id	sid	tid	token	lemma	pos
ejpam-5564	1	1	european	european	PROPN
ejpam-5564	1	2	journal	journal	PROPN
ejpam-5564	1	3	of	of	ADP
ejpam-5564	1	4	pure	pure	ADJ
ejpam-5564	1	5	and	and	CCONJ
ejpam-5564	1	6	applied	applied	ADJ
ejpam-5564	1	7	mathematics	mathematic	NOUN
ejpam-5564	1	8	2025	2025	NUM
ejpam-5564	1	9	,	,	PUNCT
ejpam-5564	1	10	vol	vol	NOUN
ejpam-5564	1	11	.	.	PROPN
ejpam-5564	1	12	18	18	NUM
ejpam-5564	1	13	,	,	PUNCT
ejpam-5564	1	14	issue	issue	NOUN
ejpam-5564	1	15	1	1	NUM
ejpam-5564	1	16	,	,	PUNCT
ejpam-5564	1	17	article	article	NOUN
ejpam-5564	1	18	number	number	NOUN
ejpam-5564	1	19	5564	5564	NUM
ejpam-5564	1	20	issn	issn	PROPN
ejpam-5564	1	21	1307	1307	NUM
ejpam-5564	1	22	-	-	SYM
ejpam-5564	1	23	5543	5543	NUM
ejpam-5564	1	24	–	–	PUNCT
ejpam-5564	1	25	ejpam.com	ejpam.com	X
ejpam-5564	1	26	published	publish	VERB
ejpam-5564	1	27	by	by	ADP
ejpam-5564	1	28	new	new	PROPN
ejpam-5564	1	29	york	york	PROPN
ejpam-5564	1	30	business	business	PROPN
ejpam-5564	1	31	global	global	ADJ
ejpam-5564	1	32	investigation	investigation	NOUN
ejpam-5564	1	33	of	of	ADP
ejpam-5564	1	34	a	a	DET
ejpam-5564	1	35	fourth	fourth	ADJ
ejpam-5564	1	36	-	-	PUNCT
ejpam-5564	1	37	order	order	NOUN
ejpam-5564	1	38	nonlinear	nonlinear	ADJ
ejpam-5564	1	39	differential	differential	ADJ
ejpam-5564	1	40	equation	equation	NOUN
ejpam-5564	1	41	with	with	ADP
ejpam-5564	1	42	moving	move	VERB
ejpam-5564	1	43	singular	singular	ADJ
ejpam-5564	1	44	points	point	NOUN
ejpam-5564	1	45	of	of	ADP
ejpam-5564	1	46	algebraic	algebraic	ADJ
ejpam-5564	1	47	type	type	NOUN
ejpam-5564	1	48	magomedyusuf	magomedyusuf	PROPN
ejpam-5564	1	49	gasanov	gasanov	NOUN
ejpam-5564	1	50	moscow	moscow	PROPN
ejpam-5564	1	51	state	state	PROPN
ejpam-5564	1	52	university	university	PROPN
ejpam-5564	1	53	of	of	ADP
ejpam-5564	1	54	civil	civil	ADJ
ejpam-5564	1	55	engineering	engineering	NOUN
ejpam-5564	1	56	,	,	PUNCT
ejpam-5564	1	57	russia	russia	PROPN
ejpam-5564	1	58	abstract	abstract	NOUN
ejpam-5564	1	59	.	.	PUNCT
ejpam-5564	2	1	in	in	ADP
ejpam-5564	2	2	this	this	DET
ejpam-5564	2	3	study	study	NOUN
ejpam-5564	2	4	,	,	PUNCT
ejpam-5564	2	5	a	a	DET
ejpam-5564	2	6	fourth	fourth	ADJ
ejpam-5564	2	7	-	-	PUNCT
ejpam-5564	2	8	order	order	NOUN
ejpam-5564	2	9	nonlinear	nonlinear	ADJ
ejpam-5564	2	10	ordinary	ordinary	ADJ
ejpam-5564	2	11	differential	differential	ADJ
ejpam-5564	2	12	equation	equation	NOUN
ejpam-5564	2	13	is	be	AUX
ejpam-5564	2	14	considered	consider	VERB
ejpam-5564	2	15	.	.	PUNCT
ejpam-5564	3	1	the	the	DET
ejpam-5564	3	2	specificity	specificity	NOUN
ejpam-5564	3	3	of	of	ADP
ejpam-5564	3	4	nonlinearity	nonlinearity	NOUN
ejpam-5564	3	5	lies	lie	VERB
ejpam-5564	3	6	in	in	ADP
ejpam-5564	3	7	the	the	DET
ejpam-5564	3	8	presence	presence	NOUN
ejpam-5564	3	9	of	of	ADP
ejpam-5564	3	10	moving	move	VERB
ejpam-5564	3	11	singular	singular	ADJ
ejpam-5564	3	12	points	point	NOUN
ejpam-5564	3	13	,	,	PUNCT
ejpam-5564	3	14	which	which	PRON
ejpam-5564	3	15	hinders	hinder	VERB
ejpam-5564	3	16	the	the	DET
ejpam-5564	3	17	application	application	NOUN
ejpam-5564	3	18	of	of	ADP
ejpam-5564	3	19	classical	classical	ADJ
ejpam-5564	3	20	theory	theory	NOUN
ejpam-5564	3	21	that	that	SCONJ
ejpam-5564	3	22	only	only	ADV
ejpam-5564	3	23	works	work	VERB
ejpam-5564	3	24	in	in	ADP
ejpam-5564	3	25	the	the	DET
ejpam-5564	3	26	linear	linear	ADJ
ejpam-5564	3	27	case	case	NOUN
ejpam-5564	3	28	.	.	PUNCT
ejpam-5564	4	1	two	two	NUM
ejpam-5564	4	2	research	research	NOUN
ejpam-5564	4	3	problems	problem	NOUN
ejpam-5564	4	4	are	be	AUX
ejpam-5564	4	5	addressed	address	VERB
ejpam-5564	4	6	in	in	ADP
ejpam-5564	4	7	this	this	DET
ejpam-5564	4	8	work	work	NOUN
ejpam-5564	4	9	:	:	PUNCT
ejpam-5564	4	10	the	the	DET
ejpam-5564	4	11	theorem	theorem	NOUN
ejpam-5564	4	12	of	of	ADP
ejpam-5564	4	13	existence	existence	NOUN
ejpam-5564	4	14	and	and	CCONJ
ejpam-5564	4	15	uniqueness	uniqueness	NOUN
ejpam-5564	4	16	of	of	ADP
ejpam-5564	4	17	the	the	DET
ejpam-5564	4	18	solution	solution	NOUN
ejpam-5564	4	19	,	,	PUNCT
ejpam-5564	4	20	and	and	CCONJ
ejpam-5564	4	21	the	the	DET
ejpam-5564	4	22	precise	precise	ADJ
ejpam-5564	4	23	criteria	criterion	NOUN
ejpam-5564	4	24	for	for	ADP
ejpam-5564	4	25	the	the	DET
ejpam-5564	4	26	existence	existence	NOUN
ejpam-5564	4	27	of	of	ADP
ejpam-5564	4	28	a	a	DET
ejpam-5564	4	29	moving	move	VERB
ejpam-5564	4	30	singular	singular	ADJ
ejpam-5564	4	31	point	point	NOUN
ejpam-5564	4	32	.	.	PUNCT
ejpam-5564	5	1	these	these	DET
ejpam-5564	5	2	problems	problem	NOUN
ejpam-5564	5	3	are	be	AUX
ejpam-5564	5	4	solved	solve	VERB
ejpam-5564	5	5	in	in	ADP
ejpam-5564	5	6	both	both	CCONJ
ejpam-5564	5	7	the	the	DET
ejpam-5564	5	8	real	real	ADJ
ejpam-5564	5	9	and	and	CCONJ
ejpam-5564	5	10	complex	complex	ADJ
ejpam-5564	5	11	domains	domain	NOUN
ejpam-5564	5	12	.	.	PUNCT
ejpam-5564	6	1	the	the	DET
ejpam-5564	6	2	specificity	specificity	NOUN
ejpam-5564	6	3	of	of	ADP
ejpam-5564	6	4	transitioning	transition	VERB
ejpam-5564	6	5	to	to	ADP
ejpam-5564	6	6	the	the	DET
ejpam-5564	6	7	complex	complex	ADJ
ejpam-5564	6	8	plane	plane	NOUN
ejpam-5564	6	9	is	be	AUX
ejpam-5564	6	10	demonstrated	demonstrate	VERB
ejpam-5564	6	11	using	use	VERB
ejpam-5564	6	12	phase	phase	NOUN
ejpam-5564	6	13	spaces	space	NOUN
ejpam-5564	6	14	.	.	PUNCT
ejpam-5564	7	1	the	the	DET
ejpam-5564	7	2	obtained	obtain	VERB
ejpam-5564	7	3	results	result	NOUN
ejpam-5564	7	4	are	be	AUX
ejpam-5564	7	5	validated	validate	VERB
ejpam-5564	7	6	through	through	ADP
ejpam-5564	7	7	numerical	numerical	ADJ
ejpam-5564	7	8	experiments	experiment	NOUN
ejpam-5564	7	9	,	,	PUNCT
ejpam-5564	7	10	confirming	confirm	VERB
ejpam-5564	7	11	the	the	DET
ejpam-5564	7	12	reliability	reliability	NOUN
ejpam-5564	7	13	of	of	ADP
ejpam-5564	7	14	the	the	DET
ejpam-5564	7	15	results	result	NOUN
ejpam-5564	7	16	.	.	PUNCT
ejpam-5564	8	1	2020	2020	NUM
ejpam-5564	8	2	mathematics	mathematic	NOUN
ejpam-5564	8	3	subject	subject	NOUN
ejpam-5564	8	4	classifications	classification	NOUN
ejpam-5564	8	5	:	:	PUNCT
ejpam-5564	8	6	34a34	34a34	NUM
ejpam-5564	8	7	,	,	PUNCT
ejpam-5564	8	8	34a12	34a12	NUM
ejpam-5564	8	9	,	,	PUNCT
ejpam-5564	8	10	34m04	34m04	NUM
ejpam-5564	8	11	,	,	PUNCT
ejpam-5564	8	12	34m05	34m05	NUM
ejpam-5564	8	13	key	key	ADJ
ejpam-5564	8	14	words	word	NOUN
ejpam-5564	8	15	and	and	CCONJ
ejpam-5564	8	16	phrases	phrase	NOUN
ejpam-5564	8	17	:	:	PUNCT
ejpam-5564	8	18	cauchy	cauchy	ADJ
ejpam-5564	8	19	problem	problem	NOUN
ejpam-5564	8	20	,	,	PUNCT
ejpam-5564	8	21	movable	movable	ADJ
ejpam-5564	8	22	singular	singular	NOUN
ejpam-5564	8	23	point	point	NOUN
ejpam-5564	8	24	,	,	PUNCT
ejpam-5564	8	25	analytical	analytical	ADJ
ejpam-5564	8	26	approximate	approximate	ADJ
ejpam-5564	8	27	solution	solution	NOUN
ejpam-5564	8	28	,	,	PUNCT
ejpam-5564	8	29	phase	phase	NOUN
ejpam-5564	8	30	spaces	space	NOUN
ejpam-5564	8	31	,	,	PUNCT
ejpam-5564	8	32	puiseux	puiseux	PROPN
ejpam-5564	8	33	series	series	PROPN
ejpam-5564	8	34	,	,	PUNCT
ejpam-5564	8	35	meromorphic	meromorphic	ADJ
ejpam-5564	8	36	function	function	NOUN
ejpam-5564	8	37	1	1	NUM
ejpam-5564	8	38	.	.	PUNCT
ejpam-5564	9	1	introduction	introduction	NOUN
ejpam-5564	9	2	nonlinear	nonlinear	PROPN
ejpam-5564	9	3	differential	differential	ADJ
ejpam-5564	9	4	equations	equation	NOUN
ejpam-5564	9	5	are	be	AUX
ejpam-5564	9	6	widely	widely	ADV
ejpam-5564	9	7	used	use	VERB
ejpam-5564	9	8	in	in	ADP
ejpam-5564	9	9	science	science	NOUN
ejpam-5564	9	10	and	and	CCONJ
ejpam-5564	9	11	engineering	engineering	NOUN
ejpam-5564	9	12	,	,	PUNCT
ejpam-5564	9	13	for	for	ADP
ejpam-5564	9	14	instance	instance	NOUN
ejpam-5564	9	15	,	,	PUNCT
ejpam-5564	9	16	in	in	ADP
ejpam-5564	9	17	problems	problem	NOUN
ejpam-5564	9	18	of	of	ADP
ejpam-5564	9	19	hydrodynamics	hydrodynamic	NOUN
ejpam-5564	9	20	[	[	X
ejpam-5564	9	21	8	8	NUM
ejpam-5564	9	22	]	]	PUNCT
ejpam-5564	9	23	,	,	PUNCT
ejpam-5564	9	24	and	and	CCONJ
ejpam-5564	9	25	continuum	continuum	ADJ
ejpam-5564	9	26	mechanics	mechanic	NOUN
ejpam-5564	9	27	[	[	X
ejpam-5564	9	28	15	15	NUM
ejpam-5564	9	29	,	,	PUNCT
ejpam-5564	9	30	23	23	NUM
ejpam-5564	9	31	]	]	PUNCT
ejpam-5564	9	32	.	.	PUNCT
ejpam-5564	10	1	in	in	ADP
ejpam-5564	10	2	this	this	DET
ejpam-5564	10	3	study	study	NOUN
ejpam-5564	10	4	,	,	PUNCT
ejpam-5564	10	5	we	we	PRON
ejpam-5564	10	6	will	will	AUX
ejpam-5564	10	7	focus	focus	VERB
ejpam-5564	10	8	on	on	ADP
ejpam-5564	10	9	the	the	DET
ejpam-5564	10	10	cauchy	cauchy	ADJ
ejpam-5564	10	11	problem	problem	NOUN
ejpam-5564	10	12	for	for	ADP
ejpam-5564	10	13	a	a	DET
ejpam-5564	10	14	fourth	fourth	ADJ
ejpam-5564	10	15	-	-	PUNCT
ejpam-5564	10	16	order	order	NOUN
ejpam-5564	10	17	differential	differential	ADJ
ejpam-5564	10	18	equation	equation	NOUN
ejpam-5564	10	19	.	.	PUNCT
ejpam-5564	11	1	the	the	DET
ejpam-5564	11	2	equation	equation	NOUN
ejpam-5564	11	3	under	under	ADP
ejpam-5564	11	4	consideration	consideration	NOUN
ejpam-5564	11	5	in	in	ADP
ejpam-5564	11	6	present	present	ADJ
ejpam-5564	11	7	research	research	NOUN
ejpam-5564	11	8	has	have	VERB
ejpam-5564	11	9	the	the	DET
ejpam-5564	11	10	following	follow	VERB
ejpam-5564	11	11	form	form	NOUN
ejpam-5564	11	12	:	:	PUNCT
ejpam-5564	11	13	d4w	d4w	PROPN
ejpam-5564	11	14	dz4	dz4	PROPN
ejpam-5564	11	15	+	+	NOUN
ejpam-5564	11	16	q0w	q0w	PROPN
ejpam-5564	11	17	(	(	PUNCT
ejpam-5564	11	18	w′)2	w′)2	PROPN
ejpam-5564	11	19	=	=	SYM
ejpam-5564	11	20	f	f	PROPN
ejpam-5564	11	21	(	(	PUNCT
ejpam-5564	11	22	z	z	NOUN
ejpam-5564	11	23	)	)	PUNCT
ejpam-5564	11	24	,	,	PUNCT
ejpam-5564	11	25	(	(	PUNCT
ejpam-5564	11	26	1	1	X
ejpam-5564	11	27	)	)	PUNCT
ejpam-5564	11	28	this	this	DET
ejpam-5564	11	29	model	model	NOUN
ejpam-5564	11	30	can	can	AUX
ejpam-5564	11	31	be	be	AUX
ejpam-5564	11	32	viewed	view	VERB
ejpam-5564	11	33	as	as	ADP
ejpam-5564	11	34	a	a	DET
ejpam-5564	11	35	mechanical	mechanical	ADJ
ejpam-5564	11	36	system	system	NOUN
ejpam-5564	11	37	involving	involve	VERB
ejpam-5564	11	38	an	an	DET
ejpam-5564	11	39	oscillator	oscillator	NOUN
ejpam-5564	11	40	,	,	PUNCT
ejpam-5564	11	41	such	such	ADJ
ejpam-5564	11	42	as	as	ADP
ejpam-5564	11	43	a	a	DET
ejpam-5564	11	44	mass	mass	ADJ
ejpam-5564	11	45	-	-	PUNCT
ejpam-5564	11	46	spring	spring	NOUN
ejpam-5564	11	47	system	system	NOUN
ejpam-5564	11	48	or	or	CCONJ
ejpam-5564	11	49	a	a	DET
ejpam-5564	11	50	pendulum	pendulum	NOUN
ejpam-5564	11	51	,	,	PUNCT
ejpam-5564	11	52	where	where	SCONJ
ejpam-5564	11	53	the	the	DET
ejpam-5564	11	54	oscillator	oscillator	NOUN
ejpam-5564	11	55	’s	’s	PART
ejpam-5564	11	56	motion	motion	NOUN
ejpam-5564	11	57	is	be	AUX
ejpam-5564	11	58	influenced	influence	VERB
ejpam-5564	11	59	by	by	ADP
ejpam-5564	11	60	external	external	ADJ
ejpam-5564	11	61	forces	force	NOUN
ejpam-5564	11	62	.	.	PUNCT
ejpam-5564	12	1	the	the	DET
ejpam-5564	12	2	term	term	NOUN
ejpam-5564	12	3	w	w	PROPN
ejpam-5564	12	4	(	(	PUNCT
ejpam-5564	12	5	w′)2	w′)2	PROPN
ejpam-5564	12	6	represents	represent	VERB
ejpam-5564	12	7	the	the	DET
ejpam-5564	12	8	interaction	interaction	NOUN
ejpam-5564	12	9	between	between	ADP
ejpam-5564	12	10	the	the	DET
ejpam-5564	12	11	displacement	displacement	NOUN
ejpam-5564	12	12	w	w	PROPN
ejpam-5564	12	13	and	and	CCONJ
ejpam-5564	12	14	the	the	DET
ejpam-5564	12	15	square	square	NOUN
ejpam-5564	12	16	of	of	ADP
ejpam-5564	12	17	the	the	DET
ejpam-5564	12	18	oscillator	oscillator	NOUN
ejpam-5564	12	19	’s	’s	PART
ejpam-5564	12	20	velocity	velocity	NOUN
ejpam-5564	12	21	w′.	w′.	X
ejpam-5564	12	22	it	it	PRON
ejpam-5564	12	23	captures	capture	VERB
ejpam-5564	12	24	the	the	DET
ejpam-5564	12	25	effect	effect	NOUN
ejpam-5564	12	26	of	of	ADP
ejpam-5564	12	27	velocity	velocity	NOUN
ejpam-5564	12	28	-	-	PUNCT
ejpam-5564	12	29	dependent	dependent	ADJ
ejpam-5564	12	30	forces	force	NOUN
ejpam-5564	12	31	,	,	PUNCT
ejpam-5564	12	32	which	which	PRON
ejpam-5564	12	33	may	may	AUX
ejpam-5564	12	34	introduce	introduce	VERB
ejpam-5564	12	35	additional	additional	ADJ
ejpam-5564	12	36	nonlinear	nonlinear	ADJ
ejpam-5564	12	37	behaviors	behavior	NOUN
ejpam-5564	12	38	,	,	PUNCT
ejpam-5564	12	39	such	such	ADJ
ejpam-5564	12	40	as	as	ADP
ejpam-5564	12	41	dissipation	dissipation	NOUN
ejpam-5564	12	42	or	or	CCONJ
ejpam-5564	12	43	energy	energy	NOUN
ejpam-5564	12	44	generation	generation	NOUN
ejpam-5564	12	45	.	.	PUNCT
ejpam-5564	13	1	often	often	ADV
ejpam-5564	13	2	,	,	PUNCT
ejpam-5564	13	3	when	when	SCONJ
ejpam-5564	13	4	solving	solve	VERB
ejpam-5564	13	5	many	many	ADJ
ejpam-5564	13	6	problems	problem	NOUN
ejpam-5564	13	7	,	,	PUNCT
ejpam-5564	13	8	nonlinear	nonlinear	ADJ
ejpam-5564	13	9	terms	term	NOUN
ejpam-5564	13	10	are	be	AUX
ejpam-5564	13	11	neglected	neglect	VERB
ejpam-5564	13	12	.	.	PUNCT
ejpam-5564	14	1	however	however	ADV
ejpam-5564	14	2	,	,	PUNCT
ejpam-5564	14	3	doi	doi	PROPN
ejpam-5564	14	4	:	:	PUNCT
ejpam-5564	14	5	https://doi.org/10.29020/nybg.ejpam.v18i1.5564	https://doi.org/10.29020/nybg.ejpam.v18i1.5564	PROPN
ejpam-5564	14	6	email	email	NOUN
ejpam-5564	14	7	address	address	NOUN
ejpam-5564	14	8	:	:	PUNCT
ejpam-5564	15	1	vonasag6991@mail.ru	vonasag6991@mail.ru	PROPN
ejpam-5564	15	2	(	(	PUNCT
ejpam-5564	15	3	m.	m.	NOUN
ejpam-5564	15	4	gasanov	gasanov	NOUN
ejpam-5564	15	5	)	)	PUNCT
ejpam-5564	15	6	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5564	15	7	1	1	NUM
ejpam-5564	15	8	copyright	copyright	NOUN
ejpam-5564	15	9	:	:	PUNCT
ejpam-5564	16	1	©	©	PROPN
ejpam-5564	16	2	2025	2025	NUM
ejpam-5564	16	3	the	the	DET
ejpam-5564	16	4	author(s	author(s	NOUN
ejpam-5564	16	5	)	)	PUNCT
ejpam-5564	16	6	.	.	PUNCT
ejpam-5564	17	1	(	(	PUNCT
ejpam-5564	17	2	cc	cc	NOUN
ejpam-5564	17	3	by	by	ADP
ejpam-5564	17	4	-	-	PUNCT
ejpam-5564	17	5	nc	nc	PROPN
ejpam-5564	17	6	4.0	4.0	NUM
ejpam-5564	17	7	)	)	PUNCT
ejpam-5564	17	8	m.	m.	NOUN
ejpam-5564	17	9	gasanov	gasanov	NOUN
ejpam-5564	17	10	/	/	SYM
ejpam-5564	17	11	eur	eur	PROPN
ejpam-5564	17	12	.	.	PUNCT
ejpam-5564	18	1	j.	j.	PROPN
ejpam-5564	18	2	pure	pure	PROPN
ejpam-5564	18	3	appl	appl	PROPN
ejpam-5564	18	4	.	.	PROPN
ejpam-5564	18	5	math	math	PROPN
ejpam-5564	18	6	,	,	PUNCT
ejpam-5564	18	7	18	18	NUM
ejpam-5564	18	8	(	(	PUNCT
ejpam-5564	18	9	1	1	NUM
ejpam-5564	18	10	)	)	PUNCT
ejpam-5564	18	11	(	(	PUNCT
ejpam-5564	18	12	2025	2025	NUM
ejpam-5564	18	13	)	)	PUNCT
ejpam-5564	18	14	,	,	PUNCT
ejpam-5564	18	15	5564	5564	NUM
ejpam-5564	18	16	2	2	NUM
ejpam-5564	18	17	of	of	ADP
ejpam-5564	18	18	19	19	NUM
ejpam-5564	18	19	as	as	SCONJ
ejpam-5564	18	20	shown	show	VERB
ejpam-5564	18	21	in	in	ADP
ejpam-5564	18	22	studies	study	NOUN
ejpam-5564	18	23	[	[	X
ejpam-5564	18	24	4–6	4–6	NOUN
ejpam-5564	18	25	,	,	PUNCT
ejpam-5564	18	26	9	9	NUM
ejpam-5564	18	27	,	,	PUNCT
ejpam-5564	18	28	10	10	NUM
ejpam-5564	18	29	,	,	PUNCT
ejpam-5564	18	30	12	12	NUM
ejpam-5564	18	31	,	,	PUNCT
ejpam-5564	18	32	14	14	NUM
ejpam-5564	18	33	,	,	PUNCT
ejpam-5564	18	34	17	17	NUM
ejpam-5564	18	35	,	,	PUNCT
ejpam-5564	18	36	22	22	NUM
ejpam-5564	18	37	,	,	PUNCT
ejpam-5564	18	38	25	25	NUM
ejpam-5564	18	39	,	,	PUNCT
ejpam-5564	18	40	44	44	NUM
ejpam-5564	18	41	,	,	PUNCT
ejpam-5564	18	42	48	48	NUM
ejpam-5564	18	43	]	]	PUNCT
ejpam-5564	18	44	,	,	PUNCT
ejpam-5564	18	45	accounting	account	VERB
ejpam-5564	18	46	for	for	ADP
ejpam-5564	18	47	nonlinearity	nonlinearity	NOUN
ejpam-5564	18	48	in	in	ADP
ejpam-5564	18	49	the	the	DET
ejpam-5564	18	50	form	form	NOUN
ejpam-5564	18	51	of	of	ADP
ejpam-5564	18	52	the	the	DET
ejpam-5564	18	53	derivative	derivative	ADJ
ejpam-5564	18	54	squared	squared	NOUN
ejpam-5564	18	55	can	can	AUX
ejpam-5564	18	56	impact	impact	VERB
ejpam-5564	18	57	the	the	DET
ejpam-5564	18	58	solution	solution	NOUN
ejpam-5564	18	59	of	of	ADP
ejpam-5564	18	60	the	the	DET
ejpam-5564	18	61	investigated	investigate	VERB
ejpam-5564	18	62	problems	problem	NOUN
ejpam-5564	18	63	.	.	PUNCT
ejpam-5564	19	1	the	the	DET
ejpam-5564	19	2	complexity	complexity	NOUN
ejpam-5564	19	3	of	of	ADP
ejpam-5564	19	4	investigating	investigate	VERB
ejpam-5564	19	5	such	such	DET
ejpam-5564	19	6	a	a	DET
ejpam-5564	19	7	class	class	NOUN
ejpam-5564	19	8	of	of	ADP
ejpam-5564	19	9	equations	equation	NOUN
ejpam-5564	19	10	lies	lie	VERB
ejpam-5564	19	11	in	in	ADP
ejpam-5564	19	12	their	their	PRON
ejpam-5564	19	13	nonlinearity	nonlinearity	NOUN
ejpam-5564	19	14	,	,	PUNCT
ejpam-5564	19	15	which	which	PRON
ejpam-5564	19	16	is	be	AUX
ejpam-5564	19	17	a	a	DET
ejpam-5564	19	18	condition	condition	NOUN
ejpam-5564	19	19	for	for	ADP
ejpam-5564	19	20	the	the	DET
ejpam-5564	19	21	emergence	emergence	NOUN
ejpam-5564	19	22	of	of	ADP
ejpam-5564	19	23	movable	movable	ADJ
ejpam-5564	19	24	singular	singular	NOUN
ejpam-5564	19	25	points	point	NOUN
ejpam-5564	19	26	.	.	PUNCT
ejpam-5564	20	1	the	the	DET
ejpam-5564	20	2	presence	presence	NOUN
ejpam-5564	20	3	of	of	ADP
ejpam-5564	20	4	movable	movable	ADJ
ejpam-5564	20	5	singular	singular	ADJ
ejpam-5564	20	6	points	point	NOUN
ejpam-5564	20	7	of	of	ADP
ejpam-5564	20	8	algebraic	algebraic	ADJ
ejpam-5564	20	9	type	type	NOUN
ejpam-5564	20	10	poses	pose	VERB
ejpam-5564	20	11	a	a	DET
ejpam-5564	20	12	challenge	challenge	NOUN
ejpam-5564	20	13	for	for	ADP
ejpam-5564	20	14	finding	find	VERB
ejpam-5564	20	15	an	an	DET
ejpam-5564	20	16	analytical	analytical	ADJ
ejpam-5564	20	17	solution	solution	NOUN
ejpam-5564	20	18	.	.	PUNCT
ejpam-5564	21	1	movable	movable	ADJ
ejpam-5564	21	2	singular	singular	PROPN
ejpam-5564	21	3	points	point	NOUN
ejpam-5564	21	4	make	make	VERB
ejpam-5564	21	5	nonlinear	nonlinear	ADJ
ejpam-5564	21	6	differential	differential	ADJ
ejpam-5564	21	7	equations	equation	NOUN
ejpam-5564	21	8	in	in	ADP
ejpam-5564	21	9	general	general	ADJ
ejpam-5564	21	10	unsolvable	unsolvable	ADJ
ejpam-5564	21	11	in	in	ADP
ejpam-5564	21	12	quadratures	quadrature	NOUN
ejpam-5564	21	13	.	.	PUNCT
ejpam-5564	22	1	the	the	DET
ejpam-5564	22	2	classification	classification	NOUN
ejpam-5564	22	3	and	and	CCONJ
ejpam-5564	22	4	characteristics	characteristic	NOUN
ejpam-5564	22	5	of	of	ADP
ejpam-5564	22	6	movable	movable	ADJ
ejpam-5564	22	7	and	and	CCONJ
ejpam-5564	22	8	fixed	fix	VERB
ejpam-5564	22	9	singular	singular	ADJ
ejpam-5564	22	10	points	point	NOUN
ejpam-5564	22	11	are	be	AUX
ejpam-5564	22	12	well	well	ADV
ejpam-5564	22	13	-	-	PUNCT
ejpam-5564	22	14	described	describe	VERB
ejpam-5564	22	15	in	in	ADP
ejpam-5564	22	16	the	the	DET
ejpam-5564	22	17	works	work	NOUN
ejpam-5564	22	18	[	[	X
ejpam-5564	22	19	11	11	NUM
ejpam-5564	22	20	,	,	PUNCT
ejpam-5564	22	21	18	18	NUM
ejpam-5564	22	22	]	]	PUNCT
ejpam-5564	22	23	.	.	PUNCT
ejpam-5564	23	1	singular	singular	PROPN
ejpam-5564	23	2	points	point	NOUN
ejpam-5564	23	3	of	of	ADP
ejpam-5564	23	4	the	the	DET
ejpam-5564	23	5	integrals	integral	NOUN
ejpam-5564	23	6	of	of	ADP
ejpam-5564	23	7	differential	differential	ADJ
ejpam-5564	23	8	equations	equation	NOUN
ejpam-5564	23	9	,	,	PUNCT
ejpam-5564	23	10	whose	whose	DET
ejpam-5564	23	11	position	position	NOUN
ejpam-5564	23	12	does	do	AUX
ejpam-5564	23	13	not	not	PART
ejpam-5564	23	14	depend	depend	VERB
ejpam-5564	23	15	on	on	ADP
ejpam-5564	23	16	the	the	DET
ejpam-5564	23	17	initial	initial	ADJ
ejpam-5564	23	18	data	datum	NOUN
ejpam-5564	23	19	that	that	PRON
ejpam-5564	23	20	determine	determine	VERB
ejpam-5564	23	21	these	these	DET
ejpam-5564	23	22	integrals	integral	NOUN
ejpam-5564	23	23	,	,	PUNCT
ejpam-5564	23	24	are	be	AUX
ejpam-5564	23	25	called	call	VERB
ejpam-5564	23	26	fixed	fix	VERB
ejpam-5564	23	27	singular	singular	ADJ
ejpam-5564	23	28	points	point	NOUN
ejpam-5564	23	29	.	.	PUNCT
ejpam-5564	24	1	singular	singular	ADJ
ejpam-5564	24	2	points	point	NOUN
ejpam-5564	24	3	of	of	ADP
ejpam-5564	24	4	the	the	DET
ejpam-5564	24	5	integrals	integral	NOUN
ejpam-5564	24	6	of	of	ADP
ejpam-5564	24	7	differential	differential	ADJ
ejpam-5564	24	8	equations	equation	NOUN
ejpam-5564	24	9	,	,	PUNCT
ejpam-5564	24	10	whose	whose	DET
ejpam-5564	24	11	position	position	NOUN
ejpam-5564	24	12	depends	depend	VERB
ejpam-5564	24	13	on	on	ADP
ejpam-5564	24	14	the	the	DET
ejpam-5564	24	15	initial	initial	ADJ
ejpam-5564	24	16	data	datum	NOUN
ejpam-5564	24	17	,	,	PUNCT
ejpam-5564	24	18	are	be	AUX
ejpam-5564	24	19	called	call	VERB
ejpam-5564	24	20	movable	movable	ADJ
ejpam-5564	24	21	singular	singular	PROPN
ejpam-5564	24	22	points	point	NOUN
ejpam-5564	24	23	.	.	PUNCT
ejpam-5564	25	1	algebraic	algebraic	ADJ
ejpam-5564	25	2	movable	movable	ADJ
ejpam-5564	25	3	singular	singular	PROPN
ejpam-5564	25	4	points	point	NOUN
ejpam-5564	25	5	include	include	VERB
ejpam-5564	25	6	simple	simple	ADJ
ejpam-5564	25	7	and	and	CCONJ
ejpam-5564	25	8	multiple	multiple	ADJ
ejpam-5564	25	9	poles	pole	NOUN
ejpam-5564	25	10	,	,	PUNCT
ejpam-5564	25	11	as	as	ADV
ejpam-5564	25	12	well	well	ADV
ejpam-5564	25	13	as	as	ADP
ejpam-5564	25	14	branch	branch	NOUN
ejpam-5564	25	15	points	point	NOUN
ejpam-5564	25	16	of	of	ADP
ejpam-5564	25	17	finite	finite	ADJ
ejpam-5564	25	18	order	order	NOUN
ejpam-5564	25	19	.	.	PUNCT
ejpam-5564	26	1	in	in	ADP
ejpam-5564	26	2	the	the	DET
ejpam-5564	26	3	neighborhood	neighborhood	NOUN
ejpam-5564	26	4	of	of	ADP
ejpam-5564	26	5	such	such	ADJ
ejpam-5564	26	6	points	point	NOUN
ejpam-5564	26	7	,	,	PUNCT
ejpam-5564	26	8	a	a	DET
ejpam-5564	26	9	puiseux	puiseux	PROPN
ejpam-5564	26	10	series	series	PROPN
ejpam-5564	26	11	expansion	expansion	NOUN
ejpam-5564	26	12	is	be	AUX
ejpam-5564	26	13	assumed	assume	VERB
ejpam-5564	26	14	.	.	PUNCT
ejpam-5564	27	1	despite	despite	SCONJ
ejpam-5564	27	2	the	the	DET
ejpam-5564	27	3	presence	presence	NOUN
ejpam-5564	27	4	of	of	ADP
ejpam-5564	27	5	movable	movable	ADJ
ejpam-5564	27	6	singular	singular	NOUN
ejpam-5564	27	7	points	point	NOUN
ejpam-5564	27	8	,	,	PUNCT
ejpam-5564	27	9	there	there	PRON
ejpam-5564	27	10	are	be	VERB
ejpam-5564	27	11	methods	method	NOUN
ejpam-5564	27	12	for	for	ADP
ejpam-5564	27	13	studying	study	VERB
ejpam-5564	27	14	such	such	ADJ
ejpam-5564	27	15	equations	equation	NOUN
ejpam-5564	27	16	.	.	PUNCT
ejpam-5564	28	1	the	the	DET
ejpam-5564	28	2	process	process	NOUN
ejpam-5564	28	3	of	of	ADP
ejpam-5564	28	4	finding	find	VERB
ejpam-5564	28	5	a	a	DET
ejpam-5564	28	6	solution	solution	NOUN
ejpam-5564	28	7	and	and	CCONJ
ejpam-5564	28	8	investigating	investigate	VERB
ejpam-5564	28	9	its	its	PRON
ejpam-5564	28	10	behavior	behavior	NOUN
ejpam-5564	28	11	can	can	AUX
ejpam-5564	28	12	be	be	AUX
ejpam-5564	28	13	divided	divide	VERB
ejpam-5564	28	14	into	into	ADP
ejpam-5564	28	15	two	two	NUM
ejpam-5564	28	16	domains	domain	NOUN
ejpam-5564	28	17	:	:	PUNCT
ejpam-5564	28	18	the	the	DET
ejpam-5564	28	19	domain	domain	NOUN
ejpam-5564	28	20	of	of	ADP
ejpam-5564	28	21	analyticity	analyticity	NOUN
ejpam-5564	28	22	and	and	CCONJ
ejpam-5564	28	23	the	the	DET
ejpam-5564	28	24	neighborhood	neighborhood	NOUN
ejpam-5564	28	25	of	of	ADP
ejpam-5564	28	26	the	the	DET
ejpam-5564	28	27	movable	movable	ADJ
ejpam-5564	28	28	singular	singular	NOUN
ejpam-5564	28	29	point	point	NOUN
ejpam-5564	28	30	.	.	PUNCT
ejpam-5564	29	1	in	in	ADP
ejpam-5564	29	2	the	the	DET
ejpam-5564	29	3	domain	domain	NOUN
ejpam-5564	29	4	of	of	ADP
ejpam-5564	29	5	analyticity	analyticity	NOUN
ejpam-5564	29	6	,	,	PUNCT
ejpam-5564	29	7	linearization	linearization	NOUN
ejpam-5564	29	8	is	be	AUX
ejpam-5564	29	9	possible	possible	ADJ
ejpam-5564	29	10	,	,	PUNCT
ejpam-5564	29	11	and	and	CCONJ
ejpam-5564	29	12	numerical	numerical	ADJ
ejpam-5564	29	13	methods	method	NOUN
ejpam-5564	29	14	can	can	AUX
ejpam-5564	29	15	be	be	AUX
ejpam-5564	29	16	applied	apply	VERB
ejpam-5564	29	17	to	to	PART
ejpam-5564	29	18	solve	solve	VERB
ejpam-5564	29	19	such	such	ADJ
ejpam-5564	29	20	problems	problem	NOUN
ejpam-5564	29	21	.	.	PUNCT
ejpam-5564	30	1	in	in	ADP
ejpam-5564	30	2	[	[	X
ejpam-5564	30	3	21	21	NUM
ejpam-5564	30	4	]	]	PUNCT
ejpam-5564	30	5	,	,	PUNCT
ejpam-5564	30	6	two	two	NUM
ejpam-5564	30	7	algorithms	algorithm	NOUN
ejpam-5564	30	8	are	be	AUX
ejpam-5564	30	9	developed	develop	VERB
ejpam-5564	30	10	to	to	PART
ejpam-5564	30	11	check	check	VERB
ejpam-5564	30	12	the	the	DET
ejpam-5564	30	13	possibility	possibility	NOUN
ejpam-5564	30	14	of	of	ADP
ejpam-5564	30	15	reducing	reduce	VERB
ejpam-5564	30	16	a	a	DET
ejpam-5564	30	17	nonlinear	nonlinear	ADJ
ejpam-5564	30	18	differential	differential	ADJ
ejpam-5564	30	19	equation	equation	NOUN
ejpam-5564	30	20	to	to	ADP
ejpam-5564	30	21	a	a	DET
ejpam-5564	30	22	linear	linear	ADJ
ejpam-5564	30	23	one	one	NOUN
ejpam-5564	30	24	using	use	VERB
ejpam-5564	30	25	lie	lie	NOUN
ejpam-5564	30	26	algebra	algebra	NOUN
ejpam-5564	30	27	and	and	CCONJ
ejpam-5564	30	28	point	point	NOUN
ejpam-5564	30	29	transformations	transformation	NOUN
ejpam-5564	30	30	.	.	PUNCT
ejpam-5564	31	1	in	in	ADP
ejpam-5564	31	2	[	[	X
ejpam-5564	31	3	16	16	NUM
ejpam-5564	31	4	]	]	PUNCT
ejpam-5564	31	5	,	,	PUNCT
ejpam-5564	31	6	linearization	linearization	NOUN
ejpam-5564	31	7	is	be	AUX
ejpam-5564	31	8	based	base	VERB
ejpam-5564	31	9	on	on	ADP
ejpam-5564	31	10	the	the	DET
ejpam-5564	31	11	method	method	NOUN
ejpam-5564	31	12	of	of	ADP
ejpam-5564	31	13	new	new	ADJ
ejpam-5564	31	14	approximation	approximation	NOUN
ejpam-5564	31	15	,	,	PUNCT
ejpam-5564	31	16	taking	take	VERB
ejpam-5564	31	17	into	into	ADP
ejpam-5564	31	18	account	account	NOUN
ejpam-5564	31	19	both	both	DET
ejpam-5564	31	20	local	local	ADJ
ejpam-5564	31	21	and	and	CCONJ
ejpam-5564	31	22	global	global	ADJ
ejpam-5564	31	23	properties	property	NOUN
ejpam-5564	31	24	obtained	obtain	VERB
ejpam-5564	31	25	through	through	ADP
ejpam-5564	31	26	global	global	ADJ
ejpam-5564	31	27	approximation	approximation	NOUN
ejpam-5564	31	28	of	of	ADP
ejpam-5564	31	29	lie	lie	NOUN
ejpam-5564	31	30	derivatives	derivative	NOUN
ejpam-5564	31	31	.	.	PUNCT
ejpam-5564	32	1	in	in	ADP
ejpam-5564	32	2	[	[	X
ejpam-5564	32	3	43	43	NUM
ejpam-5564	32	4	]	]	PUNCT
ejpam-5564	32	5	,	,	PUNCT
ejpam-5564	32	6	the	the	DET
ejpam-5564	32	7	linearization	linearization	NOUN
ejpam-5564	32	8	problem	problem	NOUN
ejpam-5564	32	9	was	be	AUX
ejpam-5564	32	10	solved	solve	VERB
ejpam-5564	32	11	using	use	VERB
ejpam-5564	32	12	a	a	DET
ejpam-5564	32	13	generalized	generalized	ADJ
ejpam-5564	32	14	linearizing	linearize	VERB
ejpam-5564	32	15	transformation	transformation	NOUN
ejpam-5564	32	16	.	.	PUNCT
ejpam-5564	33	1	in	in	ADP
ejpam-5564	33	2	[	[	X
ejpam-5564	33	3	41	41	NUM
ejpam-5564	33	4	,	,	PUNCT
ejpam-5564	33	5	42	42	NUM
ejpam-5564	33	6	,	,	PUNCT
ejpam-5564	33	7	45	45	NUM
ejpam-5564	33	8	,	,	PUNCT
ejpam-5564	33	9	46	46	NUM
ejpam-5564	33	10	]	]	PUNCT
ejpam-5564	33	11	,	,	PUNCT
ejpam-5564	33	12	the	the	DET
ejpam-5564	33	13	authors	author	NOUN
ejpam-5564	33	14	used	use	VERB
ejpam-5564	33	15	homotopy	homotopy	NOUN
ejpam-5564	33	16	analysis	analysis	NOUN
ejpam-5564	33	17	methods	method	NOUN
ejpam-5564	33	18	and	and	CCONJ
ejpam-5564	33	19	numerical	numerical	ADJ
ejpam-5564	33	20	methods	method	NOUN
ejpam-5564	33	21	.	.	PUNCT
ejpam-5564	34	1	the	the	DET
ejpam-5564	34	2	second	second	ADJ
ejpam-5564	34	3	method	method	NOUN
ejpam-5564	34	4	for	for	ADP
ejpam-5564	34	5	solving	solve	VERB
ejpam-5564	34	6	this	this	DET
ejpam-5564	34	7	type	type	NOUN
ejpam-5564	34	8	of	of	ADP
ejpam-5564	34	9	nonlinear	nonlinear	ADJ
ejpam-5564	34	10	differential	differential	ADJ
ejpam-5564	34	11	equations	equation	NOUN
ejpam-5564	34	12	is	be	AUX
ejpam-5564	34	13	analytical	analytical	ADJ
ejpam-5564	34	14	.	.	PUNCT
ejpam-5564	35	1	finding	find	VERB
ejpam-5564	35	2	an	an	DET
ejpam-5564	35	3	analytical	analytical	ADJ
ejpam-5564	35	4	solution	solution	NOUN
ejpam-5564	35	5	is	be	AUX
ejpam-5564	35	6	rare	rare	ADJ
ejpam-5564	35	7	due	due	ADP
ejpam-5564	35	8	to	to	ADP
ejpam-5564	35	9	the	the	DET
ejpam-5564	35	10	complexity	complexity	NOUN
ejpam-5564	35	11	of	of	ADP
ejpam-5564	35	12	the	the	DET
ejpam-5564	35	13	considered	consider	VERB
ejpam-5564	35	14	physical	physical	ADJ
ejpam-5564	35	15	phenomenon	phenomenon	NOUN
ejpam-5564	35	16	[	[	X
ejpam-5564	35	17	49	49	NUM
ejpam-5564	35	18	]	]	PUNCT
ejpam-5564	35	19	.	.	PUNCT
ejpam-5564	36	1	as	as	SCONJ
ejpam-5564	36	2	shown	show	VERB
ejpam-5564	36	3	in	in	ADP
ejpam-5564	36	4	the	the	DET
ejpam-5564	36	5	works	work	NOUN
ejpam-5564	36	6	[	[	X
ejpam-5564	36	7	7	7	NUM
ejpam-5564	36	8	,	,	PUNCT
ejpam-5564	36	9	13	13	NUM
ejpam-5564	36	10	,	,	PUNCT
ejpam-5564	36	11	19	19	NUM
ejpam-5564	36	12	,	,	PUNCT
ejpam-5564	36	13	24	24	NUM
ejpam-5564	36	14	,	,	PUNCT
ejpam-5564	36	15	26	26	NUM
ejpam-5564	36	16	,	,	PUNCT
ejpam-5564	36	17	38	38	NUM
ejpam-5564	36	18	,	,	PUNCT
ejpam-5564	36	19	39	39	NUM
ejpam-5564	36	20	,	,	PUNCT
ejpam-5564	36	21	47	47	NUM
ejpam-5564	36	22	]	]	PUNCT
ejpam-5564	36	23	,	,	PUNCT
ejpam-5564	36	24	these	these	DET
ejpam-5564	36	25	problems	problem	NOUN
ejpam-5564	36	26	are	be	AUX
ejpam-5564	36	27	solved	solve	VERB
ejpam-5564	36	28	using	use	VERB
ejpam-5564	36	29	a	a	DET
ejpam-5564	36	30	specific	specific	ADJ
ejpam-5564	36	31	variable	variable	ADJ
ejpam-5564	36	32	substitution	substitution	NOUN
ejpam-5564	36	33	or	or	CCONJ
ejpam-5564	36	34	special	special	ADJ
ejpam-5564	36	35	functions	function	NOUN
ejpam-5564	36	36	.	.	PUNCT
ejpam-5564	37	1	the	the	DET
ejpam-5564	37	2	third	third	ADJ
ejpam-5564	37	3	method	method	NOUN
ejpam-5564	37	4	is	be	AUX
ejpam-5564	37	5	asymptotic	asymptotic	ADJ
ejpam-5564	37	6	.	.	PUNCT
ejpam-5564	38	1	the	the	DET
ejpam-5564	38	2	main	main	ADJ
ejpam-5564	38	3	task	task	NOUN
ejpam-5564	38	4	of	of	ADP
ejpam-5564	38	5	this	this	DET
ejpam-5564	38	6	method	method	NOUN
ejpam-5564	38	7	is	be	AUX
ejpam-5564	38	8	to	to	PART
ejpam-5564	38	9	investigate	investigate	VERB
ejpam-5564	38	10	the	the	DET
ejpam-5564	38	11	behavior	behavior	NOUN
ejpam-5564	38	12	of	of	ADP
ejpam-5564	38	13	the	the	DET
ejpam-5564	38	14	solution	solution	NOUN
ejpam-5564	38	15	near	near	ADP
ejpam-5564	38	16	singular	singular	ADJ
ejpam-5564	38	17	points	point	NOUN
ejpam-5564	38	18	(	(	PUNCT
ejpam-5564	38	19	both	both	PRON
ejpam-5564	38	20	moving	move	VERB
ejpam-5564	38	21	and	and	CCONJ
ejpam-5564	38	22	stationary	stationary	ADJ
ejpam-5564	38	23	)	)	PUNCT
ejpam-5564	38	24	as	as	ADV
ejpam-5564	38	25	well	well	ADV
ejpam-5564	38	26	as	as	ADP
ejpam-5564	38	27	at	at	ADP
ejpam-5564	38	28	infinity	infinity	NOUN
ejpam-5564	38	29	[	[	X
ejpam-5564	38	30	1	1	NUM
ejpam-5564	38	31	,	,	PUNCT
ejpam-5564	38	32	2	2	NUM
ejpam-5564	38	33	,	,	PUNCT
ejpam-5564	38	34	50	50	NUM
ejpam-5564	38	35	]	]	PUNCT
ejpam-5564	38	36	.	.	PUNCT
ejpam-5564	39	1	the	the	DET
ejpam-5564	39	2	author	author	NOUN
ejpam-5564	39	3	’s	’s	PART
ejpam-5564	39	4	method	method	NOUN
ejpam-5564	39	5	for	for	ADP
ejpam-5564	39	6	studying	study	VERB
ejpam-5564	39	7	nonlinear	nonlinear	ADJ
ejpam-5564	39	8	differential	differential	ADJ
ejpam-5564	39	9	equations	equation	NOUN
ejpam-5564	39	10	is	be	AUX
ejpam-5564	39	11	based	base	VERB
ejpam-5564	39	12	on	on	ADP
ejpam-5564	39	13	solving	solve	VERB
ejpam-5564	39	14	four	four	NUM
ejpam-5564	39	15	mathematical	mathematical	ADJ
ejpam-5564	39	16	problems	problem	NOUN
ejpam-5564	39	17	:	:	PUNCT
ejpam-5564	39	18	the	the	DET
ejpam-5564	39	19	theorem	theorem	NOUN
ejpam-5564	39	20	of	of	ADP
ejpam-5564	39	21	existence	existence	NOUN
ejpam-5564	39	22	and	and	CCONJ
ejpam-5564	39	23	uniqueness	uniqueness	NOUN
ejpam-5564	39	24	(	(	PUNCT
ejpam-5564	39	25	in	in	ADP
ejpam-5564	39	26	the	the	DET
ejpam-5564	39	27	domain	domain	NOUN
ejpam-5564	39	28	of	of	ADP
ejpam-5564	39	29	analyticity	analyticity	NOUN
ejpam-5564	39	30	and	and	CCONJ
ejpam-5564	39	31	the	the	DET
ejpam-5564	39	32	neighborhood	neighborhood	NOUN
ejpam-5564	39	33	of	of	ADP
ejpam-5564	39	34	the	the	DET
ejpam-5564	39	35	movable	movable	ADJ
ejpam-5564	39	36	singular	singular	NOUN
ejpam-5564	39	37	point	point	NOUN
ejpam-5564	39	38	)	)	PUNCT
ejpam-5564	39	39	;	;	PUNCT
ejpam-5564	39	40	the	the	DET
ejpam-5564	39	41	influence	influence	NOUN
ejpam-5564	39	42	of	of	ADP
ejpam-5564	39	43	perturbation	perturbation	NOUN
ejpam-5564	39	44	of	of	ADP
ejpam-5564	39	45	initial	initial	ADJ
ejpam-5564	39	46	data	datum	NOUN
ejpam-5564	39	47	(	(	PUNCT
ejpam-5564	39	48	movable	movable	ADJ
ejpam-5564	39	49	singular	singular	NOUN
ejpam-5564	39	50	point	point	NOUN
ejpam-5564	39	51	)	)	PUNCT
ejpam-5564	39	52	on	on	ADP
ejpam-5564	39	53	the	the	DET
ejpam-5564	39	54	structure	structure	NOUN
ejpam-5564	39	55	of	of	ADP
ejpam-5564	39	56	the	the	DET
ejpam-5564	39	57	analytical	analytical	ADJ
ejpam-5564	39	58	approximate	approximate	ADJ
ejpam-5564	39	59	solution	solution	NOUN
ejpam-5564	39	60	;	;	PUNCT
ejpam-5564	39	61	precise	precise	ADJ
ejpam-5564	39	62	criteria	criterion	NOUN
ejpam-5564	39	63	for	for	ADP
ejpam-5564	39	64	the	the	DET
ejpam-5564	39	65	existence	existence	NOUN
ejpam-5564	39	66	of	of	ADP
ejpam-5564	39	67	movable	movable	ADJ
ejpam-5564	39	68	singular	singular	NOUN
ejpam-5564	39	69	points	point	NOUN
ejpam-5564	39	70	;	;	PUNCT
ejpam-5564	39	71	precise	precise	ADJ
ejpam-5564	39	72	boundaries	boundary	NOUN
ejpam-5564	39	73	for	for	ADP
ejpam-5564	39	74	the	the	DET
ejpam-5564	39	75	application	application	NOUN
ejpam-5564	39	76	of	of	ADP
ejpam-5564	39	77	the	the	DET
ejpam-5564	39	78	analytical	analytical	ADJ
ejpam-5564	39	79	approximate	approximate	ADJ
ejpam-5564	39	80	solution	solution	NOUN
ejpam-5564	39	81	.	.	PUNCT
ejpam-5564	40	1	solving	solve	VERB
ejpam-5564	40	2	these	these	DET
ejpam-5564	40	3	problems	problem	NOUN
ejpam-5564	40	4	allows	allow	VERB
ejpam-5564	40	5	for	for	ADP
ejpam-5564	40	6	the	the	DET
ejpam-5564	40	7	development	development	NOUN
ejpam-5564	40	8	of	of	ADP
ejpam-5564	40	9	an	an	DET
ejpam-5564	40	10	algorithm	algorithm	NOUN
ejpam-5564	40	11	to	to	PART
ejpam-5564	40	12	find	find	VERB
ejpam-5564	40	13	a	a	DET
ejpam-5564	40	14	movable	movable	ADJ
ejpam-5564	40	15	singular	singular	NOUN
ejpam-5564	40	16	point	point	NOUN
ejpam-5564	40	17	with	with	ADP
ejpam-5564	40	18	a	a	DET
ejpam-5564	40	19	predetermined	predetermine	VERB
ejpam-5564	40	20	accuracy	accuracy	NOUN
ejpam-5564	40	21	and	and	CCONJ
ejpam-5564	40	22	to	to	PART
ejpam-5564	40	23	combine	combine	VERB
ejpam-5564	40	24	the	the	DET
ejpam-5564	40	25	obtained	obtain	VERB
ejpam-5564	40	26	results	result	NOUN
ejpam-5564	40	27	with	with	ADP
ejpam-5564	40	28	existing	exist	VERB
ejpam-5564	40	29	numerical	numerical	ADJ
ejpam-5564	40	30	methods	method	NOUN
ejpam-5564	40	31	[	[	X
ejpam-5564	40	32	35	35	NUM
ejpam-5564	40	33	]	]	PUNCT
ejpam-5564	40	34	.	.	PUNCT
ejpam-5564	41	1	this	this	DET
ejpam-5564	41	2	method	method	NOUN
ejpam-5564	41	3	has	have	AUX
ejpam-5564	41	4	already	already	ADV
ejpam-5564	41	5	been	be	AUX
ejpam-5564	41	6	successfully	successfully	ADV
ejpam-5564	41	7	tested	test	VERB
ejpam-5564	41	8	in	in	ADP
ejpam-5564	41	9	solving	solve	VERB
ejpam-5564	41	10	certain	certain	ADJ
ejpam-5564	41	11	classes	class	NOUN
ejpam-5564	41	12	of	of	ADP
ejpam-5564	41	13	equations	equation	NOUN
ejpam-5564	41	14	.	.	PUNCT
ejpam-5564	42	1	m.	m.	NOUN
ejpam-5564	42	2	gasanov	gasanov	PROPN
ejpam-5564	42	3	/	/	SYM
ejpam-5564	42	4	eur	eur	PROPN
ejpam-5564	42	5	.	.	PUNCT
ejpam-5564	43	1	j.	j.	PROPN
ejpam-5564	43	2	pure	pure	PROPN
ejpam-5564	43	3	appl	appl	PROPN
ejpam-5564	43	4	.	.	PROPN
ejpam-5564	43	5	math	math	PROPN
ejpam-5564	43	6	,	,	PUNCT
ejpam-5564	43	7	18	18	NUM
ejpam-5564	43	8	(	(	PUNCT
ejpam-5564	43	9	1	1	NUM
ejpam-5564	43	10	)	)	PUNCT
ejpam-5564	43	11	(	(	PUNCT
ejpam-5564	43	12	2025	2025	NUM
ejpam-5564	43	13	)	)	PUNCT
ejpam-5564	43	14	,	,	PUNCT
ejpam-5564	43	15	5564	5564	NUM
ejpam-5564	43	16	3	3	NUM
ejpam-5564	43	17	of	of	ADP
ejpam-5564	43	18	19	19	NUM
ejpam-5564	43	19	in	in	ADP
ejpam-5564	43	20	the	the	DET
ejpam-5564	43	21	works	work	NOUN
ejpam-5564	43	22	[	[	X
ejpam-5564	43	23	27–30	27–30	NUM
ejpam-5564	43	24	]	]	PUNCT
ejpam-5564	43	25	,	,	PUNCT
ejpam-5564	43	26	the	the	DET
ejpam-5564	43	27	described	describe	VERB
ejpam-5564	43	28	method	method	NOUN
ejpam-5564	43	29	has	have	AUX
ejpam-5564	43	30	been	be	AUX
ejpam-5564	43	31	used	use	VERB
ejpam-5564	43	32	to	to	PART
ejpam-5564	43	33	investigate	investigate	VERB
ejpam-5564	43	34	the	the	DET
ejpam-5564	43	35	van	van	PROPN
ejpam-5564	43	36	der	der	ADJ
ejpam-5564	43	37	pol	pol	NOUN
ejpam-5564	43	38	equation	equation	NOUN
ejpam-5564	43	39	in	in	ADP
ejpam-5564	43	40	the	the	DET
ejpam-5564	43	41	complex	complex	ADJ
ejpam-5564	43	42	domain	domain	NOUN
ejpam-5564	43	43	.	.	PUNCT
ejpam-5564	44	1	in	in	ADP
ejpam-5564	44	2	[	[	X
ejpam-5564	44	3	29	29	NUM
ejpam-5564	44	4	]	]	PUNCT
ejpam-5564	44	5	,	,	PUNCT
ejpam-5564	44	6	an	an	DET
ejpam-5564	44	7	approximate	approximate	ADJ
ejpam-5564	44	8	analytical	analytical	ADJ
ejpam-5564	44	9	solution	solution	NOUN
ejpam-5564	44	10	to	to	ADP
ejpam-5564	44	11	the	the	DET
ejpam-5564	44	12	initial	initial	ADJ
ejpam-5564	44	13	value	value	NOUN
ejpam-5564	44	14	problem	problem	NOUN
ejpam-5564	44	15	in	in	ADP
ejpam-5564	44	16	the	the	DET
ejpam-5564	44	17	domain	domain	NOUN
ejpam-5564	44	18	of	of	ADP
ejpam-5564	44	19	analyticity	analyticity	NOUN
ejpam-5564	44	20	is	be	AUX
ejpam-5564	44	21	found	find	VERB
ejpam-5564	44	22	.	.	PUNCT
ejpam-5564	45	1	the	the	DET
ejpam-5564	45	2	work	work	NOUN
ejpam-5564	45	3	[	[	X
ejpam-5564	45	4	30	30	NUM
ejpam-5564	45	5	]	]	PUNCT
ejpam-5564	45	6	is	be	AUX
ejpam-5564	45	7	dedicated	dedicate	VERB
ejpam-5564	45	8	to	to	ADP
ejpam-5564	45	9	studying	study	VERB
ejpam-5564	45	10	the	the	DET
ejpam-5564	45	11	influence	influence	NOUN
ejpam-5564	45	12	of	of	ADP
ejpam-5564	45	13	perturbations	perturbation	NOUN
ejpam-5564	45	14	in	in	ADP
ejpam-5564	45	15	initial	initial	ADJ
ejpam-5564	45	16	data	datum	NOUN
ejpam-5564	45	17	on	on	ADP
ejpam-5564	45	18	the	the	DET
ejpam-5564	45	19	structure	structure	NOUN
ejpam-5564	45	20	of	of	ADP
ejpam-5564	45	21	the	the	DET
ejpam-5564	45	22	approximate	approximate	ADJ
ejpam-5564	45	23	analytical	analytical	ADJ
ejpam-5564	45	24	solution	solution	NOUN
ejpam-5564	45	25	.	.	PUNCT
ejpam-5564	46	1	in	in	ADP
ejpam-5564	46	2	the	the	DET
ejpam-5564	46	3	article	article	NOUN
ejpam-5564	46	4	[	[	X
ejpam-5564	46	5	28	28	NUM
ejpam-5564	46	6	]	]	PUNCT
ejpam-5564	46	7	,	,	PUNCT
ejpam-5564	46	8	the	the	DET
ejpam-5564	46	9	authors	author	NOUN
ejpam-5564	46	10	found	find	VERB
ejpam-5564	46	11	an	an	DET
ejpam-5564	46	12	approximate	approximate	ADJ
ejpam-5564	46	13	analytical	analytical	ADJ
ejpam-5564	46	14	solution	solution	NOUN
ejpam-5564	46	15	in	in	ADP
ejpam-5564	46	16	the	the	DET
ejpam-5564	46	17	neighborhood	neighborhood	NOUN
ejpam-5564	46	18	of	of	ADP
ejpam-5564	46	19	the	the	DET
ejpam-5564	46	20	movable	movable	ADJ
ejpam-5564	46	21	singular	singular	NOUN
ejpam-5564	46	22	point	point	NOUN
ejpam-5564	46	23	,	,	PUNCT
ejpam-5564	46	24	while	while	SCONJ
ejpam-5564	46	25	[	[	X
ejpam-5564	46	26	27	27	NUM
ejpam-5564	46	27	]	]	PUNCT
ejpam-5564	46	28	addressed	address	VERB
ejpam-5564	46	29	the	the	DET
ejpam-5564	46	30	problem	problem	NOUN
ejpam-5564	46	31	of	of	ADP
ejpam-5564	46	32	the	the	DET
ejpam-5564	46	33	influence	influence	NOUN
ejpam-5564	46	34	of	of	ADP
ejpam-5564	46	35	perturbations	perturbation	NOUN
ejpam-5564	46	36	in	in	ADP
ejpam-5564	46	37	the	the	DET
ejpam-5564	46	38	movable	movable	ADJ
ejpam-5564	46	39	singular	singular	NOUN
ejpam-5564	46	40	point	point	NOUN
ejpam-5564	46	41	on	on	ADP
ejpam-5564	46	42	the	the	DET
ejpam-5564	46	43	structure	structure	NOUN
ejpam-5564	46	44	of	of	ADP
ejpam-5564	46	45	the	the	DET
ejpam-5564	46	46	approximate	approximate	ADJ
ejpam-5564	46	47	analytical	analytical	ADJ
ejpam-5564	46	48	solution	solution	NOUN
ejpam-5564	46	49	.	.	PUNCT
ejpam-5564	47	1	in	in	ADP
ejpam-5564	47	2	[	[	X
ejpam-5564	47	3	31–36	31–36	NUM
ejpam-5564	47	4	]	]	PUNCT
ejpam-5564	47	5	,	,	PUNCT
ejpam-5564	47	6	the	the	DET
ejpam-5564	47	7	authors	author	NOUN
ejpam-5564	47	8	have	have	AUX
ejpam-5564	47	9	successfully	successfully	ADV
ejpam-5564	47	10	solved	solve	VERB
ejpam-5564	47	11	all	all	DET
ejpam-5564	47	12	research	research	NOUN
ejpam-5564	47	13	problems	problem	NOUN
ejpam-5564	47	14	related	relate	VERB
ejpam-5564	47	15	to	to	ADP
ejpam-5564	47	16	thirdorder	thirdorder	PROPN
ejpam-5564	47	17	nonlinear	nonlinear	PROPN
ejpam-5564	47	18	differential	differential	ADJ
ejpam-5564	47	19	equations	equation	NOUN
ejpam-5564	47	20	with	with	ADP
ejpam-5564	47	21	polynomial	polynomial	ADJ
ejpam-5564	47	22	right	right	ADJ
ejpam-5564	47	23	-	-	PUNCT
ejpam-5564	47	24	hand	hand	NOUN
ejpam-5564	47	25	side	side	NOUN
ejpam-5564	47	26	of	of	ADP
ejpam-5564	47	27	both	both	CCONJ
ejpam-5564	47	28	second	second	ADJ
ejpam-5564	47	29	and	and	CCONJ
ejpam-5564	47	30	seventh	seventh	ADJ
ejpam-5564	47	31	degrees	degree	NOUN
ejpam-5564	47	32	.	.	PUNCT
ejpam-5564	48	1	for	for	ADP
ejpam-5564	48	2	other	other	ADJ
ejpam-5564	48	3	classes	class	NOUN
ejpam-5564	48	4	of	of	ADP
ejpam-5564	48	5	equations	equation	NOUN
ejpam-5564	48	6	,	,	PUNCT
ejpam-5564	48	7	the	the	DET
ejpam-5564	48	8	same	same	ADJ
ejpam-5564	48	9	method	method	NOUN
ejpam-5564	48	10	for	for	ADP
ejpam-5564	48	11	finding	find	VERB
ejpam-5564	48	12	analytical	analytical	ADJ
ejpam-5564	48	13	approximate	approximate	ADJ
ejpam-5564	48	14	solutions	solution	NOUN
ejpam-5564	48	15	has	have	AUX
ejpam-5564	48	16	been	be	AUX
ejpam-5564	48	17	explored	explore	VERB
ejpam-5564	48	18	in	in	ADP
ejpam-5564	48	19	[	[	X
ejpam-5564	48	20	3	3	NUM
ejpam-5564	48	21	,	,	PUNCT
ejpam-5564	48	22	20	20	NUM
ejpam-5564	48	23	,	,	PUNCT
ejpam-5564	48	24	37	37	NUM
ejpam-5564	48	25	,	,	PUNCT
ejpam-5564	48	26	40	40	NUM
ejpam-5564	48	27	]	]	PUNCT
ejpam-5564	48	28	.	.	PUNCT
ejpam-5564	49	1	for	for	ADP
ejpam-5564	49	2	the	the	DET
ejpam-5564	49	3	equation	equation	NOUN
ejpam-5564	49	4	(	(	PUNCT
ejpam-5564	49	5	1	1	NUM
ejpam-5564	49	6	)	)	PUNCT
ejpam-5564	49	7	,	,	PUNCT
ejpam-5564	49	8	two	two	NUM
ejpam-5564	49	9	problems	problem	NOUN
ejpam-5564	49	10	are	be	AUX
ejpam-5564	49	11	addressed	address	VERB
ejpam-5564	49	12	:	:	PUNCT
ejpam-5564	49	13	the	the	DET
ejpam-5564	49	14	classical	classical	ADJ
ejpam-5564	49	15	problem	problem	NOUN
ejpam-5564	49	16	of	of	ADP
ejpam-5564	49	17	the	the	DET
ejpam-5564	49	18	theory	theory	NOUN
ejpam-5564	49	19	of	of	ADP
ejpam-5564	49	20	differential	differential	ADJ
ejpam-5564	49	21	equations	equation	NOUN
ejpam-5564	49	22	,	,	PUNCT
ejpam-5564	49	23	the	the	DET
ejpam-5564	49	24	proof	proof	NOUN
ejpam-5564	49	25	of	of	ADP
ejpam-5564	49	26	the	the	DET
ejpam-5564	49	27	existence	existence	NOUN
ejpam-5564	49	28	and	and	CCONJ
ejpam-5564	49	29	uniqueness	uniqueness	NOUN
ejpam-5564	49	30	theorem	theorem	VERB
ejpam-5564	49	31	,	,	PUNCT
ejpam-5564	49	32	and	and	CCONJ
ejpam-5564	49	33	the	the	DET
ejpam-5564	49	34	precise	precise	ADJ
ejpam-5564	49	35	criteria	criterion	NOUN
ejpam-5564	49	36	for	for	ADP
ejpam-5564	49	37	the	the	DET
ejpam-5564	49	38	existence	existence	NOUN
ejpam-5564	49	39	of	of	ADP
ejpam-5564	49	40	a	a	DET
ejpam-5564	49	41	moving	move	VERB
ejpam-5564	49	42	singular	singular	ADJ
ejpam-5564	49	43	point	point	NOUN
ejpam-5564	49	44	.	.	PUNCT
ejpam-5564	50	1	the	the	DET
ejpam-5564	50	2	existence	existence	NOUN
ejpam-5564	50	3	theorem	theorem	NOUN
ejpam-5564	50	4	is	be	AUX
ejpam-5564	50	5	considered	consider	VERB
ejpam-5564	50	6	in	in	ADP
ejpam-5564	50	7	the	the	DET
ejpam-5564	50	8	complex	complex	ADJ
ejpam-5564	50	9	domain	domain	NOUN
ejpam-5564	50	10	.	.	PUNCT
ejpam-5564	51	1	the	the	DET
ejpam-5564	51	2	solution	solution	NOUN
ejpam-5564	51	3	is	be	AUX
ejpam-5564	51	4	sought	seek	VERB
ejpam-5564	51	5	in	in	ADP
ejpam-5564	51	6	the	the	DET
ejpam-5564	51	7	form	form	NOUN
ejpam-5564	51	8	of	of	ADP
ejpam-5564	51	9	a	a	DET
ejpam-5564	51	10	puiseux	puiseux	NOUN
ejpam-5564	51	11	series	series	NOUN
ejpam-5564	51	12	.	.	PUNCT
ejpam-5564	52	1	estimates	estimate	NOUN
ejpam-5564	52	2	for	for	ADP
ejpam-5564	52	3	the	the	DET
ejpam-5564	52	4	series	series	NOUN
ejpam-5564	52	5	coefficients	coefficient	NOUN
ejpam-5564	52	6	are	be	AUX
ejpam-5564	52	7	provided	provide	VERB
ejpam-5564	52	8	to	to	PART
ejpam-5564	52	9	determine	determine	VERB
ejpam-5564	52	10	the	the	DET
ejpam-5564	52	11	convergence	convergence	NOUN
ejpam-5564	52	12	region	region	NOUN
ejpam-5564	52	13	of	of	ADP
ejpam-5564	52	14	the	the	DET
ejpam-5564	52	15	analytic	analytic	ADJ
ejpam-5564	52	16	part	part	NOUN
ejpam-5564	52	17	of	of	ADP
ejpam-5564	52	18	the	the	DET
ejpam-5564	52	19	series	series	NOUN
ejpam-5564	52	20	.	.	PUNCT
ejpam-5564	53	1	an	an	DET
ejpam-5564	53	2	analytical	analytical	ADJ
ejpam-5564	53	3	approximate	approximate	ADJ
ejpam-5564	53	4	solution	solution	NOUN
ejpam-5564	53	5	is	be	AUX
ejpam-5564	53	6	obtained	obtain	VERB
ejpam-5564	53	7	,	,	PUNCT
ejpam-5564	53	8	along	along	ADP
ejpam-5564	53	9	with	with	ADP
ejpam-5564	53	10	estimates	estimate	NOUN
ejpam-5564	53	11	of	of	ADP
ejpam-5564	53	12	its	its	PRON
ejpam-5564	53	13	error	error	NOUN
ejpam-5564	53	14	.	.	PUNCT
ejpam-5564	54	1	the	the	DET
ejpam-5564	54	2	second	second	ADJ
ejpam-5564	54	3	problem	problem	NOUN
ejpam-5564	54	4	,	,	PUNCT
ejpam-5564	54	5	finding	find	VERB
ejpam-5564	54	6	precise	precise	ADJ
ejpam-5564	54	7	criteria	criterion	NOUN
ejpam-5564	54	8	for	for	ADP
ejpam-5564	54	9	the	the	DET
ejpam-5564	54	10	existence	existence	NOUN
ejpam-5564	54	11	of	of	ADP
ejpam-5564	54	12	a	a	DET
ejpam-5564	54	13	moving	move	VERB
ejpam-5564	54	14	singular	singular	ADJ
ejpam-5564	54	15	point	point	NOUN
ejpam-5564	54	16	,	,	PUNCT
ejpam-5564	54	17	which	which	PRON
ejpam-5564	54	18	has	have	AUX
ejpam-5564	54	19	been	be	AUX
ejpam-5564	54	20	solved	solve	VERB
ejpam-5564	54	21	in	in	ADP
ejpam-5564	54	22	both	both	CCONJ
ejpam-5564	54	23	real	real	ADJ
ejpam-5564	54	24	and	and	CCONJ
ejpam-5564	54	25	complex	complex	ADJ
ejpam-5564	54	26	domains	domain	NOUN
ejpam-5564	54	27	due	due	ADP
ejpam-5564	54	28	to	to	ADP
ejpam-5564	54	29	the	the	DET
ejpam-5564	54	30	different	different	ADJ
ejpam-5564	54	31	approaches	approach	NOUN
ejpam-5564	54	32	to	to	ADP
ejpam-5564	54	33	solving	solve	VERB
ejpam-5564	54	34	these	these	DET
ejpam-5564	54	35	problems	problem	NOUN
ejpam-5564	54	36	.	.	PUNCT
ejpam-5564	55	1	2	2	X
ejpam-5564	55	2	.	.	X
ejpam-5564	55	3	main	main	ADJ
ejpam-5564	55	4	results	result	NOUN
ejpam-5564	55	5	2.1	2.1	NUM
ejpam-5564	55	6	.	.	PUNCT
ejpam-5564	56	1	the	the	DET
ejpam-5564	56	2	theorem	theorem	NOUN
ejpam-5564	56	3	of	of	ADP
ejpam-5564	56	4	existence	existence	NOUN
ejpam-5564	56	5	and	and	CCONJ
ejpam-5564	56	6	uniqueness	uniqueness	NOUN
ejpam-5564	56	7	.	.	PUNCT
ejpam-5564	57	1	modification	modification	NOUN
ejpam-5564	57	2	of	of	ADP
ejpam-5564	57	3	the	the	DET
ejpam-5564	57	4	cauchy	cauchy	PROPN
ejpam-5564	57	5	–	–	PUNCT
ejpam-5564	57	6	kovalevskaya	kovalevskaya	NOUN
ejpam-5564	57	7	theorem	theorem	VERB
ejpam-5564	57	8	.	.	PUNCT
ejpam-5564	58	1	let	let	VERB
ejpam-5564	58	2	’s	’s	NOUN
ejpam-5564	58	3	consider	consider	VERB
ejpam-5564	58	4	the	the	DET
ejpam-5564	58	5	following	follow	VERB
ejpam-5564	58	6	cauchy	cauchy	PROPN
ejpam-5564	58	7	problem	problem	NOUN
ejpam-5564	58	8	:	:	PUNCT
ejpam-5564	58	9	w(4	w(4	X
ejpam-5564	58	10	)	)	PUNCT
ejpam-5564	59	1	+	+	ADP
ejpam-5564	59	2	q0w	q0w	PROPN
ejpam-5564	59	3	(	(	PUNCT
ejpam-5564	59	4	w′)2	w′)2	PROPN
ejpam-5564	59	5	=	=	SYM
ejpam-5564	59	6	f	f	PROPN
ejpam-5564	59	7	(	(	PUNCT
ejpam-5564	59	8	z	z	NOUN
ejpam-5564	59	9	)	)	PUNCT
ejpam-5564	59	10	,	,	PUNCT
ejpam-5564	59	11	(	(	PUNCT
ejpam-5564	59	12	2)	2)	NUM
ejpam-5564	59	13	w	w	PROPN
ejpam-5564	59	14	(	(	PUNCT
ejpam-5564	59	15	z0	z0	PROPN
ejpam-5564	59	16	)	)	PUNCT
ejpam-5564	59	17	=	=	NOUN
ejpam-5564	59	18	w0	w0	PROPN
ejpam-5564	59	19	,	,	PUNCT
ejpam-5564	59	20	w′	w′	PROPN
ejpam-5564	59	21	(	(	PUNCT
ejpam-5564	59	22	z0	z0	PROPN
ejpam-5564	59	23	)	)	PUNCT
ejpam-5564	59	24	=	=	PUNCT
ejpam-5564	59	25	w′	w′	NOUN
ejpam-5564	59	26	0	0	NUM
ejpam-5564	59	27	,	,	PUNCT
ejpam-5564	59	28	w′′	w′′	NOUN
ejpam-5564	59	29	(	(	PUNCT
ejpam-5564	59	30	z0	z0	PROPN
ejpam-5564	59	31	)	)	PUNCT
ejpam-5564	59	32	=	=	SYM
ejpam-5564	59	33	w′′	w′′	NOUN
ejpam-5564	59	34	0	0	NUM
ejpam-5564	59	35	,	,	PUNCT
ejpam-5564	59	36	w′′′	w′′′	NOUN
ejpam-5564	59	37	(	(	PUNCT
ejpam-5564	59	38	z0	z0	PROPN
ejpam-5564	59	39	)	)	PUNCT
ejpam-5564	59	40	=	=	PUNCT
ejpam-5564	59	41	w′′′	w′′′	NOUN
ejpam-5564	59	42	0	0	NUM
ejpam-5564	59	43	,	,	PUNCT
ejpam-5564	59	44	(	(	PUNCT
ejpam-5564	59	45	3	3	X
ejpam-5564	59	46	)	)	PUNCT
ejpam-5564	60	1	where	where	SCONJ
ejpam-5564	60	2	w′	w′	PROPN
ejpam-5564	60	3	0	0	NUM
ejpam-5564	60	4	,	,	PUNCT
ejpam-5564	60	5	w	w	ADP
ejpam-5564	60	6	′′	′′	PROPN
ejpam-5564	60	7	0	0	NUM
ejpam-5564	60	8	,	,	PUNCT
ejpam-5564	60	9	w	w	PROPN
ejpam-5564	60	10	′′′	′′′	PROPN
ejpam-5564	60	11	0	0	NUM
ejpam-5564	60	12	,	,	PUNCT
ejpam-5564	60	13	q0	q0	PROPN
ejpam-5564	60	14	∈	∈	PROPN
ejpam-5564	60	15	c.	c.	PROPN
ejpam-5564	60	16	theorem	theorem	VERB
ejpam-5564	60	17	1	1	X
ejpam-5564	60	18	.	.	PUNCT
ejpam-5564	61	1	let	let	VERB
ejpam-5564	61	2	z∗	z∗	PROPN
ejpam-5564	61	3	be	be	AUX
ejpam-5564	61	4	a	a	DET
ejpam-5564	61	5	moving	move	VERB
ejpam-5564	61	6	singular	singular	ADJ
ejpam-5564	61	7	point	point	NOUN
ejpam-5564	61	8	of	of	ADP
ejpam-5564	61	9	the	the	DET
ejpam-5564	61	10	cauchy	cauchy	ADJ
ejpam-5564	61	11	problem	problem	NOUN
ejpam-5564	61	12	(	(	PUNCT
ejpam-5564	61	13	2	2	NUM
ejpam-5564	61	14	)	)	PUNCT
ejpam-5564	61	15	—	—	PUNCT
ejpam-5564	61	16	(	(	PUNCT
ejpam-5564	61	17	3	3	NUM
ejpam-5564	61	18	)	)	PUNCT
ejpam-5564	61	19	,	,	PUNCT
ejpam-5564	61	20	and	and	CCONJ
ejpam-5564	61	21	let	let	VERB
ejpam-5564	61	22	the	the	DET
ejpam-5564	61	23	function	function	NOUN
ejpam-5564	61	24	f	f	PROPN
ejpam-5564	61	25	(	(	PUNCT
ejpam-5564	61	26	z	z	NOUN
ejpam-5564	61	27	)	)	PUNCT
ejpam-5564	61	28	be	be	AUX
ejpam-5564	61	29	holomorphic	holomorphic	ADJ
ejpam-5564	61	30	in	in	ADP
ejpam-5564	61	31	the	the	DET
ejpam-5564	61	32	domain	domain	NOUN
ejpam-5564	61	33	|z∗	|z∗	PROPN
ejpam-5564	61	34	−	−	PROPN
ejpam-5564	61	35	z|	z|	PROPN
ejpam-5564	61	36	<	<	X
ejpam-5564	61	37	ρ1	ρ1	PROPN
ejpam-5564	61	38	,	,	PUNCT
ejpam-5564	61	39	then	then	ADV
ejpam-5564	61	40	the	the	DET
ejpam-5564	61	41	solution	solution	NOUN
ejpam-5564	61	42	w	w	PROPN
ejpam-5564	61	43	(	(	PUNCT
ejpam-5564	61	44	z	z	NOUN
ejpam-5564	61	45	)	)	PUNCT
ejpam-5564	61	46	is	be	AUX
ejpam-5564	61	47	representable	representable	ADJ
ejpam-5564	61	48	in	in	ADP
ejpam-5564	61	49	the	the	DET
ejpam-5564	61	50	form	form	NOUN
ejpam-5564	61	51	of	of	ADP
ejpam-5564	61	52	a	a	DET
ejpam-5564	61	53	meromorphic	meromorphic	ADJ
ejpam-5564	61	54	function	function	NOUN
ejpam-5564	61	55	:	:	PUNCT
ejpam-5564	62	1	w	w	X
ejpam-5564	62	2	(	(	PUNCT
ejpam-5564	62	3	z	z	NOUN
ejpam-5564	62	4	)	)	PUNCT
ejpam-5564	62	5	=	=	SYM
ejpam-5564	62	6	(	(	PUNCT
ejpam-5564	62	7	z∗	z∗	NOUN
ejpam-5564	62	8	−	−	PROPN
ejpam-5564	62	9	z)−1	z)−1	NUM
ejpam-5564	62	10	∑	∑	PROPN
ejpam-5564	62	11	n≥0	n≥0	PROPN
ejpam-5564	62	12	an	an	DET
ejpam-5564	62	13	(	(	PUNCT
ejpam-5564	62	14	z	z	NOUN
ejpam-5564	62	15	∗	∗	NOUN
ejpam-5564	62	16	−	−	PROPN
ejpam-5564	62	17	z)n	z)n	PUNCT
ejpam-5564	62	18	,	,	PUNCT
ejpam-5564	62	19	(	(	PUNCT
ejpam-5564	62	20	4	4	X
ejpam-5564	62	21	)	)	PUNCT
ejpam-5564	62	22	m.	m.	NOUN
ejpam-5564	62	23	gasanov	gasanov	NOUN
ejpam-5564	62	24	/	/	SYM
ejpam-5564	62	25	eur	eur	PROPN
ejpam-5564	62	26	.	.	PUNCT
ejpam-5564	63	1	j.	j.	PROPN
ejpam-5564	63	2	pure	pure	PROPN
ejpam-5564	63	3	appl	appl	PROPN
ejpam-5564	63	4	.	.	PROPN
ejpam-5564	63	5	math	math	PROPN
ejpam-5564	63	6	,	,	PUNCT
ejpam-5564	63	7	18	18	NUM
ejpam-5564	63	8	(	(	PUNCT
ejpam-5564	63	9	1	1	NUM
ejpam-5564	63	10	)	)	PUNCT
ejpam-5564	63	11	(	(	PUNCT
ejpam-5564	63	12	2025	2025	NUM
ejpam-5564	63	13	)	)	PUNCT
ejpam-5564	63	14	,	,	PUNCT
ejpam-5564	63	15	5564	5564	NUM
ejpam-5564	63	16	4	4	NUM
ejpam-5564	63	17	of	of	ADP
ejpam-5564	63	18	19	19	NUM
ejpam-5564	63	19	in	in	ADP
ejpam-5564	63	20	the	the	DET
ejpam-5564	63	21	domain	domain	NOUN
ejpam-5564	63	22	|z	|z	PROPN
ejpam-5564	63	23	−	−	PROPN
ejpam-5564	63	24	z∗|	z∗|	X
ejpam-5564	63	25	<	<	X
ejpam-5564	63	26	ρ2	ρ2	PROPN
ejpam-5564	63	27	.	.	PUNCT
ejpam-5564	64	1	here	here	ADV
ejpam-5564	64	2	ρ2	ρ2	NOUN
ejpam-5564	64	3	=	=	SYM
ejpam-5564	64	4	max	max	PROPN
ejpam-5564	64	5	{	{	PUNCT
ejpam-5564	64	6	ρ1	ρ1	PROPN
ejpam-5564	64	7	,	,	PUNCT
ejpam-5564	64	8	1	1	NUM
ejpam-5564	64	9	5	5	NUM
ejpam-5564	64	10	√	√	NOUN
ejpam-5564	64	11	|γ|	|γ|	PROPN
ejpam-5564	64	12	}	}	PUNCT
ejpam-5564	64	13	,	,	PUNCT
ejpam-5564	64	14	where	where	SCONJ
ejpam-5564	64	15	|γ|	|γ|	PROPN
ejpam-5564	64	16	=	=	SYM
ejpam-5564	64	17	max	max	PROPN
ejpam-5564	64	18	{	{	PUNCT
ejpam-5564	64	19	sup	sup	NOUN
ejpam-5564	64	20	n	n	CCONJ
ejpam-5564	64	21	(	(	PUNCT
ejpam-5564	64	22	∣∣∣∣∣f	∣∣∣∣∣f	NOUN
ejpam-5564	64	23	(	(	PUNCT
ejpam-5564	64	24	n	n	CCONJ
ejpam-5564	64	25	)	)	PUNCT
ejpam-5564	64	26	(	(	PUNCT
ejpam-5564	64	27	z∗	z∗	NOUN
ejpam-5564	64	28	)	)	PUNCT
ejpam-5564	64	29	n	n	CCONJ
ejpam-5564	64	30	!	!	PUNCT
ejpam-5564	64	31	∣∣∣∣∣	∣∣∣∣∣	NUM
ejpam-5564	64	32	)	)	PUNCT
ejpam-5564	64	33	,	,	PUNCT
ejpam-5564	64	34	|w0|	|w0|	NOUN
ejpam-5564	64	35	,	,	PUNCT
ejpam-5564	64	36	∣∣w′	∣∣w′	NOUN
ejpam-5564	64	37	0	0	NUM
ejpam-5564	64	38	∣∣	∣∣	NUM
ejpam-5564	64	39	,	,	PUNCT
ejpam-5564	64	40	∣∣w′′	∣∣w′′	X
ejpam-5564	64	41	0	0	NUM
ejpam-5564	64	42	∣∣	∣∣	NUM
ejpam-5564	64	43	,	,	PUNCT
ejpam-5564	64	44	∣∣w′′′	∣∣w′′′	PROPN
ejpam-5564	64	45	0	0	PUNCT
ejpam-5564	64	46	∣∣	∣∣	NUM
ejpam-5564	64	47	}	}	PUNCT
ejpam-5564	64	48	.	.	PUNCT
ejpam-5564	65	1	proof	proof	NOUN
ejpam-5564	65	2	.	.	PUNCT
ejpam-5564	66	1	we	we	PRON
ejpam-5564	66	2	will	will	AUX
ejpam-5564	66	3	seek	seek	VERB
ejpam-5564	66	4	the	the	DET
ejpam-5564	66	5	solution	solution	NOUN
ejpam-5564	66	6	in	in	ADP
ejpam-5564	66	7	the	the	DET
ejpam-5564	66	8	form	form	NOUN
ejpam-5564	66	9	of	of	ADP
ejpam-5564	66	10	a	a	DET
ejpam-5564	66	11	generalized	generalized	ADJ
ejpam-5564	66	12	power	power	NOUN
ejpam-5564	66	13	series	series	NOUN
ejpam-5564	66	14	:	:	PUNCT
ejpam-5564	66	15	w	w	PROPN
ejpam-5564	66	16	(	(	PUNCT
ejpam-5564	66	17	z	z	NOUN
ejpam-5564	66	18	)	)	PUNCT
ejpam-5564	66	19	=	=	PUNCT
ejpam-5564	67	1	∑	∑	PUNCT
ejpam-5564	67	2	n≥0	n≥0	PROPN
ejpam-5564	67	3	an	an	DET
ejpam-5564	67	4	(	(	PUNCT
ejpam-5564	67	5	z	z	NOUN
ejpam-5564	67	6	∗	∗	NOUN
ejpam-5564	67	7	−	−	PROPN
ejpam-5564	67	8	z)n+r	z)n+r	PROPN
ejpam-5564	67	9	.	.	PUNCT
ejpam-5564	68	1	(	(	PUNCT
ejpam-5564	68	2	5	5	X
ejpam-5564	68	3	)	)	PUNCT
ejpam-5564	68	4	let	let	VERB
ejpam-5564	68	5	’s	’s	NOUN
ejpam-5564	68	6	substitute	substitute	VERB
ejpam-5564	68	7	the	the	DET
ejpam-5564	68	8	formula	formula	NOUN
ejpam-5564	68	9	(	(	PUNCT
ejpam-5564	68	10	5	5	NUM
ejpam-5564	68	11	)	)	PUNCT
ejpam-5564	68	12	into	into	ADP
ejpam-5564	68	13	the	the	DET
ejpam-5564	68	14	equation	equation	NOUN
ejpam-5564	68	15	(	(	PUNCT
ejpam-5564	68	16	2	2	NUM
ejpam-5564	68	17	)	)	PUNCT
ejpam-5564	68	18	,	,	PUNCT
ejpam-5564	68	19	and	and	CCONJ
ejpam-5564	68	20	obtain	obtain	VERB
ejpam-5564	68	21	:	:	PUNCT
ejpam-5564	68	22	∑	∑	PUNCT
ejpam-5564	68	23	n≥0	n≥0	ADP
ejpam-5564	68	24	an	an	DET
ejpam-5564	68	25	(	(	PUNCT
ejpam-5564	68	26	n+	n+	NOUN
ejpam-5564	68	27	r	r	NOUN
ejpam-5564	68	28	)	)	PUNCT
ejpam-5564	68	29	(	(	PUNCT
ejpam-5564	68	30	n+	n+	INTJ
ejpam-5564	68	31	r	r	NOUN
ejpam-5564	68	32	−	−	NOUN
ejpam-5564	68	33	1	1	NUM
ejpam-5564	68	34	)	)	PUNCT
ejpam-5564	68	35	(	(	PUNCT
ejpam-5564	68	36	n+	n+	INTJ
ejpam-5564	68	37	r	r	NOUN
ejpam-5564	68	38	−	−	NOUN
ejpam-5564	68	39	2	2	NUM
ejpam-5564	68	40	)	)	PUNCT
ejpam-5564	68	41	(	(	PUNCT
ejpam-5564	68	42	n+	n+	ADP
ejpam-5564	68	43	r	r	NOUN
ejpam-5564	68	44	−	−	NOUN
ejpam-5564	68	45	3	3	NUM
ejpam-5564	68	46	)	)	PUNCT
ejpam-5564	68	47	(	(	PUNCT
ejpam-5564	69	1	z	z	NOUN
ejpam-5564	69	2	−	−	PROPN
ejpam-5564	69	3	z∗)n+r−4	z∗)n+r−4	PROPN
ejpam-5564	69	4	+	+	ADP
ejpam-5564	69	5	q0	q0	ADJ
ejpam-5564	69	6	∑	∑	NOUN
ejpam-5564	69	7	n≥0	n≥0	NOUN
ejpam-5564	69	8	an	an	DET
ejpam-5564	69	9	(	(	PUNCT
ejpam-5564	69	10	z	z	NOUN
ejpam-5564	69	11	∗	∗	NOUN
ejpam-5564	69	12	−	−	PROPN
ejpam-5564	69	13	z)n+r	z)n+r	NOUN
ejpam-5564	69	14	∑	∑	PROPN
ejpam-5564	69	15	n≥0	n≥0	ADP
ejpam-5564	69	16	an	an	DET
ejpam-5564	69	17	(	(	PUNCT
ejpam-5564	69	18	n+	n+	NOUN
ejpam-5564	69	19	r	r	NOUN
ejpam-5564	69	20	)	)	PUNCT
ejpam-5564	69	21	(	(	PUNCT
ejpam-5564	69	22	z∗	z∗	NOUN
ejpam-5564	69	23	−	−	PROPN
ejpam-5564	69	24	z)n+r−1	z)n+r−1	PROPN
ejpam-5564	69	25	2	2	PUNCT
ejpam-5564	70	1	=	=	PUNCT
ejpam-5564	70	2	∑	∑	PUNCT
ejpam-5564	70	3	n≥0	n≥0	PROPN
ejpam-5564	70	4	dn	dn	PROPN
ejpam-5564	70	5	(	(	PUNCT
ejpam-5564	70	6	z	z	NOUN
ejpam-5564	70	7	∗	∗	NOUN
ejpam-5564	70	8	−	−	PROPN
ejpam-5564	70	9	z)n	z)n	PUNCT
ejpam-5564	70	10	.	.	PUNCT
ejpam-5564	71	1	after	after	ADP
ejpam-5564	71	2	cubing	cube	VERB
ejpam-5564	71	3	the	the	DET
ejpam-5564	71	4	first	first	ADJ
ejpam-5564	71	5	term	term	NOUN
ejpam-5564	71	6	on	on	ADP
ejpam-5564	71	7	the	the	DET
ejpam-5564	71	8	right	right	ADJ
ejpam-5564	71	9	-	-	PUNCT
ejpam-5564	71	10	hand	hand	NOUN
ejpam-5564	71	11	side	side	NOUN
ejpam-5564	71	12	,	,	PUNCT
ejpam-5564	71	13	we	we	PRON
ejpam-5564	71	14	get	get	VERB
ejpam-5564	71	15	:	:	PUNCT
ejpam-5564	71	16	∑	∑	PUNCT
ejpam-5564	71	17	n≥0	n≥0	ADP
ejpam-5564	71	18	an	an	DET
ejpam-5564	71	19	(	(	PUNCT
ejpam-5564	71	20	n+	n+	NOUN
ejpam-5564	71	21	r	r	NOUN
ejpam-5564	71	22	)	)	PUNCT
ejpam-5564	71	23	(	(	PUNCT
ejpam-5564	71	24	n+	n+	INTJ
ejpam-5564	71	25	r	r	NOUN
ejpam-5564	71	26	−	−	NOUN
ejpam-5564	71	27	1	1	NUM
ejpam-5564	71	28	)	)	PUNCT
ejpam-5564	71	29	(	(	PUNCT
ejpam-5564	71	30	n+	n+	INTJ
ejpam-5564	71	31	r	r	NOUN
ejpam-5564	71	32	−	−	NOUN
ejpam-5564	71	33	2	2	NUM
ejpam-5564	71	34	)	)	PUNCT
ejpam-5564	71	35	(	(	PUNCT
ejpam-5564	71	36	n+	n+	ADP
ejpam-5564	71	37	r	r	NOUN
ejpam-5564	71	38	−	−	NOUN
ejpam-5564	71	39	3	3	NUM
ejpam-5564	71	40	)	)	PUNCT
ejpam-5564	71	41	(	(	PUNCT
ejpam-5564	71	42	z∗	z∗	NOUN
ejpam-5564	71	43	−	−	PROPN
ejpam-5564	71	44	z)n+r−4	z)n+r−4	NOUN
ejpam-5564	71	45	=	=	SYM
ejpam-5564	71	46	−q0	−q0	NOUN
ejpam-5564	71	47	∑	∑	VERB
ejpam-5564	71	48	n≥0	n≥0	NOUN
ejpam-5564	71	49	an	an	DET
ejpam-5564	71	50	(	(	PUNCT
ejpam-5564	71	51	z	z	NOUN
ejpam-5564	71	52	∗	∗	NOUN
ejpam-5564	71	53	−	−	PROPN
ejpam-5564	71	54	z)n+r	z)n+r	NOUN
ejpam-5564	71	55	∑	∑	NOUN
ejpam-5564	72	1	n≥0	n≥0	PROPN
ejpam-5564	72	2	ã∗	ã∗	PROPN
ejpam-5564	72	3	n	n	PROPN
ejpam-5564	72	4	(	(	PUNCT
ejpam-5564	72	5	z	z	NOUN
ejpam-5564	72	6	∗	∗	NOUN
ejpam-5564	72	7	−	−	PROPN
ejpam-5564	72	8	z)n+2r−2	z)n+2r−2	NOUN
ejpam-5564	72	9			PROPN
ejpam-5564	73	1	+	+	CCONJ
ejpam-5564	73	2	∑	∑	PROPN
ejpam-5564	73	3	n≥0	n≥0	PROPN
ejpam-5564	73	4	dn	dn	PROPN
ejpam-5564	73	5	(	(	PUNCT
ejpam-5564	73	6	z	z	NOUN
ejpam-5564	73	7	∗	∗	NOUN
ejpam-5564	73	8	−	−	PROPN
ejpam-5564	73	9	z)n	z)n	PUNCT
ejpam-5564	73	10	,	,	PUNCT
ejpam-5564	73	11	∑	∑	PUNCT
ejpam-5564	73	12	n≥0	n≥0	ADP
ejpam-5564	73	13	an	an	DET
ejpam-5564	73	14	(	(	PUNCT
ejpam-5564	73	15	n+	n+	NOUN
ejpam-5564	73	16	r	r	NOUN
ejpam-5564	73	17	)	)	PUNCT
ejpam-5564	73	18	(	(	PUNCT
ejpam-5564	73	19	n+	n+	INTJ
ejpam-5564	73	20	r	r	NOUN
ejpam-5564	73	21	−	−	NOUN
ejpam-5564	73	22	1	1	NUM
ejpam-5564	73	23	)	)	PUNCT
ejpam-5564	73	24	(	(	PUNCT
ejpam-5564	73	25	n+	n+	INTJ
ejpam-5564	73	26	r	r	NOUN
ejpam-5564	73	27	−	−	NOUN
ejpam-5564	73	28	2	2	NUM
ejpam-5564	73	29	)	)	PUNCT
ejpam-5564	73	30	(	(	PUNCT
ejpam-5564	73	31	n+	n+	ADP
ejpam-5564	73	32	r	r	NOUN
ejpam-5564	73	33	−	−	NOUN
ejpam-5564	73	34	3	3	NUM
ejpam-5564	73	35	)	)	PUNCT
ejpam-5564	73	36	(	(	PUNCT
ejpam-5564	73	37	z∗	z∗	NOUN
ejpam-5564	73	38	−	−	PROPN
ejpam-5564	73	39	z)n+r−4	z)n+r−4	NOUN
ejpam-5564	73	40	=	=	SYM
ejpam-5564	73	41	−q0	−q0	VERB
ejpam-5564	73	42	∑	∑	PROPN
ejpam-5564	73	43	n≥0	n≥0	PROPN
ejpam-5564	73	44	c∗	c∗	PROPN
ejpam-5564	73	45	n	n	CCONJ
ejpam-5564	73	46	(	(	PUNCT
ejpam-5564	73	47	z	z	NOUN
ejpam-5564	73	48	∗	∗	NOUN
ejpam-5564	73	49	−	−	PROPN
ejpam-5564	73	50	z)n+3r−2	z)n+3r−2	NOUN
ejpam-5564	74	1	+	+	CCONJ
ejpam-5564	74	2	∑	∑	PROPN
ejpam-5564	74	3	n≥0	n≥0	PROPN
ejpam-5564	74	4	dn	dn	PROPN
ejpam-5564	74	5	(	(	PUNCT
ejpam-5564	74	6	z	z	NOUN
ejpam-5564	74	7	∗	∗	NOUN
ejpam-5564	74	8	−	−	PROPN
ejpam-5564	74	9	z)n	z)n	PUNCT
ejpam-5564	74	10	,	,	PUNCT
ejpam-5564	74	11	m.	m.	NOUN
ejpam-5564	74	12	gasanov	gasanov	PROPN
ejpam-5564	74	13	/	/	SYM
ejpam-5564	74	14	eur	eur	PROPN
ejpam-5564	74	15	.	.	PUNCT
ejpam-5564	75	1	j.	j.	PROPN
ejpam-5564	75	2	pure	pure	PROPN
ejpam-5564	75	3	appl	appl	PROPN
ejpam-5564	75	4	.	.	PROPN
ejpam-5564	75	5	math	math	PROPN
ejpam-5564	75	6	,	,	PUNCT
ejpam-5564	75	7	18	18	NUM
ejpam-5564	75	8	(	(	PUNCT
ejpam-5564	75	9	1	1	NUM
ejpam-5564	75	10	)	)	PUNCT
ejpam-5564	75	11	(	(	PUNCT
ejpam-5564	75	12	2025	2025	NUM
ejpam-5564	75	13	)	)	PUNCT
ejpam-5564	75	14	,	,	PUNCT
ejpam-5564	75	15	5564	5564	NUM
ejpam-5564	75	16	5	5	NUM
ejpam-5564	75	17	of	of	ADP
ejpam-5564	75	18	19	19	NUM
ejpam-5564	76	1	where	where	SCONJ
ejpam-5564	76	2			NUM
ejpam-5564	76	3	a∗	a∗	PROPN
ejpam-5564	76	4	n	n	NOUN
ejpam-5564	76	5	=	=	SYM
ejpam-5564	76	6	∑n	∑n	PROPN
ejpam-5564	76	7	i=0aian−i	i=0aian−i	NOUN
ejpam-5564	76	8	,	,	PUNCT
ejpam-5564	76	9	c∗	c∗	PROPN
ejpam-5564	76	10	n	n	NOUN
ejpam-5564	76	11	=	=	SYM
ejpam-5564	76	12	∑n	∑n	PROPN
ejpam-5564	76	13	i=0	i=0	PROPN
ejpam-5564	76	14	ã	ã	PROPN
ejpam-5564	76	15	∗	∗	VERB
ejpam-5564	76	16	ian−i	ian−i	PROPN
ejpam-5564	76	17	,	,	PUNCT
ejpam-5564	76	18	ã∗	ã∗	PROPN
ejpam-5564	76	19	n	n	NOUN
ejpam-5564	76	20	=	=	SYM
ejpam-5564	76	21	∑n	∑n	PROPN
ejpam-5564	76	22	i=0bibn−i	i=0bibn−i	NOUN
ejpam-5564	76	23	,	,	PUNCT
ejpam-5564	76	24	bn	bn	NOUN
ejpam-5564	76	25	=	=	SYM
ejpam-5564	76	26	an	an	DET
ejpam-5564	76	27	(	(	PUNCT
ejpam-5564	76	28	n+	n+	NOUN
ejpam-5564	76	29	r	r	NOUN
ejpam-5564	76	30	)	)	PUNCT
ejpam-5564	76	31	.	.	PUNCT
ejpam-5564	77	1	the	the	DET
ejpam-5564	77	2	left	left	ADJ
ejpam-5564	77	3	and	and	CCONJ
ejpam-5564	77	4	right	right	ADJ
ejpam-5564	77	5	sides	side	NOUN
ejpam-5564	77	6	are	be	AUX
ejpam-5564	77	7	identically	identically	ADV
ejpam-5564	77	8	equal	equal	ADJ
ejpam-5564	77	9	,	,	PUNCT
ejpam-5564	77	10	from	from	ADP
ejpam-5564	77	11	which	which	PRON
ejpam-5564	77	12	the	the	DET
ejpam-5564	77	13	following	follow	VERB
ejpam-5564	77	14	conditions	condition	NOUN
ejpam-5564	77	15	follow	follow	VERB
ejpam-5564	77	16	:	:	PUNCT
ejpam-5564	77	17			NUM
ejpam-5564	77	18	n+	n+	ADP
ejpam-5564	77	19	r	r	NOUN
ejpam-5564	77	20	−	−	PROPN
ejpam-5564	77	21	4	4	NUM
ejpam-5564	77	22	=	=	SYM
ejpam-5564	77	23	n+	n+	ADP
ejpam-5564	77	24	3r	3r	NUM
ejpam-5564	77	25	−	−	PROPN
ejpam-5564	77	26	2	2	NUM
ejpam-5564	77	27	an	an	DET
ejpam-5564	77	28	(	(	PUNCT
ejpam-5564	77	29	n+	n+	NOUN
ejpam-5564	77	30	r	r	NOUN
ejpam-5564	77	31	)	)	PUNCT
ejpam-5564	77	32	(	(	PUNCT
ejpam-5564	77	33	n+	n+	INTJ
ejpam-5564	77	34	r	r	NOUN
ejpam-5564	77	35	−	−	NOUN
ejpam-5564	77	36	1	1	NUM
ejpam-5564	77	37	)	)	PUNCT
ejpam-5564	77	38	(	(	PUNCT
ejpam-5564	77	39	n+	n+	INTJ
ejpam-5564	77	40	r	r	NOUN
ejpam-5564	77	41	−	−	NOUN
ejpam-5564	77	42	2	2	NUM
ejpam-5564	77	43	)	)	PUNCT
ejpam-5564	77	44	(	(	PUNCT
ejpam-5564	77	45	n+	n+	ADP
ejpam-5564	77	46	r	r	NOUN
ejpam-5564	77	47	−	−	NOUN
ejpam-5564	77	48	3	3	NUM
ejpam-5564	77	49	)	)	PUNCT
ejpam-5564	77	50	=	=	SYM
ejpam-5564	77	51	−q0c	−q0c	NUM
ejpam-5564	77	52	∗	∗	NOUN
ejpam-5564	77	53	n	n	CCONJ
ejpam-5564	77	54	,	,	PUNCT
ejpam-5564	77	55	if	if	SCONJ
ejpam-5564	77	56	n	n	CCONJ
ejpam-5564	77	57	=	=	SYM
ejpam-5564	77	58	0	0	NUM
ejpam-5564	77	59	,	,	PUNCT
ejpam-5564	77	60	1	1	NUM
ejpam-5564	77	61	,	,	PUNCT
ejpam-5564	77	62	2	2	NUM
ejpam-5564	77	63	,	,	PUNCT
ejpam-5564	77	64	3	3	NUM
ejpam-5564	77	65	,	,	PUNCT
ejpam-5564	77	66	4	4	NUM
ejpam-5564	77	67	an	an	DET
ejpam-5564	77	68	(	(	PUNCT
ejpam-5564	77	69	n+	n+	NOUN
ejpam-5564	77	70	r	r	NOUN
ejpam-5564	77	71	)	)	PUNCT
ejpam-5564	77	72	(	(	PUNCT
ejpam-5564	77	73	n+	n+	INTJ
ejpam-5564	77	74	r	r	NOUN
ejpam-5564	77	75	−	−	NOUN
ejpam-5564	77	76	1	1	NUM
ejpam-5564	77	77	)	)	PUNCT
ejpam-5564	77	78	(	(	PUNCT
ejpam-5564	77	79	n+	n+	INTJ
ejpam-5564	77	80	r	r	NOUN
ejpam-5564	77	81	−	−	NOUN
ejpam-5564	77	82	2	2	NUM
ejpam-5564	77	83	)	)	PUNCT
ejpam-5564	77	84	(	(	PUNCT
ejpam-5564	77	85	n+	n+	ADP
ejpam-5564	77	86	r	r	NOUN
ejpam-5564	77	87	−	−	NOUN
ejpam-5564	77	88	3	3	NUM
ejpam-5564	77	89	)	)	PUNCT
ejpam-5564	77	90	=	=	SYM
ejpam-5564	77	91	−q0c	−q0c	NUM
ejpam-5564	77	92	∗	∗	NOUN
ejpam-5564	77	93	n	n	CCONJ
ejpam-5564	77	94	+	+	ADJ
ejpam-5564	77	95	dn−5	dn−5	PROPN
ejpam-5564	77	96	,	,	PUNCT
ejpam-5564	77	97	if	if	SCONJ
ejpam-5564	77	98	n	n	NUM
ejpam-5564	77	99	≥	≥	NOUN
ejpam-5564	77	100	5	5	NUM
ejpam-5564	77	101	(	(	PUNCT
ejpam-5564	77	102	6	6	NUM
ejpam-5564	77	103	)	)	PUNCT
ejpam-5564	77	104	from	from	ADP
ejpam-5564	77	105	the	the	DET
ejpam-5564	77	106	first	first	ADJ
ejpam-5564	77	107	equality	equality	NOUN
ejpam-5564	77	108	,	,	PUNCT
ejpam-5564	77	109	it	it	PRON
ejpam-5564	77	110	follows	follow	VERB
ejpam-5564	77	111	that	that	SCONJ
ejpam-5564	77	112	r	r	NOUN
ejpam-5564	77	113	=	=	SYM
ejpam-5564	77	114	−1	−1	NOUN
ejpam-5564	77	115	.	.	PUNCT
ejpam-5564	78	1	as	as	SCONJ
ejpam-5564	78	2	shown	show	VERB
ejpam-5564	78	3	in	in	ADP
ejpam-5564	78	4	[	[	X
ejpam-5564	78	5	11	11	NUM
ejpam-5564	78	6	]	]	PUNCT
ejpam-5564	78	7	,	,	PUNCT
ejpam-5564	78	8	if	if	SCONJ
ejpam-5564	78	9	r	r	NOUN
ejpam-5564	78	10	∈	∈	PROPN
ejpam-5564	78	11	q−	q−	PROPN
ejpam-5564	78	12	,	,	PUNCT
ejpam-5564	78	13	then	then	ADV
ejpam-5564	78	14	z∗	z∗	PROPN
ejpam-5564	78	15	is	be	AUX
ejpam-5564	78	16	a	a	DET
ejpam-5564	78	17	movable	movable	ADJ
ejpam-5564	78	18	singular	singular	NOUN
ejpam-5564	78	19	point	point	NOUN
ejpam-5564	78	20	for	for	ADP
ejpam-5564	78	21	solving	solve	VERB
ejpam-5564	78	22	the	the	DET
ejpam-5564	78	23	cauchy	cauchy	ADJ
ejpam-5564	78	24	problem	problem	NOUN
ejpam-5564	78	25	(	(	PUNCT
ejpam-5564	78	26	2	2	NUM
ejpam-5564	78	27	)	)	PUNCT
ejpam-5564	78	28	—	—	PUNCT
ejpam-5564	78	29	(	(	PUNCT
ejpam-5564	78	30	3	3	NUM
ejpam-5564	78	31	)	)	PUNCT
ejpam-5564	78	32	.	.	PUNCT
ejpam-5564	79	1	the	the	DET
ejpam-5564	79	2	second	second	ADJ
ejpam-5564	79	3	and	and	CCONJ
ejpam-5564	79	4	third	third	ADJ
ejpam-5564	79	5	equalities	equality	NOUN
ejpam-5564	79	6	are	be	AUX
ejpam-5564	79	7	recurrent	recurrent	ADJ
ejpam-5564	79	8	relations	relation	NOUN
ejpam-5564	79	9	that	that	PRON
ejpam-5564	79	10	allow	allow	VERB
ejpam-5564	79	11	for	for	ADP
ejpam-5564	79	12	the	the	DET
ejpam-5564	79	13	unique	unique	ADJ
ejpam-5564	79	14	determination	determination	NOUN
ejpam-5564	79	15	of	of	ADP
ejpam-5564	79	16	the	the	DET
ejpam-5564	79	17	coefficients	coefficient	NOUN
ejpam-5564	79	18	of	of	ADP
ejpam-5564	79	19	the	the	DET
ejpam-5564	79	20	series	series	NOUN
ejpam-5564	79	21	(	(	PUNCT
ejpam-5564	79	22	2.1	2.1	NUM
ejpam-5564	79	23	)	)	PUNCT
ejpam-5564	79	24	.	.	PUNCT
ejpam-5564	80	1	writing	write	VERB
ejpam-5564	80	2	the	the	DET
ejpam-5564	80	3	initial	initial	ADJ
ejpam-5564	80	4	values	value	NOUN
ejpam-5564	80	5	for	for	ADP
ejpam-5564	80	6	n	n	CCONJ
ejpam-5564	80	7	,	,	PUNCT
ejpam-5564	80	8	we	we	PRON
ejpam-5564	80	9	obtain	obtain	VERB
ejpam-5564	80	10	the	the	DET
ejpam-5564	80	11	first	first	ADJ
ejpam-5564	80	12	few	few	ADJ
ejpam-5564	80	13	recurrent	recurrent	ADJ
ejpam-5564	80	14	relations:	relations:	NOUN
ejpam-5564	80	15	a0	a0	NOUN
ejpam-5564	80	16	=	=	PUNCT
ejpam-5564	81	1	√	√	PROPN
ejpam-5564	81	2	−	−	NUM
ejpam-5564	81	3	24	24	NUM
ejpam-5564	81	4	q0	q0	ADJ
ejpam-5564	81	5	a1	a1	NOUN
ejpam-5564	81	6	=	=	PROPN
ejpam-5564	81	7	a2	a2	PROPN
ejpam-5564	81	8	=	=	SYM
ejpam-5564	81	9	a3	a3	NOUN
ejpam-5564	81	10	=	=	SYM
ejpam-5564	81	11	a4	a4	PROPN
ejpam-5564	81	12	=	=	SYM
ejpam-5564	81	13	0	0	NUM
ejpam-5564	81	14	a5	a5	NOUN
ejpam-5564	81	15	=	=	SYM
ejpam-5564	81	16	d0	d0	NOUN
ejpam-5564	81	17	192	192	NUM
ejpam-5564	81	18	a6	a6	NOUN
ejpam-5564	81	19	=	=	SYM
ejpam-5564	81	20	d1	d1	PROPN
ejpam-5564	81	21	336	336	NUM
ejpam-5564	81	22	a7	a7	NOUN
ejpam-5564	81	23	=	=	SYM
ejpam-5564	81	24	d2	d2	PROPN
ejpam-5564	81	25	1152	1152	NUM
ejpam-5564	81	26	.	.	PUNCT
ejpam-5564	81	27	.	.	PUNCT
ejpam-5564	81	28	.	.	PUNCT
ejpam-5564	81	29	.	.	PUNCT
ejpam-5564	81	30	.	.	PUNCT
ejpam-5564	81	31	.	.	PUNCT
ejpam-5564	81	32	.	.	PUNCT
ejpam-5564	81	33	.	.	PUNCT
ejpam-5564	81	34	.	.	PUNCT
ejpam-5564	82	1	taking	take	VERB
ejpam-5564	82	2	into	into	ADP
ejpam-5564	82	3	account	account	NOUN
ejpam-5564	82	4	the	the	DET
ejpam-5564	82	5	regularity	regularity	NOUN
ejpam-5564	82	6	,	,	PUNCT
ejpam-5564	82	7	it	it	PRON
ejpam-5564	82	8	is	be	AUX
ejpam-5564	82	9	evident	evident	ADJ
ejpam-5564	82	10	that	that	SCONJ
ejpam-5564	82	11	:	:	PUNCT
ejpam-5564	82	12	an	an	DET
ejpam-5564	82	13	=	=	SYM
ejpam-5564	82	14	dn−5	dn−5	PROPN
ejpam-5564	82	15	c	c	NOUN
ejpam-5564	82	16	−a0	−a0	PROPN
ejpam-5564	82	17	·	·	PUNCT
ejpam-5564	82	18	f	f	X
ejpam-5564	82	19	(	(	PUNCT
ejpam-5564	82	20	d0dn−10	d0dn−10	PROPN
ejpam-5564	82	21	,	,	PUNCT
ejpam-5564	82	22	d1dn−9	d1dn−9	PROPN
ejpam-5564	82	23	,	,	PUNCT
ejpam-5564	82	24	.	.	PUNCT
ejpam-5564	82	25	.	.	PUNCT
ejpam-5564	83	1	.	.	PUNCT
ejpam-5564	84	1	,	,	PUNCT
ejpam-5564	84	2	dldk	dldk	NOUN
ejpam-5564	84	3	)	)	PUNCT
ejpam-5564	84	4	,	,	PUNCT
ejpam-5564	85	1	l	l	PROPN
ejpam-5564	86	1	+	+	CCONJ
ejpam-5564	86	2	k	k	X
ejpam-5564	86	3	=	=	PUNCT
ejpam-5564	86	4	n−	n−	NOUN
ejpam-5564	86	5	10	10	NUM
ejpam-5564	86	6	,	,	PUNCT
ejpam-5564	86	7	c	c	NOUN
ejpam-5564	86	8	=	=	SYM
ejpam-5564	86	9	const	const	PROPN
ejpam-5564	86	10	,	,	PUNCT
ejpam-5564	86	11	n	n	X
ejpam-5564	86	12	≥	≥	NOUN
ejpam-5564	86	13	5	5	NUM
ejpam-5564	86	14	.	.	PUNCT
ejpam-5564	87	1	since	since	SCONJ
ejpam-5564	87	2	the	the	DET
ejpam-5564	87	3	series	series	NOUN
ejpam-5564	87	4	is	be	AUX
ejpam-5564	87	5	formal	formal	ADJ
ejpam-5564	87	6	,	,	PUNCT
ejpam-5564	87	7	it	it	PRON
ejpam-5564	87	8	is	be	AUX
ejpam-5564	87	9	necessary	necessary	ADJ
ejpam-5564	87	10	to	to	PART
ejpam-5564	87	11	find	find	VERB
ejpam-5564	87	12	its	its	PRON
ejpam-5564	87	13	convergence	convergence	NOUN
ejpam-5564	87	14	domain	domain	NOUN
ejpam-5564	87	15	.	.	PUNCT
ejpam-5564	88	1	to	to	PART
ejpam-5564	88	2	do	do	VERB
ejpam-5564	88	3	this	this	PRON
ejpam-5564	88	4	,	,	PUNCT
ejpam-5564	88	5	we	we	PRON
ejpam-5564	88	6	will	will	AUX
ejpam-5564	88	7	use	use	VERB
ejpam-5564	88	8	the	the	DET
ejpam-5564	88	9	modified	modify	VERB
ejpam-5564	88	10	majorant	majorant	NOUN
ejpam-5564	88	11	method	method	NOUN
ejpam-5564	88	12	used	use	VERB
ejpam-5564	88	13	in	in	ADP
ejpam-5564	88	14	the	the	DET
ejpam-5564	88	15	cauchy	cauchy	PROPN
ejpam-5564	88	16	–	–	PUNCT
ejpam-5564	88	17	kovalevskaya	kovalevskaya	NOUN
ejpam-5564	88	18	theorem	theorem	VERB
ejpam-5564	88	19	.	.	PUNCT
ejpam-5564	89	1	this	this	DET
ejpam-5564	89	2	method	method	NOUN
ejpam-5564	89	3	is	be	AUX
ejpam-5564	89	4	based	base	VERB
ejpam-5564	89	5	on	on	ADP
ejpam-5564	89	6	the	the	DET
ejpam-5564	89	7	estimation	estimation	NOUN
ejpam-5564	89	8	of	of	ADP
ejpam-5564	89	9	the	the	DET
ejpam-5564	89	10	coefficients	coefficient	NOUN
ejpam-5564	90	1	an	an	PRON
ejpam-5564	90	2	on	on	ADP
ejpam-5564	90	3	the	the	DET
ejpam-5564	90	4	basis	basis	NOUN
ejpam-5564	90	5	of	of	ADP
ejpam-5564	90	6	which	which	PRON
ejpam-5564	90	7	the	the	DET
ejpam-5564	90	8	majority	majority	NOUN
ejpam-5564	90	9	series	series	NOUN
ejpam-5564	90	10	is	be	AUX
ejpam-5564	90	11	constructed	construct	VERB
ejpam-5564	90	12	.	.	PUNCT
ejpam-5564	91	1	theorem	theorem	NOUN
ejpam-5564	91	2	2	2	NUM
ejpam-5564	91	3	.	.	X
ejpam-5564	91	4	assume	assume	VERB
ejpam-5564	91	5	that	that	SCONJ
ejpam-5564	91	6	all	all	DET
ejpam-5564	91	7	conditions	condition	NOUN
ejpam-5564	91	8	of	of	ADP
ejpam-5564	91	9	theorem	theorem	NOUN
ejpam-5564	91	10	1	1	NUM
ejpam-5564	91	11	be	be	AUX
ejpam-5564	91	12	satisfied	satisfied	ADJ
ejpam-5564	91	13	;	;	PUNCT
ejpam-5564	91	14	then	then	ADV
ejpam-5564	91	15	the	the	DET
ejpam-5564	91	16	estimate	estimate	NOUN
ejpam-5564	91	17	for	for	ADP
ejpam-5564	91	18	the	the	DET
ejpam-5564	91	19	coefficients	coefficient	NOUN
ejpam-5564	91	20	of	of	ADP
ejpam-5564	91	21	the	the	DET
ejpam-5564	91	22	series	series	NOUN
ejpam-5564	91	23	expansion	expansion	NOUN
ejpam-5564	91	24	(	(	PUNCT
ejpam-5564	91	25	2.1	2.1	NUM
ejpam-5564	91	26	)	)	PUNCT
ejpam-5564	91	27	,	,	PUNCT
ejpam-5564	91	28	for	for	ADP
ejpam-5564	91	29	sufficiently	sufficiently	ADV
ejpam-5564	91	30	large	large	ADJ
ejpam-5564	91	31	values	value	NOUN
ejpam-5564	91	32	of	of	ADP
ejpam-5564	91	33	n	n	CCONJ
ejpam-5564	91	34	,	,	PUNCT
ejpam-5564	91	35	takes	take	VERB
ejpam-5564	91	36	the	the	DET
ejpam-5564	91	37	following	follow	VERB
ejpam-5564	91	38	form	form	NOUN
ejpam-5564	91	39	:	:	PUNCT
ejpam-5564	91	40	|an|	|an|	NOUN
ejpam-5564	91	41	≤	≤	PUNCT
ejpam-5564	92	1	|γ|	|γ|	PROPN
ejpam-5564	92	2	[	[	PUNCT
ejpam-5564	92	3	n	n	NOUN
ejpam-5564	92	4	5	5	NUM
ejpam-5564	92	5	]	]	PUNCT
ejpam-5564	92	6	(	(	PUNCT
ejpam-5564	92	7	|q0a0|	|q0a0|	NUM
ejpam-5564	92	8	∣∣[n−9	∣∣[n−9	PROPN
ejpam-5564	92	9	2	2	NUM
ejpam-5564	92	10	]	]	PUNCT
ejpam-5564	93	1	+	+	CCONJ
ejpam-5564	93	2	1	1	NUM
ejpam-5564	93	3	∣∣+	∣∣+	NOUN
ejpam-5564	93	4	1	1	NUM
ejpam-5564	93	5	)	)	PUNCT
ejpam-5564	93	6	|(n−	|(n−	NOUN
ejpam-5564	93	7	1	1	NUM
ejpam-5564	93	8	)	)	PUNCT
ejpam-5564	93	9	(	(	PUNCT
ejpam-5564	93	10	n−	n−	NOUN
ejpam-5564	93	11	2	2	NUM
ejpam-5564	93	12	)	)	PUNCT
ejpam-5564	93	13	(	(	PUNCT
ejpam-5564	93	14	n−	n−	NOUN
ejpam-5564	93	15	3	3	NUM
ejpam-5564	93	16	)	)	PUNCT
ejpam-5564	93	17	(	(	PUNCT
ejpam-5564	93	18	n−	n−	NOUN
ejpam-5564	93	19	4	4	NUM
ejpam-5564	93	20	)	)	PUNCT
ejpam-5564	93	21	+	+	CCONJ
ejpam-5564	93	22	24	24	NUM
ejpam-5564	93	23	(	(	PUNCT
ejpam-5564	93	24	2n−	2n−	PROPN
ejpam-5564	93	25	3)|	3)|	NUM
ejpam-5564	93	26	,	,	PUNCT
ejpam-5564	93	27	(	(	PUNCT
ejpam-5564	93	28	7	7	NUM
ejpam-5564	93	29	)	)	PUNCT
ejpam-5564	93	30	where	where	SCONJ
ejpam-5564	93	31	[	[	X
ejpam-5564	93	32	α	α	X
ejpam-5564	93	33	]	]	X
ejpam-5564	93	34	denotes	denote	VERB
ejpam-5564	93	35	the	the	DET
ejpam-5564	93	36	integer	integer	NOUN
ejpam-5564	93	37	part	part	NOUN
ejpam-5564	93	38	of	of	ADP
ejpam-5564	93	39	the	the	DET
ejpam-5564	93	40	number	number	NOUN
ejpam-5564	93	41	.	.	PUNCT
ejpam-5564	94	1	proof	proof	NOUN
ejpam-5564	94	2	.	.	PUNCT
ejpam-5564	95	1	from	from	ADP
ejpam-5564	95	2	the	the	DET
ejpam-5564	95	3	system	system	NOUN
ejpam-5564	95	4	(	(	PUNCT
ejpam-5564	95	5	2.1	2.1	NUM
ejpam-5564	95	6	)	)	PUNCT
ejpam-5564	95	7	,	,	PUNCT
ejpam-5564	95	8	it	it	PRON
ejpam-5564	95	9	follows	follow	VERB
ejpam-5564	95	10	that	that	SCONJ
ejpam-5564	95	11	for	for	ADP
ejpam-5564	95	12	sufficiently	sufficiently	ADV
ejpam-5564	95	13	large	large	ADJ
ejpam-5564	95	14	values	value	NOUN
ejpam-5564	95	15	of	of	ADP
ejpam-5564	95	16	the	the	DET
ejpam-5564	95	17	index	index	NOUN
ejpam-5564	95	18	,	,	PUNCT
ejpam-5564	95	19	the	the	DET
ejpam-5564	95	20	following	follow	VERB
ejpam-5564	95	21	equality	equality	NOUN
ejpam-5564	95	22	can	can	AUX
ejpam-5564	95	23	be	be	AUX
ejpam-5564	95	24	used	use	VERB
ejpam-5564	95	25	:	:	PUNCT
ejpam-5564	95	26	m.	m.	NOUN
ejpam-5564	95	27	gasanov	gasanov	PROPN
ejpam-5564	95	28	/	/	SYM
ejpam-5564	95	29	eur	eur	PROPN
ejpam-5564	95	30	.	.	PUNCT
ejpam-5564	96	1	j.	j.	PROPN
ejpam-5564	96	2	pure	pure	PROPN
ejpam-5564	96	3	appl	appl	PROPN
ejpam-5564	96	4	.	.	PROPN
ejpam-5564	96	5	math	math	PROPN
ejpam-5564	96	6	,	,	PUNCT
ejpam-5564	96	7	18	18	NUM
ejpam-5564	96	8	(	(	PUNCT
ejpam-5564	96	9	1	1	NUM
ejpam-5564	96	10	)	)	PUNCT
ejpam-5564	96	11	(	(	PUNCT
ejpam-5564	96	12	2025	2025	NUM
ejpam-5564	96	13	)	)	PUNCT
ejpam-5564	96	14	,	,	PUNCT
ejpam-5564	96	15	5564	5564	NUM
ejpam-5564	96	16	6	6	NUM
ejpam-5564	96	17	of	of	ADP
ejpam-5564	96	18	19	19	NUM
ejpam-5564	96	19	an	an	DET
ejpam-5564	96	20	(	(	PUNCT
ejpam-5564	96	21	n−	n−	NOUN
ejpam-5564	96	22	1	1	NUM
ejpam-5564	96	23	)	)	PUNCT
ejpam-5564	96	24	(	(	PUNCT
ejpam-5564	96	25	n−	n−	NOUN
ejpam-5564	96	26	2	2	NUM
ejpam-5564	96	27	)	)	PUNCT
ejpam-5564	96	28	(	(	PUNCT
ejpam-5564	96	29	n−	n−	NOUN
ejpam-5564	96	30	3	3	NUM
ejpam-5564	96	31	)	)	PUNCT
ejpam-5564	96	32	(	(	PUNCT
ejpam-5564	96	33	n−	n−	NOUN
ejpam-5564	96	34	4	4	NUM
ejpam-5564	96	35	)	)	PUNCT
ejpam-5564	96	36	=	=	SYM
ejpam-5564	97	1	−q0c	−q0c	NUM
ejpam-5564	97	2	∗	∗	NOUN
ejpam-5564	97	3	n	n	CCONJ
ejpam-5564	97	4	+	+	NOUN
ejpam-5564	97	5	dn−5	dn−5	PROPN
ejpam-5564	97	6	.	.	PUNCT
ejpam-5564	98	1	(	(	PUNCT
ejpam-5564	98	2	8)	8)	NUM
ejpam-5564	98	3	let	let	VERB
ejpam-5564	98	4	’s	’s	NOUN
ejpam-5564	98	5	expand	expand	VERB
ejpam-5564	98	6	the	the	DET
ejpam-5564	98	7	right	right	ADJ
ejpam-5564	98	8	-	-	PUNCT
ejpam-5564	98	9	hand	hand	NOUN
ejpam-5564	98	10	side	side	NOUN
ejpam-5564	98	11	:	:	PUNCT
ejpam-5564	98	12	−q0	−q0	NOUN
ejpam-5564	98	13	n∑	n∑	NOUN
ejpam-5564	98	14	i=0	i=0	PROPN
ejpam-5564	98	15	ã∗	ã∗	NOUN
ejpam-5564	98	16	ian−i	ian−i	ADP
ejpam-5564	98	17	+	+	ADJ
ejpam-5564	98	18	dn−5	dn−5	NOUN
ejpam-5564	98	19	=	=	SYM
ejpam-5564	98	20	−q0	−q0	VERB
ejpam-5564	98	21	n∑	n∑	NOUN
ejpam-5564	98	22	i=0	i=0	PROPN
ejpam-5564	98	23			PROPN
ejpam-5564	98	24	i∑	i∑	NUM
ejpam-5564	98	25	j=0	j=0	PROPN
ejpam-5564	98	26	bjbi−j	bjbi−j	PROPN
ejpam-5564	98	27	an−i	an−i	NOUN
ejpam-5564	99	1	+	+	PROPN
ejpam-5564	99	2	dn−5	dn−5	PROPN
ejpam-5564	99	3	=	=	SYM
ejpam-5564	99	4	−q0	−q0	VERB
ejpam-5564	99	5	n∑	n∑	NOUN
ejpam-5564	99	6	i=0	i=0	PROPN
ejpam-5564	99	7			PROPN
ejpam-5564	99	8	i∑	i∑	PROPN
ejpam-5564	99	9	j=0	j=0	PROPN
ejpam-5564	99	10	aj	aj	PROPN
ejpam-5564	99	11	(	(	PUNCT
ejpam-5564	99	12	j	j	PROPN
ejpam-5564	99	13	−	−	PROPN
ejpam-5564	99	14	1)ai−j	1)ai−j	PROPN
ejpam-5564	99	15	(	(	PUNCT
ejpam-5564	99	16	i−	i−	PROPN
ejpam-5564	99	17	j	j	PROPN
ejpam-5564	99	18	−	−	PROPN
ejpam-5564	99	19	1	1	NUM
ejpam-5564	99	20	)	)	PUNCT
ejpam-5564	99	21	an−i	an−i	NOUN
ejpam-5564	100	1	+	+	PROPN
ejpam-5564	100	2	dn−5	dn−5	PROPN
ejpam-5564	100	3	=	=	SYM
ejpam-5564	100	4	−q0	−q0	NOUN
ejpam-5564	100	5	(	(	PUNCT
ejpam-5564	100	6	n∑	n∑	PROPN
ejpam-5564	100	7	i=0	i=0	PROPN
ejpam-5564	100	8	(	(	PUNCT
ejpam-5564	100	9	−	−	PROPN
ejpam-5564	100	10	(	(	PUNCT
ejpam-5564	100	11	i−	i−	PROPN
ejpam-5564	100	12	1)a0ai	1)a0ai	NUM
ejpam-5564	100	13	+	+	PROPN
ejpam-5564	100	14	.	.	PUNCT
ejpam-5564	100	15	.	.	PUNCT
ejpam-5564	101	1	.−	.−	PUNCT
ejpam-5564	101	2	(	(	PUNCT
ejpam-5564	101	3	i−	i−	PROPN
ejpam-5564	101	4	1)aia0)an−i	1)aia0)an−i	NUM
ejpam-5564	101	5	)	)	PUNCT
ejpam-5564	102	1	+	+	NUM
ejpam-5564	102	2	dn−5	dn−5	NOUN
ejpam-5564	102	3	=	=	SYM
ejpam-5564	102	4	−q0	−q0	NOUN
ejpam-5564	102	5	(	(	PUNCT
ejpam-5564	102	6	−ana	−ana	X
ejpam-5564	102	7	2	2	NUM
ejpam-5564	102	8	0	0	NUM
ejpam-5564	102	9	−	−	NUM
ejpam-5564	102	10	2	2	NUM
ejpam-5564	102	11	(	(	PUNCT
ejpam-5564	102	12	n−	n−	NOUN
ejpam-5564	102	13	1)ana	1)ana	NUM
ejpam-5564	102	14	2	2	NUM
ejpam-5564	102	15	0	0	NUM
ejpam-5564	103	1	+	+	CCONJ
ejpam-5564	103	2	p	p	X
ejpam-5564	103	3	(	(	PUNCT
ejpam-5564	103	4	a1	a1	NOUN
ejpam-5564	103	5	,	,	PUNCT
ejpam-5564	103	6	.	.	PUNCT
ejpam-5564	103	7	.	.	PUNCT
ejpam-5564	104	1	.	.	PUNCT
ejpam-5564	105	1	,	,	PUNCT
ejpam-5564	105	2	an−1	an−1	ADJ
ejpam-5564	105	3	)	)	PUNCT
ejpam-5564	105	4	)	)	PUNCT
ejpam-5564	106	1	+	+	PUNCT
ejpam-5564	106	2	dn−5	dn−5	PROPN
ejpam-5564	106	3	.	.	PUNCT
ejpam-5564	107	1	considering	consider	VERB
ejpam-5564	107	2	the	the	DET
ejpam-5564	107	3	obtained	obtain	VERB
ejpam-5564	107	4	equality	equality	NOUN
ejpam-5564	107	5	,	,	PUNCT
ejpam-5564	107	6	equation	equation	NOUN
ejpam-5564	107	7	(	(	PUNCT
ejpam-5564	107	8	8)	8)	NUM
ejpam-5564	107	9	can	can	AUX
ejpam-5564	107	10	be	be	AUX
ejpam-5564	107	11	expressed	express	VERB
ejpam-5564	107	12	as	as	ADP
ejpam-5564	107	13	:	:	PUNCT
ejpam-5564	107	14	an	an	DET
ejpam-5564	107	15	(	(	PUNCT
ejpam-5564	107	16	n−	n−	NOUN
ejpam-5564	107	17	1	1	NUM
ejpam-5564	107	18	)	)	PUNCT
ejpam-5564	107	19	(	(	PUNCT
ejpam-5564	107	20	n−	n−	NOUN
ejpam-5564	107	21	2	2	NUM
ejpam-5564	107	22	)	)	PUNCT
ejpam-5564	107	23	(	(	PUNCT
ejpam-5564	107	24	n−	n−	NOUN
ejpam-5564	107	25	3	3	NUM
ejpam-5564	107	26	)	)	PUNCT
ejpam-5564	107	27	(	(	PUNCT
ejpam-5564	107	28	n−	n−	NOUN
ejpam-5564	107	29	4	4	NUM
ejpam-5564	107	30	)	)	PUNCT
ejpam-5564	107	31	=	=	SYM
ejpam-5564	108	1	−q0	−q0	NOUN
ejpam-5564	108	2	(	(	PUNCT
ejpam-5564	108	3	−ana	−ana	X
ejpam-5564	108	4	2	2	NUM
ejpam-5564	108	5	0	0	NUM
ejpam-5564	108	6	−	−	NUM
ejpam-5564	108	7	2	2	NUM
ejpam-5564	108	8	(	(	PUNCT
ejpam-5564	108	9	n−	n−	NOUN
ejpam-5564	108	10	1)ana	1)ana	NUM
ejpam-5564	108	11	2	2	NUM
ejpam-5564	108	12	0	0	NUM
ejpam-5564	108	13	+	+	CCONJ
ejpam-5564	108	14	p	p	X
ejpam-5564	108	15	(	(	PUNCT
ejpam-5564	108	16	a0	a0	NOUN
ejpam-5564	108	17	,	,	PUNCT
ejpam-5564	108	18	.	.	PUNCT
ejpam-5564	108	19	.	.	PUNCT
ejpam-5564	108	20	.	.	PUNCT
ejpam-5564	109	1	,	,	PUNCT
ejpam-5564	109	2	an−1	an−1	ADJ
ejpam-5564	109	3	)	)	PUNCT
ejpam-5564	109	4	)	)	PUNCT
ejpam-5564	110	1	+	+	PUNCT
ejpam-5564	110	2	dn−5	dn−5	PROPN
ejpam-5564	110	3	,	,	PUNCT
ejpam-5564	110	4	an	an	DET
ejpam-5564	110	5	(	(	PUNCT
ejpam-5564	110	6	(	(	PUNCT
ejpam-5564	110	7	n−	n−	NOUN
ejpam-5564	110	8	1	1	NUM
ejpam-5564	110	9	)	)	PUNCT
ejpam-5564	110	10	(	(	PUNCT
ejpam-5564	110	11	n−	n−	NOUN
ejpam-5564	110	12	2	2	NUM
ejpam-5564	110	13	)	)	PUNCT
ejpam-5564	110	14	(	(	PUNCT
ejpam-5564	110	15	n−	n−	NOUN
ejpam-5564	110	16	3	3	NUM
ejpam-5564	110	17	)	)	PUNCT
ejpam-5564	110	18	(	(	PUNCT
ejpam-5564	110	19	n−	n−	NOUN
ejpam-5564	110	20	4	4	NUM
ejpam-5564	110	21	)	)	PUNCT
ejpam-5564	110	22	+	+	CCONJ
ejpam-5564	110	23	24	24	NUM
ejpam-5564	110	24	(	(	PUNCT
ejpam-5564	110	25	2n−	2n−	PROPN
ejpam-5564	110	26	3	3	NUM
ejpam-5564	110	27	)	)	PUNCT
ejpam-5564	110	28	)	)	PUNCT
ejpam-5564	111	1	=	=	PUNCT
ejpam-5564	111	2	−q0	−q0	NOUN
ejpam-5564	111	3	·	·	PUNCT
ejpam-5564	111	4	p	p	X
ejpam-5564	111	5	(	(	PUNCT
ejpam-5564	111	6	a0	a0	NOUN
ejpam-5564	111	7	,	,	PUNCT
ejpam-5564	111	8	.	.	PUNCT
ejpam-5564	111	9	.	.	PUNCT
ejpam-5564	111	10	.	.	PUNCT
ejpam-5564	112	1	,	,	PUNCT
ejpam-5564	112	2	an−1	an−1	ADJ
ejpam-5564	112	3	)	)	PUNCT
ejpam-5564	113	1	+	+	NUM
ejpam-5564	113	2	dn−5	dn−5	PROPN
ejpam-5564	113	3	,	,	PUNCT
ejpam-5564	113	4	an	an	DET
ejpam-5564	113	5	=	=	SYM
ejpam-5564	113	6	dn−5	dn−5	PROPN
ejpam-5564	113	7	−q0	−q0	NOUN
ejpam-5564	113	8	·	·	PUNCT
ejpam-5564	113	9	p	p	X
ejpam-5564	113	10	(	(	PUNCT
ejpam-5564	113	11	a0	a0	NOUN
ejpam-5564	113	12	,	,	PUNCT
ejpam-5564	113	13	.	.	PUNCT
ejpam-5564	113	14	.	.	PUNCT
ejpam-5564	114	1	.	.	PUNCT
ejpam-5564	115	1	,	,	PUNCT
ejpam-5564	115	2	an−1	an−1	ADJ
ejpam-5564	115	3	)	)	PUNCT
ejpam-5564	115	4	(	(	PUNCT
ejpam-5564	115	5	n−	n−	NOUN
ejpam-5564	115	6	1	1	NUM
ejpam-5564	115	7	)	)	PUNCT
ejpam-5564	115	8	(	(	PUNCT
ejpam-5564	115	9	n−	n−	NOUN
ejpam-5564	115	10	2	2	NUM
ejpam-5564	115	11	)	)	PUNCT
ejpam-5564	115	12	(	(	PUNCT
ejpam-5564	115	13	n−	n−	NOUN
ejpam-5564	115	14	3	3	NUM
ejpam-5564	115	15	)	)	PUNCT
ejpam-5564	115	16	(	(	PUNCT
ejpam-5564	115	17	n−	n−	NOUN
ejpam-5564	115	18	4	4	NUM
ejpam-5564	115	19	)	)	PUNCT
ejpam-5564	115	20	+	+	CCONJ
ejpam-5564	115	21	24	24	NUM
ejpam-5564	115	22	(	(	PUNCT
ejpam-5564	115	23	2n−	2n−	PROPN
ejpam-5564	115	24	3	3	NUM
ejpam-5564	115	25	)	)	PUNCT
ejpam-5564	115	26	.	.	PUNCT
ejpam-5564	116	1	considering	consider	VERB
ejpam-5564	116	2	the	the	DET
ejpam-5564	116	3	form	form	NOUN
ejpam-5564	116	4	of	of	ADP
ejpam-5564	116	5	the	the	DET
ejpam-5564	116	6	function	function	NOUN
ejpam-5564	116	7	p	p	PROPN
ejpam-5564	116	8	(	(	PUNCT
ejpam-5564	116	9	a0	a0	NOUN
ejpam-5564	116	10	,	,	PUNCT
ejpam-5564	116	11	.	.	PUNCT
ejpam-5564	116	12	.	.	PUNCT
ejpam-5564	117	1	.	.	PUNCT
ejpam-5564	118	1	,	,	PUNCT
ejpam-5564	118	2	an−1	an−1	ADJ
ejpam-5564	118	3	)	)	PUNCT
ejpam-5564	118	4	and	and	CCONJ
ejpam-5564	118	5	the	the	DET
ejpam-5564	118	6	initial	initial	ADJ
ejpam-5564	118	7	values	value	NOUN
ejpam-5564	118	8	ai	ai	VERB
ejpam-5564	118	9	,	,	PUNCT
ejpam-5564	118	10	as	as	ADV
ejpam-5564	118	11	well	well	ADV
ejpam-5564	118	12	as	as	ADP
ejpam-5564	118	13	the	the	DET
ejpam-5564	118	14	condition	condition	NOUN
ejpam-5564	118	15	of	of	ADP
ejpam-5564	118	16	analyticity	analyticity	NOUN
ejpam-5564	118	17	of	of	ADP
ejpam-5564	118	18	the	the	DET
ejpam-5564	118	19	function	function	NOUN
ejpam-5564	118	20	f	f	PROPN
ejpam-5564	118	21	(	(	PUNCT
ejpam-5564	118	22	z	z	NOUN
ejpam-5564	118	23	)	)	PUNCT
ejpam-5564	118	24	,	,	PUNCT
ejpam-5564	118	25	which	which	PRON
ejpam-5564	118	26	implies	imply	VERB
ejpam-5564	118	27	the	the	DET
ejpam-5564	118	28	boundedness	boundedness	NOUN
ejpam-5564	118	29	of	of	ADP
ejpam-5564	118	30	the	the	DET
ejpam-5564	118	31	coefficients	coefficient	NOUN
ejpam-5564	118	32	|dn|	|dn|	PROPN
ejpam-5564	118	33	=	=	SYM
ejpam-5564	119	1	∣∣∣f	∣∣∣f	PROPN
ejpam-5564	119	2	(	(	PUNCT
ejpam-5564	119	3	n)(x0	n)(x0	PROPN
ejpam-5564	119	4	)	)	PUNCT
ejpam-5564	119	5	n	n	CCONJ
ejpam-5564	119	6	!	!	X
ejpam-5564	119	7	∣∣∣	∣∣∣	PROPN
ejpam-5564	119	8	≤	≤	NUM
ejpam-5564	119	9	θn	θn	PROPN
ejpam-5564	119	10	,	,	PUNCT
ejpam-5564	119	11	we	we	PRON
ejpam-5564	119	12	obtain	obtain	VERB
ejpam-5564	119	13	the	the	DET
ejpam-5564	119	14	following	follow	VERB
ejpam-5564	119	15	estimate	estimate	NOUN
ejpam-5564	119	16	for	for	ADP
ejpam-5564	119	17	the	the	DET
ejpam-5564	119	18	coefficients	coefficient	NOUN
ejpam-5564	119	19	:	:	PUNCT
ejpam-5564	119	20	|an|	|an|	NOUN
ejpam-5564	119	21	=	=	NOUN
ejpam-5564	119	22	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5564	119	23	dn−5	dn−5	PROPN
ejpam-5564	119	24	−q0	−q0	NOUN
ejpam-5564	119	25	·	·	PUNCT
ejpam-5564	119	26	p	p	X
ejpam-5564	119	27	(	(	PUNCT
ejpam-5564	119	28	a0	a0	NOUN
ejpam-5564	119	29	,	,	PUNCT
ejpam-5564	119	30	.	.	PUNCT
ejpam-5564	119	31	.	.	PUNCT
ejpam-5564	120	1	.	.	PUNCT
ejpam-5564	121	1	,	,	PUNCT
ejpam-5564	121	2	an−1	an−1	ADJ
ejpam-5564	121	3	)	)	PUNCT
ejpam-5564	121	4	(	(	PUNCT
ejpam-5564	121	5	n−	n−	NOUN
ejpam-5564	121	6	1	1	NUM
ejpam-5564	121	7	)	)	PUNCT
ejpam-5564	121	8	(	(	PUNCT
ejpam-5564	121	9	n−	n−	NOUN
ejpam-5564	121	10	2	2	NUM
ejpam-5564	121	11	)	)	PUNCT
ejpam-5564	121	12	(	(	PUNCT
ejpam-5564	121	13	n−	n−	NOUN
ejpam-5564	121	14	3	3	NUM
ejpam-5564	121	15	)	)	PUNCT
ejpam-5564	121	16	(	(	PUNCT
ejpam-5564	121	17	n−	n−	NOUN
ejpam-5564	121	18	4	4	NUM
ejpam-5564	121	19	)	)	PUNCT
ejpam-5564	121	20	+	+	CCONJ
ejpam-5564	121	21	24	24	NUM
ejpam-5564	121	22	(	(	PUNCT
ejpam-5564	121	23	2n−	2n−	PROPN
ejpam-5564	121	24	3	3	NUM
ejpam-5564	121	25	)	)	PUNCT
ejpam-5564	121	26	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5564	121	27	≤	≤	NOUN
ejpam-5564	121	28	≤	≤	NUM
ejpam-5564	121	29	|dn−5|+	|dn−5|+	NOUN
ejpam-5564	121	30	|q0	|q0	NOUN
ejpam-5564	121	31	·	·	PUNCT
ejpam-5564	122	1	p	p	X
ejpam-5564	122	2	(	(	PUNCT
ejpam-5564	122	3	a0	a0	NOUN
ejpam-5564	122	4	,	,	PUNCT
ejpam-5564	122	5	.	.	PUNCT
ejpam-5564	122	6	.	.	PUNCT
ejpam-5564	122	7	.	.	PUNCT
ejpam-5564	123	1	,	,	PUNCT
ejpam-5564	123	2	an−1)|	an−1)|	VERB
ejpam-5564	123	3	|(n−	|(n−	ADJ
ejpam-5564	123	4	1	1	X
ejpam-5564	123	5	)	)	PUNCT
ejpam-5564	123	6	(	(	PUNCT
ejpam-5564	123	7	n−	n−	NOUN
ejpam-5564	123	8	2	2	NUM
ejpam-5564	123	9	)	)	PUNCT
ejpam-5564	123	10	(	(	PUNCT
ejpam-5564	123	11	n−	n−	NOUN
ejpam-5564	123	12	3	3	NUM
ejpam-5564	123	13	)	)	PUNCT
ejpam-5564	123	14	(	(	PUNCT
ejpam-5564	123	15	n−	n−	NOUN
ejpam-5564	123	16	4	4	NUM
ejpam-5564	123	17	)	)	PUNCT
ejpam-5564	123	18	+	+	CCONJ
ejpam-5564	123	19	24	24	NUM
ejpam-5564	123	20	(	(	PUNCT
ejpam-5564	123	21	2n−	2n−	PROPN
ejpam-5564	123	22	3)|	3)|	NUM
ejpam-5564	123	23	≤	≤	NOUN
ejpam-5564	123	24	m.	m.	NOUN
ejpam-5564	123	25	gasanov	gasanov	NOUN
ejpam-5564	123	26	/	/	SYM
ejpam-5564	123	27	eur	eur	PROPN
ejpam-5564	123	28	.	.	PUNCT
ejpam-5564	124	1	j.	j.	PROPN
ejpam-5564	124	2	pure	pure	PROPN
ejpam-5564	124	3	appl	appl	PROPN
ejpam-5564	124	4	.	.	PROPN
ejpam-5564	124	5	math	math	PROPN
ejpam-5564	124	6	,	,	PUNCT
ejpam-5564	124	7	18	18	NUM
ejpam-5564	124	8	(	(	PUNCT
ejpam-5564	124	9	1	1	NUM
ejpam-5564	124	10	)	)	PUNCT
ejpam-5564	124	11	(	(	PUNCT
ejpam-5564	124	12	2025	2025	NUM
ejpam-5564	124	13	)	)	PUNCT
ejpam-5564	124	14	,	,	PUNCT
ejpam-5564	124	15	5564	5564	NUM
ejpam-5564	124	16	7	7	NUM
ejpam-5564	124	17	of	of	ADP
ejpam-5564	124	18	19	19	NUM
ejpam-5564	124	19	≤	≤	NOUN
ejpam-5564	124	20	|dn−5|+	|dn−5|+	NOUN
ejpam-5564	124	21	∣∣∣∣∣∣∣∣q0a0	∣∣∣∣∣∣∣∣q0a0	NOUN
ejpam-5564	124	22	∑	∑	PUNCT
ejpam-5564	124	23	k+l	k+l	X
ejpam-5564	124	24	=	=	SYM
ejpam-5564	124	25	n−9	n−9	PROPN
ejpam-5564	124	26	k	k	NOUN
ejpam-5564	124	27	,	,	PUNCT
ejpam-5564	124	28	l∈n∪{0	l∈n∪{0	NOUN
ejpam-5564	124	29	}	}	PUNCT
ejpam-5564	124	30	dkdl	dkdl	NOUN
ejpam-5564	124	31	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ejpam-5564	124	32	|(n−	|(n−	NOUN
ejpam-5564	124	33	1	1	NUM
ejpam-5564	124	34	)	)	PUNCT
ejpam-5564	124	35	(	(	PUNCT
ejpam-5564	124	36	n−	n−	NOUN
ejpam-5564	124	37	2	2	NUM
ejpam-5564	124	38	)	)	PUNCT
ejpam-5564	124	39	(	(	PUNCT
ejpam-5564	124	40	n−	n−	NOUN
ejpam-5564	124	41	3	3	NUM
ejpam-5564	124	42	)	)	PUNCT
ejpam-5564	124	43	(	(	PUNCT
ejpam-5564	124	44	n−	n−	NOUN
ejpam-5564	124	45	4	4	NUM
ejpam-5564	124	46	)	)	PUNCT
ejpam-5564	124	47	+	+	CCONJ
ejpam-5564	125	1	24	24	NUM
ejpam-5564	125	2	(	(	PUNCT
ejpam-5564	125	3	2n−	2n−	PROPN
ejpam-5564	125	4	3)|	3)|	NUM
ejpam-5564	125	5	≤	≤	NOUN
ejpam-5564	125	6	≤	≤	PUNCT
ejpam-5564	125	7	|γ|	|γ|	PROPN
ejpam-5564	125	8	[	[	PUNCT
ejpam-5564	125	9	n	n	NOUN
ejpam-5564	125	10	5	5	NUM
ejpam-5564	125	11	]	]	PUNCT
ejpam-5564	125	12	+	+	NUM
ejpam-5564	125	13	∣∣∣q0a0γ	∣∣∣q0a0γ	X
ejpam-5564	126	1	[	[	X
ejpam-5564	126	2	n5	n5	X
ejpam-5564	126	3	]	]	PUNCT
ejpam-5564	126	4	∣∣∣	∣∣∣	NOUN
ejpam-5564	126	5	∣∣[n−9	∣∣[n−9	PROPN
ejpam-5564	126	6	2	2	NUM
ejpam-5564	126	7	]	]	PUNCT
ejpam-5564	127	1	+	+	CCONJ
ejpam-5564	127	2	1	1	NUM
ejpam-5564	127	3	∣∣	∣∣	NUM
ejpam-5564	127	4	|(n−	|(n−	VERB
ejpam-5564	127	5	1	1	NUM
ejpam-5564	127	6	)	)	PUNCT
ejpam-5564	127	7	(	(	PUNCT
ejpam-5564	127	8	n−	n−	NOUN
ejpam-5564	127	9	2	2	NUM
ejpam-5564	127	10	)	)	PUNCT
ejpam-5564	127	11	(	(	PUNCT
ejpam-5564	127	12	n−	n−	NOUN
ejpam-5564	127	13	3	3	NUM
ejpam-5564	127	14	)	)	PUNCT
ejpam-5564	127	15	(	(	PUNCT
ejpam-5564	127	16	n−	n−	NOUN
ejpam-5564	127	17	4	4	NUM
ejpam-5564	127	18	)	)	PUNCT
ejpam-5564	127	19	+	+	CCONJ
ejpam-5564	127	20	24	24	NUM
ejpam-5564	127	21	(	(	PUNCT
ejpam-5564	127	22	2n−	2n−	PROPN
ejpam-5564	127	23	3)|	3)|	NUM
ejpam-5564	127	24	=	=	SYM
ejpam-5564	128	1	=	=	PUNCT
ejpam-5564	128	2	|γ|	|γ|	PROPN
ejpam-5564	128	3	[	[	PUNCT
ejpam-5564	128	4	n	n	NOUN
ejpam-5564	128	5	5	5	NUM
ejpam-5564	128	6	]	]	PUNCT
ejpam-5564	128	7	(	(	PUNCT
ejpam-5564	128	8	|q0a0|	|q0a0|	NUM
ejpam-5564	128	9	∣∣[n−9	∣∣[n−9	PROPN
ejpam-5564	128	10	2	2	NUM
ejpam-5564	128	11	]	]	PUNCT
ejpam-5564	128	12	+	+	CCONJ
ejpam-5564	128	13	1	1	NUM
ejpam-5564	128	14	∣∣+	∣∣+	NOUN
ejpam-5564	128	15	1	1	NUM
ejpam-5564	128	16	)	)	PUNCT
ejpam-5564	128	17	|(n−	|(n−	NOUN
ejpam-5564	128	18	1	1	NUM
ejpam-5564	128	19	)	)	PUNCT
ejpam-5564	128	20	(	(	PUNCT
ejpam-5564	128	21	n−	n−	NOUN
ejpam-5564	128	22	2	2	NUM
ejpam-5564	128	23	)	)	PUNCT
ejpam-5564	128	24	(	(	PUNCT
ejpam-5564	128	25	n−	n−	NOUN
ejpam-5564	128	26	3	3	NUM
ejpam-5564	128	27	)	)	PUNCT
ejpam-5564	128	28	(	(	PUNCT
ejpam-5564	128	29	n−	n−	NOUN
ejpam-5564	128	30	4	4	NUM
ejpam-5564	128	31	)	)	PUNCT
ejpam-5564	128	32	+	+	CCONJ
ejpam-5564	128	33	24	24	NUM
ejpam-5564	128	34	(	(	PUNCT
ejpam-5564	128	35	2n−	2n−	PROPN
ejpam-5564	128	36	3)|	3)|	NUM
ejpam-5564	128	37	.	.	PUNCT
ejpam-5564	129	1	let	let	VERB
ejpam-5564	129	2	’s	’s	NOUN
ejpam-5564	129	3	find	find	VERB
ejpam-5564	129	4	the	the	DET
ejpam-5564	129	5	radius	radius	NOUN
ejpam-5564	129	6	of	of	ADP
ejpam-5564	129	7	convergence	convergence	NOUN
ejpam-5564	129	8	of	of	ADP
ejpam-5564	129	9	the	the	DET
ejpam-5564	129	10	analytic	analytic	ADJ
ejpam-5564	129	11	part	part	NOUN
ejpam-5564	129	12	of	of	ADP
ejpam-5564	129	13	the	the	DET
ejpam-5564	129	14	series	series	NOUN
ejpam-5564	129	15	(	(	PUNCT
ejpam-5564	129	16	2.1	2.1	NUM
ejpam-5564	129	17	)	)	PUNCT
ejpam-5564	129	18	,	,	PUNCT
ejpam-5564	129	19	taking	take	VERB
ejpam-5564	129	20	into	into	ADP
ejpam-5564	129	21	account	account	NOUN
ejpam-5564	129	22	the	the	DET
ejpam-5564	129	23	obtained	obtain	VERB
ejpam-5564	129	24	estimate	estimate	NOUN
ejpam-5564	129	25	(	(	PUNCT
ejpam-5564	129	26	7	7	NUM
ejpam-5564	129	27	):	):	PUNCT
ejpam-5564	129	28	|z∗	|z∗	PROPN
ejpam-5564	129	29	−	−	PROPN
ejpam-5564	129	30	z|5	z|5	PROPN
ejpam-5564	129	31	<	<	X
ejpam-5564	129	32	1	1	NUM
ejpam-5564	129	33	|γ|	|γ|	PROPN
ejpam-5564	129	34	⇒	⇒	VERB
ejpam-5564	129	35	|z∗	|z∗	PROPN
ejpam-5564	129	36	−	−	PROPN
ejpam-5564	130	1	z|	z|	PROPN
ejpam-5564	130	2	<	<	X
ejpam-5564	130	3	1	1	NUM
ejpam-5564	130	4	5	5	NUM
ejpam-5564	130	5	√	√	NOUN
ejpam-5564	130	6	|γ|	|γ|	PROPN
ejpam-5564	130	7	.	.	PUNCT
ejpam-5564	131	1	taking	take	VERB
ejpam-5564	131	2	into	into	ADP
ejpam-5564	131	3	account	account	NOUN
ejpam-5564	131	4	the	the	DET
ejpam-5564	131	5	existing	exist	VERB
ejpam-5564	131	6	estimates	estimate	NOUN
ejpam-5564	131	7	for	for	ADP
ejpam-5564	131	8	the	the	DET
ejpam-5564	131	9	series	series	NOUN
ejpam-5564	131	10	coefficients	coefficient	NOUN
ejpam-5564	131	11	,	,	PUNCT
ejpam-5564	131	12	we	we	PRON
ejpam-5564	131	13	can	can	AUX
ejpam-5564	131	14	write	write	VERB
ejpam-5564	131	15	the	the	DET
ejpam-5564	131	16	analytical	analytical	ADJ
ejpam-5564	131	17	approximate	approximate	ADJ
ejpam-5564	131	18	solution	solution	NOUN
ejpam-5564	131	19	:	:	PUNCT
ejpam-5564	132	1	wn	wn	PROPN
ejpam-5564	132	2	(	(	PUNCT
ejpam-5564	132	3	z	z	NOUN
ejpam-5564	132	4	)	)	PUNCT
ejpam-5564	132	5	=	=	SYM
ejpam-5564	132	6	(	(	PUNCT
ejpam-5564	132	7	z∗	z∗	NOUN
ejpam-5564	132	8	−	−	PROPN
ejpam-5564	132	9	z)−1	z)−1	NUM
ejpam-5564	132	10	n∑	n∑	PROPN
ejpam-5564	132	11	n=0	n=0	PUNCT
ejpam-5564	132	12	an	an	DET
ejpam-5564	132	13	(	(	PUNCT
ejpam-5564	132	14	z	z	NOUN
ejpam-5564	132	15	∗	∗	NOUN
ejpam-5564	132	16	−	−	PROPN
ejpam-5564	132	17	z)n	z)n	PUNCT
ejpam-5564	132	18	,	,	PUNCT
ejpam-5564	132	19	(	(	PUNCT
ejpam-5564	132	20	9	9	X
ejpam-5564	132	21	)	)	PUNCT
ejpam-5564	132	22	in	in	ADP
ejpam-5564	132	23	the	the	DET
ejpam-5564	132	24	domain	domain	NOUN
ejpam-5564	132	25	|z∗	|z∗	PROPN
ejpam-5564	132	26	−	−	PROPN
ejpam-5564	132	27	z|	z|	PROPN
ejpam-5564	132	28	<	<	X
ejpam-5564	132	29	ρ2	ρ2	PROPN
ejpam-5564	132	30	.	.	PUNCT
ejpam-5564	133	1	next	next	ADV
ejpam-5564	133	2	,	,	PUNCT
ejpam-5564	133	3	let	let	VERB
ejpam-5564	133	4	’s	’s	PRON
ejpam-5564	133	5	proceed	proceed	VERB
ejpam-5564	133	6	to	to	PART
ejpam-5564	133	7	estimate	estimate	VERB
ejpam-5564	133	8	the	the	DET
ejpam-5564	133	9	error	error	NOUN
ejpam-5564	133	10	of	of	ADP
ejpam-5564	133	11	the	the	DET
ejpam-5564	133	12	analytical	analytical	ADJ
ejpam-5564	133	13	approximate	approximate	ADJ
ejpam-5564	133	14	solution	solution	NOUN
ejpam-5564	133	15	.	.	PUNCT
ejpam-5564	134	1	theorem	theorem	NOUN
ejpam-5564	134	2	3	3	NUM
ejpam-5564	134	3	.	.	PUNCT
ejpam-5564	134	4	assume	assume	VERB
ejpam-5564	134	5	that	that	SCONJ
ejpam-5564	134	6	all	all	DET
ejpam-5564	134	7	conditions	condition	NOUN
ejpam-5564	134	8	of	of	ADP
ejpam-5564	134	9	theorem	theorem	ADJ
ejpam-5564	134	10	1	1	NUM
ejpam-5564	134	11	and	and	CCONJ
ejpam-5564	134	12	theorem	theorem	VERB
ejpam-5564	134	13	2	2	NUM
ejpam-5564	134	14	be	be	AUX
ejpam-5564	134	15	satisfied	satisfied	ADJ
ejpam-5564	134	16	,	,	PUNCT
ejpam-5564	134	17	then	then	ADV
ejpam-5564	134	18	the	the	DET
ejpam-5564	134	19	analytical	analytical	ADJ
ejpam-5564	134	20	approximate	approximate	ADJ
ejpam-5564	134	21	solution	solution	NOUN
ejpam-5564	134	22	(	(	PUNCT
ejpam-5564	134	23	9	9	NUM
ejpam-5564	134	24	)	)	PUNCT
ejpam-5564	134	25	of	of	ADP
ejpam-5564	134	26	the	the	DET
ejpam-5564	134	27	cauchy	cauchy	ADJ
ejpam-5564	134	28	problem	problem	NOUN
ejpam-5564	134	29	(	(	PUNCT
ejpam-5564	134	30	2	2	NUM
ejpam-5564	134	31	)	)	PUNCT
ejpam-5564	134	32	—	—	PUNCT
ejpam-5564	134	33	(	(	PUNCT
ejpam-5564	134	34	3	3	NUM
ejpam-5564	134	35	)	)	PUNCT
ejpam-5564	134	36	,	,	PUNCT
ejpam-5564	134	37	for	for	ADP
ejpam-5564	134	38	sufficiently	sufficiently	ADV
ejpam-5564	134	39	large	large	ADJ
ejpam-5564	134	40	values	value	NOUN
ejpam-5564	134	41	of	of	ADP
ejpam-5564	134	42	n	n	PROPN
ejpam-5564	134	43	,	,	PUNCT
ejpam-5564	134	44	has	have	VERB
ejpam-5564	134	45	the	the	DET
ejpam-5564	134	46	following	follow	VERB
ejpam-5564	134	47	error	error	NOUN
ejpam-5564	134	48	estimates	estimate	NOUN
ejpam-5564	134	49	:	:	PUNCT
ejpam-5564	134	50	∆wn	∆wn	PROPN
ejpam-5564	134	51	≤	≤	ADV
ejpam-5564	134	52	4∑	4∑	NUM
ejpam-5564	134	53	k=0	k=0	PROPN
ejpam-5564	134	54	|γ|n+1+k	|γ|n+1+k	PROPN
ejpam-5564	134	55	(	(	PUNCT
ejpam-5564	134	56	|q0a0|	|q0a0|	NUM
ejpam-5564	134	57	∣∣∣[5(n+1)+k−9	∣∣∣[5(n+1)+k−9	NOUN
ejpam-5564	134	58	2	2	NUM
ejpam-5564	134	59	]	]	PUNCT
ejpam-5564	135	1	+	+	CCONJ
ejpam-5564	135	2	1	1	NUM
ejpam-5564	135	3	∣∣∣+	∣∣∣+	NUM
ejpam-5564	135	4	1	1	NUM
ejpam-5564	135	5	)	)	PUNCT
ejpam-5564	135	6	|z∗	|z∗	PROPN
ejpam-5564	135	7	−	−	PROPN
ejpam-5564	135	8	z|n+k∣∣∣∏4	z|n+k∣∣∣∏4	NOUN
ejpam-5564	135	9	i=1	i=1	X
ejpam-5564	136	1	(	(	PUNCT
ejpam-5564	136	2	5	5	NUM
ejpam-5564	136	3	(	(	PUNCT
ejpam-5564	136	4	n	n	NOUN
ejpam-5564	136	5	+	+	NOUN
ejpam-5564	136	6	1	1	NUM
ejpam-5564	136	7	)	)	PUNCT
ejpam-5564	136	8	+	+	CCONJ
ejpam-5564	137	1	k	k	PROPN
ejpam-5564	137	2	−	−	PROPN
ejpam-5564	138	1	i	i	PROPN
ejpam-5564	138	2	)	)	PUNCT
ejpam-5564	139	1	+	+	CCONJ
ejpam-5564	139	2	24	24	NUM
ejpam-5564	139	3	(	(	PUNCT
ejpam-5564	139	4	(	(	PUNCT
ejpam-5564	139	5	2	2	NUM
ejpam-5564	139	6	(	(	PUNCT
ejpam-5564	139	7	5	5	NUM
ejpam-5564	139	8	(	(	PUNCT
ejpam-5564	139	9	n	n	NOUN
ejpam-5564	139	10	+	+	CCONJ
ejpam-5564	139	11	1	1	NUM
ejpam-5564	139	12	)	)	PUNCT
ejpam-5564	139	13	+	+	CCONJ
ejpam-5564	139	14	k)−	k)−	PROPN
ejpam-5564	139	15	3	3	NUM
ejpam-5564	139	16	)	)	PUNCT
ejpam-5564	139	17	)	)	PUNCT
ejpam-5564	139	18	∣∣∣	∣∣∣	ADP
ejpam-5564	139	19	×	×	PROPN
ejpam-5564	139	20	1	1	NUM
ejpam-5564	139	21	1−	1−	NUM
ejpam-5564	139	22	|γ	|γ	X
ejpam-5564	139	23	·	·	PUNCT
ejpam-5564	139	24	(	(	PUNCT
ejpam-5564	139	25	z∗	z∗	NOUN
ejpam-5564	139	26	−	−	PROPN
ejpam-5564	139	27	z)|5	z)|5	PROPN
ejpam-5564	139	28	.	.	PUNCT
ejpam-5564	140	1	(	(	PUNCT
ejpam-5564	140	2	10	10	NUM
ejpam-5564	140	3	)	)	PUNCT
ejpam-5564	140	4	proof	proof	NOUN
ejpam-5564	140	5	.	.	PUNCT
ejpam-5564	141	1	let	let	VERB
ejpam-5564	141	2	’s	’s	PRON
ejpam-5564	141	3	use	use	VERB
ejpam-5564	141	4	the	the	DET
ejpam-5564	141	5	triangle	triangle	NOUN
ejpam-5564	141	6	inequality	inequality	NOUN
ejpam-5564	141	7	:	:	PUNCT
ejpam-5564	142	1	∆wn	∆wn	PROPN
ejpam-5564	142	2	=	=	SYM
ejpam-5564	143	1	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-5564	143	2	∑	∑	PROPN
ejpam-5564	143	3	n≥0	n≥0	PROPN
ejpam-5564	143	4	an	an	DET
ejpam-5564	143	5	(	(	PUNCT
ejpam-5564	143	6	z	z	NOUN
ejpam-5564	143	7	∗	∗	NOUN
ejpam-5564	143	8	−	−	PROPN
ejpam-5564	143	9	z)n−1	z)n−1	NOUN
ejpam-5564	143	10	−	−	PROPN
ejpam-5564	143	11	n∑	n∑	PROPN
ejpam-5564	143	12	n=0	n=0	PUNCT
ejpam-5564	143	13	an	an	DET
ejpam-5564	143	14	(	(	PUNCT
ejpam-5564	143	15	z	z	NOUN
ejpam-5564	143	16	∗	∗	NOUN
ejpam-5564	143	17	−	−	PROPN
ejpam-5564	143	18	z)n−1	z)n−1	PROPN
ejpam-5564	143	19	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-5564	143	20	=	=	SYM
ejpam-5564	143	21	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-5564	143	22	∑	∑	PROPN
ejpam-5564	143	23	n≥n+1	n≥n+1	PROPN
ejpam-5564	143	24	an	an	DET
ejpam-5564	143	25	(	(	PUNCT
ejpam-5564	143	26	z	z	NOUN
ejpam-5564	143	27	∗	∗	NOUN
ejpam-5564	143	28	−	−	PROPN
ejpam-5564	143	29	z)n−1	z)n−1	PROPN
ejpam-5564	143	30	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-5564	143	31	m.	m.	NOUN
ejpam-5564	143	32	gasanov	gasanov	PROPN
ejpam-5564	143	33	/	/	SYM
ejpam-5564	143	34	eur	eur	PROPN
ejpam-5564	143	35	.	.	PUNCT
ejpam-5564	144	1	j.	j.	PROPN
ejpam-5564	144	2	pure	pure	PROPN
ejpam-5564	144	3	appl	appl	PROPN
ejpam-5564	144	4	.	.	PROPN
ejpam-5564	144	5	math	math	PROPN
ejpam-5564	144	6	,	,	PUNCT
ejpam-5564	144	7	18	18	NUM
ejpam-5564	144	8	(	(	PUNCT
ejpam-5564	144	9	1	1	NUM
ejpam-5564	144	10	)	)	PUNCT
ejpam-5564	144	11	(	(	PUNCT
ejpam-5564	144	12	2025	2025	NUM
ejpam-5564	144	13	)	)	PUNCT
ejpam-5564	144	14	,	,	PUNCT
ejpam-5564	144	15	5564	5564	NUM
ejpam-5564	144	16	8	8	NUM
ejpam-5564	144	17	of	of	ADP
ejpam-5564	144	18	19	19	NUM
ejpam-5564	144	19	considering	consider	VERB
ejpam-5564	144	20	that	that	SCONJ
ejpam-5564	144	21	|	|	ADV
ejpam-5564	144	22	∑	∑	ADP
ejpam-5564	144	23	ai|	ai|	PROPN
ejpam-5564	144	24	≤	≤	X
ejpam-5564	144	25	∑	∑	PUNCT
ejpam-5564	144	26	|ai|	|ai|	PROPN
ejpam-5564	144	27	,	,	PUNCT
ejpam-5564	144	28	∀ai	∀ai	NUM
ejpam-5564	144	29	∈	∈	PROPN
ejpam-5564	144	30	c	c	X
ejpam-5564	144	31	,	,	PUNCT
ejpam-5564	144	32	we	we	PRON
ejpam-5564	144	33	have	have	VERB
ejpam-5564	144	34	:	:	PUNCT
ejpam-5564	144	35	∆wn	∆wn	PROPN
ejpam-5564	145	1	=	=	SYM
ejpam-5564	146	1	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-5564	146	2	∑	∑	PROPN
ejpam-5564	146	3	n≥n+1	n≥n+1	PROPN
ejpam-5564	146	4	an	an	DET
ejpam-5564	146	5	(	(	PUNCT
ejpam-5564	146	6	z	z	NOUN
ejpam-5564	146	7	∗	∗	NOUN
ejpam-5564	146	8	−	−	PROPN
ejpam-5564	146	9	z)n−1	z)n−1	NOUN
ejpam-5564	146	10	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5564	146	11	≤	≤	PROPN
ejpam-5564	146	12	∑	∑	PUNCT
ejpam-5564	146	13	n≥n+1	n≥n+1	PROPN
ejpam-5564	146	14	|an|	|an|	NOUN
ejpam-5564	147	1	|z∗	|z∗	NOUN
ejpam-5564	147	2	−	−	PROPN
ejpam-5564	147	3	z|n−1	z|n−1	NOUN
ejpam-5564	147	4	≤	≤	NOUN
ejpam-5564	147	5	∑	∑	PUNCT
ejpam-5564	147	6	n≥n+1	n≥n+1	PROPN
ejpam-5564	147	7	|γ|	|γ|	PROPN
ejpam-5564	147	8	[	[	PUNCT
ejpam-5564	147	9	n	n	NOUN
ejpam-5564	147	10	5	5	NUM
ejpam-5564	147	11	]	]	PUNCT
ejpam-5564	147	12	(	(	PUNCT
ejpam-5564	147	13	|q0a0|	|q0a0|	NUM
ejpam-5564	147	14	∣∣[n−9	∣∣[n−9	PROPN
ejpam-5564	147	15	2	2	NUM
ejpam-5564	147	16	]	]	PUNCT
ejpam-5564	148	1	+	+	CCONJ
ejpam-5564	148	2	1	1	NUM
ejpam-5564	148	3	∣∣+	∣∣+	NOUN
ejpam-5564	148	4	1	1	NUM
ejpam-5564	148	5	)	)	PUNCT
ejpam-5564	148	6	|(n−	|(n−	NOUN
ejpam-5564	148	7	1	1	NUM
ejpam-5564	148	8	)	)	PUNCT
ejpam-5564	148	9	(	(	PUNCT
ejpam-5564	148	10	n−	n−	NOUN
ejpam-5564	148	11	2	2	NUM
ejpam-5564	148	12	)	)	PUNCT
ejpam-5564	148	13	(	(	PUNCT
ejpam-5564	148	14	n−	n−	NOUN
ejpam-5564	148	15	3	3	NUM
ejpam-5564	148	16	)	)	PUNCT
ejpam-5564	148	17	(	(	PUNCT
ejpam-5564	148	18	n−	n−	NOUN
ejpam-5564	148	19	4	4	NUM
ejpam-5564	148	20	)	)	PUNCT
ejpam-5564	148	21	+	+	CCONJ
ejpam-5564	148	22	24	24	NUM
ejpam-5564	148	23	(	(	PUNCT
ejpam-5564	148	24	2n−	2n−	PROPN
ejpam-5564	148	25	3)|	3)|	NUM
ejpam-5564	148	26	|z∗	|z∗	NOUN
ejpam-5564	148	27	−	−	PROPN
ejpam-5564	148	28	z|n−1	z|n−1	NOUN
ejpam-5564	148	29	≤	≤	NOUN
ejpam-5564	148	30	∑	∑	PUNCT
ejpam-5564	148	31	n≥n+1	n≥n+1	PROPN
ejpam-5564	148	32	4∑	4∑	PROPN
ejpam-5564	148	33	k=0	k=0	PROPN
ejpam-5564	148	34	|γ|n+k	|γ|n+k	PUNCT
ejpam-5564	148	35	(	(	PUNCT
ejpam-5564	148	36	|q0a0|	|q0a0|	NUM
ejpam-5564	148	37	∣∣[5n+k−9	∣∣[5n+k−9	PROPN
ejpam-5564	148	38	2	2	NUM
ejpam-5564	148	39	]	]	PUNCT
ejpam-5564	148	40	+	+	CCONJ
ejpam-5564	148	41	1	1	NUM
ejpam-5564	148	42	∣∣+	∣∣+	NOUN
ejpam-5564	148	43	1	1	NUM
ejpam-5564	148	44	)	)	PUNCT
ejpam-5564	148	45	∣∣∣∏4	∣∣∣∏4	NOUN
ejpam-5564	148	46	i=1	i=1	X
ejpam-5564	149	1	(	(	PUNCT
ejpam-5564	149	2	5n+	5n+	NUM
ejpam-5564	149	3	k	k	NOUN
ejpam-5564	149	4	−	−	PROPN
ejpam-5564	149	5	i	i	NOUN
ejpam-5564	149	6	)	)	PUNCT
ejpam-5564	150	1	+	+	CCONJ
ejpam-5564	150	2	24	24	NUM
ejpam-5564	150	3	(	(	PUNCT
ejpam-5564	150	4	2	2	NUM
ejpam-5564	150	5	(	(	PUNCT
ejpam-5564	150	6	5n+	5n+	NUM
ejpam-5564	150	7	k)−	k)−	PROPN
ejpam-5564	150	8	3	3	NUM
ejpam-5564	150	9	)	)	PUNCT
ejpam-5564	150	10	∣∣∣	∣∣∣	NOUN
ejpam-5564	151	1	|z∗	|z∗	PROPN
ejpam-5564	151	2	−	−	PROPN
ejpam-5564	151	3	z|n+k−1	z|n+k−1	PROPN
ejpam-5564	151	4	≤	≤	NOUN
ejpam-5564	151	5	4∑	4∑	PROPN
ejpam-5564	151	6	k=0	k=0	PROPN
ejpam-5564	151	7	|γ|(n+1)+k	|γ|(n+1)+k	ADV
ejpam-5564	151	8	(	(	PUNCT
ejpam-5564	151	9	|q0a0|	|q0a0|	NUM
ejpam-5564	151	10	∣∣∣[5(n+1)+k−9	∣∣∣[5(n+1)+k−9	NOUN
ejpam-5564	151	11	2	2	NUM
ejpam-5564	151	12	]	]	PUNCT
ejpam-5564	151	13	+	+	CCONJ
ejpam-5564	151	14	1	1	NUM
ejpam-5564	151	15	∣∣∣+	∣∣∣+	NUM
ejpam-5564	151	16	1	1	NUM
ejpam-5564	151	17	)	)	PUNCT
ejpam-5564	151	18	|z∗	|z∗	PROPN
ejpam-5564	151	19	−	−	PROPN
ejpam-5564	151	20	z|5(n+1)+k−1∣∣∣∏4	z|5(n+1)+k−1∣∣∣∏4	PROPN
ejpam-5564	151	21	i=1	i=1	X
ejpam-5564	152	1	(	(	PUNCT
ejpam-5564	152	2	5	5	NUM
ejpam-5564	152	3	(	(	PUNCT
ejpam-5564	152	4	n	n	NOUN
ejpam-5564	152	5	+	+	NOUN
ejpam-5564	152	6	1	1	NUM
ejpam-5564	152	7	)	)	PUNCT
ejpam-5564	152	8	+	+	CCONJ
ejpam-5564	153	1	k	k	PROPN
ejpam-5564	153	2	−	−	PROPN
ejpam-5564	154	1	i	i	PROPN
ejpam-5564	154	2	)	)	PUNCT
ejpam-5564	155	1	+	+	CCONJ
ejpam-5564	155	2	24	24	NUM
ejpam-5564	155	3	(	(	PUNCT
ejpam-5564	155	4	2	2	NUM
ejpam-5564	155	5	(	(	PUNCT
ejpam-5564	155	6	5	5	NUM
ejpam-5564	155	7	(	(	PUNCT
ejpam-5564	155	8	n	n	NOUN
ejpam-5564	155	9	+	+	CCONJ
ejpam-5564	155	10	1	1	NUM
ejpam-5564	155	11	)	)	PUNCT
ejpam-5564	155	12	+	+	CCONJ
ejpam-5564	155	13	k)−	k)−	PROPN
ejpam-5564	155	14	3	3	NUM
ejpam-5564	155	15	)	)	PUNCT
ejpam-5564	155	16	∣∣∣	∣∣∣	NOUN
ejpam-5564	155	17	×	×	PROPN
ejpam-5564	155	18	1	1	NUM
ejpam-5564	155	19	1−	1−	NUM
ejpam-5564	155	20	|γ	|γ	X
ejpam-5564	155	21	·	·	PUNCT
ejpam-5564	155	22	(	(	PUNCT
ejpam-5564	155	23	z∗	z∗	NOUN
ejpam-5564	155	24	−	−	PROPN
ejpam-5564	155	25	z)|5	z)|5	NOUN
ejpam-5564	155	26	.	.	PUNCT
ejpam-5564	156	1	2.2	2.2	NUM
ejpam-5564	156	2	.	.	PUNCT
ejpam-5564	156	3	numerical	numerical	PROPN
ejpam-5564	156	4	experiment	experiment	NOUN
ejpam-5564	156	5	let	let	VERB
ejpam-5564	156	6	’s	’s	NOUN
ejpam-5564	156	7	consider	consider	VERB
ejpam-5564	156	8	the	the	DET
ejpam-5564	156	9	cauchy	cauchy	ADJ
ejpam-5564	156	10	problem	problem	NOUN
ejpam-5564	156	11	(	(	PUNCT
ejpam-5564	156	12	2	2	NUM
ejpam-5564	156	13	)	)	PUNCT
ejpam-5564	156	14	—	—	PUNCT
ejpam-5564	156	15	(	(	PUNCT
ejpam-5564	156	16	3	3	X
ejpam-5564	156	17	)	)	PUNCT
ejpam-5564	156	18	with	with	ADP
ejpam-5564	156	19	a	a	DET
ejpam-5564	156	20	specific	specific	ADJ
ejpam-5564	156	21	example	example	NOUN
ejpam-5564	156	22	,	,	PUNCT
ejpam-5564	156	23	when	when	SCONJ
ejpam-5564	156	24	q0	q0	PROPN
ejpam-5564	156	25	=	=	PUNCT
ejpam-5564	156	26	−4	−4	X
ejpam-5564	156	27	and	and	CCONJ
ejpam-5564	156	28	f	f	PROPN
ejpam-5564	156	29	(	(	PUNCT
ejpam-5564	156	30	z	z	NOUN
ejpam-5564	156	31	)	)	PUNCT
ejpam-5564	156	32	=	=	VERB
ejpam-5564	156	33	sin	sin	NOUN
ejpam-5564	156	34	(	(	PUNCT
ejpam-5564	156	35	z	z	NOUN
ejpam-5564	156	36	)	)	PUNCT
ejpam-5564	156	37	with	with	ADP
ejpam-5564	156	38	given	give	VERB
ejpam-5564	156	39	initial	initial	ADJ
ejpam-5564	156	40	conditions	condition	NOUN
ejpam-5564	156	41	:	:	PUNCT
ejpam-5564	156	42	w(4	w(4	X
ejpam-5564	156	43	)	)	PUNCT
ejpam-5564	156	44	−	−	PROPN
ejpam-5564	156	45	4w	4w	NOUN
ejpam-5564	156	46	(	(	PUNCT
ejpam-5564	156	47	w′)2	w′)2	NOUN
ejpam-5564	156	48	=	=	SYM
ejpam-5564	156	49	sin	sin	PROPN
ejpam-5564	156	50	z	z	PROPN
ejpam-5564	156	51	(	(	PUNCT
ejpam-5564	156	52	11)	11)	PROPN
ejpam-5564	156	53	w	w	PROPN
ejpam-5564	156	54	(	(	PUNCT
ejpam-5564	156	55	0	0	NUM
ejpam-5564	156	56	)	)	PUNCT
ejpam-5564	156	57	=	=	SYM
ejpam-5564	156	58	0.2	0.2	NUM
ejpam-5564	156	59	w′	w′	NOUN
ejpam-5564	156	60	(	(	PUNCT
ejpam-5564	156	61	0	0	NUM
ejpam-5564	156	62	)	)	PUNCT
ejpam-5564	156	63	=	=	SYM
ejpam-5564	156	64	0.3	0.3	NUM
ejpam-5564	156	65	w′′	w′′	NOUN
ejpam-5564	156	66	(	(	PUNCT
ejpam-5564	156	67	0	0	NUM
ejpam-5564	156	68	)	)	PUNCT
ejpam-5564	156	69	=	=	SYM
ejpam-5564	156	70	0	0	NUM
ejpam-5564	156	71	w′′′	w′′′	NOUN
ejpam-5564	156	72	(	(	PUNCT
ejpam-5564	156	73	0	0	NUM
ejpam-5564	156	74	)	)	PUNCT
ejpam-5564	156	75	=	=	SYM
ejpam-5564	156	76	0	0	PUNCT
ejpam-5564	157	1	(	(	PUNCT
ejpam-5564	157	2	12	12	NUM
ejpam-5564	157	3	)	)	PUNCT
ejpam-5564	157	4	the	the	DET
ejpam-5564	157	5	coefficients	coefficient	NOUN
ejpam-5564	157	6	of	of	ADP
ejpam-5564	157	7	the	the	DET
ejpam-5564	157	8	series	series	NOUN
ejpam-5564	157	9	expansion	expansion	NOUN
ejpam-5564	157	10	(	(	PUNCT
ejpam-5564	157	11	2.1	2.1	NUM
ejpam-5564	157	12	)	)	PUNCT
ejpam-5564	157	13	for	for	ADP
ejpam-5564	157	14	the	the	DET
ejpam-5564	157	15	solution	solution	NOUN
ejpam-5564	157	16	to	to	ADP
ejpam-5564	157	17	the	the	DET
ejpam-5564	157	18	cauchy	cauchy	ADJ
ejpam-5564	157	19	problem	problem	NOUN
ejpam-5564	157	20	(	(	PUNCT
ejpam-5564	157	21	11	11	NUM
ejpam-5564	157	22	)	)	PUNCT
ejpam-5564	157	23	—	—	PUNCT
ejpam-5564	157	24	(	(	PUNCT
ejpam-5564	157	25	12	12	NUM
ejpam-5564	157	26	)	)	PUNCT
ejpam-5564	157	27	take	take	VERB
ejpam-5564	157	28	the	the	DET
ejpam-5564	157	29	following	follow	VERB
ejpam-5564	157	30	form:	form:	PROPN
ejpam-5564	157	31	a0	a0	PROPN
ejpam-5564	157	32	=	=	SYM
ejpam-5564	157	33	√	√	PROPN
ejpam-5564	157	34	6	6	NUM
ejpam-5564	157	35	a1	a1	NOUN
ejpam-5564	157	36	=	=	SYM
ejpam-5564	157	37	a2	a2	PROPN
ejpam-5564	157	38	=	=	SYM
ejpam-5564	157	39	a3	a3	NOUN
ejpam-5564	157	40	=	=	SYM
ejpam-5564	157	41	a4	a4	PROPN
ejpam-5564	157	42	=	=	SYM
ejpam-5564	157	43	0	0	NUM
ejpam-5564	157	44	a5	a5	NOUN
ejpam-5564	157	45	=	=	SYM
ejpam-5564	157	46	1	1	NUM
ejpam-5564	157	47	192	192	NUM
ejpam-5564	157	48	a6	a6	NOUN
ejpam-5564	157	49	=	=	PUNCT
ejpam-5564	158	1	−	−	PROPN
ejpam-5564	158	2	1	1	NUM
ejpam-5564	158	3	2016	2016	NUM
ejpam-5564	158	4	a7	a7	NOUN
ejpam-5564	158	5	=	=	SYM
ejpam-5564	158	6	1	1	NUM
ejpam-5564	158	7	40320	40320	NUM
ejpam-5564	158	8	.	.	PUNCT
ejpam-5564	158	9	.	.	PUNCT
ejpam-5564	158	10	.	.	PUNCT
ejpam-5564	158	11	.	.	PUNCT
ejpam-5564	158	12	.	.	PUNCT
ejpam-5564	158	13	.	.	PUNCT
ejpam-5564	158	14	.	.	PUNCT
ejpam-5564	158	15	.	.	PUNCT
ejpam-5564	158	16	.	.	PUNCT
ejpam-5564	159	1	m.	m.	NOUN
ejpam-5564	159	2	gasanov	gasanov	PROPN
ejpam-5564	159	3	/	/	SYM
ejpam-5564	159	4	eur	eur	PROPN
ejpam-5564	159	5	.	.	PUNCT
ejpam-5564	160	1	j.	j.	PROPN
ejpam-5564	160	2	pure	pure	PROPN
ejpam-5564	160	3	appl	appl	PROPN
ejpam-5564	160	4	.	.	PROPN
ejpam-5564	160	5	math	math	PROPN
ejpam-5564	160	6	,	,	PUNCT
ejpam-5564	160	7	18	18	NUM
ejpam-5564	160	8	(	(	PUNCT
ejpam-5564	160	9	1	1	NUM
ejpam-5564	160	10	)	)	PUNCT
ejpam-5564	160	11	(	(	PUNCT
ejpam-5564	160	12	2025	2025	NUM
ejpam-5564	160	13	)	)	PUNCT
ejpam-5564	160	14	,	,	PUNCT
ejpam-5564	160	15	5564	5564	NUM
ejpam-5564	160	16	9	9	NUM
ejpam-5564	160	17	of	of	ADP
ejpam-5564	160	18	19	19	NUM
ejpam-5564	160	19	the	the	DET
ejpam-5564	160	20	estimate	estimate	NOUN
ejpam-5564	160	21	for	for	ADP
ejpam-5564	160	22	the	the	DET
ejpam-5564	160	23	coefficients	coefficient	NOUN
ejpam-5564	160	24	of	of	ADP
ejpam-5564	160	25	the	the	DET
ejpam-5564	160	26	series	series	NOUN
ejpam-5564	160	27	expansion	expansion	NOUN
ejpam-5564	160	28	(	(	PUNCT
ejpam-5564	160	29	2.1	2.1	NUM
ejpam-5564	160	30	)	)	PUNCT
ejpam-5564	160	31	according	accord	VERB
ejpam-5564	160	32	to	to	ADP
ejpam-5564	160	33	theorem	theorem	NOUN
ejpam-5564	160	34	2	2	NUM
ejpam-5564	160	35	for	for	ADP
ejpam-5564	160	36	the	the	DET
ejpam-5564	160	37	cauchy	cauchy	ADJ
ejpam-5564	160	38	problem	problem	NOUN
ejpam-5564	160	39	(	(	PUNCT
ejpam-5564	160	40	11	11	NUM
ejpam-5564	160	41	)	)	PUNCT
ejpam-5564	160	42	—	—	PUNCT
ejpam-5564	160	43	(	(	PUNCT
ejpam-5564	160	44	12	12	NUM
ejpam-5564	160	45	)	)	PUNCT
ejpam-5564	160	46	is	be	AUX
ejpam-5564	160	47	given	give	VERB
ejpam-5564	160	48	by	by	ADP
ejpam-5564	160	49	:	:	PUNCT
ejpam-5564	160	50	|an|	|an|	NOUN
ejpam-5564	160	51	≤	≤	NUM
ejpam-5564	160	52	4	4	NUM
ejpam-5564	160	53	√	√	NUM
ejpam-5564	160	54	6	6	NUM
ejpam-5564	160	55	∣∣[n−9	∣∣[n−9	NOUN
ejpam-5564	160	56	2	2	NUM
ejpam-5564	160	57	]	]	PUNCT
ejpam-5564	161	1	+	+	CCONJ
ejpam-5564	161	2	1	1	NUM
ejpam-5564	161	3	∣∣+	∣∣+	NOUN
ejpam-5564	161	4	1	1	NUM
ejpam-5564	161	5	|(n−	|(n−	NOUN
ejpam-5564	161	6	1	1	NUM
ejpam-5564	161	7	)	)	PUNCT
ejpam-5564	161	8	(	(	PUNCT
ejpam-5564	161	9	n−	n−	NOUN
ejpam-5564	161	10	2	2	NUM
ejpam-5564	161	11	)	)	PUNCT
ejpam-5564	161	12	(	(	PUNCT
ejpam-5564	161	13	n−	n−	NOUN
ejpam-5564	161	14	3	3	NUM
ejpam-5564	161	15	)	)	PUNCT
ejpam-5564	161	16	(	(	PUNCT
ejpam-5564	161	17	n−	n−	NOUN
ejpam-5564	161	18	4	4	NUM
ejpam-5564	161	19	)	)	PUNCT
ejpam-5564	161	20	+	+	CCONJ
ejpam-5564	161	21	24	24	NUM
ejpam-5564	161	22	(	(	PUNCT
ejpam-5564	161	23	2n−	2n−	PROPN
ejpam-5564	161	24	3)|	3)|	NUM
ejpam-5564	161	25	.	.	PUNCT
ejpam-5564	162	1	next	next	ADV
ejpam-5564	162	2	,	,	PUNCT
ejpam-5564	162	3	according	accord	VERB
ejpam-5564	162	4	to	to	ADP
ejpam-5564	162	5	theorem	theorem	NOUN
ejpam-5564	162	6	3	3	NUM
ejpam-5564	162	7	,	,	PUNCT
ejpam-5564	162	8	we	we	PRON
ejpam-5564	162	9	determine	determine	VERB
ejpam-5564	162	10	the	the	DET
ejpam-5564	162	11	error	error	NOUN
ejpam-5564	162	12	estimate	estimate	NOUN
ejpam-5564	162	13	of	of	ADP
ejpam-5564	162	14	the	the	DET
ejpam-5564	162	15	analytical	analytical	ADJ
ejpam-5564	162	16	approximate	approximate	ADJ
ejpam-5564	162	17	solution	solution	NOUN
ejpam-5564	162	18	:	:	PUNCT
ejpam-5564	162	19	∆wn	∆wn	VERB
ejpam-5564	162	20	≤	≤	ADV
ejpam-5564	162	21	4∑	4∑	NUM
ejpam-5564	162	22	k=0	k=0	PROPN
ejpam-5564	162	23	(	(	PUNCT
ejpam-5564	162	24	4	4	NUM
ejpam-5564	162	25	√	√	NUM
ejpam-5564	162	26	6	6	NUM
ejpam-5564	162	27	∣∣∣[5(n+1)+k−9	∣∣∣[5(n+1)+k−9	NOUN
ejpam-5564	162	28	2	2	NUM
ejpam-5564	162	29	]	]	PUNCT
ejpam-5564	163	1	+	+	CCONJ
ejpam-5564	163	2	1	1	NUM
ejpam-5564	163	3	∣∣∣+	∣∣∣+	NUM
ejpam-5564	163	4	1	1	NUM
ejpam-5564	163	5	)	)	PUNCT
ejpam-5564	163	6	|z∗	|z∗	PROPN
ejpam-5564	163	7	−	−	PROPN
ejpam-5564	163	8	z|5(n+1)+k−1∣∣∣∏4	z|5(n+1)+k−1∣∣∣∏4	PROPN
ejpam-5564	163	9	i=1	i=1	X
ejpam-5564	164	1	(	(	PUNCT
ejpam-5564	164	2	5	5	NUM
ejpam-5564	164	3	(	(	PUNCT
ejpam-5564	164	4	n	n	NOUN
ejpam-5564	164	5	+	+	NOUN
ejpam-5564	164	6	1	1	NUM
ejpam-5564	164	7	)	)	PUNCT
ejpam-5564	164	8	+	+	CCONJ
ejpam-5564	165	1	k	k	PROPN
ejpam-5564	165	2	−	−	PROPN
ejpam-5564	166	1	i	i	PROPN
ejpam-5564	166	2	)	)	PUNCT
ejpam-5564	167	1	+	+	CCONJ
ejpam-5564	167	2	24	24	NUM
ejpam-5564	167	3	(	(	PUNCT
ejpam-5564	167	4	2	2	NUM
ejpam-5564	167	5	(	(	PUNCT
ejpam-5564	167	6	5	5	NUM
ejpam-5564	167	7	(	(	PUNCT
ejpam-5564	167	8	n	n	NOUN
ejpam-5564	167	9	+	+	NOUN
ejpam-5564	167	10	1	1	NUM
ejpam-5564	167	11	)	)	PUNCT
ejpam-5564	167	12	)	)	PUNCT
ejpam-5564	168	1	+	+	CCONJ
ejpam-5564	169	1	k	k	X
ejpam-5564	169	2	−	−	NOUN
ejpam-5564	169	3	3	3	NUM
ejpam-5564	169	4	)	)	PUNCT
ejpam-5564	169	5	∣∣∣	∣∣∣	NOUN
ejpam-5564	169	6	1	1	NUM
ejpam-5564	169	7	1−	1−	NUM
ejpam-5564	169	8	|z∗	|z∗	PROPN
ejpam-5564	169	9	−	−	PROPN
ejpam-5564	169	10	z|5	z|5	PROPN
ejpam-5564	169	11	.	.	PUNCT
ejpam-5564	170	1	the	the	DET
ejpam-5564	170	2	value	value	NOUN
ejpam-5564	170	3	of	of	ADP
ejpam-5564	170	4	the	the	DET
ejpam-5564	170	5	moving	move	VERB
ejpam-5564	170	6	singular	singular	ADJ
ejpam-5564	170	7	point	point	NOUN
ejpam-5564	170	8	is	be	AUX
ejpam-5564	170	9	z∗	z∗	NOUN
ejpam-5564	170	10	=	=	SYM
ejpam-5564	170	11	3.513	3.513	NUM
ejpam-5564	170	12	,	,	PUNCT
ejpam-5564	170	13	and	and	CCONJ
ejpam-5564	170	14	the	the	DET
ejpam-5564	170	15	convergence	convergence	NOUN
ejpam-5564	170	16	radius	radius	NOUN
ejpam-5564	170	17	is	be	AUX
ejpam-5564	170	18	ρ	ρ	NOUN
ejpam-5564	170	19	=	=	SYM
ejpam-5564	170	20	1	1	NUM
ejpam-5564	170	21	.	.	X
ejpam-5564	171	1	for	for	ADP
ejpam-5564	171	2	a	a	DET
ejpam-5564	171	3	solution	solution	NOUN
ejpam-5564	171	4	error	error	NOUN
ejpam-5564	171	5	of	of	ADP
ejpam-5564	171	6	ε	ε	PROPN
ejpam-5564	171	7	≈	≈	PROPN
ejpam-5564	171	8	10−7	10−7	NUM
ejpam-5564	171	9	at	at	ADP
ejpam-5564	171	10	the	the	DET
ejpam-5564	171	11	point	point	NOUN
ejpam-5564	171	12	z1	z1	X
ejpam-5564	171	13	=	=	SYM
ejpam-5564	171	14	3.2	3.2	NUM
ejpam-5564	171	15	,	,	PUNCT
ejpam-5564	171	16	according	accord	VERB
ejpam-5564	171	17	to	to	ADP
ejpam-5564	171	18	theorem	theorem	NOUN
ejpam-5564	171	19	3	3	NUM
ejpam-5564	171	20	,	,	PUNCT
ejpam-5564	171	21	it	it	PRON
ejpam-5564	171	22	is	be	AUX
ejpam-5564	171	23	sufficient	sufficient	ADJ
ejpam-5564	171	24	to	to	PART
ejpam-5564	171	25	take	take	VERB
ejpam-5564	171	26	n	n	PRON
ejpam-5564	171	27	=	=	SYM
ejpam-5564	171	28	7	7	X
ejpam-5564	171	29	.	.	PUNCT
ejpam-5564	172	1	in	in	ADP
ejpam-5564	172	2	this	this	DET
ejpam-5564	172	3	case	case	NOUN
ejpam-5564	172	4	,	,	PUNCT
ejpam-5564	172	5	the	the	DET
ejpam-5564	172	6	analytical	analytical	ADJ
ejpam-5564	172	7	approximate	approximate	ADJ
ejpam-5564	172	8	solution	solution	NOUN
ejpam-5564	172	9	is	be	AUX
ejpam-5564	172	10	given	give	VERB
ejpam-5564	172	11	by	by	ADP
ejpam-5564	172	12	:	:	PUNCT
ejpam-5564	172	13	w7	w7	ADJ
ejpam-5564	172	14	(	(	PUNCT
ejpam-5564	172	15	z	z	NOUN
ejpam-5564	172	16	)	)	PUNCT
ejpam-5564	172	17	=	=	PUNCT
ejpam-5564	173	1	√	√	NUM
ejpam-5564	173	2	6	6	NUM
ejpam-5564	173	3	(	(	PUNCT
ejpam-5564	173	4	3.513−	3.513−	NUM
ejpam-5564	173	5	z)−1	z)−1	NUM
ejpam-5564	173	6	+	+	CCONJ
ejpam-5564	173	7	1	1	NUM
ejpam-5564	173	8	192	192	NUM
ejpam-5564	173	9	(	(	PUNCT
ejpam-5564	173	10	3.513−	3.513−	NUM
ejpam-5564	173	11	z)4	z)4	PROPN
ejpam-5564	173	12	−	−	NUM
ejpam-5564	174	1	1	1	NUM
ejpam-5564	174	2	2016	2016	NUM
ejpam-5564	174	3	(	(	PUNCT
ejpam-5564	174	4	3.513−	3.513−	NUM
ejpam-5564	174	5	z)5	z)5	NOUN
ejpam-5564	174	6	+	+	CCONJ
ejpam-5564	174	7	1	1	NUM
ejpam-5564	174	8	40320	40320	NUM
ejpam-5564	174	9	(	(	PUNCT
ejpam-5564	174	10	3.513−	3.513−	NUM
ejpam-5564	174	11	z)6	z)6	PROPN
ejpam-5564	174	12	.	.	PUNCT
ejpam-5564	175	1	below	below	ADP
ejpam-5564	175	2	is	be	AUX
ejpam-5564	175	3	a	a	DET
ejpam-5564	175	4	table	table	NOUN
ejpam-5564	175	5	of	of	ADP
ejpam-5564	175	6	characteristics	characteristic	NOUN
ejpam-5564	175	7	and	and	CCONJ
ejpam-5564	175	8	a	a	DET
ejpam-5564	175	9	graph	graph	NOUN
ejpam-5564	175	10	comparing	compare	VERB
ejpam-5564	175	11	the	the	DET
ejpam-5564	175	12	solution	solution	NOUN
ejpam-5564	175	13	of	of	ADP
ejpam-5564	175	14	the	the	DET
ejpam-5564	175	15	cauchy	cauchy	ADJ
ejpam-5564	175	16	problem	problem	NOUN
ejpam-5564	175	17	(	(	PUNCT
ejpam-5564	175	18	11	11	NUM
ejpam-5564	175	19	)	)	PUNCT
ejpam-5564	175	20	—	—	PUNCT
ejpam-5564	175	21	(	(	PUNCT
ejpam-5564	175	22	12	12	NUM
ejpam-5564	175	23	)	)	PUNCT
ejpam-5564	175	24	obtained	obtain	VERB
ejpam-5564	175	25	using	use	VERB
ejpam-5564	175	26	the	the	DET
ejpam-5564	175	27	analytical	analytical	ADJ
ejpam-5564	175	28	approximate	approximate	ADJ
ejpam-5564	175	29	method	method	NOUN
ejpam-5564	175	30	proposed	propose	VERB
ejpam-5564	175	31	by	by	ADP
ejpam-5564	175	32	the	the	DET
ejpam-5564	175	33	authors	author	NOUN
ejpam-5564	175	34	and	and	CCONJ
ejpam-5564	175	35	the	the	DET
ejpam-5564	175	36	solution	solution	NOUN
ejpam-5564	175	37	obtained	obtain	VERB
ejpam-5564	175	38	numerically	numerically	ADV
ejpam-5564	175	39	using	use	VERB
ejpam-5564	175	40	the	the	DET
ejpam-5564	175	41	runge	runge	NOUN
ejpam-5564	175	42	-	-	PUNCT
ejpam-5564	175	43	kutta	kutta	NOUN
ejpam-5564	175	44	method	method	NOUN
ejpam-5564	175	45	.	.	PUNCT
ejpam-5564	176	1	table	table	NOUN
ejpam-5564	176	2	1	1	NUM
ejpam-5564	176	3	.	.	PUNCT
ejpam-5564	176	4	numerical	numerical	ADJ
ejpam-5564	176	5	characteristics	characteristic	NOUN
ejpam-5564	176	6	of	of	ADP
ejpam-5564	176	7	the	the	DET
ejpam-5564	176	8	analytical	analytical	ADJ
ejpam-5564	176	9	approximate	approximate	ADJ
ejpam-5564	176	10	solution	solution	NOUN
ejpam-5564	176	11	.	.	PUNCT
ejpam-5564	177	1	z1	z1	VERB
ejpam-5564	177	2	w7(z1	w7(z1	NOUN
ejpam-5564	177	3	)	)	PUNCT
ejpam-5564	177	4	∆1	∆1	NUM
ejpam-5564	177	5	3.2	3.2	NUM
ejpam-5564	177	6	7.6125622	7.6125622	NUM
ejpam-5564	177	7	10−7	10−7	NUM
ejpam-5564	177	8	2.3	2.3	NUM
ejpam-5564	177	9	.	.	PUNCT
ejpam-5564	178	1	exact	exact	ADJ
ejpam-5564	178	2	criteria	criterion	NOUN
ejpam-5564	178	3	for	for	ADP
ejpam-5564	178	4	the	the	DET
ejpam-5564	178	5	existence	existence	NOUN
ejpam-5564	178	6	of	of	ADP
ejpam-5564	178	7	a	a	DET
ejpam-5564	178	8	moving	move	VERB
ejpam-5564	178	9	singular	singular	ADJ
ejpam-5564	178	10	point	point	NOUN
ejpam-5564	178	11	in	in	ADP
ejpam-5564	178	12	the	the	DET
ejpam-5564	178	13	real	real	ADJ
ejpam-5564	178	14	and	and	CCONJ
ejpam-5564	178	15	complex	complex	ADJ
ejpam-5564	178	16	domains	domain	NOUN
ejpam-5564	178	17	this	this	DET
ejpam-5564	178	18	section	section	NOUN
ejpam-5564	178	19	is	be	AUX
ejpam-5564	178	20	dedicated	dedicate	VERB
ejpam-5564	178	21	to	to	ADP
ejpam-5564	178	22	criteria	criterion	NOUN
ejpam-5564	178	23	for	for	ADP
ejpam-5564	178	24	the	the	DET
ejpam-5564	178	25	existence	existence	NOUN
ejpam-5564	178	26	of	of	ADP
ejpam-5564	178	27	a	a	DET
ejpam-5564	178	28	moving	move	VERB
ejpam-5564	178	29	singular	singular	ADJ
ejpam-5564	178	30	point	point	NOUN
ejpam-5564	178	31	.	.	PUNCT
ejpam-5564	179	1	both	both	PRON
ejpam-5564	179	2	point	point	NOUN
ejpam-5564	179	3	and	and	CCONJ
ejpam-5564	179	4	interval	interval	NOUN
ejpam-5564	179	5	criteria	criterion	NOUN
ejpam-5564	179	6	are	be	AUX
ejpam-5564	179	7	considered	consider	VERB
ejpam-5564	179	8	.	.	PUNCT
ejpam-5564	180	1	point	point	NOUN
ejpam-5564	180	2	criteria	criterion	NOUN
ejpam-5564	180	3	only	only	ADV
ejpam-5564	180	4	guarantee	guarantee	VERB
ejpam-5564	180	5	the	the	DET
ejpam-5564	180	6	existence	existence	NOUN
ejpam-5564	180	7	of	of	ADP
ejpam-5564	180	8	a	a	DET
ejpam-5564	180	9	moving	move	VERB
ejpam-5564	180	10	singular	singular	ADJ
ejpam-5564	180	11	point	point	NOUN
ejpam-5564	180	12	,	,	PUNCT
ejpam-5564	180	13	while	while	SCONJ
ejpam-5564	180	14	interval	interval	NOUN
ejpam-5564	180	15	criteria	criterion	NOUN
ejpam-5564	180	16	allow	allow	VERB
ejpam-5564	180	17	determining	determine	VERB
ejpam-5564	180	18	their	their	PRON
ejpam-5564	180	19	location	location	NOUN
ejpam-5564	180	20	.	.	PUNCT
ejpam-5564	181	1	to	to	PART
ejpam-5564	181	2	define	define	VERB
ejpam-5564	181	3	such	such	ADJ
ejpam-5564	181	4	criteria	criterion	NOUN
ejpam-5564	181	5	in	in	ADP
ejpam-5564	181	6	the	the	DET
ejpam-5564	181	7	complex	complex	ADJ
ejpam-5564	181	8	plane	plane	NOUN
ejpam-5564	181	9	,	,	PUNCT
ejpam-5564	181	10	a	a	DET
ejpam-5564	181	11	transition	transition	NOUN
ejpam-5564	181	12	to	to	PART
ejpam-5564	181	13	phase	phase	NOUN
ejpam-5564	181	14	spaces	space	NOUN
ejpam-5564	181	15	is	be	AUX
ejpam-5564	181	16	necessary	necessary	ADJ
ejpam-5564	181	17	.	.	PUNCT
ejpam-5564	182	1	before	before	ADP
ejpam-5564	182	2	formulating	formulate	VERB
ejpam-5564	182	3	the	the	DET
ejpam-5564	182	4	theorems	theorem	NOUN
ejpam-5564	182	5	,	,	PUNCT
ejpam-5564	182	6	it	it	PRON
ejpam-5564	182	7	is	be	AUX
ejpam-5564	182	8	necessary	necessary	ADJ
ejpam-5564	182	9	to	to	PART
ejpam-5564	182	10	transform	transform	VERB
ejpam-5564	182	11	the	the	DET
ejpam-5564	182	12	cauchy	cauchy	ADJ
ejpam-5564	182	13	problem	problem	NOUN
ejpam-5564	182	14	(	(	PUNCT
ejpam-5564	182	15	2	2	NUM
ejpam-5564	182	16	)	)	PUNCT
ejpam-5564	182	17	—	—	PUNCT
ejpam-5564	182	18	(	(	PUNCT
ejpam-5564	182	19	3	3	X
ejpam-5564	182	20	)	)	PUNCT
ejpam-5564	182	21	into	into	ADP
ejpam-5564	182	22	the	the	DET
ejpam-5564	182	23	inverse	inverse	NOUN
ejpam-5564	182	24	cauchy	cauchy	NOUN
ejpam-5564	182	25	problem	problem	NOUN
ejpam-5564	182	26	by	by	ADP
ejpam-5564	182	27	a	a	DET
ejpam-5564	182	28	change	change	NOUN
ejpam-5564	182	29	of	of	ADP
ejpam-5564	182	30	variable	variable	ADJ
ejpam-5564	182	31	w	w	PROPN
ejpam-5564	182	32	(	(	PUNCT
ejpam-5564	182	33	z	z	NOUN
ejpam-5564	182	34	)	)	PUNCT
ejpam-5564	182	35	=	=	SYM
ejpam-5564	182	36	1	1	NUM
ejpam-5564	182	37	u(z	u(z	NOUN
ejpam-5564	182	38	)	)	PUNCT
ejpam-5564	182	39	:	:	PUNCT
ejpam-5564	183	1	w′	w′	PROPN
ejpam-5564	183	2	=	=	SYM
ejpam-5564	184	1	−u−2u′	−u−2u′	PROPN
ejpam-5564	184	2	,	,	PUNCT
ejpam-5564	184	3	w′′	w′′	NOUN
ejpam-5564	184	4	=	=	SYM
ejpam-5564	184	5	2u−3	2u−3	NUM
ejpam-5564	184	6	(	(	PUNCT
ejpam-5564	184	7	u′	u′	PROPN
ejpam-5564	184	8	)	)	PUNCT
ejpam-5564	184	9	2	2	NUM
ejpam-5564	184	10	−	−	PROPN
ejpam-5564	184	11	u−2u′′	u−2u′′	PROPN
ejpam-5564	184	12	,	,	PUNCT
ejpam-5564	184	13	w′′′	w′′′	NOUN
ejpam-5564	184	14	=	=	X
ejpam-5564	184	15	−6	−6	PROPN
ejpam-5564	184	16	(	(	PUNCT
ejpam-5564	184	17	u′	u′	PROPN
ejpam-5564	184	18	)	)	PUNCT
ejpam-5564	184	19	3	3	NUM
ejpam-5564	185	1	u−4	u−4	ADP
ejpam-5564	185	2	+	+	SYM
ejpam-5564	185	3	6u′u′′u−3	6u′u′′u−3	ADJ
ejpam-5564	185	4	−	−	NOUN
ejpam-5564	185	5	u′′′u−2	u′′′u−2	ADJ
ejpam-5564	185	6	,	,	PUNCT
ejpam-5564	185	7	w(4	w(4	ADJ
ejpam-5564	185	8	)	)	PUNCT
ejpam-5564	185	9	=	=	SYM
ejpam-5564	185	10	24	24	NUM
ejpam-5564	185	11	(	(	PUNCT
ejpam-5564	185	12	u′	u′	PROPN
ejpam-5564	185	13	)	)	PUNCT
ejpam-5564	185	14	4	4	NUM
ejpam-5564	185	15	u−5	u−5	PROPN
ejpam-5564	185	16	−	−	PROPN
ejpam-5564	185	17	36	36	NUM
ejpam-5564	185	18	(	(	PUNCT
ejpam-5564	185	19	u′	u′	PROPN
ejpam-5564	185	20	)	)	PUNCT
ejpam-5564	185	21	2	2	NUM
ejpam-5564	185	22	u′′u−4	u′′u−4	ADJ
ejpam-5564	185	23	+	+	NUM
ejpam-5564	185	24	6	6	NUM
ejpam-5564	185	25	(	(	PUNCT
ejpam-5564	185	26	u′′	u′′	PROPN
ejpam-5564	185	27	)	)	PUNCT
ejpam-5564	185	28	2	2	NUM
ejpam-5564	186	1	u−3	u−3	ADJ
ejpam-5564	186	2	+	+	CCONJ
ejpam-5564	186	3	3u′u′′′u−3	3u′u′′′u−3	ADV
ejpam-5564	186	4	−	−	ADP
ejpam-5564	186	5	u(4)u−2	u(4)u−2	PROPN
ejpam-5564	186	6	.	.	PUNCT
ejpam-5564	186	7	m.	m.	NOUN
ejpam-5564	186	8	gasanov	gasanov	PROPN
ejpam-5564	186	9	/	/	SYM
ejpam-5564	186	10	eur	eur	PROPN
ejpam-5564	186	11	.	.	PUNCT
ejpam-5564	187	1	j.	j.	PROPN
ejpam-5564	187	2	pure	pure	PROPN
ejpam-5564	187	3	appl	appl	PROPN
ejpam-5564	187	4	.	.	PROPN
ejpam-5564	187	5	math	math	PROPN
ejpam-5564	187	6	,	,	PUNCT
ejpam-5564	187	7	18	18	NUM
ejpam-5564	187	8	(	(	PUNCT
ejpam-5564	187	9	1	1	NUM
ejpam-5564	187	10	)	)	PUNCT
ejpam-5564	187	11	(	(	PUNCT
ejpam-5564	187	12	2025	2025	NUM
ejpam-5564	187	13	)	)	PUNCT
ejpam-5564	187	14	,	,	PUNCT
ejpam-5564	187	15	5564	5564	NUM
ejpam-5564	187	16	10	10	NUM
ejpam-5564	187	17	of	of	ADP
ejpam-5564	187	18	19	19	NUM
ejpam-5564	187	19	figure	figure	NOUN
ejpam-5564	187	20	1	1	NUM
ejpam-5564	187	21	:	:	PUNCT
ejpam-5564	187	22	the	the	DET
ejpam-5564	187	23	solution	solution	NOUN
ejpam-5564	187	24	to	to	ADP
ejpam-5564	187	25	the	the	DET
ejpam-5564	187	26	cauchy	cauchy	ADJ
ejpam-5564	187	27	problem	problem	NOUN
ejpam-5564	187	28	(	(	PUNCT
ejpam-5564	187	29	11	11	NUM
ejpam-5564	187	30	)	)	PUNCT
ejpam-5564	187	31	—	—	PUNCT
ejpam-5564	187	32	(	(	PUNCT
ejpam-5564	187	33	12	12	NUM
ejpam-5564	187	34	)	)	PUNCT
ejpam-5564	187	35	the	the	DET
ejpam-5564	187	36	analytical	analytical	ADJ
ejpam-5564	187	37	approximate	approximate	ADJ
ejpam-5564	187	38	method	method	NOUN
ejpam-5564	187	39	(	(	PUNCT
ejpam-5564	187	40	dashed	dash	VERB
ejpam-5564	187	41	blue	blue	ADJ
ejpam-5564	187	42	line	line	NOUN
ejpam-5564	187	43	)	)	PUNCT
ejpam-5564	187	44	and	and	CCONJ
ejpam-5564	187	45	the	the	DET
ejpam-5564	187	46	runge	runge	NOUN
ejpam-5564	187	47	-	-	PUNCT
ejpam-5564	187	48	kutta	kutta	NOUN
ejpam-5564	187	49	method	method	NOUN
ejpam-5564	187	50	(	(	PUNCT
ejpam-5564	187	51	solid	solid	ADJ
ejpam-5564	187	52	red	red	ADJ
ejpam-5564	187	53	line	line	NOUN
ejpam-5564	187	54	)	)	PUNCT
ejpam-5564	187	55	thus	thus	ADV
ejpam-5564	187	56	,	,	PUNCT
ejpam-5564	187	57	the	the	DET
ejpam-5564	187	58	inverse	inverse	NOUN
ejpam-5564	187	59	cauchy	cauchy	NOUN
ejpam-5564	187	60	problem	problem	NOUN
ejpam-5564	187	61	will	will	AUX
ejpam-5564	187	62	have	have	VERB
ejpam-5564	187	63	the	the	DET
ejpam-5564	187	64	form	form	NOUN
ejpam-5564	187	65	:	:	PUNCT
ejpam-5564	187	66	−	−	ADP
ejpam-5564	187	67	u(4)u3	u(4)u3	NOUN
ejpam-5564	187	68	+	+	CCONJ
ejpam-5564	187	69	33u′u′′′u2	33u′u′′′u2	NUM
ejpam-5564	188	1	+	+	SYM
ejpam-5564	188	2	6	6	NUM
ejpam-5564	188	3	(	(	PUNCT
ejpam-5564	188	4	u′′	u′′	ADJ
ejpam-5564	188	5	)	)	PUNCT
ejpam-5564	188	6	2	2	NUM
ejpam-5564	188	7	u2	u2	NOUN
ejpam-5564	188	8	−	−	PROPN
ejpam-5564	188	9	36	36	NUM
ejpam-5564	188	10	(	(	PUNCT
ejpam-5564	188	11	u′	u′	PROPN
ejpam-5564	188	12	)	)	PUNCT
ejpam-5564	188	13	2	2	NUM
ejpam-5564	188	14	u′′u	u′′u	PROPN
ejpam-5564	188	15	+	+	NUM
ejpam-5564	188	16	24	24	NUM
ejpam-5564	188	17	(	(	PUNCT
ejpam-5564	188	18	u′	u′	PROPN
ejpam-5564	188	19	)	)	PUNCT
ejpam-5564	188	20	4	4	NUM
ejpam-5564	188	21	−q0u	−q0u	NUM
ejpam-5564	188	22	′u2	′u2	NOUN
ejpam-5564	188	23	−	−	PROPN
ejpam-5564	188	24	u5f	u5f	PROPN
ejpam-5564	188	25	(	(	PUNCT
ejpam-5564	188	26	z	z	NOUN
ejpam-5564	188	27	)	)	PUNCT
ejpam-5564	188	28	=	=	SYM
ejpam-5564	188	29	0	0	NUM
ejpam-5564	188	30	(	(	PUNCT
ejpam-5564	188	31	13)	13)	NUM
ejpam-5564	188	32	u	u	NOUN
ejpam-5564	188	33	(	(	PUNCT
ejpam-5564	188	34	z0	z0	PROPN
ejpam-5564	188	35	)	)	PUNCT
ejpam-5564	188	36	=	=	PUNCT
ejpam-5564	188	37	u0	u0	ADJ
ejpam-5564	188	38	,	,	PUNCT
ejpam-5564	188	39	u′	u′	PROPN
ejpam-5564	188	40	(	(	PUNCT
ejpam-5564	188	41	z0	z0	PROPN
ejpam-5564	188	42	)	)	PUNCT
ejpam-5564	188	43	=	=	SYM
ejpam-5564	189	1	u′0	u′0	NOUN
ejpam-5564	189	2	,	,	PUNCT
ejpam-5564	189	3	u′′	u′′	PROPN
ejpam-5564	189	4	(	(	PUNCT
ejpam-5564	189	5	z0	z0	PROPN
ejpam-5564	189	6	)	)	PUNCT
ejpam-5564	189	7	=	=	SYM
ejpam-5564	189	8	u′′0	u′′0	PROPN
ejpam-5564	189	9	,	,	PUNCT
ejpam-5564	189	10	u′′′	u′′′	PROPN
ejpam-5564	189	11	(	(	PUNCT
ejpam-5564	189	12	z0	z0	PROPN
ejpam-5564	189	13	)	)	PUNCT
ejpam-5564	189	14	=	=	PUNCT
ejpam-5564	190	1	u′′′0	u′′′0	PROPN
ejpam-5564	190	2	.	.	PUNCT
ejpam-5564	191	1	(	(	PUNCT
ejpam-5564	191	2	14	14	NUM
ejpam-5564	191	3	)	)	PUNCT
ejpam-5564	191	4	since	since	SCONJ
ejpam-5564	191	5	(	(	PUNCT
ejpam-5564	191	6	13	13	NUM
ejpam-5564	191	7	)	)	PUNCT
ejpam-5564	191	8	—	—	PUNCT
ejpam-5564	191	9	(	(	PUNCT
ejpam-5564	191	10	14	14	NUM
ejpam-5564	191	11	)	)	PUNCT
ejpam-5564	191	12	is	be	AUX
ejpam-5564	191	13	the	the	DET
ejpam-5564	191	14	inverse	inverse	ADJ
ejpam-5564	191	15	cauchy	cauchy	PROPN
ejpam-5564	191	16	problem	problem	NOUN
ejpam-5564	191	17	,	,	PUNCT
ejpam-5564	191	18	the	the	DET
ejpam-5564	191	19	solution	solution	NOUN
ejpam-5564	191	20	u	u	NOUN
ejpam-5564	191	21	(	(	PUNCT
ejpam-5564	191	22	z	z	NOUN
ejpam-5564	191	23	)	)	PUNCT
ejpam-5564	191	24	will	will	AUX
ejpam-5564	191	25	take	take	VERB
ejpam-5564	191	26	a	a	DET
ejpam-5564	191	27	regular	regular	ADJ
ejpam-5564	191	28	value	value	NOUN
ejpam-5564	191	29	at	at	ADP
ejpam-5564	191	30	the	the	DET
ejpam-5564	191	31	point	point	NOUN
ejpam-5564	191	32	z∗	z∗	NOUN
ejpam-5564	191	33	,	,	PUNCT
ejpam-5564	191	34	namely	namely	ADV
ejpam-5564	191	35	,	,	PUNCT
ejpam-5564	191	36	it	it	PRON
ejpam-5564	191	37	will	will	AUX
ejpam-5564	191	38	be	be	AUX
ejpam-5564	191	39	equal	equal	ADJ
ejpam-5564	191	40	to	to	ADP
ejpam-5564	191	41	zero	zero	NUM
ejpam-5564	191	42	.	.	PUNCT
ejpam-5564	192	1	let	let	VERB
ejpam-5564	192	2	’s	’s	NOUN
ejpam-5564	192	3	proceed	proceed	VERB
ejpam-5564	192	4	to	to	PART
ejpam-5564	192	5	formulate	formulate	VERB
ejpam-5564	192	6	the	the	DET
ejpam-5564	192	7	criteria	criterion	NOUN
ejpam-5564	192	8	for	for	ADP
ejpam-5564	192	9	the	the	DET
ejpam-5564	192	10	existence	existence	NOUN
ejpam-5564	192	11	of	of	ADP
ejpam-5564	192	12	a	a	DET
ejpam-5564	192	13	moving	move	VERB
ejpam-5564	192	14	singular	singular	ADJ
ejpam-5564	192	15	point	point	NOUN
ejpam-5564	192	16	.	.	PUNCT
ejpam-5564	193	1	to	to	PART
ejpam-5564	193	2	begin	begin	VERB
ejpam-5564	193	3	with	with	ADP
ejpam-5564	193	4	,	,	PUNCT
ejpam-5564	193	5	let	let	VERB
ejpam-5564	193	6	’s	’s	PRON
ejpam-5564	193	7	formulate	formulate	VERB
ejpam-5564	193	8	them	they	PRON
ejpam-5564	193	9	for	for	ADP
ejpam-5564	193	10	the	the	DET
ejpam-5564	193	11	real	real	ADJ
ejpam-5564	193	12	domain	domain	NOUN
ejpam-5564	193	13	.	.	PUNCT
ejpam-5564	194	1	the	the	DET
ejpam-5564	194	2	following	follow	VERB
ejpam-5564	194	3	lemma	lemma	PROPN
ejpam-5564	194	4	helps	help	VERB
ejpam-5564	194	5	to	to	PART
ejpam-5564	194	6	take	take	VERB
ejpam-5564	194	7	into	into	ADP
ejpam-5564	194	8	account	account	NOUN
ejpam-5564	194	9	the	the	DET
ejpam-5564	194	10	specifics	specific	NOUN
ejpam-5564	194	11	of	of	ADP
ejpam-5564	194	12	the	the	DET
ejpam-5564	194	13	regularization	regularization	NOUN
ejpam-5564	194	14	method	method	NOUN
ejpam-5564	194	15	when	when	SCONJ
ejpam-5564	194	16	constructing	construct	VERB
ejpam-5564	194	17	an	an	DET
ejpam-5564	194	18	algorithm	algorithm	NOUN
ejpam-5564	194	19	for	for	ADP
ejpam-5564	194	20	finding	find	VERB
ejpam-5564	194	21	a	a	DET
ejpam-5564	194	22	moving	move	VERB
ejpam-5564	194	23	singular	singular	ADJ
ejpam-5564	194	24	point	point	NOUN
ejpam-5564	194	25	.	.	PUNCT
ejpam-5564	195	1	lemma	lemma	PROPN
ejpam-5564	195	2	1	1	X
ejpam-5564	195	3	.	.	PUNCT
ejpam-5564	196	1	let	let	VERB
ejpam-5564	196	2	the	the	DET
ejpam-5564	196	3	function	function	NOUN
ejpam-5564	196	4	be	be	AUX
ejpam-5564	196	5	u	u	NOUN
ejpam-5564	196	6	(	(	PUNCT
ejpam-5564	196	7	z	z	NOUN
ejpam-5564	196	8	)	)	PUNCT
ejpam-5564	196	9	does	do	AUX
ejpam-5564	196	10	not	not	PART
ejpam-5564	196	11	change	change	VERB
ejpam-5564	196	12	the	the	DET
ejpam-5564	196	13	sign	sign	NOUN
ejpam-5564	196	14	on	on	ADP
ejpam-5564	196	15	some	some	DET
ejpam-5564	196	16	segment	segment	NOUN
ejpam-5564	196	17	[	[	X
ejpam-5564	196	18	a	a	X
ejpam-5564	196	19	,	,	PUNCT
ejpam-5564	196	20	b	b	NOUN
ejpam-5564	196	21	]	]	X
ejpam-5564	196	22	.	.	PUNCT
ejpam-5564	197	1	then	then	ADV
ejpam-5564	197	2	in	in	ADP
ejpam-5564	197	3	order	order	NOUN
ejpam-5564	197	4	for	for	SCONJ
ejpam-5564	197	5	w	w	PROPN
ejpam-5564	197	6	(	(	PUNCT
ejpam-5564	197	7	z	z	NOUN
ejpam-5564	197	8	)	)	PUNCT
ejpam-5564	197	9	to	to	PART
ejpam-5564	197	10	reach	reach	VERB
ejpam-5564	197	11	a	a	DET
ejpam-5564	197	12	local	local	ADJ
ejpam-5564	197	13	maximum	maximum	NOUN
ejpam-5564	197	14	at	at	ADP
ejpam-5564	197	15	point	point	NOUN
ejpam-5564	197	16	c	c	NOUN
ejpam-5564	197	17	∈	∈	PROPN
ejpam-5564	197	18	(	(	PUNCT
ejpam-5564	197	19	a	a	DET
ejpam-5564	197	20	,	,	PUNCT
ejpam-5564	197	21	b	b	NOUN
ejpam-5564	197	22	)	)	PUNCT
ejpam-5564	197	23	,	,	PUNCT
ejpam-5564	197	24	it	it	PRON
ejpam-5564	197	25	is	be	AUX
ejpam-5564	197	26	necessary	necessary	ADJ
ejpam-5564	197	27	and	and	CCONJ
ejpam-5564	197	28	sufficient	sufficient	ADJ
ejpam-5564	197	29	that	that	SCONJ
ejpam-5564	197	30	at	at	ADP
ejpam-5564	197	31	this	this	DET
ejpam-5564	197	32	point	point	NOUN
ejpam-5564	197	33	u	u	NOUN
ejpam-5564	197	34	(	(	PUNCT
ejpam-5564	197	35	z	z	NOUN
ejpam-5564	197	36	)	)	PUNCT
ejpam-5564	197	37	had	have	VERB
ejpam-5564	197	38	a	a	DET
ejpam-5564	197	39	local	local	ADJ
ejpam-5564	197	40	minimum	minimum	NOUN
ejpam-5564	197	41	.	.	PUNCT
ejpam-5564	198	1	m.	m.	NOUN
ejpam-5564	198	2	gasanov	gasanov	PROPN
ejpam-5564	198	3	/	/	SYM
ejpam-5564	198	4	eur	eur	PROPN
ejpam-5564	198	5	.	.	PUNCT
ejpam-5564	199	1	j.	j.	PROPN
ejpam-5564	199	2	pure	pure	PROPN
ejpam-5564	199	3	appl	appl	PROPN
ejpam-5564	199	4	.	.	PROPN
ejpam-5564	199	5	math	math	PROPN
ejpam-5564	199	6	,	,	PUNCT
ejpam-5564	199	7	18	18	NUM
ejpam-5564	199	8	(	(	PUNCT
ejpam-5564	199	9	1	1	NUM
ejpam-5564	199	10	)	)	PUNCT
ejpam-5564	199	11	(	(	PUNCT
ejpam-5564	199	12	2025	2025	NUM
ejpam-5564	199	13	)	)	PUNCT
ejpam-5564	199	14	,	,	PUNCT
ejpam-5564	199	15	5564	5564	NUM
ejpam-5564	199	16	11	11	NUM
ejpam-5564	199	17	of	of	ADP
ejpam-5564	199	18	19	19	NUM
ejpam-5564	199	19	proof	proof	NOUN
ejpam-5564	199	20	.	.	PUNCT
ejpam-5564	200	1	the	the	DET
ejpam-5564	200	2	proof	proof	NOUN
ejpam-5564	200	3	obviously	obviously	ADV
ejpam-5564	200	4	follows	follow	VERB
ejpam-5564	200	5	from	from	ADP
ejpam-5564	200	6	classical	classical	ADJ
ejpam-5564	200	7	analysis	analysis	NOUN
ejpam-5564	200	8	,	,	PUNCT
ejpam-5564	200	9	a	a	DET
ejpam-5564	200	10	necessary	necessary	ADJ
ejpam-5564	200	11	and	and	CCONJ
ejpam-5564	200	12	sufficient	sufficient	ADJ
ejpam-5564	200	13	condition	condition	NOUN
ejpam-5564	200	14	for	for	ADP
ejpam-5564	200	15	a	a	DET
ejpam-5564	200	16	local	local	ADJ
ejpam-5564	200	17	extremum	extremum	NOUN
ejpam-5564	200	18	.	.	PUNCT
ejpam-5564	201	1	theorem	theorem	NOUN
ejpam-5564	201	2	4	4	NUM
ejpam-5564	201	3	.	.	PUNCT
ejpam-5564	202	1	if	if	SCONJ
ejpam-5564	202	2	z∗	z∗	PROPN
ejpam-5564	202	3	is	be	AUX
ejpam-5564	202	4	a	a	DET
ejpam-5564	202	5	movable	movable	ADJ
ejpam-5564	202	6	singular	singular	ADJ
ejpam-5564	202	7	point	point	NOUN
ejpam-5564	202	8	of	of	ADP
ejpam-5564	202	9	the	the	DET
ejpam-5564	202	10	cauchy	cauchy	ADJ
ejpam-5564	202	11	problem	problem	NOUN
ejpam-5564	202	12	(	(	PUNCT
ejpam-5564	202	13	2	2	NUM
ejpam-5564	202	14	)	)	PUNCT
ejpam-5564	202	15	—	—	PUNCT
ejpam-5564	202	16	(	(	PUNCT
ejpam-5564	202	17	3	3	NUM
ejpam-5564	202	18	)	)	PUNCT
ejpam-5564	202	19	,	,	PUNCT
ejpam-5564	202	20	and	and	CCONJ
ejpam-5564	202	21	the	the	DET
ejpam-5564	202	22	function	function	NOUN
ejpam-5564	202	23	w	w	PROPN
ejpam-5564	202	24	(	(	PUNCT
ejpam-5564	202	25	z	z	NOUN
ejpam-5564	202	26	)	)	PUNCT
ejpam-5564	202	27	defined	define	VERB
ejpam-5564	202	28	on	on	ADP
ejpam-5564	202	29	the	the	DET
ejpam-5564	202	30	half	half	ADJ
ejpam-5564	202	31	-	-	PUNCT
ejpam-5564	202	32	interval	interval	NOUN
ejpam-5564	202	33	[	[	X
ejpam-5564	202	34	z0	z0	NOUN
ejpam-5564	202	35	;	;	PUNCT
ejpam-5564	202	36	z	z	NOUN
ejpam-5564	202	37	∗	∗	NOUN
ejpam-5564	202	38	)	)	PUNCT
ejpam-5564	202	39	.	.	PUNCT
ejpam-5564	203	1	then	then	ADV
ejpam-5564	203	2	there	there	PRON
ejpam-5564	203	3	is	be	VERB
ejpam-5564	203	4	a	a	DET
ejpam-5564	203	5	number	number	NOUN
ejpam-5564	203	6	γ	γ	NOUN
ejpam-5564	203	7	,	,	PUNCT
ejpam-5564	203	8	such	such	ADJ
ejpam-5564	203	9	that	that	SCONJ
ejpam-5564	203	10	the	the	DET
ejpam-5564	203	11	function	function	NOUN
ejpam-5564	203	12	w	w	PROPN
ejpam-5564	203	13	(	(	PUNCT
ejpam-5564	203	14	z	z	NOUN
ejpam-5564	203	15	)	)	PUNCT
ejpam-5564	203	16	on	on	ADP
ejpam-5564	203	17	the	the	DET
ejpam-5564	203	18	half	half	ADJ
ejpam-5564	203	19	-	-	PUNCT
ejpam-5564	203	20	interval	interval	NOUN
ejpam-5564	203	21	[	[	X
ejpam-5564	203	22	γ	γ	X
ejpam-5564	203	23	;	;	PUNCT
ejpam-5564	203	24	z∗	z∗	NOUN
ejpam-5564	203	25	)	)	PUNCT
ejpam-5564	203	26	has	have	VERB
ejpam-5564	203	27	the	the	DET
ejpam-5564	203	28	following	follow	VERB
ejpam-5564	203	29	property	property	NOUN
ejpam-5564	203	30	:	:	PUNCT
ejpam-5564	203	31	[	[	PUNCT
ejpam-5564	203	32	w	w	X
ejpam-5564	203	33	(	(	PUNCT
ejpam-5564	203	34	z	z	NOUN
ejpam-5564	203	35	)	)	PUNCT
ejpam-5564	203	36	,	,	PUNCT
ejpam-5564	203	37	w′	w′	PROPN
ejpam-5564	203	38	(	(	PUNCT
ejpam-5564	203	39	z	z	NOUN
ejpam-5564	203	40	)	)	PUNCT
ejpam-5564	203	41	,	,	PUNCT
ejpam-5564	203	42	w′′	w′′	NOUN
ejpam-5564	203	43	(	(	PUNCT
ejpam-5564	203	44	z	z	NOUN
ejpam-5564	203	45	)	)	PUNCT
ejpam-5564	203	46	,	,	PUNCT
ejpam-5564	203	47	w′′′	w′′′	NOUN
ejpam-5564	203	48	(	(	PUNCT
ejpam-5564	203	49	z	z	NOUN
ejpam-5564	203	50	)	)	PUNCT
ejpam-5564	203	51	>	>	X
ejpam-5564	204	1	0	0	NUM
ejpam-5564	204	2	,	,	PUNCT
ejpam-5564	204	3	w	w	X
ejpam-5564	204	4	(	(	PUNCT
ejpam-5564	204	5	z	z	NOUN
ejpam-5564	204	6	)	)	PUNCT
ejpam-5564	204	7	,	,	PUNCT
ejpam-5564	204	8	w′	w′	PROPN
ejpam-5564	204	9	(	(	PUNCT
ejpam-5564	204	10	z	z	NOUN
ejpam-5564	204	11	)	)	PUNCT
ejpam-5564	204	12	,	,	PUNCT
ejpam-5564	204	13	w′′	w′′	NOUN
ejpam-5564	204	14	(	(	PUNCT
ejpam-5564	204	15	z	z	NOUN
ejpam-5564	204	16	)	)	PUNCT
ejpam-5564	204	17	,	,	PUNCT
ejpam-5564	204	18	w′′′	w′′′	NOUN
ejpam-5564	204	19	(	(	PUNCT
ejpam-5564	204	20	z	z	NOUN
ejpam-5564	204	21	)	)	PUNCT
ejpam-5564	204	22	<	<	X
ejpam-5564	204	23	0	0	X
ejpam-5564	204	24	.	.	PUNCT
ejpam-5564	204	25	proof	proof	NOUN
ejpam-5564	204	26	.	.	PUNCT
ejpam-5564	205	1	consider	consider	VERB
ejpam-5564	205	2	formula	formula	NOUN
ejpam-5564	205	3	(	(	PUNCT
ejpam-5564	205	4	2.1	2.1	NUM
ejpam-5564	205	5	)	)	PUNCT
ejpam-5564	205	6	obtained	obtain	VERB
ejpam-5564	205	7	in	in	ADP
ejpam-5564	205	8	theorem	theorem	NOUN
ejpam-5564	205	9	1	1	NUM
ejpam-5564	205	10	.	.	PUNCT
ejpam-5564	205	11	according	accord	VERB
ejpam-5564	205	12	to	to	ADP
ejpam-5564	205	13	the	the	DET
ejpam-5564	205	14	existence	existence	NOUN
ejpam-5564	205	15	theorem	theorem	VERB
ejpam-5564	205	16	∃ξ	∃ξ	NOUN
ejpam-5564	205	17	:	:	PUNCT
ejpam-5564	206	1	ξ	ξ	X
ejpam-5564	206	2	∈	∈	PROPN
ejpam-5564	206	3	[	[	X
ejpam-5564	206	4	z0	z0	NOUN
ejpam-5564	206	5	;	;	PUNCT
ejpam-5564	206	6	z	z	NOUN
ejpam-5564	206	7	∗	∗	NOUN
ejpam-5564	206	8	)	)	PUNCT
ejpam-5564	206	9	such	such	ADJ
ejpam-5564	206	10	that	that	SCONJ
ejpam-5564	206	11	the	the	DET
ejpam-5564	206	12	analytic	analytic	ADJ
ejpam-5564	206	13	part	part	NOUN
ejpam-5564	206	14	of	of	ADP
ejpam-5564	206	15	(	(	PUNCT
ejpam-5564	206	16	2.1	2.1	NUM
ejpam-5564	206	17	)	)	PUNCT
ejpam-5564	206	18	converges	converge	NOUN
ejpam-5564	206	19	in	in	ADP
ejpam-5564	206	20	the	the	DET
ejpam-5564	206	21	area	area	NOUN
ejpam-5564	206	22	[	[	X
ejpam-5564	206	23	ξ	ξ	X
ejpam-5564	206	24	;	;	PUNCT
ejpam-5564	206	25	z∗	z∗	PROPN
ejpam-5564	206	26	)	)	PUNCT
ejpam-5564	206	27	,	,	PUNCT
ejpam-5564	206	28	then	then	ADV
ejpam-5564	206	29	we	we	PRON
ejpam-5564	206	30	get	get	VERB
ejpam-5564	206	31	:	:	PUNCT
ejpam-5564	206	32	w	w	X
ejpam-5564	206	33	(	(	PUNCT
ejpam-5564	206	34	z	z	NOUN
ejpam-5564	206	35	)	)	PUNCT
ejpam-5564	206	36	=	=	SYM
ejpam-5564	207	1	√	√	NUM
ejpam-5564	207	2	−	−	NUM
ejpam-5564	207	3	24	24	NUM
ejpam-5564	207	4	q0	q0	PROPN
ejpam-5564	207	5	(	(	PUNCT
ejpam-5564	207	6	z∗	z∗	NOUN
ejpam-5564	207	7	−	−	PROPN
ejpam-5564	207	8	z)−1	z)−1	PROPN
ejpam-5564	207	9	+	+	NUM
ejpam-5564	207	10	d0	d0	NOUN
ejpam-5564	207	11	192	192	NUM
ejpam-5564	207	12	(	(	PUNCT
ejpam-5564	207	13	z∗	z∗	NOUN
ejpam-5564	207	14	−	−	NOUN
ejpam-5564	207	15	z)4	z)4	PROPN
ejpam-5564	207	16	+	+	CCONJ
ejpam-5564	207	17	d1	d1	PROPN
ejpam-5564	207	18	336	336	NUM
ejpam-5564	207	19	(	(	PUNCT
ejpam-5564	207	20	z∗	z∗	NOUN
ejpam-5564	207	21	−	−	PROPN
ejpam-5564	207	22	z)5	z)5	PROPN
ejpam-5564	207	23	+	+	PUNCT
ejpam-5564	207	24	.	.	PUNCT
ejpam-5564	207	25	.	.	PUNCT
ejpam-5564	207	26	.	.	PUNCT
ejpam-5564	208	1	since	since	SCONJ
ejpam-5564	208	2	1√	1√	PROPN
ejpam-5564	208	3	q0	q0	PROPN
ejpam-5564	208	4	(	(	PUNCT
ejpam-5564	208	5	z∗	z∗	NOUN
ejpam-5564	208	6	−	−	PROPN
ejpam-5564	208	7	z)−1	z)−1	NUM
ejpam-5564	208	8	z→z∗−0→	z→z∗−0→	NOUN
ejpam-5564	208	9	+	+	NOUN
ejpam-5564	208	10	∞	∞	PROPN
ejpam-5564	208	11	,	,	PUNCT
ejpam-5564	208	12	and	and	CCONJ
ejpam-5564	208	13	(	(	PUNCT
ejpam-5564	208	14	d0	d0	NOUN
ejpam-5564	208	15	192	192	NUM
ejpam-5564	208	16	(	(	PUNCT
ejpam-5564	208	17	z∗	z∗	NOUN
ejpam-5564	208	18	−	−	NOUN
ejpam-5564	208	19	z)4	z)4	PROPN
ejpam-5564	208	20	+	+	CCONJ
ejpam-5564	208	21	d1	d1	PROPN
ejpam-5564	208	22	336	336	NUM
ejpam-5564	208	23	(	(	PUNCT
ejpam-5564	208	24	z∗	z∗	NOUN
ejpam-5564	208	25	−	−	PROPN
ejpam-5564	208	26	z)5	z)5	PROPN
ejpam-5564	208	27	+	+	PUNCT
ejpam-5564	208	28	.	.	PUNCT
ejpam-5564	208	29	.	.	PUNCT
ejpam-5564	208	30	.	.	PUNCT
ejpam-5564	208	31	)	)	PUNCT
ejpam-5564	209	1	z→z∗−0→	z→z∗−0→	NOUN
ejpam-5564	209	2	0	0	NUM
ejpam-5564	209	3	,	,	PUNCT
ejpam-5564	209	4	there	there	PRON
ejpam-5564	209	5	is	be	VERB
ejpam-5564	209	6	such	such	DET
ejpam-5564	209	7	a	a	DET
ejpam-5564	209	8	point	point	NOUN
ejpam-5564	209	9	ξ1	ξ1	NOUN
ejpam-5564	209	10	≥	≥	NOUN
ejpam-5564	209	11	ξ	ξ	NOUN
ejpam-5564	209	12	:	:	PUNCT
ejpam-5564	209	13	∀z	∀z	X
ejpam-5564	209	14	∈	∈	PROPN
ejpam-5564	210	1	[	[	X
ejpam-5564	210	2	ξ1	ξ1	NOUN
ejpam-5564	210	3	;	;	PUNCT
ejpam-5564	210	4	z	z	NOUN
ejpam-5564	210	5	∗	∗	NOUN
ejpam-5564	210	6	)	)	PUNCT
ejpam-5564	210	7	the	the	DET
ejpam-5564	210	8	condition	condition	NOUN
ejpam-5564	210	9	w	w	ADP
ejpam-5564	210	10	>	>	X
ejpam-5564	210	11	0	0	NUM
ejpam-5564	210	12	is	be	AUX
ejpam-5564	210	13	fulfilled	fulfil	VERB
ejpam-5564	210	14	.	.	PUNCT
ejpam-5564	211	1	similarly	similarly	ADV
ejpam-5564	211	2	,	,	PUNCT
ejpam-5564	211	3	in	in	ADP
ejpam-5564	211	4	the	the	DET
ejpam-5564	211	5	case	case	NOUN
ejpam-5564	211	6	of	of	ADP
ejpam-5564	211	7	the	the	DET
ejpam-5564	211	8	derivative	derivative	NOUN
ejpam-5564	211	9	:	:	PUNCT
ejpam-5564	211	10	w′	w′	PROPN
ejpam-5564	211	11	(	(	PUNCT
ejpam-5564	211	12	z	z	X
ejpam-5564	211	13	)	)	PUNCT
ejpam-5564	211	14	=	=	SYM
ejpam-5564	212	1	√	√	NUM
ejpam-5564	212	2	−	−	NUM
ejpam-5564	212	3	24	24	NUM
ejpam-5564	212	4	q0	q0	PROPN
ejpam-5564	212	5	(	(	PUNCT
ejpam-5564	212	6	z∗	z∗	NOUN
ejpam-5564	212	7	−	−	NOUN
ejpam-5564	212	8	z)−2	z)−2	NOUN
ejpam-5564	212	9	+	+	CCONJ
ejpam-5564	212	10	d0	d0	NOUN
ejpam-5564	212	11	48	48	NUM
ejpam-5564	212	12	(	(	PUNCT
ejpam-5564	212	13	z∗	z∗	NOUN
ejpam-5564	212	14	−	−	PROPN
ejpam-5564	212	15	z)3	z)3	NOUN
ejpam-5564	212	16	+	+	CCONJ
ejpam-5564	212	17	5d1	5d1	NUM
ejpam-5564	212	18	336	336	NUM
ejpam-5564	212	19	(	(	PUNCT
ejpam-5564	212	20	z∗	z∗	NOUN
ejpam-5564	212	21	−	−	NOUN
ejpam-5564	212	22	z)4	z)4	PROPN
ejpam-5564	212	23	+	+	PUNCT
ejpam-5564	212	24	.	.	PUNCT
ejpam-5564	212	25	.	.	PUNCT
ejpam-5564	212	26	.	.	PUNCT
ejpam-5564	213	1	since	since	SCONJ
ejpam-5564	213	2	√	√	PROPN
ejpam-5564	213	3	−	−	NUM
ejpam-5564	213	4	24	24	NUM
ejpam-5564	213	5	q0	q0	PROPN
ejpam-5564	213	6	(	(	PUNCT
ejpam-5564	213	7	z∗	z∗	NOUN
ejpam-5564	213	8	−	−	PROPN
ejpam-5564	213	9	z)−2	z)−2	PROPN
ejpam-5564	213	10	z→z∗−0→	z→z∗−0→	NOUN
ejpam-5564	213	11	+	+	NOUN
ejpam-5564	213	12	∞	∞	PROPN
ejpam-5564	213	13	,	,	PUNCT
ejpam-5564	213	14	and	and	CCONJ
ejpam-5564	213	15	(	(	PUNCT
ejpam-5564	213	16	d0	d0	NOUN
ejpam-5564	213	17	48	48	NUM
ejpam-5564	213	18	(	(	PUNCT
ejpam-5564	213	19	z∗	z∗	NOUN
ejpam-5564	213	20	−	−	PROPN
ejpam-5564	213	21	z)3	z)3	NOUN
ejpam-5564	213	22	+	+	CCONJ
ejpam-5564	213	23	5d1	5d1	NUM
ejpam-5564	213	24	336	336	NUM
ejpam-5564	213	25	(	(	PUNCT
ejpam-5564	213	26	z∗	z∗	NOUN
ejpam-5564	213	27	−	−	NOUN
ejpam-5564	213	28	z)4	z)4	PROPN
ejpam-5564	213	29	+	+	PUNCT
ejpam-5564	213	30	.	.	PUNCT
ejpam-5564	213	31	.	.	PUNCT
ejpam-5564	213	32	.	.	PUNCT
ejpam-5564	213	33	)	)	PUNCT
ejpam-5564	214	1	→	→	SYM
ejpam-5564	214	2	0	0	NUM
ejpam-5564	214	3	,	,	PUNCT
ejpam-5564	214	4	there	there	PRON
ejpam-5564	214	5	is	be	VERB
ejpam-5564	214	6	such	such	DET
ejpam-5564	214	7	a	a	DET
ejpam-5564	214	8	point	point	NOUN
ejpam-5564	214	9	ξ1	ξ1	NOUN
ejpam-5564	214	10	≥	≥	NOUN
ejpam-5564	214	11	ξ	ξ	NOUN
ejpam-5564	214	12	:	:	PUNCT
ejpam-5564	214	13	∀z	∀z	X
ejpam-5564	214	14	∈	∈	PROPN
ejpam-5564	215	1	[	[	X
ejpam-5564	215	2	ξ1	ξ1	NOUN
ejpam-5564	215	3	;	;	PUNCT
ejpam-5564	215	4	z	z	NOUN
ejpam-5564	215	5	∗	∗	NOUN
ejpam-5564	215	6	)	)	PUNCT
ejpam-5564	215	7	the	the	DET
ejpam-5564	215	8	condition	condition	NOUN
ejpam-5564	215	9	w′	w′	VERB
ejpam-5564	215	10	>	>	X
ejpam-5564	215	11	0	0	PUNCT
ejpam-5564	215	12	is	be	AUX
ejpam-5564	215	13	fulfilled	fulfil	VERB
ejpam-5564	215	14	.	.	PUNCT
ejpam-5564	216	1	similarly	similarly	ADV
ejpam-5564	216	2	for	for	ADP
ejpam-5564	216	3	w′′	w′′	NOUN
ejpam-5564	216	4	,	,	PUNCT
ejpam-5564	216	5	w′′′.	w′′′.	PROPN
ejpam-5564	216	6	theorem	theorem	VERB
ejpam-5564	216	7	5	5	NUM
ejpam-5564	216	8	.	.	PUNCT
ejpam-5564	217	1	let	let	VERB
ejpam-5564	217	2	z	z	NOUN
ejpam-5564	217	3	(	(	PUNCT
ejpam-5564	217	4	u	u	NOUN
ejpam-5564	217	5	)	)	PUNCT
ejpam-5564	217	6	be	be	VERB
ejpam-5564	217	7	the	the	DET
ejpam-5564	217	8	inverse	inverse	NOUN
ejpam-5564	217	9	function	function	NOUN
ejpam-5564	217	10	to	to	ADP
ejpam-5564	217	11	the	the	DET
ejpam-5564	217	12	solution	solution	NOUN
ejpam-5564	217	13	of	of	ADP
ejpam-5564	217	14	the	the	DET
ejpam-5564	217	15	inverse	inverse	NOUN
ejpam-5564	217	16	cauchy	cauchy	NOUN
ejpam-5564	217	17	problem	problem	NOUN
ejpam-5564	217	18	(	(	PUNCT
ejpam-5564	217	19	13	13	NUM
ejpam-5564	217	20	)	)	PUNCT
ejpam-5564	217	21	—	—	PUNCT
ejpam-5564	217	22	(	(	PUNCT
ejpam-5564	217	23	14	14	NUM
ejpam-5564	217	24	)	)	PUNCT
ejpam-5564	217	25	,	,	PUNCT
ejpam-5564	217	26	and	and	CCONJ
ejpam-5564	217	27	the	the	DET
ejpam-5564	217	28	following	follow	VERB
ejpam-5564	217	29	conditions	condition	NOUN
ejpam-5564	217	30	hold	hold	VERB
ejpam-5564	217	31	:	:	PUNCT
ejpam-5564	217	32	z	z	NOUN
ejpam-5564	217	33	(	(	PUNCT
ejpam-5564	217	34	0	0	NUM
ejpam-5564	217	35	)	)	PUNCT
ejpam-5564	218	1	=	=	SYM
ejpam-5564	218	2	z∗	z∗	NOUN
ejpam-5564	218	3	,	,	PUNCT
ejpam-5564	218	4	z′	z′	NUM
ejpam-5564	218	5	(	(	PUNCT
ejpam-5564	218	6	0	0	NUM
ejpam-5564	218	7	)	)	PUNCT
ejpam-5564	218	8	=	=	SYM
ejpam-5564	219	1	−	−	PROPN
ejpam-5564	219	2	√	√	PROPN
ejpam-5564	219	3	−q0	−q0	NOUN
ejpam-5564	219	4	24	24	NUM
ejpam-5564	219	5	,	,	PUNCT
ejpam-5564	219	6	z	z	NOUN
ejpam-5564	219	7	′′	′′	PROPN
ejpam-5564	219	8	(	(	PUNCT
ejpam-5564	219	9	0	0	NUM
ejpam-5564	219	10	)	)	PUNCT
ejpam-5564	219	11	=	=	SYM
ejpam-5564	219	12	z′′′	z′′′	X
ejpam-5564	219	13	(	(	PUNCT
ejpam-5564	219	14	0	0	NUM
ejpam-5564	219	15	)	)	PUNCT
ejpam-5564	219	16	=	=	SYM
ejpam-5564	219	17	0	0	NUM
ejpam-5564	219	18	,	,	PUNCT
ejpam-5564	219	19	then	then	ADV
ejpam-5564	219	20	z∗	z∗	PROPN
ejpam-5564	219	21	is	be	AUX
ejpam-5564	219	22	a	a	DET
ejpam-5564	219	23	moving	move	VERB
ejpam-5564	219	24	singular	singular	ADJ
ejpam-5564	219	25	point	point	NOUN
ejpam-5564	219	26	of	of	ADP
ejpam-5564	219	27	the	the	DET
ejpam-5564	219	28	cauchy	cauchy	ADJ
ejpam-5564	219	29	problem	problem	NOUN
ejpam-5564	219	30	(	(	PUNCT
ejpam-5564	219	31	2	2	NUM
ejpam-5564	219	32	)	)	PUNCT
ejpam-5564	219	33	—	—	PUNCT
ejpam-5564	219	34	(	(	PUNCT
ejpam-5564	219	35	3	3	NUM
ejpam-5564	219	36	)	)	PUNCT
ejpam-5564	219	37	.	.	PUNCT
ejpam-5564	220	1	this	this	DET
ejpam-5564	220	2	condition	condition	NOUN
ejpam-5564	220	3	is	be	AUX
ejpam-5564	220	4	necessary	necessary	ADJ
ejpam-5564	220	5	and	and	CCONJ
ejpam-5564	220	6	sufficient	sufficient	ADJ
ejpam-5564	220	7	.	.	PUNCT
ejpam-5564	221	1	m.	m.	NOUN
ejpam-5564	221	2	gasanov	gasanov	PROPN
ejpam-5564	221	3	/	/	SYM
ejpam-5564	221	4	eur	eur	PROPN
ejpam-5564	221	5	.	.	PUNCT
ejpam-5564	222	1	j.	j.	PROPN
ejpam-5564	222	2	pure	pure	PROPN
ejpam-5564	222	3	appl	appl	PROPN
ejpam-5564	222	4	.	.	PROPN
ejpam-5564	222	5	math	math	PROPN
ejpam-5564	222	6	,	,	PUNCT
ejpam-5564	222	7	18	18	NUM
ejpam-5564	222	8	(	(	PUNCT
ejpam-5564	222	9	1	1	NUM
ejpam-5564	222	10	)	)	PUNCT
ejpam-5564	222	11	(	(	PUNCT
ejpam-5564	222	12	2025	2025	NUM
ejpam-5564	222	13	)	)	PUNCT
ejpam-5564	222	14	,	,	PUNCT
ejpam-5564	222	15	5564	5564	NUM
ejpam-5564	222	16	12	12	NUM
ejpam-5564	222	17	of	of	ADP
ejpam-5564	222	18	19	19	NUM
ejpam-5564	222	19	proof	proof	NOUN
ejpam-5564	222	20	.	.	PUNCT
ejpam-5564	223	1	necessity	necessity	NOUN
ejpam-5564	223	2	.	.	PUNCT
ejpam-5564	224	1	let	let	VERB
ejpam-5564	224	2	z∗	z∗	PROPN
ejpam-5564	224	3	be	be	AUX
ejpam-5564	224	4	a	a	DET
ejpam-5564	224	5	moving	move	VERB
ejpam-5564	224	6	singular	singular	ADJ
ejpam-5564	224	7	point	point	NOUN
ejpam-5564	224	8	of	of	ADP
ejpam-5564	224	9	the	the	DET
ejpam-5564	224	10	cauchy	cauchy	ADJ
ejpam-5564	224	11	problem	problem	NOUN
ejpam-5564	224	12	(	(	PUNCT
ejpam-5564	224	13	2	2	NUM
ejpam-5564	224	14	)	)	PUNCT
ejpam-5564	224	15	—	—	PUNCT
ejpam-5564	224	16	(	(	PUNCT
ejpam-5564	224	17	3	3	NUM
ejpam-5564	224	18	)	)	PUNCT
ejpam-5564	224	19	,	,	PUNCT
ejpam-5564	224	20	then	then	ADV
ejpam-5564	224	21	the	the	DET
ejpam-5564	224	22	previously	previously	ADV
ejpam-5564	224	23	proven	prove	VERB
ejpam-5564	224	24	theorems	theorem	NOUN
ejpam-5564	224	25	1	1	NUM
ejpam-5564	224	26	,	,	PUNCT
ejpam-5564	224	27	2	2	NUM
ejpam-5564	224	28	,	,	PUNCT
ejpam-5564	224	29	3	3	NUM
ejpam-5564	224	30	hold	hold	NOUN
ejpam-5564	224	31	.	.	PUNCT
ejpam-5564	225	1	with	with	ADP
ejpam-5564	225	2	the	the	DET
ejpam-5564	225	3	substitution	substitution	NOUN
ejpam-5564	225	4	w	w	NOUN
ejpam-5564	225	5	(	(	PUNCT
ejpam-5564	225	6	z	z	NOUN
ejpam-5564	225	7	)	)	PUNCT
ejpam-5564	225	8	=	=	SYM
ejpam-5564	225	9	1	1	NUM
ejpam-5564	225	10	u(z	u(z	NOUN
ejpam-5564	225	11	)	)	PUNCT
ejpam-5564	225	12	,	,	PUNCT
ejpam-5564	225	13	it	it	PRON
ejpam-5564	225	14	is	be	AUX
ejpam-5564	225	15	evident	evident	ADJ
ejpam-5564	225	16	that	that	SCONJ
ejpam-5564	225	17	u	u	PROPN
ejpam-5564	225	18	(	(	PUNCT
ejpam-5564	225	19	z∗	z∗	NOUN
ejpam-5564	225	20	)	)	PUNCT
ejpam-5564	225	21	=	=	SYM
ejpam-5564	226	1	0	0	X
ejpam-5564	226	2	.	.	PUNCT
ejpam-5564	227	1	using	use	VERB
ejpam-5564	227	2	this	this	DET
ejpam-5564	227	3	substitution	substitution	NOUN
ejpam-5564	227	4	to	to	PART
ejpam-5564	227	5	transition	transition	VERB
ejpam-5564	227	6	to	to	ADP
ejpam-5564	227	7	the	the	DET
ejpam-5564	227	8	inverse	inverse	NOUN
ejpam-5564	227	9	equation	equation	NOUN
ejpam-5564	227	10	,	,	PUNCT
ejpam-5564	227	11	we	we	PRON
ejpam-5564	227	12	get	get	VERB
ejpam-5564	227	13	:	:	PUNCT
ejpam-5564	227	14	u	u	NOUN
ejpam-5564	227	15	(	(	PUNCT
ejpam-5564	227	16	z	z	NOUN
ejpam-5564	227	17	)	)	PUNCT
ejpam-5564	227	18	=	=	SYM
ejpam-5564	228	1	1	1	NUM
ejpam-5564	228	2	(	(	PUNCT
ejpam-5564	228	3	z∗	z∗	NOUN
ejpam-5564	228	4	−	−	PROPN
ejpam-5564	228	5	z)−1∑	z)−1∑	PROPN
ejpam-5564	228	6	n≥0an	n≥0an	PROPN
ejpam-5564	228	7	(	(	PUNCT
ejpam-5564	228	8	z∗	z∗	PROPN
ejpam-5564	228	9	−	−	NOUN
ejpam-5564	228	10	z)n	z)n	PUNCT
ejpam-5564	228	11	=	=	PUNCT
ejpam-5564	229	1	∑	∑	PUNCT
ejpam-5564	229	2	n≥0	n≥0	PROPN
ejpam-5564	229	3	ãn	ãn	PROPN
ejpam-5564	229	4	(	(	PUNCT
ejpam-5564	229	5	z	z	NOUN
ejpam-5564	229	6	∗	∗	NOUN
ejpam-5564	229	7	−	−	PROPN
ejpam-5564	229	8	z)n+1	z)n+1	PROPN
ejpam-5564	229	9	,	,	PUNCT
ejpam-5564	229	10	(	(	PUNCT
ejpam-5564	229	11	15	15	NUM
ejpam-5564	229	12	)	)	PUNCT
ejpam-5564	229	13	where	where	SCONJ
ejpam-5564	229	14	ã0	ã0	PROPN
ejpam-5564	229	15	=	=	PROPN
ejpam-5564	229	16	1	1	NUM
ejpam-5564	229	17	a0	a0	NOUN
ejpam-5564	229	18	,	,	PUNCT
ejpam-5564	229	19	ã1	ã1	NOUN
ejpam-5564	229	20	=	=	PUNCT
ejpam-5564	229	21	ã2	ã2	PROPN
ejpam-5564	229	22	=	=	PUNCT
ejpam-5564	229	23	ã3	ã3	PROPN
ejpam-5564	229	24	=	=	PUNCT
ejpam-5564	229	25	ã4	ã4	PROPN
ejpam-5564	229	26	=	=	PUNCT
ejpam-5564	229	27	0	0	X
ejpam-5564	229	28	.	.	PUNCT
ejpam-5564	229	29	based	base	VERB
ejpam-5564	229	30	on	on	ADP
ejpam-5564	229	31	the	the	DET
ejpam-5564	229	32	theorem	theorem	NOUN
ejpam-5564	229	33	on	on	ADP
ejpam-5564	229	34	the	the	DET
ejpam-5564	229	35	inversion	inversion	NOUN
ejpam-5564	229	36	of	of	ADP
ejpam-5564	229	37	series	series	NOUN
ejpam-5564	229	38	[	[	X
ejpam-5564	229	39	11	11	NUM
ejpam-5564	229	40	]	]	PUNCT
ejpam-5564	229	41	,	,	PUNCT
ejpam-5564	229	42	we	we	PRON
ejpam-5564	229	43	obtain	obtain	VERB
ejpam-5564	229	44	the	the	DET
ejpam-5564	229	45	following	follow	VERB
ejpam-5564	229	46	equality	equality	NOUN
ejpam-5564	229	47	:	:	PUNCT
ejpam-5564	229	48	z∗	z∗	NOUN
ejpam-5564	229	49	−	−	PROPN
ejpam-5564	229	50	z	z	NOUN
ejpam-5564	229	51	(	(	PUNCT
ejpam-5564	229	52	u	u	NOUN
ejpam-5564	229	53	)	)	PUNCT
ejpam-5564	229	54	=	=	PUNCT
ejpam-5564	230	1	∑	∑	PUNCT
ejpam-5564	230	2	n≥0	n≥0	PROPN
ejpam-5564	230	3	bnu	bnu	NOUN
ejpam-5564	230	4	n+1	n+1	NOUN
ejpam-5564	230	5	,	,	PUNCT
ejpam-5564	230	6	b0	b0	NOUN
ejpam-5564	230	7	=	=	SYM
ejpam-5564	230	8	1	1	NUM
ejpam-5564	230	9	a0	a0	NOUN
ejpam-5564	230	10	,	,	PUNCT
ejpam-5564	230	11	b1	b1	NOUN
ejpam-5564	230	12	=	=	SYM
ejpam-5564	230	13	0	0	NUM
ejpam-5564	230	14	,	,	PUNCT
ejpam-5564	230	15	b2	b2	NOUN
ejpam-5564	230	16	=	=	SYM
ejpam-5564	230	17	0	0	NUM
ejpam-5564	230	18	.	.	PUNCT
ejpam-5564	231	1	(	(	PUNCT
ejpam-5564	231	2	16	16	NUM
ejpam-5564	231	3	)	)	PUNCT
ejpam-5564	231	4	from	from	ADP
ejpam-5564	231	5	equality	equality	NOUN
ejpam-5564	231	6	(	(	PUNCT
ejpam-5564	231	7	16	16	NUM
ejpam-5564	231	8	)	)	PUNCT
ejpam-5564	231	9	,	,	PUNCT
ejpam-5564	231	10	it	it	PRON
ejpam-5564	231	11	is	be	AUX
ejpam-5564	231	12	evident	evident	ADJ
ejpam-5564	231	13	that	that	SCONJ
ejpam-5564	231	14	z	z	NOUN
ejpam-5564	231	15	(	(	PUNCT
ejpam-5564	231	16	0	0	NUM
ejpam-5564	231	17	)	)	PUNCT
ejpam-5564	231	18	=	=	NOUN
ejpam-5564	231	19	z∗.	z∗.	NOUN
ejpam-5564	231	20	further	far	ADV
ejpam-5564	231	21	,	,	PUNCT
ejpam-5564	231	22	by	by	ADP
ejpam-5564	231	23	differentiating	differentiate	VERB
ejpam-5564	231	24	(	(	PUNCT
ejpam-5564	231	25	16	16	NUM
ejpam-5564	231	26	)	)	PUNCT
ejpam-5564	231	27	,	,	PUNCT
ejpam-5564	231	28	we	we	PRON
ejpam-5564	231	29	get	get	VERB
ejpam-5564	231	30	:	:	PUNCT
ejpam-5564	231	31	z′	z′	NUM
ejpam-5564	231	32	(	(	PUNCT
ejpam-5564	231	33	u	u	NOUN
ejpam-5564	231	34	)	)	PUNCT
ejpam-5564	231	35	=	=	SYM
ejpam-5564	232	1	−	−	PROPN
ejpam-5564	232	2	(	(	PUNCT
ejpam-5564	232	3	b0u+b3u	b0u+b3u	NOUN
ejpam-5564	232	4	4	4	NUM
ejpam-5564	232	5	+	+	CCONJ
ejpam-5564	232	6	.	.	PUNCT
ejpam-5564	232	7	.	.	PUNCT
ejpam-5564	232	8	.	.	PUNCT
ejpam-5564	232	9	)	)	PUNCT
ejpam-5564	233	1	′	′	NUM
ejpam-5564	234	1	=	=	PUNCT
ejpam-5564	235	1	−b0	−b0	NOUN
ejpam-5564	235	2	−	−	NUM
ejpam-5564	235	3	4b3u	4b3u	NOUN
ejpam-5564	235	4	3	3	NUM
ejpam-5564	235	5	−	−	NOUN
ejpam-5564	235	6	.	.	PUNCT
ejpam-5564	235	7	.	.	PUNCT
ejpam-5564	235	8	.	.	PUNCT
ejpam-5564	236	1	(	(	PUNCT
ejpam-5564	236	2	17	17	NUM
ejpam-5564	236	3	)	)	PUNCT
ejpam-5564	236	4	from	from	ADP
ejpam-5564	236	5	(	(	PUNCT
ejpam-5564	236	6	17	17	NUM
ejpam-5564	236	7	)	)	PUNCT
ejpam-5564	236	8	,	,	PUNCT
ejpam-5564	236	9	it	it	PRON
ejpam-5564	236	10	follows	follow	VERB
ejpam-5564	236	11	that	that	SCONJ
ejpam-5564	236	12	z′	z′	NUM
ejpam-5564	236	13	(	(	PUNCT
ejpam-5564	236	14	0	0	NUM
ejpam-5564	236	15	)	)	PUNCT
ejpam-5564	236	16	=	=	NOUN
ejpam-5564	237	1	−b0	−b0	NOUN
ejpam-5564	237	2	=	=	PUNCT
ejpam-5564	237	3	−	−	PROPN
ejpam-5564	237	4	1	1	NUM
ejpam-5564	237	5	a0	a0	NOUN
ejpam-5564	237	6	=	=	PUNCT
ejpam-5564	237	7	−	−	PROPN
ejpam-5564	237	8	√	√	PROPN
ejpam-5564	237	9	−q0	−q0	NOUN
ejpam-5564	237	10	24	24	NUM
ejpam-5564	237	11	.	.	PUNCT
ejpam-5564	238	1	differentiating	differentiate	VERB
ejpam-5564	238	2	(	(	PUNCT
ejpam-5564	238	3	17	17	NUM
ejpam-5564	238	4	)	)	PUNCT
ejpam-5564	238	5	,	,	PUNCT
ejpam-5564	238	6	we	we	PRON
ejpam-5564	238	7	obtain	obtain	VERB
ejpam-5564	238	8	:	:	PUNCT
ejpam-5564	238	9	z′′	z′′	PROPN
ejpam-5564	238	10	(	(	PUNCT
ejpam-5564	238	11	u	u	NOUN
ejpam-5564	238	12	)	)	PUNCT
ejpam-5564	238	13	=	=	SYM
ejpam-5564	239	1	(	(	PUNCT
ejpam-5564	239	2	−b0	−b0	ADV
ejpam-5564	239	3	−	−	PROPN
ejpam-5564	239	4	4b3u	4b3u	NOUN
ejpam-5564	239	5	3	3	NUM
ejpam-5564	239	6	−	−	NOUN
ejpam-5564	239	7	.	.	PUNCT
ejpam-5564	239	8	.	.	PUNCT
ejpam-5564	239	9	.	.	PUNCT
ejpam-5564	239	10	)	)	PUNCT
ejpam-5564	240	1	′	′	NUM
ejpam-5564	241	1	=	=	PUNCT
ejpam-5564	241	2	−12b3u	−12b3u	NOUN
ejpam-5564	241	3	2	2	NUM
ejpam-5564	241	4	−	−	NOUN
ejpam-5564	241	5	.	.	PUNCT
ejpam-5564	241	6	.	.	PUNCT
ejpam-5564	241	7	.	.	PUNCT
ejpam-5564	242	1	(	(	PUNCT
ejpam-5564	242	2	18	18	NUM
ejpam-5564	242	3	)	)	PUNCT
ejpam-5564	242	4	from	from	ADP
ejpam-5564	242	5	(	(	PUNCT
ejpam-5564	242	6	18	18	NUM
ejpam-5564	242	7	)	)	PUNCT
ejpam-5564	242	8	,	,	PUNCT
ejpam-5564	242	9	we	we	PRON
ejpam-5564	242	10	get	get	VERB
ejpam-5564	242	11	that	that	DET
ejpam-5564	242	12	z′′	z′′	NOUN
ejpam-5564	242	13	(	(	PUNCT
ejpam-5564	242	14	0	0	NUM
ejpam-5564	242	15	)	)	PUNCT
ejpam-5564	242	16	=	=	SYM
ejpam-5564	243	1	0	0	X
ejpam-5564	243	2	.	.	PUNCT
ejpam-5564	244	1	following	follow	VERB
ejpam-5564	244	2	a	a	DET
ejpam-5564	244	3	similar	similar	ADJ
ejpam-5564	244	4	algorithm	algorithm	NOUN
ejpam-5564	244	5	as	as	ADP
ejpam-5564	244	6	before	before	ADV
ejpam-5564	244	7	,	,	PUNCT
ejpam-5564	244	8	we	we	PRON
ejpam-5564	244	9	obtain	obtain	VERB
ejpam-5564	244	10	z′′′	z′′′	PROPN
ejpam-5564	244	11	(	(	PUNCT
ejpam-5564	244	12	0	0	NUM
ejpam-5564	244	13	)	)	PUNCT
ejpam-5564	244	14	=	=	SYM
ejpam-5564	245	1	0	0	X
ejpam-5564	245	2	.	.	X
ejpam-5564	245	3	sufficiency	sufficiency	PROPN
ejpam-5564	245	4	.	.	PUNCT
ejpam-5564	246	1	let	let	VERB
ejpam-5564	246	2	z	z	NOUN
ejpam-5564	246	3	(	(	PUNCT
ejpam-5564	246	4	u	u	NOUN
ejpam-5564	246	5	)	)	PUNCT
ejpam-5564	246	6	be	be	VERB
ejpam-5564	246	7	the	the	DET
ejpam-5564	246	8	inverse	inverse	NOUN
ejpam-5564	246	9	function	function	NOUN
ejpam-5564	246	10	to	to	ADP
ejpam-5564	246	11	the	the	DET
ejpam-5564	246	12	solution	solution	NOUN
ejpam-5564	246	13	of	of	ADP
ejpam-5564	246	14	the	the	DET
ejpam-5564	246	15	inverse	inverse	NOUN
ejpam-5564	246	16	cauchy	cauchy	NOUN
ejpam-5564	246	17	problem	problem	NOUN
ejpam-5564	246	18	(	(	PUNCT
ejpam-5564	246	19	13	13	NUM
ejpam-5564	246	20	)	)	PUNCT
ejpam-5564	246	21	—	—	PUNCT
ejpam-5564	246	22	(	(	PUNCT
ejpam-5564	246	23	14	14	NUM
ejpam-5564	246	24	)	)	PUNCT
ejpam-5564	246	25	,	,	PUNCT
ejpam-5564	246	26	and	and	CCONJ
ejpam-5564	246	27	the	the	DET
ejpam-5564	246	28	following	follow	VERB
ejpam-5564	246	29	conditions	condition	NOUN
ejpam-5564	246	30	hold	hold	VERB
ejpam-5564	246	31	:	:	PUNCT
ejpam-5564	246	32	z	z	NOUN
ejpam-5564	246	33	(	(	PUNCT
ejpam-5564	246	34	0	0	NUM
ejpam-5564	246	35	)	)	PUNCT
ejpam-5564	247	1	=	=	SYM
ejpam-5564	247	2	z∗	z∗	NOUN
ejpam-5564	247	3	,	,	PUNCT
ejpam-5564	247	4	z′	z′	NUM
ejpam-5564	247	5	(	(	PUNCT
ejpam-5564	247	6	0	0	NUM
ejpam-5564	247	7	)	)	PUNCT
ejpam-5564	247	8	=	=	SYM
ejpam-5564	248	1	−	−	PROPN
ejpam-5564	248	2	√	√	PROPN
ejpam-5564	248	3	−q0	−q0	NOUN
ejpam-5564	248	4	24	24	NUM
ejpam-5564	248	5	,	,	PUNCT
ejpam-5564	248	6	z′′	z′′	NOUN
ejpam-5564	248	7	(	(	PUNCT
ejpam-5564	248	8	0	0	NUM
ejpam-5564	248	9	)	)	PUNCT
ejpam-5564	248	10	=	=	SYM
ejpam-5564	248	11	z′′′	z′′′	X
ejpam-5564	248	12	(	(	PUNCT
ejpam-5564	248	13	0	0	NUM
ejpam-5564	248	14	)	)	PUNCT
ejpam-5564	248	15	=	=	SYM
ejpam-5564	249	1	0	0	X
ejpam-5564	249	2	.	.	PUNCT
ejpam-5564	250	1	let	let	VERB
ejpam-5564	250	2	’s	’s	PRON
ejpam-5564	250	3	prove	prove	VERB
ejpam-5564	250	4	that	that	SCONJ
ejpam-5564	250	5	z∗	z∗	NOUN
ejpam-5564	250	6	is	be	AUX
ejpam-5564	250	7	a	a	DET
ejpam-5564	250	8	moving	move	VERB
ejpam-5564	250	9	singular	singular	ADJ
ejpam-5564	250	10	point	point	NOUN
ejpam-5564	250	11	of	of	ADP
ejpam-5564	250	12	the	the	DET
ejpam-5564	250	13	cauchy	cauchy	ADJ
ejpam-5564	250	14	problem	problem	NOUN
ejpam-5564	250	15	(	(	PUNCT
ejpam-5564	250	16	2	2	NUM
ejpam-5564	250	17	)	)	PUNCT
ejpam-5564	250	18	—	—	PUNCT
ejpam-5564	250	19	(	(	PUNCT
ejpam-5564	250	20	3	3	NUM
ejpam-5564	250	21	)	)	PUNCT
ejpam-5564	250	22	.	.	PUNCT
ejpam-5564	251	1	since	since	SCONJ
ejpam-5564	251	2	u	u	PRON
ejpam-5564	251	3	(	(	PUNCT
ejpam-5564	251	4	z	z	NOUN
ejpam-5564	251	5	)	)	PUNCT
ejpam-5564	251	6	is	be	AUX
ejpam-5564	251	7	an	an	DET
ejpam-5564	251	8	analytic	analytic	ADJ
ejpam-5564	251	9	function	function	NOUN
ejpam-5564	251	10	in	in	ADP
ejpam-5564	251	11	the	the	DET
ejpam-5564	251	12	vicinity	vicinity	NOUN
ejpam-5564	251	13	of	of	ADP
ejpam-5564	251	14	the	the	DET
ejpam-5564	251	15	point	point	NOUN
ejpam-5564	251	16	z∗	z∗	PROPN
ejpam-5564	251	17	,	,	PUNCT
ejpam-5564	251	18	its	its	PRON
ejpam-5564	251	19	inverse	inverse	NOUN
ejpam-5564	251	20	is	be	AUX
ejpam-5564	251	21	also	also	ADV
ejpam-5564	251	22	analytic	analytic	ADJ
ejpam-5564	251	23	in	in	ADP
ejpam-5564	251	24	this	this	DET
ejpam-5564	251	25	domain	domain	NOUN
ejpam-5564	251	26	and	and	CCONJ
ejpam-5564	251	27	can	can	AUX
ejpam-5564	251	28	be	be	AUX
ejpam-5564	251	29	expanded	expand	VERB
ejpam-5564	251	30	into	into	ADP
ejpam-5564	251	31	a	a	DET
ejpam-5564	251	32	taylor	taylor	PROPN
ejpam-5564	251	33	series	series	NOUN
ejpam-5564	251	34	:	:	PUNCT
ejpam-5564	251	35	z	z	PROPN
ejpam-5564	251	36	(	(	PUNCT
ejpam-5564	251	37	u	u	NOUN
ejpam-5564	251	38	)	)	PUNCT
ejpam-5564	251	39	=	=	PUNCT
ejpam-5564	251	40	∑	∑	PUNCT
ejpam-5564	251	41	n≥0	n≥0	PROPN
ejpam-5564	251	42	dnu	dnu	PROPN
ejpam-5564	251	43	n	n	CCONJ
ejpam-5564	251	44	(	(	PUNCT
ejpam-5564	251	45	19	19	NUM
ejpam-5564	251	46	)	)	PUNCT
ejpam-5564	251	47	given	give	VERB
ejpam-5564	251	48	that	that	DET
ejpam-5564	251	49	z	z	NOUN
ejpam-5564	251	50	(	(	PUNCT
ejpam-5564	251	51	0	0	NUM
ejpam-5564	251	52	)	)	PUNCT
ejpam-5564	251	53	=	=	SYM
ejpam-5564	251	54	z∗	z∗	NOUN
ejpam-5564	251	55	and	and	CCONJ
ejpam-5564	251	56	the	the	DET
ejpam-5564	251	57	existing	exist	VERB
ejpam-5564	251	58	expansion	expansion	NOUN
ejpam-5564	251	59	(	(	PUNCT
ejpam-5564	251	60	19	19	NUM
ejpam-5564	251	61	)	)	PUNCT
ejpam-5564	251	62	,	,	PUNCT
ejpam-5564	251	63	we	we	PRON
ejpam-5564	251	64	obtain	obtain	VERB
ejpam-5564	251	65	d0	d0	NOUN
ejpam-5564	251	66	=	=	SYM
ejpam-5564	251	67	z∗.	z∗.	PUNCT
ejpam-5564	251	68	further	far	ADV
ejpam-5564	251	69	,	,	PUNCT
ejpam-5564	251	70	by	by	ADP
ejpam-5564	251	71	differentiating	differentiate	VERB
ejpam-5564	251	72	equality	equality	NOUN
ejpam-5564	251	73	(	(	PUNCT
ejpam-5564	251	74	19	19	NUM
ejpam-5564	251	75	)	)	PUNCT
ejpam-5564	251	76	,	,	PUNCT
ejpam-5564	251	77	we	we	PRON
ejpam-5564	251	78	get	get	VERB
ejpam-5564	251	79	:	:	PUNCT
ejpam-5564	251	80	z′	z′	NUM
ejpam-5564	251	81	(	(	PUNCT
ejpam-5564	251	82	u	u	NOUN
ejpam-5564	251	83	)	)	PUNCT
ejpam-5564	251	84	=	=	SYM
ejpam-5564	251	85	∑	∑	PUNCT
ejpam-5564	251	86	n≥1	n≥1	PROPN
ejpam-5564	251	87	ndnu	ndnu	PROPN
ejpam-5564	251	88	n−1	n−1	PROPN
ejpam-5564	251	89	,	,	PUNCT
ejpam-5564	251	90	thus	thus	ADV
ejpam-5564	251	91	,	,	PUNCT
ejpam-5564	251	92	taking	take	VERB
ejpam-5564	251	93	into	into	ADP
ejpam-5564	251	94	account	account	NOUN
ejpam-5564	251	95	the	the	DET
ejpam-5564	251	96	condition	condition	NOUN
ejpam-5564	251	97	z′	z′	NUM
ejpam-5564	251	98	(	(	PUNCT
ejpam-5564	251	99	0	0	NUM
ejpam-5564	251	100	)	)	PUNCT
ejpam-5564	251	101	=	=	SYM
ejpam-5564	252	1	−	−	PROPN
ejpam-5564	252	2	√	√	PROPN
ejpam-5564	252	3	−q0	−q0	NOUN
ejpam-5564	252	4	24	24	NUM
ejpam-5564	252	5	,	,	PUNCT
ejpam-5564	252	6	we	we	PRON
ejpam-5564	252	7	obtain	obtain	VERB
ejpam-5564	252	8	d1	d1	NOUN
ejpam-5564	252	9	=	=	PUNCT
ejpam-5564	253	1	−	−	PROPN
ejpam-5564	253	2	√	√	PROPN
ejpam-5564	253	3	−q0	−q0	NOUN
ejpam-5564	253	4	24	24	NUM
ejpam-5564	253	5	.	.	PUNCT
ejpam-5564	254	1	similarly	similarly	ADV
ejpam-5564	254	2	,	,	PUNCT
ejpam-5564	254	3	we	we	PRON
ejpam-5564	254	4	find	find	VERB
ejpam-5564	254	5	d2	d2	PROPN
ejpam-5564	254	6	=	=	SYM
ejpam-5564	254	7	d3	d3	PROPN
ejpam-5564	254	8	=	=	SYM
ejpam-5564	254	9	0	0	NUM
ejpam-5564	254	10	.	.	PUNCT
ejpam-5564	255	1	thus	thus	ADV
ejpam-5564	255	2	,	,	PUNCT
ejpam-5564	255	3	equality	equality	NOUN
ejpam-5564	255	4	(	(	PUNCT
ejpam-5564	255	5	19	19	NUM
ejpam-5564	255	6	)	)	PUNCT
ejpam-5564	255	7	takes	take	VERB
ejpam-5564	255	8	the	the	DET
ejpam-5564	255	9	form	form	NOUN
ejpam-5564	255	10	:	:	PUNCT
ejpam-5564	255	11	z	z	NOUN
ejpam-5564	255	12	(	(	PUNCT
ejpam-5564	255	13	u	u	NOUN
ejpam-5564	255	14	)	)	PUNCT
ejpam-5564	255	15	=	=	SYM
ejpam-5564	255	16	z∗	z∗	NOUN
ejpam-5564	255	17	−	−	NOUN
ejpam-5564	255	18	√	√	PROPN
ejpam-5564	255	19	−q0	−q0	VERB
ejpam-5564	255	20	24	24	NUM
ejpam-5564	255	21	u+d4u	u+d4u	ADV
ejpam-5564	255	22	4	4	NUM
ejpam-5564	255	23	+	+	CCONJ
ejpam-5564	255	24	.	.	PUNCT
ejpam-5564	255	25	.	.	PUNCT
ejpam-5564	256	1	.	.	PUNCT
ejpam-5564	257	1	,	,	PUNCT
ejpam-5564	257	2	m.	m.	NOUN
ejpam-5564	257	3	gasanov	gasanov	PROPN
ejpam-5564	257	4	/	/	SYM
ejpam-5564	257	5	eur	eur	PROPN
ejpam-5564	257	6	.	.	PUNCT
ejpam-5564	258	1	j.	j.	PROPN
ejpam-5564	258	2	pure	pure	PROPN
ejpam-5564	258	3	appl	appl	PROPN
ejpam-5564	258	4	.	.	PROPN
ejpam-5564	258	5	math	math	PROPN
ejpam-5564	258	6	,	,	PUNCT
ejpam-5564	258	7	18	18	NUM
ejpam-5564	258	8	(	(	PUNCT
ejpam-5564	258	9	1	1	NUM
ejpam-5564	258	10	)	)	PUNCT
ejpam-5564	258	11	(	(	PUNCT
ejpam-5564	258	12	2025	2025	NUM
ejpam-5564	258	13	)	)	PUNCT
ejpam-5564	258	14	,	,	PUNCT
ejpam-5564	258	15	5564	5564	NUM
ejpam-5564	258	16	13	13	NUM
ejpam-5564	258	17	of	of	ADP
ejpam-5564	258	18	19	19	NUM
ejpam-5564	258	19	z∗	z∗	NOUN
ejpam-5564	258	20	−	−	NOUN
ejpam-5564	258	21	z	z	NOUN
ejpam-5564	258	22	(	(	PUNCT
ejpam-5564	258	23	u	u	NOUN
ejpam-5564	258	24	)	)	PUNCT
ejpam-5564	258	25	=	=	SYM
ejpam-5564	259	1	√	√	PROPN
ejpam-5564	259	2	−q0	−q0	NOUN
ejpam-5564	259	3	24	24	NUM
ejpam-5564	259	4	u−d4u	u−d4u	NUM
ejpam-5564	259	5	4	4	NUM
ejpam-5564	259	6	+	+	CCONJ
ejpam-5564	259	7	.	.	PUNCT
ejpam-5564	259	8	.	.	PUNCT
ejpam-5564	259	9	.	.	PUNCT
ejpam-5564	260	1	(	(	PUNCT
ejpam-5564	260	2	20	20	NUM
ejpam-5564	260	3	)	)	PUNCT
ejpam-5564	260	4	based	base	VERB
ejpam-5564	260	5	on	on	ADP
ejpam-5564	260	6	the	the	DET
ejpam-5564	260	7	theorem	theorem	NOUN
ejpam-5564	260	8	on	on	ADP
ejpam-5564	260	9	the	the	DET
ejpam-5564	260	10	inversion	inversion	NOUN
ejpam-5564	260	11	of	of	ADP
ejpam-5564	260	12	series	series	NOUN
ejpam-5564	260	13	[	[	X
ejpam-5564	260	14	11	11	NUM
ejpam-5564	260	15	]	]	PUNCT
ejpam-5564	260	16	,	,	PUNCT
ejpam-5564	260	17	we	we	PRON
ejpam-5564	260	18	obtain	obtain	VERB
ejpam-5564	260	19	:	:	PUNCT
ejpam-5564	260	20	u	u	NOUN
ejpam-5564	260	21	(	(	PUNCT
ejpam-5564	260	22	z	z	NOUN
ejpam-5564	260	23	)	)	PUNCT
ejpam-5564	260	24	=	=	SYM
ejpam-5564	260	25	√	√	PROPN
ejpam-5564	260	26	−q0	−q0	NOUN
ejpam-5564	260	27	24	24	NUM
ejpam-5564	260	28	(	(	PUNCT
ejpam-5564	260	29	z∗	z∗	NOUN
ejpam-5564	260	30	−	−	PROPN
ejpam-5564	261	1	z)−	z)−	PROPN
ejpam-5564	262	1	d̃4	d̃4	PROPN
ejpam-5564	262	2	(	(	PUNCT
ejpam-5564	262	3	z	z	NOUN
ejpam-5564	262	4	∗	∗	NOUN
ejpam-5564	262	5	−	−	PROPN
ejpam-5564	262	6	z)4	z)4	PROPN
ejpam-5564	262	7	+	+	PUNCT
ejpam-5564	262	8	.	.	PUNCT
ejpam-5564	262	9	.	.	PUNCT
ejpam-5564	262	10	.	.	PUNCT
ejpam-5564	263	1	(	(	PUNCT
ejpam-5564	263	2	21	21	X
ejpam-5564	263	3	)	)	PUNCT
ejpam-5564	263	4	taking	take	VERB
ejpam-5564	263	5	into	into	ADP
ejpam-5564	263	6	account	account	NOUN
ejpam-5564	263	7	the	the	DET
ejpam-5564	263	8	relationship	relationship	NOUN
ejpam-5564	263	9	between	between	ADP
ejpam-5564	263	10	the	the	DET
ejpam-5564	263	11	solutions	solution	NOUN
ejpam-5564	263	12	of	of	ADP
ejpam-5564	263	13	the	the	DET
ejpam-5564	263	14	cauchy	cauchy	ADJ
ejpam-5564	263	15	problems	problem	NOUN
ejpam-5564	263	16	(	(	PUNCT
ejpam-5564	263	17	2	2	NUM
ejpam-5564	263	18	)	)	PUNCT
ejpam-5564	263	19	—	—	PUNCT
ejpam-5564	263	20	(	(	PUNCT
ejpam-5564	263	21	3	3	X
ejpam-5564	263	22	)	)	PUNCT
ejpam-5564	263	23	and	and	CCONJ
ejpam-5564	263	24	(	(	PUNCT
ejpam-5564	263	25	13	13	NUM
ejpam-5564	263	26	)	)	PUNCT
ejpam-5564	263	27	—	—	PUNCT
ejpam-5564	263	28	(	(	PUNCT
ejpam-5564	263	29	14	14	NUM
ejpam-5564	263	30	)	)	PUNCT
ejpam-5564	263	31	,	,	PUNCT
ejpam-5564	263	32	we	we	PRON
ejpam-5564	263	33	have	have	VERB
ejpam-5564	263	34	:	:	PUNCT
ejpam-5564	263	35	w	w	X
ejpam-5564	263	36	(	(	PUNCT
ejpam-5564	263	37	z	z	NOUN
ejpam-5564	263	38	)	)	PUNCT
ejpam-5564	263	39	=	=	SYM
ejpam-5564	263	40	1	1	NUM
ejpam-5564	263	41	u	u	NOUN
ejpam-5564	263	42	(	(	PUNCT
ejpam-5564	263	43	z	z	NOUN
ejpam-5564	263	44	)	)	PUNCT
ejpam-5564	263	45	=	=	SYM
ejpam-5564	263	46	1√	1√	PROPN
ejpam-5564	263	47	−q0	−q0	NOUN
ejpam-5564	263	48	24	24	NUM
ejpam-5564	263	49	(	(	PUNCT
ejpam-5564	263	50	z∗	z∗	NOUN
ejpam-5564	263	51	−	−	PROPN
ejpam-5564	263	52	z	z	PROPN
ejpam-5564	263	53	)	)	PUNCT
ejpam-5564	263	54	+	+	CCONJ
ejpam-5564	263	55	.	.	PUNCT
ejpam-5564	263	56	.	.	PUNCT
ejpam-5564	263	57	.	.	PUNCT
ejpam-5564	264	1	=	=	PUNCT
ejpam-5564	265	1	√	√	NUM
ejpam-5564	265	2	−	−	NUM
ejpam-5564	265	3	24	24	NUM
ejpam-5564	265	4	q0	q0	PROPN
ejpam-5564	265	5	(	(	PUNCT
ejpam-5564	265	6	z∗	z∗	NOUN
ejpam-5564	265	7	−	−	PROPN
ejpam-5564	265	8	z)−1	z)−1	PROPN
ejpam-5564	265	9	+	+	PROPN
ejpam-5564	265	10	c1	c1	PROPN
ejpam-5564	265	11	(	(	PUNCT
ejpam-5564	265	12	z	z	NOUN
ejpam-5564	265	13	∗	∗	NOUN
ejpam-5564	265	14	−	−	PROPN
ejpam-5564	265	15	z	z	X
ejpam-5564	265	16	)	)	PUNCT
ejpam-5564	266	1	+	+	CCONJ
ejpam-5564	266	2	c2	c2	PROPN
ejpam-5564	266	3	(	(	PUNCT
ejpam-5564	266	4	z	z	NOUN
ejpam-5564	266	5	∗	∗	NOUN
ejpam-5564	266	6	−	−	PROPN
ejpam-5564	266	7	z)3	z)3	PROPN
ejpam-5564	266	8	+	+	PUNCT
ejpam-5564	266	9	.	.	PUNCT
ejpam-5564	266	10	.	.	PUNCT
ejpam-5564	266	11	.	.	PUNCT
ejpam-5564	267	1	,	,	PUNCT
ejpam-5564	267	2	thus	thus	ADV
ejpam-5564	267	3	,	,	PUNCT
ejpam-5564	267	4	z∗	z∗	PROPN
ejpam-5564	267	5	is	be	AUX
ejpam-5564	267	6	a	a	DET
ejpam-5564	267	7	moving	move	VERB
ejpam-5564	267	8	singular	singular	ADJ
ejpam-5564	267	9	point	point	NOUN
ejpam-5564	267	10	of	of	ADP
ejpam-5564	267	11	algebraic	algebraic	ADJ
ejpam-5564	267	12	type	type	NOUN
ejpam-5564	267	13	of	of	ADP
ejpam-5564	267	14	the	the	DET
ejpam-5564	267	15	cauchy	cauchy	ADJ
ejpam-5564	267	16	problem	problem	NOUN
ejpam-5564	267	17	(	(	PUNCT
ejpam-5564	267	18	2	2	NUM
ejpam-5564	267	19	)	)	PUNCT
ejpam-5564	267	20	—	—	PUNCT
ejpam-5564	267	21	(	(	PUNCT
ejpam-5564	267	22	3	3	NUM
ejpam-5564	267	23	)	)	PUNCT
ejpam-5564	267	24	.	.	PUNCT
ejpam-5564	268	1	theorem	theorem	VERB
ejpam-5564	268	2	6	6	NUM
ejpam-5564	268	3	.	.	PUNCT
ejpam-5564	269	1	the	the	DET
ejpam-5564	269	2	fact	fact	NOUN
ejpam-5564	269	3	that	that	SCONJ
ejpam-5564	269	4	z∗	z∗	NOUN
ejpam-5564	269	5	is	be	AUX
ejpam-5564	269	6	a	a	DET
ejpam-5564	269	7	moving	move	VERB
ejpam-5564	269	8	singular	singular	ADJ
ejpam-5564	269	9	point	point	NOUN
ejpam-5564	269	10	of	of	ADP
ejpam-5564	269	11	the	the	DET
ejpam-5564	269	12	function	function	NOUN
ejpam-5564	269	13	w	w	PROPN
ejpam-5564	269	14	(	(	PUNCT
ejpam-5564	269	15	z	z	NOUN
ejpam-5564	269	16	)	)	PUNCT
ejpam-5564	269	17	is	be	AUX
ejpam-5564	269	18	equivalent	equivalent	ADJ
ejpam-5564	269	19	to	to	ADP
ejpam-5564	269	20	the	the	DET
ejpam-5564	269	21	existence	existence	NOUN
ejpam-5564	269	22	of	of	ADP
ejpam-5564	269	23	a	a	DET
ejpam-5564	269	24	certain	certain	ADJ
ejpam-5564	269	25	neighborhood	neighborhood	NOUN
ejpam-5564	269	26	of	of	ADP
ejpam-5564	269	27	this	this	DET
ejpam-5564	269	28	point	point	NOUN
ejpam-5564	269	29	in	in	ADP
ejpam-5564	269	30	which	which	PRON
ejpam-5564	269	31	the	the	DET
ejpam-5564	269	32	function	function	NOUN
ejpam-5564	269	33	u	u	NOUN
ejpam-5564	269	34	(	(	PUNCT
ejpam-5564	269	35	z	z	NOUN
ejpam-5564	269	36	)	)	PUNCT
ejpam-5564	269	37	is	be	AUX
ejpam-5564	269	38	continuous	continuous	ADJ
ejpam-5564	269	39	and	and	CCONJ
ejpam-5564	269	40	has	have	VERB
ejpam-5564	269	41	different	different	ADJ
ejpam-5564	269	42	signs	sign	NOUN
ejpam-5564	269	43	at	at	ADP
ejpam-5564	269	44	the	the	DET
ejpam-5564	269	45	endpoints	endpoint	NOUN
ejpam-5564	269	46	of	of	ADP
ejpam-5564	269	47	this	this	DET
ejpam-5564	269	48	interval	interval	NOUN
ejpam-5564	269	49	.	.	PUNCT
ejpam-5564	270	1	proof	proof	NOUN
ejpam-5564	270	2	.	.	PUNCT
ejpam-5564	271	1	necessity	necessity	NOUN
ejpam-5564	271	2	.	.	PUNCT
ejpam-5564	272	1	given	give	VERB
ejpam-5564	272	2	that	that	DET
ejpam-5564	272	3	u	u	NOUN
ejpam-5564	272	4	(	(	PUNCT
ejpam-5564	272	5	z	z	NOUN
ejpam-5564	272	6	)	)	PUNCT
ejpam-5564	272	7	is	be	AUX
ejpam-5564	272	8	the	the	DET
ejpam-5564	272	9	inverse	inverse	NOUN
ejpam-5564	272	10	function	function	NOUN
ejpam-5564	272	11	,	,	PUNCT
ejpam-5564	272	12	then	then	ADV
ejpam-5564	272	13	u	u	X
ejpam-5564	272	14	(	(	PUNCT
ejpam-5564	272	15	z∗	z∗	NOUN
ejpam-5564	272	16	)	)	PUNCT
ejpam-5564	272	17	=	=	SYM
ejpam-5564	272	18	0	0	NUM
ejpam-5564	272	19	,	,	PUNCT
ejpam-5564	272	20	and	and	CCONJ
ejpam-5564	272	21	the	the	DET
ejpam-5564	272	22	function	function	NOUN
ejpam-5564	272	23	is	be	AUX
ejpam-5564	272	24	continuous	continuous	ADJ
ejpam-5564	272	25	in	in	ADP
ejpam-5564	272	26	some	some	DET
ejpam-5564	272	27	neighborhood	neighborhood	NOUN
ejpam-5564	272	28	of	of	ADP
ejpam-5564	272	29	this	this	DET
ejpam-5564	272	30	point	point	NOUN
ejpam-5564	272	31	.	.	PUNCT
ejpam-5564	273	1	considering	consider	VERB
ejpam-5564	273	2	that	that	SCONJ
ejpam-5564	273	3	u	u	PROPN
ejpam-5564	273	4	(	(	PUNCT
ejpam-5564	273	5	z	z	NOUN
ejpam-5564	273	6	)	)	PUNCT
ejpam-5564	273	7	=	=	NOUN
ejpam-5564	273	8	√	√	ADP
ejpam-5564	273	9	−q0	−q0	NUM
ejpam-5564	273	10	24	24	NUM
ejpam-5564	273	11	(	(	PUNCT
ejpam-5564	273	12	z∗	z∗	PROPN
ejpam-5564	273	13	−	−	PROPN
ejpam-5564	273	14	z)+o	z)+o	PROPN
ejpam-5564	273	15	(	(	PUNCT
ejpam-5564	273	16	z∗	z∗	PROPN
ejpam-5564	273	17	−	−	PROPN
ejpam-5564	273	18	z	z	PROPN
ejpam-5564	273	19	)	)	PUNCT
ejpam-5564	273	20	,	,	PUNCT
ejpam-5564	273	21	when	when	SCONJ
ejpam-5564	273	22	crossing	cross	VERB
ejpam-5564	273	23	the	the	DET
ejpam-5564	273	24	moving	move	VERB
ejpam-5564	273	25	singular	singular	ADJ
ejpam-5564	273	26	point	point	NOUN
ejpam-5564	273	27	,	,	PUNCT
ejpam-5564	273	28	the	the	DET
ejpam-5564	273	29	function	function	NOUN
ejpam-5564	273	30	changes	change	VERB
ejpam-5564	273	31	its	its	PRON
ejpam-5564	273	32	sign	sign	NOUN
ejpam-5564	273	33	.	.	PUNCT
ejpam-5564	274	1	thus	thus	ADV
ejpam-5564	274	2	,	,	PUNCT
ejpam-5564	274	3	there	there	PRON
ejpam-5564	274	4	exists	exist	VERB
ejpam-5564	274	5	an	an	DET
ejpam-5564	274	6	interval	interval	NOUN
ejpam-5564	274	7	on	on	ADP
ejpam-5564	274	8	the	the	DET
ejpam-5564	274	9	ends	end	NOUN
ejpam-5564	274	10	of	of	ADP
ejpam-5564	274	11	which	which	PRON
ejpam-5564	274	12	the	the	DET
ejpam-5564	274	13	function	function	NOUN
ejpam-5564	274	14	takes	take	VERB
ejpam-5564	274	15	values	value	NOUN
ejpam-5564	274	16	of	of	ADP
ejpam-5564	274	17	different	different	ADJ
ejpam-5564	274	18	signs	sign	NOUN
ejpam-5564	274	19	.	.	PUNCT
ejpam-5564	275	1	sufficiency	sufficiency	NOUN
ejpam-5564	275	2	.	.	PUNCT
ejpam-5564	276	1	due	due	ADP
ejpam-5564	276	2	to	to	ADP
ejpam-5564	276	3	the	the	DET
ejpam-5564	276	4	continuity	continuity	NOUN
ejpam-5564	276	5	of	of	ADP
ejpam-5564	276	6	the	the	DET
ejpam-5564	276	7	function	function	NOUN
ejpam-5564	276	8	u	u	NOUN
ejpam-5564	276	9	(	(	PUNCT
ejpam-5564	276	10	z	z	NOUN
ejpam-5564	276	11	)	)	PUNCT
ejpam-5564	276	12	and	and	CCONJ
ejpam-5564	276	13	the	the	DET
ejpam-5564	276	14	different	different	ADJ
ejpam-5564	276	15	signs	sign	NOUN
ejpam-5564	276	16	at	at	ADP
ejpam-5564	276	17	the	the	DET
ejpam-5564	276	18	ends	end	NOUN
ejpam-5564	276	19	of	of	ADP
ejpam-5564	276	20	a	a	DET
ejpam-5564	276	21	certain	certain	ADJ
ejpam-5564	276	22	interval	interval	NOUN
ejpam-5564	276	23	,	,	PUNCT
ejpam-5564	276	24	according	accord	VERB
ejpam-5564	276	25	to	to	ADP
ejpam-5564	276	26	the	the	DET
ejpam-5564	276	27	bolzano	bolzano	NOUN
ejpam-5564	276	28	-	-	PUNCT
ejpam-5564	276	29	cauchy	cauchy	NOUN
ejpam-5564	276	30	theorem	theorem	NOUN
ejpam-5564	276	31	∃	∃	PROPN
ejpam-5564	276	32	ξ	ξ	PROPN
ejpam-5564	276	33	:	:	PUNCT
ejpam-5564	276	34	u	u	NOUN
ejpam-5564	276	35	(	(	PUNCT
ejpam-5564	276	36	ξ	ξ	NOUN
ejpam-5564	276	37	)	)	PUNCT
ejpam-5564	276	38	=	=	SYM
ejpam-5564	276	39	0	0	X
ejpam-5564	276	40	.	.	X
ejpam-5564	276	41	taking	take	VERB
ejpam-5564	276	42	into	into	ADP
ejpam-5564	276	43	account	account	NOUN
ejpam-5564	276	44	the	the	DET
ejpam-5564	276	45	relation	relation	NOUN
ejpam-5564	276	46	w	w	PROPN
ejpam-5564	276	47	(	(	PUNCT
ejpam-5564	276	48	z	z	NOUN
ejpam-5564	276	49	)	)	PUNCT
ejpam-5564	276	50	=	=	SYM
ejpam-5564	276	51	1	1	NUM
ejpam-5564	276	52	u(z	u(z	NOUN
ejpam-5564	276	53	)	)	PUNCT
ejpam-5564	276	54	,	,	PUNCT
ejpam-5564	276	55	we	we	PRON
ejpam-5564	276	56	obtain	obtain	VERB
ejpam-5564	276	57	that	that	SCONJ
ejpam-5564	276	58	ξ	ξ	PROPN
ejpam-5564	276	59	is	be	AUX
ejpam-5564	276	60	a	a	DET
ejpam-5564	276	61	moving	move	VERB
ejpam-5564	276	62	singular	singular	ADJ
ejpam-5564	276	63	point	point	NOUN
ejpam-5564	276	64	of	of	ADP
ejpam-5564	276	65	the	the	DET
ejpam-5564	276	66	solution	solution	NOUN
ejpam-5564	276	67	to	to	ADP
ejpam-5564	276	68	the	the	DET
ejpam-5564	276	69	cauchy	cauchy	ADJ
ejpam-5564	276	70	problem	problem	NOUN
ejpam-5564	276	71	(	(	PUNCT
ejpam-5564	276	72	2	2	NUM
ejpam-5564	276	73	)	)	PUNCT
ejpam-5564	276	74	—	—	PUNCT
ejpam-5564	276	75	(	(	PUNCT
ejpam-5564	276	76	3	3	NUM
ejpam-5564	276	77	)	)	PUNCT
ejpam-5564	276	78	.	.	PUNCT
ejpam-5564	277	1	next	next	ADV
ejpam-5564	277	2	,	,	PUNCT
ejpam-5564	277	3	let	let	VERB
ejpam-5564	277	4	’s	’s	NOUN
ejpam-5564	277	5	proceed	proceed	VERB
ejpam-5564	277	6	to	to	ADP
ejpam-5564	277	7	the	the	DET
ejpam-5564	277	8	formulation	formulation	NOUN
ejpam-5564	277	9	of	of	ADP
ejpam-5564	277	10	the	the	DET
ejpam-5564	277	11	exact	exact	ADJ
ejpam-5564	277	12	criteria	criterion	NOUN
ejpam-5564	277	13	for	for	ADP
ejpam-5564	277	14	the	the	DET
ejpam-5564	277	15	existence	existence	NOUN
ejpam-5564	277	16	of	of	ADP
ejpam-5564	277	17	a	a	DET
ejpam-5564	277	18	moving	move	VERB
ejpam-5564	277	19	singular	singular	ADJ
ejpam-5564	277	20	point	point	NOUN
ejpam-5564	277	21	in	in	ADP
ejpam-5564	277	22	the	the	DET
ejpam-5564	277	23	complex	complex	ADJ
ejpam-5564	277	24	domain	domain	NOUN
ejpam-5564	277	25	.	.	PUNCT
ejpam-5564	278	1	for	for	ADP
ejpam-5564	278	2	the	the	DET
ejpam-5564	278	3	complex	complex	ADJ
ejpam-5564	278	4	domain	domain	NOUN
ejpam-5564	278	5	,	,	PUNCT
ejpam-5564	278	6	these	these	DET
ejpam-5564	278	7	criteria	criterion	NOUN
ejpam-5564	278	8	are	be	AUX
ejpam-5564	278	9	related	relate	VERB
ejpam-5564	278	10	to	to	ADP
ejpam-5564	278	11	the	the	DET
ejpam-5564	278	12	specifics	specific	NOUN
ejpam-5564	278	13	of	of	ADP
ejpam-5564	278	14	transitioning	transition	VERB
ejpam-5564	278	15	to	to	PART
ejpam-5564	278	16	phase	phase	NOUN
ejpam-5564	278	17	spaces	space	NOUN
ejpam-5564	278	18	.	.	PUNCT
ejpam-5564	279	1	let	let	VERB
ejpam-5564	279	2	’s	’s	NOUN
ejpam-5564	279	3	express	express	VERB
ejpam-5564	279	4	the	the	DET
ejpam-5564	279	5	solution	solution	NOUN
ejpam-5564	279	6	to	to	ADP
ejpam-5564	279	7	the	the	DET
ejpam-5564	279	8	inverse	inverse	NOUN
ejpam-5564	279	9	cauchy	cauchy	NOUN
ejpam-5564	279	10	problem	problem	NOUN
ejpam-5564	279	11	(	(	PUNCT
ejpam-5564	279	12	13	13	NUM
ejpam-5564	279	13	)	)	PUNCT
ejpam-5564	279	14	—	—	PUNCT
ejpam-5564	279	15	(	(	PUNCT
ejpam-5564	279	16	14	14	NUM
ejpam-5564	279	17	)	)	PUNCT
ejpam-5564	279	18	as	as	ADP
ejpam-5564	279	19	u	u	PROPN
ejpam-5564	279	20	(	(	PUNCT
ejpam-5564	279	21	z	z	NOUN
ejpam-5564	279	22	)	)	PUNCT
ejpam-5564	280	1	=	=	SYM
ejpam-5564	280	2	p	p	X
ejpam-5564	280	3	(	(	PUNCT
ejpam-5564	280	4	x	x	X
ejpam-5564	280	5	,	,	PUNCT
ejpam-5564	280	6	y)+iq	y)+iq	X
ejpam-5564	280	7	(	(	PUNCT
ejpam-5564	280	8	x	x	X
ejpam-5564	280	9	,	,	PUNCT
ejpam-5564	280	10	y	y	PROPN
ejpam-5564	280	11	)	)	PUNCT
ejpam-5564	280	12	where	where	SCONJ
ejpam-5564	280	13	the	the	DET
ejpam-5564	280	14	functions	function	NOUN
ejpam-5564	280	15	p	p	X
ejpam-5564	280	16	(	(	PUNCT
ejpam-5564	280	17	x	x	NOUN
ejpam-5564	280	18	,	,	PUNCT
ejpam-5564	280	19	y	y	PROPN
ejpam-5564	280	20	)	)	PUNCT
ejpam-5564	280	21	and	and	CCONJ
ejpam-5564	280	22	q	q	ADJ
ejpam-5564	280	23	(	(	PUNCT
ejpam-5564	280	24	x	x	NOUN
ejpam-5564	280	25	,	,	PUNCT
ejpam-5564	280	26	y	y	NOUN
ejpam-5564	280	27	)	)	PUNCT
ejpam-5564	280	28	are	be	AUX
ejpam-5564	280	29	characterized	characterize	VERB
ejpam-5564	280	30	,	,	PUNCT
ejpam-5564	280	31	respectively	respectively	ADV
ejpam-5564	280	32	,	,	PUNCT
ejpam-5564	280	33	by	by	ADP
ejpam-5564	280	34	the	the	DET
ejpam-5564	280	35	phase	phase	NOUN
ejpam-5564	280	36	spaces	space	VERB
ejpam-5564	280	37	φ1	φ1	NOUN
ejpam-5564	280	38	(	(	PUNCT
ejpam-5564	280	39	x	x	X
ejpam-5564	280	40	,	,	PUNCT
ejpam-5564	280	41	y	y	PROPN
ejpam-5564	280	42	,	,	PUNCT
ejpam-5564	280	43	p	p	X
ejpam-5564	280	44	(	(	PUNCT
ejpam-5564	280	45	x	x	NOUN
ejpam-5564	280	46	,	,	PUNCT
ejpam-5564	280	47	y	y	NOUN
ejpam-5564	280	48	)	)	PUNCT
ejpam-5564	280	49	)	)	PUNCT
ejpam-5564	280	50	and	and	CCONJ
ejpam-5564	280	51	φ2	φ2	PROPN
ejpam-5564	280	52	(	(	PUNCT
ejpam-5564	280	53	x	x	X
ejpam-5564	280	54	,	,	PUNCT
ejpam-5564	280	55	y	y	PROPN
ejpam-5564	280	56	,	,	PUNCT
ejpam-5564	280	57	q	q	X
ejpam-5564	280	58	(	(	PUNCT
ejpam-5564	280	59	x	x	NOUN
ejpam-5564	280	60	,	,	PUNCT
ejpam-5564	280	61	y	y	NOUN
ejpam-5564	280	62	)	)	PUNCT
ejpam-5564	280	63	)	)	PUNCT
ejpam-5564	280	64	.	.	PUNCT
ejpam-5564	281	1	let	let	VERB
ejpam-5564	281	2	’s	’s	PRON
ejpam-5564	281	3	use	use	VERB
ejpam-5564	281	4	the	the	DET
ejpam-5564	281	5	terminology	terminology	NOUN
ejpam-5564	281	6	introduced	introduce	VERB
ejpam-5564	281	7	in	in	ADP
ejpam-5564	281	8	the	the	DET
ejpam-5564	281	9	work	work	NOUN
ejpam-5564	281	10	[	[	X
ejpam-5564	281	11	32	32	NUM
ejpam-5564	281	12	]	]	PUNCT
ejpam-5564	281	13	to	to	PART
ejpam-5564	281	14	define	define	VERB
ejpam-5564	281	15	correct	correct	ADJ
ejpam-5564	281	16	and	and	CCONJ
ejpam-5564	281	17	incorrect	incorrect	ADJ
ejpam-5564	281	18	lines	line	NOUN
ejpam-5564	281	19	to	to	PART
ejpam-5564	281	20	facilitate	facilitate	VERB
ejpam-5564	281	21	the	the	DET
ejpam-5564	281	22	statement	statement	NOUN
ejpam-5564	281	23	of	of	ADP
ejpam-5564	281	24	the	the	DET
ejpam-5564	281	25	following	follow	VERB
ejpam-5564	281	26	theorems	theorem	NOUN
ejpam-5564	281	27	.	.	PUNCT
ejpam-5564	282	1	theorem	theorem	NOUN
ejpam-5564	282	2	7	7	NUM
ejpam-5564	282	3	.	.	NOUN
ejpam-5564	282	4	for	for	SCONJ
ejpam-5564	282	5	z∗	z∗	PROPN
ejpam-5564	282	6	to	to	PART
ejpam-5564	282	7	be	be	AUX
ejpam-5564	282	8	a	a	DET
ejpam-5564	282	9	moving	move	VERB
ejpam-5564	282	10	singular	singular	ADJ
ejpam-5564	282	11	point	point	NOUN
ejpam-5564	282	12	of	of	ADP
ejpam-5564	282	13	algebraic	algebraic	ADJ
ejpam-5564	282	14	type	type	NOUN
ejpam-5564	282	15	of	of	ADP
ejpam-5564	282	16	the	the	DET
ejpam-5564	282	17	solution	solution	NOUN
ejpam-5564	282	18	w	w	PROPN
ejpam-5564	282	19	(	(	PUNCT
ejpam-5564	282	20	z	z	NOUN
ejpam-5564	282	21	)	)	PUNCT
ejpam-5564	282	22	of	of	ADP
ejpam-5564	282	23	the	the	DET
ejpam-5564	282	24	cauchy	cauchy	ADJ
ejpam-5564	282	25	problem	problem	NOUN
ejpam-5564	282	26	(	(	PUNCT
ejpam-5564	282	27	2	2	NUM
ejpam-5564	282	28	)	)	PUNCT
ejpam-5564	282	29	—	—	PUNCT
ejpam-5564	282	30	(	(	PUNCT
ejpam-5564	282	31	3	3	NUM
ejpam-5564	282	32	)	)	PUNCT
ejpam-5564	282	33	,	,	PUNCT
ejpam-5564	282	34	it	it	PRON
ejpam-5564	282	35	is	be	AUX
ejpam-5564	282	36	necessary	necessary	ADJ
ejpam-5564	282	37	and	and	CCONJ
ejpam-5564	282	38	sufficient	sufficient	ADJ
ejpam-5564	282	39	that	that	SCONJ
ejpam-5564	282	40	for	for	ADP
ejpam-5564	282	41	re	re	ADP
ejpam-5564	282	42	(	(	PUNCT
ejpam-5564	282	43	u	u	PROPN
ejpam-5564	282	44	(	(	PUNCT
ejpam-5564	282	45	z	z	NOUN
ejpam-5564	282	46	)	)	PUNCT
ejpam-5564	282	47	)	)	PUNCT
ejpam-5564	283	1	and	and	CCONJ
ejpam-5564	283	2	i	i	PRON
ejpam-5564	283	3	m	m	VERB
ejpam-5564	283	4	(	(	PUNCT
ejpam-5564	283	5	u	u	NOUN
ejpam-5564	283	6	(	(	PUNCT
ejpam-5564	283	7	z	z	NOUN
ejpam-5564	283	8	)	)	PUNCT
ejpam-5564	283	9	)	)	PUNCT
ejpam-5564	283	10	,	,	PUNCT
ejpam-5564	283	11	where	where	SCONJ
ejpam-5564	283	12	the	the	DET
ejpam-5564	283	13	function	function	NOUN
ejpam-5564	283	14	u	u	NOUN
ejpam-5564	283	15	(	(	PUNCT
ejpam-5564	283	16	z	z	NOUN
ejpam-5564	283	17	)	)	PUNCT
ejpam-5564	283	18	is	be	AUX
ejpam-5564	283	19	the	the	DET
ejpam-5564	283	20	solution	solution	NOUN
ejpam-5564	283	21	to	to	ADP
ejpam-5564	283	22	the	the	DET
ejpam-5564	283	23	inverse	inverse	NOUN
ejpam-5564	283	24	cauchy	cauchy	NOUN
ejpam-5564	283	25	problem	problem	NOUN
ejpam-5564	283	26	(	(	PUNCT
ejpam-5564	283	27	5	5	NUM
ejpam-5564	283	28	)	)	PUNCT
ejpam-5564	283	29	—	—	PUNCT
ejpam-5564	283	30	(	(	PUNCT
ejpam-5564	283	31	6	6	NUM
ejpam-5564	283	32	)	)	PUNCT
ejpam-5564	283	33	,	,	PUNCT
ejpam-5564	283	34	in	in	ADP
ejpam-5564	283	35	some	some	DET
ejpam-5564	283	36	region	region	NOUN
ejpam-5564	283	37	g	g	NOUN
ejpam-5564	283	38	,	,	PUNCT
ejpam-5564	283	39	which	which	PRON
ejpam-5564	283	40	is	be	AUX
ejpam-5564	283	41	the	the	DET
ejpam-5564	283	42	neighborhood	neighborhood	NOUN
ejpam-5564	283	43	of	of	ADP
ejpam-5564	283	44	the	the	DET
ejpam-5564	283	45	regular	regular	ADJ
ejpam-5564	283	46	point	point	NOUN
ejpam-5564	283	47	z∗	z∗	NOUN
ejpam-5564	283	48	(	(	PUNCT
ejpam-5564	283	49	x∗	x∗	PROPN
ejpam-5564	283	50	,	,	PUNCT
ejpam-5564	283	51	y∗	y∗	PROPN
ejpam-5564	283	52	)	)	PUNCT
ejpam-5564	283	53	of	of	ADP
ejpam-5564	283	54	the	the	DET
ejpam-5564	283	55	function	function	NOUN
ejpam-5564	283	56	u	u	NOUN
ejpam-5564	283	57	(	(	PUNCT
ejpam-5564	283	58	z	z	NOUN
ejpam-5564	283	59	)	)	PUNCT
ejpam-5564	283	60	,	,	PUNCT
ejpam-5564	283	61	the	the	DET
ejpam-5564	283	62	phase	phase	NOUN
ejpam-5564	283	63	spaces	space	VERB
ejpam-5564	283	64	φ1	φ1	PROPN
ejpam-5564	283	65	and	and	CCONJ
ejpam-5564	283	66	φ2	φ2	PROPN
ejpam-5564	283	67	satisfy	satisfy	VERB
ejpam-5564	283	68	the	the	DET
ejpam-5564	283	69	following	follow	VERB
ejpam-5564	283	70	conditions	condition	NOUN
ejpam-5564	283	71	:	:	PUNCT
ejpam-5564	283	72	m.	m.	NOUN
ejpam-5564	283	73	gasanov	gasanov	PROPN
ejpam-5564	283	74	/	/	SYM
ejpam-5564	283	75	eur	eur	PROPN
ejpam-5564	283	76	.	.	PUNCT
ejpam-5564	284	1	j.	j.	PROPN
ejpam-5564	284	2	pure	pure	PROPN
ejpam-5564	284	3	appl	appl	PROPN
ejpam-5564	284	4	.	.	PROPN
ejpam-5564	284	5	math	math	PROPN
ejpam-5564	284	6	,	,	PUNCT
ejpam-5564	284	7	18	18	NUM
ejpam-5564	284	8	(	(	PUNCT
ejpam-5564	284	9	1	1	NUM
ejpam-5564	284	10	)	)	PUNCT
ejpam-5564	284	11	(	(	PUNCT
ejpam-5564	284	12	2025	2025	NUM
ejpam-5564	284	13	)	)	PUNCT
ejpam-5564	284	14	,	,	PUNCT
ejpam-5564	284	15	5564	5564	NUM
ejpam-5564	284	16	14	14	NUM
ejpam-5564	284	17	of	of	ADP
ejpam-5564	284	18	19	19	NUM
ejpam-5564	284	19	(	(	PUNCT
ejpam-5564	284	20	i	i	NOUN
ejpam-5564	284	21	)	)	PUNCT
ejpam-5564	284	22	p	p	X
ejpam-5564	284	23	(	(	PUNCT
ejpam-5564	284	24	x	x	NOUN
ejpam-5564	284	25	,	,	PUNCT
ejpam-5564	284	26	y	y	PROPN
ejpam-5564	284	27	)	)	PUNCT
ejpam-5564	284	28	and	and	CCONJ
ejpam-5564	284	29	q	q	ADJ
ejpam-5564	284	30	(	(	PUNCT
ejpam-5564	284	31	x	x	NOUN
ejpam-5564	284	32	,	,	PUNCT
ejpam-5564	284	33	y	y	NOUN
ejpam-5564	284	34	)	)	PUNCT
ejpam-5564	284	35	are	be	AUX
ejpam-5564	284	36	continuous	continuous	ADJ
ejpam-5564	284	37	with	with	ADP
ejpam-5564	284	38	respect	respect	NOUN
ejpam-5564	284	39	to	to	ADP
ejpam-5564	284	40	their	their	PRON
ejpam-5564	284	41	arguments	argument	NOUN
ejpam-5564	284	42	;	;	PUNCT
ejpam-5564	284	43	(	(	PUNCT
ejpam-5564	284	44	ii	ii	NOUN
ejpam-5564	284	45	)	)	PUNCT
ejpam-5564	284	46	when	when	SCONJ
ejpam-5564	284	47	crossing	cross	VERB
ejpam-5564	284	48	the	the	DET
ejpam-5564	284	49	point	point	NOUN
ejpam-5564	284	50	z∗	z∗	NOUN
ejpam-5564	284	51	(	(	PUNCT
ejpam-5564	284	52	x∗	x∗	PROPN
ejpam-5564	284	53	,	,	PUNCT
ejpam-5564	284	54	y∗	y∗	PROPN
ejpam-5564	284	55	)	)	PUNCT
ejpam-5564	284	56	,	,	PUNCT
ejpam-5564	284	57	moving	move	VERB
ejpam-5564	284	58	along	along	ADP
ejpam-5564	284	59	the	the	DET
ejpam-5564	284	60	regular	regular	ADJ
ejpam-5564	284	61	line	line	NOUN
ejpam-5564	284	62	l	l	NOUN
ejpam-5564	284	63	in	in	ADP
ejpam-5564	284	64	the	the	DET
ejpam-5564	284	65	direction	direction	NOUN
ejpam-5564	284	66	of	of	ADP
ejpam-5564	284	67	the	the	DET
ejpam-5564	284	68	axes	axis	NOUN
ejpam-5564	284	69	ox	ox	NOUN
ejpam-5564	284	70	and	and	CCONJ
ejpam-5564	284	71	oy	oy	PROPN
ejpam-5564	284	72	,	,	PUNCT
ejpam-5564	284	73	the	the	DET
ejpam-5564	284	74	functions	function	NOUN
ejpam-5564	284	75	p	p	X
ejpam-5564	284	76	(	(	PUNCT
ejpam-5564	284	77	x	x	NOUN
ejpam-5564	284	78	,	,	PUNCT
ejpam-5564	284	79	y	y	PROPN
ejpam-5564	284	80	)	)	PUNCT
ejpam-5564	284	81	and	and	CCONJ
ejpam-5564	284	82	q	q	ADJ
ejpam-5564	284	83	(	(	PUNCT
ejpam-5564	284	84	x	x	NOUN
ejpam-5564	284	85	,	,	PUNCT
ejpam-5564	284	86	y	y	NOUN
ejpam-5564	284	87	)	)	PUNCT
ejpam-5564	284	88	change	change	NOUN
ejpam-5564	284	89	signs	sign	NOUN
ejpam-5564	284	90	,	,	PUNCT
ejpam-5564	284	91	where	where	SCONJ
ejpam-5564	284	92	l	l	NOUN
ejpam-5564	284	93	:	:	PUNCT
ejpam-5564	284	94	{	{	PUNCT
ejpam-5564	284	95	z∗	z∗	PROPN
ejpam-5564	284	96	∈	∈	PROPN
ejpam-5564	284	97	l	l	X
ejpam-5564	284	98	⊂	⊂	X
ejpam-5564	284	99	g	g	PROPN
ejpam-5564	284	100	,	,	PUNCT
ejpam-5564	284	101	l	l	PROPN
ejpam-5564	284	102	∈	∈	PROPN
ejpam-5564	284	103	(	(	PUNCT
ejpam-5564	284	104	φ1	φ1	NOUN
ejpam-5564	284	105	∪	∪	ADP
ejpam-5564	284	106	φ2	φ2	PROPN
ejpam-5564	284	107	)	)	PUNCT
ejpam-5564	284	108	}	}	PUNCT
ejpam-5564	284	109	.	.	PUNCT
ejpam-5564	285	1	proof	proof	NOUN
ejpam-5564	285	2	.	.	PUNCT
ejpam-5564	286	1	necessity	necessity	NOUN
ejpam-5564	286	2	.	.	PUNCT
ejpam-5564	287	1	according	accord	VERB
ejpam-5564	287	2	to	to	ADP
ejpam-5564	287	3	the	the	DET
ejpam-5564	287	4	theorem	theorem	ADJ
ejpam-5564	287	5	statement	statement	NOUN
ejpam-5564	287	6	,	,	PUNCT
ejpam-5564	287	7	we	we	PRON
ejpam-5564	287	8	have	have	VERB
ejpam-5564	287	9	that	that	PRON
ejpam-5564	287	10	z∗	z∗	PROPN
ejpam-5564	287	11	is	be	AUX
ejpam-5564	287	12	a	a	DET
ejpam-5564	287	13	moving	move	VERB
ejpam-5564	287	14	singular	singular	ADJ
ejpam-5564	287	15	point	point	NOUN
ejpam-5564	287	16	of	of	ADP
ejpam-5564	287	17	y	y	PROPN
ejpam-5564	287	18	(	(	PUNCT
ejpam-5564	287	19	z	z	NOUN
ejpam-5564	287	20	)	)	PUNCT
ejpam-5564	287	21	of	of	ADP
ejpam-5564	287	22	the	the	DET
ejpam-5564	287	23	cauchy	cauchy	ADJ
ejpam-5564	287	24	problem	problem	NOUN
ejpam-5564	287	25	(	(	PUNCT
ejpam-5564	287	26	2	2	NUM
ejpam-5564	287	27	)	)	PUNCT
ejpam-5564	287	28	—	—	PUNCT
ejpam-5564	287	29	(	(	PUNCT
ejpam-5564	287	30	3	3	NUM
ejpam-5564	287	31	)	)	PUNCT
ejpam-5564	287	32	.	.	PUNCT
ejpam-5564	288	1	let	let	VERB
ejpam-5564	288	2	’s	’s	PRON
ejpam-5564	288	3	demonstrate	demonstrate	VERB
ejpam-5564	288	4	that	that	SCONJ
ejpam-5564	288	5	in	in	ADP
ejpam-5564	288	6	this	this	DET
ejpam-5564	288	7	case	case	NOUN
ejpam-5564	288	8	re	re	ADP
ejpam-5564	288	9	(	(	PUNCT
ejpam-5564	288	10	w	w	PROPN
ejpam-5564	288	11	(	(	PUNCT
ejpam-5564	288	12	z	z	NOUN
ejpam-5564	288	13	)	)	PUNCT
ejpam-5564	288	14	)	)	PUNCT
ejpam-5564	289	1	and	and	CCONJ
ejpam-5564	289	2	i	i	PRON
ejpam-5564	289	3	m	m	VERB
ejpam-5564	289	4	(	(	PUNCT
ejpam-5564	289	5	w	w	PROPN
ejpam-5564	289	6	(	(	PUNCT
ejpam-5564	289	7	z	z	NOUN
ejpam-5564	289	8	)	)	PUNCT
ejpam-5564	289	9	)	)	PUNCT
ejpam-5564	289	10	satisfy	satisfy	NOUN
ejpam-5564	289	11	theorem	theorem	VERB
ejpam-5564	289	12	7	7	NUM
ejpam-5564	289	13	.	.	PUNCT
ejpam-5564	289	14	since	since	SCONJ
ejpam-5564	289	15	theorem	theorem	VERB
ejpam-5564	289	16	1	1	NUM
ejpam-5564	289	17	holds	hold	NOUN
ejpam-5564	289	18	,	,	PUNCT
ejpam-5564	289	19	the	the	DET
ejpam-5564	289	20	principal	principal	ADJ
ejpam-5564	289	21	part	part	NOUN
ejpam-5564	289	22	of	of	ADP
ejpam-5564	289	23	the	the	DET
ejpam-5564	289	24	series	series	NOUN
ejpam-5564	289	25	representing	represent	VERB
ejpam-5564	289	26	the	the	DET
ejpam-5564	289	27	solution	solution	NOUN
ejpam-5564	289	28	to	to	ADP
ejpam-5564	289	29	the	the	DET
ejpam-5564	289	30	cauchy	cauchy	ADJ
ejpam-5564	289	31	problem	problem	NOUN
ejpam-5564	289	32	(	(	PUNCT
ejpam-5564	289	33	2	2	NUM
ejpam-5564	289	34	)	)	PUNCT
ejpam-5564	289	35	—	—	PUNCT
ejpam-5564	289	36	(	(	PUNCT
ejpam-5564	289	37	3	3	X
ejpam-5564	289	38	)	)	PUNCT
ejpam-5564	289	39	takes	take	VERB
ejpam-5564	289	40	the	the	DET
ejpam-5564	289	41	form	form	NOUN
ejpam-5564	289	42	w	w	ADP
ejpam-5564	289	43	(	(	PUNCT
ejpam-5564	289	44	z	z	NOUN
ejpam-5564	289	45	)	)	PUNCT
ejpam-5564	290	1	=	=	SYM
ejpam-5564	290	2	o	o	PROPN
ejpam-5564	290	3	(	(	PUNCT
ejpam-5564	290	4	a0	a0	NOUN
ejpam-5564	290	5	/	/	SYM
ejpam-5564	290	6	z∗	z∗	PROPN
ejpam-5564	290	7	−	−	PROPN
ejpam-5564	290	8	z	z	PROPN
ejpam-5564	290	9	)	)	PUNCT
ejpam-5564	290	10	,	,	PUNCT
ejpam-5564	290	11	therefore	therefore	ADV
ejpam-5564	290	12	,	,	PUNCT
ejpam-5564	290	13	for	for	ADP
ejpam-5564	290	14	the	the	DET
ejpam-5564	290	15	inverse	inverse	NOUN
ejpam-5564	290	16	solution	solution	NOUN
ejpam-5564	290	17	in	in	ADP
ejpam-5564	290	18	the	the	DET
ejpam-5564	290	19	region	region	NOUN
ejpam-5564	290	20	g	g	NOUN
ejpam-5564	290	21	,	,	PUNCT
ejpam-5564	290	22	we	we	PRON
ejpam-5564	290	23	can	can	AUX
ejpam-5564	290	24	assert	assert	VERB
ejpam-5564	290	25	that	that	SCONJ
ejpam-5564	290	26	u	u	PROPN
ejpam-5564	290	27	(	(	PUNCT
ejpam-5564	290	28	z	z	NOUN
ejpam-5564	290	29	)	)	PUNCT
ejpam-5564	291	1	=	=	SYM
ejpam-5564	291	2	o	o	X
ejpam-5564	291	3	(	(	PUNCT
ejpam-5564	291	4	z∗	z∗	NOUN
ejpam-5564	291	5	−	−	PROPN
ejpam-5564	291	6	z	z	PROPN
ejpam-5564	291	7	/	/	SYM
ejpam-5564	291	8	a0	a0	PROPN
ejpam-5564	291	9	)	)	PUNCT
ejpam-5564	291	10	.	.	PUNCT
ejpam-5564	292	1	in	in	ADP
ejpam-5564	292	2	this	this	DET
ejpam-5564	292	3	situation	situation	NOUN
ejpam-5564	292	4	,	,	PUNCT
ejpam-5564	292	5	we	we	PRON
ejpam-5564	292	6	have	have	VERB
ejpam-5564	292	7	the	the	DET
ejpam-5564	292	8	following	following	NOUN
ejpam-5564	292	9	:	:	PUNCT
ejpam-5564	292	10	sgn	sgn	NOUN
ejpam-5564	292	11	(	(	PUNCT
ejpam-5564	292	12	p	p	X
ejpam-5564	292	13	(	(	PUNCT
ejpam-5564	292	14	x	x	NOUN
ejpam-5564	292	15	,	,	PUNCT
ejpam-5564	292	16	y	y	NOUN
ejpam-5564	292	17	)	)	PUNCT
ejpam-5564	292	18	)	)	PUNCT
ejpam-5564	293	1	=	=	SYM
ejpam-5564	293	2	sgn	sgn	NOUN
ejpam-5564	293	3	(	(	PUNCT
ejpam-5564	293	4	(	(	PUNCT
ejpam-5564	293	5	x∗	x∗	PROPN
ejpam-5564	293	6	−	−	PROPN
ejpam-5564	293	7	x	x	NOUN
ejpam-5564	293	8	)	)	PUNCT
ejpam-5564	293	9	)	)	PUNCT
ejpam-5564	293	10	(	(	PUNCT
ejpam-5564	293	11	22	22	X
ejpam-5564	293	12	)	)	PUNCT
ejpam-5564	293	13	sgn	sgn	NOUN
ejpam-5564	293	14	(	(	PUNCT
ejpam-5564	293	15	q	q	PROPN
ejpam-5564	293	16	(	(	PUNCT
ejpam-5564	293	17	x	x	NOUN
ejpam-5564	293	18	,	,	PUNCT
ejpam-5564	293	19	y	y	NOUN
ejpam-5564	293	20	)	)	PUNCT
ejpam-5564	293	21	)	)	PUNCT
ejpam-5564	294	1	=	=	SYM
ejpam-5564	294	2	sgn	sgn	NOUN
ejpam-5564	294	3	(	(	PUNCT
ejpam-5564	294	4	(	(	PUNCT
ejpam-5564	294	5	y∗	y∗	ADV
ejpam-5564	294	6	−	−	PROPN
ejpam-5564	294	7	y	y	NOUN
ejpam-5564	294	8	)	)	PUNCT
ejpam-5564	294	9	)	)	PUNCT
ejpam-5564	294	10	.	.	PUNCT
ejpam-5564	295	1	(	(	PUNCT
ejpam-5564	295	2	23	23	X
ejpam-5564	295	3	)	)	PUNCT
ejpam-5564	295	4	analysis	analysis	NOUN
ejpam-5564	295	5	of	of	ADP
ejpam-5564	295	6	the	the	DET
ejpam-5564	295	7	analytic	analytic	ADJ
ejpam-5564	295	8	part	part	NOUN
ejpam-5564	295	9	u	u	NOUN
ejpam-5564	295	10	(	(	PUNCT
ejpam-5564	295	11	z	z	NOUN
ejpam-5564	295	12	):	):	PUNCT
ejpam-5564	295	13	the	the	DET
ejpam-5564	295	14	sign	sign	NOUN
ejpam-5564	295	15	of	of	ADP
ejpam-5564	295	16	the	the	DET
ejpam-5564	295	17	function	function	NOUN
ejpam-5564	295	18	p	p	NOUN
ejpam-5564	295	19	(	(	PUNCT
ejpam-5564	295	20	x	x	NOUN
ejpam-5564	295	21	,	,	PUNCT
ejpam-5564	295	22	y	y	NOUN
ejpam-5564	295	23	)	)	PUNCT
ejpam-5564	295	24	is	be	AUX
ejpam-5564	295	25	determined	determine	VERB
ejpam-5564	295	26	by	by	ADP
ejpam-5564	295	27	the	the	DET
ejpam-5564	295	28	sign	sign	NOUN
ejpam-5564	295	29	of	of	ADP
ejpam-5564	295	30	x	x	PRON
ejpam-5564	295	31	,	,	PUNCT
ejpam-5564	295	32	while	while	SCONJ
ejpam-5564	295	33	the	the	DET
ejpam-5564	295	34	sign	sign	NOUN
ejpam-5564	295	35	of	of	ADP
ejpam-5564	295	36	the	the	DET
ejpam-5564	295	37	function	function	NOUN
ejpam-5564	295	38	q	q	PROPN
ejpam-5564	295	39	(	(	PUNCT
ejpam-5564	295	40	x	x	NOUN
ejpam-5564	295	41	,	,	PUNCT
ejpam-5564	295	42	y	y	NOUN
ejpam-5564	295	43	)	)	PUNCT
ejpam-5564	295	44	is	be	AUX
ejpam-5564	295	45	determined	determine	VERB
ejpam-5564	295	46	by	by	ADP
ejpam-5564	295	47	the	the	DET
ejpam-5564	295	48	sign	sign	NOUN
ejpam-5564	295	49	of	of	ADP
ejpam-5564	295	50	y.	y.	PROPN
ejpam-5564	295	51	without	without	ADP
ejpam-5564	295	52	loss	loss	NOUN
ejpam-5564	295	53	of	of	ADP
ejpam-5564	295	54	generality	generality	NOUN
ejpam-5564	295	55	,	,	PUNCT
ejpam-5564	295	56	let	let	VERB
ejpam-5564	295	57	’s	’s	PRON
ejpam-5564	295	58	assume	assume	VERB
ejpam-5564	295	59	that	that	SCONJ
ejpam-5564	295	60	the	the	DET
ejpam-5564	295	61	moving	move	VERB
ejpam-5564	295	62	singular	singular	ADJ
ejpam-5564	295	63	point	point	NOUN
ejpam-5564	295	64	z∗	z∗	PROPN
ejpam-5564	295	65	is	be	AUX
ejpam-5564	295	66	located	locate	VERB
ejpam-5564	295	67	in	in	ADP
ejpam-5564	295	68	the	the	DET
ejpam-5564	295	69	first	first	ADJ
ejpam-5564	295	70	quadrant	quadrant	NOUN
ejpam-5564	295	71	of	of	ADP
ejpam-5564	295	72	the	the	DET
ejpam-5564	295	73	phase	phase	NOUN
ejpam-5564	295	74	plane	plane	NOUN
ejpam-5564	295	75	.	.	PUNCT
ejpam-5564	296	1	as	as	ADP
ejpam-5564	296	2	a	a	DET
ejpam-5564	296	3	correct	correct	ADJ
ejpam-5564	296	4	line	line	NOUN
ejpam-5564	296	5	,	,	PUNCT
ejpam-5564	296	6	we	we	PRON
ejpam-5564	296	7	can	can	AUX
ejpam-5564	296	8	consider	consider	VERB
ejpam-5564	296	9	a	a	DET
ejpam-5564	296	10	segment	segment	NOUN
ejpam-5564	296	11	of	of	ADP
ejpam-5564	296	12	the	the	DET
ejpam-5564	296	13	circle	circle	NOUN
ejpam-5564	296	14	|z|	|z|	NOUN
ejpam-5564	296	15	=	=	SYM
ejpam-5564	296	16	|z∗|	|z∗|	NOUN
ejpam-5564	296	17	in	in	ADP
ejpam-5564	296	18	the	the	DET
ejpam-5564	296	19	region	region	NOUN
ejpam-5564	296	20	g.	g.	PROPN
ejpam-5564	296	21	moving	move	VERB
ejpam-5564	296	22	along	along	ADP
ejpam-5564	296	23	this	this	DET
ejpam-5564	296	24	circle	circle	NOUN
ejpam-5564	296	25	in	in	ADP
ejpam-5564	296	26	the	the	DET
ejpam-5564	296	27	direction	direction	NOUN
ejpam-5564	296	28	of	of	ADP
ejpam-5564	296	29	the	the	DET
ejpam-5564	296	30	correct	correct	ADJ
ejpam-5564	296	31	line	line	NOUN
ejpam-5564	296	32	l	l	NOUN
ejpam-5564	296	33	,	,	PUNCT
ejpam-5564	296	34	we	we	PRON
ejpam-5564	296	35	observe	observe	VERB
ejpam-5564	296	36	that	that	SCONJ
ejpam-5564	296	37	for	for	ADP
ejpam-5564	296	38	points	point	NOUN
ejpam-5564	296	39	z	z	PROPN
ejpam-5564	296	40	∈	∈	PROPN
ejpam-5564	296	41	l	l	NOUN
ejpam-5564	296	42	:	:	PUNCT
ejpam-5564	296	43	arg	arg	NOUN
ejpam-5564	296	44	z	z	X
ejpam-5564	296	45	<	<	X
ejpam-5564	296	46	arg	arg	NOUN
ejpam-5564	296	47	z∗	z∗	NOUN
ejpam-5564	296	48	⇒	⇒	NOUN
ejpam-5564	296	49	{	{	PUNCT
ejpam-5564	296	50	x	x	PUNCT
ejpam-5564	296	51	>	>	X
ejpam-5564	296	52	x∗	x∗	PROPN
ejpam-5564	297	1	y	y	X
ejpam-5564	297	2	<	<	X
ejpam-5564	297	3	y∗	y∗	PROPN
ejpam-5564	297	4	and	and	CCONJ
ejpam-5564	297	5	for	for	ADP
ejpam-5564	297	6	points	point	NOUN
ejpam-5564	297	7	z	z	PROPN
ejpam-5564	297	8	∈	∈	PROPN
ejpam-5564	297	9	l	l	NOUN
ejpam-5564	297	10	:	:	PUNCT
ejpam-5564	297	11	arg	arg	NOUN
ejpam-5564	297	12	z	z	X
ejpam-5564	297	13	>	>	X
ejpam-5564	297	14	arg	arg	NOUN
ejpam-5564	297	15	z∗	z∗	PROPN
ejpam-5564	297	16	⇒	⇒	NOUN
ejpam-5564	297	17	{	{	PUNCT
ejpam-5564	297	18	x	x	PUNCT
ejpam-5564	297	19	<	<	X
ejpam-5564	297	20	x∗	x∗	PROPN
ejpam-5564	298	1	y	y	PROPN
ejpam-5564	298	2	>	>	X
ejpam-5564	298	3	y∗	y∗	PROPN
ejpam-5564	298	4	,	,	PUNCT
ejpam-5564	298	5	therefore	therefore	ADV
ejpam-5564	298	6	,	,	PUNCT
ejpam-5564	298	7	the	the	DET
ejpam-5564	298	8	imaginary	imaginary	ADJ
ejpam-5564	298	9	and	and	CCONJ
ejpam-5564	298	10	real	real	ADJ
ejpam-5564	298	11	parts	part	NOUN
ejpam-5564	298	12	of	of	ADP
ejpam-5564	298	13	the	the	DET
ejpam-5564	298	14	function	function	NOUN
ejpam-5564	298	15	u	u	NOUN
ejpam-5564	298	16	(	(	PUNCT
ejpam-5564	298	17	z	z	NOUN
ejpam-5564	298	18	)	)	PUNCT
ejpam-5564	298	19	are	be	AUX
ejpam-5564	298	20	continuous	continuous	ADJ
ejpam-5564	298	21	functions	function	NOUN
ejpam-5564	298	22	with	with	ADP
ejpam-5564	298	23	respect	respect	NOUN
ejpam-5564	298	24	to	to	ADP
ejpam-5564	298	25	the	the	DET
ejpam-5564	298	26	arguments	argument	NOUN
ejpam-5564	298	27	,	,	PUNCT
ejpam-5564	298	28	and	and	CCONJ
ejpam-5564	298	29	they	they	PRON
ejpam-5564	298	30	change	change	VERB
ejpam-5564	298	31	their	their	PRON
ejpam-5564	298	32	sign	sign	NOUN
ejpam-5564	298	33	when	when	SCONJ
ejpam-5564	298	34	passing	pass	VERB
ejpam-5564	298	35	through	through	ADP
ejpam-5564	298	36	the	the	DET
ejpam-5564	298	37	point	point	NOUN
ejpam-5564	298	38	z∗.	z∗.	NOUN
ejpam-5564	298	39	since	since	SCONJ
ejpam-5564	298	40	,	,	PUNCT
ejpam-5564	298	41	without	without	ADP
ejpam-5564	298	42	loss	loss	NOUN
ejpam-5564	298	43	of	of	ADP
ejpam-5564	298	44	generality	generality	NOUN
ejpam-5564	298	45	,	,	PUNCT
ejpam-5564	298	46	only	only	ADV
ejpam-5564	298	47	the	the	DET
ejpam-5564	298	48	first	first	ADJ
ejpam-5564	298	49	quadrant	quadrant	NOUN
ejpam-5564	298	50	was	be	AUX
ejpam-5564	298	51	considered	consider	VERB
ejpam-5564	298	52	,	,	PUNCT
ejpam-5564	298	53	the	the	DET
ejpam-5564	298	54	necessity	necessity	NOUN
ejpam-5564	298	55	is	be	AUX
ejpam-5564	298	56	similarly	similarly	ADV
ejpam-5564	298	57	proven	prove	VERB
ejpam-5564	298	58	in	in	ADP
ejpam-5564	298	59	the	the	DET
ejpam-5564	298	60	other	other	ADJ
ejpam-5564	298	61	quadrants	quadrant	NOUN
ejpam-5564	298	62	.	.	PUNCT
ejpam-5564	299	1	theorem	theorem	VERB
ejpam-5564	299	2	8	8	NUM
ejpam-5564	299	3	.	.	PUNCT
ejpam-5564	300	1	in	in	ADP
ejpam-5564	300	2	order	order	NOUN
ejpam-5564	300	3	for	for	SCONJ
ejpam-5564	300	4	z∗	z∗	NOUN
ejpam-5564	300	5	to	to	PART
ejpam-5564	300	6	be	be	AUX
ejpam-5564	300	7	a	a	DET
ejpam-5564	300	8	moving	move	VERB
ejpam-5564	300	9	singular	singular	ADJ
ejpam-5564	300	10	point	point	NOUN
ejpam-5564	300	11	of	of	ADP
ejpam-5564	300	12	the	the	DET
ejpam-5564	300	13	function	function	NOUN
ejpam-5564	300	14	w	w	PROPN
ejpam-5564	300	15	(	(	PUNCT
ejpam-5564	300	16	z	z	NOUN
ejpam-5564	300	17	)	)	PUNCT
ejpam-5564	300	18	,	,	PUNCT
ejpam-5564	300	19	which	which	PRON
ejpam-5564	300	20	is	be	AUX
ejpam-5564	300	21	a	a	DET
ejpam-5564	300	22	solution	solution	NOUN
ejpam-5564	300	23	to	to	ADP
ejpam-5564	300	24	the	the	DET
ejpam-5564	300	25	cauchy	cauchy	ADJ
ejpam-5564	300	26	problem	problem	NOUN
ejpam-5564	300	27	(	(	PUNCT
ejpam-5564	300	28	2	2	NUM
ejpam-5564	300	29	)	)	PUNCT
ejpam-5564	300	30	—	—	PUNCT
ejpam-5564	300	31	(	(	PUNCT
ejpam-5564	300	32	3	3	NUM
ejpam-5564	300	33	)	)	PUNCT
ejpam-5564	300	34	,	,	PUNCT
ejpam-5564	300	35	it	it	PRON
ejpam-5564	300	36	is	be	AUX
ejpam-5564	300	37	necessary	necessary	ADJ
ejpam-5564	300	38	and	and	CCONJ
ejpam-5564	300	39	sufficient	sufficient	ADJ
ejpam-5564	300	40	for	for	ADP
ejpam-5564	300	41	the	the	DET
ejpam-5564	300	42	imaginary	imaginary	ADJ
ejpam-5564	300	43	and	and	CCONJ
ejpam-5564	300	44	real	real	ADJ
ejpam-5564	300	45	parts	part	NOUN
ejpam-5564	300	46	of	of	ADP
ejpam-5564	300	47	u	u	NOUN
ejpam-5564	300	48	(	(	PUNCT
ejpam-5564	300	49	z	z	NOUN
ejpam-5564	300	50	)	)	PUNCT
ejpam-5564	300	51	in	in	ADP
ejpam-5564	300	52	some	some	DET
ejpam-5564	300	53	sufficiently	sufficiently	ADV
ejpam-5564	300	54	small	small	ADJ
ejpam-5564	300	55	neighborhood	neighborhood	NOUN
ejpam-5564	300	56	g	g	NOUN
ejpam-5564	300	57	of	of	ADP
ejpam-5564	300	58	the	the	DET
ejpam-5564	300	59	point	point	NOUN
ejpam-5564	300	60	z∗	z∗	NOUN
ejpam-5564	300	61	in	in	ADP
ejpam-5564	300	62	the	the	DET
ejpam-5564	300	63	phase	phase	NOUN
ejpam-5564	300	64	spaces	space	VERB
ejpam-5564	300	65	φ1	φ1	NOUN
ejpam-5564	300	66	and	and	CCONJ
ejpam-5564	300	67	φ2	φ2	PROPN
ejpam-5564	300	68	,	,	PUNCT
ejpam-5564	300	69	to	to	PART
ejpam-5564	300	70	be	be	AUX
ejpam-5564	300	71	continuous	continuous	ADJ
ejpam-5564	300	72	functions	function	NOUN
ejpam-5564	300	73	with	with	ADP
ejpam-5564	300	74	respect	respect	NOUN
ejpam-5564	300	75	to	to	ADP
ejpam-5564	300	76	their	their	PRON
ejpam-5564	300	77	arguments	argument	NOUN
ejpam-5564	300	78	and	and	CCONJ
ejpam-5564	300	79	to	to	PART
ejpam-5564	300	80	change	change	VERB
ejpam-5564	300	81	their	their	PRON
ejpam-5564	300	82	signs	sign	NOUN
ejpam-5564	300	83	when	when	SCONJ
ejpam-5564	300	84	passing	pass	VERB
ejpam-5564	300	85	through	through	ADP
ejpam-5564	300	86	the	the	DET
ejpam-5564	300	87	point	point	NOUN
ejpam-5564	300	88	z∗	z∗	NOUN
ejpam-5564	300	89	(	(	PUNCT
ejpam-5564	300	90	x∗	x∗	PROPN
ejpam-5564	300	91	,	,	PUNCT
ejpam-5564	300	92	y∗	y∗	PROPN
ejpam-5564	300	93	)	)	PUNCT
ejpam-5564	300	94	,	,	PUNCT
ejpam-5564	300	95	moving	move	VERB
ejpam-5564	300	96	sequentially	sequentially	ADV
ejpam-5564	300	97	along	along	ADP
ejpam-5564	300	98	certain	certain	ADJ
ejpam-5564	300	99	incorrect	incorrect	ADJ
ejpam-5564	300	100	lines	line	NOUN
ejpam-5564	300	101	l1	l1	PROPN
ejpam-5564	300	102	,	,	PUNCT
ejpam-5564	300	103	l2	l2	NOUN
ejpam-5564	300	104	:	:	PUNCT
ejpam-5564	300	105	{	{	PUNCT
ejpam-5564	300	106	z∗	z∗	PROPN
ejpam-5564	300	107	∈	∈	PROPN
ejpam-5564	300	108	l1	l1	PROPN
ejpam-5564	300	109	⊂	⊂	PROPN
ejpam-5564	300	110	g	g	PROPN
ejpam-5564	300	111	,	,	PUNCT
ejpam-5564	300	112	z∗	z∗	PROPN
ejpam-5564	300	113	∈	∈	PROPN
ejpam-5564	300	114	l2	l2	NOUN
ejpam-5564	300	115	⊂	⊂	X
ejpam-5564	300	116	g	g	PROPN
ejpam-5564	300	117	,	,	PUNCT
ejpam-5564	300	118	l1	l1	PROPN
ejpam-5564	300	119	∈	∈	PROPN
ejpam-5564	300	120	φ1	φ1	PROPN
ejpam-5564	300	121	,	,	PUNCT
ejpam-5564	300	122	l2	l2	NOUN
ejpam-5564	300	123	∈	∈	PROPN
ejpam-5564	300	124	φ2	φ2	PROPN
ejpam-5564	300	125	}	}	PUNCT
ejpam-5564	300	126	.	.	PUNCT
ejpam-5564	301	1	proof	proof	NOUN
ejpam-5564	301	2	.	.	PUNCT
ejpam-5564	302	1	necessity	necessity	NOUN
ejpam-5564	302	2	.	.	PUNCT
ejpam-5564	303	1	similar	similar	ADJ
ejpam-5564	303	2	to	to	ADP
ejpam-5564	303	3	theorem	theorem	NOUN
ejpam-5564	303	4	7	7	NUM
ejpam-5564	303	5	,	,	PUNCT
ejpam-5564	303	6	we	we	PRON
ejpam-5564	303	7	have	have	VERB
ejpam-5564	303	8	the	the	DET
ejpam-5564	303	9	principal	principal	ADJ
ejpam-5564	303	10	part	part	NOUN
ejpam-5564	303	11	of	of	ADP
ejpam-5564	303	12	the	the	DET
ejpam-5564	303	13	series	series	NOUN
ejpam-5564	303	14	,	,	PUNCT
ejpam-5564	303	15	which	which	PRON
ejpam-5564	303	16	is	be	AUX
ejpam-5564	303	17	the	the	DET
ejpam-5564	303	18	solution	solution	NOUN
ejpam-5564	303	19	to	to	ADP
ejpam-5564	303	20	the	the	DET
ejpam-5564	303	21	cauchy	cauchy	ADJ
ejpam-5564	303	22	problem	problem	NOUN
ejpam-5564	303	23	(	(	PUNCT
ejpam-5564	303	24	2	2	NUM
ejpam-5564	303	25	)	)	PUNCT
ejpam-5564	303	26	—	—	PUNCT
ejpam-5564	304	1	(	(	PUNCT
ejpam-5564	304	2	3	3	NUM
ejpam-5564	304	3	):	):	PUNCT
ejpam-5564	304	4	w	w	PROPN
ejpam-5564	304	5	(	(	PUNCT
ejpam-5564	304	6	z	z	NOUN
ejpam-5564	304	7	)	)	PUNCT
ejpam-5564	304	8	=	=	SYM
ejpam-5564	304	9	o	o	PROPN
ejpam-5564	304	10	(	(	PUNCT
ejpam-5564	304	11	a0	a0	NOUN
ejpam-5564	304	12	/	/	SYM
ejpam-5564	304	13	z∗	z∗	PROPN
ejpam-5564	304	14	−	−	PROPN
ejpam-5564	304	15	z	z	NOUN
ejpam-5564	304	16	)	)	PUNCT
ejpam-5564	304	17	,	,	PUNCT
ejpam-5564	304	18	and	and	CCONJ
ejpam-5564	304	19	the	the	DET
ejpam-5564	304	20	analytic	analytic	ADJ
ejpam-5564	304	21	part	part	NOUN
ejpam-5564	304	22	of	of	ADP
ejpam-5564	304	23	the	the	DET
ejpam-5564	304	24	inverse	inverse	NOUN
ejpam-5564	304	25	function	function	NOUN
ejpam-5564	304	26	u	u	PROPN
ejpam-5564	304	27	(	(	PUNCT
ejpam-5564	304	28	z	z	NOUN
ejpam-5564	304	29	)	)	PUNCT
ejpam-5564	304	30	=	=	SYM
ejpam-5564	305	1	o	o	X
ejpam-5564	305	2	(	(	PUNCT
ejpam-5564	305	3	z∗	z∗	NOUN
ejpam-5564	305	4	−	−	PROPN
ejpam-5564	305	5	z	z	PROPN
ejpam-5564	305	6	/	/	SYM
ejpam-5564	305	7	a0	a0	PROPN
ejpam-5564	305	8	)	)	PUNCT
ejpam-5564	305	9	.	.	PUNCT
ejpam-5564	306	1	let	let	VERB
ejpam-5564	306	2	’s	’s	NOUN
ejpam-5564	306	3	consider	consider	VERB
ejpam-5564	306	4	the	the	DET
ejpam-5564	306	5	line	line	NOUN
ejpam-5564	306	6	l1	l1	PROPN
ejpam-5564	306	7	:	:	PUNCT
ejpam-5564	307	1	y	y	NOUN
ejpam-5564	307	2	=	=	PUNCT
ejpam-5564	307	3	y∗	y∗	PROPN
ejpam-5564	307	4	=	=	SYM
ejpam-5564	307	5	const	const	NOUN
ejpam-5564	307	6	—	—	PUNCT
ejpam-5564	307	7	an	an	DET
ejpam-5564	307	8	incorrect	incorrect	ADJ
ejpam-5564	307	9	line	line	NOUN
ejpam-5564	307	10	with	with	ADP
ejpam-5564	307	11	respect	respect	NOUN
ejpam-5564	307	12	to	to	ADP
ejpam-5564	307	13	the	the	DET
ejpam-5564	307	14	ox	ox	ADJ
ejpam-5564	307	15	axis	axis	NOUN
ejpam-5564	307	16	.	.	PUNCT
ejpam-5564	308	1	moving	move	VERB
ejpam-5564	308	2	along	along	ADP
ejpam-5564	308	3	this	this	DET
ejpam-5564	308	4	line	line	NOUN
ejpam-5564	308	5	,	,	PUNCT
ejpam-5564	308	6	taking	take	VERB
ejpam-5564	308	7	into	into	ADP
ejpam-5564	308	8	account	account	NOUN
ejpam-5564	308	9	the	the	DET
ejpam-5564	308	10	signs	sign	NOUN
ejpam-5564	308	11	of	of	ADP
ejpam-5564	308	12	the	the	DET
ejpam-5564	308	13	arguments	argument	NOUN
ejpam-5564	308	14	(	(	PUNCT
ejpam-5564	308	15	9	9	NUM
ejpam-5564	308	16	)	)	PUNCT
ejpam-5564	308	17	and	and	CCONJ
ejpam-5564	308	18	the	the	DET
ejpam-5564	308	19	m.	m.	NOUN
ejpam-5564	308	20	gasanov	gasanov	PROPN
ejpam-5564	308	21	/	/	SYM
ejpam-5564	308	22	eur	eur	PROPN
ejpam-5564	308	23	.	.	PUNCT
ejpam-5564	309	1	j.	j.	PROPN
ejpam-5564	309	2	pure	pure	PROPN
ejpam-5564	309	3	appl	appl	PROPN
ejpam-5564	309	4	.	.	PROPN
ejpam-5564	309	5	math	math	PROPN
ejpam-5564	309	6	,	,	PUNCT
ejpam-5564	309	7	18	18	NUM
ejpam-5564	309	8	(	(	PUNCT
ejpam-5564	309	9	1	1	NUM
ejpam-5564	309	10	)	)	PUNCT
ejpam-5564	309	11	(	(	PUNCT
ejpam-5564	309	12	2025	2025	NUM
ejpam-5564	309	13	)	)	PUNCT
ejpam-5564	309	14	,	,	PUNCT
ejpam-5564	309	15	5564	5564	NUM
ejpam-5564	309	16	15	15	NUM
ejpam-5564	309	17	of	of	ADP
ejpam-5564	309	18	19	19	NUM
ejpam-5564	309	19	theorem	theorem	NOUN
ejpam-5564	309	20	of	of	ADP
ejpam-5564	309	21	existence	existence	NOUN
ejpam-5564	309	22	and	and	CCONJ
ejpam-5564	309	23	uniqueness	uniqueness	NOUN
ejpam-5564	309	24	of	of	ADP
ejpam-5564	309	25	the	the	DET
ejpam-5564	309	26	solution	solution	NOUN
ejpam-5564	309	27	,	,	PUNCT
ejpam-5564	309	28	u	u	NOUN
ejpam-5564	309	29	(	(	PUNCT
ejpam-5564	309	30	z	z	NOUN
ejpam-5564	309	31	)	)	PUNCT
ejpam-5564	309	32	as	as	ADP
ejpam-5564	309	33	a	a	DET
ejpam-5564	309	34	function	function	NOUN
ejpam-5564	309	35	of	of	ADP
ejpam-5564	309	36	a	a	DET
ejpam-5564	309	37	single	single	ADJ
ejpam-5564	309	38	variable	variable	ADJ
ejpam-5564	309	39	changes	change	NOUN
ejpam-5564	309	40	sign	sign	VERB
ejpam-5564	309	41	when	when	SCONJ
ejpam-5564	309	42	crossing	cross	VERB
ejpam-5564	309	43	the	the	DET
ejpam-5564	309	44	point	point	NOUN
ejpam-5564	309	45	z∗.	z∗.	NOUN
ejpam-5564	309	46	similarly	similarly	ADV
ejpam-5564	309	47	,	,	PUNCT
ejpam-5564	309	48	we	we	PRON
ejpam-5564	309	49	consider	consider	VERB
ejpam-5564	309	50	the	the	DET
ejpam-5564	309	51	line	line	NOUN
ejpam-5564	309	52	l2	l2	NOUN
ejpam-5564	309	53	:	:	PUNCT
ejpam-5564	309	54	x	x	SYM
ejpam-5564	309	55	=	=	PUNCT
ejpam-5564	309	56	x∗	x∗	X
ejpam-5564	309	57	=	=	SYM
ejpam-5564	309	58	const	const	PROPN
ejpam-5564	309	59	,	,	PUNCT
ejpam-5564	309	60	which	which	PRON
ejpam-5564	309	61	is	be	AUX
ejpam-5564	309	62	an	an	DET
ejpam-5564	309	63	incorrect	incorrect	ADJ
ejpam-5564	309	64	line	line	NOUN
ejpam-5564	309	65	with	with	ADP
ejpam-5564	309	66	respect	respect	NOUN
ejpam-5564	309	67	to	to	ADP
ejpam-5564	309	68	the	the	DET
ejpam-5564	309	69	oy	oy	NOUN
ejpam-5564	309	70	axis	axis	NOUN
ejpam-5564	309	71	,	,	PUNCT
ejpam-5564	309	72	which	which	PRON
ejpam-5564	309	73	completes	complete	VERB
ejpam-5564	309	74	the	the	DET
ejpam-5564	309	75	proof	proof	NOUN
ejpam-5564	309	76	of	of	ADP
ejpam-5564	309	77	the	the	DET
ejpam-5564	309	78	necessity	necessity	NOUN
ejpam-5564	309	79	.	.	PUNCT
ejpam-5564	310	1	sufficiency	sufficiency	PROPN
ejpam-5564	310	2	.	.	PUNCT
ejpam-5564	311	1	based	base	VERB
ejpam-5564	311	2	on	on	ADP
ejpam-5564	311	3	the	the	DET
ejpam-5564	311	4	theorem	theorem	NOUN
ejpam-5564	311	5	,	,	PUNCT
ejpam-5564	311	6	we	we	PRON
ejpam-5564	311	7	conclude	conclude	VERB
ejpam-5564	311	8	that	that	SCONJ
ejpam-5564	311	9	the	the	DET
ejpam-5564	311	10	imaginary	imaginary	ADJ
ejpam-5564	311	11	and	and	CCONJ
ejpam-5564	311	12	real	real	ADJ
ejpam-5564	311	13	parts	part	NOUN
ejpam-5564	311	14	of	of	ADP
ejpam-5564	311	15	the	the	DET
ejpam-5564	311	16	function	function	NOUN
ejpam-5564	311	17	u	u	NOUN
ejpam-5564	311	18	(	(	PUNCT
ejpam-5564	311	19	z	z	NOUN
ejpam-5564	311	20	)	)	PUNCT
ejpam-5564	311	21	are	be	AUX
ejpam-5564	311	22	continuous	continuous	ADJ
ejpam-5564	311	23	functions	function	NOUN
ejpam-5564	311	24	with	with	ADP
ejpam-5564	311	25	respect	respect	NOUN
ejpam-5564	311	26	to	to	ADP
ejpam-5564	311	27	their	their	PRON
ejpam-5564	311	28	arguments	argument	NOUN
ejpam-5564	311	29	in	in	ADP
ejpam-5564	311	30	some	some	DET
ejpam-5564	311	31	neighborhood	neighborhood	NOUN
ejpam-5564	311	32	of	of	ADP
ejpam-5564	311	33	the	the	DET
ejpam-5564	311	34	point	point	NOUN
ejpam-5564	311	35	z∗	z∗	NOUN
ejpam-5564	311	36	in	in	ADP
ejpam-5564	311	37	the	the	DET
ejpam-5564	311	38	phase	phase	NOUN
ejpam-5564	311	39	spaces	space	VERB
ejpam-5564	311	40	φ1	φ1	NOUN
ejpam-5564	311	41	and	and	CCONJ
ejpam-5564	311	42	φ2	φ2	PROPN
ejpam-5564	311	43	,	,	PUNCT
ejpam-5564	311	44	and	and	CCONJ
ejpam-5564	311	45	change	change	VERB
ejpam-5564	311	46	their	their	PRON
ejpam-5564	311	47	signs	sign	NOUN
ejpam-5564	311	48	when	when	SCONJ
ejpam-5564	311	49	crossing	cross	VERB
ejpam-5564	311	50	the	the	DET
ejpam-5564	311	51	point	point	NOUN
ejpam-5564	311	52	z∗	z∗	NOUN
ejpam-5564	311	53	(	(	PUNCT
ejpam-5564	311	54	x∗	x∗	PROPN
ejpam-5564	311	55	,	,	PUNCT
ejpam-5564	311	56	y∗	y∗	PROPN
ejpam-5564	311	57	)	)	PUNCT
ejpam-5564	311	58	,	,	PUNCT
ejpam-5564	311	59	moving	move	VERB
ejpam-5564	311	60	sequentially	sequentially	ADV
ejpam-5564	311	61	along	along	ADP
ejpam-5564	311	62	incorrect	incorrect	ADJ
ejpam-5564	311	63	lines	line	NOUN
ejpam-5564	311	64	l1	l1	PROPN
ejpam-5564	311	65	and	and	CCONJ
ejpam-5564	311	66	l2	l2	NOUN
ejpam-5564	311	67	in	in	ADP
ejpam-5564	311	68	the	the	DET
ejpam-5564	311	69	direction	direction	NOUN
ejpam-5564	311	70	of	of	ADP
ejpam-5564	311	71	the	the	DET
ejpam-5564	311	72	corresponding	corresponding	ADJ
ejpam-5564	311	73	axes	axis	NOUN
ejpam-5564	311	74	l1	l1	PROPN
ejpam-5564	311	75	,	,	PUNCT
ejpam-5564	311	76	l2	l2	NOUN
ejpam-5564	311	77	:	:	PUNCT
ejpam-5564	311	78	{	{	PUNCT
ejpam-5564	311	79	z∗	z∗	PROPN
ejpam-5564	311	80	∈	∈	PROPN
ejpam-5564	311	81	l1	l1	PROPN
ejpam-5564	311	82	⊂	⊂	PROPN
ejpam-5564	311	83	g	g	PROPN
ejpam-5564	311	84	,	,	PUNCT
ejpam-5564	311	85	z∗	z∗	PROPN
ejpam-5564	311	86	∈	∈	PROPN
ejpam-5564	311	87	l2	l2	NOUN
ejpam-5564	311	88	⊂	⊂	X
ejpam-5564	311	89	g	g	PROPN
ejpam-5564	311	90	,	,	PUNCT
ejpam-5564	311	91	l1	l1	PROPN
ejpam-5564	311	92	∈	∈	PROPN
ejpam-5564	311	93	φ1	φ1	PROPN
ejpam-5564	311	94	,	,	PUNCT
ejpam-5564	311	95	l2	l2	NOUN
ejpam-5564	311	96	∈	∈	PROPN
ejpam-5564	311	97	φ2	φ2	PROPN
ejpam-5564	311	98	}	}	PUNCT
ejpam-5564	311	99	.	.	PUNCT
ejpam-5564	312	1	utilizing	utilize	VERB
ejpam-5564	312	2	this	this	DET
ejpam-5564	312	3	fact	fact	NOUN
ejpam-5564	312	4	,	,	PUNCT
ejpam-5564	312	5	we	we	PRON
ejpam-5564	312	6	obtain	obtain	VERB
ejpam-5564	312	7	that	that	DET
ejpam-5564	312	8	u	u	NOUN
ejpam-5564	312	9	(	(	PUNCT
ejpam-5564	312	10	z∗	z∗	NOUN
ejpam-5564	312	11	)	)	PUNCT
ejpam-5564	312	12	=	=	SYM
ejpam-5564	312	13	0	0	NUM
ejpam-5564	312	14	,	,	PUNCT
ejpam-5564	312	15	and	and	CCONJ
ejpam-5564	312	16	the	the	DET
ejpam-5564	312	17	function	function	NOUN
ejpam-5564	312	18	w	w	PROPN
ejpam-5564	312	19	(	(	PUNCT
ejpam-5564	312	20	z	z	NOUN
ejpam-5564	312	21	)	)	PUNCT
ejpam-5564	312	22	=	=	SYM
ejpam-5564	313	1	p	p	X
ejpam-5564	313	2	(	(	PUNCT
ejpam-5564	313	3	x	x	NOUN
ejpam-5564	313	4	,	,	PUNCT
ejpam-5564	313	5	y	y	PROPN
ejpam-5564	313	6	)	)	PUNCT
ejpam-5564	314	1	+	+	CCONJ
ejpam-5564	314	2	iq	iq	INTJ
ejpam-5564	314	3	(	(	PUNCT
ejpam-5564	314	4	x	x	NOUN
ejpam-5564	314	5	,	,	PUNCT
ejpam-5564	314	6	y	y	PROPN
ejpam-5564	314	7	)	)	PUNCT
ejpam-5564	314	8	can	can	AUX
ejpam-5564	314	9	be	be	AUX
ejpam-5564	314	10	represented	represent	VERB
ejpam-5564	314	11	as	as	ADP
ejpam-5564	314	12	:	:	PUNCT
ejpam-5564	314	13	u	u	NOUN
ejpam-5564	314	14	(	(	PUNCT
ejpam-5564	314	15	z	z	NOUN
ejpam-5564	314	16	)	)	PUNCT
ejpam-5564	314	17	=	=	PUNCT
ejpam-5564	315	1	∑	∑	PUNCT
ejpam-5564	315	2	n≥0	n≥0	PROPN
ejpam-5564	315	3	ãn	ãn	PROPN
ejpam-5564	315	4	(	(	PUNCT
ejpam-5564	315	5	z	z	NOUN
ejpam-5564	315	6	∗	∗	NOUN
ejpam-5564	315	7	−	−	PROPN
ejpam-5564	315	8	z)n+1	z)n+1	PROPN
ejpam-5564	315	9	.	.	PUNCT
ejpam-5564	316	1	taking	take	VERB
ejpam-5564	316	2	into	into	ADP
ejpam-5564	316	3	account	account	NOUN
ejpam-5564	316	4	the	the	DET
ejpam-5564	316	5	introduced	introduce	VERB
ejpam-5564	316	6	substitution	substitution	NOUN
ejpam-5564	316	7	u	u	NOUN
ejpam-5564	316	8	(	(	PUNCT
ejpam-5564	316	9	z	z	NOUN
ejpam-5564	316	10	)	)	PUNCT
ejpam-5564	316	11	=	=	SYM
ejpam-5564	316	12	1	1	NUM
ejpam-5564	316	13	w(z	w(z	NOUN
ejpam-5564	316	14	)	)	PUNCT
ejpam-5564	316	15	,	,	PUNCT
ejpam-5564	316	16	we	we	PRON
ejpam-5564	316	17	get	get	VERB
ejpam-5564	316	18	w	w	ADP
ejpam-5564	316	19	(	(	PUNCT
ejpam-5564	316	20	z	z	NOUN
ejpam-5564	316	21	)	)	PUNCT
ejpam-5564	316	22	=	=	SYM
ejpam-5564	316	23	(	(	PUNCT
ejpam-5564	316	24	z∗	z∗	NOUN
ejpam-5564	316	25	−	−	PROPN
ejpam-5564	316	26	z)−1	z)−1	NUM
ejpam-5564	316	27	∑	∑	PROPN
ejpam-5564	316	28	n≥0	n≥0	PROPN
ejpam-5564	316	29	an	an	DET
ejpam-5564	316	30	(	(	PUNCT
ejpam-5564	316	31	z	z	NOUN
ejpam-5564	316	32	∗	∗	NOUN
ejpam-5564	316	33	−	−	PROPN
ejpam-5564	316	34	z)n	z)n	PUNCT
ejpam-5564	316	35	.	.	PUNCT
ejpam-5564	317	1	3	3	X
ejpam-5564	317	2	.	.	X
ejpam-5564	317	3	conclusion	conclusion	NOUN
ejpam-5564	317	4	in	in	ADP
ejpam-5564	317	5	this	this	DET
ejpam-5564	317	6	paper	paper	NOUN
ejpam-5564	317	7	,	,	PUNCT
ejpam-5564	317	8	we	we	PRON
ejpam-5564	317	9	considered	consider	VERB
ejpam-5564	317	10	a	a	DET
ejpam-5564	317	11	nonlinear	nonlinear	ADJ
ejpam-5564	317	12	fourth	fourth	ADJ
ejpam-5564	317	13	-	-	PUNCT
ejpam-5564	317	14	order	order	NOUN
ejpam-5564	317	15	differential	differential	ADJ
ejpam-5564	317	16	equation	equation	NOUN
ejpam-5564	317	17	with	with	ADP
ejpam-5564	317	18	a	a	DET
ejpam-5564	317	19	movable	movable	ADJ
ejpam-5564	317	20	singular	singular	ADJ
ejpam-5564	317	21	point	point	NOUN
ejpam-5564	317	22	of	of	ADP
ejpam-5564	317	23	algebraic	algebraic	ADJ
ejpam-5564	317	24	type	type	NOUN
ejpam-5564	317	25	.	.	PUNCT
ejpam-5564	318	1	the	the	DET
ejpam-5564	318	2	author	author	NOUN
ejpam-5564	318	3	proposed	propose	VERB
ejpam-5564	318	4	an	an	DET
ejpam-5564	318	5	analytical	analytical	ADJ
ejpam-5564	318	6	approximate	approximate	ADJ
ejpam-5564	318	7	solution	solution	NOUN
ejpam-5564	318	8	method	method	NOUN
ejpam-5564	318	9	based	base	VERB
ejpam-5564	318	10	on	on	ADP
ejpam-5564	318	11	splitting	split	VERB
ejpam-5564	318	12	the	the	DET
ejpam-5564	318	13	solution	solution	NOUN
ejpam-5564	318	14	search	search	NOUN
ejpam-5564	318	15	into	into	ADP
ejpam-5564	318	16	the	the	DET
ejpam-5564	318	17	area	area	NOUN
ejpam-5564	318	18	of	of	ADP
ejpam-5564	318	19	analyticity	analyticity	NOUN
ejpam-5564	318	20	and	and	CCONJ
ejpam-5564	318	21	the	the	DET
ejpam-5564	318	22	neighborhood	neighborhood	NOUN
ejpam-5564	318	23	of	of	ADP
ejpam-5564	318	24	a	a	DET
ejpam-5564	318	25	moving	move	VERB
ejpam-5564	318	26	singular	singular	ADJ
ejpam-5564	318	27	point	point	NOUN
ejpam-5564	318	28	.	.	PUNCT
ejpam-5564	319	1	in	in	ADP
ejpam-5564	319	2	this	this	DET
ejpam-5564	319	3	paper	paper	NOUN
ejpam-5564	319	4	,	,	PUNCT
ejpam-5564	319	5	the	the	DET
ejpam-5564	319	6	theorem	theorem	NOUN
ejpam-5564	319	7	of	of	ADP
ejpam-5564	319	8	existence	existence	NOUN
ejpam-5564	319	9	and	and	CCONJ
ejpam-5564	319	10	uniqueness	uniqueness	NOUN
ejpam-5564	319	11	in	in	ADP
ejpam-5564	319	12	the	the	DET
ejpam-5564	319	13	vicinity	vicinity	NOUN
ejpam-5564	319	14	of	of	ADP
ejpam-5564	319	15	a	a	DET
ejpam-5564	319	16	moving	move	VERB
ejpam-5564	319	17	singular	singular	ADJ
ejpam-5564	319	18	point	point	NOUN
ejpam-5564	319	19	was	be	AUX
ejpam-5564	319	20	formulated	formulate	VERB
ejpam-5564	319	21	and	and	CCONJ
ejpam-5564	319	22	proved	prove	VERB
ejpam-5564	319	23	.	.	PUNCT
ejpam-5564	320	1	the	the	DET
ejpam-5564	320	2	solution	solution	NOUN
ejpam-5564	320	3	obtained	obtain	VERB
ejpam-5564	320	4	during	during	ADP
ejpam-5564	320	5	the	the	DET
ejpam-5564	320	6	proof	proof	NOUN
ejpam-5564	320	7	has	have	VERB
ejpam-5564	320	8	a	a	DET
ejpam-5564	320	9	simple	simple	ADJ
ejpam-5564	320	10	pole	pole	NOUN
ejpam-5564	320	11	at	at	ADP
ejpam-5564	320	12	the	the	DET
ejpam-5564	320	13	point	point	NOUN
ejpam-5564	320	14	z∗.	z∗.	NOUN
ejpam-5564	320	15	using	use	VERB
ejpam-5564	320	16	the	the	DET
ejpam-5564	320	17	modified	modify	VERB
ejpam-5564	320	18	majorant	majorant	NOUN
ejpam-5564	320	19	method	method	NOUN
ejpam-5564	320	20	,	,	PUNCT
ejpam-5564	320	21	estimates	estimate	NOUN
ejpam-5564	320	22	for	for	ADP
ejpam-5564	320	23	the	the	DET
ejpam-5564	320	24	coefficients	coefficient	NOUN
ejpam-5564	320	25	were	be	AUX
ejpam-5564	320	26	obtained	obtain	VERB
ejpam-5564	320	27	,	,	PUNCT
ejpam-5564	320	28	and	and	CCONJ
ejpam-5564	320	29	as	as	ADP
ejpam-5564	320	30	a	a	DET
ejpam-5564	320	31	result	result	NOUN
ejpam-5564	320	32	,	,	PUNCT
ejpam-5564	320	33	the	the	DET
ejpam-5564	320	34	convergence	convergence	NOUN
ejpam-5564	320	35	domain	domain	NOUN
ejpam-5564	320	36	of	of	ADP
ejpam-5564	320	37	the	the	DET
ejpam-5564	320	38	solution	solution	NOUN
ejpam-5564	320	39	under	under	ADP
ejpam-5564	320	40	consideration	consideration	NOUN
ejpam-5564	320	41	.	.	PUNCT
ejpam-5564	321	1	the	the	DET
ejpam-5564	321	2	second	second	ADJ
ejpam-5564	321	3	task	task	NOUN
ejpam-5564	321	4	of	of	ADP
ejpam-5564	321	5	the	the	DET
ejpam-5564	321	6	study	study	NOUN
ejpam-5564	321	7	was	be	AUX
ejpam-5564	321	8	to	to	PART
ejpam-5564	321	9	formulate	formulate	VERB
ejpam-5564	321	10	the	the	DET
ejpam-5564	321	11	necessary	necessary	ADJ
ejpam-5564	321	12	,	,	PUNCT
ejpam-5564	321	13	as	as	ADV
ejpam-5564	321	14	well	well	ADV
ejpam-5564	321	15	as	as	ADP
ejpam-5564	321	16	necessary	necessary	ADJ
ejpam-5564	321	17	and	and	CCONJ
ejpam-5564	321	18	sufficient	sufficient	ADJ
ejpam-5564	321	19	conditions	condition	NOUN
ejpam-5564	321	20	for	for	ADP
ejpam-5564	321	21	the	the	DET
ejpam-5564	321	22	existence	existence	NOUN
ejpam-5564	321	23	of	of	ADP
ejpam-5564	321	24	a	a	DET
ejpam-5564	321	25	mobile	mobile	ADJ
ejpam-5564	321	26	singular	singular	ADJ
ejpam-5564	321	27	point	point	NOUN
ejpam-5564	321	28	in	in	ADP
ejpam-5564	321	29	both	both	CCONJ
ejpam-5564	321	30	the	the	DET
ejpam-5564	321	31	real	real	ADJ
ejpam-5564	321	32	and	and	CCONJ
ejpam-5564	321	33	complex	complex	ADJ
ejpam-5564	321	34	domains	domain	NOUN
ejpam-5564	321	35	.	.	PUNCT
ejpam-5564	322	1	the	the	DET
ejpam-5564	322	2	main	main	ADJ
ejpam-5564	322	3	idea	idea	NOUN
ejpam-5564	322	4	of	of	ADP
ejpam-5564	322	5	solving	solve	VERB
ejpam-5564	322	6	this	this	DET
ejpam-5564	322	7	problem	problem	NOUN
ejpam-5564	322	8	was	be	AUX
ejpam-5564	322	9	the	the	DET
ejpam-5564	322	10	regularization	regularization	NOUN
ejpam-5564	322	11	of	of	ADP
ejpam-5564	322	12	a	a	DET
ejpam-5564	322	13	moving	move	VERB
ejpam-5564	322	14	singular	singular	ADJ
ejpam-5564	322	15	point	point	NOUN
ejpam-5564	322	16	.	.	PUNCT
ejpam-5564	323	1	the	the	DET
ejpam-5564	323	2	theoretical	theoretical	ADJ
ejpam-5564	323	3	results	result	NOUN
ejpam-5564	323	4	were	be	AUX
ejpam-5564	323	5	tested	test	VERB
ejpam-5564	323	6	in	in	ADP
ejpam-5564	323	7	a	a	DET
ejpam-5564	323	8	numerical	numerical	ADJ
ejpam-5564	323	9	experiment	experiment	NOUN
ejpam-5564	323	10	.	.	PUNCT
ejpam-5564	324	1	the	the	DET
ejpam-5564	324	2	results	result	NOUN
ejpam-5564	324	3	of	of	ADP
ejpam-5564	324	4	the	the	DET
ejpam-5564	324	5	numerical	numerical	ADJ
ejpam-5564	324	6	experiment	experiment	NOUN
ejpam-5564	324	7	were	be	AUX
ejpam-5564	324	8	compared	compare	VERB
ejpam-5564	324	9	with	with	ADP
ejpam-5564	324	10	existing	existing	ADJ
ejpam-5564	324	11	numerical	numerical	ADJ
ejpam-5564	324	12	methods	method	NOUN
ejpam-5564	324	13	.	.	PUNCT
ejpam-5564	325	1	the	the	DET
ejpam-5564	325	2	analytical	analytical	ADJ
ejpam-5564	325	3	approximate	approximate	ADJ
ejpam-5564	325	4	method	method	NOUN
ejpam-5564	325	5	used	use	VERB
ejpam-5564	325	6	by	by	ADP
ejpam-5564	325	7	the	the	DET
ejpam-5564	325	8	author	author	NOUN
ejpam-5564	325	9	can	can	AUX
ejpam-5564	325	10	be	be	AUX
ejpam-5564	325	11	applied	apply	VERB
ejpam-5564	325	12	to	to	ADP
ejpam-5564	325	13	other	other	ADJ
ejpam-5564	325	14	classes	class	NOUN
ejpam-5564	325	15	of	of	ADP
ejpam-5564	325	16	equations	equation	NOUN
ejpam-5564	325	17	,	,	PUNCT
ejpam-5564	325	18	as	as	SCONJ
ejpam-5564	325	19	it	it	PRON
ejpam-5564	325	20	was	be	AUX
ejpam-5564	325	21	previously	previously	ADV
ejpam-5564	325	22	indicated	indicate	VERB
ejpam-5564	325	23	in	in	ADP
ejpam-5564	325	24	the	the	DET
ejpam-5564	325	25	introduction	introduction	NOUN
ejpam-5564	325	26	.	.	PUNCT
ejpam-5564	326	1	this	this	DET
ejpam-5564	326	2	method	method	NOUN
ejpam-5564	326	3	complements	complement	VERB
ejpam-5564	326	4	the	the	DET
ejpam-5564	326	5	existing	exist	VERB
ejpam-5564	326	6	methods	method	NOUN
ejpam-5564	326	7	for	for	ADP
ejpam-5564	326	8	solving	solve	VERB
ejpam-5564	326	9	nonlinear	nonlinear	ADJ
ejpam-5564	326	10	differential	differential	ADJ
ejpam-5564	326	11	equations	equation	NOUN
ejpam-5564	326	12	,	,	PUNCT
ejpam-5564	326	13	such	such	ADJ
ejpam-5564	326	14	as	as	ADP
ejpam-5564	326	15	asymptotic	asymptotic	ADJ
ejpam-5564	326	16	,	,	PUNCT
ejpam-5564	326	17	exact	exact	ADJ
ejpam-5564	326	18	methods	method	NOUN
ejpam-5564	326	19	and	and	CCONJ
ejpam-5564	326	20	others	other	NOUN
ejpam-5564	326	21	.	.	PUNCT
ejpam-5564	327	1	this	this	DET
ejpam-5564	327	2	work	work	NOUN
ejpam-5564	327	3	can	can	AUX
ejpam-5564	327	4	be	be	AUX
ejpam-5564	327	5	utilized	utilize	VERB
ejpam-5564	327	6	to	to	PART
ejpam-5564	327	7	formulate	formulate	VERB
ejpam-5564	327	8	an	an	DET
ejpam-5564	327	9	algorithm	algorithm	NOUN
ejpam-5564	327	10	for	for	ADP
ejpam-5564	327	11	finding	find	VERB
ejpam-5564	327	12	a	a	DET
ejpam-5564	327	13	movable	movable	ADJ
ejpam-5564	327	14	singular	singular	NOUN
ejpam-5564	327	15	point	point	NOUN
ejpam-5564	327	16	with	with	ADP
ejpam-5564	327	17	a	a	DET
ejpam-5564	327	18	specified	specified	ADJ
ejpam-5564	327	19	accuracy	accuracy	NOUN
ejpam-5564	327	20	,	,	PUNCT
ejpam-5564	327	21	by	by	ADP
ejpam-5564	327	22	combining	combine	VERB
ejpam-5564	327	23	the	the	DET
ejpam-5564	327	24	obtained	obtain	VERB
ejpam-5564	327	25	results	result	NOUN
ejpam-5564	327	26	with	with	ADP
ejpam-5564	327	27	numerical	numerical	ADJ
ejpam-5564	327	28	methods	method	NOUN
ejpam-5564	327	29	[	[	X
ejpam-5564	327	30	35	35	NUM
ejpam-5564	327	31	]	]	PUNCT
ejpam-5564	327	32	.	.	PUNCT
ejpam-5564	328	1	m.	m.	NOUN
ejpam-5564	328	2	gasanov	gasanov	PROPN
ejpam-5564	328	3	/	/	SYM
ejpam-5564	328	4	eur	eur	PROPN
ejpam-5564	328	5	.	.	PUNCT
ejpam-5564	329	1	j.	j.	PROPN
ejpam-5564	329	2	pure	pure	PROPN
ejpam-5564	329	3	appl	appl	PROPN
ejpam-5564	329	4	.	.	PROPN
ejpam-5564	329	5	math	math	PROPN
ejpam-5564	329	6	,	,	PUNCT
ejpam-5564	329	7	18	18	NUM
ejpam-5564	329	8	(	(	PUNCT
ejpam-5564	329	9	1	1	NUM
ejpam-5564	329	10	)	)	PUNCT
ejpam-5564	329	11	(	(	PUNCT
ejpam-5564	329	12	2025	2025	NUM
ejpam-5564	329	13	)	)	PUNCT
ejpam-5564	329	14	,	,	PUNCT
ejpam-5564	329	15	5564	5564	NUM
ejpam-5564	329	16	16	16	NUM
ejpam-5564	329	17	of	of	ADP
ejpam-5564	329	18	19	19	NUM
ejpam-5564	329	19	references	reference	NOUN
ejpam-5564	329	20	[	[	X
ejpam-5564	329	21	1	1	NUM
ejpam-5564	329	22	]	]	PUNCT
ejpam-5564	329	23	i.	i.	PROPN
ejpam-5564	329	24	astashova	astashova	PROPN
ejpam-5564	329	25	.	.	PUNCT
ejpam-5564	330	1	on	on	ADP
ejpam-5564	330	2	asymptotic	asymptotic	ADJ
ejpam-5564	330	3	classification	classification	NOUN
ejpam-5564	330	4	of	of	ADP
ejpam-5564	330	5	solutions	solution	NOUN
ejpam-5564	330	6	to	to	PART
ejpam-5564	330	7	nonlinear	nonlinear	VERB
ejpam-5564	330	8	regular	regular	ADJ
ejpam-5564	330	9	and	and	CCONJ
ejpam-5564	330	10	singular	singular	ADJ
ejpam-5564	330	11	thirdand	thirdand	NOUN
ejpam-5564	330	12	fourth	fourth	ADJ
ejpam-5564	330	13	-	-	PUNCT
ejpam-5564	330	14	order	order	NOUN
ejpam-5564	330	15	differential	differential	ADJ
ejpam-5564	330	16	equations	equation	NOUN
ejpam-5564	330	17	with	with	ADP
ejpam-5564	330	18	power	power	NOUN
ejpam-5564	330	19	nonlinearity	nonlinearity	NOUN
ejpam-5564	330	20	.	.	PUNCT
ejpam-5564	331	1	springer	springer	NOUN
ejpam-5564	331	2	proceedings	proceeding	NOUN
ejpam-5564	331	3	in	in	ADP
ejpam-5564	331	4	mathematics	mathematics	PROPN
ejpam-5564	331	5	&	&	CCONJ
ejpam-5564	331	6	statistics	statistic	NOUN
ejpam-5564	331	7	,	,	PUNCT
ejpam-5564	331	8	page	page	NOUN
ejpam-5564	331	9	191–203	191–203	NUM
ejpam-5564	331	10	,	,	PUNCT
ejpam-5564	331	11	2016	2016	NUM
ejpam-5564	331	12	.	.	PUNCT
ejpam-5564	332	1	[	[	X
ejpam-5564	332	2	2	2	NUM
ejpam-5564	332	3	]	]	PUNCT
ejpam-5564	332	4	i.	i.	PROPN
ejpam-5564	332	5	astashova	astashova	PROPN
ejpam-5564	332	6	,	,	PUNCT
ejpam-5564	332	7	m.	m.	NOUN
ejpam-5564	332	8	bartušek	bartušek	PROPN
ejpam-5564	332	9	,	,	PUNCT
ejpam-5564	332	10	z.	z.	PROPN
ejpam-5564	332	11	došlá	došlá	PROPN
ejpam-5564	332	12	,	,	PUNCT
ejpam-5564	332	13	and	and	CCONJ
ejpam-5564	332	14	m.	m.	NOUN
ejpam-5564	332	15	marini	marini	PROPN
ejpam-5564	332	16	.	.	PUNCT
ejpam-5564	333	1	asymptotic	asymptotic	ADJ
ejpam-5564	333	2	proximity	proximity	NOUN
ejpam-5564	333	3	to	to	ADP
ejpam-5564	333	4	higher	high	ADJ
ejpam-5564	333	5	order	order	NOUN
ejpam-5564	333	6	nonlinear	nonlinear	ADJ
ejpam-5564	333	7	differential	differential	ADJ
ejpam-5564	333	8	equations	equation	NOUN
ejpam-5564	333	9	.	.	PUNCT
ejpam-5564	334	1	advances	advance	NOUN
ejpam-5564	334	2	in	in	ADP
ejpam-5564	334	3	nonlinear	nonlinear	ADJ
ejpam-5564	334	4	analysis	analysis	NOUN
ejpam-5564	334	5	,	,	PUNCT
ejpam-5564	334	6	pages	page	NOUN
ejpam-5564	334	7	1598	1598	NUM
ejpam-5564	334	8	–	–	PUNCT
ejpam-5564	334	9	1613	1613	NUM
ejpam-5564	334	10	,	,	PUNCT
ejpam-5564	334	11	2022	2022	NUM
ejpam-5564	334	12	.	.	PUNCT
ejpam-5564	335	1	[	[	X
ejpam-5564	335	2	3	3	X
ejpam-5564	335	3	]	]	X
ejpam-5564	335	4	e.	e.	PROPN
ejpam-5564	335	5	az	az	PROPN
ejpam-5564	335	6	-	-	PROPN
ejpam-5564	335	7	zo’bi	zo’bi	PROPN
ejpam-5564	335	8	,	,	PUNCT
ejpam-5564	335	9	k.	k.	PROPN
ejpam-5564	335	10	al	al	PROPN
ejpam-5564	335	11	-	-	PUNCT
ejpam-5564	335	12	khaled	khaled	PROPN
ejpam-5564	335	13	,	,	PUNCT
ejpam-5564	335	14	and	and	CCONJ
ejpam-5564	335	15	a.	a.	NOUN
ejpam-5564	335	16	darweesh	darweesh	NOUN
ejpam-5564	335	17	.	.	PUNCT
ejpam-5564	336	1	numeric	numeric	ADJ
ejpam-5564	336	2	-	-	PUNCT
ejpam-5564	336	3	analytic	analytic	ADJ
ejpam-5564	336	4	solutions	solution	NOUN
ejpam-5564	336	5	for	for	ADP
ejpam-5564	336	6	nonlinear	nonlinear	ADJ
ejpam-5564	336	7	oscillators	oscillator	NOUN
ejpam-5564	336	8	via	via	ADP
ejpam-5564	336	9	the	the	DET
ejpam-5564	336	10	modified	modify	VERB
ejpam-5564	336	11	multi	multi	ADJ
ejpam-5564	336	12	-	-	ADJ
ejpam-5564	336	13	stage	stage	NOUN
ejpam-5564	336	14	decomposition	decomposition	NOUN
ejpam-5564	336	15	method	method	NOUN
ejpam-5564	336	16	.	.	PUNCT
ejpam-5564	337	1	mathematics	mathematic	NOUN
ejpam-5564	337	2	,	,	PUNCT
ejpam-5564	337	3	2019	2019	NUM
ejpam-5564	337	4	.	.	PUNCT
ejpam-5564	338	1	[	[	X
ejpam-5564	338	2	4	4	NUM
ejpam-5564	338	3	]	]	X
ejpam-5564	338	4	f.	f.	PROPN
ejpam-5564	338	5	bernal	bernal	PROPN
ejpam-5564	338	6	-	-	PUNCT
ejpam-5564	338	7	vı́lchis	vı́lchis	PROPN
ejpam-5564	338	8	,	,	PUNCT
ejpam-5564	338	9	n.	n.	PROPN
ejpam-5564	338	10	hayashi	hayashi	PROPN
ejpam-5564	338	11	,	,	PUNCT
ejpam-5564	338	12	and	and	CCONJ
ejpam-5564	338	13	p.	p.	NOUN
ejpam-5564	338	14	naumkin	naumkin	PROPN
ejpam-5564	338	15	.	.	PUNCT
ejpam-5564	339	1	quadratic	quadratic	ADJ
ejpam-5564	339	2	derivative	derivative	ADJ
ejpam-5564	339	3	nonlinear	nonlinear	NOUN
ejpam-5564	339	4	schrödinger	schrödinger	NOUN
ejpam-5564	339	5	equations	equation	NOUN
ejpam-5564	339	6	in	in	ADP
ejpam-5564	339	7	two	two	NUM
ejpam-5564	339	8	space	space	NOUN
ejpam-5564	339	9	dimensions	dimension	NOUN
ejpam-5564	339	10	.	.	PUNCT
ejpam-5564	340	1	nonlinear	nonlinear	ADJ
ejpam-5564	340	2	differential	differential	ADJ
ejpam-5564	340	3	equations	equation	NOUN
ejpam-5564	340	4	and	and	CCONJ
ejpam-5564	340	5	applications	application	NOUN
ejpam-5564	340	6	,	,	PUNCT
ejpam-5564	340	7	18:329–355	18:329–355	NUM
ejpam-5564	340	8	,	,	PUNCT
ejpam-5564	340	9	2011	2011	NUM
ejpam-5564	340	10	.	.	PUNCT
ejpam-5564	341	1	[	[	X
ejpam-5564	341	2	5	5	X
ejpam-5564	341	3	]	]	X
ejpam-5564	341	4	g.	g.	PROPN
ejpam-5564	341	5	bonanno	bonanno	PROPN
ejpam-5564	341	6	and	and	CCONJ
ejpam-5564	341	7	b.	b.	PROPN
ejpam-5564	341	8	di	di	PROPN
ejpam-5564	341	9	bella	bella	PROPN
ejpam-5564	341	10	.	.	PUNCT
ejpam-5564	342	1	a	a	DET
ejpam-5564	342	2	boundary	boundary	ADJ
ejpam-5564	342	3	value	value	NOUN
ejpam-5564	342	4	problem	problem	NOUN
ejpam-5564	342	5	for	for	ADP
ejpam-5564	342	6	fourth	fourth	ADJ
ejpam-5564	342	7	-	-	PUNCT
ejpam-5564	342	8	order	order	NOUN
ejpam-5564	342	9	elastic	elastic	ADJ
ejpam-5564	342	10	beam	beam	NOUN
ejpam-5564	342	11	equations	equation	NOUN
ejpam-5564	342	12	.	.	PUNCT
ejpam-5564	343	1	journal	journal	PROPN
ejpam-5564	343	2	of	of	ADP
ejpam-5564	343	3	mathematical	mathematical	ADJ
ejpam-5564	343	4	analysis	analysis	NOUN
ejpam-5564	343	5	and	and	CCONJ
ejpam-5564	343	6	applications	application	NOUN
ejpam-5564	343	7	,	,	PUNCT
ejpam-5564	343	8	55:1166–1176	55:1166–1176	NUM
ejpam-5564	343	9	,	,	PUNCT
ejpam-5564	343	10	2008	2008	NUM
ejpam-5564	343	11	.	.	PUNCT
ejpam-5564	344	1	[	[	X
ejpam-5564	344	2	6	6	NUM
ejpam-5564	344	3	]	]	X
ejpam-5564	344	4	g.	g.	PROPN
ejpam-5564	344	5	bonanno	bonanno	PROPN
ejpam-5564	344	6	,	,	PUNCT
ejpam-5564	344	7	b.	b.	PROPN
ejpam-5564	344	8	di	di	PROPN
ejpam-5564	344	9	bella	bella	PROPN
ejpam-5564	344	10	,	,	PUNCT
ejpam-5564	344	11	and	and	CCONJ
ejpam-5564	344	12	d.	d.	PROPN
ejpam-5564	344	13	o’regan	o’regan	PROPN
ejpam-5564	344	14	.	.	PUNCT
ejpam-5564	345	1	non	non	ADJ
ejpam-5564	345	2	-	-	ADJ
ejpam-5564	345	3	trivial	trivial	ADJ
ejpam-5564	345	4	solutions	solution	NOUN
ejpam-5564	345	5	for	for	ADP
ejpam-5564	345	6	nonlinear	nonlinear	ADJ
ejpam-5564	345	7	fourthorder	fourthorder	NOUN
ejpam-5564	345	8	elastic	elastic	ADJ
ejpam-5564	345	9	beam	beam	NOUN
ejpam-5564	345	10	equations	equation	NOUN
ejpam-5564	345	11	.	.	PUNCT
ejpam-5564	346	1	computers	computer	NOUN
ejpam-5564	346	2	&	&	CCONJ
ejpam-5564	346	3	mathematics	mathematics	PROPN
ejpam-5564	346	4	with	with	ADP
ejpam-5564	346	5	applications	application	NOUN
ejpam-5564	346	6	,	,	PUNCT
ejpam-5564	346	7	page	page	NOUN
ejpam-5564	346	8	1862–1869	1862–1869	NUM
ejpam-5564	346	9	,	,	PUNCT
ejpam-5564	346	10	2011	2011	NUM
ejpam-5564	346	11	.	.	PUNCT
ejpam-5564	347	1	[	[	X
ejpam-5564	347	2	7	7	X
ejpam-5564	347	3	]	]	X
ejpam-5564	347	4	v.	v.	ADP
ejpam-5564	347	5	chandrasekar	chandrasekar	PROPN
ejpam-5564	347	6	,	,	PUNCT
ejpam-5564	347	7	m.	m.	NOUN
ejpam-5564	347	8	senthilvelan	senthilvelan	PROPN
ejpam-5564	347	9	,	,	PUNCT
ejpam-5564	347	10	and	and	CCONJ
ejpam-5564	347	11	m.	m.	PROPN
ejpam-5564	347	12	lakshmanan	lakshmanan	PROPN
ejpam-5564	347	13	.	.	PUNCT
ejpam-5564	348	1	on	on	ADP
ejpam-5564	348	2	the	the	DET
ejpam-5564	348	3	complete	complete	ADJ
ejpam-5564	348	4	integrability	integrability	NOUN
ejpam-5564	348	5	and	and	CCONJ
ejpam-5564	348	6	linearization	linearization	NOUN
ejpam-5564	348	7	of	of	ADP
ejpam-5564	348	8	certain	certain	ADJ
ejpam-5564	348	9	second	second	ADJ
ejpam-5564	348	10	-	-	PUNCT
ejpam-5564	348	11	order	order	NOUN
ejpam-5564	348	12	nonlinear	nonlinear	ADJ
ejpam-5564	348	13	ordinary	ordinary	ADJ
ejpam-5564	348	14	differential	differential	ADJ
ejpam-5564	348	15	equations	equation	NOUN
ejpam-5564	348	16	.	.	PUNCT
ejpam-5564	349	1	proceedings	proceeding	NOUN
ejpam-5564	349	2	of	of	ADP
ejpam-5564	349	3	the	the	DET
ejpam-5564	349	4	royal	royal	ADJ
ejpam-5564	349	5	society	society	NOUN
ejpam-5564	349	6	a	a	DET
ejpam-5564	349	7	:	:	PUNCT
ejpam-5564	349	8	mathematical	mathematical	ADJ
ejpam-5564	349	9	,	,	PUNCT
ejpam-5564	349	10	physical	physical	ADJ
ejpam-5564	349	11	and	and	CCONJ
ejpam-5564	349	12	engineering	engineering	NOUN
ejpam-5564	349	13	sciences	science	NOUN
ejpam-5564	349	14	,	,	PUNCT
ejpam-5564	349	15	page	page	NOUN
ejpam-5564	349	16	2451–2477	2451–2477	NUM
ejpam-5564	349	17	,	,	PUNCT
ejpam-5564	349	18	2005	2005	NUM
ejpam-5564	349	19	.	.	PUNCT
ejpam-5564	350	1	[	[	X
ejpam-5564	350	2	8	8	NUM
ejpam-5564	350	3	]	]	X
ejpam-5564	350	4	w.	w.	PROPN
ejpam-5564	350	5	durand	durand	PROPN
ejpam-5564	350	6	.	.	PUNCT
ejpam-5564	351	1	aerodynamic	aerodynamic	ADJ
ejpam-5564	351	2	theory	theory	NOUN
ejpam-5564	351	3	.	.	PUNCT
ejpam-5564	352	1	springer	springer	NOUN
ejpam-5564	352	2	,	,	PUNCT
ejpam-5564	352	3	2013	2013	NUM
ejpam-5564	352	4	.	.	PUNCT
ejpam-5564	353	1	[	[	X
ejpam-5564	353	2	9	9	NUM
ejpam-5564	353	3	]	]	PUNCT
ejpam-5564	353	4	m.	m.	NOUN
ejpam-5564	353	5	galewski	galewski	PROPN
ejpam-5564	353	6	.	.	PUNCT
ejpam-5564	354	1	on	on	ADP
ejpam-5564	354	2	the	the	DET
ejpam-5564	354	3	nonlinear	nonlinear	ADJ
ejpam-5564	354	4	elastic	elastic	NOUN
ejpam-5564	354	5	simply	simply	ADV
ejpam-5564	354	6	supported	support	VERB
ejpam-5564	354	7	beam	beam	NOUN
ejpam-5564	354	8	equation	equation	NOUN
ejpam-5564	354	9	.	.	PUNCT
ejpam-5564	355	1	analele	analele	ADP
ejpam-5564	355	2	stiintifice	stiintifice	PROPN
ejpam-5564	355	3	ale	ale	PROPN
ejpam-5564	355	4	universitatii	universitatii	PROPN
ejpam-5564	355	5	ovidius	ovidius	PROPN
ejpam-5564	355	6	constanta	constanta	PROPN
ejpam-5564	355	7	,	,	PUNCT
ejpam-5564	355	8	seria	seria	PROPN
ejpam-5564	355	9	matematica	matematica	PROPN
ejpam-5564	355	10	,	,	PUNCT
ejpam-5564	355	11	page	page	NOUN
ejpam-5564	355	12	109–120	109–120	NUM
ejpam-5564	355	13	,	,	PUNCT
ejpam-5564	355	14	2011	2011	NUM
ejpam-5564	355	15	.	.	PUNCT
ejpam-5564	356	1	[	[	X
ejpam-5564	356	2	10	10	NUM
ejpam-5564	356	3	]	]	PUNCT
ejpam-5564	356	4	m.	m.	NOUN
ejpam-5564	356	5	galewski	galewski	PROPN
ejpam-5564	356	6	and	and	CCONJ
ejpam-5564	356	7	j.	j.	PROPN
ejpam-5564	356	8	smejda	smejda	PROPN
ejpam-5564	356	9	.	.	PUNCT
ejpam-5564	357	1	a	a	DET
ejpam-5564	357	2	note	note	NOUN
ejpam-5564	357	3	on	on	ADP
ejpam-5564	357	4	a	a	DET
ejpam-5564	357	5	fourth	fourth	ADJ
ejpam-5564	357	6	order	order	NOUN
ejpam-5564	357	7	discrete	discrete	ADJ
ejpam-5564	357	8	boundary	boundary	ADJ
ejpam-5564	357	9	value	value	NOUN
ejpam-5564	357	10	problem	problem	NOUN
ejpam-5564	357	11	.	.	PUNCT
ejpam-5564	358	1	opuscula	opuscula	PROPN
ejpam-5564	358	2	mathematica	mathematica	PROPN
ejpam-5564	358	3	,	,	PUNCT
ejpam-5564	358	4	pages	page	NOUN
ejpam-5564	358	5	115–123	115–123	NUM
ejpam-5564	358	6	,	,	PUNCT
ejpam-5564	358	7	2012	2012	NUM
ejpam-5564	358	8	.	.	PUNCT
ejpam-5564	359	1	[	[	X
ejpam-5564	359	2	11	11	NUM
ejpam-5564	359	3	]	]	X
ejpam-5564	359	4	v.	v.	CCONJ
ejpam-5564	359	5	golubev	golubev	PROPN
ejpam-5564	359	6	.	.	PUNCT
ejpam-5564	360	1	lectures	lecture	NOUN
ejpam-5564	360	2	on	on	ADP
ejpam-5564	360	3	analytical	analytical	ADJ
ejpam-5564	360	4	theory	theory	NOUN
ejpam-5564	360	5	of	of	ADP
ejpam-5564	360	6	differential	differential	ADJ
ejpam-5564	360	7	equations	equation	NOUN
ejpam-5564	360	8	.	.	PUNCT
ejpam-5564	361	1	gostekhizdat	gostekhizdat	NOUN
ejpam-5564	361	2	,	,	PUNCT
ejpam-5564	361	3	moscow	moscow	PROPN
ejpam-5564	361	4	,	,	PUNCT
ejpam-5564	361	5	1950	1950	NUM
ejpam-5564	361	6	.	.	PUNCT
ejpam-5564	362	1	[	[	X
ejpam-5564	362	2	12	12	NUM
ejpam-5564	362	3	]	]	X
ejpam-5564	362	4	v.	v.	CCONJ
ejpam-5564	362	5	grigoryan	grigoryan	NOUN
ejpam-5564	362	6	and	and	CCONJ
ejpam-5564	362	7	a.	a.	NOUN
ejpam-5564	362	8	tanguay	tanguay	PROPN
ejpam-5564	362	9	.	.	PUNCT
ejpam-5564	363	1	improved	improve	VERB
ejpam-5564	363	2	well	well	ADV
ejpam-5564	363	3	-	-	PUNCT
ejpam-5564	363	4	posedness	posedness	NOUN
ejpam-5564	363	5	for	for	ADP
ejpam-5564	363	6	the	the	DET
ejpam-5564	363	7	quadratic	quadratic	ADJ
ejpam-5564	363	8	derivative	derivative	ADJ
ejpam-5564	363	9	nonlinear	nonlinear	ADJ
ejpam-5564	363	10	wave	wave	NOUN
ejpam-5564	363	11	equation	equation	NOUN
ejpam-5564	363	12	in	in	ADP
ejpam-5564	363	13	2d	2d	NOUN
ejpam-5564	363	14	.	.	PUNCT
ejpam-5564	364	1	journal	journal	PROPN
ejpam-5564	364	2	of	of	ADP
ejpam-5564	364	3	mathematical	mathematical	ADJ
ejpam-5564	364	4	analysis	analysis	NOUN
ejpam-5564	364	5	and	and	CCONJ
ejpam-5564	364	6	applications	application	NOUN
ejpam-5564	364	7	,	,	PUNCT
ejpam-5564	364	8	475	475	NUM
ejpam-5564	364	9	,	,	PUNCT
ejpam-5564	364	10	2019	2019	NUM
ejpam-5564	364	11	.	.	PUNCT
ejpam-5564	365	1	[	[	X
ejpam-5564	365	2	13	13	NUM
ejpam-5564	365	3	]	]	PUNCT
ejpam-5564	365	4	t.	t.	PROPN
ejpam-5564	365	5	harkó	harkó	PROPN
ejpam-5564	365	6	,	,	PUNCT
ejpam-5564	365	7	s.	s.	PROPN
ejpam-5564	365	8	lobo	lobo	PROPN
ejpam-5564	365	9	,	,	PUNCT
ejpam-5564	365	10	and	and	CCONJ
ejpam-5564	365	11	m.	m.	PROPN
ejpam-5564	365	12	mak	mak	PROPN
ejpam-5564	365	13	.	.	PUNCT
ejpam-5564	366	1	a	a	DET
ejpam-5564	366	2	class	class	NOUN
ejpam-5564	366	3	of	of	ADP
ejpam-5564	366	4	exact	exact	ADJ
ejpam-5564	366	5	solutions	solution	NOUN
ejpam-5564	366	6	of	of	ADP
ejpam-5564	366	7	the	the	DET
ejpam-5564	366	8	liénard	liénard	NOUN
ejpam-5564	366	9	-	-	PUNCT
ejpam-5564	366	10	type	type	NOUN
ejpam-5564	366	11	ordinary	ordinary	ADJ
ejpam-5564	366	12	nonlinear	nonlinear	ADJ
ejpam-5564	366	13	differential	differential	ADJ
ejpam-5564	366	14	equation	equation	NOUN
ejpam-5564	366	15	.	.	PUNCT
ejpam-5564	367	1	journal	journal	NOUN
ejpam-5564	367	2	of	of	ADP
ejpam-5564	367	3	engineering	engineering	NOUN
ejpam-5564	367	4	mathematics	mathematic	NOUN
ejpam-5564	367	5	,	,	PUNCT
ejpam-5564	367	6	page	page	NOUN
ejpam-5564	367	7	193–205	193–205	NUM
ejpam-5564	367	8	,	,	PUNCT
ejpam-5564	367	9	2014	2014	NUM
ejpam-5564	367	10	.	.	PUNCT
ejpam-5564	368	1	[	[	X
ejpam-5564	368	2	14	14	NUM
ejpam-5564	368	3	]	]	X
ejpam-5564	368	4	h.	h.	PROPN
ejpam-5564	368	5	hirayama	hirayama	PROPN
ejpam-5564	368	6	,	,	PUNCT
ejpam-5564	368	7	s.	s.	PROPN
ejpam-5564	368	8	kinoshita	kinoshita	PROPN
ejpam-5564	368	9	,	,	PUNCT
ejpam-5564	368	10	and	and	CCONJ
ejpam-5564	368	11	m.	m.	NOUN
ejpam-5564	368	12	okamoto	okamoto	PROPN
ejpam-5564	368	13	.	.	PUNCT
ejpam-5564	369	1	well	well	ADJ
ejpam-5564	369	2	-	-	PUNCT
ejpam-5564	369	3	posedness	posedness	NOUN
ejpam-5564	369	4	for	for	ADP
ejpam-5564	369	5	a	a	DET
ejpam-5564	369	6	system	system	NOUN
ejpam-5564	369	7	of	of	ADP
ejpam-5564	369	8	quadratic	quadratic	ADJ
ejpam-5564	369	9	derivative	derivative	ADJ
ejpam-5564	369	10	nonlinear	nonlinear	NOUN
ejpam-5564	369	11	schrödinger	schrödinger	NOUN
ejpam-5564	369	12	equations	equation	NOUN
ejpam-5564	369	13	in	in	ADP
ejpam-5564	369	14	almost	almost	ADV
ejpam-5564	369	15	critical	critical	ADJ
ejpam-5564	369	16	spaces	space	NOUN
ejpam-5564	369	17	.	.	PUNCT
ejpam-5564	370	1	journal	journal	NOUN
ejpam-5564	370	2	of	of	ADP
ejpam-5564	370	3	mathematical	mathematical	ADJ
ejpam-5564	370	4	analysis	analysis	NOUN
ejpam-5564	370	5	and	and	CCONJ
ejpam-5564	370	6	applications	application	NOUN
ejpam-5564	370	7	,	,	PUNCT
ejpam-5564	370	8	499	499	NUM
ejpam-5564	370	9	,	,	PUNCT
ejpam-5564	370	10	2021	2021	NUM
ejpam-5564	370	11	.	.	PUNCT
ejpam-5564	371	1	[	[	X
ejpam-5564	371	2	15	15	NUM
ejpam-5564	371	3	]	]	X
ejpam-5564	371	4	m.	m.	NOUN
ejpam-5564	371	5	fontelos	fontelos	PROPN
ejpam-5564	371	6	j.	j.	PROPN
ejpam-5564	371	7	eggers	eggers	PROPN
ejpam-5564	371	8	.	.	PUNCT
ejpam-5564	372	1	singularities	singularity	NOUN
ejpam-5564	372	2	:	:	PUNCT
ejpam-5564	372	3	formation	formation	NOUN
ejpam-5564	372	4	,	,	PUNCT
ejpam-5564	372	5	structure	structure	NOUN
ejpam-5564	372	6	,	,	PUNCT
ejpam-5564	372	7	and	and	CCONJ
ejpam-5564	372	8	propagation	propagation	NOUN
ejpam-5564	372	9	.	.	PUNCT
ejpam-5564	373	1	cambridge	cambridge	PROPN
ejpam-5564	373	2	university	university	PROPN
ejpam-5564	373	3	press	press	NOUN
ejpam-5564	373	4	,	,	PUNCT
ejpam-5564	373	5	2015	2015	NUM
ejpam-5564	373	6	.	.	PUNCT
ejpam-5564	374	1	[	[	X
ejpam-5564	374	2	16	16	NUM
ejpam-5564	374	3	]	]	X
ejpam-5564	374	4	r.	r.	PROPN
ejpam-5564	374	5	jungers	jungers	PROPN
ejpam-5564	374	6	and	and	CCONJ
ejpam-5564	374	7	p.	p.	PROPN
ejpam-5564	374	8	tabuada	tabuada	PROPN
ejpam-5564	374	9	.	.	PUNCT
ejpam-5564	375	1	non	non	ADJ
ejpam-5564	375	2	-	-	ADJ
ejpam-5564	375	3	local	local	ADJ
ejpam-5564	375	4	linearization	linearization	NOUN
ejpam-5564	375	5	of	of	ADP
ejpam-5564	375	6	nonlinear	nonlinear	ADJ
ejpam-5564	375	7	differential	differential	ADJ
ejpam-5564	375	8	equations	equation	NOUN
ejpam-5564	375	9	via	via	ADP
ejpam-5564	375	10	polyflows	polyflow	NOUN
ejpam-5564	375	11	.	.	PUNCT
ejpam-5564	376	1	2019	2019	NUM
ejpam-5564	376	2	american	american	PROPN
ejpam-5564	376	3	control	control	PROPN
ejpam-5564	376	4	conference	conference	PROPN
ejpam-5564	376	5	,	,	PUNCT
ejpam-5564	376	6	pages	page	NOUN
ejpam-5564	376	7	1–6	1–6	NUM
ejpam-5564	376	8	,	,	PUNCT
ejpam-5564	376	9	2019	2019	NUM
ejpam-5564	376	10	.	.	PUNCT
ejpam-5564	377	1	[	[	X
ejpam-5564	377	2	17	17	NUM
ejpam-5564	377	3	]	]	PUNCT
ejpam-5564	377	4	a.	a.	NOUN
ejpam-5564	377	5	khanfer	khanfer	NOUN
ejpam-5564	377	6	and	and	CCONJ
ejpam-5564	377	7	l.	l.	PROPN
ejpam-5564	377	8	bougoffa	bougoffa	PROPN
ejpam-5564	377	9	.	.	PUNCT
ejpam-5564	378	1	on	on	ADP
ejpam-5564	378	2	the	the	DET
ejpam-5564	378	3	fourth	fourth	ADJ
ejpam-5564	378	4	-	-	PUNCT
ejpam-5564	378	5	order	order	NOUN
ejpam-5564	378	6	nonlinear	nonlinear	ADJ
ejpam-5564	378	7	beam	beam	NOUN
ejpam-5564	378	8	equation	equation	NOUN
ejpam-5564	378	9	of	of	ADP
ejpam-5564	378	10	a	a	DET
ejpam-5564	378	11	small	small	ADJ
ejpam-5564	378	12	m.	m.	NOUN
ejpam-5564	378	13	gasanov	gasanov	NOUN
ejpam-5564	378	14	/	/	SYM
ejpam-5564	378	15	eur	eur	PROPN
ejpam-5564	378	16	.	.	PUNCT
ejpam-5564	379	1	j.	j.	PROPN
ejpam-5564	379	2	pure	pure	PROPN
ejpam-5564	379	3	appl	appl	PROPN
ejpam-5564	379	4	.	.	PROPN
ejpam-5564	379	5	math	math	PROPN
ejpam-5564	379	6	,	,	PUNCT
ejpam-5564	379	7	18	18	NUM
ejpam-5564	379	8	(	(	PUNCT
ejpam-5564	379	9	1	1	NUM
ejpam-5564	379	10	)	)	PUNCT
ejpam-5564	379	11	(	(	PUNCT
ejpam-5564	379	12	2025	2025	NUM
ejpam-5564	379	13	)	)	PUNCT
ejpam-5564	379	14	,	,	PUNCT
ejpam-5564	379	15	5564	5564	NUM
ejpam-5564	379	16	17	17	NUM
ejpam-5564	379	17	of	of	ADP
ejpam-5564	379	18	19	19	NUM
ejpam-5564	379	19	deflection	deflection	NOUN
ejpam-5564	379	20	with	with	ADP
ejpam-5564	379	21	nonlocal	nonlocal	ADJ
ejpam-5564	379	22	conditions	condition	NOUN
ejpam-5564	379	23	.	.	PUNCT
ejpam-5564	380	1	aims	aim	VERB
ejpam-5564	380	2	mathematics	mathematic	NOUN
ejpam-5564	380	3	,	,	PUNCT
ejpam-5564	380	4	page	page	NOUN
ejpam-5564	380	5	9899–9910	9899–9910	NOUN
ejpam-5564	380	6	,	,	PUNCT
ejpam-5564	380	7	2021	2021	NUM
ejpam-5564	380	8	.	.	PUNCT
ejpam-5564	381	1	[	[	X
ejpam-5564	381	2	18	18	NUM
ejpam-5564	381	3	]	]	X
ejpam-5564	381	4	n.	n.	PROPN
ejpam-5564	381	5	kudryashov	kudryashov	PROPN
ejpam-5564	381	6	.	.	PUNCT
ejpam-5564	382	1	analitical	analitical	ADJ
ejpam-5564	382	2	theory	theory	NOUN
ejpam-5564	382	3	of	of	ADP
ejpam-5564	382	4	nonlinear	nonlinear	ADJ
ejpam-5564	382	5	differential	differential	ADJ
ejpam-5564	382	6	equations	equation	NOUN
ejpam-5564	382	7	.	.	PUNCT
ejpam-5564	383	1	institute	institute	PROPN
ejpam-5564	383	2	of	of	ADP
ejpam-5564	383	3	computer	computer	PROPN
ejpam-5564	383	4	research	research	NOUN
ejpam-5564	383	5	,	,	PUNCT
ejpam-5564	383	6	moskow	moskow	PROPN
ejpam-5564	383	7	igevsk	igevsk	PROPN
ejpam-5564	383	8	,	,	PUNCT
ejpam-5564	383	9	2004	2004	NUM
ejpam-5564	383	10	.	.	PUNCT
ejpam-5564	384	1	[	[	X
ejpam-5564	384	2	19	19	NUM
ejpam-5564	384	3	]	]	X
ejpam-5564	384	4	n.	n.	PROPN
ejpam-5564	384	5	kudryashov	kudryashov	PROPN
ejpam-5564	384	6	.	.	PUNCT
ejpam-5564	385	1	nonlinear	nonlinear	ADJ
ejpam-5564	385	2	differential	differential	ADJ
ejpam-5564	385	3	equations	equation	NOUN
ejpam-5564	385	4	with	with	ADP
ejpam-5564	385	5	exact	exact	ADJ
ejpam-5564	385	6	solutions	solution	NOUN
ejpam-5564	385	7	expressed	express	VERB
ejpam-5564	385	8	via	via	ADP
ejpam-5564	385	9	the	the	DET
ejpam-5564	385	10	weierstrass	weierstrass	NOUN
ejpam-5564	385	11	function	function	NOUN
ejpam-5564	385	12	.	.	PUNCT
ejpam-5564	386	1	zeitschrift	zeitschrift	NOUN
ejpam-5564	386	2	für	für	PROPN
ejpam-5564	386	3	naturforschung	naturforschung	VERB
ejpam-5564	386	4	a	a	PRON
ejpam-5564	386	5	,	,	PUNCT
ejpam-5564	386	6	pages	page	NOUN
ejpam-5564	386	7	443–454	443–454	NUM
ejpam-5564	386	8	,	,	PUNCT
ejpam-5564	386	9	2004	2004	NUM
ejpam-5564	386	10	.	.	PUNCT
ejpam-5564	387	1	[	[	X
ejpam-5564	387	2	20	20	NUM
ejpam-5564	387	3	]	]	PUNCT
ejpam-5564	387	4	t.	t.	PROPN
ejpam-5564	387	5	leont’eva	leont’eva	PROPN
ejpam-5564	387	6	.	.	PUNCT
ejpam-5564	388	1	about	about	ADV
ejpam-5564	388	2	one	one	NUM
ejpam-5564	388	3	generalization	generalization	NOUN
ejpam-5564	388	4	of	of	ADP
ejpam-5564	388	5	exact	exact	ADJ
ejpam-5564	388	6	criteria	criterion	NOUN
ejpam-5564	388	7	for	for	ADP
ejpam-5564	388	8	the	the	DET
ejpam-5564	388	9	existence	existence	NOUN
ejpam-5564	388	10	moving	move	VERB
ejpam-5564	388	11	singular	singular	ADJ
ejpam-5564	388	12	points	point	NOUN
ejpam-5564	388	13	of	of	ADP
ejpam-5564	388	14	one	one	NUM
ejpam-5564	388	15	class	class	NOUN
ejpam-5564	388	16	of	of	ADP
ejpam-5564	388	17	nonlinear	nonlinear	ADJ
ejpam-5564	388	18	ordinary	ordinary	ADJ
ejpam-5564	388	19	differential	differential	ADJ
ejpam-5564	388	20	equations	equation	NOUN
ejpam-5564	388	21	in	in	ADP
ejpam-5564	388	22	the	the	DET
ejpam-5564	388	23	complex	complex	ADJ
ejpam-5564	388	24	area	area	NOUN
ejpam-5564	388	25	.	.	PUNCT
ejpam-5564	389	1	belgorod	belgorod	PROPN
ejpam-5564	389	2	state	state	PROPN
ejpam-5564	389	3	univ	univ	PROPN
ejpam-5564	389	4	.	.	PUNCT
ejpam-5564	390	1	sci	sci	PROPN
ejpam-5564	390	2	.	.	PUNCT
ejpam-5564	390	3	bull	bull	PROPN
ejpam-5564	390	4	.	.	PUNCT
ejpam-5564	391	1	math	math	NOUN
ejpam-5564	391	2	.	.	PUNCT
ejpam-5564	392	1	phys	phy	NOUN
ejpam-5564	392	2	.	.	PUNCT
ejpam-5564	392	3	,	,	PUNCT
ejpam-5564	392	4	page	page	NOUN
ejpam-5564	392	5	51–57	51–57	NUM
ejpam-5564	392	6	,	,	PUNCT
ejpam-5564	392	7	2017	2017	NUM
ejpam-5564	392	8	.	.	PUNCT
ejpam-5564	393	1	[	[	X
ejpam-5564	393	2	21	21	NUM
ejpam-5564	393	3	]	]	X
ejpam-5564	393	4	d.	d.	PROPN
ejpam-5564	393	5	lyakhov	lyakhov	PROPN
ejpam-5564	393	6	,	,	PUNCT
ejpam-5564	393	7	v.	v.	PROPN
ejpam-5564	393	8	gerdt	gerdt	NOUN
ejpam-5564	393	9	,	,	PUNCT
ejpam-5564	393	10	and	and	CCONJ
ejpam-5564	393	11	d.	d.	PROPN
ejpam-5564	393	12	michels	michels	PROPN
ejpam-5564	393	13	.	.	PUNCT
ejpam-5564	394	1	on	on	ADP
ejpam-5564	394	2	the	the	DET
ejpam-5564	394	3	algorithmic	algorithmic	ADJ
ejpam-5564	394	4	linearizability	linearizability	NOUN
ejpam-5564	394	5	of	of	ADP
ejpam-5564	394	6	nonlinear	nonlinear	ADJ
ejpam-5564	394	7	ordinary	ordinary	ADJ
ejpam-5564	394	8	differential	differential	ADJ
ejpam-5564	394	9	equations	equation	NOUN
ejpam-5564	394	10	.	.	PUNCT
ejpam-5564	395	1	journal	journal	PROPN
ejpam-5564	395	2	of	of	ADP
ejpam-5564	395	3	symbolic	symbolic	ADJ
ejpam-5564	395	4	computation	computation	NOUN
ejpam-5564	395	5	,	,	PUNCT
ejpam-5564	395	6	page	page	NOUN
ejpam-5564	395	7	3–22	3–22	NOUN
ejpam-5564	395	8	,	,	PUNCT
ejpam-5564	395	9	2020	2020	NUM
ejpam-5564	395	10	.	.	PUNCT
ejpam-5564	396	1	[	[	X
ejpam-5564	396	2	22	22	NUM
ejpam-5564	396	3	]	]	PUNCT
ejpam-5564	396	4	r.	r.	PROPN
ejpam-5564	396	5	ma	ma	PROPN
ejpam-5564	396	6	,	,	PUNCT
ejpam-5564	396	7	j.	j.	PROPN
ejpam-5564	396	8	li	li	PROPN
ejpam-5564	396	9	,	,	PUNCT
ejpam-5564	396	10	and	and	CCONJ
ejpam-5564	396	11	c.	c.	PROPN
ejpam-5564	396	12	gao	gao	PROPN
ejpam-5564	396	13	.	.	PUNCT
ejpam-5564	397	1	existence	existence	NOUN
ejpam-5564	397	2	of	of	ADP
ejpam-5564	397	3	positive	positive	ADJ
ejpam-5564	397	4	solutions	solution	NOUN
ejpam-5564	397	5	of	of	ADP
ejpam-5564	397	6	a	a	DET
ejpam-5564	397	7	discrete	discrete	ADJ
ejpam-5564	397	8	elastic	elastic	ADJ
ejpam-5564	397	9	beam	beam	NOUN
ejpam-5564	397	10	equation	equation	NOUN
ejpam-5564	397	11	.	.	PUNCT
ejpam-5564	398	1	discrete	discrete	ADJ
ejpam-5564	398	2	dynamics	dynamic	NOUN
ejpam-5564	398	3	in	in	ADP
ejpam-5564	398	4	nature	nature	NOUN
ejpam-5564	398	5	and	and	CCONJ
ejpam-5564	398	6	society	society	NOUN
ejpam-5564	398	7	,	,	PUNCT
ejpam-5564	398	8	page	page	NOUN
ejpam-5564	398	9	1–15	1–15	NUM
ejpam-5564	398	10	,	,	PUNCT
ejpam-5564	398	11	2010	2010	NUM
ejpam-5564	398	12	.	.	PUNCT
ejpam-5564	399	1	[	[	X
ejpam-5564	399	2	23	23	NUM
ejpam-5564	399	3	]	]	PUNCT
ejpam-5564	399	4	k.	k.	PROPN
ejpam-5564	399	5	maekawa	maekawa	PROPN
ejpam-5564	399	6	,	,	PUNCT
ejpam-5564	399	7	h.	h.	PROPN
ejpam-5564	399	8	okamura	okamura	PROPN
ejpam-5564	399	9	,	,	PUNCT
ejpam-5564	399	10	and	and	CCONJ
ejpam-5564	399	11	a.	a.	NOUN
ejpam-5564	399	12	pimanmas	pimanmas	PROPN
ejpam-5564	399	13	.	.	PUNCT
ejpam-5564	400	1	nonlinear	nonlinear	ADJ
ejpam-5564	400	2	mechanics	mechanic	NOUN
ejpam-5564	400	3	of	of	ADP
ejpam-5564	400	4	reinforced	reinforce	VERB
ejpam-5564	400	5	concrete	concrete	NOUN
ejpam-5564	400	6	.	.	PUNCT
ejpam-5564	401	1	boca	boca	PROPN
ejpam-5564	401	2	raton	raton	PROPN
ejpam-5564	401	3	,	,	PUNCT
ejpam-5564	401	4	fl	fl	PROPN
ejpam-5564	401	5	:	:	PUNCT
ejpam-5564	401	6	crc	crc	NOUN
ejpam-5564	401	7	press	press	NOUN
ejpam-5564	401	8	,	,	PUNCT
ejpam-5564	401	9	2019	2019	NUM
ejpam-5564	401	10	.	.	PUNCT
ejpam-5564	402	1	[	[	X
ejpam-5564	402	2	24	24	NUM
ejpam-5564	402	3	]	]	PUNCT
ejpam-5564	402	4	s.	s.	PROPN
ejpam-5564	402	5	mancas	mancas	PROPN
ejpam-5564	402	6	and	and	CCONJ
ejpam-5564	402	7	h.	h.	PROPN
ejpam-5564	402	8	rosu	rosu	PROPN
ejpam-5564	402	9	.	.	PUNCT
ejpam-5564	403	1	integrable	integrable	ADJ
ejpam-5564	403	2	dissipative	dissipative	ADJ
ejpam-5564	403	3	nonlinear	nonlinear	ADJ
ejpam-5564	403	4	second	second	ADJ
ejpam-5564	403	5	order	order	NOUN
ejpam-5564	403	6	differential	differential	ADJ
ejpam-5564	403	7	equations	equation	NOUN
ejpam-5564	403	8	via	via	ADP
ejpam-5564	403	9	factorizations	factorization	NOUN
ejpam-5564	403	10	and	and	CCONJ
ejpam-5564	403	11	abel	abel	PROPN
ejpam-5564	403	12	equations	equation	NOUN
ejpam-5564	403	13	.	.	PUNCT
ejpam-5564	404	1	physics	physics	NOUN
ejpam-5564	404	2	letters	letter	NOUN
ejpam-5564	404	3	,	,	PUNCT
ejpam-5564	404	4	page	page	NOUN
ejpam-5564	404	5	1434–1438	1434–1438	NUM
ejpam-5564	404	6	,	,	PUNCT
ejpam-5564	404	7	2013	2013	NUM
ejpam-5564	404	8	.	.	PUNCT
ejpam-5564	405	1	[	[	X
ejpam-5564	405	2	25	25	NUM
ejpam-5564	405	3	]	]	PUNCT
ejpam-5564	405	4	k.	k.	PROPN
ejpam-5564	405	5	mohsen	mohsen	PROPN
ejpam-5564	405	6	,	,	PUNCT
ejpam-5564	405	7	y.	y.	PROPN
ejpam-5564	405	8	khalili	khalili	PROPN
ejpam-5564	405	9	,	,	PUNCT
ejpam-5564	405	10	and	and	CCONJ
ejpam-5564	405	11	r.	r.	PROPN
ejpam-5564	405	12	wieteska	wieteska	PROPN
ejpam-5564	405	13	.	.	PUNCT
ejpam-5564	406	1	existence	existence	NOUN
ejpam-5564	406	2	of	of	ADP
ejpam-5564	406	3	two	two	NUM
ejpam-5564	406	4	solutions	solution	NOUN
ejpam-5564	406	5	for	for	ADP
ejpam-5564	406	6	a	a	DET
ejpam-5564	406	7	fourth	fourth	ADJ
ejpam-5564	406	8	-	-	PUNCT
ejpam-5564	406	9	order	order	NOUN
ejpam-5564	406	10	difference	difference	NOUN
ejpam-5564	406	11	problem	problem	NOUN
ejpam-5564	406	12	with	with	ADP
ejpam-5564	406	13	p(k	p(k	NOUN
ejpam-5564	406	14	)	)	PUNCT
ejpam-5564	406	15	exponent	exponent	NOUN
ejpam-5564	406	16	.	.	PUNCT
ejpam-5564	407	1	afrika	afrika	PROPN
ejpam-5564	407	2	matematika	matematika	PROPN
ejpam-5564	407	3	,	,	PUNCT
ejpam-5564	407	4	page	page	NOUN
ejpam-5564	407	5	959–970	959–970	NUM
ejpam-5564	407	6	,	,	PUNCT
ejpam-5564	407	7	2020	2020	NUM
ejpam-5564	407	8	.	.	PUNCT
ejpam-5564	408	1	[	[	X
ejpam-5564	408	2	26	26	NUM
ejpam-5564	408	3	]	]	X
ejpam-5564	408	4	w.	w.	PROPN
ejpam-5564	408	5	nakpim	nakpim	PROPN
ejpam-5564	408	6	.	.	PUNCT
ejpam-5564	409	1	linearization	linearization	NOUN
ejpam-5564	409	2	of	of	ADP
ejpam-5564	409	3	second	second	ADJ
ejpam-5564	409	4	-	-	PUNCT
ejpam-5564	409	5	order	order	NOUN
ejpam-5564	409	6	ordinary	ordinary	ADJ
ejpam-5564	409	7	differential	differential	ADJ
ejpam-5564	409	8	equations	equation	NOUN
ejpam-5564	409	9	by	by	ADP
ejpam-5564	409	10	generalized	generalized	ADJ
ejpam-5564	409	11	sundman	sundman	NOUN
ejpam-5564	409	12	transformations	transformation	NOUN
ejpam-5564	409	13	.	.	PUNCT
ejpam-5564	410	1	symmetry	symmetry	NOUN
ejpam-5564	410	2	,	,	PUNCT
ejpam-5564	410	3	integrability	integrability	NOUN
ejpam-5564	410	4	and	and	CCONJ
ejpam-5564	410	5	geometry	geometry	NOUN
ejpam-5564	410	6	:	:	PUNCT
ejpam-5564	410	7	methods	method	NOUN
ejpam-5564	410	8	and	and	CCONJ
ejpam-5564	410	9	applications	application	NOUN
ejpam-5564	410	10	,	,	PUNCT
ejpam-5564	410	11	2010	2010	NUM
ejpam-5564	410	12	.	.	PUNCT
ejpam-5564	411	1	[	[	X
ejpam-5564	411	2	27	27	NUM
ejpam-5564	411	3	]	]	X
ejpam-5564	411	4	v.	v.	CCONJ
ejpam-5564	411	5	orlov	orlov	PROPN
ejpam-5564	411	6	.	.	PUNCT
ejpam-5564	412	1	dependence	dependence	NOUN
ejpam-5564	412	2	of	of	ADP
ejpam-5564	412	3	the	the	DET
ejpam-5564	412	4	analytical	analytical	ADJ
ejpam-5564	412	5	approximate	approximate	ADJ
ejpam-5564	412	6	solution	solution	NOUN
ejpam-5564	412	7	to	to	ADP
ejpam-5564	412	8	the	the	DET
ejpam-5564	412	9	van	van	PROPN
ejpam-5564	412	10	der	der	ADJ
ejpam-5564	412	11	pol	pol	NOUN
ejpam-5564	412	12	equation	equation	NOUN
ejpam-5564	412	13	on	on	ADP
ejpam-5564	412	14	the	the	DET
ejpam-5564	412	15	perturbation	perturbation	NOUN
ejpam-5564	412	16	of	of	ADP
ejpam-5564	412	17	a	a	DET
ejpam-5564	412	18	moving	move	VERB
ejpam-5564	412	19	singular	singular	ADJ
ejpam-5564	412	20	point	point	NOUN
ejpam-5564	412	21	in	in	ADP
ejpam-5564	412	22	the	the	DET
ejpam-5564	412	23	complex	complex	ADJ
ejpam-5564	412	24	domain	domain	NOUN
ejpam-5564	412	25	.	.	PUNCT
ejpam-5564	413	1	axioms	axiom	NOUN
ejpam-5564	413	2	,	,	PUNCT
ejpam-5564	413	3	2023	2023	NUM
ejpam-5564	413	4	.	.	PUNCT
ejpam-5564	414	1	[	[	X
ejpam-5564	414	2	28	28	NUM
ejpam-5564	414	3	]	]	X
ejpam-5564	414	4	v.	v.	CCONJ
ejpam-5564	414	5	orlov	orlov	NOUN
ejpam-5564	414	6	.	.	PUNCT
ejpam-5564	415	1	moving	move	VERB
ejpam-5564	415	2	singular	singular	ADJ
ejpam-5564	415	3	points	point	NOUN
ejpam-5564	415	4	and	and	CCONJ
ejpam-5564	415	5	the	the	DET
ejpam-5564	415	6	van	van	PROPN
ejpam-5564	415	7	der	der	ADJ
ejpam-5564	415	8	pol	pol	NOUN
ejpam-5564	415	9	equation	equation	NOUN
ejpam-5564	415	10	,	,	PUNCT
ejpam-5564	415	11	as	as	ADV
ejpam-5564	415	12	well	well	ADV
ejpam-5564	415	13	as	as	ADP
ejpam-5564	415	14	the	the	DET
ejpam-5564	415	15	uniqueness	uniqueness	NOUN
ejpam-5564	415	16	of	of	ADP
ejpam-5564	415	17	its	its	PRON
ejpam-5564	415	18	solution	solution	NOUN
ejpam-5564	415	19	.	.	PUNCT
ejpam-5564	416	1	mathematics	mathematic	NOUN
ejpam-5564	416	2	,	,	PUNCT
ejpam-5564	416	3	2023	2023	NUM
ejpam-5564	416	4	.	.	PUNCT
ejpam-5564	417	1	[	[	X
ejpam-5564	417	2	29	29	NUM
ejpam-5564	417	3	]	]	X
ejpam-5564	417	4	v.	v.	CCONJ
ejpam-5564	417	5	orlov	orlov	PROPN
ejpam-5564	417	6	and	and	CCONJ
ejpam-5564	417	7	a.	a.	NOUN
ejpam-5564	417	8	chichurin	chichurin	PROPN
ejpam-5564	417	9	.	.	PUNCT
ejpam-5564	418	1	about	about	ADP
ejpam-5564	418	2	analytical	analytical	ADJ
ejpam-5564	418	3	approximate	approximate	ADJ
ejpam-5564	418	4	solutions	solution	NOUN
ejpam-5564	418	5	of	of	ADP
ejpam-5564	418	6	the	the	DET
ejpam-5564	418	7	van	van	PROPN
ejpam-5564	418	8	der	der	ADJ
ejpam-5564	418	9	pol	pol	NOUN
ejpam-5564	418	10	equation	equation	NOUN
ejpam-5564	418	11	in	in	ADP
ejpam-5564	418	12	the	the	DET
ejpam-5564	418	13	complex	complex	ADJ
ejpam-5564	418	14	domain	domain	NOUN
ejpam-5564	418	15	.	.	PUNCT
ejpam-5564	419	1	fractal	fractal	ADJ
ejpam-5564	419	2	and	and	CCONJ
ejpam-5564	419	3	fractional	fractional	ADJ
ejpam-5564	419	4	,	,	PUNCT
ejpam-5564	419	5	2023	2023	NUM
ejpam-5564	419	6	.	.	PUNCT
ejpam-5564	420	1	[	[	X
ejpam-5564	420	2	30	30	NUM
ejpam-5564	420	3	]	]	X
ejpam-5564	420	4	v.	v.	CCONJ
ejpam-5564	420	5	orlov	orlov	PROPN
ejpam-5564	420	6	and	and	CCONJ
ejpam-5564	420	7	a.	a.	NOUN
ejpam-5564	420	8	chichurin	chichurin	PROPN
ejpam-5564	420	9	.	.	PUNCT
ejpam-5564	421	1	the	the	DET
ejpam-5564	421	2	influence	influence	NOUN
ejpam-5564	421	3	of	of	ADP
ejpam-5564	421	4	the	the	DET
ejpam-5564	421	5	perturbation	perturbation	NOUN
ejpam-5564	421	6	of	of	ADP
ejpam-5564	421	7	the	the	DET
ejpam-5564	421	8	initial	initial	ADJ
ejpam-5564	421	9	data	datum	NOUN
ejpam-5564	421	10	on	on	ADP
ejpam-5564	421	11	the	the	DET
ejpam-5564	421	12	analytic	analytic	ADJ
ejpam-5564	421	13	approximate	approximate	ADJ
ejpam-5564	421	14	solution	solution	NOUN
ejpam-5564	421	15	of	of	ADP
ejpam-5564	421	16	the	the	DET
ejpam-5564	421	17	van	van	PROPN
ejpam-5564	421	18	der	der	ADJ
ejpam-5564	421	19	pol	pol	NOUN
ejpam-5564	421	20	equation	equation	NOUN
ejpam-5564	421	21	in	in	ADP
ejpam-5564	421	22	the	the	DET
ejpam-5564	421	23	complex	complex	ADJ
ejpam-5564	421	24	domain	domain	NOUN
ejpam-5564	421	25	.	.	PUNCT
ejpam-5564	422	1	symmetry	symmetry	NOUN
ejpam-5564	422	2	,	,	PUNCT
ejpam-5564	422	3	2023	2023	NUM
ejpam-5564	422	4	.	.	PUNCT
ejpam-5564	423	1	[	[	X
ejpam-5564	423	2	31	31	NUM
ejpam-5564	423	3	]	]	X
ejpam-5564	423	4	v.	v.	CCONJ
ejpam-5564	423	5	orlov	orlov	PROPN
ejpam-5564	423	6	and	and	CCONJ
ejpam-5564	423	7	m.	m.	NOUN
ejpam-5564	423	8	gasanov	gasanov	PROPN
ejpam-5564	423	9	.	.	PUNCT
ejpam-5564	423	10	analytic	analytic	ADJ
ejpam-5564	423	11	approximate	approximate	ADJ
ejpam-5564	423	12	solution	solution	NOUN
ejpam-5564	423	13	in	in	ADP
ejpam-5564	423	14	the	the	DET
ejpam-5564	423	15	neighborhood	neighborhood	NOUN
ejpam-5564	423	16	of	of	ADP
ejpam-5564	423	17	a	a	DET
ejpam-5564	423	18	moving	move	VERB
ejpam-5564	423	19	singular	singular	ADJ
ejpam-5564	423	20	point	point	NOUN
ejpam-5564	423	21	of	of	ADP
ejpam-5564	423	22	a	a	DET
ejpam-5564	423	23	class	class	NOUN
ejpam-5564	423	24	of	of	ADP
ejpam-5564	423	25	nonlinear	nonlinear	ADJ
ejpam-5564	423	26	equations	equation	NOUN
ejpam-5564	423	27	.	.	PUNCT
ejpam-5564	424	1	axioms	axiom	NOUN
ejpam-5564	424	2	,	,	PUNCT
ejpam-5564	424	3	2022	2022	NUM
ejpam-5564	424	4	.	.	PUNCT
ejpam-5564	425	1	[	[	X
ejpam-5564	425	2	32	32	NUM
ejpam-5564	425	3	]	]	X
ejpam-5564	425	4	v.	v.	CCONJ
ejpam-5564	425	5	orlov	orlov	PROPN
ejpam-5564	425	6	and	and	CCONJ
ejpam-5564	425	7	m.	m.	NOUN
ejpam-5564	425	8	gasanov	gasanov	PROPN
ejpam-5564	425	9	.	.	PUNCT
ejpam-5564	426	1	exact	exact	ADJ
ejpam-5564	426	2	criteria	criterion	NOUN
ejpam-5564	426	3	for	for	ADP
ejpam-5564	426	4	the	the	DET
ejpam-5564	426	5	existence	existence	NOUN
ejpam-5564	426	6	of	of	ADP
ejpam-5564	426	7	a	a	DET
ejpam-5564	426	8	moving	move	VERB
ejpam-5564	426	9	singular	singular	ADJ
ejpam-5564	426	10	point	point	NOUN
ejpam-5564	426	11	in	in	ADP
ejpam-5564	426	12	a	a	DET
ejpam-5564	426	13	complex	complex	ADJ
ejpam-5564	426	14	domain	domain	NOUN
ejpam-5564	426	15	for	for	ADP
ejpam-5564	426	16	a	a	DET
ejpam-5564	426	17	nonlinear	nonlinear	ADJ
ejpam-5564	426	18	differential	differential	ADJ
ejpam-5564	426	19	third	third	ADJ
ejpam-5564	426	20	-	-	PUNCT
ejpam-5564	426	21	degree	degree	NOUN
ejpam-5564	426	22	equation	equation	NOUN
ejpam-5564	426	23	with	with	ADP
ejpam-5564	426	24	a	a	DET
ejpam-5564	426	25	polynomial	polynomial	ADJ
ejpam-5564	426	26	seventh	seventh	ADJ
ejpam-5564	426	27	-	-	PUNCT
ejpam-5564	426	28	degree	degree	NOUN
ejpam-5564	426	29	right	right	ADJ
ejpam-5564	426	30	-	-	PUNCT
ejpam-5564	426	31	hand	hand	NOUN
ejpam-5564	426	32	side	side	NOUN
ejpam-5564	426	33	.	.	PUNCT
ejpam-5564	427	1	axioms	axiom	NOUN
ejpam-5564	427	2	,	,	PUNCT
ejpam-5564	427	3	2022	2022	NUM
ejpam-5564	427	4	.	.	PUNCT
ejpam-5564	428	1	[	[	X
ejpam-5564	428	2	33	33	NUM
ejpam-5564	428	3	]	]	X
ejpam-5564	428	4	v.	v.	CCONJ
ejpam-5564	428	5	orlov	orlov	PROPN
ejpam-5564	428	6	and	and	CCONJ
ejpam-5564	428	7	m.	m.	NOUN
ejpam-5564	428	8	gasanov	gasanov	PROPN
ejpam-5564	428	9	.	.	PUNCT
ejpam-5564	429	1	existence	existence	NOUN
ejpam-5564	429	2	and	and	CCONJ
ejpam-5564	429	3	uniqueness	uniqueness	NOUN
ejpam-5564	429	4	theorem	theorem	VERB
ejpam-5564	429	5	for	for	ADP
ejpam-5564	429	6	a	a	DET
ejpam-5564	429	7	solution	solution	NOUN
ejpam-5564	429	8	to	to	ADP
ejpam-5564	429	9	a	a	DET
ejpam-5564	429	10	class	class	NOUN
ejpam-5564	429	11	of	of	ADP
ejpam-5564	429	12	a	a	DET
ejpam-5564	429	13	third	third	ADJ
ejpam-5564	429	14	-	-	PUNCT
ejpam-5564	429	15	order	order	NOUN
ejpam-5564	429	16	nonlinear	nonlinear	ADJ
ejpam-5564	429	17	differential	differential	ADJ
ejpam-5564	429	18	equation	equation	NOUN
ejpam-5564	429	19	in	in	ADP
ejpam-5564	429	20	the	the	DET
ejpam-5564	429	21	domain	domain	NOUN
ejpam-5564	429	22	of	of	ADP
ejpam-5564	429	23	analyticity	analyticity	NOUN
ejpam-5564	429	24	.	.	PUNCT
ejpam-5564	430	1	axioms	axiom	NOUN
ejpam-5564	430	2	,	,	PUNCT
ejpam-5564	430	3	2022	2022	NUM
ejpam-5564	430	4	.	.	PUNCT
ejpam-5564	431	1	[	[	X
ejpam-5564	431	2	34	34	NUM
ejpam-5564	431	3	]	]	X
ejpam-5564	431	4	v.	v.	CCONJ
ejpam-5564	431	5	orlov	orlov	PROPN
ejpam-5564	431	6	and	and	CCONJ
ejpam-5564	431	7	m.	m.	NOUN
ejpam-5564	431	8	gasanov	gasanov	PROPN
ejpam-5564	431	9	.	.	PUNCT
ejpam-5564	432	1	the	the	DET
ejpam-5564	432	2	influence	influence	NOUN
ejpam-5564	432	3	of	of	ADP
ejpam-5564	432	4	a	a	DET
ejpam-5564	432	5	perturbation	perturbation	NOUN
ejpam-5564	432	6	of	of	ADP
ejpam-5564	432	7	a	a	DET
ejpam-5564	432	8	moving	move	VERB
ejpam-5564	432	9	singular	singular	ADJ
ejpam-5564	432	10	point	point	NOUN
ejpam-5564	432	11	on	on	ADP
ejpam-5564	432	12	the	the	DET
ejpam-5564	432	13	structure	structure	NOUN
ejpam-5564	432	14	of	of	ADP
ejpam-5564	432	15	an	an	DET
ejpam-5564	432	16	analytical	analytical	ADJ
ejpam-5564	432	17	approximate	approximate	ADJ
ejpam-5564	432	18	solution	solution	NOUN
ejpam-5564	432	19	of	of	ADP
ejpam-5564	432	20	a	a	DET
ejpam-5564	432	21	class	class	NOUN
ejpam-5564	432	22	of	of	ADP
ejpam-5564	432	23	third	third	ADJ
ejpam-5564	432	24	-	-	PUNCT
ejpam-5564	432	25	order	order	NOUN
ejpam-5564	432	26	nonlinear	nonlinear	ADJ
ejpam-5564	432	27	differential	differential	ADJ
ejpam-5564	432	28	equations	equation	NOUN
ejpam-5564	432	29	in	in	ADP
ejpam-5564	432	30	a	a	DET
ejpam-5564	432	31	complex	complex	ADJ
ejpam-5564	432	32	domain	domain	NOUN
ejpam-5564	432	33	.	.	PUNCT
ejpam-5564	433	1	herald	herald	NOUN
ejpam-5564	433	2	of	of	ADP
ejpam-5564	433	3	the	the	DET
ejpam-5564	433	4	bauman	bauman	PROPN
ejpam-5564	433	5	moscow	moscow	PROPN
ejpam-5564	433	6	m.	m.	NOUN
ejpam-5564	433	7	gasanov	gasanov	PROPN
ejpam-5564	433	8	/	/	SYM
ejpam-5564	433	9	eur	eur	PROPN
ejpam-5564	433	10	.	.	PUNCT
ejpam-5564	434	1	j.	j.	PROPN
ejpam-5564	434	2	pure	pure	PROPN
ejpam-5564	434	3	appl	appl	PROPN
ejpam-5564	434	4	.	.	PROPN
ejpam-5564	434	5	math	math	PROPN
ejpam-5564	434	6	,	,	PUNCT
ejpam-5564	434	7	18	18	NUM
ejpam-5564	434	8	(	(	PUNCT
ejpam-5564	434	9	1	1	NUM
ejpam-5564	434	10	)	)	PUNCT
ejpam-5564	434	11	(	(	PUNCT
ejpam-5564	434	12	2025	2025	NUM
ejpam-5564	434	13	)	)	PUNCT
ejpam-5564	434	14	,	,	PUNCT
ejpam-5564	434	15	5564	5564	NUM
ejpam-5564	434	16	18	18	NUM
ejpam-5564	434	17	of	of	ADP
ejpam-5564	434	18	19	19	NUM
ejpam-5564	434	19	state	state	NOUN
ejpam-5564	434	20	tech	tech	NOUN
ejpam-5564	434	21	.	.	PUNCT
ejpam-5564	435	1	univ	univ	PROPN
ejpam-5564	435	2	.	.	PROPN
ejpam-5564	435	3	,	,	PUNCT
ejpam-5564	435	4	nat	nat	PROPN
ejpam-5564	435	5	.	.	PUNCT
ejpam-5564	436	1	sci	sci	PROPN
ejpam-5564	436	2	.	.	PROPN
ejpam-5564	436	3	,	,	PUNCT
ejpam-5564	436	4	page	page	NOUN
ejpam-5564	436	5	60–76	60–76	NUM
ejpam-5564	436	6	,	,	PUNCT
ejpam-5564	436	7	2022	2022	NUM
ejpam-5564	436	8	.	.	PUNCT
ejpam-5564	437	1	[	[	X
ejpam-5564	437	2	35	35	NUM
ejpam-5564	437	3	]	]	X
ejpam-5564	437	4	v.	v.	CCONJ
ejpam-5564	437	5	orlov	orlov	PROPN
ejpam-5564	437	6	and	and	CCONJ
ejpam-5564	437	7	m.	m.	NOUN
ejpam-5564	437	8	gasanov	gasanov	PROPN
ejpam-5564	437	9	.	.	PUNCT
ejpam-5564	438	1	technology	technology	NOUN
ejpam-5564	438	2	for	for	ADP
ejpam-5564	438	3	obtaining	obtain	VERB
ejpam-5564	438	4	the	the	DET
ejpam-5564	438	5	approximate	approximate	ADJ
ejpam-5564	438	6	value	value	NOUN
ejpam-5564	438	7	of	of	ADP
ejpam-5564	438	8	moving	move	VERB
ejpam-5564	438	9	singular	singular	ADJ
ejpam-5564	438	10	points	point	NOUN
ejpam-5564	438	11	for	for	ADP
ejpam-5564	438	12	a	a	DET
ejpam-5564	438	13	class	class	NOUN
ejpam-5564	438	14	of	of	ADP
ejpam-5564	438	15	nonlinear	nonlinear	ADJ
ejpam-5564	438	16	differential	differential	ADJ
ejpam-5564	438	17	equations	equation	NOUN
ejpam-5564	438	18	in	in	ADP
ejpam-5564	438	19	a	a	DET
ejpam-5564	438	20	complex	complex	ADJ
ejpam-5564	438	21	domain	domain	NOUN
ejpam-5564	438	22	.	.	PUNCT
ejpam-5564	439	1	mathematics	mathematic	NOUN
ejpam-5564	439	2	,	,	PUNCT
ejpam-5564	439	3	2022	2022	NUM
ejpam-5564	439	4	.	.	PUNCT
ejpam-5564	440	1	[	[	X
ejpam-5564	440	2	36	36	NUM
ejpam-5564	440	3	]	]	X
ejpam-5564	440	4	v.	v.	CCONJ
ejpam-5564	440	5	orlov	orlov	PROPN
ejpam-5564	440	6	and	and	CCONJ
ejpam-5564	440	7	m.	m.	NOUN
ejpam-5564	440	8	gasanov	gasanov	PROPN
ejpam-5564	440	9	.	.	PUNCT
ejpam-5564	441	1	the	the	DET
ejpam-5564	441	2	maximum	maximum	ADJ
ejpam-5564	441	3	domain	domain	NOUN
ejpam-5564	441	4	for	for	ADP
ejpam-5564	441	5	an	an	DET
ejpam-5564	441	6	analytical	analytical	ADJ
ejpam-5564	441	7	approximate	approximate	ADJ
ejpam-5564	441	8	solution	solution	NOUN
ejpam-5564	441	9	to	to	ADP
ejpam-5564	441	10	a	a	DET
ejpam-5564	441	11	nonlinear	nonlinear	ADJ
ejpam-5564	441	12	differential	differential	ADJ
ejpam-5564	441	13	equation	equation	NOUN
ejpam-5564	441	14	in	in	ADP
ejpam-5564	441	15	the	the	DET
ejpam-5564	441	16	neighborhood	neighborhood	NOUN
ejpam-5564	441	17	of	of	ADP
ejpam-5564	441	18	a	a	DET
ejpam-5564	441	19	moving	move	VERB
ejpam-5564	441	20	singular	singular	ADJ
ejpam-5564	441	21	point	point	NOUN
ejpam-5564	441	22	.	.	PUNCT
ejpam-5564	442	1	axioms	axiom	NOUN
ejpam-5564	442	2	,	,	PUNCT
ejpam-5564	442	3	2023	2023	NUM
ejpam-5564	442	4	.	.	PUNCT
ejpam-5564	443	1	[	[	X
ejpam-5564	443	2	37	37	NUM
ejpam-5564	443	3	]	]	X
ejpam-5564	443	4	v.	v.	CCONJ
ejpam-5564	443	5	orlov	orlov	PROPN
ejpam-5564	443	6	and	and	CCONJ
ejpam-5564	443	7	t.	t.	PROPN
ejpam-5564	443	8	leontieva	leontieva	PROPN
ejpam-5564	443	9	.	.	PUNCT
ejpam-5564	444	1	on	on	ADP
ejpam-5564	444	2	the	the	DET
ejpam-5564	444	3	expansion	expansion	NOUN
ejpam-5564	444	4	of	of	ADP
ejpam-5564	444	5	the	the	DET
ejpam-5564	444	6	domain	domain	NOUN
ejpam-5564	444	7	for	for	ADP
ejpam-5564	444	8	an	an	DET
ejpam-5564	444	9	analytical	analytical	ADJ
ejpam-5564	444	10	approximate	approximate	ADJ
ejpam-5564	444	11	solution	solution	NOUN
ejpam-5564	444	12	of	of	ADP
ejpam-5564	444	13	one	one	NUM
ejpam-5564	444	14	class	class	NOUN
ejpam-5564	444	15	of	of	ADP
ejpam-5564	444	16	second	second	ADJ
ejpam-5564	444	17	-	-	PUNCT
ejpam-5564	444	18	order	order	NOUN
ejpam-5564	444	19	nonlinear	nonlinear	ADJ
ejpam-5564	444	20	differential	differential	ADJ
ejpam-5564	444	21	equations	equation	NOUN
ejpam-5564	444	22	in	in	ADP
ejpam-5564	444	23	the	the	DET
ejpam-5564	444	24	complex	complex	ADJ
ejpam-5564	444	25	domain	domain	NOUN
ejpam-5564	444	26	.	.	PUNCT
ejpam-5564	445	1	j.	j.	PROPN
ejpam-5564	445	2	samara	samara	PROPN
ejpam-5564	445	3	state	state	PROPN
ejpam-5564	445	4	tech	tech	PROPN
ejpam-5564	445	5	.	.	PUNCT
ejpam-5564	446	1	univ	univ	PROPN
ejpam-5564	446	2	.	.	PROPN
ejpam-5564	446	3	,	,	PUNCT
ejpam-5564	446	4	ser	ser	PROPN
ejpam-5564	446	5	.	.	PUNCT
ejpam-5564	447	1	phys	phys	PROPN
ejpam-5564	447	2	.	.	PUNCT
ejpam-5564	448	1	math	math	NOUN
ejpam-5564	448	2	.	.	PUNCT
ejpam-5564	449	1	sci	sci	PROPN
ejpam-5564	449	2	.	.	PROPN
ejpam-5564	449	3	,	,	PUNCT
ejpam-5564	449	4	page	page	NOUN
ejpam-5564	449	5	174–186	174–186	NUM
ejpam-5564	449	6	,	,	PUNCT
ejpam-5564	449	7	2020	2020	NUM
ejpam-5564	449	8	.	.	PUNCT
ejpam-5564	450	1	[	[	X
ejpam-5564	450	2	38	38	NUM
ejpam-5564	450	3	]	]	PUNCT
ejpam-5564	450	4	s.	s.	PROPN
ejpam-5564	450	5	pandey	pandey	PROPN
ejpam-5564	450	6	,	,	PUNCT
ejpam-5564	450	7	p.	p.	NOUN
ejpam-5564	450	8	bindu	bindu	PROPN
ejpam-5564	450	9	,	,	PUNCT
ejpam-5564	450	10	m.	m.	NOUN
ejpam-5564	450	11	senthilvelan	senthilvelan	NOUN
ejpam-5564	450	12	,	,	PUNCT
ejpam-5564	450	13	and	and	CCONJ
ejpam-5564	450	14	m.	m.	PROPN
ejpam-5564	450	15	lakshmanan	lakshmanan	PROPN
ejpam-5564	450	16	.	.	PUNCT
ejpam-5564	451	1	a	a	DET
ejpam-5564	451	2	group	group	NOUN
ejpam-5564	451	3	theoretical	theoretical	ADJ
ejpam-5564	451	4	identification	identification	NOUN
ejpam-5564	451	5	of	of	ADP
ejpam-5564	451	6	integrable	integrable	ADJ
ejpam-5564	451	7	cases	case	NOUN
ejpam-5564	451	8	of	of	ADP
ejpam-5564	451	9	the	the	DET
ejpam-5564	451	10	liénard	liénard	NOUN
ejpam-5564	451	11	-	-	PUNCT
ejpam-5564	451	12	type	type	NOUN
ejpam-5564	451	13	equation	equation	NOUN
ejpam-5564	451	14	ẍ+	ẍ+	PROPN
ejpam-5564	452	1	f(x)ẋ+	f(x)ẋ+	X
ejpam-5564	452	2	g(x	g(x	NOUN
ejpam-5564	452	3	)	)	PUNCT
ejpam-5564	453	1	=	=	SYM
ejpam-5564	453	2	0	0	NUM
ejpam-5564	453	3	i.	i.	NOUN
ejpam-5564	453	4	equations	equation	NOUN
ejpam-5564	453	5	having	have	VERB
ejpam-5564	453	6	nonmaximal	nonmaximal	ADJ
ejpam-5564	453	7	number	number	NOUN
ejpam-5564	453	8	of	of	ADP
ejpam-5564	453	9	lie	lie	NOUN
ejpam-5564	453	10	point	point	NOUN
ejpam-5564	453	11	symmetries	symmetry	NOUN
ejpam-5564	453	12	.	.	PUNCT
ejpam-5564	454	1	journal	journal	PROPN
ejpam-5564	454	2	of	of	ADP
ejpam-5564	454	3	mathematical	mathematical	ADJ
ejpam-5564	454	4	physics	physics	NOUN
ejpam-5564	454	5	,	,	PUNCT
ejpam-5564	454	6	2009	2009	NUM
ejpam-5564	454	7	.	.	PUNCT
ejpam-5564	455	1	[	[	X
ejpam-5564	455	2	39	39	NUM
ejpam-5564	455	3	]	]	PUNCT
ejpam-5564	455	4	s.	s.	PROPN
ejpam-5564	455	5	pandey	pandey	PROPN
ejpam-5564	455	6	,	,	PUNCT
ejpam-5564	455	7	p.	p.	NOUN
ejpam-5564	455	8	bindu	bindu	PROPN
ejpam-5564	455	9	,	,	PUNCT
ejpam-5564	455	10	m.	m.	NOUN
ejpam-5564	455	11	senthilvelan	senthilvelan	NOUN
ejpam-5564	455	12	,	,	PUNCT
ejpam-5564	455	13	and	and	CCONJ
ejpam-5564	455	14	m.	m.	PROPN
ejpam-5564	455	15	lakshmanan	lakshmanan	PROPN
ejpam-5564	455	16	.	.	PUNCT
ejpam-5564	456	1	a	a	DET
ejpam-5564	456	2	group	group	NOUN
ejpam-5564	456	3	theoretical	theoretical	ADJ
ejpam-5564	456	4	identification	identification	NOUN
ejpam-5564	456	5	of	of	ADP
ejpam-5564	456	6	integrable	integrable	ADJ
ejpam-5564	456	7	cases	case	NOUN
ejpam-5564	456	8	of	of	ADP
ejpam-5564	456	9	the	the	DET
ejpam-5564	456	10	liénard	liénard	NOUN
ejpam-5564	456	11	-	-	PUNCT
ejpam-5564	456	12	type	type	NOUN
ejpam-5564	456	13	equation	equation	NOUN
ejpam-5564	456	14	ẍ	ẍ	PUNCT
ejpam-5564	457	1	+	+	CCONJ
ejpam-5564	457	2	f(x)ẋ	f(x)ẋ	NOUN
ejpam-5564	457	3	+	+	X
ejpam-5564	457	4	g(x	g(x	NOUN
ejpam-5564	457	5	)	)	PUNCT
ejpam-5564	457	6	=	=	SYM
ejpam-5564	457	7	0	0	NUM
ejpam-5564	457	8	ii	ii	PROPN
ejpam-5564	457	9	.	.	PUNCT
ejpam-5564	458	1	equations	equation	NOUN
ejpam-5564	458	2	having	have	VERB
ejpam-5564	458	3	nonmaximal	nonmaximal	ADJ
ejpam-5564	458	4	number	number	NOUN
ejpam-5564	458	5	of	of	ADP
ejpam-5564	458	6	lie	lie	NOUN
ejpam-5564	458	7	point	point	NOUN
ejpam-5564	458	8	symmetries	symmetry	NOUN
ejpam-5564	458	9	.	.	PUNCT
ejpam-5564	459	1	journal	journal	PROPN
ejpam-5564	459	2	of	of	ADP
ejpam-5564	459	3	mathematical	mathematical	ADJ
ejpam-5564	459	4	physics	physics	NOUN
ejpam-5564	459	5	,	,	PUNCT
ejpam-5564	459	6	2009	2009	NUM
ejpam-5564	459	7	.	.	PUNCT
ejpam-5564	460	1	[	[	X
ejpam-5564	460	2	40	40	NUM
ejpam-5564	460	3	]	]	PUNCT
ejpam-5564	460	4	a.	a.	NOUN
ejpam-5564	460	5	pchelova	pchelova	PROPN
ejpam-5564	460	6	.	.	PUNCT
ejpam-5564	461	1	construction	construction	NOUN
ejpam-5564	461	2	of	of	ADP
ejpam-5564	461	3	approximate	approximate	ADJ
ejpam-5564	461	4	solutions	solution	NOUN
ejpam-5564	461	5	for	for	ADP
ejpam-5564	461	6	a	a	DET
ejpam-5564	461	7	class	class	NOUN
ejpam-5564	461	8	of	of	ADP
ejpam-5564	461	9	first	first	ADJ
ejpam-5564	461	10	-	-	PUNCT
ejpam-5564	461	11	order	order	NOUN
ejpam-5564	461	12	nonlinear	nonlinear	ADJ
ejpam-5564	461	13	differential	differential	ADJ
ejpam-5564	461	14	equations	equation	NOUN
ejpam-5564	461	15	in	in	ADP
ejpam-5564	461	16	the	the	DET
ejpam-5564	461	17	analyticity	analyticity	NOUN
ejpam-5564	461	18	region	region	NOUN
ejpam-5564	461	19	.	.	PUNCT
ejpam-5564	462	1	herald	herald	NOUN
ejpam-5564	462	2	of	of	ADP
ejpam-5564	462	3	the	the	DET
ejpam-5564	462	4	bauman	bauman	NOUN
ejpam-5564	462	5	moscow	moscow	PROPN
ejpam-5564	462	6	state	state	PROPN
ejpam-5564	462	7	tech	tech	PROPN
ejpam-5564	462	8	.	.	PUNCT
ejpam-5564	463	1	univ	univ	PROPN
ejpam-5564	463	2	.	.	PROPN
ejpam-5564	463	3	,	,	PUNCT
ejpam-5564	463	4	nat	nat	PROPN
ejpam-5564	463	5	.	.	PUNCT
ejpam-5564	464	1	sci	sci	PROPN
ejpam-5564	464	2	.	.	PROPN
ejpam-5564	464	3	,	,	PUNCT
ejpam-5564	464	4	2016	2016	NUM
ejpam-5564	464	5	.	.	PUNCT
ejpam-5564	465	1	[	[	X
ejpam-5564	465	2	41	41	NUM
ejpam-5564	465	3	]	]	PUNCT
ejpam-5564	465	4	k.	k.	PROPN
ejpam-5564	465	5	p.	p.	PROPN
ejpam-5564	465	6	v.	v.	CCONJ
ejpam-5564	466	1	preethi	preethi	ADV
ejpam-5564	466	2	,	,	PUNCT
ejpam-5564	466	3	h.	h.	PROPN
ejpam-5564	466	4	alotaibi	alotaibi	PROPN
ejpam-5564	466	5	,	,	PUNCT
ejpam-5564	466	6	and	and	CCONJ
ejpam-5564	466	7	j.	j.	PROPN
ejpam-5564	466	8	visuvasam	visuvasam	PROPN
ejpam-5564	466	9	.	.	PUNCT
ejpam-5564	467	1	analysis	analysis	NOUN
ejpam-5564	467	2	of	of	ADP
ejpam-5564	467	3	amperometric	amperometric	NOUN
ejpam-5564	467	4	biosensor	biosensor	NOUN
ejpam-5564	467	5	utilizing	utilize	VERB
ejpam-5564	467	6	synergistic	synergistic	ADJ
ejpam-5564	467	7	substrates	substrate	NOUN
ejpam-5564	467	8	conversion	conversion	NOUN
ejpam-5564	467	9	:	:	PUNCT
ejpam-5564	467	10	akbari	akbari	PROPN
ejpam-5564	467	11	-	-	PUNCT
ejpam-5564	467	12	ganji	ganji	NOUN
ejpam-5564	467	13	’s	’s	PART
ejpam-5564	467	14	method	method	NOUN
ejpam-5564	467	15	.	.	PUNCT
ejpam-5564	468	1	mathematical	mathematical	ADJ
ejpam-5564	468	2	modelling	modelling	NOUN
ejpam-5564	468	3	and	and	CCONJ
ejpam-5564	468	4	control	control	NOUN
ejpam-5564	468	5	,	,	PUNCT
ejpam-5564	468	6	pages	page	NOUN
ejpam-5564	468	7	350–360	350–360	NUM
ejpam-5564	468	8	,	,	PUNCT
ejpam-5564	468	9	2024	2024	NUM
ejpam-5564	468	10	.	.	PUNCT
ejpam-5564	469	1	[	[	X
ejpam-5564	469	2	42	42	NUM
ejpam-5564	469	3	]	]	PUNCT
ejpam-5564	469	4	r.	r.	PROPN
ejpam-5564	469	5	shanthi	shanthi	PROPN
ejpam-5564	469	6	,	,	PUNCT
ejpam-5564	469	7	t.	t.	PROPN
ejpam-5564	469	8	iswarya	iswarya	PROPN
ejpam-5564	469	9	,	,	PUNCT
ejpam-5564	469	10	j.	j.	PROPN
ejpam-5564	469	11	visuvasam	visuvasam	PROPN
ejpam-5564	469	12	,	,	PUNCT
ejpam-5564	469	13	l.	l.	PROPN
ejpam-5564	469	14	rajendran	rajendran	PROPN
ejpam-5564	469	15	,	,	PUNCT
ejpam-5564	469	16	and	and	CCONJ
ejpam-5564	469	17	michael	michael	PROPN
ejpam-5564	469	18	e.g.	e.g.	ADV
ejpam-5564	469	19	lyons	lyons	PROPN
ejpam-5564	469	20	.	.	PUNCT
ejpam-5564	470	1	voltammetric	voltammetric	ADJ
ejpam-5564	470	2	and	and	CCONJ
ejpam-5564	470	3	mathematical	mathematical	ADJ
ejpam-5564	470	4	analysis	analysis	NOUN
ejpam-5564	470	5	of	of	ADP
ejpam-5564	470	6	adsorption	adsorption	NOUN
ejpam-5564	470	7	of	of	ADP
ejpam-5564	470	8	enzymes	enzyme	NOUN
ejpam-5564	470	9	at	at	ADP
ejpam-5564	470	10	rotating	rotate	VERB
ejpam-5564	470	11	disk	disk	NOUN
ejpam-5564	470	12	electrode	electrode	NOUN
ejpam-5564	470	13	.	.	PUNCT
ejpam-5564	471	1	international	international	ADJ
ejpam-5564	471	2	journal	journal	PROPN
ejpam-5564	471	3	of	of	ADP
ejpam-5564	471	4	electrochemical	electrochemical	ADJ
ejpam-5564	471	5	science	science	NOUN
ejpam-5564	471	6	,	,	PUNCT
ejpam-5564	471	7	2022	2022	NUM
ejpam-5564	471	8	.	.	PUNCT
ejpam-5564	472	1	[	[	X
ejpam-5564	472	2	43	43	NUM
ejpam-5564	472	3	]	]	X
ejpam-5564	472	4	e.	e.	PROPN
ejpam-5564	472	5	thailert	thailert	PROPN
ejpam-5564	472	6	and	and	CCONJ
ejpam-5564	472	7	s.	s.	PROPN
ejpam-5564	472	8	suksern	suksern	PROPN
ejpam-5564	472	9	.	.	PUNCT
ejpam-5564	473	1	linearizability	linearizability	NOUN
ejpam-5564	473	2	of	of	ADP
ejpam-5564	473	3	nonlinear	nonlinear	ADJ
ejpam-5564	473	4	third	third	ADJ
ejpam-5564	473	5	-	-	PUNCT
ejpam-5564	473	6	order	order	NOUN
ejpam-5564	473	7	ordinary	ordinary	ADJ
ejpam-5564	473	8	differential	differential	ADJ
ejpam-5564	473	9	equations	equation	NOUN
ejpam-5564	473	10	by	by	ADP
ejpam-5564	473	11	using	use	VERB
ejpam-5564	473	12	a	a	DET
ejpam-5564	473	13	generalized	generalized	ADJ
ejpam-5564	473	14	linearizing	linearize	VERB
ejpam-5564	473	15	transformation	transformation	NOUN
ejpam-5564	473	16	.	.	PUNCT
ejpam-5564	474	1	journal	journal	NOUN
ejpam-5564	474	2	of	of	ADP
ejpam-5564	474	3	applied	apply	VERB
ejpam-5564	474	4	mathematics	mathematic	NOUN
ejpam-5564	474	5	,	,	PUNCT
ejpam-5564	474	6	page	page	NOUN
ejpam-5564	474	7	1–12	1–12	NOUN
ejpam-5564	474	8	,	,	PUNCT
ejpam-5564	474	9	2014	2014	NUM
ejpam-5564	474	10	.	.	PUNCT
ejpam-5564	475	1	[	[	X
ejpam-5564	475	2	44	44	NUM
ejpam-5564	475	3	]	]	PUNCT
ejpam-5564	475	4	o.	o.	PROPN
ejpam-5564	475	5	urszula	urszula	PROPN
ejpam-5564	475	6	,	,	PUNCT
ejpam-5564	475	7	e.	e.	PROPN
ejpam-5564	475	8	schmeidel	schmeidel	PROPN
ejpam-5564	475	9	,	,	PUNCT
ejpam-5564	475	10	and	and	CCONJ
ejpam-5564	475	11	m.	m.	NOUN
ejpam-5564	475	12	zdanowicz	zdanowicz	PROPN
ejpam-5564	475	13	.	.	PUNCT
ejpam-5564	476	1	existence	existence	NOUN
ejpam-5564	476	2	of	of	ADP
ejpam-5564	476	3	solutions	solution	NOUN
ejpam-5564	476	4	to	to	AUX
ejpam-5564	476	5	nonlinear	nonlinear	ADJ
ejpam-5564	476	6	fourth	fourth	ADJ
ejpam-5564	476	7	-	-	PUNCT
ejpam-5564	476	8	order	order	NOUN
ejpam-5564	476	9	beam	beam	NOUN
ejpam-5564	476	10	equation	equation	NOUN
ejpam-5564	476	11	.	.	PUNCT
ejpam-5564	477	1	qualitative	qualitative	ADJ
ejpam-5564	477	2	theory	theory	NOUN
ejpam-5564	477	3	of	of	ADP
ejpam-5564	477	4	dynamical	dynamical	ADJ
ejpam-5564	477	5	systems	system	NOUN
ejpam-5564	477	6	,	,	PUNCT
ejpam-5564	477	7	2023	2023	NUM
ejpam-5564	477	8	.	.	PUNCT
ejpam-5564	478	1	[	[	X
ejpam-5564	478	2	45	45	NUM
ejpam-5564	478	3	]	]	PUNCT
ejpam-5564	478	4	j.	j.	PROPN
ejpam-5564	478	5	visuvasam	visuvasam	PROPN
ejpam-5564	478	6	and	and	CCONJ
ejpam-5564	478	7	h.	h.	PROPN
ejpam-5564	478	8	alotaibi	alotaibi	PROPN
ejpam-5564	478	9	.	.	PUNCT
ejpam-5564	479	1	analysis	analysis	NOUN
ejpam-5564	479	2	of	of	ADP
ejpam-5564	479	3	von	von	PROPN
ejpam-5564	479	4	kármán	kármán	PROPN
ejpam-5564	479	5	swirling	swirl	VERB
ejpam-5564	479	6	flows	flow	NOUN
ejpam-5564	479	7	due	due	ADJ
ejpam-5564	479	8	to	to	ADP
ejpam-5564	479	9	a	a	DET
ejpam-5564	479	10	porous	porous	ADJ
ejpam-5564	479	11	rotating	rotating	NOUN
ejpam-5564	479	12	disk	disk	NOUN
ejpam-5564	479	13	electrode	electrode	NOUN
ejpam-5564	479	14	.	.	PUNCT
ejpam-5564	480	1	micromachines	micromachine	NOUN
ejpam-5564	480	2	,	,	PUNCT
ejpam-5564	480	3	2023	2023	NUM
ejpam-5564	480	4	.	.	PUNCT
ejpam-5564	481	1	[	[	X
ejpam-5564	481	2	46	46	NUM
ejpam-5564	481	3	]	]	X
ejpam-5564	481	4	j.	j.	PROPN
ejpam-5564	481	5	visuvasam	visuvasam	PROPN
ejpam-5564	481	6	,	,	PUNCT
ejpam-5564	481	7	a.	a.	NOUN
ejpam-5564	481	8	meena	meena	PROPN
ejpam-5564	481	9	,	,	PUNCT
ejpam-5564	481	10	and	and	CCONJ
ejpam-5564	481	11	l.	l.	PROPN
ejpam-5564	481	12	rajendran	rajendran	PROPN
ejpam-5564	481	13	.	.	PUNCT
ejpam-5564	482	1	new	new	ADJ
ejpam-5564	482	2	analytical	analytical	ADJ
ejpam-5564	482	3	method	method	NOUN
ejpam-5564	482	4	for	for	ADP
ejpam-5564	482	5	solving	solve	VERB
ejpam-5564	482	6	nonlinear	nonlinear	ADJ
ejpam-5564	482	7	equation	equation	NOUN
ejpam-5564	482	8	in	in	ADP
ejpam-5564	482	9	rotating	rotate	VERB
ejpam-5564	482	10	disk	disk	NOUN
ejpam-5564	482	11	electrodes	electrode	NOUN
ejpam-5564	482	12	for	for	ADP
ejpam-5564	482	13	second	second	ADJ
ejpam-5564	482	14	-	-	PUNCT
ejpam-5564	482	15	order	order	NOUN
ejpam-5564	482	16	ece	ece	PROPN
ejpam-5564	482	17	reactions	reaction	NOUN
ejpam-5564	482	18	.	.	PUNCT
ejpam-5564	483	1	journal	journal	NOUN
ejpam-5564	483	2	of	of	ADP
ejpam-5564	483	3	electroanalytical	electroanalytical	ADJ
ejpam-5564	483	4	chemistry	chemistry	NOUN
ejpam-5564	483	5	,	,	PUNCT
ejpam-5564	483	6	2020	2020	NUM
ejpam-5564	483	7	.	.	PUNCT
ejpam-5564	484	1	[	[	X
ejpam-5564	484	2	47	47	NUM
ejpam-5564	484	3	]	]	X
ejpam-5564	484	4	n.	n.	PROPN
ejpam-5564	484	5	vitanov	vitanov	PROPN
ejpam-5564	484	6	.	.	PUNCT
ejpam-5564	485	1	simple	simple	ADJ
ejpam-5564	485	2	equations	equation	NOUN
ejpam-5564	485	3	method	method	NOUN
ejpam-5564	485	4	(	(	PUNCT
ejpam-5564	485	5	sesm	sesm	PROPN
ejpam-5564	485	6	):	):	PUNCT
ejpam-5564	485	7	an	an	DET
ejpam-5564	485	8	effective	effective	ADJ
ejpam-5564	485	9	algorithm	algorithm	NOUN
ejpam-5564	485	10	for	for	ADP
ejpam-5564	485	11	obtaining	obtain	VERB
ejpam-5564	485	12	exact	exact	ADJ
ejpam-5564	485	13	solutions	solution	NOUN
ejpam-5564	485	14	of	of	ADP
ejpam-5564	485	15	nonlinear	nonlinear	ADJ
ejpam-5564	485	16	differential	differential	ADJ
ejpam-5564	485	17	equations	equation	NOUN
ejpam-5564	485	18	.	.	PUNCT
ejpam-5564	486	1	entropy	entropy	PROPN
ejpam-5564	486	2	,	,	PUNCT
ejpam-5564	486	3	2022	2022	NUM
ejpam-5564	486	4	.	.	PUNCT
ejpam-5564	487	1	[	[	X
ejpam-5564	487	2	48	48	NUM
ejpam-5564	487	3	]	]	PUNCT
ejpam-5564	487	4	q.	q.	PROPN
ejpam-5564	487	5	yao	yao	PROPN
ejpam-5564	487	6	.	.	PUNCT
ejpam-5564	488	1	positive	positive	ADJ
ejpam-5564	488	2	solutions	solution	NOUN
ejpam-5564	488	3	of	of	ADP
ejpam-5564	488	4	a	a	DET
ejpam-5564	488	5	nonlinear	nonlinear	ADJ
ejpam-5564	488	6	elastic	elastic	ADJ
ejpam-5564	488	7	beam	beam	NOUN
ejpam-5564	488	8	equation	equation	NOUN
ejpam-5564	488	9	rigidly	rigidly	ADV
ejpam-5564	488	10	fastened	fasten	VERB
ejpam-5564	488	11	on	on	ADP
ejpam-5564	488	12	the	the	DET
ejpam-5564	488	13	left	left	NOUN
ejpam-5564	488	14	and	and	CCONJ
ejpam-5564	488	15	simply	simply	ADV
ejpam-5564	488	16	supported	support	VERB
ejpam-5564	488	17	on	on	ADP
ejpam-5564	488	18	the	the	DET
ejpam-5564	488	19	right	right	NOUN
ejpam-5564	488	20	.	.	PUNCT
ejpam-5564	489	1	nonlinear	nonlinear	ADJ
ejpam-5564	489	2	analysis	analysis	NOUN
ejpam-5564	489	3	:	:	PUNCT
ejpam-5564	489	4	theory	theory	NOUN
ejpam-5564	489	5	,	,	PUNCT
ejpam-5564	489	6	methods	method	NOUN
ejpam-5564	489	7	&	&	CCONJ
ejpam-5564	489	8	applications	application	NOUN
ejpam-5564	489	9	,	,	PUNCT
ejpam-5564	489	10	2008	2008	NUM
ejpam-5564	489	11	.	.	PUNCT
ejpam-5564	490	1	m.	m.	NOUN
ejpam-5564	490	2	gasanov	gasanov	PROPN
ejpam-5564	490	3	/	/	SYM
ejpam-5564	490	4	eur	eur	PROPN
ejpam-5564	490	5	.	.	PUNCT
ejpam-5564	491	1	j.	j.	PROPN
ejpam-5564	491	2	pure	pure	PROPN
ejpam-5564	491	3	appl	appl	PROPN
ejpam-5564	491	4	.	.	PROPN
ejpam-5564	491	5	math	math	PROPN
ejpam-5564	491	6	,	,	PUNCT
ejpam-5564	491	7	18	18	NUM
ejpam-5564	491	8	(	(	PUNCT
ejpam-5564	491	9	1	1	NUM
ejpam-5564	491	10	)	)	PUNCT
ejpam-5564	491	11	(	(	PUNCT
ejpam-5564	491	12	2025	2025	NUM
ejpam-5564	491	13	)	)	PUNCT
ejpam-5564	491	14	,	,	PUNCT
ejpam-5564	491	15	5564	5564	NUM
ejpam-5564	491	16	19	19	NUM
ejpam-5564	491	17	of	of	ADP
ejpam-5564	491	18	19	19	NUM
ejpam-5564	492	1	[	[	SYM
ejpam-5564	492	2	49	49	NUM
ejpam-5564	492	3	]	]	PUNCT
ejpam-5564	492	4	v.	v.	CCONJ
ejpam-5564	492	5	zaitsev	zaitsev	NOUN
ejpam-5564	492	6	and	and	CCONJ
ejpam-5564	492	7	a.	a.	NOUN
ejpam-5564	492	8	polyanin	polyanin	PROPN
ejpam-5564	492	9	.	.	PUNCT
ejpam-5564	493	1	handbook	handbook	NOUN
ejpam-5564	493	2	of	of	ADP
ejpam-5564	493	3	exact	exact	ADJ
ejpam-5564	493	4	solutions	solution	NOUN
ejpam-5564	493	5	for	for	ADP
ejpam-5564	493	6	ordinary	ordinary	ADJ
ejpam-5564	493	7	differential	differential	ADJ
ejpam-5564	493	8	equations	equation	NOUN
ejpam-5564	493	9	.	.	PUNCT
ejpam-5564	494	1	crc	crc	PROPN
ejpam-5564	494	2	press	press	PROPN
ejpam-5564	494	3	,	,	PUNCT
ejpam-5564	494	4	new	new	PROPN
ejpam-5564	494	5	york	york	PROPN
ejpam-5564	494	6	,	,	PUNCT
ejpam-5564	494	7	2002	2002	NUM
ejpam-5564	494	8	.	.	PUNCT
ejpam-5564	495	1	[	[	X
ejpam-5564	495	2	50	50	NUM
ejpam-5564	495	3	]	]	PUNCT
ejpam-5564	495	4	p.	p.	NOUN
ejpam-5564	495	5	řehák	řehák	PROPN
ejpam-5564	495	6	.	.	PUNCT
ejpam-5564	496	1	on	on	ADP
ejpam-5564	496	2	asymptotic	asymptotic	ADJ
ejpam-5564	496	3	relationships	relationship	NOUN
ejpam-5564	496	4	between	between	ADP
ejpam-5564	496	5	two	two	NUM
ejpam-5564	496	6	higher	high	ADJ
ejpam-5564	496	7	order	order	NOUN
ejpam-5564	496	8	dynamic	dynamic	ADJ
ejpam-5564	496	9	equations	equation	NOUN
ejpam-5564	496	10	on	on	ADP
ejpam-5564	496	11	time	time	NOUN
ejpam-5564	496	12	scales	scale	NOUN
ejpam-5564	496	13	.	.	PUNCT
ejpam-5564	497	1	applied	apply	VERB
ejpam-5564	497	2	mathematics	mathematics	NOUN
ejpam-5564	497	3	letters	letter	NOUN
ejpam-5564	497	4	,	,	PUNCT
ejpam-5564	497	5	page	page	NOUN
ejpam-5564	497	6	84–90	84–90	NUM
ejpam-5564	497	7	,	,	PUNCT
ejpam-5564	497	8	2017	2017	NUM
ejpam-5564	497	9	.	.	PUNCT