id	sid	tid	token	lemma	pos
ejpam-3736	1	1	european	european	PROPN
ejpam-3736	1	2	journal	journal	PROPN
ejpam-3736	1	3	of	of	ADP
ejpam-3736	1	4	pure	pure	ADJ
ejpam-3736	1	5	and	and	CCONJ
ejpam-3736	1	6	applied	apply	VERB
ejpam-3736	1	7	mathematics	mathematic	NOUN
ejpam-3736	1	8	vol	vol	NOUN
ejpam-3736	1	9	.	.	PROPN
ejpam-3736	2	1	13	13	NUM
ejpam-3736	2	2	,	,	PUNCT
ejpam-3736	2	3	no	no	INTJ
ejpam-3736	2	4	.	.	NOUN
ejpam-3736	2	5	3	3	NUM
ejpam-3736	2	6	,	,	PUNCT
ejpam-3736	2	7	2020	2020	NUM
ejpam-3736	2	8	,	,	PUNCT
ejpam-3736	2	9	663	663	NUM
ejpam-3736	2	10	-	-	SYM
ejpam-3736	2	11	673	673	NUM
ejpam-3736	2	12	issn	issn	PROPN
ejpam-3736	2	13	1307	1307	NUM
ejpam-3736	2	14	-	-	SYM
ejpam-3736	2	15	5543	5543	NUM
ejpam-3736	2	16	–	–	PUNCT
ejpam-3736	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3736	2	18	published	publish	VERB
ejpam-3736	2	19	by	by	ADP
ejpam-3736	2	20	new	new	PROPN
ejpam-3736	2	21	york	york	PROPN
ejpam-3736	2	22	business	business	PROPN
ejpam-3736	2	23	global	global	ADJ
ejpam-3736	2	24	some	some	DET
ejpam-3736	2	25	localization	localization	NOUN
ejpam-3736	2	26	of	of	ADP
ejpam-3736	2	27	the	the	DET
ejpam-3736	2	28	zeros	zero	NOUN
ejpam-3736	2	29	of	of	ADP
ejpam-3736	2	30	the	the	DET
ejpam-3736	2	31	third	third	ADJ
ejpam-3736	2	32	derivative	derivative	NOUN
ejpam-3736	2	33	of	of	ADP
ejpam-3736	2	34	a	a	DET
ejpam-3736	2	35	complex	complex	ADJ
ejpam-3736	2	36	polynomial	polynomial	NOUN
ejpam-3736	2	37	in	in	ADP
ejpam-3736	2	38	the	the	DET
ejpam-3736	2	39	disks	disk	NOUN
ejpam-3736	2	40	or	or	CCONJ
ejpam-3736	2	41	generalized	generalize	VERB
ejpam-3736	2	42	cardioid	cardioid	NOUN
ejpam-3736	2	43	interiors	interior	NOUN
ejpam-3736	2	44	todor	todor	PROPN
ejpam-3736	2	45	stoyanov	stoyanov	PROPN
ejpam-3736	2	46	stoyanov	stoyanov	PROPN
ejpam-3736	2	47	department	department	PROPN
ejpam-3736	2	48	of	of	ADP
ejpam-3736	2	49	mathematics	mathematics	PROPN
ejpam-3736	2	50	,	,	PUNCT
ejpam-3736	2	51	university	university	NOUN
ejpam-3736	2	52	of	of	ADP
ejpam-3736	2	53	economics	economics	PROPN
ejpam-3736	2	54	,	,	PUNCT
ejpam-3736	2	55	bul	bul	PROPN
ejpam-3736	2	56	.	.	PUNCT
ejpam-3736	3	1	knyaz	knyaz	PROPN
ejpam-3736	3	2	boris	boris	PROPN
ejpam-3736	3	3	i	i	PRON
ejpam-3736	3	4	77	77	NUM
ejpam-3736	3	5	,	,	PUNCT
ejpam-3736	3	6	varna	varna	ADJ
ejpam-3736	3	7	9002	9002	NUM
ejpam-3736	3	8	,	,	PUNCT
ejpam-3736	3	9	bulgaria	bulgaria	PROPN
ejpam-3736	3	10	abstract	abstract	NOUN
ejpam-3736	3	11	.	.	PUNCT
ejpam-3736	4	1	in	in	ADP
ejpam-3736	4	2	this	this	DET
ejpam-3736	4	3	paper	paper	NOUN
ejpam-3736	4	4	,	,	PUNCT
ejpam-3736	4	5	we	we	PRON
ejpam-3736	4	6	localize	localize	VERB
ejpam-3736	4	7	the	the	DET
ejpam-3736	4	8	zeros	zero	NOUN
ejpam-3736	4	9	of	of	ADP
ejpam-3736	4	10	the	the	DET
ejpam-3736	4	11	third	third	ADJ
ejpam-3736	4	12	derivatives	derivative	NOUN
ejpam-3736	4	13	of	of	ADP
ejpam-3736	4	14	a	a	DET
ejpam-3736	4	15	complex	complex	ADJ
ejpam-3736	4	16	polynomial	polynomial	NOUN
ejpam-3736	4	17	in	in	ADP
ejpam-3736	4	18	some	some	DET
ejpam-3736	4	19	sets	set	NOUN
ejpam-3736	4	20	.	.	PUNCT
ejpam-3736	5	1	these	these	DET
ejpam-3736	5	2	sets	set	NOUN
ejpam-3736	5	3	are	be	AUX
ejpam-3736	5	4	relevant	relevant	ADJ
ejpam-3736	5	5	to	to	ADP
ejpam-3736	5	6	the	the	DET
ejpam-3736	5	7	first	first	ADJ
ejpam-3736	5	8	,	,	PUNCT
ejpam-3736	5	9	second	second	ADJ
ejpam-3736	5	10	and	and	CCONJ
ejpam-3736	5	11	third	third	ADJ
ejpam-3736	5	12	derivative	derivative	NOUN
ejpam-3736	5	13	of	of	ADP
ejpam-3736	5	14	the	the	DET
ejpam-3736	5	15	polynomial	polynomial	ADJ
ejpam-3736	5	16	,	,	PUNCT
ejpam-3736	5	17	and	and	CCONJ
ejpam-3736	5	18	they	they	PRON
ejpam-3736	5	19	are	be	AUX
ejpam-3736	5	20	respectively	respectively	ADV
ejpam-3736	5	21	disks	disk	NOUN
ejpam-3736	5	22	and	and	CCONJ
ejpam-3736	5	23	cardioid	cardioid	NOUN
ejpam-3736	5	24	interiors	interior	NOUN
ejpam-3736	5	25	or	or	CCONJ
ejpam-3736	5	26	generalized	generalize	VERB
ejpam-3736	5	27	cardioid	cardioid	NOUN
ejpam-3736	5	28	interiors	interior	NOUN
ejpam-3736	5	29	.	.	PUNCT
ejpam-3736	6	1	here	here	ADV
ejpam-3736	6	2	,	,	PUNCT
ejpam-3736	6	3	for	for	ADP
ejpam-3736	6	4	the	the	DET
ejpam-3736	6	5	first	first	ADJ
ejpam-3736	6	6	time	time	NOUN
ejpam-3736	6	7	we	we	PRON
ejpam-3736	6	8	consider	consider	VERB
ejpam-3736	6	9	generalized	generalized	ADJ
ejpam-3736	6	10	cardioids	cardioid	NOUN
ejpam-3736	6	11	,	,	PUNCT
ejpam-3736	6	12	as	as	ADP
ejpam-3736	6	13	the	the	DET
ejpam-3736	6	14	areas	area	NOUN
ejpam-3736	6	15	of	of	ADP
ejpam-3736	6	16	zeros	zero	NOUN
ejpam-3736	6	17	.	.	PUNCT
ejpam-3736	6	18	2020	2020	NUM
ejpam-3736	6	19	mathematics	mathematic	NOUN
ejpam-3736	6	20	subject	subject	NOUN
ejpam-3736	6	21	classifications	classification	NOUN
ejpam-3736	6	22	:	:	PUNCT
ejpam-3736	6	23	30d20	30d20	NUM
ejpam-3736	6	24	key	key	ADJ
ejpam-3736	6	25	words	word	NOUN
ejpam-3736	6	26	and	and	CCONJ
ejpam-3736	6	27	phrases	phrase	NOUN
ejpam-3736	6	28	:	:	PUNCT
ejpam-3736	6	29	zeros	zero	NOUN
ejpam-3736	6	30	,	,	PUNCT
ejpam-3736	6	31	complex	complex	ADJ
ejpam-3736	6	32	polynomial	polynomial	ADJ
ejpam-3736	6	33	,	,	PUNCT
ejpam-3736	6	34	disks	disk	NOUN
ejpam-3736	6	35	,	,	PUNCT
ejpam-3736	6	36	cardioid	cardioid	X
ejpam-3736	6	37	interiorities	interioritie	NOUN
ejpam-3736	6	38	1	1	NUM
ejpam-3736	6	39	.	.	PUNCT
ejpam-3736	6	40	introduction	introduction	NOUN
ejpam-3736	6	41	the	the	DET
ejpam-3736	6	42	localization	localization	NOUN
ejpam-3736	6	43	of	of	ADP
ejpam-3736	6	44	the	the	DET
ejpam-3736	6	45	zeros	zero	NOUN
ejpam-3736	6	46	of	of	ADP
ejpam-3736	6	47	the	the	DET
ejpam-3736	6	48	complex	complex	ADJ
ejpam-3736	6	49	polynomials	polynomial	NOUN
ejpam-3736	6	50	is	be	AUX
ejpam-3736	6	51	very	very	ADV
ejpam-3736	6	52	important	important	ADJ
ejpam-3736	6	53	area	area	NOUN
ejpam-3736	6	54	of	of	ADP
ejpam-3736	6	55	the	the	DET
ejpam-3736	6	56	mathematics	mathematic	NOUN
ejpam-3736	6	57	.	.	PUNCT
ejpam-3736	7	1	the	the	DET
ejpam-3736	7	2	impossibility	impossibility	NOUN
ejpam-3736	7	3	to	to	PART
ejpam-3736	7	4	find	find	VERB
ejpam-3736	7	5	the	the	DET
ejpam-3736	7	6	zeros	zero	NOUN
ejpam-3736	7	7	of	of	ADP
ejpam-3736	7	8	any	any	DET
ejpam-3736	7	9	polynomials	polynomial	NOUN
ejpam-3736	7	10	using	use	VERB
ejpam-3736	7	11	the	the	DET
ejpam-3736	7	12	coefficients	coefficient	NOUN
ejpam-3736	7	13	makes	make	VERB
ejpam-3736	7	14	every	every	DET
ejpam-3736	7	15	statement	statement	NOUN
ejpam-3736	7	16	here	here	ADV
ejpam-3736	7	17	very	very	ADV
ejpam-3736	7	18	significant	significant	ADJ
ejpam-3736	7	19	.	.	PUNCT
ejpam-3736	8	1	there	there	PRON
ejpam-3736	8	2	exist	exist	VERB
ejpam-3736	8	3	many	many	ADJ
ejpam-3736	8	4	conjectures	conjecture	NOUN
ejpam-3736	8	5	which	which	PRON
ejpam-3736	8	6	are	be	AUX
ejpam-3736	8	7	not	not	PART
ejpam-3736	8	8	proved	prove	VERB
ejpam-3736	8	9	,	,	PUNCT
ejpam-3736	8	10	like	like	ADP
ejpam-3736	8	11	sendov	sendov	PROPN
ejpam-3736	8	12	’s	’s	PART
ejpam-3736	8	13	conjecture	conjecture	NOUN
ejpam-3736	8	14	,	,	PUNCT
ejpam-3736	8	15	obreshkoff	obreshkoff	ADJ
ejpam-3736	8	16	’s	’s	PART
ejpam-3736	8	17	conjecture	conjecture	NOUN
ejpam-3736	8	18	.	.	PUNCT
ejpam-3736	9	1	the	the	DET
ejpam-3736	9	2	assertions	assertion	NOUN
ejpam-3736	9	3	localize	localize	VERB
ejpam-3736	9	4	the	the	DET
ejpam-3736	9	5	zeros	zero	NOUN
ejpam-3736	9	6	of	of	ADP
ejpam-3736	9	7	the	the	DET
ejpam-3736	9	8	derivative	derivative	NOUN
ejpam-3736	9	9	of	of	ADP
ejpam-3736	9	10	the	the	DET
ejpam-3736	9	11	any	any	DET
ejpam-3736	9	12	complex	complex	ADJ
ejpam-3736	9	13	polynomial	polynomial	NOUN
ejpam-3736	9	14	in	in	ADP
ejpam-3736	9	15	some	some	DET
ejpam-3736	9	16	areas	area	NOUN
ejpam-3736	9	17	.	.	PUNCT
ejpam-3736	10	1	here	here	ADV
ejpam-3736	10	2	we	we	PRON
ejpam-3736	10	3	present	present	VERB
ejpam-3736	10	4	some	some	DET
ejpam-3736	10	5	new	new	ADJ
ejpam-3736	10	6	results	result	NOUN
ejpam-3736	10	7	about	about	ADP
ejpam-3736	10	8	the	the	DET
ejpam-3736	10	9	zeros	zero	NOUN
ejpam-3736	10	10	of	of	ADP
ejpam-3736	10	11	the	the	DET
ejpam-3736	10	12	derivative	derivative	NOUN
ejpam-3736	10	13	of	of	ADP
ejpam-3736	10	14	the	the	DET
ejpam-3736	10	15	complex	complex	ADJ
ejpam-3736	10	16	polynomials	polynomial	NOUN
ejpam-3736	10	17	.	.	PUNCT
ejpam-3736	11	1	theorem	theorem	NOUN
ejpam-3736	11	2	1	1	NUM
ejpam-3736	11	3	could	could	AUX
ejpam-3736	11	4	be	be	AUX
ejpam-3736	11	5	seen	see	VERB
ejpam-3736	11	6	in	in	ADP
ejpam-3736	11	7	[	[	X
ejpam-3736	11	8	3	3	NUM
ejpam-3736	11	9	]	]	PUNCT
ejpam-3736	11	10	.	.	PUNCT
ejpam-3736	12	1	theorem	theorem	ADJ
ejpam-3736	12	2	3	3	NUM
ejpam-3736	12	3	,	,	PUNCT
ejpam-3736	12	4	theorem	theorem	VERB
ejpam-3736	12	5	4	4	NUM
ejpam-3736	12	6	and	and	CCONJ
ejpam-3736	12	7	theorem	theorem	VERB
ejpam-3736	12	8	5	5	NUM
ejpam-3736	12	9	we	we	PRON
ejpam-3736	12	10	can	can	AUX
ejpam-3736	12	11	see	see	VERB
ejpam-3736	12	12	in	in	ADP
ejpam-3736	12	13	[	[	X
ejpam-3736	12	14	4	4	NUM
ejpam-3736	12	15	]	]	PUNCT
ejpam-3736	12	16	.	.	PUNCT
ejpam-3736	13	1	their	their	PRON
ejpam-3736	13	2	results	result	NOUN
ejpam-3736	13	3	could	could	AUX
ejpam-3736	13	4	be	be	AUX
ejpam-3736	13	5	applied	apply	VERB
ejpam-3736	13	6	for	for	ADP
ejpam-3736	13	7	the	the	DET
ejpam-3736	13	8	localization	localization	NOUN
ejpam-3736	13	9	of	of	ADP
ejpam-3736	13	10	the	the	DET
ejpam-3736	13	11	zeros	zero	NOUN
ejpam-3736	13	12	of	of	ADP
ejpam-3736	13	13	the	the	DET
ejpam-3736	13	14	derivative	derivative	NOUN
ejpam-3736	13	15	of	of	ADP
ejpam-3736	13	16	the	the	DET
ejpam-3736	13	17	polynomialsthese	polynomialsthese	NOUN
ejpam-3736	13	18	are	be	AUX
ejpam-3736	13	19	theorem	theorem	VERB
ejpam-3736	13	20	3	3	NUM
ejpam-3736	13	21	and	and	CCONJ
ejpam-3736	13	22	theorem	theorem	VERB
ejpam-3736	13	23	4	4	NUM
ejpam-3736	13	24	.	.	PUNCT
ejpam-3736	13	25	in	in	ADP
ejpam-3736	13	26	theorem	theorem	NOUN
ejpam-3736	13	27	5	5	NUM
ejpam-3736	13	28	we	we	PRON
ejpam-3736	13	29	localize	localize	VERB
ejpam-3736	13	30	the	the	DET
ejpam-3736	13	31	zeros	zero	NOUN
ejpam-3736	13	32	of	of	ADP
ejpam-3736	13	33	the	the	DET
ejpam-3736	13	34	second	second	ADJ
ejpam-3736	13	35	derivative	derivative	NOUN
ejpam-3736	13	36	of	of	ADP
ejpam-3736	13	37	the	the	DET
ejpam-3736	13	38	complex	complex	ADJ
ejpam-3736	13	39	polynomial	polynomial	ADJ
ejpam-3736	13	40	.	.	PUNCT
ejpam-3736	14	1	theorem	theorem	NOUN
ejpam-3736	14	2	6	6	NUM
ejpam-3736	14	3	and	and	CCONJ
ejpam-3736	14	4	the	the	DET
ejpam-3736	14	5	corollary	corollary	NOUN
ejpam-3736	14	6	could	could	AUX
ejpam-3736	14	7	be	be	AUX
ejpam-3736	14	8	used	use	VERB
ejpam-3736	14	9	everywhere	everywhere	ADV
ejpam-3736	14	10	in	in	ADP
ejpam-3736	14	11	the	the	DET
ejpam-3736	14	12	fields	field	NOUN
ejpam-3736	14	13	of	of	ADP
ejpam-3736	14	14	mathematics	mathematic	NOUN
ejpam-3736	14	15	,	,	PUNCT
ejpam-3736	14	16	independently	independently	ADV
ejpam-3736	14	17	of	of	ADP
ejpam-3736	14	18	their	their	PRON
ejpam-3736	14	19	application	application	NOUN
ejpam-3736	14	20	here	here	ADV
ejpam-3736	14	21	in	in	ADP
ejpam-3736	14	22	theorem	theorem	ADJ
ejpam-3736	14	23	7	7	NUM
ejpam-3736	14	24	.	.	PUNCT
ejpam-3736	14	25	theorem	theorem	VERB
ejpam-3736	14	26	7	7	NUM
ejpam-3736	14	27	appears	appear	VERB
ejpam-3736	14	28	the	the	DET
ejpam-3736	14	29	main	main	ADJ
ejpam-3736	14	30	result	result	NOUN
ejpam-3736	14	31	of	of	ADP
ejpam-3736	14	32	the	the	DET
ejpam-3736	14	33	article	article	NOUN
ejpam-3736	14	34	.	.	PUNCT
ejpam-3736	15	1	for	for	ADP
ejpam-3736	15	2	the	the	DET
ejpam-3736	15	3	first	first	ADJ
ejpam-3736	15	4	time	time	NOUN
ejpam-3736	15	5	here	here	ADV
ejpam-3736	15	6	,	,	PUNCT
ejpam-3736	15	7	we	we	PRON
ejpam-3736	15	8	consider	consider	VERB
ejpam-3736	15	9	a	a	DET
ejpam-3736	15	10	generalized	generalized	ADJ
ejpam-3736	15	11	cardioid	cardioid	NOUN
ejpam-3736	15	12	.	.	PUNCT
ejpam-3736	16	1	we	we	PRON
ejpam-3736	16	2	see	see	VERB
ejpam-3736	16	3	that	that	SCONJ
ejpam-3736	16	4	the	the	DET
ejpam-3736	16	5	roots	root	NOUN
ejpam-3736	16	6	of	of	ADP
ejpam-3736	16	7	polynomial	polynomial	ADJ
ejpam-3736	16	8	must	must	AUX
ejpam-3736	16	9	belong	belong	VERB
ejpam-3736	16	10	to	to	ADP
ejpam-3736	16	11	the	the	DET
ejpam-3736	16	12	generalized	generalized	ADJ
ejpam-3736	16	13	cardioid	cardioid	NOUN
ejpam-3736	16	14	interiorities	interioritie	NOUN
ejpam-3736	16	15	,	,	PUNCT
ejpam-3736	16	16	created	create	VERB
ejpam-3736	16	17	by	by	ADP
ejpam-3736	16	18	the	the	DET
ejpam-3736	16	19	zeros	zero	NOUN
ejpam-3736	16	20	of	of	ADP
ejpam-3736	16	21	the	the	DET
ejpam-3736	16	22	given	give	VERB
ejpam-3736	16	23	polynomial	polynomial	NOUN
ejpam-3736	16	24	.	.	PUNCT
ejpam-3736	17	1	many	many	ADJ
ejpam-3736	17	2	of	of	ADP
ejpam-3736	17	3	these	these	DET
ejpam-3736	17	4	results	result	NOUN
ejpam-3736	17	5	could	could	AUX
ejpam-3736	17	6	be	be	AUX
ejpam-3736	17	7	applied	apply	VERB
ejpam-3736	17	8	for	for	ADP
ejpam-3736	17	9	the	the	DET
ejpam-3736	17	10	solving	solving	NOUN
ejpam-3736	17	11	of	of	ADP
ejpam-3736	17	12	the	the	DET
ejpam-3736	17	13	unproved	unproved	ADJ
ejpam-3736	17	14	conjectures	conjecture	NOUN
ejpam-3736	17	15	.	.	PUNCT
ejpam-3736	18	1	especially	especially	ADV
ejpam-3736	18	2	that	that	PRON
ejpam-3736	18	3	could	could	AUX
ejpam-3736	18	4	be	be	AUX
ejpam-3736	18	5	seen	see	VERB
ejpam-3736	18	6	in	in	ADP
ejpam-3736	18	7	[	[	X
ejpam-3736	18	8	1	1	NUM
ejpam-3736	18	9	]	]	PUNCT
ejpam-3736	18	10	.	.	PUNCT
ejpam-3736	19	1	other	other	ADJ
ejpam-3736	19	2	possibilities	possibility	NOUN
ejpam-3736	19	3	are	be	AUX
ejpam-3736	19	4	[	[	X
ejpam-3736	19	5	2	2	NUM
ejpam-3736	19	6	,	,	PUNCT
ejpam-3736	19	7	5	5	NUM
ejpam-3736	19	8	]	]	PUNCT
ejpam-3736	19	9	and	and	CCONJ
ejpam-3736	19	10	[	[	X
ejpam-3736	19	11	6	6	NUM
ejpam-3736	19	12	]	]	PUNCT
ejpam-3736	19	13	.	.	PUNCT
ejpam-3736	20	1	doi	doi	NOUN
ejpam-3736	20	2	:	:	PUNCT
ejpam-3736	20	3	https://doi.org/10.29020/nybg.ejpam.v13i3.3736	https://doi.org/10.29020/nybg.ejpam.v13i3.3736	PROPN
ejpam-3736	20	4	email	email	NOUN
ejpam-3736	20	5	address	address	NOUN
ejpam-3736	20	6	:	:	PUNCT
ejpam-3736	20	7	todstoyanov@yahoo.com	todstoyanov@yahoo.com	X
ejpam-3736	20	8	(	(	PUNCT
ejpam-3736	20	9	t.	t.	PROPN
ejpam-3736	20	10	s.	s.	PROPN
ejpam-3736	20	11	stoyanov	stoyanov	PROPN
ejpam-3736	20	12	)	)	PUNCT
ejpam-3736	20	13	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-3736	21	1	663	663	NUM
ejpam-3736	22	1	c	c	NOUN
ejpam-3736	22	2	©	©	NOUN
ejpam-3736	22	3	2020	2020	NUM
ejpam-3736	22	4	ejpam	ejpam	VERB
ejpam-3736	22	5	all	all	DET
ejpam-3736	22	6	rights	right	NOUN
ejpam-3736	22	7	reserved	reserve	VERB
ejpam-3736	22	8	.	.	PUNCT
ejpam-3736	23	1	t.	t.	PROPN
ejpam-3736	23	2	s.	s.	PROPN
ejpam-3736	23	3	stoyanov	stoyanov	PROPN
ejpam-3736	23	4	/	/	SYM
ejpam-3736	23	5	eur	eur	PROPN
ejpam-3736	23	6	.	.	PUNCT
ejpam-3736	24	1	j.	j.	PROPN
ejpam-3736	24	2	pure	pure	PROPN
ejpam-3736	24	3	appl	appl	PROPN
ejpam-3736	24	4	.	.	PROPN
ejpam-3736	24	5	math	math	PROPN
ejpam-3736	24	6	,	,	PUNCT
ejpam-3736	24	7	13	13	NUM
ejpam-3736	24	8	(	(	PUNCT
ejpam-3736	24	9	3	3	NUM
ejpam-3736	24	10	)	)	PUNCT
ejpam-3736	24	11	(	(	PUNCT
ejpam-3736	24	12	2020	2020	NUM
ejpam-3736	24	13	)	)	PUNCT
ejpam-3736	24	14	,	,	PUNCT
ejpam-3736	24	15	663	663	NUM
ejpam-3736	24	16	-	-	SYM
ejpam-3736	24	17	673	673	NUM
ejpam-3736	24	18	664	664	NUM
ejpam-3736	24	19	2	2	NUM
ejpam-3736	24	20	.	.	PUNCT
ejpam-3736	24	21	preliminaries	preliminary	NOUN
ejpam-3736	24	22	we	we	PRON
ejpam-3736	24	23	note	note	VERB
ejpam-3736	24	24	:	:	PUNCT
ejpam-3736	24	25	d	d	X
ejpam-3736	24	26	(	(	PUNCT
ejpam-3736	24	27	a	a	DET
ejpam-3736	24	28	,	,	PUNCT
ejpam-3736	24	29	r	r	NOUN
ejpam-3736	24	30	)	)	PUNCT
ejpam-3736	24	31	=	=	NOUN
ejpam-3736	24	32	{	{	PUNCT
ejpam-3736	24	33	z	z	NOUN
ejpam-3736	24	34	∈	∈	PROPN
ejpam-3736	24	35	c	c	NOUN
ejpam-3736	24	36	:	:	PUNCT
ejpam-3736	24	37	|z	|z	PROPN
ejpam-3736	25	1	−	−	PROPN
ejpam-3736	25	2	a|	a|	X
ejpam-3736	25	3	<	<	X
ejpam-3736	25	4	r	r	X
ejpam-3736	25	5	}	}	PUNCT
ejpam-3736	25	6	is	be	AUX
ejpam-3736	25	7	the	the	DET
ejpam-3736	25	8	open	open	ADJ
ejpam-3736	25	9	disk	disk	NOUN
ejpam-3736	25	10	.	.	PUNCT
ejpam-3736	26	1	d	d	X
ejpam-3736	26	2	(	(	PUNCT
ejpam-3736	26	3	a	a	PRON
ejpam-3736	26	4	,	,	PUNCT
ejpam-3736	26	5	r	r	NOUN
ejpam-3736	26	6	)	)	PUNCT
ejpam-3736	26	7	=	=	NOUN
ejpam-3736	26	8	{	{	PUNCT
ejpam-3736	26	9	z	z	NOUN
ejpam-3736	26	10	∈	∈	PROPN
ejpam-3736	26	11	c	c	NOUN
ejpam-3736	26	12	:	:	PUNCT
ejpam-3736	26	13	|z	|z	PROPN
ejpam-3736	27	1	−	−	PROPN
ejpam-3736	27	2	a|	a|	PROPN
ejpam-3736	27	3	≤	≤	PROPN
ejpam-3736	27	4	r	r	NOUN
ejpam-3736	27	5	}	}	PUNCT
ejpam-3736	27	6	is	be	AUX
ejpam-3736	27	7	the	the	DET
ejpam-3736	27	8	closed	closed	ADJ
ejpam-3736	27	9	disk	disk	NOUN
ejpam-3736	27	10	.	.	PUNCT
ejpam-3736	28	1	c(a	c(a	PROPN
ejpam-3736	28	2	,	,	PUNCT
ejpam-3736	28	3	r	r	NOUN
ejpam-3736	28	4	)	)	PUNCT
ejpam-3736	28	5	–	–	PUNCT
ejpam-3736	28	6	the	the	DET
ejpam-3736	28	7	open	open	ADJ
ejpam-3736	28	8	cardioid	cardioid	ADJ
ejpam-3736	28	9	interior	interior	NOUN
ejpam-3736	28	10	–	–	PUNCT
ejpam-3736	28	11	how	how	SCONJ
ejpam-3736	28	12	to	to	PART
ejpam-3736	28	13	define	define	VERB
ejpam-3736	28	14	it	it	PRON
ejpam-3736	28	15	:	:	PUNCT
ejpam-3736	28	16	after	after	SCONJ
ejpam-3736	28	17	translation	translation	PROPN
ejpam-3736	28	18	t	t	PROPN
ejpam-3736	28	19	,	,	PUNCT
ejpam-3736	28	20	t	t	PROPN
ejpam-3736	28	21	(	(	PUNCT
ejpam-3736	28	22	a	a	NOUN
ejpam-3736	28	23	)	)	PUNCT
ejpam-3736	28	24	=	=	SYM
ejpam-3736	28	25	r	r	NOUN
ejpam-3736	28	26	∈	∈	NOUN
ejpam-3736	28	27	r	r	NOUN
ejpam-3736	28	28	and	and	CCONJ
ejpam-3736	28	29	then	then	ADV
ejpam-3736	28	30	rotation	rotation	VERB
ejpam-3736	28	31	with	with	ADP
ejpam-3736	28	32	angle	angle	NOUN
ejpam-3736	28	33	ϕ	ϕ	NOUN
ejpam-3736	28	34	=	=	PROPN
ejpam-3736	28	35	−arg	−arg	NOUN
ejpam-3736	28	36	a	a	NOUN
ejpam-3736	28	37	;	;	PUNCT
ejpam-3736	28	38	a	a	DET
ejpam-3736	28	39	∈	∈	PROPN
ejpam-3736	28	40	c.	c.	NOUN
ejpam-3736	28	41	then	then	ADV
ejpam-3736	28	42	coordinates	coordinate	NOUN
ejpam-3736	28	43	must	must	AUX
ejpam-3736	28	44	satisfy	satisfy	VERB
ejpam-3736	28	45	(	(	PUNCT
ejpam-3736	28	46	x2	x2	PROPN
ejpam-3736	29	1	+	+	CCONJ
ejpam-3736	29	2	y2	y2	NOUN
ejpam-3736	29	3	−	−	PROPN
ejpam-3736	29	4	2rx	2rx	NOUN
ejpam-3736	29	5	)	)	PUNCT
ejpam-3736	29	6	2	2	NUM
ejpam-3736	29	7	<	<	X
ejpam-3736	29	8	4r2(x2	4r2(x2	NOUN
ejpam-3736	29	9	+	+	CCONJ
ejpam-3736	29	10	y2	y2	NOUN
ejpam-3736	29	11	)	)	PUNCT
ejpam-3736	29	12	.	.	PUNCT
ejpam-3736	30	1	figure	figure	NOUN
ejpam-3736	30	2	1	1	NUM
ejpam-3736	30	3	:	:	PUNCT
ejpam-3736	30	4	c(a	c(a	ADV
ejpam-3736	30	5	,	,	PUNCT
ejpam-3736	30	6	r	r	NOUN
ejpam-3736	30	7	)	)	PUNCT
ejpam-3736	30	8	–	–	PUNCT
ejpam-3736	30	9	the	the	DET
ejpam-3736	30	10	closed	closed	ADJ
ejpam-3736	30	11	cardioid	cardioid	NOUN
ejpam-3736	30	12	interior	interior	NOUN
ejpam-3736	30	13	.	.	PUNCT
ejpam-3736	31	1	cq(a	cq(a	NOUN
ejpam-3736	31	2	,	,	PUNCT
ejpam-3736	31	3	r	r	NOUN
ejpam-3736	31	4	)	)	PUNCT
ejpam-3736	31	5	–	–	PUNCT
ejpam-3736	31	6	the	the	DET
ejpam-3736	31	7	open	open	ADJ
ejpam-3736	31	8	generalized	generalized	ADJ
ejpam-3736	31	9	cardioid	cardioid	ADJ
ejpam-3736	31	10	interior	interior	NOUN
ejpam-3736	31	11	–	–	PUNCT
ejpam-3736	31	12	how	how	SCONJ
ejpam-3736	31	13	define	define	VERB
ejpam-3736	31	14	it	it	PRON
ejpam-3736	31	15	:	:	PUNCT
ejpam-3736	31	16	after	after	SCONJ
ejpam-3736	31	17	translation	translation	PROPN
ejpam-3736	31	18	t	t	PROPN
ejpam-3736	31	19	,	,	PUNCT
ejpam-3736	31	20	t	t	PROPN
ejpam-3736	31	21	(	(	PUNCT
ejpam-3736	31	22	a	a	NOUN
ejpam-3736	31	23	)	)	PUNCT
ejpam-3736	31	24	=	=	SYM
ejpam-3736	31	25	r	r	NOUN
ejpam-3736	31	26	∈	∈	NOUN
ejpam-3736	31	27	r	r	NOUN
ejpam-3736	31	28	and	and	CCONJ
ejpam-3736	31	29	then	then	ADV
ejpam-3736	31	30	a	a	DET
ejpam-3736	31	31	rotation	rotation	NOUN
ejpam-3736	31	32	with	with	ADP
ejpam-3736	31	33	angle	angle	NOUN
ejpam-3736	31	34	ϕ	ϕ	NOUN
ejpam-3736	31	35	=	=	PROPN
ejpam-3736	31	36	−arg	−arg	NOUN
ejpam-3736	31	37	a	a	NOUN
ejpam-3736	31	38	;	;	PUNCT
ejpam-3736	31	39	a	a	DET
ejpam-3736	31	40	∈	∈	PROPN
ejpam-3736	31	41	r.	r.	NOUN
ejpam-3736	31	42	the	the	DET
ejpam-3736	31	43	coordinates	coordinate	NOUN
ejpam-3736	31	44	must	must	AUX
ejpam-3736	31	45	satisfy	satisfy	VERB
ejpam-3736	31	46	(	(	PUNCT
ejpam-3736	31	47	x2	x2	PROPN
ejpam-3736	31	48	+	+	CCONJ
ejpam-3736	32	1	y2	y2	NOUN
ejpam-3736	32	2	−	−	PROPN
ejpam-3736	32	3	2rx	2rx	ADV
ejpam-3736	32	4	)	)	PUNCT
ejpam-3736	33	1	<	<	X
ejpam-3736	33	2	4q2r2	4q2r2	PRON
ejpam-3736	34	1	(	(	PUNCT
ejpam-3736	34	2	x2	x2	NOUN
ejpam-3736	34	3	+	+	CCONJ
ejpam-3736	34	4	y2	y2	NOUN
ejpam-3736	34	5	)	)	PUNCT
ejpam-3736	34	6	cq(a	cq(a	NOUN
ejpam-3736	34	7	,	,	PUNCT
ejpam-3736	34	8	r	r	NOUN
ejpam-3736	34	9	)	)	PUNCT
ejpam-3736	34	10	–	–	PUNCT
ejpam-3736	34	11	the	the	DET
ejpam-3736	34	12	closed	closed	ADJ
ejpam-3736	34	13	generalized	generalized	ADJ
ejpam-3736	34	14	cardioid	cardioid	NOUN
ejpam-3736	34	15	interior	interior	NOUN
ejpam-3736	34	16	.	.	PUNCT
ejpam-3736	35	1	sendov	sendov	PROPN
ejpam-3736	35	2	’s	’s	PART
ejpam-3736	35	3	conjecture	conjecture	NOUN
ejpam-3736	35	4	:	:	PUNCT
ejpam-3736	35	5	let	let	VERB
ejpam-3736	35	6	us	we	PRON
ejpam-3736	35	7	put	put	VERB
ejpam-3736	35	8	for	for	ADP
ejpam-3736	35	9	n	n	PRON
ejpam-3736	35	10	≥	≥	NOUN
ejpam-3736	35	11	2	2	NUM
ejpam-3736	35	12	,	,	PUNCT
ejpam-3736	35	13	p	p	X
ejpam-3736	35	14	(	(	PUNCT
ejpam-3736	35	15	z	z	NOUN
ejpam-3736	35	16	)	)	PUNCT
ejpam-3736	35	17	=	=	PRON
ejpam-3736	35	18	∏n	∏n	ADJ
ejpam-3736	35	19	k=1	k=1	X
ejpam-3736	36	1	(	(	PUNCT
ejpam-3736	36	2	z	z	NOUN
ejpam-3736	36	3	−	−	PROPN
ejpam-3736	36	4	zk	zk	PROPN
ejpam-3736	36	5	)	)	PUNCT
ejpam-3736	36	6	,	,	PUNCT
ejpam-3736	36	7	where	where	SCONJ
ejpam-3736	36	8	zk	zk	PROPN
ejpam-3736	36	9	∈	∈	PROPN
ejpam-3736	36	10	d	d	X
ejpam-3736	36	11	(	(	PUNCT
ejpam-3736	36	12	0	0	NUM
ejpam-3736	36	13	,	,	PUNCT
ejpam-3736	36	14	1	1	NUM
ejpam-3736	36	15	)	)	PUNCT
ejpam-3736	36	16	,	,	PUNCT
ejpam-3736	36	17	k	k	PROPN
ejpam-3736	36	18	=	=	SYM
ejpam-3736	36	19	1	1	NUM
ejpam-3736	36	20	,	,	PUNCT
ejpam-3736	36	21	2	2	NUM
ejpam-3736	36	22	,	,	PUNCT
ejpam-3736	36	23	.	.	PUNCT
ejpam-3736	36	24	.	.	PUNCT
ejpam-3736	37	1	.	.	PUNCT
ejpam-3736	38	1	,	,	PUNCT
ejpam-3736	38	2	n.	n.	PROPN
ejpam-3736	38	3	then	then	ADV
ejpam-3736	38	4	p′(z	p′(z	NOUN
ejpam-3736	38	5	)	)	PUNCT
ejpam-3736	38	6	has	have	VERB
ejpam-3736	38	7	at	at	ADV
ejpam-3736	38	8	least	least	ADJ
ejpam-3736	38	9	one	one	NUM
ejpam-3736	38	10	zero	zero	NUM
ejpam-3736	38	11	in	in	ADP
ejpam-3736	38	12	each	each	PRON
ejpam-3736	38	13	of	of	ADP
ejpam-3736	38	14	the	the	DET
ejpam-3736	38	15	disks	disk	NOUN
ejpam-3736	38	16	d	d	X
ejpam-3736	38	17	(	(	PUNCT
ejpam-3736	38	18	zk	zk	PROPN
ejpam-3736	38	19	,	,	PUNCT
ejpam-3736	38	20	1	1	NUM
ejpam-3736	38	21	)	)	PUNCT
ejpam-3736	38	22	,	,	PUNCT
ejpam-3736	38	23	k	k	PROPN
ejpam-3736	39	1	=	=	SYM
ejpam-3736	39	2	1	1	NUM
ejpam-3736	39	3	,	,	PUNCT
ejpam-3736	39	4	2	2	NUM
ejpam-3736	39	5	,	,	PUNCT
ejpam-3736	39	6	.	.	PUNCT
ejpam-3736	39	7	.	.	PUNCT
ejpam-3736	39	8	.	.	PUNCT
ejpam-3736	40	1	n.	n.	NOUN
ejpam-3736	40	2	3	3	NUM
ejpam-3736	40	3	.	.	PUNCT
ejpam-3736	40	4	related	relate	VERB
ejpam-3736	40	5	results	result	NOUN
ejpam-3736	40	6	theorem	theorem	VERB
ejpam-3736	40	7	1	1	NUM
ejpam-3736	40	8	.	.	PUNCT
ejpam-3736	41	1	let	let	VERB
ejpam-3736	41	2	the	the	DET
ejpam-3736	41	3	zeros	zero	NOUN
ejpam-3736	41	4	zk	zk	PROPN
ejpam-3736	41	5	,	,	PUNCT
ejpam-3736	41	6	k	k	PROPN
ejpam-3736	41	7	=	=	SYM
ejpam-3736	41	8	1	1	NUM
ejpam-3736	41	9	,	,	PUNCT
ejpam-3736	41	10	2	2	NUM
ejpam-3736	41	11	,	,	PUNCT
ejpam-3736	41	12	.	.	PUNCT
ejpam-3736	41	13	.	.	PUNCT
ejpam-3736	42	1	.	.	PUNCT
ejpam-3736	43	1	,	,	PUNCT
ejpam-3736	43	2	n	n	PROPN
ejpam-3736	43	3	of	of	ADP
ejpam-3736	43	4	a	a	DET
ejpam-3736	43	5	polynomial	polynomial	ADJ
ejpam-3736	43	6	p(z	p(z	NOUN
ejpam-3736	43	7	)	)	PUNCT
ejpam-3736	43	8	∈	∈	PROPN
ejpam-3736	43	9	c[z	c[z	PROPN
ejpam-3736	43	10	]	]	X
ejpam-3736	43	11	satisfy	satisfy	NOUN
ejpam-3736	43	12	zk	zk	PROPN
ejpam-3736	43	13	∈	∈	PROPN
ejpam-3736	43	14	d(0	d(0	PROPN
ejpam-3736	43	15	,	,	PUNCT
ejpam-3736	43	16	1	1	NUM
ejpam-3736	43	17	)	)	PUNCT
ejpam-3736	43	18	.	.	PUNCT
ejpam-3736	44	1	then	then	ADV
ejpam-3736	44	2	the	the	DET
ejpam-3736	44	3	zeros	zero	NOUN
ejpam-3736	44	4	z	z	PROPN
ejpam-3736	44	5	of	of	ADP
ejpam-3736	44	6	the	the	DET
ejpam-3736	44	7	polynomial	polynomial	ADJ
ejpam-3736	44	8	q	q	NOUN
ejpam-3736	44	9	(	(	PUNCT
ejpam-3736	44	10	z	z	NOUN
ejpam-3736	44	11	)	)	PUNCT
ejpam-3736	44	12	=	=	SYM
ejpam-3736	44	13	γp	γp	PROPN
ejpam-3736	44	14	(	(	PUNCT
ejpam-3736	44	15	z	z	NOUN
ejpam-3736	44	16	)	)	PUNCT
ejpam-3736	44	17	+	+	CCONJ
ejpam-3736	44	18	zp′(z	zp′(z	NOUN
ejpam-3736	44	19	)	)	PUNCT
ejpam-3736	44	20	,	,	PUNCT
ejpam-3736	44	21	where	where	SCONJ
ejpam-3736	44	22	re	re	PRON
ejpam-3736	44	23	γ	γ	X
ejpam-3736	44	24	≥	≥	X
ejpam-3736	44	25	−n	−n	ADV
ejpam-3736	44	26	2	2	NUM
ejpam-3736	44	27	,	,	PUNCT
ejpam-3736	44	28	t.	t.	PROPN
ejpam-3736	44	29	s.	s.	PROPN
ejpam-3736	44	30	stoyanov	stoyanov	PROPN
ejpam-3736	44	31	/	/	SYM
ejpam-3736	44	32	eur	eur	PROPN
ejpam-3736	44	33	.	.	PUNCT
ejpam-3736	45	1	j.	j.	PROPN
ejpam-3736	45	2	pure	pure	PROPN
ejpam-3736	45	3	appl	appl	PROPN
ejpam-3736	45	4	.	.	PROPN
ejpam-3736	45	5	math	math	PROPN
ejpam-3736	45	6	,	,	PUNCT
ejpam-3736	45	7	13	13	NUM
ejpam-3736	45	8	(	(	PUNCT
ejpam-3736	45	9	3	3	NUM
ejpam-3736	45	10	)	)	PUNCT
ejpam-3736	45	11	(	(	PUNCT
ejpam-3736	45	12	2020	2020	NUM
ejpam-3736	45	13	)	)	PUNCT
ejpam-3736	45	14	,	,	PUNCT
ejpam-3736	45	15	663	663	NUM
ejpam-3736	45	16	-	-	SYM
ejpam-3736	45	17	673	673	NUM
ejpam-3736	45	18	665	665	NUM
ejpam-3736	45	19	satisfy	satisfy	NOUN
ejpam-3736	45	20	z	z	PROPN
ejpam-3736	45	21	∈	∈	PROPN
ejpam-3736	45	22	d(0	d(0	NOUN
ejpam-3736	45	23	,	,	PUNCT
ejpam-3736	45	24	1	1	NUM
ejpam-3736	45	25	)	)	PUNCT
ejpam-3736	45	26	.	.	PUNCT
ejpam-3736	46	1	proof	proof	NOUN
ejpam-3736	46	2	.	.	PUNCT
ejpam-3736	47	1	let	let	VERB
ejpam-3736	47	2	z	z	PRON
ejpam-3736	47	3	be	be	AUX
ejpam-3736	47	4	such	such	ADJ
ejpam-3736	47	5	that	that	DET
ejpam-3736	47	6	q(z	q(z	PROPN
ejpam-3736	47	7	)	)	PUNCT
ejpam-3736	47	8	=	=	SYM
ejpam-3736	47	9	0	0	NUM
ejpam-3736	47	10	and	and	CCONJ
ejpam-3736	47	11	p(z	p(z	NOUN
ejpam-3736	47	12	)	)	PUNCT
ejpam-3736	47	13	6=	6=	ADP
ejpam-3736	47	14	0	0	X
ejpam-3736	47	15	.	.	PUNCT
ejpam-3736	48	1	then	then	ADV
ejpam-3736	48	2	q	q	X
ejpam-3736	48	3	(	(	PUNCT
ejpam-3736	48	4	z	z	NOUN
ejpam-3736	48	5	)	)	PUNCT
ejpam-3736	48	6	p(z	p(z	NOUN
ejpam-3736	48	7	)	)	PUNCT
ejpam-3736	48	8	=	=	SYM
ejpam-3736	48	9	γ	γ	X
ejpam-3736	48	10	+	+	NOUN
ejpam-3736	48	11	z	z	PROPN
ejpam-3736	48	12	z	z	NOUN
ejpam-3736	48	13	−	−	NOUN
ejpam-3736	48	14	z1	z1	NOUN
ejpam-3736	48	15	+	+	CCONJ
ejpam-3736	48	16	·	·	PUNCT
ejpam-3736	48	17	·	·	PUNCT
ejpam-3736	48	18	·	·	PUNCT
ejpam-3736	49	1	+	+	NUM
ejpam-3736	49	2	z	z	NOUN
ejpam-3736	49	3	z	z	NOUN
ejpam-3736	49	4	−	−	PROPN
ejpam-3736	49	5	zk	zk	PROPN
ejpam-3736	49	6	=	=	SYM
ejpam-3736	49	7	0	0	PROPN
ejpam-3736	49	8	.	.	PUNCT
ejpam-3736	50	1	hence	hence	ADV
ejpam-3736	50	2	q	q	X
ejpam-3736	50	3	(	(	PUNCT
ejpam-3736	50	4	z	z	NOUN
ejpam-3736	50	5	)	)	PUNCT
ejpam-3736	50	6	p(z	p(z	NOUN
ejpam-3736	50	7	)	)	PUNCT
ejpam-3736	51	1	=	=	NOUN
ejpam-3736	51	2	γ	γ	X
ejpam-3736	51	3	+	+	NOUN
ejpam-3736	51	4	z	z	NOUN
ejpam-3736	51	5	2	2	NUM
ejpam-3736	51	6	−	−	PROPN
ejpam-3736	51	7	z1	z1	NOUN
ejpam-3736	51	8	2	2	NUM
ejpam-3736	51	9	+	+	CCONJ
ejpam-3736	51	10	z	z	NOUN
ejpam-3736	51	11	2	2	NUM
ejpam-3736	51	12	+	+	NOUN
ejpam-3736	51	13	z1	z1	X
ejpam-3736	51	14	2	2	NUM
ejpam-3736	51	15	z	z	NOUN
ejpam-3736	51	16	−	−	NOUN
ejpam-3736	51	17	z1	z1	NOUN
ejpam-3736	51	18	+	+	CCONJ
ejpam-3736	51	19	·	·	PUNCT
ejpam-3736	51	20	·	·	PUNCT
ejpam-3736	51	21	·	·	PUNCT
ejpam-3736	52	1	+	+	NUM
ejpam-3736	52	2	z	z	NOUN
ejpam-3736	52	3	2	2	NUM
ejpam-3736	52	4	−	−	NOUN
ejpam-3736	52	5	zn	zn	NOUN
ejpam-3736	52	6	2	2	NUM
ejpam-3736	52	7	+	+	CCONJ
ejpam-3736	52	8	z	z	NOUN
ejpam-3736	52	9	2	2	NUM
ejpam-3736	52	10	+	+	CCONJ
ejpam-3736	52	11	zn	zn	PROPN
ejpam-3736	52	12	2	2	NUM
ejpam-3736	52	13	z	z	NOUN
ejpam-3736	52	14	−	−	PROPN
ejpam-3736	52	15	zk	zk	X
ejpam-3736	52	16	=	=	SYM
ejpam-3736	52	17	0	0	PROPN
ejpam-3736	52	18	.	.	PUNCT
ejpam-3736	52	19	q	q	X
ejpam-3736	53	1	(	(	PUNCT
ejpam-3736	53	2	z	z	NOUN
ejpam-3736	53	3	)	)	PUNCT
ejpam-3736	53	4	p(z	p(z	NOUN
ejpam-3736	53	5	)	)	PUNCT
ejpam-3736	54	1	=	=	NOUN
ejpam-3736	54	2	γ	γ	X
ejpam-3736	54	3	+	+	NOUN
ejpam-3736	54	4	n	n	NUM
ejpam-3736	54	5	2	2	NUM
ejpam-3736	54	6	+	+	CCONJ
ejpam-3736	54	7	1	1	NUM
ejpam-3736	54	8	2	2	NUM
ejpam-3736	54	9	[	[	PUNCT
ejpam-3736	54	10	(	(	PUNCT
ejpam-3736	54	11	z	z	NOUN
ejpam-3736	54	12	+	+	NOUN
ejpam-3736	54	13	z1	z1	NUM
ejpam-3736	54	14	)	)	PUNCT
ejpam-3736	54	15	(	(	PUNCT
ejpam-3736	54	16	z	z	NOUN
ejpam-3736	54	17	−	−	PROPN
ejpam-3736	54	18	z1	z1	PROPN
ejpam-3736	54	19	)	)	PUNCT
ejpam-3736	54	20	|z	|z	PROPN
ejpam-3736	55	1	−	−	PROPN
ejpam-3736	55	2	z1|2	z1|2	PROPN
ejpam-3736	55	3	+	+	CCONJ
ejpam-3736	55	4	·	·	PUNCT
ejpam-3736	55	5	·	·	PUNCT
ejpam-3736	55	6	·	·	PUNCT
ejpam-3736	56	1	+	+	PUNCT
ejpam-3736	56	2	(	(	PUNCT
ejpam-3736	56	3	z	z	NOUN
ejpam-3736	56	4	+	+	NOUN
ejpam-3736	56	5	zn	zn	NUM
ejpam-3736	56	6	)	)	PUNCT
ejpam-3736	56	7	(	(	PUNCT
ejpam-3736	56	8	z	z	NOUN
ejpam-3736	56	9	−	−	NOUN
ejpam-3736	56	10	zn	zn	NUM
ejpam-3736	56	11	)	)	PUNCT
ejpam-3736	56	12	|z	|z	PROPN
ejpam-3736	57	1	−	−	PROPN
ejpam-3736	57	2	zn|2	zn|2	PROPN
ejpam-3736	57	3	]	]	X
ejpam-3736	58	1	=	=	PUNCT
ejpam-3736	58	2	0	0	X
ejpam-3736	58	3	.	.	PUNCT
ejpam-3736	58	4	therefore	therefore	ADV
ejpam-3736	58	5	re	re	VERB
ejpam-3736	58	6	q	q	X
ejpam-3736	58	7	(	(	PUNCT
ejpam-3736	58	8	z	z	NOUN
ejpam-3736	58	9	)	)	PUNCT
ejpam-3736	58	10	p(z	p(z	NOUN
ejpam-3736	58	11	)	)	PUNCT
ejpam-3736	58	12	=	=	SYM
ejpam-3736	58	13	re	re	ADP
ejpam-3736	58	14	γ	γ	X
ejpam-3736	58	15	+	+	X
ejpam-3736	58	16	n	n	NUM
ejpam-3736	58	17	2	2	NUM
ejpam-3736	58	18	+	+	CCONJ
ejpam-3736	58	19	1	1	NUM
ejpam-3736	58	20	2	2	NUM
ejpam-3736	58	21	[	[	PUNCT
ejpam-3736	58	22	|z|2	|z|2	NOUN
ejpam-3736	58	23	−	−	NOUN
ejpam-3736	58	24	|z1|2	|z1|2	PROPN
ejpam-3736	58	25	|z	|z	PROPN
ejpam-3736	58	26	−	−	PROPN
ejpam-3736	58	27	z1|2	z1|2	PROPN
ejpam-3736	58	28	+	+	CCONJ
ejpam-3736	58	29	·	·	PUNCT
ejpam-3736	58	30	·	·	PUNCT
ejpam-3736	58	31	·	·	PUNCT
ejpam-3736	58	32	+	+	NUM
ejpam-3736	58	33	|z|	|z|	VERB
ejpam-3736	58	34	2	2	NUM
ejpam-3736	58	35	−	−	PROPN
ejpam-3736	58	36	|zn|2	|zn|2	PROPN
ejpam-3736	58	37	|z	|z	PROPN
ejpam-3736	59	1	−	−	PROPN
ejpam-3736	59	2	zn|2	zn|2	PROPN
ejpam-3736	59	3	]	]	X
ejpam-3736	59	4	=	=	PUNCT
ejpam-3736	60	1	0	0	X
ejpam-3736	60	2	.	.	PUNCT
ejpam-3736	61	1	if	if	SCONJ
ejpam-3736	61	2	we	we	PRON
ejpam-3736	61	3	assume	assume	VERB
ejpam-3736	61	4	z	z	X
ejpam-3736	61	5	/∈	/∈	PUNCT
ejpam-3736	62	1	d(0	d(0	NOUN
ejpam-3736	62	2	,	,	PUNCT
ejpam-3736	62	3	1	1	NUM
ejpam-3736	62	4	)	)	PUNCT
ejpam-3736	62	5	,	,	PUNCT
ejpam-3736	62	6	then	then	ADV
ejpam-3736	62	7	we	we	PRON
ejpam-3736	62	8	obtain	obtain	VERB
ejpam-3736	62	9	re	re	ADP
ejpam-3736	62	10	γ	γ	X
ejpam-3736	62	11	>	>	X
ejpam-3736	62	12	0	0	NUM
ejpam-3736	63	1	,	,	PUNCT
ejpam-3736	63	2	when	when	SCONJ
ejpam-3736	63	3	is	be	AUX
ejpam-3736	63	4	impossible	impossible	ADJ
ejpam-3736	63	5	.	.	PUNCT
ejpam-3736	64	1	theorem	theorem	NOUN
ejpam-3736	64	2	2	2	NUM
ejpam-3736	64	3	.	.	PUNCT
ejpam-3736	65	1	if	if	SCONJ
ejpam-3736	65	2	all	all	DET
ejpam-3736	65	3	the	the	DET
ejpam-3736	65	4	zeros	zeros	X
ejpam-3736	65	5	zk	zk	PROPN
ejpam-3736	65	6	,	,	PUNCT
ejpam-3736	65	7	k	k	PROPN
ejpam-3736	65	8	=	=	SYM
ejpam-3736	65	9	1	1	NUM
ejpam-3736	65	10	,	,	PUNCT
ejpam-3736	65	11	2	2	NUM
ejpam-3736	65	12	,	,	PUNCT
ejpam-3736	65	13	.	.	PUNCT
ejpam-3736	65	14	.	.	PUNCT
ejpam-3736	65	15	.	.	PUNCT
ejpam-3736	66	1	n	n	CCONJ
ejpam-3736	66	2	;	;	PUNCT
ejpam-3736	66	3	of	of	ADP
ejpam-3736	66	4	a	a	DET
ejpam-3736	66	5	polynomial	polynomial	ADJ
ejpam-3736	66	6	p(z	p(z	NOUN
ejpam-3736	66	7	)	)	PUNCT
ejpam-3736	66	8	∈	∈	PROPN
ejpam-3736	67	1	c[z	c[z	PROPN
ejpam-3736	67	2	]	]	X
ejpam-3736	67	3	satisfy	satisfy	NOUN
ejpam-3736	67	4	zk	zk	PROPN
ejpam-3736	67	5	∈	∈	PROPN
ejpam-3736	67	6	d(0	d(0	PROPN
ejpam-3736	67	7	,	,	PUNCT
ejpam-3736	67	8	1	1	NUM
ejpam-3736	67	9	)	)	PUNCT
ejpam-3736	67	10	and	and	CCONJ
ejpam-3736	67	11	a	a	PRON
ejpam-3736	67	12	is	be	AUX
ejpam-3736	67	13	a	a	DET
ejpam-3736	67	14	zero	zero	NUM
ejpam-3736	67	15	of	of	ADP
ejpam-3736	67	16	p(z	p(z	NOUN
ejpam-3736	67	17	)	)	PUNCT
ejpam-3736	67	18	of	of	ADP
ejpam-3736	67	19	modulus	modulus	NOUN
ejpam-3736	67	20	1	1	NUM
ejpam-3736	67	21	,	,	PUNCT
ejpam-3736	67	22	then	then	ADV
ejpam-3736	67	23	the	the	DET
ejpam-3736	67	24	derivative	derivative	ADJ
ejpam-3736	67	25	p′(z	p′(z	NOUN
ejpam-3736	67	26	)	)	PUNCT
ejpam-3736	67	27	has	have	VERB
ejpam-3736	67	28	at	at	ADV
ejpam-3736	67	29	least	least	ADJ
ejpam-3736	67	30	one	one	NUM
ejpam-3736	67	31	zero	zero	NUM
ejpam-3736	67	32	in	in	ADP
ejpam-3736	67	33	d	d	PROPN
ejpam-3736	67	34	(	(	PUNCT
ejpam-3736	67	35	a	a	DET
ejpam-3736	67	36	2	2	NUM
ejpam-3736	67	37	,	,	PUNCT
ejpam-3736	67	38	1	1	NUM
ejpam-3736	67	39	2	2	NUM
ejpam-3736	67	40	)	)	PUNCT
ejpam-3736	67	41	.	.	PUNCT
ejpam-3736	68	1	proof	proof	NOUN
ejpam-3736	68	2	.	.	PUNCT
ejpam-3736	69	1	let	let	VERB
ejpam-3736	69	2	p	p	NOUN
ejpam-3736	69	3	(	(	PUNCT
ejpam-3736	69	4	z	z	NOUN
ejpam-3736	69	5	)	)	PUNCT
ejpam-3736	69	6	=	=	SYM
ejpam-3736	70	1	(	(	PUNCT
ejpam-3736	70	2	z	z	NOUN
ejpam-3736	70	3	−	−	PROPN
ejpam-3736	70	4	a)q(z	a)q(z	PROPN
ejpam-3736	70	5	)	)	PUNCT
ejpam-3736	70	6	.	.	PUNCT
ejpam-3736	71	1	if	if	SCONJ
ejpam-3736	71	2	we	we	PRON
ejpam-3736	71	3	denote	denote	VERB
ejpam-3736	71	4	by	by	ADP
ejpam-3736	71	5	z1	z1	PROPN
ejpam-3736	71	6	,	,	PUNCT
ejpam-3736	71	7	z2	z2	PROPN
ejpam-3736	71	8	,	,	PUNCT
ejpam-3736	71	9	.	.	PUNCT
ejpam-3736	71	10	.	.	PUNCT
ejpam-3736	72	1	.	.	PUNCT
ejpam-3736	73	1	,	,	PUNCT
ejpam-3736	73	2	zn−1	zn−1	VERB
ejpam-3736	73	3	the	the	DET
ejpam-3736	73	4	zeros	zero	NOUN
ejpam-3736	73	5	of	of	ADP
ejpam-3736	73	6	q(z	q(z	PROPN
ejpam-3736	73	7	)	)	PUNCT
ejpam-3736	73	8	and	and	CCONJ
ejpam-3736	73	9	by	by	ADP
ejpam-3736	73	10	w1	w1	NOUN
ejpam-3736	73	11	,	,	PUNCT
ejpam-3736	73	12	w2	w2	NOUN
ejpam-3736	73	13	,	,	PUNCT
ejpam-3736	73	14	.	.	PUNCT
ejpam-3736	73	15	.	.	PUNCT
ejpam-3736	73	16	.	.	PUNCT
ejpam-3736	74	1	wn−1	wn−1	VERB
ejpam-3736	74	2	those	those	PRON
ejpam-3736	74	3	of	of	ADP
ejpam-3736	74	4	p′(z	p′(z	NOUN
ejpam-3736	74	5	)	)	PUNCT
ejpam-3736	74	6	,	,	PUNCT
ejpam-3736	74	7	then	then	ADV
ejpam-3736	74	8	in	in	ADP
ejpam-3736	74	9	the	the	DET
ejpam-3736	74	10	non	non	ADJ
ejpam-3736	74	11	-	-	ADJ
ejpam-3736	74	12	trivial	trivial	ADJ
ejpam-3736	74	13	case	case	NOUN
ejpam-3736	74	14	q	q	X
ejpam-3736	74	15	(	(	PUNCT
ejpam-3736	74	16	a	a	NOUN
ejpam-3736	74	17	)	)	PUNCT
ejpam-3736	74	18	6=	6=	SYM
ejpam-3736	74	19	0	0	NUM
ejpam-3736	74	20	we	we	PRON
ejpam-3736	74	21	obtain	obtain	VERB
ejpam-3736	74	22	n−1∑	n−1∑	PROPN
ejpam-3736	74	23	k=1	k=1	X
ejpam-3736	74	24	re	re	ADP
ejpam-3736	74	25	a	a	DET
ejpam-3736	74	26	a−	a−	PROPN
ejpam-3736	74	27	wk	wk	X
ejpam-3736	74	28	=	=	NOUN
ejpam-3736	74	29	re	re	X
ejpam-3736	74	30	ap′′(a	ap′′(a	PROPN
ejpam-3736	74	31	)	)	PUNCT
ejpam-3736	74	32	p′(a	p′(a	X
ejpam-3736	74	33	)	)	PUNCT
ejpam-3736	75	1	=	=	NOUN
ejpam-3736	75	2	=	=	SYM
ejpam-3736	75	3	2re	2re	NOUN
ejpam-3736	75	4	q′(a	q′(a	NOUN
ejpam-3736	75	5	)	)	PUNCT
ejpam-3736	75	6	q(a	q(a	PROPN
ejpam-3736	75	7	)	)	PUNCT
ejpam-3736	76	1	=	=	SYM
ejpam-3736	76	2	2	2	NUM
ejpam-3736	76	3	n−1∑	n−1∑	PROPN
ejpam-3736	76	4	k=1	k=1	X
ejpam-3736	76	5	re	re	VERB
ejpam-3736	76	6	a	a	DET
ejpam-3736	76	7	a−	a−	PROPN
ejpam-3736	76	8	zk	zk	PROPN
ejpam-3736	76	9	≥	≥	NUM
ejpam-3736	76	10	2	2	NUM
ejpam-3736	76	11	n−	n−	NOUN
ejpam-3736	76	12	1	1	NUM
ejpam-3736	76	13	2	2	NUM
ejpam-3736	76	14	=	=	SYM
ejpam-3736	76	15	n−	n−	NOUN
ejpam-3736	76	16	1	1	NUM
ejpam-3736	76	17	.	.	PUNCT
ejpam-3736	77	1	here	here	ADV
ejpam-3736	77	2	we	we	PRON
ejpam-3736	77	3	essentially	essentially	ADV
ejpam-3736	77	4	,	,	PUNCT
ejpam-3736	77	5	that	that	SCONJ
ejpam-3736	77	6	p	p	ADJ
ejpam-3736	77	7	′	′	X
ejpam-3736	77	8	(	(	PUNCT
ejpam-3736	77	9	z	z	NOUN
ejpam-3736	77	10	)	)	PUNCT
ejpam-3736	77	11	=	=	SYM
ejpam-3736	77	12	(	(	PUNCT
ejpam-3736	77	13	z	z	NOUN
ejpam-3736	77	14	−	−	PROPN
ejpam-3736	77	15	a	a	NOUN
ejpam-3736	77	16	)	)	PUNCT
ejpam-3736	77	17	q	q	NOUN
ejpam-3736	78	1	′	′	NUM
ejpam-3736	78	2	(	(	PUNCT
ejpam-3736	78	3	z	z	NOUN
ejpam-3736	78	4	)	)	PUNCT
ejpam-3736	78	5	+	+	NOUN
ejpam-3736	78	6	q	q	X
ejpam-3736	78	7	(	(	PUNCT
ejpam-3736	78	8	z	z	NOUN
ejpam-3736	78	9	)	)	PUNCT
ejpam-3736	78	10	,	,	PUNCT
ejpam-3736	78	11	p	p	PROPN
ejpam-3736	78	12	′′	′′	PROPN
ejpam-3736	78	13	(	(	PUNCT
ejpam-3736	78	14	z	z	PROPN
ejpam-3736	78	15	)	)	PUNCT
ejpam-3736	78	16	=	=	PUNCT
ejpam-3736	78	17	(	(	PUNCT
ejpam-3736	78	18	z	z	NOUN
ejpam-3736	78	19	−	−	PROPN
ejpam-3736	78	20	a	a	X
ejpam-3736	78	21	)	)	PUNCT
ejpam-3736	78	22	q	q	NOUN
ejpam-3736	79	1	′′	′′	PROPN
ejpam-3736	79	2	(	(	PUNCT
ejpam-3736	79	3	z	z	NOUN
ejpam-3736	79	4	)	)	PUNCT
ejpam-3736	79	5	+	+	NUM
ejpam-3736	79	6	2q	2q	NUM
ejpam-3736	79	7	(	(	PUNCT
ejpam-3736	79	8	z	z	NOUN
ejpam-3736	79	9	)	)	PUNCT
ejpam-3736	79	10	,	,	PUNCT
ejpam-3736	79	11	and	and	CCONJ
ejpam-3736	79	12	|a|	|a|	NOUN
ejpam-3736	79	13	=	=	SYM
ejpam-3736	79	14	1	1	NUM
ejpam-3736	79	15	.	.	PUNCT
ejpam-3736	79	16	hence	hence	ADV
ejpam-3736	79	17	re	re	ADP
ejpam-3736	79	18	a	a	DET
ejpam-3736	79	19	a−wk	a−wk	NOUN
ejpam-3736	79	20	≥	≥	NUM
ejpam-3736	79	21	1	1	NUM
ejpam-3736	79	22	for	for	ADP
ejpam-3736	79	23	some	some	DET
ejpam-3736	79	24	k	k	NOUN
ejpam-3736	79	25	,	,	PUNCT
ejpam-3736	79	26	(	(	PUNCT
ejpam-3736	79	27	1	1	NUM
ejpam-3736	79	28	≤	≤	NUM
ejpam-3736	79	29	k	k	X
ejpam-3736	79	30	≤	≤	PROPN
ejpam-3736	79	31	n−	n−	PROPN
ejpam-3736	79	32	1	1	NUM
ejpam-3736	79	33	)	)	PUNCT
ejpam-3736	79	34	.	.	PUNCT
ejpam-3736	80	1	that	that	PRON
ejpam-3736	80	2	means	mean	VERB
ejpam-3736	80	3	re	re	VERB
ejpam-3736	80	4	a	a	DET
ejpam-3736	80	5	2	2	NUM
ejpam-3736	80	6	−	−	NOUN
ejpam-3736	80	7	wk	wk	INTJ
ejpam-3736	80	8	2	2	NUM
ejpam-3736	80	9	+	+	CCONJ
ejpam-3736	80	10	a	a	DET
ejpam-3736	80	11	2	2	NUM
ejpam-3736	80	12	+	+	CCONJ
ejpam-3736	80	13	wk	wk	NOUN
ejpam-3736	80	14	2	2	NUM
ejpam-3736	80	15	a−	a−	PROPN
ejpam-3736	80	16	wk	wk	X
ejpam-3736	81	1	=	=	NOUN
ejpam-3736	81	2	re	re	X
ejpam-3736	81	3	(	(	PUNCT
ejpam-3736	81	4	1	1	NUM
ejpam-3736	81	5	2	2	NUM
ejpam-3736	81	6	+	+	CCONJ
ejpam-3736	81	7	1	1	NUM
ejpam-3736	81	8	2	2	NUM
ejpam-3736	81	9	a+	a+	PUNCT
ejpam-3736	81	10	wk	wk	X
ejpam-3736	81	11	a−	a−	PROPN
ejpam-3736	81	12	wk	wk	NOUN
ejpam-3736	81	13	)	)	PUNCT
ejpam-3736	81	14	t.	t.	PROPN
ejpam-3736	81	15	s.	s.	PROPN
ejpam-3736	81	16	stoyanov	stoyanov	PROPN
ejpam-3736	81	17	/	/	SYM
ejpam-3736	81	18	eur	eur	PROPN
ejpam-3736	81	19	.	.	PUNCT
ejpam-3736	82	1	j.	j.	PROPN
ejpam-3736	82	2	pure	pure	PROPN
ejpam-3736	82	3	appl	appl	PROPN
ejpam-3736	82	4	.	.	PROPN
ejpam-3736	82	5	math	math	PROPN
ejpam-3736	82	6	,	,	PUNCT
ejpam-3736	82	7	13	13	NUM
ejpam-3736	82	8	(	(	PUNCT
ejpam-3736	82	9	3	3	NUM
ejpam-3736	82	10	)	)	PUNCT
ejpam-3736	82	11	(	(	PUNCT
ejpam-3736	82	12	2020	2020	NUM
ejpam-3736	82	13	)	)	PUNCT
ejpam-3736	82	14	,	,	PUNCT
ejpam-3736	82	15	663	663	NUM
ejpam-3736	82	16	-	-	SYM
ejpam-3736	82	17	673	673	NUM
ejpam-3736	82	18	666	666	NUM
ejpam-3736	82	19	=	=	NOUN
ejpam-3736	82	20	re	re	X
ejpam-3736	82	21	[	[	PUNCT
ejpam-3736	82	22	1	1	NUM
ejpam-3736	82	23	2	2	NUM
ejpam-3736	82	24	+	+	CCONJ
ejpam-3736	82	25	1	1	NUM
ejpam-3736	82	26	2	2	NUM
ejpam-3736	82	27	(	(	PUNCT
ejpam-3736	82	28	a+	a+	X
ejpam-3736	82	29	wk	wk	NOUN
ejpam-3736	82	30	)	)	PUNCT
ejpam-3736	82	31	(	(	PUNCT
ejpam-3736	82	32	a−	a−	PROPN
ejpam-3736	82	33	wk	wk	PROPN
ejpam-3736	82	34	)	)	PUNCT
ejpam-3736	82	35	|a−	|a−	NOUN
ejpam-3736	82	36	wk|2	wk|2	PROPN
ejpam-3736	82	37	]	]	PUNCT
ejpam-3736	82	38	=	=	SYM
ejpam-3736	82	39	1	1	NUM
ejpam-3736	82	40	2	2	NUM
ejpam-3736	82	41	+	+	CCONJ
ejpam-3736	82	42	1	1	NUM
ejpam-3736	82	43	2	2	NUM
ejpam-3736	82	44	|a|2	|a|2	PROPN
ejpam-3736	82	45	−	−	PROPN
ejpam-3736	82	46	|wk|2	|wk|2	PUNCT
ejpam-3736	82	47	|a−	|a−	NOUN
ejpam-3736	82	48	wk|2	wk|2	NOUN
ejpam-3736	82	49	≥	≥	NUM
ejpam-3736	82	50	1	1	NUM
ejpam-3736	82	51	,	,	PUNCT
ejpam-3736	82	52	i.e.	i.e.	X
ejpam-3736	82	53	|a−	|a−	NOUN
ejpam-3736	82	54	wk|2	wk|2	NOUN
ejpam-3736	82	55	+	+	PUNCT
ejpam-3736	82	56	|wk|2	|wk|2	PROPN
ejpam-3736	82	57	≤	≤	ADJ
ejpam-3736	82	58	|a|2	|a|2	PROPN
ejpam-3736	82	59	which	which	PRON
ejpam-3736	82	60	confirms	confirm	VERB
ejpam-3736	82	61	that	that	SCONJ
ejpam-3736	82	62	wk	wk	X
ejpam-3736	82	63	∈	∈	PROPN
ejpam-3736	82	64	d	d	X
ejpam-3736	82	65	(	(	PUNCT
ejpam-3736	82	66	a	a	DET
ejpam-3736	82	67	2	2	NUM
ejpam-3736	82	68	,	,	PUNCT
ejpam-3736	82	69	1	1	NUM
ejpam-3736	82	70	2	2	NUM
ejpam-3736	82	71	)	)	PUNCT
ejpam-3736	82	72	.	.	PUNCT
ejpam-3736	83	1	theorem	theorem	VERB
ejpam-3736	83	2	3	3	NUM
ejpam-3736	83	3	.	.	PUNCT
ejpam-3736	84	1	if	if	SCONJ
ejpam-3736	84	2	all	all	DET
ejpam-3736	84	3	the	the	DET
ejpam-3736	84	4	zeros	zero	NOUN
ejpam-3736	84	5	of	of	ADP
ejpam-3736	84	6	a	a	DET
ejpam-3736	84	7	polynomial	polynomial	ADJ
ejpam-3736	84	8	p(z	p(z	NOUN
ejpam-3736	84	9	)	)	PUNCT
ejpam-3736	84	10	∈	∈	PROPN
ejpam-3736	84	11	c[z	c[z	PROPN
ejpam-3736	84	12	]	]	X
ejpam-3736	84	13	are	be	AUX
ejpam-3736	84	14	zk	zk	PROPN
ejpam-3736	84	15	,	,	PUNCT
ejpam-3736	84	16	k	k	PROPN
ejpam-3736	84	17	=	=	SYM
ejpam-3736	84	18	1	1	NUM
ejpam-3736	84	19	,	,	PUNCT
ejpam-3736	84	20	2	2	NUM
ejpam-3736	84	21	,	,	PUNCT
ejpam-3736	84	22	.	.	PUNCT
ejpam-3736	84	23	.	.	PUNCT
ejpam-3736	85	1	.	.	PUNCT
ejpam-3736	86	1	,	,	PUNCT
ejpam-3736	86	2	n.	n.	NOUN
ejpam-3736	86	3	then	then	ADV
ejpam-3736	86	4	for	for	ADP
ejpam-3736	86	5	each	each	DET
ejpam-3736	86	6	zero	zero	NUM
ejpam-3736	86	7	w	w	PROPN
ejpam-3736	86	8	of	of	ADP
ejpam-3736	86	9	the	the	DET
ejpam-3736	86	10	derivative	derivative	ADJ
ejpam-3736	86	11	p′(z	p′(z	NOUN
ejpam-3736	86	12	)	)	PUNCT
ejpam-3736	86	13	exists	exist	VERB
ejpam-3736	86	14	some	some	DET
ejpam-3736	86	15	k0	k0	PROPN
ejpam-3736	86	16	∈	∈	PROPN
ejpam-3736	86	17	n	n	CCONJ
ejpam-3736	86	18	,	,	PUNCT
ejpam-3736	86	19	1	1	NUM
ejpam-3736	86	20	≤	≤	PROPN
ejpam-3736	86	21	k0	k0	PROPN
ejpam-3736	86	22	≤	≤	PROPN
ejpam-3736	86	23	n	n	CCONJ
ejpam-3736	86	24	,	,	PUNCT
ejpam-3736	86	25	such	such	ADJ
ejpam-3736	86	26	that	that	SCONJ
ejpam-3736	87	1	w	w	PROPN
ejpam-3736	87	2	∈	∈	PROPN
ejpam-3736	87	3	d	d	X
ejpam-3736	87	4	(	(	PUNCT
ejpam-3736	87	5	zk0	zk0	NOUN
ejpam-3736	87	6	2	2	NUM
ejpam-3736	87	7	,	,	PUNCT
ejpam-3736	87	8	|zk0	|zk0	PROPN
ejpam-3736	87	9	|	|	NOUN
ejpam-3736	87	10	2	2	NUM
ejpam-3736	87	11	)	)	PUNCT
ejpam-3736	87	12	.	.	PUNCT
ejpam-3736	88	1	proof	proof	NOUN
ejpam-3736	88	2	.	.	PUNCT
ejpam-3736	89	1	let	let	VERB
ejpam-3736	89	2	w	w	X
ejpam-3736	89	3	∈	∈	PROPN
ejpam-3736	89	4	c	c	AUX
ejpam-3736	89	5	be	be	AUX
ejpam-3736	89	6	such	such	ADJ
ejpam-3736	90	1	that	that	SCONJ
ejpam-3736	90	2	p	p	NOUN
ejpam-3736	91	1	′	′	X
ejpam-3736	91	2	(	(	PUNCT
ejpam-3736	91	3	w	w	NOUN
ejpam-3736	91	4	)	)	PUNCT
ejpam-3736	91	5	=	=	SYM
ejpam-3736	92	1	0	0	X
ejpam-3736	92	2	.	.	PUNCT
ejpam-3736	93	1	we	we	PRON
ejpam-3736	93	2	except	except	SCONJ
ejpam-3736	93	3	the	the	DET
ejpam-3736	93	4	trivial	trivial	ADJ
ejpam-3736	93	5	case	case	NOUN
ejpam-3736	93	6	p	p	X
ejpam-3736	93	7	(	(	PUNCT
ejpam-3736	93	8	w	w	NOUN
ejpam-3736	93	9	)	)	PUNCT
ejpam-3736	93	10	=	=	SYM
ejpam-3736	93	11	0	0	NUM
ejpam-3736	93	12	,	,	PUNCT
ejpam-3736	93	13	which	which	PRON
ejpam-3736	93	14	confirms	confirm	VERB
ejpam-3736	93	15	the	the	DET
ejpam-3736	93	16	assertion	assertion	NOUN
ejpam-3736	93	17	.	.	PUNCT
ejpam-3736	94	1	then	then	ADV
ejpam-3736	94	2	w	w	PROPN
ejpam-3736	94	3	p	p	X
ejpam-3736	94	4	′	′	PRON
ejpam-3736	94	5	(	(	PUNCT
ejpam-3736	94	6	w	w	NOUN
ejpam-3736	94	7	)	)	PUNCT
ejpam-3736	94	8	p(w	p(w	NOUN
ejpam-3736	94	9	)	)	PUNCT
ejpam-3736	95	1	=	=	PUNCT
ejpam-3736	95	2	w	w	PROPN
ejpam-3736	95	3	w	w	PROPN
ejpam-3736	95	4	−	−	PROPN
ejpam-3736	95	5	z1	z1	NOUN
ejpam-3736	95	6	+	+	CCONJ
ejpam-3736	95	7	w	w	PROPN
ejpam-3736	95	8	w	w	PROPN
ejpam-3736	95	9	−	−	PROPN
ejpam-3736	95	10	z2	z2	NOUN
ejpam-3736	95	11	+	+	CCONJ
ejpam-3736	95	12	·	·	PUNCT
ejpam-3736	95	13	·	·	PUNCT
ejpam-3736	95	14	·	·	PUNCT
ejpam-3736	96	1	+	+	NUM
ejpam-3736	96	2	w	w	PROPN
ejpam-3736	96	3	w	w	PROPN
ejpam-3736	96	4	−	−	PROPN
ejpam-3736	96	5	zn	zn	NOUN
ejpam-3736	96	6	=	=	SYM
ejpam-3736	96	7	w	w	PROPN
ejpam-3736	96	8	2	2	NUM
ejpam-3736	96	9	−	−	PROPN
ejpam-3736	96	10	z1	z1	NOUN
ejpam-3736	96	11	2	2	NUM
ejpam-3736	96	12	+	+	CCONJ
ejpam-3736	96	13	w	w	PROPN
ejpam-3736	96	14	2	2	NUM
ejpam-3736	96	15	+	+	NOUN
ejpam-3736	96	16	z1	z1	NOUN
ejpam-3736	96	17	2	2	NUM
ejpam-3736	96	18	w	w	NOUN
ejpam-3736	96	19	−	−	PROPN
ejpam-3736	96	20	z1	z1	NOUN
ejpam-3736	96	21	+	+	CCONJ
ejpam-3736	96	22	w	w	PROPN
ejpam-3736	96	23	2	2	NUM
ejpam-3736	96	24	−	−	PROPN
ejpam-3736	96	25	z2	z2	NOUN
ejpam-3736	96	26	2	2	NUM
ejpam-3736	96	27	+	+	CCONJ
ejpam-3736	96	28	w	w	PROPN
ejpam-3736	96	29	2	2	NUM
ejpam-3736	96	30	+	+	NOUN
ejpam-3736	96	31	z2	z2	NUM
ejpam-3736	96	32	2	2	NUM
ejpam-3736	96	33	w	w	NOUN
ejpam-3736	96	34	−	−	PROPN
ejpam-3736	96	35	z2	z2	NOUN
ejpam-3736	96	36	+	+	CCONJ
ejpam-3736	96	37	·	·	PUNCT
ejpam-3736	96	38	·	·	PUNCT
ejpam-3736	96	39	·	·	PUNCT
ejpam-3736	97	1	+	+	NUM
ejpam-3736	97	2	w	w	PROPN
ejpam-3736	97	3	2	2	NUM
ejpam-3736	97	4	−	−	NOUN
ejpam-3736	97	5	zn	zn	NOUN
ejpam-3736	97	6	2	2	NUM
ejpam-3736	97	7	+	+	CCONJ
ejpam-3736	97	8	w	w	PROPN
ejpam-3736	97	9	2	2	NUM
ejpam-3736	97	10	+	+	CCONJ
ejpam-3736	97	11	zn	zn	PROPN
ejpam-3736	97	12	2	2	NUM
ejpam-3736	97	13	w	w	NOUN
ejpam-3736	97	14	−	−	PROPN
ejpam-3736	97	15	zk	zk	PROPN
ejpam-3736	97	16	=	=	PUNCT
ejpam-3736	97	17	n	n	PRON
ejpam-3736	97	18	2	2	NUM
ejpam-3736	97	19	+	+	CCONJ
ejpam-3736	97	20	1	1	NUM
ejpam-3736	97	21	2	2	NUM
ejpam-3736	97	22	[	[	PUNCT
ejpam-3736	97	23	(	(	PUNCT
ejpam-3736	97	24	w	w	NOUN
ejpam-3736	97	25	+	+	X
ejpam-3736	97	26	z1	z1	ADJ
ejpam-3736	97	27	)	)	PUNCT
ejpam-3736	97	28	(	(	PUNCT
ejpam-3736	97	29	w	w	PROPN
ejpam-3736	97	30	−	−	PROPN
ejpam-3736	97	31	z1	z1	PROPN
ejpam-3736	97	32	)	)	PUNCT
ejpam-3736	97	33	|w	|w	NOUN
ejpam-3736	97	34	−	−	PROPN
ejpam-3736	97	35	z1|2	z1|2	X
ejpam-3736	97	36	+	+	CCONJ
ejpam-3736	97	37	·	·	PUNCT
ejpam-3736	97	38	·	·	PUNCT
ejpam-3736	97	39	·	·	PUNCT
ejpam-3736	98	1	+	+	PUNCT
ejpam-3736	98	2	(	(	PUNCT
ejpam-3736	98	3	w	w	PROPN
ejpam-3736	98	4	+	+	PROPN
ejpam-3736	98	5	zn	zn	NUM
ejpam-3736	98	6	)	)	PUNCT
ejpam-3736	98	7	(	(	PUNCT
ejpam-3736	98	8	w	w	PROPN
ejpam-3736	98	9	−	−	PROPN
ejpam-3736	98	10	zn	zn	NUM
ejpam-3736	98	11	)	)	PUNCT
ejpam-3736	98	12	|w	|w	NOUN
ejpam-3736	98	13	−	−	PROPN
ejpam-3736	98	14	zn|2	zn|2	NOUN
ejpam-3736	98	15	]	]	X
ejpam-3736	99	1	=	=	PUNCT
ejpam-3736	99	2	0	0	X
ejpam-3736	99	3	.	.	PUNCT
ejpam-3736	99	4	therefore	therefore	ADV
ejpam-3736	99	5	re	re	VERB
ejpam-3736	99	6	w	w	NOUN
ejpam-3736	99	7	p	p	NOUN
ejpam-3736	99	8	′	′	NUM
ejpam-3736	99	9	(	(	PUNCT
ejpam-3736	99	10	w	w	NOUN
ejpam-3736	99	11	)	)	PUNCT
ejpam-3736	99	12	p(w	p(w	NOUN
ejpam-3736	99	13	)	)	PUNCT
ejpam-3736	100	1	=	=	SYM
ejpam-3736	100	2	n	n	PRON
ejpam-3736	100	3	2	2	NUM
ejpam-3736	100	4	+	+	CCONJ
ejpam-3736	100	5	1	1	NUM
ejpam-3736	100	6	2	2	NUM
ejpam-3736	100	7	[	[	PUNCT
ejpam-3736	100	8	|w|2	|w|2	NOUN
ejpam-3736	100	9	−	−	PROPN
ejpam-3736	100	10	|z1|2	|z1|2	PROPN
ejpam-3736	100	11	|w	|w	NOUN
ejpam-3736	100	12	−	−	PROPN
ejpam-3736	100	13	z1|2	z1|2	PROPN
ejpam-3736	100	14	+	+	CCONJ
ejpam-3736	100	15	·	·	PUNCT
ejpam-3736	100	16	·	·	PUNCT
ejpam-3736	100	17	·	·	PUNCT
ejpam-3736	100	18	+	+	CCONJ
ejpam-3736	100	19	|w|	|w|	VERB
ejpam-3736	100	20	2	2	NUM
ejpam-3736	100	21	−	−	NOUN
ejpam-3736	100	22	|zn|2	|zn|2	PROPN
ejpam-3736	100	23	|w	|w	ADJ
ejpam-3736	100	24	−	−	PROPN
ejpam-3736	100	25	zn|2	zn|2	NOUN
ejpam-3736	100	26	]	]	X
ejpam-3736	101	1	=	=	PUNCT
ejpam-3736	101	2	0	0	X
ejpam-3736	101	3	.	.	PUNCT
ejpam-3736	102	1	we	we	PRON
ejpam-3736	102	2	put	put	VERB
ejpam-3736	102	3	αk	αk	NOUN
ejpam-3736	102	4	=	=	SYM
ejpam-3736	102	5	|w|2	|w|2	PROPN
ejpam-3736	102	6	−	−	PROPN
ejpam-3736	102	7	|zn|2	|zn|2	PROPN
ejpam-3736	102	8	|w	|w	ADJ
ejpam-3736	102	9	−	−	PROPN
ejpam-3736	102	10	zn|2	zn|2	PROPN
ejpam-3736	102	11	,	,	PUNCT
ejpam-3736	102	12	k	k	NOUN
ejpam-3736	102	13	=	=	SYM
ejpam-3736	102	14	1	1	NUM
ejpam-3736	102	15	,	,	PUNCT
ejpam-3736	102	16	2	2	NUM
ejpam-3736	102	17	,	,	PUNCT
ejpam-3736	102	18	.	.	PUNCT
ejpam-3736	102	19	.	.	PUNCT
ejpam-3736	102	20	.	.	PUNCT
ejpam-3736	103	1	n.	n.	PROPN
ejpam-3736	103	2	then	then	ADV
ejpam-3736	103	3	α1	α1	PROPN
ejpam-3736	103	4	+	+	CCONJ
ejpam-3736	103	5	α2	α2	ADJ
ejpam-3736	103	6	+	+	X
ejpam-3736	103	7	·	·	PUNCT
ejpam-3736	103	8	·	·	PUNCT
ejpam-3736	103	9	·	·	PUNCT
ejpam-3736	104	1	+	+	NUM
ejpam-3736	104	2	αn	αn	NOUN
ejpam-3736	104	3	=	=	SYM
ejpam-3736	104	4	−n	−n	ADJ
ejpam-3736	104	5	.	.	PUNCT
ejpam-3736	105	1	consequently	consequently	ADV
ejpam-3736	105	2	there	there	PRON
ejpam-3736	105	3	exists	exist	VERB
ejpam-3736	105	4	k0	k0	PROPN
ejpam-3736	105	5	∈	∈	PROPN
ejpam-3736	105	6	n	n	CCONJ
ejpam-3736	105	7	,	,	PUNCT
ejpam-3736	105	8	1	1	NUM
ejpam-3736	105	9	≤	≤	PROPN
ejpam-3736	105	10	k0	k0	PROPN
ejpam-3736	105	11	≤	≤	PROPN
ejpam-3736	105	12	n	n	CCONJ
ejpam-3736	105	13	such	such	ADJ
ejpam-3736	105	14	that	that	DET
ejpam-3736	105	15	αk0	αk0	NOUN
ejpam-3736	105	16	≤	≤	NUM
ejpam-3736	105	17	−1	−1	NOUN
ejpam-3736	105	18	.	.	PUNCT
ejpam-3736	106	1	it	it	PRON
ejpam-3736	106	2	means	mean	VERB
ejpam-3736	106	3	that	that	SCONJ
ejpam-3736	106	4	|w|2	|w|2	NOUN
ejpam-3736	106	5	+	+	CCONJ
ejpam-3736	106	6	|w	|w	ADJ
ejpam-3736	106	7	−	−	PROPN
ejpam-3736	106	8	zk0	zk0	NOUN
ejpam-3736	106	9	|	|	ADV
ejpam-3736	106	10	2	2	NUM
ejpam-3736	106	11	≤	≤	NOUN
ejpam-3736	106	12	|zk0	|zk0	ADP
ejpam-3736	106	13	|	|	ADV
ejpam-3736	106	14	2	2	NUM
ejpam-3736	106	15	,	,	PUNCT
ejpam-3736	106	16	i.e.	i.e.	X
ejpam-3736	106	17	w	w	ADP
ejpam-3736	106	18	∈	∈	PROPN
ejpam-3736	106	19	d	d	X
ejpam-3736	106	20	(	(	PUNCT
ejpam-3736	106	21	zk0	zk0	NOUN
ejpam-3736	106	22	2	2	NUM
ejpam-3736	106	23	,	,	PUNCT
ejpam-3736	106	24	|zk0	|zk0	PROPN
ejpam-3736	106	25	|	|	NOUN
ejpam-3736	106	26	2	2	NUM
ejpam-3736	106	27	)	)	PUNCT
ejpam-3736	106	28	.	.	PUNCT
ejpam-3736	107	1	theorem	theorem	VERB
ejpam-3736	107	2	4	4	NUM
ejpam-3736	107	3	.	.	PUNCT
ejpam-3736	108	1	if	if	SCONJ
ejpam-3736	108	2	all	all	DET
ejpam-3736	108	3	the	the	DET
ejpam-3736	108	4	zeros	zero	NOUN
ejpam-3736	108	5	of	of	ADP
ejpam-3736	108	6	a	a	DET
ejpam-3736	108	7	polynomial	polynomial	ADJ
ejpam-3736	108	8	p(z	p(z	NOUN
ejpam-3736	108	9	)	)	PUNCT
ejpam-3736	108	10	∈	∈	PROPN
ejpam-3736	108	11	c[z	c[z	PROPN
ejpam-3736	108	12	]	]	X
ejpam-3736	108	13	are	be	AUX
ejpam-3736	108	14	zk	zk	PROPN
ejpam-3736	108	15	,	,	PUNCT
ejpam-3736	108	16	k	k	PROPN
ejpam-3736	108	17	=	=	SYM
ejpam-3736	108	18	1	1	NUM
ejpam-3736	108	19	,	,	PUNCT
ejpam-3736	108	20	2	2	NUM
ejpam-3736	108	21	,	,	PUNCT
ejpam-3736	108	22	.	.	PUNCT
ejpam-3736	108	23	.	.	PUNCT
ejpam-3736	109	1	.	.	PUNCT
ejpam-3736	110	1	,	,	PUNCT
ejpam-3736	110	2	n.	n.	NOUN
ejpam-3736	110	3	then	then	ADV
ejpam-3736	110	4	for	for	ADP
ejpam-3736	110	5	each	each	DET
ejpam-3736	110	6	zero	zero	NUM
ejpam-3736	110	7	w	w	PROPN
ejpam-3736	110	8	of	of	ADP
ejpam-3736	110	9	the	the	DET
ejpam-3736	110	10	derivative	derivative	ADJ
ejpam-3736	110	11	p′(z	p′(z	NOUN
ejpam-3736	110	12	)	)	PUNCT
ejpam-3736	110	13	exists	exist	VERB
ejpam-3736	110	14	some	some	DET
ejpam-3736	110	15	k0	k0	PROPN
ejpam-3736	110	16	∈	∈	PROPN
ejpam-3736	110	17	n	n	CCONJ
ejpam-3736	110	18	,	,	PUNCT
ejpam-3736	110	19	1	1	NUM
ejpam-3736	110	20	≤	≤	PROPN
ejpam-3736	110	21	k0	k0	PROPN
ejpam-3736	110	22	≤	≤	PROPN
ejpam-3736	110	23	n	n	CCONJ
ejpam-3736	110	24	,	,	PUNCT
ejpam-3736	110	25	such	such	ADJ
ejpam-3736	110	26	that	that	PRON
ejpam-3736	110	27	w	w	PROPN
ejpam-3736	110	28	/∈	/∈	PUNCT
ejpam-3736	111	1	d	d	NOUN
ejpam-3736	111	2	(	(	PUNCT
ejpam-3736	111	3	zk0	zk0	NOUN
ejpam-3736	111	4	2	2	NUM
ejpam-3736	111	5	,	,	PUNCT
ejpam-3736	111	6	|zk0	|zk0	PROPN
ejpam-3736	111	7	|	|	NOUN
ejpam-3736	111	8	2	2	NUM
ejpam-3736	111	9	)	)	PUNCT
ejpam-3736	111	10	.	.	PUNCT
ejpam-3736	112	1	proof	proof	NOUN
ejpam-3736	112	2	.	.	PUNCT
ejpam-3736	113	1	let	let	VERB
ejpam-3736	113	2	w	w	X
ejpam-3736	113	3	∈	∈	PROPN
ejpam-3736	113	4	c	c	AUX
ejpam-3736	113	5	be	be	AUX
ejpam-3736	113	6	such	such	ADJ
ejpam-3736	114	1	that	that	SCONJ
ejpam-3736	114	2	p	p	NOUN
ejpam-3736	115	1	′	′	X
ejpam-3736	115	2	(	(	PUNCT
ejpam-3736	115	3	w	w	NOUN
ejpam-3736	115	4	)	)	PUNCT
ejpam-3736	115	5	=	=	SYM
ejpam-3736	116	1	0	0	X
ejpam-3736	116	2	.	.	PUNCT
ejpam-3736	117	1	we	we	PRON
ejpam-3736	117	2	except	except	SCONJ
ejpam-3736	117	3	the	the	DET
ejpam-3736	117	4	trivial	trivial	ADJ
ejpam-3736	117	5	case	case	NOUN
ejpam-3736	117	6	p	p	X
ejpam-3736	117	7	(	(	PUNCT
ejpam-3736	117	8	w	w	NOUN
ejpam-3736	117	9	)	)	PUNCT
ejpam-3736	117	10	=	=	SYM
ejpam-3736	117	11	0	0	NUM
ejpam-3736	117	12	,	,	PUNCT
ejpam-3736	117	13	which	which	PRON
ejpam-3736	117	14	confirms	confirm	VERB
ejpam-3736	117	15	the	the	DET
ejpam-3736	117	16	assertion	assertion	NOUN
ejpam-3736	117	17	.	.	PUNCT
ejpam-3736	118	1	further	far	ADV
ejpam-3736	118	2	we	we	PRON
ejpam-3736	118	3	repeat	repeat	VERB
ejpam-3736	118	4	the	the	DET
ejpam-3736	118	5	proof	proof	NOUN
ejpam-3736	118	6	of	of	ADP
ejpam-3736	118	7	theorem	theorem	NOUN
ejpam-3736	118	8	3	3	NUM
ejpam-3736	119	1	and	and	CCONJ
ejpam-3736	119	2	we	we	PRON
ejpam-3736	119	3	get	get	VERB
ejpam-3736	119	4	α1	α1	PROPN
ejpam-3736	119	5	+	+	CCONJ
ejpam-3736	119	6	α2	α2	ADJ
ejpam-3736	119	7	+	+	X
ejpam-3736	119	8	·	·	PUNCT
ejpam-3736	119	9	·	·	PUNCT
ejpam-3736	119	10	·	·	PUNCT
ejpam-3736	120	1	+	+	NUM
ejpam-3736	120	2	αn	αn	NOUN
ejpam-3736	120	3	=	=	SYM
ejpam-3736	120	4	−1	−1	NOUN
ejpam-3736	120	5	.	.	PUNCT
ejpam-3736	121	1	consequently	consequently	ADV
ejpam-3736	121	2	,	,	PUNCT
ejpam-3736	121	3	there	there	PRON
ejpam-3736	121	4	exists	exist	VERB
ejpam-3736	121	5	k0	k0	PROPN
ejpam-3736	121	6	∈	∈	PROPN
ejpam-3736	121	7	n	n	CCONJ
ejpam-3736	121	8	,	,	PUNCT
ejpam-3736	121	9	1	1	NUM
ejpam-3736	121	10	≤	≤	PROPN
ejpam-3736	121	11	k0	k0	PROPN
ejpam-3736	121	12	≤	≤	PROPN
ejpam-3736	121	13	n	n	CCONJ
ejpam-3736	121	14	such	such	ADJ
ejpam-3736	121	15	that	that	SCONJ
ejpam-3736	121	16	αk0	αk0	NOUN
ejpam-3736	121	17	≥	≥	NOUN
ejpam-3736	121	18	−1	−1	NOUN
ejpam-3736	121	19	.	.	PUNCT
ejpam-3736	122	1	it	it	PRON
ejpam-3736	122	2	means	mean	VERB
ejpam-3736	122	3	that	that	SCONJ
ejpam-3736	122	4	|w|2	|w|2	NOUN
ejpam-3736	122	5	+	+	CCONJ
ejpam-3736	122	6	|w	|w	ADJ
ejpam-3736	122	7	−	−	PROPN
ejpam-3736	122	8	zk0	zk0	NOUN
ejpam-3736	122	9	|	|	ADV
ejpam-3736	122	10	2	2	NUM
ejpam-3736	122	11	≥	≥	NOUN
ejpam-3736	122	12	|zk0	|zk0	ADP
ejpam-3736	122	13	|	|	ADV
ejpam-3736	122	14	2	2	NUM
ejpam-3736	122	15	,	,	PUNCT
ejpam-3736	122	16	i.e.	i.e.	X
ejpam-3736	122	17	w	w	NOUN
ejpam-3736	122	18	/∈	/∈	PUNCT
ejpam-3736	123	1	d	d	NOUN
ejpam-3736	123	2	(	(	PUNCT
ejpam-3736	123	3	zk0	zk0	NOUN
ejpam-3736	123	4	2	2	NUM
ejpam-3736	123	5	,	,	PUNCT
ejpam-3736	123	6	|zk0	|zk0	PROPN
ejpam-3736	123	7	|	|	ADV
ejpam-3736	123	8	2	2	NUM
ejpam-3736	123	9	)	)	PUNCT
ejpam-3736	123	10	.	.	PUNCT
ejpam-3736	124	1	t.	t.	PROPN
ejpam-3736	124	2	s.	s.	PROPN
ejpam-3736	124	3	stoyanov	stoyanov	PROPN
ejpam-3736	124	4	/	/	SYM
ejpam-3736	124	5	eur	eur	PROPN
ejpam-3736	124	6	.	.	PUNCT
ejpam-3736	125	1	j.	j.	PROPN
ejpam-3736	125	2	pure	pure	PROPN
ejpam-3736	125	3	appl	appl	PROPN
ejpam-3736	125	4	.	.	PROPN
ejpam-3736	125	5	math	math	PROPN
ejpam-3736	125	6	,	,	PUNCT
ejpam-3736	125	7	13	13	NUM
ejpam-3736	125	8	(	(	PUNCT
ejpam-3736	125	9	3	3	NUM
ejpam-3736	125	10	)	)	PUNCT
ejpam-3736	125	11	(	(	PUNCT
ejpam-3736	125	12	2020	2020	NUM
ejpam-3736	125	13	)	)	PUNCT
ejpam-3736	125	14	,	,	PUNCT
ejpam-3736	125	15	663	663	NUM
ejpam-3736	125	16	-	-	SYM
ejpam-3736	125	17	673	673	NUM
ejpam-3736	125	18	667	667	NUM
ejpam-3736	125	19	theorem	theorem	NOUN
ejpam-3736	125	20	5	5	NUM
ejpam-3736	125	21	.	.	PUNCT
ejpam-3736	126	1	if	if	SCONJ
ejpam-3736	126	2	all	all	DET
ejpam-3736	126	3	the	the	DET
ejpam-3736	126	4	zeros	zero	NOUN
ejpam-3736	126	5	of	of	ADP
ejpam-3736	126	6	the	the	DET
ejpam-3736	126	7	polynomial	polynomial	ADJ
ejpam-3736	126	8	p(z	p(z	NOUN
ejpam-3736	126	9	)	)	PUNCT
ejpam-3736	126	10	∈	∈	PROPN
ejpam-3736	126	11	c[z	c[z	PROPN
ejpam-3736	126	12	]	]	X
ejpam-3736	126	13	are	be	AUX
ejpam-3736	126	14	zk	zk	PROPN
ejpam-3736	126	15	,	,	PUNCT
ejpam-3736	126	16	k	k	PROPN
ejpam-3736	126	17	=	=	SYM
ejpam-3736	126	18	1	1	NUM
ejpam-3736	126	19	,	,	PUNCT
ejpam-3736	126	20	2	2	NUM
ejpam-3736	126	21	,	,	PUNCT
ejpam-3736	126	22	.	.	PUNCT
ejpam-3736	126	23	.	.	PUNCT
ejpam-3736	127	1	.	.	PUNCT
ejpam-3736	128	1	,	,	PUNCT
ejpam-3736	128	2	n.	n.	NOUN
ejpam-3736	128	3	then	then	ADV
ejpam-3736	128	4	for	for	ADP
ejpam-3736	128	5	each	each	DET
ejpam-3736	128	6	zero	zero	NUM
ejpam-3736	128	7	t	t	NOUN
ejpam-3736	128	8	of	of	ADP
ejpam-3736	128	9	the	the	DET
ejpam-3736	128	10	second	second	ADJ
ejpam-3736	128	11	derivative	derivative	ADJ
ejpam-3736	128	12	p′′(z	p′′(z	NOUN
ejpam-3736	128	13	)	)	PUNCT
ejpam-3736	128	14	exists	exist	VERB
ejpam-3736	128	15	some	some	PRON
ejpam-3736	128	16	,	,	PUNCT
ejpam-3736	128	17	k0	k0	PROPN
ejpam-3736	128	18	∈	∈	PROPN
ejpam-3736	128	19	n	n	CCONJ
ejpam-3736	128	20	,	,	PUNCT
ejpam-3736	128	21	1	1	NUM
ejpam-3736	128	22	≤	≤	PROPN
ejpam-3736	128	23	k0	k0	PROPN
ejpam-3736	128	24	≤	≤	PROPN
ejpam-3736	128	25	n	n	CCONJ
ejpam-3736	128	26	,	,	PUNCT
ejpam-3736	128	27	such	such	ADJ
ejpam-3736	128	28	that	that	SCONJ
ejpam-3736	128	29	t	t	PROPN
ejpam-3736	128	30	∈	∈	PROPN
ejpam-3736	128	31	c	c	PROPN
ejpam-3736	128	32	(	(	PUNCT
ejpam-3736	128	33	zk0	zk0	NOUN
ejpam-3736	128	34	2	2	NUM
ejpam-3736	128	35	,	,	PUNCT
ejpam-3736	128	36	|zk0	|zk0	PROPN
ejpam-3736	128	37	|	|	NOUN
ejpam-3736	128	38	2	2	NUM
ejpam-3736	128	39	)	)	PUNCT
ejpam-3736	128	40	.	.	PUNCT
ejpam-3736	129	1	proof	proof	NOUN
ejpam-3736	129	2	.	.	PUNCT
ejpam-3736	130	1	we	we	PRON
ejpam-3736	130	2	denote	denote	VERB
ejpam-3736	130	3	by	by	ADP
ejpam-3736	130	4	t	t	PROPN
ejpam-3736	130	5	the	the	DET
ejpam-3736	130	6	zero	zero	NUM
ejpam-3736	130	7	of	of	ADP
ejpam-3736	130	8	the	the	DET
ejpam-3736	130	9	second	second	ADJ
ejpam-3736	130	10	derivative	derivative	NOUN
ejpam-3736	130	11	,	,	PUNCT
ejpam-3736	130	12	i.e.	i.e.	X
ejpam-3736	130	13	p	p	X
ejpam-3736	130	14	′′	′′	PROPN
ejpam-3736	130	15	(	(	PUNCT
ejpam-3736	130	16	t	t	PROPN
ejpam-3736	130	17	)	)	PUNCT
ejpam-3736	130	18	=	=	NOUN
ejpam-3736	131	1	0	0	X
ejpam-3736	131	2	.	.	PUNCT
ejpam-3736	132	1	according	accord	VERB
ejpam-3736	132	2	to	to	ADP
ejpam-3736	132	3	theorem	theorem	NOUN
ejpam-3736	132	4	3	3	NUM
ejpam-3736	132	5	there	there	ADV
ejpam-3736	132	6	exists	exist	VERB
ejpam-3736	132	7	such	such	DET
ejpam-3736	132	8	a	a	DET
ejpam-3736	132	9	zero	zero	NUM
ejpam-3736	132	10	w	w	NOUN
ejpam-3736	132	11	of	of	ADP
ejpam-3736	132	12	the	the	DET
ejpam-3736	132	13	derivative	derivative	ADJ
ejpam-3736	132	14	p′(z	p′(z	NOUN
ejpam-3736	132	15	)	)	PUNCT
ejpam-3736	132	16	,	,	PUNCT
ejpam-3736	132	17	that	that	SCONJ
ejpam-3736	132	18	t	t	PROPN
ejpam-3736	132	19	∈	∈	PROPN
ejpam-3736	132	20	d	d	X
ejpam-3736	132	21	(	(	PUNCT
ejpam-3736	132	22	w	w	PROPN
ejpam-3736	132	23	2	2	NUM
ejpam-3736	132	24	,	,	PUNCT
ejpam-3736	132	25	|w|	|w|	ADJ
ejpam-3736	132	26	2	2	NUM
ejpam-3736	132	27	)	)	PUNCT
ejpam-3736	132	28	.	.	PUNCT
ejpam-3736	133	1	for	for	ADP
ejpam-3736	133	2	this	this	DET
ejpam-3736	133	3	zero	zero	NUM
ejpam-3736	133	4	w	w	NOUN
ejpam-3736	133	5	of	of	ADP
ejpam-3736	133	6	the	the	DET
ejpam-3736	133	7	derivative	derivative	ADJ
ejpam-3736	133	8	p′(z	p′(z	NOUN
ejpam-3736	133	9	)	)	PUNCT
ejpam-3736	133	10	,	,	PUNCT
ejpam-3736	133	11	according	accord	VERB
ejpam-3736	133	12	to	to	ADP
ejpam-3736	133	13	theorem	theorem	NOUN
ejpam-3736	133	14	3	3	NUM
ejpam-3736	133	15	,	,	PUNCT
ejpam-3736	133	16	there	there	PRON
ejpam-3736	133	17	exists	exist	VERB
ejpam-3736	133	18	a	a	DET
ejpam-3736	133	19	zero	zero	NUM
ejpam-3736	133	20	of	of	ADP
ejpam-3736	133	21	the	the	DET
ejpam-3736	133	22	polynomial	polynomial	ADJ
ejpam-3736	133	23	p	p	NOUN
ejpam-3736	133	24	(	(	PUNCT
ejpam-3736	133	25	z)−	z)−	PROPN
ejpam-3736	133	26	zk0	zk0	NOUN
ejpam-3736	133	27	,	,	PUNCT
ejpam-3736	133	28	such	such	ADJ
ejpam-3736	133	29	that	that	SCONJ
ejpam-3736	133	30	w	w	PROPN
ejpam-3736	133	31	∈	∈	PROPN
ejpam-3736	133	32	d	d	X
ejpam-3736	133	33	(	(	PUNCT
ejpam-3736	133	34	zk0	zk0	NOUN
ejpam-3736	133	35	2	2	NUM
ejpam-3736	133	36	,	,	PUNCT
ejpam-3736	133	37	|zk0	|zk0	PROPN
ejpam-3736	133	38	|	|	NOUN
ejpam-3736	133	39	2	2	NUM
ejpam-3736	133	40	)	)	PUNCT
ejpam-3736	133	41	.	.	PUNCT
ejpam-3736	134	1	in	in	ADP
ejpam-3736	134	2	order	order	NOUN
ejpam-3736	134	3	to	to	PART
ejpam-3736	134	4	find	find	VERB
ejpam-3736	134	5	the	the	DET
ejpam-3736	134	6	geometric	geometric	ADJ
ejpam-3736	134	7	places	place	NOUN
ejpam-3736	134	8	of	of	ADP
ejpam-3736	134	9	the	the	DET
ejpam-3736	134	10	points	point	NOUN
ejpam-3736	134	11	t	t	PROPN
ejpam-3736	134	12	,	,	PUNCT
ejpam-3736	134	13	let	let	VERB
ejpam-3736	134	14	us	we	PRON
ejpam-3736	134	15	take	take	VERB
ejpam-3736	134	16	w	w	NOUN
ejpam-3736	134	17	on	on	ADP
ejpam-3736	134	18	the	the	DET
ejpam-3736	134	19	boundary	boundary	NOUN
ejpam-3736	134	20	of	of	ADP
ejpam-3736	134	21	the	the	DET
ejpam-3736	134	22	disk	disk	NOUN
ejpam-3736	134	23	d	d	NOUN
ejpam-3736	134	24	(	(	PUNCT
ejpam-3736	134	25	zk0	zk0	NOUN
ejpam-3736	134	26	2	2	NUM
ejpam-3736	134	27	,	,	PUNCT
ejpam-3736	134	28	|zk0	|zk0	PROPN
ejpam-3736	134	29	|	|	NOUN
ejpam-3736	134	30	2	2	NUM
ejpam-3736	134	31	)	)	PUNCT
ejpam-3736	134	32	and	and	CCONJ
ejpam-3736	134	33	t	t	X
ejpam-3736	134	34	on	on	ADP
ejpam-3736	134	35	the	the	DET
ejpam-3736	134	36	boundary	boundary	NOUN
ejpam-3736	134	37	of	of	ADP
ejpam-3736	134	38	the	the	DET
ejpam-3736	134	39	disk	disk	NOUN
ejpam-3736	134	40	d	d	NOUN
ejpam-3736	134	41	(	(	PUNCT
ejpam-3736	134	42	w	w	PROPN
ejpam-3736	134	43	2	2	NUM
ejpam-3736	134	44	,	,	PUNCT
ejpam-3736	134	45	|w|	|w|	ADJ
ejpam-3736	134	46	2	2	NUM
ejpam-3736	134	47	)	)	PUNCT
ejpam-3736	134	48	.	.	PUNCT
ejpam-3736	135	1	for	for	ADP
ejpam-3736	135	2	better	well	ADJ
ejpam-3736	135	3	understanding	understanding	NOUN
ejpam-3736	135	4	,	,	PUNCT
ejpam-3736	135	5	let	let	VERB
ejpam-3736	135	6	us	we	PRON
ejpam-3736	135	7	take	take	VERB
ejpam-3736	135	8	zk0	zk0	NOUN
ejpam-3736	135	9	∈	∈	NOUN
ejpam-3736	135	10	x	x	NOUN
ejpam-3736	135	11	,	,	PUNCT
ejpam-3736	135	12	and	and	CCONJ
ejpam-3736	135	13	arg	arg	NOUN
ejpam-3736	135	14	w	w	PROPN
ejpam-3736	135	15	=	=	SYM
ejpam-3736	135	16	α	α	PROPN
ejpam-3736	135	17	,	,	PUNCT
ejpam-3736	135	18	arg	arg	NOUN
ejpam-3736	135	19	t	t	NOUN
ejpam-3736	135	20	=	=	SYM
ejpam-3736	135	21	α+	α+	X
ejpam-3736	135	22	β	β	X
ejpam-3736	135	23	.	.	PUNCT
ejpam-3736	135	24	figure	figure	NOUN
ejpam-3736	135	25	2	2	NUM
ejpam-3736	135	26	:	:	PUNCT
ejpam-3736	135	27	here	here	ADV
ejpam-3736	135	28	we	we	PRON
ejpam-3736	135	29	have	have	VERB
ejpam-3736	135	30	α	α	PRON
ejpam-3736	135	31	,	,	PUNCT
ejpam-3736	135	32	β	β	X
ejpam-3736	135	33	∈	∈	PROPN
ejpam-3736	135	34	[	[	PUNCT
ejpam-3736	135	35	0	0	NUM
ejpam-3736	135	36	,	,	PUNCT
ejpam-3736	135	37	π2	π2	NOUN
ejpam-3736	135	38	]	]	PUNCT
ejpam-3736	135	39	.	.	PUNCT
ejpam-3736	136	1	let	let	VERB
ejpam-3736	136	2	us	we	PRON
ejpam-3736	136	3	put	put	VERB
ejpam-3736	136	4	|zk0	|zk0	PROPN
ejpam-3736	137	1	|	|	NOUN
ejpam-3736	137	2	=	=	PUNCT
ejpam-3736	137	3	a.	a.	NOUN
ejpam-3736	137	4	then	then	ADV
ejpam-3736	137	5	x	x	PUNCT
ejpam-3736	138	1	=	=	NOUN
ejpam-3736	138	2	a	a	X
ejpam-3736	138	3	cos	cos	PROPN
ejpam-3736	138	4	α	α	PROPN
ejpam-3736	138	5	cos	cos	PROPN
ejpam-3736	138	6	β	β	PROPN
ejpam-3736	138	7	cos	cos	PROPN
ejpam-3736	138	8	(	(	PUNCT
ejpam-3736	138	9	α+	α+	X
ejpam-3736	138	10	β	β	NOUN
ejpam-3736	138	11	)	)	PUNCT
ejpam-3736	138	12	,	,	PUNCT
ejpam-3736	138	13	y	y	PROPN
ejpam-3736	138	14	=	=	PROPN
ejpam-3736	138	15	a	a	X
ejpam-3736	138	16	cos	cos	PROPN
ejpam-3736	138	17	α	α	PROPN
ejpam-3736	138	18	cos	cos	PROPN
ejpam-3736	138	19	β	β	X
ejpam-3736	138	20	sin	sin	NOUN
ejpam-3736	138	21	(	(	PUNCT
ejpam-3736	138	22	α+	α+	X
ejpam-3736	138	23	β	β	NOUN
ejpam-3736	138	24	)	)	PUNCT
ejpam-3736	138	25	,	,	PUNCT
ejpam-3736	138	26	x2	x2	PROPN
ejpam-3736	139	1	+	+	CCONJ
ejpam-3736	139	2	y2	y2	PROPN
ejpam-3736	139	3	=	=	SYM
ejpam-3736	139	4	a2	a2	PROPN
ejpam-3736	139	5	cos2α	cos2α	NOUN
ejpam-3736	139	6	cos2β	cos2β	NOUN
ejpam-3736	139	7	,	,	PUNCT
ejpam-3736	139	8	(	(	PUNCT
ejpam-3736	139	9	x2	x2	NOUN
ejpam-3736	140	1	+	+	CCONJ
ejpam-3736	140	2	y2	y2	NOUN
ejpam-3736	140	3	−	−	NOUN
ejpam-3736	140	4	ax	ax	NOUN
ejpam-3736	140	5	)	)	PUNCT
ejpam-3736	140	6	2	2	NUM
ejpam-3736	140	7	=	=	SYM
ejpam-3736	140	8	(	(	PUNCT
ejpam-3736	140	9	a2	a2	PROPN
ejpam-3736	140	10	cos2α	cos2α	PROPN
ejpam-3736	141	1	cos2β	cos2β	NOUN
ejpam-3736	141	2	−	−	PROPN
ejpam-3736	141	3	a2	a2	PROPN
ejpam-3736	141	4	cos	cos	PROPN
ejpam-3736	141	5	α	α	PROPN
ejpam-3736	141	6	cos	cos	PROPN
ejpam-3736	141	7	β	β	PROPN
ejpam-3736	141	8	cos	cos	PROPN
ejpam-3736	141	9	(	(	PUNCT
ejpam-3736	141	10	α+	α+	X
ejpam-3736	141	11	β	β	NOUN
ejpam-3736	141	12	)	)	PUNCT
ejpam-3736	141	13	)	)	PUNCT
ejpam-3736	141	14	2	2	NUM
ejpam-3736	141	15	=	=	SYM
ejpam-3736	141	16	a4	a4	NOUN
ejpam-3736	141	17	cos2α	cos2α	NOUN
ejpam-3736	141	18	cos2β	cos2β	NOUN
ejpam-3736	141	19	sin2α	sin2α	PROPN
ejpam-3736	141	20	sin2β	sin2β	NOUN
ejpam-3736	141	21	≤	≤	PUNCT
ejpam-3736	141	22	a2a2	a2a2	PROPN
ejpam-3736	141	23	cos2α	cos2α	X
ejpam-3736	141	24	cos2β	cos2β	NOUN
ejpam-3736	141	25	=	=	SYM
ejpam-3736	141	26	a2(x2	a2(x2	NOUN
ejpam-3736	141	27	+	+	CCONJ
ejpam-3736	141	28	y2	y2	NOUN
ejpam-3736	141	29	)	)	PUNCT
ejpam-3736	141	30	.	.	PUNCT
ejpam-3736	142	1	this	this	PRON
ejpam-3736	142	2	means	mean	VERB
ejpam-3736	142	3	that	that	SCONJ
ejpam-3736	142	4	our	our	PRON
ejpam-3736	142	5	geometric	geometric	ADJ
ejpam-3736	142	6	place	place	NOUN
ejpam-3736	142	7	belongs	belong	VERB
ejpam-3736	142	8	to	to	ADP
ejpam-3736	142	9	c	c	PROPN
ejpam-3736	142	10	(	(	PUNCT
ejpam-3736	142	11	zk0	zk0	NOUN
ejpam-3736	142	12	2	2	NUM
ejpam-3736	142	13	,	,	PUNCT
ejpam-3736	142	14	|zk0	|zk0	PROPN
ejpam-3736	142	15	|	|	ADV
ejpam-3736	142	16	2	2	NUM
ejpam-3736	142	17	)	)	PUNCT
ejpam-3736	142	18	.	.	PUNCT
ejpam-3736	143	1	t.	t.	PROPN
ejpam-3736	143	2	s.	s.	PROPN
ejpam-3736	143	3	stoyanov	stoyanov	PROPN
ejpam-3736	143	4	/	/	SYM
ejpam-3736	143	5	eur	eur	PROPN
ejpam-3736	143	6	.	.	PUNCT
ejpam-3736	144	1	j.	j.	PROPN
ejpam-3736	144	2	pure	pure	PROPN
ejpam-3736	144	3	appl	appl	PROPN
ejpam-3736	144	4	.	.	PROPN
ejpam-3736	144	5	math	math	PROPN
ejpam-3736	144	6	,	,	PUNCT
ejpam-3736	144	7	13	13	NUM
ejpam-3736	144	8	(	(	PUNCT
ejpam-3736	144	9	3	3	NUM
ejpam-3736	144	10	)	)	PUNCT
ejpam-3736	144	11	(	(	PUNCT
ejpam-3736	144	12	2020	2020	NUM
ejpam-3736	144	13	)	)	PUNCT
ejpam-3736	144	14	,	,	PUNCT
ejpam-3736	144	15	663	663	NUM
ejpam-3736	144	16	-	-	SYM
ejpam-3736	144	17	673	673	NUM
ejpam-3736	144	18	668	668	NUM
ejpam-3736	144	19	figure	figure	NOUN
ejpam-3736	144	20	3	3	NUM
ejpam-3736	144	21	:	:	SYM
ejpam-3736	144	22	4	4	NUM
ejpam-3736	144	23	.	.	X
ejpam-3736	144	24	main	main	ADJ
ejpam-3736	144	25	results	result	NOUN
ejpam-3736	144	26	lemma	lemma	PROPN
ejpam-3736	145	1	1	1	X
ejpam-3736	145	2	.	.	PUNCT
ejpam-3736	146	1	if	if	SCONJ
ejpam-3736	146	2	x	x	X
ejpam-3736	146	3	,	,	PUNCT
ejpam-3736	146	4	y	y	PROPN
ejpam-3736	146	5	∈	∈	PROPN
ejpam-3736	147	1	[	[	X
ejpam-3736	147	2	0	0	NUM
ejpam-3736	147	3	,	,	PUNCT
ejpam-3736	147	4	1	1	NUM
ejpam-3736	147	5	]	]	PUNCT
ejpam-3736	147	6	,	,	PUNCT
ejpam-3736	147	7	then	then	ADV
ejpam-3736	147	8	the	the	DET
ejpam-3736	147	9	function	function	NOUN
ejpam-3736	147	10	h	h	NOUN
ejpam-3736	147	11	(	(	PUNCT
ejpam-3736	147	12	x	x	NOUN
ejpam-3736	147	13	,	,	PUNCT
ejpam-3736	147	14	y	y	NOUN
ejpam-3736	147	15	)	)	PUNCT
ejpam-3736	147	16	=	=	PUNCT
ejpam-3736	148	1	x	x	PUNCT
ejpam-3736	148	2	√	√	ADP
ejpam-3736	148	3	1−	1−	NUM
ejpam-3736	149	1	y2	y2	INTJ
ejpam-3736	150	1	+	+	CCONJ
ejpam-3736	150	2	y	y	PROPN
ejpam-3736	150	3	√	√	PROPN
ejpam-3736	150	4	1−	1−	NUM
ejpam-3736	150	5	x2	x2	INTJ
ejpam-3736	150	6	≤	≤	ADV
ejpam-3736	150	7	1	1	NUM
ejpam-3736	150	8	.	.	PUNCT
ejpam-3736	151	1	proof	proof	NOUN
ejpam-3736	151	2	.	.	PUNCT
ejpam-3736	152	1	if	if	SCONJ
ejpam-3736	152	2	we	we	PRON
ejpam-3736	152	3	fix	fix	VERB
ejpam-3736	152	4	y	y	PROPN
ejpam-3736	152	5	∈	∈	PROPN
ejpam-3736	153	1	[	[	X
ejpam-3736	153	2	0	0	NUM
ejpam-3736	153	3	,	,	PUNCT
ejpam-3736	153	4	1	1	NUM
ejpam-3736	153	5	]	]	PUNCT
ejpam-3736	153	6	,	,	PUNCT
ejpam-3736	153	7	then	then	ADV
ejpam-3736	153	8	t	t	PROPN
ejpam-3736	153	9	(	(	PUNCT
ejpam-3736	153	10	x	x	X
ejpam-3736	153	11	)	)	PUNCT
ejpam-3736	153	12	=	=	SYM
ejpam-3736	153	13	h(x	h(x	PROPN
ejpam-3736	153	14	,	,	PUNCT
ejpam-3736	153	15	y	y	PROPN
ejpam-3736	153	16	)	)	PUNCT
ejpam-3736	153	17	=	=	PUNCT
ejpam-3736	154	1	x	x	PUNCT
ejpam-3736	154	2	√	√	ADP
ejpam-3736	154	3	1−	1−	NUM
ejpam-3736	155	1	y2	y2	INTJ
ejpam-3736	156	1	+	+	CCONJ
ejpam-3736	156	2	y	y	PROPN
ejpam-3736	156	3	√	√	PROPN
ejpam-3736	156	4	1−	1−	NUM
ejpam-3736	156	5	x2	x2	PROPN
ejpam-3736	156	6	.	.	PUNCT
ejpam-3736	157	1	∂t	∂t	PROPN
ejpam-3736	157	2	∂x	∂x	PROPN
ejpam-3736	157	3	=	=	PUNCT
ejpam-3736	158	1	√	√	PROPN
ejpam-3736	158	2	1−	1−	NUM
ejpam-3736	159	1	y2	y2	NOUN
ejpam-3736	159	2	−	−	PROPN
ejpam-3736	159	3	xy√	xy√	PUNCT
ejpam-3736	160	1	1−	1−	NUM
ejpam-3736	160	2	x2	x2	NOUN
ejpam-3736	160	3	=	=	PUNCT
ejpam-3736	161	1	√	√	PROPN
ejpam-3736	161	2	1−	1−	NUM
ejpam-3736	162	1	x2	x2	NOUN
ejpam-3736	162	2	−	−	PROPN
ejpam-3736	162	3	y2+x2y2	y2+x2y2	NOUN
ejpam-3736	163	1	−	−	PROPN
ejpam-3736	163	2	xy	xy	NOUN
ejpam-3736	164	1	√	√	PROPN
ejpam-3736	164	2	1−	1−	NUM
ejpam-3736	165	1	x2	x2	INTJ
ejpam-3736	165	2	,	,	PUNCT
ejpam-3736	165	3	where	where	SCONJ
ejpam-3736	165	4	x	x	PUNCT
ejpam-3736	165	5	6=	6=	ADP
ejpam-3736	165	6	1	1	NUM
ejpam-3736	165	7	.	.	PUNCT
ejpam-3736	166	1	the	the	DET
ejpam-3736	166	2	function	function	NOUN
ejpam-3736	166	3	l(x	l(x	PROPN
ejpam-3736	166	4	)	)	PUNCT
ejpam-3736	166	5	=	=	SYM
ejpam-3736	166	6	√	√	PROPN
ejpam-3736	166	7	1−	1−	NUM
ejpam-3736	167	1	x2	x2	NOUN
ejpam-3736	167	2	−	−	PROPN
ejpam-3736	167	3	y2+x2y2	y2+x2y2	NOUN
ejpam-3736	168	1	−	−	PROPN
ejpam-3736	168	2	xy	xy	NOUN
ejpam-3736	169	1	=	=	SYM
ejpam-3736	169	2	0	0	PROPN
ejpam-3736	169	3	,	,	PUNCT
ejpam-3736	169	4	when	when	SCONJ
ejpam-3736	169	5	1	1	NUM
ejpam-3736	169	6	−	−	NOUN
ejpam-3736	169	7	x2	x2	INTJ
ejpam-3736	170	1	−	−	PROPN
ejpam-3736	170	2	y2	y2	NOUN
ejpam-3736	170	3	=	=	NOUN
ejpam-3736	170	4	0	0	NUM
ejpam-3736	170	5	⇐	⇐	ADJ
ejpam-3736	170	6	⇒	⇒	NOUN
ejpam-3736	170	7	x	x	PUNCT
ejpam-3736	171	1	=	=	VERB
ejpam-3736	171	2	√	√	ADP
ejpam-3736	171	3	1−	1−	NUM
ejpam-3736	171	4	y2	y2	NOUN
ejpam-3736	171	5	.	.	PUNCT
ejpam-3736	172	1	we	we	PRON
ejpam-3736	172	2	know	know	VERB
ejpam-3736	172	3	l(x	l(x	PROPN
ejpam-3736	172	4	)	)	PUNCT
ejpam-3736	172	5	>	>	X
ejpam-3736	172	6	0	0	PUNCT
ejpam-3736	173	1	with	with	ADP
ejpam-3736	173	2	x	x	X
ejpam-3736	173	3	<	<	X
ejpam-3736	173	4	√	√	PROPN
ejpam-3736	173	5	1−	1−	NUM
ejpam-3736	173	6	y2	y2	NOUN
ejpam-3736	173	7	,	,	PUNCT
ejpam-3736	173	8	l(x	l(x	PROPN
ejpam-3736	173	9	)	)	PUNCT
ejpam-3736	173	10	<	<	X
ejpam-3736	173	11	0	0	PUNCT
ejpam-3736	173	12	with	with	ADP
ejpam-3736	173	13	x	x	PROPN
ejpam-3736	173	14	>	>	PUNCT
ejpam-3736	173	15	√	√	PROPN
ejpam-3736	173	16	1−	1−	NUM
ejpam-3736	173	17	y2	y2	NOUN
ejpam-3736	173	18	,	,	PUNCT
ejpam-3736	173	19	l	l	X
ejpam-3736	173	20	(	(	PUNCT
ejpam-3736	173	21	0	0	NUM
ejpam-3736	173	22	)	)	PUNCT
ejpam-3736	173	23	=	=	SYM
ejpam-3736	173	24	√	√	ADP
ejpam-3736	173	25	1−	1−	NUM
ejpam-3736	174	1	y2	y2	NOUN
ejpam-3736	174	2	>	>	X
ejpam-3736	174	3	0	0	NUM
ejpam-3736	174	4	,	,	PUNCT
ejpam-3736	174	5	l	l	NOUN
ejpam-3736	174	6	(	(	PUNCT
ejpam-3736	174	7	1	1	NUM
ejpam-3736	174	8	)	)	PUNCT
ejpam-3736	174	9	=	=	SYM
ejpam-3736	175	1	−	−	PROPN
ejpam-3736	175	2	y	y	NOUN
ejpam-3736	175	3	<	<	X
ejpam-3736	175	4	0	0	PROPN
ejpam-3736	175	5	.	.	PUNCT
ejpam-3736	176	1	then	then	ADV
ejpam-3736	176	2	h(x	h(x	PROPN
ejpam-3736	176	3	,	,	PUNCT
ejpam-3736	176	4	y	y	PROPN
ejpam-3736	176	5	)	)	PUNCT
ejpam-3736	176	6	≤	≤	NOUN
ejpam-3736	176	7	t	t	NOUN
ejpam-3736	176	8	(	(	PUNCT
ejpam-3736	176	9	√	√	PROPN
ejpam-3736	176	10	1−	1−	NUM
ejpam-3736	176	11	y2	y2	NOUN
ejpam-3736	176	12	)	)	PUNCT
ejpam-3736	177	1	=	=	SYM
ejpam-3736	178	1	1−	1−	NUM
ejpam-3736	178	2	y2	y2	NOUN
ejpam-3736	178	3	+	+	CCONJ
ejpam-3736	179	1	y2	y2	NOUN
ejpam-3736	180	1	=	=	SYM
ejpam-3736	181	1	1	1	NUM
ejpam-3736	181	2	,	,	PUNCT
ejpam-3736	181	3	which	which	PRON
ejpam-3736	181	4	confirms	confirm	VERB
ejpam-3736	181	5	the	the	DET
ejpam-3736	181	6	lemma	lemma	PROPN
ejpam-3736	181	7	.	.	PUNCT
ejpam-3736	181	8	theorem	theorem	VERB
ejpam-3736	181	9	6	6	NUM
ejpam-3736	181	10	.	.	PUNCT
ejpam-3736	182	1	let	let	VERB
ejpam-3736	182	2	x	x	PRON
ejpam-3736	182	3	,	,	PUNCT
ejpam-3736	182	4	y	y	PROPN
ejpam-3736	182	5	,	,	PUNCT
ejpam-3736	182	6	z	z	NOUN
ejpam-3736	182	7	∈	∈	PROPN
ejpam-3736	183	1	[	[	X
ejpam-3736	183	2	0	0	NUM
ejpam-3736	183	3	,	,	PUNCT
ejpam-3736	183	4	1	1	NUM
ejpam-3736	183	5	]	]	PUNCT
ejpam-3736	183	6	.	.	PUNCT
ejpam-3736	184	1	then	then	ADV
ejpam-3736	184	2	the	the	DET
ejpam-3736	184	3	function	function	NOUN
ejpam-3736	184	4	f	f	X
ejpam-3736	184	5	(	(	PUNCT
ejpam-3736	184	6	x	x	PROPN
ejpam-3736	184	7	,	,	PUNCT
ejpam-3736	184	8	y	y	PROPN
ejpam-3736	184	9	,	,	PUNCT
ejpam-3736	184	10	z	z	NOUN
ejpam-3736	184	11	)	)	PUNCT
ejpam-3736	184	12	=	=	PUNCT
ejpam-3736	185	1	xy	xy	PROPN
ejpam-3736	185	2	√	√	PROPN
ejpam-3736	185	3	1−	1−	NUM
ejpam-3736	185	4	z2	z2	PROPN
ejpam-3736	185	5	+	+	PROPN
ejpam-3736	185	6	yz	yz	PROPN
ejpam-3736	185	7	√	√	ADP
ejpam-3736	185	8	1−	1−	NUM
ejpam-3736	186	1	x2	x2	PROPN
ejpam-3736	187	1	+	+	CCONJ
ejpam-3736	187	2	zx	zx	NUM
ejpam-3736	187	3	√	√	NUM
ejpam-3736	187	4	1−	1−	NUM
ejpam-3736	187	5	y2	y2	NOUN
ejpam-3736	187	6	satisfies	satisfy	VERB
ejpam-3736	187	7	f	f	PROPN
ejpam-3736	187	8	(	(	PUNCT
ejpam-3736	187	9	x	x	PROPN
ejpam-3736	187	10	,	,	PUNCT
ejpam-3736	187	11	y	y	PROPN
ejpam-3736	187	12	,	,	PUNCT
ejpam-3736	187	13	z	z	NOUN
ejpam-3736	187	14	)	)	PUNCT
ejpam-3736	187	15	≤	≤	NUM
ejpam-3736	187	16	2	2	NUM
ejpam-3736	187	17	√	√	NUM
ejpam-3736	187	18	3	3	NUM
ejpam-3736	187	19	3	3	NUM
ejpam-3736	187	20	.	.	PUNCT
ejpam-3736	188	1	t.	t.	PROPN
ejpam-3736	188	2	s.	s.	PROPN
ejpam-3736	188	3	stoyanov	stoyanov	PROPN
ejpam-3736	188	4	/	/	SYM
ejpam-3736	188	5	eur	eur	PROPN
ejpam-3736	188	6	.	.	PUNCT
ejpam-3736	189	1	j.	j.	PROPN
ejpam-3736	189	2	pure	pure	PROPN
ejpam-3736	189	3	appl	appl	PROPN
ejpam-3736	189	4	.	.	PROPN
ejpam-3736	189	5	math	math	PROPN
ejpam-3736	189	6	,	,	PUNCT
ejpam-3736	189	7	13	13	NUM
ejpam-3736	189	8	(	(	PUNCT
ejpam-3736	189	9	3	3	NUM
ejpam-3736	189	10	)	)	PUNCT
ejpam-3736	189	11	(	(	PUNCT
ejpam-3736	189	12	2020	2020	NUM
ejpam-3736	189	13	)	)	PUNCT
ejpam-3736	189	14	,	,	PUNCT
ejpam-3736	189	15	663	663	NUM
ejpam-3736	189	16	-	-	SYM
ejpam-3736	189	17	673	673	NUM
ejpam-3736	189	18	669	669	NUM
ejpam-3736	189	19	proof	proof	NOUN
ejpam-3736	189	20	.	.	PUNCT
ejpam-3736	190	1	let	let	VERB
ejpam-3736	190	2	us	we	PRON
ejpam-3736	190	3	calculate	calculate	VERB
ejpam-3736	190	4	∂f	∂f	PROPN
ejpam-3736	190	5	∂x	∂x	PROPN
ejpam-3736	190	6	=	=	SYM
ejpam-3736	190	7	y	y	PROPN
ejpam-3736	190	8	√	√	PROPN
ejpam-3736	190	9	1−	1−	NUM
ejpam-3736	190	10	z2	z2	PROPN
ejpam-3736	190	11	+	+	CCONJ
ejpam-3736	190	12	z	z	PROPN
ejpam-3736	190	13	√	√	PROPN
ejpam-3736	190	14	1−	1−	NUM
ejpam-3736	191	1	y2	y2	NOUN
ejpam-3736	191	2	−	−	PROPN
ejpam-3736	192	1	xyz√	xyz√	PROPN
ejpam-3736	192	2	1−	1−	NUM
ejpam-3736	192	3	x2	x2	NOUN
ejpam-3736	192	4	,	,	PUNCT
ejpam-3736	192	5	∂f	∂f	PROPN
ejpam-3736	192	6	∂y	∂y	SYM
ejpam-3736	193	1	=	=	PUNCT
ejpam-3736	193	2	x	x	SYM
ejpam-3736	193	3	√	√	PROPN
ejpam-3736	193	4	1−	1−	NUM
ejpam-3736	193	5	z2	z2	PROPN
ejpam-3736	193	6	+	+	CCONJ
ejpam-3736	193	7	z	z	PROPN
ejpam-3736	193	8	√	√	PROPN
ejpam-3736	193	9	1−	1−	NUM
ejpam-3736	194	1	x2	x2	INTJ
ejpam-3736	194	2	−	−	PROPN
ejpam-3736	194	3	xyz√	xyz√	PROPN
ejpam-3736	194	4	1−	1−	NUM
ejpam-3736	195	1	y2	y2	INTJ
ejpam-3736	195	2	,	,	PUNCT
ejpam-3736	195	3	∂f	∂f	PROPN
ejpam-3736	195	4	∂z	∂z	PROPN
ejpam-3736	196	1	=	=	PUNCT
ejpam-3736	196	2	x	x	PUNCT
ejpam-3736	196	3	√	√	ADP
ejpam-3736	196	4	1−	1−	NUM
ejpam-3736	197	1	y2	y2	INTJ
ejpam-3736	198	1	+	+	CCONJ
ejpam-3736	198	2	y	y	PROPN
ejpam-3736	198	3	√	√	PROPN
ejpam-3736	198	4	1−	1−	NUM
ejpam-3736	199	1	x2	x2	INTJ
ejpam-3736	199	2	−	−	PROPN
ejpam-3736	199	3	xyz√	xyz√	PROPN
ejpam-3736	199	4	1−	1−	PROPN
ejpam-3736	199	5	z2	z2	PROPN
ejpam-3736	199	6	.	.	PUNCT
ejpam-3736	200	1	we	we	PRON
ejpam-3736	200	2	want	want	VERB
ejpam-3736	200	3	x	x	X
ejpam-3736	200	4	6=	6=	ADP
ejpam-3736	200	5	1	1	NUM
ejpam-3736	200	6	,	,	PUNCT
ejpam-3736	200	7	y	y	PROPN
ejpam-3736	200	8	6=	6=	PROPN
ejpam-3736	200	9	1	1	NUM
ejpam-3736	200	10	,	,	PUNCT
ejpam-3736	200	11	z	z	NOUN
ejpam-3736	200	12	6=	6=	NUM
ejpam-3736	200	13	1	1	X
ejpam-3736	200	14	.	.	PUNCT
ejpam-3736	201	1	we	we	PRON
ejpam-3736	201	2	need	need	VERB
ejpam-3736	201	3	to	to	PART
ejpam-3736	201	4	solve	solve	VERB
ejpam-3736	201	5	the	the	DET
ejpam-3736	201	6	system	system	NOUN
ejpam-3736	201	7	y	y	PROPN
ejpam-3736	201	8	√	√	PROPN
ejpam-3736	201	9	1−	1−	NUM
ejpam-3736	201	10	z2	z2	PROPN
ejpam-3736	201	11	+	+	CCONJ
ejpam-3736	201	12	z	z	PROPN
ejpam-3736	201	13	√	√	PROPN
ejpam-3736	201	14	1−	1−	NUM
ejpam-3736	202	1	y2	y2	NOUN
ejpam-3736	202	2	−	−	PROPN
ejpam-3736	203	1	xyz√	xyz√	PROPN
ejpam-3736	203	2	1−	1−	NUM
ejpam-3736	204	1	x2	x2	PROPN
ejpam-3736	205	1	=	=	SYM
ejpam-3736	206	1	0	0	PROPN
ejpam-3736	206	2	,	,	PUNCT
ejpam-3736	206	3	x	x	PUNCT
ejpam-3736	206	4	√	√	ADP
ejpam-3736	206	5	1−	1−	NUM
ejpam-3736	206	6	z2	z2	PROPN
ejpam-3736	206	7	+	+	CCONJ
ejpam-3736	206	8	z	z	PROPN
ejpam-3736	207	1	√	√	PROPN
ejpam-3736	207	2	1−	1−	NUM
ejpam-3736	208	1	x2	x2	INTJ
ejpam-3736	208	2	−	−	PROPN
ejpam-3736	209	1	xyz√	xyz√	PROPN
ejpam-3736	209	2	1−	1−	NUM
ejpam-3736	210	1	y2	y2	NOUN
ejpam-3736	210	2	=	=	SYM
ejpam-3736	210	3	0	0	PROPN
ejpam-3736	210	4	,	,	PUNCT
ejpam-3736	210	5	y	y	PROPN
ejpam-3736	210	6	√	√	PROPN
ejpam-3736	210	7	1−	1−	NUM
ejpam-3736	211	1	x2	x2	NOUN
ejpam-3736	212	1	+	+	CCONJ
ejpam-3736	212	2	x	x	PUNCT
ejpam-3736	212	3	√	√	ADP
ejpam-3736	212	4	1−	1−	NUM
ejpam-3736	213	1	y2	y2	NOUN
ejpam-3736	213	2	−	−	PROPN
ejpam-3736	214	1	xyz√	xyz√	PROPN
ejpam-3736	214	2	1−	1−	NUM
ejpam-3736	214	3	z2	z2	PROPN
ejpam-3736	214	4	=	=	SYM
ejpam-3736	214	5	0	0	PROPN
ejpam-3736	214	6	.	.	PUNCT
ejpam-3736	215	1	if	if	SCONJ
ejpam-3736	215	2	x	x	PROPN
ejpam-3736	215	3	6=	6=	ADP
ejpam-3736	215	4	0	0	NUM
ejpam-3736	215	5	,	,	PUNCT
ejpam-3736	215	6	y	y	PROPN
ejpam-3736	215	7	6=	6=	PROPN
ejpam-3736	215	8	0	0	NUM
ejpam-3736	215	9	,	,	PUNCT
ejpam-3736	215	10	z	z	NOUN
ejpam-3736	215	11	6=	6=	NUM
ejpam-3736	215	12	0	0	NUM
ejpam-3736	215	13	,	,	PUNCT
ejpam-3736	215	14	the	the	DET
ejpam-3736	215	15	system	system	NOUN
ejpam-3736	215	16	is	be	AUX
ejpam-3736	215	17	√	√	ADJ
ejpam-3736	215	18	1−	1−	NUM
ejpam-3736	215	19	z2	z2	PROPN
ejpam-3736	215	20	z	z	PROPN
ejpam-3736	216	1	+	+	CCONJ
ejpam-3736	216	2	√	√	INTJ
ejpam-3736	216	3	1−	1−	NUM
ejpam-3736	216	4	y2	y2	NOUN
ejpam-3736	216	5	y	y	NOUN
ejpam-3736	217	1	=	=	SYM
ejpam-3736	217	2	x√	x√	PROPN
ejpam-3736	217	3	1−	1−	NUM
ejpam-3736	217	4	x2	x2	NOUN
ejpam-3736	217	5	,	,	PUNCT
ejpam-3736	217	6	√	√	PROPN
ejpam-3736	217	7	1−	1−	NUM
ejpam-3736	217	8	z2	z2	PROPN
ejpam-3736	217	9	z	z	PROPN
ejpam-3736	217	10	+	+	CCONJ
ejpam-3736	217	11	√	√	PROPN
ejpam-3736	217	12	1−	1−	NUM
ejpam-3736	217	13	x2	x2	NOUN
ejpam-3736	217	14	x	x	PUNCT
ejpam-3736	217	15	=	=	SYM
ejpam-3736	217	16	y√	y√	NOUN
ejpam-3736	217	17	1−	1−	NUM
ejpam-3736	217	18	y2	y2	INTJ
ejpam-3736	217	19	,	,	PUNCT
ejpam-3736	217	20	√	√	PROPN
ejpam-3736	217	21	1−	1−	NUM
ejpam-3736	218	1	x2	x2	NOUN
ejpam-3736	218	2	x	x	PUNCT
ejpam-3736	219	1	+	+	CCONJ
ejpam-3736	219	2	√	√	NUM
ejpam-3736	219	3	1−	1−	NUM
ejpam-3736	219	4	y2	y2	NOUN
ejpam-3736	219	5	y	y	PROPN
ejpam-3736	219	6	=	=	SYM
ejpam-3736	219	7	z√	z√	PROPN
ejpam-3736	219	8	1−	1−	NUM
ejpam-3736	219	9	z2	z2	PROPN
ejpam-3736	219	10	.	.	PUNCT
ejpam-3736	220	1	we	we	PRON
ejpam-3736	220	2	put	put	VERB
ejpam-3736	220	3	√	√	PROPN
ejpam-3736	220	4	1−	1−	NUM
ejpam-3736	221	1	x2	x2	NOUN
ejpam-3736	221	2	x	x	X
ejpam-3736	222	1	=	=	SYM
ejpam-3736	222	2	p	p	NOUN
ejpam-3736	222	3	,	,	PUNCT
ejpam-3736	222	4	√	√	PROPN
ejpam-3736	222	5	1−	1−	NUM
ejpam-3736	223	1	y2	y2	NOUN
ejpam-3736	223	2	y	y	NOUN
ejpam-3736	224	1	=	=	SYM
ejpam-3736	224	2	q	q	NOUN
ejpam-3736	224	3	,	,	PUNCT
ejpam-3736	224	4	√	√	PROPN
ejpam-3736	224	5	1−	1−	NUM
ejpam-3736	224	6	z2	z2	PROPN
ejpam-3736	224	7	z	z	PROPN
ejpam-3736	224	8	=	=	SYM
ejpam-3736	224	9	s.	s.	PROPN
ejpam-3736	224	10	(	(	PUNCT
ejpam-3736	224	11	1	1	X
ejpam-3736	224	12	)	)	PUNCT
ejpam-3736	224	13	then	then	ADV
ejpam-3736	224	14	we	we	PRON
ejpam-3736	224	15	have	have	VERB
ejpam-3736	224	16	q	q	NOUN
ejpam-3736	225	1	+	+	NUM
ejpam-3736	225	2	s	s	NOUN
ejpam-3736	225	3	=	=	SYM
ejpam-3736	225	4	1	1	NUM
ejpam-3736	225	5	p	p	NOUN
ejpam-3736	225	6	,	,	PUNCT
ejpam-3736	225	7	(	(	PUNCT
ejpam-3736	225	8	2	2	NUM
ejpam-3736	225	9	)	)	PUNCT
ejpam-3736	225	10	s+	s+	PUNCT
ejpam-3736	225	11	p	p	X
ejpam-3736	225	12	=	=	SYM
ejpam-3736	225	13	1	1	NUM
ejpam-3736	225	14	q	q	NOUN
ejpam-3736	225	15	,	,	PUNCT
ejpam-3736	225	16	(	(	PUNCT
ejpam-3736	225	17	3	3	X
ejpam-3736	225	18	)	)	PUNCT
ejpam-3736	225	19	p+	p+	NOUN
ejpam-3736	225	20	q	q	NOUN
ejpam-3736	225	21	=	=	SYM
ejpam-3736	225	22	1	1	NUM
ejpam-3736	225	23	s	s	NOUN
ejpam-3736	225	24	.	.	PUNCT
ejpam-3736	226	1	(	(	PUNCT
ejpam-3736	226	2	4	4	NUM
ejpam-3736	226	3	)	)	PUNCT
ejpam-3736	226	4	after	after	ADP
ejpam-3736	226	5	the	the	DET
ejpam-3736	226	6	subtraction	subtraction	NOUN
ejpam-3736	226	7	(	(	PUNCT
ejpam-3736	226	8	2	2	NUM
ejpam-3736	226	9	)	)	PUNCT
ejpam-3736	226	10	–	–	PUNCT
ejpam-3736	226	11	(	(	PUNCT
ejpam-3736	226	12	3	3	NUM
ejpam-3736	226	13	)	)	PUNCT
ejpam-3736	226	14	,	,	PUNCT
ejpam-3736	226	15	we	we	PRON
ejpam-3736	226	16	get	get	VERB
ejpam-3736	226	17	q	q	NOUN
ejpam-3736	227	1	+	+	NUM
ejpam-3736	227	2	1	1	NUM
ejpam-3736	227	3	q	q	NOUN
ejpam-3736	227	4	=	=	X
ejpam-3736	227	5	p+	p+	NOUN
ejpam-3736	227	6	1	1	NUM
ejpam-3736	227	7	p	p	NOUN
ejpam-3736	227	8	,	,	PUNCT
ejpam-3736	227	9	i.e.	i.e.	X
ejpam-3736	227	10	p	p	X
ejpam-3736	227	11	=	=	PUNCT
ejpam-3736	227	12	q	q	X
ejpam-3736	227	13	or	or	CCONJ
ejpam-3736	227	14	p	p	NOUN
ejpam-3736	227	15	=	=	NOUN
ejpam-3736	227	16	1	1	NUM
ejpam-3736	227	17	q	q	NOUN
ejpam-3736	227	18	.	.	PUNCT
ejpam-3736	228	1	t.	t.	PROPN
ejpam-3736	228	2	s.	s.	PROPN
ejpam-3736	228	3	stoyanov	stoyanov	PROPN
ejpam-3736	228	4	/	/	SYM
ejpam-3736	228	5	eur	eur	PROPN
ejpam-3736	228	6	.	.	PUNCT
ejpam-3736	229	1	j.	j.	PROPN
ejpam-3736	229	2	pure	pure	PROPN
ejpam-3736	229	3	appl	appl	PROPN
ejpam-3736	229	4	.	.	PROPN
ejpam-3736	229	5	math	math	PROPN
ejpam-3736	229	6	,	,	PUNCT
ejpam-3736	229	7	13	13	NUM
ejpam-3736	229	8	(	(	PUNCT
ejpam-3736	229	9	3	3	NUM
ejpam-3736	229	10	)	)	PUNCT
ejpam-3736	229	11	(	(	PUNCT
ejpam-3736	229	12	2020	2020	NUM
ejpam-3736	229	13	)	)	PUNCT
ejpam-3736	229	14	,	,	PUNCT
ejpam-3736	229	15	663	663	NUM
ejpam-3736	229	16	-	-	SYM
ejpam-3736	229	17	673	673	NUM
ejpam-3736	229	18	670	670	NUM
ejpam-3736	229	19	analogously	analogously	ADV
ejpam-3736	229	20	q	q	NOUN
ejpam-3736	229	21	=	=	SYM
ejpam-3736	229	22	s	s	X
ejpam-3736	229	23	or	or	CCONJ
ejpam-3736	229	24	q	q	NOUN
ejpam-3736	229	25	=	=	SYM
ejpam-3736	229	26	1	1	NUM
ejpam-3736	229	27	s	s	NOUN
ejpam-3736	229	28	,	,	PUNCT
ejpam-3736	229	29	and	and	CCONJ
ejpam-3736	229	30	s	s	VERB
ejpam-3736	229	31	=	=	PUNCT
ejpam-3736	229	32	p	p	PROPN
ejpam-3736	229	33	or	or	CCONJ
ejpam-3736	229	34	s	s	NOUN
ejpam-3736	229	35	=	=	SYM
ejpam-3736	229	36	1	1	NUM
ejpam-3736	229	37	p	p	NOUN
ejpam-3736	229	38	.	.	PUNCT
ejpam-3736	230	1	because	because	SCONJ
ejpam-3736	230	2	of	of	ADP
ejpam-3736	230	3	(	(	PUNCT
ejpam-3736	230	4	1	1	NUM
ejpam-3736	230	5	)	)	PUNCT
ejpam-3736	230	6	,	,	PUNCT
ejpam-3736	230	7	the	the	DET
ejpam-3736	230	8	only	only	ADJ
ejpam-3736	230	9	possibility	possibility	NOUN
ejpam-3736	230	10	is	be	AUX
ejpam-3736	230	11	p	p	NOUN
ejpam-3736	230	12	=	=	PUNCT
ejpam-3736	230	13	q	q	X
ejpam-3736	230	14	=	=	SYM
ejpam-3736	230	15	s	s	PROPN
ejpam-3736	230	16	and	and	CCONJ
ejpam-3736	230	17	therefore	therefore	ADV
ejpam-3736	230	18	p+	p+	VERB
ejpam-3736	230	19	p	p	NOUN
ejpam-3736	230	20	=	=	PROPN
ejpam-3736	230	21	1	1	NUM
ejpam-3736	230	22	p	p	NOUN
ejpam-3736	230	23	,	,	PUNCT
ejpam-3736	230	24	i.e.	i.e.	X
ejpam-3736	230	25	p	p	X
ejpam-3736	230	26	=	=	NOUN
ejpam-3736	230	27	√	√	NUM
ejpam-3736	230	28	1	1	NUM
ejpam-3736	230	29	2	2	NUM
ejpam-3736	230	30	,	,	PUNCT
ejpam-3736	230	31	i.e.	i.e.	X
ejpam-3736	230	32	x	x	X
ejpam-3736	230	33	=	=	SYM
ejpam-3736	230	34	y	y	NOUN
ejpam-3736	230	35	=	=	PUNCT
ejpam-3736	230	36	z	z	PROPN
ejpam-3736	230	37	=	=	PUNCT
ejpam-3736	230	38	√	√	NUM
ejpam-3736	230	39	2	2	NUM
ejpam-3736	230	40	3	3	NUM
ejpam-3736	230	41	.	.	PUNCT
ejpam-3736	231	1	the	the	DET
ejpam-3736	231	2	critical	critical	ADJ
ejpam-3736	231	3	point	point	NOUN
ejpam-3736	231	4	is	be	AUX
ejpam-3736	231	5	m	m	PROPN
ejpam-3736	231	6	(	(	PUNCT
ejpam-3736	231	7	√	√	PROPN
ejpam-3736	231	8	2	2	NUM
ejpam-3736	231	9	3	3	NUM
ejpam-3736	231	10	,	,	PUNCT
ejpam-3736	231	11	√	√	NUM
ejpam-3736	231	12	2	2	NUM
ejpam-3736	231	13	3	3	NUM
ejpam-3736	231	14	,	,	PUNCT
ejpam-3736	231	15	√	√	NUM
ejpam-3736	231	16	2	2	NUM
ejpam-3736	231	17	3	3	NUM
ejpam-3736	231	18	)	)	PUNCT
ejpam-3736	231	19	.	.	PUNCT
ejpam-3736	232	1	we	we	PRON
ejpam-3736	232	2	have	have	AUX
ejpam-3736	232	3	:	:	PUNCT
ejpam-3736	232	4	∂2f	∂2f	VERB
ejpam-3736	232	5	∂x2	∂x2	NOUN
ejpam-3736	232	6	=	=	SYM
ejpam-3736	232	7	−yz	−yz	PROPN
ejpam-3736	232	8	(	(	PUNCT
ejpam-3736	232	9	1−	1−	NUM
ejpam-3736	232	10	x2	x2	NOUN
ejpam-3736	232	11	)	)	PUNCT
ejpam-3736	232	12	3	3	NUM
ejpam-3736	232	13	2	2	NUM
ejpam-3736	232	14	,	,	PUNCT
ejpam-3736	232	15	∂2f	∂2f	VERB
ejpam-3736	232	16	∂y2	∂y2	NOUN
ejpam-3736	232	17	=	=	SYM
ejpam-3736	232	18	−zx	−zx	ADJ
ejpam-3736	232	19	(	(	PUNCT
ejpam-3736	232	20	1−	1−	NUM
ejpam-3736	232	21	y2	y2	NOUN
ejpam-3736	232	22	)	)	PUNCT
ejpam-3736	232	23	3	3	NUM
ejpam-3736	232	24	2	2	NUM
ejpam-3736	232	25	,	,	PUNCT
ejpam-3736	232	26	∂2f	∂2f	VERB
ejpam-3736	232	27	∂z2	∂z2	NOUN
ejpam-3736	232	28	=	=	SYM
ejpam-3736	232	29	−xy	−xy	PROPN
ejpam-3736	232	30	(	(	PUNCT
ejpam-3736	232	31	1−	1−	NUM
ejpam-3736	232	32	z2	z2	NUM
ejpam-3736	232	33	)	)	PUNCT
ejpam-3736	232	34	3	3	NUM
ejpam-3736	232	35	2	2	NUM
ejpam-3736	232	36	∂2f	∂2f	VERB
ejpam-3736	232	37	∂x∂y	∂x∂y	NOUN
ejpam-3736	232	38	=	=	PUNCT
ejpam-3736	233	1	√	√	PROPN
ejpam-3736	233	2	1−	1−	NUM
ejpam-3736	233	3	z2	z2	NOUN
ejpam-3736	233	4	−	−	PROPN
ejpam-3736	233	5	zy√	zy√	NOUN
ejpam-3736	233	6	1−	1−	NUM
ejpam-3736	234	1	y2	y2	NOUN
ejpam-3736	234	2	−	−	PROPN
ejpam-3736	234	3	zx√	zx√	NOUN
ejpam-3736	235	1	1−	1−	NUM
ejpam-3736	235	2	x2	x2	NOUN
ejpam-3736	235	3	,	,	PUNCT
ejpam-3736	235	4	∂2f	∂2f	VERB
ejpam-3736	235	5	∂y∂z	∂y∂z	PROPN
ejpam-3736	235	6	=	=	PUNCT
ejpam-3736	235	7	√	√	PROPN
ejpam-3736	235	8	1−	1−	NUM
ejpam-3736	236	1	x2	x2	NOUN
ejpam-3736	236	2	−	−	PROPN
ejpam-3736	236	3	xy√	xy√	PUNCT
ejpam-3736	237	1	1−	1−	NUM
ejpam-3736	238	1	y2	y2	NOUN
ejpam-3736	238	2	−	−	PROPN
ejpam-3736	238	3	xz√	xz√	PROPN
ejpam-3736	239	1	1−	1−	NUM
ejpam-3736	239	2	z2	z2	PROPN
ejpam-3736	239	3	,	,	PUNCT
ejpam-3736	239	4	∂2f	∂2f	VERB
ejpam-3736	239	5	∂z∂x	∂z∂x	NOUN
ejpam-3736	239	6	=	=	SYM
ejpam-3736	239	7	√	√	PROPN
ejpam-3736	239	8	1−	1−	NUM
ejpam-3736	240	1	y2	y2	NOUN
ejpam-3736	240	2	−	−	PROPN
ejpam-3736	240	3	yx√	yx√	NOUN
ejpam-3736	240	4	1−	1−	NUM
ejpam-3736	241	1	x2	x2	NUM
ejpam-3736	242	1	−	−	PROPN
ejpam-3736	242	2	zy√	zy√	NUM
ejpam-3736	242	3	1−	1−	NUM
ejpam-3736	242	4	z2	z2	PROPN
ejpam-3736	242	5	.	.	PUNCT
ejpam-3736	243	1	then	then	ADV
ejpam-3736	243	2	for	for	ADP
ejpam-3736	243	3	the	the	DET
ejpam-3736	243	4	matrix	matrix	NOUN
ejpam-3736	243	5	h	h	NOUN
ejpam-3736	243	6	=	=	SYM
ejpam-3736	243	7			PROPN
ejpam-3736	243	8	∂2f	∂2f	VERB
ejpam-3736	243	9	∂x2	∂x2	NOUN
ejpam-3736	243	10	∂2f	∂2f	VERB
ejpam-3736	243	11	∂x∂y	∂x∂y	NOUN
ejpam-3736	243	12	∂2f	∂2f	VERB
ejpam-3736	243	13	∂x∂z	∂x∂z	NOUN
ejpam-3736	243	14	∂2f	∂2f	VERB
ejpam-3736	244	1	∂y∂x	∂y∂x	ADV
ejpam-3736	244	2	∂2f	∂2f	VERB
ejpam-3736	244	3	∂y2	∂y2	NOUN
ejpam-3736	244	4	∂2f	∂2f	VERB
ejpam-3736	244	5	∂y∂z	∂y∂z	PROPN
ejpam-3736	244	6	∂2f	∂2f	VERB
ejpam-3736	244	7	∂z∂x	∂z∂x	NOUN
ejpam-3736	244	8	∂2f	∂2f	VERB
ejpam-3736	244	9	∂z∂y	∂z∂y	PROPN
ejpam-3736	244	10	∂2f	∂2f	VERB
ejpam-3736	244	11	∂z2	∂z2	NOUN
ejpam-3736	244	12			NOUN
ejpam-3736	244	13	,	,	PUNCT
ejpam-3736	244	14	we	we	PRON
ejpam-3736	244	15	get	get	VERB
ejpam-3736	244	16	h	h	NOUN
ejpam-3736	244	17	(	(	PUNCT
ejpam-3736	244	18	m	m	NOUN
ejpam-3736	244	19	)	)	PUNCT
ejpam-3736	244	20	=	=	SYM
ejpam-3736	244	21	−2	−2	PROPN
ejpam-3736	245	1	√	√	ADV
ejpam-3736	245	2	3	3	NUM
ejpam-3736	245	3	−	−	NOUN
ejpam-3736	245	4	√	√	NUM
ejpam-3736	245	5	3	3	NUM
ejpam-3736	245	6	−	−	NOUN
ejpam-3736	245	7	√	√	NUM
ejpam-3736	245	8	3	3	NUM
ejpam-3736	245	9	−	−	NOUN
ejpam-3736	245	10	√	√	NUM
ejpam-3736	245	11	3	3	NUM
ejpam-3736	245	12	−2	−2	NOUN
ejpam-3736	245	13	√	√	NOUN
ejpam-3736	245	14	3	3	NUM
ejpam-3736	245	15	−	−	NOUN
ejpam-3736	245	16	√	√	NUM
ejpam-3736	245	17	3	3	NUM
ejpam-3736	245	18	−	−	NOUN
ejpam-3736	245	19	√	√	NUM
ejpam-3736	245	20	3	3	NUM
ejpam-3736	245	21	−	−	NOUN
ejpam-3736	245	22	√	√	NUM
ejpam-3736	245	23	3	3	NUM
ejpam-3736	245	24	−2	−2	NOUN
ejpam-3736	245	25	√	√	NOUN
ejpam-3736	245	26	3	3	NUM
ejpam-3736	245	27			PROPN
ejpam-3736	245	28	=	=	PUNCT
ejpam-3736	246	1	+	+	CCONJ
ejpam-3736	246	2	√	√	NUM
ejpam-3736	246	3	3	3	NUM
ejpam-3736	246	4	−2	−2	NUM
ejpam-3736	246	5	−1	−1	NOUN
ejpam-3736	246	6	−1	−1	NOUN
ejpam-3736	246	7	−1	−1	NOUN
ejpam-3736	246	8	−2	−2	NOUN
ejpam-3736	246	9	−1	−1	NOUN
ejpam-3736	246	10	−1	−1	NOUN
ejpam-3736	246	11	−1	−1	NOUN
ejpam-3736	246	12	−2	−2	NOUN
ejpam-3736	246	13			PROPN
ejpam-3736	246	14	.	.	PUNCT
ejpam-3736	247	1	the	the	DET
ejpam-3736	247	2	determinants	determinant	NOUN
ejpam-3736	247	3	:	:	PUNCT
ejpam-3736	247	4	d1	d1	PROPN
ejpam-3736	247	5	=	=	PUNCT
ejpam-3736	247	6	|−2|	|−2|	X
ejpam-3736	247	7	=	=	SYM
ejpam-3736	247	8	−2	−2	X
ejpam-3736	247	9	<	<	X
ejpam-3736	247	10	0	0	PROPN
ejpam-3736	247	11	,	,	PUNCT
ejpam-3736	247	12	d2	d2	PROPN
ejpam-3736	247	13	=	=	SYM
ejpam-3736	247	14	∣∣∣∣−2	∣∣∣∣−2	X
ejpam-3736	247	15	−1	−1	NOUN
ejpam-3736	247	16	−1	−1	NOUN
ejpam-3736	247	17	−2	−2	NOUN
ejpam-3736	247	18	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3736	247	19	=	=	NOUN
ejpam-3736	247	20	3	3	NUM
ejpam-3736	247	21	>	>	SYM
ejpam-3736	247	22	0	0	NUM
ejpam-3736	247	23	,	,	PUNCT
ejpam-3736	247	24	d3	d3	PROPN
ejpam-3736	247	25	=	=	SYM
ejpam-3736	247	26	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3736	247	27	−2	−2	PROPN
ejpam-3736	247	28	−1	−1	NOUN
ejpam-3736	247	29	−1	−1	NOUN
ejpam-3736	247	30	−1	−1	NOUN
ejpam-3736	247	31	−2	−2	NOUN
ejpam-3736	247	32	−1	−1	NOUN
ejpam-3736	247	33	−1	−1	NOUN
ejpam-3736	247	34	−1	−1	NOUN
ejpam-3736	247	35	−2	−2	NOUN
ejpam-3736	247	36	∣∣∣∣∣∣	∣∣∣∣∣∣	ADV
ejpam-3736	247	37	=	=	PUNCT
ejpam-3736	247	38	−4	−4	X
ejpam-3736	247	39	<	<	X
ejpam-3736	247	40	0	0	NUM
ejpam-3736	247	41	.	.	PUNCT
ejpam-3736	248	1	that	that	PRON
ejpam-3736	248	2	means	mean	VERB
ejpam-3736	248	3	:	:	PUNCT
ejpam-3736	248	4	m	m	PRON
ejpam-3736	248	5	is	be	AUX
ejpam-3736	248	6	a	a	DET
ejpam-3736	248	7	local	local	ADJ
ejpam-3736	248	8	maximum	maximum	ADJ
ejpam-3736	248	9	f	f	X
ejpam-3736	248	10	(	(	PUNCT
ejpam-3736	248	11	m	m	PROPN
ejpam-3736	248	12	)	)	PUNCT
ejpam-3736	249	1	=	=	SYM
ejpam-3736	249	2	2	2	NUM
ejpam-3736	249	3	√	√	NUM
ejpam-3736	249	4	3	3	NUM
ejpam-3736	249	5	3	3	NUM
ejpam-3736	249	6	.	.	PUNCT
ejpam-3736	250	1	on	on	ADP
ejpam-3736	250	2	the	the	DET
ejpam-3736	250	3	plane	plane	NOUN
ejpam-3736	250	4	z	z	NOUN
ejpam-3736	250	5	=	=	SYM
ejpam-3736	250	6	0	0	NUM
ejpam-3736	250	7	we	we	PRON
ejpam-3736	250	8	have	have	VERB
ejpam-3736	250	9	r(x	r(x	PROPN
ejpam-3736	250	10	,	,	PUNCT
ejpam-3736	250	11	y	y	NOUN
ejpam-3736	250	12	)	)	PUNCT
ejpam-3736	250	13	=	=	SYM
ejpam-3736	250	14	f(x	f(x	PROPN
ejpam-3736	250	15	,	,	PUNCT
ejpam-3736	250	16	y	y	PROPN
ejpam-3736	250	17	,	,	PUNCT
ejpam-3736	250	18	0	0	NUM
ejpam-3736	250	19	)	)	PUNCT
ejpam-3736	250	20	=	=	PUNCT
ejpam-3736	251	1	xy	xy	PROPN
ejpam-3736	251	2	≤	≤	ADV
ejpam-3736	251	3	1	1	NUM
ejpam-3736	251	4	.	.	PUNCT
ejpam-3736	252	1	on	on	ADP
ejpam-3736	252	2	the	the	DET
ejpam-3736	252	3	plane	plane	NOUN
ejpam-3736	252	4	z	z	NOUN
ejpam-3736	252	5	=	=	SYM
ejpam-3736	252	6	1	1	NUM
ejpam-3736	252	7	we	we	PRON
ejpam-3736	252	8	have	have	VERB
ejpam-3736	252	9	h(x	h(x	PROPN
ejpam-3736	252	10	,	,	PUNCT
ejpam-3736	252	11	y	y	PROPN
ejpam-3736	252	12	)	)	PUNCT
ejpam-3736	252	13	=	=	SYM
ejpam-3736	252	14	f(x	f(x	PROPN
ejpam-3736	252	15	,	,	PUNCT
ejpam-3736	252	16	y	y	PROPN
ejpam-3736	252	17	,	,	PUNCT
ejpam-3736	252	18	1	1	NUM
ejpam-3736	252	19	)	)	PUNCT
ejpam-3736	252	20	=	=	SYM
ejpam-3736	253	1	x	x	PUNCT
ejpam-3736	253	2	√	√	ADP
ejpam-3736	253	3	1−	1−	NUM
ejpam-3736	253	4	y2	y2	INTJ
ejpam-3736	254	1	+	+	CCONJ
ejpam-3736	254	2	y	y	PROPN
ejpam-3736	254	3	√	√	PROPN
ejpam-3736	254	4	1−	1−	NUM
ejpam-3736	255	1	x2	x2	SYM
ejpam-3736	255	2	≤	≤	ADV
ejpam-3736	255	3	1	1	NUM
ejpam-3736	255	4	,	,	PUNCT
ejpam-3736	255	5	according	accord	VERB
ejpam-3736	255	6	to	to	ADP
ejpam-3736	255	7	the	the	DET
ejpam-3736	255	8	lemma	lemma	PROPN
ejpam-3736	255	9	1	1	NUM
ejpam-3736	255	10	.	.	PUNCT
ejpam-3736	256	1	because	because	SCONJ
ejpam-3736	256	2	f	f	PROPN
ejpam-3736	256	3	is	be	AUX
ejpam-3736	256	4	a	a	DET
ejpam-3736	256	5	symmetric	symmetric	ADJ
ejpam-3736	256	6	function	function	NOUN
ejpam-3736	256	7	and	and	CCONJ
ejpam-3736	256	8	defined	define	VERB
ejpam-3736	256	9	in	in	ADP
ejpam-3736	256	10	the	the	DET
ejpam-3736	256	11	cube	cube	NOUN
ejpam-3736	256	12	[	[	X
ejpam-3736	256	13	0	0	NUM
ejpam-3736	256	14	,	,	PUNCT
ejpam-3736	256	15	1]3	1]3	NUM
ejpam-3736	256	16	,	,	PUNCT
ejpam-3736	256	17	therefore	therefore	ADV
ejpam-3736	256	18	f	f	PROPN
ejpam-3736	256	19	≤	≤	ADV
ejpam-3736	256	20	2	2	NUM
ejpam-3736	256	21	√	√	NUM
ejpam-3736	256	22	3	3	NUM
ejpam-3736	256	23	3	3	NUM
ejpam-3736	256	24	.	.	PUNCT
ejpam-3736	257	1	t.	t.	PROPN
ejpam-3736	257	2	s.	s.	PROPN
ejpam-3736	257	3	stoyanov	stoyanov	PROPN
ejpam-3736	257	4	/	/	SYM
ejpam-3736	257	5	eur	eur	PROPN
ejpam-3736	257	6	.	.	PUNCT
ejpam-3736	258	1	j.	j.	PROPN
ejpam-3736	258	2	pure	pure	PROPN
ejpam-3736	258	3	appl	appl	PROPN
ejpam-3736	258	4	.	.	PROPN
ejpam-3736	258	5	math	math	PROPN
ejpam-3736	258	6	,	,	PUNCT
ejpam-3736	258	7	13	13	NUM
ejpam-3736	258	8	(	(	PUNCT
ejpam-3736	258	9	3	3	NUM
ejpam-3736	258	10	)	)	PUNCT
ejpam-3736	258	11	(	(	PUNCT
ejpam-3736	258	12	2020	2020	NUM
ejpam-3736	258	13	)	)	PUNCT
ejpam-3736	258	14	,	,	PUNCT
ejpam-3736	258	15	663	663	NUM
ejpam-3736	258	16	-	-	SYM
ejpam-3736	258	17	673	673	NUM
ejpam-3736	258	18	671	671	NUM
ejpam-3736	258	19	corollary	corollary	ADJ
ejpam-3736	258	20	1	1	NUM
ejpam-3736	258	21	.	.	PUNCT
ejpam-3736	259	1	if	if	SCONJ
ejpam-3736	259	2	α	α	PROPN
ejpam-3736	259	3	,	,	PUNCT
ejpam-3736	259	4	β	β	X
ejpam-3736	259	5	,	,	PUNCT
ejpam-3736	259	6	γ	γ	PROPN
ejpam-3736	259	7	∈	∈	PROPN
ejpam-3736	259	8	[	[	PUNCT
ejpam-3736	259	9	0	0	NUM
ejpam-3736	259	10	,	,	PUNCT
ejpam-3736	259	11	π2	π2	X
ejpam-3736	259	12	]	]	PUNCT
ejpam-3736	259	13	,	,	PUNCT
ejpam-3736	259	14	then	then	ADV
ejpam-3736	259	15	the	the	DET
ejpam-3736	259	16	function	function	NOUN
ejpam-3736	259	17	g	g	PROPN
ejpam-3736	259	18	(	(	PUNCT
ejpam-3736	259	19	α	α	PROPN
ejpam-3736	259	20	,	,	PUNCT
ejpam-3736	259	21	β	β	X
ejpam-3736	259	22	,	,	PUNCT
ejpam-3736	259	23	γ	γ	NOUN
ejpam-3736	259	24	)	)	PUNCT
ejpam-3736	259	25	=	=	PUNCT
ejpam-3736	259	26	sin	sin	NOUN
ejpam-3736	259	27	α	α	PROPN
ejpam-3736	259	28	sin	sin	VERB
ejpam-3736	259	29	β	β	X
ejpam-3736	259	30	cos	cos	PROPN
ejpam-3736	259	31	γ	γ	PROPN
ejpam-3736	259	32	+	+	CCONJ
ejpam-3736	259	33	sin	sin	NOUN
ejpam-3736	259	34	α	α	PROPN
ejpam-3736	259	35	sin	sin	PROPN
ejpam-3736	259	36	γ	γ	X
ejpam-3736	259	37	cos	cos	PROPN
ejpam-3736	259	38	β	β	PROPN
ejpam-3736	259	39	+	+	CCONJ
ejpam-3736	259	40	sin	sin	NOUN
ejpam-3736	259	41	β	β	PROPN
ejpam-3736	259	42	sin	sin	PROPN
ejpam-3736	259	43	γ	γ	X
ejpam-3736	259	44	cos	cos	PROPN
ejpam-3736	259	45	α	α	NOUN
ejpam-3736	259	46	≤	≤	ADV
ejpam-3736	259	47	2	2	NUM
ejpam-3736	259	48	√	√	NUM
ejpam-3736	259	49	3	3	NUM
ejpam-3736	259	50	3	3	NUM
ejpam-3736	259	51	.	.	PUNCT
ejpam-3736	260	1	proof	proof	NOUN
ejpam-3736	260	2	.	.	PUNCT
ejpam-3736	261	1	if	if	SCONJ
ejpam-3736	261	2	in	in	ADP
ejpam-3736	261	3	the	the	DET
ejpam-3736	261	4	conditions	condition	NOUN
ejpam-3736	261	5	of	of	ADP
ejpam-3736	261	6	theorem	theorem	NOUN
ejpam-3736	261	7	6	6	NUM
ejpam-3736	261	8	we	we	PRON
ejpam-3736	261	9	put	put	VERB
ejpam-3736	261	10	x	x	PUNCT
ejpam-3736	261	11	=	=	SYM
ejpam-3736	261	12	sin	sin	NOUN
ejpam-3736	261	13	α	α	NOUN
ejpam-3736	261	14	,	,	PUNCT
ejpam-3736	261	15	y	y	PROPN
ejpam-3736	261	16	=	=	PUNCT
ejpam-3736	261	17	sin	sin	VERB
ejpam-3736	261	18	β	β	NOUN
ejpam-3736	261	19	,	,	PUNCT
ejpam-3736	261	20	z	z	NOUN
ejpam-3736	261	21	=	=	PUNCT
ejpam-3736	261	22	sin	sin	NOUN
ejpam-3736	261	23	γ	γ	X
ejpam-3736	261	24	,	,	PUNCT
ejpam-3736	261	25	and	and	CCONJ
ejpam-3736	261	26	we	we	PRON
ejpam-3736	261	27	obtain	obtain	VERB
ejpam-3736	261	28	that	that	DET
ejpam-3736	261	29	g	g	PROPN
ejpam-3736	261	30	(	(	PUNCT
ejpam-3736	261	31	α	α	PROPN
ejpam-3736	261	32	,	,	PUNCT
ejpam-3736	261	33	β	β	X
ejpam-3736	261	34	,	,	PUNCT
ejpam-3736	261	35	γ	γ	NOUN
ejpam-3736	261	36	)	)	PUNCT
ejpam-3736	261	37	=	=	SYM
ejpam-3736	261	38	f	f	PROPN
ejpam-3736	261	39	(	(	PUNCT
ejpam-3736	261	40	x	x	X
ejpam-3736	261	41	,	,	PUNCT
ejpam-3736	261	42	y	y	PROPN
ejpam-3736	261	43	,	,	PUNCT
ejpam-3736	261	44	z	z	NOUN
ejpam-3736	261	45	)	)	PUNCT
ejpam-3736	261	46	≤	≤	NUM
ejpam-3736	261	47	2	2	NUM
ejpam-3736	261	48	√	√	NUM
ejpam-3736	261	49	3	3	NUM
ejpam-3736	261	50	3	3	NUM
ejpam-3736	261	51	.	.	PUNCT
ejpam-3736	262	1	theorem	theorem	VERB
ejpam-3736	262	2	7	7	NUM
ejpam-3736	262	3	.	.	PUNCT
ejpam-3736	263	1	if	if	SCONJ
ejpam-3736	263	2	all	all	DET
ejpam-3736	263	3	the	the	DET
ejpam-3736	263	4	zeros	zero	NOUN
ejpam-3736	263	5	of	of	ADP
ejpam-3736	263	6	the	the	DET
ejpam-3736	263	7	polynomial	polynomial	ADJ
ejpam-3736	263	8	p(z	p(z	NOUN
ejpam-3736	263	9	)	)	PUNCT
ejpam-3736	263	10	∈	∈	PROPN
ejpam-3736	263	11	c[z	c[z	PROPN
ejpam-3736	263	12	]	]	X
ejpam-3736	263	13	are	be	AUX
ejpam-3736	263	14	zk	zk	PROPN
ejpam-3736	263	15	,	,	PUNCT
ejpam-3736	263	16	k	k	PROPN
ejpam-3736	263	17	=	=	SYM
ejpam-3736	263	18	1	1	NUM
ejpam-3736	263	19	,	,	PUNCT
ejpam-3736	263	20	2	2	NUM
ejpam-3736	263	21	,	,	PUNCT
ejpam-3736	263	22	.	.	PUNCT
ejpam-3736	263	23	.	.	PUNCT
ejpam-3736	264	1	.	.	PUNCT
ejpam-3736	265	1	,	,	PUNCT
ejpam-3736	265	2	n.	n.	NOUN
ejpam-3736	265	3	then	then	ADV
ejpam-3736	265	4	for	for	ADP
ejpam-3736	265	5	each	each	DET
ejpam-3736	265	6	zero	zero	NUM
ejpam-3736	265	7	v	v	NOUN
ejpam-3736	265	8	of	of	ADP
ejpam-3736	265	9	the	the	DET
ejpam-3736	265	10	third	third	ADJ
ejpam-3736	265	11	derivative	derivative	ADJ
ejpam-3736	265	12	p′′′(z	p′′′(z	NOUN
ejpam-3736	265	13	)	)	PUNCT
ejpam-3736	265	14	exists	exist	VERB
ejpam-3736	265	15	some	some	DET
ejpam-3736	265	16	k0	k0	PROPN
ejpam-3736	265	17	∈	∈	PROPN
ejpam-3736	265	18	n	n	CCONJ
ejpam-3736	265	19	,	,	PUNCT
ejpam-3736	265	20	1	1	NUM
ejpam-3736	265	21	≤	≤	PROPN
ejpam-3736	265	22	k0	k0	PROPN
ejpam-3736	265	23	≤	≤	PROPN
ejpam-3736	265	24	n	n	CCONJ
ejpam-3736	265	25	,	,	PUNCT
ejpam-3736	266	1	such	such	ADJ
ejpam-3736	266	2	that	that	DET
ejpam-3736	266	3	v	v	NUM
ejpam-3736	266	4	∈	∈	PROPN
ejpam-3736	266	5	cq	cq	NOUN
ejpam-3736	266	6	(	(	PUNCT
ejpam-3736	266	7	zk0	zk0	NOUN
ejpam-3736	266	8	2	2	NUM
ejpam-3736	266	9	,	,	PUNCT
ejpam-3736	266	10	|zk0	|zk0	PROPN
ejpam-3736	267	1	|	|	NOUN
ejpam-3736	268	1	2	2	NUM
ejpam-3736	268	2	)	)	PUNCT
ejpam-3736	268	3	,	,	PUNCT
ejpam-3736	269	1	where	where	SCONJ
ejpam-3736	269	2	q	q	NOUN
ejpam-3736	269	3	=	=	SYM
ejpam-3736	269	4	2	2	NUM
ejpam-3736	269	5	√	√	NUM
ejpam-3736	269	6	3	3	NUM
ejpam-3736	269	7	3	3	NUM
ejpam-3736	269	8	.	.	PUNCT
ejpam-3736	270	1	proof	proof	NOUN
ejpam-3736	270	2	.	.	PUNCT
ejpam-3736	271	1	we	we	PRON
ejpam-3736	271	2	denote	denote	VERB
ejpam-3736	271	3	by	by	ADP
ejpam-3736	271	4	v	v	NUM
ejpam-3736	271	5	zero	zero	NUM
ejpam-3736	271	6	of	of	ADP
ejpam-3736	271	7	the	the	DET
ejpam-3736	271	8	third	third	ADJ
ejpam-3736	271	9	derivative	derivative	NOUN
ejpam-3736	271	10	,	,	PUNCT
ejpam-3736	271	11	i.e.	i.e.	X
ejpam-3736	271	12	p′′′	p′′′	PROPN
ejpam-3736	271	13	(	(	PUNCT
ejpam-3736	271	14	v	v	NOUN
ejpam-3736	271	15	)	)	PUNCT
ejpam-3736	271	16	=	=	SYM
ejpam-3736	272	1	0	0	X
ejpam-3736	272	2	.	.	PUNCT
ejpam-3736	273	1	according	accord	VERB
ejpam-3736	273	2	to	to	ADP
ejpam-3736	273	3	theorem	theorem	NOUN
ejpam-3736	273	4	3	3	NUM
ejpam-3736	273	5	there	there	ADV
ejpam-3736	273	6	exists	exist	VERB
ejpam-3736	273	7	such	such	DET
ejpam-3736	273	8	a	a	DET
ejpam-3736	273	9	zero	zero	NUM
ejpam-3736	273	10	t	t	NOUN
ejpam-3736	273	11	of	of	ADP
ejpam-3736	273	12	the	the	DET
ejpam-3736	273	13	second	second	ADJ
ejpam-3736	273	14	derivative	derivative	ADJ
ejpam-3736	273	15	p′′(z	p′′(z	NOUN
ejpam-3736	273	16	)	)	PUNCT
ejpam-3736	273	17	,	,	PUNCT
ejpam-3736	273	18	that	that	PRON
ejpam-3736	273	19	v	v	X
ejpam-3736	273	20	∈	∈	PROPN
ejpam-3736	273	21	d	d	X
ejpam-3736	273	22	(	(	PUNCT
ejpam-3736	273	23	t	t	PROPN
ejpam-3736	273	24	2	2	NUM
ejpam-3736	273	25	,	,	PUNCT
ejpam-3736	273	26	|t|	|t|	VERB
ejpam-3736	273	27	2	2	NUM
ejpam-3736	273	28	)	)	PUNCT
ejpam-3736	273	29	.	.	PUNCT
ejpam-3736	274	1	for	for	ADP
ejpam-3736	274	2	this	this	DET
ejpam-3736	274	3	zero	zero	NUM
ejpam-3736	274	4	t	t	NOUN
ejpam-3736	274	5	according	accord	VERB
ejpam-3736	274	6	again	again	ADV
ejpam-3736	274	7	to	to	PART
ejpam-3736	274	8	theorem	theorem	NOUN
ejpam-3736	274	9	3	3	NUM
ejpam-3736	274	10	,	,	PUNCT
ejpam-3736	274	11	there	there	PRON
ejpam-3736	274	12	exists	exist	VERB
ejpam-3736	274	13	a	a	DET
ejpam-3736	274	14	zero	zero	NUM
ejpam-3736	274	15	w	w	NOUN
ejpam-3736	274	16	of	of	ADP
ejpam-3736	274	17	the	the	DET
ejpam-3736	274	18	polynomial	polynomial	ADJ
ejpam-3736	274	19	p′	p′	NOUN
ejpam-3736	274	20	(	(	PUNCT
ejpam-3736	274	21	z	z	NOUN
ejpam-3736	274	22	)	)	PUNCT
ejpam-3736	274	23	,	,	PUNCT
ejpam-3736	274	24	such	such	ADJ
ejpam-3736	274	25	that	that	SCONJ
ejpam-3736	274	26	t	t	PROPN
ejpam-3736	274	27	∈	∈	PROPN
ejpam-3736	275	1	d	d	X
ejpam-3736	275	2	(	(	PUNCT
ejpam-3736	275	3	w	w	PROPN
ejpam-3736	275	4	2	2	NUM
ejpam-3736	275	5	,	,	PUNCT
ejpam-3736	275	6	|w|	|w|	ADJ
ejpam-3736	275	7	2	2	NUM
ejpam-3736	275	8	)	)	PUNCT
ejpam-3736	275	9	.	.	PUNCT
ejpam-3736	276	1	and	and	CCONJ
ejpam-3736	276	2	again	again	ADV
ejpam-3736	276	3	for	for	ADP
ejpam-3736	276	4	this	this	DET
ejpam-3736	276	5	zero	zero	NUM
ejpam-3736	276	6	w	w	NOUN
ejpam-3736	276	7	of	of	ADP
ejpam-3736	276	8	the	the	DET
ejpam-3736	276	9	derivative	derivative	ADJ
ejpam-3736	276	10	p′	p′	NOUN
ejpam-3736	276	11	(	(	PUNCT
ejpam-3736	276	12	z	z	NOUN
ejpam-3736	276	13	)	)	PUNCT
ejpam-3736	276	14	,	,	PUNCT
ejpam-3736	276	15	there	there	PRON
ejpam-3736	276	16	exists	exist	VERB
ejpam-3736	276	17	a	a	DET
ejpam-3736	276	18	zero	zero	NUM
ejpam-3736	276	19	zk0	zk0	NOUN
ejpam-3736	276	20	of	of	ADP
ejpam-3736	276	21	the	the	DET
ejpam-3736	276	22	polynomial	polynomial	ADJ
ejpam-3736	276	23	p(z	p(z	NOUN
ejpam-3736	276	24	)	)	PUNCT
ejpam-3736	276	25	,	,	PUNCT
ejpam-3736	276	26	such	such	ADJ
ejpam-3736	276	27	that	that	SCONJ
ejpam-3736	276	28	w	w	PROPN
ejpam-3736	276	29	∈	∈	PROPN
ejpam-3736	276	30	d	d	X
ejpam-3736	276	31	(	(	PUNCT
ejpam-3736	276	32	zk0	zk0	NOUN
ejpam-3736	276	33	2	2	NUM
ejpam-3736	276	34	,	,	PUNCT
ejpam-3736	276	35	|zk0	|zk0	PROPN
ejpam-3736	276	36	|	|	NOUN
ejpam-3736	276	37	2	2	NUM
ejpam-3736	276	38	)	)	PUNCT
ejpam-3736	276	39	.	.	PUNCT
ejpam-3736	277	1	in	in	ADP
ejpam-3736	277	2	order	order	NOUN
ejpam-3736	277	3	to	to	PART
ejpam-3736	277	4	find	find	VERB
ejpam-3736	277	5	the	the	DET
ejpam-3736	277	6	geometric	geometric	ADJ
ejpam-3736	277	7	places	place	NOUN
ejpam-3736	277	8	of	of	ADP
ejpam-3736	277	9	the	the	DET
ejpam-3736	277	10	points	point	NOUN
ejpam-3736	277	11	t	t	PROPN
ejpam-3736	277	12	,	,	PUNCT
ejpam-3736	277	13	let	let	VERB
ejpam-3736	277	14	us	we	PRON
ejpam-3736	277	15	take	take	VERB
ejpam-3736	277	16	w	w	NOUN
ejpam-3736	277	17	on	on	ADP
ejpam-3736	277	18	the	the	DET
ejpam-3736	277	19	boundary	boundary	NOUN
ejpam-3736	277	20	of	of	ADP
ejpam-3736	277	21	the	the	DET
ejpam-3736	277	22	disk	disk	NOUN
ejpam-3736	277	23	d	d	NOUN
ejpam-3736	277	24	(	(	PUNCT
ejpam-3736	277	25	zk0	zk0	NOUN
ejpam-3736	277	26	2	2	NUM
ejpam-3736	277	27	,	,	PUNCT
ejpam-3736	277	28	|zk0	|zk0	PROPN
ejpam-3736	277	29	|	|	NOUN
ejpam-3736	277	30	2	2	NUM
ejpam-3736	277	31	)	)	PUNCT
ejpam-3736	277	32	and	and	CCONJ
ejpam-3736	277	33	t	t	X
ejpam-3736	277	34	on	on	ADP
ejpam-3736	277	35	the	the	DET
ejpam-3736	277	36	boundary	boundary	NOUN
ejpam-3736	277	37	of	of	ADP
ejpam-3736	277	38	the	the	DET
ejpam-3736	277	39	disk	disk	NOUN
ejpam-3736	277	40	d	d	NOUN
ejpam-3736	277	41	(	(	PUNCT
ejpam-3736	277	42	w	w	PROPN
ejpam-3736	277	43	2	2	NUM
ejpam-3736	277	44	,	,	PUNCT
ejpam-3736	277	45	|w|	|w|	ADJ
ejpam-3736	277	46	2	2	NUM
ejpam-3736	277	47	)	)	PUNCT
ejpam-3736	277	48	.	.	PUNCT
ejpam-3736	278	1	for	for	ADP
ejpam-3736	278	2	better	well	ADJ
ejpam-3736	278	3	understanding	understanding	NOUN
ejpam-3736	278	4	,	,	PUNCT
ejpam-3736	278	5	let	let	VERB
ejpam-3736	278	6	us	we	PRON
ejpam-3736	278	7	take	take	VERB
ejpam-3736	278	8	zk0	zk0	NOUN
ejpam-3736	278	9	∈	∈	NOUN
ejpam-3736	278	10	x	x	NOUN
ejpam-3736	278	11	,	,	PUNCT
ejpam-3736	278	12	and	and	CCONJ
ejpam-3736	278	13	arg	arg	NOUN
ejpam-3736	278	14	w	w	PROPN
ejpam-3736	278	15	=	=	SYM
ejpam-3736	278	16	α	α	PROPN
ejpam-3736	278	17	,	,	PUNCT
ejpam-3736	278	18	arg	arg	NOUN
ejpam-3736	278	19	t	t	NOUN
ejpam-3736	278	20	=	=	SYM
ejpam-3736	278	21	α+	α+	X
ejpam-3736	278	22	β	β	X
ejpam-3736	278	23	,	,	PUNCT
ejpam-3736	278	24	arg	arg	NOUN
ejpam-3736	278	25	v	v	NOUN
ejpam-3736	278	26	=	=	SYM
ejpam-3736	278	27	α+	α+	PUNCT
ejpam-3736	278	28	β	β	X
ejpam-3736	278	29	+	+	CCONJ
ejpam-3736	278	30	γ	γ	PROPN
ejpam-3736	278	31	.	.	PROPN
ejpam-3736	278	32	figure	figure	NOUN
ejpam-3736	278	33	4	4	NUM
ejpam-3736	278	34	:	:	PUNCT
ejpam-3736	278	35	here	here	ADV
ejpam-3736	278	36	we	we	PRON
ejpam-3736	278	37	have	have	VERB
ejpam-3736	278	38	α	α	NUM
ejpam-3736	278	39	,	,	PUNCT
ejpam-3736	278	40	β	β	X
ejpam-3736	278	41	,	,	PUNCT
ejpam-3736	278	42	γ	γ	PROPN
ejpam-3736	278	43	∈	∈	PROPN
ejpam-3736	278	44	[	[	PUNCT
ejpam-3736	278	45	0	0	NUM
ejpam-3736	278	46	,	,	PUNCT
ejpam-3736	278	47	π2	π2	NOUN
ejpam-3736	278	48	]	]	PUNCT
ejpam-3736	278	49	.	.	PUNCT
ejpam-3736	279	1	references	reference	NOUN
ejpam-3736	279	2	672	672	NUM
ejpam-3736	279	3	let	let	VERB
ejpam-3736	279	4	us	we	PRON
ejpam-3736	279	5	put	put	VERB
ejpam-3736	279	6	|zk0	|zk0	PROPN
ejpam-3736	280	1	|	|	NOUN
ejpam-3736	280	2	=	=	PUNCT
ejpam-3736	280	3	a.	a.	NOUN
ejpam-3736	280	4	then	then	ADV
ejpam-3736	280	5	x	x	X
ejpam-3736	280	6	=	=	PUNCT
ejpam-3736	280	7	a	a	DET
ejpam-3736	280	8	cos	cos	PROPN
ejpam-3736	280	9	α	α	PROPN
ejpam-3736	280	10	cos	cos	PROPN
ejpam-3736	280	11	β	β	PROPN
ejpam-3736	280	12	cos	cos	PROPN
ejpam-3736	280	13	γ	γ	PROPN
ejpam-3736	280	14	cos	cos	PROPN
ejpam-3736	280	15	(	(	PUNCT
ejpam-3736	280	16	α+	α+	X
ejpam-3736	280	17	β	β	X
ejpam-3736	280	18	+	+	X
ejpam-3736	280	19	γ	γ	X
ejpam-3736	280	20	)	)	PUNCT
ejpam-3736	280	21	,	,	PUNCT
ejpam-3736	280	22	y	y	PROPN
ejpam-3736	280	23	=	=	PUNCT
ejpam-3736	280	24	a	a	DET
ejpam-3736	280	25	cos	cos	PROPN
ejpam-3736	280	26	α	α	PROPN
ejpam-3736	280	27	cos	cos	PROPN
ejpam-3736	280	28	β	β	PROPN
ejpam-3736	280	29	cos	cos	PROPN
ejpam-3736	280	30	γ	γ	X
ejpam-3736	280	31	sin	sin	X
ejpam-3736	280	32	(	(	PUNCT
ejpam-3736	280	33	α+	α+	X
ejpam-3736	280	34	β	β	X
ejpam-3736	280	35	+	+	X
ejpam-3736	280	36	γ	γ	X
ejpam-3736	280	37	)	)	PUNCT
ejpam-3736	280	38	.	.	PUNCT
ejpam-3736	281	1	let	let	VERB
ejpam-3736	281	2	us	we	PRON
ejpam-3736	281	3	calculate	calculate	VERB
ejpam-3736	281	4	ax	ax	NOUN
ejpam-3736	281	5	=	=	SYM
ejpam-3736	281	6	a2	a2	PROPN
ejpam-3736	281	7	cos	cos	PROPN
ejpam-3736	281	8	α	α	PROPN
ejpam-3736	281	9	cos	cos	PROPN
ejpam-3736	281	10	β	β	PROPN
ejpam-3736	281	11	cos	cos	PROPN
ejpam-3736	281	12	γ	γ	PROPN
ejpam-3736	281	13	[	[	X
ejpam-3736	281	14	cos	cos	X
ejpam-3736	281	15	(	(	PUNCT
ejpam-3736	281	16	α+	α+	X
ejpam-3736	281	17	β	β	X
ejpam-3736	281	18	)	)	PUNCT
ejpam-3736	281	19	cos	cos	ADP
ejpam-3736	281	20	γ	γ	NOUN
ejpam-3736	281	21	−	−	PROPN
ejpam-3736	281	22	sin	sin	NOUN
ejpam-3736	281	23	(	(	PUNCT
ejpam-3736	281	24	α+	α+	X
ejpam-3736	281	25	β	β	X
ejpam-3736	281	26	)	)	PUNCT
ejpam-3736	281	27	sin	sin	NOUN
ejpam-3736	281	28	γ	γ	X
ejpam-3736	281	29	]	]	PUNCT
ejpam-3736	281	30	=	=	PUNCT
ejpam-3736	281	31	a2	a2	PROPN
ejpam-3736	281	32	cos	cos	PROPN
ejpam-3736	281	33	α	α	PROPN
ejpam-3736	281	34	cos	cos	PROPN
ejpam-3736	281	35	β	β	PROPN
ejpam-3736	281	36	cos	cos	PROPN
ejpam-3736	281	37	γ	γ	PROPN
ejpam-3736	281	38	[	[	X
ejpam-3736	281	39	cos	cos	PROPN
ejpam-3736	281	40	α	α	PROPN
ejpam-3736	281	41	cos	cos	PROPN
ejpam-3736	281	42	β	β	PROPN
ejpam-3736	281	43	cos	cos	PROPN
ejpam-3736	281	44	γ	γ	PROPN
ejpam-3736	281	45	−	−	PROPN
ejpam-3736	281	46	sin	sin	NOUN
ejpam-3736	281	47	α	α	PROPN
ejpam-3736	281	48	sin	sin	NOUN
ejpam-3736	281	49	β	β	X
ejpam-3736	281	50	cos	cos	ADP
ejpam-3736	282	1	γ	γ	PROPN
ejpam-3736	282	2	−	−	PROPN
ejpam-3736	282	3	sin	sin	NOUN
ejpam-3736	282	4	α	α	PROPN
ejpam-3736	282	5	sin	sin	PROPN
ejpam-3736	282	6	γ	γ	X
ejpam-3736	282	7	cos	cos	PROPN
ejpam-3736	282	8	β	β	PROPN
ejpam-3736	282	9	−	−	PROPN
ejpam-3736	282	10	sin	sin	NOUN
ejpam-3736	282	11	β	β	PROPN
ejpam-3736	282	12	sin	sin	PROPN
ejpam-3736	282	13	γ	γ	X
ejpam-3736	282	14	cos	cos	PROPN
ejpam-3736	282	15	α	α	PROPN
ejpam-3736	282	16	]	]	PUNCT
ejpam-3736	282	17	.	.	PUNCT
ejpam-3736	283	1	obviously	obviously	ADV
ejpam-3736	283	2	x2	x2	PROPN
ejpam-3736	284	1	+	+	CCONJ
ejpam-3736	284	2	y2	y2	NOUN
ejpam-3736	284	3	=	=	SYM
ejpam-3736	284	4	a2	a2	PROPN
ejpam-3736	284	5	cos2α	cos2α	PROPN
ejpam-3736	284	6	cos2β	cos2β	PUNCT
ejpam-3736	284	7	cos2γ	cos2γ	PROPN
ejpam-3736	284	8	.	.	PUNCT
ejpam-3736	285	1	then	then	ADV
ejpam-3736	285	2	we	we	PRON
ejpam-3736	285	3	have	have	VERB
ejpam-3736	285	4	x2	x2	PROPN
ejpam-3736	286	1	+	+	CCONJ
ejpam-3736	287	1	y2	y2	NOUN
ejpam-3736	287	2	−	−	NOUN
ejpam-3736	287	3	ax	ax	NOUN
ejpam-3736	287	4	=	=	PROPN
ejpam-3736	287	5	a2	a2	PROPN
ejpam-3736	287	6	cos	cos	PROPN
ejpam-3736	287	7	α	α	PROPN
ejpam-3736	287	8	cos	cos	PROPN
ejpam-3736	287	9	β	β	PROPN
ejpam-3736	287	10	cos	cos	PROPN
ejpam-3736	287	11	γ	γ	PROPN
ejpam-3736	287	12	[	[	X
ejpam-3736	287	13	sin	sin	NOUN
ejpam-3736	287	14	α	α	PROPN
ejpam-3736	287	15	sin	sin	NOUN
ejpam-3736	287	16	β	β	X
ejpam-3736	287	17	cos	cos	PROPN
ejpam-3736	287	18	γ	γ	PROPN
ejpam-3736	287	19	+	+	CCONJ
ejpam-3736	287	20	sin	sin	NOUN
ejpam-3736	287	21	α	α	PROPN
ejpam-3736	287	22	sin	sin	PROPN
ejpam-3736	287	23	γ	γ	X
ejpam-3736	287	24	cos	cos	PROPN
ejpam-3736	287	25	β	β	PROPN
ejpam-3736	287	26	+	+	CCONJ
ejpam-3736	287	27	sin	sin	NOUN
ejpam-3736	287	28	β	β	PROPN
ejpam-3736	287	29	sin	sin	PROPN
ejpam-3736	287	30	γ	γ	X
ejpam-3736	287	31	cos	cos	PROPN
ejpam-3736	287	32	α	α	PROPN
ejpam-3736	287	33	]	]	PUNCT
ejpam-3736	287	34	.	.	PUNCT
ejpam-3736	288	1	but	but	CCONJ
ejpam-3736	288	2	sin	sin	NOUN
ejpam-3736	288	3	α	α	PROPN
ejpam-3736	288	4	sin	sin	NOUN
ejpam-3736	288	5	β	β	X
ejpam-3736	288	6	cos	cos	PROPN
ejpam-3736	288	7	γ	γ	PROPN
ejpam-3736	288	8	+	+	CCONJ
ejpam-3736	288	9	sin	sin	NOUN
ejpam-3736	288	10	α	α	PROPN
ejpam-3736	288	11	sin	sin	PROPN
ejpam-3736	288	12	γ	γ	X
ejpam-3736	288	13	cos	cos	PROPN
ejpam-3736	288	14	β	β	PROPN
ejpam-3736	288	15	+	+	CCONJ
ejpam-3736	288	16	sin	sin	NOUN
ejpam-3736	288	17	β	β	PROPN
ejpam-3736	288	18	sin	sin	PROPN
ejpam-3736	288	19	γ	γ	X
ejpam-3736	288	20	cos	cos	PROPN
ejpam-3736	288	21	α	α	NOUN
ejpam-3736	288	22	≤	≤	ADV
ejpam-3736	288	23	2	2	NUM
ejpam-3736	288	24	√	√	NUM
ejpam-3736	288	25	3	3	NUM
ejpam-3736	288	26	3	3	NUM
ejpam-3736	288	27	,	,	PUNCT
ejpam-3736	288	28	according	accord	VERB
ejpam-3736	288	29	to	to	ADP
ejpam-3736	288	30	the	the	DET
ejpam-3736	288	31	corollary	corollary	NOUN
ejpam-3736	288	32	.	.	PUNCT
ejpam-3736	289	1	from	from	ADP
ejpam-3736	289	2	here	here	ADV
ejpam-3736	289	3	we	we	PRON
ejpam-3736	289	4	state	state	VERB
ejpam-3736	289	5	(	(	PUNCT
ejpam-3736	289	6	x2	x2	PROPN
ejpam-3736	290	1	+	+	CCONJ
ejpam-3736	291	1	y2	y2	NOUN
ejpam-3736	291	2	−	−	NOUN
ejpam-3736	291	3	ax	ax	NOUN
ejpam-3736	291	4	)	)	PUNCT
ejpam-3736	291	5	2	2	NUM
ejpam-3736	291	6	≤	≤	NUM
ejpam-3736	291	7	4	4	NUM
ejpam-3736	291	8	3	3	NUM
ejpam-3736	291	9	a2	a2	NOUN
ejpam-3736	291	10	(	(	PUNCT
ejpam-3736	291	11	x2	x2	PROPN
ejpam-3736	291	12	+	+	CCONJ
ejpam-3736	291	13	y2	y2	INTJ
ejpam-3736	291	14	)	)	PUNCT
ejpam-3736	291	15	.	.	PUNCT
ejpam-3736	292	1	that	that	PRON
ejpam-3736	292	2	means	mean	VERB
ejpam-3736	292	3	that	that	SCONJ
ejpam-3736	292	4	our	our	PRON
ejpam-3736	292	5	geometric	geometric	ADJ
ejpam-3736	292	6	place	place	NOUN
ejpam-3736	292	7	belongs	belong	VERB
ejpam-3736	292	8	to	to	ADP
ejpam-3736	292	9	c	c	PROPN
ejpam-3736	292	10	2	2	NUM
ejpam-3736	292	11	√	√	NUM
ejpam-3736	292	12	3	3	NUM
ejpam-3736	292	13	3	3	NUM
ejpam-3736	292	14	(	(	PUNCT
ejpam-3736	292	15	zk0	zk0	NOUN
ejpam-3736	292	16	2	2	NUM
ejpam-3736	292	17	,	,	PUNCT
ejpam-3736	292	18	|zk0	|zk0	PROPN
ejpam-3736	292	19	|	|	NOUN
ejpam-3736	292	20	2	2	NUM
ejpam-3736	292	21	)	)	PUNCT
ejpam-3736	292	22	,	,	PUNCT
ejpam-3736	292	23	which	which	PRON
ejpam-3736	292	24	confirms	confirm	VERB
ejpam-3736	292	25	this	this	DET
ejpam-3736	292	26	assertion	assertion	NOUN
ejpam-3736	292	27	.	.	PUNCT
ejpam-3736	293	1	acknowledgements	acknowledgement	NOUN
ejpam-3736	293	2	this	this	DET
ejpam-3736	293	3	research	research	NOUN
ejpam-3736	293	4	was	be	AUX
ejpam-3736	293	5	financed	finance	VERB
ejpam-3736	293	6	from	from	ADP
ejpam-3736	293	7	university	university	NOUN
ejpam-3736	293	8	of	of	ADP
ejpam-3736	293	9	economics	economic	NOUN
ejpam-3736	293	10	of	of	ADP
ejpam-3736	293	11	varna	varna	ADJ
ejpam-3736	293	12	research	research	NOUN
ejpam-3736	293	13	grants	grant	NOUN
ejpam-3736	293	14	no.19	no.19	PROPN
ejpam-3736	293	15	2018	2018	NUM
ejpam-3736	293	16	-	-	PUNCT
ejpam-3736	293	17	04	04	NUM
ejpam-3736	293	18	-	-	PUNCT
ejpam-3736	293	19	27	27	NUM
ejpam-3736	293	20	.	.	PUNCT
ejpam-3736	294	1	references	reference	NOUN
ejpam-3736	294	2	[	[	X
ejpam-3736	294	3	1	1	NUM
ejpam-3736	294	4	]	]	X
ejpam-3736	294	5	q	q	X
ejpam-3736	295	1	i	i	PRON
ejpam-3736	295	2	rahman	rahman	PROPN
ejpam-3736	295	3	and	and	CCONJ
ejpam-3736	295	4	g	g	PROPN
ejpam-3736	295	5	schmeisser	schmeisser	NOUN
ejpam-3736	295	6	.	.	PUNCT
ejpam-3736	296	1	analytic	analytic	ADJ
ejpam-3736	296	2	theory	theory	NOUN
ejpam-3736	296	3	of	of	ADP
ejpam-3736	296	4	polynomials	polynomial	NOUN
ejpam-3736	296	5	:	:	PUNCT
ejpam-3736	296	6	critical	critical	ADJ
ejpam-3736	296	7	points	point	NOUN
ejpam-3736	296	8	,	,	PUNCT
ejpam-3736	296	9	zeros	zero	NOUN
ejpam-3736	296	10	and	and	CCONJ
ejpam-3736	296	11	extremal	extremal	ADJ
ejpam-3736	296	12	properties	property	NOUN
ejpam-3736	296	13	.	.	PUNCT
ejpam-3736	297	1	clarendon	clarendon	PROPN
ejpam-3736	297	2	press	press	PROPN
ejpam-3736	297	3	,	,	PUNCT
ejpam-3736	297	4	london	london	PROPN
ejpam-3736	297	5	,	,	PUNCT
ejpam-3736	297	6	2002	2002	NUM
ejpam-3736	297	7	.	.	PUNCT
ejpam-3736	298	1	[	[	X
ejpam-3736	298	2	2	2	NUM
ejpam-3736	298	3	]	]	PUNCT
ejpam-3736	298	4	d	d	NOUN
ejpam-3736	298	5	m	m	NOUN
ejpam-3736	298	6	souroujon	souroujon	NOUN
ejpam-3736	298	7	and	and	CCONJ
ejpam-3736	298	8	t	t	PROPN
ejpam-3736	298	9	zapryanova	zapryanova	PROPN
ejpam-3736	298	10	.	.	PUNCT
ejpam-3736	299	1	on	on	ADP
ejpam-3736	299	2	the	the	DET
ejpam-3736	299	3	relation	relation	NOUN
ejpam-3736	299	4	between	between	ADP
ejpam-3736	299	5	the	the	DET
ejpam-3736	299	6	number	number	NOUN
ejpam-3736	299	7	of	of	ADP
ejpam-3736	299	8	real	real	ADJ
ejpam-3736	299	9	and	and	CCONJ
ejpam-3736	299	10	complex	complex	ADJ
ejpam-3736	299	11	zeros	zero	NOUN
ejpam-3736	299	12	of	of	ADP
ejpam-3736	299	13	polynomials	polynomial	NOUN
ejpam-3736	299	14	of	of	ADP
ejpam-3736	299	15	a	a	DET
ejpam-3736	299	16	certain	certain	ADJ
ejpam-3736	299	17	kind	kind	NOUN
ejpam-3736	299	18	.	.	PUNCT
ejpam-3736	300	1	in	in	ADP
ejpam-3736	300	2	aip	aip	PROPN
ejpam-3736	300	3	conference	conference	NOUN
ejpam-3736	300	4	proceeding	proceeding	NOUN
ejpam-3736	300	5	.	.	PUNCT
ejpam-3736	301	1	,	,	PUNCT
ejpam-3736	301	2	volume	volume	NOUN
ejpam-3736	301	3	2159	2159	NUM
ejpam-3736	301	4	,	,	PUNCT
ejpam-3736	301	5	st	st	PROPN
ejpam-3736	301	6	constantine	constantine	PROPN
ejpam-3736	301	7	and	and	CCONJ
ejpam-3736	301	8	helena	helena	PROPN
ejpam-3736	301	9	,	,	PUNCT
ejpam-3736	301	10	2019	2019	NUM
ejpam-3736	301	11	.	.	PUNCT
ejpam-3736	302	1	sixth	sixth	ADJ
ejpam-3736	302	2	international	international	ADJ
ejpam-3736	302	3	conference	conference	NOUN
ejpam-3736	302	4	on	on	ADP
ejpam-3736	302	5	new	new	ADJ
ejpam-3736	302	6	trends	trend	NOUN
ejpam-3736	302	7	in	in	ADP
ejpam-3736	302	8	the	the	DET
ejpam-3736	302	9	applications	application	NOUN
ejpam-3736	302	10	of	of	ADP
ejpam-3736	302	11	differential	differential	ADJ
ejpam-3736	302	12	equations	equation	NOUN
ejpam-3736	302	13	in	in	ADP
ejpam-3736	302	14	sciences	science	NOUN
ejpam-3736	302	15	.	.	PUNCT
ejpam-3736	303	1	references	reference	NOUN
ejpam-3736	303	2	673	673	NUM
ejpam-3736	304	1	[	[	X
ejpam-3736	304	2	3	3	NUM
ejpam-3736	304	3	]	]	PUNCT
ejpam-3736	304	4	t	t	PROPN
ejpam-3736	304	5	stoyanov	stoyanov	PROPN
ejpam-3736	304	6	.	.	PUNCT
ejpam-3736	305	1	about	about	ADP
ejpam-3736	305	2	the	the	DET
ejpam-3736	305	3	zeros	zero	NOUN
ejpam-3736	305	4	of	of	ADP
ejpam-3736	305	5	some	some	DET
ejpam-3736	305	6	entire	entire	ADJ
ejpam-3736	305	7	functions	function	NOUN
ejpam-3736	305	8	and	and	CCONJ
ejpam-3736	305	9	their	their	PRON
ejpam-3736	305	10	derivatives	derivative	NOUN
ejpam-3736	305	11	.	.	PUNCT
ejpam-3736	306	1	journal	journal	NOUN
ejpam-3736	306	2	of	of	ADP
ejpam-3736	306	3	the	the	DET
ejpam-3736	306	4	australian	australian	ADJ
ejpam-3736	306	5	mathematical	mathematical	ADJ
ejpam-3736	306	6	society	society	NOUN
ejpam-3736	306	7	,	,	PUNCT
ejpam-3736	306	8	68:165–169	68:165–169	PROPN
ejpam-3736	306	9	,	,	PUNCT
ejpam-3736	306	10	2000	2000	NUM
ejpam-3736	306	11	.	.	PUNCT
ejpam-3736	307	1	[	[	X
ejpam-3736	307	2	4	4	X
ejpam-3736	307	3	]	]	PUNCT
ejpam-3736	307	4	t	t	PROPN
ejpam-3736	307	5	stoyanov	stoyanov	PROPN
ejpam-3736	307	6	.	.	PUNCT
ejpam-3736	308	1	some	some	DET
ejpam-3736	308	2	localization	localization	NOUN
ejpam-3736	308	3	of	of	ADP
ejpam-3736	308	4	the	the	DET
ejpam-3736	308	5	zeros	zero	NOUN
ejpam-3736	308	6	of	of	ADP
ejpam-3736	308	7	the	the	DET
ejpam-3736	308	8	derivatives	derivative	NOUN
ejpam-3736	308	9	of	of	ADP
ejpam-3736	308	10	a	a	DET
ejpam-3736	308	11	complex	complex	ADJ
ejpam-3736	308	12	polynomial	polynomial	NOUN
ejpam-3736	308	13	in	in	ADP
ejpam-3736	308	14	the	the	DET
ejpam-3736	308	15	disks	disk	NOUN
ejpam-3736	308	16	or	or	CCONJ
ejpam-3736	308	17	cardioid	cardioid	VERB
ejpam-3736	308	18	interiorities	interioritie	NOUN
ejpam-3736	308	19	.	.	PUNCT
ejpam-3736	309	1	international	international	ADJ
ejpam-3736	309	2	journal	journal	PROPN
ejpam-3736	309	3	of	of	ADP
ejpam-3736	309	4	mathematical	mathematical	ADJ
ejpam-3736	309	5	analysis	analysis	NOUN
ejpam-3736	309	6	,	,	PUNCT
ejpam-3736	309	7	9(58):2849–2855	9(58):2849–2855	NUM
ejpam-3736	309	8	,	,	PUNCT
ejpam-3736	309	9	2015	2015	NUM
ejpam-3736	309	10	.	.	PUNCT
ejpam-3736	310	1	[	[	X
ejpam-3736	310	2	5	5	NUM
ejpam-3736	310	3	]	]	PUNCT
ejpam-3736	310	4	t	t	PROPN
ejpam-3736	310	5	zapryanova	zapryanova	PROPN
ejpam-3736	310	6	.	.	PUNCT
ejpam-3736	311	1	best	good	ADJ
ejpam-3736	311	2	approximation	approximation	NOUN
ejpam-3736	311	3	and	and	CCONJ
ejpam-3736	311	4	moduli	modulus	NOUN
ejpam-3736	311	5	of	of	ADP
ejpam-3736	311	6	smoothness	smoothness	NOUN
ejpam-3736	311	7	.	.	PUNCT
ejpam-3736	312	1	pliska	pliska	PROPN
ejpam-3736	312	2	studia	studia	PROPN
ejpam-3736	312	3	mathematica	mathematica	PROPN
ejpam-3736	312	4	bulgarica	bulgarica	PROPN
ejpam-3736	312	5	,	,	PUNCT
ejpam-3736	312	6	21(1):299–306	21(1):299–306	PROPN
ejpam-3736	312	7	,	,	PUNCT
ejpam-3736	312	8	2012	2012	NUM
ejpam-3736	312	9	.	.	PUNCT
ejpam-3736	313	1	[	[	X
ejpam-3736	313	2	6	6	NUM
ejpam-3736	313	3	]	]	PUNCT
ejpam-3736	313	4	t	t	X
ejpam-3736	313	5	zapryanova	zapryanova	PROPN
ejpam-3736	313	6	and	and	CCONJ
ejpam-3736	313	7	d	d	NOUN
ejpam-3736	313	8	souroujon	souroujon	NOUN
ejpam-3736	313	9	.	.	PUNCT
ejpam-3736	314	1	on	on	ADP
ejpam-3736	314	2	the	the	DET
ejpam-3736	314	3	iterates	iterate	NOUN
ejpam-3736	314	4	of	of	ADP
ejpam-3736	314	5	jackson	jackson	PROPN
ejpam-3736	314	6	type	type	PROPN
ejpam-3736	314	7	operator	operator	NOUN
ejpam-3736	314	8	gs	gs	PROPN
ejpam-3736	314	9	,	,	PUNCT
ejpam-3736	314	10	n.	n.	PROPN
ejpam-3736	314	11	mediterr	mediterr	PROPN
ejpam-3736	314	12	.	.	PUNCT
ejpam-3736	315	1	j.	j.	PROPN
ejpam-3736	315	2	math	math	PROPN
ejpam-3736	315	3	,	,	PUNCT
ejpam-3736	315	4	13:5053–5061	13:5053–5061	NUM
ejpam-3736	315	5	,	,	PUNCT
ejpam-3736	315	6	2016	2016	NUM
ejpam-3736	315	7	.	.	PUNCT