id	sid	tid	token	lemma	pos
ejpam-447	1	1	10_447_zayed.dvi	10_447_zayed.dvi	NUM
ejpam-447	1	2	european	european	ADJ
ejpam-447	1	3	journal	journal	NOUN
ejpam-447	1	4	of	of	ADP
ejpam-447	1	5	pure	pure	ADJ
ejpam-447	1	6	and	and	CCONJ
ejpam-447	1	7	applied	apply	VERB
ejpam-447	1	8	mathematics	mathematic	NOUN
ejpam-447	1	9	vol	vol	NOUN
ejpam-447	1	10	.	.	PUNCT
ejpam-447	2	1	3	3	NUM
ejpam-447	2	2	,	,	PUNCT
ejpam-447	2	3	no	no	INTJ
ejpam-447	2	4	.	.	NOUN
ejpam-447	2	5	2	2	NUM
ejpam-447	2	6	,	,	PUNCT
ejpam-447	2	7	2010	2010	NUM
ejpam-447	2	8	,	,	PUNCT
ejpam-447	2	9	254	254	NUM
ejpam-447	2	10	-	-	SYM
ejpam-447	2	11	268	268	NUM
ejpam-447	2	12	issn	issn	PROPN
ejpam-447	2	13	1307	1307	NUM
ejpam-447	2	14	-	-	SYM
ejpam-447	2	15	5543	5543	NUM
ejpam-447	2	16	–	–	PUNCT
ejpam-447	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-447	2	18	dynamics	dynamic	NOUN
ejpam-447	2	19	of	of	ADP
ejpam-447	2	20	the	the	DET
ejpam-447	2	21	nonlinear	nonlinear	ADJ
ejpam-447	2	22	rational	rational	ADJ
ejpam-447	2	23	difference	difference	NOUN
ejpam-447	2	24	equation	equation	NOUN
ejpam-447	2	25	xn+1	xn+1	NUM
ejpam-447	2	26	=	=	SYM
ejpam-447	2	27	axn+	axn+	PUNCT
ejpam-447	2	28	bxn−k+	bxn−k+	PROPN
ejpam-447	2	29	pxn+xn−k	pxn+xn−k	PROPN
ejpam-447	2	30	q+xn−k	q+xn−k	PROPN
ejpam-447	2	31	e.	e.	PROPN
ejpam-447	2	32	m.	m.	PROPN
ejpam-447	2	33	e.	e.	PROPN
ejpam-447	2	34	zayed	zayed	PROPN
ejpam-447	2	35	mathematics	mathematics	PROPN
ejpam-447	2	36	department	department	PROPN
ejpam-447	2	37	,	,	PUNCT
ejpam-447	2	38	faculty	faculty	NOUN
ejpam-447	2	39	of	of	ADP
ejpam-447	2	40	science	science	NOUN
ejpam-447	2	41	,	,	PUNCT
ejpam-447	2	42	taif	taif	PROPN
ejpam-447	2	43	university	university	PROPN
ejpam-447	2	44	,	,	PUNCT
ejpam-447	2	45	el	el	PROPN
ejpam-447	2	46	-	-	PUNCT
ejpam-447	2	47	taif	taif	PROPN
ejpam-447	2	48	,	,	PUNCT
ejpam-447	2	49	el	el	PROPN
ejpam-447	2	50	-	-	PUNCT
ejpam-447	2	51	hawiyah	hawiyah	NOUN
ejpam-447	2	52	,	,	PUNCT
ejpam-447	2	53	kingdom	kingdom	NOUN
ejpam-447	2	54	of	of	ADP
ejpam-447	2	55	saudi	saudi	PROPN
ejpam-447	2	56	arabia	arabia	PROPN
ejpam-447	2	57	previously	previously	ADV
ejpam-447	2	58	:	:	PUNCT
ejpam-447	2	59	mathematics	mathematics	PROPN
ejpam-447	2	60	department	department	PROPN
ejpam-447	2	61	,	,	PUNCT
ejpam-447	2	62	faculty	faculty	NOUN
ejpam-447	2	63	of	of	ADP
ejpam-447	2	64	science	science	NOUN
ejpam-447	2	65	,	,	PUNCT
ejpam-447	2	66	zagazig	zagazig	PROPN
ejpam-447	2	67	university	university	PROPN
ejpam-447	2	68	,	,	PUNCT
ejpam-447	2	69	zagazig	zagazig	PROPN
ejpam-447	2	70	,	,	PUNCT
ejpam-447	2	71	egypt	egypt	PROPN
ejpam-447	2	72	abstract	abstract	PROPN
ejpam-447	2	73	.	.	PUNCT
ejpam-447	3	1	in	in	ADP
ejpam-447	3	2	this	this	DET
ejpam-447	3	3	article	article	NOUN
ejpam-447	3	4	,	,	PUNCT
ejpam-447	3	5	we	we	PRON
ejpam-447	3	6	study	study	VERB
ejpam-447	3	7	the	the	DET
ejpam-447	3	8	global	global	ADJ
ejpam-447	3	9	stability	stability	NOUN
ejpam-447	3	10	and	and	CCONJ
ejpam-447	3	11	the	the	DET
ejpam-447	3	12	asymptotic	asymptotic	ADJ
ejpam-447	3	13	properties	property	NOUN
ejpam-447	3	14	of	of	ADP
ejpam-447	3	15	the	the	DET
ejpam-447	3	16	nonnegative	nonnegative	ADJ
ejpam-447	3	17	solutions	solution	NOUN
ejpam-447	3	18	of	of	ADP
ejpam-447	3	19	the	the	DET
ejpam-447	3	20	nonlinear	nonlinear	ADJ
ejpam-447	3	21	difference	difference	NOUN
ejpam-447	3	22	equation	equation	NOUN
ejpam-447	3	23	xn+1	xn+1	PROPN
ejpam-447	4	1	=	=	PUNCT
ejpam-447	4	2	axn	axn	PROPN
ejpam-447	4	3	+	+	CCONJ
ejpam-447	4	4	bxn−k	bxn−k	PROPN
ejpam-447	4	5	+	+	CCONJ
ejpam-447	4	6	�	�	PROPN
ejpam-447	4	7	pxn	pxn	VERB
ejpam-447	4	8	+	+	CCONJ
ejpam-447	4	9	xn−k	xn−k	PROPN
ejpam-447	4	10	�	�	PROPN
ejpam-447	4	11	/	/	SYM
ejpam-447	4	12	�	�	PROPN
ejpam-447	4	13	q+	q+	PUNCT
ejpam-447	4	14	xn−k	xn−k	PROPN
ejpam-447	4	15	�	�	PROPN
ejpam-447	4	16	,	,	PUNCT
ejpam-447	4	17	n=	n=	ADJ
ejpam-447	4	18	0,1,2	0,1,2	NOUN
ejpam-447	4	19	,	,	PUNCT
ejpam-447	4	20	.....	.....	PUNCT
ejpam-447	4	21	where	where	SCONJ
ejpam-447	4	22	the	the	DET
ejpam-447	4	23	parameters	parameter	NOUN
ejpam-447	4	24	a	a	DET
ejpam-447	4	25	,	,	PUNCT
ejpam-447	4	26	b	b	PROPN
ejpam-447	4	27	,	,	PUNCT
ejpam-447	4	28	p	p	X
ejpam-447	4	29	,	,	PUNCT
ejpam-447	4	30	q	q	NOUN
ejpam-447	4	31	and	and	CCONJ
ejpam-447	4	32	the	the	DET
ejpam-447	4	33	initial	initial	ADJ
ejpam-447	4	34	conditions	condition	NOUN
ejpam-447	4	35	x−k	x−k	PROPN
ejpam-447	4	36	,	,	PUNCT
ejpam-447	4	37	...	...	PUNCT
ejpam-447	4	38	,	,	PUNCT
ejpam-447	4	39	x−1	x−1	PROPN
ejpam-447	4	40	,	,	PUNCT
ejpam-447	4	41	x0	x0	PROPN
ejpam-447	4	42	are	be	AUX
ejpam-447	4	43	arbitrary	arbitrary	ADJ
ejpam-447	4	44	nonnegative	nonnegative	ADJ
ejpam-447	4	45	real	real	ADJ
ejpam-447	4	46	numbers	number	NOUN
ejpam-447	4	47	,	,	PUNCT
ejpam-447	4	48	while	while	SCONJ
ejpam-447	4	49	k	k	PROPN
ejpam-447	4	50	is	be	AUX
ejpam-447	4	51	a	a	DET
ejpam-447	4	52	positive	positive	ADJ
ejpam-447	4	53	integer	integer	NOUN
ejpam-447	4	54	number	number	NOUN
ejpam-447	4	55	.	.	PUNCT
ejpam-447	5	1	some	some	DET
ejpam-447	5	2	numerical	numerical	ADJ
ejpam-447	5	3	examples	example	NOUN
ejpam-447	5	4	will	will	AUX
ejpam-447	5	5	be	be	AUX
ejpam-447	5	6	given	give	VERB
ejpam-447	5	7	to	to	PART
ejpam-447	5	8	illustrate	illustrate	VERB
ejpam-447	5	9	our	our	PRON
ejpam-447	5	10	results	result	NOUN
ejpam-447	5	11	.	.	PUNCT
ejpam-447	6	1	2000	2000	NUM
ejpam-447	6	2	mathematics	mathematic	NOUN
ejpam-447	6	3	subject	subject	NOUN
ejpam-447	6	4	classifications	classification	NOUN
ejpam-447	6	5	:	:	PUNCT
ejpam-447	6	6	39a10,39a11,39a99,34c99	39a10,39a11,39a99,34c99	NUM
ejpam-447	6	7	key	key	ADJ
ejpam-447	6	8	words	word	NOUN
ejpam-447	6	9	and	and	CCONJ
ejpam-447	6	10	phrases	phrase	NOUN
ejpam-447	6	11	:	:	PUNCT
ejpam-447	6	12	difference	difference	NOUN
ejpam-447	6	13	equations	equation	NOUN
ejpam-447	6	14	,	,	PUNCT
ejpam-447	6	15	prime	prime	ADJ
ejpam-447	6	16	period	period	NOUN
ejpam-447	6	17	two	two	NUM
ejpam-447	6	18	solution	solution	NOUN
ejpam-447	6	19	,	,	PUNCT
ejpam-447	6	20	locally	locally	ADV
ejpam-447	6	21	asymptotically	asymptotically	ADV
ejpam-447	6	22	stable	stable	ADJ
ejpam-447	6	23	,	,	PUNCT
ejpam-447	6	24	global	global	ADJ
ejpam-447	6	25	attractor	attractor	NOUN
ejpam-447	6	26	,	,	PUNCT
ejpam-447	6	27	global	global	ADJ
ejpam-447	6	28	stability	stability	NOUN
ejpam-447	6	29	.	.	PUNCT
ejpam-447	7	1	1	1	X
ejpam-447	7	2	.	.	X
ejpam-447	7	3	introduction	introduction	NOUN
ejpam-447	7	4	the	the	DET
ejpam-447	7	5	qualitative	qualitative	ADJ
ejpam-447	7	6	study	study	NOUN
ejpam-447	7	7	of	of	ADP
ejpam-447	7	8	difference	difference	NOUN
ejpam-447	7	9	equations	equation	NOUN
ejpam-447	7	10	is	be	AUX
ejpam-447	7	11	a	a	DET
ejpam-447	7	12	fertile	fertile	ADJ
ejpam-447	7	13	research	research	NOUN
ejpam-447	7	14	area	area	NOUN
ejpam-447	7	15	and	and	CCONJ
ejpam-447	7	16	increasingly	increasingly	ADV
ejpam-447	7	17	attracts	attract	VERB
ejpam-447	7	18	many	many	ADJ
ejpam-447	7	19	mathematicians	mathematician	NOUN
ejpam-447	7	20	.	.	PUNCT
ejpam-447	8	1	this	this	DET
ejpam-447	8	2	topic	topic	NOUN
ejpam-447	8	3	draws	draw	VERB
ejpam-447	8	4	its	its	PRON
ejpam-447	8	5	importance	importance	NOUN
ejpam-447	8	6	from	from	ADP
ejpam-447	8	7	the	the	DET
ejpam-447	8	8	fact	fact	NOUN
ejpam-447	8	9	that	that	SCONJ
ejpam-447	8	10	many	many	ADJ
ejpam-447	8	11	real	real	ADJ
ejpam-447	8	12	life	life	NOUN
ejpam-447	8	13	phenomena	phenomenon	NOUN
ejpam-447	8	14	are	be	AUX
ejpam-447	8	15	modeled	model	VERB
ejpam-447	8	16	using	use	VERB
ejpam-447	8	17	difference	difference	NOUN
ejpam-447	8	18	equations	equation	NOUN
ejpam-447	8	19	.	.	PUNCT
ejpam-447	9	1	examples	example	NOUN
ejpam-447	9	2	from	from	ADP
ejpam-447	9	3	economy	economy	NOUN
ejpam-447	9	4	,	,	PUNCT
ejpam-447	9	5	biology	biology	NOUN
ejpam-447	9	6	,	,	PUNCT
ejpam-447	9	7	etc	etc	X
ejpam-447	9	8	.	.	X
ejpam-447	9	9	can	can	AUX
ejpam-447	9	10	be	be	AUX
ejpam-447	9	11	found	find	VERB
ejpam-447	9	12	in	in	ADP
ejpam-447	9	13	[	[	X
ejpam-447	9	14	2,16,19,29	2,16,19,29	NUM
ejpam-447	9	15	]	]	PUNCT
ejpam-447	9	16	.	.	PUNCT
ejpam-447	10	1	it	it	PRON
ejpam-447	10	2	is	be	AUX
ejpam-447	10	3	known	know	VERB
ejpam-447	10	4	that	that	SCONJ
ejpam-447	10	5	nonlinear	nonlinear	ADJ
ejpam-447	10	6	difference	difference	NOUN
ejpam-447	10	7	equations	equation	NOUN
ejpam-447	10	8	are	be	AUX
ejpam-447	10	9	capable	capable	ADJ
ejpam-447	10	10	of	of	ADP
ejpam-447	10	11	producing	produce	VERB
ejpam-447	10	12	a	a	DET
ejpam-447	10	13	complicated	complicated	ADJ
ejpam-447	10	14	behavior	behavior	NOUN
ejpam-447	10	15	regardless	regardless	ADV
ejpam-447	10	16	its	its	PRON
ejpam-447	10	17	order	order	NOUN
ejpam-447	10	18	.	.	PUNCT
ejpam-447	11	1	this	this	PRON
ejpam-447	11	2	can	can	AUX
ejpam-447	11	3	be	be	AUX
ejpam-447	11	4	easily	easily	ADV
ejpam-447	11	5	seen	see	VERB
ejpam-447	11	6	from	from	ADP
ejpam-447	11	7	the	the	DET
ejpam-447	11	8	family	family	NOUN
ejpam-447	11	9	xn+1	xn+1	PROPN
ejpam-447	11	10	=	=	SYM
ejpam-447	11	11	gµ	gµ	PROPN
ejpam-447	11	12	�	�	PROPN
ejpam-447	11	13	xn	xn	PROPN
ejpam-447	11	14	�	�	PROPN
ejpam-447	11	15	,	,	PUNCT
ejpam-447	11	16	µ	µ	X
ejpam-447	11	17	>	>	X
ejpam-447	11	18	0	0	PROPN
ejpam-447	11	19	,	,	PUNCT
ejpam-447	11	20	n≥	n≥	PROPN
ejpam-447	11	21	0	0	NUM
ejpam-447	11	22	.	.	PUNCT
ejpam-447	12	1	this	this	DET
ejpam-447	12	2	behavior	behavior	NOUN
ejpam-447	12	3	is	be	AUX
ejpam-447	12	4	ranging	range	VERB
ejpam-447	12	5	according	accord	VERB
ejpam-447	12	6	to	to	ADP
ejpam-447	12	7	the	the	DET
ejpam-447	12	8	value	value	NOUN
ejpam-447	12	9	of	of	ADP
ejpam-447	12	10	µ	µ	NOUN
ejpam-447	12	11	,	,	PUNCT
ejpam-447	12	12	from	from	ADP
ejpam-447	12	13	the	the	DET
ejpam-447	12	14	existence	existence	NOUN
ejpam-447	12	15	of	of	ADP
ejpam-447	12	16	a	a	DET
ejpam-447	12	17	bounded	bounded	ADJ
ejpam-447	12	18	number	number	NOUN
ejpam-447	12	19	of	of	ADP
ejpam-447	12	20	periodic	periodic	ADJ
ejpam-447	12	21	solutions	solution	NOUN
ejpam-447	12	22	to	to	PART
ejpam-447	12	23	chaos	chaos	VERB
ejpam-447	12	24	.	.	PUNCT
ejpam-447	13	1	there	there	PRON
ejpam-447	13	2	has	have	AUX
ejpam-447	13	3	been	be	AUX
ejpam-447	13	4	a	a	DET
ejpam-447	13	5	great	great	ADJ
ejpam-447	13	6	interest	interest	NOUN
ejpam-447	13	7	in	in	ADP
ejpam-447	13	8	studying	study	VERB
ejpam-447	13	9	the	the	DET
ejpam-447	13	10	global	global	ADJ
ejpam-447	13	11	attractivity	attractivity	PROPN
ejpam-447	13	12	,	,	PUNCT
ejpam-447	13	13	the	the	DET
ejpam-447	13	14	boundedness	boundedness	NOUN
ejpam-447	13	15	character	character	NOUN
ejpam-447	13	16	and	and	CCONJ
ejpam-447	13	17	the	the	DET
ejpam-447	13	18	periodicity	periodicity	NOUN
ejpam-447	13	19	nature	nature	NOUN
ejpam-447	13	20	of	of	ADP
ejpam-447	13	21	nonlinear	nonlinear	ADJ
ejpam-447	13	22	difference	difference	NOUN
ejpam-447	13	23	equations	equation	NOUN
ejpam-447	13	24	.	.	PUNCT
ejpam-447	14	1	for	for	ADP
ejpam-447	14	2	example	example	NOUN
ejpam-447	14	3	,	,	PUNCT
ejpam-447	14	4	in	in	ADP
ejpam-447	14	5	the	the	DET
ejpam-447	14	6	articles	article	NOUN
ejpam-447	14	7	[	[	X
ejpam-447	14	8	1,7	1,7	NUM
ejpam-447	14	9	-	-	SYM
ejpam-447	14	10	14,21–31	14,21–31	NUM
ejpam-447	14	11	]	]	PUNCT
ejpam-447	14	12	closely	closely	ADV
ejpam-447	14	13	related	relate	VERB
ejpam-447	14	14	global	global	ADJ
ejpam-447	14	15	convergence	convergence	NOUN
ejpam-447	14	16	results	result	NOUN
ejpam-447	14	17	were	be	AUX
ejpam-447	14	18	obtained	obtain	VERB
ejpam-447	14	19	which	which	PRON
ejpam-447	14	20	can	can	AUX
ejpam-447	14	21	be	be	AUX
ejpam-447	14	22	applied	apply	VERB
ejpam-447	14	23	to	to	ADP
ejpam-447	14	24	nonlinear	nonlinear	ADJ
ejpam-447	14	25	difference	difference	NOUN
ejpam-447	14	26	equations	equation	NOUN
ejpam-447	14	27	in	in	ADP
ejpam-447	14	28	proving	prove	VERB
ejpam-447	14	29	that	that	SCONJ
ejpam-447	14	30	every	every	DET
ejpam-447	14	31	solution	solution	NOUN
ejpam-447	14	32	of	of	ADP
ejpam-447	14	33	these	these	DET
ejpam-447	14	34	equations	equation	NOUN
ejpam-447	14	35	converges	converge	VERB
ejpam-447	14	36	email	email	NOUN
ejpam-447	14	37	address	address	NOUN
ejpam-447	14	38	:	:	PUNCT
ejpam-447	14	39	emezayed	emezaye	VERB
ejpam-447	14	40	�	�	NOUN
ejpam-447	14	41	hotmail	hotmail	NOUN
ejpam-447	14	42	.	.	PUNCT
ejpam-447	15	1	om	om	PROPN
ejpam-447	15	2	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-447	16	1	254	254	NUM
ejpam-447	16	2	c	c	X
ejpam-447	16	3	©	©	PROPN
ejpam-447	16	4	2010	2010	NUM
ejpam-447	16	5	ejpam	ejpam	NOUN
ejpam-447	16	6	all	all	DET
ejpam-447	16	7	rights	right	NOUN
ejpam-447	16	8	reserved	reserve	VERB
ejpam-447	16	9	.	.	PUNCT
ejpam-447	17	1	e.	e.	PROPN
ejpam-447	17	2	zayed	zayed	PROPN
ejpam-447	17	3	/	/	SYM
ejpam-447	17	4	eur	eur	PROPN
ejpam-447	17	5	.	.	PUNCT
ejpam-447	18	1	j.	j.	PROPN
ejpam-447	18	2	pure	pure	PROPN
ejpam-447	18	3	appl	appl	PROPN
ejpam-447	18	4	.	.	PROPN
ejpam-447	18	5	math	math	PROPN
ejpam-447	18	6	,	,	PUNCT
ejpam-447	18	7	3	3	NUM
ejpam-447	18	8	(	(	PUNCT
ejpam-447	18	9	2010	2010	NUM
ejpam-447	18	10	)	)	PUNCT
ejpam-447	18	11	,	,	PUNCT
ejpam-447	18	12	254	254	NUM
ejpam-447	18	13	-	-	SYM
ejpam-447	18	14	268	268	NUM
ejpam-447	18	15	255	255	NUM
ejpam-447	18	16	to	to	ADP
ejpam-447	18	17	a	a	DET
ejpam-447	18	18	period	period	NOUN
ejpam-447	18	19	two	two	NUM
ejpam-447	18	20	solution	solution	NOUN
ejpam-447	18	21	.	.	PUNCT
ejpam-447	19	1	for	for	ADP
ejpam-447	19	2	other	other	ADJ
ejpam-447	19	3	closely	closely	ADV
ejpam-447	19	4	related	relate	VERB
ejpam-447	19	5	results	result	NOUN
ejpam-447	19	6	,	,	PUNCT
ejpam-447	19	7	(	(	PUNCT
ejpam-447	19	8	see	see	VERB
ejpam-447	19	9	[	[	X
ejpam-447	19	10	3	3	NUM
ejpam-447	19	11	-	-	NUM
ejpam-447	19	12	7,10,17,18	7,10,17,18	NOUN
ejpam-447	19	13	]	]	PUNCT
ejpam-447	19	14	)	)	PUNCT
ejpam-447	19	15	and	and	CCONJ
ejpam-447	19	16	the	the	DET
ejpam-447	19	17	references	reference	NOUN
ejpam-447	19	18	cited	cite	VERB
ejpam-447	19	19	therein	therein	ADV
ejpam-447	19	20	.	.	PUNCT
ejpam-447	20	1	the	the	DET
ejpam-447	20	2	study	study	NOUN
ejpam-447	20	3	of	of	ADP
ejpam-447	20	4	these	these	DET
ejpam-447	20	5	equations	equation	NOUN
ejpam-447	20	6	is	be	AUX
ejpam-447	20	7	challenging	challenge	VERB
ejpam-447	20	8	and	and	CCONJ
ejpam-447	20	9	rewarding	rewarding	ADJ
ejpam-447	20	10	and	and	CCONJ
ejpam-447	20	11	is	be	AUX
ejpam-447	20	12	still	still	ADV
ejpam-447	20	13	in	in	ADP
ejpam-447	20	14	its	its	PRON
ejpam-447	20	15	infancy	infancy	NOUN
ejpam-447	20	16	.	.	PUNCT
ejpam-447	21	1	we	we	PRON
ejpam-447	21	2	believe	believe	VERB
ejpam-447	21	3	that	that	SCONJ
ejpam-447	21	4	the	the	DET
ejpam-447	21	5	nonlinear	nonlinear	ADJ
ejpam-447	21	6	rational	rational	ADJ
ejpam-447	21	7	difference	difference	NOUN
ejpam-447	21	8	equations	equation	NOUN
ejpam-447	21	9	are	be	AUX
ejpam-447	21	10	of	of	ADP
ejpam-447	21	11	paramount	paramount	ADJ
ejpam-447	21	12	importance	importance	NOUN
ejpam-447	21	13	in	in	ADP
ejpam-447	21	14	their	their	PRON
ejpam-447	21	15	own	own	ADJ
ejpam-447	21	16	right	right	NOUN
ejpam-447	21	17	.	.	PUNCT
ejpam-447	22	1	furthermore	furthermore	ADV
ejpam-447	22	2	the	the	DET
ejpam-447	22	3	results	result	NOUN
ejpam-447	22	4	about	about	ADP
ejpam-447	22	5	such	such	ADJ
ejpam-447	22	6	equations	equation	NOUN
ejpam-447	22	7	offer	offer	VERB
ejpam-447	22	8	prototypes	prototype	NOUN
ejpam-447	22	9	for	for	ADP
ejpam-447	22	10	the	the	DET
ejpam-447	22	11	development	development	NOUN
ejpam-447	22	12	of	of	ADP
ejpam-447	22	13	the	the	DET
ejpam-447	22	14	basic	basic	ADJ
ejpam-447	22	15	theory	theory	NOUN
ejpam-447	22	16	of	of	ADP
ejpam-447	22	17	the	the	DET
ejpam-447	22	18	global	global	ADJ
ejpam-447	22	19	behavior	behavior	NOUN
ejpam-447	22	20	of	of	ADP
ejpam-447	22	21	nonlinear	nonlinear	ADJ
ejpam-447	22	22	difference	difference	NOUN
ejpam-447	22	23	equations	equation	NOUN
ejpam-447	22	24	.	.	PUNCT
ejpam-447	23	1	our	our	PRON
ejpam-447	23	2	goal	goal	NOUN
ejpam-447	23	3	in	in	ADP
ejpam-447	23	4	this	this	DET
ejpam-447	23	5	article	article	NOUN
ejpam-447	23	6	is	be	AUX
ejpam-447	23	7	to	to	PART
ejpam-447	23	8	investigate	investigate	VERB
ejpam-447	23	9	some	some	DET
ejpam-447	23	10	qualitative	qualitative	ADJ
ejpam-447	23	11	behavior	behavior	NOUN
ejpam-447	23	12	of	of	ADP
ejpam-447	23	13	the	the	DET
ejpam-447	23	14	solutions	solution	NOUN
ejpam-447	23	15	of	of	ADP
ejpam-447	23	16	the	the	DET
ejpam-447	23	17	nonlinear	nonlinear	ADJ
ejpam-447	23	18	difference	difference	NOUN
ejpam-447	23	19	equation	equation	NOUN
ejpam-447	23	20	xn+1	xn+1	PUNCT
ejpam-447	23	21	=	=	PUNCT
ejpam-447	23	22	axn+	axn+	PROPN
ejpam-447	23	23	bxn−k	bxn−k	PROPN
ejpam-447	23	24	+	+	CCONJ
ejpam-447	23	25	pxn+	pxn+	PROPN
ejpam-447	23	26	xn−k	xn−k	PROPN
ejpam-447	23	27	q+	q+	PROPN
ejpam-447	23	28	xn−k	xn−k	PROPN
ejpam-447	23	29	,	,	PUNCT
ejpam-447	23	30	n	n	PROPN
ejpam-447	23	31	=	=	SYM
ejpam-447	23	32	0,1,2	0,1,2	NUM
ejpam-447	23	33	,	,	PUNCT
ejpam-447	23	34	..	..	PUNCT
ejpam-447	23	35	.	.	PUNCT
ejpam-447	23	36	.	.	PUNCT
ejpam-447	23	37	.	.	PUNCT
ejpam-447	24	1	(	(	PUNCT
ejpam-447	24	2	1	1	X
ejpam-447	24	3	)	)	PUNCT
ejpam-447	24	4	where	where	SCONJ
ejpam-447	24	5	the	the	DET
ejpam-447	24	6	parameters	parameter	NOUN
ejpam-447	24	7	a	a	PRON
ejpam-447	24	8	,	,	PUNCT
ejpam-447	24	9	b	b	PROPN
ejpam-447	24	10	,	,	PUNCT
ejpam-447	24	11	p	p	X
ejpam-447	24	12	,	,	PUNCT
ejpam-447	24	13	q	q	NOUN
ejpam-447	24	14	and	and	CCONJ
ejpam-447	24	15	the	the	DET
ejpam-447	24	16	initial	initial	ADJ
ejpam-447	24	17	conditions	condition	NOUN
ejpam-447	24	18	x−k	x−k	PROPN
ejpam-447	24	19	,	,	PUNCT
ejpam-447	24	20	.	.	PUNCT
ejpam-447	24	21	.	.	PUNCT
ejpam-447	24	22	.	.	PUNCT
ejpam-447	25	1	x−1	x−1	PROPN
ejpam-447	25	2	,	,	PUNCT
ejpam-447	25	3	x0	x0	PROPN
ejpam-447	25	4	are	be	AUX
ejpam-447	25	5	arbitrary	arbitrary	ADJ
ejpam-447	25	6	nonnegative	nonnegative	ADJ
ejpam-447	25	7	real	real	ADJ
ejpam-447	25	8	numbers	number	NOUN
ejpam-447	25	9	,	,	PUNCT
ejpam-447	25	10	while	while	SCONJ
ejpam-447	25	11	k	k	PROPN
ejpam-447	25	12	is	be	AUX
ejpam-447	25	13	a	a	DET
ejpam-447	25	14	positive	positive	ADJ
ejpam-447	25	15	integer	integer	NOUN
ejpam-447	25	16	number	number	NOUN
ejpam-447	25	17	.	.	PUNCT
ejpam-447	26	1	the	the	DET
ejpam-447	26	2	global	global	ADJ
ejpam-447	26	3	stability	stability	NOUN
ejpam-447	26	4	of	of	ADP
ejpam-447	26	5	eq.(1	eq.(1	ADJ
ejpam-447	26	6	)	)	PUNCT
ejpam-447	26	7	for	for	ADP
ejpam-447	26	8	a=	a=	PROPN
ejpam-447	26	9	b	b	X
ejpam-447	26	10	=	=	SYM
ejpam-447	26	11	0	0	PROPN
ejpam-447	26	12	has	have	AUX
ejpam-447	26	13	been	be	AUX
ejpam-447	26	14	investigated	investigate	VERB
ejpam-447	26	15	in	in	ADP
ejpam-447	26	16	[	[	X
ejpam-447	26	17	29	29	NUM
ejpam-447	26	18	]	]	PUNCT
ejpam-447	26	19	.	.	PUNCT
ejpam-447	27	1	kulenvic	kulenvic	PROPN
ejpam-447	27	2	et	et	PROPN
ejpam-447	27	3	al.[22	al.[22	PROPN
ejpam-447	27	4	]	]	PUNCT
ejpam-447	27	5	studied	study	VERB
ejpam-447	27	6	eq.(1	eq.(1	ADJ
ejpam-447	27	7	)	)	PUNCT
ejpam-447	28	1	when	when	SCONJ
ejpam-447	28	2	a=	a=	PROPN
ejpam-447	28	3	b	b	X
ejpam-447	28	4	=	=	SYM
ejpam-447	28	5	0	0	PROPN
ejpam-447	28	6	and	and	CCONJ
ejpam-447	28	7	k	k	X
ejpam-447	28	8	=	=	NOUN
ejpam-447	28	9	1	1	X
ejpam-447	28	10	.	.	PUNCT
ejpam-447	29	1	our	our	PRON
ejpam-447	29	2	interest	interest	NOUN
ejpam-447	29	3	now	now	ADV
ejpam-447	29	4	is	be	AUX
ejpam-447	29	5	to	to	PART
ejpam-447	29	6	study	study	VERB
ejpam-447	29	7	the	the	DET
ejpam-447	29	8	behavior	behavior	NOUN
ejpam-447	29	9	of	of	ADP
ejpam-447	29	10	solutions	solution	NOUN
ejpam-447	29	11	of	of	ADP
ejpam-447	29	12	eq.(1	eq.(1	ADJ
ejpam-447	29	13	)	)	PUNCT
ejpam-447	29	14	in	in	ADP
ejpam-447	29	15	the	the	DET
ejpam-447	29	16	general	general	ADJ
ejpam-447	29	17	case	case	NOUN
ejpam-447	29	18	where	where	SCONJ
ejpam-447	29	19	a	a	DET
ejpam-447	29	20	6=	6=	NUM
ejpam-447	29	21	0	0	NUM
ejpam-447	29	22	,	,	PUNCT
ejpam-447	29	23	b	b	PROPN
ejpam-447	29	24	6=	6=	ADP
ejpam-447	29	25	0	0	NUM
ejpam-447	29	26	and	and	CCONJ
ejpam-447	29	27	k	k	PROPN
ejpam-447	29	28	is	be	AUX
ejpam-447	29	29	a	a	DET
ejpam-447	29	30	positive	positive	ADJ
ejpam-447	29	31	integer	integer	NOUN
ejpam-447	29	32	number	number	NOUN
ejpam-447	29	33	.	.	PUNCT
ejpam-447	30	1	for	for	SCONJ
ejpam-447	30	2	the	the	DET
ejpam-447	30	3	related	related	ADJ
ejpam-447	30	4	work	work	NOUN
ejpam-447	30	5	see	see	VERB
ejpam-447	30	6	[	[	X
ejpam-447	30	7	32	32	NUM
ejpam-447	30	8	-	-	SYM
ejpam-447	30	9	45	45	NUM
ejpam-447	30	10	]	]	PUNCT
ejpam-447	30	11	.	.	PUNCT
ejpam-447	31	1	the	the	DET
ejpam-447	31	2	study	study	NOUN
ejpam-447	31	3	of	of	ADP
ejpam-447	31	4	these	these	DET
ejpam-447	31	5	equations	equation	NOUN
ejpam-447	31	6	is	be	AUX
ejpam-447	31	7	challenging	challenge	VERB
ejpam-447	31	8	and	and	CCONJ
ejpam-447	31	9	rewarding	rewarding	ADJ
ejpam-447	31	10	and	and	CCONJ
ejpam-447	31	11	is	be	AUX
ejpam-447	31	12	still	still	ADV
ejpam-447	31	13	in	in	ADP
ejpam-447	31	14	its	its	PRON
ejpam-447	31	15	infancy	infancy	NOUN
ejpam-447	31	16	.	.	PUNCT
ejpam-447	32	1	we	we	PRON
ejpam-447	32	2	believe	believe	VERB
ejpam-447	32	3	that	that	SCONJ
ejpam-447	32	4	the	the	DET
ejpam-447	32	5	nonlinear	nonlinear	ADJ
ejpam-447	32	6	rational	rational	ADJ
ejpam-447	32	7	difference	difference	NOUN
ejpam-447	32	8	equations	equation	NOUN
ejpam-447	32	9	are	be	AUX
ejpam-447	32	10	of	of	ADP
ejpam-447	32	11	paramount	paramount	ADJ
ejpam-447	32	12	importance	importance	NOUN
ejpam-447	32	13	in	in	ADP
ejpam-447	32	14	their	their	PRON
ejpam-447	32	15	own	own	ADJ
ejpam-447	32	16	right	right	NOUN
ejpam-447	32	17	.	.	PUNCT
ejpam-447	33	1	furthermore	furthermore	ADV
ejpam-447	33	2	the	the	DET
ejpam-447	33	3	results	result	NOUN
ejpam-447	33	4	about	about	ADP
ejpam-447	33	5	such	such	ADJ
ejpam-447	33	6	equations	equation	NOUN
ejpam-447	33	7	offer	offer	VERB
ejpam-447	33	8	prototypes	prototype	NOUN
ejpam-447	33	9	for	for	ADP
ejpam-447	33	10	the	the	DET
ejpam-447	33	11	development	development	NOUN
ejpam-447	33	12	of	of	ADP
ejpam-447	33	13	the	the	DET
ejpam-447	33	14	basic	basic	ADJ
ejpam-447	33	15	theory	theory	NOUN
ejpam-447	33	16	of	of	ADP
ejpam-447	33	17	the	the	DET
ejpam-447	33	18	global	global	ADJ
ejpam-447	33	19	behavior	behavior	NOUN
ejpam-447	33	20	of	of	ADP
ejpam-447	33	21	nonlinear	nonlinear	ADJ
ejpam-447	33	22	difference	difference	NOUN
ejpam-447	33	23	equations	equation	NOUN
ejpam-447	33	24	.	.	PUNCT
ejpam-447	34	1	let	let	VERB
ejpam-447	34	2	us	we	PRON
ejpam-447	34	3	now	now	ADV
ejpam-447	34	4	recall	recall	VERB
ejpam-447	34	5	some	some	PRON
ejpam-447	34	6	well	well	ADV
ejpam-447	34	7	know	know	VERB
ejpam-447	34	8	results	result	NOUN
ejpam-447	34	9	[	[	X
ejpam-447	34	10	15	15	NUM
ejpam-447	34	11	]	]	PUNCT
ejpam-447	34	12	which	which	PRON
ejpam-447	34	13	will	will	AUX
ejpam-447	34	14	be	be	AUX
ejpam-447	34	15	useful	useful	ADJ
ejpam-447	34	16	in	in	ADP
ejpam-447	34	17	the	the	DET
ejpam-447	34	18	sequel	sequel	NOUN
ejpam-447	34	19	.	.	PUNCT
ejpam-447	35	1	definition	definition	NOUN
ejpam-447	35	2	1	1	NUM
ejpam-447	35	3	.	.	PUNCT
ejpam-447	36	1	a	a	DET
ejpam-447	36	2	difference	difference	NOUN
ejpam-447	36	3	equation	equation	NOUN
ejpam-447	36	4	of	of	ADP
ejpam-447	36	5	order	order	NOUN
ejpam-447	36	6	(	(	PUNCT
ejpam-447	36	7	k+	k+	NOUN
ejpam-447	36	8	1	1	X
ejpam-447	36	9	)	)	PUNCT
ejpam-447	36	10	is	be	AUX
ejpam-447	36	11	of	of	ADP
ejpam-447	36	12	the	the	DET
ejpam-447	36	13	form	form	NOUN
ejpam-447	36	14	xn+1	xn+1	NUM
ejpam-447	36	15	=	=	SYM
ejpam-447	36	16	f(xn	f(xn	PROPN
ejpam-447	36	17	,	,	PUNCT
ejpam-447	36	18	xn−k	xn−k	PROPN
ejpam-447	36	19	)	)	PUNCT
ejpam-447	36	20	,	,	PUNCT
ejpam-447	36	21	n=	n=	ADJ
ejpam-447	36	22	0,1,2	0,1,2	NOUN
ejpam-447	36	23	,	,	PUNCT
ejpam-447	36	24	.....	.....	PUNCT
ejpam-447	37	1	(	(	PUNCT
ejpam-447	37	2	2	2	X
ejpam-447	37	3	)	)	PUNCT
ejpam-447	37	4	where	where	SCONJ
ejpam-447	37	5	f	f	PROPN
ejpam-447	37	6	is	be	AUX
ejpam-447	37	7	a	a	DET
ejpam-447	37	8	continuous	continuous	ADJ
ejpam-447	37	9	function	function	NOUN
ejpam-447	37	10	which	which	PRON
ejpam-447	37	11	maps	map	VERB
ejpam-447	37	12	some	some	DET
ejpam-447	37	13	set	set	NOUN
ejpam-447	37	14	j	j	PROPN
ejpam-447	37	15	k+1	k+1	X
ejpam-447	37	16	into	into	ADP
ejpam-447	37	17	j	j	PROPN
ejpam-447	37	18	where	where	SCONJ
ejpam-447	37	19	j	j	PROPN
ejpam-447	37	20	is	be	AUX
ejpam-447	37	21	a	a	DET
ejpam-447	37	22	set	set	NOUN
ejpam-447	37	23	of	of	ADP
ejpam-447	37	24	real	real	ADJ
ejpam-447	37	25	numbers	number	NOUN
ejpam-447	37	26	.	.	PUNCT
ejpam-447	38	1	an	an	DET
ejpam-447	38	2	equilibrium	equilibrium	NOUN
ejpam-447	38	3	point	point	NOUN
ejpam-447	38	4	ex	ex	PRON
ejpam-447	38	5	of	of	ADP
ejpam-447	38	6	this	this	DET
ejpam-447	38	7	equation	equation	NOUN
ejpam-447	38	8	is	be	AUX
ejpam-447	38	9	a	a	DET
ejpam-447	38	10	point	point	NOUN
ejpam-447	38	11	that	that	PRON
ejpam-447	38	12	satisfies	satisfy	VERB
ejpam-447	38	13	the	the	DET
ejpam-447	38	14	condition	condition	NOUN
ejpam-447	38	15	ex	ex	NOUN
ejpam-447	38	16	=	=	SYM
ejpam-447	38	17	f	f	X
ejpam-447	38	18	(	(	PUNCT
ejpam-447	38	19	ex	ex	X
ejpam-447	38	20	,	,	PUNCT
ejpam-447	38	21	ex	ex	NOUN
ejpam-447	38	22	)	)	PUNCT
ejpam-447	38	23	.	.	PUNCT
ejpam-447	39	1	that	that	PRON
ejpam-447	39	2	is	be	AUX
ejpam-447	39	3	,	,	PUNCT
ejpam-447	39	4	the	the	DET
ejpam-447	39	5	constant	constant	ADJ
ejpam-447	39	6	sequence	sequence	NOUN
ejpam-447	39	7	�	�	PROPN
ejpam-447	39	8	xn	xn	PROPN
ejpam-447	39	9	∞	∞	NUM
ejpam-447	39	10	n=−k	n=−k	VERB
ejpam-447	39	11	with	with	ADP
ejpam-447	39	12	xn	xn	PROPN
ejpam-447	40	1	=	=	SYM
ejpam-447	40	2	ex	ex	PROPN
ejpam-447	40	3	for	for	ADP
ejpam-447	40	4	all	all	DET
ejpam-447	40	5	n	n	PRON
ejpam-447	40	6	≥	≥	NOUN
ejpam-447	40	7	−k	−k	PROPN
ejpam-447	40	8	is	be	AUX
ejpam-447	40	9	a	a	DET
ejpam-447	40	10	solution	solution	NOUN
ejpam-447	40	11	of	of	ADP
ejpam-447	40	12	that	that	DET
ejpam-447	40	13	equation	equation	NOUN
ejpam-447	40	14	.	.	PUNCT
ejpam-447	41	1	definition	definition	NOUN
ejpam-447	41	2	2	2	NUM
ejpam-447	41	3	.	.	PUNCT
ejpam-447	42	1	let	let	VERB
ejpam-447	42	2	ex	ex	PRON
ejpam-447	42	3	∈	∈	PROPN
ejpam-447	42	4	(	(	PUNCT
ejpam-447	42	5	0,∞	0,∞	NOUN
ejpam-447	42	6	)	)	PUNCT
ejpam-447	42	7	be	be	VERB
ejpam-447	42	8	an	an	DET
ejpam-447	42	9	equilibrium	equilibrium	NOUN
ejpam-447	42	10	point	point	NOUN
ejpam-447	42	11	of	of	ADP
ejpam-447	42	12	the	the	DET
ejpam-447	42	13	difference	difference	NOUN
ejpam-447	42	14	equation	equation	NOUN
ejpam-447	42	15	(	(	PUNCT
ejpam-447	42	16	2	2	NUM
ejpam-447	42	17	)	)	PUNCT
ejpam-447	42	18	.	.	PUNCT
ejpam-447	43	1	then	then	ADV
ejpam-447	43	2	(	(	PUNCT
ejpam-447	43	3	i	i	NOUN
ejpam-447	43	4	)	)	PUNCT
ejpam-447	43	5	an	an	DET
ejpam-447	43	6	equilibrium	equilibrium	NOUN
ejpam-447	43	7	point	point	NOUN
ejpam-447	43	8	ex	ex	PRON
ejpam-447	43	9	of	of	ADP
ejpam-447	43	10	the	the	DET
ejpam-447	43	11	difference	difference	NOUN
ejpam-447	43	12	equation	equation	NOUN
ejpam-447	43	13	(	(	PUNCT
ejpam-447	43	14	2	2	X
ejpam-447	43	15	)	)	PUNCT
ejpam-447	43	16	is	be	AUX
ejpam-447	43	17	called	call	VERB
ejpam-447	43	18	locally	locally	ADV
ejpam-447	43	19	stable	stable	ADJ
ejpam-447	43	20	if	if	SCONJ
ejpam-447	43	21	for	for	ADP
ejpam-447	43	22	every	every	DET
ejpam-447	43	23	ǫ	ǫ	NOUN
ejpam-447	43	24	>	>	X
ejpam-447	43	25	0	0	PUNCT
ejpam-447	44	1	there	there	PRON
ejpam-447	44	2	exists	exist	VERB
ejpam-447	44	3	δ	δ	PROPN
ejpam-447	44	4	>	>	X
ejpam-447	44	5	0	0	NUM
ejpam-447	45	1	such	such	ADJ
ejpam-447	45	2	that	that	SCONJ
ejpam-447	45	3	,	,	PUNCT
ejpam-447	45	4	if	if	SCONJ
ejpam-447	45	5	x−k	x−k	PROPN
ejpam-447	45	6	,	,	PUNCT
ejpam-447	45	7	.	.	PUNCT
ejpam-447	45	8	.	.	PUNCT
ejpam-447	46	1	.	.	PUNCT
ejpam-447	47	1	,	,	PUNCT
ejpam-447	47	2	x−1	x−1	PROPN
ejpam-447	47	3	,	,	PUNCT
ejpam-447	47	4	x0	x0	PROPN
ejpam-447	47	5	∈	∈	PROPN
ejpam-447	47	6	(	(	PUNCT
ejpam-447	47	7	0,∞	0,∞	NOUN
ejpam-447	47	8	)	)	PUNCT
ejpam-447	47	9	with	with	ADP
ejpam-447	47	10	�	�	PROPN
ejpam-447	47	11	�	�	PROPN
ejpam-447	47	12	x−k	x−k	X
ejpam-447	47	13	−	−	PROPN
ejpam-447	47	14	ex	ex	PRON
ejpam-447	47	15	�	�	PROPN
ejpam-447	47	16	�	�	PROPN
ejpam-447	47	17	+	+	NUM
ejpam-447	47	18	.	.	PUNCT
ejpam-447	47	19	.	.	PUNCT
ejpam-447	47	20	.	.	PUNCT
ejpam-447	48	1	+	+	NOUN
ejpam-447	48	2	�	�	PROPN
ejpam-447	48	3	�	�	PROPN
ejpam-447	48	4	x−1−	x−1−	PROPN
ejpam-447	48	5	ex	ex	PROPN
ejpam-447	48	6	�	�	PROPN
ejpam-447	48	7	�	�	PROPN
ejpam-447	48	8	+	+	SYM
ejpam-447	48	9	�	�	PROPN
ejpam-447	48	10	�	�	PROPN
ejpam-447	48	11	x0	x0	PROPN
ejpam-447	48	12	−	−	PROPN
ejpam-447	48	13	ex	ex	PRON
ejpam-447	48	14	�	�	PROPN
ejpam-447	48	15	�	�	PROPN
ejpam-447	48	16	<	<	X
ejpam-447	48	17	δ	δ	PROPN
ejpam-447	48	18	,	,	PUNCT
ejpam-447	48	19	then	then	ADV
ejpam-447	48	20	�	�	PROPN
ejpam-447	48	21	�	�	PROPN
ejpam-447	48	22	xn−	xn−	PROPN
ejpam-447	48	23	ex	ex	PROPN
ejpam-447	48	24	�	�	PROPN
ejpam-447	48	25	�	�	X
ejpam-447	48	26	<	<	X
ejpam-447	48	27	ǫ	ǫ	NOUN
ejpam-447	48	28	for	for	ADP
ejpam-447	48	29	all	all	DET
ejpam-447	48	30	n≥	n≥	PRON
ejpam-447	48	31	−k	−k	NOUN
ejpam-447	48	32	.	.	PUNCT
ejpam-447	49	1	(	(	PUNCT
ejpam-447	49	2	ii	ii	X
ejpam-447	49	3	)	)	PUNCT
ejpam-447	49	4	an	an	DET
ejpam-447	49	5	equilibrium	equilibrium	NOUN
ejpam-447	49	6	point	point	NOUN
ejpam-447	49	7	ex	ex	PRON
ejpam-447	49	8	of	of	ADP
ejpam-447	49	9	the	the	DET
ejpam-447	49	10	difference	difference	NOUN
ejpam-447	49	11	equation	equation	NOUN
ejpam-447	49	12	(	(	PUNCT
ejpam-447	49	13	2	2	X
ejpam-447	49	14	)	)	PUNCT
ejpam-447	49	15	is	be	AUX
ejpam-447	49	16	called	call	VERB
ejpam-447	49	17	locally	locally	ADV
ejpam-447	49	18	asymptotically	asymptotically	ADV
ejpam-447	49	19	stable	stable	ADJ
ejpam-447	49	20	if	if	SCONJ
ejpam-447	49	21	it	it	PRON
ejpam-447	49	22	is	be	AUX
ejpam-447	49	23	locally	locally	ADV
ejpam-447	49	24	stable	stable	ADJ
ejpam-447	49	25	and	and	CCONJ
ejpam-447	49	26	there	there	PRON
ejpam-447	49	27	exists	exist	VERB
ejpam-447	49	28	γ	γ	PROPN
ejpam-447	49	29	>	>	X
ejpam-447	49	30	0	0	NUM
ejpam-447	49	31	such	such	ADJ
ejpam-447	49	32	that	that	SCONJ
ejpam-447	49	33	,	,	PUNCT
ejpam-447	49	34	if	if	SCONJ
ejpam-447	49	35	x−k	x−k	PROPN
ejpam-447	49	36	,	,	PUNCT
ejpam-447	49	37	.	.	PUNCT
ejpam-447	49	38	.	.	PUNCT
ejpam-447	50	1	.	.	PUNCT
ejpam-447	51	1	,	,	PUNCT
ejpam-447	51	2	x−1	x−1	PROPN
ejpam-447	51	3	,	,	PUNCT
ejpam-447	51	4	x0	x0	PROPN
ejpam-447	51	5	∈	∈	PROPN
ejpam-447	51	6	(	(	PUNCT
ejpam-447	51	7	0,∞	0,∞	NOUN
ejpam-447	51	8	)	)	PUNCT
ejpam-447	51	9	with	with	ADP
ejpam-447	51	10	�	�	PROPN
ejpam-447	51	11	�	�	PROPN
ejpam-447	51	12	x−k	x−k	X
ejpam-447	51	13	−	−	PROPN
ejpam-447	51	14	ex	ex	PRON
ejpam-447	51	15	�	�	PROPN
ejpam-447	51	16	�	�	PROPN
ejpam-447	51	17	+	+	NUM
ejpam-447	51	18	...	...	PUNCT
ejpam-447	52	1	+	+	ADJ
ejpam-447	52	2	�	�	PROPN
ejpam-447	52	3	�	�	PROPN
ejpam-447	52	4	x−1−	x−1−	PROPN
ejpam-447	52	5	ex	ex	PROPN
ejpam-447	52	6	�	�	PROPN
ejpam-447	52	7	�	�	PROPN
ejpam-447	52	8	+	+	SYM
ejpam-447	52	9	�	�	PROPN
ejpam-447	52	10	�	�	PROPN
ejpam-447	52	11	x0	x0	PROPN
ejpam-447	52	12	−	−	PROPN
ejpam-447	52	13	ex	ex	PRON
ejpam-447	52	14	�	�	PROPN
ejpam-447	52	15	�	�	PROPN
ejpam-447	52	16	<	<	X
ejpam-447	52	17	γ	γ	X
ejpam-447	52	18	,	,	PUNCT
ejpam-447	52	19	then	then	ADV
ejpam-447	52	20	lim	lim	PROPN
ejpam-447	52	21	n→∞	n→∞	X
ejpam-447	52	22	xn	xn	PROPN
ejpam-447	53	1	=	=	SYM
ejpam-447	53	2	ex	ex	X
ejpam-447	53	3	.	.	PUNCT
ejpam-447	54	1	(	(	PUNCT
ejpam-447	54	2	iii	iii	X
ejpam-447	54	3	)	)	PUNCT
ejpam-447	54	4	an	an	DET
ejpam-447	54	5	equilibrium	equilibrium	NOUN
ejpam-447	54	6	point	point	NOUN
ejpam-447	54	7	ex	ex	PRON
ejpam-447	54	8	of	of	ADP
ejpam-447	54	9	the	the	DET
ejpam-447	54	10	difference	difference	NOUN
ejpam-447	54	11	equation	equation	NOUN
ejpam-447	54	12	(	(	PUNCT
ejpam-447	54	13	2	2	X
ejpam-447	54	14	)	)	PUNCT
ejpam-447	54	15	is	be	AUX
ejpam-447	54	16	called	call	VERB
ejpam-447	54	17	a	a	DET
ejpam-447	54	18	global	global	ADJ
ejpam-447	54	19	attractor	attractor	NOUN
ejpam-447	54	20	if	if	SCONJ
ejpam-447	54	21	for	for	ADP
ejpam-447	54	22	every	every	DET
ejpam-447	54	23	x−k	x−k	NOUN
ejpam-447	54	24	,	,	PUNCT
ejpam-447	54	25	.	.	PUNCT
ejpam-447	54	26	.	.	PUNCT
ejpam-447	55	1	.	.	PUNCT
ejpam-447	56	1	,	,	PUNCT
ejpam-447	56	2	x−1	x−1	PROPN
ejpam-447	56	3	,	,	PUNCT
ejpam-447	56	4	x0	x0	PROPN
ejpam-447	56	5	∈	∈	PROPN
ejpam-447	56	6	(	(	PUNCT
ejpam-447	56	7	0,∞	0,∞	NUM
ejpam-447	56	8	)	)	PUNCT
ejpam-447	57	1	we	we	PRON
ejpam-447	57	2	have	have	VERB
ejpam-447	57	3	lim	lim	PROPN
ejpam-447	57	4	n→∞	n→∞	X
ejpam-447	57	5	xn	xn	PROPN
ejpam-447	58	1	=	=	SYM
ejpam-447	58	2	ex	ex	X
ejpam-447	58	3	.	.	PUNCT
ejpam-447	59	1	e.	e.	PROPN
ejpam-447	59	2	zayed	zayed	PROPN
ejpam-447	59	3	/	/	SYM
ejpam-447	59	4	eur	eur	PROPN
ejpam-447	59	5	.	.	PUNCT
ejpam-447	60	1	j.	j.	PROPN
ejpam-447	60	2	pure	pure	PROPN
ejpam-447	60	3	appl	appl	PROPN
ejpam-447	60	4	.	.	PROPN
ejpam-447	60	5	math	math	PROPN
ejpam-447	60	6	,	,	PUNCT
ejpam-447	60	7	3	3	NUM
ejpam-447	60	8	(	(	PUNCT
ejpam-447	60	9	2010	2010	NUM
ejpam-447	60	10	)	)	PUNCT
ejpam-447	60	11	,	,	PUNCT
ejpam-447	60	12	254	254	NUM
ejpam-447	60	13	-	-	SYM
ejpam-447	60	14	268	268	NUM
ejpam-447	60	15	256	256	NUM
ejpam-447	60	16	(	(	PUNCT
ejpam-447	60	17	iv	iv	X
ejpam-447	60	18	)	)	PUNCT
ejpam-447	60	19	an	an	DET
ejpam-447	60	20	equilibrium	equilibrium	NOUN
ejpam-447	60	21	point	point	NOUN
ejpam-447	60	22	ex	ex	PRON
ejpam-447	60	23	of	of	ADP
ejpam-447	60	24	the	the	DET
ejpam-447	60	25	equation	equation	NOUN
ejpam-447	60	26	(	(	PUNCT
ejpam-447	60	27	2	2	X
ejpam-447	60	28	)	)	PUNCT
ejpam-447	60	29	is	be	AUX
ejpam-447	60	30	called	call	VERB
ejpam-447	60	31	globally	globally	ADV
ejpam-447	60	32	asymptotically	asymptotically	ADV
ejpam-447	60	33	stable	stable	ADJ
ejpam-447	60	34	if	if	SCONJ
ejpam-447	60	35	it	it	PRON
ejpam-447	60	36	is	be	AUX
ejpam-447	60	37	locally	locally	ADV
ejpam-447	60	38	stable	stable	ADJ
ejpam-447	60	39	and	and	CCONJ
ejpam-447	60	40	a	a	DET
ejpam-447	60	41	global	global	ADJ
ejpam-447	60	42	attractor	attractor	NOUN
ejpam-447	60	43	.	.	PUNCT
ejpam-447	61	1	(	(	PUNCT
ejpam-447	61	2	v	v	NOUN
ejpam-447	61	3	)	)	PUNCT
ejpam-447	61	4	an	an	DET
ejpam-447	61	5	equilibrium	equilibrium	NOUN
ejpam-447	61	6	point	point	NOUN
ejpam-447	61	7	ex	ex	PRON
ejpam-447	61	8	of	of	ADP
ejpam-447	61	9	the	the	DET
ejpam-447	61	10	difference	difference	NOUN
ejpam-447	61	11	equation	equation	NOUN
ejpam-447	61	12	(	(	PUNCT
ejpam-447	61	13	2	2	X
ejpam-447	61	14	)	)	PUNCT
ejpam-447	61	15	is	be	AUX
ejpam-447	61	16	called	call	VERB
ejpam-447	61	17	unstable	unstable	ADJ
ejpam-447	61	18	if	if	SCONJ
ejpam-447	61	19	it	it	PRON
ejpam-447	61	20	is	be	AUX
ejpam-447	61	21	not	not	PART
ejpam-447	61	22	locally	locally	ADV
ejpam-447	61	23	stable	stable	ADJ
ejpam-447	61	24	.	.	PUNCT
ejpam-447	62	1	definition	definition	NOUN
ejpam-447	62	2	3	3	NUM
ejpam-447	62	3	.	.	PUNCT
ejpam-447	63	1	a	a	DET
ejpam-447	63	2	sequence	sequence	NOUN
ejpam-447	63	3	�	�	PROPN
ejpam-447	63	4	xn	xn	PROPN
ejpam-447	63	5	∞	∞	NUM
ejpam-447	63	6	n=−k	n=−k	PROPN
ejpam-447	63	7	is	be	AUX
ejpam-447	63	8	said	say	VERB
ejpam-447	63	9	to	to	PART
ejpam-447	63	10	be	be	AUX
ejpam-447	63	11	periodic	periodic	ADJ
ejpam-447	63	12	with	with	ADP
ejpam-447	63	13	period	period	NOUN
ejpam-447	63	14	p	p	NOUN
ejpam-447	64	1	if	if	SCONJ
ejpam-447	64	2	xn+p	xn+p	PROPN
ejpam-447	64	3	=	=	PUNCT
ejpam-447	64	4	xn	xn	PROPN
ejpam-447	64	5	for	for	ADP
ejpam-447	64	6	all	all	DET
ejpam-447	64	7	n	n	DET
ejpam-447	64	8	≥	≥	NOUN
ejpam-447	64	9	−k	−k	PROPN
ejpam-447	64	10	.	.	PUNCT
ejpam-447	65	1	a	a	DET
ejpam-447	65	2	sequence	sequence	NOUN
ejpam-447	65	3	�	�	PROPN
ejpam-447	65	4	xn	xn	PROPN
ejpam-447	65	5	∞	∞	NUM
ejpam-447	65	6	n=−k	n=−k	PROPN
ejpam-447	65	7	is	be	AUX
ejpam-447	65	8	said	say	VERB
ejpam-447	65	9	to	to	PART
ejpam-447	65	10	be	be	AUX
ejpam-447	65	11	periodic	periodic	ADJ
ejpam-447	65	12	with	with	ADP
ejpam-447	65	13	prime	prime	ADJ
ejpam-447	65	14	period	period	NOUN
ejpam-447	65	15	p	p	NOUN
ejpam-447	66	1	if	if	SCONJ
ejpam-447	66	2	p	p	NOUN
ejpam-447	66	3	is	be	AUX
ejpam-447	66	4	the	the	DET
ejpam-447	66	5	smallest	small	ADJ
ejpam-447	66	6	positive	positive	ADJ
ejpam-447	66	7	integer	integer	NOUN
ejpam-447	66	8	having	have	VERB
ejpam-447	66	9	this	this	DET
ejpam-447	66	10	property	property	NOUN
ejpam-447	66	11	.	.	PUNCT
ejpam-447	67	1	definition	definition	NOUN
ejpam-447	67	2	4	4	NUM
ejpam-447	67	3	.	.	PUNCT
ejpam-447	68	1	a	a	DET
ejpam-447	68	2	positive	positive	ADJ
ejpam-447	68	3	semi	semi	NOUN
ejpam-447	68	4	-	-	NOUN
ejpam-447	68	5	cycle	cycle	NOUN
ejpam-447	68	6	of	of	ADP
ejpam-447	68	7	�	�	PROPN
ejpam-447	68	8	xn	xn	PROPN
ejpam-447	68	9	∞	∞	PROPN
ejpam-447	68	10	n=−k	n=−k	PROPN
ejpam-447	68	11	consists	consist	VERB
ejpam-447	68	12	of	of	ADP
ejpam-447	68	13	"	"	PUNCT
ejpam-447	68	14	a	a	DET
ejpam-447	68	15	string	string	NOUN
ejpam-447	68	16	"	"	PUNCT
ejpam-447	68	17	of	of	ADP
ejpam-447	68	18	terms	term	NOUN
ejpam-447	68	19	�	�	PROPN
ejpam-447	68	20	x	x	SYM
ejpam-447	68	21	l	l	NOUN
ejpam-447	68	22	,	,	PUNCT
ejpam-447	68	23	x	x	X
ejpam-447	68	24	l+1	l+1	PROPN
ejpam-447	68	25	,	,	PUNCT
ejpam-447	68	26	.	.	PUNCT
ejpam-447	68	27	.	.	PUNCT
ejpam-447	69	1	.	.	PUNCT
ejpam-447	70	1	xm	xm	PROPN
ejpam-447	70	2	all	all	ADV
ejpam-447	70	3	greater	great	ADJ
ejpam-447	70	4	than	than	ADP
ejpam-447	70	5	or	or	CCONJ
ejpam-447	70	6	equal	equal	ADJ
ejpam-447	70	7	to	to	ADP
ejpam-447	70	8	ex	ex	PRON
ejpam-447	70	9	,	,	PUNCT
ejpam-447	70	10	with	with	ADP
ejpam-447	70	11	l	l	PROPN
ejpam-447	70	12	≥	≥	NOUN
ejpam-447	70	13	−k	−k	VERB
ejpam-447	70	14	and	and	CCONJ
ejpam-447	70	15	m≤∞	m≤∞	PRON
ejpam-447	70	16	such	such	ADJ
ejpam-447	70	17	that	that	SCONJ
ejpam-447	70	18	either	either	CCONJ
ejpam-447	70	19	l	l	NOUN
ejpam-447	70	20	=	=	PUNCT
ejpam-447	70	21	−k	−k	ADJ
ejpam-447	70	22	or	or	CCONJ
ejpam-447	70	23	+	+	NUM
ejpam-447	70	24	l	l	X
ejpam-447	70	25	>	>	X
ejpam-447	70	26	−k	−k	PROPN
ejpam-447	70	27	and	and	CCONJ
ejpam-447	70	28	x	x	SYM
ejpam-447	70	29	l−1	l−1	PROPN
ejpam-447	70	30	<	<	X
ejpam-447	70	31	ex	ex	NOUN
ejpam-447	70	32	,	,	PUNCT
ejpam-447	70	33	and	and	CCONJ
ejpam-447	70	34	either	either	CCONJ
ejpam-447	70	35	m=∞	m=∞	PROPN
ejpam-447	70	36	or	or	CCONJ
ejpam-447	70	37	+	+	NOUN
ejpam-447	70	38	m	m	NOUN
ejpam-447	70	39	<	<	X
ejpam-447	70	40	∞and	∞and	ADV
ejpam-447	70	41	xm−1	xm−1	PROPN
ejpam-447	70	42	<	<	X
ejpam-447	71	1	ex	ex	X
ejpam-447	71	2	,	,	PUNCT
ejpam-447	71	3	a	a	DET
ejpam-447	71	4	negative	negative	ADJ
ejpam-447	71	5	semi	semi	NOUN
ejpam-447	71	6	-	-	NOUN
ejpam-447	71	7	cycle	cycle	NOUN
ejpam-447	71	8	of	of	ADP
ejpam-447	71	9	�	�	PROPN
ejpam-447	71	10	xn	xn	PROPN
ejpam-447	71	11	∞	∞	PROPN
ejpam-447	71	12	n=−k	n=−k	PROPN
ejpam-447	71	13	consists	consist	VERB
ejpam-447	71	14	of	of	ADP
ejpam-447	71	15	"	"	PUNCT
ejpam-447	71	16	a	a	DET
ejpam-447	71	17	string	string	NOUN
ejpam-447	71	18	"	"	PUNCT
ejpam-447	71	19	of	of	ADP
ejpam-447	71	20	terms	term	NOUN
ejpam-447	71	21	�	�	PROPN
ejpam-447	71	22	x	x	SYM
ejpam-447	71	23	l	l	NOUN
ejpam-447	71	24	,	,	PUNCT
ejpam-447	71	25	x	x	X
ejpam-447	71	26	l+1	l+1	PROPN
ejpam-447	71	27	,	,	PUNCT
ejpam-447	71	28	.	.	PUNCT
ejpam-447	71	29	.	.	PUNCT
ejpam-447	71	30	.	.	PUNCT
ejpam-447	72	1	xm	xm	PROPN
ejpam-447	73	1	all	all	PRON
ejpam-447	73	2	less	less	ADJ
ejpam-447	73	3	than	than	ADP
ejpam-447	73	4	ex	ex	PRON
ejpam-447	73	5	,	,	PUNCT
ejpam-447	73	6	with	with	ADP
ejpam-447	73	7	l	l	PROPN
ejpam-447	73	8	≥	≥	NOUN
ejpam-447	73	9	−k	−k	VERB
ejpam-447	73	10	and	and	CCONJ
ejpam-447	73	11	m	m	AUX
ejpam-447	73	12	≤∞	≤∞	VERB
ejpam-447	73	13	such	such	ADJ
ejpam-447	73	14	that	that	SCONJ
ejpam-447	73	15	either	either	CCONJ
ejpam-447	73	16	l	l	NOUN
ejpam-447	73	17	=	=	PUNCT
ejpam-447	73	18	−k	−k	ADJ
ejpam-447	73	19	or	or	CCONJ
ejpam-447	73	20	+	+	NUM
ejpam-447	73	21	l	l	X
ejpam-447	73	22	>	>	X
ejpam-447	73	23	−k	−k	PROPN
ejpam-447	73	24	and	and	CCONJ
ejpam-447	73	25	x	x	SYM
ejpam-447	73	26	l−1	l−1	PROPN
ejpam-447	73	27	≥	≥	NOUN
ejpam-447	73	28	ex	ex	NOUN
ejpam-447	73	29	,	,	PUNCT
ejpam-447	73	30	and	and	CCONJ
ejpam-447	73	31	either	either	CCONJ
ejpam-447	73	32	m=∞	m=∞	PROPN
ejpam-447	73	33	or	or	CCONJ
ejpam-447	73	34	+	+	NOUN
ejpam-447	73	35	m	m	NOUN
ejpam-447	73	36	<	<	X
ejpam-447	73	37	∞and	∞and	ADJ
ejpam-447	73	38	xm−1	xm−1	PROPN
ejpam-447	73	39	≥	≥	NUM
ejpam-447	73	40	ex	ex	NOUN
ejpam-447	73	41	,	,	PUNCT
ejpam-447	73	42	definition	definition	NOUN
ejpam-447	73	43	5	5	NUM
ejpam-447	73	44	.	.	PUNCT
ejpam-447	73	45	eq.(2	eq.(2	PROPN
ejpam-447	73	46	)	)	PUNCT
ejpam-447	73	47	is	be	AUX
ejpam-447	73	48	said	say	VERB
ejpam-447	73	49	to	to	PART
ejpam-447	73	50	be	be	AUX
ejpam-447	73	51	permanent	permanent	ADJ
ejpam-447	73	52	if	if	SCONJ
ejpam-447	73	53	there	there	PRON
ejpam-447	73	54	exist	exist	VERB
ejpam-447	73	55	positive	positive	ADJ
ejpam-447	73	56	real	real	ADJ
ejpam-447	73	57	numbers	number	NOUN
ejpam-447	73	58	m	m	VERB
ejpam-447	73	59	and	and	CCONJ
ejpam-447	73	60	m	m	VERB
ejpam-447	73	61	such	such	ADJ
ejpam-447	73	62	that	that	SCONJ
ejpam-447	73	63	for	for	ADP
ejpam-447	73	64	every	every	DET
ejpam-447	73	65	solution	solution	NOUN
ejpam-447	73	66	�	�	PROPN
ejpam-447	73	67	xn	xn	PROPN
ejpam-447	73	68	∞	∞	NUM
ejpam-447	73	69	n=−k	n=−k	PROPN
ejpam-447	73	70	of	of	ADP
ejpam-447	73	71	eq.(2	eq.(2	NOUN
ejpam-447	73	72	)	)	PUNCT
ejpam-447	73	73	there	there	PRON
ejpam-447	73	74	exists	exist	VERB
ejpam-447	73	75	a	a	DET
ejpam-447	73	76	positive	positive	ADJ
ejpam-447	73	77	integer	integer	NOUN
ejpam-447	73	78	n	n	PRON
ejpam-447	73	79	≥	≥	NOUN
ejpam-447	73	80	−k	−k	PROPN
ejpam-447	73	81	which	which	PRON
ejpam-447	73	82	depends	depend	VERB
ejpam-447	73	83	on	on	ADP
ejpam-447	73	84	the	the	DET
ejpam-447	73	85	initial	initial	ADJ
ejpam-447	73	86	conditions	condition	NOUN
ejpam-447	73	87	,	,	PUNCT
ejpam-447	73	88	such	such	ADJ
ejpam-447	73	89	that	that	SCONJ
ejpam-447	73	90	m	m	VERB
ejpam-447	73	91	≤	≤	ADJ
ejpam-447	73	92	xn	xn	PUNCT
ejpam-447	74	1	≤	≤	NUM
ejpam-447	74	2	m	m	VERB
ejpam-447	74	3	,	,	PUNCT
ejpam-447	74	4	for	for	ADP
ejpam-447	74	5	all	all	DET
ejpam-447	74	6	n≥	n≥	NOUN
ejpam-447	74	7	n	n	NOUN
ejpam-447	74	8	.	.	PUNCT
ejpam-447	75	1	the	the	DET
ejpam-447	75	2	linearized	linearize	VERB
ejpam-447	75	3	equation	equation	NOUN
ejpam-447	75	4	of	of	ADP
ejpam-447	75	5	the	the	DET
ejpam-447	75	6	difference	difference	NOUN
ejpam-447	75	7	equation	equation	NOUN
ejpam-447	75	8	(	(	PUNCT
ejpam-447	75	9	2	2	NUM
ejpam-447	75	10	)	)	PUNCT
ejpam-447	75	11	about	about	ADP
ejpam-447	75	12	the	the	DET
ejpam-447	75	13	equilibrium	equilibrium	NOUN
ejpam-447	75	14	point	point	NOUN
ejpam-447	75	15	ex	ex	PROPN
ejpam-447	75	16	is	be	AUX
ejpam-447	75	17	the	the	DET
ejpam-447	75	18	linear	linear	ADJ
ejpam-447	75	19	difference	difference	NOUN
ejpam-447	75	20	equation	equation	NOUN
ejpam-447	75	21	zn+1	zn+1	NUM
ejpam-447	75	22	=	=	SYM
ejpam-447	75	23	∂	∂	NUM
ejpam-447	75	24	f	f	NOUN
ejpam-447	75	25	(	(	PUNCT
ejpam-447	75	26	ex	ex	X
ejpam-447	75	27	,	,	PUNCT
ejpam-447	75	28	ex	ex	NOUN
ejpam-447	75	29	)	)	PUNCT
ejpam-447	75	30	∂	∂	NOUN
ejpam-447	75	31	xn	xn	PROPN
ejpam-447	75	32	zn+	zn+	PROPN
ejpam-447	75	33	∂	∂	PROPN
ejpam-447	76	1	f	f	PROPN
ejpam-447	76	2	(	(	PUNCT
ejpam-447	76	3	ex	ex	X
ejpam-447	76	4	,	,	PUNCT
ejpam-447	76	5	ex	ex	NOUN
ejpam-447	76	6	)	)	PUNCT
ejpam-447	76	7	∂	∂	NOUN
ejpam-447	76	8	xn−k	xn−k	PROPN
ejpam-447	76	9	zn−k	zn−k	PROPN
ejpam-447	76	10	,	,	PUNCT
ejpam-447	76	11	(	(	PUNCT
ejpam-447	76	12	3	3	X
ejpam-447	76	13	)	)	PUNCT
ejpam-447	76	14	the	the	DET
ejpam-447	76	15	characteristic	characteristic	ADJ
ejpam-447	76	16	equation	equation	NOUN
ejpam-447	76	17	associated	associate	VERB
ejpam-447	76	18	with	with	ADP
ejpam-447	76	19	eq.(3	eq.(3	NOUN
ejpam-447	76	20	)	)	PUNCT
ejpam-447	76	21	is	be	AUX
ejpam-447	76	22	p	p	X
ejpam-447	76	23	(	(	PUNCT
ejpam-447	76	24	λ	λ	NOUN
ejpam-447	76	25	)	)	PUNCT
ejpam-447	76	26	=	=	SYM
ejpam-447	77	1	λk+1−	λk+1−	PROPN
ejpam-447	78	1	p0λ	p0λ	X
ejpam-447	78	2	k	k	NOUN
ejpam-447	78	3	−	−	PROPN
ejpam-447	78	4	p1	p1	NOUN
ejpam-447	78	5	=	=	SYM
ejpam-447	78	6	0	0	PROPN
ejpam-447	78	7	,	,	PUNCT
ejpam-447	78	8	(	(	PUNCT
ejpam-447	78	9	4	4	X
ejpam-447	78	10	)	)	PUNCT
ejpam-447	79	1	where	where	SCONJ
ejpam-447	79	2	p0	p0	NOUN
ejpam-447	79	3	=	=	SYM
ejpam-447	79	4	∂	∂	NUM
ejpam-447	79	5	f	f	NOUN
ejpam-447	79	6	(	(	PUNCT
ejpam-447	79	7	ex	ex	X
ejpam-447	79	8	,	,	PUNCT
ejpam-447	79	9	ex	ex	NOUN
ejpam-447	79	10	)	)	PUNCT
ejpam-447	79	11	∂	∂	NOUN
ejpam-447	79	12	xn	xn	PROPN
ejpam-447	79	13	,	,	PUNCT
ejpam-447	79	14	p1	p1	PROPN
ejpam-447	79	15	=	=	SYM
ejpam-447	79	16	∂	∂	NUM
ejpam-447	79	17	f	f	NOUN
ejpam-447	79	18	(	(	PUNCT
ejpam-447	79	19	ex	ex	X
ejpam-447	79	20	,	,	PUNCT
ejpam-447	79	21	ex	ex	NOUN
ejpam-447	79	22	)	)	PUNCT
ejpam-447	79	23	∂	∂	PROPN
ejpam-447	79	24	xn−k	xn−k	PROPN
ejpam-447	79	25	.	.	PUNCT
ejpam-447	79	26	theorem	theorem	NOUN
ejpam-447	79	27	1	1	NUM
ejpam-447	79	28	.	.	PUNCT
ejpam-447	80	1	(	(	PUNCT
ejpam-447	80	2	[	[	X
ejpam-447	80	3	15	15	NUM
ejpam-447	80	4	]	]	NUM
ejpam-447	80	5	)	)	PUNCT
ejpam-447	80	6	.	.	PUNCT
ejpam-447	81	1	the	the	DET
ejpam-447	81	2	linearized	linearize	VERB
ejpam-447	81	3	stability	stability	NOUN
ejpam-447	81	4	theorem	theorem	VERB
ejpam-447	81	5	.	.	PUNCT
ejpam-447	82	1	suppose	suppose	VERB
ejpam-447	82	2	f	f	PROPN
ejpam-447	82	3	is	be	AUX
ejpam-447	82	4	a	a	DET
ejpam-447	82	5	continuously	continuously	ADV
ejpam-447	82	6	differentiable	differentiable	ADJ
ejpam-447	82	7	function	function	NOUN
ejpam-447	82	8	defined	define	VERB
ejpam-447	82	9	on	on	ADP
ejpam-447	82	10	an	an	DET
ejpam-447	82	11	open	open	ADJ
ejpam-447	82	12	neighbourhood	neighbourhood	NOUN
ejpam-447	82	13	of	of	ADP
ejpam-447	82	14	the	the	DET
ejpam-447	82	15	equilibrium	equilibrium	NOUN
ejpam-447	82	16	ex	ex	X
ejpam-447	82	17	.	.	PUNCT
ejpam-447	83	1	then	then	ADV
ejpam-447	83	2	the	the	DET
ejpam-447	83	3	following	follow	VERB
ejpam-447	83	4	statements	statement	NOUN
ejpam-447	83	5	are	be	AUX
ejpam-447	83	6	true	true	ADJ
ejpam-447	83	7	.	.	PUNCT
ejpam-447	84	1	e.	e.	PROPN
ejpam-447	84	2	zayed	zayed	PROPN
ejpam-447	84	3	/	/	SYM
ejpam-447	84	4	eur	eur	PROPN
ejpam-447	84	5	.	.	PUNCT
ejpam-447	85	1	j.	j.	PROPN
ejpam-447	85	2	pure	pure	PROPN
ejpam-447	85	3	appl	appl	PROPN
ejpam-447	85	4	.	.	PROPN
ejpam-447	85	5	math	math	PROPN
ejpam-447	85	6	,	,	PUNCT
ejpam-447	85	7	3	3	NUM
ejpam-447	85	8	(	(	PUNCT
ejpam-447	85	9	2010	2010	NUM
ejpam-447	85	10	)	)	PUNCT
ejpam-447	85	11	,	,	PUNCT
ejpam-447	85	12	254	254	NUM
ejpam-447	85	13	-	-	SYM
ejpam-447	85	14	268	268	NUM
ejpam-447	85	15	257	257	NUM
ejpam-447	85	16	(	(	PUNCT
ejpam-447	85	17	i	i	NOUN
ejpam-447	85	18	)	)	PUNCT
ejpam-447	85	19	if	if	SCONJ
ejpam-447	85	20	all	all	DET
ejpam-447	85	21	the	the	DET
ejpam-447	85	22	roots	root	NOUN
ejpam-447	85	23	of	of	ADP
ejpam-447	85	24	the	the	DET
ejpam-447	85	25	characteristic	characteristic	ADJ
ejpam-447	85	26	equation	equation	NOUN
ejpam-447	85	27	(	(	PUNCT
ejpam-447	85	28	4	4	NUM
ejpam-447	85	29	)	)	PUNCT
ejpam-447	85	30	of	of	ADP
ejpam-447	85	31	the	the	DET
ejpam-447	85	32	linearized	linearize	VERB
ejpam-447	85	33	equation	equation	NOUN
ejpam-447	85	34	(	(	PUNCT
ejpam-447	85	35	3	3	X
ejpam-447	85	36	)	)	PUNCT
ejpam-447	85	37	have	have	VERB
ejpam-447	85	38	absolute	absolute	ADJ
ejpam-447	85	39	value	value	NOUN
ejpam-447	85	40	less	less	ADJ
ejpam-447	85	41	than	than	ADP
ejpam-447	85	42	one	one	NUM
ejpam-447	85	43	,	,	PUNCT
ejpam-447	85	44	then	then	ADV
ejpam-447	85	45	the	the	DET
ejpam-447	85	46	equilibrium	equilibrium	NOUN
ejpam-447	85	47	point	point	NOUN
ejpam-447	85	48	ex	ex	PRON
ejpam-447	85	49	of	of	ADP
ejpam-447	85	50	eq.(2	eq.(2	NOUN
ejpam-447	85	51	)	)	PUNCT
ejpam-447	85	52	is	be	AUX
ejpam-447	85	53	locally	locally	ADV
ejpam-447	85	54	asymptotically	asymptotically	ADV
ejpam-447	85	55	stable	stable	ADJ
ejpam-447	85	56	.	.	PUNCT
ejpam-447	86	1	(	(	PUNCT
ejpam-447	86	2	ii	ii	NOUN
ejpam-447	86	3	)	)	PUNCT
ejpam-447	86	4	if	if	SCONJ
ejpam-447	86	5	at	at	ADV
ejpam-447	86	6	least	least	ADV
ejpam-447	86	7	one	one	NUM
ejpam-447	86	8	root	root	NOUN
ejpam-447	86	9	of	of	ADP
ejpam-447	86	10	eq.(4	eq.(4	ADJ
ejpam-447	86	11	)	)	PUNCT
ejpam-447	86	12	has	have	VERB
ejpam-447	86	13	absolute	absolute	ADJ
ejpam-447	86	14	value	value	NOUN
ejpam-447	86	15	greater	great	ADJ
ejpam-447	86	16	than	than	ADP
ejpam-447	86	17	one	one	NUM
ejpam-447	86	18	,	,	PUNCT
ejpam-447	86	19	then	then	ADV
ejpam-447	86	20	the	the	DET
ejpam-447	86	21	equilibrium	equilibrium	NOUN
ejpam-447	86	22	point	point	NOUN
ejpam-447	86	23	ex	ex	PRON
ejpam-447	86	24	of	of	ADP
ejpam-447	86	25	eq.(2	eq.(2	NOUN
ejpam-447	86	26	)	)	PUNCT
ejpam-447	86	27	(	(	PUNCT
ejpam-447	86	28	iii	iii	X
ejpam-447	86	29	)	)	PUNCT
ejpam-447	86	30	if	if	SCONJ
ejpam-447	86	31	all	all	DET
ejpam-447	86	32	the	the	DET
ejpam-447	86	33	roots	root	NOUN
ejpam-447	86	34	of	of	ADP
ejpam-447	86	35	eq.(4	eq.(4	NOUN
ejpam-447	86	36	)	)	PUNCT
ejpam-447	86	37	have	have	VERB
ejpam-447	86	38	absolute	absolute	ADJ
ejpam-447	86	39	value	value	NOUN
ejpam-447	86	40	greater	great	ADJ
ejpam-447	86	41	than	than	ADP
ejpam-447	86	42	one	one	NUM
ejpam-447	86	43	,	,	PUNCT
ejpam-447	86	44	then	then	ADV
ejpam-447	86	45	the	the	DET
ejpam-447	86	46	equilibrium	equilibrium	NOUN
ejpam-447	86	47	point	point	NOUN
ejpam-447	86	48	ex	ex	PRON
ejpam-447	86	49	of	of	ADP
ejpam-447	86	50	eq.(2	eq.(2	NOUN
ejpam-447	86	51	)	)	PUNCT
ejpam-447	86	52	is	be	AUX
ejpam-447	86	53	a	a	DET
ejpam-447	86	54	source	source	NOUN
ejpam-447	86	55	.	.	PUNCT
ejpam-447	87	1	1.1	1.1	NUM
ejpam-447	87	2	.	.	PUNCT
ejpam-447	88	1	equilibrium	equilibrium	NOUN
ejpam-447	88	2	points	point	NOUN
ejpam-447	88	3	in	in	ADP
ejpam-447	88	4	this	this	DET
ejpam-447	88	5	section	section	NOUN
ejpam-447	88	6	,	,	PUNCT
ejpam-447	88	7	we	we	PRON
ejpam-447	88	8	examine	examine	VERB
ejpam-447	88	9	the	the	DET
ejpam-447	88	10	nonnegative	nonnegative	ADJ
ejpam-447	88	11	equilibrium	equilibrium	NOUN
ejpam-447	88	12	points	point	NOUN
ejpam-447	88	13	ex	ex	PRON
ejpam-447	88	14	of	of	ADP
ejpam-447	88	15	eq.(1	eq.(1	ADJ
ejpam-447	88	16	)	)	PUNCT
ejpam-447	88	17	and	and	CCONJ
ejpam-447	88	18	their	their	PRON
ejpam-447	88	19	local	local	ADJ
ejpam-447	88	20	asymptotic	asymptotic	ADJ
ejpam-447	88	21	behavior	behavior	NOUN
ejpam-447	88	22	.	.	PUNCT
ejpam-447	89	1	the	the	DET
ejpam-447	89	2	equilibrium	equilibrium	NOUN
ejpam-447	89	3	points	point	NOUN
ejpam-447	89	4	of	of	ADP
ejpam-447	89	5	eq.(1	eq.(1	ADJ
ejpam-447	89	6	)	)	PUNCT
ejpam-447	89	7	are	be	AUX
ejpam-447	89	8	the	the	DET
ejpam-447	89	9	nonnegative	nonnegative	ADJ
ejpam-447	89	10	solutions	solution	NOUN
ejpam-447	89	11	of	of	ADP
ejpam-447	89	12	the	the	DET
ejpam-447	89	13	equation	equation	NOUN
ejpam-447	89	14	ex	ex	X
ejpam-447	90	1	=	=	SYM
ejpam-447	91	1	(	(	PUNCT
ejpam-447	91	2	a+	a+	NOUN
ejpam-447	91	3	b	b	X
ejpam-447	91	4	)	)	PUNCT
ejpam-447	91	5	ex	ex	X
ejpam-447	91	6	+	+	PROPN
ejpam-447	91	7	�	�	PROPN
ejpam-447	91	8	p+	p+	PART
ejpam-447	91	9	1	1	NUM
ejpam-447	91	10	�	�	PROPN
ejpam-447	91	11	ex	ex	X
ejpam-447	91	12	q+	q+	ADP
ejpam-447	91	13	ex	ex	X
ejpam-447	91	14	.	.	PUNCT
ejpam-447	92	1	(	(	PUNCT
ejpam-447	92	2	5	5	NUM
ejpam-447	92	3	)	)	PUNCT
ejpam-447	92	4	so	so	ADV
ejpam-447	92	5	,	,	PUNCT
ejpam-447	92	6	ex	ex	X
ejpam-447	92	7	=	=	NOUN
ejpam-447	92	8	0	0	NUM
ejpam-447	92	9	is	be	AUX
ejpam-447	92	10	always	always	ADV
ejpam-447	92	11	an	an	DET
ejpam-447	92	12	equilibrium	equilibrium	NOUN
ejpam-447	92	13	point	point	NOUN
ejpam-447	92	14	of	of	ADP
ejpam-447	92	15	eq.(1	eq.(1	ADJ
ejpam-447	92	16	)	)	PUNCT
ejpam-447	92	17	.	.	PUNCT
ejpam-447	93	1	if	if	SCONJ
ejpam-447	93	2	0	0	NUM
ejpam-447	93	3	<	<	X
ejpam-447	93	4	a+b	a+b	NUM
ejpam-447	93	5	<	<	X
ejpam-447	93	6	1	1	NUM
ejpam-447	93	7	,	,	PUNCT
ejpam-447	93	8	p−q	p−q	NOUN
ejpam-447	93	9	>	>	X
ejpam-447	93	10	−	−	PUNCT
ejpam-447	93	11	�	�	PROPN
ejpam-447	93	12	1	1	NUM
ejpam-447	93	13	+	+	NOUN
ejpam-447	93	14	q	q	NOUN
ejpam-447	93	15	(	(	PUNCT
ejpam-447	93	16	a+	a+	NOUN
ejpam-447	93	17	b	b	X
ejpam-447	93	18	)	)	PUNCT
ejpam-447	93	19	�	�	PROPN
ejpam-447	93	20	and	and	CCONJ
ejpam-447	93	21	p	p	X
ejpam-447	93	22	>	>	X
ejpam-447	93	23	q	q	X
ejpam-447	94	1	then	then	ADV
ejpam-447	94	2	the	the	DET
ejpam-447	94	3	positive	positive	ADJ
ejpam-447	94	4	equilibrium	equilibrium	NOUN
ejpam-447	94	5	point	point	NOUN
ejpam-447	94	6	is	be	AUX
ejpam-447	94	7	ex	ex	X
ejpam-447	94	8	=	=	PUNCT
ejpam-447	94	9	�	�	PROPN
ejpam-447	94	10	p−	p−	NOUN
ejpam-447	94	11	q	q	PROPN
ejpam-447	94	12	�	�	PROPN
ejpam-447	94	13	+	+	CCONJ
ejpam-447	94	14	�	�	PROPN
ejpam-447	94	15	1	1	NUM
ejpam-447	94	16	+	+	NOUN
ejpam-447	94	17	q	q	NOUN
ejpam-447	94	18	(	(	PUNCT
ejpam-447	94	19	a+	a+	NOUN
ejpam-447	94	20	b	b	X
ejpam-447	94	21	)	)	PUNCT
ejpam-447	94	22	�	�	PROPN
ejpam-447	95	1	[	[	X
ejpam-447	95	2	1−	1−	NUM
ejpam-447	95	3	(	(	PUNCT
ejpam-447	95	4	a+	a+	NOUN
ejpam-447	95	5	b	b	NOUN
ejpam-447	95	6	)	)	PUNCT
ejpam-447	95	7	]	]	PUNCT
ejpam-447	95	8	.	.	PUNCT
ejpam-447	96	1	(	(	PUNCT
ejpam-447	96	2	6	6	X
ejpam-447	96	3	)	)	PUNCT
ejpam-447	96	4	lemma	lemma	PROPN
ejpam-447	96	5	1	1	NUM
ejpam-447	96	6	.	.	PUNCT
ejpam-447	97	1	if	if	SCONJ
ejpam-447	97	2	p	p	X
ejpam-447	97	3	>	>	X
ejpam-447	97	4	q	q	X
ejpam-447	97	5	and	and	CCONJ
ejpam-447	97	6	0	0	NUM
ejpam-447	97	7	<	<	X
ejpam-447	97	8	a+	a+	X
ejpam-447	97	9	b	b	X
ejpam-447	97	10	<	<	X
ejpam-447	97	11	1	1	NUM
ejpam-447	97	12	,	,	PUNCT
ejpam-447	97	13	then	then	ADV
ejpam-447	97	14	the	the	DET
ejpam-447	97	15	positive	positive	ADJ
ejpam-447	97	16	equilibrium	equilibrium	NOUN
ejpam-447	97	17	point	point	NOUN
ejpam-447	97	18	(	(	PUNCT
ejpam-447	97	19	6	6	NUM
ejpam-447	97	20	satisfies	satisfy	VERB
ejpam-447	97	21	the	the	DET
ejpam-447	97	22	inequality	inequality	NOUN
ejpam-447	97	23	ex	ex	X
ejpam-447	97	24	>	>	X
ejpam-447	97	25	q	q	PROPN
ejpam-447	98	1	p	p	NOUN
ejpam-447	98	2	.	.	PUNCT
ejpam-447	99	1	proof	proof	NOUN
ejpam-447	99	2	.	.	PUNCT
ejpam-447	100	1	from	from	ADP
ejpam-447	100	2	(	(	PUNCT
ejpam-447	100	3	6	6	NUM
ejpam-447	100	4	we	we	PRON
ejpam-447	100	5	deduce	deduce	VERB
ejpam-447	100	6	that	that	SCONJ
ejpam-447	100	7	ex	ex	PUNCT
ejpam-447	100	8	=	=	SYM
ejpam-447	100	9	p+	p+	PROPN
ejpam-447	100	10	1	1	NUM
ejpam-447	100	11	1−	1−	NUM
ejpam-447	100	12	(	(	PUNCT
ejpam-447	100	13	a+	a+	NOUN
ejpam-447	100	14	b	b	NOUN
ejpam-447	100	15	)	)	PUNCT
ejpam-447	100	16	−	−	PROPN
ejpam-447	100	17	q	q	X
ejpam-447	101	1	>	>	X
ejpam-447	101	2	q+	q+	PUNCT
ejpam-447	101	3	1	1	NUM
ejpam-447	101	4	1−	1−	NUM
ejpam-447	101	5	(	(	PUNCT
ejpam-447	101	6	a+	a+	NOUN
ejpam-447	101	7	b	b	NOUN
ejpam-447	101	8	)	)	PUNCT
ejpam-447	101	9	−	−	NOUN
ejpam-447	101	10	q	q	NOUN
ejpam-447	102	1	=	=	PUNCT
ejpam-447	102	2	1	1	NUM
ejpam-447	102	3	+	+	NUM
ejpam-447	102	4	q	q	X
ejpam-447	102	5	(	(	PUNCT
ejpam-447	102	6	a+	a+	NOUN
ejpam-447	102	7	b	b	NOUN
ejpam-447	102	8	)	)	PUNCT
ejpam-447	102	9	1−	1−	NUM
ejpam-447	102	10	(	(	PUNCT
ejpam-447	102	11	a+	a+	NOUN
ejpam-447	102	12	b	b	NOUN
ejpam-447	102	13	)	)	PUNCT
ejpam-447	102	14	=	=	SYM
ejpam-447	102	15	�	�	PROPN
ejpam-447	102	16	1	1	NUM
ejpam-447	102	17	+	+	NUM
ejpam-447	102	18	q	q	NOUN
ejpam-447	102	19	(	(	PUNCT
ejpam-447	102	20	a+	a+	NOUN
ejpam-447	102	21	b	b	NOUN
ejpam-447	102	22	)	)	PUNCT
ejpam-447	102	23	�	�	PROPN
ejpam-447	102	24	�	�	PROPN
ejpam-447	102	25	1	1	NUM
ejpam-447	102	26	+	+	CCONJ
ejpam-447	102	27	(	(	PUNCT
ejpam-447	102	28	a+	a+	X
ejpam-447	102	29	b	b	NOUN
ejpam-447	102	30	)	)	PUNCT
ejpam-447	102	31	+	+	CCONJ
ejpam-447	102	32	(	(	PUNCT
ejpam-447	102	33	a+	a+	PRON
ejpam-447	102	34	b)2	b)2	PROPN
ejpam-447	102	35	+	+	PROPN
ejpam-447	102	36	......	......	PUNCT
ejpam-447	102	37	�	�	PROPN
ejpam-447	102	38	>	>	X
ejpam-447	102	39	1	1	NUM
ejpam-447	102	40	>	>	X
ejpam-447	102	41	q	q	PROPN
ejpam-447	102	42	p	p	NOUN
ejpam-447	102	43	.	.	PUNCT
ejpam-447	103	1	the	the	DET
ejpam-447	103	2	proof	proof	NOUN
ejpam-447	103	3	of	of	ADP
ejpam-447	103	4	lemma	lemma	PROPN
ejpam-447	103	5	1	1	NUM
ejpam-447	103	6	is	be	AUX
ejpam-447	103	7	now	now	ADV
ejpam-447	103	8	completed	complete	VERB
ejpam-447	103	9	.	.	PUNCT
ejpam-447	104	1	1.2	1.2	NUM
ejpam-447	104	2	.	.	PUNCT
ejpam-447	104	3	linearization	linearization	NOUN
ejpam-447	104	4	in	in	ADP
ejpam-447	104	5	this	this	DET
ejpam-447	104	6	section	section	NOUN
ejpam-447	104	7	,	,	PUNCT
ejpam-447	104	8	we	we	PRON
ejpam-447	104	9	derive	derive	VERB
ejpam-447	104	10	the	the	DET
ejpam-447	104	11	linearized	linearize	VERB
ejpam-447	104	12	equation	equation	NOUN
ejpam-447	104	13	of	of	ADP
ejpam-447	104	14	eq.(1	eq.(1	ADJ
ejpam-447	104	15	)	)	PUNCT
ejpam-447	104	16	.	.	PUNCT
ejpam-447	105	1	to	to	ADP
ejpam-447	105	2	this	this	DET
ejpam-447	105	3	end	end	NOUN
ejpam-447	105	4	,	,	PUNCT
ejpam-447	105	5	we	we	PRON
ejpam-447	105	6	introduce	introduce	VERB
ejpam-447	105	7	a	a	DET
ejpam-447	105	8	continuous	continuous	ADJ
ejpam-447	105	9	function	function	NOUN
ejpam-447	105	10	f	f	NOUN
ejpam-447	105	11	:	:	PUNCT
ejpam-447	105	12	(	(	PUNCT
ejpam-447	105	13	0,∞)2→	0,∞)2→	NUM
ejpam-447	105	14	(	(	PUNCT
ejpam-447	105	15	0,∞	0,∞	NOUN
ejpam-447	105	16	)	)	PUNCT
ejpam-447	105	17	which	which	PRON
ejpam-447	105	18	is	be	AUX
ejpam-447	105	19	defined	define	VERB
ejpam-447	105	20	by	by	ADP
ejpam-447	105	21	f(u0,u1	f(u0,u1	ADJ
ejpam-447	105	22	)	)	PUNCT
ejpam-447	105	23	=	=	PUNCT
ejpam-447	105	24	au0	au0	VERB
ejpam-447	106	1	+	+	NUM
ejpam-447	106	2	bu1	bu1	NOUN
ejpam-447	106	3	+	+	CCONJ
ejpam-447	106	4	pu0	pu0	NOUN
ejpam-447	106	5	+	+	CCONJ
ejpam-447	106	6	u1	u1	PROPN
ejpam-447	106	7	q+	q+	NOUN
ejpam-447	106	8	u1	u1	NOUN
ejpam-447	106	9	.	.	PUNCT
ejpam-447	107	1	(	(	PUNCT
ejpam-447	107	2	7	7	NUM
ejpam-447	107	3	)	)	PUNCT
ejpam-447	107	4	therefore	therefore	ADV
ejpam-447	107	5	,	,	PUNCT
ejpam-447	107	6			PROPN
ejpam-447	107	7			PROPN
ejpam-447	107	8			PROPN
ejpam-447	107	9	∂	∂	NUM
ejpam-447	107	10	f(u0	f(u0	ADJ
ejpam-447	107	11	,	,	PUNCT
ejpam-447	107	12	u1	u1	NOUN
ejpam-447	107	13	)	)	PUNCT
ejpam-447	107	14	∂	∂	NOUN
ejpam-447	107	15	u0	u0	NOUN
ejpam-447	107	16	=	=	NOUN
ejpam-447	107	17	a+	a+	PUNCT
ejpam-447	107	18	p	p	NOUN
ejpam-447	107	19	q+u1	q+u1	NOUN
ejpam-447	107	20	,	,	PUNCT
ejpam-447	107	21	∂	∂	X
ejpam-447	107	22	f(u0,u1	f(u0,u1	ADJ
ejpam-447	107	23	)	)	PUNCT
ejpam-447	107	24	∂	∂	NUM
ejpam-447	107	25	u1	u1	NOUN
ejpam-447	107	26	=	=	PUNCT
ejpam-447	107	27	b+	b+	NUM
ejpam-447	107	28	q−pu0	q−pu0	NOUN
ejpam-447	107	29	(	(	PUNCT
ejpam-447	107	30	q+u1	q+u1	PROPN
ejpam-447	107	31	)	)	PUNCT
ejpam-447	107	32	2	2	NUM
ejpam-447	107	33	.	.	PUNCT
ejpam-447	108	1	(	(	PUNCT
ejpam-447	108	2	8)	8)	NUM
ejpam-447	108	3	e.	e.	PROPN
ejpam-447	108	4	zayed	zayed	PROPN
ejpam-447	108	5	/	/	SYM
ejpam-447	108	6	eur	eur	PROPN
ejpam-447	108	7	.	.	PUNCT
ejpam-447	109	1	j.	j.	PROPN
ejpam-447	109	2	pure	pure	PROPN
ejpam-447	109	3	appl	appl	PROPN
ejpam-447	109	4	.	.	PROPN
ejpam-447	109	5	math	math	PROPN
ejpam-447	109	6	,	,	PUNCT
ejpam-447	109	7	3	3	NUM
ejpam-447	109	8	(	(	PUNCT
ejpam-447	109	9	2010	2010	NUM
ejpam-447	109	10	)	)	PUNCT
ejpam-447	109	11	,	,	PUNCT
ejpam-447	109	12	254	254	NUM
ejpam-447	109	13	-	-	SYM
ejpam-447	109	14	268	268	NUM
ejpam-447	109	15	258	258	NUM
ejpam-447	109	16	from	from	ADP
ejpam-447	109	17	(	(	PUNCT
ejpam-447	109	18	6	6	NUM
ejpam-447	109	19	and	and	CCONJ
ejpam-447	109	20	(	(	PUNCT
ejpam-447	109	21	8)	8)	NUM
ejpam-447	109	22	we	we	PRON
ejpam-447	109	23	have	have	AUX
ejpam-447	109	24			PROPN
ejpam-447	109	25			PRON
ejpam-447	109	26			NOUN
ejpam-447	109	27	∂	∂	NOUN
ejpam-447	109	28	f(ex	f(ex	NUM
ejpam-447	109	29	,	,	PUNCT
ejpam-447	109	30	ex	ex	NOUN
ejpam-447	109	31	)	)	PUNCT
ejpam-447	109	32	∂	∂	NOUN
ejpam-447	109	33	u0	u0	NOUN
ejpam-447	109	34	=	=	SYM
ejpam-447	109	35	a+	a+	PUNCT
ejpam-447	109	36	p[1−(a+b	p[1−(a+b	PROPN
ejpam-447	109	37	)	)	PUNCT
ejpam-447	109	38	]	]	PUNCT
ejpam-447	110	1	p+1	p+1	NOUN
ejpam-447	110	2	=	=	SYM
ejpam-447	110	3	ρ0	ρ0	PROPN
ejpam-447	110	4	,	,	PUNCT
ejpam-447	110	5	∂	∂	PRON
ejpam-447	110	6	f(ex	f(ex	NUM
ejpam-447	110	7	,	,	PUNCT
ejpam-447	110	8	ex	ex	NOUN
ejpam-447	110	9	)	)	PUNCT
ejpam-447	110	10	∂	∂	NUM
ejpam-447	110	11	u1	u1	NOUN
ejpam-447	110	12	=	=	SYM
ejpam-447	110	13	b	b	NOUN
ejpam-447	110	14	−	−	PROPN
ejpam-447	111	1	[	[	X
ejpam-447	111	2	1−(a+b)][(p−q)+q(a+b	1−(a+b)][(p−q)+q(a+b	NUM
ejpam-447	111	3	)	)	PUNCT
ejpam-447	111	4	]	]	PUNCT
ejpam-447	112	1	p+1	p+1	NOUN
ejpam-447	112	2	=	=	SYM
ejpam-447	112	3	ρ1	ρ1	PROPN
ejpam-447	112	4	.	.	PUNCT
ejpam-447	113	1	(	(	PUNCT
ejpam-447	113	2	9	9	X
ejpam-447	113	3	)	)	PUNCT
ejpam-447	113	4	the	the	DET
ejpam-447	113	5	linearized	linearize	VERB
ejpam-447	113	6	equation	equation	NOUN
ejpam-447	113	7	of	of	ADP
ejpam-447	113	8	eq.(1	eq.(1	ADJ
ejpam-447	113	9	)	)	PUNCT
ejpam-447	113	10	about	about	ADP
ejpam-447	113	11	the	the	DET
ejpam-447	113	12	zero	zero	NUM
ejpam-447	113	13	equilibrium	equilibrium	NOUN
ejpam-447	113	14	point	point	NOUN
ejpam-447	113	15	ex	ex	X
ejpam-447	113	16	=	=	NOUN
ejpam-447	113	17	0	0	NUM
ejpam-447	113	18	is	be	AUX
ejpam-447	113	19	zn+1	zn+1	NUM
ejpam-447	113	20	−	−	PROPN
ejpam-447	113	21	�	�	PROPN
ejpam-447	113	22	a+	a+	PUNCT
ejpam-447	113	23	p	p	PROPN
ejpam-447	113	24	q	q	X
ejpam-447	113	25	�	�	PROPN
ejpam-447	113	26	zn	zn	PROPN
ejpam-447	113	27	−	−	PROPN
ejpam-447	113	28	�	�	PROPN
ejpam-447	113	29	b+	b+	VERB
ejpam-447	113	30	1	1	NUM
ejpam-447	113	31	q	q	PROPN
ejpam-447	113	32	�	�	PROPN
ejpam-447	113	33	zn−k	zn−k	NOUN
ejpam-447	113	34	=	=	SYM
ejpam-447	113	35	0	0	NUM
ejpam-447	113	36	,	,	PUNCT
ejpam-447	113	37	(	(	PUNCT
ejpam-447	113	38	10	10	NUM
ejpam-447	113	39	)	)	PUNCT
ejpam-447	113	40	and	and	CCONJ
ejpam-447	113	41	the	the	DET
ejpam-447	113	42	linearized	linearize	VERB
ejpam-447	113	43	equation	equation	NOUN
ejpam-447	113	44	of	of	ADP
ejpam-447	113	45	eq.(1	eq.(1	ADJ
ejpam-447	113	46	)	)	PUNCT
ejpam-447	113	47	about	about	ADP
ejpam-447	113	48	the	the	DET
ejpam-447	113	49	positive	positive	ADJ
ejpam-447	113	50	equilibrium	equilibrium	NOUN
ejpam-447	113	51	point	point	NOUN
ejpam-447	113	52	ex	ex	X
ejpam-447	113	53	is	be	AUX
ejpam-447	113	54	zn+1	zn+1	NUM
ejpam-447	113	55	−ρ0	−ρ0	NOUN
ejpam-447	113	56	zn−ρ1	zn−ρ1	NOUN
ejpam-447	113	57	zn−k	zn−k	NOUN
ejpam-447	113	58	=	=	SYM
ejpam-447	113	59	0	0	NUM
ejpam-447	113	60	,	,	PUNCT
ejpam-447	113	61	(	(	PUNCT
ejpam-447	113	62	11	11	NUM
ejpam-447	113	63	)	)	PUNCT
ejpam-447	113	64	where	where	SCONJ
ejpam-447	113	65	ρ0	ρ0	PROPN
ejpam-447	113	66	and	and	CCONJ
ejpam-447	113	67	ρ1	ρ1	NOUN
ejpam-447	113	68	are	be	AUX
ejpam-447	113	69	given	give	VERB
ejpam-447	113	70	by	by	ADP
ejpam-447	113	71	(	(	PUNCT
ejpam-447	113	72	9	9	NUM
ejpam-447	113	73	)	)	PUNCT
ejpam-447	113	74	.	.	PUNCT
ejpam-447	114	1	theorem	theorem	NOUN
ejpam-447	114	2	2	2	NUM
ejpam-447	114	3	.	.	PUNCT
ejpam-447	115	1	[	[	X
ejpam-447	115	2	20	20	NUM
ejpam-447	115	3	]	]	PUNCT
ejpam-447	115	4	assume	assume	VERB
ejpam-447	115	5	that	that	SCONJ
ejpam-447	115	6	ρ0,ρ1	ρ0,ρ1	PROPN
ejpam-447	115	7	∈	∈	PROPN
ejpam-447	115	8	r	r	NOUN
ejpam-447	115	9	and	and	CCONJ
ejpam-447	115	10	k	k	PROPN
ejpam-447	115	11	∈	∈	PROPN
ejpam-447	115	12	{	{	PUNCT
ejpam-447	115	13	1,2	1,2	NUM
ejpam-447	115	14	,	,	PUNCT
ejpam-447	115	15	...	...	PUNCT
ejpam-447	115	16	}	}	PUNCT
ejpam-447	115	17	.	.	PUNCT
ejpam-447	116	1	then	then	ADV
ejpam-447	116	2	�	�	PROPN
ejpam-447	116	3	�	�	PROPN
ejpam-447	116	4	ρ0	ρ0	PROPN
ejpam-447	116	5	�	�	PROPN
ejpam-447	116	6	�	�	PROPN
ejpam-447	116	7	+	+	SYM
ejpam-447	116	8	�	�	PROPN
ejpam-447	116	9	�	�	PROPN
ejpam-447	116	10	ρ1	ρ1	PROPN
ejpam-447	116	11	�	�	PROPN
ejpam-447	116	12	�	�	PROPN
ejpam-447	116	13	<	<	X
ejpam-447	116	14	1	1	NUM
ejpam-447	116	15	,	,	PUNCT
ejpam-447	116	16	(	(	PUNCT
ejpam-447	116	17	12	12	NUM
ejpam-447	116	18	)	)	PUNCT
ejpam-447	116	19	is	be	AUX
ejpam-447	116	20	a	a	DET
ejpam-447	116	21	sufficient	sufficient	ADJ
ejpam-447	116	22	condition	condition	NOUN
ejpam-447	116	23	for	for	ADP
ejpam-447	116	24	the	the	DET
ejpam-447	116	25	asymptotic	asymptotic	ADJ
ejpam-447	116	26	stability	stability	NOUN
ejpam-447	116	27	of	of	ADP
ejpam-447	116	28	the	the	DET
ejpam-447	116	29	difference	difference	NOUN
ejpam-447	116	30	equation	equation	NOUN
ejpam-447	116	31	(	(	PUNCT
ejpam-447	116	32	2	2	NUM
ejpam-447	116	33	)	)	PUNCT
ejpam-447	116	34	.	.	PUNCT
ejpam-447	117	1	suppose	suppose	VERB
ejpam-447	117	2	in	in	ADP
ejpam-447	117	3	addition	addition	NOUN
ejpam-447	117	4	that	that	SCONJ
ejpam-447	117	5	one	one	NUM
ejpam-447	117	6	of	of	ADP
ejpam-447	117	7	the	the	DET
ejpam-447	117	8	following	follow	VERB
ejpam-447	117	9	two	two	NUM
ejpam-447	117	10	cases	case	NOUN
ejpam-447	117	11	holds	hold	VERB
ejpam-447	117	12	:	:	PUNCT
ejpam-447	117	13	(	(	PUNCT
ejpam-447	117	14	i	i	NOUN
ejpam-447	117	15	)	)	PUNCT
ejpam-447	117	16	k	k	X
ejpam-447	117	17	is	be	AUX
ejpam-447	117	18	an	an	DET
ejpam-447	117	19	odd	odd	ADJ
ejpam-447	117	20	integer	integer	NOUN
ejpam-447	117	21	and	and	CCONJ
ejpam-447	117	22	ρ1	ρ1	NOUN
ejpam-447	117	23	>	>	X
ejpam-447	117	24	0	0	X
ejpam-447	117	25	.	.	PUNCT
ejpam-447	118	1	(	(	PUNCT
ejpam-447	118	2	ii	ii	X
ejpam-447	118	3	)	)	PUNCT
ejpam-447	118	4	k	k	PROPN
ejpam-447	118	5	is	be	AUX
ejpam-447	118	6	an	an	DET
ejpam-447	118	7	even	even	ADV
ejpam-447	118	8	integer	integer	NOUN
ejpam-447	118	9	and	and	CCONJ
ejpam-447	118	10	ρ0ρ1	ρ0ρ1	NOUN
ejpam-447	118	11	>	>	X
ejpam-447	118	12	0	0	X
ejpam-447	118	13	.	.	PUNCT
ejpam-447	119	1	then	then	ADV
ejpam-447	119	2	(	(	PUNCT
ejpam-447	119	3	12	12	NUM
ejpam-447	119	4	)	)	PUNCT
ejpam-447	119	5	is	be	AUX
ejpam-447	119	6	also	also	ADV
ejpam-447	119	7	a	a	DET
ejpam-447	119	8	necessary	necessary	ADJ
ejpam-447	119	9	condition	condition	NOUN
ejpam-447	119	10	for	for	ADP
ejpam-447	119	11	the	the	DET
ejpam-447	119	12	asymptotic	asymptotic	ADJ
ejpam-447	119	13	stability	stability	NOUN
ejpam-447	119	14	of	of	ADP
ejpam-447	119	15	eq.(2	eq.(2	ADJ
ejpam-447	119	16	)	)	PUNCT
ejpam-447	119	17	.	.	PUNCT
ejpam-447	120	1	theorem	theorem	VERB
ejpam-447	120	2	3	3	NUM
ejpam-447	120	3	.	.	PUNCT
ejpam-447	121	1	[	[	X
ejpam-447	121	2	15	15	NUM
ejpam-447	121	3	]	]	PUNCT
ejpam-447	121	4	consider	consider	VERB
ejpam-447	121	5	the	the	DET
ejpam-447	121	6	difference	difference	NOUN
ejpam-447	121	7	equation	equation	NOUN
ejpam-447	121	8	(	(	PUNCT
ejpam-447	121	9	2	2	NUM
ejpam-447	121	10	)	)	PUNCT
ejpam-447	121	11	where	where	SCONJ
ejpam-447	121	12	the	the	DET
ejpam-447	121	13	function	function	NOUN
ejpam-447	121	14	f	f	PROPN
ejpam-447	121	15	∈	∈	PROPN
ejpam-447	121	16	c	c	PROPN
ejpam-447	121	17	�	�	PROPN
ejpam-447	121	18	ik+1,r	ik+1,r	PROPN
ejpam-447	121	19	�	�	PROPN
ejpam-447	121	20	and	and	CCONJ
ejpam-447	121	21	i	i	PRON
ejpam-447	121	22	is	be	AUX
ejpam-447	121	23	an	an	DET
ejpam-447	121	24	open	open	ADJ
ejpam-447	121	25	interval	interval	NOUN
ejpam-447	121	26	of	of	ADP
ejpam-447	121	27	real	real	ADJ
ejpam-447	121	28	numbers	number	NOUN
ejpam-447	121	29	.	.	PUNCT
ejpam-447	122	1	let	let	VERB
ejpam-447	122	2	ex	ex	PRON
ejpam-447	122	3	∈	∈	NOUN
ejpam-447	123	1	i	i	PRON
ejpam-447	123	2	be	be	VERB
ejpam-447	123	3	an	an	DET
ejpam-447	123	4	equilibrium	equilibrium	NOUN
ejpam-447	123	5	point	point	NOUN
ejpam-447	123	6	of	of	ADP
ejpam-447	123	7	eq.(2	eq.(2	NOUN
ejpam-447	123	8	)	)	PUNCT
ejpam-447	123	9	.	.	PUNCT
ejpam-447	124	1	suppose	suppose	VERB
ejpam-447	124	2	also	also	ADV
ejpam-447	124	3	that	that	SCONJ
ejpam-447	124	4	(	(	PUNCT
ejpam-447	124	5	i	i	NOUN
ejpam-447	124	6	)	)	PUNCT
ejpam-447	124	7	f	f	PROPN
ejpam-447	124	8	is	be	AUX
ejpam-447	124	9	a	a	DET
ejpam-447	124	10	nondecreasing	nondecrease	VERB
ejpam-447	124	11	function	function	NOUN
ejpam-447	124	12	in	in	ADP
ejpam-447	124	13	each	each	PRON
ejpam-447	124	14	of	of	ADP
ejpam-447	124	15	its	its	PRON
ejpam-447	124	16	arguments	argument	NOUN
ejpam-447	124	17	.	.	PUNCT
ejpam-447	125	1	(	(	PUNCT
ejpam-447	125	2	ii	ii	NOUN
ejpam-447	125	3	)	)	PUNCT
ejpam-447	125	4	the	the	DET
ejpam-447	125	5	function	function	NOUN
ejpam-447	125	6	f	f	PROPN
ejpam-447	125	7	satisfies	satisfy	VERB
ejpam-447	125	8	the	the	DET
ejpam-447	125	9	negative	negative	ADJ
ejpam-447	125	10	feedback	feedback	NOUN
ejpam-447	125	11	property	property	NOUN
ejpam-447	126	1	[	[	X
ejpam-447	126	2	f	f	X
ejpam-447	126	3	(	(	PUNCT
ejpam-447	126	4	x	x	INTJ
ejpam-447	126	5	,	,	PUNCT
ejpam-447	126	6	x)−	x)−	PROPN
ejpam-447	126	7	x	x	X
ejpam-447	126	8	]	]	X
ejpam-447	126	9	(	(	PUNCT
ejpam-447	126	10	x	x	X
ejpam-447	126	11	−	−	X
ejpam-447	126	12	ex	ex	NOUN
ejpam-447	126	13	)	)	PUNCT
ejpam-447	126	14	<	<	X
ejpam-447	126	15	0	0	NUM
ejpam-447	126	16	for	for	ADP
ejpam-447	126	17	all	all	DET
ejpam-447	126	18	x	x	SYM
ejpam-447	126	19	∈	∈	PROPN
ejpam-447	127	1	i	i	PRON
ejpam-447	127	2	−	−	PROPN
ejpam-447	127	3	{	{	PUNCT
ejpam-447	127	4	ex	ex	NOUN
ejpam-447	127	5	}	}	PUNCT
ejpam-447	127	6	.	.	PUNCT
ejpam-447	128	1	then	then	ADV
ejpam-447	128	2	the	the	DET
ejpam-447	128	3	equilibrium	equilibrium	NOUN
ejpam-447	128	4	point	point	NOUN
ejpam-447	128	5	ex	ex	PRON
ejpam-447	128	6	of	of	ADP
ejpam-447	128	7	eq.(2	eq.(2	NOUN
ejpam-447	128	8	)	)	PUNCT
ejpam-447	128	9	is	be	AUX
ejpam-447	128	10	a	a	DET
ejpam-447	128	11	global	global	ADJ
ejpam-447	128	12	attractor	attractor	NOUN
ejpam-447	128	13	for	for	ADP
ejpam-447	128	14	all	all	DET
ejpam-447	128	15	solutions	solution	NOUN
ejpam-447	128	16	of	of	ADP
ejpam-447	128	17	eq.(2	eq.(2	NOUN
ejpam-447	128	18	)	)	PUNCT
ejpam-447	128	19	.	.	PUNCT
ejpam-447	129	1	e.	e.	PROPN
ejpam-447	129	2	zayed	zayed	PROPN
ejpam-447	129	3	/	/	SYM
ejpam-447	129	4	eur	eur	PROPN
ejpam-447	129	5	.	.	PUNCT
ejpam-447	130	1	j.	j.	PROPN
ejpam-447	130	2	pure	pure	PROPN
ejpam-447	130	3	appl	appl	PROPN
ejpam-447	130	4	.	.	PROPN
ejpam-447	130	5	math	math	PROPN
ejpam-447	130	6	,	,	PUNCT
ejpam-447	130	7	3	3	NUM
ejpam-447	130	8	(	(	PUNCT
ejpam-447	130	9	2010	2010	NUM
ejpam-447	130	10	)	)	PUNCT
ejpam-447	130	11	,	,	PUNCT
ejpam-447	130	12	254	254	NUM
ejpam-447	130	13	-	-	SYM
ejpam-447	130	14	268	268	NUM
ejpam-447	130	15	259	259	NUM
ejpam-447	130	16	2	2	NUM
ejpam-447	130	17	.	.	PUNCT
ejpam-447	130	18	semi	semi	ADJ
ejpam-447	130	19	-	-	ADJ
ejpam-447	130	20	cycle	cycle	ADJ
ejpam-447	130	21	analysis	analysis	NOUN
ejpam-447	130	22	theorem	theorem	VERB
ejpam-447	130	23	4	4	NUM
ejpam-447	130	24	.	.	PUNCT
ejpam-447	130	25	assume	assume	VERB
ejpam-447	130	26	that	that	SCONJ
ejpam-447	130	27	f	f	X
ejpam-447	130	28	:	:	PUNCT
ejpam-447	130	29	(	(	PUNCT
ejpam-447	130	30	0,∞)2	0,∞)2	NUM
ejpam-447	130	31	→	→	PUNCT
ejpam-447	130	32	(	(	PUNCT
ejpam-447	130	33	0,∞	0,∞	NUM
ejpam-447	130	34	)	)	PUNCT
ejpam-447	130	35	is	be	AUX
ejpam-447	130	36	a	a	DET
ejpam-447	130	37	continuous	continuous	ADJ
ejpam-447	130	38	function	function	NOUN
ejpam-447	130	39	such	such	ADJ
ejpam-447	130	40	that	that	SCONJ
ejpam-447	130	41	f(x	f(x	PROPN
ejpam-447	130	42	,	,	PUNCT
ejpam-447	130	43	y	y	PROPN
ejpam-447	130	44	)	)	PUNCT
ejpam-447	130	45	is	be	AUX
ejpam-447	130	46	increasing	increase	VERB
ejpam-447	130	47	in	in	ADP
ejpam-447	130	48	x	x	PUNCT
ejpam-447	130	49	for	for	ADP
ejpam-447	130	50	fixed	fix	VERB
ejpam-447	130	51	y	y	PROPN
ejpam-447	130	52	,	,	PUNCT
ejpam-447	130	53	and	and	CCONJ
ejpam-447	130	54	f(x	f(x	PROPN
ejpam-447	130	55	,	,	PUNCT
ejpam-447	130	56	y	y	PROPN
ejpam-447	130	57	)	)	PUNCT
ejpam-447	130	58	is	be	AUX
ejpam-447	130	59	increasing	increase	VERB
ejpam-447	130	60	in	in	ADP
ejpam-447	130	61	y	y	PROPN
ejpam-447	130	62	for	for	ADP
ejpam-447	130	63	fixed	fixed	ADJ
ejpam-447	131	1	x	x	X
ejpam-447	131	2	.	.	PUNCT
ejpam-447	132	1	let	let	VERB
ejpam-447	132	2	ex	ex	PRON
ejpam-447	132	3	be	be	AUX
ejpam-447	132	4	a	a	DET
ejpam-447	132	5	positive	positive	ADJ
ejpam-447	132	6	equilibrium	equilibrium	NOUN
ejpam-447	132	7	of	of	ADP
ejpam-447	132	8	eq.(1	eq.(1	ADJ
ejpam-447	132	9	)	)	PUNCT
ejpam-447	132	10	.	.	PUNCT
ejpam-447	133	1	then	then	ADV
ejpam-447	133	2	,	,	PUNCT
ejpam-447	133	3	except	except	SCONJ
ejpam-447	133	4	possibly	possibly	ADV
ejpam-447	133	5	for	for	ADP
ejpam-447	133	6	the	the	DET
ejpam-447	133	7	first	first	ADJ
ejpam-447	133	8	semi	semi	NOUN
ejpam-447	133	9	-	-	NOUN
ejpam-447	133	10	cycle	cycle	NOUN
ejpam-447	133	11	,	,	PUNCT
ejpam-447	133	12	every	every	DET
ejpam-447	133	13	oscillatory	oscillatory	ADJ
ejpam-447	133	14	solution	solution	NOUN
ejpam-447	133	15	of	of	ADP
ejpam-447	133	16	eq.(1	eq.(1	ADJ
ejpam-447	133	17	)	)	PUNCT
ejpam-447	133	18	has	have	VERB
ejpam-447	133	19	semi	semi	ADJ
ejpam-447	133	20	-	-	NOUN
ejpam-447	133	21	cycle	cycle	NOUN
ejpam-447	133	22	of	of	ADP
ejpam-447	133	23	length	length	NOUN
ejpam-447	133	24	at	at	ADP
ejpam-447	133	25	least	least	ADJ
ejpam-447	133	26	k.	k.	NOUN
ejpam-447	133	27	proof	proof	NOUN
ejpam-447	133	28	.	.	PUNCT
ejpam-447	134	1	we	we	PRON
ejpam-447	134	2	just	just	ADV
ejpam-447	134	3	give	give	VERB
ejpam-447	134	4	the	the	DET
ejpam-447	134	5	proof	proof	NOUN
ejpam-447	134	6	of	of	ADP
ejpam-447	134	7	the	the	DET
ejpam-447	134	8	theorem	theorem	NOUN
ejpam-447	134	9	4	4	NUM
ejpam-447	134	10	for	for	ADP
ejpam-447	134	11	k	k	NOUN
ejpam-447	134	12	=	=	SYM
ejpam-447	134	13	2	2	X
ejpam-447	134	14	.	.	PUNCT
ejpam-447	135	1	the	the	DET
ejpam-447	135	2	proof	proof	NOUN
ejpam-447	135	3	of	of	ADP
ejpam-447	135	4	the	the	DET
ejpam-447	135	5	theorem	theorem	NOUN
ejpam-447	135	6	4	4	NUM
ejpam-447	135	7	for	for	ADP
ejpam-447	135	8	k	k	PROPN
ejpam-447	135	9	≥	≥	NUM
ejpam-447	135	10	3	3	NUM
ejpam-447	135	11	,	,	PUNCT
ejpam-447	135	12	is	be	AUX
ejpam-447	135	13	similar	similar	ADJ
ejpam-447	135	14	and	and	CCONJ
ejpam-447	135	15	omitted	omit	VERB
ejpam-447	135	16	here	here	ADV
ejpam-447	135	17	.	.	PUNCT
ejpam-447	136	1	let	let	VERB
ejpam-447	136	2	�	�	PROPN
ejpam-447	136	3	xn	xn	PROPN
ejpam-447	136	4	be	be	AUX
ejpam-447	136	5	a	a	DET
ejpam-447	136	6	solution	solution	NOUN
ejpam-447	136	7	of	of	ADP
ejpam-447	136	8	eq.(1	eq.(1	ADJ
ejpam-447	136	9	)	)	PUNCT
ejpam-447	136	10	with	with	ADP
ejpam-447	136	11	at	at	ADV
ejpam-447	136	12	least	least	ADV
ejpam-447	136	13	three	three	NUM
ejpam-447	136	14	semi	semi	NOUN
ejpam-447	136	15	-	-	NOUN
ejpam-447	136	16	cycles	cycle	NOUN
ejpam-447	136	17	.	.	PUNCT
ejpam-447	137	1	then	then	ADV
ejpam-447	137	2	,	,	PUNCT
ejpam-447	137	3	there	there	PRON
ejpam-447	137	4	exists	exist	VERB
ejpam-447	137	5	n	n	PRON
ejpam-447	137	6	≥	≥	NOUN
ejpam-447	137	7	0	0	NUM
ejpam-447	137	8	such	such	ADJ
ejpam-447	137	9	that	that	SCONJ
ejpam-447	137	10	either	either	CCONJ
ejpam-447	137	11	xn+1	xn+1	PROPN
ejpam-447	137	12	≥	≥	NOUN
ejpam-447	137	13	xn−1	xn−1	PROPN
ejpam-447	137	14	≥	≥	NUM
ejpam-447	137	15	ex	ex	X
ejpam-447	137	16	,	,	PUNCT
ejpam-447	137	17	or	or	CCONJ
ejpam-447	137	18	xn−1	xn−1	PROPN
ejpam-447	137	19	≥	≥	NUM
ejpam-447	137	20	xn+1	xn+1	NUM
ejpam-447	137	21	≥	≥	NUM
ejpam-447	137	22	ex	ex	X
ejpam-447	137	23	.	.	PUNCT
ejpam-447	138	1	we	we	PRON
ejpam-447	138	2	first	first	ADV
ejpam-447	138	3	assume	assume	VERB
ejpam-447	138	4	that	that	SCONJ
ejpam-447	138	5	xn+1	xn+1	PROPN
ejpam-447	138	6	≥	≥	NUM
ejpam-447	138	7	xn−1	xn−1	PROPN
ejpam-447	138	8	≥	≥	NUM
ejpam-447	138	9	ex	ex	X
ejpam-447	138	10	.	.	PUNCT
ejpam-447	139	1	since	since	SCONJ
ejpam-447	139	2	the	the	DET
ejpam-447	139	3	function	function	NOUN
ejpam-447	139	4	f(x	f(x	PROPN
ejpam-447	139	5	,	,	PUNCT
ejpam-447	139	6	y	y	NOUN
ejpam-447	139	7	)	)	PUNCT
ejpam-447	139	8	given	give	VERB
ejpam-447	139	9	by	by	ADP
ejpam-447	139	10	(	(	PUNCT
ejpam-447	139	11	7	7	NUM
ejpam-447	139	12	)	)	PUNCT
ejpam-447	139	13	is	be	AUX
ejpam-447	139	14	increasing	increase	VERB
ejpam-447	139	15	in	in	ADP
ejpam-447	139	16	x	x	PUNCT
ejpam-447	139	17	for	for	ADP
ejpam-447	139	18	fixed	fixed	ADJ
ejpam-447	139	19	y	y	PROPN
ejpam-447	139	20	and	and	CCONJ
ejpam-447	139	21	increasing	increase	VERB
ejpam-447	139	22	in	in	ADP
ejpam-447	139	23	y	y	PROPN
ejpam-447	139	24	for	for	ADP
ejpam-447	139	25	fixed	fixed	ADJ
ejpam-447	139	26	x	x	SYM
ejpam-447	139	27	,	,	PUNCT
ejpam-447	139	28	then	then	ADV
ejpam-447	139	29	we	we	PRON
ejpam-447	139	30	get	get	VERB
ejpam-447	139	31	xn+2	xn+2	NUM
ejpam-447	139	32	=	=	SYM
ejpam-447	139	33	f(xn+1	f(xn+1	PROPN
ejpam-447	139	34	,	,	PUNCT
ejpam-447	139	35	xn−1	xn−1	PROPN
ejpam-447	139	36	)	)	PUNCT
ejpam-447	139	37	=	=	PUNCT
ejpam-447	139	38	axn+1	axn+1	PROPN
ejpam-447	139	39	+	+	X
ejpam-447	139	40	bxn−1	bxn−1	PROPN
ejpam-447	139	41	+	+	CCONJ
ejpam-447	139	42	pxn+1	pxn+1	PROPN
ejpam-447	139	43	+	+	CCONJ
ejpam-447	139	44	xn−1	xn−1	PROPN
ejpam-447	139	45	q+	q+	PUNCT
ejpam-447	139	46	xn−1	xn−1	PROPN
ejpam-447	139	47	≥	≥	PROPN
ejpam-447	139	48	aex	aex	PROPN
ejpam-447	139	49	+	+	CCONJ
ejpam-447	139	50	bxn−1	bxn−1	PROPN
ejpam-447	139	51	+	+	CCONJ
ejpam-447	139	52	pex	pex	PROPN
ejpam-447	139	53	+	+	CCONJ
ejpam-447	139	54	xn−1	xn−1	PROPN
ejpam-447	139	55	q+	q+	PUNCT
ejpam-447	139	56	xn−1	xn−1	PROPN
ejpam-447	139	57	=	=	PROPN
ejpam-447	139	58	f(ex	f(ex	NUM
ejpam-447	139	59	,	,	PUNCT
ejpam-447	139	60	xn−1)≥	xn−1)≥	PROPN
ejpam-447	139	61	f(ex	f(ex	NUM
ejpam-447	139	62	,	,	PUNCT
ejpam-447	139	63	ex	ex	NOUN
ejpam-447	139	64	)	)	PUNCT
ejpam-447	139	65	=	=	SYM
ejpam-447	139	66	ex	ex	X
ejpam-447	139	67	,	,	PUNCT
ejpam-447	139	68	and	and	CCONJ
ejpam-447	139	69	xn+3	xn+3	PROPN
ejpam-447	139	70	=	=	SYM
ejpam-447	139	71	f(xn+2	f(xn+2	PROPN
ejpam-447	139	72	,	,	PUNCT
ejpam-447	139	73	xn	xn	PROPN
ejpam-447	139	74	)	)	PUNCT
ejpam-447	139	75	>	>	X
ejpam-447	139	76	f(ex	f(ex	NUM
ejpam-447	139	77	,	,	PUNCT
ejpam-447	139	78	xn	xn	PROPN
ejpam-447	139	79	)	)	PUNCT
ejpam-447	139	80	>	>	X
ejpam-447	140	1	f(ex	f(ex	PUNCT
ejpam-447	140	2	,	,	PUNCT
ejpam-447	140	3	ex	ex	NOUN
ejpam-447	140	4	)	)	PUNCT
ejpam-447	140	5	=	=	SYM
ejpam-447	141	1	ex	ex	X
ejpam-447	141	2	f	f	NOUN
ejpam-447	141	3	or	or	CCONJ
ejpam-447	141	4	xn	xn	PROPN
ejpam-447	141	5	>	>	X
ejpam-447	141	6	ex	ex	X
ejpam-447	141	7	.	.	PUNCT
ejpam-447	142	1	similarly	similarly	ADV
ejpam-447	142	2	,	,	PUNCT
ejpam-447	142	3	we	we	PRON
ejpam-447	142	4	can	can	AUX
ejpam-447	142	5	prove	prove	VERB
ejpam-447	142	6	the	the	DET
ejpam-447	142	7	theorem	theorem	NOUN
ejpam-447	142	8	if	if	SCONJ
ejpam-447	142	9	xn−1	xn−1	PROPN
ejpam-447	142	10	≥	≥	AUX
ejpam-447	142	11	xn+1	xn+1	NUM
ejpam-447	142	12	≥	≥	NUM
ejpam-447	142	13	ex	ex	X
ejpam-447	142	14	which	which	PRON
ejpam-447	142	15	is	be	AUX
ejpam-447	142	16	omitted	omit	VERB
ejpam-447	142	17	.	.	PUNCT
ejpam-447	143	1	now	now	ADV
ejpam-447	143	2	,	,	PUNCT
ejpam-447	143	3	the	the	DET
ejpam-447	143	4	proof	proof	NOUN
ejpam-447	143	5	of	of	ADP
ejpam-447	143	6	theorem	theorem	ADJ
ejpam-447	143	7	4	4	NUM
ejpam-447	143	8	is	be	AUX
ejpam-447	143	9	completed	complete	VERB
ejpam-447	143	10	.	.	PUNCT
ejpam-447	144	1	3	3	X
ejpam-447	144	2	.	.	X
ejpam-447	144	3	local	local	ADJ
ejpam-447	144	4	stability	stability	NOUN
ejpam-447	144	5	in	in	ADP
ejpam-447	144	6	this	this	DET
ejpam-447	144	7	section	section	NOUN
ejpam-447	144	8	,	,	PUNCT
ejpam-447	144	9	we	we	PRON
ejpam-447	144	10	investigate	investigate	VERB
ejpam-447	144	11	the	the	DET
ejpam-447	144	12	local	local	ADJ
ejpam-447	144	13	stability	stability	NOUN
ejpam-447	144	14	of	of	ADP
ejpam-447	144	15	the	the	DET
ejpam-447	144	16	positive	positive	ADJ
ejpam-447	144	17	solutions	solution	NOUN
ejpam-447	144	18	of	of	ADP
ejpam-447	144	19	eq.(1	eq.(1	ADJ
ejpam-447	144	20	)	)	PUNCT
ejpam-447	144	21	.	.	PUNCT
ejpam-447	145	1	by	by	ADP
ejpam-447	145	2	using	use	VERB
ejpam-447	145	3	theorems	theorem	NOUN
ejpam-447	145	4	1	1	NUM
ejpam-447	145	5	and	and	CCONJ
ejpam-447	145	6	3	3	NUM
ejpam-447	145	7	,	,	PUNCT
ejpam-447	145	8	we	we	PRON
ejpam-447	145	9	have	have	VERB
ejpam-447	145	10	the	the	DET
ejpam-447	145	11	following	follow	VERB
ejpam-447	145	12	result	result	NOUN
ejpam-447	145	13	.	.	PUNCT
ejpam-447	146	1	theorem	theorem	ADJ
ejpam-447	146	2	5	5	NUM
ejpam-447	146	3	.	.	PUNCT
ejpam-447	147	1	the	the	DET
ejpam-447	147	2	zero	zero	NUM
ejpam-447	147	3	equilibrium	equilibrium	NOUN
ejpam-447	147	4	point	point	NOUN
ejpam-447	147	5	ex	ex	X
ejpam-447	147	6	=	=	NOUN
ejpam-447	147	7	0	0	NUM
ejpam-447	147	8	is	be	AUX
ejpam-447	147	9	locally	locally	ADV
ejpam-447	147	10	asymptotically	asymptotically	ADV
ejpam-447	147	11	stable	stable	ADJ
ejpam-447	147	12	if	if	SCONJ
ejpam-447	147	13	p	p	NOUN
ejpam-447	147	14	−	−	PROPN
ejpam-447	147	15	q	q	NOUN
ejpam-447	148	1	<	<	X
ejpam-447	148	2	−	−	X
ejpam-447	148	3	�	�	PROPN
ejpam-447	148	4	1	1	NUM
ejpam-447	148	5	+	+	NOUN
ejpam-447	148	6	q	q	NOUN
ejpam-447	148	7	(	(	PUNCT
ejpam-447	148	8	a+	a+	NOUN
ejpam-447	148	9	b	b	PROPN
ejpam-447	148	10	)	)	PUNCT
ejpam-447	148	11	�	�	PROPN
ejpam-447	148	12	.	.	PUNCT
ejpam-447	149	1	in	in	ADP
ejpam-447	149	2	particular	particular	ADJ
ejpam-447	149	3	,	,	PUNCT
ejpam-447	149	4	if	if	SCONJ
ejpam-447	149	5	p−	p−	PRON
ejpam-447	149	6	q	q	NOUN
ejpam-447	149	7	≥	≥	PUNCT
ejpam-447	149	8	−	−	PROPN
ejpam-447	149	9	�	�	PROPN
ejpam-447	149	10	1	1	NUM
ejpam-447	149	11	+	+	NOUN
ejpam-447	149	12	q	q	NOUN
ejpam-447	149	13	(	(	PUNCT
ejpam-447	149	14	a+	a+	NOUN
ejpam-447	149	15	b	b	X
ejpam-447	149	16	)	)	PUNCT
ejpam-447	149	17	�	�	PROPN
ejpam-447	149	18	,	,	PUNCT
ejpam-447	149	19	then	then	ADV
ejpam-447	149	20	ex	ex	ADJ
ejpam-447	149	21	=	=	SYM
ejpam-447	149	22	0	0	NUM
ejpam-447	149	23	is	be	AUX
ejpam-447	149	24	unstable	unstable	ADJ
ejpam-447	149	25	.	.	PUNCT
ejpam-447	150	1	proof	proof	NOUN
ejpam-447	150	2	.	.	PUNCT
ejpam-447	151	1	first	first	ADV
ejpam-447	151	2	,	,	PUNCT
ejpam-447	151	3	suppose	suppose	VERB
ejpam-447	151	4	that	that	SCONJ
ejpam-447	151	5	p−	p−	NOUN
ejpam-447	151	6	q	q	NOUN
ejpam-447	151	7	<	<	X
ejpam-447	151	8	−	−	PROPN
ejpam-447	151	9	�	�	PROPN
ejpam-447	151	10	1	1	NUM
ejpam-447	151	11	+	+	NOUN
ejpam-447	151	12	q	q	NOUN
ejpam-447	151	13	(	(	PUNCT
ejpam-447	151	14	a+	a+	NOUN
ejpam-447	151	15	b	b	PROPN
ejpam-447	151	16	)	)	PUNCT
ejpam-447	151	17	�	�	PROPN
ejpam-447	151	18	.	.	PUNCT
ejpam-447	152	1	then	then	ADV
ejpam-447	152	2	,	,	PUNCT
ejpam-447	152	3	from	from	ADP
ejpam-447	152	4	eq.(10	eq.(10	ADJ
ejpam-447	152	5	)	)	PUNCT
ejpam-447	152	6	we	we	PRON
ejpam-447	152	7	deduce	deduce	VERB
ejpam-447	152	8	that	that	SCONJ
ejpam-447	152	9	�	�	PROPN
ejpam-447	152	10	�	�	PROPN
ejpam-447	152	11	�	�	PROPN
ejpam-447	152	12	�	�	PROPN
ejpam-447	152	13	a+	a+	PUNCT
ejpam-447	152	14	p	p	PROPN
ejpam-447	152	15	q	q	PROPN
ejpam-447	152	16	�	�	PROPN
ejpam-447	152	17	�	�	PROPN
ejpam-447	152	18	�	�	PROPN
ejpam-447	152	19	�	�	PROPN
ejpam-447	152	20	+	+	SYM
ejpam-447	152	21	�	�	PROPN
ejpam-447	152	22	�	�	PROPN
ejpam-447	152	23	�	�	PROPN
ejpam-447	152	24	�	�	PROPN
ejpam-447	152	25	b+	b+	AUX
ejpam-447	152	26	1	1	NUM
ejpam-447	152	27	q	q	PROPN
ejpam-447	152	28	�	�	PROPN
ejpam-447	152	29	�	�	PROPN
ejpam-447	152	30	�	�	PROPN
ejpam-447	152	31	�	�	PROPN
ejpam-447	152	32	=	=	PUNCT
ejpam-447	152	33	(	(	PUNCT
ejpam-447	152	34	a+	a+	NOUN
ejpam-447	152	35	b	b	X
ejpam-447	152	36	)	)	PUNCT
ejpam-447	152	37	+	+	X
ejpam-447	152	38	p+	p+	VERB
ejpam-447	152	39	1	1	NUM
ejpam-447	152	40	q	q	NOUN
ejpam-447	152	41	<	<	X
ejpam-447	152	42	(	(	PUNCT
ejpam-447	152	43	a+	a+	NOUN
ejpam-447	152	44	b	b	NOUN
ejpam-447	152	45	)	)	PUNCT
ejpam-447	153	1	+	+	NUM
ejpam-447	153	2	q	q	X
ejpam-447	154	1	[	[	X
ejpam-447	154	2	1−	1−	NUM
ejpam-447	154	3	(	(	PUNCT
ejpam-447	154	4	a+	a+	NOUN
ejpam-447	154	5	b	b	NOUN
ejpam-447	154	6	)	)	PUNCT
ejpam-447	154	7	]	]	PUNCT
ejpam-447	154	8	q	q	X
ejpam-447	154	9	=	=	NOUN
ejpam-447	154	10	1	1	X
ejpam-447	154	11	.	.	PUNCT
ejpam-447	154	12	e.	e.	PROPN
ejpam-447	154	13	zayed	zayed	PROPN
ejpam-447	154	14	/	/	SYM
ejpam-447	154	15	eur	eur	PROPN
ejpam-447	154	16	.	.	PUNCT
ejpam-447	155	1	j.	j.	PROPN
ejpam-447	155	2	pure	pure	PROPN
ejpam-447	155	3	appl	appl	PROPN
ejpam-447	155	4	.	.	PROPN
ejpam-447	155	5	math	math	PROPN
ejpam-447	155	6	,	,	PUNCT
ejpam-447	155	7	3	3	NUM
ejpam-447	155	8	(	(	PUNCT
ejpam-447	155	9	2010	2010	NUM
ejpam-447	155	10	)	)	PUNCT
ejpam-447	155	11	,	,	PUNCT
ejpam-447	155	12	254	254	NUM
ejpam-447	155	13	-	-	SYM
ejpam-447	155	14	268	268	NUM
ejpam-447	155	15	260	260	NUM
ejpam-447	155	16	thus	thus	ADV
ejpam-447	155	17	ex	ex	X
ejpam-447	155	18	=	=	SYM
ejpam-447	155	19	0	0	NUM
ejpam-447	155	20	is	be	AUX
ejpam-447	155	21	locally	locally	ADV
ejpam-447	155	22	asymptotically	asymptotically	ADV
ejpam-447	155	23	stable	stable	ADJ
ejpam-447	155	24	.	.	PUNCT
ejpam-447	156	1	in	in	ADP
ejpam-447	156	2	particular	particular	ADJ
ejpam-447	156	3	,	,	PUNCT
ejpam-447	156	4	assume	assume	VERB
ejpam-447	156	5	p−	p−	ADJ
ejpam-447	156	6	q	q	NOUN
ejpam-447	156	7	≥	≥	PUNCT
ejpam-447	156	8	−	−	PROPN
ejpam-447	156	9	�	�	PROPN
ejpam-447	156	10	1	1	NUM
ejpam-447	156	11	+	+	NOUN
ejpam-447	156	12	q	q	NOUN
ejpam-447	156	13	(	(	PUNCT
ejpam-447	156	14	a+	a+	NOUN
ejpam-447	156	15	b	b	X
ejpam-447	156	16	)	)	PUNCT
ejpam-447	156	17	�	�	PROPN
ejpam-447	156	18	,	,	PUNCT
ejpam-447	156	19	then	then	ADV
ejpam-447	156	20	we	we	PRON
ejpam-447	156	21	have	have	VERB
ejpam-447	156	22	�	�	PROPN
ejpam-447	156	23	�	�	PROPN
ejpam-447	156	24	�	�	PROPN
ejpam-447	156	25	�	�	PROPN
ejpam-447	156	26	a+	a+	PUNCT
ejpam-447	156	27	p	p	PROPN
ejpam-447	156	28	q	q	PROPN
ejpam-447	156	29	�	�	PROPN
ejpam-447	156	30	�	�	PROPN
ejpam-447	156	31	�	�	PROPN
ejpam-447	156	32	�	�	PROPN
ejpam-447	156	33	+	+	SYM
ejpam-447	156	34	�	�	PROPN
ejpam-447	156	35	�	�	PROPN
ejpam-447	156	36	�	�	PROPN
ejpam-447	156	37	�	�	PROPN
ejpam-447	156	38	b+	b+	AUX
ejpam-447	156	39	1	1	NUM
ejpam-447	156	40	q	q	PROPN
ejpam-447	156	41	�	�	PROPN
ejpam-447	156	42	�	�	PROPN
ejpam-447	156	43	�	�	PROPN
ejpam-447	156	44	�	�	PROPN
ejpam-447	156	45	=	=	PUNCT
ejpam-447	156	46	(	(	PUNCT
ejpam-447	156	47	a+	a+	NOUN
ejpam-447	156	48	b	b	X
ejpam-447	156	49	)	)	PUNCT
ejpam-447	157	1	+	+	X
ejpam-447	157	2	p+	p+	VERB
ejpam-447	157	3	1	1	NUM
ejpam-447	157	4	q	q	NOUN
ejpam-447	157	5	≥	≥	X
ejpam-447	157	6	(	(	PUNCT
ejpam-447	157	7	a+	a+	X
ejpam-447	157	8	b	b	X
ejpam-447	157	9	)	)	PUNCT
ejpam-447	157	10	+	+	NUM
ejpam-447	157	11	q	q	X
ejpam-447	158	1	[	[	X
ejpam-447	158	2	1−	1−	NUM
ejpam-447	158	3	(	(	PUNCT
ejpam-447	158	4	a+	a+	NOUN
ejpam-447	158	5	b	b	NOUN
ejpam-447	158	6	)	)	PUNCT
ejpam-447	158	7	]	]	PUNCT
ejpam-447	158	8	q	q	X
ejpam-447	158	9	=	=	NOUN
ejpam-447	158	10	1	1	X
ejpam-447	158	11	.	.	PUNCT
ejpam-447	158	12	thus	thus	ADV
ejpam-447	158	13	ex	ex	X
ejpam-447	158	14	=	=	SYM
ejpam-447	158	15	0	0	NUM
ejpam-447	158	16	is	be	AUX
ejpam-447	158	17	unstable	unstable	ADJ
ejpam-447	158	18	.	.	PUNCT
ejpam-447	159	1	the	the	DET
ejpam-447	159	2	proof	proof	NOUN
ejpam-447	159	3	of	of	ADP
ejpam-447	159	4	theorem	theorem	NOUN
ejpam-447	159	5	6	6	NUM
ejpam-447	159	6	is	be	AUX
ejpam-447	159	7	now	now	ADV
ejpam-447	159	8	completed	complete	VERB
ejpam-447	159	9	.	.	PUNCT
ejpam-447	160	1	theorem	theorem	VERB
ejpam-447	160	2	6	6	NUM
ejpam-447	160	3	.	.	PUNCT
ejpam-447	161	1	if	if	SCONJ
ejpam-447	161	2	�	�	PROPN
ejpam-447	161	3	p−	p−	PROPN
ejpam-447	161	4	q	q	PROPN
ejpam-447	161	5	�	�	PROPN
ejpam-447	161	6	>	>	X
ejpam-447	161	7	−	−	PROPN
ejpam-447	161	8	�	�	PROPN
ejpam-447	161	9	1	1	NUM
ejpam-447	161	10	+	+	NOUN
ejpam-447	161	11	q	q	NOUN
ejpam-447	161	12	(	(	PUNCT
ejpam-447	161	13	a+	a+	NOUN
ejpam-447	161	14	b	b	X
ejpam-447	161	15	)	)	PUNCT
ejpam-447	161	16	�	�	PROPN
ejpam-447	161	17	,	,	PUNCT
ejpam-447	161	18	0	0	PUNCT
ejpam-447	161	19	<	<	X
ejpam-447	161	20	a+	a+	PRON
ejpam-447	161	21	b	b	X
ejpam-447	161	22	<	<	X
ejpam-447	161	23	1	1	NUM
ejpam-447	161	24	,	,	PUNCT
ejpam-447	161	25	p	p	X
ejpam-447	161	26	>	>	X
ejpam-447	161	27	q	q	PROPN
ejpam-447	161	28	and	and	CCONJ
ejpam-447	161	29	b	b	X
ejpam-447	161	30	>	>	X
ejpam-447	162	1	[	[	X
ejpam-447	162	2	1−	1−	NUM
ejpam-447	162	3	(	(	PUNCT
ejpam-447	162	4	a+	a+	NOUN
ejpam-447	162	5	b	b	NOUN
ejpam-447	162	6	)	)	PUNCT
ejpam-447	162	7	]	]	PUNCT
ejpam-447	162	8	�	�	PROPN
ejpam-447	162	9	�	�	PROPN
ejpam-447	162	10	p−	p−	PROPN
ejpam-447	162	11	q	q	PROPN
ejpam-447	162	12	�	�	PROPN
ejpam-447	162	13	+	+	CCONJ
ejpam-447	162	14	q	q	X
ejpam-447	162	15	(	(	PUNCT
ejpam-447	162	16	a+	a+	PRON
ejpam-447	162	17	b	b	X
ejpam-447	162	18	)	)	PUNCT
ejpam-447	162	19	�	�	PROPN
ejpam-447	162	20	�	�	PROPN
ejpam-447	162	21	p+	p+	PART
ejpam-447	162	22	1	1	NUM
ejpam-447	162	23	�	�	PROPN
ejpam-447	162	24	�	�	PROPN
ejpam-447	162	25	q+	q+	ADP
ejpam-447	162	26	1	1	NUM
ejpam-447	162	27	�	�	PROPN
ejpam-447	162	28	.	.	PUNCT
ejpam-447	163	1	then	then	ADV
ejpam-447	163	2	,	,	PUNCT
ejpam-447	163	3	the	the	DET
ejpam-447	163	4	positive	positive	ADJ
ejpam-447	163	5	equilibrium	equilibrium	NOUN
ejpam-447	163	6	point	point	NOUN
ejpam-447	163	7	ex	ex	X
ejpam-447	163	8	is	be	AUX
ejpam-447	163	9	locally	locally	ADV
ejpam-447	163	10	asymptotically	asymptotically	ADV
ejpam-447	163	11	stable	stable	ADJ
ejpam-447	163	12	.	.	PUNCT
ejpam-447	164	1	furthermore	furthermore	ADV
ejpam-447	164	2	,	,	PUNCT
ejpam-447	164	3	the	the	DET
ejpam-447	164	4	condition	condition	NOUN
ejpam-447	164	5	(	(	PUNCT
ejpam-447	164	6	12	12	NUM
ejpam-447	164	7	)	)	PUNCT
ejpam-447	164	8	can	can	AUX
ejpam-447	164	9	be	be	AUX
ejpam-447	164	10	considered	consider	VERB
ejpam-447	164	11	as	as	ADP
ejpam-447	164	12	a	a	DET
ejpam-447	164	13	necessary	necessary	ADJ
ejpam-447	164	14	and	and	CCONJ
ejpam-447	164	15	sufficient	sufficient	ADJ
ejpam-447	164	16	condition	condition	NOUN
ejpam-447	164	17	for	for	ADP
ejpam-447	164	18	the	the	DET
ejpam-447	164	19	asymptotically	asymptotically	ADJ
ejpam-447	164	20	stability	stability	NOUN
ejpam-447	164	21	of	of	ADP
ejpam-447	164	22	eq.(1	eq.(1	ADJ
ejpam-447	164	23	)	)	PUNCT
ejpam-447	164	24	.	.	PUNCT
ejpam-447	165	1	proof	proof	NOUN
ejpam-447	165	2	.	.	PUNCT
ejpam-447	166	1	under	under	ADP
ejpam-447	166	2	these	these	DET
ejpam-447	166	3	assumptions	assumption	NOUN
ejpam-447	166	4	we	we	PRON
ejpam-447	166	5	deduce	deduce	VERB
ejpam-447	166	6	from	from	ADP
ejpam-447	166	7	(	(	PUNCT
ejpam-447	166	8	9	9	NUM
ejpam-447	166	9	)	)	PUNCT
ejpam-447	167	1	that	that	PRON
ejpam-447	167	2	�	�	PROPN
ejpam-447	167	3	�	�	PROPN
ejpam-447	167	4	ρ0	ρ0	PROPN
ejpam-447	167	5	�	�	PROPN
ejpam-447	167	6	�	�	PROPN
ejpam-447	167	7	+	+	SYM
ejpam-447	167	8	�	�	PROPN
ejpam-447	167	9	�	�	PROPN
ejpam-447	167	10	ρ1	ρ1	PROPN
ejpam-447	167	11	�	�	PROPN
ejpam-447	167	12	�	�	PROPN
ejpam-447	167	13	=	=	SYM
ejpam-447	167	14	�	�	PROPN
ejpam-447	167	15	�	�	PROPN
ejpam-447	167	16	�	�	PROPN
ejpam-447	167	17	�	�	PROPN
ejpam-447	167	18	a+	a+	PUNCT
ejpam-447	167	19	p	p	X
ejpam-447	168	1	[	[	X
ejpam-447	168	2	1−	1−	NUM
ejpam-447	168	3	(	(	PUNCT
ejpam-447	168	4	a+	a+	NOUN
ejpam-447	168	5	b	b	NOUN
ejpam-447	168	6	)	)	PUNCT
ejpam-447	168	7	]	]	PUNCT
ejpam-447	168	8	p+	p+	VERB
ejpam-447	168	9	1	1	NUM
ejpam-447	168	10	�	�	PROPN
ejpam-447	168	11	�	�	PROPN
ejpam-447	168	12	�	�	PROPN
ejpam-447	168	13	�	�	PROPN
ejpam-447	168	14	+	+	SYM
ejpam-447	168	15	�	�	PROPN
ejpam-447	168	16	�	�	PROPN
ejpam-447	168	17	�	�	PROPN
ejpam-447	168	18	�	�	NOUN
ejpam-447	168	19	b−	b−	PROPN
ejpam-447	168	20	[	[	X
ejpam-447	168	21	1−	1−	NUM
ejpam-447	168	22	(	(	PUNCT
ejpam-447	168	23	a+	a+	NOUN
ejpam-447	168	24	b	b	NOUN
ejpam-447	168	25	)	)	PUNCT
ejpam-447	168	26	]	]	PUNCT
ejpam-447	168	27	�	�	PROPN
ejpam-447	168	28	�	�	PROPN
ejpam-447	168	29	p−	p−	PROPN
ejpam-447	168	30	q	q	PROPN
ejpam-447	168	31	�	�	PROPN
ejpam-447	168	32	+	+	CCONJ
ejpam-447	168	33	q	q	X
ejpam-447	168	34	(	(	PUNCT
ejpam-447	168	35	a+	a+	PRON
ejpam-447	168	36	b	b	X
ejpam-447	168	37	)	)	PUNCT
ejpam-447	168	38	�	�	PROPN
ejpam-447	168	39	p+	p+	PART
ejpam-447	168	40	1	1	NUM
ejpam-447	168	41	�	�	PROPN
ejpam-447	168	42	�	�	PROPN
ejpam-447	168	43	�	�	PROPN
ejpam-447	168	44	�	�	PROPN
ejpam-447	168	45	=	=	X
ejpam-447	168	46	a+	a+	PUNCT
ejpam-447	168	47	p	p	X
ejpam-447	169	1	[	[	X
ejpam-447	169	2	1−	1−	NUM
ejpam-447	169	3	(	(	PUNCT
ejpam-447	169	4	a+	a+	NOUN
ejpam-447	169	5	b	b	NOUN
ejpam-447	169	6	)	)	PUNCT
ejpam-447	169	7	]	]	PUNCT
ejpam-447	169	8	p+	p+	VERB
ejpam-447	169	9	1	1	NUM
ejpam-447	170	1	+	+	SYM
ejpam-447	170	2	b	b	NOUN
ejpam-447	170	3	−	−	NOUN
ejpam-447	171	1	[	[	X
ejpam-447	171	2	1−	1−	NUM
ejpam-447	171	3	(	(	PUNCT
ejpam-447	171	4	a+	a+	NOUN
ejpam-447	171	5	b	b	NOUN
ejpam-447	171	6	)	)	PUNCT
ejpam-447	171	7	]	]	PUNCT
ejpam-447	171	8	�	�	PROPN
ejpam-447	171	9	�	�	PROPN
ejpam-447	171	10	p−	p−	PROPN
ejpam-447	171	11	q	q	PROPN
ejpam-447	171	12	�	�	PROPN
ejpam-447	171	13	+	+	CCONJ
ejpam-447	171	14	q	q	X
ejpam-447	171	15	(	(	PUNCT
ejpam-447	171	16	a+	a+	PRON
ejpam-447	171	17	b	b	X
ejpam-447	171	18	)	)	PUNCT
ejpam-447	171	19	�	�	PROPN
ejpam-447	171	20	p+	p+	VERB
ejpam-447	171	21	1	1	NUM
ejpam-447	171	22	<	<	X
ejpam-447	171	23	(	(	PUNCT
ejpam-447	171	24	a+	a+	PRON
ejpam-447	171	25	b	b	X
ejpam-447	171	26	)	)	PUNCT
ejpam-447	171	27	�	�	PROPN
ejpam-447	171	28	p+	p+	PART
ejpam-447	171	29	1	1	NUM
ejpam-447	171	30	�	�	PROPN
ejpam-447	171	31	+	+	CCONJ
ejpam-447	171	32	�	�	PROPN
ejpam-447	171	33	p+	p+	PART
ejpam-447	171	34	1	1	NUM
ejpam-447	171	35	�	�	PROPN
ejpam-447	172	1	[	[	X
ejpam-447	172	2	1−	1−	NUM
ejpam-447	172	3	(	(	PUNCT
ejpam-447	172	4	a+	a+	NOUN
ejpam-447	172	5	b	b	NOUN
ejpam-447	172	6	)	)	PUNCT
ejpam-447	172	7	]	]	PUNCT
ejpam-447	172	8	p+	p+	VERB
ejpam-447	172	9	1	1	NUM
ejpam-447	172	10	=	=	SYM
ejpam-447	172	11	1	1	NUM
ejpam-447	172	12	.	.	PUNCT
ejpam-447	173	1	this	this	PRON
ejpam-447	173	2	proves	prove	VERB
ejpam-447	173	3	that	that	SCONJ
ejpam-447	173	4	the	the	DET
ejpam-447	173	5	positive	positive	ADJ
ejpam-447	173	6	equilibrium	equilibrium	NOUN
ejpam-447	173	7	point	point	NOUN
ejpam-447	173	8	ex	ex	PRON
ejpam-447	173	9	of	of	ADP
ejpam-447	173	10	eq.(1	eq.(1	ADJ
ejpam-447	173	11	)	)	PUNCT
ejpam-447	173	12	is	be	AUX
ejpam-447	173	13	locally	locally	ADV
ejpam-447	173	14	asymptotically	asymptotically	ADV
ejpam-447	173	15	stable	stable	ADJ
ejpam-447	173	16	.	.	PUNCT
ejpam-447	174	1	thus	thus	ADV
ejpam-447	174	2	,	,	PUNCT
ejpam-447	174	3	the	the	DET
ejpam-447	174	4	condition	condition	NOUN
ejpam-447	174	5	(	(	PUNCT
ejpam-447	174	6	12	12	NUM
ejpam-447	174	7	)	)	PUNCT
ejpam-447	174	8	is	be	AUX
ejpam-447	174	9	sufficient	sufficient	ADJ
ejpam-447	174	10	for	for	ADP
ejpam-447	174	11	the	the	DET
ejpam-447	174	12	asymptotic	asymptotic	ADJ
ejpam-447	174	13	stability	stability	NOUN
ejpam-447	174	14	of	of	ADP
ejpam-447	174	15	eq.(1	eq.(1	ADJ
ejpam-447	174	16	)	)	PUNCT
ejpam-447	174	17	.	.	PUNCT
ejpam-447	175	1	in	in	ADP
ejpam-447	175	2	addition	addition	NOUN
ejpam-447	175	3	to	to	ADP
ejpam-447	175	4	that	that	DET
ejpam-447	175	5	condition	condition	NOUN
ejpam-447	175	6	,	,	PUNCT
ejpam-447	175	7	we	we	PRON
ejpam-447	175	8	see	see	VERB
ejpam-447	175	9	that	that	SCONJ
ejpam-447	175	10	if	if	SCONJ
ejpam-447	175	11	k	k	PROPN
ejpam-447	175	12	is	be	AUX
ejpam-447	175	13	an	an	DET
ejpam-447	175	14	odd	odd	ADJ
ejpam-447	175	15	positive	positive	ADJ
ejpam-447	175	16	integer	integer	NOUN
ejpam-447	175	17	and	and	CCONJ
ejpam-447	175	18	ρ1	ρ1	NOUN
ejpam-447	175	19	=	=	PUNCT
ejpam-447	175	20	b−	b−	PROPN
ejpam-447	175	21	[	[	X
ejpam-447	175	22	1−	1−	NUM
ejpam-447	175	23	(	(	PUNCT
ejpam-447	175	24	a+	a+	NOUN
ejpam-447	175	25	b	b	NOUN
ejpam-447	175	26	)	)	PUNCT
ejpam-447	175	27	]	]	PUNCT
ejpam-447	175	28	�	�	PROPN
ejpam-447	175	29	�	�	PROPN
ejpam-447	175	30	p−	p−	PROPN
ejpam-447	175	31	q	q	PROPN
ejpam-447	175	32	�	�	PROPN
ejpam-447	175	33	+	+	CCONJ
ejpam-447	175	34	q	q	X
ejpam-447	175	35	(	(	PUNCT
ejpam-447	175	36	a+	a+	PRON
ejpam-447	175	37	b	b	X
ejpam-447	175	38	)	)	PUNCT
ejpam-447	175	39	�	�	PROPN
ejpam-447	175	40	p+	p+	VERB
ejpam-447	175	41	1	1	NUM
ejpam-447	175	42	>	>	SYM
ejpam-447	175	43	0	0	NUM
ejpam-447	175	44	,	,	PUNCT
ejpam-447	175	45	or	or	CCONJ
ejpam-447	175	46	if	if	SCONJ
ejpam-447	175	47	k	k	PROPN
ejpam-447	175	48	is	be	AUX
ejpam-447	175	49	an	an	DET
ejpam-447	175	50	even	even	ADV
ejpam-447	175	51	positive	positive	ADJ
ejpam-447	175	52	integer	integer	NOUN
ejpam-447	175	53	and	and	CCONJ
ejpam-447	175	54	ρ0ρ1	ρ0ρ1	NOUN
ejpam-447	175	55	=	=	SYM
ejpam-447	175	56	�	�	PROPN
ejpam-447	175	57	a+	a+	PUNCT
ejpam-447	175	58	p	p	X
ejpam-447	176	1	[	[	X
ejpam-447	176	2	1−	1−	NUM
ejpam-447	176	3	(	(	PUNCT
ejpam-447	176	4	a+	a+	NOUN
ejpam-447	176	5	b	b	NOUN
ejpam-447	176	6	)	)	PUNCT
ejpam-447	176	7	]	]	PUNCT
ejpam-447	176	8	p+	p+	VERB
ejpam-447	176	9	1	1	NUM
ejpam-447	176	10	�	�	NOUN
ejpam-447	176	11	�	�	NOUN
ejpam-447	176	12	b−	b−	PROPN
ejpam-447	176	13	[	[	X
ejpam-447	176	14	1−	1−	NUM
ejpam-447	176	15	(	(	PUNCT
ejpam-447	176	16	a+	a+	NOUN
ejpam-447	176	17	b	b	NOUN
ejpam-447	176	18	)	)	PUNCT
ejpam-447	176	19	]	]	PUNCT
ejpam-447	176	20	�	�	PROPN
ejpam-447	176	21	�	�	PROPN
ejpam-447	176	22	p−	p−	PROPN
ejpam-447	176	23	q	q	PROPN
ejpam-447	176	24	�	�	PROPN
ejpam-447	176	25	+	+	CCONJ
ejpam-447	176	26	q	q	X
ejpam-447	176	27	(	(	PUNCT
ejpam-447	176	28	a+	a+	PRON
ejpam-447	176	29	b	b	X
ejpam-447	176	30	)	)	PUNCT
ejpam-447	176	31	�	�	PROPN
ejpam-447	176	32	p+	p+	PART
ejpam-447	176	33	1	1	NUM
ejpam-447	176	34	�	�	PROPN
ejpam-447	176	35	>	>	X
ejpam-447	176	36	0	0	PROPN
ejpam-447	176	37	,	,	PUNCT
ejpam-447	176	38	then	then	ADV
ejpam-447	176	39	the	the	DET
ejpam-447	176	40	condition	condition	NOUN
ejpam-447	176	41	(	(	PUNCT
ejpam-447	176	42	12	12	NUM
ejpam-447	176	43	)	)	PUNCT
ejpam-447	176	44	is	be	AUX
ejpam-447	176	45	also	also	ADV
ejpam-447	176	46	necessary	necessary	ADJ
ejpam-447	176	47	for	for	ADP
ejpam-447	176	48	the	the	DET
ejpam-447	176	49	asymptotic	asymptotic	ADJ
ejpam-447	176	50	stability	stability	NOUN
ejpam-447	176	51	of	of	ADP
ejpam-447	176	52	eq.(1	eq.(1	ADJ
ejpam-447	176	53	)	)	PUNCT
ejpam-447	176	54	.	.	PUNCT
ejpam-447	177	1	according	accord	VERB
ejpam-447	177	2	to	to	ADP
ejpam-447	177	3	theorem	theorem	NOUN
ejpam-447	177	4	2	2	NUM
ejpam-447	177	5	,	,	PUNCT
ejpam-447	177	6	the	the	DET
ejpam-447	177	7	proof	proof	NOUN
ejpam-447	177	8	of	of	ADP
ejpam-447	177	9	theorem	theorem	ADJ
ejpam-447	177	10	7	7	NUM
ejpam-447	177	11	is	be	AUX
ejpam-447	177	12	now	now	ADV
ejpam-447	177	13	completed	complete	VERB
ejpam-447	177	14	.	.	PUNCT
ejpam-447	178	1	4	4	X
ejpam-447	178	2	.	.	X
ejpam-447	178	3	periodic	periodic	ADJ
ejpam-447	178	4	solutions	solution	NOUN
ejpam-447	178	5	in	in	ADP
ejpam-447	178	6	this	this	DET
ejpam-447	178	7	section	section	NOUN
ejpam-447	178	8	,	,	PUNCT
ejpam-447	178	9	we	we	PRON
ejpam-447	178	10	investigate	investigate	VERB
ejpam-447	178	11	the	the	DET
ejpam-447	178	12	periodic	periodic	ADJ
ejpam-447	178	13	character	character	NOUN
ejpam-447	178	14	of	of	ADP
ejpam-447	178	15	the	the	DET
ejpam-447	178	16	positive	positive	ADJ
ejpam-447	178	17	solutions	solution	NOUN
ejpam-447	178	18	of	of	ADP
ejpam-447	178	19	eq.(1	eq.(1	ADJ
ejpam-447	178	20	)	)	PUNCT
ejpam-447	178	21	.	.	PUNCT
ejpam-447	179	1	e.	e.	PROPN
ejpam-447	179	2	zayed	zayed	PROPN
ejpam-447	179	3	/	/	SYM
ejpam-447	179	4	eur	eur	PROPN
ejpam-447	179	5	.	.	PUNCT
ejpam-447	180	1	j.	j.	PROPN
ejpam-447	180	2	pure	pure	PROPN
ejpam-447	180	3	appl	appl	PROPN
ejpam-447	180	4	.	.	PROPN
ejpam-447	180	5	math	math	PROPN
ejpam-447	180	6	,	,	PUNCT
ejpam-447	180	7	3	3	NUM
ejpam-447	180	8	(	(	PUNCT
ejpam-447	180	9	2010	2010	NUM
ejpam-447	180	10	)	)	PUNCT
ejpam-447	180	11	,	,	PUNCT
ejpam-447	180	12	254	254	NUM
ejpam-447	180	13	-	-	SYM
ejpam-447	180	14	268	268	NUM
ejpam-447	180	15	261	261	NUM
ejpam-447	180	16	theorem	theorem	NOUN
ejpam-447	180	17	7	7	NUM
ejpam-447	180	18	.	.	PUNCT
ejpam-447	181	1	if	if	SCONJ
ejpam-447	181	2	k	k	PROPN
ejpam-447	181	3	is	be	AUX
ejpam-447	181	4	an	an	DET
ejpam-447	181	5	even	even	ADV
ejpam-447	181	6	positive	positive	ADJ
ejpam-447	181	7	integer	integer	NOUN
ejpam-447	181	8	,	,	PUNCT
ejpam-447	181	9	then	then	ADV
ejpam-447	181	10	eq.(1	eq.(1	NUM
ejpam-447	181	11	)	)	PUNCT
ejpam-447	181	12	has	have	VERB
ejpam-447	181	13	no	no	DET
ejpam-447	181	14	positive	positive	ADJ
ejpam-447	181	15	solutions	solution	NOUN
ejpam-447	181	16	of	of	ADP
ejpam-447	181	17	prime	prime	ADJ
ejpam-447	181	18	period	period	NOUN
ejpam-447	181	19	two	two	NUM
ejpam-447	181	20	for	for	ADP
ejpam-447	181	21	all	all	DET
ejpam-447	181	22	a	a	DET
ejpam-447	181	23	,	,	PUNCT
ejpam-447	181	24	b	b	NOUN
ejpam-447	181	25	,	,	PUNCT
ejpam-447	181	26	p	p	X
ejpam-447	181	27	,	,	PUNCT
ejpam-447	181	28	q	q	NOUN
ejpam-447	181	29	∈	∈	PROPN
ejpam-447	181	30	(	(	PUNCT
ejpam-447	181	31	0,∞	0,∞	NOUN
ejpam-447	181	32	)	)	PUNCT
ejpam-447	181	33	.	.	PUNCT
ejpam-447	182	1	proof	proof	NOUN
ejpam-447	182	2	.	.	PUNCT
ejpam-447	183	1	assume	assume	VERB
ejpam-447	183	2	for	for	ADP
ejpam-447	183	3	the	the	DET
ejpam-447	183	4	sake	sake	NOUN
ejpam-447	183	5	of	of	ADP
ejpam-447	183	6	contradiction	contradiction	NOUN
ejpam-447	183	7	that	that	PRON
ejpam-447	183	8	there	there	PRON
ejpam-447	183	9	exists	exist	VERB
ejpam-447	183	10	distinctive	distinctive	ADJ
ejpam-447	183	11	positive	positive	ADJ
ejpam-447	183	12	real	real	ADJ
ejpam-447	183	13	numbers	number	NOUN
ejpam-447	183	14	φ	φ	X
ejpam-447	183	15	and	and	CCONJ
ejpam-447	183	16	ψ	ψ	PROPN
ejpam-447	183	17	,	,	PUNCT
ejpam-447	183	18	such	such	ADJ
ejpam-447	183	19	that	that	PRON
ejpam-447	183	20	.	.	PUNCT
ejpam-447	183	21	.	.	PUNCT
ejpam-447	184	1	.φ	.φ	PROPN
ejpam-447	184	2	,	,	PUNCT
ejpam-447	184	3	ψ	ψ	PROPN
ejpam-447	184	4	,	,	PUNCT
ejpam-447	184	5	φ	φ	NOUN
ejpam-447	184	6	,	,	PUNCT
ejpam-447	184	7	ψ	ψ	X
ejpam-447	184	8	,	,	PUNCT
ejpam-447	184	9	.	.	PUNCT
ejpam-447	184	10	.	.	PUNCT
ejpam-447	184	11	.	.	PUNCT
ejpam-447	184	12	is	be	AUX
ejpam-447	184	13	a	a	DET
ejpam-447	184	14	prime	prime	ADJ
ejpam-447	184	15	period	period	NOUN
ejpam-447	184	16	two	two	NUM
ejpam-447	184	17	solution	solution	NOUN
ejpam-447	184	18	of	of	ADP
ejpam-447	184	19	eq.(1	eq.(1	ADJ
ejpam-447	184	20	)	)	PUNCT
ejpam-447	184	21	.	.	PUNCT
ejpam-447	185	1	if	if	SCONJ
ejpam-447	185	2	k	k	PROPN
ejpam-447	185	3	is	be	AUX
ejpam-447	185	4	even	even	ADV
ejpam-447	185	5	,	,	PUNCT
ejpam-447	185	6	then	then	ADV
ejpam-447	185	7	xn	xn	PROPN
ejpam-447	185	8	=	=	SYM
ejpam-447	185	9	xn−k	xn−k	PROPN
ejpam-447	185	10	.	.	PUNCT
ejpam-447	186	1	it	it	PRON
ejpam-447	186	2	follows	follow	VERB
ejpam-447	186	3	from	from	ADP
ejpam-447	186	4	the	the	DET
ejpam-447	186	5	difference	difference	NOUN
ejpam-447	186	6	equation	equation	NOUN
ejpam-447	186	7	(	(	PUNCT
ejpam-447	186	8	1	1	NUM
ejpam-447	186	9	)	)	PUNCT
ejpam-447	187	1	that	that	PRON
ejpam-447	187	2	φ	φ	PROPN
ejpam-447	187	3	=	=	SYM
ejpam-447	187	4	(	(	PUNCT
ejpam-447	187	5	a+	a+	PUNCT
ejpam-447	187	6	b)ψ+	b)ψ+	PROPN
ejpam-447	187	7	�	�	PROPN
ejpam-447	187	8	p+	p+	PART
ejpam-447	187	9	1	1	NUM
ejpam-447	187	10	�	�	PROPN
ejpam-447	187	11	ψ	ψ	NOUN
ejpam-447	187	12	q+ψ	q+ψ	PROPN
ejpam-447	187	13	and	and	CCONJ
ejpam-447	187	14	ψ	ψ	X
ejpam-447	187	15	=	=	SYM
ejpam-447	187	16	(	(	PUNCT
ejpam-447	187	17	a+	a+	PROPN
ejpam-447	187	18	b)φ+	b)φ+	PROPN
ejpam-447	187	19	�	�	PROPN
ejpam-447	187	20	p+	p+	PART
ejpam-447	187	21	1	1	NUM
ejpam-447	187	22	�	�	PROPN
ejpam-447	187	23	φ	φ	NUM
ejpam-447	187	24	q+φ	q+φ	PROPN
ejpam-447	187	25	.	.	PUNCT
ejpam-447	188	1	consequently	consequently	ADV
ejpam-447	188	2	,	,	PUNCT
ejpam-447	188	3	we	we	PRON
ejpam-447	188	4	obtain	obtain	VERB
ejpam-447	188	5	qφ+φψ	qφ+φψ	NOUN
ejpam-447	188	6	=	=	SYM
ejpam-447	188	7	qaψ+	qaψ+	NOUN
ejpam-447	188	8	aψ2	aψ2	VERB
ejpam-447	188	9	+	+	CCONJ
ejpam-447	188	10	qbψ+	qbψ+	ADJ
ejpam-447	188	11	bψ2	bψ2	NOUN
ejpam-447	188	12	+	+	X
ejpam-447	188	13	pψ+ψ	pψ+ψ	PROPN
ejpam-447	188	14	,	,	PUNCT
ejpam-447	188	15	and	and	CCONJ
ejpam-447	188	16	qψ+φψ	qψ+φψ	NOUN
ejpam-447	188	17	=	=	PUNCT
ejpam-447	189	1	qaφ+	qaφ+	NOUN
ejpam-447	189	2	aφ2	aφ2	NOUN
ejpam-447	189	3	+	+	X
ejpam-447	189	4	qbφ+	qbφ+	ADP
ejpam-447	189	5	bφ2	bφ2	ADP
ejpam-447	189	6	+	+	X
ejpam-447	189	7	pφ+φ	pφ+φ	PROPN
ejpam-447	189	8	.	.	PUNCT
ejpam-447	190	1	by	by	ADP
ejpam-447	190	2	subtracting	subtract	VERB
ejpam-447	190	3	,	,	PUNCT
ejpam-447	190	4	we	we	PRON
ejpam-447	190	5	deduce	deduce	VERB
ejpam-447	190	6	that	that	PRON
ejpam-447	190	7	(	(	PUNCT
ejpam-447	190	8	φ−ψ	φ−ψ	PROPN
ejpam-447	190	9	)	)	PUNCT
ejpam-447	190	10	�	�	PROPN
ejpam-447	190	11	q	q	PROPN
ejpam-447	190	12	(	(	PUNCT
ejpam-447	190	13	a+	a+	X
ejpam-447	190	14	b+	b+	NUM
ejpam-447	190	15	1)+	1)+	NUM
ejpam-447	190	16	(	(	PUNCT
ejpam-447	190	17	φ+ψ)(a+	φ+ψ)(a+	PROPN
ejpam-447	190	18	b	b	NOUN
ejpam-447	190	19	)	)	PUNCT
ejpam-447	190	20	+	+	X
ejpam-447	190	21	p+	p+	VERB
ejpam-447	190	22	1	1	NUM
ejpam-447	190	23	=	=	SYM
ejpam-447	190	24	0	0	NUM
ejpam-447	190	25	.	.	PUNCT
ejpam-447	191	1	this	this	PRON
ejpam-447	191	2	implies	imply	VERB
ejpam-447	191	3	φ	φ	PROPN
ejpam-447	191	4	=	=	SYM
ejpam-447	191	5	ψ	ψ	X
ejpam-447	191	6	.	.	PUNCT
ejpam-447	192	1	this	this	PRON
ejpam-447	192	2	contradicts	contradict	VERB
ejpam-447	192	3	the	the	DET
ejpam-447	192	4	hypothesis	hypothesis	NOUN
ejpam-447	192	5	φ	φ	X
ejpam-447	192	6	6=	6=	PROPN
ejpam-447	192	7	ψ	ψ	SYM
ejpam-447	192	8	.	.	PUNCT
ejpam-447	193	1	thus	thus	ADV
ejpam-447	193	2	,	,	PUNCT
ejpam-447	193	3	the	the	DET
ejpam-447	193	4	proof	proof	NOUN
ejpam-447	193	5	of	of	ADP
ejpam-447	193	6	theorem	theorem	ADJ
ejpam-447	193	7	7	7	NUM
ejpam-447	193	8	is	be	AUX
ejpam-447	193	9	completed	complete	VERB
ejpam-447	193	10	.	.	PUNCT
ejpam-447	194	1	theorem	theorem	VERB
ejpam-447	194	2	8	8	NUM
ejpam-447	194	3	.	.	PUNCT
ejpam-447	195	1	if	if	SCONJ
ejpam-447	195	2	k	k	PROPN
ejpam-447	195	3	is	be	AUX
ejpam-447	195	4	an	an	DET
ejpam-447	195	5	odd	odd	ADJ
ejpam-447	195	6	positive	positive	ADJ
ejpam-447	195	7	integer	integer	NOUN
ejpam-447	195	8	then	then	ADV
ejpam-447	195	9	for	for	SCONJ
ejpam-447	195	10	all	all	DET
ejpam-447	195	11	a	a	DET
ejpam-447	195	12	,	,	PUNCT
ejpam-447	195	13	b	b	NOUN
ejpam-447	195	14	,	,	PUNCT
ejpam-447	195	15	p	p	X
ejpam-447	195	16	,	,	PUNCT
ejpam-447	195	17	q	q	NOUN
ejpam-447	195	18	∈	∈	PROPN
ejpam-447	195	19	(	(	PUNCT
ejpam-447	195	20	0,∞	0,∞	NOUN
ejpam-447	195	21	)	)	PUNCT
ejpam-447	195	22	eq.(1	eq.(1	NUM
ejpam-447	195	23	)	)	PUNCT
ejpam-447	195	24	has	have	VERB
ejpam-447	195	25	no	no	DET
ejpam-447	195	26	prime	prime	ADJ
ejpam-447	195	27	period	period	NOUN
ejpam-447	195	28	two	two	NUM
ejpam-447	195	29	solutions	solution	NOUN
ejpam-447	195	30	if	if	SCONJ
ejpam-447	195	31	a−	a−	PROPN
ejpam-447	195	32	b+	b+	ADJ
ejpam-447	195	33	1	1	NUM
ejpam-447	195	34	>	>	SYM
ejpam-447	195	35	0	0	NUM
ejpam-447	195	36	.	.	PUNCT
ejpam-447	196	1	proof	proof	NOUN
ejpam-447	196	2	.	.	PUNCT
ejpam-447	197	1	assume	assume	VERB
ejpam-447	197	2	for	for	ADP
ejpam-447	197	3	the	the	DET
ejpam-447	197	4	sake	sake	NOUN
ejpam-447	197	5	of	of	ADP
ejpam-447	197	6	contradiction	contradiction	NOUN
ejpam-447	197	7	that	that	PRON
ejpam-447	197	8	there	there	PRON
ejpam-447	197	9	exists	exist	VERB
ejpam-447	197	10	distinctive	distinctive	ADJ
ejpam-447	197	11	positive	positive	ADJ
ejpam-447	197	12	real	real	ADJ
ejpam-447	197	13	numbers	number	NOUN
ejpam-447	197	14	φ	φ	X
ejpam-447	197	15	and	and	CCONJ
ejpam-447	197	16	ψ	ψ	PROPN
ejpam-447	197	17	,	,	PUNCT
ejpam-447	197	18	such	such	ADJ
ejpam-447	197	19	that	that	PRON
ejpam-447	197	20	.	.	PUNCT
ejpam-447	197	21	.	.	PUNCT
ejpam-447	198	1	.φ	.φ	PROPN
ejpam-447	198	2	,	,	PUNCT
ejpam-447	198	3	ψ	ψ	PROPN
ejpam-447	198	4	,	,	PUNCT
ejpam-447	198	5	φ	φ	NOUN
ejpam-447	198	6	,	,	PUNCT
ejpam-447	198	7	ψ	ψ	X
ejpam-447	198	8	,	,	PUNCT
ejpam-447	198	9	.	.	PUNCT
ejpam-447	198	10	.	.	PUNCT
ejpam-447	198	11	.	.	PUNCT
ejpam-447	198	12	is	be	AUX
ejpam-447	198	13	a	a	DET
ejpam-447	198	14	prime	prime	ADJ
ejpam-447	198	15	period	period	NOUN
ejpam-447	198	16	two	two	NUM
ejpam-447	198	17	solution	solution	NOUN
ejpam-447	198	18	of	of	ADP
ejpam-447	198	19	eq.(1	eq.(1	ADJ
ejpam-447	198	20	)	)	PUNCT
ejpam-447	198	21	.	.	PUNCT
ejpam-447	199	1	if	if	SCONJ
ejpam-447	199	2	k	k	PROPN
ejpam-447	199	3	is	be	AUX
ejpam-447	199	4	odd	odd	ADJ
ejpam-447	199	5	,	,	PUNCT
ejpam-447	199	6	then	then	ADV
ejpam-447	199	7	yn+1	yn+1	PROPN
ejpam-447	199	8	=	=	PROPN
ejpam-447	199	9	yn−k	yn−k	PROPN
ejpam-447	199	10	.	.	PUNCT
ejpam-447	200	1	it	it	PRON
ejpam-447	200	2	follows	follow	VERB
ejpam-447	200	3	from	from	ADP
ejpam-447	200	4	eq.(1	eq.(1	ADJ
ejpam-447	200	5	)	)	PUNCT
ejpam-447	201	1	that	that	SCONJ
ejpam-447	201	2	φ	φ	NOUN
ejpam-447	201	3	=	=	SYM
ejpam-447	201	4	aψ+	aψ+	NOUN
ejpam-447	201	5	bφ+	bφ+	PROPN
ejpam-447	201	6	pψ+φ	pψ+φ	PROPN
ejpam-447	201	7	q+φ	q+φ	PROPN
ejpam-447	201	8	and	and	CCONJ
ejpam-447	201	9	ψ	ψ	X
ejpam-447	201	10	=	=	PUNCT
ejpam-447	201	11	aφ+	aφ+	ADJ
ejpam-447	201	12	bψ+	bψ+	ADJ
ejpam-447	202	1	pφ+ψ	pφ+ψ	PROPN
ejpam-447	202	2	q+ψ	q+ψ	PROPN
ejpam-447	202	3	.	.	PUNCT
ejpam-447	203	1	consequently	consequently	ADV
ejpam-447	203	2	,	,	PUNCT
ejpam-447	203	3	we	we	PRON
ejpam-447	203	4	obtain	obtain	VERB
ejpam-447	203	5	qφ+φ2	qφ+φ2	NOUN
ejpam-447	203	6	=	=	PUNCT
ejpam-447	203	7	qaψ+	qaψ+	NOUN
ejpam-447	203	8	aφψ+	aφψ+	ADJ
ejpam-447	203	9	qbφ+	qbφ+	ADP
ejpam-447	203	10	bφ2	bφ2	ADP
ejpam-447	203	11	+	+	CCONJ
ejpam-447	203	12	pψ+φ	pψ+φ	PROPN
ejpam-447	203	13	,	,	PUNCT
ejpam-447	203	14	(	(	PUNCT
ejpam-447	203	15	13	13	NUM
ejpam-447	203	16	)	)	PUNCT
ejpam-447	203	17	and	and	CCONJ
ejpam-447	203	18	qψ+ψ2	qψ+ψ2	PROPN
ejpam-447	203	19	=	=	SYM
ejpam-447	203	20	qaφ+	qaφ+	PROPN
ejpam-447	203	21	aφψ+	aφψ+	VERB
ejpam-447	203	22	qbψ+	qbψ+	ADJ
ejpam-447	203	23	bψ2	bψ2	NOUN
ejpam-447	203	24	+	+	CCONJ
ejpam-447	203	25	pφ+ψ	pφ+ψ	PROPN
ejpam-447	203	26	.	.	PUNCT
ejpam-447	204	1	(	(	PUNCT
ejpam-447	204	2	14	14	NUM
ejpam-447	204	3	)	)	PUNCT
ejpam-447	204	4	by	by	ADP
ejpam-447	204	5	subtracting	subtract	VERB
ejpam-447	204	6	(	(	PUNCT
ejpam-447	204	7	13	13	NUM
ejpam-447	204	8	)	)	PUNCT
ejpam-447	204	9	from	from	ADP
ejpam-447	204	10	(	(	PUNCT
ejpam-447	204	11	14	14	NUM
ejpam-447	204	12	)	)	PUNCT
ejpam-447	204	13	,	,	PUNCT
ejpam-447	204	14	we	we	PRON
ejpam-447	204	15	deduce	deduce	VERB
ejpam-447	204	16	that	that	SCONJ
ejpam-447	204	17	φ+ψ	φ+ψ	VERB
ejpam-447	204	18	=	=	SYM
ejpam-447	204	19	�	�	PROPN
ejpam-447	204	20	�	�	PROPN
ejpam-447	204	21	p+	p+	PART
ejpam-447	204	22	q	q	PROPN
ejpam-447	204	23	�	�	PROPN
ejpam-447	204	24	−	−	PROPN
ejpam-447	204	25	�	�	PROPN
ejpam-447	204	26	q	q	PROPN
ejpam-447	204	27	(	(	PUNCT
ejpam-447	204	28	b−	b−	NOUN
ejpam-447	204	29	a	a	NOUN
ejpam-447	204	30	)	)	PUNCT
ejpam-447	205	1	+	+	CCONJ
ejpam-447	205	2	1	1	NUM
ejpam-447	205	3	�	�	PROPN
ejpam-447	205	4	b	b	PROPN
ejpam-447	205	5	−	−	PROPN
ejpam-447	205	6	1	1	NUM
ejpam-447	205	7	,	,	PUNCT
ejpam-447	205	8	(	(	PUNCT
ejpam-447	205	9	15	15	NUM
ejpam-447	205	10	)	)	PUNCT
ejpam-447	205	11	e.	e.	PROPN
ejpam-447	205	12	zayed	zayed	PROPN
ejpam-447	205	13	/	/	SYM
ejpam-447	205	14	eur	eur	PROPN
ejpam-447	205	15	.	.	PUNCT
ejpam-447	206	1	j.	j.	PROPN
ejpam-447	206	2	pure	pure	PROPN
ejpam-447	206	3	appl	appl	PROPN
ejpam-447	206	4	.	.	PROPN
ejpam-447	206	5	math	math	PROPN
ejpam-447	206	6	,	,	PUNCT
ejpam-447	206	7	3	3	NUM
ejpam-447	206	8	(	(	PUNCT
ejpam-447	206	9	2010	2010	NUM
ejpam-447	206	10	)	)	PUNCT
ejpam-447	206	11	,	,	PUNCT
ejpam-447	206	12	254	254	NUM
ejpam-447	206	13	-	-	SYM
ejpam-447	206	14	268	268	NUM
ejpam-447	206	15	262	262	NUM
ejpam-447	206	16	while	while	NOUN
ejpam-447	206	17	,	,	PUNCT
ejpam-447	206	18	by	by	ADP
ejpam-447	206	19	adding	add	VERB
ejpam-447	206	20	(	(	PUNCT
ejpam-447	206	21	13	13	NUM
ejpam-447	206	22	)	)	PUNCT
ejpam-447	206	23	,	,	PUNCT
ejpam-447	206	24	(	(	PUNCT
ejpam-447	206	25	14	14	NUM
ejpam-447	206	26	)	)	PUNCT
ejpam-447	206	27	and	and	CCONJ
ejpam-447	206	28	using	use	VERB
ejpam-447	206	29	(	(	PUNCT
ejpam-447	206	30	15	15	NUM
ejpam-447	206	31	)	)	PUNCT
ejpam-447	206	32	we	we	PRON
ejpam-447	206	33	get	get	VERB
ejpam-447	206	34	φψ	φψ	NOUN
ejpam-447	206	35	=	=	PUNCT
ejpam-447	206	36	�	�	PROPN
ejpam-447	206	37	qa+	qa+	PROPN
ejpam-447	206	38	p	p	PROPN
ejpam-447	206	39	�	�	PROPN
ejpam-447	206	40	�	�	PROPN
ejpam-447	206	41	�	�	PROPN
ejpam-447	206	42	p+	p+	PART
ejpam-447	206	43	q	q	PROPN
ejpam-447	206	44	�	�	PROPN
ejpam-447	206	45	−	−	PROPN
ejpam-447	206	46	�	�	PROPN
ejpam-447	206	47	q	q	PROPN
ejpam-447	206	48	(	(	PUNCT
ejpam-447	206	49	b−	b−	NOUN
ejpam-447	206	50	a	a	NOUN
ejpam-447	206	51	)	)	PUNCT
ejpam-447	207	1	+	+	CCONJ
ejpam-447	207	2	1	1	NUM
ejpam-447	207	3	�	�	PROPN
ejpam-447	207	4	(	(	PUNCT
ejpam-447	207	5	b−	b−	NOUN
ejpam-447	207	6	1	1	NUM
ejpam-447	207	7	)	)	PUNCT
ejpam-447	208	1	[	[	X
ejpam-447	208	2	b−	b−	NOUN
ejpam-447	208	3	(	(	PUNCT
ejpam-447	208	4	a+	a+	X
ejpam-447	208	5	1	1	NUM
ejpam-447	208	6	)	)	PUNCT
ejpam-447	208	7	]	]	PUNCT
ejpam-447	208	8	.	.	PUNCT
ejpam-447	209	1	(	(	PUNCT
ejpam-447	209	2	16	16	NUM
ejpam-447	209	3	)	)	PUNCT
ejpam-447	209	4	from	from	ADP
ejpam-447	209	5	(	(	PUNCT
ejpam-447	209	6	15	15	NUM
ejpam-447	209	7	)	)	PUNCT
ejpam-447	209	8	and	and	CCONJ
ejpam-447	209	9	(	(	PUNCT
ejpam-447	209	10	16	16	NUM
ejpam-447	209	11	)	)	PUNCT
ejpam-447	209	12	we	we	PRON
ejpam-447	209	13	have	have	VERB
ejpam-447	209	14	φψ(φ+ψ	φψ(φ+ψ	VERB
ejpam-447	209	15	)	)	PUNCT
ejpam-447	209	16	=	=	SYM
ejpam-447	210	1	−	−	PROPN
ejpam-447	210	2	�	�	PROPN
ejpam-447	210	3	qa+	qa+	PROPN
ejpam-447	210	4	p	p	PROPN
ejpam-447	210	5	�	�	PROPN
ejpam-447	210	6	(	(	PUNCT
ejpam-447	210	7	1	1	NUM
ejpam-447	210	8	+	+	NUM
ejpam-447	210	9	a−	a−	PROPN
ejpam-447	210	10	b	b	NOUN
ejpam-447	210	11	)	)	PUNCT
ejpam-447	210	12	¨	¨	NOUN
ejpam-447	210	13	�	�	PROPN
ejpam-447	210	14	p+	p+	PROPN
ejpam-447	210	15	q	q	PROPN
ejpam-447	210	16	�	�	PROPN
ejpam-447	210	17	−	−	PROPN
ejpam-447	210	18	�	�	PROPN
ejpam-447	210	19	1	1	NUM
ejpam-447	210	20	+	+	NUM
ejpam-447	210	21	q	q	X
ejpam-447	210	22	(	(	PUNCT
ejpam-447	210	23	b−	b−	PROPN
ejpam-447	210	24	a	a	PRON
ejpam-447	210	25	)	)	PUNCT
ejpam-447	210	26	�	�	PROPN
ejpam-447	210	27	b−	b−	PROPN
ejpam-447	210	28	1	1	NUM
ejpam-447	210	29	«	«	SYM
ejpam-447	210	30	2	2	NUM
ejpam-447	210	31	<	<	X
ejpam-447	210	32	0	0	NUM
ejpam-447	210	33	.	.	PUNCT
ejpam-447	211	1	(	(	PUNCT
ejpam-447	211	2	17	17	NUM
ejpam-447	211	3	)	)	PUNCT
ejpam-447	211	4	this	this	PRON
ejpam-447	211	5	contradicts	contradict	VERB
ejpam-447	211	6	the	the	DET
ejpam-447	211	7	hypothesis	hypothesis	NOUN
ejpam-447	211	8	that	that	PRON
ejpam-447	211	9	both	both	DET
ejpam-447	211	10	φ	φ	NOUN
ejpam-447	211	11	,	,	PUNCT
ejpam-447	211	12	ψ	ψ	X
ejpam-447	211	13	are	be	AUX
ejpam-447	211	14	positive	positive	ADJ
ejpam-447	211	15	.	.	PUNCT
ejpam-447	212	1	thus	thus	ADV
ejpam-447	212	2	,	,	PUNCT
ejpam-447	212	3	the	the	DET
ejpam-447	212	4	proof	proof	NOUN
ejpam-447	212	5	of	of	ADP
ejpam-447	212	6	theorem	theorem	ADJ
ejpam-447	212	7	8	8	NUM
ejpam-447	212	8	is	be	AUX
ejpam-447	212	9	now	now	ADV
ejpam-447	212	10	completed	complete	VERB
ejpam-447	212	11	.	.	PUNCT
ejpam-447	213	1	5	5	X
ejpam-447	213	2	.	.	X
ejpam-447	213	3	boundedness	boundedness	NOUN
ejpam-447	213	4	character	character	NOUN
ejpam-447	213	5	in	in	ADP
ejpam-447	213	6	this	this	DET
ejpam-447	213	7	section	section	NOUN
ejpam-447	213	8	,	,	PUNCT
ejpam-447	213	9	we	we	PRON
ejpam-447	213	10	investigate	investigate	VERB
ejpam-447	213	11	the	the	DET
ejpam-447	213	12	boundedness	boundedness	NOUN
ejpam-447	213	13	character	character	NOUN
ejpam-447	213	14	of	of	ADP
ejpam-447	213	15	the	the	DET
ejpam-447	213	16	positive	positive	ADJ
ejpam-447	213	17	solutions	solution	NOUN
ejpam-447	213	18	of	of	ADP
ejpam-447	213	19	eq.(1	eq.(1	ADJ
ejpam-447	213	20	)	)	PUNCT
ejpam-447	213	21	.	.	PUNCT
ejpam-447	214	1	theorem	theorem	VERB
ejpam-447	214	2	9	9	NUM
ejpam-447	214	3	.	.	PUNCT
ejpam-447	215	1	let	let	VERB
ejpam-447	215	2	�	�	PROPN
ejpam-447	215	3	xn	xn	PROPN
ejpam-447	215	4	∞	∞	PROPN
ejpam-447	215	5	n=−k	n=−k	NOUN
ejpam-447	215	6	be	be	VERB
ejpam-447	215	7	a	a	DET
ejpam-447	215	8	solution	solution	NOUN
ejpam-447	215	9	of	of	ADP
ejpam-447	215	10	eq.(1	eq.(1	ADJ
ejpam-447	215	11	)	)	PUNCT
ejpam-447	215	12	.	.	PUNCT
ejpam-447	216	1	then	then	ADV
ejpam-447	216	2	the	the	DET
ejpam-447	216	3	following	follow	VERB
ejpam-447	216	4	statements	statement	NOUN
ejpam-447	216	5	are	be	AUX
ejpam-447	216	6	true	true	ADJ
ejpam-447	216	7	:	:	PUNCT
ejpam-447	216	8	(	(	PUNCT
ejpam-447	216	9	i	i	NOUN
ejpam-447	216	10	)	)	PUNCT
ejpam-447	216	11	suppose	suppose	VERB
ejpam-447	216	12	p	p	PRON
ejpam-447	216	13	<	<	X
ejpam-447	216	14	q	q	X
ejpam-447	216	15	and	and	CCONJ
ejpam-447	216	16	for	for	ADP
ejpam-447	216	17	some	some	DET
ejpam-447	216	18	n	n	PRON
ejpam-447	216	19	≥	≥	NOUN
ejpam-447	216	20	0	0	NUM
ejpam-447	216	21	,	,	PUNCT
ejpam-447	216	22	the	the	DET
ejpam-447	216	23	initial	initial	ADJ
ejpam-447	216	24	conditions	condition	NOUN
ejpam-447	216	25	xn−k+1	xn−k+1	VERB
ejpam-447	216	26	,	,	PUNCT
ejpam-447	216	27	.	.	PUNCT
ejpam-447	216	28	.	.	PUNCT
ejpam-447	216	29	.	.	PUNCT
ejpam-447	217	1	xn−1	xn−1	PROPN
ejpam-447	217	2	,	,	PUNCT
ejpam-447	217	3	xn	xn	PROPN
ejpam-447	217	4	∈	∈	PROPN
ejpam-447	217	5	�	�	PROPN
ejpam-447	217	6	p	p	NOUN
ejpam-447	217	7	q	q	PROPN
ejpam-447	217	8	,	,	PUNCT
ejpam-447	217	9	1	1	NUM
ejpam-447	217	10	�	�	PROPN
ejpam-447	217	11	,	,	PUNCT
ejpam-447	217	12	then	then	ADV
ejpam-447	217	13	xn	xn	PROPN
ejpam-447	217	14	∈	∈	PROPN
ejpam-447	217	15	�	�	PROPN
ejpam-447	217	16	p	p	PROPN
ejpam-447	217	17	q	q	PROPN
ejpam-447	217	18	�	�	PROPN
ejpam-447	217	19	a+	a+	PUNCT
ejpam-447	217	20	b+	b+	X
ejpam-447	217	21	p+	p+	VERB
ejpam-447	217	22	1	1	NUM
ejpam-447	217	23	q+	q+	ADP
ejpam-447	217	24	1	1	NUM
ejpam-447	217	25	�	�	PROPN
ejpam-447	217	26	,	,	PUNCT
ejpam-447	217	27	q	q	PROPN
ejpam-447	217	28	p	p	X
ejpam-447	217	29	(	(	PUNCT
ejpam-447	217	30	a+	a+	X
ejpam-447	217	31	b+	b+	NUM
ejpam-447	217	32	1	1	X
ejpam-447	217	33	)	)	PUNCT
ejpam-447	217	34	�	�	PROPN
ejpam-447	217	35	,	,	PUNCT
ejpam-447	217	36	for	for	ADP
ejpam-447	217	37	all	all	DET
ejpam-447	217	38	n≥	n≥	NOUN
ejpam-447	217	39	n	n	X
ejpam-447	217	40	.	.	PUNCT
ejpam-447	218	1	(	(	PUNCT
ejpam-447	218	2	ii	ii	NOUN
ejpam-447	218	3	)	)	PUNCT
ejpam-447	218	4	suppose	suppose	VERB
ejpam-447	218	5	p	p	PRON
ejpam-447	218	6	>	>	X
ejpam-447	218	7	q	q	PROPN
ejpam-447	219	1	and	and	CCONJ
ejpam-447	219	2	for	for	ADP
ejpam-447	219	3	some	some	DET
ejpam-447	219	4	n	n	PRON
ejpam-447	219	5	≥	≥	NOUN
ejpam-447	219	6	0	0	NUM
ejpam-447	219	7	,	,	PUNCT
ejpam-447	219	8	the	the	DET
ejpam-447	219	9	initial	initial	ADJ
ejpam-447	219	10	conditions	condition	NOUN
ejpam-447	219	11	xn−k+1	xn−k+1	VERB
ejpam-447	219	12	,	,	PUNCT
ejpam-447	219	13	.	.	PUNCT
ejpam-447	219	14	.	.	PUNCT
ejpam-447	219	15	.	.	PUNCT
ejpam-447	220	1	xn−1	xn−1	PROPN
ejpam-447	220	2	,	,	PUNCT
ejpam-447	220	3	xn	xn	PROPN
ejpam-447	220	4	∈	∈	PROPN
ejpam-447	220	5	�	�	PROPN
ejpam-447	220	6	1	1	NUM
ejpam-447	220	7	,	,	PUNCT
ejpam-447	220	8	p	p	DET
ejpam-447	220	9	q	q	PROPN
ejpam-447	220	10	�	�	PROPN
ejpam-447	220	11	,	,	PUNCT
ejpam-447	220	12	then	then	ADV
ejpam-447	220	13	xn	xn	PROPN
ejpam-447	220	14	∈	∈	PROPN
ejpam-447	220	15	�	�	PROPN
ejpam-447	220	16	q	q	PROPN
ejpam-447	220	17	p	p	X
ejpam-447	220	18	(	(	PUNCT
ejpam-447	220	19	a+	a+	X
ejpam-447	220	20	b+	b+	X
ejpam-447	220	21	1	1	NUM
ejpam-447	220	22	)	)	PUNCT
ejpam-447	220	23	,	,	PUNCT
ejpam-447	220	24	p	p	X
ejpam-447	220	25	q	q	PROPN
ejpam-447	220	26	�	�	PROPN
ejpam-447	220	27	a+	a+	PUNCT
ejpam-447	220	28	b+	b+	X
ejpam-447	220	29	p+	p+	VERB
ejpam-447	220	30	1	1	NUM
ejpam-447	220	31	q+	q+	ADP
ejpam-447	220	32	1	1	NUM
ejpam-447	220	33	�	�	PROPN
ejpam-447	220	34	�	�	PROPN
ejpam-447	220	35	,	,	PUNCT
ejpam-447	220	36	for	for	ADP
ejpam-447	220	37	all	all	PRON
ejpam-447	220	38	n≥	n≥	NOUN
ejpam-447	220	39	n	n	NOUN
ejpam-447	220	40	.	.	PUNCT
ejpam-447	221	1	proof	proof	NOUN
ejpam-447	221	2	.	.	PUNCT
ejpam-447	222	1	first	first	ADV
ejpam-447	222	2	of	of	ADP
ejpam-447	222	3	all	all	PRON
ejpam-447	222	4	,	,	PUNCT
ejpam-447	222	5	if	if	SCONJ
ejpam-447	222	6	for	for	ADP
ejpam-447	222	7	some	some	DET
ejpam-447	222	8	n	n	PRON
ejpam-447	222	9	≥	≥	NOUN
ejpam-447	222	10	0	0	NUM
ejpam-447	223	1	and	and	CCONJ
ejpam-447	223	2	p	p	X
ejpam-447	223	3	q	q	PROPN
ejpam-447	223	4	≤	≤	NUM
ejpam-447	223	5	xn	xn	PUNCT
ejpam-447	223	6	≤	≤	NUM
ejpam-447	223	7	1	1	NUM
ejpam-447	223	8	and	and	CCONJ
ejpam-447	223	9	p	p	X
ejpam-447	223	10	<	<	X
ejpam-447	223	11	q	q	X
ejpam-447	223	12	,	,	PUNCT
ejpam-447	223	13	then	then	ADV
ejpam-447	223	14	xn+1	xn+1	NOUN
ejpam-447	223	15	=	=	PUNCT
ejpam-447	223	16	axn+	axn+	PROPN
ejpam-447	223	17	bxn−k	bxn−k	X
ejpam-447	223	18	+	+	CCONJ
ejpam-447	223	19	pxn	pxn	VERB
ejpam-447	223	20	+	+	X
ejpam-447	223	21	xn−k	xn−k	PROPN
ejpam-447	223	22	q+	q+	PROPN
ejpam-447	223	23	xn−k	xn−k	PROPN
ejpam-447	223	24	≤	≤	PROPN
ejpam-447	223	25	axn+	axn+	PUNCT
ejpam-447	224	1	bxn−k	bxn−k	ADP
ejpam-447	224	2	+	+	PUNCT
ejpam-447	224	3	qxn+	qxn+	PROPN
ejpam-447	224	4	xn−k	xn−k	PROPN
ejpam-447	224	5	q+	q+	PROPN
ejpam-447	224	6	xn−k	xn−k	PROPN
ejpam-447	224	7	≤	≤	PROPN
ejpam-447	224	8	a+	a+	PUNCT
ejpam-447	225	1	b	b	X
ejpam-447	225	2	+	+	NUM
ejpam-447	225	3	1≤	1≤	NUM
ejpam-447	225	4	q	q	X
ejpam-447	225	5	p	p	X
ejpam-447	225	6	(	(	PUNCT
ejpam-447	225	7	a+	a+	PROPN
ejpam-447	225	8	b	b	NOUN
ejpam-447	225	9	+	+	CCONJ
ejpam-447	225	10	1	1	NUM
ejpam-447	225	11	)	)	PUNCT
ejpam-447	225	12	,	,	PUNCT
ejpam-447	225	13	and	and	CCONJ
ejpam-447	225	14	xn+1	xn+1	X
ejpam-447	225	15	=	=	PUNCT
ejpam-447	226	1	axn+	axn+	NOUN
ejpam-447	226	2	bxn−k	bxn−k	X
ejpam-447	226	3	+	+	CCONJ
ejpam-447	226	4	pxn	pxn	VERB
ejpam-447	226	5	+	+	CCONJ
ejpam-447	226	6	xn−k	xn−k	PROPN
ejpam-447	226	7	q+	q+	PROPN
ejpam-447	226	8	xn−k	xn−k	PROPN
ejpam-447	226	9	≥	≥	PROPN
ejpam-447	226	10	p	p	X
ejpam-447	226	11	q	q	PROPN
ejpam-447	226	12	�	�	PROPN
ejpam-447	226	13	a+	a+	PUNCT
ejpam-447	226	14	b+	b+	X
ejpam-447	226	15	p+	p+	VERB
ejpam-447	226	16	1	1	NUM
ejpam-447	226	17	q+	q+	ADP
ejpam-447	226	18	1	1	NUM
ejpam-447	226	19	�	�	PROPN
ejpam-447	226	20	.	.	PUNCT
ejpam-447	227	1	e.	e.	PROPN
ejpam-447	227	2	zayed	zayed	PROPN
ejpam-447	227	3	/	/	SYM
ejpam-447	227	4	eur	eur	PROPN
ejpam-447	227	5	.	.	PUNCT
ejpam-447	228	1	j.	j.	PROPN
ejpam-447	228	2	pure	pure	PROPN
ejpam-447	228	3	appl	appl	PROPN
ejpam-447	228	4	.	.	PROPN
ejpam-447	228	5	math	math	PROPN
ejpam-447	228	6	,	,	PUNCT
ejpam-447	228	7	3	3	NUM
ejpam-447	228	8	(	(	PUNCT
ejpam-447	228	9	2010	2010	NUM
ejpam-447	228	10	)	)	PUNCT
ejpam-447	228	11	,	,	PUNCT
ejpam-447	228	12	254	254	NUM
ejpam-447	228	13	-	-	SYM
ejpam-447	228	14	268	268	NUM
ejpam-447	228	15	263	263	NUM
ejpam-447	228	16	thus	thus	ADV
ejpam-447	228	17	,	,	PUNCT
ejpam-447	228	18	the	the	DET
ejpam-447	228	19	proof	proof	NOUN
ejpam-447	228	20	of	of	ADP
ejpam-447	228	21	part	part	NOUN
ejpam-447	228	22	(	(	PUNCT
ejpam-447	228	23	i	i	NOUN
ejpam-447	228	24	)	)	PUNCT
ejpam-447	228	25	is	be	AUX
ejpam-447	228	26	completed	complete	VERB
ejpam-447	228	27	.	.	PUNCT
ejpam-447	229	1	secondly	secondly	ADV
ejpam-447	229	2	,	,	PUNCT
ejpam-447	229	3	if	if	SCONJ
ejpam-447	229	4	for	for	ADP
ejpam-447	229	5	some	some	DET
ejpam-447	229	6	n	n	PRON
ejpam-447	229	7	≥	≥	NOUN
ejpam-447	229	8	0	0	NUM
ejpam-447	229	9	and	and	CCONJ
ejpam-447	229	10	1	1	NUM
ejpam-447	229	11	≤	≤	NUM
ejpam-447	229	12	xn	xn	PUNCT
ejpam-447	229	13	≤	≤	NUM
ejpam-447	230	1	p	p	PRON
ejpam-447	230	2	q	q	NOUN
ejpam-447	230	3	and	and	CCONJ
ejpam-447	230	4	p	p	X
ejpam-447	230	5	>	>	X
ejpam-447	230	6	q	q	X
ejpam-447	230	7	,	,	PUNCT
ejpam-447	230	8	then	then	ADV
ejpam-447	230	9	xn+1	xn+1	NOUN
ejpam-447	230	10	=	=	PUNCT
ejpam-447	230	11	axn+	axn+	PROPN
ejpam-447	230	12	bxn−k	bxn−k	X
ejpam-447	230	13	+	+	CCONJ
ejpam-447	230	14	pxn	pxn	VERB
ejpam-447	230	15	+	+	X
ejpam-447	230	16	xn−k	xn−k	PROPN
ejpam-447	230	17	q+	q+	PROPN
ejpam-447	230	18	xn−k	xn−k	PROPN
ejpam-447	230	19	≤	≤	PROPN
ejpam-447	231	1	p	p	PRON
ejpam-447	231	2	q	q	PROPN
ejpam-447	231	3	�	�	PROPN
ejpam-447	231	4	a+	a+	PUNCT
ejpam-447	231	5	b+	b+	X
ejpam-447	231	6	p+	p+	VERB
ejpam-447	231	7	1	1	NUM
ejpam-447	231	8	q+	q+	ADP
ejpam-447	231	9	1	1	NUM
ejpam-447	231	10	�	�	PROPN
ejpam-447	231	11	,	,	PUNCT
ejpam-447	231	12	and	and	CCONJ
ejpam-447	231	13	xn+1	xn+1	X
ejpam-447	231	14	=	=	PUNCT
ejpam-447	231	15	axn+	axn+	NOUN
ejpam-447	231	16	bxn−k	bxn−k	X
ejpam-447	231	17	+	+	CCONJ
ejpam-447	231	18	pxn	pxn	VERB
ejpam-447	231	19	+	+	CCONJ
ejpam-447	231	20	xn−k	xn−k	PROPN
ejpam-447	231	21	q+	q+	PROPN
ejpam-447	231	22	xn−k	xn−k	PROPN
ejpam-447	231	23	≥	≥	PROPN
ejpam-447	231	24	axn+	axn+	PUNCT
ejpam-447	232	1	bxn−k	bxn−k	X
ejpam-447	232	2	+	+	PUNCT
ejpam-447	232	3	qxn+	qxn+	PROPN
ejpam-447	232	4	xn−k	xn−k	PROPN
ejpam-447	232	5	q+	q+	PROPN
ejpam-447	232	6	xn−k	xn−k	PROPN
ejpam-447	232	7	≥	≥	X
ejpam-447	232	8	a+	a+	PUNCT
ejpam-447	232	9	b+	b+	NUM
ejpam-447	232	10	1	1	NUM
ejpam-447	232	11	≥	≥	NOUN
ejpam-447	232	12	q	q	NOUN
ejpam-447	232	13	p	p	X
ejpam-447	232	14	(	(	PUNCT
ejpam-447	232	15	a+	a+	X
ejpam-447	232	16	b+	b+	X
ejpam-447	232	17	1	1	NUM
ejpam-447	232	18	)	)	PUNCT
ejpam-447	232	19	.	.	PUNCT
ejpam-447	233	1	thus	thus	ADV
ejpam-447	233	2	,	,	PUNCT
ejpam-447	233	3	the	the	DET
ejpam-447	233	4	proof	proof	NOUN
ejpam-447	233	5	of	of	ADP
ejpam-447	233	6	part	part	NOUN
ejpam-447	233	7	(	(	PUNCT
ejpam-447	233	8	ii	ii	NOUN
ejpam-447	233	9	)	)	PUNCT
ejpam-447	233	10	is	be	AUX
ejpam-447	233	11	completed	complete	VERB
ejpam-447	233	12	.	.	PUNCT
ejpam-447	234	1	the	the	DET
ejpam-447	234	2	proof	proof	NOUN
ejpam-447	234	3	of	of	ADP
ejpam-447	234	4	theorem	theorem	ADJ
ejpam-447	234	5	9	9	NUM
ejpam-447	234	6	is	be	AUX
ejpam-447	234	7	now	now	ADV
ejpam-447	234	8	finished	finish	VERB
ejpam-447	234	9	.	.	PUNCT
ejpam-447	235	1	6	6	X
ejpam-447	235	2	.	.	X
ejpam-447	235	3	global	global	ADJ
ejpam-447	235	4	stability	stability	NOUN
ejpam-447	235	5	in	in	ADP
ejpam-447	235	6	this	this	DET
ejpam-447	235	7	section	section	NOUN
ejpam-447	235	8	,	,	PUNCT
ejpam-447	235	9	we	we	PRON
ejpam-447	235	10	investigate	investigate	VERB
ejpam-447	235	11	the	the	DET
ejpam-447	235	12	global	global	ADJ
ejpam-447	235	13	stability	stability	NOUN
ejpam-447	235	14	of	of	ADP
ejpam-447	235	15	the	the	DET
ejpam-447	235	16	positive	positive	ADJ
ejpam-447	235	17	solutions	solution	NOUN
ejpam-447	235	18	of	of	ADP
ejpam-447	235	19	eq.(1	eq.(1	ADJ
ejpam-447	235	20	)	)	PUNCT
ejpam-447	235	21	.	.	PUNCT
ejpam-447	236	1	theorem	theorem	VERB
ejpam-447	236	2	10	10	NUM
ejpam-447	236	3	.	.	PUNCT
ejpam-447	237	1	if	if	SCONJ
ejpam-447	237	2	p−	p−	PRON
ejpam-447	237	3	q	q	NOUN
ejpam-447	237	4	<	<	X
ejpam-447	237	5	−	−	PROPN
ejpam-447	237	6	�	�	PROPN
ejpam-447	237	7	1	1	NUM
ejpam-447	237	8	+	+	NOUN
ejpam-447	237	9	q	q	NOUN
ejpam-447	237	10	(	(	PUNCT
ejpam-447	237	11	a+	a+	NOUN
ejpam-447	237	12	b	b	X
ejpam-447	237	13	)	)	PUNCT
ejpam-447	237	14	�	�	PROPN
ejpam-447	237	15	,	,	PUNCT
ejpam-447	237	16	then	then	ADV
ejpam-447	237	17	,	,	PUNCT
ejpam-447	237	18	the	the	DET
ejpam-447	237	19	zero	zero	NUM
ejpam-447	237	20	equilibrium	equilibrium	NOUN
ejpam-447	237	21	point	point	NOUN
ejpam-447	237	22	ex	ex	X
ejpam-447	237	23	=	=	NOUN
ejpam-447	237	24	0	0	NUM
ejpam-447	237	25	of	of	ADP
ejpam-447	237	26	eq.(1	eq.(1	ADJ
ejpam-447	237	27	)	)	PUNCT
ejpam-447	237	28	is	be	AUX
ejpam-447	237	29	globally	globally	ADV
ejpam-447	237	30	asymptotically	asymptotically	ADV
ejpam-447	237	31	stable	stable	ADJ
ejpam-447	237	32	.	.	PUNCT
ejpam-447	238	1	proof	proof	NOUN
ejpam-447	238	2	.	.	PUNCT
ejpam-447	239	1	under	under	ADP
ejpam-447	239	2	this	this	DET
ejpam-447	239	3	condition	condition	NOUN
ejpam-447	239	4	,	,	PUNCT
ejpam-447	239	5	we	we	PRON
ejpam-447	239	6	have	have	AUX
ejpam-447	239	7	shown	show	VERB
ejpam-447	239	8	in	in	ADP
ejpam-447	239	9	theorem	theorem	NOUN
ejpam-447	239	10	5	5	NUM
ejpam-447	239	11	that	that	SCONJ
ejpam-447	239	12	ex	ex	PRON
ejpam-447	239	13	=	=	NOUN
ejpam-447	239	14	0	0	PUNCT
ejpam-447	239	15	is	be	AUX
ejpam-447	239	16	locally	locally	ADV
ejpam-447	239	17	asymptotically	asymptotically	ADV
ejpam-447	239	18	stable	stable	ADJ
ejpam-447	239	19	.	.	PUNCT
ejpam-447	240	1	it	it	PRON
ejpam-447	240	2	remains	remain	VERB
ejpam-447	240	3	to	to	PART
ejpam-447	240	4	prove	prove	VERB
ejpam-447	240	5	that	that	SCONJ
ejpam-447	240	6	ex	ex	PRON
ejpam-447	240	7	=	=	NOUN
ejpam-447	240	8	0	0	NUM
ejpam-447	240	9	is	be	AUX
ejpam-447	240	10	a	a	DET
ejpam-447	240	11	global	global	ADJ
ejpam-447	240	12	attractor	attractor	NOUN
ejpam-447	240	13	.	.	PUNCT
ejpam-447	241	1	to	to	ADP
ejpam-447	241	2	this	this	DET
ejpam-447	241	3	end	end	NOUN
ejpam-447	241	4	,	,	PUNCT
ejpam-447	241	5	we	we	PRON
ejpam-447	241	6	consider	consider	VERB
ejpam-447	241	7	the	the	DET
ejpam-447	241	8	function	function	NOUN
ejpam-447	241	9	f(x	f(x	PROPN
ejpam-447	241	10	,	,	PUNCT
ejpam-447	241	11	y	y	NOUN
ejpam-447	241	12	)	)	PUNCT
ejpam-447	242	1	=	=	NOUN
ejpam-447	242	2	ax	ax	NOUN
ejpam-447	242	3	+	+	CCONJ
ejpam-447	242	4	b	b	PROPN
ejpam-447	242	5	y	y	PROPN
ejpam-447	242	6	+	+	PROPN
ejpam-447	242	7	px	px	PROPN
ejpam-447	243	1	+	+	CCONJ
ejpam-447	243	2	y	y	PROPN
ejpam-447	243	3	q+	q+	ADP
ejpam-447	243	4	y	y	PROPN
ejpam-447	243	5	.	.	PUNCT
ejpam-447	244	1	(	(	PUNCT
ejpam-447	244	2	18	18	NUM
ejpam-447	244	3	)	)	PUNCT
ejpam-447	244	4	we	we	PRON
ejpam-447	244	5	note	note	VERB
ejpam-447	244	6	that	that	SCONJ
ejpam-447	244	7	the	the	DET
ejpam-447	244	8	function	function	NOUN
ejpam-447	244	9	(	(	PUNCT
ejpam-447	244	10	18	18	NUM
ejpam-447	244	11	)	)	PUNCT
ejpam-447	244	12	is	be	AUX
ejpam-447	244	13	continuous	continuous	ADJ
ejpam-447	244	14	and	and	CCONJ
ejpam-447	244	15	satisfying	satisfy	VERB
ejpam-447	244	16	the	the	DET
ejpam-447	244	17	following	follow	VERB
ejpam-447	244	18	conditions	condition	NOUN
ejpam-447	244	19	:	:	PUNCT
ejpam-447	244	20	(	(	PUNCT
ejpam-447	244	21	i	i	NOUN
ejpam-447	244	22	)	)	PUNCT
ejpam-447	244	23	f(x	f(x	PROPN
ejpam-447	244	24	,	,	PUNCT
ejpam-447	244	25	y	y	PROPN
ejpam-447	244	26	)	)	PUNCT
ejpam-447	244	27	is	be	AUX
ejpam-447	244	28	nondecreasing	nondecrease	VERB
ejpam-447	244	29	in	in	ADP
ejpam-447	244	30	x	x	PUNCT
ejpam-447	244	31	∈	∈	PROPN
ejpam-447	244	32	[	[	PUNCT
ejpam-447	244	33	q	q	X
ejpam-447	244	34	p	p	X
ejpam-447	244	35	,	,	PUNCT
ejpam-447	244	36	∞	∞	PROPN
ejpam-447	244	37	)	)	PUNCT
ejpam-447	244	38	for	for	ADP
ejpam-447	244	39	fixed	fix	VERB
ejpam-447	244	40	y	y	PROPN
ejpam-447	244	41	>	>	X
ejpam-447	244	42	−q	−q	NOUN
ejpam-447	244	43	.	.	PUNCT
ejpam-447	245	1	(	(	PUNCT
ejpam-447	245	2	ii	ii	NOUN
ejpam-447	245	3	)	)	PUNCT
ejpam-447	245	4	f(x	f(x	PROPN
ejpam-447	245	5	,	,	PUNCT
ejpam-447	245	6	y	y	PROPN
ejpam-447	245	7	)	)	PUNCT
ejpam-447	245	8	satisfies	satisfy	VERB
ejpam-447	245	9	the	the	DET
ejpam-447	245	10	inequality	inequality	NOUN
ejpam-447	246	1	[	[	X
ejpam-447	246	2	f(x	f(x	PROPN
ejpam-447	246	3	,	,	PUNCT
ejpam-447	246	4	x)−	x)−	PROPN
ejpam-447	246	5	x][x	x][x	PROPN
ejpam-447	246	6	−	−	PROPN
ejpam-447	247	1	ex	ex	NOUN
ejpam-447	247	2	]	]	X
ejpam-447	247	3	<	<	X
ejpam-447	247	4	0	0	NUM
ejpam-447	247	5	for	for	ADP
ejpam-447	247	6	ex	ex	X
ejpam-447	247	7	=	=	NOUN
ejpam-447	247	8	0	0	X
ejpam-447	247	9	.	.	PUNCT
ejpam-447	248	1	let	let	VERB
ejpam-447	248	2	us	we	PRON
ejpam-447	248	3	now	now	ADV
ejpam-447	248	4	prove	prove	VERB
ejpam-447	248	5	(	(	PUNCT
ejpam-447	248	6	ii	ii	NOUN
ejpam-447	248	7	)	)	PUNCT
ejpam-447	248	8	as	as	SCONJ
ejpam-447	248	9	follows	follow	VERB
ejpam-447	248	10	:	:	PUNCT
ejpam-447	249	1	[	[	X
ejpam-447	249	2	f(x	f(x	PROPN
ejpam-447	249	3	,	,	PUNCT
ejpam-447	249	4	x)−	x)−	PROPN
ejpam-447	249	5	x	x	X
ejpam-447	249	6	]	]	X
ejpam-447	250	1	[	[	X
ejpam-447	250	2	x	x	X
ejpam-447	250	3	−	−	NOUN
ejpam-447	250	4	0	0	NUM
ejpam-447	250	5	]	]	X
ejpam-447	250	6	=	=	SYM
ejpam-447	250	7	�	�	PROPN
ejpam-447	250	8	(	(	PUNCT
ejpam-447	250	9	a+	a+	NOUN
ejpam-447	250	10	b	b	X
ejpam-447	250	11	)	)	PUNCT
ejpam-447	250	12	x	x	PUNCT
ejpam-447	250	13	+	+	PUNCT
ejpam-447	250	14	�	�	PROPN
ejpam-447	250	15	p+	p+	PART
ejpam-447	250	16	1	1	NUM
ejpam-447	250	17	�	�	PROPN
ejpam-447	250	18	x	x	SYM
ejpam-447	250	19	q+	q+	ADP
ejpam-447	250	20	x	x	SYM
ejpam-447	250	21	−	−	NOUN
ejpam-447	250	22	x	x	SYM
ejpam-447	250	23	�	�	PROPN
ejpam-447	250	24	x	x	X
ejpam-447	250	25	.	.	PUNCT
ejpam-447	251	1	since	since	SCONJ
ejpam-447	251	2	x	x	PROPN
ejpam-447	251	3	∈	∈	PROPN
ejpam-447	251	4	[	[	PUNCT
ejpam-447	251	5	q	q	X
ejpam-447	251	6	p	p	NOUN
ejpam-447	251	7	,	,	PUNCT
ejpam-447	251	8	∞	∞	PROPN
ejpam-447	251	9	)	)	PUNCT
ejpam-447	251	10	,	,	PUNCT
ejpam-447	251	11	then	then	ADV
ejpam-447	251	12	p+1	p+1	PROPN
ejpam-447	251	13	q+x	q+x	PROPN
ejpam-447	251	14	<	<	X
ejpam-447	251	15	p	p	X
ejpam-447	251	16	q	q	NOUN
ejpam-447	252	1	and	and	CCONJ
ejpam-447	252	2	we	we	PRON
ejpam-447	252	3	have	have	VERB
ejpam-447	252	4	[	[	X
ejpam-447	252	5	f(x	f(x	PROPN
ejpam-447	252	6	,	,	PUNCT
ejpam-447	252	7	x)−	x)−	PROPN
ejpam-447	252	8	x][x	x][x	PROPN
ejpam-447	253	1	−	−	PROPN
ejpam-447	253	2	0	0	NUM
ejpam-447	253	3	]	]	X
ejpam-447	253	4	<	<	X
ejpam-447	253	5	�	�	PROPN
ejpam-447	253	6	(	(	PUNCT
ejpam-447	253	7	a+	a+	PUNCT
ejpam-447	253	8	b)q+	b)q+	X
ejpam-447	253	9	�	�	PROPN
ejpam-447	253	10	p−	p−	PROPN
ejpam-447	253	11	q	q	PROPN
ejpam-447	253	12	�	�	PROPN
ejpam-447	253	13	q	q	PROPN
ejpam-447	253	14	�	�	PROPN
ejpam-447	253	15	x2	x2	PROPN
ejpam-447	253	16	<	<	X
ejpam-447	253	17	�	�	PROPN
ejpam-447	253	18	(	(	PUNCT
ejpam-447	253	19	a+	a+	X
ejpam-447	253	20	b)q−	b)q−	PROPN
ejpam-447	253	21	�	�	PROPN
ejpam-447	253	22	1	1	NUM
ejpam-447	253	23	+	+	NOUN
ejpam-447	253	24	q	q	NOUN
ejpam-447	253	25	(	(	PUNCT
ejpam-447	253	26	a+	a+	NOUN
ejpam-447	253	27	b	b	NOUN
ejpam-447	253	28	)	)	PUNCT
ejpam-447	253	29	q	q	PROPN
ejpam-447	253	30	�	�	PROPN
ejpam-447	253	31	x2	x2	NOUN
ejpam-447	253	32	=	=	PUNCT
ejpam-447	254	1	−	−	PROPN
ejpam-447	255	1	x2	x2	INTJ
ejpam-447	255	2	q	q	X
ejpam-447	255	3	<	<	X
ejpam-447	255	4	0	0	NUM
ejpam-447	255	5	.	.	PUNCT
ejpam-447	256	1	e.	e.	PROPN
ejpam-447	256	2	zayed	zayed	PROPN
ejpam-447	256	3	/	/	SYM
ejpam-447	256	4	eur	eur	PROPN
ejpam-447	256	5	.	.	PUNCT
ejpam-447	257	1	j.	j.	PROPN
ejpam-447	257	2	pure	pure	PROPN
ejpam-447	257	3	appl	appl	PROPN
ejpam-447	257	4	.	.	PROPN
ejpam-447	257	5	math	math	PROPN
ejpam-447	257	6	,	,	PUNCT
ejpam-447	257	7	3	3	NUM
ejpam-447	257	8	(	(	PUNCT
ejpam-447	257	9	2010	2010	NUM
ejpam-447	257	10	)	)	PUNCT
ejpam-447	257	11	,	,	PUNCT
ejpam-447	257	12	254	254	NUM
ejpam-447	257	13	-	-	SYM
ejpam-447	257	14	268	268	NUM
ejpam-447	257	15	264	264	NUM
ejpam-447	257	16	according	accord	VERB
ejpam-447	257	17	to	to	ADP
ejpam-447	257	18	theorem	theorem	ADJ
ejpam-447	257	19	4	4	NUM
ejpam-447	257	20	,	,	PUNCT
ejpam-447	257	21	the	the	DET
ejpam-447	257	22	zero	zero	NUM
ejpam-447	257	23	equilibrium	equilibrium	NOUN
ejpam-447	257	24	point	point	NOUN
ejpam-447	257	25	ex	ex	X
ejpam-447	258	1	=	=	NOUN
ejpam-447	258	2	0	0	NUM
ejpam-447	258	3	is	be	AUX
ejpam-447	258	4	a	a	DET
ejpam-447	258	5	global	global	ADJ
ejpam-447	258	6	attractor	attractor	NOUN
ejpam-447	258	7	.	.	PUNCT
ejpam-447	259	1	the	the	DET
ejpam-447	259	2	proof	proof	NOUN
ejpam-447	259	3	of	of	ADP
ejpam-447	259	4	theorem	theorem	ADJ
ejpam-447	259	5	11	11	NUM
ejpam-447	259	6	is	be	AUX
ejpam-447	259	7	now	now	ADV
ejpam-447	259	8	completed	complete	VERB
ejpam-447	259	9	.	.	PUNCT
ejpam-447	260	1	theorem	theorem	ADJ
ejpam-447	260	2	11	11	NUM
ejpam-447	260	3	.	.	PUNCT
ejpam-447	261	1	assume	assume	VERB
ejpam-447	261	2	that	that	SCONJ
ejpam-447	261	3	p	p	PROPN
ejpam-447	262	1	−	−	PROPN
ejpam-447	262	2	q	q	NOUN
ejpam-447	262	3	>	>	PUNCT
ejpam-447	262	4	−	−	PROPN
ejpam-447	262	5	�	�	PROPN
ejpam-447	262	6	1	1	NUM
ejpam-447	262	7	+	+	NOUN
ejpam-447	262	8	q	q	NOUN
ejpam-447	262	9	(	(	PUNCT
ejpam-447	262	10	a+	a+	NOUN
ejpam-447	262	11	b	b	X
ejpam-447	262	12	)	)	PUNCT
ejpam-447	262	13	�	�	PROPN
ejpam-447	262	14	,	,	PUNCT
ejpam-447	262	15	p	p	X
ejpam-447	262	16	>	>	X
ejpam-447	262	17	q	q	X
ejpam-447	262	18	,	,	PUNCT
ejpam-447	262	19	0	0	PUNCT
ejpam-447	262	20	<	<	X
ejpam-447	262	21	a	a	DET
ejpam-447	262	22	+	+	X
ejpam-447	262	23	b	b	NOUN
ejpam-447	262	24	<	<	X
ejpam-447	262	25	1	1	NUM
ejpam-447	262	26	and	and	CCONJ
ejpam-447	262	27	b	b	NOUN
ejpam-447	262	28	>	>	X
ejpam-447	263	1	[	[	X
ejpam-447	263	2	1−(a+b)][(p−q)+q(a+b	1−(a+b)][(p−q)+q(a+b	NUM
ejpam-447	263	3	)	)	PUNCT
ejpam-447	263	4	]	]	PUNCT
ejpam-447	264	1	p+1	p+1	NOUN
ejpam-447	264	2	,	,	PUNCT
ejpam-447	264	3	then	then	ADV
ejpam-447	264	4	,	,	PUNCT
ejpam-447	264	5	the	the	DET
ejpam-447	264	6	positive	positive	ADJ
ejpam-447	264	7	equilibrium	equilibrium	NOUN
ejpam-447	264	8	point	point	NOUN
ejpam-447	264	9	ex	ex	PRON
ejpam-447	264	10	of	of	ADP
ejpam-447	264	11	eq.(1	eq.(1	ADJ
ejpam-447	264	12	)	)	PUNCT
ejpam-447	264	13	is	be	AUX
ejpam-447	264	14	globally	globally	ADV
ejpam-447	264	15	asymptotically	asymptotically	ADV
ejpam-447	264	16	stable	stable	ADJ
ejpam-447	264	17	.	.	PUNCT
ejpam-447	265	1	proof	proof	NOUN
ejpam-447	265	2	.	.	PUNCT
ejpam-447	266	1	under	under	ADP
ejpam-447	266	2	these	these	DET
ejpam-447	266	3	assumptions	assumption	NOUN
ejpam-447	266	4	,	,	PUNCT
ejpam-447	266	5	we	we	PRON
ejpam-447	266	6	have	have	AUX
ejpam-447	266	7	shown	show	VERB
ejpam-447	266	8	in	in	ADP
ejpam-447	266	9	theorem	theorem	NOUN
ejpam-447	266	10	6	6	NUM
ejpam-447	266	11	that	that	SCONJ
ejpam-447	266	12	the	the	DET
ejpam-447	266	13	positive	positive	ADJ
ejpam-447	266	14	equilibrium	equilibrium	NOUN
ejpam-447	266	15	point	point	NOUN
ejpam-447	266	16	ex	ex	PRON
ejpam-447	266	17	of	of	ADP
ejpam-447	266	18	eq.(1	eq.(1	ADJ
ejpam-447	266	19	)	)	PUNCT
ejpam-447	266	20	is	be	AUX
ejpam-447	266	21	locally	locally	ADV
ejpam-447	266	22	asymptotically	asymptotically	ADV
ejpam-447	266	23	stable	stable	ADJ
ejpam-447	266	24	.	.	PUNCT
ejpam-447	267	1	it	it	PRON
ejpam-447	267	2	remains	remain	VERB
ejpam-447	267	3	to	to	PART
ejpam-447	267	4	prove	prove	VERB
ejpam-447	267	5	that	that	SCONJ
ejpam-447	267	6	the	the	DET
ejpam-447	267	7	positive	positive	ADJ
ejpam-447	267	8	equilibrium	equilibrium	NOUN
ejpam-447	267	9	point	point	NOUN
ejpam-447	267	10	ex	ex	NOUN
ejpam-447	267	11	is	be	AUX
ejpam-447	267	12	a	a	DET
ejpam-447	267	13	global	global	ADJ
ejpam-447	267	14	attractor	attractor	NOUN
ejpam-447	267	15	.	.	PUNCT
ejpam-447	268	1	to	to	ADP
ejpam-447	268	2	this	this	DET
ejpam-447	268	3	end	end	NOUN
ejpam-447	268	4	,	,	PUNCT
ejpam-447	268	5	we	we	PRON
ejpam-447	268	6	consider	consider	VERB
ejpam-447	268	7	the	the	DET
ejpam-447	268	8	function	function	NOUN
ejpam-447	268	9	f	f	PROPN
ejpam-447	268	10	�	�	PROPN
ejpam-447	268	11	x	x	SYM
ejpam-447	268	12	,	,	PUNCT
ejpam-447	268	13	y	y	PROPN
ejpam-447	268	14	�	�	PROPN
ejpam-447	268	15	given	give	VERB
ejpam-447	268	16	by	by	ADP
ejpam-447	268	17	(	(	PUNCT
ejpam-447	268	18	18	18	NUM
ejpam-447	268	19	)	)	PUNCT
ejpam-447	268	20	which	which	PRON
ejpam-447	268	21	satisfies	satisfy	VERB
ejpam-447	268	22	the	the	DET
ejpam-447	268	23	following	follow	VERB
ejpam-447	268	24	conditions	condition	NOUN
ejpam-447	268	25	:	:	PUNCT
ejpam-447	268	26	(	(	PUNCT
ejpam-447	268	27	i	i	NOUN
ejpam-447	268	28	)	)	PUNCT
ejpam-447	268	29	f(x	f(x	PROPN
ejpam-447	268	30	,	,	PUNCT
ejpam-447	268	31	y	y	PROPN
ejpam-447	268	32	)	)	PUNCT
ejpam-447	268	33	is	be	AUX
ejpam-447	268	34	nondecreasing	nondecrease	VERB
ejpam-447	268	35	in	in	ADP
ejpam-447	268	36	x	x	PUNCT
ejpam-447	268	37	∈	∈	PROPN
ejpam-447	268	38	[	[	PUNCT
ejpam-447	268	39	q	q	X
ejpam-447	268	40	p	p	X
ejpam-447	268	41	,	,	PUNCT
ejpam-447	268	42	∞	∞	PROPN
ejpam-447	268	43	)	)	PUNCT
ejpam-447	268	44	for	for	ADP
ejpam-447	268	45	fixed	fix	VERB
ejpam-447	268	46	y	y	PROPN
ejpam-447	268	47	>	>	X
ejpam-447	268	48	−q	−q	NOUN
ejpam-447	268	49	.	.	PUNCT
ejpam-447	269	1	(	(	PUNCT
ejpam-447	269	2	ii	ii	NOUN
ejpam-447	269	3	)	)	PUNCT
ejpam-447	269	4	f(x	f(x	PROPN
ejpam-447	269	5	,	,	PUNCT
ejpam-447	269	6	y	y	PROPN
ejpam-447	269	7	)	)	PUNCT
ejpam-447	269	8	satisfies	satisfy	VERB
ejpam-447	269	9	the	the	DET
ejpam-447	269	10	inequality	inequality	NOUN
ejpam-447	270	1	[	[	X
ejpam-447	270	2	f(x	f(x	PROPN
ejpam-447	270	3	,	,	PUNCT
ejpam-447	270	4	x)−	x)−	PROPN
ejpam-447	270	5	x][x	x][x	PROPN
ejpam-447	270	6	−	−	PROPN
ejpam-447	271	1	ex	ex	NOUN
ejpam-447	271	2	]	]	X
ejpam-447	271	3	<	<	X
ejpam-447	271	4	0	0	PROPN
ejpam-447	271	5	,	,	PUNCT
ejpam-447	271	6	where	where	SCONJ
ejpam-447	271	7	ex	ex	PRON
ejpam-447	271	8	given	give	VERB
ejpam-447	271	9	by	by	ADP
ejpam-447	271	10	(	(	PUNCT
ejpam-447	271	11	6	6	X
ejpam-447	271	12	.	.	PUNCT
ejpam-447	272	1	let	let	VERB
ejpam-447	272	2	us	we	PRON
ejpam-447	272	3	now	now	ADV
ejpam-447	272	4	prove	prove	VERB
ejpam-447	272	5	the	the	DET
ejpam-447	272	6	inequality	inequality	NOUN
ejpam-447	272	7	(	(	PUNCT
ejpam-447	272	8	ii	ii	NOUN
ejpam-447	272	9	)	)	PUNCT
ejpam-447	272	10	using	use	VERB
ejpam-447	272	11	lemma	lemma	PROPN
ejpam-447	272	12	1	1	NUM
ejpam-447	272	13	as	as	SCONJ
ejpam-447	272	14	follows	follow	VERB
ejpam-447	272	15	:	:	PUNCT
ejpam-447	273	1	[	[	X
ejpam-447	273	2	f(x	f(x	PROPN
ejpam-447	273	3	,	,	PUNCT
ejpam-447	273	4	x)−	x)−	PROPN
ejpam-447	273	5	x][x	x][x	PROPN
ejpam-447	273	6	−	−	PROPN
ejpam-447	273	7	ex	ex	NOUN
ejpam-447	273	8	]	]	X
ejpam-447	273	9	=	=	SYM
ejpam-447	273	10	�	�	PROPN
ejpam-447	273	11	(	(	PUNCT
ejpam-447	273	12	a+	a+	NOUN
ejpam-447	273	13	b	b	X
ejpam-447	273	14	)	)	PUNCT
ejpam-447	273	15	+	+	CCONJ
ejpam-447	273	16	�	�	PROPN
ejpam-447	273	17	p+	p+	PART
ejpam-447	273	18	1	1	NUM
ejpam-447	273	19	�	�	PROPN
ejpam-447	273	20	q+	q+	ADP
ejpam-447	273	21	x	x	NOUN
ejpam-447	273	22	−	−	PROPN
ejpam-447	273	23	1	1	NUM
ejpam-447	273	24	�	�	PROPN
ejpam-447	273	25	�	�	PROPN
ejpam-447	273	26	x2−	x2−	PROPN
ejpam-447	273	27	xex	xex	PROPN
ejpam-447	273	28	�	�	PROPN
ejpam-447	273	29	<	<	X
ejpam-447	273	30	�	�	PROPN
ejpam-447	273	31	(	(	PUNCT
ejpam-447	273	32	a+	a+	NOUN
ejpam-447	273	33	b	b	X
ejpam-447	273	34	)	)	PUNCT
ejpam-447	273	35	+	+	CCONJ
ejpam-447	273	36	�	�	PROPN
ejpam-447	273	37	p−	p−	PROPN
ejpam-447	273	38	q	q	PROPN
ejpam-447	273	39	�	�	PROPN
ejpam-447	273	40	q	q	PROPN
ejpam-447	273	41	�	�	PROPN
ejpam-447	273	42	�	�	PROPN
ejpam-447	273	43	q2	q2	PROPN
ejpam-447	273	44	p2	p2	PROPN
ejpam-447	274	1	−	−	PROPN
ejpam-447	274	2	q	q	PROPN
ejpam-447	275	1	p	p	X
ejpam-447	275	2	ex	ex	PRON
ejpam-447	275	3	�	�	PROPN
ejpam-447	275	4	=	=	PUNCT
ejpam-447	275	5	−	−	PROPN
ejpam-447	275	6	q	q	PROPN
ejpam-447	275	7	p	p	X
ejpam-447	275	8	�	�	PROPN
ejpam-447	275	9	(	(	PUNCT
ejpam-447	275	10	a+	a+	NOUN
ejpam-447	275	11	b	b	X
ejpam-447	275	12	)	)	PUNCT
ejpam-447	275	13	+	+	CCONJ
ejpam-447	275	14	�	�	PROPN
ejpam-447	275	15	p−	p−	PROPN
ejpam-447	275	16	q	q	PROPN
ejpam-447	275	17	�	�	PROPN
ejpam-447	275	18	q	q	PROPN
ejpam-447	275	19	�	�	PROPN
ejpam-447	275	20	�	�	PROPN
ejpam-447	275	21	ex	ex	PRON
ejpam-447	275	22	−	−	PROPN
ejpam-447	275	23	q	q	PROPN
ejpam-447	275	24	p	p	X
ejpam-447	275	25	�	�	PROPN
ejpam-447	275	26	<	<	X
ejpam-447	275	27	0	0	NUM
ejpam-447	275	28	.	.	PUNCT
ejpam-447	276	1	according	accord	VERB
ejpam-447	276	2	to	to	ADP
ejpam-447	276	3	theorem	theorem	NOUN
ejpam-447	276	4	3	3	NUM
ejpam-447	276	5	,	,	PUNCT
ejpam-447	276	6	the	the	DET
ejpam-447	276	7	positive	positive	ADJ
ejpam-447	276	8	equilibrium	equilibrium	NOUN
ejpam-447	276	9	point	point	NOUN
ejpam-447	276	10	ex	ex	NOUN
ejpam-447	276	11	is	be	AUX
ejpam-447	276	12	a	a	DET
ejpam-447	276	13	global	global	ADJ
ejpam-447	276	14	attractor	attractor	NOUN
ejpam-447	276	15	.	.	PUNCT
ejpam-447	277	1	the	the	DET
ejpam-447	277	2	proof	proof	NOUN
ejpam-447	277	3	of	of	ADP
ejpam-447	277	4	theorem	theorem	ADJ
ejpam-447	277	5	11	11	NUM
ejpam-447	277	6	is	be	AUX
ejpam-447	277	7	now	now	ADV
ejpam-447	277	8	completed	complete	VERB
ejpam-447	277	9	.	.	PUNCT
ejpam-447	278	1	7	7	X
ejpam-447	278	2	.	.	X
ejpam-447	278	3	numerical	numerical	ADJ
ejpam-447	278	4	examples	example	NOUN
ejpam-447	278	5	in	in	ADP
ejpam-447	278	6	order	order	NOUN
ejpam-447	278	7	to	to	PART
ejpam-447	278	8	illustrate	illustrate	VERB
ejpam-447	278	9	the	the	DET
ejpam-447	278	10	results	result	NOUN
ejpam-447	278	11	of	of	ADP
ejpam-447	278	12	the	the	DET
ejpam-447	278	13	previous	previous	ADJ
ejpam-447	278	14	sections	section	NOUN
ejpam-447	278	15	and	and	CCONJ
ejpam-447	278	16	to	to	PART
ejpam-447	278	17	support	support	VERB
ejpam-447	278	18	our	our	PRON
ejpam-447	278	19	theoretical	theoretical	ADJ
ejpam-447	278	20	discussions	discussion	NOUN
ejpam-447	278	21	,	,	PUNCT
ejpam-447	278	22	we	we	PRON
ejpam-447	278	23	consider	consider	VERB
ejpam-447	278	24	several	several	ADJ
ejpam-447	278	25	interesting	interesting	ADJ
ejpam-447	278	26	numerical	numerical	ADJ
ejpam-447	278	27	examples	example	NOUN
ejpam-447	278	28	in	in	ADP
ejpam-447	278	29	this	this	DET
ejpam-447	278	30	section	section	NOUN
ejpam-447	278	31	.	.	PUNCT
ejpam-447	279	1	these	these	DET
ejpam-447	279	2	examples	example	NOUN
ejpam-447	279	3	represent	represent	VERB
ejpam-447	279	4	different	different	ADJ
ejpam-447	279	5	types	type	NOUN
ejpam-447	279	6	of	of	ADP
ejpam-447	279	7	qualitative	qualitative	ADJ
ejpam-447	279	8	behavior	behavior	NOUN
ejpam-447	279	9	of	of	ADP
ejpam-447	279	10	solutions	solution	NOUN
ejpam-447	279	11	to	to	ADP
ejpam-447	279	12	the	the	DET
ejpam-447	279	13	nonlinear	nonlinear	ADJ
ejpam-447	279	14	difference	difference	NOUN
ejpam-447	279	15	equation	equation	NOUN
ejpam-447	279	16	(	(	PUNCT
ejpam-447	279	17	1	1	NUM
ejpam-447	279	18	)	)	PUNCT
ejpam-447	279	19	.	.	PUNCT
ejpam-447	280	1	references	reference	NOUN
ejpam-447	280	2	265	265	NUM
ejpam-447	280	3	example	example	NOUN
ejpam-447	280	4	1	1	NUM
ejpam-447	280	5	.	.	PUNCT
ejpam-447	280	6	figure	figure	NOUN
ejpam-447	280	7	1	1	NUM
ejpam-447	280	8	shows	show	VERB
ejpam-447	280	9	that	that	SCONJ
ejpam-447	280	10	the	the	DET
ejpam-447	280	11	solution	solution	NOUN
ejpam-447	280	12	of	of	ADP
ejpam-447	280	13	eq.(1	eq.(1	ADJ
ejpam-447	280	14	)	)	PUNCT
ejpam-447	280	15	is	be	AUX
ejpam-447	280	16	global	global	ADJ
ejpam-447	280	17	stability	stability	NOUN
ejpam-447	280	18	if	if	SCONJ
ejpam-447	280	19	k	k	PROPN
ejpam-447	280	20	=	=	SYM
ejpam-447	280	21	1	1	PROPN
ejpam-447	280	22	,	,	PUNCT
ejpam-447	280	23	x−1	x−1	PUNCT
ejpam-447	280	24	=	=	NOUN
ejpam-447	280	25	1	1	NUM
ejpam-447	280	26	,	,	PUNCT
ejpam-447	280	27	x0	x0	PROPN
ejpam-447	280	28	=	=	SYM
ejpam-447	280	29	2	2	NUM
ejpam-447	280	30	,	,	PUNCT
ejpam-447	280	31	a=	a=	ADV
ejpam-447	280	32	0.25	0.25	NUM
ejpam-447	280	33	,	,	PUNCT
ejpam-447	280	34	b	b	X
ejpam-447	280	35	=	=	SYM
ejpam-447	280	36	0.3	0.3	NUM
ejpam-447	280	37	,	,	PUNCT
ejpam-447	280	38	p	p	X
ejpam-447	280	39	=	=	NOUN
ejpam-447	280	40	2	2	NUM
ejpam-447	280	41	,	,	PUNCT
ejpam-447	280	42	q	q	NOUN
ejpam-447	280	43	=	=	NOUN
ejpam-447	280	44	1	1	NUM
ejpam-447	280	45	,	,	PUNCT
ejpam-447	280	46	(	(	PUNCT
ejpam-447	280	47	p	p	X
ejpam-447	280	48	>	>	X
ejpam-447	280	49	q	q	PROPN
ejpam-447	280	50	)	)	PUNCT
ejpam-447	280	51	.	.	PUNCT
ejpam-447	281	1	0	0	NUM
ejpam-447	282	1	20	20	NUM
ejpam-447	282	2	40	40	NUM
ejpam-447	282	3	60	60	NUM
ejpam-447	282	4	80	80	NUM
ejpam-447	282	5	100	100	NUM
ejpam-447	282	6	120	120	NUM
ejpam-447	282	7	140	140	NUM
ejpam-447	282	8	160	160	NUM
ejpam-447	282	9	180	180	NUM
ejpam-447	282	10	200	200	NUM
ejpam-447	282	11	1	1	NUM
ejpam-447	282	12	2	2	NUM
ejpam-447	282	13	3	3	NUM
ejpam-447	282	14	4	4	NUM
ejpam-447	282	15	5	5	NUM
ejpam-447	282	16	6	6	NUM
ejpam-447	282	17	7	7	NUM
ejpam-447	282	18	n−iteration	n−iteration	NOUN
ejpam-447	282	19	so	so	ADV
ejpam-447	282	20	lu	lu	PROPN
ejpam-447	282	21	tio	tio	PROPN
ejpam-447	282	22	n	n	PROPN
ejpam-447	282	23	of	of	ADP
ejpam-447	282	24	x	x	X
ejpam-447	282	25	(	(	PUNCT
ejpam-447	282	26	n	n	NOUN
ejpam-447	282	27	+	+	CCONJ
ejpam-447	282	28	1	1	NUM
ejpam-447	282	29	)	)	PUNCT
ejpam-447	282	30	=	=	NOUN
ejpam-447	282	31	(	(	PUNCT
ejpam-447	282	32	a	a	DET
ejpam-447	282	33	*	*	ADJ
ejpam-447	282	34	x	x	X
ejpam-447	282	35	(	(	PUNCT
ejpam-447	282	36	n	n	NOUN
ejpam-447	282	37	)	)	PUNCT
ejpam-447	283	1	+	+	NUM
ejpam-447	284	1	b	b	X
ejpam-447	284	2	*	*	PUNCT
ejpam-447	284	3	x	x	X
ejpam-447	284	4	(	(	PUNCT
ejpam-447	284	5	n	n	CCONJ
ejpam-447	284	6	−	−	PROPN
ejpam-447	284	7	1	1	NUM
ejpam-447	284	8	)	)	PUNCT
ejpam-447	284	9	)	)	PUNCT
ejpam-447	284	10	+	+	CCONJ
ejpam-447	284	11	(	(	PUNCT
ejpam-447	284	12	(	(	PUNCT
ejpam-447	284	13	p	p	X
ejpam-447	284	14	*	*	X
ejpam-447	284	15	x	x	X
ejpam-447	284	16	(	(	PUNCT
ejpam-447	284	17	n	n	NOUN
ejpam-447	284	18	)	)	PUNCT
ejpam-447	284	19	+	+	CCONJ
ejpam-447	284	20	x	x	SYM
ejpam-447	284	21	(	(	PUNCT
ejpam-447	284	22	n	n	CCONJ
ejpam-447	284	23	−	−	PROPN
ejpam-447	284	24	1	1	NUM
ejpam-447	284	25	)	)	PUNCT
ejpam-447	284	26	)	)	PUNCT
ejpam-447	284	27	/	/	SYM
ejpam-447	284	28	(	(	PUNCT
ejpam-447	284	29	q	q	PROPN
ejpam-447	284	30	+	+	NUM
ejpam-447	284	31	x	x	SYM
ejpam-447	284	32	(	(	PUNCT
ejpam-447	284	33	n	n	CCONJ
ejpam-447	284	34	−	−	PROPN
ejpam-447	284	35	1	1	NUM
ejpam-447	284	36	)	)	PUNCT
ejpam-447	284	37	)	)	PUNCT
ejpam-447	284	38	)	)	PUNCT
ejpam-447	284	39	plot	plot	NOUN
ejpam-447	284	40	of	of	ADP
ejpam-447	284	41	x(n+1)=(a*x(n)+b*x(n−1))+((p*x(n)+x(n−1))/(q+x(n−1	x(n+1)=(a*x(n)+b*x(n−1))+((p*x(n)+x(n−1))/(q+x(n−1	PROPN
ejpam-447	284	42	)	)	PUNCT
ejpam-447	284	43	)	)	PUNCT
ejpam-447	284	44	)	)	PUNCT
ejpam-447	284	45	figure	figure	NOUN
ejpam-447	284	46	1	1	NUM
ejpam-447	284	47	:	:	SYM
ejpam-447	284	48	xn+1	xn+1	NUM
ejpam-447	284	49	=	=	SYM
ejpam-447	284	50	0.25xn	0.25xn	NOUN
ejpam-447	285	1	+	+	CCONJ
ejpam-447	285	2	0.3xn−1	0.3xn−1	ADJ
ejpam-447	285	3	+	+	CCONJ
ejpam-447	285	4	2xn+xn−1	2xn+xn−1	NUM
ejpam-447	285	5	1+xn−1	1+xn−1	NUM
ejpam-447	285	6	example	example	NOUN
ejpam-447	285	7	2	2	NUM
ejpam-447	285	8	.	.	PUNCT
ejpam-447	285	9	figure	figure	NOUN
ejpam-447	285	10	2	2	NUM
ejpam-447	285	11	shows	show	VERB
ejpam-447	285	12	that	that	SCONJ
ejpam-447	285	13	the	the	DET
ejpam-447	285	14	solution	solution	NOUN
ejpam-447	285	15	of	of	ADP
ejpam-447	285	16	eq.(1	eq.(1	ADJ
ejpam-447	285	17	)	)	PUNCT
ejpam-447	285	18	is	be	AUX
ejpam-447	285	19	global	global	ADJ
ejpam-447	285	20	stability	stability	NOUN
ejpam-447	285	21	if	if	SCONJ
ejpam-447	285	22	k	k	PROPN
ejpam-447	285	23	=	=	SYM
ejpam-447	285	24	2	2	NUM
ejpam-447	285	25	,	,	PUNCT
ejpam-447	285	26	x−2	x−2	PROPN
ejpam-447	285	27	=	=	SYM
ejpam-447	285	28	1	1	PROPN
ejpam-447	285	29	,	,	PUNCT
ejpam-447	285	30	x−1	x−1	PROPN
ejpam-447	285	31	=	=	PROPN
ejpam-447	285	32	2	2	NUM
ejpam-447	285	33	,	,	PUNCT
ejpam-447	285	34	x0	x0	PROPN
ejpam-447	285	35	=	=	SYM
ejpam-447	285	36	3	3	NUM
ejpam-447	285	37	,	,	PUNCT
ejpam-447	285	38	a=	a=	ADV
ejpam-447	285	39	0.25	0.25	NUM
ejpam-447	285	40	,	,	PUNCT
ejpam-447	285	41	b	b	X
ejpam-447	285	42	=	=	SYM
ejpam-447	285	43	0.3	0.3	NUM
ejpam-447	285	44	,	,	PUNCT
ejpam-447	285	45	p	p	X
ejpam-447	285	46	=	=	NOUN
ejpam-447	285	47	20	20	NUM
ejpam-447	285	48	,	,	PUNCT
ejpam-447	285	49	q	q	NOUN
ejpam-447	285	50	=	=	SYM
ejpam-447	285	51	5	5	NUM
ejpam-447	285	52	,	,	PUNCT
ejpam-447	285	53	(	(	PUNCT
ejpam-447	285	54	p	p	X
ejpam-447	285	55	>	>	X
ejpam-447	285	56	q	q	PROPN
ejpam-447	285	57	)	)	PUNCT
ejpam-447	285	58	.	.	PUNCT
ejpam-447	286	1	0	0	NUM
ejpam-447	287	1	20	20	NUM
ejpam-447	287	2	40	40	NUM
ejpam-447	287	3	60	60	NUM
ejpam-447	287	4	80	80	NUM
ejpam-447	287	5	100	100	NUM
ejpam-447	287	6	120	120	NUM
ejpam-447	287	7	140	140	NUM
ejpam-447	287	8	160	160	NUM
ejpam-447	287	9	180	180	NUM
ejpam-447	287	10	200	200	NUM
ejpam-447	287	11	0	0	NUM
ejpam-447	287	12	20	20	NUM
ejpam-447	287	13	40	40	NUM
ejpam-447	287	14	60	60	NUM
ejpam-447	287	15	80	80	NUM
ejpam-447	287	16	100	100	NUM
ejpam-447	287	17	120	120	NUM
ejpam-447	287	18	140	140	NUM
ejpam-447	287	19	160	160	NUM
ejpam-447	287	20	n−iteration	n−iteration	NOUN
ejpam-447	287	21	so	so	ADV
ejpam-447	287	22	lu	lu	PROPN
ejpam-447	287	23	tio	tio	PROPN
ejpam-447	287	24	n	n	PROPN
ejpam-447	287	25	of	of	ADP
ejpam-447	287	26	x	x	X
ejpam-447	287	27	(	(	PUNCT
ejpam-447	287	28	n	n	NOUN
ejpam-447	287	29	+	+	CCONJ
ejpam-447	287	30	1	1	NUM
ejpam-447	287	31	)	)	PUNCT
ejpam-447	287	32	=	=	NOUN
ejpam-447	287	33	(	(	PUNCT
ejpam-447	287	34	a	a	DET
ejpam-447	287	35	*	*	ADJ
ejpam-447	287	36	x	x	X
ejpam-447	287	37	(	(	PUNCT
ejpam-447	287	38	n	n	NOUN
ejpam-447	287	39	)	)	PUNCT
ejpam-447	288	1	+	+	NUM
ejpam-447	289	1	b	b	X
ejpam-447	289	2	*	*	PUNCT
ejpam-447	289	3	x	x	X
ejpam-447	289	4	(	(	PUNCT
ejpam-447	289	5	n	n	CCONJ
ejpam-447	289	6	−	−	PROPN
ejpam-447	289	7	2	2	NUM
ejpam-447	289	8	)	)	PUNCT
ejpam-447	289	9	)	)	PUNCT
ejpam-447	290	1	+	+	CCONJ
ejpam-447	290	2	(	(	PUNCT
ejpam-447	290	3	(	(	PUNCT
ejpam-447	290	4	p	p	X
ejpam-447	290	5	*	*	X
ejpam-447	290	6	x	x	X
ejpam-447	290	7	(	(	PUNCT
ejpam-447	290	8	n	n	NOUN
ejpam-447	290	9	)	)	PUNCT
ejpam-447	290	10	+	+	CCONJ
ejpam-447	290	11	x	x	SYM
ejpam-447	290	12	(	(	PUNCT
ejpam-447	290	13	n	n	CCONJ
ejpam-447	290	14	−	−	PROPN
ejpam-447	290	15	2	2	NUM
ejpam-447	290	16	)	)	PUNCT
ejpam-447	290	17	)	)	PUNCT
ejpam-447	290	18	/	/	SYM
ejpam-447	290	19	(	(	PUNCT
ejpam-447	290	20	q	q	PROPN
ejpam-447	290	21	+	+	NUM
ejpam-447	290	22	x	x	SYM
ejpam-447	290	23	(	(	PUNCT
ejpam-447	290	24	n	n	CCONJ
ejpam-447	290	25	−	−	PROPN
ejpam-447	290	26	2	2	NUM
ejpam-447	290	27	)	)	PUNCT
ejpam-447	290	28	)	)	PUNCT
ejpam-447	290	29	)	)	PUNCT
ejpam-447	290	30	plot	plot	NOUN
ejpam-447	290	31	of	of	ADP
ejpam-447	290	32	x(n+1)=(a*x(n)+b*x(n−2))+((p*x(n)+x(n−2))/(q+x(n−2	x(n+1)=(a*x(n)+b*x(n−2))+((p*x(n)+x(n−2))/(q+x(n−2	PROPN
ejpam-447	290	33	)	)	PUNCT
ejpam-447	290	34	)	)	PUNCT
ejpam-447	290	35	)	)	PUNCT
ejpam-447	290	36	figure	figure	NOUN
ejpam-447	290	37	2	2	NUM
ejpam-447	290	38	:	:	SYM
ejpam-447	290	39	xn+1	xn+1	NUM
ejpam-447	290	40	=	=	SYM
ejpam-447	290	41	0.25xn	0.25xn	NOUN
ejpam-447	291	1	+	+	CCONJ
ejpam-447	291	2	0.3xn−2	0.3xn−2	NOUN
ejpam-447	291	3	+	+	CCONJ
ejpam-447	291	4	20xn+xn−2	20xn+xn−2	NUM
ejpam-447	291	5	5+xn−2	5+xn−2	NUM
ejpam-447	291	6	references	reference	NOUN
ejpam-447	291	7	[	[	X
ejpam-447	291	8	1	1	NUM
ejpam-447	291	9	]	]	PUNCT
ejpam-447	291	10	m.	m.	NOUN
ejpam-447	291	11	t.	t.	PROPN
ejpam-447	291	12	aboutaleb	aboutaleb	PROPN
ejpam-447	291	13	,	,	PUNCT
ejpam-447	291	14	m.	m.	NOUN
ejpam-447	291	15	a.	a.	PROPN
ejpam-447	291	16	el	el	PROPN
ejpam-447	291	17	-	-	PUNCT
ejpam-447	291	18	sayed	say	VERB
ejpam-447	291	19	and	and	CCONJ
ejpam-447	291	20	a.	a.	PROPN
ejpam-447	291	21	e.	e.	PROPN
ejpam-447	291	22	hamza	hamza	PROPN
ejpam-447	291	23	,	,	PUNCT
ejpam-447	291	24	stability	stability	NOUN
ejpam-447	291	25	of	of	ADP
ejpam-447	291	26	the	the	DET
ejpam-447	291	27	recursive	recursive	ADJ
ejpam-447	291	28	sequence	sequence	NOUN
ejpam-447	291	29	xn+1	xn+1	PROPN
ejpam-447	291	30	=	=	SYM
ejpam-447	291	31	(	(	PUNCT
ejpam-447	291	32	α−	α−	ADP
ejpam-447	291	33	β	β	X
ejpam-447	291	34	xn)/(γ+	xn)/(γ+	NOUN
ejpam-447	291	35	xn−1	xn−1	PROPN
ejpam-447	291	36	)	)	PUNCT
ejpam-447	291	37	,	,	PUNCT
ejpam-447	291	38	j.	j.	PROPN
ejpam-447	291	39	math	math	PROPN
ejpam-447	291	40	.	.	PUNCT
ejpam-447	292	1	anal	anal	PROPN
ejpam-447	292	2	.	.	PUNCT
ejpam-447	292	3	appl	appl	PROPN
ejpam-447	292	4	;	;	PUNCT
ejpam-447	292	5	261	261	NUM
ejpam-447	292	6	(	(	PUNCT
ejpam-447	292	7	2001	2001	NUM
ejpam-447	292	8	)	)	PUNCT
ejpam-447	292	9	,	,	PUNCT
ejpam-447	292	10	126	126	NUM
ejpam-447	292	11	-	-	SYM
ejpam-447	292	12	133	133	NUM
ejpam-447	292	13	.	.	PUNCT
ejpam-447	293	1	[	[	X
ejpam-447	293	2	2	2	NUM
ejpam-447	293	3	]	]	X
ejpam-447	293	4	r.	r.	PROPN
ejpam-447	293	5	agarwal	agarwal	PROPN
ejpam-447	293	6	,	,	PUNCT
ejpam-447	293	7	difference	difference	NOUN
ejpam-447	293	8	equations	equation	NOUN
ejpam-447	293	9	and	and	CCONJ
ejpam-447	293	10	inequalities	inequality	NOUN
ejpam-447	293	11	.	.	PUNCT
ejpam-447	294	1	theory	theory	NOUN
ejpam-447	294	2	,	,	PUNCT
ejpam-447	294	3	methods	method	NOUN
ejpam-447	294	4	and	and	CCONJ
ejpam-447	294	5	applications	application	NOUN
ejpam-447	294	6	,	,	PUNCT
ejpam-447	294	7	marcel	marcel	PROPN
ejpam-447	294	8	dekker	dekker	PROPN
ejpam-447	294	9	inc	inc	PROPN
ejpam-447	294	10	,	,	PUNCT
ejpam-447	294	11	new	new	PROPN
ejpam-447	294	12	york	york	PROPN
ejpam-447	294	13	,	,	PUNCT
ejpam-447	294	14	1992	1992	NUM
ejpam-447	294	15	.	.	PUNCT
ejpam-447	295	1	[	[	X
ejpam-447	295	2	3	3	NUM
ejpam-447	295	3	]	]	PUNCT
ejpam-447	295	4	a.	a.	NOUN
ejpam-447	295	5	m.	m.	NOUN
ejpam-447	295	6	amleh	amleh	PROPN
ejpam-447	295	7	,	,	PUNCT
ejpam-447	295	8	e.	e.	PROPN
ejpam-447	295	9	a.	a.	PROPN
ejpam-447	295	10	grove	grove	PROPN
ejpam-447	295	11	,	,	PUNCT
ejpam-447	295	12	g.	g.	PROPN
ejpam-447	295	13	ladas	ladas	PROPN
ejpam-447	295	14	and	and	CCONJ
ejpam-447	295	15	d.	d.	PROPN
ejpam-447	295	16	a.	a.	PROPN
ejpam-447	295	17	georgiou	georgiou	PROPN
ejpam-447	295	18	,	,	PUNCT
ejpam-447	295	19	on	on	ADP
ejpam-447	295	20	the	the	DET
ejpam-447	295	21	recursive	recursive	ADJ
ejpam-447	295	22	sequence	sequence	NOUN
ejpam-447	295	23	xn+1	xn+1	PROPN
ejpam-447	295	24	=	=	SYM
ejpam-447	295	25	α+	α+	PUNCT
ejpam-447	295	26	(	(	PUNCT
ejpam-447	295	27	xn−1	xn−1	PROPN
ejpam-447	295	28	/	/	SYM
ejpam-447	295	29	xn	xn	PROPN
ejpam-447	295	30	)	)	PUNCT
ejpam-447	295	31	,	,	PUNCT
ejpam-447	295	32	j.	j.	PROPN
ejpam-447	295	33	math	math	PROPN
ejpam-447	295	34	.	.	PUNCT
ejpam-447	296	1	anal	anal	PROPN
ejpam-447	296	2	.	.	PUNCT
ejpam-447	296	3	appl	appl	PROPN
ejpam-447	296	4	;	;	PUNCT
ejpam-447	296	5	233	233	NUM
ejpam-447	296	6	(	(	PUNCT
ejpam-447	296	7	1999	1999	NUM
ejpam-447	296	8	)	)	PUNCT
ejpam-447	296	9	,	,	PUNCT
ejpam-447	296	10	790	790	NUM
ejpam-447	296	11	-	-	SYM
ejpam-447	296	12	798	798	NUM
ejpam-447	296	13	.	.	PUNCT
ejpam-447	297	1	[	[	X
ejpam-447	297	2	4	4	NUM
ejpam-447	297	3	]	]	PUNCT
ejpam-447	297	4	c.	c.	PROPN
ejpam-447	297	5	w.	w.	PROPN
ejpam-447	297	6	clark	clark	PROPN
ejpam-447	297	7	,	,	PUNCT
ejpam-447	297	8	a	a	DET
ejpam-447	297	9	delayed	delay	VERB
ejpam-447	297	10	recruitment	recruitment	NOUN
ejpam-447	297	11	model	model	NOUN
ejpam-447	297	12	of	of	ADP
ejpam-447	297	13	population	population	NOUN
ejpam-447	297	14	dynamics	dynamic	NOUN
ejpam-447	297	15	with	with	ADP
ejpam-447	297	16	an	an	DET
ejpam-447	297	17	application	application	NOUN
ejpam-447	297	18	to	to	ADP
ejpam-447	297	19	baleen	baleen	ADJ
ejpam-447	297	20	whale	whale	NOUN
ejpam-447	297	21	populations	population	NOUN
ejpam-447	297	22	,	,	PUNCT
ejpam-447	297	23	j.	j.	PROPN
ejpam-447	297	24	math	math	PROPN
ejpam-447	297	25	.	.	PUNCT
ejpam-447	298	1	biol	biol	PROPN
ejpam-447	298	2	;	;	PUNCT
ejpam-447	298	3	3	3	NUM
ejpam-447	298	4	(	(	PUNCT
ejpam-447	298	5	1976	1976	NUM
ejpam-447	298	6	)	)	PUNCT
ejpam-447	298	7	,	,	PUNCT
ejpam-447	298	8	381	381	NUM
ejpam-447	298	9	-	-	SYM
ejpam-447	298	10	391	391	NUM
ejpam-447	298	11	.	.	PUNCT
ejpam-447	298	12	references	reference	NOUN
ejpam-447	298	13	266	266	NUM
ejpam-447	298	14	[	[	X
ejpam-447	298	15	5	5	NUM
ejpam-447	298	16	]	]	PUNCT
ejpam-447	298	17	r.	r.	PROPN
ejpam-447	298	18	devault	devault	PROPN
ejpam-447	298	19	,	,	PUNCT
ejpam-447	298	20	w.	w.	PROPN
ejpam-447	298	21	kosmala	kosmala	PROPN
ejpam-447	298	22	,	,	PUNCT
ejpam-447	298	23	g.	g.	PROPN
ejpam-447	298	24	ladas	ladas	PROPN
ejpam-447	298	25	and	and	CCONJ
ejpam-447	298	26	s.	s.	PROPN
ejpam-447	298	27	w.	w.	PROPN
ejpam-447	298	28	schultz	schultz	PROPN
ejpam-447	298	29	,	,	PUNCT
ejpam-447	298	30	global	global	ADJ
ejpam-447	298	31	behavior	behavior	NOUN
ejpam-447	298	32	of	of	ADP
ejpam-447	298	33	yn+1	yn+1	PROPN
ejpam-447	298	34	=	=	PUNCT
ejpam-447	298	35	(	(	PUNCT
ejpam-447	298	36	p	p	X
ejpam-447	299	1	+	+	X
ejpam-447	299	2	yn−k)/(q	yn−k)/(q	NUM
ejpam-447	299	3	yn	yn	PROPN
ejpam-447	299	4	+	+	NUM
ejpam-447	299	5	yn−k	yn−k	PROPN
ejpam-447	299	6	)	)	PUNCT
ejpam-447	299	7	,	,	PUNCT
ejpam-447	299	8	nonlinear	nonlinear	ADJ
ejpam-447	299	9	analysis	analysis	NOUN
ejpam-447	299	10	,	,	PUNCT
ejpam-447	299	11	47	47	NUM
ejpam-447	299	12	(	(	PUNCT
ejpam-447	299	13	2001	2001	NUM
ejpam-447	299	14	)	)	PUNCT
ejpam-447	299	15	,	,	PUNCT
ejpam-447	299	16	4743	4743	NUM
ejpam-447	299	17	-	-	SYM
ejpam-447	299	18	4751	4751	NUM
ejpam-447	299	19	.	.	PUNCT
ejpam-447	300	1	[	[	X
ejpam-447	300	2	6	6	NUM
ejpam-447	300	3	]	]	PUNCT
ejpam-447	300	4	r.	r.	PROPN
ejpam-447	300	5	devault	devault	PROPN
ejpam-447	300	6	,	,	PUNCT
ejpam-447	300	7	g.	g.	PROPN
ejpam-447	300	8	ladas	ladas	PROPN
ejpam-447	300	9	and	and	CCONJ
ejpam-447	300	10	s.	s.	PROPN
ejpam-447	300	11	w.	w.	PROPN
ejpam-447	300	12	schultz	schultz	PROPN
ejpam-447	300	13	,	,	PUNCT
ejpam-447	300	14	on	on	ADP
ejpam-447	300	15	the	the	DET
ejpam-447	300	16	recursive	recursive	ADJ
ejpam-447	300	17	sequence	sequence	NOUN
ejpam-447	300	18	xn+1	xn+1	PROPN
ejpam-447	300	19	=	=	SYM
ejpam-447	300	20	α+(xn	α+(xn	PROPN
ejpam-447	300	21	/	/	SYM
ejpam-447	300	22	xn−1	xn−1	PROPN
ejpam-447	300	23	)	)	PUNCT
ejpam-447	300	24	,	,	PUNCT
ejpam-447	300	25	proc	proc	PROPN
ejpam-447	300	26	.	.	PUNCT
ejpam-447	301	1	amer	amer	PROPN
ejpam-447	301	2	.	.	PUNCT
ejpam-447	301	3	math	math	PROPN
ejpam-447	301	4	.	.	PUNCT
ejpam-447	302	1	soc	soc	PROPN
ejpam-447	302	2	;	;	PUNCT
ejpam-447	302	3	126(11	126(11	NUM
ejpam-447	302	4	)	)	PUNCT
ejpam-447	302	5	(	(	PUNCT
ejpam-447	302	6	1998	1998	NUM
ejpam-447	302	7	)	)	PUNCT
ejpam-447	302	8	,	,	PUNCT
ejpam-447	302	9	3257	3257	NUM
ejpam-447	302	10	-	-	SYM
ejpam-447	302	11	3261	3261	NUM
ejpam-447	302	12	.	.	PUNCT
ejpam-447	303	1	[	[	X
ejpam-447	303	2	7	7	X
ejpam-447	303	3	]	]	X
ejpam-447	303	4	r.	r.	PROPN
ejpam-447	303	5	devault	devault	PROPN
ejpam-447	303	6	and	and	CCONJ
ejpam-447	303	7	s.	s.	PROPN
ejpam-447	303	8	w.	w.	PROPN
ejpam-447	303	9	schultz	schultz	PROPN
ejpam-447	303	10	,	,	PUNCT
ejpam-447	303	11	on	on	ADP
ejpam-447	303	12	the	the	DET
ejpam-447	303	13	dynamics	dynamic	NOUN
ejpam-447	303	14	of	of	ADP
ejpam-447	303	15	xn+1	xn+1	PROPN
ejpam-447	303	16	=	=	SYM
ejpam-447	303	17	(	(	PUNCT
ejpam-447	303	18	β	β	X
ejpam-447	303	19	xn+γxn−1)/(bxn+dxn−2	xn+γxn−1)/(bxn+dxn−2	PROPN
ejpam-447	303	20	)	)	PUNCT
ejpam-447	303	21	,	,	PUNCT
ejpam-447	303	22	comm	comm	NOUN
ejpam-447	303	23	.	.	PUNCT
ejpam-447	303	24	appl	appl	PROPN
ejpam-447	303	25	.	.	PUNCT
ejpam-447	304	1	nonlinear	nonlinear	ADJ
ejpam-447	304	2	analysis	analysis	NOUN
ejpam-447	304	3	,	,	PUNCT
ejpam-447	304	4	12(2005	12(2005	NUM
ejpam-447	304	5	)	)	PUNCT
ejpam-447	304	6	,	,	PUNCT
ejpam-447	304	7	35	35	NUM
ejpam-447	304	8	-	-	SYM
ejpam-447	304	9	40	40	NUM
ejpam-447	304	10	.	.	PUNCT
ejpam-447	305	1	[	[	X
ejpam-447	305	2	8	8	NUM
ejpam-447	305	3	]	]	X
ejpam-447	305	4	e.	e.	PROPN
ejpam-447	305	5	m.	m.	PROPN
ejpam-447	305	6	elabbasy	elabbasy	PROPN
ejpam-447	305	7	,	,	PUNCT
ejpam-447	305	8	h.	h.	PROPN
ejpam-447	305	9	elmetwally	elmetwally	ADV
ejpam-447	305	10	and	and	CCONJ
ejpam-447	305	11	e.	e.	PROPN
ejpam-447	305	12	m.	m.	PROPN
ejpam-447	305	13	elsayed	elsaye	VERB
ejpam-447	305	14	,	,	PUNCT
ejpam-447	305	15	on	on	ADP
ejpam-447	305	16	the	the	DET
ejpam-447	305	17	difference	difference	NOUN
ejpam-447	305	18	equation	equation	NOUN
ejpam-447	305	19	xn+1	xn+1	PROPN
ejpam-447	306	1	=	=	PUNCT
ejpam-447	306	2	axn	axn	PROPN
ejpam-447	306	3	−	−	PROPN
ejpam-447	306	4	bxn/	bxn/	PROPN
ejpam-447	306	5	�	�	PROPN
ejpam-447	306	6	cxn	cxn	VERB
ejpam-447	306	7	−	−	PROPN
ejpam-447	306	8	d	d	PROPN
ejpam-447	306	9	xn−1	xn−1	PROPN
ejpam-447	306	10	�	�	PROPN
ejpam-447	306	11	,	,	PUNCT
ejpam-447	306	12	advances	advance	NOUN
ejpam-447	306	13	in	in	ADP
ejpam-447	306	14	difference	difference	NOUN
ejpam-447	306	15	equations	equation	NOUN
ejpam-447	306	16	,	,	PUNCT
ejpam-447	306	17	volume	volume	NOUN
ejpam-447	306	18	2006	2006	NUM
ejpam-447	306	19	,	,	PUNCT
ejpam-447	306	20	article	article	NOUN
ejpam-447	306	21	i	i	PROPN
ejpam-447	306	22	d	d	PROPN
ejpam-447	306	23	82579	82579	NUM
ejpam-447	306	24	,	,	PUNCT
ejpam-447	306	25	pages	page	NOUN
ejpam-447	306	26	1	1	NUM
ejpam-447	306	27	-	-	SYM
ejpam-447	306	28	10	10	NUM
ejpam-447	306	29	,	,	PUNCT
ejpam-447	306	30	doi	doi	NOUN
ejpam-447	306	31	:	:	PUNCT
ejpam-447	306	32	10.1155/2006/82579	10.1155/2006/82579	NUM
ejpam-447	306	33	.	.	PUNCT
ejpam-447	307	1	[	[	X
ejpam-447	307	2	9	9	NUM
ejpam-447	307	3	]	]	X
ejpam-447	307	4	h.	h.	PROPN
ejpam-447	307	5	elmetwally	elmetwally	PROPN
ejpam-447	307	6	,	,	PUNCT
ejpam-447	307	7	e.	e.	PROPN
ejpam-447	307	8	a.	a.	PROPN
ejpam-447	307	9	grove	grove	PROPN
ejpam-447	307	10	and	and	CCONJ
ejpam-447	307	11	g.	g.	PROPN
ejpam-447	307	12	ladas	ladas	PROPN
ejpam-447	307	13	,	,	PUNCT
ejpam-447	307	14	a	a	DET
ejpam-447	307	15	global	global	ADJ
ejpam-447	307	16	convergence	convergence	NOUN
ejpam-447	307	17	result	result	VERB
ejpam-447	307	18	with	with	ADP
ejpam-447	307	19	applications	application	NOUN
ejpam-447	307	20	to	to	ADP
ejpam-447	307	21	periodic	periodic	ADJ
ejpam-447	307	22	solutions	solution	NOUN
ejpam-447	307	23	,	,	PUNCT
ejpam-447	307	24	j.	j.	PROPN
ejpam-447	307	25	math	math	PROPN
ejpam-447	307	26	.	.	PUNCT
ejpam-447	308	1	anal	anal	PROPN
ejpam-447	308	2	.	.	PUNCT
ejpam-447	308	3	appl	appl	PROPN
ejpam-447	308	4	;	;	PUNCT
ejpam-447	308	5	245	245	NUM
ejpam-447	308	6	(	(	PUNCT
ejpam-447	308	7	2000	2000	NUM
ejpam-447	308	8	)	)	PUNCT
ejpam-447	308	9	,	,	PUNCT
ejpam-447	308	10	161	161	NUM
ejpam-447	308	11	-	-	SYM
ejpam-447	308	12	170	170	NUM
ejpam-447	308	13	.	.	PUNCT
ejpam-447	309	1	[	[	X
ejpam-447	309	2	10	10	NUM
ejpam-447	309	3	]	]	X
ejpam-447	309	4	h.	h.	PROPN
ejpam-447	309	5	elmetwally	elmetwally	PROPN
ejpam-447	309	6	,	,	PUNCT
ejpam-447	309	7	g.	g.	PROPN
ejpam-447	309	8	ladas	ladas	PROPN
ejpam-447	309	9	,	,	PUNCT
ejpam-447	309	10	e.	e.	PROPN
ejpam-447	309	11	a.	a.	PROPN
ejpam-447	309	12	grove	grove	PROPN
ejpam-447	309	13	and	and	CCONJ
ejpam-447	309	14	h.	h.	PROPN
ejpam-447	309	15	d.	d.	PROPN
ejpam-447	309	16	voulov	voulov	PROPN
ejpam-447	309	17	,	,	PUNCT
ejpam-447	309	18	on	on	ADP
ejpam-447	309	19	the	the	DET
ejpam-447	309	20	global	global	ADJ
ejpam-447	309	21	attractivity	attractivity	NOUN
ejpam-447	309	22	and	and	CCONJ
ejpam-447	309	23	the	the	DET
ejpam-447	309	24	periodic	periodic	ADJ
ejpam-447	309	25	character	character	NOUN
ejpam-447	309	26	of	of	ADP
ejpam-447	309	27	some	some	DET
ejpam-447	309	28	difference	difference	NOUN
ejpam-447	309	29	equations	equation	NOUN
ejpam-447	309	30	,	,	PUNCT
ejpam-447	309	31	j.	j.	PROPN
ejpam-447	309	32	difference	difference	NOUN
ejpam-447	309	33	equations	equation	NOUN
ejpam-447	309	34	and	and	CCONJ
ejpam-447	309	35	appl	appl	NOUN
ejpam-447	309	36	;	;	PUNCT
ejpam-447	309	37	7(2001	7(2001	NUM
ejpam-447	309	38	)	)	PUNCT
ejpam-447	309	39	,	,	PUNCT
ejpam-447	309	40	837850	837850	NUM
ejpam-447	309	41	.	.	PUNCT
ejpam-447	310	1	[	[	X
ejpam-447	310	2	11	11	NUM
ejpam-447	310	3	]	]	PUNCT
ejpam-447	310	4	h.	h.	PROPN
ejpam-447	310	5	a.	a.	PROPN
ejpam-447	310	6	el	el	PROPN
ejpam-447	310	7	-	-	PUNCT
ejpam-447	310	8	morshedy	morshedy	PROPN
ejpam-447	310	9	,	,	PUNCT
ejpam-447	310	10	new	new	ADJ
ejpam-447	310	11	explicit	explicit	ADJ
ejpam-447	310	12	global	global	ADJ
ejpam-447	310	13	asymptotic	asymptotic	ADJ
ejpam-447	310	14	stability	stability	NOUN
ejpam-447	310	15	criteria	criterion	NOUN
ejpam-447	310	16	for	for	ADP
ejpam-447	310	17	higher	high	ADJ
ejpam-447	310	18	order	order	NOUN
ejpam-447	310	19	difference	difference	NOUN
ejpam-447	310	20	equations	equation	NOUN
ejpam-447	310	21	,	,	PUNCT
ejpam-447	310	22	j.	j.	PROPN
ejpam-447	310	23	math	math	PROPN
ejpam-447	310	24	.	.	PUNCT
ejpam-447	311	1	anal	anal	PROPN
ejpam-447	311	2	.	.	PUNCT
ejpam-447	311	3	appl	appl	PROPN
ejpam-447	311	4	;	;	PUNCT
ejpam-447	311	5	336(2007	336(2007	NUM
ejpam-447	311	6	)	)	PUNCT
ejpam-447	311	7	,	,	PUNCT
ejpam-447	311	8	262	262	NUM
ejpam-447	311	9	-	-	SYM
ejpam-447	311	10	276	276	NUM
ejpam-447	311	11	.	.	PUNCT
ejpam-447	312	1	[	[	X
ejpam-447	312	2	12	12	NUM
ejpam-447	312	3	]	]	X
ejpam-447	312	4	h.	h.	PROPN
ejpam-447	312	5	m.	m.	PROPN
ejpam-447	312	6	elowaidy	elowaidy	PROPN
ejpam-447	312	7	,	,	PUNCT
ejpam-447	312	8	a.	a.	NOUN
ejpam-447	312	9	m.	m.	PROPN
ejpam-447	312	10	ahmed	ahmed	PROPN
ejpam-447	312	11	and	and	CCONJ
ejpam-447	312	12	m.	m.	PROPN
ejpam-447	312	13	s.	s.	PROPN
ejpam-447	312	14	mousa	mousa	PROPN
ejpam-447	312	15	,	,	PUNCT
ejpam-447	312	16	on	on	ADP
ejpam-447	312	17	asymptotic	asymptotic	ADJ
ejpam-447	312	18	behavior	behavior	NOUN
ejpam-447	312	19	of	of	ADP
ejpam-447	312	20	the	the	DET
ejpam-447	312	21	difference	difference	NOUN
ejpam-447	312	22	equation	equation	NOUN
ejpam-447	312	23	xn+1	xn+1	PROPN
ejpam-447	312	24	=	=	SYM
ejpam-447	312	25	α+	α+	PUNCT
ejpam-447	312	26	(	(	PUNCT
ejpam-447	312	27	x	x	SYM
ejpam-447	312	28	p	p	PROPN
ejpam-447	312	29	n−1	n−1	PROPN
ejpam-447	312	30	/	/	SYM
ejpam-447	312	31	x	x	PROPN
ejpam-447	312	32	p	p	NOUN
ejpam-447	312	33	n	n	CCONJ
ejpam-447	312	34	)	)	PUNCT
ejpam-447	312	35	,	,	PUNCT
ejpam-447	312	36	j.	j.	PROPN
ejpam-447	312	37	appl	appl	PROPN
ejpam-447	312	38	.	.	PROPN
ejpam-447	312	39	math	math	PROPN
ejpam-447	312	40	.	.	PUNCT
ejpam-447	313	1	&	&	CCONJ
ejpam-447	313	2	computing	computing	PROPN
ejpam-447	313	3	,	,	PUNCT
ejpam-447	313	4	12(2003	12(2003	NUM
ejpam-447	313	5	)	)	PUNCT
ejpam-447	313	6	,	,	PUNCT
ejpam-447	313	7	3137	3137	NUM
ejpam-447	313	8	.	.	PUNCT
ejpam-447	314	1	[	[	X
ejpam-447	314	2	13	13	NUM
ejpam-447	314	3	]	]	X
ejpam-447	314	4	h.	h.	PROPN
ejpam-447	314	5	m.	m.	PROPN
ejpam-447	314	6	elowaidy	elowaidy	PROPN
ejpam-447	314	7	,	,	PUNCT
ejpam-447	314	8	a.	a.	NOUN
ejpam-447	314	9	m.	m.	PROPN
ejpam-447	314	10	ahmed	ahmed	PROPN
ejpam-447	314	11	and	and	CCONJ
ejpam-447	314	12	z.	z.	PROPN
ejpam-447	314	13	elsady	elsady	PROPN
ejpam-447	314	14	,	,	PUNCT
ejpam-447	314	15	global	global	ADJ
ejpam-447	314	16	attractivity	attractivity	NOUN
ejpam-447	314	17	of	of	ADP
ejpam-447	314	18	the	the	DET
ejpam-447	314	19	recursive	recursive	ADJ
ejpam-447	314	20	sequence	sequence	NOUN
ejpam-447	314	21	xn+1	xn+1	PROPN
ejpam-447	314	22	=	=	SYM
ejpam-447	315	1	(	(	PUNCT
ejpam-447	315	2	α−	α−	ADP
ejpam-447	315	3	β	β	PROPN
ejpam-447	315	4	xn−k)/(γ+	xn−k)/(γ+	PROPN
ejpam-447	315	5	xn	xn	PROPN
ejpam-447	315	6	)	)	PUNCT
ejpam-447	315	7	,	,	PUNCT
ejpam-447	315	8	j.	j.	PROPN
ejpam-447	315	9	appl	appl	PROPN
ejpam-447	315	10	.	.	PROPN
ejpam-447	315	11	math	math	PROPN
ejpam-447	315	12	.	.	PUNCT
ejpam-447	316	1	&	&	CCONJ
ejpam-447	316	2	computing	computing	PROPN
ejpam-447	316	3	,	,	PUNCT
ejpam-447	316	4	16(2004	16(2004	NUM
ejpam-447	316	5	)	)	PUNCT
ejpam-447	316	6	,	,	PUNCT
ejpam-447	316	7	243249	243249	NUM
ejpam-447	316	8	.	.	PUNCT
ejpam-447	317	1	[	[	X
ejpam-447	317	2	14	14	NUM
ejpam-447	317	3	]	]	X
ejpam-447	317	4	c.	c.	PROPN
ejpam-447	317	5	h.	h.	PROPN
ejpam-447	317	6	gibbons	gibbons	PROPN
ejpam-447	317	7	,	,	PUNCT
ejpam-447	317	8	m.	m.	PROPN
ejpam-447	317	9	r.	r.	PROPN
ejpam-447	317	10	s.	s.	PROPN
ejpam-447	317	11	kulenovic	kulenovic	PROPN
ejpam-447	317	12	and	and	CCONJ
ejpam-447	317	13	g.	g.	PROPN
ejpam-447	317	14	ladas	ladas	PROPN
ejpam-447	317	15	,	,	PUNCT
ejpam-447	317	16	on	on	ADP
ejpam-447	317	17	the	the	DET
ejpam-447	317	18	recursive	recursive	ADJ
ejpam-447	317	19	sequence	sequence	NOUN
ejpam-447	317	20	xn+1	xn+1	PROPN
ejpam-447	317	21	=	=	SYM
ejpam-447	317	22	(	(	PUNCT
ejpam-447	317	23	α+	α+	X
ejpam-447	317	24	β	β	X
ejpam-447	317	25	xn−1)/(γ+	xn−1)/(γ+	PROPN
ejpam-447	317	26	xn	xn	PROPN
ejpam-447	317	27	)	)	PUNCT
ejpam-447	317	28	,	,	PUNCT
ejpam-447	317	29	math	math	NOUN
ejpam-447	317	30	.	.	PUNCT
ejpam-447	318	1	sci	sci	PROPN
ejpam-447	318	2	.	.	PUNCT
ejpam-447	318	3	res	re	NOUN
ejpam-447	318	4	.	.	PUNCT
ejpam-447	319	1	hot	hot	ADJ
ejpam-447	319	2	-	-	PUNCT
ejpam-447	319	3	line	line	NOUN
ejpam-447	319	4	,	,	PUNCT
ejpam-447	319	5	4	4	NUM
ejpam-447	319	6	(	(	PUNCT
ejpam-447	319	7	2	2	NUM
ejpam-447	319	8	)	)	PUNCT
ejpam-447	319	9	,	,	PUNCT
ejpam-447	319	10	(	(	PUNCT
ejpam-447	319	11	2000	2000	NUM
ejpam-447	319	12	)	)	PUNCT
ejpam-447	319	13	,	,	PUNCT
ejpam-447	319	14	1	1	NUM
ejpam-447	319	15	-	-	SYM
ejpam-447	319	16	11	11	NUM
ejpam-447	319	17	.	.	PUNCT
ejpam-447	320	1	[	[	X
ejpam-447	320	2	15	15	NUM
ejpam-447	320	3	]	]	X
ejpam-447	320	4	e.	e.	PROPN
ejpam-447	320	5	a.	a.	PROPN
ejpam-447	320	6	grove	grove	PROPN
ejpam-447	320	7	and	and	CCONJ
ejpam-447	320	8	g.	g.	PROPN
ejpam-447	320	9	ladas	ladas	PROPN
ejpam-447	320	10	,	,	PUNCT
ejpam-447	320	11	periodicities	periodicity	NOUN
ejpam-447	320	12	in	in	ADP
ejpam-447	320	13	nonlinear	nonlinear	ADJ
ejpam-447	320	14	difference	difference	NOUN
ejpam-447	320	15	equations	equation	NOUN
ejpam-447	320	16	,	,	PUNCT
ejpam-447	320	17	vol.4	vol.4	PROPN
ejpam-447	320	18	,	,	PUNCT
ejpam-447	320	19	chapman	chapman	PROPN
ejpam-447	320	20	&	&	CCONJ
ejpam-447	320	21	hall	hall	PROPN
ejpam-447	320	22	/	/	SYM
ejpam-447	320	23	crc	crc	PROPN
ejpam-447	320	24	,	,	PUNCT
ejpam-447	320	25	2005	2005	NUM
ejpam-447	320	26	.	.	PUNCT
ejpam-447	321	1	[	[	X
ejpam-447	321	2	16	16	NUM
ejpam-447	321	3	]	]	X
ejpam-447	321	4	i.	i.	NOUN
ejpam-447	321	5	gyori	gyori	NOUN
ejpam-447	321	6	and	and	CCONJ
ejpam-447	321	7	g.	g.	PROPN
ejpam-447	321	8	ladas	ladas	PROPN
ejpam-447	321	9	,	,	PUNCT
ejpam-447	321	10	oscillation	oscillation	NOUN
ejpam-447	321	11	theory	theory	NOUN
ejpam-447	321	12	of	of	ADP
ejpam-447	321	13	delay	delay	NOUN
ejpam-447	321	14	differential	differential	ADJ
ejpam-447	321	15	equations	equation	NOUN
ejpam-447	321	16	with	with	ADP
ejpam-447	321	17	applications	application	NOUN
ejpam-447	321	18	,	,	PUNCT
ejpam-447	321	19	clarendon	clarendon	PROPN
ejpam-447	321	20	,	,	PUNCT
ejpam-447	321	21	oxford	oxford	NOUN
ejpam-447	321	22	,	,	PUNCT
ejpam-447	321	23	1991	1991	NUM
ejpam-447	321	24	.	.	PUNCT
ejpam-447	322	1	[	[	X
ejpam-447	322	2	17	17	NUM
ejpam-447	322	3	]	]	X
ejpam-447	322	4	g.	g.	PROPN
ejpam-447	322	5	karakostas	karakostas	PROPN
ejpam-447	322	6	,	,	PUNCT
ejpam-447	322	7	convergence	convergence	NOUN
ejpam-447	322	8	of	of	ADP
ejpam-447	322	9	a	a	DET
ejpam-447	322	10	difference	difference	NOUN
ejpam-447	322	11	equation	equation	NOUN
ejpam-447	322	12	via	via	ADP
ejpam-447	322	13	the	the	DET
ejpam-447	322	14	full	full	ADJ
ejpam-447	322	15	limiting	limit	VERB
ejpam-447	322	16	sequences	sequence	NOUN
ejpam-447	322	17	method	method	NOUN
ejpam-447	322	18	,	,	PUNCT
ejpam-447	322	19	diff	diff	PROPN
ejpam-447	322	20	.	.	PUNCT
ejpam-447	323	1	equations	equation	NOUN
ejpam-447	323	2	and	and	CCONJ
ejpam-447	323	3	dynamical	dynamical	ADJ
ejpam-447	323	4	.	.	PUNCT
ejpam-447	324	1	system	system	NOUN
ejpam-447	324	2	,	,	PUNCT
ejpam-447	324	3	1(1993	1(1993	NUM
ejpam-447	324	4	)	)	PUNCT
ejpam-447	324	5	,	,	PUNCT
ejpam-447	324	6	289	289	NUM
ejpam-447	324	7	-	-	SYM
ejpam-447	324	8	294	294	NUM
ejpam-447	324	9	.	.	PUNCT
ejpam-447	325	1	[	[	X
ejpam-447	325	2	18	18	NUM
ejpam-447	325	3	]	]	X
ejpam-447	325	4	g.	g.	PROPN
ejpam-447	325	5	karakostas	karakostas	PROPN
ejpam-447	325	6	and	and	CCONJ
ejpam-447	325	7	s.	s.	PROPN
ejpam-447	325	8	stevic′	stevic′	PROPN
ejpam-447	325	9	,	,	PUNCT
ejpam-447	325	10	on	on	ADP
ejpam-447	325	11	the	the	DET
ejpam-447	325	12	recursive	recursive	ADJ
ejpam-447	325	13	sequences	sequence	NOUN
ejpam-447	325	14	xn+1	xn+1	PROPN
ejpam-447	325	15	=	=	PUNCT
ejpam-447	326	1	a	a	DET
ejpam-447	326	2	+	+	NUM
ejpam-447	326	3	f	f	X
ejpam-447	326	4	(	(	PUNCT
ejpam-447	326	5	xn	xn	PROPN
ejpam-447	326	6	,	,	PUNCT
ejpam-447	326	7	.	.	PUNCT
ejpam-447	326	8	.	.	PUNCT
ejpam-447	326	9	.	.	PUNCT
ejpam-447	327	1	xn−k+1)/xn−1	xn−k+1)/xn−1	PROPN
ejpam-447	327	2	,	,	PUNCT
ejpam-447	327	3	comm	comm	NOUN
ejpam-447	327	4	.	.	PUNCT
ejpam-447	328	1	appl	appl	PROPN
ejpam-447	328	2	.	.	PUNCT
ejpam-447	329	1	nonlinear	nonlinear	ADJ
ejpam-447	329	2	analysis	analysis	NOUN
ejpam-447	329	3	,	,	PUNCT
ejpam-447	329	4	11(2004	11(2004	NUM
ejpam-447	329	5	)	)	PUNCT
ejpam-447	329	6	,	,	PUNCT
ejpam-447	329	7	87	87	NUM
ejpam-447	329	8	-	-	SYM
ejpam-447	329	9	100	100	NUM
ejpam-447	329	10	.	.	PUNCT
ejpam-447	330	1	[	[	X
ejpam-447	330	2	19	19	NUM
ejpam-447	330	3	]	]	X
ejpam-447	330	4	v.	v.	X
ejpam-447	330	5	l.	l.	PROPN
ejpam-447	330	6	kocic	kocic	PROPN
ejpam-447	330	7	and	and	CCONJ
ejpam-447	330	8	g.	g.	PROPN
ejpam-447	330	9	ladas	ladas	PROPN
ejpam-447	330	10	,	,	PUNCT
ejpam-447	330	11	global	global	ADJ
ejpam-447	330	12	behavior	behavior	NOUN
ejpam-447	330	13	of	of	ADP
ejpam-447	330	14	nonlinear	nonlinear	ADJ
ejpam-447	330	15	difference	difference	NOUN
ejpam-447	330	16	equations	equation	NOUN
ejpam-447	330	17	of	of	ADP
ejpam-447	330	18	higher	high	ADJ
ejpam-447	330	19	order	order	NOUN
ejpam-447	330	20	with	with	ADP
ejpam-447	330	21	applications	application	NOUN
ejpam-447	330	22	,	,	PUNCT
ejpam-447	330	23	kluwer	kluwer	NOUN
ejpam-447	330	24	academic	academic	ADJ
ejpam-447	330	25	publishers	publisher	NOUN
ejpam-447	330	26	,	,	PUNCT
ejpam-447	330	27	dordrecht	dordrecht	PROPN
ejpam-447	330	28	,	,	PUNCT
ejpam-447	330	29	1993	1993	NUM
ejpam-447	330	30	.	.	PUNCT
ejpam-447	331	1	references	reference	NOUN
ejpam-447	331	2	267	267	NUM
ejpam-447	331	3	[	[	SYM
ejpam-447	331	4	20	20	NUM
ejpam-447	331	5	]	]	PUNCT
ejpam-447	331	6	m.	m.	PROPN
ejpam-447	331	7	r.	r.	PROPN
ejpam-447	331	8	s.	s.	PROPN
ejpam-447	331	9	kulenovic	kulenovic	PROPN
ejpam-447	331	10	and	and	CCONJ
ejpam-447	331	11	g.	g.	PROPN
ejpam-447	331	12	ladas	ladas	PROPN
ejpam-447	331	13	,	,	PUNCT
ejpam-447	331	14	dynamics	dynamic	NOUN
ejpam-447	331	15	of	of	ADP
ejpam-447	331	16	second	second	ADJ
ejpam-447	331	17	order	order	NOUN
ejpam-447	331	18	rational	rational	ADJ
ejpam-447	331	19	difference	difference	NOUN
ejpam-447	331	20	equations	equation	NOUN
ejpam-447	331	21	with	with	ADP
ejpam-447	331	22	open	open	ADJ
ejpam-447	331	23	problems	problem	NOUN
ejpam-447	331	24	and	and	CCONJ
ejpam-447	331	25	conjectures	conjecture	VERB
ejpam-447	331	26	,	,	PUNCT
ejpam-447	331	27	chapman	chapman	NOUN
ejpam-447	331	28	&	&	CCONJ
ejpam-447	331	29	hall	hall	PROPN
ejpam-447	331	30	/	/	SYM
ejpam-447	331	31	crc	crc	PROPN
ejpam-447	331	32	,	,	PUNCT
ejpam-447	331	33	florida	florida	PROPN
ejpam-447	331	34	,	,	PUNCT
ejpam-447	331	35	2001	2001	NUM
ejpam-447	331	36	.	.	PUNCT
ejpam-447	332	1	[	[	X
ejpam-447	332	2	21	21	NUM
ejpam-447	332	3	]	]	PUNCT
ejpam-447	332	4	m.	m.	PROPN
ejpam-447	332	5	r.	r.	PROPN
ejpam-447	332	6	s.	s.	PROPN
ejpam-447	332	7	kulenovic	kulenovic	PROPN
ejpam-447	332	8	,	,	PUNCT
ejpam-447	332	9	g.	g.	PROPN
ejpam-447	332	10	ladas	ladas	PROPN
ejpam-447	332	11	and	and	CCONJ
ejpam-447	332	12	w.	w.	PROPN
ejpam-447	332	13	s.	s.	PROPN
ejpam-447	332	14	sizer	sizer	PROPN
ejpam-447	332	15	,	,	PUNCT
ejpam-447	332	16	on	on	ADP
ejpam-447	332	17	the	the	DET
ejpam-447	332	18	recursive	recursive	ADJ
ejpam-447	332	19	sequence	sequence	NOUN
ejpam-447	332	20	xn+1	xn+1	PROPN
ejpam-447	332	21	=	=	SYM
ejpam-447	332	22	(	(	PUNCT
ejpam-447	332	23	αxn	αxn	PROPN
ejpam-447	332	24	+	+	X
ejpam-447	332	25	β	β	X
ejpam-447	332	26	xn−1)/(γxn+δxn−1	xn−1)/(γxn+δxn−1	NOUN
ejpam-447	332	27	)	)	PUNCT
ejpam-447	332	28	,	,	PUNCT
ejpam-447	332	29	math	math	NOUN
ejpam-447	332	30	.	.	PUNCT
ejpam-447	333	1	sci	sci	PROPN
ejpam-447	333	2	.	.	PUNCT
ejpam-447	333	3	res	re	NOUN
ejpam-447	333	4	.	.	PUNCT
ejpam-447	334	1	hot	hot	ADJ
ejpam-447	334	2	-	-	PUNCT
ejpam-447	334	3	line	line	NOUN
ejpam-447	334	4	2	2	NUM
ejpam-447	334	5	(	(	PUNCT
ejpam-447	334	6	5	5	NUM
ejpam-447	334	7	)	)	PUNCT
ejpam-447	334	8	(	(	PUNCT
ejpam-447	334	9	1998	1998	NUM
ejpam-447	334	10	)	)	PUNCT
ejpam-447	334	11	,	,	PUNCT
ejpam-447	334	12	1	1	NUM
ejpam-447	334	13	-	-	SYM
ejpam-447	334	14	16	16	NUM
ejpam-447	334	15	.	.	PUNCT
ejpam-447	335	1	[	[	X
ejpam-447	335	2	22	22	NUM
ejpam-447	335	3	]	]	PUNCT
ejpam-447	335	4	m.	m.	PROPN
ejpam-447	335	5	r.	r.	PROPN
ejpam-447	335	6	s.	s.	PROPN
ejpam-447	335	7	kulenovic	kulenovic	PROPN
ejpam-447	335	8	,	,	PUNCT
ejpam-447	335	9	g.	g.	PROPN
ejpam-447	335	10	ladas	ladas	PROPN
ejpam-447	335	11	and	and	CCONJ
ejpam-447	335	12	n.	n.	PROPN
ejpam-447	335	13	r.	r.	PROPN
ejpam-447	335	14	prokup	prokup	PROPN
ejpam-447	335	15	,	,	PUNCT
ejpam-447	335	16	a	a	DET
ejpam-447	335	17	recursive	recursive	ADJ
ejpam-447	335	18	difference	difference	NOUN
ejpam-447	335	19	equation	equation	NOUN
ejpam-447	335	20	,	,	PUNCT
ejpam-447	335	21	comput	comput	NOUN
ejpam-447	335	22	.	.	PUNCT
ejpam-447	336	1	math	math	NOUN
ejpam-447	336	2	.	.	PUNCT
ejpam-447	337	1	appl	appl	PROPN
ejpam-447	337	2	.	.	PUNCT
ejpam-447	338	1	41(2001	41(2001	NUM
ejpam-447	338	2	)	)	PUNCT
ejpam-447	338	3	,	,	PUNCT
ejpam-447	339	1	671	671	NUM
ejpam-447	339	2	-	-	SYM
ejpam-447	339	3	678	678	NUM
ejpam-447	339	4	.	.	PUNCT
ejpam-447	340	1	[	[	X
ejpam-447	340	2	23	23	NUM
ejpam-447	340	3	]	]	PUNCT
ejpam-447	340	4	s.	s.	PROPN
ejpam-447	340	5	a.	a.	PROPN
ejpam-447	340	6	kuruklis	kuruklis	PROPN
ejpam-447	340	7	,	,	PUNCT
ejpam-447	340	8	the	the	DET
ejpam-447	340	9	asymptotic	asymptotic	ADJ
ejpam-447	340	10	stability	stability	NOUN
ejpam-447	340	11	of	of	ADP
ejpam-447	340	12	xn+1−axn+	xn+1−axn+	PUNCT
ejpam-447	340	13	bxn−k	bxn−k	PROPN
ejpam-447	340	14	=	=	SYM
ejpam-447	340	15	0	0	PROPN
ejpam-447	340	16	,	,	PUNCT
ejpam-447	340	17	j.	j.	PROPN
ejpam-447	340	18	math	math	PROPN
ejpam-447	340	19	.	.	PUNCT
ejpam-447	341	1	anal	anal	PROPN
ejpam-447	341	2	.	.	PUNCT
ejpam-447	341	3	appl	appl	PROPN
ejpam-447	341	4	;	;	PUNCT
ejpam-447	341	5	188(1994	188(1994	NUM
ejpam-447	341	6	)	)	PUNCT
ejpam-447	341	7	,	,	PUNCT
ejpam-447	341	8	719	719	NUM
ejpam-447	341	9	-	-	SYM
ejpam-447	341	10	731	731	NUM
ejpam-447	341	11	.	.	PUNCT
ejpam-447	342	1	[	[	X
ejpam-447	342	2	24	24	NUM
ejpam-447	342	3	]	]	X
ejpam-447	342	4	g.	g.	PROPN
ejpam-447	342	5	ladas	ladas	PROPN
ejpam-447	342	6	,	,	PUNCT
ejpam-447	342	7	c.	c.	PROPN
ejpam-447	342	8	h.	h.	PROPN
ejpam-447	342	9	gibbons	gibbons	PROPN
ejpam-447	342	10	,	,	PUNCT
ejpam-447	342	11	m.	m.	PROPN
ejpam-447	342	12	r.	r.	PROPN
ejpam-447	342	13	s.	s.	PROPN
ejpam-447	342	14	kulenovic	kulenovic	PROPN
ejpam-447	342	15	and	and	CCONJ
ejpam-447	342	16	h.	h.	PROPN
ejpam-447	342	17	d.	d.	PROPN
ejpam-447	342	18	voulov	voulov	PROPN
ejpam-447	342	19	,	,	PUNCT
ejpam-447	342	20	on	on	ADP
ejpam-447	342	21	the	the	DET
ejpam-447	342	22	trichotomy	trichotomy	ADJ
ejpam-447	342	23	character	character	NOUN
ejpam-447	342	24	of	of	ADP
ejpam-447	342	25	xn+1	xn+1	PROPN
ejpam-447	342	26	=	=	SYM
ejpam-447	342	27	(	(	PUNCT
ejpam-447	342	28	α+	α+	X
ejpam-447	342	29	β	β	X
ejpam-447	342	30	xn	xn	PROPN
ejpam-447	343	1	+	+	CCONJ
ejpam-447	343	2	γxn−1)/(a+	γxn−1)/(a+	NOUN
ejpam-447	343	3	xn	xn	PROPN
ejpam-447	343	4	)	)	PUNCT
ejpam-447	344	1	,	,	PUNCT
ejpam-447	344	2	j.	j.	PROPN
ejpam-447	344	3	difference	difference	NOUN
ejpam-447	344	4	equations	equation	NOUN
ejpam-447	344	5	and	and	CCONJ
ejpam-447	344	6	appl	appl	NOUN
ejpam-447	344	7	;	;	PUNCT
ejpam-447	344	8	8(2002	8(2002	NUM
ejpam-447	344	9	)	)	PUNCT
ejpam-447	344	10	,	,	PUNCT
ejpam-447	344	11	75	75	NUM
ejpam-447	344	12	-	-	SYM
ejpam-447	344	13	92	92	NUM
ejpam-447	344	14	.	.	PUNCT
ejpam-447	345	1	[	[	X
ejpam-447	345	2	25	25	NUM
ejpam-447	345	3	]	]	X
ejpam-447	345	4	g.	g.	PROPN
ejpam-447	345	5	ladas	ladas	PROPN
ejpam-447	345	6	,	,	PUNCT
ejpam-447	345	7	c.	c.	PROPN
ejpam-447	345	8	h.	h.	PROPN
ejpam-447	345	9	gibbons	gibbons	PROPN
ejpam-447	345	10	and	and	CCONJ
ejpam-447	345	11	m.	m.	PROPN
ejpam-447	345	12	r.	r.	PROPN
ejpam-447	345	13	s.	s.	PROPN
ejpam-447	345	14	kulenovic	kulenovic	PROPN
ejpam-447	345	15	,	,	PUNCT
ejpam-447	345	16	on	on	ADP
ejpam-447	345	17	the	the	DET
ejpam-447	345	18	dynamics	dynamic	NOUN
ejpam-447	345	19	of	of	ADP
ejpam-447	345	20	xn+1	xn+1	PROPN
ejpam-447	345	21	=	=	SYM
ejpam-447	345	22	(	(	PUNCT
ejpam-447	345	23	α	α	X
ejpam-447	345	24	+	+	X
ejpam-447	345	25	β	β	PROPN
ejpam-447	345	26	xn+γxn−1)/(a+bxn	xn+γxn−1)/(a+bxn	NUM
ejpam-447	345	27	)	)	PUNCT
ejpam-447	345	28	,	,	PUNCT
ejpam-447	345	29	proceeding	proceed	VERB
ejpam-447	345	30	of	of	ADP
ejpam-447	345	31	the	the	DET
ejpam-447	345	32	fifth	fifth	ADJ
ejpam-447	345	33	international	international	ADJ
ejpam-447	345	34	conference	conference	NOUN
ejpam-447	345	35	on	on	ADP
ejpam-447	345	36	difference	difference	NOUN
ejpam-447	345	37	equations	equation	NOUN
ejpam-447	345	38	and	and	CCONJ
ejpam-447	345	39	applications	application	NOUN
ejpam-447	345	40	,	,	PUNCT
ejpam-447	345	41	temuco	temuco	PROPN
ejpam-447	345	42	,	,	PUNCT
ejpam-447	345	43	chile	chile	PROPN
ejpam-447	345	44	,	,	PUNCT
ejpam-447	345	45	jan	jan	PROPN
ejpam-447	345	46	.	.	PROPN
ejpam-447	345	47	3	3	NUM
ejpam-447	345	48	-	-	SYM
ejpam-447	345	49	7	7	NUM
ejpam-447	345	50	,	,	PUNCT
ejpam-447	345	51	2000	2000	NUM
ejpam-447	345	52	,	,	PUNCT
ejpam-447	345	53	taylor	taylor	PROPN
ejpam-447	345	54	and	and	CCONJ
ejpam-447	345	55	francis	francis	PROPN
ejpam-447	345	56	,	,	PUNCT
ejpam-447	345	57	london	london	PROPN
ejpam-447	345	58	(	(	PUNCT
ejpam-447	345	59	2002	2002	NUM
ejpam-447	345	60	)	)	PUNCT
ejpam-447	345	61	,	,	PUNCT
ejpam-447	345	62	141	141	NUM
ejpam-447	345	63	-	-	SYM
ejpam-447	345	64	158	158	NUM
ejpam-447	345	65	.	.	PUNCT
ejpam-447	346	1	[	[	X
ejpam-447	346	2	26	26	NUM
ejpam-447	346	3	]	]	X
ejpam-447	346	4	g.	g.	PROPN
ejpam-447	346	5	ladas	ladas	PROPN
ejpam-447	346	6	,	,	PUNCT
ejpam-447	346	7	e.	e.	PROPN
ejpam-447	346	8	camouzis	camouzis	PROPN
ejpam-447	346	9	and	and	CCONJ
ejpam-447	346	10	h.	h.	PROPN
ejpam-447	346	11	d.	d.	PROPN
ejpam-447	346	12	voulov	voulov	PROPN
ejpam-447	346	13	,	,	PUNCT
ejpam-447	346	14	on	on	ADP
ejpam-447	346	15	the	the	DET
ejpam-447	346	16	dynamic	dynamic	NOUN
ejpam-447	346	17	of	of	ADP
ejpam-447	346	18	xn+1	xn+1	PROPN
ejpam-447	346	19	=	=	SYM
ejpam-447	346	20	(	(	PUNCT
ejpam-447	346	21	α	α	NOUN
ejpam-447	346	22	+	+	X
ejpam-447	346	23	γxn−1	γxn−1	PRON
ejpam-447	346	24	+	+	CCONJ
ejpam-447	346	25	δxn−2)/(a+	δxn−2)/(a+	VERB
ejpam-447	346	26	xn−2	xn−2	PROPN
ejpam-447	346	27	)	)	PUNCT
ejpam-447	346	28	,	,	PUNCT
ejpam-447	346	29	j.	j.	PROPN
ejpam-447	346	30	difference	difference	NOUN
ejpam-447	346	31	equations	equation	NOUN
ejpam-447	346	32	and	and	CCONJ
ejpam-447	346	33	appl	appl	NOUN
ejpam-447	346	34	;	;	PUNCT
ejpam-447	346	35	9(2003	9(2003	NUM
ejpam-447	346	36	)	)	PUNCT
ejpam-447	346	37	,	,	PUNCT
ejpam-447	346	38	731	731	NUM
ejpam-447	346	39	-	-	SYM
ejpam-447	346	40	738	738	NUM
ejpam-447	346	41	.	.	PUNCT
ejpam-447	347	1	[	[	X
ejpam-447	347	2	27	27	NUM
ejpam-447	347	3	]	]	X
ejpam-447	347	4	g.	g.	PROPN
ejpam-447	347	5	ladas	ladas	PROPN
ejpam-447	347	6	,	,	PUNCT
ejpam-447	347	7	on	on	ADP
ejpam-447	347	8	the	the	DET
ejpam-447	347	9	rational	rational	ADJ
ejpam-447	347	10	recursive	recursive	ADJ
ejpam-447	347	11	sequence	sequence	NOUN
ejpam-447	347	12	xn+1	xn+1	PROPN
ejpam-447	347	13	=	=	SYM
ejpam-447	347	14	(	(	PUNCT
ejpam-447	347	15	α	α	X
ejpam-447	348	1	+	+	X
ejpam-447	348	2	β	β	X
ejpam-447	348	3	xn	xn	NOUN
ejpam-447	349	1	+	+	PUNCT
ejpam-447	349	2	γxn−1)/(a+	γxn−1)/(a+	NOUN
ejpam-447	349	3	bxn	bxn	NOUN
ejpam-447	349	4	+	+	CCONJ
ejpam-447	349	5	c	c	X
ejpam-447	349	6	xn−1	xn−1	PROPN
ejpam-447	349	7	)	)	PUNCT
ejpam-447	349	8	,	,	PUNCT
ejpam-447	349	9	j.	j.	PROPN
ejpam-447	349	10	difference	difference	NOUN
ejpam-447	349	11	equations	equation	NOUN
ejpam-447	349	12	and	and	CCONJ
ejpam-447	349	13	appl	appl	NOUN
ejpam-447	349	14	;	;	PUNCT
ejpam-447	349	15	1(1995	1(1995	NUM
ejpam-447	349	16	)	)	PUNCT
ejpam-447	349	17	,	,	PUNCT
ejpam-447	349	18	317	317	NUM
ejpam-447	349	19	-	-	SYM
ejpam-447	349	20	321	321	NUM
ejpam-447	349	21	.	.	PUNCT
ejpam-447	350	1	[	[	X
ejpam-447	350	2	28	28	NUM
ejpam-447	350	3	]	]	X
ejpam-447	350	4	w.	w.	PROPN
ejpam-447	350	5	t.	t.	PROPN
ejpam-447	350	6	li	li	PROPN
ejpam-447	350	7	and	and	CCONJ
ejpam-447	350	8	h.	h.	PROPN
ejpam-447	350	9	r.	r.	PROPN
ejpam-447	350	10	sun	sun	PROPN
ejpam-447	350	11	,	,	PUNCT
ejpam-447	350	12	global	global	ADJ
ejpam-447	350	13	attractivity	attractivity	NOUN
ejpam-447	350	14	in	in	ADP
ejpam-447	350	15	a	a	DET
ejpam-447	350	16	rational	rational	ADJ
ejpam-447	350	17	recursive	recursive	ADJ
ejpam-447	350	18	sequence	sequence	NOUN
ejpam-447	350	19	,	,	PUNCT
ejpam-447	350	20	dynamical	dynamical	ADJ
ejpam-447	350	21	systems	system	NOUN
ejpam-447	350	22	.	.	PUNCT
ejpam-447	351	1	appl	appl	NOUN
ejpam-447	351	2	;	;	PUNCT
ejpam-447	351	3	11	11	NUM
ejpam-447	351	4	(	(	PUNCT
ejpam-447	351	5	2002	2002	NUM
ejpam-447	351	6	)	)	PUNCT
ejpam-447	351	7	,	,	PUNCT
ejpam-447	351	8	339	339	NUM
ejpam-447	351	9	346	346	NUM
ejpam-447	351	10	.	.	PUNCT
ejpam-447	352	1	[	[	X
ejpam-447	352	2	29	29	NUM
ejpam-447	352	3	]	]	X
ejpam-447	352	4	w.	w.	PROPN
ejpam-447	352	5	t.	t.	PROPN
ejpam-447	352	6	li	li	PROPN
ejpam-447	352	7	and	and	CCONJ
ejpam-447	352	8	h.	h.	PROPN
ejpam-447	352	9	r.	r.	PROPN
ejpam-447	352	10	sun	sun	PROPN
ejpam-447	352	11	,	,	PUNCT
ejpam-447	352	12	dynamics	dynamic	NOUN
ejpam-447	352	13	of	of	ADP
ejpam-447	352	14	a	a	DET
ejpam-447	352	15	rational	rational	ADJ
ejpam-447	352	16	difference	difference	NOUN
ejpam-447	352	17	equation	equation	NOUN
ejpam-447	352	18	,	,	PUNCT
ejpam-447	352	19	appl	appl	PROPN
ejpam-447	352	20	.	.	PROPN
ejpam-447	352	21	math	math	PROPN
ejpam-447	352	22	.	.	PUNCT
ejpam-447	353	1	comput	comput	NOUN
ejpam-447	353	2	.	.	PUNCT
ejpam-447	353	3	,	,	PUNCT
ejpam-447	353	4	163(2005	163(2005	NUM
ejpam-447	353	5	)	)	PUNCT
ejpam-447	353	6	,	,	PUNCT
ejpam-447	353	7	577	577	NUM
ejpam-447	353	8	-	-	SYM
ejpam-447	353	9	591	591	NUM
ejpam-447	353	10	.	.	PUNCT
ejpam-447	354	1	[	[	X
ejpam-447	354	2	30	30	NUM
ejpam-447	354	3	]	]	X
ejpam-447	354	4	r.	r.	PROPN
ejpam-447	354	5	e.	e.	PROPN
ejpam-447	354	6	mickens	mickens	PROPN
ejpam-447	354	7	,	,	PUNCT
ejpam-447	354	8	difference	difference	NOUN
ejpam-447	354	9	equations	equation	NOUN
ejpam-447	354	10	,	,	PUNCT
ejpam-447	354	11	theory	theory	NOUN
ejpam-447	354	12	and	and	CCONJ
ejpam-447	354	13	applications	application	NOUN
ejpam-447	354	14	,	,	PUNCT
ejpam-447	354	15	van	van	PROPN
ejpam-447	354	16	nostrand	nostrand	PROPN
ejpam-447	354	17	,	,	PUNCT
ejpam-447	354	18	new	new	PROPN
ejpam-447	354	19	york	york	PROPN
ejpam-447	354	20	,	,	PUNCT
ejpam-447	354	21	1990	1990	NUM
ejpam-447	354	22	.	.	PUNCT
ejpam-447	355	1	[	[	X
ejpam-447	355	2	31	31	NUM
ejpam-447	355	3	]	]	PUNCT
ejpam-447	355	4	m.	m.	NOUN
ejpam-447	355	5	saleh	saleh	NOUN
ejpam-447	355	6	and	and	CCONJ
ejpam-447	355	7	s.	s.	PROPN
ejpam-447	355	8	abu	abu	PROPN
ejpam-447	355	9	-	-	PUNCT
ejpam-447	355	10	baha	baha	PROPN
ejpam-447	355	11	,	,	PUNCT
ejpam-447	355	12	dynamics	dynamic	NOUN
ejpam-447	355	13	of	of	ADP
ejpam-447	355	14	a	a	DET
ejpam-447	355	15	higher	high	ADJ
ejpam-447	355	16	order	order	NOUN
ejpam-447	355	17	rational	rational	ADJ
ejpam-447	355	18	difference	difference	NOUN
ejpam-447	355	19	equation	equation	NOUN
ejpam-447	355	20	,	,	PUNCT
ejpam-447	355	21	appl	appl	PROPN
ejpam-447	355	22	.	.	PROPN
ejpam-447	355	23	math	math	PROPN
ejpam-447	355	24	.	.	PUNCT
ejpam-447	356	1	comput	comput	NOUN
ejpam-447	356	2	;	;	PUNCT
ejpam-447	356	3	181(2006	181(2006	NUM
ejpam-447	356	4	)	)	PUNCT
ejpam-447	356	5	,	,	PUNCT
ejpam-447	356	6	84	84	NUM
ejpam-447	356	7	-	-	SYM
ejpam-447	356	8	102	102	NUM
ejpam-447	356	9	.	.	PUNCT
ejpam-447	357	1	[	[	X
ejpam-447	357	2	32	32	NUM
ejpam-447	357	3	]	]	PUNCT
ejpam-447	357	4	s.	s.	PROPN
ejpam-447	357	5	stevic′	stevic′	PROPN
ejpam-447	357	6	,	,	PUNCT
ejpam-447	357	7	on	on	ADP
ejpam-447	357	8	the	the	DET
ejpam-447	357	9	recursive	recursive	ADJ
ejpam-447	357	10	sequences	sequence	NOUN
ejpam-447	357	11	xn+1	xn+1	PROPN
ejpam-447	357	12	=	=	PUNCT
ejpam-447	357	13	xn−1	xn−1	PROPN
ejpam-447	357	14	/	/	SYM
ejpam-447	357	15	g(xn	g(xn	NOUN
ejpam-447	357	16	)	)	PUNCT
ejpam-447	357	17	,	,	PUNCT
ejpam-447	357	18	taiwanese	taiwanese	PROPN
ejpam-447	357	19	j.	j.	PROPN
ejpam-447	357	20	math	math	PROPN
ejpam-447	357	21	;	;	PUNCT
ejpam-447	357	22	6(2002	6(2002	NUM
ejpam-447	357	23	)	)	PUNCT
ejpam-447	357	24	,	,	PUNCT
ejpam-447	357	25	405	405	NUM
ejpam-447	357	26	-	-	SYM
ejpam-447	357	27	414	414	NUM
ejpam-447	357	28	.	.	PUNCT
ejpam-447	358	1	[	[	X
ejpam-447	358	2	33	33	NUM
ejpam-447	358	3	]	]	PUNCT
ejpam-447	358	4	s.	s.	PROPN
ejpam-447	358	5	stevic′	stevic′	PROPN
ejpam-447	358	6	,	,	PUNCT
ejpam-447	358	7	on	on	ADP
ejpam-447	358	8	the	the	DET
ejpam-447	358	9	recursive	recursive	ADJ
ejpam-447	358	10	sequences	sequence	NOUN
ejpam-447	358	11	xn+1	xn+1	PROPN
ejpam-447	358	12	=	=	SYM
ejpam-447	358	13	g(xn	g(xn	NOUN
ejpam-447	358	14	,	,	PUNCT
ejpam-447	358	15	xn−1)/(a+	xn−1)/(a+	PROPN
ejpam-447	358	16	xn	xn	PROPN
ejpam-447	358	17	)	)	PUNCT
ejpam-447	358	18	,	,	PUNCT
ejpam-447	358	19	appl	appl	PROPN
ejpam-447	358	20	.	.	PROPN
ejpam-447	358	21	math	math	PROPN
ejpam-447	358	22	.	.	PUNCT
ejpam-447	358	23	letter	letter	PROPN
ejpam-447	358	24	,	,	PUNCT
ejpam-447	358	25	15(2002	15(2002	NUM
ejpam-447	358	26	)	)	PUNCT
ejpam-447	358	27	,	,	PUNCT
ejpam-447	358	28	305	305	NUM
ejpam-447	358	29	-	-	SYM
ejpam-447	358	30	308	308	NUM
ejpam-447	358	31	.	.	PUNCT
ejpam-447	359	1	[	[	X
ejpam-447	359	2	34	34	NUM
ejpam-447	359	3	]	]	X
ejpam-447	359	4	s.	s.	PROPN
ejpam-447	359	5	stevic′	stevic′	PROPN
ejpam-447	359	6	,	,	PUNCT
ejpam-447	359	7	on	on	ADP
ejpam-447	359	8	the	the	DET
ejpam-447	359	9	recursive	recursive	ADJ
ejpam-447	359	10	sequences	sequence	NOUN
ejpam-447	359	11	xn+1	xn+1	PROPN
ejpam-447	359	12	=	=	SYM
ejpam-447	360	1	α+(x	α+(x	NUM
ejpam-447	360	2	p	p	DET
ejpam-447	360	3	n−1	n−1	PROPN
ejpam-447	360	4	/x	/x	PUNCT
ejpam-447	360	5	p	p	NOUN
ejpam-447	360	6	n	n	CCONJ
ejpam-447	360	7	)	)	PUNCT
ejpam-447	360	8	,	,	PUNCT
ejpam-447	361	1	j.	j.	PROPN
ejpam-447	361	2	appl	appl	PROPN
ejpam-447	361	3	.	.	PROPN
ejpam-447	361	4	math	math	PROPN
ejpam-447	361	5	.	.	PUNCT
ejpam-447	361	6	&	&	CCONJ
ejpam-447	361	7	computing	computing	PROPN
ejpam-447	361	8	,	,	PUNCT
ejpam-447	361	9	18(2005	18(2005	NUM
ejpam-447	361	10	)	)	PUNCT
ejpam-447	361	11	,	,	PUNCT
ejpam-447	361	12	229	229	NUM
ejpam-447	361	13	-	-	SYM
ejpam-447	361	14	234	234	NUM
ejpam-447	361	15	.	.	PUNCT
ejpam-447	361	16	references	reference	NOUN
ejpam-447	361	17	268	268	NUM
ejpam-447	362	1	[	[	X
ejpam-447	362	2	35	35	NUM
ejpam-447	362	3	]	]	X
ejpam-447	362	4	e.	e.	PROPN
ejpam-447	362	5	m.	m.	PROPN
ejpam-447	362	6	e.	e.	PROPN
ejpam-447	362	7	zayed	zayed	PROPN
ejpam-447	362	8	and	and	CCONJ
ejpam-447	362	9	m.	m.	PROPN
ejpam-447	362	10	a.	a.	PROPN
ejpam-447	362	11	el	el	PROPN
ejpam-447	362	12	-	-	PROPN
ejpam-447	362	13	moneam	moneam	PROPN
ejpam-447	362	14	,	,	PUNCT
ejpam-447	362	15	on	on	ADP
ejpam-447	362	16	the	the	DET
ejpam-447	362	17	rational	rational	ADJ
ejpam-447	362	18	recursive	recursive	ADJ
ejpam-447	362	19	sequence	sequence	NOUN
ejpam-447	362	20	xn+1	xn+1	PROPN
ejpam-447	362	21	=	=	SYM
ejpam-447	362	22	(	(	PUNCT
ejpam-447	362	23	d+	d+	X
ejpam-447	362	24	αxn	αxn	PROPN
ejpam-447	362	25	+	+	X
ejpam-447	362	26	β	β	X
ejpam-447	362	27	xn−1	xn−1	PROPN
ejpam-447	362	28	+	+	CCONJ
ejpam-447	362	29	γxn−2)/(axn+	γxn−2)/(axn+	PUNCT
ejpam-447	362	30	bxn−1	bxn−1	PROPN
ejpam-447	362	31	+	+	PROPN
ejpam-447	362	32	c	c	PROPN
ejpam-447	362	33	xn−2	xn−2	PROPN
ejpam-447	362	34	)	)	PUNCT
ejpam-447	362	35	,	,	PUNCT
ejpam-447	362	36	comm	comm	NOUN
ejpam-447	362	37	.	.	PUNCT
ejpam-447	362	38	appl	appl	PROPN
ejpam-447	362	39	.	.	PUNCT
ejpam-447	363	1	nonlinear	nonlinear	ADJ
ejpam-447	363	2	analysis	analysis	NOUN
ejpam-447	363	3	,	,	PUNCT
ejpam-447	363	4	12(2005	12(2005	NUM
ejpam-447	363	5	)	)	PUNCT
ejpam-447	363	6	,	,	PUNCT
ejpam-447	363	7	15	15	NUM
ejpam-447	363	8	-	-	SYM
ejpam-447	363	9	28	28	NUM
ejpam-447	363	10	.	.	PUNCT
ejpam-447	364	1	[	[	X
ejpam-447	364	2	36	36	NUM
ejpam-447	364	3	]	]	X
ejpam-447	364	4	e.	e.	PROPN
ejpam-447	364	5	m.	m.	PROPN
ejpam-447	364	6	e.	e.	PROPN
ejpam-447	364	7	zayed	zayed	PROPN
ejpam-447	364	8	and	and	CCONJ
ejpam-447	364	9	m.	m.	PROPN
ejpam-447	364	10	a.	a.	PROPN
ejpam-447	364	11	el	el	PROPN
ejpam-447	364	12	-	-	PROPN
ejpam-447	364	13	moneam	moneam	PROPN
ejpam-447	364	14	,	,	PUNCT
ejpam-447	364	15	on	on	ADP
ejpam-447	364	16	the	the	DET
ejpam-447	364	17	rational	rational	ADJ
ejpam-447	364	18	recursive	recursive	ADJ
ejpam-447	364	19	sequence	sequence	NOUN
ejpam-447	364	20	xn+1	xn+1	PROPN
ejpam-447	364	21	=	=	SYM
ejpam-447	364	22	(	(	PUNCT
ejpam-447	364	23	αxn+	αxn+	PROPN
ejpam-447	364	24	β	β	PROPN
ejpam-447	364	25	xn−1+γxn−2+δxn−3)/(axn+	xn−1+γxn−2+δxn−3)/(axn+	ADP
ejpam-447	364	26	bxn−1+c	bxn−1+c	PROPN
ejpam-447	364	27	xn−2	xn−2	PROPN
ejpam-447	364	28	+	+	PROPN
ejpam-447	364	29	dxn−3	dxn−3	PROPN
ejpam-447	364	30	)	)	PUNCT
ejpam-447	364	31	,	,	PUNCT
ejpam-447	364	32	j.	j.	PROPN
ejpam-447	364	33	appl	appl	PROPN
ejpam-447	364	34	.	.	PROPN
ejpam-447	364	35	math	math	PROPN
ejpam-447	364	36	.	.	PUNCT
ejpam-447	365	1	&	&	CCONJ
ejpam-447	365	2	computing	computing	PROPN
ejpam-447	365	3	,	,	PUNCT
ejpam-447	365	4	22(2006	22(2006	NUM
ejpam-447	365	5	)	)	PUNCT
ejpam-447	365	6	,	,	PUNCT
ejpam-447	365	7	247	247	NUM
ejpam-447	365	8	-	-	SYM
ejpam-447	365	9	262	262	NUM
ejpam-447	365	10	.	.	PUNCT
ejpam-447	366	1	[	[	X
ejpam-447	366	2	37	37	NUM
ejpam-447	366	3	]	]	X
ejpam-447	366	4	e.	e.	PROPN
ejpam-447	366	5	m.	m.	PROPN
ejpam-447	366	6	e.	e.	PROPN
ejpam-447	366	7	zayed	zayed	PROPN
ejpam-447	366	8	and	and	CCONJ
ejpam-447	366	9	m.	m.	PROPN
ejpam-447	366	10	a.	a.	PROPN
ejpam-447	366	11	el	el	PROPN
ejpam-447	366	12	-	-	PROPN
ejpam-447	366	13	moneam	moneam	PROPN
ejpam-447	366	14	,	,	PUNCT
ejpam-447	366	15	on	on	ADP
ejpam-447	366	16	the	the	DET
ejpam-447	366	17	rational	rational	ADJ
ejpam-447	366	18	recursive	recursive	ADJ
ejpam-447	366	19	sequence	sequence	NOUN
ejpam-447	366	20	xn+1	xn+1	PROPN
ejpam-447	366	21	=	=	SYM
ejpam-447	366	22	�	�	PROPN
ejpam-447	366	23	a+	a+	PUNCT
ejpam-447	366	24	∑k	∑k	PROPN
ejpam-447	366	25	i=0αi	i=0αi	PROPN
ejpam-447	367	1	xn−i	xn−i	PROPN
ejpam-447	367	2	�	�	PROPN
ejpam-447	367	3	/	/	SYM
ejpam-447	367	4	∑k	∑k	PROPN
ejpam-447	367	5	i=0	i=0	PROPN
ejpam-447	367	6	βi	βi	PROPN
ejpam-447	367	7	xn−i	xn−i	PROPN
ejpam-447	367	8	,	,	PUNCT
ejpam-447	367	9	mathematica	mathematica	PROPN
ejpam-447	367	10	bohemica	bohemica	PROPN
ejpam-447	367	11	,	,	PUNCT
ejpam-447	367	12	133(2008	133(2008	NUM
ejpam-447	367	13	)	)	PUNCT
ejpam-447	367	14	,	,	PUNCT
ejpam-447	367	15	no.3	no.3	VERB
ejpam-447	367	16	,	,	PUNCT
ejpam-447	367	17	225	225	NUM
ejpam-447	367	18	-	-	SYM
ejpam-447	367	19	239	239	NUM
ejpam-447	367	20	.	.	PUNCT
ejpam-447	368	1	[	[	X
ejpam-447	368	2	38	38	NUM
ejpam-447	368	3	]	]	PUNCT
ejpam-447	368	4	e.	e.	PROPN
ejpam-447	368	5	m.	m.	PROPN
ejpam-447	368	6	e.	e.	PROPN
ejpam-447	368	7	zayed	zayed	PROPN
ejpam-447	368	8	and	and	CCONJ
ejpam-447	368	9	m.	m.	PROPN
ejpam-447	368	10	a.	a.	PROPN
ejpam-447	368	11	el	el	PROPN
ejpam-447	368	12	-	-	PROPN
ejpam-447	368	13	moneam	moneam	PROPN
ejpam-447	368	14	,	,	PUNCT
ejpam-447	368	15	on	on	ADP
ejpam-447	368	16	the	the	DET
ejpam-447	368	17	rational	rational	ADJ
ejpam-447	368	18	recursive	recursive	ADJ
ejpam-447	368	19	sequence	sequence	NOUN
ejpam-447	368	20	xn+1	xn+1	PROPN
ejpam-447	368	21	=	=	SYM
ejpam-447	368	22	�	�	PROPN
ejpam-447	368	23	a+	a+	PUNCT
ejpam-447	368	24	∑k	∑k	PROPN
ejpam-447	368	25	i=0αi	i=0αi	PROPN
ejpam-447	368	26	xn−i	xn−i	PROPN
ejpam-447	368	27	�	�	PROPN
ejpam-447	368	28	/	/	SYM
ejpam-447	368	29	�	�	PROPN
ejpam-447	368	30	b+	b+	SYM
ejpam-447	368	31	∑k	∑k	PROPN
ejpam-447	368	32	i=0	i=0	PROPN
ejpam-447	368	33	βi	βi	PROPN
ejpam-447	368	34	xn−i	xn−i	PROPN
ejpam-447	368	35	�	�	PROPN
ejpam-447	368	36	,	,	PUNCT
ejpam-447	368	37	int	int	PROPN
ejpam-447	368	38	.	.	PUNCT
ejpam-447	369	1	j.	j.	PROPN
ejpam-447	369	2	math	math	PROPN
ejpam-447	369	3	.	.	PUNCT
ejpam-447	369	4	&	&	CCONJ
ejpam-447	369	5	math	math	PROPN
ejpam-447	369	6	.	.	PUNCT
ejpam-447	370	1	sci	sci	PROPN
ejpam-447	370	2	;	;	PUNCT
ejpam-447	370	3	volume	volume	NOUN
ejpam-447	370	4	2007	2007	NUM
ejpam-447	370	5	,	,	PUNCT
ejpam-447	370	6	article	article	NOUN
ejpam-447	370	7	i	i	PROPN
ejpam-447	370	8	d	d	PROPN
ejpam-447	370	9	23618	23618	NUM
ejpam-447	370	10	,	,	PUNCT
ejpam-447	370	11	12	12	NUM
ejpam-447	370	12	pages	page	NOUN
ejpam-447	370	13	,	,	PUNCT
ejpam-447	370	14	doi	doi	NOUN
ejpam-447	370	15	:	:	PUNCT
ejpam-447	370	16	10.1155/2007/23618	10.1155/2007/23618	NUM
ejpam-447	370	17	.	.	PUNCT
ejpam-447	371	1	[	[	X
ejpam-447	371	2	39	39	NUM
ejpam-447	371	3	]	]	PUNCT
ejpam-447	371	4	e.	e.	PROPN
ejpam-447	371	5	m.	m.	PROPN
ejpam-447	371	6	e.	e.	PROPN
ejpam-447	371	7	zayed	zayed	PROPN
ejpam-447	371	8	and	and	CCONJ
ejpam-447	371	9	m.	m.	PROPN
ejpam-447	371	10	a.	a.	PROPN
ejpam-447	371	11	el	el	PROPN
ejpam-447	371	12	-	-	PROPN
ejpam-447	371	13	moneam	moneam	PROPN
ejpam-447	371	14	,	,	PUNCT
ejpam-447	371	15	on	on	ADP
ejpam-447	371	16	the	the	DET
ejpam-447	371	17	rational	rational	ADJ
ejpam-447	371	18	recursive	recursive	ADJ
ejpam-447	371	19	sequence	sequence	NOUN
ejpam-447	371	20	xn+1	xn+1	PROPN
ejpam-447	371	21	=	=	PUNCT
ejpam-447	372	1	axn	axn	PROPN
ejpam-447	372	2	−	−	PROPN
ejpam-447	372	3	bxn/	bxn/	PROPN
ejpam-447	372	4	�	�	PROPN
ejpam-447	372	5	cxn−	cxn−	PROPN
ejpam-447	372	6	d	d	PROPN
ejpam-447	372	7	xn−k	xn−k	PROPN
ejpam-447	372	8	�	�	PROPN
ejpam-447	372	9	,	,	PUNCT
ejpam-447	372	10	comm	comm	NOUN
ejpam-447	372	11	.	.	PUNCT
ejpam-447	373	1	appl	appl	PROPN
ejpam-447	373	2	.	.	PUNCT
ejpam-447	374	1	nonlinear	nonlinear	ADJ
ejpam-447	374	2	analysis	analysis	NOUN
ejpam-447	374	3	,	,	PUNCT
ejpam-447	374	4	15(2008	15(2008	NUM
ejpam-447	374	5	)	)	PUNCT
ejpam-447	374	6	,	,	PUNCT
ejpam-447	374	7	47	47	NUM
ejpam-447	374	8	-	-	SYM
ejpam-447	374	9	57	57	NUM
ejpam-447	374	10	.	.	PUNCT
ejpam-447	375	1	[	[	X
ejpam-447	375	2	40	40	NUM
ejpam-447	375	3	]	]	PUNCT
ejpam-447	375	4	e.	e.	PROPN
ejpam-447	375	5	m.	m.	PROPN
ejpam-447	375	6	e.	e.	PROPN
ejpam-447	375	7	zayed	zayed	PROPN
ejpam-447	375	8	and	and	CCONJ
ejpam-447	375	9	m.	m.	PROPN
ejpam-447	375	10	a.	a.	PROPN
ejpam-447	375	11	el	el	PROPN
ejpam-447	375	12	-	-	PROPN
ejpam-447	375	13	moneam	moneam	PROPN
ejpam-447	375	14	,	,	PUNCT
ejpam-447	375	15	on	on	ADP
ejpam-447	375	16	the	the	DET
ejpam-447	375	17	rational	rational	ADJ
ejpam-447	375	18	recursive	recursive	ADJ
ejpam-447	375	19	sequence	sequence	NOUN
ejpam-447	375	20	xn+1	xn+1	PROPN
ejpam-447	376	1	=	=	SYM
ejpam-447	376	2	�	�	PROPN
ejpam-447	376	3	α+	α+	NUM
ejpam-447	376	4	β	β	PROPN
ejpam-447	376	5	xn−k	xn−k	PROPN
ejpam-447	376	6	�	�	PROPN
ejpam-447	376	7	/	/	SYM
ejpam-447	376	8	�	�	PROPN
ejpam-447	376	9	γ−	γ−	PROPN
ejpam-447	376	10	xn	xn	PROPN
ejpam-447	376	11	�	�	PROPN
ejpam-447	376	12	,	,	PUNCT
ejpam-447	376	13	j.	j.	PROPN
ejpam-447	376	14	appl	appl	PROPN
ejpam-447	376	15	.	.	PROPN
ejpam-447	376	16	math	math	PROPN
ejpam-447	376	17	.	.	PUNCT
ejpam-447	377	1	&	&	CCONJ
ejpam-447	378	1	computing	computing	PROPN
ejpam-447	378	2	,	,	PUNCT
ejpam-447	378	3	31(2009	31(2009	NUM
ejpam-447	378	4	)	)	PUNCT
ejpam-447	378	5	,	,	PUNCT
ejpam-447	378	6	229	229	NUM
ejpam-447	378	7	-	-	SYM
ejpam-447	378	8	237	237	NUM
ejpam-447	378	9	.	.	PUNCT
ejpam-447	379	1	[	[	X
ejpam-447	379	2	41	41	NUM
ejpam-447	379	3	]	]	X
ejpam-447	379	4	e.	e.	PROPN
ejpam-447	379	5	m.	m.	PROPN
ejpam-447	379	6	e.	e.	PROPN
ejpam-447	379	7	zayed	zayed	PROPN
ejpam-447	379	8	and	and	CCONJ
ejpam-447	379	9	m.	m.	PROPN
ejpam-447	379	10	a.	a.	PROPN
ejpam-447	379	11	el	el	PROPN
ejpam-447	379	12	-	-	PROPN
ejpam-447	379	13	moneam	moneam	PROPN
ejpam-447	379	14	,	,	PUNCT
ejpam-447	379	15	on	on	ADP
ejpam-447	379	16	the	the	DET
ejpam-447	379	17	rational	rational	ADJ
ejpam-447	379	18	recursive	recursive	ADJ
ejpam-447	379	19	sequence	sequence	NOUN
ejpam-447	379	20	xn+1	xn+1	PROPN
ejpam-447	379	21	=	=	PUNCT
ejpam-447	379	22	axn+	axn+	PROPN
ejpam-447	379	23	�	�	PROPN
ejpam-447	379	24	β	β	PROPN
ejpam-447	379	25	xn+	xn+	PROPN
ejpam-447	379	26	γxn−k	γxn−k	PROPN
ejpam-447	379	27	�	�	PROPN
ejpam-447	379	28	/	/	SYM
ejpam-447	379	29	�	�	PROPN
ejpam-447	379	30	c	c	PROPN
ejpam-447	379	31	xn+	xn+	PROPN
ejpam-447	379	32	dxn−k	dxn−k	PROPN
ejpam-447	379	33	�	�	PROPN
ejpam-447	379	34	,	,	PUNCT
ejpam-447	379	35	comm	comm	NOUN
ejpam-447	379	36	.	.	PUNCT
ejpam-447	379	37	appl	appl	PROPN
ejpam-447	379	38	.	.	PUNCT
ejpam-447	380	1	nonlinear	nonlinear	ADJ
ejpam-447	380	2	analysis	analysis	NOUN
ejpam-447	380	3	,	,	PUNCT
ejpam-447	380	4	16(2009	16(2009	NUM
ejpam-447	380	5	)	)	PUNCT
ejpam-447	380	6	,	,	PUNCT
ejpam-447	380	7	91	91	NUM
ejpam-447	380	8	-	-	SYM
ejpam-447	380	9	106	106	NUM
ejpam-447	380	10	.	.	PUNCT
ejpam-447	381	1	[	[	X
ejpam-447	381	2	42	42	NUM
ejpam-447	381	3	]	]	X
ejpam-447	381	4	e.	e.	PROPN
ejpam-447	381	5	m.	m.	PROPN
ejpam-447	381	6	e.	e.	PROPN
ejpam-447	381	7	zayed	zayed	PROPN
ejpam-447	381	8	and	and	CCONJ
ejpam-447	381	9	m.	m.	PROPN
ejpam-447	381	10	a.	a.	PROPN
ejpam-447	381	11	el	el	PROPN
ejpam-447	381	12	-	-	PROPN
ejpam-447	381	13	moneam	moneam	PROPN
ejpam-447	381	14	,	,	PUNCT
ejpam-447	381	15	on	on	ADP
ejpam-447	381	16	the	the	DET
ejpam-447	381	17	rational	rational	ADJ
ejpam-447	381	18	recursive	recursive	ADJ
ejpam-447	381	19	sequence	sequence	NOUN
ejpam-447	381	20	xn+1	xn+1	NOUN
ejpam-447	381	21	=	=	PUNCT
ejpam-447	381	22	γxn−k	γxn−k	PROPN
ejpam-447	381	23	+	+	CCONJ
ejpam-447	381	24	�	�	PROPN
ejpam-447	381	25	axn+	axn+	VERB
ejpam-447	381	26	bxn−k	bxn−k	PROPN
ejpam-447	381	27	�	�	PROPN
ejpam-447	381	28	/	/	SYM
ejpam-447	381	29	�	�	PROPN
ejpam-447	381	30	cxn	cxn	VERB
ejpam-447	381	31	−	−	PROPN
ejpam-447	381	32	d	d	PROPN
ejpam-447	381	33	xn−k	xn−k	PROPN
ejpam-447	381	34	�	�	PROPN
ejpam-447	381	35	,	,	PUNCT
ejpam-447	381	36	bulletin	bulletin	NOUN
ejpam-447	381	37	of	of	ADP
ejpam-447	381	38	the	the	DET
ejpam-447	381	39	iranian	iranian	PROPN
ejpam-447	381	40	mathematical	mathematical	ADJ
ejpam-447	381	41	society	society	NOUN
ejpam-447	381	42	,	,	PUNCT
ejpam-447	381	43	(	(	PUNCT
ejpam-447	381	44	to	to	PART
ejpam-447	381	45	appear	appear	VERB
ejpam-447	381	46	)	)	PUNCT
ejpam-447	381	47	.	.	PUNCT
ejpam-447	382	1	[	[	X
ejpam-447	382	2	43	43	NUM
ejpam-447	382	3	]	]	X
ejpam-447	382	4	e.	e.	PROPN
ejpam-447	382	5	m.	m.	PROPN
ejpam-447	382	6	e.	e.	PROPN
ejpam-447	382	7	zayed	zayed	PROPN
ejpam-447	382	8	and	and	CCONJ
ejpam-447	382	9	m.	m.	PROPN
ejpam-447	382	10	a.	a.	PROPN
ejpam-447	382	11	el	el	PROPN
ejpam-447	382	12	-	-	PROPN
ejpam-447	382	13	moneam	moneam	PROPN
ejpam-447	382	14	,	,	PUNCT
ejpam-447	382	15	on	on	ADP
ejpam-447	382	16	the	the	DET
ejpam-447	382	17	global	global	ADJ
ejpam-447	382	18	attractivity	attractivity	NOUN
ejpam-447	382	19	of	of	ADP
ejpam-447	382	20	two	two	NUM
ejpam-447	382	21	nonlinear	nonlinear	ADJ
ejpam-447	382	22	difference	difference	NOUN
ejpam-447	382	23	equations	equation	NOUN
ejpam-447	382	24	,	,	PUNCT
ejpam-447	382	25	j.	j.	PROPN
ejpam-447	382	26	math	math	PROPN
ejpam-447	382	27	.	.	PUNCT
ejpam-447	383	1	sci	sci	PROPN
ejpam-447	383	2	;	;	PUNCT
ejpam-447	383	3	(	(	PUNCT
ejpam-447	383	4	to	to	PART
ejpam-447	383	5	appear	appear	VERB
ejpam-447	383	6	)	)	PUNCT
ejpam-447	383	7	.	.	PUNCT
ejpam-447	384	1	[	[	X
ejpam-447	384	2	44	44	NUM
ejpam-447	384	3	]	]	PUNCT
ejpam-447	384	4	e.	e.	PROPN
ejpam-447	384	5	m.	m.	PROPN
ejpam-447	384	6	e.	e.	PROPN
ejpam-447	384	7	zayed	zayed	PROPN
ejpam-447	384	8	and	and	CCONJ
ejpam-447	384	9	m.	m.	PROPN
ejpam-447	384	10	a.	a.	PROPN
ejpam-447	384	11	el	el	PROPN
ejpam-447	384	12	-	-	PROPN
ejpam-447	384	13	moneam	moneam	PROPN
ejpam-447	384	14	,	,	PUNCT
ejpam-447	384	15	on	on	ADP
ejpam-447	384	16	the	the	DET
ejpam-447	384	17	rational	rational	ADJ
ejpam-447	384	18	recursive	recursive	ADJ
ejpam-447	384	19	two	two	NUM
ejpam-447	384	20	sequences	sequence	NOUN
ejpam-447	384	21	xn+1	xn+1	PROPN
ejpam-447	384	22	=	=	SYM
ejpam-447	384	23	axn−k	axn−k	PROPN
ejpam-447	384	24	+	+	CCONJ
ejpam-447	384	25	bxn−k/	bxn−k/	ADJ
ejpam-447	384	26	�	�	PROPN
ejpam-447	384	27	cxn	cxn	VERB
ejpam-447	384	28	+	+	CCONJ
ejpam-447	384	29	δd	δd	PROPN
ejpam-447	384	30	xn−k	xn−k	PROPN
ejpam-447	384	31	�	�	PROPN
ejpam-447	384	32	,	,	PUNCT
ejpam-447	384	33	acta	acta	PROPN
ejpam-447	384	34	math	math	PROPN
ejpam-447	384	35	.	.	PUNCT
ejpam-447	385	1	vietnamica	vietnamica	PROPN
ejpam-447	385	2	,	,	PUNCT
ejpam-447	385	3	(	(	PUNCT
ejpam-447	385	4	to	to	PART
ejpam-447	385	5	appear	appear	VERB
ejpam-447	385	6	)	)	PUNCT
ejpam-447	385	7	.	.	PUNCT
ejpam-447	386	1	[	[	X
ejpam-447	386	2	45	45	NUM
ejpam-447	386	3	]	]	X
ejpam-447	386	4	e.	e.	PROPN
ejpam-447	386	5	m.	m.	PROPN
ejpam-447	386	6	e.	e.	PROPN
ejpam-447	386	7	zayed	zayed	PROPN
ejpam-447	386	8	and	and	CCONJ
ejpam-447	386	9	m.	m.	PROPN
ejpam-447	386	10	a.	a.	PROPN
ejpam-447	386	11	el	el	PROPN
ejpam-447	386	12	-	-	PROPN
ejpam-447	386	13	moneam	moneam	PROPN
ejpam-447	386	14	,	,	PUNCT
ejpam-447	386	15	on	on	ADP
ejpam-447	386	16	the	the	DET
ejpam-447	386	17	rational	rational	ADJ
ejpam-447	386	18	recursive	recursive	ADJ
ejpam-447	386	19	sequence	sequence	NOUN
ejpam-447	386	20	xn+1	xn+1	PROPN
ejpam-447	386	21	=	=	PUNCT
ejpam-447	387	1	axn	axn	PROPN
ejpam-447	387	2	+	+	CCONJ
ejpam-447	387	3	bxn−k	bxn−k	PROPN
ejpam-447	387	4	+	+	CCONJ
ejpam-447	387	5	�	�	PROPN
ejpam-447	387	6	β	β	X
ejpam-447	387	7	xn+	xn+	PROPN
ejpam-447	387	8	γxn−k	γxn−k	PROPN
ejpam-447	387	9	�	�	PROPN
ejpam-447	387	10	/	/	SYM
ejpam-447	387	11	�	�	PROPN
ejpam-447	387	12	c	c	PROPN
ejpam-447	387	13	xn+	xn+	PROPN
ejpam-447	387	14	dxn−k	dxn−k	PROPN
ejpam-447	387	15	�	�	PROPN
ejpam-447	387	16	,	,	PUNCT
ejpam-447	387	17	acta	acta	PROPN
ejpam-447	387	18	appl	appl	PROPN
ejpam-447	387	19	.	.	PROPN
ejpam-447	387	20	math	math	NOUN
ejpam-447	387	21	;	;	PUNCT
ejpam-447	387	22	10.1007	10.1007	NUM
ejpam-447	387	23	/	/	SYM
ejpam-447	387	24	s10440009	s10440009	PROPN
ejpam-447	387	25	-	-	PUNCT
ejpam-447	387	26	9545	9545	NUM
ejpam-447	387	27	-	-	PUNCT
ejpam-447	387	28	y	y	NOUN
ejpam-447	387	29	,	,	PUNCT
ejpam-447	387	30	in	in	ADP
ejpam-447	387	31	press	press	NOUN
ejpam-447	387	32	.	.	PUNCT