id	sid	tid	token	lemma	pos
ejpam-6473	1	1	european	european	PROPN
ejpam-6473	1	2	journal	journal	PROPN
ejpam-6473	1	3	of	of	ADP
ejpam-6473	1	4	pure	pure	ADJ
ejpam-6473	1	5	and	and	CCONJ
ejpam-6473	1	6	applied	applied	ADJ
ejpam-6473	1	7	mathematics	mathematic	NOUN
ejpam-6473	1	8	2025	2025	NUM
ejpam-6473	1	9	,	,	PUNCT
ejpam-6473	1	10	vol	vol	NOUN
ejpam-6473	1	11	.	.	PROPN
ejpam-6473	1	12	18	18	NUM
ejpam-6473	1	13	,	,	PUNCT
ejpam-6473	1	14	issue	issue	NOUN
ejpam-6473	1	15	4	4	NUM
ejpam-6473	1	16	,	,	PUNCT
ejpam-6473	1	17	article	article	NOUN
ejpam-6473	1	18	number	number	NOUN
ejpam-6473	1	19	6473	6473	NUM
ejpam-6473	1	20	issn	issn	VERB
ejpam-6473	1	21	1307	1307	NUM
ejpam-6473	1	22	-	-	SYM
ejpam-6473	1	23	5543	5543	NUM
ejpam-6473	1	24	–	–	PUNCT
ejpam-6473	1	25	ejpam.com	ejpam.com	X
ejpam-6473	1	26	published	publish	VERB
ejpam-6473	1	27	by	by	ADP
ejpam-6473	1	28	new	new	PROPN
ejpam-6473	1	29	york	york	PROPN
ejpam-6473	1	30	business	business	PROPN
ejpam-6473	1	31	global	global	ADJ
ejpam-6473	1	32	optimal	optimal	ADJ
ejpam-6473	1	33	control	control	NOUN
ejpam-6473	1	34	strategies	strategy	NOUN
ejpam-6473	1	35	in	in	ADP
ejpam-6473	1	36	a	a	DET
ejpam-6473	1	37	nonlinear	nonlinear	ADJ
ejpam-6473	1	38	smoking	smoking	NOUN
ejpam-6473	1	39	cessation	cessation	NOUN
ejpam-6473	1	40	model	model	PROPN
ejpam-6473	1	41	sameera	sameera	PROPN
ejpam-6473	1	42	bano1	bano1	PROPN
ejpam-6473	1	43	,	,	PUNCT
ejpam-6473	1	44	shifa	shifa	PROPN
ejpam-6473	1	45	siddiqui1	siddiqui1	PROPN
ejpam-6473	1	46	,	,	PUNCT
ejpam-6473	1	47	anwar	anwar	PROPN
ejpam-6473	1	48	zeb1,∗	zeb1,∗	PROPN
ejpam-6473	1	49	,	,	PUNCT
ejpam-6473	1	50	thoraya	thoraya	PROPN
ejpam-6473	1	51	n.	n.	PROPN
ejpam-6473	1	52	alharthi2	alharthi2	PROPN
ejpam-6473	1	53	,	,	PUNCT
ejpam-6473	1	54	ilyas	ilyas	PROPN
ejpam-6473	1	55	khan3,4,5	khan3,4,5	PROPN
ejpam-6473	1	56	,	,	PUNCT
ejpam-6473	1	57	osama	osama	PROPN
ejpam-6473	1	58	oqilat6	oqilat6	PROPN
ejpam-6473	1	59	,	,	PUNCT
ejpam-6473	1	60	wei	wei	PROPN
ejpam-6473	1	61	sin	sin	PROPN
ejpam-6473	1	62	koh7	koh7	PROPN
ejpam-6473	1	63	1	1	NUM
ejpam-6473	1	64	department	department	NOUN
ejpam-6473	1	65	of	of	ADP
ejpam-6473	1	66	mathematics	mathematic	NOUN
ejpam-6473	1	67	,	,	PUNCT
ejpam-6473	1	68	comsats	comsats	PROPN
ejpam-6473	1	69	university	university	PROPN
ejpam-6473	1	70	islamabad	islamabad	PROPN
ejpam-6473	1	71	,	,	PUNCT
ejpam-6473	1	72	abbottabad	abbottabad	PROPN
ejpam-6473	1	73	campus	campus	PROPN
ejpam-6473	1	74	,	,	PUNCT
ejpam-6473	1	75	kpk	kpk	PROPN
ejpam-6473	1	76	,	,	PUNCT
ejpam-6473	1	77	pakistan	pakistan	PROPN
ejpam-6473	1	78	2	2	NUM
ejpam-6473	1	79	department	department	NOUN
ejpam-6473	1	80	of	of	ADP
ejpam-6473	1	81	mathematics	mathematic	NOUN
ejpam-6473	1	82	,	,	PUNCT
ejpam-6473	1	83	college	college	NOUN
ejpam-6473	1	84	of	of	ADP
ejpam-6473	1	85	science	science	NOUN
ejpam-6473	1	86	,	,	PUNCT
ejpam-6473	1	87	university	university	NOUN
ejpam-6473	1	88	of	of	ADP
ejpam-6473	1	89	bisha	bisha	PROPN
ejpam-6473	1	90	,	,	PUNCT
ejpam-6473	1	91	p.o	p.o	PROPN
ejpam-6473	1	92	.	.	PROPN
ejpam-6473	1	93	box	box	PROPN
ejpam-6473	1	94	551	551	NUM
ejpam-6473	1	95	,	,	PUNCT
ejpam-6473	1	96	bisha	bisha	PROPN
ejpam-6473	1	97	61922	61922	NUM
ejpam-6473	1	98	,	,	PUNCT
ejpam-6473	1	99	saudi	saudi	PROPN
ejpam-6473	1	100	arabia	arabia	PROPN
ejpam-6473	1	101	3	3	NUM
ejpam-6473	1	102	department	department	NOUN
ejpam-6473	1	103	of	of	ADP
ejpam-6473	1	104	mathematical	mathematical	ADJ
ejpam-6473	1	105	sciences	sciences	PROPN
ejpam-6473	1	106	,	,	PUNCT
ejpam-6473	1	107	saveetha	saveetha	PROPN
ejpam-6473	1	108	school	school	NOUN
ejpam-6473	1	109	of	of	ADP
ejpam-6473	1	110	engineering	engineering	NOUN
ejpam-6473	1	111	,	,	PUNCT
ejpam-6473	1	112	simats	simat	NOUN
ejpam-6473	1	113	,	,	PUNCT
ejpam-6473	1	114	chennai	chennai	PROPN
ejpam-6473	1	115	,	,	PUNCT
ejpam-6473	1	116	tamil	tamil	PROPN
ejpam-6473	1	117	nadu	nadu	PROPN
ejpam-6473	1	118	,	,	PUNCT
ejpam-6473	1	119	india	india	PROPN
ejpam-6473	1	120	4	4	NUM
ejpam-6473	1	121	hourani	hourani	PROPN
ejpam-6473	1	122	center	center	NOUN
ejpam-6473	1	123	for	for	ADP
ejpam-6473	1	124	applied	apply	VERB
ejpam-6473	1	125	scientific	scientific	ADJ
ejpam-6473	1	126	research	research	NOUN
ejpam-6473	1	127	,	,	PUNCT
ejpam-6473	1	128	al	al	PROPN
ejpam-6473	1	129	-	-	PUNCT
ejpam-6473	1	130	ahliyya	ahliyya	PROPN
ejpam-6473	1	131	amman	amman	PROPN
ejpam-6473	1	132	university	university	PROPN
ejpam-6473	1	133	,	,	PUNCT
ejpam-6473	1	134	amman	amman	PROPN
ejpam-6473	1	135	,	,	PUNCT
ejpam-6473	1	136	jordan	jordan	PROPN
ejpam-6473	1	137	5	5	NUM
ejpam-6473	1	138	department	department	NOUN
ejpam-6473	1	139	of	of	ADP
ejpam-6473	1	140	mathematics	mathematic	NOUN
ejpam-6473	1	141	,	,	PUNCT
ejpam-6473	1	142	college	college	NOUN
ejpam-6473	1	143	of	of	ADP
ejpam-6473	1	144	science	science	PROPN
ejpam-6473	1	145	al	al	PROPN
ejpam-6473	1	146	-	-	PUNCT
ejpam-6473	1	147	zulfi	zulfi	PROPN
ejpam-6473	1	148	,	,	PUNCT
ejpam-6473	1	149	majmaah	majmaah	PROPN
ejpam-6473	1	150	university	university	PROPN
ejpam-6473	1	151	,	,	PUNCT
ejpam-6473	1	152	al	al	PROPN
ejpam-6473	1	153	-	-	PUNCT
ejpam-6473	1	154	majmaah	majmaah	PROPN
ejpam-6473	1	155	11952	11952	NUM
ejpam-6473	1	156	,	,	PUNCT
ejpam-6473	1	157	saudi	saudi	PROPN
ejpam-6473	1	158	arabia	arabia	PROPN
ejpam-6473	1	159	6	6	NUM
ejpam-6473	1	160	hourani	hourani	NOUN
ejpam-6473	1	161	center	center	NOUN
ejpam-6473	1	162	for	for	ADP
ejpam-6473	1	163	applied	apply	VERB
ejpam-6473	1	164	scientific	scientific	ADJ
ejpam-6473	1	165	research	research	NOUN
ejpam-6473	1	166	,	,	PUNCT
ejpam-6473	1	167	department	department	NOUN
ejpam-6473	1	168	of	of	ADP
ejpam-6473	1	169	basic	basic	ADJ
ejpam-6473	1	170	sciences	science	NOUN
ejpam-6473	1	171	,	,	PUNCT
ejpam-6473	1	172	faculty	faculty	NOUN
ejpam-6473	1	173	of	of	ADP
ejpam-6473	1	174	arts	art	NOUN
ejpam-6473	1	175	and	and	CCONJ
ejpam-6473	1	176	science	science	NOUN
ejpam-6473	1	177	,	,	PUNCT
ejpam-6473	1	178	al	al	PROPN
ejpam-6473	1	179	-	-	PUNCT
ejpam-6473	1	180	ahliyya	ahliyya	PROPN
ejpam-6473	1	181	amman	amman	PROPN
ejpam-6473	1	182	university	university	PROPN
ejpam-6473	1	183	,	,	PUNCT
ejpam-6473	1	184	amman	amman	PROPN
ejpam-6473	1	185	,	,	PUNCT
ejpam-6473	1	186	jordan	jordan	PROPN
ejpam-6473	1	187	7	7	NUM
ejpam-6473	1	188	inti	inti	PROPN
ejpam-6473	1	189	international	international	PROPN
ejpam-6473	1	190	university	university	PROPN
ejpam-6473	1	191	,	,	PUNCT
ejpam-6473	1	192	persiaran	persiaran	VERB
ejpam-6473	1	193	perdana	perdana	PROPN
ejpam-6473	1	194	bbn	bbn	PROPN
ejpam-6473	1	195	putra	putra	PROPN
ejpam-6473	1	196	nilai	nilai	PROPN
ejpam-6473	1	197	,	,	PUNCT
ejpam-6473	1	198	71800	71800	PROPN
ejpam-6473	1	199	nilai	nilai	PROPN
ejpam-6473	1	200	,	,	PUNCT
ejpam-6473	1	201	negeri	negeri	PROPN
ejpam-6473	1	202	sembilan	sembilan	PROPN
ejpam-6473	1	203	,	,	PUNCT
ejpam-6473	1	204	malaysia	malaysia	PROPN
ejpam-6473	1	205	abstract	abstract	NOUN
ejpam-6473	1	206	.	.	PUNCT
ejpam-6473	2	1	this	this	DET
ejpam-6473	2	2	study	study	NOUN
ejpam-6473	2	3	introduces	introduce	VERB
ejpam-6473	2	4	a	a	DET
ejpam-6473	2	5	novel	novel	ADJ
ejpam-6473	2	6	nonlinear	nonlinear	ADJ
ejpam-6473	2	7	smoking	smoking	NOUN
ejpam-6473	2	8	cessation	cessation	NOUN
ejpam-6473	2	9	model	model	NOUN
ejpam-6473	2	10	with	with	ADP
ejpam-6473	2	11	optimal	optimal	ADJ
ejpam-6473	2	12	control	control	NOUN
ejpam-6473	2	13	strategies	strategy	NOUN
ejpam-6473	2	14	and	and	CCONJ
ejpam-6473	2	15	time	time	NOUN
ejpam-6473	2	16	delays	delay	NOUN
ejpam-6473	2	17	.	.	PUNCT
ejpam-6473	3	1	the	the	DET
ejpam-6473	3	2	model	model	NOUN
ejpam-6473	3	3	incorporates	incorporate	VERB
ejpam-6473	3	4	a	a	DET
ejpam-6473	3	5	convex	convex	ADJ
ejpam-6473	3	6	incidence	incidence	NOUN
ejpam-6473	3	7	rate	rate	NOUN
ejpam-6473	3	8	and	and	CCONJ
ejpam-6473	3	9	divides	divide	VERB
ejpam-6473	3	10	the	the	DET
ejpam-6473	3	11	total	total	ADJ
ejpam-6473	3	12	population	population	NOUN
ejpam-6473	3	13	into	into	ADP
ejpam-6473	3	14	four	four	NUM
ejpam-6473	3	15	classes	class	NOUN
ejpam-6473	3	16	.	.	PUNCT
ejpam-6473	4	1	we	we	PRON
ejpam-6473	4	2	first	first	ADV
ejpam-6473	4	3	establish	establish	VERB
ejpam-6473	4	4	positivity	positivity	NOUN
ejpam-6473	4	5	,	,	PUNCT
ejpam-6473	4	6	compute	compute	VERB
ejpam-6473	4	7	equilibrium	equilibrium	NOUN
ejpam-6473	4	8	points	point	NOUN
ejpam-6473	4	9	,	,	PUNCT
ejpam-6473	4	10	and	and	CCONJ
ejpam-6473	4	11	determine	determine	VERB
ejpam-6473	4	12	the	the	DET
ejpam-6473	4	13	basic	basic	ADJ
ejpam-6473	4	14	reproduction	reproduction	NOUN
ejpam-6473	4	15	number	number	NOUN
ejpam-6473	4	16	using	use	VERB
ejpam-6473	4	17	the	the	DET
ejpam-6473	4	18	next	next	ADJ
ejpam-6473	4	19	generation	generation	NOUN
ejpam-6473	4	20	method	method	NOUN
ejpam-6473	4	21	.	.	PUNCT
ejpam-6473	5	1	global	global	ADJ
ejpam-6473	5	2	stability	stability	NOUN
ejpam-6473	5	3	is	be	AUX
ejpam-6473	5	4	analyzed	analyze	VERB
ejpam-6473	5	5	via	via	ADP
ejpam-6473	5	6	the	the	DET
ejpam-6473	5	7	castillo	castillo	PROPN
ejpam-6473	5	8	–	–	PUNCT
ejpam-6473	5	9	chavez	chavez	PROPN
ejpam-6473	5	10	principle	principle	NOUN
ejpam-6473	5	11	for	for	ADP
ejpam-6473	5	12	the	the	DET
ejpam-6473	5	13	smoking	smoking	NOUN
ejpam-6473	5	14	-	-	PUNCT
ejpam-6473	5	15	free	free	ADJ
ejpam-6473	5	16	equilibrium	equilibrium	NOUN
ejpam-6473	5	17	and	and	CCONJ
ejpam-6473	5	18	the	the	DET
ejpam-6473	5	19	geometric	geometric	ADJ
ejpam-6473	5	20	approach	approach	NOUN
ejpam-6473	5	21	for	for	ADP
ejpam-6473	5	22	the	the	DET
ejpam-6473	5	23	endemic	endemic	ADJ
ejpam-6473	5	24	equilibrium	equilibrium	NOUN
ejpam-6473	5	25	.	.	PUNCT
ejpam-6473	6	1	sensitivity	sensitivity	NOUN
ejpam-6473	6	2	analysis	analysis	NOUN
ejpam-6473	6	3	is	be	AUX
ejpam-6473	6	4	performed	perform	VERB
ejpam-6473	6	5	to	to	PART
ejpam-6473	6	6	identify	identify	VERB
ejpam-6473	6	7	influential	influential	ADJ
ejpam-6473	6	8	parameters	parameter	NOUN
ejpam-6473	6	9	.	.	PUNCT
ejpam-6473	7	1	the	the	DET
ejpam-6473	7	2	model	model	NOUN
ejpam-6473	7	3	is	be	AUX
ejpam-6473	7	4	extended	extend	VERB
ejpam-6473	7	5	to	to	PART
ejpam-6473	7	6	include	include	VERB
ejpam-6473	7	7	optimal	optimal	ADJ
ejpam-6473	7	8	control	control	NOUN
ejpam-6473	7	9	,	,	PUNCT
ejpam-6473	7	10	where	where	SCONJ
ejpam-6473	7	11	the	the	DET
ejpam-6473	7	12	existence	existence	NOUN
ejpam-6473	7	13	and	and	CCONJ
ejpam-6473	7	14	uniqueness	uniqueness	NOUN
ejpam-6473	7	15	are	be	AUX
ejpam-6473	7	16	established	establish	VERB
ejpam-6473	7	17	,	,	PUNCT
ejpam-6473	7	18	and	and	CCONJ
ejpam-6473	7	19	the	the	DET
ejpam-6473	7	20	impact	impact	NOUN
ejpam-6473	7	21	of	of	ADP
ejpam-6473	7	22	time	time	NOUN
ejpam-6473	7	23	delays	delay	NOUN
ejpam-6473	7	24	is	be	AUX
ejpam-6473	7	25	examined	examine	VERB
ejpam-6473	7	26	.	.	PUNCT
ejpam-6473	8	1	a	a	DET
ejpam-6473	8	2	hopf	hopf	ADJ
ejpam-6473	8	3	bifurcation	bifurcation	NOUN
ejpam-6473	8	4	is	be	AUX
ejpam-6473	8	5	shown	show	VERB
ejpam-6473	8	6	to	to	PART
ejpam-6473	8	7	occur	occur	VERB
ejpam-6473	8	8	at	at	ADP
ejpam-6473	8	9	a	a	DET
ejpam-6473	8	10	critical	critical	ADJ
ejpam-6473	8	11	delay	delay	NOUN
ejpam-6473	8	12	,	,	PUNCT
ejpam-6473	8	13	indicating	indicate	VERB
ejpam-6473	8	14	oscillatory	oscillatory	ADJ
ejpam-6473	8	15	behavior	behavior	NOUN
ejpam-6473	8	16	.	.	PUNCT
ejpam-6473	9	1	numerical	numerical	ADJ
ejpam-6473	9	2	simulations	simulation	NOUN
ejpam-6473	9	3	validate	validate	VERB
ejpam-6473	9	4	the	the	DET
ejpam-6473	9	5	theoretical	theoretical	ADJ
ejpam-6473	9	6	results	result	NOUN
ejpam-6473	9	7	and	and	CCONJ
ejpam-6473	9	8	demonstrate	demonstrate	VERB
ejpam-6473	9	9	improved	improved	ADJ
ejpam-6473	9	10	performance	performance	NOUN
ejpam-6473	9	11	over	over	ADP
ejpam-6473	9	12	existing	exist	VERB
ejpam-6473	9	13	methods	method	NOUN
ejpam-6473	9	14	in	in	ADP
ejpam-6473	9	15	reducing	reduce	VERB
ejpam-6473	9	16	smoking	smoking	NOUN
ejpam-6473	9	17	prevalence	prevalence	NOUN
ejpam-6473	9	18	and	and	CCONJ
ejpam-6473	9	19	associated	associated	ADJ
ejpam-6473	9	20	costs	cost	NOUN
ejpam-6473	9	21	.	.	PUNCT
ejpam-6473	10	1	2020	2020	NUM
ejpam-6473	10	2	mathematics	mathematic	NOUN
ejpam-6473	10	3	subject	subject	NOUN
ejpam-6473	10	4	classifications	classification	NOUN
ejpam-6473	10	5	:	:	PUNCT
ejpam-6473	10	6	34h05	34h05	NUM
ejpam-6473	10	7	,	,	PUNCT
ejpam-6473	10	8	92d30	92d30	NUM
ejpam-6473	10	9	,	,	PUNCT
ejpam-6473	10	10	93c15	93c15	NOUN
ejpam-6473	10	11	key	key	ADJ
ejpam-6473	10	12	words	word	NOUN
ejpam-6473	10	13	and	and	CCONJ
ejpam-6473	10	14	phrases	phrase	NOUN
ejpam-6473	10	15	:	:	PUNCT
ejpam-6473	10	16	convex	convex	VERB
ejpam-6473	10	17	incidence	incidence	NOUN
ejpam-6473	10	18	rate	rate	NOUN
ejpam-6473	10	19	,	,	PUNCT
ejpam-6473	10	20	castillo	castillo	PROPN
ejpam-6473	10	21	-	-	PUNCT
ejpam-6473	10	22	chavez	chavez	PROPN
ejpam-6473	10	23	principle	principle	PROPN
ejpam-6473	10	24	,	,	PUNCT
ejpam-6473	10	25	geometric	geometric	ADJ
ejpam-6473	10	26	approach	approach	NOUN
ejpam-6473	10	27	,	,	PUNCT
ejpam-6473	10	28	sensitivity	sensitivity	NOUN
ejpam-6473	10	29	analysis	analysis	NOUN
ejpam-6473	10	30	,	,	PUNCT
ejpam-6473	10	31	optimal	optimal	ADJ
ejpam-6473	10	32	control	control	NOUN
ejpam-6473	10	33	,	,	PUNCT
ejpam-6473	10	34	time	time	NOUN
ejpam-6473	10	35	-	-	PUNCT
ejpam-6473	10	36	delay	delay	NOUN
ejpam-6473	10	37	∗corresponding	∗corresponde	VERB
ejpam-6473	10	38	author	author	NOUN
ejpam-6473	10	39	.	.	PUNCT
ejpam-6473	11	1	doi	doi	NOUN
ejpam-6473	11	2	:	:	PUNCT
ejpam-6473	11	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6473	https://doi.org/10.29020/nybg.ejpam.v18i4.6473	ADJ
ejpam-6473	11	4	email	email	NOUN
ejpam-6473	11	5	addresses	address	NOUN
ejpam-6473	11	6	:	:	PUNCT
ejpam-6473	11	7	sameera@cuiatd.edu.pk	sameera@cuiatd.edu.pk	PROPN
ejpam-6473	11	8	(	(	PUNCT
ejpam-6473	11	9	s.	s.	PROPN
ejpam-6473	11	10	bano	bano	PROPN
ejpam-6473	11	11	)	)	PUNCT
ejpam-6473	11	12	,	,	PUNCT
ejpam-6473	11	13	swadah827@gmail.com	swadah827@gmail.com	X
ejpam-6473	11	14	(	(	PUNCT
ejpam-6473	11	15	s.	s.	PROPN
ejpam-6473	11	16	siddiqui	siddiqui	PROPN
ejpam-6473	11	17	)	)	PUNCT
ejpam-6473	11	18	,	,	PUNCT
ejpam-6473	11	19	anwar@cuiatd.edu.pk	anwar@cuiatd.edu.pk	NOUN
ejpam-6473	11	20	(	(	PUNCT
ejpam-6473	11	21	a.	a.	NOUN
ejpam-6473	11	22	zeb	zeb	PROPN
ejpam-6473	11	23	)	)	PUNCT
ejpam-6473	11	24	,	,	PUNCT
ejpam-6473	11	25	talhrthe@ub.edu.sa	talhrthe@ub.edu.sa	PROPN
ejpam-6473	11	26	(	(	PUNCT
ejpam-6473	11	27	t.	t.	PROPN
ejpam-6473	11	28	n.	n.	PROPN
ejpam-6473	11	29	alharthi	alharthi	PROPN
ejpam-6473	11	30	)	)	PUNCT
ejpam-6473	11	31	,	,	PUNCT
ejpam-6473	11	32	i.said@mu.edu.sa	i.said@mu.edu.sa	PROPN
ejpam-6473	11	33	(	(	PUNCT
ejpam-6473	11	34	i.	i.	PROPN
ejpam-6473	11	35	khan	khan	PROPN
ejpam-6473	11	36	)	)	PUNCT
ejpam-6473	11	37	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6473	12	1	1	1	NUM
ejpam-6473	12	2	copyright	copyright	NOUN
ejpam-6473	12	3	:	:	PUNCT
ejpam-6473	12	4	©	©	PROPN
ejpam-6473	12	5	2025	2025	NUM
ejpam-6473	12	6	the	the	DET
ejpam-6473	12	7	author(s	author(s	NOUN
ejpam-6473	12	8	)	)	PUNCT
ejpam-6473	12	9	.	.	PUNCT
ejpam-6473	13	1	(	(	PUNCT
ejpam-6473	13	2	cc	cc	NOUN
ejpam-6473	13	3	by	by	ADP
ejpam-6473	13	4	-	-	PUNCT
ejpam-6473	13	5	nc	nc	PROPN
ejpam-6473	13	6	4.0	4.0	NUM
ejpam-6473	13	7	)	)	PUNCT
ejpam-6473	13	8	s.	s.	PROPN
ejpam-6473	13	9	bano	bano	PROPN
ejpam-6473	13	10	et	et	PROPN
ejpam-6473	13	11	al	al	PROPN
ejpam-6473	13	12	.	.	PUNCT
ejpam-6473	13	13	/	/	SYM
ejpam-6473	13	14	eur	eur	PROPN
ejpam-6473	13	15	.	.	PUNCT
ejpam-6473	14	1	j.	j.	PROPN
ejpam-6473	14	2	pure	pure	PROPN
ejpam-6473	14	3	appl	appl	PROPN
ejpam-6473	14	4	.	.	PROPN
ejpam-6473	14	5	math	math	PROPN
ejpam-6473	14	6	,	,	PUNCT
ejpam-6473	14	7	18	18	NUM
ejpam-6473	14	8	(	(	PUNCT
ejpam-6473	14	9	4	4	NUM
ejpam-6473	14	10	)	)	PUNCT
ejpam-6473	14	11	(	(	PUNCT
ejpam-6473	14	12	2025	2025	NUM
ejpam-6473	14	13	)	)	PUNCT
ejpam-6473	14	14	,	,	PUNCT
ejpam-6473	14	15	6473	6473	NUM
ejpam-6473	14	16	2	2	NUM
ejpam-6473	14	17	of	of	ADP
ejpam-6473	14	18	38	38	NUM
ejpam-6473	14	19	1	1	NUM
ejpam-6473	14	20	.	.	PUNCT
ejpam-6473	15	1	introduction	introduction	NOUN
ejpam-6473	15	2	research	research	NOUN
ejpam-6473	15	3	in	in	ADP
ejpam-6473	15	4	mathematical	mathematical	ADJ
ejpam-6473	15	5	biology	biology	NOUN
ejpam-6473	15	6	was	be	AUX
ejpam-6473	15	7	first	first	ADV
ejpam-6473	15	8	started	start	VERB
ejpam-6473	15	9	in	in	ADP
ejpam-6473	15	10	the	the	DET
ejpam-6473	15	11	19th	19th	ADJ
ejpam-6473	15	12	century	century	NOUN
ejpam-6473	15	13	;	;	PUNCT
ejpam-6473	15	14	initially	initially	ADV
ejpam-6473	15	15	,	,	PUNCT
ejpam-6473	15	16	it	it	PRON
ejpam-6473	15	17	has	have	VERB
ejpam-6473	15	18	a	a	DET
ejpam-6473	15	19	slow	slow	ADJ
ejpam-6473	15	20	progress	progress	NOUN
ejpam-6473	15	21	,	,	PUNCT
ejpam-6473	15	22	but	but	CCONJ
ejpam-6473	15	23	later	later	ADV
ejpam-6473	15	24	at	at	ADP
ejpam-6473	15	25	the	the	DET
ejpam-6473	15	26	end	end	NOUN
ejpam-6473	15	27	of	of	ADP
ejpam-6473	15	28	the	the	DET
ejpam-6473	15	29	20th	20th	ADJ
ejpam-6473	15	30	century	century	NOUN
ejpam-6473	15	31	it	it	PRON
ejpam-6473	15	32	became	become	VERB
ejpam-6473	15	33	more	more	ADV
ejpam-6473	15	34	attractive	attractive	ADJ
ejpam-6473	15	35	.	.	PUNCT
ejpam-6473	16	1	john	john	PROPN
ejpam-6473	16	2	led	lead	VERB
ejpam-6473	16	3	the	the	DET
ejpam-6473	16	4	development	development	NOUN
ejpam-6473	16	5	of	of	ADP
ejpam-6473	16	6	mathematical	mathematical	ADJ
ejpam-6473	16	7	biology	biology	NOUN
ejpam-6473	16	8	in	in	ADP
ejpam-6473	16	9	1909	1909	NUM
ejpam-6473	16	10	and	and	CCONJ
ejpam-6473	16	11	in	in	ADP
ejpam-6473	16	12	1912	1912	NUM
ejpam-6473	16	13	,	,	PUNCT
ejpam-6473	16	14	he	he	PRON
ejpam-6473	16	15	gave	give	VERB
ejpam-6473	16	16	the	the	DET
ejpam-6473	16	17	basic	basic	ADJ
ejpam-6473	16	18	law	law	NOUN
ejpam-6473	16	19	of	of	ADP
ejpam-6473	16	20	epidemic	epidemic	NOUN
ejpam-6473	16	21	spread	spread	NOUN
ejpam-6473	16	22	.	.	PUNCT
ejpam-6473	17	1	kermack	kermack	NOUN
ejpam-6473	17	2	and	and	CCONJ
ejpam-6473	17	3	mckendrick	mckendrick	PROPN
ejpam-6473	17	4	proposed	propose	VERB
ejpam-6473	17	5	the	the	DET
ejpam-6473	17	6	first	first	ADJ
ejpam-6473	17	7	dynamic	dynamic	ADJ
ejpam-6473	17	8	model	model	NOUN
ejpam-6473	17	9	in	in	ADP
ejpam-6473	17	10	1927	1927	NUM
ejpam-6473	18	1	[	[	X
ejpam-6473	18	2	1	1	NUM
ejpam-6473	18	3	]	]	PUNCT
ejpam-6473	18	4	.	.	PUNCT
ejpam-6473	19	1	later	later	ADV
ejpam-6473	19	2	,	,	PUNCT
ejpam-6473	19	3	his	his	PRON
ejpam-6473	19	4	work	work	NOUN
ejpam-6473	19	5	was	be	AUX
ejpam-6473	19	6	further	far	ADV
ejpam-6473	19	7	extended	extend	VERB
ejpam-6473	19	8	by	by	ADP
ejpam-6473	19	9	andrea	andrea	PROPN
ejpam-6473	19	10	,	,	PUNCT
ejpam-6473	19	11	who	who	PRON
ejpam-6473	19	12	applied	apply	VERB
ejpam-6473	19	13	a	a	DET
ejpam-6473	19	14	time	time	NOUN
ejpam-6473	19	15	delay	delay	NOUN
ejpam-6473	19	16	on	on	ADP
ejpam-6473	19	17	the	the	DET
ejpam-6473	19	18	model	model	NOUN
ejpam-6473	19	19	[	[	X
ejpam-6473	19	20	2	2	NUM
ejpam-6473	19	21	]	]	PUNCT
ejpam-6473	19	22	.	.	PUNCT
ejpam-6473	20	1	many	many	ADJ
ejpam-6473	20	2	models	model	NOUN
ejpam-6473	20	3	proposed	propose	VERB
ejpam-6473	20	4	based	base	VERB
ejpam-6473	20	5	on	on	ADP
ejpam-6473	20	6	the	the	DET
ejpam-6473	20	7	sir	sir	PROPN
ejpam-6473	20	8	model	model	NOUN
ejpam-6473	20	9	,	,	PUNCT
ejpam-6473	20	10	like	like	ADP
ejpam-6473	20	11	seir	seir	NOUN
ejpam-6473	20	12	[	[	X
ejpam-6473	20	13	3	3	NUM
ejpam-6473	20	14	]	]	PUNCT
ejpam-6473	20	15	presented	present	VERB
ejpam-6473	20	16	by	by	ADP
ejpam-6473	20	17	nh	nh	PROPN
ejpam-6473	20	18	shah	shah	PROPN
ejpam-6473	20	19	,	,	PUNCT
ejpam-6473	20	20	other	other	ADJ
ejpam-6473	20	21	seir	seir	NOUN
ejpam-6473	20	22	[	[	X
ejpam-6473	20	23	4	4	NUM
ejpam-6473	20	24	]	]	PUNCT
ejpam-6473	20	25	which	which	PRON
ejpam-6473	20	26	include	include	VERB
ejpam-6473	20	27	delay	delay	NOUN
ejpam-6473	20	28	information	information	NOUN
ejpam-6473	20	29	and	and	CCONJ
ejpam-6473	20	30	feedback	feedback	NOUN
ejpam-6473	20	31	mechanisms	mechanism	NOUN
ejpam-6473	20	32	influencing	influence	VERB
ejpam-6473	20	33	susceptible	susceptible	ADJ
ejpam-6473	20	34	individuals	individual	NOUN
ejpam-6473	20	35	’	'	PUNCT
ejpam-6473	20	36	behavior	behavior	NOUN
ejpam-6473	20	37	,	,	PUNCT
ejpam-6473	20	38	this	this	DET
ejpam-6473	20	39	model	model	NOUN
ejpam-6473	20	40	analysis	analysis	NOUN
ejpam-6473	20	41	the	the	DET
ejpam-6473	20	42	global	global	ADJ
ejpam-6473	20	43	stability	stability	NOUN
ejpam-6473	20	44	at	at	ADP
ejpam-6473	20	45	both	both	DET
ejpam-6473	20	46	equilibrium	equilibrium	NOUN
ejpam-6473	20	47	points	point	NOUN
ejpam-6473	20	48	.	.	PUNCT
ejpam-6473	21	1	sis	sis	PRON
ejpam-6473	21	2	model	model	NOUN
ejpam-6473	21	3	[	[	X
ejpam-6473	21	4	5	5	NUM
ejpam-6473	21	5	]	]	PUNCT
ejpam-6473	21	6	investigate	investigate	VERB
ejpam-6473	21	7	model	model	NOUN
ejpam-6473	21	8	within	within	ADP
ejpam-6473	21	9	the	the	DET
ejpam-6473	21	10	time	time	NOUN
ejpam-6473	21	11	scales	scale	VERB
ejpam-6473	21	12	framework	framework	NOUN
ejpam-6473	21	13	,	,	PUNCT
ejpam-6473	21	14	analyzing	analyze	VERB
ejpam-6473	21	15	its	its	PRON
ejpam-6473	21	16	dynamics	dynamic	NOUN
ejpam-6473	21	17	and	and	CCONJ
ejpam-6473	21	18	incorporating	incorporate	VERB
ejpam-6473	21	19	births	birth	NOUN
ejpam-6473	21	20	and	and	CCONJ
ejpam-6473	21	21	deaths	death	NOUN
ejpam-6473	21	22	.	.	PUNCT
ejpam-6473	22	1	in	in	ADP
ejpam-6473	22	2	mathematical	mathematical	ADJ
ejpam-6473	22	3	biology	biology	NOUN
ejpam-6473	22	4	models	model	NOUN
ejpam-6473	22	5	incidence	incidence	NOUN
ejpam-6473	22	6	rate	rate	NOUN
ejpam-6473	22	7	plays	play	VERB
ejpam-6473	22	8	very	very	ADV
ejpam-6473	22	9	significant	significant	ADJ
ejpam-6473	22	10	role	role	NOUN
ejpam-6473	22	11	.	.	PUNCT
ejpam-6473	23	1	yorke	yorke	NOUN
ejpam-6473	23	2	and	and	CCONJ
ejpam-6473	23	3	london	london	PROPN
ejpam-6473	23	4	present	present	VERB
ejpam-6473	23	5	a	a	DET
ejpam-6473	23	6	model	model	NOUN
ejpam-6473	23	7	[	[	X
ejpam-6473	23	8	6	6	NUM
ejpam-6473	23	9	]	]	PUNCT
ejpam-6473	23	10	on	on	ADP
ejpam-6473	23	11	the	the	DET
ejpam-6473	23	12	outbreak	outbreak	NOUN
ejpam-6473	23	13	of	of	ADP
ejpam-6473	23	14	measles	measle	NOUN
ejpam-6473	23	15	,	,	PUNCT
ejpam-6473	23	16	chickenpox	chickenpox	NOUN
ejpam-6473	23	17	,	,	PUNCT
ejpam-6473	23	18	and	and	CCONJ
ejpam-6473	23	19	mumps	mump	NOUN
ejpam-6473	23	20	.	.	PUNCT
ejpam-6473	24	1	in	in	ADP
ejpam-6473	24	2	this	this	DET
ejpam-6473	24	3	model	model	NOUN
ejpam-6473	24	4	,	,	PUNCT
ejpam-6473	24	5	they	they	PRON
ejpam-6473	24	6	use	use	VERB
ejpam-6473	24	7	an	an	DET
ejpam-6473	24	8	incidence	incidence	NOUN
ejpam-6473	24	9	rate	rate	NOUN
ejpam-6473	24	10	of	of	ADP
ejpam-6473	24	11	the	the	DET
ejpam-6473	24	12	form	form	NOUN
ejpam-6473	24	13	fis	fis	PROPN
ejpam-6473	24	14	=	=	PROPN
ejpam-6473	24	15	is(1	is(1	PROPN
ejpam-6473	24	16	−	−	PROPN
ejpam-6473	24	17	ci	ci	PROPN
ejpam-6473	24	18	)	)	PUNCT
ejpam-6473	24	19	.	.	PUNCT
ejpam-6473	25	1	liu	liu	PROPN
ejpam-6473	25	2	and	and	CCONJ
ejpam-6473	25	3	his	his	PRON
ejpam-6473	25	4	co	co	NOUN
ejpam-6473	25	5	-	-	NOUN
ejpam-6473	25	6	workers	worker	NOUN
ejpam-6473	25	7	present	present	VERB
ejpam-6473	25	8	a	a	DET
ejpam-6473	25	9	model	model	NOUN
ejpam-6473	25	10	in	in	ADP
ejpam-6473	25	11	which	which	PRON
ejpam-6473	25	12	they	they	PRON
ejpam-6473	25	13	use	use	VERB
ejpam-6473	25	14	the	the	DET
ejpam-6473	25	15	contact	contact	NOUN
ejpam-6473	25	16	rate	rate	NOUN
ejpam-6473	25	17	of	of	ADP
ejpam-6473	25	18	the	the	DET
ejpam-6473	25	19	form	form	NOUN
ejpam-6473	25	20	βias	βias	NOUN
ejpam-6473	25	21	(	(	PUNCT
ejpam-6473	25	22	1+αic	1+αic	NUM
ejpam-6473	25	23	)	)	PUNCT
ejpam-6473	25	24	,	,	PUNCT
ejpam-6473	25	25	where	where	SCONJ
ejpam-6473	25	26	β	β	X
ejpam-6473	25	27	,	,	PUNCT
ejpam-6473	25	28	α	α	PROPN
ejpam-6473	25	29	,	,	PUNCT
ejpam-6473	25	30	c	c	NOUN
ejpam-6473	25	31	,	,	PUNCT
ejpam-6473	25	32	and	and	CCONJ
ejpam-6473	25	33	a	a	DET
ejpam-6473	25	34	>	>	X
ejpam-6473	25	35	0	0	NUM
ejpam-6473	25	36	.	.	PUNCT
ejpam-6473	26	1	a	a	DET
ejpam-6473	26	2	saturated	saturate	VERB
ejpam-6473	26	3	incidence	incidence	NOUN
ejpam-6473	26	4	rate	rate	NOUN
ejpam-6473	26	5	model	model	NOUN
ejpam-6473	26	6	of	of	ADP
ejpam-6473	26	7	cholera	cholera	NOUN
ejpam-6473	26	8	was	be	AUX
ejpam-6473	26	9	proposed	propose	VERB
ejpam-6473	26	10	by	by	ADP
ejpam-6473	26	11	capasso	capasso	PROPN
ejpam-6473	26	12	and	and	CCONJ
ejpam-6473	26	13	serio	serio	PROPN
ejpam-6473	26	14	,	,	PUNCT
ejpam-6473	26	15	which	which	PRON
ejpam-6473	26	16	also	also	ADV
ejpam-6473	26	17	highlights	highlight	VERB
ejpam-6473	26	18	the	the	DET
ejpam-6473	26	19	importance	importance	NOUN
ejpam-6473	26	20	of	of	ADP
ejpam-6473	26	21	the	the	DET
ejpam-6473	26	22	non	non	ADJ
ejpam-6473	26	23	-	-	ADJ
ejpam-6473	26	24	linear	linear	ADJ
ejpam-6473	26	25	contact	contact	NOUN
ejpam-6473	26	26	rate	rate	NOUN
ejpam-6473	26	27	for	for	ADP
ejpam-6473	26	28	the	the	DET
ejpam-6473	26	29	spread	spread	NOUN
ejpam-6473	26	30	of	of	ADP
ejpam-6473	26	31	the	the	DET
ejpam-6473	26	32	disease	disease	NOUN
ejpam-6473	26	33	.	.	PUNCT
ejpam-6473	27	1	some	some	DET
ejpam-6473	27	2	other	other	ADJ
ejpam-6473	27	3	models	model	NOUN
ejpam-6473	27	4	related	relate	VERB
ejpam-6473	27	5	to	to	ADP
ejpam-6473	27	6	nonlinear	nonlinear	ADJ
ejpam-6473	27	7	incidence	incidence	NOUN
ejpam-6473	27	8	rates	rate	NOUN
ejpam-6473	27	9	like	like	ADP
ejpam-6473	27	10	nonmonotone	nonmonotone	NOUN
ejpam-6473	27	11	incidence	incidence	NOUN
ejpam-6473	27	12	rate	rate	NOUN
ejpam-6473	27	13	[	[	X
ejpam-6473	27	14	7	7	NUM
ejpam-6473	27	15	]	]	PUNCT
ejpam-6473	27	16	,	,	PUNCT
ejpam-6473	27	17	harmonic	harmonic	ADJ
ejpam-6473	27	18	mean	mean	ADJ
ejpam-6473	27	19	type	type	NOUN
ejpam-6473	27	20	incidence	incidence	NOUN
ejpam-6473	27	21	rate	rate	NOUN
ejpam-6473	27	22	[	[	X
ejpam-6473	27	23	8	8	NUM
ejpam-6473	27	24	]	]	PUNCT
ejpam-6473	27	25	,	,	PUNCT
ejpam-6473	27	26	saturated	saturate	VERB
ejpam-6473	27	27	incidence	incidence	NOUN
ejpam-6473	27	28	rate	rate	NOUN
ejpam-6473	27	29	[	[	X
ejpam-6473	27	30	9	9	NUM
ejpam-6473	27	31	]	]	PUNCT
ejpam-6473	27	32	and	and	CCONJ
ejpam-6473	27	33	some	some	DET
ejpam-6473	27	34	other	other	ADJ
ejpam-6473	27	35	model	model	NOUN
ejpam-6473	27	36	with	with	ADP
ejpam-6473	27	37	different	different	ADJ
ejpam-6473	27	38	incidence	incidence	NOUN
ejpam-6473	27	39	rate	rate	NOUN
ejpam-6473	27	40	[	[	X
ejpam-6473	27	41	10	10	NUM
ejpam-6473	27	42	]	]	PUNCT
ejpam-6473	27	43	are	be	AUX
ejpam-6473	27	44	given	give	VERB
ejpam-6473	27	45	in	in	ADP
ejpam-6473	27	46	the	the	DET
ejpam-6473	27	47	literature	literature	NOUN
ejpam-6473	27	48	review	review	NOUN
ejpam-6473	27	49	.	.	PUNCT
ejpam-6473	28	1	another	another	DET
ejpam-6473	28	2	interesting	interesting	ADJ
ejpam-6473	28	3	contact	contact	NOUN
ejpam-6473	28	4	rate	rate	NOUN
ejpam-6473	28	5	is	be	AUX
ejpam-6473	28	6	the	the	DET
ejpam-6473	28	7	convex	convex	ADJ
ejpam-6473	28	8	contact	contact	NOUN
ejpam-6473	28	9	rate	rate	NOUN
ejpam-6473	28	10	,	,	PUNCT
ejpam-6473	28	11	which	which	PRON
ejpam-6473	28	12	is	be	AUX
ejpam-6473	28	13	expressed	express	VERB
ejpam-6473	28	14	as	as	ADP
ejpam-6473	28	15	g(s	g(	NOUN
ejpam-6473	28	16	)	)	PUNCT
ejpam-6473	28	17	=	=	SYM
ejpam-6473	28	18	βsi(1	βsi(1	X
ejpam-6473	29	1	+	+	CCONJ
ejpam-6473	29	2	αi	αi	NOUN
ejpam-6473	29	3	)	)	PUNCT
ejpam-6473	29	4	.	.	PUNCT
ejpam-6473	30	1	this	this	DET
ejpam-6473	30	2	incidence	incidence	NOUN
ejpam-6473	30	3	rate	rate	NOUN
ejpam-6473	30	4	shows	show	VERB
ejpam-6473	30	5	the	the	DET
ejpam-6473	30	6	increase	increase	NOUN
ejpam-6473	30	7	rate	rate	NOUN
ejpam-6473	30	8	of	of	ADP
ejpam-6473	30	9	infection	infection	NOUN
ejpam-6473	30	10	due	due	ADP
ejpam-6473	30	11	to	to	ADP
ejpam-6473	30	12	double	double	ADJ
ejpam-6473	30	13	exposure	exposure	NOUN
ejpam-6473	30	14	.	.	PUNCT
ejpam-6473	31	1	βsi	βsi	NOUN
ejpam-6473	31	2	is	be	AUX
ejpam-6473	31	3	the	the	DET
ejpam-6473	31	4	contact	contact	NOUN
ejpam-6473	31	5	rate	rate	NOUN
ejpam-6473	31	6	produced	produce	VERB
ejpam-6473	31	7	due	due	ADP
ejpam-6473	31	8	to	to	ADP
ejpam-6473	31	9	single	single	ADJ
ejpam-6473	31	10	interaction	interaction	NOUN
ejpam-6473	31	11	,	,	PUNCT
ejpam-6473	31	12	while	while	SCONJ
ejpam-6473	31	13	βαsi2	βαsi2	NOUN
ejpam-6473	31	14	is	be	AUX
ejpam-6473	31	15	due	due	ADJ
ejpam-6473	31	16	to	to	ADP
ejpam-6473	31	17	the	the	DET
ejpam-6473	31	18	newly	newly	ADV
ejpam-6473	31	19	formed	form	VERB
ejpam-6473	31	20	infection	infection	NOUN
ejpam-6473	31	21	due	due	ADP
ejpam-6473	31	22	to	to	ADP
ejpam-6473	31	23	double	double	ADJ
ejpam-6473	31	24	exposure	exposure	NOUN
ejpam-6473	31	25	.	.	PUNCT
ejpam-6473	32	1	a.	a.	PROPN
ejpam-6473	32	2	khan	khan	PROPN
ejpam-6473	32	3	developed	develop	VERB
ejpam-6473	32	4	a	a	DET
ejpam-6473	32	5	model	model	NOUN
ejpam-6473	32	6	of	of	ADP
ejpam-6473	32	7	covid-19	covid-19	PROPN
ejpam-6473	33	1	[	[	X
ejpam-6473	33	2	11	11	NUM
ejpam-6473	33	3	]	]	PUNCT
ejpam-6473	33	4	and	and	CCONJ
ejpam-6473	33	5	hepatitis	hepatitis	PROPN
ejpam-6473	33	6	b	b	PROPN
ejpam-6473	34	1	[	[	X
ejpam-6473	34	2	12	12	NUM
ejpam-6473	34	3	]	]	PUNCT
ejpam-6473	34	4	with	with	ADP
ejpam-6473	34	5	a	a	DET
ejpam-6473	34	6	convex	convex	ADJ
ejpam-6473	34	7	incidence	incidence	NOUN
ejpam-6473	34	8	rate	rate	NOUN
ejpam-6473	34	9	.	.	PUNCT
ejpam-6473	35	1	other	other	ADJ
ejpam-6473	35	2	models	model	NOUN
ejpam-6473	35	3	with	with	ADP
ejpam-6473	35	4	convex	convex	ADJ
ejpam-6473	35	5	incidence	incidence	NOUN
ejpam-6473	35	6	rate	rate	NOUN
ejpam-6473	35	7	are	be	AUX
ejpam-6473	35	8	[	[	X
ejpam-6473	35	9	13	13	NUM
ejpam-6473	35	10	]	]	PUNCT
ejpam-6473	35	11	,	,	PUNCT
ejpam-6473	35	12	[	[	X
ejpam-6473	35	13	14	14	NUM
ejpam-6473	35	14	]	]	PUNCT
ejpam-6473	35	15	,	,	PUNCT
ejpam-6473	35	16	[	[	X
ejpam-6473	35	17	15	15	NUM
ejpam-6473	35	18	]	]	PUNCT
ejpam-6473	35	19	.	.	PUNCT
ejpam-6473	36	1	recent	recent	ADJ
ejpam-6473	36	2	studies	study	NOUN
ejpam-6473	36	3	have	have	AUX
ejpam-6473	36	4	used	use	VERB
ejpam-6473	36	5	mathematical	mathematical	ADJ
ejpam-6473	36	6	models	model	NOUN
ejpam-6473	36	7	to	to	PART
ejpam-6473	36	8	explore	explore	VERB
ejpam-6473	36	9	how	how	SCONJ
ejpam-6473	36	10	infectious	infectious	ADJ
ejpam-6473	36	11	diseases	disease	NOUN
ejpam-6473	36	12	like	like	ADP
ejpam-6473	36	13	rabies	rabie	NOUN
ejpam-6473	36	14	affect	affect	VERB
ejpam-6473	36	15	the	the	DET
ejpam-6473	36	16	brain	brain	NOUN
ejpam-6473	36	17	,	,	PUNCT
ejpam-6473	36	18	focusing	focus	VERB
ejpam-6473	36	19	on	on	ADP
ejpam-6473	36	20	transmission	transmission	NOUN
ejpam-6473	36	21	dynamics	dynamic	NOUN
ejpam-6473	36	22	and	and	CCONJ
ejpam-6473	36	23	control	control	NOUN
ejpam-6473	36	24	strategies	strategy	NOUN
ejpam-6473	36	25	.	.	PUNCT
ejpam-6473	37	1	this	this	PRON
ejpam-6473	37	2	reflects	reflect	VERB
ejpam-6473	37	3	the	the	DET
ejpam-6473	37	4	expanding	expand	VERB
ejpam-6473	37	5	role	role	NOUN
ejpam-6473	37	6	of	of	ADP
ejpam-6473	37	7	mathematical	mathematical	ADJ
ejpam-6473	37	8	biology	biology	NOUN
ejpam-6473	37	9	in	in	ADP
ejpam-6473	37	10	tackling	tackle	VERB
ejpam-6473	37	11	neurological	neurological	ADJ
ejpam-6473	37	12	health	health	NOUN
ejpam-6473	37	13	issues	issue	NOUN
ejpam-6473	37	14	[	[	X
ejpam-6473	37	15	16	16	NUM
ejpam-6473	37	16	]	]	PUNCT
ejpam-6473	37	17	.	.	PUNCT
ejpam-6473	38	1	researcher	researcher	NOUN
ejpam-6473	38	2	often	often	ADV
ejpam-6473	38	3	use	use	VERB
ejpam-6473	38	4	incidence	incidence	NOUN
ejpam-6473	38	5	functions	function	NOUN
ejpam-6473	38	6	to	to	PART
ejpam-6473	38	7	model	model	VERB
ejpam-6473	38	8	the	the	DET
ejpam-6473	38	9	spread	spread	NOUN
ejpam-6473	38	10	of	of	ADP
ejpam-6473	38	11	infectious	infectious	ADJ
ejpam-6473	38	12	diseases	disease	NOUN
ejpam-6473	38	13	[	[	X
ejpam-6473	38	14	17	17	NUM
ejpam-6473	38	15	–	–	PUNCT
ejpam-6473	38	16	19	19	NUM
ejpam-6473	38	17	]	]	PUNCT
ejpam-6473	38	18	,	,	PUNCT
ejpam-6473	38	19	but	but	CCONJ
ejpam-6473	38	20	they	they	PRON
ejpam-6473	38	21	can	can	AUX
ejpam-6473	38	22	also	also	ADV
ejpam-6473	38	23	be	be	AUX
ejpam-6473	38	24	used	use	VERB
ejpam-6473	38	25	to	to	PART
ejpam-6473	38	26	model	model	VERB
ejpam-6473	38	27	the	the	DET
ejpam-6473	38	28	spread	spread	NOUN
ejpam-6473	38	29	of	of	ADP
ejpam-6473	38	30	behaviors	behavior	NOUN
ejpam-6473	38	31	like	like	ADP
ejpam-6473	38	32	smoking	smoking	NOUN
ejpam-6473	38	33	.	.	PUNCT
ejpam-6473	39	1	smoking	smoking	NOUN
ejpam-6473	39	2	has	have	VERB
ejpam-6473	39	3	a	a	DET
ejpam-6473	39	4	knack	knack	NOUN
ejpam-6473	39	5	for	for	ADP
ejpam-6473	39	6	influencing	influence	VERB
ejpam-6473	39	7	the	the	DET
ejpam-6473	39	8	non	non	NOUN
ejpam-6473	39	9	-	-	NOUN
ejpam-6473	39	10	smokers	smoker	NOUN
ejpam-6473	39	11	and	and	CCONJ
ejpam-6473	39	12	quit	quit	VERB
ejpam-6473	39	13	smokers	smoker	NOUN
ejpam-6473	39	14	to	to	PART
ejpam-6473	39	15	start	start	VERB
ejpam-6473	39	16	smoking	smoke	VERB
ejpam-6473	39	17	,	,	PUNCT
ejpam-6473	39	18	making	make	VERB
ejpam-6473	39	19	smoking	smoke	VERB
ejpam-6473	39	20	contagious	contagious	ADJ
ejpam-6473	39	21	like	like	ADP
ejpam-6473	39	22	infectious	infectious	ADJ
ejpam-6473	39	23	disease	disease	NOUN
ejpam-6473	39	24	.	.	PUNCT
ejpam-6473	40	1	in	in	ADP
ejpam-6473	40	2	500	500	NUM
ejpam-6473	40	3	bc	bc	PROPN
ejpam-6473	40	4	in	in	ADP
ejpam-6473	40	5	america	america	PROPN
ejpam-6473	40	6	,	,	PUNCT
ejpam-6473	40	7	it	it	PRON
ejpam-6473	40	8	was	be	AUX
ejpam-6473	40	9	used	use	VERB
ejpam-6473	40	10	in	in	ADP
ejpam-6473	40	11	rituals	ritual	NOUN
ejpam-6473	40	12	and	and	CCONJ
ejpam-6473	40	13	ceremonies	ceremony	NOUN
ejpam-6473	40	14	.	.	PUNCT
ejpam-6473	41	1	it	it	PRON
ejpam-6473	41	2	was	be	AUX
ejpam-6473	41	3	brought	bring	VERB
ejpam-6473	41	4	to	to	ADP
ejpam-6473	41	5	europe	europe	PROPN
ejpam-6473	41	6	in	in	ADP
ejpam-6473	41	7	the	the	DET
ejpam-6473	41	8	15th	15th	ADJ
ejpam-6473	41	9	and	and	CCONJ
ejpam-6473	41	10	16th	16th	ADJ
ejpam-6473	41	11	centuries	century	NOUN
ejpam-6473	41	12	.	.	PUNCT
ejpam-6473	42	1	in	in	ADP
ejpam-6473	42	2	1880	1880	NUM
ejpam-6473	42	3	james	james	PROPN
ejpam-6473	42	4	a.	a.	PROPN
ejpam-6473	42	5	bonsack	bonsack	PROPN
ejpam-6473	42	6	invented	invent	VERB
ejpam-6473	42	7	the	the	DET
ejpam-6473	42	8	first	first	ADJ
ejpam-6473	42	9	smoking	smoking	NOUN
ejpam-6473	42	10	machine	machine	NOUN
ejpam-6473	42	11	that	that	PRON
ejpam-6473	42	12	increases	increase	VERB
ejpam-6473	42	13	the	the	DET
ejpam-6473	42	14	smoking	smoking	NOUN
ejpam-6473	42	15	rate	rate	NOUN
ejpam-6473	42	16	.	.	PUNCT
ejpam-6473	43	1	it	it	PRON
ejpam-6473	43	2	causes	cause	VERB
ejpam-6473	43	3	5	5	NUM
ejpam-6473	43	4	million	million	NUM
ejpam-6473	43	5	deaths	death	NOUN
ejpam-6473	43	6	around	around	ADP
ejpam-6473	43	7	the	the	DET
ejpam-6473	43	8	world	world	NOUN
ejpam-6473	43	9	,	,	PUNCT
ejpam-6473	43	10	making	make	VERB
ejpam-6473	43	11	it	it	PRON
ejpam-6473	43	12	the	the	DET
ejpam-6473	43	13	largest	large	ADJ
ejpam-6473	43	14	cause	cause	NOUN
ejpam-6473	43	15	of	of	ADP
ejpam-6473	43	16	death	death	NOUN
ejpam-6473	43	17	.	.	PUNCT
ejpam-6473	44	1	the	the	DET
ejpam-6473	44	2	harmful	harmful	ADJ
ejpam-6473	44	3	chemical	chemical	NOUN
ejpam-6473	44	4	enter	enter	VERB
ejpam-6473	44	5	our	our	PRON
ejpam-6473	44	6	bodies	body	NOUN
ejpam-6473	44	7	by	by	ADP
ejpam-6473	44	8	smoking	smoke	VERB
ejpam-6473	44	9	and	and	CCONJ
ejpam-6473	44	10	affect	affect	VERB
ejpam-6473	44	11	our	our	PRON
ejpam-6473	44	12	hearts	heart	NOUN
ejpam-6473	44	13	,	,	PUNCT
ejpam-6473	44	14	nervous	nervous	ADJ
ejpam-6473	44	15	systems	system	NOUN
ejpam-6473	44	16	,	,	PUNCT
ejpam-6473	44	17	respiratory	respiratory	ADJ
ejpam-6473	44	18	system	system	NOUN
ejpam-6473	44	19	,	,	PUNCT
ejpam-6473	44	20	stomach	stomach	NOUN
ejpam-6473	44	21	,	,	PUNCT
ejpam-6473	44	22	etc	etc	X
ejpam-6473	44	23	.	.	X
ejpam-6473	45	1	among	among	ADP
ejpam-6473	45	2	teenagers	teenager	NOUN
ejpam-6473	45	3	,	,	PUNCT
ejpam-6473	45	4	as	as	SCONJ
ejpam-6473	45	5	they	they	PRON
ejpam-6473	45	6	grow	grow	VERB
ejpam-6473	45	7	and	and	CCONJ
ejpam-6473	45	8	develop	develop	VERB
ejpam-6473	45	9	,	,	PUNCT
ejpam-6473	45	10	smoking	smoking	NOUN
ejpam-6473	45	11	leads	lead	VERB
ejpam-6473	45	12	to	to	ADP
ejpam-6473	45	13	headaches	headache	NOUN
ejpam-6473	45	14	,	,	PUNCT
ejpam-6473	45	15	dizziness	dizziness	NOUN
ejpam-6473	45	16	,	,	PUNCT
ejpam-6473	45	17	and	and	CCONJ
ejpam-6473	45	18	memory	memory	NOUN
ejpam-6473	45	19	loss	loss	NOUN
ejpam-6473	45	20	.	.	PUNCT
ejpam-6473	46	1	due	due	ADP
ejpam-6473	46	2	to	to	ADP
ejpam-6473	46	3	the	the	DET
ejpam-6473	46	4	strong	strong	ADJ
ejpam-6473	46	5	addiction	addiction	NOUN
ejpam-6473	46	6	to	to	ADP
ejpam-6473	46	7	smoking	smoke	VERB
ejpam-6473	46	8	only	only	ADV
ejpam-6473	46	9	20	20	NUM
ejpam-6473	46	10	-	-	SYM
ejpam-6473	46	11	22	22	NUM
ejpam-6473	46	12	percent	percent	NOUN
ejpam-6473	46	13	of	of	ADP
ejpam-6473	46	14	people	people	NOUN
ejpam-6473	46	15	can	can	AUX
ejpam-6473	46	16	quit	quit	VERB
ejpam-6473	46	17	smoking	smoking	NOUN
ejpam-6473	46	18	.	.	PUNCT
ejpam-6473	47	1	in	in	ADP
ejpam-6473	47	2	1997	1997	NUM
ejpam-6473	47	3	castillo	castillo	PROPN
ejpam-6473	47	4	garsow	garsow	PROPN
ejpam-6473	47	5	first	first	ADV
ejpam-6473	47	6	established	establish	VERB
ejpam-6473	47	7	a	a	DET
ejpam-6473	47	8	smoking	smoking	NOUN
ejpam-6473	47	9	model	model	NOUN
ejpam-6473	47	10	in	in	ADP
ejpam-6473	47	11	which	which	PRON
ejpam-6473	47	12	he	he	PRON
ejpam-6473	47	13	divides	divide	VERB
ejpam-6473	47	14	the	the	DET
ejpam-6473	47	15	total	total	ADJ
ejpam-6473	47	16	community	community	NOUN
ejpam-6473	47	17	into	into	ADP
ejpam-6473	47	18	3	3	NUM
ejpam-6473	47	19	classes	class	NOUN
ejpam-6473	47	20	p	p	NOUN
ejpam-6473	47	21	,	,	PUNCT
ejpam-6473	47	22	l	l	NOUN
ejpam-6473	47	23	and	and	CCONJ
ejpam-6473	47	24	s	s	VERB
ejpam-6473	47	25	that	that	PRON
ejpam-6473	47	26	are	be	AUX
ejpam-6473	47	27	potential	potential	ADJ
ejpam-6473	47	28	,	,	PUNCT
ejpam-6473	47	29	regular	regular	ADJ
ejpam-6473	47	30	,	,	PUNCT
ejpam-6473	47	31	and	and	CCONJ
ejpam-6473	47	32	quit	quit	VERB
ejpam-6473	47	33	smokers	smoker	NOUN
ejpam-6473	47	34	[	[	X
ejpam-6473	47	35	20	20	NUM
ejpam-6473	47	36	]	]	PUNCT
ejpam-6473	47	37	.	.	PUNCT
ejpam-6473	48	1	later	later	ADV
ejpam-6473	48	2	,	,	PUNCT
ejpam-6473	48	3	castillo	castillo	PROPN
ejpam-6473	48	4	’s	’s	PART
ejpam-6473	48	5	work	work	NOUN
ejpam-6473	48	6	was	be	AUX
ejpam-6473	48	7	expanded	expand	VERB
ejpam-6473	48	8	by	by	ADP
ejpam-6473	48	9	zamman	zamman	NOUN
ejpam-6473	48	10	[	[	X
ejpam-6473	48	11	21	21	NUM
ejpam-6473	48	12	]	]	X
ejpam-6473	48	13	,	,	PUNCT
ejpam-6473	48	14	in	in	ADP
ejpam-6473	48	15	s.	s.	PROPN
ejpam-6473	48	16	bano	bano	PROPN
ejpam-6473	48	17	et	et	PROPN
ejpam-6473	48	18	al	al	PROPN
ejpam-6473	48	19	.	.	PUNCT
ejpam-6473	48	20	/	/	SYM
ejpam-6473	48	21	eur	eur	PROPN
ejpam-6473	48	22	.	.	PUNCT
ejpam-6473	49	1	j.	j.	PROPN
ejpam-6473	49	2	pure	pure	PROPN
ejpam-6473	49	3	appl	appl	PROPN
ejpam-6473	49	4	.	.	PROPN
ejpam-6473	49	5	math	math	PROPN
ejpam-6473	49	6	,	,	PUNCT
ejpam-6473	49	7	18	18	NUM
ejpam-6473	49	8	(	(	PUNCT
ejpam-6473	49	9	4	4	NUM
ejpam-6473	49	10	)	)	PUNCT
ejpam-6473	49	11	(	(	PUNCT
ejpam-6473	49	12	2025	2025	NUM
ejpam-6473	49	13	)	)	PUNCT
ejpam-6473	49	14	,	,	PUNCT
ejpam-6473	49	15	6473	6473	NUM
ejpam-6473	49	16	3	3	NUM
ejpam-6473	49	17	of	of	ADP
ejpam-6473	49	18	38	38	NUM
ejpam-6473	49	19	which	which	PRON
ejpam-6473	49	20	he	he	PRON
ejpam-6473	49	21	applies	apply	VERB
ejpam-6473	49	22	two	two	NUM
ejpam-6473	49	23	control	control	NOUN
ejpam-6473	49	24	measures	measure	NOUN
ejpam-6473	49	25	.	.	PUNCT
ejpam-6473	50	1	okhyar	okhyar	NOUN
ejpam-6473	50	2	proposed	propose	VERB
ejpam-6473	50	3	a	a	DET
ejpam-6473	50	4	model	model	NOUN
ejpam-6473	50	5	in	in	ADP
ejpam-6473	50	6	which	which	PRON
ejpam-6473	50	7	he	he	PRON
ejpam-6473	50	8	divides	divide	VERB
ejpam-6473	50	9	the	the	DET
ejpam-6473	50	10	population	population	NOUN
ejpam-6473	50	11	of	of	ADP
ejpam-6473	50	12	quit	quit	VERB
ejpam-6473	50	13	smokers	smoker	NOUN
ejpam-6473	50	14	into	into	ADP
ejpam-6473	50	15	temporary	temporary	ADJ
ejpam-6473	50	16	and	and	CCONJ
ejpam-6473	50	17	permanent	permanent	ADJ
ejpam-6473	50	18	quit	quit	ADJ
ejpam-6473	50	19	smokers	smoker	NOUN
ejpam-6473	50	20	[	[	X
ejpam-6473	50	21	22	22	NUM
ejpam-6473	50	22	]	]	PUNCT
ejpam-6473	50	23	.	.	PUNCT
ejpam-6473	51	1	some	some	DET
ejpam-6473	51	2	other	other	ADJ
ejpam-6473	51	3	smoking	smoking	NOUN
ejpam-6473	51	4	-	-	PUNCT
ejpam-6473	51	5	related	relate	VERB
ejpam-6473	51	6	model	model	NOUN
ejpam-6473	51	7	includes	include	VERB
ejpam-6473	51	8	the	the	DET
ejpam-6473	51	9	works	work	NOUN
ejpam-6473	51	10	of	of	ADP
ejpam-6473	51	11	j.singh	j.singh	PROPN
ejpam-6473	51	12	,	,	PUNCT
ejpam-6473	51	13	who	who	PRON
ejpam-6473	51	14	developed	develop	VERB
ejpam-6473	51	15	a	a	DET
ejpam-6473	51	16	fractional	fractional	ADJ
ejpam-6473	51	17	model	model	NOUN
ejpam-6473	51	18	[	[	X
ejpam-6473	51	19	23	23	NUM
ejpam-6473	51	20	]	]	PUNCT
ejpam-6473	51	21	,	,	PUNCT
ejpam-6473	51	22	o	o	X
ejpam-6473	51	23	sharmoni	sharmoni	PROPN
ejpam-6473	51	24	,	,	PUNCT
ejpam-6473	51	25	who	who	PRON
ejpam-6473	51	26	presented	present	VERB
ejpam-6473	51	27	a	a	DET
ejpam-6473	51	28	model	model	NOUN
ejpam-6473	51	29	in	in	ADP
ejpam-6473	51	30	which	which	PRON
ejpam-6473	51	31	quit	quit	VERB
ejpam-6473	51	32	smokers	smoker	NOUN
ejpam-6473	51	33	are	be	AUX
ejpam-6473	51	34	divided	divide	VERB
ejpam-6473	51	35	into	into	ADP
ejpam-6473	51	36	temporary	temporary	ADJ
ejpam-6473	51	37	and	and	CCONJ
ejpam-6473	51	38	permanent	permanent	ADJ
ejpam-6473	51	39	quit	quit	ADJ
ejpam-6473	51	40	smokers	smoker	NOUN
ejpam-6473	51	41	and	and	CCONJ
ejpam-6473	51	42	he	he	PRON
ejpam-6473	51	43	also	also	ADV
ejpam-6473	51	44	added	add	VERB
ejpam-6473	51	45	the	the	DET
ejpam-6473	51	46	control	control	NOUN
ejpam-6473	51	47	strategies	strategy	NOUN
ejpam-6473	51	48	to	to	PART
ejpam-6473	51	49	analyze	analyze	VERB
ejpam-6473	51	50	most	most	ADV
ejpam-6473	51	51	effective	effective	ADJ
ejpam-6473	51	52	intervention	intervention	NOUN
ejpam-6473	51	53	to	to	PART
ejpam-6473	51	54	reduce	reduce	VERB
ejpam-6473	51	55	the	the	DET
ejpam-6473	51	56	smoking	smoking	NOUN
ejpam-6473	51	57	impact	impact	NOUN
ejpam-6473	51	58	[	[	X
ejpam-6473	51	59	24	24	NUM
ejpam-6473	51	60	]	]	PUNCT
ejpam-6473	51	61	,	,	PUNCT
ejpam-6473	51	62	mi	mi	PROPN
ejpam-6473	51	63	.	.	PROPN
ejpam-6473	51	64	chuhan	chuhan	PROPN
ejpam-6473	51	65	,	,	PUNCT
ejpam-6473	51	66	who	who	PRON
ejpam-6473	51	67	developed	develop	VERB
ejpam-6473	51	68	a	a	DET
ejpam-6473	51	69	smoking	smoking	NOUN
ejpam-6473	51	70	model	model	NOUN
ejpam-6473	51	71	in	in	ADP
ejpam-6473	51	72	which	which	PRON
ejpam-6473	51	73	homotopic	homotopic	ADJ
ejpam-6473	51	74	analysis	analysis	NOUN
ejpam-6473	51	75	method	method	NOUN
ejpam-6473	51	76	is	be	AUX
ejpam-6473	51	77	used	use	VERB
ejpam-6473	51	78	[	[	PUNCT
ejpam-6473	51	79	25	25	NUM
ejpam-6473	51	80	]	]	PUNCT
ejpam-6473	51	81	.	.	PUNCT
ejpam-6473	52	1	smoking	smoking	NOUN
ejpam-6473	52	2	remains	remain	VERB
ejpam-6473	52	3	a	a	DET
ejpam-6473	52	4	leading	lead	VERB
ejpam-6473	52	5	cause	cause	NOUN
ejpam-6473	52	6	of	of	ADP
ejpam-6473	52	7	preventable	preventable	ADJ
ejpam-6473	52	8	deaths	death	NOUN
ejpam-6473	52	9	globally	globally	ADV
ejpam-6473	52	10	.	.	PUNCT
ejpam-6473	53	1	current	current	ADJ
ejpam-6473	53	2	work	work	NOUN
ejpam-6473	53	3	is	be	AUX
ejpam-6473	53	4	related	relate	VERB
ejpam-6473	53	5	to	to	ADP
ejpam-6473	53	6	a	a	DET
ejpam-6473	53	7	new	new	ADJ
ejpam-6473	53	8	smoking	smoking	NOUN
ejpam-6473	53	9	model	model	NOUN
ejpam-6473	53	10	with	with	ADP
ejpam-6473	53	11	intervention	intervention	NOUN
ejpam-6473	53	12	-	-	PUNCT
ejpam-6473	53	13	based	base	VERB
ejpam-6473	53	14	time	time	NOUN
ejpam-6473	53	15	delay	delay	NOUN
ejpam-6473	53	16	and	and	CCONJ
ejpam-6473	53	17	controls	control	NOUN
ejpam-6473	53	18	not	not	PART
ejpam-6473	53	19	previously	previously	ADV
ejpam-6473	53	20	explored	explore	VERB
ejpam-6473	53	21	to	to	PART
ejpam-6473	53	22	fill	fill	VERB
ejpam-6473	53	23	the	the	DET
ejpam-6473	53	24	gap	gap	NOUN
ejpam-6473	53	25	.	.	PUNCT
ejpam-6473	54	1	we	we	PRON
ejpam-6473	54	2	offer	offer	VERB
ejpam-6473	54	3	theoretical	theoretical	ADJ
ejpam-6473	54	4	insights	insight	NOUN
ejpam-6473	54	5	and	and	CCONJ
ejpam-6473	54	6	numerical	numerical	ADJ
ejpam-6473	54	7	validations	validation	NOUN
ejpam-6473	54	8	,	,	PUNCT
ejpam-6473	54	9	with	with	ADP
ejpam-6473	54	10	sensitivity	sensitivity	NOUN
ejpam-6473	54	11	analysis	analysis	NOUN
ejpam-6473	54	12	and	and	CCONJ
ejpam-6473	54	13	optimization	optimization	NOUN
ejpam-6473	54	14	-	-	PUNCT
ejpam-6473	54	15	based	base	VERB
ejpam-6473	54	16	techniques	technique	NOUN
ejpam-6473	54	17	to	to	PART
ejpam-6473	54	18	validate	validate	VERB
ejpam-6473	54	19	efficacy	efficacy	NOUN
ejpam-6473	54	20	.	.	PUNCT
ejpam-6473	55	1	the	the	DET
ejpam-6473	55	2	main	main	ADJ
ejpam-6473	55	3	contributions	contribution	NOUN
ejpam-6473	55	4	of	of	ADP
ejpam-6473	55	5	this	this	DET
ejpam-6473	55	6	work	work	NOUN
ejpam-6473	55	7	are	be	AUX
ejpam-6473	55	8	as	as	SCONJ
ejpam-6473	55	9	follows	follow	VERB
ejpam-6473	55	10	:	:	PUNCT
ejpam-6473	55	11	formulation	formulation	NOUN
ejpam-6473	55	12	of	of	ADP
ejpam-6473	55	13	a	a	DET
ejpam-6473	55	14	novel	novel	ADJ
ejpam-6473	55	15	delay	delay	NOUN
ejpam-6473	55	16	-	-	PUNCT
ejpam-6473	55	17	free	free	ADJ
ejpam-6473	55	18	optimal	optimal	ADJ
ejpam-6473	55	19	control	control	NOUN
ejpam-6473	55	20	model	model	NOUN
ejpam-6473	55	21	.	.	PUNCT
ejpam-6473	56	1	stability	stability	NOUN
ejpam-6473	56	2	analysis	analysis	NOUN
ejpam-6473	56	3	using	use	VERB
ejpam-6473	56	4	lyapunov	lyapunov	NOUN
ejpam-6473	56	5	and	and	CCONJ
ejpam-6473	56	6	sensitivity	sensitivity	NOUN
ejpam-6473	56	7	theory	theory	NOUN
ejpam-6473	56	8	.	.	PUNCT
ejpam-6473	57	1	derivation	derivation	NOUN
ejpam-6473	57	2	and	and	CCONJ
ejpam-6473	57	3	verification	verification	NOUN
ejpam-6473	57	4	of	of	ADP
ejpam-6473	57	5	effective	effective	ADJ
ejpam-6473	57	6	control	control	NOUN
ejpam-6473	57	7	strategies	strategy	NOUN
ejpam-6473	57	8	through	through	ADP
ejpam-6473	57	9	numerical	numerical	ADJ
ejpam-6473	57	10	simulations	simulation	NOUN
ejpam-6473	57	11	.	.	PUNCT
ejpam-6473	58	1	the	the	DET
ejpam-6473	58	2	rest	rest	NOUN
ejpam-6473	58	3	of	of	ADP
ejpam-6473	58	4	the	the	DET
ejpam-6473	58	5	paper	paper	NOUN
ejpam-6473	58	6	is	be	AUX
ejpam-6473	58	7	organized	organize	VERB
ejpam-6473	58	8	as	as	SCONJ
ejpam-6473	58	9	follows	follow	VERB
ejpam-6473	58	10	:	:	PUNCT
ejpam-6473	58	11	section	section	NOUN
ejpam-6473	58	12	2	2	NUM
ejpam-6473	58	13	develops	develop	VERB
ejpam-6473	58	14	the	the	DET
ejpam-6473	58	15	new	new	ADJ
ejpam-6473	58	16	model	model	NOUN
ejpam-6473	58	17	formulation	formulation	NOUN
ejpam-6473	58	18	.	.	PUNCT
ejpam-6473	59	1	section	section	NOUN
ejpam-6473	59	2	3	3	NUM
ejpam-6473	59	3	provides	provide	VERB
ejpam-6473	59	4	a	a	DET
ejpam-6473	59	5	theoretical	theoretical	ADJ
ejpam-6473	59	6	analysis	analysis	NOUN
ejpam-6473	59	7	.	.	PUNCT
ejpam-6473	60	1	section	section	NOUN
ejpam-6473	60	2	4	4	NUM
ejpam-6473	60	3	discusses	discuss	VERB
ejpam-6473	60	4	the	the	DET
ejpam-6473	60	5	control	control	NOUN
ejpam-6473	60	6	problem	problem	NOUN
ejpam-6473	60	7	.	.	PUNCT
ejpam-6473	61	1	section	section	NOUN
ejpam-6473	61	2	5	5	NUM
ejpam-6473	61	3	is	be	AUX
ejpam-6473	61	4	related	relate	VERB
ejpam-6473	61	5	the	the	DET
ejpam-6473	61	6	delay	delay	NOUN
ejpam-6473	61	7	model	model	NOUN
ejpam-6473	61	8	with	with	ADP
ejpam-6473	61	9	stability	stability	NOUN
ejpam-6473	61	10	analysis	analysis	NOUN
ejpam-6473	61	11	,	,	PUNCT
ejpam-6473	61	12	section	section	NOUN
ejpam-6473	61	13	6	6	NUM
ejpam-6473	61	14	shows	show	VERB
ejpam-6473	61	15	the	the	DET
ejpam-6473	61	16	numerical	numerical	ADJ
ejpam-6473	61	17	simulations	simulation	NOUN
ejpam-6473	61	18	and	and	CCONJ
ejpam-6473	61	19	section	section	NOUN
ejpam-6473	61	20	7	7	NUM
ejpam-6473	61	21	provides	provide	VERB
ejpam-6473	61	22	the	the	DET
ejpam-6473	61	23	discussion	discussion	NOUN
ejpam-6473	61	24	of	of	ADP
ejpam-6473	61	25	model	model	NOUN
ejpam-6473	61	26	,	,	PUNCT
ejpam-6473	61	27	control	control	NOUN
ejpam-6473	61	28	and	and	CCONJ
ejpam-6473	61	29	delay	delay	NOUN
ejpam-6473	61	30	applied	apply	VERB
ejpam-6473	61	31	on	on	ADP
ejpam-6473	61	32	system	system	NOUN
ejpam-6473	61	33	and	and	CCONJ
ejpam-6473	61	34	finally	finally	ADV
ejpam-6473	61	35	in	in	ADP
ejpam-6473	61	36	section	section	NOUN
ejpam-6473	61	37	8	8	NUM
ejpam-6473	61	38	,	,	PUNCT
ejpam-6473	61	39	we	we	PRON
ejpam-6473	61	40	present	present	VERB
ejpam-6473	61	41	the	the	DET
ejpam-6473	61	42	conclusion	conclusion	NOUN
ejpam-6473	61	43	of	of	ADP
ejpam-6473	61	44	this	this	DET
ejpam-6473	61	45	work	work	NOUN
ejpam-6473	61	46	.	.	PUNCT
ejpam-6473	62	1	2	2	X
ejpam-6473	62	2	.	.	X
ejpam-6473	62	3	model	model	NOUN
ejpam-6473	62	4	formation	formation	NOUN
ejpam-6473	62	5	in	in	ADP
ejpam-6473	62	6	the	the	DET
ejpam-6473	62	7	proposed	propose	VERB
ejpam-6473	62	8	model	model	NOUN
ejpam-6473	62	9	,	,	PUNCT
ejpam-6473	62	10	the	the	DET
ejpam-6473	62	11	total	total	ADJ
ejpam-6473	62	12	community	community	NOUN
ejpam-6473	62	13	was	be	AUX
ejpam-6473	62	14	divided	divide	VERB
ejpam-6473	62	15	into	into	ADP
ejpam-6473	62	16	four	four	NUM
ejpam-6473	62	17	distinct	distinct	ADJ
ejpam-6473	62	18	classes	class	NOUN
ejpam-6473	62	19	,	,	PUNCT
ejpam-6473	62	20	which	which	PRON
ejpam-6473	62	21	are	be	AUX
ejpam-6473	62	22	plsq	plsq	NOUN
ejpam-6473	62	23	.	.	PUNCT
ejpam-6473	63	1	here	here	ADV
ejpam-6473	63	2	,	,	PUNCT
ejpam-6473	63	3	p	p	NOUN
ejpam-6473	63	4	stands	stand	VERB
ejpam-6473	63	5	for	for	ADP
ejpam-6473	63	6	potential	potential	ADJ
ejpam-6473	63	7	smokers	smoker	NOUN
ejpam-6473	63	8	,	,	PUNCT
ejpam-6473	63	9	l	l	NOUN
ejpam-6473	63	10	stands	stand	VERB
ejpam-6473	63	11	for	for	ADP
ejpam-6473	63	12	light	light	ADJ
ejpam-6473	63	13	smokers	smoker	NOUN
ejpam-6473	63	14	,	,	PUNCT
ejpam-6473	63	15	s	s	VERB
ejpam-6473	63	16	stands	stand	VERB
ejpam-6473	63	17	for	for	ADP
ejpam-6473	63	18	regular	regular	ADJ
ejpam-6473	63	19	smokers	smoker	NOUN
ejpam-6473	63	20	,	,	PUNCT
ejpam-6473	63	21	and	and	CCONJ
ejpam-6473	63	22	q	q	PROPN
ejpam-6473	63	23	stands	stand	VERB
ejpam-6473	63	24	for	for	ADP
ejpam-6473	63	25	quit	quit	ADJ
ejpam-6473	63	26	smokers	smoker	NOUN
ejpam-6473	63	27	.	.	PUNCT
ejpam-6473	64	1	n	n	PRON
ejpam-6473	64	2	is	be	AUX
ejpam-6473	64	3	used	use	VERB
ejpam-6473	64	4	to	to	PART
ejpam-6473	64	5	denote	denote	VERB
ejpam-6473	64	6	the	the	DET
ejpam-6473	64	7	total	total	ADJ
ejpam-6473	64	8	population	population	NOUN
ejpam-6473	64	9	as	as	ADP
ejpam-6473	64	10	n	n	NOUN
ejpam-6473	64	11	=	=	SYM
ejpam-6473	64	12	p	p	PROPN
ejpam-6473	65	1	+	+	NOUN
ejpam-6473	65	2	l	l	NOUN
ejpam-6473	65	3	+	+	SYM
ejpam-6473	65	4	s	s	PART
ejpam-6473	66	1	+	+	X
ejpam-6473	66	2	q.	q.	NOUN
ejpam-6473	66	3	the	the	DET
ejpam-6473	66	4	smoking	smoking	NOUN
ejpam-6473	66	5	cessation	cessation	NOUN
ejpam-6473	66	6	model	model	NOUN
ejpam-6473	66	7	with	with	ADP
ejpam-6473	66	8	convex	convex	ADJ
ejpam-6473	66	9	incidence	incidence	NOUN
ejpam-6473	66	10	rate	rate	NOUN
ejpam-6473	66	11	is	be	AUX
ejpam-6473	66	12	given	give	VERB
ejpam-6473	66	13	as	as	ADP
ejpam-6473	66	14	:	:	PUNCT
ejpam-6473	66	15	dp	dp	NOUN
ejpam-6473	66	16	dt	dt	NOUN
ejpam-6473	66	17	=	=	SYM
ejpam-6473	66	18	λ−	λ−	PROPN
ejpam-6473	66	19	(	(	PUNCT
ejpam-6473	66	20	b+	b+	X
ejpam-6473	66	21	µ)p	µ)p	PUNCT
ejpam-6473	66	22	−	−	PROPN
ejpam-6473	66	23	βps(1	βps(1	NOUN
ejpam-6473	66	24	+	+	CCONJ
ejpam-6473	66	25	νs	νs	NOUN
ejpam-6473	66	26	)	)	PUNCT
ejpam-6473	66	27	,	,	PUNCT
ejpam-6473	66	28	dl	dl	PROPN
ejpam-6473	66	29	dt	dt	NOUN
ejpam-6473	66	30	=	=	PUNCT
ejpam-6473	66	31	βps(1	βps(1	X
ejpam-6473	66	32	+	+	X
ejpam-6473	66	33	νs)−	νs)−	NOUN
ejpam-6473	66	34	(	(	PUNCT
ejpam-6473	66	35	b+	b+	X
ejpam-6473	66	36	µ+	µ+	DET
ejpam-6473	66	37	ζ)l	ζ)l	NOUN
ejpam-6473	66	38	,	,	PUNCT
ejpam-6473	66	39	ds	ds	ADJ
ejpam-6473	66	40	dt	dt	X
ejpam-6473	66	41	=	=	SYM
ejpam-6473	66	42	ζl−	ζl−	X
ejpam-6473	66	43	(	(	PUNCT
ejpam-6473	66	44	b+	b+	X
ejpam-6473	66	45	µ+	µ+	X
ejpam-6473	66	46	δ)s	δ)s	NOUN
ejpam-6473	66	47	,	,	PUNCT
ejpam-6473	66	48	dq	dq	NOUN
ejpam-6473	66	49	dt	dt	NOUN
ejpam-6473	66	50	=	=	NOUN
ejpam-6473	66	51	δs	δs	NOUN
ejpam-6473	66	52	−	−	PROPN
ejpam-6473	66	53	(	(	PUNCT
ejpam-6473	66	54	b+	b+	X
ejpam-6473	66	55	µ)q	µ)q	X
ejpam-6473	66	56	.	.	PUNCT
ejpam-6473	67	1	(	(	PUNCT
ejpam-6473	67	2	1	1	X
ejpam-6473	67	3	)	)	PUNCT
ejpam-6473	67	4	the	the	DET
ejpam-6473	67	5	initial	initial	ADJ
ejpam-6473	67	6	conditions	condition	NOUN
ejpam-6473	67	7	are	be	AUX
ejpam-6473	67	8	p0	p0	NOUN
ejpam-6473	67	9	≥	≥	NUM
ejpam-6473	67	10	0	0	NUM
ejpam-6473	67	11	,	,	PUNCT
ejpam-6473	67	12	l0	l0	PROPN
ejpam-6473	67	13	≥	≥	NOUN
ejpam-6473	67	14	0	0	NUM
ejpam-6473	67	15	,	,	PUNCT
ejpam-6473	67	16	s0	s0	PROPN
ejpam-6473	67	17	≥	≥	NUM
ejpam-6473	67	18	0	0	NUM
ejpam-6473	67	19	,	,	PUNCT
ejpam-6473	67	20	q0	q0	VERB
ejpam-6473	67	21	≥	≥	NOUN
ejpam-6473	67	22	0	0	NUM
ejpam-6473	67	23	.	.	PUNCT
ejpam-6473	68	1	here	here	ADV
ejpam-6473	68	2	β	β	X
ejpam-6473	68	3	and	and	CCONJ
ejpam-6473	68	4	ν	ν	PROPN
ejpam-6473	68	5	are	be	AUX
ejpam-6473	68	6	the	the	DET
ejpam-6473	68	7	smoking	smoking	NOUN
ejpam-6473	68	8	transmission	transmission	NOUN
ejpam-6473	68	9	coefficient	coefficient	NOUN
ejpam-6473	68	10	,	,	PUNCT
ejpam-6473	68	11	b	b	PROPN
ejpam-6473	68	12	represents	represent	VERB
ejpam-6473	68	13	the	the	DET
ejpam-6473	68	14	death	death	NOUN
ejpam-6473	68	15	rate	rate	NOUN
ejpam-6473	68	16	due	due	ADP
ejpam-6473	68	17	to	to	ADP
ejpam-6473	68	18	smoking	smoking	NOUN
ejpam-6473	68	19	-	-	PUNCT
ejpam-6473	68	20	related	relate	VERB
ejpam-6473	68	21	complications	complication	NOUN
ejpam-6473	68	22	.	.	PUNCT
ejpam-6473	69	1	while	while	SCONJ
ejpam-6473	69	2	it	it	PRON
ejpam-6473	69	3	is	be	AUX
ejpam-6473	69	4	generally	generally	ADV
ejpam-6473	69	5	associated	associate	VERB
ejpam-6473	69	6	with	with	ADP
ejpam-6473	69	7	active	active	ADJ
ejpam-6473	69	8	smokers	smoker	NOUN
ejpam-6473	69	9	,	,	PUNCT
ejpam-6473	69	10	we	we	PRON
ejpam-6473	69	11	also	also	ADV
ejpam-6473	69	12	include	include	VERB
ejpam-6473	69	13	it	it	PRON
ejpam-6473	69	14	in	in	ADP
ejpam-6473	69	15	the	the	DET
ejpam-6473	69	16	p	p	NOUN
ejpam-6473	69	17	(	(	PUNCT
ejpam-6473	69	18	potential	potential	ADJ
ejpam-6473	69	19	smokers	smoker	NOUN
ejpam-6473	69	20	)	)	PUNCT
ejpam-6473	69	21	class	class	NOUN
ejpam-6473	69	22	to	to	PART
ejpam-6473	69	23	capture	capture	VERB
ejpam-6473	69	24	individuals	individual	NOUN
ejpam-6473	69	25	who	who	PRON
ejpam-6473	69	26	may	may	AUX
ejpam-6473	69	27	already	already	ADV
ejpam-6473	69	28	be	be	AUX
ejpam-6473	69	29	affected	affect	VERB
ejpam-6473	69	30	by	by	ADP
ejpam-6473	69	31	early	early	ADJ
ejpam-6473	69	32	-	-	PUNCT
ejpam-6473	69	33	stage	stage	NOUN
ejpam-6473	69	34	health	health	NOUN
ejpam-6473	69	35	issues	issue	NOUN
ejpam-6473	69	36	(	(	PUNCT
ejpam-6473	69	37	such	such	ADJ
ejpam-6473	69	38	as	as	ADP
ejpam-6473	69	39	heart	heart	NOUN
ejpam-6473	69	40	or	or	CCONJ
ejpam-6473	69	41	lung	lung	NOUN
ejpam-6473	69	42	problems	problem	NOUN
ejpam-6473	69	43	)	)	PUNCT
ejpam-6473	69	44	or	or	CCONJ
ejpam-6473	69	45	second	second	ADJ
ejpam-6473	69	46	-	-	PUNCT
ejpam-6473	69	47	hand	hand	NOUN
ejpam-6473	69	48	smoke	smoke	NOUN
ejpam-6473	69	49	exposure	exposure	NOUN
ejpam-6473	69	50	.	.	PUNCT
ejpam-6473	70	1	this	this	PRON
ejpam-6473	70	2	reflects	reflect	VERB
ejpam-6473	70	3	real	real	ADJ
ejpam-6473	70	4	-	-	PUNCT
ejpam-6473	70	5	world	world	NOUN
ejpam-6473	70	6	situations	situation	NOUN
ejpam-6473	70	7	where	where	SCONJ
ejpam-6473	70	8	people	people	NOUN
ejpam-6473	70	9	are	be	AUX
ejpam-6473	70	10	at	at	ADP
ejpam-6473	70	11	risk	risk	NOUN
ejpam-6473	70	12	due	due	ADP
ejpam-6473	70	13	to	to	ADP
ejpam-6473	70	14	environmental	environmental	ADJ
ejpam-6473	70	15	s.	s.	PROPN
ejpam-6473	70	16	bano	bano	PROPN
ejpam-6473	70	17	et	et	PROPN
ejpam-6473	70	18	al	al	PROPN
ejpam-6473	70	19	.	.	PUNCT
ejpam-6473	70	20	/	/	SYM
ejpam-6473	70	21	eur	eur	PROPN
ejpam-6473	70	22	.	.	PUNCT
ejpam-6473	71	1	j.	j.	PROPN
ejpam-6473	71	2	pure	pure	PROPN
ejpam-6473	71	3	appl	appl	PROPN
ejpam-6473	71	4	.	.	PROPN
ejpam-6473	71	5	math	math	PROPN
ejpam-6473	71	6	,	,	PUNCT
ejpam-6473	71	7	18	18	NUM
ejpam-6473	71	8	(	(	PUNCT
ejpam-6473	71	9	4	4	NUM
ejpam-6473	71	10	)	)	PUNCT
ejpam-6473	71	11	(	(	PUNCT
ejpam-6473	71	12	2025	2025	NUM
ejpam-6473	71	13	)	)	PUNCT
ejpam-6473	71	14	,	,	PUNCT
ejpam-6473	71	15	6473	6473	NUM
ejpam-6473	71	16	4	4	NUM
ejpam-6473	71	17	of	of	ADP
ejpam-6473	71	18	38	38	NUM
ejpam-6473	71	19	figure	figure	NOUN
ejpam-6473	71	20	1	1	NUM
ejpam-6473	71	21	:	:	PUNCT
ejpam-6473	71	22	the	the	DET
ejpam-6473	71	23	graph	graph	NOUN
ejpam-6473	71	24	of	of	ADP
ejpam-6473	71	25	the	the	DET
ejpam-6473	71	26	proposed	propose	VERB
ejpam-6473	71	27	model	model	NOUN
ejpam-6473	71	28	is	be	AUX
ejpam-6473	71	29	given	give	VERB
ejpam-6473	71	30	above	above	ADV
ejpam-6473	71	31	.	.	PUNCT
ejpam-6473	72	1	exposure	exposure	NOUN
ejpam-6473	72	2	or	or	CCONJ
ejpam-6473	72	3	the	the	DET
ejpam-6473	72	4	smoking	smoking	NOUN
ejpam-6473	72	5	behavior	behavior	NOUN
ejpam-6473	72	6	of	of	ADP
ejpam-6473	72	7	friends	friend	NOUN
ejpam-6473	72	8	and	and	CCONJ
ejpam-6473	72	9	family	family	NOUN
ejpam-6473	72	10	,	,	PUNCT
ejpam-6473	72	11	even	even	ADV
ejpam-6473	72	12	before	before	SCONJ
ejpam-6473	72	13	they	they	PRON
ejpam-6473	72	14	themselves	themselves	PRON
ejpam-6473	72	15	begin	begin	VERB
ejpam-6473	72	16	smoking	smoke	VERB
ejpam-6473	72	17	.	.	PUNCT
ejpam-6473	73	1	λ	λ	X
ejpam-6473	73	2	the	the	DET
ejpam-6473	73	3	continuous	continuous	ADJ
ejpam-6473	73	4	influx	influx	NOUN
ejpam-6473	73	5	of	of	ADP
ejpam-6473	73	6	the	the	DET
ejpam-6473	73	7	potential	potential	ADJ
ejpam-6473	73	8	smokers	smoker	NOUN
ejpam-6473	73	9	(	(	PUNCT
ejpam-6473	73	10	vulnerable	vulnerable	ADJ
ejpam-6473	73	11	smokers	smoker	NOUN
ejpam-6473	73	12	)	)	PUNCT
ejpam-6473	74	1	ν	ν	NOUN
ejpam-6473	74	2	constant	constant	ADJ
ejpam-6473	74	3	rate	rate	NOUN
ejpam-6473	74	4	β	β	X
ejpam-6473	74	5	constant	constant	ADJ
ejpam-6473	74	6	rate	rate	NOUN
ejpam-6473	74	7	ζ	ζ	VERB
ejpam-6473	74	8	the	the	DET
ejpam-6473	74	9	transition	transition	NOUN
ejpam-6473	74	10	rate	rate	NOUN
ejpam-6473	74	11	from	from	ADP
ejpam-6473	74	12	light	light	ADJ
ejpam-6473	74	13	smokers	smoker	NOUN
ejpam-6473	74	14	to	to	ADP
ejpam-6473	74	15	full	full	ADJ
ejpam-6473	74	16	smoker	smoker	NOUN
ejpam-6473	74	17	δ	δ	PROPN
ejpam-6473	74	18	the	the	DET
ejpam-6473	74	19	smoking	smoking	NOUN
ejpam-6473	74	20	cessation	cessation	NOUN
ejpam-6473	74	21	rate	rate	PROPN
ejpam-6473	74	22	µ	µ	PRON
ejpam-6473	74	23	natural	natural	ADJ
ejpam-6473	74	24	mortality	mortality	NOUN
ejpam-6473	74	25	rate	rate	NOUN
ejpam-6473	74	26	b	b	NOUN
ejpam-6473	74	27	smoking	smoking	NOUN
ejpam-6473	74	28	related	relate	VERB
ejpam-6473	74	29	mortality	mortality	NOUN
ejpam-6473	74	30	rate	rate	NOUN
ejpam-6473	74	31	table	table	NOUN
ejpam-6473	74	32	1	1	NUM
ejpam-6473	74	33	:	:	PUNCT
ejpam-6473	74	34	description	description	NOUN
ejpam-6473	74	35	of	of	ADP
ejpam-6473	74	36	the	the	DET
ejpam-6473	74	37	parameter	parameter	NOUN
ejpam-6473	74	38	s.	s.	PROPN
ejpam-6473	74	39	bano	bano	PROPN
ejpam-6473	74	40	et	et	PROPN
ejpam-6473	74	41	al	al	PROPN
ejpam-6473	74	42	.	.	PUNCT
ejpam-6473	74	43	/	/	SYM
ejpam-6473	74	44	eur	eur	PROPN
ejpam-6473	74	45	.	.	PUNCT
ejpam-6473	75	1	j.	j.	PROPN
ejpam-6473	75	2	pure	pure	PROPN
ejpam-6473	75	3	appl	appl	PROPN
ejpam-6473	75	4	.	.	PROPN
ejpam-6473	75	5	math	math	PROPN
ejpam-6473	75	6	,	,	PUNCT
ejpam-6473	75	7	18	18	NUM
ejpam-6473	75	8	(	(	PUNCT
ejpam-6473	75	9	4	4	NUM
ejpam-6473	75	10	)	)	PUNCT
ejpam-6473	75	11	(	(	PUNCT
ejpam-6473	75	12	2025	2025	NUM
ejpam-6473	75	13	)	)	PUNCT
ejpam-6473	75	14	,	,	PUNCT
ejpam-6473	75	15	6473	6473	NUM
ejpam-6473	75	16	5	5	NUM
ejpam-6473	75	17	of	of	ADP
ejpam-6473	75	18	38	38	NUM
ejpam-6473	75	19	as	as	SCONJ
ejpam-6473	75	20	the	the	DET
ejpam-6473	75	21	total	total	ADJ
ejpam-6473	75	22	population	population	NOUN
ejpam-6473	75	23	is	be	AUX
ejpam-6473	75	24	equal	equal	ADJ
ejpam-6473	75	25	to	to	ADP
ejpam-6473	75	26	the	the	DET
ejpam-6473	75	27	sum	sum	NOUN
ejpam-6473	75	28	of	of	ADP
ejpam-6473	75	29	all	all	DET
ejpam-6473	75	30	classes	class	NOUN
ejpam-6473	76	1	,	,	PUNCT
ejpam-6473	76	2	this	this	PRON
ejpam-6473	76	3	implies	imply	VERB
ejpam-6473	76	4	that	that	SCONJ
ejpam-6473	76	5	n	n	NOUN
ejpam-6473	76	6	=	=	SYM
ejpam-6473	76	7	p	p	X
ejpam-6473	77	1	+	+	NUM
ejpam-6473	77	2	l+	l+	NOUN
ejpam-6473	77	3	s	s	PART
ejpam-6473	77	4	+	+	NOUN
ejpam-6473	77	5	q	q	ADJ
ejpam-6473	77	6	,	,	PUNCT
ejpam-6473	77	7	dn	dn	ADJ
ejpam-6473	77	8	dt	dt	NOUN
ejpam-6473	77	9	=	=	SYM
ejpam-6473	77	10	λ−	λ−	PROPN
ejpam-6473	77	11	(	(	PUNCT
ejpam-6473	77	12	b+	b+	X
ejpam-6473	77	13	µ)n	µ)n	X
ejpam-6473	77	14	.	.	PUNCT
ejpam-6473	77	15	by	by	ADP
ejpam-6473	77	16	using	use	VERB
ejpam-6473	77	17	the	the	DET
ejpam-6473	77	18	integrating	integrate	VERB
ejpam-6473	77	19	factor	factor	NOUN
ejpam-6473	77	20	e(b+µ)t	e(b+µ)t	PROPN
ejpam-6473	77	21	and	and	CCONJ
ejpam-6473	77	22	after	after	ADP
ejpam-6473	77	23	some	some	DET
ejpam-6473	77	24	computation	computation	NOUN
ejpam-6473	77	25	,	,	PUNCT
ejpam-6473	77	26	we	we	PRON
ejpam-6473	77	27	get	get	VERB
ejpam-6473	77	28	n	n	PRON
ejpam-6473	77	29	=	=	SYM
ejpam-6473	77	30	λ	λ	X
ejpam-6473	77	31	(	(	PUNCT
ejpam-6473	77	32	b+µ	b+µ	NOUN
ejpam-6473	77	33	)	)	PUNCT
ejpam-6473	77	34	as	as	ADP
ejpam-6473	77	35	t	t	PROPN
ejpam-6473	77	36	→	→	SYM
ejpam-6473	77	37	∞.	∞.	PROPN
ejpam-6473	77	38	this	this	PRON
ejpam-6473	77	39	implies	imply	VERB
ejpam-6473	77	40	that	that	SCONJ
ejpam-6473	77	41	all	all	DET
ejpam-6473	77	42	the	the	DET
ejpam-6473	77	43	system	system	NOUN
ejpam-6473	77	44	trajectory	trajectory	NOUN
ejpam-6473	77	45	is	be	AUX
ejpam-6473	77	46	bounded	bound	VERB
ejpam-6473	77	47	within	within	ADP
ejpam-6473	77	48	a	a	DET
ejpam-6473	77	49	feasible	feasible	ADJ
ejpam-6473	77	50	region	region	NOUN
ejpam-6473	77	51	ω	ω	PROPN
ejpam-6473	77	52	.	.	PUNCT
ejpam-6473	78	1	ω	ω	PROPN
ejpam-6473	78	2	=	=	SYM
ejpam-6473	78	3	{	{	PUNCT
ejpam-6473	78	4	(	(	PUNCT
ejpam-6473	78	5	p	p	X
ejpam-6473	78	6	,	,	PUNCT
ejpam-6473	78	7	l	l	NOUN
ejpam-6473	78	8	,	,	PUNCT
ejpam-6473	78	9	s	s	X
ejpam-6473	78	10	,	,	PUNCT
ejpam-6473	78	11	q	q	NOUN
ejpam-6473	78	12	)	)	PUNCT
ejpam-6473	78	13	:	:	PUNCT
ejpam-6473	78	14	0	0	NUM
ejpam-6473	78	15	≤	≤	NUM
ejpam-6473	78	16	n	n	CCONJ
ejpam-6473	78	17	≤	≤	NOUN
ejpam-6473	78	18	λ	λ	PROPN
ejpam-6473	78	19	(	(	PUNCT
ejpam-6473	78	20	b+µ	b+µ	NOUN
ejpam-6473	78	21	)	)	PUNCT
ejpam-6473	78	22	}	}	PUNCT
ejpam-6473	78	23	.	.	PUNCT
ejpam-6473	79	1	(	(	PUNCT
ejpam-6473	79	2	2	2	NUM
ejpam-6473	79	3	)	)	PUNCT
ejpam-6473	79	4	3	3	NUM
ejpam-6473	79	5	.	.	X
ejpam-6473	79	6	positivity	positivity	NOUN
ejpam-6473	79	7	and	and	CCONJ
ejpam-6473	79	8	boundedness	boundedness	NOUN
ejpam-6473	79	9	since	since	SCONJ
ejpam-6473	79	10	positivity	positivity	NOUN
ejpam-6473	79	11	can	can	AUX
ejpam-6473	79	12	be	be	AUX
ejpam-6473	79	13	assumed	assume	VERB
ejpam-6473	79	14	due	due	ADP
ejpam-6473	79	15	to	to	ADP
ejpam-6473	79	16	non	non	ADJ
ejpam-6473	79	17	-	-	ADJ
ejpam-6473	79	18	negative	negative	ADJ
ejpam-6473	79	19	initial	initial	ADJ
ejpam-6473	79	20	conditions	condition	NOUN
ejpam-6473	79	21	and	and	CCONJ
ejpam-6473	79	22	biological	biological	ADJ
ejpam-6473	79	23	feasibility	feasibility	NOUN
ejpam-6473	79	24	.	.	PUNCT
ejpam-6473	80	1	3.1	3.1	NUM
ejpam-6473	80	2	.	.	PUNCT
ejpam-6473	80	3	existence	existence	NOUN
ejpam-6473	80	4	of	of	ADP
ejpam-6473	80	5	equilibrium	equilibrium	NOUN
ejpam-6473	80	6	point	point	NOUN
ejpam-6473	80	7	in	in	ADP
ejpam-6473	80	8	this	this	DET
ejpam-6473	80	9	subsection	subsection	NOUN
ejpam-6473	80	10	,	,	PUNCT
ejpam-6473	80	11	we	we	PRON
ejpam-6473	80	12	discuss	discuss	VERB
ejpam-6473	80	13	the	the	DET
ejpam-6473	80	14	equilibrium	equilibrium	NOUN
ejpam-6473	80	15	points	point	NOUN
ejpam-6473	80	16	of	of	ADP
ejpam-6473	80	17	the	the	DET
ejpam-6473	80	18	plsq	plsq	NOUN
ejpam-6473	80	19	model	model	NOUN
ejpam-6473	80	20	.	.	PUNCT
ejpam-6473	81	1	there	there	PRON
ejpam-6473	81	2	are	be	VERB
ejpam-6473	81	3	two	two	NUM
ejpam-6473	81	4	equilibrium	equilibrium	NOUN
ejpam-6473	81	5	points	point	NOUN
ejpam-6473	81	6	of	of	ADP
ejpam-6473	81	7	the	the	DET
ejpam-6473	81	8	model	model	NOUN
ejpam-6473	81	9	(	(	PUNCT
ejpam-6473	81	10	1	1	NUM
ejpam-6473	81	11	)	)	PUNCT
ejpam-6473	81	12	that	that	PRON
ejpam-6473	81	13	are	be	AUX
ejpam-6473	81	14	smoking	smoking	NOUN
ejpam-6473	81	15	-	-	PUNCT
ejpam-6473	81	16	free	free	ADJ
ejpam-6473	81	17	and	and	CCONJ
ejpam-6473	81	18	endemic	endemic	ADJ
ejpam-6473	81	19	equilibrium	equilibrium	NOUN
ejpam-6473	81	20	points	point	NOUN
ejpam-6473	81	21	.	.	PUNCT
ejpam-6473	82	1	3.2	3.2	NUM
ejpam-6473	82	2	.	.	PUNCT
ejpam-6473	82	3	smoking	smoking	NOUN
ejpam-6473	82	4	-	-	PUNCT
ejpam-6473	82	5	free	free	ADJ
ejpam-6473	82	6	equilibrium	equilibrium	NOUN
ejpam-6473	82	7	point	point	NOUN
ejpam-6473	82	8	to	to	PART
ejpam-6473	82	9	determine	determine	VERB
ejpam-6473	82	10	the	the	DET
ejpam-6473	82	11	equilibrium	equilibrium	NOUN
ejpam-6473	82	12	points	point	NOUN
ejpam-6473	82	13	of	of	ADP
ejpam-6473	82	14	system	system	NOUN
ejpam-6473	82	15	(	(	PUNCT
ejpam-6473	82	16	1	1	NUM
ejpam-6473	82	17	)	)	PUNCT
ejpam-6473	82	18	,	,	PUNCT
ejpam-6473	82	19	we	we	PRON
ejpam-6473	82	20	set	set	VERB
ejpam-6473	82	21	the	the	DET
ejpam-6473	82	22	right	right	ADJ
ejpam-6473	82	23	-	-	PUNCT
ejpam-6473	82	24	hand	hand	NOUN
ejpam-6473	82	25	sides	side	NOUN
ejpam-6473	82	26	of	of	ADP
ejpam-6473	82	27	the	the	DET
ejpam-6473	82	28	differential	differential	ADJ
ejpam-6473	82	29	equations	equation	NOUN
ejpam-6473	82	30	(	(	PUNCT
ejpam-6473	82	31	1	1	X
ejpam-6473	82	32	)	)	PUNCT
ejpam-6473	82	33	equal	equal	ADJ
ejpam-6473	82	34	to	to	ADP
ejpam-6473	82	35	zero	zero	NUM
ejpam-6473	82	36	.	.	PUNCT
ejpam-6473	83	1	this	this	PRON
ejpam-6473	83	2	corresponds	correspond	VERB
ejpam-6473	83	3	to	to	ADP
ejpam-6473	83	4	the	the	DET
ejpam-6473	83	5	state	state	NOUN
ejpam-6473	83	6	where	where	SCONJ
ejpam-6473	83	7	all	all	DET
ejpam-6473	83	8	time	time	NOUN
ejpam-6473	83	9	derivatives	derivative	NOUN
ejpam-6473	83	10	vanish	vanish	VERB
ejpam-6473	83	11	,	,	PUNCT
ejpam-6473	83	12	indicating	indicate	VERB
ejpam-6473	83	13	no	no	DET
ejpam-6473	83	14	change	change	NOUN
ejpam-6473	83	15	in	in	ADP
ejpam-6473	83	16	the	the	DET
ejpam-6473	83	17	population	population	NOUN
ejpam-6473	83	18	compartments	compartment	NOUN
ejpam-6473	83	19	over	over	ADP
ejpam-6473	83	20	time	time	NOUN
ejpam-6473	83	21	.	.	PUNCT
ejpam-6473	84	1	in	in	ADP
ejpam-6473	84	2	case	case	NOUN
ejpam-6473	84	3	of	of	ADP
ejpam-6473	84	4	a	a	DET
ejpam-6473	84	5	smoking	smoking	NOUN
ejpam-6473	84	6	-	-	PUNCT
ejpam-6473	84	7	free	free	ADJ
ejpam-6473	84	8	equilibrium	equilibrium	NOUN
ejpam-6473	84	9	point	point	NOUN
ejpam-6473	84	10	,	,	PUNCT
ejpam-6473	84	11	it	it	PRON
ejpam-6473	84	12	shows	show	VERB
ejpam-6473	84	13	that	that	SCONJ
ejpam-6473	84	14	there	there	PRON
ejpam-6473	84	15	is	be	VERB
ejpam-6473	84	16	no	no	DET
ejpam-6473	84	17	case	case	NOUN
ejpam-6473	84	18	of	of	ADP
ejpam-6473	84	19	smoking	smoking	NOUN
ejpam-6473	84	20	that	that	PRON
ejpam-6473	84	21	is	be	AUX
ejpam-6473	84	22	l	l	NOUN
ejpam-6473	84	23	=	=	X
ejpam-6473	84	24	s=0	s=0	X
ejpam-6473	84	25	and	and	CCONJ
ejpam-6473	84	26	after	after	ADP
ejpam-6473	84	27	using	use	VERB
ejpam-6473	84	28	the	the	DET
ejpam-6473	84	29	value	value	NOUN
ejpam-6473	84	30	of	of	ADP
ejpam-6473	84	31	s	s	PRON
ejpam-6473	84	32	we	we	PRON
ejpam-6473	84	33	get	get	VERB
ejpam-6473	84	34	q	q	NOUN
ejpam-6473	84	35	=	=	SYM
ejpam-6473	84	36	0	0	NUM
ejpam-6473	84	37	and	and	CCONJ
ejpam-6473	84	38	p	p	NOUN
ejpam-6473	84	39	having	have	VERB
ejpam-6473	84	40	value	value	NOUN
ejpam-6473	84	41	which	which	PRON
ejpam-6473	84	42	is	be	AUX
ejpam-6473	84	43	λ	λ	PROPN
ejpam-6473	84	44	b+µ	b+µ	PROPN
ejpam-6473	84	45	.	.	PUNCT
ejpam-6473	85	1	smoking	smoking	NOUN
ejpam-6473	85	2	-	-	PUNCT
ejpam-6473	85	3	free	free	ADJ
ejpam-6473	85	4	equilibrium	equilibrium	NOUN
ejpam-6473	85	5	point	point	NOUN
ejpam-6473	85	6	of	of	ADP
ejpam-6473	85	7	the	the	DET
ejpam-6473	85	8	proposed	propose	VERB
ejpam-6473	85	9	model	model	NOUN
ejpam-6473	85	10	is	be	AUX
ejpam-6473	85	11	e0	e0	PROPN
ejpam-6473	85	12	=	=	PUNCT
ejpam-6473	85	13	(	(	PUNCT
ejpam-6473	85	14	p0	p0	PROPN
ejpam-6473	85	15	,	,	PUNCT
ejpam-6473	85	16	l0	l0	PROPN
ejpam-6473	85	17	,	,	PUNCT
ejpam-6473	85	18	s0	s0	PROPN
ejpam-6473	85	19	,	,	PUNCT
ejpam-6473	85	20	q0	q0	PROPN
ejpam-6473	85	21	)	)	PUNCT
ejpam-6473	85	22	=	=	SYM
ejpam-6473	86	1	(	(	PUNCT
ejpam-6473	86	2	λ	λ	X
ejpam-6473	86	3	(	(	PUNCT
ejpam-6473	86	4	b+	b+	X
ejpam-6473	86	5	µ	µ	NUM
ejpam-6473	86	6	)	)	PUNCT
ejpam-6473	86	7	,	,	PUNCT
ejpam-6473	86	8	0	0	NUM
ejpam-6473	86	9	,	,	PUNCT
ejpam-6473	86	10	0	0	NUM
ejpam-6473	86	11	,	,	PUNCT
ejpam-6473	86	12	0	0	NUM
ejpam-6473	86	13	)	)	PUNCT
ejpam-6473	86	14	.	.	PUNCT
ejpam-6473	87	1	3.3	3.3	NUM
ejpam-6473	87	2	.	.	PUNCT
ejpam-6473	87	3	smoking	smoke	VERB
ejpam-6473	87	4	endemic	endemic	ADJ
ejpam-6473	87	5	equilibrium	equilibrium	NOUN
ejpam-6473	87	6	point	point	NOUN
ejpam-6473	87	7	the	the	DET
ejpam-6473	87	8	model	model	NOUN
ejpam-6473	87	9	(	(	PUNCT
ejpam-6473	87	10	1	1	NUM
ejpam-6473	87	11	)	)	PUNCT
ejpam-6473	87	12	endemic	endemic	ADJ
ejpam-6473	87	13	equilibrium	equilibrium	NOUN
ejpam-6473	87	14	point	point	NOUN
ejpam-6473	87	15	entries	entry	NOUN
ejpam-6473	87	16	are	be	AUX
ejpam-6473	87	17	given	give	VERB
ejpam-6473	87	18	below	below	ADV
ejpam-6473	87	19	:	:	PUNCT
ejpam-6473	87	20	l∗	l∗	PROPN
ejpam-6473	87	21	=	=	SYM
ejpam-6473	87	22	(	(	PUNCT
ejpam-6473	87	23	b+µ+δ)s∗	b+µ+δ)s∗	ADJ
ejpam-6473	87	24	ζ	ζ	NOUN
ejpam-6473	87	25	,	,	PUNCT
ejpam-6473	87	26	q∗	q∗	NOUN
ejpam-6473	87	27	=	=	SYM
ejpam-6473	87	28	δs∗	δs∗	NOUN
ejpam-6473	87	29	(	(	PUNCT
ejpam-6473	87	30	b+µ	b+µ	NOUN
ejpam-6473	87	31	)	)	PUNCT
ejpam-6473	87	32	,	,	PUNCT
ejpam-6473	87	33	p	p	NOUN
ejpam-6473	87	34	∗	∗	NOUN
ejpam-6473	87	35	=	=	PUNCT
ejpam-6473	87	36	(	(	PUNCT
ejpam-6473	87	37	b+µ+ζ)(b+µ+δ	b+µ+ζ)(b+µ+δ	NOUN
ejpam-6473	87	38	)	)	PUNCT
ejpam-6473	87	39	βζ(1+νs∗	βζ(1+νs∗	NUM
ejpam-6473	87	40	)	)	PUNCT
ejpam-6473	87	41	,	,	PUNCT
ejpam-6473	87	42	s∗	s∗	PROPN
ejpam-6473	87	43	=	=	SYM
ejpam-6473	87	44	√	√	PROPN
ejpam-6473	87	45	e2−4fg−e	e2−4fg−e	PROPN
ejpam-6473	87	46	2f	2f	NUM
ejpam-6473	87	47	.	.	PUNCT
ejpam-6473	88	1	here	here	ADV
ejpam-6473	88	2	,	,	PUNCT
ejpam-6473	88	3	f	f	PROPN
ejpam-6473	88	4	=	=	SYM
ejpam-6473	88	5	νβζ(b+	νβζ(b+	PROPN
ejpam-6473	88	6	µ+	µ+	X
ejpam-6473	88	7	δ)(b+	δ)(b+	NUM
ejpam-6473	88	8	µ+	µ+	PUNCT
ejpam-6473	88	9	ζ	ζ	NOUN
ejpam-6473	88	10	)	)	PUNCT
ejpam-6473	88	11	,	,	PUNCT
ejpam-6473	88	12	e	e	X
ejpam-6473	88	13	=	=	PUNCT
ejpam-6473	88	14	ζβ(b+	ζβ(b+	PROPN
ejpam-6473	88	15	µ+	µ+	X
ejpam-6473	88	16	δ)(b+	δ)(b+	NUM
ejpam-6473	88	17	µ+	µ+	DET
ejpam-6473	88	18	ζ)−	ζ)−	PROPN
ejpam-6473	88	19	νβλζ2	νβλζ2	NOUN
ejpam-6473	88	20	,	,	PUNCT
ejpam-6473	88	21	g	g	PROPN
ejpam-6473	88	22	=	=	SYM
ejpam-6473	88	23	ζ(b+	ζ(b+	PROPN
ejpam-6473	88	24	µ)(b+	µ)(b+	VERB
ejpam-6473	88	25	µ+	µ+	X
ejpam-6473	88	26	δ)(b+	δ)(b+	NUM
ejpam-6473	88	27	µ+	µ+	DET
ejpam-6473	88	28	ζ)−	ζ)−	PROPN
ejpam-6473	88	29	λβζ2	λβζ2	PROPN
ejpam-6473	88	30	.	.	PUNCT
ejpam-6473	89	1	s.	s.	PROPN
ejpam-6473	89	2	bano	bano	PROPN
ejpam-6473	89	3	et	et	PROPN
ejpam-6473	89	4	al	al	PROPN
ejpam-6473	89	5	.	.	PUNCT
ejpam-6473	89	6	/	/	SYM
ejpam-6473	89	7	eur	eur	PROPN
ejpam-6473	89	8	.	.	PUNCT
ejpam-6473	90	1	j.	j.	PROPN
ejpam-6473	90	2	pure	pure	PROPN
ejpam-6473	90	3	appl	appl	PROPN
ejpam-6473	90	4	.	.	PROPN
ejpam-6473	90	5	math	math	PROPN
ejpam-6473	90	6	,	,	PUNCT
ejpam-6473	90	7	18	18	NUM
ejpam-6473	90	8	(	(	PUNCT
ejpam-6473	90	9	4	4	NUM
ejpam-6473	90	10	)	)	PUNCT
ejpam-6473	90	11	(	(	PUNCT
ejpam-6473	90	12	2025	2025	NUM
ejpam-6473	90	13	)	)	PUNCT
ejpam-6473	90	14	,	,	PUNCT
ejpam-6473	90	15	6473	6473	NUM
ejpam-6473	90	16	6	6	NUM
ejpam-6473	90	17	of	of	ADP
ejpam-6473	90	18	38	38	NUM
ejpam-6473	90	19	3.4	3.4	NUM
ejpam-6473	90	20	.	.	PUNCT
ejpam-6473	90	21	reproductive	reproductive	ADJ
ejpam-6473	90	22	number	number	NOUN
ejpam-6473	90	23	in	in	ADP
ejpam-6473	90	24	this	this	DET
ejpam-6473	90	25	subsection	subsection	NOUN
ejpam-6473	90	26	,	,	PUNCT
ejpam-6473	90	27	r0	r0	NOUN
ejpam-6473	90	28	is	be	AUX
ejpam-6473	90	29	computed	compute	VERB
ejpam-6473	90	30	with	with	ADP
ejpam-6473	90	31	the	the	DET
ejpam-6473	90	32	help	help	NOUN
ejpam-6473	90	33	of	of	ADP
ejpam-6473	90	34	the	the	DET
ejpam-6473	90	35	next	next	ADJ
ejpam-6473	90	36	-	-	PUNCT
ejpam-6473	90	37	generation	generation	NOUN
ejpam-6473	90	38	method	method	NOUN
ejpam-6473	90	39	.	.	PUNCT
ejpam-6473	91	1	according	accord	VERB
ejpam-6473	91	2	to	to	ADP
ejpam-6473	91	3	this	this	DET
ejpam-6473	91	4	method	method	NOUN
ejpam-6473	91	5	,	,	PUNCT
ejpam-6473	91	6	the	the	DET
ejpam-6473	91	7	reduced	reduce	VERB
ejpam-6473	91	8	system	system	NOUN
ejpam-6473	91	9	is	be	AUX
ejpam-6473	91	10	written	write	VERB
ejpam-6473	91	11	in	in	ADP
ejpam-6473	91	12	the	the	DET
ejpam-6473	91	13	form	form	NOUN
ejpam-6473	91	14	of	of	ADP
ejpam-6473	91	15	dy	dy	NOUN
ejpam-6473	91	16	dt	dt	PROPN
ejpam-6473	92	1	=	=	SYM
ejpam-6473	93	1	f	f	PROPN
ejpam-6473	94	1	−	−	PROPN
ejpam-6473	94	2	v.	v.	CCONJ
ejpam-6473	94	3	(	(	PUNCT
ejpam-6473	94	4	3	3	NUM
ejpam-6473	94	5	)	)	PUNCT
ejpam-6473	94	6	here	here	ADV
ejpam-6473	94	7	,	,	PUNCT
ejpam-6473	94	8	y	y	PROPN
ejpam-6473	94	9	consists	consist	VERB
ejpam-6473	94	10	of	of	ADP
ejpam-6473	94	11	three	three	NUM
ejpam-6473	94	12	classes	class	NOUN
ejpam-6473	94	13	;	;	PUNCT
ejpam-6473	94	14	potential	potential	ADJ
ejpam-6473	94	15	smokers	smoker	NOUN
ejpam-6473	94	16	,	,	PUNCT
ejpam-6473	94	17	light	light	ADJ
ejpam-6473	94	18	smokers	smoker	NOUN
ejpam-6473	94	19	,	,	PUNCT
ejpam-6473	94	20	and	and	CCONJ
ejpam-6473	94	21	regular	regular	ADJ
ejpam-6473	94	22	smokers	smoker	NOUN
ejpam-6473	94	23	.	.	PUNCT
ejpam-6473	95	1	f	f	PROPN
ejpam-6473	95	2	contains	contain	VERB
ejpam-6473	95	3	the	the	DET
ejpam-6473	95	4	transmission	transmission	NOUN
ejpam-6473	95	5	rate	rate	NOUN
ejpam-6473	95	6	(	(	PUNCT
ejpam-6473	95	7	the	the	DET
ejpam-6473	95	8	rate	rate	NOUN
ejpam-6473	95	9	at	at	ADP
ejpam-6473	95	10	which	which	PRON
ejpam-6473	95	11	the	the	DET
ejpam-6473	95	12	individual	individual	NOUN
ejpam-6473	95	13	starts	start	VERB
ejpam-6473	95	14	smoking	smoking	NOUN
ejpam-6473	95	15	)	)	PUNCT
ejpam-6473	95	16	and	and	CCONJ
ejpam-6473	95	17	v	v	NOUN
ejpam-6473	95	18	includes	include	VERB
ejpam-6473	95	19	the	the	DET
ejpam-6473	95	20	transition	transition	NOUN
ejpam-6473	95	21	rate	rate	NOUN
ejpam-6473	95	22	(	(	PUNCT
ejpam-6473	95	23	the	the	DET
ejpam-6473	95	24	rate	rate	NOUN
ejpam-6473	95	25	at	at	ADP
ejpam-6473	95	26	which	which	PRON
ejpam-6473	95	27	the	the	DET
ejpam-6473	95	28	individual	individual	ADJ
ejpam-6473	95	29	moves	move	NOUN
ejpam-6473	95	30	between	between	ADP
ejpam-6473	95	31	the	the	DET
ejpam-6473	95	32	smoking	smoking	NOUN
ejpam-6473	95	33	stages	stage	NOUN
ejpam-6473	95	34	and	and	CCONJ
ejpam-6473	95	35	exists	exist	VERB
ejpam-6473	95	36	from	from	ADP
ejpam-6473	95	37	these	these	DET
ejpam-6473	95	38	compartments	compartment	NOUN
ejpam-6473	95	39	)	)	PUNCT
ejpam-6473	95	40	and	and	CCONJ
ejpam-6473	95	41	these	these	DET
ejpam-6473	95	42	techniques	technique	NOUN
ejpam-6473	95	43	are	be	AUX
ejpam-6473	95	44	used	use	VERB
ejpam-6473	95	45	to	to	PART
ejpam-6473	95	46	compute	compute	VERB
ejpam-6473	95	47	r0	r0	NOUN
ejpam-6473	95	48	.	.	PUNCT
ejpam-6473	96	1	here	here	ADV
ejpam-6473	96	2	,	,	PUNCT
ejpam-6473	96	3	f	f	PROPN
ejpam-6473	96	4	=	=	PUNCT
ejpam-6473	96	5	−βps(1	−βps(1	PROPN
ejpam-6473	96	6	+	+	PROPN
ejpam-6473	96	7	νs	νs	NOUN
ejpam-6473	96	8	)	)	PUNCT
ejpam-6473	96	9	βps(1	βps(1	NOUN
ejpam-6473	96	10	+	+	CCONJ
ejpam-6473	96	11	νs	νs	NOUN
ejpam-6473	96	12	)	)	PUNCT
ejpam-6473	96	13	0	0	NUM
ejpam-6473	97	1			PROPN
ejpam-6473	97	2	,	,	PUNCT
ejpam-6473	97	3	v	v	NOUN
ejpam-6473	97	4	=	=	SYM
ejpam-6473	97	5			PROPN
ejpam-6473	97	6	−λ	−λ	NOUN
ejpam-6473	97	7	+	+	CCONJ
ejpam-6473	97	8	(	(	PUNCT
ejpam-6473	97	9	b+	b+	NOUN
ejpam-6473	97	10	µ)p	µ)p	NOUN
ejpam-6473	97	11	(	(	PUNCT
ejpam-6473	97	12	b+	b+	X
ejpam-6473	97	13	µ+	µ+	DET
ejpam-6473	97	14	ζ)l	ζ)l	ADJ
ejpam-6473	97	15	−ζl+	−ζl+	X
ejpam-6473	97	16	(	(	PUNCT
ejpam-6473	97	17	b+	b+	X
ejpam-6473	97	18	µ+	µ+	X
ejpam-6473	97	19	δ)s	δ)s	ADJ
ejpam-6473	97	20			PROPN
ejpam-6473	97	21	.	.	PUNCT
ejpam-6473	98	1	the	the	DET
ejpam-6473	98	2	jacobian	jacobian	NOUN
ejpam-6473	98	3	of	of	ADP
ejpam-6473	98	4	f	f	PROPN
ejpam-6473	98	5	and	and	CCONJ
ejpam-6473	98	6	v	v	NOUN
ejpam-6473	98	7	at	at	ADP
ejpam-6473	98	8	e0	e0	PROPN
ejpam-6473	98	9	are	be	AUX
ejpam-6473	98	10	:	:	PUNCT
ejpam-6473	98	11	f	f	PROPN
ejpam-6473	98	12	=	=	PUNCT
ejpam-6473	98	13	0	0	PROPN
ejpam-6473	98	14	0	0	NUM
ejpam-6473	99	1	−	−	NOUN
ejpam-6473	99	2	βλ	βλ	INTJ
ejpam-6473	99	3	(	(	PUNCT
ejpam-6473	99	4	b+µ	b+µ	NOUN
ejpam-6473	99	5	)	)	PUNCT
ejpam-6473	99	6	0	0	NUM
ejpam-6473	99	7	0	0	NUM
ejpam-6473	100	1	βλ	βλ	PROPN
ejpam-6473	100	2	(	(	PUNCT
ejpam-6473	100	3	b+µ	b+µ	NOUN
ejpam-6473	100	4	)	)	PUNCT
ejpam-6473	100	5	0	0	NUM
ejpam-6473	100	6	0	0	NUM
ejpam-6473	100	7	0	0	NUM
ejpam-6473	100	8			NUM
ejpam-6473	100	9	,	,	PUNCT
ejpam-6473	100	10	v	v	NOUN
ejpam-6473	100	11	=	=	SYM
ejpam-6473	100	12	(b+	(b+	X
ejpam-6473	100	13	µ	µ	NUM
ejpam-6473	100	14	)	)	PUNCT
ejpam-6473	100	15	0	0	NUM
ejpam-6473	100	16	0	0	NUM
ejpam-6473	100	17	0	0	NUM
ejpam-6473	100	18	(	(	PUNCT
ejpam-6473	100	19	b+	b+	X
ejpam-6473	100	20	µ+	µ+	X
ejpam-6473	100	21	ζ	ζ	NOUN
ejpam-6473	100	22	)	)	PUNCT
ejpam-6473	100	23	0	0	NUM
ejpam-6473	100	24	0	0	NUM
ejpam-6473	100	25	−ζ	−ζ	NOUN
ejpam-6473	100	26	(	(	PUNCT
ejpam-6473	100	27	b+	b+	X
ejpam-6473	100	28	µ+	µ+	X
ejpam-6473	100	29	δ	δ	NOUN
ejpam-6473	100	30	)	)	PUNCT
ejpam-6473	100	31			NOUN
ejpam-6473	100	32	,	,	PUNCT
ejpam-6473	100	33	fv	fv	X
ejpam-6473	100	34	−1	−1	NOUN
ejpam-6473	100	35	=	=	PUNCT
ejpam-6473	100	36	0	0	PROPN
ejpam-6473	100	37	−	−	PROPN
ejpam-6473	100	38	βλζ	βλζ	NOUN
ejpam-6473	100	39	(	(	PUNCT
ejpam-6473	100	40	µ+b)(µ+b+ζ)(µ+b+δ	µ+b)(µ+b+ζ)(µ+b+δ	PROPN
ejpam-6473	100	41	)	)	PUNCT
ejpam-6473	100	42	−	−	PROPN
ejpam-6473	100	43	βλ	βλ	INTJ
ejpam-6473	100	44	(	(	PUNCT
ejpam-6473	100	45	µ+b)(µ+b+δ	µ+b)(µ+b+δ	PROPN
ejpam-6473	100	46	)	)	PUNCT
ejpam-6473	100	47	0	0	NUM
ejpam-6473	100	48	βλζ	βλζ	NOUN
ejpam-6473	100	49	(	(	PUNCT
ejpam-6473	100	50	µ+b)(µ+b+ζ)(µ+b+δ	µ+b)(µ+b+ζ)(µ+b+δ	NOUN
ejpam-6473	100	51	)	)	PUNCT
ejpam-6473	100	52	βλ	βλ	INTJ
ejpam-6473	100	53	(	(	PUNCT
ejpam-6473	100	54	µ+b)(µ+b+δ	µ+b)(µ+b+δ	PROPN
ejpam-6473	100	55	)	)	PUNCT
ejpam-6473	100	56	0	0	NUM
ejpam-6473	100	57	0	0	NUM
ejpam-6473	100	58	0	0	NUM
ejpam-6473	100	59			NUM
ejpam-6473	100	60	.	.	PUNCT
ejpam-6473	101	1	as	as	SCONJ
ejpam-6473	101	2	r0	r0	NOUN
ejpam-6473	101	3	is	be	AUX
ejpam-6473	101	4	the	the	DET
ejpam-6473	101	5	dominant	dominant	ADJ
ejpam-6473	101	6	eigenvalue	eigenvalue	PROPN
ejpam-6473	101	7	of	of	ADP
ejpam-6473	101	8	fv	fv	PROPN
ejpam-6473	101	9	−1	−1	NOUN
ejpam-6473	101	10	,	,	PUNCT
ejpam-6473	101	11	first	first	ADJ
ejpam-6473	101	12	2	2	NUM
ejpam-6473	101	13	eigen	eigen	PROPN
ejpam-6473	101	14	values	value	NOUN
ejpam-6473	101	15	are	be	AUX
ejpam-6473	101	16	zero	zero	NUM
ejpam-6473	101	17	and	and	CCONJ
ejpam-6473	101	18	the	the	DET
ejpam-6473	101	19	third	third	ADJ
ejpam-6473	101	20	eigen	eigen	PROPN
ejpam-6473	101	21	value	value	NOUN
ejpam-6473	101	22	is	be	AUX
ejpam-6473	101	23	βλζ	βλζ	PROPN
ejpam-6473	101	24	r1r2r3	r1r2r3	PROPN
ejpam-6473	101	25	.	.	PUNCT
ejpam-6473	102	1	so	so	ADV
ejpam-6473	102	2	,	,	PUNCT
ejpam-6473	102	3	r0	r0	NOUN
ejpam-6473	102	4	=	=	SYM
ejpam-6473	102	5	βλζ	βλζ	X
ejpam-6473	102	6	r1r2r3	r1r2r3	PROPN
ejpam-6473	102	7	.	.	PUNCT
ejpam-6473	103	1	(	(	PUNCT
ejpam-6473	103	2	4	4	X
ejpam-6473	103	3	)	)	PUNCT
ejpam-6473	103	4	here	here	ADV
ejpam-6473	103	5	,	,	PUNCT
ejpam-6473	103	6	r1	r1	PROPN
ejpam-6473	103	7	=	=	SYM
ejpam-6473	103	8	(	(	PUNCT
ejpam-6473	103	9	µ+b	µ+b	NUM
ejpam-6473	103	10	)	)	PUNCT
ejpam-6473	103	11	,	,	PUNCT
ejpam-6473	103	12	r2	r2	PROPN
ejpam-6473	103	13	=	=	SYM
ejpam-6473	103	14	(	(	PUNCT
ejpam-6473	103	15	µ+b+ζ	µ+b+ζ	PROPN
ejpam-6473	103	16	)	)	PUNCT
ejpam-6473	103	17	,	,	PUNCT
ejpam-6473	103	18	r3	r3	PROPN
ejpam-6473	103	19	=	=	SYM
ejpam-6473	103	20	(	(	PUNCT
ejpam-6473	103	21	µ+b+δ	µ+b+δ	PROPN
ejpam-6473	103	22	)	)	PUNCT
ejpam-6473	103	23	.	.	PUNCT
ejpam-6473	104	1	f	f	PROPN
ejpam-6473	104	2	and	and	CCONJ
ejpam-6473	104	3	v	v	PROPN
ejpam-6473	104	4	represent	represent	ADJ
ejpam-6473	104	5	matrices	matrix	NOUN
ejpam-6473	104	6	in	in	ADP
ejpam-6473	104	7	r3×3	r3×3	NOUN
ejpam-6473	104	8	;	;	PUNCT
ejpam-6473	104	9	the	the	DET
ejpam-6473	104	10	vectors	vector	NOUN
ejpam-6473	104	11	used	use	VERB
ejpam-6473	104	12	in	in	ADP
ejpam-6473	104	13	the	the	DET
ejpam-6473	104	14	next	next	ADJ
ejpam-6473	104	15	-	-	PUNCT
ejpam-6473	104	16	generation	generation	NOUN
ejpam-6473	104	17	matrix	matrix	NOUN
ejpam-6473	104	18	approach	approach	NOUN
ejpam-6473	104	19	are	be	AUX
ejpam-6473	104	20	fi	fi	NOUN
ejpam-6473	104	21	,	,	PUNCT
ejpam-6473	104	22	vi	vi	PROPN
ejpam-6473	104	23	.	.	PUNCT
ejpam-6473	105	1	we	we	PRON
ejpam-6473	105	2	include	include	VERB
ejpam-6473	105	3	below	below	ADP
ejpam-6473	105	4	a	a	DET
ejpam-6473	105	5	concrete	concrete	ADJ
ejpam-6473	105	6	example	example	NOUN
ejpam-6473	105	7	using	use	VERB
ejpam-6473	105	8	assumed	assume	VERB
ejpam-6473	105	9	parameters	parameter	NOUN
ejpam-6473	105	10	to	to	PART
ejpam-6473	105	11	demonstrate	demonstrate	VERB
ejpam-6473	105	12	that	that	SCONJ
ejpam-6473	105	13	r0	r0	NOUN
ejpam-6473	105	14	is	be	AUX
ejpam-6473	105	15	the	the	DET
ejpam-6473	105	16	dominant	dominant	ADJ
ejpam-6473	105	17	eigenvalue	eigenvalue	NOUN
ejpam-6473	105	18	of	of	ADP
ejpam-6473	105	19	|fv	|fv	NOUN
ejpam-6473	105	20	−1	−1	NOUN
ejpam-6473	105	21	−	−	PROPN
ejpam-6473	106	1	λi|	λi|	PROPN
ejpam-6473	106	2	.	.	PROPN
ejpam-6473	106	3	entries	entry	NOUN
ejpam-6473	106	4	(	(	PUNCT
ejpam-6473	106	5	1,2	1,2	NUM
ejpam-6473	106	6	)	)	PUNCT
ejpam-6473	106	7	and	and	CCONJ
ejpam-6473	106	8	(	(	PUNCT
ejpam-6473	106	9	2,2	2,2	NUM
ejpam-6473	106	10	)	)	PUNCT
ejpam-6473	106	11	show	show	VERB
ejpam-6473	106	12	this	this	PRON
ejpam-6473	106	13	,	,	PUNCT
ejpam-6473	106	14	while	while	SCONJ
ejpam-6473	106	15	(	(	PUNCT
ejpam-6473	106	16	1,3	1,3	NUM
ejpam-6473	106	17	)	)	PUNCT
ejpam-6473	106	18	and	and	CCONJ
ejpam-6473	106	19	(	(	PUNCT
ejpam-6473	106	20	2,3	2,3	NOUN
ejpam-6473	106	21	)	)	PUNCT
ejpam-6473	106	22	do	do	AUX
ejpam-6473	106	23	not	not	PART
ejpam-6473	106	24	contribute	contribute	VERB
ejpam-6473	106	25	dominantly	dominantly	ADV
ejpam-6473	106	26	.	.	PUNCT
ejpam-6473	107	1	now	now	ADV
ejpam-6473	107	2	the	the	DET
ejpam-6473	107	3	smoking	smoke	VERB
ejpam-6473	107	4	endemic	endemic	ADJ
ejpam-6473	107	5	equilibrium	equilibrium	NOUN
ejpam-6473	107	6	point	point	NOUN
ejpam-6473	107	7	e∗	e∗	NOUN
ejpam-6473	107	8	=	=	SYM
ejpam-6473	107	9	(	(	PUNCT
ejpam-6473	107	10	p	p	NOUN
ejpam-6473	107	11	∗	∗	NOUN
ejpam-6473	107	12	,	,	PUNCT
ejpam-6473	107	13	l∗	l∗	PROPN
ejpam-6473	107	14	,	,	PUNCT
ejpam-6473	107	15	s∗	s∗	PROPN
ejpam-6473	107	16	,	,	PUNCT
ejpam-6473	107	17	q∗	q∗	PROPN
ejpam-6473	107	18	)	)	PUNCT
ejpam-6473	107	19	in	in	ADP
ejpam-6473	107	20	term	term	NOUN
ejpam-6473	107	21	of	of	ADP
ejpam-6473	107	22	the	the	DET
ejpam-6473	107	23	reproductive	reproductive	ADJ
ejpam-6473	107	24	number	number	NOUN
ejpam-6473	107	25	are	be	AUX
ejpam-6473	107	26	as	as	ADP
ejpam-6473	107	27	given	give	VERB
ejpam-6473	107	28	:	:	PUNCT
ejpam-6473	107	29	p	p	NOUN
ejpam-6473	107	30	∗	∗	NOUN
ejpam-6473	107	31	=	=	PUNCT
ejpam-6473	107	32	λ	λ	X
ejpam-6473	107	33	r0r1(1	r0r1(1	PROPN
ejpam-6473	107	34	+	+	CCONJ
ejpam-6473	107	35	νs∗	νs∗	NOUN
ejpam-6473	107	36	)	)	PUNCT
ejpam-6473	107	37	,	,	PUNCT
ejpam-6473	107	38	l∗	l∗	NOUN
ejpam-6473	107	39	=	=	PUNCT
ejpam-6473	107	40	r3s	r3s	ADJ
ejpam-6473	107	41	∗	∗	NOUN
ejpam-6473	107	42	ζ	ζ	NOUN
ejpam-6473	107	43	,	,	PUNCT
ejpam-6473	107	44	q∗	q∗	NOUN
ejpam-6473	107	45	=	=	PUNCT
ejpam-6473	107	46	δs∗	δs∗	NOUN
ejpam-6473	107	47	r1	r1	NOUN
ejpam-6473	107	48	,	,	PUNCT
ejpam-6473	107	49	s∗	s∗	PROPN
ejpam-6473	107	50	=	=	SYM
ejpam-6473	107	51	√	√	PROPN
ejpam-6473	107	52	e2	e2	PROPN
ejpam-6473	107	53	−	−	PROPN
ejpam-6473	107	54	4fg	4fg	ADJ
ejpam-6473	107	55	−	−	NOUN
ejpam-6473	107	56	e	e	NOUN
ejpam-6473	107	57	2f	2f	NUM
ejpam-6473	107	58	.	.	PUNCT
ejpam-6473	108	1	here	here	ADV
ejpam-6473	108	2	,	,	PUNCT
ejpam-6473	108	3	f	f	PROPN
ejpam-6473	108	4	=	=	PROPN
ejpam-6473	108	5	νβ2ζ2λ	νβ2ζ2λ	PROPN
ejpam-6473	108	6	r0(µ+b	r0(µ+b	PROPN
ejpam-6473	108	7	)	)	PUNCT
ejpam-6473	108	8	,	,	PUNCT
ejpam-6473	108	9	e	e	X
ejpam-6473	108	10	=	=	PUNCT
ejpam-6473	108	11	λβζ2	λβζ2	PROPN
ejpam-6473	108	12	[	[	PUNCT
ejpam-6473	108	13	β	β	X
ejpam-6473	108	14	r0(µ+b	r0(µ+b	PROPN
ejpam-6473	108	15	)	)	PUNCT
ejpam-6473	108	16	−	−	PROPN
ejpam-6473	108	17	ν	ν	NOUN
ejpam-6473	108	18	]	]	PUNCT
ejpam-6473	108	19	,	,	PUNCT
ejpam-6473	108	20	g	g	PROPN
ejpam-6473	108	21	=	=	PUNCT
ejpam-6473	108	22	λβζ2	λβζ2	PROPN
ejpam-6473	108	23	[	[	PUNCT
ejpam-6473	108	24	1	1	NUM
ejpam-6473	108	25	r0	r0	NOUN
ejpam-6473	108	26	−	−	NOUN
ejpam-6473	108	27	1	1	NUM
ejpam-6473	108	28	]	]	PUNCT
ejpam-6473	108	29	.	.	PUNCT
ejpam-6473	109	1	s∗	s∗	PROPN
ejpam-6473	109	2	is	be	AUX
ejpam-6473	109	3	positive	positive	ADJ
ejpam-6473	109	4	for	for	ADP
ejpam-6473	109	5	r0	r0	NOUN
ejpam-6473	109	6	>	>	X
ejpam-6473	109	7	1	1	X
ejpam-6473	109	8	.	.	PUNCT
ejpam-6473	110	1	s.	s.	PROPN
ejpam-6473	110	2	bano	bano	PROPN
ejpam-6473	110	3	et	et	PROPN
ejpam-6473	110	4	al	al	PROPN
ejpam-6473	110	5	.	.	PUNCT
ejpam-6473	110	6	/	/	SYM
ejpam-6473	110	7	eur	eur	PROPN
ejpam-6473	110	8	.	.	PUNCT
ejpam-6473	111	1	j.	j.	PROPN
ejpam-6473	111	2	pure	pure	PROPN
ejpam-6473	111	3	appl	appl	PROPN
ejpam-6473	111	4	.	.	PROPN
ejpam-6473	111	5	math	math	PROPN
ejpam-6473	111	6	,	,	PUNCT
ejpam-6473	111	7	18	18	NUM
ejpam-6473	111	8	(	(	PUNCT
ejpam-6473	111	9	4	4	NUM
ejpam-6473	111	10	)	)	PUNCT
ejpam-6473	111	11	(	(	PUNCT
ejpam-6473	111	12	2025	2025	NUM
ejpam-6473	111	13	)	)	PUNCT
ejpam-6473	111	14	,	,	PUNCT
ejpam-6473	111	15	6473	6473	NUM
ejpam-6473	111	16	7	7	NUM
ejpam-6473	111	17	of	of	ADP
ejpam-6473	111	18	38	38	NUM
ejpam-6473	111	19	3.5	3.5	NUM
ejpam-6473	111	20	.	.	PUNCT
ejpam-6473	112	1	stability	stability	NOUN
ejpam-6473	112	2	in	in	ADP
ejpam-6473	112	3	this	this	DET
ejpam-6473	112	4	section	section	NOUN
ejpam-6473	112	5	,	,	PUNCT
ejpam-6473	112	6	local	local	ADJ
ejpam-6473	112	7	as	as	ADV
ejpam-6473	112	8	well	well	ADV
ejpam-6473	112	9	as	as	ADP
ejpam-6473	112	10	global	global	ADJ
ejpam-6473	112	11	stability	stability	NOUN
ejpam-6473	112	12	of	of	ADP
ejpam-6473	112	13	the	the	DET
ejpam-6473	112	14	equilibrium	equilibrium	NOUN
ejpam-6473	112	15	points	point	NOUN
ejpam-6473	112	16	are	be	AUX
ejpam-6473	112	17	evaluated	evaluate	VERB
ejpam-6473	112	18	.	.	PUNCT
ejpam-6473	113	1	3.5.1	3.5.1	X
ejpam-6473	113	2	.	.	PUNCT
ejpam-6473	113	3	local	local	ADJ
ejpam-6473	113	4	stability	stability	NOUN
ejpam-6473	113	5	for	for	ADP
ejpam-6473	113	6	local	local	ADJ
ejpam-6473	113	7	stability	stability	NOUN
ejpam-6473	113	8	of	of	ADP
ejpam-6473	113	9	the	the	DET
ejpam-6473	113	10	equilibrium	equilibrium	NOUN
ejpam-6473	113	11	points	point	NOUN
ejpam-6473	113	12	,	,	PUNCT
ejpam-6473	113	13	we	we	PRON
ejpam-6473	113	14	will	will	AUX
ejpam-6473	113	15	first	first	ADV
ejpam-6473	113	16	linearized	linearize	VERB
ejpam-6473	113	17	the	the	DET
ejpam-6473	113	18	model	model	NOUN
ejpam-6473	113	19	by	by	ADP
ejpam-6473	113	20	using	use	VERB
ejpam-6473	113	21	taylor	taylor	PROPN
ejpam-6473	113	22	series	series	PROPN
ejpam-6473	113	23	method	method	PROPN
ejpam-6473	113	24	.	.	PUNCT
ejpam-6473	114	1	now	now	ADV
ejpam-6473	114	2	let	let	VERB
ejpam-6473	114	3	y1	y1	NOUN
ejpam-6473	114	4	=	=	PUNCT
ejpam-6473	115	1	p	p	NOUN
ejpam-6473	115	2	−	−	PROPN
ejpam-6473	115	3	p	p	NOUN
ejpam-6473	115	4	∗	∗	NOUN
ejpam-6473	115	5	,	,	PUNCT
ejpam-6473	115	6	y2	y2	NOUN
ejpam-6473	115	7	=	=	SYM
ejpam-6473	116	1	l	l	NOUN
ejpam-6473	116	2	−	−	PROPN
ejpam-6473	116	3	l∗	l∗	NOUN
ejpam-6473	116	4	,	,	PUNCT
ejpam-6473	116	5	y3	y3	NOUN
ejpam-6473	116	6	=	=	SYM
ejpam-6473	116	7	s	s	PART
ejpam-6473	116	8	−	−	NOUN
ejpam-6473	116	9	s∗	s∗	PROPN
ejpam-6473	116	10	,	,	PUNCT
ejpam-6473	116	11	y4	y4	PROPN
ejpam-6473	116	12	=	=	PUNCT
ejpam-6473	116	13	q	q	X
ejpam-6473	116	14	−	−	NOUN
ejpam-6473	116	15	q∗	q∗	NOUN
ejpam-6473	116	16	as	as	ADP
ejpam-6473	116	17	the	the	DET
ejpam-6473	116	18	system(1	system(1	NOUN
ejpam-6473	116	19	)	)	PUNCT
ejpam-6473	116	20	first	first	ADV
ejpam-6473	116	21	three	three	NUM
ejpam-6473	116	22	equation	equation	NOUN
ejpam-6473	116	23	are	be	AUX
ejpam-6473	116	24	independent	independent	ADJ
ejpam-6473	116	25	of	of	ADP
ejpam-6473	116	26	the	the	DET
ejpam-6473	116	27	q	q	NOUN
ejpam-6473	116	28	,	,	PUNCT
ejpam-6473	116	29	so	so	SCONJ
ejpam-6473	116	30	we	we	PRON
ejpam-6473	116	31	use	use	VERB
ejpam-6473	116	32	only	only	ADV
ejpam-6473	116	33	first	first	ADJ
ejpam-6473	116	34	three	three	NUM
ejpam-6473	116	35	equation	equation	NOUN
ejpam-6473	116	36	of	of	ADP
ejpam-6473	116	37	proposed	propose	VERB
ejpam-6473	116	38	model	model	NOUN
ejpam-6473	116	39	.	.	PUNCT
ejpam-6473	117	1	linearized	linearize	VERB
ejpam-6473	117	2	system	system	NOUN
ejpam-6473	117	3	is	be	AUX
ejpam-6473	117	4	given	give	VERB
ejpam-6473	117	5	as	as	ADP
ejpam-6473	117	6	:	:	PUNCT
ejpam-6473	117	7	ẏ1	ẏ1	PROPN
ejpam-6473	117	8	=	=	PUNCT
ejpam-6473	117	9	[	[	PUNCT
ejpam-6473	117	10	−	−	NOUN
ejpam-6473	117	11	βs∗(1	βs∗(1	NOUN
ejpam-6473	117	12	+	+	ADJ
ejpam-6473	117	13	νs∗)−	νs∗)−	NOUN
ejpam-6473	117	14	(	(	PUNCT
ejpam-6473	117	15	b+	b+	X
ejpam-6473	117	16	µ	µ	NUM
ejpam-6473	117	17	)	)	PUNCT
ejpam-6473	117	18	]	]	PUNCT
ejpam-6473	118	1	y1	y1	INTJ
ejpam-6473	118	2	+	+	CCONJ
ejpam-6473	118	3	[	[	PUNCT
ejpam-6473	118	4	−	−	NUM
ejpam-6473	118	5	βp	βp	NUM
ejpam-6473	118	6	∗(1	∗(1	NOUN
ejpam-6473	118	7	+	+	CCONJ
ejpam-6473	118	8	2νs∗)]y3	2νs∗)]y3	NUM
ejpam-6473	118	9	,	,	PUNCT
ejpam-6473	118	10	ẏ2	ẏ2	PROPN
ejpam-6473	118	11	=	=	PUNCT
ejpam-6473	118	12	[	[	PUNCT
ejpam-6473	118	13	βs∗(1	βs∗(1	NOUN
ejpam-6473	118	14	+	+	CCONJ
ejpam-6473	118	15	νs∗	νs∗	NOUN
ejpam-6473	118	16	)	)	PUNCT
ejpam-6473	118	17	]	]	PUNCT
ejpam-6473	119	1	y1	y1	INTJ
ejpam-6473	119	2	−	−	PROPN
ejpam-6473	119	3	[	[	PUNCT
ejpam-6473	119	4	(	(	PUNCT
ejpam-6473	119	5	b+	b+	X
ejpam-6473	119	6	µ+	µ+	X
ejpam-6473	119	7	ζ	ζ	NOUN
ejpam-6473	119	8	)	)	PUNCT
ejpam-6473	119	9	]	]	PUNCT
ejpam-6473	120	1	y2	y2	INTJ
ejpam-6473	121	1	+	+	CCONJ
ejpam-6473	121	2	[	[	PUNCT
ejpam-6473	121	3	βp	βp	ADJ
ejpam-6473	121	4	∗(1	∗(1	PROPN
ejpam-6473	121	5	+	+	CCONJ
ejpam-6473	121	6	2νs∗	2νs∗	NUM
ejpam-6473	121	7	)	)	PUNCT
ejpam-6473	121	8	]	]	PUNCT
ejpam-6473	122	1	y3	y3	PROPN
ejpam-6473	122	2	,	,	PUNCT
ejpam-6473	122	3	ẏ3	ẏ3	PROPN
ejpam-6473	122	4	=	=	PUNCT
ejpam-6473	122	5	ζy2	ζy2	ADJ
ejpam-6473	122	6	−	−	PROPN
ejpam-6473	122	7	(	(	PUNCT
ejpam-6473	122	8	b+	b+	X
ejpam-6473	122	9	µ+	µ+	DET
ejpam-6473	122	10	δ)y3	δ)y3	PROPN
ejpam-6473	122	11	.	.	PUNCT
ejpam-6473	122	12	jacobian	jacobian	ADJ
ejpam-6473	122	13	matrix	matrix	NOUN
ejpam-6473	122	14	corresponding	correspond	VERB
ejpam-6473	122	15	to	to	ADP
ejpam-6473	122	16	the	the	DET
ejpam-6473	122	17	linearized	linearize	VERB
ejpam-6473	122	18	system	system	NOUN
ejpam-6473	122	19	is	be	AUX
ejpam-6473	122	20	j	j	NOUN
ejpam-6473	122	21	=	=	PUNCT
ejpam-6473	122	22	−βs∗(1	−βs∗(1	NOUN
ejpam-6473	122	23	+	+	PUNCT
ejpam-6473	122	24	νs∗)−	νs∗)−	NOUN
ejpam-6473	122	25	r1	r1	NOUN
ejpam-6473	122	26	0	0	PUNCT
ejpam-6473	123	1	−βp	−βp	PROPN
ejpam-6473	123	2	∗(1	∗(1	PROPN
ejpam-6473	123	3	+	+	CCONJ
ejpam-6473	123	4	2νs∗	2νs∗	NUM
ejpam-6473	123	5	)	)	PUNCT
ejpam-6473	123	6	βs∗(1	βs∗(1	VERB
ejpam-6473	123	7	+	+	CCONJ
ejpam-6473	123	8	νs∗	νs∗	NOUN
ejpam-6473	123	9	)	)	PUNCT
ejpam-6473	124	1	−r2	−r2	PROPN
ejpam-6473	124	2	βp	βp	ADJ
ejpam-6473	124	3	∗(1	∗(1	NOUN
ejpam-6473	124	4	+	+	CCONJ
ejpam-6473	124	5	2νs∗	2νs∗	NUM
ejpam-6473	124	6	)	)	PUNCT
ejpam-6473	124	7	0	0	NUM
ejpam-6473	125	1	ζ	ζ	NOUN
ejpam-6473	125	2	−r3	−r3	NOUN
ejpam-6473	125	3			NOUN
ejpam-6473	125	4	.	.	PUNCT
ejpam-6473	126	1	(	(	PUNCT
ejpam-6473	126	2	5	5	X
ejpam-6473	126	3	)	)	PUNCT
ejpam-6473	126	4	theorem	theorem	NOUN
ejpam-6473	126	5	1	1	NUM
ejpam-6473	126	6	.	.	PUNCT
ejpam-6473	127	1	the	the	DET
ejpam-6473	127	2	smoking	smoking	NOUN
ejpam-6473	127	3	-	-	PUNCT
ejpam-6473	127	4	free	free	ADJ
ejpam-6473	127	5	equilibrium	equilibrium	NOUN
ejpam-6473	127	6	point	point	NOUN
ejpam-6473	127	7	is	be	AUX
ejpam-6473	127	8	locally	locally	ADV
ejpam-6473	127	9	stable	stable	ADJ
ejpam-6473	127	10	for	for	ADP
ejpam-6473	127	11	r0	r0	NOUN
ejpam-6473	127	12	<	<	X
ejpam-6473	127	13	1	1	NUM
ejpam-6473	127	14	and	and	CCONJ
ejpam-6473	127	15	unstable	unstable	ADJ
ejpam-6473	127	16	if	if	SCONJ
ejpam-6473	127	17	r0	r0	NOUN
ejpam-6473	127	18	>	>	X
ejpam-6473	127	19	1	1	NUM
ejpam-6473	127	20	.	.	PUNCT
ejpam-6473	128	1	proof	proof	NOUN
ejpam-6473	128	2	.	.	PUNCT
ejpam-6473	129	1	jacobian	jacobian	ADJ
ejpam-6473	129	2	matrix	matrix	NOUN
ejpam-6473	129	3	at	at	ADP
ejpam-6473	129	4	e0	e0	PROPN
ejpam-6473	129	5	is	be	AUX
ejpam-6473	129	6	je0	je0	NOUN
ejpam-6473	129	7	=	=	SYM
ejpam-6473	129	8	−r1	−r1	X
ejpam-6473	129	9	0	0	NUM
ejpam-6473	129	10	−βλ	−βλ	PROPN
ejpam-6473	129	11	r1	r1	PROPN
ejpam-6473	129	12	0	0	PUNCT
ejpam-6473	130	1	−r2	−r2	PROPN
ejpam-6473	130	2	βλ	βλ	PROPN
ejpam-6473	130	3	r1	r1	PROPN
ejpam-6473	130	4	0	0	PUNCT
ejpam-6473	131	1	ζ	ζ	PROPN
ejpam-6473	131	2	−r3	−r3	PROPN
ejpam-6473	131	3			NUM
ejpam-6473	131	4	,	,	PUNCT
ejpam-6473	131	5	the	the	DET
ejpam-6473	131	6	first	first	ADJ
ejpam-6473	131	7	eigen	eigen	PROPN
ejpam-6473	131	8	value	value	NOUN
ejpam-6473	131	9	of	of	ADP
ejpam-6473	131	10	the	the	DET
ejpam-6473	131	11	je0	je0	NOUN
ejpam-6473	131	12	is	be	AUX
ejpam-6473	131	13	λ1	λ1	ADJ
ejpam-6473	131	14	=	=	SYM
ejpam-6473	131	15	−r1	−r1	PROPN
ejpam-6473	131	16	and	and	CCONJ
ejpam-6473	131	17	for	for	ADP
ejpam-6473	131	18	second	second	ADJ
ejpam-6473	131	19	and	and	CCONJ
ejpam-6473	131	20	third	third	ADJ
ejpam-6473	131	21	eigen	eigen	PROPN
ejpam-6473	131	22	value	value	NOUN
ejpam-6473	131	23	we	we	PRON
ejpam-6473	131	24	have	have	VERB
ejpam-6473	131	25	an	an	DET
ejpam-6473	131	26	equation	equation	NOUN
ejpam-6473	131	27	that	that	PRON
ejpam-6473	131	28	is	be	AUX
ejpam-6473	131	29	λ2	λ2	NOUN
ejpam-6473	131	30	+	+	CCONJ
ejpam-6473	131	31	(	(	PUNCT
ejpam-6473	131	32	r2	r2	PROPN
ejpam-6473	131	33	+	+	CCONJ
ejpam-6473	131	34	r3)λ	r3)λ	NOUN
ejpam-6473	131	35	+	+	CCONJ
ejpam-6473	131	36	(	(	PUNCT
ejpam-6473	131	37	r2r3	r2r3	X
ejpam-6473	131	38	−	−	PROPN
ejpam-6473	131	39	βλζ	βλζ	PROPN
ejpam-6473	131	40	r1	r1	PROPN
ejpam-6473	131	41	)	)	PUNCT
ejpam-6473	132	1	=	=	SYM
ejpam-6473	132	2	0	0	NUM
ejpam-6473	132	3	,	,	PUNCT
ejpam-6473	132	4	which	which	PRON
ejpam-6473	132	5	is	be	AUX
ejpam-6473	132	6	solve	solve	NOUN
ejpam-6473	132	7	by	by	ADP
ejpam-6473	132	8	using	use	VERB
ejpam-6473	132	9	routh	routh	PROPN
ejpam-6473	132	10	horwitz	horwitz	PROPN
ejpam-6473	132	11	criteria	criteria	PROPN
ejpam-6473	132	12	.	.	PUNCT
ejpam-6473	133	1	clearly	clearly	ADV
ejpam-6473	133	2	,	,	PUNCT
ejpam-6473	133	3	(	(	PUNCT
ejpam-6473	133	4	r2	r2	PROPN
ejpam-6473	133	5	+	+	CCONJ
ejpam-6473	133	6	r3	r3	PROPN
ejpam-6473	133	7	)	)	PUNCT
ejpam-6473	133	8	>	>	X
ejpam-6473	133	9	0	0	PUNCT
ejpam-6473	134	1	and	and	CCONJ
ejpam-6473	134	2	(	(	PUNCT
ejpam-6473	134	3	r2r3	r2r3	X
ejpam-6473	134	4	−	−	PROPN
ejpam-6473	134	5	βλζ	βλζ	PROPN
ejpam-6473	134	6	r1	r1	PROPN
ejpam-6473	134	7	)	)	PUNCT
ejpam-6473	134	8	>	>	X
ejpam-6473	134	9	0	0	PUNCT
ejpam-6473	135	1	if	if	SCONJ
ejpam-6473	135	2	r0	r0	NOUN
ejpam-6473	135	3	<	<	X
ejpam-6473	135	4	1	1	NUM
ejpam-6473	135	5	.	.	PUNCT
ejpam-6473	136	1	it	it	PRON
ejpam-6473	136	2	is	be	AUX
ejpam-6473	136	3	proven	prove	VERB
ejpam-6473	136	4	that	that	SCONJ
ejpam-6473	136	5	the	the	DET
ejpam-6473	136	6	smoking	smoking	NOUN
ejpam-6473	136	7	-	-	PUNCT
ejpam-6473	136	8	free	free	ADJ
ejpam-6473	136	9	equilibrium	equilibrium	NOUN
ejpam-6473	136	10	points	point	NOUN
ejpam-6473	136	11	are	be	AUX
ejpam-6473	136	12	locally	locally	ADV
ejpam-6473	136	13	asymptotically	asymptotically	ADV
ejpam-6473	136	14	stable	stable	ADJ
ejpam-6473	136	15	for	for	ADP
ejpam-6473	136	16	r0	r0	NOUN
ejpam-6473	136	17	<	<	X
ejpam-6473	136	18	1	1	NUM
ejpam-6473	136	19	.	.	PUNCT
ejpam-6473	136	20	theorem	theorem	NOUN
ejpam-6473	136	21	2	2	NUM
ejpam-6473	136	22	.	.	PUNCT
ejpam-6473	137	1	the	the	DET
ejpam-6473	137	2	smoking	smoke	VERB
ejpam-6473	137	3	endemic	endemic	ADJ
ejpam-6473	137	4	equilibrium	equilibrium	NOUN
ejpam-6473	137	5	point	point	NOUN
ejpam-6473	137	6	are	be	AUX
ejpam-6473	137	7	locally	locally	ADV
ejpam-6473	137	8	stable	stable	ADJ
ejpam-6473	137	9	for	for	ADP
ejpam-6473	137	10	r0	r0	PROPN
ejpam-6473	137	11	>	>	X
ejpam-6473	137	12	1	1	NUM
ejpam-6473	137	13	and	and	CCONJ
ejpam-6473	137	14	unstable	unstable	ADJ
ejpam-6473	137	15	for	for	ADP
ejpam-6473	137	16	r0	r0	NOUN
ejpam-6473	137	17	<	<	X
ejpam-6473	137	18	1	1	NUM
ejpam-6473	137	19	.	.	PUNCT
ejpam-6473	137	20	proof	proof	NOUN
ejpam-6473	137	21	.	.	PUNCT
ejpam-6473	138	1	jacobian	jacobian	ADJ
ejpam-6473	138	2	matrix	matrix	NOUN
ejpam-6473	138	3	at	at	ADP
ejpam-6473	138	4	smoking	smoke	VERB
ejpam-6473	138	5	endemic	endemic	ADJ
ejpam-6473	138	6	equilibrium	equilibrium	NOUN
ejpam-6473	138	7	point	point	NOUN
ejpam-6473	138	8	is	be	AUX
ejpam-6473	138	9	je∗	je∗	NOUN
ejpam-6473	138	10	=	=	NUM
ejpam-6473	138	11	−βs∗(1	−βs∗(1	NOUN
ejpam-6473	138	12	+	+	PUNCT
ejpam-6473	138	13	νs∗)−	νs∗)−	NOUN
ejpam-6473	138	14	r1	r1	NOUN
ejpam-6473	138	15	0	0	PUNCT
ejpam-6473	138	16	−βp	−βp	PROPN
ejpam-6473	138	17	∗(1	∗(1	PROPN
ejpam-6473	138	18	+	+	CCONJ
ejpam-6473	138	19	2νs∗	2νs∗	NUM
ejpam-6473	138	20	)	)	PUNCT
ejpam-6473	138	21	βs∗(1	βs∗(1	VERB
ejpam-6473	138	22	+	+	CCONJ
ejpam-6473	138	23	νs∗	νs∗	NOUN
ejpam-6473	138	24	)	)	PUNCT
ejpam-6473	139	1	−r2	−r2	PROPN
ejpam-6473	139	2	βp	βp	ADJ
ejpam-6473	139	3	∗(1	∗(1	NOUN
ejpam-6473	139	4	+	+	CCONJ
ejpam-6473	139	5	2νs∗	2νs∗	NUM
ejpam-6473	139	6	)	)	PUNCT
ejpam-6473	139	7	0	0	NUM
ejpam-6473	140	1	ζ	ζ	NOUN
ejpam-6473	140	2	−r3	−r3	NOUN
ejpam-6473	140	3			NOUN
ejpam-6473	140	4	.	.	PUNCT
ejpam-6473	141	1	(	(	PUNCT
ejpam-6473	141	2	6	6	NUM
ejpam-6473	141	3	)	)	PUNCT
ejpam-6473	141	4	after	after	SCONJ
ejpam-6473	141	5	some	some	DET
ejpam-6473	141	6	row	row	NOUN
ejpam-6473	141	7	operation	operation	NOUN
ejpam-6473	141	8	applied	apply	VERB
ejpam-6473	141	9	on	on	ADP
ejpam-6473	141	10	je∗	je∗	NOUN
ejpam-6473	141	11	,	,	PUNCT
ejpam-6473	141	12	we	we	PRON
ejpam-6473	141	13	get	get	VERB
ejpam-6473	141	14	the	the	DET
ejpam-6473	141	15	two	two	NUM
ejpam-6473	141	16	eigen	eigen	PROPN
ejpam-6473	141	17	values	value	NOUN
ejpam-6473	141	18	that	that	PRON
ejpam-6473	141	19	are	be	AUX
ejpam-6473	141	20	λ1	λ1	ADJ
ejpam-6473	141	21	=	=	SYM
ejpam-6473	141	22	−r2	−r2	PROPN
ejpam-6473	141	23	<	<	X
ejpam-6473	141	24	0	0	NUM
ejpam-6473	141	25	,	,	PUNCT
ejpam-6473	141	26	λ2	λ2	NOUN
ejpam-6473	141	27	=	=	PUNCT
ejpam-6473	141	28	−ζr1	−ζr1	PUNCT
ejpam-6473	141	29	<	<	X
ejpam-6473	141	30	0	0	NUM
ejpam-6473	141	31	.	.	PUNCT
ejpam-6473	142	1	for	for	ADP
ejpam-6473	142	2	third	third	ADJ
ejpam-6473	142	3	eigen	eigen	PROPN
ejpam-6473	142	4	value	value	NOUN
ejpam-6473	142	5	,	,	PUNCT
ejpam-6473	142	6	we	we	PRON
ejpam-6473	142	7	have	have	VERB
ejpam-6473	142	8	λ3	λ3	PROPN
ejpam-6473	142	9	=	=	SYM
ejpam-6473	142	10	βζp	βζp	NUM
ejpam-6473	142	11	∗(1	∗(1	NOUN
ejpam-6473	142	12	+	+	CCONJ
ejpam-6473	142	13	2νs∗)r1	2νs∗)r1	NUM
ejpam-6473	142	14	−	−	NOUN
ejpam-6473	142	15	r1r2r3	r1r2r3	PROPN
ejpam-6473	142	16	−	−	PROPN
ejpam-6473	142	17	r2r3βs	r2r3βs	X
ejpam-6473	143	1	∗(1	∗(1	PROPN
ejpam-6473	143	2	+	+	CCONJ
ejpam-6473	143	3	νs∗	νs∗	NOUN
ejpam-6473	143	4	)	)	PUNCT
ejpam-6473	143	5	,	,	PUNCT
ejpam-6473	143	6	s.	s.	PROPN
ejpam-6473	143	7	bano	bano	PROPN
ejpam-6473	143	8	et	et	PROPN
ejpam-6473	143	9	al	al	PROPN
ejpam-6473	143	10	.	.	PUNCT
ejpam-6473	143	11	/	/	SYM
ejpam-6473	143	12	eur	eur	PROPN
ejpam-6473	143	13	.	.	PUNCT
ejpam-6473	144	1	j.	j.	PROPN
ejpam-6473	144	2	pure	pure	PROPN
ejpam-6473	144	3	appl	appl	PROPN
ejpam-6473	144	4	.	.	PROPN
ejpam-6473	144	5	math	math	PROPN
ejpam-6473	144	6	,	,	PUNCT
ejpam-6473	144	7	18	18	NUM
ejpam-6473	144	8	(	(	PUNCT
ejpam-6473	144	9	4	4	NUM
ejpam-6473	144	10	)	)	PUNCT
ejpam-6473	144	11	(	(	PUNCT
ejpam-6473	144	12	2025	2025	NUM
ejpam-6473	144	13	)	)	PUNCT
ejpam-6473	144	14	,	,	PUNCT
ejpam-6473	144	15	6473	6473	NUM
ejpam-6473	144	16	8	8	NUM
ejpam-6473	144	17	of	of	ADP
ejpam-6473	144	18	38	38	NUM
ejpam-6473	144	19	after	after	ADP
ejpam-6473	144	20	putting	put	VERB
ejpam-6473	144	21	the	the	DET
ejpam-6473	144	22	value	value	NOUN
ejpam-6473	144	23	of	of	ADP
ejpam-6473	144	24	p	p	NOUN
ejpam-6473	144	25	∗	∗	NOUN
ejpam-6473	144	26	λ3	λ3	PROPN
ejpam-6473	144	27	=	=	SYM
ejpam-6473	144	28	r2r3s	r2r3s	X
ejpam-6473	144	29	∗[νr1	∗[νr1	NOUN
ejpam-6473	144	30	−	−	PUNCT
ejpam-6473	145	1	β(1	β(1	PROPN
ejpam-6473	145	2	+	+	CCONJ
ejpam-6473	145	3	νs∗)2	νs∗)2	DET
ejpam-6473	145	4	(	(	PUNCT
ejpam-6473	145	5	1	1	NUM
ejpam-6473	145	6	+	+	CCONJ
ejpam-6473	145	7	νs∗	νs∗	NOUN
ejpam-6473	145	8	)	)	PUNCT
ejpam-6473	145	9	]	]	PUNCT
ejpam-6473	145	10	.	.	PUNCT
ejpam-6473	146	1	=	=	PUNCT
ejpam-6473	146	2	⇒	⇒	NOUN
ejpam-6473	146	3	r1ν	r1ν	VERB
ejpam-6473	146	4	<	<	X
ejpam-6473	146	5	β(1	β(1	PROPN
ejpam-6473	146	6	+	+	NUM
ejpam-6473	146	7	νs∗)2	νs∗)2	ADJ
ejpam-6473	146	8	,	,	PUNCT
ejpam-6473	146	9	where	where	SCONJ
ejpam-6473	146	10	r1	r1	PROPN
ejpam-6473	146	11	is	be	AUX
ejpam-6473	146	12	sum	sum	NOUN
ejpam-6473	146	13	of	of	ADP
ejpam-6473	146	14	parameters	parameter	NOUN
ejpam-6473	146	15	and	and	CCONJ
ejpam-6473	146	16	these	these	DET
ejpam-6473	146	17	prameter	prameter	NOUN
ejpam-6473	146	18	values	value	NOUN
ejpam-6473	146	19	are	be	AUX
ejpam-6473	146	20	between	between	ADP
ejpam-6473	146	21	0	0	NUM
ejpam-6473	146	22	and	and	CCONJ
ejpam-6473	146	23	1	1	NUM
ejpam-6473	146	24	and	and	CCONJ
ejpam-6473	146	25	β(1	β(1	PROPN
ejpam-6473	147	1	+	+	CCONJ
ejpam-6473	147	2	νs∗)2	νs∗)2	PRON
ejpam-6473	147	3	contain	contain	VERB
ejpam-6473	147	4	the	the	DET
ejpam-6473	147	5	square	square	NOUN
ejpam-6473	147	6	of	of	ADP
ejpam-6473	147	7	s∗	s∗	PROPN
ejpam-6473	147	8	which	which	PRON
ejpam-6473	147	9	is	be	AUX
ejpam-6473	147	10	positive	positive	ADJ
ejpam-6473	147	11	value	value	NOUN
ejpam-6473	147	12	for	for	ADP
ejpam-6473	147	13	r0	r0	NOUN
ejpam-6473	147	14	>	>	X
ejpam-6473	147	15	1	1	NUM
ejpam-6473	147	16	above	above	ADP
ejpam-6473	147	17	inequality	inequality	NOUN
ejpam-6473	147	18	hold	hold	NOUN
ejpam-6473	147	19	which	which	PRON
ejpam-6473	147	20	proves	prove	VERB
ejpam-6473	147	21	that	that	SCONJ
ejpam-6473	147	22	third	third	ADJ
ejpam-6473	147	23	eigen	eigen	PROPN
ejpam-6473	147	24	value	value	NOUN
ejpam-6473	147	25	is	be	AUX
ejpam-6473	147	26	negative	negative	ADJ
ejpam-6473	147	27	.	.	PUNCT
ejpam-6473	148	1	=	=	NOUN
ejpam-6473	148	2	⇒	⇒	VERB
ejpam-6473	148	3	λ3	λ3	PROPN
ejpam-6473	148	4	<	<	X
ejpam-6473	148	5	0	0	NUM
ejpam-6473	148	6	.	.	PUNCT
ejpam-6473	149	1	as	as	ADV
ejpam-6473	149	2	all	all	DET
ejpam-6473	149	3	eigenvalues	eigenvalue	NOUN
ejpam-6473	149	4	are	be	AUX
ejpam-6473	149	5	negative	negative	ADJ
ejpam-6473	149	6	,	,	PUNCT
ejpam-6473	149	7	it	it	PRON
ejpam-6473	149	8	is	be	AUX
ejpam-6473	149	9	proven	prove	VERB
ejpam-6473	149	10	that	that	SCONJ
ejpam-6473	149	11	the	the	DET
ejpam-6473	149	12	endemic	endemic	ADJ
ejpam-6473	149	13	equilibrium	equilibrium	NOUN
ejpam-6473	149	14	points	point	NOUN
ejpam-6473	149	15	are	be	AUX
ejpam-6473	149	16	locally	locally	ADV
ejpam-6473	149	17	asymptotically	asymptotically	ADV
ejpam-6473	149	18	stable	stable	ADJ
ejpam-6473	149	19	for	for	ADP
ejpam-6473	149	20	r0	r0	PROPN
ejpam-6473	149	21	>	>	X
ejpam-6473	149	22	1	1	NUM
ejpam-6473	149	23	.	.	X
ejpam-6473	150	1	3.5.2	3.5.2	NUM
ejpam-6473	150	2	.	.	PUNCT
ejpam-6473	150	3	global	global	ADJ
ejpam-6473	150	4	stability	stability	NOUN
ejpam-6473	150	5	to	to	ADP
ejpam-6473	150	6	proof	proof	NOUN
ejpam-6473	150	7	that	that	SCONJ
ejpam-6473	150	8	the	the	DET
ejpam-6473	150	9	smoking	smoking	NOUN
ejpam-6473	150	10	-	-	PUNCT
ejpam-6473	150	11	free	free	ADJ
ejpam-6473	150	12	and	and	CCONJ
ejpam-6473	150	13	endemic	endemic	ADJ
ejpam-6473	150	14	equilibrium	equilibrium	NOUN
ejpam-6473	150	15	points	point	NOUN
ejpam-6473	150	16	are	be	AUX
ejpam-6473	150	17	globally	globally	ADV
ejpam-6473	150	18	asymptotically	asymptotically	ADV
ejpam-6473	150	19	stable	stable	ADJ
ejpam-6473	150	20	,	,	PUNCT
ejpam-6473	150	21	we	we	PRON
ejpam-6473	150	22	will	will	AUX
ejpam-6473	150	23	use	use	VERB
ejpam-6473	150	24	the	the	DET
ejpam-6473	150	25	castillo	castillo	PROPN
ejpam-6473	150	26	chavez	chavez	PROPN
ejpam-6473	150	27	principle	principle	PROPN
ejpam-6473	150	28	and	and	CCONJ
ejpam-6473	150	29	the	the	DET
ejpam-6473	150	30	geometric	geometric	ADJ
ejpam-6473	150	31	approach	approach	NOUN
ejpam-6473	150	32	[	[	X
ejpam-6473	150	33	26]-[27	26]-[27	PROPN
ejpam-6473	150	34	]	]	PUNCT
ejpam-6473	150	35	,	,	PUNCT
ejpam-6473	150	36	respectively	respectively	ADV
ejpam-6473	150	37	.	.	PUNCT
ejpam-6473	151	1	global	global	ADJ
ejpam-6473	151	2	stability	stability	NOUN
ejpam-6473	151	3	at	at	ADP
ejpam-6473	151	4	smoking	smoke	VERB
ejpam-6473	151	5	free	free	ADJ
ejpam-6473	151	6	equilibrium	equilibrium	NOUN
ejpam-6473	151	7	point	point	NOUN
ejpam-6473	151	8	to	to	PART
ejpam-6473	151	9	apply	apply	VERB
ejpam-6473	151	10	the	the	DET
ejpam-6473	151	11	castillo	castillo	PROPN
ejpam-6473	151	12	chavez	chavez	PROPN
ejpam-6473	151	13	principle	principle	PROPN
ejpam-6473	151	14	,	,	PUNCT
ejpam-6473	151	15	we	we	PRON
ejpam-6473	151	16	divide	divide	VERB
ejpam-6473	151	17	the	the	DET
ejpam-6473	151	18	system	system	NOUN
ejpam-6473	151	19	(	(	PUNCT
ejpam-6473	151	20	1	1	NUM
ejpam-6473	151	21	)	)	PUNCT
ejpam-6473	151	22	into	into	ADP
ejpam-6473	151	23	dk	dk	PROPN
ejpam-6473	151	24	dt	dt	X
ejpam-6473	151	25	=	=	SYM
ejpam-6473	151	26	e(k	e(k	NOUN
ejpam-6473	151	27	,	,	PUNCT
ejpam-6473	151	28	w	w	NOUN
ejpam-6473	151	29	)	)	PUNCT
ejpam-6473	151	30	,	,	PUNCT
ejpam-6473	151	31	dw	dw	PROPN
ejpam-6473	151	32	dt	dt	NOUN
ejpam-6473	152	1	=	=	SYM
ejpam-6473	152	2	f	f	PROPN
ejpam-6473	152	3	(	(	PUNCT
ejpam-6473	152	4	k	k	X
ejpam-6473	152	5	,	,	PUNCT
ejpam-6473	152	6	w	w	PROPN
ejpam-6473	152	7	)	)	PUNCT
ejpam-6473	152	8	.	.	PUNCT
ejpam-6473	153	1	here	here	ADV
ejpam-6473	153	2	,	,	PUNCT
ejpam-6473	153	3	k	k	PROPN
ejpam-6473	153	4	represents	represent	VERB
ejpam-6473	153	5	the	the	DET
ejpam-6473	153	6	nonsmokers	nonsmoker	NOUN
ejpam-6473	153	7	population	population	NOUN
ejpam-6473	153	8	(	(	PUNCT
ejpam-6473	153	9	p	p	X
ejpam-6473	153	10	,	,	PUNCT
ejpam-6473	153	11	q	q	NOUN
ejpam-6473	153	12	)	)	PUNCT
ejpam-6473	153	13	and	and	CCONJ
ejpam-6473	153	14	w	w	PROPN
ejpam-6473	153	15	represents	represent	VERB
ejpam-6473	153	16	the	the	DET
ejpam-6473	153	17	smoker	smoker	ADJ
ejpam-6473	153	18	population	population	NOUN
ejpam-6473	153	19	(	(	PUNCT
ejpam-6473	153	20	l	l	NOUN
ejpam-6473	153	21	,	,	PUNCT
ejpam-6473	153	22	s	s	PART
ejpam-6473	153	23	)	)	PUNCT
ejpam-6473	153	24	.	.	PUNCT
ejpam-6473	154	1	e0	e0	PROPN
ejpam-6473	154	2	=	=	PUNCT
ejpam-6473	154	3	(	(	PUNCT
ejpam-6473	154	4	k0	k0	PROPN
ejpam-6473	154	5	,	,	PUNCT
ejpam-6473	154	6	0̄	0̄	PROPN
ejpam-6473	154	7	)	)	PUNCT
ejpam-6473	154	8	is	be	AUX
ejpam-6473	154	9	the	the	DET
ejpam-6473	154	10	smoking	smoking	NOUN
ejpam-6473	154	11	-	-	PUNCT
ejpam-6473	154	12	free	free	ADJ
ejpam-6473	154	13	equilibrium	equilibrium	NOUN
ejpam-6473	154	14	point	point	NOUN
ejpam-6473	154	15	.	.	PUNCT
ejpam-6473	155	1	according	accord	VERB
ejpam-6473	155	2	to	to	ADP
ejpam-6473	155	3	the	the	DET
ejpam-6473	155	4	castillo	castillo	PROPN
ejpam-6473	155	5	chavez	chavez	PROPN
ejpam-6473	155	6	principle	principle	PROPN
ejpam-6473	155	7	if	if	SCONJ
ejpam-6473	155	8	the	the	DET
ejpam-6473	155	9	following	follow	VERB
ejpam-6473	155	10	two	two	NUM
ejpam-6473	155	11	conditions	condition	NOUN
ejpam-6473	155	12	are	be	AUX
ejpam-6473	155	13	fulfilled	fulfil	VERB
ejpam-6473	155	14	,	,	PUNCT
ejpam-6473	155	15	then	then	ADV
ejpam-6473	155	16	smoking	smoke	VERB
ejpam-6473	155	17	free	free	ADJ
ejpam-6473	155	18	equilibrium	equilibrium	NOUN
ejpam-6473	155	19	point	point	NOUN
ejpam-6473	155	20	is	be	AUX
ejpam-6473	155	21	globally	globally	ADV
ejpam-6473	155	22	stable	stable	ADJ
ejpam-6473	155	23	at	at	ADP
ejpam-6473	155	24	r0	r0	NOUN
ejpam-6473	155	25	<	<	X
ejpam-6473	155	26	1	1	NUM
ejpam-6473	155	27	.	.	X
ejpam-6473	156	1	n1	n1	NOUN
ejpam-6473	156	2	dk	dk	PRON
ejpam-6473	156	3	dt	dt	X
ejpam-6473	156	4	=	=	PUNCT
ejpam-6473	156	5	e(k	e(k	NOUN
ejpam-6473	156	6	,	,	PUNCT
ejpam-6473	156	7	0	0	NUM
ejpam-6473	156	8	)	)	PUNCT
ejpam-6473	156	9	,	,	PUNCT
ejpam-6473	156	10	k0	k0	PROPN
ejpam-6473	156	11	is	be	AUX
ejpam-6473	156	12	globally	globally	ADV
ejpam-6473	156	13	stable	stable	ADJ
ejpam-6473	156	14	.	.	PUNCT
ejpam-6473	157	1	n2	n2	ADJ
ejpam-6473	157	2	the	the	DET
ejpam-6473	157	3	formula	formula	NOUN
ejpam-6473	157	4	for	for	ADP
ejpam-6473	157	5	f	f	NOUN
ejpam-6473	157	6	=	=	SYM
ejpam-6473	157	7	f(k	f(k	VERB
ejpam-6473	157	8	,	,	PUNCT
ejpam-6473	157	9	w	w	NOUN
ejpam-6473	157	10	)	)	PUNCT
ejpam-6473	157	11	is	be	AUX
ejpam-6473	157	12	f	f	PROPN
ejpam-6473	157	13	(	(	PUNCT
ejpam-6473	157	14	k	k	X
ejpam-6473	157	15	,	,	PUNCT
ejpam-6473	157	16	w	w	NOUN
ejpam-6473	157	17	)	)	PUNCT
ejpam-6473	158	1	=	=	SYM
ejpam-6473	158	2	yw	yw	PROPN
ejpam-6473	158	3	−	−	PROPN
ejpam-6473	158	4	f̄	f̄	PROPN
ejpam-6473	158	5	(	(	PUNCT
ejpam-6473	158	6	k	k	PROPN
ejpam-6473	158	7	,	,	PUNCT
ejpam-6473	158	8	w	w	PROPN
ejpam-6473	158	9	)	)	PUNCT
ejpam-6473	158	10	,	,	PUNCT
ejpam-6473	158	11	where	where	SCONJ
ejpam-6473	158	12	f̄r(k	f̄r(k	PROPN
ejpam-6473	158	13	,	,	PUNCT
ejpam-6473	158	14	w	w	NOUN
ejpam-6473	158	15	)	)	PUNCT
ejpam-6473	158	16	≥	≥	NOUN
ejpam-6473	158	17	0∀	0∀	NUM
ejpam-6473	158	18	(	(	PUNCT
ejpam-6473	158	19	k	k	X
ejpam-6473	158	20	,	,	PUNCT
ejpam-6473	158	21	w	w	NOUN
ejpam-6473	158	22	)	)	PUNCT
ejpam-6473	158	23	in	in	ADP
ejpam-6473	158	24	feasible	feasible	ADJ
ejpam-6473	158	25	region	region	NOUN
ejpam-6473	158	26	ω	ω	PROPN
ejpam-6473	158	27	for	for	ADP
ejpam-6473	158	28	r=1,2	r=1,2	NOUN
ejpam-6473	158	29	.	.	PUNCT
ejpam-6473	159	1	y	y	PROPN
ejpam-6473	159	2	is	be	AUX
ejpam-6473	159	3	m	m	NOUN
ejpam-6473	159	4	-	-	NOUN
ejpam-6473	159	5	matrix	matrix	NOUN
ejpam-6473	159	6	,	,	PUNCT
ejpam-6473	159	7	which	which	PRON
ejpam-6473	159	8	is	be	AUX
ejpam-6473	159	9	defined	define	VERB
ejpam-6473	159	10	as	as	ADP
ejpam-6473	159	11	y	y	PROPN
ejpam-6473	159	12	=	=	PROPN
ejpam-6473	159	13	dwf	dwf	PROPN
ejpam-6473	159	14	(	(	PUNCT
ejpam-6473	159	15	k0	k0	PROPN
ejpam-6473	159	16	,	,	PUNCT
ejpam-6473	159	17	0̄	0̄	PROPN
ejpam-6473	159	18	)	)	PUNCT
ejpam-6473	159	19	,	,	PUNCT
ejpam-6473	159	20	f̄r(k	f̄r(k	PROPN
ejpam-6473	159	21	,	,	PUNCT
ejpam-6473	159	22	w	w	NOUN
ejpam-6473	159	23	)	)	PUNCT
ejpam-6473	159	24	is	be	AUX
ejpam-6473	159	25	the	the	DET
ejpam-6473	159	26	individual	individual	ADJ
ejpam-6473	159	27	component	component	NOUN
ejpam-6473	159	28	of	of	ADP
ejpam-6473	159	29	f̄	f̄	PROPN
ejpam-6473	159	30	(	(	PUNCT
ejpam-6473	159	31	k	k	PROPN
ejpam-6473	159	32	,	,	PUNCT
ejpam-6473	159	33	w	w	PROPN
ejpam-6473	159	34	)	)	PUNCT
ejpam-6473	159	35	,	,	PUNCT
ejpam-6473	159	36	dw	dw	PROPN
ejpam-6473	159	37	is	be	AUX
ejpam-6473	159	38	the	the	DET
ejpam-6473	159	39	partial	partial	ADJ
ejpam-6473	159	40	derivative	derivative	NOUN
ejpam-6473	159	41	of	of	ADP
ejpam-6473	159	42	the	the	DET
ejpam-6473	159	43	sub	sub	NOUN
ejpam-6473	159	44	matrix	matrix	NOUN
ejpam-6473	159	45	f	f	PROPN
ejpam-6473	159	46	(	(	PUNCT
ejpam-6473	159	47	k	k	X
ejpam-6473	159	48	,	,	PUNCT
ejpam-6473	159	49	w	w	NOUN
ejpam-6473	159	50	)	)	PUNCT
ejpam-6473	159	51	with	with	ADP
ejpam-6473	159	52	respect	respect	NOUN
ejpam-6473	159	53	to	to	ADP
ejpam-6473	159	54	smoker	smoker	VERB
ejpam-6473	159	55	class	class	NOUN
ejpam-6473	159	56	(	(	PUNCT
ejpam-6473	159	57	l	l	NOUN
ejpam-6473	159	58	,	,	PUNCT
ejpam-6473	159	59	s	s	PART
ejpam-6473	159	60	)	)	PUNCT
ejpam-6473	159	61	and	and	CCONJ
ejpam-6473	159	62	y	y	PROPN
ejpam-6473	159	63	=	=	SYM
ejpam-6473	159	64	dwf	dwf	PROPN
ejpam-6473	159	65	(	(	PUNCT
ejpam-6473	159	66	k0	k0	PROPN
ejpam-6473	159	67	,	,	PUNCT
ejpam-6473	159	68	0̄	0̄	PROPN
ejpam-6473	159	69	)	)	PUNCT
ejpam-6473	159	70	is	be	AUX
ejpam-6473	159	71	the	the	DET
ejpam-6473	159	72	jacobian	jacobian	NOUN
ejpam-6473	159	73	of	of	ADP
ejpam-6473	159	74	the	the	DET
ejpam-6473	159	75	sub	sub	NOUN
ejpam-6473	159	76	matrix	matrix	NOUN
ejpam-6473	159	77	f	f	PROPN
ejpam-6473	159	78	of	of	ADP
ejpam-6473	159	79	smoker	smoker	ADJ
ejpam-6473	159	80	classes	class	NOUN
ejpam-6473	159	81	at	at	ADP
ejpam-6473	159	82	smoking	smoke	VERB
ejpam-6473	159	83	free	free	ADJ
ejpam-6473	159	84	equilibrium	equilibrium	NOUN
ejpam-6473	159	85	point	point	NOUN
ejpam-6473	159	86	.	.	PUNCT
ejpam-6473	160	1	lemma	lemma	PROPN
ejpam-6473	160	2	1	1	X
ejpam-6473	160	3	.	.	X
ejpam-6473	160	4	smoking	smoking	NOUN
ejpam-6473	160	5	-	-	PUNCT
ejpam-6473	160	6	free	free	ADJ
ejpam-6473	160	7	equilibrium	equilibrium	NOUN
ejpam-6473	160	8	point	point	NOUN
ejpam-6473	160	9	e0	e0	PROPN
ejpam-6473	160	10	=	=	SYM
ejpam-6473	160	11	(	(	PUNCT
ejpam-6473	160	12	k0	k0	PROPN
ejpam-6473	160	13	,	,	PUNCT
ejpam-6473	160	14	0̄	0̄	PROPN
ejpam-6473	160	15	)	)	PUNCT
ejpam-6473	160	16	is	be	AUX
ejpam-6473	160	17	globally	globally	ADV
ejpam-6473	160	18	asymptotically	asymptotically	ADV
ejpam-6473	160	19	stable	stable	ADJ
ejpam-6473	160	20	,	,	PUNCT
ejpam-6473	160	21	provided	provide	VERB
ejpam-6473	160	22	that	that	SCONJ
ejpam-6473	160	23	above	above	ADP
ejpam-6473	160	24	conditions	condition	NOUN
ejpam-6473	160	25	are	be	AUX
ejpam-6473	160	26	satisfied	satisfied	ADJ
ejpam-6473	160	27	.	.	PUNCT
ejpam-6473	161	1	theorem	theorem	VERB
ejpam-6473	161	2	3	3	NUM
ejpam-6473	161	3	.	.	PUNCT
ejpam-6473	162	1	at	at	ADP
ejpam-6473	162	2	smoking	smoking	NOUN
ejpam-6473	162	3	-	-	PUNCT
ejpam-6473	162	4	free	free	ADJ
ejpam-6473	162	5	equilibrium	equilibrium	NOUN
ejpam-6473	162	6	point	point	NOUN
ejpam-6473	162	7	,	,	PUNCT
ejpam-6473	162	8	proposed	propose	VERB
ejpam-6473	162	9	model	model	NOUN
ejpam-6473	162	10	(	(	PUNCT
ejpam-6473	162	11	1	1	X
ejpam-6473	162	12	)	)	PUNCT
ejpam-6473	162	13	is	be	AUX
ejpam-6473	162	14	globally	globally	ADV
ejpam-6473	162	15	asymptotically	asymptotically	ADV
ejpam-6473	162	16	stable	stable	ADJ
ejpam-6473	162	17	if	if	SCONJ
ejpam-6473	162	18	r0	r0	NOUN
ejpam-6473	162	19	<	<	X
ejpam-6473	162	20	1	1	NUM
ejpam-6473	162	21	.	.	PUNCT
ejpam-6473	162	22	proof	proof	NOUN
ejpam-6473	162	23	.	.	PUNCT
ejpam-6473	163	1	as	as	SCONJ
ejpam-6473	163	2	the	the	DET
ejpam-6473	163	3	system	system	NOUN
ejpam-6473	163	4	(	(	PUNCT
ejpam-6473	163	5	1	1	X
ejpam-6473	163	6	)	)	PUNCT
ejpam-6473	163	7	is	be	AUX
ejpam-6473	163	8	divided	divide	VERB
ejpam-6473	163	9	into	into	ADP
ejpam-6473	163	10	two	two	NUM
ejpam-6473	163	11	sub	sub	NOUN
ejpam-6473	163	12	systems	system	NOUN
ejpam-6473	163	13	e	e	PROPN
ejpam-6473	163	14	and	and	CCONJ
ejpam-6473	163	15	f	f	PROPN
ejpam-6473	163	16	which	which	PRON
ejpam-6473	163	17	are	be	AUX
ejpam-6473	163	18	defined	define	VERB
ejpam-6473	163	19	as	as	ADP
ejpam-6473	163	20	;	;	PUNCT
ejpam-6473	163	21	dk	dk	PRON
ejpam-6473	163	22	dt	dt	X
ejpam-6473	163	23	=	=	PROPN
ejpam-6473	163	24	e(k	e(k	NOUN
ejpam-6473	163	25	,	,	PUNCT
ejpam-6473	163	26	w	w	NOUN
ejpam-6473	163	27	)	)	PUNCT
ejpam-6473	163	28	=	=	SYM
ejpam-6473	163	29	(	(	PUNCT
ejpam-6473	163	30	λ−	λ−	PROPN
ejpam-6473	163	31	βps(1	βps(1	NOUN
ejpam-6473	163	32	+	+	CCONJ
ejpam-6473	163	33	νs)−	νs)−	NOUN
ejpam-6473	163	34	(	(	PUNCT
ejpam-6473	163	35	b+	b+	X
ejpam-6473	163	36	µ)p	µ)p	NOUN
ejpam-6473	163	37	δs	δs	ADP
ejpam-6473	163	38	−	−	PROPN
ejpam-6473	163	39	(	(	PUNCT
ejpam-6473	163	40	b+	b+	X
ejpam-6473	163	41	µ)q	µ)q	NOUN
ejpam-6473	163	42	)	)	PUNCT
ejpam-6473	163	43	,	,	PUNCT
ejpam-6473	163	44	s.	s.	PROPN
ejpam-6473	163	45	bano	bano	PROPN
ejpam-6473	163	46	et	et	PROPN
ejpam-6473	163	47	al	al	PROPN
ejpam-6473	163	48	.	.	PUNCT
ejpam-6473	163	49	/	/	SYM
ejpam-6473	163	50	eur	eur	PROPN
ejpam-6473	163	51	.	.	PUNCT
ejpam-6473	164	1	j.	j.	PROPN
ejpam-6473	164	2	pure	pure	PROPN
ejpam-6473	164	3	appl	appl	PROPN
ejpam-6473	164	4	.	.	PROPN
ejpam-6473	164	5	math	math	PROPN
ejpam-6473	164	6	,	,	PUNCT
ejpam-6473	164	7	18	18	NUM
ejpam-6473	164	8	(	(	PUNCT
ejpam-6473	164	9	4	4	NUM
ejpam-6473	164	10	)	)	PUNCT
ejpam-6473	164	11	(	(	PUNCT
ejpam-6473	164	12	2025	2025	NUM
ejpam-6473	164	13	)	)	PUNCT
ejpam-6473	164	14	,	,	PUNCT
ejpam-6473	164	15	6473	6473	NUM
ejpam-6473	164	16	9	9	NUM
ejpam-6473	164	17	of	of	ADP
ejpam-6473	164	18	38	38	NUM
ejpam-6473	164	19	dw	dw	NOUN
ejpam-6473	164	20	dt	dt	NOUN
ejpam-6473	165	1	=	=	SYM
ejpam-6473	165	2	f	f	PROPN
ejpam-6473	165	3	(	(	PUNCT
ejpam-6473	165	4	k	k	X
ejpam-6473	165	5	,	,	PUNCT
ejpam-6473	165	6	w	w	NOUN
ejpam-6473	165	7	)	)	PUNCT
ejpam-6473	165	8	=	=	SYM
ejpam-6473	165	9	(	(	PUNCT
ejpam-6473	165	10	βps(1	βps(1	NOUN
ejpam-6473	165	11	+	+	CCONJ
ejpam-6473	165	12	νs)−	νs)−	NOUN
ejpam-6473	165	13	(	(	PUNCT
ejpam-6473	165	14	b+	b+	X
ejpam-6473	165	15	µ+	µ+	PRON
ejpam-6473	165	16	ζ)l	ζ)l	NOUN
ejpam-6473	165	17	ζl−	ζl−	PUNCT
ejpam-6473	165	18	(	(	PUNCT
ejpam-6473	165	19	b+	b+	X
ejpam-6473	165	20	µ+	µ+	X
ejpam-6473	165	21	δ)s	δ)s	NOUN
ejpam-6473	165	22	)	)	PUNCT
ejpam-6473	165	23	,	,	PUNCT
ejpam-6473	165	24	the	the	DET
ejpam-6473	165	25	smoking	smoking	NOUN
ejpam-6473	165	26	-	-	PUNCT
ejpam-6473	165	27	free	free	ADJ
ejpam-6473	165	28	equilibrium	equilibrium	NOUN
ejpam-6473	165	29	point	point	NOUN
ejpam-6473	165	30	is	be	AUX
ejpam-6473	165	31	e0	e0	PROPN
ejpam-6473	165	32	=	=	PUNCT
ejpam-6473	165	33	(	(	PUNCT
ejpam-6473	165	34	k0	k0	PROPN
ejpam-6473	165	35	,	,	PUNCT
ejpam-6473	165	36	0̄	0̄	PROPN
ejpam-6473	165	37	)	)	PUNCT
ejpam-6473	165	38	,	,	PUNCT
ejpam-6473	165	39	where	where	SCONJ
ejpam-6473	165	40	k0	k0	PROPN
ejpam-6473	165	41	=	=	SYM
ejpam-6473	165	42	(	(	PUNCT
ejpam-6473	165	43	λ	λ	X
ejpam-6473	165	44	(	(	PUNCT
ejpam-6473	165	45	b+µ	b+µ	NOUN
ejpam-6473	165	46	)	)	PUNCT
ejpam-6473	165	47	,	,	PUNCT
ejpam-6473	165	48	0	0	NUM
ejpam-6473	165	49	)	)	PUNCT
ejpam-6473	165	50	and	and	CCONJ
ejpam-6473	165	51	0̄	0̄	NUM
ejpam-6473	165	52	=	=	SYM
ejpam-6473	165	53	(	(	PUNCT
ejpam-6473	165	54	0	0	NUM
ejpam-6473	165	55	,	,	PUNCT
ejpam-6473	165	56	0	0	NUM
ejpam-6473	165	57	)	)	PUNCT
ejpam-6473	165	58	.	.	PUNCT
ejpam-6473	166	1	for	for	ADP
ejpam-6473	166	2	p	p	NOUN
ejpam-6473	166	3	=	=	PROPN
ejpam-6473	166	4	p0	p0	NOUN
ejpam-6473	166	5	and	and	CCONJ
ejpam-6473	166	6	q	q	NOUN
ejpam-6473	167	1	=	=	PRON
ejpam-6473	167	2	q0	q0	PROPN
ejpam-6473	167	3	,	,	PUNCT
ejpam-6473	167	4	dk	dk	INTJ
ejpam-6473	167	5	dt	dt	X
ejpam-6473	167	6	=	=	PRON
ejpam-6473	167	7	(	(	PUNCT
ejpam-6473	167	8	λ−	λ−	PROPN
ejpam-6473	167	9	(	(	PUNCT
ejpam-6473	167	10	b+	b+	X
ejpam-6473	167	11	µ	µ	X
ejpam-6473	167	12	)	)	PUNCT
ejpam-6473	167	13	λ	λ	PROPN
ejpam-6473	167	14	(	(	PUNCT
ejpam-6473	167	15	b+µ	b+µ	NOUN
ejpam-6473	167	16	)	)	PUNCT
ejpam-6473	167	17	0	0	NUM
ejpam-6473	167	18	)	)	PUNCT
ejpam-6473	168	1	=	=	SYM
ejpam-6473	168	2	0	0	NUM
ejpam-6473	168	3	,	,	PUNCT
ejpam-6473	168	4	(	(	PUNCT
ejpam-6473	168	5	7	7	X
ejpam-6473	168	6	)	)	PUNCT
ejpam-6473	168	7	dk	dk	PRON
ejpam-6473	168	8	dt	dt	NOUN
ejpam-6473	168	9	=	=	SYM
ejpam-6473	168	10	λ−	λ−	PROPN
ejpam-6473	168	11	(	(	PUNCT
ejpam-6473	168	12	b+	b+	NOUN
ejpam-6473	168	13	µ)k	µ)k	NOUN
ejpam-6473	168	14	,	,	PUNCT
ejpam-6473	168	15	now	now	ADV
ejpam-6473	168	16	by	by	ADP
ejpam-6473	168	17	using	use	VERB
ejpam-6473	168	18	integrating	integrate	VERB
ejpam-6473	168	19	factor	factor	NOUN
ejpam-6473	168	20	e(b+µ)t	e(b+µ)t	NOUN
ejpam-6473	168	21	,	,	PUNCT
ejpam-6473	168	22	we	we	PRON
ejpam-6473	168	23	get	get	VERB
ejpam-6473	168	24	k	k	PROPN
ejpam-6473	168	25	→	→	SYM
ejpam-6473	168	26	k0	k0	PROPN
ejpam-6473	168	27	as	as	ADP
ejpam-6473	168	28	t	t	PROPN
ejpam-6473	168	29	→	→	SYM
ejpam-6473	168	30	∞.	∞.	PROPN
ejpam-6473	168	31	this	this	PRON
ejpam-6473	168	32	proves	prove	VERB
ejpam-6473	168	33	the	the	DET
ejpam-6473	168	34	condition	condition	NOUN
ejpam-6473	168	35	(	(	PUNCT
ejpam-6473	168	36	n1	n1	NOUN
ejpam-6473	168	37	)	)	PUNCT
ejpam-6473	168	38	that	that	PRON
ejpam-6473	168	39	is	be	AUX
ejpam-6473	168	40	k0	k0	PROPN
ejpam-6473	168	41	is	be	AUX
ejpam-6473	168	42	globally	globally	ADV
ejpam-6473	168	43	stable	stable	ADJ
ejpam-6473	168	44	for	for	ADP
ejpam-6473	168	45	subsystem	subsystem	NOUN
ejpam-6473	169	1	dk	dk	PRON
ejpam-6473	169	2	dt	dt	X
ejpam-6473	169	3	=	=	SYM
ejpam-6473	169	4	e(k	e(k	NOUN
ejpam-6473	169	5	,	,	PUNCT
ejpam-6473	169	6	0	0	NUM
ejpam-6473	169	7	)	)	PUNCT
ejpam-6473	169	8	.	.	PUNCT
ejpam-6473	170	1	for	for	ADP
ejpam-6473	170	2	condition	condition	NOUN
ejpam-6473	170	3	(	(	PUNCT
ejpam-6473	170	4	n2	n2	NOUN
ejpam-6473	170	5	)	)	PUNCT
ejpam-6473	170	6	we	we	PRON
ejpam-6473	170	7	first	first	ADV
ejpam-6473	170	8	defined	define	VERB
ejpam-6473	170	9	y	y	PROPN
ejpam-6473	170	10	matrix	matrix	NOUN
ejpam-6473	170	11	for	for	ADP
ejpam-6473	170	12	(	(	PUNCT
ejpam-6473	170	13	k	k	X
ejpam-6473	170	14	,	,	PUNCT
ejpam-6473	170	15	w	w	NOUN
ejpam-6473	170	16	)	)	PUNCT
ejpam-6473	171	1	=	=	SYM
ejpam-6473	171	2	(	(	PUNCT
ejpam-6473	171	3	k0	k0	PROPN
ejpam-6473	171	4	,	,	PUNCT
ejpam-6473	171	5	0̄	0̄	PROPN
ejpam-6473	171	6	)	)	PUNCT
ejpam-6473	171	7	y	y	NOUN
ejpam-6473	172	1	=	=	PUNCT
ejpam-6473	173	1	[	[	PUNCT
ejpam-6473	173	2	−(b+	−(b+	NUM
ejpam-6473	173	3	µ+	µ+	X
ejpam-6473	173	4	ζ	ζ	NOUN
ejpam-6473	173	5	)	)	PUNCT
ejpam-6473	173	6	βp0(1	βp0(1	NOUN
ejpam-6473	174	1	+	+	CCONJ
ejpam-6473	174	2	2νs0	2νs0	X
ejpam-6473	174	3	)	)	PUNCT
ejpam-6473	174	4	ζ	ζ	NOUN
ejpam-6473	174	5	−(b+	−(b+	NUM
ejpam-6473	174	6	µ+	µ+	PROPN
ejpam-6473	174	7	δ	δ	PROPN
ejpam-6473	174	8	)	)	PUNCT
ejpam-6473	174	9	]	]	PUNCT
ejpam-6473	175	1	f̄	f̄	PROPN
ejpam-6473	175	2	(	(	PUNCT
ejpam-6473	175	3	k	k	NOUN
ejpam-6473	175	4	,	,	PUNCT
ejpam-6473	175	5	w	w	NOUN
ejpam-6473	175	6	)	)	PUNCT
ejpam-6473	175	7	=	=	PUNCT
ejpam-6473	176	1	[	[	PUNCT
ejpam-6473	176	2	−(b+	−(b+	NUM
ejpam-6473	176	3	µ+	µ+	X
ejpam-6473	176	4	ζ	ζ	NOUN
ejpam-6473	176	5	)	)	PUNCT
ejpam-6473	176	6	βp0(1	βp0(1	NOUN
ejpam-6473	177	1	+	+	CCONJ
ejpam-6473	177	2	2νs0	2νs0	X
ejpam-6473	177	3	)	)	PUNCT
ejpam-6473	177	4	ζ	ζ	NOUN
ejpam-6473	177	5	−(b+	−(b+	NUM
ejpam-6473	177	6	µ+	µ+	PROPN
ejpam-6473	177	7	δ	δ	PROPN
ejpam-6473	177	8	)	)	PUNCT
ejpam-6473	177	9	]	]	PUNCT
ejpam-6473	177	10	·	·	PUNCT
ejpam-6473	178	1	[	[	PUNCT
ejpam-6473	178	2	l	l	NOUN
ejpam-6473	178	3	s	s	X
ejpam-6473	178	4	]	]	X
ejpam-6473	178	5	−	−	PROPN
ejpam-6473	178	6	[	[	PUNCT
ejpam-6473	178	7	−(b+	−(b+	NUM
ejpam-6473	178	8	µ+	µ+	X
ejpam-6473	178	9	ζ	ζ	NOUN
ejpam-6473	178	10	)	)	PUNCT
ejpam-6473	178	11	βp	βp	NOUN
ejpam-6473	178	12	(	(	PUNCT
ejpam-6473	178	13	1	1	NUM
ejpam-6473	178	14	+	+	NUM
ejpam-6473	178	15	νs	νs	NOUN
ejpam-6473	178	16	)	)	PUNCT
ejpam-6473	178	17	ζ	ζ	NOUN
ejpam-6473	178	18	−(b+	−(b+	NUM
ejpam-6473	178	19	µ+	µ+	PROPN
ejpam-6473	178	20	δ	δ	PROPN
ejpam-6473	178	21	)	)	PUNCT
ejpam-6473	178	22	]	]	PUNCT
ejpam-6473	178	23	·	·	PUNCT
ejpam-6473	179	1	[	[	PUNCT
ejpam-6473	179	2	l	l	NOUN
ejpam-6473	179	3	s	s	X
ejpam-6473	179	4	]	]	X
ejpam-6473	179	5	=	=	X
ejpam-6473	179	6	[	[	PUNCT
ejpam-6473	179	7	βp0s(1	βp0s(1	PROPN
ejpam-6473	179	8	+	+	NUM
ejpam-6473	179	9	2νs0)−	2νs0)−	NOUN
ejpam-6473	179	10	βps(1	βps(1	NOUN
ejpam-6473	179	11	+	+	CCONJ
ejpam-6473	179	12	νs	νs	NOUN
ejpam-6473	179	13	)	)	PUNCT
ejpam-6473	179	14	0	0	NUM
ejpam-6473	179	15	]	]	PUNCT
ejpam-6473	179	16	.	.	PUNCT
ejpam-6473	180	1	now	now	ADV
ejpam-6473	180	2	f̄1	f̄1	VERB
ejpam-6473	180	3	≥	≥	NOUN
ejpam-6473	180	4	0	0	NUM
ejpam-6473	180	5	,	,	PUNCT
ejpam-6473	180	6	if	if	SCONJ
ejpam-6473	180	7	βp0s(1	βp0s(1	PROPN
ejpam-6473	180	8	+	+	NUM
ejpam-6473	180	9	2νs0)−	2νs0)−	NOUN
ejpam-6473	180	10	βps(1	βps(1	NOUN
ejpam-6473	180	11	+	+	CCONJ
ejpam-6473	180	12	νs	νs	NOUN
ejpam-6473	180	13	)	)	PUNCT
ejpam-6473	180	14	≥	≥	NOUN
ejpam-6473	180	15	0	0	NUM
ejpam-6473	180	16	.	.	PUNCT
ejpam-6473	181	1	this	this	PRON
ejpam-6473	181	2	implies	imply	VERB
ejpam-6473	181	3	that	that	SCONJ
ejpam-6473	181	4	βp0s(1	βp0s(1	PROPN
ejpam-6473	181	5	+	+	CCONJ
ejpam-6473	181	6	2νs0	2νs0	NUM
ejpam-6473	181	7	)	)	PUNCT
ejpam-6473	181	8	≥	≥	NOUN
ejpam-6473	181	9	βps(1	βps(1	PUNCT
ejpam-6473	181	10	+	+	CCONJ
ejpam-6473	181	11	νs	νs	NOUN
ejpam-6473	181	12	)	)	PUNCT
ejpam-6473	181	13	.	.	PUNCT
ejpam-6473	182	1	and	and	CCONJ
ejpam-6473	182	2	f̄2	f̄2	NUM
ejpam-6473	182	3	=	=	SYM
ejpam-6473	182	4	0	0	NUM
ejpam-6473	182	5	.	.	PUNCT
ejpam-6473	183	1	f(k	f(k	VERB
ejpam-6473	183	2	,	,	PUNCT
ejpam-6473	183	3	w	w	NOUN
ejpam-6473	183	4	)	)	PUNCT
ejpam-6473	183	5	is	be	AUX
ejpam-6473	183	6	the	the	DET
ejpam-6473	183	7	sub	sub	NOUN
ejpam-6473	183	8	matrix	matrix	NOUN
ejpam-6473	183	9	which	which	PRON
ejpam-6473	183	10	contain	contain	VERB
ejpam-6473	183	11	the	the	DET
ejpam-6473	183	12	smoker	smoker	ADJ
ejpam-6473	183	13	population	population	NOUN
ejpam-6473	183	14	and	and	CCONJ
ejpam-6473	183	15	f̄	f̄	PROPN
ejpam-6473	183	16	(	(	PUNCT
ejpam-6473	183	17	k	k	NOUN
ejpam-6473	183	18	,	,	PUNCT
ejpam-6473	183	19	w	w	NOUN
ejpam-6473	183	20	)	)	PUNCT
ejpam-6473	183	21	is	be	AUX
ejpam-6473	183	22	obtain	obtain	ADJ
ejpam-6473	183	23	after	after	ADP
ejpam-6473	183	24	rearranging	rearrange	VERB
ejpam-6473	183	25	the	the	DET
ejpam-6473	183	26	formula	formula	NOUN
ejpam-6473	183	27	in	in	ADP
ejpam-6473	183	28	the	the	DET
ejpam-6473	183	29	condition	condition	NOUN
ejpam-6473	183	30	n2	n2	NOUN
ejpam-6473	183	31	that	that	PRON
ejpam-6473	183	32	is	be	AUX
ejpam-6473	183	33	f̄	f̄	PROPN
ejpam-6473	183	34	(	(	PUNCT
ejpam-6473	183	35	k	k	NOUN
ejpam-6473	183	36	,	,	PUNCT
ejpam-6473	183	37	w	w	NOUN
ejpam-6473	183	38	)	)	PUNCT
ejpam-6473	184	1	=	=	SYM
ejpam-6473	184	2	yw	yw	PROPN
ejpam-6473	185	1	−	−	PROPN
ejpam-6473	186	1	f	f	PROPN
ejpam-6473	187	1	(	(	PUNCT
ejpam-6473	187	2	k	k	X
ejpam-6473	187	3	,	,	PUNCT
ejpam-6473	187	4	w	w	PROPN
ejpam-6473	187	5	)	)	PUNCT
ejpam-6473	187	6	.	.	PUNCT
ejpam-6473	188	1	here	here	ADV
ejpam-6473	188	2	,	,	PUNCT
ejpam-6473	188	3	w	w	PROPN
ejpam-6473	188	4	is	be	AUX
ejpam-6473	188	5	the	the	DET
ejpam-6473	188	6	smoker	smoker	ADJ
ejpam-6473	188	7	class	class	NOUN
ejpam-6473	188	8	(	(	PUNCT
ejpam-6473	188	9	l	l	NOUN
ejpam-6473	188	10	,	,	PUNCT
ejpam-6473	188	11	s	s	PART
ejpam-6473	188	12	)	)	PUNCT
ejpam-6473	188	13	and	and	CCONJ
ejpam-6473	188	14	f̄1(k	f̄1(k	NOUN
ejpam-6473	188	15	,	,	PUNCT
ejpam-6473	188	16	w	w	NOUN
ejpam-6473	188	17	)	)	PUNCT
ejpam-6473	188	18	and	and	CCONJ
ejpam-6473	188	19	f̄2(k	f̄2(k	NOUN
ejpam-6473	188	20	,	,	PUNCT
ejpam-6473	188	21	w	w	NOUN
ejpam-6473	188	22	)	)	PUNCT
ejpam-6473	188	23	are	be	AUX
ejpam-6473	188	24	the	the	DET
ejpam-6473	188	25	entries	entry	NOUN
ejpam-6473	188	26	of	of	ADP
ejpam-6473	188	27	the	the	DET
ejpam-6473	188	28	f̄	f̄	PROPN
ejpam-6473	188	29	(	(	PUNCT
ejpam-6473	188	30	k	k	PROPN
ejpam-6473	188	31	,	,	PUNCT
ejpam-6473	188	32	w	w	NOUN
ejpam-6473	188	33	)	)	PUNCT
ejpam-6473	188	34	.	.	PUNCT
ejpam-6473	189	1	hence	hence	ADV
ejpam-6473	189	2	,	,	PUNCT
ejpam-6473	189	3	both	both	DET
ejpam-6473	189	4	conditions	condition	NOUN
ejpam-6473	189	5	(	(	PUNCT
ejpam-6473	189	6	n1	n1	NOUN
ejpam-6473	189	7	,	,	PUNCT
ejpam-6473	189	8	n2	n2	ADJ
ejpam-6473	189	9	)	)	PUNCT
ejpam-6473	189	10	are	be	AUX
ejpam-6473	189	11	satisfied	satisfied	ADJ
ejpam-6473	189	12	,	,	PUNCT
ejpam-6473	189	13	this	this	PRON
ejpam-6473	189	14	proves	prove	VERB
ejpam-6473	189	15	the	the	DET
ejpam-6473	189	16	global	global	ADJ
ejpam-6473	189	17	stability	stability	NOUN
ejpam-6473	189	18	of	of	ADP
ejpam-6473	189	19	the	the	DET
ejpam-6473	189	20	smoking	smoking	NOUN
ejpam-6473	189	21	-	-	PUNCT
ejpam-6473	189	22	free	free	ADJ
ejpam-6473	189	23	equilibrium	equilibrium	NOUN
ejpam-6473	189	24	point	point	NOUN
ejpam-6473	189	25	.	.	PUNCT
ejpam-6473	190	1	global	global	ADJ
ejpam-6473	190	2	stability	stability	NOUN
ejpam-6473	190	3	at	at	ADP
ejpam-6473	190	4	smoking	smoking	NOUN
ejpam-6473	190	5	present	present	ADJ
ejpam-6473	190	6	equilibrium	equilibrium	NOUN
ejpam-6473	190	7	point	point	NOUN
ejpam-6473	190	8	now	now	ADV
ejpam-6473	190	9	,	,	PUNCT
ejpam-6473	190	10	to	to	PART
ejpam-6473	190	11	check	check	VERB
ejpam-6473	190	12	the	the	DET
ejpam-6473	190	13	global	global	ADJ
ejpam-6473	190	14	stability	stability	NOUN
ejpam-6473	190	15	at	at	ADP
ejpam-6473	190	16	the	the	DET
ejpam-6473	190	17	endemic	endemic	ADJ
ejpam-6473	190	18	equilibrium	equilibrium	NOUN
ejpam-6473	190	19	point	point	NOUN
ejpam-6473	190	20	,	,	PUNCT
ejpam-6473	190	21	we	we	PRON
ejpam-6473	190	22	apply	apply	VERB
ejpam-6473	190	23	geometric	geometric	ADJ
ejpam-6473	190	24	approach	approach	NOUN
ejpam-6473	190	25	,	,	PUNCT
ejpam-6473	190	26	which	which	PRON
ejpam-6473	190	27	was	be	AUX
ejpam-6473	190	28	introduced	introduce	VERB
ejpam-6473	190	29	by	by	ADP
ejpam-6473	190	30	li	li	PROPN
ejpam-6473	190	31	and	and	CCONJ
ejpam-6473	190	32	muldowney	muldowney	PROPN
ejpam-6473	190	33	.	.	PUNCT
ejpam-6473	191	1	the	the	DET
ejpam-6473	191	2	lemma	lemma	PROPN
ejpam-6473	191	3	and	and	CCONJ
ejpam-6473	191	4	condition	condition	NOUN
ejpam-6473	191	5	for	for	ADP
ejpam-6473	191	6	this	this	DET
ejpam-6473	191	7	approach	approach	NOUN
ejpam-6473	191	8	is	be	AUX
ejpam-6473	191	9	given	give	VERB
ejpam-6473	191	10	as	as	SCONJ
ejpam-6473	191	11	s1	s1	NOUN
ejpam-6473	191	12	system	system	NOUN
ejpam-6473	191	13	has	have	VERB
ejpam-6473	191	14	a	a	DET
ejpam-6473	191	15	unique	unique	ADJ
ejpam-6473	191	16	equilibrium	equilibrium	NOUN
ejpam-6473	191	17	.	.	PUNCT
ejpam-6473	192	1	s2	s2	NOUN
ejpam-6473	192	2	compact	compact	ADJ
ejpam-6473	192	3	absorbing	absorbing	NOUN
ejpam-6473	192	4	set	set	NOUN
ejpam-6473	192	5	exists	exist	VERB
ejpam-6473	192	6	.	.	PUNCT
ejpam-6473	193	1	s.	s.	PROPN
ejpam-6473	193	2	bano	bano	PROPN
ejpam-6473	193	3	et	et	PROPN
ejpam-6473	193	4	al	al	PROPN
ejpam-6473	193	5	.	.	PUNCT
ejpam-6473	193	6	/	/	SYM
ejpam-6473	193	7	eur	eur	PROPN
ejpam-6473	193	8	.	.	PUNCT
ejpam-6473	194	1	j.	j.	PROPN
ejpam-6473	194	2	pure	pure	PROPN
ejpam-6473	194	3	appl	appl	PROPN
ejpam-6473	194	4	.	.	PROPN
ejpam-6473	194	5	math	math	PROPN
ejpam-6473	194	6	,	,	PUNCT
ejpam-6473	194	7	18	18	NUM
ejpam-6473	194	8	(	(	PUNCT
ejpam-6473	194	9	4	4	NUM
ejpam-6473	194	10	)	)	PUNCT
ejpam-6473	194	11	(	(	PUNCT
ejpam-6473	194	12	2025	2025	NUM
ejpam-6473	194	13	)	)	PUNCT
ejpam-6473	194	14	,	,	PUNCT
ejpam-6473	194	15	6473	6473	NUM
ejpam-6473	194	16	10	10	NUM
ejpam-6473	194	17	of	of	ADP
ejpam-6473	194	18	38	38	NUM
ejpam-6473	194	19	lemma	lemma	PROPN
ejpam-6473	194	20	2	2	NUM
ejpam-6473	194	21	.	.	PUNCT
ejpam-6473	195	1	if	if	SCONJ
ejpam-6473	195	2	the	the	DET
ejpam-6473	195	3	conditions	condition	NOUN
ejpam-6473	195	4	s1	s1	NOUN
ejpam-6473	195	5	,	,	PUNCT
ejpam-6473	195	6	s2	s2	PROPN
ejpam-6473	195	7	are	be	AUX
ejpam-6473	195	8	met	meet	VERB
ejpam-6473	195	9	and	and	CCONJ
ejpam-6473	195	10	bendixson	bendixson	VERB
ejpam-6473	195	11	criteria	criterion	NOUN
ejpam-6473	195	12	are	be	AUX
ejpam-6473	195	13	met	meet	VERB
ejpam-6473	195	14	then	then	ADV
ejpam-6473	195	15	equilirium	equilirium	NOUN
ejpam-6473	195	16	point	point	NOUN
ejpam-6473	195	17	is	be	AUX
ejpam-6473	195	18	globally	globally	ADV
ejpam-6473	195	19	asymptotically	asymptotically	ADV
ejpam-6473	195	20	stable	stable	ADJ
ejpam-6473	195	21	.	.	PUNCT
ejpam-6473	196	1	for	for	ADP
ejpam-6473	196	2	the	the	DET
ejpam-6473	196	3	proof	proof	NOUN
ejpam-6473	196	4	of	of	ADP
ejpam-6473	196	5	bendixson	bendixson	NOUN
ejpam-6473	196	6	criteria	criterion	NOUN
ejpam-6473	196	7	,	,	PUNCT
ejpam-6473	196	8	we	we	PRON
ejpam-6473	196	9	first	first	ADV
ejpam-6473	196	10	suppose	suppose	VERB
ejpam-6473	196	11	the	the	DET
ejpam-6473	196	12	matrix	matrix	NOUN
ejpam-6473	196	13	-	-	PUNCT
ejpam-6473	196	14	valued	value	VERB
ejpam-6473	196	15	function	function	NOUN
ejpam-6473	196	16	p	p	NOUN
ejpam-6473	196	17	such	such	ADJ
ejpam-6473	196	18	that	that	SCONJ
ejpam-6473	196	19	its	its	PRON
ejpam-6473	196	20	inverse	inverse	NOUN
ejpam-6473	196	21	exists	exist	VERB
ejpam-6473	196	22	.	.	PUNCT
ejpam-6473	197	1	p	p	NOUN
ejpam-6473	197	2	is	be	AUX
ejpam-6473	197	3	defined	define	VERB
ejpam-6473	197	4	as	as	ADP
ejpam-6473	197	5	:	:	PUNCT
ejpam-6473	197	6	p	p	X
ejpam-6473	197	7	=	=	PUNCT
ejpam-6473	197	8	(	(	PUNCT
ejpam-6473	197	9	n	n	NOUN
ejpam-6473	197	10	2	2	NUM
ejpam-6473	197	11	)	)	PUNCT
ejpam-6473	197	12	×	×	NOUN
ejpam-6473	197	13	(	(	PUNCT
ejpam-6473	197	14	n	n	NOUN
ejpam-6473	197	15	2	2	NUM
ejpam-6473	197	16	)	)	PUNCT
ejpam-6473	197	17	,	,	PUNCT
ejpam-6473	197	18	bendixson	bendixson	VERB
ejpam-6473	197	19	criteria	criterion	NOUN
ejpam-6473	197	20	is	be	AUX
ejpam-6473	197	21	given	give	VERB
ejpam-6473	197	22	as	as	ADP
ejpam-6473	197	23	q2	q2	NOUN
ejpam-6473	197	24	=	=	SYM
ejpam-6473	198	1	∫	∫	PROPN
ejpam-6473	198	2	t	t	PROPN
ejpam-6473	198	3	0	0	NUM
ejpam-6473	198	4	(	(	PUNCT
ejpam-6473	198	5	µ(b)dt	µ(b)dt	NUM
ejpam-6473	198	6	)	)	PUNCT
ejpam-6473	198	7	<	<	X
ejpam-6473	198	8	0	0	NUM
ejpam-6473	198	9	,	,	PUNCT
ejpam-6473	198	10	where	where	SCONJ
ejpam-6473	198	11	the	the	DET
ejpam-6473	198	12	b	b	PROPN
ejpam-6473	198	13	matrix	matrix	NOUN
ejpam-6473	198	14	is	be	AUX
ejpam-6473	198	15	defined	define	VERB
ejpam-6473	198	16	as	as	ADP
ejpam-6473	198	17	b	b	X
ejpam-6473	198	18	=	=	SYM
ejpam-6473	198	19	pfp	pfp	PROPN
ejpam-6473	198	20	1	1	NUM
ejpam-6473	198	21	+	+	CCONJ
ejpam-6473	198	22	pj2p−1	pj2p−1	NUM
ejpam-6473	198	23	,	,	PUNCT
ejpam-6473	198	24	µ(b	µ(b	NOUN
ejpam-6473	198	25	)	)	PUNCT
ejpam-6473	198	26	is	be	AUX
ejpam-6473	198	27	the	the	DET
ejpam-6473	198	28	lozinski	lozinski	ADJ
ejpam-6473	198	29	measure	measure	NOUN
ejpam-6473	198	30	of	of	ADP
ejpam-6473	198	31	matrix	matrix	NOUN
ejpam-6473	198	32	b	b	NOUN
ejpam-6473	198	33	and	and	CCONJ
ejpam-6473	198	34	j2	j2	PROPN
ejpam-6473	198	35	is	be	AUX
ejpam-6473	198	36	the	the	DET
ejpam-6473	198	37	second	second	ADJ
ejpam-6473	198	38	additive	additive	ADJ
ejpam-6473	198	39	compound	compound	NOUN
ejpam-6473	198	40	matrix	matrix	NOUN
ejpam-6473	198	41	of	of	ADP
ejpam-6473	198	42	jacobian	jacobian	PROPN
ejpam-6473	198	43	.	.	PUNCT
ejpam-6473	198	44	lozinski	lozinski	ADJ
ejpam-6473	198	45	measure	measure	NOUN
ejpam-6473	198	46	of	of	ADP
ejpam-6473	198	47	b	b	NOUN
ejpam-6473	198	48	matrix	matrix	NOUN
ejpam-6473	198	49	with	with	ADP
ejpam-6473	198	50	respect	respect	NOUN
ejpam-6473	198	51	to	to	ADP
ejpam-6473	198	52	the	the	DET
ejpam-6473	198	53	vector	vector	NOUN
ejpam-6473	198	54	norm	norm	NOUN
ejpam-6473	198	55	||.||	||.||	NOUN
ejpam-6473	198	56	is	be	AUX
ejpam-6473	198	57	defined	define	VERB
ejpam-6473	198	58	as	as	ADP
ejpam-6473	198	59	:	:	PUNCT
ejpam-6473	198	60	µ(b	µ(b	NOUN
ejpam-6473	198	61	)	)	PUNCT
ejpam-6473	199	1	=	=	SYM
ejpam-6473	199	2	lim	lim	PROPN
ejpam-6473	199	3	h→0	h→0	ADV
ejpam-6473	199	4	|i	|i	VERB
ejpam-6473	199	5	+	+	NOUN
ejpam-6473	199	6	bh|	bh|	NOUN
ejpam-6473	199	7	−	−	NOUN
ejpam-6473	199	8	1	1	NUM
ejpam-6473	199	9	h	h	NOUN
ejpam-6473	199	10	.	.	PUNCT
ejpam-6473	200	1	for	for	ADP
ejpam-6473	200	2	system	system	NOUN
ejpam-6473	200	3	lozinski	lozinski	NOUN
ejpam-6473	200	4	measure	measure	NOUN
ejpam-6473	200	5	can	can	AUX
ejpam-6473	200	6	also	also	ADV
ejpam-6473	200	7	be	be	AUX
ejpam-6473	200	8	expressed	express	VERB
ejpam-6473	200	9	as	as	ADP
ejpam-6473	200	10	µ(b	µ(b	NOUN
ejpam-6473	200	11	)	)	PUNCT
ejpam-6473	200	12	≤	≤	NOUN
ejpam-6473	200	13	sup{si	sup{si	NOUN
ejpam-6473	200	14	,	,	PUNCT
ejpam-6473	200	15	i	i	PRON
ejpam-6473	200	16	=	=	NOUN
ejpam-6473	200	17	1	1	NUM
ejpam-6473	200	18	,	,	PUNCT
ejpam-6473	200	19	2	2	NUM
ejpam-6473	200	20	}	}	PUNCT
ejpam-6473	200	21	,	,	PUNCT
ejpam-6473	200	22	si	si	PROPN
ejpam-6473	200	23	=	=	PUNCT
ejpam-6473	200	24	∥bij∥+	∥bij∥+	NOUN
ejpam-6473	200	25	µ1(bii	µ1(bii	NOUN
ejpam-6473	200	26	)	)	PUNCT
ejpam-6473	200	27	,	,	PUNCT
ejpam-6473	200	28	where	where	SCONJ
ejpam-6473	200	29	(	(	PUNCT
ejpam-6473	200	30	i	i	PRON
ejpam-6473	200	31	̸=	̸=	PROPN
ejpam-6473	200	32	j	j	PROPN
ejpam-6473	200	33	,	,	PUNCT
ejpam-6473	200	34	i	i	PRON
ejpam-6473	200	35	,	,	PUNCT
ejpam-6473	200	36	j	j	PROPN
ejpam-6473	200	37	=	=	SYM
ejpam-6473	200	38	1	1	NUM
ejpam-6473	200	39	,	,	PUNCT
ejpam-6473	200	40	2	2	NUM
ejpam-6473	200	41	)	)	PUNCT
ejpam-6473	200	42	.	.	PUNCT
ejpam-6473	201	1	above	above	ADP
ejpam-6473	201	2	explanation	explanation	NOUN
ejpam-6473	201	3	is	be	AUX
ejpam-6473	201	4	the	the	DET
ejpam-6473	201	5	general	general	ADJ
ejpam-6473	201	6	introduction	introduction	NOUN
ejpam-6473	201	7	of	of	ADP
ejpam-6473	201	8	the	the	DET
ejpam-6473	201	9	geometric	geometric	ADJ
ejpam-6473	201	10	approach	approach	NOUN
ejpam-6473	201	11	.	.	PUNCT
ejpam-6473	202	1	lemma	lemma	PROPN
ejpam-6473	202	2	3	3	X
ejpam-6473	202	3	.	.	PUNCT
ejpam-6473	203	1	let	let	VERB
ejpam-6473	203	2	us	we	PRON
ejpam-6473	203	3	assume	assume	VERB
ejpam-6473	203	4	q1	q1	PROPN
ejpam-6473	203	5	is	be	AUX
ejpam-6473	203	6	a	a	DET
ejpam-6473	203	7	simply	simply	ADV
ejpam-6473	203	8	connect	connect	ADJ
ejpam-6473	203	9	ste	ste	NOUN
ejpam-6473	203	10	and	and	CCONJ
ejpam-6473	203	11	both	both	DET
ejpam-6473	203	12	conditions	condition	NOUN
ejpam-6473	203	13	s1	s1	NOUN
ejpam-6473	203	14	and	and	CCONJ
ejpam-6473	203	15	s2	s2	PROPN
ejpam-6473	203	16	hold	hold	VERB
ejpam-6473	203	17	;	;	PUNCT
ejpam-6473	203	18	if	if	SCONJ
ejpam-6473	203	19	q2	q2	PROPN
ejpam-6473	203	20	<	<	X
ejpam-6473	203	21	0	0	PROPN
ejpam-6473	203	22	,	,	PUNCT
ejpam-6473	203	23	then	then	ADV
ejpam-6473	203	24	the	the	DET
ejpam-6473	203	25	endemic	endemic	ADJ
ejpam-6473	203	26	equilibrium	equilibrium	NOUN
ejpam-6473	203	27	points	point	NOUN
ejpam-6473	203	28	are	be	AUX
ejpam-6473	203	29	globally	globally	ADV
ejpam-6473	203	30	asymptotically	asymptotically	ADV
ejpam-6473	203	31	stable	stable	ADJ
ejpam-6473	203	32	.	.	PUNCT
ejpam-6473	204	1	clarification	clarification	NOUN
ejpam-6473	204	2	of	of	ADP
ejpam-6473	204	3	above	above	ADP
ejpam-6473	204	4	lemma	lemma	PROPN
ejpam-6473	204	5	:	:	PUNCT
ejpam-6473	204	6	ω	ω	PROPN
ejpam-6473	204	7	=	=	SYM
ejpam-6473	204	8	{	{	PUNCT
ejpam-6473	204	9	(	(	PUNCT
ejpam-6473	204	10	p	p	X
ejpam-6473	204	11	,	,	PUNCT
ejpam-6473	204	12	l	l	NOUN
ejpam-6473	204	13	,	,	PUNCT
ejpam-6473	204	14	s	s	X
ejpam-6473	204	15	,	,	PUNCT
ejpam-6473	204	16	q	q	NOUN
ejpam-6473	204	17	)	)	PUNCT
ejpam-6473	204	18	such	such	ADJ
ejpam-6473	204	19	that	that	SCONJ
ejpam-6473	204	20	0	0	NUM
ejpam-6473	204	21	≤	≤	NOUN
ejpam-6473	205	1	p	p	X
ejpam-6473	205	2	+	+	NUM
ejpam-6473	205	3	l+	l+	X
ejpam-6473	205	4	s	s	PART
ejpam-6473	205	5	+	+	ADJ
ejpam-6473	205	6	q	q	ADJ
ejpam-6473	205	7	≤	≤	NUM
ejpam-6473	205	8	λ	λ	NOUN
ejpam-6473	205	9	b+µ	b+µ	NOUN
ejpam-6473	205	10	}	}	PUNCT
ejpam-6473	205	11	and	and	CCONJ
ejpam-6473	205	12	q1	q1	PROPN
ejpam-6473	205	13	=	=	SYM
ejpam-6473	205	14	{	{	PUNCT
ejpam-6473	205	15	(	(	PUNCT
ejpam-6473	205	16	p	p	X
ejpam-6473	205	17	,	,	PUNCT
ejpam-6473	205	18	l	l	NOUN
ejpam-6473	205	19	,	,	PUNCT
ejpam-6473	205	20	s	s	PART
ejpam-6473	205	21	)	)	PUNCT
ejpam-6473	205	22	such	such	ADJ
ejpam-6473	205	23	that	that	SCONJ
ejpam-6473	205	24	0	0	NUM
ejpam-6473	205	25	≤	≤	NOUN
ejpam-6473	205	26	p	p	NOUN
ejpam-6473	206	1	+	+	NOUN
ejpam-6473	206	2	l	l	NOUN
ejpam-6473	206	3	+	+	SYM
ejpam-6473	206	4	s	s	PART
ejpam-6473	206	5	≤	≤	NUM
ejpam-6473	206	6	λ	λ	NOUN
ejpam-6473	206	7	b+µ	b+µ	PROPN
ejpam-6473	206	8	}	}	PUNCT
ejpam-6473	206	9	is	be	AUX
ejpam-6473	206	10	subset	subset	VERB
ejpam-6473	206	11	of	of	ADP
ejpam-6473	206	12	ω	ω	NUM
ejpam-6473	206	13	it	it	PRON
ejpam-6473	206	14	is	be	AUX
ejpam-6473	206	15	compact	compact	ADJ
ejpam-6473	206	16	absorbing	absorbing	NOUN
ejpam-6473	206	17	set	set	NOUN
ejpam-6473	206	18	,	,	PUNCT
ejpam-6473	206	19	simply	simply	ADV
ejpam-6473	206	20	connected	connect	VERB
ejpam-6473	206	21	and	and	CCONJ
ejpam-6473	206	22	e∗	e∗	NOUN
ejpam-6473	206	23	is	be	AUX
ejpam-6473	206	24	the	the	DET
ejpam-6473	206	25	unique	unique	ADJ
ejpam-6473	206	26	equilibrium	equilibrium	NOUN
ejpam-6473	206	27	point	point	NOUN
ejpam-6473	206	28	.	.	PUNCT
ejpam-6473	207	1	for	for	ADP
ejpam-6473	207	2	the	the	DET
ejpam-6473	207	3	bendixson	bendixson	NOUN
ejpam-6473	207	4	criteria	criterion	NOUN
ejpam-6473	207	5	we	we	PRON
ejpam-6473	207	6	will	will	AUX
ejpam-6473	207	7	prove	prove	VERB
ejpam-6473	207	8	the	the	DET
ejpam-6473	207	9	below	below	NOUN
ejpam-6473	207	10	theorem	theorem	NOUN
ejpam-6473	207	11	4	4	NUM
ejpam-6473	207	12	.	.	PUNCT
ejpam-6473	207	13	theorem	theorem	VERB
ejpam-6473	207	14	4	4	NUM
ejpam-6473	207	15	.	.	PUNCT
ejpam-6473	207	16	endemic	endemic	ADJ
ejpam-6473	207	17	equilibrium	equilibrium	NOUN
ejpam-6473	207	18	point	point	NOUN
ejpam-6473	207	19	is	be	AUX
ejpam-6473	207	20	globally	globally	ADV
ejpam-6473	207	21	stable	stable	ADJ
ejpam-6473	207	22	if	if	SCONJ
ejpam-6473	207	23	r0	r0	NOUN
ejpam-6473	207	24	>	>	X
ejpam-6473	207	25	1	1	NUM
ejpam-6473	207	26	and	and	CCONJ
ejpam-6473	207	27	βs(1	βs(1	PROPN
ejpam-6473	207	28	+	+	NUM
ejpam-6473	207	29	νs	νs	NOUN
ejpam-6473	207	30	)	)	PUNCT
ejpam-6473	207	31	>	>	X
ejpam-6473	207	32	βps(1	βps(1	PROPN
ejpam-6473	208	1	+	+	NOUN
ejpam-6473	208	2	2νs	2νs	ADJ
ejpam-6473	208	3	)	)	PUNCT
ejpam-6473	208	4	l	l	NOUN
ejpam-6473	208	5	.	.	PUNCT
ejpam-6473	209	1	proof	proof	NOUN
ejpam-6473	209	2	.	.	PUNCT
ejpam-6473	210	1	the	the	DET
ejpam-6473	210	2	second	second	ADJ
ejpam-6473	210	3	additive	additive	ADJ
ejpam-6473	210	4	compound	compound	NOUN
ejpam-6473	210	5	matrix	matrix	NOUN
ejpam-6473	210	6	for	for	ADP
ejpam-6473	210	7	jacobian	jacobian	PROPN
ejpam-6473	210	8	is	be	AUX
ejpam-6473	210	9	(	(	PUNCT
ejpam-6473	210	10	considering	consider	VERB
ejpam-6473	210	11	only	only	ADV
ejpam-6473	210	12	first	first	ADJ
ejpam-6473	210	13	3	3	NUM
ejpam-6473	210	14	classes	class	NOUN
ejpam-6473	210	15	pls	pls	NOUN
ejpam-6473	210	16	)	)	PUNCT
ejpam-6473	210	17	j2	j2	PROPN
ejpam-6473	210	18	=	=	PUNCT
ejpam-6473	210	19	a1	a1	X
ejpam-6473	210	20	βp	βp	INTJ
ejpam-6473	210	21	(	(	PUNCT
ejpam-6473	210	22	1	1	NUM
ejpam-6473	210	23	+	+	NUM
ejpam-6473	210	24	2νs	2ν	NOUN
ejpam-6473	210	25	)	)	PUNCT
ejpam-6473	210	26	βp	βp	NOUN
ejpam-6473	211	1	(	(	PUNCT
ejpam-6473	211	2	1	1	NUM
ejpam-6473	211	3	+	+	NUM
ejpam-6473	211	4	2νs	2νs	ADJ
ejpam-6473	211	5	)	)	PUNCT
ejpam-6473	211	6	ζ	ζ	PROPN
ejpam-6473	211	7	a2	a2	NOUN
ejpam-6473	211	8	0	0	NUM
ejpam-6473	211	9	0	0	NUM
ejpam-6473	212	1	βs(1	βs(1	NUM
ejpam-6473	212	2	+	+	NUM
ejpam-6473	212	3	νs	νs	NOUN
ejpam-6473	212	4	)	)	PUNCT
ejpam-6473	212	5	−(b+	−(b+	NUM
ejpam-6473	212	6	µ+	µ+	DET
ejpam-6473	212	7	ζ)−	ζ)−	PROPN
ejpam-6473	212	8	(	(	PUNCT
ejpam-6473	212	9	b+	b+	X
ejpam-6473	212	10	µ+	µ+	X
ejpam-6473	212	11	δ	δ	NOUN
ejpam-6473	212	12	)	)	PUNCT
ejpam-6473	212	13			NOUN
ejpam-6473	212	14	,	,	PUNCT
ejpam-6473	212	15	s.	s.	PROPN
ejpam-6473	212	16	bano	bano	PROPN
ejpam-6473	212	17	et	et	PROPN
ejpam-6473	212	18	al	al	PROPN
ejpam-6473	212	19	.	.	PUNCT
ejpam-6473	212	20	/	/	SYM
ejpam-6473	212	21	eur	eur	PROPN
ejpam-6473	212	22	.	.	PUNCT
ejpam-6473	213	1	j.	j.	PROPN
ejpam-6473	213	2	pure	pure	PROPN
ejpam-6473	213	3	appl	appl	PROPN
ejpam-6473	213	4	.	.	PROPN
ejpam-6473	213	5	math	math	PROPN
ejpam-6473	213	6	,	,	PUNCT
ejpam-6473	213	7	18	18	NUM
ejpam-6473	213	8	(	(	PUNCT
ejpam-6473	213	9	4	4	NUM
ejpam-6473	213	10	)	)	PUNCT
ejpam-6473	213	11	(	(	PUNCT
ejpam-6473	213	12	2025	2025	NUM
ejpam-6473	213	13	)	)	PUNCT
ejpam-6473	213	14	,	,	PUNCT
ejpam-6473	213	15	6473	6473	NUM
ejpam-6473	213	16	11	11	NUM
ejpam-6473	213	17	of	of	ADP
ejpam-6473	213	18	38	38	NUM
ejpam-6473	213	19	where	where	SCONJ
ejpam-6473	213	20	a1	a1	NOUN
ejpam-6473	213	21	=	=	SYM
ejpam-6473	213	22	−βs(1+νs)−	−βs(1+νs)−	PROPN
ejpam-6473	213	23	(	(	PUNCT
ejpam-6473	213	24	b+µ)−	b+µ)−	X
ejpam-6473	213	25	(	(	PUNCT
ejpam-6473	213	26	b+µ+ζ	b+µ+ζ	NOUN
ejpam-6473	213	27	)	)	PUNCT
ejpam-6473	213	28	,	,	PUNCT
ejpam-6473	213	29	a2	a2	PROPN
ejpam-6473	213	30	=	=	SYM
ejpam-6473	214	1	−βs(1+νs)−	−βs(1+νs)−	PROPN
ejpam-6473	214	2	(	(	PUNCT
ejpam-6473	214	3	b+µ)−	b+µ)−	X
ejpam-6473	214	4	(	(	PUNCT
ejpam-6473	214	5	b+µ+δ	b+µ+δ	NOUN
ejpam-6473	214	6	)	)	PUNCT
ejpam-6473	214	7	.	.	PUNCT
ejpam-6473	215	1	the	the	DET
ejpam-6473	215	2	p	p	PROPN
ejpam-6473	215	3	function	function	NOUN
ejpam-6473	215	4	is	be	AUX
ejpam-6473	215	5	defined	define	VERB
ejpam-6473	215	6	as	as	ADP
ejpam-6473	215	7	p	p	NOUN
ejpam-6473	215	8	=	=	SYM
ejpam-6473	215	9	diag(1	diag(1	PROPN
ejpam-6473	215	10	,	,	PUNCT
ejpam-6473	215	11	ls	ls	INTJ
ejpam-6473	215	12	,	,	PUNCT
ejpam-6473	215	13	l	l	PROPN
ejpam-6473	215	14	s	s	PART
ejpam-6473	215	15	)	)	PUNCT
ejpam-6473	215	16	,	,	PUNCT
ejpam-6473	215	17	now	now	ADV
ejpam-6473	215	18	pfp	pfp	PROPN
ejpam-6473	215	19	−1	−1	NOUN
ejpam-6473	216	1	=	=	PUNCT
ejpam-6473	216	2	diag	diag	NOUN
ejpam-6473	216	3	(	(	PUNCT
ejpam-6473	216	4	0	0	NUM
ejpam-6473	216	5	,	,	PUNCT
ejpam-6473	216	6	l̇l	l̇l	PROPN
ejpam-6473	216	7	−	−	PROPN
ejpam-6473	216	8	ṡ	ṡ	NOUN
ejpam-6473	216	9	s	s	NOUN
ejpam-6473	216	10	,	,	PUNCT
ejpam-6473	216	11	l̇	l̇	PROPN
ejpam-6473	216	12	l	l	NOUN
ejpam-6473	217	1	−	−	PROPN
ejpam-6473	217	2	ṡ	ṡ	PROPN
ejpam-6473	217	3	s	s	PART
ejpam-6473	217	4	)	)	PUNCT
ejpam-6473	217	5	.	.	PUNCT
ejpam-6473	218	1	to	to	PART
ejpam-6473	218	2	find	find	VERB
ejpam-6473	218	3	matrix	matrix	NOUN
ejpam-6473	218	4	b	b	NOUN
ejpam-6473	218	5	,	,	PUNCT
ejpam-6473	218	6	we	we	PRON
ejpam-6473	218	7	have	have	VERB
ejpam-6473	218	8	the	the	DET
ejpam-6473	218	9	formula	formula	NOUN
ejpam-6473	218	10	b	b	NOUN
ejpam-6473	218	11	=	=	SYM
ejpam-6473	218	12	pfp	pfp	PROPN
ejpam-6473	218	13	−1	−1	NOUN
ejpam-6473	218	14	+	+	CCONJ
ejpam-6473	218	15	pj2p−1	pj2p−1	PROPN
ejpam-6473	218	16	.	.	PUNCT
ejpam-6473	219	1	b	b	X
ejpam-6473	219	2	=	=	PRON
ejpam-6473	219	3	(	(	PUNCT
ejpam-6473	219	4	b11	b11	PROPN
ejpam-6473	219	5	b12	b12	PROPN
ejpam-6473	219	6	b21	b21	PROPN
ejpam-6473	219	7	b22	b22	PROPN
ejpam-6473	219	8	)	)	PUNCT
ejpam-6473	219	9	,	,	PUNCT
ejpam-6473	219	10	where	where	SCONJ
ejpam-6473	219	11	b11	b11	PROPN
ejpam-6473	219	12	=	=	SYM
ejpam-6473	219	13	a1	a1	PROPN
ejpam-6473	219	14	,	,	PUNCT
ejpam-6473	219	15	b12	b12	NOUN
ejpam-6473	219	16	=	=	SYM
ejpam-6473	219	17	(	(	PUNCT
ejpam-6473	219	18	sβp	sβp	NOUN
ejpam-6473	219	19	(	(	PUNCT
ejpam-6473	219	20	1	1	NUM
ejpam-6473	219	21	+	+	NOUN
ejpam-6473	219	22	2νs	2νs	ADJ
ejpam-6473	219	23	)	)	PUNCT
ejpam-6473	219	24	l	l	NOUN
ejpam-6473	219	25	sβp	sβp	NOUN
ejpam-6473	219	26	(	(	PUNCT
ejpam-6473	219	27	1	1	NUM
ejpam-6473	219	28	+	+	NUM
ejpam-6473	219	29	2νs	2νs	ADJ
ejpam-6473	219	30	)	)	PUNCT
ejpam-6473	219	31	l	l	NOUN
ejpam-6473	219	32	)	)	PUNCT
ejpam-6473	219	33	,	,	PUNCT
ejpam-6473	219	34	b21	b21	PROPN
ejpam-6473	219	35	=	=	SYM
ejpam-6473	219	36	(	(	PUNCT
ejpam-6473	219	37	ζl	ζl	ADV
ejpam-6473	219	38	s	s	NOUN
ejpam-6473	219	39	0	0	NUM
ejpam-6473	219	40	)	)	PUNCT
ejpam-6473	219	41	,	,	PUNCT
ejpam-6473	219	42	b22	b22	PROPN
ejpam-6473	219	43	=	=	SYM
ejpam-6473	219	44	(	(	PUNCT
ejpam-6473	219	45	w11	w11	PROPN
ejpam-6473	219	46	w12	w12	PROPN
ejpam-6473	219	47	w21	w21	PROPN
ejpam-6473	219	48	w22	w22	PROPN
ejpam-6473	219	49	)	)	PUNCT
ejpam-6473	219	50	.	.	PUNCT
ejpam-6473	220	1	here	here	ADV
ejpam-6473	220	2	,	,	PUNCT
ejpam-6473	220	3	w11	w11	NOUN
ejpam-6473	220	4	=	=	SYM
ejpam-6473	220	5	l̇	l̇	PROPN
ejpam-6473	220	6	l	l	NOUN
ejpam-6473	221	1	−	−	PROPN
ejpam-6473	221	2	ṡ	ṡ	PROPN
ejpam-6473	221	3	s	s	PART
ejpam-6473	221	4	+	+	NOUN
ejpam-6473	221	5	a2	a2	NOUN
ejpam-6473	221	6	,	,	PUNCT
ejpam-6473	221	7	w12	w12	NOUN
ejpam-6473	221	8	=	=	SYM
ejpam-6473	221	9	0	0	PROPN
ejpam-6473	221	10	,	,	PUNCT
ejpam-6473	221	11	w21	w21	NOUN
ejpam-6473	221	12	=	=	PUNCT
ejpam-6473	222	1	βs(1	βs(1	PROPN
ejpam-6473	222	2	+	+	NUM
ejpam-6473	222	3	νs	νs	NOUN
ejpam-6473	222	4	)	)	PUNCT
ejpam-6473	222	5	,	,	PUNCT
ejpam-6473	222	6	w22	w22	NOUN
ejpam-6473	222	7	=	=	SYM
ejpam-6473	222	8	l̇	l̇	PROPN
ejpam-6473	222	9	l	l	NOUN
ejpam-6473	223	1	−	−	PROPN
ejpam-6473	223	2	ṡ	ṡ	PROPN
ejpam-6473	223	3	s	s	PRON
ejpam-6473	223	4	−	−	PROPN
ejpam-6473	223	5	(	(	PUNCT
ejpam-6473	223	6	b+	b+	X
ejpam-6473	223	7	µ+	µ+	ADJ
ejpam-6473	223	8	ζ)−	ζ)−	PROPN
ejpam-6473	223	9	(	(	PUNCT
ejpam-6473	223	10	b+	b+	X
ejpam-6473	223	11	µ+	µ+	X
ejpam-6473	223	12	δ	δ	PROPN
ejpam-6473	223	13	)	)	PUNCT
ejpam-6473	223	14	.	.	PUNCT
ejpam-6473	224	1	the	the	DET
ejpam-6473	224	2	norm	norm	NOUN
ejpam-6473	224	3	is	be	AUX
ejpam-6473	224	4	defined	define	VERB
ejpam-6473	224	5	as	as	ADP
ejpam-6473	224	6	;	;	PUNCT
ejpam-6473	224	7	∥(n1	∥(n1	NOUN
ejpam-6473	224	8	,	,	PUNCT
ejpam-6473	224	9	n2	n2	NOUN
ejpam-6473	224	10	,	,	PUNCT
ejpam-6473	224	11	n3)∥	n3)∥	X
ejpam-6473	224	12	=	=	SYM
ejpam-6473	224	13	max(∥n1∥	max(∥n1∥	PROPN
ejpam-6473	224	14	,	,	PUNCT
ejpam-6473	224	15	∥n2∥+	∥n2∥+	ADP
ejpam-6473	224	16	∥n3∥	∥n3∥	PROPN
ejpam-6473	224	17	)	)	PUNCT
ejpam-6473	224	18	.	.	PUNCT
ejpam-6473	225	1	µ(b	µ(b	NOUN
ejpam-6473	225	2	)	)	PUNCT
ejpam-6473	225	3	≤	≤	NOUN
ejpam-6473	225	4	sup{si	sup{si	NOUN
ejpam-6473	225	5	,	,	PUNCT
ejpam-6473	225	6	i	i	PRON
ejpam-6473	225	7	=	=	NOUN
ejpam-6473	225	8	1	1	NUM
ejpam-6473	225	9	,	,	PUNCT
ejpam-6473	225	10	2	2	NUM
ejpam-6473	225	11	}	}	PUNCT
ejpam-6473	225	12	,	,	PUNCT
ejpam-6473	225	13	(	(	PUNCT
ejpam-6473	225	14	8)	8)	NUM
ejpam-6473	225	15	si	si	NOUN
ejpam-6473	225	16	=	=	PUNCT
ejpam-6473	225	17	∥bij∥+	∥bij∥+	NOUN
ejpam-6473	225	18	µ1(bii	µ1(bii	NOUN
ejpam-6473	225	19	)	)	PUNCT
ejpam-6473	225	20	where	where	SCONJ
ejpam-6473	225	21	(	(	PUNCT
ejpam-6473	225	22	i	i	PRON
ejpam-6473	225	23	̸=	̸=	PROPN
ejpam-6473	225	24	j	j	PROPN
ejpam-6473	225	25	,	,	PUNCT
ejpam-6473	225	26	i	i	PRON
ejpam-6473	225	27	,	,	PUNCT
ejpam-6473	225	28	j	j	PROPN
ejpam-6473	225	29	=	=	SYM
ejpam-6473	225	30	1	1	NUM
ejpam-6473	225	31	,	,	PUNCT
ejpam-6473	225	32	2	2	NUM
ejpam-6473	225	33	)	)	PUNCT
ejpam-6473	225	34	,	,	PUNCT
ejpam-6473	225	35	µ1(b11	µ1(b11	PROPN
ejpam-6473	225	36	)	)	PUNCT
ejpam-6473	225	37	=	=	SYM
ejpam-6473	225	38	a1	a1	NOUN
ejpam-6473	225	39	,	,	PUNCT
ejpam-6473	225	40	µ1(b11	µ1(b11	NOUN
ejpam-6473	225	41	)	)	PUNCT
ejpam-6473	225	42	=	=	PUNCT
ejpam-6473	226	1	−βs(1	−βs(1	X
ejpam-6473	226	2	+	+	NUM
ejpam-6473	226	3	νs)−	νs)−	NOUN
ejpam-6473	226	4	(	(	PUNCT
ejpam-6473	226	5	b+	b+	X
ejpam-6473	226	6	µ)−	µ)−	X
ejpam-6473	226	7	(	(	PUNCT
ejpam-6473	226	8	b+	b+	X
ejpam-6473	226	9	µ+	µ+	X
ejpam-6473	226	10	ζ	ζ	NOUN
ejpam-6473	226	11	)	)	PUNCT
ejpam-6473	226	12	,	,	PUNCT
ejpam-6473	226	13	∥b12∥	∥b12∥	PROPN
ejpam-6473	226	14	=	=	SYM
ejpam-6473	226	15	sβp	sβp	NOUN
ejpam-6473	226	16	(	(	PUNCT
ejpam-6473	226	17	1	1	NUM
ejpam-6473	226	18	+	+	NUM
ejpam-6473	226	19	2νs	2νs	ADJ
ejpam-6473	226	20	)	)	PUNCT
ejpam-6473	226	21	l	l	NOUN
ejpam-6473	226	22	,	,	PUNCT
ejpam-6473	226	23	∥b21∥	∥b21∥	PROPN
ejpam-6473	226	24	=	=	PUNCT
ejpam-6473	226	25	ζl	ζl	ADP
ejpam-6473	226	26	s	s	PROPN
ejpam-6473	226	27	.	.	PUNCT
ejpam-6473	226	28	µ1(b22	µ1(b22	PROPN
ejpam-6473	226	29	)	)	PUNCT
ejpam-6473	226	30	=	=	SYM
ejpam-6473	226	31	max	max	PROPN
ejpam-6473	226	32	{	{	PUNCT
ejpam-6473	226	33	l̇	l̇	NOUN
ejpam-6473	226	34	l	l	NOUN
ejpam-6473	227	1	−	−	PROPN
ejpam-6473	227	2	ṡ	ṡ	PROPN
ejpam-6473	227	3	s	s	PART
ejpam-6473	227	4	+	+	NOUN
ejpam-6473	227	5	a2	a2	PROPN
ejpam-6473	227	6	+	+	X
ejpam-6473	227	7	βs(1	βs(1	PROPN
ejpam-6473	227	8	+	+	NUM
ejpam-6473	227	9	νs	νs	NOUN
ejpam-6473	227	10	)	)	PUNCT
ejpam-6473	227	11	,	,	PUNCT
ejpam-6473	227	12	l̇	l̇	PROPN
ejpam-6473	227	13	l	l	NOUN
ejpam-6473	228	1	−	−	PROPN
ejpam-6473	228	2	ṡ	ṡ	PROPN
ejpam-6473	228	3	s	s	PRON
ejpam-6473	228	4	−	−	PROPN
ejpam-6473	228	5	(	(	PUNCT
ejpam-6473	228	6	b+	b+	X
ejpam-6473	228	7	µ+	µ+	ADJ
ejpam-6473	228	8	ζ)−	ζ)−	PROPN
ejpam-6473	228	9	(	(	PUNCT
ejpam-6473	228	10	b+	b+	X
ejpam-6473	228	11	µ+	µ+	X
ejpam-6473	228	12	δ	δ	NOUN
ejpam-6473	228	13	)	)	PUNCT
ejpam-6473	228	14	}	}	PUNCT
ejpam-6473	228	15	,	,	PUNCT
ejpam-6473	228	16	after	after	ADP
ejpam-6473	228	17	using	use	VERB
ejpam-6473	228	18	the	the	DET
ejpam-6473	228	19	value	value	NOUN
ejpam-6473	228	20	of	of	ADP
ejpam-6473	228	21	a2	a2	PROPN
ejpam-6473	228	22	,	,	PUNCT
ejpam-6473	228	23	we	we	PRON
ejpam-6473	228	24	get	get	VERB
ejpam-6473	228	25	:	:	PUNCT
ejpam-6473	228	26	µ1(b22	µ1(b22	NOUN
ejpam-6473	228	27	)	)	PUNCT
ejpam-6473	228	28	=	=	SYM
ejpam-6473	229	1	l̇	l̇	PROPN
ejpam-6473	229	2	l	l	NOUN
ejpam-6473	230	1	−	−	PROPN
ejpam-6473	230	2	ṡ	ṡ	PROPN
ejpam-6473	230	3	s	s	PRON
ejpam-6473	230	4	−	−	PROPN
ejpam-6473	230	5	(	(	PUNCT
ejpam-6473	230	6	b+	b+	X
ejpam-6473	230	7	µ+	µ+	PUNCT
ejpam-6473	230	8	δ)−min{(b+	δ)−min{(b+	PROPN
ejpam-6473	230	9	µ	µ	NUM
ejpam-6473	230	10	)	)	PUNCT
ejpam-6473	230	11	,	,	PUNCT
ejpam-6473	230	12	(	(	PUNCT
ejpam-6473	230	13	b+	b+	X
ejpam-6473	230	14	µ+	µ+	X
ejpam-6473	230	15	ζ	ζ	NOUN
ejpam-6473	230	16	)	)	PUNCT
ejpam-6473	230	17	}	}	PUNCT
ejpam-6473	230	18	,	,	PUNCT
ejpam-6473	230	19	µ1(b22	µ1(b22	PROPN
ejpam-6473	230	20	)	)	PUNCT
ejpam-6473	230	21	=	=	SYM
ejpam-6473	231	1	l̇	l̇	PROPN
ejpam-6473	231	2	l	l	NOUN
ejpam-6473	232	1	−	−	PROPN
ejpam-6473	232	2	ṡ	ṡ	PROPN
ejpam-6473	232	3	s	s	PRON
ejpam-6473	232	4	−	−	PROPN
ejpam-6473	232	5	(	(	PUNCT
ejpam-6473	232	6	b+	b+	X
ejpam-6473	232	7	µ+	µ+	X
ejpam-6473	232	8	δ)−	δ)−	PROPN
ejpam-6473	232	9	(	(	PUNCT
ejpam-6473	232	10	b+	b+	X
ejpam-6473	232	11	µ	µ	NUM
ejpam-6473	232	12	)	)	PUNCT
ejpam-6473	232	13	.	.	PUNCT
ejpam-6473	233	1	using	use	VERB
ejpam-6473	233	2	all	all	PRON
ejpam-6473	233	3	above	above	ADJ
ejpam-6473	233	4	values	value	NOUN
ejpam-6473	233	5	in	in	ADP
ejpam-6473	233	6	si	si	NOUN
ejpam-6473	233	7	,	,	PUNCT
ejpam-6473	233	8	where	where	SCONJ
ejpam-6473	233	9	i=1,2	i=1,2	ADJ
ejpam-6473	233	10	s1	s1	NOUN
ejpam-6473	233	11	=	=	PUNCT
ejpam-6473	233	12	−βs(1	−βs(1	X
ejpam-6473	233	13	+	+	NUM
ejpam-6473	233	14	νs)−	νs)−	NOUN
ejpam-6473	233	15	(	(	PUNCT
ejpam-6473	233	16	b+	b+	X
ejpam-6473	233	17	µ)−	µ)−	X
ejpam-6473	233	18	(	(	PUNCT
ejpam-6473	233	19	b+	b+	X
ejpam-6473	233	20	µ+	µ+	X
ejpam-6473	233	21	ζ	ζ	NOUN
ejpam-6473	233	22	)	)	PUNCT
ejpam-6473	233	23	+	+	NUM
ejpam-6473	233	24	sβp	sβp	NOUN
ejpam-6473	233	25	(	(	PUNCT
ejpam-6473	233	26	1	1	NUM
ejpam-6473	233	27	+	+	NUM
ejpam-6473	233	28	2νs	2νs	ADJ
ejpam-6473	233	29	)	)	PUNCT
ejpam-6473	233	30	l	l	NOUN
ejpam-6473	233	31	,	,	PUNCT
ejpam-6473	233	32	s.	s.	PROPN
ejpam-6473	233	33	bano	bano	PROPN
ejpam-6473	233	34	et	et	PROPN
ejpam-6473	233	35	al	al	PROPN
ejpam-6473	233	36	.	.	PUNCT
ejpam-6473	233	37	/	/	SYM
ejpam-6473	233	38	eur	eur	PROPN
ejpam-6473	233	39	.	.	PUNCT
ejpam-6473	234	1	j.	j.	PROPN
ejpam-6473	234	2	pure	pure	PROPN
ejpam-6473	234	3	appl	appl	PROPN
ejpam-6473	234	4	.	.	PROPN
ejpam-6473	234	5	math	math	PROPN
ejpam-6473	234	6	,	,	PUNCT
ejpam-6473	234	7	18	18	NUM
ejpam-6473	234	8	(	(	PUNCT
ejpam-6473	234	9	4	4	NUM
ejpam-6473	234	10	)	)	PUNCT
ejpam-6473	234	11	(	(	PUNCT
ejpam-6473	234	12	2025	2025	NUM
ejpam-6473	234	13	)	)	PUNCT
ejpam-6473	234	14	,	,	PUNCT
ejpam-6473	234	15	6473	6473	NUM
ejpam-6473	234	16	12	12	NUM
ejpam-6473	234	17	of	of	ADP
ejpam-6473	234	18	38	38	NUM
ejpam-6473	234	19	using	use	VERB
ejpam-6473	234	20	equation	equation	NOUN
ejpam-6473	234	21	2	2	NUM
ejpam-6473	234	22	of	of	ADP
ejpam-6473	234	23	system	system	NOUN
ejpam-6473	234	24	(	(	PUNCT
ejpam-6473	234	25	1	1	NUM
ejpam-6473	234	26	)	)	PUNCT
ejpam-6473	234	27	in	in	ADP
ejpam-6473	234	28	s1	s1	PROPN
ejpam-6473	234	29	l̇	l̇	PROPN
ejpam-6473	234	30	l	l	NOUN
ejpam-6473	234	31	=	=	PUNCT
ejpam-6473	234	32	βps(1	βps(1	X
ejpam-6473	234	33	+	+	NUM
ejpam-6473	234	34	νs	νs	NOUN
ejpam-6473	234	35	)	)	PUNCT
ejpam-6473	234	36	l	l	NOUN
ejpam-6473	234	37	−	−	PROPN
ejpam-6473	234	38	(	(	PUNCT
ejpam-6473	234	39	b+	b+	X
ejpam-6473	234	40	µ+	µ+	X
ejpam-6473	234	41	ζ	ζ	NOUN
ejpam-6473	234	42	)	)	PUNCT
ejpam-6473	234	43	,	,	PUNCT
ejpam-6473	234	44	=	=	SYM
ejpam-6473	234	45	⇒	⇒	NOUN
ejpam-6473	234	46	s1	s1	NOUN
ejpam-6473	234	47	≤	≤	PUNCT
ejpam-6473	234	48	−βs(1	−βs(1	X
ejpam-6473	234	49	+	+	NUM
ejpam-6473	234	50	νs)−	νs)−	PROPN
ejpam-6473	234	51	(	(	PUNCT
ejpam-6473	234	52	b+	b+	X
ejpam-6473	234	53	µ	µ	X
ejpam-6473	234	54	)	)	PUNCT
ejpam-6473	234	55	+	+	NUM
ejpam-6473	234	56	l̇	l̇	PROPN
ejpam-6473	234	57	l	l	NOUN
ejpam-6473	235	1	+	+	CCONJ
ejpam-6473	235	2	sβp	sβp	NOUN
ejpam-6473	235	3	(	(	PUNCT
ejpam-6473	235	4	1	1	NUM
ejpam-6473	235	5	+	+	NUM
ejpam-6473	235	6	2νs	2νs	ADJ
ejpam-6473	235	7	)	)	PUNCT
ejpam-6473	235	8	l	l	NOUN
ejpam-6473	235	9	.	.	PUNCT
ejpam-6473	236	1	s2	s2	NOUN
ejpam-6473	236	2	=	=	PUNCT
ejpam-6473	236	3	l̇	l̇	PROPN
ejpam-6473	236	4	l	l	NOUN
ejpam-6473	237	1	−	−	PROPN
ejpam-6473	237	2	ṡ	ṡ	PROPN
ejpam-6473	237	3	s	s	PRON
ejpam-6473	237	4	−	−	PROPN
ejpam-6473	237	5	(	(	PUNCT
ejpam-6473	237	6	b+	b+	X
ejpam-6473	237	7	µ+	µ+	X
ejpam-6473	237	8	δ)−	δ)−	PROPN
ejpam-6473	237	9	(	(	PUNCT
ejpam-6473	237	10	b+	b+	X
ejpam-6473	237	11	µ	µ	NUM
ejpam-6473	237	12	)	)	PUNCT
ejpam-6473	238	1	+	+	CCONJ
ejpam-6473	238	2	ζl	ζl	ADV
ejpam-6473	238	3	s	s	X
ejpam-6473	238	4	,	,	PUNCT
ejpam-6473	238	5	use	use	VERB
ejpam-6473	238	6	equation	equation	NOUN
ejpam-6473	238	7	3	3	NUM
ejpam-6473	238	8	of	of	ADP
ejpam-6473	238	9	system	system	NOUN
ejpam-6473	238	10	(	(	PUNCT
ejpam-6473	238	11	1	1	NUM
ejpam-6473	238	12	)	)	PUNCT
ejpam-6473	238	13	in	in	ADP
ejpam-6473	238	14	above	above	ADP
ejpam-6473	238	15	equation	equation	NOUN
ejpam-6473	238	16	s2	s2	NOUN
ejpam-6473	238	17	ṡ	ṡ	PROPN
ejpam-6473	238	18	s	s	PART
ejpam-6473	238	19	=	=	X
ejpam-6473	238	20	ζl	ζl	NOUN
ejpam-6473	238	21	s	s	NOUN
ejpam-6473	238	22	−	−	PROPN
ejpam-6473	238	23	(	(	PUNCT
ejpam-6473	238	24	b+	b+	X
ejpam-6473	238	25	µ+	µ+	X
ejpam-6473	238	26	δ	δ	PROPN
ejpam-6473	238	27	)	)	PUNCT
ejpam-6473	238	28	,	,	PUNCT
ejpam-6473	238	29	=	=	SYM
ejpam-6473	238	30	⇒	⇒	NOUN
ejpam-6473	238	31	s2	s2	NOUN
ejpam-6473	238	32	=	=	PUNCT
ejpam-6473	238	33	l̇	l̇	PROPN
ejpam-6473	238	34	l	l	NOUN
ejpam-6473	239	1	−	−	PROPN
ejpam-6473	239	2	(	(	PUNCT
ejpam-6473	239	3	b+	b+	X
ejpam-6473	239	4	µ	µ	NUM
ejpam-6473	239	5	)	)	PUNCT
ejpam-6473	239	6	,	,	PUNCT
ejpam-6473	239	7	put	put	VERB
ejpam-6473	239	8	values	value	NOUN
ejpam-6473	239	9	in	in	ADP
ejpam-6473	239	10	equation	equation	NOUN
ejpam-6473	239	11	(	(	PUNCT
ejpam-6473	239	12	8)	8)	NUM
ejpam-6473	239	13	µ(b	µ(b	NOUN
ejpam-6473	239	14	)	)	PUNCT
ejpam-6473	239	15	≤	≤	PUNCT
ejpam-6473	239	16	l̇	l̇	PROPN
ejpam-6473	239	17	l	l	NOUN
ejpam-6473	240	1	−	−	PROPN
ejpam-6473	240	2	(	(	PUNCT
ejpam-6473	240	3	b+	b+	X
ejpam-6473	240	4	µ	µ	NUM
ejpam-6473	240	5	)	)	PUNCT
ejpam-6473	241	1	+	+	NUM
ejpam-6473	241	2	sup{−βs(1	sup{−βs(1	NOUN
ejpam-6473	241	3	+	+	NUM
ejpam-6473	241	4	νs	νs	NOUN
ejpam-6473	241	5	)	)	PUNCT
ejpam-6473	242	1	+	+	CCONJ
ejpam-6473	242	2	sβp	sβp	NOUN
ejpam-6473	242	3	(	(	PUNCT
ejpam-6473	242	4	1	1	NUM
ejpam-6473	242	5	+	+	NUM
ejpam-6473	242	6	2νs	2νs	ADJ
ejpam-6473	242	7	)	)	PUNCT
ejpam-6473	242	8	l	l	NOUN
ejpam-6473	242	9	,	,	PUNCT
ejpam-6473	242	10	0	0	NUM
ejpam-6473	242	11	}	}	PUNCT
ejpam-6473	242	12	,	,	PUNCT
ejpam-6473	242	13	we	we	PRON
ejpam-6473	242	14	can	can	AUX
ejpam-6473	242	15	deduce	deduce	VERB
ejpam-6473	242	16	that	that	SCONJ
ejpam-6473	242	17	if	if	SCONJ
ejpam-6473	242	18	βs(1	βs(1	PROPN
ejpam-6473	242	19	+	+	X
ejpam-6473	242	20	νs	νs	NOUN
ejpam-6473	242	21	)	)	PUNCT
ejpam-6473	242	22	>	>	X
ejpam-6473	242	23	sβp	sβp	NOUN
ejpam-6473	242	24	(	(	PUNCT
ejpam-6473	242	25	1	1	NUM
ejpam-6473	242	26	+	+	NUM
ejpam-6473	242	27	2νs	2νs	ADJ
ejpam-6473	242	28	)	)	PUNCT
ejpam-6473	242	29	l	l	NOUN
ejpam-6473	242	30	,	,	PUNCT
ejpam-6473	242	31	(	(	PUNCT
ejpam-6473	242	32	9	9	NUM
ejpam-6473	242	33	)	)	PUNCT
ejpam-6473	242	34	then	then	ADV
ejpam-6473	242	35	µ(b	µ(b	NOUN
ejpam-6473	242	36	)	)	PUNCT
ejpam-6473	242	37	≤	≤	NUM
ejpam-6473	242	38	l̇	l̇	PROPN
ejpam-6473	242	39	l	l	NOUN
ejpam-6473	242	40	−	−	PROPN
ejpam-6473	242	41	(	(	PUNCT
ejpam-6473	242	42	b+	b+	X
ejpam-6473	242	43	µ	µ	NUM
ejpam-6473	242	44	)	)	PUNCT
ejpam-6473	242	45	,	,	PUNCT
ejpam-6473	242	46	q2	q2	PROPN
ejpam-6473	242	47	=	=	PROPN
ejpam-6473	242	48	lim	lim	PROPN
ejpam-6473	242	49	t→∞	t→∞	PRON
ejpam-6473	242	50	sup	sup	NOUN
ejpam-6473	242	51	sup	sup	NOUN
ejpam-6473	242	52	1	1	NUM
ejpam-6473	242	53	t	t	NOUN
ejpam-6473	242	54	∫	∫	PROPN
ejpam-6473	242	55	t	t	PROPN
ejpam-6473	242	56	0	0	NUM
ejpam-6473	242	57	l(b	l(b	PROPN
ejpam-6473	242	58	)	)	PUNCT
ejpam-6473	242	59	dl	dl	X
ejpam-6473	242	60	<	<	X
ejpam-6473	242	61	−(b+	−(b+	NUM
ejpam-6473	242	62	µ	µ	NUM
ejpam-6473	242	63	)	)	PUNCT
ejpam-6473	242	64	.	.	PUNCT
ejpam-6473	243	1	(	(	PUNCT
ejpam-6473	243	2	10	10	NUM
ejpam-6473	243	3	)	)	PUNCT
ejpam-6473	243	4	the	the	DET
ejpam-6473	243	5	bendixson	bendixson	NOUN
ejpam-6473	243	6	criteria	criterion	NOUN
ejpam-6473	243	7	is	be	AUX
ejpam-6473	243	8	satisfied	satisfied	ADJ
ejpam-6473	243	9	as	as	ADP
ejpam-6473	243	10	q2	q2	NOUN
ejpam-6473	243	11	<	<	X
ejpam-6473	243	12	0	0	NUM
ejpam-6473	243	13	.	.	PUNCT
ejpam-6473	244	1	this	this	PRON
ejpam-6473	244	2	implies	imply	VERB
ejpam-6473	244	3	that	that	SCONJ
ejpam-6473	244	4	endemic	endemic	ADJ
ejpam-6473	244	5	equilibrium	equilibrium	NOUN
ejpam-6473	244	6	point	point	NOUN
ejpam-6473	244	7	(	(	PUNCT
ejpam-6473	244	8	p	p	NOUN
ejpam-6473	244	9	∗	∗	NOUN
ejpam-6473	244	10	,	,	PUNCT
ejpam-6473	244	11	l∗	l∗	PROPN
ejpam-6473	244	12	,	,	PUNCT
ejpam-6473	244	13	s∗	s∗	PROPN
ejpam-6473	244	14	)	)	PUNCT
ejpam-6473	244	15	is	be	AUX
ejpam-6473	244	16	globally	globally	ADV
ejpam-6473	244	17	asymptotically	asymptotically	ADV
ejpam-6473	244	18	stable	stable	ADJ
ejpam-6473	244	19	.	.	PUNCT
ejpam-6473	245	1	from	from	ADP
ejpam-6473	245	2	equation	equation	NOUN
ejpam-6473	245	3	4	4	NUM
ejpam-6473	245	4	of	of	ADP
ejpam-6473	245	5	system	system	NOUN
ejpam-6473	245	6	(	(	PUNCT
ejpam-6473	245	7	1	1	X
ejpam-6473	245	8	)	)	PUNCT
ejpam-6473	245	9	dq	dq	NOUN
ejpam-6473	245	10	dt	dt	NOUN
ejpam-6473	246	1	=	=	NOUN
ejpam-6473	246	2	δs	δs	NOUN
ejpam-6473	246	3	−	−	PROPN
ejpam-6473	246	4	(	(	PUNCT
ejpam-6473	246	5	b+	b+	X
ejpam-6473	246	6	µ)q	µ)q	NOUN
ejpam-6473	246	7	,	,	PUNCT
ejpam-6473	246	8	limit	limit	NOUN
ejpam-6473	246	9	equation	equation	NOUN
ejpam-6473	246	10	is	be	AUX
ejpam-6473	246	11	dq	dq	PART
ejpam-6473	246	12	dt	dt	NOUN
ejpam-6473	246	13	=	=	PUNCT
ejpam-6473	246	14	δs∗	δs∗	NOUN
ejpam-6473	246	15	−	−	PROPN
ejpam-6473	246	16	(	(	PUNCT
ejpam-6473	246	17	b+	b+	X
ejpam-6473	246	18	µ)q	µ)q	NOUN
ejpam-6473	246	19	,	,	PUNCT
ejpam-6473	246	20	from	from	ADP
ejpam-6473	246	21	integrating	integrate	VERB
ejpam-6473	246	22	factor	factor	NOUN
ejpam-6473	246	23	e(b+µ)t	e(b+µ)t	PROPN
ejpam-6473	246	24	and	and	CCONJ
ejpam-6473	246	25	let	let	VERB
ejpam-6473	246	26	t	t	NOUN
ejpam-6473	246	27	→	→	SYM
ejpam-6473	246	28	∞	∞	PROPN
ejpam-6473	246	29	q(t	q(t	PROPN
ejpam-6473	246	30	)	)	PUNCT
ejpam-6473	246	31	→	→	SYM
ejpam-6473	246	32	q∗.	q∗.	NOUN
ejpam-6473	246	33	hence	hence	ADV
ejpam-6473	246	34	,	,	PUNCT
ejpam-6473	246	35	the	the	DET
ejpam-6473	246	36	endemic	endemic	ADJ
ejpam-6473	246	37	equilibrium	equilibrium	NOUN
ejpam-6473	246	38	point	point	NOUN
ejpam-6473	246	39	e∗	e∗	PROPN
ejpam-6473	246	40	is	be	AUX
ejpam-6473	246	41	globally	globally	ADV
ejpam-6473	246	42	asymptotically	asymptotically	ADV
ejpam-6473	246	43	stable	stable	ADJ
ejpam-6473	246	44	.	.	PUNCT
ejpam-6473	247	1	s.	s.	PROPN
ejpam-6473	247	2	bano	bano	PROPN
ejpam-6473	247	3	et	et	PROPN
ejpam-6473	247	4	al	al	PROPN
ejpam-6473	247	5	.	.	PUNCT
ejpam-6473	247	6	/	/	SYM
ejpam-6473	247	7	eur	eur	PROPN
ejpam-6473	247	8	.	.	PUNCT
ejpam-6473	248	1	j.	j.	PROPN
ejpam-6473	248	2	pure	pure	PROPN
ejpam-6473	248	3	appl	appl	PROPN
ejpam-6473	248	4	.	.	PROPN
ejpam-6473	248	5	math	math	PROPN
ejpam-6473	248	6	,	,	PUNCT
ejpam-6473	248	7	18	18	NUM
ejpam-6473	248	8	(	(	PUNCT
ejpam-6473	248	9	4	4	NUM
ejpam-6473	248	10	)	)	PUNCT
ejpam-6473	248	11	(	(	PUNCT
ejpam-6473	248	12	2025	2025	NUM
ejpam-6473	248	13	)	)	PUNCT
ejpam-6473	248	14	,	,	PUNCT
ejpam-6473	248	15	6473	6473	NUM
ejpam-6473	248	16	13	13	NUM
ejpam-6473	248	17	of	of	ADP
ejpam-6473	248	18	38	38	NUM
ejpam-6473	248	19	3.6	3.6	NUM
ejpam-6473	248	20	.	.	PUNCT
ejpam-6473	249	1	sensitivity	sensitivity	NOUN
ejpam-6473	249	2	in	in	ADP
ejpam-6473	249	3	this	this	DET
ejpam-6473	249	4	part	part	NOUN
ejpam-6473	249	5	of	of	ADP
ejpam-6473	249	6	the	the	DET
ejpam-6473	249	7	paper	paper	NOUN
ejpam-6473	249	8	,	,	PUNCT
ejpam-6473	249	9	the	the	DET
ejpam-6473	249	10	sensitivity	sensitivity	NOUN
ejpam-6473	249	11	analysis	analysis	NOUN
ejpam-6473	249	12	is	be	AUX
ejpam-6473	249	13	conducted	conduct	VERB
ejpam-6473	249	14	.	.	PUNCT
ejpam-6473	250	1	sensitivity	sensitivity	NOUN
ejpam-6473	250	2	analysis	analysis	NOUN
ejpam-6473	250	3	is	be	AUX
ejpam-6473	250	4	an	an	DET
ejpam-6473	250	5	essential	essential	ADJ
ejpam-6473	250	6	part	part	NOUN
ejpam-6473	250	7	of	of	ADP
ejpam-6473	250	8	infectious	infectious	ADJ
ejpam-6473	250	9	disease	disease	NOUN
ejpam-6473	250	10	modeling	modeling	NOUN
ejpam-6473	250	11	because	because	SCONJ
ejpam-6473	250	12	it	it	PRON
ejpam-6473	250	13	facilitates	facilitate	VERB
ejpam-6473	250	14	the	the	DET
ejpam-6473	250	15	researcher	researcher	NOUN
ejpam-6473	250	16	to	to	PART
ejpam-6473	250	17	identify	identify	VERB
ejpam-6473	250	18	which	which	DET
ejpam-6473	250	19	parameter	parameter	NOUN
ejpam-6473	250	20	has	have	VERB
ejpam-6473	250	21	the	the	DET
ejpam-6473	250	22	greatest	great	ADJ
ejpam-6473	250	23	influence	influence	NOUN
ejpam-6473	250	24	on	on	ADP
ejpam-6473	250	25	the	the	DET
ejpam-6473	250	26	propagation	propagation	NOUN
ejpam-6473	250	27	and	and	CCONJ
ejpam-6473	250	28	control	control	NOUN
ejpam-6473	250	29	of	of	ADP
ejpam-6473	250	30	the	the	DET
ejpam-6473	250	31	infection	infection	NOUN
ejpam-6473	250	32	.	.	PUNCT
ejpam-6473	251	1	the	the	DET
ejpam-6473	251	2	forward	forward	ADJ
ejpam-6473	251	3	index	index	NOUN
ejpam-6473	251	4	method	method	NOUN
ejpam-6473	251	5	is	be	AUX
ejpam-6473	251	6	used	use	VERB
ejpam-6473	251	7	to	to	PART
ejpam-6473	251	8	check	check	VERB
ejpam-6473	251	9	sensitivity	sensitivity	NOUN
ejpam-6473	251	10	,	,	PUNCT
ejpam-6473	251	11	which	which	PRON
ejpam-6473	251	12	involves	involve	VERB
ejpam-6473	251	13	computing	compute	VERB
ejpam-6473	251	14	the	the	DET
ejpam-6473	251	15	partial	partial	ADJ
ejpam-6473	251	16	derivative	derivative	NOUN
ejpam-6473	251	17	of	of	ADP
ejpam-6473	251	18	r0	r0	NOUN
ejpam-6473	251	19	with	with	ADP
ejpam-6473	251	20	respect	respect	NOUN
ejpam-6473	251	21	to	to	ADP
ejpam-6473	251	22	each	each	DET
ejpam-6473	251	23	parameter	parameter	NOUN
ejpam-6473	251	24	.	.	PUNCT
ejpam-6473	252	1	the	the	DET
ejpam-6473	252	2	sensitivity	sensitivity	NOUN
ejpam-6473	252	3	is	be	AUX
ejpam-6473	252	4	checked	check	VERB
ejpam-6473	252	5	by	by	ADP
ejpam-6473	252	6	using	use	VERB
ejpam-6473	252	7	the	the	DET
ejpam-6473	252	8	formula	formula	NOUN
ejpam-6473	252	9	that	that	PRON
ejpam-6473	252	10	is	be	AUX
ejpam-6473	252	11	xr0	xr0	PROPN
ejpam-6473	252	12	p	p	X
ejpam-6473	253	1	=	=	PUNCT
ejpam-6473	253	2	∂r0	∂r0	ADP
ejpam-6473	253	3	∂p	∂p	PROPN
ejpam-6473	253	4	×	×	NOUN
ejpam-6473	253	5	p	p	PROPN
ejpam-6473	253	6	r0	r0	NOUN
ejpam-6473	253	7	.	.	PUNCT
ejpam-6473	254	1	here	here	ADV
ejpam-6473	254	2	p	p	PROPN
ejpam-6473	254	3	∈	∈	PROPN
ejpam-6473	254	4	(	(	PUNCT
ejpam-6473	254	5	λ	λ	PROPN
ejpam-6473	254	6	,	,	PUNCT
ejpam-6473	254	7	β	β	NOUN
ejpam-6473	254	8	,	,	PUNCT
ejpam-6473	254	9	ζ	ζ	PROPN
ejpam-6473	254	10	,	,	PUNCT
ejpam-6473	254	11	δ	δ	PROPN
ejpam-6473	254	12	,	,	PUNCT
ejpam-6473	254	13	µ	µ	X
ejpam-6473	254	14	,	,	PUNCT
ejpam-6473	254	15	b	b	NOUN
ejpam-6473	254	16	)	)	PUNCT
ejpam-6473	254	17	,	,	PUNCT
ejpam-6473	254	18	xr0	xr0	PROPN
ejpam-6473	254	19	λ	λ	NOUN
ejpam-6473	254	20	=	=	NOUN
ejpam-6473	254	21	1	1	NUM
ejpam-6473	254	22	>	>	SYM
ejpam-6473	254	23	0	0	NUM
ejpam-6473	254	24	,	,	PUNCT
ejpam-6473	254	25	xr0	xr0	PROPN
ejpam-6473	254	26	β	β	X
ejpam-6473	254	27	=	=	SYM
ejpam-6473	254	28	1	1	NUM
ejpam-6473	254	29	>	>	SYM
ejpam-6473	254	30	0	0	NUM
ejpam-6473	254	31	,	,	PUNCT
ejpam-6473	254	32	xr0	xr0	NOUN
ejpam-6473	254	33	ζ	ζ	NOUN
ejpam-6473	254	34	=	=	SYM
ejpam-6473	254	35	(	(	PUNCT
ejpam-6473	254	36	b+	b+	X
ejpam-6473	254	37	µ	µ	NUM
ejpam-6473	254	38	)	)	PUNCT
ejpam-6473	254	39	(	(	PUNCT
ejpam-6473	254	40	b+	b+	X
ejpam-6473	254	41	µ+	µ+	X
ejpam-6473	254	42	ζ	ζ	NOUN
ejpam-6473	254	43	)	)	PUNCT
ejpam-6473	254	44	>	>	X
ejpam-6473	254	45	0	0	NUM
ejpam-6473	254	46	,	,	PUNCT
ejpam-6473	254	47	xr0	xr0	PROPN
ejpam-6473	254	48	δ	δ	PROPN
ejpam-6473	254	49	=	=	PUNCT
ejpam-6473	254	50	−δ	−δ	ADJ
ejpam-6473	254	51	(	(	PUNCT
ejpam-6473	254	52	b+	b+	X
ejpam-6473	254	53	µ+	µ+	X
ejpam-6473	254	54	δ	δ	NOUN
ejpam-6473	254	55	)	)	PUNCT
ejpam-6473	254	56	<	<	X
ejpam-6473	254	57	0	0	PROPN
ejpam-6473	254	58	,	,	PUNCT
ejpam-6473	254	59	xr0	xr0	PROPN
ejpam-6473	254	60	µ	µ	X
ejpam-6473	254	61	=	=	PUNCT
ejpam-6473	254	62	−µ(3µ2	−µ(3µ2	X
ejpam-6473	254	63	+	+	X
ejpam-6473	254	64	3b2	3b2	NUM
ejpam-6473	254	65	+	+	CCONJ
ejpam-6473	254	66	2bζ	2bζ	ADJ
ejpam-6473	254	67	+	+	CCONJ
ejpam-6473	254	68	2bδ	2bδ	NOUN
ejpam-6473	254	69	+	+	CCONJ
ejpam-6473	254	70	6µb+	6µb+	NOUN
ejpam-6473	254	71	2µδ	2µδ	NOUN
ejpam-6473	254	72	+	+	CCONJ
ejpam-6473	254	73	2µζ	2µζ	ADJ
ejpam-6473	254	74	+	+	CCONJ
ejpam-6473	254	75	δζ	δζ	NOUN
ejpam-6473	254	76	)	)	PUNCT
ejpam-6473	254	77	(	(	PUNCT
ejpam-6473	254	78	b+	b+	X
ejpam-6473	254	79	µ)(b+	µ)(b+	X
ejpam-6473	254	80	µ+	µ+	X
ejpam-6473	254	81	ζ)(b+	ζ)(b+	NUM
ejpam-6473	254	82	µ+	µ+	PROPN
ejpam-6473	254	83	δ	δ	PROPN
ejpam-6473	254	84	)	)	PUNCT
ejpam-6473	254	85	<	<	X
ejpam-6473	254	86	0	0	PROPN
ejpam-6473	254	87	,	,	PUNCT
ejpam-6473	254	88	xr0	xr0	PROPN
ejpam-6473	254	89	b	b	PROPN
ejpam-6473	254	90	=	=	SYM
ejpam-6473	254	91	−b(3d2	−b(3d2	PROPN
ejpam-6473	254	92	+	+	CCONJ
ejpam-6473	254	93	6µb+	6µb+	NOUN
ejpam-6473	254	94	2bδ	2bδ	NOUN
ejpam-6473	254	95	+	+	CCONJ
ejpam-6473	254	96	2bζ	2bζ	ADJ
ejpam-6473	254	97	+	+	CCONJ
ejpam-6473	254	98	2ζµ+	2ζµ+	NUM
ejpam-6473	254	99	2µδ	2µδ	NOUN
ejpam-6473	255	1	+	+	CCONJ
ejpam-6473	255	2	ζδ	ζδ	X
ejpam-6473	256	1	+	+	NUM
ejpam-6473	256	2	3µ2	3µ2	NUM
ejpam-6473	256	3	)	)	PUNCT
ejpam-6473	257	1	(	(	PUNCT
ejpam-6473	257	2	b+	b+	X
ejpam-6473	257	3	µ)(b+	µ)(b+	X
ejpam-6473	257	4	µ+	µ+	X
ejpam-6473	257	5	ζ)(b+	ζ)(b+	NUM
ejpam-6473	257	6	µ+	µ+	PROPN
ejpam-6473	257	7	δ	δ	PROPN
ejpam-6473	257	8	)	)	PUNCT
ejpam-6473	257	9	<	<	X
ejpam-6473	257	10	0	0	X
ejpam-6473	257	11	.	.	PUNCT
ejpam-6473	258	1	(	(	PUNCT
ejpam-6473	258	2	11	11	NUM
ejpam-6473	258	3	)	)	PUNCT
ejpam-6473	258	4	from	from	ADP
ejpam-6473	258	5	the	the	DET
ejpam-6473	258	6	above	above	ADJ
ejpam-6473	258	7	computation	computation	NOUN
ejpam-6473	258	8	,	,	PUNCT
ejpam-6473	258	9	it	it	PRON
ejpam-6473	258	10	is	be	AUX
ejpam-6473	258	11	shown	show	VERB
ejpam-6473	258	12	that	that	SCONJ
ejpam-6473	258	13	β	β	NOUN
ejpam-6473	258	14	,	,	PUNCT
ejpam-6473	258	15	ζ	ζ	NOUN
ejpam-6473	258	16	,	,	PUNCT
ejpam-6473	258	17	λ	λ	PROPN
ejpam-6473	258	18	has	have	VERB
ejpam-6473	258	19	positive	positive	ADJ
ejpam-6473	258	20	influence	influence	NOUN
ejpam-6473	258	21	on	on	ADP
ejpam-6473	258	22	r0	r0	NOUN
ejpam-6473	258	23	and	and	CCONJ
ejpam-6473	258	24	the	the	DET
ejpam-6473	258	25	index	index	NOUN
ejpam-6473	258	26	of	of	ADP
ejpam-6473	258	27	b	b	PROPN
ejpam-6473	258	28	,	,	PUNCT
ejpam-6473	258	29	δ	δ	PROPN
ejpam-6473	258	30	,	,	PUNCT
ejpam-6473	259	1	µ	µ	X
ejpam-6473	259	2	show	show	VERB
ejpam-6473	259	3	that	that	SCONJ
ejpam-6473	259	4	increasing	increase	VERB
ejpam-6473	259	5	their	their	PRON
ejpam-6473	259	6	value	value	NOUN
ejpam-6473	259	7	decreases	decrease	VERB
ejpam-6473	259	8	the	the	DET
ejpam-6473	259	9	value	value	NOUN
ejpam-6473	259	10	of	of	ADP
ejpam-6473	259	11	r0	r0	NOUN
ejpam-6473	259	12	.	.	PUNCT
ejpam-6473	260	1	parameter	parameter	PROPN
ejpam-6473	260	2	sensitive	sensitive	ADJ
ejpam-6473	260	3	index	index	NOUN
ejpam-6473	260	4	formula	formula	NOUN
ejpam-6473	260	5	index	index	NOUN
ejpam-6473	260	6	values	value	NOUN
ejpam-6473	260	7	base	base	NOUN
ejpam-6473	260	8	value	value	NOUN
ejpam-6473	260	9	used	use	VERB
ejpam-6473	260	10	source	source	NOUN
ejpam-6473	260	11	λ	λ	PROPN
ejpam-6473	260	12	xr0	xr0	PROPN
ejpam-6473	260	13	λ	λ	PROPN
ejpam-6473	260	14	1	1	NUM
ejpam-6473	260	15	1.025	1.025	NUM
ejpam-6473	260	16	assumed	assume	VERB
ejpam-6473	260	17	β	β	PROPN
ejpam-6473	260	18	xr0	xr0	PROPN
ejpam-6473	260	19	β	β	X
ejpam-6473	260	20	1	1	NUM
ejpam-6473	260	21	0.00038	0.00038	NUM
ejpam-6473	261	1	[	[	X
ejpam-6473	261	2	28	28	NUM
ejpam-6473	261	3	]	]	X
ejpam-6473	261	4	ζ	ζ	NOUN
ejpam-6473	261	5	xr0	xr0	PROPN
ejpam-6473	261	6	ζ	ζ	NOUN
ejpam-6473	261	7	0.3805	0.3805	NUM
ejpam-6473	261	8	0.21	0.21	NUM
ejpam-6473	261	9	[	[	X
ejpam-6473	261	10	29	29	NUM
ejpam-6473	261	11	]	]	X
ejpam-6473	261	12	δ	δ	PROPN
ejpam-6473	261	13	xr0	xr0	PROPN
ejpam-6473	261	14	δ	δ	PROPN
ejpam-6473	261	15	-0.5686	-0.5686	PROPN
ejpam-6473	261	16	0.017	0.017	NUM
ejpam-6473	261	17	assumed	assume	VERB
ejpam-6473	261	18	b	b	PROPN
ejpam-6473	261	19	xr0	xr0	PROPN
ejpam-6473	261	20	b	b	PROPN
ejpam-6473	261	21	-0.2669	-0.2669	PROPN
ejpam-6473	261	22	0.0019	0.0019	NUM
ejpam-6473	262	1	[	[	X
ejpam-6473	262	2	29	29	NUM
ejpam-6473	262	3	]	]	SYM
ejpam-6473	262	4	µ	µ	X
ejpam-6473	262	5	xr0	xr0	X
ejpam-6473	262	6	µ	µ	NOUN
ejpam-6473	262	7	-1.5451	-1.5451	NOUN
ejpam-6473	262	8	0.011	0.011	NUM
ejpam-6473	262	9	[	[	X
ejpam-6473	262	10	29	29	NUM
ejpam-6473	262	11	]	]	SYM
ejpam-6473	262	12	table	table	NOUN
ejpam-6473	262	13	2	2	NUM
ejpam-6473	262	14	:	:	PUNCT
ejpam-6473	262	15	sensitive	sensitive	ADJ
ejpam-6473	262	16	index	index	NOUN
ejpam-6473	262	17	of	of	ADP
ejpam-6473	262	18	the	the	DET
ejpam-6473	262	19	r0	r0	NOUN
ejpam-6473	262	20	figure	figure	NOUN
ejpam-6473	262	21	2	2	NUM
ejpam-6473	262	22	of	of	ADP
ejpam-6473	262	23	the	the	DET
ejpam-6473	262	24	sensitivity	sensitivity	NOUN
ejpam-6473	262	25	analysis	analysis	NOUN
ejpam-6473	262	26	is	be	AUX
ejpam-6473	262	27	constructed	construct	VERB
ejpam-6473	262	28	by	by	ADP
ejpam-6473	262	29	using	use	VERB
ejpam-6473	262	30	matlab	matlab	PROPN
ejpam-6473	262	31	.	.	PUNCT
ejpam-6473	263	1	figure	figure	NOUN
ejpam-6473	263	2	2	2	NUM
ejpam-6473	263	3	shows	show	VERB
ejpam-6473	263	4	that	that	SCONJ
ejpam-6473	263	5	µ	µ	X
ejpam-6473	263	6	,	,	PUNCT
ejpam-6473	263	7	b	b	PROPN
ejpam-6473	263	8	,	,	PUNCT
ejpam-6473	263	9	δ	δ	PROPN
ejpam-6473	263	10	has	have	VERB
ejpam-6473	263	11	a	a	DET
ejpam-6473	263	12	negative	negative	ADJ
ejpam-6473	263	13	impact	impact	NOUN
ejpam-6473	263	14	on	on	ADP
ejpam-6473	263	15	disease	disease	NOUN
ejpam-6473	263	16	propagation	propagation	NOUN
ejpam-6473	263	17	.	.	PUNCT
ejpam-6473	264	1	by	by	ADP
ejpam-6473	264	2	increasing	increase	VERB
ejpam-6473	264	3	these	these	DET
ejpam-6473	264	4	parameter	parameter	NOUN
ejpam-6473	264	5	values	value	NOUN
ejpam-6473	264	6	will	will	AUX
ejpam-6473	264	7	reduce	reduce	VERB
ejpam-6473	264	8	the	the	DET
ejpam-6473	264	9	spread	spread	NOUN
ejpam-6473	264	10	of	of	ADP
ejpam-6473	264	11	smoking	smoking	NOUN
ejpam-6473	264	12	.	.	PUNCT
ejpam-6473	265	1	the	the	DET
ejpam-6473	265	2	parameter	parameter	NOUN
ejpam-6473	265	3	values	value	NOUN
ejpam-6473	265	4	that	that	PRON
ejpam-6473	265	5	are	be	AUX
ejpam-6473	265	6	used	use	VERB
ejpam-6473	265	7	in	in	ADP
ejpam-6473	265	8	the	the	DET
ejpam-6473	265	9	sensitivity	sensitivity	NOUN
ejpam-6473	265	10	analysis	analysis	NOUN
ejpam-6473	265	11	are	be	AUX
ejpam-6473	265	12	given	give	VERB
ejpam-6473	265	13	below	below	ADV
ejpam-6473	265	14	.	.	PUNCT
ejpam-6473	266	1	s.	s.	PROPN
ejpam-6473	266	2	bano	bano	PROPN
ejpam-6473	266	3	et	et	PROPN
ejpam-6473	266	4	al	al	PROPN
ejpam-6473	266	5	.	.	PUNCT
ejpam-6473	266	6	/	/	SYM
ejpam-6473	266	7	eur	eur	PROPN
ejpam-6473	266	8	.	.	PUNCT
ejpam-6473	267	1	j.	j.	PROPN
ejpam-6473	267	2	pure	pure	PROPN
ejpam-6473	267	3	appl	appl	PROPN
ejpam-6473	267	4	.	.	PROPN
ejpam-6473	267	5	math	math	PROPN
ejpam-6473	267	6	,	,	PUNCT
ejpam-6473	267	7	18	18	NUM
ejpam-6473	267	8	(	(	PUNCT
ejpam-6473	267	9	4	4	NUM
ejpam-6473	267	10	)	)	PUNCT
ejpam-6473	267	11	(	(	PUNCT
ejpam-6473	267	12	2025	2025	NUM
ejpam-6473	267	13	)	)	PUNCT
ejpam-6473	267	14	,	,	PUNCT
ejpam-6473	267	15	6473	6473	NUM
ejpam-6473	267	16	14	14	NUM
ejpam-6473	267	17	of	of	ADP
ejpam-6473	267	18	38	38	NUM
ejpam-6473	267	19	figure	figure	NOUN
ejpam-6473	267	20	2	2	NUM
ejpam-6473	267	21	:	:	PUNCT
ejpam-6473	267	22	sensitivity	sensitivity	NOUN
ejpam-6473	267	23	index	index	NOUN
ejpam-6473	267	24	graph	graph	NOUN
ejpam-6473	267	25	.	.	PUNCT
ejpam-6473	268	1	4	4	X
ejpam-6473	268	2	.	.	X
ejpam-6473	268	3	optimal	optimal	ADJ
ejpam-6473	268	4	control	control	NOUN
ejpam-6473	268	5	we	we	PRON
ejpam-6473	268	6	have	have	AUX
ejpam-6473	268	7	extended	extend	VERB
ejpam-6473	268	8	the	the	DET
ejpam-6473	268	9	dynamics	dynamic	NOUN
ejpam-6473	268	10	to	to	PART
ejpam-6473	268	11	include	include	VERB
ejpam-6473	268	12	new	new	ADJ
ejpam-6473	268	13	compartments	compartment	NOUN
ejpam-6473	268	14	and	and	CCONJ
ejpam-6473	268	15	control	control	NOUN
ejpam-6473	268	16	functions	function	NOUN
ejpam-6473	268	17	,	,	PUNCT
ejpam-6473	268	18	making	make	VERB
ejpam-6473	268	19	it	it	PRON
ejpam-6473	268	20	a	a	DET
ejpam-6473	268	21	novel	novel	ADJ
ejpam-6473	268	22	contribution	contribution	NOUN
ejpam-6473	268	23	.	.	PUNCT
ejpam-6473	269	1	in	in	ADP
ejpam-6473	269	2	this	this	DET
ejpam-6473	269	3	part	part	NOUN
ejpam-6473	269	4	of	of	ADP
ejpam-6473	269	5	the	the	DET
ejpam-6473	269	6	paper	paper	NOUN
ejpam-6473	269	7	,	,	PUNCT
ejpam-6473	269	8	we	we	PRON
ejpam-6473	269	9	employ	employ	VERB
ejpam-6473	269	10	the	the	DET
ejpam-6473	269	11	method	method	NOUN
ejpam-6473	269	12	from	from	ADP
ejpam-6473	269	13	the	the	DET
ejpam-6473	269	14	optimal	optimal	ADJ
ejpam-6473	269	15	control	control	NOUN
ejpam-6473	269	16	theory	theory	NOUN
ejpam-6473	269	17	to	to	PART
ejpam-6473	269	18	forecast	forecast	VERB
ejpam-6473	269	19	the	the	DET
ejpam-6473	269	20	decrease	decrease	NOUN
ejpam-6473	269	21	and	and	CCONJ
ejpam-6473	269	22	analyze	analyze	VERB
ejpam-6473	269	23	the	the	DET
ejpam-6473	269	24	eradication	eradication	NOUN
ejpam-6473	269	25	of	of	ADP
ejpam-6473	269	26	smoking	smoking	NOUN
ejpam-6473	269	27	habits	habit	NOUN
ejpam-6473	269	28	in	in	ADP
ejpam-6473	269	29	the	the	DET
ejpam-6473	269	30	population	population	NOUN
ejpam-6473	269	31	.	.	PUNCT
ejpam-6473	270	1	to	to	PART
ejpam-6473	270	2	achieve	achieve	VERB
ejpam-6473	270	3	this	this	PRON
ejpam-6473	270	4	,	,	PUNCT
ejpam-6473	270	5	we	we	PRON
ejpam-6473	270	6	modified	modify	VERB
ejpam-6473	270	7	the	the	DET
ejpam-6473	270	8	model	model	NOUN
ejpam-6473	270	9	(	(	PUNCT
ejpam-6473	270	10	1	1	NUM
ejpam-6473	270	11	)	)	PUNCT
ejpam-6473	270	12	with	with	ADP
ejpam-6473	270	13	optimal	optimal	ADJ
ejpam-6473	270	14	control	control	NOUN
ejpam-6473	270	15	by	by	ADP
ejpam-6473	270	16	using	use	VERB
ejpam-6473	270	17	three	three	NUM
ejpam-6473	270	18	control	control	NOUN
ejpam-6473	270	19	measures	measure	NOUN
ejpam-6473	270	20	that	that	PRON
ejpam-6473	270	21	are	be	AUX
ejpam-6473	270	22	the	the	DET
ejpam-6473	270	23	media	medium	NOUN
ejpam-6473	270	24	campaign	campaign	NOUN
ejpam-6473	270	25	for	for	ADP
ejpam-6473	270	26	the	the	DET
ejpam-6473	270	27	potential	potential	ADJ
ejpam-6473	270	28	smokers	smoker	NOUN
ejpam-6473	270	29	,	,	PUNCT
ejpam-6473	270	30	antismoking	antismoke	VERB
ejpam-6473	270	31	gum	gum	NOUN
ejpam-6473	270	32	for	for	ADP
ejpam-6473	270	33	light	light	ADJ
ejpam-6473	270	34	smokers	smoker	NOUN
ejpam-6473	270	35	,	,	PUNCT
ejpam-6473	270	36	and	and	CCONJ
ejpam-6473	270	37	medicine	medicine	NOUN
ejpam-6473	270	38	for	for	ADP
ejpam-6473	270	39	regular	regular	ADJ
ejpam-6473	270	40	smokers	smoker	NOUN
ejpam-6473	270	41	.	.	PUNCT
ejpam-6473	271	1	in	in	ADP
ejpam-6473	271	2	[	[	X
ejpam-6473	271	3	30	30	NUM
ejpam-6473	271	4	]	]	PUNCT
ejpam-6473	271	5	and	and	CCONJ
ejpam-6473	271	6	[	[	X
ejpam-6473	271	7	31	31	NUM
ejpam-6473	271	8	]	]	PUNCT
ejpam-6473	271	9	researchers	researcher	NOUN
ejpam-6473	271	10	found	find	VERB
ejpam-6473	271	11	that	that	SCONJ
ejpam-6473	271	12	the	the	DET
ejpam-6473	271	13	media	medium	NOUN
ejpam-6473	271	14	campaign	campaign	NOUN
ejpam-6473	271	15	is	be	AUX
ejpam-6473	271	16	very	very	ADV
ejpam-6473	271	17	helpful	helpful	ADJ
ejpam-6473	271	18	in	in	ADP
ejpam-6473	271	19	reducing	reduce	VERB
ejpam-6473	271	20	the	the	DET
ejpam-6473	271	21	use	use	NOUN
ejpam-6473	271	22	of	of	ADP
ejpam-6473	271	23	tobacco	tobacco	NOUN
ejpam-6473	271	24	among	among	ADP
ejpam-6473	271	25	adults	adult	NOUN
ejpam-6473	271	26	and	and	CCONJ
ejpam-6473	271	27	young	young	ADJ
ejpam-6473	271	28	generations	generation	NOUN
ejpam-6473	271	29	and	and	CCONJ
ejpam-6473	271	30	decreases	decrease	VERB
ejpam-6473	271	31	the	the	DET
ejpam-6473	271	32	smoking	smoking	NOUN
ejpam-6473	271	33	rate	rate	NOUN
ejpam-6473	271	34	.	.	PUNCT
ejpam-6473	272	1	the	the	DET
ejpam-6473	272	2	modified	modify	VERB
ejpam-6473	272	3	model	model	NOUN
ejpam-6473	272	4	of	of	ADP
ejpam-6473	272	5	the	the	DET
ejpam-6473	272	6	optimal	optimal	ADJ
ejpam-6473	272	7	control	control	NOUN
ejpam-6473	272	8	problem	problem	NOUN
ejpam-6473	272	9	is	be	AUX
ejpam-6473	272	10	given	give	VERB
ejpam-6473	272	11	below.	below.	PROPN
ejpam-6473	272	12	dp	dp	NOUN
ejpam-6473	272	13	dt	dt	NOUN
ejpam-6473	272	14	=	=	SYM
ejpam-6473	272	15	λ−	λ−	PROPN
ejpam-6473	272	16	(	(	PUNCT
ejpam-6473	272	17	b+	b+	X
ejpam-6473	272	18	µ)p	µ)p	PUNCT
ejpam-6473	272	19	−	−	PROPN
ejpam-6473	272	20	βps(1	βps(1	NOUN
ejpam-6473	272	21	+	+	CCONJ
ejpam-6473	272	22	νs)−	νs)−	NOUN
ejpam-6473	272	23	a0u1p	a0u1p	PUNCT
ejpam-6473	272	24	+	+	PUNCT
ejpam-6473	272	25	π1u2l+	π1u2l+	NOUN
ejpam-6473	272	26	π2u3s	π2u3s	NUM
ejpam-6473	272	27	,	,	PUNCT
ejpam-6473	272	28	dl	dl	PROPN
ejpam-6473	272	29	dt	dt	NOUN
ejpam-6473	272	30	=	=	PUNCT
ejpam-6473	272	31	βps(1	βps(1	X
ejpam-6473	272	32	+	+	X
ejpam-6473	272	33	νs)−	νs)−	NOUN
ejpam-6473	272	34	(	(	PUNCT
ejpam-6473	272	35	b+	b+	X
ejpam-6473	272	36	µ+	µ+	X
ejpam-6473	272	37	ζ	ζ	NOUN
ejpam-6473	272	38	+	+	CCONJ
ejpam-6473	272	39	u2)l	u2)l	NOUN
ejpam-6473	272	40	,	,	PUNCT
ejpam-6473	272	41	ds	ds	ADJ
ejpam-6473	272	42	dt	dt	NOUN
ejpam-6473	272	43	=	=	SYM
ejpam-6473	272	44	ζl−	ζl−	X
ejpam-6473	272	45	(	(	PUNCT
ejpam-6473	272	46	b+	b+	X
ejpam-6473	272	47	µ+	µ+	X
ejpam-6473	272	48	δ	δ	NOUN
ejpam-6473	272	49	+	+	CCONJ
ejpam-6473	272	50	u3)s	u3)s	NOUN
ejpam-6473	272	51	,	,	PUNCT
ejpam-6473	272	52	dq	dq	NOUN
ejpam-6473	272	53	dt	dt	NOUN
ejpam-6473	272	54	=	=	NOUN
ejpam-6473	272	55	δs	δs	NOUN
ejpam-6473	272	56	−	−	PROPN
ejpam-6473	272	57	(	(	PUNCT
ejpam-6473	272	58	b+	b+	X
ejpam-6473	272	59	µ)q+	µ)q+	NOUN
ejpam-6473	272	60	a0u1p	a0u1p	PUNCT
ejpam-6473	272	61	+	+	CCONJ
ejpam-6473	272	62	(	(	PUNCT
ejpam-6473	272	63	1−	1−	NUM
ejpam-6473	272	64	π1)u2l+	π1)u2l+	NOUN
ejpam-6473	272	65	(	(	PUNCT
ejpam-6473	272	66	1−	1−	NUM
ejpam-6473	272	67	π2)u3s	π2)u3s	NOUN
ejpam-6473	272	68	.	.	PUNCT
ejpam-6473	272	69	,	,	PUNCT
ejpam-6473	272	70	(	(	PUNCT
ejpam-6473	272	71	12	12	NUM
ejpam-6473	272	72	)	)	PUNCT
ejpam-6473	272	73	with	with	ADP
ejpam-6473	272	74	initial	initial	ADJ
ejpam-6473	272	75	condition	condition	NOUN
ejpam-6473	272	76	p0	p0	NOUN
ejpam-6473	272	77	≥	≥	NOUN
ejpam-6473	272	78	0	0	NUM
ejpam-6473	272	79	,	,	PUNCT
ejpam-6473	272	80	l0	l0	PROPN
ejpam-6473	272	81	≥	≥	NOUN
ejpam-6473	272	82	0	0	NUM
ejpam-6473	272	83	,	,	PUNCT
ejpam-6473	272	84	s0	s0	PROPN
ejpam-6473	272	85	≥	≥	NUM
ejpam-6473	272	86	0	0	NUM
ejpam-6473	272	87	,	,	PUNCT
ejpam-6473	272	88	q0	q0	VERB
ejpam-6473	272	89	≥	≥	NOUN
ejpam-6473	272	90	0	0	NUM
ejpam-6473	273	1	the	the	DET
ejpam-6473	273	2	goal	goal	NOUN
ejpam-6473	273	3	of	of	ADP
ejpam-6473	273	4	the	the	DET
ejpam-6473	273	5	control	control	NOUN
ejpam-6473	273	6	strategies	strategy	NOUN
ejpam-6473	273	7	is	be	AUX
ejpam-6473	273	8	to	to	PART
ejpam-6473	273	9	decrease	decrease	VERB
ejpam-6473	273	10	the	the	DET
ejpam-6473	273	11	population	population	NOUN
ejpam-6473	273	12	of	of	ADP
ejpam-6473	273	13	light	light	ADJ
ejpam-6473	273	14	smokers	smoker	NOUN
ejpam-6473	273	15	and	and	CCONJ
ejpam-6473	273	16	regular	regular	ADJ
ejpam-6473	273	17	smokers	smoker	NOUN
ejpam-6473	273	18	and	and	CCONJ
ejpam-6473	273	19	enhancing	enhance	VERB
ejpam-6473	273	20	the	the	DET
ejpam-6473	273	21	population	population	NOUN
ejpam-6473	273	22	of	of	ADP
ejpam-6473	273	23	quit	quit	VERB
ejpam-6473	273	24	smokers	smoker	NOUN
ejpam-6473	273	25	and	and	CCONJ
ejpam-6473	273	26	potential	potential	ADJ
ejpam-6473	273	27	smokers	smoker	NOUN
ejpam-6473	273	28	,	,	PUNCT
ejpam-6473	273	29	which	which	PRON
ejpam-6473	273	30	can	can	AUX
ejpam-6473	273	31	be	be	AUX
ejpam-6473	273	32	accomplished	accomplish	VERB
ejpam-6473	273	33	by	by	ADP
ejpam-6473	273	34	reducing	reduce	VERB
ejpam-6473	273	35	the	the	DET
ejpam-6473	273	36	contact	contact	NOUN
ejpam-6473	273	37	between	between	ADP
ejpam-6473	273	38	smokers	smoker	NOUN
ejpam-6473	273	39	and	and	CCONJ
ejpam-6473	273	40	nonsmokers	nonsmoker	NOUN
ejpam-6473	273	41	.	.	PUNCT
ejpam-6473	274	1	the	the	DET
ejpam-6473	274	2	cost	cost	NOUN
ejpam-6473	274	3	(	(	PUNCT
ejpam-6473	274	4	objective	objective	ADJ
ejpam-6473	274	5	function	function	NOUN
ejpam-6473	274	6	)	)	PUNCT
ejpam-6473	274	7	of	of	ADP
ejpam-6473	274	8	the	the	DET
ejpam-6473	274	9	above	above	ADJ
ejpam-6473	274	10	control	control	NOUN
ejpam-6473	274	11	problem	problem	NOUN
ejpam-6473	274	12	is	be	AUX
ejpam-6473	274	13	given	give	VERB
ejpam-6473	274	14	bellow	bellow	ADJ
ejpam-6473	274	15	j	j	PROPN
ejpam-6473	274	16	=	=	SYM
ejpam-6473	274	17	∫	∫	PROPN
ejpam-6473	274	18	t	t	PROPN
ejpam-6473	274	19	0	0	NUM
ejpam-6473	275	1	(	(	PUNCT
ejpam-6473	275	2	d1l+d2s	d1l+d2s	PROPN
ejpam-6473	275	3	−d3p	−d3p	NUM
ejpam-6473	275	4	−d4q+	−d4q+	NOUN
ejpam-6473	275	5	1	1	NUM
ejpam-6473	275	6	2(b1u	2(b1u	NUM
ejpam-6473	275	7	2	2	NUM
ejpam-6473	275	8	1	1	NUM
ejpam-6473	275	9	+	+	NOUN
ejpam-6473	275	10	b2u	b2u	PROPN
ejpam-6473	275	11	2	2	NUM
ejpam-6473	275	12	2	2	NUM
ejpam-6473	275	13	+	+	NOUN
ejpam-6473	275	14	b3u	b3u	NOUN
ejpam-6473	275	15	2	2	NUM
ejpam-6473	275	16	3))dt	3))dt	NUM
ejpam-6473	275	17	.	.	PUNCT
ejpam-6473	276	1	in	in	ADP
ejpam-6473	276	2	the	the	DET
ejpam-6473	276	3	above	above	ADJ
ejpam-6473	276	4	objective	objective	ADJ
ejpam-6473	276	5	function	function	NOUN
ejpam-6473	276	6	(	(	PUNCT
ejpam-6473	276	7	d1	d1	PROPN
ejpam-6473	276	8	,	,	PUNCT
ejpam-6473	276	9	d2	d2	PROPN
ejpam-6473	276	10	,	,	PUNCT
ejpam-6473	276	11	d3	d3	PROPN
ejpam-6473	276	12	,	,	PUNCT
ejpam-6473	276	13	d4	d4	PROPN
ejpam-6473	276	14	)	)	PUNCT
ejpam-6473	276	15	are	be	AUX
ejpam-6473	276	16	positive	positive	ADJ
ejpam-6473	276	17	constant	constant	ADJ
ejpam-6473	276	18	for	for	ADP
ejpam-6473	276	19	the	the	DET
ejpam-6473	276	20	classes	class	NOUN
ejpam-6473	276	21	p	p	X
ejpam-6473	276	22	,	,	PUNCT
ejpam-6473	276	23	l	l	NOUN
ejpam-6473	276	24	,	,	PUNCT
ejpam-6473	276	25	s	s	X
ejpam-6473	276	26	,	,	PUNCT
ejpam-6473	276	27	q	q	X
ejpam-6473	276	28	respectively	respectively	ADV
ejpam-6473	276	29	.	.	PUNCT
ejpam-6473	277	1	the	the	DET
ejpam-6473	277	2	second	second	ADJ
ejpam-6473	277	3	term	term	NOUN
ejpam-6473	277	4	includes	include	VERB
ejpam-6473	277	5	(	(	PUNCT
ejpam-6473	277	6	b1	b1	NOUN
ejpam-6473	277	7	,	,	PUNCT
ejpam-6473	277	8	b2	b2	NOUN
ejpam-6473	277	9	,	,	PUNCT
ejpam-6473	277	10	b3	b3	PROPN
ejpam-6473	277	11	)	)	PUNCT
ejpam-6473	277	12	are	be	AUX
ejpam-6473	277	13	the	the	DET
ejpam-6473	277	14	positive	positive	ADJ
ejpam-6473	277	15	weight	weight	NOUN
ejpam-6473	277	16	parameters	parameter	NOUN
ejpam-6473	277	17	associated	associate	VERB
ejpam-6473	277	18	with	with	ADP
ejpam-6473	277	19	the	the	DET
ejpam-6473	277	20	control	control	NOUN
ejpam-6473	277	21	variables	variable	NOUN
ejpam-6473	277	22	(	(	PUNCT
ejpam-6473	277	23	u1	u1	NOUN
ejpam-6473	277	24	,	,	PUNCT
ejpam-6473	277	25	u2	u2	NOUN
ejpam-6473	277	26	,	,	PUNCT
ejpam-6473	277	27	u3	u3	NOUN
ejpam-6473	277	28	)	)	PUNCT
ejpam-6473	277	29	.	.	PUNCT
ejpam-6473	278	1	the	the	DET
ejpam-6473	278	2	objective	objective	NOUN
ejpam-6473	278	3	of	of	ADP
ejpam-6473	278	4	the	the	DET
ejpam-6473	278	5	cost	cost	NOUN
ejpam-6473	278	6	function	function	NOUN
ejpam-6473	278	7	s.	s.	PROPN
ejpam-6473	278	8	bano	bano	PROPN
ejpam-6473	278	9	et	et	PROPN
ejpam-6473	278	10	al	al	PROPN
ejpam-6473	278	11	.	.	PUNCT
ejpam-6473	278	12	/	/	SYM
ejpam-6473	278	13	eur	eur	PROPN
ejpam-6473	278	14	.	.	PUNCT
ejpam-6473	279	1	j.	j.	PROPN
ejpam-6473	279	2	pure	pure	PROPN
ejpam-6473	279	3	appl	appl	PROPN
ejpam-6473	279	4	.	.	PROPN
ejpam-6473	279	5	math	math	PROPN
ejpam-6473	279	6	,	,	PUNCT
ejpam-6473	279	7	18	18	NUM
ejpam-6473	279	8	(	(	PUNCT
ejpam-6473	279	9	4	4	NUM
ejpam-6473	279	10	)	)	PUNCT
ejpam-6473	279	11	(	(	PUNCT
ejpam-6473	279	12	2025	2025	NUM
ejpam-6473	279	13	)	)	PUNCT
ejpam-6473	279	14	,	,	PUNCT
ejpam-6473	279	15	6473	6473	NUM
ejpam-6473	279	16	15	15	NUM
ejpam-6473	279	17	of	of	ADP
ejpam-6473	279	18	38	38	NUM
ejpam-6473	279	19	is	be	AUX
ejpam-6473	279	20	to	to	PART
ejpam-6473	279	21	decrease	decrease	VERB
ejpam-6473	279	22	smoking	smoke	VERB
ejpam-6473	279	23	and	and	CCONJ
ejpam-6473	279	24	increase	increase	VERB
ejpam-6473	279	25	quit	quit	VERB
ejpam-6473	279	26	smokers	smoker	NOUN
ejpam-6473	279	27	.	.	PUNCT
ejpam-6473	280	1	u	u	NOUN
ejpam-6473	280	2	is	be	AUX
ejpam-6473	280	3	the	the	DET
ejpam-6473	280	4	admissible	admissible	ADJ
ejpam-6473	280	5	control	control	NOUN
ejpam-6473	280	6	set	set	VERB
ejpam-6473	280	7	and	and	CCONJ
ejpam-6473	280	8	is	be	AUX
ejpam-6473	280	9	defined	define	VERB
ejpam-6473	280	10	as	as	ADP
ejpam-6473	280	11	u	u	NOUN
ejpam-6473	280	12	=	=	PUNCT
ejpam-6473	280	13	{	{	PUNCT
ejpam-6473	280	14	u	u	NOUN
ejpam-6473	280	15	=	=	PUNCT
ejpam-6473	280	16	(	(	PUNCT
ejpam-6473	280	17	u1	u1	PROPN
ejpam-6473	280	18	,	,	PUNCT
ejpam-6473	280	19	u2	u2	NOUN
ejpam-6473	280	20	,	,	PUNCT
ejpam-6473	280	21	u3)|uj(t	u3)|uj(t	PROPN
ejpam-6473	280	22	)	)	PUNCT
ejpam-6473	280	23	,	,	PUNCT
ejpam-6473	280	24	0	0	NUM
ejpam-6473	280	25	≤	≤	NUM
ejpam-6473	280	26	uj(t	uj(t	PUNCT
ejpam-6473	280	27	)	)	PUNCT
ejpam-6473	280	28	≤	≤	NOUN
ejpam-6473	280	29	uj(t	uj(t	PUNCT
ejpam-6473	280	30	)	)	PUNCT
ejpam-6473	280	31	max	max	PROPN
ejpam-6473	280	32	≤	≤	PROPN
ejpam-6473	280	33	1	1	NUM
ejpam-6473	280	34	,	,	PUNCT
ejpam-6473	280	35	t	t	PROPN
ejpam-6473	280	36	∈	∈	PROPN
ejpam-6473	281	1	[	[	X
ejpam-6473	281	2	0	0	NUM
ejpam-6473	281	3	,	,	PUNCT
ejpam-6473	281	4	t	t	X
ejpam-6473	281	5	]	]	PUNCT
ejpam-6473	281	6	,	,	PUNCT
ejpam-6473	281	7	j	j	PROPN
ejpam-6473	281	8	=	=	SYM
ejpam-6473	281	9	1	1	NUM
ejpam-6473	281	10	,	,	PUNCT
ejpam-6473	281	11	2	2	NUM
ejpam-6473	281	12	,	,	PUNCT
ejpam-6473	281	13	3	3	NUM
ejpam-6473	281	14	}	}	PUNCT
ejpam-6473	281	15	in	in	ADP
ejpam-6473	281	16	the	the	DET
ejpam-6473	281	17	above	above	ADJ
ejpam-6473	281	18	set	set	NOUN
ejpam-6473	281	19	u	u	PROPN
ejpam-6473	281	20	,	,	PUNCT
ejpam-6473	281	21	uj(t	uj(t	PUNCT
ejpam-6473	281	22	)	)	PUNCT
ejpam-6473	281	23	are	be	AUX
ejpam-6473	281	24	the	the	DET
ejpam-6473	281	25	control	control	NOUN
ejpam-6473	281	26	variables	variable	NOUN
ejpam-6473	281	27	for	for	ADP
ejpam-6473	281	28	j=1,2,3	j=1,2,3	NUM
ejpam-6473	281	29	and	and	CCONJ
ejpam-6473	281	30	set	set	VERB
ejpam-6473	281	31	u	u	NOUN
ejpam-6473	281	32	is	be	AUX
ejpam-6473	281	33	the	the	DET
ejpam-6473	281	34	lebesgue	lebesgue	ADJ
ejpam-6473	281	35	measurable	measurable	ADJ
ejpam-6473	281	36	function	function	NOUN
ejpam-6473	281	37	.	.	PUNCT
ejpam-6473	282	1	in	in	ADP
ejpam-6473	282	2	above	above	ADP
ejpam-6473	282	3	set	set	VERB
ejpam-6473	282	4	u	u	NOUN
ejpam-6473	282	5	,	,	PUNCT
ejpam-6473	282	6	(	(	PUNCT
ejpam-6473	282	7	umax	umax	PROPN
ejpam-6473	282	8	1	1	NUM
ejpam-6473	282	9	,	,	PUNCT
ejpam-6473	282	10	umax	umax	ADJ
ejpam-6473	282	11	2	2	NUM
ejpam-6473	282	12	,	,	PUNCT
ejpam-6473	282	13	and	and	CCONJ
ejpam-6473	282	14	umax	umax	ADJ
ejpam-6473	282	15	3	3	NUM
ejpam-6473	282	16	)	)	PUNCT
ejpam-6473	282	17	denotes	denote	VERB
ejpam-6473	282	18	the	the	DET
ejpam-6473	282	19	maximum	maximum	ADJ
ejpam-6473	282	20	achievable	achievable	ADJ
ejpam-6473	282	21	values	value	NOUN
ejpam-6473	282	22	of	of	ADP
ejpam-6473	282	23	u1	u1	NOUN
ejpam-6473	282	24	,	,	PUNCT
ejpam-6473	282	25	u2	u2	NOUN
ejpam-6473	282	26	,	,	PUNCT
ejpam-6473	282	27	and	and	CCONJ
ejpam-6473	282	28	u3	u3	NOUN
ejpam-6473	282	29	respectively	respectively	ADV
ejpam-6473	282	30	,	,	PUNCT
ejpam-6473	282	31	and	and	CCONJ
ejpam-6473	282	32	t	t	PROPN
ejpam-6473	282	33	is	be	AUX
ejpam-6473	282	34	the	the	DET
ejpam-6473	282	35	terminal	terminal	ADJ
ejpam-6473	282	36	time	time	NOUN
ejpam-6473	282	37	.	.	PUNCT
ejpam-6473	283	1	the	the	DET
ejpam-6473	283	2	model	model	NOUN
ejpam-6473	283	3	(	(	PUNCT
ejpam-6473	283	4	12	12	NUM
ejpam-6473	283	5	)	)	PUNCT
ejpam-6473	283	6	all	all	DET
ejpam-6473	283	7	solutions	solution	NOUN
ejpam-6473	283	8	lie	lie	VERB
ejpam-6473	283	9	in	in	ADP
ejpam-6473	283	10	the	the	DET
ejpam-6473	283	11	feasible	feasible	ADJ
ejpam-6473	283	12	region	region	NOUN
ejpam-6473	283	13	ω	ω	PROPN
ejpam-6473	283	14	,	,	PUNCT
ejpam-6473	283	15	i	i	PROPN
ejpam-6473	283	16	-	-	PROPN
ejpam-6473	283	17	e.	e.	PROPN
ejpam-6473	283	18	ω	ω	PROPN
ejpam-6473	283	19	=	=	X
ejpam-6473	283	20	{	{	PUNCT
ejpam-6473	283	21	(	(	PUNCT
ejpam-6473	283	22	p	p	X
ejpam-6473	283	23	,	,	PUNCT
ejpam-6473	283	24	l	l	NOUN
ejpam-6473	283	25	,	,	PUNCT
ejpam-6473	283	26	s	s	X
ejpam-6473	283	27	,	,	PUNCT
ejpam-6473	283	28	q	q	NOUN
ejpam-6473	283	29	)	)	PUNCT
ejpam-6473	283	30	∈	∈	PROPN
ejpam-6473	283	31	r4	r4	NOUN
ejpam-6473	283	32	,	,	PUNCT
ejpam-6473	283	33	0	0	NUM
ejpam-6473	283	34	≤	≤	NUM
ejpam-6473	283	35	n	n	CCONJ
ejpam-6473	283	36	≤	≤	NUM
ejpam-6473	283	37	λ	λ	X
ejpam-6473	283	38	b+	b+	X
ejpam-6473	283	39	µ	µ	X
ejpam-6473	283	40	}	}	PUNCT
ejpam-6473	283	41	.	.	PUNCT
ejpam-6473	284	1	4.1	4.1	NUM
ejpam-6473	284	2	.	.	PUNCT
ejpam-6473	284	3	optimal	optimal	ADJ
ejpam-6473	284	4	control	control	NOUN
ejpam-6473	284	5	existence	existence	NOUN
ejpam-6473	284	6	theorem	theorem	VERB
ejpam-6473	284	7	5	5	NUM
ejpam-6473	284	8	.	.	PUNCT
ejpam-6473	285	1	there	there	PRON
ejpam-6473	285	2	exists	exist	VERB
ejpam-6473	285	3	an	an	DET
ejpam-6473	285	4	optimal	optimal	ADJ
ejpam-6473	285	5	control	control	NOUN
ejpam-6473	285	6	(	(	PUNCT
ejpam-6473	285	7	u∗1	u∗1	NOUN
ejpam-6473	285	8	,	,	PUNCT
ejpam-6473	285	9	u	u	NOUN
ejpam-6473	285	10	∗	∗	NOUN
ejpam-6473	285	11	2	2	NUM
ejpam-6473	285	12	,	,	PUNCT
ejpam-6473	285	13	u	u	NOUN
ejpam-6473	285	14	∗	∗	NOUN
ejpam-6473	285	15	3	3	NUM
ejpam-6473	285	16	)	)	PUNCT
ejpam-6473	285	17	that	that	PRON
ejpam-6473	285	18	minimizes	minimize	VERB
ejpam-6473	285	19	the	the	DET
ejpam-6473	285	20	objective	objective	ADJ
ejpam-6473	285	21	function	function	NOUN
ejpam-6473	285	22	j.	j.	PROPN
ejpam-6473	285	23	proof	proof	PROPN
ejpam-6473	285	24	.	.	PUNCT
ejpam-6473	286	1	to	to	PART
ejpam-6473	286	2	prove	prove	VERB
ejpam-6473	286	3	the	the	DET
ejpam-6473	286	4	existence	existence	NOUN
ejpam-6473	286	5	of	of	ADP
ejpam-6473	286	6	optimal	optimal	ADJ
ejpam-6473	286	7	control	control	NOUN
ejpam-6473	286	8	,	,	PUNCT
ejpam-6473	286	9	we	we	PRON
ejpam-6473	286	10	must	must	AUX
ejpam-6473	286	11	satisfied	satisfied	VERB
ejpam-6473	286	12	the	the	DET
ejpam-6473	286	13	following	follow	VERB
ejpam-6473	286	14	condition	condition	NOUN
ejpam-6473	286	15	:	:	PUNCT
ejpam-6473	286	16	(	(	PUNCT
ejpam-6473	286	17	i	i	NOUN
ejpam-6473	286	18	)	)	PUNCT
ejpam-6473	286	19	both	both	CCONJ
ejpam-6473	286	20	the	the	DET
ejpam-6473	286	21	control	control	NOUN
ejpam-6473	286	22	set	set	VERB
ejpam-6473	286	23	and	and	CCONJ
ejpam-6473	286	24	the	the	DET
ejpam-6473	286	25	state	state	NOUN
ejpam-6473	286	26	variable	variable	NOUN
ejpam-6473	286	27	are	be	AUX
ejpam-6473	286	28	non	non	X
ejpam-6473	286	29	empty	empty	ADJ
ejpam-6473	286	30	.	.	PUNCT
ejpam-6473	287	1	(	(	PUNCT
ejpam-6473	287	2	ii	ii	X
ejpam-6473	287	3	)	)	PUNCT
ejpam-6473	287	4	the	the	DET
ejpam-6473	287	5	control	control	NOUN
ejpam-6473	287	6	set	set	NOUN
ejpam-6473	287	7	is	be	AUX
ejpam-6473	287	8	closed	close	VERB
ejpam-6473	287	9	as	as	ADV
ejpam-6473	287	10	well	well	ADV
ejpam-6473	287	11	as	as	ADP
ejpam-6473	287	12	convex	convex	NOUN
ejpam-6473	287	13	.	.	PUNCT
ejpam-6473	288	1	(	(	PUNCT
ejpam-6473	288	2	iii	iii	X
ejpam-6473	288	3	)	)	PUNCT
ejpam-6473	288	4	objective	objective	ADJ
ejpam-6473	288	5	function	function	NOUN
ejpam-6473	288	6	integrand	integrand	PROPN
ejpam-6473	288	7	is	be	AUX
ejpam-6473	288	8	convex	convex	NOUN
ejpam-6473	288	9	.	.	PUNCT
ejpam-6473	289	1	(	(	PUNCT
ejpam-6473	289	2	iv	iv	X
ejpam-6473	289	3	)	)	PUNCT
ejpam-6473	289	4	r(t	r(t	NOUN
ejpam-6473	289	5	,	,	PUNCT
ejpam-6473	289	6	x	x	X
ejpam-6473	289	7	,	,	PUNCT
ejpam-6473	289	8	u	u	NOUN
ejpam-6473	289	9	)	)	PUNCT
ejpam-6473	289	10	=	=	SYM
ejpam-6473	290	1	a(t	a(t	NOUN
ejpam-6473	290	2	,	,	PUNCT
ejpam-6473	290	3	x	x	X
ejpam-6473	290	4	)	)	PUNCT
ejpam-6473	290	5	+	+	NOUN
ejpam-6473	290	6	b(t	b(t	PROPN
ejpam-6473	290	7	,	,	PUNCT
ejpam-6473	290	8	x)u	x)u	PUNCT
ejpam-6473	290	9	.	.	PUNCT
ejpam-6473	291	1	(	(	PUNCT
ejpam-6473	291	2	v	v	X
ejpam-6473	291	3	)	)	PUNCT
ejpam-6473	291	4	there	there	PRON
ejpam-6473	291	5	exist	exist	VERB
ejpam-6473	291	6	y1	y1	PROPN
ejpam-6473	291	7	>	>	X
ejpam-6473	291	8	0	0	NUM
ejpam-6473	291	9	,	,	PUNCT
ejpam-6473	291	10	positive	positive	ADJ
ejpam-6473	291	11	numbers	number	NOUN
ejpam-6473	291	12	y2	y2	PROPN
ejpam-6473	291	13	,	,	PUNCT
ejpam-6473	291	14	y3	y3	PROPN
ejpam-6473	291	15	,	,	PUNCT
ejpam-6473	291	16	the	the	DET
ejpam-6473	291	17	integrand	integrand	NOUN
ejpam-6473	291	18	of	of	ADP
ejpam-6473	291	19	the	the	DET
ejpam-6473	291	20	objective	objective	ADJ
ejpam-6473	291	21	function	function	NOUN
ejpam-6473	291	22	fulfill	fulfill	NOUN
ejpam-6473	291	23	.	.	PUNCT
ejpam-6473	292	1	l	l	NOUN
ejpam-6473	292	2	≥	≥	NOUN
ejpam-6473	293	1	y2(|u1|2	y2(|u1|2	X
ejpam-6473	293	2	+	+	CCONJ
ejpam-6473	293	3	|u2|2	|u2|2	PROPN
ejpam-6473	293	4	+	+	CCONJ
ejpam-6473	293	5	|u3|2	|u3|2	PROPN
ejpam-6473	293	6	)	)	PUNCT
ejpam-6473	293	7	y1	y1	NOUN
ejpam-6473	293	8	2	2	NUM
ejpam-6473	293	9	−	−	NOUN
ejpam-6473	293	10	y3	y3	NOUN
ejpam-6473	293	11	,	,	PUNCT
ejpam-6473	293	12	where	where	SCONJ
ejpam-6473	293	13	y1	y1	NOUN
ejpam-6473	293	14	=	=	SYM
ejpam-6473	293	15	2	2	NUM
ejpam-6473	293	16	,	,	PUNCT
ejpam-6473	293	17	y2	y2	NOUN
ejpam-6473	293	18	=	=	NOUN
ejpam-6473	293	19	1	1	NUM
ejpam-6473	293	20	2min(b1	2min(b1	NUM
ejpam-6473	293	21	,	,	PUNCT
ejpam-6473	293	22	b2	b2	NOUN
ejpam-6473	293	23	,	,	PUNCT
ejpam-6473	293	24	b3	b3	PROPN
ejpam-6473	293	25	)	)	PUNCT
ejpam-6473	293	26	,	,	PUNCT
ejpam-6473	293	27	y3	y3	NOUN
ejpam-6473	293	28	=	=	SYM
ejpam-6473	293	29	b3u3	b3u3	NOUN
ejpam-6473	293	30	2	2	NUM
ejpam-6473	293	31	.	.	PUNCT
ejpam-6473	294	1	(	(	PUNCT
ejpam-6473	294	2	i	i	NOUN
ejpam-6473	294	3	)	)	PUNCT
ejpam-6473	294	4	to	to	PART
ejpam-6473	294	5	proof	proof	VERB
ejpam-6473	294	6	the	the	DET
ejpam-6473	294	7	above	above	ADJ
ejpam-6473	294	8	conditions	condition	NOUN
ejpam-6473	294	9	,	,	PUNCT
ejpam-6473	294	10	we	we	PRON
ejpam-6473	294	11	use	use	VERB
ejpam-6473	294	12	the	the	DET
ejpam-6473	294	13	result	result	NOUN
ejpam-6473	294	14	by	by	ADP
ejpam-6473	294	15	luke	luke	PROPN
ejpam-6473	295	1	[	[	X
ejpam-6473	295	2	28	28	NUM
ejpam-6473	295	3	]	]	PUNCT
ejpam-6473	295	4	to	to	PART
ejpam-6473	295	5	establish	establish	VERB
ejpam-6473	295	6	the	the	DET
ejpam-6473	295	7	existence	existence	NOUN
ejpam-6473	295	8	solution	solution	NOUN
ejpam-6473	295	9	of	of	ADP
ejpam-6473	295	10	system	system	NOUN
ejpam-6473	295	11	with	with	ADP
ejpam-6473	295	12	bounded	bounded	ADJ
ejpam-6473	295	13	coefficient	coefficient	NOUN
ejpam-6473	295	14	,	,	PUNCT
ejpam-6473	295	15	which	which	PRON
ejpam-6473	295	16	verified	verify	VERB
ejpam-6473	295	17	the	the	DET
ejpam-6473	295	18	condition	condition	NOUN
ejpam-6473	295	19	1	1	NUM
ejpam-6473	295	20	.	.	PUNCT
ejpam-6473	296	1	the	the	DET
ejpam-6473	296	2	system	system	NOUN
ejpam-6473	296	3	can	can	AUX
ejpam-6473	296	4	be	be	AUX
ejpam-6473	296	5	expressed	express	VERB
ejpam-6473	296	6	as	as	ADP
ejpam-6473	296	7	r(x	r(x	PROPN
ejpam-6473	296	8	)	)	PUNCT
ejpam-6473	297	1	=	=	SYM
ejpam-6473	297	2	y	y	PROPN
ejpam-6473	297	3	x+o(x	x+o(x	NUM
ejpam-6473	297	4	)	)	PUNCT
ejpam-6473	297	5	,	,	PUNCT
ejpam-6473	297	6	where	where	SCONJ
ejpam-6473	297	7	state	state	NOUN
ejpam-6473	297	8	variables	variable	NOUN
ejpam-6473	297	9	are	be	AUX
ejpam-6473	297	10	x(t	x(t	PROPN
ejpam-6473	297	11	)	)	PUNCT
ejpam-6473	298	1	=	=	SYM
ejpam-6473	298	2	(	(	PUNCT
ejpam-6473	298	3	p	p	X
ejpam-6473	298	4	(	(	PUNCT
ejpam-6473	298	5	t	t	PROPN
ejpam-6473	298	6	)	)	PUNCT
ejpam-6473	298	7	,	,	PUNCT
ejpam-6473	298	8	l(t	l(t	PROPN
ejpam-6473	298	9	)	)	PUNCT
ejpam-6473	298	10	,	,	PUNCT
ejpam-6473	298	11	s(t	s(t	PROPN
ejpam-6473	298	12	)	)	PUNCT
ejpam-6473	298	13	,	,	PUNCT
ejpam-6473	298	14	q(t))t	q(t))t	ADV
ejpam-6473	298	15	and	and	CCONJ
ejpam-6473	298	16	matrix	matrix	VERB
ejpam-6473	298	17	y	y	PROPN
ejpam-6473	298	18	and	and	CCONJ
ejpam-6473	298	19	o(x	o(x	PROPN
ejpam-6473	298	20	)	)	PUNCT
ejpam-6473	298	21	nonlinear	nonlinear	ADJ
ejpam-6473	298	22	function	function	NOUN
ejpam-6473	298	23	are	be	AUX
ejpam-6473	298	24	defined	define	VERB
ejpam-6473	298	25	as	as	ADP
ejpam-6473	298	26	below	below	ADV
ejpam-6473	298	27	:	:	PUNCT
ejpam-6473	298	28	y	y	NOUN
ejpam-6473	298	29	=	=	PUNCT
ejpam-6473	298	30			NOUN
ejpam-6473	298	31	−(b+	−(b+	ADP
ejpam-6473	298	32	µ+	µ+	X
ejpam-6473	298	33	a0u1	a0u1	X
ejpam-6473	298	34	)	)	PUNCT
ejpam-6473	299	1	π1u2	π1u2	X
ejpam-6473	299	2	π2u3	π2u3	X
ejpam-6473	299	3	0	0	NUM
ejpam-6473	299	4	0	0	NUM
ejpam-6473	299	5	−(b+	−(b+	NUM
ejpam-6473	299	6	µ+	µ+	PRON
ejpam-6473	299	7	ζ	ζ	NOUN
ejpam-6473	299	8	+	+	CCONJ
ejpam-6473	299	9	u2	u2	NOUN
ejpam-6473	299	10	)	)	PUNCT
ejpam-6473	299	11	0	0	NUM
ejpam-6473	299	12	0	0	NUM
ejpam-6473	299	13	0	0	NUM
ejpam-6473	299	14	ζ	ζ	NOUN
ejpam-6473	299	15	−(b+	−(b+	NUM
ejpam-6473	299	16	µ+	µ+	PROPN
ejpam-6473	299	17	δ	δ	PROPN
ejpam-6473	299	18	+	+	CCONJ
ejpam-6473	299	19	u3	u3	NOUN
ejpam-6473	299	20	)	)	PUNCT
ejpam-6473	299	21	0	0	PUNCT
ejpam-6473	300	1	a0u1	a0u1	PROPN
ejpam-6473	300	2	(	(	PUNCT
ejpam-6473	300	3	1−	1−	NUM
ejpam-6473	300	4	π1)u2	π1)u2	NOUN
ejpam-6473	300	5	(	(	PUNCT
ejpam-6473	300	6	1−	1−	NUM
ejpam-6473	300	7	π2)u3	π2)u3	NOUN
ejpam-6473	300	8	+	+	CCONJ
ejpam-6473	300	9	δ	δ	PROPN
ejpam-6473	300	10	−(b+	−(b+	NUM
ejpam-6473	300	11	µ	µ	NOUN
ejpam-6473	300	12	)	)	PUNCT
ejpam-6473	300	13			PROPN
ejpam-6473	300	14	,	,	PUNCT
ejpam-6473	300	15	s.	s.	PROPN
ejpam-6473	300	16	bano	bano	PROPN
ejpam-6473	300	17	et	et	PROPN
ejpam-6473	300	18	al	al	PROPN
ejpam-6473	300	19	.	.	PUNCT
ejpam-6473	300	20	/	/	SYM
ejpam-6473	300	21	eur	eur	PROPN
ejpam-6473	300	22	.	.	PUNCT
ejpam-6473	301	1	j.	j.	PROPN
ejpam-6473	301	2	pure	pure	PROPN
ejpam-6473	301	3	appl	appl	PROPN
ejpam-6473	301	4	.	.	PROPN
ejpam-6473	301	5	math	math	PROPN
ejpam-6473	301	6	,	,	PUNCT
ejpam-6473	301	7	18	18	NUM
ejpam-6473	301	8	(	(	PUNCT
ejpam-6473	301	9	4	4	NUM
ejpam-6473	301	10	)	)	PUNCT
ejpam-6473	301	11	(	(	PUNCT
ejpam-6473	301	12	2025	2025	NUM
ejpam-6473	301	13	)	)	PUNCT
ejpam-6473	301	14	,	,	PUNCT
ejpam-6473	301	15	6473	6473	NUM
ejpam-6473	301	16	16	16	NUM
ejpam-6473	301	17	of	of	ADP
ejpam-6473	301	18	38	38	NUM
ejpam-6473	301	19	o(x	o(x	NUM
ejpam-6473	301	20	)	)	PUNCT
ejpam-6473	302	1	=	=	SYM
ejpam-6473	302	2			NOUN
ejpam-6473	303	1	λ−	λ−	PROPN
ejpam-6473	303	2	βps(1	βps(1	X
ejpam-6473	303	3	+	+	CCONJ
ejpam-6473	303	4	νs	νs	NOUN
ejpam-6473	303	5	)	)	PUNCT
ejpam-6473	303	6	βps(1	βps(1	NOUN
ejpam-6473	303	7	+	+	CCONJ
ejpam-6473	303	8	νs	νs	NOUN
ejpam-6473	303	9	)	)	PUNCT
ejpam-6473	303	10	0	0	NUM
ejpam-6473	303	11	0	0	NUM
ejpam-6473	303	12			NOUN
ejpam-6473	303	13	,	,	PUNCT
ejpam-6473	303	14	let	let	AUX
ejpam-6473	303	15	set	set	VERB
ejpam-6473	303	16	x1	x1	NOUN
ejpam-6473	303	17	=	=	SYM
ejpam-6473	303	18	(	(	PUNCT
ejpam-6473	303	19	p1	p1	PROPN
ejpam-6473	303	20	,	,	PUNCT
ejpam-6473	303	21	l1	l1	PROPN
ejpam-6473	303	22	,	,	PUNCT
ejpam-6473	303	23	s1	s1	PROPN
ejpam-6473	303	24	,	,	PUNCT
ejpam-6473	303	25	q1	q1	PROPN
ejpam-6473	303	26	)	)	PUNCT
ejpam-6473	303	27	,	,	PUNCT
ejpam-6473	303	28	x2	x2	NOUN
ejpam-6473	303	29	=	=	PRON
ejpam-6473	303	30	(	(	PUNCT
ejpam-6473	303	31	p2	p2	NOUN
ejpam-6473	303	32	,	,	PUNCT
ejpam-6473	303	33	l2	l2	NOUN
ejpam-6473	303	34	,	,	PUNCT
ejpam-6473	303	35	s2	s2	NOUN
ejpam-6473	303	36	,	,	PUNCT
ejpam-6473	303	37	q2	q2	NOUN
ejpam-6473	303	38	)	)	PUNCT
ejpam-6473	303	39	done	do	VERB
ejpam-6473	303	40	in	in	ADP
ejpam-6473	303	41	similar	similar	ADJ
ejpam-6473	303	42	manner	manner	NOUN
ejpam-6473	303	43	as	as	SCONJ
ejpam-6473	303	44	it	it	PRON
ejpam-6473	303	45	is	be	AUX
ejpam-6473	303	46	done	do	VERB
ejpam-6473	303	47	in	in	ADP
ejpam-6473	303	48	[	[	X
ejpam-6473	303	49	32	32	NUM
ejpam-6473	303	50	]	]	PUNCT
ejpam-6473	303	51	|r(x1)−r(x2)|	|r(x1)−r(x2)|	X
ejpam-6473	303	52	≤	≤	PUNCT
ejpam-6473	303	53	||y	||y	PROPN
ejpam-6473	304	1	|||x1	|||x1	ADP
ejpam-6473	304	2	−	−	PROPN
ejpam-6473	304	3	x2|+	x2|+	PROPN
ejpam-6473	304	4	|o(x1)−o(x2)|	|o(x1)−o(x2)|	PROPN
ejpam-6473	304	5	,	,	PUNCT
ejpam-6473	304	6	o(x1)−o(x2	o(x1)−o(x2	NOUN
ejpam-6473	304	7	)	)	PUNCT
ejpam-6473	304	8	=	=	SYM
ejpam-6473	304	9	(	(	PUNCT
ejpam-6473	304	10	−βp1s1(1	−βp1s1(1	PROPN
ejpam-6473	304	11	+	+	CCONJ
ejpam-6473	304	12	νs1	νs1	ADJ
ejpam-6473	304	13	)	)	PUNCT
ejpam-6473	305	1	+	+	NUM
ejpam-6473	305	2	βp2s2(1	βp2s2(1	NOUN
ejpam-6473	305	3	+	+	CCONJ
ejpam-6473	305	4	νs2	νs2	NOUN
ejpam-6473	305	5	)	)	PUNCT
ejpam-6473	305	6	βp1s1(1	βp1s1(1	VERB
ejpam-6473	305	7	+	+	CCONJ
ejpam-6473	305	8	νs1)−	νs1)−	PROPN
ejpam-6473	305	9	βp2s2(1	βp2s2(1	NOUN
ejpam-6473	305	10	+	+	CCONJ
ejpam-6473	305	11	νs2	νs2	NOUN
ejpam-6473	305	12	)	)	PUNCT
ejpam-6473	305	13	)	)	PUNCT
ejpam-6473	305	14	,	,	PUNCT
ejpam-6473	305	15	now	now	ADV
ejpam-6473	305	16	,	,	PUNCT
ejpam-6473	305	17	|o(x1)−o(x2)|	|o(x1)−o(x2)|	PROPN
ejpam-6473	305	18	=	=	SYM
ejpam-6473	305	19	|	|	ADV
ejpam-6473	305	20	−	−	NOUN
ejpam-6473	305	21	βp1s1(1	βp1s1(1	VERB
ejpam-6473	305	22	+	+	CCONJ
ejpam-6473	305	23	νs1	νs1	ADJ
ejpam-6473	305	24	)	)	PUNCT
ejpam-6473	306	1	+	+	CCONJ
ejpam-6473	306	2	βp2s2(1	βp2s2(1	NOUN
ejpam-6473	306	3	+	+	CCONJ
ejpam-6473	306	4	νs2)|	νs2)|	PROPN
ejpam-6473	306	5	+	+	PROPN
ejpam-6473	306	6	|βp1s1(1	|βp1s1(1	NOUN
ejpam-6473	306	7	+	+	CCONJ
ejpam-6473	306	8	νs1)−	νs1)−	PROPN
ejpam-6473	306	9	βp2s2(1	βp2s2(1	NOUN
ejpam-6473	306	10	+	+	CCONJ
ejpam-6473	306	11	νs2)|	νs2)|	PROPN
ejpam-6473	306	12	,	,	PUNCT
ejpam-6473	306	13	|o(x1)−o(x2)|	|o(x1)−o(x2)|	VERB
ejpam-6473	306	14	≤	≤	NOUN
ejpam-6473	306	15	(	(	PUNCT
ejpam-6473	306	16	2β|s1|+	2β|s1|+	NUM
ejpam-6473	306	17	2νβ|s2	2νβ|s2	NUM
ejpam-6473	306	18	1	1	NUM
ejpam-6473	306	19	|)|p1	|)|p1	NOUN
ejpam-6473	306	20	−	−	NOUN
ejpam-6473	306	21	p2|	p2|	PROPN
ejpam-6473	307	1	+	+	PROPN
ejpam-6473	307	2	(	(	PUNCT
ejpam-6473	307	3	2β|p2|+	2β|p2|+	NUM
ejpam-6473	307	4	2νβ|p2||s1	2νβ|p2||s1	NUM
ejpam-6473	308	1	+	+	CCONJ
ejpam-6473	308	2	s2|)|s1	s2|)|s1	PROPN
ejpam-6473	308	3	−	−	PROPN
ejpam-6473	308	4	s2|	s2|	PROPN
ejpam-6473	308	5	,	,	PUNCT
ejpam-6473	308	6	|o(x1)−o(x2)|	|o(x1)−o(x2)|	VERB
ejpam-6473	308	7	≤	≤	ADJ
ejpam-6473	308	8	2βλ	2βλ	NOUN
ejpam-6473	308	9	(	(	PUNCT
ejpam-6473	308	10	b+µ	b+µ	NOUN
ejpam-6473	308	11	)	)	PUNCT
ejpam-6473	308	12	(	(	PUNCT
ejpam-6473	308	13	1	1	X
ejpam-6473	308	14	+	+	NUM
ejpam-6473	308	15	νλ	νλ	INTJ
ejpam-6473	308	16	(	(	PUNCT
ejpam-6473	308	17	b+µ	b+µ	NOUN
ejpam-6473	308	18	)	)	PUNCT
ejpam-6473	308	19	)	)	PUNCT
ejpam-6473	309	1	(	(	PUNCT
ejpam-6473	309	2	|p1	|p1	NUM
ejpam-6473	309	3	−	−	PROPN
ejpam-6473	309	4	p2|+	p2|+	ADJ
ejpam-6473	309	5	|s1	|s1	NOUN
ejpam-6473	309	6	−	−	PROPN
ejpam-6473	309	7	s2|	s2|	PROPN
ejpam-6473	309	8	)	)	PUNCT
ejpam-6473	309	9	,	,	PUNCT
ejpam-6473	309	10	|r(x1)−r(x2)|	|r(x1)−r(x2)|	X
ejpam-6473	309	11	≤	≤	PUNCT
ejpam-6473	309	12	h|x1	h|x1	PROPN
ejpam-6473	309	13	−	−	PROPN
ejpam-6473	309	14	x2|	x2|	PROPN
ejpam-6473	309	15	.	.	PUNCT
ejpam-6473	310	1	here	here	ADV
ejpam-6473	310	2	,	,	PUNCT
ejpam-6473	310	3	h	h	NOUN
ejpam-6473	310	4	=	=	SYM
ejpam-6473	310	5	max	max	PROPN
ejpam-6473	310	6	{	{	PUNCT
ejpam-6473	310	7	(	(	PUNCT
ejpam-6473	310	8	2βλ	2βλ	NOUN
ejpam-6473	310	9	(	(	PUNCT
ejpam-6473	310	10	b+µ	b+µ	NOUN
ejpam-6473	310	11	)	)	PUNCT
ejpam-6473	311	1	[	[	X
ejpam-6473	311	2	1	1	NUM
ejpam-6473	311	3	+	+	NUM
ejpam-6473	311	4	νλ	νλ	INTJ
ejpam-6473	311	5	(	(	PUNCT
ejpam-6473	311	6	b+µ	b+µ	NOUN
ejpam-6473	311	7	)	)	PUNCT
ejpam-6473	311	8	]	]	PUNCT
ejpam-6473	311	9	,	,	PUNCT
ejpam-6473	311	10	||y	||y	PROPN
ejpam-6473	311	11	||	||	NOUN
ejpam-6473	311	12	}	}	PUNCT
ejpam-6473	311	13	<	<	X
ejpam-6473	311	14	∞.	∞.	PROPN
ejpam-6473	311	15	this	this	DET
ejpam-6473	311	16	show	show	VERB
ejpam-6473	311	17	that	that	SCONJ
ejpam-6473	311	18	function	function	NOUN
ejpam-6473	311	19	r(x	r(x	PROPN
ejpam-6473	311	20	)	)	PUNCT
ejpam-6473	311	21	is	be	AUX
ejpam-6473	311	22	uniformly	uniformly	ADV
ejpam-6473	311	23	lipchitz	lipchitz	VERB
ejpam-6473	311	24	continuous	continuous	ADJ
ejpam-6473	311	25	(	(	PUNCT
ejpam-6473	311	26	satisfy	satisfy	VERB
ejpam-6473	311	27	the	the	DET
ejpam-6473	311	28	assumption	assumption	NOUN
ejpam-6473	311	29	of	of	ADP
ejpam-6473	311	30	condition	condition	NOUN
ejpam-6473	311	31	1	1	NUM
ejpam-6473	311	32	)	)	PUNCT
ejpam-6473	311	33	.	.	PUNCT
ejpam-6473	312	1	u	u	PRON
ejpam-6473	312	2	control	control	NOUN
ejpam-6473	312	3	set	set	VERB
ejpam-6473	312	4	is	be	AUX
ejpam-6473	312	5	nonempty	nonempty	ADJ
ejpam-6473	312	6	because	because	SCONJ
ejpam-6473	312	7	it	it	PRON
ejpam-6473	312	8	contain	contain	VERB
ejpam-6473	312	9	the	the	DET
ejpam-6473	312	10	measurable	measurable	ADJ
ejpam-6473	312	11	function	function	NOUN
ejpam-6473	312	12	and	and	CCONJ
ejpam-6473	312	13	bounded	bound	VERB
ejpam-6473	312	14	by	by	ADP
ejpam-6473	312	15	0	0	NUM
ejpam-6473	312	16	≤	≤	NUM
ejpam-6473	312	17	uj(t	uj(t	PUNCT
ejpam-6473	312	18	)	)	PUNCT
ejpam-6473	312	19	≤	≤	NUM
ejpam-6473	312	20	umax	umax	ADJ
ejpam-6473	312	21	j	j	PROPN
ejpam-6473	312	22	where	where	SCONJ
ejpam-6473	312	23	j	j	PROPN
ejpam-6473	312	24	=	=	SYM
ejpam-6473	312	25	1	1	NUM
ejpam-6473	312	26	,	,	PUNCT
ejpam-6473	312	27	2	2	NUM
ejpam-6473	312	28	,	,	PUNCT
ejpam-6473	312	29	3	3	NUM
ejpam-6473	312	30	for	for	ADP
ejpam-6473	312	31	example	example	NOUN
ejpam-6473	312	32	constant	constant	ADJ
ejpam-6473	312	33	zero	zero	NUM
ejpam-6473	312	34	control	control	NOUN
ejpam-6473	312	35	u(t)=(0,0,0	u(t)=(0,0,0	NOUN
ejpam-6473	312	36	)	)	PUNCT
ejpam-6473	312	37	.	.	PUNCT
ejpam-6473	313	1	(	(	PUNCT
ejpam-6473	313	2	ii	ii	NOUN
ejpam-6473	313	3	)	)	PUNCT
ejpam-6473	313	4	as	as	SCONJ
ejpam-6473	313	5	control	control	NOUN
ejpam-6473	313	6	set	set	VERB
ejpam-6473	313	7	u	u	NOUN
ejpam-6473	313	8	is	be	AUX
ejpam-6473	313	9	closed	close	VERB
ejpam-6473	313	10	by	by	ADP
ejpam-6473	313	11	definition	definition	NOUN
ejpam-6473	313	12	and	and	CCONJ
ejpam-6473	313	13	each	each	DET
ejpam-6473	313	14	component	component	NOUN
ejpam-6473	313	15	of	of	ADP
ejpam-6473	313	16	u	u	PRON
ejpam-6473	313	17	lies	lie	VERB
ejpam-6473	313	18	in	in	ADP
ejpam-6473	313	19	[	[	X
ejpam-6473	313	20	0,1	0,1	NUM
ejpam-6473	313	21	]	]	PUNCT
ejpam-6473	313	22	and	and	CCONJ
ejpam-6473	313	23	for	for	ADP
ejpam-6473	313	24	any	any	DET
ejpam-6473	313	25	u1	u1	NOUN
ejpam-6473	313	26	=	=	SYM
ejpam-6473	313	27	(	(	PUNCT
ejpam-6473	313	28	u11	u11	PROPN
ejpam-6473	313	29	,	,	PUNCT
ejpam-6473	313	30	u	u	NOUN
ejpam-6473	313	31	1	1	NUM
ejpam-6473	313	32	2	2	NUM
ejpam-6473	313	33	,	,	PUNCT
ejpam-6473	313	34	u	u	NOUN
ejpam-6473	313	35	1	1	NUM
ejpam-6473	313	36	3	3	NUM
ejpam-6473	313	37	)	)	PUNCT
ejpam-6473	313	38	∈	∈	PROPN
ejpam-6473	313	39	u	u	NOUN
ejpam-6473	313	40	and	and	CCONJ
ejpam-6473	313	41	u2	u2	PROPN
ejpam-6473	313	42	=	=	SYM
ejpam-6473	313	43	(	(	PUNCT
ejpam-6473	313	44	u21	u21	PROPN
ejpam-6473	313	45	,	,	PUNCT
ejpam-6473	313	46	u	u	NOUN
ejpam-6473	313	47	2	2	NUM
ejpam-6473	313	48	2	2	NUM
ejpam-6473	313	49	,	,	PUNCT
ejpam-6473	313	50	u	u	NOUN
ejpam-6473	313	51	2	2	NUM
ejpam-6473	313	52	3	3	NUM
ejpam-6473	313	53	)	)	PUNCT
ejpam-6473	313	54	∈	∈	PROPN
ejpam-6473	313	55	u	u	NOUN
ejpam-6473	313	56	and	and	CCONJ
ejpam-6473	313	57	q	q	NOUN
ejpam-6473	313	58	∈	∈	PROPN
ejpam-6473	314	1	[	[	X
ejpam-6473	314	2	0	0	NUM
ejpam-6473	314	3	,	,	PUNCT
ejpam-6473	314	4	1	1	NUM
ejpam-6473	314	5	]	]	PUNCT
ejpam-6473	314	6	and	and	CCONJ
ejpam-6473	314	7	u	u	X
ejpam-6473	314	8	=	=	SYM
ejpam-6473	314	9	ru1	ru1	PROPN
ejpam-6473	314	10	+	+	CCONJ
ejpam-6473	314	11	(	(	PUNCT
ejpam-6473	314	12	1	1	NUM
ejpam-6473	314	13	−	−	NOUN
ejpam-6473	314	14	r)u2	r)u2	NOUN
ejpam-6473	314	15	for	for	ADP
ejpam-6473	314	16	each	each	DET
ejpam-6473	314	17	j	j	PROPN
ejpam-6473	314	18	,	,	PUNCT
ejpam-6473	314	19	0	0	NUM
ejpam-6473	314	20	≤	≤	X
ejpam-6473	314	21	u1j	u1j	ADV
ejpam-6473	314	22	≤	≤	NUM
ejpam-6473	314	23	umax	umax	ADJ
ejpam-6473	314	24	j	j	PROPN
ejpam-6473	314	25	≤	≤	ADV
ejpam-6473	314	26	1	1	NUM
ejpam-6473	314	27	,	,	PUNCT
ejpam-6473	314	28	0	0	NUM
ejpam-6473	314	29	≤	≤	NUM
ejpam-6473	314	30	u2j	u2j	ADJ
ejpam-6473	314	31	≤	≤	PROPN
ejpam-6473	314	32	umax	umax	ADJ
ejpam-6473	314	33	j	j	PROPN
ejpam-6473	314	34	≤	≤	ADV
ejpam-6473	314	35	1	1	NUM
ejpam-6473	314	36	this	this	PRON
ejpam-6473	314	37	shows	show	VERB
ejpam-6473	314	38	the	the	DET
ejpam-6473	314	39	convex	convex	ADJ
ejpam-6473	314	40	combination	combination	NOUN
ejpam-6473	314	41	defined	define	VERB
ejpam-6473	314	42	by	by	ADP
ejpam-6473	314	43	0	0	NUM
ejpam-6473	314	44	≤	≤	NOUN
ejpam-6473	314	45	qu1j	qu1j	ADV
ejpam-6473	314	46	+	+	SYM
ejpam-6473	314	47	(	(	PUNCT
ejpam-6473	314	48	1	1	NUM
ejpam-6473	314	49	−	−	PRON
ejpam-6473	314	50	q)u2j	q)u2j	NOUN
ejpam-6473	314	51	≤	≤	NUM
ejpam-6473	314	52	umax	umax	ADJ
ejpam-6473	314	53	j	j	PROPN
ejpam-6473	314	54	≤	≤	ADV
ejpam-6473	314	55	1	1	NUM
ejpam-6473	314	56	,	,	PUNCT
ejpam-6473	314	57	where	where	SCONJ
ejpam-6473	314	58	j=1,2,3	j=1,2,3	NUM
ejpam-6473	314	59	remain	remain	VERB
ejpam-6473	314	60	in	in	ADP
ejpam-6473	314	61	[	[	X
ejpam-6473	314	62	0,1	0,1	NUM
ejpam-6473	314	63	]	]	PUNCT
ejpam-6473	314	64	,	,	PUNCT
ejpam-6473	314	65	this	this	PRON
ejpam-6473	314	66	means	mean	VERB
ejpam-6473	314	67	u	u	PROPN
ejpam-6473	314	68	∈	∈	PROPN
ejpam-6473	314	69	u	u	NOUN
ejpam-6473	314	70	.	.	PUNCT
ejpam-6473	315	1	this	this	PRON
ejpam-6473	315	2	implies	imply	VERB
ejpam-6473	315	3	that	that	SCONJ
ejpam-6473	315	4	u	u	NOUN
ejpam-6473	315	5	is	be	AUX
ejpam-6473	315	6	convex	convex	ADJ
ejpam-6473	315	7	.	.	PUNCT
ejpam-6473	316	1	this	this	PRON
ejpam-6473	316	2	proves	prove	VERB
ejpam-6473	316	3	the	the	DET
ejpam-6473	316	4	condition	condition	NOUN
ejpam-6473	316	5	(	(	PUNCT
ejpam-6473	316	6	2	2	NUM
ejpam-6473	316	7	)	)	PUNCT
ejpam-6473	316	8	(	(	PUNCT
ejpam-6473	316	9	iii	iii	NOUN
ejpam-6473	316	10	)	)	PUNCT
ejpam-6473	316	11	to	to	PART
ejpam-6473	316	12	prove	prove	VERB
ejpam-6473	316	13	the	the	DET
ejpam-6473	316	14	integrand	integrand	NOUN
ejpam-6473	316	15	function	function	NOUN
ejpam-6473	316	16	is	be	AUX
ejpam-6473	316	17	convex	convex	ADJ
ejpam-6473	316	18	,	,	PUNCT
ejpam-6473	316	19	we	we	PRON
ejpam-6473	316	20	let	let	VERB
ejpam-6473	316	21	λ	λ	X
ejpam-6473	316	22	∈	∈	PROPN
ejpam-6473	316	23	[	[	X
ejpam-6473	316	24	0	0	NUM
ejpam-6473	316	25	,	,	PUNCT
ejpam-6473	316	26	1	1	NUM
ejpam-6473	316	27	]	]	PUNCT
ejpam-6473	316	28	,	,	PUNCT
ejpam-6473	316	29	s	s	PROPN
ejpam-6473	316	30	∈	∈	PROPN
ejpam-6473	316	31	(	(	PUNCT
ejpam-6473	316	32	s1	s1	NOUN
ejpam-6473	316	33	,	,	PUNCT
ejpam-6473	316	34	s2	s2	PROPN
ejpam-6473	316	35	,	,	PUNCT
ejpam-6473	316	36	s3	s3	PROPN
ejpam-6473	316	37	)	)	PUNCT
ejpam-6473	316	38	and	and	CCONJ
ejpam-6473	316	39	a	a	DET
ejpam-6473	316	40	∈	∈	PROPN
ejpam-6473	316	41	(	(	PUNCT
ejpam-6473	316	42	a1	a1	PROPN
ejpam-6473	316	43	,	,	PUNCT
ejpam-6473	316	44	a2	a2	PROPN
ejpam-6473	316	45	,	,	PUNCT
ejpam-6473	316	46	a3	a3	NOUN
ejpam-6473	316	47	)	)	PUNCT
ejpam-6473	316	48	,	,	PUNCT
ejpam-6473	316	49	x	x	PUNCT
ejpam-6473	316	50	∈	∈	PROPN
ejpam-6473	316	51	(	(	PUNCT
ejpam-6473	316	52	p	p	X
ejpam-6473	316	53	,	,	PUNCT
ejpam-6473	316	54	l	l	NOUN
ejpam-6473	316	55	,	,	PUNCT
ejpam-6473	316	56	s	s	X
ejpam-6473	316	57	,	,	PUNCT
ejpam-6473	316	58	q	q	NOUN
ejpam-6473	316	59	)	)	PUNCT
ejpam-6473	316	60	and	and	CCONJ
ejpam-6473	316	61	we	we	PRON
ejpam-6473	316	62	need	need	VERB
ejpam-6473	316	63	to	to	PART
ejpam-6473	316	64	show	show	VERB
ejpam-6473	316	65	that	that	SCONJ
ejpam-6473	316	66	l(x	l(x	PROPN
ejpam-6473	316	67	,	,	PUNCT
ejpam-6473	316	68	(	(	PUNCT
ejpam-6473	316	69	1−	1−	NUM
ejpam-6473	316	70	λ)s+	λ)s+	NUM
ejpam-6473	316	71	λa	λa	NOUN
ejpam-6473	316	72	)	)	PUNCT
ejpam-6473	316	73	)	)	PUNCT
ejpam-6473	316	74	≤	≤	NOUN
ejpam-6473	316	75	(	(	PUNCT
ejpam-6473	316	76	1−	1−	NUM
ejpam-6473	316	77	λ)l(x	λ)l(x	PROPN
ejpam-6473	316	78	,	,	PUNCT
ejpam-6473	316	79	s	s	PART
ejpam-6473	316	80	)	)	PUNCT
ejpam-6473	317	1	+	+	NUM
ejpam-6473	317	2	λl(x	λl(x	PROPN
ejpam-6473	317	3	,	,	PUNCT
ejpam-6473	317	4	a	a	PRON
ejpam-6473	317	5	)	)	PUNCT
ejpam-6473	317	6	l(x	l(x	PROPN
ejpam-6473	317	7	,	,	PUNCT
ejpam-6473	317	8	(	(	PUNCT
ejpam-6473	317	9	1−	1−	NUM
ejpam-6473	317	10	λ)s+	λ)s+	NOUN
ejpam-6473	317	11	λa))−	λa))−	NOUN
ejpam-6473	317	12	(	(	PUNCT
ejpam-6473	317	13	1−	1−	NUM
ejpam-6473	317	14	λ)l(x	λ)l(x	PROPN
ejpam-6473	317	15	,	,	PUNCT
ejpam-6473	317	16	s)−	s)−	PROPN
ejpam-6473	317	17	λl(x	λl(x	X
ejpam-6473	317	18	,	,	PUNCT
ejpam-6473	317	19	a	a	PRON
ejpam-6473	317	20	)	)	PUNCT
ejpam-6473	317	21	s.	s.	PROPN
ejpam-6473	317	22	bano	bano	PROPN
ejpam-6473	317	23	et	et	PROPN
ejpam-6473	317	24	al	al	PROPN
ejpam-6473	317	25	.	.	PUNCT
ejpam-6473	317	26	/	/	SYM
ejpam-6473	317	27	eur	eur	PROPN
ejpam-6473	317	28	.	.	PUNCT
ejpam-6473	318	1	j.	j.	PROPN
ejpam-6473	318	2	pure	pure	PROPN
ejpam-6473	318	3	appl	appl	PROPN
ejpam-6473	318	4	.	.	PROPN
ejpam-6473	318	5	math	math	PROPN
ejpam-6473	318	6	,	,	PUNCT
ejpam-6473	318	7	18	18	NUM
ejpam-6473	318	8	(	(	PUNCT
ejpam-6473	318	9	4	4	NUM
ejpam-6473	318	10	)	)	PUNCT
ejpam-6473	318	11	(	(	PUNCT
ejpam-6473	318	12	2025	2025	NUM
ejpam-6473	318	13	)	)	PUNCT
ejpam-6473	318	14	,	,	PUNCT
ejpam-6473	318	15	6473	6473	NUM
ejpam-6473	318	16	17	17	NUM
ejpam-6473	318	17	of	of	ADP
ejpam-6473	318	18	38	38	NUM
ejpam-6473	318	19	=	=	NOUN
ejpam-6473	318	20	d1l+d2s	d1l+d2s	PROPN
ejpam-6473	318	21	−d3p	−d3p	NUM
ejpam-6473	318	22	−d4q+	−d4q+	NOUN
ejpam-6473	318	23	b1	b1	NOUN
ejpam-6473	318	24	2	2	NUM
ejpam-6473	318	25	(	(	PUNCT
ejpam-6473	318	26	(	(	PUNCT
ejpam-6473	318	27	1−	1−	NUM
ejpam-6473	318	28	λ)s1	λ)s1	NOUN
ejpam-6473	318	29	+	+	NUM
ejpam-6473	318	30	λa1	λa1	PROPN
ejpam-6473	318	31	)	)	PUNCT
ejpam-6473	318	32	2	2	NUM
ejpam-6473	319	1	+	+	NUM
ejpam-6473	319	2	b2	b2	NOUN
ejpam-6473	319	3	2	2	NUM
ejpam-6473	319	4	(	(	PUNCT
ejpam-6473	319	5	(	(	PUNCT
ejpam-6473	319	6	1−	1−	NUM
ejpam-6473	319	7	λ)s2	λ)s2	NOUN
ejpam-6473	319	8	+	+	CCONJ
ejpam-6473	319	9	λa2	λa2	NOUN
ejpam-6473	319	10	)	)	PUNCT
ejpam-6473	319	11	2	2	NUM
ejpam-6473	319	12	+	+	NUM
ejpam-6473	319	13	b3	b3	NOUN
ejpam-6473	319	14	2	2	NUM
ejpam-6473	319	15	(	(	PUNCT
ejpam-6473	319	16	(	(	PUNCT
ejpam-6473	319	17	1−	1−	NUM
ejpam-6473	319	18	λ)s3	λ)s3	PROPN
ejpam-6473	319	19	+	+	CCONJ
ejpam-6473	319	20	λa3	λa3	NOUN
ejpam-6473	319	21	)	)	PUNCT
ejpam-6473	319	22	2	2	NUM
ejpam-6473	319	23	−	−	PROPN
ejpam-6473	319	24	(	(	PUNCT
ejpam-6473	319	25	1−	1−	NUM
ejpam-6473	319	26	λ	λ	NOUN
ejpam-6473	319	27	)	)	PUNCT
ejpam-6473	319	28	(	(	PUNCT
ejpam-6473	319	29	d1l+d2s	d1l+d2s	PROPN
ejpam-6473	319	30	−d3p	−d3p	PROPN
ejpam-6473	319	31	−d4q	−d4q	PROPN
ejpam-6473	319	32	)	)	PUNCT
ejpam-6473	319	33	−	−	PROPN
ejpam-6473	320	1	(	(	PUNCT
ejpam-6473	320	2	1−	1−	NUM
ejpam-6473	320	3	λ	λ	NOUN
ejpam-6473	320	4	)	)	PUNCT
ejpam-6473	320	5	b1	b1	NOUN
ejpam-6473	320	6	2	2	NUM
ejpam-6473	320	7	s21	s21	NOUN
ejpam-6473	320	8	−	−	NOUN
ejpam-6473	320	9	(	(	PUNCT
ejpam-6473	320	10	1−	1−	NUM
ejpam-6473	320	11	λ	λ	NOUN
ejpam-6473	320	12	)	)	PUNCT
ejpam-6473	320	13	b2	b2	NOUN
ejpam-6473	320	14	2	2	NUM
ejpam-6473	320	15	s22	s22	NOUN
ejpam-6473	320	16	−	−	PROPN
ejpam-6473	321	1	(	(	PUNCT
ejpam-6473	321	2	1−	1−	NUM
ejpam-6473	321	3	λ	λ	NOUN
ejpam-6473	321	4	)	)	PUNCT
ejpam-6473	321	5	b3	b3	PROPN
ejpam-6473	321	6	2	2	NUM
ejpam-6473	321	7	s23	s23	NOUN
ejpam-6473	321	8	−	−	PROPN
ejpam-6473	321	9	λ	λ	PROPN
ejpam-6473	321	10	(	(	PUNCT
ejpam-6473	321	11	d1l+d2s	d1l+d2s	PROPN
ejpam-6473	321	12	−d3p	−d3p	PROPN
ejpam-6473	321	13	−d4q	−d4q	PROPN
ejpam-6473	321	14	)	)	PUNCT
ejpam-6473	321	15	−λ	−λ	PROPN
ejpam-6473	321	16	b1	b1	PROPN
ejpam-6473	321	17	2	2	NUM
ejpam-6473	321	18	a21	a21	NOUN
ejpam-6473	321	19	−	−	PROPN
ejpam-6473	321	20	λ	λ	PROPN
ejpam-6473	321	21	b2	b2	NOUN
ejpam-6473	321	22	2	2	NUM
ejpam-6473	321	23	a22	a22	NOUN
ejpam-6473	321	24	−	−	PROPN
ejpam-6473	321	25	λ	λ	PROPN
ejpam-6473	321	26	b3	b3	PROPN
ejpam-6473	321	27	2	2	NUM
ejpam-6473	321	28	a23	a23	NOUN
ejpam-6473	321	29	,	,	PUNCT
ejpam-6473	321	30	=	=	SYM
ejpam-6473	321	31	b1	b1	NOUN
ejpam-6473	321	32	2	2	NUM
ejpam-6473	321	33	(	(	PUNCT
ejpam-6473	321	34	(	(	PUNCT
ejpam-6473	321	35	1−	1−	NUM
ejpam-6473	321	36	λ)2s21	λ)2s21	PUNCT
ejpam-6473	321	37	+	+	NUM
ejpam-6473	321	38	λ2a21	λ2a21	X
ejpam-6473	321	39	+	+	NOUN
ejpam-6473	321	40	2(1−	2(1−	NUM
ejpam-6473	321	41	λ)λs1a1	λ)λs1a1	X
ejpam-6473	321	42	−	−	PROPN
ejpam-6473	321	43	(	(	PUNCT
ejpam-6473	321	44	1−	1−	NUM
ejpam-6473	321	45	λ)a21	λ)a21	X
ejpam-6473	321	46	−	−	PROPN
ejpam-6473	321	47	λa21	λa21	PROPN
ejpam-6473	321	48	)	)	PUNCT
ejpam-6473	322	1	+	+	NUM
ejpam-6473	322	2	b2	b2	NOUN
ejpam-6473	322	3	2	2	NUM
ejpam-6473	322	4	(	(	PUNCT
ejpam-6473	322	5	(	(	PUNCT
ejpam-6473	322	6	1−	1−	NUM
ejpam-6473	322	7	λ)2s22	λ)2s22	SYM
ejpam-6473	322	8	+	+	PUNCT
ejpam-6473	322	9	λ2a22	λ2a22	NOUN
ejpam-6473	322	10	+	+	CCONJ
ejpam-6473	322	11	2(1−	2(1−	NUM
ejpam-6473	322	12	λ)λs2a2	λ)λs2a2	X
ejpam-6473	322	13	−	−	PROPN
ejpam-6473	322	14	(	(	PUNCT
ejpam-6473	322	15	1−	1−	NUM
ejpam-6473	322	16	λ)s22	λ)s22	PUNCT
ejpam-6473	322	17	−	−	PROPN
ejpam-6473	322	18	λa22	λa22	PROPN
ejpam-6473	322	19	)	)	PUNCT
ejpam-6473	323	1	+	+	NUM
ejpam-6473	323	2	b3	b3	PROPN
ejpam-6473	323	3	2	2	NUM
ejpam-6473	323	4	(	(	PUNCT
ejpam-6473	323	5	(	(	PUNCT
ejpam-6473	323	6	1−	1−	NUM
ejpam-6473	323	7	λ)2s23	λ)2s23	X
ejpam-6473	323	8	+	+	CCONJ
ejpam-6473	323	9	λ2a23	λ2a23	PROPN
ejpam-6473	323	10	+	+	NUM
ejpam-6473	323	11	2(1−	2(1−	X
ejpam-6473	323	12	λ)λs3a3	λ)λs3a3	SYM
ejpam-6473	323	13	−	−	PROPN
ejpam-6473	323	14	(	(	PUNCT
ejpam-6473	323	15	1−	1−	NUM
ejpam-6473	323	16	λ)s23	λ)s23	PUNCT
ejpam-6473	323	17	−	−	PROPN
ejpam-6473	323	18	λa23	λa23	PROPN
ejpam-6473	323	19	)	)	PUNCT
ejpam-6473	323	20	,	,	PUNCT
ejpam-6473	323	21	=	=	PRON
ejpam-6473	323	22	(	(	PUNCT
ejpam-6473	323	23	λ−	λ−	PROPN
ejpam-6473	323	24	1)(λ	1)(λ	NUM
ejpam-6473	323	25	)	)	PUNCT
ejpam-6473	323	26	(	(	PUNCT
ejpam-6473	323	27	b1	b1	NOUN
ejpam-6473	323	28	2	2	NUM
ejpam-6473	323	29	(	(	PUNCT
ejpam-6473	323	30	s1	s1	PROPN
ejpam-6473	323	31	−	−	PROPN
ejpam-6473	323	32	a1	a1	NOUN
ejpam-6473	323	33	)	)	PUNCT
ejpam-6473	323	34	2	2	NUM
ejpam-6473	323	35	+	+	NUM
ejpam-6473	323	36	b2	b2	NOUN
ejpam-6473	323	37	2	2	NUM
ejpam-6473	323	38	(	(	PUNCT
ejpam-6473	323	39	s2	s2	NOUN
ejpam-6473	323	40	−	−	PROPN
ejpam-6473	323	41	a2	a2	PROPN
ejpam-6473	323	42	)	)	PUNCT
ejpam-6473	323	43	2	2	NUM
ejpam-6473	323	44	+	+	SYM
ejpam-6473	323	45	b3	b3	NOUN
ejpam-6473	323	46	2	2	NUM
ejpam-6473	323	47	(	(	PUNCT
ejpam-6473	323	48	s3	s3	PROPN
ejpam-6473	323	49	−	−	PROPN
ejpam-6473	323	50	a3	a3	NOUN
ejpam-6473	323	51	)	)	PUNCT
ejpam-6473	323	52	2	2	NUM
ejpam-6473	323	53	)	)	PUNCT
ejpam-6473	323	54	≤	≤	NOUN
ejpam-6473	323	55	0	0	NUM
ejpam-6473	323	56	.	.	PUNCT
ejpam-6473	324	1	=	=	NOUN
ejpam-6473	324	2	⇒	⇒	VERB
ejpam-6473	324	3	l(x	l(x	PROPN
ejpam-6473	324	4	,	,	PUNCT
ejpam-6473	324	5	(	(	PUNCT
ejpam-6473	324	6	1−	1−	NUM
ejpam-6473	324	7	λ)s+	λ)s+	NUM
ejpam-6473	324	8	λa	λa	NOUN
ejpam-6473	324	9	)	)	PUNCT
ejpam-6473	324	10	)	)	PUNCT
ejpam-6473	324	11	≤	≤	NOUN
ejpam-6473	324	12	(	(	PUNCT
ejpam-6473	324	13	1−	1−	NUM
ejpam-6473	324	14	λ)l(x	λ)l(x	PROPN
ejpam-6473	324	15	,	,	PUNCT
ejpam-6473	324	16	s	s	PART
ejpam-6473	324	17	)	)	PUNCT
ejpam-6473	324	18	+	+	NUM
ejpam-6473	324	19	λl(x	λl(x	PROPN
ejpam-6473	324	20	,	,	PUNCT
ejpam-6473	324	21	a	a	PRON
ejpam-6473	324	22	)	)	PUNCT
ejpam-6473	324	23	.	.	PUNCT
ejpam-6473	325	1	condition	condition	NOUN
ejpam-6473	325	2	(	(	PUNCT
ejpam-6473	325	3	3	3	X
ejpam-6473	325	4	)	)	PUNCT
ejpam-6473	325	5	holds	hold	NOUN
ejpam-6473	325	6	.	.	PUNCT
ejpam-6473	326	1	(	(	PUNCT
ejpam-6473	326	2	iv	iv	X
ejpam-6473	326	3	)	)	PUNCT
ejpam-6473	326	4	now	now	ADV
ejpam-6473	326	5	x	x	X
ejpam-6473	326	6	=	=	SYM
ejpam-6473	326	7	(	(	PUNCT
ejpam-6473	326	8	p	p	X
ejpam-6473	326	9	,	,	PUNCT
ejpam-6473	326	10	l	l	NOUN
ejpam-6473	326	11	,	,	PUNCT
ejpam-6473	326	12	s	s	X
ejpam-6473	326	13	,	,	PUNCT
ejpam-6473	326	14	q)t	q)t	ADJ
ejpam-6473	326	15	,	,	PUNCT
ejpam-6473	326	16	u	u	NOUN
ejpam-6473	326	17	=	=	PUNCT
ejpam-6473	326	18	(	(	PUNCT
ejpam-6473	326	19	u1	u1	PROPN
ejpam-6473	326	20	,	,	PUNCT
ejpam-6473	326	21	u2	u2	NOUN
ejpam-6473	326	22	,	,	PUNCT
ejpam-6473	326	23	u3	u3	PROPN
ejpam-6473	326	24	)	)	PUNCT
ejpam-6473	326	25	t	t	NOUN
ejpam-6473	326	26	.	.	PUNCT
ejpam-6473	327	1	now	now	ADV
ejpam-6473	327	2	for	for	ADP
ejpam-6473	327	3	the	the	DET
ejpam-6473	327	4	proof	proof	ADJ
ejpam-6473	327	5	condition	condition	NOUN
ejpam-6473	327	6	4	4	NUM
ejpam-6473	327	7	,	,	PUNCT
ejpam-6473	327	8	we	we	PRON
ejpam-6473	327	9	separate	separate	VERB
ejpam-6473	327	10	the	the	DET
ejpam-6473	327	11	system	system	NOUN
ejpam-6473	327	12	(	(	PUNCT
ejpam-6473	327	13	12	12	NUM
ejpam-6473	327	14	)	)	PUNCT
ejpam-6473	327	15	into	into	ADP
ejpam-6473	327	16	sub	sub	NOUN
ejpam-6473	327	17	matrix	matrix	NOUN
ejpam-6473	327	18	a(t	a(t	NOUN
ejpam-6473	327	19	,	,	PUNCT
ejpam-6473	327	20	x	x	NOUN
ejpam-6473	327	21	)	)	PUNCT
ejpam-6473	327	22	and	and	CCONJ
ejpam-6473	327	23	b(t	b(t	PROPN
ejpam-6473	327	24	,	,	PUNCT
ejpam-6473	327	25	x	x	NOUN
ejpam-6473	327	26	)	)	PUNCT
ejpam-6473	327	27	,	,	PUNCT
ejpam-6473	327	28	where	where	SCONJ
ejpam-6473	327	29	a(t	a(t	NOUN
ejpam-6473	327	30	,	,	PUNCT
ejpam-6473	327	31	x	x	X
ejpam-6473	327	32	)	)	PUNCT
ejpam-6473	327	33	is	be	AUX
ejpam-6473	327	34	the	the	DET
ejpam-6473	327	35	matrix	matrix	NOUN
ejpam-6473	327	36	of	of	ADP
ejpam-6473	327	37	dynamic	dynamic	ADJ
ejpam-6473	327	38	without	without	ADP
ejpam-6473	327	39	control	control	NOUN
ejpam-6473	327	40	,	,	PUNCT
ejpam-6473	327	41	b(t	b(t	PROPN
ejpam-6473	327	42	,	,	PUNCT
ejpam-6473	327	43	x	x	X
ejpam-6473	327	44	)	)	PUNCT
ejpam-6473	327	45	is	be	AUX
ejpam-6473	327	46	the	the	DET
ejpam-6473	327	47	state	state	NOUN
ejpam-6473	327	48	dependent	dependent	ADJ
ejpam-6473	327	49	control	control	NOUN
ejpam-6473	327	50	coefficient	coefficient	NOUN
ejpam-6473	327	51	matrix	matrix	NOUN
ejpam-6473	327	52	.	.	PUNCT
ejpam-6473	328	1	a(t	a(t	NOUN
ejpam-6473	328	2	,	,	PUNCT
ejpam-6473	328	3	x	x	NOUN
ejpam-6473	328	4	)	)	PUNCT
ejpam-6473	328	5	=	=	SYM
ejpam-6473	328	6			NOUN
ejpam-6473	329	1	λ−	λ−	PROPN
ejpam-6473	329	2	βps(1	βps(1	NOUN
ejpam-6473	329	3	+	+	CCONJ
ejpam-6473	329	4	νs)−	νs)−	NOUN
ejpam-6473	329	5	(	(	PUNCT
ejpam-6473	329	6	b+	b+	X
ejpam-6473	329	7	µ)p	µ)p	PUNCT
ejpam-6473	329	8	βps(1	βps(1	NOUN
ejpam-6473	329	9	+	+	CCONJ
ejpam-6473	329	10	νs)−	νs)−	NOUN
ejpam-6473	329	11	(	(	PUNCT
ejpam-6473	329	12	b+	b+	X
ejpam-6473	329	13	µ+	µ+	PRON
ejpam-6473	329	14	ζ)l	ζ)l	NOUN
ejpam-6473	329	15	ζl−	ζl−	PUNCT
ejpam-6473	329	16	(	(	PUNCT
ejpam-6473	329	17	b+	b+	X
ejpam-6473	329	18	µ+	µ+	X
ejpam-6473	329	19	δ)s	δ)s	ADJ
ejpam-6473	329	20	δs	δs	NOUN
ejpam-6473	329	21	−	−	PROPN
ejpam-6473	329	22	(	(	PUNCT
ejpam-6473	329	23	b+	b+	X
ejpam-6473	329	24	µ)q	µ)q	NOUN
ejpam-6473	329	25			NOUN
ejpam-6473	329	26	,	,	PUNCT
ejpam-6473	329	27	a(t	a(t	PROPN
ejpam-6473	329	28	,	,	PUNCT
ejpam-6473	329	29	x	x	X
ejpam-6473	329	30	)	)	PUNCT
ejpam-6473	329	31	is	be	AUX
ejpam-6473	329	32	the	the	DET
ejpam-6473	329	33	matrix	matrix	NOUN
ejpam-6473	329	34	that	that	PRON
ejpam-6473	329	35	represent	represent	VERB
ejpam-6473	329	36	the	the	DET
ejpam-6473	329	37	part	part	NOUN
ejpam-6473	329	38	of	of	ADP
ejpam-6473	329	39	system	system	NOUN
ejpam-6473	329	40	that	that	PRON
ejpam-6473	329	41	depend	depend	VERB
ejpam-6473	329	42	only	only	ADV
ejpam-6473	329	43	on	on	ADP
ejpam-6473	329	44	state	state	NOUN
ejpam-6473	329	45	variable	variable	NOUN
ejpam-6473	329	46	and	and	CCONJ
ejpam-6473	329	47	independent	independent	ADJ
ejpam-6473	329	48	of	of	ADP
ejpam-6473	329	49	control	control	NOUN
ejpam-6473	329	50	and	and	CCONJ
ejpam-6473	329	51	it	it	PRON
ejpam-6473	329	52	reflect	reflect	VERB
ejpam-6473	329	53	natural	natural	ADJ
ejpam-6473	329	54	behavior	behavior	NOUN
ejpam-6473	329	55	of	of	ADP
ejpam-6473	329	56	system	system	NOUN
ejpam-6473	329	57	,	,	PUNCT
ejpam-6473	329	58	including	include	VERB
ejpam-6473	329	59	its	its	PRON
ejpam-6473	329	60	inherent	inherent	ADJ
ejpam-6473	329	61	nonlinear	nonlinear	ADJ
ejpam-6473	329	62	behavior	behavior	NOUN
ejpam-6473	329	63	.	.	PUNCT
ejpam-6473	330	1	b(t	b(t	PROPN
ejpam-6473	330	2	,	,	PUNCT
ejpam-6473	330	3	x	x	NOUN
ejpam-6473	330	4	)	)	PUNCT
ejpam-6473	330	5	=	=	SYM
ejpam-6473	330	6			NOUN
ejpam-6473	330	7	−a0p	−a0p	X
ejpam-6473	330	8	π1l	π1l	PROPN
ejpam-6473	330	9	π2s	π2s	PROPN
ejpam-6473	330	10	0	0	PUNCT
ejpam-6473	331	1	−l	−l	NOUN
ejpam-6473	331	2	0	0	NUM
ejpam-6473	331	3	0	0	NUM
ejpam-6473	331	4	0	0	NUM
ejpam-6473	331	5	−s	−s	NOUN
ejpam-6473	331	6	a0p	a0p	NOUN
ejpam-6473	331	7	(	(	PUNCT
ejpam-6473	331	8	1−	1−	NUM
ejpam-6473	331	9	π1)l	π1)l	NOUN
ejpam-6473	331	10	(	(	PUNCT
ejpam-6473	331	11	1−	1−	NUM
ejpam-6473	331	12	π2)s	π2)s	ADJ
ejpam-6473	331	13			NOUN
ejpam-6473	331	14	,	,	PUNCT
ejpam-6473	331	15	s.	s.	PROPN
ejpam-6473	331	16	bano	bano	PROPN
ejpam-6473	331	17	et	et	PROPN
ejpam-6473	331	18	al	al	PROPN
ejpam-6473	331	19	.	.	PUNCT
ejpam-6473	331	20	/	/	SYM
ejpam-6473	331	21	eur	eur	PROPN
ejpam-6473	331	22	.	.	PUNCT
ejpam-6473	332	1	j.	j.	PROPN
ejpam-6473	332	2	pure	pure	PROPN
ejpam-6473	332	3	appl	appl	PROPN
ejpam-6473	332	4	.	.	PROPN
ejpam-6473	332	5	math	math	PROPN
ejpam-6473	332	6	,	,	PUNCT
ejpam-6473	332	7	18	18	NUM
ejpam-6473	332	8	(	(	PUNCT
ejpam-6473	332	9	4	4	NUM
ejpam-6473	332	10	)	)	PUNCT
ejpam-6473	332	11	(	(	PUNCT
ejpam-6473	332	12	2025	2025	NUM
ejpam-6473	332	13	)	)	PUNCT
ejpam-6473	332	14	,	,	PUNCT
ejpam-6473	332	15	6473	6473	NUM
ejpam-6473	332	16	18	18	NUM
ejpam-6473	332	17	of	of	ADP
ejpam-6473	332	18	38	38	NUM
ejpam-6473	332	19	b(t	b(t	NOUN
ejpam-6473	332	20	,	,	PUNCT
ejpam-6473	332	21	x	x	X
ejpam-6473	332	22	)	)	PUNCT
ejpam-6473	332	23	shows	show	VERB
ejpam-6473	332	24	the	the	DET
ejpam-6473	332	25	influence	influence	NOUN
ejpam-6473	332	26	of	of	ADP
ejpam-6473	332	27	control	control	NOUN
ejpam-6473	332	28	on	on	ADP
ejpam-6473	332	29	system	system	NOUN
ejpam-6473	332	30	.	.	PUNCT
ejpam-6473	333	1	the	the	DET
ejpam-6473	333	2	system	system	NOUN
ejpam-6473	333	3	(	(	PUNCT
ejpam-6473	333	4	12	12	NUM
ejpam-6473	333	5	)	)	PUNCT
ejpam-6473	333	6	is	be	AUX
ejpam-6473	333	7	linear	linear	ADJ
ejpam-6473	333	8	in	in	ADP
ejpam-6473	333	9	control	control	NOUN
ejpam-6473	333	10	,	,	PUNCT
ejpam-6473	333	11	and	and	CCONJ
ejpam-6473	333	12	can	can	AUX
ejpam-6473	333	13	be	be	AUX
ejpam-6473	333	14	rewritten	rewrite	VERB
ejpam-6473	333	15	as	as	ADP
ejpam-6473	333	16	:	:	PUNCT
ejpam-6473	333	17	r(t	r(t	NOUN
ejpam-6473	333	18	,	,	PUNCT
ejpam-6473	333	19	x	x	NOUN
ejpam-6473	333	20	,	,	PUNCT
ejpam-6473	333	21	u)=a(t	u)=a(t	PROPN
ejpam-6473	333	22	,	,	PUNCT
ejpam-6473	333	23	x)+b(x	x)+b(x	PROPN
ejpam-6473	333	24	,	,	PUNCT
ejpam-6473	333	25	t)u	t)u	NUM
ejpam-6473	333	26	dx	dx	PROPN
ejpam-6473	333	27	dt	dt	NOUN
ejpam-6473	333	28	=	=	SYM
ejpam-6473	333	29	r(t	r(t	PROPN
ejpam-6473	333	30	,	,	PUNCT
ejpam-6473	333	31	x	x	NOUN
ejpam-6473	333	32	,	,	PUNCT
ejpam-6473	333	33	u	u	NOUN
ejpam-6473	333	34	)	)	PUNCT
ejpam-6473	334	1	=	=	SYM
ejpam-6473	334	2			NOUN
ejpam-6473	334	3	λ−	λ−	PROPN
ejpam-6473	334	4	βps(1	βps(1	NOUN
ejpam-6473	334	5	+	+	CCONJ
ejpam-6473	334	6	νs)−	νs)−	NOUN
ejpam-6473	334	7	(	(	PUNCT
ejpam-6473	334	8	b+	b+	X
ejpam-6473	334	9	µ)p	µ)p	PUNCT
ejpam-6473	334	10	βps(1	βps(1	NOUN
ejpam-6473	334	11	+	+	CCONJ
ejpam-6473	334	12	νs)−	νs)−	NOUN
ejpam-6473	334	13	(	(	PUNCT
ejpam-6473	334	14	b+	b+	X
ejpam-6473	334	15	µ+	µ+	PRON
ejpam-6473	334	16	ζ)l	ζ)l	NOUN
ejpam-6473	334	17	ζl−	ζl−	PUNCT
ejpam-6473	334	18	(	(	PUNCT
ejpam-6473	334	19	b+	b+	X
ejpam-6473	334	20	µ+	µ+	X
ejpam-6473	334	21	δ)s	δ)s	ADJ
ejpam-6473	334	22	δs	δs	NOUN
ejpam-6473	334	23	−	−	PROPN
ejpam-6473	334	24	(	(	PUNCT
ejpam-6473	334	25	b+	b+	X
ejpam-6473	335	1	µ)q	µ)q	NOUN
ejpam-6473	335	2			NOUN
ejpam-6473	335	3	+	+	PUNCT
ejpam-6473	335	4			NOUN
ejpam-6473	335	5	−a0p	−a0p	NOUN
ejpam-6473	335	6	π1l	π1l	PROPN
ejpam-6473	335	7	π2s	π2s	PROPN
ejpam-6473	335	8	0	0	PUNCT
ejpam-6473	336	1	−l	−l	NOUN
ejpam-6473	336	2	0	0	NUM
ejpam-6473	336	3	0	0	NUM
ejpam-6473	336	4	0	0	NUM
ejpam-6473	336	5	−s	−s	NOUN
ejpam-6473	336	6	a0p	a0p	NOUN
ejpam-6473	336	7	(	(	PUNCT
ejpam-6473	336	8	1−	1−	NUM
ejpam-6473	336	9	π1)l	π1)l	NOUN
ejpam-6473	336	10	(	(	PUNCT
ejpam-6473	336	11	1−	1−	NUM
ejpam-6473	336	12	π2)s	π2)s	ADJ
ejpam-6473	336	13			NOUN
ejpam-6473	336	14	·	·	PUNCT
ejpam-6473	336	15	u1u2	u1u2	NOUN
ejpam-6473	336	16	u3	u3	NOUN
ejpam-6473	336	17			NOUN
ejpam-6473	336	18	.	.	PUNCT
ejpam-6473	337	1	condition	condition	NOUN
ejpam-6473	337	2	(	(	PUNCT
ejpam-6473	337	3	4	4	X
ejpam-6473	337	4	)	)	PUNCT
ejpam-6473	337	5	holds	hold	VERB
ejpam-6473	337	6	.	.	PUNCT
ejpam-6473	338	1	(	(	PUNCT
ejpam-6473	338	2	v	v	NOUN
ejpam-6473	338	3	)	)	PUNCT
ejpam-6473	338	4	as	as	ADP
ejpam-6473	338	5	integrand	integrand	NOUN
ejpam-6473	338	6	of	of	ADP
ejpam-6473	338	7	the	the	DET
ejpam-6473	338	8	objective	objective	ADJ
ejpam-6473	338	9	function	function	NOUN
ejpam-6473	338	10	is	be	AUX
ejpam-6473	338	11	l	l	NOUN
ejpam-6473	338	12	=	=	PUNCT
ejpam-6473	338	13	d1l+d2s	d1l+d2s	PROPN
ejpam-6473	338	14	−d3p	−d3p	NUM
ejpam-6473	338	15	−d4q+	−d4q+	NOUN
ejpam-6473	338	16	1	1	NUM
ejpam-6473	338	17	2	2	NUM
ejpam-6473	338	18	(	(	PUNCT
ejpam-6473	338	19	b1u	b1u	ADP
ejpam-6473	338	20	2	2	NUM
ejpam-6473	338	21	1	1	NUM
ejpam-6473	338	22	+	+	NOUN
ejpam-6473	338	23	b2u	b2u	PROPN
ejpam-6473	338	24	2	2	NUM
ejpam-6473	338	25	2	2	NUM
ejpam-6473	338	26	+	+	NOUN
ejpam-6473	338	27	b3u	b3u	NOUN
ejpam-6473	338	28	2	2	NUM
ejpam-6473	338	29	3	3	NUM
ejpam-6473	338	30	)	)	PUNCT
ejpam-6473	338	31	for	for	ADP
ejpam-6473	338	32	the	the	DET
ejpam-6473	338	33	proof	proof	NOUN
ejpam-6473	338	34	of	of	ADP
ejpam-6473	338	35	condition	condition	NOUN
ejpam-6473	338	36	5	5	NUM
ejpam-6473	338	37	,	,	PUNCT
ejpam-6473	338	38	we	we	PRON
ejpam-6473	338	39	use	use	VERB
ejpam-6473	338	40	(	(	PUNCT
ejpam-6473	338	41	p	p	X
ejpam-6473	338	42	,	,	PUNCT
ejpam-6473	338	43	l	l	NOUN
ejpam-6473	338	44	,	,	PUNCT
ejpam-6473	338	45	s	s	X
ejpam-6473	338	46	,	,	PUNCT
ejpam-6473	338	47	q	q	NOUN
ejpam-6473	338	48	)	)	PUNCT
ejpam-6473	338	49	≥	≥	NOUN
ejpam-6473	338	50	0	0	NUM
ejpam-6473	339	1	and	and	CCONJ
ejpam-6473	339	2	we	we	PRON
ejpam-6473	339	3	assume	assume	VERB
ejpam-6473	339	4	that	that	SCONJ
ejpam-6473	339	5	weighted	weight	VERB
ejpam-6473	339	6	sum	sum	NOUN
ejpam-6473	339	7	of	of	ADP
ejpam-6473	339	8	the	the	DET
ejpam-6473	339	9	smoker	smoker	NOUN
ejpam-6473	339	10	class(l	class(l	PROPN
ejpam-6473	339	11	,	,	PUNCT
ejpam-6473	339	12	s	s	PART
ejpam-6473	339	13	)	)	PUNCT
ejpam-6473	339	14	are	be	AUX
ejpam-6473	339	15	greater	great	ADJ
ejpam-6473	339	16	than	than	ADP
ejpam-6473	339	17	that	that	PRON
ejpam-6473	339	18	of	of	ADP
ejpam-6473	339	19	nonsmoker	nonsmoker	NOUN
ejpam-6473	339	20	class(p	class(p	PROPN
ejpam-6473	339	21	,	,	PUNCT
ejpam-6473	339	22	q	q	NOUN
ejpam-6473	339	23	)	)	PUNCT
ejpam-6473	339	24	that	that	PRON
ejpam-6473	339	25	is	be	AUX
ejpam-6473	339	26	d1l+d2s	d1l+d2s	PROPN
ejpam-6473	339	27	>	>	X
ejpam-6473	339	28	d3p	d3p	PROPN
ejpam-6473	339	29	+	+	PROPN
ejpam-6473	339	30	d4q	d4q	PROPN
ejpam-6473	339	31	,	,	PUNCT
ejpam-6473	339	32	where	where	SCONJ
ejpam-6473	339	33	di	di	X
ejpam-6473	339	34	>	>	X
ejpam-6473	339	35	0	0	PROPN
ejpam-6473	339	36	,	,	PUNCT
ejpam-6473	339	37	i	i	PRON
ejpam-6473	339	38	=	=	NOUN
ejpam-6473	339	39	1	1	NUM
ejpam-6473	339	40	,	,	PUNCT
ejpam-6473	339	41	2	2	NUM
ejpam-6473	339	42	,	,	PUNCT
ejpam-6473	339	43	3	3	NUM
ejpam-6473	339	44	,	,	PUNCT
ejpam-6473	339	45	4	4	NUM
ejpam-6473	339	46	l	l	NOUN
ejpam-6473	339	47	>	>	X
ejpam-6473	339	48	1	1	NUM
ejpam-6473	339	49	2	2	NUM
ejpam-6473	339	50	(	(	PUNCT
ejpam-6473	339	51	b1u	b1u	ADP
ejpam-6473	339	52	2	2	NUM
ejpam-6473	339	53	1	1	NUM
ejpam-6473	339	54	+	+	NOUN
ejpam-6473	339	55	b2u	b2u	PROPN
ejpam-6473	339	56	2	2	NUM
ejpam-6473	339	57	2	2	NUM
ejpam-6473	340	1	+	+	NOUN
ejpam-6473	340	2	b3u	b3u	NOUN
ejpam-6473	340	3	2	2	NUM
ejpam-6473	340	4	3	3	NUM
ejpam-6473	340	5	)	)	PUNCT
ejpam-6473	340	6	.	.	PUNCT
ejpam-6473	341	1	as	as	ADP
ejpam-6473	341	2	b3u3	b3u3	PROPN
ejpam-6473	341	3	2	2	NUM
ejpam-6473	341	4	≤	≤	NOUN
ejpam-6473	341	5	b3	b3	NOUN
ejpam-6473	341	6	2	2	NUM
ejpam-6473	341	7	l	l	NOUN
ejpam-6473	341	8	≥	≥	NOUN
ejpam-6473	341	9	y2(|u1|2	y2(|u1|2	X
ejpam-6473	341	10	+	+	CCONJ
ejpam-6473	341	11	|u2|2	|u2|2	PROPN
ejpam-6473	341	12	+	+	CCONJ
ejpam-6473	341	13	|u3|2	|u3|2	PROPN
ejpam-6473	341	14	)	)	PUNCT
ejpam-6473	341	15	y1	y1	NOUN
ejpam-6473	341	16	2	2	NUM
ejpam-6473	341	17	−	−	NOUN
ejpam-6473	341	18	y3	y3	NOUN
ejpam-6473	341	19	.	.	PUNCT
ejpam-6473	342	1	y1	y1	NOUN
ejpam-6473	342	2	=	=	SYM
ejpam-6473	342	3	2	2	NUM
ejpam-6473	342	4	,	,	PUNCT
ejpam-6473	342	5	y2	y2	NOUN
ejpam-6473	342	6	=	=	NOUN
ejpam-6473	342	7	1	1	NUM
ejpam-6473	342	8	2min(b1	2min(b1	NUM
ejpam-6473	342	9	,	,	PUNCT
ejpam-6473	342	10	b2	b2	NOUN
ejpam-6473	342	11	,	,	PUNCT
ejpam-6473	342	12	b3	b3	PROPN
ejpam-6473	342	13	)	)	PUNCT
ejpam-6473	342	14	,	,	PUNCT
ejpam-6473	342	15	y3	y3	NOUN
ejpam-6473	342	16	=	=	SYM
ejpam-6473	342	17	b3u3	b3u3	NOUN
ejpam-6473	342	18	2	2	NUM
ejpam-6473	342	19	.	.	PUNCT
ejpam-6473	343	1	this	this	PRON
ejpam-6473	343	2	prove	prove	VERB
ejpam-6473	343	3	the	the	DET
ejpam-6473	343	4	condition	condition	NOUN
ejpam-6473	343	5	(	(	PUNCT
ejpam-6473	343	6	5	5	NUM
ejpam-6473	343	7	)	)	PUNCT
ejpam-6473	343	8	.	.	PUNCT
ejpam-6473	344	1	hence	hence	ADV
ejpam-6473	344	2	all	all	DET
ejpam-6473	344	3	the	the	DET
ejpam-6473	344	4	five	five	NUM
ejpam-6473	344	5	condition	condition	NOUN
ejpam-6473	344	6	are	be	AUX
ejpam-6473	344	7	proof	proof	ADJ
ejpam-6473	344	8	,	,	PUNCT
ejpam-6473	344	9	this	this	PRON
ejpam-6473	344	10	implies	imply	VERB
ejpam-6473	344	11	that	that	SCONJ
ejpam-6473	344	12	optimal	optimal	ADJ
ejpam-6473	344	13	control	control	NOUN
ejpam-6473	344	14	exists	exist	VERB
ejpam-6473	344	15	that	that	PRON
ejpam-6473	344	16	minimizes	minimize	VERB
ejpam-6473	344	17	the	the	DET
ejpam-6473	344	18	objective	objective	ADJ
ejpam-6473	344	19	function	function	NOUN
ejpam-6473	344	20	.	.	PUNCT
ejpam-6473	345	1	4.2	4.2	NUM
ejpam-6473	345	2	.	.	PUNCT
ejpam-6473	346	1	optimal	optimal	ADJ
ejpam-6473	346	2	control	control	NOUN
ejpam-6473	346	3	characteristic	characteristic	ADJ
ejpam-6473	346	4	of	of	ADP
ejpam-6473	346	5	the	the	DET
ejpam-6473	346	6	plsq	plsq	NOUN
ejpam-6473	346	7	system	system	NOUN
ejpam-6473	346	8	the	the	DET
ejpam-6473	346	9	hamiltonian	hamiltonian	ADJ
ejpam-6473	346	10	function	function	NOUN
ejpam-6473	346	11	is	be	AUX
ejpam-6473	346	12	given	give	VERB
ejpam-6473	346	13	as	as	ADP
ejpam-6473	346	14	:	:	PUNCT
ejpam-6473	346	15	h	h	NOUN
ejpam-6473	346	16	=	=	PUNCT
ejpam-6473	346	17	l+	l+	X
ejpam-6473	346	18	∑4	∑4	PROPN
ejpam-6473	346	19	n=1	n=1	PROPN
ejpam-6473	346	20	λnhn	λnhn	PROPN
ejpam-6473	346	21	.	.	PUNCT
ejpam-6473	347	1	here	here	ADV
ejpam-6473	347	2	hn	hn	PROPN
ejpam-6473	347	3	=	=	PUNCT
ejpam-6473	347	4	(	(	PUNCT
ejpam-6473	347	5	dpdt	dpdt	X
ejpam-6473	347	6	,	,	PUNCT
ejpam-6473	347	7	dl	dl	PROPN
ejpam-6473	347	8	dt	dt	X
ejpam-6473	347	9	,	,	PUNCT
ejpam-6473	347	10	ds	ds	ADP
ejpam-6473	347	11	dt	dt	X
ejpam-6473	347	12	,	,	PUNCT
ejpam-6473	347	13	dq	dq	PROPN
ejpam-6473	347	14	dt	dt	NOUN
ejpam-6473	347	15	)	)	PUNCT
ejpam-6473	347	16	,	,	PUNCT
ejpam-6473	347	17	where	where	SCONJ
ejpam-6473	347	18	n	n	NOUN
ejpam-6473	347	19	=	=	SYM
ejpam-6473	347	20	1	1	NUM
ejpam-6473	347	21	,	,	PUNCT
ejpam-6473	347	22	2	2	NUM
ejpam-6473	347	23	,	,	PUNCT
ejpam-6473	347	24	3	3	NUM
ejpam-6473	347	25	,	,	PUNCT
ejpam-6473	347	26	4	4	NUM
ejpam-6473	347	27	.	.	PUNCT
ejpam-6473	348	1	and	and	CCONJ
ejpam-6473	348	2	x	x	X
ejpam-6473	348	3	=	=	PUNCT
ejpam-6473	349	1	[	[	X
ejpam-6473	349	2	p	p	X
ejpam-6473	349	3	,	,	PUNCT
ejpam-6473	349	4	l	l	NOUN
ejpam-6473	349	5	,	,	PUNCT
ejpam-6473	349	6	s	s	PART
ejpam-6473	349	7	,	,	PUNCT
ejpam-6473	349	8	q]t	q]t	NOUN
ejpam-6473	349	9	,	,	PUNCT
ejpam-6473	349	10	l	l	PROPN
ejpam-6473	349	11	=	=	PUNCT
ejpam-6473	350	1	d1l+d2s	d1l+d2s	PROPN
ejpam-6473	350	2	−d3p	−d3p	NUM
ejpam-6473	350	3	−d4q+	−d4q+	NOUN
ejpam-6473	350	4	1	1	NUM
ejpam-6473	350	5	2(b1u	2(b1u	NUM
ejpam-6473	350	6	2	2	NUM
ejpam-6473	350	7	1	1	NUM
ejpam-6473	350	8	+	+	NOUN
ejpam-6473	350	9	b2u	b2u	PROPN
ejpam-6473	350	10	2	2	NUM
ejpam-6473	350	11	2	2	NUM
ejpam-6473	350	12	+	+	NOUN
ejpam-6473	350	13	b3u	b3u	NOUN
ejpam-6473	350	14	2	2	NUM
ejpam-6473	350	15	3	3	NUM
ejpam-6473	350	16	)	)	PUNCT
ejpam-6473	350	17	,	,	PUNCT
ejpam-6473	350	18	pontraygin	pontraygin	PROPN
ejpam-6473	350	19	’s	’s	PART
ejpam-6473	350	20	maximum	maximum	ADJ
ejpam-6473	350	21	principle	principle	ADJ
ejpam-6473	350	22	conditions	condition	NOUN
ejpam-6473	350	23	are	be	AUX
ejpam-6473	350	24	λ̇n	λ̇n	PROPN
ejpam-6473	350	25	=	=	PUNCT
ejpam-6473	350	26	−∂h	−∂h	PROPN
ejpam-6473	350	27	∂x	∂x	PROPN
ejpam-6473	350	28	,	,	PUNCT
ejpam-6473	350	29	s.	s.	PROPN
ejpam-6473	350	30	bano	bano	PROPN
ejpam-6473	350	31	et	et	PROPN
ejpam-6473	351	1	al	al	PROPN
ejpam-6473	351	2	.	.	PUNCT
ejpam-6473	351	3	/	/	SYM
ejpam-6473	351	4	eur	eur	PROPN
ejpam-6473	351	5	.	.	PUNCT
ejpam-6473	352	1	j.	j.	PROPN
ejpam-6473	352	2	pure	pure	PROPN
ejpam-6473	352	3	appl	appl	PROPN
ejpam-6473	352	4	.	.	PROPN
ejpam-6473	352	5	math	math	PROPN
ejpam-6473	352	6	,	,	PUNCT
ejpam-6473	352	7	18	18	NUM
ejpam-6473	352	8	(	(	PUNCT
ejpam-6473	352	9	4	4	NUM
ejpam-6473	352	10	)	)	PUNCT
ejpam-6473	352	11	(	(	PUNCT
ejpam-6473	352	12	2025	2025	NUM
ejpam-6473	352	13	)	)	PUNCT
ejpam-6473	352	14	,	,	PUNCT
ejpam-6473	352	15	6473	6473	NUM
ejpam-6473	352	16	19	19	NUM
ejpam-6473	352	17	of	of	ADP
ejpam-6473	352	18	38	38	NUM
ejpam-6473	352	19	∂h	∂h	PROPN
ejpam-6473	352	20	∂u	∂u	PROPN
ejpam-6473	352	21	=	=	SYM
ejpam-6473	352	22	0	0	NUM
ejpam-6473	352	23	,	,	PUNCT
ejpam-6473	352	24	λn(t	λn(t	PUNCT
ejpam-6473	352	25	)	)	PUNCT
ejpam-6473	353	1	=	=	SYM
ejpam-6473	353	2	0	0	NUM
ejpam-6473	353	3	,	,	PUNCT
ejpam-6473	353	4	where	where	SCONJ
ejpam-6473	353	5	x	x	X
ejpam-6473	353	6	=	=	PRON
ejpam-6473	353	7	(	(	PUNCT
ejpam-6473	353	8	p	p	X
ejpam-6473	353	9	,	,	PUNCT
ejpam-6473	353	10	l	l	NOUN
ejpam-6473	353	11	,	,	PUNCT
ejpam-6473	353	12	s	s	X
ejpam-6473	353	13	,	,	PUNCT
ejpam-6473	353	14	q)t	q)t	ADJ
ejpam-6473	353	15	and	and	CCONJ
ejpam-6473	353	16	n	n	CCONJ
ejpam-6473	353	17	=	=	SYM
ejpam-6473	353	18	1	1	NUM
ejpam-6473	353	19	,	,	PUNCT
ejpam-6473	353	20	2	2	NUM
ejpam-6473	353	21	,	,	PUNCT
ejpam-6473	353	22	3	3	NUM
ejpam-6473	353	23	,	,	PUNCT
ejpam-6473	353	24	4	4	NUM
ejpam-6473	353	25	.	.	X
ejpam-6473	353	26	theorem	theorem	VERB
ejpam-6473	353	27	6	6	NUM
ejpam-6473	353	28	.	.	PUNCT
ejpam-6473	354	1	if	if	SCONJ
ejpam-6473	354	2	u∗1	u∗1	PROPN
ejpam-6473	354	3	,	,	PUNCT
ejpam-6473	354	4	u∗2	u∗2	NOUN
ejpam-6473	354	5	,	,	PUNCT
ejpam-6473	354	6	u∗3	u∗3	NOUN
ejpam-6473	354	7	are	be	AUX
ejpam-6473	354	8	the	the	DET
ejpam-6473	354	9	control	control	NOUN
ejpam-6473	354	10	pair	pair	NOUN
ejpam-6473	354	11	and	and	CCONJ
ejpam-6473	354	12	p	p	NOUN
ejpam-6473	354	13	∗	∗	NOUN
ejpam-6473	354	14	,	,	PUNCT
ejpam-6473	354	15	l∗	l∗	PROPN
ejpam-6473	354	16	,	,	PUNCT
ejpam-6473	354	17	s∗	s∗	PROPN
ejpam-6473	354	18	,	,	PUNCT
ejpam-6473	354	19	q∗	q∗	PROPN
ejpam-6473	354	20	are	be	AUX
ejpam-6473	354	21	the	the	DET
ejpam-6473	354	22	control	control	NOUN
ejpam-6473	354	23	path	path	NOUN
ejpam-6473	354	24	and	and	CCONJ
ejpam-6473	354	25	λn	λn	PROPN
ejpam-6473	354	26	are	be	AUX
ejpam-6473	354	27	the	the	DET
ejpam-6473	354	28	adjoint	adjoint	NOUN
ejpam-6473	354	29	variables	variable	NOUN
ejpam-6473	354	30	then	then	ADV
ejpam-6473	354	31	the	the	DET
ejpam-6473	354	32	following	follow	VERB
ejpam-6473	354	33	conditions	condition	NOUN
ejpam-6473	354	34	should	should	AUX
ejpam-6473	354	35	be	be	AUX
ejpam-6473	354	36	satisfied	satisfied	ADJ
ejpam-6473	354	37	λ̇1	λ̇1	PROPN
ejpam-6473	354	38	=	=	SYM
ejpam-6473	354	39	d3	d3	PROPN
ejpam-6473	354	40	−	−	PROPN
ejpam-6473	354	41	λ1(−βs(1	λ1(−βs(1	PROPN
ejpam-6473	354	42	+	+	NUM
ejpam-6473	354	43	νs)−	νs)−	NOUN
ejpam-6473	354	44	(	(	PUNCT
ejpam-6473	354	45	b+	b+	X
ejpam-6473	354	46	µ)−	µ)−	VERB
ejpam-6473	354	47	a0u1)−	a0u1)−	NOUN
ejpam-6473	354	48	λ2(βs(1	λ2(βs(1	NOUN
ejpam-6473	354	49	+	+	CCONJ
ejpam-6473	354	50	νs))−	νs))−	NOUN
ejpam-6473	354	51	λ4(a0u1	λ4(a0u1	ADV
ejpam-6473	354	52	)	)	PUNCT
ejpam-6473	354	53	,	,	PUNCT
ejpam-6473	355	1	λ̇2	λ̇2	PROPN
ejpam-6473	355	2	=	=	PROPN
ejpam-6473	355	3	−d1	−d1	NOUN
ejpam-6473	355	4	−	−	PROPN
ejpam-6473	355	5	λ1(π1u2)−	λ1(π1u2)−	PROPN
ejpam-6473	355	6	λ2(−(b+	λ2(−(b+	PUNCT
ejpam-6473	355	7	µ+	µ+	PUNCT
ejpam-6473	355	8	ζ	ζ	NOUN
ejpam-6473	355	9	+	+	CCONJ
ejpam-6473	355	10	u2))−	u2))−	PROPN
ejpam-6473	355	11	λ3ζ	λ3ζ	X
ejpam-6473	355	12	−	−	PROPN
ejpam-6473	355	13	λ4((1−	λ4((1−	VERB
ejpam-6473	355	14	π1)u2	π1)u2	NOUN
ejpam-6473	355	15	)	)	PUNCT
ejpam-6473	355	16	,	,	PUNCT
ejpam-6473	356	1	λ̇3	λ̇3	PROPN
ejpam-6473	356	2	=	=	PUNCT
ejpam-6473	357	1	−d2	−d2	PRON
ejpam-6473	357	2	−	−	NOUN
ejpam-6473	358	1	λ1(−βp	λ1(−βp	X
ejpam-6473	358	2	(	(	PUNCT
ejpam-6473	358	3	1	1	NUM
ejpam-6473	358	4	+	+	NUM
ejpam-6473	358	5	2νs	2νs	ADJ
ejpam-6473	358	6	)	)	PUNCT
ejpam-6473	359	1	+	+	CCONJ
ejpam-6473	359	2	π2u3)−	π2u3)−	PROPN
ejpam-6473	359	3	λ2(βp	λ2(βp	PROPN
ejpam-6473	359	4	(	(	PUNCT
ejpam-6473	359	5	1	1	NUM
ejpam-6473	359	6	+	+	NUM
ejpam-6473	359	7	2νs	2νs	ADJ
ejpam-6473	359	8	)	)	PUNCT
ejpam-6473	359	9	)	)	PUNCT
ejpam-6473	360	1	−	−	PROPN
ejpam-6473	360	2	λ3(−(b+	λ3(−(b+	PROPN
ejpam-6473	360	3	µ+	µ+	PUNCT
ejpam-6473	360	4	δ	δ	NOUN
ejpam-6473	360	5	+	+	CCONJ
ejpam-6473	360	6	u3))−	u3))−	PROPN
ejpam-6473	360	7	λ4(δ	λ4(δ	X
ejpam-6473	360	8	+	+	CCONJ
ejpam-6473	360	9	(	(	PUNCT
ejpam-6473	360	10	1−	1−	NUM
ejpam-6473	360	11	π2)u3	π2)u3	NOUN
ejpam-6473	360	12	)	)	PUNCT
ejpam-6473	360	13	,	,	PUNCT
ejpam-6473	360	14	λ̇4	λ̇4	PROPN
ejpam-6473	360	15	=	=	PROPN
ejpam-6473	360	16	d4	d4	PROPN
ejpam-6473	360	17	−	−	PROPN
ejpam-6473	360	18	λ4(−(b+	λ4(−(b+	SYM
ejpam-6473	360	19	µ	µ	NUM
ejpam-6473	360	20	)	)	PUNCT
ejpam-6473	360	21	)	)	PUNCT
ejpam-6473	360	22	,	,	PUNCT
ejpam-6473	360	23	(	(	PUNCT
ejpam-6473	360	24	13	13	NUM
ejpam-6473	360	25	)	)	PUNCT
ejpam-6473	360	26	along	along	ADP
ejpam-6473	360	27	with	with	ADP
ejpam-6473	360	28	the	the	DET
ejpam-6473	360	29	transversality	transversality	NOUN
ejpam-6473	360	30	conditions	condition	NOUN
ejpam-6473	360	31	:	:	PUNCT
ejpam-6473	360	32	λn(t	λn(t	X
ejpam-6473	360	33	)	)	PUNCT
ejpam-6473	361	1	=	=	PUNCT
ejpam-6473	361	2	0	0	NUM
ejpam-6473	361	3	where	where	SCONJ
ejpam-6473	361	4	n	n	ADV
ejpam-6473	361	5	=	=	SYM
ejpam-6473	361	6	1	1	NUM
ejpam-6473	361	7	,	,	PUNCT
ejpam-6473	361	8	2	2	NUM
ejpam-6473	361	9	,	,	PUNCT
ejpam-6473	361	10	3	3	NUM
ejpam-6473	361	11	,	,	PUNCT
ejpam-6473	361	12	4	4	NUM
ejpam-6473	361	13	.	.	PUNCT
ejpam-6473	361	14	furthermore	furthermore	ADV
ejpam-6473	361	15	,	,	PUNCT
ejpam-6473	361	16	the	the	DET
ejpam-6473	361	17	optimal	optimal	ADJ
ejpam-6473	361	18	pair	pair	NOUN
ejpam-6473	361	19	are	be	AUX
ejpam-6473	361	20	given	give	VERB
ejpam-6473	361	21	as	as	ADP
ejpam-6473	361	22	u∗1	u∗1	NOUN
ejpam-6473	361	23	=	=	SYM
ejpam-6473	361	24	max	max	PROPN
ejpam-6473	361	25	(	(	PUNCT
ejpam-6473	361	26	min	min	NOUN
ejpam-6473	361	27	(	(	PUNCT
ejpam-6473	361	28	(	(	PUNCT
ejpam-6473	361	29	λ1	λ1	PROPN
ejpam-6473	361	30	−	−	PROPN
ejpam-6473	361	31	λ4)a0p	λ4)a0p	X
ejpam-6473	361	32	∗	∗	NOUN
ejpam-6473	361	33	b1	b1	NOUN
ejpam-6473	361	34	,	,	PUNCT
ejpam-6473	361	35	umax	umax	ADJ
ejpam-6473	361	36	1	1	NUM
ejpam-6473	361	37	)	)	PUNCT
ejpam-6473	361	38	,	,	PUNCT
ejpam-6473	361	39	0	0	NUM
ejpam-6473	361	40	)	)	PUNCT
ejpam-6473	361	41	,	,	PUNCT
ejpam-6473	361	42	u∗2	u∗2	NOUN
ejpam-6473	361	43	=	=	SYM
ejpam-6473	361	44	max	max	PROPN
ejpam-6473	361	45	(	(	PUNCT
ejpam-6473	361	46	min	min	NOUN
ejpam-6473	361	47	(	(	PUNCT
ejpam-6473	361	48	(	(	PUNCT
ejpam-6473	361	49	λ4	λ4	VERB
ejpam-6473	361	50	−	−	PROPN
ejpam-6473	361	51	λ1)π1l	λ1)π1l	PROPN
ejpam-6473	362	1	∗	∗	NOUN
ejpam-6473	362	2	+	+	NUM
ejpam-6473	362	3	(	(	PUNCT
ejpam-6473	362	4	λ2	λ2	NOUN
ejpam-6473	362	5	−	−	PROPN
ejpam-6473	362	6	λ4)l	λ4)l	PROPN
ejpam-6473	362	7	∗	∗	NOUN
ejpam-6473	362	8	b2	b2	NOUN
ejpam-6473	362	9	,	,	PUNCT
ejpam-6473	362	10	umax	umax	ADJ
ejpam-6473	362	11	2	2	NUM
ejpam-6473	362	12	)	)	PUNCT
ejpam-6473	362	13	,	,	PUNCT
ejpam-6473	362	14	0	0	NUM
ejpam-6473	362	15	)	)	PUNCT
ejpam-6473	362	16	,	,	PUNCT
ejpam-6473	362	17	u∗3	u∗3	NOUN
ejpam-6473	362	18	=	=	X
ejpam-6473	362	19	max	max	PROPN
ejpam-6473	362	20	(	(	PUNCT
ejpam-6473	362	21	min	min	NOUN
ejpam-6473	362	22	(	(	PUNCT
ejpam-6473	362	23	(	(	PUNCT
ejpam-6473	362	24	λ4	λ4	VERB
ejpam-6473	362	25	−	−	PROPN
ejpam-6473	362	26	λ1)π2s	λ1)π2s	X
ejpam-6473	362	27	∗	∗	VERB
ejpam-6473	362	28	+	+	X
ejpam-6473	362	29	(	(	PUNCT
ejpam-6473	362	30	λ3	λ3	PROPN
ejpam-6473	362	31	−	−	PROPN
ejpam-6473	362	32	λ4)s	λ4)s	PROPN
ejpam-6473	362	33	∗	∗	NOUN
ejpam-6473	362	34	b3	b3	PROPN
ejpam-6473	362	35	,	,	PUNCT
ejpam-6473	362	36	umax	umax	ADJ
ejpam-6473	362	37	3	3	NUM
ejpam-6473	362	38	)	)	PUNCT
ejpam-6473	362	39	,	,	PUNCT
ejpam-6473	362	40	0	0	NUM
ejpam-6473	362	41	)	)	PUNCT
ejpam-6473	362	42	.	.	PUNCT
ejpam-6473	363	1	(	(	PUNCT
ejpam-6473	363	2	14	14	NUM
ejpam-6473	363	3	)	)	PUNCT
ejpam-6473	363	4	proof	proof	NOUN
ejpam-6473	363	5	.	.	PUNCT
ejpam-6473	364	1	by	by	ADP
ejpam-6473	364	2	applying	apply	VERB
ejpam-6473	364	3	the	the	DET
ejpam-6473	364	4	first	first	ADJ
ejpam-6473	364	5	condition	condition	NOUN
ejpam-6473	364	6	of	of	ADP
ejpam-6473	364	7	pontryagin	pontryagin	NOUN
ejpam-6473	364	8	maximum	maximum	PROPN
ejpam-6473	364	9	principle	principle	NOUN
ejpam-6473	364	10	,	,	PUNCT
ejpam-6473	364	11	we	we	PRON
ejpam-6473	364	12	get	get	VERB
ejpam-6473	364	13	λ̇1	λ̇1	ADP
ejpam-6473	364	14	=	=	X
ejpam-6473	364	15	−∂h	−∂h	NOUN
ejpam-6473	364	16	∂p	∂p	ADJ
ejpam-6473	364	17	,	,	PUNCT
ejpam-6473	364	18	λ̇2	λ̇2	PROPN
ejpam-6473	364	19	=	=	PUNCT
ejpam-6473	364	20	−∂h	−∂h	PROPN
ejpam-6473	364	21	∂l	∂l	NOUN
ejpam-6473	364	22	,	,	PUNCT
ejpam-6473	365	1	λ̇3	λ̇3	PROPN
ejpam-6473	365	2	=	=	PUNCT
ejpam-6473	365	3	−∂h	−∂h	PROPN
ejpam-6473	365	4	∂s	∂s	PROPN
ejpam-6473	365	5	,	,	PUNCT
ejpam-6473	366	1	λ̇4	λ̇4	PROPN
ejpam-6473	366	2	=	=	PUNCT
ejpam-6473	366	3	−∂h	−∂h	PROPN
ejpam-6473	366	4	∂q	∂q	PROPN
ejpam-6473	366	5	,	,	PUNCT
ejpam-6473	366	6	and	and	CCONJ
ejpam-6473	366	7	transversality	transversality	NOUN
ejpam-6473	366	8	condition	condition	NOUN
ejpam-6473	366	9	of	of	ADP
ejpam-6473	366	10	the	the	DET
ejpam-6473	366	11	pontryagin	pontryagin	NOUN
ejpam-6473	366	12	maximum	maximum	ADJ
ejpam-6473	366	13	principle	principle	NOUN
ejpam-6473	366	14	λn(t	λn(t	X
ejpam-6473	366	15	)	)	PUNCT
ejpam-6473	367	1	=	=	SYM
ejpam-6473	367	2	0	0	NUM
ejpam-6473	367	3	,	,	PUNCT
ejpam-6473	367	4	which	which	PRON
ejpam-6473	367	5	gives	give	VERB
ejpam-6473	367	6	λ1(t	λ1(t	ADP
ejpam-6473	367	7	)	)	PUNCT
ejpam-6473	367	8	=	=	SYM
ejpam-6473	367	9	0	0	NUM
ejpam-6473	367	10	,	,	PUNCT
ejpam-6473	367	11	λ2(t	λ2(t	NUM
ejpam-6473	367	12	)	)	PUNCT
ejpam-6473	367	13	=	=	SYM
ejpam-6473	367	14	0	0	NUM
ejpam-6473	367	15	,	,	PUNCT
ejpam-6473	367	16	λ3(t	λ3(t	NUM
ejpam-6473	367	17	)	)	PUNCT
ejpam-6473	367	18	=	=	SYM
ejpam-6473	367	19	0	0	NUM
ejpam-6473	367	20	,	,	PUNCT
ejpam-6473	367	21	λ4(t	λ4(t	PROPN
ejpam-6473	367	22	)	)	PUNCT
ejpam-6473	367	23	=	=	SYM
ejpam-6473	368	1	0	0	X
ejpam-6473	368	2	.	.	PUNCT
ejpam-6473	369	1	from	from	ADP
ejpam-6473	369	2	the	the	DET
ejpam-6473	369	3	2	2	NUM
ejpam-6473	369	4	condition	condition	NOUN
ejpam-6473	369	5	of	of	ADP
ejpam-6473	369	6	pontryagin	pontryagin	NOUN
ejpam-6473	369	7	’s	’s	PART
ejpam-6473	369	8	maximum	maximum	ADJ
ejpam-6473	369	9	principle	principle	NOUN
ejpam-6473	369	10	∂h	∂h	PROPN
ejpam-6473	369	11	∂u1	∂u1	PROPN
ejpam-6473	369	12	=	=	SYM
ejpam-6473	369	13	0	0	NUM
ejpam-6473	369	14	,	,	PUNCT
ejpam-6473	369	15	at	at	ADP
ejpam-6473	369	16	u1	u1	NOUN
ejpam-6473	369	17	=	=	SYM
ejpam-6473	369	18	u∗1	u∗1	NOUN
ejpam-6473	369	19	,	,	PUNCT
ejpam-6473	369	20	=	=	PRON
ejpam-6473	369	21	⇒	⇒	NOUN
ejpam-6473	369	22	u∗1	u∗1	NOUN
ejpam-6473	369	23	=	=	SYM
ejpam-6473	369	24	(	(	PUNCT
ejpam-6473	369	25	λ1	λ1	PROPN
ejpam-6473	369	26	−	−	PROPN
ejpam-6473	369	27	λ4)a0p	λ4)a0p	X
ejpam-6473	369	28	∗	∗	NOUN
ejpam-6473	369	29	b1	b1	NOUN
ejpam-6473	369	30	,	,	PUNCT
ejpam-6473	369	31	∂h	∂h	PROPN
ejpam-6473	369	32	∂u2	∂u2	NOUN
ejpam-6473	369	33	=	=	SYM
ejpam-6473	369	34	0	0	NUM
ejpam-6473	369	35	,	,	PUNCT
ejpam-6473	369	36	at	at	ADP
ejpam-6473	369	37	u2	u2	NOUN
ejpam-6473	369	38	=	=	SYM
ejpam-6473	369	39	u∗2	u∗2	NOUN
ejpam-6473	369	40	=	=	NOUN
ejpam-6473	369	41	⇒	⇒	X
ejpam-6473	369	42	u∗2	u∗2	NOUN
ejpam-6473	369	43	=	=	SYM
ejpam-6473	369	44	(	(	PUNCT
ejpam-6473	369	45	λ4	λ4	PROPN
ejpam-6473	369	46	−	−	PROPN
ejpam-6473	369	47	λ1)π1l	λ1)π1l	PROPN
ejpam-6473	369	48	∗	∗	NOUN
ejpam-6473	369	49	+	+	NUM
ejpam-6473	369	50	(	(	PUNCT
ejpam-6473	369	51	λ2	λ2	NOUN
ejpam-6473	369	52	−	−	PROPN
ejpam-6473	369	53	λ4)l	λ4)l	PROPN
ejpam-6473	369	54	∗	∗	NOUN
ejpam-6473	369	55	b2	b2	NOUN
ejpam-6473	369	56	,	,	PUNCT
ejpam-6473	369	57	s.	s.	PROPN
ejpam-6473	369	58	bano	bano	PROPN
ejpam-6473	369	59	et	et	PROPN
ejpam-6473	369	60	al	al	PROPN
ejpam-6473	369	61	.	.	PUNCT
ejpam-6473	369	62	/	/	SYM
ejpam-6473	369	63	eur	eur	PROPN
ejpam-6473	369	64	.	.	PUNCT
ejpam-6473	370	1	j.	j.	PROPN
ejpam-6473	370	2	pure	pure	PROPN
ejpam-6473	370	3	appl	appl	PROPN
ejpam-6473	370	4	.	.	PROPN
ejpam-6473	370	5	math	math	PROPN
ejpam-6473	370	6	,	,	PUNCT
ejpam-6473	370	7	18	18	NUM
ejpam-6473	370	8	(	(	PUNCT
ejpam-6473	370	9	4	4	NUM
ejpam-6473	370	10	)	)	PUNCT
ejpam-6473	370	11	(	(	PUNCT
ejpam-6473	370	12	2025	2025	NUM
ejpam-6473	370	13	)	)	PUNCT
ejpam-6473	370	14	,	,	PUNCT
ejpam-6473	370	15	6473	6473	NUM
ejpam-6473	370	16	20	20	NUM
ejpam-6473	370	17	of	of	ADP
ejpam-6473	370	18	38	38	NUM
ejpam-6473	370	19	∂h	∂h	PROPN
ejpam-6473	370	20	∂u3	∂u3	NOUN
ejpam-6473	370	21	=	=	SYM
ejpam-6473	370	22	0	0	NUM
ejpam-6473	370	23	,	,	PUNCT
ejpam-6473	370	24	at	at	ADP
ejpam-6473	370	25	u3	u3	NOUN
ejpam-6473	370	26	=	=	SYM
ejpam-6473	370	27	u∗3	u∗3	NOUN
ejpam-6473	370	28	=	=	X
ejpam-6473	370	29	⇒	⇒	VERB
ejpam-6473	370	30	u∗3	u∗3	NOUN
ejpam-6473	370	31	=	=	PUNCT
ejpam-6473	370	32	(	(	PUNCT
ejpam-6473	370	33	λ4	λ4	ADJ
ejpam-6473	370	34	−	−	PROPN
ejpam-6473	371	1	λ1)π2s	λ1)π2s	X
ejpam-6473	371	2	∗	∗	VERB
ejpam-6473	371	3	+	+	X
ejpam-6473	371	4	(	(	PUNCT
ejpam-6473	371	5	λ3	λ3	PROPN
ejpam-6473	371	6	−	−	PROPN
ejpam-6473	371	7	λ4)s	λ4)s	PROPN
ejpam-6473	371	8	∗	∗	NOUN
ejpam-6473	371	9	b3	b3	PROPN
ejpam-6473	371	10	.	.	PUNCT
ejpam-6473	372	1	using	use	VERB
ejpam-6473	372	2	the	the	DET
ejpam-6473	372	3	control	control	NOUN
ejpam-6473	372	4	set	set	VERB
ejpam-6473	372	5	property	property	NOUN
ejpam-6473	372	6	,	,	PUNCT
ejpam-6473	372	7	we	we	PRON
ejpam-6473	372	8	get	get	VERB
ejpam-6473	372	9	:	:	PUNCT
ejpam-6473	372	10	u∗1	u∗1	NOUN
ejpam-6473	372	11	=	=	PUNCT
ejpam-6473	373	1			NOUN
ejpam-6473	373	2	0	0	NUM
ejpam-6473	373	3	,	,	PUNCT
ejpam-6473	373	4	if	if	SCONJ
ejpam-6473	373	5	(	(	PUNCT
ejpam-6473	373	6	λ1−λ4)a0p	λ1−λ4)a0p	NOUN
ejpam-6473	373	7	∗	∗	NOUN
ejpam-6473	373	8	b1	b1	NOUN
ejpam-6473	373	9	≤	≤	ADJ
ejpam-6473	373	10	0	0	NUM
ejpam-6473	373	11	,	,	PUNCT
ejpam-6473	373	12	(	(	PUNCT
ejpam-6473	373	13	λ1−λ4)a0p	λ1−λ4)a0p	X
ejpam-6473	373	14	∗	∗	NOUN
ejpam-6473	373	15	b1	b1	NOUN
ejpam-6473	373	16	,	,	PUNCT
ejpam-6473	373	17	if	if	SCONJ
ejpam-6473	373	18	0	0	NUM
ejpam-6473	373	19	<	<	X
ejpam-6473	373	20	(	(	PUNCT
ejpam-6473	373	21	λ1−λ4)a0p	λ1−λ4)a0p	X
ejpam-6473	373	22	∗	∗	NOUN
ejpam-6473	373	23	b1	b1	NOUN
ejpam-6473	373	24	<	<	X
ejpam-6473	373	25	umax	umax	PROPN
ejpam-6473	373	26	1	1	NUM
ejpam-6473	373	27	,	,	PUNCT
ejpam-6473	373	28	umax	umax	ADJ
ejpam-6473	373	29	1	1	NUM
ejpam-6473	373	30	,	,	PUNCT
ejpam-6473	373	31	if	if	SCONJ
ejpam-6473	373	32	(	(	PUNCT
ejpam-6473	373	33	λ1−λ4)a0p	λ1−λ4)a0p	NOUN
ejpam-6473	373	34	∗	∗	NOUN
ejpam-6473	373	35	b1	b1	PROPN
ejpam-6473	373	36	≥	≥	PRON
ejpam-6473	373	37	umax	umax	ADJ
ejpam-6473	373	38	1	1	NUM
ejpam-6473	373	39	.	.	PUNCT
ejpam-6473	374	1	u∗2	u∗2	NOUN
ejpam-6473	374	2	=	=	PUNCT
ejpam-6473	374	3			NOUN
ejpam-6473	374	4	0	0	NUM
ejpam-6473	374	5	,	,	PUNCT
ejpam-6473	374	6	if	if	SCONJ
ejpam-6473	374	7	(	(	PUNCT
ejpam-6473	374	8	λ4−λ1)π1l∗+(λ2−λ4)l∗	λ4−λ1)π1l∗+(λ2−λ4)l∗	ADP
ejpam-6473	374	9	b2	b2	NOUN
ejpam-6473	374	10	≤	≤	NOUN
ejpam-6473	374	11	0	0	NUM
ejpam-6473	374	12	,	,	PUNCT
ejpam-6473	374	13	(	(	PUNCT
ejpam-6473	374	14	λ4−λ1)π1l∗+(λ2−λ4)l∗	λ4−λ1)π1l∗+(λ2−λ4)l∗	CCONJ
ejpam-6473	374	15	b2	b2	NOUN
ejpam-6473	374	16	,	,	PUNCT
ejpam-6473	374	17	if	if	SCONJ
ejpam-6473	374	18	0	0	NUM
ejpam-6473	374	19	<	<	X
ejpam-6473	374	20	(	(	PUNCT
ejpam-6473	374	21	λ4−λ1)π1l∗+(λ2−λ4)l∗	λ4−λ1)π1l∗+(λ2−λ4)l∗	PROPN
ejpam-6473	374	22	b2	b2	PROPN
ejpam-6473	374	23	<	<	X
ejpam-6473	374	24	umax	umax	X
ejpam-6473	374	25	2	2	NUM
ejpam-6473	374	26	,	,	PUNCT
ejpam-6473	374	27	umax	umax	ADJ
ejpam-6473	374	28	2	2	NUM
ejpam-6473	374	29	,	,	PUNCT
ejpam-6473	374	30	if	if	SCONJ
ejpam-6473	374	31	(	(	PUNCT
ejpam-6473	374	32	λ4−λ1)π1l∗+(λ2−λ4)l∗	λ4−λ1)π1l∗+(λ2−λ4)l∗	PROPN
ejpam-6473	374	33	b2	b2	PROPN
ejpam-6473	374	34	≥	≥	NUM
ejpam-6473	374	35	umax	umax	ADJ
ejpam-6473	374	36	2	2	NUM
ejpam-6473	374	37	.	.	PUNCT
ejpam-6473	375	1	u∗3	u∗3	NOUN
ejpam-6473	376	1	=	=	PUNCT
ejpam-6473	376	2			NOUN
ejpam-6473	376	3	0	0	NUM
ejpam-6473	376	4	,	,	PUNCT
ejpam-6473	376	5	if	if	SCONJ
ejpam-6473	376	6	(	(	PUNCT
ejpam-6473	376	7	λ4−λ1)π2s∗+(λ3−λ4)s∗	λ4−λ1)π2s∗+(λ3−λ4)s∗	NOUN
ejpam-6473	376	8	b3	b3	NOUN
ejpam-6473	376	9	≤	≤	NOUN
ejpam-6473	376	10	0	0	NUM
ejpam-6473	376	11	,	,	PUNCT
ejpam-6473	376	12	(	(	PUNCT
ejpam-6473	376	13	λ4−λ1)π2s∗+(λ3−λ4)s∗	λ4−λ1)π2s∗+(λ3−λ4)s∗	PROPN
ejpam-6473	376	14	b3	b3	NOUN
ejpam-6473	376	15	,	,	PUNCT
ejpam-6473	376	16	if	if	SCONJ
ejpam-6473	376	17	0	0	NUM
ejpam-6473	376	18	<	<	X
ejpam-6473	376	19	(	(	PUNCT
ejpam-6473	376	20	λ4−λ1)π2s∗+(λ3−λ4)s∗	λ4−λ1)π2s∗+(λ3−λ4)s∗	PROPN
ejpam-6473	376	21	b3	b3	PROPN
ejpam-6473	376	22	<	<	X
ejpam-6473	376	23	umax	umax	X
ejpam-6473	376	24	3	3	NUM
ejpam-6473	376	25	,	,	PUNCT
ejpam-6473	376	26	umax	umax	VERB
ejpam-6473	376	27	3	3	NUM
ejpam-6473	376	28	,	,	PUNCT
ejpam-6473	376	29	if	if	SCONJ
ejpam-6473	376	30	(	(	PUNCT
ejpam-6473	376	31	λ4−λ1)π2s∗+(λ3−λ4)s∗	λ4−λ1)π2s∗+(λ3−λ4)s∗	PROPN
ejpam-6473	376	32	b3	b3	PROPN
ejpam-6473	376	33	≥	≥	PRON
ejpam-6473	376	34	umax	umax	VERB
ejpam-6473	376	35	3	3	NUM
ejpam-6473	376	36	.	.	PUNCT
ejpam-6473	377	1	this	this	PRON
ejpam-6473	377	2	completes	complete	VERB
ejpam-6473	377	3	the	the	DET
ejpam-6473	377	4	proof	proof	NOUN
ejpam-6473	377	5	.	.	PUNCT
ejpam-6473	378	1	4.3	4.3	NUM
ejpam-6473	378	2	.	.	PUNCT
ejpam-6473	378	3	uniqueness	uniqueness	NOUN
ejpam-6473	378	4	of	of	ADP
ejpam-6473	378	5	optimal	optimal	ADJ
ejpam-6473	378	6	control	control	NOUN
ejpam-6473	378	7	system	system	NOUN
ejpam-6473	378	8	the	the	DET
ejpam-6473	378	9	optimal	optimal	ADJ
ejpam-6473	378	10	system	system	NOUN
ejpam-6473	378	11	consists	consist	VERB
ejpam-6473	378	12	of	of	ADP
ejpam-6473	378	13	the	the	DET
ejpam-6473	378	14	state	state	NOUN
ejpam-6473	378	15	system	system	NOUN
ejpam-6473	378	16	(	(	PUNCT
ejpam-6473	378	17	12	12	NUM
ejpam-6473	378	18	)	)	PUNCT
ejpam-6473	378	19	with	with	ADP
ejpam-6473	378	20	initial	initial	ADJ
ejpam-6473	378	21	condition	condition	NOUN
ejpam-6473	378	22	,	,	PUNCT
ejpam-6473	378	23	adjoint	adjoint	NOUN
ejpam-6473	378	24	system	system	NOUN
ejpam-6473	378	25	(	(	PUNCT
ejpam-6473	378	26	13	13	NUM
ejpam-6473	378	27	)	)	PUNCT
ejpam-6473	378	28	with	with	ADP
ejpam-6473	378	29	transversality	transversality	NOUN
ejpam-6473	378	30	condition	condition	NOUN
ejpam-6473	378	31	,	,	PUNCT
ejpam-6473	378	32	and	and	CCONJ
ejpam-6473	378	33	optimality	optimality	NOUN
ejpam-6473	378	34	condition	condition	NOUN
ejpam-6473	378	35	(	(	PUNCT
ejpam-6473	378	36	14	14	NUM
ejpam-6473	378	37	)	)	PUNCT
ejpam-6473	378	38	.	.	PUNCT
ejpam-6473	379	1	thus	thus	ADV
ejpam-6473	379	2	,	,	PUNCT
ejpam-6473	379	3	optimality	optimality	NOUN
ejpam-6473	379	4	system	system	NOUN
ejpam-6473	379	5	is	be	AUX
ejpam-6473	379	6	given	give	VERB
ejpam-6473	379	7	as	as	NUM
ejpam-6473	379	8	dp	dp	NOUN
ejpam-6473	379	9	dt	dt	NOUN
ejpam-6473	379	10	=	=	SYM
ejpam-6473	379	11	λ−	λ−	PROPN
ejpam-6473	379	12	βps(1	βps(1	NOUN
ejpam-6473	379	13	+	+	CCONJ
ejpam-6473	379	14	νs)−	νs)−	NOUN
ejpam-6473	379	15	(	(	PUNCT
ejpam-6473	379	16	b+	b+	X
ejpam-6473	379	17	µ)p	µ)p	PUNCT
ejpam-6473	379	18	−	−	NOUN
ejpam-6473	379	19	a0u1p	a0u1p	SYM
ejpam-6473	379	20	+	+	NUM
ejpam-6473	379	21	π1u2l+	π1u2l+	NOUN
ejpam-6473	379	22	π2u3s	π2u3s	NUM
ejpam-6473	379	23	,	,	PUNCT
ejpam-6473	379	24	dl	dl	PROPN
ejpam-6473	379	25	dt	dt	NOUN
ejpam-6473	379	26	=	=	PUNCT
ejpam-6473	379	27	βps(1	βps(1	X
ejpam-6473	379	28	+	+	X
ejpam-6473	379	29	νs)−	νs)−	NOUN
ejpam-6473	379	30	(	(	PUNCT
ejpam-6473	379	31	b+	b+	X
ejpam-6473	379	32	µ+	µ+	X
ejpam-6473	379	33	ζ	ζ	NOUN
ejpam-6473	379	34	+	+	CCONJ
ejpam-6473	379	35	u2)l	u2)l	NOUN
ejpam-6473	379	36	,	,	PUNCT
ejpam-6473	379	37	ds	ds	ADJ
ejpam-6473	379	38	dt	dt	NOUN
ejpam-6473	379	39	=	=	SYM
ejpam-6473	379	40	ζl−	ζl−	X
ejpam-6473	379	41	(	(	PUNCT
ejpam-6473	379	42	b+	b+	X
ejpam-6473	379	43	µ+	µ+	X
ejpam-6473	379	44	δ	δ	NOUN
ejpam-6473	379	45	+	+	CCONJ
ejpam-6473	379	46	u3)s	u3)s	NOUN
ejpam-6473	379	47	,	,	PUNCT
ejpam-6473	379	48	dq	dq	NOUN
ejpam-6473	379	49	dt	dt	NOUN
ejpam-6473	379	50	=	=	NOUN
ejpam-6473	379	51	δs	δs	NOUN
ejpam-6473	379	52	−	−	PROPN
ejpam-6473	379	53	(	(	PUNCT
ejpam-6473	379	54	b+	b+	X
ejpam-6473	379	55	µ)q+	µ)q+	NOUN
ejpam-6473	379	56	a0u1p	a0u1p	PUNCT
ejpam-6473	379	57	+	+	CCONJ
ejpam-6473	379	58	(	(	PUNCT
ejpam-6473	379	59	1−	1−	NUM
ejpam-6473	379	60	π1)u2l+	π1)u2l+	NOUN
ejpam-6473	379	61	(	(	PUNCT
ejpam-6473	379	62	1−	1−	NUM
ejpam-6473	379	63	π2)u3s	π2)u3	NOUN
ejpam-6473	379	64	,	,	PUNCT
ejpam-6473	379	65	λ̇1	λ̇1	PROPN
ejpam-6473	379	66	=	=	SYM
ejpam-6473	379	67	d3	d3	PROPN
ejpam-6473	379	68	−	−	PROPN
ejpam-6473	379	69	λ1(−βs(1	λ1(−βs(1	PROPN
ejpam-6473	379	70	+	+	NUM
ejpam-6473	379	71	νs)−	νs)−	NOUN
ejpam-6473	379	72	(	(	PUNCT
ejpam-6473	379	73	b+	b+	X
ejpam-6473	379	74	µ)−	µ)−	VERB
ejpam-6473	379	75	a0u1	a0u1	X
ejpam-6473	379	76	)	)	PUNCT
ejpam-6473	379	77	−λ2(βs(1	−λ2(βs(1	NOUN
ejpam-6473	379	78	+	+	CCONJ
ejpam-6473	379	79	νs))−	νs))−	NOUN
ejpam-6473	379	80	λ4(a0u1	λ4(a0u1	ADV
ejpam-6473	379	81	)	)	PUNCT
ejpam-6473	379	82	,	,	PUNCT
ejpam-6473	379	83	λ̇2	λ̇2	PROPN
ejpam-6473	379	84	=	=	PROPN
ejpam-6473	379	85	−d1	−d1	NOUN
ejpam-6473	379	86	−	−	PROPN
ejpam-6473	379	87	λ1(π1u2)−	λ1(π1u2)−	PROPN
ejpam-6473	379	88	λ2(−(b+	λ2(−(b+	PUNCT
ejpam-6473	379	89	µ+	µ+	PUNCT
ejpam-6473	379	90	ζ	ζ	NOUN
ejpam-6473	379	91	+	+	CCONJ
ejpam-6473	379	92	u2))−	u2))−	PROPN
ejpam-6473	379	93	λ3ζ	λ3ζ	VERB
ejpam-6473	379	94	−λ4((1−	−λ4((1−	ADJ
ejpam-6473	379	95	π1)u2	π1)u2	PROPN
ejpam-6473	379	96	)	)	PUNCT
ejpam-6473	379	97	,	,	PUNCT
ejpam-6473	379	98	λ̇3	λ̇3	PROPN
ejpam-6473	379	99	=	=	PUNCT
ejpam-6473	380	1	−d2	−d2	PRON
ejpam-6473	380	2	−	−	NOUN
ejpam-6473	381	1	λ1(−βp	λ1(−βp	X
ejpam-6473	381	2	(	(	PUNCT
ejpam-6473	381	3	1	1	NUM
ejpam-6473	381	4	+	+	NUM
ejpam-6473	381	5	2νs	2νs	ADJ
ejpam-6473	381	6	)	)	PUNCT
ejpam-6473	382	1	+	+	CCONJ
ejpam-6473	382	2	π2u3)−	π2u3)−	PROPN
ejpam-6473	382	3	λ2(βp	λ2(βp	PROPN
ejpam-6473	382	4	(	(	PUNCT
ejpam-6473	382	5	1	1	NUM
ejpam-6473	382	6	+	+	NUM
ejpam-6473	382	7	2νs	2ν	NOUN
ejpam-6473	382	8	)	)	PUNCT
ejpam-6473	382	9	)	)	PUNCT
ejpam-6473	383	1	−λ3(−(b+	−λ3(−(b+	ADP
ejpam-6473	383	2	µ+	µ+	PROPN
ejpam-6473	383	3	δ	δ	PROPN
ejpam-6473	383	4	+	+	CCONJ
ejpam-6473	383	5	u3))−	u3))−	PROPN
ejpam-6473	383	6	λ4(δ	λ4(δ	X
ejpam-6473	383	7	+	+	CCONJ
ejpam-6473	383	8	(	(	PUNCT
ejpam-6473	383	9	1−	1−	NUM
ejpam-6473	383	10	π2)u3	π2)u3	NOUN
ejpam-6473	383	11	)	)	PUNCT
ejpam-6473	383	12	,	,	PUNCT
ejpam-6473	383	13	λ̇4	λ̇4	PROPN
ejpam-6473	383	14	=	=	PROPN
ejpam-6473	383	15	d4	d4	PROPN
ejpam-6473	383	16	−	−	PROPN
ejpam-6473	383	17	λ4(−(b+	λ4(−(b+	SYM
ejpam-6473	383	18	µ	µ	NUM
ejpam-6473	383	19	)	)	PUNCT
ejpam-6473	383	20	)	)	PUNCT
ejpam-6473	383	21	.	.	PUNCT
ejpam-6473	384	1	,	,	PUNCT
ejpam-6473	384	2	(	(	PUNCT
ejpam-6473	384	3	15	15	NUM
ejpam-6473	384	4	)	)	PUNCT
ejpam-6473	384	5	where	where	SCONJ
ejpam-6473	384	6	p	p	NOUN
ejpam-6473	384	7	(	(	PUNCT
ejpam-6473	384	8	0	0	NUM
ejpam-6473	384	9	)	)	PUNCT
ejpam-6473	384	10	,	,	PUNCT
ejpam-6473	384	11	l(0	l(0	PROPN
ejpam-6473	384	12	)	)	PUNCT
ejpam-6473	384	13	,	,	PUNCT
ejpam-6473	384	14	s(0	s(0	PROPN
ejpam-6473	384	15	)	)	PUNCT
ejpam-6473	384	16	,	,	PUNCT
ejpam-6473	384	17	q(0	q(0	PROPN
ejpam-6473	384	18	)	)	PUNCT
ejpam-6473	384	19	≥	≥	NOUN
ejpam-6473	384	20	0	0	NUM
ejpam-6473	384	21	and	and	CCONJ
ejpam-6473	384	22	λi(t	λi(t	NUM
ejpam-6473	384	23	)	)	PUNCT
ejpam-6473	384	24	=	=	SYM
ejpam-6473	384	25	0	0	NUM
ejpam-6473	384	26	,	,	PUNCT
ejpam-6473	384	27	for	for	ADP
ejpam-6473	384	28	i	i	PROPN
ejpam-6473	384	29	=	=	SYM
ejpam-6473	384	30	1	1	NUM
ejpam-6473	384	31	,	,	PUNCT
ejpam-6473	384	32	2	2	NUM
ejpam-6473	384	33	,	,	PUNCT
ejpam-6473	384	34	3	3	NUM
ejpam-6473	384	35	,	,	PUNCT
ejpam-6473	384	36	4	4	NUM
ejpam-6473	384	37	.	.	PUNCT
ejpam-6473	384	38	u1	u1	NOUN
ejpam-6473	384	39	=	=	SYM
ejpam-6473	384	40	max	max	PROPN
ejpam-6473	384	41	(	(	PUNCT
ejpam-6473	384	42	min	min	NOUN
ejpam-6473	384	43	(	(	PUNCT
ejpam-6473	384	44	(	(	PUNCT
ejpam-6473	384	45	λ1	λ1	PROPN
ejpam-6473	384	46	−	−	PROPN
ejpam-6473	384	47	λ4)a0p	λ4)a0p	X
ejpam-6473	384	48	b1	b1	PROPN
ejpam-6473	384	49	,	,	PUNCT
ejpam-6473	384	50	umax	umax	ADJ
ejpam-6473	384	51	1	1	NUM
ejpam-6473	384	52	)	)	PUNCT
ejpam-6473	384	53	,	,	PUNCT
ejpam-6473	384	54	0	0	NUM
ejpam-6473	384	55	)	)	PUNCT
ejpam-6473	384	56	,	,	PUNCT
ejpam-6473	384	57	s.	s.	PROPN
ejpam-6473	384	58	bano	bano	PROPN
ejpam-6473	384	59	et	et	PROPN
ejpam-6473	384	60	al	al	PROPN
ejpam-6473	384	61	.	.	PUNCT
ejpam-6473	384	62	/	/	SYM
ejpam-6473	384	63	eur	eur	PROPN
ejpam-6473	384	64	.	.	PUNCT
ejpam-6473	385	1	j.	j.	PROPN
ejpam-6473	385	2	pure	pure	PROPN
ejpam-6473	385	3	appl	appl	PROPN
ejpam-6473	385	4	.	.	PROPN
ejpam-6473	385	5	math	math	PROPN
ejpam-6473	385	6	,	,	PUNCT
ejpam-6473	385	7	18	18	NUM
ejpam-6473	385	8	(	(	PUNCT
ejpam-6473	385	9	4	4	NUM
ejpam-6473	385	10	)	)	PUNCT
ejpam-6473	385	11	(	(	PUNCT
ejpam-6473	385	12	2025	2025	NUM
ejpam-6473	385	13	)	)	PUNCT
ejpam-6473	385	14	,	,	PUNCT
ejpam-6473	385	15	6473	6473	NUM
ejpam-6473	385	16	21	21	NUM
ejpam-6473	385	17	of	of	ADP
ejpam-6473	385	18	38	38	NUM
ejpam-6473	385	19	u2	u2	NOUN
ejpam-6473	385	20	=	=	PUNCT
ejpam-6473	385	21	max	max	PROPN
ejpam-6473	385	22	(	(	PUNCT
ejpam-6473	385	23	min	min	NOUN
ejpam-6473	385	24	(	(	PUNCT
ejpam-6473	385	25	(	(	PUNCT
ejpam-6473	385	26	λ4	λ4	VERB
ejpam-6473	385	27	−	−	X
ejpam-6473	386	1	λ1)π1l+	λ1)π1l+	CCONJ
ejpam-6473	387	1	(	(	PUNCT
ejpam-6473	387	2	λ2	λ2	NOUN
ejpam-6473	387	3	−	−	PROPN
ejpam-6473	387	4	λ4)l	λ4)l	ADJ
ejpam-6473	387	5	b2	b2	NOUN
ejpam-6473	387	6	,	,	PUNCT
ejpam-6473	387	7	umax	umax	ADJ
ejpam-6473	387	8	2	2	NUM
ejpam-6473	387	9	)	)	PUNCT
ejpam-6473	387	10	,	,	PUNCT
ejpam-6473	387	11	0	0	NUM
ejpam-6473	387	12	)	)	PUNCT
ejpam-6473	387	13	,	,	PUNCT
ejpam-6473	387	14	u3	u3	NOUN
ejpam-6473	387	15	=	=	SYM
ejpam-6473	387	16	max	max	PROPN
ejpam-6473	387	17	(	(	PUNCT
ejpam-6473	387	18	min	min	NOUN
ejpam-6473	387	19	(	(	PUNCT
ejpam-6473	387	20	(	(	PUNCT
ejpam-6473	387	21	λ4	λ4	VERB
ejpam-6473	387	22	−	−	NOUN
ejpam-6473	387	23	λ1)π2s	λ1)π2s	X
ejpam-6473	388	1	+	+	CCONJ
ejpam-6473	388	2	(	(	PUNCT
ejpam-6473	388	3	λ3	λ3	PROPN
ejpam-6473	388	4	−	−	PROPN
ejpam-6473	388	5	λ4)s	λ4)s	PROPN
ejpam-6473	388	6	b3	b3	PROPN
ejpam-6473	388	7	,	,	PUNCT
ejpam-6473	388	8	umax	umax	ADJ
ejpam-6473	388	9	3	3	NUM
ejpam-6473	388	10	)	)	PUNCT
ejpam-6473	388	11	,	,	PUNCT
ejpam-6473	388	12	0	0	NUM
ejpam-6473	388	13	)	)	PUNCT
ejpam-6473	388	14	.	.	PUNCT
ejpam-6473	389	1	figure	figure	VERB
ejpam-6473	389	2	3	3	NUM
ejpam-6473	389	3	:	:	PUNCT
ejpam-6473	389	4	the	the	DET
ejpam-6473	389	5	flowchart	flowchart	NOUN
ejpam-6473	389	6	of	of	ADP
ejpam-6473	389	7	the	the	DET
ejpam-6473	389	8	optimality	optimality	NOUN
ejpam-6473	389	9	system	system	NOUN
ejpam-6473	389	10	is	be	AUX
ejpam-6473	389	11	given	give	VERB
ejpam-6473	389	12	above	above	ADV
ejpam-6473	389	13	.	.	PUNCT
ejpam-6473	390	1	s.	s.	PROPN
ejpam-6473	390	2	bano	bano	PROPN
ejpam-6473	390	3	et	et	PROPN
ejpam-6473	390	4	al	al	PROPN
ejpam-6473	390	5	.	.	PUNCT
ejpam-6473	390	6	/	/	SYM
ejpam-6473	390	7	eur	eur	PROPN
ejpam-6473	390	8	.	.	PUNCT
ejpam-6473	391	1	j.	j.	PROPN
ejpam-6473	391	2	pure	pure	PROPN
ejpam-6473	391	3	appl	appl	PROPN
ejpam-6473	391	4	.	.	PROPN
ejpam-6473	391	5	math	math	PROPN
ejpam-6473	391	6	,	,	PUNCT
ejpam-6473	391	7	18	18	NUM
ejpam-6473	391	8	(	(	PUNCT
ejpam-6473	391	9	4	4	NUM
ejpam-6473	391	10	)	)	PUNCT
ejpam-6473	391	11	(	(	PUNCT
ejpam-6473	391	12	2025	2025	NUM
ejpam-6473	391	13	)	)	PUNCT
ejpam-6473	391	14	,	,	PUNCT
ejpam-6473	391	15	6473	6473	NUM
ejpam-6473	391	16	22	22	NUM
ejpam-6473	391	17	of	of	ADP
ejpam-6473	391	18	38	38	NUM
ejpam-6473	391	19	the	the	DET
ejpam-6473	391	20	adjoint	adjoint	NOUN
ejpam-6473	391	21	system	system	NOUN
ejpam-6473	391	22	has	have	VERB
ejpam-6473	391	23	a	a	DET
ejpam-6473	391	24	linear	linear	ADJ
ejpam-6473	391	25	bounded	bounded	ADJ
ejpam-6473	391	26	coefficient	coefficient	NOUN
ejpam-6473	391	27	in	in	ADP
ejpam-6473	391	28	each	each	PRON
ejpam-6473	391	29	of	of	ADP
ejpam-6473	391	30	the	the	DET
ejpam-6473	391	31	adjoint	adjoint	NOUN
ejpam-6473	391	32	variables	variable	NOUN
ejpam-6473	391	33	because	because	SCONJ
ejpam-6473	391	34	the	the	DET
ejpam-6473	391	35	state	state	NOUN
ejpam-6473	391	36	system	system	NOUN
ejpam-6473	391	37	is	be	AUX
ejpam-6473	391	38	bounded	bound	VERB
ejpam-6473	391	39	.	.	PUNCT
ejpam-6473	392	1	thus	thus	ADV
ejpam-6473	392	2	,	,	PUNCT
ejpam-6473	392	3	the	the	DET
ejpam-6473	392	4	upper	upper	ADJ
ejpam-6473	392	5	bound	bound	NOUN
ejpam-6473	392	6	of	of	ADP
ejpam-6473	392	7	the	the	DET
ejpam-6473	392	8	adjoint	adjoint	NOUN
ejpam-6473	392	9	system	system	NOUN
ejpam-6473	392	10	is	be	AUX
ejpam-6473	392	11	finite	finite	ADJ
ejpam-6473	392	12	.	.	PUNCT
ejpam-6473	393	1	in	in	ADP
ejpam-6473	393	2	order	order	NOUN
ejpam-6473	393	3	to	to	PART
ejpam-6473	393	4	prove	prove	VERB
ejpam-6473	393	5	the	the	DET
ejpam-6473	393	6	uniqueness	uniqueness	NOUN
ejpam-6473	393	7	of	of	ADP
ejpam-6473	393	8	the	the	DET
ejpam-6473	393	9	optimality	optimality	NOUN
ejpam-6473	393	10	system	system	NOUN
ejpam-6473	393	11	for	for	ADP
ejpam-6473	393	12	small	small	ADJ
ejpam-6473	393	13	time	time	NOUN
ejpam-6473	393	14	,	,	PUNCT
ejpam-6473	393	15	we	we	PRON
ejpam-6473	393	16	state	state	VERB
ejpam-6473	393	17	the	the	DET
ejpam-6473	393	18	following	follow	VERB
ejpam-6473	393	19	statement	statement	NOUN
ejpam-6473	393	20	lemma	lemma	PROPN
ejpam-6473	393	21	4	4	X
ejpam-6473	393	22	.	.	PUNCT
ejpam-6473	394	1	the	the	DET
ejpam-6473	394	2	function	function	NOUN
ejpam-6473	394	3	v∗(r	v∗(r	NOUN
ejpam-6473	394	4	)	)	PUNCT
ejpam-6473	394	5	=	=	SYM
ejpam-6473	394	6	max{min{r	max{min{r	PROPN
ejpam-6473	394	7	,	,	PUNCT
ejpam-6473	394	8	c	c	NOUN
ejpam-6473	394	9	}	}	PUNCT
ejpam-6473	394	10	,	,	PUNCT
ejpam-6473	394	11	d	d	X
ejpam-6473	394	12	}	}	PUNCT
ejpam-6473	394	13	is	be	AUX
ejpam-6473	394	14	lipchitz	lipchitz	NOUN
ejpam-6473	394	15	continuous	continuous	ADJ
ejpam-6473	394	16	in	in	ADP
ejpam-6473	394	17	r	r	NOUN
ejpam-6473	394	18	with	with	ADP
ejpam-6473	394	19	c	c	NOUN
ejpam-6473	394	20	<	<	X
ejpam-6473	394	21	d	d	NOUN
ejpam-6473	394	22	for	for	ADP
ejpam-6473	394	23	some	some	DET
ejpam-6473	394	24	non	non	ADJ
ejpam-6473	394	25	-	-	ADJ
ejpam-6473	394	26	negative	negative	ADJ
ejpam-6473	394	27	constant	constant	ADJ
ejpam-6473	394	28	.	.	PUNCT
ejpam-6473	395	1	the	the	DET
ejpam-6473	395	2	uniqueness	uniqueness	NOUN
ejpam-6473	395	3	of	of	ADP
ejpam-6473	395	4	the	the	DET
ejpam-6473	395	5	above	above	ADJ
ejpam-6473	395	6	model	model	NOUN
ejpam-6473	395	7	is	be	AUX
ejpam-6473	395	8	evaluated	evaluate	VERB
ejpam-6473	395	9	in	in	ADP
ejpam-6473	395	10	the	the	DET
ejpam-6473	395	11	similar	similar	ADJ
ejpam-6473	395	12	way	way	NOUN
ejpam-6473	395	13	it	it	PRON
ejpam-6473	395	14	is	be	AUX
ejpam-6473	395	15	found	find	VERB
ejpam-6473	395	16	in	in	ADP
ejpam-6473	395	17	[	[	X
ejpam-6473	395	18	33	33	NUM
ejpam-6473	395	19	]	]	PUNCT
ejpam-6473	395	20	,	,	PUNCT
ejpam-6473	395	21	[	[	X
ejpam-6473	395	22	34	34	NUM
ejpam-6473	395	23	]	]	PUNCT
ejpam-6473	395	24	.	.	PUNCT
ejpam-6473	396	1	theorem	theorem	VERB
ejpam-6473	396	2	7	7	NUM
ejpam-6473	396	3	.	.	X
ejpam-6473	396	4	for	for	ADP
ejpam-6473	396	5	a	a	DET
ejpam-6473	396	6	sufficiently	sufficiently	ADV
ejpam-6473	396	7	short	short	ADJ
ejpam-6473	396	8	time	time	NOUN
ejpam-6473	396	9	interval	interval	PROPN
ejpam-6473	396	10	t	t	PROPN
ejpam-6473	396	11	,	,	PUNCT
ejpam-6473	396	12	the	the	DET
ejpam-6473	396	13	solution	solution	NOUN
ejpam-6473	396	14	of	of	ADP
ejpam-6473	396	15	the	the	DET
ejpam-6473	396	16	optimal	optimal	ADJ
ejpam-6473	396	17	system	system	NOUN
ejpam-6473	396	18	(	(	PUNCT
ejpam-6473	396	19	15	15	NUM
ejpam-6473	396	20	)	)	PUNCT
ejpam-6473	396	21	is	be	AUX
ejpam-6473	396	22	unique	unique	ADJ
ejpam-6473	396	23	.	.	PUNCT
ejpam-6473	397	1	proof	proof	NOUN
ejpam-6473	397	2	.	.	PUNCT
ejpam-6473	398	1	contradiction	contradiction	NOUN
ejpam-6473	398	2	is	be	AUX
ejpam-6473	398	3	used	use	VERB
ejpam-6473	398	4	to	to	PART
ejpam-6473	398	5	prove	prove	VERB
ejpam-6473	398	6	this	this	DET
ejpam-6473	398	7	theorem	theorem	NOUN
ejpam-6473	398	8	.	.	PUNCT
ejpam-6473	399	1	contradiction	contradiction	NOUN
ejpam-6473	399	2	is	be	AUX
ejpam-6473	399	3	obtained	obtain	VERB
ejpam-6473	399	4	by	by	ADP
ejpam-6473	399	5	taking	take	VERB
ejpam-6473	399	6	into	into	ADP
ejpam-6473	399	7	account	account	NOUN
ejpam-6473	399	8	optimum	optimum	ADJ
ejpam-6473	399	9	control	control	NOUN
ejpam-6473	399	10	function	function	NOUN
ejpam-6473	399	11	lipschitz	lipschitz	NOUN
ejpam-6473	399	12	continuity	continuity	NOUN
ejpam-6473	399	13	,	,	PUNCT
ejpam-6473	399	14	state	state	NOUN
ejpam-6473	399	15	system	system	NOUN
ejpam-6473	399	16	,	,	PUNCT
ejpam-6473	399	17	and	and	CCONJ
ejpam-6473	399	18	adjoint	adjoint	NOUN
ejpam-6473	399	19	system	system	NOUN
ejpam-6473	399	20	boundedness	boundedness	NOUN
ejpam-6473	399	21	,	,	PUNCT
ejpam-6473	399	22	and	and	CCONJ
ejpam-6473	399	23	some	some	DET
ejpam-6473	399	24	few	few	ADJ
ejpam-6473	399	25	basic	basic	ADJ
ejpam-6473	399	26	inequalities	inequality	NOUN
ejpam-6473	399	27	.	.	PUNCT
ejpam-6473	400	1	let	let	VERB
ejpam-6473	400	2	the	the	DET
ejpam-6473	400	3	two	two	NUM
ejpam-6473	400	4	solutions	solution	NOUN
ejpam-6473	400	5	of	of	ADP
ejpam-6473	400	6	system	system	NOUN
ejpam-6473	400	7	(	(	PUNCT
ejpam-6473	400	8	15	15	NUM
ejpam-6473	400	9	)	)	PUNCT
ejpam-6473	400	10	be	be	AUX
ejpam-6473	400	11	(	(	PUNCT
ejpam-6473	400	12	p	p	X
ejpam-6473	400	13	,	,	PUNCT
ejpam-6473	400	14	l	l	NOUN
ejpam-6473	400	15	,	,	PUNCT
ejpam-6473	400	16	s	s	X
ejpam-6473	400	17	,	,	PUNCT
ejpam-6473	400	18	q	q	NOUN
ejpam-6473	400	19	)	)	PUNCT
ejpam-6473	400	20	and	and	CCONJ
ejpam-6473	400	21	(	(	PUNCT
ejpam-6473	400	22	p̄	p̄	INTJ
ejpam-6473	400	23	,	,	PUNCT
ejpam-6473	400	24	l̄	l̄	NOUN
ejpam-6473	400	25	,	,	PUNCT
ejpam-6473	400	26	s̄	s̄	NOUN
ejpam-6473	400	27	,	,	PUNCT
ejpam-6473	400	28	q̄	q̄	NOUN
ejpam-6473	400	29	)	)	PUNCT
ejpam-6473	400	30	.	.	PUNCT
ejpam-6473	401	1	it	it	PRON
ejpam-6473	401	2	is	be	AUX
ejpam-6473	401	3	convenient	convenient	ADJ
ejpam-6473	401	4	to	to	PART
ejpam-6473	401	5	modify	modify	VERB
ejpam-6473	401	6	the	the	DET
ejpam-6473	401	7	variable	variable	NOUN
ejpam-6473	401	8	to	to	PART
ejpam-6473	401	9	demonstrate	demonstrate	VERB
ejpam-6473	401	10	that	that	SCONJ
ejpam-6473	401	11	two	two	NUM
ejpam-6473	401	12	solutions	solution	NOUN
ejpam-6473	401	13	are	be	AUX
ejpam-6473	401	14	equivalent	equivalent	ADJ
ejpam-6473	401	15	.	.	PUNCT
ejpam-6473	402	1	now	now	ADV
ejpam-6473	402	2	,	,	PUNCT
ejpam-6473	402	3	let	let	VERB
ejpam-6473	402	4	p	p	NOUN
ejpam-6473	402	5	=	=	NOUN
ejpam-6473	402	6	eλta1	eλta1	NOUN
ejpam-6473	402	7	,	,	PUNCT
ejpam-6473	402	8	l	l	NOUN
ejpam-6473	402	9	=	=	SYM
ejpam-6473	402	10	eλta2	eλta2	PROPN
ejpam-6473	402	11	,	,	PUNCT
ejpam-6473	402	12	s	s	PART
ejpam-6473	402	13	=	=	PUNCT
ejpam-6473	402	14	eλta3	eλta3	PROPN
ejpam-6473	402	15	,	,	PUNCT
ejpam-6473	402	16	q	q	PROPN
ejpam-6473	402	17	=	=	SYM
ejpam-6473	402	18	eλta4	eλta4	NOUN
ejpam-6473	402	19	,	,	PUNCT
ejpam-6473	402	20	p̄	p̄	NOUN
ejpam-6473	402	21	=	=	PUNCT
ejpam-6473	402	22	eλtā1	eλtā1	PROPN
ejpam-6473	402	23	,	,	PUNCT
ejpam-6473	402	24	l̄	l̄	NOUN
ejpam-6473	402	25	=	=	PUNCT
ejpam-6473	402	26	eλtā2	eλtā2	NOUN
ejpam-6473	402	27	,	,	PUNCT
ejpam-6473	402	28	s̄	s̄	NOUN
ejpam-6473	402	29	=	=	SYM
ejpam-6473	402	30	eλtā3	eλtā3	NOUN
ejpam-6473	402	31	,	,	PUNCT
ejpam-6473	402	32	q̄	q̄	ADJ
ejpam-6473	402	33	=	=	SYM
ejpam-6473	402	34	eλtā4	eλtā4	NOUN
ejpam-6473	402	35	,	,	PUNCT
ejpam-6473	402	36	λ1	λ1	PROPN
ejpam-6473	402	37	=	=	PUNCT
ejpam-6473	402	38	e−λtb1	e−λtb1	NOUN
ejpam-6473	402	39	,	,	PUNCT
ejpam-6473	402	40	λ2	λ2	PROPN
ejpam-6473	402	41	=	=	SYM
ejpam-6473	402	42	e−λtb2	e−λtb2	NOUN
ejpam-6473	402	43	,	,	PUNCT
ejpam-6473	403	1	λ3	λ3	PROPN
ejpam-6473	403	2	=	=	SYM
ejpam-6473	403	3	e−λtb3	e−λtb3	PROPN
ejpam-6473	403	4	,	,	PUNCT
ejpam-6473	403	5	λ4	λ4	PROPN
ejpam-6473	403	6	=	=	SYM
ejpam-6473	403	7	e−λtb4	e−λtb4	PROPN
ejpam-6473	403	8	,	,	PUNCT
ejpam-6473	403	9	λ̄1	λ̄1	X
ejpam-6473	403	10	=	=	PUNCT
ejpam-6473	403	11	e−λtb̄1	e−λtb̄1	PROPN
ejpam-6473	403	12	,	,	PUNCT
ejpam-6473	403	13	λ̄2	λ̄2	X
ejpam-6473	403	14	=	=	SYM
ejpam-6473	403	15	e−λtb̄2	e−λtb̄2	PROPN
ejpam-6473	403	16	,	,	PUNCT
ejpam-6473	403	17	λ̄3	λ̄3	PROPN
ejpam-6473	403	18	=	=	SYM
ejpam-6473	403	19	e−λtb̄3	e−λtb̄3	PROPN
ejpam-6473	403	20	,	,	PUNCT
ejpam-6473	403	21	λ̄4	λ̄4	NOUN
ejpam-6473	403	22	=	=	SYM
ejpam-6473	403	23	e−λtb̄4	e−λtb̄4	PROPN
ejpam-6473	403	24	.	.	PUNCT
ejpam-6473	404	1	λ	λ	PROPN
ejpam-6473	404	2	is	be	AUX
ejpam-6473	404	3	the	the	DET
ejpam-6473	404	4	constant	constant	ADJ
ejpam-6473	404	5	,	,	PUNCT
ejpam-6473	404	6	whose	whose	DET
ejpam-6473	404	7	value	value	NOUN
ejpam-6473	404	8	is	be	AUX
ejpam-6473	404	9	chosen	choose	VERB
ejpam-6473	404	10	at	at	ADP
ejpam-6473	404	11	the	the	DET
ejpam-6473	404	12	end	end	NOUN
ejpam-6473	404	13	.	.	PUNCT
ejpam-6473	405	1	u1	u1	NOUN
ejpam-6473	405	2	=	=	SYM
ejpam-6473	405	3	max	max	PROPN
ejpam-6473	405	4	(	(	PUNCT
ejpam-6473	405	5	min	min	NOUN
ejpam-6473	405	6	(	(	PUNCT
ejpam-6473	405	7	(	(	PUNCT
ejpam-6473	405	8	b1−b4)a0a1	b1−b4)a0a1	ADP
ejpam-6473	405	9	b1	b1	NOUN
ejpam-6473	405	10	,	,	PUNCT
ejpam-6473	405	11	umax	umax	ADJ
ejpam-6473	405	12	1	1	NUM
ejpam-6473	405	13	)	)	PUNCT
ejpam-6473	405	14	,	,	PUNCT
ejpam-6473	405	15	0	0	NUM
ejpam-6473	405	16	)	)	PUNCT
ejpam-6473	405	17	,	,	PUNCT
ejpam-6473	405	18	u2	u2	PROPN
ejpam-6473	405	19	=	=	PUNCT
ejpam-6473	405	20	max	max	PROPN
ejpam-6473	405	21	(	(	PUNCT
ejpam-6473	405	22	min	min	NOUN
ejpam-6473	405	23	(	(	PUNCT
ejpam-6473	405	24	(	(	PUNCT
ejpam-6473	405	25	b4−b1)π1a2+(b2−b4)a2	b4−b1)π1a2+(b2−b4)a2	NOUN
ejpam-6473	405	26	b2	b2	NOUN
ejpam-6473	405	27	,	,	PUNCT
ejpam-6473	405	28	umax	umax	ADJ
ejpam-6473	405	29	2	2	NUM
ejpam-6473	405	30	)	)	PUNCT
ejpam-6473	405	31	,	,	PUNCT
ejpam-6473	405	32	0	0	NUM
ejpam-6473	405	33	)	)	PUNCT
ejpam-6473	405	34	,	,	PUNCT
ejpam-6473	405	35	u3	u3	NOUN
ejpam-6473	405	36	=	=	SYM
ejpam-6473	405	37	max	max	PROPN
ejpam-6473	405	38	(	(	PUNCT
ejpam-6473	405	39	min	min	NOUN
ejpam-6473	405	40	(	(	PUNCT
ejpam-6473	405	41	(	(	PUNCT
ejpam-6473	405	42	b4−b1)π2a3+(b3−b4)a3	b4−b1)π2a3+(b3−b4)a3	PROPN
ejpam-6473	405	43	b3	b3	PROPN
ejpam-6473	405	44	,	,	PUNCT
ejpam-6473	405	45	umax	umax	ADJ
ejpam-6473	405	46	3	3	NUM
ejpam-6473	405	47	)	)	PUNCT
ejpam-6473	405	48	,	,	PUNCT
ejpam-6473	405	49	0	0	NUM
ejpam-6473	405	50	)	)	PUNCT
ejpam-6473	405	51	,	,	PUNCT
ejpam-6473	405	52	ū1	ū1	NOUN
ejpam-6473	405	53	=	=	SYM
ejpam-6473	405	54	max	max	PROPN
ejpam-6473	405	55	(	(	PUNCT
ejpam-6473	405	56	min	min	NOUN
ejpam-6473	405	57	(	(	PUNCT
ejpam-6473	405	58	(	(	PUNCT
ejpam-6473	405	59	b̄1−b̄4)a0ā1	b̄1−b̄4)a0ā1	PROPN
ejpam-6473	405	60	b1	b1	NOUN
ejpam-6473	405	61	,	,	PUNCT
ejpam-6473	405	62	umax	umax	ADJ
ejpam-6473	405	63	1	1	NUM
ejpam-6473	405	64	)	)	PUNCT
ejpam-6473	405	65	,	,	PUNCT
ejpam-6473	405	66	0	0	NUM
ejpam-6473	405	67	)	)	PUNCT
ejpam-6473	405	68	,	,	PUNCT
ejpam-6473	405	69	ū2	ū2	ADJ
ejpam-6473	405	70	=	=	SYM
ejpam-6473	405	71	max	max	PROPN
ejpam-6473	405	72	(	(	PUNCT
ejpam-6473	405	73	min	min	PROPN
ejpam-6473	405	74	(	(	PUNCT
ejpam-6473	405	75	(	(	PUNCT
ejpam-6473	405	76	b̄4−b̄1)π1ā2+(b̄2−b̄4)ā2	b̄4−b̄1)π1ā2+(b̄2−b̄4)ā2	NUM
ejpam-6473	405	77	b2	b2	NOUN
ejpam-6473	405	78	,	,	PUNCT
ejpam-6473	405	79	umax	umax	ADJ
ejpam-6473	405	80	2	2	NUM
ejpam-6473	405	81	)	)	PUNCT
ejpam-6473	405	82	,	,	PUNCT
ejpam-6473	405	83	0	0	NUM
ejpam-6473	405	84	)	)	PUNCT
ejpam-6473	405	85	,	,	PUNCT
ejpam-6473	405	86	ū3	ū3	PROPN
ejpam-6473	405	87	=	=	SYM
ejpam-6473	405	88	max	max	PROPN
ejpam-6473	405	89	(	(	PUNCT
ejpam-6473	405	90	min	min	NOUN
ejpam-6473	405	91	(	(	PUNCT
ejpam-6473	405	92	(	(	PUNCT
ejpam-6473	405	93	b̄4−b̄1)π2ā3+(b̄3−b̄4)ā3	b̄4−b̄1)π2ā3+(b̄3−b̄4)ā3	PROPN
ejpam-6473	405	94	b3	b3	PROPN
ejpam-6473	405	95	,	,	PUNCT
ejpam-6473	405	96	umax	umax	ADJ
ejpam-6473	405	97	3	3	NUM
ejpam-6473	405	98	)	)	PUNCT
ejpam-6473	405	99	,	,	PUNCT
ejpam-6473	405	100	0	0	NUM
ejpam-6473	405	101	)	)	PUNCT
ejpam-6473	405	102	.	.	PUNCT
ejpam-6473	406	1	some	some	DET
ejpam-6473	406	2	inequality	inequality	NOUN
ejpam-6473	406	3	conditions	condition	NOUN
ejpam-6473	406	4	that	that	SCONJ
ejpam-6473	406	5	we	we	PRON
ejpam-6473	406	6	will	will	AUX
ejpam-6473	406	7	use	use	VERB
ejpam-6473	406	8	later	later	ADV
ejpam-6473	406	9	are	be	AUX
ejpam-6473	406	10	taken	take	VERB
ejpam-6473	406	11	from	from	ADP
ejpam-6473	406	12	[	[	X
ejpam-6473	406	13	33	33	NUM
ejpam-6473	406	14	]	]	PUNCT
ejpam-6473	406	15	(	(	PUNCT
ejpam-6473	406	16	w	w	ADP
ejpam-6473	406	17	+	+	CCONJ
ejpam-6473	406	18	y)2	y)2	NOUN
ejpam-6473	406	19	≤	≤	NOUN
ejpam-6473	407	1	2(w2	2(w2	NUM
ejpam-6473	408	1	+	+	CCONJ
ejpam-6473	408	2	y2	y2	NOUN
ejpam-6473	408	3	)	)	PUNCT
ejpam-6473	408	4	,	,	PUNCT
ejpam-6473	408	5	(	(	PUNCT
ejpam-6473	408	6	w	w	PROPN
ejpam-6473	408	7	−	−	PROPN
ejpam-6473	408	8	w̄)(y	w̄)(y	PROPN
ejpam-6473	408	9	−	−	PROPN
ejpam-6473	408	10	ȳ	ȳ	PROPN
ejpam-6473	408	11	)	)	PUNCT
ejpam-6473	408	12	≤	≤	NOUN
ejpam-6473	408	13	(	(	PUNCT
ejpam-6473	408	14	w	w	NOUN
ejpam-6473	408	15	−	−	PROPN
ejpam-6473	408	16	w̄)2	w̄)2	PROPN
ejpam-6473	409	1	+	+	CCONJ
ejpam-6473	409	2	(	(	PUNCT
ejpam-6473	409	3	y	y	PROPN
ejpam-6473	409	4	−	−	PROPN
ejpam-6473	409	5	ȳ)2	ȳ)2	PROPN
ejpam-6473	409	6	)	)	PUNCT
ejpam-6473	409	7	.	.	PUNCT
ejpam-6473	410	1	(	(	PUNCT
ejpam-6473	410	2	ab−	ab−	PUNCT
ejpam-6473	410	3	āb̄)2	āb̄)2	NOUN
ejpam-6473	410	4	=	=	SYM
ejpam-6473	410	5	(	(	PUNCT
ejpam-6473	410	6	ab−	ab−	PUNCT
ejpam-6473	410	7	āb+	āb+	X
ejpam-6473	410	8	āb−	āb−	PROPN
ejpam-6473	410	9	āb̄)2	āb̄)2	PROPN
ejpam-6473	410	10	,	,	PUNCT
ejpam-6473	410	11	≤	≤	NUM
ejpam-6473	410	12	max{2b2	max{2b2	ADJ
ejpam-6473	410	13	,	,	PUNCT
ejpam-6473	410	14	2ā2}[(a−	2ā2}[(a−	NUM
ejpam-6473	410	15	ā)2	ā)2	NOUN
ejpam-6473	410	16	+	+	CCONJ
ejpam-6473	410	17	(	(	PUNCT
ejpam-6473	410	18	b−	b−	PROPN
ejpam-6473	410	19	b̄)2	b̄)2	PROPN
ejpam-6473	410	20	]	]	PUNCT
ejpam-6473	410	21	,	,	PUNCT
ejpam-6473	410	22	≤	≤	NUM
ejpam-6473	410	23	d0[(a−	d0[(a−	PART
ejpam-6473	410	24	ā)2	ā)2	NOUN
ejpam-6473	410	25	+	+	CCONJ
ejpam-6473	410	26	(	(	PUNCT
ejpam-6473	410	27	b−	b−	PROPN
ejpam-6473	410	28	b̄)2	b̄)2	PROPN
ejpam-6473	410	29	]	]	PUNCT
ejpam-6473	410	30	.	.	PUNCT
ejpam-6473	411	1	(	(	PUNCT
ejpam-6473	411	2	c−	c−	NOUN
ejpam-6473	411	3	c̄)(ab−	c̄)(ab−	NOUN
ejpam-6473	411	4	āb̄	āb̄	ADJ
ejpam-6473	411	5	)	)	PUNCT
ejpam-6473	411	6	=	=	SYM
ejpam-6473	411	7	(	(	PUNCT
ejpam-6473	411	8	c−	c−	X
ejpam-6473	411	9	c̄)(ab−	c̄)(ab−	NOUN
ejpam-6473	411	10	āb+	āb+	NOUN
ejpam-6473	411	11	āb−	āb−	PROPN
ejpam-6473	411	12	āb̄	āb̄	PROPN
ejpam-6473	411	13	)	)	PUNCT
ejpam-6473	411	14	,	,	PUNCT
ejpam-6473	411	15	s.	s.	PROPN
ejpam-6473	411	16	bano	bano	PROPN
ejpam-6473	411	17	et	et	PROPN
ejpam-6473	411	18	al	al	PROPN
ejpam-6473	411	19	.	.	PUNCT
ejpam-6473	411	20	/	/	SYM
ejpam-6473	411	21	eur	eur	PROPN
ejpam-6473	411	22	.	.	PUNCT
ejpam-6473	412	1	j.	j.	PROPN
ejpam-6473	412	2	pure	pure	PROPN
ejpam-6473	412	3	appl	appl	PROPN
ejpam-6473	412	4	.	.	PROPN
ejpam-6473	412	5	math	math	PROPN
ejpam-6473	412	6	,	,	PUNCT
ejpam-6473	412	7	18	18	NUM
ejpam-6473	412	8	(	(	PUNCT
ejpam-6473	412	9	4	4	NUM
ejpam-6473	412	10	)	)	PUNCT
ejpam-6473	412	11	(	(	PUNCT
ejpam-6473	412	12	2025	2025	NUM
ejpam-6473	412	13	)	)	PUNCT
ejpam-6473	412	14	,	,	PUNCT
ejpam-6473	412	15	6473	6473	NUM
ejpam-6473	412	16	23	23	NUM
ejpam-6473	412	17	of	of	ADP
ejpam-6473	412	18	38	38	NUM
ejpam-6473	412	19	=	=	SYM
ejpam-6473	412	20	(	(	PUNCT
ejpam-6473	412	21	c−	c−	X
ejpam-6473	412	22	c̄)(b(a−	c̄)(b(a−	PROPN
ejpam-6473	412	23	ā	ā	VERB
ejpam-6473	412	24	)	)	PUNCT
ejpam-6473	412	25	+	+	NUM
ejpam-6473	412	26	ā(b−	ā(b−	NOUN
ejpam-6473	412	27	b̄	b̄	NOUN
ejpam-6473	412	28	)	)	PUNCT
ejpam-6473	412	29	)	)	PUNCT
ejpam-6473	412	30	,	,	PUNCT
ejpam-6473	412	31	≤	≤	NUM
ejpam-6473	412	32	d1((a−	d1((a−	NOUN
ejpam-6473	412	33	ā)2	ā)2	PROPN
ejpam-6473	412	34	+	+	CCONJ
ejpam-6473	412	35	(	(	PUNCT
ejpam-6473	412	36	b−	b−	PROPN
ejpam-6473	412	37	b̄)2	b̄)2	PROPN
ejpam-6473	412	38	+	+	CCONJ
ejpam-6473	412	39	(	(	PUNCT
ejpam-6473	412	40	c−	c−	ADJ
ejpam-6473	412	41	c̄)2	c̄)2	NOUN
ejpam-6473	412	42	)	)	PUNCT
ejpam-6473	412	43	.	.	PUNCT
ejpam-6473	413	1	from	from	ADP
ejpam-6473	413	2	first	first	ADJ
ejpam-6473	413	3	equation	equation	NOUN
ejpam-6473	413	4	of	of	ADP
ejpam-6473	413	5	system(15	system(15	NOUN
ejpam-6473	413	6	)	)	PUNCT
ejpam-6473	413	7	,	,	PUNCT
ejpam-6473	413	8	we	we	PRON
ejpam-6473	413	9	get	get	VERB
ejpam-6473	413	10	λa1e	λa1e	PROPN
ejpam-6473	413	11	λt	λt	ADP
ejpam-6473	413	12	+	+	NOUN
ejpam-6473	413	13	eλta′1	eλta′1	X
ejpam-6473	413	14	=	=	SYM
ejpam-6473	413	15	λ−	λ−	PROPN
ejpam-6473	413	16	βe2λta1a3(1	βe2λta1a3(1	PROPN
ejpam-6473	414	1	+	+	NUM
ejpam-6473	414	2	νeλta3)−	νeλta3)−	NOUN
ejpam-6473	414	3	(	(	PUNCT
ejpam-6473	414	4	b+	b+	X
ejpam-6473	414	5	µ)eλta1	µ)eλta1	ADP
ejpam-6473	414	6	−a0u1a1e	−a0u1a1e	NOUN
ejpam-6473	414	7	λt	λt	ADP
ejpam-6473	414	8	+	+	CCONJ
ejpam-6473	414	9	π1u2a2e	π1u2a2e	PROPN
ejpam-6473	414	10	λt	λt	X
ejpam-6473	414	11	+	+	CCONJ
ejpam-6473	414	12	π2u3a3e	π2u3a3e	NOUN
ejpam-6473	414	13	λt	λt	ADP
ejpam-6473	414	14	,	,	PUNCT
ejpam-6473	414	15	=	=	SYM
ejpam-6473	414	16	⇒	⇒	NOUN
ejpam-6473	414	17	(	(	PUNCT
ejpam-6473	414	18	λ+	λ+	X
ejpam-6473	414	19	b+	b+	X
ejpam-6473	414	20	µ)a1	µ)a1	PROPN
ejpam-6473	414	21	+	+	CCONJ
ejpam-6473	414	22	a′1	a′1	ADJ
ejpam-6473	414	23	=	=	SYM
ejpam-6473	414	24	λe−λt	λe−λt	X
ejpam-6473	414	25	−	−	NOUN
ejpam-6473	414	26	βa1a3e	βa1a3e	PROPN
ejpam-6473	414	27	λt	λt	ADP
ejpam-6473	414	28	−	−	PROPN
ejpam-6473	414	29	νβa1a	νβa1a	NOUN
ejpam-6473	414	30	2	2	NUM
ejpam-6473	414	31	3e	3e	NOUN
ejpam-6473	414	32	2λt	2λt	NOUN
ejpam-6473	414	33	−a0u1a1	−a0u1a1	NOUN
ejpam-6473	414	34	+	+	CCONJ
ejpam-6473	414	35	π1a2u2	π1a2u2	PROPN
ejpam-6473	414	36	+	+	CCONJ
ejpam-6473	414	37	π2u3a3	π2u3a3	PROPN
ejpam-6473	414	38	.	.	PUNCT
ejpam-6473	414	39	similarly	similarly	ADV
ejpam-6473	414	40	,	,	PUNCT
ejpam-6473	414	41	=	=	NOUN
ejpam-6473	414	42	⇒	⇒	NOUN
ejpam-6473	414	43	(	(	PUNCT
ejpam-6473	414	44	λ+	λ+	X
ejpam-6473	414	45	b+	b+	X
ejpam-6473	414	46	µ)ā1	µ)ā1	ADV
ejpam-6473	414	47	+	+	CCONJ
ejpam-6473	414	48	ā1	ā1	NOUN
ejpam-6473	414	49	′	′	NUM
ejpam-6473	415	1	=	=	PUNCT
ejpam-6473	415	2	λe−λt	λe−λt	NOUN
ejpam-6473	415	3	−	−	NOUN
ejpam-6473	415	4	βā1ā3e	βā1ā3e	NOUN
ejpam-6473	415	5	λt	λt	ADP
ejpam-6473	415	6	−	−	PROPN
ejpam-6473	415	7	νβā1ā3	νβā1ā3	PRON
ejpam-6473	415	8	2e2λt	2e2λt	PROPN
ejpam-6473	415	9	−a0u1ā1	−a0u1ā1	PROPN
ejpam-6473	416	1	+	+	CCONJ
ejpam-6473	416	2	π1ā2ū2	π1ā2ū2	NOUN
ejpam-6473	416	3	+	+	CCONJ
ejpam-6473	416	4	π2ū3ā3	π2ū3ā3	NOUN
ejpam-6473	416	5	,	,	PUNCT
ejpam-6473	416	6	by	by	ADP
ejpam-6473	416	7	subtracting	subtract	VERB
ejpam-6473	416	8	and	and	CCONJ
ejpam-6473	416	9	integrating	integrate	VERB
ejpam-6473	416	10	the	the	DET
ejpam-6473	416	11	above	above	ADJ
ejpam-6473	416	12	two	two	NUM
ejpam-6473	416	13	equations	equation	NOUN
ejpam-6473	416	14	,	,	PUNCT
ejpam-6473	416	15	we	we	PRON
ejpam-6473	416	16	get	get	VERB
ejpam-6473	417	1	=	=	PRON
ejpam-6473	417	2	⇒	⇒	NOUN
ejpam-6473	417	3	(	(	PUNCT
ejpam-6473	417	4	λ+	λ+	X
ejpam-6473	417	5	b+	b+	X
ejpam-6473	417	6	µ	µ	X
ejpam-6473	417	7	)	)	PUNCT
ejpam-6473	417	8	∫	∫	PROPN
ejpam-6473	417	9	t	t	PROPN
ejpam-6473	417	10	0	0	NUM
ejpam-6473	418	1	(	(	PUNCT
ejpam-6473	418	2	a1	a1	NOUN
ejpam-6473	418	3	−	−	NOUN
ejpam-6473	418	4	ā1	ā1	NOUN
ejpam-6473	418	5	)	)	PUNCT
ejpam-6473	418	6	2	2	NUM
ejpam-6473	418	7	dt+	dt+	NOUN
ejpam-6473	418	8	1	1	NUM
ejpam-6473	418	9	2	2	NUM
ejpam-6473	418	10	(	(	PUNCT
ejpam-6473	418	11	a1(t	a1(t	ADV
ejpam-6473	418	12	)	)	PUNCT
ejpam-6473	418	13	−	−	NOUN
ejpam-6473	418	14	ā1(t	ā1(t	NUM
ejpam-6473	418	15	)	)	PUNCT
ejpam-6473	418	16	)	)	PUNCT
ejpam-6473	418	17	2	2	NUM
ejpam-6473	419	1	=	=	SYM
ejpam-6473	419	2	−β	−β	NOUN
ejpam-6473	419	3	∫	∫	PROPN
ejpam-6473	419	4	t	t	PROPN
ejpam-6473	419	5	0	0	NUM
ejpam-6473	419	6	(	(	PUNCT
ejpam-6473	419	7	eλt(a1a3	eλt(a1a3	X
ejpam-6473	419	8	−	−	NOUN
ejpam-6473	419	9	ā1ā3)(a1	ā1ā3)(a1	PUNCT
ejpam-6473	419	10	−	−	NUM
ejpam-6473	419	11	ā1	ā1	NOUN
ejpam-6473	419	12	)	)	PUNCT
ejpam-6473	419	13	)	)	PUNCT
ejpam-6473	420	1	dt	dt	X
ejpam-6473	421	1	−	−	PROPN
ejpam-6473	421	2	νβ	νβ	PROPN
ejpam-6473	421	3	∫	∫	PROPN
ejpam-6473	421	4	t	t	PROPN
ejpam-6473	421	5	0	0	NUM
ejpam-6473	422	1	(	(	PUNCT
ejpam-6473	422	2	e2λt(a1a	e2λt(a1a	PROPN
ejpam-6473	422	3	2	2	NUM
ejpam-6473	422	4	3	3	NUM
ejpam-6473	422	5	−	−	PROPN
ejpam-6473	422	6	ā1ā3	ā1ā3	PROPN
ejpam-6473	422	7	2)(a1	2)(a1	NUM
ejpam-6473	422	8	−	−	NOUN
ejpam-6473	422	9	ā1	ā1	NOUN
ejpam-6473	422	10	)	)	PUNCT
ejpam-6473	422	11	)	)	PUNCT
ejpam-6473	422	12	dt	dt	PUNCT
ejpam-6473	423	1	−	−	PROPN
ejpam-6473	423	2	a0	a0	PROPN
ejpam-6473	423	3	∫	∫	PROPN
ejpam-6473	423	4	t	t	PROPN
ejpam-6473	423	5	0	0	NUM
ejpam-6473	423	6	(	(	PUNCT
ejpam-6473	423	7	(	(	PUNCT
ejpam-6473	423	8	u1a1	u1a1	NOUN
ejpam-6473	423	9	−	−	NOUN
ejpam-6473	423	10	ū1ā1)(a1	ū1ā1)(a1	PUNCT
ejpam-6473	423	11	−	−	PROPN
ejpam-6473	423	12	ā1	ā1	NOUN
ejpam-6473	423	13	)	)	PUNCT
ejpam-6473	423	14	)	)	PUNCT
ejpam-6473	423	15	dt	dt	PUNCT
ejpam-6473	424	1	+	+	CCONJ
ejpam-6473	424	2	π1	π1	ADJ
ejpam-6473	424	3	∫	∫	PROPN
ejpam-6473	424	4	t	t	PROPN
ejpam-6473	424	5	0	0	NUM
ejpam-6473	424	6	(	(	PUNCT
ejpam-6473	424	7	(	(	PUNCT
ejpam-6473	424	8	u2a2	u2a2	INTJ
ejpam-6473	424	9	−	−	NOUN
ejpam-6473	424	10	ā2ū2)(a1	ā2ū2)(a1	PUNCT
ejpam-6473	424	11	−	−	NUM
ejpam-6473	424	12	ā1	ā1	NOUN
ejpam-6473	424	13	)	)	PUNCT
ejpam-6473	424	14	)	)	PUNCT
ejpam-6473	424	15	dt	dt	PUNCT
ejpam-6473	425	1	+	+	CCONJ
ejpam-6473	425	2	π2	π2	ADJ
ejpam-6473	425	3	∫	∫	PROPN
ejpam-6473	425	4	t	t	PROPN
ejpam-6473	425	5	0	0	NUM
ejpam-6473	425	6	(	(	PUNCT
ejpam-6473	425	7	(	(	PUNCT
ejpam-6473	425	8	u3a3	u3a3	ADP
ejpam-6473	425	9	−	−	NOUN
ejpam-6473	425	10	ā3ū3)(a1	ā3ū3)(a1	X
ejpam-6473	425	11	−	−	PROPN
ejpam-6473	425	12	ā1	ā1	NOUN
ejpam-6473	425	13	)	)	PUNCT
ejpam-6473	425	14	)	)	PUNCT
ejpam-6473	426	1	dt	dt	X
ejpam-6473	426	2	.	.	PUNCT
ejpam-6473	427	1	(	(	PUNCT
ejpam-6473	427	2	16	16	NUM
ejpam-6473	427	3	)	)	PUNCT
ejpam-6473	427	4	now	now	ADV
ejpam-6473	427	5	(	(	PUNCT
ejpam-6473	427	6	a1a3	a1a3	ADP
ejpam-6473	427	7	−	−	NOUN
ejpam-6473	427	8	ā1ā3)(a1	ā1ā3)(a1	PUNCT
ejpam-6473	427	9	−	−	NUM
ejpam-6473	427	10	ā1	ā1	NOUN
ejpam-6473	427	11	)	)	PUNCT
ejpam-6473	427	12	≤	≤	PUNCT
ejpam-6473	427	13	b1[(a1	b1[(a1	NOUN
ejpam-6473	427	14	−	−	NOUN
ejpam-6473	427	15	ā1	ā1	NOUN
ejpam-6473	427	16	)	)	PUNCT
ejpam-6473	427	17	2	2	NUM
ejpam-6473	427	18	+	+	CCONJ
ejpam-6473	427	19	(	(	PUNCT
ejpam-6473	427	20	a3	a3	NOUN
ejpam-6473	427	21	−	−	PROPN
ejpam-6473	427	22	ā3	ā3	NOUN
ejpam-6473	427	23	)	)	PUNCT
ejpam-6473	427	24	2	2	NUM
ejpam-6473	427	25	]	]	PUNCT
ejpam-6473	427	26	.	.	PUNCT
ejpam-6473	428	1	(	(	PUNCT
ejpam-6473	428	2	a1a	a1a	PROPN
ejpam-6473	428	3	2	2	NUM
ejpam-6473	428	4	3	3	NUM
ejpam-6473	428	5	−	−	PROPN
ejpam-6473	428	6	ā1ā3	ā1ā3	PROPN
ejpam-6473	428	7	2)(a1	2)(a1	NUM
ejpam-6473	428	8	−	−	NOUN
ejpam-6473	428	9	ā1	ā1	NOUN
ejpam-6473	428	10	)	)	PUNCT
ejpam-6473	428	11	≤	≤	PUNCT
ejpam-6473	429	1	b2[(a1	b2[(a1	PROPN
ejpam-6473	429	2	−	−	PROPN
ejpam-6473	429	3	ā1	ā1	NOUN
ejpam-6473	429	4	)	)	PUNCT
ejpam-6473	429	5	2	2	NUM
ejpam-6473	430	1	+	+	CCONJ
ejpam-6473	430	2	(	(	PUNCT
ejpam-6473	430	3	a3	a3	NOUN
ejpam-6473	430	4	−	−	PROPN
ejpam-6473	430	5	ā3	ā3	NOUN
ejpam-6473	430	6	)	)	PUNCT
ejpam-6473	430	7	2	2	NUM
ejpam-6473	430	8	]	]	PUNCT
ejpam-6473	430	9	.	.	PUNCT
ejpam-6473	431	1	(	(	PUNCT
ejpam-6473	431	2	a1u1	a1u1	X
ejpam-6473	431	3	−	−	NOUN
ejpam-6473	431	4	ā1ū1)(a1	ā1ū1)(a1	PUNCT
ejpam-6473	431	5	−	−	NUM
ejpam-6473	431	6	ā1	ā1	NOUN
ejpam-6473	431	7	)	)	PUNCT
ejpam-6473	431	8	≤	≤	NOUN
ejpam-6473	431	9	b3[(a1	b3[(a1	NOUN
ejpam-6473	431	10	−	−	PROPN
ejpam-6473	431	11	ā1	ā1	NOUN
ejpam-6473	431	12	)	)	PUNCT
ejpam-6473	431	13	2	2	NUM
ejpam-6473	432	1	+	+	CCONJ
ejpam-6473	432	2	(	(	PUNCT
ejpam-6473	432	3	u1	u1	PROPN
ejpam-6473	432	4	−	−	PROPN
ejpam-6473	432	5	ū1	ū1	NUM
ejpam-6473	432	6	)	)	PUNCT
ejpam-6473	432	7	2	2	NUM
ejpam-6473	432	8	]	]	PUNCT
ejpam-6473	432	9	.	.	PUNCT
ejpam-6473	433	1	(	(	PUNCT
ejpam-6473	433	2	u1	u1	NOUN
ejpam-6473	433	3	−	−	PROPN
ejpam-6473	433	4	ū1	ū1	NUM
ejpam-6473	433	5	)	)	PUNCT
ejpam-6473	433	6	2	2	NUM
ejpam-6473	433	7	=	=	SYM
ejpam-6473	433	8	(	(	PUNCT
ejpam-6473	433	9	a0	a0	NOUN
ejpam-6473	433	10	b1	b1	PROPN
ejpam-6473	433	11	)	)	PUNCT
ejpam-6473	433	12	2	2	NUM
ejpam-6473	434	1	[	[	X
ejpam-6473	434	2	(	(	PUNCT
ejpam-6473	434	3	b1	b1	NOUN
ejpam-6473	434	4	−	−	PROPN
ejpam-6473	434	5	b4)a1	b4)a1	NOUN
ejpam-6473	434	6	−	−	PROPN
ejpam-6473	434	7	(	(	PUNCT
ejpam-6473	434	8	b̄1	b̄1	PROPN
ejpam-6473	434	9	−	−	PROPN
ejpam-6473	434	10	b̄4)ā1	b̄4)ā1	PROPN
ejpam-6473	434	11	]	]	X
ejpam-6473	434	12	2	2	NUM
ejpam-6473	434	13	,	,	PUNCT
ejpam-6473	434	14	≤	≤	NUM
ejpam-6473	434	15	b4[(a1	b4[(a1	VERB
ejpam-6473	434	16	−	−	PROPN
ejpam-6473	434	17	ā1	ā1	NOUN
ejpam-6473	434	18	)	)	PUNCT
ejpam-6473	434	19	2	2	NUM
ejpam-6473	434	20	+	+	CCONJ
ejpam-6473	434	21	(	(	PUNCT
ejpam-6473	434	22	b1	b1	NOUN
ejpam-6473	434	23	−	−	PROPN
ejpam-6473	434	24	b̄1	b̄1	NUM
ejpam-6473	434	25	)	)	PUNCT
ejpam-6473	434	26	2	2	NUM
ejpam-6473	435	1	+	+	CCONJ
ejpam-6473	435	2	(	(	PUNCT
ejpam-6473	435	3	b4	b4	NOUN
ejpam-6473	435	4	−	−	PROPN
ejpam-6473	435	5	b̄4	b̄4	NOUN
ejpam-6473	435	6	)	)	PUNCT
ejpam-6473	435	7	2	2	NUM
ejpam-6473	435	8	]	]	PUNCT
ejpam-6473	435	9	.	.	PUNCT
ejpam-6473	436	1	s.	s.	PROPN
ejpam-6473	436	2	bano	bano	PROPN
ejpam-6473	436	3	et	et	PROPN
ejpam-6473	436	4	al	al	PROPN
ejpam-6473	436	5	.	.	PUNCT
ejpam-6473	436	6	/	/	SYM
ejpam-6473	436	7	eur	eur	PROPN
ejpam-6473	436	8	.	.	PUNCT
ejpam-6473	437	1	j.	j.	PROPN
ejpam-6473	437	2	pure	pure	PROPN
ejpam-6473	437	3	appl	appl	PROPN
ejpam-6473	437	4	.	.	PROPN
ejpam-6473	437	5	math	math	PROPN
ejpam-6473	437	6	,	,	PUNCT
ejpam-6473	437	7	18	18	NUM
ejpam-6473	437	8	(	(	PUNCT
ejpam-6473	437	9	4	4	NUM
ejpam-6473	437	10	)	)	PUNCT
ejpam-6473	437	11	(	(	PUNCT
ejpam-6473	437	12	2025	2025	NUM
ejpam-6473	437	13	)	)	PUNCT
ejpam-6473	437	14	,	,	PUNCT
ejpam-6473	437	15	6473	6473	NUM
ejpam-6473	437	16	24	24	NUM
ejpam-6473	437	17	of	of	ADP
ejpam-6473	437	18	38	38	NUM
ejpam-6473	437	19	use	use	VERB
ejpam-6473	437	20	the	the	DET
ejpam-6473	437	21	value	value	NOUN
ejpam-6473	437	22	of	of	ADP
ejpam-6473	437	23	(	(	PUNCT
ejpam-6473	437	24	u1	u1	NOUN
ejpam-6473	437	25	−	−	PROPN
ejpam-6473	437	26	ū1	ū1	NUM
ejpam-6473	437	27	)	)	PUNCT
ejpam-6473	437	28	in	in	ADP
ejpam-6473	437	29	the	the	DET
ejpam-6473	437	30	above	above	ADJ
ejpam-6473	437	31	equation	equation	NOUN
ejpam-6473	437	32	(	(	PUNCT
ejpam-6473	437	33	a1u1	a1u1	X
ejpam-6473	437	34	−	−	PROPN
ejpam-6473	437	35	ā1ū1)(a1	ā1ū1)(a1	PUNCT
ejpam-6473	437	36	−	−	NOUN
ejpam-6473	437	37	ā1	ā1	NOUN
ejpam-6473	437	38	)	)	PUNCT
ejpam-6473	437	39	≤	≤	NOUN
ejpam-6473	437	40	b5[(a1	b5[(a1	PROPN
ejpam-6473	437	41	−	−	PROPN
ejpam-6473	437	42	ā1	ā1	NOUN
ejpam-6473	437	43	)	)	PUNCT
ejpam-6473	437	44	2	2	NUM
ejpam-6473	438	1	+	+	CCONJ
ejpam-6473	438	2	(	(	PUNCT
ejpam-6473	438	3	b1	b1	NOUN
ejpam-6473	438	4	−	−	PROPN
ejpam-6473	438	5	b̄1	b̄1	NUM
ejpam-6473	438	6	)	)	PUNCT
ejpam-6473	438	7	2	2	NUM
ejpam-6473	439	1	+	+	CCONJ
ejpam-6473	439	2	(	(	PUNCT
ejpam-6473	439	3	b4	b4	NOUN
ejpam-6473	439	4	−	−	PROPN
ejpam-6473	439	5	b̄4	b̄4	NOUN
ejpam-6473	439	6	)	)	PUNCT
ejpam-6473	439	7	2	2	NUM
ejpam-6473	439	8	]	]	PUNCT
ejpam-6473	439	9	.	.	PUNCT
ejpam-6473	440	1	(	(	PUNCT
ejpam-6473	440	2	a2u2	a2u2	PROPN
ejpam-6473	440	3	−	−	PROPN
ejpam-6473	440	4	ā2ū2)(a1	ā2ū2)(a1	PUNCT
ejpam-6473	440	5	−	−	NUM
ejpam-6473	440	6	ā1	ā1	NOUN
ejpam-6473	440	7	)	)	PUNCT
ejpam-6473	440	8	≤	≤	PUNCT
ejpam-6473	441	1	b6[(u2	b6[(u2	PROPN
ejpam-6473	441	2	−	−	PROPN
ejpam-6473	441	3	ū2	ū2	ADJ
ejpam-6473	441	4	)	)	PUNCT
ejpam-6473	441	5	2	2	NUM
ejpam-6473	442	1	+	+	CCONJ
ejpam-6473	442	2	(	(	PUNCT
ejpam-6473	442	3	a1	a1	NOUN
ejpam-6473	442	4	−	−	NOUN
ejpam-6473	442	5	ā1	ā1	NOUN
ejpam-6473	442	6	)	)	PUNCT
ejpam-6473	442	7	2	2	NUM
ejpam-6473	443	1	+	+	CCONJ
ejpam-6473	443	2	(	(	PUNCT
ejpam-6473	443	3	a2	a2	PROPN
ejpam-6473	443	4	−	−	PROPN
ejpam-6473	443	5	ā2	ā2	PROPN
ejpam-6473	443	6	)	)	PUNCT
ejpam-6473	443	7	2	2	NUM
ejpam-6473	443	8	]	]	PUNCT
ejpam-6473	443	9	.	.	PUNCT
ejpam-6473	444	1	(	(	PUNCT
ejpam-6473	444	2	u2	u2	PROPN
ejpam-6473	444	3	−	−	PROPN
ejpam-6473	444	4	ū2	ū2	ADJ
ejpam-6473	444	5	)	)	PUNCT
ejpam-6473	444	6	2	2	NUM
ejpam-6473	445	1	=	=	SYM
ejpam-6473	445	2	(	(	PUNCT
ejpam-6473	445	3	1	1	NUM
ejpam-6473	445	4	b2	b2	NOUN
ejpam-6473	445	5	)	)	PUNCT
ejpam-6473	445	6	2	2	NUM
ejpam-6473	446	1	[	[	X
ejpam-6473	446	2	π1a2(b4	π1a2(b4	NOUN
ejpam-6473	446	3	−	−	PROPN
ejpam-6473	446	4	b1	b1	NOUN
ejpam-6473	446	5	)	)	PUNCT
ejpam-6473	447	1	+	+	NUM
ejpam-6473	448	1	a2(b2	a2(b2	NOUN
ejpam-6473	448	2	−	−	NOUN
ejpam-6473	448	3	b4)−	b4)−	NOUN
ejpam-6473	448	4	π1ā2(b̄4	π1ā2(b̄4	VERB
ejpam-6473	448	5	−	−	PROPN
ejpam-6473	448	6	b̄1	b̄1	NUM
ejpam-6473	448	7	)	)	PUNCT
ejpam-6473	448	8	−	−	PROPN
ejpam-6473	448	9	ā2(b̄2	ā2(b̄2	ADV
ejpam-6473	448	10	−	−	PROPN
ejpam-6473	448	11	b̄4	b̄4	ADJ
ejpam-6473	448	12	)	)	PUNCT
ejpam-6473	448	13	]	]	PUNCT
ejpam-6473	449	1	2	2	NUM
ejpam-6473	449	2	,	,	PUNCT
ejpam-6473	449	3	≤	≤	NUM
ejpam-6473	449	4	b7[(a2	b7[(a2	PROPN
ejpam-6473	449	5	−	−	PROPN
ejpam-6473	449	6	ā2	ā2	PROPN
ejpam-6473	449	7	)	)	PUNCT
ejpam-6473	449	8	2	2	NUM
ejpam-6473	450	1	+	+	CCONJ
ejpam-6473	450	2	(	(	PUNCT
ejpam-6473	450	3	b1	b1	NOUN
ejpam-6473	450	4	−	−	PROPN
ejpam-6473	450	5	b̄1	b̄1	NUM
ejpam-6473	450	6	)	)	PUNCT
ejpam-6473	450	7	2	2	NUM
ejpam-6473	451	1	+	+	CCONJ
ejpam-6473	451	2	(	(	PUNCT
ejpam-6473	451	3	b2	b2	NOUN
ejpam-6473	451	4	−	−	NOUN
ejpam-6473	451	5	b̄2	b̄2	NOUN
ejpam-6473	451	6	)	)	PUNCT
ejpam-6473	451	7	2	2	NUM
ejpam-6473	452	1	+	+	CCONJ
ejpam-6473	452	2	(	(	PUNCT
ejpam-6473	452	3	b4	b4	NOUN
ejpam-6473	452	4	−	−	PROPN
ejpam-6473	452	5	b̄4	b̄4	NOUN
ejpam-6473	452	6	)	)	PUNCT
ejpam-6473	452	7	2	2	NUM
ejpam-6473	452	8	]	]	PUNCT
ejpam-6473	452	9	.	.	PUNCT
ejpam-6473	453	1	use	use	VERB
ejpam-6473	453	2	the	the	DET
ejpam-6473	453	3	value	value	NOUN
ejpam-6473	453	4	of	of	ADP
ejpam-6473	453	5	(	(	PUNCT
ejpam-6473	453	6	u2	u2	PROPN
ejpam-6473	453	7	−	−	PROPN
ejpam-6473	453	8	ū2	ū2	ADJ
ejpam-6473	453	9	)	)	PUNCT
ejpam-6473	453	10	2,we	2,we	NUM
ejpam-6473	453	11	get	get	VERB
ejpam-6473	453	12	(	(	PUNCT
ejpam-6473	453	13	a2u2	a2u2	NOUN
ejpam-6473	453	14	−	−	PROPN
ejpam-6473	453	15	ā2ū2)(a1	ā2ū2)(a1	PUNCT
ejpam-6473	453	16	−	−	NUM
ejpam-6473	453	17	ā1	ā1	NOUN
ejpam-6473	453	18	)	)	PUNCT
ejpam-6473	453	19	≤	≤	NOUN
ejpam-6473	453	20	b8[(a1	b8[(a1	PRON
ejpam-6473	453	21	−	−	NUM
ejpam-6473	453	22	ā1	ā1	NOUN
ejpam-6473	453	23	)	)	PUNCT
ejpam-6473	453	24	2	2	NUM
ejpam-6473	454	1	+	+	CCONJ
ejpam-6473	454	2	(	(	PUNCT
ejpam-6473	454	3	a2	a2	PROPN
ejpam-6473	454	4	−	−	PROPN
ejpam-6473	454	5	ā2	ā2	PROPN
ejpam-6473	454	6	)	)	PUNCT
ejpam-6473	454	7	2	2	NUM
ejpam-6473	455	1	+	+	CCONJ
ejpam-6473	455	2	(	(	PUNCT
ejpam-6473	455	3	b1	b1	NOUN
ejpam-6473	455	4	−	−	PROPN
ejpam-6473	455	5	b̄1	b̄1	NUM
ejpam-6473	455	6	)	)	PUNCT
ejpam-6473	455	7	2	2	NUM
ejpam-6473	456	1	+	+	CCONJ
ejpam-6473	456	2	(	(	PUNCT
ejpam-6473	456	3	b2	b2	NOUN
ejpam-6473	456	4	−	−	NOUN
ejpam-6473	456	5	b̄2	b̄2	NOUN
ejpam-6473	456	6	)	)	PUNCT
ejpam-6473	456	7	2	2	NUM
ejpam-6473	457	1	+	+	CCONJ
ejpam-6473	457	2	(	(	PUNCT
ejpam-6473	457	3	b4	b4	NOUN
ejpam-6473	457	4	−	−	PROPN
ejpam-6473	457	5	b̄4	b̄4	NOUN
ejpam-6473	457	6	)	)	PUNCT
ejpam-6473	457	7	2	2	NUM
ejpam-6473	457	8	]	]	PUNCT
ejpam-6473	457	9	.	.	PUNCT
ejpam-6473	458	1	(	(	PUNCT
ejpam-6473	458	2	a3u3	a3u3	ADV
ejpam-6473	458	3	−	−	X
ejpam-6473	458	4	ā3ū3)(a1	ā3ū3)(a1	PUNCT
ejpam-6473	458	5	−	−	PROPN
ejpam-6473	458	6	ā1	ā1	NOUN
ejpam-6473	458	7	)	)	PUNCT
ejpam-6473	458	8	≤	≤	NOUN
ejpam-6473	458	9	b9[(u3	b9[(u3	PROPN
ejpam-6473	458	10	−	−	PROPN
ejpam-6473	458	11	ū3	ū3	NOUN
ejpam-6473	458	12	)	)	PUNCT
ejpam-6473	458	13	2	2	NUM
ejpam-6473	459	1	+	+	CCONJ
ejpam-6473	459	2	(	(	PUNCT
ejpam-6473	459	3	a1	a1	NOUN
ejpam-6473	459	4	−	−	NOUN
ejpam-6473	459	5	ā1	ā1	NOUN
ejpam-6473	459	6	)	)	PUNCT
ejpam-6473	459	7	2	2	NUM
ejpam-6473	460	1	+	+	CCONJ
ejpam-6473	460	2	(	(	PUNCT
ejpam-6473	460	3	a3	a3	NOUN
ejpam-6473	460	4	−	−	PROPN
ejpam-6473	460	5	ā3	ā3	NOUN
ejpam-6473	460	6	)	)	PUNCT
ejpam-6473	460	7	2	2	NUM
ejpam-6473	460	8	]	]	PUNCT
ejpam-6473	460	9	,	,	PUNCT
ejpam-6473	460	10	(	(	PUNCT
ejpam-6473	460	11	u3	u3	NOUN
ejpam-6473	460	12	−	−	PROPN
ejpam-6473	460	13	ū3	ū3	PROPN
ejpam-6473	460	14	)	)	PUNCT
ejpam-6473	460	15	2	2	NUM
ejpam-6473	460	16	=	=	SYM
ejpam-6473	460	17	(	(	PUNCT
ejpam-6473	460	18	1	1	NUM
ejpam-6473	460	19	b3	b3	NOUN
ejpam-6473	460	20	)	)	PUNCT
ejpam-6473	460	21	2	2	NUM
ejpam-6473	461	1	[	[	X
ejpam-6473	461	2	π2a3(b4	π2a3(b4	NOUN
ejpam-6473	461	3	−	−	NOUN
ejpam-6473	461	4	b1	b1	NOUN
ejpam-6473	461	5	)	)	PUNCT
ejpam-6473	462	1	+	+	CCONJ
ejpam-6473	463	1	a3(b3	a3(b3	NOUN
ejpam-6473	463	2	−	−	NOUN
ejpam-6473	463	3	b4)−	b4)−	NOUN
ejpam-6473	463	4	π2ā3(b̄4	π2ā3(b̄4	NOUN
ejpam-6473	463	5	−	−	PROPN
ejpam-6473	463	6	b̄1	b̄1	NUM
ejpam-6473	463	7	)	)	PUNCT
ejpam-6473	463	8	−	−	PROPN
ejpam-6473	463	9	ā3(b̄3	ā3(b̄3	PRON
ejpam-6473	463	10	−	−	PROPN
ejpam-6473	463	11	b̄4	b̄4	ADJ
ejpam-6473	463	12	)	)	PUNCT
ejpam-6473	463	13	]	]	PUNCT
ejpam-6473	463	14	2	2	NUM
ejpam-6473	463	15	,	,	PUNCT
ejpam-6473	463	16	≤	≤	NUM
ejpam-6473	463	17	b10[(a3	b10[(a3	PROPN
ejpam-6473	463	18	−	−	PUNCT
ejpam-6473	463	19	ā3	ā3	ADJ
ejpam-6473	463	20	)	)	PUNCT
ejpam-6473	463	21	2	2	NUM
ejpam-6473	464	1	+	+	CCONJ
ejpam-6473	464	2	(	(	PUNCT
ejpam-6473	464	3	b1	b1	NOUN
ejpam-6473	464	4	−	−	PROPN
ejpam-6473	464	5	b̄1	b̄1	NUM
ejpam-6473	464	6	)	)	PUNCT
ejpam-6473	464	7	2	2	NUM
ejpam-6473	465	1	+	+	CCONJ
ejpam-6473	465	2	(	(	PUNCT
ejpam-6473	465	3	b3	b3	PROPN
ejpam-6473	465	4	−	−	PROPN
ejpam-6473	465	5	b̄3	b̄3	NOUN
ejpam-6473	465	6	)	)	PUNCT
ejpam-6473	465	7	2	2	NUM
ejpam-6473	466	1	+	+	CCONJ
ejpam-6473	466	2	(	(	PUNCT
ejpam-6473	466	3	b4	b4	NOUN
ejpam-6473	466	4	−	−	PROPN
ejpam-6473	466	5	b̄4	b̄4	NOUN
ejpam-6473	466	6	)	)	PUNCT
ejpam-6473	466	7	2	2	NUM
ejpam-6473	466	8	]	]	PUNCT
ejpam-6473	466	9	.	.	PUNCT
ejpam-6473	467	1	using	use	VERB
ejpam-6473	467	2	the	the	DET
ejpam-6473	467	3	value	value	NOUN
ejpam-6473	467	4	of	of	ADP
ejpam-6473	467	5	(	(	PUNCT
ejpam-6473	467	6	u3	u3	NOUN
ejpam-6473	467	7	−	−	PROPN
ejpam-6473	467	8	ū3	ū3	NOUN
ejpam-6473	467	9	)	)	PUNCT
ejpam-6473	467	10	2	2	NUM
ejpam-6473	467	11	,	,	PUNCT
ejpam-6473	467	12	we	we	PRON
ejpam-6473	467	13	get	get	VERB
ejpam-6473	467	14	(	(	PUNCT
ejpam-6473	467	15	a3u3	a3u3	ADV
ejpam-6473	467	16	−	−	X
ejpam-6473	467	17	ā3ū3)(a1	ā3ū3)(a1	PUNCT
ejpam-6473	467	18	−	−	PROPN
ejpam-6473	467	19	ā1	ā1	NOUN
ejpam-6473	467	20	)	)	PUNCT
ejpam-6473	467	21	≤	≤	NOUN
ejpam-6473	468	1	b11[(a1	b11[(a1	SCONJ
ejpam-6473	468	2	−	−	NUM
ejpam-6473	468	3	ā1	ā1	NOUN
ejpam-6473	468	4	)	)	PUNCT
ejpam-6473	468	5	2	2	NUM
ejpam-6473	469	1	+	+	CCONJ
ejpam-6473	469	2	(	(	PUNCT
ejpam-6473	469	3	a3	a3	NOUN
ejpam-6473	469	4	−	−	PROPN
ejpam-6473	469	5	ā3	ā3	NOUN
ejpam-6473	469	6	)	)	PUNCT
ejpam-6473	469	7	2	2	NUM
ejpam-6473	470	1	+	+	CCONJ
ejpam-6473	470	2	(	(	PUNCT
ejpam-6473	470	3	b1	b1	NOUN
ejpam-6473	470	4	−	−	PROPN
ejpam-6473	470	5	b̄1	b̄1	NUM
ejpam-6473	470	6	)	)	PUNCT
ejpam-6473	470	7	2	2	NUM
ejpam-6473	471	1	+	+	CCONJ
ejpam-6473	471	2	(	(	PUNCT
ejpam-6473	471	3	b3	b3	PROPN
ejpam-6473	471	4	−	−	PROPN
ejpam-6473	471	5	b̄3	b̄3	NOUN
ejpam-6473	471	6	)	)	PUNCT
ejpam-6473	471	7	2	2	NUM
ejpam-6473	472	1	+	+	CCONJ
ejpam-6473	472	2	(	(	PUNCT
ejpam-6473	472	3	b4	b4	NOUN
ejpam-6473	472	4	−	−	PROPN
ejpam-6473	472	5	b̄4	b̄4	NOUN
ejpam-6473	472	6	)	)	PUNCT
ejpam-6473	472	7	2	2	NUM
ejpam-6473	472	8	]	]	PUNCT
ejpam-6473	472	9	.	.	PUNCT
ejpam-6473	473	1	bi	bi	NOUN
ejpam-6473	473	2	where	where	SCONJ
ejpam-6473	473	3	i=1,2,3,	i=1,2,3,	NOUN
ejpam-6473	473	4	...	...	PUNCT
ejpam-6473	473	5	11	11	NUM
ejpam-6473	473	6	depend	depend	VERB
ejpam-6473	473	7	on	on	ADP
ejpam-6473	473	8	the	the	DET
ejpam-6473	473	9	bound	bind	VERB
ejpam-6473	473	10	of	of	ADP
ejpam-6473	473	11	the	the	DET
ejpam-6473	473	12	state	state	NOUN
ejpam-6473	473	13	variable	variable	NOUN
ejpam-6473	473	14	.	.	PUNCT
ejpam-6473	474	1	now	now	ADV
ejpam-6473	474	2	substitute	substitute	VERB
ejpam-6473	474	3	the	the	DET
ejpam-6473	474	4	vales	vale	NOUN
ejpam-6473	474	5	in	in	ADP
ejpam-6473	474	6	equation	equation	NOUN
ejpam-6473	474	7	(	(	PUNCT
ejpam-6473	474	8	16	16	NUM
ejpam-6473	474	9	)	)	PUNCT
ejpam-6473	475	1	=	=	NOUN
ejpam-6473	475	2	⇒	⇒	NOUN
ejpam-6473	475	3	(	(	PUNCT
ejpam-6473	475	4	λ+	λ+	X
ejpam-6473	475	5	b+	b+	X
ejpam-6473	475	6	µ	µ	X
ejpam-6473	475	7	)	)	PUNCT
ejpam-6473	475	8	∫	∫	PROPN
ejpam-6473	475	9	t	t	PROPN
ejpam-6473	475	10	0	0	NUM
ejpam-6473	475	11	(	(	PUNCT
ejpam-6473	475	12	a1	a1	NOUN
ejpam-6473	475	13	−	−	NOUN
ejpam-6473	475	14	ā1	ā1	NOUN
ejpam-6473	475	15	)	)	PUNCT
ejpam-6473	475	16	2	2	NUM
ejpam-6473	475	17	dt+	dt+	NOUN
ejpam-6473	475	18	1	1	NUM
ejpam-6473	475	19	2	2	NUM
ejpam-6473	475	20	(	(	PUNCT
ejpam-6473	475	21	a1(t	a1(t	ADV
ejpam-6473	475	22	)	)	PUNCT
ejpam-6473	475	23	−	−	NOUN
ejpam-6473	475	24	ā1(t	ā1(t	NUM
ejpam-6473	475	25	)	)	PUNCT
ejpam-6473	475	26	)	)	PUNCT
ejpam-6473	475	27	2	2	NUM
ejpam-6473	475	28	≤	≤	NOUN
ejpam-6473	475	29	m1e	m1e	NOUN
ejpam-6473	475	30	λt	λt	ADP
ejpam-6473	475	31	∫	∫	PROPN
ejpam-6473	475	32	t	t	PROPN
ejpam-6473	475	33	0	0	NUM
ejpam-6473	476	1	(	(	PUNCT
ejpam-6473	476	2	(	(	PUNCT
ejpam-6473	476	3	a1	a1	NOUN
ejpam-6473	476	4	−	−	NOUN
ejpam-6473	476	5	ā1	ā1	NOUN
ejpam-6473	476	6	)	)	PUNCT
ejpam-6473	476	7	2	2	NUM
ejpam-6473	477	1	+	+	CCONJ
ejpam-6473	477	2	(	(	PUNCT
ejpam-6473	477	3	a3	a3	NOUN
ejpam-6473	477	4	−	−	PROPN
ejpam-6473	477	5	ā3	ā3	ADJ
ejpam-6473	477	6	)	)	PUNCT
ejpam-6473	477	7	2	2	NUM
ejpam-6473	477	8	)	)	PUNCT
ejpam-6473	477	9	dt	dt	PUNCT
ejpam-6473	478	1	+	+	NOUN
ejpam-6473	478	2	k1e	k1e	PROPN
ejpam-6473	478	3	2λt	2λt	ADJ
ejpam-6473	478	4	∫	∫	PROPN
ejpam-6473	478	5	t	t	PROPN
ejpam-6473	478	6	0	0	NUM
ejpam-6473	479	1	(	(	PUNCT
ejpam-6473	479	2	(	(	PUNCT
ejpam-6473	479	3	a1	a1	NOUN
ejpam-6473	479	4	−	−	NOUN
ejpam-6473	479	5	ā1	ā1	NOUN
ejpam-6473	479	6	)	)	PUNCT
ejpam-6473	479	7	2	2	NUM
ejpam-6473	480	1	+	+	CCONJ
ejpam-6473	480	2	(	(	PUNCT
ejpam-6473	480	3	a3	a3	NOUN
ejpam-6473	480	4	−	−	PROPN
ejpam-6473	480	5	ā3	ā3	ADJ
ejpam-6473	480	6	)	)	PUNCT
ejpam-6473	480	7	2	2	NUM
ejpam-6473	480	8	)	)	PUNCT
ejpam-6473	480	9	dt	dt	PUNCT
ejpam-6473	481	1	+	+	CCONJ
ejpam-6473	481	2	p1	p1	PROPN
ejpam-6473	481	3	∫	∫	PROPN
ejpam-6473	481	4	t	t	PROPN
ejpam-6473	481	5	0	0	NUM
ejpam-6473	482	1	(	(	PUNCT
ejpam-6473	482	2	(	(	PUNCT
ejpam-6473	482	3	a1	a1	NOUN
ejpam-6473	482	4	−	−	NOUN
ejpam-6473	482	5	ā1	ā1	NOUN
ejpam-6473	482	6	)	)	PUNCT
ejpam-6473	482	7	2	2	NUM
ejpam-6473	483	1	+	+	CCONJ
ejpam-6473	483	2	(	(	PUNCT
ejpam-6473	483	3	a2	a2	PROPN
ejpam-6473	483	4	−	−	PROPN
ejpam-6473	483	5	ā2	ā2	PROPN
ejpam-6473	483	6	)	)	PUNCT
ejpam-6473	483	7	2	2	NUM
ejpam-6473	483	8	+	+	CCONJ
ejpam-6473	483	9	(	(	PUNCT
ejpam-6473	483	10	a3	a3	NOUN
ejpam-6473	483	11	−	−	PROPN
ejpam-6473	483	12	ā3	ā3	NOUN
ejpam-6473	483	13	)	)	PUNCT
ejpam-6473	483	14	2	2	NUM
ejpam-6473	484	1	+	+	CCONJ
ejpam-6473	484	2	(	(	PUNCT
ejpam-6473	484	3	b1	b1	NOUN
ejpam-6473	484	4	−	−	PROPN
ejpam-6473	484	5	b̄1	b̄1	PROPN
ejpam-6473	484	6	2	2	NUM
ejpam-6473	484	7	)	)	PUNCT
ejpam-6473	484	8	+	+	PROPN
ejpam-6473	484	9	(	(	PUNCT
ejpam-6473	484	10	b2	b2	NOUN
ejpam-6473	484	11	−	−	NOUN
ejpam-6473	484	12	b̄2	b̄2	NOUN
ejpam-6473	484	13	)	)	PUNCT
ejpam-6473	484	14	2	2	NUM
ejpam-6473	484	15	+	+	CCONJ
ejpam-6473	484	16	(	(	PUNCT
ejpam-6473	484	17	b3	b3	PROPN
ejpam-6473	484	18	−	−	PROPN
ejpam-6473	484	19	b̄3	b̄3	NOUN
ejpam-6473	484	20	)	)	PUNCT
ejpam-6473	484	21	2	2	NUM
ejpam-6473	485	1	+	+	CCONJ
ejpam-6473	485	2	(	(	PUNCT
ejpam-6473	485	3	b4	b4	NOUN
ejpam-6473	485	4	−	−	PROPN
ejpam-6473	485	5	b̄4	b̄4	ADJ
ejpam-6473	485	6	)	)	PUNCT
ejpam-6473	485	7	2	2	NUM
ejpam-6473	486	1	)	)	PUNCT
ejpam-6473	486	2	dt	dt	X
ejpam-6473	486	3	.	.	PUNCT
ejpam-6473	487	1	(	(	PUNCT
ejpam-6473	487	2	17	17	NUM
ejpam-6473	487	3	)	)	PUNCT
ejpam-6473	487	4	similarly	similarly	ADV
ejpam-6473	487	5	=	=	SYM
ejpam-6473	487	6	⇒	⇒	NOUN
ejpam-6473	487	7	(	(	PUNCT
ejpam-6473	487	8	λ+	λ+	X
ejpam-6473	487	9	b+	b+	X
ejpam-6473	487	10	µ+	µ+	X
ejpam-6473	487	11	ζ	ζ	NOUN
ejpam-6473	487	12	)	)	PUNCT
ejpam-6473	487	13	∫	∫	PROPN
ejpam-6473	487	14	t	t	PROPN
ejpam-6473	487	15	0	0	NUM
ejpam-6473	487	16	(	(	PUNCT
ejpam-6473	487	17	a2	a2	PROPN
ejpam-6473	487	18	−	−	PROPN
ejpam-6473	487	19	ā2	ā2	PROPN
ejpam-6473	487	20	)	)	PUNCT
ejpam-6473	487	21	2	2	NUM
ejpam-6473	487	22	dt+	dt+	NOUN
ejpam-6473	487	23	1	1	NUM
ejpam-6473	487	24	2	2	NUM
ejpam-6473	487	25	(	(	PUNCT
ejpam-6473	487	26	a2(t	a2(t	NOUN
ejpam-6473	487	27	)	)	PUNCT
ejpam-6473	487	28	−	−	PROPN
ejpam-6473	487	29	¯a2(t	¯a2(t	PROPN
ejpam-6473	487	30	)	)	PUNCT
ejpam-6473	487	31	)	)	PUNCT
ejpam-6473	487	32	2	2	NUM
ejpam-6473	487	33	s.	s.	PROPN
ejpam-6473	487	34	bano	bano	PROPN
ejpam-6473	487	35	et	et	PROPN
ejpam-6473	487	36	al	al	PROPN
ejpam-6473	487	37	.	.	PUNCT
ejpam-6473	487	38	/	/	SYM
ejpam-6473	487	39	eur	eur	PROPN
ejpam-6473	487	40	.	.	PUNCT
ejpam-6473	488	1	j.	j.	PROPN
ejpam-6473	488	2	pure	pure	PROPN
ejpam-6473	488	3	appl	appl	PROPN
ejpam-6473	488	4	.	.	PROPN
ejpam-6473	488	5	math	math	PROPN
ejpam-6473	488	6	,	,	PUNCT
ejpam-6473	488	7	18	18	NUM
ejpam-6473	488	8	(	(	PUNCT
ejpam-6473	488	9	4	4	NUM
ejpam-6473	488	10	)	)	PUNCT
ejpam-6473	488	11	(	(	PUNCT
ejpam-6473	488	12	2025	2025	NUM
ejpam-6473	488	13	)	)	PUNCT
ejpam-6473	488	14	,	,	PUNCT
ejpam-6473	488	15	6473	6473	NUM
ejpam-6473	488	16	25	25	NUM
ejpam-6473	488	17	of	of	ADP
ejpam-6473	488	18	38	38	NUM
ejpam-6473	488	19	≤	≤	NUM
ejpam-6473	488	20	m2e	m2e	PUNCT
ejpam-6473	488	21	λt	λt	ADP
ejpam-6473	488	22	∫	∫	PROPN
ejpam-6473	488	23	t	t	PROPN
ejpam-6473	488	24	0	0	NUM
ejpam-6473	488	25	(	(	PUNCT
ejpam-6473	488	26	(	(	PUNCT
ejpam-6473	488	27	a1	a1	NOUN
ejpam-6473	488	28	−	−	NOUN
ejpam-6473	488	29	ā1	ā1	NOUN
ejpam-6473	488	30	)	)	PUNCT
ejpam-6473	488	31	2	2	NUM
ejpam-6473	488	32	+	+	CCONJ
ejpam-6473	488	33	(	(	PUNCT
ejpam-6473	488	34	a2	a2	PROPN
ejpam-6473	488	35	−	−	PROPN
ejpam-6473	488	36	ā2	ā2	PROPN
ejpam-6473	488	37	)	)	PUNCT
ejpam-6473	488	38	2	2	NUM
ejpam-6473	488	39	+	+	CCONJ
ejpam-6473	488	40	(	(	PUNCT
ejpam-6473	488	41	a3	a3	NOUN
ejpam-6473	488	42	−	−	PROPN
ejpam-6473	488	43	ā3	ā3	ADJ
ejpam-6473	488	44	)	)	PUNCT
ejpam-6473	488	45	2	2	NUM
ejpam-6473	488	46	)	)	PUNCT
ejpam-6473	488	47	dt	dt	PUNCT
ejpam-6473	489	1	+	+	NOUN
ejpam-6473	489	2	k2e	k2e	PROPN
ejpam-6473	489	3	2λt	2λt	NOUN
ejpam-6473	489	4	∫	∫	PROPN
ejpam-6473	489	5	t	t	PROPN
ejpam-6473	489	6	0	0	NUM
ejpam-6473	490	1	(	(	PUNCT
ejpam-6473	490	2	(	(	PUNCT
ejpam-6473	490	3	a1	a1	NOUN
ejpam-6473	490	4	−	−	NOUN
ejpam-6473	490	5	ā1	ā1	NOUN
ejpam-6473	490	6	)	)	PUNCT
ejpam-6473	490	7	2	2	NUM
ejpam-6473	491	1	+	+	CCONJ
ejpam-6473	491	2	(	(	PUNCT
ejpam-6473	491	3	a2	a2	PROPN
ejpam-6473	491	4	−	−	PROPN
ejpam-6473	491	5	ā2	ā2	PROPN
ejpam-6473	491	6	)	)	PUNCT
ejpam-6473	491	7	2	2	NUM
ejpam-6473	491	8	+	+	CCONJ
ejpam-6473	491	9	(	(	PUNCT
ejpam-6473	491	10	a3	a3	NOUN
ejpam-6473	491	11	−	−	PROPN
ejpam-6473	491	12	ā3	ā3	ADJ
ejpam-6473	491	13	)	)	PUNCT
ejpam-6473	491	14	2	2	NUM
ejpam-6473	491	15	)	)	PUNCT
ejpam-6473	491	16	dt	dt	NOUN
ejpam-6473	492	1	+	+	CCONJ
ejpam-6473	492	2	p2	p2	PROPN
ejpam-6473	492	3	∫	∫	PROPN
ejpam-6473	492	4	t	t	PROPN
ejpam-6473	492	5	0	0	NUM
ejpam-6473	492	6	(	(	PUNCT
ejpam-6473	492	7	(	(	PUNCT
ejpam-6473	492	8	a2	a2	PROPN
ejpam-6473	492	9	−	−	PROPN
ejpam-6473	492	10	ā2	ā2	PROPN
ejpam-6473	492	11	)	)	PUNCT
ejpam-6473	492	12	2	2	NUM
ejpam-6473	492	13	+	+	CCONJ
ejpam-6473	492	14	(	(	PUNCT
ejpam-6473	492	15	b1	b1	NOUN
ejpam-6473	492	16	−	−	PROPN
ejpam-6473	492	17	b̄1	b̄1	NUM
ejpam-6473	492	18	)	)	PUNCT
ejpam-6473	492	19	+	+	CCONJ
ejpam-6473	492	20	(	(	PUNCT
ejpam-6473	492	21	b2	b2	NOUN
ejpam-6473	492	22	−	−	NOUN
ejpam-6473	492	23	b̄2	b̄2	NUM
ejpam-6473	492	24	)	)	PUNCT
ejpam-6473	492	25	+	+	CCONJ
ejpam-6473	492	26	(	(	PUNCT
ejpam-6473	492	27	b4	b4	NOUN
ejpam-6473	492	28	−	−	PROPN
ejpam-6473	492	29	b̄4	b̄4	ADJ
ejpam-6473	492	30	)	)	PUNCT
ejpam-6473	492	31	2	2	NUM
ejpam-6473	493	1	)	)	PUNCT
ejpam-6473	493	2	dt	dt	NOUN
ejpam-6473	493	3	.	.	PUNCT
ejpam-6473	494	1	(	(	PUNCT
ejpam-6473	494	2	18	18	NUM
ejpam-6473	494	3	)	)	PUNCT
ejpam-6473	494	4	=	=	NOUN
ejpam-6473	494	5	⇒	⇒	NOUN
ejpam-6473	494	6	(	(	PUNCT
ejpam-6473	494	7	λ+	λ+	X
ejpam-6473	494	8	b+	b+	X
ejpam-6473	494	9	µ+	µ+	X
ejpam-6473	494	10	δ	δ	PROPN
ejpam-6473	494	11	)	)	PUNCT
ejpam-6473	494	12	∫	∫	PROPN
ejpam-6473	494	13	t	t	PROPN
ejpam-6473	494	14	0	0	NUM
ejpam-6473	494	15	(	(	PUNCT
ejpam-6473	494	16	a3	a3	NOUN
ejpam-6473	494	17	−	−	PROPN
ejpam-6473	494	18	ā3	ā3	ADJ
ejpam-6473	494	19	)	)	PUNCT
ejpam-6473	494	20	2	2	NUM
ejpam-6473	494	21	dt+	dt+	NOUN
ejpam-6473	494	22	1	1	NUM
ejpam-6473	494	23	2	2	NUM
ejpam-6473	494	24	(	(	PUNCT
ejpam-6473	494	25	a3(t	a3(t	PROPN
ejpam-6473	494	26	)	)	PUNCT
ejpam-6473	494	27	−	−	PROPN
ejpam-6473	494	28	ā3(t	ā3(t	NUM
ejpam-6473	494	29	)	)	PUNCT
ejpam-6473	494	30	)	)	PUNCT
ejpam-6473	494	31	2	2	NUM
ejpam-6473	494	32	≤	≤	PROPN
ejpam-6473	494	33	p3	p3	PROPN
ejpam-6473	494	34	∫	∫	PROPN
ejpam-6473	494	35	t	t	PROPN
ejpam-6473	494	36	0	0	NUM
ejpam-6473	495	1	(	(	PUNCT
ejpam-6473	495	2	(	(	PUNCT
ejpam-6473	495	3	a2	a2	PROPN
ejpam-6473	495	4	−	−	PROPN
ejpam-6473	495	5	ā2	ā2	PROPN
ejpam-6473	495	6	)	)	PUNCT
ejpam-6473	495	7	2	2	NUM
ejpam-6473	496	1	+	+	CCONJ
ejpam-6473	496	2	(	(	PUNCT
ejpam-6473	496	3	a3	a3	NOUN
ejpam-6473	496	4	−	−	PROPN
ejpam-6473	496	5	ā3	ā3	NOUN
ejpam-6473	496	6	)	)	PUNCT
ejpam-6473	496	7	2	2	NUM
ejpam-6473	496	8	+	+	CCONJ
ejpam-6473	496	9	(	(	PUNCT
ejpam-6473	496	10	b1	b1	NOUN
ejpam-6473	496	11	−	−	PROPN
ejpam-6473	496	12	b̄1	b̄1	NUM
ejpam-6473	496	13	)	)	PUNCT
ejpam-6473	496	14	2	2	NUM
ejpam-6473	496	15	+	+	PROPN
ejpam-6473	496	16	(	(	PUNCT
ejpam-6473	496	17	b3	b3	PROPN
ejpam-6473	496	18	−	−	PROPN
ejpam-6473	496	19	b̄3	b̄3	NOUN
ejpam-6473	496	20	)	)	PUNCT
ejpam-6473	496	21	2	2	NUM
ejpam-6473	497	1	+	+	CCONJ
ejpam-6473	497	2	(	(	PUNCT
ejpam-6473	497	3	b4	b4	NOUN
ejpam-6473	497	4	−	−	PROPN
ejpam-6473	497	5	b̄4	b̄4	ADJ
ejpam-6473	497	6	)	)	PUNCT
ejpam-6473	497	7	2	2	NUM
ejpam-6473	498	1	)	)	PUNCT
ejpam-6473	498	2	dt	dt	NOUN
ejpam-6473	498	3	.	.	PUNCT
ejpam-6473	499	1	(	(	PUNCT
ejpam-6473	499	2	19	19	NUM
ejpam-6473	499	3	)	)	PUNCT
ejpam-6473	499	4	=	=	NOUN
ejpam-6473	499	5	⇒	⇒	NOUN
ejpam-6473	499	6	(	(	PUNCT
ejpam-6473	499	7	λ+	λ+	X
ejpam-6473	499	8	b+	b+	X
ejpam-6473	499	9	µ	µ	X
ejpam-6473	499	10	)	)	PUNCT
ejpam-6473	499	11	∫	∫	PROPN
ejpam-6473	499	12	t	t	PROPN
ejpam-6473	499	13	0	0	NUM
ejpam-6473	499	14	(	(	PUNCT
ejpam-6473	499	15	a4	a4	NOUN
ejpam-6473	499	16	−	−	NOUN
ejpam-6473	499	17	ā4	ā4	NOUN
ejpam-6473	499	18	)	)	PUNCT
ejpam-6473	499	19	2	2	NUM
ejpam-6473	499	20	dt+	dt+	NOUN
ejpam-6473	499	21	1	1	NUM
ejpam-6473	499	22	2	2	NUM
ejpam-6473	499	23	(	(	PUNCT
ejpam-6473	499	24	a4(t	a4(t	NUM
ejpam-6473	499	25	)	)	PUNCT
ejpam-6473	499	26	−	−	PROPN
ejpam-6473	499	27	ā4(t	ā4(t	NOUN
ejpam-6473	499	28	)	)	PUNCT
ejpam-6473	499	29	)	)	PUNCT
ejpam-6473	499	30	2	2	NUM
ejpam-6473	499	31	≤	≤	ADV
ejpam-6473	499	32	p4	p4	ADJ
ejpam-6473	499	33	∫	∫	PROPN
ejpam-6473	499	34	t	t	PROPN
ejpam-6473	499	35	0	0	NUM
ejpam-6473	500	1	(	(	PUNCT
ejpam-6473	500	2	(	(	PUNCT
ejpam-6473	500	3	a1	a1	NOUN
ejpam-6473	500	4	−	−	NOUN
ejpam-6473	500	5	ā1	ā1	NOUN
ejpam-6473	500	6	)	)	PUNCT
ejpam-6473	500	7	2	2	NUM
ejpam-6473	501	1	+	+	CCONJ
ejpam-6473	501	2	(	(	PUNCT
ejpam-6473	501	3	a2	a2	PROPN
ejpam-6473	501	4	−	−	PROPN
ejpam-6473	501	5	ā2	ā2	PROPN
ejpam-6473	501	6	)	)	PUNCT
ejpam-6473	501	7	2	2	NUM
ejpam-6473	501	8	+	+	CCONJ
ejpam-6473	501	9	(	(	PUNCT
ejpam-6473	501	10	a3	a3	NOUN
ejpam-6473	501	11	−	−	PROPN
ejpam-6473	501	12	ā3	ā3	NOUN
ejpam-6473	501	13	)	)	PUNCT
ejpam-6473	501	14	2	2	NUM
ejpam-6473	502	1	+	+	ADJ
ejpam-6473	502	2	(	(	PUNCT
ejpam-6473	502	3	a4	a4	NOUN
ejpam-6473	502	4	−	−	NOUN
ejpam-6473	502	5	ā4	ā4	NOUN
ejpam-6473	502	6	)	)	PUNCT
ejpam-6473	502	7	2	2	NUM
ejpam-6473	502	8	+	+	CCONJ
ejpam-6473	502	9	(	(	PUNCT
ejpam-6473	502	10	b1	b1	NOUN
ejpam-6473	502	11	−	−	PROPN
ejpam-6473	502	12	b̄1	b̄1	NUM
ejpam-6473	502	13	)	)	PUNCT
ejpam-6473	502	14	2	2	NUM
ejpam-6473	502	15	+	+	CCONJ
ejpam-6473	502	16	(	(	PUNCT
ejpam-6473	502	17	b2	b2	NOUN
ejpam-6473	502	18	−	−	NOUN
ejpam-6473	502	19	b̄2	b̄2	NOUN
ejpam-6473	502	20	)	)	PUNCT
ejpam-6473	502	21	2	2	NUM
ejpam-6473	502	22	+	+	NOUN
ejpam-6473	502	23	(	(	PUNCT
ejpam-6473	502	24	b3	b3	PROPN
ejpam-6473	502	25	−	−	PROPN
ejpam-6473	502	26	b̄3	b̄3	NOUN
ejpam-6473	502	27	)	)	PUNCT
ejpam-6473	502	28	2	2	NUM
ejpam-6473	503	1	+	+	CCONJ
ejpam-6473	503	2	(	(	PUNCT
ejpam-6473	503	3	b4	b4	NOUN
ejpam-6473	503	4	−	−	PROPN
ejpam-6473	503	5	b̄4	b̄4	ADJ
ejpam-6473	503	6	)	)	PUNCT
ejpam-6473	503	7	2	2	NUM
ejpam-6473	504	1	)	)	PUNCT
ejpam-6473	504	2	dt	dt	NOUN
ejpam-6473	504	3	.	.	PUNCT
ejpam-6473	505	1	(	(	PUNCT
ejpam-6473	505	2	20	20	NUM
ejpam-6473	505	3	)	)	PUNCT
ejpam-6473	506	1	=	=	NOUN
ejpam-6473	506	2	⇒	⇒	NOUN
ejpam-6473	506	3	(	(	PUNCT
ejpam-6473	506	4	λ+	λ+	X
ejpam-6473	506	5	b+	b+	X
ejpam-6473	506	6	µ	µ	X
ejpam-6473	506	7	)	)	PUNCT
ejpam-6473	506	8	∫	∫	PROPN
ejpam-6473	506	9	t	t	PROPN
ejpam-6473	506	10	0	0	NUM
ejpam-6473	506	11	(	(	PUNCT
ejpam-6473	506	12	b1	b1	NOUN
ejpam-6473	506	13	−	−	PROPN
ejpam-6473	506	14	b̄1	b̄1	NUM
ejpam-6473	506	15	)	)	PUNCT
ejpam-6473	506	16	2	2	NUM
ejpam-6473	506	17	dt+	dt+	NOUN
ejpam-6473	506	18	1	1	NUM
ejpam-6473	506	19	2	2	NUM
ejpam-6473	506	20	(	(	PUNCT
ejpam-6473	506	21	b1(0)−	b1(0)−	PROPN
ejpam-6473	506	22	b̄1(0	b̄1(0	PROPN
ejpam-6473	506	23	)	)	PUNCT
ejpam-6473	506	24	)	)	PUNCT
ejpam-6473	506	25	2	2	NUM
ejpam-6473	506	26	≤	≤	NUM
ejpam-6473	506	27	m5e	m5e	X
ejpam-6473	506	28	λt	λt	ADP
ejpam-6473	506	29	∫	∫	PROPN
ejpam-6473	506	30	t	t	PROPN
ejpam-6473	506	31	0	0	NUM
ejpam-6473	507	1	(	(	PUNCT
ejpam-6473	507	2	(	(	PUNCT
ejpam-6473	507	3	a3	a3	NOUN
ejpam-6473	507	4	−	−	PROPN
ejpam-6473	507	5	ā3	ā3	NOUN
ejpam-6473	507	6	)	)	PUNCT
ejpam-6473	507	7	2	2	NUM
ejpam-6473	508	1	+	+	CCONJ
ejpam-6473	508	2	(	(	PUNCT
ejpam-6473	508	3	b1	b1	NOUN
ejpam-6473	508	4	−	−	PROPN
ejpam-6473	508	5	b̄1	b̄1	NUM
ejpam-6473	508	6	)	)	PUNCT
ejpam-6473	508	7	2	2	NUM
ejpam-6473	509	1	+	+	CCONJ
ejpam-6473	509	2	(	(	PUNCT
ejpam-6473	509	3	b2	b2	NOUN
ejpam-6473	509	4	−	−	NOUN
ejpam-6473	509	5	b̄2	b̄2	NUM
ejpam-6473	509	6	)	)	PUNCT
ejpam-6473	509	7	2	2	NUM
ejpam-6473	509	8	)	)	PUNCT
ejpam-6473	509	9	)	)	PUNCT
ejpam-6473	510	1	dt	dt	PUNCT
ejpam-6473	511	1	+	+	NOUN
ejpam-6473	511	2	k5e	k5e	PROPN
ejpam-6473	511	3	2λt	2λt	ADJ
ejpam-6473	511	4	∫	∫	PROPN
ejpam-6473	511	5	t	t	PROPN
ejpam-6473	511	6	0	0	NUM
ejpam-6473	512	1	(	(	PUNCT
ejpam-6473	512	2	(	(	PUNCT
ejpam-6473	512	3	a3	a3	NOUN
ejpam-6473	512	4	−	−	PROPN
ejpam-6473	512	5	ā3	ā3	NOUN
ejpam-6473	512	6	)	)	PUNCT
ejpam-6473	512	7	2	2	NUM
ejpam-6473	513	1	+	+	CCONJ
ejpam-6473	513	2	(	(	PUNCT
ejpam-6473	513	3	b1	b1	NOUN
ejpam-6473	513	4	−	−	PROPN
ejpam-6473	513	5	b̄1	b̄1	NUM
ejpam-6473	513	6	)	)	PUNCT
ejpam-6473	513	7	2	2	NUM
ejpam-6473	514	1	+	+	CCONJ
ejpam-6473	514	2	(	(	PUNCT
ejpam-6473	514	3	b2	b2	NOUN
ejpam-6473	514	4	−	−	NOUN
ejpam-6473	514	5	b̄2	b̄2	NUM
ejpam-6473	514	6	)	)	PUNCT
ejpam-6473	514	7	2	2	NUM
ejpam-6473	514	8	)	)	PUNCT
ejpam-6473	514	9	)	)	PUNCT
ejpam-6473	515	1	dt	dt	PUNCT
ejpam-6473	516	1	+	+	CCONJ
ejpam-6473	516	2	p5	p5	ADJ
ejpam-6473	516	3	∫	∫	PROPN
ejpam-6473	516	4	t	t	PROPN
ejpam-6473	516	5	0	0	NUM
ejpam-6473	516	6	(	(	PUNCT
ejpam-6473	516	7	(	(	PUNCT
ejpam-6473	516	8	a1	a1	NOUN
ejpam-6473	516	9	−	−	NOUN
ejpam-6473	516	10	ā1	ā1	NOUN
ejpam-6473	516	11	)	)	PUNCT
ejpam-6473	516	12	2	2	NUM
ejpam-6473	516	13	+	+	CCONJ
ejpam-6473	516	14	(	(	PUNCT
ejpam-6473	516	15	b1	b1	NOUN
ejpam-6473	516	16	−	−	PROPN
ejpam-6473	516	17	b̄1	b̄1	NUM
ejpam-6473	516	18	)	)	PUNCT
ejpam-6473	516	19	2	2	NUM
ejpam-6473	516	20	+	+	CCONJ
ejpam-6473	516	21	(	(	PUNCT
ejpam-6473	516	22	b4	b4	NOUN
ejpam-6473	516	23	−	−	PROPN
ejpam-6473	516	24	b̄4	b̄4	ADJ
ejpam-6473	516	25	)	)	PUNCT
ejpam-6473	516	26	2	2	NUM
ejpam-6473	517	1	)	)	PUNCT
ejpam-6473	517	2	dt	dt	NOUN
ejpam-6473	517	3	.	.	PUNCT
ejpam-6473	518	1	(	(	PUNCT
ejpam-6473	518	2	21	21	NUM
ejpam-6473	518	3	)	)	PUNCT
ejpam-6473	519	1	=	=	NOUN
ejpam-6473	519	2	⇒	⇒	NOUN
ejpam-6473	519	3	(	(	PUNCT
ejpam-6473	519	4	λ+	λ+	X
ejpam-6473	519	5	b+	b+	X
ejpam-6473	519	6	µ+	µ+	X
ejpam-6473	519	7	ζ	ζ	NOUN
ejpam-6473	519	8	)	)	PUNCT
ejpam-6473	519	9	∫	∫	PROPN
ejpam-6473	519	10	t	t	PROPN
ejpam-6473	519	11	0	0	NUM
ejpam-6473	519	12	(	(	PUNCT
ejpam-6473	519	13	b2	b2	NOUN
ejpam-6473	519	14	−	−	NOUN
ejpam-6473	519	15	b̄2	b̄2	NOUN
ejpam-6473	519	16	)	)	PUNCT
ejpam-6473	519	17	2	2	NUM
ejpam-6473	519	18	dt+	dt+	NOUN
ejpam-6473	519	19	1	1	NUM
ejpam-6473	519	20	2	2	NUM
ejpam-6473	519	21	(	(	PUNCT
ejpam-6473	519	22	b2(0)−	b2(0)−	PROPN
ejpam-6473	519	23	b̄2(0	b̄2(0	NOUN
ejpam-6473	519	24	)	)	PUNCT
ejpam-6473	519	25	)	)	PUNCT
ejpam-6473	519	26	2	2	NUM
ejpam-6473	519	27	≤	≤	NUM
ejpam-6473	519	28	p6	p6	PROPN
ejpam-6473	519	29	∫	∫	PROPN
ejpam-6473	519	30	t	t	PROPN
ejpam-6473	519	31	0	0	NUM
ejpam-6473	520	1	(	(	PUNCT
ejpam-6473	520	2	(	(	PUNCT
ejpam-6473	520	3	a2	a2	PROPN
ejpam-6473	520	4	−	−	PROPN
ejpam-6473	520	5	ā2	ā2	PROPN
ejpam-6473	520	6	)	)	PUNCT
ejpam-6473	520	7	2	2	NUM
ejpam-6473	521	1	+	+	CCONJ
ejpam-6473	521	2	(	(	PUNCT
ejpam-6473	521	3	b1	b1	NOUN
ejpam-6473	521	4	−	−	PROPN
ejpam-6473	521	5	b̄1	b̄1	NUM
ejpam-6473	521	6	)	)	PUNCT
ejpam-6473	521	7	2	2	NUM
ejpam-6473	522	1	+	+	CCONJ
ejpam-6473	522	2	(	(	PUNCT
ejpam-6473	522	3	b2	b2	NOUN
ejpam-6473	522	4	−	−	NOUN
ejpam-6473	522	5	b̄2	b̄2	NOUN
ejpam-6473	522	6	)	)	PUNCT
ejpam-6473	522	7	2	2	NUM
ejpam-6473	523	1	+	+	NOUN
ejpam-6473	523	2	(	(	PUNCT
ejpam-6473	523	3	b3	b3	PROPN
ejpam-6473	523	4	−	−	PROPN
ejpam-6473	523	5	b̄3	b̄3	NOUN
ejpam-6473	523	6	)	)	PUNCT
ejpam-6473	523	7	2	2	NUM
ejpam-6473	524	1	+	+	CCONJ
ejpam-6473	524	2	(	(	PUNCT
ejpam-6473	524	3	b4	b4	NOUN
ejpam-6473	524	4	−	−	PROPN
ejpam-6473	524	5	b̄4	b̄4	ADJ
ejpam-6473	524	6	)	)	PUNCT
ejpam-6473	524	7	2	2	NUM
ejpam-6473	525	1	)	)	PUNCT
ejpam-6473	525	2	dt	dt	NOUN
ejpam-6473	525	3	.	.	PUNCT
ejpam-6473	526	1	(	(	PUNCT
ejpam-6473	526	2	22	22	NUM
ejpam-6473	526	3	)	)	PUNCT
ejpam-6473	527	1	=	=	NOUN
ejpam-6473	527	2	⇒	⇒	NOUN
ejpam-6473	527	3	(	(	PUNCT
ejpam-6473	527	4	λ+	λ+	X
ejpam-6473	527	5	b+	b+	X
ejpam-6473	527	6	µ+	µ+	X
ejpam-6473	527	7	δ	δ	PROPN
ejpam-6473	527	8	)	)	PUNCT
ejpam-6473	527	9	∫	∫	PROPN
ejpam-6473	527	10	t	t	PROPN
ejpam-6473	527	11	0	0	NUM
ejpam-6473	527	12	(	(	PUNCT
ejpam-6473	527	13	b3	b3	PROPN
ejpam-6473	527	14	−	−	PROPN
ejpam-6473	527	15	b̄3	b̄3	NOUN
ejpam-6473	527	16	)	)	PUNCT
ejpam-6473	527	17	2	2	NUM
ejpam-6473	527	18	dt+	dt+	NOUN
ejpam-6473	527	19	1	1	NUM
ejpam-6473	527	20	2	2	NUM
ejpam-6473	527	21	(	(	PUNCT
ejpam-6473	527	22	b3(0)−	b3(0)−	NOUN
ejpam-6473	527	23	b̄3(0	b̄3(0	PROPN
ejpam-6473	527	24	)	)	PUNCT
ejpam-6473	527	25	)	)	PUNCT
ejpam-6473	527	26	2	2	NUM
ejpam-6473	527	27	s.	s.	PROPN
ejpam-6473	527	28	bano	bano	PROPN
ejpam-6473	527	29	et	et	PROPN
ejpam-6473	527	30	al	al	PROPN
ejpam-6473	527	31	.	.	PUNCT
ejpam-6473	527	32	/	/	SYM
ejpam-6473	527	33	eur	eur	PROPN
ejpam-6473	527	34	.	.	PUNCT
ejpam-6473	528	1	j.	j.	PROPN
ejpam-6473	528	2	pure	pure	PROPN
ejpam-6473	528	3	appl	appl	PROPN
ejpam-6473	528	4	.	.	PROPN
ejpam-6473	528	5	math	math	PROPN
ejpam-6473	528	6	,	,	PUNCT
ejpam-6473	528	7	18	18	NUM
ejpam-6473	528	8	(	(	PUNCT
ejpam-6473	528	9	4	4	NUM
ejpam-6473	528	10	)	)	PUNCT
ejpam-6473	528	11	(	(	PUNCT
ejpam-6473	528	12	2025	2025	NUM
ejpam-6473	528	13	)	)	PUNCT
ejpam-6473	528	14	,	,	PUNCT
ejpam-6473	528	15	6473	6473	NUM
ejpam-6473	528	16	26	26	NUM
ejpam-6473	528	17	of	of	ADP
ejpam-6473	528	18	38	38	NUM
ejpam-6473	528	19	≤	≤	NUM
ejpam-6473	528	20	m7e	m7e	NOUN
ejpam-6473	528	21	λt	λt	ADP
ejpam-6473	528	22	∫	∫	PROPN
ejpam-6473	528	23	t	t	PROPN
ejpam-6473	528	24	0	0	NUM
ejpam-6473	529	1	(	(	PUNCT
ejpam-6473	529	2	(	(	PUNCT
ejpam-6473	529	3	a1	a1	NOUN
ejpam-6473	529	4	−	−	NOUN
ejpam-6473	529	5	ā1	ā1	NOUN
ejpam-6473	529	6	)	)	PUNCT
ejpam-6473	529	7	2	2	NUM
ejpam-6473	530	1	+	+	CCONJ
ejpam-6473	530	2	(	(	PUNCT
ejpam-6473	530	3	b1	b1	NOUN
ejpam-6473	530	4	−	−	PROPN
ejpam-6473	530	5	b̄1	b̄1	NUM
ejpam-6473	530	6	)	)	PUNCT
ejpam-6473	530	7	2	2	NUM
ejpam-6473	531	1	+	+	CCONJ
ejpam-6473	531	2	(	(	PUNCT
ejpam-6473	531	3	b2	b2	NOUN
ejpam-6473	531	4	−	−	NOUN
ejpam-6473	531	5	b̄2	b̄2	NOUN
ejpam-6473	531	6	)	)	PUNCT
ejpam-6473	531	7	2	2	NUM
ejpam-6473	532	1	+	+	NOUN
ejpam-6473	532	2	(	(	PUNCT
ejpam-6473	532	3	b3	b3	PROPN
ejpam-6473	532	4	−	−	PROPN
ejpam-6473	532	5	b̄3	b̄3	NOUN
ejpam-6473	532	6	)	)	PUNCT
ejpam-6473	532	7	2	2	NUM
ejpam-6473	532	8	)	)	PUNCT
ejpam-6473	532	9	dt	dt	X
ejpam-6473	533	1	+	+	PROPN
ejpam-6473	533	2	k7e	k7e	PROPN
ejpam-6473	533	3	2λt	2λt	PROPN
ejpam-6473	533	4	∫	∫	PROPN
ejpam-6473	533	5	t	t	PROPN
ejpam-6473	533	6	0	0	NUM
ejpam-6473	533	7	(	(	PUNCT
ejpam-6473	533	8	(	(	PUNCT
ejpam-6473	533	9	a1	a1	NOUN
ejpam-6473	533	10	−	−	NOUN
ejpam-6473	533	11	ā1	ā1	NOUN
ejpam-6473	533	12	)	)	PUNCT
ejpam-6473	533	13	2	2	NUM
ejpam-6473	533	14	+	+	CCONJ
ejpam-6473	533	15	(	(	PUNCT
ejpam-6473	533	16	a3	a3	NOUN
ejpam-6473	533	17	−	−	PROPN
ejpam-6473	533	18	ā3	ā3	NOUN
ejpam-6473	533	19	)	)	PUNCT
ejpam-6473	533	20	2	2	NUM
ejpam-6473	533	21	+	+	CCONJ
ejpam-6473	533	22	(	(	PUNCT
ejpam-6473	533	23	b1	b1	NOUN
ejpam-6473	533	24	−	−	PROPN
ejpam-6473	533	25	b̄1	b̄1	NUM
ejpam-6473	533	26	)	)	PUNCT
ejpam-6473	533	27	2	2	NUM
ejpam-6473	533	28	+	+	ADJ
ejpam-6473	533	29	(	(	PUNCT
ejpam-6473	533	30	b2	b2	NOUN
ejpam-6473	533	31	−	−	NOUN
ejpam-6473	533	32	b̄2	b̄2	NOUN
ejpam-6473	533	33	)	)	PUNCT
ejpam-6473	533	34	2	2	NUM
ejpam-6473	533	35	+	+	CCONJ
ejpam-6473	533	36	(	(	PUNCT
ejpam-6473	533	37	b3	b3	PROPN
ejpam-6473	533	38	−	−	PROPN
ejpam-6473	533	39	b̄3	b̄3	NOUN
ejpam-6473	533	40	)	)	PUNCT
ejpam-6473	533	41	2	2	NUM
ejpam-6473	533	42	)	)	PUNCT
ejpam-6473	533	43	dt	dt	PUNCT
ejpam-6473	534	1	+	+	CCONJ
ejpam-6473	534	2	p7	p7	ADJ
ejpam-6473	534	3	∫	∫	PROPN
ejpam-6473	534	4	t	t	PROPN
ejpam-6473	534	5	0	0	NUM
ejpam-6473	534	6	(	(	PUNCT
ejpam-6473	534	7	(	(	PUNCT
ejpam-6473	534	8	a3	a3	NOUN
ejpam-6473	534	9	−	−	PROPN
ejpam-6473	534	10	ā3	ā3	NOUN
ejpam-6473	534	11	)	)	PUNCT
ejpam-6473	534	12	2	2	NUM
ejpam-6473	535	1	+	+	CCONJ
ejpam-6473	535	2	(	(	PUNCT
ejpam-6473	535	3	b1	b1	NOUN
ejpam-6473	535	4	−	−	PROPN
ejpam-6473	535	5	b̄1	b̄1	NUM
ejpam-6473	535	6	)	)	PUNCT
ejpam-6473	535	7	2	2	NUM
ejpam-6473	536	1	+	+	CCONJ
ejpam-6473	536	2	(	(	PUNCT
ejpam-6473	536	3	b3	b3	PROPN
ejpam-6473	536	4	−	−	PROPN
ejpam-6473	536	5	b̄3	b̄3	NOUN
ejpam-6473	536	6	)	)	PUNCT
ejpam-6473	536	7	2	2	NUM
ejpam-6473	537	1	+	+	NOUN
ejpam-6473	537	2	(	(	PUNCT
ejpam-6473	537	3	b4	b4	NOUN
ejpam-6473	537	4	−	−	PROPN
ejpam-6473	537	5	b̄4	b̄4	ADJ
ejpam-6473	537	6	)	)	PUNCT
ejpam-6473	537	7	2	2	NUM
ejpam-6473	537	8	)	)	PUNCT
ejpam-6473	537	9	dt	dt	NOUN
ejpam-6473	537	10	,	,	PUNCT
ejpam-6473	537	11	(	(	PUNCT
ejpam-6473	537	12	23	23	NUM
ejpam-6473	537	13	)	)	PUNCT
ejpam-6473	537	14	(	(	PUNCT
ejpam-6473	537	15	λ+	λ+	X
ejpam-6473	537	16	b+	b+	X
ejpam-6473	537	17	µ	µ	X
ejpam-6473	537	18	)	)	PUNCT
ejpam-6473	537	19	∫	∫	PROPN
ejpam-6473	537	20	t	t	PROPN
ejpam-6473	537	21	0	0	NUM
ejpam-6473	538	1	(	(	PUNCT
ejpam-6473	538	2	b4	b4	NOUN
ejpam-6473	538	3	−	−	PROPN
ejpam-6473	538	4	b̄4	b̄4	ADJ
ejpam-6473	538	5	)	)	PUNCT
ejpam-6473	538	6	2	2	NUM
ejpam-6473	538	7	dt+	dt+	NOUN
ejpam-6473	538	8	1	1	NUM
ejpam-6473	538	9	2	2	NUM
ejpam-6473	538	10	(	(	PUNCT
ejpam-6473	538	11	b4(0)−	b4(0)−	NOUN
ejpam-6473	538	12	b̄4(0	b̄4(0	NOUN
ejpam-6473	538	13	)	)	PUNCT
ejpam-6473	538	14	)	)	PUNCT
ejpam-6473	538	15	2	2	NUM
ejpam-6473	538	16	+	+	NUM
ejpam-6473	538	17	ā	ā	ADJ
ejpam-6473	538	18	=	=	SYM
ejpam-6473	538	19	0	0	PROPN
ejpam-6473	538	20	.	.	PUNCT
ejpam-6473	539	1	(	(	PUNCT
ejpam-6473	539	2	24	24	NUM
ejpam-6473	539	3	)	)	PUNCT
ejpam-6473	539	4	here	here	ADV
ejpam-6473	539	5	,	,	PUNCT
ejpam-6473	539	6	(	(	PUNCT
ejpam-6473	539	7	mi	mi	PROPN
ejpam-6473	539	8	,	,	PUNCT
ejpam-6473	539	9	kj	kj	PROPN
ejpam-6473	539	10	,	,	PUNCT
ejpam-6473	539	11	pr	pr	NOUN
ejpam-6473	539	12	)	)	PUNCT
ejpam-6473	539	13	,	,	PUNCT
ejpam-6473	539	14	where	where	SCONJ
ejpam-6473	539	15	(	(	PUNCT
ejpam-6473	539	16	i	i	NOUN
ejpam-6473	539	17	=	=	NOUN
ejpam-6473	539	18	1	1	NUM
ejpam-6473	539	19	,	,	PUNCT
ejpam-6473	539	20	2	2	NUM
ejpam-6473	539	21	,	,	PUNCT
ejpam-6473	539	22	,	,	PUNCT
ejpam-6473	539	23	5	5	NUM
ejpam-6473	539	24	,	,	PUNCT
ejpam-6473	539	25	7	7	NUM
ejpam-6473	539	26	)	)	PUNCT
ejpam-6473	539	27	,	,	PUNCT
ejpam-6473	539	28	(	(	PUNCT
ejpam-6473	539	29	j	j	NOUN
ejpam-6473	539	30	=	=	SYM
ejpam-6473	539	31	1	1	NUM
ejpam-6473	539	32	,	,	PUNCT
ejpam-6473	539	33	2	2	NUM
ejpam-6473	539	34	,	,	PUNCT
ejpam-6473	539	35	3	3	NUM
ejpam-6473	539	36	,	,	PUNCT
ejpam-6473	539	37	..	..	PUNCT
ejpam-6473	539	38	7	7	NUM
ejpam-6473	539	39	)	)	PUNCT
ejpam-6473	539	40	and	and	CCONJ
ejpam-6473	539	41	r	r	NOUN
ejpam-6473	539	42	=	=	SYM
ejpam-6473	539	43	1	1	NUM
ejpam-6473	539	44	,	,	PUNCT
ejpam-6473	539	45	2	2	NUM
ejpam-6473	539	46	,	,	PUNCT
ejpam-6473	539	47	5	5	NUM
ejpam-6473	539	48	,	,	PUNCT
ejpam-6473	539	49	7	7	NUM
ejpam-6473	539	50	depend	depend	VERB
ejpam-6473	539	51	on	on	ADP
ejpam-6473	539	52	the	the	DET
ejpam-6473	539	53	bounds	bound	NOUN
ejpam-6473	539	54	and	and	CCONJ
ejpam-6473	539	55	coefficients	coefficient	NOUN
ejpam-6473	539	56	of	of	ADP
ejpam-6473	539	57	the	the	DET
ejpam-6473	539	58	state	state	NOUN
ejpam-6473	539	59	variable	variable	NOUN
ejpam-6473	539	60	and	and	CCONJ
ejpam-6473	539	61	the	the	DET
ejpam-6473	539	62	costate	costate	ADJ
ejpam-6473	539	63	variable	variable	NOUN
ejpam-6473	539	64	.	.	PUNCT
ejpam-6473	540	1	from	from	ADP
ejpam-6473	540	2	equation	equation	NOUN
ejpam-6473	540	3	(	(	PUNCT
ejpam-6473	540	4	17)-(24	17)-(24	NUM
ejpam-6473	540	5	)	)	PUNCT
ejpam-6473	540	6	[	[	PUNCT
ejpam-6473	540	7	(	(	PUNCT
ejpam-6473	540	8	λ+	λ+	X
ejpam-6473	540	9	b+	b+	ADJ
ejpam-6473	540	10	µ)−	µ)−	NOUN
ejpam-6473	540	11	(	(	PUNCT
ejpam-6473	540	12	m1	m1	PROPN
ejpam-6473	540	13	+	+	PROPN
ejpam-6473	540	14	m2	m2	PROPN
ejpam-6473	540	15	+	+	CCONJ
ejpam-6473	540	16	m7)e	m7)e	PROPN
ejpam-6473	540	17	λt	λt	ADP
ejpam-6473	540	18	−	−	PROPN
ejpam-6473	540	19	(	(	PUNCT
ejpam-6473	540	20	k1	k1	NOUN
ejpam-6473	540	21	+	+	PROPN
ejpam-6473	540	22	k2	k2	ADJ
ejpam-6473	540	23	+	+	ADP
ejpam-6473	540	24	k7)e	k7)e	ADJ
ejpam-6473	540	25	2λt	2λt	ADJ
ejpam-6473	540	26	−(p1	−(p1	NOUN
ejpam-6473	540	27	+	+	CCONJ
ejpam-6473	540	28	p4	p4	ADJ
ejpam-6473	540	29	+	+	CCONJ
ejpam-6473	540	30	p5	p5	ADJ
ejpam-6473	540	31	)	)	PUNCT
ejpam-6473	540	32	]	]	PUNCT
ejpam-6473	541	1	∫	∫	PROPN
ejpam-6473	541	2	t	t	PROPN
ejpam-6473	541	3	0	0	NUM
ejpam-6473	542	1	(	(	PUNCT
ejpam-6473	542	2	(	(	PUNCT
ejpam-6473	542	3	a1	a1	NOUN
ejpam-6473	542	4	−	−	NOUN
ejpam-6473	542	5	ā1	ā1	NOUN
ejpam-6473	542	6	)	)	PUNCT
ejpam-6473	542	7	2	2	NUM
ejpam-6473	542	8	)	)	PUNCT
ejpam-6473	542	9	dt	dt	NOUN
ejpam-6473	543	1	+	+	CCONJ
ejpam-6473	543	2	[	[	PUNCT
ejpam-6473	543	3	(	(	PUNCT
ejpam-6473	543	4	λ+	λ+	X
ejpam-6473	543	5	b+	b+	X
ejpam-6473	543	6	µ+	µ+	X
ejpam-6473	543	7	ζ)−m2e	ζ)−m2e	PROPN
ejpam-6473	543	8	λt	λt	ADP
ejpam-6473	543	9	−k2e	−k2e	NUM
ejpam-6473	543	10	2λt	2λt	ADJ
ejpam-6473	543	11	−(p1	−(p1	NOUN
ejpam-6473	543	12	+	+	CCONJ
ejpam-6473	543	13	p2	p2	PROPN
ejpam-6473	543	14	+	+	CCONJ
ejpam-6473	543	15	p3	p3	NOUN
ejpam-6473	543	16	+	+	CCONJ
ejpam-6473	543	17	p4	p4	ADJ
ejpam-6473	543	18	+	+	CCONJ
ejpam-6473	543	19	p6	p6	PROPN
ejpam-6473	543	20	)	)	PUNCT
ejpam-6473	543	21	]	]	PUNCT
ejpam-6473	544	1	∫	∫	PROPN
ejpam-6473	544	2	t	t	PROPN
ejpam-6473	544	3	0	0	NUM
ejpam-6473	545	1	(	(	PUNCT
ejpam-6473	545	2	(	(	PUNCT
ejpam-6473	545	3	a2	a2	PROPN
ejpam-6473	545	4	−	−	PROPN
ejpam-6473	545	5	ā2	ā2	PROPN
ejpam-6473	545	6	)	)	PUNCT
ejpam-6473	545	7	2	2	NUM
ejpam-6473	545	8	)	)	PUNCT
ejpam-6473	545	9	dt	dt	NOUN
ejpam-6473	546	1	+	+	CCONJ
ejpam-6473	546	2	[	[	PUNCT
ejpam-6473	546	3	(	(	PUNCT
ejpam-6473	546	4	λ+	λ+	X
ejpam-6473	546	5	b+	b+	X
ejpam-6473	546	6	µ+	µ+	X
ejpam-6473	546	7	δ)−	δ)−	PROPN
ejpam-6473	546	8	(	(	PUNCT
ejpam-6473	546	9	m1	m1	PROPN
ejpam-6473	546	10	+	+	PROPN
ejpam-6473	546	11	m2	m2	PROPN
ejpam-6473	546	12	+	+	CCONJ
ejpam-6473	546	13	m5)e	m5)e	NOUN
ejpam-6473	546	14	λt	λt	INTJ
ejpam-6473	546	15	−	−	PROPN
ejpam-6473	546	16	(	(	PUNCT
ejpam-6473	546	17	k1	k1	NOUN
ejpam-6473	546	18	+	+	PROPN
ejpam-6473	546	19	k2	k2	PROPN
ejpam-6473	546	20	+	+	PROPN
ejpam-6473	546	21	k5	k5	PROPN
ejpam-6473	546	22	+	+	ADP
ejpam-6473	546	23	k7)e	k7)e	ADJ
ejpam-6473	546	24	2λt	2λt	ADJ
ejpam-6473	546	25	−(p1	−(p1	NOUN
ejpam-6473	546	26	+	+	CCONJ
ejpam-6473	546	27	p3	p3	PROPN
ejpam-6473	546	28	+	+	CCONJ
ejpam-6473	546	29	p4	p4	ADJ
ejpam-6473	546	30	+	+	CCONJ
ejpam-6473	546	31	p7	p7	ADJ
ejpam-6473	546	32	)	)	PUNCT
ejpam-6473	546	33	]	]	PUNCT
ejpam-6473	547	1	∫	∫	PROPN
ejpam-6473	547	2	t	t	PROPN
ejpam-6473	547	3	0	0	NUM
ejpam-6473	547	4	(	(	PUNCT
ejpam-6473	547	5	(	(	PUNCT
ejpam-6473	547	6	a3	a3	NOUN
ejpam-6473	547	7	−	−	PROPN
ejpam-6473	547	8	ā3	ā3	ADJ
ejpam-6473	547	9	)	)	PUNCT
ejpam-6473	547	10	2	2	NUM
ejpam-6473	547	11	)	)	PUNCT
ejpam-6473	547	12	dt	dt	NOUN
ejpam-6473	548	1	+	+	CCONJ
ejpam-6473	548	2	[	[	X
ejpam-6473	548	3	(	(	PUNCT
ejpam-6473	548	4	λ+	λ+	AUX
ejpam-6473	548	5	b+	b+	ADJ
ejpam-6473	548	6	µ)−	µ)−	VERB
ejpam-6473	548	7	p4	p4	ADJ
ejpam-6473	548	8	]	]	PUNCT
ejpam-6473	548	9	∫	∫	PROPN
ejpam-6473	548	10	t	t	PROPN
ejpam-6473	548	11	0	0	NUM
ejpam-6473	548	12	(	(	PUNCT
ejpam-6473	548	13	(	(	PUNCT
ejpam-6473	548	14	a4	a4	INTJ
ejpam-6473	548	15	−	−	NOUN
ejpam-6473	548	16	ā4	ā4	NOUN
ejpam-6473	548	17	)	)	PUNCT
ejpam-6473	548	18	2	2	NUM
ejpam-6473	548	19	)	)	PUNCT
ejpam-6473	548	20	dt	dt	NOUN
ejpam-6473	549	1	+	+	CCONJ
ejpam-6473	549	2	[	[	PUNCT
ejpam-6473	549	3	(	(	PUNCT
ejpam-6473	549	4	λ+	λ+	X
ejpam-6473	549	5	b+	b+	ADJ
ejpam-6473	549	6	µ)−	µ)−	X
ejpam-6473	549	7	(	(	PUNCT
ejpam-6473	549	8	m5	m5	PROPN
ejpam-6473	549	9	+	+	CCONJ
ejpam-6473	549	10	m7)e	m7)e	NOUN
ejpam-6473	549	11	λt	λt	ADP
ejpam-6473	549	12	−	−	PROPN
ejpam-6473	549	13	(	(	PUNCT
ejpam-6473	549	14	k5	k5	PROPN
ejpam-6473	549	15	+	+	ADP
ejpam-6473	549	16	k7)e	k7)e	PROPN
ejpam-6473	549	17	2λt	2λt	ADJ
ejpam-6473	549	18	−(p1	−(p1	NOUN
ejpam-6473	549	19	+	+	CCONJ
ejpam-6473	549	20	p2	p2	PROPN
ejpam-6473	549	21	+	+	CCONJ
ejpam-6473	549	22	p3	p3	NOUN
ejpam-6473	549	23	+	+	CCONJ
ejpam-6473	549	24	p4	p4	ADJ
ejpam-6473	549	25	+	+	CCONJ
ejpam-6473	549	26	p5	p5	ADJ
ejpam-6473	549	27	+	+	CCONJ
ejpam-6473	549	28	p6	p6	ADJ
ejpam-6473	549	29	+	+	CCONJ
ejpam-6473	549	30	p7	p7	ADJ
ejpam-6473	549	31	)	)	PUNCT
ejpam-6473	549	32	]	]	PUNCT
ejpam-6473	550	1	∫	∫	PROPN
ejpam-6473	550	2	t	t	PROPN
ejpam-6473	550	3	0	0	NUM
ejpam-6473	551	1	(	(	PUNCT
ejpam-6473	551	2	(	(	PUNCT
ejpam-6473	551	3	b1	b1	NOUN
ejpam-6473	551	4	−	−	PROPN
ejpam-6473	551	5	b̄1	b̄1	NUM
ejpam-6473	551	6	)	)	PUNCT
ejpam-6473	551	7	2	2	NUM
ejpam-6473	551	8	)	)	PUNCT
ejpam-6473	551	9	dt	dt	NOUN
ejpam-6473	552	1	+	+	CCONJ
ejpam-6473	552	2	[	[	PUNCT
ejpam-6473	552	3	(	(	PUNCT
ejpam-6473	552	4	λ+	λ+	X
ejpam-6473	552	5	b+	b+	X
ejpam-6473	552	6	µ+	µ+	ADJ
ejpam-6473	552	7	ζ)−	ζ)−	PROPN
ejpam-6473	552	8	(	(	PUNCT
ejpam-6473	552	9	m5	m5	PROPN
ejpam-6473	552	10	+	+	CCONJ
ejpam-6473	552	11	m7)e	m7)e	NOUN
ejpam-6473	552	12	λt	λt	ADP
ejpam-6473	552	13	−	−	PROPN
ejpam-6473	552	14	(	(	PUNCT
ejpam-6473	552	15	k5	k5	PROPN
ejpam-6473	552	16	+	+	ADP
ejpam-6473	552	17	k7)e	k7)e	PROPN
ejpam-6473	552	18	2λt	2λt	ADJ
ejpam-6473	552	19	−(p1	−(p1	NOUN
ejpam-6473	552	20	+	+	CCONJ
ejpam-6473	552	21	p2	p2	X
ejpam-6473	552	22	+	+	CCONJ
ejpam-6473	552	23	p4	p4	ADJ
ejpam-6473	552	24	+	+	CCONJ
ejpam-6473	552	25	p6	p6	PROPN
ejpam-6473	552	26	)	)	PUNCT
ejpam-6473	552	27	]	]	PUNCT
ejpam-6473	553	1	∫	∫	PROPN
ejpam-6473	553	2	t	t	PROPN
ejpam-6473	553	3	0	0	NUM
ejpam-6473	554	1	(	(	PUNCT
ejpam-6473	554	2	(	(	PUNCT
ejpam-6473	554	3	b2	b2	NOUN
ejpam-6473	554	4	−	−	NOUN
ejpam-6473	554	5	b̄2	b̄2	NUM
ejpam-6473	554	6	)	)	PUNCT
ejpam-6473	554	7	2	2	NUM
ejpam-6473	554	8	)	)	PUNCT
ejpam-6473	554	9	dt	dt	NOUN
ejpam-6473	555	1	+	+	CCONJ
ejpam-6473	555	2	[	[	PUNCT
ejpam-6473	555	3	(	(	PUNCT
ejpam-6473	555	4	λ+	λ+	X
ejpam-6473	555	5	b+	b+	X
ejpam-6473	555	6	µ+	µ+	X
ejpam-6473	555	7	δ)−m7e	δ)−m7e	NOUN
ejpam-6473	555	8	λt	λt	ADP
ejpam-6473	555	9	−k7e	−k7e	NUM
ejpam-6473	555	10	2λt	2λt	NOUN
ejpam-6473	555	11	s.	s.	PROPN
ejpam-6473	555	12	bano	bano	PROPN
ejpam-6473	555	13	et	et	PROPN
ejpam-6473	555	14	al	al	PROPN
ejpam-6473	555	15	.	.	PUNCT
ejpam-6473	555	16	/	/	SYM
ejpam-6473	555	17	eur	eur	PROPN
ejpam-6473	555	18	.	.	PUNCT
ejpam-6473	556	1	j.	j.	PROPN
ejpam-6473	556	2	pure	pure	PROPN
ejpam-6473	556	3	appl	appl	PROPN
ejpam-6473	556	4	.	.	PROPN
ejpam-6473	556	5	math	math	PROPN
ejpam-6473	556	6	,	,	PUNCT
ejpam-6473	556	7	18	18	NUM
ejpam-6473	556	8	(	(	PUNCT
ejpam-6473	556	9	4	4	NUM
ejpam-6473	556	10	)	)	PUNCT
ejpam-6473	556	11	(	(	PUNCT
ejpam-6473	556	12	2025	2025	NUM
ejpam-6473	556	13	)	)	PUNCT
ejpam-6473	556	14	,	,	PUNCT
ejpam-6473	556	15	6473	6473	NUM
ejpam-6473	556	16	27	27	NUM
ejpam-6473	556	17	of	of	ADP
ejpam-6473	556	18	38	38	NUM
ejpam-6473	556	19	−(p1	−(p1	NUM
ejpam-6473	556	20	+	+	CCONJ
ejpam-6473	556	21	p3	p3	PROPN
ejpam-6473	556	22	+	+	CCONJ
ejpam-6473	556	23	p4	p4	ADJ
ejpam-6473	556	24	+	+	CCONJ
ejpam-6473	556	25	p6	p6	ADJ
ejpam-6473	556	26	+	+	CCONJ
ejpam-6473	556	27	p7	p7	ADJ
ejpam-6473	556	28	)	)	PUNCT
ejpam-6473	556	29	]	]	PUNCT
ejpam-6473	557	1	∫	∫	PROPN
ejpam-6473	557	2	t	t	PROPN
ejpam-6473	557	3	0	0	NUM
ejpam-6473	558	1	(	(	PUNCT
ejpam-6473	558	2	(	(	PUNCT
ejpam-6473	558	3	b3	b3	PROPN
ejpam-6473	558	4	−	−	PROPN
ejpam-6473	558	5	b̄3	b̄3	NOUN
ejpam-6473	558	6	)	)	PUNCT
ejpam-6473	558	7	2	2	NUM
ejpam-6473	558	8	)	)	PUNCT
ejpam-6473	558	9	dt	dt	NOUN
ejpam-6473	559	1	+	+	CCONJ
ejpam-6473	559	2	[	[	X
ejpam-6473	559	3	(	(	PUNCT
ejpam-6473	559	4	λ+	λ+	PUNCT
ejpam-6473	559	5	b+	b+	ADJ
ejpam-6473	559	6	µ)−	µ)−	X
ejpam-6473	559	7	(	(	PUNCT
ejpam-6473	559	8	p1	p1	NOUN
ejpam-6473	559	9	+	+	CCONJ
ejpam-6473	559	10	p2	p2	PROPN
ejpam-6473	559	11	+	+	CCONJ
ejpam-6473	559	12	p3	p3	NOUN
ejpam-6473	559	13	+	+	CCONJ
ejpam-6473	559	14	p4	p4	ADJ
ejpam-6473	559	15	+	+	CCONJ
ejpam-6473	559	16	p5	p5	ADJ
ejpam-6473	559	17	+	+	CCONJ
ejpam-6473	559	18	p6	p6	ADJ
ejpam-6473	559	19	+	+	CCONJ
ejpam-6473	559	20	p7	p7	ADJ
ejpam-6473	559	21	)	)	PUNCT
ejpam-6473	559	22	]	]	PUNCT
ejpam-6473	560	1	∫	∫	PROPN
ejpam-6473	560	2	t	t	PROPN
ejpam-6473	560	3	0	0	NUM
ejpam-6473	561	1	(	(	PUNCT
ejpam-6473	561	2	(	(	PUNCT
ejpam-6473	561	3	b4	b4	NOUN
ejpam-6473	561	4	−	−	PROPN
ejpam-6473	561	5	b̄4	b̄4	ADJ
ejpam-6473	561	6	)	)	PUNCT
ejpam-6473	561	7	2	2	NUM
ejpam-6473	561	8	)	)	PUNCT
ejpam-6473	561	9	dt	dt	NOUN
ejpam-6473	561	10	≤	≤	NUM
ejpam-6473	561	11	0	0	NUM
ejpam-6473	561	12	.	.	PUNCT
ejpam-6473	562	1	(	(	PUNCT
ejpam-6473	562	2	25	25	NUM
ejpam-6473	562	3	)	)	PUNCT
ejpam-6473	562	4	the	the	DET
ejpam-6473	562	5	coefficient	coefficient	NOUN
ejpam-6473	562	6	of	of	ADP
ejpam-6473	562	7	each	each	DET
ejpam-6473	562	8	integral	integral	ADJ
ejpam-6473	562	9	of	of	ADP
ejpam-6473	562	10	equation	equation	NOUN
ejpam-6473	562	11	(	(	PUNCT
ejpam-6473	562	12	25	25	NUM
ejpam-6473	562	13	)	)	PUNCT
ejpam-6473	562	14	are	be	AUX
ejpam-6473	562	15	non	non	X
ejpam-6473	562	16	negative	negative	ADJ
ejpam-6473	562	17	if	if	SCONJ
ejpam-6473	562	18	we	we	PRON
ejpam-6473	562	19	choose	choose	VERB
ejpam-6473	562	20	sufficiently	sufficiently	ADV
ejpam-6473	562	21	small	small	ADJ
ejpam-6473	562	22	t	t	NOUN
ejpam-6473	562	23	and	and	CCONJ
ejpam-6473	562	24	sufficiently	sufficiently	ADV
ejpam-6473	562	25	large	large	ADJ
ejpam-6473	562	26	λ	λ	NOUN
ejpam-6473	562	27	.	.	PROPN
ejpam-6473	563	1	for	for	ADP
ejpam-6473	563	2	example	example	NOUN
ejpam-6473	563	3	,	,	PUNCT
ejpam-6473	563	4	if	if	SCONJ
ejpam-6473	563	5	we	we	PRON
ejpam-6473	563	6	fix	fix	VERB
ejpam-6473	563	7	λ	λ	X
ejpam-6473	563	8	>	>	X
ejpam-6473	563	9	m1	m1	PROPN
ejpam-6473	563	10	+	+	CCONJ
ejpam-6473	563	11	m2	m2	PROPN
ejpam-6473	563	12	+	+	CCONJ
ejpam-6473	563	13	m7	m7	PROPN
ejpam-6473	563	14	+	+	CCONJ
ejpam-6473	563	15	k1	k1	NOUN
ejpam-6473	563	16	+	+	CCONJ
ejpam-6473	563	17	k2	k2	NOUN
ejpam-6473	563	18	+	+	CCONJ
ejpam-6473	563	19	k7	k7	PROPN
ejpam-6473	563	20	+	+	CCONJ
ejpam-6473	563	21	p1	p1	PROPN
ejpam-6473	563	22	+	+	CCONJ
ejpam-6473	563	23	p4	p4	ADJ
ejpam-6473	563	24	+	+	CCONJ
ejpam-6473	563	25	p5	p5	ADJ
ejpam-6473	563	26	−	−	PROPN
ejpam-6473	563	27	b	b	PROPN
ejpam-6473	563	28	−	−	PROPN
ejpam-6473	563	29	µ	µ	PROPN
ejpam-6473	563	30	and	and	CCONJ
ejpam-6473	563	31	t	t	X
ejpam-6473	563	32	<	<	X
ejpam-6473	563	33	1	1	NUM
ejpam-6473	563	34	2λ	2λ	NUM
ejpam-6473	563	35	ln	ln	ADJ
ejpam-6473	563	36	(	(	PUNCT
ejpam-6473	563	37	(	(	PUNCT
ejpam-6473	563	38	λ+b+µ)−(p1+p4+p5	λ+b+µ)−(p1+p4+p5	NOUN
ejpam-6473	563	39	)	)	PUNCT
ejpam-6473	563	40	)	)	PUNCT
ejpam-6473	564	1	m1+m2+m7+k1+k2+k7	m1+m2+m7+k1+k2+k7	PROPN
ejpam-6473	564	2	.	.	PUNCT
ejpam-6473	565	1	then	then	ADV
ejpam-6473	565	2	the	the	DET
ejpam-6473	565	3	coefficient	coefficient	NOUN
ejpam-6473	565	4	of	of	ADP
ejpam-6473	565	5	integral	integral	ADJ
ejpam-6473	565	6	∫	∫	PROPN
ejpam-6473	565	7	t	t	PROPN
ejpam-6473	565	8	0	0	NUM
ejpam-6473	566	1	(	(	PUNCT
ejpam-6473	566	2	a1	a1	NOUN
ejpam-6473	566	3	−	−	NOUN
ejpam-6473	566	4	ā1	ā1	NOUN
ejpam-6473	566	5	)	)	PUNCT
ejpam-6473	566	6	2	2	NUM
ejpam-6473	566	7	dt	dt	NOUN
ejpam-6473	566	8	is	be	AUX
ejpam-6473	566	9	nonnegative	nonnegative	ADJ
ejpam-6473	566	10	.	.	PUNCT
ejpam-6473	567	1	the	the	DET
ejpam-6473	567	2	same	same	ADJ
ejpam-6473	567	3	method	method	NOUN
ejpam-6473	567	4	is	be	AUX
ejpam-6473	567	5	applied	apply	VERB
ejpam-6473	567	6	to	to	ADP
ejpam-6473	567	7	the	the	DET
ejpam-6473	567	8	remaining	remain	VERB
ejpam-6473	567	9	integral	integral	ADJ
ejpam-6473	567	10	terms	term	NOUN
ejpam-6473	567	11	.	.	PUNCT
ejpam-6473	568	1	we	we	PRON
ejpam-6473	568	2	obtain	obtain	VERB
ejpam-6473	568	3	the	the	DET
ejpam-6473	568	4	others	other	NOUN
ejpam-6473	568	5	λs	λs	ADP
ejpam-6473	568	6	,	,	PUNCT
ejpam-6473	568	7	ts	ts	PROPN
ejpam-6473	568	8	.	.	PUNCT
ejpam-6473	568	9	take	take	VERB
ejpam-6473	568	10	the	the	DET
ejpam-6473	568	11	maximum	maximum	NOUN
ejpam-6473	568	12	of	of	ADP
ejpam-6473	568	13	the	the	DET
ejpam-6473	568	14	all	all	DET
ejpam-6473	568	15	λs	λs	NOUN
ejpam-6473	568	16	and	and	CCONJ
ejpam-6473	568	17	minimum	minimum	NOUN
ejpam-6473	568	18	of	of	ADP
ejpam-6473	568	19	the	the	DET
ejpam-6473	568	20	ts	ts	NOUN
ejpam-6473	568	21	,	,	PUNCT
ejpam-6473	568	22	then	then	ADV
ejpam-6473	568	23	used	use	VERB
ejpam-6473	568	24	it	it	PRON
ejpam-6473	568	25	as	as	ADP
ejpam-6473	568	26	λ	λ	PROPN
ejpam-6473	568	27	and	and	CCONJ
ejpam-6473	568	28	t	t	PROPN
ejpam-6473	568	29	,	,	PUNCT
ejpam-6473	568	30	then	then	ADV
ejpam-6473	568	31	all	all	DET
ejpam-6473	568	32	the	the	DET
ejpam-6473	568	33	integral	integral	ADJ
ejpam-6473	568	34	coefficients	coefficient	NOUN
ejpam-6473	568	35	will	will	AUX
ejpam-6473	568	36	be	be	AUX
ejpam-6473	568	37	non	non	ADJ
ejpam-6473	568	38	-	-	ADJ
ejpam-6473	568	39	negative	negative	ADJ
ejpam-6473	568	40	.	.	PUNCT
ejpam-6473	569	1	this	this	PRON
ejpam-6473	569	2	implies	imply	VERB
ejpam-6473	569	3	that	that	SCONJ
ejpam-6473	569	4	ā1	ā1	NOUN
ejpam-6473	569	5	=	=	SYM
ejpam-6473	569	6	a1	a1	PROPN
ejpam-6473	569	7	,	,	PUNCT
ejpam-6473	569	8	ā2	ā2	X
ejpam-6473	569	9	=	=	SYM
ejpam-6473	569	10	a2	a2	PROPN
ejpam-6473	569	11	,	,	PUNCT
ejpam-6473	569	12	ā3	ā3	ADJ
ejpam-6473	569	13	=	=	SYM
ejpam-6473	569	14	a3	a3	NOUN
ejpam-6473	569	15	,	,	PUNCT
ejpam-6473	569	16	ā4	ā4	NOUN
ejpam-6473	569	17	=	=	SYM
ejpam-6473	569	18	a4	a4	PROPN
ejpam-6473	569	19	,	,	PUNCT
ejpam-6473	569	20	b̄1	b̄1	NOUN
ejpam-6473	569	21	=	=	SYM
ejpam-6473	569	22	b1	b1	NOUN
ejpam-6473	569	23	,	,	PUNCT
ejpam-6473	569	24	b̄2	b̄2	X
ejpam-6473	569	25	=	=	SYM
ejpam-6473	569	26	b2	b2	NOUN
ejpam-6473	569	27	,	,	PUNCT
ejpam-6473	569	28	b̄3	b̄3	X
ejpam-6473	569	29	=	=	SYM
ejpam-6473	569	30	b3	b3	PROPN
ejpam-6473	569	31	,	,	PUNCT
ejpam-6473	569	32	b̄4	b̄4	ADJ
ejpam-6473	569	33	=	=	NOUN
ejpam-6473	569	34	b4	b4	NOUN
ejpam-6473	569	35	,	,	PUNCT
ejpam-6473	569	36	p̄	p̄	PROPN
ejpam-6473	570	1	=	=	SYM
ejpam-6473	570	2	p	p	PROPN
ejpam-6473	570	3	,	,	PUNCT
ejpam-6473	570	4	l̄	l̄	NOUN
ejpam-6473	570	5	=	=	SYM
ejpam-6473	570	6	l	l	NOUN
ejpam-6473	570	7	,	,	PUNCT
ejpam-6473	570	8	s̄	s̄	NOUN
ejpam-6473	570	9	=	=	SYM
ejpam-6473	570	10	s	s	NOUN
ejpam-6473	570	11	,	,	PUNCT
ejpam-6473	570	12	q̄	q̄	ADJ
ejpam-6473	570	13	=	=	SYM
ejpam-6473	570	14	q	q	NOUN
ejpam-6473	570	15	,	,	PUNCT
ejpam-6473	570	16	λ̄1	λ̄1	X
ejpam-6473	570	17	=	=	SYM
ejpam-6473	570	18	λ1	λ1	PROPN
ejpam-6473	570	19	,	,	PUNCT
ejpam-6473	570	20	λ̄2	λ̄2	NOUN
ejpam-6473	570	21	=	=	SYM
ejpam-6473	570	22	λ2	λ2	NOUN
ejpam-6473	570	23	,	,	PUNCT
ejpam-6473	570	24	λ̄3	λ̄3	PUNCT
ejpam-6473	570	25	=	=	SYM
ejpam-6473	570	26	λ3	λ3	PROPN
ejpam-6473	570	27	,	,	PUNCT
ejpam-6473	570	28	λ̄4	λ̄4	X
ejpam-6473	570	29	=	=	SYM
ejpam-6473	570	30	λ4	λ4	NOUN
ejpam-6473	570	31	.	.	PUNCT
ejpam-6473	571	1	hence	hence	ADV
ejpam-6473	571	2	,	,	PUNCT
ejpam-6473	571	3	the	the	DET
ejpam-6473	571	4	solution	solution	NOUN
ejpam-6473	571	5	of	of	ADP
ejpam-6473	571	6	equation	equation	NOUN
ejpam-6473	571	7	(	(	PUNCT
ejpam-6473	571	8	15	15	NUM
ejpam-6473	571	9	)	)	PUNCT
ejpam-6473	571	10	is	be	AUX
ejpam-6473	571	11	unique	unique	ADJ
ejpam-6473	571	12	.	.	PUNCT
ejpam-6473	572	1	5	5	X
ejpam-6473	572	2	.	.	X
ejpam-6473	572	3	delay	delay	NOUN
ejpam-6473	572	4	we	we	PRON
ejpam-6473	572	5	modify	modify	VERB
ejpam-6473	572	6	the	the	DET
ejpam-6473	572	7	classical	classical	ADJ
ejpam-6473	572	8	plsq	plsq	NOUN
ejpam-6473	572	9	model	model	NOUN
ejpam-6473	572	10	to	to	PART
ejpam-6473	572	11	incorporate	incorporate	VERB
ejpam-6473	572	12	intervention	intervention	NOUN
ejpam-6473	572	13	-	-	PUNCT
ejpam-6473	572	14	based	base	VERB
ejpam-6473	572	15	dynamics	dynamic	NOUN
ejpam-6473	572	16	and	and	CCONJ
ejpam-6473	572	17	time	time	NOUN
ejpam-6473	572	18	delay	delay	NOUN
ejpam-6473	572	19	.	.	PUNCT
ejpam-6473	573	1	unlike	unlike	ADP
ejpam-6473	573	2	previous	previous	ADJ
ejpam-6473	573	3	models	model	NOUN
ejpam-6473	573	4	,	,	PUNCT
ejpam-6473	573	5	our	our	PRON
ejpam-6473	573	6	structure	structure	NOUN
ejpam-6473	573	7	captures	capture	VERB
ejpam-6473	573	8	the	the	DET
ejpam-6473	573	9	relapse	relapse	NOUN
ejpam-6473	573	10	and	and	CCONJ
ejpam-6473	573	11	partial	partial	ADJ
ejpam-6473	573	12	immunity	immunity	NOUN
ejpam-6473	573	13	.	.	PUNCT
ejpam-6473	574	1	the	the	DET
ejpam-6473	574	2	modified	modify	VERB
ejpam-6473	574	3	model	model	NOUN
ejpam-6473	574	4	is	be	AUX
ejpam-6473	574	5	given	give	VERB
ejpam-6473	574	6	below	below	NOUN
ejpam-6473	574	7	dp	dp	NOUN
ejpam-6473	574	8	dt	dt	NOUN
ejpam-6473	574	9	=	=	SYM
ejpam-6473	574	10	λ−	λ−	PROPN
ejpam-6473	574	11	(	(	PUNCT
ejpam-6473	574	12	b+	b+	X
ejpam-6473	574	13	µ)p	µ)p	PUNCT
ejpam-6473	574	14	−	−	PROPN
ejpam-6473	574	15	βps(1	βps(1	NOUN
ejpam-6473	574	16	+	+	CCONJ
ejpam-6473	574	17	νs	νs	NOUN
ejpam-6473	574	18	)	)	PUNCT
ejpam-6473	574	19	,	,	PUNCT
ejpam-6473	574	20	dl	dl	PROPN
ejpam-6473	574	21	dt	dt	NOUN
ejpam-6473	574	22	=	=	PUNCT
ejpam-6473	574	23	βps(1	βps(1	X
ejpam-6473	574	24	+	+	CCONJ
ejpam-6473	574	25	νs)−	νs)−	NOUN
ejpam-6473	574	26	(	(	PUNCT
ejpam-6473	574	27	µ+	µ+	DET
ejpam-6473	574	28	b)l−	b)l−	PROPN
ejpam-6473	574	29	ζl(t−	ζl(t−	PROPN
ejpam-6473	574	30	τ	τ	PROPN
ejpam-6473	574	31	)	)	PUNCT
ejpam-6473	574	32	,	,	PUNCT
ejpam-6473	574	33	ds	ds	ADP
ejpam-6473	574	34	dt	dt	NOUN
ejpam-6473	574	35	=	=	SYM
ejpam-6473	574	36	ζl(t−	ζl(t−	PROPN
ejpam-6473	574	37	τ)−	τ)−	PROPN
ejpam-6473	574	38	(	(	PUNCT
ejpam-6473	574	39	µ+	µ+	X
ejpam-6473	574	40	b+	b+	NOUN
ejpam-6473	574	41	δ)s	δ)s	X
ejpam-6473	574	42	,	,	PUNCT
ejpam-6473	574	43	dq	dq	NOUN
ejpam-6473	574	44	dt	dt	NOUN
ejpam-6473	574	45	=	=	NOUN
ejpam-6473	574	46	δs	δs	NOUN
ejpam-6473	574	47	−	−	PROPN
ejpam-6473	574	48	(	(	PUNCT
ejpam-6473	574	49	µ+	µ+	X
ejpam-6473	574	50	b)q	b)q	X
ejpam-6473	574	51	.	.	PUNCT
ejpam-6473	575	1	(	(	PUNCT
ejpam-6473	575	2	26	26	NUM
ejpam-6473	575	3	)	)	PUNCT
ejpam-6473	575	4	here	here	ADV
ejpam-6473	575	5	,	,	PUNCT
ejpam-6473	575	6	τ	τ	PROPN
ejpam-6473	575	7	is	be	AUX
ejpam-6473	575	8	the	the	DET
ejpam-6473	575	9	delay	delay	NOUN
ejpam-6473	575	10	parameter	parameter	NOUN
ejpam-6473	575	11	.	.	PUNCT
ejpam-6473	576	1	now	now	ADV
ejpam-6473	576	2	we	we	PRON
ejpam-6473	576	3	linearize	linearize	VERB
ejpam-6473	576	4	the	the	DET
ejpam-6473	576	5	delay	delay	NOUN
ejpam-6473	576	6	system	system	NOUN
ejpam-6473	576	7	by	by	ADP
ejpam-6473	576	8	choosing	choose	VERB
ejpam-6473	576	9	the	the	DET
ejpam-6473	576	10	variable	variable	NOUN
ejpam-6473	576	11	as	as	ADP
ejpam-6473	576	12	a	a	DET
ejpam-6473	576	13	=	=	NOUN
ejpam-6473	576	14	p	p	NOUN
ejpam-6473	576	15	−	−	PROPN
ejpam-6473	576	16	p	p	NOUN
ejpam-6473	576	17	∗	∗	NOUN
ejpam-6473	576	18	,	,	PUNCT
ejpam-6473	576	19	b	b	X
ejpam-6473	576	20	=	=	SYM
ejpam-6473	576	21	l−l∗	l−l∗	PROPN
ejpam-6473	576	22	,	,	PUNCT
ejpam-6473	576	23	c	c	X
ejpam-6473	576	24	=	=	SYM
ejpam-6473	576	25	s	s	PART
ejpam-6473	576	26	−	−	NOUN
ejpam-6473	576	27	s∗.	s∗.	ADJ
ejpam-6473	576	28	as	as	SCONJ
ejpam-6473	576	29	the	the	DET
ejpam-6473	576	30	above	above	ADJ
ejpam-6473	576	31	system	system	NOUN
ejpam-6473	576	32	is	be	AUX
ejpam-6473	576	33	independent	independent	ADJ
ejpam-6473	576	34	of	of	ADP
ejpam-6473	576	35	the	the	DET
ejpam-6473	576	36	q	q	NOUN
ejpam-6473	576	37	,	,	PUNCT
ejpam-6473	576	38	so	so	ADV
ejpam-6473	576	39	the	the	DET
ejpam-6473	576	40	linearized	linearize	VERB
ejpam-6473	576	41	system	system	NOUN
ejpam-6473	576	42	is	be	AUX
ejpam-6473	576	43	given	give	VERB
ejpam-6473	576	44	as	as	ADP
ejpam-6473	576	45	ȧ	ȧ	PROPN
ejpam-6473	576	46	=	=	PRON
ejpam-6473	577	1	[	[	X
ejpam-6473	577	2	−βs∗(1	−βs∗(1	NOUN
ejpam-6473	577	3	+	+	PUNCT
ejpam-6473	577	4	νs∗)−	νs∗)−	NOUN
ejpam-6473	577	5	(	(	PUNCT
ejpam-6473	577	6	b+	b+	X
ejpam-6473	577	7	µ)]a+	µ)]a+	VERB
ejpam-6473	577	8	[	[	PUNCT
ejpam-6473	577	9	−βp	−βp	PROPN
ejpam-6473	577	10	∗(1	∗(1	PROPN
ejpam-6473	577	11	+	+	CCONJ
ejpam-6473	577	12	2νs∗)]c	2νs∗)]c	NUM
ejpam-6473	577	13	,	,	PUNCT
ejpam-6473	577	14	ḃ	ḃ	PROPN
ejpam-6473	578	1	=	=	PUNCT
ejpam-6473	578	2	[	[	PUNCT
ejpam-6473	578	3	βs∗(1	βs∗(1	NOUN
ejpam-6473	578	4	+	+	CCONJ
ejpam-6473	578	5	νs∗	νs∗	NOUN
ejpam-6473	578	6	)	)	PUNCT
ejpam-6473	578	7	]	]	PUNCT
ejpam-6473	579	1	a−	a−	PROPN
ejpam-6473	579	2	[	[	PUNCT
ejpam-6473	579	3	b+	b+	X
ejpam-6473	579	4	µ+	µ+	DET
ejpam-6473	579	5	ζe−λτ	ζe−λτ	NOUN
ejpam-6473	579	6	]	]	PUNCT
ejpam-6473	579	7	b+	b+	X
ejpam-6473	579	8	[	[	PUNCT
ejpam-6473	579	9	βp	βp	PROPN
ejpam-6473	579	10	∗(1	∗(1	PROPN
ejpam-6473	579	11	+	+	CCONJ
ejpam-6473	579	12	2νs∗	2νs∗	NUM
ejpam-6473	579	13	)	)	PUNCT
ejpam-6473	579	14	]	]	PUNCT
ejpam-6473	580	1	c	c	X
ejpam-6473	580	2	,	,	PUNCT
ejpam-6473	580	3	ċ	ċ	NOUN
ejpam-6473	580	4	=	=	SYM
ejpam-6473	580	5	[	[	PUNCT
ejpam-6473	580	6	ζe−λτ	ζe−λτ	NOUN
ejpam-6473	580	7	]	]	X
ejpam-6473	580	8	b−	b−	PROPN
ejpam-6473	580	9	[	[	PUNCT
ejpam-6473	580	10	b+	b+	X
ejpam-6473	580	11	µ+	µ+	X
ejpam-6473	580	12	δ	δ	PROPN
ejpam-6473	580	13	]	]	PUNCT
ejpam-6473	580	14	c.	c.	PROPN
ejpam-6473	581	1	the	the	DET
ejpam-6473	581	2	jacobian	jacobian	PROPN
ejpam-6473	581	3	of	of	ADP
ejpam-6473	581	4	the	the	DET
ejpam-6473	581	5	linearized	linearize	VERB
ejpam-6473	581	6	system	system	NOUN
ejpam-6473	581	7	is	be	AUX
ejpam-6473	581	8	j	j	NOUN
ejpam-6473	581	9	=	=	PUNCT
ejpam-6473	581	10	−βs∗(1	−βs∗(1	NOUN
ejpam-6473	582	1	+	+	X
ejpam-6473	582	2	νs∗)−	νs∗)−	NOUN
ejpam-6473	582	3	(	(	PUNCT
ejpam-6473	582	4	b+	b+	X
ejpam-6473	582	5	µ	µ	NUM
ejpam-6473	582	6	)	)	PUNCT
ejpam-6473	582	7	0	0	NUM
ejpam-6473	583	1	−βp	−βp	PROPN
ejpam-6473	583	2	∗(1	∗(1	PROPN
ejpam-6473	583	3	+	+	CCONJ
ejpam-6473	583	4	2νs∗	2νs∗	NUM
ejpam-6473	583	5	)	)	PUNCT
ejpam-6473	583	6	βs∗(1	βs∗(1	VERB
ejpam-6473	583	7	+	+	CCONJ
ejpam-6473	583	8	νs∗	νs∗	NOUN
ejpam-6473	583	9	)	)	PUNCT
ejpam-6473	584	1	−(b+	−(b+	NUM
ejpam-6473	584	2	µ+	µ+	DET
ejpam-6473	584	3	ζe−λτ	ζe−λτ	NOUN
ejpam-6473	584	4	)	)	PUNCT
ejpam-6473	584	5	βp	βp	PROPN
ejpam-6473	584	6	∗(1	∗(1	NOUN
ejpam-6473	584	7	+	+	CCONJ
ejpam-6473	584	8	2νs∗	2νs∗	NUM
ejpam-6473	584	9	)	)	PUNCT
ejpam-6473	584	10	0	0	NUM
ejpam-6473	585	1	ζe−λτ	ζe−λτ	NOUN
ejpam-6473	585	2	−(b+	−(b+	NUM
ejpam-6473	585	3	µ+	µ+	PROPN
ejpam-6473	585	4	δ	δ	PROPN
ejpam-6473	585	5	)	)	PUNCT
ejpam-6473	585	6	.	.	NOUN
ejpam-6473	585	7	(	(	PUNCT
ejpam-6473	585	8	27	27	NUM
ejpam-6473	585	9	)	)	PUNCT
ejpam-6473	586	1	s.	s.	PROPN
ejpam-6473	586	2	bano	bano	PROPN
ejpam-6473	586	3	et	et	PROPN
ejpam-6473	586	4	al	al	PROPN
ejpam-6473	586	5	.	.	PUNCT
ejpam-6473	586	6	/	/	SYM
ejpam-6473	586	7	eur	eur	PROPN
ejpam-6473	586	8	.	.	PUNCT
ejpam-6473	587	1	j.	j.	PROPN
ejpam-6473	587	2	pure	pure	PROPN
ejpam-6473	587	3	appl	appl	PROPN
ejpam-6473	587	4	.	.	PROPN
ejpam-6473	587	5	math	math	PROPN
ejpam-6473	587	6	,	,	PUNCT
ejpam-6473	587	7	18	18	NUM
ejpam-6473	587	8	(	(	PUNCT
ejpam-6473	587	9	4	4	NUM
ejpam-6473	587	10	)	)	PUNCT
ejpam-6473	587	11	(	(	PUNCT
ejpam-6473	587	12	2025	2025	NUM
ejpam-6473	587	13	)	)	PUNCT
ejpam-6473	587	14	,	,	PUNCT
ejpam-6473	587	15	6473	6473	NUM
ejpam-6473	587	16	28	28	NUM
ejpam-6473	587	17	of	of	ADP
ejpam-6473	587	18	38	38	NUM
ejpam-6473	587	19	the	the	DET
ejpam-6473	587	20	characteristic	characteristic	ADJ
ejpam-6473	587	21	equation	equation	NOUN
ejpam-6473	587	22	from	from	ADP
ejpam-6473	587	23	above	above	ADP
ejpam-6473	587	24	equation	equation	NOUN
ejpam-6473	587	25	is	be	AUX
ejpam-6473	587	26	λ3	λ3	PROPN
ejpam-6473	587	27	+	+	NOUN
ejpam-6473	587	28	λ2(d1	λ2(d1	PRON
ejpam-6473	587	29	+	+	CCONJ
ejpam-6473	587	30	f1e	f1e	PROPN
ejpam-6473	587	31	−λτ	−λτ	X
ejpam-6473	587	32	)	)	PUNCT
ejpam-6473	588	1	+	+	CCONJ
ejpam-6473	588	2	λ(d2	λ(d2	X
ejpam-6473	588	3	+	+	CCONJ
ejpam-6473	588	4	f2e	f2e	PROPN
ejpam-6473	588	5	−λτ	−λτ	PROPN
ejpam-6473	588	6	)	)	PUNCT
ejpam-6473	589	1	+	+	CCONJ
ejpam-6473	589	2	(	(	PUNCT
ejpam-6473	589	3	d3	d3	PROPN
ejpam-6473	589	4	+	+	CCONJ
ejpam-6473	589	5	f3e	f3e	PROPN
ejpam-6473	589	6	−λτ	−λτ	NOUN
ejpam-6473	589	7	)	)	PUNCT
ejpam-6473	589	8	=	=	PUNCT
ejpam-6473	589	9	0	0	X
ejpam-6473	589	10	.	.	PUNCT
ejpam-6473	590	1	(	(	PUNCT
ejpam-6473	590	2	28	28	NUM
ejpam-6473	590	3	)	)	PUNCT
ejpam-6473	590	4	the	the	DET
ejpam-6473	590	5	values	value	NOUN
ejpam-6473	590	6	of	of	ADP
ejpam-6473	590	7	the	the	DET
ejpam-6473	590	8	coefficients	coefficient	NOUN
ejpam-6473	590	9	of	of	ADP
ejpam-6473	590	10	the	the	DET
ejpam-6473	590	11	characteristic	characteristic	ADJ
ejpam-6473	590	12	equation	equation	NOUN
ejpam-6473	590	13	are	be	AUX
ejpam-6473	590	14	as	as	SCONJ
ejpam-6473	590	15	given	give	VERB
ejpam-6473	590	16	d1	d1	PROPN
ejpam-6473	590	17	=	=	PUNCT
ejpam-6473	590	18	−k1	−k1	NOUN
ejpam-6473	590	19	−	−	NOUN
ejpam-6473	590	20	k4	k4	NOUN
ejpam-6473	590	21	−	−	PROPN
ejpam-6473	590	22	k8	k8	PROPN
ejpam-6473	590	23	,	,	PUNCT
ejpam-6473	590	24	d2	d2	PROPN
ejpam-6473	590	25	=	=	SYM
ejpam-6473	591	1	k1k4	k1k4	PROPN
ejpam-6473	592	1	+	+	NUM
ejpam-6473	592	2	k4k8	k4k8	NOUN
ejpam-6473	592	3	+	+	CCONJ
ejpam-6473	592	4	k1k8	k1k8	PROPN
ejpam-6473	592	5	,	,	PUNCT
ejpam-6473	592	6	d3	d3	PROPN
ejpam-6473	592	7	=	=	SYM
ejpam-6473	592	8	−k1k4k8	−k1k4k8	PROPN
ejpam-6473	592	9	,	,	PUNCT
ejpam-6473	592	10	f1	f1	NOUN
ejpam-6473	592	11	=	=	SYM
ejpam-6473	592	12	−k5	−k5	PROPN
ejpam-6473	592	13	,	,	PUNCT
ejpam-6473	592	14	f2	f2	PROPN
ejpam-6473	592	15	=	=	SYM
ejpam-6473	592	16	k1k5	k1k5	PROPN
ejpam-6473	592	17	+	+	CCONJ
ejpam-6473	593	1	k5k8	k5k8	X
ejpam-6473	593	2	−	−	PRON
ejpam-6473	593	3	k6k7	k6k7	NOUN
ejpam-6473	593	4	,	,	PUNCT
ejpam-6473	593	5	f3	f3	NOUN
ejpam-6473	593	6	=	=	PUNCT
ejpam-6473	594	1	−k1k5k8	−k1k5k8	X
ejpam-6473	594	2	+	+	CCONJ
ejpam-6473	594	3	k1k6k7	k1k6k7	NOUN
ejpam-6473	594	4	−	−	PROPN
ejpam-6473	594	5	k2k3k7	k2k3k7	PROPN
ejpam-6473	594	6	,	,	PUNCT
ejpam-6473	594	7	k1	k1	NOUN
ejpam-6473	594	8	=	=	SYM
ejpam-6473	594	9	−βs∗(1	−βs∗(1	NOUN
ejpam-6473	594	10	+	+	PUNCT
ejpam-6473	594	11	νs∗)−	νs∗)−	NOUN
ejpam-6473	594	12	(	(	PUNCT
ejpam-6473	594	13	b+	b+	X
ejpam-6473	594	14	µ	µ	NUM
ejpam-6473	594	15	)	)	PUNCT
ejpam-6473	594	16	,	,	PUNCT
ejpam-6473	594	17	k2	k2	NOUN
ejpam-6473	594	18	=	=	SYM
ejpam-6473	594	19	−βp	−βp	PROPN
ejpam-6473	594	20	∗(1	∗(1	PROPN
ejpam-6473	594	21	+	+	CCONJ
ejpam-6473	594	22	2νs∗	2νs∗	NUM
ejpam-6473	594	23	)	)	PUNCT
ejpam-6473	594	24	,	,	PUNCT
ejpam-6473	594	25	k3	k3	VERB
ejpam-6473	594	26	=	=	PUNCT
ejpam-6473	594	27	βs∗(1	βs∗(1	NOUN
ejpam-6473	594	28	+	+	CCONJ
ejpam-6473	594	29	νs∗	νs∗	NOUN
ejpam-6473	594	30	)	)	PUNCT
ejpam-6473	594	31	,	,	PUNCT
ejpam-6473	594	32	k4	k4	NOUN
ejpam-6473	594	33	=	=	SYM
ejpam-6473	594	34	−(b+	−(b+	NUM
ejpam-6473	594	35	µ	µ	NOUN
ejpam-6473	594	36	)	)	PUNCT
ejpam-6473	594	37	,	,	PUNCT
ejpam-6473	594	38	k5	k5	PROPN
ejpam-6473	594	39	=	=	SYM
ejpam-6473	594	40	−ζ	−ζ	PROPN
ejpam-6473	594	41	,	,	PUNCT
ejpam-6473	594	42	k6	k6	NOUN
ejpam-6473	594	43	=	=	SYM
ejpam-6473	594	44	βp	βp	PROPN
ejpam-6473	594	45	∗(1	∗(1	PROPN
ejpam-6473	594	46	+	+	CCONJ
ejpam-6473	594	47	2νs∗	2νs∗	NUM
ejpam-6473	594	48	)	)	PUNCT
ejpam-6473	594	49	,	,	PUNCT
ejpam-6473	594	50	k7	k7	PROPN
ejpam-6473	594	51	=	=	SYM
ejpam-6473	594	52	ζ	ζ	X
ejpam-6473	594	53	,	,	PUNCT
ejpam-6473	594	54	k8	k8	NOUN
ejpam-6473	594	55	=	=	SYM
ejpam-6473	594	56	−(b+	−(b+	NUM
ejpam-6473	594	57	µ+	µ+	PROPN
ejpam-6473	594	58	δ	δ	PROPN
ejpam-6473	594	59	)	)	PUNCT
ejpam-6473	594	60	.	.	PUNCT
ejpam-6473	595	1	5.1	5.1	NUM
ejpam-6473	595	2	.	.	PUNCT
ejpam-6473	596	1	stability	stability	NOUN
ejpam-6473	596	2	analysis	analysis	NOUN
ejpam-6473	596	3	the	the	DET
ejpam-6473	596	4	stability	stability	NOUN
ejpam-6473	596	5	of	of	ADP
ejpam-6473	596	6	the	the	DET
ejpam-6473	596	7	delay	delay	NOUN
ejpam-6473	596	8	system	system	NOUN
ejpam-6473	596	9	of	of	ADP
ejpam-6473	596	10	the	the	DET
ejpam-6473	596	11	smoking	smoking	NOUN
ejpam-6473	596	12	cessation	cessation	NOUN
ejpam-6473	596	13	model	model	NOUN
ejpam-6473	596	14	with	with	ADP
ejpam-6473	596	15	convex	convex	ADJ
ejpam-6473	596	16	incidence	incidence	NOUN
ejpam-6473	596	17	rate	rate	NOUN
ejpam-6473	596	18	is	be	AUX
ejpam-6473	596	19	computed	compute	VERB
ejpam-6473	596	20	in	in	ADP
ejpam-6473	596	21	the	the	DET
ejpam-6473	596	22	same	same	ADJ
ejpam-6473	596	23	way	way	NOUN
ejpam-6473	596	24	as	as	SCONJ
ejpam-6473	596	25	already	already	ADV
ejpam-6473	596	26	done	do	VERB
ejpam-6473	596	27	in	in	ADP
ejpam-6473	596	28	[	[	X
ejpam-6473	596	29	35	35	NUM
ejpam-6473	596	30	]	]	PUNCT
ejpam-6473	596	31	.	.	PUNCT
ejpam-6473	597	1	we	we	PRON
ejpam-6473	597	2	will	will	AUX
ejpam-6473	597	3	check	check	VERB
ejpam-6473	597	4	the	the	DET
ejpam-6473	597	5	two	two	NUM
ejpam-6473	597	6	cases	case	NOUN
ejpam-6473	597	7	that	that	PRON
ejpam-6473	597	8	are	be	AUX
ejpam-6473	597	9	(	(	PUNCT
ejpam-6473	597	10	1	1	NUM
ejpam-6473	597	11	)	)	PUNCT
ejpam-6473	597	12	when	when	SCONJ
ejpam-6473	597	13	delay	delay	NOUN
ejpam-6473	597	14	parameter	parameter	NOUN
ejpam-6473	597	15	τ	τ	PROPN
ejpam-6473	597	16	=	=	SYM
ejpam-6473	597	17	0	0	PROPN
ejpam-6473	597	18	,	,	PUNCT
ejpam-6473	597	19	(	(	PUNCT
ejpam-6473	597	20	2	2	X
ejpam-6473	597	21	)	)	PUNCT
ejpam-6473	597	22	when	when	SCONJ
ejpam-6473	597	23	delay	delay	NOUN
ejpam-6473	597	24	parameter	parameter	PROPN
ejpam-6473	597	25	τ	τ	PROPN
ejpam-6473	597	26	>	>	X
ejpam-6473	597	27	0	0	NUM
ejpam-6473	597	28	.	.	PUNCT
ejpam-6473	597	29	5.1.1	5.1.1	NOUN
ejpam-6473	597	30	.	.	PUNCT
ejpam-6473	598	1	in	in	ADP
ejpam-6473	598	2	the	the	DET
ejpam-6473	598	3	absence	absence	NOUN
ejpam-6473	598	4	of	of	ADP
ejpam-6473	598	5	delay	delay	NOUN
ejpam-6473	598	6	in	in	ADP
ejpam-6473	598	7	this	this	DET
ejpam-6473	598	8	case	case	NOUN
ejpam-6473	598	9	,	,	PUNCT
ejpam-6473	598	10	we	we	PRON
ejpam-6473	598	11	put	put	VERB
ejpam-6473	598	12	τ	τ	X
ejpam-6473	598	13	=	=	SYM
ejpam-6473	598	14	0	0	NUM
ejpam-6473	598	15	in	in	ADP
ejpam-6473	598	16	equation	equation	NOUN
ejpam-6473	598	17	(	(	PUNCT
ejpam-6473	598	18	28	28	NUM
ejpam-6473	598	19	)	)	PUNCT
ejpam-6473	598	20	=	=	NOUN
ejpam-6473	598	21	⇒	⇒	X
ejpam-6473	599	1	λ3	λ3	PROPN
ejpam-6473	599	2	+	+	CCONJ
ejpam-6473	599	3	λ2(d1	λ2(d1	PRON
ejpam-6473	599	4	+	+	CCONJ
ejpam-6473	599	5	f1	f1	NOUN
ejpam-6473	599	6	)	)	PUNCT
ejpam-6473	600	1	+	+	NUM
ejpam-6473	600	2	λ(d2	λ(d2	X
ejpam-6473	600	3	+	+	X
ejpam-6473	600	4	f2	f2	PROPN
ejpam-6473	600	5	)	)	PUNCT
ejpam-6473	600	6	+	+	CCONJ
ejpam-6473	600	7	d3	d3	PROPN
ejpam-6473	600	8	+	+	CCONJ
ejpam-6473	600	9	f3	f3	PROPN
ejpam-6473	600	10	=	=	SYM
ejpam-6473	600	11	0	0	NUM
ejpam-6473	600	12	,	,	PUNCT
ejpam-6473	600	13	let	let	VERB
ejpam-6473	600	14	,	,	PUNCT
ejpam-6473	600	15	d2	d2	NOUN
ejpam-6473	600	16	=	=	SYM
ejpam-6473	600	17	d1	d1	PROPN
ejpam-6473	600	18	+	+	CCONJ
ejpam-6473	600	19	f1	f1	NOUN
ejpam-6473	600	20	,	,	PUNCT
ejpam-6473	600	21	d1	d1	PROPN
ejpam-6473	600	22	=	=	SYM
ejpam-6473	600	23	d2	d2	PROPN
ejpam-6473	600	24	+	+	CCONJ
ejpam-6473	600	25	f2	f2	PROPN
ejpam-6473	600	26	,	,	PUNCT
ejpam-6473	600	27	d0	d0	NOUN
ejpam-6473	600	28	=	=	PUNCT
ejpam-6473	600	29	d3	d3	PROPN
ejpam-6473	600	30	+	+	X
ejpam-6473	600	31	f3	f3	ADJ
ejpam-6473	600	32	.	.	PUNCT
ejpam-6473	601	1	then	then	ADV
ejpam-6473	601	2	equation	equation	NOUN
ejpam-6473	601	3	becomes	become	VERB
ejpam-6473	601	4	=	=	PRON
ejpam-6473	601	5	⇒	⇒	NOUN
ejpam-6473	601	6	λ3	λ3	PROPN
ejpam-6473	601	7	+	+	X
ejpam-6473	601	8	λ2d2	λ2d2	X
ejpam-6473	601	9	+	+	ADJ
ejpam-6473	601	10	λd1	λd1	ADJ
ejpam-6473	601	11	+	+	NOUN
ejpam-6473	601	12	d0	d0	NOUN
ejpam-6473	601	13	=	=	SYM
ejpam-6473	601	14	0	0	X
ejpam-6473	601	15	.	.	PUNCT
ejpam-6473	602	1	according	accord	VERB
ejpam-6473	602	2	to	to	ADP
ejpam-6473	602	3	the	the	DET
ejpam-6473	602	4	routh	routh	PROPN
ejpam-6473	602	5	hurwitz	hurwitz	PROPN
ejpam-6473	602	6	criteria	criterion	NOUN
ejpam-6473	602	7	,	,	PUNCT
ejpam-6473	602	8	if	if	SCONJ
ejpam-6473	602	9	the	the	DET
ejpam-6473	602	10	below	below	ADP
ejpam-6473	602	11	conditions	condition	NOUN
ejpam-6473	602	12	hold	hold	VERB
ejpam-6473	602	13	,	,	PUNCT
ejpam-6473	602	14	then	then	ADV
ejpam-6473	602	15	the	the	DET
ejpam-6473	602	16	equilibrium	equilibrium	NOUN
ejpam-6473	602	17	points	point	NOUN
ejpam-6473	602	18	are	be	AUX
ejpam-6473	602	19	locally	locally	ADV
ejpam-6473	602	20	stable	stable	ADJ
ejpam-6473	602	21	.	.	PUNCT
ejpam-6473	603	1	det1	det1	NOUN
ejpam-6473	603	2	=	=	SYM
ejpam-6473	603	3	d2	d2	PROPN
ejpam-6473	603	4	>	>	X
ejpam-6473	603	5	0	0	PROPN
ejpam-6473	603	6	,	,	PUNCT
ejpam-6473	603	7	det2	det2	NOUN
ejpam-6473	603	8	=	=	SYM
ejpam-6473	603	9	(	(	PUNCT
ejpam-6473	603	10	d2	d2	NOUN
ejpam-6473	603	11	d0	d0	NOUN
ejpam-6473	603	12	1	1	NUM
ejpam-6473	603	13	d1	d1	PROPN
ejpam-6473	603	14	)	)	PUNCT
ejpam-6473	603	15	>	>	X
ejpam-6473	603	16	0	0	NUM
ejpam-6473	603	17	,	,	PUNCT
ejpam-6473	603	18	det3	det3	ADJ
ejpam-6473	603	19	=	=	SYM
ejpam-6473	603	20	d2	d2	X
ejpam-6473	603	21	d0	d0	NOUN
ejpam-6473	603	22	0	0	NUM
ejpam-6473	603	23	1	1	NUM
ejpam-6473	603	24	d1	d1	NOUN
ejpam-6473	603	25	0	0	NUM
ejpam-6473	603	26	0	0	NUM
ejpam-6473	603	27	d2	d2	PROPN
ejpam-6473	603	28	d0	d0	NOUN
ejpam-6473	603	29			PROPN
ejpam-6473	603	30	>	>	X
ejpam-6473	603	31	0	0	NUM
ejpam-6473	603	32	.	.	PUNCT
ejpam-6473	604	1	(	(	PUNCT
ejpam-6473	604	2	29	29	NUM
ejpam-6473	604	3	)	)	PUNCT
ejpam-6473	604	4	5.1.2	5.1.2	NUM
ejpam-6473	604	5	.	.	PUNCT
ejpam-6473	604	6	presence	presence	NOUN
ejpam-6473	604	7	of	of	ADP
ejpam-6473	604	8	delay	delay	NOUN
ejpam-6473	604	9	in	in	ADP
ejpam-6473	604	10	this	this	DET
ejpam-6473	604	11	case	case	NOUN
ejpam-6473	604	12	we	we	PRON
ejpam-6473	604	13	let	let	VERB
ejpam-6473	604	14	τ	τ	PROPN
ejpam-6473	604	15	>	>	X
ejpam-6473	604	16	0	0	PUNCT
ejpam-6473	605	1	and	and	CCONJ
ejpam-6473	605	2	λ	λ	X
ejpam-6473	605	3	=	=	VERB
ejpam-6473	605	4	ιω	ιω	PROPN
ejpam-6473	605	5	where	where	SCONJ
ejpam-6473	605	6	ω	ω	X
ejpam-6473	605	7	>	>	X
ejpam-6473	605	8	0	0	PROPN
ejpam-6473	605	9	.	.	PUNCT
ejpam-6473	606	1	after	after	ADP
ejpam-6473	606	2	using	use	VERB
ejpam-6473	606	3	the	the	DET
ejpam-6473	606	4	value	value	NOUN
ejpam-6473	606	5	λ	λ	NOUN
ejpam-6473	606	6	equation	equation	NOUN
ejpam-6473	606	7	(	(	PUNCT
ejpam-6473	606	8	28	28	NUM
ejpam-6473	606	9	)	)	PUNCT
ejpam-6473	606	10	becomes	become	VERB
ejpam-6473	606	11	(	(	PUNCT
ejpam-6473	606	12	(	(	PUNCT
ejpam-6473	606	13	ιω)3	ιω)3	PROPN
ejpam-6473	606	14	+	+	CCONJ
ejpam-6473	606	15	(	(	PUNCT
ejpam-6473	606	16	ιω)2d1	ιω)2d1	NOUN
ejpam-6473	606	17	+	+	CCONJ
ejpam-6473	606	18	(	(	PUNCT
ejpam-6473	606	19	ιω)d2	ιω)d2	PROPN
ejpam-6473	606	20	+	+	CCONJ
ejpam-6473	606	21	d3	d3	PROPN
ejpam-6473	606	22	)	)	PUNCT
ejpam-6473	606	23	+	+	CCONJ
ejpam-6473	606	24	(	(	PUNCT
ejpam-6473	606	25	(	(	PUNCT
ejpam-6473	606	26	ιω)2f1	ιω)2f1	NOUN
ejpam-6473	606	27	+	+	CCONJ
ejpam-6473	606	28	(	(	PUNCT
ejpam-6473	606	29	ιω)f2	ιω)f2	NOUN
ejpam-6473	606	30	+	+	CCONJ
ejpam-6473	606	31	f3)e	f3)e	ADJ
ejpam-6473	606	32	−ιωτ	−ιωτ	PUNCT
ejpam-6473	606	33	=	=	NOUN
ejpam-6473	607	1	0	0	X
ejpam-6473	607	2	.	.	PUNCT
ejpam-6473	608	1	as	as	ADP
ejpam-6473	608	2	e−ιθ	e−ιθ	NOUN
ejpam-6473	608	3	=	=	SYM
ejpam-6473	608	4	cos	co	NOUN
ejpam-6473	608	5	θ	θ	PROPN
ejpam-6473	608	6	−	−	NOUN
ejpam-6473	608	7	ι	ι	X
ejpam-6473	608	8	sin	sin	NOUN
ejpam-6473	608	9	θ	θ	PROPN
ejpam-6473	608	10	,	,	PUNCT
ejpam-6473	608	11	after	after	ADP
ejpam-6473	608	12	some	some	DET
ejpam-6473	608	13	simple	simple	ADJ
ejpam-6473	608	14	calculation	calculation	NOUN
ejpam-6473	608	15	we	we	PRON
ejpam-6473	608	16	get	get	VERB
ejpam-6473	608	17	cosωτ	cosωτ	NOUN
ejpam-6473	608	18	=	=	PUNCT
ejpam-6473	609	1	ω4y1	ω4y1	ADP
ejpam-6473	609	2	+	+	NUM
ejpam-6473	609	3	ω2y2	ω2y2	NOUN
ejpam-6473	609	4	+	+	X
ejpam-6473	609	5	y3	y3	NOUN
ejpam-6473	609	6	ω4y4	ω4y4	ADV
ejpam-6473	609	7	+	+	CCONJ
ejpam-6473	609	8	ω2y5	ω2y5	PUNCT
ejpam-6473	609	9	+	+	CCONJ
ejpam-6473	609	10	y6	y6	ADJ
ejpam-6473	609	11	.	.	PUNCT
ejpam-6473	610	1	(	(	PUNCT
ejpam-6473	610	2	30	30	NUM
ejpam-6473	610	3	)	)	PUNCT
ejpam-6473	610	4	sinωτ	sinωτ	NOUN
ejpam-6473	610	5	=	=	PUNCT
ejpam-6473	611	1	ω5y7	ω5y7	PUNCT
ejpam-6473	612	1	+	+	NOUN
ejpam-6473	612	2	ω3y8	ω3y8	PUNCT
ejpam-6473	612	3	+	+	NUM
ejpam-6473	612	4	ωy9	ωy9	NUM
ejpam-6473	612	5	ω4y4	ω4y4	ADV
ejpam-6473	612	6	+	+	CCONJ
ejpam-6473	612	7	ω2y5	ω2y5	PUNCT
ejpam-6473	612	8	+	+	CCONJ
ejpam-6473	612	9	y6	y6	ADJ
ejpam-6473	612	10	.	.	PUNCT
ejpam-6473	613	1	(	(	PUNCT
ejpam-6473	613	2	31	31	NUM
ejpam-6473	613	3	)	)	PUNCT
ejpam-6473	613	4	s.	s.	PROPN
ejpam-6473	613	5	bano	bano	PROPN
ejpam-6473	613	6	et	et	PROPN
ejpam-6473	613	7	al	al	PROPN
ejpam-6473	613	8	.	.	PUNCT
ejpam-6473	613	9	/	/	SYM
ejpam-6473	613	10	eur	eur	PROPN
ejpam-6473	613	11	.	.	PUNCT
ejpam-6473	614	1	j.	j.	PROPN
ejpam-6473	614	2	pure	pure	PROPN
ejpam-6473	614	3	appl	appl	PROPN
ejpam-6473	614	4	.	.	PROPN
ejpam-6473	614	5	math	math	PROPN
ejpam-6473	614	6	,	,	PUNCT
ejpam-6473	614	7	18	18	NUM
ejpam-6473	614	8	(	(	PUNCT
ejpam-6473	614	9	4	4	NUM
ejpam-6473	614	10	)	)	PUNCT
ejpam-6473	614	11	(	(	PUNCT
ejpam-6473	614	12	2025	2025	NUM
ejpam-6473	614	13	)	)	PUNCT
ejpam-6473	614	14	,	,	PUNCT
ejpam-6473	614	15	6473	6473	NUM
ejpam-6473	614	16	29	29	NUM
ejpam-6473	614	17	of	of	ADP
ejpam-6473	614	18	38	38	NUM
ejpam-6473	614	19	here	here	ADV
ejpam-6473	614	20	,	,	PUNCT
ejpam-6473	614	21	y1	y1	INTJ
ejpam-6473	614	22	=	=	PUNCT
ejpam-6473	614	23	f2	f2	PROPN
ejpam-6473	614	24	−	−	NOUN
ejpam-6473	614	25	d1f1	d1f1	NOUN
ejpam-6473	614	26	,	,	PUNCT
ejpam-6473	614	27	y2	y2	NOUN
ejpam-6473	614	28	=	=	PUNCT
ejpam-6473	615	1	d1f3	d1f3	PROPN
ejpam-6473	615	2	+	+	X
ejpam-6473	615	3	d3f1	d3f1	VERB
ejpam-6473	615	4	−	−	PROPN
ejpam-6473	615	5	d2f2	d2f2	NOUN
ejpam-6473	615	6	,	,	PUNCT
ejpam-6473	615	7	y3	y3	NOUN
ejpam-6473	615	8	=	=	PUNCT
ejpam-6473	615	9	−d3f3	−d3f3	PROPN
ejpam-6473	615	10	,	,	PUNCT
ejpam-6473	615	11	y4	y4	PROPN
ejpam-6473	615	12	=	=	SYM
ejpam-6473	615	13	f2	f2	PROPN
ejpam-6473	615	14	1	1	NUM
ejpam-6473	615	15	,	,	PUNCT
ejpam-6473	615	16	y5	y5	NOUN
ejpam-6473	615	17	=	=	SYM
ejpam-6473	615	18	f2	f2	PROPN
ejpam-6473	615	19	2	2	NUM
ejpam-6473	615	20	−2f1f3	−2f1f3	PROPN
ejpam-6473	615	21	,	,	PUNCT
ejpam-6473	615	22	y6	y6	NOUN
ejpam-6473	615	23	=	=	SYM
ejpam-6473	615	24	f2	f2	PROPN
ejpam-6473	615	25	3	3	NUM
ejpam-6473	615	26	,	,	PUNCT
ejpam-6473	615	27	y7	y7	ADJ
ejpam-6473	615	28	=	=	NOUN
ejpam-6473	615	29	f1	f1	NOUN
ejpam-6473	615	30	,	,	PUNCT
ejpam-6473	615	31	y8	y8	PROPN
ejpam-6473	615	32	=	=	PUNCT
ejpam-6473	615	33	d1f2−d2f1−f3	d1f2−d2f1−f3	PROPN
ejpam-6473	615	34	,	,	PUNCT
ejpam-6473	615	35	y9	y9	PROPN
ejpam-6473	615	36	=	=	SYM
ejpam-6473	615	37	d2f3−d3f2	d2f3−d3f2	PROPN
ejpam-6473	615	38	.	.	PUNCT
ejpam-6473	616	1	after	after	ADP
ejpam-6473	616	2	utilizing	utilize	VERB
ejpam-6473	616	3	cos2	cos2	NOUN
ejpam-6473	616	4	ωτ	ωτ	ADP
ejpam-6473	616	5	+	+	CCONJ
ejpam-6473	616	6	sin2	sin2	NOUN
ejpam-6473	616	7	ωτ	ωτ	X
ejpam-6473	616	8	=	=	SYM
ejpam-6473	616	9	1	1	NUM
ejpam-6473	616	10	,	,	PUNCT
ejpam-6473	616	11	we	we	PRON
ejpam-6473	616	12	get	get	VERB
ejpam-6473	616	13	ω10u1	ω10u1	PRON
ejpam-6473	616	14	+	+	NOUN
ejpam-6473	616	15	ω8u2	ω8u2	X
ejpam-6473	617	1	+	+	CCONJ
ejpam-6473	617	2	ω6u3	ω6u3	PUNCT
ejpam-6473	617	3	+	+	CCONJ
ejpam-6473	617	4	ω4u4	ω4u4	NUM
ejpam-6473	617	5	+	+	SYM
ejpam-6473	617	6	ω2u5	ω2u5	X
ejpam-6473	617	7	+	+	CCONJ
ejpam-6473	617	8	ωu6	ωu6	NOUN
ejpam-6473	617	9	=	=	SYM
ejpam-6473	617	10	0	0	NUM
ejpam-6473	617	11	,	,	PUNCT
ejpam-6473	617	12	where	where	SCONJ
ejpam-6473	617	13	,	,	PUNCT
ejpam-6473	617	14	u1	u1	PROPN
ejpam-6473	617	15	=	=	SYM
ejpam-6473	617	16	y	y	PROPN
ejpam-6473	617	17	2	2	NUM
ejpam-6473	617	18	7	7	NUM
ejpam-6473	617	19	,	,	PUNCT
ejpam-6473	617	20	u2	u2	NOUN
ejpam-6473	617	21	=	=	SYM
ejpam-6473	617	22	y	y	PROPN
ejpam-6473	617	23	2	2	NUM
ejpam-6473	617	24	1	1	NUM
ejpam-6473	617	25	+	+	NUM
ejpam-6473	617	26	2y7y8	2y7y8	NUM
ejpam-6473	617	27	−	−	NOUN
ejpam-6473	617	28	y	y	PROPN
ejpam-6473	617	29	2	2	NUM
ejpam-6473	617	30	4	4	NUM
ejpam-6473	617	31	,	,	PUNCT
ejpam-6473	617	32	u3	u3	NOUN
ejpam-6473	617	33	=	=	SYM
ejpam-6473	617	34	2y1y2	2y1y2	PROPN
ejpam-6473	618	1	+	+	NUM
ejpam-6473	618	2	y	y	PROPN
ejpam-6473	618	3	2	2	NUM
ejpam-6473	618	4	8	8	NUM
ejpam-6473	618	5	+	+	NUM
ejpam-6473	618	6	2y7y9	2y7y9	NUM
ejpam-6473	618	7	−	−	NOUN
ejpam-6473	618	8	2y4y5	2y4y5	NUM
ejpam-6473	618	9	,	,	PUNCT
ejpam-6473	618	10	u4	u4	PROPN
ejpam-6473	618	11	=	=	SYM
ejpam-6473	618	12	y	y	PROPN
ejpam-6473	618	13	2	2	NUM
ejpam-6473	618	14	2	2	NUM
ejpam-6473	618	15	+	+	NUM
ejpam-6473	618	16	2y1y3	2y1y3	NUM
ejpam-6473	618	17	+	+	NUM
ejpam-6473	618	18	2y8y9	2y8y9	NUM
ejpam-6473	618	19	−	−	NOUN
ejpam-6473	618	20	y	y	NOUN
ejpam-6473	618	21	2	2	NUM
ejpam-6473	618	22	5	5	NUM
ejpam-6473	618	23	−	−	PROPN
ejpam-6473	618	24	2y4y6	2y4y6	NUM
ejpam-6473	618	25	,	,	PUNCT
ejpam-6473	618	26	u5	u5	NOUN
ejpam-6473	618	27	=	=	SYM
ejpam-6473	618	28	2y2y3	2y2y3	PROPN
ejpam-6473	619	1	+	+	CCONJ
ejpam-6473	619	2	y	y	PROPN
ejpam-6473	619	3	2	2	NUM
ejpam-6473	619	4	9	9	NUM
ejpam-6473	619	5	−	−	NUM
ejpam-6473	619	6	2y5y6	2y5y6	NUM
ejpam-6473	619	7	,	,	PUNCT
ejpam-6473	619	8	u6	u6	NOUN
ejpam-6473	619	9	=	=	SYM
ejpam-6473	619	10	y	y	PROPN
ejpam-6473	619	11	2	2	NUM
ejpam-6473	619	12	3	3	NUM
ejpam-6473	619	13	−	−	PROPN
ejpam-6473	619	14	y	y	PROPN
ejpam-6473	619	15	2	2	NUM
ejpam-6473	619	16	6	6	NUM
ejpam-6473	619	17	.	.	PUNCT
ejpam-6473	620	1	let	let	AUX
ejpam-6473	620	2	suppose	suppose	VERB
ejpam-6473	620	3	ω2	ω2	PROPN
ejpam-6473	620	4	=	=	SYM
ejpam-6473	620	5	t	t	X
ejpam-6473	621	1	t5u1	t5u1	PROPN
ejpam-6473	621	2	+	+	CCONJ
ejpam-6473	621	3	t4u2	t4u2	X
ejpam-6473	621	4	+	+	PUNCT
ejpam-6473	621	5	t3r3	t3r3	NUM
ejpam-6473	621	6	+	+	CCONJ
ejpam-6473	621	7	t2u4	t2u4	SYM
ejpam-6473	621	8	+	+	CCONJ
ejpam-6473	621	9	tu5	tu5	NOUN
ejpam-6473	621	10	+	+	CCONJ
ejpam-6473	621	11	u6	u6	NOUN
ejpam-6473	621	12	=	=	SYM
ejpam-6473	621	13	0	0	NUM
ejpam-6473	621	14	.	.	PUNCT
ejpam-6473	622	1	(	(	PUNCT
ejpam-6473	622	2	32	32	NUM
ejpam-6473	622	3	)	)	PUNCT
ejpam-6473	622	4	one	one	NUM
ejpam-6473	622	5	of	of	ADP
ejpam-6473	622	6	the	the	DET
ejpam-6473	622	7	positive	positive	ADJ
ejpam-6473	622	8	roots	root	NOUN
ejpam-6473	622	9	of	of	ADP
ejpam-6473	622	10	the	the	DET
ejpam-6473	622	11	equation(32	equation(32	NOUN
ejpam-6473	622	12	)	)	PUNCT
ejpam-6473	622	13	is	be	AUX
ejpam-6473	622	14	ω0	ω0	ADV
ejpam-6473	622	15	and	and	CCONJ
ejpam-6473	622	16	for	for	ADP
ejpam-6473	622	17	ω0	ω0	NOUN
ejpam-6473	622	18	there	there	PRON
ejpam-6473	622	19	exists	exist	VERB
ejpam-6473	622	20	τn0	τn0	ADV
ejpam-6473	622	21	=	=	SYM
ejpam-6473	623	1	1	1	NUM
ejpam-6473	623	2	ω0	ω0	NOUN
ejpam-6473	623	3	(	(	PUNCT
ejpam-6473	623	4	cos−1	cos−1	PROPN
ejpam-6473	623	5	g1(ω0	g1(ω0	PROPN
ejpam-6473	623	6	)	)	PUNCT
ejpam-6473	623	7	+	+	NUM
ejpam-6473	623	8	2nπ	2nπ	NOUN
ejpam-6473	623	9	)	)	PUNCT
ejpam-6473	623	10	,	,	PUNCT
ejpam-6473	623	11	where	where	SCONJ
ejpam-6473	623	12	,	,	PUNCT
ejpam-6473	623	13	τ0	τ0	NOUN
ejpam-6473	623	14	=	=	SYM
ejpam-6473	623	15	min{τn0	min{τn0	PROPN
ejpam-6473	623	16	,	,	PUNCT
ejpam-6473	623	17	n	n	NOUN
ejpam-6473	623	18	=	=	SYM
ejpam-6473	623	19	0	0	NUM
ejpam-6473	623	20	,	,	PUNCT
ejpam-6473	623	21	2	2	NUM
ejpam-6473	623	22	,	,	PUNCT
ejpam-6473	623	23	3	3	NUM
ejpam-6473	623	24	..	..	PUNCT
ejpam-6473	623	25	}	}	PUNCT
ejpam-6473	623	26	.	.	PUNCT
ejpam-6473	624	1	g1(ω0	g1(ω0	X
ejpam-6473	624	2	)	)	PUNCT
ejpam-6473	624	3	=	=	SYM
ejpam-6473	624	4	ω4	ω4	NUM
ejpam-6473	624	5	0(f2	0(f2	NOUN
ejpam-6473	625	1	−	−	NOUN
ejpam-6473	625	2	d1f1	d1f1	NOUN
ejpam-6473	625	3	)	)	PUNCT
ejpam-6473	625	4	+	+	NUM
ejpam-6473	625	5	ω2	ω2	PROPN
ejpam-6473	625	6	0(d1f3	0(d1f3	PROPN
ejpam-6473	626	1	+	+	CCONJ
ejpam-6473	626	2	d3f1	d3f1	VERB
ejpam-6473	626	3	−	−	VERB
ejpam-6473	626	4	d2f2)−	d2f2)−	NOUN
ejpam-6473	626	5	d3f3	d3f3	DET
ejpam-6473	626	6	ω4	ω4	NOUN
ejpam-6473	626	7	0d	0d	NUM
ejpam-6473	626	8	2	2	NUM
ejpam-6473	626	9	1	1	NUM
ejpam-6473	626	10	+	+	CCONJ
ejpam-6473	626	11	ω2	ω2	ADJ
ejpam-6473	626	12	0(f	0(f	NUM
ejpam-6473	626	13	2	2	NUM
ejpam-6473	626	14	2	2	NUM
ejpam-6473	626	15	−	−	PROPN
ejpam-6473	626	16	2f3f1	2f3f1	NUM
ejpam-6473	626	17	)	)	PUNCT
ejpam-6473	626	18	+	+	CCONJ
ejpam-6473	626	19	f2	f2	PROPN
ejpam-6473	626	20	3	3	NUM
ejpam-6473	626	21	.	.	PUNCT
ejpam-6473	627	1	after	after	ADP
ejpam-6473	627	2	differentiating	differentiate	VERB
ejpam-6473	627	3	characteristic	characteristic	ADJ
ejpam-6473	627	4	equation	equation	NOUN
ejpam-6473	627	5	[	[	PUNCT
ejpam-6473	627	6	∂λ	∂λ	PROPN
ejpam-6473	627	7	∂τ	∂τ	PROPN
ejpam-6473	627	8	]	]	X
ejpam-6473	627	9	−1	−1	NOUN
ejpam-6473	627	10	=	=	PUNCT
ejpam-6473	627	11	(	(	PUNCT
ejpam-6473	627	12	3λ2	3λ2	NUM
ejpam-6473	627	13	+	+	CCONJ
ejpam-6473	627	14	2d1λ+	2d1λ+	NUM
ejpam-6473	627	15	d2	d2	NOUN
ejpam-6473	627	16	)	)	PUNCT
ejpam-6473	627	17	+	+	SYM
ejpam-6473	627	18	e−λτ	e−λτ	PROPN
ejpam-6473	627	19	(	(	PUNCT
ejpam-6473	627	20	2f1λ+	2f1λ+	NUM
ejpam-6473	627	21	f2	f2	PROPN
ejpam-6473	627	22	)	)	PUNCT
ejpam-6473	627	23	λe−λτ	λe−λτ	X
ejpam-6473	627	24	(	(	PUNCT
ejpam-6473	627	25	f1λ2	f1λ2	VERB
ejpam-6473	627	26	+	+	NUM
ejpam-6473	627	27	f2λ+	f2λ+	ADJ
ejpam-6473	627	28	f3	f3	ADJ
ejpam-6473	627	29	)	)	PUNCT
ejpam-6473	627	30	−	−	PROPN
ejpam-6473	628	1	τ	τ	PROPN
ejpam-6473	628	2	λ	λ	PROPN
ejpam-6473	628	3	.	.	PUNCT
ejpam-6473	629	1	now	now	ADV
ejpam-6473	629	2	after	after	ADP
ejpam-6473	629	3	putting	put	VERB
ejpam-6473	629	4	λ	λ	PROPN
ejpam-6473	629	5	=	=	PUNCT
ejpam-6473	629	6	ιω0	ιω0	PROPN
ejpam-6473	629	7	,	,	PUNCT
ejpam-6473	629	8	we	we	PRON
ejpam-6473	629	9	get	get	VERB
ejpam-6473	629	10	[	[	PUNCT
ejpam-6473	629	11	∂λ	∂λ	PROPN
ejpam-6473	629	12	∂τ	∂τ	PROPN
ejpam-6473	629	13	]	]	X
ejpam-6473	629	14	−1	−1	NOUN
ejpam-6473	629	15	|τ	|τ	ADJ
ejpam-6473	629	16	=	=	NOUN
ejpam-6473	629	17	τ0	τ0	NOUN
ejpam-6473	629	18	=	=	SYM
ejpam-6473	630	1	e	e	X
ejpam-6473	630	2	+	+	CCONJ
ejpam-6473	630	3	fι	fι	VERB
ejpam-6473	630	4	g+hι	g+hι	PROPN
ejpam-6473	630	5	+	+	CCONJ
ejpam-6473	630	6	ιτ	ιτ	PROPN
ejpam-6473	630	7	ω	ω	PROPN
ejpam-6473	630	8	,	,	PUNCT
ejpam-6473	630	9	ℜ	ℜ	PROPN
ejpam-6473	630	10	[	[	PUNCT
ejpam-6473	630	11	∂λ	∂λ	PROPN
ejpam-6473	630	12	∂τ	∂τ	PROPN
ejpam-6473	630	13	]	]	X
ejpam-6473	630	14	−1	−1	NOUN
ejpam-6473	630	15	|τ	|τ	ADJ
ejpam-6473	630	16	=	=	NOUN
ejpam-6473	630	17	τ0	τ0	NOUN
ejpam-6473	630	18	=	=	SYM
ejpam-6473	630	19	eg+	eg+	PROPN
ejpam-6473	630	20	fh	fh	PROPN
ejpam-6473	630	21	g2	g2	PROPN
ejpam-6473	631	1	+	+	PROPN
ejpam-6473	631	2	h2	h2	PROPN
ejpam-6473	631	3	̸=	̸=	PROPN
ejpam-6473	631	4	0	0	NUM
ejpam-6473	631	5	.	.	PUNCT
ejpam-6473	631	6	here	here	ADV
ejpam-6473	631	7	,	,	PUNCT
ejpam-6473	631	8	e	e	X
ejpam-6473	631	9	=	=	SYM
ejpam-6473	631	10	d2−3ω2	d2−3ω2	NOUN
ejpam-6473	631	11	0+f2	0+f2	NOUN
ejpam-6473	631	12	cosω0τ+2f1ω0	cosω0τ+2f1ω0	NUM
ejpam-6473	631	13	sinω0τ	sinω0τ	PROPN
ejpam-6473	631	14	,	,	PUNCT
ejpam-6473	631	15	f	f	PROPN
ejpam-6473	631	16	=	=	SYM
ejpam-6473	631	17	2ω0d1	2ω0d1	NUM
ejpam-6473	631	18	+	+	SYM
ejpam-6473	631	19	2ω0f1	2ω0f1	PROPN
ejpam-6473	631	20	cosω0τ−f2	cosω0τ−f2	PROPN
ejpam-6473	631	21	sinω0τ	sinω0τ	PROPN
ejpam-6473	631	22	,	,	PUNCT
ejpam-6473	631	23	g	g	NOUN
ejpam-6473	631	24	=	=	PUNCT
ejpam-6473	631	25	−ω2	−ω2	NOUN
ejpam-6473	631	26	0f2	0f2	NOUN
ejpam-6473	631	27	cosω0τ−ω3	cosω0τ−ω3	NOUN
ejpam-6473	631	28	0f1	0f1	NUM
ejpam-6473	632	1	sinω0τ+ω0f3	sinω0τ+ω0f3	PROPN
ejpam-6473	632	2	sinω0τ	sinω0τ	PROPN
ejpam-6473	632	3	,	,	PUNCT
ejpam-6473	632	4	h	h	NOUN
ejpam-6473	632	5	=	=	PUNCT
ejpam-6473	632	6	−ω3	−ω3	PROPN
ejpam-6473	632	7	0f1	0f1	NUM
ejpam-6473	633	1	cosω0τ+ω0f3	cosω0τ+ω0f3	NOUN
ejpam-6473	633	2	cosω0τ+ω2	cosω0τ+ω2	NOUN
ejpam-6473	633	3	0f2	0f2	NUM
ejpam-6473	634	1	sinω0τ	sinω0τ	PROPN
ejpam-6473	634	2	.	.	PUNCT
ejpam-6473	635	1	hence	hence	ADV
ejpam-6473	635	2	,	,	PUNCT
ejpam-6473	635	3	hopf	hopf	ADJ
ejpam-6473	635	4	bifurcation	bifurcation	NOUN
ejpam-6473	635	5	exists	exist	VERB
ejpam-6473	635	6	at	at	ADP
ejpam-6473	635	7	τ	τ	PROPN
ejpam-6473	635	8	=	=	PROPN
ejpam-6473	635	9	τ0	τ0	NOUN
ejpam-6473	635	10	.	.	PUNCT
ejpam-6473	636	1	6	6	NUM
ejpam-6473	636	2	.	.	X
ejpam-6473	636	3	numerical	numerical	PROPN
ejpam-6473	636	4	simulation	simulation	PROPN
ejpam-6473	636	5	in	in	ADP
ejpam-6473	636	6	this	this	DET
ejpam-6473	636	7	part	part	NOUN
ejpam-6473	636	8	of	of	ADP
ejpam-6473	636	9	the	the	DET
ejpam-6473	636	10	paper	paper	NOUN
ejpam-6473	636	11	,	,	PUNCT
ejpam-6473	636	12	we	we	PRON
ejpam-6473	636	13	use	use	VERB
ejpam-6473	636	14	a	a	DET
ejpam-6473	636	15	numerical	numerical	ADJ
ejpam-6473	636	16	method	method	NOUN
ejpam-6473	636	17	to	to	PART
ejpam-6473	636	18	solve	solve	VERB
ejpam-6473	636	19	the	the	DET
ejpam-6473	636	20	optimal	optimal	ADJ
ejpam-6473	636	21	control	control	NOUN
ejpam-6473	636	22	and	and	CCONJ
ejpam-6473	636	23	delay	delay	NOUN
ejpam-6473	636	24	problem	problem	NOUN
ejpam-6473	636	25	.	.	PUNCT
ejpam-6473	637	1	for	for	ADP
ejpam-6473	637	2	numerical	numerical	PROPN
ejpam-6473	637	3	simulation	simulation	PROPN
ejpam-6473	637	4	fourth	fourth	ADJ
ejpam-6473	637	5	order	order	NOUN
ejpam-6473	637	6	runge	runge	VERB
ejpam-6473	637	7	kutta	kutta	NOUN
ejpam-6473	637	8	method	method	NOUN
ejpam-6473	637	9	is	be	AUX
ejpam-6473	637	10	employed	employ	VERB
ejpam-6473	637	11	.	.	PUNCT
ejpam-6473	638	1	all	all	DET
ejpam-6473	638	2	the	the	DET
ejpam-6473	638	3	numerical	numerical	ADJ
ejpam-6473	638	4	simulations	simulation	NOUN
ejpam-6473	638	5	are	be	AUX
ejpam-6473	638	6	done	do	VERB
ejpam-6473	638	7	in	in	ADP
ejpam-6473	638	8	matlab	matlab	PROPN
ejpam-6473	638	9	.	.	PUNCT
ejpam-6473	639	1	a	a	DET
ejpam-6473	639	2	fixed	fix	VERB
ejpam-6473	639	3	step	step	NOUN
ejpam-6473	639	4	size	size	NOUN
ejpam-6473	639	5	of	of	ADP
ejpam-6473	639	6	0.1	0.1	NUM
ejpam-6473	639	7	was	be	AUX
ejpam-6473	639	8	used	use	VERB
ejpam-6473	639	9	throughout	throughout	ADP
ejpam-6473	639	10	the	the	DET
ejpam-6473	639	11	simulations	simulation	NOUN
ejpam-6473	639	12	.	.	PUNCT
ejpam-6473	640	1	for	for	ADP
ejpam-6473	640	2	the	the	DET
ejpam-6473	640	3	delay	delay	NOUN
ejpam-6473	640	4	model	model	NOUN
ejpam-6473	640	5	,	,	PUNCT
ejpam-6473	640	6	a	a	DET
ejpam-6473	640	7	constant	constant	ADJ
ejpam-6473	640	8	delay	delay	NOUN
ejpam-6473	640	9	value	value	NOUN
ejpam-6473	640	10	of	of	ADP
ejpam-6473	640	11	10	10	NUM
ejpam-6473	640	12	days	day	NOUN
ejpam-6473	640	13	was	be	AUX
ejpam-6473	640	14	implemented	implement	VERB
ejpam-6473	640	15	using	use	VERB
ejpam-6473	640	16	discrete	discrete	ADJ
ejpam-6473	640	17	delay	delay	NOUN
ejpam-6473	640	18	approximation	approximation	NOUN
ejpam-6473	640	19	based	base	VERB
ejpam-6473	640	20	on	on	ADP
ejpam-6473	640	21	past	past	ADJ
ejpam-6473	640	22	state	state	NOUN
ejpam-6473	640	23	values	value	NOUN
ejpam-6473	640	24	.	.	PUNCT
ejpam-6473	641	1	the	the	DET
ejpam-6473	641	2	implementation	implementation	NOUN
ejpam-6473	641	3	covers	cover	VERB
ejpam-6473	641	4	three	three	NUM
ejpam-6473	641	5	scenarios	scenario	NOUN
ejpam-6473	641	6	:	:	PUNCT
ejpam-6473	641	7	the	the	DET
ejpam-6473	641	8	basic	basic	ADJ
ejpam-6473	641	9	model	model	NOUN
ejpam-6473	641	10	,	,	PUNCT
ejpam-6473	641	11	a	a	DET
ejpam-6473	641	12	model	model	NOUN
ejpam-6473	641	13	with	with	ADP
ejpam-6473	641	14	delay	delay	NOUN
ejpam-6473	641	15	in	in	ADP
ejpam-6473	641	16	the	the	DET
ejpam-6473	641	17	light	light	NOUN
ejpam-6473	641	18	s.	s.	PROPN
ejpam-6473	641	19	bano	bano	PROPN
ejpam-6473	642	1	et	et	PROPN
ejpam-6473	642	2	al	al	PROPN
ejpam-6473	642	3	.	.	PUNCT
ejpam-6473	642	4	/	/	SYM
ejpam-6473	642	5	eur	eur	PROPN
ejpam-6473	642	6	.	.	PUNCT
ejpam-6473	643	1	j.	j.	PROPN
ejpam-6473	643	2	pure	pure	PROPN
ejpam-6473	643	3	appl	appl	PROPN
ejpam-6473	643	4	.	.	PROPN
ejpam-6473	643	5	math	math	PROPN
ejpam-6473	643	6	,	,	PUNCT
ejpam-6473	643	7	18	18	NUM
ejpam-6473	643	8	(	(	PUNCT
ejpam-6473	643	9	4	4	NUM
ejpam-6473	643	10	)	)	PUNCT
ejpam-6473	643	11	(	(	PUNCT
ejpam-6473	643	12	2025	2025	NUM
ejpam-6473	643	13	)	)	PUNCT
ejpam-6473	643	14	,	,	PUNCT
ejpam-6473	643	15	6473	6473	NUM
ejpam-6473	643	16	30	30	NUM
ejpam-6473	643	17	of	of	ADP
ejpam-6473	643	18	38	38	NUM
ejpam-6473	643	19	smoker	smoker	ADJ
ejpam-6473	643	20	class	class	NOUN
ejpam-6473	643	21	,	,	PUNCT
ejpam-6473	643	22	and	and	CCONJ
ejpam-6473	643	23	a	a	DET
ejpam-6473	643	24	model	model	NOUN
ejpam-6473	643	25	with	with	ADP
ejpam-6473	643	26	control	control	NOUN
ejpam-6473	643	27	interventions	intervention	NOUN
ejpam-6473	643	28	applied	apply	VERB
ejpam-6473	643	29	to	to	ADP
ejpam-6473	643	30	potential	potential	ADJ
ejpam-6473	643	31	,	,	PUNCT
ejpam-6473	643	32	light	light	ADJ
ejpam-6473	643	33	,	,	PUNCT
ejpam-6473	643	34	and	and	CCONJ
ejpam-6473	643	35	regular	regular	ADJ
ejpam-6473	643	36	smokers	smoker	NOUN
ejpam-6473	643	37	.	.	PUNCT
ejpam-6473	644	1	the	the	DET
ejpam-6473	644	2	parameter	parameter	NOUN
ejpam-6473	644	3	values	value	NOUN
ejpam-6473	644	4	that	that	PRON
ejpam-6473	644	5	are	be	AUX
ejpam-6473	644	6	used	use	VERB
ejpam-6473	644	7	in	in	ADP
ejpam-6473	644	8	the	the	DET
ejpam-6473	644	9	simulation	simulation	NOUN
ejpam-6473	644	10	are	be	AUX
ejpam-6473	644	11	presented	present	VERB
ejpam-6473	644	12	in	in	ADP
ejpam-6473	644	13	the	the	DET
ejpam-6473	644	14	table	table	NOUN
ejpam-6473	644	15	4	4	NUM
ejpam-6473	644	16	.	.	PUNCT
ejpam-6473	645	1	the	the	DET
ejpam-6473	645	2	baseline	baseline	PROPN
ejpam-6473	645	3	parameters	parameter	NOUN
ejpam-6473	645	4	(	(	PUNCT
ejpam-6473	645	5	β	β	X
ejpam-6473	645	6	,	,	PUNCT
ejpam-6473	645	7	ζ	ζ	PROPN
ejpam-6473	645	8	,	,	PUNCT
ejpam-6473	645	9	δ	δ	PROPN
ejpam-6473	645	10	,	,	PUNCT
ejpam-6473	645	11	µ	µ	NOUN
ejpam-6473	645	12	,	,	PUNCT
ejpam-6473	645	13	ν	ν	PROPN
ejpam-6473	645	14	,	,	PUNCT
ejpam-6473	645	15	b	b	NOUN
ejpam-6473	645	16	)	)	PUNCT
ejpam-6473	645	17	are	be	AUX
ejpam-6473	645	18	kept	keep	VERB
ejpam-6473	645	19	constant	constant	ADJ
ejpam-6473	645	20	across	across	ADP
ejpam-6473	645	21	all	all	DET
ejpam-6473	645	22	three	three	NUM
ejpam-6473	645	23	scenarios	scenario	NOUN
ejpam-6473	645	24	.	.	PUNCT
ejpam-6473	646	1	the	the	DET
ejpam-6473	646	2	only	only	ADJ
ejpam-6473	646	3	difference	difference	NOUN
ejpam-6473	646	4	in	in	ADP
ejpam-6473	646	5	the	the	DET
ejpam-6473	646	6	controlled	control	VERB
ejpam-6473	646	7	model	model	NOUN
ejpam-6473	646	8	is	be	AUX
ejpam-6473	646	9	the	the	DET
ejpam-6473	646	10	inclusion	inclusion	NOUN
ejpam-6473	646	11	of	of	ADP
ejpam-6473	646	12	three	three	NUM
ejpam-6473	646	13	intervention	intervention	NOUN
ejpam-6473	646	14	controls	control	NOUN
ejpam-6473	646	15	,	,	PUNCT
ejpam-6473	646	16	which	which	PRON
ejpam-6473	646	17	influence	influence	VERB
ejpam-6473	646	18	the	the	DET
ejpam-6473	646	19	system	system	NOUN
ejpam-6473	646	20	dynamics	dynamic	NOUN
ejpam-6473	646	21	.	.	PUNCT
ejpam-6473	647	1	therefore	therefore	ADV
ejpam-6473	647	2	,	,	PUNCT
ejpam-6473	647	3	the	the	DET
ejpam-6473	647	4	change	change	NOUN
ejpam-6473	647	5	in	in	ADP
ejpam-6473	647	6	behavior	behavior	NOUN
ejpam-6473	647	7	between	between	ADP
ejpam-6473	647	8	models	model	NOUN
ejpam-6473	647	9	arises	arise	VERB
ejpam-6473	647	10	from	from	ADP
ejpam-6473	647	11	the	the	DET
ejpam-6473	647	12	control	control	NOUN
ejpam-6473	647	13	functions	function	NOUN
ejpam-6473	647	14	,	,	PUNCT
ejpam-6473	647	15	not	not	PART
ejpam-6473	647	16	from	from	ADP
ejpam-6473	647	17	changes	change	NOUN
ejpam-6473	647	18	in	in	ADP
ejpam-6473	647	19	the	the	DET
ejpam-6473	647	20	original	original	ADJ
ejpam-6473	647	21	parameter	parameter	NOUN
ejpam-6473	647	22	values	value	NOUN
ejpam-6473	647	23	.	.	PUNCT
ejpam-6473	648	1	parameter	parameter	NOUN
ejpam-6473	648	2	values	value	NOUN
ejpam-6473	648	3	source	source	NOUN
ejpam-6473	648	4	λ	λ	PROPN
ejpam-6473	648	5	8	8	NUM
ejpam-6473	648	6	assumed	assume	VERB
ejpam-6473	648	7	β	β	PROPN
ejpam-6473	648	8	0.0038	0.0038	NUM
ejpam-6473	649	1	[	[	X
ejpam-6473	649	2	28	28	NUM
ejpam-6473	649	3	]	]	X
ejpam-6473	649	4	ζ	ζ	NOUN
ejpam-6473	649	5	0.021	0.021	NUM
ejpam-6473	649	6	[	[	X
ejpam-6473	649	7	29	29	NUM
ejpam-6473	649	8	]	]	PUNCT
ejpam-6473	649	9	δ	δ	PROPN
ejpam-6473	649	10	0.017	0.017	NUM
ejpam-6473	649	11	assumed	assume	VERB
ejpam-6473	649	12	b	b	PROPN
ejpam-6473	649	13	0.0019	0.0019	NUM
ejpam-6473	649	14	[	[	X
ejpam-6473	649	15	29	29	NUM
ejpam-6473	649	16	]	]	SYM
ejpam-6473	649	17	µ	µ	X
ejpam-6473	649	18	0.011	0.011	NUM
ejpam-6473	649	19	[	[	X
ejpam-6473	649	20	29	29	NUM
ejpam-6473	649	21	]	]	PUNCT
ejpam-6473	649	22	ν	ν	X
ejpam-6473	649	23	0.0009	0.0009	NUM
ejpam-6473	649	24	[	[	PUNCT
ejpam-6473	649	25	13	13	NUM
ejpam-6473	649	26	]	]	PUNCT
ejpam-6473	649	27	u1	u1	NOUN
ejpam-6473	649	28	0.01	0.01	NUM
ejpam-6473	649	29	[	[	X
ejpam-6473	649	30	29	29	NUM
ejpam-6473	649	31	]	]	X
ejpam-6473	649	32	u2	u2	NOUN
ejpam-6473	649	33	0.01	0.01	NUM
ejpam-6473	649	34	[	[	X
ejpam-6473	649	35	29	29	NUM
ejpam-6473	649	36	]	]	X
ejpam-6473	649	37	u3	u3	NOUN
ejpam-6473	649	38	0.05	0.05	NUM
ejpam-6473	649	39	[	[	X
ejpam-6473	649	40	29	29	NUM
ejpam-6473	649	41	]	]	PUNCT
ejpam-6473	649	42	a0	a0	PROPN
ejpam-6473	649	43	0.0051	0.0051	NUM
ejpam-6473	649	44	[	[	X
ejpam-6473	649	45	29	29	NUM
ejpam-6473	649	46	]	]	PUNCT
ejpam-6473	649	47	π1	π1	NOUN
ejpam-6473	649	48	0.085	0.085	NUM
ejpam-6473	649	49	[	[	X
ejpam-6473	649	50	29	29	NUM
ejpam-6473	649	51	]	]	X
ejpam-6473	649	52	π2	π2	NOUN
ejpam-6473	649	53	0.095	0.095	NUM
ejpam-6473	649	54	[	[	X
ejpam-6473	649	55	29	29	NUM
ejpam-6473	649	56	]	]	SYM
ejpam-6473	649	57	table	table	NOUN
ejpam-6473	649	58	3	3	NUM
ejpam-6473	649	59	:	:	PUNCT
ejpam-6473	649	60	parameter	parameter	NOUN
ejpam-6473	649	61	values	value	NOUN
ejpam-6473	649	62	for	for	ADP
ejpam-6473	649	63	proposed	propose	VERB
ejpam-6473	649	64	model	model	PROPN
ejpam-6473	649	65	s.	s.	PROPN
ejpam-6473	649	66	bano	bano	PROPN
ejpam-6473	649	67	et	et	PROPN
ejpam-6473	649	68	al	al	PROPN
ejpam-6473	649	69	.	.	PUNCT
ejpam-6473	649	70	/	/	SYM
ejpam-6473	649	71	eur	eur	PROPN
ejpam-6473	649	72	.	.	PUNCT
ejpam-6473	650	1	j.	j.	PROPN
ejpam-6473	650	2	pure	pure	PROPN
ejpam-6473	650	3	appl	appl	PROPN
ejpam-6473	650	4	.	.	PROPN
ejpam-6473	650	5	math	math	PROPN
ejpam-6473	650	6	,	,	PUNCT
ejpam-6473	650	7	18	18	NUM
ejpam-6473	650	8	(	(	PUNCT
ejpam-6473	650	9	4	4	NUM
ejpam-6473	650	10	)	)	PUNCT
ejpam-6473	650	11	(	(	PUNCT
ejpam-6473	650	12	2025	2025	NUM
ejpam-6473	650	13	)	)	PUNCT
ejpam-6473	650	14	,	,	PUNCT
ejpam-6473	650	15	6473	6473	NUM
ejpam-6473	650	16	31	31	NUM
ejpam-6473	650	17	of	of	ADP
ejpam-6473	650	18	38	38	NUM
ejpam-6473	650	19	the	the	DET
ejpam-6473	650	20	evolution	evolution	NOUN
ejpam-6473	650	21	of	of	ADP
ejpam-6473	650	22	each	each	DET
ejpam-6473	650	23	population	population	NOUN
ejpam-6473	650	24	class	class	NOUN
ejpam-6473	650	25	over	over	ADP
ejpam-6473	650	26	the	the	DET
ejpam-6473	650	27	300	300	NUM
ejpam-6473	650	28	-	-	PUNCT
ejpam-6473	650	29	day	day	NOUN
ejpam-6473	650	30	simulation	simulation	NOUN
ejpam-6473	650	31	period	period	NOUN
ejpam-6473	650	32	is	be	AUX
ejpam-6473	650	33	shown	show	VERB
ejpam-6473	650	34	in	in	ADP
ejpam-6473	650	35	fig	fig	NOUN
ejpam-6473	650	36	.	.	PUNCT
ejpam-6473	651	1	(	(	PUNCT
ejpam-6473	651	2	4	4	NUM
ejpam-6473	651	3	)	)	PUNCT
ejpam-6473	651	4	.	.	PUNCT
ejpam-6473	652	1	fig	fig	NOUN
ejpam-6473	652	2	.	.	PUNCT
ejpam-6473	653	1	4(a	4(a	NUM
ejpam-6473	653	2	)	)	PUNCT
ejpam-6473	654	1	demonstrates	demonstrate	VERB
ejpam-6473	654	2	the	the	DET
ejpam-6473	654	3	natural	natural	ADJ
ejpam-6473	654	4	progression	progression	NOUN
ejpam-6473	654	5	of	of	ADP
ejpam-6473	654	6	each	each	DET
ejpam-6473	654	7	class	class	NOUN
ejpam-6473	654	8	without	without	ADP
ejpam-6473	654	9	the	the	DET
ejpam-6473	654	10	effect	effect	NOUN
ejpam-6473	654	11	of	of	ADP
ejpam-6473	654	12	external	external	ADJ
ejpam-6473	654	13	intervention	intervention	NOUN
ejpam-6473	654	14	like	like	ADP
ejpam-6473	654	15	delay	delay	NOUN
ejpam-6473	654	16	and	and	CCONJ
ejpam-6473	654	17	control	control	NOUN
ejpam-6473	654	18	.	.	PUNCT
ejpam-6473	655	1	the	the	DET
ejpam-6473	655	2	light	light	ADJ
ejpam-6473	655	3	smokers	smoker	NOUN
ejpam-6473	655	4	population	population	NOUN
ejpam-6473	655	5	increases	increase	VERB
ejpam-6473	655	6	rapidly	rapidly	ADV
ejpam-6473	655	7	as	as	SCONJ
ejpam-6473	655	8	compared	compare	VERB
ejpam-6473	655	9	to	to	ADP
ejpam-6473	655	10	other	other	ADJ
ejpam-6473	655	11	classes	class	NOUN
ejpam-6473	655	12	due	due	ADJ
ejpam-6473	655	13	to	to	ADP
ejpam-6473	655	14	the	the	DET
ejpam-6473	655	15	fast	fast	ADJ
ejpam-6473	655	16	transition	transition	NOUN
ejpam-6473	655	17	into	into	ADP
ejpam-6473	655	18	light	light	ADJ
ejpam-6473	655	19	smokers	smoker	NOUN
ejpam-6473	655	20	,	,	PUNCT
ejpam-6473	655	21	while	while	SCONJ
ejpam-6473	655	22	regular	regular	ADJ
ejpam-6473	655	23	and	and	CCONJ
ejpam-6473	655	24	quit	quit	VERB
ejpam-6473	655	25	smokers	smoker	NOUN
ejpam-6473	655	26	gradually	gradually	ADV
ejpam-6473	655	27	rises	rise	VERB
ejpam-6473	655	28	before	before	ADP
ejpam-6473	655	29	stabilizing	stabilize	VERB
ejpam-6473	655	30	.	.	PUNCT
ejpam-6473	656	1	figure	figure	NOUN
ejpam-6473	656	2	4(b	4(b	NUM
ejpam-6473	656	3	)	)	PUNCT
ejpam-6473	656	4	introduces	introduce	VERB
ejpam-6473	656	5	the	the	DET
ejpam-6473	656	6	three	three	NUM
ejpam-6473	656	7	controls	control	NOUN
ejpam-6473	656	8	in	in	ADP
ejpam-6473	656	9	the	the	DET
ejpam-6473	656	10	simulation	simulation	NOUN
ejpam-6473	656	11	,	,	PUNCT
ejpam-6473	656	12	namely	namely	ADV
ejpam-6473	656	13	education	education	NOUN
ejpam-6473	656	14	campaign	campaign	NOUN
ejpam-6473	656	15	,	,	PUNCT
ejpam-6473	656	16	the	the	DET
ejpam-6473	656	17	anti	anti	ADJ
ejpam-6473	656	18	-	-	ADJ
ejpam-6473	656	19	smoking	smoking	ADJ
ejpam-6473	656	20	gum	gum	NOUN
ejpam-6473	656	21	,	,	PUNCT
ejpam-6473	656	22	and	and	CCONJ
ejpam-6473	656	23	the	the	DET
ejpam-6473	656	24	medicine	medicine	NOUN
ejpam-6473	656	25	whose	whose	DET
ejpam-6473	656	26	values	value	NOUN
ejpam-6473	656	27	are	be	AUX
ejpam-6473	656	28	given	give	VERB
ejpam-6473	656	29	in	in	ADP
ejpam-6473	656	30	the	the	DET
ejpam-6473	656	31	above	above	ADJ
ejpam-6473	656	32	table	table	NOUN
ejpam-6473	656	33	.	.	PUNCT
ejpam-6473	657	1	the	the	DET
ejpam-6473	657	2	control	control	NOUN
ejpam-6473	657	3	measures	measure	NOUN
ejpam-6473	657	4	decreasing	decrease	VERB
ejpam-6473	657	5	the	the	DET
ejpam-6473	657	6	spread	spread	NOUN
ejpam-6473	657	7	of	of	ADP
ejpam-6473	657	8	smoking	smoking	NOUN
ejpam-6473	657	9	,	,	PUNCT
ejpam-6473	657	10	lowering	lower	VERB
ejpam-6473	657	11	the	the	DET
ejpam-6473	657	12	potential	potential	ADJ
ejpam-6473	657	13	,	,	PUNCT
ejpam-6473	657	14	light	light	ADJ
ejpam-6473	657	15	and	and	CCONJ
ejpam-6473	657	16	regular	regular	ADJ
ejpam-6473	657	17	smokers	smoker	NOUN
ejpam-6473	657	18	population	population	NOUN
ejpam-6473	657	19	and	and	CCONJ
ejpam-6473	657	20	increasing	increase	VERB
ejpam-6473	657	21	the	the	DET
ejpam-6473	657	22	quit	quit	ADJ
ejpam-6473	657	23	smokers	smoker	NOUN
ejpam-6473	657	24	population	population	NOUN
ejpam-6473	657	25	,	,	PUNCT
ejpam-6473	657	26	which	which	PRON
ejpam-6473	657	27	suggest	suggest	VERB
ejpam-6473	657	28	that	that	SCONJ
ejpam-6473	657	29	more	more	ADJ
ejpam-6473	657	30	people	people	NOUN
ejpam-6473	657	31	stop	stop	VERB
ejpam-6473	657	32	smoking	smoke	VERB
ejpam-6473	657	33	.	.	PUNCT
ejpam-6473	658	1	figure	figure	NOUN
ejpam-6473	658	2	4(c	4(c	NUM
ejpam-6473	658	3	)	)	PUNCT
ejpam-6473	658	4	shows	show	VERB
ejpam-6473	658	5	the	the	DET
ejpam-6473	658	6	impact	impact	NOUN
ejpam-6473	658	7	of	of	ADP
ejpam-6473	658	8	the	the	DET
ejpam-6473	658	9	delay	delay	NOUN
ejpam-6473	658	10	(	(	PUNCT
ejpam-6473	658	11	τ	τ	X
ejpam-6473	658	12	=	=	NOUN
ejpam-6473	658	13	10	10	NUM
ejpam-6473	658	14	)	)	PUNCT
ejpam-6473	658	15	in	in	ADP
ejpam-6473	658	16	the	the	DET
ejpam-6473	658	17	simulation	simulation	NOUN
ejpam-6473	658	18	.	.	PUNCT
ejpam-6473	659	1	delay	delay	PROPN
ejpam-6473	659	2	affects	affect	VERB
ejpam-6473	659	3	the	the	DET
ejpam-6473	659	4	magnitude	magnitude	NOUN
ejpam-6473	659	5	and	and	CCONJ
ejpam-6473	659	6	timing	timing	NOUN
ejpam-6473	659	7	of	of	ADP
ejpam-6473	659	8	the	the	DET
ejpam-6473	659	9	transition	transition	NOUN
ejpam-6473	659	10	between	between	ADP
ejpam-6473	659	11	classes	class	NOUN
ejpam-6473	659	12	,	,	PUNCT
ejpam-6473	659	13	such	such	ADJ
ejpam-6473	659	14	as	as	ADP
ejpam-6473	659	15	delay	delay	NOUN
ejpam-6473	659	16	increases	increase	VERB
ejpam-6473	659	17	light	light	ADJ
ejpam-6473	659	18	and	and	CCONJ
ejpam-6473	659	19	potential	potential	ADJ
ejpam-6473	659	20	smokers	smoker	NOUN
ejpam-6473	659	21	population	population	NOUN
ejpam-6473	659	22	as	as	SCONJ
ejpam-6473	659	23	compared	compare	VERB
ejpam-6473	659	24	to	to	ADP
ejpam-6473	659	25	the	the	DET
ejpam-6473	659	26	case	case	NOUN
ejpam-6473	659	27	of	of	ADP
ejpam-6473	659	28	without	without	ADP
ejpam-6473	659	29	delay	delay	NOUN
ejpam-6473	659	30	.	.	PUNCT
ejpam-6473	660	1	the	the	DET
ejpam-6473	660	2	rapid	rapid	ADJ
ejpam-6473	660	3	increase	increase	NOUN
ejpam-6473	660	4	in	in	ADP
ejpam-6473	660	5	light	light	ADJ
ejpam-6473	660	6	smokers	smoker	NOUN
ejpam-6473	660	7	suggests	suggest	VERB
ejpam-6473	660	8	that	that	SCONJ
ejpam-6473	660	9	delays	delay	NOUN
ejpam-6473	660	10	prolong	prolong	VERB
ejpam-6473	660	11	the	the	DET
ejpam-6473	660	12	time	time	NOUN
ejpam-6473	660	13	smokers	smoker	NOUN
ejpam-6473	660	14	spend	spend	VERB
ejpam-6473	660	15	as	as	ADP
ejpam-6473	660	16	light	light	ADJ
ejpam-6473	660	17	smokers	smoker	NOUN
ejpam-6473	660	18	and	and	CCONJ
ejpam-6473	660	19	postpone	postpone	VERB
ejpam-6473	660	20	the	the	DET
ejpam-6473	660	21	transition	transition	NOUN
ejpam-6473	660	22	to	to	ADP
ejpam-6473	660	23	regular	regular	ADJ
ejpam-6473	660	24	and	and	CCONJ
ejpam-6473	660	25	quit	quit	VERB
ejpam-6473	660	26	smokers	smoker	NOUN
ejpam-6473	660	27	.	.	PUNCT
ejpam-6473	661	1	control	control	NOUN
ejpam-6473	661	2	measures	measure	NOUN
ejpam-6473	661	3	are	be	AUX
ejpam-6473	661	4	very	very	ADV
ejpam-6473	661	5	effective	effective	ADJ
ejpam-6473	661	6	in	in	ADP
ejpam-6473	661	7	stabilizing	stabilize	VERB
ejpam-6473	661	8	the	the	DET
ejpam-6473	661	9	system	system	NOUN
ejpam-6473	661	10	and	and	CCONJ
ejpam-6473	661	11	decreasing	decrease	VERB
ejpam-6473	661	12	the	the	DET
ejpam-6473	661	13	light	light	ADJ
ejpam-6473	661	14	,	,	PUNCT
ejpam-6473	661	15	regular	regular	ADJ
ejpam-6473	661	16	smokers	smoker	NOUN
ejpam-6473	661	17	and	and	CCONJ
ejpam-6473	661	18	increasing	increase	VERB
ejpam-6473	661	19	quit	quit	ADJ
ejpam-6473	661	20	smokers	smoker	NOUN
ejpam-6473	661	21	population	population	NOUN
ejpam-6473	661	22	compared	compare	VERB
ejpam-6473	661	23	to	to	ADP
ejpam-6473	661	24	with	with	ADP
ejpam-6473	661	25	and	and	CCONJ
ejpam-6473	661	26	without	without	ADP
ejpam-6473	661	27	delay	delay	NOUN
ejpam-6473	661	28	cases	case	NOUN
ejpam-6473	661	29	.	.	PUNCT
ejpam-6473	662	1	s.	s.	PROPN
ejpam-6473	662	2	bano	bano	PROPN
ejpam-6473	662	3	et	et	PROPN
ejpam-6473	662	4	al	al	PROPN
ejpam-6473	662	5	.	.	PUNCT
ejpam-6473	662	6	/	/	SYM
ejpam-6473	662	7	eur	eur	PROPN
ejpam-6473	662	8	.	.	PUNCT
ejpam-6473	663	1	j.	j.	PROPN
ejpam-6473	663	2	pure	pure	PROPN
ejpam-6473	663	3	appl	appl	PROPN
ejpam-6473	663	4	.	.	PROPN
ejpam-6473	663	5	math	math	PROPN
ejpam-6473	663	6	,	,	PUNCT
ejpam-6473	663	7	18	18	NUM
ejpam-6473	663	8	(	(	PUNCT
ejpam-6473	663	9	4	4	NUM
ejpam-6473	663	10	)	)	PUNCT
ejpam-6473	663	11	(	(	PUNCT
ejpam-6473	663	12	2025	2025	NUM
ejpam-6473	663	13	)	)	PUNCT
ejpam-6473	663	14	,	,	PUNCT
ejpam-6473	663	15	6473	6473	NUM
ejpam-6473	663	16	32	32	NUM
ejpam-6473	663	17	of	of	ADP
ejpam-6473	663	18	38	38	NUM
ejpam-6473	663	19	(	(	PUNCT
ejpam-6473	663	20	a	a	NOUN
ejpam-6473	663	21	)	)	PUNCT
ejpam-6473	663	22	plsq	plsq	NOUN
ejpam-6473	663	23	model	model	NOUN
ejpam-6473	663	24	without	without	ADP
ejpam-6473	663	25	control	control	NOUN
ejpam-6473	663	26	and	and	CCONJ
ejpam-6473	663	27	delay	delay	NOUN
ejpam-6473	663	28	(	(	PUNCT
ejpam-6473	663	29	b	b	NOUN
ejpam-6473	663	30	)	)	PUNCT
ejpam-6473	663	31	control	control	NOUN
ejpam-6473	663	32	plsq	plsq	NOUN
ejpam-6473	663	33	model	model	PROPN
ejpam-6473	663	34	(	(	PUNCT
ejpam-6473	663	35	c	c	NOUN
ejpam-6473	663	36	)	)	PUNCT
ejpam-6473	663	37	delay	delay	NOUN
ejpam-6473	663	38	plsq	plsq	PROPN
ejpam-6473	663	39	model	model	PROPN
ejpam-6473	663	40	figure	figure	NOUN
ejpam-6473	663	41	4	4	NUM
ejpam-6473	663	42	:	:	PUNCT
ejpam-6473	663	43	(	(	PUNCT
ejpam-6473	663	44	a	a	X
ejpam-6473	663	45	)	)	PUNCT
ejpam-6473	663	46	plot	plot	NOUN
ejpam-6473	663	47	of	of	ADP
ejpam-6473	663	48	proposed	propose	VERB
ejpam-6473	663	49	model	model	NOUN
ejpam-6473	663	50	without	without	ADP
ejpam-6473	663	51	control	control	NOUN
ejpam-6473	663	52	and	and	CCONJ
ejpam-6473	663	53	delay	delay	NOUN
ejpam-6473	663	54	.	.	PUNCT
ejpam-6473	664	1	(	(	PUNCT
ejpam-6473	664	2	b	b	X
ejpam-6473	664	3	)	)	PUNCT
ejpam-6473	664	4	plot	plot	NOUN
ejpam-6473	664	5	of	of	ADP
ejpam-6473	664	6	proposed	propose	VERB
ejpam-6473	664	7	model	model	NOUN
ejpam-6473	664	8	with	with	ADP
ejpam-6473	664	9	control	control	NOUN
ejpam-6473	664	10	and	and	CCONJ
ejpam-6473	664	11	without	without	ADP
ejpam-6473	664	12	delay	delay	NOUN
ejpam-6473	664	13	.	.	PUNCT
ejpam-6473	665	1	(	(	PUNCT
ejpam-6473	665	2	c	c	X
ejpam-6473	665	3	)	)	PUNCT
ejpam-6473	665	4	plot	plot	NOUN
ejpam-6473	665	5	of	of	ADP
ejpam-6473	665	6	the	the	DET
ejpam-6473	665	7	proposed	propose	VERB
ejpam-6473	665	8	model	model	NOUN
ejpam-6473	665	9	without	without	ADP
ejpam-6473	665	10	control	control	NOUN
ejpam-6473	665	11	and	and	CCONJ
ejpam-6473	665	12	with	with	ADP
ejpam-6473	665	13	delay	delay	NOUN
ejpam-6473	665	14	.	.	PUNCT
ejpam-6473	666	1	s.	s.	PROPN
ejpam-6473	666	2	bano	bano	PROPN
ejpam-6473	666	3	et	et	PROPN
ejpam-6473	666	4	al	al	PROPN
ejpam-6473	666	5	.	.	PUNCT
ejpam-6473	666	6	/	/	SYM
ejpam-6473	666	7	eur	eur	PROPN
ejpam-6473	666	8	.	.	PUNCT
ejpam-6473	667	1	j.	j.	PROPN
ejpam-6473	667	2	pure	pure	PROPN
ejpam-6473	667	3	appl	appl	PROPN
ejpam-6473	667	4	.	.	PROPN
ejpam-6473	667	5	math	math	PROPN
ejpam-6473	667	6	,	,	PUNCT
ejpam-6473	667	7	18	18	NUM
ejpam-6473	667	8	(	(	PUNCT
ejpam-6473	667	9	4	4	NUM
ejpam-6473	667	10	)	)	PUNCT
ejpam-6473	667	11	(	(	PUNCT
ejpam-6473	667	12	2025	2025	NUM
ejpam-6473	667	13	)	)	PUNCT
ejpam-6473	667	14	,	,	PUNCT
ejpam-6473	667	15	6473	6473	NUM
ejpam-6473	667	16	33	33	NUM
ejpam-6473	667	17	of	of	ADP
ejpam-6473	667	18	38	38	NUM
ejpam-6473	667	19	fig	fig	NOUN
ejpam-6473	667	20	.	.	PUNCT
ejpam-6473	668	1	5	5	NUM
ejpam-6473	668	2	shows	show	VERB
ejpam-6473	668	3	the	the	DET
ejpam-6473	668	4	effect	effect	NOUN
ejpam-6473	668	5	of	of	ADP
ejpam-6473	668	6	control	control	NOUN
ejpam-6473	668	7	and	and	CCONJ
ejpam-6473	668	8	delay	delay	VERB
ejpam-6473	668	9	on	on	ADP
ejpam-6473	668	10	each	each	DET
ejpam-6473	668	11	population	population	NOUN
ejpam-6473	668	12	separately	separately	ADV
ejpam-6473	668	13	.	.	PUNCT
ejpam-6473	669	1	in	in	ADP
ejpam-6473	669	2	the	the	DET
ejpam-6473	669	3	potential	potential	ADJ
ejpam-6473	669	4	smokers	smoker	NOUN
ejpam-6473	669	5	graph	graph	NOUN
ejpam-6473	669	6	,	,	PUNCT
ejpam-6473	669	7	without	without	ADP
ejpam-6473	669	8	delay	delay	NOUN
ejpam-6473	669	9	and	and	CCONJ
ejpam-6473	669	10	control	control	NOUN
ejpam-6473	669	11	curves	curve	NOUN
ejpam-6473	669	12	show	show	VERB
ejpam-6473	669	13	the	the	DET
ejpam-6473	669	14	slow	slow	ADJ
ejpam-6473	669	15	transition	transition	NOUN
ejpam-6473	669	16	of	of	ADP
ejpam-6473	669	17	potential	potential	ADJ
ejpam-6473	669	18	smokers	smoker	NOUN
ejpam-6473	669	19	to	to	ADP
ejpam-6473	669	20	other	other	ADJ
ejpam-6473	669	21	classes	class	NOUN
ejpam-6473	669	22	,	,	PUNCT
ejpam-6473	669	23	while	while	SCONJ
ejpam-6473	669	24	the	the	DET
ejpam-6473	669	25	delay	delay	NOUN
ejpam-6473	669	26	curve	curve	NOUN
ejpam-6473	669	27	shows	show	VERB
ejpam-6473	669	28	that	that	SCONJ
ejpam-6473	669	29	the	the	DET
ejpam-6473	669	30	transition	transition	NOUN
ejpam-6473	669	31	from	from	ADP
ejpam-6473	669	32	potential	potential	NOUN
ejpam-6473	669	33	to	to	ADP
ejpam-6473	669	34	other	other	ADJ
ejpam-6473	669	35	classes	class	NOUN
ejpam-6473	669	36	stabilizes	stabilize	VERB
ejpam-6473	669	37	faster	fast	ADV
ejpam-6473	669	38	than	than	ADP
ejpam-6473	669	39	the	the	DET
ejpam-6473	669	40	simple	simple	ADJ
ejpam-6473	669	41	curve	curve	NOUN
ejpam-6473	669	42	,	,	PUNCT
ejpam-6473	669	43	but	but	CCONJ
ejpam-6473	669	44	with	with	ADP
ejpam-6473	669	45	the	the	DET
ejpam-6473	669	46	introduction	introduction	NOUN
ejpam-6473	669	47	of	of	ADP
ejpam-6473	669	48	controls	control	NOUN
ejpam-6473	669	49	,	,	PUNCT
ejpam-6473	669	50	rapidly	rapidly	ADV
ejpam-6473	669	51	potential	potential	ADJ
ejpam-6473	669	52	smokers	smoker	NOUN
ejpam-6473	669	53	move	move	VERB
ejpam-6473	669	54	to	to	ADP
ejpam-6473	669	55	the	the	DET
ejpam-6473	669	56	other	other	ADJ
ejpam-6473	669	57	classes	class	NOUN
ejpam-6473	669	58	and	and	CCONJ
ejpam-6473	669	59	reach	reach	VERB
ejpam-6473	669	60	the	the	DET
ejpam-6473	669	61	stability	stability	NOUN
ejpam-6473	669	62	more	more	ADV
ejpam-6473	669	63	quickly	quickly	ADV
ejpam-6473	669	64	than	than	ADP
ejpam-6473	669	65	the	the	DET
ejpam-6473	669	66	delay	delay	NOUN
ejpam-6473	669	67	and	and	CCONJ
ejpam-6473	669	68	simple	simple	ADJ
ejpam-6473	669	69	curve	curve	NOUN
ejpam-6473	669	70	.	.	PUNCT
ejpam-6473	670	1	in	in	ADP
ejpam-6473	670	2	the	the	DET
ejpam-6473	670	3	case	case	NOUN
ejpam-6473	670	4	of	of	ADP
ejpam-6473	670	5	the	the	DET
ejpam-6473	670	6	light	light	ADJ
ejpam-6473	670	7	smokers	smoker	NOUN
ejpam-6473	670	8	,	,	PUNCT
ejpam-6473	670	9	with	with	ADP
ejpam-6473	670	10	delay	delay	NOUN
ejpam-6473	670	11	,	,	PUNCT
ejpam-6473	670	12	the	the	DET
ejpam-6473	670	13	population	population	NOUN
ejpam-6473	670	14	increases	increase	VERB
ejpam-6473	670	15	rapidly	rapidly	ADV
ejpam-6473	670	16	and	and	CCONJ
ejpam-6473	670	17	then	then	ADV
ejpam-6473	670	18	declines	decline	VERB
ejpam-6473	670	19	as	as	SCONJ
ejpam-6473	670	20	it	it	PRON
ejpam-6473	670	21	moves	move	VERB
ejpam-6473	670	22	to	to	ADP
ejpam-6473	670	23	another	another	DET
ejpam-6473	670	24	class	class	NOUN
ejpam-6473	670	25	and	and	CCONJ
ejpam-6473	670	26	stabilizes	stabilize	VERB
ejpam-6473	670	27	at	at	ADP
ejpam-6473	670	28	the	the	DET
ejpam-6473	670	29	same	same	ADJ
ejpam-6473	670	30	level	level	NOUN
ejpam-6473	670	31	as	as	ADP
ejpam-6473	670	32	the	the	DET
ejpam-6473	670	33	simple	simple	ADJ
ejpam-6473	670	34	curve	curve	NOUN
ejpam-6473	670	35	.	.	PUNCT
ejpam-6473	671	1	this	this	PRON
ejpam-6473	671	2	shows	show	VERB
ejpam-6473	671	3	that	that	DET
ejpam-6473	671	4	delay	delay	NOUN
ejpam-6473	671	5	causes	cause	VERB
ejpam-6473	671	6	a	a	DET
ejpam-6473	671	7	temporary	temporary	ADJ
ejpam-6473	671	8	rise	rise	NOUN
ejpam-6473	671	9	in	in	ADP
ejpam-6473	671	10	light	light	ADJ
ejpam-6473	671	11	smokers	smoker	NOUN
ejpam-6473	671	12	due	due	ADJ
ejpam-6473	671	13	to	to	ADP
ejpam-6473	671	14	the	the	DET
ejpam-6473	671	15	slow	slow	ADJ
ejpam-6473	671	16	transition	transition	NOUN
ejpam-6473	671	17	to	to	PART
ejpam-6473	671	18	quit	quit	VERB
ejpam-6473	671	19	or	or	CCONJ
ejpam-6473	671	20	regular	regular	ADJ
ejpam-6473	671	21	smokers	smoker	NOUN
ejpam-6473	671	22	.	.	PUNCT
ejpam-6473	672	1	while	while	SCONJ
ejpam-6473	672	2	control	control	NOUN
ejpam-6473	672	3	measures	measure	NOUN
ejpam-6473	672	4	(	(	PUNCT
ejpam-6473	672	5	like	like	ADP
ejpam-6473	672	6	anti	anti	ADJ
ejpam-6473	672	7	smoking	smoking	NOUN
ejpam-6473	672	8	gums	gum	NOUN
ejpam-6473	672	9	)	)	PUNCT
ejpam-6473	672	10	accelerate	accelerate	VERB
ejpam-6473	672	11	the	the	DET
ejpam-6473	672	12	reduction	reduction	NOUN
ejpam-6473	672	13	in	in	ADP
ejpam-6473	672	14	the	the	DET
ejpam-6473	672	15	light	light	ADJ
ejpam-6473	672	16	smoker	smoker	NOUN
ejpam-6473	672	17	population	population	NOUN
ejpam-6473	672	18	.	.	PUNCT
ejpam-6473	673	1	the	the	DET
ejpam-6473	673	2	population	population	NOUN
ejpam-6473	673	3	of	of	ADP
ejpam-6473	673	4	regular	regular	ADJ
ejpam-6473	673	5	smokers	smoker	NOUN
ejpam-6473	673	6	,	,	PUNCT
ejpam-6473	673	7	without	without	ADP
ejpam-6473	673	8	the	the	DET
ejpam-6473	673	9	effect	effect	NOUN
ejpam-6473	673	10	of	of	ADP
ejpam-6473	673	11	delay	delay	NOUN
ejpam-6473	673	12	and	and	CCONJ
ejpam-6473	673	13	control	control	NOUN
ejpam-6473	673	14	population	population	NOUN
ejpam-6473	673	15	,	,	PUNCT
ejpam-6473	673	16	increases	increase	VERB
ejpam-6473	673	17	rapidly	rapidly	ADV
ejpam-6473	673	18	before	before	ADP
ejpam-6473	673	19	stabilization	stabilization	NOUN
ejpam-6473	673	20	,	,	PUNCT
ejpam-6473	673	21	which	which	PRON
ejpam-6473	673	22	shows	show	VERB
ejpam-6473	673	23	a	a	DET
ejpam-6473	673	24	swifter	swifter	ADJ
ejpam-6473	673	25	transition	transition	NOUN
ejpam-6473	673	26	to	to	ADP
ejpam-6473	673	27	the	the	DET
ejpam-6473	673	28	regular	regular	ADJ
ejpam-6473	673	29	smoking	smoking	NOUN
ejpam-6473	673	30	population	population	NOUN
ejpam-6473	673	31	,	,	PUNCT
ejpam-6473	673	32	but	but	CCONJ
ejpam-6473	673	33	with	with	ADP
ejpam-6473	673	34	delay	delay	NOUN
ejpam-6473	673	35	,	,	PUNCT
ejpam-6473	673	36	this	this	DET
ejpam-6473	673	37	transition	transition	NOUN
ejpam-6473	673	38	slows	slow	VERB
ejpam-6473	673	39	down	down	ADP
ejpam-6473	673	40	.	.	PUNCT
ejpam-6473	674	1	a	a	DET
ejpam-6473	674	2	control	control	NOUN
ejpam-6473	674	3	measure	measure	NOUN
ejpam-6473	674	4	(	(	PUNCT
ejpam-6473	674	5	like	like	ADP
ejpam-6473	674	6	medicine	medicine	NOUN
ejpam-6473	674	7	)	)	PUNCT
ejpam-6473	674	8	,	,	PUNCT
ejpam-6473	674	9	further	far	ADV
ejpam-6473	674	10	decreases	decrease	VERB
ejpam-6473	674	11	this	this	DET
ejpam-6473	674	12	transition	transition	NOUN
ejpam-6473	674	13	and	and	CCONJ
ejpam-6473	674	14	reaches	reach	VERB
ejpam-6473	674	15	a	a	DET
ejpam-6473	674	16	lower	low	ADJ
ejpam-6473	674	17	peak	peak	NOUN
ejpam-6473	674	18	,	,	PUNCT
ejpam-6473	674	19	which	which	PRON
ejpam-6473	674	20	shows	show	VERB
ejpam-6473	674	21	the	the	DET
ejpam-6473	674	22	effectiveness	effectiveness	NOUN
ejpam-6473	674	23	of	of	ADP
ejpam-6473	674	24	the	the	DET
ejpam-6473	674	25	control	control	NOUN
ejpam-6473	674	26	.	.	PUNCT
ejpam-6473	675	1	finally	finally	ADV
ejpam-6473	675	2	,	,	PUNCT
ejpam-6473	675	3	for	for	ADP
ejpam-6473	675	4	the	the	DET
ejpam-6473	675	5	quit	quit	NOUN
ejpam-6473	675	6	smoker	smoker	NOUN
ejpam-6473	675	7	,	,	PUNCT
ejpam-6473	675	8	there	there	PRON
ejpam-6473	675	9	is	be	VERB
ejpam-6473	675	10	a	a	DET
ejpam-6473	675	11	gradual	gradual	ADJ
ejpam-6473	675	12	increase	increase	NOUN
ejpam-6473	675	13	in	in	ADP
ejpam-6473	675	14	the	the	DET
ejpam-6473	675	15	population	population	NOUN
ejpam-6473	675	16	in	in	ADP
ejpam-6473	675	17	all	all	DET
ejpam-6473	675	18	three	three	NUM
ejpam-6473	675	19	cases	case	NOUN
ejpam-6473	675	20	,	,	PUNCT
ejpam-6473	675	21	which	which	PRON
ejpam-6473	675	22	indicates	indicate	VERB
ejpam-6473	675	23	a	a	DET
ejpam-6473	675	24	slow	slow	ADJ
ejpam-6473	675	25	growth	growth	NOUN
ejpam-6473	675	26	rate	rate	NOUN
ejpam-6473	675	27	,	,	PUNCT
ejpam-6473	675	28	but	but	CCONJ
ejpam-6473	675	29	the	the	DET
ejpam-6473	675	30	delay	delay	NOUN
ejpam-6473	675	31	curve	curve	NOUN
ejpam-6473	675	32	is	be	AUX
ejpam-6473	675	33	slightly	slightly	ADV
ejpam-6473	675	34	lower	low	ADJ
ejpam-6473	675	35	than	than	ADP
ejpam-6473	675	36	the	the	DET
ejpam-6473	675	37	simple	simple	ADJ
ejpam-6473	675	38	curve	curve	NOUN
ejpam-6473	675	39	,	,	PUNCT
ejpam-6473	675	40	showing	show	VERB
ejpam-6473	675	41	a	a	DET
ejpam-6473	675	42	minor	minor	ADJ
ejpam-6473	675	43	reduction	reduction	NOUN
ejpam-6473	675	44	in	in	ADP
ejpam-6473	675	45	growth	growth	NOUN
ejpam-6473	675	46	.	.	PUNCT
ejpam-6473	676	1	on	on	ADP
ejpam-6473	676	2	the	the	DET
ejpam-6473	676	3	other	other	ADJ
ejpam-6473	676	4	hand	hand	NOUN
ejpam-6473	676	5	,	,	PUNCT
ejpam-6473	676	6	control	control	NOUN
ejpam-6473	676	7	measures	measure	NOUN
ejpam-6473	676	8	speed	speed	VERB
ejpam-6473	676	9	up	up	ADP
ejpam-6473	676	10	the	the	DET
ejpam-6473	676	11	process	process	NOUN
ejpam-6473	676	12	of	of	ADP
ejpam-6473	676	13	quitting	quit	VERB
ejpam-6473	676	14	smoking	smoking	NOUN
ejpam-6473	676	15	and	and	CCONJ
ejpam-6473	676	16	result	result	VERB
ejpam-6473	676	17	in	in	ADP
ejpam-6473	676	18	the	the	DET
ejpam-6473	676	19	increase	increase	NOUN
ejpam-6473	676	20	in	in	ADP
ejpam-6473	676	21	the	the	DET
ejpam-6473	676	22	quit	quit	ADJ
ejpam-6473	676	23	smokers	smoker	NOUN
ejpam-6473	676	24	population	population	NOUN
ejpam-6473	676	25	.	.	PUNCT
ejpam-6473	677	1	in	in	ADP
ejpam-6473	677	2	general	general	ADJ
ejpam-6473	677	3	,	,	PUNCT
ejpam-6473	677	4	by	by	ADP
ejpam-6473	677	5	implementing	implement	VERB
ejpam-6473	677	6	delay	delay	NOUN
ejpam-6473	677	7	(	(	PUNCT
ejpam-6473	677	8	τ	τ	X
ejpam-6473	677	9	=	=	NOUN
ejpam-6473	677	10	10	10	NUM
ejpam-6473	677	11	)	)	PUNCT
ejpam-6473	677	12	,	,	PUNCT
ejpam-6473	677	13	transition	transition	NOUN
ejpam-6473	677	14	becomes	become	VERB
ejpam-6473	677	15	slow	slow	ADJ
ejpam-6473	677	16	and	and	CCONJ
ejpam-6473	677	17	prolongs	prolong	VERB
ejpam-6473	677	18	the	the	DET
ejpam-6473	677	19	quitting	quit	VERB
ejpam-6473	677	20	process	process	NOUN
ejpam-6473	677	21	.	.	PUNCT
ejpam-6473	678	1	however	however	ADV
ejpam-6473	678	2	,	,	PUNCT
ejpam-6473	678	3	control	control	NOUN
ejpam-6473	678	4	measures	measure	NOUN
ejpam-6473	678	5	increase	increase	VERB
ejpam-6473	678	6	the	the	DET
ejpam-6473	678	7	rate	rate	NOUN
ejpam-6473	678	8	of	of	ADP
ejpam-6473	678	9	quitting	quitting	NOUN
ejpam-6473	678	10	and	and	CCONJ
ejpam-6473	678	11	reduce	reduce	VERB
ejpam-6473	678	12	the	the	DET
ejpam-6473	678	13	smoking	smoking	NOUN
ejpam-6473	678	14	rate	rate	NOUN
ejpam-6473	678	15	.	.	PUNCT
ejpam-6473	679	1	s.	s.	PROPN
ejpam-6473	679	2	bano	bano	PROPN
ejpam-6473	679	3	et	et	PROPN
ejpam-6473	679	4	al	al	PROPN
ejpam-6473	679	5	.	.	PUNCT
ejpam-6473	679	6	/	/	SYM
ejpam-6473	679	7	eur	eur	PROPN
ejpam-6473	679	8	.	.	PUNCT
ejpam-6473	680	1	j.	j.	PROPN
ejpam-6473	680	2	pure	pure	PROPN
ejpam-6473	680	3	appl	appl	PROPN
ejpam-6473	680	4	.	.	PROPN
ejpam-6473	680	5	math	math	PROPN
ejpam-6473	680	6	,	,	PUNCT
ejpam-6473	680	7	18	18	NUM
ejpam-6473	680	8	(	(	PUNCT
ejpam-6473	680	9	4	4	NUM
ejpam-6473	680	10	)	)	PUNCT
ejpam-6473	680	11	(	(	PUNCT
ejpam-6473	680	12	2025	2025	NUM
ejpam-6473	680	13	)	)	PUNCT
ejpam-6473	680	14	,	,	PUNCT
ejpam-6473	680	15	6473	6473	NUM
ejpam-6473	680	16	34	34	NUM
ejpam-6473	680	17	of	of	ADP
ejpam-6473	680	18	38	38	NUM
ejpam-6473	680	19	(	(	PUNCT
ejpam-6473	680	20	a	a	NOUN
ejpam-6473	680	21	)	)	PUNCT
ejpam-6473	680	22	potential	potential	ADJ
ejpam-6473	680	23	smokers	smoker	NOUN
ejpam-6473	680	24	(	(	PUNCT
ejpam-6473	680	25	b	b	NOUN
ejpam-6473	680	26	)	)	PUNCT
ejpam-6473	680	27	regular	regular	ADJ
ejpam-6473	680	28	smokers	smoker	NOUN
ejpam-6473	680	29	(	(	PUNCT
ejpam-6473	680	30	c	c	NOUN
ejpam-6473	680	31	)	)	PUNCT
ejpam-6473	680	32	light	light	ADJ
ejpam-6473	680	33	smokers	smoker	NOUN
ejpam-6473	680	34	(	(	PUNCT
ejpam-6473	680	35	d	d	X
ejpam-6473	680	36	)	)	PUNCT
ejpam-6473	680	37	quit	quit	VERB
ejpam-6473	680	38	smokers	smoker	NOUN
ejpam-6473	680	39	figure	figure	VERB
ejpam-6473	680	40	5	5	NUM
ejpam-6473	680	41	:	:	PUNCT
ejpam-6473	680	42	(	(	PUNCT
ejpam-6473	680	43	a	a	X
ejpam-6473	680	44	)	)	PUNCT
ejpam-6473	680	45	the	the	DET
ejpam-6473	680	46	potential	potential	ADJ
ejpam-6473	680	47	smokers	smoker	NOUN
ejpam-6473	680	48	population	population	NOUN
ejpam-6473	680	49	who	who	PRON
ejpam-6473	680	50	are	be	AUX
ejpam-6473	680	51	vulnerable	vulnerable	ADJ
ejpam-6473	680	52	to	to	ADP
ejpam-6473	680	53	smoking	smoke	VERB
ejpam-6473	680	54	with	with	ADP
ejpam-6473	680	55	and	and	CCONJ
ejpam-6473	680	56	without	without	ADP
ejpam-6473	680	57	control	control	NOUN
ejpam-6473	680	58	and	and	CCONJ
ejpam-6473	680	59	delay	delay	NOUN
ejpam-6473	680	60	.	.	PUNCT
ejpam-6473	681	1	(	(	PUNCT
ejpam-6473	681	2	b	b	X
ejpam-6473	681	3	)	)	PUNCT
ejpam-6473	681	4	the	the	DET
ejpam-6473	681	5	population	population	NOUN
ejpam-6473	681	6	of	of	ADP
ejpam-6473	681	7	smokers	smoker	NOUN
ejpam-6473	681	8	who	who	PRON
ejpam-6473	681	9	smoke	smoke	VERB
ejpam-6473	681	10	occasionally	occasionally	ADV
ejpam-6473	681	11	with	with	ADP
ejpam-6473	681	12	and	and	CCONJ
ejpam-6473	681	13	without	without	ADP
ejpam-6473	681	14	control	control	NOUN
ejpam-6473	681	15	and	and	CCONJ
ejpam-6473	681	16	delay	delay	NOUN
ejpam-6473	681	17	.	.	PUNCT
ejpam-6473	682	1	(	(	PUNCT
ejpam-6473	682	2	c	c	X
ejpam-6473	682	3	)	)	PUNCT
ejpam-6473	682	4	the	the	DET
ejpam-6473	682	5	population	population	NOUN
ejpam-6473	682	6	of	of	ADP
ejpam-6473	682	7	smokers	smoker	NOUN
ejpam-6473	682	8	who	who	PRON
ejpam-6473	682	9	smoke	smoke	VERB
ejpam-6473	682	10	regularly	regularly	ADV
ejpam-6473	682	11	with	with	ADP
ejpam-6473	682	12	and	and	CCONJ
ejpam-6473	682	13	without	without	ADP
ejpam-6473	682	14	control	control	NOUN
ejpam-6473	682	15	and	and	CCONJ
ejpam-6473	682	16	delay	delay	NOUN
ejpam-6473	682	17	.	.	PUNCT
ejpam-6473	683	1	(	(	PUNCT
ejpam-6473	683	2	d	d	X
ejpam-6473	683	3	)	)	PUNCT
ejpam-6473	683	4	the	the	DET
ejpam-6473	683	5	population	population	NOUN
ejpam-6473	683	6	of	of	ADP
ejpam-6473	683	7	individuals	individual	NOUN
ejpam-6473	683	8	who	who	PRON
ejpam-6473	683	9	quit	quit	VERB
ejpam-6473	683	10	smoking	smoking	NOUN
ejpam-6473	683	11	permanently	permanently	ADV
ejpam-6473	683	12	with	with	ADP
ejpam-6473	683	13	and	and	CCONJ
ejpam-6473	683	14	without	without	ADP
ejpam-6473	683	15	control	control	NOUN
ejpam-6473	683	16	and	and	CCONJ
ejpam-6473	683	17	delay	delay	NOUN
ejpam-6473	683	18	.	.	PUNCT
ejpam-6473	684	1	s.	s.	PROPN
ejpam-6473	684	2	bano	bano	PROPN
ejpam-6473	684	3	et	et	PROPN
ejpam-6473	684	4	al	al	PROPN
ejpam-6473	684	5	.	.	PUNCT
ejpam-6473	684	6	/	/	SYM
ejpam-6473	684	7	eur	eur	PROPN
ejpam-6473	684	8	.	.	PUNCT
ejpam-6473	685	1	j.	j.	PROPN
ejpam-6473	685	2	pure	pure	PROPN
ejpam-6473	685	3	appl	appl	PROPN
ejpam-6473	685	4	.	.	PROPN
ejpam-6473	685	5	math	math	PROPN
ejpam-6473	685	6	,	,	PUNCT
ejpam-6473	685	7	18	18	NUM
ejpam-6473	685	8	(	(	PUNCT
ejpam-6473	685	9	4	4	NUM
ejpam-6473	685	10	)	)	PUNCT
ejpam-6473	685	11	(	(	PUNCT
ejpam-6473	685	12	2025	2025	NUM
ejpam-6473	685	13	)	)	PUNCT
ejpam-6473	685	14	,	,	PUNCT
ejpam-6473	685	15	6473	6473	NUM
ejpam-6473	685	16	35	35	NUM
ejpam-6473	685	17	of	of	ADP
ejpam-6473	685	18	38	38	NUM
ejpam-6473	685	19	7	7	NUM
ejpam-6473	685	20	.	.	PUNCT
ejpam-6473	686	1	discussion	discussion	NOUN
ejpam-6473	686	2	the	the	DET
ejpam-6473	686	3	present	present	ADJ
ejpam-6473	686	4	study	study	NOUN
ejpam-6473	686	5	examines	examine	VERB
ejpam-6473	686	6	a	a	DET
ejpam-6473	686	7	smoking	smoking	NOUN
ejpam-6473	686	8	behavior	behavior	NOUN
ejpam-6473	686	9	model	model	NOUN
ejpam-6473	686	10	that	that	PRON
ejpam-6473	686	11	incorporates	incorporate	VERB
ejpam-6473	686	12	both	both	CCONJ
ejpam-6473	686	13	optimal	optimal	ADJ
ejpam-6473	686	14	control	control	NOUN
ejpam-6473	686	15	strategies	strategy	NOUN
ejpam-6473	686	16	and	and	CCONJ
ejpam-6473	686	17	a	a	DET
ejpam-6473	686	18	discrete	discrete	ADJ
ejpam-6473	686	19	time	time	NOUN
ejpam-6473	686	20	delay	delay	NOUN
ejpam-6473	686	21	in	in	ADP
ejpam-6473	686	22	the	the	DET
ejpam-6473	686	23	transmission	transmission	NOUN
ejpam-6473	686	24	dynamics	dynamic	NOUN
ejpam-6473	686	25	.	.	PUNCT
ejpam-6473	687	1	by	by	ADP
ejpam-6473	687	2	integrating	integrate	VERB
ejpam-6473	687	3	these	these	DET
ejpam-6473	687	4	elements	element	NOUN
ejpam-6473	687	5	,	,	PUNCT
ejpam-6473	687	6	the	the	DET
ejpam-6473	687	7	model	model	NOUN
ejpam-6473	687	8	captures	capture	VERB
ejpam-6473	687	9	more	more	ADV
ejpam-6473	687	10	realistic	realistic	ADJ
ejpam-6473	687	11	behavioral	behavioral	ADJ
ejpam-6473	687	12	patterns	pattern	NOUN
ejpam-6473	687	13	,	,	PUNCT
ejpam-6473	687	14	such	such	ADJ
ejpam-6473	687	15	as	as	ADP
ejpam-6473	687	16	the	the	DET
ejpam-6473	687	17	gradual	gradual	ADJ
ejpam-6473	687	18	transition	transition	NOUN
ejpam-6473	687	19	between	between	ADP
ejpam-6473	687	20	smoking	smoking	NOUN
ejpam-6473	687	21	states	state	NOUN
ejpam-6473	687	22	and	and	CCONJ
ejpam-6473	687	23	the	the	DET
ejpam-6473	687	24	delayed	delay	VERB
ejpam-6473	687	25	impact	impact	NOUN
ejpam-6473	687	26	of	of	ADP
ejpam-6473	687	27	intervention	intervention	NOUN
ejpam-6473	687	28	measures	measure	NOUN
ejpam-6473	687	29	.	.	PUNCT
ejpam-6473	688	1	this	this	DET
ejpam-6473	688	2	framework	framework	NOUN
ejpam-6473	688	3	extends	extend	VERB
ejpam-6473	688	4	previous	previous	ADJ
ejpam-6473	688	5	models	model	NOUN
ejpam-6473	688	6	that	that	PRON
ejpam-6473	688	7	neglected	neglect	VERB
ejpam-6473	688	8	either	either	CCONJ
ejpam-6473	688	9	the	the	DET
ejpam-6473	688	10	influence	influence	NOUN
ejpam-6473	688	11	of	of	ADP
ejpam-6473	688	12	time	time	NOUN
ejpam-6473	688	13	delays	delay	NOUN
ejpam-6473	688	14	or	or	CCONJ
ejpam-6473	688	15	the	the	DET
ejpam-6473	688	16	role	role	NOUN
ejpam-6473	688	17	of	of	ADP
ejpam-6473	688	18	systematically	systematically	ADV
ejpam-6473	688	19	designed	design	VERB
ejpam-6473	688	20	control	control	NOUN
ejpam-6473	688	21	strategies	strategy	NOUN
ejpam-6473	688	22	.	.	PUNCT
ejpam-6473	689	1	numerical	numerical	ADJ
ejpam-6473	689	2	simulations	simulation	NOUN
ejpam-6473	689	3	were	be	AUX
ejpam-6473	689	4	performed	perform	VERB
ejpam-6473	689	5	using	use	VERB
ejpam-6473	689	6	the	the	DET
ejpam-6473	689	7	classical	classical	ADJ
ejpam-6473	689	8	fourth	fourth	ADJ
ejpam-6473	689	9	-	-	PUNCT
ejpam-6473	689	10	order	order	NOUN
ejpam-6473	689	11	runge	runge	NOUN
ejpam-6473	689	12	–	–	PUNCT
ejpam-6473	689	13	kutta	kutta	NOUN
ejpam-6473	689	14	(	(	PUNCT
ejpam-6473	689	15	rk4	rk4	NOUN
ejpam-6473	689	16	)	)	PUNCT
ejpam-6473	689	17	method	method	NOUN
ejpam-6473	689	18	implemented	implement	VERB
ejpam-6473	689	19	in	in	ADP
ejpam-6473	689	20	matlab	matlab	PROPN
ejpam-6473	689	21	,	,	PUNCT
ejpam-6473	689	22	enabling	enable	VERB
ejpam-6473	689	23	accurate	accurate	ADJ
ejpam-6473	689	24	and	and	CCONJ
ejpam-6473	689	25	efficient	efficient	ADJ
ejpam-6473	689	26	approximation	approximation	NOUN
ejpam-6473	689	27	of	of	ADP
ejpam-6473	689	28	the	the	DET
ejpam-6473	689	29	system	system	NOUN
ejpam-6473	689	30	’s	’s	PART
ejpam-6473	689	31	trajectories	trajectory	NOUN
ejpam-6473	689	32	over	over	ADP
ejpam-6473	689	33	time	time	NOUN
ejpam-6473	689	34	.	.	PUNCT
ejpam-6473	690	1	the	the	DET
ejpam-6473	690	2	computational	computational	ADJ
ejpam-6473	690	3	results	result	NOUN
ejpam-6473	690	4	demonstrate	demonstrate	VERB
ejpam-6473	690	5	that	that	SCONJ
ejpam-6473	690	6	the	the	DET
ejpam-6473	690	7	introduction	introduction	NOUN
ejpam-6473	690	8	of	of	ADP
ejpam-6473	690	9	a	a	DET
ejpam-6473	690	10	time	time	NOUN
ejpam-6473	690	11	delay	delay	NOUN
ejpam-6473	690	12	can	can	AUX
ejpam-6473	690	13	significantly	significantly	ADV
ejpam-6473	690	14	alter	alter	VERB
ejpam-6473	690	15	system	system	NOUN
ejpam-6473	690	16	behavior	behavior	NOUN
ejpam-6473	690	17	,	,	PUNCT
ejpam-6473	690	18	potentially	potentially	ADV
ejpam-6473	690	19	inducing	induce	VERB
ejpam-6473	690	20	oscillations	oscillation	NOUN
ejpam-6473	690	21	or	or	CCONJ
ejpam-6473	690	22	changing	change	VERB
ejpam-6473	690	23	the	the	DET
ejpam-6473	690	24	stability	stability	NOUN
ejpam-6473	690	25	of	of	ADP
ejpam-6473	690	26	equilibria	equilibrium	NOUN
ejpam-6473	690	27	,	,	PUNCT
ejpam-6473	690	28	thereby	thereby	ADV
ejpam-6473	690	29	influencing	influence	VERB
ejpam-6473	690	30	the	the	DET
ejpam-6473	690	31	effectiveness	effectiveness	NOUN
ejpam-6473	690	32	of	of	ADP
ejpam-6473	690	33	intervention	intervention	NOUN
ejpam-6473	690	34	strategies	strategy	NOUN
ejpam-6473	690	35	.	.	PUNCT
ejpam-6473	691	1	moreover	moreover	ADV
ejpam-6473	691	2	,	,	PUNCT
ejpam-6473	691	3	the	the	DET
ejpam-6473	691	4	application	application	NOUN
ejpam-6473	691	5	of	of	ADP
ejpam-6473	691	6	optimal	optimal	ADJ
ejpam-6473	691	7	control	control	NOUN
ejpam-6473	691	8	provides	provide	VERB
ejpam-6473	691	9	a	a	DET
ejpam-6473	691	10	systematic	systematic	ADJ
ejpam-6473	691	11	means	mean	NOUN
ejpam-6473	691	12	to	to	PART
ejpam-6473	691	13	minimize	minimize	VERB
ejpam-6473	691	14	the	the	DET
ejpam-6473	691	15	prevalence	prevalence	NOUN
ejpam-6473	691	16	of	of	ADP
ejpam-6473	691	17	smokers	smoker	NOUN
ejpam-6473	691	18	while	while	SCONJ
ejpam-6473	691	19	balancing	balance	VERB
ejpam-6473	691	20	the	the	DET
ejpam-6473	691	21	associated	associated	ADJ
ejpam-6473	691	22	implementation	implementation	NOUN
ejpam-6473	691	23	costs	cost	NOUN
ejpam-6473	691	24	.	.	PUNCT
ejpam-6473	692	1	compared	compare	VERB
ejpam-6473	692	2	with	with	ADP
ejpam-6473	692	3	earlier	early	ADJ
ejpam-6473	692	4	formulations	formulation	NOUN
ejpam-6473	692	5	in	in	ADP
ejpam-6473	692	6	the	the	DET
ejpam-6473	692	7	literature	literature	NOUN
ejpam-6473	692	8	,	,	PUNCT
ejpam-6473	692	9	our	our	PRON
ejpam-6473	692	10	model	model	NOUN
ejpam-6473	692	11	delivers	deliver	VERB
ejpam-6473	692	12	a	a	DET
ejpam-6473	692	13	more	more	ADV
ejpam-6473	692	14	comprehensive	comprehensive	ADJ
ejpam-6473	692	15	and	and	CCONJ
ejpam-6473	692	16	practical	practical	ADJ
ejpam-6473	692	17	representation	representation	NOUN
ejpam-6473	692	18	of	of	ADP
ejpam-6473	692	19	smoking	smoking	NOUN
ejpam-6473	692	20	behavior	behavior	NOUN
ejpam-6473	692	21	and	and	CCONJ
ejpam-6473	692	22	its	its	PRON
ejpam-6473	692	23	control	control	NOUN
ejpam-6473	692	24	.	.	PUNCT
ejpam-6473	693	1	the	the	DET
ejpam-6473	693	2	combination	combination	NOUN
ejpam-6473	693	3	of	of	ADP
ejpam-6473	693	4	time	time	NOUN
ejpam-6473	693	5	delay	delay	NOUN
ejpam-6473	693	6	and	and	CCONJ
ejpam-6473	693	7	optimal	optimal	ADJ
ejpam-6473	693	8	control	control	NOUN
ejpam-6473	693	9	allows	allow	VERB
ejpam-6473	693	10	for	for	ADP
ejpam-6473	693	11	more	more	ADV
ejpam-6473	693	12	precise	precise	ADJ
ejpam-6473	693	13	predictions	prediction	NOUN
ejpam-6473	693	14	of	of	ADP
ejpam-6473	693	15	intervention	intervention	NOUN
ejpam-6473	693	16	outcomes	outcome	NOUN
ejpam-6473	693	17	and	and	CCONJ
ejpam-6473	693	18	facilitates	facilitate	VERB
ejpam-6473	693	19	the	the	DET
ejpam-6473	693	20	identification	identification	NOUN
ejpam-6473	693	21	of	of	ADP
ejpam-6473	693	22	critical	critical	ADJ
ejpam-6473	693	23	time	time	NOUN
ejpam-6473	693	24	thresholds	threshold	NOUN
ejpam-6473	693	25	for	for	ADP
ejpam-6473	693	26	policy	policy	NOUN
ejpam-6473	693	27	actions	action	NOUN
ejpam-6473	693	28	.	.	PUNCT
ejpam-6473	694	1	such	such	ADJ
ejpam-6473	694	2	insights	insight	NOUN
ejpam-6473	694	3	are	be	AUX
ejpam-6473	694	4	highly	highly	ADV
ejpam-6473	694	5	valuable	valuable	ADJ
ejpam-6473	694	6	for	for	ADP
ejpam-6473	694	7	public	public	ADJ
ejpam-6473	694	8	health	health	NOUN
ejpam-6473	694	9	authorities	authority	NOUN
ejpam-6473	694	10	,	,	PUNCT
ejpam-6473	694	11	as	as	SCONJ
ejpam-6473	694	12	they	they	PRON
ejpam-6473	694	13	inform	inform	VERB
ejpam-6473	694	14	the	the	DET
ejpam-6473	694	15	timing	timing	NOUN
ejpam-6473	694	16	and	and	CCONJ
ejpam-6473	694	17	intensity	intensity	NOUN
ejpam-6473	694	18	of	of	ADP
ejpam-6473	694	19	anti	anti	ADJ
ejpam-6473	694	20	-	-	ADJ
ejpam-6473	694	21	smoking	smoking	ADJ
ejpam-6473	694	22	campaigns	campaign	NOUN
ejpam-6473	694	23	,	,	PUNCT
ejpam-6473	694	24	resource	resource	NOUN
ejpam-6473	694	25	allocation	allocation	NOUN
ejpam-6473	694	26	,	,	PUNCT
ejpam-6473	694	27	and	and	CCONJ
ejpam-6473	694	28	awareness	awareness	NOUN
ejpam-6473	694	29	programs	program	NOUN
ejpam-6473	694	30	.	.	PUNCT
ejpam-6473	695	1	overall	overall	ADV
ejpam-6473	695	2	,	,	PUNCT
ejpam-6473	695	3	this	this	DET
ejpam-6473	695	4	work	work	NOUN
ejpam-6473	695	5	enhances	enhance	VERB
ejpam-6473	695	6	existing	exist	VERB
ejpam-6473	695	7	methodological	methodological	ADJ
ejpam-6473	695	8	approaches	approach	NOUN
ejpam-6473	695	9	by	by	ADP
ejpam-6473	695	10	integrating	integrate	VERB
ejpam-6473	695	11	behavioral	behavioral	ADJ
ejpam-6473	695	12	delay	delay	NOUN
ejpam-6473	695	13	effects	effect	NOUN
ejpam-6473	695	14	with	with	ADP
ejpam-6473	695	15	mathematically	mathematically	ADV
ejpam-6473	695	16	optimized	optimize	VERB
ejpam-6473	695	17	intervention	intervention	NOUN
ejpam-6473	695	18	strategies	strategy	NOUN
ejpam-6473	695	19	.	.	PUNCT
ejpam-6473	696	1	the	the	DET
ejpam-6473	696	2	results	result	NOUN
ejpam-6473	696	3	not	not	PART
ejpam-6473	696	4	only	only	ADV
ejpam-6473	696	5	strengthen	strengthen	VERB
ejpam-6473	696	6	the	the	DET
ejpam-6473	696	7	theoretical	theoretical	ADJ
ejpam-6473	696	8	understanding	understanding	NOUN
ejpam-6473	696	9	of	of	ADP
ejpam-6473	696	10	smoking	smoking	NOUN
ejpam-6473	696	11	dynamics	dynamic	NOUN
ejpam-6473	696	12	but	but	CCONJ
ejpam-6473	696	13	also	also	ADV
ejpam-6473	696	14	provide	provide	VERB
ejpam-6473	696	15	actionable	actionable	ADJ
ejpam-6473	696	16	guidance	guidance	NOUN
ejpam-6473	696	17	for	for	ADP
ejpam-6473	696	18	evidence	evidence	NOUN
ejpam-6473	696	19	-	-	PUNCT
ejpam-6473	696	20	based	base	VERB
ejpam-6473	696	21	policymaking	policymaking	NOUN
ejpam-6473	696	22	aimed	aim	VERB
ejpam-6473	696	23	at	at	ADP
ejpam-6473	696	24	reducing	reduce	VERB
ejpam-6473	696	25	smoking	smoking	NOUN
ejpam-6473	696	26	prevalence	prevalence	NOUN
ejpam-6473	696	27	and	and	CCONJ
ejpam-6473	696	28	its	its	PRON
ejpam-6473	696	29	associated	associated	ADJ
ejpam-6473	696	30	health	health	NOUN
ejpam-6473	696	31	and	and	CCONJ
ejpam-6473	696	32	economic	economic	ADJ
ejpam-6473	696	33	burdens	burden	NOUN
ejpam-6473	696	34	.	.	PUNCT
ejpam-6473	697	1	8	8	X
ejpam-6473	697	2	.	.	X
ejpam-6473	697	3	conclusion	conclusion	NOUN
ejpam-6473	697	4	in	in	ADP
ejpam-6473	697	5	this	this	DET
ejpam-6473	697	6	article	article	NOUN
ejpam-6473	697	7	,	,	PUNCT
ejpam-6473	697	8	we	we	PRON
ejpam-6473	697	9	examine	examine	VERB
ejpam-6473	697	10	the	the	DET
ejpam-6473	697	11	smoking	smoking	NOUN
ejpam-6473	697	12	cessation	cessation	NOUN
ejpam-6473	697	13	model	model	NOUN
ejpam-6473	697	14	considering	consider	VERB
ejpam-6473	697	15	the	the	DET
ejpam-6473	697	16	important	important	ADJ
ejpam-6473	697	17	feature	feature	NOUN
ejpam-6473	697	18	of	of	ADP
ejpam-6473	697	19	the	the	DET
ejpam-6473	697	20	convex	convex	ADJ
ejpam-6473	697	21	incidence	incidence	NOUN
ejpam-6473	697	22	rate	rate	NOUN
ejpam-6473	697	23	with	with	ADP
ejpam-6473	697	24	and	and	CCONJ
ejpam-6473	697	25	without	without	ADP
ejpam-6473	697	26	control	control	NOUN
ejpam-6473	697	27	and	and	CCONJ
ejpam-6473	697	28	delay	delay	NOUN
ejpam-6473	697	29	.	.	PUNCT
ejpam-6473	698	1	this	this	DET
ejpam-6473	698	2	model	model	NOUN
ejpam-6473	698	3	is	be	AUX
ejpam-6473	698	4	constructed	construct	VERB
ejpam-6473	698	5	using	use	VERB
ejpam-6473	698	6	the	the	DET
ejpam-6473	698	7	current	current	ADJ
ejpam-6473	698	8	literature	literature	NOUN
ejpam-6473	698	9	in	in	ADP
ejpam-6473	698	10	this	this	DET
ejpam-6473	698	11	field	field	NOUN
ejpam-6473	698	12	.	.	PUNCT
ejpam-6473	699	1	we	we	PRON
ejpam-6473	699	2	examine	examine	VERB
ejpam-6473	699	3	the	the	DET
ejpam-6473	699	4	boundedness	boundedness	NOUN
ejpam-6473	699	5	and	and	CCONJ
ejpam-6473	699	6	positive	positive	ADJ
ejpam-6473	699	7	of	of	ADP
ejpam-6473	699	8	the	the	DET
ejpam-6473	699	9	solution	solution	NOUN
ejpam-6473	699	10	once	once	SCONJ
ejpam-6473	699	11	the	the	DET
ejpam-6473	699	12	model	model	NOUN
ejpam-6473	699	13	was	be	AUX
ejpam-6473	699	14	constructed	construct	VERB
ejpam-6473	699	15	,	,	PUNCT
ejpam-6473	699	16	provided	provide	VERB
ejpam-6473	699	17	that	that	SCONJ
ejpam-6473	699	18	the	the	DET
ejpam-6473	699	19	initial	initial	ADJ
ejpam-6473	699	20	conditions	condition	NOUN
ejpam-6473	699	21	are	be	AUX
ejpam-6473	699	22	satisfied	satisfied	ADJ
ejpam-6473	699	23	.	.	PUNCT
ejpam-6473	700	1	two	two	NUM
ejpam-6473	700	2	equilibrium	equilibrium	NOUN
ejpam-6473	700	3	points	point	NOUN
ejpam-6473	700	4	of	of	ADP
ejpam-6473	700	5	the	the	DET
ejpam-6473	700	6	model	model	NOUN
ejpam-6473	700	7	are	be	AUX
ejpam-6473	700	8	determined	determine	VERB
ejpam-6473	700	9	,	,	PUNCT
ejpam-6473	700	10	namely	namely	ADV
ejpam-6473	700	11	smoking	smoking	NOUN
ejpam-6473	700	12	-	-	PUNCT
ejpam-6473	700	13	free	free	ADJ
ejpam-6473	700	14	and	and	CCONJ
ejpam-6473	700	15	endemic	endemic	ADJ
ejpam-6473	700	16	equilibrium	equilibrium	NOUN
ejpam-6473	700	17	points	point	NOUN
ejpam-6473	700	18	,	,	PUNCT
ejpam-6473	700	19	through	through	ADP
ejpam-6473	700	20	simple	simple	ADJ
ejpam-6473	700	21	computation	computation	NOUN
ejpam-6473	700	22	.	.	PUNCT
ejpam-6473	701	1	then	then	ADV
ejpam-6473	701	2	the	the	DET
ejpam-6473	701	3	basic	basic	ADJ
ejpam-6473	701	4	reproductive	reproductive	ADJ
ejpam-6473	701	5	number	number	NOUN
ejpam-6473	701	6	is	be	AUX
ejpam-6473	701	7	computed	compute	VERB
ejpam-6473	701	8	,	,	PUNCT
ejpam-6473	701	9	which	which	PRON
ejpam-6473	701	10	is	be	AUX
ejpam-6473	701	11	very	very	ADV
ejpam-6473	701	12	important	important	ADJ
ejpam-6473	701	13	in	in	ADP
ejpam-6473	701	14	understanding	understand	VERB
ejpam-6473	701	15	the	the	DET
ejpam-6473	701	16	propagation	propagation	NOUN
ejpam-6473	701	17	of	of	ADP
ejpam-6473	701	18	smoking	smoking	NOUN
ejpam-6473	701	19	.	.	PUNCT
ejpam-6473	702	1	with	with	ADP
ejpam-6473	702	2	the	the	DET
ejpam-6473	702	3	help	help	NOUN
ejpam-6473	702	4	of	of	ADP
ejpam-6473	702	5	the	the	DET
ejpam-6473	702	6	reproductive	reproductive	ADJ
ejpam-6473	702	7	number	number	NOUN
ejpam-6473	702	8	,	,	PUNCT
ejpam-6473	702	9	sufficient	sufficient	ADJ
ejpam-6473	702	10	conditions	condition	NOUN
ejpam-6473	702	11	for	for	ADP
ejpam-6473	702	12	local	local	ADJ
ejpam-6473	702	13	and	and	CCONJ
ejpam-6473	702	14	global	global	ADJ
ejpam-6473	702	15	stability	stability	NOUN
ejpam-6473	702	16	are	be	AUX
ejpam-6473	702	17	determined	determine	VERB
ejpam-6473	702	18	.	.	PUNCT
ejpam-6473	703	1	sensitivity	sensitivity	NOUN
ejpam-6473	703	2	analysis	analysis	NOUN
ejpam-6473	703	3	is	be	AUX
ejpam-6473	703	4	performed	perform	VERB
ejpam-6473	703	5	,	,	PUNCT
ejpam-6473	703	6	which	which	PRON
ejpam-6473	703	7	shows	show	VERB
ejpam-6473	703	8	that	that	SCONJ
ejpam-6473	703	9	the	the	DET
ejpam-6473	703	10	dynamic	dynamic	ADJ
ejpam-6473	703	11	behavior	behavior	NOUN
ejpam-6473	703	12	of	of	ADP
ejpam-6473	703	13	the	the	DET
ejpam-6473	703	14	system	system	NOUN
ejpam-6473	703	15	is	be	AUX
ejpam-6473	703	16	affected	affect	VERB
ejpam-6473	703	17	by	by	ADP
ejpam-6473	703	18	changing	change	VERB
ejpam-6473	703	19	the	the	DET
ejpam-6473	703	20	values	value	NOUN
ejpam-6473	703	21	of	of	ADP
ejpam-6473	703	22	the	the	DET
ejpam-6473	703	23	parameters	parameter	NOUN
ejpam-6473	703	24	.	.	PUNCT
ejpam-6473	704	1	after	after	ADP
ejpam-6473	704	2	that	that	PRON
ejpam-6473	704	3	,	,	PUNCT
ejpam-6473	704	4	control	control	NOUN
ejpam-6473	704	5	problem	problem	NOUN
ejpam-6473	704	6	are	be	AUX
ejpam-6473	704	7	established	establish	VERB
ejpam-6473	704	8	by	by	ADP
ejpam-6473	704	9	utilizing	utilize	VERB
ejpam-6473	704	10	three	three	NUM
ejpam-6473	704	11	control	control	NOUN
ejpam-6473	704	12	measures	measure	NOUN
ejpam-6473	704	13	.	.	PUNCT
ejpam-6473	705	1	here	here	ADV
ejpam-6473	705	2	pontryagin	pontryagin	VERB
ejpam-6473	705	3	maximum	maximum	ADJ
ejpam-6473	705	4	principle	principle	NOUN
ejpam-6473	705	5	is	be	AUX
ejpam-6473	705	6	utilize	utilize	ADJ
ejpam-6473	705	7	to	to	PART
ejpam-6473	705	8	establish	establish	VERB
ejpam-6473	705	9	the	the	DET
ejpam-6473	705	10	best	good	ADJ
ejpam-6473	705	11	control	control	NOUN
ejpam-6473	705	12	strategies	strategy	NOUN
ejpam-6473	705	13	.	.	PUNCT
ejpam-6473	706	1	the	the	DET
ejpam-6473	706	2	model	model	NOUN
ejpam-6473	706	3	is	be	AUX
ejpam-6473	706	4	modified	modify	VERB
ejpam-6473	706	5	with	with	ADP
ejpam-6473	706	6	delay	delay	NOUN
ejpam-6473	706	7	,	,	PUNCT
ejpam-6473	706	8	where	where	SCONJ
ejpam-6473	706	9	delay	delay	NOUN
ejpam-6473	706	10	is	be	AUX
ejpam-6473	706	11	treated	treat	VERB
ejpam-6473	706	12	as	as	ADP
ejpam-6473	706	13	a	a	DET
ejpam-6473	706	14	bifurcation	bifurcation	NOUN
ejpam-6473	706	15	parameter	parameter	NOUN
ejpam-6473	706	16	.	.	PUNCT
ejpam-6473	707	1	in	in	ADP
ejpam-6473	707	2	delay	delay	NOUN
ejpam-6473	707	3	model	model	NOUN
ejpam-6473	707	4	stability	stability	NOUN
ejpam-6473	707	5	is	be	AUX
ejpam-6473	707	6	s.	s.	PROPN
ejpam-6473	707	7	bano	bano	PROPN
ejpam-6473	707	8	et	et	PROPN
ejpam-6473	707	9	al	al	PROPN
ejpam-6473	707	10	.	.	PUNCT
ejpam-6473	707	11	/	/	SYM
ejpam-6473	707	12	eur	eur	PROPN
ejpam-6473	707	13	.	.	PUNCT
ejpam-6473	708	1	j.	j.	PROPN
ejpam-6473	708	2	pure	pure	PROPN
ejpam-6473	708	3	appl	appl	PROPN
ejpam-6473	708	4	.	.	PROPN
ejpam-6473	708	5	math	math	PROPN
ejpam-6473	708	6	,	,	PUNCT
ejpam-6473	708	7	18	18	NUM
ejpam-6473	708	8	(	(	PUNCT
ejpam-6473	708	9	4	4	NUM
ejpam-6473	708	10	)	)	PUNCT
ejpam-6473	708	11	(	(	PUNCT
ejpam-6473	708	12	2025	2025	NUM
ejpam-6473	708	13	)	)	PUNCT
ejpam-6473	708	14	,	,	PUNCT
ejpam-6473	708	15	6473	6473	NUM
ejpam-6473	708	16	36	36	NUM
ejpam-6473	708	17	of	of	ADP
ejpam-6473	708	18	38	38	NUM
ejpam-6473	708	19	checked	check	VERB
ejpam-6473	708	20	with	with	ADP
ejpam-6473	708	21	help	help	NOUN
ejpam-6473	708	22	of	of	ADP
ejpam-6473	708	23	the	the	DET
ejpam-6473	708	24	routh	routh	PROPN
ejpam-6473	708	25	-	-	PUNCT
ejpam-6473	708	26	hurwitz	hurwitz	PROPN
ejpam-6473	708	27	criteria	criterion	NOUN
ejpam-6473	708	28	.	.	PUNCT
ejpam-6473	709	1	finally	finally	ADV
ejpam-6473	709	2	,	,	PUNCT
ejpam-6473	709	3	to	to	PART
ejpam-6473	709	4	verify	verify	VERB
ejpam-6473	709	5	the	the	DET
ejpam-6473	709	6	theoretical	theoretical	ADJ
ejpam-6473	709	7	results	result	NOUN
ejpam-6473	709	8	,	,	PUNCT
ejpam-6473	709	9	numerical	numerical	ADJ
ejpam-6473	709	10	computation	computation	NOUN
ejpam-6473	709	11	is	be	AUX
ejpam-6473	709	12	performed	perform	VERB
ejpam-6473	709	13	.	.	PUNCT
ejpam-6473	710	1	the	the	DET
ejpam-6473	710	2	effectiveness	effectiveness	NOUN
ejpam-6473	710	3	of	of	ADP
ejpam-6473	710	4	control	control	NOUN
ejpam-6473	710	5	and	and	CCONJ
ejpam-6473	710	6	delay	delay	NOUN
ejpam-6473	710	7	are	be	AUX
ejpam-6473	710	8	shown	show	VERB
ejpam-6473	710	9	by	by	ADP
ejpam-6473	710	10	comparing	compare	VERB
ejpam-6473	710	11	the	the	DET
ejpam-6473	710	12	curves	curve	NOUN
ejpam-6473	710	13	with	with	ADP
ejpam-6473	710	14	and	and	CCONJ
ejpam-6473	710	15	without	without	ADP
ejpam-6473	710	16	control	control	NOUN
ejpam-6473	710	17	and	and	CCONJ
ejpam-6473	710	18	delay	delay	NOUN
ejpam-6473	710	19	.	.	PUNCT
ejpam-6473	711	1	references	reference	NOUN
ejpam-6473	711	2	[	[	X
ejpam-6473	711	3	1	1	NUM
ejpam-6473	711	4	]	]	PUNCT
ejpam-6473	711	5	w.	w.	PROPN
ejpam-6473	711	6	o.	o.	PROPN
ejpam-6473	711	7	kermack	kermack	PROPN
ejpam-6473	711	8	and	and	CCONJ
ejpam-6473	711	9	a.	a.	PROPN
ejpam-6473	711	10	g.	g.	PROPN
ejpam-6473	711	11	mckendrick	mckendrick	PROPN
ejpam-6473	711	12	.	.	PUNCT
ejpam-6473	712	1	a	a	DET
ejpam-6473	712	2	contribution	contribution	NOUN
ejpam-6473	712	3	to	to	ADP
ejpam-6473	712	4	the	the	DET
ejpam-6473	712	5	mathematical	mathematical	ADJ
ejpam-6473	712	6	theory	theory	NOUN
ejpam-6473	712	7	of	of	ADP
ejpam-6473	712	8	epidemics	epidemic	NOUN
ejpam-6473	712	9	.	.	PUNCT
ejpam-6473	713	1	proceedings	proceeding	NOUN
ejpam-6473	713	2	of	of	ADP
ejpam-6473	713	3	the	the	DET
ejpam-6473	713	4	royal	royal	ADJ
ejpam-6473	713	5	society	society	NOUN
ejpam-6473	713	6	of	of	ADP
ejpam-6473	713	7	london	london	PROPN
ejpam-6473	713	8	.	.	PUNCT
ejpam-6473	714	1	series	series	PROPN
ejpam-6473	714	2	a	a	PROPN
ejpam-6473	714	3	,	,	PUNCT
ejpam-6473	714	4	containing	contain	VERB
ejpam-6473	714	5	papers	paper	NOUN
ejpam-6473	714	6	of	of	ADP
ejpam-6473	714	7	a	a	DET
ejpam-6473	714	8	mathematical	mathematical	ADJ
ejpam-6473	714	9	and	and	CCONJ
ejpam-6473	714	10	physical	physical	ADJ
ejpam-6473	714	11	character	character	NOUN
ejpam-6473	714	12	,	,	PUNCT
ejpam-6473	714	13	115:700–721	115:700–721	NUM
ejpam-6473	714	14	,	,	PUNCT
ejpam-6473	714	15	1927	1927	NUM
ejpam-6473	714	16	.	.	PUNCT
ejpam-6473	715	1	[	[	X
ejpam-6473	715	2	2	2	NUM
ejpam-6473	715	3	]	]	PUNCT
ejpam-6473	715	4	andrea	andrea	PROPN
ejpam-6473	715	5	.	.	PUNCT
ejpam-6473	716	1	a	a	DET
ejpam-6473	716	2	s.i.r	s.i.r	ADJ
ejpam-6473	716	3	vector	vector	NOUN
ejpam-6473	716	4	disease	disease	NOUN
ejpam-6473	716	5	model	model	NOUN
ejpam-6473	716	6	with	with	ADP
ejpam-6473	716	7	delay	delay	NOUN
ejpam-6473	716	8	.	.	PUNCT
ejpam-6473	717	1	mathematical	mathematical	ADJ
ejpam-6473	717	2	modelling	modelling	NOUN
ejpam-6473	717	3	,	,	PUNCT
ejpam-6473	717	4	7:793–802	7:793–802	NUM
ejpam-6473	717	5	,	,	PUNCT
ejpam-6473	717	6	1986	1986	NUM
ejpam-6473	717	7	.	.	PUNCT
ejpam-6473	718	1	[	[	X
ejpam-6473	718	2	3	3	NUM
ejpam-6473	718	3	]	]	X
ejpam-6473	718	4	n.	n.	PROPN
ejpam-6473	718	5	h.	h.	PROPN
ejpam-6473	718	6	shah	shah	PROPN
ejpam-6473	718	7	and	and	CCONJ
ejpam-6473	718	8	j.	j.	PROPN
ejpam-6473	718	9	gupta	gupta	PROPN
ejpam-6473	718	10	.	.	PUNCT
ejpam-6473	718	11	seir	seir	ADJ
ejpam-6473	718	12	model	model	NOUN
ejpam-6473	718	13	and	and	CCONJ
ejpam-6473	718	14	simulation	simulation	NOUN
ejpam-6473	718	15	for	for	ADP
ejpam-6473	718	16	vector	vector	NOUN
ejpam-6473	718	17	borne	borne	NOUN
ejpam-6473	718	18	diseases	disease	NOUN
ejpam-6473	718	19	.	.	PUNCT
ejpam-6473	719	1	scientific	scientific	ADJ
ejpam-6473	719	2	research	research	NOUN
ejpam-6473	719	3	publisher	publisher	NOUN
ejpam-6473	719	4	,	,	PUNCT
ejpam-6473	719	5	2013	2013	NUM
ejpam-6473	719	6	.	.	PUNCT
ejpam-6473	720	1	[	[	X
ejpam-6473	720	2	4	4	X
ejpam-6473	720	3	]	]	X
ejpam-6473	720	4	g.	g.	PROPN
ejpam-6473	720	5	zaman	zaman	PROPN
ejpam-6473	720	6	,	,	PUNCT
ejpam-6473	720	7	y.	y.	PROPN
ejpam-6473	720	8	h.	h.	PROPN
ejpam-6473	720	9	kang	kang	PROPN
ejpam-6473	720	10	,	,	PUNCT
ejpam-6473	720	11	and	and	CCONJ
ejpam-6473	720	12	i.	i.	PROPN
ejpam-6473	720	13	h.	h.	PROPN
ejpam-6473	720	14	jung	jung	PROPN
ejpam-6473	720	15	.	.	PUNCT
ejpam-6473	721	1	stability	stability	NOUN
ejpam-6473	721	2	analysis	analysis	NOUN
ejpam-6473	721	3	and	and	CCONJ
ejpam-6473	721	4	optimal	optimal	ADJ
ejpam-6473	721	5	vaccination	vaccination	NOUN
ejpam-6473	721	6	of	of	ADP
ejpam-6473	721	7	sir	sir	NOUN
ejpam-6473	721	8	epidemic	epidemic	NOUN
ejpam-6473	721	9	model	model	NOUN
ejpam-6473	721	10	.	.	PUNCT
ejpam-6473	722	1	biosystems	biosystems	PROPN
ejpam-6473	722	2	,	,	PUNCT
ejpam-6473	722	3	93(3):240–249	93(3):240–249	PROPN
ejpam-6473	722	4	,	,	PUNCT
ejpam-6473	722	5	2008	2008	NUM
ejpam-6473	722	6	.	.	PUNCT
ejpam-6473	723	1	[	[	X
ejpam-6473	723	2	5	5	NUM
ejpam-6473	723	3	]	]	PUNCT
ejpam-6473	723	4	m.	m.	NOUN
ejpam-6473	723	5	bohner	bohner	NOUN
ejpam-6473	723	6	and	and	CCONJ
ejpam-6473	723	7	s.	s.	PROPN
ejpam-6473	723	8	h.	h.	PROPN
ejpam-6473	723	9	streipert	streipert	PROPN
ejpam-6473	723	10	.	.	PUNCT
ejpam-6473	724	1	the	the	DET
ejpam-6473	724	2	sis	sis	PROPN
ejpam-6473	724	3	model	model	NOUN
ejpam-6473	724	4	on	on	ADP
ejpam-6473	724	5	time	time	NOUN
ejpam-6473	724	6	scales	scale	NOUN
ejpam-6473	724	7	.	.	PUNCT
ejpam-6473	725	1	pliska	pliska	PROPN
ejpam-6473	725	2	studia	studia	PROPN
ejpam-6473	725	3	mathematica	mathematica	PROPN
ejpam-6473	725	4	bulgarica	bulgarica	PROPN
ejpam-6473	725	5	,	,	PUNCT
ejpam-6473	725	6	26:11–28	26:11–28	PROPN
ejpam-6473	725	7	,	,	PUNCT
ejpam-6473	725	8	2016	2016	NUM
ejpam-6473	725	9	.	.	PUNCT
ejpam-6473	726	1	[	[	X
ejpam-6473	726	2	6	6	NUM
ejpam-6473	726	3	]	]	PUNCT
ejpam-6473	726	4	wayne	wayne	PROPN
ejpam-6473	726	5	p.	p.	PROPN
ejpam-6473	726	6	london	london	PROPN
ejpam-6473	726	7	and	and	CCONJ
ejpam-6473	726	8	james	james	PROPN
ejpam-6473	726	9	a.	a.	PROPN
ejpam-6473	726	10	yorke	yorke	PROPN
ejpam-6473	726	11	.	.	PUNCT
ejpam-6473	727	1	recurrent	recurrent	ADJ
ejpam-6473	727	2	outbreaks	outbreak	NOUN
ejpam-6473	727	3	of	of	ADP
ejpam-6473	727	4	measles	measle	NOUN
ejpam-6473	727	5	,	,	PUNCT
ejpam-6473	727	6	chickenpox	chickenpox	NOUN
ejpam-6473	727	7	and	and	CCONJ
ejpam-6473	727	8	mumps	mump	NOUN
ejpam-6473	727	9	:	:	PUNCT
ejpam-6473	727	10	i.	i.	PROPN
ejpam-6473	727	11	seasonal	seasonal	ADJ
ejpam-6473	727	12	variation	variation	NOUN
ejpam-6473	727	13	in	in	ADP
ejpam-6473	727	14	contact	contact	NOUN
ejpam-6473	727	15	rates	rate	NOUN
ejpam-6473	727	16	.	.	PUNCT
ejpam-6473	728	1	american	american	ADJ
ejpam-6473	728	2	journal	journal	PROPN
ejpam-6473	728	3	of	of	ADP
ejpam-6473	728	4	epidemiology	epidemiology	NOUN
ejpam-6473	728	5	,	,	PUNCT
ejpam-6473	728	6	98(6):453–468	98(6):453–468	PROPN
ejpam-6473	728	7	,	,	PUNCT
ejpam-6473	728	8	1973	1973	NUM
ejpam-6473	728	9	.	.	PUNCT
ejpam-6473	729	1	[	[	X
ejpam-6473	729	2	7	7	X
ejpam-6473	729	3	]	]	X
ejpam-6473	729	4	d.	d.	PROPN
ejpam-6473	729	5	xiao	xiao	PROPN
ejpam-6473	729	6	and	and	CCONJ
ejpam-6473	729	7	s.	s.	PROPN
ejpam-6473	729	8	ruan	ruan	PROPN
ejpam-6473	729	9	.	.	PUNCT
ejpam-6473	730	1	global	global	ADJ
ejpam-6473	730	2	analysis	analysis	NOUN
ejpam-6473	730	3	of	of	ADP
ejpam-6473	730	4	an	an	DET
ejpam-6473	730	5	epidemic	epidemic	NOUN
ejpam-6473	730	6	model	model	NOUN
ejpam-6473	730	7	with	with	ADP
ejpam-6473	730	8	non	non	ADJ
ejpam-6473	730	9	-	-	ADJ
ejpam-6473	730	10	monotone	monotone	ADJ
ejpam-6473	730	11	incidence	incidence	NOUN
ejpam-6473	730	12	rate	rate	NOUN
ejpam-6473	730	13	.	.	PUNCT
ejpam-6473	731	1	mathematical	mathematical	ADJ
ejpam-6473	731	2	biosciences	bioscience	NOUN
ejpam-6473	731	3	,	,	PUNCT
ejpam-6473	731	4	208(2):419–429	208(2):419–429	PROPN
ejpam-6473	731	5	,	,	PUNCT
ejpam-6473	731	6	2007	2007	NUM
ejpam-6473	731	7	.	.	PUNCT
ejpam-6473	732	1	[	[	X
ejpam-6473	732	2	8	8	NUM
ejpam-6473	732	3	]	]	X
ejpam-6473	732	4	g.	g.	PROPN
ejpam-6473	732	5	ur	ur	PROPN
ejpam-6473	732	6	rahman	rahman	PROPN
ejpam-6473	732	7	,	,	PUNCT
ejpam-6473	732	8	r.	r.	PROPN
ejpam-6473	732	9	p.	p.	PROPN
ejpam-6473	732	10	agarwal	agarwal	PROPN
ejpam-6473	732	11	,	,	PUNCT
ejpam-6473	732	12	and	and	CCONJ
ejpam-6473	732	13	q.	q.	PROPN
ejpam-6473	732	14	din	din	PROPN
ejpam-6473	732	15	.	.	PROPN
ejpam-6473	732	16	mathematical	mathematical	ADJ
ejpam-6473	732	17	analysis	analysis	NOUN
ejpam-6473	732	18	of	of	ADP
ejpam-6473	732	19	giving	give	VERB
ejpam-6473	732	20	up	up	ADP
ejpam-6473	732	21	smoking	smoking	NOUN
ejpam-6473	732	22	model	model	NOUN
ejpam-6473	732	23	via	via	ADP
ejpam-6473	732	24	harmonic	harmonic	ADJ
ejpam-6473	732	25	mean	mean	NOUN
ejpam-6473	732	26	type	type	NOUN
ejpam-6473	732	27	incidence	incidence	NOUN
ejpam-6473	732	28	rate	rate	NOUN
ejpam-6473	732	29	.	.	PUNCT
ejpam-6473	733	1	applied	apply	VERB
ejpam-6473	733	2	mathematics	mathematic	NOUN
ejpam-6473	733	3	and	and	CCONJ
ejpam-6473	733	4	computation	computation	NOUN
ejpam-6473	733	5	,	,	PUNCT
ejpam-6473	733	6	354:128–148	354:128–148	NUM
ejpam-6473	733	7	,	,	PUNCT
ejpam-6473	733	8	2019	2019	NUM
ejpam-6473	733	9	.	.	PUNCT
ejpam-6473	734	1	[	[	X
ejpam-6473	734	2	9	9	NUM
ejpam-6473	734	3	]	]	PUNCT
ejpam-6473	734	4	a.	a.	NOUN
ejpam-6473	734	5	kaddar	kaddar	PROPN
ejpam-6473	734	6	.	.	PUNCT
ejpam-6473	735	1	stability	stability	NOUN
ejpam-6473	735	2	analysis	analysis	NOUN
ejpam-6473	735	3	in	in	ADP
ejpam-6473	735	4	a	a	DET
ejpam-6473	735	5	delayed	delay	VERB
ejpam-6473	735	6	sir	sir	NOUN
ejpam-6473	735	7	epidemic	epidemic	NOUN
ejpam-6473	735	8	model	model	NOUN
ejpam-6473	735	9	with	with	ADP
ejpam-6473	735	10	saturated	saturate	VERB
ejpam-6473	735	11	incidence	incidence	NOUN
ejpam-6473	735	12	rate	rate	NOUN
ejpam-6473	735	13	.	.	PUNCT
ejpam-6473	736	1	nonlinear	nonlinear	ADJ
ejpam-6473	736	2	analysis	analysis	NOUN
ejpam-6473	736	3	:	:	PUNCT
ejpam-6473	736	4	modelling	modelling	NOUN
ejpam-6473	736	5	and	and	CCONJ
ejpam-6473	736	6	control	control	NOUN
ejpam-6473	736	7	,	,	PUNCT
ejpam-6473	736	8	15(3):299–306	15(3):299–306	NOUN
ejpam-6473	736	9	,	,	PUNCT
ejpam-6473	736	10	2010	2010	NUM
ejpam-6473	736	11	.	.	PUNCT
ejpam-6473	737	1	[	[	X
ejpam-6473	737	2	10	10	NUM
ejpam-6473	737	3	]	]	X
ejpam-6473	737	4	y.	y.	PROPN
ejpam-6473	737	5	jin	jin	PROPN
ejpam-6473	737	6	,	,	PUNCT
ejpam-6473	737	7	w.	w.	PROPN
ejpam-6473	737	8	wang	wang	PROPN
ejpam-6473	737	9	,	,	PUNCT
ejpam-6473	737	10	and	and	CCONJ
ejpam-6473	737	11	s.	s.	PROPN
ejpam-6473	737	12	xiao	xiao	PROPN
ejpam-6473	737	13	.	.	PUNCT
ejpam-6473	738	1	an	an	DET
ejpam-6473	738	2	sirs	sirs	PROPN
ejpam-6473	738	3	model	model	NOUN
ejpam-6473	738	4	with	with	ADP
ejpam-6473	738	5	a	a	DET
ejpam-6473	738	6	nonlinear	nonlinear	ADJ
ejpam-6473	738	7	incidence	incidence	NOUN
ejpam-6473	738	8	rate	rate	NOUN
ejpam-6473	738	9	.	.	PUNCT
ejpam-6473	739	1	chaos	chaos	NOUN
ejpam-6473	739	2	,	,	PUNCT
ejpam-6473	739	3	solitons	soliton	NOUN
ejpam-6473	739	4	fractals	fractal	NOUN
ejpam-6473	739	5	,	,	PUNCT
ejpam-6473	739	6	34(5):1482–1497	34(5):1482–1497	NUM
ejpam-6473	739	7	,	,	PUNCT
ejpam-6473	739	8	2007	2007	NUM
ejpam-6473	739	9	.	.	PUNCT
ejpam-6473	740	1	[	[	X
ejpam-6473	740	2	11	11	NUM
ejpam-6473	740	3	]	]	PUNCT
ejpam-6473	740	4	a.	a.	PROPN
ejpam-6473	740	5	khan	khan	PROPN
ejpam-6473	740	6	,	,	PUNCT
ejpam-6473	740	7	r.	r.	PROPN
ejpam-6473	740	8	zarin	zarin	PROPN
ejpam-6473	740	9	,	,	PUNCT
ejpam-6473	740	10	g.	g.	PROPN
ejpam-6473	740	11	hussain	hussain	PROPN
ejpam-6473	740	12	,	,	PUNCT
ejpam-6473	740	13	n.	n.	PROPN
ejpam-6473	740	14	a.	a.	PROPN
ejpam-6473	740	15	ahmad	ahmad	PROPN
ejpam-6473	740	16	,	,	PUNCT
ejpam-6473	740	17	m.	m.	PROPN
ejpam-6473	740	18	hafiz	hafiz	PROPN
ejpam-6473	740	19	,	,	PUNCT
ejpam-6473	740	20	and	and	CCONJ
ejpam-6473	740	21	a.	a.	PROPN
ejpam-6473	740	22	yusuf	yusuf	PROPN
ejpam-6473	740	23	.	.	PUNCT
ejpam-6473	741	1	stability	stability	NOUN
ejpam-6473	741	2	analysis	analysis	NOUN
ejpam-6473	741	3	and	and	CCONJ
ejpam-6473	741	4	optimal	optimal	ADJ
ejpam-6473	741	5	control	control	NOUN
ejpam-6473	741	6	of	of	ADP
ejpam-6473	741	7	covid-19	covid-19	PROPN
ejpam-6473	741	8	with	with	ADP
ejpam-6473	741	9	convex	convex	ADJ
ejpam-6473	741	10	incidence	incidence	NOUN
ejpam-6473	741	11	rate	rate	NOUN
ejpam-6473	741	12	in	in	ADP
ejpam-6473	741	13	khyber	khyber	PROPN
ejpam-6473	741	14	pakhtunkhwa	pakhtunkhwa	PROPN
ejpam-6473	741	15	(	(	PUNCT
ejpam-6473	741	16	pakistan	pakistan	PROPN
ejpam-6473	741	17	)	)	PUNCT
ejpam-6473	741	18	.	.	PUNCT
ejpam-6473	742	1	results	result	NOUN
ejpam-6473	742	2	in	in	ADP
ejpam-6473	742	3	physics	physics	NOUN
ejpam-6473	742	4	,	,	PUNCT
ejpam-6473	742	5	20:103703	20:103703	NUM
ejpam-6473	742	6	,	,	PUNCT
ejpam-6473	742	7	2021	2021	NUM
ejpam-6473	742	8	.	.	PUNCT
ejpam-6473	743	1	[	[	X
ejpam-6473	743	2	12	12	NUM
ejpam-6473	743	3	]	]	PUNCT
ejpam-6473	743	4	a.	a.	NOUN
ejpam-6473	743	5	khan	khan	PROPN
ejpam-6473	743	6	,	,	PUNCT
ejpam-6473	743	7	r.	r.	PROPN
ejpam-6473	743	8	zarin	zarin	PROPN
ejpam-6473	743	9	,	,	PUNCT
ejpam-6473	743	10	g.	g.	PROPN
ejpam-6473	743	11	hussain	hussain	PROPN
ejpam-6473	743	12	,	,	PUNCT
ejpam-6473	743	13	a.	a.	PROPN
ejpam-6473	743	14	h.	h.	PROPN
ejpam-6473	743	15	usman	usman	PROPN
ejpam-6473	743	16	,	,	PUNCT
ejpam-6473	743	17	u.	u.	PROPN
ejpam-6473	743	18	w.	w.	PROPN
ejpam-6473	743	19	humphries	humphries	PROPN
ejpam-6473	743	20	,	,	PUNCT
ejpam-6473	743	21	and	and	CCONJ
ejpam-6473	743	22	j.	j.	PROPN
ejpam-6473	743	23	f.	f.	PROPN
ejpam-6473	743	24	gomezaguilar	gomezaguilar	PROPN
ejpam-6473	743	25	.	.	PUNCT
ejpam-6473	744	1	modelling	modelling	NOUN
ejpam-6473	744	2	and	and	CCONJ
ejpam-6473	744	3	sensitivity	sensitivity	NOUN
ejpam-6473	744	4	analysis	analysis	NOUN
ejpam-6473	744	5	of	of	ADP
ejpam-6473	744	6	hbv	hbv	NOUN
ejpam-6473	744	7	epidemic	epidemic	NOUN
ejpam-6473	744	8	model	model	NOUN
ejpam-6473	744	9	with	with	ADP
ejpam-6473	744	10	convex	convex	ADJ
ejpam-6473	744	11	incidence	incidence	NOUN
ejpam-6473	744	12	rate	rate	NOUN
ejpam-6473	744	13	.	.	PUNCT
ejpam-6473	745	1	results	result	NOUN
ejpam-6473	745	2	in	in	ADP
ejpam-6473	745	3	physics	physics	NOUN
ejpam-6473	745	4	,	,	PUNCT
ejpam-6473	745	5	22:103836	22:103836	NUM
ejpam-6473	745	6	,	,	PUNCT
ejpam-6473	745	7	2021	2021	NUM
ejpam-6473	745	8	.	.	PUNCT
ejpam-6473	746	1	[	[	X
ejpam-6473	746	2	13	13	NUM
ejpam-6473	746	3	]	]	X
ejpam-6473	746	4	o.	o.	PROPN
ejpam-6473	746	5	babasola	babasola	PROPN
ejpam-6473	746	6	,	,	PUNCT
ejpam-6473	746	7	o.	o.	PROPN
ejpam-6473	746	8	kayobe	kayobe	PROPN
ejpam-6473	746	9	,	,	PUNCT
ejpam-6473	746	10	o.	o.	PROPN
ejpam-6473	746	11	j.	j.	PROPN
ejpam-6473	746	12	peter	peter	PROPN
ejpam-6473	746	13	,	,	PUNCT
ejpam-6473	746	14	f.	f.	PROPN
ejpam-6473	746	15	c.	c.	PROPN
ejpam-6473	746	16	onwuegbuche	onwuegbuche	PROPN
ejpam-6473	746	17	,	,	PUNCT
ejpam-6473	746	18	and	and	CCONJ
ejpam-6473	746	19	f.	f.	PROPN
ejpam-6473	746	20	a.	a.	PROPN
ejpam-6473	746	21	oguntolu	oguntolu	PROPN
ejpam-6473	746	22	.	.	PUNCT
ejpam-6473	747	1	time	time	NOUN
ejpam-6473	747	2	delayed	delay	VERB
ejpam-6473	747	3	modelling	modelling	NOUN
ejpam-6473	747	4	of	of	ADP
ejpam-6473	747	5	covid-19	covid-19	PROPN
ejpam-6473	747	6	dynamics	dynamic	NOUN
ejpam-6473	747	7	with	with	ADP
ejpam-6473	747	8	a	a	DET
ejpam-6473	747	9	convex	convex	ADJ
ejpam-6473	747	10	incidence	incidence	NOUN
ejpam-6473	747	11	rate	rate	NOUN
ejpam-6473	747	12	.	.	PUNCT
ejpam-6473	748	1	informatics	informatic	NOUN
ejpam-6473	748	2	in	in	ADP
ejpam-6473	748	3	medicine	medicine	NOUN
ejpam-6473	748	4	unlocked	unlock	VERB
ejpam-6473	748	5	,	,	PUNCT
ejpam-6473	748	6	33:101124	33:101124	NUM
ejpam-6473	748	7	,	,	PUNCT
ejpam-6473	748	8	2022	2022	NUM
ejpam-6473	748	9	.	.	PUNCT
ejpam-6473	749	1	[	[	X
ejpam-6473	749	2	14	14	NUM
ejpam-6473	749	3	]	]	X
ejpam-6473	749	4	r.	r.	PROPN
ejpam-6473	749	5	zarin	zarin	PROPN
ejpam-6473	749	6	,	,	PUNCT
ejpam-6473	749	7	a.	a.	PROPN
ejpam-6473	749	8	raouf	raouf	PROPN
ejpam-6473	749	9	,	,	PUNCT
ejpam-6473	749	10	a.	a.	PROPN
ejpam-6473	749	11	khan	khan	PROPN
ejpam-6473	749	12	,	,	PUNCT
ejpam-6473	749	13	and	and	CCONJ
ejpam-6473	749	14	u.	u.	PROPN
ejpam-6473	749	15	w.	w.	PROPN
ejpam-6473	749	16	humphries	humphries	PROPN
ejpam-6473	749	17	.	.	PUNCT
ejpam-6473	750	1	modelling	model	VERB
ejpam-6473	750	2	hepatitis	hepatitis	PROPN
ejpam-6473	750	3	b	b	PROPN
ejpam-6473	750	4	infection	infection	NOUN
ejpam-6473	750	5	dynamics	dynamic	NOUN
ejpam-6473	750	6	with	with	ADP
ejpam-6473	750	7	a	a	DET
ejpam-6473	750	8	novel	novel	ADJ
ejpam-6473	750	9	mathematical	mathematical	ADJ
ejpam-6473	750	10	model	model	NOUN
ejpam-6473	750	11	incorporating	incorporate	VERB
ejpam-6473	750	12	convex	convex	ADJ
ejpam-6473	750	13	incidence	incidence	NOUN
ejpam-6473	750	14	rate	rate	NOUN
ejpam-6473	750	15	and	and	CCONJ
ejpam-6473	750	16	real	real	ADJ
ejpam-6473	750	17	data	datum	NOUN
ejpam-6473	750	18	.	.	PUNCT
ejpam-6473	751	1	the	the	DET
ejpam-6473	751	2	european	european	PROPN
ejpam-6473	751	3	physical	physical	PROPN
ejpam-6473	751	4	journal	journal	PROPN
ejpam-6473	751	5	plus	plus	CCONJ
ejpam-6473	751	6	,	,	PUNCT
ejpam-6473	751	7	138(11):1056	138(11):1056	PROPN
ejpam-6473	751	8	,	,	PUNCT
ejpam-6473	751	9	2023	2023	NUM
ejpam-6473	751	10	.	.	PUNCT
ejpam-6473	752	1	[	[	X
ejpam-6473	752	2	15	15	NUM
ejpam-6473	752	3	]	]	X
ejpam-6473	752	4	b.	b.	PROPN
ejpam-6473	752	5	buonomo	buonomo	PROPN
ejpam-6473	752	6	and	and	CCONJ
ejpam-6473	752	7	d.	d.	PROPN
ejpam-6473	752	8	lacitignola	lacitignola	PROPN
ejpam-6473	752	9	.	.	PUNCT
ejpam-6473	753	1	on	on	ADP
ejpam-6473	753	2	the	the	DET
ejpam-6473	753	3	dynamics	dynamic	NOUN
ejpam-6473	753	4	of	of	ADP
ejpam-6473	753	5	an	an	DET
ejpam-6473	753	6	seir	seir	ADJ
ejpam-6473	753	7	epidemic	epidemic	NOUN
ejpam-6473	753	8	model	model	NOUN
ejpam-6473	753	9	with	with	ADP
ejpam-6473	753	10	convex	convex	ADJ
ejpam-6473	753	11	incidence	incidence	NOUN
ejpam-6473	753	12	rate	rate	NOUN
ejpam-6473	753	13	.	.	PUNCT
ejpam-6473	754	1	ricerche	ricerche	PROPN
ejpam-6473	754	2	di	di	PROPN
ejpam-6473	754	3	matematica	matematica	PROPN
ejpam-6473	754	4	,	,	PUNCT
ejpam-6473	754	5	57:261–281	57:261–281	NUM
ejpam-6473	754	6	,	,	PUNCT
ejpam-6473	754	7	2008	2008	NUM
ejpam-6473	754	8	.	.	PUNCT
ejpam-6473	755	1	s.	s.	PROPN
ejpam-6473	755	2	bano	bano	PROPN
ejpam-6473	755	3	et	et	PROPN
ejpam-6473	755	4	al	al	PROPN
ejpam-6473	755	5	.	.	PUNCT
ejpam-6473	755	6	/	/	SYM
ejpam-6473	755	7	eur	eur	PROPN
ejpam-6473	755	8	.	.	PUNCT
ejpam-6473	756	1	j.	j.	PROPN
ejpam-6473	756	2	pure	pure	PROPN
ejpam-6473	756	3	appl	appl	PROPN
ejpam-6473	756	4	.	.	PROPN
ejpam-6473	756	5	math	math	PROPN
ejpam-6473	756	6	,	,	PUNCT
ejpam-6473	756	7	18	18	NUM
ejpam-6473	756	8	(	(	PUNCT
ejpam-6473	756	9	4	4	NUM
ejpam-6473	756	10	)	)	PUNCT
ejpam-6473	756	11	(	(	PUNCT
ejpam-6473	756	12	2025	2025	NUM
ejpam-6473	756	13	)	)	PUNCT
ejpam-6473	756	14	,	,	PUNCT
ejpam-6473	756	15	6473	6473	NUM
ejpam-6473	756	16	37	37	NUM
ejpam-6473	756	17	of	of	ADP
ejpam-6473	756	18	38	38	NUM
ejpam-6473	756	19	[	[	SYM
ejpam-6473	756	20	16	16	NUM
ejpam-6473	756	21	]	]	X
ejpam-6473	756	22	kamel	kamel	PROPN
ejpam-6473	756	23	guedri	guedri	PROPN
ejpam-6473	756	24	et	et	PROPN
ejpam-6473	756	25	al	al	PROPN
ejpam-6473	756	26	.	.	PUNCT
ejpam-6473	757	1	rabies	rabie	NOUN
ejpam-6473	757	2	-	-	PUNCT
ejpam-6473	757	3	related	relate	VERB
ejpam-6473	757	4	brain	brain	NOUN
ejpam-6473	757	5	disorders	disorder	NOUN
ejpam-6473	757	6	:	:	PUNCT
ejpam-6473	757	7	transmission	transmission	NOUN
ejpam-6473	757	8	dynamics	dynamic	NOUN
ejpam-6473	757	9	and	and	CCONJ
ejpam-6473	757	10	epidemic	epidemic	NOUN
ejpam-6473	757	11	management	management	NOUN
ejpam-6473	757	12	via	via	ADP
ejpam-6473	757	13	educational	educational	ADJ
ejpam-6473	757	14	campaigns	campaign	NOUN
ejpam-6473	757	15	and	and	CCONJ
ejpam-6473	757	16	application	application	NOUN
ejpam-6473	757	17	of	of	ADP
ejpam-6473	757	18	nanotechnology	nanotechnology	NOUN
ejpam-6473	757	19	.	.	PUNCT
ejpam-6473	758	1	the	the	DET
ejpam-6473	758	2	european	european	PROPN
ejpam-6473	758	3	physical	physical	PROPN
ejpam-6473	758	4	journal	journal	PROPN
ejpam-6473	758	5	plus	plus	CCONJ
ejpam-6473	758	6	,	,	PUNCT
ejpam-6473	758	7	139(1):1–16	139(1):1–16	NUM
ejpam-6473	758	8	,	,	PUNCT
ejpam-6473	758	9	2024	2024	NUM
ejpam-6473	758	10	.	.	PUNCT
ejpam-6473	759	1	[	[	X
ejpam-6473	759	2	17	17	NUM
ejpam-6473	759	3	]	]	PUNCT
ejpam-6473	759	4	v.	v.	ADP
ejpam-6473	759	5	ambalarajan	ambalarajan	NOUN
ejpam-6473	759	6	,	,	PUNCT
ejpam-6473	759	7	a.	a.	PROPN
ejpam-6473	759	8	r.	r.	PROPN
ejpam-6473	759	9	mallela	mallela	PROPN
ejpam-6473	759	10	,	,	PUNCT
ejpam-6473	759	11	v.	v.	PROPN
ejpam-6473	759	12	sivakumar	sivakumar	PROPN
ejpam-6473	759	13	,	,	PUNCT
ejpam-6473	759	14	p.	p.	PROPN
ejpam-6473	759	15	b.	b.	PROPN
ejpam-6473	759	16	dhandapani	dhandapani	PROPN
ejpam-6473	759	17	,	,	PUNCT
ejpam-6473	759	18	v.	v.	X
ejpam-6473	759	19	leiva	leiva	PROPN
ejpam-6473	759	20	,	,	PUNCT
ejpam-6473	759	21	c.	c.	PROPN
ejpam-6473	759	22	martinbarreiro	martinbarreiro	PROPN
ejpam-6473	759	23	,	,	PUNCT
ejpam-6473	759	24	and	and	CCONJ
ejpam-6473	759	25	c.	c.	PROPN
ejpam-6473	759	26	castro	castro	PROPN
ejpam-6473	759	27	.	.	PUNCT
ejpam-6473	760	1	a	a	DET
ejpam-6473	760	2	six	six	NUM
ejpam-6473	760	3	-	-	PUNCT
ejpam-6473	760	4	compartment	compartment	NOUN
ejpam-6473	760	5	model	model	NOUN
ejpam-6473	760	6	for	for	ADP
ejpam-6473	760	7	covid-19	covid-19	PROPN
ejpam-6473	760	8	with	with	ADP
ejpam-6473	760	9	transmission	transmission	NOUN
ejpam-6473	760	10	dynamics	dynamic	NOUN
ejpam-6473	760	11	and	and	CCONJ
ejpam-6473	760	12	public	public	ADJ
ejpam-6473	760	13	health	health	NOUN
ejpam-6473	760	14	strategies	strategy	NOUN
ejpam-6473	760	15	.	.	PUNCT
ejpam-6473	761	1	scientific	scientific	ADJ
ejpam-6473	761	2	reports	report	NOUN
ejpam-6473	761	3	,	,	PUNCT
ejpam-6473	761	4	14(1):22226	14(1):22226	NUM
ejpam-6473	761	5	,	,	PUNCT
ejpam-6473	761	6	2024	2024	NUM
ejpam-6473	761	7	.	.	PUNCT
ejpam-6473	762	1	[	[	X
ejpam-6473	762	2	18	18	NUM
ejpam-6473	762	3	]	]	PUNCT
ejpam-6473	762	4	t.	t.	NOUN
ejpam-6473	762	5	mathivanan	mathivanan	PROPN
ejpam-6473	762	6	,	,	PUNCT
ejpam-6473	762	7	r.	r.	PROPN
ejpam-6473	762	8	bheeman	bheeman	PROPN
ejpam-6473	762	9	,	,	PUNCT
ejpam-6473	762	10	p.	p.	PROPN
ejpam-6473	762	11	b.	b.	PROPN
ejpam-6473	762	12	dhandapani	dhandapani	PROPN
ejpam-6473	762	13	,	,	PUNCT
ejpam-6473	762	14	i.	i.	NOUN
ejpam-6473	762	15	alraddadi	alraddadi	PROPN
ejpam-6473	762	16	,	,	PUNCT
ejpam-6473	762	17	h.	h.	PROPN
ejpam-6473	762	18	ahmad	ahmad	PROPN
ejpam-6473	762	19	,	,	PUNCT
ejpam-6473	762	20	and	and	CCONJ
ejpam-6473	762	21	t.	t.	NOUN
ejpam-6473	762	22	radwan	radwan	NOUN
ejpam-6473	762	23	.	.	PUNCT
ejpam-6473	763	1	monkeypox	monkeypox	PROPN
ejpam-6473	763	2	:	:	PUNCT
ejpam-6473	763	3	a	a	DET
ejpam-6473	763	4	new	new	ADJ
ejpam-6473	763	5	mathematical	mathematical	ADJ
ejpam-6473	763	6	model	model	NOUN
ejpam-6473	763	7	using	use	VERB
ejpam-6473	763	8	the	the	DET
ejpam-6473	763	9	caputo	caputo	PROPN
ejpam-6473	763	10	-	-	PUNCT
ejpam-6473	763	11	fabrizio	fabrizio	PROPN
ejpam-6473	763	12	fractional	fractional	ADJ
ejpam-6473	763	13	derivative	derivative	NOUN
ejpam-6473	763	14	.	.	PUNCT
ejpam-6473	764	1	fractals	fractal	NOUN
ejpam-6473	764	2	,	,	PUNCT
ejpam-6473	764	3	page	page	NOUN
ejpam-6473	764	4	2540128	2540128	NUM
ejpam-6473	764	5	,	,	PUNCT
ejpam-6473	764	6	2025	2025	NUM
ejpam-6473	764	7	.	.	PUNCT
ejpam-6473	765	1	[	[	X
ejpam-6473	765	2	19	19	NUM
ejpam-6473	765	3	]	]	X
ejpam-6473	765	4	p.	p.	PROPN
ejpam-6473	765	5	r.	r.	PROPN
ejpam-6473	765	6	murugadoss	murugadoss	PROPN
ejpam-6473	765	7	,	,	PUNCT
ejpam-6473	765	8	v.	v.	ADP
ejpam-6473	765	9	ambalarajan	ambalarajan	NOUN
ejpam-6473	765	10	,	,	PUNCT
ejpam-6473	765	11	v.	v.	PROPN
ejpam-6473	765	12	sivakumar	sivakumar	PROPN
ejpam-6473	765	13	,	,	PUNCT
ejpam-6473	765	14	p.	p.	PROPN
ejpam-6473	765	15	b.	b.	PROPN
ejpam-6473	765	16	dhandapani	dhandapani	PROPN
ejpam-6473	765	17	,	,	PUNCT
ejpam-6473	765	18	and	and	CCONJ
ejpam-6473	765	19	d.	d.	PROPN
ejpam-6473	765	20	baleanu	baleanu	PROPN
ejpam-6473	765	21	.	.	PUNCT
ejpam-6473	766	1	analysis	analysis	NOUN
ejpam-6473	766	2	of	of	ADP
ejpam-6473	766	3	dengue	dengue	NOUN
ejpam-6473	766	4	transmission	transmission	NOUN
ejpam-6473	766	5	dynamic	dynamic	ADJ
ejpam-6473	766	6	model	model	NOUN
ejpam-6473	766	7	by	by	ADP
ejpam-6473	766	8	stability	stability	NOUN
ejpam-6473	766	9	and	and	CCONJ
ejpam-6473	766	10	hopf	hopf	ADJ
ejpam-6473	766	11	bifurcation	bifurcation	NOUN
ejpam-6473	766	12	with	with	ADP
ejpam-6473	766	13	two	two	NUM
ejpam-6473	766	14	-	-	PUNCT
ejpam-6473	766	15	time	time	NOUN
ejpam-6473	766	16	delays	delay	NOUN
ejpam-6473	766	17	.	.	PUNCT
ejpam-6473	767	1	frontiers	frontier	NOUN
ejpam-6473	767	2	in	in	ADP
ejpam-6473	767	3	bioscience	bioscience	NOUN
ejpam-6473	767	4	-	-	PUNCT
ejpam-6473	767	5	landmark	landmark	NOUN
ejpam-6473	767	6	,	,	PUNCT
ejpam-6473	767	7	28(6):117	28(6):117	NUM
ejpam-6473	767	8	,	,	PUNCT
ejpam-6473	767	9	2023	2023	NUM
ejpam-6473	767	10	.	.	PUNCT
ejpam-6473	768	1	[	[	X
ejpam-6473	768	2	20	20	NUM
ejpam-6473	768	3	]	]	X
ejpam-6473	768	4	c.	c.	PROPN
ejpam-6473	768	5	castillo	castillo	PROPN
ejpam-6473	768	6	-	-	PUNCT
ejpam-6473	768	7	garsow	garsow	PROPN
ejpam-6473	768	8	,	,	PUNCT
ejpam-6473	768	9	g.	g.	PROPN
ejpam-6473	768	10	jordan	jordan	PROPN
ejpam-6473	768	11	-	-	PUNCT
ejpam-6473	768	12	salivia	salivia	PROPN
ejpam-6473	768	13	,	,	PUNCT
ejpam-6473	768	14	and	and	CCONJ
ejpam-6473	768	15	a.	a.	NOUN
ejpam-6473	768	16	rodriguez	rodriguez	PROPN
ejpam-6473	768	17	-	-	PUNCT
ejpam-6473	768	18	herrera	herrera	NOUN
ejpam-6473	768	19	.	.	PUNCT
ejpam-6473	769	1	mathematical	mathematical	ADJ
ejpam-6473	769	2	models	model	NOUN
ejpam-6473	769	3	for	for	ADP
ejpam-6473	769	4	the	the	DET
ejpam-6473	769	5	dynamics	dynamic	NOUN
ejpam-6473	769	6	of	of	ADP
ejpam-6473	769	7	tobacco	tobacco	NOUN
ejpam-6473	769	8	use	use	NOUN
ejpam-6473	769	9	,	,	PUNCT
ejpam-6473	769	10	recovery	recovery	NOUN
ejpam-6473	769	11	and	and	CCONJ
ejpam-6473	769	12	relapse	relapse	NOUN
ejpam-6473	769	13	.	.	PUNCT
ejpam-6473	770	1	1997	1997	NUM
ejpam-6473	770	2	.	.	PUNCT
ejpam-6473	771	1	[	[	X
ejpam-6473	771	2	21	21	NUM
ejpam-6473	771	3	]	]	X
ejpam-6473	771	4	g.	g.	PROPN
ejpam-6473	771	5	zaman	zaman	PROPN
ejpam-6473	771	6	.	.	PUNCT
ejpam-6473	771	7	qualitative	qualitative	ADJ
ejpam-6473	771	8	behavior	behavior	NOUN
ejpam-6473	771	9	of	of	ADP
ejpam-6473	771	10	giving	give	VERB
ejpam-6473	771	11	up	up	ADP
ejpam-6473	771	12	smoking	smoking	NOUN
ejpam-6473	771	13	models	model	NOUN
ejpam-6473	771	14	.	.	PUNCT
ejpam-6473	772	1	bulletin	bulletin	NOUN
ejpam-6473	772	2	of	of	ADP
ejpam-6473	772	3	the	the	DET
ejpam-6473	772	4	malaysian	malaysian	PROPN
ejpam-6473	772	5	mathematical	mathematical	PROPN
ejpam-6473	772	6	sciences	sciences	PROPN
ejpam-6473	772	7	society	society	NOUN
ejpam-6473	772	8	.	.	PUNCT
ejpam-6473	773	1	second	second	ADJ
ejpam-6473	773	2	series	series	NOUN
ejpam-6473	773	3	,	,	PUNCT
ejpam-6473	773	4	34(2):403–415	34(2):403–415	PROPN
ejpam-6473	773	5	,	,	PUNCT
ejpam-6473	773	6	2011	2011	NUM
ejpam-6473	773	7	.	.	PUNCT
ejpam-6473	774	1	[	[	X
ejpam-6473	774	2	22	22	NUM
ejpam-6473	774	3	]	]	X
ejpam-6473	774	4	o.	o.	PROPN
ejpam-6473	774	5	khyar	khyar	PROPN
ejpam-6473	774	6	,	,	PUNCT
ejpam-6473	774	7	j.	j.	PROPN
ejpam-6473	774	8	danane	danane	PROPN
ejpam-6473	774	9	,	,	PUNCT
ejpam-6473	774	10	and	and	CCONJ
ejpam-6473	774	11	k.	k.	PROPN
ejpam-6473	774	12	allali	allali	PROPN
ejpam-6473	774	13	.	.	PUNCT
ejpam-6473	775	1	mathematical	mathematical	ADJ
ejpam-6473	775	2	analysis	analysis	NOUN
ejpam-6473	775	3	and	and	CCONJ
ejpam-6473	775	4	optimal	optimal	ADJ
ejpam-6473	775	5	control	control	NOUN
ejpam-6473	775	6	of	of	ADP
ejpam-6473	775	7	giving	give	VERB
ejpam-6473	775	8	up	up	ADP
ejpam-6473	775	9	smoking	smoking	NOUN
ejpam-6473	775	10	model	model	NOUN
ejpam-6473	775	11	.	.	PUNCT
ejpam-6473	776	1	international	international	ADJ
ejpam-6473	776	2	journal	journal	PROPN
ejpam-6473	776	3	of	of	ADP
ejpam-6473	776	4	differential	differential	ADJ
ejpam-6473	776	5	equations	equation	NOUN
ejpam-6473	776	6	,	,	PUNCT
ejpam-6473	776	7	2021(1):8673020	2021(1):8673020	NUM
ejpam-6473	776	8	,	,	PUNCT
ejpam-6473	776	9	2021	2021	NUM
ejpam-6473	776	10	.	.	PUNCT
ejpam-6473	777	1	[	[	X
ejpam-6473	777	2	23	23	NUM
ejpam-6473	777	3	]	]	PUNCT
ejpam-6473	777	4	j.	j.	PROPN
ejpam-6473	777	5	singh	singh	PROPN
ejpam-6473	777	6	,	,	PUNCT
ejpam-6473	777	7	d.	d.	PROPN
ejpam-6473	777	8	kumar	kumar	PROPN
ejpam-6473	777	9	,	,	PUNCT
ejpam-6473	777	10	m.	m.	NOUN
ejpam-6473	777	11	a.	a.	NOUN
ejpam-6473	777	12	qurashi	qurashi	PROPN
ejpam-6473	777	13	,	,	PUNCT
ejpam-6473	777	14	and	and	CCONJ
ejpam-6473	777	15	d.	d.	PROPN
ejpam-6473	777	16	baleanu	baleanu	PROPN
ejpam-6473	777	17	.	.	PUNCT
ejpam-6473	778	1	a	a	DET
ejpam-6473	778	2	fractional	fractional	ADJ
ejpam-6473	778	3	model	model	NOUN
ejpam-6473	778	4	for	for	ADP
ejpam-6473	778	5	giving	give	VERB
ejpam-6473	778	6	up	up	ADP
ejpam-6473	778	7	smoking	smoking	NOUN
ejpam-6473	778	8	dynamics	dynamic	NOUN
ejpam-6473	778	9	.	.	PUNCT
ejpam-6473	779	1	advances	advance	NOUN
ejpam-6473	779	2	in	in	ADP
ejpam-6473	779	3	difference	difference	NOUN
ejpam-6473	779	4	equations	equation	NOUN
ejpam-6473	779	5	,	,	PUNCT
ejpam-6473	779	6	2017:1–16	2017:1–16	NUM
ejpam-6473	779	7	,	,	PUNCT
ejpam-6473	779	8	2017	2017	NUM
ejpam-6473	779	9	.	.	PUNCT
ejpam-6473	780	1	[	[	X
ejpam-6473	780	2	24	24	NUM
ejpam-6473	780	3	]	]	X
ejpam-6473	780	4	o.	o.	NOUN
ejpam-6473	780	5	sharomi	sharomi	PROPN
ejpam-6473	780	6	and	and	CCONJ
ejpam-6473	780	7	a.	a.	PROPN
ejpam-6473	780	8	b.	b.	PROPN
ejpam-6473	780	9	gumel	gumel	PROPN
ejpam-6473	780	10	.	.	PUNCT
ejpam-6473	781	1	curtailing	curtail	VERB
ejpam-6473	781	2	smoking	smoking	NOUN
ejpam-6473	781	3	dynamics	dynamic	NOUN
ejpam-6473	781	4	:	:	PUNCT
ejpam-6473	781	5	a	a	DET
ejpam-6473	781	6	mathematical	mathematical	ADJ
ejpam-6473	781	7	modeling	modeling	NOUN
ejpam-6473	781	8	approach	approach	NOUN
ejpam-6473	781	9	.	.	PUNCT
ejpam-6473	782	1	applied	apply	VERB
ejpam-6473	782	2	mathematics	mathematic	NOUN
ejpam-6473	782	3	and	and	CCONJ
ejpam-6473	782	4	computation	computation	NOUN
ejpam-6473	782	5	,	,	PUNCT
ejpam-6473	782	6	195(2):475–499	195(2):475–499	NUM
ejpam-6473	782	7	,	,	PUNCT
ejpam-6473	782	8	2008	2008	NUM
ejpam-6473	782	9	.	.	PUNCT
ejpam-6473	783	1	[	[	X
ejpam-6473	783	2	25	25	NUM
ejpam-6473	783	3	]	]	PUNCT
ejpam-6473	783	4	a.	a.	NOUN
ejpam-6473	783	5	zeb	zeb	PROPN
ejpam-6473	783	6	,	,	PUNCT
ejpam-6473	783	7	m.	m.	PROPN
ejpam-6473	783	8	i.	i.	PROPN
ejpam-6473	783	9	chohan	chohan	PROPN
ejpam-6473	783	10	,	,	PUNCT
ejpam-6473	783	11	and	and	CCONJ
ejpam-6473	783	12	g.	g.	PROPN
ejpam-6473	783	13	zaman	zaman	PROPN
ejpam-6473	783	14	.	.	PUNCT
ejpam-6473	784	1	the	the	DET
ejpam-6473	784	2	homotopic	homotopic	ADJ
ejpam-6473	784	3	analysis	analysis	NOUN
ejpam-6473	784	4	method	method	NOUN
ejpam-6473	784	5	for	for	ADP
ejpam-6473	784	6	approximating	approximate	VERB
ejpam-6473	784	7	of	of	ADP
ejpam-6473	784	8	giving	give	VERB
ejpam-6473	784	9	up	up	ADP
ejpam-6473	784	10	smoking	smoking	NOUN
ejpam-6473	784	11	model	model	NOUN
ejpam-6473	784	12	in	in	ADP
ejpam-6473	784	13	fractional	fractional	ADJ
ejpam-6473	784	14	order	order	NOUN
ejpam-6473	784	15	.	.	PUNCT
ejpam-6473	785	1	scientific	scientific	ADJ
ejpam-6473	785	2	research	research	NOUN
ejpam-6473	785	3	publishing	publishing	NOUN
ejpam-6473	785	4	,	,	PUNCT
ejpam-6473	785	5	2012	2012	NUM
ejpam-6473	785	6	.	.	PUNCT
ejpam-6473	786	1	[	[	X
ejpam-6473	786	2	26	26	NUM
ejpam-6473	786	3	]	]	X
ejpam-6473	786	4	d.	d.	PROPN
ejpam-6473	786	5	p.	p.	PROPN
ejpam-6473	786	6	gao	gao	PROPN
ejpam-6473	786	7	,	,	PUNCT
ejpam-6473	786	8	n.	n.	PROPN
ejpam-6473	786	9	j.	j.	PROPN
ejpam-6473	786	10	huang	huang	PROPN
ejpam-6473	786	11	,	,	PUNCT
ejpam-6473	786	12	s.	s.	PROPN
ejpam-6473	786	13	m.	m.	PROPN
ejpam-6473	786	14	kang	kang	PROPN
ejpam-6473	786	15	,	,	PUNCT
ejpam-6473	786	16	and	and	CCONJ
ejpam-6473	786	17	c.	c.	PROPN
ejpam-6473	786	18	zhang	zhang	PROPN
ejpam-6473	786	19	.	.	PUNCT
ejpam-6473	787	1	global	global	ADJ
ejpam-6473	787	2	stability	stability	NOUN
ejpam-6473	787	3	analysis	analysis	NOUN
ejpam-6473	787	4	of	of	ADP
ejpam-6473	787	5	an	an	DET
ejpam-6473	787	6	sveir	sveir	ADJ
ejpam-6473	787	7	epidemic	epidemic	NOUN
ejpam-6473	787	8	model	model	NOUN
ejpam-6473	787	9	with	with	ADP
ejpam-6473	787	10	general	general	ADJ
ejpam-6473	787	11	incidence	incidence	NOUN
ejpam-6473	787	12	rate	rate	NOUN
ejpam-6473	787	13	.	.	PUNCT
ejpam-6473	788	1	boundary	boundary	ADJ
ejpam-6473	788	2	value	value	NOUN
ejpam-6473	788	3	problems	problem	NOUN
ejpam-6473	788	4	,	,	PUNCT
ejpam-6473	788	5	2018(1):42	2018(1):42	NUM
ejpam-6473	788	6	,	,	PUNCT
ejpam-6473	788	7	2018	2018	NUM
ejpam-6473	788	8	.	.	PUNCT
ejpam-6473	789	1	[	[	X
ejpam-6473	789	2	27	27	NUM
ejpam-6473	789	3	]	]	PUNCT
ejpam-6473	789	4	m.	m.	NOUN
ejpam-6473	789	5	y.	y.	PROPN
ejpam-6473	789	6	li	li	PROPN
ejpam-6473	789	7	and	and	CCONJ
ejpam-6473	789	8	j.	j.	PROPN
ejpam-6473	789	9	s.	s.	PROPN
ejpam-6473	789	10	muldowney	muldowney	PROPN
ejpam-6473	789	11	.	.	PUNCT
ejpam-6473	790	1	a	a	DET
ejpam-6473	790	2	geometric	geometric	ADJ
ejpam-6473	790	3	approach	approach	NOUN
ejpam-6473	790	4	to	to	ADP
ejpam-6473	790	5	global	global	ADJ
ejpam-6473	790	6	-	-	PUNCT
ejpam-6473	790	7	stability	stability	NOUN
ejpam-6473	790	8	problems	problem	NOUN
ejpam-6473	790	9	.	.	PUNCT
ejpam-6473	791	1	siam	siam	PROPN
ejpam-6473	791	2	journal	journal	PROPN
ejpam-6473	791	3	on	on	ADP
ejpam-6473	791	4	mathematical	mathematical	ADJ
ejpam-6473	791	5	analysis	analysis	NOUN
ejpam-6473	791	6	,	,	PUNCT
ejpam-6473	791	7	27(4):1070–1083	27(4):1070–1083	NUM
ejpam-6473	791	8	,	,	PUNCT
ejpam-6473	791	9	1996	1996	NUM
ejpam-6473	791	10	.	.	PUNCT
ejpam-6473	792	1	[	[	X
ejpam-6473	792	2	28	28	NUM
ejpam-6473	792	3	]	]	X
ejpam-6473	792	4	d.	d.	PROPN
ejpam-6473	792	5	l.	l.	PROPN
ejpam-6473	792	6	lukes	lukes	PROPN
ejpam-6473	792	7	.	.	PUNCT
ejpam-6473	793	1	differential	differential	ADJ
ejpam-6473	793	2	equations	equation	NOUN
ejpam-6473	793	3	:	:	PUNCT
ejpam-6473	793	4	classical	classical	ADJ
ejpam-6473	793	5	to	to	ADP
ejpam-6473	793	6	controlled	control	VERB
ejpam-6473	793	7	,	,	PUNCT
ejpam-6473	793	8	volume	volume	NOUN
ejpam-6473	793	9	162	162	NUM
ejpam-6473	793	10	of	of	ADP
ejpam-6473	793	11	mathematics	mathematic	NOUN
ejpam-6473	793	12	in	in	ADP
ejpam-6473	793	13	science	science	NOUN
ejpam-6473	793	14	and	and	CCONJ
ejpam-6473	793	15	engineering	engineering	NOUN
ejpam-6473	793	16	.	.	PUNCT
ejpam-6473	794	1	academic	academic	ADJ
ejpam-6473	794	2	press	press	NOUN
ejpam-6473	794	3	,	,	PUNCT
ejpam-6473	794	4	new	new	PROPN
ejpam-6473	794	5	york	york	PROPN
ejpam-6473	794	6	,	,	PUNCT
ejpam-6473	794	7	ny	ny	PROPN
ejpam-6473	794	8	,	,	PUNCT
ejpam-6473	794	9	usa	usa	PROPN
ejpam-6473	794	10	,	,	PUNCT
ejpam-6473	794	11	1982	1982	NUM
ejpam-6473	794	12	.	.	PUNCT
ejpam-6473	795	1	[	[	X
ejpam-6473	795	2	29	29	NUM
ejpam-6473	795	3	]	]	PUNCT
ejpam-6473	795	4	s.	s.	PROPN
ejpam-6473	795	5	s.	s.	PROPN
ejpam-6473	795	6	alzaid	alzaid	PROPN
ejpam-6473	795	7	and	and	CCONJ
ejpam-6473	795	8	b.	b.	PROPN
ejpam-6473	795	9	s.	s.	PROPN
ejpam-6473	795	10	t.	t.	PROPN
ejpam-6473	795	11	alkahtani	alkahtani	PROPN
ejpam-6473	795	12	.	.	PUNCT
ejpam-6473	796	1	asymptotic	asymptotic	ADJ
ejpam-6473	796	2	analysis	analysis	NOUN
ejpam-6473	796	3	of	of	ADP
ejpam-6473	796	4	a	a	DET
ejpam-6473	796	5	giving	giving	NOUN
ejpam-6473	796	6	up	up	ADP
ejpam-6473	796	7	smoking	smoking	NOUN
ejpam-6473	796	8	model	model	NOUN
ejpam-6473	796	9	with	with	ADP
ejpam-6473	796	10	relapse	relapse	NOUN
ejpam-6473	796	11	and	and	CCONJ
ejpam-6473	796	12	harmonic	harmonic	ADJ
ejpam-6473	796	13	mean	mean	NOUN
ejpam-6473	796	14	type	type	NOUN
ejpam-6473	796	15	incidence	incidence	NOUN
ejpam-6473	796	16	rate	rate	NOUN
ejpam-6473	796	17	.	.	PUNCT
ejpam-6473	797	1	results	result	NOUN
ejpam-6473	797	2	in	in	ADP
ejpam-6473	797	3	physics	physics	NOUN
ejpam-6473	797	4	,	,	PUNCT
ejpam-6473	797	5	28:104437	28:104437	NUM
ejpam-6473	797	6	,	,	PUNCT
ejpam-6473	797	7	2021	2021	NUM
ejpam-6473	797	8	.	.	PUNCT
ejpam-6473	798	1	[	[	X
ejpam-6473	798	2	30	30	NUM
ejpam-6473	798	3	]	]	X
ejpam-6473	798	4	sarah	sarah	PROPN
ejpam-6473	798	5	durkin	durkin	PROPN
ejpam-6473	798	6	,	,	PUNCT
ejpam-6473	798	7	emily	emily	PROPN
ejpam-6473	798	8	brennan	brennan	PROPN
ejpam-6473	798	9	,	,	PUNCT
ejpam-6473	798	10	and	and	CCONJ
ejpam-6473	798	11	melanie	melanie	PROPN
ejpam-6473	798	12	wakefield	wakefield	PROPN
ejpam-6473	798	13	.	.	PUNCT
ejpam-6473	799	1	mass	mass	ADJ
ejpam-6473	799	2	media	medium	NOUN
ejpam-6473	799	3	campaigns	campaign	NOUN
ejpam-6473	799	4	to	to	PART
ejpam-6473	799	5	promote	promote	VERB
ejpam-6473	799	6	smoking	smoking	NOUN
ejpam-6473	799	7	cessation	cessation	NOUN
ejpam-6473	799	8	among	among	ADP
ejpam-6473	799	9	adults	adult	NOUN
ejpam-6473	799	10	:	:	PUNCT
ejpam-6473	799	11	an	an	DET
ejpam-6473	799	12	integrative	integrative	ADJ
ejpam-6473	799	13	review	review	NOUN
ejpam-6473	799	14	.	.	PUNCT
ejpam-6473	799	15	tobacco	tobacco	NOUN
ejpam-6473	799	16	control	control	NOUN
ejpam-6473	799	17	,	,	PUNCT
ejpam-6473	799	18	21(2):127–138	21(2):127–138	PROPN
ejpam-6473	799	19	,	,	PUNCT
ejpam-6473	799	20	2012	2012	NUM
ejpam-6473	799	21	.	.	PUNCT
ejpam-6473	800	1	[	[	X
ejpam-6473	800	2	31	31	NUM
ejpam-6473	800	3	]	]	PUNCT
ejpam-6473	800	4	us	us	PROPN
ejpam-6473	800	5	department	department	PROPN
ejpam-6473	800	6	of	of	ADP
ejpam-6473	800	7	health	health	PROPN
ejpam-6473	800	8	and	and	CCONJ
ejpam-6473	800	9	human	human	ADJ
ejpam-6473	800	10	services	service	NOUN
ejpam-6473	800	11	.	.	PUNCT
ejpam-6473	801	1	preventing	prevent	VERB
ejpam-6473	801	2	tobacco	tobacco	NOUN
ejpam-6473	801	3	use	use	NOUN
ejpam-6473	801	4	among	among	ADP
ejpam-6473	801	5	youth	youth	NOUN
ejpam-6473	801	6	and	and	CCONJ
ejpam-6473	801	7	young	young	ADJ
ejpam-6473	801	8	adults	adult	NOUN
ejpam-6473	801	9	:	:	PUNCT
ejpam-6473	801	10	a	a	DET
ejpam-6473	801	11	report	report	NOUN
ejpam-6473	801	12	of	of	ADP
ejpam-6473	801	13	the	the	DET
ejpam-6473	801	14	surgeon	surgeon	NOUN
ejpam-6473	801	15	general	general	ADJ
ejpam-6473	801	16	.	.	PUNCT
ejpam-6473	802	1	technical	technical	ADJ
ejpam-6473	802	2	report	report	PROPN
ejpam-6473	802	3	,	,	PUNCT
ejpam-6473	802	4	2012	2012	NUM
ejpam-6473	802	5	.	.	PUNCT
ejpam-6473	803	1	[	[	X
ejpam-6473	803	2	32	32	NUM
ejpam-6473	803	3	]	]	PUNCT
ejpam-6473	803	4	nur	nur	VERB
ejpam-6473	803	5	ilmayasinta	ilmayasinta	NOUN
ejpam-6473	803	6	and	and	CCONJ
ejpam-6473	803	7	heri	heri	NOUN
ejpam-6473	803	8	purnawan	purnawan	NOUN
ejpam-6473	803	9	.	.	PUNCT
ejpam-6473	804	1	optimal	optimal	ADJ
ejpam-6473	804	2	control	control	NOUN
ejpam-6473	804	3	in	in	ADP
ejpam-6473	804	4	a	a	DET
ejpam-6473	804	5	mathematical	mathematical	ADJ
ejpam-6473	804	6	model	model	NOUN
ejpam-6473	804	7	of	of	ADP
ejpam-6473	804	8	smoking	smoking	NOUN
ejpam-6473	804	9	.	.	PUNCT
ejpam-6473	805	1	journal	journal	PROPN
ejpam-6473	805	2	of	of	ADP
ejpam-6473	805	3	mathematical	mathematical	ADJ
ejpam-6473	805	4	and	and	CCONJ
ejpam-6473	805	5	fundamental	fundamental	ADJ
ejpam-6473	805	6	sciences	science	NOUN
ejpam-6473	805	7	,	,	PUNCT
ejpam-6473	805	8	53(3	53(3	NUM
ejpam-6473	805	9	)	)	PUNCT
ejpam-6473	805	10	,	,	PUNCT
ejpam-6473	805	11	2021	2021	NUM
ejpam-6473	805	12	.	.	PUNCT
ejpam-6473	806	1	s.	s.	PROPN
ejpam-6473	806	2	bano	bano	PROPN
ejpam-6473	806	3	et	et	PROPN
ejpam-6473	806	4	al	al	PROPN
ejpam-6473	806	5	.	.	PUNCT
ejpam-6473	806	6	/	/	SYM
ejpam-6473	806	7	eur	eur	PROPN
ejpam-6473	806	8	.	.	PUNCT
ejpam-6473	807	1	j.	j.	PROPN
ejpam-6473	807	2	pure	pure	PROPN
ejpam-6473	807	3	appl	appl	PROPN
ejpam-6473	807	4	.	.	PROPN
ejpam-6473	807	5	math	math	PROPN
ejpam-6473	807	6	,	,	PUNCT
ejpam-6473	807	7	18	18	NUM
ejpam-6473	807	8	(	(	PUNCT
ejpam-6473	807	9	4	4	NUM
ejpam-6473	807	10	)	)	PUNCT
ejpam-6473	807	11	(	(	PUNCT
ejpam-6473	807	12	2025	2025	NUM
ejpam-6473	807	13	)	)	PUNCT
ejpam-6473	807	14	,	,	PUNCT
ejpam-6473	807	15	6473	6473	NUM
ejpam-6473	807	16	38	38	NUM
ejpam-6473	807	17	of	of	ADP
ejpam-6473	807	18	38	38	NUM
ejpam-6473	807	19	[	[	SYM
ejpam-6473	807	20	33	33	NUM
ejpam-6473	807	21	]	]	X
ejpam-6473	807	22	da	da	PROPN
ejpam-6473	807	23	-	-	PUNCT
ejpam-6473	807	24	peng	peng	PROPN
ejpam-6473	807	25	gao	gao	PROPN
ejpam-6473	807	26	and	and	CCONJ
ejpam-6473	807	27	nan	nan	PROPN
ejpam-6473	807	28	-	-	PROPN
ejpam-6473	807	29	jing	jing	PROPN
ejpam-6473	807	30	huang	huang	PROPN
ejpam-6473	807	31	.	.	PUNCT
ejpam-6473	808	1	optimal	optimal	ADJ
ejpam-6473	808	2	control	control	NOUN
ejpam-6473	808	3	analysis	analysis	NOUN
ejpam-6473	808	4	of	of	ADP
ejpam-6473	808	5	a	a	DET
ejpam-6473	808	6	tuberculosis	tuberculosis	NOUN
ejpam-6473	808	7	model	model	NOUN
ejpam-6473	808	8	.	.	PUNCT
ejpam-6473	809	1	applied	apply	VERB
ejpam-6473	809	2	mathematical	mathematical	ADJ
ejpam-6473	809	3	modelling	modelling	NOUN
ejpam-6473	809	4	,	,	PUNCT
ejpam-6473	809	5	58:46–64	58:46–64	NUM
ejpam-6473	809	6	,	,	PUNCT
ejpam-6473	809	7	2018	2018	NUM
ejpam-6473	809	8	.	.	PUNCT
ejpam-6473	810	1	[	[	X
ejpam-6473	810	2	34	34	NUM
ejpam-6473	810	3	]	]	X
ejpam-6473	810	4	yinggao	yinggao	NOUN
ejpam-6473	810	5	zhou	zhou	PROPN
ejpam-6473	810	6	,	,	PUNCT
ejpam-6473	810	7	yiting	yiting	PROPN
ejpam-6473	810	8	liang	liang	PROPN
ejpam-6473	810	9	,	,	PUNCT
ejpam-6473	810	10	and	and	CCONJ
ejpam-6473	810	11	jianhong	jianhong	PROPN
ejpam-6473	810	12	wu	wu	PROPN
ejpam-6473	810	13	.	.	PUNCT
ejpam-6473	811	1	an	an	DET
ejpam-6473	811	2	optimal	optimal	ADJ
ejpam-6473	811	3	strategy	strategy	NOUN
ejpam-6473	811	4	for	for	ADP
ejpam-6473	811	5	hiv	hiv	PROPN
ejpam-6473	811	6	multitherapy	multitherapy	PROPN
ejpam-6473	811	7	.	.	PUNCT
ejpam-6473	812	1	journal	journal	PROPN
ejpam-6473	812	2	of	of	ADP
ejpam-6473	812	3	computational	computational	ADJ
ejpam-6473	812	4	and	and	CCONJ
ejpam-6473	812	5	applied	applied	ADJ
ejpam-6473	812	6	mathematics	mathematic	NOUN
ejpam-6473	812	7	,	,	PUNCT
ejpam-6473	812	8	263:326–337	263:326–337	NUM
ejpam-6473	812	9	,	,	PUNCT
ejpam-6473	812	10	2014	2014	NUM
ejpam-6473	812	11	.	.	PUNCT
ejpam-6473	813	1	[	[	X
ejpam-6473	813	2	35	35	NUM
ejpam-6473	813	3	]	]	X
ejpam-6473	813	4	haojie	haojie	PROPN
ejpam-6473	813	5	yang	yang	PROPN
ejpam-6473	813	6	,	,	PUNCT
ejpam-6473	813	7	yougang	yougang	PROPN
ejpam-6473	813	8	wang	wang	PROPN
ejpam-6473	813	9	,	,	PUNCT
ejpam-6473	813	10	soumen	soumen	PROPN
ejpam-6473	813	11	kundu	kundu	PROPN
ejpam-6473	813	12	,	,	PUNCT
ejpam-6473	813	13	zhiqiang	zhiqiang	PROPN
ejpam-6473	813	14	song	song	NOUN
ejpam-6473	813	15	,	,	PUNCT
ejpam-6473	813	16	and	and	CCONJ
ejpam-6473	813	17	zizhen	zizhen	PROPN
ejpam-6473	813	18	zhang	zhang	PROPN
ejpam-6473	813	19	.	.	PUNCT
ejpam-6473	814	1	dynamics	dynamic	NOUN
ejpam-6473	814	2	of	of	ADP
ejpam-6473	814	3	an	an	DET
ejpam-6473	814	4	sir	sir	NOUN
ejpam-6473	814	5	epidemic	epidemic	NOUN
ejpam-6473	814	6	model	model	NOUN
ejpam-6473	814	7	incorporating	incorporate	VERB
ejpam-6473	814	8	time	time	NOUN
ejpam-6473	814	9	delay	delay	NOUN
ejpam-6473	814	10	and	and	CCONJ
ejpam-6473	814	11	convex	convex	VERB
ejpam-6473	814	12	incidence	incidence	NOUN
ejpam-6473	814	13	rate	rate	NOUN
ejpam-6473	814	14	.	.	PUNCT
ejpam-6473	815	1	results	result	NOUN
ejpam-6473	815	2	in	in	ADP
ejpam-6473	815	3	physics	physics	NOUN
ejpam-6473	815	4	,	,	PUNCT
ejpam-6473	815	5	32:105025	32:105025	NUM
ejpam-6473	815	6	,	,	PUNCT
ejpam-6473	815	7	2022	2022	NUM
ejpam-6473	815	8	.	.	PUNCT
ejpam-6473	816	1	appendix	appendix	VERB
ejpam-6473	816	2	a	a	DET
ejpam-6473	816	3	:	:	PUNCT
ejpam-6473	816	4	pseudocode	pseudocode	NOUN
ejpam-6473	816	5	for	for	ADP
ejpam-6473	816	6	numerical	numerical	ADJ
ejpam-6473	816	7	scheme	scheme	NOUN
ejpam-6473	816	8	implementing	implement	VERB
ejpam-6473	816	9	optimal	optimal	ADJ
ejpam-6473	816	10	control	control	NOUN
ejpam-6473	816	11	strategy	strategy	NOUN
ejpam-6473	816	12	algorithm	algorithm	NOUN
ejpam-6473	816	13	1	1	NUM
ejpam-6473	816	14	forward	forward	ADV
ejpam-6473	816	15	-	-	PUNCT
ejpam-6473	816	16	backward	backward	ADJ
ejpam-6473	816	17	sweep	sweep	NOUN
ejpam-6473	816	18	method	method	NOUN
ejpam-6473	816	19	for	for	ADP
ejpam-6473	816	20	optimal	optimal	ADJ
ejpam-6473	816	21	control	control	NOUN
ejpam-6473	816	22	1	1	NUM
ejpam-6473	816	23	:	:	PUNCT
ejpam-6473	816	24	input	input	NOUN
ejpam-6473	816	25	:	:	PUNCT
ejpam-6473	816	26	initial	initial	ADJ
ejpam-6473	816	27	state	state	NOUN
ejpam-6473	816	28	values	value	NOUN
ejpam-6473	816	29	s(0	s(0	PROPN
ejpam-6473	816	30	)	)	PUNCT
ejpam-6473	816	31	,	,	PUNCT
ejpam-6473	816	32	e(0	e(0	NOUN
ejpam-6473	816	33	)	)	PUNCT
ejpam-6473	816	34	,	,	PUNCT
ejpam-6473	816	35	i(0	i(0	PROPN
ejpam-6473	816	36	)	)	PUNCT
ejpam-6473	816	37	,	,	PUNCT
ejpam-6473	816	38	r(0	r(0	PROPN
ejpam-6473	816	39	)	)	PUNCT
ejpam-6473	816	40	,	,	PUNCT
ejpam-6473	816	41	.	.	PUNCT
ejpam-6473	816	42	.	.	PUNCT
ejpam-6473	816	43	.	.	PUNCT
ejpam-6473	817	1	2	2	NUM
ejpam-6473	817	2	:	:	PUNCT
ejpam-6473	817	3	time	time	NOUN
ejpam-6473	817	4	step	step	NOUN
ejpam-6473	817	5	size	size	NOUN
ejpam-6473	817	6	∆t	∆t	PROPN
ejpam-6473	817	7	3	3	NUM
ejpam-6473	817	8	:	:	PUNCT
ejpam-6473	817	9	total	total	ADJ
ejpam-6473	817	10	time	time	NOUN
ejpam-6473	817	11	t	t	PROPN
ejpam-6473	817	12	4	4	NUM
ejpam-6473	817	13	:	:	PUNCT
ejpam-6473	817	14	initial	initial	ADJ
ejpam-6473	817	15	guess	guess	NOUN
ejpam-6473	817	16	for	for	ADP
ejpam-6473	817	17	controls	control	NOUN
ejpam-6473	817	18	u1(t	u1(t	ADP
ejpam-6473	817	19	)	)	PUNCT
ejpam-6473	817	20	,	,	PUNCT
ejpam-6473	817	21	u2(t	u2(t	NOUN
ejpam-6473	817	22	)	)	PUNCT
ejpam-6473	817	23	,	,	PUNCT
ejpam-6473	817	24	.	.	PUNCT
ejpam-6473	817	25	.	.	PUNCT
ejpam-6473	817	26	.	.	PUNCT
ejpam-6473	818	1	,	,	PUNCT
ejpam-6473	818	2	uk(t	uk(t	ADJ
ejpam-6473	818	3	)	)	PUNCT
ejpam-6473	818	4	5	5	NUM
ejpam-6473	818	5	:	:	PUNCT
ejpam-6473	818	6	maximum	maximum	ADJ
ejpam-6473	818	7	number	number	NOUN
ejpam-6473	818	8	of	of	ADP
ejpam-6473	818	9	iterations	iteration	NOUN
ejpam-6473	818	10	nmax	nmax	ADJ
ejpam-6473	818	11	6	6	NUM
ejpam-6473	818	12	:	:	PUNCT
ejpam-6473	818	13	convergence	convergence	NOUN
ejpam-6473	818	14	tolerance	tolerance	NOUN
ejpam-6473	818	15	ε	ε	PROPN
ejpam-6473	818	16	7	7	NUM
ejpam-6473	818	17	:	:	PUNCT
ejpam-6473	818	18	output	output	NOUN
ejpam-6473	818	19	:	:	PUNCT
ejpam-6473	818	20	optimal	optimal	ADJ
ejpam-6473	818	21	state	state	NOUN
ejpam-6473	818	22	trajectories	trajectory	NOUN
ejpam-6473	818	23	s(t	s(t	PROPN
ejpam-6473	818	24	)	)	PUNCT
ejpam-6473	818	25	,	,	PUNCT
ejpam-6473	818	26	e(t	e(t	NOUN
ejpam-6473	818	27	)	)	PUNCT
ejpam-6473	818	28	,	,	PUNCT
ejpam-6473	818	29	i(t	i(t	PROPN
ejpam-6473	818	30	)	)	PUNCT
ejpam-6473	818	31	,	,	PUNCT
ejpam-6473	818	32	r(t	r(t	NOUN
ejpam-6473	818	33	)	)	PUNCT
ejpam-6473	818	34	,	,	PUNCT
ejpam-6473	818	35	.	.	PUNCT
ejpam-6473	818	36	.	.	PUNCT
ejpam-6473	819	1	.	.	PUNCT
ejpam-6473	820	1	8	8	NUM
ejpam-6473	820	2	:	:	PUNCT
ejpam-6473	820	3	optimal	optimal	ADJ
ejpam-6473	820	4	control	control	NOUN
ejpam-6473	820	5	functions	function	NOUN
ejpam-6473	820	6	u∗1(t	u∗1(t	PROPN
ejpam-6473	820	7	)	)	PUNCT
ejpam-6473	820	8	,	,	PUNCT
ejpam-6473	820	9	u	u	NOUN
ejpam-6473	820	10	∗	∗	NOUN
ejpam-6473	820	11	2(t	2(t	NUM
ejpam-6473	820	12	)	)	PUNCT
ejpam-6473	820	13	,	,	PUNCT
ejpam-6473	820	14	.	.	PUNCT
ejpam-6473	820	15	.	.	PUNCT
ejpam-6473	820	16	.	.	PUNCT
ejpam-6473	821	1	,	,	PUNCT
ejpam-6473	821	2	u	u	NOUN
ejpam-6473	821	3	∗	∗	X
ejpam-6473	821	4	k(t	k(t	PROPN
ejpam-6473	821	5	)	)	PUNCT
ejpam-6473	821	6	9	9	NUM
ejpam-6473	821	7	:	:	PUNCT
ejpam-6473	821	8	step	step	NOUN
ejpam-6473	821	9	1	1	NUM
ejpam-6473	821	10	:	:	PUNCT
ejpam-6473	821	11	initialize	initialize	VERB
ejpam-6473	821	12	time	time	NOUN
ejpam-6473	821	13	grid	grid	PROPN
ejpam-6473	821	14	t	t	PROPN
ejpam-6473	821	15	∈	∈	PROPN
ejpam-6473	822	1	[	[	X
ejpam-6473	822	2	0	0	NUM
ejpam-6473	822	3	,	,	PUNCT
ejpam-6473	822	4	t	t	X
ejpam-6473	822	5	]	]	PUNCT
ejpam-6473	822	6	with	with	ADP
ejpam-6473	822	7	step	step	NOUN
ejpam-6473	822	8	size	size	NOUN
ejpam-6473	822	9	∆t	∆t	PROPN
ejpam-6473	822	10	10	10	NUM
ejpam-6473	822	11	:	:	PUNCT
ejpam-6473	822	12	step	step	NOUN
ejpam-6473	822	13	2	2	NUM
ejpam-6473	822	14	:	:	PUNCT
ejpam-6473	822	15	initialize	initialize	VERB
ejpam-6473	822	16	control	control	NOUN
ejpam-6473	822	17	functions	function	NOUN
ejpam-6473	822	18	u1(t	u1(t	ADP
ejpam-6473	822	19	)	)	PUNCT
ejpam-6473	822	20	,	,	PUNCT
ejpam-6473	822	21	u2(t	u2(t	NOUN
ejpam-6473	822	22	)	)	PUNCT
ejpam-6473	822	23	,	,	PUNCT
ejpam-6473	822	24	.	.	PUNCT
ejpam-6473	822	25	.	.	PUNCT
ejpam-6473	823	1	.	.	PUNCT
ejpam-6473	824	1	,	,	PUNCT
ejpam-6473	824	2	uk(t	uk(t	ADJ
ejpam-6473	824	3	)	)	PUNCT
ejpam-6473	824	4	11	11	NUM
ejpam-6473	824	5	:	:	PUNCT
ejpam-6473	824	6	step	step	NOUN
ejpam-6473	824	7	3	3	NUM
ejpam-6473	824	8	:	:	PUNCT
ejpam-6473	824	9	repeat	repeat	VERB
ejpam-6473	824	10	for	for	ADP
ejpam-6473	824	11	n	n	NOUN
ejpam-6473	824	12	=	=	SYM
ejpam-6473	824	13	1	1	NUM
ejpam-6473	824	14	to	to	ADP
ejpam-6473	824	15	nmax	nmax	PROPN
ejpam-6473	824	16	a	a	PRON
ejpam-6473	824	17	)	)	PUNCT
ejpam-6473	824	18	forward	forward	ADV
ejpam-6473	824	19	sweep	sweep	NOUN
ejpam-6473	824	20	:	:	PUNCT
ejpam-6473	824	21	–	–	PUNCT
ejpam-6473	824	22	integrate	integrate	VERB
ejpam-6473	824	23	the	the	DET
ejpam-6473	824	24	state	state	NOUN
ejpam-6473	824	25	system	system	NOUN
ejpam-6473	824	26	using	use	VERB
ejpam-6473	824	27	initial	initial	ADJ
ejpam-6473	824	28	conditions	condition	NOUN
ejpam-6473	824	29	–	–	PUNCT
ejpam-6473	824	30	use	use	VERB
ejpam-6473	824	31	current	current	ADJ
ejpam-6473	824	32	control	control	NOUN
ejpam-6473	824	33	functions	function	NOUN
ejpam-6473	824	34	u1(t	u1(t	ADP
ejpam-6473	824	35	)	)	PUNCT
ejpam-6473	824	36	,	,	PUNCT
ejpam-6473	824	37	.	.	PUNCT
ejpam-6473	824	38	.	.	PUNCT
ejpam-6473	825	1	.	.	PUNCT
ejpam-6473	826	1	,	,	PUNCT
ejpam-6473	826	2	uk(t	uk(t	NOUN
ejpam-6473	826	3	)	)	PUNCT
ejpam-6473	826	4	–	–	PUNCT
ejpam-6473	826	5	solve	solve	VERB
ejpam-6473	826	6	using	use	VERB
ejpam-6473	826	7	a	a	DET
ejpam-6473	826	8	numerical	numerical	ADJ
ejpam-6473	826	9	method	method	NOUN
ejpam-6473	826	10	(	(	PUNCT
ejpam-6473	826	11	e.g.	e.g.	ADV
ejpam-6473	826	12	,	,	PUNCT
ejpam-6473	826	13	4th	4th	ADJ
ejpam-6473	826	14	order	order	NOUN
ejpam-6473	826	15	runge	runge	NOUN
ejpam-6473	826	16	-	-	PUNCT
ejpam-6473	826	17	kutta	kutta	NOUN
ejpam-6473	826	18	)	)	PUNCT
ejpam-6473	826	19	b	b	NOUN
ejpam-6473	826	20	)	)	PUNCT
ejpam-6473	826	21	backward	backward	ADJ
ejpam-6473	826	22	sweep	sweep	NOUN
ejpam-6473	826	23	:	:	PUNCT
ejpam-6473	826	24	–	–	PUNCT
ejpam-6473	826	25	initialize	initialize	VERB
ejpam-6473	826	26	adjoint	adjoint	NOUN
ejpam-6473	826	27	variables	variable	NOUN
ejpam-6473	826	28	λi(t	λi(t	PRON
ejpam-6473	826	29	)	)	PUNCT
ejpam-6473	827	1	=	=	SYM
ejpam-6473	827	2	0	0	PUNCT
ejpam-6473	827	3	–	–	PUNCT
ejpam-6473	827	4	integrate	integrate	VERB
ejpam-6473	827	5	the	the	DET
ejpam-6473	827	6	adjoint	adjoint	NOUN
ejpam-6473	827	7	system	system	NOUN
ejpam-6473	827	8	backward	backward	ADV
ejpam-6473	827	9	in	in	ADP
ejpam-6473	827	10	time	time	NOUN
ejpam-6473	827	11	–	–	PUNCT
ejpam-6473	827	12	use	use	VERB
ejpam-6473	827	13	state	state	NOUN
ejpam-6473	827	14	trajectories	trajectory	NOUN
ejpam-6473	827	15	from	from	ADP
ejpam-6473	827	16	the	the	DET
ejpam-6473	827	17	forward	forward	ADJ
ejpam-6473	827	18	sweep	sweep	NOUN
ejpam-6473	827	19	c	c	NOUN
ejpam-6473	827	20	)	)	PUNCT
ejpam-6473	827	21	control	control	NOUN
ejpam-6473	827	22	update	update	NOUN
ejpam-6473	827	23	:	:	PUNCT
ejpam-6473	827	24	–	–	PUNCT
ejpam-6473	827	25	update	update	NOUN
ejpam-6473	827	26	controls	control	VERB
ejpam-6473	827	27	u1(t	u1(t	PRON
ejpam-6473	827	28	)	)	PUNCT
ejpam-6473	827	29	,	,	PUNCT
ejpam-6473	827	30	.	.	PUNCT
ejpam-6473	827	31	.	.	PUNCT
ejpam-6473	827	32	.	.	PUNCT
ejpam-6473	828	1	,	,	PUNCT
ejpam-6473	828	2	uk(t	uk(t	X
ejpam-6473	828	3	)	)	PUNCT
ejpam-6473	828	4	using	use	VERB
ejpam-6473	828	5	optimality	optimality	NOUN
ejpam-6473	828	6	conditions	condition	NOUN
ejpam-6473	828	7	–	–	PUNCT
ejpam-6473	828	8	apply	apply	VERB
ejpam-6473	828	9	projection	projection	NOUN
ejpam-6473	828	10	if	if	SCONJ
ejpam-6473	828	11	control	control	NOUN
ejpam-6473	828	12	bounds	bound	NOUN
ejpam-6473	828	13	exist	exist	VERB
ejpam-6473	828	14	(	(	PUNCT
ejpam-6473	828	15	e.g.	e.g.	ADV
ejpam-6473	828	16	,	,	PUNCT
ejpam-6473	828	17	0	0	NUM
ejpam-6473	828	18	≤	≤	NUM
ejpam-6473	828	19	u	u	NOUN
ejpam-6473	828	20	≤	≤	NUM
ejpam-6473	828	21	1	1	NUM
ejpam-6473	828	22	)	)	PUNCT
ejpam-6473	828	23	d	d	NOUN
ejpam-6473	828	24	)	)	PUNCT
ejpam-6473	828	25	check	check	VERB
ejpam-6473	828	26	convergence	convergence	NOUN
ejpam-6473	828	27	:	:	PUNCT
ejpam-6473	828	28	–	–	PUNCT
ejpam-6473	828	29	if	if	SCONJ
ejpam-6473	828	30	change	change	NOUN
ejpam-6473	828	31	in	in	ADP
ejpam-6473	828	32	control	control	NOUN
ejpam-6473	828	33	functions	function	NOUN
ejpam-6473	828	34	<	<	X
ejpam-6473	828	35	ε	ε	PROPN
ejpam-6473	828	36	,	,	PUNCT
ejpam-6473	828	37	then	then	ADV
ejpam-6473	828	38	break	break	VERB
ejpam-6473	828	39	loop	loop	NOUN
ejpam-6473	828	40	12	12	NUM
ejpam-6473	828	41	:	:	PUNCT
ejpam-6473	828	42	step	step	NOUN
ejpam-6473	828	43	4	4	NUM
ejpam-6473	828	44	:	:	PUNCT
ejpam-6473	828	45	return	return	VERB
ejpam-6473	828	46	final	final	ADJ
ejpam-6473	828	47	state	state	NOUN
ejpam-6473	828	48	and	and	CCONJ
ejpam-6473	828	49	control	control	NOUN
ejpam-6473	828	50	trajectories	trajectory	NOUN
ejpam-6473	828	51	introduction	introduction	NOUN
ejpam-6473	828	52	model	model	NOUN
ejpam-6473	828	53	formation	formation	NOUN
ejpam-6473	828	54	positivity	positivity	NOUN
ejpam-6473	828	55	and	and	CCONJ
ejpam-6473	828	56	boundedness	boundedness	NOUN
ejpam-6473	828	57	existence	existence	NOUN
ejpam-6473	828	58	of	of	ADP
ejpam-6473	828	59	equilibrium	equilibrium	NOUN
ejpam-6473	828	60	point	point	NOUN
ejpam-6473	828	61	smoking	smoking	NOUN
ejpam-6473	828	62	-	-	PUNCT
ejpam-6473	828	63	free	free	ADJ
ejpam-6473	828	64	equilibrium	equilibrium	NOUN
ejpam-6473	828	65	point	point	NOUN
ejpam-6473	828	66	smoking	smoke	VERB
ejpam-6473	828	67	endemic	endemic	ADJ
ejpam-6473	828	68	equilibrium	equilibrium	NOUN
ejpam-6473	828	69	point	point	NOUN
ejpam-6473	828	70	reproductive	reproductive	ADJ
ejpam-6473	828	71	number	number	NOUN
ejpam-6473	828	72	stability	stability	NOUN
ejpam-6473	828	73	local	local	ADJ
ejpam-6473	828	74	stability	stability	NOUN
ejpam-6473	828	75	global	global	ADJ
ejpam-6473	828	76	stability	stability	NOUN
ejpam-6473	828	77	sensitivity	sensitivity	NOUN
ejpam-6473	828	78	optimal	optimal	ADJ
ejpam-6473	828	79	control	control	NOUN
ejpam-6473	828	80	optimal	optimal	ADJ
ejpam-6473	828	81	control	control	NOUN
ejpam-6473	828	82	existence	existence	PROPN
ejpam-6473	828	83	optimal	optimal	ADJ
ejpam-6473	828	84	control	control	NOUN
ejpam-6473	828	85	characteristic	characteristic	ADJ
ejpam-6473	828	86	of	of	ADP
ejpam-6473	828	87	the	the	DET
ejpam-6473	828	88	plsq	plsq	NOUN
ejpam-6473	828	89	system	system	NOUN
ejpam-6473	828	90	uniqueness	uniqueness	NOUN
ejpam-6473	828	91	of	of	ADP
ejpam-6473	828	92	optimal	optimal	ADJ
ejpam-6473	828	93	control	control	NOUN
ejpam-6473	828	94	system	system	NOUN
ejpam-6473	828	95	delay	delay	VERB
ejpam-6473	828	96	stability	stability	NOUN
ejpam-6473	828	97	analysis	analysis	NOUN
ejpam-6473	828	98	in	in	ADP
ejpam-6473	828	99	the	the	DET
ejpam-6473	828	100	absence	absence	NOUN
ejpam-6473	828	101	of	of	ADP
ejpam-6473	828	102	delay	delay	NOUN
ejpam-6473	828	103	presence	presence	NOUN
ejpam-6473	828	104	of	of	ADP
ejpam-6473	828	105	delay	delay	PROPN
ejpam-6473	828	106	numerical	numerical	PROPN
ejpam-6473	828	107	simulation	simulation	PROPN
ejpam-6473	828	108	discussion	discussion	NOUN
ejpam-6473	828	109	conclusion	conclusion	NOUN