id	sid	tid	token	lemma	pos
ejpam-3372	1	1	european	european	PROPN
ejpam-3372	1	2	journal	journal	PROPN
ejpam-3372	1	3	of	of	ADP
ejpam-3372	1	4	pure	pure	ADJ
ejpam-3372	1	5	and	and	CCONJ
ejpam-3372	1	6	applied	apply	VERB
ejpam-3372	1	7	mathematics	mathematic	NOUN
ejpam-3372	1	8	vol	vol	NOUN
ejpam-3372	1	9	.	.	PROPN
ejpam-3372	2	1	12	12	NUM
ejpam-3372	2	2	,	,	PUNCT
ejpam-3372	2	3	no	no	INTJ
ejpam-3372	2	4	.	.	NOUN
ejpam-3372	2	5	2	2	NUM
ejpam-3372	2	6	,	,	PUNCT
ejpam-3372	2	7	2019	2019	NUM
ejpam-3372	2	8	,	,	PUNCT
ejpam-3372	2	9	649	649	NUM
ejpam-3372	2	10	-	-	SYM
ejpam-3372	2	11	653	653	NUM
ejpam-3372	2	12	issn	issn	PROPN
ejpam-3372	2	13	1307	1307	NUM
ejpam-3372	2	14	-	-	SYM
ejpam-3372	2	15	5543	5543	NUM
ejpam-3372	2	16	–	–	PUNCT
ejpam-3372	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3372	2	18	published	publish	VERB
ejpam-3372	2	19	by	by	ADP
ejpam-3372	2	20	new	new	PROPN
ejpam-3372	2	21	york	york	PROPN
ejpam-3372	2	22	business	business	PROPN
ejpam-3372	2	23	global	global	PROPN
ejpam-3372	2	24	some	some	DET
ejpam-3372	2	25	estimates	estimate	NOUN
ejpam-3372	2	26	below	below	ADP
ejpam-3372	2	27	the	the	DET
ejpam-3372	2	28	modulus	modulus	NOUN
ejpam-3372	2	29	of	of	ADP
ejpam-3372	2	30	integrals	integral	NOUN
ejpam-3372	2	31	of	of	ADP
ejpam-3372	2	32	some	some	DET
ejpam-3372	2	33	polynomials	polynomial	NOUN
ejpam-3372	2	34	in	in	ADP
ejpam-3372	2	35	the	the	DET
ejpam-3372	2	36	complex	complex	ADJ
ejpam-3372	2	37	plane	plane	NOUN
ejpam-3372	2	38	todor	todor	NOUN
ejpam-3372	2	39	stoyanov	stoyanov	NOUN
ejpam-3372	2	40	stoyanov	stoyanov	PROPN
ejpam-3372	2	41	1	1	NUM
ejpam-3372	2	42	university	university	NOUN
ejpam-3372	2	43	of	of	ADP
ejpam-3372	2	44	economics	economic	NOUN
ejpam-3372	2	45	,	,	PUNCT
ejpam-3372	2	46	department	department	NOUN
ejpam-3372	2	47	of	of	ADP
ejpam-3372	2	48	mathematics	mathematics	PROPN
ejpam-3372	2	49	bul	bul	PROPN
ejpam-3372	2	50	.	.	PUNCT
ejpam-3372	3	1	knyaz	knyaz	PROPN
ejpam-3372	3	2	boris	boris	PROPN
ejpam-3372	3	3	i	i	PRON
ejpam-3372	3	4	77	77	NUM
ejpam-3372	3	5	,	,	PUNCT
ejpam-3372	3	6	varna	varna	ADJ
ejpam-3372	3	7	9002	9002	NUM
ejpam-3372	3	8	,	,	PUNCT
ejpam-3372	3	9	bulgaria	bulgaria	PROPN
ejpam-3372	3	10	abstract	abstract	NOUN
ejpam-3372	3	11	.	.	PUNCT
ejpam-3372	4	1	in	in	ADP
ejpam-3372	4	2	this	this	DET
ejpam-3372	4	3	paper	paper	NOUN
ejpam-3372	4	4	,	,	PUNCT
ejpam-3372	4	5	we	we	PRON
ejpam-3372	4	6	make	make	VERB
ejpam-3372	4	7	some	some	DET
ejpam-3372	4	8	estimates	estimate	NOUN
ejpam-3372	4	9	below	below	ADP
ejpam-3372	4	10	the	the	DET
ejpam-3372	4	11	modulus	modulus	NOUN
ejpam-3372	4	12	of	of	ADP
ejpam-3372	4	13	some	some	DET
ejpam-3372	4	14	integrals	integral	NOUN
ejpam-3372	4	15	in	in	ADP
ejpam-3372	4	16	the	the	DET
ejpam-3372	4	17	complex	complex	ADJ
ejpam-3372	4	18	plane	plane	NOUN
ejpam-3372	4	19	.	.	PUNCT
ejpam-3372	5	1	our	our	PRON
ejpam-3372	5	2	aim	aim	NOUN
ejpam-3372	5	3	is	be	AUX
ejpam-3372	5	4	to	to	PART
ejpam-3372	5	5	prove	prove	VERB
ejpam-3372	5	6	the	the	DET
ejpam-3372	5	7	conjecture1	conjecture1	NUM
ejpam-3372	5	8	,	,	PUNCT
ejpam-3372	5	9	which	which	PRON
ejpam-3372	5	10	we	we	PRON
ejpam-3372	5	11	could	could	AUX
ejpam-3372	5	12	see	see	VERB
ejpam-3372	5	13	in	in	ADP
ejpam-3372	5	14	[	[	X
ejpam-3372	5	15	2–4	2–4	NUM
ejpam-3372	5	16	]	]	X
ejpam-3372	5	17	.	.	PUNCT
ejpam-3372	6	1	the	the	DET
ejpam-3372	6	2	proof	proof	NOUN
ejpam-3372	6	3	of	of	ADP
ejpam-3372	6	4	the	the	DET
ejpam-3372	6	5	conjecture	conjecture	NOUN
ejpam-3372	6	6	appears	appear	VERB
ejpam-3372	6	7	the	the	DET
ejpam-3372	6	8	corollary	corollary	NOUN
ejpam-3372	6	9	.	.	PUNCT
ejpam-3372	7	1	2010	2010	NUM
ejpam-3372	7	2	mathematics	mathematic	NOUN
ejpam-3372	7	3	subject	subject	NOUN
ejpam-3372	7	4	classifications	classification	NOUN
ejpam-3372	7	5	:	:	PUNCT
ejpam-3372	7	6	30a10	30a10	NUM
ejpam-3372	7	7	key	key	ADJ
ejpam-3372	7	8	words	word	NOUN
ejpam-3372	7	9	and	and	CCONJ
ejpam-3372	7	10	phrases	phrase	NOUN
ejpam-3372	7	11	:	:	PUNCT
ejpam-3372	7	12	zeros	zero	NOUN
ejpam-3372	7	13	,	,	PUNCT
ejpam-3372	7	14	complex	complex	ADJ
ejpam-3372	7	15	polynomial	polynomial	ADJ
ejpam-3372	7	16	,	,	PUNCT
ejpam-3372	7	17	real	real	ADJ
ejpam-3372	7	18	polynomial	polynomial	ADJ
ejpam-3372	7	19	,	,	PUNCT
ejpam-3372	7	20	disk	disk	NOUN
ejpam-3372	7	21	,	,	PUNCT
ejpam-3372	7	22	derivative	derivative	ADJ
ejpam-3372	7	23	,	,	PUNCT
ejpam-3372	7	24	integral	integral	ADJ
ejpam-3372	7	25	1	1	NUM
ejpam-3372	7	26	.	.	PUNCT
ejpam-3372	7	27	introduction	introduction	NOUN
ejpam-3372	7	28	in	in	ADP
ejpam-3372	7	29	papers	paper	NOUN
ejpam-3372	7	30	[	[	X
ejpam-3372	7	31	2–4	2–4	NUM
ejpam-3372	7	32	]	]	PUNCT
ejpam-3372	7	33	,	,	PUNCT
ejpam-3372	7	34	we	we	PRON
ejpam-3372	7	35	consider	consider	VERB
ejpam-3372	7	36	the	the	DET
ejpam-3372	7	37	conjecture	conjecture	NOUN
ejpam-3372	7	38	1	1	NUM
ejpam-3372	7	39	:	:	PUNCT
ejpam-3372	7	40	if	if	SCONJ
ejpam-3372	7	41	ak	ak	PROPN
ejpam-3372	7	42	≥	≥	PROPN
ejpam-3372	7	43	0	0	NUM
ejpam-3372	7	44	,	,	PUNCT
ejpam-3372	7	45	ak	ak	PROPN
ejpam-3372	7	46	∈	∈	PROPN
ejpam-3372	7	47	r	r	NOUN
ejpam-3372	7	48	,	,	PUNCT
ejpam-3372	7	49	then	then	ADV
ejpam-3372	7	50	we	we	PRON
ejpam-3372	7	51	assert∣∣∣∣∣∣∣	assert∣∣∣∣∣∣∣	ADJ
ejpam-3372	7	52	eiϕ∫	eiϕ∫	NOUN
ejpam-3372	7	53	0	0	NUM
ejpam-3372	7	54	n∏	n∏	NOUN
ejpam-3372	7	55	k=1	k=1	NOUN
ejpam-3372	8	1	(	(	PUNCT
ejpam-3372	8	2	x+	x+	PROPN
ejpam-3372	8	3	ak	ak	PROPN
ejpam-3372	8	4	)	)	PUNCT
ejpam-3372	8	5	dx	dx	PROPN
ejpam-3372	8	6	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	PROPN
ejpam-3372	8	7	≥	≥	NUM
ejpam-3372	8	8	1	1	NUM
ejpam-3372	8	9	n+	n+	ADP
ejpam-3372	8	10	1	1	NUM
ejpam-3372	8	11	,	,	PUNCT
ejpam-3372	8	12	for	for	ADP
ejpam-3372	8	13	arbitrary	arbitrary	ADJ
ejpam-3372	8	14	natural	natural	ADJ
ejpam-3372	8	15	n	n	NOUN
ejpam-3372	8	16	,	,	PUNCT
ejpam-3372	8	17	ϕ	ϕ	PROPN
ejpam-3372	8	18	∈	∈	PROPN
ejpam-3372	8	19	[	[	PUNCT
ejpam-3372	8	20	0	0	NUM
ejpam-3372	8	21	,	,	PUNCT
ejpam-3372	8	22	π2	π2	NOUN
ejpam-3372	8	23	]	]	PUNCT
ejpam-3372	8	24	.	.	PUNCT
ejpam-3372	9	1	there	there	PRON
ejpam-3372	9	2	exists	exist	VERB
ejpam-3372	9	3	a	a	DET
ejpam-3372	9	4	connection	connection	NOUN
ejpam-3372	9	5	between	between	ADP
ejpam-3372	9	6	this	this	DET
ejpam-3372	9	7	conjecture	conjecture	NOUN
ejpam-3372	9	8	and	and	CCONJ
ejpam-3372	9	9	conjecture2	conjecture2	PROPN
ejpam-3372	9	10	:	:	PUNCT
ejpam-3372	9	11	if	if	SCONJ
ejpam-3372	9	12	φk	φk	ADP
ejpam-3372	9	13	∈	∈	PROPN
ejpam-3372	9	14	[	[	PUNCT
ejpam-3372	9	15	π	π	PROPN
ejpam-3372	9	16	2	2	NUM
ejpam-3372	9	17	,	,	PUNCT
ejpam-3372	9	18	π	π	X
ejpam-3372	9	19	]	]	PUNCT
ejpam-3372	9	20	,	,	PUNCT
ejpam-3372	9	21	then∣∣∣∣∣∣	then∣∣∣∣∣∣	PROPN
ejpam-3372	9	22	0∫	0∫	NUM
ejpam-3372	9	23	−1	−1	NOUN
ejpam-3372	9	24	(	(	PUNCT
ejpam-3372	9	25	x+	x+	ADJ
ejpam-3372	9	26	1	1	NUM
ejpam-3372	9	27	)	)	PUNCT
ejpam-3372	9	28	n∏	n∏	NOUN
ejpam-3372	9	29	k=1	k=1	NOUN
ejpam-3372	10	1	(	(	PUNCT
ejpam-3372	10	2	x−	x−	PROPN
ejpam-3372	10	3	eiφk	eiφk	PROPN
ejpam-3372	10	4	)	)	PUNCT
ejpam-3372	11	1	dx	dx	PROPN
ejpam-3372	12	1	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3372	12	2	≥	≥	NUM
ejpam-3372	12	3	1	1	NUM
ejpam-3372	12	4	n+	n+	SYM
ejpam-3372	12	5	2	2	NUM
ejpam-3372	12	6	.	.	PUNCT
ejpam-3372	13	1	both	both	PRON
ejpam-3372	13	2	conjectures	conjecture	VERB
ejpam-3372	13	3	are	be	AUX
ejpam-3372	13	4	very	very	ADV
ejpam-3372	13	5	important	important	ADJ
ejpam-3372	13	6	for	for	ADP
ejpam-3372	13	7	the	the	DET
ejpam-3372	13	8	proofs	proof	NOUN
ejpam-3372	13	9	of	of	ADP
ejpam-3372	13	10	some	some	DET
ejpam-3372	13	11	famous	famous	ADJ
ejpam-3372	13	12	conjectures	conjecture	NOUN
ejpam-3372	13	13	,	,	PUNCT
ejpam-3372	13	14	like	like	ADP
ejpam-3372	13	15	sendov	sendov	PROPN
ejpam-3372	13	16	’s	’s	PART
ejpam-3372	13	17	and	and	CCONJ
ejpam-3372	13	18	obreshkoff	obreshkoff	NOUN
ejpam-3372	13	19	’s	’s	PART
ejpam-3372	13	20	ones	one	NOUN
ejpam-3372	13	21	.	.	PUNCT
ejpam-3372	14	1	a	a	DET
ejpam-3372	14	2	possible	possible	ADJ
ejpam-3372	14	3	connection	connection	NOUN
ejpam-3372	14	4	between	between	ADP
ejpam-3372	14	5	both	both	DET
ejpam-3372	14	6	conjctures	conjcture	NOUN
ejpam-3372	14	7	appears	appear	VERB
ejpam-3372	14	8	[	[	X
ejpam-3372	14	9	5	5	NUM
ejpam-3372	14	10	]	]	PUNCT
ejpam-3372	14	11	.	.	PUNCT
ejpam-3372	15	1	here	here	ADV
ejpam-3372	15	2	we	we	PRON
ejpam-3372	15	3	shall	shall	AUX
ejpam-3372	15	4	extend	extend	VERB
ejpam-3372	15	5	this	this	DET
ejpam-3372	15	6	problem	problem	NOUN
ejpam-3372	15	7	(	(	PUNCT
ejpam-3372	15	8	conjecture1	conjecture1	X
ejpam-3372	15	9	):	):	PUNCT
ejpam-3372	15	10	what	what	PRON
ejpam-3372	15	11	kind	kind	NOUN
ejpam-3372	15	12	of	of	ADP
ejpam-3372	15	13	set	set	ADJ
ejpam-3372	15	14	l	l	NOUN
ejpam-3372	15	15	satisfies	satisfie	NOUN
ejpam-3372	15	16	this	this	DET
ejpam-3372	15	17	assertion	assertion	NOUN
ejpam-3372	15	18	,	,	PUNCT
ejpam-3372	15	19	i.e.	i.e.	X
ejpam-3372	15	20	if	if	SCONJ
ejpam-3372	15	21	ak	ak	PROPN
ejpam-3372	15	22	belongs	belong	VERB
ejpam-3372	15	23	to	to	ADP
ejpam-3372	15	24	the	the	DET
ejpam-3372	15	25	set	set	PROPN
ejpam-3372	15	26	l	l	NOUN
ejpam-3372	15	27	,	,	PUNCT
ejpam-3372	15	28	then	then	ADV
ejpam-3372	15	29	the	the	DET
ejpam-3372	15	30	upper	upper	ADJ
ejpam-3372	15	31	inequality	inequality	NOUN
ejpam-3372	15	32	is	be	AUX
ejpam-3372	15	33	true	true	ADJ
ejpam-3372	15	34	.	.	PUNCT
ejpam-3372	16	1	the	the	DET
ejpam-3372	16	2	results	result	NOUN
ejpam-3372	16	3	related	relate	VERB
ejpam-3372	16	4	with	with	ADP
ejpam-3372	16	5	the	the	DET
ejpam-3372	16	6	conjecture	conjecture	NOUN
ejpam-3372	16	7	1	1	NUM
ejpam-3372	16	8	,	,	PUNCT
ejpam-3372	16	9	we	we	PRON
ejpam-3372	16	10	observe	observe	VERB
ejpam-3372	16	11	in	in	ADP
ejpam-3372	16	12	theorem	theorem	NOUN
ejpam-3372	16	13	1	1	NUM
ejpam-3372	16	14	,	,	PUNCT
ejpam-3372	16	15	theorem	theorem	VERB
ejpam-3372	16	16	2	2	NUM
ejpam-3372	16	17	.	.	PUNCT
ejpam-3372	16	18	in	in	ADP
ejpam-3372	16	19	theorem	theorem	NOUN
ejpam-3372	16	20	4	4	NUM
ejpam-3372	16	21	we	we	PRON
ejpam-3372	16	22	generalize	generalize	VERB
ejpam-3372	16	23	and	and	CCONJ
ejpam-3372	16	24	prove	prove	VERB
ejpam-3372	16	25	the	the	DET
ejpam-3372	16	26	extended	extended	ADJ
ejpam-3372	16	27	conjecture	conjecture	NOUN
ejpam-3372	16	28	.	.	PUNCT
ejpam-3372	17	1	we	we	PRON
ejpam-3372	17	2	can	can	AUX
ejpam-3372	17	3	see	see	VERB
ejpam-3372	17	4	the	the	DET
ejpam-3372	17	5	results	result	NOUN
ejpam-3372	17	6	of	of	ADP
ejpam-3372	17	7	theorem	theorem	NOUN
ejpam-3372	17	8	1	1	NUM
ejpam-3372	17	9	in	in	ADP
ejpam-3372	17	10	doi	doi	NOUN
ejpam-3372	17	11	:	:	PUNCT
ejpam-3372	17	12	https://doi.org/10.29020/nybg.ejpam.v12i2.3372	https://doi.org/10.29020/nybg.ejpam.v12i2.3372	PROPN
ejpam-3372	17	13	email	email	NOUN
ejpam-3372	17	14	address	address	NOUN
ejpam-3372	17	15	:	:	PUNCT
ejpam-3372	17	16	todstoyanov@yahoo.com	todstoyanov@yahoo.com	X
ejpam-3372	17	17	(	(	PUNCT
ejpam-3372	17	18	t.	t.	PROPN
ejpam-3372	17	19	s.	s.	PROPN
ejpam-3372	17	20	stoyanov	stoyanov	PROPN
ejpam-3372	17	21	)	)	PUNCT
ejpam-3372	17	22	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3372	18	1	649	649	NUM
ejpam-3372	18	2	c	c	X
ejpam-3372	18	3	©	©	PROPN
ejpam-3372	18	4	2019	2019	NUM
ejpam-3372	18	5	ejpam	ejpam	NOUN
ejpam-3372	18	6	all	all	DET
ejpam-3372	18	7	rights	right	NOUN
ejpam-3372	18	8	reserved	reserve	VERB
ejpam-3372	18	9	.	.	PUNCT
ejpam-3372	19	1	t.	t.	PROPN
ejpam-3372	19	2	s.	s.	PROPN
ejpam-3372	19	3	stoyanov	stoyanov	PROPN
ejpam-3372	19	4	/	/	SYM
ejpam-3372	19	5	eur	eur	PROPN
ejpam-3372	19	6	.	.	PUNCT
ejpam-3372	20	1	j.	j.	PROPN
ejpam-3372	20	2	pure	pure	PROPN
ejpam-3372	20	3	appl	appl	PROPN
ejpam-3372	20	4	.	.	PROPN
ejpam-3372	20	5	math	math	PROPN
ejpam-3372	20	6	,	,	PUNCT
ejpam-3372	20	7	12	12	NUM
ejpam-3372	20	8	(	(	PUNCT
ejpam-3372	20	9	2	2	NUM
ejpam-3372	20	10	)	)	PUNCT
ejpam-3372	20	11	(	(	PUNCT
ejpam-3372	20	12	2019	2019	NUM
ejpam-3372	20	13	)	)	PUNCT
ejpam-3372	20	14	,	,	PUNCT
ejpam-3372	20	15	649	649	NUM
ejpam-3372	20	16	-	-	SYM
ejpam-3372	20	17	653	653	NUM
ejpam-3372	20	18	650	650	NUM
ejpam-3372	21	1	[	[	SYM
ejpam-3372	21	2	2	2	NUM
ejpam-3372	21	3	,	,	PUNCT
ejpam-3372	21	4	4	4	NUM
ejpam-3372	21	5	]	]	PUNCT
ejpam-3372	21	6	.	.	PUNCT
ejpam-3372	22	1	such	such	ADJ
ejpam-3372	22	2	one	one	NUM
ejpam-3372	22	3	of	of	ADP
ejpam-3372	22	4	theorem	theorem	ADJ
ejpam-3372	22	5	2	2	NUM
ejpam-3372	22	6	could	could	AUX
ejpam-3372	22	7	be	be	AUX
ejpam-3372	22	8	seen	see	VERB
ejpam-3372	22	9	in	in	ADP
ejpam-3372	22	10	[	[	X
ejpam-3372	22	11	3	3	NUM
ejpam-3372	22	12	]	]	PUNCT
ejpam-3372	22	13	.	.	PUNCT
ejpam-3372	23	1	many	many	ADJ
ejpam-3372	23	2	authors	author	NOUN
ejpam-3372	23	3	use	use	VERB
ejpam-3372	23	4	some	some	DET
ejpam-3372	23	5	modulus	modulus	NOUN
ejpam-3372	23	6	of	of	ADP
ejpam-3372	23	7	some	some	DET
ejpam-3372	23	8	integrals	integral	NOUN
ejpam-3372	23	9	in	in	ADP
ejpam-3372	23	10	the	the	DET
ejpam-3372	23	11	complex	complex	ADJ
ejpam-3372	23	12	plane	plane	NOUN
ejpam-3372	23	13	for	for	ADP
ejpam-3372	23	14	various	various	ADJ
ejpam-3372	23	15	estimates	estimate	NOUN
ejpam-3372	23	16	in	in	ADP
ejpam-3372	23	17	their	their	PRON
ejpam-3372	23	18	works	work	NOUN
ejpam-3372	23	19	.	.	PUNCT
ejpam-3372	24	1	for	for	ADP
ejpam-3372	24	2	example	example	NOUN
ejpam-3372	24	3	we	we	PRON
ejpam-3372	24	4	can	can	AUX
ejpam-3372	24	5	see	see	VERB
ejpam-3372	24	6	how	how	SCONJ
ejpam-3372	24	7	bojanov	bojanov	NOUN
ejpam-3372	24	8	and	and	CCONJ
ejpam-3372	24	9	rahman	rahman	NOUN
ejpam-3372	24	10	in	in	ADP
ejpam-3372	24	11	[	[	X
ejpam-3372	24	12	1	1	X
ejpam-3372	24	13	]	]	PUNCT
ejpam-3372	24	14	use	use	NOUN
ejpam-3372	24	15	this	this	DET
ejpam-3372	24	16	method	method	NOUN
ejpam-3372	24	17	.	.	PUNCT
ejpam-3372	25	1	these	these	DET
ejpam-3372	25	2	estimates	estimate	NOUN
ejpam-3372	25	3	are	be	AUX
ejpam-3372	25	4	explored	explore	VERB
ejpam-3372	25	5	for	for	ADP
ejpam-3372	25	6	the	the	DET
ejpam-3372	25	7	localization	localization	NOUN
ejpam-3372	25	8	of	of	ADP
ejpam-3372	25	9	the	the	DET
ejpam-3372	25	10	zeros	zero	NOUN
ejpam-3372	25	11	of	of	ADP
ejpam-3372	25	12	some	some	DET
ejpam-3372	25	13	polynomials	polynomial	NOUN
ejpam-3372	25	14	.	.	PUNCT
ejpam-3372	26	1	the	the	DET
ejpam-3372	26	2	results	result	NOUN
ejpam-3372	26	3	are	be	AUX
ejpam-3372	26	4	useful	useful	ADJ
ejpam-3372	26	5	in	in	ADP
ejpam-3372	26	6	the	the	DET
ejpam-3372	26	7	(	(	PUNCT
ejpam-3372	26	8	open	open	ADJ
ejpam-3372	26	9	)	)	PUNCT
ejpam-3372	26	10	problems	problem	NOUN
ejpam-3372	26	11	of	of	ADP
ejpam-3372	26	12	[	[	X
ejpam-3372	26	13	6–9	6–9	NOUN
ejpam-3372	26	14	]	]	PUNCT
ejpam-3372	26	15	.	.	PUNCT
ejpam-3372	27	1	2	2	X
ejpam-3372	27	2	.	.	NUM
ejpam-3372	27	3	related	relate	VERB
ejpam-3372	27	4	results	result	NOUN
ejpam-3372	27	5	theorem	theorem	VERB
ejpam-3372	27	6	1	1	NUM
ejpam-3372	27	7	.	.	PUNCT
ejpam-3372	28	1	let	let	VERB
ejpam-3372	28	2	k	k	NOUN
ejpam-3372	28	3	=	=	SYM
ejpam-3372	28	4	1	1	NUM
ejpam-3372	28	5	,	,	PUNCT
ejpam-3372	28	6	2	2	NUM
ejpam-3372	28	7	,	,	PUNCT
ejpam-3372	28	8	...	...	PUNCT
ejpam-3372	28	9	n	n	CCONJ
ejpam-3372	28	10	,	,	PUNCT
ejpam-3372	28	11	n	n	PROPN
ejpam-3372	28	12	∈	∈	PROPN
ejpam-3372	28	13	n	n	CCONJ
ejpam-3372	28	14	,	,	PUNCT
ejpam-3372	28	15	ak	ak	PROPN
ejpam-3372	28	16	∈	∈	PROPN
ejpam-3372	29	1	[	[	X
ejpam-3372	29	2	0	0	NUM
ejpam-3372	29	3	,	,	PUNCT
ejpam-3372	29	4	1]ϕ	1]ϕ	NUM
ejpam-3372	29	5	∈	∈	PROPN
ejpam-3372	29	6	[	[	PUNCT
ejpam-3372	29	7	0	0	NUM
ejpam-3372	29	8	,	,	PUNCT
ejpam-3372	29	9	π2	π2	NOUN
ejpam-3372	29	10	]	]	PUNCT
ejpam-3372	29	11	.	.	PUNCT
ejpam-3372	30	1	then	then	ADV
ejpam-3372	30	2	the	the	DET
ejpam-3372	30	3	function∣∣∣∣∣∣∣	function∣∣∣∣∣∣∣	ADJ
ejpam-3372	30	4	eiϕ∫	eiϕ∫	NOUN
ejpam-3372	30	5	−1	−1	NOUN
ejpam-3372	30	6	x	x	PUNCT
ejpam-3372	30	7	n	n	PROPN
ejpam-3372	30	8	π	π	X
ejpam-3372	30	9	k=1	k=1	X
ejpam-3372	30	10	(	(	PUNCT
ejpam-3372	30	11	x+	x+	PROPN
ejpam-3372	30	12	ak	ak	PROPN
ejpam-3372	30	13	)	)	PUNCT
ejpam-3372	30	14	dx	dx	PROPN
ejpam-3372	30	15	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	PROPN
ejpam-3372	30	16	≥	≥	NUM
ejpam-3372	30	17	1	1	NUM
ejpam-3372	30	18	n+	n+	ADP
ejpam-3372	30	19	2	2	NUM
ejpam-3372	30	20	for	for	ADP
ejpam-3372	30	21	n	n	NOUN
ejpam-3372	30	22	=	=	SYM
ejpam-3372	30	23	1	1	NUM
ejpam-3372	30	24	,	,	PUNCT
ejpam-3372	30	25	2	2	NUM
ejpam-3372	30	26	,	,	PUNCT
ejpam-3372	30	27	3	3	NUM
ejpam-3372	30	28	.	.	X
ejpam-3372	30	29	theorem	theorem	NOUN
ejpam-3372	30	30	2	2	NUM
ejpam-3372	30	31	.	.	PUNCT
ejpam-3372	31	1	let	let	VERB
ejpam-3372	31	2	k	k	PROPN
ejpam-3372	31	3	∈	∈	PROPN
ejpam-3372	31	4	n	n	CCONJ
ejpam-3372	31	5	,	,	PUNCT
ejpam-3372	31	6	a	a	DET
ejpam-3372	31	7	∈	∈	PROPN
ejpam-3372	31	8	r	r	NOUN
ejpam-3372	31	9	,	,	PUNCT
ejpam-3372	31	10	a	a	DET
ejpam-3372	31	11	∈	∈	NOUN
ejpam-3372	32	1	[	[	X
ejpam-3372	32	2	0	0	NUM
ejpam-3372	32	3	,	,	PUNCT
ejpam-3372	32	4	1	1	NUM
ejpam-3372	32	5	]	]	PUNCT
ejpam-3372	32	6	.	.	PUNCT
ejpam-3372	33	1	then	then	ADV
ejpam-3372	33	2	the	the	DET
ejpam-3372	33	3	function∣∣∣∣∣∣	function∣∣∣∣∣∣	ADJ
ejpam-3372	33	4	i∫	i∫	PROPN
ejpam-3372	33	5	0	0	PUNCT
ejpam-3372	33	6	x	x	SYM
ejpam-3372	33	7	(	(	PUNCT
ejpam-3372	33	8	x+	x+	ADJ
ejpam-3372	33	9	a)k	a)k	ADJ
ejpam-3372	33	10	dx	dx	PROPN
ejpam-3372	33	11	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3372	33	12	≥	≥	NUM
ejpam-3372	33	13	1	1	NUM
ejpam-3372	33	14	n+	n+	ADP
ejpam-3372	33	15	2	2	NUM
ejpam-3372	33	16	.	.	X
ejpam-3372	33	17	3	3	X
ejpam-3372	33	18	.	.	X
ejpam-3372	33	19	preliminaries	preliminary	NOUN
ejpam-3372	33	20	we	we	PRON
ejpam-3372	33	21	note	note	VERB
ejpam-3372	33	22	:	:	PUNCT
ejpam-3372	33	23	d	d	X
ejpam-3372	33	24	(	(	PUNCT
ejpam-3372	33	25	a	a	DET
ejpam-3372	33	26	,	,	PUNCT
ejpam-3372	33	27	r	r	NOUN
ejpam-3372	33	28	)	)	PUNCT
ejpam-3372	33	29	=	=	NOUN
ejpam-3372	33	30	{	{	PUNCT
ejpam-3372	33	31	z	z	NOUN
ejpam-3372	33	32	∈	∈	PROPN
ejpam-3372	33	33	c	c	NOUN
ejpam-3372	33	34	:	:	PUNCT
ejpam-3372	33	35	|z	|z	PROPN
ejpam-3372	33	36	−	−	PROPN
ejpam-3372	33	37	a|	a|	X
ejpam-3372	33	38	<	<	X
ejpam-3372	33	39	r	r	X
ejpam-3372	33	40	}	}	PUNCT
ejpam-3372	33	41	is	be	AUX
ejpam-3372	33	42	the	the	DET
ejpam-3372	33	43	open	open	ADJ
ejpam-3372	33	44	disk	disk	NOUN
ejpam-3372	33	45	with	with	ADP
ejpam-3372	33	46	center	center	NOUN
ejpam-3372	33	47	a	a	PRON
ejpam-3372	33	48	and	and	CCONJ
ejpam-3372	33	49	radius	radius	PROPN
ejpam-3372	33	50	r.	r.	PROPN
ejpam-3372	33	51	d	d	PROPN
ejpam-3372	33	52	(	(	PUNCT
ejpam-3372	33	53	0	0	NUM
ejpam-3372	33	54	,	,	PUNCT
ejpam-3372	33	55	r	r	NOUN
ejpam-3372	33	56	)	)	PUNCT
ejpam-3372	33	57	=	=	NOUN
ejpam-3372	34	1	{	{	PUNCT
ejpam-3372	34	2	z	z	NOUN
ejpam-3372	34	3	∈	∈	PROPN
ejpam-3372	34	4	c	c	NOUN
ejpam-3372	34	5	:	:	PUNCT
ejpam-3372	34	6	|z	|z	PROPN
ejpam-3372	35	1	−	−	PROPN
ejpam-3372	35	2	a|	a|	PROPN
ejpam-3372	35	3	≤	≤	PROPN
ejpam-3372	35	4	r	r	NOUN
ejpam-3372	35	5	}	}	PUNCT
ejpam-3372	35	6	is	be	AUX
ejpam-3372	35	7	the	the	DET
ejpam-3372	35	8	closed	closed	ADJ
ejpam-3372	35	9	disk	disk	NOUN
ejpam-3372	35	10	with	with	ADP
ejpam-3372	35	11	center	center	NOUN
ejpam-3372	35	12	a	a	PRON
ejpam-3372	35	13	and	and	CCONJ
ejpam-3372	35	14	radius	radius	PROPN
ejpam-3372	35	15	r.	r.	PROPN
ejpam-3372	35	16	a	a	PROPN
ejpam-3372	35	17	=	=	X
ejpam-3372	35	18	{	{	PUNCT
ejpam-3372	35	19	z	z	NOUN
ejpam-3372	35	20	∈	∈	PROPN
ejpam-3372	35	21	c	c	NOUN
ejpam-3372	35	22	,	,	PUNCT
ejpam-3372	35	23	rez	rez	NOUN
ejpam-3372	35	24	≤	≤	NOUN
ejpam-3372	35	25	0	0	NUM
ejpam-3372	35	26	}	}	PUNCT
ejpam-3372	35	27	is	be	AUX
ejpam-3372	35	28	the	the	DET
ejpam-3372	35	29	left	left	ADJ
ejpam-3372	35	30	semiplane	semiplane	NOUN
ejpam-3372	35	31	.	.	PUNCT
ejpam-3372	36	1	4	4	X
ejpam-3372	36	2	.	.	X
ejpam-3372	36	3	main	main	ADJ
ejpam-3372	36	4	results	result	NOUN
ejpam-3372	36	5	theorem	theorem	VERB
ejpam-3372	36	6	3	3	X
ejpam-3372	36	7	.	.	X
ejpam-3372	37	1	we	we	PRON
ejpam-3372	37	2	consider	consider	VERB
ejpam-3372	37	3	a	a	DET
ejpam-3372	37	4	polynomial	polynomial	ADJ
ejpam-3372	37	5	r(z	r(z	NOUN
ejpam-3372	37	6	)	)	PUNCT
ejpam-3372	38	1	=	=	PUNCT
ejpam-3372	38	2	zn−1	zn−1	PROPN
ejpam-3372	38	3	+	+	CCONJ
ejpam-3372	38	4	rn−1z	rn−1z	NUM
ejpam-3372	38	5	n−1	n−1	PROPN
ejpam-3372	38	6	+	+	CCONJ
ejpam-3372	38	7	...	...	PUNCT
ejpam-3372	39	1	+	+	CCONJ
ejpam-3372	39	2	r1z	r1z	PROPN
ejpam-3372	39	3	+	+	CCONJ
ejpam-3372	39	4	r0	r0	NOUN
ejpam-3372	39	5	.	.	PUNCT
ejpam-3372	40	1	where	where	SCONJ
ejpam-3372	40	2	rk	rk	VERB
ejpam-3372	40	3	∈	∈	PROPN
ejpam-3372	40	4	r	r	NOUN
ejpam-3372	40	5	,	,	PUNCT
ejpam-3372	40	6	n	n	PRON
ejpam-3372	40	7	≥	≥	NOUN
ejpam-3372	40	8	1	1	NUM
ejpam-3372	40	9	,	,	PUNCT
ejpam-3372	40	10	n	n	PRON
ejpam-3372	40	11	∈	∈	PROPN
ejpam-3372	40	12	n	n	CCONJ
ejpam-3372	40	13	,	,	PUNCT
ejpam-3372	40	14	k	k	PROPN
ejpam-3372	40	15	=	=	SYM
ejpam-3372	40	16	0	0	PROPN
ejpam-3372	40	17	,	,	PUNCT
ejpam-3372	40	18	n−	n−	NOUN
ejpam-3372	40	19	1	1	NUM
ejpam-3372	40	20	.	.	PUNCT
ejpam-3372	40	21	the	the	DET
ejpam-3372	40	22	zeros	zero	NOUN
ejpam-3372	40	23	zk	zk	PROPN
ejpam-3372	40	24	of	of	ADP
ejpam-3372	40	25	r	r	PROPN
ejpam-3372	40	26	(	(	PUNCT
ejpam-3372	40	27	z	z	NOUN
ejpam-3372	40	28	)	)	PUNCT
ejpam-3372	40	29	satisfy	satisfy	VERB
ejpam-3372	40	30	the	the	DET
ejpam-3372	40	31	condition	condition	NOUN
ejpam-3372	40	32	rezk	rezk	ADJ
ejpam-3372	40	33	≤	≤	ADJ
ejpam-3372	40	34	0	0	NUM
ejpam-3372	40	35	.	.	PUNCT
ejpam-3372	41	1	if	if	SCONJ
ejpam-3372	41	2	a	a	DET
ejpam-3372	41	3	≥	≥	NOUN
ejpam-3372	41	4	0	0	NUM
ejpam-3372	41	5	,	,	PUNCT
ejpam-3372	41	6	then	then	ADV
ejpam-3372	41	7	i	i	PRON
ejpam-3372	41	8	=	=	SYM
ejpam-3372	41	9	n	n	PROPN
ejpam-3372	41	10	a∫	a∫	NOUN
ejpam-3372	41	11	0	0	NUM
ejpam-3372	41	12	r	r	NOUN
ejpam-3372	41	13	(	(	PUNCT
ejpam-3372	41	14	z	z	NOUN
ejpam-3372	41	15	)	)	PUNCT
ejpam-3372	41	16	dz	dz	PROPN
ejpam-3372	41	17	≥	≥	X
ejpam-3372	41	18	an	an	X
ejpam-3372	41	19	.	.	PUNCT
ejpam-3372	41	20	proof	proof	NOUN
ejpam-3372	41	21	.	.	PUNCT
ejpam-3372	42	1	let	let	VERB
ejpam-3372	42	2	r	r	NOUN
ejpam-3372	42	3	(	(	PUNCT
ejpam-3372	42	4	z	z	NOUN
ejpam-3372	42	5	)	)	PUNCT
ejpam-3372	42	6	=	=	PUNCT
ejpam-3372	43	1	(	(	PUNCT
ejpam-3372	43	2	z	z	NOUN
ejpam-3372	43	3	+	+	CCONJ
ejpam-3372	43	4	a1	a1	NOUN
ejpam-3372	43	5	)	)	PUNCT
ejpam-3372	43	6	(	(	PUNCT
ejpam-3372	43	7	z	z	NOUN
ejpam-3372	43	8	+	+	NUM
ejpam-3372	43	9	a2	a2	PROPN
ejpam-3372	43	10	)	)	PUNCT
ejpam-3372	43	11	...	...	PUNCT
ejpam-3372	44	1	(	(	PUNCT
ejpam-3372	44	2	z	z	X
ejpam-3372	44	3	+	+	CCONJ
ejpam-3372	44	4	a1	a1	NOUN
ejpam-3372	44	5	)	)	PUNCT
ejpam-3372	44	6	(	(	PUNCT
ejpam-3372	44	7	z	z	NOUN
ejpam-3372	44	8	−	−	PROPN
ejpam-3372	44	9	b1	b1	PROPN
ejpam-3372	44	10	)	)	PUNCT
ejpam-3372	44	11	(	(	PUNCT
ejpam-3372	44	12	z	z	NOUN
ejpam-3372	44	13	−	−	PROPN
ejpam-3372	44	14	b1	b1	PROPN
ejpam-3372	44	15	)	)	PUNCT
ejpam-3372	44	16	...	...	PUNCT
ejpam-3372	45	1	(	(	PUNCT
ejpam-3372	45	2	z	z	NOUN
ejpam-3372	45	3	−	−	NOUN
ejpam-3372	45	4	bs	bs	NOUN
ejpam-3372	45	5	)	)	PUNCT
ejpam-3372	45	6	(	(	PUNCT
ejpam-3372	45	7	z	z	NOUN
ejpam-3372	45	8	−	−	NOUN
ejpam-3372	45	9	bs	bs	PROPN
ejpam-3372	45	10	)	)	PUNCT
ejpam-3372	45	11	,	,	PUNCT
ejpam-3372	45	12	where	where	SCONJ
ejpam-3372	45	13	1	1	NUM
ejpam-3372	45	14	+	+	NOUN
ejpam-3372	45	15	2s	2s	NOUN
ejpam-3372	45	16	=	=	SYM
ejpam-3372	45	17	n−1	n−1	PROPN
ejpam-3372	45	18	,	,	PUNCT
ejpam-3372	45	19	ak	ak	PROPN
ejpam-3372	45	20	≥	≥	PROPN
ejpam-3372	45	21	0	0	NUM
ejpam-3372	45	22	,	,	PUNCT
ejpam-3372	45	23	bm	bm	PROPN
ejpam-3372	45	24	∈	∈	PROPN
ejpam-3372	45	25	c	c	PROPN
ejpam-3372	45	26	,	,	PUNCT
ejpam-3372	45	27	k	k	NOUN
ejpam-3372	45	28	=	=	SYM
ejpam-3372	45	29	1	1	NUM
ejpam-3372	45	30	,	,	PUNCT
ejpam-3372	45	31	l	l	NOUN
ejpam-3372	45	32	,	,	PUNCT
ejpam-3372	45	33	m	m	VERB
ejpam-3372	45	34	=	=	NOUN
ejpam-3372	45	35	1	1	NUM
ejpam-3372	45	36	,	,	PUNCT
ejpam-3372	45	37	s	s	PROPN
ejpam-3372	45	38	,	,	PUNCT
ejpam-3372	45	39	ak	ak	PROPN
ejpam-3372	45	40	∈	∈	PROPN
ejpam-3372	45	41	r	r	PROPN
ejpam-3372	45	42	,	,	PUNCT
ejpam-3372	45	43	k	k	NOUN
ejpam-3372	45	44	,	,	PUNCT
ejpam-3372	45	45	m	m	PROPN
ejpam-3372	45	46	∈	∈	PROPN
ejpam-3372	45	47	n.	n.	PROPN
ejpam-3372	45	48	and	and	CCONJ
ejpam-3372	45	49	bm	bm	PROPN
ejpam-3372	45	50	=	=	PROPN
ejpam-3372	45	51	ρme	ρme	PROPN
ejpam-3372	45	52	iϕm	iϕm	PROPN
ejpam-3372	45	53	,	,	PUNCT
ejpam-3372	45	54	ρm	ρm	PRON
ejpam-3372	45	55	≥	≥	NOUN
ejpam-3372	45	56	0	0	NUM
ejpam-3372	45	57	,	,	PUNCT
ejpam-3372	45	58	ϕm	ϕm	X
ejpam-3372	45	59	∈	∈	PROPN
ejpam-3372	45	60	[	[	PUNCT
ejpam-3372	45	61	π	π	NOUN
ejpam-3372	45	62	2	2	NUM
ejpam-3372	45	63	,	,	PUNCT
ejpam-3372	45	64	π	π	X
ejpam-3372	45	65	]	]	PUNCT
ejpam-3372	45	66	,	,	PUNCT
ejpam-3372	45	67	(	(	PUNCT
ejpam-3372	45	68	z	z	NOUN
ejpam-3372	45	69	−	−	PROPN
ejpam-3372	45	70	bm	bm	PROPN
ejpam-3372	45	71	)	)	PUNCT
ejpam-3372	45	72	(	(	PUNCT
ejpam-3372	45	73	z	z	NOUN
ejpam-3372	45	74	−	−	PROPN
ejpam-3372	45	75	bm	bm	PROPN
ejpam-3372	45	76	)	)	PUNCT
ejpam-3372	45	77	=	=	SYM
ejpam-3372	45	78	z2	z2	PROPN
ejpam-3372	45	79	−	−	NUM
ejpam-3372	45	80	2ρm	2ρm	ADJ
ejpam-3372	45	81	cosϕmz	cosϕmz	PROPN
ejpam-3372	45	82	+	+	CCONJ
ejpam-3372	45	83	ρ2	ρ2	PROPN
ejpam-3372	45	84	m	m	PROPN
ejpam-3372	45	85	≥	≥	NOUN
ejpam-3372	45	86	z2	z2	PROPN
ejpam-3372	45	87	.	.	PUNCT
ejpam-3372	46	1	then	then	ADV
ejpam-3372	46	2	n	n	PROPN
ejpam-3372	46	3	a∫	a∫	NOUN
ejpam-3372	46	4	0	0	NUM
ejpam-3372	46	5	r	r	NOUN
ejpam-3372	46	6	(	(	PUNCT
ejpam-3372	46	7	z	z	NOUN
ejpam-3372	46	8	)	)	PUNCT
ejpam-3372	46	9	dz	dz	NOUN
ejpam-3372	46	10	=	=	PUNCT
ejpam-3372	46	11	n	n	PROPN
ejpam-3372	46	12	a∫	a∫	NOUN
ejpam-3372	46	13	0	0	PUNCT
ejpam-3372	47	1	(	(	PUNCT
ejpam-3372	47	2	z	z	NOUN
ejpam-3372	47	3	+	+	CCONJ
ejpam-3372	47	4	a1	a1	NOUN
ejpam-3372	47	5	)	)	PUNCT
ejpam-3372	47	6	(	(	PUNCT
ejpam-3372	47	7	z	z	NOUN
ejpam-3372	47	8	+	+	NUM
ejpam-3372	47	9	a2	a2	PROPN
ejpam-3372	47	10	)	)	PUNCT
ejpam-3372	47	11	...	...	PUNCT
ejpam-3372	48	1	(	(	PUNCT
ejpam-3372	48	2	z	z	X
ejpam-3372	48	3	+	+	CCONJ
ejpam-3372	48	4	a1	a1	NOUN
ejpam-3372	48	5	)	)	PUNCT
ejpam-3372	48	6	(	(	PUNCT
ejpam-3372	48	7	z	z	NOUN
ejpam-3372	48	8	−	−	PROPN
ejpam-3372	48	9	b1	b1	PROPN
ejpam-3372	48	10	)	)	PUNCT
ejpam-3372	48	11	(	(	PUNCT
ejpam-3372	48	12	z	z	NOUN
ejpam-3372	48	13	−	−	PROPN
ejpam-3372	48	14	b1	b1	PROPN
ejpam-3372	48	15	)	)	PUNCT
ejpam-3372	48	16	...	...	PUNCT
ejpam-3372	49	1	(	(	PUNCT
ejpam-3372	49	2	z	z	NOUN
ejpam-3372	49	3	−	−	NOUN
ejpam-3372	49	4	bs	bs	NOUN
ejpam-3372	49	5	)	)	PUNCT
ejpam-3372	49	6	(	(	PUNCT
ejpam-3372	49	7	z	z	NOUN
ejpam-3372	49	8	−	−	NOUN
ejpam-3372	49	9	bs	bs	NOUN
ejpam-3372	49	10	)	)	PUNCT
ejpam-3372	50	1	d	d	NOUN
ejpam-3372	50	2	≥	≥	NOUN
ejpam-3372	50	3	n	n	CCONJ
ejpam-3372	50	4	a∫	a∫	NOUN
ejpam-3372	50	5	0	0	NUM
ejpam-3372	50	6	zn−1dz	zn−1dz	NUM
ejpam-3372	50	7	=	=	SYM
ejpam-3372	50	8	an	an	X
ejpam-3372	50	9	.	.	PUNCT
ejpam-3372	51	1	t.	t.	PROPN
ejpam-3372	51	2	s.	s.	PROPN
ejpam-3372	51	3	stoyanov	stoyanov	PROPN
ejpam-3372	51	4	/	/	SYM
ejpam-3372	51	5	eur	eur	PROPN
ejpam-3372	51	6	.	.	PUNCT
ejpam-3372	52	1	j.	j.	PROPN
ejpam-3372	52	2	pure	pure	PROPN
ejpam-3372	52	3	appl	appl	PROPN
ejpam-3372	52	4	.	.	PROPN
ejpam-3372	52	5	math	math	PROPN
ejpam-3372	52	6	,	,	PUNCT
ejpam-3372	52	7	12	12	NUM
ejpam-3372	52	8	(	(	PUNCT
ejpam-3372	52	9	2	2	NUM
ejpam-3372	52	10	)	)	PUNCT
ejpam-3372	52	11	(	(	PUNCT
ejpam-3372	52	12	2019	2019	NUM
ejpam-3372	52	13	)	)	PUNCT
ejpam-3372	52	14	,	,	PUNCT
ejpam-3372	52	15	649	649	NUM
ejpam-3372	52	16	-	-	SYM
ejpam-3372	52	17	653	653	NUM
ejpam-3372	52	18	651	651	NUM
ejpam-3372	52	19	theorem	theorem	NOUN
ejpam-3372	52	20	4	4	NUM
ejpam-3372	52	21	.	.	PUNCT
ejpam-3372	53	1	we	we	PRON
ejpam-3372	53	2	consider	consider	VERB
ejpam-3372	53	3	a	a	DET
ejpam-3372	53	4	polynomial	polynomial	ADJ
ejpam-3372	53	5	r	r	NOUN
ejpam-3372	53	6	(	(	PUNCT
ejpam-3372	53	7	z	z	NOUN
ejpam-3372	53	8	)	)	PUNCT
ejpam-3372	53	9	=	=	SYM
ejpam-3372	53	10	zn−1	zn−1	PROPN
ejpam-3372	53	11	+	+	CCONJ
ejpam-3372	53	12	rn−1z	rn−1z	NUM
ejpam-3372	53	13	n−2	n−2	PROPN
ejpam-3372	53	14	+	+	CCONJ
ejpam-3372	53	15	...	...	PUNCT
ejpam-3372	54	1	+	+	CCONJ
ejpam-3372	54	2	r1z	r1z	PROPN
ejpam-3372	54	3	+	+	CCONJ
ejpam-3372	54	4	r0	r0	NOUN
ejpam-3372	54	5	,	,	PUNCT
ejpam-3372	54	6	where	where	SCONJ
ejpam-3372	54	7	rk	rk	VERB
ejpam-3372	54	8	∈	∈	PROPN
ejpam-3372	54	9	r	r	NOUN
ejpam-3372	54	10	,	,	PUNCT
ejpam-3372	54	11	n	n	PRON
ejpam-3372	54	12	≥	≥	NOUN
ejpam-3372	54	13	1	1	NUM
ejpam-3372	54	14	,	,	PUNCT
ejpam-3372	54	15	n	n	PRON
ejpam-3372	54	16	∈	∈	PROPN
ejpam-3372	54	17	n	n	CCONJ
ejpam-3372	54	18	,	,	PUNCT
ejpam-3372	54	19	k	k	PROPN
ejpam-3372	54	20	=	=	SYM
ejpam-3372	54	21	0	0	PROPN
ejpam-3372	54	22	,	,	PUNCT
ejpam-3372	54	23	n−	n−	NOUN
ejpam-3372	54	24	1	1	NUM
ejpam-3372	54	25	.	.	PUNCT
ejpam-3372	55	1	the	the	DET
ejpam-3372	55	2	zeros	zero	NOUN
ejpam-3372	55	3	zk	zk	PROPN
ejpam-3372	55	4	of	of	ADP
ejpam-3372	55	5	r	r	PROPN
ejpam-3372	55	6	(	(	PUNCT
ejpam-3372	55	7	z	z	NOUN
ejpam-3372	55	8	)	)	PUNCT
ejpam-3372	55	9	satisfy	satisfy	VERB
ejpam-3372	55	10	the	the	DET
ejpam-3372	55	11	condition	condition	NOUN
ejpam-3372	55	12	zk	zk	PROPN
ejpam-3372	55	13	∈	∈	PROPN
ejpam-3372	55	14	a	a	DET
ejpam-3372	55	15	\d	\d	NOUN
ejpam-3372	55	16	(	(	PUNCT
ejpam-3372	55	17	z0	z0	PROPN
ejpam-3372	55	18	,	,	PUNCT
ejpam-3372	55	19	a	a	PRON
ejpam-3372	55	20	)	)	PUNCT
ejpam-3372	55	21	\d	\d	NOUN
ejpam-3372	55	22	(	(	PUNCT
ejpam-3372	55	23	z0	z0	PROPN
ejpam-3372	55	24	,	,	PUNCT
ejpam-3372	55	25	a	a	PRON
ejpam-3372	55	26	)	)	PUNCT
ejpam-3372	55	27	,	,	PUNCT
ejpam-3372	55	28	z0	z0	PROPN
ejpam-3372	55	29	=	=	SYM
ejpam-3372	55	30	aeiθ0	aeiθ0	PROPN
ejpam-3372	55	31	,	,	PUNCT
ejpam-3372	55	32	where	where	SCONJ
ejpam-3372	55	33	a	a	DET
ejpam-3372	55	34	≥	≥	NOUN
ejpam-3372	55	35	0	0	NUM
ejpam-3372	55	36	,	,	PUNCT
ejpam-3372	55	37	θ0	θ0	PROPN
ejpam-3372	55	38	∈	∈	PROPN
ejpam-3372	55	39	[	[	PUNCT
ejpam-3372	55	40	0	0	NUM
ejpam-3372	55	41	,	,	PUNCT
ejpam-3372	55	42	π2	π2	NOUN
ejpam-3372	55	43	]	]	PUNCT
ejpam-3372	55	44	.	.	PUNCT
ejpam-3372	56	1	then	then	ADV
ejpam-3372	56	2	i	i	PRON
ejpam-3372	56	3	=	=	PUNCT
ejpam-3372	56	4	∣∣∣∣∣∣n	∣∣∣∣∣∣n	ADJ
ejpam-3372	56	5	z0∫	z0∫	NUM
ejpam-3372	56	6	0	0	NUM
ejpam-3372	56	7	r	r	NOUN
ejpam-3372	56	8	(	(	PUNCT
ejpam-3372	56	9	z	z	NOUN
ejpam-3372	56	10	)	)	PUNCT
ejpam-3372	56	11	dz	dz	PROPN
ejpam-3372	56	12	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3372	56	13	≥	≥	X
ejpam-3372	56	14	an	an	PRON
ejpam-3372	56	15	.	.	PUNCT
ejpam-3372	56	16	proof	proof	NOUN
ejpam-3372	56	17	.	.	PUNCT
ejpam-3372	57	1	let	let	VERB
ejpam-3372	57	2	us	we	PRON
ejpam-3372	57	3	put	put	VERB
ejpam-3372	57	4	v	v	NOUN
ejpam-3372	57	5	(	(	PUNCT
ejpam-3372	57	6	θ	θ	NOUN
ejpam-3372	57	7	)	)	PUNCT
ejpam-3372	57	8	=	=	SYM
ejpam-3372	57	9	aeiθ	aeiθ	PROPN
ejpam-3372	57	10	,	,	PUNCT
ejpam-3372	57	11	θ	θ	PROPN
ejpam-3372	57	12	∈	∈	PROPN
ejpam-3372	58	1	[	[	X
ejpam-3372	58	2	0	0	NUM
ejpam-3372	58	3	,	,	PUNCT
ejpam-3372	58	4	θ0	θ0	PROPN
ejpam-3372	58	5	]	]	PUNCT
ejpam-3372	58	6	,	,	PUNCT
ejpam-3372	58	7	i	i	PRON
ejpam-3372	59	1	+	+	X
ejpam-3372	59	2	2s	2s	NUM
ejpam-3372	59	3	=	=	SYM
ejpam-3372	59	4	n−	n−	NOUN
ejpam-3372	59	5	1	1	NUM
ejpam-3372	59	6	,	,	PUNCT
ejpam-3372	59	7	r	r	NOUN
ejpam-3372	59	8	(	(	PUNCT
ejpam-3372	59	9	z	z	NOUN
ejpam-3372	59	10	)	)	PUNCT
ejpam-3372	60	1	=	=	SYM
ejpam-3372	61	1	l	l	PUNCT
ejpam-3372	61	2	π	π	X
ejpam-3372	61	3	p=1	p=1	X
ejpam-3372	61	4	(	(	PUNCT
ejpam-3372	61	5	z	z	NOUN
ejpam-3372	61	6	+	+	CCONJ
ejpam-3372	61	7	ap	ap	PROPN
ejpam-3372	61	8	)	)	PUNCT
ejpam-3372	61	9	s	s	PART
ejpam-3372	62	1	π	π	X
ejpam-3372	62	2	p=1	p=1	X
ejpam-3372	62	3	(	(	PUNCT
ejpam-3372	62	4	z	z	NOUN
ejpam-3372	62	5	−	−	PROPN
ejpam-3372	62	6	bp	bp	PROPN
ejpam-3372	62	7	)	)	PUNCT
ejpam-3372	62	8	(	(	PUNCT
ejpam-3372	62	9	z	z	NOUN
ejpam-3372	62	10	−	−	PROPN
ejpam-3372	62	11	bp	bp	PROPN
ejpam-3372	62	12	)	)	PUNCT
ejpam-3372	62	13	,	,	PUNCT
ejpam-3372	62	14	l	l	NOUN
ejpam-3372	62	15	,	,	PUNCT
ejpam-3372	62	16	s	s	VERB
ejpam-3372	62	17	∈	∈	PROPN
ejpam-3372	62	18	n	n	CCONJ
ejpam-3372	62	19	(	(	PUNCT
ejpam-3372	62	20	one	one	NUM
ejpam-3372	62	21	of	of	ADP
ejpam-3372	62	22	the	the	DET
ejpam-3372	62	23	factors	factor	NOUN
ejpam-3372	62	24	could	could	AUX
ejpam-3372	62	25	be	be	AUX
ejpam-3372	62	26	not	not	PART
ejpam-3372	62	27	existing	exist	VERB
ejpam-3372	62	28	,	,	PUNCT
ejpam-3372	62	29	i.e.	i.e.	X
ejpam-3372	62	30	,l	,l	PUNCT
ejpam-3372	62	31	=	=	SYM
ejpam-3372	62	32	0	0	NUM
ejpam-3372	62	33	or	or	CCONJ
ejpam-3372	62	34	s	s	X
ejpam-3372	62	35	=	=	NOUN
ejpam-3372	62	36	0	0	NUM
ejpam-3372	62	37	)	)	PUNCT
ejpam-3372	62	38	.	.	PUNCT
ejpam-3372	63	1	we	we	PRON
ejpam-3372	63	2	put	put	VERB
ejpam-3372	63	3	f	f	PROPN
ejpam-3372	63	4	(	(	PUNCT
ejpam-3372	63	5	θ	θ	NOUN
ejpam-3372	63	6	)	)	PUNCT
ejpam-3372	63	7	=	=	SYM
ejpam-3372	63	8	n	n	PRON
ejpam-3372	63	9	v(θ)∫	v(θ)∫	NOUN
ejpam-3372	63	10	0	0	NUM
ejpam-3372	64	1	r	r	NOUN
ejpam-3372	64	2	(	(	PUNCT
ejpam-3372	64	3	z	z	NOUN
ejpam-3372	64	4	)	)	PUNCT
ejpam-3372	64	5	dz	dz	PROPN
ejpam-3372	64	6	,	,	PUNCT
ejpam-3372	64	7	g	g	PROPN
ejpam-3372	64	8	(	(	PUNCT
ejpam-3372	64	9	θ	θ	NOUN
ejpam-3372	64	10	)	)	PUNCT
ejpam-3372	64	11	=	=	SYM
ejpam-3372	64	12	f	f	PROPN
ejpam-3372	64	13	(	(	PUNCT
ejpam-3372	64	14	θ	θ	NOUN
ejpam-3372	64	15	)	)	PUNCT
ejpam-3372	64	16	.f	.f	NOUN
ejpam-3372	64	17	(	(	PUNCT
ejpam-3372	64	18	θ	θ	NOUN
ejpam-3372	64	19	)	)	PUNCT
ejpam-3372	64	20	.	.	PUNCT
ejpam-3372	65	1	let	let	VERB
ejpam-3372	65	2	us	we	PRON
ejpam-3372	65	3	calculate	calculate	VERB
ejpam-3372	65	4	dg	dg	PROPN
ejpam-3372	65	5	dθ	dθ	PROPN
ejpam-3372	65	6	=	=	PROPN
ejpam-3372	65	7	n	n	PROPN
ejpam-3372	65	8	[	[	PUNCT
ejpam-3372	65	9	r	r	NOUN
ejpam-3372	65	10	(	(	PUNCT
ejpam-3372	65	11	v	v	NOUN
ejpam-3372	65	12	(	(	PUNCT
ejpam-3372	65	13	θ	θ	NOUN
ejpam-3372	65	14	)	)	PUNCT
ejpam-3372	65	15	)	)	PUNCT
ejpam-3372	66	1	dv	dv	PROPN
ejpam-3372	66	2	dθ	dθ	PROPN
ejpam-3372	66	3	f	f	PROPN
ejpam-3372	66	4	(	(	PUNCT
ejpam-3372	66	5	θ	θ	NOUN
ejpam-3372	66	6	)	)	PUNCT
ejpam-3372	67	1	+	+	NOUN
ejpam-3372	67	2	r	r	NOUN
ejpam-3372	67	3	(	(	PUNCT
ejpam-3372	67	4	v	v	NOUN
ejpam-3372	67	5	(	(	PUNCT
ejpam-3372	67	6	θ	θ	NOUN
ejpam-3372	67	7	)	)	PUNCT
ejpam-3372	67	8	)	)	PUNCT
ejpam-3372	68	1	dv	dv	PROPN
ejpam-3372	68	2	dθ	dθ	PROPN
ejpam-3372	68	3	f	f	PROPN
ejpam-3372	68	4	(	(	PUNCT
ejpam-3372	68	5	θ	θ	PROPN
ejpam-3372	68	6	)	)	PUNCT
ejpam-3372	68	7	]	]	PUNCT
ejpam-3372	68	8	,	,	PUNCT
ejpam-3372	68	9	dv	dv	PROPN
ejpam-3372	68	10	dθ	dθ	PROPN
ejpam-3372	68	11	=	=	PROPN
ejpam-3372	69	1	daeiθ	daeiθ	PROPN
ejpam-3372	69	2	dθ	dθ	PROPN
ejpam-3372	69	3	=	=	PROPN
ejpam-3372	69	4	iaeiθ	iaeiθ	PROPN
ejpam-3372	69	5	,	,	PUNCT
ejpam-3372	69	6	and	and	CCONJ
ejpam-3372	69	7	if	if	SCONJ
ejpam-3372	69	8	we	we	PRON
ejpam-3372	69	9	put	put	VERB
ejpam-3372	69	10	u0	u0	ADJ
ejpam-3372	69	11	=	=	NOUN
ejpam-3372	69	12	v	v	X
ejpam-3372	69	13	(	(	PUNCT
ejpam-3372	69	14	θ	θ	NOUN
ejpam-3372	69	15	)	)	PUNCT
ejpam-3372	69	16	=	=	SYM
ejpam-3372	69	17	aeiθ	aeiθ	PROPN
ejpam-3372	69	18	,	,	PUNCT
ejpam-3372	69	19	up	up	ADV
ejpam-3372	69	20	=	=	SYM
ejpam-3372	69	21	v	v	NOUN
ejpam-3372	69	22	(	(	PUNCT
ejpam-3372	69	23	θ	θ	NOUN
ejpam-3372	69	24	)	)	PUNCT
ejpam-3372	70	1	+	+	CCONJ
ejpam-3372	70	2	ap	ap	PROPN
ejpam-3372	70	3	,	,	PUNCT
ejpam-3372	70	4	p	p	NOUN
ejpam-3372	70	5	=	=	NOUN
ejpam-3372	70	6	1	1	NUM
ejpam-3372	70	7	,	,	PUNCT
ejpam-3372	70	8	l	l	NOUN
ejpam-3372	70	9	,	,	PUNCT
ejpam-3372	70	10	ul+2p+1	ul+2p+1	VERB
ejpam-3372	70	11	=	=	SYM
ejpam-3372	70	12	v	v	NOUN
ejpam-3372	70	13	(	(	PUNCT
ejpam-3372	70	14	θ)−	θ)−	PROPN
ejpam-3372	70	15	bp	bp	PROPN
ejpam-3372	70	16	,	,	PUNCT
ejpam-3372	70	17	ul+2p+2	ul+2p+2	PROPN
ejpam-3372	70	18	=	=	SYM
ejpam-3372	70	19	v	v	NOUN
ejpam-3372	70	20	(	(	PUNCT
ejpam-3372	70	21	θ)−	θ)−	PROPN
ejpam-3372	70	22	bp	bp	PROPN
ejpam-3372	70	23	,	,	PUNCT
ejpam-3372	70	24	p	p	X
ejpam-3372	70	25	=	=	NOUN
ejpam-3372	70	26	0	0	NUM
ejpam-3372	70	27	,	,	PUNCT
ejpam-3372	70	28	s−	s−	PROPN
ejpam-3372	70	29	1	1	NUM
ejpam-3372	70	30	.	.	PUNCT
ejpam-3372	71	1	knowing	know	VERB
ejpam-3372	71	2	df	df	PROPN
ejpam-3372	71	3	dθ	dθ	PROPN
ejpam-3372	71	4	.πn−1	.πn−1	PROPN
ejpam-3372	72	1	p=0up	p=0up	NOUN
ejpam-3372	72	2	=	=	PUNCT
ejpam-3372	72	3	df	df	PROPN
ejpam-3372	72	4	dθ	dθ	X
ejpam-3372	72	5	.πn−1	.πn−1	PROPN
ejpam-3372	73	1	p=0up	p=0up	NUM
ejpam-3372	73	2	,	,	PUNCT
ejpam-3372	73	3	we	we	PRON
ejpam-3372	73	4	have	have	VERB
ejpam-3372	73	5	dg	dg	PROPN
ejpam-3372	73	6	dθ	dθ	NOUN
ejpam-3372	73	7	=	=	PROPN
ejpam-3372	73	8	in	in	ADP
ejpam-3372	73	9	[	[	PUNCT
ejpam-3372	73	10	f	f	X
ejpam-3372	73	11	(	(	PUNCT
ejpam-3372	73	12	θ	θ	PROPN
ejpam-3372	73	13	)	)	PUNCT
ejpam-3372	73	14	n−1	n−1	PROPN
ejpam-3372	73	15	π	π	PROPN
ejpam-3372	73	16	p=0	p=0	PROPN
ejpam-3372	73	17	up	up	ADP
ejpam-3372	73	18	−	−	PROPN
ejpam-3372	73	19	f	f	PROPN
ejpam-3372	73	20	(	(	PUNCT
ejpam-3372	73	21	θ	θ	PROPN
ejpam-3372	73	22	)	)	PUNCT
ejpam-3372	74	1	n−1	n−1	PROPN
ejpam-3372	74	2	π	π	PROPN
ejpam-3372	74	3	p=0	p=0	PROPN
ejpam-3372	74	4	up	up	ADP
ejpam-3372	74	5	]	]	PUNCT
ejpam-3372	74	6	,	,	PUNCT
ejpam-3372	74	7	d2	d2	PROPN
ejpam-3372	74	8	g	g	NOUN
ejpam-3372	74	9	dθ2	dθ2	NOUN
ejpam-3372	74	10	=	=	SYM
ejpam-3372	74	11	n	n	CCONJ
ejpam-3372	75	1	[	[	PUNCT
ejpam-3372	75	2	2	2	NUM
ejpam-3372	75	3	df	df	NOUN
ejpam-3372	75	4	dθ	dθ	PROPN
ejpam-3372	75	5	n−1	n−1	PROPN
ejpam-3372	75	6	π	π	PROPN
ejpam-3372	75	7	p=0	p=0	PROPN
ejpam-3372	75	8	up	up	ADP
ejpam-3372	76	1	+	+	CCONJ
ejpam-3372	76	2	i	i	PRON
ejpam-3372	76	3	dπn−1	dπn−1	VERB
ejpam-3372	76	4	p=0up	p=0up	NUM
ejpam-3372	77	1	dθ	dθ	PROPN
ejpam-3372	77	2	f	f	PROPN
ejpam-3372	77	3	(	(	PUNCT
ejpam-3372	77	4	θ)−	θ)−	PROPN
ejpam-3372	77	5	i	i	PRON
ejpam-3372	77	6	dπn−1	dπn−1	PROPN
ejpam-3372	77	7	p=0up	p=0up	NUM
ejpam-3372	77	8	dθ	dθ	PROPN
ejpam-3372	77	9	f	f	PROPN
ejpam-3372	77	10	(	(	PUNCT
ejpam-3372	77	11	θ	θ	PROPN
ejpam-3372	77	12	)	)	PUNCT
ejpam-3372	77	13	]	]	PUNCT
ejpam-3372	77	14	,	,	PUNCT
ejpam-3372	77	15	d2	d2	PROPN
ejpam-3372	77	16	g	g	NOUN
ejpam-3372	77	17	dθ2	dθ2	NOUN
ejpam-3372	77	18	=	=	SYM
ejpam-3372	77	19	n	n	CCONJ
ejpam-3372	77	20	[	[	PUNCT
ejpam-3372	77	21	2n	2n	NUM
ejpam-3372	77	22	n−1	n−1	PROPN
ejpam-3372	77	23	π	π	X
ejpam-3372	77	24	p=0	p=0	X
ejpam-3372	77	25	|up|2	|up|2	PUNCT
ejpam-3372	77	26	−	−	PROPN
ejpam-3372	77	27	(	(	PUNCT
ejpam-3372	77	28	u0	u0	PROPN
ejpam-3372	77	29	n−1	n−1	PROPN
ejpam-3372	78	1	σ	σ	PROPN
ejpam-3372	79	1	p=0	p=0	PROPN
ejpam-3372	80	1	π	π	PROPN
ejpam-3372	80	2	j	j	PROPN
ejpam-3372	80	3	6	6	NUM
ejpam-3372	80	4	=	=	PROPN
ejpam-3372	80	5	p	p	X
ejpam-3372	80	6	uj	uj	PROPN
ejpam-3372	80	7	)	)	PUNCT
ejpam-3372	80	8	f	f	PROPN
ejpam-3372	81	1	(	(	PUNCT
ejpam-3372	81	2	θ)−	θ)−	PROPN
ejpam-3372	81	3	(	(	PUNCT
ejpam-3372	81	4	u0	u0	PROPN
ejpam-3372	81	5	n−1	n−1	PROPN
ejpam-3372	81	6	σ	σ	PROPN
ejpam-3372	81	7	p=0	p=0	PROPN
ejpam-3372	82	1	π	π	PROPN
ejpam-3372	82	2	j	j	PROPN
ejpam-3372	82	3	6	6	NUM
ejpam-3372	82	4	=	=	PROPN
ejpam-3372	82	5	p	p	X
ejpam-3372	82	6	uj	uj	PROPN
ejpam-3372	82	7	)	)	PUNCT
ejpam-3372	82	8	f	f	PROPN
ejpam-3372	82	9	(	(	PUNCT
ejpam-3372	82	10	θ	θ	PROPN
ejpam-3372	82	11	)	)	PUNCT
ejpam-3372	82	12	]	]	PUNCT
ejpam-3372	82	13	,	,	PUNCT
ejpam-3372	82	14	d2	d2	PROPN
ejpam-3372	82	15	g	g	NOUN
ejpam-3372	82	16	dθ2	dθ2	NOUN
ejpam-3372	82	17	=	=	SYM
ejpam-3372	82	18	2n	2n	NUM
ejpam-3372	82	19	[	[	PUNCT
ejpam-3372	82	20	n	n	NUM
ejpam-3372	83	1	n−1	n−1	PROPN
ejpam-3372	83	2	π	π	X
ejpam-3372	83	3	p=0	p=0	X
ejpam-3372	83	4	|up|2	|up|2	PUNCT
ejpam-3372	83	5	−re	−re	PROPN
ejpam-3372	83	6	(	(	PUNCT
ejpam-3372	83	7	u0	u0	PROPN
ejpam-3372	83	8	n−1	n−1	PROPN
ejpam-3372	83	9	σ	σ	PROPN
ejpam-3372	84	1	p=0	p=0	PROPN
ejpam-3372	84	2	π	π	PROPN
ejpam-3372	84	3	j	j	PROPN
ejpam-3372	84	4	6	6	NUM
ejpam-3372	84	5	=	=	PROPN
ejpam-3372	84	6	p	p	X
ejpam-3372	84	7	uj	uj	PROPN
ejpam-3372	84	8	)	)	PUNCT
ejpam-3372	84	9	f	f	PROPN
ejpam-3372	84	10	(	(	PUNCT
ejpam-3372	84	11	θ	θ	PROPN
ejpam-3372	84	12	)	)	PUNCT
ejpam-3372	84	13	]	]	PUNCT
ejpam-3372	84	14	,	,	PUNCT
ejpam-3372	84	15	t.	t.	PROPN
ejpam-3372	84	16	s.	s.	PROPN
ejpam-3372	84	17	stoyanov	stoyanov	PROPN
ejpam-3372	84	18	/	/	SYM
ejpam-3372	84	19	eur	eur	PROPN
ejpam-3372	84	20	.	.	PUNCT
ejpam-3372	85	1	j.	j.	PROPN
ejpam-3372	85	2	pure	pure	PROPN
ejpam-3372	85	3	appl	appl	PROPN
ejpam-3372	85	4	.	.	PROPN
ejpam-3372	85	5	math	math	PROPN
ejpam-3372	85	6	,	,	PUNCT
ejpam-3372	85	7	12	12	NUM
ejpam-3372	85	8	(	(	PUNCT
ejpam-3372	85	9	2	2	NUM
ejpam-3372	85	10	)	)	PUNCT
ejpam-3372	85	11	(	(	PUNCT
ejpam-3372	85	12	2019	2019	NUM
ejpam-3372	85	13	)	)	PUNCT
ejpam-3372	85	14	,	,	PUNCT
ejpam-3372	85	15	649	649	NUM
ejpam-3372	85	16	-	-	SYM
ejpam-3372	85	17	653	653	NUM
ejpam-3372	85	18	652	652	NUM
ejpam-3372	85	19	and	and	CCONJ
ejpam-3372	85	20	consequently	consequently	ADV
ejpam-3372	85	21	d2	d2	PROPN
ejpam-3372	85	22	g	g	PROPN
ejpam-3372	85	23	dθ2	dθ2	NOUN
ejpam-3372	85	24	≥	≥	NUM
ejpam-3372	85	25	2n	2n	NUM
ejpam-3372	85	26	n−1	n−1	PROPN
ejpam-3372	85	27	π	π	PROPN
ejpam-3372	85	28	p=0	p=0	PROPN
ejpam-3372	85	29	|up|	|up|	PROPN
ejpam-3372	85	30	nn−1π	nn−1π	PUNCT
ejpam-3372	85	31	p=0	p=0	PROPN
ejpam-3372	85	32	|up|	|up|	PROPN
ejpam-3372	85	33	−	−	PROPN
ejpam-3372	85	34	∣∣∣∣u0	∣∣∣∣u0	PROPN
ejpam-3372	86	1	n−1	n−1	PROPN
ejpam-3372	86	2	σ	σ	PROPN
ejpam-3372	87	1	p=0	p=0	PROPN
ejpam-3372	87	2	π	π	PROPN
ejpam-3372	87	3	j	j	PROPN
ejpam-3372	87	4	6	6	NUM
ejpam-3372	87	5	=	=	PROPN
ejpam-3372	87	6	p	p	X
ejpam-3372	87	7	uj	uj	PROPN
ejpam-3372	87	8	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3372	87	9	.	.	PUNCT
ejpam-3372	88	1	∣∣f	∣∣f	NOUN
ejpam-3372	88	2	(	(	PUNCT
ejpam-3372	88	3	θ	θ	NOUN
ejpam-3372	88	4	)	)	PUNCT
ejpam-3372	88	5	∣∣	∣∣	NUM
ejpam-3372	88	6	πn−1	πn−1	PROPN
ejpam-3372	88	7	p=0up	p=0up	NUM
ejpam-3372	88	8			NOUN
ejpam-3372	88	9	.	.	PUNCT
ejpam-3372	89	1	if	if	SCONJ
ejpam-3372	89	2	we	we	PRON
ejpam-3372	89	3	note	note	VERB
ejpam-3372	89	4	b	b	NOUN
ejpam-3372	89	5	=	=	X
ejpam-3372	89	6	{	{	PUNCT
ejpam-3372	89	7	a	a	DET
ejpam-3372	89	8	\d	\d	NOUN
ejpam-3372	89	9	(	(	PUNCT
ejpam-3372	89	10	z	z	PROPN
ejpam-3372	89	11	,	,	PUNCT
ejpam-3372	89	12	a	a	PRON
ejpam-3372	89	13	)	)	PUNCT
ejpam-3372	89	14	\d	\d	NOUN
ejpam-3372	89	15	(	(	PUNCT
ejpam-3372	89	16	z	z	PROPN
ejpam-3372	89	17	,	,	PUNCT
ejpam-3372	89	18	a	a	NOUN
ejpam-3372	89	19	)	)	PUNCT
ejpam-3372	89	20	}	}	PUNCT
ejpam-3372	89	21	,	,	PUNCT
ejpam-3372	89	22	b0	b0	NOUN
ejpam-3372	89	23	=	=	SYM
ejpam-3372	89	24	{	{	PUNCT
ejpam-3372	89	25	a	a	DET
ejpam-3372	89	26	\d	\d	NOUN
ejpam-3372	89	27	(	(	PUNCT
ejpam-3372	89	28	z0	z0	PROPN
ejpam-3372	89	29	,	,	PUNCT
ejpam-3372	89	30	a	a	PRON
ejpam-3372	89	31	)	)	PUNCT
ejpam-3372	89	32	\d	\d	NOUN
ejpam-3372	89	33	(	(	PUNCT
ejpam-3372	89	34	z0	z0	PROPN
ejpam-3372	89	35	,	,	PUNCT
ejpam-3372	89	36	a	a	NOUN
ejpam-3372	89	37	)	)	PUNCT
ejpam-3372	89	38	}	}	PUNCT
ejpam-3372	89	39	and	and	CCONJ
ejpam-3372	89	40	since	since	SCONJ
ejpam-3372	89	41	θ	θ	PROPN
ejpam-3372	89	42	∈	∈	PROPN
ejpam-3372	90	1	[	[	X
ejpam-3372	90	2	0	0	NUM
ejpam-3372	90	3	,	,	PUNCT
ejpam-3372	90	4	θ0	θ0	PROPN
ejpam-3372	90	5	]	]	X
ejpam-3372	90	6	=	=	NOUN
ejpam-3372	90	7	⇒	⇒	NOUN
ejpam-3372	90	8	b0	b0	NOUN
ejpam-3372	90	9	⊂	⊂	PROPN
ejpam-3372	90	10	b	b	PROPN
ejpam-3372	90	11	,	,	PUNCT
ejpam-3372	90	12	i.e.	i.e.	X
ejpam-3372	90	13	,	,	PUNCT
ejpam-3372	90	14	|up	|up	NUM
ejpam-3372	90	15	(	(	PUNCT
ejpam-3372	90	16	θ)|	θ)|	PROPN
ejpam-3372	90	17	≥	≥	PRON
ejpam-3372	90	18	a	a	NOUN
ejpam-3372	90	19	,	,	PUNCT
ejpam-3372	90	20	p	p	X
ejpam-3372	90	21	=	=	NOUN
ejpam-3372	90	22	1	1	NUM
ejpam-3372	90	23	,	,	PUNCT
ejpam-3372	90	24	n−	n−	NOUN
ejpam-3372	90	25	1	1	NUM
ejpam-3372	90	26	.	.	PUNCT
ejpam-3372	91	1	if	if	SCONJ
ejpam-3372	91	2	we	we	PRON
ejpam-3372	91	3	assume	assume	VERB
ejpam-3372	91	4	|f	|f	PROPN
ejpam-3372	91	5	(	(	PUNCT
ejpam-3372	91	6	θ)|	θ)|	PROPN
ejpam-3372	91	7	=	=	SYM
ejpam-3372	91	8	∣∣f	∣∣f	PROPN
ejpam-3372	91	9	(	(	PUNCT
ejpam-3372	91	10	θ	θ	NOUN
ejpam-3372	91	11	)	)	PUNCT
ejpam-3372	91	12	∣∣	∣∣	X
ejpam-3372	91	13	≤	≤	ADV
ejpam-3372	91	14	an	an	DET
ejpam-3372	91	15	,	,	PUNCT
ejpam-3372	91	16	then	then	ADV
ejpam-3372	91	17	d2	d2	PROPN
ejpam-3372	91	18	g	g	PROPN
ejpam-3372	91	19	dθ2	dθ2	NOUN
ejpam-3372	91	20	≥	≥	NUM
ejpam-3372	91	21	2n	2n	NUM
ejpam-3372	91	22	n−1	n−1	PROPN
ejpam-3372	91	23	π	π	PROPN
ejpam-3372	91	24	p=0	p=0	PROPN
ejpam-3372	91	25	|up|	|up|	PROPN
ejpam-3372	91	26	[	[	PUNCT
ejpam-3372	91	27	naan−1	naan−1	PROPN
ejpam-3372	91	28	−	−	PROPN
ejpam-3372	91	29	(	(	PUNCT
ejpam-3372	91	30	1	1	NUM
ejpam-3372	91	31	+	+	NUM
ejpam-3372	91	32	∣∣∣∣u0	∣∣∣∣u0	PROPN
ejpam-3372	91	33	u1	u1	NOUN
ejpam-3372	91	34	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-3372	91	35	...	...	PUNCT
ejpam-3372	91	36	+	+	CCONJ
ejpam-3372	91	37	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3372	91	38	u0	u0	ADJ
ejpam-3372	91	39	un−1	un−1	PROPN
ejpam-3372	91	40	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3372	91	41	)	)	PUNCT
ejpam-3372	91	42	.an	.an	PUNCT
ejpam-3372	91	43	]	]	PUNCT
ejpam-3372	91	44	≥	≥	X
ejpam-3372	91	45	2na.πn−1	2na.πn−1	NUM
ejpam-3372	91	46	p=0	p=0	PROPN
ejpam-3372	91	47	|up|	|up|	PROPN
ejpam-3372	91	48	[	[	PUNCT
ejpam-3372	91	49	nan−1	nan−1	PROPN
ejpam-3372	91	50	−	−	PROPN
ejpam-3372	91	51	(	(	PUNCT
ejpam-3372	91	52	1	1	NUM
ejpam-3372	91	53	+	+	CCONJ
ejpam-3372	91	54	a	a	DET
ejpam-3372	91	55	(	(	PUNCT
ejpam-3372	91	56	n−	n−	NOUN
ejpam-3372	91	57	1	1	NUM
ejpam-3372	91	58	)	)	PUNCT
ejpam-3372	91	59	a	a	PRON
ejpam-3372	91	60	)	)	PUNCT
ejpam-3372	91	61	.an−1	.an−1	NOUN
ejpam-3372	91	62	]	]	PUNCT
ejpam-3372	92	1	=	=	PUNCT
ejpam-3372	92	2	0	0	X
ejpam-3372	92	3	.	.	PUNCT
ejpam-3372	92	4	then	then	ADV
ejpam-3372	92	5	d2	d2	PROPN
ejpam-3372	92	6	g	g	PROPN
ejpam-3372	92	7	dθ2	dθ2	NOUN
ejpam-3372	92	8	≥	≥	NOUN
ejpam-3372	92	9	0	0	NUM
ejpam-3372	92	10	.	.	PUNCT
ejpam-3372	93	1	hence	hence	ADV
ejpam-3372	93	2	dg	dg	PROPN
ejpam-3372	93	3	dθ	dθ	PROPN
ejpam-3372	93	4	(	(	PUNCT
ejpam-3372	93	5	θ	θ	PROPN
ejpam-3372	93	6	)	)	PUNCT
ejpam-3372	93	7	≥	≥	NOUN
ejpam-3372	93	8	dg	dg	PROPN
ejpam-3372	93	9	dθ	dθ	PROPN
ejpam-3372	93	10	(	(	PUNCT
ejpam-3372	93	11	0	0	NUM
ejpam-3372	93	12	)	)	PUNCT
ejpam-3372	93	13	=	=	SYM
ejpam-3372	93	14	0	0	X
ejpam-3372	93	15	.	.	PUNCT
ejpam-3372	94	1	consequently	consequently	ADV
ejpam-3372	94	2	g	g	PROPN
ejpam-3372	94	3	(	(	PUNCT
ejpam-3372	94	4	θ0	θ0	PROPN
ejpam-3372	94	5	)	)	PUNCT
ejpam-3372	94	6	>	>	X
ejpam-3372	95	1	g	g	PROPN
ejpam-3372	95	2	(	(	PUNCT
ejpam-3372	95	3	0	0	NUM
ejpam-3372	95	4	)	)	PUNCT
ejpam-3372	95	5	,	,	PUNCT
ejpam-3372	95	6	i.e.	i.e.	X
ejpam-3372	95	7	,	,	PUNCT
ejpam-3372	95	8	|f	|f	PROPN
ejpam-3372	95	9	(	(	PUNCT
ejpam-3372	95	10	θ0)|	θ0)|	X
ejpam-3372	95	11	>	>	X
ejpam-3372	95	12	an	an	PROPN
ejpam-3372	95	13	,	,	PUNCT
ejpam-3372	95	14	according	accord	VERB
ejpam-3372	95	15	to	to	ADP
ejpam-3372	95	16	the	the	DET
ejpam-3372	95	17	proof	proof	NOUN
ejpam-3372	95	18	of	of	ADP
ejpam-3372	95	19	theorem	theorem	NOUN
ejpam-3372	95	20	3	3	X
ejpam-3372	95	21	.	.	PUNCT
ejpam-3372	96	1	therefore	therefore	ADV
ejpam-3372	96	2	an	an	DET
ejpam-3372	96	3	<	<	X
ejpam-3372	96	4	|f	|f	PROPN
ejpam-3372	96	5	(	(	PUNCT
ejpam-3372	96	6	θ0)|	θ0)|	NOUN
ejpam-3372	96	7	≤	≤	NOUN
ejpam-3372	96	8	an	an	PRON
ejpam-3372	96	9	,	,	PUNCT
ejpam-3372	96	10	which	which	PRON
ejpam-3372	96	11	is	be	AUX
ejpam-3372	96	12	impossible	impossible	ADJ
ejpam-3372	96	13	.	.	PUNCT
ejpam-3372	97	1	the	the	DET
ejpam-3372	97	2	contradiction	contradiction	NOUN
ejpam-3372	97	3	proves	prove	VERB
ejpam-3372	97	4	the	the	DET
ejpam-3372	97	5	theorem	theorem	NOUN
ejpam-3372	97	6	4	4	NUM
ejpam-3372	97	7	.	.	PUNCT
ejpam-3372	97	8	corollary	corollary	NOUN
ejpam-3372	97	9	.	.	PUNCT
ejpam-3372	98	1	if	if	SCONJ
ejpam-3372	98	2	in	in	ADP
ejpam-3372	98	3	the	the	DET
ejpam-3372	98	4	condition	condition	NOUN
ejpam-3372	98	5	of	of	ADP
ejpam-3372	98	6	theorem	theorem	ADJ
ejpam-3372	98	7	4	4	NUM
ejpam-3372	98	8	,	,	PUNCT
ejpam-3372	98	9	we	we	PRON
ejpam-3372	98	10	put	put	VERB
ejpam-3372	98	11	a=1	a=1	ADP
ejpam-3372	98	12	,	,	PUNCT
ejpam-3372	98	13	and	and	CCONJ
ejpam-3372	98	14	s=0	s=0	PROPN
ejpam-3372	98	15	,	,	PUNCT
ejpam-3372	98	16	i.e.	i.e.	X
ejpam-3372	98	17	,	,	PUNCT
ejpam-3372	98	18	all	all	DET
ejpam-3372	98	19	the	the	DET
ejpam-3372	98	20	zeros	zero	NOUN
ejpam-3372	98	21	of	of	ADP
ejpam-3372	98	22	r(z	r(z	PROPN
ejpam-3372	98	23	)	)	PUNCT
ejpam-3372	98	24	are	be	AUX
ejpam-3372	98	25	real	real	ADJ
ejpam-3372	98	26	and	and	CCONJ
ejpam-3372	98	27	negative	negative	ADJ
ejpam-3372	98	28	,	,	PUNCT
ejpam-3372	98	29	then	then	ADV
ejpam-3372	98	30	we	we	PRON
ejpam-3372	98	31	get	get	VERB
ejpam-3372	98	32	that	that	SCONJ
ejpam-3372	98	33	the	the	DET
ejpam-3372	98	34	conjecture	conjecture	NOUN
ejpam-3372	98	35	1	1	NUM
ejpam-3372	98	36	is	be	AUX
ejpam-3372	98	37	true	true	ADJ
ejpam-3372	98	38	.	.	PUNCT
ejpam-3372	99	1	acknowledgements	acknowledgement	NOUN
ejpam-3372	99	2	this	this	DET
ejpam-3372	99	3	research	research	NOUN
ejpam-3372	99	4	was	be	AUX
ejpam-3372	99	5	financed	finance	VERB
ejpam-3372	99	6	from	from	ADP
ejpam-3372	99	7	university	university	NOUN
ejpam-3372	99	8	of	of	ADP
ejpam-3372	99	9	economics	economic	NOUN
ejpam-3372	99	10	of	of	ADP
ejpam-3372	99	11	varna	varna	ADJ
ejpam-3372	99	12	research	research	NOUN
ejpam-3372	99	13	grants	grant	NOUN
ejpam-3372	99	14	no	no	INTJ
ejpam-3372	99	15	.	.	NOUN
ejpam-3372	99	16	19	19	NUM
ejpam-3372	99	17	2018	2018	NUM
ejpam-3372	99	18	-	-	PUNCT
ejpam-3372	99	19	04	04	NUM
ejpam-3372	99	20	-	-	PUNCT
ejpam-3372	99	21	27	27	NUM
ejpam-3372	99	22	references	reference	NOUN
ejpam-3372	99	23	653	653	NUM
ejpam-3372	99	24	references	reference	NOUN
ejpam-3372	99	25	[	[	X
ejpam-3372	99	26	1	1	X
ejpam-3372	99	27	]	]	X
ejpam-3372	99	28	q.i	q.i	PROPN
ejpam-3372	99	29	.	.	PUNCT
ejpam-3372	99	30	rahman	rahman	PROPN
ejpam-3372	99	31	b.	b.	PROPN
ejpam-3372	99	32	bojanov	bojanov	PROPN
ejpam-3372	99	33	and	and	CCONJ
ejpam-3372	99	34	j.	j.	PROPN
ejpam-3372	99	35	szynal	szynal	PROPN
ejpam-3372	99	36	.	.	PUNCT
ejpam-3372	100	1	on	on	ADP
ejpam-3372	100	2	a	a	DET
ejpam-3372	100	3	conjecture	conjecture	NOUN
ejpam-3372	100	4	of	of	ADP
ejpam-3372	100	5	sendov	sendov	NOUN
ejpam-3372	100	6	about	about	ADP
ejpam-3372	100	7	the	the	DET
ejpam-3372	100	8	critical	critical	ADJ
ejpam-3372	100	9	points	point	NOUN
ejpam-3372	100	10	of	of	ADP
ejpam-3372	100	11	a	a	DET
ejpam-3372	100	12	polynomial	polynomial	NOUN
ejpam-3372	100	13	.	.	PUNCT
ejpam-3372	101	1	math.z	math.z	PROPN
ejpam-3372	101	2	,	,	PUNCT
ejpam-3372	101	3	190:281–285	190:281–285	NUM
ejpam-3372	101	4	,	,	PUNCT
ejpam-3372	101	5	1985	1985	NUM
ejpam-3372	101	6	.	.	PUNCT
ejpam-3372	102	1	[	[	X
ejpam-3372	102	2	2	2	X
ejpam-3372	102	3	]	]	PUNCT
ejpam-3372	102	4	t.	t.	PROPN
ejpam-3372	102	5	stoyanov	stoyanov	PROPN
ejpam-3372	102	6	.	.	PUNCT
ejpam-3372	103	1	inequalities	inequality	NOUN
ejpam-3372	103	2	of	of	ADP
ejpam-3372	103	3	the	the	DET
ejpam-3372	103	4	modulus	modulus	NOUN
ejpam-3372	103	5	of	of	ADP
ejpam-3372	103	6	some	some	DET
ejpam-3372	103	7	complex	complex	ADJ
ejpam-3372	103	8	integrals	integral	NOUN
ejpam-3372	103	9	,	,	PUNCT
ejpam-3372	103	10	theory	theory	NOUN
ejpam-3372	103	11	and	and	CCONJ
ejpam-3372	103	12	practice	practice	NOUN
ejpam-3372	103	13	of	of	ADP
ejpam-3372	103	14	modern	modern	ADJ
ejpam-3372	103	15	science	science	NOUN
ejpam-3372	103	16	.	.	PUNCT
ejpam-3372	104	1	[	[	X
ejpam-3372	104	2	3	3	X
ejpam-3372	104	3	]	]	PUNCT
ejpam-3372	104	4	t.	t.	PROPN
ejpam-3372	104	5	stoyanov	stoyanov	PROPN
ejpam-3372	104	6	.	.	PUNCT
ejpam-3372	105	1	some	some	DET
ejpam-3372	105	2	estimates	estimate	NOUN
ejpam-3372	105	3	below	below	ADP
ejpam-3372	105	4	the	the	DET
ejpam-3372	105	5	modulus	modulus	NOUN
ejpam-3372	105	6	of	of	ADP
ejpam-3372	105	7	integrals	integral	NOUN
ejpam-3372	105	8	in	in	ADP
ejpam-3372	105	9	the	the	DET
ejpam-3372	105	10	complex	complex	ADJ
ejpam-3372	105	11	plane	plane	NOUN
ejpam-3372	105	12	.	.	PUNCT
ejpam-3372	106	1	international	international	ADJ
ejpam-3372	106	2	scientific	scientific	ADJ
ejpam-3372	106	3	conference	conference	NOUN
ejpam-3372	106	4	,	,	PUNCT
ejpam-3372	106	5	tendencies	tendency	NOUN
ejpam-3372	106	6	and	and	CCONJ
ejpam-3372	106	7	prospects	prospect	NOUN
ejpam-3372	106	8	of	of	ADP
ejpam-3372	106	9	development	development	NOUN
ejpam-3372	106	10	of	of	ADP
ejpam-3372	106	11	modern	modern	ADJ
ejpam-3372	106	12	scientific	scientific	ADJ
ejpam-3372	106	13	knowledge	knowledge	NOUN
ejpam-3372	106	14	,	,	PUNCT
ejpam-3372	107	1	v.	v.	X
ejpam-3372	108	1	[	[	X
ejpam-3372	108	2	4	4	X
ejpam-3372	108	3	]	]	PUNCT
ejpam-3372	108	4	t.	t.	PROPN
ejpam-3372	108	5	stoyanov	stoyanov	PROPN
ejpam-3372	108	6	.	.	PUNCT
ejpam-3372	109	1	some	some	DET
ejpam-3372	109	2	estimates	estimate	NOUN
ejpam-3372	109	3	of	of	ADP
ejpam-3372	109	4	the	the	DET
ejpam-3372	109	5	modulus	modulus	NOUN
ejpam-3372	109	6	of	of	ADP
ejpam-3372	109	7	some	some	DET
ejpam-3372	109	8	complex	complex	ADJ
ejpam-3372	109	9	integrals	integral	NOUN
ejpam-3372	109	10	using	use	VERB
ejpam-3372	109	11	division	division	NOUN
ejpam-3372	109	12	of	of	ADP
ejpam-3372	109	13	polynomials	polynomial	NOUN
ejpam-3372	109	14	.	.	PUNCT
ejpam-3372	110	1	international	international	ADJ
ejpam-3372	110	2	scientific	scientific	ADJ
ejpam-3372	110	3	conference	conference	NOUN
ejpam-3372	110	4	,	,	PUNCT
ejpam-3372	110	5	tendencies	tendency	NOUN
ejpam-3372	110	6	and	and	CCONJ
ejpam-3372	110	7	prospects	prospect	NOUN
ejpam-3372	110	8	of	of	ADP
ejpam-3372	110	9	development	development	NOUN
ejpam-3372	110	10	of	of	ADP
ejpam-3372	110	11	modern	modern	ADJ
ejpam-3372	110	12	scientific	scientific	ADJ
ejpam-3372	110	13	knowledge	knowledge	NOUN
ejpam-3372	110	14	,	,	PUNCT
ejpam-3372	110	15	moskwa	moskwa	NOUN
ejpam-3372	110	16	,	,	PUNCT
ejpam-3372	110	17	iv	iv	X
ejpam-3372	110	18	.	.	PUNCT
ejpam-3372	111	1	[	[	X
ejpam-3372	111	2	5	5	X
ejpam-3372	111	3	]	]	PUNCT
ejpam-3372	111	4	t.	t.	PROPN
ejpam-3372	111	5	stoyanov	stoyanov	PROPN
ejpam-3372	111	6	.	.	PUNCT
ejpam-3372	112	1	some	some	DET
ejpam-3372	112	2	new	new	ADJ
ejpam-3372	112	3	methods	method	NOUN
ejpam-3372	112	4	for	for	ADP
ejpam-3372	112	5	the	the	DET
ejpam-3372	112	6	estimates	estimate	NOUN
ejpam-3372	112	7	of	of	ADP
ejpam-3372	112	8	the	the	DET
ejpam-3372	112	9	modulus	modulus	NOUN
ejpam-3372	112	10	of	of	ADP
ejpam-3372	112	11	some	some	DET
ejpam-3372	112	12	integrals	integral	NOUN
ejpam-3372	112	13	of	of	ADP
ejpam-3372	112	14	the	the	DET
ejpam-3372	112	15	unit	unit	NOUN
ejpam-3372	112	16	circle	circle	NOUN
ejpam-3372	112	17	in	in	ADP
ejpam-3372	112	18	the	the	DET
ejpam-3372	112	19	complex	complex	ADJ
ejpam-3372	112	20	plane	plane	NOUN
ejpam-3372	112	21	.	.	PUNCT
ejpam-3372	113	1	journal	journal	NOUN
ejpam-3372	113	2	of	of	ADP
ejpam-3372	113	3	analysis	analysis	NOUN
ejpam-3372	113	4	and	and	CCONJ
ejpam-3372	113	5	applications	application	NOUN
ejpam-3372	113	6	,	,	PUNCT
ejpam-3372	113	7	17(2):119	17(2):119	NUM
ejpam-3372	113	8	–	–	PUNCT
ejpam-3372	113	9	130	130	NUM
ejpam-3372	113	10	,	,	PUNCT
ejpam-3372	113	11	2019	2019	NUM
ejpam-3372	113	12	.	.	PUNCT
ejpam-3372	114	1	[	[	X
ejpam-3372	114	2	6	6	NUM
ejpam-3372	114	3	]	]	PUNCT
ejpam-3372	114	4	t.	t.	PROPN
ejpam-3372	114	5	zapryanova	zapryanova	PROPN
ejpam-3372	114	6	.	.	PUNCT
ejpam-3372	115	1	approximation	approximation	NOUN
ejpam-3372	115	2	by	by	ADP
ejpam-3372	115	3	the	the	DET
ejpam-3372	115	4	operators	operator	NOUN
ejpam-3372	115	5	of	of	ADP
ejpam-3372	115	6	cao	cao	ADJ
ejpam-3372	115	7	-	-	ADJ
ejpam-3372	115	8	gonska	gonska	NOUN
ejpam-3372	115	9	type	type	NOUN
ejpam-3372	115	10	g+s	g+s	PROPN
ejpam-3372	115	11	,	,	PUNCT
ejpam-3372	115	12	n.	n.	NOUN
ejpam-3372	115	13	direct	direct	ADJ
ejpam-3372	115	14	and	and	CCONJ
ejpam-3372	115	15	converse	converse	NOUN
ejpam-3372	115	16	theorem	theorem	NOUN
ejpam-3372	115	17	.	.	PUNCT
ejpam-3372	116	1	mathematics	mathematic	NOUN
ejpam-3372	116	2	and	and	CCONJ
ejpam-3372	116	3	education	education	NOUN
ejpam-3372	116	4	in	in	ADP
ejpam-3372	116	5	mathematics	mathematic	NOUN
ejpam-3372	116	6	.	.	PUNCT
ejpam-3372	117	1	[	[	X
ejpam-3372	117	2	7	7	X
ejpam-3372	117	3	]	]	PUNCT
ejpam-3372	117	4	t.	t.	PROPN
ejpam-3372	117	5	zapryanova	zapryanova	PROPN
ejpam-3372	117	6	.	.	PUNCT
ejpam-3372	118	1	approximation	approximation	NOUN
ejpam-3372	118	2	by	by	ADP
ejpam-3372	118	3	the	the	DET
ejpam-3372	118	4	operators	operator	NOUN
ejpam-3372	118	5	of	of	ADP
ejpam-3372	118	6	cao	cao	ADJ
ejpam-3372	118	7	-	-	ADJ
ejpam-3372	118	8	gonska	gonska	ADJ
ejpam-3372	118	9	type	type	NOUN
ejpam-3372	118	10	gs	gs	NOUN
ejpam-3372	118	11	,	,	PUNCT
ejpam-3372	118	12	n	n	PROPN
ejpam-3372	118	13	and	and	CCONJ
ejpam-3372	118	14	g*s	g*s	PROPN
ejpam-3372	118	15	,	,	PUNCT
ejpam-3372	118	16	n.	n.	NOUN
ejpam-3372	118	17	direct	direct	ADJ
ejpam-3372	118	18	and	and	CCONJ
ejpam-3372	118	19	converse	converse	NOUN
ejpam-3372	118	20	theorem	theorem	NOUN
ejpam-3372	118	21	.	.	PUNCT
ejpam-3372	119	1	mathematics	mathematic	NOUN
ejpam-3372	119	2	and	and	CCONJ
ejpam-3372	119	3	education	education	NOUN
ejpam-3372	119	4	in	in	ADP
ejpam-3372	119	5	mathematics	mathematic	NOUN
ejpam-3372	119	6	,	,	PUNCT
ejpam-3372	119	7	pages	page	NOUN
ejpam-3372	119	8	189	189	NUM
ejpam-3372	119	9	–	–	SYM
ejpam-3372	119	10	194	194	NUM
ejpam-3372	119	11	,	,	PUNCT
ejpam-3372	119	12	2008	2008	NUM
ejpam-3372	119	13	.	.	PUNCT
ejpam-3372	120	1	[	[	X
ejpam-3372	120	2	8	8	X
ejpam-3372	120	3	]	]	PUNCT
ejpam-3372	120	4	t.	t.	PROPN
ejpam-3372	120	5	zapryanova	zapryanova	PROPN
ejpam-3372	120	6	.	.	PUNCT
ejpam-3372	121	1	a	a	DET
ejpam-3372	121	2	characterization	characterization	NOUN
ejpam-3372	121	3	of	of	ADP
ejpam-3372	121	4	the	the	DET
ejpam-3372	121	5	k	k	NOUN
ejpam-3372	121	6	-	-	NOUN
ejpam-3372	121	7	functional	functional	ADJ
ejpam-3372	121	8	for	for	ADP
ejpam-3372	121	9	the	the	DET
ejpam-3372	121	10	algebraic	algebraic	ADJ
ejpam-3372	121	11	version	version	NOUN
ejpam-3372	121	12	of	of	ADP
ejpam-3372	121	13	the	the	DET
ejpam-3372	121	14	trigonometric	trigonometric	PROPN
ejpam-3372	121	15	jackson	jackson	PROPN
ejpam-3372	121	16	integrals	integral	VERB
ejpam-3372	121	17	gs	gs	PROPN
ejpam-3372	121	18	,	,	PUNCT
ejpam-3372	121	19	n	n	PROPN
ejpam-3372	121	20	and	and	CCONJ
ejpam-3372	121	21	the	the	DET
ejpam-3372	121	22	k	k	NOUN
ejpam-3372	121	23	-	-	PUNCT
ejpam-3372	121	24	functionals	functional	NOUN
ejpam-3372	121	25	for	for	ADP
ejpam-3372	121	26	cao	cao	ADJ
ejpam-3372	121	27	-	-	ADJ
ejpam-3372	121	28	gonska	gonska	ADJ
ejpam-3372	121	29	operators	operator	NOUN
ejpam-3372	121	30	g*s	g*s	PROPN
ejpam-3372	121	31	,	,	PUNCT
ejpam-3372	121	32	n	n	PROPN
ejpam-3372	121	33	and	and	CCONJ
ejpam-3372	121	34	g+s	g+s	PROPN
ejpam-3372	121	35	,	,	PUNCT
ejpam-3372	121	36	n.	n.	NOUN
ejpam-3372	121	37	result	result	NOUN
ejpam-3372	121	38	.	.	PUNCT
ejpam-3372	122	1	math	math	NOUN
ejpam-3372	122	2	.	.	PUNCT
ejpam-3372	122	3	,	,	PUNCT
ejpam-3372	123	1	54:397–413	54:397–413	NUM
ejpam-3372	123	2	,	,	PUNCT
ejpam-3372	123	3	2009	2009	NUM
ejpam-3372	123	4	.	.	PUNCT
ejpam-3372	124	1	[	[	X
ejpam-3372	124	2	9	9	NUM
ejpam-3372	124	3	]	]	PUNCT
ejpam-3372	124	4	t.	t.	PROPN
ejpam-3372	124	5	zapryanova	zapryanova	PROPN
ejpam-3372	124	6	and	and	CCONJ
ejpam-3372	124	7	d.	d.	PROPN
ejpam-3372	124	8	souroujon	souroujon	PROPN
ejpam-3372	124	9	.	.	PUNCT
ejpam-3372	125	1	on	on	ADP
ejpam-3372	125	2	the	the	DET
ejpam-3372	125	3	iterates	iterate	NOUN
ejpam-3372	125	4	of	of	ADP
ejpam-3372	125	5	jackson	jackson	PROPN
ejpam-3372	125	6	type	type	PROPN
ejpam-3372	125	7	operator	operator	NOUN
ejpam-3372	125	8	gs	gs	PROPN
ejpam-3372	125	9	,	,	PUNCT
ejpam-3372	125	10	n.	n.	PROPN
ejpam-3372	125	11	mediterr	mediterr	PROPN
ejpam-3372	125	12	.	.	PUNCT
ejpam-3372	126	1	j.	j.	PROPN
ejpam-3372	126	2	math	math	PROPN
ejpam-3372	126	3	.	.	PUNCT