id	sid	tid	token	lemma	pos
ejpam-6007	1	1	european	european	PROPN
ejpam-6007	1	2	journal	journal	PROPN
ejpam-6007	1	3	of	of	ADP
ejpam-6007	1	4	pure	pure	ADJ
ejpam-6007	1	5	and	and	CCONJ
ejpam-6007	1	6	applied	applied	ADJ
ejpam-6007	1	7	mathematics	mathematic	NOUN
ejpam-6007	1	8	2025	2025	NUM
ejpam-6007	1	9	,	,	PUNCT
ejpam-6007	1	10	vol	vol	NOUN
ejpam-6007	1	11	.	.	PROPN
ejpam-6007	1	12	18	18	NUM
ejpam-6007	1	13	,	,	PUNCT
ejpam-6007	1	14	issue	issue	NOUN
ejpam-6007	1	15	4	4	NUM
ejpam-6007	1	16	,	,	PUNCT
ejpam-6007	1	17	article	article	NOUN
ejpam-6007	1	18	number	number	NOUN
ejpam-6007	1	19	6007	6007	NUM
ejpam-6007	1	20	issn	issn	PROPN
ejpam-6007	1	21	1307	1307	NUM
ejpam-6007	1	22	-	-	SYM
ejpam-6007	1	23	5543	5543	NUM
ejpam-6007	1	24	–	–	PUNCT
ejpam-6007	1	25	ejpam.com	ejpam.com	X
ejpam-6007	1	26	published	publish	VERB
ejpam-6007	1	27	by	by	ADP
ejpam-6007	1	28	new	new	PROPN
ejpam-6007	1	29	york	york	PROPN
ejpam-6007	1	30	business	business	PROPN
ejpam-6007	1	31	global	global	PROPN
ejpam-6007	1	32	a	a	DET
ejpam-6007	1	33	numerical	numerical	ADJ
ejpam-6007	1	34	solution	solution	NOUN
ejpam-6007	1	35	for	for	ADP
ejpam-6007	1	36	nash	nash	PROPN
ejpam-6007	1	37	differential	differential	PROPN
ejpam-6007	1	38	games	game	NOUN
ejpam-6007	1	39	based	base	VERB
ejpam-6007	1	40	on	on	ADP
ejpam-6007	1	41	the	the	DET
ejpam-6007	1	42	runge	runge	NOUN
ejpam-6007	1	43	kutta	kutta	PROPN
ejpam-6007	1	44	4th	4th	ADJ
ejpam-6007	1	45	-	-	PUNCT
ejpam-6007	1	46	order	order	NOUN
ejpam-6007	1	47	method	method	NOUN
ejpam-6007	1	48	abd	abd	PROPN
ejpam-6007	1	49	el	el	PROPN
ejpam-6007	1	50	-	-	PROPN
ejpam-6007	1	51	monem	monem	PROPN
ejpam-6007	1	52	a.	a.	NOUN
ejpam-6007	1	53	megahed1,∗	megahed1,∗	PROPN
ejpam-6007	1	54	,	,	PUNCT
ejpam-6007	1	55	nesreen	nesreen	PROPN
ejpam-6007	1	56	m.	m.	PROPN
ejpam-6007	1	57	kamel1	kamel1	PROPN
ejpam-6007	1	58	,	,	PUNCT
ejpam-6007	1	59	i.	i.	PROPN
ejpam-6007	1	60	m.	m.	PROPN
ejpam-6007	1	61	hanafy2	hanafy2	PROPN
ejpam-6007	1	62	,	,	PUNCT
ejpam-6007	1	63	nora	nora	PROPN
ejpam-6007	1	64	a.	a.	PROPN
ejpam-6007	1	65	omar2	omar2	PROPN
ejpam-6007	1	66	1	1	NUM
ejpam-6007	1	67	department	department	NOUN
ejpam-6007	1	68	of	of	ADP
ejpam-6007	1	69	basic	basic	ADJ
ejpam-6007	1	70	science	science	NOUN
ejpam-6007	1	71	,	,	PUNCT
ejpam-6007	1	72	faculty	faculty	NOUN
ejpam-6007	1	73	of	of	ADP
ejpam-6007	1	74	computers	computer	NOUN
ejpam-6007	1	75	and	and	CCONJ
ejpam-6007	1	76	informatics	informatic	NOUN
ejpam-6007	1	77	,	,	PUNCT
ejpam-6007	1	78	suez	suez	PROPN
ejpam-6007	1	79	canal	canal	PROPN
ejpam-6007	1	80	university	university	PROPN
ejpam-6007	1	81	,	,	PUNCT
ejpam-6007	1	82	ismailia	ismailia	PROPN
ejpam-6007	1	83	41522	41522	NUM
ejpam-6007	1	84	,	,	PUNCT
ejpam-6007	1	85	egypt	egypt	PROPN
ejpam-6007	1	86	2	2	NUM
ejpam-6007	1	87	department	department	NOUN
ejpam-6007	1	88	of	of	ADP
ejpam-6007	1	89	mathematics	mathematic	NOUN
ejpam-6007	1	90	and	and	CCONJ
ejpam-6007	1	91	computer	computer	NOUN
ejpam-6007	1	92	science	science	NOUN
ejpam-6007	1	93	,	,	PUNCT
ejpam-6007	1	94	faculty	faculty	NOUN
ejpam-6007	1	95	of	of	ADP
ejpam-6007	1	96	science	science	NOUN
ejpam-6007	1	97	,	,	PUNCT
ejpam-6007	1	98	port	port	NOUN
ejpam-6007	1	99	said	say	VERB
ejpam-6007	1	100	university	university	NOUN
ejpam-6007	1	101	,	,	PUNCT
ejpam-6007	1	102	egypt	egypt	PROPN
ejpam-6007	1	103	abstract	abstract	PROPN
ejpam-6007	1	104	.	.	PUNCT
ejpam-6007	2	1	in	in	ADP
ejpam-6007	2	2	this	this	DET
ejpam-6007	2	3	paper	paper	NOUN
ejpam-6007	2	4	,	,	PUNCT
ejpam-6007	2	5	we	we	PRON
ejpam-6007	2	6	present	present	VERB
ejpam-6007	2	7	a	a	DET
ejpam-6007	2	8	numerical	numerical	ADJ
ejpam-6007	2	9	solution	solution	NOUN
ejpam-6007	2	10	for	for	ADP
ejpam-6007	2	11	an	an	DET
ejpam-6007	2	12	open	open	ADJ
ejpam-6007	2	13	-	-	PUNCT
ejpam-6007	2	14	loop	loop	NOUN
ejpam-6007	2	15	nash	nash	NOUN
ejpam-6007	2	16	differential	differential	ADJ
ejpam-6007	2	17	game	game	NOUN
ejpam-6007	2	18	modeling	modeling	NOUN
ejpam-6007	2	19	competition	competition	NOUN
ejpam-6007	2	20	between	between	ADP
ejpam-6007	2	21	two	two	NUM
ejpam-6007	2	22	firms	firm	NOUN
ejpam-6007	2	23	.	.	PUNCT
ejpam-6007	3	1	using	use	VERB
ejpam-6007	3	2	the	the	DET
ejpam-6007	3	3	fourth	fourth	ADJ
ejpam-6007	3	4	-	-	PUNCT
ejpam-6007	3	5	order	order	NOUN
ejpam-6007	3	6	runge	runge	NOUN
ejpam-6007	3	7	-	-	PUNCT
ejpam-6007	3	8	kutta	kutta	NOUN
ejpam-6007	3	9	method	method	NOUN
ejpam-6007	3	10	,	,	PUNCT
ejpam-6007	3	11	we	we	PRON
ejpam-6007	3	12	computed	compute	VERB
ejpam-6007	3	13	the	the	DET
ejpam-6007	3	14	numerical	numerical	ADJ
ejpam-6007	3	15	solution	solution	NOUN
ejpam-6007	3	16	and	and	CCONJ
ejpam-6007	3	17	analyzed	analyze	VERB
ejpam-6007	3	18	the	the	DET
ejpam-6007	3	19	stability	stability	NOUN
ejpam-6007	3	20	of	of	ADP
ejpam-6007	3	21	the	the	DET
ejpam-6007	3	22	open	open	ADJ
ejpam-6007	3	23	-	-	PUNCT
ejpam-6007	3	24	loop	loop	NOUN
ejpam-6007	3	25	nash	nash	PROPN
ejpam-6007	3	26	equilibrium	equilibrium	NOUN
ejpam-6007	3	27	.	.	PUNCT
ejpam-6007	4	1	additionally	additionally	ADV
ejpam-6007	4	2	,	,	PUNCT
ejpam-6007	4	3	we	we	PRON
ejpam-6007	4	4	examined	examine	VERB
ejpam-6007	4	5	the	the	DET
ejpam-6007	4	6	uniform	uniform	ADJ
ejpam-6007	4	7	convergence	convergence	NOUN
ejpam-6007	4	8	of	of	ADP
ejpam-6007	4	9	the	the	DET
ejpam-6007	4	10	solution	solution	NOUN
ejpam-6007	4	11	.	.	PUNCT
ejpam-6007	5	1	finally	finally	ADV
ejpam-6007	5	2	,	,	PUNCT
ejpam-6007	5	3	an	an	DET
ejpam-6007	5	4	illustrative	illustrative	ADJ
ejpam-6007	5	5	example	example	NOUN
ejpam-6007	5	6	is	be	AUX
ejpam-6007	5	7	presented	present	VERB
ejpam-6007	5	8	to	to	PART
ejpam-6007	5	9	clarify	clarify	VERB
ejpam-6007	5	10	the	the	DET
ejpam-6007	5	11	results	result	NOUN
ejpam-6007	5	12	,	,	PUNCT
ejpam-6007	5	13	accompanied	accompany	VERB
ejpam-6007	5	14	by	by	ADP
ejpam-6007	5	15	figures	figure	NOUN
ejpam-6007	5	16	to	to	PART
ejpam-6007	5	17	illustrate	illustrate	VERB
ejpam-6007	5	18	the	the	DET
ejpam-6007	5	19	findings	finding	NOUN
ejpam-6007	5	20	.	.	PUNCT
ejpam-6007	6	1	2020	2020	NUM
ejpam-6007	6	2	mathematics	mathematic	NOUN
ejpam-6007	6	3	subject	subject	NOUN
ejpam-6007	6	4	classifications	classification	NOUN
ejpam-6007	6	5	:	:	PUNCT
ejpam-6007	6	6	91a23	91a23	NUM
ejpam-6007	6	7	,	,	PUNCT
ejpam-6007	6	8	49n05	49n05	NUM
ejpam-6007	6	9	,	,	PUNCT
ejpam-6007	6	10	49n70	49n70	NUM
ejpam-6007	6	11	,	,	PUNCT
ejpam-6007	6	12	49n90	49n90	NUM
ejpam-6007	6	13	key	key	ADJ
ejpam-6007	6	14	words	word	NOUN
ejpam-6007	6	15	and	and	CCONJ
ejpam-6007	6	16	phrases	phrase	NOUN
ejpam-6007	6	17	:	:	PUNCT
ejpam-6007	6	18	open	open	ADJ
ejpam-6007	6	19	-	-	PUNCT
ejpam-6007	6	20	loop	loop	NOUN
ejpam-6007	6	21	nash	nash	NOUN
ejpam-6007	6	22	differential	differential	ADJ
ejpam-6007	6	23	game	game	NOUN
ejpam-6007	6	24	,	,	PUNCT
ejpam-6007	6	25	runge	runge	NOUN
ejpam-6007	6	26	-	-	PUNCT
ejpam-6007	6	27	kutta	kutta	NOUN
ejpam-6007	6	28	fourth	fourth	ADJ
ejpam-6007	6	29	-	-	PUNCT
ejpam-6007	6	30	order	order	NOUN
ejpam-6007	6	31	method	method	NOUN
ejpam-6007	6	32	,	,	PUNCT
ejpam-6007	6	33	stability	stability	NOUN
ejpam-6007	6	34	,	,	PUNCT
ejpam-6007	6	35	uniform	uniform	ADJ
ejpam-6007	6	36	convergence	convergence	NOUN
ejpam-6007	6	37	1	1	NUM
ejpam-6007	6	38	.	.	PUNCT
ejpam-6007	7	1	introduction	introduction	NOUN
ejpam-6007	7	2	differential	differential	NOUN
ejpam-6007	7	3	games	game	NOUN
ejpam-6007	7	4	are	be	AUX
ejpam-6007	7	5	a	a	DET
ejpam-6007	7	6	branch	branch	NOUN
ejpam-6007	7	7	of	of	ADP
ejpam-6007	7	8	game	game	NOUN
ejpam-6007	7	9	theory	theory	NOUN
ejpam-6007	7	10	that	that	PRON
ejpam-6007	7	11	focus	focus	VERB
ejpam-6007	7	12	on	on	ADP
ejpam-6007	7	13	studying	study	VERB
ejpam-6007	7	14	and	and	CCONJ
ejpam-6007	7	15	developing	develop	VERB
ejpam-6007	7	16	optimal	optimal	ADJ
ejpam-6007	7	17	control	control	NOUN
ejpam-6007	7	18	strategies	strategy	NOUN
ejpam-6007	7	19	for	for	ADP
ejpam-6007	7	20	dynamic	dynamic	ADJ
ejpam-6007	7	21	systems	system	NOUN
ejpam-6007	7	22	influenced	influence	VERB
ejpam-6007	7	23	by	by	ADP
ejpam-6007	7	24	the	the	DET
ejpam-6007	7	25	decisions	decision	NOUN
ejpam-6007	7	26	of	of	ADP
ejpam-6007	7	27	multiple	multiple	ADJ
ejpam-6007	7	28	players	player	NOUN
ejpam-6007	7	29	[	[	X
ejpam-6007	7	30	1	1	NUM
ejpam-6007	7	31	]	]	PUNCT
ejpam-6007	7	32	.	.	PUNCT
ejpam-6007	8	1	an	an	DET
ejpam-6007	8	2	open	open	ADJ
ejpam-6007	8	3	-	-	PUNCT
ejpam-6007	8	4	loop	loop	NOUN
ejpam-6007	8	5	nash	nash	NOUN
ejpam-6007	8	6	differential	differential	NOUN
ejpam-6007	8	7	game	game	NOUN
ejpam-6007	8	8	is	be	AUX
ejpam-6007	8	9	a	a	DET
ejpam-6007	8	10	specific	specific	ADJ
ejpam-6007	8	11	type	type	NOUN
ejpam-6007	8	12	of	of	ADP
ejpam-6007	8	13	differential	differential	ADJ
ejpam-6007	8	14	game	game	NOUN
ejpam-6007	8	15	in	in	ADP
ejpam-6007	8	16	which	which	PRON
ejpam-6007	8	17	the	the	DET
ejpam-6007	8	18	strategies	strategy	NOUN
ejpam-6007	8	19	of	of	ADP
ejpam-6007	8	20	the	the	DET
ejpam-6007	8	21	players	player	NOUN
ejpam-6007	8	22	depend	depend	VERB
ejpam-6007	8	23	solely	solely	ADV
ejpam-6007	8	24	on	on	ADP
ejpam-6007	8	25	time	time	NOUN
ejpam-6007	8	26	(	(	PUNCT
ejpam-6007	8	27	t	t	NOUN
ejpam-6007	8	28	)	)	PUNCT
ejpam-6007	8	29	rather	rather	ADV
ejpam-6007	8	30	than	than	ADP
ejpam-6007	8	31	the	the	DET
ejpam-6007	8	32	current	current	ADJ
ejpam-6007	8	33	state	state	NOUN
ejpam-6007	8	34	of	of	ADP
ejpam-6007	8	35	the	the	DET
ejpam-6007	8	36	dynamic	dynamic	ADJ
ejpam-6007	8	37	system	system	NOUN
ejpam-6007	8	38	.	.	PUNCT
ejpam-6007	9	1	in	in	ADP
ejpam-6007	9	2	other	other	ADJ
ejpam-6007	9	3	words	word	NOUN
ejpam-6007	9	4	,	,	PUNCT
ejpam-6007	9	5	players	player	NOUN
ejpam-6007	9	6	predefine	predefine	VERB
ejpam-6007	9	7	their	their	PRON
ejpam-6007	9	8	strategies	strategy	NOUN
ejpam-6007	9	9	at	at	ADP
ejpam-6007	9	10	the	the	DET
ejpam-6007	9	11	start	start	NOUN
ejpam-6007	9	12	of	of	ADP
ejpam-6007	9	13	the	the	DET
ejpam-6007	9	14	game	game	NOUN
ejpam-6007	9	15	and	and	CCONJ
ejpam-6007	9	16	do	do	AUX
ejpam-6007	9	17	not	not	PART
ejpam-6007	9	18	update	update	VERB
ejpam-6007	9	19	them	they	PRON
ejpam-6007	9	20	based	base	VERB
ejpam-6007	9	21	on	on	ADP
ejpam-6007	9	22	subsequent	subsequent	ADJ
ejpam-6007	9	23	observations	observation	NOUN
ejpam-6007	9	24	or	or	CCONJ
ejpam-6007	9	25	system	system	NOUN
ejpam-6007	9	26	states	state	NOUN
ejpam-6007	9	27	.	.	PUNCT
ejpam-6007	10	1	in	in	ADP
ejpam-6007	10	2	game	game	NOUN
ejpam-6007	10	3	theory	theory	NOUN
ejpam-6007	10	4	,	,	PUNCT
ejpam-6007	10	5	differential	differential	ADJ
ejpam-6007	10	6	games	game	NOUN
ejpam-6007	10	7	are	be	AUX
ejpam-6007	10	8	used	use	VERB
ejpam-6007	10	9	to	to	PART
ejpam-6007	10	10	model	model	VERB
ejpam-6007	10	11	and	and	CCONJ
ejpam-6007	10	12	analyze	analyze	VERB
ejpam-6007	10	13	conflicts	conflict	NOUN
ejpam-6007	10	14	,	,	PUNCT
ejpam-6007	10	15	such	such	ADJ
ejpam-6007	10	16	as	as	ADP
ejpam-6007	10	17	competition	competition	NOUN
ejpam-6007	10	18	,	,	PUNCT
ejpam-6007	10	19	within	within	ADP
ejpam-6007	10	20	dynamical	dynamical	ADJ
ejpam-6007	10	21	systems	system	NOUN
ejpam-6007	10	22	.	.	PUNCT
ejpam-6007	11	1	differential	differential	ADJ
ejpam-6007	11	2	equations	equation	NOUN
ejpam-6007	11	3	play	play	VERB
ejpam-6007	11	4	a	a	DET
ejpam-6007	11	5	key	key	ADJ
ejpam-6007	11	6	role	role	NOUN
ejpam-6007	11	7	in	in	ADP
ejpam-6007	11	8	many	many	ADJ
ejpam-6007	11	9	applications	application	NOUN
ejpam-6007	11	10	in	in	ADP
ejpam-6007	11	11	physics	physics	NOUN
ejpam-6007	11	12	,	,	PUNCT
ejpam-6007	11	13	engineering	engineering	NOUN
ejpam-6007	11	14	,	,	PUNCT
ejpam-6007	11	15	and	and	CCONJ
ejpam-6007	11	16	the	the	DET
ejpam-6007	11	17	modeling	modeling	NOUN
ejpam-6007	11	18	of	of	ADP
ejpam-6007	11	19	natural	natural	ADJ
ejpam-6007	11	20	phenomena	phenomenon	NOUN
ejpam-6007	11	21	[	[	X
ejpam-6007	11	22	2	2	NUM
ejpam-6007	11	23	]	]	PUNCT
ejpam-6007	11	24	.	.	PUNCT
ejpam-6007	12	1	an	an	DET
ejpam-6007	12	2	effective	effective	ADJ
ejpam-6007	12	3	approach	approach	NOUN
ejpam-6007	12	4	for	for	ADP
ejpam-6007	12	5	solving	solve	VERB
ejpam-6007	12	6	differential	differential	NOUN
ejpam-6007	12	7	games	game	NOUN
ejpam-6007	12	8	is	be	AUX
ejpam-6007	12	9	through	through	ADP
ejpam-6007	12	10	numerical	numerical	ADJ
ejpam-6007	12	11	methods	method	NOUN
ejpam-6007	12	12	.	.	PUNCT
ejpam-6007	13	1	for	for	ADP
ejpam-6007	13	2	example	example	NOUN
ejpam-6007	13	3	,	,	PUNCT
ejpam-6007	13	4	dehghan	dehghan	PROPN
ejpam-6007	13	5	banadaki	banadaki	NOUN
ejpam-6007	13	6	and	and	CCONJ
ejpam-6007	13	7	navidi	navidi	NOUN
ejpam-6007	14	1	[	[	X
ejpam-6007	14	2	3	3	NUM
ejpam-6007	14	3	]	]	PUNCT
ejpam-6007	14	4	studied	study	VERB
ejpam-6007	14	5	open	open	ADJ
ejpam-6007	14	6	-	-	PUNCT
ejpam-6007	14	7	loop	loop	NOUN
ejpam-6007	14	8	nash	nash	NOUN
ejpam-6007	14	9	differential	differential	NOUN
ejpam-6007	14	10	games	game	NOUN
ejpam-6007	14	11	using	use	VERB
ejpam-6007	14	12	∗corresponding	∗corresponde	VERB
ejpam-6007	14	13	author	author	NOUN
ejpam-6007	14	14	.	.	PUNCT
ejpam-6007	15	1	doi	doi	NOUN
ejpam-6007	15	2	:	:	PUNCT
ejpam-6007	15	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6007	https://doi.org/10.29020/nybg.ejpam.v18i4.6007	ADJ
ejpam-6007	15	4	email	email	NOUN
ejpam-6007	15	5	addresses	address	NOUN
ejpam-6007	15	6	:	:	PUNCT
ejpam-6007	15	7	abdelmoneam	abdelmoneam	NOUN
ejpam-6007	15	8	mgahed@ci.suez.edu.eg	mgahed@ci.suez.edu.eg	PROPN
ejpam-6007	15	9	(	(	PUNCT
ejpam-6007	15	10	a.	a.	NOUN
ejpam-6007	15	11	a.	a.	NOUN
ejpam-6007	15	12	megahed	megahe	VERB
ejpam-6007	15	13	)	)	PUNCT
ejpam-6007	15	14	,	,	PUNCT
ejpam-6007	15	15	nesreenmostafakamelbs@ci.suez.edu.eg	nesreenmostafakamelbs@ci.suez.edu.eg	NUM
ejpam-6007	15	16	(	(	PUNCT
ejpam-6007	15	17	n.	n.	PROPN
ejpam-6007	15	18	m.	m.	PROPN
ejpam-6007	15	19	kamel	kamel	PROPN
ejpam-6007	15	20	)	)	PUNCT
ejpam-6007	15	21	,	,	PUNCT
ejpam-6007	15	22	ihanafy@hotmail.com	ihanafy@hotmail.com	PROPN
ejpam-6007	15	23	(	(	PUNCT
ejpam-6007	15	24	i.	i.	PROPN
ejpam-6007	15	25	m.	m.	PROPN
ejpam-6007	15	26	hanafy	hanafy	PROPN
ejpam-6007	15	27	)	)	PUNCT
ejpam-6007	15	28	,	,	PUNCT
ejpam-6007	15	29	noraalaa19862013@gmail.com	noraalaa19862013@gmail.com	X
ejpam-6007	16	1	(	(	PUNCT
ejpam-6007	16	2	n.	n.	NOUN
ejpam-6007	16	3	a.	a.	PROPN
ejpam-6007	16	4	omar	omar	PROPN
ejpam-6007	16	5	)	)	PUNCT
ejpam-6007	16	6	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6007	17	1	1	1	NUM
ejpam-6007	17	2	copyright	copyright	NOUN
ejpam-6007	17	3	:	:	PUNCT
ejpam-6007	17	4	©	©	PROPN
ejpam-6007	17	5	2025	2025	NUM
ejpam-6007	17	6	the	the	DET
ejpam-6007	17	7	author(s	author(s	NOUN
ejpam-6007	17	8	)	)	PUNCT
ejpam-6007	17	9	.	.	PUNCT
ejpam-6007	18	1	(	(	PUNCT
ejpam-6007	18	2	cc	cc	NOUN
ejpam-6007	18	3	by	by	ADP
ejpam-6007	18	4	-	-	PUNCT
ejpam-6007	18	5	nc	nc	PROPN
ejpam-6007	18	6	4.0	4.0	NUM
ejpam-6007	18	7	)	)	PUNCT
ejpam-6007	18	8	a.	a.	NOUN
ejpam-6007	18	9	a.	a.	NOUN
ejpam-6007	18	10	megahed	megahe	VERB
ejpam-6007	18	11	et	et	PROPN
ejpam-6007	18	12	al	al	PROPN
ejpam-6007	18	13	.	.	PUNCT
ejpam-6007	18	14	/	/	SYM
ejpam-6007	18	15	eur	eur	PROPN
ejpam-6007	18	16	.	.	PUNCT
ejpam-6007	19	1	j.	j.	PROPN
ejpam-6007	19	2	pure	pure	PROPN
ejpam-6007	19	3	appl	appl	PROPN
ejpam-6007	19	4	.	.	PROPN
ejpam-6007	19	5	math	math	PROPN
ejpam-6007	19	6	,	,	PUNCT
ejpam-6007	19	7	18	18	NUM
ejpam-6007	19	8	(	(	PUNCT
ejpam-6007	19	9	4	4	NUM
ejpam-6007	19	10	)	)	PUNCT
ejpam-6007	19	11	(	(	PUNCT
ejpam-6007	19	12	2025	2025	NUM
ejpam-6007	19	13	)	)	PUNCT
ejpam-6007	19	14	,	,	PUNCT
ejpam-6007	19	15	6007	6007	NUM
ejpam-6007	19	16	2	2	NUM
ejpam-6007	19	17	of	of	ADP
ejpam-6007	19	18	22	22	NUM
ejpam-6007	19	19	the	the	DET
ejpam-6007	19	20	legendre	legendre	PROPN
ejpam-6007	19	21	tau	tau	PROPN
ejpam-6007	19	22	method	method	NOUN
ejpam-6007	19	23	combined	combine	VERB
ejpam-6007	19	24	with	with	ADP
ejpam-6007	19	25	the	the	DET
ejpam-6007	19	26	fourth	fourth	ADJ
ejpam-6007	19	27	-	-	PUNCT
ejpam-6007	19	28	order	order	NOUN
ejpam-6007	19	29	runge	runge	NOUN
ejpam-6007	19	30	–	–	PUNCT
ejpam-6007	19	31	kutta	kutta	NOUN
ejpam-6007	19	32	method	method	NOUN
ejpam-6007	19	33	.	.	PUNCT
ejpam-6007	20	1	kuvshinov	kuvshinov	NOUN
ejpam-6007	20	2	and	and	CCONJ
ejpam-6007	20	3	osipov	osipov	NOUN
ejpam-6007	21	1	[	[	X
ejpam-6007	21	2	4	4	NUM
ejpam-6007	21	3	]	]	PUNCT
ejpam-6007	21	4	investigated	investigate	VERB
ejpam-6007	21	5	stackelberg	stackelberg	PROPN
ejpam-6007	21	6	solutions	solution	NOUN
ejpam-6007	21	7	for	for	ADP
ejpam-6007	21	8	linear	linear	ADJ
ejpam-6007	21	9	positional	positional	ADJ
ejpam-6007	21	10	differential	differential	NOUN
ejpam-6007	21	11	games	game	NOUN
ejpam-6007	21	12	by	by	ADP
ejpam-6007	21	13	applying	apply	VERB
ejpam-6007	21	14	the	the	DET
ejpam-6007	21	15	polyhedron	polyhedron	NOUN
ejpam-6007	21	16	method	method	NOUN
ejpam-6007	21	17	.	.	PUNCT
ejpam-6007	22	1	megahed	megahe	VERB
ejpam-6007	22	2	et	et	PROPN
ejpam-6007	22	3	al	al	PROPN
ejpam-6007	22	4	.	.	PUNCT
ejpam-6007	23	1	[	[	X
ejpam-6007	23	2	5	5	NUM
ejpam-6007	23	3	]	]	PUNCT
ejpam-6007	23	4	studied	study	VERB
ejpam-6007	23	5	an	an	DET
ejpam-6007	23	6	open	open	ADJ
ejpam-6007	23	7	-	-	PUNCT
ejpam-6007	23	8	loop	loop	NOUN
ejpam-6007	23	9	nash	nash	NOUN
ejpam-6007	23	10	differential	differential	ADJ
ejpam-6007	23	11	game	game	NOUN
ejpam-6007	23	12	and	and	CCONJ
ejpam-6007	23	13	employed	employ	VERB
ejpam-6007	23	14	the	the	DET
ejpam-6007	23	15	picard	picard	NOUN
ejpam-6007	23	16	method	method	NOUN
ejpam-6007	23	17	to	to	PART
ejpam-6007	23	18	approximate	approximate	VERB
ejpam-6007	23	19	the	the	DET
ejpam-6007	23	20	solution	solution	NOUN
ejpam-6007	23	21	of	of	ADP
ejpam-6007	23	22	a	a	DET
ejpam-6007	23	23	model	model	NOUN
ejpam-6007	23	24	describing	describe	VERB
ejpam-6007	23	25	competition	competition	NOUN
ejpam-6007	23	26	between	between	ADP
ejpam-6007	23	27	two	two	NUM
ejpam-6007	23	28	firms	firm	NOUN
ejpam-6007	23	29	,	,	PUNCT
ejpam-6007	23	30	incorporating	incorporate	VERB
ejpam-6007	23	31	market	market	NOUN
ejpam-6007	23	32	share	share	NOUN
ejpam-6007	23	33	,	,	PUNCT
ejpam-6007	23	34	advertising	advertising	NOUN
ejpam-6007	23	35	efforts	effort	NOUN
ejpam-6007	23	36	,	,	PUNCT
ejpam-6007	23	37	and	and	CCONJ
ejpam-6007	23	38	advertising	advertising	NOUN
ejpam-6007	23	39	costs	cost	NOUN
ejpam-6007	23	40	.	.	PUNCT
ejpam-6007	24	1	megahed	megahe	VERB
ejpam-6007	24	2	et	et	PROPN
ejpam-6007	24	3	al	al	PROPN
ejpam-6007	24	4	.	.	PUNCT
ejpam-6007	25	1	[	[	X
ejpam-6007	25	2	6	6	NUM
ejpam-6007	25	3	]	]	PUNCT
ejpam-6007	25	4	studied	study	VERB
ejpam-6007	25	5	a	a	DET
ejpam-6007	25	6	zero	zero	NUM
ejpam-6007	25	7	-	-	PUNCT
ejpam-6007	25	8	sum	sum	NOUN
ejpam-6007	25	9	differential	differential	ADJ
ejpam-6007	25	10	game	game	NOUN
ejpam-6007	25	11	for	for	ADP
ejpam-6007	25	12	modeling	model	VERB
ejpam-6007	25	13	coronavirus	coronavirus	NOUN
ejpam-6007	25	14	dynamics	dynamic	NOUN
ejpam-6007	25	15	,	,	PUNCT
ejpam-6007	25	16	solving	solve	VERB
ejpam-6007	25	17	it	it	PRON
ejpam-6007	25	18	using	use	VERB
ejpam-6007	25	19	the	the	DET
ejpam-6007	25	20	homotopy	homotopy	NOUN
ejpam-6007	25	21	perturbation	perturbation	NOUN
ejpam-6007	25	22	method	method	NOUN
ejpam-6007	25	23	combined	combine	VERB
ejpam-6007	25	24	with	with	ADP
ejpam-6007	25	25	a	a	DET
ejpam-6007	25	26	new	new	ADJ
ejpam-6007	25	27	iterative	iterative	NOUN
ejpam-6007	25	28	approach	approach	NOUN
ejpam-6007	25	29	.	.	PUNCT
ejpam-6007	26	1	the	the	DET
ejpam-6007	26	2	stackelberg	stackelberg	PROPN
ejpam-6007	26	3	differential	differential	ADJ
ejpam-6007	26	4	game	game	NOUN
ejpam-6007	26	5	of	of	ADP
ejpam-6007	26	6	e	e	NOUN
ejpam-6007	26	7	-	-	NOUN
ejpam-6007	26	8	differentiable	differentiable	ADJ
ejpam-6007	26	9	and	and	CCONJ
ejpam-6007	26	10	e	e	ADJ
ejpam-6007	26	11	-	-	ADJ
ejpam-6007	26	12	convex	convex	ADJ
ejpam-6007	26	13	functions	function	NOUN
ejpam-6007	26	14	was	be	AUX
ejpam-6007	26	15	applied	apply	VERB
ejpam-6007	26	16	to	to	ADP
ejpam-6007	26	17	combat	combat	NOUN
ejpam-6007	26	18	terrorism	terrorism	NOUN
ejpam-6007	26	19	,	,	PUNCT
ejpam-6007	26	20	considering	consider	VERB
ejpam-6007	26	21	government	government	NOUN
ejpam-6007	26	22	actions	action	NOUN
ejpam-6007	26	23	[	[	X
ejpam-6007	26	24	7	7	NUM
ejpam-6007	26	25	]	]	PUNCT
ejpam-6007	26	26	.	.	PUNCT
ejpam-6007	27	1	hemeda	hemeda	PROPN
ejpam-6007	28	1	[	[	X
ejpam-6007	28	2	8	8	NUM
ejpam-6007	28	3	]	]	PUNCT
ejpam-6007	28	4	introduced	introduce	VERB
ejpam-6007	28	5	the	the	DET
ejpam-6007	28	6	integral	integral	ADJ
ejpam-6007	28	7	iterative	iterative	NOUN
ejpam-6007	28	8	method	method	NOUN
ejpam-6007	28	9	(	(	PUNCT
ejpam-6007	28	10	iim	iim	NOUN
ejpam-6007	28	11	)	)	PUNCT
ejpam-6007	28	12	,	,	PUNCT
ejpam-6007	28	13	a	a	DET
ejpam-6007	28	14	modification	modification	NOUN
ejpam-6007	28	15	of	of	ADP
ejpam-6007	28	16	the	the	DET
ejpam-6007	28	17	picard	picard	NOUN
ejpam-6007	28	18	method	method	NOUN
ejpam-6007	28	19	,	,	PUNCT
ejpam-6007	28	20	as	as	ADP
ejpam-6007	28	21	a	a	DET
ejpam-6007	28	22	numerical	numerical	ADJ
ejpam-6007	28	23	technique	technique	NOUN
ejpam-6007	28	24	for	for	ADP
ejpam-6007	28	25	solving	solve	VERB
ejpam-6007	28	26	nonlinear	nonlinear	ADJ
ejpam-6007	28	27	integro	integro	ADJ
ejpam-6007	28	28	-	-	PUNCT
ejpam-6007	28	29	differential	differential	NOUN
ejpam-6007	28	30	equations	equation	NOUN
ejpam-6007	28	31	and	and	CCONJ
ejpam-6007	28	32	systems	system	NOUN
ejpam-6007	28	33	.	.	PUNCT
ejpam-6007	29	1	megahed	megahe	VERB
ejpam-6007	29	2	et	et	PROPN
ejpam-6007	29	3	al	al	PROPN
ejpam-6007	29	4	.	.	PUNCT
ejpam-6007	30	1	[	[	X
ejpam-6007	30	2	9	9	NUM
ejpam-6007	30	3	]	]	PUNCT
ejpam-6007	30	4	investigated	investigate	VERB
ejpam-6007	30	5	an	an	DET
ejpam-6007	30	6	open	open	ADJ
ejpam-6007	30	7	-	-	PUNCT
ejpam-6007	30	8	loop	loop	NOUN
ejpam-6007	30	9	nash	nash	NOUN
ejpam-6007	30	10	differential	differential	ADJ
ejpam-6007	30	11	game	game	NOUN
ejpam-6007	30	12	,	,	PUNCT
ejpam-6007	30	13	where	where	SCONJ
ejpam-6007	30	14	they	they	PRON
ejpam-6007	30	15	derived	derive	VERB
ejpam-6007	30	16	the	the	DET
ejpam-6007	30	17	necessary	necessary	ADJ
ejpam-6007	30	18	conditions	condition	NOUN
ejpam-6007	30	19	for	for	ADP
ejpam-6007	30	20	equilibrium	equilibrium	NOUN
ejpam-6007	30	21	and	and	CCONJ
ejpam-6007	30	22	analyzed	analyze	VERB
ejpam-6007	30	23	the	the	DET
ejpam-6007	30	24	existence	existence	NOUN
ejpam-6007	30	25	and	and	CCONJ
ejpam-6007	30	26	uniform	uniform	ADJ
ejpam-6007	30	27	convergence	convergence	NOUN
ejpam-6007	30	28	of	of	ADP
ejpam-6007	30	29	the	the	DET
ejpam-6007	30	30	solutions	solution	NOUN
ejpam-6007	30	31	using	use	VERB
ejpam-6007	30	32	the	the	DET
ejpam-6007	30	33	picard	picard	NOUN
ejpam-6007	30	34	method	method	NOUN
ejpam-6007	30	35	.	.	PUNCT
ejpam-6007	31	1	illustrative	illustrative	ADJ
ejpam-6007	31	2	figures	figure	NOUN
ejpam-6007	31	3	were	be	AUX
ejpam-6007	31	4	provided	provide	VERB
ejpam-6007	31	5	to	to	PART
ejpam-6007	31	6	demonstrate	demonstrate	VERB
ejpam-6007	31	7	applications	application	NOUN
ejpam-6007	31	8	in	in	ADP
ejpam-6007	31	9	economic	economic	ADJ
ejpam-6007	31	10	,	,	PUNCT
ejpam-6007	31	11	financial	financial	ADJ
ejpam-6007	31	12	,	,	PUNCT
ejpam-6007	31	13	and	and	CCONJ
ejpam-6007	31	14	industrial	industrial	ADJ
ejpam-6007	31	15	contexts	contexts	NOUN
ejpam-6007	31	16	.	.	PUNCT
ejpam-6007	32	1	kassem	kassem	PROPN
ejpam-6007	32	2	et	et	PROPN
ejpam-6007	32	3	al	al	PROPN
ejpam-6007	32	4	.	.	PUNCT
ejpam-6007	33	1	[	[	X
ejpam-6007	33	2	10	10	NUM
ejpam-6007	33	3	]	]	PUNCT
ejpam-6007	33	4	discussed	discuss	VERB
ejpam-6007	33	5	a	a	DET
ejpam-6007	33	6	nash	nash	ADJ
ejpam-6007	33	7	-	-	PUNCT
ejpam-6007	33	8	collaborative	collaborative	ADJ
ejpam-6007	33	9	approach	approach	NOUN
ejpam-6007	33	10	for	for	ADP
ejpam-6007	33	11	a	a	DET
ejpam-6007	33	12	differential	differential	ADJ
ejpam-6007	33	13	game	game	NOUN
ejpam-6007	33	14	involving	involve	VERB
ejpam-6007	33	15	multiple	multiple	ADJ
ejpam-6007	33	16	governments	government	NOUN
ejpam-6007	33	17	and	and	CCONJ
ejpam-6007	33	18	terrorist	terrorist	ADJ
ejpam-6007	33	19	organizations	organization	NOUN
ejpam-6007	33	20	,	,	PUNCT
ejpam-6007	33	21	analyzing	analyze	VERB
ejpam-6007	33	22	government	government	NOUN
ejpam-6007	33	23	cooperation	cooperation	NOUN
ejpam-6007	33	24	and	and	CCONJ
ejpam-6007	33	25	the	the	DET
ejpam-6007	33	26	role	role	NOUN
ejpam-6007	33	27	of	of	ADP
ejpam-6007	33	28	each	each	DET
ejpam-6007	33	29	government	government	NOUN
ejpam-6007	33	30	in	in	ADP
ejpam-6007	33	31	counterterrorism	counterterrorism	NOUN
ejpam-6007	33	32	.	.	PUNCT
ejpam-6007	34	1	youness	youness	NOUN
ejpam-6007	35	1	[	[	X
ejpam-6007	35	2	11	11	NUM
ejpam-6007	35	3	]	]	PUNCT
ejpam-6007	35	4	introduced	introduce	VERB
ejpam-6007	35	5	a	a	DET
ejpam-6007	35	6	differential	differential	ADJ
ejpam-6007	35	7	game	game	NOUN
ejpam-6007	35	8	termed	term	VERB
ejpam-6007	35	9	“	"	PUNCT
ejpam-6007	35	10	nash	nash	PROPN
ejpam-6007	35	11	coalitional	coalitional	NOUN
ejpam-6007	35	12	,	,	PUNCT
ejpam-6007	35	13	”	"	PUNCT
ejpam-6007	35	14	which	which	PRON
ejpam-6007	35	15	extends	extend	VERB
ejpam-6007	35	16	the	the	DET
ejpam-6007	35	17	traditional	traditional	ADJ
ejpam-6007	35	18	nash	nash	ADJ
ejpam-6007	35	19	equilibrium	equilibrium	NOUN
ejpam-6007	35	20	framework	framework	NOUN
ejpam-6007	35	21	by	by	ADP
ejpam-6007	35	22	incorporating	incorporate	VERB
ejpam-6007	35	23	partial	partial	ADJ
ejpam-6007	35	24	cooperation	cooperation	NOUN
ejpam-6007	35	25	among	among	ADP
ejpam-6007	35	26	players	player	NOUN
ejpam-6007	35	27	,	,	PUNCT
ejpam-6007	35	28	enabling	enable	VERB
ejpam-6007	35	29	them	they	PRON
ejpam-6007	35	30	to	to	PART
ejpam-6007	35	31	achieve	achieve	VERB
ejpam-6007	35	32	mutually	mutually	ADV
ejpam-6007	35	33	beneficial	beneficial	ADJ
ejpam-6007	35	34	outcomes	outcome	NOUN
ejpam-6007	35	35	while	while	SCONJ
ejpam-6007	35	36	still	still	ADV
ejpam-6007	35	37	accounting	account	VERB
ejpam-6007	35	38	for	for	ADP
ejpam-6007	35	39	individual	individual	ADJ
ejpam-6007	35	40	objectives	objective	NOUN
ejpam-6007	35	41	.	.	PUNCT
ejpam-6007	36	1	youness	youness	NOUN
ejpam-6007	36	2	et	et	PROPN
ejpam-6007	36	3	al	al	PROPN
ejpam-6007	36	4	.	.	PUNCT
ejpam-6007	37	1	[	[	X
ejpam-6007	37	2	12	12	NUM
ejpam-6007	37	3	]	]	PUNCT
ejpam-6007	37	4	examined	examine	VERB
ejpam-6007	37	5	the	the	DET
ejpam-6007	37	6	necessary	necessary	ADJ
ejpam-6007	37	7	conditions	condition	NOUN
ejpam-6007	37	8	for	for	ADP
ejpam-6007	37	9	determining	determine	VERB
ejpam-6007	37	10	optimal	optimal	ADJ
ejpam-6007	37	11	strategies	strategy	NOUN
ejpam-6007	37	12	in	in	ADP
ejpam-6007	37	13	fuzzy	fuzzy	ADJ
ejpam-6007	37	14	continuous	continuous	ADJ
ejpam-6007	37	15	differential	differential	NOUN
ejpam-6007	37	16	games	game	NOUN
ejpam-6007	37	17	under	under	ADP
ejpam-6007	37	18	nash	nash	PROPN
ejpam-6007	37	19	equilibrium	equilibrium	NOUN
ejpam-6007	37	20	.	.	PUNCT
ejpam-6007	38	1	sun	sun	PROPN
ejpam-6007	38	2	et	et	PROPN
ejpam-6007	38	3	al	al	PROPN
ejpam-6007	38	4	.	.	PUNCT
ejpam-6007	39	1	[	[	X
ejpam-6007	39	2	13	13	NUM
ejpam-6007	39	3	]	]	PUNCT
ejpam-6007	39	4	introduced	introduce	VERB
ejpam-6007	39	5	a	a	DET
ejpam-6007	39	6	linear	linear	ADJ
ejpam-6007	39	7	–	–	PUNCT
ejpam-6007	39	8	quadratic	quadratic	ADJ
ejpam-6007	39	9	stochastic	stochastic	ADJ
ejpam-6007	39	10	two	two	NUM
ejpam-6007	39	11	-	-	PUNCT
ejpam-6007	39	12	person	person	NOUN
ejpam-6007	39	13	nonzero	nonzero	NOUN
ejpam-6007	39	14	-	-	PUNCT
ejpam-6007	39	15	sum	sum	NOUN
ejpam-6007	39	16	differential	differential	ADJ
ejpam-6007	39	17	game	game	NOUN
ejpam-6007	39	18	with	with	ADP
ejpam-6007	39	19	both	both	CCONJ
ejpam-6007	39	20	open	open	ADJ
ejpam-6007	39	21	-	-	PUNCT
ejpam-6007	39	22	loop	loop	NOUN
ejpam-6007	39	23	and	and	CCONJ
ejpam-6007	39	24	closed	closed	ADJ
ejpam-6007	39	25	-	-	PUNCT
ejpam-6007	39	26	loop	loop	NOUN
ejpam-6007	39	27	nash	nash	NOUN
ejpam-6007	39	28	equilibria	equilibria	PROPN
ejpam-6007	39	29	.	.	PUNCT
ejpam-6007	40	1	engwerda	engwerda	PROPN
ejpam-6007	41	1	[	[	X
ejpam-6007	41	2	14	14	NUM
ejpam-6007	41	3	]	]	PUNCT
ejpam-6007	41	4	analyzed	analyze	VERB
ejpam-6007	41	5	the	the	DET
ejpam-6007	41	6	open	open	ADJ
ejpam-6007	41	7	-	-	PUNCT
ejpam-6007	41	8	loop	loop	NOUN
ejpam-6007	41	9	nash	nash	NOUN
ejpam-6007	41	10	equilibrium	equilibrium	NOUN
ejpam-6007	41	11	in	in	ADP
ejpam-6007	41	12	a	a	DET
ejpam-6007	41	13	linear	linear	ADJ
ejpam-6007	41	14	-	-	PUNCT
ejpam-6007	41	15	quadratic	quadratic	ADJ
ejpam-6007	41	16	(	(	PUNCT
ejpam-6007	41	17	lq	lq	NOUN
ejpam-6007	41	18	)	)	PUNCT
ejpam-6007	41	19	differential	differential	ADJ
ejpam-6007	41	20	game	game	NOUN
ejpam-6007	41	21	.	.	PUNCT
ejpam-6007	42	1	min	min	ADJ
ejpam-6007	42	2	-	-	ADJ
ejpam-6007	42	3	max	max	PROPN
ejpam-6007	42	4	differential	differential	NOUN
ejpam-6007	42	5	games	game	NOUN
ejpam-6007	42	6	with	with	ADP
ejpam-6007	42	7	fuzzy	fuzzy	ADJ
ejpam-6007	42	8	objectives	objective	NOUN
ejpam-6007	42	9	and	and	CCONJ
ejpam-6007	42	10	controls	control	NOUN
ejpam-6007	42	11	,	,	PUNCT
ejpam-6007	42	12	as	as	ADV
ejpam-6007	42	13	well	well	ADV
ejpam-6007	42	14	as	as	ADP
ejpam-6007	42	15	large	large	ADJ
ejpam-6007	42	16	-	-	PUNCT
ejpam-6007	42	17	scale	scale	NOUN
ejpam-6007	42	18	differential	differential	NOUN
ejpam-6007	42	19	games	game	NOUN
ejpam-6007	42	20	,	,	PUNCT
ejpam-6007	42	21	have	have	AUX
ejpam-6007	42	22	been	be	AUX
ejpam-6007	42	23	discussed	discuss	VERB
ejpam-6007	42	24	in	in	ADP
ejpam-6007	42	25	[	[	X
ejpam-6007	42	26	15	15	NUM
ejpam-6007	42	27	,	,	PUNCT
ejpam-6007	42	28	16	16	NUM
ejpam-6007	42	29	]	]	PUNCT
ejpam-6007	42	30	.	.	PUNCT
ejpam-6007	43	1	megahed	megahe	VERB
ejpam-6007	43	2	[	[	X
ejpam-6007	43	3	17	17	NUM
ejpam-6007	43	4	]	]	PUNCT
ejpam-6007	43	5	analyzed	analyze	VERB
ejpam-6007	43	6	terrorism	terrorism	NOUN
ejpam-6007	43	7	dynamics	dynamic	NOUN
ejpam-6007	43	8	through	through	ADP
ejpam-6007	43	9	a	a	DET
ejpam-6007	43	10	two	two	NUM
ejpam-6007	43	11	-	-	PUNCT
ejpam-6007	43	12	player	player	NOUN
ejpam-6007	43	13	differential	differential	ADJ
ejpam-6007	43	14	game	game	NOUN
ejpam-6007	43	15	involving	involve	VERB
ejpam-6007	43	16	the	the	DET
ejpam-6007	43	17	international	international	ADJ
ejpam-6007	43	18	terrorism	terrorism	NOUN
ejpam-6007	43	19	organization	organization	NOUN
ejpam-6007	43	20	(	(	PUNCT
ejpam-6007	43	21	ito	ito	PROPN
ejpam-6007	43	22	)	)	PUNCT
ejpam-6007	43	23	.	.	PUNCT
ejpam-6007	44	1	youness	youness	NOUN
ejpam-6007	44	2	et	et	PROPN
ejpam-6007	44	3	al	al	PROPN
ejpam-6007	44	4	.	.	PUNCT
ejpam-6007	45	1	[	[	X
ejpam-6007	45	2	18	18	NUM
ejpam-6007	45	3	]	]	PUNCT
ejpam-6007	45	4	examined	examine	VERB
ejpam-6007	45	5	a	a	DET
ejpam-6007	45	6	min	min	ADJ
ejpam-6007	45	7	-	-	ADJ
ejpam-6007	45	8	max	max	PROPN
ejpam-6007	45	9	differential	differential	ADJ
ejpam-6007	45	10	game	game	NOUN
ejpam-6007	45	11	whose	whose	DET
ejpam-6007	45	12	state	state	NOUN
ejpam-6007	45	13	trajectory	trajectory	NOUN
ejpam-6007	45	14	is	be	AUX
ejpam-6007	45	15	governed	govern	VERB
ejpam-6007	45	16	by	by	ADP
ejpam-6007	45	17	a	a	DET
ejpam-6007	45	18	cauchy	cauchy	ADJ
ejpam-6007	45	19	initial	initial	ADJ
ejpam-6007	45	20	value	value	NOUN
ejpam-6007	45	21	problem	problem	NOUN
ejpam-6007	45	22	(	(	PUNCT
ejpam-6007	45	23	civp	civp	PROPN
ejpam-6007	45	24	)	)	PUNCT
ejpam-6007	45	25	.	.	PUNCT
ejpam-6007	46	1	they	they	PRON
ejpam-6007	46	2	provided	provide	VERB
ejpam-6007	46	3	both	both	CCONJ
ejpam-6007	46	4	analytical	analytical	ADJ
ejpam-6007	46	5	and	and	CCONJ
ejpam-6007	46	6	approximate	approximate	ADJ
ejpam-6007	46	7	numerical	numerical	ADJ
ejpam-6007	46	8	solutions	solution	NOUN
ejpam-6007	46	9	using	use	VERB
ejpam-6007	46	10	the	the	DET
ejpam-6007	46	11	picard	picard	NOUN
ejpam-6007	46	12	method	method	NOUN
ejpam-6007	46	13	,	,	PUNCT
ejpam-6007	46	14	demonstrating	demonstrate	VERB
ejpam-6007	46	15	the	the	DET
ejpam-6007	46	16	model	model	NOUN
ejpam-6007	46	17	’s	’s	PART
ejpam-6007	46	18	effectiveness	effectiveness	NOUN
ejpam-6007	46	19	in	in	ADP
ejpam-6007	46	20	dynamic	dynamic	ADJ
ejpam-6007	46	21	optimization	optimization	NOUN
ejpam-6007	46	22	contexts	contexts	NOUN
ejpam-6007	46	23	.	.	PUNCT
ejpam-6007	47	1	in	in	ADP
ejpam-6007	47	2	this	this	DET
ejpam-6007	47	3	paper	paper	NOUN
ejpam-6007	47	4	,	,	PUNCT
ejpam-6007	47	5	we	we	PRON
ejpam-6007	47	6	present	present	VERB
ejpam-6007	47	7	the	the	DET
ejpam-6007	47	8	numerical	numerical	ADJ
ejpam-6007	47	9	solution	solution	NOUN
ejpam-6007	47	10	of	of	ADP
ejpam-6007	47	11	an	an	DET
ejpam-6007	47	12	open	open	ADJ
ejpam-6007	47	13	-	-	PUNCT
ejpam-6007	47	14	loop	loop	NOUN
ejpam-6007	47	15	nash	nash	NOUN
ejpam-6007	47	16	differential	differential	NOUN
ejpam-6007	47	17	game	game	NOUN
ejpam-6007	47	18	using	use	VERB
ejpam-6007	47	19	the	the	DET
ejpam-6007	47	20	fourth	fourth	ADJ
ejpam-6007	47	21	-	-	PUNCT
ejpam-6007	47	22	order	order	NOUN
ejpam-6007	47	23	runge	runge	NOUN
ejpam-6007	47	24	–	–	PUNCT
ejpam-6007	47	25	kutta	kutta	NOUN
ejpam-6007	47	26	method	method	NOUN
ejpam-6007	47	27	[	[	X
ejpam-6007	47	28	19	19	NUM
ejpam-6007	47	29	]	]	PUNCT
ejpam-6007	47	30	.	.	PUNCT
ejpam-6007	48	1	the	the	DET
ejpam-6007	48	2	system	system	NOUN
ejpam-6007	48	3	dynamics	dynamic	NOUN
ejpam-6007	48	4	,	,	PUNCT
ejpam-6007	48	5	representing	represent	VERB
ejpam-6007	48	6	competition	competition	NOUN
ejpam-6007	48	7	between	between	ADP
ejpam-6007	48	8	two	two	NUM
ejpam-6007	48	9	firms	firm	NOUN
ejpam-6007	48	10	in	in	ADP
ejpam-6007	48	11	the	the	DET
ejpam-6007	48	12	market	market	NOUN
ejpam-6007	48	13	,	,	PUNCT
ejpam-6007	48	14	are	be	AUX
ejpam-6007	48	15	modeled	model	VERB
ejpam-6007	48	16	by	by	ADP
ejpam-6007	48	17	differential	differential	ADJ
ejpam-6007	48	18	equations	equation	NOUN
ejpam-6007	48	19	.	.	PUNCT
ejpam-6007	49	1	each	each	DET
ejpam-6007	49	2	player	player	NOUN
ejpam-6007	49	3	aims	aim	VERB
ejpam-6007	49	4	to	to	PART
ejpam-6007	49	5	optimize	optimize	VERB
ejpam-6007	49	6	their	their	PRON
ejpam-6007	49	7	objective	objective	NOUN
ejpam-6007	49	8	while	while	SCONJ
ejpam-6007	49	9	accounting	account	VERB
ejpam-6007	49	10	for	for	ADP
ejpam-6007	49	11	the	the	DET
ejpam-6007	49	12	impact	impact	NOUN
ejpam-6007	49	13	of	of	ADP
ejpam-6007	49	14	both	both	PRON
ejpam-6007	49	15	their	their	PRON
ejpam-6007	49	16	own	own	ADJ
ejpam-6007	49	17	actions	action	NOUN
ejpam-6007	49	18	and	and	CCONJ
ejpam-6007	49	19	those	those	PRON
ejpam-6007	49	20	of	of	ADP
ejpam-6007	49	21	the	the	DET
ejpam-6007	49	22	other	other	ADJ
ejpam-6007	49	23	player	player	NOUN
ejpam-6007	49	24	.	.	PUNCT
ejpam-6007	50	1	section	section	NOUN
ejpam-6007	50	2	2	2	NUM
ejpam-6007	50	3	formulates	formulate	VERB
ejpam-6007	50	4	the	the	DET
ejpam-6007	50	5	dynamical	dynamical	ADJ
ejpam-6007	50	6	system	system	NOUN
ejpam-6007	50	7	of	of	ADP
ejpam-6007	50	8	the	the	DET
ejpam-6007	50	9	problem	problem	NOUN
ejpam-6007	50	10	and	and	CCONJ
ejpam-6007	50	11	derives	derive	VERB
ejpam-6007	50	12	the	the	DET
ejpam-6007	50	13	necessary	necessary	ADJ
ejpam-6007	50	14	conditions	condition	NOUN
ejpam-6007	50	15	for	for	ADP
ejpam-6007	50	16	an	an	DET
ejpam-6007	50	17	open	open	ADJ
ejpam-6007	50	18	-	-	PUNCT
ejpam-6007	50	19	loop	loop	NOUN
ejpam-6007	50	20	nash	nash	PROPN
ejpam-6007	50	21	equilibrium	equilibrium	NOUN
ejpam-6007	50	22	.	.	PUNCT
ejpam-6007	51	1	section	section	NOUN
ejpam-6007	51	2	3	3	NUM
ejpam-6007	51	3	presents	present	VERB
ejpam-6007	51	4	the	the	DET
ejpam-6007	51	5	numerical	numerical	ADJ
ejpam-6007	51	6	solution	solution	NOUN
ejpam-6007	51	7	using	use	VERB
ejpam-6007	51	8	the	the	DET
ejpam-6007	51	9	fourth	fourth	ADJ
ejpam-6007	51	10	-	-	PUNCT
ejpam-6007	51	11	order	order	NOUN
ejpam-6007	51	12	runge	runge	NOUN
ejpam-6007	51	13	–	–	PUNCT
ejpam-6007	51	14	kutta	kutta	NOUN
ejpam-6007	51	15	method	method	NOUN
ejpam-6007	51	16	and	and	CCONJ
ejpam-6007	51	17	discusses	discuss	VERB
ejpam-6007	51	18	its	its	PRON
ejpam-6007	51	19	convergence	convergence	NOUN
ejpam-6007	51	20	.	.	PUNCT
ejpam-6007	52	1	section	section	NOUN
ejpam-6007	52	2	4	4	NUM
ejpam-6007	52	3	analyzes	analyze	VERB
ejpam-6007	52	4	the	the	DET
ejpam-6007	52	5	stability	stability	NOUN
ejpam-6007	52	6	of	of	ADP
ejpam-6007	52	7	the	the	DET
ejpam-6007	52	8	numerical	numerical	ADJ
ejpam-6007	52	9	solution	solution	NOUN
ejpam-6007	52	10	,	,	PUNCT
ejpam-6007	52	11	and	and	CCONJ
ejpam-6007	52	12	section	section	NOUN
ejpam-6007	52	13	5	5	NUM
ejpam-6007	52	14	concludes	conclude	VERB
ejpam-6007	52	15	the	the	DET
ejpam-6007	52	16	paper	paper	NOUN
ejpam-6007	52	17	.	.	PUNCT
ejpam-6007	53	1	a.	a.	NOUN
ejpam-6007	53	2	a.	a.	PROPN
ejpam-6007	53	3	megahed	megahe	VERB
ejpam-6007	53	4	et	et	PROPN
ejpam-6007	53	5	al	al	PROPN
ejpam-6007	53	6	.	.	PUNCT
ejpam-6007	53	7	/	/	SYM
ejpam-6007	53	8	eur	eur	PROPN
ejpam-6007	53	9	.	.	PUNCT
ejpam-6007	54	1	j.	j.	PROPN
ejpam-6007	54	2	pure	pure	PROPN
ejpam-6007	54	3	appl	appl	PROPN
ejpam-6007	54	4	.	.	PROPN
ejpam-6007	54	5	math	math	PROPN
ejpam-6007	54	6	,	,	PUNCT
ejpam-6007	54	7	18	18	NUM
ejpam-6007	54	8	(	(	PUNCT
ejpam-6007	54	9	4	4	NUM
ejpam-6007	54	10	)	)	PUNCT
ejpam-6007	54	11	(	(	PUNCT
ejpam-6007	54	12	2025	2025	NUM
ejpam-6007	54	13	)	)	PUNCT
ejpam-6007	54	14	,	,	PUNCT
ejpam-6007	54	15	6007	6007	NUM
ejpam-6007	54	16	3	3	NUM
ejpam-6007	54	17	of	of	ADP
ejpam-6007	54	18	22	22	NUM
ejpam-6007	54	19	2	2	NUM
ejpam-6007	54	20	.	.	PUNCT
ejpam-6007	54	21	problem	problem	NOUN
ejpam-6007	54	22	formulation	formulation	NOUN
ejpam-6007	54	23	in	in	ADP
ejpam-6007	54	24	this	this	DET
ejpam-6007	54	25	section	section	NOUN
ejpam-6007	54	26	,	,	PUNCT
ejpam-6007	54	27	we	we	PRON
ejpam-6007	54	28	discuss	discuss	VERB
ejpam-6007	54	29	the	the	DET
ejpam-6007	54	30	solution	solution	NOUN
ejpam-6007	54	31	of	of	ADP
ejpam-6007	54	32	an	an	DET
ejpam-6007	54	33	open	open	ADJ
ejpam-6007	54	34	-	-	PUNCT
ejpam-6007	54	35	loop	loop	NOUN
ejpam-6007	54	36	nash	nash	NOUN
ejpam-6007	54	37	differential	differential	NOUN
ejpam-6007	54	38	game	game	NOUN
ejpam-6007	54	39	between	between	ADP
ejpam-6007	54	40	two	two	NUM
ejpam-6007	54	41	firms	firm	NOUN
ejpam-6007	54	42	over	over	ADP
ejpam-6007	54	43	the	the	DET
ejpam-6007	54	44	time	time	NOUN
ejpam-6007	54	45	interval	interval	NOUN
ejpam-6007	54	46	t	t	PROPN
ejpam-6007	54	47	∈	∈	PROPN
ejpam-6007	55	1	[	[	X
ejpam-6007	55	2	0	0	NUM
ejpam-6007	55	3	,	,	PUNCT
ejpam-6007	55	4	t	t	X
ejpam-6007	55	5	]	]	PUNCT
ejpam-6007	55	6	.	.	PUNCT
ejpam-6007	56	1	the	the	DET
ejpam-6007	56	2	system	system	NOUN
ejpam-6007	56	3	dynamics	dynamic	NOUN
ejpam-6007	56	4	can	can	AUX
ejpam-6007	56	5	be	be	AUX
ejpam-6007	56	6	expressed	express	VERB
ejpam-6007	56	7	as	as	SCONJ
ejpam-6007	56	8	follows	follow	VERB
ejpam-6007	56	9	:	:	PUNCT
ejpam-6007	56	10	dx	dx	PROPN
ejpam-6007	56	11	dt	dt	X
ejpam-6007	57	1	=	=	SYM
ejpam-6007	57	2	u1(t	u1(t	PROPN
ejpam-6007	57	3	)	)	PUNCT
ejpam-6007	57	4	(	(	PUNCT
ejpam-6007	57	5	1−	1−	NUM
ejpam-6007	57	6	x(t	x(t	PROPN
ejpam-6007	57	7	)	)	PUNCT
ejpam-6007	57	8	)	)	PUNCT
ejpam-6007	58	1	−	−	PROPN
ejpam-6007	58	2	u2(t)x(t	u2(t)x(t	PROPN
ejpam-6007	58	3	)	)	PUNCT
ejpam-6007	58	4	,	,	PUNCT
ejpam-6007	58	5	(	(	PUNCT
ejpam-6007	58	6	1	1	X
ejpam-6007	58	7	)	)	PUNCT
ejpam-6007	58	8	where	where	SCONJ
ejpam-6007	58	9	t	t	PROPN
ejpam-6007	58	10	∈	∈	PROPN
ejpam-6007	59	1	[	[	X
ejpam-6007	59	2	0	0	NUM
ejpam-6007	59	3	,	,	PUNCT
ejpam-6007	59	4	t	t	X
ejpam-6007	59	5	]	]	PUNCT
ejpam-6007	59	6	,	,	PUNCT
ejpam-6007	59	7	x(0	x(0	PROPN
ejpam-6007	59	8	)	)	PUNCT
ejpam-6007	59	9	=	=	PUNCT
ejpam-6007	59	10	x0	x0	PROPN
ejpam-6007	59	11	,	,	PUNCT
ejpam-6007	59	12	subject	subject	ADJ
ejpam-6007	59	13	to	to	ADP
ejpam-6007	59	14	the	the	DET
ejpam-6007	59	15	constraint	constraint	NOUN
ejpam-6007	59	16	0	0	NUM
ejpam-6007	59	17	≤	≤	NOUN
ejpam-6007	59	18	x(t	x(t	NOUN
ejpam-6007	59	19	)	)	PUNCT
ejpam-6007	59	20	≤	≤	NUM
ejpam-6007	59	21	1	1	NUM
ejpam-6007	59	22	.	.	PUNCT
ejpam-6007	59	23	(	(	PUNCT
ejpam-6007	59	24	2	2	NUM
ejpam-6007	59	25	)	)	PUNCT
ejpam-6007	59	26	where	where	SCONJ
ejpam-6007	59	27	x(t	x(t	PROPN
ejpam-6007	59	28	)	)	PUNCT
ejpam-6007	59	29	denotes	denote	VERB
ejpam-6007	59	30	the	the	DET
ejpam-6007	59	31	market	market	NOUN
ejpam-6007	59	32	share	share	NOUN
ejpam-6007	59	33	of	of	ADP
ejpam-6007	59	34	firm	firm	NOUN
ejpam-6007	59	35	1	1	NUM
ejpam-6007	59	36	at	at	ADP
ejpam-6007	59	37	time	time	NOUN
ejpam-6007	59	38	t	t	PROPN
ejpam-6007	59	39	,	,	PUNCT
ejpam-6007	59	40	and	and	CCONJ
ejpam-6007	59	41	1	1	NUM
ejpam-6007	59	42	−	−	PRON
ejpam-6007	59	43	x(t	x(t	PROPN
ejpam-6007	59	44	)	)	PUNCT
ejpam-6007	59	45	represents	represent	VERB
ejpam-6007	59	46	the	the	DET
ejpam-6007	59	47	market	market	NOUN
ejpam-6007	59	48	share	share	NOUN
ejpam-6007	59	49	of	of	ADP
ejpam-6007	59	50	firm	firm	ADJ
ejpam-6007	59	51	2	2	NUM
ejpam-6007	59	52	.	.	PUNCT
ejpam-6007	60	1	the	the	DET
ejpam-6007	60	2	control	control	NOUN
ejpam-6007	60	3	variables	variable	VERB
ejpam-6007	60	4	u1(t	u1(t	ADP
ejpam-6007	60	5	)	)	PUNCT
ejpam-6007	60	6	and	and	CCONJ
ejpam-6007	60	7	u2(t	u2(t	NOUN
ejpam-6007	60	8	)	)	PUNCT
ejpam-6007	60	9	are	be	AUX
ejpam-6007	60	10	defined	define	VERB
ejpam-6007	60	11	as	as	SCONJ
ejpam-6007	60	12	follows	follow	VERB
ejpam-6007	60	13	:	:	PUNCT
ejpam-6007	60	14	u1(t	u1(t	X
ejpam-6007	60	15	)	)	PUNCT
ejpam-6007	60	16	corresponds	correspond	VERB
ejpam-6007	60	17	to	to	ADP
ejpam-6007	60	18	the	the	DET
ejpam-6007	60	19	advertising	advertising	NOUN
ejpam-6007	60	20	efforts	effort	NOUN
ejpam-6007	60	21	of	of	ADP
ejpam-6007	60	22	firm	firm	NOUN
ejpam-6007	60	23	1	1	NUM
ejpam-6007	60	24	at	at	ADP
ejpam-6007	60	25	time	time	NOUN
ejpam-6007	60	26	t	t	PROPN
ejpam-6007	60	27	,	,	PUNCT
ejpam-6007	60	28	while	while	SCONJ
ejpam-6007	60	29	u2(t	u2(t	NOUN
ejpam-6007	60	30	)	)	PUNCT
ejpam-6007	60	31	corresponds	correspond	VERB
ejpam-6007	60	32	to	to	ADP
ejpam-6007	60	33	the	the	DET
ejpam-6007	60	34	advertising	advertising	NOUN
ejpam-6007	60	35	efforts	effort	NOUN
ejpam-6007	60	36	of	of	ADP
ejpam-6007	60	37	firm	firm	ADJ
ejpam-6007	60	38	2	2	NUM
ejpam-6007	60	39	at	at	ADP
ejpam-6007	60	40	time	time	NOUN
ejpam-6007	60	41	t.	t.	PROPN
ejpam-6007	60	42	for	for	ADP
ejpam-6007	60	43	firm	firm	ADJ
ejpam-6007	60	44	1	1	NUM
ejpam-6007	60	45	,	,	PUNCT
ejpam-6007	60	46	the	the	DET
ejpam-6007	60	47	number	number	NOUN
ejpam-6007	60	48	of	of	ADP
ejpam-6007	60	49	customers	customer	NOUN
ejpam-6007	60	50	increases	increase	VERB
ejpam-6007	60	51	due	due	ADJ
ejpam-6007	60	52	to	to	ADP
ejpam-6007	60	53	its	its	PRON
ejpam-6007	60	54	own	own	ADJ
ejpam-6007	60	55	advertising	advertising	NOUN
ejpam-6007	60	56	efforts	effort	NOUN
ejpam-6007	60	57	,	,	PUNCT
ejpam-6007	60	58	whereas	whereas	SCONJ
ejpam-6007	60	59	the	the	DET
ejpam-6007	60	60	advertising	advertising	NOUN
ejpam-6007	60	61	efforts	effort	NOUN
ejpam-6007	60	62	of	of	ADP
ejpam-6007	60	63	firm	firm	ADJ
ejpam-6007	60	64	2	2	NUM
ejpam-6007	60	65	decrease	decrease	NOUN
ejpam-6007	60	66	the	the	DET
ejpam-6007	60	67	number	number	NOUN
ejpam-6007	60	68	of	of	ADP
ejpam-6007	60	69	customers	customer	NOUN
ejpam-6007	60	70	of	of	ADP
ejpam-6007	60	71	firm	firm	ADJ
ejpam-6007	60	72	1	1	NUM
ejpam-6007	60	73	.	.	PUNCT
ejpam-6007	61	1	the	the	DET
ejpam-6007	61	2	state	state	NOUN
ejpam-6007	61	3	dynamics	dynamic	NOUN
ejpam-6007	61	4	and	and	CCONJ
ejpam-6007	61	5	the	the	DET
ejpam-6007	61	6	payoff	payoff	NOUN
ejpam-6007	61	7	functionals	functional	NOUN
ejpam-6007	61	8	are	be	AUX
ejpam-6007	61	9	described	describe	VERB
ejpam-6007	61	10	as	as	SCONJ
ejpam-6007	61	11	follows	follow	VERB
ejpam-6007	61	12	:	:	PUNCT
ejpam-6007	61	13	ji	ji	PROPN
ejpam-6007	61	14	(	(	PUNCT
ejpam-6007	61	15	u1(t	u1(t	PROPN
ejpam-6007	61	16	)	)	PUNCT
ejpam-6007	61	17	,	,	PUNCT
ejpam-6007	61	18	u2(t	u2(t	NOUN
ejpam-6007	61	19	)	)	PUNCT
ejpam-6007	61	20	)	)	PUNCT
ejpam-6007	62	1	=	=	SYM
ejpam-6007	63	1	∫	∫	PROPN
ejpam-6007	63	2	t	t	PROPN
ejpam-6007	63	3	0	0	NUM
ejpam-6007	63	4	ii	ii	PROPN
ejpam-6007	63	5	(	(	PUNCT
ejpam-6007	63	6	x(t	x(t	PROPN
ejpam-6007	63	7	)	)	PUNCT
ejpam-6007	63	8	,	,	PUNCT
ejpam-6007	63	9	u1(t	u1(t	PROPN
ejpam-6007	63	10	)	)	PUNCT
ejpam-6007	63	11	,	,	PUNCT
ejpam-6007	63	12	u2(t	u2(t	PROPN
ejpam-6007	63	13	)	)	PUNCT
ejpam-6007	63	14	,	,	PUNCT
ejpam-6007	63	15	t	t	NOUN
ejpam-6007	63	16	)	)	PUNCT
ejpam-6007	64	1	dt	dt	PROPN
ejpam-6007	64	2	,	,	PUNCT
ejpam-6007	64	3	i	i	PRON
ejpam-6007	64	4	=	=	NOUN
ejpam-6007	64	5	1	1	NUM
ejpam-6007	64	6	,	,	PUNCT
ejpam-6007	64	7	2	2	NUM
ejpam-6007	64	8	.	.	PUNCT
ejpam-6007	64	9	(	(	PUNCT
ejpam-6007	64	10	3	3	X
ejpam-6007	64	11	)	)	PUNCT
ejpam-6007	64	12	the	the	DET
ejpam-6007	64	13	payoff	payoff	NOUN
ejpam-6007	64	14	functionals	functional	NOUN
ejpam-6007	64	15	of	of	ADP
ejpam-6007	64	16	the	the	DET
ejpam-6007	64	17	two	two	NUM
ejpam-6007	64	18	firms	firm	NOUN
ejpam-6007	64	19	in	in	ADP
ejpam-6007	64	20	problems	problem	NOUN
ejpam-6007	64	21	(	(	PUNCT
ejpam-6007	64	22	1	1	NUM
ejpam-6007	64	23	)	)	PUNCT
ejpam-6007	64	24	and	and	CCONJ
ejpam-6007	64	25	(	(	PUNCT
ejpam-6007	64	26	2	2	X
ejpam-6007	64	27	)	)	PUNCT
ejpam-6007	64	28	are	be	AUX
ejpam-6007	64	29	defined	define	VERB
ejpam-6007	64	30	as	as	ADP
ejpam-6007	64	31	follows	follow	VERB
ejpam-6007	64	32	:	:	PUNCT
ejpam-6007	64	33	j1(u1(t	j1(u1(t	NUM
ejpam-6007	64	34	)	)	PUNCT
ejpam-6007	64	35	,	,	PUNCT
ejpam-6007	64	36	u2(t	u2(t	NOUN
ejpam-6007	64	37	)	)	PUNCT
ejpam-6007	64	38	)	)	PUNCT
ejpam-6007	65	1	=	=	SYM
ejpam-6007	66	1	∫	∫	PROPN
ejpam-6007	66	2	t	t	PROPN
ejpam-6007	66	3	0	0	NUM
ejpam-6007	67	1	e−r1t[ϕ1x(t)−	e−r1t[ϕ1x(t)−	PROPN
ejpam-6007	67	2	c1u1(t	c1u1(t	PROPN
ejpam-6007	67	3	)	)	PUNCT
ejpam-6007	67	4	]	]	PUNCT
ejpam-6007	68	1	dt	dt	X
ejpam-6007	68	2	,	,	PUNCT
ejpam-6007	68	3	j2(u1(t	j2(u1(t	PROPN
ejpam-6007	68	4	)	)	PUNCT
ejpam-6007	68	5	,	,	PUNCT
ejpam-6007	68	6	u2(t	u2(t	NOUN
ejpam-6007	68	7	)	)	PUNCT
ejpam-6007	68	8	)	)	PUNCT
ejpam-6007	69	1	=	=	SYM
ejpam-6007	70	1	∫	∫	PROPN
ejpam-6007	70	2	t	t	NOUN
ejpam-6007	70	3	0	0	NUM
ejpam-6007	70	4	e−r2t[ϕ2(1−	e−r2t[ϕ2(1−	PROPN
ejpam-6007	70	5	x(t))−	x(t))−	PROPN
ejpam-6007	70	6	c2u2(t	c2u2(t	NOUN
ejpam-6007	70	7	)	)	PUNCT
ejpam-6007	70	8	]	]	PUNCT
ejpam-6007	71	1	dt	dt	X
ejpam-6007	71	2	.	.	PUNCT
ejpam-6007	72	1	(	(	PUNCT
ejpam-6007	72	2	4	4	X
ejpam-6007	72	3	)	)	PUNCT
ejpam-6007	72	4	where	where	SCONJ
ejpam-6007	72	5	ri	ri	PROPN
ejpam-6007	72	6	is	be	AUX
ejpam-6007	72	7	the	the	DET
ejpam-6007	72	8	interest	interest	NOUN
ejpam-6007	72	9	rate	rate	NOUN
ejpam-6007	72	10	of	of	ADP
ejpam-6007	72	11	firm	firm	NOUN
ejpam-6007	72	12	i	i	PRON
ejpam-6007	72	13	,	,	PUNCT
ejpam-6007	72	14	ϕi	ϕi	ADV
ejpam-6007	72	15	is	be	AUX
ejpam-6007	72	16	the	the	DET
ejpam-6007	72	17	fractional	fractional	ADJ
ejpam-6007	72	18	revenue	revenue	NOUN
ejpam-6007	72	19	potential	potential	NOUN
ejpam-6007	72	20	of	of	ADP
ejpam-6007	72	21	firm	firm	ADJ
ejpam-6007	72	22	i	i	PROPN
ejpam-6007	72	23	,	,	PUNCT
ejpam-6007	72	24	and	and	CCONJ
ejpam-6007	72	25	ci(s	ci(s	NUM
ejpam-6007	72	26	)	)	PUNCT
ejpam-6007	72	27	denotes	denote	VERB
ejpam-6007	72	28	the	the	DET
ejpam-6007	72	29	advertising	advertising	NOUN
ejpam-6007	72	30	cost	cost	NOUN
ejpam-6007	72	31	function	function	NOUN
ejpam-6007	72	32	.	.	PUNCT
ejpam-6007	73	1	we	we	PRON
ejpam-6007	73	2	assume	assume	VERB
ejpam-6007	73	3	that	that	PRON
ejpam-6007	73	4	ci(s	ci(s	PUNCT
ejpam-6007	73	5	)	)	PUNCT
ejpam-6007	73	6	=	=	PRON
ejpam-6007	73	7	pi	pi	NOUN
ejpam-6007	73	8	2	2	NUM
ejpam-6007	73	9	s2	s2	PROPN
ejpam-6007	73	10	,	,	PUNCT
ejpam-6007	73	11	pi	pi	NOUN
ejpam-6007	73	12	>	>	X
ejpam-6007	73	13	0	0	NUM
ejpam-6007	73	14	,	,	PUNCT
ejpam-6007	73	15	i	i	PRON
ejpam-6007	73	16	=	=	NOUN
ejpam-6007	73	17	1	1	NUM
ejpam-6007	73	18	,	,	PUNCT
ejpam-6007	73	19	2	2	NUM
ejpam-6007	73	20	.	.	PUNCT
ejpam-6007	73	21	f(x(t	f(x(t	PROPN
ejpam-6007	73	22	)	)	PUNCT
ejpam-6007	73	23	,	,	PUNCT
ejpam-6007	73	24	u1(t	u1(t	PROPN
ejpam-6007	73	25	)	)	PUNCT
ejpam-6007	73	26	,	,	PUNCT
ejpam-6007	73	27	u2(t	u2(t	PROPN
ejpam-6007	73	28	)	)	PUNCT
ejpam-6007	73	29	,	,	PUNCT
ejpam-6007	73	30	t	t	PROPN
ejpam-6007	73	31	)	)	PUNCT
ejpam-6007	73	32	=	=	SYM
ejpam-6007	74	1	u1(t	u1(t	PROPN
ejpam-6007	74	2	)	)	PUNCT
ejpam-6007	74	3	(	(	PUNCT
ejpam-6007	74	4	1−	1−	NUM
ejpam-6007	74	5	x(t	x(t	PROPN
ejpam-6007	74	6	)	)	PUNCT
ejpam-6007	74	7	)	)	PUNCT
ejpam-6007	75	1	−	−	PROPN
ejpam-6007	75	2	u2(t)x(t	u2(t)x(t	PROPN
ejpam-6007	75	3	)	)	PUNCT
ejpam-6007	75	4	,	,	PUNCT
ejpam-6007	75	5	i1(x(t	i1(x(t	PROPN
ejpam-6007	75	6	)	)	PUNCT
ejpam-6007	75	7	,	,	PUNCT
ejpam-6007	75	8	u1(t	u1(t	PROPN
ejpam-6007	75	9	)	)	PUNCT
ejpam-6007	75	10	,	,	PUNCT
ejpam-6007	75	11	u2(t	u2(t	PROPN
ejpam-6007	75	12	)	)	PUNCT
ejpam-6007	75	13	,	,	PUNCT
ejpam-6007	75	14	t	t	PROPN
ejpam-6007	75	15	)	)	PUNCT
ejpam-6007	75	16	=	=	VERB
ejpam-6007	76	1	ϕ1	ϕ1	NOUN
ejpam-6007	76	2	x(t)−	x(t)−	PROPN
ejpam-6007	76	3	c1	c1	PROPN
ejpam-6007	76	4	(	(	PUNCT
ejpam-6007	76	5	u1(t	u1(t	PROPN
ejpam-6007	76	6	)	)	PUNCT
ejpam-6007	76	7	)	)	PUNCT
ejpam-6007	77	1	=	=	VERB
ejpam-6007	77	2	ϕ1	ϕ1	NOUN
ejpam-6007	77	3	x(t)−	x(t)−	PROPN
ejpam-6007	77	4	p1	p1	PROPN
ejpam-6007	77	5	2	2	NUM
ejpam-6007	77	6	u1(t	u1(t	ADP
ejpam-6007	77	7	)	)	PUNCT
ejpam-6007	77	8	2	2	NUM
ejpam-6007	77	9	,	,	PUNCT
ejpam-6007	77	10	i2(x(t	i2(x(t	NOUN
ejpam-6007	77	11	)	)	PUNCT
ejpam-6007	77	12	,	,	PUNCT
ejpam-6007	77	13	u1(t	u1(t	PROPN
ejpam-6007	77	14	)	)	PUNCT
ejpam-6007	77	15	,	,	PUNCT
ejpam-6007	77	16	u2(t	u2(t	PROPN
ejpam-6007	77	17	)	)	PUNCT
ejpam-6007	77	18	,	,	PUNCT
ejpam-6007	77	19	t	t	PROPN
ejpam-6007	77	20	)	)	PUNCT
ejpam-6007	77	21	=	=	PUNCT
ejpam-6007	78	1	ϕ2	ϕ2	ADV
ejpam-6007	78	2	(	(	PUNCT
ejpam-6007	78	3	1−	1−	NUM
ejpam-6007	78	4	x(t))−	x(t))−	PROPN
ejpam-6007	78	5	c2	c2	PROPN
ejpam-6007	78	6	(	(	PUNCT
ejpam-6007	78	7	u2(t	u2(t	PROPN
ejpam-6007	78	8	)	)	PUNCT
ejpam-6007	78	9	)	)	PUNCT
ejpam-6007	79	1	=	=	PUNCT
ejpam-6007	79	2	ϕ2	ϕ2	ADV
ejpam-6007	79	3	(	(	PUNCT
ejpam-6007	79	4	1−	1−	NUM
ejpam-6007	79	5	x(t))−	x(t))−	NOUN
ejpam-6007	79	6	p2	p2	PROPN
ejpam-6007	79	7	2	2	NUM
ejpam-6007	79	8	u2(t	u2(t	NOUN
ejpam-6007	79	9	)	)	PUNCT
ejpam-6007	79	10	2	2	NUM
ejpam-6007	79	11	.	.	PUNCT
ejpam-6007	79	12	(	(	PUNCT
ejpam-6007	79	13	5	5	X
ejpam-6007	79	14	)	)	PUNCT
ejpam-6007	79	15	theorem	theorem	NOUN
ejpam-6007	79	16	1	1	NUM
ejpam-6007	79	17	.	.	PUNCT
ejpam-6007	80	1	let	let	VERB
ejpam-6007	80	2	f(x(t	f(x(t	NOUN
ejpam-6007	80	3	)	)	PUNCT
ejpam-6007	80	4	,	,	PUNCT
ejpam-6007	80	5	u1(t	u1(t	PROPN
ejpam-6007	80	6	)	)	PUNCT
ejpam-6007	80	7	,	,	PUNCT
ejpam-6007	80	8	u2(t	u2(t	PROPN
ejpam-6007	80	9	)	)	PUNCT
ejpam-6007	80	10	,	,	PUNCT
ejpam-6007	80	11	t	t	PROPN
ejpam-6007	80	12	)	)	PUNCT
ejpam-6007	80	13	and	and	CCONJ
ejpam-6007	80	14	ii(x(t	ii(x(t	NOUN
ejpam-6007	80	15	)	)	PUNCT
ejpam-6007	80	16	,	,	PUNCT
ejpam-6007	80	17	u1(t	u1(t	PROPN
ejpam-6007	80	18	)	)	PUNCT
ejpam-6007	80	19	,	,	PUNCT
ejpam-6007	80	20	u2(t	u2(t	PROPN
ejpam-6007	80	21	)	)	PUNCT
ejpam-6007	80	22	,	,	PUNCT
ejpam-6007	80	23	t	t	PROPN
ejpam-6007	80	24	)	)	PUNCT
ejpam-6007	80	25	be	be	VERB
ejpam-6007	80	26	continuously	continuously	ADV
ejpam-6007	80	27	differentiable	differentiable	ADJ
ejpam-6007	80	28	functions	function	NOUN
ejpam-6007	80	29	on	on	ADP
ejpam-6007	80	30	rn	rn	PROPN
ejpam-6007	80	31	,	,	PUNCT
ejpam-6007	80	32	i	i	PRON
ejpam-6007	80	33	=	=	NOUN
ejpam-6007	80	34	1	1	NUM
ejpam-6007	80	35	,	,	PUNCT
ejpam-6007	80	36	2	2	NUM
ejpam-6007	80	37	.	.	PUNCT
ejpam-6007	80	38	specifically	specifically	ADV
ejpam-6007	80	39	,	,	PUNCT
ejpam-6007	80	40	f(x(t	f(x(t	PROPN
ejpam-6007	80	41	)	)	PUNCT
ejpam-6007	80	42	,	,	PUNCT
ejpam-6007	80	43	u1(t	u1(t	PROPN
ejpam-6007	80	44	)	)	PUNCT
ejpam-6007	80	45	,	,	PUNCT
ejpam-6007	80	46	u2(t	u2(t	PROPN
ejpam-6007	80	47	)	)	PUNCT
ejpam-6007	80	48	,	,	PUNCT
ejpam-6007	80	49	t	t	PROPN
ejpam-6007	80	50	)	)	PUNCT
ejpam-6007	80	51	:	:	PUNCT
ejpam-6007	81	1	rn	rn	PROPN
ejpam-6007	81	2	×	×	PROPN
ejpam-6007	81	3	rs	rs	NOUN
ejpam-6007	81	4	×	×	NOUN
ejpam-6007	82	1	[	[	X
ejpam-6007	82	2	0	0	NUM
ejpam-6007	82	3	,	,	PUNCT
ejpam-6007	82	4	t	t	X
ejpam-6007	82	5	]	]	PUNCT
ejpam-6007	82	6	→	→	SYM
ejpam-6007	82	7	r	r	X
ejpam-6007	82	8	,	,	PUNCT
ejpam-6007	82	9	f	f	PROPN
ejpam-6007	82	10	∈	∈	PROPN
ejpam-6007	82	11	c1	c1	PROPN
ejpam-6007	82	12	,	,	PUNCT
ejpam-6007	82	13	a.	a.	NOUN
ejpam-6007	82	14	a.	a.	PROPN
ejpam-6007	82	15	megahed	megahe	VERB
ejpam-6007	82	16	et	et	PROPN
ejpam-6007	82	17	al	al	PROPN
ejpam-6007	82	18	.	.	PUNCT
ejpam-6007	82	19	/	/	SYM
ejpam-6007	82	20	eur	eur	PROPN
ejpam-6007	82	21	.	.	PUNCT
ejpam-6007	83	1	j.	j.	PROPN
ejpam-6007	83	2	pure	pure	PROPN
ejpam-6007	83	3	appl	appl	PROPN
ejpam-6007	83	4	.	.	PROPN
ejpam-6007	83	5	math	math	PROPN
ejpam-6007	83	6	,	,	PUNCT
ejpam-6007	83	7	18	18	NUM
ejpam-6007	83	8	(	(	PUNCT
ejpam-6007	83	9	4	4	NUM
ejpam-6007	83	10	)	)	PUNCT
ejpam-6007	83	11	(	(	PUNCT
ejpam-6007	83	12	2025	2025	NUM
ejpam-6007	83	13	)	)	PUNCT
ejpam-6007	83	14	,	,	PUNCT
ejpam-6007	83	15	6007	6007	NUM
ejpam-6007	83	16	4	4	NUM
ejpam-6007	83	17	of	of	ADP
ejpam-6007	83	18	22	22	NUM
ejpam-6007	83	19	where	where	SCONJ
ejpam-6007	83	20	s	s	VERB
ejpam-6007	83	21	=	=	PUNCT
ejpam-6007	84	1	∑n	∑n	PROPN
ejpam-6007	84	2	j=1	j=1	NOUN
ejpam-6007	84	3	sj	sj	PROPN
ejpam-6007	84	4	,	,	PUNCT
ejpam-6007	84	5	i	i	PROPN
ejpam-6007	84	6	̸=	̸=	PROPN
ejpam-6007	84	7	j	j	PROPN
ejpam-6007	84	8	,	,	PUNCT
ejpam-6007	84	9	and	and	CCONJ
ejpam-6007	84	10	ii(x(t	ii(x(t	PROPN
ejpam-6007	84	11	)	)	PUNCT
ejpam-6007	84	12	,	,	PUNCT
ejpam-6007	84	13	u1(t	u1(t	PROPN
ejpam-6007	84	14	)	)	PUNCT
ejpam-6007	84	15	,	,	PUNCT
ejpam-6007	84	16	u2(t	u2(t	PROPN
ejpam-6007	84	17	)	)	PUNCT
ejpam-6007	84	18	,	,	PUNCT
ejpam-6007	84	19	t	t	PROPN
ejpam-6007	84	20	)	)	PUNCT
ejpam-6007	84	21	:	:	PUNCT
ejpam-6007	85	1	rn	rn	PROPN
ejpam-6007	85	2	×	×	PROPN
ejpam-6007	85	3	rs	rs	NOUN
ejpam-6007	85	4	×	×	NOUN
ejpam-6007	86	1	[	[	X
ejpam-6007	86	2	0	0	NUM
ejpam-6007	86	3	,	,	PUNCT
ejpam-6007	86	4	t	t	X
ejpam-6007	86	5	]	]	PUNCT
ejpam-6007	86	6	→	→	SYM
ejpam-6007	86	7	r	r	X
ejpam-6007	86	8	,	,	PUNCT
ejpam-6007	86	9	ii	ii	PROPN
ejpam-6007	86	10	∈	∈	PROPN
ejpam-6007	86	11	c1	c1	NOUN
ejpam-6007	86	12	,	,	PUNCT
ejpam-6007	86	13	i	i	NOUN
ejpam-6007	86	14	=	=	NOUN
ejpam-6007	86	15	1	1	NUM
ejpam-6007	86	16	,	,	PUNCT
ejpam-6007	86	17	2	2	NUM
ejpam-6007	86	18	.	.	PUNCT
ejpam-6007	86	19	if	if	SCONJ
ejpam-6007	86	20	u∗i	u∗i	PUNCT
ejpam-6007	86	21	(	(	PUNCT
ejpam-6007	86	22	t	t	NOUN
ejpam-6007	86	23	)	)	PUNCT
ejpam-6007	86	24	,	,	PUNCT
ejpam-6007	86	25	0	0	NUM
ejpam-6007	86	26	≤	≤	NUM
ejpam-6007	86	27	t	t	PROPN
ejpam-6007	86	28	≤	≤	PROPN
ejpam-6007	86	29	t	t	PROPN
ejpam-6007	86	30	,	,	PUNCT
ejpam-6007	86	31	is	be	AUX
ejpam-6007	86	32	an	an	DET
ejpam-6007	86	33	open	open	ADJ
ejpam-6007	86	34	-	-	PUNCT
ejpam-6007	86	35	loop	loop	NOUN
ejpam-6007	86	36	nash	nash	NOUN
ejpam-6007	86	37	equilibrium	equilibrium	NOUN
ejpam-6007	86	38	solution	solution	NOUN
ejpam-6007	86	39	,	,	PUNCT
ejpam-6007	86	40	and	and	CCONJ
ejpam-6007	86	41	x∗(t	x∗(t	NOUN
ejpam-6007	86	42	)	)	PUNCT
ejpam-6007	86	43	,	,	PUNCT
ejpam-6007	86	44	0	0	NUM
ejpam-6007	86	45	≤	≤	NUM
ejpam-6007	86	46	t	t	PROPN
ejpam-6007	86	47	≤	≤	PROPN
ejpam-6007	86	48	t	t	PROPN
ejpam-6007	86	49	,	,	PUNCT
ejpam-6007	86	50	is	be	AUX
ejpam-6007	86	51	the	the	DET
ejpam-6007	86	52	corresponding	corresponding	ADJ
ejpam-6007	86	53	state	state	NOUN
ejpam-6007	86	54	trajectory	trajectory	NOUN
ejpam-6007	86	55	.	.	PUNCT
ejpam-6007	87	1	then	then	ADV
ejpam-6007	87	2	,	,	PUNCT
ejpam-6007	87	3	there	there	PRON
ejpam-6007	87	4	exist	exist	VERB
ejpam-6007	87	5	two	two	NUM
ejpam-6007	87	6	costate	costate	ADJ
ejpam-6007	87	7	vectors	vector	NOUN
ejpam-6007	87	8	λi(t	λi(t	NOUN
ejpam-6007	87	9	)	)	PUNCT
ejpam-6007	87	10	:	:	PUNCT
ejpam-6007	88	1	[	[	X
ejpam-6007	88	2	0	0	NUM
ejpam-6007	88	3	,	,	PUNCT
ejpam-6007	88	4	t	t	X
ejpam-6007	88	5	]	]	PUNCT
ejpam-6007	88	6	→	→	SYM
ejpam-6007	88	7	rn	rn	PROPN
ejpam-6007	88	8	and	and	CCONJ
ejpam-6007	88	9	two	two	NUM
ejpam-6007	88	10	hamiltonian	hamiltonian	ADJ
ejpam-6007	88	11	functions	function	NOUN
ejpam-6007	88	12	.	.	PUNCT
ejpam-6007	89	1	hi	hi	INTJ
ejpam-6007	89	2	(	(	PUNCT
ejpam-6007	89	3	λi(t	λi(t	NUM
ejpam-6007	89	4	)	)	PUNCT
ejpam-6007	89	5	,	,	PUNCT
ejpam-6007	89	6	x(t	x(t	PROPN
ejpam-6007	89	7	)	)	PUNCT
ejpam-6007	89	8	,	,	PUNCT
ejpam-6007	89	9	u1(t	u1(t	PROPN
ejpam-6007	89	10	)	)	PUNCT
ejpam-6007	89	11	,	,	PUNCT
ejpam-6007	89	12	u2(t	u2(t	PROPN
ejpam-6007	89	13	)	)	PUNCT
ejpam-6007	89	14	,	,	PUNCT
ejpam-6007	89	15	t	t	NOUN
ejpam-6007	89	16	)	)	PUNCT
ejpam-6007	89	17	=	=	SYM
ejpam-6007	89	18	ii	ii	PROPN
ejpam-6007	89	19	(	(	PUNCT
ejpam-6007	89	20	x(t	x(t	PROPN
ejpam-6007	89	21	)	)	PUNCT
ejpam-6007	89	22	,	,	PUNCT
ejpam-6007	89	23	u1(t	u1(t	PROPN
ejpam-6007	89	24	)	)	PUNCT
ejpam-6007	89	25	,	,	PUNCT
ejpam-6007	89	26	u2(t	u2(t	PROPN
ejpam-6007	89	27	)	)	PUNCT
ejpam-6007	89	28	,	,	PUNCT
ejpam-6007	89	29	t	t	NOUN
ejpam-6007	89	30	)	)	PUNCT
ejpam-6007	90	1	+	+	NOUN
ejpam-6007	90	2	λi(t	λi(t	X
ejpam-6007	90	3	)	)	PUNCT
ejpam-6007	90	4	⊤f	⊤f	X
ejpam-6007	90	5	(	(	PUNCT
ejpam-6007	90	6	x(t	x(t	PROPN
ejpam-6007	90	7	)	)	PUNCT
ejpam-6007	90	8	,	,	PUNCT
ejpam-6007	90	9	u1(t	u1(t	PROPN
ejpam-6007	90	10	)	)	PUNCT
ejpam-6007	90	11	,	,	PUNCT
ejpam-6007	90	12	u2(t	u2(t	PROPN
ejpam-6007	90	13	)	)	PUNCT
ejpam-6007	90	14	,	,	PUNCT
ejpam-6007	90	15	t	t	PROPN
ejpam-6007	90	16	)	)	PUNCT
ejpam-6007	90	17	,	,	PUNCT
ejpam-6007	90	18	i	i	PRON
ejpam-6007	90	19	=	=	NOUN
ejpam-6007	90	20	1	1	NUM
ejpam-6007	90	21	,	,	PUNCT
ejpam-6007	90	22	2	2	NUM
ejpam-6007	90	23	.	.	PUNCT
ejpam-6007	90	24	(	(	PUNCT
ejpam-6007	90	25	6	6	NUM
ejpam-6007	90	26	)	)	PUNCT
ejpam-6007	90	27	such	such	ADJ
ejpam-6007	90	28	that	that	SCONJ
ejpam-6007	90	29	the	the	DET
ejpam-6007	90	30	following	follow	VERB
ejpam-6007	90	31	necessary	necessary	ADJ
ejpam-6007	90	32	conditions	condition	NOUN
ejpam-6007	90	33	hold	hold	VERB
ejpam-6007	90	34	:	:	PUNCT
ejpam-6007	90	35	dx∗(t	dx∗(t	NOUN
ejpam-6007	90	36	)	)	PUNCT
ejpam-6007	90	37	dt	dt	NOUN
ejpam-6007	91	1	=	=	SYM
ejpam-6007	91	2	f	f	PROPN
ejpam-6007	91	3	(	(	PUNCT
ejpam-6007	91	4	x∗(t	x∗(t	PROPN
ejpam-6007	91	5	)	)	PUNCT
ejpam-6007	91	6	,	,	PUNCT
ejpam-6007	91	7	u∗1(t	u∗1(t	PROPN
ejpam-6007	91	8	)	)	PUNCT
ejpam-6007	91	9	,	,	PUNCT
ejpam-6007	91	10	u	u	NOUN
ejpam-6007	91	11	∗	∗	NOUN
ejpam-6007	91	12	2(t	2(t	NUM
ejpam-6007	91	13	)	)	PUNCT
ejpam-6007	91	14	,	,	PUNCT
ejpam-6007	91	15	t	t	PROPN
ejpam-6007	91	16	)	)	PUNCT
ejpam-6007	91	17	,	,	PUNCT
ejpam-6007	91	18	x∗(0	x∗(0	X
ejpam-6007	91	19	)	)	PUNCT
ejpam-6007	91	20	=	=	SYM
ejpam-6007	91	21	x0	x0	PROPN
ejpam-6007	91	22	,	,	PUNCT
ejpam-6007	91	23	dλ∗	dλ∗	PROPN
ejpam-6007	91	24	1(t	1(t	NUM
ejpam-6007	91	25	)	)	PUNCT
ejpam-6007	91	26	dt	dt	NOUN
ejpam-6007	91	27	=	=	SYM
ejpam-6007	92	1	−	−	PROPN
ejpam-6007	92	2	∂h1	∂h1	PROPN
ejpam-6007	92	3	(	(	PUNCT
ejpam-6007	92	4	λ1(t	λ1(t	PROPN
ejpam-6007	92	5	)	)	PUNCT
ejpam-6007	92	6	,	,	PUNCT
ejpam-6007	92	7	x	x	PUNCT
ejpam-6007	92	8	∗(t	∗(t	NOUN
ejpam-6007	92	9	)	)	PUNCT
ejpam-6007	92	10	,	,	PUNCT
ejpam-6007	92	11	u∗1(t	u∗1(t	PROPN
ejpam-6007	92	12	)	)	PUNCT
ejpam-6007	92	13	,	,	PUNCT
ejpam-6007	92	14	u	u	NOUN
ejpam-6007	92	15	∗	∗	NOUN
ejpam-6007	92	16	2(t	2(t	NUM
ejpam-6007	92	17	)	)	PUNCT
ejpam-6007	92	18	,	,	PUNCT
ejpam-6007	92	19	t	t	NOUN
ejpam-6007	92	20	)	)	PUNCT
ejpam-6007	92	21	∂x	∂x	PROPN
ejpam-6007	92	22	,	,	PUNCT
ejpam-6007	92	23	dλ∗	dλ∗	PROPN
ejpam-6007	92	24	2(t	2(t	NUM
ejpam-6007	92	25	)	)	PUNCT
ejpam-6007	92	26	dt	dt	NOUN
ejpam-6007	93	1	=	=	PUNCT
ejpam-6007	93	2	−	−	PROPN
ejpam-6007	93	3	∂h2	∂h2	ADP
ejpam-6007	93	4	(	(	PUNCT
ejpam-6007	93	5	λ2(t	λ2(t	NOUN
ejpam-6007	93	6	)	)	PUNCT
ejpam-6007	93	7	,	,	PUNCT
ejpam-6007	93	8	x	x	PUNCT
ejpam-6007	93	9	∗(t	∗(t	NOUN
ejpam-6007	93	10	)	)	PUNCT
ejpam-6007	93	11	,	,	PUNCT
ejpam-6007	93	12	u∗1(t	u∗1(t	PROPN
ejpam-6007	93	13	)	)	PUNCT
ejpam-6007	93	14	,	,	PUNCT
ejpam-6007	93	15	u	u	NOUN
ejpam-6007	93	16	∗	∗	NOUN
ejpam-6007	93	17	2(t	2(t	NUM
ejpam-6007	93	18	)	)	PUNCT
ejpam-6007	93	19	,	,	PUNCT
ejpam-6007	93	20	t	t	NOUN
ejpam-6007	93	21	)	)	PUNCT
ejpam-6007	93	22	∂x	∂x	PROPN
ejpam-6007	93	23	,	,	PUNCT
ejpam-6007	93	24	∂h1	∂h1	PROPN
ejpam-6007	93	25	(	(	PUNCT
ejpam-6007	93	26	λ1(t	λ1(t	PROPN
ejpam-6007	93	27	)	)	PUNCT
ejpam-6007	93	28	,	,	PUNCT
ejpam-6007	93	29	x	x	PUNCT
ejpam-6007	93	30	∗(t	∗(t	NOUN
ejpam-6007	93	31	)	)	PUNCT
ejpam-6007	93	32	,	,	PUNCT
ejpam-6007	93	33	u∗1(t	u∗1(t	PROPN
ejpam-6007	93	34	)	)	PUNCT
ejpam-6007	93	35	,	,	PUNCT
ejpam-6007	93	36	u	u	NOUN
ejpam-6007	93	37	∗	∗	NOUN
ejpam-6007	93	38	2(t	2(t	NUM
ejpam-6007	93	39	)	)	PUNCT
ejpam-6007	93	40	,	,	PUNCT
ejpam-6007	93	41	t	t	NOUN
ejpam-6007	93	42	)	)	PUNCT
ejpam-6007	93	43	∂u1	∂u1	PROPN
ejpam-6007	93	44	=	=	SYM
ejpam-6007	93	45	0	0	NUM
ejpam-6007	93	46	,	,	PUNCT
ejpam-6007	93	47	∂h2	∂h2	ADP
ejpam-6007	93	48	(	(	PUNCT
ejpam-6007	93	49	λ2(t	λ2(t	NOUN
ejpam-6007	93	50	)	)	PUNCT
ejpam-6007	93	51	,	,	PUNCT
ejpam-6007	93	52	x	x	PUNCT
ejpam-6007	93	53	∗(t	∗(t	NOUN
ejpam-6007	93	54	)	)	PUNCT
ejpam-6007	93	55	,	,	PUNCT
ejpam-6007	93	56	u∗1(t	u∗1(t	PROPN
ejpam-6007	93	57	)	)	PUNCT
ejpam-6007	93	58	,	,	PUNCT
ejpam-6007	93	59	u	u	NOUN
ejpam-6007	93	60	∗	∗	NOUN
ejpam-6007	93	61	2(t	2(t	NUM
ejpam-6007	93	62	)	)	PUNCT
ejpam-6007	93	63	,	,	PUNCT
ejpam-6007	93	64	t	t	NOUN
ejpam-6007	93	65	)	)	PUNCT
ejpam-6007	93	66	∂u2	∂u2	PROPN
ejpam-6007	93	67	=	=	PUNCT
ejpam-6007	93	68	0	0	X
ejpam-6007	93	69	.	.	PUNCT
ejpam-6007	93	70	(	(	PUNCT
ejpam-6007	93	71	7	7	NUM
ejpam-6007	93	72	)	)	PUNCT
ejpam-6007	93	73	with	with	ADP
ejpam-6007	93	74	initial	initial	ADJ
ejpam-6007	93	75	and	and	CCONJ
ejpam-6007	93	76	terminal	terminal	ADJ
ejpam-6007	93	77	conditions	condition	NOUN
ejpam-6007	93	78	x∗(0	x∗(0	NOUN
ejpam-6007	93	79	)	)	PUNCT
ejpam-6007	93	80	=	=	SYM
ejpam-6007	93	81	x0	x0	PROPN
ejpam-6007	93	82	,	,	PUNCT
ejpam-6007	93	83	λ1(t	λ1(t	PUNCT
ejpam-6007	93	84	)	)	PUNCT
ejpam-6007	93	85	=	=	SYM
ejpam-6007	93	86	0	0	NUM
ejpam-6007	93	87	,	,	PUNCT
ejpam-6007	93	88	λ2(t	λ2(t	NUM
ejpam-6007	93	89	)	)	PUNCT
ejpam-6007	93	90	=	=	SYM
ejpam-6007	93	91	0	0	X
ejpam-6007	93	92	.	.	PUNCT
ejpam-6007	94	1	(	(	PUNCT
ejpam-6007	94	2	8)	8)	NUM
ejpam-6007	94	3	the	the	DET
ejpam-6007	94	4	proof	proof	NOUN
ejpam-6007	94	5	of	of	ADP
ejpam-6007	94	6	this	this	DET
ejpam-6007	94	7	theorem	theorem	NOUN
ejpam-6007	94	8	is	be	AUX
ejpam-6007	94	9	presented	present	VERB
ejpam-6007	94	10	in	in	ADP
ejpam-6007	94	11	[	[	X
ejpam-6007	94	12	20	20	NUM
ejpam-6007	94	13	]	]	PUNCT
ejpam-6007	94	14	.	.	PUNCT
ejpam-6007	95	1	3	3	X
ejpam-6007	95	2	.	.	X
ejpam-6007	95	3	the	the	DET
ejpam-6007	95	4	numerical	numerical	ADJ
ejpam-6007	95	5	solution	solution	NOUN
ejpam-6007	95	6	by	by	ADP
ejpam-6007	95	7	using	use	VERB
ejpam-6007	95	8	the	the	DET
ejpam-6007	95	9	fourth	fourth	ADJ
ejpam-6007	95	10	-	-	PUNCT
ejpam-6007	95	11	order	order	NOUN
ejpam-6007	95	12	runge	runge	NOUN
ejpam-6007	95	13	-	-	PUNCT
ejpam-6007	95	14	kutta	kutta	NOUN
ejpam-6007	95	15	method	method	NOUN
ejpam-6007	95	16	3.1	3.1	NUM
ejpam-6007	95	17	.	.	PUNCT
ejpam-6007	96	1	existence	existence	NOUN
ejpam-6007	96	2	and	and	CCONJ
ejpam-6007	96	3	convergence	convergence	NOUN
ejpam-6007	96	4	of	of	ADP
ejpam-6007	96	5	the	the	DET
ejpam-6007	96	6	solution	solution	NOUN
ejpam-6007	96	7	existence	existence	NOUN
ejpam-6007	96	8	of	of	ADP
ejpam-6007	96	9	the	the	DET
ejpam-6007	96	10	solution	solution	NOUN
ejpam-6007	96	11	after	after	ADP
ejpam-6007	96	12	applying	apply	VERB
ejpam-6007	96	13	the	the	DET
ejpam-6007	96	14	necessary	necessary	ADJ
ejpam-6007	96	15	conditions	condition	NOUN
ejpam-6007	96	16	for	for	ADP
ejpam-6007	96	17	an	an	DET
ejpam-6007	96	18	open	open	ADJ
ejpam-6007	96	19	-	-	PUNCT
ejpam-6007	96	20	loop	loop	NOUN
ejpam-6007	96	21	nash	nash	PROPN
ejpam-6007	96	22	equilibrium	equilibrium	NOUN
ejpam-6007	96	23	differential	differential	ADJ
ejpam-6007	96	24	game	game	NOUN
ejpam-6007	96	25	,	,	PUNCT
ejpam-6007	96	26	the	the	DET
ejpam-6007	96	27	problem	problem	NOUN
ejpam-6007	96	28	(	(	PUNCT
ejpam-6007	96	29	1)–(5	1)–(5	NUM
ejpam-6007	96	30	)	)	PUNCT
ejpam-6007	96	31	is	be	AUX
ejpam-6007	96	32	reduced	reduce	VERB
ejpam-6007	96	33	to	to	ADP
ejpam-6007	96	34	the	the	DET
ejpam-6007	96	35	following	follow	VERB
ejpam-6007	96	36	hamiltonian	hamiltonian	ADJ
ejpam-6007	96	37	functions	function	NOUN
ejpam-6007	96	38	.	.	PUNCT
ejpam-6007	97	1	for	for	ADP
ejpam-6007	97	2	player	player	NOUN
ejpam-6007	97	3	1	1	NUM
ejpam-6007	97	4	,	,	PUNCT
ejpam-6007	97	5	the	the	DET
ejpam-6007	97	6	hamiltonian	hamiltonian	NOUN
ejpam-6007	97	7	is	be	AUX
ejpam-6007	97	8	defined	define	VERB
ejpam-6007	97	9	as	as	ADP
ejpam-6007	97	10	h1(λ1(t	h1(λ1(t	PROPN
ejpam-6007	97	11	)	)	PUNCT
ejpam-6007	97	12	,	,	PUNCT
ejpam-6007	97	13	x(t	x(t	PROPN
ejpam-6007	97	14	)	)	PUNCT
ejpam-6007	97	15	,	,	PUNCT
ejpam-6007	97	16	u1(t	u1(t	PROPN
ejpam-6007	97	17	)	)	PUNCT
ejpam-6007	97	18	,	,	PUNCT
ejpam-6007	97	19	u2(t	u2(t	PROPN
ejpam-6007	97	20	)	)	PUNCT
ejpam-6007	97	21	,	,	PUNCT
ejpam-6007	97	22	t	t	PROPN
ejpam-6007	97	23	)	)	PUNCT
ejpam-6007	98	1	=	=	SYM
ejpam-6007	98	2	ϕ1x(t)−	ϕ1x(t)−	PROPN
ejpam-6007	98	3	p1	p1	PROPN
ejpam-6007	98	4	2	2	NUM
ejpam-6007	98	5	u21(t)+λ1(t	u21(t)+λ1(t	ADJ
ejpam-6007	98	6	)	)	PUNCT
ejpam-6007	98	7	t	t	PROPN
ejpam-6007	98	8	[	[	PUNCT
ejpam-6007	98	9	u1(t)(1−x(t))−u2(t)x(t	u1(t)(1−x(t))−u2(t)x(t	PROPN
ejpam-6007	98	10	)	)	PUNCT
ejpam-6007	98	11	]	]	PUNCT
ejpam-6007	98	12	.	.	PUNCT
ejpam-6007	99	1	(	(	PUNCT
ejpam-6007	99	2	9	9	X
ejpam-6007	99	3	)	)	PUNCT
ejpam-6007	99	4	a.	a.	NOUN
ejpam-6007	99	5	a.	a.	NOUN
ejpam-6007	99	6	megahed	megahe	VERB
ejpam-6007	99	7	et	et	PROPN
ejpam-6007	99	8	al	al	PROPN
ejpam-6007	99	9	.	.	PUNCT
ejpam-6007	99	10	/	/	SYM
ejpam-6007	99	11	eur	eur	PROPN
ejpam-6007	99	12	.	.	PUNCT
ejpam-6007	100	1	j.	j.	PROPN
ejpam-6007	100	2	pure	pure	PROPN
ejpam-6007	100	3	appl	appl	PROPN
ejpam-6007	100	4	.	.	PROPN
ejpam-6007	100	5	math	math	PROPN
ejpam-6007	100	6	,	,	PUNCT
ejpam-6007	100	7	18	18	NUM
ejpam-6007	100	8	(	(	PUNCT
ejpam-6007	100	9	4	4	NUM
ejpam-6007	100	10	)	)	PUNCT
ejpam-6007	100	11	(	(	PUNCT
ejpam-6007	100	12	2025	2025	NUM
ejpam-6007	100	13	)	)	PUNCT
ejpam-6007	100	14	,	,	PUNCT
ejpam-6007	100	15	6007	6007	NUM
ejpam-6007	100	16	5	5	NUM
ejpam-6007	100	17	of	of	ADP
ejpam-6007	100	18	22	22	NUM
ejpam-6007	100	19	and	and	CCONJ
ejpam-6007	100	20	for	for	ADP
ejpam-6007	100	21	player	player	NOUN
ejpam-6007	100	22	2	2	NUM
ejpam-6007	100	23	,	,	PUNCT
ejpam-6007	100	24	the	the	DET
ejpam-6007	100	25	hamiltonian	hamiltonian	NOUN
ejpam-6007	100	26	is	be	AUX
ejpam-6007	100	27	h2(λ2(t	h2(λ2(t	PROPN
ejpam-6007	100	28	)	)	PUNCT
ejpam-6007	100	29	,	,	PUNCT
ejpam-6007	100	30	x(t	x(t	PROPN
ejpam-6007	100	31	)	)	PUNCT
ejpam-6007	100	32	,	,	PUNCT
ejpam-6007	100	33	u1(t	u1(t	PROPN
ejpam-6007	100	34	)	)	PUNCT
ejpam-6007	100	35	,	,	PUNCT
ejpam-6007	100	36	u2(t	u2(t	PROPN
ejpam-6007	100	37	)	)	PUNCT
ejpam-6007	100	38	,	,	PUNCT
ejpam-6007	100	39	t	t	PROPN
ejpam-6007	100	40	)	)	PUNCT
ejpam-6007	100	41	=	=	PUNCT
ejpam-6007	101	1	ϕ2	ϕ2	ADV
ejpam-6007	101	2	(	(	PUNCT
ejpam-6007	101	3	1−x(t	1−x(t	NUM
ejpam-6007	101	4	)	)	PUNCT
ejpam-6007	101	5	)	)	PUNCT
ejpam-6007	102	1	−	−	NOUN
ejpam-6007	102	2	p2	p2	PROPN
ejpam-6007	102	3	2	2	NUM
ejpam-6007	102	4	u22(t)+λ2(t	u22(t)+λ2(t	NOUN
ejpam-6007	102	5	)	)	PUNCT
ejpam-6007	102	6	t	t	NOUN
ejpam-6007	102	7	[	[	PUNCT
ejpam-6007	102	8	u1(t)(1−x(t))−u2(t)x(t	u1(t)(1−x(t))−u2(t)x(t	PROPN
ejpam-6007	102	9	)	)	PUNCT
ejpam-6007	102	10	]	]	PUNCT
ejpam-6007	102	11	.	.	PUNCT
ejpam-6007	103	1	(	(	PUNCT
ejpam-6007	103	2	10	10	NUM
ejpam-6007	103	3	)	)	PUNCT
ejpam-6007	103	4	dx	dx	PROPN
ejpam-6007	104	1	dt	dt	NOUN
ejpam-6007	104	2	=	=	SYM
ejpam-6007	104	3	u1(t	u1(t	PROPN
ejpam-6007	104	4	)	)	PUNCT
ejpam-6007	104	5	(	(	PUNCT
ejpam-6007	104	6	1−	1−	NUM
ejpam-6007	104	7	x(t	x(t	PROPN
ejpam-6007	104	8	)	)	PUNCT
ejpam-6007	104	9	)	)	PUNCT
ejpam-6007	105	1	−	−	PROPN
ejpam-6007	105	2	u2(t)x(t	u2(t)x(t	PROPN
ejpam-6007	105	3	)	)	PUNCT
ejpam-6007	105	4	,	,	PUNCT
ejpam-6007	105	5	x(0	x(0	PROPN
ejpam-6007	105	6	)	)	PUNCT
ejpam-6007	105	7	=	=	PUNCT
ejpam-6007	105	8	x0	x0	PROPN
ejpam-6007	105	9	,	,	PUNCT
ejpam-6007	105	10	dλ1(t	dλ1(t	PROPN
ejpam-6007	105	11	)	)	PUNCT
ejpam-6007	105	12	dt	dt	X
ejpam-6007	106	1	=	=	SYM
ejpam-6007	106	2	λ1(t	λ1(t	PROPN
ejpam-6007	106	3	)	)	PUNCT
ejpam-6007	106	4	[	[	PUNCT
ejpam-6007	106	5	u1(t	u1(t	X
ejpam-6007	106	6	)	)	PUNCT
ejpam-6007	106	7	+	+	PUNCT
ejpam-6007	106	8	u2(t	u2(t	NOUN
ejpam-6007	106	9	)	)	PUNCT
ejpam-6007	106	10	]	]	PUNCT
ejpam-6007	107	1	−	−	PROPN
ejpam-6007	107	2	ϕ1	ϕ1	NOUN
ejpam-6007	107	3	,	,	PUNCT
ejpam-6007	107	4	λ1(t	λ1(t	PUNCT
ejpam-6007	107	5	)	)	PUNCT
ejpam-6007	107	6	=	=	SYM
ejpam-6007	107	7	0	0	NUM
ejpam-6007	107	8	,	,	PUNCT
ejpam-6007	107	9	dλ2(t	dλ2(t	NOUN
ejpam-6007	107	10	)	)	PUNCT
ejpam-6007	107	11	dt	dt	NOUN
ejpam-6007	107	12	=	=	SYM
ejpam-6007	107	13	λ2(t	λ2(t	PROPN
ejpam-6007	107	14	)	)	PUNCT
ejpam-6007	107	15	[	[	PUNCT
ejpam-6007	107	16	u1(t	u1(t	X
ejpam-6007	107	17	)	)	PUNCT
ejpam-6007	107	18	+	+	PUNCT
ejpam-6007	107	19	u2(t	u2(t	NOUN
ejpam-6007	107	20	)	)	PUNCT
ejpam-6007	107	21	]	]	PUNCT
ejpam-6007	108	1	+	+	CCONJ
ejpam-6007	108	2	ϕ2	ϕ2	ADV
ejpam-6007	108	3	,	,	PUNCT
ejpam-6007	108	4	λ2(t	λ2(t	X
ejpam-6007	108	5	)	)	PUNCT
ejpam-6007	108	6	=	=	SYM
ejpam-6007	108	7	0	0	NUM
ejpam-6007	108	8	,	,	PUNCT
ejpam-6007	108	9	u1(t	u1(t	X
ejpam-6007	108	10	)	)	PUNCT
ejpam-6007	108	11	=	=	SYM
ejpam-6007	108	12	λ1(t	λ1(t	ADJ
ejpam-6007	108	13	)	)	PUNCT
ejpam-6007	108	14	p1	p1	NOUN
ejpam-6007	108	15	(	(	PUNCT
ejpam-6007	108	16	1−	1−	NUM
ejpam-6007	108	17	x(t	x(t	PROPN
ejpam-6007	108	18	)	)	PUNCT
ejpam-6007	108	19	)	)	PUNCT
ejpam-6007	108	20	,	,	PUNCT
ejpam-6007	108	21	u2(t	u2(t	NOUN
ejpam-6007	108	22	)	)	PUNCT
ejpam-6007	108	23	=	=	SYM
ejpam-6007	108	24	−λ2(t	−λ2(t	NOUN
ejpam-6007	108	25	)	)	PUNCT
ejpam-6007	108	26	p2	p2	PROPN
ejpam-6007	108	27	x(t	x(t	PROPN
ejpam-6007	108	28	)	)	PUNCT
ejpam-6007	108	29	,	,	PUNCT
ejpam-6007	108	30	(	(	PUNCT
ejpam-6007	108	31	ci)n	ci)n	NOUN
ejpam-6007	108	32	=	=	PUNCT
ejpam-6007	108	33	pi	pi	NOUN
ejpam-6007	108	34	2	2	NUM
ejpam-6007	108	35	(	(	PUNCT
ejpam-6007	108	36	u2i	u2i	NUM
ejpam-6007	108	37	)	)	PUNCT
ejpam-6007	108	38	n	n	CCONJ
ejpam-6007	108	39	,	,	PUNCT
ejpam-6007	108	40	i	i	PRON
ejpam-6007	108	41	=	=	NOUN
ejpam-6007	108	42	1	1	NUM
ejpam-6007	108	43	,	,	PUNCT
ejpam-6007	108	44	2	2	NUM
ejpam-6007	108	45	.	.	PUNCT
ejpam-6007	109	1	(	(	PUNCT
ejpam-6007	109	2	11	11	NUM
ejpam-6007	109	3	)	)	PUNCT
ejpam-6007	109	4	the	the	DET
ejpam-6007	109	5	existence	existence	NOUN
ejpam-6007	109	6	of	of	ADP
ejpam-6007	109	7	a	a	DET
ejpam-6007	109	8	solution	solution	NOUN
ejpam-6007	109	9	to	to	ADP
ejpam-6007	109	10	system	system	NOUN
ejpam-6007	109	11	(	(	PUNCT
ejpam-6007	109	12	11	11	NUM
ejpam-6007	109	13	)	)	PUNCT
ejpam-6007	109	14	is	be	AUX
ejpam-6007	109	15	discussed	discuss	VERB
ejpam-6007	109	16	in	in	ADP
ejpam-6007	109	17	[	[	X
ejpam-6007	109	18	9	9	NUM
ejpam-6007	109	19	]	]	PUNCT
ejpam-6007	109	20	.	.	PUNCT
ejpam-6007	110	1	uniform	uniform	ADJ
ejpam-6007	110	2	convergence	convergence	NOUN
ejpam-6007	110	3	of	of	ADP
ejpam-6007	110	4	the	the	DET
ejpam-6007	110	5	solution	solution	NOUN
ejpam-6007	110	6	now	now	ADV
ejpam-6007	110	7	,	,	PUNCT
ejpam-6007	110	8	we	we	PRON
ejpam-6007	110	9	apply	apply	VERB
ejpam-6007	110	10	the	the	DET
ejpam-6007	110	11	fourth	fourth	ADJ
ejpam-6007	110	12	-	-	PUNCT
ejpam-6007	110	13	order	order	NOUN
ejpam-6007	110	14	runge	runge	NOUN
ejpam-6007	110	15	–	–	PUNCT
ejpam-6007	110	16	kutta	kutta	NOUN
ejpam-6007	110	17	method	method	NOUN
ejpam-6007	110	18	to	to	PART
ejpam-6007	110	19	discuss	discuss	VERB
ejpam-6007	110	20	the	the	DET
ejpam-6007	110	21	uniform	uniform	ADJ
ejpam-6007	110	22	convergence	convergence	NOUN
ejpam-6007	110	23	of	of	ADP
ejpam-6007	110	24	the	the	DET
ejpam-6007	110	25	solution	solution	NOUN
ejpam-6007	110	26	.	.	PUNCT
ejpam-6007	111	1	the	the	DET
ejpam-6007	111	2	scheme	scheme	NOUN
ejpam-6007	111	3	is	be	AUX
ejpam-6007	111	4	given	give	VERB
ejpam-6007	111	5	by	by	ADP
ejpam-6007	111	6	xn+1	xn+1	PROPN
ejpam-6007	111	7	=	=	SYM
ejpam-6007	111	8	xn	xn	PROPN
ejpam-6007	112	1	+	+	NUM
ejpam-6007	112	2	h	h	NOUN
ejpam-6007	112	3	6	6	NUM
ejpam-6007	112	4	φ1(xn	φ1(xn	PROPN
ejpam-6007	112	5	,	,	PUNCT
ejpam-6007	112	6	λ1,n	λ1,n	PROPN
ejpam-6007	112	7	,	,	PUNCT
ejpam-6007	112	8	λ2,n	λ2,n	PROPN
ejpam-6007	112	9	,	,	PUNCT
ejpam-6007	112	10	tn	tn	PROPN
ejpam-6007	112	11	)	)	PUNCT
ejpam-6007	112	12	,	,	PUNCT
ejpam-6007	112	13	λ1,n+1	λ1,n+1	PUNCT
ejpam-6007	112	14	=	=	SYM
ejpam-6007	112	15	λ1,n	λ1,n	PROPN
ejpam-6007	112	16	+	+	CCONJ
ejpam-6007	112	17	h	h	PROPN
ejpam-6007	112	18	6	6	NUM
ejpam-6007	112	19	φ2(xn	φ2(xn	PROPN
ejpam-6007	112	20	,	,	PUNCT
ejpam-6007	112	21	λ1,n	λ1,n	PROPN
ejpam-6007	112	22	,	,	PUNCT
ejpam-6007	112	23	λ2,n	λ2,n	PROPN
ejpam-6007	112	24	,	,	PUNCT
ejpam-6007	112	25	ϕ1	ϕ1	NOUN
ejpam-6007	112	26	,	,	PUNCT
ejpam-6007	112	27	tn	tn	PROPN
ejpam-6007	112	28	)	)	PUNCT
ejpam-6007	112	29	,	,	PUNCT
ejpam-6007	112	30	λ2,n+1	λ2,n+1	PUNCT
ejpam-6007	112	31	=	=	SYM
ejpam-6007	113	1	λ2,n	λ2,n	X
ejpam-6007	113	2	+	+	NUM
ejpam-6007	113	3	h	h	NOUN
ejpam-6007	113	4	6	6	NUM
ejpam-6007	113	5	φ3(xn	φ3(xn	PROPN
ejpam-6007	113	6	,	,	PUNCT
ejpam-6007	113	7	λ1,n	λ1,n	PROPN
ejpam-6007	113	8	,	,	PUNCT
ejpam-6007	113	9	λ2,n	λ2,n	PROPN
ejpam-6007	113	10	,	,	PUNCT
ejpam-6007	113	11	ϕ2	ϕ2	ADV
ejpam-6007	113	12	,	,	PUNCT
ejpam-6007	113	13	tn	tn	PROPN
ejpam-6007	113	14	)	)	PUNCT
ejpam-6007	113	15	,	,	PUNCT
ejpam-6007	113	16	(	(	PUNCT
ejpam-6007	113	17	12	12	NUM
ejpam-6007	113	18	)	)	PUNCT
ejpam-6007	114	1	where	where	SCONJ
ejpam-6007	114	2	φ1(xn	φ1(xn	PROPN
ejpam-6007	114	3	,	,	PUNCT
ejpam-6007	114	4	λ1,n	λ1,n	PROPN
ejpam-6007	114	5	,	,	PUNCT
ejpam-6007	114	6	λ2,n	λ2,n	PROPN
ejpam-6007	114	7	,	,	PUNCT
ejpam-6007	114	8	tn	tn	PROPN
ejpam-6007	114	9	)	)	PUNCT
ejpam-6007	114	10	=	=	SYM
ejpam-6007	115	1	k1x	k1x	NOUN
ejpam-6007	116	1	+	+	CCONJ
ejpam-6007	116	2	2k2x	2k2x	NUM
ejpam-6007	116	3	+	+	CCONJ
ejpam-6007	116	4	2k3x	2k3x	NOUN
ejpam-6007	116	5	+	+	ADJ
ejpam-6007	116	6	k4x	k4x	PROPN
ejpam-6007	116	7	,	,	PUNCT
ejpam-6007	116	8	φ2(xn	φ2(xn	PROPN
ejpam-6007	116	9	,	,	PUNCT
ejpam-6007	116	10	λ1,n	λ1,n	PROPN
ejpam-6007	116	11	,	,	PUNCT
ejpam-6007	116	12	λ2,n	λ2,n	PROPN
ejpam-6007	116	13	,	,	PUNCT
ejpam-6007	116	14	ϕ1	ϕ1	NOUN
ejpam-6007	116	15	,	,	PUNCT
ejpam-6007	116	16	tn	tn	PROPN
ejpam-6007	116	17	)	)	PUNCT
ejpam-6007	116	18	=	=	PUNCT
ejpam-6007	117	1	k1λ1	k1λ1	PROPN
ejpam-6007	117	2	+	+	CCONJ
ejpam-6007	117	3	2k2λ1	2k2λ1	NUM
ejpam-6007	117	4	+	+	CCONJ
ejpam-6007	117	5	2k3λ1	2k3λ1	NUM
ejpam-6007	118	1	+	+	ADJ
ejpam-6007	118	2	k4λ1	k4λ1	NOUN
ejpam-6007	118	3	,	,	PUNCT
ejpam-6007	118	4	φ3(xn	φ3(xn	PROPN
ejpam-6007	118	5	,	,	PUNCT
ejpam-6007	118	6	λ1,n	λ1,n	PROPN
ejpam-6007	118	7	,	,	PUNCT
ejpam-6007	118	8	λ2,n	λ2,n	PROPN
ejpam-6007	118	9	,	,	PUNCT
ejpam-6007	118	10	ϕ2	ϕ2	ADV
ejpam-6007	118	11	,	,	PUNCT
ejpam-6007	118	12	tn	tn	PROPN
ejpam-6007	118	13	)	)	PUNCT
ejpam-6007	118	14	=	=	PUNCT
ejpam-6007	119	1	k1λ2	k1λ2	NOUN
ejpam-6007	120	1	+	+	NUM
ejpam-6007	120	2	2k2λ2	2k2λ2	NUM
ejpam-6007	120	3	+	+	CCONJ
ejpam-6007	120	4	2k3λ2	2k3λ2	NUM
ejpam-6007	121	1	+	+	NOUN
ejpam-6007	121	2	k4λ2	k4λ2	PROPN
ejpam-6007	121	3	.	.	PUNCT
ejpam-6007	122	1	(	(	PUNCT
ejpam-6007	122	2	13	13	NUM
ejpam-6007	122	3	)	)	PUNCT
ejpam-6007	122	4	a.	a.	NOUN
ejpam-6007	122	5	a.	a.	NOUN
ejpam-6007	122	6	megahed	megahe	VERB
ejpam-6007	122	7	et	et	PROPN
ejpam-6007	122	8	al	al	PROPN
ejpam-6007	122	9	.	.	PUNCT
ejpam-6007	122	10	/	/	SYM
ejpam-6007	122	11	eur	eur	PROPN
ejpam-6007	122	12	.	.	PUNCT
ejpam-6007	123	1	j.	j.	PROPN
ejpam-6007	123	2	pure	pure	PROPN
ejpam-6007	123	3	appl	appl	PROPN
ejpam-6007	123	4	.	.	PROPN
ejpam-6007	123	5	math	math	PROPN
ejpam-6007	123	6	,	,	PUNCT
ejpam-6007	123	7	18	18	NUM
ejpam-6007	123	8	(	(	PUNCT
ejpam-6007	123	9	4	4	NUM
ejpam-6007	123	10	)	)	PUNCT
ejpam-6007	123	11	(	(	PUNCT
ejpam-6007	123	12	2025	2025	NUM
ejpam-6007	123	13	)	)	PUNCT
ejpam-6007	123	14	,	,	PUNCT
ejpam-6007	123	15	6007	6007	NUM
ejpam-6007	123	16	6	6	NUM
ejpam-6007	123	17	of	of	ADP
ejpam-6007	123	18	22	22	NUM
ejpam-6007	123	19	the	the	DET
ejpam-6007	123	20	runge	runge	NOUN
ejpam-6007	123	21	-	-	PUNCT
ejpam-6007	123	22	kutta	kutta	NOUN
ejpam-6007	123	23	variables	variable	NOUN
ejpam-6007	123	24	ki	ki	PROPN
ejpam-6007	123	25	are	be	AUX
ejpam-6007	123	26	defined	define	VERB
ejpam-6007	123	27	as	as	ADP
ejpam-6007	123	28	k1x	k1x	PROPN
ejpam-6007	123	29	=	=	SYM
ejpam-6007	123	30	hfx(xn	hfx(xn	PROPN
ejpam-6007	123	31	,	,	PUNCT
ejpam-6007	123	32	tn	tn	PROPN
ejpam-6007	123	33	)	)	PUNCT
ejpam-6007	123	34	,	,	PUNCT
ejpam-6007	123	35	k2x	k2x	PROPN
ejpam-6007	123	36	=	=	SYM
ejpam-6007	123	37	hfx	hfx	PROPN
ejpam-6007	123	38	(	(	PUNCT
ejpam-6007	123	39	xn	xn	PROPN
ejpam-6007	124	1	+	+	NUM
ejpam-6007	124	2	h	h	PROPN
ejpam-6007	124	3	2	2	NUM
ejpam-6007	124	4	,	,	PUNCT
ejpam-6007	124	5	tn	tn	PROPN
ejpam-6007	125	1	+	+	CCONJ
ejpam-6007	125	2	k1x	k1x	PROPN
ejpam-6007	125	3	2	2	NUM
ejpam-6007	125	4	)	)	PUNCT
ejpam-6007	125	5	,	,	PUNCT
ejpam-6007	125	6	k3x	k3x	X
ejpam-6007	125	7	=	=	PROPN
ejpam-6007	125	8	hfx	hfx	PROPN
ejpam-6007	125	9	(	(	PUNCT
ejpam-6007	125	10	xn	xn	PROPN
ejpam-6007	126	1	+	+	NUM
ejpam-6007	126	2	h	h	PROPN
ejpam-6007	126	3	2	2	NUM
ejpam-6007	126	4	,	,	PUNCT
ejpam-6007	126	5	tn	tn	PROPN
ejpam-6007	127	1	+	+	CCONJ
ejpam-6007	127	2	k2x	k2x	X
ejpam-6007	127	3	2	2	NUM
ejpam-6007	127	4	)	)	PUNCT
ejpam-6007	127	5	,	,	PUNCT
ejpam-6007	127	6	k4x	k4x	PROPN
ejpam-6007	127	7	=	=	SYM
ejpam-6007	127	8	hfx	hfx	PROPN
ejpam-6007	127	9	(	(	PUNCT
ejpam-6007	127	10	xn	xn	PROPN
ejpam-6007	128	1	+	+	NUM
ejpam-6007	128	2	h	h	NOUN
ejpam-6007	128	3	,	,	PUNCT
ejpam-6007	128	4	tn	tn	PROPN
ejpam-6007	128	5	+	+	PROPN
ejpam-6007	128	6	k3x	k3x	PROPN
ejpam-6007	128	7	)	)	PUNCT
ejpam-6007	128	8	,	,	PUNCT
ejpam-6007	128	9	k1λ1	k1λ1	NOUN
ejpam-6007	128	10	=	=	SYM
ejpam-6007	128	11	hfλ1(xn	hfλ1(xn	PROPN
ejpam-6007	128	12	,	,	PUNCT
ejpam-6007	128	13	tn	tn	PROPN
ejpam-6007	128	14	)	)	PUNCT
ejpam-6007	128	15	,	,	PUNCT
ejpam-6007	128	16	k2λ1	k2λ1	PROPN
ejpam-6007	128	17	=	=	SYM
ejpam-6007	128	18	hfλ1	hfλ1	PROPN
ejpam-6007	128	19	(	(	PUNCT
ejpam-6007	128	20	xn	xn	PROPN
ejpam-6007	129	1	+	+	NUM
ejpam-6007	129	2	h	h	PROPN
ejpam-6007	129	3	2	2	NUM
ejpam-6007	129	4	,	,	PUNCT
ejpam-6007	129	5	tn	tn	PROPN
ejpam-6007	130	1	+	+	CCONJ
ejpam-6007	130	2	k1λ1	k1λ1	NOUN
ejpam-6007	130	3	2	2	NUM
ejpam-6007	130	4	)	)	PUNCT
ejpam-6007	130	5	,	,	PUNCT
ejpam-6007	131	1	k3λ1	k3λ1	NOUN
ejpam-6007	131	2	=	=	SYM
ejpam-6007	131	3	hfλ1	hfλ1	PROPN
ejpam-6007	131	4	(	(	PUNCT
ejpam-6007	131	5	xn	xn	PROPN
ejpam-6007	132	1	+	+	NUM
ejpam-6007	132	2	h	h	PROPN
ejpam-6007	132	3	2	2	NUM
ejpam-6007	132	4	,	,	PUNCT
ejpam-6007	132	5	tn	tn	PROPN
ejpam-6007	132	6	+	+	CCONJ
ejpam-6007	132	7	k2λ1	k2λ1	PROPN
ejpam-6007	132	8	2	2	NUM
ejpam-6007	132	9	)	)	PUNCT
ejpam-6007	132	10	,	,	PUNCT
ejpam-6007	133	1	k4λ1	k4λ1	NOUN
ejpam-6007	133	2	=	=	VERB
ejpam-6007	133	3	hfλ1	hfλ1	NOUN
ejpam-6007	133	4	(	(	PUNCT
ejpam-6007	133	5	xn	xn	PROPN
ejpam-6007	134	1	+	+	NUM
ejpam-6007	134	2	h	h	NOUN
ejpam-6007	134	3	,	,	PUNCT
ejpam-6007	134	4	tn	tn	PROPN
ejpam-6007	134	5	+	+	PROPN
ejpam-6007	134	6	k3λ1	k3λ1	NOUN
ejpam-6007	134	7	)	)	PUNCT
ejpam-6007	134	8	,	,	PUNCT
ejpam-6007	134	9	k1λ2	k1λ2	X
ejpam-6007	134	10	=	=	SYM
ejpam-6007	134	11	hfλ2(xn	hfλ2(xn	PROPN
ejpam-6007	134	12	,	,	PUNCT
ejpam-6007	134	13	tn	tn	PROPN
ejpam-6007	134	14	)	)	PUNCT
ejpam-6007	134	15	,	,	PUNCT
ejpam-6007	134	16	k2λ2	k2λ2	PROPN
ejpam-6007	134	17	=	=	SYM
ejpam-6007	134	18	hfλ2	hfλ2	PROPN
ejpam-6007	134	19	(	(	PUNCT
ejpam-6007	134	20	xn	xn	PROPN
ejpam-6007	135	1	+	+	NUM
ejpam-6007	135	2	h	h	PROPN
ejpam-6007	135	3	2	2	NUM
ejpam-6007	135	4	,	,	PUNCT
ejpam-6007	135	5	tn	tn	PROPN
ejpam-6007	135	6	+	+	CCONJ
ejpam-6007	135	7	k1λ2	k1λ2	X
ejpam-6007	135	8	2	2	NUM
ejpam-6007	135	9	)	)	PUNCT
ejpam-6007	135	10	,	,	PUNCT
ejpam-6007	135	11	k3λ2	k3λ2	PROPN
ejpam-6007	135	12	=	=	SYM
ejpam-6007	135	13	hfλ2	hfλ2	PROPN
ejpam-6007	135	14	(	(	PUNCT
ejpam-6007	135	15	xn	xn	PROPN
ejpam-6007	136	1	+	+	NUM
ejpam-6007	136	2	h	h	PROPN
ejpam-6007	136	3	2	2	NUM
ejpam-6007	136	4	,	,	PUNCT
ejpam-6007	136	5	tn	tn	PROPN
ejpam-6007	137	1	+	+	CCONJ
ejpam-6007	137	2	k2λ2	k2λ2	X
ejpam-6007	137	3	2	2	NUM
ejpam-6007	137	4	)	)	PUNCT
ejpam-6007	137	5	,	,	PUNCT
ejpam-6007	137	6	and	and	CCONJ
ejpam-6007	137	7	k4λ2	k4λ2	PROPN
ejpam-6007	137	8	=	=	SYM
ejpam-6007	137	9	hfλ2	hfλ2	PROPN
ejpam-6007	137	10	(	(	PUNCT
ejpam-6007	137	11	xn	xn	PROPN
ejpam-6007	138	1	+	+	NUM
ejpam-6007	138	2	h	h	NOUN
ejpam-6007	138	3	,	,	PUNCT
ejpam-6007	138	4	tn	tn	PROPN
ejpam-6007	138	5	+	+	PROPN
ejpam-6007	138	6	k3λ2	k3λ2	NOUN
ejpam-6007	138	7	)	)	PUNCT
ejpam-6007	138	8	.	.	PUNCT
ejpam-6007	139	1	(	(	PUNCT
ejpam-6007	139	2	14	14	NUM
ejpam-6007	139	3	)	)	PUNCT
ejpam-6007	139	4	the	the	DET
ejpam-6007	139	5	sequence	sequence	NOUN
ejpam-6007	139	6	xn+1	xn+1	PROPN
ejpam-6007	139	7	,	,	PUNCT
ejpam-6007	139	8	λ1,n+1	λ1,n+1	PROPN
ejpam-6007	139	9	,	,	PUNCT
ejpam-6007	139	10	and	and	CCONJ
ejpam-6007	139	11	λ2,n+1	λ2,n+1	PROPN
ejpam-6007	139	12	can	can	AUX
ejpam-6007	139	13	be	be	AUX
ejpam-6007	139	14	written	write	VERB
ejpam-6007	139	15	as	as	ADP
ejpam-6007	139	16	the	the	DET
ejpam-6007	139	17	finite	finite	PROPN
ejpam-6007	139	18	series	series	PROPN
ejpam-6007	139	19	xn+1	xn+1	PROPN
ejpam-6007	139	20	=	=	SYM
ejpam-6007	140	1	x0	x0	PROPN
ejpam-6007	140	2	+	+	CCONJ
ejpam-6007	140	3	n∑	n∑	PROPN
ejpam-6007	140	4	j=0	j=0	PROPN
ejpam-6007	140	5	(	(	PUNCT
ejpam-6007	140	6	xj+1	xj+1	PROPN
ejpam-6007	140	7	−	−	PROPN
ejpam-6007	140	8	xj	xj	PROPN
ejpam-6007	140	9	)	)	PUNCT
ejpam-6007	140	10	,	,	PUNCT
ejpam-6007	140	11	λ1,n+1	λ1,n+1	PROPN
ejpam-6007	140	12	=	=	PRON
ejpam-6007	141	1	λ1,0	λ1,0	PROPN
ejpam-6007	141	2	+	+	CCONJ
ejpam-6007	141	3	n∑	n∑	PROPN
ejpam-6007	141	4	j=0	j=0	PROPN
ejpam-6007	141	5	(	(	PUNCT
ejpam-6007	141	6	λ1,j+1	λ1,j+1	NOUN
ejpam-6007	141	7	−	−	PROPN
ejpam-6007	141	8	λ1,j	λ1,j	PROPN
ejpam-6007	141	9	)	)	PUNCT
ejpam-6007	141	10	,	,	PUNCT
ejpam-6007	141	11	λ2,n+1	λ2,n+1	PUNCT
ejpam-6007	142	1	=	=	SYM
ejpam-6007	142	2	λ2,0	λ2,0	X
ejpam-6007	143	1	+	+	CCONJ
ejpam-6007	143	2	n∑	n∑	ADJ
ejpam-6007	143	3	j=0	j=0	PROPN
ejpam-6007	143	4	(	(	PUNCT
ejpam-6007	143	5	λ2,j+1	λ2,j+1	PROPN
ejpam-6007	143	6	−	−	PROPN
ejpam-6007	143	7	λ2,j	λ2,j	PROPN
ejpam-6007	143	8	)	)	PUNCT
ejpam-6007	143	9	.	.	PUNCT
ejpam-6007	144	1	(	(	PUNCT
ejpam-6007	144	2	15	15	NUM
ejpam-6007	144	3	)	)	PUNCT
ejpam-6007	144	4	if	if	SCONJ
ejpam-6007	144	5	xn+1	xn+1	NUM
ejpam-6007	144	6	,	,	PUNCT
ejpam-6007	144	7	λ1,n+1	λ1,n+1	PROPN
ejpam-6007	144	8	and	and	CCONJ
ejpam-6007	144	9	λ2,n+1	λ2,n+1	PROPN
ejpam-6007	144	10	are	be	AUX
ejpam-6007	144	11	convergent	convergent	ADJ
ejpam-6007	144	12	,	,	PUNCT
ejpam-6007	144	13	then	then	ADV
ejpam-6007	144	14	the	the	DET
ejpam-6007	144	15	infinite	infinite	ADJ
ejpam-6007	144	16	series	series	NOUN
ejpam-6007	144	17	∞∑	∞∑	PROPN
ejpam-6007	144	18	j=0	j=0	PROPN
ejpam-6007	144	19	(	(	PUNCT
ejpam-6007	144	20	xj+1	xj+1	PROPN
ejpam-6007	144	21	−	−	PROPN
ejpam-6007	144	22	xj	xj	NOUN
ejpam-6007	144	23	)	)	PUNCT
ejpam-6007	144	24	,	,	PUNCT
ejpam-6007	144	25	∞∑	∞∑	NUM
ejpam-6007	144	26	j=0	j=0	PROPN
ejpam-6007	144	27	(	(	PUNCT
ejpam-6007	144	28	λ1,j+1	λ1,j+1	NOUN
ejpam-6007	144	29	−	−	PROPN
ejpam-6007	144	30	λ1,j	λ1,j	PROPN
ejpam-6007	144	31	)	)	PUNCT
ejpam-6007	144	32	,	,	PUNCT
ejpam-6007	144	33	∞∑	∞∑	NUM
ejpam-6007	144	34	j=0	j=0	PROPN
ejpam-6007	144	35	(	(	PUNCT
ejpam-6007	144	36	(	(	PUNCT
ejpam-6007	144	37	λ2,j+1	λ2,j+1	PROPN
ejpam-6007	144	38	−	−	PROPN
ejpam-6007	144	39	λ2,j	λ2,j	PROPN
ejpam-6007	144	40	)	)	PUNCT
ejpam-6007	144	41	)	)	PUNCT
ejpam-6007	144	42	are	be	AUX
ejpam-6007	144	43	convergent	convergent	ADJ
ejpam-6007	144	44	,	,	PUNCT
ejpam-6007	144	45	and	and	CCONJ
ejpam-6007	144	46	the	the	DET
ejpam-6007	144	47	solution	solution	NOUN
ejpam-6007	144	48	will	will	AUX
ejpam-6007	144	49	be	be	AUX
ejpam-6007	144	50	x	x	X
ejpam-6007	144	51	,	,	PUNCT
ejpam-6007	144	52	λ1	λ1	ADJ
ejpam-6007	144	53	and	and	CCONJ
ejpam-6007	144	54	λ2	λ2	NOUN
ejpam-6007	144	55	.	.	PUNCT
ejpam-6007	145	1	lim	lim	PROPN
ejpam-6007	145	2	n→∞	n→∞	X
ejpam-6007	145	3	xn+1	xn+1	PROPN
ejpam-6007	145	4	=	=	SYM
ejpam-6007	145	5	x	x	PROPN
ejpam-6007	145	6	,	,	PUNCT
ejpam-6007	145	7	lim	lim	PROPN
ejpam-6007	145	8	n→∞	n→∞	X
ejpam-6007	145	9	λ1,n+1	λ1,n+1	PROPN
ejpam-6007	145	10	=	=	SYM
ejpam-6007	145	11	λ1	λ1	PROPN
ejpam-6007	145	12	,	,	PUNCT
ejpam-6007	145	13	lim	lim	PROPN
ejpam-6007	145	14	n→∞	n→∞	X
ejpam-6007	145	15	λ2,n+1	λ2,n+1	PROPN
ejpam-6007	145	16	=	=	SYM
ejpam-6007	145	17	λ2	λ2	PROPN
ejpam-6007	145	18	.	.	PUNCT
ejpam-6007	146	1	(	(	PUNCT
ejpam-6007	146	2	16	16	NUM
ejpam-6007	146	3	)	)	PUNCT
ejpam-6007	146	4	assume	assume	VERB
ejpam-6007	146	5	that	that	SCONJ
ejpam-6007	146	6	1	1	X
ejpam-6007	146	7	.	.	PUNCT
ejpam-6007	146	8	the	the	DET
ejpam-6007	146	9	functions	function	NOUN
ejpam-6007	146	10	φi	φi	ADP
ejpam-6007	146	11	:	:	PUNCT
ejpam-6007	146	12	rn	rn	PROPN
ejpam-6007	146	13	×	×	PROPN
ejpam-6007	146	14	rn	rn	PROPN
ejpam-6007	146	15	×	×	PROPN
ejpam-6007	146	16	rn	rn	PROPN
ejpam-6007	146	17	×	×	NOUN
ejpam-6007	147	1	[	[	X
ejpam-6007	147	2	0	0	NUM
ejpam-6007	147	3	,	,	PUNCT
ejpam-6007	147	4	t	t	X
ejpam-6007	147	5	]	]	PUNCT
ejpam-6007	147	6	→	→	SYM
ejpam-6007	147	7	r	r	X
ejpam-6007	147	8	,	,	PUNCT
ejpam-6007	147	9	i	i	NOUN
ejpam-6007	147	10	=	=	NOUN
ejpam-6007	147	11	1	1	NUM
ejpam-6007	147	12	,	,	PUNCT
ejpam-6007	147	13	2	2	NUM
ejpam-6007	147	14	,	,	PUNCT
ejpam-6007	147	15	3	3	NUM
ejpam-6007	147	16	,	,	PUNCT
ejpam-6007	147	17	a.	a.	NOUN
ejpam-6007	147	18	a.	a.	NOUN
ejpam-6007	147	19	megahed	megahe	VERB
ejpam-6007	147	20	et	et	PROPN
ejpam-6007	147	21	al	al	PROPN
ejpam-6007	147	22	.	.	PUNCT
ejpam-6007	147	23	/	/	SYM
ejpam-6007	147	24	eur	eur	PROPN
ejpam-6007	147	25	.	.	PUNCT
ejpam-6007	148	1	j.	j.	PROPN
ejpam-6007	148	2	pure	pure	PROPN
ejpam-6007	148	3	appl	appl	PROPN
ejpam-6007	148	4	.	.	PROPN
ejpam-6007	148	5	math	math	PROPN
ejpam-6007	148	6	,	,	PUNCT
ejpam-6007	148	7	18	18	NUM
ejpam-6007	148	8	(	(	PUNCT
ejpam-6007	148	9	4	4	NUM
ejpam-6007	148	10	)	)	PUNCT
ejpam-6007	148	11	(	(	PUNCT
ejpam-6007	148	12	2025	2025	NUM
ejpam-6007	148	13	)	)	PUNCT
ejpam-6007	148	14	,	,	PUNCT
ejpam-6007	148	15	6007	6007	NUM
ejpam-6007	148	16	7	7	NUM
ejpam-6007	148	17	of	of	ADP
ejpam-6007	148	18	22	22	NUM
ejpam-6007	148	19	are	be	AUX
ejpam-6007	148	20	continuous	continuous	ADJ
ejpam-6007	148	21	,	,	PUNCT
ejpam-6007	148	22	and	and	CCONJ
ejpam-6007	148	23	there	there	PRON
ejpam-6007	148	24	exist	exist	VERB
ejpam-6007	148	25	positive	positive	ADJ
ejpam-6007	148	26	constants	constant	NOUN
ejpam-6007	148	27	mi	mi	INTJ
ejpam-6007	148	28	such	such	ADJ
ejpam-6007	148	29	that	that	DET
ejpam-6007	148	30	|φi|	|φi|	NOUN
ejpam-6007	148	31	≤	≤	X
ejpam-6007	148	32	mi	mi	PROPN
ejpam-6007	148	33	,	,	PUNCT
ejpam-6007	148	34	i	i	NOUN
ejpam-6007	148	35	=	=	NOUN
ejpam-6007	148	36	1	1	NUM
ejpam-6007	148	37	,	,	PUNCT
ejpam-6007	148	38	2	2	NUM
ejpam-6007	148	39	,	,	PUNCT
ejpam-6007	148	40	3	3	NUM
ejpam-6007	148	41	.	.	NOUN
ejpam-6007	148	42	2	2	NUM
ejpam-6007	148	43	.	.	X
ejpam-6007	148	44	each	each	DET
ejpam-6007	148	45	function	function	NOUN
ejpam-6007	148	46	φi	φi	SCONJ
ejpam-6007	148	47	satisfies	satisfy	VERB
ejpam-6007	148	48	the	the	DET
ejpam-6007	148	49	lipschitz	lipschitz	NOUN
ejpam-6007	148	50	condition	condition	NOUN
ejpam-6007	148	51	with	with	ADP
ejpam-6007	148	52	lipschitz	lipschitz	NOUN
ejpam-6007	148	53	constants	constant	NOUN
ejpam-6007	148	54	li	li	PROPN
ejpam-6007	148	55	,	,	PUNCT
ejpam-6007	148	56	where	where	SCONJ
ejpam-6007	148	57	0	0	X
ejpam-6007	148	58	<	<	X
ejpam-6007	148	59	li	li	X
ejpam-6007	148	60	<	<	X
ejpam-6007	148	61	1	1	NUM
ejpam-6007	148	62	,	,	PUNCT
ejpam-6007	148	63	i	i	PRON
ejpam-6007	148	64	=	=	NOUN
ejpam-6007	148	65	1	1	NUM
ejpam-6007	148	66	,	,	PUNCT
ejpam-6007	148	67	2	2	NUM
ejpam-6007	148	68	,	,	PUNCT
ejpam-6007	148	69	3	3	NUM
ejpam-6007	148	70	,	,	PUNCT
ejpam-6007	148	71	such	such	ADJ
ejpam-6007	148	72	that	that	SCONJ
ejpam-6007	148	73	|φi(z1)−	|φi(z1)−	PROPN
ejpam-6007	148	74	φi(z2)|	φi(z2)|	PROPN
ejpam-6007	148	75	≤	≤	PROPN
ejpam-6007	148	76	li∥z1	li∥z1	NOUN
ejpam-6007	148	77	−	−	PROPN
ejpam-6007	148	78	z2∥	z2∥	PROPN
ejpam-6007	148	79	,	,	PUNCT
ejpam-6007	148	80	∀z1	∀z1	PROPN
ejpam-6007	148	81	,	,	PUNCT
ejpam-6007	148	82	z2	z2	PROPN
ejpam-6007	148	83	∈	∈	PROPN
ejpam-6007	149	1	rn	rn	PROPN
ejpam-6007	149	2	×	×	PROPN
ejpam-6007	149	3	rn	rn	PROPN
ejpam-6007	149	4	×	×	PROPN
ejpam-6007	149	5	rn	rn	PROPN
ejpam-6007	149	6	×	×	NOUN
ejpam-6007	150	1	[	[	X
ejpam-6007	150	2	0	0	NUM
ejpam-6007	150	3	,	,	PUNCT
ejpam-6007	150	4	t	t	X
ejpam-6007	150	5	]	]	PUNCT
ejpam-6007	150	6	.	.	PUNCT
ejpam-6007	151	1	in	in	ADP
ejpam-6007	151	2	particular	particular	ADJ
ejpam-6007	151	3	,	,	PUNCT
ejpam-6007	151	4	|φ1(x	|φ1(x	NOUN
ejpam-6007	151	5	,	,	PUNCT
ejpam-6007	151	6	λ1	λ1	ADJ
ejpam-6007	151	7	,	,	PUNCT
ejpam-6007	151	8	λ2	λ2	NOUN
ejpam-6007	151	9	,	,	PUNCT
ejpam-6007	151	10	t)−	t)−	PROPN
ejpam-6007	151	11	φ1(y	φ1(y	PROPN
ejpam-6007	151	12	,	,	PUNCT
ejpam-6007	151	13	λ1	λ1	ADJ
ejpam-6007	151	14	,	,	PUNCT
ejpam-6007	151	15	λ2	λ2	NOUN
ejpam-6007	151	16	,	,	PUNCT
ejpam-6007	151	17	t)|	t)|	NOUN
ejpam-6007	151	18	<	<	X
ejpam-6007	151	19	l1|x−	l1|x−	PROPN
ejpam-6007	151	20	y|	y|	NOUN
ejpam-6007	151	21	,	,	PUNCT
ejpam-6007	151	22	(	(	PUNCT
ejpam-6007	151	23	17	17	NUM
ejpam-6007	151	24	)	)	PUNCT
ejpam-6007	151	25	|φ2(x	|φ2(x	NUM
ejpam-6007	151	26	,	,	PUNCT
ejpam-6007	151	27	λ1	λ1	ADJ
ejpam-6007	151	28	,	,	PUNCT
ejpam-6007	151	29	λ2	λ2	NOUN
ejpam-6007	151	30	,	,	PUNCT
ejpam-6007	151	31	t)−	t)−	PROPN
ejpam-6007	151	32	φ2(x	φ2(x	PROPN
ejpam-6007	151	33	,	,	PUNCT
ejpam-6007	151	34	α	α	NOUN
ejpam-6007	151	35	,	,	PUNCT
ejpam-6007	151	36	λ2	λ2	NOUN
ejpam-6007	151	37	,	,	PUNCT
ejpam-6007	151	38	t)|	t)|	NOUN
ejpam-6007	151	39	<	<	X
ejpam-6007	151	40	l2|λ1	l2|λ1	NOUN
ejpam-6007	151	41	−	−	PROPN
ejpam-6007	151	42	α|	α|	PROPN
ejpam-6007	151	43	,	,	PUNCT
ejpam-6007	151	44	(	(	PUNCT
ejpam-6007	151	45	18	18	NUM
ejpam-6007	151	46	)	)	PUNCT
ejpam-6007	151	47	|φ3(x	|φ3(x	PROPN
ejpam-6007	151	48	,	,	PUNCT
ejpam-6007	151	49	λ1	λ1	ADJ
ejpam-6007	151	50	,	,	PUNCT
ejpam-6007	151	51	λ2	λ2	NOUN
ejpam-6007	151	52	,	,	PUNCT
ejpam-6007	151	53	t)−	t)−	PROPN
ejpam-6007	151	54	φ3(x	φ3(x	PROPN
ejpam-6007	151	55	,	,	PUNCT
ejpam-6007	151	56	λ1	λ1	PROPN
ejpam-6007	151	57	,	,	PUNCT
ejpam-6007	151	58	γ	γ	X
ejpam-6007	151	59	,	,	PUNCT
ejpam-6007	151	60	t)|	t)|	ADJ
ejpam-6007	151	61	<	<	X
ejpam-6007	151	62	l3|λ2	l3|λ2	PROPN
ejpam-6007	151	63	−	−	PROPN
ejpam-6007	151	64	γ|	γ|	PROPN
ejpam-6007	151	65	.	.	PUNCT
ejpam-6007	152	1	(	(	PUNCT
ejpam-6007	152	2	19	19	NUM
ejpam-6007	152	3	)	)	PUNCT
ejpam-6007	152	4	if	if	SCONJ
ejpam-6007	152	5	the	the	DET
ejpam-6007	152	6	three	three	NUM
ejpam-6007	152	7	series	series	NOUN
ejpam-6007	152	8	converge	converge	NOUN
ejpam-6007	152	9	,	,	PUNCT
ejpam-6007	152	10	then	then	ADV
ejpam-6007	152	11	the	the	DET
ejpam-6007	152	12	three	three	NUM
ejpam-6007	152	13	sequences	sequence	NOUN
ejpam-6007	152	14	xn+1	xn+1	NUM
ejpam-6007	152	15	,	,	PUNCT
ejpam-6007	152	16	λ1,n+1	λ1,n+1	PROPN
ejpam-6007	152	17	and	and	CCONJ
ejpam-6007	152	18	λ2,n+1	λ2,n+1	PROPN
ejpam-6007	152	19	will	will	AUX
ejpam-6007	152	20	converge	converge	VERB
ejpam-6007	152	21	to	to	ADP
ejpam-6007	152	22	x	x	SYM
ejpam-6007	152	23	,	,	PUNCT
ejpam-6007	152	24	λ1	λ1	ADJ
ejpam-6007	152	25	and	and	CCONJ
ejpam-6007	152	26	λ2	λ2	NOUN
ejpam-6007	152	27	,	,	PUNCT
ejpam-6007	152	28	respectively	respectively	ADV
ejpam-6007	152	29	.	.	PUNCT
ejpam-6007	153	1	to	to	PART
ejpam-6007	153	2	discuss	discuss	VERB
ejpam-6007	153	3	the	the	DET
ejpam-6007	153	4	uniform	uniform	ADJ
ejpam-6007	153	5	convergence	convergence	NOUN
ejpam-6007	153	6	of	of	ADP
ejpam-6007	153	7	xn+1	xn+1	PROPN
ejpam-6007	153	8	,	,	PUNCT
ejpam-6007	153	9	λ1,n+1	λ1,n+1	PROPN
ejpam-6007	153	10	and	and	CCONJ
ejpam-6007	153	11	λ2,n+1	λ2,n+1	PROPN
ejpam-6007	153	12	,	,	PUNCT
ejpam-6007	153	13	we	we	PRON
ejpam-6007	153	14	consider	consider	VERB
ejpam-6007	153	15	the	the	DET
ejpam-6007	153	16	following	follow	VERB
ejpam-6007	153	17	three	three	NUM
ejpam-6007	153	18	associated	associated	ADJ
ejpam-6007	153	19	series	series	NOUN
ejpam-6007	153	20	:	:	PUNCT
ejpam-6007	153	21	∞∑	∞∑	NUM
ejpam-6007	153	22	n=0	n=0	NUM
ejpam-6007	153	23	(	(	PUNCT
ejpam-6007	153	24	xn+1	xn+1	NUM
ejpam-6007	153	25	−	−	NOUN
ejpam-6007	153	26	xn	xn	NUM
ejpam-6007	153	27	)	)	PUNCT
ejpam-6007	153	28	,	,	PUNCT
ejpam-6007	153	29	∞∑	∞∑	PROPN
ejpam-6007	153	30	n=0	n=0	NUM
ejpam-6007	153	31	(	(	PUNCT
ejpam-6007	153	32	λ1,n+1	λ1,n+1	PROPN
ejpam-6007	153	33	−	−	PROPN
ejpam-6007	153	34	λ1,n	λ1,n	PROPN
ejpam-6007	153	35	)	)	PUNCT
ejpam-6007	153	36	,	,	PUNCT
ejpam-6007	153	37	∞∑	∞∑	PROPN
ejpam-6007	153	38	n=0	n=0	NUM
ejpam-6007	153	39	(	(	PUNCT
ejpam-6007	153	40	λ2,n+1	λ2,n+1	NOUN
ejpam-6007	153	41	−	−	PROPN
ejpam-6007	153	42	λ2,n	λ2,n	NOUN
ejpam-6007	153	43	)	)	PUNCT
ejpam-6007	153	44	.	.	PUNCT
ejpam-6007	154	1	(	(	PUNCT
ejpam-6007	154	2	20	20	NUM
ejpam-6007	154	3	)	)	PUNCT
ejpam-6007	154	4	for	for	ADP
ejpam-6007	154	5	n	n	NOUN
ejpam-6007	154	6	=	=	SYM
ejpam-6007	154	7	0	0	NUM
ejpam-6007	154	8	,	,	PUNCT
ejpam-6007	154	9	x1	x1	NUM
ejpam-6007	154	10	−	−	NOUN
ejpam-6007	154	11	x0	x0	PROPN
ejpam-6007	155	1	=	=	PUNCT
ejpam-6007	155	2	h	h	NOUN
ejpam-6007	155	3	6	6	NUM
ejpam-6007	155	4	φ1(xn	φ1(xn	PROPN
ejpam-6007	155	5	,	,	PUNCT
ejpam-6007	155	6	λ1,n	λ1,n	PROPN
ejpam-6007	155	7	,	,	PUNCT
ejpam-6007	155	8	λ2,n	λ2,n	PROPN
ejpam-6007	155	9	,	,	PUNCT
ejpam-6007	155	10	t	t	PROPN
ejpam-6007	155	11	)	)	PUNCT
ejpam-6007	155	12	,	,	PUNCT
ejpam-6007	155	13	|x1	|x1	NUM
ejpam-6007	155	14	−	−	PROPN
ejpam-6007	155	15	x0|	x0|	PROPN
ejpam-6007	156	1	=	=	SYM
ejpam-6007	156	2	∣∣∣∣h6φ1(xn	∣∣∣∣h6φ1(xn	PROPN
ejpam-6007	156	3	,	,	PUNCT
ejpam-6007	156	4	λ1,n	λ1,n	PROPN
ejpam-6007	156	5	,	,	PUNCT
ejpam-6007	156	6	λ2,n	λ2,n	PROPN
ejpam-6007	156	7	,	,	PUNCT
ejpam-6007	156	8	t	t	PROPN
ejpam-6007	156	9	)	)	PUNCT
ejpam-6007	156	10	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6007	156	11	,	,	PUNCT
ejpam-6007	156	12	|x1	|x1	NUM
ejpam-6007	156	13	−	−	PROPN
ejpam-6007	156	14	x0|	x0|	PROPN
ejpam-6007	156	15	≤	≤	PROPN
ejpam-6007	156	16	h	h	NOUN
ejpam-6007	156	17	6	6	NUM
ejpam-6007	156	18	m1	m1	NOUN
ejpam-6007	156	19	.	.	PUNCT
ejpam-6007	157	1	(	(	PUNCT
ejpam-6007	157	2	21	21	NUM
ejpam-6007	157	3	)	)	PUNCT
ejpam-6007	157	4	similarly	similarly	ADV
ejpam-6007	157	5	,	,	PUNCT
ejpam-6007	157	6	|λ1,1	|λ1,1	ADP
ejpam-6007	157	7	−	−	PROPN
ejpam-6007	157	8	λ1,0|	λ1,0|	PROPN
ejpam-6007	157	9	≤	≤	NUM
ejpam-6007	157	10	h	h	NOUN
ejpam-6007	157	11	6	6	NUM
ejpam-6007	157	12	m2	m2	NOUN
ejpam-6007	157	13	,	,	PUNCT
ejpam-6007	157	14	|λ2,1	|λ2,1	NOUN
ejpam-6007	157	15	−	−	NOUN
ejpam-6007	157	16	λ2,0|	λ2,0|	NOUN
ejpam-6007	157	17	≤	≤	NUM
ejpam-6007	157	18	h	h	NOUN
ejpam-6007	157	19	6	6	NUM
ejpam-6007	157	20	m3	m3	PROPN
ejpam-6007	157	21	.	.	PUNCT
ejpam-6007	158	1	(	(	PUNCT
ejpam-6007	158	2	22	22	NUM
ejpam-6007	158	3	)	)	PUNCT
ejpam-6007	158	4	now	now	ADV
ejpam-6007	158	5	,	,	PUNCT
ejpam-6007	158	6	we	we	PRON
ejpam-6007	158	7	will	will	AUX
ejpam-6007	158	8	get	get	VERB
ejpam-6007	158	9	an	an	DET
ejpam-6007	158	10	estimation	estimation	NOUN
ejpam-6007	158	11	for(xn+1	for(xn+1	NOUN
ejpam-6007	158	12	−	−	PROPN
ejpam-6007	158	13	xn	xn	PROPN
ejpam-6007	158	14	)	)	PUNCT
ejpam-6007	158	15	,	,	PUNCT
ejpam-6007	158	16	(	(	PUNCT
ejpam-6007	158	17	λ1,n+1	λ1,n+1	PROPN
ejpam-6007	158	18	−	−	PROPN
ejpam-6007	158	19	λ1,n	λ1,n	PROPN
ejpam-6007	158	20	)	)	PUNCT
ejpam-6007	158	21	and	and	CCONJ
ejpam-6007	158	22	(	(	PUNCT
ejpam-6007	158	23	λ2,n+1	λ2,n+1	INTJ
ejpam-6007	158	24	−	−	PROPN
ejpam-6007	158	25	λ2,n	λ2,n	NOUN
ejpam-6007	158	26	)	)	PUNCT
ejpam-6007	158	27	a.	a.	NOUN
ejpam-6007	158	28	a.	a.	NOUN
ejpam-6007	158	29	megahed	megahe	VERB
ejpam-6007	158	30	et	et	PROPN
ejpam-6007	158	31	al	al	PROPN
ejpam-6007	158	32	.	.	PUNCT
ejpam-6007	158	33	/	/	SYM
ejpam-6007	158	34	eur	eur	PROPN
ejpam-6007	158	35	.	.	PUNCT
ejpam-6007	159	1	j.	j.	PROPN
ejpam-6007	159	2	pure	pure	PROPN
ejpam-6007	159	3	appl	appl	PROPN
ejpam-6007	159	4	.	.	PROPN
ejpam-6007	159	5	math	math	PROPN
ejpam-6007	159	6	,	,	PUNCT
ejpam-6007	159	7	18	18	NUM
ejpam-6007	159	8	(	(	PUNCT
ejpam-6007	159	9	4	4	NUM
ejpam-6007	159	10	)	)	PUNCT
ejpam-6007	159	11	(	(	PUNCT
ejpam-6007	159	12	2025	2025	NUM
ejpam-6007	159	13	)	)	PUNCT
ejpam-6007	159	14	,	,	PUNCT
ejpam-6007	159	15	6007	6007	NUM
ejpam-6007	159	16	8	8	NUM
ejpam-6007	159	17	of	of	ADP
ejpam-6007	159	18	22	22	NUM
ejpam-6007	159	19	|xn+1	|xn+1	NOUN
ejpam-6007	159	20	−	−	NOUN
ejpam-6007	159	21	xn|	xn|	NOUN
ejpam-6007	160	1	=	=	NOUN
ejpam-6007	160	2	∣∣∣∣(xn	∣∣∣∣(xn	PROPN
ejpam-6007	160	3	−	−	PROPN
ejpam-6007	160	4	xn−1	xn−1	PROPN
ejpam-6007	160	5	)	)	PUNCT
ejpam-6007	161	1	+	+	CCONJ
ejpam-6007	161	2	h	h	NOUN
ejpam-6007	161	3	6	6	NUM
ejpam-6007	161	4	(	(	PUNCT
ejpam-6007	161	5	φ1,n	φ1,n	NOUN
ejpam-6007	161	6	−	−	PROPN
ejpam-6007	161	7	φ1,n−1	φ1,n−1	ADJ
ejpam-6007	161	8	)	)	PUNCT
ejpam-6007	161	9	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6007	161	10	,	,	PUNCT
ejpam-6007	161	11	|xn+1	|xn+1	ADJ
ejpam-6007	161	12	−	−	PROPN
ejpam-6007	161	13	xn|	xn|	NOUN
ejpam-6007	161	14	≤	≤	ADJ
ejpam-6007	161	15	|xn	|xn	X
ejpam-6007	161	16	−	−	PROPN
ejpam-6007	161	17	xn−1|+	xn−1|+	PROPN
ejpam-6007	161	18	h	h	PROPN
ejpam-6007	161	19	6	6	NUM
ejpam-6007	161	20	|φ1,n	|φ1,n	NOUN
ejpam-6007	161	21	−	−	ADP
ejpam-6007	161	22	φ1,n−1|	φ1,n−1|	PROPN
ejpam-6007	161	23	,	,	PUNCT
ejpam-6007	161	24	|xn+1	|xn+1	VERB
ejpam-6007	161	25	−	−	PROPN
ejpam-6007	161	26	xn|	xn|	NOUN
ejpam-6007	161	27	≤	≤	ADJ
ejpam-6007	161	28	|xn	|xn	X
ejpam-6007	161	29	−	−	PROPN
ejpam-6007	161	30	xn−1|+	xn−1|+	PROPN
ejpam-6007	161	31	h	h	PROPN
ejpam-6007	161	32	6	6	NUM
ejpam-6007	161	33	|l1(xn	|l1(xn	NOUN
ejpam-6007	161	34	−	−	PROPN
ejpam-6007	161	35	xn−1)|	xn−1)|	PROPN
ejpam-6007	161	36	,	,	PUNCT
ejpam-6007	161	37	|xn+1	|xn+1	VERB
ejpam-6007	161	38	−	−	PROPN
ejpam-6007	161	39	xn|	xn|	NOUN
ejpam-6007	161	40	≤	≤	NUM
ejpam-6007	161	41	(	(	PUNCT
ejpam-6007	161	42	1	1	NUM
ejpam-6007	161	43	+	+	NUM
ejpam-6007	161	44	l1	l1	PROPN
ejpam-6007	161	45	h	h	PROPN
ejpam-6007	161	46	6	6	NUM
ejpam-6007	161	47	)	)	PUNCT
ejpam-6007	161	48	|xn	|xn	X
ejpam-6007	161	49	−	−	PROPN
ejpam-6007	161	50	xn−1|	xn−1|	NOUN
ejpam-6007	161	51	.	.	PUNCT
ejpam-6007	162	1	(	(	PUNCT
ejpam-6007	162	2	23	23	NUM
ejpam-6007	162	3	)	)	PUNCT
ejpam-6007	162	4	similarly	similarly	ADV
ejpam-6007	162	5	,	,	PUNCT
ejpam-6007	162	6	|λ1,n+1	|λ1,n+1	VERB
ejpam-6007	162	7	−	−	PROPN
ejpam-6007	162	8	λ1,n|	λ1,n|	PROPN
ejpam-6007	162	9	≤	≤	X
ejpam-6007	162	10	(	(	PUNCT
ejpam-6007	162	11	1	1	NUM
ejpam-6007	162	12	+	+	NUM
ejpam-6007	162	13	h	h	NOUN
ejpam-6007	162	14	6	6	NUM
ejpam-6007	162	15	l2	l2	NOUN
ejpam-6007	162	16	)	)	PUNCT
ejpam-6007	162	17	|λ1,n	|λ1,n	NOUN
ejpam-6007	162	18	−	−	NOUN
ejpam-6007	162	19	λ1,n−1|	λ1,n−1|	NOUN
ejpam-6007	162	20	,	,	PUNCT
ejpam-6007	162	21	|λ2,n+1	|λ2,n+1	VERB
ejpam-6007	162	22	−	−	NOUN
ejpam-6007	162	23	λ2,n|	λ2,n|	PROPN
ejpam-6007	162	24	≤	≤	NUM
ejpam-6007	162	25	(	(	PUNCT
ejpam-6007	162	26	1	1	NUM
ejpam-6007	162	27	+	+	NUM
ejpam-6007	162	28	h	h	NOUN
ejpam-6007	162	29	6	6	NUM
ejpam-6007	162	30	l3	l3	NOUN
ejpam-6007	162	31	)	)	PUNCT
ejpam-6007	162	32	|λ2,n	|λ2,n	NUM
ejpam-6007	162	33	−	−	PROPN
ejpam-6007	162	34	λ2,n−1|	λ2,n−1|	X
ejpam-6007	162	35	.	.	PUNCT
ejpam-6007	163	1	(	(	PUNCT
ejpam-6007	163	2	24	24	NUM
ejpam-6007	163	3	)	)	PUNCT
ejpam-6007	163	4	at	at	ADP
ejpam-6007	163	5	n	n	PROPN
ejpam-6007	163	6	=	=	SYM
ejpam-6007	163	7	1	1	NUM
ejpam-6007	163	8	,	,	PUNCT
ejpam-6007	163	9	|x2	|x2	ADV
ejpam-6007	163	10	−	−	PROPN
ejpam-6007	164	1	x1|	x1|	NOUN
ejpam-6007	164	2	≤	≤	NUM
ejpam-6007	164	3	(	(	PUNCT
ejpam-6007	164	4	1	1	NUM
ejpam-6007	164	5	+	+	NUM
ejpam-6007	164	6	l1	l1	PROPN
ejpam-6007	164	7	h	h	PROPN
ejpam-6007	164	8	6	6	NUM
ejpam-6007	164	9	)	)	PUNCT
ejpam-6007	164	10	|x1	|x1	ADP
ejpam-6007	164	11	−	−	PROPN
ejpam-6007	164	12	x0|	x0|	PROPN
ejpam-6007	165	1	|x2	|x2	ADV
ejpam-6007	165	2	−	−	PROPN
ejpam-6007	166	1	x1|	x1|	NOUN
ejpam-6007	167	1	≤	≤	NUM
ejpam-6007	167	2	h	h	NOUN
ejpam-6007	167	3	6	6	NUM
ejpam-6007	167	4	m1(1	m1(1	PROPN
ejpam-6007	167	5	+	+	PROPN
ejpam-6007	167	6	l1	l1	PROPN
ejpam-6007	167	7	h	h	PROPN
ejpam-6007	167	8	6	6	NUM
ejpam-6007	167	9	)	)	PUNCT
ejpam-6007	167	10	.	.	PUNCT
ejpam-6007	168	1	(	(	PUNCT
ejpam-6007	168	2	25	25	NUM
ejpam-6007	168	3	)	)	PUNCT
ejpam-6007	168	4	at	at	ADP
ejpam-6007	168	5	n	n	PROPN
ejpam-6007	168	6	=	=	SYM
ejpam-6007	168	7	2	2	NUM
ejpam-6007	168	8	,	,	PUNCT
ejpam-6007	168	9	|x3	|x3	NUM
ejpam-6007	168	10	−	−	PROPN
ejpam-6007	169	1	x2|	x2|	PROPN
ejpam-6007	170	1	≤	≤	PROPN
ejpam-6007	170	2	(	(	PUNCT
ejpam-6007	170	3	1	1	NUM
ejpam-6007	170	4	+	+	NUM
ejpam-6007	170	5	l1	l1	PROPN
ejpam-6007	170	6	h	h	PROPN
ejpam-6007	170	7	6	6	NUM
ejpam-6007	170	8	)	)	PUNCT
ejpam-6007	170	9	|x2	|x2	NOUN
ejpam-6007	170	10	−	−	PROPN
ejpam-6007	171	1	x1|	x1|	INTJ
ejpam-6007	171	2	,	,	PUNCT
ejpam-6007	171	3	|x3	|x3	NUM
ejpam-6007	172	1	−	−	PROPN
ejpam-6007	172	2	x2|	x2|	PROPN
ejpam-6007	173	1	≤	≤	PROPN
ejpam-6007	173	2	h	h	NOUN
ejpam-6007	173	3	6	6	NUM
ejpam-6007	173	4	m1(1	m1(1	PROPN
ejpam-6007	173	5	+	+	PROPN
ejpam-6007	173	6	l1	l1	PROPN
ejpam-6007	173	7	h	h	PROPN
ejpam-6007	173	8	6	6	NUM
ejpam-6007	173	9	)	)	SYM
ejpam-6007	173	10	2	2	NUM
ejpam-6007	173	11	.	.	PUNCT
ejpam-6007	174	1	(	(	PUNCT
ejpam-6007	174	2	26	26	NUM
ejpam-6007	174	3	)	)	PUNCT
ejpam-6007	174	4	at	at	ADP
ejpam-6007	174	5	n	n	PROPN
ejpam-6007	174	6	=	=	SYM
ejpam-6007	174	7	3	3	NUM
ejpam-6007	174	8	,	,	PUNCT
ejpam-6007	174	9	|x4	|x4	NOUN
ejpam-6007	174	10	−	−	PROPN
ejpam-6007	174	11	x3|	x3|	PROPN
ejpam-6007	175	1	≤	≤	NUM
ejpam-6007	175	2	(	(	PUNCT
ejpam-6007	175	3	1	1	NUM
ejpam-6007	175	4	+	+	NUM
ejpam-6007	175	5	l1	l1	PROPN
ejpam-6007	175	6	h	h	PROPN
ejpam-6007	175	7	6	6	NUM
ejpam-6007	175	8	)	)	PUNCT
ejpam-6007	175	9	|x3	|x3	NOUN
ejpam-6007	175	10	−	−	PROPN
ejpam-6007	176	1	x2|	x2|	PROPN
ejpam-6007	176	2	,	,	PUNCT
ejpam-6007	176	3	|x4	|x4	PROPN
ejpam-6007	176	4	−	−	PROPN
ejpam-6007	176	5	x3|	x3|	PUNCT
ejpam-6007	176	6	≤	≤	ADJ
ejpam-6007	176	7	h	h	NOUN
ejpam-6007	176	8	6	6	NUM
ejpam-6007	176	9	m1(1	m1(1	PROPN
ejpam-6007	176	10	+	+	PROPN
ejpam-6007	176	11	l1	l1	PROPN
ejpam-6007	176	12	h	h	PROPN
ejpam-6007	176	13	6	6	NUM
ejpam-6007	176	14	)	)	SYM
ejpam-6007	176	15	3	3	NUM
ejpam-6007	176	16	.	.	PUNCT
ejpam-6007	177	1	(	(	PUNCT
ejpam-6007	177	2	27	27	NUM
ejpam-6007	177	3	)	)	PUNCT
ejpam-6007	177	4	and	and	CCONJ
ejpam-6007	177	5	so	so	ADV
ejpam-6007	177	6	on	on	ADP
ejpam-6007	177	7	|xn+1	|xn+1	NOUN
ejpam-6007	177	8	−	−	PROPN
ejpam-6007	177	9	xn|	xn|	NOUN
ejpam-6007	177	10	≤	≤	NUM
ejpam-6007	177	11	h	h	NOUN
ejpam-6007	177	12	6	6	NUM
ejpam-6007	177	13	m1(1	m1(1	PROPN
ejpam-6007	177	14	+	+	PROPN
ejpam-6007	177	15	l1	l1	PROPN
ejpam-6007	177	16	h	h	PROPN
ejpam-6007	177	17	6	6	NUM
ejpam-6007	177	18	)	)	PUNCT
ejpam-6007	177	19	n.	n.	NOUN
ejpam-6007	177	20	(	(	PUNCT
ejpam-6007	177	21	28	28	NUM
ejpam-6007	177	22	)	)	PUNCT
ejpam-6007	177	23	similarly	similarly	ADV
ejpam-6007	177	24	,	,	PUNCT
ejpam-6007	177	25	|λ1,n+1	|λ1,n+1	VERB
ejpam-6007	177	26	−	−	PROPN
ejpam-6007	177	27	λ1,n|	λ1,n|	PROPN
ejpam-6007	177	28	≤	≤	PROPN
ejpam-6007	177	29	h	h	NOUN
ejpam-6007	177	30	6	6	NUM
ejpam-6007	177	31	m2(1	m2(1	NOUN
ejpam-6007	177	32	+	+	X
ejpam-6007	177	33	l1	l1	PROPN
ejpam-6007	177	34	h	h	PROPN
ejpam-6007	177	35	6	6	NUM
ejpam-6007	177	36	)	)	PUNCT
ejpam-6007	177	37	n	n	CCONJ
ejpam-6007	177	38	,	,	PUNCT
ejpam-6007	177	39	|λ2,n+1	|λ2,n+1	VERB
ejpam-6007	177	40	−	−	NOUN
ejpam-6007	177	41	λ2,n|	λ2,n|	PROPN
ejpam-6007	178	1	≤	≤	NUM
ejpam-6007	178	2	h	h	NOUN
ejpam-6007	178	3	6	6	NUM
ejpam-6007	178	4	m2(1	m2(1	NOUN
ejpam-6007	178	5	+	+	X
ejpam-6007	178	6	l1	l1	PROPN
ejpam-6007	178	7	h	h	PROPN
ejpam-6007	178	8	6	6	NUM
ejpam-6007	178	9	)	)	PUNCT
ejpam-6007	178	10	n.	n.	NOUN
ejpam-6007	178	11	(	(	PUNCT
ejpam-6007	178	12	29	29	NUM
ejpam-6007	178	13	)	)	PUNCT
ejpam-6007	178	14	since	since	SCONJ
ejpam-6007	178	15	li	li	PROPN
ejpam-6007	178	16	≤	≤	PROPN
ejpam-6007	178	17	1	1	NUM
ejpam-6007	178	18	,	,	PUNCT
ejpam-6007	178	19	mi	mi	PROPN
ejpam-6007	178	20	≤	≤	ADV
ejpam-6007	178	21	1	1	NUM
ejpam-6007	178	22	and	and	CCONJ
ejpam-6007	178	23	h	h	NOUN
ejpam-6007	178	24	≤	≤	NOUN
ejpam-6007	178	25	1	1	NUM
ejpam-6007	179	1	i	i	NOUN
ejpam-6007	179	2	=	=	NOUN
ejpam-6007	179	3	1	1	NUM
ejpam-6007	179	4	,	,	PUNCT
ejpam-6007	179	5	2	2	NUM
ejpam-6007	179	6	,	,	PUNCT
ejpam-6007	179	7	3	3	NUM
ejpam-6007	179	8	.	.	PUNCT
ejpam-6007	180	1	then	then	ADV
ejpam-6007	180	2	the	the	DET
ejpam-6007	180	3	series	series	NOUN
ejpam-6007	180	4	∑∞	∑∞	PROPN
ejpam-6007	180	5	n=0	n=0	NUM
ejpam-6007	180	6	(	(	PUNCT
ejpam-6007	180	7	xn+1	xn+1	NUM
ejpam-6007	180	8	−	−	NOUN
ejpam-6007	180	9	xn	xn	NUM
ejpam-6007	180	10	)	)	PUNCT
ejpam-6007	180	11	,	,	PUNCT
ejpam-6007	180	12	∑∞	∑∞	NOUN
ejpam-6007	180	13	n=0	n=0	PRON
ejpam-6007	180	14	(	(	PUNCT
ejpam-6007	180	15	λ1,n+1	λ1,n+1	PROPN
ejpam-6007	180	16	−	−	PROPN
ejpam-6007	180	17	λ1,n	λ1,n	PROPN
ejpam-6007	180	18	)	)	PUNCT
ejpam-6007	180	19	,	,	PUNCT
ejpam-6007	180	20	∑∞	∑∞	NOUN
ejpam-6007	180	21	n=0	n=0	NUM
ejpam-6007	181	1	(	(	PUNCT
ejpam-6007	181	2	λ2,n+1	λ2,n+1	NOUN
ejpam-6007	181	3	−	−	PROPN
ejpam-6007	181	4	λ2,n	λ2,n	NOUN
ejpam-6007	181	5	)	)	PUNCT
ejpam-6007	181	6	,	,	PUNCT
ejpam-6007	181	7	and	and	CCONJ
ejpam-6007	181	8	the	the	DET
ejpam-6007	181	9	sequences	sequence	NOUN
ejpam-6007	181	10	xn+1	xn+1	PROPN
ejpam-6007	181	11	,	,	PUNCT
ejpam-6007	181	12	λ1,n+1	λ1,n+1	PROPN
ejpam-6007	181	13	,	,	PUNCT
ejpam-6007	181	14	λ2,n+1	λ2,n+1	VERB
ejpam-6007	181	15	are	be	AUX
ejpam-6007	181	16	uniformly	uniformly	ADV
ejpam-6007	181	17	convergent	convergent	ADJ
ejpam-6007	181	18	.	.	PUNCT
ejpam-6007	182	1	since	since	SCONJ
ejpam-6007	182	2	li	li	PROPN
ejpam-6007	182	3	≤	≤	PROPN
ejpam-6007	182	4	1	1	NUM
ejpam-6007	182	5	,	,	PUNCT
ejpam-6007	182	6	mi	mi	PROPN
ejpam-6007	182	7	≤	≤	PROPN
ejpam-6007	182	8	1	1	NUM
ejpam-6007	182	9	,	,	PUNCT
ejpam-6007	182	10	and	and	CCONJ
ejpam-6007	182	11	h	h	NOUN
ejpam-6007	182	12	≤	≤	NOUN
ejpam-6007	182	13	1	1	NUM
ejpam-6007	182	14	for	for	ADP
ejpam-6007	182	15	i	i	PRON
ejpam-6007	182	16	=	=	NOUN
ejpam-6007	182	17	1	1	NUM
ejpam-6007	182	18	,	,	PUNCT
ejpam-6007	182	19	2	2	NUM
ejpam-6007	182	20	,	,	PUNCT
ejpam-6007	182	21	3	3	NUM
ejpam-6007	182	22	,	,	PUNCT
ejpam-6007	182	23	the	the	DET
ejpam-6007	182	24	series	series	PROPN
ejpam-6007	182	25	∑∞	∑∞	PROPN
ejpam-6007	182	26	n=0(xn+1	n=0(xn+1	NOUN
ejpam-6007	182	27	−	−	PROPN
ejpam-6007	182	28	xn),∑∞	xn),∑∞	PROPN
ejpam-6007	183	1	n=0(λ1,n+1	n=0(λ1,n+1	PROPN
ejpam-6007	183	2	−	−	PROPN
ejpam-6007	183	3	λ1,n	λ1,n	PROPN
ejpam-6007	183	4	)	)	PUNCT
ejpam-6007	183	5	,	,	PUNCT
ejpam-6007	183	6	and	and	CCONJ
ejpam-6007	183	7	∑∞	∑∞	X
ejpam-6007	184	1	n=0(λ2,n+1	n=0(λ2,n+1	DET
ejpam-6007	184	2	−	−	NOUN
ejpam-6007	184	3	λ2,n	λ2,n	NOUN
ejpam-6007	184	4	)	)	PUNCT
ejpam-6007	184	5	,	,	PUNCT
ejpam-6007	184	6	as	as	ADV
ejpam-6007	184	7	well	well	ADV
ejpam-6007	184	8	as	as	ADP
ejpam-6007	184	9	the	the	DET
ejpam-6007	184	10	sequences	sequence	NOUN
ejpam-6007	184	11	xn+1	xn+1	PROPN
ejpam-6007	184	12	,	,	PUNCT
ejpam-6007	184	13	λ1,n+1	λ1,n+1	PROPN
ejpam-6007	184	14	,	,	PUNCT
ejpam-6007	184	15	and	and	CCONJ
ejpam-6007	184	16	λ2,n+1	λ2,n+1	PROPN
ejpam-6007	184	17	,	,	PUNCT
ejpam-6007	184	18	are	be	AUX
ejpam-6007	184	19	uniformly	uniformly	ADV
ejpam-6007	184	20	convergent	convergent	ADJ
ejpam-6007	184	21	.	.	PUNCT
ejpam-6007	185	1	a.	a.	NOUN
ejpam-6007	185	2	a.	a.	PROPN
ejpam-6007	185	3	megahed	megahe	VERB
ejpam-6007	185	4	et	et	PROPN
ejpam-6007	185	5	al	al	PROPN
ejpam-6007	185	6	.	.	PUNCT
ejpam-6007	185	7	/	/	SYM
ejpam-6007	185	8	eur	eur	PROPN
ejpam-6007	185	9	.	.	PUNCT
ejpam-6007	186	1	j.	j.	PROPN
ejpam-6007	186	2	pure	pure	PROPN
ejpam-6007	186	3	appl	appl	PROPN
ejpam-6007	186	4	.	.	PROPN
ejpam-6007	186	5	math	math	PROPN
ejpam-6007	186	6	,	,	PUNCT
ejpam-6007	186	7	18	18	NUM
ejpam-6007	186	8	(	(	PUNCT
ejpam-6007	186	9	4	4	NUM
ejpam-6007	186	10	)	)	PUNCT
ejpam-6007	186	11	(	(	PUNCT
ejpam-6007	186	12	2025	2025	NUM
ejpam-6007	186	13	)	)	PUNCT
ejpam-6007	186	14	,	,	PUNCT
ejpam-6007	186	15	6007	6007	NUM
ejpam-6007	186	16	9	9	NUM
ejpam-6007	186	17	of	of	ADP
ejpam-6007	186	18	22	22	NUM
ejpam-6007	186	19	3.2	3.2	NUM
ejpam-6007	186	20	.	.	PUNCT
ejpam-6007	187	1	numerical	numerical	ADJ
ejpam-6007	187	2	solution	solution	NOUN
ejpam-6007	187	3	we	we	PRON
ejpam-6007	187	4	now	now	ADV
ejpam-6007	187	5	apply	apply	VERB
ejpam-6007	187	6	the	the	DET
ejpam-6007	187	7	fourth	fourth	ADJ
ejpam-6007	187	8	-	-	PUNCT
ejpam-6007	187	9	order	order	NOUN
ejpam-6007	187	10	runge	runge	NOUN
ejpam-6007	187	11	–	–	PUNCT
ejpam-6007	187	12	kutta	kutta	NOUN
ejpam-6007	187	13	method	method	NOUN
ejpam-6007	187	14	to	to	PART
ejpam-6007	187	15	obtain	obtain	VERB
ejpam-6007	187	16	the	the	DET
ejpam-6007	187	17	numerical	numerical	ADJ
ejpam-6007	187	18	solution	solution	NOUN
ejpam-6007	187	19	for	for	ADP
ejpam-6007	187	20	the	the	DET
ejpam-6007	187	21	problem	problem	NOUN
ejpam-6007	187	22	(	(	PUNCT
ejpam-6007	187	23	11	11	NUM
ejpam-6007	187	24	)	)	PUNCT
ejpam-6007	187	25	.	.	PUNCT
ejpam-6007	188	1	by	by	ADP
ejpam-6007	188	2	substituting	substitute	VERB
ejpam-6007	188	3	the	the	DET
ejpam-6007	188	4	controls	control	NOUN
ejpam-6007	188	5	u1	u1	NOUN
ejpam-6007	188	6	and	and	CCONJ
ejpam-6007	188	7	u2	u2	NOUN
ejpam-6007	188	8	into	into	ADP
ejpam-6007	188	9	the	the	DET
ejpam-6007	188	10	state	state	NOUN
ejpam-6007	188	11	and	and	CCONJ
ejpam-6007	188	12	costate	costate	ADJ
ejpam-6007	188	13	equations	equation	NOUN
ejpam-6007	188	14	,	,	PUNCT
ejpam-6007	188	15	we	we	PRON
ejpam-6007	188	16	obtain	obtain	VERB
ejpam-6007	188	17	:	:	PUNCT
ejpam-6007	189	1	dx	dx	PROPN
ejpam-6007	189	2	dt	dt	X
ejpam-6007	190	1	=	=	SYM
ejpam-6007	190	2	λ1	λ1	PROPN
ejpam-6007	190	3	p1	p1	PROPN
ejpam-6007	190	4	(	(	PUNCT
ejpam-6007	190	5	1−	1−	NUM
ejpam-6007	190	6	x)2	x)2	NOUN
ejpam-6007	190	7	+	+	CCONJ
ejpam-6007	190	8	λ2	λ2	NOUN
ejpam-6007	190	9	p2	p2	NOUN
ejpam-6007	190	10	x2	x2	PROPN
ejpam-6007	190	11	,	,	PUNCT
ejpam-6007	190	12	x(0	x(0	PROPN
ejpam-6007	190	13	)	)	PUNCT
ejpam-6007	190	14	=	=	PUNCT
ejpam-6007	190	15	x0	x0	PROPN
ejpam-6007	190	16	,	,	PUNCT
ejpam-6007	190	17	dλ1(t	dλ1(t	PROPN
ejpam-6007	190	18	)	)	PUNCT
ejpam-6007	190	19	dt	dt	NOUN
ejpam-6007	191	1	=	=	SYM
ejpam-6007	191	2	λ2	λ2	PROPN
ejpam-6007	191	3	1	1	NUM
ejpam-6007	191	4	p1	p1	NOUN
ejpam-6007	191	5	(	(	PUNCT
ejpam-6007	191	6	1−	1−	NUM
ejpam-6007	191	7	x)−	x)−	PROPN
ejpam-6007	191	8	λ1λ2(t	λ1λ2(t	NOUN
ejpam-6007	191	9	)	)	PUNCT
ejpam-6007	191	10	p2	p2	PROPN
ejpam-6007	191	11	x−	x−	PROPN
ejpam-6007	191	12	ϕ1	ϕ1	PROPN
ejpam-6007	191	13	,	,	PUNCT
ejpam-6007	191	14	λ1(t	λ1(t	PUNCT
ejpam-6007	191	15	)	)	PUNCT
ejpam-6007	191	16	=	=	SYM
ejpam-6007	191	17	0	0	NUM
ejpam-6007	191	18	,	,	PUNCT
ejpam-6007	191	19	dλ2(t	dλ2(t	NOUN
ejpam-6007	191	20	)	)	PUNCT
ejpam-6007	191	21	dt	dt	NOUN
ejpam-6007	192	1	=	=	PUNCT
ejpam-6007	192	2	λ1λ2(t	λ1λ2(t	NOUN
ejpam-6007	192	3	)	)	PUNCT
ejpam-6007	192	4	p1	p1	NOUN
ejpam-6007	192	5	(	(	PUNCT
ejpam-6007	192	6	1−	1−	NUM
ejpam-6007	192	7	x)−	x)−	PROPN
ejpam-6007	192	8	λ2	λ2	NOUN
ejpam-6007	192	9	2	2	NUM
ejpam-6007	192	10	p2	p2	NOUN
ejpam-6007	192	11	x+	x+	PUNCT
ejpam-6007	192	12	ϕ2	ϕ2	ADV
ejpam-6007	192	13	,	,	PUNCT
ejpam-6007	192	14	λ2(t	λ2(t	X
ejpam-6007	192	15	)	)	PUNCT
ejpam-6007	192	16	=	=	SYM
ejpam-6007	192	17	0	0	X
ejpam-6007	192	18	.	.	PUNCT
ejpam-6007	192	19	(	(	PUNCT
ejpam-6007	192	20	30	30	NUM
ejpam-6007	192	21	)	)	PUNCT
ejpam-6007	192	22	then	then	ADV
ejpam-6007	192	23	,	,	PUNCT
ejpam-6007	192	24	the	the	DET
ejpam-6007	192	25	system	system	NOUN
ejpam-6007	192	26	becomes	become	VERB
ejpam-6007	192	27	:	:	PUNCT
ejpam-6007	192	28	fx(xn	fx(xn	PROPN
ejpam-6007	192	29	,	,	PUNCT
ejpam-6007	192	30	tn	tn	PROPN
ejpam-6007	192	31	)	)	PUNCT
ejpam-6007	192	32	=	=	PUNCT
ejpam-6007	193	1	(	(	PUNCT
ejpam-6007	193	2	λ1(t))n	λ1(t))n	PROPN
ejpam-6007	193	3	p1	p1	NOUN
ejpam-6007	193	4	(	(	PUNCT
ejpam-6007	193	5	1−	1−	NUM
ejpam-6007	193	6	xn(t	xn(t	NUM
ejpam-6007	193	7	)	)	PUNCT
ejpam-6007	193	8	)	)	PUNCT
ejpam-6007	193	9	2	2	NUM
ejpam-6007	194	1	+	+	CCONJ
ejpam-6007	194	2	(	(	PUNCT
ejpam-6007	194	3	λ2(t))n	λ2(t))n	NOUN
ejpam-6007	194	4	p2	p2	VERB
ejpam-6007	194	5	x2n	x2n	PROPN
ejpam-6007	194	6	,	,	PUNCT
ejpam-6007	194	7	fλ1(xn	fλ1(xn	NOUN
ejpam-6007	194	8	,	,	PUNCT
ejpam-6007	194	9	tn	tn	PROPN
ejpam-6007	194	10	)	)	PUNCT
ejpam-6007	194	11	=	=	SYM
ejpam-6007	194	12	(	(	PUNCT
ejpam-6007	194	13	λ1(t	λ1(t	PROPN
ejpam-6007	194	14	)	)	PUNCT
ejpam-6007	194	15	2)n	2)n	NUM
ejpam-6007	194	16	p1	p1	NOUN
ejpam-6007	194	17	(	(	PUNCT
ejpam-6007	194	18	1−	1−	NUM
ejpam-6007	194	19	xn(t))−	xn(t))−	NOUN
ejpam-6007	194	20	(	(	PUNCT
ejpam-6007	194	21	λ1(t))n(λ2(t))n	λ1(t))n(λ2(t))n	PRON
ejpam-6007	194	22	p2	p2	PROPN
ejpam-6007	194	23	xn(t)−	xn(t)−	PROPN
ejpam-6007	194	24	ϕ1	ϕ1	PROPN
ejpam-6007	194	25	,	,	PUNCT
ejpam-6007	194	26	fλ2(xn	fλ2(xn	NOUN
ejpam-6007	194	27	,	,	PUNCT
ejpam-6007	194	28	tn	tn	PROPN
ejpam-6007	194	29	)	)	PUNCT
ejpam-6007	194	30	=	=	PUNCT
ejpam-6007	195	1	(	(	PUNCT
ejpam-6007	195	2	λ1(t))n(λ2(t))n	λ1(t))n(λ2(t))n	NOUN
ejpam-6007	195	3	p1	p1	NOUN
ejpam-6007	195	4	(	(	PUNCT
ejpam-6007	195	5	1−	1−	NUM
ejpam-6007	195	6	xn(t))−	xn(t))−	NOUN
ejpam-6007	195	7	(	(	PUNCT
ejpam-6007	195	8	λ2	λ2	NOUN
ejpam-6007	195	9	2(t))n	2(t))n	PROPN
ejpam-6007	195	10	p2	p2	NOUN
ejpam-6007	195	11	xn(t	xn(t	PUNCT
ejpam-6007	195	12	)	)	PUNCT
ejpam-6007	196	1	+	+	CCONJ
ejpam-6007	196	2	ϕ2	ϕ2	ADV
ejpam-6007	196	3	,	,	PUNCT
ejpam-6007	196	4	(	(	PUNCT
ejpam-6007	196	5	ci)n+1	ci)n+1	NOUN
ejpam-6007	196	6	=	=	SYM
ejpam-6007	196	7	pi	pi	NOUN
ejpam-6007	196	8	2	2	NUM
ejpam-6007	196	9	(	(	PUNCT
ejpam-6007	196	10	u2i	u2i	NUM
ejpam-6007	196	11	)	)	PUNCT
ejpam-6007	196	12	n+1	n+1	PROPN
ejpam-6007	196	13	,	,	PUNCT
ejpam-6007	196	14	i	i	PRON
ejpam-6007	196	15	=	=	NOUN
ejpam-6007	196	16	1	1	NUM
ejpam-6007	196	17	,	,	PUNCT
ejpam-6007	196	18	2	2	NUM
ejpam-6007	196	19	.	.	PUNCT
ejpam-6007	196	20	(	(	PUNCT
ejpam-6007	196	21	31	31	NUM
ejpam-6007	196	22	)	)	PUNCT
ejpam-6007	196	23	with	with	ADP
ejpam-6007	196	24	the	the	DET
ejpam-6007	196	25	initial	initial	ADJ
ejpam-6007	196	26	and	and	CCONJ
ejpam-6007	196	27	terminal	terminal	ADJ
ejpam-6007	196	28	conditions	condition	NOUN
ejpam-6007	196	29	:	:	PUNCT
ejpam-6007	196	30	x(0	x(0	PROPN
ejpam-6007	196	31	)	)	PUNCT
ejpam-6007	197	1	=	=	PUNCT
ejpam-6007	197	2	x0	x0	PROPN
ejpam-6007	197	3	,	,	PUNCT
ejpam-6007	197	4	(	(	PUNCT
ejpam-6007	197	5	λ1)0	λ1)0	PUNCT
ejpam-6007	197	6	=	=	SYM
ejpam-6007	197	7	0	0	NUM
ejpam-6007	197	8	,	,	PUNCT
ejpam-6007	197	9	(	(	PUNCT
ejpam-6007	197	10	λ2(t	λ2(t	NOUN
ejpam-6007	197	11	)	)	PUNCT
ejpam-6007	197	12	)	)	PUNCT
ejpam-6007	197	13	0	0	X
ejpam-6007	198	1	=	=	SYM
ejpam-6007	198	2	0	0	PROPN
ejpam-6007	198	3	.	.	PUNCT
ejpam-6007	199	1	the	the	DET
ejpam-6007	199	2	general	general	ADJ
ejpam-6007	199	3	form	form	NOUN
ejpam-6007	199	4	after	after	ADP
ejpam-6007	199	5	applying	apply	VERB
ejpam-6007	199	6	the	the	DET
ejpam-6007	199	7	runge	runge	NOUN
ejpam-6007	199	8	-	-	PUNCT
ejpam-6007	199	9	kutta	kutta	NOUN
ejpam-6007	199	10	4th	4th	ADJ
ejpam-6007	199	11	-	-	PUNCT
ejpam-6007	199	12	order	order	NOUN
ejpam-6007	199	13	method	method	NOUN
ejpam-6007	199	14	is	be	AUX
ejpam-6007	199	15	as	as	SCONJ
ejpam-6007	199	16	follows	follow	VERB
ejpam-6007	199	17	,	,	PUNCT
ejpam-6007	199	18	xn+1	xn+1	PROPN
ejpam-6007	199	19	=	=	SYM
ejpam-6007	199	20	xn	xn	PROPN
ejpam-6007	200	1	+	+	NUM
ejpam-6007	200	2	h	h	PROPN
ejpam-6007	200	3	6	6	NUM
ejpam-6007	200	4	(	(	PUNCT
ejpam-6007	200	5	k1x	k1x	PROPN
ejpam-6007	200	6	+	+	NUM
ejpam-6007	200	7	2k2x	2k2x	NUM
ejpam-6007	200	8	+	+	CCONJ
ejpam-6007	200	9	2k3x	2k3x	NOUN
ejpam-6007	200	10	+	+	NOUN
ejpam-6007	200	11	k4x	k4x	PROPN
ejpam-6007	200	12	)	)	PUNCT
ejpam-6007	200	13	,	,	PUNCT
ejpam-6007	200	14	λ1,n+1	λ1,n+1	PUNCT
ejpam-6007	200	15	=	=	SYM
ejpam-6007	200	16	λ1,n	λ1,n	PROPN
ejpam-6007	201	1	+	+	CCONJ
ejpam-6007	201	2	h	h	NOUN
ejpam-6007	201	3	6	6	NUM
ejpam-6007	201	4	(	(	PUNCT
ejpam-6007	201	5	k1λ1	k1λ1	X
ejpam-6007	201	6	+	+	CCONJ
ejpam-6007	201	7	2k2λ1	2k2λ1	NUM
ejpam-6007	201	8	+	+	CCONJ
ejpam-6007	201	9	2k3λ1	2k3λ1	NUM
ejpam-6007	201	10	+	+	ADJ
ejpam-6007	201	11	k4λ1	k4λ1	NOUN
ejpam-6007	201	12	)	)	PUNCT
ejpam-6007	201	13	,	,	PUNCT
ejpam-6007	201	14	λ2,n+1	λ2,n+1	PUNCT
ejpam-6007	201	15	=	=	SYM
ejpam-6007	202	1	λ2,n	λ2,n	X
ejpam-6007	202	2	+	+	NUM
ejpam-6007	202	3	h	h	NOUN
ejpam-6007	202	4	6	6	NUM
ejpam-6007	202	5	(	(	PUNCT
ejpam-6007	202	6	k1λ2	k1λ2	X
ejpam-6007	202	7	+	+	NUM
ejpam-6007	202	8	2k2λ2	2k2λ2	NUM
ejpam-6007	202	9	+	+	CCONJ
ejpam-6007	202	10	2k3λ2	2k3λ2	NUM
ejpam-6007	202	11	+	+	ADJ
ejpam-6007	202	12	k4λ2	k4λ2	NOUN
ejpam-6007	202	13	)	)	PUNCT
ejpam-6007	202	14	.	.	PUNCT
ejpam-6007	203	1	(	(	PUNCT
ejpam-6007	203	2	32	32	NUM
ejpam-6007	203	3	)	)	PUNCT
ejpam-6007	203	4	where	where	SCONJ
ejpam-6007	203	5	a.	a.	NOUN
ejpam-6007	203	6	a.	a.	PROPN
ejpam-6007	203	7	megahed	megahe	VERB
ejpam-6007	203	8	et	et	PROPN
ejpam-6007	203	9	al	al	PROPN
ejpam-6007	203	10	.	.	PUNCT
ejpam-6007	203	11	/	/	SYM
ejpam-6007	203	12	eur	eur	PROPN
ejpam-6007	203	13	.	.	PUNCT
ejpam-6007	204	1	j.	j.	PROPN
ejpam-6007	204	2	pure	pure	PROPN
ejpam-6007	204	3	appl	appl	PROPN
ejpam-6007	204	4	.	.	PROPN
ejpam-6007	204	5	math	math	PROPN
ejpam-6007	204	6	,	,	PUNCT
ejpam-6007	204	7	18	18	NUM
ejpam-6007	204	8	(	(	PUNCT
ejpam-6007	204	9	4	4	NUM
ejpam-6007	204	10	)	)	PUNCT
ejpam-6007	204	11	(	(	PUNCT
ejpam-6007	204	12	2025	2025	NUM
ejpam-6007	204	13	)	)	PUNCT
ejpam-6007	204	14	,	,	PUNCT
ejpam-6007	204	15	6007	6007	NUM
ejpam-6007	204	16	10	10	NUM
ejpam-6007	204	17	of	of	ADP
ejpam-6007	204	18	22	22	NUM
ejpam-6007	204	19	k1x	k1x	NOUN
ejpam-6007	204	20	=	=	SYM
ejpam-6007	204	21	hfx(xn	hfx(xn	PROPN
ejpam-6007	204	22	,	,	PUNCT
ejpam-6007	204	23	tn	tn	PROPN
ejpam-6007	204	24	)	)	PUNCT
ejpam-6007	204	25	,	,	PUNCT
ejpam-6007	204	26	k2x	k2x	PROPN
ejpam-6007	204	27	=	=	SYM
ejpam-6007	204	28	hfx	hfx	PROPN
ejpam-6007	204	29	(	(	PUNCT
ejpam-6007	204	30	xn	xn	PROPN
ejpam-6007	205	1	+	+	NUM
ejpam-6007	205	2	h	h	PROPN
ejpam-6007	205	3	2	2	NUM
ejpam-6007	205	4	,	,	PUNCT
ejpam-6007	205	5	tn	tn	PROPN
ejpam-6007	206	1	+	+	CCONJ
ejpam-6007	206	2	k1x	k1x	PROPN
ejpam-6007	206	3	2	2	NUM
ejpam-6007	206	4	)	)	PUNCT
ejpam-6007	206	5	,	,	PUNCT
ejpam-6007	206	6	k3x	k3x	X
ejpam-6007	206	7	=	=	PROPN
ejpam-6007	206	8	hfx	hfx	PROPN
ejpam-6007	206	9	(	(	PUNCT
ejpam-6007	206	10	xn	xn	PROPN
ejpam-6007	207	1	+	+	NUM
ejpam-6007	207	2	h	h	PROPN
ejpam-6007	207	3	2	2	NUM
ejpam-6007	207	4	,	,	PUNCT
ejpam-6007	207	5	tn	tn	PROPN
ejpam-6007	208	1	+	+	CCONJ
ejpam-6007	208	2	k2x	k2x	X
ejpam-6007	208	3	2	2	NUM
ejpam-6007	208	4	)	)	PUNCT
ejpam-6007	208	5	,	,	PUNCT
ejpam-6007	208	6	k4x	k4x	PROPN
ejpam-6007	208	7	=	=	SYM
ejpam-6007	208	8	hfx	hfx	PROPN
ejpam-6007	208	9	(	(	PUNCT
ejpam-6007	208	10	xn	xn	PROPN
ejpam-6007	209	1	+	+	NUM
ejpam-6007	209	2	h	h	NOUN
ejpam-6007	209	3	,	,	PUNCT
ejpam-6007	209	4	tn	tn	PROPN
ejpam-6007	209	5	+	+	PROPN
ejpam-6007	209	6	k3x	k3x	PROPN
ejpam-6007	209	7	)	)	PUNCT
ejpam-6007	209	8	,	,	PUNCT
ejpam-6007	209	9	k1λ1	k1λ1	NOUN
ejpam-6007	209	10	=	=	SYM
ejpam-6007	209	11	hfλ1(xn	hfλ1(xn	PROPN
ejpam-6007	209	12	,	,	PUNCT
ejpam-6007	209	13	tn	tn	PROPN
ejpam-6007	209	14	)	)	PUNCT
ejpam-6007	209	15	,	,	PUNCT
ejpam-6007	209	16	k2λ1	k2λ1	PROPN
ejpam-6007	209	17	=	=	SYM
ejpam-6007	209	18	hfλ1	hfλ1	PROPN
ejpam-6007	209	19	(	(	PUNCT
ejpam-6007	209	20	xn	xn	PROPN
ejpam-6007	210	1	+	+	NUM
ejpam-6007	210	2	h	h	PROPN
ejpam-6007	210	3	2	2	NUM
ejpam-6007	210	4	,	,	PUNCT
ejpam-6007	210	5	tn	tn	PROPN
ejpam-6007	211	1	+	+	CCONJ
ejpam-6007	211	2	k1λ1	k1λ1	NOUN
ejpam-6007	211	3	2	2	NUM
ejpam-6007	211	4	)	)	PUNCT
ejpam-6007	211	5	,	,	PUNCT
ejpam-6007	212	1	k3λ1	k3λ1	NOUN
ejpam-6007	212	2	=	=	SYM
ejpam-6007	212	3	hfλ1	hfλ1	PROPN
ejpam-6007	212	4	(	(	PUNCT
ejpam-6007	212	5	xn	xn	PROPN
ejpam-6007	213	1	+	+	NUM
ejpam-6007	213	2	h	h	PROPN
ejpam-6007	213	3	2	2	NUM
ejpam-6007	213	4	,	,	PUNCT
ejpam-6007	213	5	tn	tn	PROPN
ejpam-6007	213	6	+	+	CCONJ
ejpam-6007	213	7	k2λ1	k2λ1	PROPN
ejpam-6007	213	8	2	2	NUM
ejpam-6007	213	9	)	)	PUNCT
ejpam-6007	213	10	,	,	PUNCT
ejpam-6007	214	1	k4λ1	k4λ1	NOUN
ejpam-6007	214	2	=	=	VERB
ejpam-6007	214	3	hfλ1	hfλ1	NOUN
ejpam-6007	214	4	(	(	PUNCT
ejpam-6007	214	5	xn	xn	PROPN
ejpam-6007	215	1	+	+	NUM
ejpam-6007	215	2	h	h	NOUN
ejpam-6007	215	3	,	,	PUNCT
ejpam-6007	215	4	tn	tn	PROPN
ejpam-6007	215	5	+	+	PROPN
ejpam-6007	215	6	k3λ1	k3λ1	NOUN
ejpam-6007	215	7	)	)	PUNCT
ejpam-6007	215	8	,	,	PUNCT
ejpam-6007	215	9	k1λ2	k1λ2	X
ejpam-6007	215	10	=	=	SYM
ejpam-6007	215	11	hfλ2(xn	hfλ2(xn	PROPN
ejpam-6007	215	12	,	,	PUNCT
ejpam-6007	215	13	tn	tn	PROPN
ejpam-6007	215	14	)	)	PUNCT
ejpam-6007	215	15	,	,	PUNCT
ejpam-6007	215	16	k2λ2	k2λ2	PROPN
ejpam-6007	215	17	=	=	SYM
ejpam-6007	215	18	hfλ2	hfλ2	PROPN
ejpam-6007	215	19	(	(	PUNCT
ejpam-6007	215	20	xn	xn	PROPN
ejpam-6007	216	1	+	+	NUM
ejpam-6007	216	2	h	h	PROPN
ejpam-6007	216	3	2	2	NUM
ejpam-6007	216	4	,	,	PUNCT
ejpam-6007	216	5	tn	tn	PROPN
ejpam-6007	216	6	+	+	CCONJ
ejpam-6007	216	7	k1λ2	k1λ2	X
ejpam-6007	216	8	2	2	NUM
ejpam-6007	216	9	)	)	PUNCT
ejpam-6007	216	10	,	,	PUNCT
ejpam-6007	216	11	k3λ2	k3λ2	PROPN
ejpam-6007	216	12	=	=	SYM
ejpam-6007	216	13	hfλ2	hfλ2	PROPN
ejpam-6007	216	14	(	(	PUNCT
ejpam-6007	216	15	xn	xn	PROPN
ejpam-6007	217	1	+	+	NUM
ejpam-6007	217	2	h	h	PROPN
ejpam-6007	217	3	2	2	NUM
ejpam-6007	217	4	,	,	PUNCT
ejpam-6007	217	5	tn	tn	PROPN
ejpam-6007	218	1	+	+	CCONJ
ejpam-6007	218	2	k2λ2	k2λ2	X
ejpam-6007	218	3	2	2	NUM
ejpam-6007	218	4	)	)	PUNCT
ejpam-6007	218	5	,	,	PUNCT
ejpam-6007	218	6	and	and	CCONJ
ejpam-6007	218	7	k4λ2	k4λ2	PROPN
ejpam-6007	218	8	=	=	SYM
ejpam-6007	218	9	hfλ2	hfλ2	PROPN
ejpam-6007	218	10	(	(	PUNCT
ejpam-6007	218	11	xn	xn	PROPN
ejpam-6007	219	1	+	+	NUM
ejpam-6007	219	2	h	h	NOUN
ejpam-6007	219	3	,	,	PUNCT
ejpam-6007	219	4	tn	tn	PROPN
ejpam-6007	219	5	+	+	PROPN
ejpam-6007	219	6	k3λ2	k3λ2	NOUN
ejpam-6007	219	7	)	)	PUNCT
ejpam-6007	219	8	.	.	PUNCT
ejpam-6007	220	1	(	(	PUNCT
ejpam-6007	220	2	33	33	NUM
ejpam-6007	220	3	)	)	PUNCT
ejpam-6007	220	4	at	at	ADP
ejpam-6007	220	5	n=0	n=0	ADJ
ejpam-6007	220	6	,	,	PUNCT
ejpam-6007	220	7	x1	x1	PROPN
ejpam-6007	220	8	=	=	PUNCT
ejpam-6007	221	1	x0	x0	PROPN
ejpam-6007	221	2	+	+	CCONJ
ejpam-6007	221	3	h	h	NOUN
ejpam-6007	221	4	6	6	NUM
ejpam-6007	221	5	(	(	PUNCT
ejpam-6007	221	6	k1x	k1x	PROPN
ejpam-6007	222	1	+	+	NUM
ejpam-6007	222	2	2k2x	2k2x	NUM
ejpam-6007	222	3	+	+	CCONJ
ejpam-6007	222	4	2k3x	2k3x	NOUN
ejpam-6007	222	5	+	+	NOUN
ejpam-6007	222	6	k4x	k4x	X
ejpam-6007	222	7	)	)	PUNCT
ejpam-6007	222	8	(	(	PUNCT
ejpam-6007	222	9	34	34	NUM
ejpam-6007	222	10	)	)	PUNCT
ejpam-6007	223	1	where	where	SCONJ
ejpam-6007	223	2	k1x	k1x	NOUN
ejpam-6007	223	3	=	=	SYM
ejpam-6007	223	4	hfx(x0	hfx(x0	PROPN
ejpam-6007	223	5	,	,	PUNCT
ejpam-6007	223	6	t0	t0	PROPN
ejpam-6007	223	7	)	)	PUNCT
ejpam-6007	224	1	=	=	SYM
ejpam-6007	224	2	h	h	NOUN
ejpam-6007	224	3	[	[	PUNCT
ejpam-6007	224	4	λ1,0(t	λ1,0(t	PROPN
ejpam-6007	224	5	)	)	PUNCT
ejpam-6007	224	6	p1	p1	NOUN
ejpam-6007	224	7	(	(	PUNCT
ejpam-6007	224	8	1−	1−	NUM
ejpam-6007	224	9	x0(t	x0(t	NUM
ejpam-6007	224	10	)	)	PUNCT
ejpam-6007	224	11	)	)	PUNCT
ejpam-6007	224	12	2	2	NUM
ejpam-6007	225	1	+	+	CCONJ
ejpam-6007	225	2	(	(	PUNCT
ejpam-6007	225	3	λ2(t))0	λ2(t))0	X
ejpam-6007	225	4	p2	p2	NOUN
ejpam-6007	225	5	x20	x20	NOUN
ejpam-6007	225	6	]	]	PUNCT
ejpam-6007	225	7	=	=	SYM
ejpam-6007	225	8	0	0	NUM
ejpam-6007	225	9	,	,	PUNCT
ejpam-6007	225	10	k2x	k2x	PROPN
ejpam-6007	225	11	=	=	SYM
ejpam-6007	225	12	hfx	hfx	PROPN
ejpam-6007	225	13	(	(	PUNCT
ejpam-6007	225	14	x0	x0	PROPN
ejpam-6007	225	15	+	+	CCONJ
ejpam-6007	225	16	h	h	NOUN
ejpam-6007	225	17	2	2	NUM
ejpam-6007	225	18	,	,	PUNCT
ejpam-6007	225	19	t0	t0	PROPN
ejpam-6007	226	1	+	+	CCONJ
ejpam-6007	226	2	k1x	k1x	PROPN
ejpam-6007	226	3	2	2	X
ejpam-6007	226	4	)	)	PUNCT
ejpam-6007	227	1	=	=	SYM
ejpam-6007	227	2	h	h	NOUN
ejpam-6007	227	3	[	[	PUNCT
ejpam-6007	227	4	λ1(t0	λ1(t0	X
ejpam-6007	227	5	+	+	CCONJ
ejpam-6007	227	6	k1x	k1x	PROPN
ejpam-6007	227	7	2	2	X
ejpam-6007	227	8	)	)	PUNCT
ejpam-6007	227	9	p1	p1	NOUN
ejpam-6007	227	10	(	(	PUNCT
ejpam-6007	227	11	1−	1−	NUM
ejpam-6007	227	12	(	(	PUNCT
ejpam-6007	227	13	x0	x0	PROPN
ejpam-6007	227	14	+	+	CCONJ
ejpam-6007	227	15	h	h	NOUN
ejpam-6007	227	16	2	2	NUM
ejpam-6007	227	17	)	)	PUNCT
ejpam-6007	227	18	)	)	PUNCT
ejpam-6007	227	19	2	2	X
ejpam-6007	228	1	+	+	CCONJ
ejpam-6007	228	2	λ2(t0	λ2(t0	PROPN
ejpam-6007	228	3	+	+	NUM
ejpam-6007	228	4	k1x	k1x	PROPN
ejpam-6007	228	5	2	2	NUM
ejpam-6007	228	6	)	)	PUNCT
ejpam-6007	228	7	p2	p2	PROPN
ejpam-6007	228	8	(	(	PUNCT
ejpam-6007	228	9	x0	x0	PROPN
ejpam-6007	228	10	+	+	CCONJ
ejpam-6007	228	11	h	h	NOUN
ejpam-6007	228	12	2	2	NUM
ejpam-6007	228	13	)	)	PUNCT
ejpam-6007	228	14	2	2	NUM
ejpam-6007	228	15	]	]	PUNCT
ejpam-6007	228	16	=	=	SYM
ejpam-6007	228	17	0	0	NUM
ejpam-6007	228	18	k3x	k3x	NOUN
ejpam-6007	228	19	=	=	PROPN
ejpam-6007	228	20	hfx	hfx	PROPN
ejpam-6007	228	21	(	(	PUNCT
ejpam-6007	228	22	x0	x0	PROPN
ejpam-6007	228	23	+	+	CCONJ
ejpam-6007	228	24	h	h	NOUN
ejpam-6007	228	25	2	2	NUM
ejpam-6007	228	26	,	,	PUNCT
ejpam-6007	228	27	t0	t0	X
ejpam-6007	228	28	+	+	CCONJ
ejpam-6007	228	29	k2x	k2x	X
ejpam-6007	228	30	2	2	X
ejpam-6007	228	31	)	)	PUNCT
ejpam-6007	228	32	=	=	SYM
ejpam-6007	229	1	h	h	NOUN
ejpam-6007	229	2	[	[	PUNCT
ejpam-6007	229	3	λ1(t0	λ1(t0	X
ejpam-6007	229	4	+	+	CCONJ
ejpam-6007	229	5	k2x	k2x	NOUN
ejpam-6007	229	6	2	2	X
ejpam-6007	229	7	)	)	PUNCT
ejpam-6007	229	8	p1	p1	NOUN
ejpam-6007	229	9	(	(	PUNCT
ejpam-6007	229	10	1−	1−	NUM
ejpam-6007	229	11	(	(	PUNCT
ejpam-6007	229	12	x0	x0	PROPN
ejpam-6007	229	13	+	+	CCONJ
ejpam-6007	229	14	h	h	NOUN
ejpam-6007	229	15	2	2	NUM
ejpam-6007	229	16	)	)	PUNCT
ejpam-6007	229	17	)	)	PUNCT
ejpam-6007	229	18	2	2	X
ejpam-6007	230	1	+	+	CCONJ
ejpam-6007	230	2	λ2(t0	λ2(t0	PROPN
ejpam-6007	230	3	+	+	CCONJ
ejpam-6007	230	4	k2x	k2x	X
ejpam-6007	230	5	2	2	X
ejpam-6007	230	6	)	)	PUNCT
ejpam-6007	230	7	p2	p2	PROPN
ejpam-6007	230	8	(	(	PUNCT
ejpam-6007	230	9	x0	x0	PROPN
ejpam-6007	230	10	+	+	CCONJ
ejpam-6007	230	11	h	h	NOUN
ejpam-6007	230	12	2	2	NUM
ejpam-6007	230	13	)	)	PUNCT
ejpam-6007	230	14	2	2	NUM
ejpam-6007	230	15	]	]	PUNCT
ejpam-6007	230	16	=	=	SYM
ejpam-6007	230	17	0	0	NUM
ejpam-6007	230	18	,	,	PUNCT
ejpam-6007	230	19	k4x	k4x	PROPN
ejpam-6007	230	20	=	=	SYM
ejpam-6007	230	21	hfx	hfx	PROPN
ejpam-6007	230	22	(	(	PUNCT
ejpam-6007	230	23	x0	x0	PROPN
ejpam-6007	230	24	+	+	CCONJ
ejpam-6007	230	25	h	h	NOUN
ejpam-6007	230	26	,	,	PUNCT
ejpam-6007	230	27	t0	t0	PROPN
ejpam-6007	230	28	+	+	NOUN
ejpam-6007	230	29	k3x	k3x	X
ejpam-6007	230	30	)	)	PUNCT
ejpam-6007	231	1	=	=	SYM
ejpam-6007	231	2	h	h	NOUN
ejpam-6007	231	3	[	[	PUNCT
ejpam-6007	231	4	λ1(t0	λ1(t0	NUM
ejpam-6007	231	5	+	+	ADJ
ejpam-6007	231	6	k3x	k3x	NOUN
ejpam-6007	231	7	)	)	PUNCT
ejpam-6007	231	8	p1	p1	NOUN
ejpam-6007	231	9	(	(	PUNCT
ejpam-6007	231	10	1−	1−	NUM
ejpam-6007	231	11	(	(	PUNCT
ejpam-6007	231	12	x0	x0	PROPN
ejpam-6007	231	13	+	+	NUM
ejpam-6007	231	14	h))2	h))2	NOUN
ejpam-6007	231	15	+	+	CCONJ
ejpam-6007	231	16	λ2(t0	λ2(t0	PROPN
ejpam-6007	231	17	+	+	PROPN
ejpam-6007	231	18	k3x	k3x	NOUN
ejpam-6007	231	19	)	)	PUNCT
ejpam-6007	231	20	p2	p2	PROPN
ejpam-6007	231	21	(	(	PUNCT
ejpam-6007	231	22	x0	x0	PROPN
ejpam-6007	231	23	+	+	CCONJ
ejpam-6007	231	24	h)2	h)2	VERB
ejpam-6007	231	25	]	]	PUNCT
ejpam-6007	232	1	=	=	PUNCT
ejpam-6007	232	2	0	0	X
ejpam-6007	232	3	.	.	PUNCT
ejpam-6007	233	1	(	(	PUNCT
ejpam-6007	233	2	35	35	NUM
ejpam-6007	233	3	)	)	PUNCT
ejpam-6007	233	4	then	then	ADV
ejpam-6007	233	5	x	x	X
ejpam-6007	233	6	=	=	SYM
ejpam-6007	233	7	x0	x0	PROPN
ejpam-6007	233	8	.	.	PUNCT
ejpam-6007	234	1	(	(	PUNCT
ejpam-6007	234	2	λ1)1	λ1)1	X
ejpam-6007	234	3	=	=	SYM
ejpam-6007	234	4	(	(	PUNCT
ejpam-6007	234	5	λ1)0	λ1)0	X
ejpam-6007	234	6	+	+	NUM
ejpam-6007	234	7	h	h	NOUN
ejpam-6007	234	8	6	6	NUM
ejpam-6007	234	9	(	(	PUNCT
ejpam-6007	234	10	k1λ1	k1λ1	X
ejpam-6007	234	11	+	+	CCONJ
ejpam-6007	234	12	2k2λ1	2k2λ1	NUM
ejpam-6007	234	13	+	+	CCONJ
ejpam-6007	234	14	2k3λ1	2k3λ1	NUM
ejpam-6007	234	15	+	+	ADJ
ejpam-6007	234	16	k4λ1	k4λ1	NOUN
ejpam-6007	234	17	)	)	PUNCT
ejpam-6007	234	18	(	(	PUNCT
ejpam-6007	234	19	36	36	NUM
ejpam-6007	234	20	)	)	PUNCT
ejpam-6007	234	21	a.	a.	NOUN
ejpam-6007	234	22	a.	a.	NOUN
ejpam-6007	234	23	megahed	megahe	VERB
ejpam-6007	234	24	et	et	PROPN
ejpam-6007	234	25	al	al	PROPN
ejpam-6007	234	26	.	.	PUNCT
ejpam-6007	234	27	/	/	SYM
ejpam-6007	234	28	eur	eur	PROPN
ejpam-6007	234	29	.	.	PUNCT
ejpam-6007	235	1	j.	j.	PROPN
ejpam-6007	235	2	pure	pure	PROPN
ejpam-6007	235	3	appl	appl	PROPN
ejpam-6007	235	4	.	.	PROPN
ejpam-6007	235	5	math	math	PROPN
ejpam-6007	235	6	,	,	PUNCT
ejpam-6007	235	7	18	18	NUM
ejpam-6007	235	8	(	(	PUNCT
ejpam-6007	235	9	4	4	NUM
ejpam-6007	235	10	)	)	PUNCT
ejpam-6007	235	11	(	(	PUNCT
ejpam-6007	235	12	2025	2025	NUM
ejpam-6007	235	13	)	)	PUNCT
ejpam-6007	235	14	,	,	PUNCT
ejpam-6007	235	15	6007	6007	NUM
ejpam-6007	235	16	11	11	NUM
ejpam-6007	235	17	of	of	ADP
ejpam-6007	235	18	22	22	NUM
ejpam-6007	235	19	where	where	SCONJ
ejpam-6007	235	20	k1λ1	k1λ1	NOUN
ejpam-6007	235	21	=	=	SYM
ejpam-6007	235	22	hfλ1(x0	hfλ1(x0	PROPN
ejpam-6007	235	23	,	,	PUNCT
ejpam-6007	235	24	t0	t0	PROPN
ejpam-6007	235	25	)	)	PUNCT
ejpam-6007	236	1	=	=	SYM
ejpam-6007	236	2	h	h	NOUN
ejpam-6007	236	3	[	[	PUNCT
ejpam-6007	236	4	(	(	PUNCT
ejpam-6007	236	5	λ1(t	λ1(t	ADJ
ejpam-6007	236	6	)	)	PUNCT
ejpam-6007	236	7	2)0	2)0	PROPN
ejpam-6007	236	8	p1	p1	NOUN
ejpam-6007	236	9	(	(	PUNCT
ejpam-6007	236	10	1−	1−	NUM
ejpam-6007	236	11	x0)−	x0)−	X
ejpam-6007	236	12	λ1,0(t)(λ2(t))0	λ1,0(t)(λ2(t))0	PROPN
ejpam-6007	236	13	p2	p2	PROPN
ejpam-6007	236	14	x0(t)−	x0(t)−	PROPN
ejpam-6007	236	15	ϕ1	ϕ1	PROPN
ejpam-6007	236	16	]	]	PUNCT
ejpam-6007	236	17	=	=	SYM
ejpam-6007	236	18	−hϕ1	−hϕ1	NOUN
ejpam-6007	236	19	,	,	PUNCT
ejpam-6007	236	20	k2λ1	k2λ1	PROPN
ejpam-6007	236	21	=	=	SYM
ejpam-6007	236	22	hfλ1	hfλ1	PROPN
ejpam-6007	236	23	(	(	PUNCT
ejpam-6007	236	24	x0	x0	PROPN
ejpam-6007	236	25	+	+	CCONJ
ejpam-6007	236	26	h	h	NOUN
ejpam-6007	236	27	2	2	NUM
ejpam-6007	236	28	,	,	PUNCT
ejpam-6007	236	29	t0	t0	PROPN
ejpam-6007	236	30	+	+	CCONJ
ejpam-6007	236	31	k1λ1	k1λ1	NOUN
ejpam-6007	236	32	2	2	X
ejpam-6007	236	33	)	)	PUNCT
ejpam-6007	236	34	=	=	SYM
ejpam-6007	237	1	h	h	NOUN
ejpam-6007	238	1	[	[	X
ejpam-6007	238	2	λ1	λ1	X
ejpam-6007	238	3	(	(	PUNCT
ejpam-6007	238	4	t0	t0	NOUN
ejpam-6007	238	5	+	+	CCONJ
ejpam-6007	238	6	k1λ1	k1λ1	PROPN
ejpam-6007	238	7	2	2	NUM
ejpam-6007	238	8	)	)	SYM
ejpam-6007	238	9	2	2	NUM
ejpam-6007	238	10	p1	p1	NOUN
ejpam-6007	238	11	(	(	PUNCT
ejpam-6007	238	12	1−	1−	NUM
ejpam-6007	238	13	(	(	PUNCT
ejpam-6007	238	14	x0	x0	PROPN
ejpam-6007	238	15	+	+	CCONJ
ejpam-6007	238	16	h	h	NOUN
ejpam-6007	238	17	2	2	NUM
ejpam-6007	238	18	)	)	PUNCT
ejpam-6007	238	19	)	)	PUNCT
ejpam-6007	239	1	−	−	PROPN
ejpam-6007	239	2	λ1	λ1	INTJ
ejpam-6007	239	3	(	(	PUNCT
ejpam-6007	239	4	t0	t0	NOUN
ejpam-6007	239	5	+	+	CCONJ
ejpam-6007	239	6	k1λ1	k1λ1	PROPN
ejpam-6007	239	7	2	2	X
ejpam-6007	239	8	)	)	PUNCT
ejpam-6007	239	9	λ2	λ2	NOUN
ejpam-6007	239	10	(	(	PUNCT
ejpam-6007	239	11	t0	t0	NOUN
ejpam-6007	239	12	+	+	CCONJ
ejpam-6007	239	13	k1λ1	k1λ1	PROPN
ejpam-6007	239	14	2	2	X
ejpam-6007	239	15	)	)	PUNCT
ejpam-6007	239	16	p2	p2	PROPN
ejpam-6007	239	17	(	(	PUNCT
ejpam-6007	239	18	x0	x0	PROPN
ejpam-6007	239	19	+	+	CCONJ
ejpam-6007	239	20	h	h	NOUN
ejpam-6007	239	21	2	2	X
ejpam-6007	239	22	)	)	PUNCT
ejpam-6007	239	23	−	−	NOUN
ejpam-6007	239	24	ϕ1	ϕ1	NOUN
ejpam-6007	239	25	]	]	PUNCT
ejpam-6007	239	26	=	=	SYM
ejpam-6007	239	27	−hϕ1	−hϕ1	NOUN
ejpam-6007	239	28	,	,	PUNCT
ejpam-6007	239	29	k3λ1	k3λ1	NOUN
ejpam-6007	239	30	=	=	SYM
ejpam-6007	239	31	hfλ1	hfλ1	PROPN
ejpam-6007	239	32	(	(	PUNCT
ejpam-6007	239	33	x0	x0	PROPN
ejpam-6007	239	34	+	+	CCONJ
ejpam-6007	239	35	h	h	NOUN
ejpam-6007	239	36	2	2	NUM
ejpam-6007	239	37	,	,	PUNCT
ejpam-6007	239	38	t0	t0	PROPN
ejpam-6007	239	39	+	+	CCONJ
ejpam-6007	239	40	k2λ1	k2λ1	PROPN
ejpam-6007	239	41	2	2	X
ejpam-6007	239	42	)	)	PUNCT
ejpam-6007	239	43	=	=	SYM
ejpam-6007	240	1	h	h	NOUN
ejpam-6007	241	1	[	[	X
ejpam-6007	241	2	λ1	λ1	X
ejpam-6007	241	3	(	(	PUNCT
ejpam-6007	241	4	t0	t0	NOUN
ejpam-6007	241	5	+	+	CCONJ
ejpam-6007	241	6	k2λ1	k2λ1	PROPN
ejpam-6007	241	7	2	2	NUM
ejpam-6007	241	8	)	)	SYM
ejpam-6007	241	9	2	2	NUM
ejpam-6007	241	10	p1	p1	NOUN
ejpam-6007	241	11	(	(	PUNCT
ejpam-6007	241	12	1−	1−	NUM
ejpam-6007	241	13	(	(	PUNCT
ejpam-6007	241	14	x0	x0	PROPN
ejpam-6007	241	15	+	+	CCONJ
ejpam-6007	241	16	h	h	NOUN
ejpam-6007	241	17	2	2	NUM
ejpam-6007	241	18	)	)	PUNCT
ejpam-6007	241	19	)	)	PUNCT
ejpam-6007	242	1	−	−	PROPN
ejpam-6007	242	2	λ1	λ1	INTJ
ejpam-6007	242	3	(	(	PUNCT
ejpam-6007	242	4	t0	t0	PROPN
ejpam-6007	242	5	+	+	CCONJ
ejpam-6007	242	6	k2λ1	k2λ1	PROPN
ejpam-6007	242	7	2	2	X
ejpam-6007	242	8	)	)	PUNCT
ejpam-6007	242	9	λ2	λ2	NOUN
ejpam-6007	242	10	(	(	PUNCT
ejpam-6007	242	11	t0	t0	NOUN
ejpam-6007	242	12	+	+	CCONJ
ejpam-6007	242	13	k2λ1	k2λ1	PROPN
ejpam-6007	242	14	2	2	X
ejpam-6007	242	15	)	)	PUNCT
ejpam-6007	242	16	p2	p2	PROPN
ejpam-6007	242	17	(	(	PUNCT
ejpam-6007	242	18	x0	x0	PROPN
ejpam-6007	242	19	+	+	CCONJ
ejpam-6007	242	20	h	h	NOUN
ejpam-6007	242	21	2	2	X
ejpam-6007	242	22	)	)	PUNCT
ejpam-6007	242	23	−	−	NOUN
ejpam-6007	242	24	ϕ1	ϕ1	NOUN
ejpam-6007	242	25	]	]	PUNCT
ejpam-6007	242	26	=	=	SYM
ejpam-6007	242	27	−hϕ1	−hϕ1	NOUN
ejpam-6007	242	28	,	,	PUNCT
ejpam-6007	242	29	k4λ1	k4λ1	NOUN
ejpam-6007	242	30	=	=	VERB
ejpam-6007	242	31	hfλ1	hfλ1	NOUN
ejpam-6007	242	32	(	(	PUNCT
ejpam-6007	242	33	x0	x0	PROPN
ejpam-6007	242	34	+	+	CCONJ
ejpam-6007	242	35	h	h	NOUN
ejpam-6007	242	36	,	,	PUNCT
ejpam-6007	242	37	t0	t0	PROPN
ejpam-6007	242	38	+	+	PROPN
ejpam-6007	242	39	k3λ1	k3λ1	NOUN
ejpam-6007	242	40	)	)	PUNCT
ejpam-6007	242	41	=	=	SYM
ejpam-6007	242	42	h	h	NOUN
ejpam-6007	242	43	[	[	PUNCT
ejpam-6007	242	44	λ1	λ1	PROPN
ejpam-6007	242	45	(	(	PUNCT
ejpam-6007	242	46	t0	t0	NOUN
ejpam-6007	242	47	+	+	NOUN
ejpam-6007	242	48	k3λ1	k3λ1	NOUN
ejpam-6007	242	49	)	)	PUNCT
ejpam-6007	242	50	2	2	NUM
ejpam-6007	242	51	p1	p1	NOUN
ejpam-6007	242	52	(	(	PUNCT
ejpam-6007	242	53	1−	1−	NUM
ejpam-6007	242	54	(	(	PUNCT
ejpam-6007	242	55	x0	x0	PROPN
ejpam-6007	242	56	+	+	CCONJ
ejpam-6007	242	57	h	h	NOUN
ejpam-6007	242	58	)	)	PUNCT
ejpam-6007	242	59	)	)	PUNCT
ejpam-6007	243	1	−	−	PROPN
ejpam-6007	244	1	λ1	λ1	INTJ
ejpam-6007	244	2	(	(	PUNCT
ejpam-6007	244	3	t0	t0	NOUN
ejpam-6007	244	4	+	+	NOUN
ejpam-6007	244	5	k3λ1)λ2	k3λ1)λ2	X
ejpam-6007	244	6	(	(	PUNCT
ejpam-6007	244	7	t0	t0	NOUN
ejpam-6007	244	8	+	+	NOUN
ejpam-6007	244	9	k3λ1	k3λ1	NOUN
ejpam-6007	244	10	)	)	PUNCT
ejpam-6007	244	11	p2	p2	PROPN
ejpam-6007	244	12	(	(	PUNCT
ejpam-6007	244	13	x0	x0	PROPN
ejpam-6007	244	14	+	+	CCONJ
ejpam-6007	244	15	h)−	h)−	PROPN
ejpam-6007	244	16	ϕ1	ϕ1	NOUN
ejpam-6007	244	17	]	]	PUNCT
ejpam-6007	244	18	=	=	SYM
ejpam-6007	244	19	−hϕ1	−hϕ1	NOUN
ejpam-6007	244	20	.	.	PUNCT
ejpam-6007	245	1	(	(	PUNCT
ejpam-6007	245	2	37	37	NUM
ejpam-6007	245	3	)	)	PUNCT
ejpam-6007	246	1	then	then	ADV
ejpam-6007	246	2	λ1,1	λ1,1	X
ejpam-6007	246	3	=	=	PUNCT
ejpam-6007	247	1	−h2ϕ1	−h2ϕ1	NUM
ejpam-6007	247	2	λ2,n+1	λ2,n+1	NOUN
ejpam-6007	247	3	=	=	SYM
ejpam-6007	248	1	λ2,n	λ2,n	NOUN
ejpam-6007	248	2	+	+	NUM
ejpam-6007	248	3	h	h	NOUN
ejpam-6007	248	4	6	6	NUM
ejpam-6007	248	5	(	(	PUNCT
ejpam-6007	248	6	k1λ2	k1λ2	X
ejpam-6007	248	7	+	+	NUM
ejpam-6007	248	8	2k2λ2	2k2λ2	NUM
ejpam-6007	248	9	+	+	CCONJ
ejpam-6007	248	10	2k3λ2	2k3λ2	NUM
ejpam-6007	248	11	+	+	ADJ
ejpam-6007	248	12	k4λ2	k4λ2	ADJ
ejpam-6007	248	13	)	)	PUNCT
ejpam-6007	248	14	(	(	PUNCT
ejpam-6007	248	15	38	38	NUM
ejpam-6007	248	16	)	)	PUNCT
ejpam-6007	248	17	k1λ2	k1λ2	NOUN
ejpam-6007	248	18	=	=	SYM
ejpam-6007	248	19	hfλ2(xn	hfλ2(xn	PROPN
ejpam-6007	248	20	,	,	PUNCT
ejpam-6007	248	21	tn	tn	PROPN
ejpam-6007	248	22	)	)	PUNCT
ejpam-6007	248	23	,	,	PUNCT
ejpam-6007	248	24	k2λ2	k2λ2	PROPN
ejpam-6007	248	25	=	=	SYM
ejpam-6007	248	26	hfλ2	hfλ2	PROPN
ejpam-6007	248	27	(	(	PUNCT
ejpam-6007	248	28	xn	xn	PROPN
ejpam-6007	249	1	+	+	NUM
ejpam-6007	249	2	h	h	PROPN
ejpam-6007	249	3	2	2	NUM
ejpam-6007	249	4	,	,	PUNCT
ejpam-6007	249	5	tn	tn	PROPN
ejpam-6007	249	6	+	+	CCONJ
ejpam-6007	249	7	k1λ2	k1λ2	X
ejpam-6007	249	8	2	2	NUM
ejpam-6007	249	9	)	)	PUNCT
ejpam-6007	249	10	,	,	PUNCT
ejpam-6007	249	11	k3λ2	k3λ2	PROPN
ejpam-6007	249	12	=	=	SYM
ejpam-6007	249	13	hfλ2	hfλ2	PROPN
ejpam-6007	249	14	(	(	PUNCT
ejpam-6007	249	15	xn	xn	PROPN
ejpam-6007	250	1	+	+	NUM
ejpam-6007	250	2	h	h	PROPN
ejpam-6007	250	3	2	2	NUM
ejpam-6007	250	4	,	,	PUNCT
ejpam-6007	250	5	tn	tn	PROPN
ejpam-6007	251	1	+	+	CCONJ
ejpam-6007	251	2	k2λ2	k2λ2	X
ejpam-6007	251	3	2	2	NUM
ejpam-6007	251	4	)	)	PUNCT
ejpam-6007	251	5	,	,	PUNCT
ejpam-6007	251	6	k4λ2	k4λ2	PROPN
ejpam-6007	251	7	=	=	SYM
ejpam-6007	251	8	hfλ2	hfλ2	PROPN
ejpam-6007	251	9	(	(	PUNCT
ejpam-6007	251	10	xn	xn	PROPN
ejpam-6007	252	1	+	+	NUM
ejpam-6007	252	2	h	h	NOUN
ejpam-6007	252	3	,	,	PUNCT
ejpam-6007	252	4	tn	tn	PROPN
ejpam-6007	252	5	+	+	PROPN
ejpam-6007	252	6	k3λ2	k3λ2	NOUN
ejpam-6007	252	7	)	)	PUNCT
ejpam-6007	252	8	.	.	PUNCT
ejpam-6007	253	1	(	(	PUNCT
ejpam-6007	253	2	39	39	NUM
ejpam-6007	253	3	)	)	PUNCT
ejpam-6007	253	4	where	where	SCONJ
ejpam-6007	253	5	a.	a.	NOUN
ejpam-6007	253	6	a.	a.	PROPN
ejpam-6007	253	7	megahed	megahe	VERB
ejpam-6007	253	8	et	et	PROPN
ejpam-6007	253	9	al	al	PROPN
ejpam-6007	253	10	.	.	PUNCT
ejpam-6007	253	11	/	/	SYM
ejpam-6007	253	12	eur	eur	PROPN
ejpam-6007	253	13	.	.	PUNCT
ejpam-6007	254	1	j.	j.	PROPN
ejpam-6007	254	2	pure	pure	PROPN
ejpam-6007	254	3	appl	appl	PROPN
ejpam-6007	254	4	.	.	PROPN
ejpam-6007	254	5	math	math	PROPN
ejpam-6007	254	6	,	,	PUNCT
ejpam-6007	254	7	18	18	NUM
ejpam-6007	254	8	(	(	PUNCT
ejpam-6007	254	9	4	4	NUM
ejpam-6007	254	10	)	)	PUNCT
ejpam-6007	254	11	(	(	PUNCT
ejpam-6007	254	12	2025	2025	NUM
ejpam-6007	254	13	)	)	PUNCT
ejpam-6007	254	14	,	,	PUNCT
ejpam-6007	254	15	6007	6007	NUM
ejpam-6007	254	16	12	12	NUM
ejpam-6007	254	17	of	of	ADP
ejpam-6007	254	18	22	22	NUM
ejpam-6007	254	19	k1λ2	k1λ2	NOUN
ejpam-6007	254	20	=	=	SYM
ejpam-6007	254	21	hfλ2(x0	hfλ2(x0	PROPN
ejpam-6007	254	22	,	,	PUNCT
ejpam-6007	254	23	t0	t0	PROPN
ejpam-6007	254	24	)	)	PUNCT
ejpam-6007	254	25	=	=	SYM
ejpam-6007	255	1	h	h	NOUN
ejpam-6007	255	2	[	[	PUNCT
ejpam-6007	255	3	λ1,0(t)(λ2(t))0	λ1,0(t)(λ2(t))0	PROPN
ejpam-6007	255	4	p1	p1	NOUN
ejpam-6007	255	5	(	(	PUNCT
ejpam-6007	255	6	1−	1−	NUM
ejpam-6007	255	7	x0)−	x0)−	X
ejpam-6007	255	8	λ2	λ2	NOUN
ejpam-6007	255	9	2,0(t	2,0(t	NUM
ejpam-6007	255	10	)	)	PUNCT
ejpam-6007	255	11	p2	p2	PROPN
ejpam-6007	255	12	x0(t	x0(t	PROPN
ejpam-6007	255	13	)	)	PUNCT
ejpam-6007	256	1	+	+	NUM
ejpam-6007	256	2	ϕ1	ϕ1	NOUN
ejpam-6007	256	3	]	]	PUNCT
ejpam-6007	256	4	=	=	SYM
ejpam-6007	256	5	hϕ2	hϕ2	NOUN
ejpam-6007	256	6	,	,	PUNCT
ejpam-6007	256	7	k2λ2	k2λ2	PROPN
ejpam-6007	256	8	=	=	SYM
ejpam-6007	256	9	hfλ2	hfλ2	PROPN
ejpam-6007	256	10	(	(	PUNCT
ejpam-6007	256	11	x0	x0	PROPN
ejpam-6007	256	12	+	+	CCONJ
ejpam-6007	256	13	h	h	NOUN
ejpam-6007	256	14	2	2	NUM
ejpam-6007	256	15	,	,	PUNCT
ejpam-6007	256	16	t0	t0	X
ejpam-6007	256	17	+	+	CCONJ
ejpam-6007	256	18	k1λ2	k1λ2	X
ejpam-6007	256	19	2	2	NUM
ejpam-6007	256	20	)	)	PUNCT
ejpam-6007	256	21	=	=	SYM
ejpam-6007	257	1	h	h	NOUN
ejpam-6007	258	1	[	[	X
ejpam-6007	258	2	λ1	λ1	X
ejpam-6007	258	3	(	(	PUNCT
ejpam-6007	258	4	t0	t0	NOUN
ejpam-6007	258	5	+	+	CCONJ
ejpam-6007	258	6	k1λ2	k1λ2	VERB
ejpam-6007	258	7	2	2	X
ejpam-6007	258	8	)	)	PUNCT
ejpam-6007	258	9	λ2	λ2	NOUN
ejpam-6007	258	10	(	(	PUNCT
ejpam-6007	258	11	t0	t0	NOUN
ejpam-6007	258	12	+	+	CCONJ
ejpam-6007	258	13	k1λ2	k1λ2	VERB
ejpam-6007	258	14	2	2	X
ejpam-6007	258	15	)	)	PUNCT
ejpam-6007	258	16	p1	p1	NOUN
ejpam-6007	258	17	(	(	PUNCT
ejpam-6007	258	18	1−	1−	NUM
ejpam-6007	258	19	(	(	PUNCT
ejpam-6007	258	20	x0	x0	PROPN
ejpam-6007	258	21	+	+	CCONJ
ejpam-6007	258	22	h	h	NOUN
ejpam-6007	258	23	2	2	NUM
ejpam-6007	258	24	)	)	PUNCT
ejpam-6007	258	25	)	)	PUNCT
ejpam-6007	259	1	−	−	PROPN
ejpam-6007	259	2	λ2	λ2	NOUN
ejpam-6007	259	3	(	(	PUNCT
ejpam-6007	259	4	t0	t0	NOUN
ejpam-6007	259	5	+	+	CCONJ
ejpam-6007	259	6	k1λ2	k1λ2	X
ejpam-6007	259	7	2	2	NUM
ejpam-6007	259	8	)	)	SYM
ejpam-6007	259	9	2	2	NUM
ejpam-6007	259	10	p2	p2	NOUN
ejpam-6007	259	11	(	(	PUNCT
ejpam-6007	259	12	x0	x0	PROPN
ejpam-6007	259	13	+	+	CCONJ
ejpam-6007	259	14	h	h	NOUN
ejpam-6007	259	15	2	2	NUM
ejpam-6007	259	16	)	)	PUNCT
ejpam-6007	259	17	+	+	CCONJ
ejpam-6007	259	18	ϕ1	ϕ1	NOUN
ejpam-6007	259	19	]	]	PUNCT
ejpam-6007	259	20	=	=	SYM
ejpam-6007	260	1	hϕ2	hϕ2	NOUN
ejpam-6007	260	2	,	,	PUNCT
ejpam-6007	260	3	k3λ2	k3λ2	PROPN
ejpam-6007	260	4	=	=	SYM
ejpam-6007	260	5	hfλ2	hfλ2	PROPN
ejpam-6007	260	6	(	(	PUNCT
ejpam-6007	260	7	x0	x0	PROPN
ejpam-6007	260	8	+	+	CCONJ
ejpam-6007	260	9	h	h	NOUN
ejpam-6007	260	10	2	2	NUM
ejpam-6007	260	11	,	,	PUNCT
ejpam-6007	260	12	t0	t0	X
ejpam-6007	260	13	+	+	CCONJ
ejpam-6007	260	14	k2λ2	k2λ2	X
ejpam-6007	260	15	2	2	X
ejpam-6007	260	16	)	)	PUNCT
ejpam-6007	260	17	=	=	SYM
ejpam-6007	261	1	h	h	NOUN
ejpam-6007	262	1	[	[	X
ejpam-6007	262	2	λ1	λ1	X
ejpam-6007	262	3	(	(	PUNCT
ejpam-6007	262	4	t0	t0	NOUN
ejpam-6007	262	5	+	+	CCONJ
ejpam-6007	262	6	k2λ2	k2λ2	X
ejpam-6007	262	7	2	2	X
ejpam-6007	262	8	)	)	PUNCT
ejpam-6007	262	9	λ2	λ2	NOUN
ejpam-6007	262	10	(	(	PUNCT
ejpam-6007	262	11	t0	t0	NOUN
ejpam-6007	262	12	+	+	CCONJ
ejpam-6007	262	13	k2λ2	k2λ2	X
ejpam-6007	262	14	2	2	X
ejpam-6007	262	15	)	)	PUNCT
ejpam-6007	262	16	p1	p1	NOUN
ejpam-6007	262	17	(	(	PUNCT
ejpam-6007	262	18	1−	1−	NUM
ejpam-6007	262	19	(	(	PUNCT
ejpam-6007	262	20	x0	x0	PROPN
ejpam-6007	262	21	+	+	CCONJ
ejpam-6007	262	22	h	h	NOUN
ejpam-6007	262	23	2	2	NUM
ejpam-6007	262	24	)	)	PUNCT
ejpam-6007	262	25	)	)	PUNCT
ejpam-6007	263	1	−	−	PROPN
ejpam-6007	263	2	λ2	λ2	NOUN
ejpam-6007	263	3	(	(	PUNCT
ejpam-6007	263	4	t0	t0	NOUN
ejpam-6007	263	5	+	+	CCONJ
ejpam-6007	264	1	k2λ2	k2λ2	X
ejpam-6007	265	1	2	2	X
ejpam-6007	265	2	)	)	SYM
ejpam-6007	265	3	2	2	NUM
ejpam-6007	265	4	p2	p2	NOUN
ejpam-6007	265	5	(	(	PUNCT
ejpam-6007	265	6	x0	x0	PROPN
ejpam-6007	265	7	+	+	CCONJ
ejpam-6007	265	8	h	h	NOUN
ejpam-6007	265	9	2	2	NUM
ejpam-6007	265	10	)	)	PUNCT
ejpam-6007	265	11	+	+	CCONJ
ejpam-6007	265	12	ϕ1	ϕ1	NOUN
ejpam-6007	265	13	]	]	PUNCT
ejpam-6007	265	14	=	=	SYM
ejpam-6007	265	15	hϕ2	hϕ2	NOUN
ejpam-6007	265	16	,	,	PUNCT
ejpam-6007	265	17	k4λ2	k4λ2	PROPN
ejpam-6007	265	18	=	=	SYM
ejpam-6007	265	19	hfλ2	hfλ2	PROPN
ejpam-6007	265	20	(	(	PUNCT
ejpam-6007	265	21	x0	x0	PROPN
ejpam-6007	265	22	+	+	CCONJ
ejpam-6007	265	23	h	h	NOUN
ejpam-6007	265	24	,	,	PUNCT
ejpam-6007	265	25	t0	t0	PROPN
ejpam-6007	265	26	+	+	NOUN
ejpam-6007	265	27	k3λ2	k3λ2	NOUN
ejpam-6007	265	28	)	)	PUNCT
ejpam-6007	265	29	=	=	SYM
ejpam-6007	265	30	h	h	NOUN
ejpam-6007	265	31	[	[	PUNCT
ejpam-6007	265	32	λ1	λ1	PROPN
ejpam-6007	265	33	(	(	PUNCT
ejpam-6007	265	34	t0	t0	NOUN
ejpam-6007	265	35	+	+	NOUN
ejpam-6007	265	36	k3λ2)λ2	k3λ2)λ2	X
ejpam-6007	265	37	(	(	PUNCT
ejpam-6007	265	38	t0	t0	NOUN
ejpam-6007	265	39	+	+	NOUN
ejpam-6007	265	40	k3λ2	k3λ2	NOUN
ejpam-6007	265	41	)	)	PUNCT
ejpam-6007	265	42	p1	p1	NOUN
ejpam-6007	265	43	(	(	PUNCT
ejpam-6007	265	44	1−	1−	NUM
ejpam-6007	265	45	(	(	PUNCT
ejpam-6007	265	46	x0	x0	PROPN
ejpam-6007	265	47	+	+	CCONJ
ejpam-6007	265	48	h	h	NOUN
ejpam-6007	265	49	)	)	PUNCT
ejpam-6007	265	50	)	)	PUNCT
ejpam-6007	265	51	−	−	PROPN
ejpam-6007	266	1	λ2	λ2	NOUN
ejpam-6007	266	2	(	(	PUNCT
ejpam-6007	266	3	t0	t0	NOUN
ejpam-6007	266	4	+	+	NOUN
ejpam-6007	266	5	k3λ2	k3λ2	NOUN
ejpam-6007	266	6	)	)	PUNCT
ejpam-6007	266	7	2	2	NUM
ejpam-6007	266	8	p2	p2	NOUN
ejpam-6007	266	9	(	(	PUNCT
ejpam-6007	266	10	x0	x0	PROPN
ejpam-6007	266	11	+	+	CCONJ
ejpam-6007	266	12	h	h	NOUN
ejpam-6007	266	13	)	)	PUNCT
ejpam-6007	266	14	+	+	CCONJ
ejpam-6007	266	15	ϕ1	ϕ1	NOUN
ejpam-6007	266	16	]	]	PUNCT
ejpam-6007	266	17	=	=	PUNCT
ejpam-6007	266	18	hϕ2	hϕ2	NOUN
ejpam-6007	266	19	.	.	PUNCT
ejpam-6007	267	1	(	(	PUNCT
ejpam-6007	267	2	40	40	NUM
ejpam-6007	267	3	)	)	PUNCT
ejpam-6007	268	1	then	then	ADV
ejpam-6007	268	2	λ2,1	λ2,1	PROPN
ejpam-6007	268	3	=	=	PUNCT
ejpam-6007	268	4	h2ϕ2	h2ϕ2	VERB
ejpam-6007	268	5	u1,1	u1,1	ADJ
ejpam-6007	268	6	=	=	SYM
ejpam-6007	269	1	λ1,1	λ1,1	ADP
ejpam-6007	269	2	p1	p1	PROPN
ejpam-6007	269	3	(	(	PUNCT
ejpam-6007	269	4	1−	1−	NUM
ejpam-6007	269	5	x1	x1	NUM
ejpam-6007	269	6	)	)	PUNCT
ejpam-6007	269	7	=	=	PUNCT
ejpam-6007	270	1	−h2ϕ1	−h2ϕ1	PROPN
ejpam-6007	270	2	p1	p1	NOUN
ejpam-6007	270	3	(	(	PUNCT
ejpam-6007	270	4	1−	1−	NUM
ejpam-6007	270	5	x0	x0	NUM
ejpam-6007	270	6	)	)	PUNCT
ejpam-6007	270	7	,	,	PUNCT
ejpam-6007	270	8	u2,1	u2,1	PROPN
ejpam-6007	270	9	=	=	PUNCT
ejpam-6007	270	10	−λ2	−λ2	NOUN
ejpam-6007	270	11	p2	p2	VERB
ejpam-6007	270	12	x	x	PUNCT
ejpam-6007	270	13	=	=	PUNCT
ejpam-6007	270	14	−h2ϕ2	−h2ϕ2	PROPN
ejpam-6007	270	15	p2	p2	PROPN
ejpam-6007	270	16	x	x	NOUN
ejpam-6007	270	17	,	,	PUNCT
ejpam-6007	270	18	c1,1	c1,1	NOUN
ejpam-6007	270	19	=	=	SYM
ejpam-6007	270	20	p1	p1	NOUN
ejpam-6007	270	21	2	2	NUM
ejpam-6007	270	22	u21,1	u21,1	NOUN
ejpam-6007	270	23	=	=	SYM
ejpam-6007	270	24	p1	p1	NOUN
ejpam-6007	270	25	2	2	NUM
ejpam-6007	270	26	(	(	PUNCT
ejpam-6007	270	27	h2ϕ1	h2ϕ1	PROPN
ejpam-6007	270	28	p1	p1	NOUN
ejpam-6007	270	29	(	(	PUNCT
ejpam-6007	270	30	1−	1−	NUM
ejpam-6007	270	31	x0	x0	NUM
ejpam-6007	270	32	)	)	PUNCT
ejpam-6007	270	33	)	)	PUNCT
ejpam-6007	270	34	2	2	NUM
ejpam-6007	270	35	,	,	PUNCT
ejpam-6007	270	36	c2,1	c2,1	NOUN
ejpam-6007	270	37	=	=	NOUN
ejpam-6007	270	38	p2	p2	PROPN
ejpam-6007	270	39	2	2	NUM
ejpam-6007	270	40	u22,1	u22,1	NOUN
ejpam-6007	270	41	=	=	NOUN
ejpam-6007	270	42	p2	p2	PROPN
ejpam-6007	270	43	2	2	NUM
ejpam-6007	270	44	(	(	PUNCT
ejpam-6007	270	45	h2ϕ2	h2ϕ2	X
ejpam-6007	270	46	p2	p2	PROPN
ejpam-6007	270	47	x)2	x)2	PROPN
ejpam-6007	270	48	.	.	PUNCT
ejpam-6007	271	1	(	(	PUNCT
ejpam-6007	271	2	41	41	NUM
ejpam-6007	271	3	)	)	PUNCT
ejpam-6007	271	4	at	at	ADP
ejpam-6007	271	5	n=1	n=1	PROPN
ejpam-6007	271	6	x2	x2	PROPN
ejpam-6007	272	1	=	=	PUNCT
ejpam-6007	273	1	x1	x1	PROPN
ejpam-6007	274	1	+	+	NUM
ejpam-6007	274	2	h	h	NOUN
ejpam-6007	274	3	6	6	NUM
ejpam-6007	274	4	(	(	PUNCT
ejpam-6007	274	5	k1x	k1x	PROPN
ejpam-6007	274	6	+	+	NUM
ejpam-6007	274	7	2k2x	2k2x	NUM
ejpam-6007	274	8	+	+	CCONJ
ejpam-6007	274	9	2k3x	2k3x	NOUN
ejpam-6007	274	10	+	+	NOUN
ejpam-6007	274	11	k4x	k4x	X
ejpam-6007	274	12	)	)	PUNCT
ejpam-6007	274	13	(	(	PUNCT
ejpam-6007	274	14	42	42	NUM
ejpam-6007	274	15	)	)	PUNCT
ejpam-6007	274	16	where	where	SCONJ
ejpam-6007	274	17	a.	a.	NOUN
ejpam-6007	274	18	a.	a.	PROPN
ejpam-6007	274	19	megahed	megahe	VERB
ejpam-6007	274	20	et	et	PROPN
ejpam-6007	274	21	al	al	PROPN
ejpam-6007	274	22	.	.	PUNCT
ejpam-6007	274	23	/	/	SYM
ejpam-6007	274	24	eur	eur	PROPN
ejpam-6007	274	25	.	.	PUNCT
ejpam-6007	275	1	j.	j.	PROPN
ejpam-6007	275	2	pure	pure	PROPN
ejpam-6007	275	3	appl	appl	PROPN
ejpam-6007	275	4	.	.	PROPN
ejpam-6007	275	5	math	math	PROPN
ejpam-6007	275	6	,	,	PUNCT
ejpam-6007	275	7	18	18	NUM
ejpam-6007	275	8	(	(	PUNCT
ejpam-6007	275	9	4	4	NUM
ejpam-6007	275	10	)	)	PUNCT
ejpam-6007	275	11	(	(	PUNCT
ejpam-6007	275	12	2025	2025	NUM
ejpam-6007	275	13	)	)	PUNCT
ejpam-6007	275	14	,	,	PUNCT
ejpam-6007	275	15	6007	6007	NUM
ejpam-6007	275	16	13	13	NUM
ejpam-6007	275	17	of	of	ADP
ejpam-6007	275	18	22	22	NUM
ejpam-6007	275	19	k1x	k1x	NOUN
ejpam-6007	275	20	=	=	SYM
ejpam-6007	276	1	hfx(x1	hfx(x1	PROPN
ejpam-6007	276	2	,	,	PUNCT
ejpam-6007	276	3	t1	t1	NOUN
ejpam-6007	276	4	)	)	PUNCT
ejpam-6007	277	1	=	=	SYM
ejpam-6007	277	2	h	h	NOUN
ejpam-6007	277	3	[	[	PUNCT
ejpam-6007	277	4	(	(	PUNCT
ejpam-6007	277	5	λ1(t))1	λ1(t))1	X
ejpam-6007	277	6	p1	p1	PROPN
ejpam-6007	277	7	(	(	PUNCT
ejpam-6007	277	8	1−	1−	NUM
ejpam-6007	277	9	x1(t	x1(t	NUM
ejpam-6007	277	10	)	)	PUNCT
ejpam-6007	277	11	)	)	PUNCT
ejpam-6007	277	12	2	2	NUM
ejpam-6007	278	1	+	+	CCONJ
ejpam-6007	278	2	(	(	PUNCT
ejpam-6007	278	3	λ2(t))1	λ2(t))1	NOUN
ejpam-6007	278	4	p2	p2	VERB
ejpam-6007	278	5	x21	x21	PROPN
ejpam-6007	278	6	]	]	PUNCT
ejpam-6007	278	7	,	,	PUNCT
ejpam-6007	278	8	k2x	k2x	PROPN
ejpam-6007	278	9	=	=	SYM
ejpam-6007	278	10	hfx	hfx	PROPN
ejpam-6007	278	11	(	(	PUNCT
ejpam-6007	278	12	x1	x1	PROPN
ejpam-6007	278	13	+	+	CCONJ
ejpam-6007	278	14	h	h	NOUN
ejpam-6007	278	15	2	2	NUM
ejpam-6007	278	16	,	,	PUNCT
ejpam-6007	278	17	t1	t1	NOUN
ejpam-6007	279	1	+	+	CCONJ
ejpam-6007	279	2	k1x	k1x	PROPN
ejpam-6007	279	3	2	2	X
ejpam-6007	279	4	)	)	PUNCT
ejpam-6007	280	1	=	=	SYM
ejpam-6007	280	2	h	h	NOUN
ejpam-6007	280	3	[	[	PUNCT
ejpam-6007	280	4	λ1	λ1	PROPN
ejpam-6007	280	5	(	(	PUNCT
ejpam-6007	280	6	t1	t1	NOUN
ejpam-6007	280	7	+	+	CCONJ
ejpam-6007	280	8	k1x	k1x	PROPN
ejpam-6007	280	9	2	2	X
ejpam-6007	280	10	)	)	PUNCT
ejpam-6007	280	11	p1	p1	NOUN
ejpam-6007	280	12	(	(	PUNCT
ejpam-6007	280	13	1−	1−	NUM
ejpam-6007	280	14	(	(	PUNCT
ejpam-6007	280	15	x1	x1	PROPN
ejpam-6007	281	1	+	+	CCONJ
ejpam-6007	281	2	h	h	NOUN
ejpam-6007	281	3	2	2	NUM
ejpam-6007	281	4	)	)	PUNCT
ejpam-6007	281	5	)	)	PUNCT
ejpam-6007	281	6	2	2	NUM
ejpam-6007	282	1	+	+	NUM
ejpam-6007	282	2	λ2	λ2	NOUN
ejpam-6007	282	3	(	(	PUNCT
ejpam-6007	282	4	t1	t1	NOUN
ejpam-6007	282	5	+	+	CCONJ
ejpam-6007	282	6	k1x	k1x	PROPN
ejpam-6007	282	7	2	2	X
ejpam-6007	282	8	)	)	PUNCT
ejpam-6007	282	9	p2	p2	PROPN
ejpam-6007	282	10	(	(	PUNCT
ejpam-6007	282	11	x1	x1	PROPN
ejpam-6007	282	12	+	+	CCONJ
ejpam-6007	282	13	h	h	NOUN
ejpam-6007	282	14	2	2	NUM
ejpam-6007	282	15	)	)	PUNCT
ejpam-6007	282	16	2	2	NUM
ejpam-6007	282	17	]	]	PUNCT
ejpam-6007	282	18	,	,	PUNCT
ejpam-6007	282	19	k3x	k3x	X
ejpam-6007	282	20	=	=	PROPN
ejpam-6007	282	21	hfx	hfx	PROPN
ejpam-6007	282	22	(	(	PUNCT
ejpam-6007	282	23	x1	x1	PROPN
ejpam-6007	282	24	+	+	CCONJ
ejpam-6007	282	25	h	h	NOUN
ejpam-6007	282	26	2	2	NUM
ejpam-6007	282	27	,	,	PUNCT
ejpam-6007	282	28	t1	t1	NOUN
ejpam-6007	282	29	+	+	X
ejpam-6007	282	30	k2x	k2x	X
ejpam-6007	282	31	2	2	NUM
ejpam-6007	282	32	)	)	PUNCT
ejpam-6007	282	33	=	=	SYM
ejpam-6007	283	1	h	h	NOUN
ejpam-6007	283	2	[	[	PUNCT
ejpam-6007	283	3	λ1	λ1	PROPN
ejpam-6007	283	4	(	(	PUNCT
ejpam-6007	283	5	t1	t1	NOUN
ejpam-6007	283	6	+	+	CCONJ
ejpam-6007	283	7	k2x	k2x	PROPN
ejpam-6007	283	8	2	2	X
ejpam-6007	283	9	)	)	PUNCT
ejpam-6007	283	10	p1	p1	NOUN
ejpam-6007	283	11	(	(	PUNCT
ejpam-6007	283	12	1−	1−	NUM
ejpam-6007	283	13	(	(	PUNCT
ejpam-6007	283	14	x1	x1	PROPN
ejpam-6007	283	15	+	+	CCONJ
ejpam-6007	283	16	h	h	NOUN
ejpam-6007	283	17	2	2	NUM
ejpam-6007	283	18	)	)	PUNCT
ejpam-6007	283	19	)	)	PUNCT
ejpam-6007	283	20	2	2	NUM
ejpam-6007	284	1	+	+	NUM
ejpam-6007	284	2	λ2	λ2	NOUN
ejpam-6007	284	3	(	(	PUNCT
ejpam-6007	284	4	t1	t1	NOUN
ejpam-6007	284	5	+	+	CCONJ
ejpam-6007	285	1	k2x	k2x	X
ejpam-6007	285	2	2	2	X
ejpam-6007	285	3	)	)	PUNCT
ejpam-6007	285	4	p2	p2	PROPN
ejpam-6007	285	5	(	(	PUNCT
ejpam-6007	285	6	x1	x1	PROPN
ejpam-6007	286	1	+	+	CCONJ
ejpam-6007	286	2	h	h	NOUN
ejpam-6007	286	3	2	2	NUM
ejpam-6007	286	4	)	)	PUNCT
ejpam-6007	286	5	2	2	NUM
ejpam-6007	286	6	]	]	PUNCT
ejpam-6007	286	7	,	,	PUNCT
ejpam-6007	286	8	k4x	k4x	PROPN
ejpam-6007	286	9	=	=	SYM
ejpam-6007	286	10	hfx	hfx	PROPN
ejpam-6007	286	11	(	(	PUNCT
ejpam-6007	286	12	x1	x1	PROPN
ejpam-6007	286	13	+	+	NUM
ejpam-6007	286	14	h	h	NOUN
ejpam-6007	286	15	,	,	PUNCT
ejpam-6007	286	16	t1	t1	NOUN
ejpam-6007	286	17	+	+	NOUN
ejpam-6007	286	18	k3x	k3x	X
ejpam-6007	286	19	)	)	PUNCT
ejpam-6007	287	1	=	=	SYM
ejpam-6007	287	2	h	h	NOUN
ejpam-6007	287	3	[	[	PUNCT
ejpam-6007	287	4	λ1	λ1	PROPN
ejpam-6007	287	5	(	(	PUNCT
ejpam-6007	287	6	t1	t1	NOUN
ejpam-6007	287	7	+	+	NOUN
ejpam-6007	287	8	k3x	k3x	PROPN
ejpam-6007	287	9	)	)	PUNCT
ejpam-6007	287	10	p1	p1	NOUN
ejpam-6007	287	11	(	(	PUNCT
ejpam-6007	287	12	1−	1−	NUM
ejpam-6007	287	13	(	(	PUNCT
ejpam-6007	287	14	x1	x1	PROPN
ejpam-6007	288	1	+	+	NUM
ejpam-6007	288	2	h))2	h))2	NOUN
ejpam-6007	288	3	+	+	CCONJ
ejpam-6007	288	4	λ2	λ2	NOUN
ejpam-6007	288	5	(	(	PUNCT
ejpam-6007	288	6	t1	t1	NOUN
ejpam-6007	288	7	+	+	NOUN
ejpam-6007	288	8	k3x	k3x	PROPN
ejpam-6007	288	9	)	)	PUNCT
ejpam-6007	288	10	p2	p2	PROPN
ejpam-6007	288	11	(	(	PUNCT
ejpam-6007	288	12	x1	x1	PROPN
ejpam-6007	288	13	+	+	CCONJ
ejpam-6007	288	14	h)2	h)2	NOUN
ejpam-6007	288	15	]	]	PUNCT
ejpam-6007	288	16	.	.	PUNCT
ejpam-6007	289	1	(	(	PUNCT
ejpam-6007	289	2	43	43	NUM
ejpam-6007	289	3	)	)	PUNCT
ejpam-6007	289	4	then	then	ADV
ejpam-6007	289	5	x2	x2	PRON
ejpam-6007	290	1	=	=	PUNCT
ejpam-6007	291	1	x0	x0	PROPN
ejpam-6007	292	1	+	+	X
ejpam-6007	292	2	h4	h4	PROPN
ejpam-6007	292	3	6	6	NUM
ejpam-6007	292	4	[	[	PUNCT
ejpam-6007	292	5	ϕ1	ϕ1	PROPN
ejpam-6007	292	6	p1	p1	NOUN
ejpam-6007	292	7	(	(	PUNCT
ejpam-6007	292	8	(	(	PUNCT
ejpam-6007	292	9	1−x0	1−x0	NUM
ejpam-6007	292	10	)	)	PUNCT
ejpam-6007	292	11	2	2	NUM
ejpam-6007	293	1	+	+	NOUN
ejpam-6007	293	2	4(1−x0−	4(1−x0−	NUM
ejpam-6007	293	3	h	h	NOUN
ejpam-6007	293	4	2	2	NUM
ejpam-6007	293	5	)	)	PUNCT
ejpam-6007	293	6	2+(1−x0−h)2	2+(1−x0−h)2	NOUN
ejpam-6007	293	7	)	)	PUNCT
ejpam-6007	294	1	−ϕ2	−ϕ2	PROPN
ejpam-6007	294	2	p2	p2	PROPN
ejpam-6007	294	3	(	(	PUNCT
ejpam-6007	294	4	(	(	PUNCT
ejpam-6007	294	5	x0	x0	PROPN
ejpam-6007	294	6	)	)	PUNCT
ejpam-6007	294	7	2	2	NUM
ejpam-6007	294	8	+	+	NUM
ejpam-6007	294	9	4(x0	4(x0	NOUN
ejpam-6007	294	10	+	+	NUM
ejpam-6007	294	11	h	h	NOUN
ejpam-6007	294	12	2	2	NUM
ejpam-6007	294	13	)	)	PUNCT
ejpam-6007	294	14	2+(x0+h)2	2+(x0+h)2	NUM
ejpam-6007	294	15	)	)	PUNCT
ejpam-6007	294	16	]	]	PUNCT
ejpam-6007	294	17	.	.	PUNCT
ejpam-6007	295	1	(	(	PUNCT
ejpam-6007	295	2	λ1)2	λ1)2	X
ejpam-6007	295	3	=	=	SYM
ejpam-6007	295	4	λ1,1	λ1,1	NOUN
ejpam-6007	296	1	+	+	CCONJ
ejpam-6007	296	2	h	h	NOUN
ejpam-6007	296	3	6	6	NUM
ejpam-6007	296	4	(	(	PUNCT
ejpam-6007	296	5	k1λ1	k1λ1	X
ejpam-6007	296	6	+	+	CCONJ
ejpam-6007	296	7	2k2λ1	2k2λ1	NUM
ejpam-6007	296	8	+	+	CCONJ
ejpam-6007	296	9	2k3λ1	2k3λ1	NUM
ejpam-6007	296	10	+	+	ADJ
ejpam-6007	296	11	k4λ1	k4λ1	NOUN
ejpam-6007	296	12	)	)	PUNCT
ejpam-6007	296	13	(	(	PUNCT
ejpam-6007	296	14	44	44	NUM
ejpam-6007	296	15	)	)	PUNCT
ejpam-6007	297	1	where	where	SCONJ
ejpam-6007	297	2	k1λ1	k1λ1	NOUN
ejpam-6007	297	3	=	=	SYM
ejpam-6007	297	4	hfλ1(x1	hfλ1(x1	PROPN
ejpam-6007	297	5	,	,	PUNCT
ejpam-6007	297	6	t1	t1	NOUN
ejpam-6007	297	7	)	)	PUNCT
ejpam-6007	297	8	=	=	SYM
ejpam-6007	298	1	h	h	NOUN
ejpam-6007	298	2	[	[	PUNCT
ejpam-6007	298	3	(	(	PUNCT
ejpam-6007	298	4	λ2	λ2	NOUN
ejpam-6007	298	5	1(t))1	1(t))1	NUM
ejpam-6007	298	6	p1	p1	NOUN
ejpam-6007	298	7	(	(	PUNCT
ejpam-6007	298	8	1−	1−	NUM
ejpam-6007	298	9	x1)−	x1)−	PROPN
ejpam-6007	298	10	(	(	PUNCT
ejpam-6007	298	11	λ1(t))1(λ2(t))1	λ1(t))1(λ2(t))1	ADP
ejpam-6007	298	12	p2	p2	PROPN
ejpam-6007	298	13	x1(t)−	x1(t)−	PROPN
ejpam-6007	298	14	ϕ1	ϕ1	PROPN
ejpam-6007	298	15	]	]	PUNCT
ejpam-6007	298	16	,	,	PUNCT
ejpam-6007	298	17	k2λ1	k2λ1	PROPN
ejpam-6007	298	18	=	=	SYM
ejpam-6007	298	19	hfλ1	hfλ1	PROPN
ejpam-6007	298	20	(	(	PUNCT
ejpam-6007	298	21	x1	x1	PROPN
ejpam-6007	299	1	+	+	CCONJ
ejpam-6007	299	2	h	h	NOUN
ejpam-6007	299	3	2	2	NUM
ejpam-6007	299	4	,	,	PUNCT
ejpam-6007	299	5	t1	t1	NOUN
ejpam-6007	299	6	+	+	X
ejpam-6007	299	7	k1λ1	k1λ1	NOUN
ejpam-6007	299	8	2	2	X
ejpam-6007	299	9	)	)	PUNCT
ejpam-6007	299	10	=	=	SYM
ejpam-6007	300	1	h	h	NOUN
ejpam-6007	300	2	[	[	PUNCT
ejpam-6007	300	3	λ1(t1	λ1(t1	X
ejpam-6007	300	4	+	+	NOUN
ejpam-6007	300	5	k1λ1	k1λ1	NOUN
ejpam-6007	300	6	2	2	NUM
ejpam-6007	300	7	)	)	SYM
ejpam-6007	300	8	2	2	NUM
ejpam-6007	300	9	p1	p1	NOUN
ejpam-6007	300	10	(	(	PUNCT
ejpam-6007	300	11	1−	1−	NUM
ejpam-6007	300	12	(	(	PUNCT
ejpam-6007	300	13	x1	x1	PROPN
ejpam-6007	300	14	+	+	NUM
ejpam-6007	300	15	h	h	NOUN
ejpam-6007	300	16	2	2	NUM
ejpam-6007	300	17	)	)	PUNCT
ejpam-6007	300	18	)	)	PUNCT
ejpam-6007	301	1	−	−	PROPN
ejpam-6007	302	1	λ1(t1	λ1(t1	NUM
ejpam-6007	302	2	+	+	NOUN
ejpam-6007	302	3	k1λ1	k1λ1	NOUN
ejpam-6007	302	4	2	2	NUM
ejpam-6007	302	5	)	)	PUNCT
ejpam-6007	302	6	λ2(t1	λ2(t1	NOUN
ejpam-6007	302	7	+	+	NOUN
ejpam-6007	302	8	k1λ1	k1λ1	NOUN
ejpam-6007	302	9	2	2	X
ejpam-6007	302	10	)	)	PUNCT
ejpam-6007	302	11	p2	p2	PROPN
ejpam-6007	302	12	(	(	PUNCT
ejpam-6007	302	13	x1	x1	PROPN
ejpam-6007	302	14	+	+	NUM
ejpam-6007	302	15	h	h	NOUN
ejpam-6007	302	16	2	2	NUM
ejpam-6007	302	17	)	)	PUNCT
ejpam-6007	302	18	−	−	PROPN
ejpam-6007	302	19	ϕ1	ϕ1	NOUN
ejpam-6007	302	20	]	]	PUNCT
ejpam-6007	302	21	,	,	PUNCT
ejpam-6007	302	22	k3λ1	k3λ1	X
ejpam-6007	302	23	=	=	SYM
ejpam-6007	302	24	hfλ1	hfλ1	PROPN
ejpam-6007	302	25	(	(	PUNCT
ejpam-6007	302	26	x1	x1	PROPN
ejpam-6007	302	27	+	+	CCONJ
ejpam-6007	302	28	h	h	NOUN
ejpam-6007	302	29	2	2	NUM
ejpam-6007	302	30	,	,	PUNCT
ejpam-6007	302	31	t1	t1	NOUN
ejpam-6007	302	32	+	+	CCONJ
ejpam-6007	302	33	k2λ1	k2λ1	PROPN
ejpam-6007	302	34	2	2	X
ejpam-6007	302	35	)	)	PUNCT
ejpam-6007	302	36	=	=	SYM
ejpam-6007	303	1	h	h	NOUN
ejpam-6007	303	2	[	[	PUNCT
ejpam-6007	303	3	λ1(t1	λ1(t1	X
ejpam-6007	303	4	+	+	CCONJ
ejpam-6007	303	5	k2λ1	k2λ1	PROPN
ejpam-6007	303	6	2	2	NUM
ejpam-6007	303	7	)	)	SYM
ejpam-6007	303	8	2	2	NUM
ejpam-6007	303	9	p1	p1	NOUN
ejpam-6007	303	10	(	(	PUNCT
ejpam-6007	303	11	1−	1−	NUM
ejpam-6007	303	12	(	(	PUNCT
ejpam-6007	303	13	x1	x1	PROPN
ejpam-6007	303	14	+	+	NUM
ejpam-6007	303	15	h	h	NOUN
ejpam-6007	303	16	2	2	NUM
ejpam-6007	303	17	)	)	PUNCT
ejpam-6007	303	18	)	)	PUNCT
ejpam-6007	304	1	−	−	PROPN
ejpam-6007	305	1	λ1(t1	λ1(t1	X
ejpam-6007	305	2	+	+	CCONJ
ejpam-6007	305	3	k2λ1	k2λ1	PROPN
ejpam-6007	305	4	2	2	NUM
ejpam-6007	305	5	)	)	PUNCT
ejpam-6007	305	6	λ2(t1	λ2(t1	PROPN
ejpam-6007	305	7	+	+	CCONJ
ejpam-6007	305	8	k2λ1	k2λ1	PROPN
ejpam-6007	305	9	2	2	X
ejpam-6007	305	10	)	)	PUNCT
ejpam-6007	305	11	p2	p2	PROPN
ejpam-6007	305	12	(	(	PUNCT
ejpam-6007	305	13	x1	x1	PROPN
ejpam-6007	306	1	+	+	NUM
ejpam-6007	306	2	h	h	NOUN
ejpam-6007	306	3	2	2	NUM
ejpam-6007	306	4	)	)	PUNCT
ejpam-6007	307	1	−	−	PROPN
ejpam-6007	307	2	ϕ1	ϕ1	NOUN
ejpam-6007	307	3	]	]	PUNCT
ejpam-6007	307	4	,	,	PUNCT
ejpam-6007	307	5	k4λ1	k4λ1	NOUN
ejpam-6007	307	6	=	=	VERB
ejpam-6007	307	7	hfλ1	hfλ1	NOUN
ejpam-6007	307	8	(	(	PUNCT
ejpam-6007	307	9	x1	x1	PROPN
ejpam-6007	307	10	+	+	NUM
ejpam-6007	307	11	h	h	NOUN
ejpam-6007	307	12	,	,	PUNCT
ejpam-6007	307	13	t1	t1	NOUN
ejpam-6007	307	14	+	+	NOUN
ejpam-6007	307	15	k3x	k3x	X
ejpam-6007	307	16	)	)	PUNCT
ejpam-6007	308	1	=	=	SYM
ejpam-6007	308	2	h	h	NOUN
ejpam-6007	308	3	[	[	PUNCT
ejpam-6007	308	4	λ1(t1	λ1(t1	NUM
ejpam-6007	308	5	+	+	NOUN
ejpam-6007	308	6	k3λ1	k3λ1	NOUN
ejpam-6007	308	7	)	)	PUNCT
ejpam-6007	308	8	2	2	NUM
ejpam-6007	308	9	p1	p1	NOUN
ejpam-6007	308	10	(	(	PUNCT
ejpam-6007	308	11	1−	1−	NUM
ejpam-6007	308	12	(	(	PUNCT
ejpam-6007	308	13	x1	x1	PROPN
ejpam-6007	308	14	+	+	NUM
ejpam-6007	308	15	h	h	NOUN
ejpam-6007	308	16	)	)	PUNCT
ejpam-6007	308	17	)	)	PUNCT
ejpam-6007	309	1	−	−	PROPN
ejpam-6007	310	1	λ1(t1	λ1(t1	NUM
ejpam-6007	310	2	+	+	NOUN
ejpam-6007	310	3	k3λ1)λ2(t1	k3λ1)λ2(t1	ADJ
ejpam-6007	310	4	+	+	ADJ
ejpam-6007	310	5	k3λ1	k3λ1	NOUN
ejpam-6007	310	6	)	)	PUNCT
ejpam-6007	310	7	p2	p2	PROPN
ejpam-6007	310	8	(	(	PUNCT
ejpam-6007	310	9	x1	x1	PROPN
ejpam-6007	310	10	+	+	CCONJ
ejpam-6007	310	11	h)−	h)−	PROPN
ejpam-6007	310	12	ϕ1	ϕ1	NOUN
ejpam-6007	310	13	]	]	PUNCT
ejpam-6007	310	14	.	.	PUNCT
ejpam-6007	311	1	(	(	PUNCT
ejpam-6007	311	2	45	45	NUM
ejpam-6007	311	3	)	)	PUNCT
ejpam-6007	311	4	λ1,2	λ1,2	NOUN
ejpam-6007	311	5	=	=	PUNCT
ejpam-6007	312	1	−h2ϕ1	−h2ϕ1	PROPN
ejpam-6007	312	2	+	+	NUM
ejpam-6007	312	3	h6	h6	PROPN
ejpam-6007	312	4	6	6	NUM
ejpam-6007	312	5	[	[	PUNCT
ejpam-6007	312	6	(	(	PUNCT
ejpam-6007	312	7	ϕ1	ϕ1	NOUN
ejpam-6007	312	8	)	)	PUNCT
ejpam-6007	312	9	2	2	NUM
ejpam-6007	312	10	p1	p1	NOUN
ejpam-6007	312	11	(	(	PUNCT
ejpam-6007	312	12	(	(	PUNCT
ejpam-6007	312	13	1−	1−	NUM
ejpam-6007	312	14	x0	x0	NUM
ejpam-6007	312	15	)	)	PUNCT
ejpam-6007	313	1	+	+	CCONJ
ejpam-6007	313	2	4(1−	4(1−	NUM
ejpam-6007	313	3	x0	x0	NUM
ejpam-6007	313	4	−	−	PROPN
ejpam-6007	313	5	h	h	NOUN
ejpam-6007	313	6	2	2	NUM
ejpam-6007	313	7	)	)	PUNCT
ejpam-6007	314	1	+	+	CCONJ
ejpam-6007	314	2	(	(	PUNCT
ejpam-6007	314	3	1−	1−	NUM
ejpam-6007	314	4	x0	x0	NUM
ejpam-6007	314	5	−	−	PROPN
ejpam-6007	314	6	h	h	NOUN
ejpam-6007	314	7	)	)	PUNCT
ejpam-6007	314	8	)	)	PUNCT
ejpam-6007	315	1	−	−	PROPN
ejpam-6007	316	1	ϕ1ϕ2	ϕ1ϕ2	NOUN
ejpam-6007	316	2	p2	p2	PROPN
ejpam-6007	316	3	(	(	PUNCT
ejpam-6007	316	4	x0	x0	PROPN
ejpam-6007	316	5	+	+	CCONJ
ejpam-6007	316	6	4(x0	4(x0	PROPN
ejpam-6007	317	1	+	+	CCONJ
ejpam-6007	317	2	h	h	NOUN
ejpam-6007	317	3	2	2	NUM
ejpam-6007	317	4	)	)	PUNCT
ejpam-6007	317	5	+	+	CCONJ
ejpam-6007	317	6	(	(	PUNCT
ejpam-6007	317	7	x0	x0	PROPN
ejpam-6007	317	8	+	+	NUM
ejpam-6007	317	9	h	h	NOUN
ejpam-6007	317	10	)	)	PUNCT
ejpam-6007	317	11	)	)	PUNCT
ejpam-6007	317	12	]	]	PUNCT
ejpam-6007	318	1	+	+	CCONJ
ejpam-6007	318	2	ϕ1h	ϕ1h	SYM
ejpam-6007	318	3	2	2	NUM
ejpam-6007	318	4	(	(	PUNCT
ejpam-6007	318	5	46	46	NUM
ejpam-6007	318	6	)	)	PUNCT
ejpam-6007	318	7	a.	a.	NOUN
ejpam-6007	318	8	a.	a.	NOUN
ejpam-6007	318	9	megahed	megahe	VERB
ejpam-6007	318	10	et	et	PROPN
ejpam-6007	318	11	al	al	PROPN
ejpam-6007	318	12	.	.	PUNCT
ejpam-6007	318	13	/	/	SYM
ejpam-6007	318	14	eur	eur	PROPN
ejpam-6007	318	15	.	.	PUNCT
ejpam-6007	319	1	j.	j.	PROPN
ejpam-6007	319	2	pure	pure	PROPN
ejpam-6007	319	3	appl	appl	PROPN
ejpam-6007	319	4	.	.	PROPN
ejpam-6007	319	5	math	math	PROPN
ejpam-6007	319	6	,	,	PUNCT
ejpam-6007	319	7	18	18	NUM
ejpam-6007	319	8	(	(	PUNCT
ejpam-6007	319	9	4	4	NUM
ejpam-6007	319	10	)	)	PUNCT
ejpam-6007	319	11	(	(	PUNCT
ejpam-6007	319	12	2025	2025	NUM
ejpam-6007	319	13	)	)	PUNCT
ejpam-6007	319	14	,	,	PUNCT
ejpam-6007	319	15	6007	6007	NUM
ejpam-6007	319	16	14	14	NUM
ejpam-6007	319	17	of	of	ADP
ejpam-6007	319	18	22	22	NUM
ejpam-6007	319	19	k1λ1	k1λ1	NOUN
ejpam-6007	319	20	=	=	SYM
ejpam-6007	319	21	hfλ1(x1	hfλ1(x1	PROPN
ejpam-6007	319	22	,	,	PUNCT
ejpam-6007	319	23	t1	t1	NOUN
ejpam-6007	319	24	)	)	PUNCT
ejpam-6007	320	1	=	=	SYM
ejpam-6007	320	2	h	h	NOUN
ejpam-6007	320	3	[	[	PUNCT
ejpam-6007	320	4	λ1,1(t	λ1,1(t	PROPN
ejpam-6007	320	5	)	)	PUNCT
ejpam-6007	320	6	p1	p1	NOUN
ejpam-6007	320	7	(	(	PUNCT
ejpam-6007	320	8	1−	1−	NUM
ejpam-6007	320	9	x1)−	x1)−	PROPN
ejpam-6007	320	10	λ1,1(t)λ2,1(t	λ1,1(t)λ2,1(t	X
ejpam-6007	320	11	)	)	PUNCT
ejpam-6007	320	12	p2	p2	PROPN
ejpam-6007	320	13	x1(t)−	x1(t)−	PROPN
ejpam-6007	320	14	ϕ1	ϕ1	PROPN
ejpam-6007	320	15	]	]	PUNCT
ejpam-6007	320	16	,	,	PUNCT
ejpam-6007	320	17	k2λ1	k2λ1	PROPN
ejpam-6007	320	18	=	=	SYM
ejpam-6007	320	19	hfλ1	hfλ1	PROPN
ejpam-6007	320	20	(	(	PUNCT
ejpam-6007	320	21	x1	x1	PROPN
ejpam-6007	320	22	+	+	CCONJ
ejpam-6007	320	23	h	h	NOUN
ejpam-6007	320	24	2	2	NUM
ejpam-6007	320	25	,	,	PUNCT
ejpam-6007	320	26	t1	t1	NOUN
ejpam-6007	320	27	+	+	X
ejpam-6007	320	28	k1λ1	k1λ1	NOUN
ejpam-6007	320	29	2	2	X
ejpam-6007	320	30	)	)	PUNCT
ejpam-6007	320	31	=	=	SYM
ejpam-6007	320	32	h	h	NOUN
ejpam-6007	320	33	[	[	PUNCT
ejpam-6007	320	34	λ1	λ1	PROPN
ejpam-6007	320	35	(	(	PUNCT
ejpam-6007	320	36	t1	t1	NOUN
ejpam-6007	320	37	+	+	CCONJ
ejpam-6007	320	38	k1λ1	k1λ1	NOUN
ejpam-6007	320	39	2	2	NUM
ejpam-6007	320	40	)	)	SYM
ejpam-6007	320	41	2	2	NUM
ejpam-6007	320	42	p1	p1	NOUN
ejpam-6007	320	43	(	(	PUNCT
ejpam-6007	320	44	1−	1−	NUM
ejpam-6007	320	45	(	(	PUNCT
ejpam-6007	320	46	x1	x1	PROPN
ejpam-6007	320	47	+	+	NUM
ejpam-6007	320	48	h	h	NOUN
ejpam-6007	320	49	2	2	NUM
ejpam-6007	320	50	)	)	PUNCT
ejpam-6007	320	51	)	)	PUNCT
ejpam-6007	321	1	−	−	PROPN
ejpam-6007	321	2	λ1	λ1	INTJ
ejpam-6007	321	3	(	(	PUNCT
ejpam-6007	321	4	t1	t1	NOUN
ejpam-6007	321	5	+	+	CCONJ
ejpam-6007	321	6	k1λ1	k1λ1	NOUN
ejpam-6007	321	7	2	2	X
ejpam-6007	321	8	)	)	PUNCT
ejpam-6007	321	9	λ2	λ2	NOUN
ejpam-6007	321	10	(	(	PUNCT
ejpam-6007	321	11	t1	t1	NOUN
ejpam-6007	321	12	+	+	CCONJ
ejpam-6007	321	13	k1λ1	k1λ1	NOUN
ejpam-6007	321	14	2	2	X
ejpam-6007	321	15	)	)	PUNCT
ejpam-6007	321	16	p2	p2	PROPN
ejpam-6007	321	17	(	(	PUNCT
ejpam-6007	321	18	x1	x1	PROPN
ejpam-6007	321	19	+	+	NUM
ejpam-6007	321	20	h	h	NOUN
ejpam-6007	321	21	2	2	NUM
ejpam-6007	321	22	)	)	PUNCT
ejpam-6007	321	23	−	−	PROPN
ejpam-6007	321	24	ϕ1	ϕ1	NOUN
ejpam-6007	321	25	]	]	PUNCT
ejpam-6007	321	26	,	,	PUNCT
ejpam-6007	321	27	k3λ1	k3λ1	X
ejpam-6007	321	28	=	=	SYM
ejpam-6007	321	29	hfλ1	hfλ1	PROPN
ejpam-6007	321	30	(	(	PUNCT
ejpam-6007	321	31	x1	x1	PROPN
ejpam-6007	321	32	+	+	CCONJ
ejpam-6007	321	33	h	h	NOUN
ejpam-6007	321	34	2	2	NUM
ejpam-6007	321	35	,	,	PUNCT
ejpam-6007	321	36	t1	t1	NOUN
ejpam-6007	321	37	+	+	CCONJ
ejpam-6007	321	38	k2λ1	k2λ1	PROPN
ejpam-6007	321	39	2	2	X
ejpam-6007	321	40	)	)	PUNCT
ejpam-6007	321	41	=	=	SYM
ejpam-6007	322	1	h	h	NOUN
ejpam-6007	322	2	[	[	PUNCT
ejpam-6007	322	3	λ1	λ1	PROPN
ejpam-6007	322	4	(	(	PUNCT
ejpam-6007	322	5	t1	t1	NOUN
ejpam-6007	322	6	+	+	CCONJ
ejpam-6007	322	7	k2λ1	k2λ1	PROPN
ejpam-6007	322	8	2	2	NUM
ejpam-6007	322	9	)	)	SYM
ejpam-6007	322	10	2	2	NUM
ejpam-6007	322	11	p1	p1	NOUN
ejpam-6007	322	12	(	(	PUNCT
ejpam-6007	322	13	1−	1−	NUM
ejpam-6007	322	14	(	(	PUNCT
ejpam-6007	322	15	x1	x1	PROPN
ejpam-6007	322	16	+	+	NUM
ejpam-6007	322	17	h	h	NOUN
ejpam-6007	322	18	2	2	NUM
ejpam-6007	322	19	)	)	PUNCT
ejpam-6007	322	20	)	)	PUNCT
ejpam-6007	323	1	−	−	PROPN
ejpam-6007	323	2	λ1	λ1	INTJ
ejpam-6007	323	3	(	(	PUNCT
ejpam-6007	323	4	t1	t1	NOUN
ejpam-6007	323	5	+	+	CCONJ
ejpam-6007	323	6	k2λ1	k2λ1	PROPN
ejpam-6007	323	7	2	2	X
ejpam-6007	323	8	)	)	PUNCT
ejpam-6007	323	9	λ2	λ2	NOUN
ejpam-6007	323	10	(	(	PUNCT
ejpam-6007	323	11	t1	t1	NOUN
ejpam-6007	323	12	+	+	CCONJ
ejpam-6007	323	13	k2λ1	k2λ1	PROPN
ejpam-6007	323	14	2	2	X
ejpam-6007	323	15	)	)	PUNCT
ejpam-6007	323	16	p2	p2	PROPN
ejpam-6007	323	17	(	(	PUNCT
ejpam-6007	323	18	x1	x1	PROPN
ejpam-6007	323	19	+	+	NUM
ejpam-6007	323	20	h	h	NOUN
ejpam-6007	323	21	2	2	NUM
ejpam-6007	323	22	)	)	PUNCT
ejpam-6007	323	23	−	−	PROPN
ejpam-6007	323	24	ϕ1	ϕ1	NOUN
ejpam-6007	323	25	]	]	PUNCT
ejpam-6007	323	26	,	,	PUNCT
ejpam-6007	323	27	k4λ1	k4λ1	NOUN
ejpam-6007	323	28	=	=	VERB
ejpam-6007	323	29	hfλ1	hfλ1	NOUN
ejpam-6007	323	30	(	(	PUNCT
ejpam-6007	323	31	x1	x1	PROPN
ejpam-6007	323	32	+	+	NUM
ejpam-6007	323	33	h	h	NOUN
ejpam-6007	323	34	,	,	PUNCT
ejpam-6007	323	35	t1	t1	NOUN
ejpam-6007	323	36	+	+	NOUN
ejpam-6007	323	37	k3λ1	k3λ1	NOUN
ejpam-6007	323	38	)	)	PUNCT
ejpam-6007	324	1	=	=	SYM
ejpam-6007	324	2	h	h	NOUN
ejpam-6007	324	3	[	[	PUNCT
ejpam-6007	324	4	λ1	λ1	PROPN
ejpam-6007	324	5	(	(	PUNCT
ejpam-6007	324	6	t1	t1	NOUN
ejpam-6007	324	7	+	+	PROPN
ejpam-6007	324	8	k3λ1	k3λ1	NOUN
ejpam-6007	324	9	)	)	PUNCT
ejpam-6007	324	10	2	2	NUM
ejpam-6007	324	11	p1	p1	NOUN
ejpam-6007	324	12	(	(	PUNCT
ejpam-6007	324	13	1−	1−	NUM
ejpam-6007	324	14	(	(	PUNCT
ejpam-6007	324	15	x1	x1	PROPN
ejpam-6007	324	16	+	+	NUM
ejpam-6007	324	17	h	h	NOUN
ejpam-6007	324	18	)	)	PUNCT
ejpam-6007	324	19	)	)	PUNCT
ejpam-6007	325	1	−	−	PROPN
ejpam-6007	325	2	λ1	λ1	PROPN
ejpam-6007	325	3	(	(	PUNCT
ejpam-6007	325	4	t1	t1	NOUN
ejpam-6007	325	5	+	+	NOUN
ejpam-6007	325	6	k3λ1	k3λ1	NOUN
ejpam-6007	325	7	)	)	PUNCT
ejpam-6007	325	8	λ2	λ2	NOUN
ejpam-6007	325	9	(	(	PUNCT
ejpam-6007	325	10	t1	t1	NOUN
ejpam-6007	325	11	+	+	PROPN
ejpam-6007	325	12	k3λ1	k3λ1	NOUN
ejpam-6007	325	13	)	)	PUNCT
ejpam-6007	325	14	p2	p2	PROPN
ejpam-6007	325	15	(	(	PUNCT
ejpam-6007	325	16	x1	x1	PROPN
ejpam-6007	325	17	+	+	CCONJ
ejpam-6007	325	18	h)−	h)−	PROPN
ejpam-6007	325	19	ϕ1	ϕ1	NOUN
ejpam-6007	325	20	]	]	PUNCT
ejpam-6007	325	21	.	.	PUNCT
ejpam-6007	326	1	(	(	PUNCT
ejpam-6007	326	2	47	47	NUM
ejpam-6007	326	3	)	)	PUNCT
ejpam-6007	326	4	similarly	similarly	ADV
ejpam-6007	326	5	,	,	PUNCT
ejpam-6007	326	6	λ2,2	λ2,2	PROPN
ejpam-6007	326	7	=	=	PUNCT
ejpam-6007	326	8	h2ϕ2	h2ϕ2	PROPN
ejpam-6007	326	9	−	−	PROPN
ejpam-6007	326	10	h6	h6	PROPN
ejpam-6007	326	11	6	6	NUM
ejpam-6007	326	12	[	[	PUNCT
ejpam-6007	326	13	ϕ1ϕ2	ϕ1ϕ2	X
ejpam-6007	326	14	p1	p1	NOUN
ejpam-6007	326	15	(	(	PUNCT
ejpam-6007	326	16	(	(	PUNCT
ejpam-6007	326	17	1−	1−	NUM
ejpam-6007	326	18	x0	x0	NUM
ejpam-6007	326	19	)	)	PUNCT
ejpam-6007	327	1	+	+	CCONJ
ejpam-6007	327	2	4(1−	4(1−	NUM
ejpam-6007	327	3	x0	x0	NUM
ejpam-6007	327	4	−	−	PROPN
ejpam-6007	327	5	h	h	NOUN
ejpam-6007	327	6	2	2	NUM
ejpam-6007	327	7	)	)	PUNCT
ejpam-6007	328	1	+	+	CCONJ
ejpam-6007	328	2	(	(	PUNCT
ejpam-6007	328	3	1−	1−	NUM
ejpam-6007	328	4	x0	x0	NUM
ejpam-6007	328	5	−	−	PROPN
ejpam-6007	328	6	h	h	NOUN
ejpam-6007	328	7	)	)	PUNCT
ejpam-6007	328	8	)	)	PUNCT
ejpam-6007	329	1	+	+	CCONJ
ejpam-6007	329	2	(	(	PUNCT
ejpam-6007	329	3	ϕ2	ϕ2	ADV
ejpam-6007	329	4	)	)	PUNCT
ejpam-6007	329	5	2	2	NUM
ejpam-6007	329	6	p2	p2	NOUN
ejpam-6007	329	7	(	(	PUNCT
ejpam-6007	329	8	x0	x0	PROPN
ejpam-6007	329	9	+	+	CCONJ
ejpam-6007	329	10	4(x0	4(x0	PROPN
ejpam-6007	330	1	+	+	CCONJ
ejpam-6007	330	2	h	h	NOUN
ejpam-6007	330	3	2	2	NUM
ejpam-6007	330	4	)	)	PUNCT
ejpam-6007	330	5	+	+	CCONJ
ejpam-6007	330	6	(	(	PUNCT
ejpam-6007	330	7	x0	x0	PROPN
ejpam-6007	330	8	+	+	NUM
ejpam-6007	330	9	h	h	NOUN
ejpam-6007	330	10	)	)	PUNCT
ejpam-6007	330	11	)	)	PUNCT
ejpam-6007	330	12	]	]	PUNCT
ejpam-6007	331	1	+	+	CCONJ
ejpam-6007	331	2	ϕ2h	ϕ2h	PROPN
ejpam-6007	331	3	2	2	X
ejpam-6007	331	4	.	.	PUNCT
ejpam-6007	331	5	(	(	PUNCT
ejpam-6007	331	6	48	48	NUM
ejpam-6007	331	7	)	)	PUNCT
ejpam-6007	331	8	a.	a.	NOUN
ejpam-6007	331	9	a.	a.	NOUN
ejpam-6007	331	10	megahed	megahe	VERB
ejpam-6007	331	11	et	et	PROPN
ejpam-6007	331	12	al	al	PROPN
ejpam-6007	331	13	.	.	PUNCT
ejpam-6007	331	14	/	/	SYM
ejpam-6007	331	15	eur	eur	PROPN
ejpam-6007	331	16	.	.	PUNCT
ejpam-6007	332	1	j.	j.	PROPN
ejpam-6007	332	2	pure	pure	PROPN
ejpam-6007	332	3	appl	appl	PROPN
ejpam-6007	332	4	.	.	PROPN
ejpam-6007	332	5	math	math	PROPN
ejpam-6007	332	6	,	,	PUNCT
ejpam-6007	332	7	18	18	NUM
ejpam-6007	332	8	(	(	PUNCT
ejpam-6007	332	9	4	4	NUM
ejpam-6007	332	10	)	)	PUNCT
ejpam-6007	332	11	(	(	PUNCT
ejpam-6007	332	12	2025	2025	NUM
ejpam-6007	332	13	)	)	PUNCT
ejpam-6007	332	14	,	,	PUNCT
ejpam-6007	332	15	6007	6007	NUM
ejpam-6007	332	16	15	15	NUM
ejpam-6007	332	17	of	of	ADP
ejpam-6007	332	18	22	22	NUM
ejpam-6007	332	19	u1,2	u1,2	ADJ
ejpam-6007	332	20	=	=	SYM
ejpam-6007	333	1	λ1,2	λ1,2	PROPN
ejpam-6007	333	2	p1	p1	NOUN
ejpam-6007	333	3	(	(	PUNCT
ejpam-6007	333	4	1−	1−	NUM
ejpam-6007	333	5	x2	x2	NOUN
ejpam-6007	333	6	)	)	PUNCT
ejpam-6007	333	7	=	=	SYM
ejpam-6007	333	8	1	1	NUM
ejpam-6007	333	9	p1	p1	NOUN
ejpam-6007	333	10	[	[	X
ejpam-6007	333	11	(	(	PUNCT
ejpam-6007	333	12	1−	1−	NUM
ejpam-6007	333	13	(	(	PUNCT
ejpam-6007	333	14	x0	x0	PROPN
ejpam-6007	333	15	+	+	CCONJ
ejpam-6007	333	16	h4	h4	PROPN
ejpam-6007	333	17	6	6	NUM
ejpam-6007	333	18	[	[	PUNCT
ejpam-6007	333	19	ϕ1	ϕ1	PROPN
ejpam-6007	333	20	p1	p1	NOUN
ejpam-6007	333	21	(	(	PUNCT
ejpam-6007	333	22	(	(	PUNCT
ejpam-6007	333	23	1−	1−	NUM
ejpam-6007	333	24	x0	x0	NUM
ejpam-6007	333	25	)	)	PUNCT
ejpam-6007	333	26	2	2	NUM
ejpam-6007	334	1	+	+	CCONJ
ejpam-6007	334	2	4(1−	4(1−	NUM
ejpam-6007	334	3	x0	x0	NUM
ejpam-6007	334	4	−	−	PROPN
ejpam-6007	334	5	h	h	NOUN
ejpam-6007	334	6	2	2	NUM
ejpam-6007	334	7	)	)	SYM
ejpam-6007	334	8	2	2	NUM
ejpam-6007	334	9	+	+	CCONJ
ejpam-6007	334	10	(	(	PUNCT
ejpam-6007	334	11	1−	1−	NUM
ejpam-6007	334	12	x0	x0	NUM
ejpam-6007	334	13	−	−	PROPN
ejpam-6007	334	14	h)2	h)2	VERB
ejpam-6007	334	15	)	)	PUNCT
ejpam-6007	335	1	−	−	ADP
ejpam-6007	335	2	ϕ2	ϕ2	ADV
ejpam-6007	335	3	p2	p2	PROPN
ejpam-6007	335	4	(	(	PUNCT
ejpam-6007	335	5	x20	x20	NUM
ejpam-6007	336	1	+	+	CCONJ
ejpam-6007	336	2	4(x0	4(x0	PROPN
ejpam-6007	337	1	+	+	CCONJ
ejpam-6007	337	2	h	h	NOUN
ejpam-6007	337	3	2	2	NUM
ejpam-6007	337	4	)	)	SYM
ejpam-6007	337	5	2	2	NUM
ejpam-6007	338	1	+	+	CCONJ
ejpam-6007	338	2	(	(	PUNCT
ejpam-6007	338	3	x0	x0	PROPN
ejpam-6007	338	4	+	+	CCONJ
ejpam-6007	338	5	h)2	h)2	NOUN
ejpam-6007	338	6	)	)	PUNCT
ejpam-6007	338	7	]	]	PUNCT
ejpam-6007	338	8	)	)	PUNCT
ejpam-6007	338	9	)	)	PUNCT
ejpam-6007	338	10	]	]	PUNCT
ejpam-6007	338	11	·	·	PUNCT
ejpam-6007	338	12	[	[	PUNCT
ejpam-6007	338	13	h2ϕ1	h2ϕ1	PROPN
ejpam-6007	338	14	+	+	NUM
ejpam-6007	338	15	h6	h6	PROPN
ejpam-6007	338	16	6	6	NUM
ejpam-6007	338	17	(	(	PUNCT
ejpam-6007	338	18	(	(	PUNCT
ejpam-6007	338	19	ϕ1	ϕ1	NOUN
ejpam-6007	338	20	)	)	PUNCT
ejpam-6007	338	21	2	2	NUM
ejpam-6007	338	22	p1	p1	NOUN
ejpam-6007	338	23	(	(	PUNCT
ejpam-6007	338	24	(	(	PUNCT
ejpam-6007	338	25	1−	1−	NUM
ejpam-6007	338	26	x0	x0	NUM
ejpam-6007	338	27	)	)	PUNCT
ejpam-6007	338	28	+	+	CCONJ
ejpam-6007	339	1	4(1−	4(1−	NUM
ejpam-6007	339	2	x0	x0	NUM
ejpam-6007	339	3	−	−	PROPN
ejpam-6007	339	4	h	h	NOUN
ejpam-6007	339	5	2	2	NUM
ejpam-6007	339	6	)	)	PUNCT
ejpam-6007	340	1	+	+	CCONJ
ejpam-6007	340	2	(	(	PUNCT
ejpam-6007	340	3	1−	1−	NUM
ejpam-6007	340	4	x0	x0	NUM
ejpam-6007	340	5	−	−	PROPN
ejpam-6007	340	6	h	h	NOUN
ejpam-6007	340	7	)	)	PUNCT
ejpam-6007	340	8	)	)	PUNCT
ejpam-6007	341	1	−	−	PROPN
ejpam-6007	342	1	ϕ1ϕ2	ϕ1ϕ2	NOUN
ejpam-6007	342	2	p2	p2	PROPN
ejpam-6007	342	3	(	(	PUNCT
ejpam-6007	342	4	x0	x0	PROPN
ejpam-6007	342	5	+	+	CCONJ
ejpam-6007	342	6	4(x0	4(x0	PROPN
ejpam-6007	343	1	+	+	CCONJ
ejpam-6007	343	2	h	h	NOUN
ejpam-6007	343	3	2	2	NUM
ejpam-6007	343	4	)	)	PUNCT
ejpam-6007	343	5	+	+	CCONJ
ejpam-6007	343	6	(	(	PUNCT
ejpam-6007	343	7	x0	x0	PROPN
ejpam-6007	343	8	+	+	NUM
ejpam-6007	343	9	h	h	NOUN
ejpam-6007	343	10	)	)	PUNCT
ejpam-6007	343	11	)	)	PUNCT
ejpam-6007	343	12	)	)	PUNCT
ejpam-6007	344	1	+	+	CCONJ
ejpam-6007	344	2	ϕ1h	ϕ1h	ADP
ejpam-6007	344	3	2	2	NUM
ejpam-6007	344	4	]	]	PUNCT
ejpam-6007	344	5	,	,	PUNCT
ejpam-6007	344	6	u2,2	u2,2	PROPN
ejpam-6007	344	7	=	=	SYM
ejpam-6007	344	8	−λ2,2	−λ2,2	PROPN
ejpam-6007	344	9	p2	p2	X
ejpam-6007	344	10	x2	x2	NOUN
ejpam-6007	345	1	=	=	PUNCT
ejpam-6007	345	2	−	−	PROPN
ejpam-6007	345	3	1	1	NUM
ejpam-6007	345	4	p2	p2	NOUN
ejpam-6007	345	5	[	[	PUNCT
ejpam-6007	345	6	−	−	NOUN
ejpam-6007	345	7	h2ϕ2	h2ϕ2	X
ejpam-6007	345	8	−	−	PROPN
ejpam-6007	345	9	h6	h6	PROPN
ejpam-6007	345	10	6	6	NUM
ejpam-6007	345	11	(	(	PUNCT
ejpam-6007	345	12	ϕ1ϕ2	ϕ1ϕ2	X
ejpam-6007	345	13	p1	p1	PROPN
ejpam-6007	345	14	(	(	PUNCT
ejpam-6007	345	15	(	(	PUNCT
ejpam-6007	345	16	1−	1−	NUM
ejpam-6007	345	17	x0	x0	NUM
ejpam-6007	345	18	)	)	PUNCT
ejpam-6007	346	1	+	+	CCONJ
ejpam-6007	346	2	4(1−	4(1−	NUM
ejpam-6007	346	3	x0	x0	NUM
ejpam-6007	346	4	−	−	PROPN
ejpam-6007	346	5	h	h	NOUN
ejpam-6007	346	6	2	2	NUM
ejpam-6007	346	7	)	)	PUNCT
ejpam-6007	347	1	+	+	CCONJ
ejpam-6007	347	2	(	(	PUNCT
ejpam-6007	347	3	1−	1−	NUM
ejpam-6007	347	4	x0	x0	NUM
ejpam-6007	347	5	−	−	PROPN
ejpam-6007	347	6	h	h	NOUN
ejpam-6007	347	7	)	)	PUNCT
ejpam-6007	347	8	)	)	PUNCT
ejpam-6007	348	1	+	+	CCONJ
ejpam-6007	348	2	(	(	PUNCT
ejpam-6007	348	3	ϕ2	ϕ2	ADV
ejpam-6007	348	4	)	)	PUNCT
ejpam-6007	348	5	2	2	NUM
ejpam-6007	348	6	p2	p2	NOUN
ejpam-6007	348	7	(	(	PUNCT
ejpam-6007	348	8	x0	x0	PROPN
ejpam-6007	348	9	+	+	CCONJ
ejpam-6007	348	10	4(x0	4(x0	PROPN
ejpam-6007	349	1	+	+	CCONJ
ejpam-6007	349	2	h	h	NOUN
ejpam-6007	349	3	2	2	NUM
ejpam-6007	349	4	)	)	PUNCT
ejpam-6007	349	5	+	+	CCONJ
ejpam-6007	349	6	(	(	PUNCT
ejpam-6007	349	7	x0	x0	PROPN
ejpam-6007	349	8	+	+	NUM
ejpam-6007	349	9	h	h	NOUN
ejpam-6007	349	10	)	)	PUNCT
ejpam-6007	349	11	)	)	PUNCT
ejpam-6007	349	12	)	)	PUNCT
ejpam-6007	350	1	+	+	CCONJ
ejpam-6007	350	2	ϕ2h	ϕ2h	ADV
ejpam-6007	350	3	2	2	NUM
ejpam-6007	350	4	]	]	PUNCT
ejpam-6007	350	5	·	·	PUNCT
ejpam-6007	351	1	[	[	PUNCT
ejpam-6007	351	2	x1	x1	PROPN
ejpam-6007	351	3	+	+	NUM
ejpam-6007	351	4	h	h	NOUN
ejpam-6007	351	5	6	6	NUM
ejpam-6007	351	6	(	(	PUNCT
ejpam-6007	351	7	k1x	k1x	PROPN
ejpam-6007	351	8	+	+	NUM
ejpam-6007	351	9	2k2x	2k2x	NUM
ejpam-6007	351	10	+	+	CCONJ
ejpam-6007	351	11	2k3x	2k3x	NOUN
ejpam-6007	351	12	+	+	NOUN
ejpam-6007	351	13	k4x	k4x	PROPN
ejpam-6007	351	14	)	)	PUNCT
ejpam-6007	351	15	]	]	PUNCT
ejpam-6007	351	16	,	,	PUNCT
ejpam-6007	351	17	(	(	PUNCT
ejpam-6007	351	18	49	49	NUM
ejpam-6007	351	19	)	)	PUNCT
ejpam-6007	351	20	a.	a.	NOUN
ejpam-6007	351	21	a.	a.	NOUN
ejpam-6007	351	22	megahed	megahe	VERB
ejpam-6007	351	23	et	et	PROPN
ejpam-6007	351	24	al	al	PROPN
ejpam-6007	351	25	.	.	PUNCT
ejpam-6007	351	26	/	/	SYM
ejpam-6007	351	27	eur	eur	PROPN
ejpam-6007	351	28	.	.	PUNCT
ejpam-6007	352	1	j.	j.	PROPN
ejpam-6007	352	2	pure	pure	PROPN
ejpam-6007	352	3	appl	appl	PROPN
ejpam-6007	352	4	.	.	PROPN
ejpam-6007	352	5	math	math	PROPN
ejpam-6007	352	6	,	,	PUNCT
ejpam-6007	352	7	18	18	NUM
ejpam-6007	352	8	(	(	PUNCT
ejpam-6007	352	9	4	4	NUM
ejpam-6007	352	10	)	)	PUNCT
ejpam-6007	352	11	(	(	PUNCT
ejpam-6007	352	12	2025	2025	NUM
ejpam-6007	352	13	)	)	PUNCT
ejpam-6007	352	14	,	,	PUNCT
ejpam-6007	352	15	6007	6007	NUM
ejpam-6007	352	16	16	16	NUM
ejpam-6007	352	17	of	of	ADP
ejpam-6007	352	18	22	22	NUM
ejpam-6007	352	19	c1,2	c1,2	PROPN
ejpam-6007	352	20	=	=	SYM
ejpam-6007	352	21	p1	p1	NOUN
ejpam-6007	352	22	2	2	NUM
ejpam-6007	352	23	(	(	PUNCT
ejpam-6007	352	24	u21)2	u21)2	NOUN
ejpam-6007	352	25	=	=	SYM
ejpam-6007	352	26	p1	p1	NOUN
ejpam-6007	352	27	2	2	NUM
ejpam-6007	352	28	[	[	PUNCT
ejpam-6007	352	29	1	1	NUM
ejpam-6007	352	30	p1	p1	NOUN
ejpam-6007	352	31	[	[	PUNCT
ejpam-6007	352	32	1−	1−	NUM
ejpam-6007	352	33	(	(	PUNCT
ejpam-6007	352	34	x0	x0	PROPN
ejpam-6007	352	35	+	+	CCONJ
ejpam-6007	352	36	h4	h4	PROPN
ejpam-6007	352	37	6	6	NUM
ejpam-6007	352	38	[	[	PUNCT
ejpam-6007	352	39	ϕ1	ϕ1	PROPN
ejpam-6007	352	40	p1	p1	NOUN
ejpam-6007	352	41	(	(	PUNCT
ejpam-6007	352	42	(	(	PUNCT
ejpam-6007	352	43	1−	1−	NUM
ejpam-6007	352	44	x0	x0	NUM
ejpam-6007	352	45	)	)	PUNCT
ejpam-6007	352	46	2	2	NUM
ejpam-6007	353	1	+	+	CCONJ
ejpam-6007	353	2	4(1−	4(1−	NUM
ejpam-6007	353	3	x0	x0	NUM
ejpam-6007	353	4	−	−	PROPN
ejpam-6007	353	5	h	h	NOUN
ejpam-6007	353	6	2	2	NUM
ejpam-6007	353	7	)	)	SYM
ejpam-6007	353	8	2	2	NUM
ejpam-6007	353	9	+	+	CCONJ
ejpam-6007	353	10	(	(	PUNCT
ejpam-6007	353	11	1−	1−	NUM
ejpam-6007	353	12	x0	x0	NUM
ejpam-6007	353	13	−	−	PROPN
ejpam-6007	353	14	h)2	h)2	VERB
ejpam-6007	353	15	)	)	PUNCT
ejpam-6007	354	1	−	−	ADP
ejpam-6007	354	2	ϕ2	ϕ2	ADV
ejpam-6007	354	3	p2	p2	PROPN
ejpam-6007	354	4	(	(	PUNCT
ejpam-6007	354	5	x20	x20	NUM
ejpam-6007	355	1	+	+	CCONJ
ejpam-6007	355	2	4(x0	4(x0	PROPN
ejpam-6007	356	1	+	+	CCONJ
ejpam-6007	356	2	h	h	NOUN
ejpam-6007	356	3	2	2	NUM
ejpam-6007	356	4	)	)	SYM
ejpam-6007	356	5	2	2	NUM
ejpam-6007	357	1	+	+	CCONJ
ejpam-6007	357	2	(	(	PUNCT
ejpam-6007	357	3	x0	x0	PROPN
ejpam-6007	357	4	+	+	CCONJ
ejpam-6007	357	5	h)2	h)2	NOUN
ejpam-6007	357	6	)	)	PUNCT
ejpam-6007	357	7	]	]	PUNCT
ejpam-6007	357	8	)	)	PUNCT
ejpam-6007	357	9	]	]	PUNCT
ejpam-6007	357	10	·	·	PUNCT
ejpam-6007	358	1	[	[	PUNCT
ejpam-6007	358	2	h2ϕ1	h2ϕ1	PROPN
ejpam-6007	358	3	+	+	NUM
ejpam-6007	358	4	h6	h6	PROPN
ejpam-6007	358	5	6	6	NUM
ejpam-6007	358	6	(	(	PUNCT
ejpam-6007	358	7	(	(	PUNCT
ejpam-6007	358	8	ϕ1	ϕ1	NOUN
ejpam-6007	358	9	)	)	PUNCT
ejpam-6007	358	10	2	2	NUM
ejpam-6007	358	11	p1	p1	NOUN
ejpam-6007	358	12	(	(	PUNCT
ejpam-6007	358	13	(	(	PUNCT
ejpam-6007	358	14	1−	1−	NUM
ejpam-6007	358	15	x0	x0	NUM
ejpam-6007	358	16	)	)	PUNCT
ejpam-6007	359	1	+	+	CCONJ
ejpam-6007	359	2	4(1−	4(1−	NUM
ejpam-6007	359	3	x0	x0	NUM
ejpam-6007	359	4	−	−	PROPN
ejpam-6007	359	5	h	h	NOUN
ejpam-6007	359	6	2	2	NUM
ejpam-6007	359	7	)	)	PUNCT
ejpam-6007	360	1	+	+	CCONJ
ejpam-6007	360	2	(	(	PUNCT
ejpam-6007	360	3	1−	1−	NUM
ejpam-6007	360	4	x0	x0	NUM
ejpam-6007	360	5	−	−	PROPN
ejpam-6007	360	6	h	h	NOUN
ejpam-6007	360	7	)	)	PUNCT
ejpam-6007	360	8	)	)	PUNCT
ejpam-6007	361	1	−	−	PROPN
ejpam-6007	362	1	ϕ1ϕ2	ϕ1ϕ2	NOUN
ejpam-6007	362	2	p2	p2	PROPN
ejpam-6007	362	3	(	(	PUNCT
ejpam-6007	362	4	x0	x0	PROPN
ejpam-6007	362	5	+	+	CCONJ
ejpam-6007	362	6	4(x0	4(x0	PROPN
ejpam-6007	363	1	+	+	CCONJ
ejpam-6007	363	2	h	h	NOUN
ejpam-6007	363	3	2	2	NUM
ejpam-6007	363	4	)	)	PUNCT
ejpam-6007	363	5	+	+	CCONJ
ejpam-6007	363	6	(	(	PUNCT
ejpam-6007	363	7	x0	x0	PROPN
ejpam-6007	363	8	+	+	NUM
ejpam-6007	363	9	h	h	NOUN
ejpam-6007	363	10	)	)	PUNCT
ejpam-6007	363	11	)	)	PUNCT
ejpam-6007	363	12	)	)	PUNCT
ejpam-6007	364	1	+	+	CCONJ
ejpam-6007	364	2	ϕ1h	ϕ1h	ADP
ejpam-6007	364	3	2	2	NUM
ejpam-6007	364	4	]	]	PUNCT
ejpam-6007	364	5	]	]	SYM
ejpam-6007	364	6	2	2	NUM
ejpam-6007	364	7	,	,	PUNCT
ejpam-6007	364	8	c2,2	c2,2	NOUN
ejpam-6007	364	9	=	=	NOUN
ejpam-6007	364	10	p2	p2	X
ejpam-6007	364	11	2	2	NUM
ejpam-6007	364	12	(	(	PUNCT
ejpam-6007	364	13	u22)2	u22)2	NOUN
ejpam-6007	364	14	=	=	SYM
ejpam-6007	364	15	p2	p2	X
ejpam-6007	364	16	2	2	NUM
ejpam-6007	364	17	[	[	PUNCT
ejpam-6007	364	18	−	−	PROPN
ejpam-6007	364	19	1	1	NUM
ejpam-6007	364	20	p2	p2	NOUN
ejpam-6007	364	21	[	[	PUNCT
ejpam-6007	364	22	−	−	NOUN
ejpam-6007	364	23	h2ϕ2	h2ϕ2	X
ejpam-6007	364	24	−	−	PROPN
ejpam-6007	364	25	h6	h6	PROPN
ejpam-6007	364	26	6	6	NUM
ejpam-6007	364	27	(	(	PUNCT
ejpam-6007	364	28	ϕ1ϕ2	ϕ1ϕ2	X
ejpam-6007	364	29	p1	p1	PROPN
ejpam-6007	364	30	(	(	PUNCT
ejpam-6007	364	31	(	(	PUNCT
ejpam-6007	364	32	1−	1−	NUM
ejpam-6007	364	33	x0	x0	NUM
ejpam-6007	364	34	)	)	PUNCT
ejpam-6007	365	1	+	+	CCONJ
ejpam-6007	365	2	4(1−	4(1−	NUM
ejpam-6007	365	3	x0	x0	NUM
ejpam-6007	365	4	−	−	PROPN
ejpam-6007	365	5	h	h	NOUN
ejpam-6007	365	6	2	2	NUM
ejpam-6007	365	7	)	)	PUNCT
ejpam-6007	366	1	+	+	CCONJ
ejpam-6007	366	2	(	(	PUNCT
ejpam-6007	366	3	1−	1−	NUM
ejpam-6007	366	4	x0	x0	NUM
ejpam-6007	366	5	−	−	PROPN
ejpam-6007	366	6	h	h	NOUN
ejpam-6007	366	7	)	)	PUNCT
ejpam-6007	366	8	)	)	PUNCT
ejpam-6007	367	1	+	+	CCONJ
ejpam-6007	367	2	(	(	PUNCT
ejpam-6007	367	3	ϕ2	ϕ2	ADV
ejpam-6007	367	4	)	)	PUNCT
ejpam-6007	367	5	2	2	NUM
ejpam-6007	367	6	p2	p2	NOUN
ejpam-6007	367	7	(	(	PUNCT
ejpam-6007	367	8	x0	x0	PROPN
ejpam-6007	367	9	+	+	CCONJ
ejpam-6007	367	10	4(x0	4(x0	PROPN
ejpam-6007	368	1	+	+	CCONJ
ejpam-6007	368	2	h	h	NOUN
ejpam-6007	368	3	2	2	NUM
ejpam-6007	368	4	)	)	PUNCT
ejpam-6007	368	5	+	+	CCONJ
ejpam-6007	368	6	(	(	PUNCT
ejpam-6007	368	7	x0	x0	PROPN
ejpam-6007	368	8	+	+	NUM
ejpam-6007	368	9	h	h	NOUN
ejpam-6007	368	10	)	)	PUNCT
ejpam-6007	368	11	)	)	PUNCT
ejpam-6007	368	12	)	)	PUNCT
ejpam-6007	369	1	+	+	CCONJ
ejpam-6007	369	2	ϕ2h	ϕ2h	ADV
ejpam-6007	369	3	2	2	NUM
ejpam-6007	369	4	]	]	PUNCT
ejpam-6007	369	5	·	·	PUNCT
ejpam-6007	370	1	[	[	PUNCT
ejpam-6007	370	2	x1	x1	PROPN
ejpam-6007	370	3	+	+	NUM
ejpam-6007	370	4	h	h	NOUN
ejpam-6007	370	5	6	6	NUM
ejpam-6007	370	6	(	(	PUNCT
ejpam-6007	370	7	k1x	k1x	PROPN
ejpam-6007	370	8	+	+	NUM
ejpam-6007	370	9	2k2x	2k2x	NUM
ejpam-6007	370	10	+	+	CCONJ
ejpam-6007	370	11	2k3x	2k3x	NOUN
ejpam-6007	370	12	+	+	NOUN
ejpam-6007	370	13	k4x	k4x	PROPN
ejpam-6007	370	14	)	)	PUNCT
ejpam-6007	370	15	]	]	PUNCT
ejpam-6007	370	16	]	]	X
ejpam-6007	370	17	2	2	NUM
ejpam-6007	370	18	(	(	PUNCT
ejpam-6007	370	19	50	50	NUM
ejpam-6007	370	20	)	)	PUNCT
ejpam-6007	370	21	suppose	suppose	VERB
ejpam-6007	370	22	that	that	SCONJ
ejpam-6007	370	23	firm	firm	NOUN
ejpam-6007	370	24	2	2	NUM
ejpam-6007	370	25	is	be	AUX
ejpam-6007	370	26	already	already	ADV
ejpam-6007	370	27	present	present	ADJ
ejpam-6007	370	28	in	in	ADP
ejpam-6007	370	29	the	the	DET
ejpam-6007	370	30	market	market	NOUN
ejpam-6007	370	31	,	,	PUNCT
ejpam-6007	370	32	with	with	ADP
ejpam-6007	370	33	its	its	PRON
ejpam-6007	370	34	market	market	NOUN
ejpam-6007	370	35	share	share	NOUN
ejpam-6007	370	36	represented	represent	VERB
ejpam-6007	370	37	by	by	ADP
ejpam-6007	370	38	1	1	NUM
ejpam-6007	370	39	−	−	PRON
ejpam-6007	370	40	x(t	x(t	PROPN
ejpam-6007	370	41	)	)	PUNCT
ejpam-6007	370	42	.	.	PUNCT
ejpam-6007	371	1	firm	firm	NOUN
ejpam-6007	371	2	1	1	NUM
ejpam-6007	371	3	enters	enter	VERB
ejpam-6007	371	4	the	the	DET
ejpam-6007	371	5	market	market	NOUN
ejpam-6007	371	6	to	to	PART
ejpam-6007	371	7	compete	compete	VERB
ejpam-6007	371	8	with	with	ADP
ejpam-6007	371	9	firm	firm	ADJ
ejpam-6007	371	10	2	2	NUM
ejpam-6007	371	11	,	,	PUNCT
ejpam-6007	371	12	and	and	CCONJ
ejpam-6007	371	13	its	its	PRON
ejpam-6007	371	14	market	market	NOUN
ejpam-6007	371	15	share	share	NOUN
ejpam-6007	371	16	at	at	ADP
ejpam-6007	371	17	time	time	NOUN
ejpam-6007	371	18	t	t	PROPN
ejpam-6007	371	19	is	be	AUX
ejpam-6007	371	20	represented	represent	VERB
ejpam-6007	371	21	by	by	ADP
ejpam-6007	371	22	x(t	x(t	PROPN
ejpam-6007	371	23	)	)	PUNCT
ejpam-6007	371	24	.	.	PUNCT
ejpam-6007	372	1	we	we	PRON
ejpam-6007	372	2	assume	assume	VERB
ejpam-6007	372	3	that	that	SCONJ
ejpam-6007	372	4	at	at	ADP
ejpam-6007	372	5	the	the	DET
ejpam-6007	372	6	beginning	beginning	NOUN
ejpam-6007	372	7	of	of	ADP
ejpam-6007	372	8	the	the	DET
ejpam-6007	372	9	competition	competition	NOUN
ejpam-6007	372	10	,	,	PUNCT
ejpam-6007	372	11	the	the	DET
ejpam-6007	372	12	initial	initial	ADJ
ejpam-6007	372	13	market	market	NOUN
ejpam-6007	372	14	share	share	NOUN
ejpam-6007	372	15	of	of	ADP
ejpam-6007	372	16	firm	firm	ADJ
ejpam-6007	372	17	1	1	NUM
ejpam-6007	372	18	is	be	AUX
ejpam-6007	372	19	x0	x0	PROPN
ejpam-6007	372	20	=	=	PUNCT
ejpam-6007	372	21	0	0	X
ejpam-6007	372	22	.	.	PUNCT
ejpam-6007	373	1	the	the	DET
ejpam-6007	373	2	parameters	parameter	NOUN
ejpam-6007	373	3	are	be	AUX
ejpam-6007	373	4	set	set	VERB
ejpam-6007	373	5	as	as	SCONJ
ejpam-6007	373	6	follows	follow	VERB
ejpam-6007	373	7	:	:	PUNCT
ejpam-6007	373	8	ϕ1	ϕ1	NOUN
ejpam-6007	373	9	=	=	SYM
ejpam-6007	373	10	0.1	0.1	NUM
ejpam-6007	373	11	,	,	PUNCT
ejpam-6007	373	12	ϕ2	ϕ2	ADV
ejpam-6007	373	13	=	=	SYM
ejpam-6007	373	14	0.3	0.3	NUM
ejpam-6007	373	15	,	,	PUNCT
ejpam-6007	373	16	p1	p1	NOUN
ejpam-6007	373	17	=	=	NOUN
ejpam-6007	373	18	0.25	0.25	NUM
ejpam-6007	373	19	,	,	PUNCT
ejpam-6007	373	20	p2	p2	PROPN
ejpam-6007	373	21	=	=	SYM
ejpam-6007	373	22	0.5	0.5	NUM
ejpam-6007	373	23	,	,	PUNCT
ejpam-6007	373	24	the	the	DET
ejpam-6007	373	25	time	time	NOUN
ejpam-6007	373	26	interval	interval	NOUN
ejpam-6007	373	27	t	t	PROPN
ejpam-6007	373	28	∈	∈	PROPN
ejpam-6007	374	1	[	[	X
ejpam-6007	374	2	0	0	NUM
ejpam-6007	374	3	,	,	PUNCT
ejpam-6007	374	4	1.5	1.5	NUM
ejpam-6007	374	5	]	]	PUNCT
ejpam-6007	374	6	,	,	PUNCT
ejpam-6007	374	7	and	and	CCONJ
ejpam-6007	374	8	the	the	DET
ejpam-6007	374	9	step	step	NOUN
ejpam-6007	374	10	size	size	NOUN
ejpam-6007	374	11	h	h	NOUN
ejpam-6007	374	12	=	=	NOUN
ejpam-6007	374	13	0.5	0.5	NUM
ejpam-6007	374	14	.	.	PUNCT
ejpam-6007	375	1	then	then	ADV
ejpam-6007	375	2	we	we	PRON
ejpam-6007	375	3	have	have	VERB
ejpam-6007	375	4	a	a	DET
ejpam-6007	375	5	comparison	comparison	NOUN
ejpam-6007	375	6	between	between	ADP
ejpam-6007	375	7	the	the	DET
ejpam-6007	375	8	two	two	NUM
ejpam-6007	375	9	firms	firm	NOUN
ejpam-6007	375	10	.	.	PUNCT
ejpam-6007	376	1	at	at	ADP
ejpam-6007	376	2	n=0	n=0	ADV
ejpam-6007	376	3	,	,	PUNCT
ejpam-6007	376	4	x0	x0	PROPN
ejpam-6007	376	5	=	=	SYM
ejpam-6007	376	6	0	0	NUM
ejpam-6007	376	7	,	,	PUNCT
ejpam-6007	376	8	1−	1−	NUM
ejpam-6007	376	9	x0	x0	NUM
ejpam-6007	376	10	=	=	SYM
ejpam-6007	376	11	1	1	NUM
ejpam-6007	376	12	,	,	PUNCT
ejpam-6007	376	13	u1,0	u1,0	PROPN
ejpam-6007	376	14	=	=	SYM
ejpam-6007	376	15	0	0	NUM
ejpam-6007	376	16	,	,	PUNCT
ejpam-6007	376	17	u2,0	u2,0	PROPN
ejpam-6007	376	18	=	=	SYM
ejpam-6007	376	19	0	0	PROPN
ejpam-6007	376	20	,	,	PUNCT
ejpam-6007	376	21	c1,0	c1,0	PROPN
ejpam-6007	376	22	=	=	SYM
ejpam-6007	376	23	0	0	NUM
ejpam-6007	376	24	,	,	PUNCT
ejpam-6007	376	25	c2,0	c2,0	PROPN
ejpam-6007	376	26	=	=	SYM
ejpam-6007	376	27	0	0	PROPN
ejpam-6007	376	28	,	,	PUNCT
ejpam-6007	376	29	λ1,0	λ1,0	PROPN
ejpam-6007	376	30	=	=	SYM
ejpam-6007	376	31	0	0	NUM
ejpam-6007	376	32	,	,	PUNCT
ejpam-6007	376	33	λ2,0	λ2,0	X
ejpam-6007	376	34	=	=	PUNCT
ejpam-6007	376	35	0	0	X
ejpam-6007	376	36	.	.	PUNCT
ejpam-6007	377	1	(	(	PUNCT
ejpam-6007	377	2	51	51	NUM
ejpam-6007	377	3	)	)	PUNCT
ejpam-6007	377	4	this	this	PRON
ejpam-6007	377	5	indicates	indicate	VERB
ejpam-6007	377	6	that	that	SCONJ
ejpam-6007	377	7	,	,	PUNCT
ejpam-6007	377	8	initially	initially	ADV
ejpam-6007	377	9	,	,	PUNCT
ejpam-6007	377	10	firm	firm	ADJ
ejpam-6007	377	11	2	2	NUM
ejpam-6007	377	12	was	be	AUX
ejpam-6007	377	13	the	the	DET
ejpam-6007	377	14	only	only	ADJ
ejpam-6007	377	15	firm	firm	NOUN
ejpam-6007	377	16	in	in	ADP
ejpam-6007	377	17	the	the	DET
ejpam-6007	377	18	market	market	NOUN
ejpam-6007	377	19	and	and	CCONJ
ejpam-6007	377	20	did	do	AUX
ejpam-6007	377	21	not	not	PART
ejpam-6007	377	22	undertake	undertake	VERB
ejpam-6007	377	23	any	any	DET
ejpam-6007	377	24	advertising	advertising	NOUN
ejpam-6007	377	25	efforts	effort	NOUN
ejpam-6007	377	26	.	.	PUNCT
ejpam-6007	378	1	at	at	ADP
ejpam-6007	378	2	n=1	n=1	PROPN
ejpam-6007	378	3	x1	x1	PROPN
ejpam-6007	378	4	=	=	SYM
ejpam-6007	378	5	0	0	NUM
ejpam-6007	378	6	,	,	PUNCT
ejpam-6007	378	7	1−	1−	NUM
ejpam-6007	378	8	x1	x1	NUM
ejpam-6007	378	9	=	=	SYM
ejpam-6007	378	10	1	1	NUM
ejpam-6007	378	11	,	,	PUNCT
ejpam-6007	378	12	u1,1	u1,1	ADJ
ejpam-6007	378	13	=	=	SYM
ejpam-6007	378	14	0.1	0.1	NUM
ejpam-6007	378	15	,	,	PUNCT
ejpam-6007	378	16	u2,1	u2,1	PROPN
ejpam-6007	378	17	=	=	SYM
ejpam-6007	378	18	0	0	NUM
ejpam-6007	378	19	,	,	PUNCT
ejpam-6007	378	20	c1,1	c1,1	NOUN
ejpam-6007	378	21	=	=	SYM
ejpam-6007	378	22	0.00125	0.00125	NUM
ejpam-6007	378	23	,	,	PUNCT
ejpam-6007	378	24	c2,1	c2,1	NOUN
ejpam-6007	378	25	=	=	SYM
ejpam-6007	378	26	0	0	NUM
ejpam-6007	378	27	,	,	PUNCT
ejpam-6007	378	28	λ1,1	λ1,1	NOUN
ejpam-6007	378	29	=	=	PUNCT
ejpam-6007	378	30	0.25	0.25	NUM
ejpam-6007	378	31	,	,	PUNCT
ejpam-6007	378	32	λ2,1	λ2,1	PROPN
ejpam-6007	378	33	=	=	PUNCT
ejpam-6007	378	34	−0.075	−0.075	PROPN
ejpam-6007	378	35	.	.	PUNCT
ejpam-6007	379	1	(	(	PUNCT
ejpam-6007	379	2	52	52	NUM
ejpam-6007	379	3	)	)	PUNCT
ejpam-6007	379	4	a.	a.	NOUN
ejpam-6007	379	5	a.	a.	NOUN
ejpam-6007	379	6	megahed	megahe	VERB
ejpam-6007	379	7	et	et	PROPN
ejpam-6007	379	8	al	al	PROPN
ejpam-6007	379	9	.	.	PUNCT
ejpam-6007	379	10	/	/	SYM
ejpam-6007	379	11	eur	eur	PROPN
ejpam-6007	379	12	.	.	PUNCT
ejpam-6007	380	1	j.	j.	PROPN
ejpam-6007	380	2	pure	pure	PROPN
ejpam-6007	380	3	appl	appl	PROPN
ejpam-6007	380	4	.	.	PROPN
ejpam-6007	380	5	math	math	PROPN
ejpam-6007	380	6	,	,	PUNCT
ejpam-6007	380	7	18	18	NUM
ejpam-6007	380	8	(	(	PUNCT
ejpam-6007	380	9	4	4	NUM
ejpam-6007	380	10	)	)	PUNCT
ejpam-6007	380	11	(	(	PUNCT
ejpam-6007	380	12	2025	2025	NUM
ejpam-6007	380	13	)	)	PUNCT
ejpam-6007	380	14	,	,	PUNCT
ejpam-6007	380	15	6007	6007	NUM
ejpam-6007	380	16	17	17	NUM
ejpam-6007	380	17	of	of	ADP
ejpam-6007	380	18	22	22	NUM
ejpam-6007	380	19	this	this	PRON
ejpam-6007	380	20	indicates	indicate	VERB
ejpam-6007	380	21	that	that	SCONJ
ejpam-6007	380	22	initially	initially	ADV
ejpam-6007	380	23	,	,	PUNCT
ejpam-6007	380	24	firm	firm	ADJ
ejpam-6007	380	25	1	1	NUM
ejpam-6007	380	26	entered	enter	VERB
ejpam-6007	380	27	the	the	DET
ejpam-6007	380	28	market	market	NOUN
ejpam-6007	380	29	without	without	ADP
ejpam-6007	380	30	holding	hold	VERB
ejpam-6007	380	31	any	any	DET
ejpam-6007	380	32	market	market	NOUN
ejpam-6007	380	33	share	share	NOUN
ejpam-6007	380	34	.	.	PUNCT
ejpam-6007	381	1	consequently	consequently	ADV
ejpam-6007	381	2	,	,	PUNCT
ejpam-6007	381	3	it	it	PRON
ejpam-6007	381	4	launched	launch	VERB
ejpam-6007	381	5	advertising	advertising	NOUN
ejpam-6007	381	6	campaigns	campaign	NOUN
ejpam-6007	381	7	to	to	PART
ejpam-6007	381	8	increase	increase	VERB
ejpam-6007	381	9	its	its	PRON
ejpam-6007	381	10	market	market	NOUN
ejpam-6007	381	11	share	share	NOUN
ejpam-6007	381	12	,	,	PUNCT
ejpam-6007	381	13	while	while	SCONJ
ejpam-6007	381	14	firm	firm	ADJ
ejpam-6007	381	15	2	2	NUM
ejpam-6007	381	16	did	do	AUX
ejpam-6007	381	17	not	not	PART
ejpam-6007	381	18	engage	engage	VERB
ejpam-6007	381	19	in	in	ADP
ejpam-6007	381	20	any	any	DET
ejpam-6007	381	21	advertising	advertising	NOUN
ejpam-6007	381	22	.	.	PUNCT
ejpam-6007	382	1	as	as	ADP
ejpam-6007	382	2	a	a	DET
ejpam-6007	382	3	result	result	NOUN
ejpam-6007	382	4	,	,	PUNCT
ejpam-6007	382	5	the	the	DET
ejpam-6007	382	6	number	number	NOUN
ejpam-6007	382	7	of	of	ADP
ejpam-6007	382	8	customers	customer	NOUN
ejpam-6007	382	9	for	for	ADP
ejpam-6007	382	10	firm	firm	ADJ
ejpam-6007	382	11	1	1	NUM
ejpam-6007	382	12	increased	increase	VERB
ejpam-6007	382	13	.	.	PUNCT
ejpam-6007	383	1	at	at	ADP
ejpam-6007	383	2	n=2	n=2	ADV
ejpam-6007	383	3	,	,	PUNCT
ejpam-6007	383	4	x2	x2	PROPN
ejpam-6007	383	5	=	=	SYM
ejpam-6007	383	6	0.00989583	0.00989583	NUM
ejpam-6007	383	7	,	,	PUNCT
ejpam-6007	383	8	1−	1−	NUM
ejpam-6007	383	9	x2	x2	NOUN
ejpam-6007	383	10	=	=	SYM
ejpam-6007	383	11	0.99010417	0.99010417	NUM
ejpam-6007	383	12	,	,	PUNCT
ejpam-6007	383	13	u1,2	u1,2	ADJ
ejpam-6007	383	14	=	=	SYM
ejpam-6007	383	15	0.18533512	0.18533512	NUM
ejpam-6007	383	16	,	,	PUNCT
ejpam-6007	383	17	u2,2	u2,2	PROPN
ejpam-6007	383	18	=	=	SYM
ejpam-6007	383	19	−0.0001182685	−0.0001182685	PROPN
ejpam-6007	383	20	,	,	PUNCT
ejpam-6007	383	21	c1,2	c1,2	PROPN
ejpam-6007	383	22	=	=	SYM
ejpam-6007	383	23	0.004293638	0.004293638	NUM
ejpam-6007	383	24	,	,	PUNCT
ejpam-6007	383	25	c2,2	c2,2	NOUN
ejpam-6007	383	26	=	=	NOUN
ejpam-6007	383	27	3.496865×	3.496865×	NUM
ejpam-6007	383	28	10−9	10−9	NUM
ejpam-6007	383	29	,	,	PUNCT
ejpam-6007	383	30	λ1,2	λ1,2	PROPN
ejpam-6007	383	31	=	=	SYM
ejpam-6007	383	32	0.04679687	0.04679687	NUM
ejpam-6007	383	33	,	,	PUNCT
ejpam-6007	383	34	λ2,2	λ2,2	PROPN
ejpam-6007	383	35	=	=	SYM
ejpam-6007	383	36	−0.005976	−0.005976	PROPN
ejpam-6007	383	37	.	.	PUNCT
ejpam-6007	384	1	(	(	PUNCT
ejpam-6007	384	2	53	53	NUM
ejpam-6007	384	3	)	)	PUNCT
ejpam-6007	384	4	this	this	PRON
ejpam-6007	384	5	indicates	indicate	VERB
ejpam-6007	384	6	that	that	SCONJ
ejpam-6007	384	7	initially	initially	ADV
ejpam-6007	384	8	,	,	PUNCT
ejpam-6007	384	9	firm	firm	ADJ
ejpam-6007	384	10	1	1	NUM
ejpam-6007	384	11	’s	’s	PART
ejpam-6007	384	12	market	market	NOUN
ejpam-6007	384	13	share	share	NOUN
ejpam-6007	384	14	increased	increase	VERB
ejpam-6007	384	15	,	,	PUNCT
ejpam-6007	384	16	while	while	SCONJ
ejpam-6007	384	17	firm	firm	ADJ
ejpam-6007	384	18	2	2	NUM
ejpam-6007	384	19	began	begin	VERB
ejpam-6007	384	20	to	to	PART
ejpam-6007	384	21	lose	lose	VERB
ejpam-6007	384	22	market	market	NOUN
ejpam-6007	384	23	share	share	NOUN
ejpam-6007	384	24	and	and	CCONJ
ejpam-6007	384	25	experienced	experience	VERB
ejpam-6007	384	26	a	a	DET
ejpam-6007	384	27	decrease	decrease	NOUN
ejpam-6007	384	28	in	in	ADP
ejpam-6007	384	29	sales	sale	NOUN
ejpam-6007	384	30	.	.	PUNCT
ejpam-6007	385	1	as	as	ADP
ejpam-6007	385	2	a	a	DET
ejpam-6007	385	3	result	result	NOUN
ejpam-6007	385	4	of	of	ADP
ejpam-6007	385	5	these	these	DET
ejpam-6007	385	6	losses	loss	NOUN
ejpam-6007	385	7	,	,	PUNCT
ejpam-6007	385	8	firm	firm	NOUN
ejpam-6007	385	9	2	2	NUM
ejpam-6007	385	10	obtained	obtain	VERB
ejpam-6007	385	11	a	a	DET
ejpam-6007	385	12	loan	loan	NOUN
ejpam-6007	385	13	to	to	PART
ejpam-6007	385	14	finance	finance	VERB
ejpam-6007	385	15	its	its	PRON
ejpam-6007	385	16	advertising	advertising	NOUN
ejpam-6007	385	17	campaigns	campaign	NOUN
ejpam-6007	385	18	.	.	PUNCT
ejpam-6007	386	1	at	at	ADP
ejpam-6007	386	2	n=3	n=3	ADV
ejpam-6007	386	3	,	,	PUNCT
ejpam-6007	386	4	x3	x3	NOUN
ejpam-6007	386	5	=	=	SYM
ejpam-6007	386	6	0.0362395	0.0362395	NUM
ejpam-6007	386	7	,	,	PUNCT
ejpam-6007	386	8	1−	1−	NUM
ejpam-6007	386	9	x3	x3	NOUN
ejpam-6007	386	10	=	=	SYM
ejpam-6007	386	11	0.96376	0.96376	NUM
ejpam-6007	386	12	,	,	PUNCT
ejpam-6007	386	13	u1,3	u1,3	PROPN
ejpam-6007	386	14	=	=	SYM
ejpam-6007	386	15	0.283165810	0.283165810	NUM
ejpam-6007	386	16	,	,	PUNCT
ejpam-6007	386	17	u2,3	u2,3	ADJ
ejpam-6007	386	18	=	=	NOUN
ejpam-6007	386	19	0.010028594	0.010028594	NUM
ejpam-6007	386	20	,	,	PUNCT
ejpam-6007	386	21	c1,3	c1,3	PROPN
ejpam-6007	386	22	=	=	SYM
ejpam-6007	386	23	0.005976423	0.005976423	NUM
ejpam-6007	386	24	,	,	PUNCT
ejpam-6007	386	25	c2,3	c2,3	NOUN
ejpam-6007	386	26	=	=	SYM
ejpam-6007	386	27	0.00446470	0.00446470	NUM
ejpam-6007	386	28	,	,	PUNCT
ejpam-6007	386	29	λ1,3	λ1,3	NOUN
ejpam-6007	386	30	=	=	SYM
ejpam-6007	386	31	0.0734531	0.0734531	NUM
ejpam-6007	386	32	,	,	PUNCT
ejpam-6007	386	33	λ2,3	λ2,3	NOUN
ejpam-6007	386	34	=	=	SYM
ejpam-6007	386	35	−0.082457305	−0.082457305	PROPN
ejpam-6007	386	36	.	.	PUNCT
ejpam-6007	387	1	(	(	PUNCT
ejpam-6007	387	2	54	54	NUM
ejpam-6007	387	3	)	)	PUNCT
ejpam-6007	387	4	now	now	ADV
ejpam-6007	387	5	,	,	PUNCT
ejpam-6007	387	6	we	we	PRON
ejpam-6007	387	7	present	present	VERB
ejpam-6007	387	8	a	a	DET
ejpam-6007	387	9	comparison	comparison	NOUN
ejpam-6007	387	10	of	of	ADP
ejpam-6007	387	11	the	the	DET
ejpam-6007	387	12	obtained	obtain	VERB
ejpam-6007	387	13	numerical	numerical	ADJ
ejpam-6007	387	14	solutions	solution	NOUN
ejpam-6007	387	15	for	for	ADP
ejpam-6007	387	16	the	the	DET
ejpam-6007	387	17	two	two	NUM
ejpam-6007	387	18	firms	firm	NOUN
ejpam-6007	387	19	in	in	ADP
ejpam-6007	387	20	the	the	DET
ejpam-6007	387	21	following	follow	VERB
ejpam-6007	387	22	figures	figure	NOUN
ejpam-6007	387	23	:	:	PUNCT
ejpam-6007	387	24	figure	figure	NOUN
ejpam-6007	387	25	1	1	NUM
ejpam-6007	387	26	shows	show	VERB
ejpam-6007	387	27	the	the	DET
ejpam-6007	387	28	market	market	NOUN
ejpam-6007	387	29	shares	share	NOUN
ejpam-6007	387	30	x	x	PUNCT
ejpam-6007	387	31	and	and	CCONJ
ejpam-6007	387	32	1	1	NUM
ejpam-6007	387	33	−	−	NOUN
ejpam-6007	387	34	x	x	SYM
ejpam-6007	387	35	,	,	PUNCT
ejpam-6007	387	36	representing	represent	VERB
ejpam-6007	387	37	firm	firm	NOUN
ejpam-6007	387	38	1	1	NUM
ejpam-6007	387	39	and	and	CCONJ
ejpam-6007	387	40	firm	firm	ADJ
ejpam-6007	387	41	2	2	NUM
ejpam-6007	387	42	,	,	PUNCT
ejpam-6007	387	43	respectively	respectively	ADV
ejpam-6007	387	44	,	,	PUNCT
ejpam-6007	387	45	at	at	ADP
ejpam-6007	387	46	time	time	NOUN
ejpam-6007	387	47	t.	t.	PROPN
ejpam-6007	387	48	it	it	PRON
ejpam-6007	387	49	is	be	AUX
ejpam-6007	387	50	observed	observe	VERB
ejpam-6007	387	51	that	that	SCONJ
ejpam-6007	387	52	firm	firm	ADJ
ejpam-6007	387	53	1	1	NUM
ejpam-6007	387	54	’s	’s	PART
ejpam-6007	387	55	market	market	NOUN
ejpam-6007	387	56	share	share	NOUN
ejpam-6007	387	57	increases	increase	NOUN
ejpam-6007	387	58	over	over	ADP
ejpam-6007	387	59	time	time	NOUN
ejpam-6007	387	60	,	,	PUNCT
ejpam-6007	387	61	while	while	SCONJ
ejpam-6007	387	62	firm	firm	ADJ
ejpam-6007	387	63	2	2	NUM
ejpam-6007	387	64	’s	’s	PART
ejpam-6007	387	65	market	market	NOUN
ejpam-6007	387	66	share	share	NOUN
ejpam-6007	387	67	decreases	decrease	VERB
ejpam-6007	387	68	.	.	PUNCT
ejpam-6007	388	1	figure	figure	NOUN
ejpam-6007	388	2	2	2	NUM
ejpam-6007	388	3	illustrates	illustrate	VERB
ejpam-6007	388	4	the	the	DET
ejpam-6007	388	5	controls	control	NOUN
ejpam-6007	388	6	u1	u1	NOUN
ejpam-6007	388	7	and	and	CCONJ
ejpam-6007	388	8	u2	u2	NOUN
ejpam-6007	388	9	,	,	PUNCT
ejpam-6007	388	10	representing	represent	VERB
ejpam-6007	388	11	the	the	DET
ejpam-6007	388	12	advertising	advertising	NOUN
ejpam-6007	388	13	efforts	effort	NOUN
ejpam-6007	388	14	of	of	ADP
ejpam-6007	388	15	firm	firm	ADJ
ejpam-6007	388	16	1	1	NUM
ejpam-6007	388	17	and	and	CCONJ
ejpam-6007	388	18	firm	firm	ADJ
ejpam-6007	388	19	2	2	NUM
ejpam-6007	388	20	,	,	PUNCT
ejpam-6007	388	21	respectively	respectively	ADV
ejpam-6007	388	22	.	.	PUNCT
ejpam-6007	389	1	initially	initially	ADV
ejpam-6007	389	2	,	,	PUNCT
ejpam-6007	389	3	firm	firm	ADJ
ejpam-6007	389	4	1	1	NUM
ejpam-6007	389	5	increased	increase	VERB
ejpam-6007	389	6	its	its	PRON
ejpam-6007	389	7	advertising	advertising	NOUN
ejpam-6007	389	8	efforts	effort	NOUN
ejpam-6007	389	9	to	to	PART
ejpam-6007	389	10	attract	attract	VERB
ejpam-6007	389	11	more	more	ADJ
ejpam-6007	389	12	customers	customer	NOUN
ejpam-6007	389	13	,	,	PUNCT
ejpam-6007	389	14	while	while	SCONJ
ejpam-6007	389	15	firm	firm	ADJ
ejpam-6007	389	16	2	2	NUM
ejpam-6007	389	17	had	have	VERB
ejpam-6007	389	18	no	no	DET
ejpam-6007	389	19	advertising	advertising	NOUN
ejpam-6007	389	20	.	.	PUNCT
ejpam-6007	390	1	over	over	ADP
ejpam-6007	390	2	time	time	NOUN
ejpam-6007	390	3	,	,	PUNCT
ejpam-6007	390	4	firm	firm	NOUN
ejpam-6007	390	5	2	2	NUM
ejpam-6007	390	6	gradually	gradually	ADV
ejpam-6007	390	7	increased	increase	VERB
ejpam-6007	390	8	its	its	PRON
ejpam-6007	390	9	advertising	advertising	NOUN
ejpam-6007	390	10	to	to	PART
ejpam-6007	390	11	reduce	reduce	VERB
ejpam-6007	390	12	firm	firm	ADJ
ejpam-6007	390	13	1	1	NUM
ejpam-6007	390	14	’s	’s	PART
ejpam-6007	390	15	market	market	NOUN
ejpam-6007	390	16	share	share	NOUN
ejpam-6007	390	17	.	.	PUNCT
ejpam-6007	391	1	figure	figure	VERB
ejpam-6007	391	2	3	3	NUM
ejpam-6007	391	3	presents	present	VERB
ejpam-6007	391	4	the	the	DET
ejpam-6007	391	5	advertising	advertising	NOUN
ejpam-6007	391	6	cost	cost	NOUN
ejpam-6007	391	7	functions	function	NOUN
ejpam-6007	391	8	for	for	ADP
ejpam-6007	391	9	the	the	DET
ejpam-6007	391	10	two	two	NUM
ejpam-6007	391	11	firms	firm	NOUN
ejpam-6007	391	12	,	,	PUNCT
ejpam-6007	391	13	c1	c1	PROPN
ejpam-6007	391	14	for	for	ADP
ejpam-6007	391	15	firm	firm	NOUN
ejpam-6007	391	16	1	1	NUM
ejpam-6007	391	17	and	and	CCONJ
ejpam-6007	391	18	c2	c2	PROPN
ejpam-6007	391	19	for	for	ADP
ejpam-6007	391	20	firm	firm	ADJ
ejpam-6007	391	21	2	2	NUM
ejpam-6007	391	22	.	.	PUNCT
ejpam-6007	391	23	firm	firm	ADJ
ejpam-6007	391	24	1	1	NUM
ejpam-6007	391	25	’s	’s	PART
ejpam-6007	391	26	cost	cost	NOUN
ejpam-6007	391	27	is	be	AUX
ejpam-6007	391	28	noticeably	noticeably	ADV
ejpam-6007	391	29	higher	high	ADJ
ejpam-6007	391	30	due	due	ADP
ejpam-6007	391	31	to	to	ADP
ejpam-6007	391	32	its	its	PRON
ejpam-6007	391	33	stronger	strong	ADJ
ejpam-6007	391	34	advertising	advertising	NOUN
ejpam-6007	391	35	intensity	intensity	NOUN
ejpam-6007	391	36	,	,	PUNCT
ejpam-6007	391	37	whereas	whereas	SCONJ
ejpam-6007	391	38	firm	firm	ADJ
ejpam-6007	391	39	2	2	NUM
ejpam-6007	391	40	incurs	incur	VERB
ejpam-6007	391	41	minimal	minimal	ADJ
ejpam-6007	391	42	costs	cost	NOUN
ejpam-6007	391	43	during	during	ADP
ejpam-6007	391	44	the	the	DET
ejpam-6007	391	45	early	early	ADJ
ejpam-6007	391	46	stages	stage	NOUN
ejpam-6007	391	47	of	of	ADP
ejpam-6007	391	48	the	the	DET
ejpam-6007	391	49	competition	competition	NOUN
ejpam-6007	391	50	.	.	PUNCT
ejpam-6007	392	1	figure	figure	VERB
ejpam-6007	392	2	4	4	NUM
ejpam-6007	392	3	depicts	depict	VERB
ejpam-6007	392	4	the	the	DET
ejpam-6007	392	5	costate	costate	NOUN
ejpam-6007	392	6	variables	variable	NOUN
ejpam-6007	392	7	λ1	λ1	ADJ
ejpam-6007	392	8	and	and	CCONJ
ejpam-6007	392	9	λ2	λ2	NOUN
ejpam-6007	392	10	for	for	ADP
ejpam-6007	392	11	firm	firm	ADJ
ejpam-6007	392	12	1	1	NUM
ejpam-6007	392	13	and	and	CCONJ
ejpam-6007	392	14	firm	firm	ADJ
ejpam-6007	392	15	2	2	NUM
ejpam-6007	392	16	,	,	PUNCT
ejpam-6007	392	17	respectively	respectively	ADV
ejpam-6007	392	18	.	.	PUNCT
ejpam-6007	393	1	for	for	ADP
ejpam-6007	393	2	firm	firm	ADJ
ejpam-6007	393	3	1	1	NUM
ejpam-6007	393	4	,	,	PUNCT
ejpam-6007	393	5	the	the	DET
ejpam-6007	393	6	costate	costate	ADJ
ejpam-6007	393	7	variable	variable	NOUN
ejpam-6007	393	8	starts	start	VERB
ejpam-6007	393	9	at	at	ADP
ejpam-6007	393	10	zero	zero	NUM
ejpam-6007	393	11	since	since	SCONJ
ejpam-6007	393	12	it	it	PRON
ejpam-6007	393	13	is	be	AUX
ejpam-6007	393	14	new	new	ADJ
ejpam-6007	393	15	to	to	ADP
ejpam-6007	393	16	the	the	DET
ejpam-6007	393	17	market	market	NOUN
ejpam-6007	393	18	and	and	CCONJ
ejpam-6007	393	19	initially	initially	ADV
ejpam-6007	393	20	has	have	VERB
ejpam-6007	393	21	no	no	DET
ejpam-6007	393	22	impact	impact	NOUN
ejpam-6007	393	23	.	.	PUNCT
ejpam-6007	394	1	it	it	PRON
ejpam-6007	394	2	then	then	ADV
ejpam-6007	394	3	rises	rise	VERB
ejpam-6007	394	4	as	as	ADP
ejpam-6007	394	5	firm	firm	ADJ
ejpam-6007	394	6	1	1	NUM
ejpam-6007	394	7	gains	gain	NOUN
ejpam-6007	394	8	influence	influence	NOUN
ejpam-6007	394	9	and	and	CCONJ
ejpam-6007	394	10	faces	face	VERB
ejpam-6007	394	11	competition	competition	NOUN
ejpam-6007	394	12	,	,	PUNCT
ejpam-6007	394	13	and	and	CCONJ
ejpam-6007	394	14	later	later	ADV
ejpam-6007	394	15	decreases	decrease	NOUN
ejpam-6007	394	16	as	as	SCONJ
ejpam-6007	394	17	it	it	PRON
ejpam-6007	394	18	approaches	approach	VERB
ejpam-6007	394	19	the	the	DET
ejpam-6007	394	20	optimal	optimal	ADJ
ejpam-6007	394	21	strategy	strategy	NOUN
ejpam-6007	394	22	,	,	PUNCT
ejpam-6007	394	23	indicating	indicate	VERB
ejpam-6007	394	24	a	a	DET
ejpam-6007	394	25	balanced	balanced	ADJ
ejpam-6007	394	26	state	state	NOUN
ejpam-6007	394	27	.	.	PUNCT
ejpam-6007	395	1	conversely	conversely	ADV
ejpam-6007	395	2	,	,	PUNCT
ejpam-6007	395	3	λ2	λ2	NOUN
ejpam-6007	395	4	initially	initially	ADV
ejpam-6007	395	5	starts	start	VERB
ejpam-6007	395	6	at	at	ADP
ejpam-6007	395	7	zero	zero	NUM
ejpam-6007	395	8	and	and	CCONJ
ejpam-6007	395	9	then	then	ADV
ejpam-6007	395	10	decreases	decrease	VERB
ejpam-6007	395	11	to	to	ADP
ejpam-6007	395	12	negative	negative	ADJ
ejpam-6007	395	13	values	value	NOUN
ejpam-6007	395	14	as	as	SCONJ
ejpam-6007	395	15	firm	firm	ADJ
ejpam-6007	395	16	2	2	NUM
ejpam-6007	395	17	loses	lose	VERB
ejpam-6007	395	18	market	market	NOUN
ejpam-6007	395	19	share	share	NOUN
ejpam-6007	395	20	due	due	ADJ
ejpam-6007	395	21	to	to	PART
ejpam-6007	395	22	firm	firm	VERB
ejpam-6007	395	23	1	1	NUM
ejpam-6007	395	24	’s	’s	PART
ejpam-6007	395	25	entry	entry	NOUN
ejpam-6007	395	26	.	.	PUNCT
ejpam-6007	396	1	the	the	DET
ejpam-6007	396	2	negative	negative	ADJ
ejpam-6007	396	3	values	value	NOUN
ejpam-6007	396	4	indicate	indicate	VERB
ejpam-6007	396	5	that	that	SCONJ
ejpam-6007	396	6	maintaining	maintain	VERB
ejpam-6007	396	7	its	its	PRON
ejpam-6007	396	8	market	market	NOUN
ejpam-6007	396	9	share	share	NOUN
ejpam-6007	396	10	becomes	become	VERB
ejpam-6007	396	11	increasingly	increasingly	ADV
ejpam-6007	396	12	costly	costly	ADJ
ejpam-6007	396	13	,	,	PUNCT
ejpam-6007	396	14	highlighting	highlight	VERB
ejpam-6007	396	15	the	the	DET
ejpam-6007	396	16	competitive	competitive	ADJ
ejpam-6007	396	17	pressure	pressure	NOUN
ejpam-6007	396	18	imposed	impose	VERB
ejpam-6007	396	19	by	by	ADP
ejpam-6007	396	20	firm	firm	ADJ
ejpam-6007	396	21	1	1	NUM
ejpam-6007	396	22	.	.	PUNCT
ejpam-6007	396	23	a.	a.	NOUN
ejpam-6007	396	24	a.	a.	PROPN
ejpam-6007	396	25	megahed	megahe	VERB
ejpam-6007	396	26	et	et	PROPN
ejpam-6007	396	27	al	al	PROPN
ejpam-6007	396	28	.	.	PUNCT
ejpam-6007	396	29	/	/	SYM
ejpam-6007	396	30	eur	eur	PROPN
ejpam-6007	396	31	.	.	PUNCT
ejpam-6007	397	1	j.	j.	PROPN
ejpam-6007	397	2	pure	pure	PROPN
ejpam-6007	397	3	appl	appl	PROPN
ejpam-6007	397	4	.	.	PROPN
ejpam-6007	397	5	math	math	PROPN
ejpam-6007	397	6	,	,	PUNCT
ejpam-6007	397	7	18	18	NUM
ejpam-6007	397	8	(	(	PUNCT
ejpam-6007	397	9	4	4	NUM
ejpam-6007	397	10	)	)	PUNCT
ejpam-6007	397	11	(	(	PUNCT
ejpam-6007	397	12	2025	2025	NUM
ejpam-6007	397	13	)	)	PUNCT
ejpam-6007	397	14	,	,	PUNCT
ejpam-6007	397	15	6007	6007	NUM
ejpam-6007	397	16	18	18	NUM
ejpam-6007	397	17	of	of	ADP
ejpam-6007	397	18	22	22	NUM
ejpam-6007	397	19	1	1	NUM
ejpam-6007	397	20	2	2	NUM
ejpam-6007	397	21	3	3	NUM
ejpam-6007	397	22	4	4	NUM
ejpam-6007	397	23	t	t	NOUN
ejpam-6007	397	24	0.2	0.2	NUM
ejpam-6007	397	25	0.4	0.4	NUM
ejpam-6007	397	26	0.6	0.6	NUM
ejpam-6007	397	27	0.8	0.8	NUM
ejpam-6007	397	28	1.0	1.0	NUM
ejpam-6007	397	29	x	x	SYM
ejpam-6007	397	30	figure	figure	NOUN
ejpam-6007	397	31	1	1	NUM
ejpam-6007	397	32	:	:	PUNCT
ejpam-6007	397	33	market	market	NOUN
ejpam-6007	397	34	shares	share	NOUN
ejpam-6007	397	35	of	of	ADP
ejpam-6007	397	36	firm	firm	ADJ
ejpam-6007	397	37	1	1	NUM
ejpam-6007	397	38	and	and	CCONJ
ejpam-6007	397	39	firm	firm	ADJ
ejpam-6007	397	40	2	2	NUM
ejpam-6007	397	41	at	at	ADP
ejpam-6007	397	42	time	time	NOUN
ejpam-6007	397	43	t.	t.	PROPN
ejpam-6007	397	44	0.5	0.5	NUM
ejpam-6007	397	45	1.0	1.0	NUM
ejpam-6007	397	46	1.5	1.5	NUM
ejpam-6007	397	47	2.0	2.0	NUM
ejpam-6007	397	48	2.5	2.5	NUM
ejpam-6007	397	49	3.0	3.0	NUM
ejpam-6007	397	50	t	t	NOUN
ejpam-6007	397	51	0.05	0.05	NUM
ejpam-6007	397	52	0.10	0.10	NUM
ejpam-6007	397	53	0.15	0.15	NUM
ejpam-6007	397	54	0.20	0.20	NUM
ejpam-6007	397	55	0.25	0.25	NUM
ejpam-6007	398	1	u	u	NOUN
ejpam-6007	398	2	figure	figure	NOUN
ejpam-6007	398	3	2	2	NUM
ejpam-6007	398	4	:	:	PUNCT
ejpam-6007	398	5	the	the	DET
ejpam-6007	398	6	advertising	advertising	NOUN
ejpam-6007	398	7	efforts	effort	NOUN
ejpam-6007	398	8	of	of	ADP
ejpam-6007	398	9	firm	firm	ADJ
ejpam-6007	398	10	1	1	NUM
ejpam-6007	398	11	and	and	CCONJ
ejpam-6007	398	12	firm	firm	ADJ
ejpam-6007	398	13	2	2	NUM
ejpam-6007	398	14	at	at	ADP
ejpam-6007	398	15	time	time	NOUN
ejpam-6007	398	16	t.	t.	PROPN
ejpam-6007	398	17	0.5	0.5	NUM
ejpam-6007	398	18	1.0	1.0	NUM
ejpam-6007	398	19	1.5	1.5	NUM
ejpam-6007	398	20	2.0	2.0	NUM
ejpam-6007	398	21	2.5	2.5	NUM
ejpam-6007	398	22	3.0	3.0	NUM
ejpam-6007	398	23	t	t	NOUN
ejpam-6007	398	24	0.002	0.002	NUM
ejpam-6007	398	25	0.004	0.004	NUM
ejpam-6007	398	26	0.006	0.006	NUM
ejpam-6007	398	27	0.008	0.008	NUM
ejpam-6007	398	28	0.010	0.010	NUM
ejpam-6007	398	29	c	c	NOUN
ejpam-6007	398	30	figure	figure	NOUN
ejpam-6007	398	31	3	3	NUM
ejpam-6007	398	32	:	:	PUNCT
ejpam-6007	398	33	the	the	DET
ejpam-6007	398	34	advertising	advertising	NOUN
ejpam-6007	398	35	cost	cost	NOUN
ejpam-6007	398	36	functions	function	NOUN
ejpam-6007	398	37	of	of	ADP
ejpam-6007	398	38	firm	firm	ADJ
ejpam-6007	398	39	1	1	NUM
ejpam-6007	398	40	and	and	CCONJ
ejpam-6007	398	41	firm	firm	ADJ
ejpam-6007	398	42	2	2	NUM
ejpam-6007	398	43	at	at	ADP
ejpam-6007	398	44	the	the	DET
ejpam-6007	398	45	time	time	NOUN
ejpam-6007	398	46	t	t	PROPN
ejpam-6007	398	47	0.5	0.5	NUM
ejpam-6007	398	48	1.0	1.0	NUM
ejpam-6007	398	49	1.5	1.5	NUM
ejpam-6007	398	50	2.0	2.0	NUM
ejpam-6007	398	51	2.5	2.5	NUM
ejpam-6007	398	52	3.0	3.0	NUM
ejpam-6007	398	53	-0.05	-0.05	NUM
ejpam-6007	398	54	0.05	0.05	NUM
ejpam-6007	398	55	0.10	0.10	NUM
ejpam-6007	398	56	0.15	0.15	NUM
ejpam-6007	398	57	0.20	0.20	NUM
ejpam-6007	398	58	0.25	0.25	NUM
ejpam-6007	398	59	figure	figure	NOUN
ejpam-6007	398	60	4	4	NUM
ejpam-6007	398	61	:	:	PUNCT
ejpam-6007	398	62	the	the	DET
ejpam-6007	398	63	costate	costate	ADJ
ejpam-6007	398	64	variables	variable	NOUN
ejpam-6007	398	65	of	of	ADP
ejpam-6007	398	66	firm	firm	ADJ
ejpam-6007	398	67	1	1	NUM
ejpam-6007	398	68	and	and	CCONJ
ejpam-6007	398	69	firm	firm	ADJ
ejpam-6007	398	70	2	2	NUM
ejpam-6007	398	71	at	at	ADP
ejpam-6007	398	72	time	time	NOUN
ejpam-6007	398	73	t.	t.	PROPN
ejpam-6007	398	74	a.	a.	NOUN
ejpam-6007	398	75	a.	a.	PROPN
ejpam-6007	398	76	megahed	megahe	VERB
ejpam-6007	398	77	et	et	PROPN
ejpam-6007	398	78	al	al	PROPN
ejpam-6007	398	79	.	.	PUNCT
ejpam-6007	398	80	/	/	SYM
ejpam-6007	398	81	eur	eur	PROPN
ejpam-6007	398	82	.	.	PUNCT
ejpam-6007	399	1	j.	j.	PROPN
ejpam-6007	399	2	pure	pure	PROPN
ejpam-6007	399	3	appl	appl	PROPN
ejpam-6007	399	4	.	.	PROPN
ejpam-6007	399	5	math	math	PROPN
ejpam-6007	399	6	,	,	PUNCT
ejpam-6007	399	7	18	18	NUM
ejpam-6007	399	8	(	(	PUNCT
ejpam-6007	399	9	4	4	NUM
ejpam-6007	399	10	)	)	PUNCT
ejpam-6007	399	11	(	(	PUNCT
ejpam-6007	399	12	2025	2025	NUM
ejpam-6007	399	13	)	)	PUNCT
ejpam-6007	399	14	,	,	PUNCT
ejpam-6007	399	15	6007	6007	NUM
ejpam-6007	399	16	19	19	NUM
ejpam-6007	399	17	of	of	ADP
ejpam-6007	399	18	22	22	NUM
ejpam-6007	399	19	4	4	NUM
ejpam-6007	399	20	.	.	PUNCT
ejpam-6007	400	1	stability	stability	NOUN
ejpam-6007	400	2	analysis	analysis	NOUN
ejpam-6007	400	3	of	of	ADP
ejpam-6007	400	4	the	the	DET
ejpam-6007	400	5	fourth	fourth	ADJ
ejpam-6007	400	6	-	-	PUNCT
ejpam-6007	400	7	order	order	NOUN
ejpam-6007	400	8	runge	runge	NOUN
ejpam-6007	400	9	-	-	PUNCT
ejpam-6007	400	10	kutta	kutta	NOUN
ejpam-6007	400	11	method	method	NOUN
ejpam-6007	400	12	using	use	VERB
ejpam-6007	400	13	the	the	DET
ejpam-6007	400	14	jacobian	jacobian	ADJ
ejpam-6007	400	15	matrix	matrix	NOUN
ejpam-6007	400	16	in	in	ADP
ejpam-6007	400	17	a	a	DET
ejpam-6007	400	18	system	system	NOUN
ejpam-6007	400	19	of	of	ADP
ejpam-6007	400	20	differential	differential	ADJ
ejpam-6007	400	21	equations	equation	NOUN
ejpam-6007	400	22	,	,	PUNCT
ejpam-6007	400	23	stability	stability	NOUN
ejpam-6007	400	24	analysis	analysis	NOUN
ejpam-6007	400	25	is	be	AUX
ejpam-6007	400	26	performed	perform	VERB
ejpam-6007	400	27	to	to	PART
ejpam-6007	400	28	determine	determine	VERB
ejpam-6007	400	29	whether	whether	SCONJ
ejpam-6007	400	30	small	small	ADJ
ejpam-6007	400	31	perturbations	perturbation	NOUN
ejpam-6007	400	32	around	around	ADP
ejpam-6007	400	33	equilibrium	equilibrium	NOUN
ejpam-6007	400	34	points	point	NOUN
ejpam-6007	400	35	cause	cause	VERB
ejpam-6007	400	36	the	the	DET
ejpam-6007	400	37	system	system	NOUN
ejpam-6007	400	38	to	to	PART
ejpam-6007	400	39	return	return	VERB
ejpam-6007	400	40	to	to	ADP
ejpam-6007	400	41	equilibrium	equilibrium	NOUN
ejpam-6007	400	42	(	(	PUNCT
ejpam-6007	400	43	stable	stable	ADJ
ejpam-6007	400	44	)	)	PUNCT
ejpam-6007	400	45	or	or	CCONJ
ejpam-6007	400	46	to	to	PART
ejpam-6007	400	47	diverge	diverge	VERB
ejpam-6007	400	48	away	away	ADV
ejpam-6007	400	49	(	(	PUNCT
ejpam-6007	400	50	unstable	unstable	ADJ
ejpam-6007	400	51	)	)	PUNCT
ejpam-6007	400	52	.	.	PUNCT
ejpam-6007	401	1	for	for	ADP
ejpam-6007	401	2	a	a	DET
ejpam-6007	401	3	nonlinear	nonlinear	ADJ
ejpam-6007	401	4	system	system	NOUN
ejpam-6007	401	5	:	:	PUNCT
ejpam-6007	401	6	dx	dx	PROPN
ejpam-6007	401	7	dt	dt	X
ejpam-6007	402	1	=	=	SYM
ejpam-6007	402	2	λ1	λ1	PROPN
ejpam-6007	402	3	p1	p1	PROPN
ejpam-6007	402	4	(	(	PUNCT
ejpam-6007	402	5	1−	1−	NUM
ejpam-6007	402	6	x)2	x)2	NOUN
ejpam-6007	402	7	+	+	CCONJ
ejpam-6007	402	8	λ2	λ2	NOUN
ejpam-6007	402	9	p2	p2	NOUN
ejpam-6007	402	10	x2	x2	PROPN
ejpam-6007	402	11	,	,	PUNCT
ejpam-6007	402	12	dλ1(t	dλ1(t	PROPN
ejpam-6007	402	13	)	)	PUNCT
ejpam-6007	402	14	dt	dt	NOUN
ejpam-6007	403	1	=	=	SYM
ejpam-6007	403	2	λ2	λ2	PROPN
ejpam-6007	403	3	1	1	NUM
ejpam-6007	403	4	p1	p1	NOUN
ejpam-6007	403	5	(	(	PUNCT
ejpam-6007	403	6	1−	1−	NUM
ejpam-6007	403	7	x)−	x)−	PROPN
ejpam-6007	403	8	λ1λ2(t	λ1λ2(t	NOUN
ejpam-6007	403	9	)	)	PUNCT
ejpam-6007	403	10	p2	p2	PROPN
ejpam-6007	403	11	x−	x−	PROPN
ejpam-6007	403	12	ϕ1	ϕ1	PROPN
ejpam-6007	403	13	,	,	PUNCT
ejpam-6007	403	14	dλ2(t	dλ2(t	PROPN
ejpam-6007	403	15	)	)	PUNCT
ejpam-6007	403	16	dt	dt	NOUN
ejpam-6007	404	1	=	=	PUNCT
ejpam-6007	404	2	λ1λ2(t	λ1λ2(t	NOUN
ejpam-6007	404	3	)	)	PUNCT
ejpam-6007	404	4	p1	p1	NOUN
ejpam-6007	404	5	(	(	PUNCT
ejpam-6007	404	6	1−	1−	NUM
ejpam-6007	404	7	x)−	x)−	PROPN
ejpam-6007	404	8	λ2	λ2	NOUN
ejpam-6007	404	9	2	2	NUM
ejpam-6007	404	10	p2	p2	NOUN
ejpam-6007	404	11	x+	x+	PUNCT
ejpam-6007	404	12	ϕ2	ϕ2	ADV
ejpam-6007	404	13	.	.	PUNCT
ejpam-6007	405	1	(	(	PUNCT
ejpam-6007	405	2	55	55	NUM
ejpam-6007	405	3	)	)	PUNCT
ejpam-6007	405	4	equilibrium	equilibrium	NOUN
ejpam-6007	405	5	points	point	NOUN
ejpam-6007	405	6	(	(	PUNCT
ejpam-6007	405	7	or	or	CCONJ
ejpam-6007	405	8	steady	steady	ADJ
ejpam-6007	405	9	states	state	NOUN
ejpam-6007	405	10	)	)	PUNCT
ejpam-6007	405	11	of	of	ADP
ejpam-6007	405	12	the	the	DET
ejpam-6007	405	13	system	system	NOUN
ejpam-6007	405	14	are	be	AUX
ejpam-6007	405	15	obtained	obtain	VERB
ejpam-6007	405	16	by	by	ADP
ejpam-6007	405	17	solving	solve	VERB
ejpam-6007	405	18	:	:	PUNCT
ejpam-6007	405	19	f1	f1	NOUN
ejpam-6007	405	20	=	=	SYM
ejpam-6007	405	21	λ1	λ1	PROPN
ejpam-6007	405	22	p1	p1	PROPN
ejpam-6007	405	23	(	(	PUNCT
ejpam-6007	405	24	1−	1−	NUM
ejpam-6007	405	25	x)2	x)2	NOUN
ejpam-6007	406	1	+	+	CCONJ
ejpam-6007	406	2	λ2	λ2	NOUN
ejpam-6007	406	3	p2	p2	NOUN
ejpam-6007	406	4	x2	x2	NOUN
ejpam-6007	407	1	=	=	SYM
ejpam-6007	407	2	0	0	NUM
ejpam-6007	407	3	,	,	PUNCT
ejpam-6007	407	4	f2	f2	PROPN
ejpam-6007	407	5	=	=	SYM
ejpam-6007	407	6	λ2	λ2	PROPN
ejpam-6007	407	7	1	1	NUM
ejpam-6007	407	8	p1	p1	NOUN
ejpam-6007	407	9	(	(	PUNCT
ejpam-6007	407	10	1−	1−	NUM
ejpam-6007	407	11	x)−	x)−	PROPN
ejpam-6007	407	12	λ1λ2(t	λ1λ2(t	NOUN
ejpam-6007	407	13	)	)	PUNCT
ejpam-6007	407	14	p2	p2	PROPN
ejpam-6007	407	15	x−	x−	PROPN
ejpam-6007	407	16	ϕ1	ϕ1	PROPN
ejpam-6007	407	17	=	=	SYM
ejpam-6007	407	18	0	0	NUM
ejpam-6007	407	19	,	,	PUNCT
ejpam-6007	407	20	f3	f3	NOUN
ejpam-6007	407	21	=	=	SYM
ejpam-6007	407	22	λ1λ2(t	λ1λ2(t	NOUN
ejpam-6007	407	23	)	)	PUNCT
ejpam-6007	407	24	p1	p1	NOUN
ejpam-6007	407	25	(	(	PUNCT
ejpam-6007	407	26	1−	1−	NUM
ejpam-6007	407	27	x)−	x)−	PROPN
ejpam-6007	407	28	λ2	λ2	NOUN
ejpam-6007	407	29	2	2	NUM
ejpam-6007	407	30	p2	p2	NOUN
ejpam-6007	407	31	x+	x+	PUNCT
ejpam-6007	408	1	ϕ2	ϕ2	ADV
ejpam-6007	408	2	=	=	SYM
ejpam-6007	408	3	0	0	X
ejpam-6007	408	4	.	.	PUNCT
ejpam-6007	409	1	(	(	PUNCT
ejpam-6007	409	2	56	56	NUM
ejpam-6007	409	3	)	)	PUNCT
ejpam-6007	409	4	after	after	ADP
ejpam-6007	409	5	solving	solve	VERB
ejpam-6007	409	6	the	the	DET
ejpam-6007	409	7	system	system	NOUN
ejpam-6007	409	8	(	(	PUNCT
ejpam-6007	409	9	56	56	NUM
ejpam-6007	409	10	)	)	PUNCT
ejpam-6007	409	11	simultaneously	simultaneously	ADV
ejpam-6007	409	12	,	,	PUNCT
ejpam-6007	409	13	we	we	PRON
ejpam-6007	409	14	obtain	obtain	VERB
ejpam-6007	409	15	the	the	DET
ejpam-6007	409	16	equilibrium	equilibrium	NOUN
ejpam-6007	409	17	point	point	NOUN
ejpam-6007	409	18	(	(	PUNCT
ejpam-6007	409	19	x∗	x∗	PROPN
ejpam-6007	409	20	,	,	PUNCT
ejpam-6007	409	21	λ∗	λ∗	NOUN
ejpam-6007	409	22	1	1	NUM
ejpam-6007	409	23	,	,	PUNCT
ejpam-6007	409	24	λ	λ	PROPN
ejpam-6007	409	25	∗	∗	NOUN
ejpam-6007	409	26	2	2	NUM
ejpam-6007	409	27	)	)	PUNCT
ejpam-6007	409	28	.	.	PUNCT
ejpam-6007	410	1	next	next	ADV
ejpam-6007	410	2	,	,	PUNCT
ejpam-6007	410	3	we	we	PRON
ejpam-6007	410	4	construct	construct	VERB
ejpam-6007	410	5	the	the	DET
ejpam-6007	410	6	jacobian	jacobian	ADJ
ejpam-6007	410	7	matrix	matrix	NOUN
ejpam-6007	410	8	,	,	PUNCT
ejpam-6007	410	9	which	which	PRON
ejpam-6007	410	10	is	be	AUX
ejpam-6007	410	11	a	a	DET
ejpam-6007	410	12	square	square	ADJ
ejpam-6007	410	13	matrix	matrix	NOUN
ejpam-6007	410	14	of	of	ADP
ejpam-6007	410	15	the	the	DET
ejpam-6007	410	16	first	first	ADJ
ejpam-6007	410	17	-	-	PUNCT
ejpam-6007	410	18	order	order	NOUN
ejpam-6007	410	19	partial	partial	ADJ
ejpam-6007	410	20	derivatives	derivative	NOUN
ejpam-6007	410	21	of	of	ADP
ejpam-6007	410	22	the	the	DET
ejpam-6007	410	23	system	system	NOUN
ejpam-6007	410	24	’s	’s	PART
ejpam-6007	410	25	functions	function	NOUN
ejpam-6007	410	26	with	with	ADP
ejpam-6007	410	27	respect	respect	NOUN
ejpam-6007	410	28	to	to	ADP
ejpam-6007	410	29	the	the	DET
ejpam-6007	410	30	state	state	NOUN
ejpam-6007	410	31	variables	variable	NOUN
ejpam-6007	410	32	.	.	PUNCT
ejpam-6007	411	1	the	the	DET
ejpam-6007	411	2	jacobian	jacobian	ADJ
ejpam-6007	411	3	matrix	matrix	NOUN
ejpam-6007	411	4	j	j	PROPN
ejpam-6007	411	5	is	be	AUX
ejpam-6007	411	6	defined	define	VERB
ejpam-6007	411	7	as	as	ADP
ejpam-6007	411	8	:	:	PUNCT
ejpam-6007	411	9	j	j	NOUN
ejpam-6007	411	10	=	=	PUNCT
ejpam-6007	411	11			X
ejpam-6007	411	12	∂f1	∂f1	ADJ
ejpam-6007	411	13	∂x	∂x	PROPN
ejpam-6007	411	14	∂f1	∂f1	PROPN
ejpam-6007	411	15	∂λ1	∂λ1	PROPN
ejpam-6007	411	16	∂f1	∂f1	PROPN
ejpam-6007	411	17	∂λ2	∂λ2	PROPN
ejpam-6007	411	18	∂f2	∂f2	NOUN
ejpam-6007	411	19	∂x	∂x	PROPN
ejpam-6007	411	20	∂f2	∂f2	NOUN
ejpam-6007	411	21	∂λ1	∂λ1	NOUN
ejpam-6007	411	22	∂f2	∂f2	VERB
ejpam-6007	411	23	∂λ2	∂λ2	PROPN
ejpam-6007	411	24	∂f3	∂f3	PROPN
ejpam-6007	411	25	∂x	∂x	PROPN
ejpam-6007	411	26	∂f3	∂f3	NOUN
ejpam-6007	411	27	∂λ1	∂λ1	PROPN
ejpam-6007	411	28	∂f3	∂f3	NOUN
ejpam-6007	411	29	∂λ2	∂λ2	VERB
ejpam-6007	411	30			NUM
ejpam-6007	411	31	,	,	PUNCT
ejpam-6007	411	32	then	then	ADV
ejpam-6007	411	33	the	the	DET
ejpam-6007	411	34	jacobian	jacobian	ADJ
ejpam-6007	411	35	matrix	matrix	NOUN
ejpam-6007	411	36	evaluation	evaluation	NOUN
ejpam-6007	411	37	,	,	PUNCT
ejpam-6007	411	38	j	j	NOUN
ejpam-6007	411	39	=	=	NOUN
ejpam-6007	411	40			NOUN
ejpam-6007	411	41	−2λ∗	−2λ∗	NOUN
ejpam-6007	411	42	1	1	NUM
ejpam-6007	411	43	p1	p1	NOUN
ejpam-6007	411	44	(	(	PUNCT
ejpam-6007	411	45	1−	1−	NUM
ejpam-6007	411	46	x∗	x∗	X
ejpam-6007	411	47	)	)	PUNCT
ejpam-6007	412	1	+	+	CCONJ
ejpam-6007	412	2	2λ∗	2λ∗	NUM
ejpam-6007	412	3	2	2	NUM
ejpam-6007	412	4	p2	p2	NOUN
ejpam-6007	412	5	x	x	SYM
ejpam-6007	412	6	(	(	PUNCT
ejpam-6007	412	7	1−x∗)2	1−x∗)2	PROPN
ejpam-6007	412	8	p1	p1	NOUN
ejpam-6007	412	9	(	(	PUNCT
ejpam-6007	412	10	x∗)2	x∗)2	PUNCT
ejpam-6007	412	11	p2	p2	PROPN
ejpam-6007	412	12	−(λ∗	−(λ∗	NOUN
ejpam-6007	412	13	1	1	NUM
ejpam-6007	412	14	)	)	SYM
ejpam-6007	412	15	2	2	NUM
ejpam-6007	412	16	p1	p1	NOUN
ejpam-6007	412	17	−	−	NOUN
ejpam-6007	412	18	λ1λ∗	λ1λ∗	PROPN
ejpam-6007	412	19	2	2	NUM
ejpam-6007	412	20	p2	p2	PROPN
ejpam-6007	412	21	2λ∗	2λ∗	NUM
ejpam-6007	412	22	1(1−x∗	1(1−x∗	NUM
ejpam-6007	412	23	)	)	PUNCT
ejpam-6007	412	24	p1	p1	NOUN
ejpam-6007	412	25	−	−	PROPN
ejpam-6007	412	26	λ2(t	λ2(t	PROPN
ejpam-6007	412	27	)	)	PUNCT
ejpam-6007	412	28	p2	p2	NOUN
ejpam-6007	412	29	x	x	PUNCT
ejpam-6007	413	1	−λ∗	−λ∗	NOUN
ejpam-6007	413	2	1x	1x	NUM
ejpam-6007	413	3	∗	∗	NOUN
ejpam-6007	413	4	p2	p2	PROPN
ejpam-6007	414	1	−λ∗	−λ∗	ADP
ejpam-6007	414	2	1λ	1λ	PROPN
ejpam-6007	414	3	∗	∗	NOUN
ejpam-6007	414	4	2	2	NUM
ejpam-6007	414	5	p1	p1	NOUN
ejpam-6007	414	6	−	−	PROPN
ejpam-6007	414	7	(	(	PUNCT
ejpam-6007	414	8	λ∗	λ∗	NOUN
ejpam-6007	414	9	2	2	NUM
ejpam-6007	414	10	)	)	PUNCT
ejpam-6007	414	11	2	2	NUM
ejpam-6007	414	12	p2	p2	NOUN
ejpam-6007	414	13	λ∗	λ∗	NOUN
ejpam-6007	414	14	2(1−x∗	2(1−x∗	NOUN
ejpam-6007	414	15	)	)	PUNCT
ejpam-6007	414	16	p1	p1	PROPN
ejpam-6007	414	17	λ∗	λ∗	PROPN
ejpam-6007	414	18	1(1−x∗	1(1−x∗	PROPN
ejpam-6007	414	19	)	)	PUNCT
ejpam-6007	414	20	p1	p1	NOUN
ejpam-6007	414	21	−	−	PROPN
ejpam-6007	414	22	2λ∗	2λ∗	NUM
ejpam-6007	414	23	2x	2x	NUM
ejpam-6007	414	24	∗	∗	NOUN
ejpam-6007	414	25	p2	p2	NOUN
ejpam-6007	414	26			NOUN
ejpam-6007	414	27	.	.	PUNCT
ejpam-6007	415	1	to	to	PART
ejpam-6007	415	2	analyze	analyze	VERB
ejpam-6007	415	3	the	the	DET
ejpam-6007	415	4	stability	stability	NOUN
ejpam-6007	415	5	at	at	ADP
ejpam-6007	415	6	an	an	DET
ejpam-6007	415	7	equilibrium	equilibrium	NOUN
ejpam-6007	415	8	point	point	NOUN
ejpam-6007	415	9	(	(	PUNCT
ejpam-6007	415	10	x∗	x∗	PROPN
ejpam-6007	415	11	,	,	PUNCT
ejpam-6007	415	12	λ∗	λ∗	NOUN
ejpam-6007	415	13	1	1	NUM
ejpam-6007	415	14	,	,	PUNCT
ejpam-6007	415	15	λ	λ	PROPN
ejpam-6007	415	16	∗	∗	NOUN
ejpam-6007	415	17	2	2	NUM
ejpam-6007	415	18	)	)	PUNCT
ejpam-6007	415	19	,	,	PUNCT
ejpam-6007	415	20	the	the	DET
ejpam-6007	415	21	jacobian	jacobian	ADJ
ejpam-6007	415	22	matrix	matrix	NOUN
ejpam-6007	415	23	j(x∗	j(x∗	PROPN
ejpam-6007	415	24	,	,	PUNCT
ejpam-6007	415	25	λ∗	λ∗	NOUN
ejpam-6007	415	26	1	1	NUM
ejpam-6007	415	27	,	,	PUNCT
ejpam-6007	415	28	λ	λ	PROPN
ejpam-6007	415	29	∗	∗	NOUN
ejpam-6007	415	30	2	2	NUM
ejpam-6007	415	31	)	)	PUNCT
ejpam-6007	415	32	is	be	AUX
ejpam-6007	415	33	evaluated	evaluate	VERB
ejpam-6007	415	34	at	at	ADP
ejpam-6007	415	35	the	the	DET
ejpam-6007	415	36	equilibrium	equilibrium	NOUN
ejpam-6007	415	37	.	.	PUNCT
ejpam-6007	416	1	the	the	DET
ejpam-6007	416	2	stability	stability	NOUN
ejpam-6007	416	3	of	of	ADP
ejpam-6007	416	4	the	the	DET
ejpam-6007	416	5	system	system	NOUN
ejpam-6007	416	6	depends	depend	VERB
ejpam-6007	416	7	on	on	ADP
ejpam-6007	416	8	the	the	DET
ejpam-6007	416	9	eigenvalues	eigenvalue	NOUN
ejpam-6007	416	10	µi	µi	PROPN
ejpam-6007	416	11	of	of	ADP
ejpam-6007	416	12	j(x	j(x	PROPN
ejpam-6007	416	13	∗	∗	NOUN
ejpam-6007	416	14	,	,	PUNCT
ejpam-6007	416	15	λ∗	λ∗	NOUN
ejpam-6007	416	16	1	1	NUM
ejpam-6007	416	17	,	,	PUNCT
ejpam-6007	416	18	λ	λ	PROPN
ejpam-6007	416	19	∗	∗	NOUN
ejpam-6007	416	20	2	2	NUM
ejpam-6007	416	21	)	)	PUNCT
ejpam-6007	416	22	.	.	PUNCT
ejpam-6007	417	1	stable	stable	ADJ
ejpam-6007	417	2	equilibrium	equilibrium	NOUN
ejpam-6007	417	3	:	:	PUNCT
ejpam-6007	417	4	all	all	PRON
ejpam-6007	417	5	eigenvalues	eigenvalue	VERB
ejpam-6007	417	6	satisfy	satisfy	PROPN
ejpam-6007	417	7	re(µi	re(µi	PROPN
ejpam-6007	417	8	)	)	PUNCT
ejpam-6007	417	9	<	<	X
ejpam-6007	417	10	0	0	NUM
ejpam-6007	417	11	,	,	PUNCT
ejpam-6007	417	12	implying	imply	VERB
ejpam-6007	417	13	local	local	ADJ
ejpam-6007	417	14	asymptotic	asymptotic	ADJ
ejpam-6007	417	15	stability	stability	NOUN
ejpam-6007	417	16	.	.	PUNCT
ejpam-6007	418	1	unstable	unstable	ADJ
ejpam-6007	418	2	equilibrium	equilibrium	NOUN
ejpam-6007	418	3	:	:	PUNCT
ejpam-6007	418	4	at	at	ADV
ejpam-6007	418	5	least	least	ADV
ejpam-6007	418	6	one	one	NUM
ejpam-6007	418	7	eigenvalue	eigenvalue	NOUN
ejpam-6007	418	8	satisfies	satisfie	NOUN
ejpam-6007	418	9	re(µi	re(µi	NOUN
ejpam-6007	418	10	)	)	PUNCT
ejpam-6007	418	11	>	>	X
ejpam-6007	419	1	0	0	NUM
ejpam-6007	419	2	,	,	PUNCT
ejpam-6007	419	3	implying	imply	VERB
ejpam-6007	419	4	instability	instability	NOUN
ejpam-6007	419	5	.	.	PUNCT
ejpam-6007	420	1	a.	a.	NOUN
ejpam-6007	420	2	a.	a.	PROPN
ejpam-6007	420	3	megahed	megahe	VERB
ejpam-6007	420	4	et	et	PROPN
ejpam-6007	420	5	al	al	PROPN
ejpam-6007	420	6	.	.	PUNCT
ejpam-6007	420	7	/	/	SYM
ejpam-6007	420	8	eur	eur	PROPN
ejpam-6007	420	9	.	.	PUNCT
ejpam-6007	421	1	j.	j.	PROPN
ejpam-6007	421	2	pure	pure	PROPN
ejpam-6007	421	3	appl	appl	PROPN
ejpam-6007	421	4	.	.	PROPN
ejpam-6007	421	5	math	math	PROPN
ejpam-6007	421	6	,	,	PUNCT
ejpam-6007	421	7	18	18	NUM
ejpam-6007	421	8	(	(	PUNCT
ejpam-6007	421	9	4	4	NUM
ejpam-6007	421	10	)	)	PUNCT
ejpam-6007	421	11	(	(	PUNCT
ejpam-6007	421	12	2025	2025	NUM
ejpam-6007	421	13	)	)	PUNCT
ejpam-6007	421	14	,	,	PUNCT
ejpam-6007	421	15	6007	6007	NUM
ejpam-6007	421	16	20	20	NUM
ejpam-6007	421	17	of	of	ADP
ejpam-6007	421	18	22	22	NUM
ejpam-6007	421	19	marginally	marginally	ADV
ejpam-6007	421	20	stable	stable	ADJ
ejpam-6007	421	21	equilibrium	equilibrium	NOUN
ejpam-6007	421	22	:	:	PUNCT
ejpam-6007	421	23	all	all	PRON
ejpam-6007	421	24	eigenvalues	eigenvalue	VERB
ejpam-6007	421	25	satisfy	satisfy	ADJ
ejpam-6007	421	26	re(µi	re(µi	PROPN
ejpam-6007	421	27	)	)	PUNCT
ejpam-6007	422	1	=	=	SYM
ejpam-6007	422	2	0	0	NUM
ejpam-6007	422	3	;	;	PUNCT
ejpam-6007	422	4	stability	stability	NOUN
ejpam-6007	422	5	can	can	AUX
ejpam-6007	422	6	not	not	PART
ejpam-6007	422	7	be	be	AUX
ejpam-6007	422	8	fully	fully	ADV
ejpam-6007	422	9	determined	determine	VERB
ejpam-6007	422	10	and	and	CCONJ
ejpam-6007	422	11	the	the	DET
ejpam-6007	422	12	system	system	NOUN
ejpam-6007	422	13	may	may	AUX
ejpam-6007	422	14	be	be	AUX
ejpam-6007	422	15	marginally	marginally	ADV
ejpam-6007	422	16	stable	stable	ADJ
ejpam-6007	422	17	or	or	CCONJ
ejpam-6007	422	18	exhibit	exhibit	VERB
ejpam-6007	422	19	oscillatory	oscillatory	ADJ
ejpam-6007	422	20	behavior	behavior	NOUN
ejpam-6007	422	21	.	.	PUNCT
ejpam-6007	423	1	to	to	PART
ejpam-6007	423	2	study	study	VERB
ejpam-6007	423	3	the	the	DET
ejpam-6007	423	4	stability	stability	NOUN
ejpam-6007	423	5	of	of	ADP
ejpam-6007	423	6	the	the	DET
ejpam-6007	423	7	system	system	NOUN
ejpam-6007	423	8	(	(	PUNCT
ejpam-6007	423	9	55	55	NUM
ejpam-6007	423	10	)	)	PUNCT
ejpam-6007	423	11	,	,	PUNCT
ejpam-6007	423	12	we	we	PRON
ejpam-6007	423	13	first	first	ADV
ejpam-6007	423	14	determine	determine	VERB
ejpam-6007	423	15	the	the	DET
ejpam-6007	423	16	equilibrium	equilibrium	NOUN
ejpam-6007	423	17	points	point	NOUN
ejpam-6007	423	18	by	by	ADP
ejpam-6007	423	19	solving	solve	VERB
ejpam-6007	423	20	the	the	DET
ejpam-6007	423	21	system	system	NOUN
ejpam-6007	423	22	(	(	PUNCT
ejpam-6007	423	23	56	56	NUM
ejpam-6007	423	24	)	)	PUNCT
ejpam-6007	423	25	.	.	PUNCT
ejpam-6007	424	1	we	we	PRON
ejpam-6007	424	2	obtain	obtain	VERB
ejpam-6007	424	3	the	the	DET
ejpam-6007	424	4	following	follow	VERB
ejpam-6007	424	5	equilibrium	equilibrium	NOUN
ejpam-6007	424	6	points	point	NOUN
ejpam-6007	424	7	:	:	PUNCT
ejpam-6007	424	8	(	(	PUNCT
ejpam-6007	424	9	x∗	x∗	X
ejpam-6007	424	10	,	,	PUNCT
ejpam-6007	424	11	λ∗	λ∗	NOUN
ejpam-6007	424	12	1	1	NUM
ejpam-6007	424	13	,	,	PUNCT
ejpam-6007	424	14	λ	λ	PROPN
ejpam-6007	424	15	∗	∗	NOUN
ejpam-6007	424	16	2)1	2)1	NUM
ejpam-6007	425	1	=	=	SYM
ejpam-6007	426	1	(	(	PUNCT
ejpam-6007	426	2	1.85786	1.85786	NUM
ejpam-6007	426	3	,	,	PUNCT
ejpam-6007	426	4	0−	0−	NUM
ejpam-6007	426	5	0.617178i	0.617178i	PROPN
ejpam-6007	426	6	,	,	PUNCT
ejpam-6007	426	7	0	0	NUM
ejpam-6007	427	1	+	+	CCONJ
ejpam-6007	427	2	0.263177i	0.263177i	NUM
ejpam-6007	427	3	)	)	PUNCT
ejpam-6007	427	4	,	,	PUNCT
ejpam-6007	427	5	(	(	PUNCT
ejpam-6007	427	6	x∗	x∗	PROPN
ejpam-6007	427	7	,	,	PUNCT
ejpam-6007	427	8	λ∗	λ∗	NOUN
ejpam-6007	427	9	1	1	NUM
ejpam-6007	427	10	,	,	PUNCT
ejpam-6007	427	11	λ	λ	PROPN
ejpam-6007	427	12	∗	∗	NOUN
ejpam-6007	427	13	2)2	2)2	NUM
ejpam-6007	427	14	=	=	SYM
ejpam-6007	427	15	(	(	PUNCT
ejpam-6007	427	16	1.85786	1.85786	NUM
ejpam-6007	427	17	,	,	PUNCT
ejpam-6007	427	18	0	0	NUM
ejpam-6007	428	1	+	+	CCONJ
ejpam-6007	428	2	0.617178i	0.617178i	PROPN
ejpam-6007	428	3	,	,	PUNCT
ejpam-6007	428	4	0−	0−	NUM
ejpam-6007	428	5	0.263177i	0.263177i	NUM
ejpam-6007	428	6	)	)	PUNCT
ejpam-6007	428	7	,	,	PUNCT
ejpam-6007	428	8	(	(	PUNCT
ejpam-6007	428	9	x∗	x∗	PROPN
ejpam-6007	428	10	,	,	PUNCT
ejpam-6007	428	11	λ∗	λ∗	NOUN
ejpam-6007	428	12	1	1	NUM
ejpam-6007	428	13	,	,	PUNCT
ejpam-6007	428	14	λ	λ	PROPN
ejpam-6007	428	15	∗	∗	NOUN
ejpam-6007	428	16	2)3	2)3	NUM
ejpam-6007	428	17	=	=	SYM
ejpam-6007	428	18	(	(	PUNCT
ejpam-6007	428	19	−0.916188	−0.916188	PROPN
ejpam-6007	428	20	,	,	PUNCT
ejpam-6007	428	21	0	0	NUM
ejpam-6007	429	1	+	+	CCONJ
ejpam-6007	429	2	0.0640229i	0.0640229i	NOUN
ejpam-6007	429	3	,	,	PUNCT
ejpam-6007	429	4	0−	0−	NUM
ejpam-6007	429	5	0.560109i	0.560109i	NUM
ejpam-6007	429	6	)	)	PUNCT
ejpam-6007	429	7	,	,	PUNCT
ejpam-6007	429	8	(	(	PUNCT
ejpam-6007	429	9	x∗	x∗	PROPN
ejpam-6007	429	10	,	,	PUNCT
ejpam-6007	429	11	λ∗	λ∗	NOUN
ejpam-6007	429	12	1	1	NUM
ejpam-6007	429	13	,	,	PUNCT
ejpam-6007	429	14	λ	λ	NOUN
ejpam-6007	429	15	∗	∗	VERB
ejpam-6007	429	16	2)4	2)4	NUM
ejpam-6007	429	17	=	=	SYM
ejpam-6007	429	18	(	(	PUNCT
ejpam-6007	429	19	−0.916188	−0.916188	PROPN
ejpam-6007	429	20	,	,	PUNCT
ejpam-6007	429	21	0−	0−	NUM
ejpam-6007	429	22	0.0640229i	0.0640229i	NUM
ejpam-6007	429	23	,	,	PUNCT
ejpam-6007	429	24	0	0	NUM
ejpam-6007	430	1	+	+	CCONJ
ejpam-6007	430	2	0.560109i	0.560109i	NOUN
ejpam-6007	430	3	)	)	PUNCT
ejpam-6007	430	4	,	,	PUNCT
ejpam-6007	430	5	(	(	PUNCT
ejpam-6007	430	6	x∗	x∗	PROPN
ejpam-6007	430	7	,	,	PUNCT
ejpam-6007	430	8	λ∗	λ∗	NOUN
ejpam-6007	430	9	1	1	NUM
ejpam-6007	430	10	,	,	PUNCT
ejpam-6007	430	11	λ	λ	PROPN
ejpam-6007	430	12	∗	∗	NOUN
ejpam-6007	430	13	2)5	2)5	NUM
ejpam-6007	430	14	=	=	SYM
ejpam-6007	430	15	(	(	PUNCT
ejpam-6007	430	16	0.391662	0.391662	NUM
ejpam-6007	430	17	,	,	PUNCT
ejpam-6007	430	18	0.100038,−0.482684	0.100038,−0.482684	NUM
ejpam-6007	430	19	)	)	PUNCT
ejpam-6007	430	20	,	,	PUNCT
ejpam-6007	430	21	(	(	PUNCT
ejpam-6007	430	22	x∗	x∗	PROPN
ejpam-6007	430	23	,	,	PUNCT
ejpam-6007	430	24	λ∗	λ∗	NOUN
ejpam-6007	430	25	1	1	NUM
ejpam-6007	430	26	,	,	PUNCT
ejpam-6007	430	27	λ	λ	NOUN
ejpam-6007	430	28	∗	∗	NOUN
ejpam-6007	430	29	2)6	2)6	NUM
ejpam-6007	430	30	=	=	SYM
ejpam-6007	430	31	(	(	PUNCT
ejpam-6007	430	32	0.391662,−0.100038	0.391662,−0.100038	NOUN
ejpam-6007	430	33	,	,	PUNCT
ejpam-6007	430	34	0.482684	0.482684	NUM
ejpam-6007	430	35	)	)	PUNCT
ejpam-6007	430	36	,	,	PUNCT
ejpam-6007	430	37	then	then	ADV
ejpam-6007	430	38	the	the	DET
ejpam-6007	430	39	jacobian	jacobian	ADJ
ejpam-6007	430	40	matrix	matrix	NOUN
ejpam-6007	430	41	evaluation	evaluation	NOUN
ejpam-6007	430	42	,	,	PUNCT
ejpam-6007	430	43	j	j	X
ejpam-6007	430	44	=	=	PUNCT
ejpam-6007	430	45			NUM
ejpam-6007	430	46	−2λ∗	−2λ∗	NOUN
ejpam-6007	430	47	1	1	NUM
ejpam-6007	430	48	0.25	0.25	NUM
ejpam-6007	430	49	(	(	PUNCT
ejpam-6007	430	50	1−	1−	NUM
ejpam-6007	430	51	x∗	x∗	X
ejpam-6007	430	52	)	)	PUNCT
ejpam-6007	431	1	+	+	CCONJ
ejpam-6007	431	2	2λ∗	2λ∗	NUM
ejpam-6007	431	3	2	2	NUM
ejpam-6007	431	4	0.5	0.5	NUM
ejpam-6007	431	5	x	x	SYM
ejpam-6007	431	6	−	−	PROPN
ejpam-6007	431	7	(	(	PUNCT
ejpam-6007	431	8	1−x∗)2	1−x∗)2	NUM
ejpam-6007	431	9	0.25	0.25	NUM
ejpam-6007	431	10	(	(	PUNCT
ejpam-6007	431	11	x∗)2	x∗)2	SYM
ejpam-6007	431	12	0.5	0.5	NUM
ejpam-6007	432	1	−(λ∗	−(λ∗	NUM
ejpam-6007	432	2	1	1	NUM
ejpam-6007	432	3	)	)	PUNCT
ejpam-6007	432	4	2	2	NUM
ejpam-6007	432	5	0.25	0.25	NUM
ejpam-6007	432	6	−	−	PROPN
ejpam-6007	432	7	λ∗	λ∗	PROPN
ejpam-6007	432	8	1λ	1λ	NUM
ejpam-6007	432	9	∗	∗	NOUN
ejpam-6007	432	10	2	2	NUM
ejpam-6007	432	11	0.5	0.5	NUM
ejpam-6007	432	12	2λ∗	2λ∗	NUM
ejpam-6007	432	13	1(1−x∗	1(1−x∗	NUM
ejpam-6007	432	14	)	)	PUNCT
ejpam-6007	432	15	0.25	0.25	NUM
ejpam-6007	433	1	−λ∗	−λ∗	PROPN
ejpam-6007	433	2	1x	1x	PROPN
ejpam-6007	433	3	∗	∗	VERB
ejpam-6007	433	4	0.5	0.5	NUM
ejpam-6007	434	1	−λ∗	−λ∗	NUM
ejpam-6007	434	2	1λ	1λ	PROPN
ejpam-6007	434	3	∗	∗	NOUN
ejpam-6007	434	4	2	2	NUM
ejpam-6007	434	5	0.25	0.25	NUM
ejpam-6007	434	6	−	−	PROPN
ejpam-6007	434	7	(	(	PUNCT
ejpam-6007	434	8	λ∗	λ∗	NOUN
ejpam-6007	434	9	2	2	NUM
ejpam-6007	434	10	)	)	PUNCT
ejpam-6007	434	11	2	2	NUM
ejpam-6007	434	12	0.5	0.5	NUM
ejpam-6007	434	13	λ∗	λ∗	PROPN
ejpam-6007	434	14	2(1−x∗	2(1−x∗	NOUN
ejpam-6007	434	15	)	)	PUNCT
ejpam-6007	434	16	0.25	0.25	NUM
ejpam-6007	434	17	λ∗	λ∗	NOUN
ejpam-6007	434	18	1(1−x∗	1(1−x∗	NUM
ejpam-6007	434	19	)	)	PUNCT
ejpam-6007	434	20	0.25	0.25	NUM
ejpam-6007	434	21	−	−	PROPN
ejpam-6007	434	22	2λ∗	2λ∗	NUM
ejpam-6007	434	23	2x	2x	NUM
ejpam-6007	434	24	∗	∗	NOUN
ejpam-6007	434	25	0.5	0.5	NUM
ejpam-6007	434	26			NUM
ejpam-6007	434	27	.	.	PUNCT
ejpam-6007	435	1	the	the	DET
ejpam-6007	435	2	eigenvalues	eigenvalue	NOUN
ejpam-6007	435	3	µi	µi	PROPN
ejpam-6007	435	4	of	of	ADP
ejpam-6007	435	5	the	the	DET
ejpam-6007	435	6	jacobian	jacobian	ADJ
ejpam-6007	435	7	matrix	matrix	NOUN
ejpam-6007	435	8	are	be	AUX
ejpam-6007	435	9	computed	compute	VERB
ejpam-6007	435	10	,	,	PUNCT
ejpam-6007	435	11	j(x∗	j(x∗	PROPN
ejpam-6007	435	12	,	,	PUNCT
ejpam-6007	435	13	λ∗	λ∗	NOUN
ejpam-6007	435	14	1	1	NUM
ejpam-6007	435	15	,	,	PUNCT
ejpam-6007	435	16	λ	λ	PROPN
ejpam-6007	435	17	∗	∗	NOUN
ejpam-6007	435	18	2)1	2)1	NUM
ejpam-6007	435	19	=(	=(	ADJ
ejpam-6007	436	1	−2.23227−	−2.23227−	PROPN
ejpam-6007	436	2	4.23449i,−2.23227−	4.23449i,−2.23227−	NUM
ejpam-6007	436	3	0.97901i,−6.85728×	0.97901i,−6.85728×	NUM
ejpam-6007	436	4	10−15	10−15	NOUN
ejpam-6007	436	5	−	−	PROPN
ejpam-6007	436	6	2.279837i	2.279837i	NUM
ejpam-6007	436	7	)	)	PUNCT
ejpam-6007	437	1	,	,	PUNCT
ejpam-6007	437	2	j(x∗	j(x∗	PROPN
ejpam-6007	437	3	,	,	PUNCT
ejpam-6007	437	4	λ∗	λ∗	NOUN
ejpam-6007	437	5	1	1	NUM
ejpam-6007	437	6	,	,	PUNCT
ejpam-6007	437	7	λ	λ	PROPN
ejpam-6007	437	8	∗	∗	VERB
ejpam-6007	437	9	2)2	2)2	NUM
ejpam-6007	437	10	=(	=(	NOUN
ejpam-6007	437	11	−2.23227	−2.23227	PRON
ejpam-6007	438	1	+	+	CCONJ
ejpam-6007	438	2	4.23449i,−2.23227	4.23449i,−2.23227	PROPN
ejpam-6007	438	3	+	+	CCONJ
ejpam-6007	438	4	0.97901i,−6.85728×	0.97901i,−6.85728×	NUM
ejpam-6007	438	5	10−15	10−15	PROPN
ejpam-6007	438	6	+	+	CCONJ
ejpam-6007	438	7	2.279837i	2.279837i	NUM
ejpam-6007	438	8	)	)	PUNCT
ejpam-6007	438	9	,	,	PUNCT
ejpam-6007	438	10	j(x∗	j(x∗	PROPN
ejpam-6007	438	11	,	,	PUNCT
ejpam-6007	438	12	λ∗	λ∗	NOUN
ejpam-6007	438	13	1	1	NUM
ejpam-6007	438	14	,	,	PUNCT
ejpam-6007	438	15	λ	λ	PROPN
ejpam-6007	438	16	∗	∗	NOUN
ejpam-6007	438	17	2)3	2)3	NUM
ejpam-6007	438	18	=(	=(	ADJ
ejpam-6007	438	19	−1.04710−	−1.04710−	PROPN
ejpam-6007	438	20	2.79990i,−1.04710−	2.79990i,−1.04710−	PROPN
ejpam-6007	438	21	0.79213i	0.79213i	NUM
ejpam-6007	438	22	,	,	PUNCT
ejpam-6007	438	23	8.88260×	8.88260×	VERB
ejpam-6007	438	24	10−16	10−16	PROPN
ejpam-6007	438	25	−	−	PROPN
ejpam-6007	438	26	1.07122i	1.07122i	NUM
ejpam-6007	438	27	)	)	PUNCT
ejpam-6007	438	28	,	,	PUNCT
ejpam-6007	438	29	j(x∗	j(x∗	PROPN
ejpam-6007	438	30	,	,	PUNCT
ejpam-6007	438	31	λ∗	λ∗	NOUN
ejpam-6007	438	32	1	1	NUM
ejpam-6007	438	33	,	,	PUNCT
ejpam-6007	438	34	λ	λ	PROPN
ejpam-6007	438	35	∗	∗	NOUN
ejpam-6007	438	36	2)4	2)4	NUM
ejpam-6007	438	37	=(	=(	NOUN
ejpam-6007	438	38	−1.04710	−1.04710	PRON
ejpam-6007	438	39	+	+	CCONJ
ejpam-6007	438	40	2.79990i,−1.04710	2.79990i,−1.04710	PROPN
ejpam-6007	438	41	+	+	CCONJ
ejpam-6007	438	42	0.79213i	0.79213i	PROPN
ejpam-6007	438	43	,	,	PUNCT
ejpam-6007	438	44	8.88260×	8.88260×	VERB
ejpam-6007	438	45	10−16	10−16	PROPN
ejpam-6007	438	46	+	+	CCONJ
ejpam-6007	438	47	1.07122i	1.07122i	NUM
ejpam-6007	438	48	)	)	PUNCT
ejpam-6007	438	49	,	,	PUNCT
ejpam-6007	438	50	j(x∗	j(x∗	PROPN
ejpam-6007	438	51	,	,	PUNCT
ejpam-6007	438	52	λ∗	λ∗	NOUN
ejpam-6007	438	53	1	1	NUM
ejpam-6007	438	54	,	,	PUNCT
ejpam-6007	438	55	λ	λ	PROPN
ejpam-6007	438	56	∗	∗	NOUN
ejpam-6007	438	57	2)5	2)5	NUM
ejpam-6007	438	58	=(	=(	PROPN
ejpam-6007	438	59	−1.24304,−0.62152,−0.51276	−1.24304,−0.62152,−0.51276	PROPN
ejpam-6007	438	60	)	)	PUNCT
ejpam-6007	438	61	,	,	PUNCT
ejpam-6007	438	62	j(x∗	j(x∗	PROPN
ejpam-6007	438	63	,	,	PUNCT
ejpam-6007	438	64	λ∗	λ∗	NOUN
ejpam-6007	438	65	1	1	NUM
ejpam-6007	438	66	,	,	PUNCT
ejpam-6007	438	67	λ	λ	PROPN
ejpam-6007	438	68	∗	∗	NOUN
ejpam-6007	438	69	2)6	2)6	NUM
ejpam-6007	438	70	=(	=(	NOUN
ejpam-6007	438	71	−1.24304,−1.24304,−0.62152	−1.24304,−1.24304,−0.62152	PROPN
ejpam-6007	438	72	)	)	PUNCT
ejpam-6007	438	73	.	.	PUNCT
ejpam-6007	439	1	from	from	ADP
ejpam-6007	439	2	the	the	DET
ejpam-6007	439	3	computed	compute	VERB
ejpam-6007	439	4	eigenvalues	eigenvalue	NOUN
ejpam-6007	439	5	of	of	ADP
ejpam-6007	439	6	the	the	DET
ejpam-6007	439	7	jacobian	jacobian	ADJ
ejpam-6007	439	8	matrix	matrix	NOUN
ejpam-6007	439	9	,	,	PUNCT
ejpam-6007	439	10	all	all	DET
ejpam-6007	439	11	eigenvalues	eigenvalue	NOUN
ejpam-6007	439	12	have	have	VERB
ejpam-6007	439	13	negative	negative	ADJ
ejpam-6007	439	14	real	real	ADJ
ejpam-6007	439	15	parts	part	NOUN
ejpam-6007	439	16	,	,	PUNCT
ejpam-6007	439	17	indicating	indicate	VERB
ejpam-6007	439	18	that	that	SCONJ
ejpam-6007	439	19	the	the	DET
ejpam-6007	439	20	equilibrium	equilibrium	NOUN
ejpam-6007	439	21	point	point	NOUN
ejpam-6007	439	22	of	of	ADP
ejpam-6007	439	23	the	the	DET
ejpam-6007	439	24	system	system	NOUN
ejpam-6007	439	25	is	be	AUX
ejpam-6007	439	26	locally	locally	ADV
ejpam-6007	439	27	asymptotically	asymptotically	ADV
ejpam-6007	439	28	stable	stable	ADJ
ejpam-6007	439	29	.	.	PUNCT
ejpam-6007	440	1	this	this	PRON
ejpam-6007	440	2	means	mean	VERB
ejpam-6007	440	3	that	that	SCONJ
ejpam-6007	440	4	small	small	ADJ
ejpam-6007	440	5	perturbations	perturbation	NOUN
ejpam-6007	440	6	in	in	ADP
ejpam-6007	440	7	the	the	DET
ejpam-6007	440	8	market	market	NOUN
ejpam-6007	440	9	shares	share	NOUN
ejpam-6007	440	10	or	or	CCONJ
ejpam-6007	440	11	advertising	advertising	NOUN
ejpam-6007	440	12	efforts	effort	NOUN
ejpam-6007	440	13	of	of	ADP
ejpam-6007	440	14	either	either	CCONJ
ejpam-6007	440	15	firm	firm	NOUN
ejpam-6007	440	16	will	will	AUX
ejpam-6007	440	17	decay	decay	VERB
ejpam-6007	440	18	over	over	ADP
ejpam-6007	440	19	time	time	NOUN
ejpam-6007	440	20	,	,	PUNCT
ejpam-6007	440	21	and	and	CCONJ
ejpam-6007	440	22	the	the	DET
ejpam-6007	440	23	system	system	NOUN
ejpam-6007	440	24	will	will	AUX
ejpam-6007	440	25	return	return	VERB
ejpam-6007	440	26	to	to	ADP
ejpam-6007	440	27	the	the	DET
ejpam-6007	440	28	equilibrium	equilibrium	NOUN
ejpam-6007	440	29	state	state	NOUN
ejpam-6007	440	30	.	.	PUNCT
ejpam-6007	441	1	economically	economically	ADV
ejpam-6007	441	2	,	,	PUNCT
ejpam-6007	441	3	this	this	PRON
ejpam-6007	441	4	implies	imply	VERB
ejpam-6007	441	5	that	that	SCONJ
ejpam-6007	441	6	both	both	CCONJ
ejpam-6007	441	7	firm	firm	ADJ
ejpam-6007	441	8	1	1	NUM
ejpam-6007	441	9	and	and	CCONJ
ejpam-6007	441	10	firm	firm	ADJ
ejpam-6007	441	11	2	2	NUM
ejpam-6007	441	12	can	can	AUX
ejpam-6007	441	13	maintain	maintain	VERB
ejpam-6007	441	14	stable	stable	ADJ
ejpam-6007	441	15	market	market	NOUN
ejpam-6007	441	16	shares	share	NOUN
ejpam-6007	441	17	under	under	ADP
ejpam-6007	441	18	the	the	DET
ejpam-6007	441	19	given	give	VERB
ejpam-6007	441	20	dynamics	dynamic	NOUN
ejpam-6007	441	21	,	,	PUNCT
ejpam-6007	441	22	and	and	CCONJ
ejpam-6007	441	23	neither	neither	DET
ejpam-6007	441	24	firm	firm	NOUN
ejpam-6007	441	25	will	will	AUX
ejpam-6007	441	26	experience	experience	VERB
ejpam-6007	441	27	unbounded	unbounded	ADJ
ejpam-6007	441	28	fluctuations	fluctuation	NOUN
ejpam-6007	441	29	in	in	ADP
ejpam-6007	441	30	influence	influence	NOUN
ejpam-6007	441	31	or	or	CCONJ
ejpam-6007	441	32	costs	cost	NOUN
ejpam-6007	441	33	.	.	PUNCT
ejpam-6007	442	1	5	5	X
ejpam-6007	442	2	.	.	X
ejpam-6007	442	3	conclusion	conclusion	NOUN
ejpam-6007	442	4	in	in	ADP
ejpam-6007	442	5	this	this	DET
ejpam-6007	442	6	paper	paper	NOUN
ejpam-6007	442	7	,	,	PUNCT
ejpam-6007	442	8	we	we	PRON
ejpam-6007	442	9	discussed	discuss	VERB
ejpam-6007	442	10	the	the	DET
ejpam-6007	442	11	numerical	numerical	ADJ
ejpam-6007	442	12	solution	solution	NOUN
ejpam-6007	442	13	of	of	ADP
ejpam-6007	442	14	an	an	DET
ejpam-6007	442	15	open	open	ADJ
ejpam-6007	442	16	-	-	PUNCT
ejpam-6007	442	17	loop	loop	NOUN
ejpam-6007	442	18	nash	nash	NOUN
ejpam-6007	442	19	differential	differential	NOUN
ejpam-6007	442	20	game	game	NOUN
ejpam-6007	442	21	using	use	VERB
ejpam-6007	442	22	the	the	DET
ejpam-6007	442	23	fourth	fourth	ADJ
ejpam-6007	442	24	-	-	PUNCT
ejpam-6007	442	25	order	order	NOUN
ejpam-6007	442	26	runge	runge	NOUN
ejpam-6007	442	27	-	-	PUNCT
ejpam-6007	442	28	kutta	kutta	NOUN
ejpam-6007	442	29	method	method	NOUN
ejpam-6007	442	30	.	.	PUNCT
ejpam-6007	443	1	this	this	DET
ejpam-6007	443	2	approach	approach	NOUN
ejpam-6007	443	3	allowed	allow	VERB
ejpam-6007	443	4	us	we	PRON
ejpam-6007	443	5	to	to	PART
ejpam-6007	443	6	analyze	analyze	VERB
ejpam-6007	443	7	competition	competition	NOUN
ejpam-6007	443	8	between	between	ADP
ejpam-6007	443	9	firms	firm	NOUN
ejpam-6007	443	10	in	in	ADP
ejpam-6007	443	11	a	a	DET
ejpam-6007	443	12	dynamic	dynamic	ADJ
ejpam-6007	443	13	market	market	NOUN
ejpam-6007	443	14	environment	environment	NOUN
ejpam-6007	443	15	.	.	PUNCT
ejpam-6007	444	1	we	we	PRON
ejpam-6007	444	2	studied	study	VERB
ejpam-6007	444	3	the	the	DET
ejpam-6007	444	4	convergence	convergence	NOUN
ejpam-6007	444	5	a.	a.	NOUN
ejpam-6007	444	6	a.	a.	NOUN
ejpam-6007	444	7	megahed	megahe	VERB
ejpam-6007	444	8	et	et	PROPN
ejpam-6007	444	9	al	al	PROPN
ejpam-6007	444	10	.	.	PUNCT
ejpam-6007	444	11	/	/	SYM
ejpam-6007	444	12	eur	eur	PROPN
ejpam-6007	444	13	.	.	PUNCT
ejpam-6007	445	1	j.	j.	PROPN
ejpam-6007	445	2	pure	pure	PROPN
ejpam-6007	445	3	appl	appl	PROPN
ejpam-6007	445	4	.	.	PROPN
ejpam-6007	445	5	math	math	PROPN
ejpam-6007	445	6	,	,	PUNCT
ejpam-6007	445	7	18	18	NUM
ejpam-6007	445	8	(	(	PUNCT
ejpam-6007	445	9	4	4	NUM
ejpam-6007	445	10	)	)	PUNCT
ejpam-6007	445	11	(	(	PUNCT
ejpam-6007	445	12	2025	2025	NUM
ejpam-6007	445	13	)	)	PUNCT
ejpam-6007	445	14	,	,	PUNCT
ejpam-6007	445	15	6007	6007	NUM
ejpam-6007	445	16	21	21	NUM
ejpam-6007	445	17	of	of	ADP
ejpam-6007	445	18	22	22	NUM
ejpam-6007	445	19	of	of	ADP
ejpam-6007	445	20	the	the	DET
ejpam-6007	445	21	runge	runge	NOUN
ejpam-6007	445	22	-	-	PUNCT
ejpam-6007	445	23	kutta	kutta	NOUN
ejpam-6007	445	24	method	method	NOUN
ejpam-6007	445	25	to	to	PART
ejpam-6007	445	26	ensure	ensure	VERB
ejpam-6007	445	27	the	the	DET
ejpam-6007	445	28	reliability	reliability	NOUN
ejpam-6007	445	29	of	of	ADP
ejpam-6007	445	30	the	the	DET
ejpam-6007	445	31	numerical	numerical	ADJ
ejpam-6007	445	32	solution	solution	NOUN
ejpam-6007	445	33	,	,	PUNCT
ejpam-6007	445	34	and	and	CCONJ
ejpam-6007	445	35	we	we	PRON
ejpam-6007	445	36	examined	examine	VERB
ejpam-6007	445	37	the	the	DET
ejpam-6007	445	38	stability	stability	NOUN
ejpam-6007	445	39	of	of	ADP
ejpam-6007	445	40	the	the	DET
ejpam-6007	445	41	solution	solution	NOUN
ejpam-6007	445	42	to	to	PART
ejpam-6007	445	43	confirm	confirm	VERB
ejpam-6007	445	44	that	that	SCONJ
ejpam-6007	445	45	numerical	numerical	ADJ
ejpam-6007	445	46	errors	error	NOUN
ejpam-6007	445	47	do	do	AUX
ejpam-6007	445	48	not	not	PART
ejpam-6007	445	49	amplify	amplify	VERB
ejpam-6007	445	50	over	over	ADP
ejpam-6007	445	51	time	time	NOUN
ejpam-6007	445	52	.	.	PUNCT
ejpam-6007	446	1	we	we	PRON
ejpam-6007	446	2	also	also	ADV
ejpam-6007	446	3	demonstrated	demonstrate	VERB
ejpam-6007	446	4	that	that	SCONJ
ejpam-6007	446	5	increasing	increase	VERB
ejpam-6007	446	6	advertising	advertising	NOUN
ejpam-6007	446	7	campaigns	campaign	NOUN
ejpam-6007	446	8	leads	lead	VERB
ejpam-6007	446	9	to	to	ADP
ejpam-6007	446	10	higher	high	ADJ
ejpam-6007	446	11	market	market	NOUN
ejpam-6007	446	12	participation	participation	NOUN
ejpam-6007	446	13	for	for	ADP
ejpam-6007	446	14	the	the	DET
ejpam-6007	446	15	firms	firm	NOUN
ejpam-6007	446	16	.	.	PUNCT
ejpam-6007	447	1	finally	finally	ADV
ejpam-6007	447	2	,	,	PUNCT
ejpam-6007	447	3	illustrative	illustrative	ADJ
ejpam-6007	447	4	figures	figure	NOUN
ejpam-6007	447	5	were	be	AUX
ejpam-6007	447	6	presented	present	VERB
ejpam-6007	447	7	to	to	PART
ejpam-6007	447	8	demonstrate	demonstrate	VERB
ejpam-6007	447	9	the	the	DET
ejpam-6007	447	10	effect	effect	NOUN
ejpam-6007	447	11	of	of	ADP
ejpam-6007	447	12	advertising	advertising	NOUN
ejpam-6007	447	13	campaigns	campaign	NOUN
ejpam-6007	447	14	on	on	ADP
ejpam-6007	447	15	each	each	DET
ejpam-6007	447	16	firm	firm	NOUN
ejpam-6007	447	17	’s	’s	PART
ejpam-6007	447	18	market	market	NOUN
ejpam-6007	447	19	share	share	NOUN
ejpam-6007	447	20	.	.	PUNCT
ejpam-6007	448	1	in	in	ADP
ejpam-6007	448	2	future	future	ADJ
ejpam-6007	448	3	work	work	NOUN
ejpam-6007	448	4	,	,	PUNCT
ejpam-6007	448	5	we	we	PRON
ejpam-6007	448	6	plan	plan	VERB
ejpam-6007	448	7	to	to	PART
ejpam-6007	448	8	expand	expand	VERB
ejpam-6007	448	9	this	this	DET
ejpam-6007	448	10	study	study	NOUN
ejpam-6007	448	11	in	in	ADP
ejpam-6007	448	12	several	several	ADJ
ejpam-6007	448	13	ways	way	NOUN
ejpam-6007	448	14	.	.	PUNCT
ejpam-6007	449	1	first	first	ADV
ejpam-6007	449	2	,	,	PUNCT
ejpam-6007	449	3	we	we	PRON
ejpam-6007	449	4	aim	aim	VERB
ejpam-6007	449	5	to	to	PART
ejpam-6007	449	6	incorporate	incorporate	VERB
ejpam-6007	449	7	stochastic	stochastic	ADJ
ejpam-6007	449	8	elements	element	NOUN
ejpam-6007	449	9	into	into	ADP
ejpam-6007	449	10	the	the	DET
ejpam-6007	449	11	model	model	NOUN
ejpam-6007	449	12	to	to	PART
ejpam-6007	449	13	analyze	analyze	VERB
ejpam-6007	449	14	how	how	SCONJ
ejpam-6007	449	15	uncertainty	uncertainty	NOUN
ejpam-6007	449	16	influences	influence	VERB
ejpam-6007	449	17	market	market	NOUN
ejpam-6007	449	18	behavior	behavior	NOUN
ejpam-6007	449	19	and	and	CCONJ
ejpam-6007	449	20	firm	firm	ADJ
ejpam-6007	449	21	strategies	strategy	NOUN
ejpam-6007	449	22	.	.	PUNCT
ejpam-6007	450	1	second	second	ADJ
ejpam-6007	450	2	,	,	PUNCT
ejpam-6007	450	3	we	we	PRON
ejpam-6007	450	4	plan	plan	VERB
ejpam-6007	450	5	to	to	PART
ejpam-6007	450	6	include	include	VERB
ejpam-6007	450	7	more	more	ADJ
ejpam-6007	450	8	firms	firm	NOUN
ejpam-6007	450	9	,	,	PUNCT
ejpam-6007	450	10	allowing	allow	VERB
ejpam-6007	450	11	multiple	multiple	ADJ
ejpam-6007	450	12	companies	company	NOUN
ejpam-6007	450	13	to	to	PART
ejpam-6007	450	14	compete	compete	VERB
ejpam-6007	450	15	simultaneously	simultaneously	ADV
ejpam-6007	450	16	,	,	PUNCT
ejpam-6007	450	17	which	which	PRON
ejpam-6007	450	18	increases	increase	VERB
ejpam-6007	450	19	the	the	DET
ejpam-6007	450	20	complexity	complexity	NOUN
ejpam-6007	450	21	of	of	ADP
ejpam-6007	450	22	interactions	interaction	NOUN
ejpam-6007	450	23	and	and	CCONJ
ejpam-6007	450	24	may	may	AUX
ejpam-6007	450	25	reveal	reveal	VERB
ejpam-6007	450	26	new	new	ADJ
ejpam-6007	450	27	patterns	pattern	NOUN
ejpam-6007	450	28	.	.	PUNCT
ejpam-6007	451	1	third	third	ADJ
ejpam-6007	451	2	,	,	PUNCT
ejpam-6007	451	3	we	we	PRON
ejpam-6007	451	4	aim	aim	VERB
ejpam-6007	451	5	to	to	PART
ejpam-6007	451	6	allow	allow	VERB
ejpam-6007	451	7	strategies	strategy	NOUN
ejpam-6007	451	8	to	to	PART
ejpam-6007	451	9	adapt	adapt	VERB
ejpam-6007	451	10	based	base	VERB
ejpam-6007	451	11	on	on	ADP
ejpam-6007	451	12	the	the	DET
ejpam-6007	451	13	current	current	ADJ
ejpam-6007	451	14	state	state	NOUN
ejpam-6007	451	15	of	of	ADP
ejpam-6007	451	16	the	the	DET
ejpam-6007	451	17	system	system	NOUN
ejpam-6007	451	18	,	,	PUNCT
ejpam-6007	451	19	using	use	VERB
ejpam-6007	451	20	feedback	feedback	NOUN
ejpam-6007	451	21	nash	nash	NOUN
ejpam-6007	451	22	equilibria	equilibrium	NOUN
ejpam-6007	451	23	,	,	PUNCT
ejpam-6007	451	24	making	make	VERB
ejpam-6007	451	25	the	the	DET
ejpam-6007	451	26	model	model	NOUN
ejpam-6007	451	27	more	more	ADV
ejpam-6007	451	28	flexible	flexible	ADJ
ejpam-6007	451	29	and	and	CCONJ
ejpam-6007	451	30	closer	close	ADJ
ejpam-6007	451	31	to	to	ADP
ejpam-6007	451	32	real	real	ADJ
ejpam-6007	451	33	-	-	PUNCT
ejpam-6007	451	34	world	world	NOUN
ejpam-6007	451	35	competition	competition	NOUN
ejpam-6007	451	36	.	.	PUNCT
ejpam-6007	452	1	references	reference	NOUN
ejpam-6007	452	2	[	[	X
ejpam-6007	452	3	1	1	X
ejpam-6007	452	4	]	]	PUNCT
ejpam-6007	452	5	john	john	PROPN
ejpam-6007	452	6	von	von	PROPN
ejpam-6007	452	7	neumann	neumann	PROPN
ejpam-6007	452	8	and	and	CCONJ
ejpam-6007	452	9	oskar	oskar	PROPN
ejpam-6007	452	10	morgenstern	morgenstern	PROPN
ejpam-6007	452	11	.	.	PUNCT
ejpam-6007	453	1	theory	theory	NOUN
ejpam-6007	453	2	of	of	ADP
ejpam-6007	453	3	games	game	NOUN
ejpam-6007	453	4	and	and	CCONJ
ejpam-6007	453	5	economic	economic	ADJ
ejpam-6007	453	6	behavior	behavior	NOUN
ejpam-6007	453	7	.	.	PUNCT
ejpam-6007	454	1	princeton	princeton	PROPN
ejpam-6007	454	2	university	university	PROPN
ejpam-6007	454	3	press	press	NOUN
ejpam-6007	454	4	,	,	PUNCT
ejpam-6007	454	5	1944	1944	NUM
ejpam-6007	454	6	.	.	PUNCT
ejpam-6007	455	1	[	[	X
ejpam-6007	455	2	2	2	NUM
ejpam-6007	455	3	]	]	X
ejpam-6007	455	4	fred	fred	PROPN
ejpam-6007	455	5	brauer	brauer	PROPN
ejpam-6007	455	6	and	and	CCONJ
ejpam-6007	455	7	john	john	PROPN
ejpam-6007	455	8	a.	a.	PROPN
ejpam-6007	455	9	nohel	nohel	PROPN
ejpam-6007	455	10	.	.	PUNCT
ejpam-6007	456	1	differential	differential	ADJ
ejpam-6007	456	2	equations	equation	NOUN
ejpam-6007	456	3	and	and	CCONJ
ejpam-6007	456	4	their	their	PRON
ejpam-6007	456	5	applications	application	NOUN
ejpam-6007	456	6	.	.	PUNCT
ejpam-6007	457	1	springer	springer	NOUN
ejpam-6007	457	2	,	,	PUNCT
ejpam-6007	457	3	1989	1989	NUM
ejpam-6007	457	4	.	.	PUNCT
ejpam-6007	458	1	[	[	X
ejpam-6007	458	2	3	3	X
ejpam-6007	458	3	]	]	PUNCT
ejpam-6007	458	4	mojtaba	mojtaba	NOUN
ejpam-6007	458	5	dehghan	dehghan	PROPN
ejpam-6007	458	6	banadaki	banadaki	PROPN
ejpam-6007	458	7	and	and	CCONJ
ejpam-6007	458	8	hamidreza	hamidreza	PROPN
ejpam-6007	458	9	navidi	navidi	PROPN
ejpam-6007	458	10	.	.	PUNCT
ejpam-6007	459	1	numerical	numerical	ADJ
ejpam-6007	459	2	solution	solution	NOUN
ejpam-6007	459	3	of	of	ADP
ejpam-6007	459	4	open	open	ADJ
ejpam-6007	459	5	-	-	PUNCT
ejpam-6007	459	6	loop	loop	NOUN
ejpam-6007	459	7	nash	nash	NOUN
ejpam-6007	459	8	differential	differential	NOUN
ejpam-6007	459	9	games	game	NOUN
ejpam-6007	459	10	based	base	VERB
ejpam-6007	459	11	on	on	ADP
ejpam-6007	459	12	the	the	DET
ejpam-6007	459	13	legendre	legendre	PROPN
ejpam-6007	459	14	tau	tau	PROPN
ejpam-6007	459	15	method	method	PROPN
ejpam-6007	459	16	.	.	PUNCT
ejpam-6007	460	1	games	game	NOUN
ejpam-6007	460	2	,	,	PUNCT
ejpam-6007	460	3	11:28	11:28	NUM
ejpam-6007	460	4	,	,	PUNCT
ejpam-6007	460	5	2020	2020	NUM
ejpam-6007	460	6	.	.	PUNCT
ejpam-6007	461	1	[	[	X
ejpam-6007	461	2	4	4	X
ejpam-6007	461	3	]	]	PUNCT
ejpam-6007	461	4	dmitry	dmitry	PROPN
ejpam-6007	461	5	r.	r.	PROPN
ejpam-6007	461	6	kuvshinov	kuvshinov	PROPN
ejpam-6007	461	7	and	and	CCONJ
ejpam-6007	461	8	sergei	sergei	PROPN
ejpam-6007	461	9	i.	i.	PROPN
ejpam-6007	461	10	osipov	osipov	PROPN
ejpam-6007	461	11	.	.	PUNCT
ejpam-6007	462	1	numerical	numerical	ADJ
ejpam-6007	462	2	construction	construction	NOUN
ejpam-6007	462	3	of	of	ADP
ejpam-6007	462	4	stackelberg	stackelberg	PROPN
ejpam-6007	462	5	solutions	solution	NOUN
ejpam-6007	462	6	in	in	ADP
ejpam-6007	462	7	a	a	DET
ejpam-6007	462	8	linear	linear	ADJ
ejpam-6007	462	9	positional	positional	ADJ
ejpam-6007	462	10	differential	differential	ADJ
ejpam-6007	462	11	game	game	NOUN
ejpam-6007	462	12	based	base	VERB
ejpam-6007	462	13	on	on	ADP
ejpam-6007	462	14	the	the	DET
ejpam-6007	462	15	method	method	NOUN
ejpam-6007	462	16	of	of	ADP
ejpam-6007	462	17	polyhedra	polyhedra	PROPN
ejpam-6007	462	18	.	.	PUNCT
ejpam-6007	462	19	automation	automation	NOUN
ejpam-6007	462	20	and	and	CCONJ
ejpam-6007	462	21	remote	remote	ADJ
ejpam-6007	462	22	control	control	NOUN
ejpam-6007	462	23	,	,	PUNCT
ejpam-6007	462	24	79:479–491	79:479–491	NOUN
ejpam-6007	462	25	,	,	PUNCT
ejpam-6007	462	26	2018	2018	NUM
ejpam-6007	462	27	.	.	PUNCT
ejpam-6007	463	1	[	[	X
ejpam-6007	463	2	5	5	NUM
ejpam-6007	463	3	]	]	SYM
ejpam-6007	463	4	a.a	a.a	PROPN
ejpam-6007	463	5	.	.	PROPN
ejpam-6007	463	6	megahed	megahed	PROPN
ejpam-6007	463	7	and	and	CCONJ
ejpam-6007	463	8	s.e	s.e	PROPN
ejpam-6007	463	9	.	.	PROPN
ejpam-6007	463	10	mohamed	mohamed	PROPN
ejpam-6007	463	11	.	.	PROPN
ejpam-6007	464	1	on	on	ADP
ejpam-6007	464	2	the	the	DET
ejpam-6007	464	3	solution	solution	NOUN
ejpam-6007	464	4	of	of	ADP
ejpam-6007	464	5	differential	differential	ADJ
ejpam-6007	464	6	games	game	NOUN
ejpam-6007	464	7	by	by	ADP
ejpam-6007	464	8	picard	picard	PROPN
ejpam-6007	464	9	method	method	NOUN
ejpam-6007	464	10	.	.	PUNCT
ejpam-6007	465	1	applied	apply	VERB
ejpam-6007	465	2	mathematics	mathematic	NOUN
ejpam-6007	465	3	and	and	CCONJ
ejpam-6007	465	4	computation	computation	NOUN
ejpam-6007	465	5	,	,	PUNCT
ejpam-6007	465	6	184:432–440	184:432–440	PROPN
ejpam-6007	465	7	,	,	PUNCT
ejpam-6007	465	8	2007	2007	NUM
ejpam-6007	465	9	.	.	PUNCT
ejpam-6007	466	1	[	[	X
ejpam-6007	466	2	6	6	NUM
ejpam-6007	466	3	]	]	X
ejpam-6007	466	4	a.a	a.a	PROPN
ejpam-6007	466	5	.	.	PROPN
ejpam-6007	466	6	megahed	megahed	PROPN
ejpam-6007	466	7	and	and	CCONJ
ejpam-6007	466	8	a.m.	a.m.	PROPN
ejpam-6007	466	9	kassem	kassem	PROPN
ejpam-6007	466	10	.	.	PUNCT
ejpam-6007	467	1	a	a	DET
ejpam-6007	467	2	zero	zero	NUM
ejpam-6007	467	3	-	-	PUNCT
ejpam-6007	467	4	sum	sum	NOUN
ejpam-6007	467	5	differential	differential	ADJ
ejpam-6007	467	6	game	game	NOUN
ejpam-6007	467	7	model	model	NOUN
ejpam-6007	467	8	for	for	ADP
ejpam-6007	467	9	the	the	DET
ejpam-6007	467	10	spread	spread	NOUN
ejpam-6007	467	11	of	of	ADP
ejpam-6007	467	12	coronavirus	coronavirus	NOUN
ejpam-6007	467	13	.	.	PUNCT
ejpam-6007	468	1	chaos	chaos	NOUN
ejpam-6007	468	2	,	,	PUNCT
ejpam-6007	468	3	solitons	soliton	NOUN
ejpam-6007	468	4	&	&	CCONJ
ejpam-6007	468	5	fractals	fractal	NOUN
ejpam-6007	468	6	,	,	PUNCT
ejpam-6007	468	7	140:110–117	140:110–117	NUM
ejpam-6007	468	8	,	,	PUNCT
ejpam-6007	468	9	2020	2020	NUM
ejpam-6007	468	10	.	.	PUNCT
ejpam-6007	469	1	[	[	X
ejpam-6007	469	2	7	7	X
ejpam-6007	469	3	]	]	X
ejpam-6007	469	4	e.	e.	PROPN
ejpam-6007	469	5	youness	youness	NOUN
ejpam-6007	469	6	and	and	CCONJ
ejpam-6007	469	7	a.m.a	a.m.a	NOUN
ejpam-6007	469	8	.	.	PUNCT
ejpam-6007	470	1	el	el	PROPN
ejpam-6007	470	2	-	-	PUNCT
ejpam-6007	470	3	sayed	say	VERB
ejpam-6007	470	4	.	.	PUNCT
ejpam-6007	471	1	a	a	DET
ejpam-6007	471	2	stackelberg	stackelberg	PROPN
ejpam-6007	471	3	differential	differential	ADJ
ejpam-6007	471	4	game	game	NOUN
ejpam-6007	471	5	approach	approach	NOUN
ejpam-6007	471	6	to	to	AUX
ejpam-6007	471	7	combat	combat	VERB
ejpam-6007	471	8	terrorism	terrorism	NOUN
ejpam-6007	471	9	.	.	PUNCT
ejpam-6007	472	1	nonlinear	nonlinear	ADJ
ejpam-6007	472	2	dynamics	dynamic	NOUN
ejpam-6007	472	3	,	,	PUNCT
ejpam-6007	472	4	63:671–682	63:671–682	PROPN
ejpam-6007	472	5	,	,	PUNCT
ejpam-6007	472	6	2011	2011	NUM
ejpam-6007	472	7	.	.	PUNCT
ejpam-6007	473	1	[	[	X
ejpam-6007	473	2	8	8	NUM
ejpam-6007	473	3	]	]	X
ejpam-6007	473	4	a.a	a.a	PROPN
ejpam-6007	473	5	.	.	PROPN
ejpam-6007	473	6	hemeda	hemeda	PROPN
ejpam-6007	473	7	.	.	PUNCT
ejpam-6007	474	1	on	on	ADP
ejpam-6007	474	2	iterative	iterative	ADJ
ejpam-6007	474	3	methods	method	NOUN
ejpam-6007	474	4	for	for	ADP
ejpam-6007	474	5	nonlinear	nonlinear	ADJ
ejpam-6007	474	6	integro	integro	ADJ
ejpam-6007	474	7	-	-	PUNCT
ejpam-6007	474	8	differential	differential	NOUN
ejpam-6007	474	9	equations	equation	NOUN
ejpam-6007	474	10	.	.	PUNCT
ejpam-6007	475	1	applied	apply	VERB
ejpam-6007	475	2	mathematics	mathematic	NOUN
ejpam-6007	475	3	and	and	CCONJ
ejpam-6007	475	4	computation	computation	NOUN
ejpam-6007	475	5	,	,	PUNCT
ejpam-6007	475	6	219:7625–7635	219:7625–7635	NOUN
ejpam-6007	475	7	,	,	PUNCT
ejpam-6007	475	8	2013	2013	NUM
ejpam-6007	475	9	.	.	PUNCT
ejpam-6007	476	1	[	[	X
ejpam-6007	476	2	9	9	NUM
ejpam-6007	476	3	]	]	PUNCT
ejpam-6007	476	4	a.	a.	NOUN
ejpam-6007	476	5	a.	a.	NOUN
ejpam-6007	476	6	megahed	megahe	VERB
ejpam-6007	476	7	,	,	PUNCT
ejpam-6007	476	8	a.	a.	NOUN
ejpam-6007	476	9	a.	a.	PROPN
ejpam-6007	476	10	hemeda	hemeda	PROPN
ejpam-6007	476	11	,	,	PUNCT
ejpam-6007	476	12	and	and	CCONJ
ejpam-6007	476	13	h.	h.	PROPN
ejpam-6007	476	14	f.	f.	PROPN
ejpam-6007	476	15	a.	a.	PROPN
ejpam-6007	476	16	madkour	madkour	PROPN
ejpam-6007	476	17	.	.	PROPN
ejpam-6007	477	1	approximate	approximate	ADJ
ejpam-6007	477	2	solutions	solution	NOUN
ejpam-6007	477	3	for	for	ADP
ejpam-6007	477	4	nash	nash	PROPN
ejpam-6007	477	5	differential	differential	PROPN
ejpam-6007	477	6	games	games	PROPN
ejpam-6007	477	7	.	.	PUNCT
ejpam-6007	478	1	journal	journal	PROPN
ejpam-6007	478	2	of	of	ADP
ejpam-6007	478	3	mathematics	mathematic	NOUN
ejpam-6007	478	4	,	,	PUNCT
ejpam-6007	478	5	2023:7374882	2023:7374882	NUM
ejpam-6007	478	6	,	,	PUNCT
ejpam-6007	478	7	2023	2023	NUM
ejpam-6007	478	8	.	.	PUNCT
ejpam-6007	479	1	[	[	X
ejpam-6007	479	2	10	10	NUM
ejpam-6007	479	3	]	]	PUNCT
ejpam-6007	479	4	a.m.	a.m.	PROPN
ejpam-6007	480	1	kassem	kassem	PROPN
ejpam-6007	480	2	and	and	CCONJ
ejpam-6007	480	3	a.a	a.a	PROPN
ejpam-6007	480	4	.	.	PROPN
ejpam-6007	480	5	megahed	megahed	PROPN
ejpam-6007	480	6	.	.	PUNCT
ejpam-6007	481	1	a	a	DET
ejpam-6007	481	2	differential	differential	ADJ
ejpam-6007	481	3	game	game	NOUN
ejpam-6007	481	4	approach	approach	NOUN
ejpam-6007	481	5	to	to	ADP
ejpam-6007	481	6	counter	counter	NOUN
ejpam-6007	481	7	-	-	NOUN
ejpam-6007	481	8	terrorism	terrorism	NOUN
ejpam-6007	481	9	.	.	PUNCT
ejpam-6007	482	1	applied	apply	VERB
ejpam-6007	482	2	mathematics	mathematic	NOUN
ejpam-6007	482	3	and	and	CCONJ
ejpam-6007	482	4	computation	computation	NOUN
ejpam-6007	482	5	,	,	PUNCT
ejpam-6007	482	6	190:607–618	190:607–618	NUM
ejpam-6007	482	7	,	,	PUNCT
ejpam-6007	482	8	2007	2007	NUM
ejpam-6007	482	9	.	.	PUNCT
ejpam-6007	483	1	[	[	X
ejpam-6007	483	2	11	11	NUM
ejpam-6007	483	3	]	]	PUNCT
ejpam-6007	483	4	e.	e.	PROPN
ejpam-6007	483	5	youness	youness	PROPN
ejpam-6007	483	6	.	.	PUNCT
ejpam-6007	484	1	nash	nash	NOUN
ejpam-6007	484	2	-	-	PUNCT
ejpam-6007	484	3	collaborative	collaborative	ADJ
ejpam-6007	484	4	solutions	solution	NOUN
ejpam-6007	484	5	for	for	ADP
ejpam-6007	484	6	differential	differential	ADJ
ejpam-6007	484	7	games	game	NOUN
ejpam-6007	484	8	.	.	PUNCT
ejpam-6007	485	1	applied	apply	VERB
ejpam-6007	485	2	mathematics	mathematic	NOUN
ejpam-6007	485	3	and	and	CCONJ
ejpam-6007	485	4	computation	computation	NOUN
ejpam-6007	485	5	,	,	PUNCT
ejpam-6007	485	6	138:289–300	138:289–300	NUM
ejpam-6007	485	7	,	,	PUNCT
ejpam-6007	485	8	2003	2003	NUM
ejpam-6007	485	9	.	.	PUNCT
ejpam-6007	486	1	[	[	X
ejpam-6007	486	2	12	12	NUM
ejpam-6007	486	3	]	]	X
ejpam-6007	486	4	e.	e.	PROPN
ejpam-6007	486	5	youness	youness	PROPN
ejpam-6007	486	6	and	and	CCONJ
ejpam-6007	486	7	a.a	a.a	PROPN
ejpam-6007	486	8	.	.	PROPN
ejpam-6007	486	9	megahed	megahe	VERB
ejpam-6007	486	10	.	.	PUNCT
ejpam-6007	487	1	on	on	ADP
ejpam-6007	487	2	nash	nash	PROPN
ejpam-6007	487	3	equilibrium	equilibrium	NOUN
ejpam-6007	487	4	strategies	strategy	NOUN
ejpam-6007	487	5	of	of	ADP
ejpam-6007	487	6	fuzzy	fuzzy	ADJ
ejpam-6007	487	7	differential	differential	NOUN
ejpam-6007	487	8	games	game	NOUN
ejpam-6007	487	9	.	.	PUNCT
ejpam-6007	488	1	fuzzy	fuzzy	ADJ
ejpam-6007	488	2	sets	set	NOUN
ejpam-6007	488	3	and	and	CCONJ
ejpam-6007	488	4	systems	system	NOUN
ejpam-6007	488	5	,	,	PUNCT
ejpam-6007	488	6	113:439–445	113:439–445	NUM
ejpam-6007	488	7	,	,	PUNCT
ejpam-6007	488	8	2000	2000	NUM
ejpam-6007	488	9	.	.	PUNCT
ejpam-6007	489	1	[	[	X
ejpam-6007	489	2	13	13	NUM
ejpam-6007	489	3	]	]	X
ejpam-6007	489	4	h.	h.	PROPN
ejpam-6007	489	5	sun	sun	PROPN
ejpam-6007	489	6	and	and	CCONJ
ejpam-6007	489	7	j.	j.	PROPN
ejpam-6007	489	8	yong	yong	PROPN
ejpam-6007	489	9	.	.	PUNCT
ejpam-6007	489	10	open	open	ADJ
ejpam-6007	489	11	-	-	PUNCT
ejpam-6007	489	12	loop	loop	NOUN
ejpam-6007	489	13	and	and	CCONJ
ejpam-6007	489	14	closed	closed	ADJ
ejpam-6007	489	15	-	-	PUNCT
ejpam-6007	489	16	loop	loop	NOUN
ejpam-6007	489	17	nash	nash	NOUN
ejpam-6007	489	18	equilibria	equilibrium	NOUN
ejpam-6007	489	19	in	in	ADP
ejpam-6007	489	20	linear	linear	ADJ
ejpam-6007	489	21	-	-	PUNCT
ejpam-6007	489	22	quadratic	quadratic	ADJ
ejpam-6007	489	23	stochastic	stochastic	ADJ
ejpam-6007	489	24	differential	differential	NOUN
ejpam-6007	489	25	games	game	NOUN
ejpam-6007	489	26	.	.	PUNCT
ejpam-6007	490	1	siam	siam	PROPN
ejpam-6007	490	2	journal	journal	PROPN
ejpam-6007	490	3	on	on	ADP
ejpam-6007	490	4	control	control	NOUN
ejpam-6007	490	5	and	and	CCONJ
ejpam-6007	490	6	optimization	optimization	NOUN
ejpam-6007	490	7	,	,	PUNCT
ejpam-6007	490	8	41:737	41:737	NUM
ejpam-6007	490	9	–	–	PUNCT
ejpam-6007	490	10	756	756	NUM
ejpam-6007	490	11	,	,	PUNCT
ejpam-6007	490	12	2002	2002	NUM
ejpam-6007	490	13	.	.	PUNCT
ejpam-6007	491	1	a.	a.	NOUN
ejpam-6007	491	2	a.	a.	PROPN
ejpam-6007	491	3	megahed	megahe	VERB
ejpam-6007	491	4	et	et	PROPN
ejpam-6007	491	5	al	al	PROPN
ejpam-6007	491	6	.	.	PUNCT
ejpam-6007	491	7	/	/	SYM
ejpam-6007	491	8	eur	eur	PROPN
ejpam-6007	491	9	.	.	PUNCT
ejpam-6007	492	1	j.	j.	PROPN
ejpam-6007	492	2	pure	pure	PROPN
ejpam-6007	492	3	appl	appl	PROPN
ejpam-6007	492	4	.	.	PROPN
ejpam-6007	492	5	math	math	PROPN
ejpam-6007	492	6	,	,	PUNCT
ejpam-6007	492	7	18	18	NUM
ejpam-6007	492	8	(	(	PUNCT
ejpam-6007	492	9	4	4	NUM
ejpam-6007	492	10	)	)	PUNCT
ejpam-6007	492	11	(	(	PUNCT
ejpam-6007	492	12	2025	2025	NUM
ejpam-6007	492	13	)	)	PUNCT
ejpam-6007	492	14	,	,	PUNCT
ejpam-6007	492	15	6007	6007	NUM
ejpam-6007	492	16	22	22	NUM
ejpam-6007	492	17	of	of	ADP
ejpam-6007	492	18	22	22	NUM
ejpam-6007	492	19	[	[	X
ejpam-6007	492	20	14	14	NUM
ejpam-6007	492	21	]	]	X
ejpam-6007	492	22	j.c	j.c	PROPN
ejpam-6007	492	23	.	.	PROPN
ejpam-6007	492	24	engwerda	engwerda	PROPN
ejpam-6007	492	25	.	.	PUNCT
ejpam-6007	493	1	open	open	ADJ
ejpam-6007	493	2	-	-	PUNCT
ejpam-6007	493	3	loop	loop	NOUN
ejpam-6007	493	4	nash	nash	NOUN
ejpam-6007	493	5	equilibria	equilibrium	NOUN
ejpam-6007	493	6	in	in	ADP
ejpam-6007	493	7	lq	lq	NOUN
ejpam-6007	493	8	-	-	PUNCT
ejpam-6007	493	9	games	game	NOUN
ejpam-6007	493	10	.	.	PUNCT
ejpam-6007	494	1	journal	journal	PROPN
ejpam-6007	494	2	of	of	ADP
ejpam-6007	494	3	economic	economic	ADJ
ejpam-6007	494	4	dynamics	dynamic	NOUN
ejpam-6007	494	5	and	and	CCONJ
ejpam-6007	494	6	control	control	NOUN
ejpam-6007	494	7	,	,	PUNCT
ejpam-6007	494	8	22:29–50	22:29–50	NUM
ejpam-6007	494	9	,	,	PUNCT
ejpam-6007	494	10	1998	1998	NUM
ejpam-6007	494	11	.	.	PUNCT
ejpam-6007	495	1	[	[	X
ejpam-6007	495	2	15	15	NUM
ejpam-6007	495	3	]	]	X
ejpam-6007	495	4	e.	e.	PROPN
ejpam-6007	495	5	youness	youness	PROPN
ejpam-6007	495	6	.	.	PUNCT
ejpam-6007	496	1	a	a	DET
ejpam-6007	496	2	fuzzy	fuzzy	ADJ
ejpam-6007	496	3	min	min	ADJ
ejpam-6007	496	4	-	-	ADJ
ejpam-6007	496	5	max	max	ADJ
ejpam-6007	496	6	differential	differential	ADJ
ejpam-6007	496	7	game	game	NOUN
ejpam-6007	496	8	problem	problem	NOUN
ejpam-6007	496	9	.	.	PUNCT
ejpam-6007	497	1	fuzzy	fuzzy	ADJ
ejpam-6007	497	2	sets	set	NOUN
ejpam-6007	497	3	and	and	CCONJ
ejpam-6007	497	4	systems	system	NOUN
ejpam-6007	497	5	,	,	PUNCT
ejpam-6007	497	6	122:465–474	122:465–474	NUM
ejpam-6007	497	7	,	,	PUNCT
ejpam-6007	497	8	2001	2001	NUM
ejpam-6007	497	9	.	.	PUNCT
ejpam-6007	498	1	[	[	X
ejpam-6007	498	2	16	16	NUM
ejpam-6007	498	3	]	]	X
ejpam-6007	498	4	e.	e.	PROPN
ejpam-6007	498	5	youness	youness	PROPN
ejpam-6007	498	6	.	.	PUNCT
ejpam-6007	499	1	large	large	ADJ
ejpam-6007	499	2	scale	scale	NOUN
ejpam-6007	499	3	fuzzy	fuzzy	ADJ
ejpam-6007	499	4	differential	differential	NOUN
ejpam-6007	499	5	games	game	NOUN
ejpam-6007	499	6	.	.	PUNCT
ejpam-6007	500	1	applied	apply	VERB
ejpam-6007	500	2	mathematics	mathematic	NOUN
ejpam-6007	500	3	and	and	CCONJ
ejpam-6007	500	4	computation	computation	NOUN
ejpam-6007	500	5	,	,	PUNCT
ejpam-6007	500	6	142:225–234	142:225–234	NUM
ejpam-6007	500	7	,	,	PUNCT
ejpam-6007	500	8	2003	2003	NUM
ejpam-6007	500	9	.	.	PUNCT
ejpam-6007	501	1	[	[	X
ejpam-6007	501	2	17	17	NUM
ejpam-6007	501	3	]	]	X
ejpam-6007	501	4	a.a	a.a	PROPN
ejpam-6007	501	5	.	.	PROPN
ejpam-6007	501	6	megahed	megahed	PROPN
ejpam-6007	501	7	.	.	PUNCT
ejpam-6007	502	1	a	a	DET
ejpam-6007	502	2	min	min	ADJ
ejpam-6007	502	3	-	-	ADJ
ejpam-6007	502	4	max	max	PROPN
ejpam-6007	502	5	differential	differential	ADJ
ejpam-6007	502	6	game	game	NOUN
ejpam-6007	502	7	applied	apply	VERB
ejpam-6007	502	8	to	to	ADP
ejpam-6007	502	9	terrorism	terrorism	NOUN
ejpam-6007	502	10	.	.	PUNCT
ejpam-6007	503	1	applied	apply	VERB
ejpam-6007	503	2	mathematics	mathematic	NOUN
ejpam-6007	503	3	and	and	CCONJ
ejpam-6007	503	4	computation	computation	NOUN
ejpam-6007	503	5	,	,	PUNCT
ejpam-6007	503	6	198:446–455	198:446–455	NUM
ejpam-6007	503	7	,	,	PUNCT
ejpam-6007	503	8	2008	2008	NUM
ejpam-6007	503	9	.	.	PUNCT
ejpam-6007	504	1	[	[	X
ejpam-6007	504	2	18	18	NUM
ejpam-6007	504	3	]	]	PUNCT
ejpam-6007	504	4	ebrahim	ebrahim	PROPN
ejpam-6007	504	5	a.	a.	PROPN
ejpam-6007	504	6	youness	youness	PROPN
ejpam-6007	504	7	et	et	PROPN
ejpam-6007	504	8	al	al	PROPN
ejpam-6007	504	9	.	.	PROPN
ejpam-6007	504	10	min	min	PROPN
ejpam-6007	504	11	-	-	ADJ
ejpam-6007	504	12	max	max	PROPN
ejpam-6007	504	13	differential	differential	ADJ
ejpam-6007	504	14	game	game	NOUN
ejpam-6007	504	15	with	with	ADP
ejpam-6007	504	16	partial	partial	ADJ
ejpam-6007	504	17	differential	differential	NOUN
ejpam-6007	504	18	equation	equation	NOUN
ejpam-6007	504	19	.	.	PUNCT
ejpam-6007	505	1	aims	aim	VERB
ejpam-6007	505	2	mathematics	mathematic	NOUN
ejpam-6007	505	3	,	,	PUNCT
ejpam-6007	505	4	7:13777–13789	7:13777–13789	ADV
ejpam-6007	505	5	,	,	PUNCT
ejpam-6007	505	6	2022	2022	NUM
ejpam-6007	505	7	.	.	PUNCT
ejpam-6007	506	1	[	[	X
ejpam-6007	506	2	19	19	NUM
ejpam-6007	506	3	]	]	X
ejpam-6007	506	4	kendall	kendall	PROPN
ejpam-6007	506	5	e.	e.	PROPN
ejpam-6007	506	6	atkinson	atkinson	PROPN
ejpam-6007	506	7	.	.	PUNCT
ejpam-6007	507	1	numerical	numerical	ADJ
ejpam-6007	507	2	methods	method	NOUN
ejpam-6007	507	3	for	for	ADP
ejpam-6007	507	4	ordinary	ordinary	ADJ
ejpam-6007	507	5	differential	differential	ADJ
ejpam-6007	507	6	equations	equation	NOUN
ejpam-6007	507	7	.	.	PUNCT
ejpam-6007	508	1	wiley	wiley	PROPN
ejpam-6007	508	2	,	,	PUNCT
ejpam-6007	508	3	1989	1989	NUM
ejpam-6007	508	4	.	.	PUNCT
ejpam-6007	509	1	[	[	X
ejpam-6007	509	2	20	20	NUM
ejpam-6007	509	3	]	]	PUNCT
ejpam-6007	509	4	ebrahim	ebrahim	PROPN
ejpam-6007	509	5	youness	youness	NOUN
ejpam-6007	509	6	and	and	CCONJ
ejpam-6007	509	7	abd	abd	PROPN
ejpam-6007	509	8	el	el	PROPN
ejpam-6007	509	9	-	-	PUNCT
ejpam-6007	509	10	moneim	moneim	NOUN
ejpam-6007	509	11	megahed	megahe	VERB
ejpam-6007	509	12	.	.	PUNCT
ejpam-6007	510	1	a	a	DET
ejpam-6007	510	2	study	study	NOUN
ejpam-6007	510	3	on	on	ADP
ejpam-6007	510	4	fuzzy	fuzzy	ADJ
ejpam-6007	510	5	differential	differential	ADJ
ejpam-6007	510	6	game	game	NOUN
ejpam-6007	510	7	.	.	PUNCT
ejpam-6007	511	1	le	le	PROPN
ejpam-6007	511	2	matematiche	matematiche	PROPN
ejpam-6007	511	3	,	,	PUNCT
ejpam-6007	511	4	56:97–107	56:97–107	NUM
ejpam-6007	511	5	,	,	PUNCT
ejpam-6007	511	6	2001	2001	NUM
ejpam-6007	511	7	.	.	PUNCT