id	sid	tid	token	lemma	pos
ejpam-4772	1	1	european	european	PROPN
ejpam-4772	1	2	journal	journal	PROPN
ejpam-4772	1	3	of	of	ADP
ejpam-4772	1	4	pure	pure	ADJ
ejpam-4772	1	5	and	and	CCONJ
ejpam-4772	1	6	applied	apply	VERB
ejpam-4772	1	7	mathematics	mathematic	NOUN
ejpam-4772	1	8	vol	vol	NOUN
ejpam-4772	1	9	.	.	PUNCT
ejpam-4772	2	1	16	16	NUM
ejpam-4772	2	2	,	,	PUNCT
ejpam-4772	2	3	no	no	INTJ
ejpam-4772	2	4	.	.	NOUN
ejpam-4772	2	5	2	2	NUM
ejpam-4772	2	6	,	,	PUNCT
ejpam-4772	2	7	2023	2023	NUM
ejpam-4772	2	8	,	,	PUNCT
ejpam-4772	2	9	1290	1290	NUM
ejpam-4772	2	10	-	-	SYM
ejpam-4772	2	11	1301	1301	NUM
ejpam-4772	2	12	issn	issn	PROPN
ejpam-4772	2	13	1307	1307	NUM
ejpam-4772	2	14	-	-	SYM
ejpam-4772	2	15	5543	5543	NUM
ejpam-4772	2	16	–	–	PUNCT
ejpam-4772	3	1	ejpam.com	ejpam.com	X
ejpam-4772	3	2	published	publish	VERB
ejpam-4772	3	3	by	by	ADP
ejpam-4772	3	4	new	new	PROPN
ejpam-4772	3	5	york	york	PROPN
ejpam-4772	3	6	business	business	PROPN
ejpam-4772	3	7	global	global	ADJ
ejpam-4772	3	8	hankel	hankel	NOUN
ejpam-4772	3	9	determinant	determinant	ADJ
ejpam-4772	3	10	and	and	CCONJ
ejpam-4772	3	11	toeplitz	toeplitz	NOUN
ejpam-4772	3	12	determinant	determinant	ADJ
ejpam-4772	3	13	on	on	ADP
ejpam-4772	3	14	the	the	DET
ejpam-4772	3	15	class	class	NOUN
ejpam-4772	3	16	of	of	ADP
ejpam-4772	3	17	bazilevič	bazilevič	NOUN
ejpam-4772	3	18	functions	function	NOUN
ejpam-4772	3	19	related	relate	VERB
ejpam-4772	3	20	to	to	ADP
ejpam-4772	3	21	the	the	DET
ejpam-4772	3	22	bernoulli	bernoulli	PROPN
ejpam-4772	3	23	lemniscate	lemniscate	PROPN
ejpam-4772	3	24	ni	ni	PROPN
ejpam-4772	3	25	made	make	VERB
ejpam-4772	3	26	asih1,2,∗	asih1,2,∗	PROPN
ejpam-4772	3	27	,	,	PUNCT
ejpam-4772	3	28	sa’adatul	sa’adatul	VERB
ejpam-4772	3	29	fitri1	fitri1	NOUN
ejpam-4772	3	30	,	,	PUNCT
ejpam-4772	3	31	ratno	ratno	PROPN
ejpam-4772	3	32	bagus	bagus	PROPN
ejpam-4772	3	33	edy	edy	PROPN
ejpam-4772	3	34	wibowo1	wibowo1	PROPN
ejpam-4772	3	35	,	,	PUNCT
ejpam-4772	3	36	marjono1	marjono1	NOUN
ejpam-4772	3	37	1	1	NUM
ejpam-4772	3	38	department	department	NOUN
ejpam-4772	3	39	of	of	ADP
ejpam-4772	3	40	mathematics	mathematic	NOUN
ejpam-4772	3	41	,	,	PUNCT
ejpam-4772	3	42	faculty	faculty	NOUN
ejpam-4772	3	43	of	of	ADP
ejpam-4772	3	44	mathematics	mathematic	NOUN
ejpam-4772	3	45	and	and	CCONJ
ejpam-4772	3	46	natural	natural	ADJ
ejpam-4772	3	47	sciences	science	NOUN
ejpam-4772	3	48	,	,	PUNCT
ejpam-4772	3	49	university	university	NOUN
ejpam-4772	3	50	of	of	ADP
ejpam-4772	3	51	brawijaya	brawijaya	PROPN
ejpam-4772	3	52	,	,	PUNCT
ejpam-4772	3	53	jl	jl	PROPN
ejpam-4772	3	54	.	.	PROPN
ejpam-4772	3	55	veteran	veteran	PROPN
ejpam-4772	3	56	malang	malang	PROPN
ejpam-4772	3	57	65145	65145	NUM
ejpam-4772	3	58	,	,	PUNCT
ejpam-4772	3	59	indonesia	indonesia	PROPN
ejpam-4772	3	60	,	,	PUNCT
ejpam-4772	3	61	2	2	NUM
ejpam-4772	3	62	department	department	NOUN
ejpam-4772	3	63	of	of	ADP
ejpam-4772	3	64	mathematics	mathematic	NOUN
ejpam-4772	3	65	,	,	PUNCT
ejpam-4772	3	66	faculty	faculty	NOUN
ejpam-4772	3	67	of	of	ADP
ejpam-4772	3	68	mathematics	mathematic	NOUN
ejpam-4772	3	69	and	and	CCONJ
ejpam-4772	3	70	natural	natural	ADJ
ejpam-4772	3	71	sciences	science	NOUN
ejpam-4772	3	72	,	,	PUNCT
ejpam-4772	3	73	university	university	NOUN
ejpam-4772	3	74	of	of	ADP
ejpam-4772	3	75	udayana	udayana	PROPN
ejpam-4772	3	76	,	,	PUNCT
ejpam-4772	3	77	indonesia	indonesia	PROPN
ejpam-4772	3	78	abstract	abstract	NOUN
ejpam-4772	3	79	.	.	PUNCT
ejpam-4772	4	1	in	in	ADP
ejpam-4772	4	2	this	this	DET
ejpam-4772	4	3	papers	paper	NOUN
ejpam-4772	4	4	,	,	PUNCT
ejpam-4772	4	5	we	we	PRON
ejpam-4772	4	6	investigate	investigate	VERB
ejpam-4772	4	7	the	the	DET
ejpam-4772	4	8	hankel	hankel	NOUN
ejpam-4772	4	9	determinant	determinant	ADJ
ejpam-4772	4	10	and	and	CCONJ
ejpam-4772	4	11	toeplitz	toeplitz	NOUN
ejpam-4772	4	12	determinant	determinant	ADJ
ejpam-4772	4	13	for	for	ADP
ejpam-4772	4	14	the	the	DET
ejpam-4772	4	15	class	class	NOUN
ejpam-4772	4	16	bazilevič	bazilevič	NOUN
ejpam-4772	4	17	function	function	PROPN
ejpam-4772	4	18	b1(α	b1(α	PROPN
ejpam-4772	4	19	,	,	PUNCT
ejpam-4772	4	20	δ	δ	PROPN
ejpam-4772	4	21	)	)	PUNCT
ejpam-4772	4	22	related	relate	VERB
ejpam-4772	4	23	to	to	ADP
ejpam-4772	4	24	the	the	DET
ejpam-4772	4	25	bernoulli	bernoulli	PROPN
ejpam-4772	4	26	lemniscate	lemniscate	PROPN
ejpam-4772	4	27	function	function	PROPN
ejpam-4772	4	28	on	on	ADP
ejpam-4772	4	29	the	the	DET
ejpam-4772	4	30	unit	unit	NOUN
ejpam-4772	4	31	disk	disk	NOUN
ejpam-4772	4	32	d	d	NOUN
ejpam-4772	4	33	=	=	PUNCT
ejpam-4772	4	34	{	{	PUNCT
ejpam-4772	4	35	z	z	NOUN
ejpam-4772	4	36	:	:	PUNCT
ejpam-4772	4	37	|z|	|z|	NOUN
ejpam-4772	4	38	<	<	X
ejpam-4772	4	39	1	1	NUM
ejpam-4772	4	40	}	}	PUNCT
ejpam-4772	4	41	and	and	CCONJ
ejpam-4772	4	42	obtain	obtain	VERB
ejpam-4772	4	43	the	the	DET
ejpam-4772	4	44	upper	upper	ADJ
ejpam-4772	4	45	bounds	bound	NOUN
ejpam-4772	4	46	of	of	ADP
ejpam-4772	4	47	the	the	DET
ejpam-4772	4	48	determinant	determinant	ADJ
ejpam-4772	4	49	h2(1	h2(1	NOUN
ejpam-4772	4	50	)	)	PUNCT
ejpam-4772	4	51	,	,	PUNCT
ejpam-4772	4	52	h2(2	h2(2	PROPN
ejpam-4772	4	53	)	)	PUNCT
ejpam-4772	4	54	,	,	PUNCT
ejpam-4772	4	55	t2(1	t2(1	PROPN
ejpam-4772	4	56	)	)	PUNCT
ejpam-4772	4	57	,	,	PUNCT
ejpam-4772	4	58	and	and	CCONJ
ejpam-4772	4	59	investigate	investigate	VERB
ejpam-4772	4	60	h2(1	h2(1	NOUN
ejpam-4772	4	61	)	)	PUNCT
ejpam-4772	4	62	using	use	VERB
ejpam-4772	4	63	coefficients	coefficient	NOUN
ejpam-4772	4	64	invers	inver	NOUN
ejpam-4772	4	65	function	function	PROPN
ejpam-4772	4	66	.	.	PUNCT
ejpam-4772	5	1	we	we	PRON
ejpam-4772	5	2	used	use	VERB
ejpam-4772	5	3	lemma	lemma	PROPN
ejpam-4772	5	4	from	from	ADP
ejpam-4772	5	5	charateodory	charateodory	NOUN
ejpam-4772	5	6	-	-	PUNCT
ejpam-4772	5	7	toeplitz	toeplitz	NOUN
ejpam-4772	5	8	and	and	CCONJ
ejpam-4772	5	9	libera	libera	NOUN
ejpam-4772	5	10	about	about	ADP
ejpam-4772	5	11	sharp	sharp	ADJ
ejpam-4772	5	12	inequalities	inequality	NOUN
ejpam-4772	5	13	for	for	ADP
ejpam-4772	5	14	functions	function	NOUN
ejpam-4772	5	15	with	with	ADP
ejpam-4772	5	16	positive	positive	ADJ
ejpam-4772	5	17	real	real	ADJ
ejpam-4772	5	18	part	part	NOUN
ejpam-4772	5	19	.	.	PUNCT
ejpam-4772	6	1	2020	2020	NUM
ejpam-4772	6	2	mathematics	mathematic	NOUN
ejpam-4772	6	3	subject	subject	NOUN
ejpam-4772	6	4	classifications	classification	NOUN
ejpam-4772	6	5	:	:	PUNCT
ejpam-4772	6	6	30c45	30c45	NUM
ejpam-4772	6	7	,	,	PUNCT
ejpam-4772	6	8	30c50	30c50	NUM
ejpam-4772	6	9	,	,	PUNCT
ejpam-4772	6	10	30c55	30c55	NUM
ejpam-4772	6	11	,	,	PUNCT
ejpam-4772	6	12	30c80	30c80	NUM
ejpam-4772	6	13	key	key	ADJ
ejpam-4772	6	14	words	word	NOUN
ejpam-4772	6	15	and	and	CCONJ
ejpam-4772	6	16	phrases	phrase	NOUN
ejpam-4772	6	17	:	:	PUNCT
ejpam-4772	6	18	coefficients	coefficient	NOUN
ejpam-4772	6	19	,	,	PUNCT
ejpam-4772	6	20	bazilevič	bazilevič	NOUN
ejpam-4772	6	21	functions	function	NOUN
ejpam-4772	6	22	,	,	PUNCT
ejpam-4772	6	23	bernoulli	bernoulli	PROPN
ejpam-4772	6	24	lemniscate	lemniscate	PROPN
ejpam-4772	6	25	,	,	PUNCT
ejpam-4772	6	26	subordination	subordination	NOUN
ejpam-4772	6	27	,	,	PUNCT
ejpam-4772	6	28	hankel	hankel	NOUN
ejpam-4772	6	29	determinant	determinant	ADJ
ejpam-4772	6	30	,	,	PUNCT
ejpam-4772	6	31	toeplitz	toeplitz	NOUN
ejpam-4772	6	32	determinant	determinant	ADJ
ejpam-4772	6	33	.	.	PUNCT
ejpam-4772	7	1	1	1	X
ejpam-4772	7	2	.	.	X
ejpam-4772	7	3	introduction	introduction	NOUN
ejpam-4772	7	4	let	let	VERB
ejpam-4772	7	5	s	s	PRON
ejpam-4772	7	6	denotes	denote	VERB
ejpam-4772	7	7	the	the	DET
ejpam-4772	7	8	class	class	NOUN
ejpam-4772	7	9	of	of	ADP
ejpam-4772	7	10	analytic	analytic	ADJ
ejpam-4772	7	11	univalent	univalent	ADJ
ejpam-4772	7	12	function	function	NOUN
ejpam-4772	7	13	f	f	PROPN
ejpam-4772	7	14	defined	define	VERB
ejpam-4772	7	15	on	on	ADP
ejpam-4772	7	16	the	the	DET
ejpam-4772	7	17	unit	unit	NOUN
ejpam-4772	7	18	disk	disk	NOUN
ejpam-4772	7	19	d	d	NOUN
ejpam-4772	7	20	=	=	PUNCT
ejpam-4772	7	21	{	{	PUNCT
ejpam-4772	7	22	z	z	NOUN
ejpam-4772	7	23	:	:	PUNCT
ejpam-4772	7	24	|z|	|z|	NOUN
ejpam-4772	7	25	<	<	X
ejpam-4772	7	26	1	1	NUM
ejpam-4772	7	27	}	}	PUNCT
ejpam-4772	7	28	,	,	PUNCT
ejpam-4772	7	29	and	and	CCONJ
ejpam-4772	7	30	normalized	normalize	VERB
ejpam-4772	7	31	by	by	ADP
ejpam-4772	7	32	f(0	f(0	NOUN
ejpam-4772	7	33	)	)	PUNCT
ejpam-4772	7	34	=	=	SYM
ejpam-4772	7	35	0	0	NUM
ejpam-4772	8	1	and	and	CCONJ
ejpam-4772	8	2	f	f	PROPN
ejpam-4772	8	3	′	′	NUM
ejpam-4772	8	4	(	(	PUNCT
ejpam-4772	8	5	0	0	NUM
ejpam-4772	8	6	)	)	PUNCT
ejpam-4772	8	7	=	=	SYM
ejpam-4772	8	8	1	1	NUM
ejpam-4772	8	9	,	,	PUNCT
ejpam-4772	8	10	given	give	VERB
ejpam-4772	8	11	by	by	ADP
ejpam-4772	8	12	f(z	f(z	PROPN
ejpam-4772	8	13	)	)	PUNCT
ejpam-4772	8	14	=	=	SYM
ejpam-4772	9	1	z	z	NOUN
ejpam-4772	10	1	+	+	NOUN
ejpam-4772	10	2	∞∑	∞∑	NUM
ejpam-4772	10	3	n=2	n=2	CCONJ
ejpam-4772	10	4	anz	anz	NOUN
ejpam-4772	10	5	n.	n.	NOUN
ejpam-4772	10	6	(	(	PUNCT
ejpam-4772	10	7	1	1	X
ejpam-4772	10	8	)	)	PUNCT
ejpam-4772	10	9	let	let	VERB
ejpam-4772	10	10	p	p	NOUN
ejpam-4772	10	11	denotes	denote	VERB
ejpam-4772	10	12	the	the	DET
ejpam-4772	10	13	class	class	NOUN
ejpam-4772	10	14	of	of	ADP
ejpam-4772	10	15	analytic	analytic	ADJ
ejpam-4772	10	16	p	p	NOUN
ejpam-4772	10	17	and	and	CCONJ
ejpam-4772	10	18	satisfies	satisfy	VERB
ejpam-4772	10	19	the	the	DET
ejpam-4772	10	20	condition	condition	NOUN
ejpam-4772	10	21	re(p(z	re(p(z	VERB
ejpam-4772	10	22	)	)	PUNCT
ejpam-4772	10	23	)	)	PUNCT
ejpam-4772	11	1	>	>	X
ejpam-4772	11	2	0	0	PUNCT
ejpam-4772	12	1	for	for	ADP
ejpam-4772	12	2	z	z	PROPN
ejpam-4772	12	3	∈	∈	PROPN
ejpam-4772	12	4	d	d	NOUN
ejpam-4772	12	5	=	=	PRON
ejpam-4772	12	6	{	{	PUNCT
ejpam-4772	12	7	z	z	NOUN
ejpam-4772	12	8	:	:	PUNCT
ejpam-4772	12	9	|z|	|z|	NOUN
ejpam-4772	12	10	<	<	X
ejpam-4772	12	11	1	1	NUM
ejpam-4772	12	12	}	}	PUNCT
ejpam-4772	12	13	,	,	PUNCT
ejpam-4772	12	14	p	p	PROPN
ejpam-4772	12	15	∈	∈	PROPN
ejpam-4772	12	16	p	p	NOUN
ejpam-4772	12	17	gives	give	VERB
ejpam-4772	12	18	,	,	PUNCT
ejpam-4772	12	19	p(z	p(z	NOUN
ejpam-4772	12	20	)	)	PUNCT
ejpam-4772	12	21	=	=	SYM
ejpam-4772	13	1	1	1	NUM
ejpam-4772	13	2	+	+	CCONJ
ejpam-4772	13	3	∞∑	∞∑	NUM
ejpam-4772	13	4	n=1	n=1	PROPN
ejpam-4772	13	5	pnz	pnz	NOUN
ejpam-4772	13	6	n	n	CCONJ
ejpam-4772	13	7	,	,	PUNCT
ejpam-4772	13	8	n	n	NOUN
ejpam-4772	13	9	=	=	SYM
ejpam-4772	13	10	1	1	NUM
ejpam-4772	13	11	,	,	PUNCT
ejpam-4772	13	12	2	2	NUM
ejpam-4772	13	13	,	,	PUNCT
ejpam-4772	13	14	3	3	NUM
ejpam-4772	13	15	,	,	PUNCT
ejpam-4772	13	16	..	..	PUNCT
ejpam-4772	13	17	(	(	PUNCT
ejpam-4772	13	18	2	2	X
ejpam-4772	13	19	)	)	PUNCT
ejpam-4772	13	20	where	where	SCONJ
ejpam-4772	13	21	pn	pn	PROPN
ejpam-4772	13	22	is	be	AUX
ejpam-4772	13	23	the	the	DET
ejpam-4772	13	24	positive	positive	ADJ
ejpam-4772	13	25	real	real	ADJ
ejpam-4772	13	26	part	part	NOUN
ejpam-4772	13	27	[	[	X
ejpam-4772	13	28	1	1	NUM
ejpam-4772	13	29	]	]	PUNCT
ejpam-4772	13	30	.	.	PUNCT
ejpam-4772	14	1	∗corresponding	∗corresponde	VERB
ejpam-4772	14	2	author	author	NOUN
ejpam-4772	14	3	.	.	PUNCT
ejpam-4772	15	1	doi	doi	NOUN
ejpam-4772	15	2	:	:	PUNCT
ejpam-4772	15	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4772	https://doi.org/10.29020/nybg.ejpam.v16i2.4772	ADP
ejpam-4772	15	4	email	email	NOUN
ejpam-4772	15	5	addresses	address	NOUN
ejpam-4772	15	6	:	:	PUNCT
ejpam-4772	15	7	madeasih2@student.ub.ac.id	madeasih2@student.ub.ac.id	PROPN
ejpam-4772	15	8	(	(	PUNCT
ejpam-4772	15	9	n.m	n.m	PROPN
ejpam-4772	15	10	.	.	PROPN
ejpam-4772	15	11	asih	asih	PROPN
ejpam-4772	15	12	)	)	PUNCT
ejpam-4772	15	13	,	,	PUNCT
ejpam-4772	15	14	saadatulfitri@ub.ac.id	saadatulfitri@ub.ac.id	NOUN
ejpam-4772	15	15	(	(	PUNCT
ejpam-4772	15	16	s.	s.	PROPN
ejpam-4772	15	17	fitri	fitri	PROPN
ejpam-4772	15	18	)	)	PUNCT
ejpam-4772	15	19	,	,	PUNCT
ejpam-4772	15	20	rbagus@ub.ac.id	rbagus@ub.ac.id	NOUN
ejpam-4772	15	21	(	(	PUNCT
ejpam-4772	15	22	r.b.e	r.b.e	NOUN
ejpam-4772	15	23	.	.	PUNCT
ejpam-4772	15	24	wibowo	wibowo	PROPN
ejpam-4772	15	25	)	)	PUNCT
ejpam-4772	15	26	,	,	PUNCT
ejpam-4772	15	27	marjono@ub.ac.id	marjono@ub.ac.id	PROPN
ejpam-4772	15	28	(	(	PUNCT
ejpam-4772	15	29	marjono	marjono	PROPN
ejpam-4772	15	30	)	)	PUNCT
ejpam-4772	15	31	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4772	15	32	1290	1290	NUM
ejpam-4772	16	1	©	©	PROPN
ejpam-4772	16	2	2023	2023	NUM
ejpam-4772	16	3	ejpam	ejpam	NOUN
ejpam-4772	16	4	all	all	DET
ejpam-4772	16	5	rights	right	NOUN
ejpam-4772	16	6	reserved	reserve	VERB
ejpam-4772	16	7	.	.	PUNCT
ejpam-4772	17	1	n.m	n.m	PROPN
ejpam-4772	17	2	.	.	PROPN
ejpam-4772	17	3	asih	asih	PROPN
ejpam-4772	17	4	et	et	PROPN
ejpam-4772	17	5	al	al	PROPN
ejpam-4772	17	6	.	.	PUNCT
ejpam-4772	17	7	/	/	SYM
ejpam-4772	17	8	eur	eur	PROPN
ejpam-4772	17	9	.	.	PUNCT
ejpam-4772	18	1	j.	j.	PROPN
ejpam-4772	18	2	pure	pure	PROPN
ejpam-4772	18	3	appl	appl	PROPN
ejpam-4772	18	4	.	.	PROPN
ejpam-4772	18	5	math	math	PROPN
ejpam-4772	18	6	,	,	PUNCT
ejpam-4772	18	7	16	16	NUM
ejpam-4772	18	8	(	(	PUNCT
ejpam-4772	18	9	2	2	NUM
ejpam-4772	18	10	)	)	PUNCT
ejpam-4772	18	11	(	(	PUNCT
ejpam-4772	18	12	2023	2023	NUM
ejpam-4772	18	13	)	)	PUNCT
ejpam-4772	18	14	,	,	PUNCT
ejpam-4772	18	15	1290	1290	NUM
ejpam-4772	18	16	-	-	SYM
ejpam-4772	18	17	1301	1301	NUM
ejpam-4772	18	18	1291	1291	NUM
ejpam-4772	18	19	definition	definition	NOUN
ejpam-4772	18	20	1	1	NUM
ejpam-4772	18	21	.	.	PUNCT
ejpam-4772	19	1	let	let	VERB
ejpam-4772	19	2	f	f	PROPN
ejpam-4772	19	3	∈	∈	PROPN
ejpam-4772	19	4	s	s	X
ejpam-4772	19	5	and	and	CCONJ
ejpam-4772	19	6	satisfying	satisfy	VERB
ejpam-4772	19	7	the	the	DET
ejpam-4772	19	8	condition	condition	NOUN
ejpam-4772	19	9	f(0	f(0	NOUN
ejpam-4772	19	10	)	)	PUNCT
ejpam-4772	20	1	=	=	SYM
ejpam-4772	20	2	1	1	NUM
ejpam-4772	20	3	and	and	CCONJ
ejpam-4772	20	4	f	f	PROPN
ejpam-4772	21	1	′	′	NUM
ejpam-4772	21	2	(	(	PUNCT
ejpam-4772	21	3	0	0	NUM
ejpam-4772	21	4	)	)	PUNCT
ejpam-4772	21	5	=	=	NOUN
ejpam-4772	22	1	0	0	X
ejpam-4772	22	2	.	.	PUNCT
ejpam-4772	23	1	the	the	DET
ejpam-4772	23	2	function	function	NOUN
ejpam-4772	23	3	f	f	PROPN
ejpam-4772	23	4	∈	∈	PROPN
ejpam-4772	23	5	b1(α	b1(α	PROPN
ejpam-4772	23	6	,	,	PUNCT
ejpam-4772	23	7	δ	δ	PROPN
ejpam-4772	23	8	)	)	PUNCT
ejpam-4772	23	9	for	for	ADP
ejpam-4772	23	10	α	α	DET
ejpam-4772	23	11	≥	≥	NOUN
ejpam-4772	23	12	0	0	NUM
ejpam-4772	23	13	and	and	CCONJ
ejpam-4772	23	14	δ	δ	PROPN
ejpam-4772	23	15	>	>	X
ejpam-4772	23	16	0	0	PUNCT
ejpam-4772	24	1	if	if	SCONJ
ejpam-4772	24	2	and	and	CCONJ
ejpam-4772	24	3	only	only	ADV
ejpam-4772	24	4	if	if	SCONJ
ejpam-4772	24	5	,	,	PUNCT
ejpam-4772	24	6	[	[	PUNCT
ejpam-4772	24	7	f	f	X
ejpam-4772	24	8	′	′	NUM
ejpam-4772	24	9	(	(	PUNCT
ejpam-4772	24	10	z	z	NOUN
ejpam-4772	24	11	)	)	PUNCT
ejpam-4772	24	12	f(z)α−1	f(z)α−1	PROPN
ejpam-4772	24	13	zα−1	zα−1	NOUN
ejpam-4772	24	14	]	]	PUNCT
ejpam-4772	24	15	≺	≺	NOUN
ejpam-4772	24	16	√	√	VERB
ejpam-4772	24	17	1	1	NUM
ejpam-4772	24	18	+	+	CCONJ
ejpam-4772	24	19	z	z	NOUN
ejpam-4772	24	20	=	=	NOUN
ejpam-4772	24	21	:	:	PUNCT
ejpam-4772	24	22	ξ(z	ξ(z	NOUN
ejpam-4772	24	23	)	)	PUNCT
ejpam-4772	24	24	,	,	PUNCT
ejpam-4772	24	25	for	for	ADP
ejpam-4772	24	26	z	z	PROPN
ejpam-4772	24	27	∈	∈	PROPN
ejpam-4772	24	28	d	d	X
ejpam-4772	24	29	and	and	CCONJ
ejpam-4772	24	30	ξ(0	ξ(0	PROPN
ejpam-4772	24	31	)	)	PUNCT
ejpam-4772	24	32	=	=	SYM
ejpam-4772	24	33	1	1	NUM
ejpam-4772	24	34	,	,	PUNCT
ejpam-4772	24	35	(	(	PUNCT
ejpam-4772	24	36	3	3	X
ejpam-4772	24	37	)	)	PUNCT
ejpam-4772	24	38	where	where	SCONJ
ejpam-4772	24	39	the	the	DET
ejpam-4772	24	40	branch	branch	NOUN
ejpam-4772	24	41	of	of	ADP
ejpam-4772	24	42	the	the	DET
ejpam-4772	24	43	square	square	ADJ
ejpam-4772	24	44	root	root	NOUN
ejpam-4772	24	45	is	be	AUX
ejpam-4772	24	46	chosen	choose	VERB
ejpam-4772	24	47	to	to	PART
ejpam-4772	24	48	be	be	AUX
ejpam-4772	24	49	ξ(0	ξ(0	VERB
ejpam-4772	24	50	)	)	PUNCT
ejpam-4772	24	51	=	=	SYM
ejpam-4772	24	52	1	1	NUM
ejpam-4772	24	53	,	,	PUNCT
ejpam-4772	24	54	the	the	DET
ejpam-4772	24	55	set	set	NOUN
ejpam-4772	24	56	ξ(d	ξ(d	NOUN
ejpam-4772	24	57	)	)	PUNCT
ejpam-4772	24	58	lies	lie	VERB
ejpam-4772	24	59	in	in	ADP
ejpam-4772	24	60	the	the	DET
ejpam-4772	24	61	region	region	NOUN
ejpam-4772	24	62	bounded	bound	VERB
ejpam-4772	24	63	the	the	DET
ejpam-4772	24	64	right	right	ADJ
ejpam-4772	24	65	loop	loop	NOUN
ejpam-4772	24	66	of	of	ADP
ejpam-4772	24	67	the	the	DET
ejpam-4772	24	68	bernoulli	bernoulli	PROPN
ejpam-4772	24	69	lemniscate	lemniscate	PROPN
ejpam-4772	24	70	function	function	PROPN
ejpam-4772	24	71	is	be	AUX
ejpam-4772	24	72	(	(	PUNCT
ejpam-4772	24	73	x2+y2)2−a2(x2−y2	x2+y2)2−a2(x2−y2	PROPN
ejpam-4772	24	74	)	)	PUNCT
ejpam-4772	24	75	)	)	PUNCT
ejpam-4772	25	1	=	=	SYM
ejpam-4772	25	2	0	0	NUM
ejpam-4772	25	3	,	,	PUNCT
ejpam-4772	25	4	see	see	VERB
ejpam-4772	25	5	[	[	X
ejpam-4772	25	6	2	2	NUM
ejpam-4772	25	7	]	]	PUNCT
ejpam-4772	25	8	,	,	PUNCT
ejpam-4772	25	9	[	[	X
ejpam-4772	25	10	14	14	NUM
ejpam-4772	25	11	]	]	PUNCT
ejpam-4772	25	12	.	.	PUNCT
ejpam-4772	26	1	we	we	PRON
ejpam-4772	26	2	say	say	VERB
ejpam-4772	26	3	that	that	SCONJ
ejpam-4772	26	4	an	an	DET
ejpam-4772	26	5	analytic	analytic	ADJ
ejpam-4772	26	6	function	function	NOUN
ejpam-4772	26	7	f	f	PROPN
ejpam-4772	26	8	is	be	AUX
ejpam-4772	26	9	subordinate	subordinate	ADJ
ejpam-4772	26	10	to	to	ADP
ejpam-4772	26	11	an	an	DET
ejpam-4772	26	12	analytic	analytic	ADJ
ejpam-4772	26	13	function	function	NOUN
ejpam-4772	26	14	g	g	NOUN
ejpam-4772	26	15	,	,	PUNCT
ejpam-4772	26	16	and	and	CCONJ
ejpam-4772	26	17	write	write	VERB
ejpam-4772	26	18	f(z	f(z	NOUN
ejpam-4772	26	19	)	)	PUNCT
ejpam-4772	26	20	≺	≺	NOUN
ejpam-4772	26	21	g(z	g(z	PROPN
ejpam-4772	26	22	)	)	PUNCT
ejpam-4772	26	23	,	,	PUNCT
ejpam-4772	26	24	if	if	SCONJ
ejpam-4772	26	25	and	and	CCONJ
ejpam-4772	26	26	only	only	ADV
ejpam-4772	26	27	if	if	SCONJ
ejpam-4772	26	28	there	there	PRON
ejpam-4772	26	29	exists	exist	VERB
ejpam-4772	26	30	a	a	DET
ejpam-4772	26	31	function	function	NOUN
ejpam-4772	26	32	ω	ω	NOUN
ejpam-4772	26	33	,	,	PUNCT
ejpam-4772	26	34	analytic	analytic	ADJ
ejpam-4772	26	35	in	in	ADP
ejpam-4772	26	36	d	d	PROPN
ejpam-4772	26	37	,	,	PUNCT
ejpam-4772	26	38	such	such	ADJ
ejpam-4772	26	39	that	that	DET
ejpam-4772	26	40	ω(0	ω(0	NOUN
ejpam-4772	26	41	)	)	PUNCT
ejpam-4772	26	42	=	=	SYM
ejpam-4772	26	43	0	0	NUM
ejpam-4772	26	44	,	,	PUNCT
ejpam-4772	26	45	|ω(z)|	|ω(z)|	X
ejpam-4772	26	46	<	<	X
ejpam-4772	26	47	1	1	NUM
ejpam-4772	26	48	for	for	ADP
ejpam-4772	26	49	|z|	|z|	NOUN
ejpam-4772	26	50	<	<	X
ejpam-4772	26	51	1	1	NUM
ejpam-4772	26	52	and	and	CCONJ
ejpam-4772	26	53	f(z	f(z	PROPN
ejpam-4772	26	54	)	)	PUNCT
ejpam-4772	26	55	=	=	SYM
ejpam-4772	26	56	g(ω(z	g(ω(z	ADJ
ejpam-4772	26	57	)	)	PUNCT
ejpam-4772	26	58	)	)	PUNCT
ejpam-4772	26	59	,	,	PUNCT
ejpam-4772	26	60	where	where	SCONJ
ejpam-4772	26	61	ω(z	ω(z	PUNCT
ejpam-4772	26	62	)	)	PUNCT
ejpam-4772	26	63	=	=	PUNCT
ejpam-4772	27	1	δp(z)−	δp(z)−	ADJ
ejpam-4772	27	2	1	1	NUM
ejpam-4772	27	3	δp(z	δp(z	NUM
ejpam-4772	27	4	)	)	PUNCT
ejpam-4772	28	1	+	+	CCONJ
ejpam-4772	28	2	1	1	X
ejpam-4772	28	3	.	.	PUNCT
ejpam-4772	29	1	the	the	DET
ejpam-4772	29	2	form	form	NOUN
ejpam-4772	29	3	of	of	ADP
ejpam-4772	29	4	the	the	DET
ejpam-4772	29	5	lemniscate	lemniscate	PROPN
ejpam-4772	29	6	bernoulli	bernoulli	PROPN
ejpam-4772	29	7	will	will	AUX
ejpam-4772	29	8	be	be	AUX
ejpam-4772	29	9	depended	depend	VERB
ejpam-4772	29	10	on	on	ADP
ejpam-4772	29	11	the	the	DET
ejpam-4772	29	12	value	value	NOUN
ejpam-4772	29	13	of	of	ADP
ejpam-4772	29	14	positive	positive	ADJ
ejpam-4772	29	15	real	real	ADJ
ejpam-4772	29	16	δ	δ	PROPN
ejpam-4772	29	17	.	.	PUNCT
ejpam-4772	30	1	the	the	DET
ejpam-4772	30	2	following	follow	VERB
ejpam-4772	30	3	picture	picture	NOUN
ejpam-4772	30	4	shows	show	VERB
ejpam-4772	30	5	the	the	DET
ejpam-4772	30	6	bazilevič	bazilevič	NOUN
ejpam-4772	30	7	function	function	PROPN
ejpam-4772	30	8	b1(α	b1(α	PROPN
ejpam-4772	30	9	,	,	PUNCT
ejpam-4772	30	10	δ	δ	PROPN
ejpam-4772	30	11	)	)	PUNCT
ejpam-4772	30	12	related	relate	VERB
ejpam-4772	30	13	to	to	ADP
ejpam-4772	30	14	bernoulli	bernoulli	PROPN
ejpam-4772	30	15	lemniscate	lemniscate	PROPN
ejpam-4772	30	16	function	function	PROPN
ejpam-4772	30	17	.	.	PUNCT
ejpam-4772	31	1	figure	figure	VERB
ejpam-4772	31	2	1	1	NUM
ejpam-4772	31	3	:	:	PUNCT
ejpam-4772	31	4	bazilevič	bazilevič	PROPN
ejpam-4772	31	5	b1(α	b1(α	PROPN
ejpam-4772	31	6	,	,	PUNCT
ejpam-4772	31	7	δ	δ	PROPN
ejpam-4772	31	8	)	)	PUNCT
ejpam-4772	31	9	subordination	subordination	NOUN
ejpam-4772	31	10	bernoulli	bernoulli	PROPN
ejpam-4772	31	11	lemniscate	lemniscate	PROPN
ejpam-4772	31	12	from	from	ADP
ejpam-4772	31	13	(	(	PUNCT
ejpam-4772	31	14	3	3	X
ejpam-4772	31	15	)	)	PUNCT
ejpam-4772	31	16	we	we	PRON
ejpam-4772	31	17	obtain	obtain	VERB
ejpam-4772	31	18	initial	initial	ADJ
ejpam-4772	31	19	coefficients	coefficient	NOUN
ejpam-4772	31	20	which	which	PRON
ejpam-4772	31	21	are	be	AUX
ejpam-4772	31	22	used	use	VERB
ejpam-4772	31	23	to	to	PART
ejpam-4772	31	24	determine	determine	VERB
ejpam-4772	31	25	the	the	DET
ejpam-4772	31	26	hankel	hankel	NOUN
ejpam-4772	31	27	determinant	determinant	ADJ
ejpam-4772	31	28	and	and	CCONJ
ejpam-4772	31	29	toeplitz	toeplitz	NOUN
ejpam-4772	31	30	determinant	determinant	ADJ
ejpam-4772	31	31	for	for	ADP
ejpam-4772	31	32	the	the	DET
ejpam-4772	31	33	sharp	sharp	ADJ
ejpam-4772	31	34	boundaries	boundary	NOUN
ejpam-4772	31	35	.	.	PUNCT
ejpam-4772	32	1	the	the	DET
ejpam-4772	32	2	q	q	NOUN
ejpam-4772	32	3	-	-	PUNCT
ejpam-4772	32	4	th	th	VERB
ejpam-4772	32	5	hankel	hankel	NOUN
ejpam-4772	32	6	determinant	determinant	ADJ
ejpam-4772	32	7	is	be	AUX
ejpam-4772	32	8	denoted	denote	VERB
ejpam-4772	32	9	by	by	ADP
ejpam-4772	32	10	hq(n	hq(n	NOUN
ejpam-4772	32	11	)	)	PUNCT
ejpam-4772	32	12	,	,	PUNCT
ejpam-4772	32	13	where	where	SCONJ
ejpam-4772	32	14	q	q	PROPN
ejpam-4772	32	15	≥	≥	NUM
ejpam-4772	32	16	1	1	NUM
ejpam-4772	32	17	and	and	CCONJ
ejpam-4772	32	18	n	n	PRON
ejpam-4772	32	19	≥	≥	NOUN
ejpam-4772	32	20	1	1	NUM
ejpam-4772	32	21	of	of	ADP
ejpam-4772	32	22	functions	function	NOUN
ejpam-4772	32	23	f	f	PROPN
ejpam-4772	32	24	was	be	AUX
ejpam-4772	32	25	stated	state	VERB
ejpam-4772	32	26	by	by	ADP
ejpam-4772	32	27	noonan	noonan	PROPN
ejpam-4772	32	28	and	and	CCONJ
ejpam-4772	32	29	thomas	thomas	PROPN
ejpam-4772	33	1	[	[	X
ejpam-4772	33	2	12	12	NUM
ejpam-4772	33	3	]	]	PUNCT
ejpam-4772	33	4	as	as	ADP
ejpam-4772	33	5	,	,	PUNCT
ejpam-4772	33	6	hq(n	hq(n	X
ejpam-4772	33	7	)	)	PUNCT
ejpam-4772	33	8	=	=	PUNCT
ejpam-4772	33	9	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	SCONJ
ejpam-4772	33	10	an	an	DET
ejpam-4772	33	11	an	an	DET
ejpam-4772	33	12	+	+	NOUN
ejpam-4772	33	13	1	1	NUM
ejpam-4772	33	14	....	....	PUNCT
ejpam-4772	33	15	an+q+1	an+q+1	VERB
ejpam-4772	33	16	an	an	DET
ejpam-4772	33	17	+	+	NUM
ejpam-4772	33	18	1	1	NUM
ejpam-4772	33	19	an	an	DET
ejpam-4772	33	20	+	+	NUM
ejpam-4772	33	21	2	2	NUM
ejpam-4772	33	22	...	...	PUNCT
ejpam-4772	33	23	an	an	DET
ejpam-4772	33	24	+	+	NOUN
ejpam-4772	33	25	q	q	NOUN
ejpam-4772	33	26	...	...	PUNCT
ejpam-4772	33	27	...	...	PUNCT
ejpam-4772	33	28	...	...	PUNCT
ejpam-4772	33	29	...	...	PUNCT
ejpam-4772	34	1	an+q−1	an+q−1	PRON
ejpam-4772	34	2	an	an	DET
ejpam-4772	34	3	+	+	X
ejpam-4772	34	4	q	q	NOUN
ejpam-4772	34	5	...	...	PUNCT
ejpam-4772	34	6	an+2q−2	an+2q−2	X
ejpam-4772	34	7	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ejpam-4772	34	8	(	(	PUNCT
ejpam-4772	34	9	4	4	NUM
ejpam-4772	34	10	)	)	PUNCT
ejpam-4772	34	11	since	since	SCONJ
ejpam-4772	34	12	f	f	PROPN
ejpam-4772	34	13	∈	∈	PROPN
ejpam-4772	34	14	s	s	PROPN
ejpam-4772	34	15	,	,	PUNCT
ejpam-4772	34	16	a1	a1	NOUN
ejpam-4772	34	17	=	=	SYM
ejpam-4772	34	18	1	1	NUM
ejpam-4772	34	19	,	,	PUNCT
ejpam-4772	34	20	in	in	ADP
ejpam-4772	34	21	particular	particular	ADJ
ejpam-4772	34	22	we	we	PRON
ejpam-4772	34	23	have	have	VERB
ejpam-4772	34	24	h2(1	h2(1	PROPN
ejpam-4772	34	25	)	)	PUNCT
ejpam-4772	34	26	as	as	ADP
ejpam-4772	34	27	follow	follow	VERB
ejpam-4772	34	28	,	,	PUNCT
ejpam-4772	34	29	h2(1	h2(1	PROPN
ejpam-4772	34	30	)	)	PUNCT
ejpam-4772	34	31	=	=	SYM
ejpam-4772	34	32	∣∣∣∣a1	∣∣∣∣a1	NOUN
ejpam-4772	34	33	a2	a2	PROPN
ejpam-4772	34	34	a2	a2	PROPN
ejpam-4772	34	35	a3	a3	NOUN
ejpam-4772	34	36	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4772	34	37	=	=	PUNCT
ejpam-4772	34	38	(	(	PUNCT
ejpam-4772	34	39	a1a3	a1a3	X
ejpam-4772	34	40	−	−	PROPN
ejpam-4772	34	41	a22	a22	NOUN
ejpam-4772	34	42	)	)	PUNCT
ejpam-4772	34	43	.	.	PUNCT
ejpam-4772	35	1	hankel	hankel	PROPN
ejpam-4772	35	2	determinant	determinant	ADJ
ejpam-4772	35	3	h2(1	h2(1	NOUN
ejpam-4772	35	4	)	)	PUNCT
ejpam-4772	35	5	=	=	PUNCT
ejpam-4772	36	1	|a3	|a3	NOUN
ejpam-4772	36	2	−	−	NOUN
ejpam-4772	37	1	a22|	a22|	PRON
ejpam-4772	37	2	is	be	AUX
ejpam-4772	37	3	well	well	ADV
ejpam-4772	37	4	known	know	VERB
ejpam-4772	37	5	as	as	ADP
ejpam-4772	37	6	fekete	fekete	PROPN
ejpam-4772	37	7	szegö	szegö	PROPN
ejpam-4772	37	8	function	function	PROPN
ejpam-4772	37	9	.	.	PUNCT
ejpam-4772	38	1	previous	previous	ADJ
ejpam-4772	38	2	research	research	NOUN
ejpam-4772	38	3	about	about	ADP
ejpam-4772	38	4	hankel	hankel	NOUN
ejpam-4772	38	5	determinant	determinant	ADJ
ejpam-4772	38	6	on	on	ADP
ejpam-4772	38	7	starlike	starlike	NOUN
ejpam-4772	38	8	function	function	NOUN
ejpam-4772	38	9	related	relate	VERB
ejpam-4772	38	10	to	to	ADP
ejpam-4772	38	11	bernoulli	bernoulli	PROPN
ejpam-4772	38	12	lemniscate	lemniscate	PROPN
ejpam-4772	38	13	function	function	PROPN
ejpam-4772	38	14	in	in	ADP
ejpam-4772	38	15	[	[	X
ejpam-4772	38	16	4	4	NUM
ejpam-4772	38	17	]	]	PUNCT
ejpam-4772	38	18	obtained	obtain	VERB
ejpam-4772	38	19	one	one	NUM
ejpam-4772	38	20	of	of	ADP
ejpam-4772	38	21	them	they	PRON
ejpam-4772	38	22	is	be	AUX
ejpam-4772	38	23	hankel	hankel	NOUN
ejpam-4772	38	24	determinant	determinant	ADJ
ejpam-4772	38	25	h2(2	h2(2	PROPN
ejpam-4772	38	26	)	)	PUNCT
ejpam-4772	38	27	.	.	PUNCT
ejpam-4772	39	1	the	the	DET
ejpam-4772	39	2	other	other	ADJ
ejpam-4772	39	3	researches	research	VERB
ejpam-4772	39	4	n.m	n.m	PROPN
ejpam-4772	39	5	.	.	PROPN
ejpam-4772	39	6	asih	asih	PROPN
ejpam-4772	39	7	et	et	PROPN
ejpam-4772	39	8	al	al	PROPN
ejpam-4772	39	9	.	.	PUNCT
ejpam-4772	39	10	/	/	SYM
ejpam-4772	39	11	eur	eur	PROPN
ejpam-4772	39	12	.	.	PUNCT
ejpam-4772	40	1	j.	j.	PROPN
ejpam-4772	40	2	pure	pure	PROPN
ejpam-4772	40	3	appl	appl	PROPN
ejpam-4772	40	4	.	.	PROPN
ejpam-4772	40	5	math	math	PROPN
ejpam-4772	40	6	,	,	PUNCT
ejpam-4772	40	7	16	16	NUM
ejpam-4772	40	8	(	(	PUNCT
ejpam-4772	40	9	2	2	NUM
ejpam-4772	40	10	)	)	PUNCT
ejpam-4772	40	11	(	(	PUNCT
ejpam-4772	40	12	2023	2023	NUM
ejpam-4772	40	13	)	)	PUNCT
ejpam-4772	40	14	,	,	PUNCT
ejpam-4772	40	15	1290	1290	NUM
ejpam-4772	40	16	-	-	SYM
ejpam-4772	40	17	1301	1301	NUM
ejpam-4772	40	18	1292	1292	NUM
ejpam-4772	40	19	on	on	ADP
ejpam-4772	40	20	third	third	ADJ
ejpam-4772	40	21	hankel	hankel	NOUN
ejpam-4772	40	22	determinant	determinant	ADJ
ejpam-4772	40	23	are	be	AUX
ejpam-4772	40	24	studied	study	VERB
ejpam-4772	40	25	in	in	ADP
ejpam-4772	40	26	[	[	X
ejpam-4772	40	27	5	5	NUM
ejpam-4772	40	28	]	]	PUNCT
ejpam-4772	40	29	,	,	PUNCT
ejpam-4772	40	30	[	[	X
ejpam-4772	40	31	9	9	NUM
ejpam-4772	40	32	]	]	PUNCT
ejpam-4772	40	33	.	.	PUNCT
ejpam-4772	41	1	research	research	NOUN
ejpam-4772	41	2	by	by	ADP
ejpam-4772	41	3	thomas	thomas	PROPN
ejpam-4772	41	4	and	and	CCONJ
ejpam-4772	41	5	halim	halim	PROPN
ejpam-4772	42	1	[	[	X
ejpam-4772	42	2	15	15	NUM
ejpam-4772	42	3	]	]	PUNCT
ejpam-4772	42	4	defined	define	VERB
ejpam-4772	42	5	the	the	DET
ejpam-4772	42	6	symmetric	symmetric	ADJ
ejpam-4772	42	7	toeplitz	toeplitz	NOUN
ejpam-4772	42	8	determinant	determinant	ADJ
ejpam-4772	42	9	tq(n	tq(n	PUNCT
ejpam-4772	42	10	)	)	PUNCT
ejpam-4772	42	11	for	for	ADP
ejpam-4772	42	12	q	q	PROPN
ejpam-4772	42	13	≥	≥	NUM
ejpam-4772	42	14	1	1	NUM
ejpam-4772	42	15	and	and	CCONJ
ejpam-4772	42	16	n	n	PRON
ejpam-4772	42	17	≥	≥	NOUN
ejpam-4772	42	18	1	1	NUM
ejpam-4772	42	19	gives	give	NOUN
ejpam-4772	42	20	,	,	PUNCT
ejpam-4772	42	21	tq(n	tq(n	PUNCT
ejpam-4772	42	22	)	)	PUNCT
ejpam-4772	42	23	=	=	PUNCT
ejpam-4772	42	24	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ejpam-4772	42	25	an	an	DET
ejpam-4772	42	26	an	an	DET
ejpam-4772	42	27	+	+	NOUN
ejpam-4772	42	28	1	1	NUM
ejpam-4772	42	29	....	....	PUNCT
ejpam-4772	43	1	an+q−1	an+q−1	PRON
ejpam-4772	43	2	an	an	DET
ejpam-4772	43	3	+	+	NUM
ejpam-4772	43	4	1	1	NUM
ejpam-4772	43	5	an	an	PRON
ejpam-4772	43	6	...	...	PUNCT
ejpam-4772	43	7	an+q−2	an+q−2	INTJ
ejpam-4772	43	8	...	...	PUNCT
ejpam-4772	43	9	...	...	PUNCT
ejpam-4772	43	10	...	...	PUNCT
ejpam-4772	43	11	...	...	PUNCT
ejpam-4772	44	1	an+q−1	an+q−1	PRON
ejpam-4772	44	2	an+q−2	an+q−2	VERB
ejpam-4772	44	3	...	...	PUNCT
ejpam-4772	44	4	an	an	DET
ejpam-4772	44	5	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ejpam-4772	44	6	(	(	PUNCT
ejpam-4772	44	7	5	5	NUM
ejpam-4772	44	8	)	)	PUNCT
ejpam-4772	44	9	an	an	DET
ejpam-4772	44	10	example	example	NOUN
ejpam-4772	44	11	of	of	ADP
ejpam-4772	44	12	second	second	ADJ
ejpam-4772	44	13	order	order	NOUN
ejpam-4772	44	14	of	of	ADP
ejpam-4772	44	15	toeplitz	toeplitz	NOUN
ejpam-4772	44	16	determinant	determinant	ADJ
ejpam-4772	44	17	is	be	AUX
ejpam-4772	44	18	t2(1	t2(1	PROPN
ejpam-4772	44	19	)	)	PUNCT
ejpam-4772	44	20	with	with	ADP
ejpam-4772	44	21	a1	a1	NOUN
ejpam-4772	44	22	=	=	SYM
ejpam-4772	44	23	1	1	NUM
ejpam-4772	44	24	,	,	PUNCT
ejpam-4772	44	25	is	be	AUX
ejpam-4772	44	26	given	give	VERB
ejpam-4772	44	27	by	by	ADP
ejpam-4772	44	28	t2(1	t2(1	PROPN
ejpam-4772	44	29	)	)	PUNCT
ejpam-4772	44	30	=	=	SYM
ejpam-4772	44	31	∣∣∣∣a1	∣∣∣∣a1	NOUN
ejpam-4772	44	32	a2	a2	PROPN
ejpam-4772	44	33	a2	a2	PROPN
ejpam-4772	44	34	a1	a1	NOUN
ejpam-4772	44	35	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4772	44	36	=	=	SYM
ejpam-4772	44	37	(	(	PUNCT
ejpam-4772	44	38	a21	a21	PROPN
ejpam-4772	44	39	−	−	PROPN
ejpam-4772	44	40	a22	a22	PROPN
ejpam-4772	44	41	)	)	PUNCT
ejpam-4772	44	42	.	.	PUNCT
ejpam-4772	45	1	the	the	DET
ejpam-4772	45	2	well	well	ADV
ejpam-4772	45	3	known	know	VERB
ejpam-4772	45	4	research	research	NOUN
ejpam-4772	45	5	about	about	ADP
ejpam-4772	45	6	the	the	DET
ejpam-4772	45	7	contruction	contruction	NOUN
ejpam-4772	45	8	of	of	ADP
ejpam-4772	45	9	toeplitz	toeplitz	NOUN
ejpam-4772	45	10	matrices	matrix	NOUN
ejpam-4772	45	11	has	have	AUX
ejpam-4772	45	12	previously	previously	ADV
ejpam-4772	45	13	studied	study	VERB
ejpam-4772	45	14	by	by	ADP
ejpam-4772	45	15	(	(	PUNCT
ejpam-4772	45	16	see	see	VERB
ejpam-4772	45	17	[	[	X
ejpam-4772	45	18	13	13	NUM
ejpam-4772	45	19	]	]	PUNCT
ejpam-4772	45	20	for	for	ADP
ejpam-4772	45	21	more	more	ADJ
ejpam-4772	45	22	detail	detail	NOUN
ejpam-4772	45	23	)	)	PUNCT
ejpam-4772	45	24	.	.	PUNCT
ejpam-4772	46	1	in	in	ADP
ejpam-4772	46	2	his	his	PRON
ejpam-4772	46	3	work	work	NOUN
ejpam-4772	46	4	whose	whose	DET
ejpam-4772	46	5	element	element	NOUN
ejpam-4772	46	6	are	be	AUX
ejpam-4772	46	7	the	the	DET
ejpam-4772	46	8	coefficient	coefficient	NOUN
ejpam-4772	46	9	f	f	PROPN
ejpam-4772	46	10	univalent	univalent	ADJ
ejpam-4772	46	11	functions	function	NOUN
ejpam-4772	46	12	assosiated	assosiate	VERB
ejpam-4772	46	13	with	with	ADP
ejpam-4772	46	14	q	q	ADJ
ejpam-4772	46	15	-	-	ADJ
ejpam-4772	46	16	derivative	derivative	ADJ
ejpam-4772	46	17	operator	operator	NOUN
ejpam-4772	46	18	.	.	PUNCT
ejpam-4772	47	1	2	2	X
ejpam-4772	47	2	.	.	X
ejpam-4772	47	3	preliminaries	preliminary	NOUN
ejpam-4772	47	4	we	we	PRON
ejpam-4772	47	5	have	have	VERB
ejpam-4772	47	6	some	some	DET
ejpam-4772	47	7	lemmas	lemma	NOUN
ejpam-4772	47	8	used	use	VERB
ejpam-4772	47	9	to	to	PART
ejpam-4772	47	10	determine	determine	VERB
ejpam-4772	47	11	sharp	sharp	ADJ
ejpam-4772	47	12	inequalities	inequality	NOUN
ejpam-4772	47	13	boundaries	boundary	NOUN
ejpam-4772	47	14	of	of	ADP
ejpam-4772	47	15	hankel	hankel	NOUN
ejpam-4772	47	16	determinant	determinant	ADJ
ejpam-4772	47	17	and	and	CCONJ
ejpam-4772	47	18	toeplitz	toeplitz	NOUN
ejpam-4772	47	19	determinant	determinant	ADJ
ejpam-4772	47	20	.	.	PUNCT
ejpam-4772	48	1	lemma	lemma	PROPN
ejpam-4772	48	2	1	1	NUM
ejpam-4772	48	3	.	.	PUNCT
ejpam-4772	49	1	[	[	X
ejpam-4772	49	2	1	1	NUM
ejpam-4772	49	3	]	]	PUNCT
ejpam-4772	49	4	,	,	PUNCT
ejpam-4772	49	5	[	[	X
ejpam-4772	49	6	3	3	NUM
ejpam-4772	49	7	]	]	PUNCT
ejpam-4772	49	8	.	.	PUNCT
ejpam-4772	50	1	if	if	SCONJ
ejpam-4772	50	2	p	p	PROPN
ejpam-4772	50	3	∈	∈	PROPN
ejpam-4772	50	4	p	p	NOUN
ejpam-4772	50	5	analityc	analityc	NOUN
ejpam-4772	50	6	in	in	ADP
ejpam-4772	50	7	d	d	PROPN
ejpam-4772	50	8	with	with	ADP
ejpam-4772	50	9	p(z	p(z	NOUN
ejpam-4772	50	10	)	)	PUNCT
ejpam-4772	50	11	=	=	SYM
ejpam-4772	50	12	1	1	NUM
ejpam-4772	50	13	+	+	NUM
ejpam-4772	50	14	∑∞	∑∞	NOUN
ejpam-4772	50	15	n=1	n=1	PROPN
ejpam-4772	50	16	pnz	pnz	NOUN
ejpam-4772	50	17	n	n	PROPN
ejpam-4772	50	18	for	for	ADP
ejpam-4772	50	19	n	n	PRON
ejpam-4772	50	20	≥	≥	NOUN
ejpam-4772	50	21	1	1	NUM
ejpam-4772	50	22	than	than	ADP
ejpam-4772	50	23	|pn|	|pn|	NUM
ejpam-4772	50	24	≤	≤	NUM
ejpam-4772	50	25	2	2	NUM
ejpam-4772	50	26	(	(	PUNCT
ejpam-4772	50	27	6	6	NUM
ejpam-4772	50	28	)	)	PUNCT
ejpam-4772	50	29	for	for	ADP
ejpam-4772	50	30	the	the	DET
ejpam-4772	50	31	p(z	p(z	NOUN
ejpam-4772	50	32	)	)	PUNCT
ejpam-4772	50	33	=	=	PUNCT
ejpam-4772	51	1	(	(	PUNCT
ejpam-4772	51	2	1+z)/(1−z	1+z)/(1−z	NUM
ejpam-4772	51	3	)	)	PUNCT
ejpam-4772	51	4	,	,	PUNCT
ejpam-4772	51	5	this	this	PRON
ejpam-4772	51	6	lemmas	lemma	VERB
ejpam-4772	51	7	an	an	DET
ejpam-4772	51	8	know	know	NOUN
ejpam-4772	51	9	as	as	ADP
ejpam-4772	51	10	inequlity	inequlity	NOUN
ejpam-4772	51	11	caratheodory	caratheodory	NOUN
ejpam-4772	51	12	toeplitz	toeplitz	PROPN
ejpam-4772	51	13	.	.	PUNCT
ejpam-4772	52	1	lemma	lemma	PROPN
ejpam-4772	52	2	2	2	NUM
ejpam-4772	52	3	.	.	PUNCT
ejpam-4772	53	1	[	[	X
ejpam-4772	53	2	7	7	NUM
ejpam-4772	53	3	]	]	PUNCT
ejpam-4772	53	4	.	.	PUNCT
ejpam-4772	54	1	if	if	SCONJ
ejpam-4772	54	2	p	p	PROPN
ejpam-4772	54	3	∈	∈	PROPN
ejpam-4772	54	4	p	p	NOUN
ejpam-4772	54	5	analityc	analityc	NOUN
ejpam-4772	54	6	in	in	ADP
ejpam-4772	54	7	d	d	PROPN
ejpam-4772	54	8	with	with	ADP
ejpam-4772	54	9	p(z	p(z	NOUN
ejpam-4772	54	10	)	)	PUNCT
ejpam-4772	54	11	=	=	SYM
ejpam-4772	54	12	1	1	NUM
ejpam-4772	54	13	+	+	NUM
ejpam-4772	54	14	∑∞	∑∞	NOUN
ejpam-4772	54	15	n=1	n=1	PROPN
ejpam-4772	54	16	pnz	pnz	NOUN
ejpam-4772	54	17	n	n	CCONJ
ejpam-4772	54	18	then	then	ADV
ejpam-4772	54	19	for	for	ADP
ejpam-4772	54	20	some	some	DET
ejpam-4772	54	21	complex	complex	ADJ
ejpam-4772	54	22	values	value	NOUN
ejpam-4772	54	23	x	x	PUNCT
ejpam-4772	54	24	with	with	ADP
ejpam-4772	54	25	|x|	|x|	PROPN
ejpam-4772	54	26	≤	≤	NUM
ejpam-4772	54	27	1	1	NUM
ejpam-4772	54	28	and	and	CCONJ
ejpam-4772	54	29	some	some	DET
ejpam-4772	54	30	complex	complex	ADJ
ejpam-4772	54	31	values	value	NOUN
ejpam-4772	54	32	ρ	ρ	NOUN
ejpam-4772	54	33	with	with	ADP
ejpam-4772	54	34	|ρ|	|ρ|	NOUN
ejpam-4772	54	35	≤	≤	NUM
ejpam-4772	54	36	1	1	NUM
ejpam-4772	54	37	,	,	PUNCT
ejpam-4772	54	38	2p2	2p2	NUM
ejpam-4772	54	39	=	=	SYM
ejpam-4772	54	40	p21	p21	PROPN
ejpam-4772	54	41	+	+	CCONJ
ejpam-4772	54	42	x(4−	x(4−	PROPN
ejpam-4772	54	43	p21	p21	PROPN
ejpam-4772	54	44	)	)	PUNCT
ejpam-4772	54	45	(	(	PUNCT
ejpam-4772	54	46	7	7	NUM
ejpam-4772	54	47	)	)	PUNCT
ejpam-4772	54	48	4p3	4p3	NUM
ejpam-4772	55	1	=	=	NOUN
ejpam-4772	55	2	p31	p31	NOUN
ejpam-4772	55	3	+	+	CCONJ
ejpam-4772	55	4	2(4−	2(4−	NUM
ejpam-4772	55	5	p21)p1x−	p21)p1x−	PRON
ejpam-4772	55	6	p1(4−	p1(4−	NOUN
ejpam-4772	55	7	p21)x	p21)x	PROPN
ejpam-4772	55	8	2	2	NUM
ejpam-4772	55	9	+	+	CCONJ
ejpam-4772	55	10	2(4−	2(4−	NUM
ejpam-4772	55	11	p21)(1−	p21)(1−	NOUN
ejpam-4772	55	12	|x|2)ρ	|x|2)ρ	ADJ
ejpam-4772	55	13	(	(	PUNCT
ejpam-4772	55	14	8)	8)	NUM
ejpam-4772	55	15	3	3	NUM
ejpam-4772	55	16	.	.	PUNCT
ejpam-4772	56	1	results	result	NOUN
ejpam-4772	56	2	now	now	ADV
ejpam-4772	56	3	,	,	PUNCT
ejpam-4772	56	4	we	we	PRON
ejpam-4772	56	5	state	state	VERB
ejpam-4772	56	6	and	and	CCONJ
ejpam-4772	56	7	prove	prove	VERB
ejpam-4772	56	8	the	the	DET
ejpam-4772	56	9	results	result	NOUN
ejpam-4772	56	10	from	from	ADP
ejpam-4772	56	11	hankel	hankel	NOUN
ejpam-4772	56	12	determinant	determinant	ADJ
ejpam-4772	56	13	and	and	CCONJ
ejpam-4772	56	14	toeplitz	toeplitz	NOUN
ejpam-4772	56	15	determinant	determinant	ADJ
ejpam-4772	56	16	of	of	ADP
ejpam-4772	56	17	our	our	PRON
ejpam-4772	56	18	investigation	investigation	NOUN
ejpam-4772	56	19	.	.	PUNCT
ejpam-4772	57	1	theorem	theorem	NOUN
ejpam-4772	57	2	1	1	NUM
ejpam-4772	57	3	.	.	PUNCT
ejpam-4772	58	1	if	if	SCONJ
ejpam-4772	58	2	f	f	PROPN
ejpam-4772	58	3	∈	∈	PROPN
ejpam-4772	58	4	b1(α	b1(α	PROPN
ejpam-4772	58	5	,	,	PUNCT
ejpam-4772	58	6	δ	δ	PROPN
ejpam-4772	58	7	)	)	PUNCT
ejpam-4772	58	8	for	for	ADP
ejpam-4772	58	9	0	0	NUM
ejpam-4772	58	10	≤	≤	NUM
ejpam-4772	58	11	α	α	NOUN
ejpam-4772	58	12	≤	≤	NOUN
ejpam-4772	58	13	1	1	NUM
ejpam-4772	58	14	and	and	CCONJ
ejpam-4772	58	15	0	0	NUM
ejpam-4772	58	16	<	<	X
ejpam-4772	58	17	δ	δ	PROPN
ejpam-4772	58	18	≤	≤	ADV
ejpam-4772	58	19	1	1	NUM
ejpam-4772	58	20	then	then	ADV
ejpam-4772	58	21	h2(1	h2(1	PROPN
ejpam-4772	58	22	)	)	PUNCT
ejpam-4772	58	23	≤	≤	NOUN
ejpam-4772	58	24	3	3	NUM
ejpam-4772	58	25	√	√	NUM
ejpam-4772	58	26	2	2	NUM
ejpam-4772	58	27	√	√	PROPN
ejpam-4772	58	28	δ	δ	PROPN
ejpam-4772	58	29	+	+	CCONJ
ejpam-4772	58	30	2(1	2(1	NUM
ejpam-4772	58	31	+	+	CCONJ
ejpam-4772	58	32	α)(2	α)(2	NUM
ejpam-4772	58	33	+	+	NOUN
ejpam-4772	58	34	α)δ	α)δ	NOUN
ejpam-4772	58	35	√	√	VERB
ejpam-4772	58	36	1	1	NUM
ejpam-4772	58	37	+	+	NUM
ejpam-4772	58	38	δ	δ	PROPN
ejpam-4772	58	39	+	+	CCONJ
ejpam-4772	58	40	3	3	NUM
ejpam-4772	58	41	√	√	NUM
ejpam-4772	58	42	2δ3/2((3	2δ3/2((3	NUM
ejpam-4772	58	43	+	+	NUM
ejpam-4772	58	44	2α	2α	NOUN
ejpam-4772	58	45	)	)	PUNCT
ejpam-4772	58	46	)	)	PUNCT
ejpam-4772	58	47	2(2	2(2	NUM
ejpam-4772	59	1	+	+	CCONJ
ejpam-4772	59	2	α)(1	α)(1	NUM
ejpam-4772	60	1	+	+	CCONJ
ejpam-4772	60	2	δ)7/2	δ)7/2	PROPN
ejpam-4772	60	3	,	,	PUNCT
ejpam-4772	60	4	and	and	CCONJ
ejpam-4772	60	5	the	the	DET
ejpam-4772	60	6	inequality	inequality	NOUN
ejpam-4772	60	7	is	be	AUX
ejpam-4772	60	8	sharp	sharp	ADJ
ejpam-4772	60	9	.	.	PUNCT
ejpam-4772	61	1	n.m	n.m	PROPN
ejpam-4772	61	2	.	.	PROPN
ejpam-4772	61	3	asih	asih	PROPN
ejpam-4772	61	4	et	et	PROPN
ejpam-4772	61	5	al	al	PROPN
ejpam-4772	61	6	.	.	PUNCT
ejpam-4772	61	7	/	/	SYM
ejpam-4772	61	8	eur	eur	PROPN
ejpam-4772	61	9	.	.	PUNCT
ejpam-4772	62	1	j.	j.	PROPN
ejpam-4772	62	2	pure	pure	PROPN
ejpam-4772	62	3	appl	appl	PROPN
ejpam-4772	62	4	.	.	PROPN
ejpam-4772	62	5	math	math	PROPN
ejpam-4772	62	6	,	,	PUNCT
ejpam-4772	62	7	16	16	NUM
ejpam-4772	62	8	(	(	PUNCT
ejpam-4772	62	9	2	2	NUM
ejpam-4772	62	10	)	)	PUNCT
ejpam-4772	62	11	(	(	PUNCT
ejpam-4772	62	12	2023	2023	NUM
ejpam-4772	62	13	)	)	PUNCT
ejpam-4772	62	14	,	,	PUNCT
ejpam-4772	62	15	1290	1290	NUM
ejpam-4772	62	16	-	-	SYM
ejpam-4772	62	17	1301	1301	NUM
ejpam-4772	62	18	1293	1293	NUM
ejpam-4772	62	19	proof	proof	NOUN
ejpam-4772	62	20	.	.	PUNCT
ejpam-4772	63	1	first	first	ADV
ejpam-4772	63	2	consider	consider	VERB
ejpam-4772	63	3	from	from	ADP
ejpam-4772	63	4	(	(	PUNCT
ejpam-4772	63	5	3	3	NUM
ejpam-4772	63	6	)	)	PUNCT
ejpam-4772	63	7	,	,	PUNCT
ejpam-4772	63	8	we	we	PRON
ejpam-4772	63	9	have	have	VERB
ejpam-4772	63	10	initial	initial	ADJ
ejpam-4772	63	11	coefficients	coefficient	NOUN
ejpam-4772	63	12	a1	a1	NOUN
ejpam-4772	63	13	,	,	PUNCT
ejpam-4772	63	14	a2	a2	PROPN
ejpam-4772	63	15	and	and	CCONJ
ejpam-4772	63	16	a3	a3	NOUN
ejpam-4772	63	17	by	by	ADP
ejpam-4772	63	18	[	[	X
ejpam-4772	63	19	10	10	NUM
ejpam-4772	63	20	]	]	PUNCT
ejpam-4772	63	21	,	,	PUNCT
ejpam-4772	63	22	with	with	ADP
ejpam-4772	63	23	a1	a1	NOUN
ejpam-4772	63	24	=	=	SYM
ejpam-4772	63	25	1	1	NUM
ejpam-4772	63	26	,	,	PUNCT
ejpam-4772	63	27	a2	a2	PROPN
ejpam-4772	63	28	and	and	CCONJ
ejpam-4772	63	29	a3	a3	NOUN
ejpam-4772	63	30	gives	give	NOUN
ejpam-4772	63	31	,	,	PUNCT
ejpam-4772	63	32	a2	a2	PROPN
ejpam-4772	63	33	=	=	SYM
ejpam-4772	63	34	p1	p1	PROPN
ejpam-4772	63	35	√	√	NOUN
ejpam-4772	63	36	α√	α√	NUM
ejpam-4772	63	37	2(1	2(1	NUM
ejpam-4772	64	1	+	+	CCONJ
ejpam-4772	64	2	δ)3/2	δ)3/2	PROPN
ejpam-4772	64	3	,	,	PUNCT
ejpam-4772	64	4	(	(	PUNCT
ejpam-4772	64	5	9	9	X
ejpam-4772	64	6	)	)	PUNCT
ejpam-4772	64	7	a3	a3	NOUN
ejpam-4772	64	8	=	=	SYM
ejpam-4772	64	9	δ	δ	PROPN
ejpam-4772	64	10	8(2	8(2	PROPN
ejpam-4772	65	1	+	+	CCONJ
ejpam-4772	65	2	α)(1	α)(1	NUM
ejpam-4772	66	1	+	+	CCONJ
ejpam-4772	66	2	δ)7/8	δ)7/8	X
ejpam-4772	66	3	(	(	PUNCT
ejpam-4772	66	4	4	4	NUM
ejpam-4772	66	5	√	√	NUM
ejpam-4772	66	6	2p2(1	2p2(1	NUM
ejpam-4772	66	7	+	+	CCONJ
ejpam-4772	67	1	δ)2	δ)2	PROPN
ejpam-4772	67	2	−	−	PROPN
ejpam-4772	67	3	p21	p21	NOUN
ejpam-4772	67	4	(	(	PUNCT
ejpam-4772	67	5	√	√	ADV
ejpam-4772	67	6	2	2	NUM
ejpam-4772	67	7	+	+	CCONJ
ejpam-4772	67	8	5	5	NUM
ejpam-4772	67	9	√	√	NUM
ejpam-4772	67	10	2)δ	2)δ	NOUN
ejpam-4772	67	11	+4	+4	PROPN
ejpam-4772	67	12	√	√	NUM
ejpam-4772	67	13	2δ2	2δ2	NUM
ejpam-4772	68	1	−	−	ADP
ejpam-4772	68	2	2(−2	2(−2	NUM
ejpam-4772	69	1	+	+	CCONJ
ejpam-4772	69	2	α+	α+	PUNCT
ejpam-4772	69	3	α2	α2	ADJ
ejpam-4772	69	4	√	√	PROPN
ejpam-4772	69	5	δ	δ	PROPN
ejpam-4772	69	6	√	√	ADV
ejpam-4772	69	7	1	1	NUM
ejpam-4772	69	8	+	+	NUM
ejpam-4772	69	9	δ	δ	NOUN
ejpam-4772	69	10	)	)	PUNCT
ejpam-4772	69	11	)	)	PUNCT
ejpam-4772	69	12	.	.	PUNCT
ejpam-4772	70	1	(	(	PUNCT
ejpam-4772	70	2	10	10	NUM
ejpam-4772	70	3	)	)	PUNCT
ejpam-4772	70	4	from	from	ADP
ejpam-4772	70	5	(	(	PUNCT
ejpam-4772	70	6	3	3	NUM
ejpam-4772	70	7	)	)	PUNCT
ejpam-4772	70	8	and	and	CCONJ
ejpam-4772	70	9	(	(	PUNCT
ejpam-4772	70	10	4	4	NUM
ejpam-4772	70	11	)	)	PUNCT
ejpam-4772	70	12	,	,	PUNCT
ejpam-4772	70	13	we	we	PRON
ejpam-4772	70	14	can	can	AUX
ejpam-4772	70	15	write	write	VERB
ejpam-4772	70	16	hankel	hankel	NOUN
ejpam-4772	70	17	determinant	determinant	ADJ
ejpam-4772	70	18	h2(1	h2(1	NOUN
ejpam-4772	70	19	)	)	PUNCT
ejpam-4772	70	20	gives	give	VERB
ejpam-4772	70	21	,	,	PUNCT
ejpam-4772	70	22	h2(1	h2(1	PROPN
ejpam-4772	70	23	)	)	PUNCT
ejpam-4772	70	24	=	=	SYM
ejpam-4772	70	25	∣∣∣∣a1	∣∣∣∣a1	NOUN
ejpam-4772	70	26	a2	a2	PROPN
ejpam-4772	70	27	a2	a2	PROPN
ejpam-4772	70	28	a3	a3	NOUN
ejpam-4772	71	1	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4772	71	2	=	=	PUNCT
ejpam-4772	71	3	|a1a3	|a1a3	PROPN
ejpam-4772	71	4	−	−	PROPN
ejpam-4772	71	5	a22|	a22|	NUM
ejpam-4772	71	6	=	=	SYM
ejpam-4772	72	1	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-4772	72	2	p2	p2	NOUN
ejpam-4772	72	3	√	√	NUM
ejpam-4772	72	4	δ√	δ√	SYM
ejpam-4772	72	5	2(2	2(2	NUM
ejpam-4772	72	6	+	+	NUM
ejpam-4772	72	7	α)(1	α)(1	NUM
ejpam-4772	73	1	+	+	CCONJ
ejpam-4772	73	2	δ)7/2	δ)7/2	PROPN
ejpam-4772	73	3	+	+	CCONJ
ejpam-4772	73	4	p21	p21	PROPN
ejpam-4772	73	5	√	√	NUM
ejpam-4772	73	6	δ	δ	PROPN
ejpam-4772	73	7	(	(	PUNCT
ejpam-4772	73	8	√	√	ADV
ejpam-4772	73	9	2	2	NUM
ejpam-4772	73	10	+	+	CCONJ
ejpam-4772	73	11	5	5	NUM
ejpam-4772	73	12	√	√	NUM
ejpam-4772	73	13	2δ	2δ	NUM
ejpam-4772	73	14	+	+	CCONJ
ejpam-4772	73	15	4	4	NUM
ejpam-4772	73	16	√	√	NUM
ejpam-4772	73	17	2δ2	2δ2	NUM
ejpam-4772	74	1	+	+	CCONJ
ejpam-4772	74	2	2(2	2(2	NUM
ejpam-4772	74	3	+	+	SYM
ejpam-4772	74	4	3α+	3α+	NUM
ejpam-4772	74	5	α2	α2	ADJ
ejpam-4772	74	6	)	)	PUNCT
ejpam-4772	75	1	√	√	PROPN
ejpam-4772	75	2	δ	δ	NOUN
ejpam-4772	75	3	√	√	ADV
ejpam-4772	75	4	1	1	NUM
ejpam-4772	75	5	+	+	NUM
ejpam-4772	75	6	δ	δ	PROPN
ejpam-4772	75	7	)	)	PUNCT
ejpam-4772	75	8	8(2	8(2	NUM
ejpam-4772	76	1	+	+	CCONJ
ejpam-4772	76	2	α)(1	α)(1	PRON
ejpam-4772	77	1	+	+	CCONJ
ejpam-4772	77	2	δ)3/2	δ)3/2	PROPN
ejpam-4772	77	3	∣∣∣∣∣.	∣∣∣∣∣.	PROPN
ejpam-4772	77	4	(	(	PUNCT
ejpam-4772	77	5	11	11	NUM
ejpam-4772	77	6	)	)	PUNCT
ejpam-4772	77	7	next	next	ADV
ejpam-4772	77	8	,	,	PUNCT
ejpam-4772	77	9	applying	apply	VERB
ejpam-4772	77	10	lemma	lemma	PROPN
ejpam-4772	77	11	(	(	PUNCT
ejpam-4772	77	12	2	2	NUM
ejpam-4772	77	13	)	)	PUNCT
ejpam-4772	77	14	to	to	ADP
ejpam-4772	77	15	(	(	PUNCT
ejpam-4772	77	16	11	11	NUM
ejpam-4772	77	17	)	)	PUNCT
ejpam-4772	77	18	,	,	PUNCT
ejpam-4772	77	19	gives	give	VERB
ejpam-4772	77	20	h2(1	h2(1	PRON
ejpam-4772	77	21	)	)	PUNCT
ejpam-4772	77	22	=	=	PUNCT
ejpam-4772	78	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-4772	78	2	(	(	PUNCT
ejpam-4772	78	3	p21	p21	NOUN
ejpam-4772	78	4	+	+	CCONJ
ejpam-4772	78	5	(	(	PUNCT
ejpam-4772	78	6	4−	4−	NUM
ejpam-4772	78	7	p21)x	p21)x	NOUN
ejpam-4772	78	8	)	)	PUNCT
ejpam-4772	78	9	√	√	NUM
ejpam-4772	78	10	δ√	δ√	NUM
ejpam-4772	78	11	2(2	2(2	NUM
ejpam-4772	78	12	+	+	NUM
ejpam-4772	78	13	α)(1	α)(1	NUM
ejpam-4772	79	1	+	+	CCONJ
ejpam-4772	79	2	δ)7/2	δ)7/2	PROPN
ejpam-4772	79	3	+	+	CCONJ
ejpam-4772	79	4	p21	p21	PROPN
ejpam-4772	79	5	√	√	NUM
ejpam-4772	79	6	δ	δ	PROPN
ejpam-4772	79	7	(	(	PUNCT
ejpam-4772	79	8	√	√	ADV
ejpam-4772	79	9	2	2	NUM
ejpam-4772	79	10	+	+	CCONJ
ejpam-4772	79	11	5	5	NUM
ejpam-4772	79	12	√	√	NUM
ejpam-4772	79	13	2δ	2δ	NUM
ejpam-4772	79	14	+	+	CCONJ
ejpam-4772	79	15	4	4	NUM
ejpam-4772	79	16	√	√	NUM
ejpam-4772	79	17	2δ2	2δ2	NUM
ejpam-4772	80	1	+	+	CCONJ
ejpam-4772	80	2	2(2	2(2	NUM
ejpam-4772	80	3	+	+	SYM
ejpam-4772	80	4	3α+	3α+	NUM
ejpam-4772	80	5	α2	α2	ADJ
ejpam-4772	80	6	)	)	PUNCT
ejpam-4772	81	1	√	√	PROPN
ejpam-4772	81	2	δ	δ	NOUN
ejpam-4772	81	3	√	√	ADV
ejpam-4772	81	4	1	1	NUM
ejpam-4772	81	5	+	+	NUM
ejpam-4772	81	6	δ	δ	PROPN
ejpam-4772	81	7	)	)	PUNCT
ejpam-4772	81	8	8(2	8(2	NUM
ejpam-4772	82	1	+	+	CCONJ
ejpam-4772	82	2	α)(1	α)(1	PRON
ejpam-4772	83	1	+	+	CCONJ
ejpam-4772	83	2	δ)3/2	δ)3/2	PROPN
ejpam-4772	83	3	∣∣∣∣∣.	∣∣∣∣∣.	PROPN
ejpam-4772	83	4	(	(	PUNCT
ejpam-4772	83	5	12	12	NUM
ejpam-4772	83	6	)	)	PUNCT
ejpam-4772	83	7	by	by	ADP
ejpam-4772	83	8	taing	tae	VERB
ejpam-4772	83	9	p1	p1	NOUN
ejpam-4772	83	10	=	=	PROPN
ejpam-4772	83	11	p	p	PROPN
ejpam-4772	83	12	and	and	CCONJ
ejpam-4772	83	13	0	0	NUM
ejpam-4772	83	14	≤	≤	NOUN
ejpam-4772	83	15	p	p	NOUN
ejpam-4772	83	16	≤	≤	NUM
ejpam-4772	83	17	2	2	NUM
ejpam-4772	83	18	and	and	CCONJ
ejpam-4772	83	19	applying	apply	VERB
ejpam-4772	83	20	them	they	PRON
ejpam-4772	83	21	to	to	ADP
ejpam-4772	83	22	(	(	PUNCT
ejpam-4772	83	23	12	12	NUM
ejpam-4772	83	24	)	)	PUNCT
ejpam-4772	83	25	it	it	PRON
ejpam-4772	83	26	follows	follow	VERB
ejpam-4772	83	27	that	that	SCONJ
ejpam-4772	83	28	,	,	PUNCT
ejpam-4772	83	29	h2(1	h2(1	PROPN
ejpam-4772	83	30	)	)	PUNCT
ejpam-4772	83	31	≤	≤	NOUN
ejpam-4772	83	32	(	(	PUNCT
ejpam-4772	83	33	p2	p2	PROPN
ejpam-4772	83	34	+	+	CCONJ
ejpam-4772	83	35	(	(	PUNCT
ejpam-4772	83	36	4−	4−	NOUN
ejpam-4772	83	37	p2)|x|	p2)|x|	NOUN
ejpam-4772	83	38	)	)	PUNCT
ejpam-4772	83	39	√	√	PROPN
ejpam-4772	84	1	δ	δ	NOUN
ejpam-4772	84	2	2	2	NUM
ejpam-4772	84	3	√	√	NUM
ejpam-4772	84	4	2(2	2(2	NUM
ejpam-4772	85	1	+	+	CCONJ
ejpam-4772	85	2	α)(1	α)(1	NUM
ejpam-4772	86	1	+	+	CCONJ
ejpam-4772	86	2	δ)3/2	δ)3/2	VERB
ejpam-4772	87	1	+	+	CCONJ
ejpam-4772	87	2	p2	p2	PROPN
ejpam-4772	87	3	√	√	NUM
ejpam-4772	87	4	δ	δ	PROPN
ejpam-4772	87	5	(	(	PUNCT
ejpam-4772	87	6	√	√	ADV
ejpam-4772	87	7	2	2	NUM
ejpam-4772	87	8	+	+	CCONJ
ejpam-4772	87	9	5	5	NUM
ejpam-4772	87	10	√	√	NUM
ejpam-4772	87	11	2δ	2δ	NUM
ejpam-4772	87	12	+	+	CCONJ
ejpam-4772	87	13	4	4	NUM
ejpam-4772	87	14	√	√	NUM
ejpam-4772	87	15	2δ2	2δ2	NUM
ejpam-4772	87	16	+	+	CCONJ
ejpam-4772	87	17	2(2	2(2	NUM
ejpam-4772	87	18	+	+	SYM
ejpam-4772	87	19	3α+	3α+	NUM
ejpam-4772	87	20	α2	α2	ADJ
ejpam-4772	87	21	)	)	PUNCT
ejpam-4772	87	22	√	√	PROPN
ejpam-4772	88	1	δ	δ	NOUN
ejpam-4772	88	2	√	√	ADV
ejpam-4772	88	3	1	1	NUM
ejpam-4772	88	4	+	+	NUM
ejpam-4772	88	5	δ	δ	PROPN
ejpam-4772	88	6	)	)	PUNCT
ejpam-4772	88	7	8(2	8(2	NUM
ejpam-4772	89	1	+	+	CCONJ
ejpam-4772	89	2	α)(1	α)(1	NUM
ejpam-4772	90	1	+	+	CCONJ
ejpam-4772	90	2	δ)3/2	δ)3/2	NUM
ejpam-4772	90	3	:	:	PUNCT
ejpam-4772	90	4	=	=	SYM
ejpam-4772	90	5	φ1(α	φ1(α	PROPN
ejpam-4772	90	6	,	,	PUNCT
ejpam-4772	90	7	δ	δ	PROPN
ejpam-4772	90	8	,	,	PUNCT
ejpam-4772	90	9	p	p	X
ejpam-4772	90	10	,	,	PUNCT
ejpam-4772	90	11	|x|	|x|	PROPN
ejpam-4772	90	12	)	)	PUNCT
ejpam-4772	90	13	(	(	PUNCT
ejpam-4772	90	14	13	13	NUM
ejpam-4772	90	15	)	)	PUNCT
ejpam-4772	90	16	from	from	ADP
ejpam-4772	90	17	(	(	PUNCT
ejpam-4772	90	18	13	13	NUM
ejpam-4772	90	19	)	)	PUNCT
ejpam-4772	90	20	then	then	ADV
ejpam-4772	90	21	taking	take	VERB
ejpam-4772	90	22	|x|	|x|	PROPN
ejpam-4772	90	23	≤	≤	ADJ
ejpam-4772	90	24	1	1	NUM
ejpam-4772	90	25	gives	give	NOUN
ejpam-4772	90	26	,	,	PUNCT
ejpam-4772	90	27	h2(1	h2(1	PROPN
ejpam-4772	90	28	)	)	PUNCT
ejpam-4772	90	29	≤	≤	NUM
ejpam-4772	90	30	p2	p2	X
ejpam-4772	90	31	+	+	CCONJ
ejpam-4772	91	1	(	(	PUNCT
ejpam-4772	91	2	4−	4−	NOUN
ejpam-4772	91	3	p2	p2	NOUN
ejpam-4772	91	4	)	)	PUNCT
ejpam-4772	91	5	√	√	ADP
ejpam-4772	91	6	δ	δ	NOUN
ejpam-4772	91	7	2	2	NUM
ejpam-4772	91	8	√	√	NUM
ejpam-4772	91	9	2(2	2(2	NUM
ejpam-4772	92	1	+	+	CCONJ
ejpam-4772	92	2	α)(1	α)(1	NUM
ejpam-4772	93	1	+	+	CCONJ
ejpam-4772	93	2	δ)3/2	δ)3/2	PROPN
ejpam-4772	94	1	+	+	CCONJ
ejpam-4772	94	2	p2	p2	X
ejpam-4772	94	3	(	(	PUNCT
ejpam-4772	94	4	√	√	PROPN
ejpam-4772	94	5	δ	δ	PROPN
ejpam-4772	94	6	(	(	PUNCT
ejpam-4772	94	7	√	√	ADV
ejpam-4772	94	8	2	2	NUM
ejpam-4772	94	9	+	+	CCONJ
ejpam-4772	94	10	5	5	NUM
ejpam-4772	94	11	√	√	NUM
ejpam-4772	94	12	2δ	2δ	NUM
ejpam-4772	94	13	+	+	CCONJ
ejpam-4772	94	14	4	4	NUM
ejpam-4772	94	15	√	√	NUM
ejpam-4772	94	16	2δ2	2δ2	NUM
ejpam-4772	94	17	+	+	CCONJ
ejpam-4772	94	18	2(2	2(2	NUM
ejpam-4772	94	19	+	+	SYM
ejpam-4772	94	20	3α+	3α+	NUM
ejpam-4772	94	21	α2	α2	ADJ
ejpam-4772	94	22	)	)	PUNCT
ejpam-4772	94	23	√	√	PROPN
ejpam-4772	94	24	δ	δ	NOUN
ejpam-4772	94	25	√	√	ADV
ejpam-4772	94	26	1	1	NUM
ejpam-4772	94	27	+	+	NUM
ejpam-4772	94	28	δ	δ	PROPN
ejpam-4772	94	29	)	)	PUNCT
ejpam-4772	94	30	8(2	8(2	PROPN
ejpam-4772	95	1	+	+	CCONJ
ejpam-4772	95	2	α)(1	α)(1	PRON
ejpam-4772	96	1	+	+	CCONJ
ejpam-4772	96	2	δ)7/2	δ)7/2	PROPN
ejpam-4772	96	3	n.m	n.m	PROPN
ejpam-4772	96	4	.	.	PROPN
ejpam-4772	96	5	asih	asih	PROPN
ejpam-4772	96	6	et	et	PROPN
ejpam-4772	96	7	al	al	PROPN
ejpam-4772	96	8	.	.	PUNCT
ejpam-4772	96	9	/	/	SYM
ejpam-4772	96	10	eur	eur	PROPN
ejpam-4772	96	11	.	.	PUNCT
ejpam-4772	97	1	j.	j.	PROPN
ejpam-4772	97	2	pure	pure	PROPN
ejpam-4772	97	3	appl	appl	PROPN
ejpam-4772	97	4	.	.	PROPN
ejpam-4772	97	5	math	math	PROPN
ejpam-4772	97	6	,	,	PUNCT
ejpam-4772	97	7	16	16	NUM
ejpam-4772	97	8	(	(	PUNCT
ejpam-4772	97	9	2	2	NUM
ejpam-4772	97	10	)	)	PUNCT
ejpam-4772	97	11	(	(	PUNCT
ejpam-4772	97	12	2023	2023	NUM
ejpam-4772	97	13	)	)	PUNCT
ejpam-4772	97	14	,	,	PUNCT
ejpam-4772	97	15	1290	1290	NUM
ejpam-4772	97	16	-	-	SYM
ejpam-4772	97	17	1301	1301	NUM
ejpam-4772	97	18	1294	1294	NUM
ejpam-4772	97	19	=	=	SYM
ejpam-4772	97	20	√	√	NUM
ejpam-4772	97	21	δ(8	δ(8	NOUN
ejpam-4772	97	22	√	√	PROPN
ejpam-4772	97	23	2(1	2(1	NUM
ejpam-4772	97	24	+	+	CCONJ
ejpam-4772	97	25	δ)2	δ)2	PROPN
ejpam-4772	97	26	8(2	8(2	NUM
ejpam-4772	98	1	+	+	CCONJ
ejpam-4772	98	2	α)(1	α)(1	NUM
ejpam-4772	99	1	+	+	CCONJ
ejpam-4772	99	2	δ)3/2	δ)3/2	VERB
ejpam-4772	100	1	+	+	CCONJ
ejpam-4772	100	2	p2	p2	PROPN
ejpam-4772	100	3	√	√	NUM
ejpam-4772	100	4	δ	δ	PROPN
ejpam-4772	100	5	(	(	PUNCT
ejpam-4772	100	6	√	√	ADV
ejpam-4772	100	7	2	2	NUM
ejpam-4772	100	8	+	+	CCONJ
ejpam-4772	100	9	5	5	NUM
ejpam-4772	100	10	√	√	NUM
ejpam-4772	100	11	2δ	2δ	NUM
ejpam-4772	100	12	+	+	CCONJ
ejpam-4772	100	13	4	4	NUM
ejpam-4772	100	14	√	√	NUM
ejpam-4772	100	15	2δ2	2δ2	NUM
ejpam-4772	100	16	+	+	CCONJ
ejpam-4772	100	17	2(2	2(2	NUM
ejpam-4772	100	18	+	+	SYM
ejpam-4772	100	19	3α+	3α+	NUM
ejpam-4772	100	20	α2	α2	ADJ
ejpam-4772	100	21	)	)	PUNCT
ejpam-4772	100	22	√	√	PROPN
ejpam-4772	101	1	δ	δ	NOUN
ejpam-4772	101	2	√	√	ADV
ejpam-4772	101	3	1	1	NUM
ejpam-4772	101	4	+	+	NUM
ejpam-4772	101	5	δ	δ	PROPN
ejpam-4772	101	6	)	)	PUNCT
ejpam-4772	101	7	8(2	8(2	PROPN
ejpam-4772	102	1	+	+	CCONJ
ejpam-4772	102	2	α)(1	α)(1	PRON
ejpam-4772	103	1	+	+	CCONJ
ejpam-4772	103	2	δ)7/2	δ)7/2	PROPN
ejpam-4772	103	3	:	:	PUNCT
ejpam-4772	103	4	=	=	SYM
ejpam-4772	103	5	φ1(α	φ1(α	PROPN
ejpam-4772	103	6	,	,	PUNCT
ejpam-4772	103	7	δ	δ	PROPN
ejpam-4772	103	8	,	,	PUNCT
ejpam-4772	103	9	p	p	NOUN
ejpam-4772	103	10	)	)	PUNCT
ejpam-4772	103	11	(	(	PUNCT
ejpam-4772	103	12	14	14	NUM
ejpam-4772	103	13	)	)	PUNCT
ejpam-4772	103	14	next	next	ADV
ejpam-4772	103	15	,	,	PUNCT
ejpam-4772	103	16	we	we	PRON
ejpam-4772	103	17	determine	determine	VERB
ejpam-4772	103	18	the	the	DET
ejpam-4772	103	19	derivative	derivative	NOUN
ejpam-4772	103	20	of	of	ADP
ejpam-4772	103	21	φ(α	φ(α	PROPN
ejpam-4772	103	22	,	,	PUNCT
ejpam-4772	103	23	δ	δ	PROPN
ejpam-4772	103	24	,	,	PUNCT
ejpam-4772	103	25	p	p	NOUN
ejpam-4772	103	26	)	)	PUNCT
ejpam-4772	103	27	with	with	ADP
ejpam-4772	103	28	respect	respect	NOUN
ejpam-4772	103	29	to	to	ADP
ejpam-4772	103	30	p	p	NOUN
ejpam-4772	103	31	from	from	ADP
ejpam-4772	103	32	(	(	PUNCT
ejpam-4772	103	33	14)are	14)are	NUM
ejpam-4772	103	34	we	we	PRON
ejpam-4772	103	35	obtain	obtain	VERB
ejpam-4772	103	36	,	,	PUNCT
ejpam-4772	103	37	φ	φ	PROPN
ejpam-4772	103	38	′	′	NUM
ejpam-4772	103	39	1(α	1(α	NUM
ejpam-4772	103	40	,	,	PUNCT
ejpam-4772	103	41	δ	δ	PROPN
ejpam-4772	103	42	,	,	PUNCT
ejpam-4772	103	43	p	p	NOUN
ejpam-4772	103	44	)	)	PUNCT
ejpam-4772	103	45	=	=	SYM
ejpam-4772	103	46	2p	2p	NUM
ejpam-4772	103	47	√	√	NUM
ejpam-4772	103	48	δ	δ	PROPN
ejpam-4772	103	49	(	(	PUNCT
ejpam-4772	103	50	√	√	ADV
ejpam-4772	103	51	2	2	NUM
ejpam-4772	103	52	+	+	CCONJ
ejpam-4772	103	53	5	5	NUM
ejpam-4772	103	54	√	√	NUM
ejpam-4772	103	55	2δ	2δ	NUM
ejpam-4772	103	56	+	+	CCONJ
ejpam-4772	103	57	4	4	NUM
ejpam-4772	103	58	√	√	NUM
ejpam-4772	103	59	2δ2	2δ2	NUM
ejpam-4772	104	1	+	+	CCONJ
ejpam-4772	104	2	2(2	2(2	NUM
ejpam-4772	104	3	+	+	SYM
ejpam-4772	104	4	3α+	3α+	NUM
ejpam-4772	104	5	α2	α2	ADJ
ejpam-4772	104	6	)	)	PUNCT
ejpam-4772	105	1	√	√	PROPN
ejpam-4772	105	2	δ	δ	NOUN
ejpam-4772	105	3	√	√	ADV
ejpam-4772	105	4	1	1	NUM
ejpam-4772	105	5	+	+	NUM
ejpam-4772	105	6	δ	δ	PROPN
ejpam-4772	105	7	)	)	PUNCT
ejpam-4772	105	8	8(2	8(2	PROPN
ejpam-4772	106	1	+	+	CCONJ
ejpam-4772	106	2	α)(1	α)(1	PRON
ejpam-4772	107	1	+	+	CCONJ
ejpam-4772	107	2	δ)7/2	δ)7/2	PROPN
ejpam-4772	107	3	.	.	PUNCT
ejpam-4772	108	1	(	(	PUNCT
ejpam-4772	108	2	15	15	X
ejpam-4772	108	3	)	)	PUNCT
ejpam-4772	108	4	let	let	VERB
ejpam-4772	108	5	the	the	DET
ejpam-4772	108	6	derivative	derivative	NOUN
ejpam-4772	108	7	of	of	ADP
ejpam-4772	108	8	φ1(α	φ1(α	PROPN
ejpam-4772	108	9	,	,	PUNCT
ejpam-4772	108	10	δ	δ	PROPN
ejpam-4772	108	11	,	,	PUNCT
ejpam-4772	108	12	p	p	NOUN
ejpam-4772	108	13	)	)	PUNCT
ejpam-4772	108	14	with	with	ADP
ejpam-4772	108	15	respect	respect	NOUN
ejpam-4772	108	16	to	to	ADP
ejpam-4772	108	17	p	p	NOUN
ejpam-4772	108	18	is	be	AUX
ejpam-4772	108	19	φ	φ	NUM
ejpam-4772	108	20	′	′	NUM
ejpam-4772	108	21	1(α	1(α	NUM
ejpam-4772	108	22	,	,	PUNCT
ejpam-4772	108	23	δ	δ	PROPN
ejpam-4772	108	24	,	,	PUNCT
ejpam-4772	108	25	p	p	NOUN
ejpam-4772	108	26	)	)	PUNCT
ejpam-4772	108	27	.	.	PUNCT
ejpam-4772	109	1	then	then	ADV
ejpam-4772	109	2	,	,	PUNCT
ejpam-4772	109	3	from	from	ADP
ejpam-4772	109	4	(	(	PUNCT
ejpam-4772	109	5	15	15	NUM
ejpam-4772	109	6	)	)	PUNCT
ejpam-4772	109	7	,	,	PUNCT
ejpam-4772	109	8	we	we	PRON
ejpam-4772	109	9	can	can	AUX
ejpam-4772	109	10	show	show	VERB
ejpam-4772	109	11	that	that	SCONJ
ejpam-4772	109	12	φ	φ	PROPN
ejpam-4772	109	13	′	′	NUM
ejpam-4772	109	14	1	1	NUM
ejpam-4772	109	15	>	>	X
ejpam-4772	109	16	0	0	PUNCT
ejpam-4772	109	17	for	for	ADP
ejpam-4772	109	18	0	0	NUM
ejpam-4772	109	19	≤	≤	NOUN
ejpam-4772	109	20	p	p	NOUN
ejpam-4772	109	21	≤	≤	NUM
ejpam-4772	109	22	2	2	NUM
ejpam-4772	109	23	.	.	PUNCT
ejpam-4772	110	1	hence	hence	ADV
ejpam-4772	110	2	,	,	PUNCT
ejpam-4772	110	3	φ1	φ1	PROPN
ejpam-4772	110	4	is	be	AUX
ejpam-4772	110	5	an	an	DET
ejpam-4772	110	6	increasing	increase	VERB
ejpam-4772	110	7	monoton	monoton	NOUN
ejpam-4772	110	8	function	function	NOUN
ejpam-4772	110	9	.	.	PUNCT
ejpam-4772	111	1	from	from	ADP
ejpam-4772	111	2	which	which	PRON
ejpam-4772	111	3	we	we	PRON
ejpam-4772	111	4	obtain	obtain	VERB
ejpam-4772	111	5	h2(1	h2(1	NOUN
ejpam-4772	111	6	)	)	PUNCT
ejpam-4772	111	7	≤	≤	NOUN
ejpam-4772	111	8	φ1(α	φ1(α	PROPN
ejpam-4772	111	9	,	,	PUNCT
ejpam-4772	111	10	δ	δ	PROPN
ejpam-4772	111	11	,	,	PUNCT
ejpam-4772	111	12	2	2	NUM
ejpam-4772	111	13	)	)	PUNCT
ejpam-4772	111	14	=	=	SYM
ejpam-4772	112	1	3	3	NUM
ejpam-4772	112	2	√	√	NUM
ejpam-4772	112	3	2	2	NUM
ejpam-4772	112	4	√	√	PROPN
ejpam-4772	112	5	δ	δ	PROPN
ejpam-4772	112	6	+	+	CCONJ
ejpam-4772	112	7	2(1	2(1	NUM
ejpam-4772	112	8	+	+	CCONJ
ejpam-4772	112	9	α)(2	α)(2	NUM
ejpam-4772	112	10	+	+	NOUN
ejpam-4772	112	11	α)δ	α)δ	NOUN
ejpam-4772	112	12	√	√	VERB
ejpam-4772	112	13	1	1	NUM
ejpam-4772	112	14	+	+	NUM
ejpam-4772	112	15	δ	δ	PROPN
ejpam-4772	112	16	+	+	CCONJ
ejpam-4772	112	17	3	3	NUM
ejpam-4772	112	18	√	√	NUM
ejpam-4772	112	19	2δ3/2((3	2δ3/2((3	NUM
ejpam-4772	113	1	+	+	NUM
ejpam-4772	113	2	2α	2α	NOUN
ejpam-4772	113	3	)	)	PUNCT
ejpam-4772	113	4	)	)	PUNCT
ejpam-4772	114	1	2(2	2(2	NUM
ejpam-4772	115	1	+	+	CCONJ
ejpam-4772	115	2	α)(1	α)(1	NUM
ejpam-4772	116	1	+	+	CCONJ
ejpam-4772	116	2	δ)7/2	δ)7/2	PROPN
ejpam-4772	116	3	.	.	PUNCT
ejpam-4772	117	1	the	the	DET
ejpam-4772	117	2	inequality	inequality	NOUN
ejpam-4772	117	3	is	be	AUX
ejpam-4772	117	4	sharp	sharp	ADJ
ejpam-4772	118	1	when	when	SCONJ
ejpam-4772	118	2	p1	p1	PROPN
ejpam-4772	118	3	=	=	NOUN
ejpam-4772	118	4	p2	p2	PROPN
ejpam-4772	118	5	=	=	SYM
ejpam-4772	118	6	2	2	X
ejpam-4772	118	7	.	.	PUNCT
ejpam-4772	119	1	the	the	DET
ejpam-4772	119	2	proof	proof	NOUN
ejpam-4772	119	3	is	be	AUX
ejpam-4772	119	4	completed	complete	VERB
ejpam-4772	119	5	.	.	PUNCT
ejpam-4772	120	1	theorem	theorem	NOUN
ejpam-4772	120	2	2	2	NUM
ejpam-4772	120	3	.	.	PUNCT
ejpam-4772	121	1	if	if	SCONJ
ejpam-4772	121	2	f	f	PROPN
ejpam-4772	121	3	∈	∈	PROPN
ejpam-4772	121	4	b1(α	b1(α	PROPN
ejpam-4772	121	5	,	,	PUNCT
ejpam-4772	121	6	δ	δ	PROPN
ejpam-4772	121	7	)	)	PUNCT
ejpam-4772	121	8	for	for	ADP
ejpam-4772	121	9	α1	α1	PROPN
ejpam-4772	121	10	≤	≤	NUM
ejpam-4772	121	11	α	α	NOUN
ejpam-4772	121	12	≤	≤	NOUN
ejpam-4772	121	13	1	1	NUM
ejpam-4772	121	14	and	and	CCONJ
ejpam-4772	121	15	0	0	NUM
ejpam-4772	121	16	<	<	X
ejpam-4772	121	17	δ	δ	PROPN
ejpam-4772	121	18	≤	≤	ADV
ejpam-4772	121	19	1	1	NUM
ejpam-4772	121	20	then	then	ADV
ejpam-4772	121	21	h2(2	h2(2	PROPN
ejpam-4772	121	22	)	)	PUNCT
ejpam-4772	121	23	≤	≤	NOUN
ejpam-4772	121	24	(	(	PUNCT
ejpam-4772	121	25	δ(1	δ(1	PROPN
ejpam-4772	121	26	+	+	CCONJ
ejpam-4772	121	27	δ)3/2	δ)3/2	PROPN
ejpam-4772	121	28	)	)	PUNCT
ejpam-4772	121	29	6(2	6(2	NUM
ejpam-4772	122	1	+	+	CCONJ
ejpam-4772	122	2	α)2(1	α)2(1	NOUN
ejpam-4772	122	3	+	+	CCONJ
ejpam-4772	122	4	δ)8	δ)8	NOUN
ejpam-4772	122	5	)	)	PUNCT
ejpam-4772	123	1	[	[	PUNCT
ejpam-4772	123	2	(	(	PUNCT
ejpam-4772	123	3	6	6	NUM
ejpam-4772	123	4	√	√	NUM
ejpam-4772	123	5	2(−1	2(−1	NUM
ejpam-4772	123	6	+	+	CCONJ
ejpam-4772	123	7	δ)(2	δ)(2	NUM
ejpam-4772	123	8	+	+	NUM
ejpam-4772	123	9	α)2	α)2	NOUN
ejpam-4772	123	10	√	√	NOUN
ejpam-4772	123	11	δ	δ	PROPN
ejpam-4772	123	12	+	+	PROPN
ejpam-4772	123	13	30	30	NUM
ejpam-4772	123	14	√	√	NUM
ejpam-4772	123	15	2(−1	2(−1	NUM
ejpam-4772	123	16	+	+	CCONJ
ejpam-4772	123	17	α	α	X
ejpam-4772	123	18	)	)	PUNCT
ejpam-4772	123	19	(	(	PUNCT
ejpam-4772	123	20	2	2	NUM
ejpam-4772	123	21	+	+	NUM
ejpam-4772	123	22	α)2δ3/2	α)2δ3/2	ADJ
ejpam-4772	123	23	+	+	CCONJ
ejpam-4772	123	24	24	24	NUM
ejpam-4772	123	25	√	√	NUM
ejpam-4772	123	26	2(−1	2(−1	NUM
ejpam-4772	123	27	+	+	CCONJ
ejpam-4772	123	28	α)(2	α)(2	NUM
ejpam-4772	123	29	+	+	CCONJ
ejpam-4772	123	30	α)2δ5/2	α)2δ5/2	ADJ
ejpam-4772	123	31	+	+	NOUN
ejpam-4772	123	32	3(7	3(7	NUM
ejpam-4772	123	33	+	+	NUM
ejpam-4772	123	34	8α+	8α+	NUM
ejpam-4772	123	35	2α2)√	2α2)√	NUM
ejpam-4772	123	36	1	1	NUM
ejpam-4772	123	37	+	+	CCONJ
ejpam-4772	123	38	δ	δ	X
ejpam-4772	124	1	+	+	CCONJ
ejpam-4772	124	2	(	(	PUNCT
ejpam-4772	124	3	117	117	NUM
ejpam-4772	124	4	+	+	NUM
ejpam-4772	124	5	64α−	64α−	NUM
ejpam-4772	124	6	20α2	20α2	NUM
ejpam-4772	125	1	+	+	NUM
ejpam-4772	126	1	36α3	36α3	NUM
ejpam-4772	126	2	+	+	NUM
ejpam-4772	126	3	38α4	38α4	NUM
ejpam-4772	126	4	+	+	CCONJ
ejpam-4772	126	5	8α5)δ	8α5)δ	NUM
ejpam-4772	126	6	√	√	NUM
ejpam-4772	126	7	1	1	NUM
ejpam-4772	126	8	+	+	NUM
ejpam-4772	126	9	δ	δ	NOUN
ejpam-4772	126	10	+72(3	+72(3	PUNCT
ejpam-4772	127	1	+	+	CCONJ
ejpam-4772	127	2	4α+	4α+	NUM
ejpam-4772	127	3	α2)δ2	α2)δ2	NOUN
ejpam-4772	127	4	√	√	NOUN
ejpam-4772	127	5	1	1	NUM
ejpam-4772	127	6	+	+	CCONJ
ejpam-4772	127	7	δ	δ	PROPN
ejpam-4772	127	8	+	+	CCONJ
ejpam-4772	127	9	48(3	48(3	NOUN
ejpam-4772	128	1	+	+	CCONJ
ejpam-4772	128	2	4α+	4α+	NUM
ejpam-4772	128	3	α2)δ3	α2)δ3	NOUN
ejpam-4772	128	4	√	√	NOUN
ejpam-4772	128	5	1	1	NUM
ejpam-4772	128	6	+	+	NUM
ejpam-4772	128	7	δ	δ	NOUN
ejpam-4772	128	8	)	)	PUNCT
ejpam-4772	128	9	−12(1	−12(1	ADP
ejpam-4772	128	10	+	+	ADJ
ejpam-4772	128	11	5α+	5α+	NUM
ejpam-4772	128	12	10α2	10α2	NUM
ejpam-4772	128	13	+	+	NUM
ejpam-4772	128	14	10α3	10α3	NUM
ejpam-4772	129	1	+	+	CCONJ
ejpam-4772	129	2	5α4)−	5α4)−	PROPN
ejpam-4772	129	3	(	(	PUNCT
ejpam-4772	129	4	2	2	NUM
ejpam-4772	129	5	+	+	SYM
ejpam-4772	129	6	α)2(1	α)2(1	NOUN
ejpam-4772	129	7	+	+	CCONJ
ejpam-4772	129	8	δ)5	δ)5	X
ejpam-4772	129	9	]	]	PUNCT
ejpam-4772	129	10	,	,	PUNCT
ejpam-4772	129	11	with	with	ADP
ejpam-4772	129	12	α1	α1	PROPN
ejpam-4772	129	13	=	=	SYM
ejpam-4772	129	14	0	0	NUM
ejpam-4772	129	15	,	,	PUNCT
ejpam-4772	129	16	205	205	NUM
ejpam-4772	129	17	is	be	AUX
ejpam-4772	129	18	real	real	ADJ
ejpam-4772	129	19	root	root	NOUN
ejpam-4772	129	20	of	of	ADP
ejpam-4772	129	21	the	the	DET
ejpam-4772	129	22	equation	equation	NOUN
ejpam-4772	129	23	x3	x3	VERB
ejpam-4772	130	1	+	+	CCONJ
ejpam-4772	130	2	4x2	4x2	NUM
ejpam-4772	131	1	+	+	CCONJ
ejpam-4772	131	2	4x−	4x−	NOUN
ejpam-4772	131	3	1	1	NUM
ejpam-4772	131	4	=	=	SYM
ejpam-4772	131	5	0	0	NUM
ejpam-4772	131	6	,	,	PUNCT
ejpam-4772	131	7	and	and	CCONJ
ejpam-4772	131	8	the	the	DET
ejpam-4772	131	9	inequality	inequality	NOUN
ejpam-4772	131	10	is	be	AUX
ejpam-4772	131	11	sharp	sharp	ADJ
ejpam-4772	131	12	.	.	PUNCT
ejpam-4772	132	1	proof	proof	NOUN
ejpam-4772	132	2	.	.	PUNCT
ejpam-4772	133	1	based	base	VERB
ejpam-4772	133	2	on	on	ADP
ejpam-4772	133	3	equation	equation	NOUN
ejpam-4772	133	4	(	(	PUNCT
ejpam-4772	133	5	3	3	NUM
ejpam-4772	133	6	)	)	PUNCT
ejpam-4772	133	7	,	,	PUNCT
ejpam-4772	133	8	we	we	PRON
ejpam-4772	133	9	have	have	VERB
ejpam-4772	133	10	initial	initial	ADJ
ejpam-4772	133	11	coefficients	coefficient	NOUN
ejpam-4772	133	12	a2	a2	PROPN
ejpam-4772	133	13	,	,	PUNCT
ejpam-4772	133	14	and	and	CCONJ
ejpam-4772	133	15	a3	a3	VERB
ejpam-4772	133	16	in	in	ADP
ejpam-4772	133	17	equation	equation	NOUN
ejpam-4772	133	18	(	(	PUNCT
ejpam-4772	133	19	9	9	NUM
ejpam-4772	133	20	)	)	PUNCT
ejpam-4772	133	21	and	and	CCONJ
ejpam-4772	133	22	(	(	PUNCT
ejpam-4772	133	23	10	10	NUM
ejpam-4772	133	24	)	)	PUNCT
ejpam-4772	133	25	respectively	respectively	ADV
ejpam-4772	133	26	while	while	SCONJ
ejpam-4772	133	27	a4	a4	NOUN
ejpam-4772	133	28	is	be	AUX
ejpam-4772	133	29	,	,	PUNCT
ejpam-4772	133	30	a4	a4	NOUN
ejpam-4772	133	31	=	=	SYM
ejpam-4772	133	32	(	(	PUNCT
ejpam-4772	133	33	1	1	NUM
ejpam-4772	133	34	48(2	48(2	NUM
ejpam-4772	133	35	+	+	CCONJ
ejpam-4772	133	36	α)(1	α)(1	X
ejpam-4772	134	1	+	+	CCONJ
ejpam-4772	134	2	α)9/2	α)9/2	PUNCT
ejpam-4772	134	3	)	)	PUNCT
ejpam-4772	135	1	[	[	X
ejpam-4772	135	2	√	√	ADV
ejpam-4772	135	3	α(24	α(24	ADP
ejpam-4772	135	4	√	√	NUM
ejpam-4772	135	5	2p3(2	2p3(2	NUM
ejpam-4772	136	1	+	+	CCONJ
ejpam-4772	136	2	α)(1	α)(1	X
ejpam-4772	136	3	+	+	CCONJ
ejpam-4772	136	4	δ)3	δ)3	NOUN
ejpam-4772	137	1	−	−	PROPN
ejpam-4772	137	2	12p1p2(1	12p1p2(1	NUM
ejpam-4772	137	3	+	+	NUM
ejpam-4772	137	4	δ	δ	PROPN
ejpam-4772	137	5	)	)	PUNCT
ejpam-4772	137	6	(	(	PUNCT
ejpam-4772	137	7	2α2	2α2	NUM
ejpam-4772	137	8	√	√	ADV
ejpam-4772	137	9	δ	δ	PROPN
ejpam-4772	137	10	√	√	ADV
ejpam-4772	137	11	1	1	NUM
ejpam-4772	137	12	+	+	CCONJ
ejpam-4772	137	13	δ	δ	PROPN
ejpam-4772	137	14	+	+	CCONJ
ejpam-4772	137	15	2	2	NUM
ejpam-4772	137	16	(	(	PUNCT
ejpam-4772	137	17	√	√	NUM
ejpam-4772	137	18	2	2	NUM
ejpam-4772	137	19	+	+	CCONJ
ejpam-4772	137	20	5	5	NUM
ejpam-4772	137	21	√	√	NUM
ejpam-4772	137	22	2δ	2δ	NUM
ejpam-4772	137	23	+	+	CCONJ
ejpam-4772	137	24	4	4	NUM
ejpam-4772	137	25	√	√	NOUN
ejpam-4772	137	26	2δ2	2δ2	NUM
ejpam-4772	137	27	−	−	PROPN
ejpam-4772	137	28	3	3	NUM
ejpam-4772	137	29	√	√	NUM
ejpam-4772	137	30	δ	δ	PROPN
ejpam-4772	137	31	√	√	ADV
ejpam-4772	137	32	1	1	NUM
ejpam-4772	137	33	+	+	NUM
ejpam-4772	137	34	δ	δ	NOUN
ejpam-4772	137	35	)	)	PUNCT
ejpam-4772	138	1	+	+	CCONJ
ejpam-4772	138	2	α	α	PROPN
ejpam-4772	138	3	(	(	PUNCT
ejpam-4772	138	4	√	√	ADV
ejpam-4772	138	5	2	2	NUM
ejpam-4772	138	6	+	+	CCONJ
ejpam-4772	138	7	5	5	NUM
ejpam-4772	138	8	√	√	NUM
ejpam-4772	138	9	2δ	2δ	NUM
ejpam-4772	138	10	+4	+4	NUM
ejpam-4772	138	11	√	√	NUM
ejpam-4772	138	12	2δ2	2δ2	NUM
ejpam-4772	138	13	−	−	PROPN
ejpam-4772	138	14	4	4	NUM
ejpam-4772	138	15	√	√	NUM
ejpam-4772	138	16	δ	δ	NOUN
ejpam-4772	138	17	√	√	ADV
ejpam-4772	138	18	1	1	NUM
ejpam-4772	138	19	+	+	NUM
ejpam-4772	138	20	δ	δ	NOUN
ejpam-4772	138	21	)	)	PUNCT
ejpam-4772	138	22	)	)	PUNCT
ejpam-4772	139	1	+	+	PUNCT
ejpam-4772	139	2	p31(14	p31(14	NOUN
ejpam-4772	139	3	√	√	NOUN
ejpam-4772	139	4	2α3δ	2α3δ	NUM
ejpam-4772	139	5	+	+	CCONJ
ejpam-4772	139	6	4	4	NUM
ejpam-4772	139	7	√	√	NOUN
ejpam-4772	139	8	2α4δ	2α4δ	ADJ
ejpam-4772	140	1	+	+	CCONJ
ejpam-4772	140	2	6	6	NUM
ejpam-4772	140	3	(	(	PUNCT
ejpam-4772	140	4	√	√	NUM
ejpam-4772	140	5	2	2	NUM
ejpam-4772	140	6	+	+	CCONJ
ejpam-4772	140	7	7	7	NUM
ejpam-4772	140	8	√	√	NUM
ejpam-4772	140	9	2δ	2δ	NUM
ejpam-4772	141	1	n.m	n.m	PROPN
ejpam-4772	141	2	.	.	PROPN
ejpam-4772	141	3	asih	asih	PROPN
ejpam-4772	141	4	et	et	PROPN
ejpam-4772	141	5	al	al	PROPN
ejpam-4772	141	6	.	.	PUNCT
ejpam-4772	141	7	/	/	SYM
ejpam-4772	141	8	eur	eur	PROPN
ejpam-4772	141	9	.	.	PUNCT
ejpam-4772	142	1	j.	j.	PROPN
ejpam-4772	142	2	pure	pure	PROPN
ejpam-4772	142	3	appl	appl	PROPN
ejpam-4772	142	4	.	.	PROPN
ejpam-4772	142	5	math	math	PROPN
ejpam-4772	142	6	,	,	PUNCT
ejpam-4772	142	7	16	16	NUM
ejpam-4772	142	8	(	(	PUNCT
ejpam-4772	142	9	2	2	NUM
ejpam-4772	142	10	)	)	PUNCT
ejpam-4772	142	11	(	(	PUNCT
ejpam-4772	142	12	2023	2023	NUM
ejpam-4772	142	13	)	)	PUNCT
ejpam-4772	142	14	,	,	PUNCT
ejpam-4772	142	15	1290	1290	NUM
ejpam-4772	142	16	-	-	SYM
ejpam-4772	142	17	1301	1301	NUM
ejpam-4772	142	18	1295	1295	NUM
ejpam-4772	142	19	+12	+12	NOUN
ejpam-4772	142	20	√	√	NUM
ejpam-4772	142	21	2δ2	2δ2	NUM
ejpam-4772	142	22	+	+	CCONJ
ejpam-4772	142	23	8	8	NUM
ejpam-4772	142	24	√	√	NUM
ejpam-4772	142	25	2δ3	2δ3	NUM
ejpam-4772	142	26	−	−	NUM
ejpam-4772	142	27	3	3	NUM
ejpam-4772	142	28	√	√	NUM
ejpam-4772	142	29	δ	δ	PROPN
ejpam-4772	142	30	√	√	ADV
ejpam-4772	142	31	1	1	NUM
ejpam-4772	142	32	+	+	NUM
ejpam-4772	142	33	δ	δ	PROPN
ejpam-4772	143	1	−	−	PROPN
ejpam-4772	143	2	12δ3/2	12δ3/2	NUM
ejpam-4772	143	3	√	√	ADV
ejpam-4772	143	4	1	1	NUM
ejpam-4772	143	5	+	+	NUM
ejpam-4772	143	6	δ	δ	PROPN
ejpam-4772	143	7	)	)	PUNCT
ejpam-4772	144	1	+	+	NUM
ejpam-4772	144	2	δ2(−4	δ2(−4	NOUN
ejpam-4772	144	3	√	√	ADP
ejpam-4772	144	4	2δ	2δ	NUM
ejpam-4772	144	5	+6	+6	PROPN
ejpam-4772	144	6	√	√	NUM
ejpam-4772	144	7	δ	δ	PROPN
ejpam-4772	144	8	√	√	ADV
ejpam-4772	144	9	1	1	NUM
ejpam-4772	144	10	+	+	CCONJ
ejpam-4772	144	11	δ	δ	X
ejpam-4772	145	1	+	+	CCONJ
ejpam-4772	146	1	24δ3/2	24δ3/2	NUM
ejpam-4772	146	2	√	√	ADP
ejpam-4772	146	3	1	1	NUM
ejpam-4772	146	4	+	+	NUM
ejpam-4772	146	5	δ	δ	NOUN
ejpam-4772	146	6	)	)	PUNCT
ejpam-4772	147	1	+	+	CCONJ
ejpam-4772	147	2	α(3	α(3	PROPN
ejpam-4772	147	3	√	√	PROPN
ejpam-4772	147	4	2−	2−	NUM
ejpam-4772	147	5	11	11	NUM
ejpam-4772	147	6	√	√	PROPN
ejpam-4772	147	7	2δ	2δ	NUM
ejpam-4772	147	8	+	+	CCONJ
ejpam-4772	147	9	36	36	NUM
ejpam-4772	147	10	√	√	NUM
ejpam-4772	147	11	2δ2	2δ2	NUM
ejpam-4772	147	12	+24	+24	ADJ
ejpam-4772	147	13	√	√	PROPN
ejpam-4772	147	14	2δ3	2δ3	NUM
ejpam-4772	147	15	+	+	CCONJ
ejpam-4772	147	16	12δ	12δ	NOUN
ejpam-4772	147	17	√	√	ADV
ejpam-4772	147	18	1	1	NUM
ejpam-4772	147	19	+	+	CCONJ
ejpam-4772	147	20	δ	δ	PROPN
ejpam-4772	147	21	+	+	CCONJ
ejpam-4772	147	22	48δ3/2	48δ3/2	NUM
ejpam-4772	147	23	√	√	NUM
ejpam-4772	147	24	1	1	NUM
ejpam-4772	147	25	+	+	NUM
ejpam-4772	147	26	δ	δ	PROPN
ejpam-4772	147	27	)	)	PUNCT
ejpam-4772	147	28	)	)	PUNCT
ejpam-4772	147	29	)	)	PUNCT
ejpam-4772	147	30	]	]	PUNCT
ejpam-4772	147	31	.	.	PUNCT
ejpam-4772	148	1	(	(	PUNCT
ejpam-4772	148	2	16	16	NUM
ejpam-4772	148	3	)	)	PUNCT
ejpam-4772	148	4	we	we	PRON
ejpam-4772	148	5	can	can	AUX
ejpam-4772	148	6	write	write	VERB
ejpam-4772	148	7	hankel	hankel	NOUN
ejpam-4772	148	8	determinant	determinant	ADJ
ejpam-4772	148	9	h2(2	h2(2	PROPN
ejpam-4772	148	10	)	)	PUNCT
ejpam-4772	148	11	as	as	ADP
ejpam-4772	148	12	,	,	PUNCT
ejpam-4772	148	13	h2(2	h2(2	PROPN
ejpam-4772	148	14	)	)	PUNCT
ejpam-4772	148	15	=	=	SYM
ejpam-4772	148	16	∣∣∣∣a2	∣∣∣∣a2	PROPN
ejpam-4772	148	17	a3	a3	NOUN
ejpam-4772	148	18	a3	a3	PROPN
ejpam-4772	148	19	a4	a4	PROPN
ejpam-4772	148	20	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4772	148	21	=	=	PUNCT
ejpam-4772	148	22	|a2a4	|a2a4	NOUN
ejpam-4772	148	23	−	−	PROPN
ejpam-4772	148	24	a23|	a23|	X
ejpam-4772	148	25	=	=	SYM
ejpam-4772	148	26	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-4772	148	27	(	(	PUNCT
ejpam-4772	148	28	p1p3δ	p1p3δ	NUM
ejpam-4772	148	29	2(1	2(1	NUM
ejpam-4772	148	30	+	+	NUM
ejpam-4772	148	31	δ)3	δ)3	NOUN
ejpam-4772	148	32	)	)	PUNCT
ejpam-4772	148	33	−	−	PROPN
ejpam-4772	149	1	(	(	PUNCT
ejpam-4772	149	2	p22δ(1	p22δ(1	NOUN
ejpam-4772	149	3	+	+	NOUN
ejpam-4772	149	4	5α+	5α+	NUM
ejpam-4772	149	5	10α2	10α2	NUM
ejpam-4772	149	6	+	+	CCONJ
ejpam-4772	149	7	16α3	16α3	NUM
ejpam-4772	149	8	+	+	NUM
ejpam-4772	149	9	5α4	5α4	NUM
ejpam-4772	149	10	)	)	PUNCT
ejpam-4772	149	11	2(2	2(2	NUM
ejpam-4772	150	1	+	+	CCONJ
ejpam-4772	150	2	α)2(1	α)2(1	NOUN
ejpam-4772	150	3	+	+	CCONJ
ejpam-4772	150	4	δ)8	δ)8	PROPN
ejpam-4772	150	5	)	)	PUNCT
ejpam-4772	151	1	+	+	CCONJ
ejpam-4772	151	2	(	(	PUNCT
ejpam-4772	151	3	p41δ	p41δ	NOUN
ejpam-4772	151	4	96(2	96(2	X
ejpam-4772	151	5	+	+	CCONJ
ejpam-4772	151	6	α)2(1	α)2(1	NOUN
ejpam-4772	151	7	+	+	CCONJ
ejpam-4772	151	8	δ)13/2	δ)13/2	X
ejpam-4772	151	9	)	)	PUNCT
ejpam-4772	151	10	[	[	PUNCT
ejpam-4772	151	11	(	(	PUNCT
ejpam-4772	151	12	6	6	NUM
ejpam-4772	151	13	√	√	NUM
ejpam-4772	151	14	2(−1	2(−1	NUM
ejpam-4772	151	15	+	+	CCONJ
ejpam-4772	151	16	δ)(2	δ)(2	NUM
ejpam-4772	151	17	+	+	NUM
ejpam-4772	151	18	α)2	α)2	NOUN
ejpam-4772	151	19	√	√	NOUN
ejpam-4772	151	20	δ	δ	PROPN
ejpam-4772	151	21	+	+	CCONJ
ejpam-4772	151	22	30	30	NUM
ejpam-4772	151	23	√	√	NUM
ejpam-4772	151	24	2	2	NUM
ejpam-4772	151	25	(	(	PUNCT
ejpam-4772	151	26	−1	−1	NOUN
ejpam-4772	151	27	+	+	CCONJ
ejpam-4772	151	28	α)(2	α)(2	NUM
ejpam-4772	151	29	+	+	CCONJ
ejpam-4772	151	30	α)2δ3/2	α)2δ3/2	PROPN
ejpam-4772	151	31	+	+	CCONJ
ejpam-4772	151	32	24	24	NUM
ejpam-4772	151	33	√	√	NUM
ejpam-4772	151	34	2(−1	2(−1	NUM
ejpam-4772	151	35	+	+	CCONJ
ejpam-4772	151	36	α)(2	α)(2	NUM
ejpam-4772	151	37	+	+	CCONJ
ejpam-4772	152	1	α)2δ5/2	α)2δ5/2	ADJ
ejpam-4772	153	1	+	+	NOUN
ejpam-4772	153	2	3(7	3(7	NUM
ejpam-4772	153	3	+	+	NUM
ejpam-4772	153	4	8α+	8α+	NUM
ejpam-4772	153	5	2α2)√	2α2)√	NUM
ejpam-4772	153	6	1	1	NUM
ejpam-4772	153	7	+	+	CCONJ
ejpam-4772	153	8	δ	δ	X
ejpam-4772	154	1	+	+	CCONJ
ejpam-4772	154	2	(	(	PUNCT
ejpam-4772	154	3	117	117	NUM
ejpam-4772	154	4	+	+	NUM
ejpam-4772	154	5	64α−	64α−	NUM
ejpam-4772	154	6	20α2	20α2	NUM
ejpam-4772	155	1	+	+	NUM
ejpam-4772	156	1	36α3	36α3	NUM
ejpam-4772	156	2	+	+	NUM
ejpam-4772	156	3	38α4	38α4	NUM
ejpam-4772	156	4	+	+	CCONJ
ejpam-4772	156	5	8α5)δ	8α5)δ	NUM
ejpam-4772	156	6	√	√	NUM
ejpam-4772	156	7	1	1	NUM
ejpam-4772	156	8	+	+	NUM
ejpam-4772	156	9	δ	δ	NOUN
ejpam-4772	156	10	+72(3	+72(3	PUNCT
ejpam-4772	157	1	+	+	CCONJ
ejpam-4772	157	2	4α+	4α+	NUM
ejpam-4772	157	3	α2)δ2	α2)δ2	NOUN
ejpam-4772	157	4	√	√	NOUN
ejpam-4772	157	5	1	1	NUM
ejpam-4772	157	6	+	+	CCONJ
ejpam-4772	157	7	δ	δ	PROPN
ejpam-4772	157	8	+	+	CCONJ
ejpam-4772	157	9	48(3	48(3	NOUN
ejpam-4772	158	1	+	+	CCONJ
ejpam-4772	158	2	4α+	4α+	NUM
ejpam-4772	158	3	α2)δ3	α2)δ3	NOUN
ejpam-4772	158	4	√	√	NOUN
ejpam-4772	158	5	1	1	NUM
ejpam-4772	158	6	+	+	CCONJ
ejpam-4772	158	7	δ	δ	PROPN
ejpam-4772	158	8	)	)	PUNCT
ejpam-4772	158	9	]	]	PUNCT
ejpam-4772	159	1	−	−	PROPN
ejpam-4772	159	2	(	(	PUNCT
ejpam-4772	159	3	p2δ	p2δ	PROPN
ejpam-4772	159	4	4(2	4(2	PROPN
ejpam-4772	160	1	+	+	CCONJ
ejpam-4772	160	2	α)2(1	α)2(1	NOUN
ejpam-4772	160	3	+	+	CCONJ
ejpam-4772	160	4	δ)17/2	δ)17/2	NOUN
ejpam-4772	160	5	)	)	PUNCT
ejpam-4772	160	6	[	[	PUNCT
ejpam-4772	160	7	(	(	PUNCT
ejpam-4772	160	8	2p2δ	2p2δ	NUM
ejpam-4772	160	9	5	5	NUM
ejpam-4772	160	10	√	√	NUM
ejpam-4772	160	11	1	1	NUM
ejpam-4772	160	12	+	+	CCONJ
ejpam-4772	160	13	δ	δ	PROPN
ejpam-4772	160	14	+	+	CCONJ
ejpam-4772	160	15	p21	p21	NOUN
ejpam-4772	160	16	√	√	NOUN
ejpam-4772	160	17	2(−1	2(−1	NUM
ejpam-4772	160	18	+	+	CCONJ
ejpam-4772	160	19	α)(2	α)(2	NUM
ejpam-4772	160	20	+	+	ADJ
ejpam-4772	160	21	α)2	α)2	NOUN
ejpam-4772	160	22	√	√	NOUN
ejpam-4772	160	23	δ(1	δ(1	NOUN
ejpam-4772	160	24	+	+	CCONJ
ejpam-4772	160	25	δ)4	δ)4	NOUN
ejpam-4772	160	26	+	+	CCONJ
ejpam-4772	160	27	(	(	PUNCT
ejpam-4772	160	28	3	3	NUM
ejpam-4772	160	29	+	+	SYM
ejpam-4772	160	30	4α+	4α+	NUM
ejpam-4772	160	31	α2)(1	α2)(1	NOUN
ejpam-4772	160	32	+	+	CCONJ
ejpam-4772	160	33	δ)9/2	δ)9/2	PROPN
ejpam-4772	161	1	+	+	CCONJ
ejpam-4772	161	2	4(3	4(3	NUM
ejpam-4772	161	3	+	+	CCONJ
ejpam-4772	161	4	4α+	4α+	NUM
ejpam-4772	161	5	α2)(1	α2)(1	NOUN
ejpam-4772	161	6	+	+	CCONJ
ejpam-4772	161	7	δ)9/2	δ)9/2	PROPN
ejpam-4772	161	8	)	)	PUNCT
ejpam-4772	161	9	]	]	PUNCT
ejpam-4772	161	10	∣∣∣∣∣.	∣∣∣∣∣.	X
ejpam-4772	161	11	(	(	PUNCT
ejpam-4772	161	12	17	17	NUM
ejpam-4772	161	13	)	)	PUNCT
ejpam-4772	161	14	applying	apply	VERB
ejpam-4772	161	15	(	(	PUNCT
ejpam-4772	161	16	17	17	NUM
ejpam-4772	161	17	)	)	PUNCT
ejpam-4772	161	18	,	,	PUNCT
ejpam-4772	161	19	lemma	lemma	PROPN
ejpam-4772	161	20	2	2	NUM
ejpam-4772	161	21	and	and	CCONJ
ejpam-4772	161	22	taking	take	VERB
ejpam-4772	161	23	p1	p1	NOUN
ejpam-4772	161	24	=	=	PUNCT
ejpam-4772	161	25	p	p	NOUN
ejpam-4772	161	26	so	so	ADV
ejpam-4772	161	27	that	that	SCONJ
ejpam-4772	161	28	0	0	NUM
ejpam-4772	161	29	≤	≤	X
ejpam-4772	161	30	p	p	NOUN
ejpam-4772	161	31	≤	≤	ADJ
ejpam-4772	161	32	2	2	NUM
ejpam-4772	161	33	gives	give	NOUN
ejpam-4772	161	34	,	,	PUNCT
ejpam-4772	161	35	h2(2	h2(2	PROPN
ejpam-4772	161	36	)	)	PUNCT
ejpam-4772	161	37	=	=	PUNCT
ejpam-4772	162	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-4772	162	2	δ(4−	δ(4−	X
ejpam-4772	162	3	p2)x2	p2)x2	NOUN
ejpam-4772	162	4	8(2	8(2	NUM
ejpam-4772	163	1	+	+	CCONJ
ejpam-4772	163	2	α)2(1	α)2(1	NOUN
ejpam-4772	163	3	+	+	NUM
ejpam-4772	163	4	δ)3	δ)3	NOUN
ejpam-4772	163	5	+	+	CCONJ
ejpam-4772	163	6	2pδ(4−	2pδ(4−	NUM
ejpam-4772	163	7	p2)(1−	p2)(1−	PROPN
ejpam-4772	163	8	x2)ρ	x2)ρ	NOUN
ejpam-4772	163	9	8(1	8(1	NOUN
ejpam-4772	163	10	+	+	CCONJ
ejpam-4772	163	11	δ)3	δ)3	NOUN
ejpam-4772	163	12	+	+	CCONJ
ejpam-4772	163	13	(	(	PUNCT
ejpam-4772	163	14	3	3	NUM
ejpam-4772	163	15	+	+	SYM
ejpam-4772	163	16	4α+	4α+	NUM
ejpam-4772	163	17	α2	α2	ADJ
ejpam-4772	163	18	+	+	CCONJ
ejpam-4772	163	19	(	(	PUNCT
ejpam-4772	163	20	p2	p2	PROPN
ejpam-4772	163	21	8(2	8(2	PROPN
ejpam-4772	164	1	+	+	CCONJ
ejpam-4772	164	2	α)2(1	α)2(1	NOUN
ejpam-4772	164	3	+	+	CCONJ
ejpam-4772	164	4	δ)17/2	δ)17/2	NOUN
ejpam-4772	164	5	)	)	PUNCT
ejpam-4772	164	6	[	[	PUNCT
ejpam-4772	164	7	(	(	PUNCT
ejpam-4772	164	8	4−	4−	NUM
ejpam-4772	164	9	p2)x	p2)x	NOUN
ejpam-4772	164	10	(	(	PUNCT
ejpam-4772	164	11	√	√	NUM
ejpam-4772	164	12	2(−1	2(−1	NUM
ejpam-4772	165	1	+	+	CCONJ
ejpam-4772	165	2	α)(2	α)(2	NUM
ejpam-4772	165	3	+	+	CCONJ
ejpam-4772	165	4	α)2	α)2	NOUN
ejpam-4772	165	5	√	√	NUM
ejpam-4772	165	6	δ	δ	PROPN
ejpam-4772	165	7	)	)	PUNCT
ejpam-4772	165	8	√	√	ADV
ejpam-4772	165	9	1	1	NUM
ejpam-4772	165	10	+	+	CCONJ
ejpam-4772	165	11	δ	δ	PROPN
ejpam-4772	165	12	+	+	CCONJ
ejpam-4772	165	13	2(3	2(3	NUM
ejpam-4772	165	14	+	+	CCONJ
ejpam-4772	165	15	4α+	4α+	NUM
ejpam-4772	165	16	α2)δ	α2)δ	NOUN
ejpam-4772	165	17	√	√	NUM
ejpam-4772	165	18	1	1	NUM
ejpam-4772	165	19	+	+	NUM
ejpam-4772	165	20	δ	δ	PROPN
ejpam-4772	165	21	−	−	PROPN
ejpam-4772	165	22	2(3	2(3	NUM
ejpam-4772	165	23	+	+	CCONJ
ejpam-4772	165	24	4α+	4α+	NUM
ejpam-4772	165	25	α2)δ2	α2)δ2	NOUN
ejpam-4772	165	26	√	√	NOUN
ejpam-4772	165	27	1	1	NUM
ejpam-4772	165	28	+	+	NUM
ejpam-4772	165	29	δ	δ	NOUN
ejpam-4772	165	30	)	)	PUNCT
ejpam-4772	165	31	]	]	PUNCT
ejpam-4772	166	1	+	+	CCONJ
ejpam-4772	166	2	(	(	PUNCT
ejpam-4772	166	3	p4δ	p4δ	NOUN
ejpam-4772	166	4	96(2	96(2	NOUN
ejpam-4772	166	5	+	+	CCONJ
ejpam-4772	166	6	α)2(1	α)2(1	NOUN
ejpam-4772	166	7	+	+	CCONJ
ejpam-4772	166	8	δ)13/2	δ)13/2	X
ejpam-4772	166	9	)	)	PUNCT
ejpam-4772	166	10	[	[	PUNCT
ejpam-4772	166	11	(	(	PUNCT
ejpam-4772	166	12	6	6	NUM
ejpam-4772	166	13	√	√	NUM
ejpam-4772	166	14	2(−1	2(−1	NUM
ejpam-4772	166	15	+	+	CCONJ
ejpam-4772	166	16	δ)(2	δ)(2	NUM
ejpam-4772	166	17	+	+	NUM
ejpam-4772	166	18	α)2	α)2	NOUN
ejpam-4772	166	19	√	√	NOUN
ejpam-4772	166	20	δ	δ	PROPN
ejpam-4772	166	21	+	+	PROPN
ejpam-4772	166	22	30	30	NUM
ejpam-4772	166	23	√	√	NUM
ejpam-4772	166	24	2(−1	2(−1	NUM
ejpam-4772	166	25	+	+	CCONJ
ejpam-4772	166	26	α	α	X
ejpam-4772	166	27	)	)	PUNCT
ejpam-4772	166	28	(	(	PUNCT
ejpam-4772	166	29	2	2	NUM
ejpam-4772	166	30	+	+	NUM
ejpam-4772	166	31	α)2δ3/2	α)2δ3/2	ADJ
ejpam-4772	166	32	+	+	CCONJ
ejpam-4772	166	33	24	24	NUM
ejpam-4772	166	34	√	√	NUM
ejpam-4772	166	35	2(−1	2(−1	NUM
ejpam-4772	166	36	+	+	CCONJ
ejpam-4772	166	37	α)(2	α)(2	NUM
ejpam-4772	166	38	+	+	CCONJ
ejpam-4772	167	1	α)2δ5/2	α)2δ5/2	ADJ
ejpam-4772	168	1	+	+	NOUN
ejpam-4772	168	2	3(7	3(7	NUM
ejpam-4772	168	3	+	+	NUM
ejpam-4772	168	4	8α+	8α+	NUM
ejpam-4772	168	5	2α2)√	2α2)√	NUM
ejpam-4772	168	6	1	1	NUM
ejpam-4772	168	7	+	+	CCONJ
ejpam-4772	168	8	δ	δ	X
ejpam-4772	169	1	+	+	CCONJ
ejpam-4772	169	2	(	(	PUNCT
ejpam-4772	169	3	117	117	NUM
ejpam-4772	169	4	+	+	NUM
ejpam-4772	169	5	64α−	64α−	NUM
ejpam-4772	169	6	20α2	20α2	NUM
ejpam-4772	170	1	+	+	NUM
ejpam-4772	171	1	36α3	36α3	NUM
ejpam-4772	171	2	+	+	NUM
ejpam-4772	171	3	38α4	38α4	NUM
ejpam-4772	171	4	+	+	CCONJ
ejpam-4772	171	5	8α5)δ	8α5)δ	NUM
ejpam-4772	171	6	√	√	NUM
ejpam-4772	171	7	1	1	NUM
ejpam-4772	171	8	+	+	NUM
ejpam-4772	171	9	δ	δ	NOUN
ejpam-4772	171	10	+72(3	+72(3	PUNCT
ejpam-4772	172	1	+	+	CCONJ
ejpam-4772	172	2	4α+	4α+	NUM
ejpam-4772	172	3	α2)δ2	α2)δ2	NOUN
ejpam-4772	172	4	√	√	NOUN
ejpam-4772	172	5	1	1	NUM
ejpam-4772	172	6	+	+	CCONJ
ejpam-4772	172	7	δ	δ	PROPN
ejpam-4772	172	8	+	+	CCONJ
ejpam-4772	172	9	48(3	48(3	NOUN
ejpam-4772	173	1	+	+	CCONJ
ejpam-4772	173	2	4α+	4α+	NUM
ejpam-4772	173	3	α2)δ3	α2)δ3	NOUN
ejpam-4772	173	4	√	√	NOUN
ejpam-4772	173	5	1	1	NUM
ejpam-4772	173	6	+	+	CCONJ
ejpam-4772	173	7	δ	δ	PROPN
ejpam-4772	173	8	)	)	PUNCT
ejpam-4772	173	9	n.m	n.m	PROPN
ejpam-4772	173	10	.	.	PROPN
ejpam-4772	173	11	asih	asih	PROPN
ejpam-4772	173	12	et	et	PROPN
ejpam-4772	173	13	al	al	PROPN
ejpam-4772	173	14	.	.	PUNCT
ejpam-4772	173	15	/	/	SYM
ejpam-4772	173	16	eur	eur	PROPN
ejpam-4772	173	17	.	.	PUNCT
ejpam-4772	174	1	j.	j.	PROPN
ejpam-4772	174	2	pure	pure	PROPN
ejpam-4772	174	3	appl	appl	PROPN
ejpam-4772	174	4	.	.	PROPN
ejpam-4772	174	5	math	math	PROPN
ejpam-4772	174	6	,	,	PUNCT
ejpam-4772	174	7	16	16	NUM
ejpam-4772	174	8	(	(	PUNCT
ejpam-4772	174	9	2	2	NUM
ejpam-4772	174	10	)	)	PUNCT
ejpam-4772	174	11	(	(	PUNCT
ejpam-4772	174	12	2023	2023	NUM
ejpam-4772	174	13	)	)	PUNCT
ejpam-4772	174	14	,	,	PUNCT
ejpam-4772	174	15	1290	1290	NUM
ejpam-4772	174	16	-	-	SYM
ejpam-4772	174	17	1301	1301	NUM
ejpam-4772	174	18	1296	1296	NUM
ejpam-4772	174	19	−12(1	−12(1	ADP
ejpam-4772	174	20	+	+	X
ejpam-4772	174	21	5α+	5α+	NUM
ejpam-4772	174	22	10α2	10α2	NUM
ejpam-4772	174	23	+	+	NUM
ejpam-4772	174	24	10α3	10α3	NUM
ejpam-4772	175	1	+	+	CCONJ
ejpam-4772	175	2	5α4)−	5α4)−	PROPN
ejpam-4772	175	3	(	(	PUNCT
ejpam-4772	175	4	2	2	NUM
ejpam-4772	175	5	+	+	SYM
ejpam-4772	175	6	α)2(1	α)2(1	NOUN
ejpam-4772	175	7	+	+	CCONJ
ejpam-4772	175	8	δ)5	δ)5	X
ejpam-4772	175	9	]	]	PUNCT
ejpam-4772	175	10	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-4772	175	11	:	:	PUNCT
ejpam-4772	175	12	=	=	SYM
ejpam-4772	175	13	φ1(α	φ1(α	PROPN
ejpam-4772	175	14	,	,	PUNCT
ejpam-4772	175	15	δ	δ	PROPN
ejpam-4772	175	16	,	,	PUNCT
ejpam-4772	175	17	p	p	X
ejpam-4772	175	18	,	,	PUNCT
ejpam-4772	175	19	x	x	PROPN
ejpam-4772	175	20	,	,	PUNCT
ejpam-4772	175	21	ρ	ρ	PROPN
ejpam-4772	175	22	)	)	PUNCT
ejpam-4772	175	23	.	.	PUNCT
ejpam-4772	176	1	(	(	PUNCT
ejpam-4772	176	2	18	18	NUM
ejpam-4772	176	3	)	)	PUNCT
ejpam-4772	176	4	from	from	ADP
ejpam-4772	176	5	(	(	PUNCT
ejpam-4772	176	6	18	18	NUM
ejpam-4772	176	7	)	)	PUNCT
ejpam-4772	176	8	,	,	PUNCT
ejpam-4772	176	9	then	then	ADV
ejpam-4772	176	10	for	for	ADP
ejpam-4772	176	11	some	some	DET
ejpam-4772	176	12	|ρ|	|ρ|	NOUN
ejpam-4772	176	13	≤	≤	NUM
ejpam-4772	176	14	1	1	NUM
ejpam-4772	176	15	gives	give	VERB
ejpam-4772	176	16	h2(2	h2(2	PROPN
ejpam-4772	176	17	)	)	PUNCT
ejpam-4772	176	18	≤	≤	PUNCT
ejpam-4772	177	1	δ(4−	δ(4−	PUNCT
ejpam-4772	178	1	p2)|x|2	p2)|x|2	PROPN
ejpam-4772	178	2	8(2	8(2	PROPN
ejpam-4772	179	1	+	+	CCONJ
ejpam-4772	179	2	α)2(1	α)2(1	NOUN
ejpam-4772	179	3	+	+	NUM
ejpam-4772	179	4	δ)3	δ)3	NOUN
ejpam-4772	179	5	+	+	CCONJ
ejpam-4772	179	6	2pδ(4−	2pδ(4−	NUM
ejpam-4772	179	7	p2)(1−	p2)(1−	PROPN
ejpam-4772	179	8	|x|2	|x|2	PROPN
ejpam-4772	179	9	)	)	PUNCT
ejpam-4772	179	10	8(1	8(1	NOUN
ejpam-4772	179	11	+	+	CCONJ
ejpam-4772	179	12	δ)3	δ)3	NOUN
ejpam-4772	179	13	+	+	CCONJ
ejpam-4772	179	14	(	(	PUNCT
ejpam-4772	179	15	p2	p2	PROPN
ejpam-4772	179	16	8(2	8(2	PROPN
ejpam-4772	180	1	+	+	CCONJ
ejpam-4772	180	2	α)2(1	α)2(1	NOUN
ejpam-4772	180	3	+	+	CCONJ
ejpam-4772	180	4	δ)17/2	δ)17/2	NOUN
ejpam-4772	180	5	)	)	PUNCT
ejpam-4772	180	6	[	[	PUNCT
ejpam-4772	180	7	(	(	PUNCT
ejpam-4772	180	8	4−	4−	NOUN
ejpam-4772	180	9	p2)|x|	p2)|x|	X
ejpam-4772	180	10	(	(	PUNCT
ejpam-4772	180	11	√	√	NOUN
ejpam-4772	180	12	2(−1	2(−1	NUM
ejpam-4772	180	13	+	+	CCONJ
ejpam-4772	180	14	α)(2	α)(2	NUM
ejpam-4772	180	15	+	+	ADJ
ejpam-4772	180	16	α)2	α)2	NOUN
ejpam-4772	180	17	√	√	NOUN
ejpam-4772	180	18	δ	δ	PROPN
ejpam-4772	180	19	+	+	PROPN
ejpam-4772	180	20	(	(	PUNCT
ejpam-4772	180	21	3	3	NUM
ejpam-4772	180	22	+	+	CCONJ
ejpam-4772	180	23	4α+	4α+	NUM
ejpam-4772	180	24	α2	α2	ADJ
ejpam-4772	180	25	)	)	PUNCT
ejpam-4772	180	26	√	√	ADP
ejpam-4772	180	27	1	1	NUM
ejpam-4772	181	1	+	+	CCONJ
ejpam-4772	181	2	δ	δ	PROPN
ejpam-4772	181	3	+	+	CCONJ
ejpam-4772	181	4	2(3	2(3	NUM
ejpam-4772	181	5	+	+	CCONJ
ejpam-4772	181	6	4α+	4α+	NUM
ejpam-4772	181	7	α2)δ	α2)δ	NOUN
ejpam-4772	181	8	√	√	NUM
ejpam-4772	181	9	1	1	NUM
ejpam-4772	181	10	+	+	CCONJ
ejpam-4772	181	11	δ	δ	NOUN
ejpam-4772	181	12	−2(3	−2(3	NOUN
ejpam-4772	181	13	+	+	CCONJ
ejpam-4772	181	14	4α+	4α+	NUM
ejpam-4772	181	15	α2)δ2	α2)δ2	NOUN
ejpam-4772	181	16	√	√	NOUN
ejpam-4772	181	17	1	1	NUM
ejpam-4772	181	18	+	+	NUM
ejpam-4772	181	19	δ	δ	NOUN
ejpam-4772	181	20	)	)	PUNCT
ejpam-4772	181	21	]	]	PUNCT
ejpam-4772	182	1	+	+	CCONJ
ejpam-4772	182	2	(	(	PUNCT
ejpam-4772	182	3	p4δ	p4δ	NOUN
ejpam-4772	182	4	96(2	96(2	NOUN
ejpam-4772	182	5	+	+	CCONJ
ejpam-4772	182	6	α)2(1	α)2(1	NOUN
ejpam-4772	182	7	+	+	CCONJ
ejpam-4772	182	8	δ)8	δ)8	NOUN
ejpam-4772	182	9	)	)	PUNCT
ejpam-4772	182	10	[	[	PUNCT
ejpam-4772	182	11	(	(	PUNCT
ejpam-4772	182	12	6	6	NUM
ejpam-4772	182	13	√	√	NUM
ejpam-4772	182	14	2(−1	2(−1	NUM
ejpam-4772	182	15	+	+	CCONJ
ejpam-4772	182	16	δ)(2	δ)(2	NUM
ejpam-4772	182	17	+	+	NUM
ejpam-4772	182	18	α)2	α)2	NOUN
ejpam-4772	182	19	√	√	NOUN
ejpam-4772	182	20	δ	δ	PROPN
ejpam-4772	182	21	+	+	PROPN
ejpam-4772	182	22	30	30	NUM
ejpam-4772	182	23	√	√	NUM
ejpam-4772	182	24	2(−1	2(−1	NUM
ejpam-4772	182	25	+	+	CCONJ
ejpam-4772	182	26	α	α	X
ejpam-4772	182	27	)	)	PUNCT
ejpam-4772	182	28	(	(	PUNCT
ejpam-4772	182	29	2	2	NUM
ejpam-4772	182	30	+	+	NUM
ejpam-4772	182	31	α)2δ3/2	α)2δ3/2	ADJ
ejpam-4772	182	32	+	+	CCONJ
ejpam-4772	182	33	24	24	NUM
ejpam-4772	182	34	√	√	NUM
ejpam-4772	182	35	2(−1	2(−1	NUM
ejpam-4772	182	36	+	+	CCONJ
ejpam-4772	182	37	α)(2	α)(2	NUM
ejpam-4772	182	38	+	+	CCONJ
ejpam-4772	183	1	α)2δ5/2	α)2δ5/2	ADJ
ejpam-4772	184	1	+	+	NOUN
ejpam-4772	184	2	3(7	3(7	NUM
ejpam-4772	184	3	+	+	NUM
ejpam-4772	184	4	8α+	8α+	NUM
ejpam-4772	184	5	2α2)√	2α2)√	NUM
ejpam-4772	184	6	1	1	NUM
ejpam-4772	184	7	+	+	CCONJ
ejpam-4772	184	8	δ	δ	X
ejpam-4772	185	1	+	+	CCONJ
ejpam-4772	185	2	(	(	PUNCT
ejpam-4772	185	3	117	117	NUM
ejpam-4772	185	4	+	+	NUM
ejpam-4772	185	5	64α−	64α−	NUM
ejpam-4772	185	6	20α2	20α2	NUM
ejpam-4772	186	1	+	+	NUM
ejpam-4772	187	1	36α3	36α3	NUM
ejpam-4772	187	2	+	+	NUM
ejpam-4772	187	3	38α4	38α4	NUM
ejpam-4772	187	4	+	+	CCONJ
ejpam-4772	187	5	8α5)δ	8α5)δ	NUM
ejpam-4772	187	6	√	√	NUM
ejpam-4772	187	7	1	1	NUM
ejpam-4772	187	8	+	+	NUM
ejpam-4772	187	9	δ	δ	NOUN
ejpam-4772	187	10	+72(3	+72(3	PUNCT
ejpam-4772	188	1	+	+	CCONJ
ejpam-4772	188	2	4α+	4α+	NUM
ejpam-4772	188	3	α2)δ2	α2)δ2	NOUN
ejpam-4772	188	4	√	√	NOUN
ejpam-4772	188	5	1	1	NUM
ejpam-4772	188	6	+	+	CCONJ
ejpam-4772	188	7	δ	δ	PROPN
ejpam-4772	188	8	+	+	CCONJ
ejpam-4772	188	9	48(3	48(3	NOUN
ejpam-4772	189	1	+	+	CCONJ
ejpam-4772	189	2	4α+	4α+	NUM
ejpam-4772	189	3	α2)δ3	α2)δ3	NOUN
ejpam-4772	189	4	√	√	NOUN
ejpam-4772	189	5	1	1	NUM
ejpam-4772	189	6	+	+	NUM
ejpam-4772	189	7	δ	δ	NOUN
ejpam-4772	189	8	)	)	PUNCT
ejpam-4772	189	9	−12(1	−12(1	ADP
ejpam-4772	189	10	+	+	ADJ
ejpam-4772	189	11	5α+	5α+	NUM
ejpam-4772	189	12	10α2	10α2	NUM
ejpam-4772	189	13	+	+	NUM
ejpam-4772	189	14	10α3	10α3	NUM
ejpam-4772	190	1	+	+	CCONJ
ejpam-4772	190	2	5α4)−	5α4)−	PROPN
ejpam-4772	190	3	(	(	PUNCT
ejpam-4772	190	4	2	2	NUM
ejpam-4772	190	5	+	+	SYM
ejpam-4772	190	6	α)2(1	α)2(1	NOUN
ejpam-4772	190	7	+	+	CCONJ
ejpam-4772	190	8	δ)5	δ)5	X
ejpam-4772	190	9	]	]	PUNCT
ejpam-4772	190	10	:	:	PUNCT
ejpam-4772	190	11	=	=	SYM
ejpam-4772	190	12	φ1(α	φ1(α	PROPN
ejpam-4772	190	13	,	,	PUNCT
ejpam-4772	190	14	δ	δ	PROPN
ejpam-4772	190	15	,	,	PUNCT
ejpam-4772	190	16	p	p	X
ejpam-4772	190	17	,	,	PUNCT
ejpam-4772	190	18	|x|	|x|	PROPN
ejpam-4772	190	19	)	)	PUNCT
ejpam-4772	190	20	.	.	PUNCT
ejpam-4772	191	1	(	(	PUNCT
ejpam-4772	191	2	19	19	NUM
ejpam-4772	191	3	)	)	PUNCT
ejpam-4772	191	4	now	now	ADV
ejpam-4772	191	5	we	we	PRON
ejpam-4772	191	6	check	check	VERB
ejpam-4772	191	7	the	the	DET
ejpam-4772	191	8	derivative	derivative	NOUN
ejpam-4772	191	9	of	of	ADP
ejpam-4772	191	10	φ1(α	φ1(α	PROPN
ejpam-4772	191	11	,	,	PUNCT
ejpam-4772	191	12	δ	δ	PROPN
ejpam-4772	191	13	,	,	PUNCT
ejpam-4772	191	14	p	p	X
ejpam-4772	191	15	,	,	PUNCT
ejpam-4772	191	16	|x|	|x|	PROPN
ejpam-4772	191	17	)	)	PUNCT
ejpam-4772	191	18	with	with	ADP
ejpam-4772	191	19	respect	respect	NOUN
ejpam-4772	191	20	to	to	ADP
ejpam-4772	191	21	|x|	|x|	PROPN
ejpam-4772	191	22	from	from	ADP
ejpam-4772	191	23	(	(	PUNCT
ejpam-4772	191	24	18	18	NUM
ejpam-4772	191	25	)	)	PUNCT
ejpam-4772	191	26	,	,	PUNCT
ejpam-4772	191	27	φ	φ	PROPN
ejpam-4772	191	28	′	′	NUM
ejpam-4772	191	29	1(α	1(α	NUM
ejpam-4772	191	30	,	,	PUNCT
ejpam-4772	191	31	δ	δ	PROPN
ejpam-4772	191	32	,	,	PUNCT
ejpam-4772	191	33	p	p	X
ejpam-4772	191	34	,	,	PUNCT
ejpam-4772	191	35	|x|	|x|	PROPN
ejpam-4772	191	36	)	)	PUNCT
ejpam-4772	191	37	=	=	PUNCT
ejpam-4772	192	1	δ(4−	δ(4−	X
ejpam-4772	192	2	p2)2|x|	p2)2|x|	NOUN
ejpam-4772	192	3	4(2	4(2	NUM
ejpam-4772	193	1	+	+	CCONJ
ejpam-4772	193	2	α)2(1	α)2(1	NOUN
ejpam-4772	193	3	+	+	NUM
ejpam-4772	193	4	δ)3	δ)3	NOUN
ejpam-4772	193	5	−	−	PROPN
ejpam-4772	193	6	pδ(4−	pδ(4−	PROPN
ejpam-4772	193	7	p2)|x|	p2)|x|	NUM
ejpam-4772	193	8	2(1	2(1	NUM
ejpam-4772	193	9	+	+	NUM
ejpam-4772	193	10	δ)3	δ)3	NOUN
ejpam-4772	193	11	+	+	CCONJ
ejpam-4772	193	12	(	(	PUNCT
ejpam-4772	193	13	p2	p2	PROPN
ejpam-4772	193	14	8(2	8(2	PROPN
ejpam-4772	194	1	+	+	CCONJ
ejpam-4772	194	2	α)2(1	α)2(1	NOUN
ejpam-4772	194	3	+	+	CCONJ
ejpam-4772	194	4	δ)17/2	δ)17/2	NOUN
ejpam-4772	194	5	)	)	PUNCT
ejpam-4772	194	6	[	[	PUNCT
ejpam-4772	194	7	(	(	PUNCT
ejpam-4772	194	8	4−	4−	NOUN
ejpam-4772	194	9	p2	p2	NOUN
ejpam-4772	194	10	)	)	PUNCT
ejpam-4772	194	11	(	(	PUNCT
ejpam-4772	195	1	√	√	NUM
ejpam-4772	195	2	2(−1	2(−1	NUM
ejpam-4772	195	3	+	+	CCONJ
ejpam-4772	195	4	α)(2	α)(2	NUM
ejpam-4772	195	5	+	+	ADJ
ejpam-4772	195	6	α)2	α)2	NOUN
ejpam-4772	195	7	√	√	NOUN
ejpam-4772	195	8	δ	δ	PROPN
ejpam-4772	195	9	+	+	PROPN
ejpam-4772	195	10	(	(	PUNCT
ejpam-4772	195	11	3	3	NUM
ejpam-4772	195	12	+	+	CCONJ
ejpam-4772	195	13	4α+	4α+	NUM
ejpam-4772	195	14	α2	α2	ADJ
ejpam-4772	195	15	)	)	PUNCT
ejpam-4772	195	16	√	√	ADP
ejpam-4772	195	17	1	1	NUM
ejpam-4772	195	18	+	+	CCONJ
ejpam-4772	195	19	δ	δ	PROPN
ejpam-4772	195	20	+	+	CCONJ
ejpam-4772	195	21	2(3	2(3	NUM
ejpam-4772	195	22	+	+	CCONJ
ejpam-4772	195	23	4α+	4α+	NUM
ejpam-4772	195	24	α2)δ	α2)δ	NOUN
ejpam-4772	195	25	√	√	NUM
ejpam-4772	195	26	1	1	NUM
ejpam-4772	195	27	+	+	CCONJ
ejpam-4772	195	28	δ	δ	NOUN
ejpam-4772	195	29	−2(3	−2(3	NOUN
ejpam-4772	195	30	+	+	CCONJ
ejpam-4772	195	31	4α+	4α+	NUM
ejpam-4772	195	32	α2)δ2	α2)δ2	NOUN
ejpam-4772	195	33	√	√	NOUN
ejpam-4772	195	34	1	1	NUM
ejpam-4772	195	35	+	+	NUM
ejpam-4772	195	36	δ	δ	NOUN
ejpam-4772	195	37	)	)	PUNCT
ejpam-4772	195	38	]	]	PUNCT
ejpam-4772	195	39	(	(	PUNCT
ejpam-4772	195	40	20	20	NUM
ejpam-4772	195	41	)	)	PUNCT
ejpam-4772	195	42	since	since	SCONJ
ejpam-4772	195	43	φ	φ	PROPN
ejpam-4772	195	44	′	′	NUM
ejpam-4772	195	45	1(α	1(α	NUM
ejpam-4772	195	46	,	,	PUNCT
ejpam-4772	195	47	δ	δ	PROPN
ejpam-4772	195	48	,	,	PUNCT
ejpam-4772	195	49	p	p	X
ejpam-4772	195	50	,	,	PUNCT
ejpam-4772	195	51	|x|	|x|	PROPN
ejpam-4772	195	52	)	)	PUNCT
ejpam-4772	195	53	≥	≥	NOUN
ejpam-4772	195	54	0	0	NUM
ejpam-4772	195	55	when	when	SCONJ
ejpam-4772	195	56	α1	α1	PROPN
ejpam-4772	195	57	≤	≤	NUM
ejpam-4772	195	58	α	α	NOUN
ejpam-4772	195	59	≤	≤	NOUN
ejpam-4772	195	60	1	1	NUM
ejpam-4772	195	61	and	and	CCONJ
ejpam-4772	195	62	0	0	NUM
ejpam-4772	195	63	<	<	X
ejpam-4772	195	64	δ	δ	PROPN
ejpam-4772	195	65	≤	≤	ADV
ejpam-4772	195	66	1	1	NUM
ejpam-4772	195	67	,	,	PUNCT
ejpam-4772	195	68	then	then	ADV
ejpam-4772	195	69	φ1	φ1	PROPN
ejpam-4772	195	70	is	be	AUX
ejpam-4772	195	71	increasing	increase	VERB
ejpam-4772	195	72	monoton	monoton	NOUN
ejpam-4772	195	73	function	function	NOUN
ejpam-4772	195	74	.	.	PUNCT
ejpam-4772	196	1	so	so	ADV
ejpam-4772	196	2	that	that	SCONJ
ejpam-4772	196	3	the	the	DET
ejpam-4772	196	4	maximum	maximum	ADJ
ejpam-4772	196	5	value	value	NOUN
ejpam-4772	196	6	of	of	ADP
ejpam-4772	196	7	φ1(α	φ1(α	PROPN
ejpam-4772	196	8	,	,	PUNCT
ejpam-4772	196	9	δ	δ	PROPN
ejpam-4772	196	10	,	,	PUNCT
ejpam-4772	196	11	p	p	X
ejpam-4772	196	12	,	,	PUNCT
ejpam-4772	196	13	|x|	|x|	PROPN
ejpam-4772	196	14	)	)	PUNCT
ejpam-4772	196	15	is	be	AUX
ejpam-4772	196	16	provided	provide	VERB
ejpam-4772	196	17	when	when	SCONJ
ejpam-4772	196	18	|x|	|x|	PROPN
ejpam-4772	196	19	=	=	SYM
ejpam-4772	196	20	1	1	NUM
ejpam-4772	196	21	or	or	CCONJ
ejpam-4772	196	22	h2(2	h2(2	PROPN
ejpam-4772	196	23	)	)	PUNCT
ejpam-4772	196	24	≤	≤	NOUN
ejpam-4772	196	25	δ(4−	δ(4−	NOUN
ejpam-4772	196	26	p2	p2	PROPN
ejpam-4772	196	27	)	)	PUNCT
ejpam-4772	196	28	8(2	8(2	NUM
ejpam-4772	197	1	+	+	CCONJ
ejpam-4772	197	2	α)2(1	α)2(1	NOUN
ejpam-4772	197	3	+	+	NUM
ejpam-4772	197	4	δ)3	δ)3	NOUN
ejpam-4772	197	5	+	+	CCONJ
ejpam-4772	197	6	(	(	PUNCT
ejpam-4772	197	7	p2	p2	PROPN
ejpam-4772	197	8	8(2	8(2	PROPN
ejpam-4772	198	1	+	+	CCONJ
ejpam-4772	198	2	α)2(1	α)2(1	NOUN
ejpam-4772	198	3	+	+	CCONJ
ejpam-4772	198	4	δ)17/2	δ)17/2	NOUN
ejpam-4772	198	5	)	)	PUNCT
ejpam-4772	198	6	[	[	PUNCT
ejpam-4772	198	7	(	(	PUNCT
ejpam-4772	198	8	4−	4−	NOUN
ejpam-4772	198	9	p2	p2	NOUN
ejpam-4772	198	10	)	)	PUNCT
ejpam-4772	198	11	(	(	PUNCT
ejpam-4772	199	1	√	√	NUM
ejpam-4772	199	2	2(−1	2(−1	NUM
ejpam-4772	199	3	+	+	CCONJ
ejpam-4772	199	4	α	α	X
ejpam-4772	199	5	)	)	PUNCT
ejpam-4772	199	6	n.m	n.m	PROPN
ejpam-4772	199	7	.	.	PROPN
ejpam-4772	199	8	asih	asih	PROPN
ejpam-4772	199	9	et	et	PROPN
ejpam-4772	199	10	al	al	PROPN
ejpam-4772	199	11	.	.	PUNCT
ejpam-4772	199	12	/	/	SYM
ejpam-4772	199	13	eur	eur	PROPN
ejpam-4772	199	14	.	.	PUNCT
ejpam-4772	200	1	j.	j.	PROPN
ejpam-4772	200	2	pure	pure	PROPN
ejpam-4772	200	3	appl	appl	PROPN
ejpam-4772	200	4	.	.	PROPN
ejpam-4772	200	5	math	math	PROPN
ejpam-4772	200	6	,	,	PUNCT
ejpam-4772	200	7	16	16	NUM
ejpam-4772	200	8	(	(	PUNCT
ejpam-4772	200	9	2	2	NUM
ejpam-4772	200	10	)	)	PUNCT
ejpam-4772	200	11	(	(	PUNCT
ejpam-4772	200	12	2023	2023	NUM
ejpam-4772	200	13	)	)	PUNCT
ejpam-4772	200	14	,	,	PUNCT
ejpam-4772	200	15	1290	1290	NUM
ejpam-4772	200	16	-	-	SYM
ejpam-4772	200	17	1301	1301	NUM
ejpam-4772	200	18	1297	1297	NUM
ejpam-4772	200	19	(	(	PUNCT
ejpam-4772	200	20	2	2	NUM
ejpam-4772	200	21	+	+	NUM
ejpam-4772	200	22	α)2	α)2	NOUN
ejpam-4772	200	23	√	√	NOUN
ejpam-4772	200	24	δ	δ	PROPN
ejpam-4772	200	25	+	+	CCONJ
ejpam-4772	200	26	(	(	PUNCT
ejpam-4772	200	27	3	3	NUM
ejpam-4772	200	28	+	+	CCONJ
ejpam-4772	200	29	4α+	4α+	NUM
ejpam-4772	200	30	α2	α2	ADJ
ejpam-4772	200	31	)	)	PUNCT
ejpam-4772	201	1	√	√	ADP
ejpam-4772	201	2	1	1	NUM
ejpam-4772	202	1	+	+	CCONJ
ejpam-4772	202	2	δ	δ	PROPN
ejpam-4772	202	3	+	+	CCONJ
ejpam-4772	202	4	2(3	2(3	NUM
ejpam-4772	202	5	+	+	CCONJ
ejpam-4772	202	6	4α+	4α+	NUM
ejpam-4772	202	7	α2)δ	α2)δ	NOUN
ejpam-4772	202	8	√	√	NUM
ejpam-4772	202	9	1	1	NUM
ejpam-4772	202	10	+	+	CCONJ
ejpam-4772	202	11	δ	δ	NOUN
ejpam-4772	202	12	−2(3	−2(3	NOUN
ejpam-4772	202	13	+	+	CCONJ
ejpam-4772	202	14	4α+	4α+	NUM
ejpam-4772	202	15	α2)δ2	α2)δ2	NOUN
ejpam-4772	202	16	√	√	NOUN
ejpam-4772	202	17	1	1	NUM
ejpam-4772	202	18	+	+	NUM
ejpam-4772	202	19	δ	δ	NOUN
ejpam-4772	202	20	)	)	PUNCT
ejpam-4772	202	21	]	]	PUNCT
ejpam-4772	203	1	+	+	CCONJ
ejpam-4772	203	2	(	(	PUNCT
ejpam-4772	203	3	p4δ	p4δ	NOUN
ejpam-4772	203	4	96(2	96(2	NOUN
ejpam-4772	203	5	+	+	CCONJ
ejpam-4772	203	6	α)2(1	α)2(1	NOUN
ejpam-4772	203	7	+	+	CCONJ
ejpam-4772	203	8	δ)8	δ)8	NOUN
ejpam-4772	203	9	)	)	PUNCT
ejpam-4772	203	10	[	[	PUNCT
ejpam-4772	203	11	(	(	PUNCT
ejpam-4772	203	12	6	6	NUM
ejpam-4772	203	13	√	√	NUM
ejpam-4772	203	14	2(−1	2(−1	NUM
ejpam-4772	203	15	+	+	CCONJ
ejpam-4772	203	16	δ)(2	δ)(2	NUM
ejpam-4772	203	17	+	+	NUM
ejpam-4772	203	18	α)2	α)2	NOUN
ejpam-4772	203	19	√	√	NOUN
ejpam-4772	203	20	δ	δ	PROPN
ejpam-4772	203	21	+	+	PROPN
ejpam-4772	203	22	30	30	NUM
ejpam-4772	203	23	√	√	NUM
ejpam-4772	203	24	2(−1	2(−1	NUM
ejpam-4772	203	25	+	+	CCONJ
ejpam-4772	203	26	α	α	X
ejpam-4772	203	27	)	)	PUNCT
ejpam-4772	203	28	(	(	PUNCT
ejpam-4772	203	29	2	2	NUM
ejpam-4772	203	30	+	+	NUM
ejpam-4772	203	31	α)2δ3/2	α)2δ3/2	ADJ
ejpam-4772	203	32	+	+	CCONJ
ejpam-4772	203	33	24	24	NUM
ejpam-4772	203	34	√	√	NUM
ejpam-4772	203	35	2(−1	2(−1	NUM
ejpam-4772	203	36	+	+	CCONJ
ejpam-4772	203	37	α)(2	α)(2	NUM
ejpam-4772	203	38	+	+	CCONJ
ejpam-4772	204	1	α)2δ5/2	α)2δ5/2	ADJ
ejpam-4772	205	1	+	+	NOUN
ejpam-4772	205	2	3(7	3(7	NUM
ejpam-4772	205	3	+	+	NUM
ejpam-4772	205	4	8α+	8α+	NUM
ejpam-4772	205	5	2α2)√	2α2)√	NUM
ejpam-4772	205	6	1	1	NUM
ejpam-4772	205	7	+	+	CCONJ
ejpam-4772	205	8	δ	δ	X
ejpam-4772	206	1	+	+	CCONJ
ejpam-4772	206	2	(	(	PUNCT
ejpam-4772	206	3	117	117	NUM
ejpam-4772	206	4	+	+	NUM
ejpam-4772	206	5	64α−	64α−	NUM
ejpam-4772	206	6	20α2	20α2	NUM
ejpam-4772	207	1	+	+	NUM
ejpam-4772	208	1	36α3	36α3	NUM
ejpam-4772	208	2	+	+	NUM
ejpam-4772	208	3	38α4	38α4	NUM
ejpam-4772	208	4	+	+	CCONJ
ejpam-4772	208	5	8α5)δ	8α5)δ	NUM
ejpam-4772	208	6	√	√	NUM
ejpam-4772	208	7	1	1	NUM
ejpam-4772	208	8	+	+	NUM
ejpam-4772	208	9	δ	δ	NOUN
ejpam-4772	208	10	+72(3	+72(3	PUNCT
ejpam-4772	209	1	+	+	CCONJ
ejpam-4772	209	2	4α+	4α+	NUM
ejpam-4772	209	3	α2)δ2	α2)δ2	NOUN
ejpam-4772	209	4	√	√	NOUN
ejpam-4772	209	5	1	1	NUM
ejpam-4772	209	6	+	+	CCONJ
ejpam-4772	209	7	δ	δ	PROPN
ejpam-4772	209	8	+	+	CCONJ
ejpam-4772	209	9	48(3	48(3	NOUN
ejpam-4772	210	1	+	+	CCONJ
ejpam-4772	210	2	4α+	4α+	NUM
ejpam-4772	210	3	α2)δ3	α2)δ3	NOUN
ejpam-4772	210	4	√	√	NOUN
ejpam-4772	210	5	1	1	NUM
ejpam-4772	210	6	+	+	NUM
ejpam-4772	210	7	δ	δ	NOUN
ejpam-4772	210	8	)	)	PUNCT
ejpam-4772	210	9	−12(1	−12(1	ADP
ejpam-4772	210	10	+	+	ADJ
ejpam-4772	210	11	5α+	5α+	NUM
ejpam-4772	210	12	10α2	10α2	NUM
ejpam-4772	210	13	+	+	NUM
ejpam-4772	210	14	10α3	10α3	NUM
ejpam-4772	211	1	+	+	CCONJ
ejpam-4772	211	2	5α4)−	5α4)−	PROPN
ejpam-4772	211	3	(	(	PUNCT
ejpam-4772	211	4	2	2	NUM
ejpam-4772	211	5	+	+	SYM
ejpam-4772	211	6	α)2(1	α)2(1	NOUN
ejpam-4772	211	7	+	+	CCONJ
ejpam-4772	211	8	δ)5	δ)5	X
ejpam-4772	211	9	]	]	PUNCT
ejpam-4772	211	10	:	:	PUNCT
ejpam-4772	211	11	=	=	SYM
ejpam-4772	211	12	φ1(α	φ1(α	PROPN
ejpam-4772	211	13	,	,	PUNCT
ejpam-4772	211	14	δ	δ	PROPN
ejpam-4772	211	15	,	,	PUNCT
ejpam-4772	211	16	p	p	NOUN
ejpam-4772	211	17	)	)	PUNCT
ejpam-4772	211	18	.	.	PUNCT
ejpam-4772	212	1	(	(	PUNCT
ejpam-4772	212	2	21	21	NUM
ejpam-4772	212	3	)	)	PUNCT
ejpam-4772	212	4	next	next	ADV
ejpam-4772	212	5	,	,	PUNCT
ejpam-4772	212	6	the	the	DET
ejpam-4772	212	7	derivative	derivative	NOUN
ejpam-4772	212	8	of	of	ADP
ejpam-4772	212	9	φ1(α	φ1(α	PROPN
ejpam-4772	212	10	,	,	PUNCT
ejpam-4772	212	11	δ	δ	PROPN
ejpam-4772	212	12	,	,	PUNCT
ejpam-4772	212	13	p	p	NOUN
ejpam-4772	212	14	)	)	PUNCT
ejpam-4772	212	15	with	with	ADP
ejpam-4772	212	16	respect	respect	NOUN
ejpam-4772	212	17	to	to	ADP
ejpam-4772	212	18	p	p	NOUN
ejpam-4772	212	19	from	from	ADP
ejpam-4772	212	20	(	(	PUNCT
ejpam-4772	212	21	21	21	NUM
ejpam-4772	212	22	)	)	PUNCT
ejpam-4772	212	23	is	be	AUX
ejpam-4772	212	24	,	,	PUNCT
ejpam-4772	212	25	φ	φ	PROPN
ejpam-4772	212	26	′	′	NUM
ejpam-4772	212	27	1(α	1(α	NUM
ejpam-4772	212	28	,	,	PUNCT
ejpam-4772	212	29	δ	δ	PROPN
ejpam-4772	212	30	,	,	PUNCT
ejpam-4772	212	31	p	p	NOUN
ejpam-4772	212	32	)	)	PUNCT
ejpam-4772	212	33	=	=	SYM
ejpam-4772	212	34	−	−	PROPN
ejpam-4772	212	35	pδ(4−	pδ(4−	NOUN
ejpam-4772	212	36	p2	p2	NOUN
ejpam-4772	212	37	)	)	PUNCT
ejpam-4772	212	38	2(2	2(2	NUM
ejpam-4772	213	1	+	+	CCONJ
ejpam-4772	213	2	α)2(1	α)2(1	NOUN
ejpam-4772	213	3	+	+	NUM
ejpam-4772	213	4	δ)3	δ)3	NOUN
ejpam-4772	213	5	−	−	PROPN
ejpam-4772	213	6	(	(	PUNCT
ejpam-4772	213	7	p3	p3	PROPN
ejpam-4772	213	8	4(2	4(2	NUM
ejpam-4772	213	9	+	+	CCONJ
ejpam-4772	213	10	α)2(1	α)2(1	NOUN
ejpam-4772	213	11	+	+	CCONJ
ejpam-4772	213	12	δ)17/2	δ)17/2	NOUN
ejpam-4772	213	13	)	)	PUNCT
ejpam-4772	213	14	(	(	PUNCT
ejpam-4772	213	15	√	√	NUM
ejpam-4772	213	16	2(−1	2(−1	NUM
ejpam-4772	213	17	+	+	CCONJ
ejpam-4772	213	18	α	α	X
ejpam-4772	213	19	)	)	PUNCT
ejpam-4772	213	20	(	(	PUNCT
ejpam-4772	213	21	2	2	NUM
ejpam-4772	213	22	+	+	NUM
ejpam-4772	213	23	α)2	α)2	NOUN
ejpam-4772	213	24	√	√	NOUN
ejpam-4772	213	25	δ	δ	PROPN
ejpam-4772	213	26	+	+	CCONJ
ejpam-4772	213	27	(	(	PUNCT
ejpam-4772	213	28	3	3	NUM
ejpam-4772	213	29	+	+	CCONJ
ejpam-4772	213	30	4α+	4α+	NUM
ejpam-4772	213	31	α2	α2	ADJ
ejpam-4772	213	32	)	)	PUNCT
ejpam-4772	213	33	√	√	ADP
ejpam-4772	213	34	1	1	NUM
ejpam-4772	213	35	+	+	CCONJ
ejpam-4772	213	36	δ	δ	PROPN
ejpam-4772	213	37	+	+	CCONJ
ejpam-4772	213	38	2(3	2(3	NUM
ejpam-4772	213	39	+	+	CCONJ
ejpam-4772	213	40	4α+	4α+	NUM
ejpam-4772	213	41	α2)δ	α2)δ	NOUN
ejpam-4772	213	42	√	√	NUM
ejpam-4772	213	43	1	1	NUM
ejpam-4772	213	44	+	+	CCONJ
ejpam-4772	213	45	δ	δ	NOUN
ejpam-4772	213	46	−2(3	−2(3	NOUN
ejpam-4772	213	47	+	+	CCONJ
ejpam-4772	213	48	4α+	4α+	NUM
ejpam-4772	213	49	α2)δ2	α2)δ2	NOUN
ejpam-4772	213	50	√	√	NOUN
ejpam-4772	213	51	1	1	NUM
ejpam-4772	213	52	+	+	NUM
ejpam-4772	213	53	δ	δ	NOUN
ejpam-4772	213	54	)	)	PUNCT
ejpam-4772	214	1	+	+	CCONJ
ejpam-4772	214	2	(	(	PUNCT
ejpam-4772	214	3	p(4−	p(4−	NOUN
ejpam-4772	214	4	p2	p2	NOUN
ejpam-4772	214	5	)	)	PUNCT
ejpam-4772	214	6	4(2	4(2	NUM
ejpam-4772	215	1	+	+	CCONJ
ejpam-4772	215	2	α)2(1	α)2(1	NOUN
ejpam-4772	215	3	+	+	CCONJ
ejpam-4772	215	4	δ)17/2	δ)17/2	NOUN
ejpam-4772	215	5	)	)	PUNCT
ejpam-4772	215	6	(	(	PUNCT
ejpam-4772	215	7	√	√	NUM
ejpam-4772	215	8	2(−1	2(−1	NUM
ejpam-4772	215	9	+	+	CCONJ
ejpam-4772	215	10	α	α	X
ejpam-4772	215	11	)	)	PUNCT
ejpam-4772	215	12	(	(	PUNCT
ejpam-4772	215	13	2	2	NUM
ejpam-4772	215	14	+	+	NUM
ejpam-4772	215	15	α)2	α)2	NOUN
ejpam-4772	215	16	√	√	NOUN
ejpam-4772	215	17	δ	δ	PROPN
ejpam-4772	215	18	+	+	CCONJ
ejpam-4772	215	19	(	(	PUNCT
ejpam-4772	215	20	3	3	NUM
ejpam-4772	215	21	+	+	CCONJ
ejpam-4772	215	22	4α+	4α+	NUM
ejpam-4772	215	23	α2	α2	ADJ
ejpam-4772	215	24	)	)	PUNCT
ejpam-4772	215	25	√	√	ADP
ejpam-4772	215	26	1	1	NUM
ejpam-4772	216	1	+	+	CCONJ
ejpam-4772	216	2	δ	δ	PROPN
ejpam-4772	216	3	+	+	CCONJ
ejpam-4772	216	4	2(3	2(3	NUM
ejpam-4772	216	5	+	+	CCONJ
ejpam-4772	216	6	4α+	4α+	NUM
ejpam-4772	216	7	α2)δ	α2)δ	NOUN
ejpam-4772	216	8	√	√	NUM
ejpam-4772	216	9	1	1	NUM
ejpam-4772	216	10	+	+	CCONJ
ejpam-4772	216	11	δ	δ	NOUN
ejpam-4772	216	12	−2(3	−2(3	NOUN
ejpam-4772	216	13	+	+	CCONJ
ejpam-4772	216	14	4α+	4α+	NUM
ejpam-4772	216	15	α2)δ2	α2)δ2	NOUN
ejpam-4772	216	16	√	√	NOUN
ejpam-4772	216	17	1	1	NUM
ejpam-4772	216	18	+	+	NUM
ejpam-4772	216	19	δ	δ	NOUN
ejpam-4772	216	20	)	)	PUNCT
ejpam-4772	217	1	+	+	CCONJ
ejpam-4772	217	2	(	(	PUNCT
ejpam-4772	217	3	p3δ(1	p3δ(1	PROPN
ejpam-4772	217	4	+	+	CCONJ
ejpam-4772	217	5	δ)3/2	δ)3/2	PROPN
ejpam-4772	217	6	)	)	PUNCT
ejpam-4772	217	7	24(2	24(2	NUM
ejpam-4772	218	1	+	+	CCONJ
ejpam-4772	218	2	α)2(1	α)2(1	NOUN
ejpam-4772	218	3	+	+	CCONJ
ejpam-4772	218	4	δ)8	δ)8	NOUN
ejpam-4772	218	5	)	)	PUNCT
ejpam-4772	219	1	[	[	PUNCT
ejpam-4772	219	2	(	(	PUNCT
ejpam-4772	219	3	6	6	NUM
ejpam-4772	219	4	√	√	NUM
ejpam-4772	219	5	2(−1	2(−1	NUM
ejpam-4772	219	6	+	+	CCONJ
ejpam-4772	219	7	δ	δ	X
ejpam-4772	219	8	)	)	PUNCT
ejpam-4772	219	9	(	(	PUNCT
ejpam-4772	219	10	2	2	NUM
ejpam-4772	219	11	+	+	NUM
ejpam-4772	219	12	α)2	α)2	NOUN
ejpam-4772	219	13	√	√	PUNCT
ejpam-4772	219	14	δ	δ	PROPN
ejpam-4772	219	15	+	+	PROPN
ejpam-4772	219	16	30	30	NUM
ejpam-4772	219	17	√	√	NUM
ejpam-4772	219	18	2(−1	2(−1	NUM
ejpam-4772	219	19	+	+	CCONJ
ejpam-4772	219	20	α)(2	α)(2	NUM
ejpam-4772	219	21	+	+	CCONJ
ejpam-4772	219	22	α)2δ3/2	α)2δ3/2	PROPN
ejpam-4772	219	23	+	+	CCONJ
ejpam-4772	219	24	24	24	NUM
ejpam-4772	219	25	√	√	NUM
ejpam-4772	219	26	2(−1	2(−1	NUM
ejpam-4772	219	27	+	+	CCONJ
ejpam-4772	219	28	α	α	X
ejpam-4772	219	29	)	)	PUNCT
ejpam-4772	219	30	(	(	PUNCT
ejpam-4772	219	31	2	2	NUM
ejpam-4772	219	32	+	+	CCONJ
ejpam-4772	219	33	α)2δ5/2	α)2δ5/2	ADJ
ejpam-4772	219	34	+	+	NOUN
ejpam-4772	219	35	3(7	3(7	NUM
ejpam-4772	219	36	+	+	NUM
ejpam-4772	219	37	8α+	8α+	NUM
ejpam-4772	219	38	2α2	2α2	NUM
ejpam-4772	219	39	)	)	PUNCT
ejpam-4772	219	40	√	√	ADV
ejpam-4772	219	41	1	1	NUM
ejpam-4772	219	42	+	+	CCONJ
ejpam-4772	219	43	δ	δ	X
ejpam-4772	219	44	+	+	CCONJ
ejpam-4772	219	45	(	(	PUNCT
ejpam-4772	219	46	117	117	NUM
ejpam-4772	219	47	+	+	NUM
ejpam-4772	219	48	64α−	64α−	NUM
ejpam-4772	220	1	20α2	20α2	NUM
ejpam-4772	220	2	+36α3	+36α3	NOUN
ejpam-4772	220	3	+	+	NOUN
ejpam-4772	220	4	38α4	38α4	NUM
ejpam-4772	220	5	+	+	CCONJ
ejpam-4772	220	6	8α5)δ	8α5)δ	NUM
ejpam-4772	220	7	√	√	NUM
ejpam-4772	220	8	1	1	NUM
ejpam-4772	220	9	+	+	CCONJ
ejpam-4772	220	10	δ	δ	PROPN
ejpam-4772	220	11	+	+	CCONJ
ejpam-4772	220	12	72(3	72(3	NUM
ejpam-4772	220	13	+	+	CCONJ
ejpam-4772	220	14	4α+	4α+	NUM
ejpam-4772	220	15	α2)δ2	α2)δ2	NOUN
ejpam-4772	220	16	√	√	NOUN
ejpam-4772	220	17	1	1	NUM
ejpam-4772	220	18	+	+	CCONJ
ejpam-4772	220	19	δ	δ	PROPN
ejpam-4772	220	20	+48(3	+48(3	PROPN
ejpam-4772	220	21	+	+	CCONJ
ejpam-4772	220	22	4α+	4α+	NUM
ejpam-4772	220	23	α2)δ3	α2)δ3	NOUN
ejpam-4772	220	24	√	√	NOUN
ejpam-4772	220	25	1	1	NUM
ejpam-4772	220	26	+	+	CCONJ
ejpam-4772	220	27	δ)−	δ)−	PROPN
ejpam-4772	220	28	12(1	12(1	NOUN
ejpam-4772	220	29	+	+	NOUN
ejpam-4772	220	30	5α+	5α+	NUM
ejpam-4772	220	31	10α2	10α2	NUM
ejpam-4772	220	32	+10α3	+10α3	PROPN
ejpam-4772	221	1	+	+	CCONJ
ejpam-4772	221	2	5α4)−	5α4)−	PROPN
ejpam-4772	221	3	(	(	PUNCT
ejpam-4772	221	4	2	2	NUM
ejpam-4772	221	5	+	+	SYM
ejpam-4772	221	6	α)2(1	α)2(1	NOUN
ejpam-4772	221	7	+	+	CCONJ
ejpam-4772	221	8	δ)5	δ)5	X
ejpam-4772	221	9	]	]	PUNCT
ejpam-4772	221	10	(	(	PUNCT
ejpam-4772	221	11	22	22	NUM
ejpam-4772	221	12	)	)	PUNCT
ejpam-4772	221	13	from	from	ADP
ejpam-4772	221	14	(	(	PUNCT
ejpam-4772	221	15	22	22	NUM
ejpam-4772	221	16	)	)	PUNCT
ejpam-4772	221	17	we	we	PRON
ejpam-4772	221	18	find	find	VERB
ejpam-4772	221	19	the	the	DET
ejpam-4772	221	20	maximum	maximum	ADJ
ejpam-4772	221	21	value	value	NOUN
ejpam-4772	221	22	of	of	ADP
ejpam-4772	221	23	φ1(α	φ1(α	PROPN
ejpam-4772	221	24	,	,	PUNCT
ejpam-4772	221	25	δ	δ	PROPN
ejpam-4772	221	26	,	,	PUNCT
ejpam-4772	221	27	p	p	NOUN
ejpam-4772	221	28	)	)	PUNCT
ejpam-4772	221	29	when	when	SCONJ
ejpam-4772	221	30	0	0	NUM
ejpam-4772	221	31	≤	≤	NOUN
ejpam-4772	221	32	p	p	X
ejpam-4772	221	33	≤	≤	NUM
ejpam-4772	221	34	2	2	NUM
ejpam-4772	221	35	.	.	PUNCT
ejpam-4772	221	36	with	with	ADP
ejpam-4772	221	37	elementary	elementary	ADJ
ejpam-4772	221	38	calculus	calculus	NOUN
ejpam-4772	221	39	,	,	PUNCT
ejpam-4772	221	40	we	we	PRON
ejpam-4772	221	41	can	can	AUX
ejpam-4772	221	42	show	show	VERB
ejpam-4772	221	43	that	that	DET
ejpam-4772	221	44	φ1′	φ1′	NOUN
ejpam-4772	221	45	(	(	PUNCT
ejpam-4772	221	46	α	α	NOUN
ejpam-4772	221	47	,	,	PUNCT
ejpam-4772	221	48	δ	δ	PROPN
ejpam-4772	221	49	,	,	PUNCT
ejpam-4772	221	50	p	p	NOUN
ejpam-4772	221	51	)	)	PUNCT
ejpam-4772	221	52	=	=	SYM
ejpam-4772	221	53	0	0	PROPN
ejpam-4772	221	54	has	have	VERB
ejpam-4772	221	55	three	three	NUM
ejpam-4772	221	56	values	value	NOUN
ejpam-4772	221	57	of	of	ADP
ejpam-4772	221	58	p	p	NOUN
ejpam-4772	221	59	but	but	CCONJ
ejpam-4772	221	60	the	the	DET
ejpam-4772	221	61	only	only	ADJ
ejpam-4772	221	62	valid	valid	ADJ
ejpam-4772	221	63	value	value	NOUN
ejpam-4772	221	64	is	be	AUX
ejpam-4772	221	65	p	p	NOUN
ejpam-4772	221	66	=	=	SYM
ejpam-4772	221	67	0	0	NUM
ejpam-4772	221	68	while	while	SCONJ
ejpam-4772	221	69	the	the	DET
ejpam-4772	221	70	thers	ther	NOUN
ejpam-4772	221	71	are	be	AUX
ejpam-4772	221	72	not	not	PART
ejpam-4772	221	73	valid	valid	ADJ
ejpam-4772	221	74	.	.	PUNCT
ejpam-4772	222	1	since	since	SCONJ
ejpam-4772	222	2	φ1(α	φ1(α	PROPN
ejpam-4772	222	3	,	,	PUNCT
ejpam-4772	222	4	δ	δ	PROPN
ejpam-4772	222	5	,	,	PUNCT
ejpam-4772	222	6	0	0	NUM
ejpam-4772	222	7	)	)	PUNCT
ejpam-4772	222	8	≤	≤	NOUN
ejpam-4772	222	9	φ1(α	φ1(α	PROPN
ejpam-4772	222	10	,	,	PUNCT
ejpam-4772	222	11	δ	δ	PROPN
ejpam-4772	222	12	,	,	PUNCT
ejpam-4772	222	13	2	2	NUM
ejpam-4772	222	14	)	)	PUNCT
ejpam-4772	222	15	for	for	ADP
ejpam-4772	222	16	α1	α1	PROPN
ejpam-4772	222	17	≤	≤	NUM
ejpam-4772	222	18	α	α	NOUN
ejpam-4772	222	19	≤	≤	NOUN
ejpam-4772	222	20	1	1	NUM
ejpam-4772	222	21	and	and	CCONJ
ejpam-4772	222	22	0	0	NUM
ejpam-4772	222	23	<	<	X
ejpam-4772	222	24	δ	δ	PROPN
ejpam-4772	222	25	≤	≤	ADV
ejpam-4772	222	26	1	1	NUM
ejpam-4772	222	27	,	,	PUNCT
ejpam-4772	222	28	then	then	ADV
ejpam-4772	222	29	h2(2	h2(2	PROPN
ejpam-4772	222	30	)	)	PUNCT
ejpam-4772	222	31	≤	≤	PROPN
ejpam-4772	222	32	φ1(α	φ1(α	PROPN
ejpam-4772	222	33	,	,	PUNCT
ejpam-4772	222	34	δ	δ	PROPN
ejpam-4772	222	35	,	,	PUNCT
ejpam-4772	222	36	2	2	NUM
ejpam-4772	222	37	)	)	PUNCT
ejpam-4772	222	38	.	.	PUNCT
ejpam-4772	223	1	the	the	DET
ejpam-4772	223	2	inequality	inequality	NOUN
ejpam-4772	223	3	is	be	AUX
ejpam-4772	223	4	sharp	sharp	ADJ
ejpam-4772	223	5	when	when	SCONJ
ejpam-4772	223	6	p1	p1	PROPN
ejpam-4772	223	7	=	=	NOUN
ejpam-4772	223	8	p2	p2	PROPN
ejpam-4772	223	9	=	=	SYM
ejpam-4772	223	10	p3	p3	PROPN
ejpam-4772	223	11	=	=	SYM
ejpam-4772	223	12	2	2	X
ejpam-4772	223	13	.	.	PUNCT
ejpam-4772	224	1	the	the	DET
ejpam-4772	224	2	proof	proof	NOUN
ejpam-4772	224	3	is	be	AUX
ejpam-4772	224	4	completed	complete	VERB
ejpam-4772	224	5	.	.	PUNCT
ejpam-4772	225	1	theorem	theorem	NOUN
ejpam-4772	225	2	3	3	NUM
ejpam-4772	225	3	.	.	PUNCT
ejpam-4772	226	1	if	if	SCONJ
ejpam-4772	226	2	f	f	PROPN
ejpam-4772	226	3	∈	∈	PROPN
ejpam-4772	226	4	b1(α	b1(α	PROPN
ejpam-4772	226	5	,	,	PUNCT
ejpam-4772	226	6	δ	δ	PROPN
ejpam-4772	226	7	)	)	PUNCT
ejpam-4772	226	8	,	,	PUNCT
ejpam-4772	226	9	for	for	ADP
ejpam-4772	226	10	0	0	NUM
ejpam-4772	226	11	≤	≤	NUM
ejpam-4772	226	12	α	α	NOUN
ejpam-4772	226	13	≤	≤	NOUN
ejpam-4772	226	14	0	0	NUM
ejpam-4772	226	15	and	and	CCONJ
ejpam-4772	226	16	0	0	NUM
ejpam-4772	226	17	<	<	X
ejpam-4772	226	18	δ	δ	PROPN
ejpam-4772	226	19	≤	≤	ADV
ejpam-4772	226	20	1	1	NUM
ejpam-4772	226	21	then	then	ADV
ejpam-4772	226	22	t2(1	t2(1	PROPN
ejpam-4772	226	23	)	)	PUNCT
ejpam-4772	226	24	=	=	PUNCT
ejpam-4772	227	1	|a21	|a21	X
ejpam-4772	227	2	−	−	PROPN
ejpam-4772	227	3	a22|	a22|	SYM
ejpam-4772	227	4	≤	≤	NUM
ejpam-4772	227	5	1	1	NUM
ejpam-4772	227	6	,	,	PUNCT
ejpam-4772	227	7	(	(	PUNCT
ejpam-4772	227	8	23	23	X
ejpam-4772	227	9	)	)	PUNCT
ejpam-4772	227	10	n.m	n.m	PROPN
ejpam-4772	227	11	.	.	PROPN
ejpam-4772	227	12	asih	asih	PROPN
ejpam-4772	227	13	et	et	PROPN
ejpam-4772	227	14	al	al	PROPN
ejpam-4772	227	15	.	.	PUNCT
ejpam-4772	227	16	/	/	SYM
ejpam-4772	227	17	eur	eur	PROPN
ejpam-4772	227	18	.	.	PUNCT
ejpam-4772	228	1	j.	j.	PROPN
ejpam-4772	228	2	pure	pure	PROPN
ejpam-4772	228	3	appl	appl	PROPN
ejpam-4772	228	4	.	.	PROPN
ejpam-4772	228	5	math	math	PROPN
ejpam-4772	228	6	,	,	PUNCT
ejpam-4772	228	7	16	16	NUM
ejpam-4772	228	8	(	(	PUNCT
ejpam-4772	228	9	2	2	NUM
ejpam-4772	228	10	)	)	PUNCT
ejpam-4772	228	11	(	(	PUNCT
ejpam-4772	228	12	2023	2023	NUM
ejpam-4772	228	13	)	)	PUNCT
ejpam-4772	228	14	,	,	PUNCT
ejpam-4772	228	15	1290	1290	NUM
ejpam-4772	228	16	-	-	SYM
ejpam-4772	228	17	1301	1301	NUM
ejpam-4772	228	18	1298	1298	NUM
ejpam-4772	228	19	and	and	CCONJ
ejpam-4772	228	20	the	the	DET
ejpam-4772	228	21	inequality	inequality	NOUN
ejpam-4772	228	22	is	be	AUX
ejpam-4772	228	23	sharp	sharp	ADJ
ejpam-4772	228	24	.	.	PUNCT
ejpam-4772	229	1	proof	proof	NOUN
ejpam-4772	229	2	.	.	PUNCT
ejpam-4772	230	1	based	base	VERB
ejpam-4772	230	2	on	on	ADP
ejpam-4772	230	3	definition	definition	NOUN
ejpam-4772	230	4	1	1	NUM
ejpam-4772	230	5	,	,	PUNCT
ejpam-4772	230	6	we	we	PRON
ejpam-4772	230	7	have	have	VERB
ejpam-4772	230	8	initial	initial	ADJ
ejpam-4772	230	9	coefficients	coefficient	NOUN
ejpam-4772	230	10	a1	a1	NOUN
ejpam-4772	230	11	=	=	SYM
ejpam-4772	230	12	1	1	NUM
ejpam-4772	230	13	and	and	CCONJ
ejpam-4772	230	14	a2	a2	PROPN
ejpam-4772	230	15	(	(	PUNCT
ejpam-4772	230	16	see	see	VERB
ejpam-4772	230	17	(	(	PUNCT
ejpam-4772	230	18	9	9	NUM
ejpam-4772	230	19	)	)	PUNCT
ejpam-4772	230	20	)	)	PUNCT
ejpam-4772	230	21	and	and	CCONJ
ejpam-4772	230	22	we	we	PRON
ejpam-4772	230	23	can	can	AUX
ejpam-4772	230	24	write	write	VERB
ejpam-4772	230	25	toeplitz	toeplitz	NOUN
ejpam-4772	230	26	determinant	determinant	ADJ
ejpam-4772	230	27	t2(1	t2(1	PROPN
ejpam-4772	230	28	)	)	PUNCT
ejpam-4772	230	29	as	as	ADP
ejpam-4772	230	30	t2(1	t2(1	PROPN
ejpam-4772	230	31	)	)	PUNCT
ejpam-4772	230	32	=	=	SYM
ejpam-4772	231	1	∣∣∣∣a1	∣∣∣∣a1	NOUN
ejpam-4772	231	2	a2	a2	PROPN
ejpam-4772	231	3	a2	a2	PROPN
ejpam-4772	231	4	a1	a1	NOUN
ejpam-4772	231	5	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4772	231	6	=	=	PUNCT
ejpam-4772	231	7	|a21	|a21	NOUN
ejpam-4772	231	8	−	−	PROPN
ejpam-4772	231	9	a22|	a22|	PROPN
ejpam-4772	231	10	=	=	NOUN
ejpam-4772	231	11	|1−	|1−	PROPN
ejpam-4772	231	12	p21	p21	NOUN
ejpam-4772	231	13	√	√	PROPN
ejpam-4772	231	14	δ	δ	PROPN
ejpam-4772	231	15	(	(	PUNCT
ejpam-4772	231	16	2	2	NUM
ejpam-4772	231	17	+	+	NUM
ejpam-4772	231	18	δ)3	δ)3	NOUN
ejpam-4772	231	19	|	|	ADV
ejpam-4772	231	20	since	since	SCONJ
ejpam-4772	231	21	(	(	PUNCT
ejpam-4772	231	22	1−	1−	NUM
ejpam-4772	231	23	p21	p21	PROPN
ejpam-4772	231	24	√	√	PROPN
ejpam-4772	231	25	δ	δ	PROPN
ejpam-4772	231	26	(	(	PUNCT
ejpam-4772	231	27	2	2	NUM
ejpam-4772	231	28	+	+	NUM
ejpam-4772	231	29	δ)3	δ)3	NOUN
ejpam-4772	231	30	)	)	PUNCT
ejpam-4772	231	31	≥	≥	NOUN
ejpam-4772	231	32	0	0	NUM
ejpam-4772	231	33	,	,	PUNCT
ejpam-4772	231	34	if	if	SCONJ
ejpam-4772	231	35	δ	δ	PROPN
ejpam-4772	231	36	≥	≥	VERB
ejpam-4772	231	37	0	0	NUM
ejpam-4772	231	38	and	and	CCONJ
ejpam-4772	231	39	0	0	NUM
ejpam-4772	231	40	<	<	X
ejpam-4772	231	41	p1	p1	PROPN
ejpam-4772	231	42	≤	≤	ADV
ejpam-4772	231	43	2	2	NUM
ejpam-4772	231	44	,	,	PUNCT
ejpam-4772	231	45	we	we	PRON
ejpam-4772	231	46	have	have	VERB
ejpam-4772	231	47	,	,	PUNCT
ejpam-4772	231	48	t2(1	t2(1	PROPN
ejpam-4772	231	49	)	)	PUNCT
ejpam-4772	231	50	=	=	SYM
ejpam-4772	232	1	1−	1−	NUM
ejpam-4772	232	2	p21	p21	PROPN
ejpam-4772	232	3	√	√	PROPN
ejpam-4772	232	4	δ	δ	PROPN
ejpam-4772	232	5	(	(	PUNCT
ejpam-4772	232	6	2	2	NUM
ejpam-4772	232	7	+	+	NUM
ejpam-4772	232	8	δ)3	δ)3	NOUN
ejpam-4772	232	9	:	:	PUNCT
ejpam-4772	232	10	=	=	SYM
ejpam-4772	232	11	φ(p1	φ(p1	NOUN
ejpam-4772	232	12	)	)	PUNCT
ejpam-4772	232	13	(	(	PUNCT
ejpam-4772	232	14	24	24	NUM
ejpam-4772	232	15	)	)	PUNCT
ejpam-4772	232	16	the	the	DET
ejpam-4772	232	17	derivative	derivative	NOUN
ejpam-4772	232	18	of	of	ADP
ejpam-4772	232	19	(	(	PUNCT
ejpam-4772	232	20	24	24	NUM
ejpam-4772	232	21	)	)	PUNCT
ejpam-4772	232	22	is	be	AUX
ejpam-4772	232	23	,	,	PUNCT
ejpam-4772	232	24	φ	φ	PROPN
ejpam-4772	232	25	′	′	NUM
ejpam-4772	232	26	(	(	PUNCT
ejpam-4772	232	27	p1	p1	PROPN
ejpam-4772	232	28	)	)	PUNCT
ejpam-4772	232	29	=	=	NOUN
ejpam-4772	232	30	−2p1	−2p1	NOUN
ejpam-4772	232	31	√	√	PUNCT
ejpam-4772	232	32	δ	δ	PROPN
ejpam-4772	232	33	(	(	PUNCT
ejpam-4772	232	34	2	2	NUM
ejpam-4772	232	35	+	+	NUM
ejpam-4772	232	36	δ)3	δ)3	NOUN
ejpam-4772	232	37	≤	≤	X
ejpam-4772	232	38	0	0	NUM
ejpam-4772	233	1	(	(	PUNCT
ejpam-4772	233	2	25	25	NUM
ejpam-4772	233	3	)	)	PUNCT
ejpam-4772	233	4	for	for	ADP
ejpam-4772	233	5	all	all	DET
ejpam-4772	233	6	p1	p1	NOUN
ejpam-4772	233	7	∈	∈	PROPN
ejpam-4772	234	1	[	[	X
ejpam-4772	234	2	0	0	NUM
ejpam-4772	234	3	,	,	PUNCT
ejpam-4772	234	4	2	2	NUM
ejpam-4772	234	5	]	]	PUNCT
ejpam-4772	234	6	and	and	CCONJ
ejpam-4772	234	7	δ	δ	X
ejpam-4772	234	8	>	>	X
ejpam-4772	234	9	0	0	X
ejpam-4772	234	10	.	.	PUNCT
ejpam-4772	235	1	according	accord	VERB
ejpam-4772	235	2	to	to	ADP
ejpam-4772	235	3	(	(	PUNCT
ejpam-4772	235	4	25	25	NUM
ejpam-4772	235	5	)	)	PUNCT
ejpam-4772	235	6	,	,	PUNCT
ejpam-4772	235	7	φ(p1	φ(p1	NOUN
ejpam-4772	235	8	)	)	PUNCT
ejpam-4772	235	9	is	be	AUX
ejpam-4772	235	10	monoton	monoton	NOUN
ejpam-4772	235	11	decreasing	decrease	VERB
ejpam-4772	235	12	function	function	NOUN
ejpam-4772	235	13	,	,	PUNCT
ejpam-4772	235	14	so	so	CCONJ
ejpam-4772	235	15	the	the	DET
ejpam-4772	235	16	maximum	maximum	ADJ
ejpam-4772	235	17	value	value	NOUN
ejpam-4772	235	18	of	of	ADP
ejpam-4772	235	19	φ(0	φ(0	ADJ
ejpam-4772	235	20	)	)	PUNCT
ejpam-4772	235	21	=	=	SYM
ejpam-4772	236	1	1	1	X
ejpam-4772	236	2	.	.	PUNCT
ejpam-4772	237	1	the	the	DET
ejpam-4772	237	2	inequality	inequality	NOUN
ejpam-4772	237	3	boundary	boundary	NOUN
ejpam-4772	237	4	is	be	AUX
ejpam-4772	237	5	sharp	sharp	ADJ
ejpam-4772	237	6	for	for	ADP
ejpam-4772	237	7	p1	p1	NOUN
ejpam-4772	237	8	=	=	NOUN
ejpam-4772	237	9	0	0	X
ejpam-4772	237	10	.	.	PUNCT
ejpam-4772	238	1	the	the	DET
ejpam-4772	238	2	proof	proof	NOUN
ejpam-4772	238	3	is	be	AUX
ejpam-4772	238	4	completed	complete	VERB
ejpam-4772	238	5	.	.	PUNCT
ejpam-4772	239	1	this	this	DET
ejpam-4772	239	2	research	research	NOUN
ejpam-4772	239	3	,	,	PUNCT
ejpam-4772	239	4	we	we	PRON
ejpam-4772	239	5	also	also	ADV
ejpam-4772	239	6	obtain	obtain	VERB
ejpam-4772	239	7	the	the	DET
ejpam-4772	239	8	upper	upper	ADJ
ejpam-4772	239	9	bounds	bound	NOUN
ejpam-4772	239	10	of	of	ADP
ejpam-4772	239	11	the	the	DET
ejpam-4772	239	12	determinant	determinant	ADJ
ejpam-4772	239	13	hankel	hankel	NOUN
ejpam-4772	239	14	h2(1	h2(1	PROPN
ejpam-4772	239	15	)	)	PUNCT
ejpam-4772	239	16	using	use	VERB
ejpam-4772	239	17	coefficients	coefficient	NOUN
ejpam-4772	239	18	invers	inver	NOUN
ejpam-4772	239	19	function	function	PROPN
ejpam-4772	239	20	.	.	PUNCT
ejpam-4772	240	1	theorem	theorem	VERB
ejpam-4772	240	2	4	4	NUM
ejpam-4772	240	3	.	.	PUNCT
ejpam-4772	241	1	if	if	SCONJ
ejpam-4772	241	2	f	f	PROPN
ejpam-4772	241	3	∈	∈	PROPN
ejpam-4772	241	4	b1(α	b1(α	PROPN
ejpam-4772	241	5	,	,	PUNCT
ejpam-4772	241	6	δ	δ	PROPN
ejpam-4772	241	7	)	)	PUNCT
ejpam-4772	241	8	for	for	ADP
ejpam-4772	241	9	0	0	NUM
ejpam-4772	241	10	≤	≤	NUM
ejpam-4772	241	11	α	α	NOUN
ejpam-4772	241	12	≤	≤	NOUN
ejpam-4772	241	13	0	0	NUM
ejpam-4772	241	14	and	and	CCONJ
ejpam-4772	241	15	0	0	NUM
ejpam-4772	241	16	<	<	X
ejpam-4772	241	17	δ	δ	PROPN
ejpam-4772	241	18	≤	≤	ADV
ejpam-4772	241	19	1	1	NUM
ejpam-4772	241	20	then	then	ADV
ejpam-4772	241	21	h2(1	h2(1	PROPN
ejpam-4772	241	22	)	)	PUNCT
ejpam-4772	241	23	=	=	SYM
ejpam-4772	241	24	|a1a3	|a1a3	PROPN
ejpam-4772	241	25	−a2	−a2	NOUN
ejpam-4772	241	26	2|	2|	NUM
ejpam-4772	241	27	≤	≤	NUM
ejpam-4772	241	28	√	√	ADV
ejpam-4772	241	29	2	2	NUM
ejpam-4772	241	30	√	√	PROPN
ejpam-4772	241	31	δ	δ	PROPN
ejpam-4772	241	32	(	(	PUNCT
ejpam-4772	241	33	2	2	NUM
ejpam-4772	241	34	+	+	NUM
ejpam-4772	241	35	α)(1	α)(1	X
ejpam-4772	242	1	+	+	CCONJ
ejpam-4772	242	2	δ)3/2	δ)3/2	PROPN
ejpam-4772	242	3	,	,	PUNCT
ejpam-4772	242	4	(	(	PUNCT
ejpam-4772	242	5	26	26	NUM
ejpam-4772	242	6	)	)	PUNCT
ejpam-4772	242	7	and	and	CCONJ
ejpam-4772	242	8	the	the	DET
ejpam-4772	242	9	inequality	inequality	NOUN
ejpam-4772	242	10	is	be	AUX
ejpam-4772	242	11	sharp	sharp	ADJ
ejpam-4772	242	12	.	.	PUNCT
ejpam-4772	243	1	proof	proof	NOUN
ejpam-4772	243	2	.	.	PUNCT
ejpam-4772	244	1	let	let	VERB
ejpam-4772	244	2	the	the	DET
ejpam-4772	244	3	coefficients	coefficient	NOUN
ejpam-4772	244	4	on	on	ADP
ejpam-4772	244	5	the	the	DET
ejpam-4772	244	6	inverse	inverse	NOUN
ejpam-4772	244	7	function	function	NOUN
ejpam-4772	244	8	are	be	AUX
ejpam-4772	244	9	a1	a1	PROPN
ejpam-4772	244	10	,	,	PUNCT
ejpam-4772	244	11	a2	a2	PROPN
ejpam-4772	244	12	and	and	CCONJ
ejpam-4772	244	13	a3	a3	NOUN
ejpam-4772	244	14	by	by	ADP
ejpam-4772	244	15	[	[	X
ejpam-4772	244	16	11	11	NUM
ejpam-4772	244	17	]	]	PUNCT
ejpam-4772	244	18	gives	give	VERB
ejpam-4772	244	19	,	,	PUNCT
ejpam-4772	244	20	a2	a2	PROPN
ejpam-4772	244	21	=	=	SYM
ejpam-4772	244	22	−	−	PROPN
ejpam-4772	244	23	p1	p1	NOUN
ejpam-4772	244	24	√	√	NOUN
ejpam-4772	244	25	α√	α√	NUM
ejpam-4772	244	26	2(1	2(1	NUM
ejpam-4772	245	1	+	+	CCONJ
ejpam-4772	245	2	δ)3/2	δ)3/2	PROPN
ejpam-4772	245	3	,	,	PUNCT
ejpam-4772	245	4	(	(	PUNCT
ejpam-4772	245	5	27	27	NUM
ejpam-4772	245	6	)	)	PUNCT
ejpam-4772	245	7	a3	a3	NOUN
ejpam-4772	245	8	=	=	NOUN
ejpam-4772	245	9	1	1	NUM
ejpam-4772	245	10	8(2	8(2	NUM
ejpam-4772	246	1	+	+	CCONJ
ejpam-4772	246	2	α)(1	α)(1	NUM
ejpam-4772	246	3	+	+	CCONJ
ejpam-4772	246	4	δ)7/8	δ)7/8	X
ejpam-4772	246	5	(	(	PUNCT
ejpam-4772	246	6	−	−	PROPN
ejpam-4772	246	7	√	√	NOUN
ejpam-4772	246	8	δ(4	δ(4	VERB
ejpam-4772	246	9	√	√	NUM
ejpam-4772	246	10	2p2(1	2p2(1	NUM
ejpam-4772	246	11	+	+	CCONJ
ejpam-4772	246	12	δ)2	δ)2	PROPN
ejpam-4772	246	13	+	+	PROPN
ejpam-4772	246	14	p21	p21	NOUN
ejpam-4772	246	15	(	(	PUNCT
ejpam-4772	246	16	√	√	ADV
ejpam-4772	246	17	2	2	NUM
ejpam-4772	246	18	+	+	CCONJ
ejpam-4772	246	19	5	5	NUM
ejpam-4772	246	20	√	√	NUM
ejpam-4772	246	21	2)δ	2)δ	NOUN
ejpam-4772	246	22	+	+	CCONJ
ejpam-4772	246	23	4	4	NUM
ejpam-4772	246	24	√	√	NOUN
ejpam-4772	246	25	2δ2	2δ2	NUM
ejpam-4772	246	26	−	−	ADP
ejpam-4772	246	27	2(−2	2(−2	NUM
ejpam-4772	247	1	+	+	CCONJ
ejpam-4772	247	2	α+	α+	PUNCT
ejpam-4772	247	3	α2	α2	ADJ
ejpam-4772	247	4	√	√	PROPN
ejpam-4772	247	5	δ	δ	PROPN
ejpam-4772	247	6	√	√	ADV
ejpam-4772	247	7	1	1	NUM
ejpam-4772	247	8	+	+	NUM
ejpam-4772	247	9	δ	δ	NOUN
ejpam-4772	247	10	)	)	PUNCT
ejpam-4772	247	11	)	)	PUNCT
ejpam-4772	247	12	.	.	PUNCT
ejpam-4772	248	1	(	(	PUNCT
ejpam-4772	248	2	28	28	NUM
ejpam-4772	248	3	)	)	PUNCT
ejpam-4772	248	4	from	from	ADP
ejpam-4772	248	5	(	(	PUNCT
ejpam-4772	248	6	4	4	X
ejpam-4772	248	7	)	)	PUNCT
ejpam-4772	248	8	we	we	PRON
ejpam-4772	248	9	have	have	AUX
ejpam-4772	248	10	h2(1	h2(1	PROPN
ejpam-4772	248	11	)	)	PUNCT
ejpam-4772	248	12	,	,	PUNCT
ejpam-4772	248	13	h2(1	h2(1	PROPN
ejpam-4772	248	14	)	)	PUNCT
ejpam-4772	248	15	=	=	SYM
ejpam-4772	248	16	∣∣∣∣a1	∣∣∣∣a1	NOUN
ejpam-4772	248	17	a2	a2	PROPN
ejpam-4772	248	18	a2	a2	PROPN
ejpam-4772	248	19	a3	a3	NOUN
ejpam-4772	248	20	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4772	248	21	=	=	SYM
ejpam-4772	248	22	|a1a3	|a1a3	NOUN
ejpam-4772	248	23	−a2	−a2	NOUN
ejpam-4772	248	24	2|	2|	NUM
ejpam-4772	248	25	=	=	PUNCT
ejpam-4772	249	1	∣∣∣∣∣−	∣∣∣∣∣−	PROPN
ejpam-4772	249	2	p2	p2	VERB
ejpam-4772	249	3	√	√	NOUN
ejpam-4772	249	4	δ√	δ√	SYM
ejpam-4772	249	5	2(2	2(2	NUM
ejpam-4772	249	6	+	+	NUM
ejpam-4772	249	7	α)(1	α)(1	NUM
ejpam-4772	250	1	+	+	CCONJ
ejpam-4772	250	2	δ)3/2	δ)3/2	PROPN
ejpam-4772	250	3	n.m	n.m	PROPN
ejpam-4772	250	4	.	.	PROPN
ejpam-4772	250	5	asih	asih	PROPN
ejpam-4772	250	6	et	et	PROPN
ejpam-4772	250	7	al	al	PROPN
ejpam-4772	250	8	.	.	PUNCT
ejpam-4772	250	9	/	/	SYM
ejpam-4772	250	10	eur	eur	PROPN
ejpam-4772	250	11	.	.	PUNCT
ejpam-4772	251	1	j.	j.	PROPN
ejpam-4772	251	2	pure	pure	PROPN
ejpam-4772	251	3	appl	appl	PROPN
ejpam-4772	251	4	.	.	PROPN
ejpam-4772	251	5	math	math	PROPN
ejpam-4772	251	6	,	,	PUNCT
ejpam-4772	251	7	16	16	NUM
ejpam-4772	251	8	(	(	PUNCT
ejpam-4772	251	9	2	2	NUM
ejpam-4772	251	10	)	)	PUNCT
ejpam-4772	251	11	(	(	PUNCT
ejpam-4772	251	12	2023	2023	NUM
ejpam-4772	251	13	)	)	PUNCT
ejpam-4772	251	14	,	,	PUNCT
ejpam-4772	251	15	1290	1290	NUM
ejpam-4772	251	16	-	-	SYM
ejpam-4772	251	17	1301	1301	NUM
ejpam-4772	251	18	1299	1299	NUM
ejpam-4772	251	19	+	+	CCONJ
ejpam-4772	251	20	p21	p21	PROPN
ejpam-4772	251	21	√	√	NUM
ejpam-4772	251	22	δ	δ	PROPN
ejpam-4772	251	23	(	(	PUNCT
ejpam-4772	251	24	√	√	ADV
ejpam-4772	251	25	2	2	NUM
ejpam-4772	251	26	+	+	CCONJ
ejpam-4772	251	27	5	5	NUM
ejpam-4772	251	28	√	√	NUM
ejpam-4772	251	29	2δ	2δ	NUM
ejpam-4772	251	30	+	+	CCONJ
ejpam-4772	251	31	4	4	NUM
ejpam-4772	251	32	√	√	NUM
ejpam-4772	251	33	2δ2	2δ2	NUM
ejpam-4772	252	1	+	+	SYM
ejpam-4772	252	2	2(−14−	2(−14−	NUM
ejpam-4772	252	3	5α+	5α+	NUM
ejpam-4772	252	4	α2	α2	VERB
ejpam-4772	252	5	)	)	PUNCT
ejpam-4772	252	6	√	√	PROPN
ejpam-4772	253	1	δ	δ	NOUN
ejpam-4772	253	2	√	√	ADV
ejpam-4772	253	3	1	1	NUM
ejpam-4772	253	4	+	+	NUM
ejpam-4772	253	5	δ	δ	PROPN
ejpam-4772	253	6	)	)	PUNCT
ejpam-4772	253	7	8(2	8(2	PROPN
ejpam-4772	254	1	+	+	CCONJ
ejpam-4772	254	2	α)(1	α)(1	PRON
ejpam-4772	255	1	+	+	CCONJ
ejpam-4772	255	2	δ)7/2	δ)7/2	X
ejpam-4772	255	3	∣∣∣∣∣.	∣∣∣∣∣.	PROPN
ejpam-4772	255	4	(	(	PUNCT
ejpam-4772	255	5	29	29	NUM
ejpam-4772	255	6	)	)	PUNCT
ejpam-4772	255	7	applying	apply	VERB
ejpam-4772	255	8	(	(	PUNCT
ejpam-4772	255	9	29	29	NUM
ejpam-4772	255	10	)	)	PUNCT
ejpam-4772	255	11	,	,	PUNCT
ejpam-4772	255	12	lemma	lemma	PROPN
ejpam-4772	255	13	2	2	NUM
ejpam-4772	255	14	,	,	PUNCT
ejpam-4772	255	15	and	and	CCONJ
ejpam-4772	255	16	taking	take	VERB
ejpam-4772	255	17	p1	p1	NOUN
ejpam-4772	255	18	=	=	PROPN
ejpam-4772	255	19	p	p	PROPN
ejpam-4772	255	20	and	and	CCONJ
ejpam-4772	255	21	0	0	NUM
ejpam-4772	255	22	≤	≤	NOUN
ejpam-4772	255	23	p	p	NOUN
ejpam-4772	255	24	≤	≤	ADJ
ejpam-4772	255	25	2	2	NUM
ejpam-4772	255	26	gives	give	NOUN
ejpam-4772	255	27	,	,	PUNCT
ejpam-4772	255	28	h2(1	h2(1	PROPN
ejpam-4772	255	29	)	)	PUNCT
ejpam-4772	255	30	=	=	PUNCT
ejpam-4772	256	1	∣∣∣∣∣−	∣∣∣∣∣−	PROPN
ejpam-4772	256	2	(	(	PUNCT
ejpam-4772	256	3	p2	p2	PROPN
ejpam-4772	256	4	+	+	CCONJ
ejpam-4772	256	5	(	(	PUNCT
ejpam-4772	256	6	4−	4−	NOUN
ejpam-4772	256	7	p2)x	p2)x	NOUN
ejpam-4772	256	8	)	)	PUNCT
ejpam-4772	256	9	√	√	PROPN
ejpam-4772	256	10	δ	δ	NOUN
ejpam-4772	256	11	2	2	NUM
ejpam-4772	256	12	√	√	NUM
ejpam-4772	256	13	2(2	2(2	NUM
ejpam-4772	256	14	+	+	CCONJ
ejpam-4772	256	15	α)(1	α)(1	NUM
ejpam-4772	257	1	+	+	CCONJ
ejpam-4772	257	2	δ)3/2	δ)3/2	VERB
ejpam-4772	258	1	+	+	CCONJ
ejpam-4772	258	2	p2	p2	PROPN
ejpam-4772	258	3	√	√	NUM
ejpam-4772	258	4	δ	δ	PROPN
ejpam-4772	258	5	(	(	PUNCT
ejpam-4772	258	6	√	√	ADV
ejpam-4772	258	7	2	2	NUM
ejpam-4772	258	8	+	+	CCONJ
ejpam-4772	258	9	5	5	NUM
ejpam-4772	258	10	√	√	NUM
ejpam-4772	258	11	2δ	2δ	NUM
ejpam-4772	258	12	+	+	CCONJ
ejpam-4772	258	13	4	4	NUM
ejpam-4772	258	14	√	√	NUM
ejpam-4772	258	15	2δ2	2δ2	NUM
ejpam-4772	258	16	+	+	SYM
ejpam-4772	258	17	2(−14−	2(−14−	NUM
ejpam-4772	258	18	5α+	5α+	NUM
ejpam-4772	258	19	α2	α2	VERB
ejpam-4772	258	20	)	)	PUNCT
ejpam-4772	258	21	√	√	PROPN
ejpam-4772	259	1	δ	δ	NOUN
ejpam-4772	259	2	√	√	ADV
ejpam-4772	259	3	1	1	NUM
ejpam-4772	259	4	+	+	NUM
ejpam-4772	259	5	δ	δ	PROPN
ejpam-4772	259	6	)	)	PUNCT
ejpam-4772	259	7	8(2	8(2	PROPN
ejpam-4772	260	1	+	+	CCONJ
ejpam-4772	260	2	α)(1	α)(1	PRON
ejpam-4772	261	1	+	+	CCONJ
ejpam-4772	261	2	δ)7/2	δ)7/2	PUNCT
ejpam-4772	261	3	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-4772	261	4	=	=	SYM
ejpam-4772	262	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-4772	262	2	(	(	PUNCT
ejpam-4772	262	3	4−	4−	NOUN
ejpam-4772	262	4	p2)x	p2)x	NOUN
ejpam-4772	262	5	√	√	PROPN
ejpam-4772	262	6	δ	δ	PROPN
ejpam-4772	262	7	2	2	NUM
ejpam-4772	262	8	√	√	NUM
ejpam-4772	262	9	2(2	2(2	NUM
ejpam-4772	263	1	+	+	CCONJ
ejpam-4772	263	2	α)(1	α)(1	NUM
ejpam-4772	264	1	+	+	CCONJ
ejpam-4772	264	2	δ)3/2	δ)3/2	VERB
ejpam-4772	265	1	+	+	CCONJ
ejpam-4772	265	2	p2	p2	PROPN
ejpam-4772	265	3	√	√	PROPN
ejpam-4772	265	4	δ(3	δ(3	PROPN
ejpam-4772	265	5	√	√	ADP
ejpam-4772	265	6	2	2	NUM
ejpam-4772	265	7	+	+	CCONJ
ejpam-4772	265	8	9	9	NUM
ejpam-4772	265	9	√	√	NUM
ejpam-4772	265	10	2δ	2δ	NUM
ejpam-4772	265	11	+	+	CCONJ
ejpam-4772	265	12	6	6	NUM
ejpam-4772	265	13	√	√	NUM
ejpam-4772	265	14	2δ2	2δ2	NUM
ejpam-4772	265	15	+	+	SYM
ejpam-4772	265	16	2(−14−	2(−14−	NUM
ejpam-4772	265	17	5α+	5α+	NUM
ejpam-4772	265	18	α2	α2	VERB
ejpam-4772	265	19	)	)	PUNCT
ejpam-4772	265	20	√	√	PROPN
ejpam-4772	266	1	δ	δ	NOUN
ejpam-4772	266	2	√	√	ADV
ejpam-4772	266	3	1	1	NUM
ejpam-4772	266	4	+	+	NUM
ejpam-4772	266	5	δ	δ	PROPN
ejpam-4772	266	6	)	)	PUNCT
ejpam-4772	266	7	8(2	8(2	PROPN
ejpam-4772	267	1	+	+	CCONJ
ejpam-4772	267	2	α)(1	α)(1	PRON
ejpam-4772	268	1	+	+	CCONJ
ejpam-4772	268	2	δ)7/2	δ)7/2	X
ejpam-4772	268	3	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-4772	268	4	(	(	PUNCT
ejpam-4772	268	5	30	30	NUM
ejpam-4772	268	6	)	)	PUNCT
ejpam-4772	268	7	case	case	NOUN
ejpam-4772	268	8	1	1	NUM
ejpam-4772	268	9	.	.	PUNCT
ejpam-4772	269	1	when	when	SCONJ
ejpam-4772	269	2	0	0	NUM
ejpam-4772	269	3	≤	≤	NUM
ejpam-4772	269	4	α	α	NOUN
ejpam-4772	269	5	≤	≤	NOUN
ejpam-4772	269	6	1	1	NUM
ejpam-4772	269	7	and	and	CCONJ
ejpam-4772	269	8	0	0	NUM
ejpam-4772	269	9	<	<	X
ejpam-4772	269	10	δ	δ	X
ejpam-4772	269	11	<	<	X
ejpam-4772	269	12	δ1(α	δ1(α	X
ejpam-4772	269	13	)	)	PUNCT
ejpam-4772	269	14	,	,	PUNCT
ejpam-4772	269	15	with	with	ADP
ejpam-4772	269	16	δ1(α	δ1(α	NOUN
ejpam-4772	269	17	)	)	PUNCT
ejpam-4772	269	18	is	be	AUX
ejpam-4772	269	19	real	real	ADJ
ejpam-4772	269	20	number	number	NOUN
ejpam-4772	269	21	root	root	NOUN
ejpam-4772	269	22	of	of	ADP
ejpam-4772	269	23	the	the	DET
ejpam-4772	269	24	equation	equation	NOUN
ejpam-4772	269	25	1	1	NUM
ejpam-4772	269	26	+	+	CCONJ
ejpam-4772	269	27	(	(	PUNCT
ejpam-4772	269	28	−383−	−383−	ADP
ejpam-4772	269	29	280α+	280α+	NUM
ejpam-4772	269	30	6α2	6α2	NUM
ejpam-4772	270	1	+	+	CCONJ
ejpam-4772	271	1	20α3	20α3	NUM
ejpam-4772	271	2	−	−	NOUN
ejpam-4772	271	3	2α4)x+	2α4)x+	NOUN
ejpam-4772	272	1	24x2	24x2	NUM
ejpam-4772	272	2	+	+	CCONJ
ejpam-4772	272	3	16x3	16x3	NUM
ejpam-4772	272	4	=	=	SYM
ejpam-4772	272	5	0	0	X
ejpam-4772	272	6	.	.	PUNCT
ejpam-4772	273	1	from	from	ADP
ejpam-4772	273	2	(	(	PUNCT
ejpam-4772	273	3	30	30	NUM
ejpam-4772	273	4	)	)	PUNCT
ejpam-4772	273	5	,	,	PUNCT
ejpam-4772	273	6	if	if	SCONJ
ejpam-4772	273	7	|x|	|x|	PROPN
ejpam-4772	273	8	≤	≤	NOUN
ejpam-4772	273	9	1	1	NUM
ejpam-4772	273	10	then	then	ADV
ejpam-4772	273	11	,	,	PUNCT
ejpam-4772	273	12	h2(1	h2(1	PROPN
ejpam-4772	273	13	)	)	PUNCT
ejpam-4772	273	14	≤	≤	NOUN
ejpam-4772	273	15	(	(	PUNCT
ejpam-4772	273	16	4−	4−	NOUN
ejpam-4772	273	17	p2)|x|	p2)|x|	NOUN
ejpam-4772	273	18	√	√	PROPN
ejpam-4772	273	19	δ	δ	PROPN
ejpam-4772	273	20	2	2	NUM
ejpam-4772	273	21	√	√	NUM
ejpam-4772	273	22	2(2	2(2	NUM
ejpam-4772	273	23	+	+	CCONJ
ejpam-4772	273	24	α)(1	α)(1	NUM
ejpam-4772	274	1	+	+	CCONJ
ejpam-4772	274	2	δ)3/2	δ)3/2	VERB
ejpam-4772	275	1	+	+	CCONJ
ejpam-4772	275	2	p2	p2	PROPN
ejpam-4772	275	3	√	√	PROPN
ejpam-4772	275	4	δ(3	δ(3	PROPN
ejpam-4772	275	5	√	√	ADP
ejpam-4772	275	6	2	2	NUM
ejpam-4772	275	7	+	+	CCONJ
ejpam-4772	275	8	9	9	NUM
ejpam-4772	275	9	√	√	NUM
ejpam-4772	275	10	2δ	2δ	NUM
ejpam-4772	275	11	+	+	CCONJ
ejpam-4772	275	12	6	6	NUM
ejpam-4772	275	13	√	√	NUM
ejpam-4772	275	14	2δ2	2δ2	NUM
ejpam-4772	275	15	+	+	SYM
ejpam-4772	275	16	2(−14−	2(−14−	NUM
ejpam-4772	275	17	5α+	5α+	NUM
ejpam-4772	275	18	α2	α2	VERB
ejpam-4772	275	19	)	)	PUNCT
ejpam-4772	275	20	√	√	PROPN
ejpam-4772	276	1	δ	δ	NOUN
ejpam-4772	276	2	√	√	ADV
ejpam-4772	276	3	1	1	NUM
ejpam-4772	276	4	+	+	NUM
ejpam-4772	276	5	δ	δ	PROPN
ejpam-4772	276	6	)	)	PUNCT
ejpam-4772	276	7	8(2	8(2	PROPN
ejpam-4772	277	1	+	+	CCONJ
ejpam-4772	277	2	α)(1	α)(1	PRON
ejpam-4772	278	1	+	+	CCONJ
ejpam-4772	278	2	δ)7/2	δ)7/2	X
ejpam-4772	278	3	≤	≤	ADV
ejpam-4772	278	4	2	2	NUM
ejpam-4772	278	5	√	√	NOUN
ejpam-4772	278	6	δ√	δ√	NUM
ejpam-4772	278	7	2(2	2(2	NUM
ejpam-4772	278	8	+	+	NUM
ejpam-4772	278	9	α)(1	α)(1	NUM
ejpam-4772	279	1	+	+	CCONJ
ejpam-4772	279	2	δ)3/2	δ)3/2	VERB
ejpam-4772	280	1	+	+	CCONJ
ejpam-4772	280	2	p2	p2	PROPN
ejpam-4772	280	3	√	√	PROPN
ejpam-4772	280	4	δ(3	δ(3	PROPN
ejpam-4772	280	5	√	√	ADP
ejpam-4772	280	6	2	2	NUM
ejpam-4772	280	7	+	+	CCONJ
ejpam-4772	280	8	9	9	NUM
ejpam-4772	280	9	√	√	NUM
ejpam-4772	280	10	2δ	2δ	NUM
ejpam-4772	280	11	+	+	CCONJ
ejpam-4772	280	12	6	6	NUM
ejpam-4772	280	13	√	√	NUM
ejpam-4772	280	14	2δ2	2δ2	NUM
ejpam-4772	280	15	+	+	SYM
ejpam-4772	280	16	2(−14−	2(−14−	NUM
ejpam-4772	280	17	5α+	5α+	NUM
ejpam-4772	280	18	α2	α2	VERB
ejpam-4772	280	19	)	)	PUNCT
ejpam-4772	280	20	√	√	PROPN
ejpam-4772	281	1	δ	δ	NOUN
ejpam-4772	281	2	√	√	ADV
ejpam-4772	281	3	1	1	NUM
ejpam-4772	281	4	+	+	NUM
ejpam-4772	281	5	δ	δ	PROPN
ejpam-4772	281	6	)	)	PUNCT
ejpam-4772	281	7	8(2	8(2	PROPN
ejpam-4772	282	1	+	+	CCONJ
ejpam-4772	282	2	α)(1	α)(1	PRON
ejpam-4772	283	1	+	+	CCONJ
ejpam-4772	283	2	δ)7/2	δ)7/2	PROPN
ejpam-4772	283	3	:	:	PUNCT
ejpam-4772	283	4	=	=	SYM
ejpam-4772	283	5	φ1(α	φ1(α	PROPN
ejpam-4772	283	6	,	,	PUNCT
ejpam-4772	283	7	δ	δ	PROPN
ejpam-4772	283	8	,	,	PUNCT
ejpam-4772	283	9	p	p	NOUN
ejpam-4772	283	10	)	)	PUNCT
ejpam-4772	283	11	.	.	PUNCT
ejpam-4772	284	1	(	(	PUNCT
ejpam-4772	284	2	31	31	NUM
ejpam-4772	284	3	)	)	PUNCT
ejpam-4772	284	4	let	let	VERB
ejpam-4772	284	5	the	the	DET
ejpam-4772	284	6	derivative	derivative	NOUN
ejpam-4772	284	7	of	of	ADP
ejpam-4772	284	8	φ1(α	φ1(α	PROPN
ejpam-4772	284	9	,	,	PUNCT
ejpam-4772	284	10	δ	δ	PROPN
ejpam-4772	284	11	,	,	PUNCT
ejpam-4772	284	12	p	p	NOUN
ejpam-4772	284	13	)	)	PUNCT
ejpam-4772	284	14	with	with	ADP
ejpam-4772	284	15	respect	respect	NOUN
ejpam-4772	284	16	to	to	ADP
ejpam-4772	284	17	p	p	NOUN
ejpam-4772	284	18	is	be	AUX
ejpam-4772	284	19	φ′	φ′	NUM
ejpam-4772	284	20	1(α	1(α	NUM
ejpam-4772	284	21	,	,	PUNCT
ejpam-4772	284	22	δ	δ	PROPN
ejpam-4772	284	23	,	,	PUNCT
ejpam-4772	284	24	p	p	NOUN
ejpam-4772	284	25	)	)	PUNCT
ejpam-4772	284	26	.	.	PUNCT
ejpam-4772	285	1	by	by	ADP
ejpam-4772	285	2	solving	solve	VERB
ejpam-4772	285	3	φ′	φ′	NUM
ejpam-4772	285	4	1(α	1(α	NUM
ejpam-4772	285	5	,	,	PUNCT
ejpam-4772	285	6	δ	δ	PROPN
ejpam-4772	285	7	,	,	PUNCT
ejpam-4772	285	8	p	p	NOUN
ejpam-4772	285	9	)	)	PUNCT
ejpam-4772	285	10	=	=	SYM
ejpam-4772	285	11	0	0	NUM
ejpam-4772	285	12	,	,	PUNCT
ejpam-4772	285	13	we	we	PRON
ejpam-4772	285	14	obtain	obtain	VERB
ejpam-4772	285	15	stationary	stationary	ADJ
ejpam-4772	285	16	point	point	NOUN
ejpam-4772	285	17	when	when	SCONJ
ejpam-4772	285	18	p	p	PROPN
ejpam-4772	285	19	=	=	NOUN
ejpam-4772	285	20	0	0	PROPN
ejpam-4772	285	21	.	.	PUNCT
ejpam-4772	286	1	so	so	ADV
ejpam-4772	286	2	we	we	PRON
ejpam-4772	286	3	have	have	VERB
ejpam-4772	286	4	two	two	NUM
ejpam-4772	286	5	critical	critical	ADJ
ejpam-4772	286	6	points	point	NOUN
ejpam-4772	286	7	p	p	X
ejpam-4772	286	8	=	=	NOUN
ejpam-4772	286	9	0	0	NUM
ejpam-4772	286	10	and	and	CCONJ
ejpam-4772	286	11	p	p	X
ejpam-4772	286	12	=	=	ADJ
ejpam-4772	286	13	2	2	X
ejpam-4772	286	14	.	.	NOUN
ejpam-4772	286	15	case	case	NOUN
ejpam-4772	286	16	2	2	NUM
ejpam-4772	286	17	.	.	PUNCT
ejpam-4772	286	18	when	when	SCONJ
ejpam-4772	286	19	0	0	NUM
ejpam-4772	286	20	≤	≤	NUM
ejpam-4772	286	21	α	α	NOUN
ejpam-4772	286	22	≤	≤	NUM
ejpam-4772	286	23	1	1	NUM
ejpam-4772	286	24	and	and	CCONJ
ejpam-4772	286	25	δ1(α	δ1(α	NOUN
ejpam-4772	286	26	)	)	PUNCT
ejpam-4772	286	27	≤	≤	NUM
ejpam-4772	287	1	δ	δ	PROPN
ejpam-4772	287	2	≤	≤	ADV
ejpam-4772	287	3	1	1	NUM
ejpam-4772	287	4	.	.	PUNCT
ejpam-4772	287	5	from	from	ADP
ejpam-4772	287	6	(	(	PUNCT
ejpam-4772	287	7	30	30	NUM
ejpam-4772	287	8	)	)	PUNCT
ejpam-4772	287	9	,	,	PUNCT
ejpam-4772	287	10	if	if	SCONJ
ejpam-4772	287	11	|x|	|x|	PROPN
ejpam-4772	287	12	≤	≤	NOUN
ejpam-4772	287	13	1	1	NUM
ejpam-4772	287	14	then	then	ADV
ejpam-4772	287	15	,	,	PUNCT
ejpam-4772	287	16	h2(1	h2(1	PROPN
ejpam-4772	287	17	)	)	PUNCT
ejpam-4772	287	18	≤	≤	NOUN
ejpam-4772	287	19	(	(	PUNCT
ejpam-4772	287	20	4−	4−	NOUN
ejpam-4772	287	21	p2)|x|	p2)|x|	NOUN
ejpam-4772	287	22	√	√	PROPN
ejpam-4772	287	23	δ	δ	PROPN
ejpam-4772	287	24	2	2	NUM
ejpam-4772	287	25	√	√	NUM
ejpam-4772	287	26	2(2	2(2	NUM
ejpam-4772	287	27	+	+	CCONJ
ejpam-4772	287	28	α)(1	α)(1	NUM
ejpam-4772	288	1	+	+	CCONJ
ejpam-4772	288	2	δ)3/2	δ)3/2	PROPN
ejpam-4772	288	3	references	reference	NOUN
ejpam-4772	288	4	1300	1300	NUM
ejpam-4772	288	5	−p2	−p2	PROPN
ejpam-4772	288	6	√	√	PUNCT
ejpam-4772	288	7	δ(3	δ(3	PROPN
ejpam-4772	288	8	√	√	ADV
ejpam-4772	288	9	2	2	NUM
ejpam-4772	288	10	+	+	CCONJ
ejpam-4772	288	11	9	9	NUM
ejpam-4772	288	12	√	√	NUM
ejpam-4772	288	13	2δ	2δ	NUM
ejpam-4772	288	14	+	+	CCONJ
ejpam-4772	288	15	6	6	NUM
ejpam-4772	288	16	√	√	NUM
ejpam-4772	288	17	2δ2	2δ2	NUM
ejpam-4772	288	18	+	+	SYM
ejpam-4772	288	19	2(−14−	2(−14−	NUM
ejpam-4772	288	20	5α+	5α+	NUM
ejpam-4772	288	21	α2	α2	VERB
ejpam-4772	288	22	)	)	PUNCT
ejpam-4772	288	23	√	√	PROPN
ejpam-4772	289	1	δ	δ	NOUN
ejpam-4772	289	2	√	√	ADV
ejpam-4772	289	3	1	1	NUM
ejpam-4772	289	4	+	+	NUM
ejpam-4772	289	5	δ	δ	PROPN
ejpam-4772	289	6	)	)	PUNCT
ejpam-4772	289	7	8(2	8(2	PROPN
ejpam-4772	290	1	+	+	CCONJ
ejpam-4772	290	2	α)(1	α)(1	PRON
ejpam-4772	291	1	+	+	CCONJ
ejpam-4772	291	2	δ)7/2	δ)7/2	X
ejpam-4772	291	3	≤	≤	ADV
ejpam-4772	291	4	2	2	NUM
ejpam-4772	291	5	√	√	NOUN
ejpam-4772	291	6	δ√	δ√	NUM
ejpam-4772	291	7	2(2	2(2	NUM
ejpam-4772	291	8	+	+	NUM
ejpam-4772	291	9	α)(1	α)(1	NUM
ejpam-4772	292	1	+	+	CCONJ
ejpam-4772	292	2	δ)3/2	δ)3/2	PROPN
ejpam-4772	292	3	−p2	−p2	PROPN
ejpam-4772	292	4	√	√	PUNCT
ejpam-4772	293	1	δ(3	δ(3	PROPN
ejpam-4772	293	2	√	√	ADV
ejpam-4772	293	3	2	2	NUM
ejpam-4772	293	4	+	+	CCONJ
ejpam-4772	293	5	9	9	NUM
ejpam-4772	293	6	√	√	NUM
ejpam-4772	293	7	2δ	2δ	NUM
ejpam-4772	293	8	+	+	CCONJ
ejpam-4772	293	9	6	6	NUM
ejpam-4772	293	10	√	√	NUM
ejpam-4772	293	11	2δ2	2δ2	NUM
ejpam-4772	294	1	+	+	SYM
ejpam-4772	294	2	2(−14−	2(−14−	NUM
ejpam-4772	294	3	5α+	5α+	NUM
ejpam-4772	294	4	α2	α2	VERB
ejpam-4772	294	5	)	)	PUNCT
ejpam-4772	294	6	√	√	PROPN
ejpam-4772	295	1	δ	δ	NOUN
ejpam-4772	295	2	√	√	ADV
ejpam-4772	295	3	1	1	NUM
ejpam-4772	295	4	+	+	NUM
ejpam-4772	295	5	δ	δ	PROPN
ejpam-4772	295	6	)	)	PUNCT
ejpam-4772	295	7	8(2	8(2	PROPN
ejpam-4772	296	1	+	+	CCONJ
ejpam-4772	296	2	α)(1	α)(1	PRON
ejpam-4772	297	1	+	+	CCONJ
ejpam-4772	297	2	δ)7/2	δ)7/2	PROPN
ejpam-4772	297	3	:	:	PUNCT
ejpam-4772	297	4	=	=	SYM
ejpam-4772	297	5	φ1(α	φ1(α	PROPN
ejpam-4772	297	6	,	,	PUNCT
ejpam-4772	297	7	δ	δ	PROPN
ejpam-4772	297	8	,	,	PUNCT
ejpam-4772	297	9	p	p	NOUN
ejpam-4772	297	10	)	)	PUNCT
ejpam-4772	297	11	(	(	PUNCT
ejpam-4772	297	12	32	32	NUM
ejpam-4772	297	13	)	)	PUNCT
ejpam-4772	297	14	the	the	DET
ejpam-4772	297	15	same	same	ADJ
ejpam-4772	297	16	conclusion	conclusion	NOUN
ejpam-4772	297	17	of	of	ADP
ejpam-4772	297	18	case	case	NOUN
ejpam-4772	297	19	1	1	NUM
ejpam-4772	297	20	,	,	PUNCT
ejpam-4772	297	21	let	let	VERB
ejpam-4772	297	22	the	the	DET
ejpam-4772	297	23	derivative	derivative	NOUN
ejpam-4772	297	24	of	of	ADP
ejpam-4772	297	25	φ1(α	φ1(α	PROPN
ejpam-4772	297	26	,	,	PUNCT
ejpam-4772	297	27	δ	δ	PROPN
ejpam-4772	297	28	,	,	PUNCT
ejpam-4772	297	29	p	p	NOUN
ejpam-4772	297	30	)	)	PUNCT
ejpam-4772	297	31	with	with	ADP
ejpam-4772	297	32	respect	respect	NOUN
ejpam-4772	297	33	to	to	ADP
ejpam-4772	297	34	p	p	NOUN
ejpam-4772	297	35	is	be	AUX
ejpam-4772	297	36	φ′	φ′	NUM
ejpam-4772	297	37	1(α	1(α	NUM
ejpam-4772	297	38	,	,	PUNCT
ejpam-4772	297	39	δ	δ	PROPN
ejpam-4772	297	40	,	,	PUNCT
ejpam-4772	297	41	p	p	NOUN
ejpam-4772	297	42	)	)	PUNCT
ejpam-4772	297	43	.	.	PUNCT
ejpam-4772	298	1	by	by	ADP
ejpam-4772	298	2	solving	solve	VERB
ejpam-4772	298	3	φ′	φ′	NUM
ejpam-4772	298	4	1(α	1(α	NUM
ejpam-4772	298	5	,	,	PUNCT
ejpam-4772	298	6	δ	δ	PROPN
ejpam-4772	298	7	,	,	PUNCT
ejpam-4772	298	8	p	p	NOUN
ejpam-4772	298	9	)	)	PUNCT
ejpam-4772	298	10	=	=	SYM
ejpam-4772	298	11	0	0	NUM
ejpam-4772	298	12	,	,	PUNCT
ejpam-4772	298	13	we	we	PRON
ejpam-4772	298	14	obtain	obtain	VERB
ejpam-4772	298	15	stationary	stationary	ADJ
ejpam-4772	298	16	point	point	NOUN
ejpam-4772	298	17	when	when	SCONJ
ejpam-4772	298	18	p	p	PROPN
ejpam-4772	298	19	=	=	NOUN
ejpam-4772	298	20	0	0	PROPN
ejpam-4772	298	21	.	.	PUNCT
ejpam-4772	299	1	so	so	ADV
ejpam-4772	299	2	we	we	PRON
ejpam-4772	299	3	have	have	VERB
ejpam-4772	299	4	two	two	NUM
ejpam-4772	299	5	critical	critical	ADJ
ejpam-4772	299	6	points	point	NOUN
ejpam-4772	299	7	p	p	X
ejpam-4772	299	8	=	=	NOUN
ejpam-4772	299	9	0	0	NUM
ejpam-4772	299	10	and	and	CCONJ
ejpam-4772	299	11	p	p	X
ejpam-4772	299	12	=	=	ADJ
ejpam-4772	299	13	2	2	X
ejpam-4772	299	14	.	.	PUNCT
ejpam-4772	300	1	since	since	SCONJ
ejpam-4772	300	2	φ1(α	φ1(α	PROPN
ejpam-4772	300	3	,	,	PUNCT
ejpam-4772	300	4	δ	δ	PROPN
ejpam-4772	300	5	,	,	PUNCT
ejpam-4772	300	6	0	0	NUM
ejpam-4772	300	7	)	)	PUNCT
ejpam-4772	300	8	≥	≥	NOUN
ejpam-4772	300	9	φ1(α	φ1(α	PROPN
ejpam-4772	300	10	,	,	PUNCT
ejpam-4772	300	11	δ	δ	PROPN
ejpam-4772	300	12	,	,	PUNCT
ejpam-4772	300	13	2	2	NUM
ejpam-4772	300	14	)	)	PUNCT
ejpam-4772	300	15	,	,	PUNCT
ejpam-4772	300	16	then	then	ADV
ejpam-4772	300	17	h2(1	h2(1	PROPN
ejpam-4772	300	18	)	)	PUNCT
ejpam-4772	300	19	≤	≤	PROPN
ejpam-4772	300	20	φ1(α	φ1(α	PROPN
ejpam-4772	300	21	,	,	PUNCT
ejpam-4772	300	22	δ	δ	PROPN
ejpam-4772	300	23	,	,	PUNCT
ejpam-4772	300	24	0	0	NUM
ejpam-4772	300	25	)	)	PUNCT
ejpam-4772	300	26	=	=	SYM
ejpam-4772	301	1	√	√	ADP
ejpam-4772	301	2	2	2	NUM
ejpam-4772	301	3	√	√	PROPN
ejpam-4772	301	4	δ	δ	PROPN
ejpam-4772	301	5	(	(	PUNCT
ejpam-4772	301	6	2	2	NUM
ejpam-4772	301	7	+	+	NUM
ejpam-4772	301	8	α)(1	α)(1	PRON
ejpam-4772	302	1	+	+	CCONJ
ejpam-4772	302	2	δ)3/2	δ)3/2	PROPN
ejpam-4772	302	3	.	.	PUNCT
ejpam-4772	303	1	the	the	DET
ejpam-4772	303	2	inequality	inequality	NOUN
ejpam-4772	303	3	is	be	AUX
ejpam-4772	303	4	sharp	sharp	ADJ
ejpam-4772	303	5	when	when	SCONJ
ejpam-4772	303	6	p1	p1	PROPN
ejpam-4772	303	7	=	=	SYM
ejpam-4772	303	8	0	0	NUM
ejpam-4772	303	9	and	and	CCONJ
ejpam-4772	303	10	p2	p2	PROPN
ejpam-4772	303	11	=	=	SYM
ejpam-4772	303	12	2	2	X
ejpam-4772	303	13	.	.	PUNCT
ejpam-4772	304	1	the	the	DET
ejpam-4772	304	2	proof	proof	NOUN
ejpam-4772	304	3	is	be	AUX
ejpam-4772	304	4	completed	complete	VERB
ejpam-4772	304	5	.	.	PUNCT
ejpam-4772	305	1	acknowledgements	acknowledgement	NOUN
ejpam-4772	305	2	many	many	ADJ
ejpam-4772	305	3	thanks	thank	NOUN
ejpam-4772	305	4	and	and	CCONJ
ejpam-4772	305	5	appreciation	appreciation	NOUN
ejpam-4772	305	6	for	for	ADP
ejpam-4772	305	7	my	my	PRON
ejpam-4772	305	8	supervisor	supervisor	NOUN
ejpam-4772	305	9	marjono	marjono	NOUN
ejpam-4772	305	10	and	and	CCONJ
ejpam-4772	305	11	my	my	PRON
ejpam-4772	305	12	co	co	NOUN
ejpam-4772	305	13	supervisor	supervisor	NOUN
ejpam-4772	305	14	sa‘adatul	sa‘adatul	PROPN
ejpam-4772	305	15	fitri	fitri	PROPN
ejpam-4772	305	16	and	and	CCONJ
ejpam-4772	305	17	ratno	ratno	PROPN
ejpam-4772	305	18	bagus	bagus	PROPN
ejpam-4772	305	19	edy	edy	PROPN
ejpam-4772	305	20	wibowo	wibowo	PROPN
ejpam-4772	305	21	at	at	ADP
ejpam-4772	305	22	the	the	DET
ejpam-4772	305	23	department	department	NOUN
ejpam-4772	305	24	of	of	ADP
ejpam-4772	305	25	mathematics	mathematics	PROPN
ejpam-4772	305	26	and	and	CCONJ
ejpam-4772	305	27	natural	natural	ADJ
ejpam-4772	305	28	sciences	sciences	PROPN
ejpam-4772	305	29	brawijaya	brawijaya	PROPN
ejpam-4772	305	30	university	university	PROPN
ejpam-4772	305	31	,	,	PUNCT
ejpam-4772	305	32	for	for	ADP
ejpam-4772	305	33	their	their	PRON
ejpam-4772	305	34	support	support	NOUN
ejpam-4772	305	35	and	and	CCONJ
ejpam-4772	305	36	guidance	guidance	NOUN
ejpam-4772	305	37	in	in	ADP
ejpam-4772	305	38	completing	complete	VERB
ejpam-4772	305	39	this	this	DET
ejpam-4772	305	40	research	research	NOUN
ejpam-4772	305	41	and	and	CCONJ
ejpam-4772	305	42	this	this	DET
ejpam-4772	305	43	paper	paper	NOUN
ejpam-4772	305	44	.	.	PUNCT
ejpam-4772	306	1	references	reference	NOUN
ejpam-4772	306	2	[	[	X
ejpam-4772	306	3	1	1	NUM
ejpam-4772	306	4	]	]	X
ejpam-4772	306	5	duren	duren	PROPN
ejpam-4772	306	6	,	,	PUNCT
ejpam-4772	306	7	p.l	p.l	PROPN
ejpam-4772	306	8	.	.	PROPN
ejpam-4772	306	9	univalent	univalent	ADJ
ejpam-4772	306	10	function	function	NOUN
ejpam-4772	306	11	.	.	PUNCT
ejpam-4772	307	1	1983	1983	NUM
ejpam-4772	307	2	springer	springer	NOUN
ejpam-4772	307	3	-	-	PUNCT
ejpam-4772	307	4	verlag	verlag	PROPN
ejpam-4772	307	5	.	.	PUNCT
ejpam-4772	308	1	new	new	PROPN
ejpam-4772	308	2	york	york	PROPN
ejpam-4772	308	3	inc	inc	PROPN
ejpam-4772	308	4	.	.	PUNCT
ejpam-4772	309	1	[	[	X
ejpam-4772	309	2	2	2	NUM
ejpam-4772	309	3	]	]	PUNCT
ejpam-4772	309	4	f.	f.	PROPN
ejpam-4772	309	5	muge	muge	PROPN
ejpam-4772	309	6	sakar	sakar	PROPN
ejpam-4772	309	7	and	and	CCONJ
ejpam-4772	309	8	s.	s.	PROPN
ejpam-4772	309	9	melike	melike	PROPN
ejpam-4772	309	10	aydogan	aydogan	PROPN
ejpam-4772	309	11	.	.	PUNCT
ejpam-4772	310	1	inequalities	inequality	NOUN
ejpam-4772	310	2	of	of	ADP
ejpam-4772	310	3	bi	bi	ADJ
ejpam-4772	310	4	-	-	ADJ
ejpam-4772	310	5	starlike	starlike	ADJ
ejpam-4772	310	6	functions	function	NOUN
ejpam-4772	310	7	involving	involve	VERB
ejpam-4772	310	8	sigmoid	sigmoid	NOUN
ejpam-4772	310	9	function	function	NOUN
ejpam-4772	310	10	and	and	CCONJ
ejpam-4772	310	11	bernoulli	bernoulli	NOUN
ejpam-4772	310	12	lemniscate	lemniscate	PROPN
ejpam-4772	310	13	by	by	ADP
ejpam-4772	310	14	subordination	subordination	NOUN
ejpam-4772	310	15	,	,	PUNCT
ejpam-4772	310	16	int	int	NOUN
ejpam-4772	310	17	.	.	PUNCT
ejpam-4772	311	1	j.	j.	PROPN
ejpam-4772	311	2	open	open	PROPN
ejpam-4772	311	3	problems	problem	NOUN
ejpam-4772	311	4	compt	compt	VERB
ejpam-4772	311	5	.	.	PUNCT
ejpam-4772	312	1	math	math	NOUN
ejpam-4772	312	2	.	.	PUNCT
ejpam-4772	312	3	,	,	PUNCT
ejpam-4772	312	4	2023	2023	NUM
ejpam-4772	312	5	,	,	PUNCT
ejpam-4772	312	6	vol	vol	NOUN
ejpam-4772	312	7	.	.	PROPN
ejpam-4772	313	1	16	16	NUM
ejpam-4772	313	2	,	,	PUNCT
ejpam-4772	313	3	no	no	INTJ
ejpam-4772	313	4	.	.	NOUN
ejpam-4772	313	5	1	1	NUM
ejpam-4772	313	6	,	,	PUNCT
ejpam-4772	313	7	pp	pp	ADJ
ejpam-4772	313	8	.	.	PUNCT
ejpam-4772	314	1	71	71	NUM
ejpam-4772	314	2	-	-	SYM
ejpam-4772	314	3	82	82	NUM
ejpam-4772	314	4	.	.	PUNCT
ejpam-4772	315	1	[	[	X
ejpam-4772	315	2	3	3	X
ejpam-4772	315	3	]	]	PUNCT
ejpam-4772	315	4	jahangiri	jahangiri	NOUN
ejpam-4772	315	5	,	,	PUNCT
ejpam-4772	315	6	m.	m.	NOUN
ejpam-4772	315	7	on	on	ADP
ejpam-4772	315	8	the	the	DET
ejpam-4772	315	9	coefficients	coefficient	NOUN
ejpam-4772	315	10	of	of	ADP
ejpam-4772	315	11	powers	power	NOUN
ejpam-4772	315	12	of	of	ADP
ejpam-4772	315	13	a	a	DET
ejpam-4772	315	14	class	class	NOUN
ejpam-4772	315	15	of	of	ADP
ejpam-4772	315	16	bazilevič	bazilevič	NOUN
ejpam-4772	315	17	functions	function	NOUN
ejpam-4772	315	18	,	,	PUNCT
ejpam-4772	315	19	indian	indian	ADJ
ejpam-4772	315	20	j.	j.	PROPN
ejpam-4772	315	21	pure	pure	PROPN
ejpam-4772	315	22	appl	appl	PROPN
ejpam-4772	315	23	.	.	PUNCT
ejpam-4772	315	24	math	math	PROPN
ejpam-4772	315	25	.	.	PUNCT
ejpam-4772	316	1	1986	1986	NUM
ejpam-4772	316	2	,	,	PUNCT
ejpam-4772	316	3	17	17	NUM
ejpam-4772	316	4	(	(	PUNCT
ejpam-4772	316	5	9	9	NUM
ejpam-4772	316	6	)	)	PUNCT
ejpam-4772	316	7	,	,	PUNCT
ejpam-4772	316	8	1140	1140	NUM
ejpam-4772	316	9	-	-	SYM
ejpam-4772	316	10	1144	1144	NUM
ejpam-4772	316	11	.	.	PUNCT
ejpam-4772	317	1	[	[	X
ejpam-4772	317	2	4	4	NUM
ejpam-4772	317	3	]	]	X
ejpam-4772	317	4	jateng	jateng	PROPN
ejpam-4772	317	5	,	,	PUNCT
ejpam-4772	317	6	a.	a.	PROPN
ejpam-4772	317	7	,	,	PUNCT
ejpam-4772	317	8	s.	s.	PROPN
ejpam-4772	317	9	halim	halim	PROPN
ejpam-4772	317	10	,	,	PUNCT
ejpam-4772	317	11	and	and	CCONJ
ejpam-4772	317	12	m.	m.	NOUN
ejpam-4772	317	13	darus	darus	NOUN
ejpam-4772	317	14	.	.	PUNCT
ejpam-4772	318	1	hankel	hankel	NOUN
ejpam-4772	318	2	determinant	determinant	ADJ
ejpam-4772	318	3	for	for	ADP
ejpam-4772	318	4	starlike	starlike	NOUN
ejpam-4772	318	5	and	and	CCONJ
ejpam-4772	318	6	convex	convex	NOUN
ejpam-4772	318	7	functions	function	NOUN
ejpam-4772	318	8	.	.	PUNCT
ejpam-4772	319	1	int	int	NOUN
ejpam-4772	319	2	.	.	PUNCT
ejpam-4772	320	1	journal	journal	PROPN
ejpam-4772	320	2	math	math	PROPN
ejpam-4772	320	3	.	.	PUNCT
ejpam-4772	321	1	analysis	analysis	NOUN
ejpam-4772	321	2	2007	2007	NUM
ejpam-4772	321	3	,	,	PUNCT
ejpam-4772	321	4	13	13	NUM
ejpam-4772	321	5	,	,	PUNCT
ejpam-4772	321	6	619	619	NUM
ejpam-4772	321	7	-	-	SYM
ejpam-4772	321	8	625	625	NUM
ejpam-4772	321	9	.	.	PUNCT
ejpam-4772	322	1	[	[	X
ejpam-4772	322	2	5	5	NUM
ejpam-4772	322	3	]	]	X
ejpam-4772	322	4	khan	khan	PROPN
ejpam-4772	322	5	bilal	bilal	PROPN
ejpam-4772	322	6	,	,	PUNCT
ejpam-4772	322	7	ibtisam	ibtisam	PROPN
ejpam-4772	322	8	aldawish	aldawish	PROPN
ejpam-4772	322	9	,	,	PUNCT
ejpam-4772	322	10	serkan	serkan	ADJ
ejpam-4772	322	11	araci	araci	NOUN
ejpam-4772	322	12	,	,	PUNCT
ejpam-4772	322	13	and	and	CCONJ
ejpam-4772	322	14	muhammad	muhammad	PROPN
ejpam-4772	322	15	ghaffar	ghaffar	PROPN
ejpam-4772	322	16	khan	khan	PROPN
ejpam-4772	322	17	.	.	PUNCT
ejpam-4772	323	1	third	third	ADJ
ejpam-4772	323	2	hankel	hankel	NOUN
ejpam-4772	323	3	determinant	determinant	ADJ
ejpam-4772	323	4	for	for	ADP
ejpam-4772	323	5	the	the	DET
ejpam-4772	323	6	logarithimic	logarithimic	ADJ
ejpam-4772	323	7	coefficients	coefficient	NOUN
ejpam-4772	323	8	of	of	ADP
ejpam-4772	323	9	starlike	starlike	NOUN
ejpam-4772	323	10	functions	function	NOUN
ejpam-4772	323	11	assosiated	assosiate	VERB
ejpam-4772	323	12	with	with	ADP
ejpam-4772	323	13	sine	sine	ADJ
ejpam-4772	323	14	function	function	NOUN
ejpam-4772	323	15	,	,	PUNCT
ejpam-4772	323	16	fratal	fratal	ADJ
ejpam-4772	323	17	and	and	CCONJ
ejpam-4772	323	18	fractinal	fractinal	ADJ
ejpam-4772	323	19	,	,	PUNCT
ejpam-4772	323	20	mdpi	mdpi	PROPN
ejpam-4772	323	21	garman	garman	NOUN
ejpam-4772	323	22	,	,	PUNCT
ejpam-4772	323	23	1875	1875	NUM
ejpam-4772	323	24	.	.	PUNCT
ejpam-4772	323	25	2022	2022	NUM
ejpam-4772	323	26	,	,	PUNCT
ejpam-4772	323	27	vol	vol	NOUN
ejpam-4772	323	28	6	6	NUM
ejpam-4772	323	29	,	,	PUNCT
ejpam-4772	323	30	261	261	NUM
ejpam-4772	323	31	-	-	SYM
ejpam-4772	323	32	271	271	NUM
ejpam-4772	323	33	.	.	PUNCT
ejpam-4772	324	1	[	[	X
ejpam-4772	324	2	6	6	NUM
ejpam-4772	324	3	]	]	X
ejpam-4772	324	4	layman	layman	NOUN
ejpam-4772	324	5	,	,	PUNCT
ejpam-4772	324	6	j.w	j.w	PROPN
ejpam-4772	324	7	.	.	PUNCT
ejpam-4772	325	1	the	the	DET
ejpam-4772	325	2	hankel	hankel	NOUN
ejpam-4772	325	3	transform	transform	NOUN
ejpam-4772	325	4	and	and	CCONJ
ejpam-4772	325	5	some	some	PRON
ejpam-4772	325	6	of	of	ADP
ejpam-4772	325	7	it	it	PRON
ejpam-4772	325	8	properties	property	NOUN
ejpam-4772	325	9	.	.	PUNCT
ejpam-4772	326	1	j.of	j.of	NOUN
ejpam-4772	326	2	integer	integer	NOUN
ejpam-4772	326	3	sequences	sequence	NOUN
ejpam-4772	326	4	.	.	PUNCT
ejpam-4772	327	1	2001	2001	NUM
ejpam-4772	327	2	,	,	PUNCT
ejpam-4772	327	3	4	4	NUM
ejpam-4772	327	4	,	,	PUNCT
ejpam-4772	327	5	1	1	NUM
ejpam-4772	327	6	-	-	SYM
ejpam-4772	327	7	11	11	NUM
ejpam-4772	327	8	.	.	PUNCT
ejpam-4772	328	1	references	reference	NOUN
ejpam-4772	328	2	1301	1301	NUM
ejpam-4772	328	3	[	[	X
ejpam-4772	328	4	7	7	NUM
ejpam-4772	328	5	]	]	X
ejpam-4772	328	6	libera	libera	NOUN
ejpam-4772	328	7	,	,	PUNCT
ejpam-4772	328	8	r.j	r.j	PROPN
ejpam-4772	328	9	.	.	PROPN
ejpam-4772	328	10	and	and	CCONJ
ejpam-4772	328	11	e.j	e.j	PROPN
ejpam-4772	328	12	.	.	PROPN
ejpam-4772	328	13	zlotkiewicz	zlotkiewicz	PROPN
ejpam-4772	328	14	.	.	PUNCT
ejpam-4772	329	1	coefficient	coefficient	NOUN
ejpam-4772	329	2	bounds	bound	VERB
ejpam-4772	329	3	for	for	ADP
ejpam-4772	329	4	the	the	DET
ejpam-4772	329	5	invers	inver	NOUN
ejpam-4772	329	6	of	of	ADP
ejpam-4772	329	7	a	a	DET
ejpam-4772	329	8	function	function	NOUN
ejpam-4772	329	9	with	with	ADP
ejpam-4772	329	10	derivative	derivative	NOUN
ejpam-4772	329	11	in	in	ADP
ejpam-4772	329	12	p.	p.	PROPN
ejpam-4772	329	13	proc	proc	PROPN
ejpam-4772	329	14	.	.	PUNCT
ejpam-4772	330	1	amer	amer	PROPN
ejpam-4772	330	2	.	.	PUNCT
ejpam-4772	331	1	math.soc	math.soc	X
ejpam-4772	331	2	.	.	PROPN
ejpam-4772	331	3	1983	1983	NUM
ejpam-4772	331	4	,	,	PUNCT
ejpam-4772	331	5	87	87	NUM
ejpam-4772	331	6	,	,	PUNCT
ejpam-4772	331	7	251	251	NUM
ejpam-4772	331	8	-	-	SYM
ejpam-4772	331	9	257	257	NUM
ejpam-4772	331	10	.	.	PUNCT
ejpam-4772	332	1	[	[	X
ejpam-4772	332	2	8	8	NUM
ejpam-4772	332	3	]	]	X
ejpam-4772	332	4	marjono	marjono	PROPN
ejpam-4772	332	5	.	.	PUNCT
ejpam-4772	332	6	subordination	subordination	NOUN
ejpam-4772	332	7	of	of	ADP
ejpam-4772	332	8	analytic	analytic	ADJ
ejpam-4772	332	9	functions	function	NOUN
ejpam-4772	332	10	.	.	PUNCT
ejpam-4772	333	1	the	the	DET
ejpam-4772	333	2	australian	australian	ADJ
ejpam-4772	333	3	journal	journal	NOUN
ejpam-4772	333	4	of	of	ADP
ejpam-4772	333	5	mathematical	mathematical	ADJ
ejpam-4772	333	6	analysis	analysis	NOUN
ejpam-4772	333	7	and	and	CCONJ
ejpam-4772	333	8	applications(ajmaa	applications(ajmaa	NOUN
ejpam-4772	333	9	)	)	PUNCT
ejpam-4772	333	10	.	.	PUNCT
ejpam-4772	334	1	2017	2017	NUM
ejpam-4772	334	2	,	,	PUNCT
ejpam-4772	334	3	vol	vol	NOUN
ejpam-4772	334	4	14	14	NUM
ejpam-4772	334	5	,	,	PUNCT
ejpam-4772	334	6	issue	issue	NOUN
ejpam-4772	334	7	1	1	NUM
ejpam-4772	334	8	,	,	PUNCT
ejpam-4772	334	9	article	article	NOUN
ejpam-4772	334	10	2	2	NUM
ejpam-4772	334	11	,	,	PUNCT
ejpam-4772	334	12	1	1	NUM
ejpam-4772	334	13	-	-	SYM
ejpam-4772	334	14	5	5	NUM
ejpam-4772	334	15	.	.	PUNCT
ejpam-4772	335	1	[	[	X
ejpam-4772	335	2	9	9	X
ejpam-4772	335	3	]	]	PUNCT
ejpam-4772	335	4	muhammad	muhammad	PROPN
ejpam-4772	335	5	ghaffar	ghaffar	PROPN
ejpam-4772	335	6	khan	khan	PROPN
ejpam-4772	335	7	,	,	PUNCT
ejpam-4772	335	8	baktiar	baktiar	PROPN
ejpam-4772	335	9	ahmad	ahmad	PROPN
ejpam-4772	335	10	,	,	PUNCT
ejpam-4772	335	11	gangadharan	gangadharan	NOUN
ejpam-4772	335	12	murugusundaramoorthy	murugusundaramoorthy	ADJ
ejpam-4772	335	13	,	,	PUNCT
ejpam-4772	335	14	wali	wali	PROPN
ejpam-4772	335	15	khan	khan	PROPN
ejpam-4772	335	16	mashwani	mashwani	PROPN
ejpam-4772	335	17	,	,	PUNCT
ejpam-4772	335	18	sibel	sibel	PROPN
ejpam-4772	335	19	yalcin	yalcin	PROPN
ejpam-4772	335	20	,	,	PUNCT
ejpam-4772	335	21	timilehin	timilehin	PROPN
ejpam-4772	335	22	gideon	gideon	PROPN
ejpam-4772	335	23	shaba	shaba	PROPN
ejpam-4772	335	24	,	,	PUNCT
ejpam-4772	335	25	zabidin	zabidin	VERB
ejpam-4772	335	26	salleh	salleh	PROPN
ejpam-4772	335	27	.	.	PUNCT
ejpam-4772	336	1	third	third	ADJ
ejpam-4772	336	2	hankel	hankel	NOUN
ejpam-4772	336	3	determinant	determinant	ADJ
ejpam-4772	336	4	and	and	CCONJ
ejpam-4772	336	5	zalcman	zalcman	NOUN
ejpam-4772	336	6	functional	functional	PROPN
ejpam-4772	336	7	for	for	ADP
ejpam-4772	336	8	class	class	NOUN
ejpam-4772	336	9	of	of	ADP
ejpam-4772	336	10	starlike	starlike	NOUN
ejpam-4772	336	11	functions	function	NOUN
ejpam-4772	336	12	with	with	ADP
ejpam-4772	336	13	respect	respect	NOUN
ejpam-4772	336	14	to	to	ADP
ejpam-4772	336	15	symmetric	symmetric	ADJ
ejpam-4772	336	16	point	point	NOUN
ejpam-4772	336	17	related	relate	VERB
ejpam-4772	336	18	with	with	ADP
ejpam-4772	336	19	sine	sine	ADJ
ejpam-4772	336	20	function	function	NOUN
ejpam-4772	336	21	.	.	PUNCT
ejpam-4772	337	1	journal	journal	NOUN
ejpam-4772	337	2	of	of	ADP
ejpam-4772	337	3	mathematics	mathematic	NOUN
ejpam-4772	337	4	and	and	CCONJ
ejpam-4772	337	5	computer	computer	NOUN
ejpam-4772	337	6	science	science	NOUN
ejpam-4772	337	7	.	.	PUNCT
ejpam-4772	338	1	2022	2022	NUM
ejpam-4772	338	2	,	,	PUNCT
ejpam-4772	338	3	vol	vol	NOUN
ejpam-4772	338	4	.	.	PROPN
ejpam-4772	338	5	25	25	NUM
ejpam-4772	338	6	,	,	PUNCT
ejpam-4772	338	7	issue	issue	NOUN
ejpam-4772	338	8	1	1	NUM
ejpam-4772	338	9	.	.	NUM
ejpam-4772	338	10	,	,	PUNCT
ejpam-4772	338	11	pp	pp	ADJ
ejpam-4772	338	12	.	.	PUNCT
ejpam-4772	339	1	29	29	NUM
ejpam-4772	339	2	-	-	SYM
ejpam-4772	339	3	36	36	NUM
ejpam-4772	339	4	.	.	PUNCT
ejpam-4772	340	1	[	[	X
ejpam-4772	340	2	10	10	NUM
ejpam-4772	340	3	]	]	X
ejpam-4772	340	4	n.m	n.m	PROPN
ejpam-4772	340	5	.	.	PROPN
ejpam-4772	340	6	asih	asih	PROPN
ejpam-4772	340	7	,	,	PUNCT
ejpam-4772	340	8	marjono	marjono	PROPN
ejpam-4772	340	9	,	,	PUNCT
ejpam-4772	340	10	s.	s.	PROPN
ejpam-4772	340	11	fitri	fitri	PROPN
ejpam-4772	340	12	,	,	PUNCT
ejpam-4772	340	13	and	and	CCONJ
ejpam-4772	340	14	r.b.e	r.b.e	NOUN
ejpam-4772	340	15	.	.	PUNCT
ejpam-4772	341	1	wibowo	wibowo	PROPN
ejpam-4772	341	2	.	.	PUNCT
ejpam-4772	342	1	coefficients	coefficient	NOUN
ejpam-4772	342	2	estimates	estimate	NOUN
ejpam-4772	342	3	in	in	ADP
ejpam-4772	342	4	the	the	DET
ejpam-4772	342	5	class	class	NOUN
ejpam-4772	342	6	bazilevič	bazilevič	NOUN
ejpam-4772	342	7	functions	function	NOUN
ejpam-4772	342	8	b1(α	b1(α	NOUN
ejpam-4772	342	9	)	)	PUNCT
ejpam-4772	342	10	related	relate	VERB
ejpam-4772	342	11	to	to	ADP
ejpam-4772	342	12	the	the	DET
ejpam-4772	342	13	bernoulli	bernoulli	PROPN
ejpam-4772	342	14	lemniscate	lemniscate	PROPN
ejpam-4772	342	15	.	.	PUNCT
ejpam-4772	343	1	proceeding	proceed	VERB
ejpam-4772	343	2	of	of	ADP
ejpam-4772	343	3	the	the	DET
ejpam-4772	343	4	soedirman	soedirman	NOUN
ejpam-4772	343	5	international	international	ADJ
ejpam-4772	343	6	conference	conference	NOUN
ejpam-4772	343	7	on	on	ADP
ejpam-4772	343	8	applied	apply	VERB
ejpam-4772	343	9	sciences(sicomas	sciences(sicoma	NOUN
ejpam-4772	343	10	2021	2021	NUM
ejpam-4772	343	11	)	)	PUNCT
ejpam-4772	343	12	,	,	PUNCT
ejpam-4772	343	13	https://doi.org/10.2991/apr.k.220503.008	https://doi.org/10.2991/apr.k.220503.008	NOUN
ejpam-4772	343	14	.	.	PUNCT
ejpam-4772	343	15	2022	2022	NUM
ejpam-4772	343	16	,	,	PUNCT
ejpam-4772	343	17	vol	vol	NOUN
ejpam-4772	343	18	5	5	NUM
ejpam-4772	343	19	,	,	PUNCT
ejpam-4772	343	20	37	37	NUM
ejpam-4772	343	21	-	-	SYM
ejpam-4772	343	22	39	39	NUM
ejpam-4772	343	23	.	.	PUNCT
ejpam-4772	344	1	[	[	X
ejpam-4772	344	2	11	11	NUM
ejpam-4772	344	3	]	]	X
ejpam-4772	344	4	n.m	n.m	PROPN
ejpam-4772	344	5	.	.	PROPN
ejpam-4772	344	6	asih	asih	PROPN
ejpam-4772	344	7	,	,	PUNCT
ejpam-4772	344	8	marjono	marjono	PROPN
ejpam-4772	344	9	,	,	PUNCT
ejpam-4772	344	10	s.	s.	PROPN
ejpam-4772	344	11	fitri	fitri	PROPN
ejpam-4772	344	12	,	,	PUNCT
ejpam-4772	344	13	and	and	CCONJ
ejpam-4772	344	14	r.b.e	r.b.e	NOUN
ejpam-4772	344	15	.	.	PUNCT
ejpam-4772	344	16	wibowo	wibowo	PROPN
ejpam-4772	344	17	.	.	PUNCT
ejpam-4772	345	1	fekete	fekete	PROPN
ejpam-4772	345	2	zsegö	zsegö	PROPN
ejpam-4772	345	3	on	on	ADP
ejpam-4772	345	4	the	the	DET
ejpam-4772	345	5	class	class	NOUN
ejpam-4772	345	6	bazilevič	bazilevič	NOUN
ejpam-4772	345	7	functions	function	NOUN
ejpam-4772	345	8	b1(α	b1(α	NOUN
ejpam-4772	345	9	)	)	PUNCT
ejpam-4772	345	10	related	relate	VERB
ejpam-4772	345	11	to	to	ADP
ejpam-4772	345	12	the	the	DET
ejpam-4772	345	13	bernoulli	bernoulli	PROPN
ejpam-4772	345	14	lemniscate	lemniscate	PROPN
ejpam-4772	345	15	.	.	PUNCT
ejpam-4772	346	1	aust	aust	PROPN
ejpam-4772	346	2	.	.	PUNCT
ejpam-4772	347	1	j.	j.	PROPN
ejpam-4772	347	2	math	math	PROPN
ejpam-4772	347	3	.	.	PUNCT
ejpam-4772	348	1	anal	anal	PROPN
ejpam-4772	348	2	.	.	PUNCT
ejpam-4772	348	3	appl	appl	PROPN
ejpam-4772	348	4	(	(	PUNCT
ejpam-4772	348	5	ajmaa	ajmaa	NOUN
ejpam-4772	348	6	)	)	PUNCT
ejpam-4772	348	7	,	,	PUNCT
ejpam-4772	348	8	2022	2022	NUM
ejpam-4772	348	9	,	,	PUNCT
ejpam-4772	348	10	vol	vol	NOUN
ejpam-4772	348	11	19	19	NUM
ejpam-4772	348	12	,	,	PUNCT
ejpam-4772	348	13	no.2	no.2	PROPN
ejpam-4772	348	14	.	.	PUNCT
ejpam-4772	349	1	art.15	art.15	ADP
ejpam-4772	349	2	,	,	PUNCT
ejpam-4772	349	3	10	10	NUM
ejpam-4772	349	4	pp	pp	NOUN
ejpam-4772	349	5	.	.	PUNCT
ejpam-4772	350	1	ajmaa	ajmaa	NOUN
ejpam-4772	350	2	.	.	PUNCT
ejpam-4772	351	1	[	[	X
ejpam-4772	351	2	12	12	NUM
ejpam-4772	351	3	]	]	X
ejpam-4772	351	4	noonan	noonan	PROPN
ejpam-4772	351	5	,	,	PUNCT
ejpam-4772	351	6	j.w	j.w	PROPN
ejpam-4772	351	7	.	.	PROPN
ejpam-4772	351	8	and	and	CCONJ
ejpam-4772	351	9	thomas	thomas	PROPN
ejpam-4772	351	10	,	,	PUNCT
ejpam-4772	351	11	d.k	d.k	PROPN
ejpam-4772	351	12	.	.	PROPN
ejpam-4772	352	1	on	on	ADP
ejpam-4772	352	2	the	the	DET
ejpam-4772	352	3	second	second	ADJ
ejpam-4772	352	4	hankel	hankel	NOUN
ejpam-4772	352	5	determinant	determinant	ADJ
ejpam-4772	352	6	of	of	ADP
ejpam-4772	352	7	areally	areally	ADV
ejpam-4772	352	8	mean	mean	VERB
ejpam-4772	352	9	p	p	ADJ
ejpam-4772	352	10	-	-	PUNCT
ejpam-4772	352	11	value	value	NOUN
ejpam-4772	352	12	functions	function	NOUN
ejpam-4772	352	13	.	.	PUNCT
ejpam-4772	353	1	mar	mar	PROPN
ejpam-4772	353	2	.	.	PUNCT
ejpam-4772	353	3	biol	biol	PROPN
ejpam-4772	353	4	.	.	PUNCT
ejpam-4772	354	1	2017	2017	NUM
ejpam-4772	354	2	,	,	PUNCT
ejpam-4772	354	3	164	164	NUM
ejpam-4772	354	4	,	,	PUNCT
ejpam-4772	354	5	article	article	NOUN
ejpam-4772	354	6	76	76	NUM
ejpam-4772	354	7	.	.	PUNCT
ejpam-4772	355	1	[	[	X
ejpam-4772	355	2	13	13	NUM
ejpam-4772	355	3	]	]	X
ejpam-4772	355	4	sahsene	sahsene	PROPN
ejpam-4772	355	5	altin	altin	PROPN
ejpam-4772	355	6	kaya	kaya	PROPN
ejpam-4772	355	7	,	,	PUNCT
ejpam-4772	355	8	nanjundan	nanjundan	PROPN
ejpam-4772	355	9	magesh	magesh	PROPN
ejpam-4772	355	10	,	,	PUNCT
ejpam-4772	355	11	and	and	CCONJ
ejpam-4772	355	12	sibel	sibel	VERB
ejpam-4772	355	13	yalcm	yalcm	PROPN
ejpam-4772	355	14	.	.	PUNCT
ejpam-4772	356	1	contruction	contruction	NOUN
ejpam-4772	356	2	of	of	ADP
ejpam-4772	356	3	toeplitz	toeplitz	NOUN
ejpam-4772	356	4	matrices	matrix	NOUN
ejpam-4772	356	5	whose	whose	DET
ejpam-4772	356	6	element	element	NOUN
ejpam-4772	356	7	are	be	AUX
ejpam-4772	356	8	the	the	DET
ejpam-4772	356	9	coefficient	coefficient	NOUN
ejpam-4772	356	10	f	f	PROPN
ejpam-4772	356	11	univalent	univalent	ADJ
ejpam-4772	356	12	functions	function	NOUN
ejpam-4772	356	13	assosiated	assosiate	VERB
ejpam-4772	356	14	with	with	ADP
ejpam-4772	356	15	qderivative	qderivative	ADJ
ejpam-4772	356	16	operator	operator	NOUN
ejpam-4772	356	17	.	.	PUNCT
ejpam-4772	357	1	caspian	caspian	PROPN
ejpam-4772	357	2	journal	journal	PROPN
ejpam-4772	357	3	of	of	ADP
ejpam-4772	357	4	mathematics	mathematic	NOUN
ejpam-4772	357	5	.	.	PUNCT
ejpam-4772	358	1	2019	2019	NUM
ejpam-4772	358	2	,	,	PUNCT
ejpam-4772	358	3	vol	vol	NOUN
ejpam-4772	358	4	.	.	NOUN
ejpam-4772	358	5	8	8	NUM
ejpam-4772	358	6	,	,	PUNCT
ejpam-4772	358	7	no.1	no.1	NUM
ejpam-4772	358	8	,	,	PUNCT
ejpam-4772	358	9	pp	pp	ADJ
ejpam-4772	358	10	.	.	PUNCT
ejpam-4772	359	1	51	51	NUM
ejpam-4772	359	2	-	-	SYM
ejpam-4772	359	3	57	57	NUM
ejpam-4772	359	4	.	.	PUNCT
ejpam-4772	360	1	[	[	X
ejpam-4772	360	2	14	14	NUM
ejpam-4772	360	3	]	]	X
ejpam-4772	360	4	sokol	sokol	PROPN
ejpam-4772	360	5	,	,	PUNCT
ejpam-4772	360	6	j	j	PROPN
ejpam-4772	360	7	and	and	CCONJ
ejpam-4772	360	8	d.	d.	PROPN
ejpam-4772	360	9	k.	k.	PROPN
ejpam-4772	360	10	thomas	thomas	PROPN
ejpam-4772	360	11	.	.	PUNCT
ejpam-4772	361	1	further	further	ADJ
ejpam-4772	361	2	results	result	NOUN
ejpam-4772	361	3	on	on	ADP
ejpam-4772	361	4	a	a	DET
ejpam-4772	361	5	class	class	NOUN
ejpam-4772	361	6	of	of	ADP
ejpam-4772	361	7	starlike	starlike	NOUN
ejpam-4772	361	8	functions	function	NOUN
ejpam-4772	361	9	related	relate	VERB
ejpam-4772	361	10	to	to	ADP
ejpam-4772	361	11	the	the	DET
ejpam-4772	361	12	bernoulli	bernoulli	PROPN
ejpam-4772	361	13	lemniscate	lemniscate	PROPN
ejpam-4772	361	14	.	.	PUNCT
ejpam-4772	362	1	houston	houston	PROPN
ejpam-4772	362	2	journal	journal	PROPN
ejpam-4772	362	3	of	of	ADP
ejpam-4772	362	4	mathematics	mathematics	PROPN
ejpam-4772	362	5	@2018	@2018	PROPN
ejpam-4772	362	6	university	university	PROPN
ejpam-4772	362	7	of	of	ADP
ejpam-4772	362	8	houston	houston	PROPN
ejpam-4772	362	9	.	.	PUNCT
ejpam-4772	363	1	2018	2018	NUM
ejpam-4772	363	2	,	,	PUNCT
ejpam-4772	363	3	vol	vol	NOUN
ejpam-4772	363	4	44	44	NUM
ejpam-4772	363	5	,	,	PUNCT
ejpam-4772	363	6	no.1	no.1	NUM
ejpam-4772	363	7	,	,	PUNCT
ejpam-4772	363	8	pp	pp	ADJ
ejpam-4772	363	9	.	.	PUNCT
ejpam-4772	364	1	83	83	NUM
ejpam-4772	364	2	-	-	SYM
ejpam-4772	364	3	95	95	NUM
ejpam-4772	364	4	.	.	PUNCT
ejpam-4772	365	1	[	[	X
ejpam-4772	365	2	15	15	NUM
ejpam-4772	365	3	]	]	X
ejpam-4772	365	4	thomas	thomas	PROPN
ejpam-4772	365	5	,	,	PUNCT
ejpam-4772	365	6	d.k	d.k	PROPN
ejpam-4772	365	7	and	and	CCONJ
ejpam-4772	365	8	s.	s.	PROPN
ejpam-4772	365	9	a.	a.	PROPN
ejpam-4772	365	10	halim	halim	PROPN
ejpam-4772	365	11	,	,	PUNCT
ejpam-4772	365	12	2016	2016	NUM
ejpam-4772	365	13	.	.	PUNCT
ejpam-4772	366	1	toeplitz	toeplitz	NOUN
ejpam-4772	366	2	matrices	matrix	NOUN
ejpam-4772	366	3	whose	whose	DET
ejpam-4772	366	4	element	element	NOUN
ejpam-4772	366	5	are	be	AUX
ejpam-4772	366	6	the	the	DET
ejpam-4772	366	7	coefficients	coefficient	NOUN
ejpam-4772	366	8	of	of	ADP
ejpam-4772	366	9	starlike	starlike	NOUN
ejpam-4772	366	10	and	and	CCONJ
ejpam-4772	366	11	close	close	ADJ
ejpam-4772	366	12	to	to	ADP
ejpam-4772	366	13	-	-	PUNCT
ejpam-4772	366	14	convex	convex	NOUN
ejpam-4772	366	15	functions	function	NOUN
ejpam-4772	366	16	.	.	PUNCT
ejpam-4772	367	1	the	the	DET
ejpam-4772	367	2	bulletin	bulletin	NOUN
ejpam-4772	367	3	of	of	ADP
ejpam-4772	367	4	the	the	DET
ejpam-4772	367	5	malaysian	malaysian	PROPN
ejpam-4772	367	6	mathematical	mathematical	PROPN
ejpam-4772	367	7	society	society	NOUN
ejpam-4772	367	8	series	series	PROPN
ejpam-4772	367	9	2	2	NUM
ejpam-4772	367	10	.	.	NUM
ejpam-4772	367	11	2016	2016	NUM
ejpam-4772	367	12	,	,	PUNCT
ejpam-4772	367	13	doi:10.1007	doi:10.1007	VERB
ejpam-4772	367	14	/	/	SYM
ejpam-4772	367	15	s40840	s40840	PROPN
ejpam-4772	367	16	-	-	PUNCT
ejpam-4772	367	17	016	016	NUM
ejpam-4772	367	18	-	-	PUNCT
ejpam-4772	367	19	0385	0385	NUM
ejpam-4772	367	20	-	-	PUNCT
ejpam-4772	367	21	4	4	NUM
ejpam-4772	367	22	.	.	PUNCT