id	sid	tid	token	lemma	pos
ejpam-3737	1	1	european	european	PROPN
ejpam-3737	1	2	journal	journal	PROPN
ejpam-3737	1	3	of	of	ADP
ejpam-3737	1	4	pure	pure	ADJ
ejpam-3737	1	5	and	and	CCONJ
ejpam-3737	1	6	applied	apply	VERB
ejpam-3737	1	7	mathematics	mathematic	NOUN
ejpam-3737	1	8	vol	vol	NOUN
ejpam-3737	1	9	.	.	PROPN
ejpam-3737	2	1	13	13	NUM
ejpam-3737	2	2	,	,	PUNCT
ejpam-3737	2	3	no	no	INTJ
ejpam-3737	2	4	.	.	NOUN
ejpam-3737	2	5	4	4	NUM
ejpam-3737	2	6	,	,	PUNCT
ejpam-3737	2	7	2020	2020	NUM
ejpam-3737	2	8	,	,	PUNCT
ejpam-3737	2	9	807	807	NUM
ejpam-3737	2	10	-	-	SYM
ejpam-3737	2	11	813	813	NUM
ejpam-3737	2	12	issn	issn	PROPN
ejpam-3737	2	13	1307	1307	NUM
ejpam-3737	2	14	-	-	SYM
ejpam-3737	2	15	5543	5543	NUM
ejpam-3737	2	16	–	–	PUNCT
ejpam-3737	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3737	2	18	published	publish	VERB
ejpam-3737	2	19	by	by	ADP
ejpam-3737	2	20	new	new	PROPN
ejpam-3737	2	21	york	york	PROPN
ejpam-3737	2	22	business	business	PROPN
ejpam-3737	3	1	global	global	PROPN
ejpam-3737	3	2	a	a	DET
ejpam-3737	3	3	private	private	ADJ
ejpam-3737	3	4	case	case	NOUN
ejpam-3737	3	5	of	of	ADP
ejpam-3737	3	6	sendov	sendov	PROPN
ejpam-3737	3	7	’s	’s	PART
ejpam-3737	3	8	conjecture	conjecture	NOUN
ejpam-3737	3	9	todor	todor	PROPN
ejpam-3737	3	10	stoyanov	stoyanov	PROPN
ejpam-3737	3	11	stoyanov	stoyanov	PROPN
ejpam-3737	3	12	department	department	PROPN
ejpam-3737	3	13	of	of	ADP
ejpam-3737	3	14	mathematics	mathematics	PROPN
ejpam-3737	3	15	,	,	PUNCT
ejpam-3737	3	16	university	university	NOUN
ejpam-3737	3	17	of	of	ADP
ejpam-3737	3	18	economics	economics	PROPN
ejpam-3737	3	19	,	,	PUNCT
ejpam-3737	3	20	bul	bul	PROPN
ejpam-3737	3	21	.	.	PUNCT
ejpam-3737	4	1	knyaz	knyaz	PROPN
ejpam-3737	4	2	boris	boris	PROPN
ejpam-3737	4	3	i	i	PRON
ejpam-3737	4	4	77	77	NUM
ejpam-3737	4	5	,	,	PUNCT
ejpam-3737	4	6	varna	varna	ADJ
ejpam-3737	4	7	9002	9002	NUM
ejpam-3737	4	8	,	,	PUNCT
ejpam-3737	4	9	bulgaria	bulgaria	PROPN
ejpam-3737	4	10	abstract	abstract	NOUN
ejpam-3737	4	11	.	.	PUNCT
ejpam-3737	5	1	in	in	ADP
ejpam-3737	5	2	this	this	DET
ejpam-3737	5	3	paper	paper	NOUN
ejpam-3737	5	4	,	,	PUNCT
ejpam-3737	5	5	we	we	PRON
ejpam-3737	5	6	prove	prove	VERB
ejpam-3737	5	7	sendov	sendov	PROPN
ejpam-3737	5	8	’s	’s	PART
ejpam-3737	5	9	conjecture	conjecture	NOUN
ejpam-3737	5	10	,	,	PUNCT
ejpam-3737	5	11	when	when	SCONJ
ejpam-3737	5	12	a	a	DET
ejpam-3737	5	13	polynomial	polynomial	NOUN
ejpam-3737	5	14	is	be	AUX
ejpam-3737	5	15	with	with	ADP
ejpam-3737	5	16	real	real	ADJ
ejpam-3737	5	17	coefficients	coefficient	NOUN
ejpam-3737	5	18	and	and	CCONJ
ejpam-3737	5	19	the	the	DET
ejpam-3737	5	20	conjecture	conjecture	NOUN
ejpam-3737	5	21	is	be	AUX
ejpam-3737	5	22	relevant	relevant	ADJ
ejpam-3737	5	23	to	to	ADP
ejpam-3737	5	24	the	the	DET
ejpam-3737	5	25	zeros	zero	NOUN
ejpam-3737	5	26	,	,	PUNCT
ejpam-3737	5	27	which	which	PRON
ejpam-3737	5	28	belong	belong	VERB
ejpam-3737	5	29	to	to	ADP
ejpam-3737	5	30	the	the	DET
ejpam-3737	5	31	set	set	NOUN
ejpam-3737	5	32	m	m	NOUN
ejpam-3737	5	33	=	=	SYM
ejpam-3737	5	34	d	d	X
ejpam-3737	5	35	(	(	PUNCT
ejpam-3737	5	36	0	0	NUM
ejpam-3737	5	37	,	,	PUNCT
ejpam-3737	5	38	1	1	NUM
ejpam-3737	5	39	)	)	PUNCT
ejpam-3737	5	40	∩	∩	NOUN
ejpam-3737	6	1	[	[	X
ejpam-3737	6	2	d	d	X
ejpam-3737	6	3	(	(	PUNCT
ejpam-3737	6	4	1	1	NUM
ejpam-3737	6	5	,	,	PUNCT
ejpam-3737	6	6	1	1	NUM
ejpam-3737	6	7	)	)	PUNCT
ejpam-3737	6	8	∪	∪	PROPN
ejpam-3737	6	9	d	d	PROPN
ejpam-3737	6	10	(	(	PUNCT
ejpam-3737	6	11	−1	−1	NOUN
ejpam-3737	6	12	,	,	PUNCT
ejpam-3737	6	13	1	1	NUM
ejpam-3737	6	14	)	)	PUNCT
ejpam-3737	6	15	]	]	PUNCT
ejpam-3737	6	16	.	.	PUNCT
ejpam-3737	7	1	we	we	PRON
ejpam-3737	7	2	can	can	AUX
ejpam-3737	7	3	see	see	VERB
ejpam-3737	7	4	it	it	PRON
ejpam-3737	7	5	in	in	ADP
ejpam-3737	7	6	figure	figure	NOUN
ejpam-3737	7	7	1	1	NUM
ejpam-3737	7	8	.	.	PUNCT
ejpam-3737	8	1	the	the	DET
ejpam-3737	8	2	conjecture	conjecture	NOUN
ejpam-3737	8	3	is	be	AUX
ejpam-3737	8	4	true	true	ADJ
ejpam-3737	8	5	for	for	ADP
ejpam-3737	8	6	the	the	DET
ejpam-3737	8	7	filled	fill	VERB
ejpam-3737	8	8	areas	area	NOUN
ejpam-3737	8	9	.	.	PUNCT
ejpam-3737	9	1	2020	2020	NUM
ejpam-3737	9	2	mathematics	mathematic	NOUN
ejpam-3737	9	3	subject	subject	NOUN
ejpam-3737	9	4	classifications	classification	NOUN
ejpam-3737	9	5	:	:	PUNCT
ejpam-3737	9	6	30d20	30d20	NUM
ejpam-3737	9	7	,	,	PUNCT
ejpam-3737	9	8	30a10	30a10	NUM
ejpam-3737	9	9	key	key	ADJ
ejpam-3737	9	10	words	word	NOUN
ejpam-3737	9	11	and	and	CCONJ
ejpam-3737	9	12	phrases	phrase	NOUN
ejpam-3737	9	13	:	:	PUNCT
ejpam-3737	9	14	zeros	zero	NOUN
ejpam-3737	9	15	,	,	PUNCT
ejpam-3737	9	16	complex	complex	ADJ
ejpam-3737	9	17	polynomial	polynomial	ADJ
ejpam-3737	9	18	,	,	PUNCT
ejpam-3737	9	19	real	real	ADJ
ejpam-3737	9	20	polynomial	polynomial	ADJ
ejpam-3737	9	21	,	,	PUNCT
ejpam-3737	9	22	disk	disk	NOUN
ejpam-3737	9	23	,	,	PUNCT
ejpam-3737	9	24	derivative	derivative	ADJ
ejpam-3737	9	25	,	,	PUNCT
ejpam-3737	9	26	integral	integral	ADJ
ejpam-3737	9	27	1	1	NUM
ejpam-3737	9	28	.	.	PUNCT
ejpam-3737	9	29	introduction	introduction	NOUN
ejpam-3737	9	30	the	the	DET
ejpam-3737	9	31	localization	localization	NOUN
ejpam-3737	9	32	of	of	ADP
ejpam-3737	9	33	the	the	DET
ejpam-3737	9	34	zeros	zero	NOUN
ejpam-3737	9	35	of	of	ADP
ejpam-3737	9	36	the	the	DET
ejpam-3737	9	37	complex	complex	ADJ
ejpam-3737	9	38	polynomials	polynomial	NOUN
ejpam-3737	9	39	is	be	AUX
ejpam-3737	9	40	very	very	ADV
ejpam-3737	9	41	important	important	ADJ
ejpam-3737	9	42	area	area	NOUN
ejpam-3737	9	43	of	of	ADP
ejpam-3737	9	44	the	the	DET
ejpam-3737	9	45	mathematics	mathematic	NOUN
ejpam-3737	9	46	.	.	PUNCT
ejpam-3737	10	1	the	the	DET
ejpam-3737	10	2	impossibility	impossibility	NOUN
ejpam-3737	10	3	to	to	PART
ejpam-3737	10	4	find	find	VERB
ejpam-3737	10	5	the	the	DET
ejpam-3737	10	6	zeros	zero	NOUN
ejpam-3737	10	7	of	of	ADP
ejpam-3737	10	8	any	any	DET
ejpam-3737	10	9	polynomials	polynomial	NOUN
ejpam-3737	10	10	using	use	VERB
ejpam-3737	10	11	the	the	DET
ejpam-3737	10	12	coefficients	coefficient	NOUN
ejpam-3737	10	13	makes	make	VERB
ejpam-3737	10	14	every	every	DET
ejpam-3737	10	15	statement	statement	NOUN
ejpam-3737	10	16	here	here	ADV
ejpam-3737	10	17	very	very	ADV
ejpam-3737	10	18	significant	significant	ADJ
ejpam-3737	10	19	.	.	PUNCT
ejpam-3737	11	1	there	there	PRON
ejpam-3737	11	2	exist	exist	VERB
ejpam-3737	11	3	many	many	ADJ
ejpam-3737	11	4	conjectures	conjecture	NOUN
ejpam-3737	11	5	which	which	PRON
ejpam-3737	11	6	are	be	AUX
ejpam-3737	11	7	not	not	PART
ejpam-3737	11	8	proved	prove	VERB
ejpam-3737	11	9	,	,	PUNCT
ejpam-3737	11	10	like	like	ADP
ejpam-3737	11	11	sendov	sendov	PROPN
ejpam-3737	11	12	’s	’s	PART
ejpam-3737	11	13	conjecture	conjecture	NOUN
ejpam-3737	11	14	and	and	CCONJ
ejpam-3737	11	15	obreshkoff	obreshkoff	ADJ
ejpam-3737	11	16	’s	’s	PART
ejpam-3737	11	17	conjecture	conjecture	NOUN
ejpam-3737	11	18	.	.	PUNCT
ejpam-3737	12	1	they	they	PRON
ejpam-3737	12	2	localize	localize	VERB
ejpam-3737	12	3	the	the	DET
ejpam-3737	12	4	zeros	zero	NOUN
ejpam-3737	12	5	of	of	ADP
ejpam-3737	12	6	the	the	DET
ejpam-3737	12	7	derivative	derivative	NOUN
ejpam-3737	12	8	of	of	ADP
ejpam-3737	12	9	many	many	ADJ
ejpam-3737	12	10	complex	complex	ADJ
ejpam-3737	12	11	polynomial	polynomial	NOUN
ejpam-3737	12	12	in	in	ADP
ejpam-3737	12	13	some	some	DET
ejpam-3737	12	14	areas	area	NOUN
ejpam-3737	12	15	.	.	PUNCT
ejpam-3737	13	1	here	here	ADV
ejpam-3737	13	2	we	we	PRON
ejpam-3737	13	3	present	present	VERB
ejpam-3737	13	4	some	some	DET
ejpam-3737	13	5	new	new	ADJ
ejpam-3737	13	6	results	result	NOUN
ejpam-3737	13	7	about	about	ADP
ejpam-3737	13	8	the	the	DET
ejpam-3737	13	9	zeros	zero	NOUN
ejpam-3737	13	10	of	of	ADP
ejpam-3737	13	11	the	the	DET
ejpam-3737	13	12	derivative	derivative	NOUN
ejpam-3737	13	13	of	of	ADP
ejpam-3737	13	14	real	real	ADJ
ejpam-3737	13	15	polynomials	polynomial	NOUN
ejpam-3737	13	16	.	.	PUNCT
ejpam-3737	14	1	in	in	ADP
ejpam-3737	14	2	the	the	DET
ejpam-3737	14	3	second	second	ADJ
ejpam-3737	14	4	part	part	NOUN
ejpam-3737	14	5	“	"	PUNCT
ejpam-3737	14	6	preliminaries	preliminary	NOUN
ejpam-3737	14	7	”	"	PUNCT
ejpam-3737	14	8	we	we	PRON
ejpam-3737	14	9	define	define	VERB
ejpam-3737	14	10	some	some	DET
ejpam-3737	14	11	sets	set	NOUN
ejpam-3737	14	12	,	,	PUNCT
ejpam-3737	14	13	including	include	VERB
ejpam-3737	14	14	the	the	DET
ejpam-3737	14	15	set	set	NOUN
ejpam-3737	14	16	m	m	NOUN
ejpam-3737	14	17	.	.	PUNCT
ejpam-3737	15	1	here	here	ADV
ejpam-3737	15	2	we	we	PRON
ejpam-3737	15	3	formulate	formulate	VERB
ejpam-3737	15	4	sendov	sendov	PROPN
ejpam-3737	15	5	’s	’s	PART
ejpam-3737	15	6	conjecture	conjecture	NOUN
ejpam-3737	15	7	.	.	PUNCT
ejpam-3737	16	1	in	in	ADP
ejpam-3737	16	2	the	the	DET
ejpam-3737	16	3	third	third	ADJ
ejpam-3737	16	4	part	part	NOUN
ejpam-3737	16	5	“	"	PUNCT
ejpam-3737	16	6	related	related	ADJ
ejpam-3737	16	7	results	result	NOUN
ejpam-3737	16	8	”	"	PUNCT
ejpam-3737	16	9	,	,	PUNCT
ejpam-3737	16	10	we	we	PRON
ejpam-3737	16	11	present	present	VERB
ejpam-3737	16	12	three	three	NUM
ejpam-3737	16	13	statements	statement	NOUN
ejpam-3737	16	14	which	which	PRON
ejpam-3737	16	15	are	be	AUX
ejpam-3737	16	16	similar	similar	ADJ
ejpam-3737	16	17	to	to	ADP
ejpam-3737	16	18	our	our	PRON
ejpam-3737	16	19	theorems	theorem	NOUN
ejpam-3737	16	20	.	.	PUNCT
ejpam-3737	17	1	the	the	DET
ejpam-3737	17	2	proofs	proof	NOUN
ejpam-3737	17	3	of	of	ADP
ejpam-3737	17	4	statement	statement	NOUN
ejpam-3737	17	5	1	1	NUM
ejpam-3737	17	6	and	and	CCONJ
ejpam-3737	17	7	statement	statement	NOUN
ejpam-3737	17	8	2	2	NUM
ejpam-3737	17	9	,	,	PUNCT
ejpam-3737	17	10	we	we	PRON
ejpam-3737	17	11	can	can	AUX
ejpam-3737	17	12	see	see	VERB
ejpam-3737	17	13	in	in	ADP
ejpam-3737	17	14	[	[	X
ejpam-3737	17	15	3	3	NUM
ejpam-3737	17	16	]	]	PUNCT
ejpam-3737	17	17	.	.	PUNCT
ejpam-3737	18	1	if	if	SCONJ
ejpam-3737	18	2	we	we	PRON
ejpam-3737	18	3	put	put	VERB
ejpam-3737	18	4	m	m	VERB
ejpam-3737	18	5	=	=	NOUN
ejpam-3737	18	6	1	1	NUM
ejpam-3737	18	7	in	in	ADP
ejpam-3737	18	8	the	the	DET
ejpam-3737	18	9	condition	condition	NOUN
ejpam-3737	18	10	of	of	ADP
ejpam-3737	18	11	statement	statement	NOUN
ejpam-3737	18	12	2	2	NUM
ejpam-3737	18	13	we	we	PRON
ejpam-3737	18	14	obtain	obtain	VERB
ejpam-3737	18	15	statement	statement	NOUN
ejpam-3737	18	16	1	1	NUM
ejpam-3737	18	17	,	,	PUNCT
ejpam-3737	18	18	which	which	PRON
ejpam-3737	18	19	is	be	AUX
ejpam-3737	18	20	the	the	DET
ejpam-3737	18	21	famous	famous	ADJ
ejpam-3737	18	22	obreshkoff	obreshkoff	ADJ
ejpam-3737	18	23	theorem	theorem	NOUN
ejpam-3737	18	24	,	,	PUNCT
ejpam-3737	18	25	that	that	PRON
ejpam-3737	18	26	can	can	AUX
ejpam-3737	18	27	be	be	AUX
ejpam-3737	18	28	regarded	regard	VERB
ejpam-3737	18	29	as	as	ADP
ejpam-3737	18	30	a	a	DET
ejpam-3737	18	31	‘	'	PUNCT
ejpam-3737	18	32	complex	complex	ADJ
ejpam-3737	18	33	version	version	NOUN
ejpam-3737	18	34	’	'	PUNCT
ejpam-3737	18	35	of	of	ADP
ejpam-3737	18	36	a	a	DET
ejpam-3737	18	37	well	well	ADV
ejpam-3737	18	38	-	-	PUNCT
ejpam-3737	18	39	known	know	VERB
ejpam-3737	18	40	theorem	theorem	NOUN
ejpam-3737	18	41	due	due	ADP
ejpam-3737	18	42	to	to	ADP
ejpam-3737	18	43	laguerre	laguerre	NOUN
ejpam-3737	18	44	.	.	PUNCT
ejpam-3737	19	1	the	the	DET
ejpam-3737	19	2	proof	proof	NOUN
ejpam-3737	19	3	of	of	ADP
ejpam-3737	19	4	statement	statement	NOUN
ejpam-3737	19	5	3	3	NUM
ejpam-3737	19	6	we	we	PRON
ejpam-3737	19	7	can	can	AUX
ejpam-3737	19	8	see	see	VERB
ejpam-3737	19	9	in	in	ADP
ejpam-3737	19	10	[	[	X
ejpam-3737	19	11	1	1	NUM
ejpam-3737	19	12	]	]	PUNCT
ejpam-3737	19	13	.	.	PUNCT
ejpam-3737	20	1	the	the	DET
ejpam-3737	20	2	main	main	ADJ
ejpam-3737	20	3	theorems	theorem	NOUN
ejpam-3737	20	4	are	be	AUX
ejpam-3737	20	5	in	in	ADP
ejpam-3737	20	6	the	the	DET
ejpam-3737	20	7	fourth	fourth	ADJ
ejpam-3737	20	8	part	part	NOUN
ejpam-3737	20	9	“	"	PUNCT
ejpam-3737	20	10	main	main	ADJ
ejpam-3737	20	11	results	result	NOUN
ejpam-3737	20	12	”	"	PUNCT
ejpam-3737	20	13	.	.	PUNCT
ejpam-3737	21	1	theorem	theorem	NOUN
ejpam-3737	21	2	1	1	NUM
ejpam-3737	21	3	is	be	AUX
ejpam-3737	21	4	relevant	relevant	ADJ
ejpam-3737	21	5	to	to	ADP
ejpam-3737	21	6	the	the	DET
ejpam-3737	21	7	real	real	ADJ
ejpam-3737	21	8	zeros	zero	NOUN
ejpam-3737	21	9	of	of	ADP
ejpam-3737	21	10	the	the	DET
ejpam-3737	21	11	real	real	ADJ
ejpam-3737	21	12	polynomial	polynomial	ADJ
ejpam-3737	21	13	r	r	NOUN
ejpam-3737	21	14	(	(	PUNCT
ejpam-3737	21	15	z	z	NOUN
ejpam-3737	21	16	)	)	PUNCT
ejpam-3737	21	17	.	.	PUNCT
ejpam-3737	22	1	theorem	theorem	NOUN
ejpam-3737	22	2	2	2	NUM
ejpam-3737	22	3	is	be	AUX
ejpam-3737	22	4	relevant	relevant	ADJ
ejpam-3737	22	5	to	to	ADP
ejpam-3737	22	6	the	the	DET
ejpam-3737	22	7	complex	complex	ADJ
ejpam-3737	22	8	zeros	zero	NOUN
ejpam-3737	22	9	of	of	ADP
ejpam-3737	22	10	the	the	DET
ejpam-3737	22	11	real	real	ADJ
ejpam-3737	22	12	polynomial	polynomial	ADJ
ejpam-3737	22	13	r	r	NOUN
ejpam-3737	22	14	(	(	PUNCT
ejpam-3737	22	15	z	z	NOUN
ejpam-3737	22	16	)	)	PUNCT
ejpam-3737	22	17	.	.	PUNCT
ejpam-3737	23	1	all	all	DET
ejpam-3737	23	2	the	the	DET
ejpam-3737	23	3	results	result	NOUN
ejpam-3737	23	4	could	could	AUX
ejpam-3737	23	5	be	be	AUX
ejpam-3737	23	6	connected	connect	VERB
ejpam-3737	23	7	with	with	ADP
ejpam-3737	23	8	the	the	DET
ejpam-3737	23	9	results	result	NOUN
ejpam-3737	23	10	of	of	ADP
ejpam-3737	23	11	[	[	X
ejpam-3737	23	12	4	4	NUM
ejpam-3737	23	13	]	]	PUNCT
ejpam-3737	23	14	.	.	PUNCT
ejpam-3737	24	1	the	the	DET
ejpam-3737	24	2	proofs	proof	NOUN
ejpam-3737	24	3	of	of	ADP
ejpam-3737	24	4	these	these	DET
ejpam-3737	24	5	theorems	theorem	NOUN
ejpam-3737	24	6	are	be	AUX
ejpam-3737	24	7	independent	independent	ADJ
ejpam-3737	24	8	of	of	ADP
ejpam-3737	24	9	references	reference	NOUN
ejpam-3737	24	10	.	.	PUNCT
ejpam-3737	25	1	only	only	ADV
ejpam-3737	25	2	[	[	X
ejpam-3737	25	3	4	4	X
ejpam-3737	25	4	]	]	PUNCT
ejpam-3737	25	5	is	be	AUX
ejpam-3737	25	6	relevant	relevant	ADJ
ejpam-3737	25	7	to	to	ADP
ejpam-3737	25	8	them	they	PRON
ejpam-3737	25	9	.	.	PUNCT
ejpam-3737	26	1	many	many	ADJ
ejpam-3737	26	2	of	of	ADP
ejpam-3737	26	3	these	these	DET
ejpam-3737	26	4	results	result	NOUN
ejpam-3737	26	5	could	could	AUX
ejpam-3737	26	6	be	be	AUX
ejpam-3737	26	7	applied	apply	VERB
ejpam-3737	26	8	in	in	ADP
ejpam-3737	26	9	[	[	X
ejpam-3737	26	10	2	2	NUM
ejpam-3737	26	11	]	]	PUNCT
ejpam-3737	26	12	and	and	CCONJ
ejpam-3737	26	13	[	[	X
ejpam-3737	26	14	5	5	NUM
ejpam-3737	26	15	]	]	PUNCT
ejpam-3737	26	16	.	.	PUNCT
ejpam-3737	27	1	doi	doi	PROPN
ejpam-3737	27	2	:	:	PUNCT
ejpam-3737	27	3	https://doi.org/10.29020/nybg.ejpam.v13i4.3737	https://doi.org/10.29020/nybg.ejpam.v13i4.3737	PROPN
ejpam-3737	27	4	email	email	NOUN
ejpam-3737	27	5	address	address	NOUN
ejpam-3737	27	6	:	:	PUNCT
ejpam-3737	27	7	todstoyanov@yahoo.com	todstoyanov@yahoo.com	X
ejpam-3737	27	8	(	(	PUNCT
ejpam-3737	27	9	t.	t.	PROPN
ejpam-3737	27	10	s.	s.	PROPN
ejpam-3737	27	11	stoyanov	stoyanov	PROPN
ejpam-3737	27	12	)	)	PUNCT
ejpam-3737	27	13	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-3737	27	14	807	807	NUM
ejpam-3737	27	15	c	c	NOUN
ejpam-3737	27	16	©	©	NOUN
ejpam-3737	27	17	2020	2020	NUM
ejpam-3737	27	18	ejpam	ejpam	VERB
ejpam-3737	27	19	all	all	DET
ejpam-3737	27	20	rights	right	NOUN
ejpam-3737	27	21	reserved	reserve	VERB
ejpam-3737	27	22	.	.	PUNCT
ejpam-3737	28	1	t.	t.	PROPN
ejpam-3737	28	2	s.	s.	PROPN
ejpam-3737	28	3	stoyanov	stoyanov	PROPN
ejpam-3737	28	4	/	/	SYM
ejpam-3737	28	5	eur	eur	PROPN
ejpam-3737	28	6	.	.	PUNCT
ejpam-3737	29	1	j.	j.	PROPN
ejpam-3737	29	2	pure	pure	PROPN
ejpam-3737	29	3	appl	appl	PROPN
ejpam-3737	29	4	.	.	PROPN
ejpam-3737	29	5	math	math	PROPN
ejpam-3737	29	6	,	,	PUNCT
ejpam-3737	29	7	13	13	NUM
ejpam-3737	29	8	(	(	PUNCT
ejpam-3737	29	9	4	4	NUM
ejpam-3737	29	10	)	)	PUNCT
ejpam-3737	29	11	(	(	PUNCT
ejpam-3737	29	12	2020	2020	NUM
ejpam-3737	29	13	)	)	PUNCT
ejpam-3737	29	14	,	,	PUNCT
ejpam-3737	29	15	807	807	NUM
ejpam-3737	29	16	-	-	SYM
ejpam-3737	29	17	813	813	NUM
ejpam-3737	29	18	808	808	NUM
ejpam-3737	29	19	2	2	NUM
ejpam-3737	29	20	.	.	PUNCT
ejpam-3737	29	21	preliminaries	preliminary	NOUN
ejpam-3737	29	22	we	we	PRON
ejpam-3737	29	23	note	note	VERB
ejpam-3737	29	24	:	:	PUNCT
ejpam-3737	29	25	d	d	X
ejpam-3737	29	26	(	(	PUNCT
ejpam-3737	29	27	a	a	DET
ejpam-3737	29	28	,	,	PUNCT
ejpam-3737	29	29	r	r	NOUN
ejpam-3737	29	30	)	)	PUNCT
ejpam-3737	29	31	=	=	NOUN
ejpam-3737	29	32	{	{	PUNCT
ejpam-3737	29	33	z	z	NOUN
ejpam-3737	29	34	∈	∈	PROPN
ejpam-3737	29	35	c	c	NOUN
ejpam-3737	29	36	:	:	PUNCT
ejpam-3737	29	37	|z	|z	PROPN
ejpam-3737	30	1	−	−	PROPN
ejpam-3737	30	2	a|	a|	X
ejpam-3737	30	3	<	<	X
ejpam-3737	30	4	r	r	X
ejpam-3737	30	5	}	}	PUNCT
ejpam-3737	30	6	is	be	AUX
ejpam-3737	30	7	the	the	DET
ejpam-3737	30	8	open	open	ADJ
ejpam-3737	30	9	disk	disk	NOUN
ejpam-3737	30	10	with	with	ADP
ejpam-3737	30	11	center	center	NOUN
ejpam-3737	30	12	a	a	PRON
ejpam-3737	30	13	and	and	CCONJ
ejpam-3737	31	1	radius	radius	PROPN
ejpam-3737	31	2	r.	r.	PROPN
ejpam-3737	31	3	d	d	PROPN
ejpam-3737	31	4	(	(	PUNCT
ejpam-3737	31	5	a	a	DET
ejpam-3737	31	6	,	,	PUNCT
ejpam-3737	31	7	r	r	NOUN
ejpam-3737	31	8	)	)	PUNCT
ejpam-3737	31	9	=	=	NOUN
ejpam-3737	31	10	{	{	PUNCT
ejpam-3737	31	11	z	z	NOUN
ejpam-3737	31	12	∈	∈	PROPN
ejpam-3737	31	13	c	c	NOUN
ejpam-3737	31	14	:	:	PUNCT
ejpam-3737	31	15	|z	|z	PROPN
ejpam-3737	32	1	−	−	PROPN
ejpam-3737	32	2	a|	a|	PROPN
ejpam-3737	32	3	≤	≤	PROPN
ejpam-3737	32	4	r	r	NOUN
ejpam-3737	32	5	}	}	PUNCT
ejpam-3737	32	6	is	be	AUX
ejpam-3737	32	7	the	the	DET
ejpam-3737	32	8	closed	closed	ADJ
ejpam-3737	32	9	disk	disk	NOUN
ejpam-3737	32	10	with	with	ADP
ejpam-3737	32	11	center	center	NOUN
ejpam-3737	32	12	a	a	PRON
ejpam-3737	32	13	and	and	CCONJ
ejpam-3737	32	14	radius	radius	PROPN
ejpam-3737	32	15	r.	r.	PROPN
ejpam-3737	32	16	c	c	PROPN
ejpam-3737	32	17	(	(	PUNCT
ejpam-3737	32	18	a	a	PRON
ejpam-3737	32	19	,	,	PUNCT
ejpam-3737	32	20	r	r	NOUN
ejpam-3737	32	21	)	)	PUNCT
ejpam-3737	32	22	=	=	NOUN
ejpam-3737	33	1	{	{	PUNCT
ejpam-3737	33	2	z	z	NOUN
ejpam-3737	33	3	∈	∈	PROPN
ejpam-3737	33	4	c	c	NOUN
ejpam-3737	33	5	:	:	PUNCT
ejpam-3737	33	6	|z	|z	PROPN
ejpam-3737	34	1	−	−	PROPN
ejpam-3737	34	2	a|	a|	PROPN
ejpam-3737	35	1	=	=	PUNCT
ejpam-3737	35	2	r	r	X
ejpam-3737	35	3	}	}	PUNCT
ejpam-3737	35	4	is	be	AUX
ejpam-3737	35	5	the	the	DET
ejpam-3737	35	6	circle	circle	NOUN
ejpam-3737	35	7	with	with	ADP
ejpam-3737	35	8	center	center	PROPN
ejpam-3737	35	9	a	a	PRON
ejpam-3737	35	10	and	and	CCONJ
ejpam-3737	35	11	radius	radius	PROPN
ejpam-3737	35	12	r.	r.	PROPN
ejpam-3737	35	13	m	m	PROPN
ejpam-3737	36	1	=	=	SYM
ejpam-3737	36	2	d	d	X
ejpam-3737	36	3	(	(	PUNCT
ejpam-3737	36	4	0	0	NUM
ejpam-3737	36	5	,	,	PUNCT
ejpam-3737	36	6	1	1	NUM
ejpam-3737	36	7	)	)	PUNCT
ejpam-3737	36	8	∩	∩	NOUN
ejpam-3737	36	9	[	[	X
ejpam-3737	36	10	d	d	X
ejpam-3737	36	11	(	(	PUNCT
ejpam-3737	36	12	1	1	NUM
ejpam-3737	36	13	,	,	PUNCT
ejpam-3737	36	14	1	1	NUM
ejpam-3737	36	15	)	)	PUNCT
ejpam-3737	36	16	∪d	∪d	NOUN
ejpam-3737	36	17	(	(	PUNCT
ejpam-3737	36	18	−1	−1	NOUN
ejpam-3737	36	19	,	,	PUNCT
ejpam-3737	36	20	1	1	NUM
ejpam-3737	36	21	)	)	PUNCT
ejpam-3737	36	22	]	]	PUNCT
ejpam-3737	36	23	.	.	PUNCT
ejpam-3737	37	1	figure	figure	NOUN
ejpam-3737	37	2	1	1	NUM
ejpam-3737	37	3	:	:	PUNCT
ejpam-3737	37	4	sendov‘s	sendov‘s	NOUN
ejpam-3737	37	5	conjecture	conjecture	NOUN
ejpam-3737	37	6	:	:	PUNCT
ejpam-3737	37	7	let	let	VERB
ejpam-3737	37	8	us	we	PRON
ejpam-3737	37	9	put	put	VERB
ejpam-3737	37	10	for	for	ADP
ejpam-3737	37	11	n	n	PRON
ejpam-3737	37	12	≥	≥	NOUN
ejpam-3737	37	13	2	2	NUM
ejpam-3737	37	14	,	,	PUNCT
ejpam-3737	37	15	p	p	X
ejpam-3737	37	16	(	(	PUNCT
ejpam-3737	37	17	z	z	NOUN
ejpam-3737	37	18	)	)	PUNCT
ejpam-3737	38	1	=	=	PRON
ejpam-3737	38	2	∏n	∏n	ADJ
ejpam-3737	38	3	k=1	k=1	X
ejpam-3737	38	4	(	(	PUNCT
ejpam-3737	38	5	z	z	NOUN
ejpam-3737	38	6	−	−	PROPN
ejpam-3737	38	7	zk	zk	PROPN
ejpam-3737	38	8	)	)	PUNCT
ejpam-3737	38	9	,	,	PUNCT
ejpam-3737	38	10	where	where	SCONJ
ejpam-3737	38	11	zk	zk	PROPN
ejpam-3737	38	12	∈	∈	PROPN
ejpam-3737	38	13	d	d	X
ejpam-3737	38	14	(	(	PUNCT
ejpam-3737	38	15	0	0	NUM
ejpam-3737	38	16	,	,	PUNCT
ejpam-3737	38	17	1	1	NUM
ejpam-3737	38	18	)	)	PUNCT
ejpam-3737	38	19	,	,	PUNCT
ejpam-3737	38	20	k	k	X
ejpam-3737	38	21	=	=	SYM
ejpam-3737	38	22	1	1	NUM
ejpam-3737	38	23	,	,	PUNCT
ejpam-3737	38	24	2	2	NUM
ejpam-3737	38	25	,	,	PUNCT
ejpam-3737	38	26	.	.	PUNCT
ejpam-3737	38	27	.	.	PUNCT
ejpam-3737	39	1	.	.	PUNCT
ejpam-3737	40	1	,	,	PUNCT
ejpam-3737	40	2	n.	n.	PROPN
ejpam-3737	40	3	then	then	ADV
ejpam-3737	40	4	p′(z	p′(z	NOUN
ejpam-3737	40	5	)	)	PUNCT
ejpam-3737	40	6	has	have	VERB
ejpam-3737	40	7	at	at	ADV
ejpam-3737	40	8	least	least	ADJ
ejpam-3737	40	9	one	one	NUM
ejpam-3737	40	10	zero	zero	NUM
ejpam-3737	40	11	in	in	ADP
ejpam-3737	40	12	each	each	PRON
ejpam-3737	40	13	of	of	ADP
ejpam-3737	40	14	the	the	DET
ejpam-3737	40	15	disks	disk	NOUN
ejpam-3737	40	16	d	d	X
ejpam-3737	40	17	(	(	PUNCT
ejpam-3737	40	18	zk	zk	PROPN
ejpam-3737	40	19	,	,	PUNCT
ejpam-3737	40	20	1	1	NUM
ejpam-3737	40	21	)	)	PUNCT
ejpam-3737	40	22	,	,	PUNCT
ejpam-3737	41	1	k	k	X
ejpam-3737	42	1	=	=	SYM
ejpam-3737	42	2	1	1	NUM
ejpam-3737	42	3	,	,	PUNCT
ejpam-3737	42	4	2	2	NUM
ejpam-3737	42	5	,	,	PUNCT
ejpam-3737	42	6	.	.	PUNCT
ejpam-3737	42	7	.	.	PUNCT
ejpam-3737	42	8	.	.	PUNCT
ejpam-3737	43	1	n.	n.	NOUN
ejpam-3737	43	2	3	3	NUM
ejpam-3737	43	3	.	.	PUNCT
ejpam-3737	43	4	related	relate	VERB
ejpam-3737	43	5	results	result	NOUN
ejpam-3737	43	6	statement	statement	NOUN
ejpam-3737	43	7	1(obreshkoff	1(obreshkoff	NUM
ejpam-3737	43	8	)	)	PUNCT
ejpam-3737	43	9	.	.	PUNCT
ejpam-3737	44	1	let	let	VERB
ejpam-3737	44	2	the	the	DET
ejpam-3737	44	3	zeros	zero	NOUN
ejpam-3737	44	4	zk	zk	PROPN
ejpam-3737	44	5	,	,	PUNCT
ejpam-3737	44	6	k	k	PROPN
ejpam-3737	44	7	=	=	SYM
ejpam-3737	44	8	1	1	NUM
ejpam-3737	44	9	,	,	PUNCT
ejpam-3737	44	10	2	2	NUM
ejpam-3737	44	11	,	,	PUNCT
ejpam-3737	44	12	.	.	PUNCT
ejpam-3737	44	13	.	.	PUNCT
ejpam-3737	45	1	.	.	PUNCT
ejpam-3737	46	1	,	,	PUNCT
ejpam-3737	46	2	n	n	PROPN
ejpam-3737	46	3	of	of	ADP
ejpam-3737	46	4	a	a	DET
ejpam-3737	46	5	polynomial	polynomial	ADJ
ejpam-3737	46	6	p	p	NOUN
ejpam-3737	46	7	(	(	PUNCT
ejpam-3737	46	8	z	z	NOUN
ejpam-3737	46	9	)	)	PUNCT
ejpam-3737	46	10	∈	∈	PROPN
ejpam-3737	46	11	c	c	NOUN
ejpam-3737	47	1	[	[	X
ejpam-3737	47	2	z	z	X
ejpam-3737	47	3	]	]	X
ejpam-3737	47	4	satisfy	satisfy	NOUN
ejpam-3737	47	5	zk	zk	PROPN
ejpam-3737	47	6	∈	∈	PROPN
ejpam-3737	48	1	d	d	X
ejpam-3737	48	2	(	(	PUNCT
ejpam-3737	48	3	0	0	NUM
ejpam-3737	48	4	,	,	PUNCT
ejpam-3737	48	5	1	1	NUM
ejpam-3737	48	6	)	)	PUNCT
ejpam-3737	48	7	.	.	PUNCT
ejpam-3737	49	1	then	then	ADV
ejpam-3737	49	2	the	the	DET
ejpam-3737	49	3	zeros	zero	NOUN
ejpam-3737	49	4	z	z	PROPN
ejpam-3737	49	5	of	of	ADP
ejpam-3737	49	6	the	the	DET
ejpam-3737	49	7	polynomial	polynomial	ADJ
ejpam-3737	49	8	q	q	NOUN
ejpam-3737	49	9	(	(	PUNCT
ejpam-3737	49	10	z	z	NOUN
ejpam-3737	49	11	)	)	PUNCT
ejpam-3737	49	12	=	=	PUNCT
ejpam-3737	49	13	nγp	nγp	INTJ
ejpam-3737	49	14	(	(	PUNCT
ejpam-3737	49	15	z	z	NOUN
ejpam-3737	49	16	)	)	PUNCT
ejpam-3737	50	1	+	+	CCONJ
ejpam-3737	50	2	zp	zp	NOUN
ejpam-3737	50	3	′	′	NUM
ejpam-3737	50	4	(	(	PUNCT
ejpam-3737	50	5	z	z	NOUN
ejpam-3737	50	6	)	)	PUNCT
ejpam-3737	50	7	,	,	PUNCT
ejpam-3737	50	8	where	where	SCONJ
ejpam-3737	50	9	re	re	PRON
ejpam-3737	50	10	γ	γ	X
ejpam-3737	50	11	≥	≥	X
ejpam-3737	50	12	−1	−1	ADV
ejpam-3737	50	13	2	2	NUM
ejpam-3737	50	14	,	,	PUNCT
ejpam-3737	50	15	satisfy	satisfy	VERB
ejpam-3737	50	16	z	z	NOUN
ejpam-3737	50	17	∈	∈	PROPN
ejpam-3737	50	18	d	d	X
ejpam-3737	50	19	(	(	PUNCT
ejpam-3737	50	20	0	0	NUM
ejpam-3737	50	21	,	,	PUNCT
ejpam-3737	50	22	1	1	NUM
ejpam-3737	50	23	)	)	PUNCT
ejpam-3737	50	24	.	.	PUNCT
ejpam-3737	51	1	statement	statement	NOUN
ejpam-3737	51	2	2(stoyanov	2(stoyanov	NUM
ejpam-3737	51	3	)	)	PUNCT
ejpam-3737	51	4	.	.	PUNCT
ejpam-3737	52	1	let	let	VERB
ejpam-3737	52	2	the	the	DET
ejpam-3737	52	3	zeros	zero	NOUN
ejpam-3737	52	4	zk	zk	PROPN
ejpam-3737	52	5	,	,	PUNCT
ejpam-3737	52	6	k	k	PROPN
ejpam-3737	52	7	=	=	SYM
ejpam-3737	52	8	1	1	NUM
ejpam-3737	52	9	,	,	PUNCT
ejpam-3737	52	10	2	2	NUM
ejpam-3737	52	11	,	,	PUNCT
ejpam-3737	52	12	.	.	PUNCT
ejpam-3737	52	13	.	.	PUNCT
ejpam-3737	53	1	.	.	PUNCT
ejpam-3737	54	1	,	,	PUNCT
ejpam-3737	54	2	n	n	PROPN
ejpam-3737	54	3	of	of	ADP
ejpam-3737	54	4	a	a	DET
ejpam-3737	54	5	polynomial	polynomial	ADJ
ejpam-3737	54	6	p(z	p(z	NOUN
ejpam-3737	54	7	)	)	PUNCT
ejpam-3737	54	8	∈	∈	PROPN
ejpam-3737	54	9	c[z	c[z	PROPN
ejpam-3737	54	10	]	]	X
ejpam-3737	54	11	satisfy	satisfy	NOUN
ejpam-3737	54	12	zk	zk	PROPN
ejpam-3737	54	13	∈	∈	PROPN
ejpam-3737	55	1	d	d	X
ejpam-3737	55	2	(	(	PUNCT
ejpam-3737	55	3	0	0	NUM
ejpam-3737	55	4	,	,	PUNCT
ejpam-3737	55	5	1	1	NUM
ejpam-3737	55	6	)	)	PUNCT
ejpam-3737	55	7	.	.	PUNCT
ejpam-3737	56	1	then	then	ADV
ejpam-3737	56	2	if	if	SCONJ
ejpam-3737	56	3	re	re	ADJ
ejpam-3737	56	4	γ	γ	PROPN
ejpam-3737	56	5	≥	≥	NUM
ejpam-3737	56	6	−m	−m	PROPN
ejpam-3737	56	7	2	2	NUM
ejpam-3737	56	8	,	,	PUNCT
ejpam-3737	56	9	m	m	VERB
ejpam-3737	56	10	=	=	NOUN
ejpam-3737	56	11	1	1	NUM
ejpam-3737	56	12	,	,	PUNCT
ejpam-3737	56	13	2	2	NUM
ejpam-3737	56	14	,	,	PUNCT
ejpam-3737	56	15	.	.	PUNCT
ejpam-3737	56	16	.	.	PUNCT
ejpam-3737	57	1	.	.	PUNCT
ejpam-3737	58	1	,	,	PUNCT
ejpam-3737	58	2	n	n	X
ejpam-3737	58	3	,	,	PUNCT
ejpam-3737	58	4	the	the	DET
ejpam-3737	58	5	zeros	zero	NOUN
ejpam-3737	58	6	z	z	PROPN
ejpam-3737	58	7	of	of	ADP
ejpam-3737	58	8	the	the	DET
ejpam-3737	58	9	polynomial	polynomial	ADJ
ejpam-3737	58	10	q	q	NOUN
ejpam-3737	58	11	(	(	PUNCT
ejpam-3737	58	12	z	z	NOUN
ejpam-3737	58	13	)	)	PUNCT
ejpam-3737	58	14	=	=	SYM
ejpam-3737	58	15	γp	γp	PROPN
ejpam-3737	58	16	(	(	PUNCT
ejpam-3737	58	17	z	z	NOUN
ejpam-3737	58	18	)	)	PUNCT
ejpam-3737	59	1	+	+	CCONJ
ejpam-3737	59	2	∑m	∑m	INTJ
ejpam-3737	59	3	k=1	k=1	X
ejpam-3737	59	4	(	(	PUNCT
ejpam-3737	59	5	n−k	n−k	PROPN
ejpam-3737	59	6	)	)	PUNCT
ejpam-3737	59	7	!	!	PUNCT
ejpam-3737	60	1	n	n	X
ejpam-3737	60	2	!	!	X
ejpam-3737	61	1	zkp(k)(z	zkp(k)(z	NUM
ejpam-3737	61	2	)	)	PUNCT
ejpam-3737	62	1	,	,	PUNCT
ejpam-3737	62	2	satisfy	satisfy	VERB
ejpam-3737	62	3	z	z	NOUN
ejpam-3737	62	4	∈	∈	PROPN
ejpam-3737	62	5	d	d	X
ejpam-3737	62	6	(	(	PUNCT
ejpam-3737	62	7	0	0	NUM
ejpam-3737	62	8	,	,	PUNCT
ejpam-3737	62	9	θ	θ	NOUN
ejpam-3737	62	10	)	)	PUNCT
ejpam-3737	62	11	,	,	PUNCT
ejpam-3737	62	12	where	where	SCONJ
ejpam-3737	62	13	θ	θ	NOUN
ejpam-3737	62	14	=	=	PUNCT
ejpam-3737	62	15	(	(	PUNCT
ejpam-3737	62	16	2	2	NUM
ejpam-3737	62	17	1	1	NUM
ejpam-3737	62	18	m	m	NOUN
ejpam-3737	62	19	−	−	NOUN
ejpam-3737	62	20	1	1	NUM
ejpam-3737	62	21	)	)	PUNCT
ejpam-3737	62	22	−1	−1	NOUN
ejpam-3737	62	23	.	.	PUNCT
ejpam-3737	63	1	statement	statement	NOUN
ejpam-3737	63	2	3(bojanov	3(bojanov	NUM
ejpam-3737	63	3	)	)	PUNCT
ejpam-3737	63	4	.	.	PUNCT
ejpam-3737	64	1	if	if	SCONJ
ejpam-3737	64	2	all	all	DET
ejpam-3737	64	3	the	the	DET
ejpam-3737	64	4	zeros	zeros	X
ejpam-3737	64	5	zk	zk	PROPN
ejpam-3737	64	6	,	,	PUNCT
ejpam-3737	64	7	k	k	PROPN
ejpam-3737	64	8	=	=	SYM
ejpam-3737	64	9	1	1	NUM
ejpam-3737	64	10	,	,	PUNCT
ejpam-3737	64	11	2	2	NUM
ejpam-3737	64	12	,	,	PUNCT
ejpam-3737	64	13	.	.	PUNCT
ejpam-3737	64	14	.	.	PUNCT
ejpam-3737	64	15	.	.	PUNCT
ejpam-3737	65	1	n	n	CCONJ
ejpam-3737	65	2	;	;	PUNCT
ejpam-3737	65	3	of	of	ADP
ejpam-3737	65	4	a	a	DET
ejpam-3737	65	5	polynomial	polynomial	ADJ
ejpam-3737	65	6	p(z	p(z	NOUN
ejpam-3737	65	7	)	)	PUNCT
ejpam-3737	65	8	∈	∈	PROPN
ejpam-3737	66	1	c[z	c[z	PROPN
ejpam-3737	66	2	]	]	X
ejpam-3737	66	3	satisfy	satisfy	NOUN
ejpam-3737	66	4	zk	zk	PROPN
ejpam-3737	66	5	∈	∈	PROPN
ejpam-3737	66	6	d	d	X
ejpam-3737	66	7	(	(	PUNCT
ejpam-3737	66	8	0	0	NUM
ejpam-3737	66	9	,	,	PUNCT
ejpam-3737	66	10	1	1	NUM
ejpam-3737	66	11	)	)	PUNCT
ejpam-3737	66	12	and	and	CCONJ
ejpam-3737	66	13	a	a	PRON
ejpam-3737	66	14	is	be	AUX
ejpam-3737	66	15	a	a	DET
ejpam-3737	66	16	zero	zero	NUM
ejpam-3737	66	17	of	of	ADP
ejpam-3737	66	18	p(z	p(z	NOUN
ejpam-3737	66	19	)	)	PUNCT
ejpam-3737	66	20	of	of	ADP
ejpam-3737	66	21	modulus	modulus	NOUN
ejpam-3737	66	22	1	1	NUM
ejpam-3737	66	23	,	,	PUNCT
ejpam-3737	66	24	then	then	ADV
ejpam-3737	66	25	the	the	DET
ejpam-3737	66	26	derivative	derivative	ADJ
ejpam-3737	66	27	p′(z	p′(z	NOUN
ejpam-3737	66	28	)	)	PUNCT
ejpam-3737	66	29	has	have	VERB
ejpam-3737	66	30	at	at	ADV
ejpam-3737	66	31	least	least	ADJ
ejpam-3737	66	32	one	one	NUM
ejpam-3737	66	33	zero	zero	NUM
ejpam-3737	66	34	in	in	ADP
ejpam-3737	66	35	d(a2	d(a2	NOUN
ejpam-3737	66	36	,	,	PUNCT
ejpam-3737	66	37	1	1	NUM
ejpam-3737	66	38	2	2	NUM
ejpam-3737	66	39	)	)	PUNCT
ejpam-3737	66	40	.	.	PUNCT
ejpam-3737	67	1	t.	t.	PROPN
ejpam-3737	67	2	s.	s.	PROPN
ejpam-3737	67	3	stoyanov	stoyanov	PROPN
ejpam-3737	67	4	/	/	SYM
ejpam-3737	67	5	eur	eur	PROPN
ejpam-3737	67	6	.	.	PUNCT
ejpam-3737	68	1	j.	j.	PROPN
ejpam-3737	68	2	pure	pure	PROPN
ejpam-3737	68	3	appl	appl	PROPN
ejpam-3737	68	4	.	.	PROPN
ejpam-3737	68	5	math	math	PROPN
ejpam-3737	68	6	,	,	PUNCT
ejpam-3737	68	7	13	13	NUM
ejpam-3737	68	8	(	(	PUNCT
ejpam-3737	68	9	4	4	NUM
ejpam-3737	68	10	)	)	PUNCT
ejpam-3737	68	11	(	(	PUNCT
ejpam-3737	68	12	2020	2020	NUM
ejpam-3737	68	13	)	)	PUNCT
ejpam-3737	68	14	,	,	PUNCT
ejpam-3737	68	15	807	807	NUM
ejpam-3737	68	16	-	-	SYM
ejpam-3737	68	17	813	813	NUM
ejpam-3737	68	18	809	809	NUM
ejpam-3737	68	19	4	4	NUM
ejpam-3737	68	20	.	.	PUNCT
ejpam-3737	68	21	main	main	ADJ
ejpam-3737	68	22	results	result	NOUN
ejpam-3737	68	23	case	case	NOUN
ejpam-3737	68	24	1	1	NUM
ejpam-3737	68	25	.	.	PUNCT
ejpam-3737	69	1	in	in	ADP
ejpam-3737	69	2	this	this	DET
ejpam-3737	69	3	case	case	NOUN
ejpam-3737	69	4	we	we	PRON
ejpam-3737	69	5	consider	consider	VERB
ejpam-3737	69	6	a	a	DET
ejpam-3737	69	7	polynomial	polynomial	ADJ
ejpam-3737	69	8	r	r	NOUN
ejpam-3737	69	9	(	(	PUNCT
ejpam-3737	69	10	z	z	NOUN
ejpam-3737	69	11	)	)	PUNCT
ejpam-3737	69	12	=	=	SYM
ejpam-3737	70	1	zn	zn	PROPN
ejpam-3737	70	2	+	+	NUM
ejpam-3737	70	3	rn−1z	rn−1z	NUM
ejpam-3737	70	4	n−1	n−1	PROPN
ejpam-3737	70	5	+	+	CCONJ
ejpam-3737	70	6	·	·	PUNCT
ejpam-3737	70	7	·	·	PUNCT
ejpam-3737	70	8	·	·	PUNCT
ejpam-3737	71	1	+	+	NUM
ejpam-3737	71	2	r1z	r1z	PROPN
ejpam-3737	71	3	+	+	CCONJ
ejpam-3737	71	4	r0	r0	NOUN
ejpam-3737	71	5	,	,	PUNCT
ejpam-3737	71	6	where	where	SCONJ
ejpam-3737	71	7	rk	rk	VERB
ejpam-3737	71	8	∈	∈	PROPN
ejpam-3737	71	9	r	r	NOUN
ejpam-3737	71	10	,	,	PUNCT
ejpam-3737	71	11	n	n	PRON
ejpam-3737	71	12	≥	≥	NOUN
ejpam-3737	71	13	2	2	NUM
ejpam-3737	71	14	,	,	PUNCT
ejpam-3737	71	15	n	n	PRON
ejpam-3737	71	16	∈	∈	PROPN
ejpam-3737	71	17	n	n	NOUN
ejpam-3737	71	18	,	,	PUNCT
ejpam-3737	71	19	k	k	PROPN
ejpam-3737	71	20	=	=	SYM
ejpam-3737	71	21	0	0	PROPN
ejpam-3737	71	22	,	,	PUNCT
ejpam-3737	71	23	n−	n−	NOUN
ejpam-3737	71	24	1	1	NUM
ejpam-3737	71	25	.	.	PUNCT
ejpam-3737	72	1	the	the	DET
ejpam-3737	72	2	zeros	zero	NOUN
ejpam-3737	72	3	zk	zk	PROPN
ejpam-3737	72	4	of	of	ADP
ejpam-3737	72	5	r	r	PROPN
ejpam-3737	72	6	(	(	PUNCT
ejpam-3737	72	7	z	z	NOUN
ejpam-3737	72	8	)	)	PUNCT
ejpam-3737	72	9	satisfy	satisfy	VERB
ejpam-3737	72	10	the	the	DET
ejpam-3737	72	11	condition	condition	NOUN
ejpam-3737	72	12	zk	zk	PROPN
ejpam-3737	72	13	∈	∈	PROPN
ejpam-3737	73	1	d	d	X
ejpam-3737	73	2	(	(	PUNCT
ejpam-3737	73	3	−a	−a	ADJ
ejpam-3737	73	4	,	,	PUNCT
ejpam-3737	73	5	1	1	NUM
ejpam-3737	73	6	)	)	PUNCT
ejpam-3737	73	7	,	,	PUNCT
ejpam-3737	73	8	z0	z0	PROPN
ejpam-3737	73	9	∈	∈	PROPN
ejpam-3737	73	10	r	r	PROPN
ejpam-3737	73	11	,	,	PUNCT
ejpam-3737	73	12	z0	z0	PROPN
ejpam-3737	73	13	+	+	CCONJ
ejpam-3737	73	14	a	a	PRON
ejpam-3737	73	15	=	=	SYM
ejpam-3737	73	16	0	0	NUM
ejpam-3737	73	17	,	,	PUNCT
ejpam-3737	73	18	a	a	DET
ejpam-3737	73	19	∈	∈	PROPN
ejpam-3737	73	20	(	(	PUNCT
ejpam-3737	73	21	0	0	NUM
ejpam-3737	73	22	,	,	PUNCT
ejpam-3737	73	23	1	1	NUM
ejpam-3737	73	24	]	]	PUNCT
ejpam-3737	73	25	.	.	PUNCT
ejpam-3737	74	1	the	the	DET
ejpam-3737	74	2	derivative	derivative	NOUN
ejpam-3737	74	3	is	be	AUX
ejpam-3737	74	4	dr	dr	PROPN
ejpam-3737	74	5	dz	dz	PROPN
ejpam-3737	74	6	=	=	PUNCT
ejpam-3737	74	7	n	n	PROPN
ejpam-3737	74	8	(	(	PUNCT
ejpam-3737	74	9	z	z	NOUN
ejpam-3737	74	10	+	+	CCONJ
ejpam-3737	74	11	a1	a1	NOUN
ejpam-3737	74	12	)	)	PUNCT
ejpam-3737	74	13	(	(	PUNCT
ejpam-3737	74	14	z	z	NOUN
ejpam-3737	74	15	+	+	NUM
ejpam-3737	74	16	a2	a2	PROPN
ejpam-3737	74	17	)	)	PUNCT
ejpam-3737	74	18	·	·	PUNCT
ejpam-3737	74	19	·	·	PUNCT
ejpam-3737	74	20	·	·	PUNCT
ejpam-3737	75	1	(	(	PUNCT
ejpam-3737	75	2	z	z	X
ejpam-3737	75	3	+	+	CCONJ
ejpam-3737	75	4	al	al	PROPN
ejpam-3737	75	5	)	)	PUNCT
ejpam-3737	75	6	(	(	PUNCT
ejpam-3737	75	7	z	z	NOUN
ejpam-3737	75	8	−	−	PROPN
ejpam-3737	75	9	b1	b1	PROPN
ejpam-3737	75	10	)	)	PUNCT
ejpam-3737	75	11	(	(	PUNCT
ejpam-3737	75	12	z	z	NOUN
ejpam-3737	75	13	−	−	PROPN
ejpam-3737	75	14	b1	b1	PROPN
ejpam-3737	75	15	)	)	PUNCT
ejpam-3737	75	16	·	·	PUNCT
ejpam-3737	75	17	·	·	PUNCT
ejpam-3737	75	18	·	·	PUNCT
ejpam-3737	76	1	(	(	PUNCT
ejpam-3737	76	2	z	z	NOUN
ejpam-3737	76	3	−	−	NOUN
ejpam-3737	76	4	bs	bs	NOUN
ejpam-3737	76	5	)	)	PUNCT
ejpam-3737	76	6	(	(	PUNCT
ejpam-3737	76	7	z	z	NOUN
ejpam-3737	76	8	−	−	NOUN
ejpam-3737	76	9	bs	bs	PROPN
ejpam-3737	76	10	)	)	PUNCT
ejpam-3737	76	11	,	,	PUNCT
ejpam-3737	77	1	where	where	SCONJ
ejpam-3737	77	2	l	l	NOUN
ejpam-3737	77	3	+	+	CCONJ
ejpam-3737	77	4	2s	2s	NUM
ejpam-3737	77	5	=	=	SYM
ejpam-3737	77	6	n−	n−	NOUN
ejpam-3737	77	7	1	1	NUM
ejpam-3737	77	8	,	,	PUNCT
ejpam-3737	77	9	ak	ak	PROPN
ejpam-3737	77	10	,	,	PUNCT
ejpam-3737	77	11	bm	bm	PROPN
ejpam-3737	77	12	∈	∈	PROPN
ejpam-3737	77	13	d	d	X
ejpam-3737	77	14	(	(	PUNCT
ejpam-3737	77	15	−a	−a	ADJ
ejpam-3737	77	16	,	,	PUNCT
ejpam-3737	77	17	1	1	NUM
ejpam-3737	77	18	)	)	PUNCT
ejpam-3737	77	19	,	,	PUNCT
ejpam-3737	77	20	k	k	PROPN
ejpam-3737	77	21	=	=	SYM
ejpam-3737	77	22	1	1	NUM
ejpam-3737	77	23	,	,	PUNCT
ejpam-3737	77	24	l	l	NOUN
ejpam-3737	77	25	,	,	PUNCT
ejpam-3737	77	26	m	m	VERB
ejpam-3737	77	27	=	=	NOUN
ejpam-3737	77	28	1	1	NUM
ejpam-3737	77	29	,	,	PUNCT
ejpam-3737	77	30	s	s	PROPN
ejpam-3737	77	31	,	,	PUNCT
ejpam-3737	77	32	ak	ak	PROPN
ejpam-3737	77	33	∈	∈	PROPN
ejpam-3737	77	34	r	r	PROPN
ejpam-3737	77	35	,	,	PUNCT
ejpam-3737	77	36	k	k	NOUN
ejpam-3737	77	37	,	,	PUNCT
ejpam-3737	77	38	m	m	VERB
ejpam-3737	77	39	∈	∈	PROPN
ejpam-3737	77	40	n	n	X
ejpam-3737	77	41	.	.	PUNCT
ejpam-3737	77	42	theorem	theorem	NOUN
ejpam-3737	77	43	1	1	NUM
ejpam-3737	77	44	.	.	PUNCT
ejpam-3737	78	1	if	if	SCONJ
ejpam-3737	78	2	z0	z0	PROPN
ejpam-3737	78	3	=	=	SYM
ejpam-3737	78	4	0	0	NUM
ejpam-3737	78	5	∈	∈	NOUN
ejpam-3737	78	6	r	r	NOUN
ejpam-3737	78	7	is	be	AUX
ejpam-3737	78	8	a	a	DET
ejpam-3737	78	9	real	real	ADJ
ejpam-3737	78	10	zero	zero	NUM
ejpam-3737	78	11	of	of	ADP
ejpam-3737	78	12	r	r	NOUN
ejpam-3737	78	13	(	(	PUNCT
ejpam-3737	78	14	z	z	NOUN
ejpam-3737	78	15	)	)	PUNCT
ejpam-3737	78	16	,	,	PUNCT
ejpam-3737	78	17	then	then	ADV
ejpam-3737	78	18	there	there	PRON
ejpam-3737	78	19	exists	exist	VERB
ejpam-3737	78	20	a	a	DET
ejpam-3737	78	21	zero	zero	NUM
ejpam-3737	78	22	c	c	NOUN
ejpam-3737	78	23	of	of	ADP
ejpam-3737	78	24	dr	dr	PROPN
ejpam-3737	78	25	dz	dz	PROPN
ejpam-3737	78	26	which	which	PRON
ejpam-3737	78	27	satisfies	satisfy	VERB
ejpam-3737	78	28	c	c	NOUN
ejpam-3737	78	29	∈	∈	PROPN
ejpam-3737	78	30	d	d	X
ejpam-3737	78	31	(	(	PUNCT
ejpam-3737	78	32	0	0	NUM
ejpam-3737	78	33	,	,	PUNCT
ejpam-3737	78	34	1	1	NUM
ejpam-3737	78	35	)	)	PUNCT
ejpam-3737	78	36	.	.	PUNCT
ejpam-3737	79	1	proof	proof	NOUN
ejpam-3737	79	2	.	.	PUNCT
ejpam-3737	80	1	figure	figure	VERB
ejpam-3737	80	2	2	2	NUM
ejpam-3737	80	3	:	:	PUNCT
ejpam-3737	80	4	without	without	ADP
ejpam-3737	80	5	loss	loss	NOUN
ejpam-3737	80	6	of	of	ADP
ejpam-3737	80	7	generality	generality	NOUN
ejpam-3737	80	8	,	,	PUNCT
ejpam-3737	80	9	we	we	PRON
ejpam-3737	80	10	consider	consider	VERB
ejpam-3737	80	11	re	re	PART
ejpam-3737	80	12	z0	z0	VERB
ejpam-3737	80	13	≥	≥	NUM
ejpam-3737	80	14	0	0	NUM
ejpam-3737	80	15	.	.	PUNCT
ejpam-3737	81	1	about	about	ADP
ejpam-3737	81	2	the	the	DET
ejpam-3737	81	3	root	root	NOUN
ejpam-3737	81	4	z0	z0	NOUN
ejpam-3737	81	5	=	=	SYM
ejpam-3737	81	6	0	0	NUM
ejpam-3737	81	7	we	we	PRON
ejpam-3737	81	8	assume	assume	VERB
ejpam-3737	81	9	that	that	SCONJ
ejpam-3737	81	10	in	in	ADP
ejpam-3737	81	11	the	the	DET
ejpam-3737	81	12	disk	disk	NOUN
ejpam-3737	81	13	d	d	NOUN
ejpam-3737	81	14	(	(	PUNCT
ejpam-3737	81	15	0	0	NUM
ejpam-3737	81	16	,	,	PUNCT
ejpam-3737	81	17	1	1	NUM
ejpam-3737	81	18	)	)	PUNCT
ejpam-3737	81	19	there	there	PRON
ejpam-3737	81	20	is	be	VERB
ejpam-3737	81	21	not	not	PART
ejpam-3737	81	22	exists	exist	VERB
ejpam-3737	81	23	a	a	DET
ejpam-3737	81	24	root	root	NOUN
ejpam-3737	81	25	c	c	NOUN
ejpam-3737	81	26	∈	∈	PROPN
ejpam-3737	81	27	dr	dr	PROPN
ejpam-3737	81	28	dz	dz	PROPN
ejpam-3737	81	29	.	.	PUNCT
ejpam-3737	82	1	then	then	ADV
ejpam-3737	82	2	all	all	DET
ejpam-3737	82	3	the	the	DET
ejpam-3737	82	4	zeros	zero	NOUN
ejpam-3737	82	5	of	of	ADP
ejpam-3737	82	6	the	the	DET
ejpam-3737	82	7	derivative	derivative	PROPN
ejpam-3737	82	8	ak	ak	PROPN
ejpam-3737	82	9	,	,	PUNCT
ejpam-3737	82	10	bm	bm	PROPN
ejpam-3737	82	11	∈	∈	PROPN
ejpam-3737	82	12	d	d	X
ejpam-3737	82	13	(	(	PUNCT
ejpam-3737	82	14	−a	−a	ADJ
ejpam-3737	82	15	,	,	PUNCT
ejpam-3737	82	16	1	1	NUM
ejpam-3737	82	17	)	)	PUNCT
ejpam-3737	82	18	\	\	NOUN
ejpam-3737	82	19	d	d	X
ejpam-3737	82	20	(	(	PUNCT
ejpam-3737	82	21	0	0	NUM
ejpam-3737	82	22	,	,	PUNCT
ejpam-3737	82	23	1	1	NUM
ejpam-3737	82	24	)	)	PUNCT
ejpam-3737	82	25	and	and	CCONJ
ejpam-3737	82	26	we	we	PRON
ejpam-3737	82	27	have	have	VERB
ejpam-3737	82	28	r	r	NOUN
ejpam-3737	82	29	(	(	PUNCT
ejpam-3737	82	30	0)−	0)−	NOUN
ejpam-3737	82	31	r	r	NOUN
ejpam-3737	82	32	(	(	PUNCT
ejpam-3737	82	33	−a	−a	NOUN
ejpam-3737	82	34	)	)	PUNCT
ejpam-3737	82	35	=	=	SYM
ejpam-3737	83	1	∫	∫	PROPN
ejpam-3737	83	2	0	0	NUM
ejpam-3737	83	3	−a	−a	PROPN
ejpam-3737	83	4	dr	dr	PROPN
ejpam-3737	83	5	dz	dz	PROPN
ejpam-3737	83	6	dz	dz	PROPN
ejpam-3737	83	7	=	=	PUNCT
ejpam-3737	83	8	−r	−r	PROPN
ejpam-3737	83	9	(	(	PUNCT
ejpam-3737	83	10	−a	−a	NOUN
ejpam-3737	83	11	)	)	PUNCT
ejpam-3737	83	12	,	,	PUNCT
ejpam-3737	83	13	t.	t.	PROPN
ejpam-3737	83	14	s.	s.	PROPN
ejpam-3737	83	15	stoyanov	stoyanov	PROPN
ejpam-3737	83	16	/	/	SYM
ejpam-3737	83	17	eur	eur	PROPN
ejpam-3737	83	18	.	.	PUNCT
ejpam-3737	84	1	j.	j.	PROPN
ejpam-3737	84	2	pure	pure	PROPN
ejpam-3737	84	3	appl	appl	PROPN
ejpam-3737	84	4	.	.	PROPN
ejpam-3737	84	5	math	math	PROPN
ejpam-3737	84	6	,	,	PUNCT
ejpam-3737	84	7	13	13	NUM
ejpam-3737	84	8	(	(	PUNCT
ejpam-3737	84	9	4	4	NUM
ejpam-3737	84	10	)	)	PUNCT
ejpam-3737	84	11	(	(	PUNCT
ejpam-3737	84	12	2020	2020	NUM
ejpam-3737	84	13	)	)	PUNCT
ejpam-3737	84	14	,	,	PUNCT
ejpam-3737	84	15	807	807	NUM
ejpam-3737	84	16	-	-	SYM
ejpam-3737	84	17	813	813	NUM
ejpam-3737	84	18	810	810	NUM
ejpam-3737	84	19	i.e.	i.e.	X
ejpam-3737	84	20	−r	−r	PROPN
ejpam-3737	84	21	(	(	PUNCT
ejpam-3737	84	22	−a	−a	ADJ
ejpam-3737	84	23	)	)	PUNCT
ejpam-3737	84	24	=	=	SYM
ejpam-3737	84	25	n	n	NUM
ejpam-3737	84	26	∫	∫	NOUN
ejpam-3737	84	27	0	0	NUM
ejpam-3737	85	1	−a	−a	NOUN
ejpam-3737	86	1	(	(	PUNCT
ejpam-3737	86	2	z	z	NOUN
ejpam-3737	86	3	+	+	CCONJ
ejpam-3737	86	4	a1	a1	NOUN
ejpam-3737	86	5	)	)	PUNCT
ejpam-3737	86	6	(	(	PUNCT
ejpam-3737	86	7	z	z	NOUN
ejpam-3737	86	8	+	+	NUM
ejpam-3737	86	9	a2	a2	PROPN
ejpam-3737	86	10	)	)	PUNCT
ejpam-3737	86	11	·	·	PUNCT
ejpam-3737	86	12	·	·	PUNCT
ejpam-3737	86	13	·	·	PUNCT
ejpam-3737	87	1	(	(	PUNCT
ejpam-3737	87	2	z	z	X
ejpam-3737	87	3	+	+	CCONJ
ejpam-3737	87	4	al	al	PROPN
ejpam-3737	87	5	)	)	PUNCT
ejpam-3737	87	6	(	(	PUNCT
ejpam-3737	87	7	z	z	NOUN
ejpam-3737	87	8	−	−	PROPN
ejpam-3737	87	9	b1	b1	PROPN
ejpam-3737	87	10	)	)	PUNCT
ejpam-3737	87	11	(	(	PUNCT
ejpam-3737	87	12	z	z	NOUN
ejpam-3737	87	13	−	−	PROPN
ejpam-3737	87	14	b1	b1	PROPN
ejpam-3737	87	15	)	)	PUNCT
ejpam-3737	87	16	·	·	PUNCT
ejpam-3737	87	17	·	·	PUNCT
ejpam-3737	87	18	·	·	PUNCT
ejpam-3737	88	1	(	(	PUNCT
ejpam-3737	88	2	z	z	NOUN
ejpam-3737	88	3	−	−	NOUN
ejpam-3737	88	4	bs	bs	NOUN
ejpam-3737	88	5	)	)	PUNCT
ejpam-3737	88	6	(	(	PUNCT
ejpam-3737	88	7	z	z	NOUN
ejpam-3737	88	8	−	−	NOUN
ejpam-3737	88	9	bs	bs	NOUN
ejpam-3737	88	10	)	)	PUNCT
ejpam-3737	88	11	dz	dz	PROPN
ejpam-3737	88	12	where	where	SCONJ
ejpam-3737	88	13	ak	ak	PROPN
ejpam-3737	88	14	>	>	X
ejpam-3737	88	15	1	1	PROPN
ejpam-3737	88	16	,	,	PUNCT
ejpam-3737	88	17	bm	bm	PROPN
ejpam-3737	88	18	=	=	PROPN
ejpam-3737	88	19	ρme	ρme	PROPN
ejpam-3737	88	20	iϕm	iϕm	NOUN
ejpam-3737	88	21	,	,	PUNCT
ejpam-3737	88	22	ρm	ρm	INTJ
ejpam-3737	88	23	>	>	X
ejpam-3737	88	24	1	1	NUM
ejpam-3737	88	25	,	,	PUNCT
ejpam-3737	88	26	ϕm	ϕm	X
ejpam-3737	88	27	∈	∈	PROPN
ejpam-3737	88	28	[	[	PUNCT
ejpam-3737	88	29	π	π	NOUN
ejpam-3737	88	30	2	2	NUM
ejpam-3737	88	31	,	,	PUNCT
ejpam-3737	88	32	π	π	X
ejpam-3737	88	33	]	]	PUNCT
ejpam-3737	88	34	,	,	PUNCT
ejpam-3737	88	35	k	k	X
ejpam-3737	88	36	=	=	SYM
ejpam-3737	88	37	1	1	NUM
ejpam-3737	88	38	,	,	PUNCT
ejpam-3737	88	39	l	l	NOUN
ejpam-3737	88	40	,	,	PUNCT
ejpam-3737	88	41	m	m	VERB
ejpam-3737	88	42	=	=	NOUN
ejpam-3737	88	43	1	1	NUM
ejpam-3737	88	44	,	,	PUNCT
ejpam-3737	88	45	s	s	AUX
ejpam-3737	88	46	,	,	PUNCT
ejpam-3737	88	47	(	(	PUNCT
ejpam-3737	88	48	z	z	NOUN
ejpam-3737	88	49	−	−	PROPN
ejpam-3737	88	50	bm	bm	PROPN
ejpam-3737	88	51	)	)	PUNCT
ejpam-3737	88	52	(	(	PUNCT
ejpam-3737	88	53	z	z	NOUN
ejpam-3737	88	54	−	−	PROPN
ejpam-3737	88	55	bm	bm	PROPN
ejpam-3737	88	56	)	)	PUNCT
ejpam-3737	88	57	=	=	SYM
ejpam-3737	88	58	z2	z2	PROPN
ejpam-3737	88	59	−	−	PROPN
ejpam-3737	88	60	2ρm	2ρm	NOUN
ejpam-3737	88	61	cos	cos	PROPN
ejpam-3737	88	62	ϕmz	ϕmz	PROPN
ejpam-3737	88	63	+	+	CCONJ
ejpam-3737	88	64	ρ2	ρ2	NOUN
ejpam-3737	88	65	m.	m.	NOUN
ejpam-3737	88	66	then	then	ADV
ejpam-3737	88	67	we	we	PRON
ejpam-3737	88	68	obtain	obtain	VERB
ejpam-3737	88	69	−r	−r	ADJ
ejpam-3737	88	70	(	(	PUNCT
ejpam-3737	88	71	−a	−a	ADJ
ejpam-3737	88	72	)	)	PUNCT
ejpam-3737	88	73	=	=	PUNCT
ejpam-3737	89	1	=	=	PUNCT
ejpam-3737	89	2	n	n	NUM
ejpam-3737	89	3	∫	∫	NOUN
ejpam-3737	89	4	0	0	NUM
ejpam-3737	89	5	−a	−a	NOUN
ejpam-3737	89	6	(	(	PUNCT
ejpam-3737	89	7	z	z	NOUN
ejpam-3737	89	8	+	+	CCONJ
ejpam-3737	89	9	a1	a1	NOUN
ejpam-3737	89	10	)	)	PUNCT
ejpam-3737	89	11	·	·	PUNCT
ejpam-3737	89	12	·	·	PUNCT
ejpam-3737	89	13	·	·	PUNCT
ejpam-3737	90	1	(	(	PUNCT
ejpam-3737	90	2	z	z	X
ejpam-3737	90	3	+	+	CCONJ
ejpam-3737	90	4	al	al	PROPN
ejpam-3737	90	5	)	)	PUNCT
ejpam-3737	90	6	(	(	PUNCT
ejpam-3737	90	7	z2	z2	PROPN
ejpam-3737	90	8	−	−	PROPN
ejpam-3737	90	9	2ρ1	2ρ1	NUM
ejpam-3737	90	10	cos	cos	PROPN
ejpam-3737	90	11	ϕ1z	ϕ1z	PROPN
ejpam-3737	90	12	+	+	NUM
ejpam-3737	90	13	ρ21	ρ21	PROPN
ejpam-3737	90	14	)	)	PUNCT
ejpam-3737	90	15	·	·	PUNCT
ejpam-3737	90	16	·	·	PUNCT
ejpam-3737	90	17	·	·	PUNCT
ejpam-3737	90	18	(	(	PUNCT
ejpam-3737	90	19	z2	z2	PROPN
ejpam-3737	90	20	−	−	PROPN
ejpam-3737	90	21	2ρs	2ρs	PROPN
ejpam-3737	90	22	cos	cos	PROPN
ejpam-3737	90	23	ϕsz	ϕsz	PROPN
ejpam-3737	90	24	+	+	CCONJ
ejpam-3737	90	25	ρ2s	ρ2s	NOUN
ejpam-3737	90	26	)	)	PUNCT
ejpam-3737	90	27	dz	dz	PROPN
ejpam-3737	90	28	≥	≥	X
ejpam-3737	90	29	n	n	CCONJ
ejpam-3737	90	30	∫	∫	PROPN
ejpam-3737	90	31	0	0	NUM
ejpam-3737	90	32	−a	−a	NOUN
ejpam-3737	90	33	(	(	PUNCT
ejpam-3737	90	34	z	z	NOUN
ejpam-3737	90	35	+	+	NOUN
ejpam-3737	90	36	1)l	1)l	NUM
ejpam-3737	90	37	(	(	PUNCT
ejpam-3737	90	38	z2	z2	PROPN
ejpam-3737	90	39	+	+	NUM
ejpam-3737	90	40	2ρ1z	2ρ1z	NUM
ejpam-3737	90	41	+	+	CCONJ
ejpam-3737	90	42	ρ21	ρ21	NOUN
ejpam-3737	90	43	)	)	PUNCT
ejpam-3737	90	44	·	·	PUNCT
ejpam-3737	90	45	·	·	PUNCT
ejpam-3737	90	46	·	·	PUNCT
ejpam-3737	91	1	(	(	PUNCT
ejpam-3737	91	2	z2	z2	NOUN
ejpam-3737	91	3	+	+	CCONJ
ejpam-3737	91	4	2ρsz	2ρsz	NUM
ejpam-3737	91	5	+	+	CCONJ
ejpam-3737	91	6	ρ2s	ρ2s	NOUN
ejpam-3737	91	7	)	)	PUNCT
ejpam-3737	91	8	dz	dz	PROPN
ejpam-3737	91	9	>	>	X
ejpam-3737	91	10	n	n	NUM
ejpam-3737	91	11	∫	∫	PROPN
ejpam-3737	91	12	0	0	NUM
ejpam-3737	91	13	−a	−a	NOUN
ejpam-3737	92	1	(	(	PUNCT
ejpam-3737	92	2	z	z	NOUN
ejpam-3737	92	3	+	+	NOUN
ejpam-3737	92	4	1)l(z	1)l(z	NUM
ejpam-3737	92	5	+	+	SYM
ejpam-3737	92	6	1)2sdz	1)2sdz	NUM
ejpam-3737	92	7	=	=	SYM
ejpam-3737	92	8	n	n	NUM
ejpam-3737	92	9	∫	∫	NOUN
ejpam-3737	92	10	0	0	NUM
ejpam-3737	92	11	−a	−a	NOUN
ejpam-3737	92	12	(	(	PUNCT
ejpam-3737	92	13	z	z	NOUN
ejpam-3737	92	14	+	+	NOUN
ejpam-3737	92	15	1)n−1dz	1)n−1dz	NUM
ejpam-3737	92	16	=	=	SYM
ejpam-3737	92	17	(	(	PUNCT
ejpam-3737	92	18	z	z	NOUN
ejpam-3737	92	19	+	+	CCONJ
ejpam-3737	92	20	1)n	1)n	NUM
ejpam-3737	92	21	|0−a	|0−a	NOUN
ejpam-3737	92	22	=	=	SYM
ejpam-3737	92	23	1n	1n	NUM
ejpam-3737	93	1	−	−	PROPN
ejpam-3737	93	2	(	(	PUNCT
ejpam-3737	93	3	1−	1−	NUM
ejpam-3737	93	4	a)n	a)n	NOUN
ejpam-3737	93	5	>	>	X
ejpam-3737	93	6	a.	a.	NOUN
ejpam-3737	93	7	we	we	PRON
ejpam-3737	93	8	obtain	obtain	VERB
ejpam-3737	93	9	that	that	DET
ejpam-3737	93	10	|r	|r	PROPN
ejpam-3737	93	11	(	(	PUNCT
ejpam-3737	93	12	−a)|	−a)|	X
ejpam-3737	93	13	>	>	X
ejpam-3737	93	14	a.	a.	NOUN
ejpam-3737	94	1	but	but	CCONJ
ejpam-3737	94	2	all	all	DET
ejpam-3737	94	3	the	the	DET
ejpam-3737	94	4	zeros	zero	NOUN
ejpam-3737	94	5	zk	zk	PROPN
ejpam-3737	94	6	of	of	ADP
ejpam-3737	94	7	r	r	PROPN
ejpam-3737	94	8	(	(	PUNCT
ejpam-3737	94	9	z	z	NOUN
ejpam-3737	94	10	)	)	PUNCT
ejpam-3737	94	11	belong	belong	VERB
ejpam-3737	94	12	to	to	ADP
ejpam-3737	94	13	d	d	PROPN
ejpam-3737	94	14	(	(	PUNCT
ejpam-3737	94	15	−a	−a	ADJ
ejpam-3737	94	16	,	,	PUNCT
ejpam-3737	94	17	1	1	NUM
ejpam-3737	94	18	)	)	PUNCT
ejpam-3737	94	19	,	,	PUNCT
ejpam-3737	94	20	i.e.	i.e.	X
ejpam-3737	94	21	|r	|r	X
ejpam-3737	94	22	(	(	PUNCT
ejpam-3737	94	23	−a)|	−a)|	PROPN
ejpam-3737	94	24	≤	≤	PROPN
ejpam-3737	94	25	a	a	PRON
ejpam-3737	94	26	,	,	PUNCT
ejpam-3737	94	27	because	because	SCONJ
ejpam-3737	94	28	|z0	|z0	VERB
ejpam-3737	94	29	+	+	CCONJ
ejpam-3737	94	30	a|	a|	PROPN
ejpam-3737	94	31	=	=	SYM
ejpam-3737	95	1	0	0	X
ejpam-3737	95	2	.	.	PUNCT
ejpam-3737	96	1	this	this	DET
ejpam-3737	96	2	contradiction	contradiction	NOUN
ejpam-3737	96	3	confirms	confirm	VERB
ejpam-3737	96	4	the	the	DET
ejpam-3737	96	5	theorem	theorem	NOUN
ejpam-3737	96	6	1	1	NUM
ejpam-3737	96	7	.	.	PUNCT
ejpam-3737	96	8	case	case	NOUN
ejpam-3737	96	9	2	2	NUM
ejpam-3737	96	10	.	.	PUNCT
ejpam-3737	97	1	in	in	ADP
ejpam-3737	97	2	this	this	DET
ejpam-3737	97	3	case	case	NOUN
ejpam-3737	97	4	we	we	PRON
ejpam-3737	97	5	consider	consider	VERB
ejpam-3737	97	6	a	a	DET
ejpam-3737	97	7	polynomial	polynomial	ADJ
ejpam-3737	97	8	r	r	NOUN
ejpam-3737	97	9	(	(	PUNCT
ejpam-3737	97	10	z	z	NOUN
ejpam-3737	97	11	)	)	PUNCT
ejpam-3737	97	12	=	=	SYM
ejpam-3737	98	1	zn	zn	PROPN
ejpam-3737	98	2	+	+	NUM
ejpam-3737	98	3	rn−1z	rn−1z	NUM
ejpam-3737	98	4	n−1	n−1	PROPN
ejpam-3737	98	5	+	+	NUM
ejpam-3737	98	6	·	·	PUNCT
ejpam-3737	98	7	·	·	PUNCT
ejpam-3737	98	8	·	·	PUNCT
ejpam-3737	99	1	+	+	CCONJ
ejpam-3737	99	2	r1z	r1z	PROPN
ejpam-3737	99	3	+	+	CCONJ
ejpam-3737	99	4	r0	r0	NOUN
ejpam-3737	99	5	,	,	PUNCT
ejpam-3737	99	6	where	where	SCONJ
ejpam-3737	99	7	rk	rk	VERB
ejpam-3737	99	8	∈	∈	PROPN
ejpam-3737	99	9	r	r	NOUN
ejpam-3737	99	10	,	,	PUNCT
ejpam-3737	99	11	n	n	PRON
ejpam-3737	99	12	≥	≥	NOUN
ejpam-3737	99	13	2	2	NUM
ejpam-3737	99	14	,	,	PUNCT
ejpam-3737	99	15	n	n	PRON
ejpam-3737	99	16	∈	∈	PROPN
ejpam-3737	99	17	n	n	NOUN
ejpam-3737	99	18	,	,	PUNCT
ejpam-3737	99	19	k	k	PROPN
ejpam-3737	99	20	=	=	SYM
ejpam-3737	99	21	0	0	PROPN
ejpam-3737	99	22	,	,	PUNCT
ejpam-3737	99	23	n−	n−	NOUN
ejpam-3737	99	24	1	1	NUM
ejpam-3737	99	25	.	.	PUNCT
ejpam-3737	100	1	the	the	DET
ejpam-3737	100	2	zeros	zero	NOUN
ejpam-3737	100	3	zk	zk	PROPN
ejpam-3737	100	4	of	of	ADP
ejpam-3737	100	5	r	r	PROPN
ejpam-3737	100	6	(	(	PUNCT
ejpam-3737	100	7	z	z	NOUN
ejpam-3737	100	8	)	)	PUNCT
ejpam-3737	100	9	satisfy	satisfy	VERB
ejpam-3737	100	10	the	the	DET
ejpam-3737	100	11	condition	condition	NOUN
ejpam-3737	100	12	zk	zk	PROPN
ejpam-3737	100	13	∈	∈	PROPN
ejpam-3737	101	1	d	d	X
ejpam-3737	101	2	(	(	PUNCT
ejpam-3737	101	3	0	0	NUM
ejpam-3737	101	4	,	,	PUNCT
ejpam-3737	101	5	1	1	NUM
ejpam-3737	101	6	)	)	PUNCT
ejpam-3737	101	7	,	,	PUNCT
ejpam-3737	101	8	z0	z0	PROPN
ejpam-3737	101	9	=	=	SYM
ejpam-3737	101	10	aeiθ0	aeiθ0	PROPN
ejpam-3737	101	11	,	,	PUNCT
ejpam-3737	101	12	where	where	SCONJ
ejpam-3737	101	13	a	a	DET
ejpam-3737	101	14	∈	∈	NOUN
ejpam-3737	101	15	(	(	PUNCT
ejpam-3737	101	16	0	0	NUM
ejpam-3737	101	17	,	,	PUNCT
ejpam-3737	101	18	1	1	NUM
ejpam-3737	101	19	]	]	PUNCT
ejpam-3737	101	20	,	,	PUNCT
ejpam-3737	101	21	θ0	θ0	PROPN
ejpam-3737	101	22	∈	∈	PROPN
ejpam-3737	101	23	[	[	PUNCT
ejpam-3737	101	24	0	0	NUM
ejpam-3737	101	25	,	,	PUNCT
ejpam-3737	101	26	π2	π2	NOUN
ejpam-3737	101	27	]	]	PUNCT
ejpam-3737	101	28	.	.	PUNCT
ejpam-3737	102	1	the	the	DET
ejpam-3737	102	2	derivative	derivative	NOUN
ejpam-3737	102	3	is	be	AUX
ejpam-3737	102	4	dr	dr	PROPN
ejpam-3737	102	5	dz	dz	PROPN
ejpam-3737	102	6	=	=	PUNCT
ejpam-3737	102	7	n	n	PROPN
ejpam-3737	102	8	(	(	PUNCT
ejpam-3737	102	9	z	z	NOUN
ejpam-3737	102	10	−	−	PROPN
ejpam-3737	102	11	a1	a1	NOUN
ejpam-3737	102	12	)	)	PUNCT
ejpam-3737	102	13	(	(	PUNCT
ejpam-3737	102	14	z	z	NOUN
ejpam-3737	102	15	−	−	PROPN
ejpam-3737	102	16	a2	a2	PROPN
ejpam-3737	102	17	)	)	PUNCT
ejpam-3737	102	18	·	·	PUNCT
ejpam-3737	102	19	·	·	PUNCT
ejpam-3737	102	20	·	·	PUNCT
ejpam-3737	103	1	(	(	PUNCT
ejpam-3737	103	2	z	z	NOUN
ejpam-3737	103	3	−	−	PROPN
ejpam-3737	103	4	al	al	PROPN
ejpam-3737	103	5	)	)	PUNCT
ejpam-3737	103	6	(	(	PUNCT
ejpam-3737	103	7	z	z	NOUN
ejpam-3737	103	8	−	−	PROPN
ejpam-3737	103	9	b1	b1	PROPN
ejpam-3737	103	10	)	)	PUNCT
ejpam-3737	103	11	(	(	PUNCT
ejpam-3737	103	12	z	z	NOUN
ejpam-3737	103	13	−	−	PROPN
ejpam-3737	103	14	b1	b1	PROPN
ejpam-3737	103	15	)	)	PUNCT
ejpam-3737	103	16	·	·	PUNCT
ejpam-3737	103	17	·	·	PUNCT
ejpam-3737	103	18	·	·	PUNCT
ejpam-3737	104	1	(	(	PUNCT
ejpam-3737	104	2	z	z	NOUN
ejpam-3737	104	3	−	−	NOUN
ejpam-3737	104	4	bs	bs	NOUN
ejpam-3737	104	5	)	)	PUNCT
ejpam-3737	104	6	(	(	PUNCT
ejpam-3737	104	7	z	z	NOUN
ejpam-3737	104	8	−	−	NOUN
ejpam-3737	104	9	bs	bs	PROPN
ejpam-3737	104	10	)	)	PUNCT
ejpam-3737	104	11	,	,	PUNCT
ejpam-3737	105	1	where	where	SCONJ
ejpam-3737	105	2	l	l	NOUN
ejpam-3737	105	3	+	+	CCONJ
ejpam-3737	105	4	2s	2s	NUM
ejpam-3737	105	5	=	=	SYM
ejpam-3737	105	6	n−	n−	NOUN
ejpam-3737	105	7	1	1	NUM
ejpam-3737	105	8	,	,	PUNCT
ejpam-3737	105	9	ak	ak	PROPN
ejpam-3737	105	10	,	,	PUNCT
ejpam-3737	105	11	bm	bm	PROPN
ejpam-3737	105	12	∈	∈	PROPN
ejpam-3737	105	13	d	d	X
ejpam-3737	105	14	(	(	PUNCT
ejpam-3737	105	15	0	0	NUM
ejpam-3737	105	16	,	,	PUNCT
ejpam-3737	105	17	1	1	NUM
ejpam-3737	105	18	)	)	PUNCT
ejpam-3737	105	19	,	,	PUNCT
ejpam-3737	105	20	k	k	PROPN
ejpam-3737	105	21	=	=	SYM
ejpam-3737	105	22	1	1	NUM
ejpam-3737	105	23	,	,	PUNCT
ejpam-3737	105	24	l	l	NOUN
ejpam-3737	105	25	,	,	PUNCT
ejpam-3737	105	26	m	m	VERB
ejpam-3737	105	27	=	=	NOUN
ejpam-3737	105	28	1	1	NUM
ejpam-3737	105	29	,	,	PUNCT
ejpam-3737	105	30	s	s	X
ejpam-3737	105	31	,	,	PUNCT
ejpam-3737	105	32	k	k	NOUN
ejpam-3737	105	33	,	,	PUNCT
ejpam-3737	105	34	m	m	VERB
ejpam-3737	105	35	∈	∈	PROPN
ejpam-3737	105	36	n	n	X
ejpam-3737	105	37	.	.	PUNCT
ejpam-3737	105	38	theorem	theorem	NOUN
ejpam-3737	105	39	2	2	NUM
ejpam-3737	105	40	.	.	PUNCT
ejpam-3737	106	1	if	if	SCONJ
ejpam-3737	106	2	z0	z0	PROPN
ejpam-3737	106	3	=	=	PUNCT
ejpam-3737	106	4	aeiθ0	aeiθ0	PROPN
ejpam-3737	106	5	is	be	AUX
ejpam-3737	106	6	a	a	DET
ejpam-3737	106	7	zero	zero	NUM
ejpam-3737	106	8	of	of	ADP
ejpam-3737	106	9	r	r	NOUN
ejpam-3737	106	10	(	(	PUNCT
ejpam-3737	106	11	z	z	NOUN
ejpam-3737	106	12	)	)	PUNCT
ejpam-3737	106	13	belongs	belong	VERB
ejpam-3737	106	14	to	to	ADP
ejpam-3737	106	15	m	m	PROPN
ejpam-3737	106	16	(	(	PUNCT
ejpam-3737	106	17	in	in	ADP
ejpam-3737	106	18	preliminaries	preliminary	NOUN
ejpam-3737	106	19	)	)	PUNCT
ejpam-3737	106	20	,	,	PUNCT
ejpam-3737	106	21	then	then	ADV
ejpam-3737	106	22	there	there	PRON
ejpam-3737	106	23	exists	exist	VERB
ejpam-3737	106	24	a	a	DET
ejpam-3737	106	25	zero	zero	NUM
ejpam-3737	106	26	c	c	NOUN
ejpam-3737	106	27	of	of	ADP
ejpam-3737	106	28	dr	dr	PROPN
ejpam-3737	106	29	dz	dz	PROPN
ejpam-3737	106	30	which	which	PRON
ejpam-3737	106	31	satisfies	satisfy	VERB
ejpam-3737	106	32	c	c	NOUN
ejpam-3737	106	33	∈	∈	PROPN
ejpam-3737	106	34	d	d	X
ejpam-3737	106	35	(	(	PUNCT
ejpam-3737	106	36	z0	z0	PROPN
ejpam-3737	106	37	,	,	PUNCT
ejpam-3737	106	38	1	1	NUM
ejpam-3737	106	39	)	)	PUNCT
ejpam-3737	106	40	.	.	PUNCT
ejpam-3737	107	1	t.	t.	PROPN
ejpam-3737	107	2	s.	s.	PROPN
ejpam-3737	107	3	stoyanov	stoyanov	PROPN
ejpam-3737	107	4	/	/	SYM
ejpam-3737	107	5	eur	eur	PROPN
ejpam-3737	107	6	.	.	PUNCT
ejpam-3737	108	1	j.	j.	PROPN
ejpam-3737	108	2	pure	pure	PROPN
ejpam-3737	108	3	appl	appl	PROPN
ejpam-3737	108	4	.	.	PROPN
ejpam-3737	108	5	math	math	PROPN
ejpam-3737	108	6	,	,	PUNCT
ejpam-3737	108	7	13	13	NUM
ejpam-3737	108	8	(	(	PUNCT
ejpam-3737	108	9	4	4	NUM
ejpam-3737	108	10	)	)	PUNCT
ejpam-3737	108	11	(	(	PUNCT
ejpam-3737	108	12	2020	2020	NUM
ejpam-3737	108	13	)	)	PUNCT
ejpam-3737	108	14	,	,	PUNCT
ejpam-3737	108	15	807	807	NUM
ejpam-3737	108	16	-	-	SYM
ejpam-3737	108	17	813	813	NUM
ejpam-3737	108	18	811	811	NUM
ejpam-3737	108	19	proof	proof	NOUN
ejpam-3737	108	20	.	.	PUNCT
ejpam-3737	109	1	figure	figure	VERB
ejpam-3737	109	2	3	3	NUM
ejpam-3737	109	3	:	:	PUNCT
ejpam-3737	109	4	without	without	ADP
ejpam-3737	109	5	loss	loss	NOUN
ejpam-3737	109	6	of	of	ADP
ejpam-3737	109	7	generality	generality	NOUN
ejpam-3737	109	8	,	,	PUNCT
ejpam-3737	109	9	we	we	PRON
ejpam-3737	109	10	consider	consider	VERB
ejpam-3737	109	11	re	re	PART
ejpam-3737	109	12	z0	z0	VERB
ejpam-3737	109	13	≥	≥	NUM
ejpam-3737	109	14	0	0	NUM
ejpam-3737	109	15	.	.	PUNCT
ejpam-3737	110	1	let	let	VERB
ejpam-3737	110	2	us	we	PRON
ejpam-3737	110	3	assume	assume	VERB
ejpam-3737	110	4	that	that	SCONJ
ejpam-3737	110	5	in	in	ADP
ejpam-3737	110	6	the	the	DET
ejpam-3737	110	7	disk	disk	NOUN
ejpam-3737	110	8	d	d	NOUN
ejpam-3737	110	9	(	(	PUNCT
ejpam-3737	110	10	z0	z0	PROPN
ejpam-3737	110	11	,	,	PUNCT
ejpam-3737	110	12	1	1	NUM
ejpam-3737	110	13	)	)	PUNCT
ejpam-3737	110	14	there	there	PRON
ejpam-3737	110	15	is	be	VERB
ejpam-3737	110	16	not	not	PART
ejpam-3737	110	17	exists	exist	VERB
ejpam-3737	110	18	a	a	DET
ejpam-3737	110	19	root	root	NOUN
ejpam-3737	110	20	c	c	NOUN
ejpam-3737	110	21	∈	∈	PROPN
ejpam-3737	110	22	dr	dr	PROPN
ejpam-3737	110	23	dz	dz	PROPN
ejpam-3737	110	24	.	.	PUNCT
ejpam-3737	111	1	then	then	ADV
ejpam-3737	111	2	all	all	DET
ejpam-3737	111	3	the	the	DET
ejpam-3737	111	4	zeros	zero	NOUN
ejpam-3737	111	5	of	of	ADP
ejpam-3737	111	6	the	the	DET
ejpam-3737	111	7	derivative	derivative	PROPN
ejpam-3737	111	8	ak	ak	PROPN
ejpam-3737	111	9	,	,	PUNCT
ejpam-3737	111	10	bm	bm	PROPN
ejpam-3737	111	11	∈	∈	PROPN
ejpam-3737	111	12	d	d	X
ejpam-3737	111	13	(	(	PUNCT
ejpam-3737	111	14	0	0	NUM
ejpam-3737	111	15	,	,	PUNCT
ejpam-3737	111	16	1	1	NUM
ejpam-3737	111	17	)	)	PUNCT
ejpam-3737	111	18	\	\	NOUN
ejpam-3737	111	19	d	d	X
ejpam-3737	111	20	(	(	PUNCT
ejpam-3737	111	21	z0	z0	PROPN
ejpam-3737	111	22	,	,	PUNCT
ejpam-3737	111	23	1	1	NUM
ejpam-3737	111	24	)	)	PUNCT
ejpam-3737	111	25	\	\	NOUN
ejpam-3737	112	1	d	d	NOUN
ejpam-3737	112	2	(	(	PUNCT
ejpam-3737	112	3	z0,1	z0,1	NOUN
ejpam-3737	112	4	)	)	PUNCT
ejpam-3737	112	5	,	,	PUNCT
ejpam-3737	112	6	because	because	SCONJ
ejpam-3737	112	7	the	the	DET
ejpam-3737	112	8	zero	zero	NUM
ejpam-3737	112	9	z0	z0	NOUN
ejpam-3737	112	10	=	=	SYM
ejpam-3737	112	11	aeiθ0	aeiθ0	PROPN
ejpam-3737	112	12	of	of	ADP
ejpam-3737	112	13	the	the	DET
ejpam-3737	112	14	polynomial	polynomial	NOUN
ejpam-3737	112	15	must	must	AUX
ejpam-3737	112	16	belongs	belong	VERB
ejpam-3737	112	17	to	to	ADP
ejpam-3737	112	18	m	m	PROPN
ejpam-3737	112	19	.	.	PUNCT
ejpam-3737	113	1	we	we	PRON
ejpam-3737	113	2	note	note	VERB
ejpam-3737	113	3	with	with	ADP
ejpam-3737	113	4	−d	−d	PROPN
ejpam-3737	113	5	,	,	PUNCT
ejpam-3737	113	6	d	d	X
ejpam-3737	113	7	>	>	X
ejpam-3737	113	8	0	0	PUNCT
ejpam-3737	113	9	:	:	PUNCT
ejpam-3737	114	1	−d	−d	PROPN
ejpam-3737	114	2	=	=	PUNCT
ejpam-3737	114	3	c	c	PROPN
ejpam-3737	114	4	(	(	PUNCT
ejpam-3737	114	5	z0	z0	PROPN
ejpam-3737	114	6	,	,	PUNCT
ejpam-3737	114	7	1	1	NUM
ejpam-3737	114	8	)	)	PUNCT
ejpam-3737	114	9	⋂	⋂	PROPN
ejpam-3737	114	10	c	c	X
ejpam-3737	114	11	(	(	PUNCT
ejpam-3737	114	12	z0	z0	PROPN
ejpam-3737	114	13	,	,	PUNCT
ejpam-3737	114	14	1	1	NUM
ejpam-3737	114	15	)	)	PUNCT
ejpam-3737	114	16	and	and	CCONJ
ejpam-3737	114	17	let	let	VERB
ejpam-3737	114	18	us	we	PRON
ejpam-3737	114	19	put	put	VERB
ejpam-3737	114	20	v	v	NOUN
ejpam-3737	114	21	(	(	PUNCT
ejpam-3737	114	22	θ	θ	NOUN
ejpam-3737	114	23	)	)	PUNCT
ejpam-3737	114	24	=	=	SYM
ejpam-3737	114	25	aeiθ	aeiθ	PROPN
ejpam-3737	114	26	,	,	PUNCT
ejpam-3737	114	27	θ	θ	PROPN
ejpam-3737	114	28	∈	∈	PROPN
ejpam-3737	115	1	[	[	X
ejpam-3737	115	2	0	0	NUM
ejpam-3737	115	3	,	,	PUNCT
ejpam-3737	115	4	θ0	θ0	PROPN
ejpam-3737	115	5	]	]	PUNCT
ejpam-3737	115	6	,	,	PUNCT
ejpam-3737	115	7	l	l	PROPN
ejpam-3737	116	1	+	+	CCONJ
ejpam-3737	116	2	2s	2s	NUM
ejpam-3737	116	3	=	=	SYM
ejpam-3737	116	4	n−	n−	NOUN
ejpam-3737	116	5	1	1	NUM
ejpam-3737	116	6	,	,	PUNCT
ejpam-3737	116	7	t	t	PROPN
ejpam-3737	116	8	(	(	PUNCT
ejpam-3737	116	9	z	z	NOUN
ejpam-3737	116	10	)	)	PUNCT
ejpam-3737	116	11	=	=	SYM
ejpam-3737	116	12	1	1	NUM
ejpam-3737	116	13	n	n	PRON
ejpam-3737	116	14	dr	dr	PROPN
ejpam-3737	116	15	(	(	PUNCT
ejpam-3737	116	16	z	z	NOUN
ejpam-3737	116	17	)	)	PUNCT
ejpam-3737	116	18	dz	dz	PROPN
ejpam-3737	116	19	=	=	SYM
ejpam-3737	116	20	l∏	l∏	PROPN
ejpam-3737	116	21	p=1	p=1	X
ejpam-3737	116	22	(	(	PUNCT
ejpam-3737	116	23	z	z	X
ejpam-3737	116	24	+	+	CCONJ
ejpam-3737	116	25	ap	ap	ADJ
ejpam-3737	116	26	)	)	PUNCT
ejpam-3737	116	27	s∏	s∏	PROPN
ejpam-3737	117	1	p=1	p=1	X
ejpam-3737	117	2	(	(	PUNCT
ejpam-3737	117	3	z	z	NOUN
ejpam-3737	117	4	−	−	PROPN
ejpam-3737	117	5	bp	bp	PROPN
ejpam-3737	117	6	)	)	PUNCT
ejpam-3737	117	7	(	(	PUNCT
ejpam-3737	117	8	z	z	NOUN
ejpam-3737	117	9	−	−	PROPN
ejpam-3737	117	10	bp	bp	PROPN
ejpam-3737	117	11	)	)	PUNCT
ejpam-3737	117	12	,	,	PUNCT
ejpam-3737	117	13	l	l	NOUN
ejpam-3737	117	14	,	,	PUNCT
ejpam-3737	117	15	s	s	VERB
ejpam-3737	117	16	∈	∈	PROPN
ejpam-3737	117	17	n	n	CCONJ
ejpam-3737	117	18	[	[	X
ejpam-3737	117	19	one	one	NUM
ejpam-3737	117	20	of	of	ADP
ejpam-3737	117	21	these	these	DET
ejpam-3737	117	22	factors	factor	NOUN
ejpam-3737	117	23	could	could	AUX
ejpam-3737	117	24	be	be	AUX
ejpam-3737	117	25	not	not	PART
ejpam-3737	117	26	existing	exist	VERB
ejpam-3737	117	27	,	,	PUNCT
ejpam-3737	117	28	i.e.	i.e.	X
ejpam-3737	117	29	l	l	X
ejpam-3737	117	30	=	=	SYM
ejpam-3737	117	31	0	0	NUM
ejpam-3737	117	32	or	or	CCONJ
ejpam-3737	117	33	s	s	X
ejpam-3737	117	34	=	=	NOUN
ejpam-3737	117	35	0	0	NUM
ejpam-3737	117	36	]	]	PUNCT
ejpam-3737	117	37	.	.	PUNCT
ejpam-3737	118	1	we	we	PRON
ejpam-3737	118	2	put	put	VERB
ejpam-3737	118	3	f	f	PROPN
ejpam-3737	118	4	(	(	PUNCT
ejpam-3737	118	5	θ	θ	NOUN
ejpam-3737	118	6	)	)	PUNCT
ejpam-3737	118	7	=	=	SYM
ejpam-3737	118	8	∫	∫	PROPN
ejpam-3737	118	9	v(θ	v(θ	PROPN
ejpam-3737	118	10	)	)	PUNCT
ejpam-3737	118	11	0	0	NUM
ejpam-3737	119	1	dr	dr	PROPN
ejpam-3737	119	2	dz	dz	PROPN
ejpam-3737	119	3	dz	dz	PROPN
ejpam-3737	119	4	=	=	PUNCT
ejpam-3737	119	5	n	n	NUM
ejpam-3737	119	6	∫	∫	PROPN
ejpam-3737	119	7	v(θ	v(θ	PROPN
ejpam-3737	119	8	)	)	PUNCT
ejpam-3737	119	9	0	0	NUM
ejpam-3737	120	1	t	t	PROPN
ejpam-3737	120	2	(	(	PUNCT
ejpam-3737	120	3	z	z	NOUN
ejpam-3737	120	4	)	)	PUNCT
ejpam-3737	120	5	dz	dz	PROPN
ejpam-3737	120	6	,	,	PUNCT
ejpam-3737	120	7	g	g	PROPN
ejpam-3737	120	8	(	(	PUNCT
ejpam-3737	120	9	θ	θ	NOUN
ejpam-3737	120	10	)	)	PUNCT
ejpam-3737	120	11	=	=	SYM
ejpam-3737	120	12	f	f	PROPN
ejpam-3737	120	13	(	(	PUNCT
ejpam-3737	120	14	θ	θ	NOUN
ejpam-3737	120	15	)	)	PUNCT
ejpam-3737	120	16	.f	.f	NOUN
ejpam-3737	120	17	(	(	PUNCT
ejpam-3737	120	18	θ	θ	NOUN
ejpam-3737	120	19	)	)	PUNCT
ejpam-3737	120	20	.	.	PUNCT
ejpam-3737	121	1	let	let	VERB
ejpam-3737	121	2	us	we	PRON
ejpam-3737	121	3	calculate	calculate	VERB
ejpam-3737	121	4	dg	dg	PROPN
ejpam-3737	121	5	dθ	dθ	PROPN
ejpam-3737	121	6	=	=	PROPN
ejpam-3737	121	7	n	n	PROPN
ejpam-3737	121	8	[	[	PUNCT
ejpam-3737	121	9	t	t	X
ejpam-3737	121	10	(	(	PUNCT
ejpam-3737	121	11	v	v	NOUN
ejpam-3737	121	12	(	(	PUNCT
ejpam-3737	121	13	θ	θ	NOUN
ejpam-3737	121	14	)	)	PUNCT
ejpam-3737	121	15	)	)	PUNCT
ejpam-3737	122	1	dv	dv	PROPN
ejpam-3737	122	2	dθ	dθ	PROPN
ejpam-3737	122	3	f	f	PROPN
ejpam-3737	122	4	(	(	PUNCT
ejpam-3737	122	5	θ	θ	PROPN
ejpam-3737	122	6	)	)	PUNCT
ejpam-3737	123	1	+	+	NUM
ejpam-3737	123	2	t	t	PROPN
ejpam-3737	123	3	(	(	PUNCT
ejpam-3737	123	4	v	v	X
ejpam-3737	123	5	(	(	PUNCT
ejpam-3737	123	6	θ	θ	NOUN
ejpam-3737	123	7	)	)	PUNCT
ejpam-3737	123	8	)	)	PUNCT
ejpam-3737	124	1	dv	dv	PROPN
ejpam-3737	124	2	dθ	dθ	PROPN
ejpam-3737	124	3	f	f	PROPN
ejpam-3737	124	4	(	(	PUNCT
ejpam-3737	124	5	θ	θ	PROPN
ejpam-3737	124	6	)	)	PUNCT
ejpam-3737	124	7	]	]	PUNCT
ejpam-3737	124	8	,	,	PUNCT
ejpam-3737	124	9	dv	dv	PROPN
ejpam-3737	124	10	dθ	dθ	PROPN
ejpam-3737	124	11	=	=	PROPN
ejpam-3737	125	1	daeiθ	daeiθ	PROPN
ejpam-3737	125	2	dθ	dθ	PROPN
ejpam-3737	125	3	=	=	PROPN
ejpam-3737	125	4	iaeiθ	iaeiθ	PROPN
ejpam-3737	125	5	,	,	PUNCT
ejpam-3737	125	6	and	and	CCONJ
ejpam-3737	125	7	if	if	SCONJ
ejpam-3737	125	8	we	we	PRON
ejpam-3737	125	9	put	put	VERB
ejpam-3737	125	10	u0	u0	ADJ
ejpam-3737	125	11	=	=	NOUN
ejpam-3737	125	12	v	v	X
ejpam-3737	125	13	(	(	PUNCT
ejpam-3737	125	14	θ	θ	NOUN
ejpam-3737	125	15	)	)	PUNCT
ejpam-3737	125	16	=	=	SYM
ejpam-3737	125	17	aeiθ	aeiθ	PROPN
ejpam-3737	125	18	,	,	PUNCT
ejpam-3737	125	19	up	up	ADV
ejpam-3737	125	20	=	=	SYM
ejpam-3737	125	21	v	v	NOUN
ejpam-3737	125	22	(	(	PUNCT
ejpam-3737	125	23	θ	θ	NOUN
ejpam-3737	125	24	)	)	PUNCT
ejpam-3737	126	1	+	+	CCONJ
ejpam-3737	126	2	ap	ap	PROPN
ejpam-3737	126	3	,	,	PUNCT
ejpam-3737	126	4	p	p	NOUN
ejpam-3737	126	5	=	=	NOUN
ejpam-3737	126	6	1	1	NUM
ejpam-3737	126	7	,	,	PUNCT
ejpam-3737	126	8	l	l	NOUN
ejpam-3737	126	9	,	,	PUNCT
ejpam-3737	126	10	ul+2p+1	ul+2p+1	VERB
ejpam-3737	126	11	=	=	SYM
ejpam-3737	126	12	v	v	NOUN
ejpam-3737	126	13	(	(	PUNCT
ejpam-3737	126	14	θ)−	θ)−	PROPN
ejpam-3737	126	15	bp	bp	PROPN
ejpam-3737	126	16	,	,	PUNCT
ejpam-3737	126	17	ul+2p+2	ul+2p+2	PROPN
ejpam-3737	126	18	=	=	SYM
ejpam-3737	126	19	v	v	NOUN
ejpam-3737	126	20	(	(	PUNCT
ejpam-3737	126	21	θ)−	θ)−	PROPN
ejpam-3737	126	22	bp	bp	PROPN
ejpam-3737	126	23	,	,	PUNCT
ejpam-3737	126	24	p	p	X
ejpam-3737	126	25	=	=	NOUN
ejpam-3737	126	26	0	0	NUM
ejpam-3737	126	27	,	,	PUNCT
ejpam-3737	126	28	s−	s−	PROPN
ejpam-3737	126	29	1	1	NUM
ejpam-3737	126	30	.	.	PUNCT
ejpam-3737	127	1	t.	t.	PROPN
ejpam-3737	127	2	s.	s.	PROPN
ejpam-3737	127	3	stoyanov	stoyanov	PROPN
ejpam-3737	127	4	/	/	SYM
ejpam-3737	127	5	eur	eur	PROPN
ejpam-3737	127	6	.	.	PUNCT
ejpam-3737	128	1	j.	j.	PROPN
ejpam-3737	128	2	pure	pure	PROPN
ejpam-3737	128	3	appl	appl	PROPN
ejpam-3737	128	4	.	.	PROPN
ejpam-3737	128	5	math	math	PROPN
ejpam-3737	128	6	,	,	PUNCT
ejpam-3737	128	7	13	13	NUM
ejpam-3737	128	8	(	(	PUNCT
ejpam-3737	128	9	4	4	NUM
ejpam-3737	128	10	)	)	PUNCT
ejpam-3737	128	11	(	(	PUNCT
ejpam-3737	128	12	2020	2020	NUM
ejpam-3737	128	13	)	)	PUNCT
ejpam-3737	128	14	,	,	PUNCT
ejpam-3737	128	15	807	807	NUM
ejpam-3737	128	16	-	-	SYM
ejpam-3737	128	17	813	813	NUM
ejpam-3737	128	18	812	812	NUM
ejpam-3737	128	19	knowing	know	VERB
ejpam-3737	128	20	df	df	PROPN
ejpam-3737	128	21	dθ	dθ	PROPN
ejpam-3737	128	22	.	.	PUNCT
ejpam-3737	129	1	∏n−1	∏n−1	PROPN
ejpam-3737	129	2	p=0	p=0	PROPN
ejpam-3737	130	1	up	up	ADP
ejpam-3737	130	2	=	=	PUNCT
ejpam-3737	130	3	df	df	PROPN
ejpam-3737	130	4	dθ	dθ	NOUN
ejpam-3737	130	5	.	.	PUNCT
ejpam-3737	131	1	∏n−1	∏n−1	PROPN
ejpam-3737	131	2	p=0	p=0	PROPN
ejpam-3737	131	3	up	up	ADP
ejpam-3737	131	4	we	we	PRON
ejpam-3737	131	5	have	have	VERB
ejpam-3737	131	6	dg	dg	PROPN
ejpam-3737	131	7	dθ	dθ	PROPN
ejpam-3737	131	8	=	=	PROPN
ejpam-3737	131	9	in	in	ADP
ejpam-3737	131	10	f	f	PROPN
ejpam-3737	131	11	(	(	PUNCT
ejpam-3737	131	12	θ	θ	NOUN
ejpam-3737	131	13	)	)	PUNCT
ejpam-3737	131	14	n−1∏	n−1∏	PROPN
ejpam-3737	131	15	p=0	p=0	PROPN
ejpam-3737	131	16	up	up	ADP
ejpam-3737	131	17	−	−	PROPN
ejpam-3737	131	18	f	f	PROPN
ejpam-3737	131	19	(	(	PUNCT
ejpam-3737	131	20	θ	θ	PROPN
ejpam-3737	131	21	)	)	PUNCT
ejpam-3737	131	22	n−1∏	n−1∏	PROPN
ejpam-3737	131	23	p=0	p=0	PROPN
ejpam-3737	131	24	up	up	ADP
ejpam-3737	131	25			NOUN
ejpam-3737	131	26	,	,	PUNCT
ejpam-3737	131	27	d2	d2	PROPN
ejpam-3737	131	28	g	g	NOUN
ejpam-3737	131	29	dθ2	dθ2	NOUN
ejpam-3737	132	1	=	=	NOUN
ejpam-3737	132	2	n	n	NOUN
ejpam-3737	132	3	2	2	NOUN
ejpam-3737	132	4	df	df	NOUN
ejpam-3737	132	5	dθ	dθ	NOUN
ejpam-3737	132	6	.	.	PUNCT
ejpam-3737	133	1	n−1∏	n−1∏	PROPN
ejpam-3737	133	2	p=0	p=0	PROPN
ejpam-3737	133	3	up	up	ADP
ejpam-3737	134	1	+	+	CCONJ
ejpam-3737	134	2	i	i	PRON
ejpam-3737	135	1	d	d	X
ejpam-3737	135	2	∏n−1	∏n−1	PROPN
ejpam-3737	135	3	p=0	p=0	PROPN
ejpam-3737	135	4	up	up	ADP
ejpam-3737	135	5	dθ	dθ	PROPN
ejpam-3737	135	6	f	f	PROPN
ejpam-3737	136	1	(	(	PUNCT
ejpam-3737	136	2	θ)−	θ)−	PROPN
ejpam-3737	136	3	i	i	INTJ
ejpam-3737	137	1	d	d	X
ejpam-3737	137	2	∏n−1	∏n−1	PROPN
ejpam-3737	137	3	p=0	p=0	PROPN
ejpam-3737	137	4	up	up	ADP
ejpam-3737	137	5	dθ	dθ	PROPN
ejpam-3737	137	6	f	f	PROPN
ejpam-3737	137	7	(	(	PUNCT
ejpam-3737	137	8	θ	θ	NOUN
ejpam-3737	137	9	)	)	PUNCT
ejpam-3737	137	10			NOUN
ejpam-3737	137	11	d2	d2	VERB
ejpam-3737	137	12	g	g	NOUN
ejpam-3737	137	13	dθ2	dθ2	NOUN
ejpam-3737	138	1	=	=	NOUN
ejpam-3737	138	2	n	n	NUM
ejpam-3737	138	3	2n	2n	NOUN
ejpam-3737	139	1	n−1∏	n−1∏	PROPN
ejpam-3737	139	2	p=0	p=0	PROPN
ejpam-3737	139	3	|up|2	|up|2	PUNCT
ejpam-3737	139	4	−	−	PROPN
ejpam-3737	139	5	u0	u0	PRON
ejpam-3737	139	6	n−1∑	n−1∑	NUM
ejpam-3737	139	7	p=0	p=0	PROPN
ejpam-3737	139	8	∏	∏	PROPN
ejpam-3737	139	9	j	j	PROPN
ejpam-3737	139	10	6	6	NUM
ejpam-3737	139	11	=	=	PROPN
ejpam-3737	139	12	p	p	NOUN
ejpam-3737	139	13	uj	uj	NUM
ejpam-3737	140	1			PROPN
ejpam-3737	140	2	f	f	PROPN
ejpam-3737	140	3	(	(	PUNCT
ejpam-3737	140	4	θ)−	θ)−	PROPN
ejpam-3737	140	5	u0	u0	PROPN
ejpam-3737	140	6	n−1∑	n−1∑	NUM
ejpam-3737	140	7	p=0	p=0	PROPN
ejpam-3737	140	8	∏	∏	PROPN
ejpam-3737	140	9	j	j	PROPN
ejpam-3737	140	10	6	6	NUM
ejpam-3737	140	11	=	=	PROPN
ejpam-3737	140	12	p	p	NOUN
ejpam-3737	140	13	uj	uj	NUM
ejpam-3737	140	14			PROPN
ejpam-3737	140	15	f	f	PROPN
ejpam-3737	140	16	(	(	PUNCT
ejpam-3737	140	17	θ	θ	NOUN
ejpam-3737	140	18	)	)	PUNCT
ejpam-3737	140	19			NOUN
ejpam-3737	140	20	d2	d2	VERB
ejpam-3737	140	21	g	g	NOUN
ejpam-3737	140	22	dθ2	dθ2	NOUN
ejpam-3737	141	1	=	=	NOUN
ejpam-3737	141	2	2n	2n	NUM
ejpam-3737	141	3	n	n	PROPN
ejpam-3737	141	4	n−1∏	n−1∏	PROPN
ejpam-3737	141	5	p=0	p=0	PROPN
ejpam-3737	141	6	|up|2	|up|2	PUNCT
ejpam-3737	141	7	−re	−re	PROPN
ejpam-3737	141	8	u0	u0	NOUN
ejpam-3737	141	9	n−1∑	n−1∑	NUM
ejpam-3737	141	10	p=0	p=0	PROPN
ejpam-3737	141	11	∏	∏	PROPN
ejpam-3737	141	12	j	j	PROPN
ejpam-3737	141	13	6	6	NUM
ejpam-3737	141	14	=	=	PROPN
ejpam-3737	141	15	p	p	NOUN
ejpam-3737	141	16	uj	uj	NUM
ejpam-3737	141	17			PROPN
ejpam-3737	141	18	f	f	PROPN
ejpam-3737	141	19	(	(	PUNCT
ejpam-3737	141	20	θ	θ	NOUN
ejpam-3737	141	21	)	)	PUNCT
ejpam-3737	141	22			NOUN
ejpam-3737	141	23	,	,	PUNCT
ejpam-3737	141	24	and	and	CCONJ
ejpam-3737	141	25	consequently	consequently	ADV
ejpam-3737	141	26	d2	d2	PROPN
ejpam-3737	141	27	g	g	PROPN
ejpam-3737	141	28	dθ2	dθ2	NOUN
ejpam-3737	141	29	≥	≥	NUM
ejpam-3737	141	30	2n	2n	NUM
ejpam-3737	141	31	n−1∏	n−1∏	PROPN
ejpam-3737	141	32	p=0	p=0	PROPN
ejpam-3737	141	33	|up|	|up|	PROPN
ejpam-3737	141	34	n	n	PROPN
ejpam-3737	141	35	n−1∏	n−1∏	PROPN
ejpam-3737	141	36	p=0	p=0	PROPN
ejpam-3737	141	37	|up|	|up|	PROPN
ejpam-3737	141	38	−	−	ADP
ejpam-3737	141	39	∣∣∣u0	∣∣∣u0	PROPN
ejpam-3737	141	40	∑n−1	∑n−1	ADP
ejpam-3737	142	1	p=0	p=0	PROPN
ejpam-3737	142	2	∏	∏	PROPN
ejpam-3737	142	3	j	j	PROPN
ejpam-3737	142	4	6	6	NUM
ejpam-3737	142	5	=	=	PROPN
ejpam-3737	142	6	p	p	X
ejpam-3737	142	7	uj	uj	PROPN
ejpam-3737	142	8	∣∣∣	∣∣∣	NOUN
ejpam-3737	142	9	.	.	PUNCT
ejpam-3737	143	1	∣∣f	∣∣f	NOUN
ejpam-3737	143	2	(	(	PUNCT
ejpam-3737	143	3	θ	θ	NOUN
ejpam-3737	143	4	)	)	PUNCT
ejpam-3737	143	5	∣∣∏n−1	∣∣∏n−1	ADJ
ejpam-3737	143	6	p=0	p=0	PROPN
ejpam-3737	143	7	up	up	ADP
ejpam-3737	143	8			NOUN
ejpam-3737	143	9	.	.	PUNCT
ejpam-3737	144	1	since	since	SCONJ
ejpam-3737	144	2	θ	θ	PROPN
ejpam-3737	144	3	∈	∈	PROPN
ejpam-3737	144	4	[	[	X
ejpam-3737	144	5	0	0	NUM
ejpam-3737	144	6	,	,	PUNCT
ejpam-3737	144	7	θ0	θ0	PROPN
ejpam-3737	144	8	]	]	PUNCT
ejpam-3737	144	9	⇒	⇒	NOUN
ejpam-3737	144	10	|up	|up	NUM
ejpam-3737	144	11	(	(	PUNCT
ejpam-3737	144	12	θ)|	θ)|	PROPN
ejpam-3737	144	13	≥	≥	NUM
ejpam-3737	144	14	|up	|up	NUM
ejpam-3737	144	15	(	(	PUNCT
ejpam-3737	144	16	θ0)|	θ0)|	NOUN
ejpam-3737	144	17	≥	≥	NOUN
ejpam-3737	144	18	1	1	NUM
ejpam-3737	144	19	,	,	PUNCT
ejpam-3737	144	20	p	p	NOUN
ejpam-3737	144	21	=	=	NOUN
ejpam-3737	144	22	1	1	NUM
ejpam-3737	144	23	,	,	PUNCT
ejpam-3737	144	24	n−	n−	NOUN
ejpam-3737	144	25	1	1	NUM
ejpam-3737	144	26	.	.	PUNCT
ejpam-3737	145	1	if	if	SCONJ
ejpam-3737	145	2	we	we	PRON
ejpam-3737	145	3	assume	assume	VERB
ejpam-3737	145	4	|f	|f	PROPN
ejpam-3737	145	5	(	(	PUNCT
ejpam-3737	145	6	θ)|	θ)|	PROPN
ejpam-3737	145	7	=	=	SYM
ejpam-3737	145	8	∣∣f	∣∣f	PROPN
ejpam-3737	145	9	(	(	PUNCT
ejpam-3737	145	10	θ	θ	NOUN
ejpam-3737	145	11	)	)	PUNCT
ejpam-3737	145	12	∣∣	∣∣	NUM
ejpam-3737	145	13	≤	≤	PROPN
ejpam-3737	145	14	a2	a2	PROPN
ejpam-3737	145	15	,	,	PUNCT
ejpam-3737	145	16	then	then	ADV
ejpam-3737	145	17	d2	d2	PROPN
ejpam-3737	145	18	g	g	PROPN
ejpam-3737	145	19	dθ2	dθ2	NOUN
ejpam-3737	145	20	≥2n	≥2n	X
ejpam-3737	145	21	n−1∏	n−1∏	PROPN
ejpam-3737	145	22	p=0	p=0	PROPN
ejpam-3737	145	23	|up|	|up|	PROPN
ejpam-3737	145	24	[	[	PUNCT
ejpam-3737	145	25	na−	na−	PROPN
ejpam-3737	145	26	(	(	PUNCT
ejpam-3737	145	27	1	1	NUM
ejpam-3737	145	28	+	+	NUM
ejpam-3737	145	29	∣∣∣∣u0	∣∣∣∣u0	PROPN
ejpam-3737	145	30	u1	u1	NOUN
ejpam-3737	145	31	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-3737	145	32	·	·	PUNCT
ejpam-3737	145	33	·	·	PUNCT
ejpam-3737	145	34	·	·	PUNCT
ejpam-3737	145	35	+	+	NUM
ejpam-3737	145	36	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3737	145	37	u0	u0	ADJ
ejpam-3737	145	38	un−1	un−1	PROPN
ejpam-3737	145	39	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3737	145	40	)	)	PUNCT
ejpam-3737	145	41	a2	a2	PROPN
ejpam-3737	145	42	]	]	PUNCT
ejpam-3737	145	43	≥	≥	PROPN
ejpam-3737	145	44	2na	2na	PROPN
ejpam-3737	145	45	n−1∏	n−1∏	PROPN
ejpam-3737	145	46	p=0	p=0	PROPN
ejpam-3737	145	47	|up|	|up|	PROPN
ejpam-3737	146	1	[	[	X
ejpam-3737	146	2	n−	n−	NOUN
ejpam-3737	146	3	(	(	PUNCT
ejpam-3737	146	4	1	1	NUM
ejpam-3737	146	5	+	+	CCONJ
ejpam-3737	146	6	a	a	DET
ejpam-3737	146	7	(	(	PUNCT
ejpam-3737	146	8	n−	n−	NOUN
ejpam-3737	146	9	1	1	NUM
ejpam-3737	146	10	)	)	PUNCT
ejpam-3737	146	11	)	)	PUNCT
ejpam-3737	146	12	a	a	DET
ejpam-3737	146	13	]	]	X
ejpam-3737	146	14	=	=	PUNCT
ejpam-3737	146	15	2na	2na	PROPN
ejpam-3737	146	16	n−1∏	n−1∏	PROPN
ejpam-3737	146	17	p=0	p=0	PROPN
ejpam-3737	146	18	|up|	|up|	PROPN
ejpam-3737	146	19	[	[	PUNCT
ejpam-3737	146	20	n−	n−	PROPN
ejpam-3737	146	21	a−	a−	PROPN
ejpam-3737	146	22	a2	a2	PROPN
ejpam-3737	146	23	(	(	PUNCT
ejpam-3737	146	24	n−	n−	NOUN
ejpam-3737	146	25	1	1	NUM
ejpam-3737	146	26	)	)	PUNCT
ejpam-3737	146	27	]	]	PUNCT
ejpam-3737	146	28	≥	≥	PROPN
ejpam-3737	146	29	2na	2na	PROPN
ejpam-3737	146	30	n−1∏	n−1∏	PROPN
ejpam-3737	146	31	p=0	p=0	PROPN
ejpam-3737	146	32	|up|	|up|	PROPN
ejpam-3737	146	33	[	[	X
ejpam-3737	146	34	n−	n−	NOUN
ejpam-3737	146	35	a−	a−	PROPN
ejpam-3737	146	36	a	a	PRON
ejpam-3737	146	37	(	(	PUNCT
ejpam-3737	146	38	n−	n−	NOUN
ejpam-3737	146	39	1	1	NUM
ejpam-3737	146	40	)	)	PUNCT
ejpam-3737	146	41	]	]	PUNCT
ejpam-3737	147	1	=	=	SYM
ejpam-3737	147	2	2nan	2nan	X
ejpam-3737	147	3	(	(	PUNCT
ejpam-3737	147	4	1−	1−	NUM
ejpam-3737	147	5	a	a	NOUN
ejpam-3737	147	6	)	)	PUNCT
ejpam-3737	147	7	n−1∏	n−1∏	PROPN
ejpam-3737	147	8	p=0	p=0	PROPN
ejpam-3737	147	9	|up|	|up|	PROPN
ejpam-3737	147	10	.	.	PUNCT
ejpam-3737	148	1	then	then	ADV
ejpam-3737	148	2	we	we	PRON
ejpam-3737	148	3	get	get	VERB
ejpam-3737	148	4	d2	d2	PROPN
ejpam-3737	148	5	g	g	PROPN
ejpam-3737	148	6	dθ2	dθ2	NOUN
ejpam-3737	148	7	≥	≥	NOUN
ejpam-3737	148	8	0	0	NUM
ejpam-3737	148	9	.	.	PUNCT
ejpam-3737	149	1	hence	hence	ADV
ejpam-3737	149	2	dg	dg	PROPN
ejpam-3737	149	3	dθ	dθ	PROPN
ejpam-3737	149	4	(	(	PUNCT
ejpam-3737	149	5	θ	θ	PROPN
ejpam-3737	149	6	)	)	PUNCT
ejpam-3737	149	7	≥	≥	NOUN
ejpam-3737	149	8	dg	dg	PROPN
ejpam-3737	149	9	dθ	dθ	PROPN
ejpam-3737	149	10	(	(	PUNCT
ejpam-3737	149	11	0	0	NUM
ejpam-3737	149	12	)	)	PUNCT
ejpam-3737	149	13	=	=	SYM
ejpam-3737	149	14	0	0	X
ejpam-3737	149	15	.	.	PUNCT
ejpam-3737	150	1	consequently	consequently	ADV
ejpam-3737	150	2	g	g	PROPN
ejpam-3737	150	3	(	(	PUNCT
ejpam-3737	150	4	θ0	θ0	PROPN
ejpam-3737	150	5	)	)	PUNCT
ejpam-3737	150	6	>	>	X
ejpam-3737	150	7	g	g	PROPN
ejpam-3737	150	8	(	(	PUNCT
ejpam-3737	150	9	0	0	NUM
ejpam-3737	150	10	)	)	PUNCT
ejpam-3737	150	11	,	,	PUNCT
ejpam-3737	150	12	i.e.	i.e.	X
ejpam-3737	150	13	|f	|f	PROPN
ejpam-3737	150	14	(	(	PUNCT
ejpam-3737	150	15	θ0)|	θ0)|	X
ejpam-3737	150	16	>	>	X
ejpam-3737	150	17	a	a	X
ejpam-3737	150	18	,	,	PUNCT
ejpam-3737	150	19	according	accord	VERB
ejpam-3737	150	20	to	to	ADP
ejpam-3737	150	21	the	the	DET
ejpam-3737	150	22	proof	proof	NOUN
ejpam-3737	150	23	of	of	ADP
ejpam-3737	150	24	theorem	theorem	NOUN
ejpam-3737	150	25	1	1	NUM
ejpam-3737	150	26	.	.	PUNCT
ejpam-3737	150	27	therefore	therefore	ADV
ejpam-3737	150	28	a	a	DET
ejpam-3737	150	29	<	<	X
ejpam-3737	150	30	|f	|f	PROPN
ejpam-3737	150	31	(	(	PUNCT
ejpam-3737	150	32	θ0)|	θ0)|	NOUN
ejpam-3737	150	33	≤	≤	NUM
ejpam-3737	150	34	a2	a2	PROPN
ejpam-3737	150	35	,	,	PUNCT
ejpam-3737	150	36	which	which	PRON
ejpam-3737	150	37	is	be	AUX
ejpam-3737	150	38	impossible	impossible	ADJ
ejpam-3737	150	39	.	.	PUNCT
ejpam-3737	151	1	the	the	DET
ejpam-3737	151	2	contradiction	contradiction	NOUN
ejpam-3737	151	3	proves	prove	VERB
ejpam-3737	151	4	that	that	SCONJ
ejpam-3737	151	5	|f	|f	PROPN
ejpam-3737	151	6	(	(	PUNCT
ejpam-3737	151	7	θ0)|	θ0)|	PROPN
ejpam-3737	151	8	>	>	X
ejpam-3737	151	9	a2	a2	PROPN
ejpam-3737	151	10	,	,	PUNCT
ejpam-3737	151	11	but	but	CCONJ
ejpam-3737	151	12	f	f	PROPN
ejpam-3737	151	13	(	(	PUNCT
ejpam-3737	151	14	θ0	θ0	PROPN
ejpam-3737	151	15	)	)	PUNCT
ejpam-3737	151	16	=	=	SYM
ejpam-3737	152	1	∫	∫	PROPN
ejpam-3737	152	2	v(θ0	v(θ0	NOUN
ejpam-3737	152	3	)	)	PUNCT
ejpam-3737	152	4	0	0	PROPN
ejpam-3737	153	1	dr	dr	PROPN
ejpam-3737	153	2	dz	dz	PROPN
ejpam-3737	153	3	dz	dz	PROPN
ejpam-3737	153	4	=	=	SYM
ejpam-3737	153	5	∫	∫	PROPN
ejpam-3737	153	6	z0	z0	PROPN
ejpam-3737	153	7	0	0	PROPN
ejpam-3737	153	8	dr	dr	PROPN
ejpam-3737	153	9	dz	dz	PROPN
ejpam-3737	153	10	dz	dz	PROPN
ejpam-3737	153	11	=	=	SYM
ejpam-3737	153	12	r	r	NOUN
ejpam-3737	153	13	(	(	PUNCT
ejpam-3737	153	14	z0)−	z0)−	NOUN
ejpam-3737	153	15	r	r	NOUN
ejpam-3737	153	16	(	(	PUNCT
ejpam-3737	153	17	0	0	NUM
ejpam-3737	153	18	)	)	PUNCT
ejpam-3737	153	19	=	=	PRON
ejpam-3737	153	20	−r	−r	X
ejpam-3737	153	21	(	(	PUNCT
ejpam-3737	153	22	0	0	NUM
ejpam-3737	153	23	)	)	PUNCT
ejpam-3737	153	24	,	,	PUNCT
ejpam-3737	153	25	references	reference	VERB
ejpam-3737	153	26	813	813	NUM
ejpam-3737	153	27	i.e.	i.e.	X
ejpam-3737	153	28	|r	|r	PROPN
ejpam-3737	153	29	(	(	PUNCT
ejpam-3737	153	30	0)|	0)|	NOUN
ejpam-3737	153	31	≤	≤	NUM
ejpam-3737	153	32	a2	a2	NOUN
ejpam-3737	153	33	,	,	PUNCT
ejpam-3737	153	34	because	because	SCONJ
ejpam-3737	153	35	z0	z0	PROPN
ejpam-3737	153	36	,	,	PUNCT
ejpam-3737	153	37	z0	z0	PROPN
ejpam-3737	153	38	are	be	AUX
ejpam-3737	153	39	roots	root	NOUN
ejpam-3737	153	40	of	of	ADP
ejpam-3737	153	41	r	r	NOUN
ejpam-3737	153	42	(	(	PUNCT
ejpam-3737	153	43	z	z	NOUN
ejpam-3737	153	44	)	)	PUNCT
ejpam-3737	153	45	and	and	CCONJ
ejpam-3737	153	46	|z0|=|z0|	|z0|=|z0|	X
ejpam-3737	153	47	=	=	PUNCT
ejpam-3737	154	1	a.	a.	NOUN
ejpam-3737	154	2	then	then	ADV
ejpam-3737	154	3	we	we	PRON
ejpam-3737	154	4	have	have	VERB
ejpam-3737	154	5	a2	a2	PROPN
ejpam-3737	154	6	<	<	X
ejpam-3737	154	7	|r	|r	PROPN
ejpam-3737	154	8	(	(	PUNCT
ejpam-3737	154	9	0)|	0)|	NOUN
ejpam-3737	154	10	≤	≤	NUM
ejpam-3737	154	11	a2	a2	PROPN
ejpam-3737	154	12	.	.	PUNCT
ejpam-3737	155	1	this	this	DET
ejpam-3737	155	2	contradiction	contradiction	NOUN
ejpam-3737	155	3	shows	show	VERB
ejpam-3737	155	4	that	that	SCONJ
ejpam-3737	155	5	,	,	PUNCT
ejpam-3737	155	6	there	there	PRON
ejpam-3737	155	7	exists	exist	VERB
ejpam-3737	155	8	a	a	DET
ejpam-3737	155	9	zero	zero	NUM
ejpam-3737	155	10	c	c	NOUN
ejpam-3737	155	11	of	of	ADP
ejpam-3737	155	12	dr	dr	PROPN
ejpam-3737	155	13	dz	dz	PROPN
ejpam-3737	155	14	,	,	PUNCT
ejpam-3737	155	15	which	which	PRON
ejpam-3737	155	16	satisfies	satisfy	VERB
ejpam-3737	155	17	c	c	NOUN
ejpam-3737	155	18	∈	∈	PROPN
ejpam-3737	155	19	d	d	X
ejpam-3737	155	20	(	(	PUNCT
ejpam-3737	155	21	0	0	NUM
ejpam-3737	155	22	,	,	PUNCT
ejpam-3737	155	23	1	1	NUM
ejpam-3737	155	24	)	)	PUNCT
ejpam-3737	155	25	.	.	PUNCT
ejpam-3737	156	1	acknowledgements	acknowledgement	NOUN
ejpam-3737	156	2	this	this	DET
ejpam-3737	156	3	research	research	NOUN
ejpam-3737	156	4	was	be	AUX
ejpam-3737	156	5	financed	finance	VERB
ejpam-3737	156	6	from	from	ADP
ejpam-3737	156	7	university	university	NOUN
ejpam-3737	156	8	of	of	ADP
ejpam-3737	156	9	economics	economic	NOUN
ejpam-3737	156	10	of	of	ADP
ejpam-3737	156	11	varna	varna	ADJ
ejpam-3737	156	12	research	research	NOUN
ejpam-3737	156	13	grants	grant	NOUN
ejpam-3737	156	14	no.19	no.19	PROPN
ejpam-3737	156	15	2018	2018	NUM
ejpam-3737	156	16	-	-	PUNCT
ejpam-3737	156	17	04	04	NUM
ejpam-3737	156	18	-	-	PUNCT
ejpam-3737	156	19	27	27	NUM
ejpam-3737	156	20	.	.	PUNCT
ejpam-3737	157	1	references	reference	NOUN
ejpam-3737	157	2	[	[	X
ejpam-3737	157	3	1	1	NUM
ejpam-3737	157	4	]	]	SYM
ejpam-3737	157	5	b	b	NOUN
ejpam-3737	157	6	bojanov	bojanov	NOUN
ejpam-3737	157	7	,	,	PUNCT
ejpam-3737	157	8	q	q	PROPN
ejpam-3737	158	1	i	i	PRON
ejpam-3737	158	2	rahman	rahman	PROPN
ejpam-3737	158	3	,	,	PUNCT
ejpam-3737	158	4	and	and	CCONJ
ejpam-3737	158	5	j	j	PROPN
ejpam-3737	158	6	szynal	szynal	ADJ
ejpam-3737	158	7	.	.	PUNCT
ejpam-3737	159	1	on	on	ADP
ejpam-3737	159	2	a	a	DET
ejpam-3737	159	3	conjecture	conjecture	NOUN
ejpam-3737	159	4	of	of	ADP
ejpam-3737	159	5	sendov	sendov	NOUN
ejpam-3737	159	6	about	about	ADP
ejpam-3737	159	7	the	the	DET
ejpam-3737	159	8	critical	critical	ADJ
ejpam-3737	159	9	points	point	NOUN
ejpam-3737	159	10	of	of	ADP
ejpam-3737	159	11	a	a	DET
ejpam-3737	159	12	polynomial	polynomial	ADJ
ejpam-3737	159	13	.	.	PUNCT
ejpam-3737	159	14	math	math	NOUN
ejpam-3737	159	15	.	.	PUNCT
ejpam-3737	160	1	z	z	X
ejpam-3737	160	2	,	,	PUNCT
ejpam-3737	160	3	190:281–285	190:281–285	NUM
ejpam-3737	160	4	,	,	PUNCT
ejpam-3737	160	5	1985	1985	NUM
ejpam-3737	160	6	.	.	PUNCT
ejpam-3737	161	1	[	[	X
ejpam-3737	161	2	2	2	NUM
ejpam-3737	161	3	]	]	PUNCT
ejpam-3737	161	4	d	d	NOUN
ejpam-3737	161	5	m	m	NOUN
ejpam-3737	161	6	souroujon	souroujon	NOUN
ejpam-3737	161	7	and	and	CCONJ
ejpam-3737	161	8	t	t	PROPN
ejpam-3737	161	9	zapryanova	zapryanova	PROPN
ejpam-3737	161	10	.	.	PUNCT
ejpam-3737	162	1	on	on	ADP
ejpam-3737	162	2	the	the	DET
ejpam-3737	162	3	relation	relation	NOUN
ejpam-3737	162	4	between	between	ADP
ejpam-3737	162	5	the	the	DET
ejpam-3737	162	6	number	number	NOUN
ejpam-3737	162	7	of	of	ADP
ejpam-3737	162	8	real	real	ADJ
ejpam-3737	162	9	and	and	CCONJ
ejpam-3737	162	10	complex	complex	ADJ
ejpam-3737	162	11	zeros	zero	NOUN
ejpam-3737	162	12	of	of	ADP
ejpam-3737	162	13	polynomials	polynomial	NOUN
ejpam-3737	162	14	of	of	ADP
ejpam-3737	162	15	a	a	DET
ejpam-3737	162	16	certain	certain	ADJ
ejpam-3737	162	17	kind	kind	NOUN
ejpam-3737	162	18	.	.	PUNCT
ejpam-3737	163	1	in	in	ADP
ejpam-3737	163	2	aip	aip	PROPN
ejpam-3737	163	3	conference	conference	NOUN
ejpam-3737	163	4	proceeding	proceeding	NOUN
ejpam-3737	163	5	.	.	PUNCT
ejpam-3737	164	1	,	,	PUNCT
ejpam-3737	164	2	volume	volume	NOUN
ejpam-3737	164	3	2159	2159	NUM
ejpam-3737	164	4	,	,	PUNCT
ejpam-3737	164	5	st	st	PROPN
ejpam-3737	164	6	constantine	constantine	PROPN
ejpam-3737	164	7	and	and	CCONJ
ejpam-3737	164	8	helena	helena	PROPN
ejpam-3737	164	9	,	,	PUNCT
ejpam-3737	164	10	2019	2019	NUM
ejpam-3737	164	11	.	.	PUNCT
ejpam-3737	165	1	sixth	sixth	ADJ
ejpam-3737	165	2	international	international	ADJ
ejpam-3737	165	3	conference	conference	NOUN
ejpam-3737	165	4	on	on	ADP
ejpam-3737	165	5	new	new	ADJ
ejpam-3737	165	6	trends	trend	NOUN
ejpam-3737	165	7	in	in	ADP
ejpam-3737	165	8	the	the	DET
ejpam-3737	165	9	applications	application	NOUN
ejpam-3737	165	10	of	of	ADP
ejpam-3737	165	11	differential	differential	ADJ
ejpam-3737	165	12	equations	equation	NOUN
ejpam-3737	165	13	in	in	ADP
ejpam-3737	165	14	sciences	science	NOUN
ejpam-3737	165	15	.	.	PUNCT
ejpam-3737	166	1	[	[	X
ejpam-3737	166	2	3	3	X
ejpam-3737	166	3	]	]	PUNCT
ejpam-3737	166	4	t	t	PROPN
ejpam-3737	166	5	stoyanov	stoyanov	PROPN
ejpam-3737	166	6	.	.	PUNCT
ejpam-3737	167	1	about	about	ADP
ejpam-3737	167	2	the	the	DET
ejpam-3737	167	3	zeros	zero	NOUN
ejpam-3737	167	4	of	of	ADP
ejpam-3737	167	5	some	some	DET
ejpam-3737	167	6	entire	entire	ADJ
ejpam-3737	167	7	functions	function	NOUN
ejpam-3737	167	8	and	and	CCONJ
ejpam-3737	167	9	their	their	PRON
ejpam-3737	167	10	derivatives	derivative	NOUN
ejpam-3737	167	11	.	.	PUNCT
ejpam-3737	168	1	journal	journal	NOUN
ejpam-3737	168	2	of	of	ADP
ejpam-3737	168	3	the	the	DET
ejpam-3737	168	4	australian	australian	ADJ
ejpam-3737	168	5	mathematical	mathematical	ADJ
ejpam-3737	168	6	society	society	NOUN
ejpam-3737	168	7	,	,	PUNCT
ejpam-3737	168	8	68:165–169	68:165–169	PROPN
ejpam-3737	168	9	,	,	PUNCT
ejpam-3737	168	10	2000	2000	NUM
ejpam-3737	168	11	.	.	PUNCT
ejpam-3737	169	1	[	[	X
ejpam-3737	169	2	4	4	X
ejpam-3737	169	3	]	]	PUNCT
ejpam-3737	169	4	t	t	PROPN
ejpam-3737	169	5	stoyanov	stoyanov	PROPN
ejpam-3737	169	6	.	.	PUNCT
ejpam-3737	170	1	some	some	DET
ejpam-3737	170	2	estimates	estimate	NOUN
ejpam-3737	170	3	below	below	ADP
ejpam-3737	170	4	the	the	DET
ejpam-3737	170	5	modulus	modulus	NOUN
ejpam-3737	170	6	of	of	ADP
ejpam-3737	170	7	integrals	integral	NOUN
ejpam-3737	170	8	of	of	ADP
ejpam-3737	170	9	some	some	DET
ejpam-3737	170	10	polynomials	polynomial	NOUN
ejpam-3737	170	11	in	in	ADP
ejpam-3737	170	12	the	the	DET
ejpam-3737	170	13	complex	complex	ADJ
ejpam-3737	170	14	plane	plane	NOUN
ejpam-3737	170	15	.	.	PUNCT
ejpam-3737	171	1	european	european	PROPN
ejpam-3737	171	2	journal	journal	PROPN
ejpam-3737	171	3	of	of	ADP
ejpam-3737	171	4	pure	pure	ADJ
ejpam-3737	171	5	and	and	CCONJ
ejpam-3737	171	6	applied	applied	ADJ
ejpam-3737	171	7	mathematics	mathematic	NOUN
ejpam-3737	171	8	,	,	PUNCT
ejpam-3737	171	9	12(2):649	12(2):649	NUM
ejpam-3737	171	10	–	–	PUNCT
ejpam-3737	171	11	653	653	NUM
ejpam-3737	171	12	,	,	PUNCT
ejpam-3737	171	13	2019	2019	NUM
ejpam-3737	171	14	.	.	PUNCT
ejpam-3737	172	1	[	[	X
ejpam-3737	172	2	5	5	NUM
ejpam-3737	172	3	]	]	PUNCT
ejpam-3737	172	4	t	t	X
ejpam-3737	172	5	zapryanova	zapryanova	PROPN
ejpam-3737	172	6	and	and	CCONJ
ejpam-3737	172	7	d	d	NOUN
ejpam-3737	172	8	souroujon	souroujon	NOUN
ejpam-3737	172	9	.	.	PUNCT
ejpam-3737	173	1	on	on	ADP
ejpam-3737	173	2	the	the	DET
ejpam-3737	173	3	iterates	iterate	NOUN
ejpam-3737	173	4	of	of	ADP
ejpam-3737	173	5	jackson	jackson	PROPN
ejpam-3737	173	6	type	type	PROPN
ejpam-3737	173	7	operator	operator	NOUN
ejpam-3737	173	8	gs	gs	PROPN
ejpam-3737	173	9	,	,	PUNCT
ejpam-3737	173	10	n.	n.	PROPN
ejpam-3737	173	11	mediterr	mediterr	PROPN
ejpam-3737	173	12	.	.	PUNCT
ejpam-3737	174	1	j.	j.	PROPN
ejpam-3737	174	2	math	math	PROPN
ejpam-3737	174	3	,	,	PUNCT
ejpam-3737	174	4	13:5053–5061	13:5053–5061	NUM
ejpam-3737	174	5	,	,	PUNCT
ejpam-3737	174	6	2016	2016	NUM
ejpam-3737	174	7	.	.	PUNCT