id	sid	tid	token	lemma	pos
ejpam-5155	1	1	european	european	PROPN
ejpam-5155	1	2	journal	journal	PROPN
ejpam-5155	1	3	of	of	ADP
ejpam-5155	1	4	pure	pure	ADJ
ejpam-5155	1	5	and	and	CCONJ
ejpam-5155	1	6	applied	apply	VERB
ejpam-5155	1	7	mathematics	mathematic	NOUN
ejpam-5155	1	8	vol	vol	NOUN
ejpam-5155	1	9	.	.	PROPN
ejpam-5155	2	1	17	17	NUM
ejpam-5155	2	2	,	,	PUNCT
ejpam-5155	2	3	no	no	INTJ
ejpam-5155	2	4	.	.	NOUN
ejpam-5155	2	5	2	2	NUM
ejpam-5155	2	6	,	,	PUNCT
ejpam-5155	2	7	2024	2024	NUM
ejpam-5155	2	8	,	,	PUNCT
ejpam-5155	2	9	1294	1294	NUM
ejpam-5155	2	10	-	-	SYM
ejpam-5155	2	11	1305	1305	NUM
ejpam-5155	2	12	issn	issn	VERB
ejpam-5155	2	13	1307	1307	NUM
ejpam-5155	2	14	-	-	SYM
ejpam-5155	2	15	5543	5543	NUM
ejpam-5155	2	16	–	–	PUNCT
ejpam-5155	2	17	ejpam.com	ejpam.com	X
ejpam-5155	2	18	published	publish	VERB
ejpam-5155	2	19	by	by	ADP
ejpam-5155	2	20	new	new	PROPN
ejpam-5155	2	21	york	york	PROPN
ejpam-5155	2	22	business	business	PROPN
ejpam-5155	2	23	global	global	ADJ
ejpam-5155	2	24	determination	determination	NOUN
ejpam-5155	2	25	of	of	ADP
ejpam-5155	2	26	the	the	DET
ejpam-5155	2	27	fixed	fix	VERB
ejpam-5155	2	28	point	point	NOUN
ejpam-5155	2	29	of	of	ADP
ejpam-5155	2	30	lotka	lotka	PROPN
ejpam-5155	2	31	-	-	PUNCT
ejpam-5155	2	32	volterra	volterra	PROPN
ejpam-5155	2	33	function	function	PROPN
ejpam-5155	2	34	mary	mary	PROPN
ejpam-5155	2	35	osei	osei	PROPN
ejpam-5155	2	36	fokuo1	fokuo1	PROPN
ejpam-5155	2	37	,	,	PUNCT
ejpam-5155	2	38	william	william	PROPN
ejpam-5155	2	39	obeng	obeng	PROPN
ejpam-5155	2	40	-	-	PUNCT
ejpam-5155	2	41	denteh1	denteh1	PROPN
ejpam-5155	2	42	,	,	PUNCT
ejpam-5155	2	43	isaac	isaac	PROPN
ejpam-5155	2	44	kwame	kwame	PROPN
ejpam-5155	2	45	dontwi1	dontwi1	PROPN
ejpam-5155	2	46	,	,	PUNCT
ejpam-5155	2	47	patrick	patrick	PROPN
ejpam-5155	2	48	akwasi	akwasi	PROPN
ejpam-5155	2	49	anamuah	anamuah	PROPN
ejpam-5155	2	50	mensah2,∗	mensah2,∗	PROPN
ejpam-5155	2	51	1	1	NUM
ejpam-5155	2	52	department	department	NOUN
ejpam-5155	2	53	of	of	ADP
ejpam-5155	2	54	mathematics	mathematics	PROPN
ejpam-5155	2	55	,	,	PUNCT
ejpam-5155	2	56	kwame	kwame	PROPN
ejpam-5155	2	57	nkrumah	nkrumah	PROPN
ejpam-5155	2	58	university	university	PROPN
ejpam-5155	2	59	of	of	ADP
ejpam-5155	2	60	science	science	NOUN
ejpam-5155	2	61	and	and	CCONJ
ejpam-5155	2	62	technology	technology	NOUN
ejpam-5155	2	63	,	,	PUNCT
ejpam-5155	2	64	kumasi	kumasi	PROPN
ejpam-5155	2	65	,	,	PUNCT
ejpam-5155	2	66	ghana	ghana	PROPN
ejpam-5155	2	67	.	.	PUNCT
ejpam-5155	3	1	2	2	NUM
ejpam-5155	3	2	department	department	NOUN
ejpam-5155	3	3	of	of	ADP
ejpam-5155	3	4	mathematics	mathematics	PROPN
ejpam-5155	3	5	and	and	CCONJ
ejpam-5155	3	6	ict	ict	PROPN
ejpam-5155	3	7	,	,	PUNCT
ejpam-5155	3	8	st	st	PROPN
ejpam-5155	3	9	ambrose	ambrose	PROPN
ejpam-5155	3	10	college	college	PROPN
ejpam-5155	3	11	of	of	ADP
ejpam-5155	3	12	education	education	NOUN
ejpam-5155	3	13	,	,	PUNCT
ejpam-5155	3	14	dormaa	dormaa	ADV
ejpam-5155	3	15	akwamu	akwamu	ADJ
ejpam-5155	3	16	,	,	PUNCT
ejpam-5155	3	17	ghana	ghana	PROPN
ejpam-5155	3	18	abstract	abstract	PROPN
ejpam-5155	3	19	.	.	PUNCT
ejpam-5155	4	1	the	the	DET
ejpam-5155	4	2	paper	paper	NOUN
ejpam-5155	4	3	focuses	focus	VERB
ejpam-5155	4	4	on	on	ADP
ejpam-5155	4	5	the	the	DET
ejpam-5155	4	6	lotka	lotka	PROPN
ejpam-5155	4	7	-	-	PUNCT
ejpam-5155	4	8	volterra	volterra	PROPN
ejpam-5155	4	9	function	function	NOUN
ejpam-5155	4	10	in	in	ADP
ejpam-5155	4	11	its	its	PRON
ejpam-5155	4	12	discrete	discrete	ADJ
ejpam-5155	4	13	form	form	NOUN
ejpam-5155	4	14	.	.	PUNCT
ejpam-5155	5	1	the	the	DET
ejpam-5155	5	2	purpose	purpose	NOUN
ejpam-5155	5	3	of	of	ADP
ejpam-5155	5	4	the	the	DET
ejpam-5155	5	5	study	study	NOUN
ejpam-5155	5	6	was	be	AUX
ejpam-5155	5	7	to	to	PART
ejpam-5155	5	8	determine	determine	VERB
ejpam-5155	5	9	the	the	DET
ejpam-5155	5	10	fixed	fix	VERB
ejpam-5155	5	11	points	point	NOUN
ejpam-5155	5	12	of	of	ADP
ejpam-5155	5	13	the	the	DET
ejpam-5155	5	14	function	function	NOUN
ejpam-5155	5	15	.	.	PUNCT
ejpam-5155	6	1	the	the	DET
ejpam-5155	6	2	study	study	NOUN
ejpam-5155	6	3	employs	employ	VERB
ejpam-5155	6	4	the	the	DET
ejpam-5155	6	5	banach	banach	ADV
ejpam-5155	6	6	fixed	fix	VERB
ejpam-5155	6	7	point	point	NOUN
ejpam-5155	6	8	theorem	theorem	NOUN
ejpam-5155	6	9	and	and	CCONJ
ejpam-5155	6	10	contraction	contraction	NOUN
ejpam-5155	6	11	mapping	mapping	NOUN
ejpam-5155	6	12	in	in	ADP
ejpam-5155	6	13	metric	metric	ADJ
ejpam-5155	6	14	space	space	NOUN
ejpam-5155	6	15	on	on	ADP
ejpam-5155	6	16	the	the	DET
ejpam-5155	6	17	function	function	NOUN
ejpam-5155	6	18	to	to	PART
ejpam-5155	6	19	demonstrate	demonstrate	VERB
ejpam-5155	6	20	the	the	DET
ejpam-5155	6	21	uniqueness	uniqueness	NOUN
ejpam-5155	6	22	of	of	ADP
ejpam-5155	6	23	the	the	DET
ejpam-5155	6	24	fixed	fix	VERB
ejpam-5155	6	25	points	point	NOUN
ejpam-5155	6	26	and	and	CCONJ
ejpam-5155	6	27	its	its	PRON
ejpam-5155	6	28	continuous	continuous	ADJ
ejpam-5155	6	29	stability	stability	NOUN
ejpam-5155	6	30	after	after	ADP
ejpam-5155	6	31	several	several	ADJ
ejpam-5155	6	32	iterations	iteration	NOUN
ejpam-5155	6	33	,	,	PUNCT
ejpam-5155	6	34	using	use	VERB
ejpam-5155	6	35	the	the	DET
ejpam-5155	6	36	fixed	fix	VERB
ejpam-5155	6	37	points	point	NOUN
ejpam-5155	6	38	as	as	ADP
ejpam-5155	6	39	the	the	DET
ejpam-5155	6	40	initial	initial	ADJ
ejpam-5155	6	41	conditions	condition	NOUN
ejpam-5155	6	42	.	.	PUNCT
ejpam-5155	7	1	the	the	DET
ejpam-5155	7	2	study	study	NOUN
ejpam-5155	7	3	has	have	AUX
ejpam-5155	7	4	shown	show	VERB
ejpam-5155	7	5	that	that	SCONJ
ejpam-5155	7	6	(	(	PUNCT
ejpam-5155	7	7	0	0	NUM
ejpam-5155	7	8	,	,	PUNCT
ejpam-5155	7	9	0	0	NUM
ejpam-5155	7	10	)	)	PUNCT
ejpam-5155	7	11	,	,	PUNCT
ejpam-5155	7	12	(	(	PUNCT
ejpam-5155	7	13	0	0	NUM
ejpam-5155	7	14	,	,	PUNCT
ejpam-5155	7	15	α−1	α−1	PROPN
ejpam-5155	7	16	β	β	NOUN
ejpam-5155	7	17	)	)	PUNCT
ejpam-5155	7	18	,	,	PUNCT
ejpam-5155	7	19	(	(	PUNCT
ejpam-5155	7	20	1+γ	1+γ	NUM
ejpam-5155	7	21	δ	δ	PROPN
ejpam-5155	7	22	,	,	PUNCT
ejpam-5155	7	23	0	0	NUM
ejpam-5155	7	24	)	)	PUNCT
ejpam-5155	7	25	and	and	CCONJ
ejpam-5155	7	26	(	(	PUNCT
ejpam-5155	7	27	1+γ	1+γ	NUM
ejpam-5155	7	28	δ	δ	PROPN
ejpam-5155	7	29	,	,	PUNCT
ejpam-5155	7	30	α−1	α−1	PROPN
ejpam-5155	7	31	β	β	X
ejpam-5155	7	32	)	)	PUNCT
ejpam-5155	7	33	are	be	AUX
ejpam-5155	7	34	the	the	DET
ejpam-5155	7	35	fixed	fix	VERB
ejpam-5155	7	36	points	point	NOUN
ejpam-5155	7	37	of	of	ADP
ejpam-5155	7	38	the	the	DET
ejpam-5155	7	39	function	function	NOUN
ejpam-5155	7	40	,	,	PUNCT
ejpam-5155	7	41	with	with	ADP
ejpam-5155	7	42	the	the	DET
ejpam-5155	7	43	initial	initial	ADJ
ejpam-5155	7	44	pair	pair	NOUN
ejpam-5155	7	45	serving	serve	VERB
ejpam-5155	7	46	as	as	ADP
ejpam-5155	7	47	a	a	DET
ejpam-5155	7	48	trivial	trivial	ADJ
ejpam-5155	7	49	one	one	NOUN
ejpam-5155	7	50	and	and	CCONJ
ejpam-5155	7	51	the	the	DET
ejpam-5155	7	52	other	other	ADJ
ejpam-5155	7	53	three	three	NUM
ejpam-5155	7	54	solely	solely	ADV
ejpam-5155	7	55	depending	depend	VERB
ejpam-5155	7	56	on	on	ADP
ejpam-5155	7	57	the	the	DET
ejpam-5155	7	58	parameter	parameter	NOUN
ejpam-5155	7	59	values	value	NOUN
ejpam-5155	7	60	for	for	ADP
ejpam-5155	7	61	the	the	DET
ejpam-5155	7	62	behavior	behavior	NOUN
ejpam-5155	7	63	of	of	ADP
ejpam-5155	7	64	the	the	DET
ejpam-5155	7	65	function	function	NOUN
ejpam-5155	7	66	.	.	PUNCT
ejpam-5155	8	1	the	the	DET
ejpam-5155	8	2	outcome	outcome	NOUN
ejpam-5155	8	3	of	of	ADP
ejpam-5155	8	4	the	the	DET
ejpam-5155	8	5	limit	limit	NOUN
ejpam-5155	8	6	points	point	NOUN
ejpam-5155	8	7	of	of	ADP
ejpam-5155	8	8	the	the	DET
ejpam-5155	8	9	function	function	NOUN
ejpam-5155	8	10	as	as	ADP
ejpam-5155	8	11	the	the	DET
ejpam-5155	8	12	fixed	fix	VERB
ejpam-5155	8	13	points	point	NOUN
ejpam-5155	8	14	after	after	SCONJ
ejpam-5155	8	15	several	several	ADJ
ejpam-5155	8	16	iterations	iteration	NOUN
ejpam-5155	8	17	forms	form	VERB
ejpam-5155	8	18	a	a	DET
ejpam-5155	8	19	fixed	fix	VERB
ejpam-5155	8	20	orbit	orbit	NOUN
ejpam-5155	8	21	structure	structure	NOUN
ejpam-5155	8	22	of	of	ADP
ejpam-5155	8	23	the	the	DET
ejpam-5155	8	24	function	function	NOUN
ejpam-5155	8	25	,	,	PUNCT
ejpam-5155	8	26	irrespective	irrespective	ADV
ejpam-5155	8	27	of	of	ADP
ejpam-5155	8	28	the	the	DET
ejpam-5155	8	29	value	value	NOUN
ejpam-5155	8	30	of	of	ADP
ejpam-5155	8	31	the	the	DET
ejpam-5155	8	32	parameter	parameter	NOUN
ejpam-5155	8	33	.	.	PUNCT
ejpam-5155	9	1	the	the	DET
ejpam-5155	9	2	study	study	NOUN
ejpam-5155	9	3	also	also	ADV
ejpam-5155	9	4	showed	show	VERB
ejpam-5155	9	5	the	the	DET
ejpam-5155	9	6	uniqueness	uniqueness	NOUN
ejpam-5155	9	7	of	of	ADP
ejpam-5155	9	8	the	the	DET
ejpam-5155	9	9	fixed	fix	VERB
ejpam-5155	9	10	points	point	NOUN
ejpam-5155	9	11	,	,	PUNCT
ejpam-5155	9	12	demonstrating	demonstrate	VERB
ejpam-5155	9	13	the	the	DET
ejpam-5155	9	14	stability	stability	NOUN
ejpam-5155	9	15	and	and	CCONJ
ejpam-5155	9	16	continuity	continuity	NOUN
ejpam-5155	9	17	of	of	ADP
ejpam-5155	9	18	the	the	DET
ejpam-5155	9	19	function	function	NOUN
ejpam-5155	9	20	in	in	ADP
ejpam-5155	9	21	its	its	PRON
ejpam-5155	9	22	steady	steady	ADJ
ejpam-5155	9	23	state	state	NOUN
ejpam-5155	9	24	.	.	PUNCT
ejpam-5155	10	1	2020	2020	NUM
ejpam-5155	10	2	mathematics	mathematic	NOUN
ejpam-5155	10	3	subject	subject	NOUN
ejpam-5155	10	4	classifications	classification	NOUN
ejpam-5155	10	5	:	:	PUNCT
ejpam-5155	10	6	54h25	54h25	NUM
ejpam-5155	10	7	,	,	PUNCT
ejpam-5155	10	8	47h10	47h10	NUM
ejpam-5155	10	9	,	,	PUNCT
ejpam-5155	10	10	54e35	54e35	NUM
ejpam-5155	10	11	key	key	ADJ
ejpam-5155	10	12	words	word	NOUN
ejpam-5155	10	13	and	and	CCONJ
ejpam-5155	10	14	phrases	phrase	NOUN
ejpam-5155	10	15	:	:	PUNCT
ejpam-5155	10	16	lotka	lotka	PROPN
ejpam-5155	10	17	-	-	PUNCT
ejpam-5155	10	18	volterra	volterra	PROPN
ejpam-5155	10	19	,	,	PUNCT
ejpam-5155	10	20	fixed	fix	VERB
ejpam-5155	10	21	point	point	NOUN
ejpam-5155	10	22	,	,	PUNCT
ejpam-5155	10	23	parameter	parameter	NOUN
ejpam-5155	10	24	,	,	PUNCT
ejpam-5155	10	25	solution	solution	NOUN
ejpam-5155	10	26	,	,	PUNCT
ejpam-5155	10	27	function	function	NOUN
ejpam-5155	10	28	,	,	PUNCT
ejpam-5155	10	29	contraction	contraction	NOUN
ejpam-5155	10	30	mapping	mapping	NOUN
ejpam-5155	10	31	,	,	PUNCT
ejpam-5155	10	32	fixed	fix	VERB
ejpam-5155	10	33	point	point	NOUN
ejpam-5155	10	34	theorem	theorem	NOUN
ejpam-5155	10	35	1	1	NUM
ejpam-5155	10	36	.	.	PUNCT
ejpam-5155	11	1	introduction	introduction	NOUN
ejpam-5155	11	2	many	many	ADJ
ejpam-5155	11	3	researchers	researcher	NOUN
ejpam-5155	11	4	have	have	AUX
ejpam-5155	11	5	studied	study	VERB
ejpam-5155	11	6	about	about	ADP
ejpam-5155	11	7	fixed	fix	VERB
ejpam-5155	11	8	point	point	NOUN
ejpam-5155	11	9	theorem	theorem	VERB
ejpam-5155	11	10	.	.	PUNCT
ejpam-5155	12	1	all	all	DET
ejpam-5155	12	2	their	their	PRON
ejpam-5155	12	3	definitions	definition	NOUN
ejpam-5155	12	4	seem	seem	VERB
ejpam-5155	12	5	to	to	PART
ejpam-5155	12	6	have	have	VERB
ejpam-5155	12	7	one	one	NUM
ejpam-5155	12	8	idea	idea	NOUN
ejpam-5155	12	9	.	.	PUNCT
ejpam-5155	13	1	that	that	PRON
ejpam-5155	13	2	is	be	AUX
ejpam-5155	13	3	fixed	fix	VERB
ejpam-5155	13	4	point	point	NOUN
ejpam-5155	13	5	theorem	theorem	NOUN
ejpam-5155	13	6	is	be	AUX
ejpam-5155	13	7	where	where	SCONJ
ejpam-5155	13	8	each	each	DET
ejpam-5155	13	9	fixed	fix	VERB
ejpam-5155	13	10	point	point	NOUN
ejpam-5155	13	11	of	of	ADP
ejpam-5155	13	12	a	a	DET
ejpam-5155	13	13	function	function	NOUN
ejpam-5155	13	14	g	g	NOUN
ejpam-5155	13	15	must	must	AUX
ejpam-5155	13	16	exist	exist	VERB
ejpam-5155	13	17	,	,	PUNCT
ejpam-5155	13	18	x	x	PUNCT
ejpam-5155	13	19	∈	∈	NOUN
ejpam-5155	13	20	x	x	PUNCT
ejpam-5155	13	21	such	such	ADJ
ejpam-5155	13	22	that	that	SCONJ
ejpam-5155	13	23	g(x	g(x	NOUN
ejpam-5155	13	24	)	)	PUNCT
ejpam-5155	13	25	=	=	PUNCT
ejpam-5155	14	1	x.	x.	NOUN
ejpam-5155	15	1	[	[	X
ejpam-5155	15	2	9	9	NUM
ejpam-5155	15	3	]	]	PUNCT
ejpam-5155	15	4	wrote	write	VERB
ejpam-5155	15	5	a	a	DET
ejpam-5155	15	6	brief	brief	ADJ
ejpam-5155	15	7	historical	historical	ADJ
ejpam-5155	15	8	survey	survey	NOUN
ejpam-5155	15	9	on	on	ADP
ejpam-5155	15	10	fixed	fix	VERB
ejpam-5155	15	11	point	point	NOUN
ejpam-5155	15	12	theorem	theorem	VERB
ejpam-5155	15	13	.	.	PUNCT
ejpam-5155	16	1	many	many	ADJ
ejpam-5155	16	2	papers	paper	NOUN
ejpam-5155	16	3	were	be	AUX
ejpam-5155	16	4	cited	cite	VERB
ejpam-5155	16	5	in	in	ADP
ejpam-5155	16	6	that	that	DET
ejpam-5155	16	7	paper	paper	NOUN
ejpam-5155	16	8	.	.	PUNCT
ejpam-5155	17	1	many	many	ADJ
ejpam-5155	17	2	interesting	interesting	ADJ
ejpam-5155	17	3	results	result	NOUN
ejpam-5155	17	4	on	on	ADP
ejpam-5155	17	5	fixed	fix	VERB
ejpam-5155	17	6	point	point	NOUN
ejpam-5155	17	7	theorem	theorem	NOUN
ejpam-5155	17	8	were	be	AUX
ejpam-5155	17	9	also	also	ADV
ejpam-5155	17	10	given	give	VERB
ejpam-5155	17	11	like	like	ADP
ejpam-5155	17	12	generalization	generalization	NOUN
ejpam-5155	17	13	and	and	CCONJ
ejpam-5155	17	14	extension	extension	NOUN
ejpam-5155	17	15	of	of	ADP
ejpam-5155	17	16	fixed	fix	VERB
ejpam-5155	17	17	point	point	NOUN
ejpam-5155	17	18	theorem	theorem	VERB
ejpam-5155	17	19	through	through	ADP
ejpam-5155	17	20	∗corresponding	∗corresponde	VERB
ejpam-5155	17	21	author	author	NOUN
ejpam-5155	17	22	.	.	PUNCT
ejpam-5155	18	1	doi	doi	NOUN
ejpam-5155	18	2	:	:	PUNCT
ejpam-5155	18	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5155	https://doi.org/10.29020/nybg.ejpam.v17i2.5155	NUM
ejpam-5155	18	4	email	email	NOUN
ejpam-5155	18	5	addresses	address	NOUN
ejpam-5155	18	6	:	:	PUNCT
ejpam-5155	18	7	abenamof@gmail.com	abenamof@gmail.com	X
ejpam-5155	18	8	(	(	PUNCT
ejpam-5155	18	9	m.	m.	NOUN
ejpam-5155	18	10	o.	o.	PROPN
ejpam-5155	18	11	fokuo	fokuo	PROPN
ejpam-5155	18	12	)	)	PUNCT
ejpam-5155	18	13	,	,	PUNCT
ejpam-5155	18	14	wobengdenteh@gmail.com	wobengdenteh@gmail.com	X
ejpam-5155	18	15	(	(	PUNCT
ejpam-5155	18	16	w.	w.	PROPN
ejpam-5155	18	17	obeng	obeng	PROPN
ejpam-5155	18	18	-	-	PUNCT
ejpam-5155	18	19	denteh	denteh	NOUN
ejpam-5155	18	20	)	)	PUNCT
ejpam-5155	18	21	,	,	PUNCT
ejpam-5155	18	22	ikdontwi@knust.edu.gh	ikdontwi@knust.edu.gh	NOUN
ejpam-5155	18	23	(	(	PUNCT
ejpam-5155	18	24	i.	i.	PROPN
ejpam-5155	18	25	k.	k.	PROPN
ejpam-5155	18	26	dontwi	dontwi	PROPN
ejpam-5155	18	27	)	)	PUNCT
ejpam-5155	18	28	,	,	PUNCT
ejpam-5155	18	29	patrickakwasianamuahmensah@sace.edu.gh	patrickakwasianamuahmensah@sace.edu.gh	NOUN
ejpam-5155	18	30	(	(	PUNCT
ejpam-5155	18	31	p.	p.	NOUN
ejpam-5155	18	32	a.	a.	NOUN
ejpam-5155	18	33	a.	a.	PROPN
ejpam-5155	18	34	mensah	mensah	PROPN
ejpam-5155	18	35	)	)	PUNCT
ejpam-5155	18	36	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5155	18	37	1294	1294	NUM
ejpam-5155	19	1	©	©	ADP
ejpam-5155	19	2	2024	2024	NUM
ejpam-5155	19	3	ejpam	ejpam	NOUN
ejpam-5155	19	4	all	all	DET
ejpam-5155	19	5	rights	right	NOUN
ejpam-5155	19	6	reserved	reserve	VERB
ejpam-5155	19	7	.	.	PUNCT
ejpam-5155	20	1	m.	m.	NOUN
ejpam-5155	20	2	o.	o.	PROPN
ejpam-5155	20	3	fokuoet	fokuoet	PROPN
ejpam-5155	20	4	al	al	PROPN
ejpam-5155	20	5	.	.	PUNCT
ejpam-5155	20	6	/	/	SYM
ejpam-5155	20	7	eur	eur	PROPN
ejpam-5155	20	8	.	.	PUNCT
ejpam-5155	21	1	j.	j.	PROPN
ejpam-5155	21	2	pure	pure	PROPN
ejpam-5155	21	3	appl	appl	PROPN
ejpam-5155	21	4	.	.	PROPN
ejpam-5155	21	5	math	math	PROPN
ejpam-5155	21	6	,	,	PUNCT
ejpam-5155	21	7	17	17	NUM
ejpam-5155	21	8	(	(	PUNCT
ejpam-5155	21	9	2	2	NUM
ejpam-5155	21	10	)	)	PUNCT
ejpam-5155	21	11	(	(	PUNCT
ejpam-5155	21	12	2024	2024	NUM
ejpam-5155	21	13	)	)	PUNCT
ejpam-5155	21	14	,	,	PUNCT
ejpam-5155	21	15	1294	1294	NUM
ejpam-5155	21	16	-	-	SYM
ejpam-5155	21	17	1305	1305	NUM
ejpam-5155	21	18	1295	1295	NUM
ejpam-5155	21	19	different	different	ADJ
ejpam-5155	21	20	types	type	NOUN
ejpam-5155	21	21	of	of	ADP
ejpam-5155	21	22	mappings	mapping	NOUN
ejpam-5155	21	23	.	.	PUNCT
ejpam-5155	22	1	suppose	suppose	VERB
ejpam-5155	22	2	t	t	PROPN
ejpam-5155	22	3	represent	represent	VERB
ejpam-5155	22	4	a	a	DET
ejpam-5155	22	5	self	self	NOUN
ejpam-5155	22	6	-	-	PUNCT
ejpam-5155	22	7	map	map	NOUN
ejpam-5155	22	8	on	on	ADP
ejpam-5155	22	9	set	set	PROPN
ejpam-5155	22	10	x.	x.	NOUN
ejpam-5155	22	11	a	a	DET
ejpam-5155	22	12	fixed	fix	VERB
ejpam-5155	22	13	point	point	NOUN
ejpam-5155	22	14	of	of	ADP
ejpam-5155	22	15	the	the	DET
ejpam-5155	22	16	mapping	mapping	NOUN
ejpam-5155	22	17	t	t	PROPN
ejpam-5155	22	18	is	be	AUX
ejpam-5155	22	19	referred	refer	VERB
ejpam-5155	22	20	to	to	ADP
ejpam-5155	22	21	as	as	ADP
ejpam-5155	22	22	an	an	DET
ejpam-5155	22	23	element	element	NOUN
ejpam-5155	22	24	x	x	PUNCT
ejpam-5155	22	25	in	in	ADP
ejpam-5155	22	26	x	x	X
ejpam-5155	22	27	such	such	ADJ
ejpam-5155	22	28	that	that	DET
ejpam-5155	22	29	tx	tx	PROPN
ejpam-5155	23	1	=	=	PUNCT
ejpam-5155	23	2	x.	x.	NOUN
ejpam-5155	23	3	one	one	NUM
ejpam-5155	23	4	of	of	ADP
ejpam-5155	23	5	the	the	DET
ejpam-5155	23	6	most	most	ADV
ejpam-5155	23	7	important	important	ADJ
ejpam-5155	23	8	theorems	theorem	NOUN
ejpam-5155	23	9	in	in	ADP
ejpam-5155	23	10	fixed	fix	VERB
ejpam-5155	23	11	point	point	NOUN
ejpam-5155	23	12	theorem	theorem	NOUN
ejpam-5155	23	13	is	be	AUX
ejpam-5155	23	14	the	the	DET
ejpam-5155	23	15	l.e	l.e	PROPN
ejpam-5155	23	16	.	.	PUNCT
ejpam-5155	23	17	brouwer	brouwer	PROPN
ejpam-5155	23	18	’s	’s	PART
ejpam-5155	23	19	fixed	fix	VERB
ejpam-5155	23	20	point	point	NOUN
ejpam-5155	23	21	theorem	theorem	VERB
ejpam-5155	23	22	in	in	ADP
ejpam-5155	23	23	which	which	PRON
ejpam-5155	23	24	it	it	PRON
ejpam-5155	23	25	is	be	AUX
ejpam-5155	23	26	said	say	VERB
ejpam-5155	23	27	that	that	SCONJ
ejpam-5155	23	28	each	each	DET
ejpam-5155	23	29	continual	continual	ADJ
ejpam-5155	23	30	self	self	NOUN
ejpam-5155	23	31	-	-	PUNCT
ejpam-5155	23	32	mapping	mapping	NOUN
ejpam-5155	23	33	of	of	ADP
ejpam-5155	23	34	the	the	DET
ejpam-5155	23	35	sealed	seal	VERB
ejpam-5155	23	36	unit	unit	NOUN
ejpam-5155	23	37	in	in	ADP
ejpam-5155	23	38	the	the	DET
ejpam-5155	23	39	n−	n−	NOUN
ejpam-5155	23	40	dimensional	dimensional	ADJ
ejpam-5155	23	41	euclidean	euclidean	ADJ
ejpam-5155	23	42	spaces	space	NOUN
ejpam-5155	23	43	rn	rn	PROPN
ejpam-5155	23	44	,	,	PUNCT
ejpam-5155	23	45	possess	possess	VERB
ejpam-5155	23	46	a	a	DET
ejpam-5155	23	47	fixed	fix	VERB
ejpam-5155	23	48	point[5	point[5	NOUN
ejpam-5155	23	49	]	]	PUNCT
ejpam-5155	23	50	.	.	PUNCT
ejpam-5155	24	1	advanced	advanced	ADJ
ejpam-5155	24	2	fixed	fix	VERB
ejpam-5155	24	3	point	point	NOUN
ejpam-5155	24	4	theorem	theorem	NOUN
ejpam-5155	24	5	for	for	ADP
ejpam-5155	24	6	internal	internal	ADJ
ejpam-5155	24	7	mapping	mapping	NOUN
ejpam-5155	24	8	by	by	ADP
ejpam-5155	24	9	employing	employ	VERB
ejpam-5155	24	10	a	a	DET
ejpam-5155	24	11	known	know	VERB
ejpam-5155	24	12	ky	ky	PROPN
ejpam-5155	24	13	fan	fan	PROPN
ejpam-5155	24	14	type	type	NOUN
ejpam-5155	24	15	outcome	outcome	NOUN
ejpam-5155	24	16	in	in	ADP
ejpam-5155	24	17	a	a	DET
ejpam-5155	24	18	hilbert	hilbert	NOUN
ejpam-5155	24	19	space	space	NOUN
ejpam-5155	24	20	setting.[10	setting.[10	PROPN
ejpam-5155	24	21	]	]	PUNCT
ejpam-5155	24	22	for	for	ADP
ejpam-5155	24	23	two	two	NUM
ejpam-5155	24	24	species	specie	NOUN
ejpam-5155	24	25	(	(	PUNCT
ejpam-5155	24	26	prey	prey	NOUN
ejpam-5155	24	27	and	and	CCONJ
ejpam-5155	24	28	predators	predator	NOUN
ejpam-5155	24	29	)	)	PUNCT
ejpam-5155	24	30	to	to	PART
ejpam-5155	24	31	exist	exist	VERB
ejpam-5155	24	32	,	,	PUNCT
ejpam-5155	24	33	there	there	PRON
ejpam-5155	24	34	is	be	VERB
ejpam-5155	24	35	an	an	DET
ejpam-5155	24	36	equation	equation	NOUN
ejpam-5155	24	37	which	which	PRON
ejpam-5155	24	38	model	model	VERB
ejpam-5155	24	39	the	the	DET
ejpam-5155	24	40	struggle	struggle	NOUN
ejpam-5155	24	41	.	.	PUNCT
ejpam-5155	25	1	this	this	DET
ejpam-5155	25	2	model	model	NOUN
ejpam-5155	25	3	was	be	AUX
ejpam-5155	25	4	brought	bring	VERB
ejpam-5155	25	5	up	up	ADP
ejpam-5155	25	6	by	by	ADP
ejpam-5155	25	7	two	two	NUM
ejpam-5155	25	8	scientists	scientist	NOUN
ejpam-5155	25	9	:	:	PUNCT
ejpam-5155	25	10	lotka	lotka	PROPN
ejpam-5155	25	11	and	and	CCONJ
ejpam-5155	25	12	volterra.the	volterra.the	DET
ejpam-5155	25	13	scientists	scientist	NOUN
ejpam-5155	25	14	came	come	VERB
ejpam-5155	25	15	to	to	ADP
ejpam-5155	25	16	a	a	DET
ejpam-5155	25	17	conclusion	conclusion	NOUN
ejpam-5155	25	18	based	base	VERB
ejpam-5155	25	19	on	on	ADP
ejpam-5155	25	20	the	the	DET
ejpam-5155	25	21	problem	problem	NOUN
ejpam-5155	25	22	they	they	PRON
ejpam-5155	25	23	had	have	VERB
ejpam-5155	25	24	in	in	ADP
ejpam-5155	25	25	1920	1920	NUM
ejpam-5155	25	26	by	by	ADP
ejpam-5155	25	27	lotka	lotka	PROPN
ejpam-5155	25	28	and	and	CCONJ
ejpam-5155	25	29	1926	1926	NUM
ejpam-5155	25	30	by	by	ADP
ejpam-5155	25	31	volterra	volterra	PROPN
ejpam-5155	25	32	.	.	PUNCT
ejpam-5155	26	1	the	the	DET
ejpam-5155	26	2	conclusion	conclusion	NOUN
ejpam-5155	26	3	was	be	AUX
ejpam-5155	26	4	the	the	DET
ejpam-5155	26	5	same	same	ADJ
ejpam-5155	26	6	,	,	PUNCT
ejpam-5155	26	7	that	that	SCONJ
ejpam-5155	26	8	the	the	DET
ejpam-5155	26	9	interaction	interaction	NOUN
ejpam-5155	26	10	of	of	ADP
ejpam-5155	26	11	the	the	DET
ejpam-5155	26	12	two	two	NUM
ejpam-5155	26	13	species	specie	NOUN
ejpam-5155	26	14	would	would	AUX
ejpam-5155	26	15	give	give	VERB
ejpam-5155	26	16	rise	rise	NOUN
ejpam-5155	26	17	to	to	ADP
ejpam-5155	26	18	periodic	periodic	ADJ
ejpam-5155	26	19	oscillation	oscillation	NOUN
ejpam-5155	26	20	in	in	ADP
ejpam-5155	26	21	their	their	PRON
ejpam-5155	26	22	populations.[2	populations.[2	NOUN
ejpam-5155	26	23	]	]	X
ejpam-5155	26	24	many	many	ADJ
ejpam-5155	26	25	works	work	NOUN
ejpam-5155	26	26	have	have	AUX
ejpam-5155	26	27	been	be	AUX
ejpam-5155	26	28	done	do	VERB
ejpam-5155	26	29	on	on	ADP
ejpam-5155	26	30	the	the	DET
ejpam-5155	26	31	fixed	fix	VERB
ejpam-5155	26	32	-	-	PUNCT
ejpam-5155	26	33	point	point	NOUN
ejpam-5155	26	34	theorem	theorem	NOUN
ejpam-5155	26	35	and	and	CCONJ
ejpam-5155	26	36	the	the	DET
ejpam-5155	26	37	lotka	lotka	PROPN
ejpam-5155	26	38	volterra	volterra	PROPN
ejpam-5155	26	39	function	function	NOUN
ejpam-5155	26	40	,	,	PUNCT
ejpam-5155	26	41	but	but	CCONJ
ejpam-5155	26	42	our	our	PRON
ejpam-5155	26	43	focus	focus	NOUN
ejpam-5155	26	44	is	be	AUX
ejpam-5155	26	45	on	on	ADP
ejpam-5155	26	46	the	the	DET
ejpam-5155	26	47	determination	determination	NOUN
ejpam-5155	26	48	of	of	ADP
ejpam-5155	26	49	the	the	DET
ejpam-5155	26	50	fixed	fix	VERB
ejpam-5155	26	51	point	point	NOUN
ejpam-5155	26	52	of	of	ADP
ejpam-5155	26	53	the	the	DET
ejpam-5155	26	54	lotka	lotka	PROPN
ejpam-5155	26	55	volterra	volterra	PROPN
ejpam-5155	26	56	function	function	PROPN
ejpam-5155	26	57	,	,	PUNCT
ejpam-5155	26	58	applying	apply	VERB
ejpam-5155	26	59	the	the	DET
ejpam-5155	26	60	banach	banach	ADV
ejpam-5155	26	61	fixed	fix	VERB
ejpam-5155	26	62	point	point	NOUN
ejpam-5155	26	63	theorem	theorem	VERB
ejpam-5155	26	64	,	,	PUNCT
ejpam-5155	26	65	and	and	CCONJ
ejpam-5155	26	66	the	the	DET
ejpam-5155	26	67	contraction	contraction	NOUN
ejpam-5155	26	68	mapping	mapping	NOUN
ejpam-5155	26	69	on	on	ADP
ejpam-5155	26	70	the	the	DET
ejpam-5155	26	71	lotka	lotka	PROPN
ejpam-5155	26	72	volterra	volterra	PROPN
ejpam-5155	26	73	function	function	VERB
ejpam-5155	26	74	to	to	PART
ejpam-5155	26	75	find	find	VERB
ejpam-5155	26	76	the	the	DET
ejpam-5155	26	77	fixed	fix	VERB
ejpam-5155	26	78	point	point	NOUN
ejpam-5155	26	79	of	of	ADP
ejpam-5155	26	80	the	the	DET
ejpam-5155	26	81	lotka	lotka	PROPN
ejpam-5155	26	82	volterra	volterra	PROPN
ejpam-5155	26	83	function	function	NOUN
ejpam-5155	26	84	.	.	PUNCT
ejpam-5155	27	1	2	2	X
ejpam-5155	27	2	.	.	X
ejpam-5155	27	3	preliminaries	preliminary	NOUN
ejpam-5155	27	4	definition	definition	NOUN
ejpam-5155	27	5	1	1	NUM
ejpam-5155	27	6	.	.	PUNCT
ejpam-5155	28	1	a	a	DET
ejpam-5155	28	2	fixed	fix	VERB
ejpam-5155	28	3	point	point	NOUN
ejpam-5155	28	4	is	be	AUX
ejpam-5155	28	5	a	a	DET
ejpam-5155	28	6	point	point	NOUN
ejpam-5155	28	7	that	that	PRON
ejpam-5155	28	8	remains	remain	VERB
ejpam-5155	28	9	the	the	DET
ejpam-5155	28	10	same	same	ADJ
ejpam-5155	28	11	after	after	ADP
ejpam-5155	28	12	applying	apply	VERB
ejpam-5155	28	13	a	a	DET
ejpam-5155	28	14	map	map	NOUN
ejpam-5155	28	15	system	system	NOUN
ejpam-5155	28	16	of	of	ADP
ejpam-5155	28	17	differential	differential	ADJ
ejpam-5155	28	18	equations	equation	NOUN
ejpam-5155	28	19	,	,	PUNCT
ejpam-5155	28	20	etc	etc	X
ejpam-5155	28	21	.	.	X
ejpam-5155	29	1	a	a	DET
ejpam-5155	29	2	point	point	NOUN
ejpam-5155	29	3	x0	x0	PROPN
ejpam-5155	29	4	is	be	AUX
ejpam-5155	29	5	referred	refer	VERB
ejpam-5155	29	6	to	to	ADP
ejpam-5155	29	7	as	as	ADP
ejpam-5155	29	8	a	a	DET
ejpam-5155	29	9	function	function	NOUN
ejpam-5155	29	10	’s	’s	PART
ejpam-5155	29	11	fixed	fix	VERB
ejpam-5155	29	12	point	point	NOUN
ejpam-5155	29	13	,	,	PUNCT
ejpam-5155	29	14	if	if	SCONJ
ejpam-5155	29	15	g	g	PROPN
ejpam-5155	29	16	(	(	PUNCT
ejpam-5155	29	17	x0	x0	PROPN
ejpam-5155	29	18	)	)	PUNCT
ejpam-5155	30	1	=	=	PUNCT
ejpam-5155	30	2	x0	x0	PROPN
ejpam-5155	30	3	,	,	PUNCT
ejpam-5155	31	1	[	[	X
ejpam-5155	31	2	11	11	NUM
ejpam-5155	31	3	]	]	PUNCT
ejpam-5155	31	4	.	.	PUNCT
ejpam-5155	32	1	definition	definition	NOUN
ejpam-5155	32	2	2	2	NUM
ejpam-5155	32	3	.	.	PUNCT
ejpam-5155	33	1	the	the	DET
ejpam-5155	33	2	fixed	fix	VERB
ejpam-5155	33	3	point	point	NOUN
ejpam-5155	33	4	theorem	theorem	VERB
ejpam-5155	33	5	in	in	ADP
ejpam-5155	33	6	general	general	ADJ
ejpam-5155	33	7	term	term	NOUN
ejpam-5155	33	8	is	be	AUX
ejpam-5155	33	9	stated	state	VERB
ejpam-5155	33	10	as	as	ADP
ejpam-5155	33	11	an	an	DET
ejpam-5155	33	12	outcome	outcome	NOUN
ejpam-5155	33	13	of	of	ADP
ejpam-5155	33	14	a	a	DET
ejpam-5155	33	15	function	function	NOUN
ejpam-5155	33	16	having	have	VERB
ejpam-5155	33	17	at	at	ADV
ejpam-5155	33	18	least	least	ADJ
ejpam-5155	33	19	a	a	DET
ejpam-5155	33	20	fixed	fix	VERB
ejpam-5155	33	21	point	point	NOUN
ejpam-5155	33	22	under	under	ADP
ejpam-5155	33	23	a	a	DET
ejpam-5155	33	24	certain	certain	ADJ
ejpam-5155	33	25	condition	condition	NOUN
ejpam-5155	33	26	[	[	X
ejpam-5155	33	27	11	11	NUM
ejpam-5155	33	28	]	]	PUNCT
ejpam-5155	33	29	definition	definition	NOUN
ejpam-5155	33	30	3	3	X
ejpam-5155	33	31	.	.	PUNCT
ejpam-5155	34	1	let	let	VERB
ejpam-5155	34	2	u	u	PRON
ejpam-5155	34	3	be	be	AUX
ejpam-5155	34	4	a	a	DET
ejpam-5155	34	5	non	non	ADJ
ejpam-5155	34	6	-	-	ADJ
ejpam-5155	34	7	empty	empty	ADJ
ejpam-5155	34	8	set	set	NOUN
ejpam-5155	34	9	.	.	PUNCT
ejpam-5155	35	1	then	then	ADV
ejpam-5155	35	2	,	,	PUNCT
ejpam-5155	35	3	the	the	DET
ejpam-5155	35	4	real	real	ADJ
ejpam-5155	35	5	function	function	NOUN
ejpam-5155	35	6	d	d	NOUN
ejpam-5155	35	7	(	(	PUNCT
ejpam-5155	35	8	distance	distance	NOUN
ejpam-5155	35	9	function	function	NOUN
ejpam-5155	35	10	)	)	PUNCT
ejpam-5155	35	11	that	that	PRON
ejpam-5155	35	12	assign	assign	VERB
ejpam-5155	35	13	any	any	DET
ejpam-5155	35	14	ordered	ordered	ADJ
ejpam-5155	35	15	pair	pair	NOUN
ejpam-5155	35	16	d(u	d(u	PROPN
ejpam-5155	35	17	,	,	PUNCT
ejpam-5155	35	18	v	v	NOUN
ejpam-5155	35	19	)	)	PUNCT
ejpam-5155	35	20	of	of	ADP
ejpam-5155	35	21	element	element	NOUN
ejpam-5155	35	22	u	u	PROPN
ejpam-5155	35	23	,	,	PUNCT
ejpam-5155	35	24	v	v	NOUN
ejpam-5155	35	25	and	and	CCONJ
ejpam-5155	35	26	w	w	PROPN
ejpam-5155	35	27	∈	∈	PROPN
ejpam-5155	35	28	u	u	NOUN
ejpam-5155	35	29	is	be	AUX
ejpam-5155	35	30	a	a	DET
ejpam-5155	35	31	metric	metric	ADJ
ejpam-5155	35	32	space	space	NOUN
ejpam-5155	35	33	,	,	PUNCT
ejpam-5155	35	34	if	if	SCONJ
ejpam-5155	35	35	the	the	DET
ejpam-5155	35	36	following	follow	VERB
ejpam-5155	35	37	properties	property	NOUN
ejpam-5155	35	38	are	be	AUX
ejpam-5155	35	39	satisfied	satisfied	ADJ
ejpam-5155	35	40	:	:	PUNCT
ejpam-5155	35	41	1	1	X
ejpam-5155	35	42	.	.	X
ejpam-5155	36	1	d(u	d(u	PROPN
ejpam-5155	36	2	,	,	PUNCT
ejpam-5155	36	3	v	v	NOUN
ejpam-5155	36	4	)	)	PUNCT
ejpam-5155	36	5	≥	≥	NOUN
ejpam-5155	36	6	0	0	NUM
ejpam-5155	36	7	and	and	CCONJ
ejpam-5155	36	8	d(u	d(u	PROPN
ejpam-5155	36	9	,	,	PUNCT
ejpam-5155	36	10	v	v	NOUN
ejpam-5155	36	11	)	)	PUNCT
ejpam-5155	36	12	=	=	SYM
ejpam-5155	36	13	0	0	PUNCT
ejpam-5155	37	1	if	if	SCONJ
ejpam-5155	37	2	and	and	CCONJ
ejpam-5155	37	3	only	only	ADV
ejpam-5155	37	4	if	if	SCONJ
ejpam-5155	37	5	u	u	PROPN
ejpam-5155	37	6	=	=	NOUN
ejpam-5155	37	7	v	v	ADP
ejpam-5155	37	8	2	2	NUM
ejpam-5155	37	9	.	.	PUNCT
ejpam-5155	38	1	d(u	d(u	PROPN
ejpam-5155	38	2	,	,	PUNCT
ejpam-5155	38	3	v	v	NOUN
ejpam-5155	38	4	)	)	PUNCT
ejpam-5155	38	5	=	=	SYM
ejpam-5155	39	1	d(v	d(v	PROPN
ejpam-5155	39	2	,	,	PUNCT
ejpam-5155	39	3	u	u	NOUN
ejpam-5155	39	4	)	)	PUNCT
ejpam-5155	39	5	3	3	NUM
ejpam-5155	39	6	.	.	PUNCT
ejpam-5155	40	1	d(u	d(u	PROPN
ejpam-5155	40	2	,	,	PUNCT
ejpam-5155	40	3	v	v	NOUN
ejpam-5155	40	4	)	)	PUNCT
ejpam-5155	40	5	+	+	X
ejpam-5155	40	6	d(v	d(v	ADJ
ejpam-5155	40	7	,	,	PUNCT
ejpam-5155	40	8	w	w	NOUN
ejpam-5155	40	9	)	)	PUNCT
ejpam-5155	40	10	≥	≥	NOUN
ejpam-5155	40	11	d(u	d(u	PROPN
ejpam-5155	40	12	,	,	PUNCT
ejpam-5155	40	13	w	w	NOUN
ejpam-5155	40	14	)	)	PUNCT
ejpam-5155	40	15	.	.	PUNCT
ejpam-5155	41	1	a	a	DET
ejpam-5155	41	2	function	function	NOUN
ejpam-5155	41	3	d	d	ADP
ejpam-5155	41	4	satisfying	satisfy	VERB
ejpam-5155	41	5	the	the	DET
ejpam-5155	41	6	conditions	condition	NOUN
ejpam-5155	41	7	(	(	PUNCT
ejpam-5155	41	8	1)−	1)−	PROPN
ejpam-5155	41	9	(	(	PUNCT
ejpam-5155	41	10	3	3	NUM
ejpam-5155	41	11	)	)	PUNCT
ejpam-5155	41	12	is	be	AUX
ejpam-5155	41	13	a	a	DET
ejpam-5155	41	14	metric	metric	NOUN
ejpam-5155	41	15	on	on	ADP
ejpam-5155	41	16	u	u	NOUN
ejpam-5155	41	17	[	[	X
ejpam-5155	41	18	8	8	NUM
ejpam-5155	41	19	]	]	PUNCT
ejpam-5155	41	20	definition	definition	NOUN
ejpam-5155	41	21	4	4	NUM
ejpam-5155	41	22	.	.	PUNCT
ejpam-5155	42	1	a	a	DET
ejpam-5155	42	2	dynamic	dynamic	ADJ
ejpam-5155	42	3	system	system	NOUN
ejpam-5155	42	4	is	be	AUX
ejpam-5155	42	5	one	one	NUM
ejpam-5155	42	6	in	in	ADP
ejpam-5155	42	7	which	which	PRON
ejpam-5155	42	8	a	a	DET
ejpam-5155	42	9	function	function	NOUN
ejpam-5155	42	10	explains	explain	VERB
ejpam-5155	42	11	how	how	SCONJ
ejpam-5155	42	12	a	a	DET
ejpam-5155	42	13	point	point	NOUN
ejpam-5155	42	14	’s	’s	PART
ejpam-5155	42	15	relationship	relationship	NOUN
ejpam-5155	42	16	to	to	ADP
ejpam-5155	42	17	time	time	NOUN
ejpam-5155	42	18	changes	change	NOUN
ejpam-5155	42	19	with	with	ADP
ejpam-5155	42	20	a	a	DET
ejpam-5155	42	21	given	give	VERB
ejpam-5155	42	22	environment	environment	NOUN
ejpam-5155	42	23	.	.	PUNCT
ejpam-5155	43	1	examples	example	NOUN
ejpam-5155	43	2	are	be	AUX
ejpam-5155	43	3	the	the	DET
ejpam-5155	43	4	mathematical	mathematical	ADJ
ejpam-5155	43	5	formulas	formula	NOUN
ejpam-5155	43	6	that	that	PRON
ejpam-5155	43	7	explain	explain	VERB
ejpam-5155	43	8	how	how	SCONJ
ejpam-5155	43	9	water	water	NOUN
ejpam-5155	43	10	moves	move	VERB
ejpam-5155	43	11	through	through	ADP
ejpam-5155	43	12	a	a	DET
ejpam-5155	43	13	pipe	pipe	NOUN
ejpam-5155	43	14	,	,	PUNCT
ejpam-5155	43	15	how	how	SCONJ
ejpam-5155	43	16	many	many	ADJ
ejpam-5155	43	17	fish	fish	NOUN
ejpam-5155	43	18	spawn	spawn	NOUN
ejpam-5155	43	19	in	in	ADP
ejpam-5155	43	20	a	a	DET
ejpam-5155	43	21	lake	lake	NOUN
ejpam-5155	43	22	each	each	DET
ejpam-5155	43	23	springtime	springtime	NOUN
ejpam-5155	44	1	etc.[4	etc.[4	NOUN
ejpam-5155	44	2	]	]	X
ejpam-5155	44	3	definition	definition	NOUN
ejpam-5155	44	4	5	5	NUM
ejpam-5155	44	5	.	.	PUNCT
ejpam-5155	45	1	a	a	DET
ejpam-5155	45	2	steady	steady	ADJ
ejpam-5155	45	3	state	state	NOUN
ejpam-5155	45	4	of	of	ADP
ejpam-5155	45	5	ẋ	ẋ	PROPN
ejpam-5155	45	6	=	=	SYM
ejpam-5155	45	7	f(x	f(x	PROPN
ejpam-5155	45	8	)	)	PUNCT
ejpam-5155	45	9	is	be	AUX
ejpam-5155	45	10	a	a	DET
ejpam-5155	45	11	point	point	NOUN
ejpam-5155	45	12	x	x	SYM
ejpam-5155	45	13	∈	∈	NOUN
ejpam-5155	45	14	u	u	NOUN
ejpam-5155	45	15	as	as	ADP
ejpam-5155	45	16	to	to	ADP
ejpam-5155	45	17	which	which	PRON
ejpam-5155	45	18	f(x	f(x	PROPN
ejpam-5155	45	19	)	)	PUNCT
ejpam-5155	45	20	=	=	PUNCT
ejpam-5155	46	1	0	0	X
ejpam-5155	46	2	.	.	PUNCT
ejpam-5155	47	1	a	a	DET
ejpam-5155	47	2	steady	steady	ADJ
ejpam-5155	47	3	state	state	NOUN
ejpam-5155	47	4	x∗	x∗	PROPN
ejpam-5155	47	5	is	be	AUX
ejpam-5155	47	6	said	say	VERB
ejpam-5155	47	7	to	to	PART
ejpam-5155	47	8	be	be	AUX
ejpam-5155	47	9	lyapunov	lyapunov	ADJ
ejpam-5155	47	10	stable	stable	ADJ
ejpam-5155	47	11	if	if	SCONJ
ejpam-5155	47	12	for	for	ADP
ejpam-5155	47	13	any	any	DET
ejpam-5155	47	14	ε	ε	PROPN
ejpam-5155	47	15	>	>	X
ejpam-5155	47	16	0	0	PROPN
ejpam-5155	47	17	,	,	PUNCT
ejpam-5155	47	18	there	there	PRON
ejpam-5155	47	19	exist	exist	VERB
ejpam-5155	47	20	δ	δ	PROPN
ejpam-5155	47	21	>	>	X
ejpam-5155	47	22	0	0	NUM
ejpam-5155	48	1	this	this	DET
ejpam-5155	48	2	way	way	NOUN
ejpam-5155	48	3	for	for	ADP
ejpam-5155	48	4	all	all	DET
ejpam-5155	48	5	x0	x0	PROPN
ejpam-5155	48	6	with	with	ADP
ejpam-5155	48	7	|x∗	|x∗	PROPN
ejpam-5155	48	8	−	−	PROPN
ejpam-5155	49	1	x0|	x0|	PROPN
ejpam-5155	49	2	<	<	X
ejpam-5155	49	3	δ	δ	PROPN
ejpam-5155	49	4	we	we	PRON
ejpam-5155	49	5	have	have	VERB
ejpam-5155	49	6	|φ	|φ	PROPN
ejpam-5155	49	7	(	(	PUNCT
ejpam-5155	49	8	x0	x0	PROPN
ejpam-5155	49	9	,	,	PUNCT
ejpam-5155	49	10	t)−	t)−	PROPN
ejpam-5155	49	11	x∗|	x∗|	PROPN
ejpam-5155	49	12	<	<	X
ejpam-5155	49	13	ε	ε	PROPN
ejpam-5155	49	14	for	for	ADP
ejpam-5155	49	15	all	all	DET
ejpam-5155	49	16	t	t	PROPN
ejpam-5155	49	17	≥	≥	NOUN
ejpam-5155	49	18	0	0	NUM
ejpam-5155	49	19	,	,	PUNCT
ejpam-5155	49	20	[	[	X
ejpam-5155	49	21	3	3	NUM
ejpam-5155	49	22	]	]	PUNCT
ejpam-5155	49	23	.	.	PUNCT
ejpam-5155	50	1	definition	definition	NOUN
ejpam-5155	50	2	6	6	NUM
ejpam-5155	50	3	.	.	PUNCT
ejpam-5155	51	1	an	an	DET
ejpam-5155	51	2	equilibrium	equilibrium	NOUN
ejpam-5155	51	3	x	x	VERB
ejpam-5155	51	4	is	be	AUX
ejpam-5155	51	5	said	say	VERB
ejpam-5155	51	6	to	to	PART
ejpam-5155	51	7	be	be	AUX
ejpam-5155	51	8	globally	globally	ADV
ejpam-5155	51	9	asymptotically	asymptotically	ADV
ejpam-5155	51	10	stable	stable	ADJ
ejpam-5155	51	11	in	in	ADP
ejpam-5155	51	12	the	the	DET
ejpam-5155	51	13	set	set	NOUN
ejpam-5155	51	14	of	of	ADP
ejpam-5155	51	15	all	all	DET
ejpam-5155	51	16	positive	positive	ADJ
ejpam-5155	51	17	solutions.[7	solutions.[7	NOUN
ejpam-5155	51	18	]	]	PUNCT
ejpam-5155	51	19	m.	m.	NOUN
ejpam-5155	51	20	o.	o.	PROPN
ejpam-5155	51	21	fokuoet	fokuoet	PROPN
ejpam-5155	51	22	al	al	PROPN
ejpam-5155	51	23	.	.	PUNCT
ejpam-5155	51	24	/	/	SYM
ejpam-5155	51	25	eur	eur	PROPN
ejpam-5155	51	26	.	.	PUNCT
ejpam-5155	52	1	j.	j.	PROPN
ejpam-5155	52	2	pure	pure	PROPN
ejpam-5155	52	3	appl	appl	PROPN
ejpam-5155	52	4	.	.	PROPN
ejpam-5155	52	5	math	math	PROPN
ejpam-5155	52	6	,	,	PUNCT
ejpam-5155	52	7	17	17	NUM
ejpam-5155	52	8	(	(	PUNCT
ejpam-5155	52	9	2	2	NUM
ejpam-5155	52	10	)	)	PUNCT
ejpam-5155	52	11	(	(	PUNCT
ejpam-5155	52	12	2024	2024	NUM
ejpam-5155	52	13	)	)	PUNCT
ejpam-5155	52	14	,	,	PUNCT
ejpam-5155	52	15	1294	1294	NUM
ejpam-5155	52	16	-	-	SYM
ejpam-5155	52	17	1305	1305	NUM
ejpam-5155	52	18	1296	1296	NUM
ejpam-5155	52	19	definition	definition	NOUN
ejpam-5155	52	20	7	7	NUM
ejpam-5155	52	21	(	(	PUNCT
ejpam-5155	52	22	lotka	lotka	PROPN
ejpam-5155	52	23	-	-	PUNCT
ejpam-5155	52	24	volterra	volterra	PROPN
ejpam-5155	52	25	equations	equation	NOUN
ejpam-5155	52	26	)	)	PUNCT
ejpam-5155	52	27	.	.	PUNCT
ejpam-5155	53	1	xn+1	xn+1	PUNCT
ejpam-5155	54	1	=	=	SYM
ejpam-5155	54	2	αxn	αxn	PROPN
ejpam-5155	54	3	−	−	NOUN
ejpam-5155	54	4	βxnyn	βxnyn	NOUN
ejpam-5155	54	5	(	(	PUNCT
ejpam-5155	54	6	1	1	NUM
ejpam-5155	54	7	)	)	PUNCT
ejpam-5155	54	8	yn+1	yn+1	PROPN
ejpam-5155	55	1	=	=	NOUN
ejpam-5155	55	2	δxnyn	δxnyn	ADJ
ejpam-5155	55	3	−	−	NUM
ejpam-5155	55	4	γyn	γyn	NOUN
ejpam-5155	55	5	(	(	PUNCT
ejpam-5155	55	6	2	2	NUM
ejpam-5155	55	7	)	)	PUNCT
ejpam-5155	55	8	where	where	SCONJ
ejpam-5155	55	9	n	n	NOUN
ejpam-5155	55	10	=	=	SYM
ejpam-5155	55	11	0	0	NUM
ejpam-5155	55	12	,	,	PUNCT
ejpam-5155	55	13	1	1	NUM
ejpam-5155	55	14	,	,	PUNCT
ejpam-5155	55	15	2	2	NUM
ejpam-5155	55	16	,	,	PUNCT
ejpam-5155	55	17	.	.	PUNCT
ejpam-5155	55	18	.	.	PUNCT
ejpam-5155	55	19	.	.	PUNCT
ejpam-5155	56	1	,	,	PUNCT
ejpam-5155	56	2	x	x	X
ejpam-5155	56	3	is	be	AUX
ejpam-5155	56	4	the	the	DET
ejpam-5155	56	5	quantity	quantity	NOUN
ejpam-5155	56	6	of	of	ADP
ejpam-5155	56	7	preys	prey	NOUN
ejpam-5155	56	8	,	,	PUNCT
ejpam-5155	56	9	y	y	PROPN
ejpam-5155	56	10	is	be	AUX
ejpam-5155	56	11	the	the	DET
ejpam-5155	56	12	quantity	quantity	NOUN
ejpam-5155	56	13	of	of	ADP
ejpam-5155	56	14	predators	predator	NOUN
ejpam-5155	56	15	,	,	PUNCT
ejpam-5155	56	16	xn+1	xn+1	NUM
ejpam-5155	56	17	and	and	CCONJ
ejpam-5155	56	18	yn+1	yn+1	NUM
ejpam-5155	56	19	are	be	AUX
ejpam-5155	56	20	the	the	DET
ejpam-5155	56	21	two	two	NUM
ejpam-5155	56	22	population	population	NOUN
ejpam-5155	56	23	growth	growth	NOUN
ejpam-5155	56	24	rates	rate	NOUN
ejpam-5155	56	25	and	and	CCONJ
ejpam-5155	56	26	α	α	NOUN
ejpam-5155	56	27	,	,	PUNCT
ejpam-5155	56	28	β	β	PROPN
ejpam-5155	56	29	,	,	PUNCT
ejpam-5155	56	30	δ	δ	PROPN
ejpam-5155	56	31	,	,	PUNCT
ejpam-5155	56	32	γ	γ	PROPN
ejpam-5155	56	33	are	be	AUX
ejpam-5155	56	34	positive	positive	ADJ
ejpam-5155	56	35	real	real	ADJ
ejpam-5155	56	36	parameters	parameter	NOUN
ejpam-5155	56	37	defining	define	VERB
ejpam-5155	56	38	the	the	DET
ejpam-5155	56	39	interaction	interaction	NOUN
ejpam-5155	56	40	between	between	ADP
ejpam-5155	56	41	the	the	DET
ejpam-5155	56	42	two	two	NUM
ejpam-5155	56	43	species	specie	NOUN
ejpam-5155	56	44	[	[	X
ejpam-5155	56	45	2	2	NUM
ejpam-5155	56	46	]	]	PUNCT
ejpam-5155	56	47	.	.	PUNCT
ejpam-5155	57	1	definition	definition	NOUN
ejpam-5155	57	2	8	8	NUM
ejpam-5155	57	3	(	(	PUNCT
ejpam-5155	57	4	population	population	NOUN
ejpam-5155	57	5	equilibrium	equilibrium	NOUN
ejpam-5155	57	6	)	)	PUNCT
ejpam-5155	57	7	.	.	PUNCT
ejpam-5155	58	1	the	the	DET
ejpam-5155	58	2	model	model	NOUN
ejpam-5155	58	3	reaches	reach	VERB
ejpam-5155	58	4	population	population	NOUN
ejpam-5155	58	5	equilibrium	equilibrium	NOUN
ejpam-5155	58	6	when	when	SCONJ
ejpam-5155	58	7	none	none	NOUN
ejpam-5155	58	8	of	of	ADP
ejpam-5155	58	9	the	the	DET
ejpam-5155	58	10	population	population	NOUN
ejpam-5155	58	11	levels	level	NOUN
ejpam-5155	58	12	is	be	AUX
ejpam-5155	58	13	shifting	shift	VERB
ejpam-5155	58	14	.	.	PUNCT
ejpam-5155	59	1	when	when	SCONJ
ejpam-5155	59	2	both	both	DET
ejpam-5155	59	3	derivatives	derivative	NOUN
ejpam-5155	59	4	equal	equal	VERB
ejpam-5155	59	5	0	0	NUM
ejpam-5155	59	6	,	,	PUNCT
ejpam-5155	59	7	that	that	PRON
ejpam-5155	59	8	is	be	AUX
ejpam-5155	59	9	when	when	SCONJ
ejpam-5155	59	10	it	it	PRON
ejpam-5155	59	11	occurs	occur	VERB
ejpam-5155	59	12	.	.	PUNCT
ejpam-5155	60	1	xn	xn	PUNCT
ejpam-5155	61	1	(	(	PUNCT
ejpam-5155	61	2	α−	α−	ADP
ejpam-5155	61	3	βyn	βyn	NOUN
ejpam-5155	61	4	)	)	PUNCT
ejpam-5155	61	5	=	=	SYM
ejpam-5155	61	6	0	0	NUM
ejpam-5155	61	7	(	(	PUNCT
ejpam-5155	61	8	3	3	NUM
ejpam-5155	61	9	)	)	PUNCT
ejpam-5155	61	10	yn	yn	PROPN
ejpam-5155	61	11	(	(	PUNCT
ejpam-5155	61	12	γ	γ	PROPN
ejpam-5155	61	13	−	−	PROPN
ejpam-5155	61	14	δxn	δxn	NOUN
ejpam-5155	61	15	)	)	PUNCT
ejpam-5155	61	16	=	=	SYM
ejpam-5155	61	17	0	0	PUNCT
ejpam-5155	61	18	(	(	PUNCT
ejpam-5155	61	19	4	4	NUM
ejpam-5155	61	20	)	)	PUNCT
ejpam-5155	61	21	hence	hence	ADV
ejpam-5155	61	22	,	,	PUNCT
ejpam-5155	61	23	there	there	PRON
ejpam-5155	61	24	are	be	VERB
ejpam-5155	61	25	two	two	NUM
ejpam-5155	61	26	solutions	solution	NOUN
ejpam-5155	61	27	to	to	ADP
ejpam-5155	61	28	the	the	DET
ejpam-5155	61	29	equations	equation	NOUN
ejpam-5155	61	30	or	or	CCONJ
ejpam-5155	61	31	the	the	DET
ejpam-5155	61	32	systems	system	NOUN
ejpam-5155	61	33	.	.	PUNCT
ejpam-5155	62	1	{	{	PUNCT
ejpam-5155	62	2	yn	yn	X
ejpam-5155	62	3	=	=	SYM
ejpam-5155	62	4	0	0	PROPN
ejpam-5155	62	5	,	,	PUNCT
ejpam-5155	62	6	xn	xn	PUNCT
ejpam-5155	62	7	=	=	SYM
ejpam-5155	62	8	0	0	NUM
ejpam-5155	62	9	}	}	PUNCT
ejpam-5155	62	10	and	and	CCONJ
ejpam-5155	62	11	{	{	PUNCT
ejpam-5155	62	12	yn	yn	X
ejpam-5155	62	13	=	=	PUNCT
ejpam-5155	62	14	α	α	NOUN
ejpam-5155	62	15	β	β	NOUN
ejpam-5155	62	16	xn	xn	PUNCT
ejpam-5155	62	17	=	=	PUNCT
ejpam-5155	62	18	γ	γ	X
ejpam-5155	62	19	δ	δ	PROPN
ejpam-5155	62	20	}	}	PUNCT
ejpam-5155	62	21	,	,	PUNCT
ejpam-5155	62	22	hence	hence	ADV
ejpam-5155	62	23	,	,	PUNCT
ejpam-5155	62	24	there	there	PRON
ejpam-5155	62	25	are	be	VERB
ejpam-5155	62	26	two	two	NUM
ejpam-5155	62	27	equilibria.[7	equilibria.[7	NOUN
ejpam-5155	62	28	]	]	PUNCT
ejpam-5155	62	29	theorem	theorem	ADJ
ejpam-5155	62	30	1	1	NUM
ejpam-5155	62	31	(	(	PUNCT
ejpam-5155	62	32	banach	banach	NOUN
ejpam-5155	62	33	contraction	contraction	NOUN
ejpam-5155	62	34	principle	principle	NOUN
ejpam-5155	62	35	)	)	PUNCT
ejpam-5155	62	36	.	.	PUNCT
ejpam-5155	63	1	suppose(p	suppose(p	NOUN
ejpam-5155	63	2	,	,	PUNCT
ejpam-5155	63	3	d	d	NOUN
ejpam-5155	63	4	)	)	PUNCT
ejpam-5155	63	5	is	be	AUX
ejpam-5155	63	6	a	a	DET
ejpam-5155	63	7	complete	complete	ADJ
ejpam-5155	63	8	metric	metric	ADJ
ejpam-5155	63	9	space	space	NOUN
ejpam-5155	63	10	and	and	CCONJ
ejpam-5155	63	11	h	h	NOUN
ejpam-5155	63	12	:	:	PUNCT
ejpam-5155	64	1	p	p	X
ejpam-5155	64	2	→	→	PUNCT
ejpam-5155	64	3	p	p	X
ejpam-5155	64	4	is	be	AUX
ejpam-5155	64	5	a	a	DET
ejpam-5155	64	6	mapping	mapping	NOUN
ejpam-5155	64	7	of	of	ADP
ejpam-5155	64	8	contractions	contraction	NOUN
ejpam-5155	64	9	using	use	VERB
ejpam-5155	64	10	the	the	DET
ejpam-5155	64	11	lipschitz	lipschitz	NOUN
ejpam-5155	64	12	constant	constant	ADJ
ejpam-5155	64	13	k	k	X
ejpam-5155	64	14	<	<	X
ejpam-5155	64	15	1	1	NUM
ejpam-5155	64	16	.	.	PUNCT
ejpam-5155	65	1	then	then	ADV
ejpam-5155	65	2	,	,	PUNCT
ejpam-5155	65	3	the	the	DET
ejpam-5155	65	4	fixed	fix	VERB
ejpam-5155	65	5	point	point	NOUN
ejpam-5155	65	6	ω	ω	PROPN
ejpam-5155	65	7	∈	∈	PROPN
ejpam-5155	65	8	p	p	X
ejpam-5155	65	9	,	,	PUNCT
ejpam-5155	65	10	for	for	ADP
ejpam-5155	66	1	all	all	DET
ejpam-5155	66	2	x	x	SYM
ejpam-5155	66	3	∈	∈	PROPN
ejpam-5155	67	1	p	p	NOUN
ejpam-5155	67	2	is	be	AUX
ejpam-5155	67	3	a	a	DET
ejpam-5155	67	4	unique	unique	ADJ
ejpam-5155	67	5	point	point	NOUN
ejpam-5155	67	6	in	in	ADP
ejpam-5155	67	7	h.	h.	PROPN
ejpam-5155	67	8	that	that	PRON
ejpam-5155	67	9	is	be	AUX
ejpam-5155	67	10	;	;	PUNCT
ejpam-5155	67	11	limn+∞hn(x	limn+∞hn(x	X
ejpam-5155	67	12	)	)	PUNCT
ejpam-5155	67	13	=	=	PUNCT
ejpam-5155	68	1	ω.moreover	ω.moreover	ADV
ejpam-5155	68	2	,	,	PUNCT
ejpam-5155	68	3	for	for	ADP
ejpam-5155	68	4	each	each	DET
ejpam-5155	68	5	x	x	SYM
ejpam-5155	68	6	∈	∈	PROPN
ejpam-5155	68	7	p	p	X
ejpam-5155	68	8	,	,	PUNCT
ejpam-5155	68	9	we	we	PRON
ejpam-5155	68	10	have	have	VERB
ejpam-5155	68	11	d(hn(x	d(hn(x	NOUN
ejpam-5155	68	12	)	)	PUNCT
ejpam-5155	68	13	,	,	PUNCT
ejpam-5155	68	14	ω	ω	X
ejpam-5155	68	15	)	)	PUNCT
ejpam-5155	68	16	≤	≤	PUNCT
ejpam-5155	69	1	kn	kn	PROPN
ejpam-5155	69	2	1−kd(h(x	1−kd(h(x	NUM
ejpam-5155	69	3	)	)	PUNCT
ejpam-5155	69	4	,	,	PUNCT
ejpam-5155	69	5	x	x	NOUN
ejpam-5155	69	6	)	)	PUNCT
ejpam-5155	69	7	.	.	PUNCT
ejpam-5155	70	1	[	[	X
ejpam-5155	70	2	1	1	NUM
ejpam-5155	70	3	]	]	PUNCT
ejpam-5155	70	4	theorem	theorem	NOUN
ejpam-5155	70	5	2	2	NUM
ejpam-5155	70	6	.	.	PUNCT
ejpam-5155	70	7	given	give	VERB
ejpam-5155	70	8	(	(	PUNCT
ejpam-5155	70	9	p	p	X
ejpam-5155	70	10	,	,	PUNCT
ejpam-5155	70	11	d	d	NOUN
ejpam-5155	70	12	)	)	PUNCT
ejpam-5155	70	13	as	as	ADP
ejpam-5155	70	14	a	a	DET
ejpam-5155	70	15	complete	complete	ADJ
ejpam-5155	70	16	metric	metric	ADJ
ejpam-5155	70	17	space	space	NOUN
ejpam-5155	70	18	,	,	PUNCT
ejpam-5155	70	19	and	and	CCONJ
ejpam-5155	70	20	a	a	DET
ejpam-5155	70	21	mapping	mapping	NOUN
ejpam-5155	70	22	h	h	NOUN
ejpam-5155	70	23	:	:	PUNCT
ejpam-5155	71	1	p	p	X
ejpam-5155	71	2	→	→	PUNCT
ejpam-5155	71	3	p	p	NOUN
ejpam-5155	71	4	for	for	ADP
ejpam-5155	71	5	which	which	PRON
ejpam-5155	71	6	hn	hn	PROPN
ejpam-5155	71	7	is	be	AUX
ejpam-5155	71	8	a	a	DET
ejpam-5155	71	9	contraction	contraction	NOUN
ejpam-5155	71	10	mapping	mapping	NOUN
ejpam-5155	71	11	for	for	ADP
ejpam-5155	71	12	n	n	X
ejpam-5155	71	13	≥	≥	NOUN
ejpam-5155	71	14	1	1	NUM
ejpam-5155	71	15	.	.	PUNCT
ejpam-5155	72	1	as	as	ADP
ejpam-5155	72	2	a	a	DET
ejpam-5155	72	3	result	result	NOUN
ejpam-5155	72	4	,	,	PUNCT
ejpam-5155	72	5	h	h	NOUN
ejpam-5155	72	6	has	have	VERB
ejpam-5155	72	7	a	a	DET
ejpam-5155	72	8	distinct	distinct	ADJ
ejpam-5155	72	9	fixed	fix	VERB
ejpam-5155	72	10	point	point	NOUN
ejpam-5155	72	11	.	.	PUNCT
ejpam-5155	73	1	in	in	ADP
ejpam-5155	73	2	general	general	ADJ
ejpam-5155	73	3	,	,	PUNCT
ejpam-5155	73	4	it	it	PRON
ejpam-5155	73	5	is	be	AUX
ejpam-5155	73	6	unclear	unclear	ADJ
ejpam-5155	73	7	if	if	SCONJ
ejpam-5155	73	8	h	h	NOUN
ejpam-5155	73	9	has	have	VERB
ejpam-5155	73	10	a	a	DET
ejpam-5155	73	11	fixed	fix	VERB
ejpam-5155	73	12	point	point	NOUN
ejpam-5155	73	13	whenever	whenever	SCONJ
ejpam-5155	73	14	hn	hn	PROPN
ejpam-5155	73	15	has	have	VERB
ejpam-5155	73	16	a	a	DET
ejpam-5155	73	17	fixed	fix	VERB
ejpam-5155	73	18	point	point	NOUN
ejpam-5155	73	19	.	.	PUNCT
ejpam-5155	74	1	the	the	DET
ejpam-5155	74	2	term	term	NOUN
ejpam-5155	74	3	“	"	PUNCT
ejpam-5155	74	4	periodic	periodic	ADJ
ejpam-5155	74	5	points	point	NOUN
ejpam-5155	74	6	of	of	ADP
ejpam-5155	74	7	h	h	NOUN
ejpam-5155	74	8	”	"	PUNCT
ejpam-5155	74	9	also	also	ADV
ejpam-5155	74	10	applies	apply	VERB
ejpam-5155	74	11	to	to	ADP
ejpam-5155	74	12	fixed	fix	VERB
ejpam-5155	74	13	point	point	NOUN
ejpam-5155	74	14	of	of	ADP
ejpam-5155	74	15	hn	hn	PROPN
ejpam-5155	74	16	.[1	.[1	PROPN
ejpam-5155	74	17	]	]	PUNCT
ejpam-5155	74	18	.	.	PUNCT
ejpam-5155	75	1	3	3	X
ejpam-5155	75	2	.	.	X
ejpam-5155	75	3	main	main	ADJ
ejpam-5155	75	4	work	work	NOUN
ejpam-5155	75	5	under	under	ADP
ejpam-5155	75	6	this	this	DET
ejpam-5155	75	7	part	part	NOUN
ejpam-5155	75	8	we	we	PRON
ejpam-5155	75	9	look	look	VERB
ejpam-5155	75	10	for	for	ADP
ejpam-5155	75	11	the	the	DET
ejpam-5155	75	12	main	main	ADJ
ejpam-5155	75	13	solutions	solution	NOUN
ejpam-5155	75	14	of	of	ADP
ejpam-5155	75	15	the	the	DET
ejpam-5155	75	16	lotka	lotka	PROPN
ejpam-5155	75	17	volterra	volterra	PROPN
ejpam-5155	75	18	function	function	NOUN
ejpam-5155	75	19	and	and	CCONJ
ejpam-5155	75	20	also	also	ADV
ejpam-5155	75	21	determine	determine	VERB
ejpam-5155	75	22	the	the	DET
ejpam-5155	75	23	fixed	fix	VERB
ejpam-5155	75	24	point	point	NOUN
ejpam-5155	75	25	of	of	ADP
ejpam-5155	75	26	the	the	DET
ejpam-5155	75	27	function	function	NOUN
ejpam-5155	75	28	.	.	PUNCT
ejpam-5155	76	1	3.1	3.1	NUM
ejpam-5155	76	2	.	.	PUNCT
ejpam-5155	77	1	the	the	DET
ejpam-5155	77	2	zeros	zero	NOUN
ejpam-5155	77	3	of	of	ADP
ejpam-5155	77	4	the	the	DET
ejpam-5155	77	5	lotka	lotka	PROPN
ejpam-5155	77	6	volterra	volterra	PROPN
ejpam-5155	77	7	function	function	NOUN
ejpam-5155	77	8	in	in	ADP
ejpam-5155	77	9	this	this	DET
ejpam-5155	77	10	section	section	NOUN
ejpam-5155	77	11	,	,	PUNCT
ejpam-5155	77	12	we	we	PRON
ejpam-5155	77	13	look	look	VERB
ejpam-5155	77	14	for	for	ADP
ejpam-5155	77	15	the	the	DET
ejpam-5155	77	16	roots	root	NOUN
ejpam-5155	77	17	,	,	PUNCT
ejpam-5155	77	18	or	or	CCONJ
ejpam-5155	77	19	zeros	zero	NOUN
ejpam-5155	77	20	,	,	PUNCT
ejpam-5155	77	21	of	of	ADP
ejpam-5155	77	22	the	the	DET
ejpam-5155	77	23	function	function	NOUN
ejpam-5155	77	24	.	.	PUNCT
ejpam-5155	78	1	in	in	ADP
ejpam-5155	78	2	determining	determine	VERB
ejpam-5155	78	3	the	the	DET
ejpam-5155	78	4	zeros	zero	NOUN
ejpam-5155	78	5	or	or	CCONJ
ejpam-5155	78	6	roots	root	NOUN
ejpam-5155	78	7	of	of	ADP
ejpam-5155	78	8	the	the	DET
ejpam-5155	78	9	function	function	NOUN
ejpam-5155	78	10	,	,	PUNCT
ejpam-5155	78	11	let	let	VERB
ejpam-5155	78	12	xn+1	xn+1	VERB
ejpam-5155	78	13	=	=	SYM
ejpam-5155	78	14	0	0	PROPN
ejpam-5155	78	15	,	,	PUNCT
ejpam-5155	78	16	from	from	ADP
ejpam-5155	78	17	equation	equation	NOUN
ejpam-5155	78	18	(	(	PUNCT
ejpam-5155	78	19	1	1	NUM
ejpam-5155	78	20	)	)	PUNCT
ejpam-5155	78	21	,	,	PUNCT
ejpam-5155	78	22	thus	thus	ADV
ejpam-5155	78	23	xn+1	xn+1	X
ejpam-5155	78	24	=	=	SYM
ejpam-5155	78	25	αxn−βxnyn	αxn−βxnyn	NOUN
ejpam-5155	78	26	becomes	become	VERB
ejpam-5155	78	27	αxn	αxn	NOUN
ejpam-5155	78	28	−	−	NOUN
ejpam-5155	78	29	xnβyn	xnβyn	NOUN
ejpam-5155	78	30	=	=	SYM
ejpam-5155	78	31	0	0	NUM
ejpam-5155	78	32	(	(	PUNCT
ejpam-5155	78	33	5	5	NUM
ejpam-5155	78	34	)	)	PUNCT
ejpam-5155	78	35	xn(α−	xn(α−	PUNCT
ejpam-5155	79	1	βyn	βyn	NOUN
ejpam-5155	79	2	)	)	PUNCT
ejpam-5155	79	3	=	=	SYM
ejpam-5155	79	4	0	0	NUM
ejpam-5155	79	5	(	(	PUNCT
ejpam-5155	79	6	6	6	NUM
ejpam-5155	79	7	)	)	PUNCT
ejpam-5155	79	8	it	it	PRON
ejpam-5155	79	9	implies	imply	VERB
ejpam-5155	79	10	that	that	SCONJ
ejpam-5155	79	11	xn	xn	PROPN
ejpam-5155	80	1	=	=	SYM
ejpam-5155	80	2	0	0	NUM
ejpam-5155	80	3	and	and	CCONJ
ejpam-5155	80	4	α−	α−	ADP
ejpam-5155	80	5	βyn	βyn	NOUN
ejpam-5155	80	6	=	=	NOUN
ejpam-5155	80	7	0	0	NUM
ejpam-5155	81	1	then	then	ADV
ejpam-5155	81	2	yn	yn	X
ejpam-5155	81	3	=	=	PUNCT
ejpam-5155	81	4	α	α	PROPN
ejpam-5155	81	5	β	β	NOUN
ejpam-5155	81	6	hence	hence	ADV
ejpam-5155	81	7	,	,	PUNCT
ejpam-5155	81	8	the	the	DET
ejpam-5155	81	9	root	root	NOUN
ejpam-5155	81	10	of	of	ADP
ejpam-5155	81	11	xn+1	xn+1	PROPN
ejpam-5155	81	12	=	=	SYM
ejpam-5155	81	13	αxn	αxn	PROPN
ejpam-5155	81	14	−	−	NOUN
ejpam-5155	81	15	βxnyn	βxnyn	NOUN
ejpam-5155	81	16	thus	thus	ADV
ejpam-5155	81	17	(	(	PUNCT
ejpam-5155	81	18	xn	xn	PROPN
ejpam-5155	81	19	,	,	PUNCT
ejpam-5155	81	20	yn	yn	PROPN
ejpam-5155	81	21	)	)	PUNCT
ejpam-5155	81	22	is	be	AUX
ejpam-5155	81	23	(	(	PUNCT
ejpam-5155	81	24	0	0	NUM
ejpam-5155	81	25	,	,	PUNCT
ejpam-5155	81	26	αβ	αβ	NOUN
ejpam-5155	81	27	)	)	PUNCT
ejpam-5155	81	28	m.	m.	NOUN
ejpam-5155	81	29	o.	o.	PROPN
ejpam-5155	81	30	fokuoet	fokuoet	PROPN
ejpam-5155	81	31	al	al	PROPN
ejpam-5155	81	32	.	.	PUNCT
ejpam-5155	81	33	/	/	SYM
ejpam-5155	81	34	eur	eur	PROPN
ejpam-5155	81	35	.	.	PUNCT
ejpam-5155	82	1	j.	j.	PROPN
ejpam-5155	82	2	pure	pure	PROPN
ejpam-5155	82	3	appl	appl	PROPN
ejpam-5155	82	4	.	.	PROPN
ejpam-5155	82	5	math	math	PROPN
ejpam-5155	82	6	,	,	PUNCT
ejpam-5155	82	7	17	17	NUM
ejpam-5155	82	8	(	(	PUNCT
ejpam-5155	82	9	2	2	NUM
ejpam-5155	82	10	)	)	PUNCT
ejpam-5155	82	11	(	(	PUNCT
ejpam-5155	82	12	2024	2024	NUM
ejpam-5155	82	13	)	)	PUNCT
ejpam-5155	82	14	,	,	PUNCT
ejpam-5155	82	15	1294	1294	NUM
ejpam-5155	82	16	-	-	SYM
ejpam-5155	82	17	1305	1305	NUM
ejpam-5155	82	18	1297	1297	NUM
ejpam-5155	82	19	also	also	ADV
ejpam-5155	82	20	,	,	PUNCT
ejpam-5155	82	21	let	let	VERB
ejpam-5155	82	22	yn+1	yn+1	PRON
ejpam-5155	82	23	=	=	SYM
ejpam-5155	82	24	0	0	PROPN
ejpam-5155	82	25	then	then	ADV
ejpam-5155	82	26	from	from	ADP
ejpam-5155	82	27	equation	equation	NOUN
ejpam-5155	82	28	(	(	PUNCT
ejpam-5155	82	29	2	2	NUM
ejpam-5155	82	30	)	)	PUNCT
ejpam-5155	82	31	thus	thus	ADV
ejpam-5155	82	32	,	,	PUNCT
ejpam-5155	82	33	yn+1	yn+1	PROPN
ejpam-5155	82	34	=	=	NOUN
ejpam-5155	82	35	δxnyn	δxnyn	ADJ
ejpam-5155	82	36	−	−	NOUN
ejpam-5155	82	37	γyn	γyn	NOUN
ejpam-5155	82	38	also	also	ADV
ejpam-5155	82	39	becomes	become	VERB
ejpam-5155	82	40	δxnyn	δxnyn	ADJ
ejpam-5155	82	41	−	−	NOUN
ejpam-5155	82	42	γyn	γyn	NOUN
ejpam-5155	82	43	=	=	SYM
ejpam-5155	82	44	0	0	PUNCT
ejpam-5155	83	1	(	(	PUNCT
ejpam-5155	83	2	7	7	X
ejpam-5155	83	3	)	)	PUNCT
ejpam-5155	83	4	yn(δxn	yn(δxn	PROPN
ejpam-5155	83	5	−	−	PROPN
ejpam-5155	83	6	γ	γ	PROPN
ejpam-5155	83	7	)	)	PUNCT
ejpam-5155	83	8	=	=	SYM
ejpam-5155	83	9	0	0	PUNCT
ejpam-5155	83	10	(	(	PUNCT
ejpam-5155	83	11	8)	8)	NUM
ejpam-5155	83	12	then	then	ADV
ejpam-5155	83	13	yn	yn	PROPN
ejpam-5155	83	14	=	=	NOUN
ejpam-5155	83	15	0	0	NUM
ejpam-5155	83	16	and	and	CCONJ
ejpam-5155	83	17	δxn	δxn	VERB
ejpam-5155	84	1	−	−	PROPN
ejpam-5155	84	2	γ	γ	X
ejpam-5155	84	3	=	=	SYM
ejpam-5155	84	4	0	0	NUM
ejpam-5155	84	5	implies	imply	VERB
ejpam-5155	84	6	xn	xn	NOUN
ejpam-5155	84	7	=	=	SYM
ejpam-5155	84	8	γ	γ	PROPN
ejpam-5155	84	9	δ	δ	PROPN
ejpam-5155	84	10	similarly	similarly	ADV
ejpam-5155	84	11	,	,	PUNCT
ejpam-5155	84	12	the	the	DET
ejpam-5155	84	13	root	root	NOUN
ejpam-5155	84	14	of	of	ADP
ejpam-5155	84	15	yn+1	yn+1	PROPN
ejpam-5155	84	16	=	=	NOUN
ejpam-5155	84	17	δxnyn	δxnyn	ADJ
ejpam-5155	84	18	−	−	NOUN
ejpam-5155	84	19	γyn	γyn	PRON
ejpam-5155	84	20	thus	thus	ADV
ejpam-5155	84	21	(	(	PUNCT
ejpam-5155	84	22	xn	xn	PROPN
ejpam-5155	84	23	,	,	PUNCT
ejpam-5155	84	24	yn	yn	PROPN
ejpam-5155	84	25	)	)	PUNCT
ejpam-5155	84	26	is	be	AUX
ejpam-5155	84	27	(	(	PUNCT
ejpam-5155	84	28	γ	γ	X
ejpam-5155	84	29	δ	δ	PROPN
ejpam-5155	84	30	,	,	PUNCT
ejpam-5155	84	31	0	0	NUM
ejpam-5155	84	32	)	)	PUNCT
ejpam-5155	84	33	therefore	therefore	ADV
ejpam-5155	84	34	,	,	PUNCT
ejpam-5155	84	35	the	the	DET
ejpam-5155	84	36	roots	root	NOUN
ejpam-5155	84	37	are	be	AUX
ejpam-5155	84	38	(	(	PUNCT
ejpam-5155	84	39	0	0	NUM
ejpam-5155	84	40	,	,	PUNCT
ejpam-5155	84	41	0	0	NUM
ejpam-5155	84	42	)	)	PUNCT
ejpam-5155	84	43	,	,	PUNCT
ejpam-5155	84	44	(	(	PUNCT
ejpam-5155	84	45	0	0	NUM
ejpam-5155	84	46	,	,	PUNCT
ejpam-5155	84	47	αβ	αβ	NOUN
ejpam-5155	84	48	)	)	PUNCT
ejpam-5155	84	49	,	,	PUNCT
ejpam-5155	84	50	(	(	PUNCT
ejpam-5155	84	51	γ	γ	X
ejpam-5155	84	52	δ	δ	PROPN
ejpam-5155	84	53	,	,	PUNCT
ejpam-5155	84	54	0	0	NUM
ejpam-5155	84	55	)	)	PUNCT
ejpam-5155	84	56	,	,	PUNCT
ejpam-5155	84	57	and	and	CCONJ
ejpam-5155	84	58	(	(	PUNCT
ejpam-5155	84	59	γ	γ	PROPN
ejpam-5155	84	60	δ	δ	PROPN
ejpam-5155	84	61	,	,	PUNCT
ejpam-5155	84	62	α	α	NOUN
ejpam-5155	84	63	β	β	NOUN
ejpam-5155	84	64	)	)	PUNCT
ejpam-5155	84	65	3.2	3.2	NUM
ejpam-5155	84	66	.	.	PUNCT
ejpam-5155	85	1	the	the	DET
ejpam-5155	85	2	solutions	solution	NOUN
ejpam-5155	85	3	of	of	ADP
ejpam-5155	85	4	the	the	DET
ejpam-5155	85	5	lotka	lotka	PROPN
ejpam-5155	85	6	volterra	volterra	PROPN
ejpam-5155	85	7	function	function	VERB
ejpam-5155	85	8	this	this	DET
ejpam-5155	85	9	section	section	NOUN
ejpam-5155	85	10	is	be	AUX
ejpam-5155	85	11	mainly	mainly	ADV
ejpam-5155	85	12	about	about	ADP
ejpam-5155	85	13	the	the	DET
ejpam-5155	85	14	solutions	solution	NOUN
ejpam-5155	85	15	of	of	ADP
ejpam-5155	85	16	the	the	DET
ejpam-5155	85	17	function	function	NOUN
ejpam-5155	85	18	.	.	PUNCT
ejpam-5155	86	1	let	let	VERB
ejpam-5155	86	2	xn+1	xn+1	NOUN
ejpam-5155	86	3	=	=	SYM
ejpam-5155	86	4	xn	xn	PROPN
ejpam-5155	86	5	(	(	PUNCT
ejpam-5155	86	6	9	9	NUM
ejpam-5155	86	7	)	)	PUNCT
ejpam-5155	86	8	yn+1	yn+1	PROPN
ejpam-5155	86	9	=	=	SYM
ejpam-5155	86	10	yn	yn	PROPN
ejpam-5155	86	11	(	(	PUNCT
ejpam-5155	86	12	10	10	NUM
ejpam-5155	86	13	)	)	PUNCT
ejpam-5155	86	14	equating	equate	VERB
ejpam-5155	86	15	equation	equation	NOUN
ejpam-5155	86	16	(	(	PUNCT
ejpam-5155	86	17	1	1	NUM
ejpam-5155	86	18	)	)	PUNCT
ejpam-5155	86	19	and	and	CCONJ
ejpam-5155	86	20	equation	equation	NOUN
ejpam-5155	86	21	(	(	PUNCT
ejpam-5155	86	22	9	9	X
ejpam-5155	86	23	)	)	PUNCT
ejpam-5155	86	24	becomes	become	VERB
ejpam-5155	86	25	αxn	αxn	NOUN
ejpam-5155	86	26	−	−	NOUN
ejpam-5155	86	27	xnβyn	xnβyn	NOUN
ejpam-5155	86	28	=	=	SYM
ejpam-5155	86	29	xn	xn	PROPN
ejpam-5155	86	30	αxn	αxn	PROPN
ejpam-5155	86	31	−	−	PROPN
ejpam-5155	86	32	xnβyn	xnβyn	NOUN
ejpam-5155	86	33	−	−	PROPN
ejpam-5155	86	34	xn	xn	PUNCT
ejpam-5155	87	1	=	=	SYM
ejpam-5155	87	2	0	0	NUM
ejpam-5155	87	3	implies	imply	VERB
ejpam-5155	87	4	xn(α−	xn(α−	X
ejpam-5155	87	5	βyn	βyn	PROPN
ejpam-5155	87	6	−	−	PROPN
ejpam-5155	87	7	1	1	NUM
ejpam-5155	87	8	)	)	PUNCT
ejpam-5155	87	9	=	=	SYM
ejpam-5155	87	10	0	0	PUNCT
ejpam-5155	88	1	then	then	ADV
ejpam-5155	88	2	xn	xn	PUNCT
ejpam-5155	88	3	=	=	SYM
ejpam-5155	88	4	0	0	NUM
ejpam-5155	88	5	and	and	CCONJ
ejpam-5155	88	6	α−	α−	ADP
ejpam-5155	88	7	βyn	βyn	NOUN
ejpam-5155	89	1	−	−	PROPN
ejpam-5155	89	2	1	1	NUM
ejpam-5155	89	3	=	=	SYM
ejpam-5155	89	4	0	0	NUM
ejpam-5155	89	5	βyn	βyn	NOUN
ejpam-5155	89	6	=	=	SYM
ejpam-5155	89	7	α−	α−	ADP
ejpam-5155	89	8	1	1	NUM
ejpam-5155	89	9	therefore	therefore	ADV
ejpam-5155	89	10	,	,	PUNCT
ejpam-5155	89	11	yn	yn	PROPN
ejpam-5155	89	12	=	=	PUNCT
ejpam-5155	89	13	α−1	α−1	PROPN
ejpam-5155	89	14	β	β	PRON
ejpam-5155	89	15	also	also	ADV
ejpam-5155	89	16	equating	equate	VERB
ejpam-5155	89	17	equation	equation	NOUN
ejpam-5155	89	18	(	(	PUNCT
ejpam-5155	89	19	2	2	NUM
ejpam-5155	89	20	)	)	PUNCT
ejpam-5155	89	21	and	and	CCONJ
ejpam-5155	89	22	equation	equation	NOUN
ejpam-5155	89	23	(	(	PUNCT
ejpam-5155	89	24	10	10	NUM
ejpam-5155	89	25	)	)	PUNCT
ejpam-5155	89	26	becomes	become	VERB
ejpam-5155	89	27	δxnyn	δxnyn	ADJ
ejpam-5155	89	28	−	−	NOUN
ejpam-5155	89	29	γyn	γyn	NOUN
ejpam-5155	89	30	=	=	SYM
ejpam-5155	89	31	yn	yn	PROPN
ejpam-5155	89	32	(	(	PUNCT
ejpam-5155	89	33	11	11	NUM
ejpam-5155	89	34	)	)	PUNCT
ejpam-5155	89	35	then	then	ADV
ejpam-5155	89	36	δxnyn	δxnyn	ADJ
ejpam-5155	89	37	−	−	PROPN
ejpam-5155	89	38	γyn	γyn	NOUN
ejpam-5155	89	39	−	−	PROPN
ejpam-5155	90	1	yn	yn	INTJ
ejpam-5155	91	1	=	=	PUNCT
ejpam-5155	92	1	0	0	PROPN
ejpam-5155	93	1	yn(δxn	yn(δxn	PROPN
ejpam-5155	93	2	−	−	PROPN
ejpam-5155	93	3	γ	γ	PROPN
ejpam-5155	93	4	−	−	PROPN
ejpam-5155	93	5	1	1	NUM
ejpam-5155	93	6	)	)	PUNCT
ejpam-5155	93	7	=	=	SYM
ejpam-5155	93	8	0	0	PUNCT
ejpam-5155	94	1	then	then	ADV
ejpam-5155	94	2	yn	yn	PROPN
ejpam-5155	94	3	=	=	SYM
ejpam-5155	94	4	0	0	NUM
ejpam-5155	94	5	and	and	CCONJ
ejpam-5155	94	6	δxn	δxn	VERB
ejpam-5155	94	7	−	−	PROPN
ejpam-5155	94	8	γ	γ	PROPN
ejpam-5155	94	9	−	−	PROPN
ejpam-5155	94	10	1	1	NUM
ejpam-5155	94	11	=	=	SYM
ejpam-5155	94	12	0	0	NUM
ejpam-5155	94	13	δxn	δxn	NOUN
ejpam-5155	94	14	=	=	NOUN
ejpam-5155	94	15	1	1	NUM
ejpam-5155	94	16	+	+	CCONJ
ejpam-5155	94	17	γ	γ	X
ejpam-5155	94	18	therefore	therefore	ADV
ejpam-5155	94	19	,	,	PUNCT
ejpam-5155	94	20	xn	xn	PROPN
ejpam-5155	94	21	=	=	SYM
ejpam-5155	95	1	1+γ	1+γ	NUM
ejpam-5155	95	2	δ	δ	NOUN
ejpam-5155	95	3	hence	hence	ADV
ejpam-5155	95	4	,	,	PUNCT
ejpam-5155	95	5	the	the	DET
ejpam-5155	95	6	solutions	solution	NOUN
ejpam-5155	95	7	of	of	ADP
ejpam-5155	95	8	the	the	DET
ejpam-5155	95	9	function	function	NOUN
ejpam-5155	95	10	are	be	AUX
ejpam-5155	95	11	(	(	PUNCT
ejpam-5155	95	12	0	0	NUM
ejpam-5155	95	13	,	,	PUNCT
ejpam-5155	95	14	α−1	α−1	PROPN
ejpam-5155	95	15	β	β	X
ejpam-5155	95	16	)	)	PUNCT
ejpam-5155	95	17	and	and	CCONJ
ejpam-5155	95	18	(	(	PUNCT
ejpam-5155	95	19	1+γ	1+γ	NUM
ejpam-5155	95	20	δ	δ	PROPN
ejpam-5155	95	21	,	,	PUNCT
ejpam-5155	95	22	0	0	NUM
ejpam-5155	95	23	)	)	PUNCT
ejpam-5155	95	24	3.3	3.3	NUM
ejpam-5155	95	25	.	.	PUNCT
ejpam-5155	96	1	determination	determination	NOUN
ejpam-5155	96	2	of	of	ADP
ejpam-5155	96	3	the	the	DET
ejpam-5155	96	4	fixed	fix	VERB
ejpam-5155	96	5	point	point	NOUN
ejpam-5155	96	6	of	of	ADP
ejpam-5155	96	7	the	the	DET
ejpam-5155	96	8	lotka	lotka	PROPN
ejpam-5155	96	9	volterra	volterra	PROPN
ejpam-5155	96	10	function	function	NOUN
ejpam-5155	96	11	in	in	ADP
ejpam-5155	96	12	this	this	DET
ejpam-5155	96	13	section	section	NOUN
ejpam-5155	96	14	,	,	PUNCT
ejpam-5155	96	15	we	we	PRON
ejpam-5155	96	16	will	will	AUX
ejpam-5155	96	17	consider	consider	VERB
ejpam-5155	96	18	the	the	DET
ejpam-5155	96	19	two	two	NUM
ejpam-5155	96	20	definitions	definition	NOUN
ejpam-5155	96	21	of	of	ADP
ejpam-5155	96	22	the	the	DET
ejpam-5155	96	23	function	function	NOUN
ejpam-5155	96	24	.	.	PUNCT
ejpam-5155	97	1	that	that	PRON
ejpam-5155	97	2	is	be	AUX
ejpam-5155	97	3	;	;	PUNCT
ejpam-5155	97	4	xn+1	xn+1	NUM
ejpam-5155	97	5	=	=	SYM
ejpam-5155	97	6	αxn	αxn	PROPN
ejpam-5155	97	7	−	−	PROPN
ejpam-5155	97	8	xnβyn	xnβyn	NOUN
ejpam-5155	97	9	and	and	CCONJ
ejpam-5155	97	10	yn+1	yn+1	NUM
ejpam-5155	97	11	=	=	NOUN
ejpam-5155	97	12	δxnyn	δxnyn	ADJ
ejpam-5155	97	13	−	−	NUM
ejpam-5155	97	14	γyn	γyn	NOUN
ejpam-5155	97	15	and	and	CCONJ
ejpam-5155	97	16	then	then	ADV
ejpam-5155	97	17	work	work	VERB
ejpam-5155	97	18	out	out	ADP
ejpam-5155	97	19	for	for	ADP
ejpam-5155	97	20	the	the	DET
ejpam-5155	97	21	fixed	fix	VERB
ejpam-5155	97	22	point	point	NOUN
ejpam-5155	97	23	of	of	ADP
ejpam-5155	97	24	the	the	DET
ejpam-5155	97	25	function	function	NOUN
ejpam-5155	97	26	using	use	VERB
ejpam-5155	97	27	the	the	DET
ejpam-5155	97	28	solutions	solution	NOUN
ejpam-5155	97	29	,	,	PUNCT
ejpam-5155	97	30	(	(	PUNCT
ejpam-5155	97	31	0	0	NUM
ejpam-5155	97	32	,	,	PUNCT
ejpam-5155	97	33	0	0	NUM
ejpam-5155	97	34	)	)	PUNCT
ejpam-5155	97	35	,	,	PUNCT
ejpam-5155	97	36	(	(	PUNCT
ejpam-5155	97	37	0	0	NUM
ejpam-5155	97	38	,	,	PUNCT
ejpam-5155	97	39	α−1	α−1	PROPN
ejpam-5155	97	40	β	β	NOUN
ejpam-5155	97	41	)	)	PUNCT
ejpam-5155	97	42	,	,	PUNCT
ejpam-5155	97	43	(	(	PUNCT
ejpam-5155	97	44	1+γ	1+γ	NUM
ejpam-5155	97	45	δ	δ	PROPN
ejpam-5155	97	46	,	,	PUNCT
ejpam-5155	97	47	0	0	NUM
ejpam-5155	97	48	)	)	PUNCT
ejpam-5155	97	49	,	,	PUNCT
ejpam-5155	97	50	and	and	CCONJ
ejpam-5155	97	51	(	(	PUNCT
ejpam-5155	97	52	1+γ	1+γ	NUM
ejpam-5155	97	53	δ	δ	PROPN
ejpam-5155	97	54	,	,	PUNCT
ejpam-5155	97	55	α−1	α−1	PROPN
ejpam-5155	97	56	β	β	PROPN
ejpam-5155	97	57	)	)	PUNCT
ejpam-5155	97	58	.	.	PUNCT
ejpam-5155	98	1	we	we	PRON
ejpam-5155	98	2	then	then	ADV
ejpam-5155	98	3	apply	apply	VERB
ejpam-5155	98	4	the	the	DET
ejpam-5155	98	5	idea	idea	NOUN
ejpam-5155	98	6	and	and	CCONJ
ejpam-5155	98	7	the	the	DET
ejpam-5155	98	8	definition	definition	NOUN
ejpam-5155	98	9	of	of	ADP
ejpam-5155	98	10	the	the	DET
ejpam-5155	98	11	theorem	theorem	NOUN
ejpam-5155	98	12	of	of	ADP
ejpam-5155	98	13	fixed	fix	VERB
ejpam-5155	98	14	points	point	NOUN
ejpam-5155	98	15	and	and	CCONJ
ejpam-5155	98	16	fixed	fix	VERB
ejpam-5155	98	17	point	point	NOUN
ejpam-5155	98	18	.	.	PUNCT
ejpam-5155	99	1	that	that	PRON
ejpam-5155	99	2	is	be	AUX
ejpam-5155	99	3	;	;	PUNCT
ejpam-5155	99	4	a	a	DET
ejpam-5155	99	5	function	function	NOUN
ejpam-5155	99	6	g	g	NOUN
ejpam-5155	99	7	is	be	AUX
ejpam-5155	99	8	fixed	fix	VERB
ejpam-5155	99	9	point	point	NOUN
ejpam-5155	99	10	theorem	theorem	ADJ
ejpam-5155	99	11	having	have	VERB
ejpam-5155	99	12	a	a	DET
ejpam-5155	99	13	minimum	minimum	NOUN
ejpam-5155	99	14	of	of	ADP
ejpam-5155	99	15	one	one	NUM
ejpam-5155	99	16	fixed	fix	VERB
ejpam-5155	99	17	point	point	NOUN
ejpam-5155	99	18	x	x	SYM
ejpam-5155	99	19	∈	∈	NOUN
ejpam-5155	99	20	x	x	PUNCT
ejpam-5155	99	21	such	such	ADJ
ejpam-5155	99	22	that	that	SCONJ
ejpam-5155	99	23	g(x	g(x	NOUN
ejpam-5155	99	24	)	)	PUNCT
ejpam-5155	100	1	=	=	PUNCT
ejpam-5155	100	2	x.	x.	NOUN
ejpam-5155	100	3	a	a	DET
ejpam-5155	100	4	point	point	NOUN
ejpam-5155	100	5	x0	x0	PROPN
ejpam-5155	100	6	is	be	AUX
ejpam-5155	100	7	the	the	DET
ejpam-5155	100	8	fixed	fixed	ADJ
ejpam-5155	100	9	point	point	NOUN
ejpam-5155	100	10	of	of	ADP
ejpam-5155	100	11	a	a	DET
ejpam-5155	100	12	function	function	NOUN
ejpam-5155	100	13	g(x	g(x	NOUN
ejpam-5155	100	14	)	)	PUNCT
ejpam-5155	100	15	,	,	PUNCT
ejpam-5155	100	16	such	such	ADJ
ejpam-5155	100	17	that	that	SCONJ
ejpam-5155	100	18	g	g	PROPN
ejpam-5155	100	19	(	(	PUNCT
ejpam-5155	100	20	x0	x0	PROPN
ejpam-5155	100	21	)	)	PUNCT
ejpam-5155	101	1	=	=	SYM
ejpam-5155	101	2	x0	x0	PROPN
ejpam-5155	101	3	.	.	PUNCT
ejpam-5155	102	1	m.	m.	NOUN
ejpam-5155	102	2	o.	o.	PROPN
ejpam-5155	102	3	fokuoet	fokuoet	PROPN
ejpam-5155	102	4	al	al	PROPN
ejpam-5155	102	5	.	.	PUNCT
ejpam-5155	102	6	/	/	SYM
ejpam-5155	102	7	eur	eur	PROPN
ejpam-5155	102	8	.	.	PUNCT
ejpam-5155	103	1	j.	j.	PROPN
ejpam-5155	103	2	pure	pure	PROPN
ejpam-5155	103	3	appl	appl	PROPN
ejpam-5155	103	4	.	.	PROPN
ejpam-5155	103	5	math	math	PROPN
ejpam-5155	103	6	,	,	PUNCT
ejpam-5155	103	7	17	17	NUM
ejpam-5155	103	8	(	(	PUNCT
ejpam-5155	103	9	2	2	NUM
ejpam-5155	103	10	)	)	PUNCT
ejpam-5155	103	11	(	(	PUNCT
ejpam-5155	103	12	2024	2024	NUM
ejpam-5155	103	13	)	)	PUNCT
ejpam-5155	103	14	,	,	PUNCT
ejpam-5155	103	15	1294	1294	NUM
ejpam-5155	103	16	-	-	SYM
ejpam-5155	103	17	1305	1305	NUM
ejpam-5155	103	18	1298	1298	NUM
ejpam-5155	103	19	1	1	NUM
ejpam-5155	103	20	)	)	PUNCT
ejpam-5155	103	21	determining	determine	VERB
ejpam-5155	103	22	the	the	DET
ejpam-5155	103	23	fixed	fixed	ADJ
ejpam-5155	103	24	point	point	NOUN
ejpam-5155	103	25	of	of	ADP
ejpam-5155	103	26	xn+1	xn+1	PROPN
ejpam-5155	103	27	=	=	SYM
ejpam-5155	103	28	αxn	αxn	PROPN
ejpam-5155	103	29	−	−	PROPN
ejpam-5155	103	30	xnβyn	xnβyn	NOUN
ejpam-5155	103	31	at	at	ADP
ejpam-5155	103	32	(	(	PUNCT
ejpam-5155	103	33	0	0	NUM
ejpam-5155	103	34	,	,	PUNCT
ejpam-5155	103	35	0	0	NUM
ejpam-5155	103	36	)	)	PUNCT
ejpam-5155	103	37	xn+1	xn+1	PUNCT
ejpam-5155	104	1	=	=	SYM
ejpam-5155	104	2	α(0)−	α(0)−	PROPN
ejpam-5155	104	3	(	(	PUNCT
ejpam-5155	104	4	0)β(0	0)β(0	PROPN
ejpam-5155	104	5	)	)	PUNCT
ejpam-5155	104	6	implies	imply	VERB
ejpam-5155	104	7	xn+1	xn+1	PROPN
ejpam-5155	104	8	=	=	SYM
ejpam-5155	104	9	0−	0−	NUM
ejpam-5155	104	10	0	0	NUM
ejpam-5155	104	11	xn+1	xn+1	NUM
ejpam-5155	104	12	=	=	SYM
ejpam-5155	104	13	0	0	PUNCT
ejpam-5155	105	1	hence	hence	ADV
ejpam-5155	105	2	,	,	PUNCT
ejpam-5155	105	3	(	(	PUNCT
ejpam-5155	105	4	0	0	NUM
ejpam-5155	105	5	,	,	PUNCT
ejpam-5155	105	6	0	0	NUM
ejpam-5155	105	7	)	)	PUNCT
ejpam-5155	105	8	is	be	AUX
ejpam-5155	105	9	one	one	NUM
ejpam-5155	105	10	of	of	ADP
ejpam-5155	105	11	the	the	DET
ejpam-5155	105	12	fixed	fix	VERB
ejpam-5155	105	13	points	point	NOUN
ejpam-5155	105	14	but	but	CCONJ
ejpam-5155	105	15	trivial	trivial	ADJ
ejpam-5155	105	16	.	.	PUNCT
ejpam-5155	106	1	also	also	ADV
ejpam-5155	106	2	,	,	PUNCT
ejpam-5155	106	3	at	at	ADP
ejpam-5155	106	4	(	(	PUNCT
ejpam-5155	106	5	1+γ	1+γ	PROPN
ejpam-5155	106	6	δ	δ	PROPN
ejpam-5155	106	7	,	,	PUNCT
ejpam-5155	106	8	α−1	α−1	PROPN
ejpam-5155	106	9	β	β	X
ejpam-5155	106	10	)	)	PUNCT
ejpam-5155	106	11	xn+1	xn+1	PROPN
ejpam-5155	107	1	=	=	SYM
ejpam-5155	107	2	α	α	PROPN
ejpam-5155	107	3	(	(	PUNCT
ejpam-5155	107	4	1+γ	1+γ	NUM
ejpam-5155	107	5	δ	δ	NOUN
ejpam-5155	107	6	)	)	PUNCT
ejpam-5155	107	7	−	−	PROPN
ejpam-5155	108	1	(	(	PUNCT
ejpam-5155	108	2	1+γ	1+γ	NUM
ejpam-5155	108	3	δ	δ	NOUN
ejpam-5155	108	4	)	)	PUNCT
ejpam-5155	108	5	β	β	PROPN
ejpam-5155	108	6	(	(	PUNCT
ejpam-5155	108	7	α−1	α−1	PROPN
ejpam-5155	108	8	β	β	X
ejpam-5155	108	9	)	)	PUNCT
ejpam-5155	108	10	implies	imply	VERB
ejpam-5155	108	11	xn+1	xn+1	PROPN
ejpam-5155	109	1	=	=	SYM
ejpam-5155	109	2	(	(	PUNCT
ejpam-5155	109	3	α+αγ	α+αγ	PROPN
ejpam-5155	109	4	δ	δ	PROPN
ejpam-5155	109	5	)	)	PUNCT
ejpam-5155	109	6	−	−	PROPN
ejpam-5155	109	7	(	(	PUNCT
ejpam-5155	109	8	1+γ	1+γ	NUM
ejpam-5155	109	9	δ	δ	NOUN
ejpam-5155	109	10	)	)	PUNCT
ejpam-5155	109	11	(	(	PUNCT
ejpam-5155	109	12	α−	α−	ADP
ejpam-5155	109	13	1	1	NUM
ejpam-5155	109	14	)	)	PUNCT
ejpam-5155	109	15	=	=	SYM
ejpam-5155	109	16	(	(	PUNCT
ejpam-5155	109	17	α+αγ	α+αγ	PROPN
ejpam-5155	109	18	δ	δ	PROPN
ejpam-5155	109	19	)	)	PUNCT
ejpam-5155	109	20	−	−	PROPN
ejpam-5155	110	1	[	[	X
ejpam-5155	110	2	(	(	PUNCT
ejpam-5155	110	3	α+αγ	α+αγ	PROPN
ejpam-5155	110	4	δ	δ	PROPN
ejpam-5155	110	5	)	)	PUNCT
ejpam-5155	110	6	−	−	PROPN
ejpam-5155	111	1	(	(	PUNCT
ejpam-5155	111	2	1+γ	1+γ	NUM
ejpam-5155	111	3	δ	δ	NOUN
ejpam-5155	111	4	)	)	PUNCT
ejpam-5155	111	5	]	]	PUNCT
ejpam-5155	112	1	=	=	PUNCT
ejpam-5155	112	2	(	(	PUNCT
ejpam-5155	112	3	α+αγ	α+αγ	PROPN
ejpam-5155	112	4	δ	δ	PROPN
ejpam-5155	112	5	)	)	PUNCT
ejpam-5155	112	6	−	−	PROPN
ejpam-5155	113	1	(	(	PUNCT
ejpam-5155	113	2	α+αγ	α+αγ	PROPN
ejpam-5155	113	3	δ	δ	PROPN
ejpam-5155	113	4	)	)	PUNCT
ejpam-5155	114	1	+	+	CCONJ
ejpam-5155	114	2	(	(	PUNCT
ejpam-5155	114	3	1+γ	1+γ	NUM
ejpam-5155	114	4	δ	δ	NOUN
ejpam-5155	114	5	)	)	PUNCT
ejpam-5155	114	6	=	=	PUNCT
ejpam-5155	115	1	(	(	PUNCT
ejpam-5155	115	2	1+γ	1+γ	NUM
ejpam-5155	115	3	δ	δ	NOUN
ejpam-5155	115	4	)	)	PUNCT
ejpam-5155	115	5	again	again	ADV
ejpam-5155	115	6	,	,	PUNCT
ejpam-5155	115	7	(	(	PUNCT
ejpam-5155	115	8	1+γ	1+γ	NUM
ejpam-5155	115	9	δ	δ	PROPN
ejpam-5155	115	10	,	,	PUNCT
ejpam-5155	115	11	α−1	α−1	PROPN
ejpam-5155	115	12	β	β	X
ejpam-5155	115	13	)	)	PUNCT
ejpam-5155	115	14	is	be	AUX
ejpam-5155	115	15	also	also	ADV
ejpam-5155	115	16	a	a	DET
ejpam-5155	115	17	fixed	fix	VERB
ejpam-5155	115	18	point	point	NOUN
ejpam-5155	115	19	but	but	CCONJ
ejpam-5155	115	20	its	its	PRON
ejpam-5155	115	21	existence	existence	NOUN
ejpam-5155	115	22	will	will	AUX
ejpam-5155	115	23	depend	depend	VERB
ejpam-5155	115	24	on	on	ADP
ejpam-5155	115	25	the	the	DET
ejpam-5155	115	26	values	value	NOUN
ejpam-5155	115	27	of	of	ADP
ejpam-5155	115	28	the	the	DET
ejpam-5155	115	29	parameter	parameter	NOUN
ejpam-5155	115	30	of	of	ADP
ejpam-5155	115	31	the	the	DET
ejpam-5155	115	32	function	function	NOUN
ejpam-5155	115	33	.	.	PUNCT
ejpam-5155	116	1	2	2	X
ejpam-5155	116	2	)	)	PUNCT
ejpam-5155	116	3	determining	determine	VERB
ejpam-5155	116	4	the	the	DET
ejpam-5155	116	5	fixed	fixed	ADJ
ejpam-5155	116	6	point	point	NOUN
ejpam-5155	116	7	of	of	ADP
ejpam-5155	116	8	yn+1	yn+1	PROPN
ejpam-5155	116	9	=	=	NOUN
ejpam-5155	116	10	δxnyn	δxnyn	ADJ
ejpam-5155	116	11	−	−	NOUN
ejpam-5155	116	12	γyn	γyn	NOUN
ejpam-5155	116	13	then	then	ADV
ejpam-5155	116	14	at	at	ADP
ejpam-5155	116	15	(	(	PUNCT
ejpam-5155	116	16	0	0	NUM
ejpam-5155	116	17	,	,	PUNCT
ejpam-5155	116	18	0	0	NUM
ejpam-5155	116	19	)	)	PUNCT
ejpam-5155	116	20	yn+1	yn+1	PROPN
ejpam-5155	117	1	=	=	SYM
ejpam-5155	117	2	δ(0)(0)−	δ(0)(0)−	ADP
ejpam-5155	117	3	γ(0	γ(0	PROPN
ejpam-5155	117	4	)	)	PUNCT
ejpam-5155	117	5	yn+1	yn+1	PROPN
ejpam-5155	118	1	=	=	NOUN
ejpam-5155	118	2	0−	0−	NUM
ejpam-5155	118	3	0	0	NUM
ejpam-5155	118	4	yn+1	yn+1	PROPN
ejpam-5155	118	5	=	=	SYM
ejpam-5155	118	6	0	0	PUNCT
ejpam-5155	119	1	also	also	ADV
ejpam-5155	119	2	,	,	PUNCT
ejpam-5155	119	3	at	at	ADP
ejpam-5155	119	4	(	(	PUNCT
ejpam-5155	119	5	1+γ	1+γ	NUM
ejpam-5155	119	6	δ	δ	PROPN
ejpam-5155	119	7	,	,	PUNCT
ejpam-5155	119	8	α−1	α−1	PROPN
ejpam-5155	119	9	β	β	X
ejpam-5155	119	10	)	)	PUNCT
ejpam-5155	119	11	yn+1	yn+1	PROPN
ejpam-5155	119	12	=	=	PUNCT
ejpam-5155	119	13	δ	δ	PROPN
ejpam-5155	119	14	(	(	PUNCT
ejpam-5155	119	15	1+γ	1+γ	PROPN
ejpam-5155	119	16	δ	δ	NOUN
ejpam-5155	119	17	)	)	PUNCT
ejpam-5155	119	18	(	(	PUNCT
ejpam-5155	119	19	α−1	α−1	PROPN
ejpam-5155	119	20	β	β	X
ejpam-5155	119	21	)	)	PUNCT
ejpam-5155	120	1	−	−	PROPN
ejpam-5155	120	2	γ	γ	X
ejpam-5155	120	3	(	(	PUNCT
ejpam-5155	120	4	α−1	α−1	PROPN
ejpam-5155	120	5	β	β	PROPN
ejpam-5155	120	6	)	)	PUNCT
ejpam-5155	120	7	implies	imply	VERB
ejpam-5155	120	8	yn+1	yn+1	X
ejpam-5155	121	1	=	=	SYM
ejpam-5155	122	1	(	(	PUNCT
ejpam-5155	122	2	1	1	NUM
ejpam-5155	122	3	+	+	CCONJ
ejpam-5155	122	4	γ	γ	X
ejpam-5155	122	5	)	)	PUNCT
ejpam-5155	122	6	(	(	PUNCT
ejpam-5155	122	7	α−1	α−1	PROPN
ejpam-5155	122	8	β	β	X
ejpam-5155	122	9	)	)	PUNCT
ejpam-5155	122	10	−	−	PROPN
ejpam-5155	122	11	γ	γ	X
ejpam-5155	122	12	(	(	PUNCT
ejpam-5155	122	13	α−1	α−1	PROPN
ejpam-5155	122	14	β	β	X
ejpam-5155	122	15	)	)	PUNCT
ejpam-5155	122	16	=	=	PUNCT
ejpam-5155	123	1	(	(	PUNCT
ejpam-5155	123	2	1	1	NUM
ejpam-5155	123	3	+	+	CCONJ
ejpam-5155	123	4	γ	γ	X
ejpam-5155	123	5	)	)	PUNCT
ejpam-5155	123	6	(	(	PUNCT
ejpam-5155	123	7	α−1	α−1	PROPN
ejpam-5155	123	8	β	β	X
ejpam-5155	123	9	)	)	PUNCT
ejpam-5155	123	10	−	−	PROPN
ejpam-5155	123	11	γ	γ	X
ejpam-5155	123	12	(	(	PUNCT
ejpam-5155	123	13	α−1	α−1	PROPN
ejpam-5155	123	14	β	β	X
ejpam-5155	123	15	)	)	PUNCT
ejpam-5155	123	16	=	=	PUNCT
ejpam-5155	124	1	(	(	PUNCT
ejpam-5155	124	2	α−1	α−1	PROPN
ejpam-5155	124	3	β	β	X
ejpam-5155	124	4	)	)	PUNCT
ejpam-5155	125	1	+	+	CCONJ
ejpam-5155	125	2	(	(	PUNCT
ejpam-5155	125	3	γα−γ	γα−γ	NOUN
ejpam-5155	125	4	β	β	NOUN
ejpam-5155	125	5	)	)	PUNCT
ejpam-5155	125	6	−	−	PROPN
ejpam-5155	126	1	(	(	PUNCT
ejpam-5155	126	2	γα−γ	γα−γ	NOUN
ejpam-5155	126	3	β	β	X
ejpam-5155	126	4	)	)	PUNCT
ejpam-5155	126	5	=	=	PUNCT
ejpam-5155	127	1	(	(	PUNCT
ejpam-5155	127	2	α−1	α−1	PROPN
ejpam-5155	127	3	β	β	PROPN
ejpam-5155	127	4	)	)	PUNCT
ejpam-5155	127	5	hence	hence	ADV
ejpam-5155	127	6	,	,	PUNCT
ejpam-5155	127	7	(	(	PUNCT
ejpam-5155	127	8	0	0	NUM
ejpam-5155	127	9	,	,	PUNCT
ejpam-5155	127	10	0	0	NUM
ejpam-5155	127	11	)	)	PUNCT
ejpam-5155	127	12	,	,	PUNCT
ejpam-5155	127	13	(	(	PUNCT
ejpam-5155	127	14	0	0	NUM
ejpam-5155	127	15	,	,	PUNCT
ejpam-5155	127	16	α−1	α−1	PROPN
ejpam-5155	127	17	β	β	NOUN
ejpam-5155	127	18	)	)	PUNCT
ejpam-5155	127	19	,	,	PUNCT
ejpam-5155	127	20	(	(	PUNCT
ejpam-5155	127	21	1+γ	1+γ	NUM
ejpam-5155	127	22	δ	δ	PROPN
ejpam-5155	127	23	,	,	PUNCT
ejpam-5155	127	24	0	0	NUM
ejpam-5155	127	25	)	)	PUNCT
ejpam-5155	127	26	and	and	CCONJ
ejpam-5155	127	27	(	(	PUNCT
ejpam-5155	127	28	1+γ	1+γ	NUM
ejpam-5155	127	29	δ	δ	PROPN
ejpam-5155	127	30	,	,	PUNCT
ejpam-5155	127	31	α−1	α−1	PROPN
ejpam-5155	127	32	β	β	X
ejpam-5155	127	33	)	)	PUNCT
ejpam-5155	127	34	are	be	AUX
ejpam-5155	127	35	the	the	DET
ejpam-5155	127	36	fixed	fix	VERB
ejpam-5155	127	37	points	point	NOUN
ejpam-5155	127	38	of	of	ADP
ejpam-5155	127	39	the	the	DET
ejpam-5155	127	40	function	function	NOUN
ejpam-5155	127	41	.	.	PUNCT
ejpam-5155	128	1	final	final	ADJ
ejpam-5155	128	2	results	result	NOUN
ejpam-5155	128	3	in	in	ADP
ejpam-5155	128	4	this	this	DET
ejpam-5155	128	5	section	section	NOUN
ejpam-5155	128	6	we	we	PRON
ejpam-5155	128	7	impose	impose	VERB
ejpam-5155	128	8	the	the	DET
ejpam-5155	128	9	contraction	contraction	NOUN
ejpam-5155	128	10	mapping	mapping	NOUN
ejpam-5155	128	11	on	on	ADP
ejpam-5155	128	12	the	the	DET
ejpam-5155	128	13	lotka	lotka	PROPN
ejpam-5155	128	14	volterra	volterra	PROPN
ejpam-5155	128	15	to	to	PART
ejpam-5155	128	16	see	see	VERB
ejpam-5155	128	17	the	the	DET
ejpam-5155	128	18	outcome	outcome	NOUN
ejpam-5155	128	19	of	of	ADP
ejpam-5155	128	20	its	its	PRON
ejpam-5155	128	21	behaviour[6	behaviour[6	NOUN
ejpam-5155	128	22	]	]	PUNCT
ejpam-5155	128	23	.	.	PUNCT
ejpam-5155	129	1	definition	definition	NOUN
ejpam-5155	129	2	9	9	NUM
ejpam-5155	129	3	(	(	PUNCT
ejpam-5155	129	4	contraction	contraction	NOUN
ejpam-5155	129	5	mapping	mapping	NOUN
ejpam-5155	129	6	in	in	ADP
ejpam-5155	129	7	metric	metric	ADJ
ejpam-5155	129	8	space	space	NOUN
ejpam-5155	129	9	)	)	PUNCT
ejpam-5155	129	10	.	.	PUNCT
ejpam-5155	130	1	given	give	VERB
ejpam-5155	130	2	(	(	PUNCT
ejpam-5155	130	3	m	m	PROPN
ejpam-5155	130	4	,	,	PUNCT
ejpam-5155	130	5	d	d	NOUN
ejpam-5155	130	6	)	)	PUNCT
ejpam-5155	130	7	a	a	DET
ejpam-5155	130	8	metric	metric	ADJ
ejpam-5155	130	9	space	space	NOUN
ejpam-5155	130	10	,	,	PUNCT
ejpam-5155	130	11	a	a	DET
ejpam-5155	130	12	function	function	NOUN
ejpam-5155	130	13	t	t	NOUN
ejpam-5155	130	14	:	:	PUNCT
ejpam-5155	130	15	m	m	AUX
ejpam-5155	130	16	→	→	NOUN
ejpam-5155	130	17	m	m	VERB
ejpam-5155	130	18	is	be	AUX
ejpam-5155	130	19	said	say	VERB
ejpam-5155	130	20	to	to	PART
ejpam-5155	130	21	be	be	AUX
ejpam-5155	130	22	a	a	DET
ejpam-5155	130	23	contraction	contraction	NOUN
ejpam-5155	130	24	mapping	mapping	NOUN
ejpam-5155	130	25	if	if	SCONJ
ejpam-5155	130	26	there	there	PRON
ejpam-5155	130	27	is	be	VERB
ejpam-5155	130	28	a	a	DET
ejpam-5155	130	29	constant	constant	ADJ
ejpam-5155	130	30	a	a	DET
ejpam-5155	130	31	constant	constant	ADJ
ejpam-5155	130	32	m.	m.	NOUN
ejpam-5155	130	33	o.	o.	PROPN
ejpam-5155	130	34	fokuoet	fokuoet	VERB
ejpam-5155	130	35	al	al	PROPN
ejpam-5155	130	36	.	.	PUNCT
ejpam-5155	130	37	/	/	SYM
ejpam-5155	130	38	eur	eur	PROPN
ejpam-5155	130	39	.	.	PUNCT
ejpam-5155	131	1	j.	j.	PROPN
ejpam-5155	131	2	pure	pure	PROPN
ejpam-5155	131	3	appl	appl	PROPN
ejpam-5155	131	4	.	.	PROPN
ejpam-5155	131	5	math	math	PROPN
ejpam-5155	131	6	,	,	PUNCT
ejpam-5155	131	7	17	17	NUM
ejpam-5155	131	8	(	(	PUNCT
ejpam-5155	131	9	2	2	NUM
ejpam-5155	131	10	)	)	PUNCT
ejpam-5155	131	11	(	(	PUNCT
ejpam-5155	131	12	2024	2024	NUM
ejpam-5155	131	13	)	)	PUNCT
ejpam-5155	131	14	,	,	PUNCT
ejpam-5155	131	15	1294	1294	NUM
ejpam-5155	131	16	-	-	SYM
ejpam-5155	131	17	1305	1305	NUM
ejpam-5155	131	18	1299	1299	NUM
ejpam-5155	131	19	q	q	NOUN
ejpam-5155	131	20	with	with	ADP
ejpam-5155	131	21	q	q	X
ejpam-5155	131	22	<	<	X
ejpam-5155	131	23	1	1	NUM
ejpam-5155	131	24	such	such	ADJ
ejpam-5155	131	25	that	that	PRON
ejpam-5155	131	26	for	for	ADP
ejpam-5155	131	27	all	all	DET
ejpam-5155	131	28	x	x	NOUN
ejpam-5155	131	29	,	,	PUNCT
ejpam-5155	131	30	y	y	PROPN
ejpam-5155	131	31	∈	∈	PROPN
ejpam-5155	131	32	m	m	VERB
ejpam-5155	131	33	d(t	d(t	PROPN
ejpam-5155	131	34	(	(	PUNCT
ejpam-5155	131	35	x	x	NOUN
ejpam-5155	131	36	)	)	PUNCT
ejpam-5155	131	37	,	,	PUNCT
ejpam-5155	131	38	t	t	PROPN
ejpam-5155	131	39	(	(	PUNCT
ejpam-5155	131	40	y	y	NOUN
ejpam-5155	131	41	)	)	PUNCT
ejpam-5155	131	42	)	)	PUNCT
ejpam-5155	131	43	≤	≤	NUM
ejpam-5155	132	1	q	q	X
ejpam-5155	132	2	·	·	PUNCT
ejpam-5155	132	3	d(x	d(x	NOUN
ejpam-5155	132	4	,	,	PUNCT
ejpam-5155	132	5	y	y	NOUN
ejpam-5155	132	6	)	)	PUNCT
ejpam-5155	132	7	applying	apply	VERB
ejpam-5155	132	8	the	the	DET
ejpam-5155	132	9	banach	banach	ADV
ejpam-5155	132	10	fixed	fix	VERB
ejpam-5155	132	11	point	point	NOUN
ejpam-5155	132	12	theorem	theorem	NOUN
ejpam-5155	132	13	and	and	CCONJ
ejpam-5155	132	14	the	the	DET
ejpam-5155	132	15	contraction	contraction	NOUN
ejpam-5155	132	16	mapping	mapping	NOUN
ejpam-5155	132	17	on	on	ADP
ejpam-5155	132	18	the	the	DET
ejpam-5155	132	19	lotka	lotka	PROPN
ejpam-5155	132	20	volterra	volterra	PROPN
ejpam-5155	132	21	functions	function	NOUN
ejpam-5155	132	22	.	.	PUNCT
ejpam-5155	133	1	using	use	VERB
ejpam-5155	133	2	banach	banach	NOUN
ejpam-5155	133	3	fixed	fix	VERB
ejpam-5155	133	4	point	point	NOUN
ejpam-5155	133	5	theorem	theorem	VERB
ejpam-5155	133	6	to	to	PART
ejpam-5155	133	7	find	find	VERB
ejpam-5155	133	8	the	the	DET
ejpam-5155	133	9	fixed	fix	VERB
ejpam-5155	133	10	point	point	NOUN
ejpam-5155	133	11	of	of	ADP
ejpam-5155	133	12	lotka	lotka	PROPN
ejpam-5155	133	13	volterra	volterra	PROPN
ejpam-5155	133	14	functions	function	NOUN
ejpam-5155	133	15	.	.	PUNCT
ejpam-5155	134	1	from	from	ADP
ejpam-5155	134	2	the	the	DET
ejpam-5155	134	3	definition	definition	NOUN
ejpam-5155	134	4	of	of	ADP
ejpam-5155	134	5	banach	banach	ADV
ejpam-5155	134	6	fixed	fix	VERB
ejpam-5155	134	7	theorem	theorem	ADJ
ejpam-5155	134	8	,	,	PUNCT
ejpam-5155	134	9	let	let	VERB
ejpam-5155	134	10	(	(	PUNCT
ejpam-5155	134	11	m	m	NOUN
ejpam-5155	134	12	,	,	PUNCT
ejpam-5155	134	13	d	d	X
ejpam-5155	134	14	)	)	PUNCT
ejpam-5155	134	15	be	be	AUX
ejpam-5155	134	16	a	a	DET
ejpam-5155	134	17	complete	complete	ADJ
ejpam-5155	134	18	metric	metric	ADJ
ejpam-5155	134	19	space	space	NOUN
ejpam-5155	134	20	then	then	ADV
ejpam-5155	134	21	every	every	DET
ejpam-5155	134	22	contraction	contraction	NOUN
ejpam-5155	134	23	has	have	VERB
ejpam-5155	134	24	a	a	DET
ejpam-5155	134	25	unique	unique	ADJ
ejpam-5155	134	26	fixed	fix	VERB
ejpam-5155	134	27	point	point	NOUN
ejpam-5155	134	28	.	.	PUNCT
ejpam-5155	135	1	if	if	SCONJ
ejpam-5155	135	2	t	t	PROPN
ejpam-5155	135	3	(	(	PUNCT
ejpam-5155	135	4	x	x	NOUN
ejpam-5155	135	5	)	)	PUNCT
ejpam-5155	135	6	=	=	SYM
ejpam-5155	135	7	x	x	PROPN
ejpam-5155	135	8	,	,	PUNCT
ejpam-5155	135	9	t	t	PROPN
ejpam-5155	135	10	(	(	PUNCT
ejpam-5155	135	11	y	y	NOUN
ejpam-5155	135	12	)	)	PUNCT
ejpam-5155	135	13	=	=	SYM
ejpam-5155	136	1	y	y	PROPN
ejpam-5155	136	2	then	then	ADV
ejpam-5155	136	3	d(x	d(x	PROPN
ejpam-5155	136	4	,	,	PUNCT
ejpam-5155	136	5	y	y	NOUN
ejpam-5155	136	6	)	)	PUNCT
ejpam-5155	136	7	=	=	SYM
ejpam-5155	137	1	d(t	d(t	PROPN
ejpam-5155	137	2	(	(	PUNCT
ejpam-5155	137	3	x	x	NOUN
ejpam-5155	137	4	)	)	PUNCT
ejpam-5155	137	5	,	,	PUNCT
ejpam-5155	137	6	t	t	PROPN
ejpam-5155	137	7	(	(	PUNCT
ejpam-5155	137	8	y	y	NOUN
ejpam-5155	137	9	)	)	PUNCT
ejpam-5155	137	10	)	)	PUNCT
ejpam-5155	137	11	≤	≤	NUM
ejpam-5155	138	1	q	q	X
ejpam-5155	138	2	·	·	PUNCT
ejpam-5155	138	3	d(x	d(x	NOUN
ejpam-5155	138	4	,	,	PUNCT
ejpam-5155	138	5	y	y	NOUN
ejpam-5155	138	6	)	)	PUNCT
ejpam-5155	139	1	q	q	NOUN
ejpam-5155	140	1	<	<	X
ejpam-5155	140	2	1	1	NUM
ejpam-5155	140	3	so	so	ADV
ejpam-5155	140	4	d(x	d(x	PROPN
ejpam-5155	140	5	,	,	PUNCT
ejpam-5155	140	6	y	y	NOUN
ejpam-5155	140	7	)	)	PUNCT
ejpam-5155	140	8	=	=	SYM
ejpam-5155	140	9	0	0	NUM
ejpam-5155	140	10	or	or	CCONJ
ejpam-5155	140	11	x	x	SYM
ejpam-5155	140	12	=	=	SYM
ejpam-5155	140	13	y	y	PROPN
ejpam-5155	140	14	to	to	PART
ejpam-5155	140	15	show	show	VERB
ejpam-5155	140	16	that	that	SCONJ
ejpam-5155	140	17	a	a	DET
ejpam-5155	140	18	fixed	fix	VERB
ejpam-5155	140	19	point	point	NOUN
ejpam-5155	140	20	exists	exist	VERB
ejpam-5155	140	21	,	,	PUNCT
ejpam-5155	140	22	pick	pick	VERB
ejpam-5155	140	23	any	any	DET
ejpam-5155	140	24	x	x	SYM
ejpam-5155	140	25	∈	∈	PROPN
ejpam-5155	140	26	m	m	VERB
ejpam-5155	140	27	.	.	PUNCT
ejpam-5155	141	1	setting	set	VERB
ejpam-5155	141	2	x	x	PUNCT
ejpam-5155	141	3	∈	∈	PROPN
ejpam-5155	141	4	x0	x0	PROPN
ejpam-5155	141	5	,	,	PUNCT
ejpam-5155	141	6	we	we	PRON
ejpam-5155	141	7	define	define	VERB
ejpam-5155	141	8	a	a	DET
ejpam-5155	141	9	sequence	sequence	NOUN
ejpam-5155	141	10	{	{	PUNCT
ejpam-5155	141	11	xi}i∈z+	xi}i∈z+	NOUN
ejpam-5155	141	12	by	by	ADP
ejpam-5155	141	13	setting	set	VERB
ejpam-5155	141	14	xn+1	xn+1	PROPN
ejpam-5155	141	15	=	=	SYM
ejpam-5155	141	16	t	t	PROPN
ejpam-5155	141	17	(	(	PUNCT
ejpam-5155	141	18	xn	xn	PROPN
ejpam-5155	141	19	)	)	PUNCT
ejpam-5155	141	20	xn+1	xn+1	PUNCT
ejpam-5155	142	1	=	=	SYM
ejpam-5155	142	2	αt	αt	PROPN
ejpam-5155	142	3	(	(	PUNCT
ejpam-5155	142	4	xn)−βt	xn)−βt	PROPN
ejpam-5155	142	5	(	(	PUNCT
ejpam-5155	142	6	xn	xn	NUM
ejpam-5155	142	7	)	)	PUNCT
ejpam-5155	142	8	(	(	PUNCT
ejpam-5155	142	9	yn	yn	X
ejpam-5155	142	10	)	)	PUNCT
ejpam-5155	142	11	xn+1	xn+1	PROPN
ejpam-5155	142	12	=	=	SYM
ejpam-5155	142	13	(	(	PUNCT
ejpam-5155	142	14	α−β(yn))t	α−β(yn))t	NUM
ejpam-5155	142	15	(	(	PUNCT
ejpam-5155	142	16	xn	xn	X
ejpam-5155	142	17	)	)	PUNCT
ejpam-5155	142	18	rewriting	rewrite	VERB
ejpam-5155	142	19	the	the	DET
ejpam-5155	142	20	contraction	contraction	NOUN
ejpam-5155	142	21	formula	formula	NOUN
ejpam-5155	142	22	we	we	PRON
ejpam-5155	142	23	have	have	VERB
ejpam-5155	142	24	xn+1	xn+1	NUM
ejpam-5155	142	25	=	=	SYM
ejpam-5155	142	26	(	(	PUNCT
ejpam-5155	142	27	α−	α−	ADP
ejpam-5155	142	28	β(yn))t	β(yn))t	PRON
ejpam-5155	142	29	(	(	PUNCT
ejpam-5155	142	30	xn	xn	X
ejpam-5155	142	31	)	)	PUNCT
ejpam-5155	142	32	d(xn+2	d(xn+2	ADV
ejpam-5155	142	33	,	,	PUNCT
ejpam-5155	142	34	xn+1	xn+1	X
ejpam-5155	142	35	)	)	PUNCT
ejpam-5155	142	36	≤	≤	NOUN
ejpam-5155	142	37	(	(	PUNCT
ejpam-5155	142	38	α−	α−	ADP
ejpam-5155	142	39	β(yn))qd(xn+1	β(yn))qd(xn+1	NOUN
ejpam-5155	142	40	,	,	PUNCT
ejpam-5155	142	41	xn	xn	PROPN
ejpam-5155	142	42	)	)	PUNCT
ejpam-5155	142	43	d(xn+2	d(xn+2	ADV
ejpam-5155	142	44	,	,	PUNCT
ejpam-5155	142	45	xn+1	xn+1	X
ejpam-5155	142	46	)	)	PUNCT
ejpam-5155	142	47	≤	≤	NOUN
ejpam-5155	142	48	(	(	PUNCT
ejpam-5155	142	49	α−	α−	ADP
ejpam-5155	142	50	βyn)qd(xn+1	βyn)qd(xn+1	NUM
ejpam-5155	142	51	,	,	PUNCT
ejpam-5155	142	52	xn	xn	NUM
ejpam-5155	142	53	)	)	PUNCT
ejpam-5155	142	54	d	d	NOUN
ejpam-5155	142	55	(	(	PUNCT
ejpam-5155	142	56	xn+1	xn+1	PROPN
ejpam-5155	142	57	,	,	PUNCT
ejpam-5155	142	58	xn	xn	PROPN
ejpam-5155	142	59	)	)	PUNCT
ejpam-5155	142	60	≤	≤	NOUN
ejpam-5155	142	61	(	(	PUNCT
ejpam-5155	142	62	α−	α−	ADP
ejpam-5155	142	63	βyn	βyn	NOUN
ejpam-5155	142	64	)	)	PUNCT
ejpam-5155	142	65	q	q	NOUN
ejpam-5155	142	66	nd	nd	INTJ
ejpam-5155	142	67	(	(	PUNCT
ejpam-5155	142	68	x1	x1	PROPN
ejpam-5155	142	69	,	,	PUNCT
ejpam-5155	142	70	x0	x0	PROPN
ejpam-5155	142	71	)	)	PUNCT
ejpam-5155	142	72	d	d	X
ejpam-5155	142	73	(	(	PUNCT
ejpam-5155	142	74	xn+1	xn+1	PROPN
ejpam-5155	142	75	,	,	PUNCT
ejpam-5155	142	76	xn	xn	PROPN
ejpam-5155	142	77	)	)	PUNCT
ejpam-5155	142	78	≤	≤	NOUN
ejpam-5155	142	79	αqnd	αqnd	X
ejpam-5155	142	80	(	(	PUNCT
ejpam-5155	142	81	x1	x1	PROPN
ejpam-5155	142	82	,	,	PUNCT
ejpam-5155	142	83	x0)−	x0)−	PROPN
ejpam-5155	142	84	βqnynd	βqnynd	PROPN
ejpam-5155	142	85	(	(	PUNCT
ejpam-5155	142	86	x	x	NOUN
ejpam-5155	142	87	,	,	PUNCT
ejpam-5155	142	88	x0	x0	PROPN
ejpam-5155	142	89	)	)	PUNCT
ejpam-5155	142	90	≤	≤	NUM
ejpam-5155	142	91	qn[αd	qn[αd	PUNCT
ejpam-5155	142	92	(	(	PUNCT
ejpam-5155	142	93	x1	x1	PROPN
ejpam-5155	142	94	,	,	PUNCT
ejpam-5155	142	95	x0)−	x0)−	X
ejpam-5155	142	96	βynd	βynd	NOUN
ejpam-5155	142	97	(	(	PUNCT
ejpam-5155	142	98	x1	x1	PROPN
ejpam-5155	142	99	,	,	PUNCT
ejpam-5155	142	100	x0	x0	PROPN
ejpam-5155	142	101	)	)	PUNCT
ejpam-5155	142	102	]	]	PUNCT
ejpam-5155	143	1	d(xn+1	d(xn+1	PROPN
ejpam-5155	143	2	,	,	PUNCT
ejpam-5155	143	3	xn	xn	X
ejpam-5155	143	4	)	)	PUNCT
ejpam-5155	143	5	≤	≤	NOUN
ejpam-5155	143	6	qn[(α−	qn[(α−	AUX
ejpam-5155	143	7	β)ynd	β)ynd	PROPN
ejpam-5155	143	8	(	(	PUNCT
ejpam-5155	143	9	x1	x1	PROPN
ejpam-5155	143	10	,	,	PUNCT
ejpam-5155	143	11	x0	x0	PROPN
ejpam-5155	143	12	)	)	PUNCT
ejpam-5155	143	13	]	]	PUNCT
ejpam-5155	143	14	assuming	assume	VERB
ejpam-5155	143	15	n	n	PRON
ejpam-5155	143	16	<	<	X
ejpam-5155	143	17	m	m	PROPN
ejpam-5155	143	18	d	d	X
ejpam-5155	143	19	(	(	PUNCT
ejpam-5155	143	20	xm	xm	PROPN
ejpam-5155	143	21	,	,	PUNCT
ejpam-5155	143	22	xn	xn	PROPN
ejpam-5155	143	23	)	)	PUNCT
ejpam-5155	143	24	≤	≤	NUM
ejpam-5155	144	1	d	d	NOUN
ejpam-5155	144	2	(	(	PUNCT
ejpam-5155	144	3	xm	xm	PROPN
ejpam-5155	144	4	,	,	PUNCT
ejpam-5155	144	5	xm−1	xm−1	PROPN
ejpam-5155	144	6	)	)	PUNCT
ejpam-5155	145	1	+	+	CCONJ
ejpam-5155	146	1	d	d	X
ejpam-5155	146	2	(	(	PUNCT
ejpam-5155	146	3	xm−1	xm−1	PROPN
ejpam-5155	146	4	,	,	PUNCT
ejpam-5155	146	5	xm−2	xm−2	PROPN
ejpam-5155	146	6	)	)	PUNCT
ejpam-5155	146	7	+	+	CCONJ
ejpam-5155	146	8	.	.	PUNCT
ejpam-5155	146	9	.	.	PUNCT
ejpam-5155	147	1	.+	.+	NOUN
ejpam-5155	147	2	(	(	PUNCT
ejpam-5155	147	3	xn+1	xn+1	PROPN
ejpam-5155	147	4	,	,	PUNCT
ejpam-5155	147	5	xn	xn	PROPN
ejpam-5155	147	6	)	)	PUNCT
ejpam-5155	148	1	d	d	PROPN
ejpam-5155	148	2	(	(	PUNCT
ejpam-5155	148	3	xm	xm	PROPN
ejpam-5155	148	4	,	,	PUNCT
ejpam-5155	148	5	xn	xn	PROPN
ejpam-5155	148	6	)	)	PUNCT
ejpam-5155	148	7	≤	≤	NOUN
ejpam-5155	148	8	(	(	PUNCT
ejpam-5155	148	9	qm−n−1	qm−n−1	PROPN
ejpam-5155	148	10	+	+	CCONJ
ejpam-5155	148	11	qm−n−2	qm−n−2	X
ejpam-5155	148	12	+	+	NOUN
ejpam-5155	148	13	.	.	PUNCT
ejpam-5155	148	14	.	.	PUNCT
ejpam-5155	149	1	.+	.+	NOUN
ejpam-5155	149	2	q	q	X
ejpam-5155	150	1	+	+	CCONJ
ejpam-5155	150	2	1	1	X
ejpam-5155	150	3	)	)	PUNCT
ejpam-5155	150	4	d	d	NOUN
ejpam-5155	150	5	(	(	PUNCT
ejpam-5155	150	6	xn+1	xn+1	PROPN
ejpam-5155	150	7	,	,	PUNCT
ejpam-5155	150	8	xn	xn	PROPN
ejpam-5155	150	9	)	)	PUNCT
ejpam-5155	150	10	≤	≤	NOUN
ejpam-5155	150	11	(	(	PUNCT
ejpam-5155	150	12	1−	1−	NUM
ejpam-5155	150	13	qm−n	qm−n	PROPN
ejpam-5155	150	14	1−	1−	NUM
ejpam-5155	150	15	q	q	NOUN
ejpam-5155	150	16	)	)	PUNCT
ejpam-5155	150	17	d	d	NOUN
ejpam-5155	150	18	(	(	PUNCT
ejpam-5155	150	19	xn+1	xn+1	PROPN
ejpam-5155	150	20	,	,	PUNCT
ejpam-5155	150	21	xn	xn	PROPN
ejpam-5155	150	22	)	)	PUNCT
ejpam-5155	150	23	≤	≤	NOUN
ejpam-5155	150	24	(	(	PUNCT
ejpam-5155	150	25	1−	1−	NUM
ejpam-5155	150	26	qm−n	qm−n	PROPN
ejpam-5155	150	27	1−	1−	NUM
ejpam-5155	150	28	q	q	NOUN
ejpam-5155	150	29	)	)	PUNCT
ejpam-5155	150	30	qn	qn	INTJ
ejpam-5155	150	31	(	(	PUNCT
ejpam-5155	150	32	α−	α−	ADP
ejpam-5155	150	33	βyn	βyn	NOUN
ejpam-5155	150	34	)	)	PUNCT
ejpam-5155	150	35	d	d	NOUN
ejpam-5155	150	36	(	(	PUNCT
ejpam-5155	150	37	x1	x1	PROPN
ejpam-5155	150	38	,	,	PUNCT
ejpam-5155	150	39	x0	x0	PROPN
ejpam-5155	150	40	)	)	PUNCT
ejpam-5155	150	41	since	since	SCONJ
ejpam-5155	150	42	qm	qm	PROPN
ejpam-5155	150	43	=	=	PROPN
ejpam-5155	150	44	n	n	CCONJ
ejpam-5155	150	45	<	<	X
ejpam-5155	150	46	1	1	NUM
ejpam-5155	150	47	d(xm	d(xm	PROPN
ejpam-5155	150	48	,	,	PUNCT
ejpam-5155	150	49	xn	xn	PROPN
ejpam-5155	150	50	)	)	PUNCT
ejpam-5155	150	51	<	<	X
ejpam-5155	151	1	qn	qn	PROPN
ejpam-5155	151	2	1−	1−	NUM
ejpam-5155	151	3	q	q	X
ejpam-5155	151	4	(	(	PUNCT
ejpam-5155	151	5	α−	α−	ADP
ejpam-5155	151	6	βyn)d(x1	βyn)d(x1	NOUN
ejpam-5155	151	7	,	,	PUNCT
ejpam-5155	151	8	x0	x0	PROPN
ejpam-5155	151	9	)	)	PUNCT
ejpam-5155	151	10	thus	thus	ADV
ejpam-5155	151	11	{	{	PUNCT
ejpam-5155	151	12	xi	xi	NOUN
ejpam-5155	151	13	}	}	PUNCT
ejpam-5155	151	14	is	be	AUX
ejpam-5155	151	15	cauchy	cauchy	NOUN
ejpam-5155	151	16	.	.	PUNCT
ejpam-5155	152	1	this	this	PRON
ejpam-5155	152	2	shows	show	VERB
ejpam-5155	152	3	that	that	SCONJ
ejpam-5155	152	4	(	(	PUNCT
ejpam-5155	152	5	xn	xn	X
ejpam-5155	152	6	)	)	PUNCT
ejpam-5155	152	7	is	be	AUX
ejpam-5155	152	8	cauchy	cauchy	ADJ
ejpam-5155	152	9	sequence	sequence	NOUN
ejpam-5155	152	10	in	in	ADP
ejpam-5155	152	11	x.	x.	NOUN
ejpam-5155	152	12	hence	hence	ADV
ejpam-5155	152	13	,	,	PUNCT
ejpam-5155	152	14	(	(	PUNCT
ejpam-5155	152	15	xn	xn	X
ejpam-5155	152	16	)	)	PUNCT
ejpam-5155	152	17	must	must	AUX
ejpam-5155	152	18	be	be	AUX
ejpam-5155	152	19	convergent	convergent	ADJ
ejpam-5155	152	20	,	,	PUNCT
ejpam-5155	152	21	say	say	VERB
ejpam-5155	152	22	lim	lim	PROPN
ejpam-5155	152	23	n→+∞	n→+∞	VERB
ejpam-5155	152	24	xn	xn	PUNCT
ejpam-5155	153	1	=	=	PUNCT
ejpam-5155	153	2	x	x	PUNCT
ejpam-5155	153	3	m.	m.	NOUN
ejpam-5155	153	4	o.	o.	PROPN
ejpam-5155	153	5	fokuoet	fokuoet	PROPN
ejpam-5155	153	6	al	al	PROPN
ejpam-5155	153	7	.	.	PUNCT
ejpam-5155	153	8	/	/	SYM
ejpam-5155	153	9	eur	eur	PROPN
ejpam-5155	153	10	.	.	PUNCT
ejpam-5155	154	1	j.	j.	PROPN
ejpam-5155	154	2	pure	pure	PROPN
ejpam-5155	154	3	appl	appl	PROPN
ejpam-5155	154	4	.	.	PROPN
ejpam-5155	154	5	math	math	PROPN
ejpam-5155	154	6	,	,	PUNCT
ejpam-5155	154	7	17	17	NUM
ejpam-5155	154	8	(	(	PUNCT
ejpam-5155	154	9	2	2	NUM
ejpam-5155	154	10	)	)	PUNCT
ejpam-5155	154	11	(	(	PUNCT
ejpam-5155	154	12	2024	2024	NUM
ejpam-5155	154	13	)	)	PUNCT
ejpam-5155	154	14	,	,	PUNCT
ejpam-5155	154	15	1294	1294	NUM
ejpam-5155	154	16	-	-	SYM
ejpam-5155	154	17	1305	1305	NUM
ejpam-5155	154	18	1300	1300	NUM
ejpam-5155	154	19	since	since	SCONJ
ejpam-5155	154	20	t	t	PROPN
ejpam-5155	154	21	is	be	AUX
ejpam-5155	154	22	continuous	continuous	ADJ
ejpam-5155	154	23	,	,	PUNCT
ejpam-5155	154	24	we	we	PRON
ejpam-5155	154	25	have	have	VERB
ejpam-5155	154	26	tx	tx	PROPN
ejpam-5155	154	27	=	=	SYM
ejpam-5155	154	28	t	t	PROPN
ejpam-5155	154	29	(	(	PUNCT
ejpam-5155	154	30	lim	lim	PROPN
ejpam-5155	154	31	n→+∞	n→+∞	PROPN
ejpam-5155	154	32	xn	xn	PROPN
ejpam-5155	154	33	)	)	PUNCT
ejpam-5155	155	1	=	=	NOUN
ejpam-5155	155	2	lim	lim	PROPN
ejpam-5155	155	3	n→+∞	n→+∞	PROPN
ejpam-5155	155	4	t	t	PROPN
ejpam-5155	155	5	(	(	PUNCT
ejpam-5155	155	6	xn	xn	PROPN
ejpam-5155	155	7	)	)	PUNCT
ejpam-5155	156	1	=	=	NOUN
ejpam-5155	156	2	lim	lim	PROPN
ejpam-5155	156	3	n→+∞	n→+∞	VERB
ejpam-5155	156	4	xn+1	xn+1	PROPN
ejpam-5155	156	5	since	since	SCONJ
ejpam-5155	156	6	the	the	DET
ejpam-5155	156	7	limit	limit	NOUN
ejpam-5155	156	8	of	of	ADP
ejpam-5155	156	9	xn+1	xn+1	PROPN
ejpam-5155	156	10	is	be	AUX
ejpam-5155	156	11	the	the	DET
ejpam-5155	156	12	same	same	ADJ
ejpam-5155	156	13	as	as	ADP
ejpam-5155	156	14	that	that	PRON
ejpam-5155	156	15	of	of	ADP
ejpam-5155	156	16	(	(	PUNCT
ejpam-5155	156	17	xn	xn	PROPN
ejpam-5155	156	18	)	)	PUNCT
ejpam-5155	156	19	thus	thus	ADV
ejpam-5155	156	20	,	,	PUNCT
ejpam-5155	156	21	x	x	PRON
ejpam-5155	156	22	is	be	AUX
ejpam-5155	156	23	a	a	DET
ejpam-5155	156	24	fixed	fix	VERB
ejpam-5155	156	25	point	point	NOUN
ejpam-5155	156	26	of	of	ADP
ejpam-5155	156	27	t.	t.	NOUN
ejpam-5155	156	28	illustration	illustration	NOUN
ejpam-5155	156	29	1	1	NUM
ejpam-5155	156	30	xn+1	xn+1	NOUN
ejpam-5155	156	31	=	=	PUNCT
ejpam-5155	156	32	g(xn	g(xn	X
ejpam-5155	156	33	,	,	PUNCT
ejpam-5155	156	34	yn	yn	PROPN
ejpam-5155	156	35	)	)	PUNCT
ejpam-5155	156	36	=	=	SYM
ejpam-5155	156	37	αxn	αxn	PROPN
ejpam-5155	156	38	−	−	PROPN
ejpam-5155	156	39	xnβyn	xnβyn	NOUN
ejpam-5155	156	40	then	then	ADV
ejpam-5155	156	41	,	,	PUNCT
ejpam-5155	156	42	by	by	ADP
ejpam-5155	156	43	considering	consider	VERB
ejpam-5155	156	44	the	the	DET
ejpam-5155	156	45	coordinate	coordinate	NOUN
ejpam-5155	156	46	of	of	ADP
ejpam-5155	156	47	y	y	PROPN
ejpam-5155	156	48	,	,	PUNCT
ejpam-5155	156	49	that	that	PRON
ejpam-5155	156	50	is	be	AUX
ejpam-5155	156	51	yn	yn	X
ejpam-5155	156	52	=	=	PUNCT
ejpam-5155	156	53	α−	α−	ADP
ejpam-5155	156	54	1	1	NUM
ejpam-5155	156	55	β	β	PROPN
ejpam-5155	156	56	lim	lim	PROPN
ejpam-5155	156	57	yn→α−1	yn→α−1	PROPN
ejpam-5155	156	58	β	β	X
ejpam-5155	156	59	g(xn	g(xn	X
ejpam-5155	156	60	,	,	PUNCT
ejpam-5155	156	61	yn	yn	PROPN
ejpam-5155	156	62	)	)	PUNCT
ejpam-5155	156	63	=	=	PROPN
ejpam-5155	156	64	lim	lim	PROPN
ejpam-5155	156	65	yn→α−1	yn→α−1	PROPN
ejpam-5155	156	66	β	β	X
ejpam-5155	156	67	β(αxn	β(αxn	PROPN
ejpam-5155	156	68	−	−	PROPN
ejpam-5155	156	69	xnβyn	xnβyn	NOUN
ejpam-5155	156	70	)	)	PUNCT
ejpam-5155	156	71	=	=	SYM
ejpam-5155	157	1	xn	xn	PROPN
ejpam-5155	157	2	lim	lim	PROPN
ejpam-5155	157	3	yn→α−1	yn→α−1	PROPN
ejpam-5155	157	4	β	β	PROPN
ejpam-5155	157	5	(	(	PUNCT
ejpam-5155	157	6	α−	α−	ADP
ejpam-5155	157	7	βyn	βyn	NOUN
ejpam-5155	157	8	)	)	PUNCT
ejpam-5155	157	9	where	where	SCONJ
ejpam-5155	157	10	n	n	ADV
ejpam-5155	157	11	=	=	SYM
ejpam-5155	157	12	0	0	NUM
ejpam-5155	157	13	,	,	PUNCT
ejpam-5155	157	14	1	1	NUM
ejpam-5155	157	15	,	,	PUNCT
ejpam-5155	157	16	2	2	NUM
ejpam-5155	157	17	,	,	PUNCT
ejpam-5155	157	18	.	.	PUNCT
ejpam-5155	157	19	.	.	PUNCT
ejpam-5155	157	20	.	.	PUNCT
ejpam-5155	157	21	implies	imply	VERB
ejpam-5155	157	22	lim	lim	PROPN
ejpam-5155	157	23	yn→α−1	yn→α−1	PROPN
ejpam-5155	157	24	β	β	X
ejpam-5155	157	25	g(xn	g(xn	X
ejpam-5155	157	26	,	,	PUNCT
ejpam-5155	157	27	yn	yn	PROPN
ejpam-5155	157	28	)	)	PUNCT
ejpam-5155	157	29	=	=	SYM
ejpam-5155	157	30	xn	xn	PUNCT
ejpam-5155	158	1	[	[	PUNCT
ejpam-5155	158	2	lim	lim	PROPN
ejpam-5155	158	3	yn→α−1	yn→α−1	PROPN
ejpam-5155	158	4	β	β	PROPN
ejpam-5155	158	5	(	(	PUNCT
ejpam-5155	158	6	α)−	α)−	ADP
ejpam-5155	158	7	lim	lim	PROPN
ejpam-5155	158	8	yn→α−1	yn→α−1	PROPN
ejpam-5155	158	9	β	β	X
ejpam-5155	158	10	βyn	βyn	PUNCT
ejpam-5155	158	11	]	]	PUNCT
ejpam-5155	158	12	=	=	SYM
ejpam-5155	158	13	xn[α−	xn[α−	NOUN
ejpam-5155	158	14	β(α−	β(α−	NUM
ejpam-5155	158	15	1	1	NUM
ejpam-5155	158	16	)	)	PUNCT
ejpam-5155	158	17	]	]	PUNCT
ejpam-5155	159	1	=	=	PUNCT
ejpam-5155	160	1	xn	xn	NUM
ejpam-5155	160	2	×	×	NOUN
ejpam-5155	160	3	1	1	NUM
ejpam-5155	160	4	=	=	SYM
ejpam-5155	160	5	xn	xn	NOUN
ejpam-5155	160	6	hence	hence	ADV
ejpam-5155	160	7	,	,	PUNCT
ejpam-5155	160	8	lim	lim	PROPN
ejpam-5155	160	9	yn→α−1	yn→α−1	PROPN
ejpam-5155	160	10	β	β	X
ejpam-5155	160	11	xn+1	xn+1	PROPN
ejpam-5155	161	1	=	=	SYM
ejpam-5155	161	2	lim	lim	PROPN
ejpam-5155	161	3	yn→α−1	yn→α−1	PROPN
ejpam-5155	161	4	β	β	X
ejpam-5155	161	5	g(xn	g(xn	X
ejpam-5155	161	6	)	)	PUNCT
ejpam-5155	161	7	=	=	SYM
ejpam-5155	161	8	xn	xn	NUM
ejpam-5155	161	9	irrespective	irrespective	ADV
ejpam-5155	161	10	of	of	ADP
ejpam-5155	161	11	the	the	DET
ejpam-5155	161	12	values	value	NOUN
ejpam-5155	161	13	of	of	ADP
ejpam-5155	161	14	the	the	DET
ejpam-5155	161	15	parameters	parameter	NOUN
ejpam-5155	161	16	.	.	PUNCT
ejpam-5155	162	1	this	this	PRON
ejpam-5155	162	2	implies	imply	VERB
ejpam-5155	162	3	:	:	PUNCT
ejpam-5155	162	4	when	when	SCONJ
ejpam-5155	162	5	n	n	X
ejpam-5155	162	6	=	=	SYM
ejpam-5155	162	7	0	0	NUM
ejpam-5155	162	8	,	,	PUNCT
ejpam-5155	162	9	x1	x1	PROPN
ejpam-5155	162	10	=	=	SYM
ejpam-5155	162	11	g(x0	g(x0	NOUN
ejpam-5155	162	12	)	)	PUNCT
ejpam-5155	162	13	=	=	PUNCT
ejpam-5155	163	1	x0	x0	PROPN
ejpam-5155	163	2	.	.	PUNCT
ejpam-5155	164	1	when	when	SCONJ
ejpam-5155	164	2	n	n	X
ejpam-5155	164	3	=	=	SYM
ejpam-5155	164	4	1	1	NUM
ejpam-5155	164	5	,	,	PUNCT
ejpam-5155	164	6	x2	x2	NOUN
ejpam-5155	164	7	=	=	SYM
ejpam-5155	164	8	g(x1	g(x1	NOUN
ejpam-5155	164	9	)	)	PUNCT
ejpam-5155	164	10	=	=	SYM
ejpam-5155	165	1	x1	x1	PROPN
ejpam-5155	165	2	.	.	PUNCT
ejpam-5155	166	1	when	when	SCONJ
ejpam-5155	166	2	n	n	X
ejpam-5155	166	3	=	=	SYM
ejpam-5155	166	4	2	2	NUM
ejpam-5155	166	5	,	,	PUNCT
ejpam-5155	166	6	x3	x3	ADJ
ejpam-5155	166	7	=	=	SYM
ejpam-5155	166	8	g(x2	g(x2	NOUN
ejpam-5155	166	9	)	)	PUNCT
ejpam-5155	166	10	=	=	SYM
ejpam-5155	167	1	x2	x2	PROPN
ejpam-5155	167	2	.	.	PUNCT
ejpam-5155	168	1	hence	hence	ADV
ejpam-5155	168	2	,	,	PUNCT
ejpam-5155	168	3	the	the	DET
ejpam-5155	168	4	orbit	orbit	NOUN
ejpam-5155	168	5	{	{	PUNCT
ejpam-5155	168	6	x0	x0	PROPN
ejpam-5155	168	7	,	,	PUNCT
ejpam-5155	168	8	x1	x1	PROPN
ejpam-5155	168	9	=	=	SYM
ejpam-5155	168	10	g(x0	g(x0	NOUN
ejpam-5155	168	11	)	)	PUNCT
ejpam-5155	168	12	=	=	SYM
ejpam-5155	168	13	x0	x0	PROPN
ejpam-5155	168	14	,	,	PUNCT
ejpam-5155	168	15	x2	x2	PROPN
ejpam-5155	168	16	=	=	SYM
ejpam-5155	168	17	g(x1	g(x1	NOUN
ejpam-5155	168	18	)	)	PUNCT
ejpam-5155	168	19	=	=	SYM
ejpam-5155	169	1	x1	x1	ADJ
ejpam-5155	169	2	,	,	PUNCT
ejpam-5155	169	3	x3	x3	ADJ
ejpam-5155	169	4	=	=	SYM
ejpam-5155	169	5	g(x2	g(x2	NOUN
ejpam-5155	169	6	)	)	PUNCT
ejpam-5155	169	7	=	=	SYM
ejpam-5155	169	8	x2	x2	PROPN
ejpam-5155	169	9	,	,	PUNCT
ejpam-5155	169	10	.	.	PUNCT
ejpam-5155	169	11	.	.	PUNCT
ejpam-5155	169	12	.	.	PUNCT
ejpam-5155	169	13	}	}	PUNCT
ejpam-5155	169	14	serve	serve	VERB
ejpam-5155	169	15	as	as	ADP
ejpam-5155	169	16	the	the	DET
ejpam-5155	169	17	fixed	fix	VERB
ejpam-5155	169	18	points	point	NOUN
ejpam-5155	169	19	of	of	ADP
ejpam-5155	169	20	the	the	DET
ejpam-5155	169	21	function	function	NOUN
ejpam-5155	169	22	since	since	SCONJ
ejpam-5155	169	23	it	it	PRON
ejpam-5155	169	24	is	be	AUX
ejpam-5155	169	25	a	a	DET
ejpam-5155	169	26	repeated	repeat	VERB
ejpam-5155	169	27	point	point	NOUN
ejpam-5155	169	28	that	that	PRON
ejpam-5155	169	29	is	be	AUX
ejpam-5155	169	30	unique	unique	ADJ
ejpam-5155	169	31	and	and	CCONJ
ejpam-5155	169	32	asymptotically	asymptotically	ADV
ejpam-5155	169	33	stable	stable	ADJ
ejpam-5155	169	34	throughout	throughout	ADP
ejpam-5155	169	35	the	the	DET
ejpam-5155	169	36	iteration	iteration	NOUN
ejpam-5155	169	37	process	process	NOUN
ejpam-5155	169	38	.	.	PUNCT
ejpam-5155	170	1	example	example	NOUN
ejpam-5155	171	1	1	1	NUM
ejpam-5155	171	2	.	.	PUNCT
ejpam-5155	171	3	given	give	VERB
ejpam-5155	171	4	f(xn	f(xn	PROPN
ejpam-5155	171	5	,	,	PUNCT
ejpam-5155	171	6	yn	yn	PROPN
ejpam-5155	171	7	)	)	PUNCT
ejpam-5155	171	8	=	=	PUNCT
ejpam-5155	171	9	αxn	αxn	PROPN
ejpam-5155	171	10	−	−	PROPN
ejpam-5155	171	11	xnβyn	xnβyn	PROPN
ejpam-5155	171	12	.	.	PUNCT
ejpam-5155	172	1	let	let	VERB
ejpam-5155	172	2	γ	γ	X
ejpam-5155	172	3	>	>	X
ejpam-5155	172	4	1	1	PROPN
ejpam-5155	172	5	,	,	PUNCT
ejpam-5155	172	6	δ	δ	PROPN
ejpam-5155	172	7	>	>	X
ejpam-5155	172	8	1	1	NUM
ejpam-5155	172	9	,	,	PUNCT
ejpam-5155	172	10	α	α	PROPN
ejpam-5155	172	11	>	>	X
ejpam-5155	172	12	1	1	NUM
ejpam-5155	172	13	,	,	PUNCT
ejpam-5155	172	14	and	and	CCONJ
ejpam-5155	172	15	β	β	X
ejpam-5155	172	16	>	>	X
ejpam-5155	172	17	1	1	X
ejpam-5155	172	18	.	.	PUNCT
ejpam-5155	173	1	at	at	ADP
ejpam-5155	173	2	γ	γ	X
ejpam-5155	173	3	=	=	SYM
ejpam-5155	173	4	1.1	1.1	NUM
ejpam-5155	173	5	,	,	PUNCT
ejpam-5155	173	6	δ	δ	PROPN
ejpam-5155	173	7	=	=	PUNCT
ejpam-5155	173	8	2.1	2.1	NUM
ejpam-5155	173	9	,	,	PUNCT
ejpam-5155	173	10	α	α	NOUN
ejpam-5155	173	11	=	=	SYM
ejpam-5155	173	12	1.2	1.2	NUM
ejpam-5155	173	13	,	,	PUNCT
ejpam-5155	173	14	and	and	CCONJ
ejpam-5155	173	15	β	β	X
ejpam-5155	173	16	=	=	SYM
ejpam-5155	173	17	2.5	2.5	NUM
ejpam-5155	173	18	.	.	PUNCT
ejpam-5155	174	1	(	(	PUNCT
ejpam-5155	174	2	1	1	NUM
ejpam-5155	174	3	+	+	NUM
ejpam-5155	174	4	γ	γ	PROPN
ejpam-5155	174	5	δ	δ	PROPN
ejpam-5155	174	6	,	,	PUNCT
ejpam-5155	174	7	α−	α−	ADP
ejpam-5155	174	8	1	1	NUM
ejpam-5155	174	9	β	β	NOUN
ejpam-5155	174	10	)	)	PUNCT
ejpam-5155	174	11	implies	imply	VERB
ejpam-5155	174	12	(	(	PUNCT
ejpam-5155	174	13	xn	xn	PROPN
ejpam-5155	174	14	,	,	PUNCT
ejpam-5155	174	15	yn	yn	PROPN
ejpam-5155	174	16	)	)	PUNCT
ejpam-5155	174	17	then	then	ADV
ejpam-5155	174	18	,	,	PUNCT
ejpam-5155	174	19	lim	lim	PROPN
ejpam-5155	174	20	yn→α−1	yn→α−1	PROPN
ejpam-5155	174	21	β	β	X
ejpam-5155	174	22	f(xn	f(xn	PROPN
ejpam-5155	174	23	,	,	PUNCT
ejpam-5155	174	24	yn	yn	PROPN
ejpam-5155	174	25	)	)	PUNCT
ejpam-5155	174	26	=	=	PROPN
ejpam-5155	174	27	lim	lim	PROPN
ejpam-5155	174	28	yn→α−1	yn→α−1	PROPN
ejpam-5155	174	29	β	β	PROPN
ejpam-5155	174	30	(	(	PUNCT
ejpam-5155	174	31	αxn	αxn	PROPN
ejpam-5155	174	32	−	−	PROPN
ejpam-5155	174	33	xnβyn	xnβyn	NOUN
ejpam-5155	174	34	)	)	PUNCT
ejpam-5155	174	35	m.	m.	NOUN
ejpam-5155	174	36	o.	o.	PROPN
ejpam-5155	174	37	fokuoet	fokuoet	PROPN
ejpam-5155	174	38	al	al	PROPN
ejpam-5155	174	39	.	.	PUNCT
ejpam-5155	174	40	/	/	SYM
ejpam-5155	174	41	eur	eur	PROPN
ejpam-5155	174	42	.	.	PUNCT
ejpam-5155	175	1	j.	j.	PROPN
ejpam-5155	175	2	pure	pure	PROPN
ejpam-5155	175	3	appl	appl	PROPN
ejpam-5155	175	4	.	.	PROPN
ejpam-5155	175	5	math	math	PROPN
ejpam-5155	175	6	,	,	PUNCT
ejpam-5155	175	7	17	17	NUM
ejpam-5155	175	8	(	(	PUNCT
ejpam-5155	175	9	2	2	NUM
ejpam-5155	175	10	)	)	PUNCT
ejpam-5155	175	11	(	(	PUNCT
ejpam-5155	175	12	2024	2024	NUM
ejpam-5155	175	13	)	)	PUNCT
ejpam-5155	175	14	,	,	PUNCT
ejpam-5155	175	15	1294	1294	NUM
ejpam-5155	175	16	-	-	SYM
ejpam-5155	175	17	1305	1305	NUM
ejpam-5155	175	18	1301	1301	NUM
ejpam-5155	175	19	at	at	ADP
ejpam-5155	175	20	α	α	NOUN
ejpam-5155	175	21	=	=	SYM
ejpam-5155	175	22	1.2	1.2	NUM
ejpam-5155	175	23	,	,	PUNCT
ejpam-5155	175	24	β	β	X
ejpam-5155	175	25	=	=	SYM
ejpam-5155	175	26	2.5	2.5	NUM
ejpam-5155	175	27	implies	imply	VERB
ejpam-5155	175	28	lim	lim	PROPN
ejpam-5155	175	29	yn→α−1	yn→α−1	PROPN
ejpam-5155	175	30	β	β	PROPN
ejpam-5155	175	31	f(xn	f(xn	PROPN
ejpam-5155	175	32	,	,	PUNCT
ejpam-5155	175	33	yn	yn	PROPN
ejpam-5155	175	34	)	)	PUNCT
ejpam-5155	175	35	=	=	SYM
ejpam-5155	176	1	xn	xn	PROPN
ejpam-5155	176	2	lim	lim	PROPN
ejpam-5155	176	3	yn→α−1	yn→α−1	PROPN
ejpam-5155	176	4	β	β	PROPN
ejpam-5155	176	5	(	(	PUNCT
ejpam-5155	176	6	1.2−	1.2−	NOUN
ejpam-5155	176	7	2.5yn	2.5yn	NUM
ejpam-5155	176	8	)	)	PUNCT
ejpam-5155	176	9	when	when	SCONJ
ejpam-5155	176	10	n	n	X
ejpam-5155	176	11	=	=	SYM
ejpam-5155	176	12	0	0	NUM
ejpam-5155	176	13	,	,	PUNCT
ejpam-5155	176	14	x0	x0	PROPN
ejpam-5155	176	15	=	=	NOUN
ejpam-5155	176	16	1	1	NUM
ejpam-5155	176	17	+	+	CCONJ
ejpam-5155	176	18	γ	γ	X
ejpam-5155	176	19	δ	δ	NOUN
ejpam-5155	176	20	=	=	SYM
ejpam-5155	176	21	1	1	NUM
ejpam-5155	176	22	+	+	NUM
ejpam-5155	176	23	1.1	1.1	NUM
ejpam-5155	176	24	2.1	2.1	NUM
ejpam-5155	176	25	=	=	SYM
ejpam-5155	176	26	1	1	NUM
ejpam-5155	176	27	,	,	PUNCT
ejpam-5155	176	28	y0	y0	NOUN
ejpam-5155	176	29	=	=	PUNCT
ejpam-5155	176	30	α−	α−	ADP
ejpam-5155	176	31	1	1	NUM
ejpam-5155	176	32	β	β	X
ejpam-5155	176	33	=	=	SYM
ejpam-5155	176	34	1.2−	1.2−	NUM
ejpam-5155	176	35	1	1	NUM
ejpam-5155	176	36	2.5	2.5	NUM
ejpam-5155	176	37	=	=	SYM
ejpam-5155	176	38	0.08	0.08	NUM
ejpam-5155	176	39	implies	imply	VERB
ejpam-5155	176	40	(	(	PUNCT
ejpam-5155	176	41	x0	x0	PROPN
ejpam-5155	176	42	,	,	PUNCT
ejpam-5155	176	43	y0	y0	PROPN
ejpam-5155	176	44	)	)	PUNCT
ejpam-5155	176	45	=	=	PUNCT
ejpam-5155	176	46	(	(	PUNCT
ejpam-5155	176	47	1	1	NUM
ejpam-5155	176	48	,	,	PUNCT
ejpam-5155	176	49	0.08	0.08	NUM
ejpam-5155	176	50	)	)	PUNCT
ejpam-5155	176	51	impliesx1	impliesx1	NOUN
ejpam-5155	177	1	=	=	PUNCT
ejpam-5155	177	2	lim	lim	PROPN
ejpam-5155	177	3	yn→α−1	yn→α−1	PROPN
ejpam-5155	177	4	β	β	PROPN
ejpam-5155	177	5	f(x0	f(x0	PROPN
ejpam-5155	177	6	,	,	PUNCT
ejpam-5155	177	7	y0	y0	PROPN
ejpam-5155	177	8	)	)	PUNCT
ejpam-5155	177	9	=	=	SYM
ejpam-5155	177	10	lim	lim	PROPN
ejpam-5155	177	11	y0→0.08	y0→0.08	PROPN
ejpam-5155	177	12	f(x0	f(x0	PROPN
ejpam-5155	177	13	,	,	PUNCT
ejpam-5155	177	14	y0	y0	NOUN
ejpam-5155	177	15	)	)	PUNCT
ejpam-5155	177	16	=	=	PROPN
ejpam-5155	177	17	lim	lim	PROPN
ejpam-5155	177	18	y0→0.08	y0→0.08	PROPN
ejpam-5155	177	19	f(1	f(1	PROPN
ejpam-5155	177	20	,	,	PUNCT
ejpam-5155	177	21	0.08	0.08	NUM
ejpam-5155	177	22	)	)	PUNCT
ejpam-5155	177	23	=	=	SYM
ejpam-5155	178	1	x0	x0	PROPN
ejpam-5155	178	2	lim	lim	PROPN
ejpam-5155	178	3	y0→0.08	y0→0.08	PROPN
ejpam-5155	178	4	(	(	PUNCT
ejpam-5155	178	5	1.2−	1.2−	NOUN
ejpam-5155	178	6	2.5y0	2.5y0	NUM
ejpam-5155	178	7	)	)	PUNCT
ejpam-5155	178	8	=	=	PUNCT
ejpam-5155	179	1	1[1.2−	1[1.2−	NUM
ejpam-5155	179	2	2.5(0.08	2.5(0.08	NUM
ejpam-5155	179	3	)	)	PUNCT
ejpam-5155	179	4	]	]	PUNCT
ejpam-5155	180	1	this	this	PRON
ejpam-5155	180	2	implies	imply	VERB
ejpam-5155	180	3	x1	x1	PROPN
ejpam-5155	180	4	=	=	PUNCT
ejpam-5155	181	1	x0	x0	PUNCT
ejpam-5155	181	2	=	=	PUNCT
ejpam-5155	181	3	1	1	NUM
ejpam-5155	181	4	now	now	ADV
ejpam-5155	181	5	for	for	ADP
ejpam-5155	181	6	x2	x2	PROPN
ejpam-5155	181	7	,	,	PUNCT
ejpam-5155	181	8	we	we	PRON
ejpam-5155	181	9	iterate	iterate	VERB
ejpam-5155	181	10	the	the	DET
ejpam-5155	181	11	function	function	NOUN
ejpam-5155	181	12	again	again	ADV
ejpam-5155	181	13	using	use	VERB
ejpam-5155	181	14	x1	x1	PROPN
ejpam-5155	181	15	=	=	SYM
ejpam-5155	181	16	1	1	NUM
ejpam-5155	181	17	and	and	CCONJ
ejpam-5155	181	18	use	use	VERB
ejpam-5155	181	19	different	different	ADJ
ejpam-5155	181	20	values	value	NOUN
ejpam-5155	181	21	for	for	ADP
ejpam-5155	181	22	the	the	DET
ejpam-5155	181	23	parameters	parameter	NOUN
ejpam-5155	181	24	for	for	ADP
ejpam-5155	181	25	y	y	PROPN
ejpam-5155	181	26	coordinate	coordinate	NOUN
ejpam-5155	181	27	,	,	PUNCT
ejpam-5155	181	28	that	that	SCONJ
ejpam-5155	181	29	is;α	is;α	ADV
ejpam-5155	181	30	=	=	SYM
ejpam-5155	181	31	10	10	NUM
ejpam-5155	181	32	,	,	PUNCT
ejpam-5155	181	33	β	β	X
ejpam-5155	181	34	=	=	NOUN
ejpam-5155	181	35	12	12	NUM
ejpam-5155	181	36	at	at	ADP
ejpam-5155	181	37	n	n	NOUN
ejpam-5155	181	38	=	=	SYM
ejpam-5155	181	39	1	1	NUM
ejpam-5155	181	40	that	that	PRON
ejpam-5155	181	41	is	be	AUX
ejpam-5155	181	42	lim	lim	PROPN
ejpam-5155	181	43	y1→α−1	y1→α−1	PROPN
ejpam-5155	181	44	β	β	PROPN
ejpam-5155	181	45	f(x1	f(x1	PROPN
ejpam-5155	181	46	,	,	PUNCT
ejpam-5155	181	47	y1	y1	NOUN
ejpam-5155	181	48	)	)	PUNCT
ejpam-5155	181	49	=	=	SYM
ejpam-5155	182	1	x1	x1	PROPN
ejpam-5155	182	2	lim	lim	PROPN
ejpam-5155	182	3	y→	y→	X
ejpam-5155	182	4	α−1	α−1	PROPN
ejpam-5155	182	5	β	β	X
ejpam-5155	182	6	(	(	PUNCT
ejpam-5155	182	7	10−	10−	NOUN
ejpam-5155	182	8	12y1	12y1	NUM
ejpam-5155	182	9	)	)	PUNCT
ejpam-5155	182	10	.	.	PUNCT
ejpam-5155	183	1	where	where	SCONJ
ejpam-5155	183	2	y1	y1	NOUN
ejpam-5155	183	3	=	=	PUNCT
ejpam-5155	183	4	10−	10−	NOUN
ejpam-5155	183	5	1	1	NUM
ejpam-5155	183	6	12	12	NUM
ejpam-5155	183	7	=	=	SYM
ejpam-5155	183	8	9	9	NUM
ejpam-5155	183	9	12	12	NUM
ejpam-5155	183	10	=	=	SYM
ejpam-5155	183	11	0.75	0.75	NUM
ejpam-5155	183	12	.	.	PUNCT
ejpam-5155	184	1	hence	hence	ADV
ejpam-5155	184	2	(	(	PUNCT
ejpam-5155	184	3	x1	x1	PROPN
ejpam-5155	184	4	,	,	PUNCT
ejpam-5155	184	5	y1	y1	NOUN
ejpam-5155	184	6	)	)	PUNCT
ejpam-5155	184	7	=	=	PUNCT
ejpam-5155	184	8	(	(	PUNCT
ejpam-5155	184	9	1	1	NUM
ejpam-5155	184	10	,	,	PUNCT
ejpam-5155	184	11	0.75	0.75	NUM
ejpam-5155	184	12	)	)	PUNCT
ejpam-5155	184	13	therefore	therefore	ADV
ejpam-5155	184	14	x2	x2	PROPN
ejpam-5155	185	1	=	=	PROPN
ejpam-5155	185	2	lim	lim	PROPN
ejpam-5155	185	3	yn→α−1	yn→α−1	PROPN
ejpam-5155	185	4	β	β	PROPN
ejpam-5155	185	5	f(x	f(x	PROPN
ejpam-5155	185	6	,	,	PUNCT
ejpam-5155	185	7	y1	y1	NOUN
ejpam-5155	185	8	)	)	PUNCT
ejpam-5155	185	9	=	=	SYM
ejpam-5155	185	10	lim	lim	PROPN
ejpam-5155	185	11	y1→0.75	y1→0.75	PROPN
ejpam-5155	185	12	f(x1	f(x1	NOUN
ejpam-5155	185	13	,	,	PUNCT
ejpam-5155	185	14	y1	y1	NOUN
ejpam-5155	185	15	)	)	PUNCT
ejpam-5155	185	16	.	.	PUNCT
ejpam-5155	186	1	=	=	PUNCT
ejpam-5155	187	1	x1	x1	NUM
ejpam-5155	187	2	lim	lim	PROPN
ejpam-5155	187	3	y1→0.75	y1→0.75	PROPN
ejpam-5155	187	4	(	(	PUNCT
ejpam-5155	187	5	10−	10−	NOUN
ejpam-5155	187	6	12y1	12y1	NUM
ejpam-5155	187	7	)	)	PUNCT
ejpam-5155	187	8	=	=	NOUN
ejpam-5155	187	9	1[10−	1[10−	NUM
ejpam-5155	187	10	12(0.75	12(0.75	NUM
ejpam-5155	187	11	)	)	PUNCT
ejpam-5155	187	12	]	]	PUNCT
ejpam-5155	188	1	this	this	PRON
ejpam-5155	188	2	implies	imply	VERB
ejpam-5155	188	3	x2	x2	NOUN
ejpam-5155	189	1	=	=	SYM
ejpam-5155	189	2	x1	x1	PROPN
ejpam-5155	189	3	=	=	SYM
ejpam-5155	189	4	1	1	NUM
ejpam-5155	189	5	the	the	DET
ejpam-5155	189	6	iteration	iteration	NOUN
ejpam-5155	189	7	process	process	NOUN
ejpam-5155	189	8	so	so	ADV
ejpam-5155	189	9	far	far	ADV
ejpam-5155	189	10	indicates	indicate	VERB
ejpam-5155	189	11	the	the	DET
ejpam-5155	189	12	limit	limit	NOUN
ejpam-5155	189	13	of	of	ADP
ejpam-5155	189	14	xn+1	xn+1	PROPN
ejpam-5155	189	15	is	be	AUX
ejpam-5155	189	16	the	the	DET
ejpam-5155	189	17	same	same	ADJ
ejpam-5155	189	18	as	as	ADP
ejpam-5155	189	19	that	that	PRON
ejpam-5155	189	20	of	of	ADP
ejpam-5155	189	21	(	(	PUNCT
ejpam-5155	189	22	xn	xn	PROPN
ejpam-5155	189	23	)	)	PUNCT
ejpam-5155	189	24	and	and	CCONJ
ejpam-5155	189	25	keeps	keep	VERB
ejpam-5155	189	26	repeating	repeat	VERB
ejpam-5155	189	27	itself	itself	PRON
ejpam-5155	189	28	.	.	PUNCT
ejpam-5155	190	1	hence	hence	ADV
ejpam-5155	190	2	,	,	PUNCT
ejpam-5155	190	3	xn	xn	PROPN
ejpam-5155	190	4	=	=	SYM
ejpam-5155	190	5	1	1	NUM
ejpam-5155	190	6	+	+	CCONJ
ejpam-5155	190	7	γ	γ	PROPN
ejpam-5155	190	8	δ	δ	PROPN
ejpam-5155	190	9	is	be	AUX
ejpam-5155	190	10	a	a	DET
ejpam-5155	190	11	fixed	fix	VERB
ejpam-5155	190	12	point	point	NOUN
ejpam-5155	190	13	of	of	ADP
ejpam-5155	190	14	the	the	DET
ejpam-5155	190	15	function	function	NOUN
ejpam-5155	190	16	.	.	PUNCT
ejpam-5155	191	1	which	which	PRON
ejpam-5155	191	2	implies	imply	VERB
ejpam-5155	191	3	that	that	SCONJ
ejpam-5155	191	4	when	when	SCONJ
ejpam-5155	191	5	n	n	X
ejpam-5155	191	6	=	=	SYM
ejpam-5155	191	7	0	0	NUM
ejpam-5155	191	8	,	,	PUNCT
ejpam-5155	191	9	x1	x1	PROPN
ejpam-5155	191	10	=	=	SYM
ejpam-5155	191	11	g(x0	g(x0	NOUN
ejpam-5155	191	12	)	)	PUNCT
ejpam-5155	191	13	=	=	PUNCT
ejpam-5155	192	1	x0	x0	PROPN
ejpam-5155	192	2	when	when	SCONJ
ejpam-5155	192	3	n	n	X
ejpam-5155	192	4	=	=	SYM
ejpam-5155	192	5	1	1	NUM
ejpam-5155	192	6	,	,	PUNCT
ejpam-5155	192	7	x2	x2	NOUN
ejpam-5155	192	8	=	=	SYM
ejpam-5155	192	9	g(x1	g(x1	NOUN
ejpam-5155	192	10	)	)	PUNCT
ejpam-5155	192	11	=	=	PUNCT
ejpam-5155	193	1	x1	x1	NUM
ejpam-5155	193	2	when	when	SCONJ
ejpam-5155	193	3	n	n	X
ejpam-5155	193	4	=	=	SYM
ejpam-5155	193	5	2	2	NUM
ejpam-5155	193	6	,	,	PUNCT
ejpam-5155	193	7	x3	x3	ADJ
ejpam-5155	193	8	=	=	SYM
ejpam-5155	193	9	g(x2	g(x2	NOUN
ejpam-5155	193	10	)	)	PUNCT
ejpam-5155	194	1	=	=	SYM
ejpam-5155	195	1	x2	x2	INTJ
ejpam-5155	195	2	...	...	PUNCT
ejpam-5155	195	3	when	when	SCONJ
ejpam-5155	195	4	n	n	X
ejpam-5155	195	5	=	=	SYM
ejpam-5155	195	6	k	k	NOUN
ejpam-5155	195	7	,	,	PUNCT
ejpam-5155	195	8	xk+1	xk+1	PROPN
ejpam-5155	195	9	=	=	SYM
ejpam-5155	195	10	g(xk	g(xk	PROPN
ejpam-5155	195	11	)	)	PUNCT
ejpam-5155	195	12	=	=	SYM
ejpam-5155	195	13	xk	xk	NOUN
ejpam-5155	195	14	considering	consider	VERB
ejpam-5155	195	15	equation	equation	NOUN
ejpam-5155	195	16	(	(	PUNCT
ejpam-5155	195	17	12	12	NUM
ejpam-5155	195	18	)	)	PUNCT
ejpam-5155	195	19	,	,	PUNCT
ejpam-5155	195	20	that	that	PRON
ejpam-5155	195	21	is	is	ADV
ejpam-5155	195	22	yn+1	yn+1	PROPN
ejpam-5155	195	23	=	=	NOUN
ejpam-5155	195	24	δxnt	δxnt	NOUN
ejpam-5155	195	25	(	(	PUNCT
ejpam-5155	195	26	yn)−	yn)−	X
ejpam-5155	195	27	γt	γt	PROPN
ejpam-5155	195	28	(	(	PUNCT
ejpam-5155	195	29	yn	yn	NOUN
ejpam-5155	195	30	)	)	PUNCT
ejpam-5155	195	31	m.	m.	NOUN
ejpam-5155	196	1	o.	o.	PROPN
ejpam-5155	196	2	fokuoet	fokuoet	PROPN
ejpam-5155	196	3	al	al	PROPN
ejpam-5155	196	4	.	.	PUNCT
ejpam-5155	196	5	/	/	SYM
ejpam-5155	196	6	eur	eur	PROPN
ejpam-5155	196	7	.	.	PUNCT
ejpam-5155	197	1	j.	j.	PROPN
ejpam-5155	197	2	pure	pure	PROPN
ejpam-5155	197	3	appl	appl	PROPN
ejpam-5155	197	4	.	.	PROPN
ejpam-5155	197	5	math	math	PROPN
ejpam-5155	197	6	,	,	PUNCT
ejpam-5155	197	7	17	17	NUM
ejpam-5155	197	8	(	(	PUNCT
ejpam-5155	197	9	2	2	NUM
ejpam-5155	197	10	)	)	PUNCT
ejpam-5155	197	11	(	(	PUNCT
ejpam-5155	197	12	2024	2024	NUM
ejpam-5155	197	13	)	)	PUNCT
ejpam-5155	197	14	,	,	PUNCT
ejpam-5155	197	15	1294	1294	NUM
ejpam-5155	197	16	-	-	SYM
ejpam-5155	197	17	1305	1305	NUM
ejpam-5155	197	18	1302	1302	NUM
ejpam-5155	197	19	we	we	PRON
ejpam-5155	197	20	pick	pick	VERB
ejpam-5155	197	21	any	any	DET
ejpam-5155	197	22	y	y	PROPN
ejpam-5155	197	23	∈	∈	PROPN
ejpam-5155	197	24	m	m	AUX
ejpam-5155	197	25	setting	set	VERB
ejpam-5155	197	26	y	y	NOUN
ejpam-5155	197	27	=	=	SYM
ejpam-5155	197	28	y0	y0	PROPN
ejpam-5155	197	29	,	,	PUNCT
ejpam-5155	197	30	we	we	PRON
ejpam-5155	197	31	define	define	VERB
ejpam-5155	197	32	a	a	DET
ejpam-5155	197	33	sequence	sequence	NOUN
ejpam-5155	197	34	{	{	PUNCT
ejpam-5155	197	35	yi}i∈z+	yi}i∈z+	ADJ
ejpam-5155	197	36	by	by	ADP
ejpam-5155	197	37	setting	set	VERB
ejpam-5155	197	38	yn+1	yn+1	PROPN
ejpam-5155	197	39	=	=	SYM
ejpam-5155	197	40	t	t	PROPN
ejpam-5155	197	41	(	(	PUNCT
ejpam-5155	197	42	yn	yn	NOUN
ejpam-5155	197	43	)	)	PUNCT
ejpam-5155	197	44	yn+1	yn+1	PROPN
ejpam-5155	197	45	=	=	NOUN
ejpam-5155	197	46	δxnt	δxnt	NOUN
ejpam-5155	197	47	(	(	PUNCT
ejpam-5155	197	48	yn)−	yn)−	X
ejpam-5155	197	49	γt	γt	PROPN
ejpam-5155	197	50	(	(	PUNCT
ejpam-5155	197	51	yn	yn	NOUN
ejpam-5155	197	52	)	)	PUNCT
ejpam-5155	197	53	rewriting	rewrite	VERB
ejpam-5155	197	54	the	the	DET
ejpam-5155	197	55	contraction	contraction	NOUN
ejpam-5155	197	56	formula	formula	NOUN
ejpam-5155	197	57	we	we	PRON
ejpam-5155	197	58	have	have	VERB
ejpam-5155	197	59	yn+1	yn+1	NUM
ejpam-5155	197	60	=	=	SYM
ejpam-5155	197	61	(	(	PUNCT
ejpam-5155	197	62	δxn	δxn	NOUN
ejpam-5155	197	63	−	−	PROPN
ejpam-5155	197	64	γ)t	γ)t	NOUN
ejpam-5155	197	65	(	(	PUNCT
ejpam-5155	197	66	yn	yn	NOUN
ejpam-5155	197	67	)	)	PUNCT
ejpam-5155	197	68	d(yn+2	d(yn+2	PROPN
ejpam-5155	197	69	,	,	PUNCT
ejpam-5155	197	70	yn+1	yn+1	NOUN
ejpam-5155	197	71	)	)	PUNCT
ejpam-5155	197	72	≤	≤	NOUN
ejpam-5155	197	73	(	(	PUNCT
ejpam-5155	197	74	δxn	δxn	NOUN
ejpam-5155	197	75	−	−	PROPN
ejpam-5155	197	76	γ)qd(yn+1	γ)qd(yn+1	PROPN
ejpam-5155	197	77	,	,	PUNCT
ejpam-5155	197	78	yn	yn	PROPN
ejpam-5155	197	79	)	)	PUNCT
ejpam-5155	197	80	or	or	CCONJ
ejpam-5155	197	81	d(yn+1	d(yn+1	PROPN
ejpam-5155	197	82	,	,	PUNCT
ejpam-5155	197	83	yn	yn	NOUN
ejpam-5155	197	84	)	)	PUNCT
ejpam-5155	197	85	≤	≤	NOUN
ejpam-5155	197	86	(	(	PUNCT
ejpam-5155	197	87	δxn	δxn	NOUN
ejpam-5155	197	88	−	−	PROPN
ejpam-5155	197	89	γ)qnd(y1	γ)qnd(y1	PROPN
ejpam-5155	197	90	,	,	PUNCT
ejpam-5155	197	91	y0	y0	NOUN
ejpam-5155	197	92	)	)	PUNCT
ejpam-5155	197	93	d(yn+1	d(yn+1	PROPN
ejpam-5155	197	94	,	,	PUNCT
ejpam-5155	197	95	yn	yn	NOUN
ejpam-5155	197	96	)	)	PUNCT
ejpam-5155	197	97	≤	≤	PUNCT
ejpam-5155	198	1	qn(δxn	qn(δxn	ADP
ejpam-5155	198	2	−	−	PROPN
ejpam-5155	198	3	γ)d(y1	γ)d(y1	NOUN
ejpam-5155	198	4	,	,	PUNCT
ejpam-5155	198	5	y0	y0	NOUN
ejpam-5155	198	6	)	)	PUNCT
ejpam-5155	198	7	assuming	assume	VERB
ejpam-5155	198	8	n	n	PRON
ejpam-5155	198	9	<	<	X
ejpam-5155	198	10	m	m	PROPN
ejpam-5155	198	11	d(ym	d(ym	PROPN
ejpam-5155	198	12	,	,	PUNCT
ejpam-5155	198	13	yn	yn	PROPN
ejpam-5155	198	14	)	)	PUNCT
ejpam-5155	198	15	≤	≤	NUM
ejpam-5155	198	16	d(ym	d(ym	PROPN
ejpam-5155	198	17	,	,	PUNCT
ejpam-5155	198	18	ym−1	ym−1	PROPN
ejpam-5155	198	19	)	)	PUNCT
ejpam-5155	199	1	+	+	NUM
ejpam-5155	199	2	d(ym−1	d(ym−1	NOUN
ejpam-5155	199	3	,	,	PUNCT
ejpam-5155	199	4	ym−2	ym−2	PROPN
ejpam-5155	199	5	)	)	PUNCT
ejpam-5155	200	1	+	+	CCONJ
ejpam-5155	200	2	.	.	PUNCT
ejpam-5155	200	3	.	.	PUNCT
ejpam-5155	201	1	.+	.+	NOUN
ejpam-5155	201	2	d(yn+1	d(yn+1	PROPN
ejpam-5155	201	3	,	,	PUNCT
ejpam-5155	201	4	yn	yn	NOUN
ejpam-5155	201	5	)	)	PUNCT
ejpam-5155	201	6	d(ym	d(ym	PROPN
ejpam-5155	201	7	,	,	PUNCT
ejpam-5155	201	8	yn	yn	PROPN
ejpam-5155	201	9	)	)	PUNCT
ejpam-5155	201	10	≤	≤	NOUN
ejpam-5155	201	11	(	(	PUNCT
ejpam-5155	201	12	qm−n−1	qm−n−1	PROPN
ejpam-5155	201	13	+	+	CCONJ
ejpam-5155	201	14	qm−n−2	qm−n−2	X
ejpam-5155	201	15	+	+	NOUN
ejpam-5155	201	16	.	.	PUNCT
ejpam-5155	201	17	.	.	PUNCT
ejpam-5155	202	1	.+	.+	NOUN
ejpam-5155	202	2	q	q	X
ejpam-5155	203	1	+	+	NUM
ejpam-5155	203	2	1)d(yn+1	1)d(yn+1	NUM
ejpam-5155	203	3	,	,	PUNCT
ejpam-5155	203	4	yn	yn	NOUN
ejpam-5155	203	5	)	)	PUNCT
ejpam-5155	203	6	d(ym	d(ym	PROPN
ejpam-5155	203	7	,	,	PUNCT
ejpam-5155	203	8	yn	yn	PROPN
ejpam-5155	203	9	)	)	PUNCT
ejpam-5155	203	10	≤	≤	NOUN
ejpam-5155	203	11	1−	1−	NUM
ejpam-5155	203	12	qm−n	qm−n	PROPN
ejpam-5155	203	13	1−	1−	NUM
ejpam-5155	203	14	q	q	PROPN
ejpam-5155	203	15	d(yn+1	d(yn+1	PROPN
ejpam-5155	203	16	,	,	PUNCT
ejpam-5155	203	17	yn	yn	PROPN
ejpam-5155	203	18	)	)	PUNCT
ejpam-5155	203	19	since	since	SCONJ
ejpam-5155	203	20	qm−n	qm−n	PROPN
ejpam-5155	203	21	<	<	X
ejpam-5155	203	22	1	1	NUM
ejpam-5155	203	23	d(ym	d(ym	PROPN
ejpam-5155	203	24	,	,	PUNCT
ejpam-5155	203	25	yn	yn	PROPN
ejpam-5155	203	26	)	)	PUNCT
ejpam-5155	203	27	<	<	X
ejpam-5155	204	1	qn	qn	PROPN
ejpam-5155	204	2	1−	1−	NUM
ejpam-5155	204	3	q	q	NOUN
ejpam-5155	204	4	(	(	PUNCT
ejpam-5155	204	5	δxn	δxn	NOUN
ejpam-5155	204	6	−	−	PROPN
ejpam-5155	204	7	γ)d(y1	γ)d(y1	NOUN
ejpam-5155	204	8	,	,	PUNCT
ejpam-5155	204	9	y0	y0	NOUN
ejpam-5155	204	10	)	)	PUNCT
ejpam-5155	204	11	thus	thus	ADV
ejpam-5155	204	12	{	{	PUNCT
ejpam-5155	204	13	yi	yi	NOUN
ejpam-5155	204	14	}	}	PUNCT
ejpam-5155	204	15	is	be	AUX
ejpam-5155	204	16	cauchy	cauchy	NOUN
ejpam-5155	204	17	.	.	PUNCT
ejpam-5155	205	1	this	this	PRON
ejpam-5155	205	2	shows	show	VERB
ejpam-5155	205	3	that	that	SCONJ
ejpam-5155	205	4	yn	yn	PROPN
ejpam-5155	205	5	is	be	AUX
ejpam-5155	205	6	a	a	DET
ejpam-5155	205	7	cauchy	cauchy	ADJ
ejpam-5155	205	8	sequence	sequence	NOUN
ejpam-5155	205	9	in	in	ADP
ejpam-5155	205	10	m	m	VERB
ejpam-5155	205	11	hence	hence	ADV
ejpam-5155	205	12	,	,	PUNCT
ejpam-5155	205	13	(	(	PUNCT
ejpam-5155	205	14	yn	yn	NOUN
ejpam-5155	205	15	)	)	PUNCT
ejpam-5155	205	16	must	must	AUX
ejpam-5155	205	17	be	be	AUX
ejpam-5155	205	18	convergent	convergent	ADJ
ejpam-5155	205	19	,	,	PUNCT
ejpam-5155	205	20	say	say	VERB
ejpam-5155	205	21	lim	lim	PROPN
ejpam-5155	205	22	n→+∞	n→+∞	VERB
ejpam-5155	205	23	yn	yn	PROPN
ejpam-5155	205	24	=	=	PUNCT
ejpam-5155	205	25	y	y	PROPN
ejpam-5155	205	26	since	since	SCONJ
ejpam-5155	205	27	t	t	PROPN
ejpam-5155	205	28	is	be	AUX
ejpam-5155	205	29	continuous	continuous	ADJ
ejpam-5155	205	30	,	,	PUNCT
ejpam-5155	205	31	we	we	PRON
ejpam-5155	205	32	have	have	VERB
ejpam-5155	205	33	ty	ty	NOUN
ejpam-5155	205	34	=	=	SYM
ejpam-5155	205	35	t	t	PROPN
ejpam-5155	205	36	(	(	PUNCT
ejpam-5155	205	37	lim	lim	PROPN
ejpam-5155	205	38	n→+∞	n→+∞	VERB
ejpam-5155	205	39	yn	yn	PROPN
ejpam-5155	205	40	)	)	PUNCT
ejpam-5155	206	1	=	=	VERB
ejpam-5155	206	2	lim	lim	PROPN
ejpam-5155	206	3	n→+∞	n→+∞	VERB
ejpam-5155	206	4	tyn	tyn	INTJ
ejpam-5155	207	1	=	=	SYM
ejpam-5155	207	2	lim	lim	PROPN
ejpam-5155	207	3	n→+∞	n→+∞	VERB
ejpam-5155	207	4	yn+1	yn+1	X
ejpam-5155	208	1	=	=	PUNCT
ejpam-5155	208	2	y	y	PROPN
ejpam-5155	208	3	since	since	SCONJ
ejpam-5155	208	4	the	the	DET
ejpam-5155	208	5	limit	limit	NOUN
ejpam-5155	208	6	of	of	ADP
ejpam-5155	208	7	yn+1	yn+1	PROPN
ejpam-5155	208	8	is	be	AUX
ejpam-5155	208	9	the	the	DET
ejpam-5155	208	10	same	same	ADJ
ejpam-5155	208	11	as	as	ADP
ejpam-5155	208	12	that	that	PRON
ejpam-5155	208	13	of	of	ADP
ejpam-5155	208	14	yn	yn	PRON
ejpam-5155	208	15	thus	thus	ADV
ejpam-5155	208	16	,	,	PUNCT
ejpam-5155	208	17	y	y	PROPN
ejpam-5155	208	18	is	be	AUX
ejpam-5155	208	19	a	a	DET
ejpam-5155	208	20	fixed	fixed	ADJ
ejpam-5155	208	21	point	point	NOUN
ejpam-5155	208	22	of	of	ADP
ejpam-5155	208	23	t.	t.	NOUN
ejpam-5155	208	24	illustration	illustration	NOUN
ejpam-5155	208	25	2	2	NUM
ejpam-5155	208	26	similarly	similarly	ADV
ejpam-5155	208	27	,	,	PUNCT
ejpam-5155	208	28	let	let	VERB
ejpam-5155	208	29	yn+1	yn+1	PRON
ejpam-5155	208	30	=	=	SYM
ejpam-5155	208	31	h(xn	h(xn	PROPN
ejpam-5155	208	32	,	,	PUNCT
ejpam-5155	208	33	yn	yn	PROPN
ejpam-5155	208	34	)	)	PUNCT
ejpam-5155	209	1	=	=	PUNCT
ejpam-5155	209	2	δxnyn	δxnyn	ADJ
ejpam-5155	209	3	−	−	NUM
ejpam-5155	209	4	γyn	γyn	NOUN
ejpam-5155	209	5	then	then	ADV
ejpam-5155	209	6	,	,	PUNCT
ejpam-5155	209	7	by	by	ADP
ejpam-5155	209	8	considering	consider	VERB
ejpam-5155	209	9	the	the	DET
ejpam-5155	209	10	coordinate	coordinate	NOUN
ejpam-5155	209	11	of	of	ADP
ejpam-5155	209	12	x	x	PRON
ejpam-5155	209	13	,	,	PUNCT
ejpam-5155	209	14	that	that	PRON
ejpam-5155	209	15	is	is	ADV
ejpam-5155	209	16	xn	xn	PROPN
ejpam-5155	209	17	=	=	SYM
ejpam-5155	209	18	1	1	NUM
ejpam-5155	209	19	+	+	CCONJ
ejpam-5155	209	20	γ	γ	PROPN
ejpam-5155	209	21	δ	δ	PROPN
ejpam-5155	209	22	lim	lim	PROPN
ejpam-5155	209	23	xn→	xn→	PROPN
ejpam-5155	210	1	1+γ	1+γ	NUM
ejpam-5155	210	2	δ	δ	PROPN
ejpam-5155	210	3	h(xn	h(xn	PROPN
ejpam-5155	210	4	,	,	PUNCT
ejpam-5155	210	5	yn	yn	PROPN
ejpam-5155	210	6	)	)	PUNCT
ejpam-5155	211	1	=	=	VERB
ejpam-5155	211	2	lim	lim	PROPN
ejpam-5155	211	3	xn→	xn→	PROPN
ejpam-5155	212	1	1+γ	1+γ	NUM
ejpam-5155	212	2	δ	δ	NOUN
ejpam-5155	212	3	(	(	PUNCT
ejpam-5155	212	4	δxnyn	δxnyn	ADJ
ejpam-5155	212	5	−	−	PROPN
ejpam-5155	212	6	γyn	γyn	NOUN
ejpam-5155	212	7	)	)	PUNCT
ejpam-5155	212	8	=	=	SYM
ejpam-5155	212	9	yn	yn	PROPN
ejpam-5155	212	10	lim	lim	PROPN
ejpam-5155	212	11	xn→	xn→	PROPN
ejpam-5155	213	1	1+γ	1+γ	NUM
ejpam-5155	213	2	δ	δ	NOUN
ejpam-5155	213	3	(	(	PUNCT
ejpam-5155	213	4	δxn	δxn	NOUN
ejpam-5155	213	5	−	−	PROPN
ejpam-5155	213	6	γ	γ	PROPN
ejpam-5155	213	7	)	)	PUNCT
ejpam-5155	213	8	where	where	SCONJ
ejpam-5155	213	9	n	n	NOUN
ejpam-5155	213	10	=	=	SYM
ejpam-5155	213	11	0	0	NUM
ejpam-5155	213	12	,	,	PUNCT
ejpam-5155	213	13	1	1	NUM
ejpam-5155	213	14	,	,	PUNCT
ejpam-5155	213	15	2	2	NUM
ejpam-5155	213	16	,	,	PUNCT
ejpam-5155	213	17	.	.	PUNCT
ejpam-5155	213	18	.	.	PUNCT
ejpam-5155	213	19	.	.	PUNCT
ejpam-5155	214	1	=	=	PUNCT
ejpam-5155	214	2	δ	δ	PROPN
ejpam-5155	214	3	(	(	PUNCT
ejpam-5155	214	4	1	1	NUM
ejpam-5155	214	5	+	+	CCONJ
ejpam-5155	214	6	γ	γ	X
ejpam-5155	214	7	δ	δ	PROPN
ejpam-5155	214	8	)	)	PUNCT
ejpam-5155	215	1	yn	yn	PRON
ejpam-5155	215	2	−	−	PROPN
ejpam-5155	215	3	γyn	γyn	PROPN
ejpam-5155	215	4	m.	m.	NOUN
ejpam-5155	215	5	o.	o.	PROPN
ejpam-5155	215	6	fokuoet	fokuoet	VERB
ejpam-5155	215	7	al	al	PROPN
ejpam-5155	215	8	.	.	PUNCT
ejpam-5155	215	9	/	/	SYM
ejpam-5155	215	10	eur	eur	PROPN
ejpam-5155	215	11	.	.	PUNCT
ejpam-5155	216	1	j.	j.	PROPN
ejpam-5155	216	2	pure	pure	PROPN
ejpam-5155	216	3	appl	appl	PROPN
ejpam-5155	216	4	.	.	PROPN
ejpam-5155	216	5	math	math	PROPN
ejpam-5155	216	6	,	,	PUNCT
ejpam-5155	216	7	17	17	NUM
ejpam-5155	216	8	(	(	PUNCT
ejpam-5155	216	9	2	2	NUM
ejpam-5155	216	10	)	)	PUNCT
ejpam-5155	216	11	(	(	PUNCT
ejpam-5155	216	12	2024	2024	NUM
ejpam-5155	216	13	)	)	PUNCT
ejpam-5155	216	14	,	,	PUNCT
ejpam-5155	216	15	1294	1294	NUM
ejpam-5155	216	16	-	-	SYM
ejpam-5155	216	17	1305	1305	NUM
ejpam-5155	216	18	1303	1303	NUM
ejpam-5155	216	19	=	=	SYM
ejpam-5155	216	20	yn	yn	PROPN
ejpam-5155	216	21	[	[	PUNCT
ejpam-5155	216	22	δ	δ	PROPN
ejpam-5155	216	23	(	(	PUNCT
ejpam-5155	216	24	1	1	NUM
ejpam-5155	216	25	+	+	CCONJ
ejpam-5155	216	26	γ	γ	X
ejpam-5155	216	27	δ	δ	PROPN
ejpam-5155	216	28	)	)	PUNCT
ejpam-5155	216	29	−	−	PROPN
ejpam-5155	216	30	γ	γ	X
ejpam-5155	216	31	]	]	PUNCT
ejpam-5155	216	32	=	=	PUNCT
ejpam-5155	217	1	yn[(1	yn[(1	PROPN
ejpam-5155	217	2	+	+	CCONJ
ejpam-5155	217	3	γ)−	γ)−	PROPN
ejpam-5155	217	4	γ	γ	X
ejpam-5155	217	5	]	]	X
ejpam-5155	217	6	=	=	PUNCT
ejpam-5155	217	7	yn	yn	NUM
ejpam-5155	217	8	×	×	NOUN
ejpam-5155	217	9	(	(	PUNCT
ejpam-5155	217	10	1	1	NUM
ejpam-5155	217	11	)	)	PUNCT
ejpam-5155	217	12	=	=	SYM
ejpam-5155	217	13	yn	yn	PRON
ejpam-5155	217	14	hence	hence	ADV
ejpam-5155	217	15	,	,	PUNCT
ejpam-5155	217	16	yn+1	yn+1	PROPN
ejpam-5155	217	17	=	=	PUNCT
ejpam-5155	217	18	h(yn	h(yn	PROPN
ejpam-5155	217	19	)	)	PUNCT
ejpam-5155	217	20	=	=	SYM
ejpam-5155	218	1	yn	yn	PROPN
ejpam-5155	218	2	irrespective	irrespective	ADV
ejpam-5155	218	3	of	of	ADP
ejpam-5155	218	4	the	the	DET
ejpam-5155	218	5	values	value	NOUN
ejpam-5155	218	6	of	of	ADP
ejpam-5155	218	7	the	the	DET
ejpam-5155	218	8	parameters	parameter	NOUN
ejpam-5155	218	9	.	.	PUNCT
ejpam-5155	219	1	whitewhitespaceere	whitewhitespaceere	VERB
ejpam-5155	219	2	when	when	SCONJ
ejpam-5155	219	3	n	n	X
ejpam-5155	219	4	=	=	SYM
ejpam-5155	219	5	0	0	NUM
ejpam-5155	219	6	,	,	PUNCT
ejpam-5155	219	7	y1	y1	NOUN
ejpam-5155	219	8	=	=	SYM
ejpam-5155	219	9	h(y0	h(y0	ADJ
ejpam-5155	219	10	)	)	PUNCT
ejpam-5155	219	11	=	=	PUNCT
ejpam-5155	219	12	y0	y0	NOUN
ejpam-5155	219	13	when	when	SCONJ
ejpam-5155	219	14	n	n	X
ejpam-5155	219	15	=	=	SYM
ejpam-5155	219	16	1	1	NUM
ejpam-5155	219	17	,	,	PUNCT
ejpam-5155	219	18	y2	y2	NOUN
ejpam-5155	219	19	=	=	SYM
ejpam-5155	219	20	h(y1	h(y1	NOUN
ejpam-5155	219	21	)	)	PUNCT
ejpam-5155	219	22	=	=	PUNCT
ejpam-5155	220	1	y1	y1	INTJ
ejpam-5155	220	2	when	when	SCONJ
ejpam-5155	220	3	n	n	X
ejpam-5155	220	4	=	=	SYM
ejpam-5155	220	5	2	2	NUM
ejpam-5155	220	6	,	,	PUNCT
ejpam-5155	220	7	y3	y3	NOUN
ejpam-5155	220	8	=	=	SYM
ejpam-5155	220	9	h(y2	h(y2	PROPN
ejpam-5155	220	10	)	)	PUNCT
ejpam-5155	220	11	=	=	VERB
ejpam-5155	221	1	y2	y2	NOUN
ejpam-5155	221	2	this	this	PRON
ejpam-5155	221	3	forms	form	VERB
ejpam-5155	221	4	the	the	DET
ejpam-5155	221	5	orbit	orbit	NOUN
ejpam-5155	221	6	{	{	PUNCT
ejpam-5155	221	7	y0	y0	PROPN
ejpam-5155	221	8	,	,	PUNCT
ejpam-5155	221	9	y1	y1	NOUN
ejpam-5155	221	10	=	=	SYM
ejpam-5155	221	11	h(y0	h(y0	ADJ
ejpam-5155	221	12	)	)	PUNCT
ejpam-5155	221	13	=	=	SYM
ejpam-5155	221	14	y0	y0	NOUN
ejpam-5155	221	15	,	,	PUNCT
ejpam-5155	221	16	y2	y2	PROPN
ejpam-5155	221	17	=	=	SYM
ejpam-5155	221	18	h(y1	h(y1	NOUN
ejpam-5155	221	19	)	)	PUNCT
ejpam-5155	221	20	=	=	SYM
ejpam-5155	221	21	y1	y1	PROPN
ejpam-5155	221	22	,	,	PUNCT
ejpam-5155	221	23	y3	y3	NOUN
ejpam-5155	221	24	=	=	SYM
ejpam-5155	221	25	h(y2	h(y2	PROPN
ejpam-5155	221	26	)	)	PUNCT
ejpam-5155	221	27	=	=	SYM
ejpam-5155	221	28	y2	y2	PROPN
ejpam-5155	221	29	,	,	PUNCT
ejpam-5155	221	30	.	.	PUNCT
ejpam-5155	221	31	.	.	PUNCT
ejpam-5155	222	1	.	.	PUNCT
ejpam-5155	222	2	}	}	PUNCT
ejpam-5155	223	1	of	of	ADP
ejpam-5155	223	2	the	the	DET
ejpam-5155	223	3	function	function	NOUN
ejpam-5155	223	4	that	that	PRON
ejpam-5155	223	5	are	be	AUX
ejpam-5155	223	6	equilibrium	equilibrium	NOUN
ejpam-5155	223	7	in	in	ADP
ejpam-5155	223	8	nature	nature	NOUN
ejpam-5155	223	9	,	,	PUNCT
ejpam-5155	223	10	asymptotically	asymptotically	ADV
ejpam-5155	223	11	stable	stable	ADJ
ejpam-5155	223	12	and	and	CCONJ
ejpam-5155	223	13	continuous	continuous	ADJ
ejpam-5155	223	14	after	after	ADP
ejpam-5155	223	15	several	several	ADJ
ejpam-5155	223	16	iterations	iteration	NOUN
ejpam-5155	223	17	.	.	PUNCT
ejpam-5155	223	18	example	example	NOUN
ejpam-5155	224	1	2	2	NUM
ejpam-5155	224	2	.	.	PUNCT
ejpam-5155	224	3	given	give	VERB
ejpam-5155	224	4	yn+1	yn+1	PROPN
ejpam-5155	224	5	=	=	SYM
ejpam-5155	224	6	h(xn	h(xn	PROPN
ejpam-5155	224	7	,	,	PUNCT
ejpam-5155	224	8	yn	yn	PROPN
ejpam-5155	224	9	)	)	PUNCT
ejpam-5155	224	10	=	=	PUNCT
ejpam-5155	224	11	δxnyn	δxnyn	ADJ
ejpam-5155	224	12	−	−	PROPN
ejpam-5155	224	13	γyn	γyn	PROPN
ejpam-5155	224	14	.	.	PUNCT
ejpam-5155	225	1	let	let	VERB
ejpam-5155	225	2	γ	γ	X
ejpam-5155	225	3	>	>	X
ejpam-5155	225	4	1	1	PROPN
ejpam-5155	225	5	,	,	PUNCT
ejpam-5155	225	6	δ	δ	PROPN
ejpam-5155	225	7	>	>	X
ejpam-5155	225	8	1	1	NUM
ejpam-5155	225	9	,	,	PUNCT
ejpam-5155	225	10	and	and	CCONJ
ejpam-5155	225	11	α	α	X
ejpam-5155	225	12	>	>	X
ejpam-5155	225	13	1	1	NUM
ejpam-5155	225	14	,	,	PUNCT
ejpam-5155	225	15	β	β	X
ejpam-5155	225	16	>	>	X
ejpam-5155	226	1	1	1	X
ejpam-5155	226	2	.	.	PUNCT
ejpam-5155	227	1	at	at	ADP
ejpam-5155	227	2	γ	γ	X
ejpam-5155	227	3	=	=	SYM
ejpam-5155	227	4	1.1	1.1	NUM
ejpam-5155	227	5	,	,	PUNCT
ejpam-5155	227	6	δ	δ	PROPN
ejpam-5155	227	7	=	=	PUNCT
ejpam-5155	227	8	2.1	2.1	NUM
ejpam-5155	227	9	,	,	PUNCT
ejpam-5155	227	10	α	α	NOUN
ejpam-5155	227	11	=	=	SYM
ejpam-5155	227	12	1.2	1.2	NUM
ejpam-5155	227	13	,	,	PUNCT
ejpam-5155	227	14	β	β	X
ejpam-5155	227	15	=	=	SYM
ejpam-5155	227	16	2.5	2.5	NUM
ejpam-5155	227	17	.	.	PUNCT
ejpam-5155	228	1	(	(	PUNCT
ejpam-5155	228	2	1	1	NUM
ejpam-5155	228	3	+	+	NUM
ejpam-5155	228	4	γ	γ	PROPN
ejpam-5155	228	5	δ	δ	PROPN
ejpam-5155	228	6	,	,	PUNCT
ejpam-5155	228	7	α−	α−	ADP
ejpam-5155	228	8	1	1	NUM
ejpam-5155	228	9	β	β	NOUN
ejpam-5155	228	10	)	)	PUNCT
ejpam-5155	228	11	implies	imply	VERB
ejpam-5155	228	12	(	(	PUNCT
ejpam-5155	228	13	xn	xn	PROPN
ejpam-5155	228	14	,	,	PUNCT
ejpam-5155	228	15	yn	yn	PROPN
ejpam-5155	228	16	)	)	PUNCT
ejpam-5155	228	17	)	)	PUNCT
ejpam-5155	229	1	then	then	ADV
ejpam-5155	229	2	,	,	PUNCT
ejpam-5155	229	3	taking	take	VERB
ejpam-5155	229	4	the	the	DET
ejpam-5155	229	5	limit	limit	NOUN
ejpam-5155	229	6	of	of	ADP
ejpam-5155	229	7	the	the	DET
ejpam-5155	229	8	function	function	NOUN
ejpam-5155	229	9	yn+1as	yn+1as	NOUN
ejpam-5155	229	10	xn	xn	PUNCT
ejpam-5155	230	1	→	→	SYM
ejpam-5155	230	2	1	1	NUM
ejpam-5155	230	3	+	+	CCONJ
ejpam-5155	230	4	γ	γ	PROPN
ejpam-5155	230	5	δ	δ	PROPN
ejpam-5155	230	6	for	for	ADP
ejpam-5155	230	7	γ	γ	X
ejpam-5155	230	8	=	=	SYM
ejpam-5155	230	9	1.1	1.1	NUM
ejpam-5155	230	10	,	,	PUNCT
ejpam-5155	230	11	δ	δ	PROPN
ejpam-5155	230	12	=	=	NOUN
ejpam-5155	230	13	2.1	2.1	NUM
ejpam-5155	230	14	implies	imply	VERB
ejpam-5155	230	15	lim	lim	PROPN
ejpam-5155	230	16	xn→	xn→	PUNCT
ejpam-5155	231	1	1+γ	1+γ	NUM
ejpam-5155	231	2	δ	δ	PROPN
ejpam-5155	231	3	h(xn	h(xn	PROPN
ejpam-5155	231	4	,	,	PUNCT
ejpam-5155	231	5	yn	yn	PROPN
ejpam-5155	231	6	)	)	PUNCT
ejpam-5155	232	1	=	=	VERB
ejpam-5155	232	2	lim	lim	PROPN
ejpam-5155	232	3	xn→	xn→	PROPN
ejpam-5155	233	1	1+γ	1+γ	NUM
ejpam-5155	233	2	δ	δ	NOUN
ejpam-5155	233	3	(	(	PUNCT
ejpam-5155	233	4	δxnyn	δxnyn	ADJ
ejpam-5155	233	5	−	−	PROPN
ejpam-5155	233	6	γyn	γyn	PROPN
ejpam-5155	233	7	)	)	PUNCT
ejpam-5155	233	8	lim	lim	PROPN
ejpam-5155	233	9	xn→	xn→	PROPN
ejpam-5155	234	1	1+γ	1+γ	NUM
ejpam-5155	234	2	δ	δ	PROPN
ejpam-5155	234	3	h(xn	h(xn	PROPN
ejpam-5155	234	4	,	,	PUNCT
ejpam-5155	234	5	yn	yn	PROPN
ejpam-5155	234	6	)	)	PUNCT
ejpam-5155	235	1	=	=	VERB
ejpam-5155	235	2	lim	lim	PROPN
ejpam-5155	235	3	xn→	xn→	PROPN
ejpam-5155	236	1	1+γ	1+γ	NUM
ejpam-5155	236	2	δ	δ	NOUN
ejpam-5155	236	3	(	(	PUNCT
ejpam-5155	236	4	2.1xnyn	2.1xnyn	NUM
ejpam-5155	236	5	−	−	NOUN
ejpam-5155	236	6	1.1yn	1.1yn	NUM
ejpam-5155	236	7	)	)	PUNCT
ejpam-5155	236	8	=	=	SYM
ejpam-5155	236	9	yn	yn	PROPN
ejpam-5155	236	10	lim	lim	PROPN
ejpam-5155	236	11	xn→	xn→	PROPN
ejpam-5155	237	1	1+γ	1+γ	NUM
ejpam-5155	237	2	δ	δ	NOUN
ejpam-5155	237	3	(	(	PUNCT
ejpam-5155	237	4	2.1xn	2.1xn	PROPN
ejpam-5155	237	5	−	−	PROPN
ejpam-5155	237	6	1.1	1.1	NUM
ejpam-5155	237	7	)	)	PUNCT
ejpam-5155	237	8	then	then	ADV
ejpam-5155	237	9	for	for	ADP
ejpam-5155	237	10	xn	xn	PROPN
ejpam-5155	237	11	=	=	SYM
ejpam-5155	237	12	1	1	NUM
ejpam-5155	237	13	+	+	CCONJ
ejpam-5155	237	14	γ	γ	PROPN
ejpam-5155	237	15	δ	δ	PROPN
ejpam-5155	237	16	,	,	PUNCT
ejpam-5155	237	17	when	when	SCONJ
ejpam-5155	237	18	n	n	X
ejpam-5155	237	19	=	=	SYM
ejpam-5155	237	20	0	0	NUM
ejpam-5155	237	21	,	,	PUNCT
ejpam-5155	237	22	implies	imply	VERB
ejpam-5155	237	23	x0	x0	PROPN
ejpam-5155	237	24	=	=	SYM
ejpam-5155	237	25	1	1	NUM
ejpam-5155	237	26	+	+	CCONJ
ejpam-5155	237	27	γ	γ	X
ejpam-5155	237	28	δ	δ	NOUN
ejpam-5155	237	29	=	=	SYM
ejpam-5155	237	30	1	1	NUM
ejpam-5155	237	31	+	+	NUM
ejpam-5155	237	32	1.1	1.1	NUM
ejpam-5155	237	33	2.1	2.1	NUM
ejpam-5155	237	34	=	=	SYM
ejpam-5155	237	35	1	1	NUM
ejpam-5155	237	36	,	,	PUNCT
ejpam-5155	237	37	also	also	ADV
ejpam-5155	237	38	,	,	PUNCT
ejpam-5155	237	39	for	for	SCONJ
ejpam-5155	237	40	y1	y1	PROPN
ejpam-5155	237	41	implies	imply	VERB
ejpam-5155	237	42	y1	y1	NOUN
ejpam-5155	237	43	=	=	SYM
ejpam-5155	237	44	lim	lim	PROPN
ejpam-5155	237	45	xo→1	xo→1	PROPN
ejpam-5155	237	46	h(x0	h(x0	PROPN
ejpam-5155	237	47	,	,	PUNCT
ejpam-5155	237	48	y0	y0	PROPN
ejpam-5155	237	49	)	)	PUNCT
ejpam-5155	237	50	=	=	SYM
ejpam-5155	238	1	y0	y0	NUM
ejpam-5155	238	2	lim	lim	NOUN
ejpam-5155	238	3	x0→1	x0→1	PROPN
ejpam-5155	238	4	(	(	PUNCT
ejpam-5155	238	5	2.1x0	2.1x0	NUM
ejpam-5155	238	6	−	−	NOUN
ejpam-5155	238	7	1.1	1.1	NUM
ejpam-5155	238	8	)	)	PUNCT
ejpam-5155	238	9	=	=	NOUN
ejpam-5155	238	10	0.008[2.1(1)−	0.008[2.1(1)−	NOUN
ejpam-5155	238	11	1.1	1.1	NUM
ejpam-5155	238	12	]	]	PUNCT
ejpam-5155	238	13	=	=	SYM
ejpam-5155	238	14	0.08	0.08	NUM
ejpam-5155	238	15	hence	hence	ADV
ejpam-5155	238	16	,	,	PUNCT
ejpam-5155	238	17	y1	y1	NOUN
ejpam-5155	238	18	=	=	SYM
ejpam-5155	238	19	y0	y0	NOUN
ejpam-5155	238	20	=	=	NOUN
ejpam-5155	238	21	0.08	0.08	NUM
ejpam-5155	238	22	now	now	ADV
ejpam-5155	238	23	,	,	PUNCT
ejpam-5155	238	24	using	use	VERB
ejpam-5155	238	25	y1	y1	NOUN
ejpam-5155	238	26	=	=	NUM
ejpam-5155	238	27	0.08	0.08	NUM
ejpam-5155	238	28	as	as	ADP
ejpam-5155	238	29	the	the	DET
ejpam-5155	238	30	initial	initial	ADJ
ejpam-5155	238	31	value	value	NOUN
ejpam-5155	238	32	for	for	ADP
ejpam-5155	238	33	the	the	DET
ejpam-5155	238	34	next	next	ADJ
ejpam-5155	238	35	iteration	iteration	NOUN
ejpam-5155	238	36	y2	y2	PROPN
ejpam-5155	238	37	and	and	CCONJ
ejpam-5155	238	38	taking	take	VERB
ejpam-5155	238	39	different	different	ADJ
ejpam-5155	238	40	values	value	NOUN
ejpam-5155	238	41	for	for	ADP
ejpam-5155	238	42	the	the	DET
ejpam-5155	238	43	parameters	parameter	NOUN
ejpam-5155	238	44	of	of	ADP
ejpam-5155	238	45	x	x	SYM
ejpam-5155	238	46	coordinate	coordinate	NOUN
ejpam-5155	238	47	,	,	PUNCT
ejpam-5155	238	48	that	that	ADV
ejpam-5155	238	49	is	be	AUX
ejpam-5155	238	50	;	;	PUNCT
ejpam-5155	238	51	γ	γ	X
ejpam-5155	238	52	=	=	SYM
ejpam-5155	238	53	10	10	NUM
ejpam-5155	238	54	,	,	PUNCT
ejpam-5155	238	55	δ	δ	PROPN
ejpam-5155	238	56	=	=	NOUN
ejpam-5155	238	57	12	12	NUM
ejpam-5155	238	58	at	at	ADP
ejpam-5155	238	59	n	n	NOUN
ejpam-5155	238	60	=	=	SYM
ejpam-5155	238	61	1	1	NUM
ejpam-5155	238	62	that	that	PRON
ejpam-5155	238	63	is	be	AUX
ejpam-5155	238	64	lim	lim	PROPN
ejpam-5155	238	65	xn→	xn→	PROPN
ejpam-5155	239	1	1+γ	1+γ	NUM
ejpam-5155	239	2	δ	δ	PROPN
ejpam-5155	239	3	h(xn	h(xn	PROPN
ejpam-5155	239	4	,	,	PUNCT
ejpam-5155	239	5	yn	yn	PROPN
ejpam-5155	239	6	)	)	PUNCT
ejpam-5155	240	1	=	=	VERB
ejpam-5155	240	2	lim	lim	PROPN
ejpam-5155	240	3	xn→	xn→	PROPN
ejpam-5155	241	1	1+γ	1+γ	NUM
ejpam-5155	241	2	δ	δ	PROPN
ejpam-5155	241	3	(	(	PUNCT
ejpam-5155	241	4	12xnyn	12xnyn	NUM
ejpam-5155	241	5	−	−	NUM
ejpam-5155	241	6	10yn	10yn	NOUN
ejpam-5155	241	7	)	)	PUNCT
ejpam-5155	241	8	m.	m.	NOUN
ejpam-5155	242	1	o.	o.	PROPN
ejpam-5155	242	2	fokuoet	fokuoet	PROPN
ejpam-5155	242	3	al	al	PROPN
ejpam-5155	242	4	.	.	PUNCT
ejpam-5155	242	5	/	/	SYM
ejpam-5155	242	6	eur	eur	PROPN
ejpam-5155	242	7	.	.	PUNCT
ejpam-5155	243	1	j.	j.	PROPN
ejpam-5155	243	2	pure	pure	PROPN
ejpam-5155	243	3	appl	appl	PROPN
ejpam-5155	243	4	.	.	PROPN
ejpam-5155	243	5	math	math	PROPN
ejpam-5155	243	6	,	,	PUNCT
ejpam-5155	243	7	17	17	NUM
ejpam-5155	243	8	(	(	PUNCT
ejpam-5155	243	9	2	2	NUM
ejpam-5155	243	10	)	)	PUNCT
ejpam-5155	243	11	(	(	PUNCT
ejpam-5155	243	12	2024	2024	NUM
ejpam-5155	243	13	)	)	PUNCT
ejpam-5155	243	14	,	,	PUNCT
ejpam-5155	243	15	1294	1294	NUM
ejpam-5155	243	16	-	-	SYM
ejpam-5155	243	17	1305	1305	NUM
ejpam-5155	243	18	1304	1304	NUM
ejpam-5155	243	19	=	=	SYM
ejpam-5155	243	20	yn	yn	PROPN
ejpam-5155	243	21	lim	lim	PROPN
ejpam-5155	243	22	xn→	xn→	PROPN
ejpam-5155	244	1	1+γ	1+γ	NUM
ejpam-5155	244	2	δ	δ	NOUN
ejpam-5155	244	3	(	(	PUNCT
ejpam-5155	244	4	12xn	12xn	ADJ
ejpam-5155	244	5	−	−	NOUN
ejpam-5155	244	6	10	10	NUM
ejpam-5155	244	7	)	)	PUNCT
ejpam-5155	244	8	x1	x1	NOUN
ejpam-5155	245	1	=	=	SYM
ejpam-5155	245	2	11	11	NUM
ejpam-5155	245	3	12	12	NUM
ejpam-5155	245	4	=	=	SYM
ejpam-5155	245	5	0.92	0.92	NUM
ejpam-5155	245	6	(	(	PUNCT
ejpam-5155	245	7	x1	x1	PROPN
ejpam-5155	245	8	,	,	PUNCT
ejpam-5155	245	9	y1	y1	NOUN
ejpam-5155	245	10	)	)	PUNCT
ejpam-5155	245	11	=	=	SYM
ejpam-5155	245	12	(	(	PUNCT
ejpam-5155	245	13	0.92	0.92	NUM
ejpam-5155	245	14	,	,	PUNCT
ejpam-5155	245	15	0.08	0.08	NUM
ejpam-5155	245	16	)	)	PUNCT
ejpam-5155	246	1	y2	y2	NOUN
ejpam-5155	246	2	=	=	SYM
ejpam-5155	247	1	lim	lim	PROPN
ejpam-5155	247	2	x1→0.92	x1→0.92	PROPN
ejpam-5155	247	3	h(x1	h(x1	PROPN
ejpam-5155	247	4	,	,	PUNCT
ejpam-5155	247	5	y1	y1	NOUN
ejpam-5155	247	6	)	)	PUNCT
ejpam-5155	247	7	=	=	SYM
ejpam-5155	247	8	y1	y1	PROPN
ejpam-5155	247	9	lim	lim	PROPN
ejpam-5155	247	10	x1→0.92	x1→0.92	PROPN
ejpam-5155	247	11	(	(	PUNCT
ejpam-5155	247	12	12x1	12x1	NUM
ejpam-5155	247	13	−	−	NOUN
ejpam-5155	247	14	10	10	NUM
ejpam-5155	247	15	)	)	PUNCT
ejpam-5155	247	16	=	=	PUNCT
ejpam-5155	248	1	0.08[12(0.92)−	0.08[12(0.92)−	NOUN
ejpam-5155	248	2	10	10	NUM
ejpam-5155	248	3	]	]	X
ejpam-5155	248	4	=	=	SYM
ejpam-5155	248	5	0.08	0.08	NUM
ejpam-5155	248	6	again	again	ADV
ejpam-5155	248	7	the	the	DET
ejpam-5155	248	8	final	final	ADJ
ejpam-5155	248	9	value	value	NOUN
ejpam-5155	248	10	of	of	ADP
ejpam-5155	248	11	y2	y2	PROPN
ejpam-5155	248	12	=	=	PUNCT
ejpam-5155	248	13	y1	y1	NOUN
ejpam-5155	248	14	=	=	PUNCT
ejpam-5155	248	15	0.08	0.08	NUM
ejpam-5155	248	16	hence	hence	ADV
ejpam-5155	248	17	,	,	PUNCT
ejpam-5155	248	18	from	from	ADP
ejpam-5155	248	19	the	the	DET
ejpam-5155	248	20	iteration	iteration	NOUN
ejpam-5155	248	21	process	process	NOUN
ejpam-5155	248	22	so	so	ADV
ejpam-5155	248	23	far	far	ADV
ejpam-5155	248	24	,	,	PUNCT
ejpam-5155	248	25	the	the	DET
ejpam-5155	248	26	limit	limit	NOUN
ejpam-5155	248	27	of	of	ADP
ejpam-5155	248	28	yn+1	yn+1	PROPN
ejpam-5155	248	29	is	be	AUX
ejpam-5155	248	30	the	the	DET
ejpam-5155	248	31	same	same	ADJ
ejpam-5155	248	32	as	as	ADP
ejpam-5155	248	33	that	that	PRON
ejpam-5155	248	34	of	of	ADP
ejpam-5155	248	35	(	(	PUNCT
ejpam-5155	248	36	yn	yn	PROPN
ejpam-5155	248	37	)	)	PUNCT
ejpam-5155	248	38	and	and	CCONJ
ejpam-5155	248	39	keeps	keep	VERB
ejpam-5155	248	40	repeating	repeat	VERB
ejpam-5155	248	41	itself	itself	PRON
ejpam-5155	248	42	.	.	PUNCT
ejpam-5155	249	1	thus	thus	ADV
ejpam-5155	249	2	,	,	PUNCT
ejpam-5155	249	3	indicating	indicate	VERB
ejpam-5155	249	4	that	that	SCONJ
ejpam-5155	249	5	yn	yn	PRON
ejpam-5155	249	6	=	=	PUNCT
ejpam-5155	249	7	α−1	α−1	PROPN
ejpam-5155	249	8	β	β	NOUN
ejpam-5155	249	9	is	be	AUX
ejpam-5155	249	10	a	a	DET
ejpam-5155	249	11	fixed	fix	VERB
ejpam-5155	249	12	point	point	NOUN
ejpam-5155	249	13	of	of	ADP
ejpam-5155	249	14	the	the	DET
ejpam-5155	249	15	function	function	NOUN
ejpam-5155	249	16	.	.	PUNCT
ejpam-5155	250	1	which	which	PRON
ejpam-5155	250	2	implies	imply	VERB
ejpam-5155	250	3	that	that	SCONJ
ejpam-5155	250	4	:	:	PUNCT
ejpam-5155	250	5	when	when	SCONJ
ejpam-5155	250	6	n	n	X
ejpam-5155	250	7	=	=	SYM
ejpam-5155	250	8	0	0	NUM
ejpam-5155	250	9	,	,	PUNCT
ejpam-5155	250	10	y1	y1	NOUN
ejpam-5155	250	11	=	=	SYM
ejpam-5155	250	12	h(y0	h(y0	ADJ
ejpam-5155	250	13	)	)	PUNCT
ejpam-5155	251	1	=	=	PUNCT
ejpam-5155	251	2	y0	y0	NOUN
ejpam-5155	251	3	when	when	SCONJ
ejpam-5155	251	4	n	n	X
ejpam-5155	251	5	=	=	SYM
ejpam-5155	251	6	1	1	NUM
ejpam-5155	251	7	,	,	PUNCT
ejpam-5155	251	8	y2	y2	NOUN
ejpam-5155	251	9	=	=	SYM
ejpam-5155	251	10	h(y1	h(y1	NOUN
ejpam-5155	251	11	)	)	PUNCT
ejpam-5155	251	12	=	=	PUNCT
ejpam-5155	252	1	y1	y1	INTJ
ejpam-5155	252	2	when	when	SCONJ
ejpam-5155	252	3	n	n	X
ejpam-5155	252	4	=	=	SYM
ejpam-5155	252	5	2	2	NUM
ejpam-5155	252	6	,	,	PUNCT
ejpam-5155	252	7	y3	y3	NOUN
ejpam-5155	252	8	=	=	SYM
ejpam-5155	252	9	h(y2	h(y2	PROPN
ejpam-5155	252	10	)	)	PUNCT
ejpam-5155	253	1	=	=	PUNCT
ejpam-5155	253	2	y2	y2	INTJ
ejpam-5155	253	3	...	...	PUNCT
ejpam-5155	253	4	when	when	SCONJ
ejpam-5155	253	5	n	n	X
ejpam-5155	253	6	=	=	SYM
ejpam-5155	253	7	k	k	NOUN
ejpam-5155	253	8	,	,	PUNCT
ejpam-5155	253	9	yk+1	yk+1	NOUN
ejpam-5155	253	10	=	=	SYM
ejpam-5155	253	11	h(yk	h(yk	PROPN
ejpam-5155	253	12	)	)	PUNCT
ejpam-5155	253	13	=	=	SYM
ejpam-5155	253	14	yk	yk	PROPN
ejpam-5155	253	15	clearly	clearly	ADV
ejpam-5155	253	16	,	,	PUNCT
ejpam-5155	253	17	at	at	ADP
ejpam-5155	253	18	a	a	DET
ejpam-5155	253	19	fixed	fix	VERB
ejpam-5155	253	20	value	value	NOUN
ejpam-5155	253	21	of	of	ADP
ejpam-5155	253	22	γ	γ	PROPN
ejpam-5155	253	23	,	,	PUNCT
ejpam-5155	253	24	δ	δ	PROPN
ejpam-5155	253	25	,	,	PUNCT
ejpam-5155	253	26	α	α	PROPN
ejpam-5155	253	27	,	,	PUNCT
ejpam-5155	253	28	β	β	NOUN
ejpam-5155	253	29	for	for	ADP
ejpam-5155	253	30	h(xn	h(xn	PROPN
ejpam-5155	253	31	,	,	PUNCT
ejpam-5155	253	32	yn	yn	PROPN
ejpam-5155	253	33	)	)	PUNCT
ejpam-5155	253	34	and	and	CCONJ
ejpam-5155	253	35	f(xn	f(xn	PROPN
ejpam-5155	253	36	,	,	PUNCT
ejpam-5155	253	37	yn	yn	PROPN
ejpam-5155	253	38	)	)	PUNCT
ejpam-5155	253	39	,	,	PUNCT
ejpam-5155	253	40	i.e.	i.e.	X
ejpam-5155	253	41	,	,	PUNCT
ejpam-5155	253	42	(	(	PUNCT
ejpam-5155	253	43	γ	γ	X
ejpam-5155	253	44	=	=	SYM
ejpam-5155	253	45	1.1	1.1	NUM
ejpam-5155	253	46	,	,	PUNCT
ejpam-5155	253	47	δ	δ	PROPN
ejpam-5155	253	48	=	=	PUNCT
ejpam-5155	253	49	2.1	2.1	NUM
ejpam-5155	253	50	,	,	PUNCT
ejpam-5155	253	51	α	α	NOUN
ejpam-5155	253	52	=	=	SYM
ejpam-5155	253	53	1.2	1.2	NUM
ejpam-5155	253	54	,	,	PUNCT
ejpam-5155	253	55	β	β	X
ejpam-5155	253	56	=	=	X
ejpam-5155	253	57	2.5),the	2.5),the	DET
ejpam-5155	253	58	functions	function	NOUN
ejpam-5155	253	59	have	have	AUX
ejpam-5155	253	60	fixed	fix	VERB
ejpam-5155	253	61	values	value	NOUN
ejpam-5155	253	62	,	,	PUNCT
ejpam-5155	253	63	for	for	ADP
ejpam-5155	253	64	instance	instance	NOUN
ejpam-5155	253	65	,	,	PUNCT
ejpam-5155	253	66	(	(	PUNCT
ejpam-5155	253	67	1	1	NUM
ejpam-5155	253	68	,	,	PUNCT
ejpam-5155	253	69	0.08	0.08	NUM
ejpam-5155	253	70	)	)	PUNCT
ejpam-5155	253	71	irrespective	irrespective	ADV
ejpam-5155	253	72	of	of	ADP
ejpam-5155	253	73	the	the	DET
ejpam-5155	253	74	number	number	NOUN
ejpam-5155	253	75	of	of	ADP
ejpam-5155	253	76	successive	successive	ADJ
ejpam-5155	253	77	iterations	iteration	NOUN
ejpam-5155	253	78	and	and	CCONJ
ejpam-5155	253	79	the	the	DET
ejpam-5155	253	80	values	value	NOUN
ejpam-5155	253	81	for	for	ADP
ejpam-5155	253	82	the	the	DET
ejpam-5155	253	83	parameters	parameter	NOUN
ejpam-5155	253	84	of	of	ADP
ejpam-5155	253	85	the	the	DET
ejpam-5155	253	86	x	x	X
ejpam-5155	253	87	and	and	CCONJ
ejpam-5155	253	88	y	y	PROPN
ejpam-5155	253	89	coordinates	coordinate	NOUN
ejpam-5155	253	90	.	.	PUNCT
ejpam-5155	254	1	this	this	PRON
ejpam-5155	254	2	indicates	indicate	VERB
ejpam-5155	254	3	that	that	SCONJ
ejpam-5155	254	4	the	the	DET
ejpam-5155	254	5	structure	structure	NOUN
ejpam-5155	254	6	of	of	ADP
ejpam-5155	254	7	the	the	DET
ejpam-5155	254	8	fixed	fix	VERB
ejpam-5155	254	9	orbits	orbit	NOUN
ejpam-5155	254	10	of	of	ADP
ejpam-5155	254	11	the	the	DET
ejpam-5155	254	12	function	function	NOUN
ejpam-5155	254	13	is	be	AUX
ejpam-5155	254	14	in	in	ADP
ejpam-5155	254	15	equilibrium	equilibrium	NOUN
ejpam-5155	254	16	as	as	SCONJ
ejpam-5155	254	17	it	it	PRON
ejpam-5155	254	18	travels	travel	VERB
ejpam-5155	254	19	through	through	ADP
ejpam-5155	254	20	time	time	NOUN
ejpam-5155	254	21	with	with	ADP
ejpam-5155	254	22	a	a	DET
ejpam-5155	254	23	stable	stable	ADJ
ejpam-5155	254	24	and	and	CCONJ
ejpam-5155	254	25	continuous	continuous	ADJ
ejpam-5155	254	26	movement	movement	NOUN
ejpam-5155	254	27	.	.	PUNCT
ejpam-5155	255	1	4	4	X
ejpam-5155	255	2	.	.	X
ejpam-5155	255	3	conclusion	conclusion	NOUN
ejpam-5155	255	4	the	the	DET
ejpam-5155	255	5	lotka	lotka	PROPN
ejpam-5155	255	6	-	-	PUNCT
ejpam-5155	255	7	volterra	volterra	PROPN
ejpam-5155	255	8	function	function	NOUN
ejpam-5155	255	9	has	have	AUX
ejpam-5155	255	10	been	be	AUX
ejpam-5155	255	11	studied	study	VERB
ejpam-5155	255	12	,	,	PUNCT
ejpam-5155	255	13	and	and	CCONJ
ejpam-5155	255	14	it	it	PRON
ejpam-5155	255	15	shows	show	VERB
ejpam-5155	255	16	that	that	SCONJ
ejpam-5155	255	17	the	the	DET
ejpam-5155	255	18	function	function	NOUN
ejpam-5155	255	19	has	have	VERB
ejpam-5155	255	20	two	two	NUM
ejpam-5155	255	21	sets	set	NOUN
ejpam-5155	255	22	of	of	ADP
ejpam-5155	255	23	roots	root	NOUN
ejpam-5155	255	24	,	,	PUNCT
ejpam-5155	255	25	or	or	CCONJ
ejpam-5155	255	26	zeros	zero	NOUN
ejpam-5155	255	27	.	.	PUNCT
ejpam-5155	256	1	(	(	PUNCT
ejpam-5155	256	2	0	0	NUM
ejpam-5155	256	3	,	,	PUNCT
ejpam-5155	256	4	0	0	NUM
ejpam-5155	256	5	)	)	PUNCT
ejpam-5155	256	6	and	and	CCONJ
ejpam-5155	256	7	(	(	PUNCT
ejpam-5155	256	8	γ	γ	PROPN
ejpam-5155	256	9	δ	δ	PROPN
ejpam-5155	256	10	,	,	PUNCT
ejpam-5155	256	11	α	α	X
ejpam-5155	256	12	β	β	NOUN
ejpam-5155	256	13	)	)	PUNCT
ejpam-5155	256	14	where	where	SCONJ
ejpam-5155	256	15	the	the	DET
ejpam-5155	256	16	latter	latter	ADJ
ejpam-5155	256	17	depends	depend	VERB
ejpam-5155	256	18	on	on	ADP
ejpam-5155	256	19	the	the	DET
ejpam-5155	256	20	parameters	parameter	NOUN
ejpam-5155	256	21	of	of	ADP
ejpam-5155	256	22	the	the	DET
ejpam-5155	256	23	function	function	NOUN
ejpam-5155	256	24	.	.	PUNCT
ejpam-5155	257	1	again	again	ADV
ejpam-5155	257	2	,	,	PUNCT
ejpam-5155	257	3	there	there	PRON
ejpam-5155	257	4	are	be	VERB
ejpam-5155	257	5	four	four	NUM
ejpam-5155	257	6	solutions	solution	NOUN
ejpam-5155	257	7	of	of	ADP
ejpam-5155	257	8	the	the	DET
ejpam-5155	257	9	function	function	NOUN
ejpam-5155	257	10	(	(	PUNCT
ejpam-5155	257	11	0	0	NUM
ejpam-5155	257	12	,	,	PUNCT
ejpam-5155	257	13	0	0	NUM
ejpam-5155	257	14	)	)	PUNCT
ejpam-5155	257	15	,	,	PUNCT
ejpam-5155	257	16	(	(	PUNCT
ejpam-5155	257	17	0	0	NUM
ejpam-5155	257	18	,	,	PUNCT
ejpam-5155	257	19	α−1	α−1	PROPN
ejpam-5155	257	20	β	β	NOUN
ejpam-5155	257	21	)	)	PUNCT
ejpam-5155	257	22	,	,	PUNCT
ejpam-5155	257	23	(	(	PUNCT
ejpam-5155	257	24	1+γ	1+γ	NUM
ejpam-5155	257	25	δ	δ	PROPN
ejpam-5155	257	26	,	,	PUNCT
ejpam-5155	257	27	0	0	NUM
ejpam-5155	257	28	)	)	PUNCT
ejpam-5155	257	29	and	and	CCONJ
ejpam-5155	257	30	(	(	PUNCT
ejpam-5155	257	31	1+γ	1+γ	NUM
ejpam-5155	257	32	δ	δ	PROPN
ejpam-5155	257	33	,	,	PUNCT
ejpam-5155	257	34	α−1	α−1	PROPN
ejpam-5155	257	35	β	β	PROPN
ejpam-5155	257	36	)	)	PUNCT
ejpam-5155	257	37	,	,	PUNCT
ejpam-5155	257	38	where	where	SCONJ
ejpam-5155	257	39	(	(	PUNCT
ejpam-5155	257	40	0	0	NUM
ejpam-5155	257	41	,	,	PUNCT
ejpam-5155	257	42	0	0	NUM
ejpam-5155	257	43	)	)	PUNCT
ejpam-5155	257	44	as	as	ADP
ejpam-5155	257	45	a	a	DET
ejpam-5155	257	46	trivial	trivial	ADJ
ejpam-5155	257	47	solution	solution	NOUN
ejpam-5155	257	48	always	always	ADV
ejpam-5155	257	49	exits	exit	VERB
ejpam-5155	257	50	but	but	CCONJ
ejpam-5155	257	51	the	the	DET
ejpam-5155	257	52	existence	existence	NOUN
ejpam-5155	257	53	of	of	ADP
ejpam-5155	257	54	(	(	PUNCT
ejpam-5155	257	55	1+γ	1+γ	PROPN
ejpam-5155	257	56	δ	δ	PROPN
ejpam-5155	257	57	,	,	PUNCT
ejpam-5155	257	58	α−1	α−1	PROPN
ejpam-5155	257	59	β	β	X
ejpam-5155	257	60	)	)	PUNCT
ejpam-5155	257	61	depends	depend	VERB
ejpam-5155	257	62	on	on	ADP
ejpam-5155	257	63	the	the	DET
ejpam-5155	257	64	parameters	parameter	NOUN
ejpam-5155	257	65	of	of	ADP
ejpam-5155	257	66	the	the	DET
ejpam-5155	257	67	function.the	function.the	DET
ejpam-5155	257	68	study	study	NOUN
ejpam-5155	257	69	also	also	ADV
ejpam-5155	257	70	shows	show	VERB
ejpam-5155	257	71	that	that	SCONJ
ejpam-5155	257	72	the	the	DET
ejpam-5155	257	73	solutions	solution	NOUN
ejpam-5155	257	74	of	of	ADP
ejpam-5155	257	75	the	the	DET
ejpam-5155	257	76	function	function	NOUN
ejpam-5155	257	77	are	be	AUX
ejpam-5155	257	78	the	the	DET
ejpam-5155	257	79	fixed	fix	VERB
ejpam-5155	257	80	points	point	NOUN
ejpam-5155	257	81	of	of	ADP
ejpam-5155	257	82	the	the	DET
ejpam-5155	257	83	function	function	NOUN
ejpam-5155	257	84	,	,	PUNCT
ejpam-5155	257	85	and	and	CCONJ
ejpam-5155	257	86	the	the	DET
ejpam-5155	257	87	limit	limit	NOUN
ejpam-5155	257	88	points	point	NOUN
ejpam-5155	257	89	,	,	PUNCT
ejpam-5155	257	90	as	as	ADP
ejpam-5155	257	91	the	the	DET
ejpam-5155	257	92	fixed	fix	VERB
ejpam-5155	257	93	points	point	NOUN
ejpam-5155	257	94	of	of	ADP
ejpam-5155	257	95	the	the	DET
ejpam-5155	257	96	function	function	NOUN
ejpam-5155	257	97	,	,	PUNCT
ejpam-5155	257	98	are	be	AUX
ejpam-5155	257	99	asymptotically	asymptotically	ADV
ejpam-5155	257	100	stable	stable	ADJ
ejpam-5155	257	101	and	and	CCONJ
ejpam-5155	257	102	continuous	continuous	ADJ
ejpam-5155	257	103	after	after	ADP
ejpam-5155	257	104	several	several	ADJ
ejpam-5155	257	105	iterations	iteration	NOUN
ejpam-5155	257	106	.	.	PUNCT
ejpam-5155	258	1	the	the	DET
ejpam-5155	258	2	outcome	outcome	NOUN
ejpam-5155	258	3	of	of	ADP
ejpam-5155	258	4	the	the	DET
ejpam-5155	258	5	fixed	fix	VERB
ejpam-5155	258	6	points	point	NOUN
ejpam-5155	258	7	after	after	SCONJ
ejpam-5155	258	8	several	several	ADJ
ejpam-5155	258	9	iterations	iteration	NOUN
ejpam-5155	258	10	forms	form	VERB
ejpam-5155	258	11	a	a	DET
ejpam-5155	258	12	fixed	fix	VERB
ejpam-5155	258	13	orbit	orbit	NOUN
ejpam-5155	258	14	structure	structure	NOUN
ejpam-5155	258	15	of	of	ADP
ejpam-5155	258	16	the	the	DET
ejpam-5155	258	17	function	function	NOUN
ejpam-5155	258	18	,	,	PUNCT
ejpam-5155	258	19	irrespective	irrespective	ADV
ejpam-5155	258	20	of	of	ADP
ejpam-5155	258	21	the	the	DET
ejpam-5155	258	22	value	value	NOUN
ejpam-5155	258	23	of	of	ADP
ejpam-5155	258	24	the	the	DET
ejpam-5155	258	25	parameter	parameter	NOUN
ejpam-5155	258	26	.	.	PUNCT
ejpam-5155	259	1	in	in	ADP
ejpam-5155	259	2	addition	addition	NOUN
ejpam-5155	259	3	,	,	PUNCT
ejpam-5155	259	4	the	the	DET
ejpam-5155	259	5	uniqueness	uniqueness	NOUN
ejpam-5155	259	6	of	of	ADP
ejpam-5155	259	7	the	the	DET
ejpam-5155	259	8	fixed	fix	VERB
ejpam-5155	259	9	points	point	NOUN
ejpam-5155	259	10	demonstrates	demonstrate	VERB
ejpam-5155	259	11	the	the	DET
ejpam-5155	259	12	stability	stability	NOUN
ejpam-5155	259	13	and	and	CCONJ
ejpam-5155	259	14	continuity	continuity	NOUN
ejpam-5155	259	15	of	of	ADP
ejpam-5155	259	16	the	the	DET
ejpam-5155	259	17	function	function	NOUN
ejpam-5155	259	18	in	in	ADP
ejpam-5155	259	19	its	its	PRON
ejpam-5155	259	20	steady	steady	ADJ
ejpam-5155	259	21	state	state	NOUN
ejpam-5155	259	22	.	.	PUNCT
ejpam-5155	260	1	references	reference	NOUN
ejpam-5155	260	2	1305	1305	NUM
ejpam-5155	260	3	conflicts	conflict	NOUN
ejpam-5155	260	4	of	of	ADP
ejpam-5155	260	5	interest	interest	NOUN
ejpam-5155	260	6	the	the	DET
ejpam-5155	260	7	authors	author	NOUN
ejpam-5155	260	8	declare	declare	VERB
ejpam-5155	260	9	no	no	DET
ejpam-5155	260	10	conflicts	conflict	NOUN
ejpam-5155	260	11	of	of	ADP
ejpam-5155	260	12	interest	interest	NOUN
ejpam-5155	260	13	and	and	CCONJ
ejpam-5155	260	14	that	that	SCONJ
ejpam-5155	260	15	authors	author	NOUN
ejpam-5155	260	16	are	be	AUX
ejpam-5155	260	17	responsible	responsible	ADJ
ejpam-5155	260	18	for	for	ADP
ejpam-5155	260	19	coauthors	coauthor	NOUN
ejpam-5155	260	20	declaring	declare	VERB
ejpam-5155	260	21	their	their	PRON
ejpam-5155	260	22	interests	interest	NOUN
ejpam-5155	260	23	.	.	PUNCT
ejpam-5155	261	1	data	datum	NOUN
ejpam-5155	261	2	availability	availability	NOUN
ejpam-5155	261	3	no	no	DET
ejpam-5155	261	4	data	datum	NOUN
ejpam-5155	261	5	were	be	AUX
ejpam-5155	261	6	used	use	VERB
ejpam-5155	261	7	to	to	PART
ejpam-5155	261	8	support	support	VERB
ejpam-5155	261	9	this	this	DET
ejpam-5155	261	10	study	study	NOUN
ejpam-5155	261	11	.	.	PUNCT
ejpam-5155	262	1	funding	fund	VERB
ejpam-5155	262	2	this	this	DET
ejpam-5155	262	3	study	study	NOUN
ejpam-5155	262	4	did	do	AUX
ejpam-5155	262	5	not	not	PART
ejpam-5155	262	6	receive	receive	VERB
ejpam-5155	262	7	fund	fund	NOUN
ejpam-5155	262	8	in	in	ADP
ejpam-5155	262	9	any	any	DET
ejpam-5155	262	10	form	form	NOUN
ejpam-5155	262	11	.	.	PUNCT
ejpam-5155	263	1	references	reference	NOUN
ejpam-5155	263	2	[	[	X
ejpam-5155	263	3	1	1	NUM
ejpam-5155	263	4	]	]	X
ejpam-5155	263	5	saleh	saleh	PROPN
ejpam-5155	263	6	almezel	almezel	PROPN
ejpam-5155	263	7	,	,	PUNCT
ejpam-5155	263	8	qamrul	qamrul	PROPN
ejpam-5155	263	9	hasan	hasan	PROPN
ejpam-5155	263	10	ansari	ansari	PROPN
ejpam-5155	263	11	,	,	PUNCT
ejpam-5155	263	12	mohamed	mohamed	ADJ
ejpam-5155	263	13	amine	amine	ADJ
ejpam-5155	263	14	khamsi	khamsi	PROPN
ejpam-5155	263	15	,	,	PUNCT
ejpam-5155	263	16	et	et	PROPN
ejpam-5155	263	17	al	al	PROPN
ejpam-5155	263	18	.	.	PUNCT
ejpam-5155	264	1	topics	topic	NOUN
ejpam-5155	264	2	in	in	ADP
ejpam-5155	264	3	fixed	fix	VERB
ejpam-5155	264	4	point	point	NOUN
ejpam-5155	264	5	theory	theory	NOUN
ejpam-5155	264	6	,	,	PUNCT
ejpam-5155	264	7	volume	volume	NOUN
ejpam-5155	264	8	5	5	NUM
ejpam-5155	264	9	.	.	PUNCT
ejpam-5155	264	10	springer	springer	NOUN
ejpam-5155	264	11	,	,	PUNCT
ejpam-5155	264	12	2014	2014	NUM
ejpam-5155	264	13	.	.	PUNCT
ejpam-5155	265	1	[	[	X
ejpam-5155	265	2	2	2	NUM
ejpam-5155	265	3	]	]	X
ejpam-5155	265	4	mira	mira	PROPN
ejpam-5155	265	5	-	-	PUNCT
ejpam-5155	265	6	cristiana	cristiana	PROPN
ejpam-5155	265	7	anisiu	anisiu	PROPN
ejpam-5155	265	8	.	.	PUNCT
ejpam-5155	266	1	lotka	lotka	PROPN
ejpam-5155	266	2	,	,	PUNCT
ejpam-5155	266	3	volterra	volterra	NOUN
ejpam-5155	266	4	and	and	CCONJ
ejpam-5155	266	5	their	their	PRON
ejpam-5155	266	6	model	model	NOUN
ejpam-5155	266	7	.	.	PUNCT
ejpam-5155	267	1	didáctica	didáctica	PROPN
ejpam-5155	267	2	mathematica	mathematica	PROPN
ejpam-5155	267	3	,	,	PUNCT
ejpam-5155	267	4	32(01	32(01	NUM
ejpam-5155	267	5	)	)	PUNCT
ejpam-5155	267	6	,	,	PUNCT
ejpam-5155	267	7	2014	2014	NUM
ejpam-5155	267	8	.	.	PUNCT
ejpam-5155	268	1	[	[	X
ejpam-5155	268	2	3	3	X
ejpam-5155	268	3	]	]	X
ejpam-5155	268	4	stephen	stephen	PROPN
ejpam-5155	268	5	baigent	baigent	PROPN
ejpam-5155	268	6	.	.	PUNCT
ejpam-5155	269	1	lotka	lotka	PROPN
ejpam-5155	269	2	–	–	PUNCT
ejpam-5155	269	3	volterra	volterra	NOUN
ejpam-5155	269	4	dynamical	dynamical	ADJ
ejpam-5155	269	5	systems	system	NOUN
ejpam-5155	269	6	.	.	PUNCT
ejpam-5155	270	1	in	in	ADP
ejpam-5155	270	2	dynamical	dynamical	ADJ
ejpam-5155	270	3	and	and	CCONJ
ejpam-5155	270	4	complex	complex	ADJ
ejpam-5155	270	5	systems	system	NOUN
ejpam-5155	270	6	,	,	PUNCT
ejpam-5155	270	7	pages	page	NOUN
ejpam-5155	270	8	157–188	157–188	NUM
ejpam-5155	270	9	.	.	PUNCT
ejpam-5155	271	1	world	world	NOUN
ejpam-5155	271	2	scientific	scientific	ADJ
ejpam-5155	271	3	,	,	PUNCT
ejpam-5155	271	4	2017	2017	NUM
ejpam-5155	271	5	.	.	PUNCT
ejpam-5155	272	1	[	[	X
ejpam-5155	272	2	4	4	X
ejpam-5155	272	3	]	]	PUNCT
ejpam-5155	272	4	michael	michael	PROPN
ejpam-5155	272	5	brin	brin	PROPN
ejpam-5155	272	6	and	and	CCONJ
ejpam-5155	272	7	garrett	garrett	PROPN
ejpam-5155	272	8	stuck	stick	VERB
ejpam-5155	272	9	.	.	PUNCT
ejpam-5155	273	1	introduction	introduction	NOUN
ejpam-5155	273	2	to	to	ADP
ejpam-5155	273	3	dynamical	dynamical	ADJ
ejpam-5155	273	4	systems	system	NOUN
ejpam-5155	273	5	.	.	PUNCT
ejpam-5155	274	1	cambridge	cambridge	PROPN
ejpam-5155	274	2	university	university	PROPN
ejpam-5155	274	3	press	press	NOUN
ejpam-5155	274	4	,	,	PUNCT
ejpam-5155	274	5	2002	2002	NUM
ejpam-5155	274	6	.	.	PUNCT
ejpam-5155	275	1	[	[	X
ejpam-5155	275	2	5	5	NUM
ejpam-5155	275	3	]	]	X
ejpam-5155	275	4	george	george	PROPN
ejpam-5155	275	5	dinca	dinca	PROPN
ejpam-5155	275	6	and	and	CCONJ
ejpam-5155	275	7	jean	jean	PROPN
ejpam-5155	275	8	mawhin	mawhin	PROPN
ejpam-5155	275	9	.	.	PUNCT
ejpam-5155	276	1	history	history	NOUN
ejpam-5155	276	2	of	of	ADP
ejpam-5155	276	3	the	the	DET
ejpam-5155	276	4	brouwer	brouwer	PROPN
ejpam-5155	276	5	fixed	fix	VERB
ejpam-5155	276	6	point	point	NOUN
ejpam-5155	276	7	theorem	theorem	VERB
ejpam-5155	276	8	.	.	PROPN
ejpam-5155	277	1	in	in	ADP
ejpam-5155	277	2	brouwer	brouwer	PROPN
ejpam-5155	277	3	degree	degree	NOUN
ejpam-5155	277	4	:	:	PUNCT
ejpam-5155	277	5	the	the	DET
ejpam-5155	277	6	core	core	NOUN
ejpam-5155	277	7	of	of	ADP
ejpam-5155	277	8	nonlinear	nonlinear	ADJ
ejpam-5155	277	9	analysis	analysis	NOUN
ejpam-5155	277	10	,	,	PUNCT
ejpam-5155	277	11	pages	page	NOUN
ejpam-5155	277	12	391–412	391–412	NUM
ejpam-5155	277	13	.	.	PUNCT
ejpam-5155	277	14	springer	springer	NOUN
ejpam-5155	277	15	,	,	PUNCT
ejpam-5155	277	16	2020	2020	NUM
ejpam-5155	277	17	.	.	PUNCT
ejpam-5155	278	1	[	[	X
ejpam-5155	278	2	6	6	NUM
ejpam-5155	278	3	]	]	SYM
ejpam-5155	278	4	hamid	hamid	PROPN
ejpam-5155	278	5	faraji	faraji	PROPN
ejpam-5155	278	6	,	,	PUNCT
ejpam-5155	278	7	dragana	dragana	PROPN
ejpam-5155	278	8	savić	savić	ADV
ejpam-5155	278	9	,	,	PUNCT
ejpam-5155	278	10	and	and	CCONJ
ejpam-5155	278	11	stojan	stojan	ADP
ejpam-5155	278	12	radenović.	radenović.	PRON
ejpam-5155	278	13	fixed	fix	VERB
ejpam-5155	278	14	point	point	NOUN
ejpam-5155	278	15	theorems	theorem	NOUN
ejpam-5155	278	16	for	for	ADP
ejpam-5155	278	17	geraghty	geraghty	PROPN
ejpam-5155	278	18	contraction	contraction	NOUN
ejpam-5155	278	19	type	type	NOUN
ejpam-5155	278	20	mappings	mapping	NOUN
ejpam-5155	278	21	in	in	ADP
ejpam-5155	278	22	b	b	NOUN
ejpam-5155	278	23	-	-	ADJ
ejpam-5155	278	24	metric	metric	ADJ
ejpam-5155	278	25	spaces	space	NOUN
ejpam-5155	278	26	and	and	CCONJ
ejpam-5155	278	27	applications	application	NOUN
ejpam-5155	278	28	.	.	PUNCT
ejpam-5155	279	1	axioms	axiom	NOUN
ejpam-5155	279	2	,	,	PUNCT
ejpam-5155	279	3	8(1):34	8(1):34	NUM
ejpam-5155	279	4	,	,	PUNCT
ejpam-5155	279	5	2019	2019	NUM
ejpam-5155	279	6	.	.	PUNCT
ejpam-5155	280	1	[	[	X
ejpam-5155	280	2	7	7	X
ejpam-5155	280	3	]	]	X
ejpam-5155	280	4	teresa	teresa	NOUN
ejpam-5155	280	5	faria	faria	PROPN
ejpam-5155	280	6	and	and	CCONJ
ejpam-5155	280	7	josé	josé	PROPN
ejpam-5155	281	1	j	j	PROPN
ejpam-5155	281	2	oliveira	oliveira	PROPN
ejpam-5155	281	3	.	.	PUNCT
ejpam-5155	282	1	local	local	ADJ
ejpam-5155	282	2	and	and	CCONJ
ejpam-5155	282	3	global	global	ADJ
ejpam-5155	282	4	stability	stability	NOUN
ejpam-5155	282	5	for	for	ADP
ejpam-5155	282	6	lotka	lotka	PROPN
ejpam-5155	282	7	–	–	PUNCT
ejpam-5155	282	8	volterra	volterra	NOUN
ejpam-5155	282	9	systems	system	NOUN
ejpam-5155	282	10	with	with	ADP
ejpam-5155	282	11	distributed	distribute	VERB
ejpam-5155	282	12	delays	delay	NOUN
ejpam-5155	282	13	and	and	CCONJ
ejpam-5155	282	14	instantaneous	instantaneous	ADJ
ejpam-5155	282	15	negative	negative	ADJ
ejpam-5155	282	16	feedbacks	feedback	NOUN
ejpam-5155	282	17	.	.	PUNCT
ejpam-5155	283	1	journal	journal	NOUN
ejpam-5155	283	2	of	of	ADP
ejpam-5155	283	3	differential	differential	ADJ
ejpam-5155	283	4	equations	equation	NOUN
ejpam-5155	283	5	,	,	PUNCT
ejpam-5155	283	6	244(5):1049–1079	244(5):1049–1079	PROPN
ejpam-5155	283	7	,	,	PUNCT
ejpam-5155	283	8	2008	2008	NUM
ejpam-5155	283	9	.	.	PUNCT
ejpam-5155	284	1	[	[	X
ejpam-5155	284	2	8	8	NUM
ejpam-5155	284	3	]	]	X
ejpam-5155	284	4	france	france	PROPN
ejpam-5155	284	5	-	-	PUNCT
ejpam-5155	284	6	kosovo	kosovo	PROPN
ejpam-5155	284	7	.	.	PUNCT
ejpam-5155	285	1	introduction	introduction	NOUN
ejpam-5155	285	2	to	to	ADP
ejpam-5155	285	3	dynamical	dynamical	ADJ
ejpam-5155	285	4	system	system	NOUN
ejpam-5155	285	5	.	.	PUNCT
ejpam-5155	286	1	city	city	NOUN
ejpam-5155	286	2	,	,	PUNCT
ejpam-5155	286	3	2017	2017	NUM
ejpam-5155	286	4	.	.	PUNCT
ejpam-5155	287	1	[	[	X
ejpam-5155	287	2	9	9	NUM
ejpam-5155	287	3	]	]	X
ejpam-5155	287	4	rp	rp	NOUN
ejpam-5155	287	5	pant	pant	NOUN
ejpam-5155	287	6	,	,	PUNCT
ejpam-5155	287	7	ab	ab	PROPN
ejpam-5155	287	8	lohani	lohani	PROPN
ejpam-5155	287	9	,	,	PUNCT
ejpam-5155	287	10	and	and	CCONJ
ejpam-5155	287	11	k	k	PROPN
ejpam-5155	287	12	jha	jha	PROPN
ejpam-5155	287	13	.	.	PUNCT
ejpam-5155	288	1	a	a	DET
ejpam-5155	288	2	history	history	NOUN
ejpam-5155	288	3	of	of	ADP
ejpam-5155	288	4	fixed	fix	VERB
ejpam-5155	288	5	point	point	NOUN
ejpam-5155	288	6	theorems	theorem	NOUN
ejpam-5155	288	7	.	.	PUNCT
ejpam-5155	288	8	ganita	ganita	PROPN
ejpam-5155	288	9	bharati	bharati	PROPN
ejpam-5155	288	10	,	,	PUNCT
ejpam-5155	288	11	24:147–159	24:147–159	PROPN
ejpam-5155	288	12	,	,	PUNCT
ejpam-5155	288	13	2002	2002	NUM
ejpam-5155	288	14	.	.	PUNCT
ejpam-5155	289	1	[	[	X
ejpam-5155	289	2	10	10	NUM
ejpam-5155	289	3	]	]	X
ejpam-5155	289	4	kl	kl	NOUN
ejpam-5155	289	5	singh	singh	PROPN
ejpam-5155	289	6	.	.	PUNCT
ejpam-5155	290	1	on	on	ADP
ejpam-5155	290	2	some	some	DET
ejpam-5155	290	3	fixed	fix	VERB
ejpam-5155	290	4	point	point	NOUN
ejpam-5155	290	5	theorems	theorem	NOUN
ejpam-5155	290	6	.	.	PUNCT
ejpam-5155	291	1	bulletin	bulletin	PROPN
ejpam-5155	291	2	mathématique	mathématique	PROPN
ejpam-5155	291	3	de	de	X
ejpam-5155	291	4	la	la	PROPN
ejpam-5155	291	5	société	société	PROPN
ejpam-5155	291	6	des	des	PROPN
ejpam-5155	291	7	sciences	science	NOUN
ejpam-5155	291	8	mathématiques	mathématiques	PROPN
ejpam-5155	291	9	de	de	X
ejpam-5155	291	10	la	la	X
ejpam-5155	291	11	république	république	PROPN
ejpam-5155	291	12	socialiste	socialiste	PROPN
ejpam-5155	291	13	de	de	PROPN
ejpam-5155	291	14	roumanie	roumanie	PROPN
ejpam-5155	291	15	,	,	PUNCT
ejpam-5155	291	16	13(3):375–382	13(3):375–382	PROPN
ejpam-5155	291	17	,	,	PUNCT
ejpam-5155	291	18	1969	1969	NUM
ejpam-5155	291	19	.	.	PUNCT
ejpam-5155	292	1	[	[	X
ejpam-5155	292	2	11	11	NUM
ejpam-5155	292	3	]	]	SYM
ejpam-5155	292	4	jaime	jaime	NOUN
ejpam-5155	292	5	e	e	NOUN
ejpam-5155	292	6	villate	villate	NOUN
ejpam-5155	292	7	.	.	PUNCT
ejpam-5155	293	1	introduction	introduction	NOUN
ejpam-5155	293	2	to	to	ADP
ejpam-5155	293	3	dynamical	dynamical	ADJ
ejpam-5155	293	4	systems	system	NOUN
ejpam-5155	293	5	:	:	PUNCT
ejpam-5155	293	6	a	a	DET
ejpam-5155	293	7	hands	hand	NOUN
ejpam-5155	293	8	-	-	PUNCT
ejpam-5155	293	9	on	on	ADP
ejpam-5155	293	10	approach	approach	NOUN
ejpam-5155	293	11	with	with	ADP
ejpam-5155	293	12	maxima	maxima	PROPN
ejpam-5155	293	13	.	.	PUNCT
ejpam-5155	293	14	2007	2007	NUM
ejpam-5155	293	15	.	.	PUNCT