id	sid	tid	token	lemma	pos
ejpam-700	1	1	9_700_elsayed.dvi	9_700_elsayed.dvi	NUM
ejpam-700	1	2	european	european	ADJ
ejpam-700	1	3	journal	journal	NOUN
ejpam-700	1	4	of	of	ADP
ejpam-700	1	5	pure	pure	ADJ
ejpam-700	1	6	and	and	CCONJ
ejpam-700	1	7	applied	apply	VERB
ejpam-700	1	8	mathematics	mathematic	NOUN
ejpam-700	1	9	vol	vol	NOUN
ejpam-700	1	10	.	.	PROPN
ejpam-700	1	11	4	4	NUM
ejpam-700	1	12	,	,	PUNCT
ejpam-700	1	13	no	no	INTJ
ejpam-700	1	14	.	.	NOUN
ejpam-700	1	15	3	3	NUM
ejpam-700	1	16	,	,	PUNCT
ejpam-700	1	17	2011	2011	NUM
ejpam-700	1	18	,	,	PUNCT
ejpam-700	1	19	287	287	NUM
ejpam-700	1	20	-	-	SYM
ejpam-700	1	21	303	303	NUM
ejpam-700	1	22	issn	issn	PROPN
ejpam-700	1	23	1307	1307	NUM
ejpam-700	1	24	-	-	SYM
ejpam-700	1	25	5543	5543	NUM
ejpam-700	1	26	–	–	PUNCT
ejpam-700	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-700	1	28	on	on	ADP
ejpam-700	1	29	the	the	DET
ejpam-700	1	30	solution	solution	NOUN
ejpam-700	1	31	of	of	ADP
ejpam-700	1	32	some	some	DET
ejpam-700	1	33	difference	difference	NOUN
ejpam-700	1	34	equations	equation	NOUN
ejpam-700	1	35	elsayed	elsaye	VERB
ejpam-700	1	36	m.	m.	NOUN
ejpam-700	1	37	elsayed	elsaye	VERB
ejpam-700	1	38	king	king	PROPN
ejpam-700	1	39	abdulaziz	abdulaziz	PROPN
ejpam-700	1	40	university	university	PROPN
ejpam-700	1	41	,	,	PUNCT
ejpam-700	1	42	faculty	faculty	NOUN
ejpam-700	1	43	of	of	ADP
ejpam-700	1	44	science	science	NOUN
ejpam-700	1	45	,	,	PUNCT
ejpam-700	1	46	mathematics	mathematics	PROPN
ejpam-700	1	47	department	department	PROPN
ejpam-700	1	48	,	,	PUNCT
ejpam-700	1	49	p.	p.	PROPN
ejpam-700	1	50	o.	o.	PROPN
ejpam-700	1	51	box	box	PROPN
ejpam-700	1	52	80203	80203	NUM
ejpam-700	1	53	,	,	PUNCT
ejpam-700	1	54	jeddah	jeddah	PROPN
ejpam-700	1	55	21589	21589	NUM
ejpam-700	1	56	,	,	PUNCT
ejpam-700	1	57	saudi	saudi	PROPN
ejpam-700	1	58	arabia	arabia	PROPN
ejpam-700	1	59	permanent	permanent	ADJ
ejpam-700	1	60	address	address	NOUN
ejpam-700	1	61	:	:	PUNCT
ejpam-700	1	62	department	department	NOUN
ejpam-700	1	63	of	of	ADP
ejpam-700	1	64	mathematics	mathematic	NOUN
ejpam-700	1	65	,	,	PUNCT
ejpam-700	1	66	faculty	faculty	NOUN
ejpam-700	1	67	of	of	ADP
ejpam-700	1	68	science	science	NOUN
ejpam-700	1	69	,	,	PUNCT
ejpam-700	1	70	mansoura	mansoura	PROPN
ejpam-700	1	71	university	university	NOUN
ejpam-700	1	72	,	,	PUNCT
ejpam-700	1	73	mansoura	mansoura	PROPN
ejpam-700	1	74	35516	35516	NUM
ejpam-700	1	75	,	,	PUNCT
ejpam-700	1	76	egypt	egypt	PROPN
ejpam-700	1	77	.	.	PUNCT
ejpam-700	2	1	abstract	abstract	PROPN
ejpam-700	2	2	.	.	PUNCT
ejpam-700	3	1	we	we	PRON
ejpam-700	3	2	obtain	obtain	VERB
ejpam-700	3	3	in	in	ADP
ejpam-700	3	4	this	this	DET
ejpam-700	3	5	paper	paper	NOUN
ejpam-700	3	6	the	the	DET
ejpam-700	3	7	solutions	solution	NOUN
ejpam-700	3	8	of	of	ADP
ejpam-700	3	9	the	the	DET
ejpam-700	3	10	following	follow	VERB
ejpam-700	3	11	difference	difference	NOUN
ejpam-700	3	12	equations	equation	NOUN
ejpam-700	3	13	xn+1	xn+1	PROPN
ejpam-700	4	1	=	=	SYM
ejpam-700	4	2	xn−3	xn−3	PROPN
ejpam-700	4	3	±1±	±1±	NUM
ejpam-700	4	4	xn−1	xn−1	PROPN
ejpam-700	4	5	xn−3	xn−3	PROPN
ejpam-700	4	6	,	,	PUNCT
ejpam-700	4	7	n=	n=	ADJ
ejpam-700	4	8	0,1	0,1	NUM
ejpam-700	4	9	,	,	PUNCT
ejpam-700	4	10	...	...	PUNCT
ejpam-700	4	11	,	,	PUNCT
ejpam-700	4	12	where	where	SCONJ
ejpam-700	4	13	the	the	DET
ejpam-700	4	14	initial	initial	ADJ
ejpam-700	4	15	conditions	condition	NOUN
ejpam-700	4	16	are	be	AUX
ejpam-700	4	17	arbitrary	arbitrary	ADJ
ejpam-700	4	18	nonzero	nonzero	ADJ
ejpam-700	4	19	real	real	ADJ
ejpam-700	4	20	numbers	number	NOUN
ejpam-700	4	21	.	.	PUNCT
ejpam-700	5	1	2000	2000	NUM
ejpam-700	5	2	mathematics	mathematic	NOUN
ejpam-700	5	3	subject	subject	NOUN
ejpam-700	5	4	classifications	classification	NOUN
ejpam-700	5	5	:	:	PUNCT
ejpam-700	5	6	39a10	39a10	NUM
ejpam-700	5	7	key	key	ADJ
ejpam-700	5	8	words	word	NOUN
ejpam-700	5	9	and	and	CCONJ
ejpam-700	5	10	phrases	phrase	NOUN
ejpam-700	5	11	:	:	PUNCT
ejpam-700	5	12	difference	difference	NOUN
ejpam-700	5	13	equations	equation	NOUN
ejpam-700	5	14	,	,	PUNCT
ejpam-700	5	15	recursive	recursive	ADJ
ejpam-700	5	16	sequences	sequence	NOUN
ejpam-700	5	17	,	,	PUNCT
ejpam-700	5	18	periodic	periodic	ADJ
ejpam-700	5	19	solution	solution	NOUN
ejpam-700	5	20	.	.	PUNCT
ejpam-700	6	1	1	1	X
ejpam-700	6	2	.	.	X
ejpam-700	6	3	introduction	introduction	NOUN
ejpam-700	6	4	in	in	ADP
ejpam-700	6	5	this	this	DET
ejpam-700	6	6	paper	paper	NOUN
ejpam-700	6	7	we	we	PRON
ejpam-700	6	8	obtain	obtain	VERB
ejpam-700	6	9	the	the	DET
ejpam-700	6	10	solutions	solution	NOUN
ejpam-700	6	11	of	of	ADP
ejpam-700	6	12	the	the	DET
ejpam-700	6	13	following	follow	VERB
ejpam-700	6	14	difference	difference	NOUN
ejpam-700	6	15	equations	equation	NOUN
ejpam-700	6	16	xn+1	xn+1	PROPN
ejpam-700	6	17	=	=	SYM
ejpam-700	6	18	xn−3	xn−3	PROPN
ejpam-700	6	19	±1±	±1±	NUM
ejpam-700	6	20	xn−1	xn−1	PROPN
ejpam-700	6	21	xn−3	xn−3	PROPN
ejpam-700	6	22	,	,	PUNCT
ejpam-700	6	23	n=	n=	ADJ
ejpam-700	6	24	0,1	0,1	NUM
ejpam-700	6	25	,	,	PUNCT
ejpam-700	6	26	.	.	PUNCT
ejpam-700	6	27	.	.	PUNCT
ejpam-700	6	28	.	.	PUNCT
ejpam-700	7	1	,	,	PUNCT
ejpam-700	7	2	(	(	PUNCT
ejpam-700	7	3	1	1	X
ejpam-700	7	4	)	)	PUNCT
ejpam-700	7	5	where	where	SCONJ
ejpam-700	7	6	the	the	DET
ejpam-700	7	7	initial	initial	ADJ
ejpam-700	7	8	conditions	condition	NOUN
ejpam-700	7	9	are	be	AUX
ejpam-700	7	10	arbitrary	arbitrary	ADJ
ejpam-700	7	11	nonzero	nonzero	ADJ
ejpam-700	7	12	real	real	ADJ
ejpam-700	7	13	numbers	number	NOUN
ejpam-700	7	14	.	.	PUNCT
ejpam-700	8	1	the	the	DET
ejpam-700	8	2	study	study	NOUN
ejpam-700	8	3	of	of	ADP
ejpam-700	8	4	difference	difference	NOUN
ejpam-700	8	5	equations	equation	NOUN
ejpam-700	8	6	has	have	AUX
ejpam-700	8	7	been	be	AUX
ejpam-700	8	8	growing	grow	VERB
ejpam-700	8	9	continuously	continuously	ADV
ejpam-700	8	10	for	for	ADP
ejpam-700	8	11	the	the	DET
ejpam-700	8	12	last	last	ADJ
ejpam-700	8	13	decade	decade	NOUN
ejpam-700	8	14	.	.	PUNCT
ejpam-700	9	1	this	this	PRON
ejpam-700	9	2	is	be	AUX
ejpam-700	9	3	largely	largely	ADV
ejpam-700	9	4	due	due	ADJ
ejpam-700	9	5	to	to	ADP
ejpam-700	9	6	the	the	DET
ejpam-700	9	7	fact	fact	NOUN
ejpam-700	9	8	that	that	SCONJ
ejpam-700	9	9	difference	difference	NOUN
ejpam-700	9	10	equations	equation	NOUN
ejpam-700	9	11	manifest	manifest	VERB
ejpam-700	9	12	themselves	themselves	PRON
ejpam-700	9	13	as	as	ADP
ejpam-700	9	14	mathematical	mathematical	ADJ
ejpam-700	9	15	models	model	NOUN
ejpam-700	9	16	describing	describe	VERB
ejpam-700	9	17	real	real	ADJ
ejpam-700	9	18	life	life	NOUN
ejpam-700	9	19	situations	situation	NOUN
ejpam-700	9	20	in	in	ADP
ejpam-700	9	21	probability	probability	NOUN
ejpam-700	9	22	theory	theory	NOUN
ejpam-700	9	23	,	,	PUNCT
ejpam-700	9	24	queuing	queue	VERB
ejpam-700	9	25	theory	theory	NOUN
ejpam-700	9	26	,	,	PUNCT
ejpam-700	9	27	statistical	statistical	ADJ
ejpam-700	9	28	problems	problem	NOUN
ejpam-700	9	29	,	,	PUNCT
ejpam-700	9	30	stochastic	stochastic	ADJ
ejpam-700	9	31	time	time	NOUN
ejpam-700	9	32	series	series	NOUN
ejpam-700	9	33	,	,	PUNCT
ejpam-700	9	34	combinatorial	combinatorial	ADJ
ejpam-700	9	35	analysis	analysis	NOUN
ejpam-700	9	36	,	,	PUNCT
ejpam-700	9	37	number	number	NOUN
ejpam-700	9	38	theory	theory	NOUN
ejpam-700	9	39	,	,	PUNCT
ejpam-700	9	40	geometry	geometry	NOUN
ejpam-700	9	41	,	,	PUNCT
ejpam-700	9	42	electrical	electrical	ADJ
ejpam-700	9	43	network	network	NOUN
ejpam-700	9	44	,	,	PUNCT
ejpam-700	9	45	quanta	quanta	PROPN
ejpam-700	9	46	in	in	ADP
ejpam-700	9	47	radiation	radiation	NOUN
ejpam-700	9	48	,	,	PUNCT
ejpam-700	9	49	genetics	genetic	NOUN
ejpam-700	9	50	in	in	ADP
ejpam-700	9	51	biology	biology	NOUN
ejpam-700	9	52	,	,	PUNCT
ejpam-700	9	53	economics	economic	NOUN
ejpam-700	9	54	,	,	PUNCT
ejpam-700	9	55	psychology	psychology	NOUN
ejpam-700	9	56	,	,	PUNCT
ejpam-700	9	57	sociology	sociology	NOUN
ejpam-700	9	58	,	,	PUNCT
ejpam-700	9	59	etc	etc	X
ejpam-700	9	60	.	.	X
ejpam-700	10	1	in	in	ADP
ejpam-700	10	2	fact	fact	NOUN
ejpam-700	10	3	,	,	PUNCT
ejpam-700	10	4	now	now	ADV
ejpam-700	10	5	it	it	PRON
ejpam-700	10	6	occupies	occupy	VERB
ejpam-700	10	7	a	a	DET
ejpam-700	10	8	central	central	ADJ
ejpam-700	10	9	position	position	NOUN
ejpam-700	10	10	in	in	ADP
ejpam-700	10	11	applicable	applicable	ADJ
ejpam-700	10	12	analysis	analysis	NOUN
ejpam-700	10	13	and	and	CCONJ
ejpam-700	10	14	will	will	AUX
ejpam-700	10	15	no	no	ADV
ejpam-700	10	16	doubt	doubt	ADV
ejpam-700	10	17	continue	continue	VERB
ejpam-700	10	18	to	to	PART
ejpam-700	10	19	play	play	VERB
ejpam-700	10	20	an	an	DET
ejpam-700	10	21	important	important	ADJ
ejpam-700	10	22	role	role	NOUN
ejpam-700	10	23	in	in	ADP
ejpam-700	10	24	mathematics	mathematic	NOUN
ejpam-700	10	25	as	as	ADP
ejpam-700	10	26	a	a	DET
ejpam-700	10	27	whole	whole	NOUN
ejpam-700	10	28	.	.	PUNCT
ejpam-700	11	1	recently	recently	ADV
ejpam-700	11	2	there	there	PRON
ejpam-700	11	3	has	have	AUX
ejpam-700	11	4	been	be	AUX
ejpam-700	11	5	a	a	DET
ejpam-700	11	6	lot	lot	NOUN
ejpam-700	11	7	of	of	ADP
ejpam-700	11	8	interest	interest	NOUN
ejpam-700	11	9	in	in	ADP
ejpam-700	11	10	studying	study	VERB
ejpam-700	11	11	the	the	DET
ejpam-700	11	12	global	global	ADJ
ejpam-700	11	13	attractivity	attractivity	PROPN
ejpam-700	11	14	,	,	PUNCT
ejpam-700	11	15	boundedness	boundedness	NOUN
ejpam-700	11	16	character	character	NOUN
ejpam-700	11	17	,	,	PUNCT
ejpam-700	11	18	periodicity	periodicity	NOUN
ejpam-700	11	19	and	and	CCONJ
ejpam-700	11	20	the	the	DET
ejpam-700	11	21	solution	solution	NOUN
ejpam-700	11	22	form	form	NOUN
ejpam-700	11	23	of	of	ADP
ejpam-700	11	24	nonlinear	nonlinear	ADJ
ejpam-700	11	25	difference	difference	NOUN
ejpam-700	11	26	equations	equation	NOUN
ejpam-700	11	27	.	.	PUNCT
ejpam-700	12	1	for	for	ADP
ejpam-700	12	2	some	some	DET
ejpam-700	12	3	results	result	NOUN
ejpam-700	12	4	email	email	NOUN
ejpam-700	12	5	addresses	address	NOUN
ejpam-700	12	6	:	:	PUNCT
ejpam-700	12	7	emelsayed�mans.edu.eg	emelsayed�mans.edu.eg	PROPN
ejpam-700	12	8	,	,	PUNCT
ejpam-700	12	9	emmelsayed	emmelsaye	VERB
ejpam-700	12	10	�	�	PROPN
ejpam-700	12	11	yahoo	yahoo	PROPN
ejpam-700	12	12	.	.	PUNCT
ejpam-700	13	1	om	om	PROPN
ejpam-700	13	2	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-700	14	1	287	287	NUM
ejpam-700	14	2	c	c	X
ejpam-700	14	3	©	©	NOUN
ejpam-700	14	4	2011	2011	NUM
ejpam-700	14	5	ejpam	ejpam	VERB
ejpam-700	14	6	all	all	DET
ejpam-700	14	7	rights	right	NOUN
ejpam-700	14	8	reserved	reserve	VERB
ejpam-700	14	9	.	.	PUNCT
ejpam-700	15	1	e.	e.	PROPN
ejpam-700	15	2	elsayed	elsayed	PROPN
ejpam-700	15	3	/	/	SYM
ejpam-700	15	4	eur	eur	PROPN
ejpam-700	15	5	.	.	PUNCT
ejpam-700	16	1	j.	j.	PROPN
ejpam-700	16	2	pure	pure	PROPN
ejpam-700	16	3	appl	appl	PROPN
ejpam-700	16	4	.	.	PROPN
ejpam-700	16	5	math	math	PROPN
ejpam-700	16	6	,	,	PUNCT
ejpam-700	16	7	4	4	NUM
ejpam-700	16	8	(	(	PUNCT
ejpam-700	16	9	2011	2011	NUM
ejpam-700	16	10	)	)	PUNCT
ejpam-700	16	11	,	,	PUNCT
ejpam-700	16	12	287	287	NUM
ejpam-700	16	13	-	-	SYM
ejpam-700	16	14	303	303	NUM
ejpam-700	16	15	288	288	NUM
ejpam-700	16	16	in	in	ADP
ejpam-700	16	17	this	this	DET
ejpam-700	16	18	area	area	NOUN
ejpam-700	16	19	,	,	PUNCT
ejpam-700	16	20	for	for	ADP
ejpam-700	16	21	example	example	NOUN
ejpam-700	16	22	:	:	PUNCT
ejpam-700	16	23	agarwal	agarwal	PROPN
ejpam-700	16	24	et	et	PROPN
ejpam-700	16	25	al	al	PROPN
ejpam-700	16	26	.	.	PUNCT
ejpam-700	17	1	[	[	X
ejpam-700	17	2	2	2	NUM
ejpam-700	17	3	]	]	PUNCT
ejpam-700	17	4	investigated	investigate	VERB
ejpam-700	17	5	the	the	DET
ejpam-700	17	6	global	global	ADJ
ejpam-700	17	7	stability	stability	NOUN
ejpam-700	17	8	,	,	PUNCT
ejpam-700	17	9	periodicity	periodicity	NOUN
ejpam-700	17	10	character	character	NOUN
ejpam-700	17	11	and	and	CCONJ
ejpam-700	17	12	gave	give	VERB
ejpam-700	17	13	the	the	DET
ejpam-700	17	14	solution	solution	NOUN
ejpam-700	17	15	of	of	ADP
ejpam-700	17	16	some	some	DET
ejpam-700	17	17	special	special	ADJ
ejpam-700	17	18	cases	case	NOUN
ejpam-700	17	19	of	of	ADP
ejpam-700	17	20	the	the	DET
ejpam-700	17	21	difference	difference	NOUN
ejpam-700	17	22	equation	equation	NOUN
ejpam-700	17	23	xn+1	xn+1	PROPN
ejpam-700	17	24	=	=	SYM
ejpam-700	17	25	a+	a+	PUNCT
ejpam-700	17	26	d	d	X
ejpam-700	17	27	xn−l	xn−l	PROPN
ejpam-700	17	28	xn−k	xn−k	PROPN
ejpam-700	17	29	b−	b−	PROPN
ejpam-700	17	30	cxn−s	cxn−	VERB
ejpam-700	17	31	.	.	PUNCT
ejpam-700	18	1	aloqeili	aloqeili	NOUN
ejpam-700	19	1	[	[	X
ejpam-700	19	2	4	4	NUM
ejpam-700	19	3	]	]	PUNCT
ejpam-700	19	4	has	have	AUX
ejpam-700	19	5	obtained	obtain	VERB
ejpam-700	19	6	the	the	DET
ejpam-700	19	7	solutions	solution	NOUN
ejpam-700	19	8	of	of	ADP
ejpam-700	19	9	the	the	DET
ejpam-700	19	10	difference	difference	NOUN
ejpam-700	19	11	equation	equation	NOUN
ejpam-700	19	12	xn+1	xn+1	PROPN
ejpam-700	20	1	=	=	SYM
ejpam-700	20	2	xn−1	xn−1	PROPN
ejpam-700	20	3	a−	a−	PROPN
ejpam-700	20	4	xn	xn	PROPN
ejpam-700	21	1	xn−1	xn−1	PROPN
ejpam-700	21	2	.	.	PUNCT
ejpam-700	22	1	cinar	cinar	PROPN
ejpam-700	23	1	[	[	X
ejpam-700	23	2	6–8	6–8	X
ejpam-700	23	3	]	]	X
ejpam-700	23	4	obtained	obtain	VERB
ejpam-700	23	5	the	the	DET
ejpam-700	23	6	solutions	solution	NOUN
ejpam-700	23	7	of	of	ADP
ejpam-700	23	8	the	the	DET
ejpam-700	23	9	following	follow	VERB
ejpam-700	23	10	difference	difference	NOUN
ejpam-700	23	11	equations	equation	NOUN
ejpam-700	23	12	xn+1	xn+1	PUNCT
ejpam-700	24	1	=	=	PUNCT
ejpam-700	24	2	xn−1	xn−1	PROPN
ejpam-700	24	3	1	1	NUM
ejpam-700	24	4	+	+	NUM
ejpam-700	24	5	xn	xn	PROPN
ejpam-700	24	6	xn−1	xn−1	PROPN
ejpam-700	24	7	,	,	PUNCT
ejpam-700	24	8	xn+1	xn+1	PROPN
ejpam-700	24	9	=	=	PUNCT
ejpam-700	24	10	xn−1	xn−1	PROPN
ejpam-700	25	1	−1	−1	PROPN
ejpam-700	26	1	+	+	NUM
ejpam-700	26	2	xn	xn	PROPN
ejpam-700	26	3	xn−1	xn−1	PROPN
ejpam-700	26	4	,	,	PUNCT
ejpam-700	26	5	xn+1	xn+1	PROPN
ejpam-700	26	6	=	=	PUNCT
ejpam-700	27	1	axn−1	axn−1	PROPN
ejpam-700	27	2	1	1	NUM
ejpam-700	27	3	+	+	NUM
ejpam-700	27	4	bxn	bxn	VERB
ejpam-700	27	5	xn−1	xn−1	PROPN
ejpam-700	27	6	.	.	PUNCT
ejpam-700	28	1	cinar	cinar	PROPN
ejpam-700	28	2	et	et	PROPN
ejpam-700	28	3	al	al	PROPN
ejpam-700	28	4	.	.	PUNCT
ejpam-700	29	1	[	[	X
ejpam-700	29	2	9	9	NUM
ejpam-700	29	3	]	]	PUNCT
ejpam-700	29	4	studied	study	VERB
ejpam-700	29	5	the	the	DET
ejpam-700	29	6	solutions	solution	NOUN
ejpam-700	29	7	and	and	CCONJ
ejpam-700	29	8	attractivity	attractivity	NOUN
ejpam-700	29	9	of	of	ADP
ejpam-700	29	10	the	the	DET
ejpam-700	29	11	difference	difference	NOUN
ejpam-700	29	12	equation	equation	NOUN
ejpam-700	29	13	xn+1	xn+1	PROPN
ejpam-700	29	14	=	=	SYM
ejpam-700	29	15	xn−3	xn−3	PROPN
ejpam-700	29	16	−1	−1	NOUN
ejpam-700	30	1	+	+	NUM
ejpam-700	30	2	xn	xn	PROPN
ejpam-700	30	3	xn−1	xn−1	PROPN
ejpam-700	30	4	xn−2	xn−2	PROPN
ejpam-700	30	5	xn−3	xn−3	PROPN
ejpam-700	30	6	.	.	PUNCT
ejpam-700	31	1	elabbasy	elabbasy	PROPN
ejpam-700	31	2	et	et	PROPN
ejpam-700	31	3	al	al	PROPN
ejpam-700	31	4	.	.	PUNCT
ejpam-700	32	1	[	[	X
ejpam-700	32	2	11–12	11–12	NUM
ejpam-700	32	3	]	]	PUNCT
ejpam-700	32	4	investigated	investigate	VERB
ejpam-700	32	5	the	the	DET
ejpam-700	32	6	global	global	ADJ
ejpam-700	32	7	stability	stability	NOUN
ejpam-700	32	8	,	,	PUNCT
ejpam-700	32	9	periodicity	periodicity	NOUN
ejpam-700	32	10	character	character	NOUN
ejpam-700	32	11	and	and	CCONJ
ejpam-700	32	12	gave	give	VERB
ejpam-700	32	13	the	the	DET
ejpam-700	32	14	solution	solution	NOUN
ejpam-700	32	15	of	of	ADP
ejpam-700	32	16	some	some	DET
ejpam-700	32	17	special	special	ADJ
ejpam-700	32	18	cases	case	NOUN
ejpam-700	32	19	of	of	ADP
ejpam-700	32	20	the	the	DET
ejpam-700	32	21	following	follow	VERB
ejpam-700	32	22	difference	difference	NOUN
ejpam-700	32	23	equations	equation	NOUN
ejpam-700	32	24	xn+1	xn+1	PUNCT
ejpam-700	33	1	=	=	SYM
ejpam-700	33	2	axn−	axn−	PROPN
ejpam-700	33	3	bxn	bxn	VERB
ejpam-700	33	4	cxn	cxn	VERB
ejpam-700	33	5	−	−	PROPN
ejpam-700	33	6	d	d	X
ejpam-700	33	7	xn−1	xn−1	PROPN
ejpam-700	33	8	,	,	PUNCT
ejpam-700	33	9	xn+1	xn+1	PROPN
ejpam-700	33	10	=	=	PUNCT
ejpam-700	33	11	αxn−k	αxn−k	NOUN
ejpam-700	33	12	β	β	NOUN
ejpam-700	33	13	+	+	X
ejpam-700	33	14	γ	γ	X
ejpam-700	33	15	∏k	∏k	X
ejpam-700	33	16	i=0	i=0	PROPN
ejpam-700	33	17	xn−i	xn−i	PROPN
ejpam-700	33	18	.	.	PUNCT
ejpam-700	34	1	in	in	ADP
ejpam-700	34	2	[	[	X
ejpam-700	34	3	19	19	NUM
ejpam-700	34	4	]	]	PUNCT
ejpam-700	34	5	elsayed	elsaye	VERB
ejpam-700	34	6	dealed	deal	VERB
ejpam-700	34	7	with	with	ADP
ejpam-700	34	8	the	the	DET
ejpam-700	34	9	dynamics	dynamic	NOUN
ejpam-700	34	10	and	and	CCONJ
ejpam-700	34	11	found	find	VERB
ejpam-700	34	12	the	the	DET
ejpam-700	34	13	solution	solution	NOUN
ejpam-700	34	14	of	of	ADP
ejpam-700	34	15	the	the	DET
ejpam-700	34	16	following	follow	VERB
ejpam-700	34	17	rational	rational	ADJ
ejpam-700	34	18	recursive	recursive	ADJ
ejpam-700	34	19	sequences	sequence	NOUN
ejpam-700	34	20	xn+1	xn+1	PROPN
ejpam-700	35	1	=	=	SYM
ejpam-700	36	1	xn−5	xn−5	PROPN
ejpam-700	36	2	±1±	±1±	PROPN
ejpam-700	36	3	xn−1	xn−1	PROPN
ejpam-700	36	4	xn−3	xn−3	PROPN
ejpam-700	36	5	xn−5	xn−5	PROPN
ejpam-700	36	6	.	.	PUNCT
ejpam-700	37	1	karatas	karata	NOUN
ejpam-700	37	2	et	et	PROPN
ejpam-700	37	3	al	al	PROPN
ejpam-700	37	4	.	.	PUNCT
ejpam-700	38	1	[	[	X
ejpam-700	38	2	34	34	NUM
ejpam-700	38	3	]	]	PUNCT
ejpam-700	38	4	obtained	obtain	VERB
ejpam-700	38	5	the	the	DET
ejpam-700	38	6	solution	solution	NOUN
ejpam-700	38	7	of	of	ADP
ejpam-700	38	8	the	the	DET
ejpam-700	38	9	difference	difference	NOUN
ejpam-700	38	10	equation	equation	NOUN
ejpam-700	38	11	xn+1	xn+1	NOUN
ejpam-700	38	12	=	=	SYM
ejpam-700	38	13	axn−(2k+2	axn−(2k+2	NOUN
ejpam-700	38	14	)	)	PUNCT
ejpam-700	38	15	−a+	−a+	X
ejpam-700	38	16	∏2k+2	∏2k+2	PROPN
ejpam-700	38	17	i=0	i=0	PROPN
ejpam-700	38	18	xn−i	xn−i	PROPN
ejpam-700	38	19	.	.	PUNCT
ejpam-700	39	1	simsek	simsek	VERB
ejpam-700	39	2	et	et	PROPN
ejpam-700	39	3	al	al	PROPN
ejpam-700	39	4	.	.	PUNCT
ejpam-700	40	1	[	[	X
ejpam-700	40	2	38]-[39	38]-[39	NUM
ejpam-700	40	3	]	]	PUNCT
ejpam-700	40	4	obtained	obtain	VERB
ejpam-700	40	5	the	the	DET
ejpam-700	40	6	solutions	solution	NOUN
ejpam-700	40	7	of	of	ADP
ejpam-700	40	8	the	the	DET
ejpam-700	40	9	following	follow	VERB
ejpam-700	40	10	difference	difference	NOUN
ejpam-700	40	11	equations	equation	NOUN
ejpam-700	40	12	xn+1	xn+1	PROPN
ejpam-700	41	1	=	=	PUNCT
ejpam-700	41	2	xn−3	xn−3	PROPN
ejpam-700	41	3	1	1	NUM
ejpam-700	41	4	+	+	CCONJ
ejpam-700	41	5	xn−1	xn−1	PROPN
ejpam-700	41	6	,	,	PUNCT
ejpam-700	41	7	xn+1	xn+1	PROPN
ejpam-700	41	8	=	=	SYM
ejpam-700	41	9	xn−5	xn−5	PROPN
ejpam-700	41	10	1	1	NUM
ejpam-700	41	11	+	+	NUM
ejpam-700	41	12	xn−1	xn−1	PROPN
ejpam-700	41	13	xn−3	xn−3	PROPN
ejpam-700	41	14	.	.	PUNCT
ejpam-700	42	1	in	in	ADP
ejpam-700	42	2	[	[	X
ejpam-700	42	3	40	40	NUM
ejpam-700	42	4	]	]	PUNCT
ejpam-700	42	5	stevic	stevic	NOUN
ejpam-700	42	6	solved	solve	VERB
ejpam-700	42	7	the	the	DET
ejpam-700	42	8	following	follow	VERB
ejpam-700	42	9	problem	problem	NOUN
ejpam-700	42	10	xn+1	xn+1	PUNCT
ejpam-700	43	1	=	=	PUNCT
ejpam-700	43	2	xn−1	xn−1	PROPN
ejpam-700	43	3	1	1	NUM
ejpam-700	43	4	+	+	NUM
ejpam-700	43	5	xn	xn	PROPN
ejpam-700	43	6	.	.	PUNCT
ejpam-700	44	1	yalçınkaya	yalçınkaya	NOUN
ejpam-700	44	2	et	et	PROPN
ejpam-700	44	3	al	al	PROPN
ejpam-700	44	4	.	.	PUNCT
ejpam-700	45	1	[	[	X
ejpam-700	45	2	49	49	NUM
ejpam-700	45	3	]	]	PUNCT
ejpam-700	45	4	considered	consider	VERB
ejpam-700	45	5	the	the	DET
ejpam-700	45	6	dynamics	dynamic	NOUN
ejpam-700	45	7	of	of	ADP
ejpam-700	45	8	the	the	DET
ejpam-700	45	9	difference	difference	NOUN
ejpam-700	45	10	equation	equation	NOUN
ejpam-700	45	11	xn+1	xn+1	PROPN
ejpam-700	45	12	=	=	PUNCT
ejpam-700	46	1	α+	α+	PUNCT
ejpam-700	47	1	xn−m	xn−m	PROPN
ejpam-700	47	2	x	x	X
ejpam-700	48	1	k	k	NOUN
ejpam-700	48	2	n	n	PROPN
ejpam-700	48	3	.	.	PUNCT
ejpam-700	49	1	e.	e.	PROPN
ejpam-700	49	2	elsayed	elsayed	PROPN
ejpam-700	49	3	/	/	SYM
ejpam-700	49	4	eur	eur	PROPN
ejpam-700	49	5	.	.	PUNCT
ejpam-700	50	1	j.	j.	PROPN
ejpam-700	50	2	pure	pure	PROPN
ejpam-700	50	3	appl	appl	PROPN
ejpam-700	50	4	.	.	PROPN
ejpam-700	50	5	math	math	PROPN
ejpam-700	50	6	,	,	PUNCT
ejpam-700	50	7	4	4	NUM
ejpam-700	50	8	(	(	PUNCT
ejpam-700	50	9	2011	2011	NUM
ejpam-700	50	10	)	)	PUNCT
ejpam-700	50	11	,	,	PUNCT
ejpam-700	50	12	287	287	NUM
ejpam-700	50	13	-	-	SYM
ejpam-700	50	14	303	303	NUM
ejpam-700	50	15	289	289	NUM
ejpam-700	50	16	zayed	zayed	ADJ
ejpam-700	51	1	[	[	X
ejpam-700	51	2	52	52	NUM
ejpam-700	51	3	]	]	PUNCT
ejpam-700	51	4	considered	consider	VERB
ejpam-700	51	5	the	the	DET
ejpam-700	51	6	behavior	behavior	NOUN
ejpam-700	51	7	of	of	ADP
ejpam-700	51	8	the	the	DET
ejpam-700	51	9	following	follow	VERB
ejpam-700	51	10	difference	difference	NOUN
ejpam-700	51	11	equation	equation	NOUN
ejpam-700	51	12	xn+1	xn+1	PUNCT
ejpam-700	51	13	=	=	PUNCT
ejpam-700	52	1	axn+	axn+	PROPN
ejpam-700	52	2	bxn−k	bxn−k	X
ejpam-700	52	3	+	+	CCONJ
ejpam-700	52	4	pxn	pxn	VERB
ejpam-700	52	5	+	+	X
ejpam-700	52	6	xn−k	xn−k	PROPN
ejpam-700	52	7	q+	q+	PROPN
ejpam-700	52	8	xn−k	xn−k	PROPN
ejpam-700	52	9	.	.	PUNCT
ejpam-700	53	1	other	other	ADJ
ejpam-700	53	2	related	relate	VERB
ejpam-700	53	3	results	result	NOUN
ejpam-700	53	4	on	on	ADP
ejpam-700	53	5	rational	rational	ADJ
ejpam-700	53	6	difference	difference	NOUN
ejpam-700	53	7	equations	equation	NOUN
ejpam-700	53	8	can	can	AUX
ejpam-700	53	9	be	be	AUX
ejpam-700	53	10	found	find	VERB
ejpam-700	53	11	in	in	ADP
ejpam-700	53	12	refs	ref	NOUN
ejpam-700	53	13	.	.	PUNCT
ejpam-700	54	1	[	[	X
ejpam-700	54	2	2	2	NUM
ejpam-700	54	3	-	-	SYM
ejpam-700	54	4	51	51	NUM
ejpam-700	54	5	]	]	PUNCT
ejpam-700	54	6	.	.	PUNCT
ejpam-700	55	1	the	the	DET
ejpam-700	55	2	study	study	NOUN
ejpam-700	55	3	of	of	ADP
ejpam-700	55	4	these	these	DET
ejpam-700	55	5	equations	equation	NOUN
ejpam-700	55	6	is	be	AUX
ejpam-700	55	7	quite	quite	ADV
ejpam-700	55	8	challenging	challenging	ADJ
ejpam-700	55	9	and	and	CCONJ
ejpam-700	55	10	rewarding	rewarding	ADJ
ejpam-700	55	11	and	and	CCONJ
ejpam-700	55	12	is	be	AUX
ejpam-700	55	13	still	still	ADV
ejpam-700	55	14	in	in	ADP
ejpam-700	55	15	its	its	PRON
ejpam-700	55	16	infancy	infancy	NOUN
ejpam-700	55	17	.	.	PUNCT
ejpam-700	56	1	we	we	PRON
ejpam-700	56	2	believe	believe	VERB
ejpam-700	56	3	that	that	SCONJ
ejpam-700	56	4	the	the	DET
ejpam-700	56	5	nonlinear	nonlinear	ADJ
ejpam-700	56	6	rational	rational	ADJ
ejpam-700	56	7	difference	difference	NOUN
ejpam-700	56	8	equations	equation	NOUN
ejpam-700	56	9	are	be	AUX
ejpam-700	56	10	of	of	ADP
ejpam-700	56	11	paramount	paramount	ADJ
ejpam-700	56	12	importance	importance	NOUN
ejpam-700	56	13	in	in	ADP
ejpam-700	56	14	their	their	PRON
ejpam-700	56	15	own	own	ADJ
ejpam-700	56	16	right	right	NOUN
ejpam-700	56	17	,	,	PUNCT
ejpam-700	56	18	and	and	CCONJ
ejpam-700	56	19	furthermore	furthermore	ADV
ejpam-700	56	20	we	we	PRON
ejpam-700	56	21	believe	believe	VERB
ejpam-700	56	22	that	that	SCONJ
ejpam-700	56	23	these	these	DET
ejpam-700	56	24	results	result	NOUN
ejpam-700	56	25	about	about	ADP
ejpam-700	56	26	such	such	ADJ
ejpam-700	56	27	equations	equation	NOUN
ejpam-700	56	28	over	over	ADP
ejpam-700	56	29	prototypes	prototype	NOUN
ejpam-700	56	30	for	for	ADP
ejpam-700	56	31	the	the	DET
ejpam-700	56	32	development	development	NOUN
ejpam-700	56	33	of	of	ADP
ejpam-700	56	34	the	the	DET
ejpam-700	56	35	basic	basic	ADJ
ejpam-700	56	36	theory	theory	NOUN
ejpam-700	56	37	of	of	ADP
ejpam-700	56	38	the	the	DET
ejpam-700	56	39	global	global	ADJ
ejpam-700	56	40	behavior	behavior	NOUN
ejpam-700	56	41	of	of	ADP
ejpam-700	56	42	nonlinear	nonlinear	ADJ
ejpam-700	56	43	rational	rational	ADJ
ejpam-700	56	44	difference	difference	NOUN
ejpam-700	56	45	equations	equation	NOUN
ejpam-700	56	46	.	.	PUNCT
ejpam-700	57	1	let	let	VERB
ejpam-700	57	2	us	we	PRON
ejpam-700	57	3	introduce	introduce	VERB
ejpam-700	57	4	some	some	DET
ejpam-700	57	5	basic	basic	ADJ
ejpam-700	57	6	definitions	definition	NOUN
ejpam-700	57	7	and	and	CCONJ
ejpam-700	57	8	some	some	DET
ejpam-700	57	9	theorems	theorem	NOUN
ejpam-700	57	10	that	that	SCONJ
ejpam-700	57	11	we	we	PRON
ejpam-700	57	12	need	need	VERB
ejpam-700	57	13	in	in	ADP
ejpam-700	57	14	the	the	DET
ejpam-700	57	15	sequel	sequel	NOUN
ejpam-700	57	16	.	.	PUNCT
ejpam-700	58	1	let	let	VERB
ejpam-700	58	2	i	i	PRON
ejpam-700	58	3	be	be	AUX
ejpam-700	58	4	some	some	DET
ejpam-700	58	5	interval	interval	NOUN
ejpam-700	58	6	of	of	ADP
ejpam-700	58	7	real	real	ADJ
ejpam-700	58	8	numbers	number	NOUN
ejpam-700	58	9	and	and	CCONJ
ejpam-700	58	10	let	let	VERB
ejpam-700	58	11	f	f	PROPN
ejpam-700	58	12	:	:	PUNCT
ejpam-700	58	13	ik+1→	ik+1→	PROPN
ejpam-700	58	14	i	i	PRON
ejpam-700	58	15	,	,	PUNCT
ejpam-700	58	16	be	be	AUX
ejpam-700	58	17	a	a	DET
ejpam-700	58	18	continuously	continuously	ADV
ejpam-700	58	19	differentiable	differentiable	ADJ
ejpam-700	58	20	function	function	NOUN
ejpam-700	58	21	.	.	PUNCT
ejpam-700	59	1	then	then	ADV
ejpam-700	59	2	for	for	ADP
ejpam-700	59	3	every	every	DET
ejpam-700	59	4	set	set	NOUN
ejpam-700	59	5	of	of	ADP
ejpam-700	59	6	initial	initial	ADJ
ejpam-700	59	7	conditions	condition	NOUN
ejpam-700	59	8	x−k	x−k	PROPN
ejpam-700	59	9	,	,	PUNCT
ejpam-700	59	10	x−k+1	x−k+1	PROPN
ejpam-700	59	11	,	,	PUNCT
ejpam-700	59	12	.	.	PUNCT
ejpam-700	59	13	.	.	PUNCT
ejpam-700	59	14	.	.	PUNCT
ejpam-700	60	1	,	,	PUNCT
ejpam-700	60	2	x0	x0	PROPN
ejpam-700	60	3	∈	∈	PROPN
ejpam-700	61	1	i	i	PRON
ejpam-700	61	2	,	,	PUNCT
ejpam-700	61	3	the	the	DET
ejpam-700	61	4	difference	difference	NOUN
ejpam-700	61	5	equation	equation	NOUN
ejpam-700	61	6	xn+1	xn+1	PROPN
ejpam-700	61	7	=	=	SYM
ejpam-700	61	8	f	f	PROPN
ejpam-700	61	9	(	(	PUNCT
ejpam-700	61	10	xn	xn	PROPN
ejpam-700	61	11	,	,	PUNCT
ejpam-700	61	12	xn−1	xn−1	PROPN
ejpam-700	61	13	,	,	PUNCT
ejpam-700	61	14	.	.	PUNCT
ejpam-700	61	15	.	.	PUNCT
ejpam-700	61	16	.	.	PUNCT
ejpam-700	62	1	,	,	PUNCT
ejpam-700	62	2	xn−k	xn−k	PROPN
ejpam-700	62	3	)	)	PUNCT
ejpam-700	62	4	,	,	PUNCT
ejpam-700	62	5	n=	n=	ADJ
ejpam-700	62	6	0,1	0,1	NUM
ejpam-700	62	7	,	,	PUNCT
ejpam-700	62	8	.	.	PUNCT
ejpam-700	62	9	.	.	PUNCT
ejpam-700	63	1	.	.	PUNCT
ejpam-700	64	1	,	,	PUNCT
ejpam-700	64	2	(	(	PUNCT
ejpam-700	64	3	2	2	X
ejpam-700	64	4	)	)	PUNCT
ejpam-700	64	5	has	have	VERB
ejpam-700	64	6	a	a	DET
ejpam-700	64	7	unique	unique	ADJ
ejpam-700	64	8	solution	solution	NOUN
ejpam-700	64	9	{	{	PUNCT
ejpam-700	64	10	xn}∞n=−k	xn}∞n=−k	PROPN
ejpam-700	64	11	.	.	PUNCT
ejpam-700	65	1	definition	definition	NOUN
ejpam-700	65	2	1	1	NUM
ejpam-700	65	3	(	(	PUNCT
ejpam-700	65	4	equilibrium	equilibrium	NOUN
ejpam-700	65	5	point	point	NOUN
ejpam-700	65	6	)	)	PUNCT
ejpam-700	65	7	.	.	PUNCT
ejpam-700	66	1	a	a	DET
ejpam-700	66	2	point	point	NOUN
ejpam-700	66	3	x	x	X
ejpam-700	66	4	∈	∈	NOUN
ejpam-700	66	5	i	i	PRON
ejpam-700	66	6	is	be	AUX
ejpam-700	66	7	called	call	VERB
ejpam-700	66	8	an	an	DET
ejpam-700	66	9	equilibrium	equilibrium	NOUN
ejpam-700	66	10	point	point	NOUN
ejpam-700	66	11	of	of	ADP
ejpam-700	66	12	eq	eq	PROPN
ejpam-700	66	13	.	.	PUNCT
ejpam-700	67	1	(	(	PUNCT
ejpam-700	67	2	2	2	X
ejpam-700	67	3	)	)	PUNCT
ejpam-700	67	4	if	if	SCONJ
ejpam-700	67	5	x	x	PROPN
ejpam-700	67	6	=	=	SYM
ejpam-700	67	7	f	f	X
ejpam-700	67	8	(	(	PUNCT
ejpam-700	67	9	x	x	INTJ
ejpam-700	67	10	,	,	PUNCT
ejpam-700	67	11	x	x	INTJ
ejpam-700	67	12	,	,	PUNCT
ejpam-700	67	13	.	.	PUNCT
ejpam-700	67	14	.	.	PUNCT
ejpam-700	67	15	.	.	PUNCT
ejpam-700	67	16	,	,	PUNCT
ejpam-700	67	17	x	x	X
ejpam-700	67	18	)	)	PUNCT
ejpam-700	67	19	.	.	PUNCT
ejpam-700	68	1	that	that	PRON
ejpam-700	68	2	is	be	AUX
ejpam-700	68	3	,	,	PUNCT
ejpam-700	68	4	xn	xn	PUNCT
ejpam-700	69	1	=	=	PUNCT
ejpam-700	69	2	x	x	PROPN
ejpam-700	69	3	for	for	ADP
ejpam-700	69	4	n≥	n≥	PROPN
ejpam-700	69	5	0	0	NUM
ejpam-700	69	6	,	,	PUNCT
ejpam-700	69	7	is	be	AUX
ejpam-700	69	8	a	a	DET
ejpam-700	69	9	solution	solution	NOUN
ejpam-700	69	10	of	of	ADP
ejpam-700	69	11	eq	eq	PROPN
ejpam-700	69	12	.	.	PUNCT
ejpam-700	70	1	(	(	PUNCT
ejpam-700	70	2	2	2	NUM
ejpam-700	70	3	)	)	PUNCT
ejpam-700	70	4	,	,	PUNCT
ejpam-700	70	5	or	or	CCONJ
ejpam-700	70	6	equivalently	equivalently	ADV
ejpam-700	70	7	,	,	PUNCT
ejpam-700	70	8	x	x	PRON
ejpam-700	70	9	is	be	AUX
ejpam-700	70	10	a	a	DET
ejpam-700	70	11	fixed	fix	VERB
ejpam-700	70	12	point	point	NOUN
ejpam-700	70	13	of	of	ADP
ejpam-700	70	14	f	f	PROPN
ejpam-700	70	15	.	.	PUNCT
ejpam-700	71	1	definition	definition	NOUN
ejpam-700	71	2	2	2	NUM
ejpam-700	71	3	(	(	PUNCT
ejpam-700	71	4	periodicity	periodicity	NOUN
ejpam-700	71	5	)	)	PUNCT
ejpam-700	71	6	.	.	PUNCT
ejpam-700	72	1	a	a	DET
ejpam-700	72	2	sequence	sequence	NOUN
ejpam-700	72	3	{	{	PUNCT
ejpam-700	72	4	xn}∞n=−k	xn}∞n=−k	PROPN
ejpam-700	72	5	is	be	AUX
ejpam-700	72	6	said	say	VERB
ejpam-700	72	7	to	to	PART
ejpam-700	72	8	be	be	AUX
ejpam-700	72	9	periodic	periodic	ADJ
ejpam-700	72	10	with	with	ADP
ejpam-700	72	11	period	period	NOUN
ejpam-700	72	12	p	p	NOUN
ejpam-700	72	13	if	if	SCONJ
ejpam-700	72	14	xn+p	xn+p	PROPN
ejpam-700	72	15	=	=	PUNCT
ejpam-700	72	16	xn	xn	PROPN
ejpam-700	72	17	for	for	ADP
ejpam-700	72	18	all	all	DET
ejpam-700	72	19	n≥	n≥	PRON
ejpam-700	72	20	−k	−k	VERB
ejpam-700	72	21	.	.	PUNCT
ejpam-700	73	1	2	2	X
ejpam-700	73	2	.	.	X
ejpam-700	73	3	on	on	ADP
ejpam-700	73	4	the	the	DET
ejpam-700	73	5	difference	difference	NOUN
ejpam-700	73	6	equation	equation	NOUN
ejpam-700	73	7	xn+1	xn+1	PROPN
ejpam-700	73	8	=	=	SYM
ejpam-700	73	9	xn−3	xn−3	PROPN
ejpam-700	73	10	1	1	NUM
ejpam-700	73	11	+	+	NUM
ejpam-700	73	12	xn−1	xn−1	PROPN
ejpam-700	73	13	xn−3	xn−3	PROPN
ejpam-700	73	14	in	in	ADP
ejpam-700	73	15	this	this	DET
ejpam-700	73	16	section	section	NOUN
ejpam-700	73	17	we	we	PRON
ejpam-700	73	18	give	give	VERB
ejpam-700	73	19	a	a	DET
ejpam-700	73	20	specific	specific	ADJ
ejpam-700	73	21	form	form	NOUN
ejpam-700	73	22	of	of	ADP
ejpam-700	73	23	the	the	DET
ejpam-700	73	24	solutions	solution	NOUN
ejpam-700	73	25	of	of	ADP
ejpam-700	73	26	the	the	DET
ejpam-700	73	27	difference	difference	NOUN
ejpam-700	73	28	equation	equation	NOUN
ejpam-700	73	29	xn+1	xn+1	PROPN
ejpam-700	74	1	=	=	SYM
ejpam-700	74	2	xn−3	xn−3	PROPN
ejpam-700	74	3	1	1	NUM
ejpam-700	74	4	+	+	NUM
ejpam-700	74	5	xn−1	xn−1	PROPN
ejpam-700	74	6	xn−3	xn−3	PROPN
ejpam-700	74	7	,	,	PUNCT
ejpam-700	74	8	n=	n=	ADJ
ejpam-700	74	9	0,1	0,1	NUM
ejpam-700	74	10	,	,	PUNCT
ejpam-700	74	11	.	.	PUNCT
ejpam-700	74	12	.	.	PUNCT
ejpam-700	74	13	.	.	PUNCT
ejpam-700	75	1	,	,	PUNCT
ejpam-700	75	2	(	(	PUNCT
ejpam-700	75	3	3	3	X
ejpam-700	75	4	)	)	PUNCT
ejpam-700	75	5	where	where	SCONJ
ejpam-700	75	6	the	the	DET
ejpam-700	75	7	initial	initial	ADJ
ejpam-700	75	8	conditions	condition	NOUN
ejpam-700	75	9	are	be	AUX
ejpam-700	75	10	arbitrary	arbitrary	ADJ
ejpam-700	75	11	nonzero	nonzero	ADJ
ejpam-700	75	12	positive	positive	ADJ
ejpam-700	75	13	real	real	ADJ
ejpam-700	75	14	numbers	number	NOUN
ejpam-700	75	15	.	.	PUNCT
ejpam-700	76	1	theorem	theorem	NOUN
ejpam-700	76	2	1	1	NUM
ejpam-700	76	3	.	.	PUNCT
ejpam-700	77	1	let	let	VERB
ejpam-700	77	2	{	{	PUNCT
ejpam-700	77	3	xn}∞n=−3	xn}∞n=−3	AUX
ejpam-700	77	4	be	be	AUX
ejpam-700	77	5	a	a	DET
ejpam-700	77	6	solution	solution	NOUN
ejpam-700	77	7	of	of	ADP
ejpam-700	77	8	eq	eq	PROPN
ejpam-700	77	9	.	.	PUNCT
ejpam-700	78	1	(	(	PUNCT
ejpam-700	78	2	3	3	NUM
ejpam-700	78	3	)	)	PUNCT
ejpam-700	78	4	.	.	PUNCT
ejpam-700	79	1	then	then	ADV
ejpam-700	79	2	for	for	ADP
ejpam-700	79	3	n=	n=	ADJ
ejpam-700	79	4	0,1	0,1	NUM
ejpam-700	79	5	,	,	PUNCT
ejpam-700	79	6	.	.	PUNCT
ejpam-700	79	7	.	.	PUNCT
ejpam-700	79	8	.	.	PUNCT
ejpam-700	80	1	x4n−3	x4n−3	PROPN
ejpam-700	81	1	=	=	PUNCT
ejpam-700	81	2	d	d	PROPN
ejpam-700	81	3	n−1	n−1	PROPN
ejpam-700	81	4	∏	∏	PROPN
ejpam-700	81	5	i=0	i=0	PROPN
ejpam-700	81	6	(	(	PUNCT
ejpam-700	81	7	1	1	NUM
ejpam-700	81	8	+	+	NUM
ejpam-700	81	9	2i	2i	NUM
ejpam-700	81	10	bd	bd	NOUN
ejpam-700	81	11	)	)	PUNCT
ejpam-700	81	12	n−1	n−1	PROPN
ejpam-700	81	13	∏	∏	PROPN
ejpam-700	81	14	i=0	i=0	PROPN
ejpam-700	81	15	(	(	PUNCT
ejpam-700	81	16	1	1	NUM
ejpam-700	81	17	+	+	CCONJ
ejpam-700	81	18	(	(	PUNCT
ejpam-700	81	19	2i	2i	NUM
ejpam-700	81	20	+	+	CCONJ
ejpam-700	81	21	1)bd	1)bd	NUM
ejpam-700	81	22	)	)	PUNCT
ejpam-700	81	23	,	,	PUNCT
ejpam-700	81	24	x4n−1	x4n−1	PROPN
ejpam-700	82	1	=	=	SYM
ejpam-700	82	2	b	b	PROPN
ejpam-700	82	3	n−1	n−1	PROPN
ejpam-700	82	4	∏	∏	PROPN
ejpam-700	82	5	i=0	i=0	PROPN
ejpam-700	82	6	(	(	PUNCT
ejpam-700	82	7	1	1	NUM
ejpam-700	82	8	+	+	CCONJ
ejpam-700	82	9	(	(	PUNCT
ejpam-700	82	10	2i+	2i+	NUM
ejpam-700	82	11	1)bd	1)bd	NUM
ejpam-700	82	12	)	)	PUNCT
ejpam-700	82	13	n−1	n−1	PROPN
ejpam-700	82	14	∏	∏	PROPN
ejpam-700	82	15	i=0	i=0	PROPN
ejpam-700	82	16	(	(	PUNCT
ejpam-700	82	17	1	1	NUM
ejpam-700	82	18	+	+	CCONJ
ejpam-700	82	19	(	(	PUNCT
ejpam-700	82	20	2i+	2i+	NUM
ejpam-700	82	21	2)bd	2)bd	NUM
ejpam-700	82	22	)	)	PUNCT
ejpam-700	82	23	,	,	PUNCT
ejpam-700	82	24	e.	e.	PROPN
ejpam-700	82	25	elsayed	elsaye	VERB
ejpam-700	82	26	/	/	SYM
ejpam-700	82	27	eur	eur	PROPN
ejpam-700	82	28	.	.	PUNCT
ejpam-700	83	1	j.	j.	PROPN
ejpam-700	83	2	pure	pure	PROPN
ejpam-700	83	3	appl	appl	PROPN
ejpam-700	83	4	.	.	PROPN
ejpam-700	83	5	math	math	PROPN
ejpam-700	83	6	,	,	PUNCT
ejpam-700	83	7	4	4	NUM
ejpam-700	83	8	(	(	PUNCT
ejpam-700	83	9	2011	2011	NUM
ejpam-700	83	10	)	)	PUNCT
ejpam-700	83	11	,	,	PUNCT
ejpam-700	83	12	287	287	NUM
ejpam-700	83	13	-	-	SYM
ejpam-700	83	14	303	303	NUM
ejpam-700	83	15	290	290	NUM
ejpam-700	84	1	x4n−2	x4n−2	PROPN
ejpam-700	84	2	=	=	SYM
ejpam-700	85	1	c	c	PROPN
ejpam-700	85	2	n−1	n−1	PROPN
ejpam-700	85	3	∏	∏	PROPN
ejpam-700	85	4	i=0	i=0	PROPN
ejpam-700	85	5	(	(	PUNCT
ejpam-700	85	6	1	1	NUM
ejpam-700	85	7	+	+	NUM
ejpam-700	85	8	2iac	2iac	NUM
ejpam-700	85	9	)	)	PUNCT
ejpam-700	85	10	n−1	n−1	PROPN
ejpam-700	85	11	∏	∏	PROPN
ejpam-700	85	12	i=0	i=0	PROPN
ejpam-700	85	13	(	(	PUNCT
ejpam-700	85	14	1	1	NUM
ejpam-700	85	15	+	+	CCONJ
ejpam-700	85	16	(	(	PUNCT
ejpam-700	85	17	2i	2i	NUM
ejpam-700	85	18	+	+	X
ejpam-700	85	19	1)ac	1)ac	NUM
ejpam-700	85	20	)	)	PUNCT
ejpam-700	85	21	,	,	PUNCT
ejpam-700	85	22	x4n	x4n	PUNCT
ejpam-700	85	23	=	=	PUNCT
ejpam-700	86	1	a	a	DET
ejpam-700	86	2	n−1	n−1	PROPN
ejpam-700	86	3	∏	∏	PROPN
ejpam-700	86	4	i=0	i=0	X
ejpam-700	86	5	(	(	PUNCT
ejpam-700	86	6	1	1	NUM
ejpam-700	86	7	+	+	CCONJ
ejpam-700	86	8	(	(	PUNCT
ejpam-700	86	9	2i+	2i+	NUM
ejpam-700	86	10	1)ac	1)ac	NUM
ejpam-700	86	11	)	)	PUNCT
ejpam-700	86	12	n−1	n−1	PROPN
ejpam-700	86	13	∏	∏	PROPN
ejpam-700	86	14	i=0	i=0	PROPN
ejpam-700	86	15	(	(	PUNCT
ejpam-700	86	16	1	1	NUM
ejpam-700	86	17	+	+	CCONJ
ejpam-700	86	18	(	(	PUNCT
ejpam-700	86	19	2i+	2i+	NUM
ejpam-700	86	20	2)ac	2)ac	NUM
ejpam-700	86	21	)	)	PUNCT
ejpam-700	86	22	,	,	PUNCT
ejpam-700	86	23	where	where	SCONJ
ejpam-700	86	24	x−3	x−3	PROPN
ejpam-700	86	25	=	=	SYM
ejpam-700	86	26	d	d	PROPN
ejpam-700	86	27	,	,	PUNCT
ejpam-700	86	28	x−2	x−2	PROPN
ejpam-700	86	29	=	=	SYM
ejpam-700	86	30	c	c	X
ejpam-700	86	31	,	,	PUNCT
ejpam-700	86	32	x−1	x−1	PUNCT
ejpam-700	86	33	=	=	SYM
ejpam-700	86	34	b	b	PROPN
ejpam-700	86	35	,	,	PUNCT
ejpam-700	86	36	x−0	x−0	PROPN
ejpam-700	86	37	=	=	PUNCT
ejpam-700	87	1	a	a	PRON
ejpam-700	87	2	,	,	PUNCT
ejpam-700	87	3	−1	−1	NOUN
ejpam-700	87	4	∏	∏	PROPN
ejpam-700	87	5	i=0	i=0	PROPN
ejpam-700	87	6	ai	ai	VERB
ejpam-700	87	7	=	=	ADJ
ejpam-700	87	8	1	1	NUM
ejpam-700	87	9	.	.	PUNCT
ejpam-700	88	1	proof	proof	NOUN
ejpam-700	88	2	.	.	PUNCT
ejpam-700	89	1	for	for	ADP
ejpam-700	89	2	n	n	NOUN
ejpam-700	89	3	=	=	SYM
ejpam-700	89	4	0	0	NOUN
ejpam-700	89	5	the	the	DET
ejpam-700	89	6	result	result	NOUN
ejpam-700	89	7	holds	hold	VERB
ejpam-700	89	8	.	.	PUNCT
ejpam-700	90	1	now	now	ADV
ejpam-700	90	2	suppose	suppose	VERB
ejpam-700	90	3	that	that	SCONJ
ejpam-700	90	4	n	n	PROPN
ejpam-700	90	5	>	>	X
ejpam-700	90	6	0	0	PUNCT
ejpam-700	91	1	and	and	CCONJ
ejpam-700	91	2	that	that	SCONJ
ejpam-700	91	3	our	our	PRON
ejpam-700	91	4	assumption	assumption	NOUN
ejpam-700	91	5	holds	hold	VERB
ejpam-700	91	6	for	for	ADP
ejpam-700	91	7	n−	n−	NOUN
ejpam-700	91	8	1	1	NUM
ejpam-700	91	9	.	.	PUNCT
ejpam-700	92	1	that	that	PRON
ejpam-700	92	2	is	be	AUX
ejpam-700	92	3	;	;	PUNCT
ejpam-700	92	4	x4n−7	x4n−7	PROPN
ejpam-700	92	5	=	=	PUNCT
ejpam-700	93	1	d	d	PROPN
ejpam-700	93	2	n−2	n−2	PROPN
ejpam-700	93	3	∏	∏	PROPN
ejpam-700	93	4	i=0	i=0	PROPN
ejpam-700	93	5	(	(	PUNCT
ejpam-700	93	6	1	1	NUM
ejpam-700	93	7	+	+	NUM
ejpam-700	93	8	2i	2i	NUM
ejpam-700	93	9	bd	bd	NOUN
ejpam-700	93	10	)	)	PUNCT
ejpam-700	93	11	n−2	n−2	PROPN
ejpam-700	93	12	∏	∏	PROPN
ejpam-700	93	13	i=0	i=0	PROPN
ejpam-700	93	14	(	(	PUNCT
ejpam-700	93	15	1	1	NUM
ejpam-700	93	16	+	+	CCONJ
ejpam-700	93	17	(	(	PUNCT
ejpam-700	93	18	2i	2i	NUM
ejpam-700	93	19	+	+	CCONJ
ejpam-700	93	20	1)bd	1)bd	NUM
ejpam-700	93	21	)	)	PUNCT
ejpam-700	93	22	,	,	PUNCT
ejpam-700	93	23	x4n−5	x4n−5	PROPN
ejpam-700	93	24	=	=	SYM
ejpam-700	93	25	b	b	PROPN
ejpam-700	93	26	n−2	n−2	PROPN
ejpam-700	93	27	∏	∏	PROPN
ejpam-700	93	28	i=0	i=0	PROPN
ejpam-700	93	29	(	(	PUNCT
ejpam-700	93	30	1	1	NUM
ejpam-700	93	31	+	+	CCONJ
ejpam-700	93	32	(	(	PUNCT
ejpam-700	93	33	2i+	2i+	NUM
ejpam-700	93	34	1)bd	1)bd	NUM
ejpam-700	93	35	)	)	PUNCT
ejpam-700	93	36	n−2	n−2	PROPN
ejpam-700	93	37	∏	∏	PROPN
ejpam-700	93	38	i=0	i=0	PROPN
ejpam-700	93	39	(	(	PUNCT
ejpam-700	93	40	1	1	NUM
ejpam-700	93	41	+	+	CCONJ
ejpam-700	93	42	(	(	PUNCT
ejpam-700	93	43	2i+	2i+	NUM
ejpam-700	93	44	2)bd	2)bd	NUM
ejpam-700	93	45	)	)	PUNCT
ejpam-700	93	46	,	,	PUNCT
ejpam-700	93	47	x4n−6	x4n−6	PROPN
ejpam-700	93	48	=	=	PUNCT
ejpam-700	94	1	c	c	PROPN
ejpam-700	94	2	n−2	n−2	PROPN
ejpam-700	94	3	∏	∏	PROPN
ejpam-700	94	4	i=0	i=0	PROPN
ejpam-700	94	5	(	(	PUNCT
ejpam-700	94	6	1	1	NUM
ejpam-700	94	7	+	+	NUM
ejpam-700	94	8	2iac	2iac	NUM
ejpam-700	94	9	)	)	PUNCT
ejpam-700	94	10	n−2	n−2	PROPN
ejpam-700	94	11	∏	∏	PROPN
ejpam-700	94	12	i=0	i=0	PROPN
ejpam-700	94	13	(	(	PUNCT
ejpam-700	94	14	1	1	NUM
ejpam-700	94	15	+	+	CCONJ
ejpam-700	94	16	(	(	PUNCT
ejpam-700	94	17	2i	2i	NUM
ejpam-700	94	18	+	+	X
ejpam-700	94	19	1)ac	1)ac	NUM
ejpam-700	94	20	)	)	PUNCT
ejpam-700	94	21	,	,	PUNCT
ejpam-700	94	22	x4n−4	x4n−4	PROPN
ejpam-700	94	23	=	=	PUNCT
ejpam-700	95	1	a	a	DET
ejpam-700	95	2	n−2	n−2	PROPN
ejpam-700	95	3	∏	∏	PROPN
ejpam-700	95	4	i=0	i=0	PROPN
ejpam-700	95	5	(	(	PUNCT
ejpam-700	95	6	1	1	NUM
ejpam-700	95	7	+	+	CCONJ
ejpam-700	95	8	(	(	PUNCT
ejpam-700	95	9	2i+	2i+	NUM
ejpam-700	95	10	1)ac	1)ac	NUM
ejpam-700	95	11	)	)	PUNCT
ejpam-700	95	12	n−2	n−2	PROPN
ejpam-700	95	13	∏	∏	PROPN
ejpam-700	95	14	i=0	i=0	PROPN
ejpam-700	95	15	(	(	PUNCT
ejpam-700	95	16	1	1	NUM
ejpam-700	95	17	+	+	CCONJ
ejpam-700	95	18	(	(	PUNCT
ejpam-700	95	19	2i+	2i+	NUM
ejpam-700	95	20	2)ac	2)ac	NUM
ejpam-700	95	21	)	)	PUNCT
ejpam-700	95	22	.	.	PUNCT
ejpam-700	96	1	now	now	ADV
ejpam-700	96	2	,	,	PUNCT
ejpam-700	96	3	it	it	PRON
ejpam-700	96	4	follows	follow	VERB
ejpam-700	96	5	from	from	ADP
ejpam-700	96	6	eq	eq	ADP
ejpam-700	96	7	.	.	PUNCT
ejpam-700	97	1	(	(	PUNCT
ejpam-700	97	2	3	3	NUM
ejpam-700	97	3	)	)	PUNCT
ejpam-700	98	1	that	that	DET
ejpam-700	98	2	x4n−3	x4n−3	PROPN
ejpam-700	98	3	=	=	SYM
ejpam-700	98	4	x4n−7	x4n−7	PROPN
ejpam-700	98	5	1	1	NUM
ejpam-700	98	6	+	+	NUM
ejpam-700	98	7	x4n−5	x4n−5	PROPN
ejpam-700	98	8	x4n−7	x4n−7	PROPN
ejpam-700	99	1	=	=	PUNCT
ejpam-700	99	2	d	d	PROPN
ejpam-700	99	3	n−2	n−2	PROPN
ejpam-700	99	4	∏	∏	PROPN
ejpam-700	99	5	i=0	i=0	PROPN
ejpam-700	99	6	(	(	PUNCT
ejpam-700	99	7	1	1	NUM
ejpam-700	99	8	+	+	NUM
ejpam-700	99	9	2i	2i	NUM
ejpam-700	99	10	bd	bd	NOUN
ejpam-700	99	11	)	)	PUNCT
ejpam-700	99	12	n−2	n−2	PROPN
ejpam-700	99	13	∏	∏	PROPN
ejpam-700	99	14	i=0	i=0	PROPN
ejpam-700	99	15	(	(	PUNCT
ejpam-700	99	16	1	1	NUM
ejpam-700	99	17	+	+	CCONJ
ejpam-700	99	18	(	(	PUNCT
ejpam-700	99	19	2i+	2i+	NUM
ejpam-700	99	20	1)bd	1)bd	NUM
ejpam-700	99	21	)	)	PUNCT
ejpam-700	99	22	1	1	NUM
ejpam-700	99	23	+	+	SYM
ejpam-700	99	24	b	b	PROPN
ejpam-700	99	25	n−2	n−2	PROPN
ejpam-700	99	26	∏	∏	PROPN
ejpam-700	99	27	i=0	i=0	PROPN
ejpam-700	99	28	(	(	PUNCT
ejpam-700	99	29	1	1	NUM
ejpam-700	99	30	+	+	CCONJ
ejpam-700	99	31	(	(	PUNCT
ejpam-700	99	32	2i+	2i+	NUM
ejpam-700	99	33	1)bd	1)bd	NUM
ejpam-700	99	34	)	)	PUNCT
ejpam-700	99	35	n−2	n−2	PROPN
ejpam-700	99	36	∏	∏	PROPN
ejpam-700	99	37	i=0	i=0	PROPN
ejpam-700	99	38	(	(	PUNCT
ejpam-700	99	39	1	1	NUM
ejpam-700	99	40	+	+	CCONJ
ejpam-700	99	41	(	(	PUNCT
ejpam-700	99	42	2i	2i	NOUN
ejpam-700	99	43	+	+	CCONJ
ejpam-700	99	44	2)bd	2)bd	X
ejpam-700	99	45	)	)	PUNCT
ejpam-700	99	46	d	d	PROPN
ejpam-700	99	47	n−2	n−2	PROPN
ejpam-700	99	48	∏	∏	PROPN
ejpam-700	99	49	i=0	i=0	PROPN
ejpam-700	99	50	(	(	PUNCT
ejpam-700	99	51	1	1	NUM
ejpam-700	99	52	+	+	NUM
ejpam-700	99	53	2i	2i	NUM
ejpam-700	99	54	bd	bd	NOUN
ejpam-700	99	55	)	)	PUNCT
ejpam-700	99	56	n−2	n−2	PROPN
ejpam-700	99	57	∏	∏	PROPN
ejpam-700	99	58	i=0	i=0	PROPN
ejpam-700	99	59	(	(	PUNCT
ejpam-700	99	60	1	1	NUM
ejpam-700	99	61	+	+	CCONJ
ejpam-700	99	62	(	(	PUNCT
ejpam-700	99	63	2i+	2i+	NUM
ejpam-700	99	64	1)bd	1)bd	NUM
ejpam-700	99	65	)	)	PUNCT
ejpam-700	99	66	=	=	PUNCT
ejpam-700	100	1	d	d	PROPN
ejpam-700	100	2	n−2	n−2	PROPN
ejpam-700	100	3	∏	∏	PROPN
ejpam-700	100	4	i=0	i=0	PROPN
ejpam-700	100	5	(	(	PUNCT
ejpam-700	100	6	1	1	NUM
ejpam-700	100	7	+	+	NUM
ejpam-700	100	8	2i	2i	NUM
ejpam-700	100	9	bd	bd	NOUN
ejpam-700	100	10	)	)	PUNCT
ejpam-700	100	11	n−2	n−2	PROPN
ejpam-700	100	12	∏	∏	PROPN
ejpam-700	100	13	i=0	i=0	PROPN
ejpam-700	100	14	(	(	PUNCT
ejpam-700	100	15	1	1	NUM
ejpam-700	100	16	+	+	CCONJ
ejpam-700	100	17	(	(	PUNCT
ejpam-700	100	18	2i+	2i+	NUM
ejpam-700	100	19	1)bd	1)bd	NUM
ejpam-700	100	20	)	)	PUNCT
ejpam-700	100	21			PROPN
ejpam-700	100	22			NOUN
ejpam-700	100	23			NOUN
ejpam-700	100	24			NOUN
ejpam-700	100	25			NOUN
ejpam-700	100	26			NOUN
ejpam-700	100	27			NOUN
ejpam-700	100	28	1	1	NUM
ejpam-700	100	29	+	+	NUM
ejpam-700	100	30	bd	bd	PROPN
ejpam-700	100	31	n−2	n−2	PROPN
ejpam-700	100	32	∏	∏	PROPN
ejpam-700	100	33	i=0	i=0	PROPN
ejpam-700	100	34	(	(	PUNCT
ejpam-700	100	35	1	1	NUM
ejpam-700	100	36	+	+	NUM
ejpam-700	100	37	2i	2i	NUM
ejpam-700	100	38	bd	bd	NOUN
ejpam-700	100	39	)	)	PUNCT
ejpam-700	100	40	n−2	n−2	PROPN
ejpam-700	100	41	∏	∏	PROPN
ejpam-700	100	42	i=0	i=0	PROPN
ejpam-700	100	43	(	(	PUNCT
ejpam-700	100	44	1	1	NUM
ejpam-700	100	45	+	+	CCONJ
ejpam-700	100	46	(	(	PUNCT
ejpam-700	100	47	2i	2i	NOUN
ejpam-700	100	48	+	+	CCONJ
ejpam-700	100	49	2)bd	2)bd	X
ejpam-700	100	50	)	)	PUNCT
ejpam-700	100	51			NOUN
ejpam-700	100	52			NOUN
ejpam-700	100	53			VERB
ejpam-700	100	54			NOUN
ejpam-700	100	55			NOUN
ejpam-700	100	56			NOUN
ejpam-700	100	57			PUNCT
ejpam-700	101	1	e.	e.	PROPN
ejpam-700	101	2	elsayed	elsaye	VERB
ejpam-700	101	3	/	/	SYM
ejpam-700	101	4	eur	eur	PROPN
ejpam-700	101	5	.	.	PUNCT
ejpam-700	102	1	j.	j.	PROPN
ejpam-700	102	2	pure	pure	PROPN
ejpam-700	102	3	appl	appl	PROPN
ejpam-700	102	4	.	.	PROPN
ejpam-700	102	5	math	math	PROPN
ejpam-700	102	6	,	,	PUNCT
ejpam-700	102	7	4	4	NUM
ejpam-700	102	8	(	(	PUNCT
ejpam-700	102	9	2011	2011	NUM
ejpam-700	102	10	)	)	PUNCT
ejpam-700	102	11	,	,	PUNCT
ejpam-700	102	12	287	287	NUM
ejpam-700	102	13	-	-	SYM
ejpam-700	102	14	303	303	NUM
ejpam-700	102	15	291	291	NUM
ejpam-700	102	16	=	=	SYM
ejpam-700	102	17	d	d	PROPN
ejpam-700	102	18	n−2	n−2	PROPN
ejpam-700	102	19	∏	∏	PROPN
ejpam-700	102	20	i=0	i=0	PROPN
ejpam-700	102	21	(	(	PUNCT
ejpam-700	102	22	1	1	NUM
ejpam-700	102	23	+	+	NUM
ejpam-700	102	24	2i	2i	NUM
ejpam-700	102	25	bd	bd	NOUN
ejpam-700	102	26	)	)	PUNCT
ejpam-700	102	27	n−2	n−2	PROPN
ejpam-700	102	28	∏	∏	PROPN
ejpam-700	102	29	i=0	i=0	PROPN
ejpam-700	102	30	(	(	PUNCT
ejpam-700	102	31	1	1	NUM
ejpam-700	102	32	+	+	CCONJ
ejpam-700	102	33	(	(	PUNCT
ejpam-700	102	34	2i+	2i+	NUM
ejpam-700	102	35	1)bd	1)bd	NUM
ejpam-700	102	36	)	)	PUNCT
ejpam-700	102	37	�	�	PROPN
ejpam-700	102	38	1	1	NUM
ejpam-700	102	39	+	+	NUM
ejpam-700	102	40	bd	bd	PROPN
ejpam-700	102	41	(	(	PUNCT
ejpam-700	102	42	1	1	NUM
ejpam-700	102	43	+	+	CCONJ
ejpam-700	102	44	(	(	PUNCT
ejpam-700	102	45	2n−	2n−	NUM
ejpam-700	102	46	2)bd	2)bd	NUM
ejpam-700	102	47	)	)	PUNCT
ejpam-700	102	48	�	�	NOUN
ejpam-700	103	1	=	=	PUNCT
ejpam-700	103	2	d	d	PROPN
ejpam-700	103	3	n−2	n−2	PROPN
ejpam-700	103	4	∏	∏	PROPN
ejpam-700	103	5	i=0	i=0	PROPN
ejpam-700	103	6	(	(	PUNCT
ejpam-700	103	7	1	1	NUM
ejpam-700	103	8	+	+	NUM
ejpam-700	103	9	2i	2i	NUM
ejpam-700	103	10	bd	bd	NOUN
ejpam-700	103	11	)	)	PUNCT
ejpam-700	103	12	n−2	n−2	PROPN
ejpam-700	103	13	∏	∏	PROPN
ejpam-700	103	14	i=0	i=0	PROPN
ejpam-700	103	15	(	(	PUNCT
ejpam-700	103	16	1	1	NUM
ejpam-700	103	17	+	+	CCONJ
ejpam-700	103	18	(	(	PUNCT
ejpam-700	103	19	2i+	2i+	NUM
ejpam-700	103	20	1)bd	1)bd	NUM
ejpam-700	103	21	)	)	PUNCT
ejpam-700	103	22	�	�	PROPN
ejpam-700	103	23	1	1	NUM
ejpam-700	103	24	+	+	NUM
ejpam-700	103	25	bd	bd	PROPN
ejpam-700	103	26	(	(	PUNCT
ejpam-700	103	27	1	1	NUM
ejpam-700	103	28	+	+	CCONJ
ejpam-700	103	29	(	(	PUNCT
ejpam-700	103	30	2n−	2n−	NUM
ejpam-700	103	31	2)bd	2)bd	NUM
ejpam-700	103	32	)	)	PUNCT
ejpam-700	103	33	�	�	PROPN
ejpam-700	103	34	(	(	PUNCT
ejpam-700	103	35	1	1	NUM
ejpam-700	103	36	+	+	CCONJ
ejpam-700	103	37	(	(	PUNCT
ejpam-700	103	38	2n−	2n−	NUM
ejpam-700	103	39	2)bd	2)bd	NUM
ejpam-700	103	40	)	)	PUNCT
ejpam-700	103	41	(	(	PUNCT
ejpam-700	103	42	1	1	NUM
ejpam-700	103	43	+	+	CCONJ
ejpam-700	103	44	(	(	PUNCT
ejpam-700	103	45	2n−	2n−	NUM
ejpam-700	103	46	2)bd	2)bd	NUM
ejpam-700	103	47	)	)	PUNCT
ejpam-700	103	48	=	=	SYM
ejpam-700	104	1	d	d	PROPN
ejpam-700	104	2	n−1	n−1	PROPN
ejpam-700	104	3	∏	∏	PROPN
ejpam-700	104	4	i=0	i=0	PROPN
ejpam-700	104	5	(	(	PUNCT
ejpam-700	104	6	1	1	NUM
ejpam-700	104	7	+	+	NUM
ejpam-700	104	8	2i	2i	NUM
ejpam-700	104	9	bd	bd	NOUN
ejpam-700	104	10	)	)	PUNCT
ejpam-700	104	11	n−2	n−2	PROPN
ejpam-700	104	12	∏	∏	PROPN
ejpam-700	104	13	i=0	i=0	PROPN
ejpam-700	104	14	(	(	PUNCT
ejpam-700	104	15	1	1	NUM
ejpam-700	104	16	+	+	CCONJ
ejpam-700	104	17	(	(	PUNCT
ejpam-700	104	18	2i+	2i+	NUM
ejpam-700	104	19	1)bd)((1	1)bd)((1	NUM
ejpam-700	104	20	+	+	SYM
ejpam-700	104	21	(	(	PUNCT
ejpam-700	104	22	2n−	2n−	PROPN
ejpam-700	104	23	2)bd)+	2)bd)+	NUM
ejpam-700	104	24	bd	bd	PROPN
ejpam-700	104	25	)	)	PUNCT
ejpam-700	104	26	=	=	PUNCT
ejpam-700	105	1	d	d	PROPN
ejpam-700	105	2	n−1	n−1	PROPN
ejpam-700	105	3	∏	∏	PROPN
ejpam-700	105	4	i=0	i=0	PROPN
ejpam-700	105	5	(	(	PUNCT
ejpam-700	105	6	1	1	NUM
ejpam-700	105	7	+	+	NUM
ejpam-700	105	8	2i	2i	NUM
ejpam-700	105	9	bd	bd	NOUN
ejpam-700	105	10	)	)	PUNCT
ejpam-700	105	11	n−2	n−2	PROPN
ejpam-700	105	12	∏	∏	PROPN
ejpam-700	105	13	i=0	i=0	PROPN
ejpam-700	105	14	(	(	PUNCT
ejpam-700	105	15	1	1	NUM
ejpam-700	105	16	+	+	CCONJ
ejpam-700	105	17	(	(	PUNCT
ejpam-700	105	18	2i+	2i+	NUM
ejpam-700	105	19	1)bd)(1	1)bd)(1	NUM
ejpam-700	105	20	+	+	SYM
ejpam-700	105	21	(	(	PUNCT
ejpam-700	105	22	2n−	2n−	PROPN
ejpam-700	105	23	1)bd	1)bd	NUM
ejpam-700	105	24	)	)	PUNCT
ejpam-700	105	25	.	.	PUNCT
ejpam-700	106	1	hence	hence	ADV
ejpam-700	106	2	,	,	PUNCT
ejpam-700	106	3	we	we	PRON
ejpam-700	106	4	have	have	VERB
ejpam-700	106	5	x4n−3	x4n−3	PROPN
ejpam-700	106	6	=	=	SYM
ejpam-700	107	1	d	d	PROPN
ejpam-700	107	2	n−1	n−1	PROPN
ejpam-700	107	3	∏	∏	PROPN
ejpam-700	107	4	i=0	i=0	PROPN
ejpam-700	107	5	(	(	PUNCT
ejpam-700	107	6	1	1	NUM
ejpam-700	107	7	+	+	NUM
ejpam-700	107	8	2i	2i	NUM
ejpam-700	107	9	bd	bd	NOUN
ejpam-700	107	10	)	)	PUNCT
ejpam-700	107	11	n−1	n−1	PROPN
ejpam-700	107	12	∏	∏	PROPN
ejpam-700	107	13	i=0	i=0	PROPN
ejpam-700	107	14	(	(	PUNCT
ejpam-700	107	15	1	1	NUM
ejpam-700	107	16	+	+	CCONJ
ejpam-700	107	17	(	(	PUNCT
ejpam-700	107	18	2i+	2i+	NUM
ejpam-700	107	19	1)bd	1)bd	NUM
ejpam-700	107	20	)	)	PUNCT
ejpam-700	107	21	.	.	PUNCT
ejpam-700	108	1	similarly	similarly	ADV
ejpam-700	108	2	one	one	PRON
ejpam-700	108	3	can	can	AUX
ejpam-700	108	4	prove	prove	VERB
ejpam-700	108	5	the	the	DET
ejpam-700	108	6	other	other	ADJ
ejpam-700	108	7	relations	relation	NOUN
ejpam-700	108	8	.	.	PUNCT
ejpam-700	109	1	the	the	DET
ejpam-700	109	2	proof	proof	NOUN
ejpam-700	109	3	is	be	AUX
ejpam-700	109	4	complete	complete	ADJ
ejpam-700	109	5	.	.	PUNCT
ejpam-700	110	1	theorem	theorem	ADJ
ejpam-700	110	2	2	2	NUM
ejpam-700	110	3	.	.	PUNCT
ejpam-700	111	1	eq	eq	NOUN
ejpam-700	111	2	.	.	PUNCT
ejpam-700	112	1	(	(	PUNCT
ejpam-700	112	2	3	3	X
ejpam-700	112	3	)	)	PUNCT
ejpam-700	112	4	has	have	VERB
ejpam-700	112	5	a	a	DET
ejpam-700	112	6	unique	unique	ADJ
ejpam-700	112	7	equilibrium	equilibrium	NOUN
ejpam-700	112	8	point	point	NOUN
ejpam-700	112	9	which	which	PRON
ejpam-700	112	10	is	be	AUX
ejpam-700	112	11	the	the	DET
ejpam-700	112	12	number	number	NOUN
ejpam-700	112	13	zero	zero	NUM
ejpam-700	112	14	.	.	PUNCT
ejpam-700	113	1	proof	proof	NOUN
ejpam-700	113	2	.	.	PUNCT
ejpam-700	114	1	for	for	ADP
ejpam-700	114	2	the	the	DET
ejpam-700	114	3	equilibrium	equilibrium	NOUN
ejpam-700	114	4	points	point	NOUN
ejpam-700	114	5	of	of	ADP
ejpam-700	114	6	eq	eq	PROPN
ejpam-700	114	7	.	.	PUNCT
ejpam-700	115	1	(	(	PUNCT
ejpam-700	115	2	3	3	NUM
ejpam-700	115	3	)	)	PUNCT
ejpam-700	115	4	,	,	PUNCT
ejpam-700	115	5	we	we	PRON
ejpam-700	115	6	can	can	AUX
ejpam-700	115	7	write	write	VERB
ejpam-700	115	8	x	x	X
ejpam-700	116	1	=	=	SYM
ejpam-700	116	2	x	x	SYM
ejpam-700	116	3	1	1	NUM
ejpam-700	116	4	+	+	NUM
ejpam-700	116	5	x2	x2	NOUN
ejpam-700	116	6	.	.	PUNCT
ejpam-700	117	1	then	then	ADV
ejpam-700	117	2	x	x	X
ejpam-700	118	1	+	+	PUNCT
ejpam-700	119	1	x3	x3	ADJ
ejpam-700	119	2	=	=	SYM
ejpam-700	119	3	x	x	X
ejpam-700	119	4	,	,	PUNCT
ejpam-700	119	5	or	or	CCONJ
ejpam-700	119	6	,	,	PUNCT
ejpam-700	119	7	x3	x3	VERB
ejpam-700	119	8	=	=	SYM
ejpam-700	119	9	0	0	NUM
ejpam-700	119	10	.	.	PUNCT
ejpam-700	120	1	thus	thus	ADV
ejpam-700	120	2	the	the	DET
ejpam-700	120	3	equilibrium	equilibrium	NOUN
ejpam-700	120	4	point	point	NOUN
ejpam-700	120	5	of	of	ADP
ejpam-700	120	6	eq	eq	PROPN
ejpam-700	120	7	.	.	PUNCT
ejpam-700	121	1	(	(	PUNCT
ejpam-700	121	2	3	3	X
ejpam-700	121	3	)	)	PUNCT
ejpam-700	121	4	is	be	AUX
ejpam-700	121	5	x	x	X
ejpam-700	121	6	=	=	SYM
ejpam-700	121	7	0	0	PROPN
ejpam-700	121	8	.	.	PUNCT
ejpam-700	122	1	e.	e.	PROPN
ejpam-700	122	2	elsayed	elsayed	PROPN
ejpam-700	122	3	/	/	SYM
ejpam-700	122	4	eur	eur	PROPN
ejpam-700	122	5	.	.	PUNCT
ejpam-700	123	1	j.	j.	PROPN
ejpam-700	123	2	pure	pure	PROPN
ejpam-700	123	3	appl	appl	PROPN
ejpam-700	123	4	.	.	PROPN
ejpam-700	123	5	math	math	PROPN
ejpam-700	123	6	,	,	PUNCT
ejpam-700	123	7	4	4	NUM
ejpam-700	123	8	(	(	PUNCT
ejpam-700	123	9	2011	2011	NUM
ejpam-700	123	10	)	)	PUNCT
ejpam-700	123	11	,	,	PUNCT
ejpam-700	123	12	287	287	NUM
ejpam-700	123	13	-	-	SYM
ejpam-700	123	14	303	303	NUM
ejpam-700	123	15	292	292	NUM
ejpam-700	123	16	theorem	theorem	NOUN
ejpam-700	123	17	3	3	NUM
ejpam-700	123	18	.	.	PUNCT
ejpam-700	124	1	every	every	DET
ejpam-700	124	2	positive	positive	ADJ
ejpam-700	124	3	solution	solution	NOUN
ejpam-700	124	4	of	of	ADP
ejpam-700	124	5	eq	eq	PROPN
ejpam-700	124	6	.	.	PUNCT
ejpam-700	125	1	(	(	PUNCT
ejpam-700	125	2	3	3	X
ejpam-700	125	3	)	)	PUNCT
ejpam-700	125	4	is	be	AUX
ejpam-700	125	5	bounded	bound	VERB
ejpam-700	125	6	and	and	CCONJ
ejpam-700	125	7	lim	lim	PROPN
ejpam-700	125	8	n→∞xn	n→∞xn	PROPN
ejpam-700	125	9	=	=	SYM
ejpam-700	126	1	0	0	X
ejpam-700	126	2	.	.	PUNCT
ejpam-700	127	1	proof	proof	NOUN
ejpam-700	127	2	.	.	PUNCT
ejpam-700	128	1	it	it	PRON
ejpam-700	128	2	follows	follow	VERB
ejpam-700	128	3	from	from	ADP
ejpam-700	128	4	eq	eq	ADP
ejpam-700	128	5	.	.	PUNCT
ejpam-700	129	1	(	(	PUNCT
ejpam-700	129	2	3	3	NUM
ejpam-700	129	3	)	)	PUNCT
ejpam-700	129	4	that	that	PRON
ejpam-700	129	5	xn+1	xn+1	VERB
ejpam-700	130	1	=	=	SYM
ejpam-700	130	2	xn−3	xn−3	PROPN
ejpam-700	130	3	1	1	NUM
ejpam-700	130	4	+	+	CCONJ
ejpam-700	130	5	xn−1	xn−1	PROPN
ejpam-700	130	6	xn−3	xn−3	PROPN
ejpam-700	130	7	≤	≤	PROPN
ejpam-700	130	8	xn−3	xn−3	PROPN
ejpam-700	130	9	.	.	PUNCT
ejpam-700	131	1	then	then	ADV
ejpam-700	131	2	the	the	DET
ejpam-700	131	3	subsequences	subsequence	NOUN
ejpam-700	131	4	{	{	PUNCT
ejpam-700	131	5	x4n−3}∞n=0	x4n−3}∞n=0	PROPN
ejpam-700	131	6	,	,	PUNCT
ejpam-700	131	7	{	{	PUNCT
ejpam-700	131	8	x4n−2}∞n=0	x4n−2}∞n=0	PROPN
ejpam-700	131	9	,	,	PUNCT
ejpam-700	131	10	{	{	PUNCT
ejpam-700	131	11	x4n−1}∞n=0	x4n−1}∞n=0	PROPN
ejpam-700	131	12	,	,	PUNCT
ejpam-700	131	13	{	{	PUNCT
ejpam-700	131	14	x4n}∞n=0	x4n}∞n=0	PROPN
ejpam-700	131	15	are	be	AUX
ejpam-700	131	16	decreasing	decrease	VERB
ejpam-700	131	17	and	and	CCONJ
ejpam-700	131	18	so	so	ADV
ejpam-700	131	19	are	be	AUX
ejpam-700	131	20	bounded	bound	VERB
ejpam-700	131	21	from	from	ADP
ejpam-700	131	22	above	above	ADV
ejpam-700	131	23	by	by	ADP
ejpam-700	131	24	m	m	NOUN
ejpam-700	131	25	=	=	NOUN
ejpam-700	131	26	max{x−3	max{x−3	NOUN
ejpam-700	131	27	,	,	PUNCT
ejpam-700	131	28	x−2	x−2	PROPN
ejpam-700	131	29	,	,	PUNCT
ejpam-700	131	30	x−1	x−1	PROPN
ejpam-700	131	31	,	,	PUNCT
ejpam-700	131	32	x0	x0	PROPN
ejpam-700	131	33	}	}	PUNCT
ejpam-700	131	34	.	.	PUNCT
ejpam-700	132	1	lemma	lemma	PROPN
ejpam-700	132	2	1	1	NUM
ejpam-700	132	3	.	.	PUNCT
ejpam-700	133	1	eq	eq	NOUN
ejpam-700	133	2	.	.	PUNCT
ejpam-700	134	1	(	(	PUNCT
ejpam-700	134	2	3	3	X
ejpam-700	134	3	)	)	PUNCT
ejpam-700	134	4	has	have	VERB
ejpam-700	134	5	no	no	DET
ejpam-700	134	6	prime	prime	ADJ
ejpam-700	134	7	period	period	NOUN
ejpam-700	134	8	two	two	NUM
ejpam-700	134	9	solution	solution	NOUN
ejpam-700	134	10	.	.	PUNCT
ejpam-700	135	1	numerical	numerical	ADJ
ejpam-700	135	2	examples	example	NOUN
ejpam-700	135	3	for	for	ADP
ejpam-700	135	4	confirming	confirm	VERB
ejpam-700	135	5	the	the	DET
ejpam-700	135	6	results	result	NOUN
ejpam-700	135	7	of	of	ADP
ejpam-700	135	8	this	this	DET
ejpam-700	135	9	section	section	NOUN
ejpam-700	135	10	,	,	PUNCT
ejpam-700	135	11	we	we	PRON
ejpam-700	135	12	consider	consider	VERB
ejpam-700	135	13	numerical	numerical	ADJ
ejpam-700	135	14	examples	example	NOUN
ejpam-700	135	15	which	which	PRON
ejpam-700	135	16	represent	represent	VERB
ejpam-700	135	17	different	different	ADJ
ejpam-700	135	18	types	type	NOUN
ejpam-700	135	19	of	of	ADP
ejpam-700	135	20	solutions	solution	NOUN
ejpam-700	135	21	to	to	ADP
ejpam-700	135	22	eq	eq	PROPN
ejpam-700	135	23	.	.	PUNCT
ejpam-700	136	1	(	(	PUNCT
ejpam-700	136	2	3	3	NUM
ejpam-700	136	3	)	)	PUNCT
ejpam-700	136	4	.	.	PUNCT
ejpam-700	137	1	example	example	NOUN
ejpam-700	138	1	1	1	X
ejpam-700	138	2	.	.	X
ejpam-700	138	3	consider	consider	VERB
ejpam-700	138	4	x−3	x−3	NOUN
ejpam-700	138	5	=	=	NOUN
ejpam-700	138	6	4	4	NUM
ejpam-700	138	7	,	,	PUNCT
ejpam-700	138	8	x−2	x−2	PROPN
ejpam-700	138	9	=	=	NOUN
ejpam-700	138	10	9	9	NUM
ejpam-700	138	11	,	,	PUNCT
ejpam-700	138	12	x−1	x−1	PROPN
ejpam-700	139	1	=	=	NOUN
ejpam-700	139	2	6	6	NUM
ejpam-700	139	3	,	,	PUNCT
ejpam-700	139	4	x0	x0	PROPN
ejpam-700	139	5	=	=	PUNCT
ejpam-700	139	6	7	7	X
ejpam-700	139	7	.	.	X
ejpam-700	139	8	see	see	VERB
ejpam-700	139	9	fig	fig	NOUN
ejpam-700	139	10	.	.	PUNCT
ejpam-700	140	1	1	1	NUM
ejpam-700	140	2	.	.	SYM
ejpam-700	140	3	0	0	NUM
ejpam-700	141	1	5	5	NUM
ejpam-700	141	2	10	10	NUM
ejpam-700	141	3	15	15	NUM
ejpam-700	141	4	20	20	NUM
ejpam-700	141	5	25	25	NUM
ejpam-700	141	6	30	30	NUM
ejpam-700	141	7	35	35	NUM
ejpam-700	141	8	40	40	NUM
ejpam-700	141	9	45	45	NUM
ejpam-700	141	10	50	50	NUM
ejpam-700	141	11	0	0	NUM
ejpam-700	141	12	1	1	NUM
ejpam-700	141	13	2	2	NUM
ejpam-700	141	14	3	3	NUM
ejpam-700	141	15	4	4	NUM
ejpam-700	141	16	5	5	NUM
ejpam-700	141	17	6	6	NUM
ejpam-700	141	18	7	7	NUM
ejpam-700	141	19	8	8	NUM
ejpam-700	141	20	9	9	NUM
ejpam-700	141	21	n	n	NOUN
ejpam-700	141	22	x	x	PROPN
ejpam-700	141	23	(	(	PUNCT
ejpam-700	141	24	n	n	CCONJ
ejpam-700	141	25	)	)	PUNCT
ejpam-700	141	26	plot	plot	NOUN
ejpam-700	141	27	of	of	ADP
ejpam-700	141	28	x(n+1)=	x(n+1)=	PROPN
ejpam-700	141	29	(	(	PUNCT
ejpam-700	141	30	x(n−3)/(1+x(n−1)*x(n−3	x(n−3)/(1+x(n−1)*x(n−3	PROPN
ejpam-700	141	31	)	)	PUNCT
ejpam-700	141	32	)	)	PUNCT
ejpam-700	141	33	figure	figure	NOUN
ejpam-700	141	34	1	1	NUM
ejpam-700	141	35	example	example	NOUN
ejpam-700	141	36	2	2	NUM
ejpam-700	141	37	.	.	X
ejpam-700	142	1	see	see	VERB
ejpam-700	142	2	fig	fig	NOUN
ejpam-700	142	3	.	.	PUNCT
ejpam-700	143	1	2	2	NUM
ejpam-700	143	2	,	,	PUNCT
ejpam-700	143	3	since	since	SCONJ
ejpam-700	143	4	x−3	x−3	PROPN
ejpam-700	143	5	=	=	SYM
ejpam-700	143	6	1.4	1.4	NUM
ejpam-700	143	7	,	,	PUNCT
ejpam-700	143	8	x−2	x−2	PROPN
ejpam-700	143	9	=	=	PUNCT
ejpam-700	143	10	0.9	0.9	NUM
ejpam-700	143	11	,	,	PUNCT
ejpam-700	143	12	x−1	x−1	PUNCT
ejpam-700	143	13	=	=	NOUN
ejpam-700	143	14	0.6	0.6	NUM
ejpam-700	143	15	,	,	PUNCT
ejpam-700	144	1	x0	x0	PROPN
ejpam-700	144	2	=	=	PUNCT
ejpam-700	145	1	0.7	0.7	NUM
ejpam-700	145	2	.	.	PUNCT
ejpam-700	146	1	e.	e.	PROPN
ejpam-700	146	2	elsayed	elsayed	PROPN
ejpam-700	146	3	/	/	SYM
ejpam-700	146	4	eur	eur	PROPN
ejpam-700	146	5	.	.	PUNCT
ejpam-700	147	1	j.	j.	PROPN
ejpam-700	147	2	pure	pure	PROPN
ejpam-700	147	3	appl	appl	PROPN
ejpam-700	147	4	.	.	PROPN
ejpam-700	147	5	math	math	PROPN
ejpam-700	147	6	,	,	PUNCT
ejpam-700	147	7	4	4	NUM
ejpam-700	147	8	(	(	PUNCT
ejpam-700	147	9	2011	2011	NUM
ejpam-700	147	10	)	)	PUNCT
ejpam-700	147	11	,	,	PUNCT
ejpam-700	147	12	287	287	NUM
ejpam-700	147	13	-	-	SYM
ejpam-700	147	14	303	303	NUM
ejpam-700	147	15	293	293	NUM
ejpam-700	147	16	0	0	NUM
ejpam-700	147	17	5	5	NUM
ejpam-700	147	18	10	10	NUM
ejpam-700	147	19	15	15	NUM
ejpam-700	147	20	20	20	NUM
ejpam-700	147	21	25	25	NUM
ejpam-700	147	22	30	30	NUM
ejpam-700	147	23	35	35	NUM
ejpam-700	147	24	40	40	NUM
ejpam-700	147	25	45	45	NUM
ejpam-700	147	26	50	50	NUM
ejpam-700	147	27	0	0	NUM
ejpam-700	147	28	0.2	0.2	NUM
ejpam-700	147	29	0.4	0.4	NUM
ejpam-700	147	30	0.6	0.6	NUM
ejpam-700	147	31	0.8	0.8	NUM
ejpam-700	147	32	1	1	NUM
ejpam-700	147	33	1.2	1.2	NUM
ejpam-700	147	34	1.4	1.4	NUM
ejpam-700	147	35	n	n	NUM
ejpam-700	147	36	x	x	X
ejpam-700	147	37	(	(	PUNCT
ejpam-700	147	38	n	n	CCONJ
ejpam-700	147	39	)	)	PUNCT
ejpam-700	147	40	plot	plot	NOUN
ejpam-700	147	41	of	of	ADP
ejpam-700	147	42	x(n+1)=	x(n+1)=	PROPN
ejpam-700	147	43	(	(	PUNCT
ejpam-700	147	44	x(n−3)/(1+x(n−1)*x(n−3	x(n−3)/(1+x(n−1)*x(n−3	PROPN
ejpam-700	147	45	)	)	PUNCT
ejpam-700	147	46	)	)	PUNCT
ejpam-700	147	47	figure	figure	NOUN
ejpam-700	147	48	2	2	NUM
ejpam-700	147	49	3	3	NUM
ejpam-700	147	50	.	.	PUNCT
ejpam-700	148	1	on	on	ADP
ejpam-700	148	2	the	the	DET
ejpam-700	148	3	difference	difference	NOUN
ejpam-700	148	4	equation	equation	NOUN
ejpam-700	148	5	xn+1	xn+1	PROPN
ejpam-700	148	6	=	=	SYM
ejpam-700	148	7	xn−3	xn−3	PROPN
ejpam-700	148	8	1−	1−	NUM
ejpam-700	148	9	xn−1	xn−1	PROPN
ejpam-700	148	10	xn−3	xn−3	PROPN
ejpam-700	148	11	in	in	ADP
ejpam-700	148	12	this	this	DET
ejpam-700	148	13	section	section	NOUN
ejpam-700	148	14	we	we	PRON
ejpam-700	148	15	give	give	VERB
ejpam-700	148	16	a	a	DET
ejpam-700	148	17	specific	specific	ADJ
ejpam-700	148	18	form	form	NOUN
ejpam-700	148	19	of	of	ADP
ejpam-700	148	20	the	the	DET
ejpam-700	148	21	solutions	solution	NOUN
ejpam-700	148	22	of	of	ADP
ejpam-700	148	23	the	the	DET
ejpam-700	148	24	difference	difference	NOUN
ejpam-700	148	25	equation	equation	NOUN
ejpam-700	148	26	xn+1	xn+1	PROPN
ejpam-700	149	1	=	=	SYM
ejpam-700	149	2	xn−3	xn−3	PROPN
ejpam-700	149	3	1−	1−	NUM
ejpam-700	149	4	xn−1	xn−1	PROPN
ejpam-700	149	5	xn−3	xn−3	PROPN
ejpam-700	149	6	,	,	PUNCT
ejpam-700	149	7	n=	n=	ADJ
ejpam-700	149	8	0,1	0,1	NUM
ejpam-700	149	9	,	,	PUNCT
ejpam-700	149	10	.	.	PUNCT
ejpam-700	149	11	.	.	PUNCT
ejpam-700	149	12	.	.	PUNCT
ejpam-700	150	1	,	,	PUNCT
ejpam-700	150	2	(	(	PUNCT
ejpam-700	150	3	4	4	X
ejpam-700	150	4	)	)	PUNCT
ejpam-700	150	5	where	where	SCONJ
ejpam-700	150	6	the	the	DET
ejpam-700	150	7	initial	initial	ADJ
ejpam-700	150	8	conditions	condition	NOUN
ejpam-700	150	9	are	be	AUX
ejpam-700	150	10	arbitrary	arbitrary	ADJ
ejpam-700	150	11	nonzero	nonzero	ADJ
ejpam-700	150	12	positive	positive	ADJ
ejpam-700	150	13	real	real	ADJ
ejpam-700	150	14	numbers	number	NOUN
ejpam-700	150	15	.	.	PUNCT
ejpam-700	151	1	theorem	theorem	ADJ
ejpam-700	151	2	4	4	NUM
ejpam-700	151	3	.	.	PUNCT
ejpam-700	152	1	let	let	VERB
ejpam-700	152	2	{	{	PUNCT
ejpam-700	152	3	xn}∞n=−3	xn}∞n=−3	AUX
ejpam-700	152	4	be	be	AUX
ejpam-700	152	5	a	a	DET
ejpam-700	152	6	solution	solution	NOUN
ejpam-700	152	7	of	of	ADP
ejpam-700	152	8	eq	eq	PROPN
ejpam-700	152	9	.	.	PUNCT
ejpam-700	153	1	(	(	PUNCT
ejpam-700	153	2	4	4	NUM
ejpam-700	153	3	)	)	PUNCT
ejpam-700	153	4	.	.	PUNCT
ejpam-700	154	1	then	then	ADV
ejpam-700	154	2	for	for	ADP
ejpam-700	154	3	n=	n=	ADJ
ejpam-700	154	4	0,1	0,1	NUM
ejpam-700	154	5	,	,	PUNCT
ejpam-700	154	6	.	.	PUNCT
ejpam-700	154	7	.	.	PUNCT
ejpam-700	154	8	.	.	PUNCT
ejpam-700	155	1	x4n−3	x4n−3	PROPN
ejpam-700	156	1	=	=	PUNCT
ejpam-700	156	2	d	d	PROPN
ejpam-700	156	3	n−1	n−1	PROPN
ejpam-700	156	4	∏	∏	PROPN
ejpam-700	156	5	i=0	i=0	PROPN
ejpam-700	156	6	(	(	PUNCT
ejpam-700	156	7	1−	1−	NUM
ejpam-700	156	8	2i	2i	NUM
ejpam-700	156	9	bd	bd	PROPN
ejpam-700	156	10	)	)	PUNCT
ejpam-700	156	11	n−1	n−1	PROPN
ejpam-700	156	12	∏	∏	PROPN
ejpam-700	156	13	i=0	i=0	PROPN
ejpam-700	156	14	(	(	PUNCT
ejpam-700	156	15	1−	1−	NUM
ejpam-700	156	16	(	(	PUNCT
ejpam-700	156	17	2i	2i	NOUN
ejpam-700	156	18	+	+	CCONJ
ejpam-700	156	19	1)bd	1)bd	NUM
ejpam-700	156	20	)	)	PUNCT
ejpam-700	156	21	,	,	PUNCT
ejpam-700	156	22	x4n−1	x4n−1	PROPN
ejpam-700	157	1	=	=	SYM
ejpam-700	157	2	b	b	PROPN
ejpam-700	157	3	n−1	n−1	PROPN
ejpam-700	157	4	∏	∏	PROPN
ejpam-700	157	5	i=0	i=0	PROPN
ejpam-700	157	6	(	(	PUNCT
ejpam-700	157	7	1−	1−	NUM
ejpam-700	157	8	(	(	PUNCT
ejpam-700	157	9	2i+	2i+	NUM
ejpam-700	157	10	1)bd	1)bd	NUM
ejpam-700	157	11	)	)	PUNCT
ejpam-700	157	12	n−1	n−1	PROPN
ejpam-700	157	13	∏	∏	PROPN
ejpam-700	157	14	i=0	i=0	PROPN
ejpam-700	157	15	(	(	PUNCT
ejpam-700	157	16	1−	1−	NUM
ejpam-700	157	17	(	(	PUNCT
ejpam-700	157	18	2i+	2i+	NUM
ejpam-700	157	19	2)bd	2)bd	NUM
ejpam-700	157	20	)	)	PUNCT
ejpam-700	157	21	,	,	PUNCT
ejpam-700	157	22	x4n−2	x4n−2	PROPN
ejpam-700	157	23	=	=	SYM
ejpam-700	158	1	c	c	PROPN
ejpam-700	158	2	n−1	n−1	PROPN
ejpam-700	158	3	∏	∏	PROPN
ejpam-700	158	4	i=0	i=0	PROPN
ejpam-700	158	5	(	(	PUNCT
ejpam-700	158	6	1−	1−	NUM
ejpam-700	158	7	2iac	2iac	NUM
ejpam-700	158	8	)	)	PUNCT
ejpam-700	158	9	n−1	n−1	PROPN
ejpam-700	158	10	∏	∏	PROPN
ejpam-700	158	11	i=0	i=0	PROPN
ejpam-700	158	12	(	(	PUNCT
ejpam-700	158	13	1−	1−	NUM
ejpam-700	158	14	(	(	PUNCT
ejpam-700	158	15	2i	2i	NOUN
ejpam-700	158	16	+	+	X
ejpam-700	158	17	1)ac	1)ac	NUM
ejpam-700	158	18	)	)	PUNCT
ejpam-700	158	19	,	,	PUNCT
ejpam-700	158	20	x4n	x4n	PUNCT
ejpam-700	158	21	=	=	PUNCT
ejpam-700	159	1	a	a	DET
ejpam-700	159	2	n−1	n−1	PROPN
ejpam-700	159	3	∏	∏	PROPN
ejpam-700	159	4	i=0	i=0	PROPN
ejpam-700	159	5	(	(	PUNCT
ejpam-700	159	6	1−	1−	NUM
ejpam-700	159	7	(	(	PUNCT
ejpam-700	159	8	2i+	2i+	NUM
ejpam-700	159	9	1)ac	1)ac	NUM
ejpam-700	159	10	)	)	PUNCT
ejpam-700	159	11	n−1	n−1	PROPN
ejpam-700	159	12	∏	∏	PROPN
ejpam-700	159	13	i=0	i=0	PROPN
ejpam-700	159	14	(	(	PUNCT
ejpam-700	159	15	1−	1−	NUM
ejpam-700	159	16	(	(	PUNCT
ejpam-700	159	17	2i+	2i+	NUM
ejpam-700	159	18	2)ac	2)ac	NUM
ejpam-700	159	19	)	)	PUNCT
ejpam-700	159	20	,	,	PUNCT
ejpam-700	159	21	where	where	SCONJ
ejpam-700	159	22	x−3	x−3	PROPN
ejpam-700	159	23	=	=	SYM
ejpam-700	159	24	d	d	PROPN
ejpam-700	159	25	,	,	PUNCT
ejpam-700	159	26	x−2	x−2	PROPN
ejpam-700	159	27	=	=	SYM
ejpam-700	159	28	c	c	X
ejpam-700	159	29	,	,	PUNCT
ejpam-700	159	30	x−1	x−1	PUNCT
ejpam-700	159	31	=	=	SYM
ejpam-700	159	32	b	b	PROPN
ejpam-700	159	33	,	,	PUNCT
ejpam-700	159	34	x−0	x−0	PROPN
ejpam-700	159	35	=	=	PUNCT
ejpam-700	160	1	a	a	PRON
ejpam-700	160	2	,	,	PUNCT
ejpam-700	160	3	−1	−1	NOUN
ejpam-700	160	4	∏	∏	PROPN
ejpam-700	160	5	i=0	i=0	PROPN
ejpam-700	160	6	ai	ai	VERB
ejpam-700	160	7	=	=	SYM
ejpam-700	160	8	1	1	NUM
ejpam-700	160	9	and	and	CCONJ
ejpam-700	160	10	jbd	jbd	NOUN
ejpam-700	160	11	6=	6=	ADP
ejpam-700	160	12	1	1	NUM
ejpam-700	160	13	jac	jac	PROPN
ejpam-700	160	14	6=	6=	ADP
ejpam-700	160	15	1	1	NUM
ejpam-700	160	16	for	for	ADP
ejpam-700	160	17	j	j	PROPN
ejpam-700	160	18	=	=	SYM
ejpam-700	160	19	1,2,3	1,2,3	NUM
ejpam-700	160	20	,	,	PUNCT
ejpam-700	160	21	.	.	PUNCT
ejpam-700	160	22	.	.	PUNCT
ejpam-700	161	1	..	..	PUNCT
ejpam-700	161	2	proof	proof	NOUN
ejpam-700	161	3	.	.	PUNCT
ejpam-700	162	1	as	as	ADP
ejpam-700	162	2	the	the	DET
ejpam-700	162	3	proof	proof	NOUN
ejpam-700	162	4	of	of	ADP
ejpam-700	162	5	theorem	theorem	NOUN
ejpam-700	162	6	1	1	NUM
ejpam-700	162	7	.	.	PUNCT
ejpam-700	162	8	e.	e.	PROPN
ejpam-700	162	9	elsayed	elsayed	PROPN
ejpam-700	162	10	/	/	SYM
ejpam-700	162	11	eur	eur	PROPN
ejpam-700	162	12	.	.	PUNCT
ejpam-700	163	1	j.	j.	PROPN
ejpam-700	163	2	pure	pure	PROPN
ejpam-700	163	3	appl	appl	PROPN
ejpam-700	163	4	.	.	PROPN
ejpam-700	163	5	math	math	PROPN
ejpam-700	163	6	,	,	PUNCT
ejpam-700	163	7	4	4	NUM
ejpam-700	163	8	(	(	PUNCT
ejpam-700	163	9	2011	2011	NUM
ejpam-700	163	10	)	)	PUNCT
ejpam-700	163	11	,	,	PUNCT
ejpam-700	163	12	287	287	NUM
ejpam-700	163	13	-	-	SYM
ejpam-700	163	14	303	303	NUM
ejpam-700	163	15	294	294	NUM
ejpam-700	163	16	theorem	theorem	VERB
ejpam-700	163	17	5	5	NUM
ejpam-700	163	18	.	.	PUNCT
ejpam-700	164	1	eq	eq	NOUN
ejpam-700	164	2	.	.	PUNCT
ejpam-700	165	1	(	(	PUNCT
ejpam-700	165	2	4	4	X
ejpam-700	165	3	)	)	PUNCT
ejpam-700	165	4	has	have	VERB
ejpam-700	165	5	a	a	DET
ejpam-700	165	6	unique	unique	ADJ
ejpam-700	165	7	equilibrium	equilibrium	NOUN
ejpam-700	165	8	point	point	NOUN
ejpam-700	165	9	which	which	PRON
ejpam-700	165	10	is	be	AUX
ejpam-700	165	11	the	the	DET
ejpam-700	165	12	number	number	NOUN
ejpam-700	165	13	zero	zero	NUM
ejpam-700	165	14	.	.	PUNCT
ejpam-700	166	1	proof	proof	NOUN
ejpam-700	166	2	.	.	PUNCT
ejpam-700	167	1	as	as	SCONJ
ejpam-700	167	2	the	the	DET
ejpam-700	167	3	proof	proof	NOUN
ejpam-700	167	4	of	of	ADP
ejpam-700	167	5	theorem	theorem	NOUN
ejpam-700	167	6	2	2	NUM
ejpam-700	167	7	.	.	NOUN
ejpam-700	167	8	numerical	numerical	ADJ
ejpam-700	167	9	examples	example	NOUN
ejpam-700	167	10	example	example	NOUN
ejpam-700	167	11	3	3	X
ejpam-700	167	12	.	.	X
ejpam-700	167	13	consider	consider	VERB
ejpam-700	167	14	x−3	x−3	NOUN
ejpam-700	167	15	=	=	PUNCT
ejpam-700	167	16	0.7	0.7	NUM
ejpam-700	167	17	,	,	PUNCT
ejpam-700	168	1	x−2	x−2	PROPN
ejpam-700	168	2	=	=	SYM
ejpam-700	168	3	0.5	0.5	NUM
ejpam-700	168	4	,	,	PUNCT
ejpam-700	168	5	x−1	x−1	PROPN
ejpam-700	169	1	=	=	PROPN
ejpam-700	169	2	3	3	NUM
ejpam-700	169	3	,	,	PUNCT
ejpam-700	169	4	x0	x0	PROPN
ejpam-700	169	5	=	=	PUNCT
ejpam-700	170	1	4	4	X
ejpam-700	170	2	.	.	X
ejpam-700	170	3	see	see	VERB
ejpam-700	170	4	fig	fig	NOUN
ejpam-700	170	5	.	.	PUNCT
ejpam-700	171	1	3	3	NUM
ejpam-700	171	2	.	.	NOUN
ejpam-700	171	3	0	0	NUM
ejpam-700	172	1	10	10	NUM
ejpam-700	172	2	20	20	NUM
ejpam-700	172	3	30	30	NUM
ejpam-700	172	4	40	40	NUM
ejpam-700	172	5	50	50	NUM
ejpam-700	172	6	60	60	NUM
ejpam-700	172	7	70	70	NUM
ejpam-700	172	8	80	80	NUM
ejpam-700	172	9	−1	−1	NOUN
ejpam-700	172	10	−0.5	−0.5	NOUN
ejpam-700	172	11	0	0	NUM
ejpam-700	172	12	0.5	0.5	NUM
ejpam-700	172	13	1	1	NUM
ejpam-700	172	14	1.5	1.5	NUM
ejpam-700	172	15	2	2	NUM
ejpam-700	172	16	2.5	2.5	NUM
ejpam-700	172	17	3	3	NUM
ejpam-700	172	18	3.5	3.5	NUM
ejpam-700	172	19	4	4	NUM
ejpam-700	172	20	n	n	NOUN
ejpam-700	172	21	x	x	X
ejpam-700	172	22	(	(	PUNCT
ejpam-700	172	23	n	n	CCONJ
ejpam-700	172	24	)	)	PUNCT
ejpam-700	172	25	plot	plot	NOUN
ejpam-700	172	26	of	of	ADP
ejpam-700	172	27	x(n+1)=	x(n+1)=	PROPN
ejpam-700	172	28	(	(	PUNCT
ejpam-700	172	29	x(n−3)/(1−x(n−1)*x(n−3	x(n−3)/(1−x(n−1)*x(n−3	PROPN
ejpam-700	172	30	)	)	PUNCT
ejpam-700	172	31	)	)	PUNCT
ejpam-700	172	32	figure	figure	VERB
ejpam-700	172	33	3	3	NUM
ejpam-700	172	34	example	example	NOUN
ejpam-700	172	35	4	4	NUM
ejpam-700	172	36	.	.	X
ejpam-700	173	1	see	see	VERB
ejpam-700	173	2	fig	fig	NOUN
ejpam-700	173	3	.	.	PUNCT
ejpam-700	174	1	4	4	NUM
ejpam-700	174	2	,	,	PUNCT
ejpam-700	174	3	since	since	SCONJ
ejpam-700	174	4	x−3	x−3	PROPN
ejpam-700	174	5	=	=	SYM
ejpam-700	174	6	7	7	PROPN
ejpam-700	174	7	,	,	PUNCT
ejpam-700	174	8	x−2	x−2	PROPN
ejpam-700	174	9	=	=	SYM
ejpam-700	174	10	11	11	NUM
ejpam-700	174	11	,	,	PUNCT
ejpam-700	174	12	x−1	x−1	PUNCT
ejpam-700	175	1	=	=	NOUN
ejpam-700	175	2	0.3	0.3	NUM
ejpam-700	175	3	,	,	PUNCT
ejpam-700	175	4	x0	x0	PROPN
ejpam-700	175	5	=	=	PUNCT
ejpam-700	175	6	4	4	NUM
ejpam-700	175	7	.	.	NOUN
ejpam-700	175	8	0	0	NUM
ejpam-700	175	9	10	10	NUM
ejpam-700	175	10	20	20	NUM
ejpam-700	175	11	30	30	NUM
ejpam-700	175	12	40	40	NUM
ejpam-700	175	13	50	50	NUM
ejpam-700	175	14	60	60	NUM
ejpam-700	175	15	70	70	NUM
ejpam-700	175	16	80	80	NUM
ejpam-700	175	17	−8	−8	NOUN
ejpam-700	176	1	−6	−6	NOUN
ejpam-700	177	1	−4	−4	X
ejpam-700	178	1	−2	−2	NOUN
ejpam-700	178	2	0	0	NUM
ejpam-700	178	3	2	2	NUM
ejpam-700	178	4	4	4	NUM
ejpam-700	178	5	6	6	NUM
ejpam-700	178	6	8	8	NUM
ejpam-700	178	7	10	10	NUM
ejpam-700	178	8	12	12	NUM
ejpam-700	178	9	n	n	NOUN
ejpam-700	178	10	x	x	PROPN
ejpam-700	178	11	(	(	PUNCT
ejpam-700	178	12	n	n	CCONJ
ejpam-700	178	13	)	)	PUNCT
ejpam-700	178	14	plot	plot	NOUN
ejpam-700	178	15	of	of	ADP
ejpam-700	178	16	x(n+1)=	x(n+1)=	PROPN
ejpam-700	178	17	(	(	PUNCT
ejpam-700	178	18	x(n−3)/(1−x(n−1)*x(n−3	x(n−3)/(1−x(n−1)*x(n−3	PROPN
ejpam-700	178	19	)	)	PUNCT
ejpam-700	178	20	)	)	PUNCT
ejpam-700	178	21	figure	figure	NOUN
ejpam-700	178	22	4	4	NUM
ejpam-700	178	23	e.	e.	PROPN
ejpam-700	178	24	elsayed	elsayed	PROPN
ejpam-700	178	25	/	/	SYM
ejpam-700	178	26	eur	eur	PROPN
ejpam-700	178	27	.	.	PUNCT
ejpam-700	179	1	j.	j.	PROPN
ejpam-700	179	2	pure	pure	PROPN
ejpam-700	179	3	appl	appl	PROPN
ejpam-700	179	4	.	.	PROPN
ejpam-700	179	5	math	math	PROPN
ejpam-700	179	6	,	,	PUNCT
ejpam-700	179	7	4	4	NUM
ejpam-700	179	8	(	(	PUNCT
ejpam-700	179	9	2011	2011	NUM
ejpam-700	179	10	)	)	PUNCT
ejpam-700	179	11	,	,	PUNCT
ejpam-700	179	12	287	287	NUM
ejpam-700	179	13	-	-	SYM
ejpam-700	179	14	303	303	NUM
ejpam-700	179	15	295	295	NUM
ejpam-700	179	16	4	4	NUM
ejpam-700	179	17	.	.	PUNCT
ejpam-700	180	1	on	on	ADP
ejpam-700	180	2	the	the	DET
ejpam-700	180	3	difference	difference	NOUN
ejpam-700	180	4	equation	equation	NOUN
ejpam-700	180	5	xn+1	xn+1	PROPN
ejpam-700	180	6	=	=	SYM
ejpam-700	180	7	xn−3	xn−3	PROPN
ejpam-700	180	8	−1	−1	NOUN
ejpam-700	180	9	+	+	CCONJ
ejpam-700	180	10	xn−1xn−3	xn−1xn−3	PUNCT
ejpam-700	180	11	in	in	ADP
ejpam-700	180	12	this	this	DET
ejpam-700	180	13	section	section	NOUN
ejpam-700	180	14	we	we	PRON
ejpam-700	180	15	investigate	investigate	VERB
ejpam-700	180	16	the	the	DET
ejpam-700	180	17	solutions	solution	NOUN
ejpam-700	180	18	of	of	ADP
ejpam-700	180	19	the	the	DET
ejpam-700	180	20	following	follow	VERB
ejpam-700	180	21	difference	difference	NOUN
ejpam-700	180	22	equation	equation	NOUN
ejpam-700	180	23	xn+1	xn+1	PROPN
ejpam-700	181	1	=	=	SYM
ejpam-700	181	2	xn−3	xn−3	PROPN
ejpam-700	181	3	−1	−1	NOUN
ejpam-700	181	4	+	+	ADP
ejpam-700	181	5	xn−1	xn−1	PROPN
ejpam-700	181	6	xn−3	xn−3	PROPN
ejpam-700	181	7	,	,	PUNCT
ejpam-700	181	8	n=	n=	ADJ
ejpam-700	181	9	0,1	0,1	NUM
ejpam-700	181	10	,	,	PUNCT
ejpam-700	181	11	.	.	PUNCT
ejpam-700	181	12	.	.	PUNCT
ejpam-700	181	13	.	.	PUNCT
ejpam-700	182	1	,	,	PUNCT
ejpam-700	182	2	(	(	PUNCT
ejpam-700	182	3	5	5	X
ejpam-700	182	4	)	)	PUNCT
ejpam-700	182	5	where	where	SCONJ
ejpam-700	182	6	the	the	DET
ejpam-700	182	7	initial	initial	ADJ
ejpam-700	182	8	conditions	condition	NOUN
ejpam-700	182	9	are	be	AUX
ejpam-700	182	10	arbitrary	arbitrary	ADJ
ejpam-700	182	11	non	non	ADJ
ejpam-700	182	12	zero	zero	NUM
ejpam-700	182	13	real	real	ADJ
ejpam-700	182	14	numbers	number	NOUN
ejpam-700	182	15	with	with	ADP
ejpam-700	182	16	x−3	x−3	PROPN
ejpam-700	182	17	x−1	x−1	PROPN
ejpam-700	183	1	6=	6=	ADP
ejpam-700	183	2	1	1	NUM
ejpam-700	183	3	,	,	PUNCT
ejpam-700	183	4	x−2	x−2	PROPN
ejpam-700	183	5	x0	x0	PROPN
ejpam-700	183	6	6=	6=	ADP
ejpam-700	183	7	1	1	NUM
ejpam-700	183	8	.	.	PUNCT
ejpam-700	184	1	theorem	theorem	NOUN
ejpam-700	184	2	6	6	NUM
ejpam-700	184	3	.	.	PUNCT
ejpam-700	185	1	let	let	VERB
ejpam-700	185	2	{	{	PUNCT
ejpam-700	185	3	xn}∞n=−3	xn}∞n=−3	AUX
ejpam-700	185	4	be	be	AUX
ejpam-700	185	5	a	a	DET
ejpam-700	185	6	solution	solution	NOUN
ejpam-700	185	7	of	of	ADP
ejpam-700	185	8	eq	eq	PROPN
ejpam-700	185	9	.	.	PUNCT
ejpam-700	186	1	(	(	PUNCT
ejpam-700	186	2	5	5	NUM
ejpam-700	186	3	)	)	PUNCT
ejpam-700	186	4	.	.	PUNCT
ejpam-700	187	1	then	then	ADV
ejpam-700	187	2	for	for	ADP
ejpam-700	187	3	n=	n=	ADJ
ejpam-700	187	4	0,1	0,1	NUM
ejpam-700	187	5	,	,	PUNCT
ejpam-700	187	6	.	.	PUNCT
ejpam-700	187	7	.	.	PUNCT
ejpam-700	187	8	.	.	PUNCT
ejpam-700	188	1	x4n−3	x4n−3	PROPN
ejpam-700	188	2	=	=	PUNCT
ejpam-700	188	3	d	d	PROPN
ejpam-700	188	4	(	(	PUNCT
ejpam-700	188	5	−1	−1	NOUN
ejpam-700	188	6	+	+	CCONJ
ejpam-700	188	7	bd)n	bd)n	NOUN
ejpam-700	188	8	,	,	PUNCT
ejpam-700	188	9	x4n−1	x4n−1	PROPN
ejpam-700	188	10	=	=	SYM
ejpam-700	188	11	b	b	PROPN
ejpam-700	188	12	(	(	PUNCT
ejpam-700	188	13	−1	−1	NOUN
ejpam-700	188	14	+	+	CCONJ
ejpam-700	188	15	bd)n	bd)n	NOUN
ejpam-700	188	16	,	,	PUNCT
ejpam-700	188	17	x4n−2	x4n−2	PROPN
ejpam-700	188	18	=	=	SYM
ejpam-700	188	19	c	c	PROPN
ejpam-700	188	20	(	(	PUNCT
ejpam-700	188	21	−1	−1	NOUN
ejpam-700	188	22	+	+	CCONJ
ejpam-700	188	23	ac)n	ac)n	PROPN
ejpam-700	188	24	,	,	PUNCT
ejpam-700	188	25	x4n	x4n	PROPN
ejpam-700	188	26	=	=	PUNCT
ejpam-700	188	27	a	a	DET
ejpam-700	188	28	(	(	PUNCT
ejpam-700	188	29	−1	−1	NOUN
ejpam-700	188	30	+	+	CCONJ
ejpam-700	188	31	ac)n	ac)n	NOUN
ejpam-700	188	32	,	,	PUNCT
ejpam-700	189	1	where	where	SCONJ
ejpam-700	189	2	x−3	x−3	PROPN
ejpam-700	189	3	=	=	SYM
ejpam-700	189	4	d	d	PROPN
ejpam-700	189	5	,	,	PUNCT
ejpam-700	189	6	x−2	x−2	PROPN
ejpam-700	189	7	=	=	SYM
ejpam-700	189	8	c	c	X
ejpam-700	189	9	,	,	PUNCT
ejpam-700	189	10	x−1	x−1	PUNCT
ejpam-700	189	11	=	=	SYM
ejpam-700	189	12	b	b	PROPN
ejpam-700	189	13	,	,	PUNCT
ejpam-700	189	14	x−0	x−0	PROPN
ejpam-700	189	15	=	=	NOUN
ejpam-700	189	16	a.	a.	NOUN
ejpam-700	189	17	proof	proof	NOUN
ejpam-700	189	18	.	.	PUNCT
ejpam-700	190	1	for	for	ADP
ejpam-700	190	2	n	n	NOUN
ejpam-700	190	3	=	=	SYM
ejpam-700	190	4	0	0	NOUN
ejpam-700	190	5	the	the	DET
ejpam-700	190	6	result	result	NOUN
ejpam-700	190	7	holds	hold	VERB
ejpam-700	190	8	.	.	PUNCT
ejpam-700	191	1	now	now	ADV
ejpam-700	191	2	suppose	suppose	VERB
ejpam-700	191	3	that	that	SCONJ
ejpam-700	191	4	n	n	PROPN
ejpam-700	191	5	>	>	X
ejpam-700	191	6	0	0	PUNCT
ejpam-700	192	1	and	and	CCONJ
ejpam-700	192	2	that	that	SCONJ
ejpam-700	192	3	our	our	PRON
ejpam-700	192	4	assumption	assumption	NOUN
ejpam-700	192	5	holds	hold	VERB
ejpam-700	192	6	for	for	ADP
ejpam-700	192	7	n−	n−	NOUN
ejpam-700	192	8	1	1	NUM
ejpam-700	192	9	.	.	PUNCT
ejpam-700	193	1	that	that	PRON
ejpam-700	193	2	is	be	AUX
ejpam-700	193	3	;	;	PUNCT
ejpam-700	193	4	x4n−7	x4n−7	PROPN
ejpam-700	193	5	=	=	PUNCT
ejpam-700	194	1	d	d	PROPN
ejpam-700	194	2	(	(	PUNCT
ejpam-700	194	3	−1	−1	NOUN
ejpam-700	194	4	+	+	X
ejpam-700	194	5	bd)n−1	bd)n−1	PRON
ejpam-700	194	6	,	,	PUNCT
ejpam-700	194	7	x4n−5	x4n−5	PROPN
ejpam-700	194	8	=	=	SYM
ejpam-700	194	9	b	b	PROPN
ejpam-700	194	10	(	(	PUNCT
ejpam-700	194	11	−1	−1	NOUN
ejpam-700	194	12	+	+	X
ejpam-700	194	13	bd)n−1	bd)n−1	PRON
ejpam-700	194	14	,	,	PUNCT
ejpam-700	194	15	x4n−6	x4n−6	PROPN
ejpam-700	194	16	=	=	PUNCT
ejpam-700	195	1	c	c	X
ejpam-700	195	2	(	(	PUNCT
ejpam-700	195	3	−1	−1	NOUN
ejpam-700	195	4	+	+	CCONJ
ejpam-700	195	5	ac)n−1	ac)n−1	ADJ
ejpam-700	195	6	,	,	PUNCT
ejpam-700	195	7	x4n−4	x4n−4	PROPN
ejpam-700	195	8	=	=	PUNCT
ejpam-700	195	9	a	a	DET
ejpam-700	195	10	(	(	PUNCT
ejpam-700	195	11	−1	−1	NOUN
ejpam-700	195	12	+	+	X
ejpam-700	195	13	ac)n−1	ac)n−1	ADJ
ejpam-700	195	14	.	.	PUNCT
ejpam-700	196	1	now	now	ADV
ejpam-700	196	2	,	,	PUNCT
ejpam-700	196	3	it	it	PRON
ejpam-700	196	4	follows	follow	VERB
ejpam-700	196	5	from	from	ADP
ejpam-700	196	6	eq.(5	eq.(5	NOUN
ejpam-700	196	7	)	)	PUNCT
ejpam-700	196	8	that	that	SCONJ
ejpam-700	196	9	x4n−3	x4n−3	PROPN
ejpam-700	196	10	=	=	SYM
ejpam-700	196	11	x4n−7	x4n−7	PROPN
ejpam-700	196	12	−1	−1	NOUN
ejpam-700	196	13	+	+	NUM
ejpam-700	197	1	x4n−5	x4n−5	PROPN
ejpam-700	197	2	x4n−7	x4n−7	PROPN
ejpam-700	198	1	=	=	PUNCT
ejpam-700	198	2	d	d	PROPN
ejpam-700	198	3	(	(	PUNCT
ejpam-700	198	4	−1	−1	NOUN
ejpam-700	198	5	+	+	X
ejpam-700	198	6	bd)n−1	bd)n−1	NUM
ejpam-700	198	7	−1	−1	NOUN
ejpam-700	198	8	+	+	SYM
ejpam-700	198	9	b	b	X
ejpam-700	198	10	(	(	PUNCT
ejpam-700	198	11	−1	−1	NOUN
ejpam-700	198	12	+	+	X
ejpam-700	198	13	bd)n−1	bd)n−1	ADJ
ejpam-700	198	14	d	d	NOUN
ejpam-700	198	15	(	(	PUNCT
ejpam-700	198	16	−1	−1	NOUN
ejpam-700	198	17	+	+	X
ejpam-700	198	18	bd)n−1	bd)n−1	X
ejpam-700	198	19	=	=	SYM
ejpam-700	198	20	d	d	NOUN
ejpam-700	198	21	(	(	PUNCT
ejpam-700	198	22	−1	−1	NOUN
ejpam-700	198	23	+	+	X
ejpam-700	198	24	bd)n−1	bd)n−1	PRON
ejpam-700	198	25	(	(	PUNCT
ejpam-700	198	26	−1	−1	NOUN
ejpam-700	198	27	+	+	CCONJ
ejpam-700	198	28	bd	bd	NOUN
ejpam-700	198	29	)	)	PUNCT
ejpam-700	198	30	.	.	PUNCT
ejpam-700	199	1	hence	hence	ADV
ejpam-700	199	2	,	,	PUNCT
ejpam-700	199	3	we	we	PRON
ejpam-700	199	4	have	have	VERB
ejpam-700	199	5	x4n−3	x4n−3	PROPN
ejpam-700	199	6	=	=	SYM
ejpam-700	199	7	d	d	PROPN
ejpam-700	199	8	(	(	PUNCT
ejpam-700	199	9	−1	−1	NOUN
ejpam-700	199	10	+	+	CCONJ
ejpam-700	199	11	bd)n	bd)n	NOUN
ejpam-700	199	12	.	.	PUNCT
ejpam-700	200	1	similarly	similarly	ADV
ejpam-700	200	2	x4n−2	x4n−2	PROPN
ejpam-700	200	3	=	=	SYM
ejpam-700	200	4	x4n−6	x4n−6	PROPN
ejpam-700	200	5	−1	−1	PROPN
ejpam-700	200	6	+	+	CCONJ
ejpam-700	200	7	x4n−4	x4n−4	PROPN
ejpam-700	200	8	x4n−6	x4n−6	PROPN
ejpam-700	201	1	=	=	PUNCT
ejpam-700	201	2	c	c	X
ejpam-700	201	3	(	(	PUNCT
ejpam-700	201	4	−1	−1	NOUN
ejpam-700	201	5	+	+	ADP
ejpam-700	201	6	ac)n−1	ac)n−1	ADP
ejpam-700	201	7	−1	−1	NOUN
ejpam-700	201	8	+	+	CCONJ
ejpam-700	201	9	a	a	DET
ejpam-700	201	10	(	(	PUNCT
ejpam-700	201	11	−1	−1	NOUN
ejpam-700	201	12	+	+	ADP
ejpam-700	201	13	ac)n−1	ac)n−1	PROPN
ejpam-700	201	14	c	c	NOUN
ejpam-700	201	15	(	(	PUNCT
ejpam-700	201	16	−1	−1	NOUN
ejpam-700	201	17	+	+	X
ejpam-700	201	18	ac)n−1	ac)n−1	X
ejpam-700	201	19	=	=	SYM
ejpam-700	201	20	c	c	X
ejpam-700	201	21	(	(	PUNCT
ejpam-700	201	22	−1	−1	NOUN
ejpam-700	201	23	+	+	X
ejpam-700	201	24	ac)n−1	ac)n−1	NUM
ejpam-700	201	25	(	(	PUNCT
ejpam-700	201	26	−1	−1	NOUN
ejpam-700	201	27	+	+	CCONJ
ejpam-700	201	28	ac	ac	NOUN
ejpam-700	201	29	)	)	PUNCT
ejpam-700	201	30	.	.	PUNCT
ejpam-700	202	1	e.	e.	PROPN
ejpam-700	202	2	elsayed	elsayed	PROPN
ejpam-700	202	3	/	/	SYM
ejpam-700	202	4	eur	eur	PROPN
ejpam-700	202	5	.	.	PUNCT
ejpam-700	203	1	j.	j.	PROPN
ejpam-700	203	2	pure	pure	PROPN
ejpam-700	203	3	appl	appl	PROPN
ejpam-700	203	4	.	.	PROPN
ejpam-700	203	5	math	math	PROPN
ejpam-700	203	6	,	,	PUNCT
ejpam-700	203	7	4	4	NUM
ejpam-700	203	8	(	(	PUNCT
ejpam-700	203	9	2011	2011	NUM
ejpam-700	203	10	)	)	PUNCT
ejpam-700	203	11	,	,	PUNCT
ejpam-700	203	12	287	287	NUM
ejpam-700	203	13	-	-	SYM
ejpam-700	203	14	303	303	NUM
ejpam-700	203	15	296	296	NUM
ejpam-700	203	16	hence	hence	ADV
ejpam-700	203	17	,	,	PUNCT
ejpam-700	203	18	we	we	PRON
ejpam-700	203	19	have	have	VERB
ejpam-700	203	20	x4n−3	x4n−3	PROPN
ejpam-700	203	21	=	=	SYM
ejpam-700	203	22	c	c	PROPN
ejpam-700	203	23	(	(	PUNCT
ejpam-700	203	24	−1	−1	NOUN
ejpam-700	203	25	+	+	CCONJ
ejpam-700	203	26	ac)n	ac)n	NOUN
ejpam-700	203	27	.	.	PUNCT
ejpam-700	204	1	similarly	similarly	ADV
ejpam-700	204	2	,	,	PUNCT
ejpam-700	204	3	one	one	PRON
ejpam-700	204	4	can	can	AUX
ejpam-700	204	5	easily	easily	ADV
ejpam-700	204	6	obtain	obtain	VERB
ejpam-700	204	7	the	the	DET
ejpam-700	204	8	other	other	ADJ
ejpam-700	204	9	relations	relation	NOUN
ejpam-700	204	10	.	.	PUNCT
ejpam-700	205	1	thus	thus	ADV
ejpam-700	205	2	,	,	PUNCT
ejpam-700	205	3	the	the	DET
ejpam-700	205	4	proof	proof	NOUN
ejpam-700	205	5	is	be	AUX
ejpam-700	205	6	completed	complete	VERB
ejpam-700	205	7	.	.	PUNCT
ejpam-700	206	1	theorem	theorem	VERB
ejpam-700	206	2	7	7	NUM
ejpam-700	206	3	.	.	PUNCT
ejpam-700	207	1	eq	eq	NOUN
ejpam-700	207	2	.	.	PUNCT
ejpam-700	208	1	(	(	PUNCT
ejpam-700	208	2	5	5	NUM
ejpam-700	208	3	)	)	PUNCT
ejpam-700	208	4	has	have	VERB
ejpam-700	208	5	three	three	NUM
ejpam-700	208	6	equilibrium	equilibrium	NOUN
ejpam-700	208	7	points	point	NOUN
ejpam-700	208	8	which	which	PRON
ejpam-700	208	9	are	be	AUX
ejpam-700	208	10	0	0	NUM
ejpam-700	208	11	,	,	PUNCT
ejpam-700	208	12	p	p	NOUN
ejpam-700	208	13	2	2	NUM
ejpam-700	208	14	,	,	PUNCT
ejpam-700	208	15	−p2	−p2	PROPN
ejpam-700	208	16	.	.	PUNCT
ejpam-700	209	1	proof	proof	NOUN
ejpam-700	209	2	.	.	PUNCT
ejpam-700	210	1	for	for	ADP
ejpam-700	210	2	the	the	DET
ejpam-700	210	3	equilibrium	equilibrium	NOUN
ejpam-700	210	4	points	point	NOUN
ejpam-700	210	5	of	of	ADP
ejpam-700	210	6	eq	eq	PROPN
ejpam-700	210	7	.	.	PUNCT
ejpam-700	211	1	(	(	PUNCT
ejpam-700	211	2	5	5	NUM
ejpam-700	211	3	)	)	PUNCT
ejpam-700	211	4	,	,	PUNCT
ejpam-700	211	5	we	we	PRON
ejpam-700	211	6	can	can	AUX
ejpam-700	211	7	write	write	VERB
ejpam-700	211	8	x	x	X
ejpam-700	212	1	=	=	PUNCT
ejpam-700	212	2	x	x	SYM
ejpam-700	212	3	−1	−1	NOUN
ejpam-700	212	4	+	+	CCONJ
ejpam-700	212	5	x2	x2	NOUN
ejpam-700	212	6	.	.	PUNCT
ejpam-700	213	1	thus	thus	ADV
ejpam-700	213	2	we	we	PRON
ejpam-700	213	3	have	have	VERB
ejpam-700	213	4	−x	−x	NOUN
ejpam-700	214	1	+	+	CCONJ
ejpam-700	214	2	x3	x3	ADJ
ejpam-700	214	3	=	=	SYM
ejpam-700	214	4	x	x	X
ejpam-700	214	5	,	,	PUNCT
ejpam-700	214	6	or	or	CCONJ
ejpam-700	214	7	,	,	PUNCT
ejpam-700	214	8	x(x2	x(x2	PROPN
ejpam-700	215	1	−	−	NOUN
ejpam-700	215	2	2	2	NUM
ejpam-700	215	3	)	)	PUNCT
ejpam-700	215	4	=	=	SYM
ejpam-700	215	5	0	0	X
ejpam-700	215	6	.	.	PUNCT
ejpam-700	216	1	thus	thus	ADV
ejpam-700	216	2	the	the	DET
ejpam-700	216	3	equilibrium	equilibrium	NOUN
ejpam-700	216	4	points	point	NOUN
ejpam-700	216	5	of	of	ADP
ejpam-700	216	6	eq	eq	PROPN
ejpam-700	216	7	.	.	PUNCT
ejpam-700	217	1	(	(	PUNCT
ejpam-700	217	2	5	5	X
ejpam-700	217	3	)	)	PUNCT
ejpam-700	217	4	are	be	AUX
ejpam-700	217	5	0	0	NUM
ejpam-700	217	6	,	,	PUNCT
ejpam-700	217	7	p	p	NOUN
ejpam-700	217	8	2	2	NUM
ejpam-700	217	9	,	,	PUNCT
ejpam-700	217	10	−p2	−p2	PROPN
ejpam-700	217	11	.	.	PUNCT
ejpam-700	218	1	theorem	theorem	VERB
ejpam-700	218	2	8	8	NUM
ejpam-700	218	3	.	.	PUNCT
ejpam-700	219	1	eq	eq	NOUN
ejpam-700	219	2	.	.	PUNCT
ejpam-700	220	1	(	(	PUNCT
ejpam-700	220	2	5	5	NUM
ejpam-700	220	3	)	)	PUNCT
ejpam-700	220	4	has	have	VERB
ejpam-700	220	5	a	a	DET
ejpam-700	220	6	periodic	periodic	ADJ
ejpam-700	220	7	solutions	solution	NOUN
ejpam-700	220	8	of	of	ADP
ejpam-700	220	9	period	period	NOUN
ejpam-700	221	1	four	four	NUM
ejpam-700	221	2	iff	iff	PROPN
ejpam-700	221	3	ac	ac	PROPN
ejpam-700	222	1	=	=	PUNCT
ejpam-700	223	1	bd	bd	PROPN
ejpam-700	224	1	=	=	SYM
ejpam-700	224	2	2	2	NUM
ejpam-700	225	1	and	and	CCONJ
ejpam-700	225	2	will	will	AUX
ejpam-700	225	3	be	be	AUX
ejpam-700	225	4	take	take	VERB
ejpam-700	225	5	the	the	DET
ejpam-700	225	6	form	form	NOUN
ejpam-700	225	7	{	{	PUNCT
ejpam-700	225	8	d	d	NOUN
ejpam-700	225	9	,	,	PUNCT
ejpam-700	225	10	c	c	X
ejpam-700	225	11	,	,	PUNCT
ejpam-700	225	12	b	b	NOUN
ejpam-700	225	13	,	,	PUNCT
ejpam-700	225	14	a	a	DET
ejpam-700	225	15	,	,	PUNCT
ejpam-700	225	16	d	d	X
ejpam-700	225	17	,	,	PUNCT
ejpam-700	225	18	c	c	X
ejpam-700	225	19	,	,	PUNCT
ejpam-700	225	20	b	b	NOUN
ejpam-700	225	21	,	,	PUNCT
ejpam-700	225	22	a	a	PRON
ejpam-700	225	23	,	,	PUNCT
ejpam-700	225	24	.	.	PUNCT
ejpam-700	225	25	.	.	PUNCT
ejpam-700	226	1	.	.	PUNCT
ejpam-700	226	2	}	}	PUNCT
ejpam-700	226	3	.	.	PUNCT
ejpam-700	227	1	proof	proof	NOUN
ejpam-700	227	2	.	.	PUNCT
ejpam-700	228	1	first	first	ADV
ejpam-700	228	2	suppose	suppose	VERB
ejpam-700	228	3	that	that	SCONJ
ejpam-700	228	4	there	there	PRON
ejpam-700	228	5	exists	exist	VERB
ejpam-700	228	6	a	a	DET
ejpam-700	228	7	prime	prime	ADJ
ejpam-700	228	8	period	period	NOUN
ejpam-700	228	9	four	four	NUM
ejpam-700	228	10	solution	solution	NOUN
ejpam-700	228	11	d	d	X
ejpam-700	228	12	,	,	PUNCT
ejpam-700	228	13	c	c	X
ejpam-700	228	14	,	,	PUNCT
ejpam-700	228	15	b	b	NOUN
ejpam-700	228	16	,	,	PUNCT
ejpam-700	228	17	a	a	DET
ejpam-700	228	18	,	,	PUNCT
ejpam-700	228	19	d	d	X
ejpam-700	228	20	,	,	PUNCT
ejpam-700	228	21	c	c	X
ejpam-700	228	22	,	,	PUNCT
ejpam-700	228	23	b	b	NOUN
ejpam-700	228	24	,	,	PUNCT
ejpam-700	228	25	a	a	PRON
ejpam-700	228	26	,	,	PUNCT
ejpam-700	228	27	.	.	PUNCT
ejpam-700	228	28	.	.	PUNCT
ejpam-700	228	29	.	.	PUNCT
ejpam-700	229	1	,	,	PUNCT
ejpam-700	229	2	of	of	ADP
ejpam-700	229	3	eq	eq	NOUN
ejpam-700	229	4	.	.	PUNCT
ejpam-700	230	1	(	(	PUNCT
ejpam-700	230	2	5	5	NUM
ejpam-700	230	3	)	)	PUNCT
ejpam-700	230	4	,	,	PUNCT
ejpam-700	230	5	we	we	PRON
ejpam-700	230	6	see	see	VERB
ejpam-700	230	7	from	from	ADP
ejpam-700	230	8	eq	eq	PROPN
ejpam-700	230	9	.	.	PUNCT
ejpam-700	231	1	(	(	PUNCT
ejpam-700	231	2	5	5	NUM
ejpam-700	231	3	)	)	PUNCT
ejpam-700	231	4	that	that	PRON
ejpam-700	232	1	d	d	NOUN
ejpam-700	232	2	=	=	SYM
ejpam-700	232	3	d	d	PROPN
ejpam-700	232	4	(	(	PUNCT
ejpam-700	232	5	−1	−1	NOUN
ejpam-700	232	6	+	+	CCONJ
ejpam-700	232	7	bd)n	bd)n	NOUN
ejpam-700	232	8	,	,	PUNCT
ejpam-700	232	9	b	b	X
ejpam-700	232	10	=	=	SYM
ejpam-700	232	11	b	b	PROPN
ejpam-700	232	12	(	(	PUNCT
ejpam-700	232	13	−1	−1	NOUN
ejpam-700	232	14	+	+	CCONJ
ejpam-700	232	15	bd)n	bd)n	NOUN
ejpam-700	232	16	,	,	PUNCT
ejpam-700	232	17	c	c	X
ejpam-700	232	18	=	=	SYM
ejpam-700	232	19	c	c	X
ejpam-700	232	20	(	(	PUNCT
ejpam-700	232	21	−1	−1	NOUN
ejpam-700	232	22	+	+	CCONJ
ejpam-700	232	23	ac)n	ac)n	NOUN
ejpam-700	232	24	,	,	PUNCT
ejpam-700	232	25	a	a	DET
ejpam-700	232	26	=	=	SYM
ejpam-700	232	27	a(−1	a(−1	PROPN
ejpam-700	232	28	+	+	PROPN
ejpam-700	232	29	ac)n	ac)n	PROPN
ejpam-700	232	30	,	,	PUNCT
ejpam-700	232	31	or	or	CCONJ
ejpam-700	232	32	,	,	PUNCT
ejpam-700	232	33	(	(	PUNCT
ejpam-700	232	34	−1	−1	NOUN
ejpam-700	232	35	+	+	SYM
ejpam-700	232	36	bd)n	bd)n	NOUN
ejpam-700	232	37	=	=	SYM
ejpam-700	232	38	1	1	NUM
ejpam-700	232	39	,	,	PUNCT
ejpam-700	232	40	(	(	PUNCT
ejpam-700	232	41	−1	−1	NOUN
ejpam-700	232	42	+	+	CCONJ
ejpam-700	232	43	ac)n	ac)n	NOUN
ejpam-700	232	44	=	=	SYM
ejpam-700	232	45	1	1	X
ejpam-700	232	46	.	.	PUNCT
ejpam-700	233	1	then	then	ADV
ejpam-700	233	2	bd	bd	PROPN
ejpam-700	233	3	=	=	ADJ
ejpam-700	233	4	2	2	NUM
ejpam-700	233	5	,	,	PUNCT
ejpam-700	233	6	ac	ac	PROPN
ejpam-700	233	7	=	=	SYM
ejpam-700	233	8	2	2	X
ejpam-700	233	9	.	.	X
ejpam-700	233	10	second	second	ADV
ejpam-700	233	11	suppose	suppose	VERB
ejpam-700	233	12	ac	ac	PROPN
ejpam-700	233	13	=	=	SYM
ejpam-700	233	14	2	2	NUM
ejpam-700	233	15	,	,	PUNCT
ejpam-700	233	16	bd	bd	PROPN
ejpam-700	234	1	=	=	NOUN
ejpam-700	234	2	2	2	X
ejpam-700	234	3	.	.	PUNCT
ejpam-700	235	1	then	then	ADV
ejpam-700	235	2	we	we	PRON
ejpam-700	235	3	see	see	VERB
ejpam-700	235	4	from	from	ADP
ejpam-700	235	5	eq	eq	PROPN
ejpam-700	235	6	.	.	PUNCT
ejpam-700	236	1	(	(	PUNCT
ejpam-700	236	2	5	5	NUM
ejpam-700	236	3	)	)	PUNCT
ejpam-700	237	1	that	that	DET
ejpam-700	237	2	x4n−3	x4n−3	PROPN
ejpam-700	237	3	=	=	SYM
ejpam-700	237	4	d	d	PROPN
ejpam-700	237	5	,	,	PUNCT
ejpam-700	237	6	x4n−2	x4n−2	PROPN
ejpam-700	237	7	=	=	SYM
ejpam-700	237	8	c	c	PROPN
ejpam-700	237	9	,	,	PUNCT
ejpam-700	237	10	x4n−1	x4n−1	PROPN
ejpam-700	237	11	=	=	SYM
ejpam-700	237	12	b	b	PROPN
ejpam-700	237	13	,	,	PUNCT
ejpam-700	237	14	x4n	x4n	PUNCT
ejpam-700	237	15	=	=	PUNCT
ejpam-700	237	16	a.	a.	NOUN
ejpam-700	237	17	thus	thus	ADV
ejpam-700	237	18	we	we	PRON
ejpam-700	237	19	have	have	VERB
ejpam-700	237	20	a	a	DET
ejpam-700	237	21	period	period	NOUN
ejpam-700	237	22	four	four	NUM
ejpam-700	237	23	solution	solution	NOUN
ejpam-700	237	24	and	and	CCONJ
ejpam-700	237	25	the	the	DET
ejpam-700	237	26	proof	proof	NOUN
ejpam-700	237	27	is	be	AUX
ejpam-700	237	28	complete	complete	ADJ
ejpam-700	237	29	.	.	PUNCT
ejpam-700	238	1	lemma	lemma	PROPN
ejpam-700	238	2	2	2	NUM
ejpam-700	238	3	.	.	PUNCT
ejpam-700	239	1	eq	eq	NOUN
ejpam-700	239	2	.	.	PUNCT
ejpam-700	240	1	(	(	PUNCT
ejpam-700	240	2	5	5	NUM
ejpam-700	240	3	)	)	PUNCT
ejpam-700	240	4	has	have	VERB
ejpam-700	240	5	no	no	DET
ejpam-700	240	6	prime	prime	ADJ
ejpam-700	240	7	period	period	NOUN
ejpam-700	240	8	two	two	NUM
ejpam-700	240	9	solution	solution	NOUN
ejpam-700	240	10	.	.	PUNCT
ejpam-700	241	1	lemma	lemma	PROPN
ejpam-700	241	2	3	3	X
ejpam-700	241	3	.	.	PROPN
ejpam-700	241	4	assume	assume	VERB
ejpam-700	241	5	that	that	SCONJ
ejpam-700	241	6	ac	ac	PROPN
ejpam-700	241	7	,	,	PUNCT
ejpam-700	241	8	bd	bd	PROPN
ejpam-700	241	9	6=	6=	NOUN
ejpam-700	241	10	1±	1±	NUM
ejpam-700	241	11	1	1	NUM
ejpam-700	241	12	.	.	PUNCT
ejpam-700	242	1	then	then	ADV
ejpam-700	242	2	eq	eq	ADP
ejpam-700	242	3	.	.	PUNCT
ejpam-700	243	1	(	(	PUNCT
ejpam-700	243	2	5	5	NUM
ejpam-700	243	3	)	)	PUNCT
ejpam-700	243	4	has	have	VERB
ejpam-700	243	5	unbounded	unbounded	ADJ
ejpam-700	243	6	solutions	solution	NOUN
ejpam-700	243	7	.	.	PUNCT
ejpam-700	244	1	e.	e.	PROPN
ejpam-700	244	2	elsayed	elsayed	PROPN
ejpam-700	244	3	/	/	SYM
ejpam-700	244	4	eur	eur	PROPN
ejpam-700	244	5	.	.	PUNCT
ejpam-700	245	1	j.	j.	PROPN
ejpam-700	245	2	pure	pure	PROPN
ejpam-700	245	3	appl	appl	PROPN
ejpam-700	245	4	.	.	PROPN
ejpam-700	245	5	math	math	PROPN
ejpam-700	245	6	,	,	PUNCT
ejpam-700	245	7	4	4	NUM
ejpam-700	245	8	(	(	PUNCT
ejpam-700	245	9	2011	2011	NUM
ejpam-700	245	10	)	)	PUNCT
ejpam-700	245	11	,	,	PUNCT
ejpam-700	245	12	287	287	NUM
ejpam-700	245	13	-	-	SYM
ejpam-700	245	14	303	303	NUM
ejpam-700	245	15	297	297	NUM
ejpam-700	245	16	numerical	numerical	ADJ
ejpam-700	245	17	examples	example	NOUN
ejpam-700	245	18	example	example	NOUN
ejpam-700	246	1	5	5	X
ejpam-700	246	2	.	.	X
ejpam-700	246	3	we	we	PRON
ejpam-700	246	4	consider	consider	VERB
ejpam-700	246	5	x−3	x−3	NOUN
ejpam-700	246	6	=	=	PUNCT
ejpam-700	246	7	0.4	0.4	NUM
ejpam-700	246	8	,	,	PUNCT
ejpam-700	246	9	x−2	x−2	PROPN
ejpam-700	246	10	=	=	PUNCT
ejpam-700	246	11	0.9	0.9	NUM
ejpam-700	246	12	,	,	PUNCT
ejpam-700	246	13	x−1	x−1	PUNCT
ejpam-700	247	1	=	=	PROPN
ejpam-700	247	2	0.16	0.16	NUM
ejpam-700	247	3	,	,	PUNCT
ejpam-700	247	4	x0	x0	PROPN
ejpam-700	247	5	=	=	PUNCT
ejpam-700	247	6	1.7	1.7	NUM
ejpam-700	247	7	.	.	PUNCT
ejpam-700	248	1	see	see	VERB
ejpam-700	248	2	fig	fig	NOUN
ejpam-700	248	3	.	.	PUNCT
ejpam-700	249	1	5	5	NUM
ejpam-700	249	2	.	.	NOUN
ejpam-700	249	3	0	0	NUM
ejpam-700	250	1	10	10	NUM
ejpam-700	250	2	20	20	NUM
ejpam-700	250	3	30	30	NUM
ejpam-700	250	4	40	40	NUM
ejpam-700	250	5	50	50	NUM
ejpam-700	250	6	60	60	NUM
ejpam-700	250	7	70	70	NUM
ejpam-700	250	8	−0.5	−0.5	NOUN
ejpam-700	250	9	0	0	NUM
ejpam-700	250	10	0.5	0.5	NUM
ejpam-700	250	11	1	1	NUM
ejpam-700	250	12	1.5	1.5	NUM
ejpam-700	250	13	2	2	NUM
ejpam-700	250	14	2.5	2.5	NUM
ejpam-700	250	15	3	3	NUM
ejpam-700	250	16	3.5	3.5	NUM
ejpam-700	250	17	4	4	NUM
ejpam-700	250	18	4.5	4.5	NUM
ejpam-700	250	19	x	x	SYM
ejpam-700	250	20	10	10	NUM
ejpam-700	250	21	4	4	NUM
ejpam-700	250	22	n	n	NOUN
ejpam-700	250	23	x	x	X
ejpam-700	250	24	(	(	PUNCT
ejpam-700	250	25	n	n	CCONJ
ejpam-700	250	26	)	)	PUNCT
ejpam-700	250	27	plot	plot	NOUN
ejpam-700	250	28	of	of	ADP
ejpam-700	250	29	x(n+1)=	x(n+1)=	PROPN
ejpam-700	250	30	(	(	PUNCT
ejpam-700	250	31	x(n−3)/(−1+x(n−1)*x(n−3	x(n−3)/(−1+x(n−1)*x(n−3	PROPN
ejpam-700	250	32	)	)	PUNCT
ejpam-700	250	33	)	)	PUNCT
ejpam-700	250	34	figure	figure	VERB
ejpam-700	250	35	5	5	NUM
ejpam-700	250	36	example	example	NOUN
ejpam-700	250	37	6	6	NUM
ejpam-700	250	38	.	.	PUNCT
ejpam-700	251	1	see	see	VERB
ejpam-700	251	2	fig	fig	NOUN
ejpam-700	251	3	.	.	PUNCT
ejpam-700	252	1	6	6	NUM
ejpam-700	252	2	,	,	PUNCT
ejpam-700	252	3	since	since	SCONJ
ejpam-700	252	4	x−3	x−3	PROPN
ejpam-700	252	5	=	=	PUNCT
ejpam-700	252	6	0.7	0.7	NUM
ejpam-700	252	7	,	,	PUNCT
ejpam-700	252	8	x−2	x−2	PROPN
ejpam-700	252	9	=	=	SYM
ejpam-700	252	10	0.5	0.5	NUM
ejpam-700	252	11	,	,	PUNCT
ejpam-700	252	12	x−1	x−1	PROPN
ejpam-700	252	13	=	=	SYM
ejpam-700	252	14	20/7	20/7	NUM
ejpam-700	252	15	,	,	PUNCT
ejpam-700	252	16	x0	x0	PROPN
ejpam-700	252	17	=	=	PUNCT
ejpam-700	253	1	4	4	NUM
ejpam-700	253	2	.	.	NOUN
ejpam-700	253	3	0	0	NUM
ejpam-700	253	4	5	5	NUM
ejpam-700	253	5	10	10	NUM
ejpam-700	253	6	15	15	NUM
ejpam-700	253	7	20	20	NUM
ejpam-700	253	8	25	25	NUM
ejpam-700	253	9	30	30	NUM
ejpam-700	253	10	0.5	0.5	NUM
ejpam-700	253	11	1	1	NUM
ejpam-700	253	12	1.5	1.5	NUM
ejpam-700	253	13	2	2	NUM
ejpam-700	253	14	2.5	2.5	NUM
ejpam-700	253	15	3	3	NUM
ejpam-700	253	16	3.5	3.5	NUM
ejpam-700	253	17	4	4	NUM
ejpam-700	253	18	n	n	NOUN
ejpam-700	253	19	x	x	X
ejpam-700	253	20	(	(	PUNCT
ejpam-700	253	21	n	n	CCONJ
ejpam-700	253	22	)	)	PUNCT
ejpam-700	253	23	plot	plot	NOUN
ejpam-700	253	24	of	of	ADP
ejpam-700	253	25	x(n+1)=	x(n+1)=	PROPN
ejpam-700	253	26	(	(	PUNCT
ejpam-700	253	27	x(n−3)/(−1+x(n−1)*x(n−3	x(n−3)/(−1+x(n−1)*x(n−3	PROPN
ejpam-700	253	28	)	)	PUNCT
ejpam-700	253	29	)	)	PUNCT
ejpam-700	253	30	figure	figure	VERB
ejpam-700	253	31	6	6	NUM
ejpam-700	253	32	example	example	NOUN
ejpam-700	253	33	7	7	NUM
ejpam-700	253	34	.	.	PUNCT
ejpam-700	254	1	in	in	ADP
ejpam-700	254	2	fig	fig	NOUN
ejpam-700	254	3	.	.	PUNCT
ejpam-700	255	1	7	7	NUM
ejpam-700	255	2	,	,	PUNCT
ejpam-700	255	3	we	we	PRON
ejpam-700	255	4	assume	assume	VERB
ejpam-700	255	5	x−3	x−3	NOUN
ejpam-700	255	6	=	=	NOUN
ejpam-700	255	7	0.7	0.7	NUM
ejpam-700	255	8	,	,	PUNCT
ejpam-700	255	9	x−2	x−2	PROPN
ejpam-700	255	10	=	=	SYM
ejpam-700	255	11	0.5	0.5	NUM
ejpam-700	255	12	,	,	PUNCT
ejpam-700	255	13	x−1	x−1	PROPN
ejpam-700	256	1	=	=	PROPN
ejpam-700	256	2	3	3	NUM
ejpam-700	256	3	,	,	PUNCT
ejpam-700	256	4	x0	x0	PROPN
ejpam-700	256	5	=	=	PUNCT
ejpam-700	256	6	4	4	X
ejpam-700	256	7	.	.	X
ejpam-700	256	8	e.	e.	PROPN
ejpam-700	256	9	elsayed	elsayed	PROPN
ejpam-700	256	10	/	/	SYM
ejpam-700	256	11	eur	eur	PROPN
ejpam-700	256	12	.	.	PUNCT
ejpam-700	257	1	j.	j.	PROPN
ejpam-700	257	2	pure	pure	PROPN
ejpam-700	257	3	appl	appl	PROPN
ejpam-700	257	4	.	.	PROPN
ejpam-700	257	5	math	math	PROPN
ejpam-700	257	6	,	,	PUNCT
ejpam-700	257	7	4	4	NUM
ejpam-700	257	8	(	(	PUNCT
ejpam-700	257	9	2011	2011	NUM
ejpam-700	257	10	)	)	PUNCT
ejpam-700	257	11	,	,	PUNCT
ejpam-700	257	12	287	287	NUM
ejpam-700	257	13	-	-	SYM
ejpam-700	257	14	303	303	NUM
ejpam-700	257	15	298	298	NUM
ejpam-700	257	16	0	0	NUM
ejpam-700	257	17	10	10	NUM
ejpam-700	257	18	20	20	NUM
ejpam-700	257	19	30	30	NUM
ejpam-700	257	20	40	40	NUM
ejpam-700	257	21	50	50	NUM
ejpam-700	257	22	60	60	NUM
ejpam-700	257	23	70	70	NUM
ejpam-700	257	24	80	80	NUM
ejpam-700	257	25	0	0	NUM
ejpam-700	257	26	2	2	NUM
ejpam-700	257	27	4	4	NUM
ejpam-700	257	28	6	6	NUM
ejpam-700	257	29	8	8	NUM
ejpam-700	257	30	10	10	NUM
ejpam-700	257	31	12	12	NUM
ejpam-700	257	32	14	14	NUM
ejpam-700	257	33	16	16	NUM
ejpam-700	257	34	18	18	NUM
ejpam-700	257	35	20	20	NUM
ejpam-700	257	36	n	n	NUM
ejpam-700	257	37	x	x	X
ejpam-700	257	38	(	(	PUNCT
ejpam-700	257	39	n	n	CCONJ
ejpam-700	257	40	)	)	PUNCT
ejpam-700	257	41	plot	plot	NOUN
ejpam-700	257	42	of	of	ADP
ejpam-700	257	43	x(n+1)=	x(n+1)=	PROPN
ejpam-700	257	44	(	(	PUNCT
ejpam-700	257	45	x(n−3)/(−1+x(n−1)*x(n−3	x(n−3)/(−1+x(n−1)*x(n−3	PROPN
ejpam-700	257	46	)	)	PUNCT
ejpam-700	257	47	)	)	PUNCT
ejpam-700	257	48	figure	figure	VERB
ejpam-700	257	49	7	7	NUM
ejpam-700	257	50	5	5	NUM
ejpam-700	257	51	.	.	PUNCT
ejpam-700	258	1	on	on	ADP
ejpam-700	258	2	the	the	DET
ejpam-700	258	3	difference	difference	NOUN
ejpam-700	258	4	equation	equation	NOUN
ejpam-700	258	5	xn+1	xn+1	PROPN
ejpam-700	258	6	=	=	SYM
ejpam-700	258	7	xn−3	xn−3	PROPN
ejpam-700	258	8	−1−	−1−	PROPN
ejpam-700	258	9	xn−1xn−3	xn−1xn−3	NUM
ejpam-700	258	10	in	in	ADP
ejpam-700	258	11	this	this	DET
ejpam-700	258	12	section	section	NOUN
ejpam-700	258	13	we	we	PRON
ejpam-700	258	14	investigate	investigate	VERB
ejpam-700	258	15	the	the	DET
ejpam-700	258	16	solutions	solution	NOUN
ejpam-700	258	17	of	of	ADP
ejpam-700	258	18	the	the	DET
ejpam-700	258	19	following	follow	VERB
ejpam-700	258	20	difference	difference	NOUN
ejpam-700	258	21	equation	equation	NOUN
ejpam-700	258	22	xn+1	xn+1	PROPN
ejpam-700	259	1	=	=	SYM
ejpam-700	259	2	xn−3	xn−3	PROPN
ejpam-700	259	3	−1−	−1−	PROPN
ejpam-700	259	4	xn−1	xn−1	PROPN
ejpam-700	259	5	xn−3	xn−3	PROPN
ejpam-700	259	6	,	,	PUNCT
ejpam-700	259	7	n=	n=	ADJ
ejpam-700	259	8	0,1	0,1	NUM
ejpam-700	259	9	,	,	PUNCT
ejpam-700	259	10	.	.	PUNCT
ejpam-700	259	11	.	.	PUNCT
ejpam-700	260	1	.	.	PUNCT
ejpam-700	261	1	,	,	PUNCT
ejpam-700	261	2	(	(	PUNCT
ejpam-700	261	3	6	6	NUM
ejpam-700	261	4	)	)	PUNCT
ejpam-700	261	5	where	where	SCONJ
ejpam-700	261	6	the	the	DET
ejpam-700	261	7	initial	initial	ADJ
ejpam-700	261	8	conditions	condition	NOUN
ejpam-700	261	9	are	be	AUX
ejpam-700	261	10	arbitrary	arbitrary	ADJ
ejpam-700	261	11	nonzero	nonzero	ADJ
ejpam-700	261	12	real	real	ADJ
ejpam-700	261	13	numbers	number	NOUN
ejpam-700	261	14	with	with	ADP
ejpam-700	261	15	x−3	x−3	PROPN
ejpam-700	261	16	x−1	x−1	PROPN
ejpam-700	261	17	6=	6=	NUM
ejpam-700	261	18	−1	−1	NOUN
ejpam-700	261	19	,	,	PUNCT
ejpam-700	261	20	x−2	x−2	PROPN
ejpam-700	261	21	x0	x0	PROPN
ejpam-700	261	22	6=	6=	ADP
ejpam-700	261	23	−1	−1	NOUN
ejpam-700	261	24	.	.	PUNCT
ejpam-700	261	25	theorem	theorem	VERB
ejpam-700	261	26	9	9	NUM
ejpam-700	261	27	.	.	PUNCT
ejpam-700	262	1	let	let	VERB
ejpam-700	262	2	{	{	PUNCT
ejpam-700	262	3	xn}∞n=−3	xn}∞n=−3	AUX
ejpam-700	262	4	be	be	AUX
ejpam-700	262	5	a	a	DET
ejpam-700	262	6	solution	solution	NOUN
ejpam-700	262	7	of	of	ADP
ejpam-700	262	8	eq	eq	PROPN
ejpam-700	262	9	.	.	PUNCT
ejpam-700	263	1	(	(	PUNCT
ejpam-700	263	2	6	6	NUM
ejpam-700	263	3	)	)	PUNCT
ejpam-700	263	4	.	.	PUNCT
ejpam-700	264	1	then	then	ADV
ejpam-700	264	2	for	for	ADP
ejpam-700	264	3	n=	n=	ADJ
ejpam-700	264	4	0,1	0,1	NUM
ejpam-700	264	5	,	,	PUNCT
ejpam-700	264	6	.	.	PUNCT
ejpam-700	264	7	.	.	PUNCT
ejpam-700	264	8	.	.	PUNCT
ejpam-700	265	1	x4n−3	x4n−3	PROPN
ejpam-700	265	2	=	=	PRON
ejpam-700	265	3	(	(	PUNCT
ejpam-700	265	4	−1)n	−1)n	PROPN
ejpam-700	265	5	d	d	X
ejpam-700	265	6	(	(	PUNCT
ejpam-700	265	7	1	1	NUM
ejpam-700	265	8	+	+	NUM
ejpam-700	265	9	bd)n	bd)n	NOUN
ejpam-700	265	10	,	,	PUNCT
ejpam-700	265	11	x4n−1	x4n−1	PROPN
ejpam-700	265	12	=	=	SYM
ejpam-700	265	13	(	(	PUNCT
ejpam-700	265	14	−1)n	−1)n	PROPN
ejpam-700	265	15	b	b	X
ejpam-700	265	16	(	(	PUNCT
ejpam-700	265	17	1	1	NUM
ejpam-700	265	18	+	+	NUM
ejpam-700	265	19	bd)n	bd)n	NOUN
ejpam-700	265	20	,	,	PUNCT
ejpam-700	265	21	x4n−2	x4n−2	PROPN
ejpam-700	265	22	=	=	SYM
ejpam-700	265	23	(	(	PUNCT
ejpam-700	265	24	−1)n	−1)n	PROPN
ejpam-700	265	25	c	c	X
ejpam-700	265	26	(	(	PUNCT
ejpam-700	265	27	1	1	NUM
ejpam-700	265	28	+	+	NUM
ejpam-700	265	29	ac)n	ac)n	PROPN
ejpam-700	265	30	,	,	PUNCT
ejpam-700	265	31	x4n	x4n	PROPN
ejpam-700	265	32	=	=	PUNCT
ejpam-700	265	33	(	(	PUNCT
ejpam-700	265	34	−1)n	−1)n	PROPN
ejpam-700	265	35	a	a	DET
ejpam-700	265	36	(	(	PUNCT
ejpam-700	265	37	1	1	NUM
ejpam-700	265	38	+	+	NUM
ejpam-700	265	39	ac)n	ac)n	NOUN
ejpam-700	265	40	,	,	PUNCT
ejpam-700	266	1	where	where	SCONJ
ejpam-700	266	2	x−3	x−3	PROPN
ejpam-700	266	3	=	=	SYM
ejpam-700	266	4	d	d	PROPN
ejpam-700	266	5	,	,	PUNCT
ejpam-700	266	6	x−2	x−2	PROPN
ejpam-700	266	7	=	=	SYM
ejpam-700	266	8	c	c	X
ejpam-700	266	9	,	,	PUNCT
ejpam-700	266	10	x−1	x−1	PUNCT
ejpam-700	266	11	=	=	SYM
ejpam-700	266	12	b	b	PROPN
ejpam-700	266	13	,	,	PUNCT
ejpam-700	266	14	x−0	x−0	PROPN
ejpam-700	266	15	=	=	NOUN
ejpam-700	266	16	a.	a.	NOUN
ejpam-700	266	17	proof	proof	NOUN
ejpam-700	266	18	.	.	PUNCT
ejpam-700	267	1	as	as	ADP
ejpam-700	267	2	the	the	DET
ejpam-700	267	3	proof	proof	NOUN
ejpam-700	267	4	of	of	ADP
ejpam-700	267	5	theorem	theorem	ADJ
ejpam-700	267	6	6	6	NUM
ejpam-700	267	7	.	.	PUNCT
ejpam-700	267	8	theorem	theorem	VERB
ejpam-700	267	9	10	10	NUM
ejpam-700	267	10	.	.	PUNCT
ejpam-700	268	1	eq	eq	ADP
ejpam-700	268	2	.	.	PUNCT
ejpam-700	269	1	(	(	PUNCT
ejpam-700	269	2	6	6	NUM
ejpam-700	269	3	)	)	PUNCT
ejpam-700	269	4	has	have	VERB
ejpam-700	269	5	three	three	NUM
ejpam-700	269	6	equilibrium	equilibrium	NOUN
ejpam-700	269	7	points	point	NOUN
ejpam-700	269	8	which	which	PRON
ejpam-700	269	9	are	be	AUX
ejpam-700	269	10	0	0	NUM
ejpam-700	269	11	,	,	PUNCT
ejpam-700	269	12	p	p	NOUN
ejpam-700	269	13	2	2	NUM
ejpam-700	269	14	,	,	PUNCT
ejpam-700	269	15	−p2	−p2	PROPN
ejpam-700	269	16	.	.	PUNCT
ejpam-700	270	1	proof	proof	NOUN
ejpam-700	270	2	.	.	PUNCT
ejpam-700	271	1	as	as	ADP
ejpam-700	271	2	the	the	DET
ejpam-700	271	3	proof	proof	NOUN
ejpam-700	271	4	of	of	ADP
ejpam-700	271	5	theorem	theorem	ADJ
ejpam-700	271	6	7	7	NUM
ejpam-700	271	7	.	.	PUNCT
ejpam-700	271	8	theorem	theorem	VERB
ejpam-700	271	9	11	11	NUM
ejpam-700	271	10	.	.	PUNCT
ejpam-700	272	1	eq	eq	ADP
ejpam-700	272	2	.	.	PUNCT
ejpam-700	273	1	(	(	PUNCT
ejpam-700	273	2	6	6	NUM
ejpam-700	273	3	)	)	PUNCT
ejpam-700	273	4	has	have	VERB
ejpam-700	273	5	a	a	DET
ejpam-700	273	6	periodic	periodic	ADJ
ejpam-700	273	7	solutions	solution	NOUN
ejpam-700	273	8	of	of	ADP
ejpam-700	273	9	period	period	NOUN
ejpam-700	274	1	four	four	NUM
ejpam-700	274	2	iff	iff	PROPN
ejpam-700	274	3	ac	ac	PROPN
ejpam-700	275	1	=	=	PUNCT
ejpam-700	276	1	bd	bd	PROPN
ejpam-700	277	1	=	=	SYM
ejpam-700	278	1	−2	−2	NOUN
ejpam-700	279	1	and	and	CCONJ
ejpam-700	279	2	will	will	AUX
ejpam-700	279	3	be	be	AUX
ejpam-700	279	4	take	take	VERB
ejpam-700	279	5	the	the	DET
ejpam-700	279	6	form	form	NOUN
ejpam-700	279	7	{	{	PUNCT
ejpam-700	279	8	d	d	NOUN
ejpam-700	279	9	,	,	PUNCT
ejpam-700	279	10	c	c	X
ejpam-700	279	11	,	,	PUNCT
ejpam-700	279	12	b	b	NOUN
ejpam-700	279	13	,	,	PUNCT
ejpam-700	279	14	a	a	DET
ejpam-700	279	15	,	,	PUNCT
ejpam-700	279	16	d	d	X
ejpam-700	279	17	,	,	PUNCT
ejpam-700	279	18	c	c	X
ejpam-700	279	19	,	,	PUNCT
ejpam-700	279	20	b	b	NOUN
ejpam-700	279	21	,	,	PUNCT
ejpam-700	279	22	a	a	PRON
ejpam-700	279	23	,	,	PUNCT
ejpam-700	279	24	.	.	PUNCT
ejpam-700	279	25	.	.	PUNCT
ejpam-700	280	1	.	.	PUNCT
ejpam-700	280	2	}	}	PUNCT
ejpam-700	280	3	.	.	PUNCT
ejpam-700	281	1	proof	proof	NOUN
ejpam-700	281	2	.	.	PUNCT
ejpam-700	282	1	as	as	ADP
ejpam-700	282	2	the	the	DET
ejpam-700	282	3	proof	proof	NOUN
ejpam-700	282	4	of	of	ADP
ejpam-700	282	5	theorem	theorem	ADJ
ejpam-700	282	6	8	8	NUM
ejpam-700	282	7	.	.	PUNCT
ejpam-700	282	8	lemma	lemma	PROPN
ejpam-700	282	9	4	4	NUM
ejpam-700	282	10	.	.	PUNCT
ejpam-700	282	11	eq	eq	ADP
ejpam-700	282	12	.	.	PUNCT
ejpam-700	283	1	(	(	PUNCT
ejpam-700	283	2	6	6	NUM
ejpam-700	283	3	)	)	PUNCT
ejpam-700	283	4	has	have	VERB
ejpam-700	283	5	no	no	DET
ejpam-700	283	6	prime	prime	ADJ
ejpam-700	283	7	period	period	NOUN
ejpam-700	283	8	two	two	NUM
ejpam-700	283	9	solution	solution	NOUN
ejpam-700	283	10	.	.	PUNCT
ejpam-700	284	1	lemma	lemma	PROPN
ejpam-700	284	2	5	5	X
ejpam-700	284	3	.	.	PUNCT
ejpam-700	284	4	assume	assume	VERB
ejpam-700	284	5	that	that	SCONJ
ejpam-700	284	6	ac	ac	PROPN
ejpam-700	284	7	,	,	PUNCT
ejpam-700	284	8	bd	bd	PROPN
ejpam-700	284	9	6=	6=	PROPN
ejpam-700	284	10	−1±	−1±	ADP
ejpam-700	284	11	1	1	NUM
ejpam-700	284	12	.	.	PUNCT
ejpam-700	285	1	then	then	ADV
ejpam-700	285	2	eq	eq	X
ejpam-700	285	3	.	.	PUNCT
ejpam-700	286	1	(	(	PUNCT
ejpam-700	286	2	6	6	NUM
ejpam-700	286	3	)	)	PUNCT
ejpam-700	286	4	has	have	VERB
ejpam-700	286	5	unbounded	unbounded	ADJ
ejpam-700	286	6	solutions	solution	NOUN
ejpam-700	286	7	.	.	PUNCT
ejpam-700	287	1	e.	e.	PROPN
ejpam-700	287	2	elsayed	elsayed	PROPN
ejpam-700	287	3	/	/	SYM
ejpam-700	287	4	eur	eur	PROPN
ejpam-700	287	5	.	.	PUNCT
ejpam-700	288	1	j.	j.	PROPN
ejpam-700	288	2	pure	pure	PROPN
ejpam-700	288	3	appl	appl	PROPN
ejpam-700	288	4	.	.	PROPN
ejpam-700	288	5	math	math	PROPN
ejpam-700	288	6	,	,	PUNCT
ejpam-700	288	7	4	4	NUM
ejpam-700	288	8	(	(	PUNCT
ejpam-700	288	9	2011	2011	NUM
ejpam-700	288	10	)	)	PUNCT
ejpam-700	288	11	,	,	PUNCT
ejpam-700	288	12	287	287	NUM
ejpam-700	288	13	-	-	SYM
ejpam-700	288	14	303	303	NUM
ejpam-700	288	15	299	299	NUM
ejpam-700	288	16	numerical	numerical	ADJ
ejpam-700	288	17	examples	example	NOUN
ejpam-700	288	18	example	example	NOUN
ejpam-700	288	19	8	8	NUM
ejpam-700	288	20	.	.	PUNCT
ejpam-700	289	1	we	we	PRON
ejpam-700	289	2	consider	consider	VERB
ejpam-700	289	3	x−3	x−3	NOUN
ejpam-700	289	4	=	=	PUNCT
ejpam-700	289	5	0.7	0.7	NUM
ejpam-700	289	6	,	,	PUNCT
ejpam-700	289	7	x−2	x−2	PROPN
ejpam-700	289	8	=	=	SYM
ejpam-700	289	9	0.6	0.6	NUM
ejpam-700	289	10	,	,	PUNCT
ejpam-700	289	11	x−1	x−1	PROPN
ejpam-700	289	12	=	=	NOUN
ejpam-700	289	13	0.3	0.3	NUM
ejpam-700	289	14	,	,	PUNCT
ejpam-700	289	15	x0	x0	PROPN
ejpam-700	289	16	=	=	PUNCT
ejpam-700	289	17	0.4	0.4	NUM
ejpam-700	289	18	.	.	PUNCT
ejpam-700	290	1	see	see	VERB
ejpam-700	290	2	fig	fig	NOUN
ejpam-700	290	3	.	.	PUNCT
ejpam-700	291	1	8	8	NUM
ejpam-700	291	2	.	.	NOUN
ejpam-700	291	3	0	0	NUM
ejpam-700	292	1	20	20	NUM
ejpam-700	292	2	40	40	NUM
ejpam-700	292	3	60	60	NUM
ejpam-700	292	4	80	80	NUM
ejpam-700	292	5	100	100	NUM
ejpam-700	292	6	120	120	NUM
ejpam-700	292	7	140	140	NUM
ejpam-700	292	8	160	160	NUM
ejpam-700	292	9	180	180	NUM
ejpam-700	292	10	−6000	−6000	PROPN
ejpam-700	292	11	−4000	−4000	NOUN
ejpam-700	292	12	−2000	−2000	PROPN
ejpam-700	292	13	0	0	NUM
ejpam-700	292	14	2000	2000	NUM
ejpam-700	292	15	4000	4000	NUM
ejpam-700	292	16	6000	6000	NUM
ejpam-700	292	17	n	n	CCONJ
ejpam-700	292	18	x	x	X
ejpam-700	292	19	(	(	PUNCT
ejpam-700	292	20	n	n	CCONJ
ejpam-700	292	21	)	)	PUNCT
ejpam-700	292	22	plot	plot	NOUN
ejpam-700	292	23	of	of	ADP
ejpam-700	292	24	x(n+1)=	x(n+1)=	PROPN
ejpam-700	292	25	(	(	PUNCT
ejpam-700	292	26	x(n−3)/(−1−x(n−1)*x(n−3	x(n−3)/(−1−x(n−1)*x(n−3	PROPN
ejpam-700	292	27	)	)	PUNCT
ejpam-700	292	28	)	)	PUNCT
ejpam-700	292	29	figure	figure	VERB
ejpam-700	292	30	8	8	NUM
ejpam-700	292	31	example	example	NOUN
ejpam-700	292	32	9	9	NUM
ejpam-700	292	33	.	.	PUNCT
ejpam-700	293	1	see	see	VERB
ejpam-700	293	2	fig	fig	NOUN
ejpam-700	293	3	.	.	PUNCT
ejpam-700	294	1	9	9	NUM
ejpam-700	294	2	,	,	PUNCT
ejpam-700	294	3	since	since	SCONJ
ejpam-700	294	4	x−3	x−3	PROPN
ejpam-700	294	5	=	=	PUNCT
ejpam-700	294	6	0.7	0.7	NUM
ejpam-700	294	7	,	,	PUNCT
ejpam-700	294	8	x−2	x−2	PROPN
ejpam-700	294	9	=	=	SYM
ejpam-700	294	10	6	6	NUM
ejpam-700	294	11	,	,	PUNCT
ejpam-700	294	12	x−1	x−1	PUNCT
ejpam-700	295	1	=	=	PUNCT
ejpam-700	295	2	−3	−3	PROPN
ejpam-700	295	3	,	,	PUNCT
ejpam-700	295	4	x0	x0	PROPN
ejpam-700	295	5	=	=	PUNCT
ejpam-700	296	1	−0.4	−0.4	PROPN
ejpam-700	296	2	.	.	PUNCT
ejpam-700	297	1	0	0	NUM
ejpam-700	297	2	10	10	NUM
ejpam-700	297	3	20	20	NUM
ejpam-700	297	4	30	30	NUM
ejpam-700	297	5	40	40	NUM
ejpam-700	297	6	50	50	NUM
ejpam-700	297	7	60	60	NUM
ejpam-700	297	8	70	70	NUM
ejpam-700	297	9	80	80	NUM
ejpam-700	297	10	−250	−250	NOUN
ejpam-700	297	11	−200	−200	PROPN
ejpam-700	297	12	−150	−150	ADJ
ejpam-700	297	13	−100	−100	ADP
ejpam-700	297	14	−50	−50	NOUN
ejpam-700	297	15	0	0	NUM
ejpam-700	297	16	50	50	NUM
ejpam-700	297	17	n	n	NOUN
ejpam-700	297	18	x	x	X
ejpam-700	297	19	(	(	PUNCT
ejpam-700	297	20	n	n	CCONJ
ejpam-700	297	21	)	)	PUNCT
ejpam-700	297	22	plot	plot	NOUN
ejpam-700	297	23	of	of	ADP
ejpam-700	297	24	x(n+1)=	x(n+1)=	PROPN
ejpam-700	297	25	(	(	PUNCT
ejpam-700	297	26	x(n−3)/(−1−x(n−1)*x(n−3	x(n−3)/(−1−x(n−1)*x(n−3	PROPN
ejpam-700	297	27	)	)	PUNCT
ejpam-700	297	28	)	)	PUNCT
ejpam-700	297	29	figure	figure	NOUN
ejpam-700	297	30	9	9	NUM
ejpam-700	297	31	example	example	NOUN
ejpam-700	297	32	10	10	NUM
ejpam-700	297	33	.	.	PUNCT
ejpam-700	298	1	in	in	ADP
ejpam-700	298	2	fig	fig	NOUN
ejpam-700	298	3	.	.	PUNCT
ejpam-700	299	1	10	10	NUM
ejpam-700	299	2	,	,	PUNCT
ejpam-700	299	3	we	we	PRON
ejpam-700	299	4	assume	assume	VERB
ejpam-700	299	5	x−3	x−3	NOUN
ejpam-700	299	6	=	=	SYM
ejpam-700	299	7	−2.5	−2.5	PROPN
ejpam-700	299	8	,	,	PUNCT
ejpam-700	299	9	x−2	x−2	PROPN
ejpam-700	299	10	=	=	SYM
ejpam-700	299	11	−6	−6	PROPN
ejpam-700	299	12	,	,	PUNCT
ejpam-700	299	13	x−1	x−1	PROPN
ejpam-700	300	1	=	=	PROPN
ejpam-700	300	2	0.8	0.8	NUM
ejpam-700	300	3	,	,	PUNCT
ejpam-700	300	4	x0	x0	PROPN
ejpam-700	300	5	=	=	SYM
ejpam-700	300	6	1/3	1/3	NUM
ejpam-700	300	7	.	.	PUNCT
ejpam-700	301	1	references	reference	NOUN
ejpam-700	301	2	300	300	NUM
ejpam-700	301	3	0	0	NUM
ejpam-700	301	4	5	5	NUM
ejpam-700	301	5	10	10	NUM
ejpam-700	301	6	15	15	NUM
ejpam-700	301	7	20	20	NUM
ejpam-700	301	8	25	25	NUM
ejpam-700	301	9	30	30	NUM
ejpam-700	301	10	−6	−6	NOUN
ejpam-700	301	11	−5	−5	NOUN
ejpam-700	301	12	−4	−4	X
ejpam-700	302	1	−3	−3	X
ejpam-700	302	2	−2	−2	PROPN
ejpam-700	302	3	−1	−1	NOUN
ejpam-700	302	4	0	0	NUM
ejpam-700	302	5	1	1	NUM
ejpam-700	302	6	n	n	NOUN
ejpam-700	302	7	x	x	X
ejpam-700	302	8	(	(	PUNCT
ejpam-700	302	9	n	n	CCONJ
ejpam-700	302	10	)	)	PUNCT
ejpam-700	302	11	plot	plot	NOUN
ejpam-700	302	12	of	of	ADP
ejpam-700	302	13	x(n+1)=	x(n+1)=	PROPN
ejpam-700	302	14	(	(	PUNCT
ejpam-700	302	15	x(n−3)/(−1−x(n−1)*x(n−3	x(n−3)/(−1−x(n−1)*x(n−3	PROPN
ejpam-700	302	16	)	)	PUNCT
ejpam-700	302	17	)	)	PUNCT
ejpam-700	302	18	figure	figure	VERB
ejpam-700	302	19	10	10	NUM
ejpam-700	302	20	references	reference	NOUN
ejpam-700	302	21	[	[	X
ejpam-700	302	22	1	1	NUM
ejpam-700	302	23	]	]	X
ejpam-700	302	24	r	r	NOUN
ejpam-700	302	25	p	p	PROPN
ejpam-700	302	26	agarwal	agarwal	PROPN
ejpam-700	302	27	.	.	PUNCT
ejpam-700	303	1	difference	difference	NOUN
ejpam-700	303	2	equations	equation	NOUN
ejpam-700	303	3	and	and	CCONJ
ejpam-700	303	4	inequalities	inequality	NOUN
ejpam-700	303	5	.	.	PUNCT
ejpam-700	304	1	1st	1st	PROPN
ejpam-700	304	2	edition	edition	PROPN
ejpam-700	304	3	,	,	PUNCT
ejpam-700	304	4	marcel	marcel	PROPN
ejpam-700	304	5	dekker	dekker	PROPN
ejpam-700	304	6	,	,	PUNCT
ejpam-700	304	7	new	new	PROPN
ejpam-700	304	8	york	york	PROPN
ejpam-700	304	9	,	,	PUNCT
ejpam-700	304	10	1992	1992	NUM
ejpam-700	304	11	,	,	PUNCT
ejpam-700	304	12	2nd	2nd	PROPN
ejpam-700	304	13	edition	edition	NOUN
ejpam-700	304	14	,	,	PUNCT
ejpam-700	304	15	2000	2000	NUM
ejpam-700	304	16	.	.	PUNCT
ejpam-700	305	1	[	[	X
ejpam-700	305	2	2	2	NUM
ejpam-700	305	3	]	]	X
ejpam-700	305	4	r	r	NOUN
ejpam-700	305	5	p	p	PROPN
ejpam-700	305	6	agarwal	agarwal	PROPN
ejpam-700	305	7	and	and	CCONJ
ejpam-700	305	8	e	e	NOUN
ejpam-700	305	9	m	m	VERB
ejpam-700	305	10	elsayed	elsaye	VERB
ejpam-700	305	11	.	.	PUNCT
ejpam-700	306	1	periodicity	periodicity	NOUN
ejpam-700	306	2	and	and	CCONJ
ejpam-700	306	3	stability	stability	NOUN
ejpam-700	306	4	of	of	ADP
ejpam-700	306	5	solutions	solution	NOUN
ejpam-700	306	6	of	of	ADP
ejpam-700	306	7	higher	high	ADJ
ejpam-700	306	8	order	order	NOUN
ejpam-700	306	9	rational	rational	ADJ
ejpam-700	306	10	difference	difference	NOUN
ejpam-700	306	11	equation	equation	NOUN
ejpam-700	306	12	.	.	PUNCT
ejpam-700	307	1	advanced	advanced	ADJ
ejpam-700	307	2	studies	study	NOUN
ejpam-700	307	3	in	in	ADP
ejpam-700	307	4	contemporary	contemporary	ADJ
ejpam-700	307	5	mathematics	mathematic	NOUN
ejpam-700	307	6	,	,	PUNCT
ejpam-700	307	7	17(2):181201	17(2):181201	NUM
ejpam-700	307	8	,	,	PUNCT
ejpam-700	307	9	2008	2008	NUM
ejpam-700	307	10	.	.	PUNCT
ejpam-700	308	1	[	[	X
ejpam-700	308	2	3	3	NUM
ejpam-700	308	3	]	]	X
ejpam-700	308	4	r	r	NOUN
ejpam-700	308	5	p	p	PROPN
ejpam-700	308	6	agarwal	agarwal	PROPN
ejpam-700	308	7	and	and	CCONJ
ejpam-700	308	8	e	e	NOUN
ejpam-700	308	9	m	m	VERB
ejpam-700	308	10	elsayed	elsaye	VERB
ejpam-700	308	11	.	.	PUNCT
ejpam-700	309	1	on	on	ADP
ejpam-700	309	2	the	the	DET
ejpam-700	309	3	solution	solution	NOUN
ejpam-700	309	4	of	of	ADP
ejpam-700	309	5	fourth	fourth	ADJ
ejpam-700	309	6	-	-	PUNCT
ejpam-700	309	7	order	order	NOUN
ejpam-700	309	8	rational	rational	ADJ
ejpam-700	309	9	recursive	recursive	ADJ
ejpam-700	309	10	sequence	sequence	NOUN
ejpam-700	309	11	.	.	PUNCT
ejpam-700	310	1	advanced	advanced	ADJ
ejpam-700	310	2	studies	study	NOUN
ejpam-700	310	3	in	in	ADP
ejpam-700	310	4	contemporary	contemporary	ADJ
ejpam-700	310	5	mathematics	mathematic	NOUN
ejpam-700	310	6	,	,	PUNCT
ejpam-700	310	7	20(4):525–545	20(4):525–545	NUM
ejpam-700	310	8	,	,	PUNCT
ejpam-700	310	9	2010	2010	NUM
ejpam-700	310	10	.	.	PUNCT
ejpam-700	311	1	[	[	X
ejpam-700	311	2	4	4	NUM
ejpam-700	311	3	]	]	X
ejpam-700	311	4	m	m	NOUN
ejpam-700	311	5	aloqeili	aloqeili	NOUN
ejpam-700	311	6	.	.	PUNCT
ejpam-700	312	1	dynamics	dynamic	NOUN
ejpam-700	312	2	of	of	ADP
ejpam-700	312	3	a	a	DET
ejpam-700	312	4	rational	rational	ADJ
ejpam-700	312	5	difference	difference	NOUN
ejpam-700	312	6	equation	equation	NOUN
ejpam-700	312	7	.	.	PUNCT
ejpam-700	313	1	appl	appl	PROPN
ejpam-700	313	2	.	.	PROPN
ejpam-700	313	3	math	math	PROPN
ejpam-700	313	4	.	.	PUNCT
ejpam-700	314	1	comp	comp	PROPN
ejpam-700	314	2	.	.	PUNCT
ejpam-700	314	3	,	,	PUNCT
ejpam-700	314	4	176(2):768774	176(2):768774	PROPN
ejpam-700	314	5	,	,	PUNCT
ejpam-700	314	6	2006	2006	NUM
ejpam-700	314	7	.	.	PUNCT
ejpam-700	315	1	[	[	X
ejpam-700	315	2	5	5	NUM
ejpam-700	315	3	]	]	PUNCT
ejpam-700	315	4	n	n	PRON
ejpam-700	315	5	battaloglu	battaloglu	NOUN
ejpam-700	315	6	,	,	PUNCT
ejpam-700	315	7	c	c	PROPN
ejpam-700	315	8	cinar	cinar	PROPN
ejpam-700	315	9	and	and	CCONJ
ejpam-700	315	10	i	i	PRON
ejpam-700	315	11	yalçınkaya	yalçınkaya	NOUN
ejpam-700	315	12	.	.	PUNCT
ejpam-700	316	1	the	the	DET
ejpam-700	316	2	dynamics	dynamic	NOUN
ejpam-700	316	3	of	of	ADP
ejpam-700	316	4	the	the	DET
ejpam-700	316	5	difference	difference	NOUN
ejpam-700	316	6	equation	equation	NOUN
ejpam-700	316	7	.	.	PUNCT
ejpam-700	317	1	ars	ar	VERB
ejpam-700	317	2	combinatoria	combinatoria	NOUN
ejpam-700	317	3	,	,	PUNCT
ejpam-700	317	4	97:281	97:281	NUM
ejpam-700	317	5	-	-	SYM
ejpam-700	317	6	288	288	NUM
ejpam-700	317	7	,	,	PUNCT
ejpam-700	317	8	2010	2010	NUM
ejpam-700	317	9	.	.	PUNCT
ejpam-700	318	1	[	[	X
ejpam-700	318	2	6	6	NUM
ejpam-700	318	3	]	]	X
ejpam-700	318	4	c	c	PROPN
ejpam-700	318	5	cinar	cinar	PROPN
ejpam-700	318	6	.	.	PUNCT
ejpam-700	319	1	on	on	ADP
ejpam-700	319	2	the	the	DET
ejpam-700	319	3	positive	positive	ADJ
ejpam-700	319	4	solutions	solution	NOUN
ejpam-700	319	5	of	of	ADP
ejpam-700	319	6	the	the	DET
ejpam-700	319	7	difference	difference	NOUN
ejpam-700	319	8	equation	equation	NOUN
ejpam-700	319	9	xn+1	xn+1	PROPN
ejpam-700	319	10	=	=	PUNCT
ejpam-700	319	11	xn−1	xn−1	PROPN
ejpam-700	319	12	1+xn	1+xn	NUM
ejpam-700	319	13	xn−1	xn−1	PROPN
ejpam-700	319	14	.	.	PUNCT
ejpam-700	320	1	appl	appl	PROPN
ejpam-700	320	2	.	.	PROPN
ejpam-700	320	3	math	math	PROPN
ejpam-700	320	4	.	.	PUNCT
ejpam-700	321	1	comp	comp	PROPN
ejpam-700	321	2	.	.	PUNCT
ejpam-700	321	3	,	,	PUNCT
ejpam-700	321	4	150:21	150:21	NUM
ejpam-700	321	5	-	-	SYM
ejpam-700	321	6	24	24	NUM
ejpam-700	321	7	,	,	PUNCT
ejpam-700	321	8	2004	2004	NUM
ejpam-700	321	9	.	.	PUNCT
ejpam-700	322	1	[	[	X
ejpam-700	322	2	7	7	NUM
ejpam-700	322	3	]	]	X
ejpam-700	322	4	c	c	PROPN
ejpam-700	322	5	cinar	cinar	PROPN
ejpam-700	322	6	.	.	PUNCT
ejpam-700	323	1	on	on	ADP
ejpam-700	323	2	the	the	DET
ejpam-700	323	3	difference	difference	NOUN
ejpam-700	323	4	equation	equation	NOUN
ejpam-700	323	5	xn+1	xn+1	PROPN
ejpam-700	323	6	=	=	PUNCT
ejpam-700	323	7	xn−1	xn−1	PROPN
ejpam-700	323	8	−1+xn	−1+xn	PROPN
ejpam-700	323	9	xn−1	xn−1	PROPN
ejpam-700	323	10	.	.	PUNCT
ejpam-700	324	1	appl	appl	PROPN
ejpam-700	324	2	.	.	PROPN
ejpam-700	324	3	math	math	PROPN
ejpam-700	324	4	.	.	PUNCT
ejpam-700	325	1	comp	comp	PROPN
ejpam-700	325	2	.	.	PUNCT
ejpam-700	326	1	,	,	PUNCT
ejpam-700	326	2	158:813	158:813	PROPN
ejpam-700	326	3	-	-	PUNCT
ejpam-700	326	4	816	816	NUM
ejpam-700	326	5	,	,	PUNCT
ejpam-700	326	6	2004	2004	NUM
ejpam-700	326	7	.	.	PUNCT
ejpam-700	327	1	[	[	X
ejpam-700	327	2	8	8	NUM
ejpam-700	327	3	]	]	X
ejpam-700	327	4	c	c	PROPN
ejpam-700	327	5	cinar	cinar	PROPN
ejpam-700	327	6	.	.	PUNCT
ejpam-700	328	1	on	on	ADP
ejpam-700	328	2	the	the	DET
ejpam-700	328	3	positive	positive	ADJ
ejpam-700	328	4	solutions	solution	NOUN
ejpam-700	328	5	of	of	ADP
ejpam-700	328	6	the	the	DET
ejpam-700	328	7	difference	difference	NOUN
ejpam-700	328	8	equation	equation	NOUN
ejpam-700	328	9	xn+1	xn+1	PROPN
ejpam-700	329	1	=	=	SYM
ejpam-700	329	2	axn−1	axn−1	PROPN
ejpam-700	329	3	1+bxn	1+bxn	NUM
ejpam-700	329	4	xn−1	xn−1	PROPN
ejpam-700	329	5	.	.	PUNCT
ejpam-700	330	1	appl	appl	PROPN
ejpam-700	330	2	.	.	PROPN
ejpam-700	330	3	math	math	PROPN
ejpam-700	330	4	.	.	PUNCT
ejpam-700	331	1	comp	comp	PROPN
ejpam-700	331	2	.	.	PUNCT
ejpam-700	331	3	,	,	PUNCT
ejpam-700	331	4	156:587	156:587	NUM
ejpam-700	331	5	-	-	PUNCT
ejpam-700	331	6	590	590	NUM
ejpam-700	331	7	,	,	PUNCT
ejpam-700	331	8	2004	2004	NUM
ejpam-700	331	9	.	.	PUNCT
ejpam-700	332	1	[	[	X
ejpam-700	332	2	9	9	NUM
ejpam-700	332	3	]	]	X
ejpam-700	332	4	c	c	PROPN
ejpam-700	332	5	cinar	cinar	PROPN
ejpam-700	332	6	,	,	PUNCT
ejpam-700	332	7	r	r	NOUN
ejpam-700	332	8	karatas	karata	NOUN
ejpam-700	332	9	and	and	CCONJ
ejpam-700	332	10	i	i	PRON
ejpam-700	332	11	yalcinkaya	yalcinkaya	NOUN
ejpam-700	332	12	.	.	PUNCT
ejpam-700	333	1	on	on	ADP
ejpam-700	333	2	solutions	solution	NOUN
ejpam-700	333	3	of	of	ADP
ejpam-700	333	4	the	the	DET
ejpam-700	333	5	difference	difference	NOUN
ejpam-700	333	6	equation	equation	NOUN
ejpam-700	333	7	xn+1	xn+1	PROPN
ejpam-700	333	8	=	=	SYM
ejpam-700	333	9	xn−3	xn−3	PROPN
ejpam-700	333	10	−1+xn	−1+xn	PROPN
ejpam-700	333	11	xn−1	xn−1	PROPN
ejpam-700	333	12	xn−2	xn−2	PROPN
ejpam-700	333	13	xn−3	xn−3	PROPN
ejpam-700	333	14	.	.	PUNCT
ejpam-700	334	1	mathematica	mathematica	PROPN
ejpam-700	334	2	bohemica	bohemica	PROPN
ejpam-700	334	3	,	,	PUNCT
ejpam-700	334	4	132(3):257	132(3):257	NOUN
ejpam-700	334	5	-	-	SYM
ejpam-700	334	6	261	261	NUM
ejpam-700	334	7	,	,	PUNCT
ejpam-700	334	8	2007	2007	NUM
ejpam-700	334	9	.	.	PUNCT
ejpam-700	335	1	references	reference	NOUN
ejpam-700	335	2	301	301	NUM
ejpam-700	335	3	[	[	X
ejpam-700	335	4	10	10	NUM
ejpam-700	335	5	]	]	X
ejpam-700	335	6	c	c	PROPN
ejpam-700	335	7	cinar	cinar	PROPN
ejpam-700	335	8	,	,	PUNCT
ejpam-700	335	9	t	t	PROPN
ejpam-700	335	10	mansour	mansour	PROPN
ejpam-700	335	11	and	and	CCONJ
ejpam-700	335	12	i	i	PRON
ejpam-700	335	13	yalçınkaya	yalçınkaya	NOUN
ejpam-700	335	14	.	.	PUNCT
ejpam-700	336	1	on	on	ADP
ejpam-700	336	2	the	the	DET
ejpam-700	336	3	difference	difference	NOUN
ejpam-700	336	4	equation	equation	NOUN
ejpam-700	336	5	of	of	ADP
ejpam-700	336	6	higher	high	ADJ
ejpam-700	336	7	order	order	NOUN
ejpam-700	336	8	.	.	PUNCT
ejpam-700	337	1	ars	ars	PROPN
ejpam-700	337	2	combinatoria	combinatoria	PROPN
ejpam-700	337	3	,	,	PUNCT
ejpam-700	337	4	(	(	PUNCT
ejpam-700	337	5	in	in	ADP
ejpam-700	337	6	press	press	NOUN
ejpam-700	337	7	)	)	PUNCT
ejpam-700	337	8	.	.	PUNCT
ejpam-700	338	1	[	[	X
ejpam-700	338	2	11	11	NUM
ejpam-700	338	3	]	]	X
ejpam-700	338	4	e	e	PROPN
ejpam-700	338	5	m	m	NOUN
ejpam-700	338	6	elabbasy	elabbasy	ADJ
ejpam-700	338	7	,	,	PUNCT
ejpam-700	338	8	h	h	PROPN
ejpam-700	338	9	el	el	PROPN
ejpam-700	338	10	-	-	PROPN
ejpam-700	338	11	metwally	metwally	ADV
ejpam-700	338	12	and	and	CCONJ
ejpam-700	338	13	e	e	NOUN
ejpam-700	338	14	m	m	VERB
ejpam-700	338	15	elsayed	elsaye	VERB
ejpam-700	338	16	.	.	PUNCT
ejpam-700	339	1	on	on	ADP
ejpam-700	339	2	the	the	DET
ejpam-700	339	3	difference	difference	NOUN
ejpam-700	339	4	equation	equation	NOUN
ejpam-700	339	5	xn+1	xn+1	PROPN
ejpam-700	339	6	=	=	SYM
ejpam-700	339	7	axn−	axn−	PROPN
ejpam-700	339	8	bxn	bxn	VERB
ejpam-700	339	9	cxn−d	cxn−d	INTJ
ejpam-700	339	10	xn−1	xn−1	PROPN
ejpam-700	339	11	.	.	PUNCT
ejpam-700	340	1	adv	adv	PROPN
ejpam-700	340	2	.	.	PROPN
ejpam-700	340	3	differ	differ	VERB
ejpam-700	340	4	.	.	PUNCT
ejpam-700	341	1	equ	equ	PROPN
ejpam-700	341	2	.	.	PROPN
ejpam-700	341	3	,	,	PUNCT
ejpam-700	341	4	2006:1–10	2006:1–10	NOUN
ejpam-700	341	5	,	,	PUNCT
ejpam-700	341	6	article	article	NOUN
ejpam-700	341	7	i	i	PROPN
ejpam-700	341	8	d	d	PROPN
ejpam-700	341	9	82579	82579	NUM
ejpam-700	341	10	,	,	PUNCT
ejpam-700	341	11	2006	2006	NUM
ejpam-700	341	12	.	.	PUNCT
ejpam-700	342	1	[	[	X
ejpam-700	342	2	12	12	NUM
ejpam-700	342	3	]	]	X
ejpam-700	342	4	e	e	PROPN
ejpam-700	342	5	m	m	NOUN
ejpam-700	342	6	elabbasy	elabbasy	ADJ
ejpam-700	342	7	,	,	PUNCT
ejpam-700	342	8	h	h	PROPN
ejpam-700	342	9	el	el	PROPN
ejpam-700	342	10	-	-	PROPN
ejpam-700	342	11	metwally	metwally	ADV
ejpam-700	342	12	and	and	CCONJ
ejpam-700	342	13	e	e	NOUN
ejpam-700	342	14	m	m	VERB
ejpam-700	342	15	elsayed	elsaye	VERB
ejpam-700	342	16	.	.	PUNCT
ejpam-700	343	1	on	on	ADP
ejpam-700	343	2	the	the	DET
ejpam-700	343	3	difference	difference	NOUN
ejpam-700	343	4	equations	equation	NOUN
ejpam-700	343	5	xn+1	xn+1	NUM
ejpam-700	343	6	=	=	SYM
ejpam-700	343	7	αxn−k	αxn−k	X
ejpam-700	343	8	β+γ	β+γ	PUNCT
ejpam-700	343	9	∏k	∏k	ADJ
ejpam-700	343	10	i=0	i=0	PROPN
ejpam-700	343	11	xn−i	xn−i	PROPN
ejpam-700	343	12	.	.	PUNCT
ejpam-700	344	1	j.	j.	PROPN
ejpam-700	344	2	conc	conc	PROPN
ejpam-700	344	3	.	.	PUNCT
ejpam-700	345	1	appl	appl	PROPN
ejpam-700	345	2	.	.	PROPN
ejpam-700	345	3	math	math	PROPN
ejpam-700	345	4	.	.	PUNCT
ejpam-700	346	1	,	,	PUNCT
ejpam-700	346	2	5(2):101	5(2):101	NUM
ejpam-700	346	3	-	-	SYM
ejpam-700	346	4	113	113	NUM
ejpam-700	346	5	,	,	PUNCT
ejpam-700	346	6	2007	2007	NUM
ejpam-700	346	7	.	.	PUNCT
ejpam-700	347	1	[	[	X
ejpam-700	347	2	13	13	NUM
ejpam-700	347	3	]	]	X
ejpam-700	347	4	e	e	PROPN
ejpam-700	347	5	m	m	NOUN
ejpam-700	347	6	elabbasy	elabbasy	ADJ
ejpam-700	347	7	,	,	PUNCT
ejpam-700	347	8	h	h	PROPN
ejpam-700	347	9	el	el	PROPN
ejpam-700	347	10	-	-	PROPN
ejpam-700	347	11	metwally	metwally	ADV
ejpam-700	347	12	and	and	CCONJ
ejpam-700	347	13	e	e	NOUN
ejpam-700	347	14	m	m	VERB
ejpam-700	347	15	elsayed	elsaye	VERB
ejpam-700	347	16	.	.	PUNCT
ejpam-700	348	1	on	on	ADP
ejpam-700	348	2	the	the	DET
ejpam-700	348	3	solutions	solution	NOUN
ejpam-700	348	4	of	of	ADP
ejpam-700	348	5	difference	difference	NOUN
ejpam-700	348	6	equations	equation	NOUN
ejpam-700	348	7	of	of	ADP
ejpam-700	348	8	order	order	NOUN
ejpam-700	348	9	four	four	NUM
ejpam-700	348	10	.	.	PUNCT
ejpam-700	349	1	rocky	rocky	ADJ
ejpam-700	349	2	mountain	mountain	PROPN
ejpam-700	349	3	journal	journal	NOUN
ejpam-700	349	4	of	of	ADP
ejpam-700	349	5	mathematics	mathematic	NOUN
ejpam-700	349	6	,	,	PUNCT
ejpam-700	349	7	in	in	ADP
ejpam-700	349	8	press	press	NOUN
ejpam-700	349	9	.	.	PUNCT
ejpam-700	350	1	[	[	X
ejpam-700	350	2	14	14	NUM
ejpam-700	350	3	]	]	X
ejpam-700	350	4	e	e	PROPN
ejpam-700	350	5	m	m	NOUN
ejpam-700	350	6	elabbasy	elabbasy	ADJ
ejpam-700	350	7	,	,	PUNCT
ejpam-700	350	8	h	h	PROPN
ejpam-700	350	9	el	el	PROPN
ejpam-700	350	10	-	-	PROPN
ejpam-700	350	11	metwally	metwally	ADV
ejpam-700	350	12	and	and	CCONJ
ejpam-700	350	13	e	e	NOUN
ejpam-700	350	14	m	m	AUX
ejpam-700	350	15	elsayed	elsaye	VERB
ejpam-700	350	16	.	.	PUNCT
ejpam-700	351	1	global	global	ADJ
ejpam-700	351	2	behavior	behavior	NOUN
ejpam-700	351	3	of	of	ADP
ejpam-700	351	4	the	the	DET
ejpam-700	351	5	solutions	solution	NOUN
ejpam-700	351	6	of	of	ADP
ejpam-700	351	7	difference	difference	NOUN
ejpam-700	351	8	equation	equation	NOUN
ejpam-700	351	9	,	,	PUNCT
ejpam-700	351	10	advances	advance	NOUN
ejpam-700	351	11	in	in	ADP
ejpam-700	351	12	difference	difference	NOUN
ejpam-700	351	13	equations	equation	NOUN
ejpam-700	351	14	,	,	PUNCT
ejpam-700	351	15	in	in	ADP
ejpam-700	351	16	press	press	NOUN
ejpam-700	351	17	.	.	PUNCT
ejpam-700	352	1	[	[	X
ejpam-700	352	2	15	15	NUM
ejpam-700	352	3	]	]	X
ejpam-700	352	4	e	e	NOUN
ejpam-700	352	5	m	m	NOUN
ejpam-700	352	6	elabbasy	elabbasy	ADJ
ejpam-700	352	7	and	and	CCONJ
ejpam-700	352	8	e	e	NOUN
ejpam-700	352	9	m	m	VERB
ejpam-700	352	10	elsayed	elsaye	VERB
ejpam-700	352	11	.	.	PUNCT
ejpam-700	353	1	global	global	ADJ
ejpam-700	353	2	attractivity	attractivity	NOUN
ejpam-700	353	3	and	and	CCONJ
ejpam-700	353	4	periodic	periodic	ADJ
ejpam-700	353	5	nature	nature	NOUN
ejpam-700	353	6	of	of	ADP
ejpam-700	353	7	a	a	DET
ejpam-700	353	8	difference	difference	NOUN
ejpam-700	353	9	equation	equation	NOUN
ejpam-700	353	10	.	.	PUNCT
ejpam-700	354	1	world	world	NOUN
ejpam-700	354	2	applied	apply	VERB
ejpam-700	354	3	sciences	science	NOUN
ejpam-700	354	4	journal	journal	NOUN
ejpam-700	354	5	,	,	PUNCT
ejpam-700	354	6	12(1):39–47	12(1):39–47	NUM
ejpam-700	354	7	,	,	PUNCT
ejpam-700	354	8	2011	2011	NUM
ejpam-700	354	9	.	.	PUNCT
ejpam-700	355	1	[	[	X
ejpam-700	355	2	16	16	NUM
ejpam-700	355	3	]	]	X
ejpam-700	355	4	e	e	NOUN
ejpam-700	355	5	m	m	PROPN
ejpam-700	355	6	elsayed	elsaye	VERB
ejpam-700	355	7	.	.	PUNCT
ejpam-700	356	1	dynamics	dynamic	NOUN
ejpam-700	356	2	of	of	ADP
ejpam-700	356	3	a	a	DET
ejpam-700	356	4	recursive	recursive	ADJ
ejpam-700	356	5	sequence	sequence	NOUN
ejpam-700	356	6	of	of	ADP
ejpam-700	356	7	higher	high	ADJ
ejpam-700	356	8	order	order	NOUN
ejpam-700	356	9	.	.	PUNCT
ejpam-700	357	1	communications	communication	NOUN
ejpam-700	357	2	on	on	ADP
ejpam-700	357	3	applied	apply	VERB
ejpam-700	357	4	nonlinear	nonlinear	ADJ
ejpam-700	357	5	analysis	analysis	NOUN
ejpam-700	357	6	,	,	PUNCT
ejpam-700	357	7	16(2):37–50	16(2):37–50	NUM
ejpam-700	357	8	,	,	PUNCT
ejpam-700	357	9	2009	2009	NUM
ejpam-700	357	10	.	.	PUNCT
ejpam-700	358	1	[	[	X
ejpam-700	358	2	17	17	NUM
ejpam-700	358	3	]	]	X
ejpam-700	358	4	e	e	NOUN
ejpam-700	358	5	m	m	PRON
ejpam-700	358	6	elsayed	elsaye	VERB
ejpam-700	358	7	.	.	PUNCT
ejpam-700	359	1	qualitative	qualitative	ADJ
ejpam-700	359	2	behavior	behavior	NOUN
ejpam-700	359	3	of	of	ADP
ejpam-700	359	4	difference	difference	NOUN
ejpam-700	359	5	equation	equation	NOUN
ejpam-700	359	6	of	of	ADP
ejpam-700	359	7	order	order	NOUN
ejpam-700	359	8	two	two	NUM
ejpam-700	359	9	.	.	PUNCT
ejpam-700	360	1	mathematical	mathematical	ADJ
ejpam-700	360	2	and	and	CCONJ
ejpam-700	360	3	computer	computer	NOUN
ejpam-700	360	4	modelling	modelling	NOUN
ejpam-700	360	5	,	,	PUNCT
ejpam-700	360	6	50:1130–1141	50:1130–1141	NUM
ejpam-700	360	7	,	,	PUNCT
ejpam-700	360	8	2009	2009	NUM
ejpam-700	360	9	.	.	PUNCT
ejpam-700	361	1	[	[	X
ejpam-700	361	2	18	18	NUM
ejpam-700	361	3	]	]	X
ejpam-700	361	4	e	e	NOUN
ejpam-700	361	5	m	m	PRON
ejpam-700	361	6	elsayed	elsaye	VERB
ejpam-700	361	7	.	.	PUNCT
ejpam-700	362	1	qualitative	qualitative	ADJ
ejpam-700	362	2	behavior	behavior	NOUN
ejpam-700	362	3	of	of	ADP
ejpam-700	362	4	a	a	DET
ejpam-700	362	5	rational	rational	ADJ
ejpam-700	362	6	recursive	recursive	ADJ
ejpam-700	362	7	sequence	sequence	NOUN
ejpam-700	362	8	.	.	PUNCT
ejpam-700	363	1	indagationes	indagatione	NOUN
ejpam-700	363	2	mathematicae	mathematicae	PROPN
ejpam-700	363	3	,	,	PUNCT
ejpam-700	363	4	new	new	ADJ
ejpam-700	363	5	series	series	NOUN
ejpam-700	363	6	,	,	PUNCT
ejpam-700	363	7	19(2):189–201	19(2):189–201	PROPN
ejpam-700	363	8	,	,	PUNCT
ejpam-700	363	9	2008	2008	NUM
ejpam-700	363	10	.	.	PUNCT
ejpam-700	364	1	[	[	X
ejpam-700	364	2	19	19	NUM
ejpam-700	364	3	]	]	X
ejpam-700	364	4	e	e	NOUN
ejpam-700	364	5	m	m	PRON
ejpam-700	364	6	elsayed	elsaye	VERB
ejpam-700	364	7	.	.	PUNCT
ejpam-700	365	1	dynamics	dynamic	NOUN
ejpam-700	365	2	of	of	ADP
ejpam-700	365	3	a	a	DET
ejpam-700	365	4	rational	rational	ADJ
ejpam-700	365	5	recursive	recursive	ADJ
ejpam-700	365	6	sequences	sequence	NOUN
ejpam-700	365	7	.	.	PUNCT
ejpam-700	366	1	international	international	ADJ
ejpam-700	366	2	journal	journal	PROPN
ejpam-700	366	3	of	of	ADP
ejpam-700	366	4	difference	difference	NOUN
ejpam-700	366	5	equations	equation	NOUN
ejpam-700	366	6	,	,	PUNCT
ejpam-700	366	7	4(2):185–200	4(2):185–200	NUM
ejpam-700	366	8	,	,	PUNCT
ejpam-700	366	9	2009	2009	NUM
ejpam-700	366	10	.	.	PUNCT
ejpam-700	367	1	[	[	X
ejpam-700	367	2	20	20	NUM
ejpam-700	367	3	]	]	X
ejpam-700	367	4	e	e	NOUN
ejpam-700	367	5	m	m	PROPN
ejpam-700	367	6	elsayed	elsaye	VERB
ejpam-700	367	7	.	.	PUNCT
ejpam-700	368	1	dynamics	dynamic	NOUN
ejpam-700	368	2	of	of	ADP
ejpam-700	368	3	recursive	recursive	ADJ
ejpam-700	368	4	sequence	sequence	NOUN
ejpam-700	368	5	of	of	ADP
ejpam-700	368	6	order	order	NOUN
ejpam-700	368	7	two	two	NUM
ejpam-700	368	8	.	.	PUNCT
ejpam-700	369	1	kyungpook	kyungpook	PROPN
ejpam-700	369	2	mathematical	mathematical	PROPN
ejpam-700	369	3	journal	journal	PROPN
ejpam-700	369	4	,	,	PUNCT
ejpam-700	369	5	50:483	50:483	NUM
ejpam-700	369	6	-	-	SYM
ejpam-700	369	7	497	497	NUM
ejpam-700	369	8	,	,	PUNCT
ejpam-700	369	9	2010	2010	NUM
ejpam-700	369	10	.	.	PUNCT
ejpam-700	370	1	[	[	X
ejpam-700	370	2	21	21	NUM
ejpam-700	370	3	]	]	X
ejpam-700	370	4	e	e	NOUN
ejpam-700	370	5	m	m	PROPN
ejpam-700	370	6	elsayed	elsaye	VERB
ejpam-700	370	7	.	.	PUNCT
ejpam-700	371	1	on	on	ADP
ejpam-700	371	2	the	the	DET
ejpam-700	371	3	difference	difference	NOUN
ejpam-700	371	4	equation	equation	NOUN
ejpam-700	371	5	xn+1	xn+1	PROPN
ejpam-700	371	6	=	=	SYM
ejpam-700	371	7	xn−5	xn−5	PROPN
ejpam-700	371	8	−1	−1	NOUN
ejpam-700	371	9	+	+	PROPN
ejpam-700	371	10	xn−2	xn−2	PROPN
ejpam-700	371	11	xn−5	xn−5	PROPN
ejpam-700	371	12	.	.	PUNCT
ejpam-700	372	1	international	international	ADJ
ejpam-700	372	2	journal	journal	PROPN
ejpam-700	372	3	of	of	ADP
ejpam-700	372	4	contemporary	contemporary	PROPN
ejpam-700	372	5	mathematical	mathematical	PROPN
ejpam-700	372	6	sciences	sciences	PROPN
ejpam-700	372	7	,	,	PUNCT
ejpam-700	372	8	3(33):1657	3(33):1657	NUM
ejpam-700	372	9	-	-	SYM
ejpam-700	372	10	1664	1664	NUM
ejpam-700	372	11	,	,	PUNCT
ejpam-700	372	12	2008	2008	NUM
ejpam-700	372	13	.	.	PUNCT
ejpam-700	373	1	[	[	X
ejpam-700	373	2	22	22	NUM
ejpam-700	373	3	]	]	X
ejpam-700	373	4	e	e	NOUN
ejpam-700	373	5	m	m	PRON
ejpam-700	373	6	elsayed	elsaye	VERB
ejpam-700	373	7	.	.	PUNCT
ejpam-700	374	1	qualitative	qualitative	ADJ
ejpam-700	374	2	behavior	behavior	NOUN
ejpam-700	374	3	of	of	ADP
ejpam-700	374	4	difference	difference	NOUN
ejpam-700	374	5	equation	equation	NOUN
ejpam-700	374	6	of	of	ADP
ejpam-700	374	7	order	order	NOUN
ejpam-700	374	8	three	three	NUM
ejpam-700	374	9	.	.	PUNCT
ejpam-700	375	1	acta	acta	PROPN
ejpam-700	375	2	scientiarum	scientiarum	PROPN
ejpam-700	375	3	mathematicarum	mathematicarum	PROPN
ejpam-700	375	4	(	(	PUNCT
ejpam-700	375	5	szeged	szeged	PROPN
ejpam-700	375	6	)	)	PUNCT
ejpam-700	375	7	,	,	PUNCT
ejpam-700	375	8	75(1	75(1	NOUN
ejpam-700	375	9	-	-	PUNCT
ejpam-700	375	10	2):113–129	2):113–129	NUM
ejpam-700	375	11	,	,	PUNCT
ejpam-700	375	12	2009	2009	NUM
ejpam-700	375	13	.	.	PUNCT
ejpam-700	376	1	[	[	X
ejpam-700	376	2	23	23	NUM
ejpam-700	376	3	]	]	X
ejpam-700	376	4	e	e	NOUN
ejpam-700	376	5	m	m	NOUN
ejpam-700	376	6	elsayed	elsaye	VERB
ejpam-700	376	7	.	.	PUNCT
ejpam-700	377	1	on	on	ADP
ejpam-700	377	2	the	the	DET
ejpam-700	377	3	global	global	ADJ
ejpam-700	377	4	attractivity	attractivity	NOUN
ejpam-700	377	5	and	and	CCONJ
ejpam-700	377	6	the	the	DET
ejpam-700	377	7	solution	solution	NOUN
ejpam-700	377	8	of	of	ADP
ejpam-700	377	9	recursive	recursive	ADJ
ejpam-700	377	10	sequence	sequence	NOUN
ejpam-700	377	11	.	.	PUNCT
ejpam-700	378	1	studia	studia	PROPN
ejpam-700	378	2	scientiarum	scientiarum	PROPN
ejpam-700	378	3	mathematicarum	mathematicarum	PROPN
ejpam-700	378	4	hungarica	hungarica	PROPN
ejpam-700	378	5	,	,	PUNCT
ejpam-700	378	6	47(3):401	47(3):401	PROPN
ejpam-700	378	7	-	-	SYM
ejpam-700	378	8	418	418	NUM
ejpam-700	378	9	,	,	PUNCT
ejpam-700	378	10	2010	2010	NUM
ejpam-700	378	11	.	.	PUNCT
ejpam-700	379	1	[	[	X
ejpam-700	379	2	24	24	NUM
ejpam-700	379	3	]	]	X
ejpam-700	379	4	e	e	NOUN
ejpam-700	379	5	m	m	NOUN
ejpam-700	379	6	elsayed	elsaye	VERB
ejpam-700	379	7	.	.	PUNCT
ejpam-700	380	1	behavior	behavior	NOUN
ejpam-700	380	2	of	of	ADP
ejpam-700	380	3	a	a	DET
ejpam-700	380	4	rational	rational	ADJ
ejpam-700	380	5	recursive	recursive	ADJ
ejpam-700	380	6	sequences	sequence	NOUN
ejpam-700	380	7	.	.	PUNCT
ejpam-700	381	1	studia	studia	PROPN
ejpam-700	381	2	univ	univ	PROPN
ejpam-700	381	3	.	.	PUNCT
ejpam-700	381	4	"	"	PUNCT
ejpam-700	382	1	babes	babe	NOUN
ejpam-700	382	2	–	–	PUNCT
ejpam-700	382	3	bolyai	bolyai	NOUN
ejpam-700	382	4	"	"	PUNCT
ejpam-700	382	5	,	,	PUNCT
ejpam-700	382	6	mathematica	mathematica	PROPN
ejpam-700	382	7	,	,	PUNCT
ejpam-700	382	8	lvi(1):27–42	lvi(1):27–42	PROPN
ejpam-700	382	9	,	,	PUNCT
ejpam-700	382	10	2011	2011	NUM
ejpam-700	382	11	.	.	PUNCT
ejpam-700	383	1	[	[	X
ejpam-700	383	2	25	25	NUM
ejpam-700	383	3	]	]	X
ejpam-700	383	4	e	e	NOUN
ejpam-700	383	5	m	m	NOUN
ejpam-700	383	6	elsayed	elsaye	VERB
ejpam-700	383	7	.	.	PUNCT
ejpam-700	384	1	on	on	ADP
ejpam-700	384	2	the	the	DET
ejpam-700	384	3	global	global	ADJ
ejpam-700	384	4	attractivity	attractivity	NOUN
ejpam-700	384	5	and	and	CCONJ
ejpam-700	384	6	the	the	DET
ejpam-700	384	7	periodic	periodic	ADJ
ejpam-700	384	8	character	character	NOUN
ejpam-700	384	9	of	of	ADP
ejpam-700	384	10	a	a	DET
ejpam-700	384	11	recursive	recursive	ADJ
ejpam-700	384	12	sequence	sequence	NOUN
ejpam-700	384	13	.	.	PUNCT
ejpam-700	385	1	opuscula	opuscula	PROPN
ejpam-700	385	2	mathematica	mathematica	PROPN
ejpam-700	385	3	,	,	PUNCT
ejpam-700	385	4	30(4):431–446	30(4):431–446	PROPN
ejpam-700	385	5	,	,	PUNCT
ejpam-700	385	6	2010	2010	NUM
ejpam-700	385	7	.	.	PUNCT
ejpam-700	386	1	references	reference	NOUN
ejpam-700	386	2	302	302	NUM
ejpam-700	387	1	[	[	X
ejpam-700	387	2	26	26	NUM
ejpam-700	387	3	]	]	X
ejpam-700	387	4	e	e	NOUN
ejpam-700	387	5	m	m	PROPN
ejpam-700	387	6	elsayed	elsaye	VERB
ejpam-700	387	7	.	.	PUNCT
ejpam-700	388	1	solution	solution	NOUN
ejpam-700	388	2	and	and	CCONJ
ejpam-700	388	3	attractivity	attractivity	NOUN
ejpam-700	388	4	for	for	ADP
ejpam-700	388	5	a	a	DET
ejpam-700	388	6	rational	rational	ADJ
ejpam-700	388	7	recursive	recursive	ADJ
ejpam-700	388	8	sequence	sequence	NOUN
ejpam-700	388	9	.	.	PUNCT
ejpam-700	389	1	discrete	discrete	ADJ
ejpam-700	389	2	dynamics	dynamic	NOUN
ejpam-700	389	3	in	in	ADP
ejpam-700	389	4	nature	nature	NOUN
ejpam-700	389	5	and	and	CCONJ
ejpam-700	389	6	society	society	NOUN
ejpam-700	389	7	,	,	PUNCT
ejpam-700	389	8	2011:17	2011:17	NUM
ejpam-700	389	9	pages	page	NOUN
ejpam-700	389	10	,	,	PUNCT
ejpam-700	389	11	article	article	NOUN
ejpam-700	389	12	i	i	PROPN
ejpam-700	389	13	d	d	PROPN
ejpam-700	389	14	982309	982309	NUM
ejpam-700	389	15	,	,	PUNCT
ejpam-700	389	16	2011	2011	NUM
ejpam-700	389	17	.	.	PUNCT
ejpam-700	390	1	[	[	X
ejpam-700	390	2	27	27	NUM
ejpam-700	390	3	]	]	X
ejpam-700	390	4	e	e	NOUN
ejpam-700	390	5	m	m	PROPN
ejpam-700	390	6	elsayed	elsaye	VERB
ejpam-700	390	7	.	.	PUNCT
ejpam-700	391	1	on	on	ADP
ejpam-700	391	2	the	the	DET
ejpam-700	391	3	solutions	solution	NOUN
ejpam-700	391	4	of	of	ADP
ejpam-700	391	5	a	a	DET
ejpam-700	391	6	rational	rational	ADJ
ejpam-700	391	7	system	system	NOUN
ejpam-700	391	8	of	of	ADP
ejpam-700	391	9	difference	difference	NOUN
ejpam-700	391	10	equations	equation	NOUN
ejpam-700	391	11	.	.	PUNCT
ejpam-700	392	1	fasciculi	fasciculi	PROPN
ejpam-700	392	2	mathematici	mathematici	PROPN
ejpam-700	392	3	,	,	PUNCT
ejpam-700	392	4	45:25–36	45:25–36	NUM
ejpam-700	392	5	,	,	PUNCT
ejpam-700	392	6	2010	2010	NUM
ejpam-700	392	7	.	.	PUNCT
ejpam-700	393	1	[	[	X
ejpam-700	393	2	28	28	NUM
ejpam-700	393	3	]	]	X
ejpam-700	393	4	e	e	NOUN
ejpam-700	393	5	m	m	PROPN
ejpam-700	393	6	elsayed	elsaye	VERB
ejpam-700	393	7	.	.	PUNCT
ejpam-700	394	1	solution	solution	NOUN
ejpam-700	394	2	and	and	CCONJ
ejpam-700	394	3	behavior	behavior	NOUN
ejpam-700	394	4	of	of	ADP
ejpam-700	394	5	a	a	DET
ejpam-700	394	6	rational	rational	ADJ
ejpam-700	394	7	difference	difference	NOUN
ejpam-700	394	8	equations	equation	NOUN
ejpam-700	394	9	.	.	PUNCT
ejpam-700	395	1	acta	acta	PROPN
ejpam-700	395	2	universitatis	universitatis	PROPN
ejpam-700	395	3	apulensis	apulensis	NOUN
ejpam-700	395	4	,	,	PUNCT
ejpam-700	395	5	23:233–249	23:233–249	NUM
ejpam-700	395	6	,	,	PUNCT
ejpam-700	395	7	2010	2010	NUM
ejpam-700	395	8	.	.	PUNCT
ejpam-700	396	1	[	[	X
ejpam-700	396	2	29	29	NUM
ejpam-700	396	3	]	]	X
ejpam-700	396	4	e	e	NOUN
ejpam-700	396	5	m	m	PROPN
ejpam-700	396	6	elsayed	elsaye	VERB
ejpam-700	396	7	.	.	PUNCT
ejpam-700	397	1	solution	solution	NOUN
ejpam-700	397	2	of	of	ADP
ejpam-700	397	3	a	a	DET
ejpam-700	397	4	recursive	recursive	ADJ
ejpam-700	397	5	sequence	sequence	NOUN
ejpam-700	397	6	of	of	ADP
ejpam-700	397	7	order	order	NOUN
ejpam-700	397	8	ten	ten	NUM
ejpam-700	397	9	.	.	PUNCT
ejpam-700	398	1	general	general	ADJ
ejpam-700	398	2	mathematics	mathematics	PROPN
ejpam-700	398	3	,	,	PUNCT
ejpam-700	398	4	19(1):145–162	19(1):145–162	PROPN
ejpam-700	398	5	,	,	PUNCT
ejpam-700	398	6	2011	2011	NUM
ejpam-700	398	7	.	.	PUNCT
ejpam-700	399	1	[	[	X
ejpam-700	399	2	30	30	NUM
ejpam-700	399	3	]	]	X
ejpam-700	399	4	e	e	NOUN
ejpam-700	399	5	m	m	VERB
ejpam-700	399	6	elsayed	elsaye	VERB
ejpam-700	399	7	,	,	PUNCT
ejpam-700	399	8	b	b	X
ejpam-700	399	9	iricanin	iricanin	NOUN
ejpam-700	399	10	and	and	CCONJ
ejpam-700	399	11	s	s	NOUN
ejpam-700	399	12	stevic	stevic	NOUN
ejpam-700	399	13	.	.	PUNCT
ejpam-700	400	1	on	on	ADP
ejpam-700	400	2	the	the	DET
ejpam-700	400	3	max	max	PROPN
ejpam-700	400	4	-	-	PUNCT
ejpam-700	400	5	type	type	NOUN
ejpam-700	400	6	equation	equation	NOUN
ejpam-700	400	7	.	.	PUNCT
ejpam-700	401	1	ars	ar	VERB
ejpam-700	401	2	combinatoria	combinatoria	PROPN
ejpam-700	401	3	,	,	PUNCT
ejpam-700	401	4	95:187–192	95:187–192	NUM
ejpam-700	401	5	,	,	PUNCT
ejpam-700	401	6	2010	2010	NUM
ejpam-700	401	7	.	.	PUNCT
ejpam-700	402	1	[	[	X
ejpam-700	402	2	31	31	NUM
ejpam-700	402	3	]	]	PUNCT
ejpam-700	402	4	a	a	DET
ejpam-700	402	5	gelisken	gelisken	VERB
ejpam-700	402	6	,	,	PUNCT
ejpam-700	402	7	c	c	PROPN
ejpam-700	402	8	cinar	cinar	PROPN
ejpam-700	402	9	and	and	CCONJ
ejpam-700	402	10	i	i	PRON
ejpam-700	402	11	yalcinkaya	yalcinkaya	NOUN
ejpam-700	402	12	.	.	PUNCT
ejpam-700	403	1	on	on	ADP
ejpam-700	403	2	a	a	DET
ejpam-700	403	3	max	max	ADJ
ejpam-700	403	4	-	-	PUNCT
ejpam-700	403	5	type	type	NOUN
ejpam-700	403	6	difference	difference	NOUN
ejpam-700	403	7	equation	equation	NOUN
ejpam-700	403	8	.	.	PUNCT
ejpam-700	404	1	advances	advance	NOUN
ejpam-700	404	2	in	in	ADP
ejpam-700	404	3	difference	difference	NOUN
ejpam-700	404	4	equations	equation	NOUN
ejpam-700	404	5	,	,	PUNCT
ejpam-700	404	6	2010:6	2010:6	NUM
ejpam-700	404	7	pages	page	NOUN
ejpam-700	404	8	,	,	PUNCT
ejpam-700	404	9	article	article	NOUN
ejpam-700	404	10	i	i	PROPN
ejpam-700	404	11	d	d	PROPN
ejpam-700	404	12	584890	584890	NUM
ejpam-700	404	13	,	,	PUNCT
ejpam-700	404	14	2010	2010	NUM
ejpam-700	404	15	.	.	PUNCT
ejpam-700	405	1	[	[	X
ejpam-700	405	2	32	32	NUM
ejpam-700	405	3	]	]	PUNCT
ejpam-700	405	4	a	a	DET
ejpam-700	405	5	geli̧sken	geli̧sken	PROPN
ejpam-700	405	6	,	,	PUNCT
ejpam-700	405	7	c	c	PROPN
ejpam-700	405	8	cinar	cinar	PROPN
ejpam-700	405	9	and	and	CCONJ
ejpam-700	405	10	i	i	PRON
ejpam-700	405	11	yalçınkaya	yalçınkaya	NOUN
ejpam-700	405	12	.	.	PUNCT
ejpam-700	406	1	on	on	ADP
ejpam-700	406	2	the	the	DET
ejpam-700	406	3	periodicity	periodicity	NOUN
ejpam-700	406	4	of	of	ADP
ejpam-700	406	5	a	a	DET
ejpam-700	406	6	difference	difference	NOUN
ejpam-700	406	7	equation	equation	NOUN
ejpam-700	406	8	with	with	ADP
ejpam-700	406	9	maximum	maximum	ADJ
ejpam-700	406	10	.	.	PUNCT
ejpam-700	406	11	discrete	discrete	ADJ
ejpam-700	406	12	dynamics	dynamic	NOUN
ejpam-700	406	13	in	in	ADP
ejpam-700	406	14	nature	nature	NOUN
ejpam-700	406	15	and	and	CCONJ
ejpam-700	406	16	society	society	NOUN
ejpam-700	406	17	,	,	PUNCT
ejpam-700	406	18	2008:11	2008:11	NUM
ejpam-700	406	19	pages	page	NOUN
ejpam-700	406	20	,	,	PUNCT
ejpam-700	406	21	article	article	NOUN
ejpam-700	406	22	i	i	PROPN
ejpam-700	406	23	d	d	PROPN
ejpam-700	406	24	820629	820629	NUM
ejpam-700	406	25	,	,	PUNCT
ejpam-700	406	26	doi	doi	NOUN
ejpam-700	406	27	:	:	PUNCT
ejpam-700	406	28	10.1155/2008/820629	10.1155/2008/820629	NUM
ejpam-700	406	29	.	.	PUNCT
ejpam-700	407	1	[	[	X
ejpam-700	407	2	33	33	NUM
ejpam-700	407	3	]	]	PUNCT
ejpam-700	407	4	t	t	PROPN
ejpam-700	407	5	f	f	PROPN
ejpam-700	407	6	ibrahim	ibrahim	PROPN
ejpam-700	407	7	.	.	PUNCT
ejpam-700	408	1	on	on	ADP
ejpam-700	408	2	the	the	DET
ejpam-700	408	3	third	third	ADJ
ejpam-700	408	4	order	order	NOUN
ejpam-700	408	5	rational	rational	ADJ
ejpam-700	408	6	difference	difference	NOUN
ejpam-700	408	7	equation	equation	NOUN
ejpam-700	408	8	xn+1	xn+1	PUNCT
ejpam-700	408	9	=	=	SYM
ejpam-700	408	10	xn	xn	PROPN
ejpam-700	409	1	xn−2	xn−2	PROPN
ejpam-700	409	2	xn−1(a+bxn	xn−1(a+bxn	PROPN
ejpam-700	409	3	xn−2	xn−2	PROPN
ejpam-700	409	4	)	)	PUNCT
ejpam-700	409	5	.	.	PUNCT
ejpam-700	410	1	int	int	NOUN
ejpam-700	410	2	.	.	PUNCT
ejpam-700	411	1	j.	j.	PROPN
ejpam-700	411	2	contemp	contemp	PROPN
ejpam-700	411	3	.	.	PUNCT
ejpam-700	412	1	math	math	NOUN
ejpam-700	412	2	.	.	PUNCT
ejpam-700	413	1	sciences	science	NOUN
ejpam-700	413	2	,	,	PUNCT
ejpam-700	413	3	4(27):1321	4(27):1321	NUM
ejpam-700	413	4	-	-	SYM
ejpam-700	413	5	1334	1334	NUM
ejpam-700	413	6	,	,	PUNCT
ejpam-700	413	7	2009	2009	NUM
ejpam-700	413	8	.	.	PUNCT
ejpam-700	414	1	[	[	X
ejpam-700	414	2	34	34	NUM
ejpam-700	414	3	]	]	X
ejpam-700	414	4	r	r	NOUN
ejpam-700	414	5	karatas	karata	NOUN
ejpam-700	414	6	and	and	CCONJ
ejpam-700	414	7	c	c	PROPN
ejpam-700	414	8	cinar	cinar	PROPN
ejpam-700	414	9	.	.	PUNCT
ejpam-700	415	1	on	on	ADP
ejpam-700	415	2	the	the	DET
ejpam-700	415	3	solutions	solution	NOUN
ejpam-700	415	4	of	of	ADP
ejpam-700	415	5	the	the	DET
ejpam-700	415	6	difference	difference	NOUN
ejpam-700	415	7	equation	equation	NOUN
ejpam-700	415	8	xn+1	xn+1	NOUN
ejpam-700	415	9	=	=	SYM
ejpam-700	415	10	axn−(2k+2	axn−(2k+2	NOUN
ejpam-700	415	11	)	)	PUNCT
ejpam-700	415	12	−a+	−a+	X
ejpam-700	415	13	∏2k+2	∏2k+2	PROPN
ejpam-700	415	14	i=0	i=0	PROPN
ejpam-700	415	15	xn−i	xn−i	PROPN
ejpam-700	415	16	.	.	PUNCT
ejpam-700	416	1	int	int	NOUN
ejpam-700	416	2	.	.	PUNCT
ejpam-700	417	1	j.	j.	PROPN
ejpam-700	417	2	contemp	contemp	PROPN
ejpam-700	417	3	.	.	PUNCT
ejpam-700	418	1	math	math	NOUN
ejpam-700	418	2	.	.	PUNCT
ejpam-700	419	1	sciences	science	NOUN
ejpam-700	419	2	,	,	PUNCT
ejpam-700	419	3	2(13):1505	2(13):1505	NUM
ejpam-700	419	4	-	-	SYM
ejpam-700	419	5	1509	1509	NUM
ejpam-700	419	6	,	,	PUNCT
ejpam-700	419	7	2007	2007	NUM
ejpam-700	419	8	.	.	PUNCT
ejpam-700	420	1	[	[	X
ejpam-700	420	2	35	35	NUM
ejpam-700	420	3	]	]	X
ejpam-700	420	4	r	r	NOUN
ejpam-700	420	5	karatas	karata	NOUN
ejpam-700	420	6	,	,	PUNCT
ejpam-700	420	7	c	c	PROPN
ejpam-700	420	8	cinar	cinar	PROPN
ejpam-700	420	9	and	and	CCONJ
ejpam-700	420	10	d	d	ADP
ejpam-700	420	11	simsek	simsek	NOUN
ejpam-700	420	12	.	.	PUNCT
ejpam-700	421	1	on	on	ADP
ejpam-700	421	2	positive	positive	ADJ
ejpam-700	421	3	solutions	solution	NOUN
ejpam-700	421	4	of	of	ADP
ejpam-700	421	5	the	the	DET
ejpam-700	421	6	difference	difference	NOUN
ejpam-700	421	7	equation	equation	NOUN
ejpam-700	421	8	xn+1	xn+1	PROPN
ejpam-700	421	9	=	=	SYM
ejpam-700	421	10	xn−5	xn−5	PROPN
ejpam-700	421	11	1+xn−2	1+xn−2	NUM
ejpam-700	421	12	xn−5	xn−5	PROPN
ejpam-700	421	13	.	.	PUNCT
ejpam-700	422	1	int	int	NOUN
ejpam-700	422	2	.	.	PUNCT
ejpam-700	423	1	j.	j.	PROPN
ejpam-700	423	2	contemp	contemp	PROPN
ejpam-700	423	3	.	.	PUNCT
ejpam-700	424	1	math	math	NOUN
ejpam-700	424	2	.	.	PUNCT
ejpam-700	425	1	sci	sci	PROPN
ejpam-700	425	2	.	.	PROPN
ejpam-700	425	3	,	,	PUNCT
ejpam-700	425	4	1(10):495	1(10):495	PROPN
ejpam-700	425	5	-	-	SYM
ejpam-700	425	6	500	500	NUM
ejpam-700	425	7	,	,	PUNCT
ejpam-700	425	8	2006	2006	NUM
ejpam-700	425	9	.	.	PUNCT
ejpam-700	426	1	[	[	X
ejpam-700	426	2	36	36	NUM
ejpam-700	426	3	]	]	SYM
ejpam-700	426	4	v	v	ADP
ejpam-700	426	5	l	l	NOUN
ejpam-700	426	6	kocic	kocic	NOUN
ejpam-700	426	7	and	and	CCONJ
ejpam-700	426	8	g	g	PROPN
ejpam-700	426	9	ladas	ladas	PROPN
ejpam-700	426	10	.	.	PUNCT
ejpam-700	427	1	global	global	ADJ
ejpam-700	427	2	behavior	behavior	NOUN
ejpam-700	427	3	of	of	ADP
ejpam-700	427	4	nonlinear	nonlinear	ADJ
ejpam-700	427	5	difference	difference	NOUN
ejpam-700	427	6	equations	equation	NOUN
ejpam-700	427	7	of	of	ADP
ejpam-700	427	8	higher	high	ADJ
ejpam-700	427	9	order	order	NOUN
ejpam-700	427	10	with	with	ADP
ejpam-700	427	11	applications	application	NOUN
ejpam-700	427	12	.	.	PUNCT
ejpam-700	428	1	kluwer	kluwer	NOUN
ejpam-700	428	2	academic	academic	ADJ
ejpam-700	428	3	publishers	publisher	NOUN
ejpam-700	428	4	,	,	PUNCT
ejpam-700	428	5	dordrecht	dordrecht	PROPN
ejpam-700	428	6	,	,	PUNCT
ejpam-700	428	7	1993	1993	NUM
ejpam-700	428	8	.	.	PUNCT
ejpam-700	429	1	[	[	X
ejpam-700	429	2	37	37	NUM
ejpam-700	429	3	]	]	X
ejpam-700	429	4	m	m	VERB
ejpam-700	429	5	r	r	NOUN
ejpam-700	429	6	s	s	X
ejpam-700	429	7	kulenovic	kulenovic	VERB
ejpam-700	429	8	and	and	CCONJ
ejpam-700	429	9	g	g	PROPN
ejpam-700	429	10	ladas	ladas	PROPN
ejpam-700	429	11	.	.	PUNCT
ejpam-700	430	1	dynamics	dynamic	NOUN
ejpam-700	430	2	of	of	ADP
ejpam-700	430	3	second	second	ADJ
ejpam-700	430	4	order	order	NOUN
ejpam-700	430	5	rational	rational	ADJ
ejpam-700	430	6	difference	difference	NOUN
ejpam-700	430	7	equations	equation	NOUN
ejpam-700	430	8	with	with	ADP
ejpam-700	430	9	open	open	ADJ
ejpam-700	430	10	problems	problem	NOUN
ejpam-700	430	11	and	and	CCONJ
ejpam-700	430	12	conjectures	conjecture	VERB
ejpam-700	430	13	.	.	PUNCT
ejpam-700	431	1	chapman	chapman	PROPN
ejpam-700	431	2	&	&	CCONJ
ejpam-700	431	3	hall	hall	PROPN
ejpam-700	431	4	/	/	SYM
ejpam-700	431	5	crc	crc	PROPN
ejpam-700	431	6	press	press	NOUN
ejpam-700	431	7	,	,	PUNCT
ejpam-700	431	8	2001	2001	NUM
ejpam-700	431	9	.	.	PUNCT
ejpam-700	432	1	[	[	X
ejpam-700	432	2	38	38	NUM
ejpam-700	432	3	]	]	PUNCT
ejpam-700	432	4	d	d	NOUN
ejpam-700	432	5	simsek	simsek	NOUN
ejpam-700	432	6	,	,	PUNCT
ejpam-700	432	7	c	c	PROPN
ejpam-700	432	8	cinar	cinar	PROPN
ejpam-700	432	9	and	and	CCONJ
ejpam-700	432	10	i	i	PRON
ejpam-700	432	11	yalcinkaya	yalcinkaya	NOUN
ejpam-700	432	12	.	.	PUNCT
ejpam-700	433	1	on	on	ADP
ejpam-700	433	2	the	the	DET
ejpam-700	433	3	recursive	recursive	ADJ
ejpam-700	433	4	sequence	sequence	NOUN
ejpam-700	433	5	xn+1	xn+1	PROPN
ejpam-700	433	6	=	=	SYM
ejpam-700	433	7	xn−3	xn−3	PROPN
ejpam-700	433	8	1+xn−1	1+xn−1	NUM
ejpam-700	433	9	.	.	PUNCT
ejpam-700	434	1	int	int	NOUN
ejpam-700	434	2	.	.	PUNCT
ejpam-700	435	1	j.	j.	PROPN
ejpam-700	435	2	contemp	contemp	PROPN
ejpam-700	435	3	.	.	PUNCT
ejpam-700	436	1	math	math	NOUN
ejpam-700	436	2	.	.	PUNCT
ejpam-700	437	1	sci	sci	PROPN
ejpam-700	437	2	.	.	PROPN
ejpam-700	437	3	,	,	PUNCT
ejpam-700	437	4	1(10):475	1(10):475	PROPN
ejpam-700	437	5	-	-	SYM
ejpam-700	437	6	480	480	NUM
ejpam-700	437	7	,	,	PUNCT
ejpam-700	437	8	2006	2006	NUM
ejpam-700	437	9	.	.	PUNCT
ejpam-700	438	1	[	[	X
ejpam-700	438	2	39	39	NUM
ejpam-700	438	3	]	]	X
ejpam-700	438	4	d	d	NOUN
ejpam-700	438	5	simsek	simsek	NOUN
ejpam-700	438	6	,	,	PUNCT
ejpam-700	438	7	c	c	PROPN
ejpam-700	438	8	cınar	cınar	NOUN
ejpam-700	438	9	,	,	PUNCT
ejpam-700	438	10	r	r	NOUN
ejpam-700	438	11	karatas	karata	NOUN
ejpam-700	438	12	and	and	CCONJ
ejpam-700	438	13	i	i	PRON
ejpam-700	438	14	yalcinkaya	yalcinkaya	NOUN
ejpam-700	438	15	.	.	PUNCT
ejpam-700	439	1	on	on	ADP
ejpam-700	439	2	the	the	DET
ejpam-700	439	3	recursive	recursive	ADJ
ejpam-700	439	4	sequence	sequence	NOUN
ejpam-700	439	5	xn+1	xn+1	PROPN
ejpam-700	439	6	=	=	SYM
ejpam-700	439	7	xn−5	xn−5	PROPN
ejpam-700	439	8	1+xn−1	1+xn−1	PROPN
ejpam-700	439	9	xn−3	xn−3	PROPN
ejpam-700	439	10	.	.	PUNCT
ejpam-700	440	1	int	int	NOUN
ejpam-700	440	2	.	.	PUNCT
ejpam-700	441	1	j.	j.	PROPN
ejpam-700	441	2	of	of	ADP
ejpam-700	441	3	pure	pure	ADJ
ejpam-700	441	4	and	and	CCONJ
ejpam-700	441	5	appl	appl	NOUN
ejpam-700	441	6	.	.	PROPN
ejpam-700	441	7	math	math	PROPN
ejpam-700	441	8	.	.	PUNCT
ejpam-700	441	9	,	,	PUNCT
ejpam-700	441	10	28:117	28:117	NUM
ejpam-700	441	11	-	-	SYM
ejpam-700	441	12	124	124	NUM
ejpam-700	441	13	,	,	PUNCT
ejpam-700	441	14	2006	2006	NUM
ejpam-700	441	15	.	.	PUNCT
ejpam-700	442	1	[	[	X
ejpam-700	442	2	40	40	NUM
ejpam-700	442	3	]	]	PUNCT
ejpam-700	442	4	s	s	VERB
ejpam-700	442	5	stevic	stevic	NOUN
ejpam-700	442	6	.	.	PUNCT
ejpam-700	443	1	on	on	ADP
ejpam-700	443	2	the	the	DET
ejpam-700	443	3	recursive	recursive	ADJ
ejpam-700	443	4	sequence	sequence	NOUN
ejpam-700	443	5	xn+1	xn+1	PROPN
ejpam-700	443	6	=	=	SYM
ejpam-700	443	7	xn−1	xn−1	PROPN
ejpam-700	443	8	/	/	SYM
ejpam-700	443	9	g(xn	g(xn	NOUN
ejpam-700	443	10	)	)	PUNCT
ejpam-700	443	11	.	.	PUNCT
ejpam-700	444	1	taiwanese	taiwanese	PROPN
ejpam-700	444	2	j.	j.	PROPN
ejpam-700	444	3	math	math	PROPN
ejpam-700	444	4	.	.	PUNCT
ejpam-700	444	5	,	,	PUNCT
ejpam-700	444	6	6(3):405414	6(3):405414	NUM
ejpam-700	444	7	,	,	PUNCT
ejpam-700	444	8	2002	2002	NUM
ejpam-700	444	9	.	.	PUNCT
ejpam-700	445	1	[	[	X
ejpam-700	445	2	41	41	NUM
ejpam-700	445	3	]	]	X
ejpam-700	445	4	c	c	PROPN
ejpam-700	445	5	wang	wang	PROPN
ejpam-700	445	6	and	and	CCONJ
ejpam-700	445	7	s	s	PROPN
ejpam-700	445	8	wang	wang	PROPN
ejpam-700	445	9	.	.	PUNCT
ejpam-700	446	1	oscillation	oscillation	NOUN
ejpam-700	446	2	of	of	ADP
ejpam-700	446	3	partial	partial	ADJ
ejpam-700	446	4	population	population	NOUN
ejpam-700	446	5	model	model	NOUN
ejpam-700	446	6	with	with	ADP
ejpam-700	446	7	diffusion	diffusion	NOUN
ejpam-700	446	8	and	and	CCONJ
ejpam-700	446	9	delay	delay	NOUN
ejpam-700	446	10	.	.	PUNCT
ejpam-700	447	1	applied	apply	VERB
ejpam-700	447	2	mathematics	mathematics	NOUN
ejpam-700	447	3	letters	letter	NOUN
ejpam-700	447	4	,	,	PUNCT
ejpam-700	447	5	22(12):1793	22(12):1793	PROPN
ejpam-700	447	6	-	-	SYM
ejpam-700	447	7	1797	1797	NUM
ejpam-700	447	8	,	,	PUNCT
ejpam-700	447	9	2009	2009	NUM
ejpam-700	447	10	.	.	PUNCT
ejpam-700	448	1	references	reference	NOUN
ejpam-700	448	2	303	303	NUM
ejpam-700	449	1	[	[	X
ejpam-700	449	2	42	42	NUM
ejpam-700	449	3	]	]	X
ejpam-700	449	4	c	c	PROPN
ejpam-700	449	5	wang	wang	PROPN
ejpam-700	449	6	,	,	PUNCT
ejpam-700	449	7	s	s	PROPN
ejpam-700	449	8	wang	wang	PROPN
ejpam-700	449	9	and	and	CCONJ
ejpam-700	449	10	x	x	PROPN
ejpam-700	449	11	yan	yan	PROPN
ejpam-700	449	12	.	.	PUNCT
ejpam-700	450	1	global	global	ADJ
ejpam-700	450	2	asymptotic	asymptotic	ADJ
ejpam-700	450	3	stability	stability	NOUN
ejpam-700	450	4	of	of	ADP
ejpam-700	450	5	3	3	NUM
ejpam-700	450	6	-	-	PUNCT
ejpam-700	450	7	species	species	NOUN
ejpam-700	450	8	mutualism	mutualism	NOUN
ejpam-700	450	9	models	model	NOUN
ejpam-700	450	10	with	with	ADP
ejpam-700	450	11	diffusion	diffusion	NOUN
ejpam-700	450	12	and	and	CCONJ
ejpam-700	450	13	delay	delay	NOUN
ejpam-700	450	14	effects	effect	NOUN
ejpam-700	450	15	.	.	PUNCT
ejpam-700	451	1	discrete	discrete	ADJ
ejpam-700	451	2	dynamics	dynamic	NOUN
ejpam-700	451	3	in	in	ADP
ejpam-700	451	4	natural	natural	ADJ
ejpam-700	451	5	and	and	CCONJ
ejpam-700	451	6	science	science	NOUN
ejpam-700	451	7	,	,	PUNCT
ejpam-700	451	8	2009:20	2009:20	NUM
ejpam-700	451	9	pages	page	NOUN
ejpam-700	451	10	,	,	PUNCT
ejpam-700	451	11	article	article	NOUN
ejpam-700	451	12	i	i	PROPN
ejpam-700	451	13	d	d	PROPN
ejpam-700	451	14	317298	317298	NUM
ejpam-700	451	15	,	,	PUNCT
ejpam-700	451	16	2009	2009	NUM
ejpam-700	451	17	.	.	PUNCT
ejpam-700	452	1	[	[	X
ejpam-700	452	2	43	43	NUM
ejpam-700	452	3	]	]	X
ejpam-700	452	4	c	c	PROPN
ejpam-700	452	5	wang	wang	PROPN
ejpam-700	452	6	,	,	PUNCT
ejpam-700	452	7	f	f	PROPN
ejpam-700	452	8	gong	gong	PROPN
ejpam-700	452	9	,	,	PUNCT
ejpam-700	452	10	s	s	PROPN
ejpam-700	452	11	wang	wang	PROPN
ejpam-700	452	12	,	,	PUNCT
ejpam-700	452	13	l	l	PROPN
ejpam-700	452	14	li	li	PROPN
ejpam-700	452	15	and	and	CCONJ
ejpam-700	452	16	q	q	PROPN
ejpam-700	452	17	shi	shi	PROPN
ejpam-700	452	18	.	.	PUNCT
ejpam-700	453	1	asymptotic	asymptotic	ADJ
ejpam-700	453	2	behavior	behavior	NOUN
ejpam-700	453	3	of	of	ADP
ejpam-700	453	4	equilibrium	equilibrium	NOUN
ejpam-700	453	5	point	point	NOUN
ejpam-700	453	6	for	for	ADP
ejpam-700	453	7	a	a	DET
ejpam-700	453	8	class	class	NOUN
ejpam-700	453	9	of	of	ADP
ejpam-700	453	10	nonlinear	nonlinear	ADJ
ejpam-700	453	11	difference	difference	NOUN
ejpam-700	453	12	equation	equation	NOUN
ejpam-700	453	13	.	.	PUNCT
ejpam-700	454	1	advances	advance	NOUN
ejpam-700	454	2	in	in	ADP
ejpam-700	454	3	difference	difference	NOUN
ejpam-700	454	4	equations	equation	NOUN
ejpam-700	454	5	,	,	PUNCT
ejpam-700	454	6	2009:8	2009:8	DET
ejpam-700	454	7	pages	page	NOUN
ejpam-700	454	8	.	.	PUNCT
ejpam-700	454	9	,	,	PUNCT
ejpam-700	454	10	article	article	NOUN
ejpam-700	454	11	i	i	PROPN
ejpam-700	454	12	d	d	PROPN
ejpam-700	454	13	214309	214309	NUM
ejpam-700	454	14	,	,	PUNCT
ejpam-700	454	15	2008	2008	NUM
ejpam-700	454	16	.	.	PUNCT
ejpam-700	455	1	[	[	X
ejpam-700	455	2	44	44	NUM
ejpam-700	455	3	]	]	PUNCT
ejpam-700	455	4	i	i	PRON
ejpam-700	455	5	yalçınkaya	yalçınkaya	NOUN
ejpam-700	455	6	,	,	PUNCT
ejpam-700	455	7	c	c	PROPN
ejpam-700	455	8	cinar	cinar	PROPN
ejpam-700	455	9	and	and	CCONJ
ejpam-700	455	10	m	m	PROPN
ejpam-700	455	11	atalay	atalay	ADJ
ejpam-700	455	12	.	.	PUNCT
ejpam-700	456	1	on	on	ADP
ejpam-700	456	2	the	the	DET
ejpam-700	456	3	solutions	solution	NOUN
ejpam-700	456	4	of	of	ADP
ejpam-700	456	5	systems	system	NOUN
ejpam-700	456	6	of	of	ADP
ejpam-700	456	7	difference	difference	NOUN
ejpam-700	456	8	equations	equation	NOUN
ejpam-700	456	9	.	.	PUNCT
ejpam-700	457	1	advances	advance	NOUN
ejpam-700	457	2	in	in	ADP
ejpam-700	457	3	difference	difference	NOUN
ejpam-700	457	4	equations	equation	NOUN
ejpam-700	457	5	,	,	PUNCT
ejpam-700	457	6	2008:9	2008:9	NUM
ejpam-700	457	7	pages	page	NOUN
ejpam-700	457	8	,	,	PUNCT
ejpam-700	457	9	article	article	NOUN
ejpam-700	457	10	i	i	PROPN
ejpam-700	457	11	d	d	PROPN
ejpam-700	457	12	143943	143943	NUM
ejpam-700	457	13	,	,	PUNCT
ejpam-700	457	14	doi	doi	NOUN
ejpam-700	457	15	:	:	PUNCT
ejpam-700	457	16	10.1155/2008/	10.1155/2008/	NUM
ejpam-700	457	17	143943	143943	NUM
ejpam-700	457	18	.	.	PUNCT
ejpam-700	458	1	[	[	X
ejpam-700	458	2	45	45	NUM
ejpam-700	458	3	]	]	X
ejpam-700	458	4	i	i	PRON
ejpam-700	458	5	yalcinkaya	yalcinkaya	PROPN
ejpam-700	458	6	,	,	PUNCT
ejpam-700	458	7	c	c	PROPN
ejpam-700	458	8	cinar	cinar	PROPN
ejpam-700	458	9	and	and	CCONJ
ejpam-700	458	10	a	a	DET
ejpam-700	458	11	gelisken	gelisken	VERB
ejpam-700	458	12	.	.	PUNCT
ejpam-700	459	1	on	on	ADP
ejpam-700	459	2	the	the	DET
ejpam-700	459	3	recursive	recursive	ADJ
ejpam-700	459	4	sequence	sequence	NOUN
ejpam-700	459	5	xn+1	xn+1	PROPN
ejpam-700	459	6	=	=	SYM
ejpam-700	459	7	max	max	PROPN
ejpam-700	459	8	�	�	PROPN
ejpam-700	459	9	xn	xn	PROPN
ejpam-700	459	10	,	,	PUNCT
ejpam-700	459	11	a	a	DET
ejpam-700	459	12	x2	x2	NOUN
ejpam-700	459	13	n	n	PROPN
ejpam-700	459	14	xn−1	xn−1	PROPN
ejpam-700	459	15	.	.	PUNCT
ejpam-700	460	1	discrete	discrete	ADJ
ejpam-700	460	2	dynamics	dynamic	NOUN
ejpam-700	460	3	in	in	ADP
ejpam-700	460	4	nature	nature	NOUN
ejpam-700	460	5	and	and	CCONJ
ejpam-700	460	6	society	society	NOUN
ejpam-700	460	7	,	,	PUNCT
ejpam-700	460	8	2010:13	2010:13	NUM
ejpam-700	460	9	pages	page	NOUN
ejpam-700	460	10	,	,	PUNCT
ejpam-700	460	11	article	article	NOUN
ejpam-700	460	12	i	i	PROPN
ejpam-700	460	13	d	d	PROPN
ejpam-700	460	14	583230	583230	NUM
ejpam-700	460	15	,	,	PUNCT
ejpam-700	460	16	2010	2010	NUM
ejpam-700	460	17	.	.	PUNCT
ejpam-700	461	1	[	[	X
ejpam-700	461	2	46	46	NUM
ejpam-700	461	3	]	]	X
ejpam-700	461	4	i	i	PRON
ejpam-700	461	5	yalçınkaya	yalçınkaya	NOUN
ejpam-700	461	6	,	,	PUNCT
ejpam-700	461	7	c	c	PROPN
ejpam-700	461	8	cinar	cinar	PROPN
ejpam-700	461	9	and	and	CCONJ
ejpam-700	461	10	d	d	ADP
ejpam-700	461	11	simsek	simsek	NOUN
ejpam-700	461	12	.	.	PUNCT
ejpam-700	462	1	global	global	ADJ
ejpam-700	462	2	asymptotic	asymptotic	ADJ
ejpam-700	462	3	stability	stability	NOUN
ejpam-700	462	4	of	of	ADP
ejpam-700	462	5	a	a	DET
ejpam-700	462	6	system	system	NOUN
ejpam-700	462	7	of	of	ADP
ejpam-700	462	8	difference	difference	NOUN
ejpam-700	462	9	equations	equation	NOUN
ejpam-700	462	10	.	.	PUNCT
ejpam-700	463	1	applicable	applicable	ADJ
ejpam-700	463	2	analysis	analysis	NOUN
ejpam-700	463	3	,	,	PUNCT
ejpam-700	463	4	87(6):689	87(6):689	NUM
ejpam-700	463	5	-	-	SYM
ejpam-700	463	6	699	699	NUM
ejpam-700	463	7	,	,	PUNCT
ejpam-700	463	8	2008	2008	NUM
ejpam-700	463	9	.	.	PUNCT
ejpam-700	464	1	[	[	X
ejpam-700	464	2	47	47	NUM
ejpam-700	464	3	]	]	X
ejpam-700	464	4	i	i	PRON
ejpam-700	464	5	yalçınkaya	yalçınkaya	NOUN
ejpam-700	464	6	,	,	PUNCT
ejpam-700	464	7	b	b	PROPN
ejpam-700	465	1	d	d	X
ejpam-700	465	2	iricanin	iricanin	NOUN
ejpam-700	465	3	and	and	CCONJ
ejpam-700	465	4	c	c	NOUN
ejpam-700	465	5	cinar	cinar	PROPN
ejpam-700	465	6	.	.	PUNCT
ejpam-700	466	1	on	on	ADP
ejpam-700	466	2	a	a	DET
ejpam-700	466	3	max	max	ADJ
ejpam-700	466	4	-	-	PUNCT
ejpam-700	466	5	type	type	NOUN
ejpam-700	466	6	difference	difference	NOUN
ejpam-700	466	7	equation	equation	NOUN
ejpam-700	466	8	.	.	PUNCT
ejpam-700	467	1	discrete	discrete	ADJ
ejpam-700	467	2	dynamics	dynamic	NOUN
ejpam-700	467	3	in	in	ADP
ejpam-700	467	4	nature	nature	NOUN
ejpam-700	467	5	and	and	CCONJ
ejpam-700	467	6	society	society	NOUN
ejpam-700	467	7	,	,	PUNCT
ejpam-700	467	8	2007:10	2007:10	NUM
ejpam-700	467	9	pages	page	NOUN
ejpam-700	467	10	,	,	PUNCT
ejpam-700	467	11	article	article	NOUN
ejpam-700	467	12	i	i	PROPN
ejpam-700	467	13	d	d	PROPN
ejpam-700	467	14	47264	47264	NUM
ejpam-700	467	15	,	,	PUNCT
ejpam-700	467	16	doi	doi	NOUN
ejpam-700	467	17	:	:	PUNCT
ejpam-700	467	18	1155/2007/47264	1155/2007/47264	NUM
ejpam-700	467	19	.	.	PUNCT
ejpam-700	468	1	[	[	X
ejpam-700	468	2	48	48	NUM
ejpam-700	468	3	]	]	X
ejpam-700	468	4	i	i	PRON
ejpam-700	468	5	yalçınkaya	yalçınkaya	NOUN
ejpam-700	468	6	.	.	PUNCT
ejpam-700	469	1	on	on	ADP
ejpam-700	469	2	the	the	DET
ejpam-700	469	3	global	global	ADJ
ejpam-700	469	4	asymptotic	asymptotic	ADJ
ejpam-700	469	5	stability	stability	NOUN
ejpam-700	469	6	of	of	ADP
ejpam-700	469	7	a	a	DET
ejpam-700	469	8	second	second	ADJ
ejpam-700	469	9	-	-	PUNCT
ejpam-700	469	10	order	order	NOUN
ejpam-700	469	11	system	system	NOUN
ejpam-700	469	12	of	of	ADP
ejpam-700	469	13	difference	difference	NOUN
ejpam-700	469	14	equations	equation	NOUN
ejpam-700	469	15	.	.	PUNCT
ejpam-700	470	1	discrete	discrete	ADJ
ejpam-700	470	2	dynamics	dynamic	NOUN
ejpam-700	470	3	in	in	ADP
ejpam-700	470	4	nature	nature	NOUN
ejpam-700	470	5	and	and	CCONJ
ejpam-700	470	6	society	society	NOUN
ejpam-700	470	7	,	,	PUNCT
ejpam-700	470	8	2008:12	2008:12	NUM
ejpam-700	470	9	pages	page	NOUN
ejpam-700	470	10	,	,	PUNCT
ejpam-700	470	11	article	article	NOUN
ejpam-700	470	12	i	i	PROPN
ejpam-700	470	13	d	d	PROPN
ejpam-700	470	14	860152	860152	NUM
ejpam-700	470	15	,	,	PUNCT
ejpam-700	470	16	doi	doi	PROPN
ejpam-700	470	17	:	:	PUNCT
ejpam-700	470	18	10.1155/2008/	10.1155/2008/	NUM
ejpam-700	470	19	860152	860152	NUM
ejpam-700	470	20	.	.	PUNCT
ejpam-700	471	1	[	[	X
ejpam-700	471	2	49	49	NUM
ejpam-700	471	3	]	]	PUNCT
ejpam-700	471	4	i	i	PRON
ejpam-700	471	5	yalçınkaya	yalçınkaya	NOUN
ejpam-700	471	6	.	.	PUNCT
ejpam-700	472	1	on	on	ADP
ejpam-700	472	2	the	the	DET
ejpam-700	472	3	difference	difference	NOUN
ejpam-700	472	4	equation	equation	NOUN
ejpam-700	472	5	xn+1	xn+1	PROPN
ejpam-700	472	6	=	=	SYM
ejpam-700	473	1	α+	α+	PUNCT
ejpam-700	473	2	xn−m	xn−m	PROPN
ejpam-700	473	3	xk	xk	PROPN
ejpam-700	474	1	n	n	PROPN
ejpam-700	474	2	.	.	PUNCT
ejpam-700	475	1	discrete	discrete	ADJ
ejpam-700	475	2	dynamics	dynamic	NOUN
ejpam-700	475	3	in	in	ADP
ejpam-700	475	4	nature	nature	NOUN
ejpam-700	475	5	and	and	CCONJ
ejpam-700	475	6	society	society	NOUN
ejpam-700	475	7	,	,	PUNCT
ejpam-700	475	8	2008:8	2008:8	NUM
ejpam-700	475	9	pages	page	NOUN
ejpam-700	475	10	,	,	PUNCT
ejpam-700	475	11	article	article	NOUN
ejpam-700	475	12	i	i	PROPN
ejpam-700	475	13	d	d	PROPN
ejpam-700	475	14	805460	805460	NUM
ejpam-700	475	15	,	,	PUNCT
ejpam-700	475	16	doi	doi	PROPN
ejpam-700	475	17	:	:	PUNCT
ejpam-700	475	18	10.1155/2008/	10.1155/2008/	PROPN
ejpam-700	475	19	805460	805460	NUM
ejpam-700	475	20	.	.	PUNCT
ejpam-700	476	1	[	[	X
ejpam-700	476	2	50	50	NUM
ejpam-700	476	3	]	]	PUNCT
ejpam-700	476	4	i	i	PRON
ejpam-700	476	5	yalçınkaya	yalçınkaya	NOUN
ejpam-700	476	6	.	.	PUNCT
ejpam-700	477	1	on	on	ADP
ejpam-700	477	2	the	the	DET
ejpam-700	477	3	global	global	ADJ
ejpam-700	477	4	asymptotic	asymptotic	ADJ
ejpam-700	477	5	behavior	behavior	NOUN
ejpam-700	477	6	of	of	ADP
ejpam-700	477	7	a	a	DET
ejpam-700	477	8	system	system	NOUN
ejpam-700	477	9	of	of	ADP
ejpam-700	477	10	two	two	NUM
ejpam-700	477	11	nonlinear	nonlinear	ADJ
ejpam-700	477	12	difference	difference	NOUN
ejpam-700	477	13	equations	equation	NOUN
ejpam-700	477	14	.	.	PUNCT
ejpam-700	478	1	ars	ars	PROPN
ejpam-700	478	2	combinatoria	combinatoria	NOUN
ejpam-700	478	3	,	,	PUNCT
ejpam-700	478	4	95:151	95:151	NUM
ejpam-700	478	5	-	-	SYM
ejpam-700	478	6	159	159	NUM
ejpam-700	478	7	,	,	PUNCT
ejpam-700	478	8	2010	2010	NUM
ejpam-700	478	9	.	.	PUNCT
ejpam-700	479	1	[	[	X
ejpam-700	479	2	51	51	NUM
ejpam-700	479	3	]	]	X
ejpam-700	479	4	e	e	X
ejpam-700	479	5	m	m	NOUN
ejpam-700	479	6	e	e	NOUN
ejpam-700	479	7	zayed	zayed	ADJ
ejpam-700	479	8	and	and	CCONJ
ejpam-700	479	9	m	m	PROPN
ejpam-700	479	10	a	a	DET
ejpam-700	479	11	el	el	PROPN
ejpam-700	479	12	-	-	NOUN
ejpam-700	479	13	moneam	moneam	NOUN
ejpam-700	479	14	.	.	PUNCT
ejpam-700	480	1	on	on	ADP
ejpam-700	480	2	the	the	DET
ejpam-700	480	3	rational	rational	ADJ
ejpam-700	480	4	recursive	recursive	ADJ
ejpam-700	480	5	sequence	sequence	NOUN
ejpam-700	480	6	xn+1	xn+1	PROPN
ejpam-700	480	7	=	=	PUNCT
ejpam-700	480	8	axn	axn	PROPN
ejpam-700	480	9	−	−	PROPN
ejpam-700	480	10	bxn	bxn	VERB
ejpam-700	480	11	cxn−d	cxn−d	PROPN
ejpam-700	480	12	xn−k	xn−k	PROPN
ejpam-700	480	13	.	.	PUNCT
ejpam-700	481	1	communications	communication	NOUN
ejpam-700	481	2	on	on	ADP
ejpam-700	481	3	applied	apply	VERB
ejpam-700	481	4	nonlinear	nonlinear	ADJ
ejpam-700	481	5	analysis	analysis	NOUN
ejpam-700	481	6	,	,	PUNCT
ejpam-700	481	7	15(2):47	15(2):47	NUM
ejpam-700	481	8	-	-	SYM
ejpam-700	481	9	57	57	NUM
ejpam-700	481	10	,	,	PUNCT
ejpam-700	481	11	2008	2008	NUM
ejpam-700	481	12	.	.	PUNCT
ejpam-700	482	1	[	[	X
ejpam-700	482	2	52	52	NUM
ejpam-700	482	3	]	]	PUNCT
ejpam-700	482	4	e	e	NOUN
ejpam-700	482	5	m	m	PROPN
ejpam-700	482	6	e	e	X
ejpam-700	482	7	zayed	zaye	VERB
ejpam-700	482	8	.	.	PUNCT
ejpam-700	483	1	dynamics	dynamic	NOUN
ejpam-700	483	2	of	of	ADP
ejpam-700	483	3	the	the	DET
ejpam-700	483	4	nonlinear	nonlinear	ADJ
ejpam-700	483	5	rational	rational	ADJ
ejpam-700	483	6	difference	difference	NOUN
ejpam-700	483	7	equation	equation	NOUN
ejpam-700	483	8	xn+1	xn+1	PROPN
ejpam-700	484	1	=	=	PUNCT
ejpam-700	484	2	axn	axn	PROPN
ejpam-700	484	3	+	+	CCONJ
ejpam-700	484	4	bxn−k	bxn−k	PROPN
ejpam-700	484	5	+	+	CCONJ
ejpam-700	484	6	pxn+xn−k	pxn+xn−k	PROPN
ejpam-700	484	7	q+xn−k	q+xn−k	PROPN
ejpam-700	484	8	.	.	PUNCT
ejpam-700	485	1	european	european	PROPN
ejpam-700	485	2	journal	journal	PROPN
ejpam-700	485	3	of	of	ADP
ejpam-700	485	4	pure	pure	ADJ
ejpam-700	485	5	and	and	CCONJ
ejpam-700	485	6	applied	applied	ADJ
ejpam-700	485	7	mathematics	mathematic	NOUN
ejpam-700	485	8	,	,	PUNCT
ejpam-700	485	9	3(2):254	3(2):254	NUM
ejpam-700	485	10	-	-	SYM
ejpam-700	485	11	268	268	NUM
ejpam-700	485	12	,	,	PUNCT
ejpam-700	485	13	2010	2010	NUM
ejpam-700	485	14	.	.	PUNCT