id	sid	tid	token	lemma	pos
ejpam-4559	1	1	european	european	PROPN
ejpam-4559	1	2	journal	journal	PROPN
ejpam-4559	1	3	of	of	ADP
ejpam-4559	1	4	pure	pure	ADJ
ejpam-4559	1	5	and	and	CCONJ
ejpam-4559	1	6	applied	apply	VERB
ejpam-4559	1	7	mathematics	mathematic	NOUN
ejpam-4559	1	8	vol	vol	NOUN
ejpam-4559	1	9	.	.	PROPN
ejpam-4559	2	1	15	15	NUM
ejpam-4559	2	2	,	,	PUNCT
ejpam-4559	2	3	no	no	INTJ
ejpam-4559	2	4	.	.	NOUN
ejpam-4559	2	5	4	4	NUM
ejpam-4559	2	6	,	,	PUNCT
ejpam-4559	2	7	2022	2022	NUM
ejpam-4559	2	8	,	,	PUNCT
ejpam-4559	2	9	1937	1937	NUM
ejpam-4559	2	10	-	-	SYM
ejpam-4559	2	11	1947	1947	NUM
ejpam-4559	2	12	issn	issn	PROPN
ejpam-4559	2	13	1307	1307	NUM
ejpam-4559	2	14	-	-	SYM
ejpam-4559	2	15	5543	5543	NUM
ejpam-4559	2	16	–	–	PUNCT
ejpam-4559	2	17	ejpam.com	ejpam.com	X
ejpam-4559	2	18	published	publish	VERB
ejpam-4559	2	19	by	by	ADP
ejpam-4559	2	20	new	new	PROPN
ejpam-4559	2	21	york	york	PROPN
ejpam-4559	2	22	business	business	PROPN
ejpam-4559	2	23	global	global	PROPN
ejpam-4559	2	24	toeplitz	toeplitz	NOUN
ejpam-4559	2	25	determinants	determinant	NOUN
ejpam-4559	2	26	for	for	ADP
ejpam-4559	2	27	the	the	DET
ejpam-4559	2	28	class	class	NOUN
ejpam-4559	2	29	of	of	ADP
ejpam-4559	2	30	functions	function	NOUN
ejpam-4559	2	31	with	with	ADP
ejpam-4559	2	32	bounded	bounded	ADJ
ejpam-4559	2	33	turning	turn	VERB
ejpam-4559	2	34	nur	nur	PROPN
ejpam-4559	2	35	hazwani	hazwani	PROPN
ejpam-4559	2	36	aqilah	aqilah	PROPN
ejpam-4559	2	37	abdul	abdul	PROPN
ejpam-4559	2	38	wahid1,∗	wahid1,∗	PROPN
ejpam-4559	2	39	,	,	PUNCT
ejpam-4559	2	40	daud	daud	PROPN
ejpam-4559	2	41	mohamad1	mohamad1	PROPN
ejpam-4559	2	42	,	,	PUNCT
ejpam-4559	2	43	nur	nur	VERB
ejpam-4559	2	44	maziah	maziah	PROPN
ejpam-4559	2	45	kamarozzaman1	kamarozzaman1	PROPN
ejpam-4559	2	46	,	,	PUNCT
ejpam-4559	2	47	ainurraziqin	ainurraziqin	PROPN
ejpam-4559	2	48	ahmad	ahmad	PROPN
ejpam-4559	2	49	shahminan1	shahminan1	PROPN
ejpam-4559	2	50	1	1	NUM
ejpam-4559	2	51	faculty	faculty	NOUN
ejpam-4559	2	52	of	of	ADP
ejpam-4559	2	53	computer	computer	NOUN
ejpam-4559	2	54	and	and	CCONJ
ejpam-4559	2	55	mathematical	mathematical	ADJ
ejpam-4559	2	56	sciences	sciences	PROPN
ejpam-4559	2	57	,	,	PUNCT
ejpam-4559	2	58	universiti	universiti	PROPN
ejpam-4559	2	59	teknologi	teknologi	PROPN
ejpam-4559	2	60	mara	mara	PROPN
ejpam-4559	2	61	,	,	PUNCT
ejpam-4559	2	62	40450	40450	NUM
ejpam-4559	2	63	shah	shah	PROPN
ejpam-4559	2	64	alam	alam	PROPN
ejpam-4559	2	65	,	,	PUNCT
ejpam-4559	2	66	selangor	selangor	PROPN
ejpam-4559	2	67	,	,	PUNCT
ejpam-4559	2	68	malaysia	malaysia	PROPN
ejpam-4559	2	69	abstract	abstract	NOUN
ejpam-4559	2	70	.	.	PUNCT
ejpam-4559	3	1	in	in	ADP
ejpam-4559	3	2	this	this	DET
ejpam-4559	3	3	paper	paper	NOUN
ejpam-4559	3	4	,	,	PUNCT
ejpam-4559	3	5	we	we	PRON
ejpam-4559	3	6	obtain	obtain	VERB
ejpam-4559	3	7	the	the	DET
ejpam-4559	3	8	upper	upper	ADJ
ejpam-4559	3	9	bounds	bound	NOUN
ejpam-4559	3	10	of	of	ADP
ejpam-4559	3	11	the	the	DET
ejpam-4559	3	12	toeplitz	toeplitz	NOUN
ejpam-4559	3	13	determinants	determinant	NOUN
ejpam-4559	3	14	for	for	ADP
ejpam-4559	3	15	the	the	DET
ejpam-4559	3	16	class	class	NOUN
ejpam-4559	3	17	of	of	ADP
ejpam-4559	3	18	functions	function	NOUN
ejpam-4559	3	19	with	with	ADP
ejpam-4559	3	20	bounded	bounded	ADJ
ejpam-4559	3	21	turning	turning	NOUN
ejpam-4559	3	22	.	.	PUNCT
ejpam-4559	4	1	we	we	PRON
ejpam-4559	4	2	also	also	ADV
ejpam-4559	4	3	present	present	VERB
ejpam-4559	4	4	some	some	DET
ejpam-4559	4	5	consequences	consequence	NOUN
ejpam-4559	4	6	of	of	ADP
ejpam-4559	4	7	our	our	PRON
ejpam-4559	4	8	main	main	ADJ
ejpam-4559	4	9	results	result	NOUN
ejpam-4559	4	10	.	.	PUNCT
ejpam-4559	5	1	some	some	DET
ejpam-4559	5	2	estimates	estimate	NOUN
ejpam-4559	5	3	obtained	obtain	VERB
ejpam-4559	5	4	on	on	ADP
ejpam-4559	5	5	toeplitz	toeplitz	NOUN
ejpam-4559	5	6	determinants	determinant	NOUN
ejpam-4559	5	7	are	be	AUX
ejpam-4559	5	8	sharp	sharp	ADJ
ejpam-4559	5	9	.	.	PUNCT
ejpam-4559	6	1	2020	2020	NUM
ejpam-4559	6	2	mathematics	mathematic	NOUN
ejpam-4559	6	3	subject	subject	NOUN
ejpam-4559	6	4	classifications	classification	NOUN
ejpam-4559	6	5	:	:	PUNCT
ejpam-4559	6	6	30c45	30c45	NUM
ejpam-4559	6	7	,	,	PUNCT
ejpam-4559	6	8	30c50	30c50	DET
ejpam-4559	6	9	key	key	ADJ
ejpam-4559	6	10	words	word	NOUN
ejpam-4559	6	11	and	and	CCONJ
ejpam-4559	6	12	phrases	phrase	NOUN
ejpam-4559	6	13	:	:	PUNCT
ejpam-4559	6	14	bounded	bound	VERB
ejpam-4559	6	15	turning	turning	NOUN
ejpam-4559	6	16	functions	function	NOUN
ejpam-4559	6	17	,	,	PUNCT
ejpam-4559	6	18	toeplitz	toeplitz	NOUN
ejpam-4559	6	19	determinant	determinant	ADJ
ejpam-4559	6	20	,	,	PUNCT
ejpam-4559	6	21	univalent	univalent	ADJ
ejpam-4559	6	22	functions	function	NOUN
ejpam-4559	6	23	1	1	NUM
ejpam-4559	6	24	.	.	PUNCT
ejpam-4559	7	1	introduction	introduction	NOUN
ejpam-4559	7	2	let	let	VERB
ejpam-4559	7	3	a	a	DET
ejpam-4559	7	4	denote	denote	NOUN
ejpam-4559	7	5	the	the	DET
ejpam-4559	7	6	class	class	NOUN
ejpam-4559	7	7	of	of	ADP
ejpam-4559	7	8	all	all	DET
ejpam-4559	7	9	functions	function	NOUN
ejpam-4559	7	10	f	f	X
ejpam-4559	7	11	(	(	PUNCT
ejpam-4559	7	12	z	z	NOUN
ejpam-4559	7	13	)	)	PUNCT
ejpam-4559	7	14	of	of	ADP
ejpam-4559	7	15	the	the	DET
ejpam-4559	7	16	form	form	NOUN
ejpam-4559	7	17	f	f	X
ejpam-4559	7	18	(	(	PUNCT
ejpam-4559	7	19	z	z	NOUN
ejpam-4559	7	20	)	)	PUNCT
ejpam-4559	7	21	=	=	SYM
ejpam-4559	8	1	z	z	NOUN
ejpam-4559	9	1	+	+	NOUN
ejpam-4559	9	2	∞∑	∞∑	NUM
ejpam-4559	9	3	n=2	n=2	ADV
ejpam-4559	9	4	anz	anz	NOUN
ejpam-4559	9	5	n	n	CCONJ
ejpam-4559	9	6	,	,	PUNCT
ejpam-4559	9	7	(	(	PUNCT
ejpam-4559	9	8	1	1	X
ejpam-4559	9	9	)	)	PUNCT
ejpam-4559	9	10	which	which	PRON
ejpam-4559	9	11	are	be	AUX
ejpam-4559	9	12	analytic	analytic	ADJ
ejpam-4559	9	13	in	in	ADP
ejpam-4559	9	14	the	the	DET
ejpam-4559	9	15	open	open	ADJ
ejpam-4559	9	16	unit	unit	NOUN
ejpam-4559	9	17	disk	disk	NOUN
ejpam-4559	9	18	e	e	NOUN
ejpam-4559	9	19	=	=	PUNCT
ejpam-4559	9	20	{	{	PUNCT
ejpam-4559	9	21	z	z	NOUN
ejpam-4559	9	22	∈	∈	PROPN
ejpam-4559	9	23	c	c	NOUN
ejpam-4559	9	24	:	:	PUNCT
ejpam-4559	9	25	|z|	|z|	NOUN
ejpam-4559	9	26	<	<	X
ejpam-4559	9	27	1	1	NUM
ejpam-4559	9	28	}	}	PUNCT
ejpam-4559	9	29	.	.	PUNCT
ejpam-4559	10	1	we	we	PRON
ejpam-4559	10	2	denote	denote	VERB
ejpam-4559	10	3	by	by	ADP
ejpam-4559	10	4	s	s	PRON
ejpam-4559	10	5	the	the	DET
ejpam-4559	10	6	subclass	subclass	NOUN
ejpam-4559	10	7	of	of	ADP
ejpam-4559	10	8	a	a	DET
ejpam-4559	10	9	consisting	consisting	NOUN
ejpam-4559	10	10	of	of	ADP
ejpam-4559	10	11	univalent	univalent	ADJ
ejpam-4559	10	12	functions	function	NOUN
ejpam-4559	10	13	in	in	ADP
ejpam-4559	10	14	e.	e.	PROPN
ejpam-4559	10	15	let	let	VERB
ejpam-4559	10	16	p	p	PRON
ejpam-4559	10	17	denote	denote	VERB
ejpam-4559	10	18	the	the	DET
ejpam-4559	10	19	class	class	NOUN
ejpam-4559	10	20	of	of	ADP
ejpam-4559	10	21	positive	positive	ADJ
ejpam-4559	10	22	real	real	ADJ
ejpam-4559	10	23	part	part	NOUN
ejpam-4559	10	24	functions	function	NOUN
ejpam-4559	10	25	p	p	X
ejpam-4559	10	26	(	(	PUNCT
ejpam-4559	10	27	z	z	NOUN
ejpam-4559	10	28	)	)	PUNCT
ejpam-4559	10	29	of	of	ADP
ejpam-4559	10	30	the	the	DET
ejpam-4559	10	31	form	form	NOUN
ejpam-4559	10	32	p	p	X
ejpam-4559	10	33	(	(	PUNCT
ejpam-4559	10	34	z	z	NOUN
ejpam-4559	10	35	)	)	PUNCT
ejpam-4559	10	36	=	=	SYM
ejpam-4559	11	1	1	1	NUM
ejpam-4559	11	2	+	+	CCONJ
ejpam-4559	11	3	∞∑	∞∑	NUM
ejpam-4559	11	4	n=1	n=1	PROPN
ejpam-4559	11	5	pnz	pnz	NOUN
ejpam-4559	11	6	n	n	CCONJ
ejpam-4559	11	7	,	,	PUNCT
ejpam-4559	11	8	(	(	PUNCT
ejpam-4559	11	9	2	2	X
ejpam-4559	11	10	)	)	PUNCT
ejpam-4559	11	11	which	which	PRON
ejpam-4559	11	12	satisfy	satisfy	VERB
ejpam-4559	11	13	re	re	ADP
ejpam-4559	11	14	p	p	PROPN
ejpam-4559	11	15	(	(	PUNCT
ejpam-4559	11	16	z	z	NOUN
ejpam-4559	11	17	)	)	PUNCT
ejpam-4559	11	18	>	>	X
ejpam-4559	11	19	0	0	PUNCT
ejpam-4559	12	1	for	for	ADP
ejpam-4559	12	2	z	z	PROPN
ejpam-4559	12	3	∈	∈	PROPN
ejpam-4559	12	4	e.	e.	PROPN
ejpam-4559	13	1	this	this	DET
ejpam-4559	13	2	class	class	NOUN
ejpam-4559	13	3	is	be	AUX
ejpam-4559	13	4	also	also	ADV
ejpam-4559	13	5	known	know	VERB
ejpam-4559	13	6	as	as	ADP
ejpam-4559	13	7	the	the	DET
ejpam-4559	13	8	class	class	NOUN
ejpam-4559	13	9	of	of	ADP
ejpam-4559	13	10	carathéodory	carathéodory	NOUN
ejpam-4559	13	11	functions	function	NOUN
ejpam-4559	13	12	.	.	PUNCT
ejpam-4559	14	1	let	let	VERB
ejpam-4559	14	2	g	g	PROPN
ejpam-4559	14	3	(	(	PUNCT
ejpam-4559	14	4	α	α	PROPN
ejpam-4559	14	5	,	,	PUNCT
ejpam-4559	14	6	δ	δ	PROPN
ejpam-4559	14	7	)	)	PUNCT
ejpam-4559	14	8	be	be	VERB
ejpam-4559	14	9	the	the	DET
ejpam-4559	14	10	class	class	NOUN
ejpam-4559	14	11	of	of	ADP
ejpam-4559	14	12	normalized	normalize	VERB
ejpam-4559	14	13	functions	function	NOUN
ejpam-4559	14	14	f	f	X
ejpam-4559	14	15	(	(	PUNCT
ejpam-4559	14	16	z	z	NOUN
ejpam-4559	14	17	)	)	PUNCT
ejpam-4559	14	18	∈	∈	PROPN
ejpam-4559	14	19	a	a	DET
ejpam-4559	14	20	satisfying	satisfying	NOUN
ejpam-4559	14	21	the	the	DET
ejpam-4559	14	22	condition	condition	NOUN
ejpam-4559	14	23	re	re	ADP
ejpam-4559	14	24	(	(	PUNCT
ejpam-4559	14	25	eiαf	eiαf	NOUN
ejpam-4559	14	26	′	′	NUM
ejpam-4559	15	1	(	(	PUNCT
ejpam-4559	15	2	z	z	NOUN
ejpam-4559	15	3	)	)	PUNCT
ejpam-4559	15	4	)	)	PUNCT
ejpam-4559	16	1	>	>	PUNCT
ejpam-4559	16	2	δ	δ	PROPN
ejpam-4559	16	3	,	,	PUNCT
ejpam-4559	17	1	z	z	NOUN
ejpam-4559	17	2	∈	∈	PROPN
ejpam-4559	17	3	e	e	NOUN
ejpam-4559	17	4	,	,	PUNCT
ejpam-4559	17	5	where	where	SCONJ
ejpam-4559	17	6	|α|	|α|	PROPN
ejpam-4559	17	7	<	<	X
ejpam-4559	17	8	π	π	PROPN
ejpam-4559	17	9	,	,	PUNCT
ejpam-4559	17	10	0	0	NUM
ejpam-4559	17	11	⩽	⩽	PROPN
ejpam-4559	17	12	δ	δ	PROPN
ejpam-4559	17	13	<	<	X
ejpam-4559	17	14	1	1	NUM
ejpam-4559	17	15	,	,	PUNCT
ejpam-4559	17	16	and	and	CCONJ
ejpam-4559	17	17	cosα	cosα	NOUN
ejpam-4559	17	18	>	>	X
ejpam-4559	17	19	δ	δ	PROPN
ejpam-4559	17	20	.	.	PUNCT
ejpam-4559	18	1	this	this	DET
ejpam-4559	18	2	class	class	NOUN
ejpam-4559	18	3	was	be	AUX
ejpam-4559	18	4	introduced	introduce	VERB
ejpam-4559	18	5	by	by	ADP
ejpam-4559	18	6	mohamad	mohamad	PROPN
ejpam-4559	18	7	[	[	X
ejpam-4559	18	8	10	10	NUM
ejpam-4559	18	9	]	]	PUNCT
ejpam-4559	18	10	.	.	PUNCT
ejpam-4559	19	1	∗corresponding	∗corresponde	VERB
ejpam-4559	19	2	author	author	NOUN
ejpam-4559	19	3	.	.	PUNCT
ejpam-4559	20	1	doi	doi	NOUN
ejpam-4559	20	2	:	:	PUNCT
ejpam-4559	20	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4559	https://doi.org/10.29020/nybg.ejpam.v15i4.4559	DET
ejpam-4559	20	4	email	email	NOUN
ejpam-4559	20	5	addresses	address	VERB
ejpam-4559	20	6	:	:	PUNCT
ejpam-4559	20	7	hazwaniaqilah@fskm.uitm.edu.my	hazwaniaqilah@fskm.uitm.edu.my	PROPN
ejpam-4559	20	8	(	(	PUNCT
ejpam-4559	20	9	n.	n.	PROPN
ejpam-4559	20	10	h.	h.	PROPN
ejpam-4559	20	11	a.	a.	PROPN
ejpam-4559	20	12	a.	a.	PROPN
ejpam-4559	20	13	wahid	wahid	PROPN
ejpam-4559	20	14	)	)	PUNCT
ejpam-4559	20	15	,	,	PUNCT
ejpam-4559	20	16	daud@fskm.uitm.edu.my	daud@fskm.uitm.edu.my	PROPN
ejpam-4559	20	17	(	(	PUNCT
ejpam-4559	20	18	d.	d.	PROPN
ejpam-4559	20	19	mohamad	mohamad	PROPN
ejpam-4559	20	20	)	)	PUNCT
ejpam-4559	20	21	,	,	PUNCT
ejpam-4559	20	22	nurmaziah16@gmail.com	nurmaziah16@gmail.com	X
ejpam-4559	20	23	(	(	PUNCT
ejpam-4559	20	24	n.	n.	PROPN
ejpam-4559	20	25	m.	m.	PROPN
ejpam-4559	20	26	kamarozzaman	kamarozzaman	PROPN
ejpam-4559	20	27	)	)	PUNCT
ejpam-4559	20	28	,	,	PUNCT
ejpam-4559	20	29	ainurraziqin.ahmad@gmail.com	ainurraziqin.ahmad@gmail.com	X
ejpam-4559	20	30	(	(	PUNCT
ejpam-4559	20	31	a.	a.	NOUN
ejpam-4559	20	32	a.	a.	PROPN
ejpam-4559	20	33	shahminan	shahminan	PROPN
ejpam-4559	20	34	)	)	PUNCT
ejpam-4559	20	35	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4559	20	36	1937	1937	NUM
ejpam-4559	21	1	©	©	PROPN
ejpam-4559	21	2	2022	2022	NUM
ejpam-4559	21	3	ejpam	ejpam	VERB
ejpam-4559	21	4	all	all	DET
ejpam-4559	21	5	rights	right	NOUN
ejpam-4559	21	6	reserved	reserve	VERB
ejpam-4559	21	7	.	.	PUNCT
ejpam-4559	22	1	n.	n.	PROPN
ejpam-4559	22	2	h.	h.	PROPN
ejpam-4559	22	3	a.	a.	PROPN
ejpam-4559	22	4	a.	a.	PROPN
ejpam-4559	22	5	wahid	wahid	PROPN
ejpam-4559	22	6	et	et	PROPN
ejpam-4559	22	7	al	al	PROPN
ejpam-4559	22	8	.	.	PUNCT
ejpam-4559	22	9	/	/	SYM
ejpam-4559	22	10	eur	eur	PROPN
ejpam-4559	22	11	.	.	PUNCT
ejpam-4559	23	1	j.	j.	PROPN
ejpam-4559	23	2	pure	pure	PROPN
ejpam-4559	23	3	appl	appl	PROPN
ejpam-4559	23	4	.	.	PROPN
ejpam-4559	23	5	math	math	PROPN
ejpam-4559	23	6	,	,	PUNCT
ejpam-4559	23	7	15	15	NUM
ejpam-4559	23	8	(	(	PUNCT
ejpam-4559	23	9	4	4	NUM
ejpam-4559	23	10	)	)	PUNCT
ejpam-4559	23	11	(	(	PUNCT
ejpam-4559	23	12	2022	2022	NUM
ejpam-4559	23	13	)	)	PUNCT
ejpam-4559	23	14	,	,	PUNCT
ejpam-4559	23	15	1937	1937	NUM
ejpam-4559	23	16	-	-	SYM
ejpam-4559	23	17	1947	1947	NUM
ejpam-4559	23	18	1938	1938	NUM
ejpam-4559	23	19	remark	remark	NOUN
ejpam-4559	23	20	1	1	NUM
ejpam-4559	23	21	.	.	PUNCT
ejpam-4559	24	1	for	for	ADP
ejpam-4559	24	2	the	the	DET
ejpam-4559	24	3	specific	specific	ADJ
ejpam-4559	24	4	values	value	NOUN
ejpam-4559	24	5	of	of	ADP
ejpam-4559	24	6	the	the	DET
ejpam-4559	24	7	parameters	parameter	NOUN
ejpam-4559	24	8	α	α	PROPN
ejpam-4559	24	9	and	and	CCONJ
ejpam-4559	24	10	δ	δ	PROPN
ejpam-4559	24	11	,	,	PUNCT
ejpam-4559	24	12	we	we	PRON
ejpam-4559	24	13	obtain	obtain	VERB
ejpam-4559	24	14	the	the	DET
ejpam-4559	24	15	special	special	ADJ
ejpam-4559	24	16	cases	case	NOUN
ejpam-4559	24	17	of	of	ADP
ejpam-4559	24	18	g	g	PROPN
ejpam-4559	24	19	(	(	PUNCT
ejpam-4559	24	20	α	α	PROPN
ejpam-4559	24	21	,	,	PUNCT
ejpam-4559	24	22	δ	δ	PROPN
ejpam-4559	24	23	)	)	PUNCT
ejpam-4559	24	24	as	as	SCONJ
ejpam-4559	24	25	follows	follow	VERB
ejpam-4559	24	26	:	:	PUNCT
ejpam-4559	24	27	(	(	PUNCT
ejpam-4559	24	28	i	i	NOUN
ejpam-4559	24	29	)	)	PUNCT
ejpam-4559	24	30	if	if	SCONJ
ejpam-4559	24	31	we	we	PRON
ejpam-4559	24	32	let	let	VERB
ejpam-4559	24	33	α	α	NOUN
ejpam-4559	24	34	=	=	PUNCT
ejpam-4559	24	35	δ	δ	X
ejpam-4559	24	36	=	=	SYM
ejpam-4559	24	37	0	0	PROPN
ejpam-4559	24	38	,	,	PUNCT
ejpam-4559	24	39	then	then	ADV
ejpam-4559	24	40	we	we	PRON
ejpam-4559	24	41	have	have	VERB
ejpam-4559	24	42	the	the	DET
ejpam-4559	24	43	class	class	NOUN
ejpam-4559	24	44	g	g	NOUN
ejpam-4559	24	45	(	(	PUNCT
ejpam-4559	24	46	0	0	NUM
ejpam-4559	24	47	,	,	PUNCT
ejpam-4559	24	48	0	0	NUM
ejpam-4559	24	49	)	)	PUNCT
ejpam-4559	24	50	≡	≡	PROPN
ejpam-4559	24	51	r	r	NOUN
ejpam-4559	24	52	which	which	PRON
ejpam-4559	24	53	satisfies	satisfy	VERB
ejpam-4559	24	54	re	re	VERB
ejpam-4559	24	55	f	f	PROPN
ejpam-4559	24	56	′	′	NUM
ejpam-4559	25	1	(	(	PUNCT
ejpam-4559	25	2	z	z	NOUN
ejpam-4559	25	3	)	)	PUNCT
ejpam-4559	25	4	>	>	X
ejpam-4559	26	1	0	0	X
ejpam-4559	26	2	.	.	PUNCT
ejpam-4559	27	1	the	the	DET
ejpam-4559	27	2	functions	function	NOUN
ejpam-4559	27	3	from	from	ADP
ejpam-4559	27	4	r	r	NOUN
ejpam-4559	27	5	are	be	AUX
ejpam-4559	27	6	said	say	VERB
ejpam-4559	27	7	to	to	PART
ejpam-4559	27	8	be	be	AUX
ejpam-4559	27	9	of	of	ADP
ejpam-4559	27	10	bounded	bounded	ADJ
ejpam-4559	27	11	turning	turning	NOUN
ejpam-4559	27	12	.	.	PUNCT
ejpam-4559	28	1	(	(	PUNCT
ejpam-4559	28	2	ii	ii	NOUN
ejpam-4559	28	3	)	)	PUNCT
ejpam-4559	28	4	if	if	SCONJ
ejpam-4559	28	5	we	we	PRON
ejpam-4559	28	6	let	let	VERB
ejpam-4559	28	7	α	α	NOUN
ejpam-4559	28	8	=	=	SYM
ejpam-4559	28	9	0	0	NUM
ejpam-4559	28	10	,	,	PUNCT
ejpam-4559	28	11	then	then	ADV
ejpam-4559	28	12	we	we	PRON
ejpam-4559	28	13	have	have	VERB
ejpam-4559	28	14	the	the	DET
ejpam-4559	28	15	class	class	NOUN
ejpam-4559	28	16	g	g	NOUN
ejpam-4559	28	17	(	(	PUNCT
ejpam-4559	28	18	0	0	NUM
ejpam-4559	28	19	,	,	PUNCT
ejpam-4559	28	20	δ	δ	PROPN
ejpam-4559	28	21	)	)	PUNCT
ejpam-4559	28	22	≡	≡	PROPN
ejpam-4559	28	23	r	r	PROPN
ejpam-4559	28	24	(	(	PUNCT
ejpam-4559	28	25	δ	δ	PROPN
ejpam-4559	28	26	)	)	PUNCT
ejpam-4559	28	27	which	which	PRON
ejpam-4559	28	28	satisfies	satisfy	VERB
ejpam-4559	28	29	re	re	VERB
ejpam-4559	28	30	(	(	PUNCT
ejpam-4559	28	31	f	f	NOUN
ejpam-4559	28	32	′	′	NUM
ejpam-4559	28	33	(	(	PUNCT
ejpam-4559	28	34	z	z	NOUN
ejpam-4559	28	35	)	)	PUNCT
ejpam-4559	28	36	)	)	PUNCT
ejpam-4559	28	37	>	>	PUNCT
ejpam-4559	29	1	δ	δ	PROPN
ejpam-4559	29	2	.	.	PUNCT
ejpam-4559	30	1	the	the	DET
ejpam-4559	30	2	class	class	NOUN
ejpam-4559	30	3	r	r	NOUN
ejpam-4559	30	4	(	(	PUNCT
ejpam-4559	30	5	δ	δ	NOUN
ejpam-4559	30	6	)	)	PUNCT
ejpam-4559	30	7	is	be	AUX
ejpam-4559	30	8	called	call	VERB
ejpam-4559	30	9	the	the	DET
ejpam-4559	30	10	class	class	NOUN
ejpam-4559	30	11	of	of	ADP
ejpam-4559	30	12	bounded	bounded	ADJ
ejpam-4559	30	13	turning	turning	NOUN
ejpam-4559	30	14	functions	function	NOUN
ejpam-4559	30	15	of	of	ADP
ejpam-4559	30	16	order	order	NOUN
ejpam-4559	30	17	δ	δ	PROPN
ejpam-4559	30	18	.	.	PUNCT
ejpam-4559	31	1	(	(	PUNCT
ejpam-4559	31	2	iii	iii	X
ejpam-4559	31	3	)	)	PUNCT
ejpam-4559	31	4	if	if	SCONJ
ejpam-4559	31	5	we	we	PRON
ejpam-4559	31	6	let	let	VERB
ejpam-4559	31	7	δ	δ	PROPN
ejpam-4559	31	8	=	=	SYM
ejpam-4559	31	9	0	0	PROPN
ejpam-4559	31	10	,	,	PUNCT
ejpam-4559	31	11	then	then	ADV
ejpam-4559	31	12	we	we	PRON
ejpam-4559	31	13	have	have	VERB
ejpam-4559	31	14	the	the	DET
ejpam-4559	31	15	class	class	NOUN
ejpam-4559	31	16	g	g	PROPN
ejpam-4559	31	17	(	(	PUNCT
ejpam-4559	31	18	α	α	NOUN
ejpam-4559	31	19	,	,	PUNCT
ejpam-4559	31	20	0	0	NUM
ejpam-4559	31	21	)	)	PUNCT
ejpam-4559	31	22	≡	≡	PROPN
ejpam-4559	31	23	r	r	NOUN
ejpam-4559	31	24	(	(	PUNCT
ejpam-4559	31	25	α	α	NOUN
ejpam-4559	31	26	)	)	PUNCT
ejpam-4559	31	27	which	which	PRON
ejpam-4559	31	28	satisfies	satisfy	VERB
ejpam-4559	31	29	re	re	VERB
ejpam-4559	31	30	(	(	PUNCT
ejpam-4559	31	31	eiαf	eiαf	NOUN
ejpam-4559	31	32	′	′	NUM
ejpam-4559	31	33	(	(	PUNCT
ejpam-4559	31	34	z	z	NOUN
ejpam-4559	31	35	)	)	PUNCT
ejpam-4559	31	36	)	)	PUNCT
ejpam-4559	31	37	>	>	X
ejpam-4559	32	1	0	0	X
ejpam-4559	32	2	.	.	X
ejpam-4559	33	1	goel	goel	PROPN
ejpam-4559	33	2	and	and	CCONJ
ejpam-4559	33	3	mehrok	mehrok	ADJ
ejpam-4559	34	1	[	[	X
ejpam-4559	34	2	8	8	NUM
ejpam-4559	34	3	]	]	PUNCT
ejpam-4559	34	4	,	,	PUNCT
ejpam-4559	34	5	macgregor	macgregor	PROPN
ejpam-4559	35	1	[	[	X
ejpam-4559	35	2	9	9	NUM
ejpam-4559	35	3	]	]	PUNCT
ejpam-4559	35	4	,	,	PUNCT
ejpam-4559	35	5	and	and	CCONJ
ejpam-4559	35	6	silverman	silverman	NOUN
ejpam-4559	35	7	and	and	CCONJ
ejpam-4559	35	8	silvia	silvia	PROPN
ejpam-4559	35	9	[	[	X
ejpam-4559	35	10	17	17	NUM
ejpam-4559	35	11	]	]	PUNCT
ejpam-4559	35	12	were	be	AUX
ejpam-4559	35	13	among	among	ADP
ejpam-4559	35	14	the	the	DET
ejpam-4559	35	15	first	first	ADJ
ejpam-4559	35	16	researchers	researcher	NOUN
ejpam-4559	35	17	to	to	PART
ejpam-4559	35	18	study	study	VERB
ejpam-4559	35	19	the	the	DET
ejpam-4559	35	20	classes	class	NOUN
ejpam-4559	35	21	r	r	NOUN
ejpam-4559	35	22	,	,	PUNCT
ejpam-4559	35	23	r	r	NOUN
ejpam-4559	35	24	(	(	PUNCT
ejpam-4559	35	25	δ	δ	PROPN
ejpam-4559	35	26	)	)	PUNCT
ejpam-4559	35	27	,	,	PUNCT
ejpam-4559	35	28	and	and	CCONJ
ejpam-4559	35	29	r	r	NOUN
ejpam-4559	35	30	(	(	PUNCT
ejpam-4559	35	31	α	α	NOUN
ejpam-4559	35	32	)	)	PUNCT
ejpam-4559	35	33	.	.	PUNCT
ejpam-4559	36	1	recently	recently	ADV
ejpam-4559	36	2	,	,	PUNCT
ejpam-4559	36	3	the	the	DET
ejpam-4559	36	4	investigation	investigation	NOUN
ejpam-4559	36	5	into	into	ADP
ejpam-4559	36	6	the	the	DET
ejpam-4559	36	7	class	class	NOUN
ejpam-4559	36	8	of	of	ADP
ejpam-4559	36	9	bounded	bounded	ADJ
ejpam-4559	36	10	turning	turning	NOUN
ejpam-4559	36	11	functions	function	NOUN
ejpam-4559	36	12	and	and	CCONJ
ejpam-4559	36	13	coefficient	coefficient	NOUN
ejpam-4559	36	14	problems	problem	NOUN
ejpam-4559	36	15	such	such	ADJ
ejpam-4559	36	16	as	as	ADP
ejpam-4559	36	17	the	the	DET
ejpam-4559	36	18	hankel	hankel	NOUN
ejpam-4559	36	19	determinant	determinant	ADJ
ejpam-4559	36	20	for	for	ADP
ejpam-4559	36	21	the	the	DET
ejpam-4559	36	22	higher	high	ADJ
ejpam-4559	36	23	order	order	NOUN
ejpam-4559	36	24	has	have	AUX
ejpam-4559	36	25	been	be	AUX
ejpam-4559	36	26	extensively	extensively	ADV
ejpam-4559	36	27	studied	study	VERB
ejpam-4559	36	28	by	by	ADP
ejpam-4559	36	29	other	other	ADJ
ejpam-4559	36	30	researchers	researcher	NOUN
ejpam-4559	36	31	,	,	PUNCT
ejpam-4559	36	32	see	see	VERB
ejpam-4559	36	33	for	for	ADP
ejpam-4559	36	34	example	example	NOUN
ejpam-4559	37	1	[	[	X
ejpam-4559	37	2	3	3	NUM
ejpam-4559	37	3	,	,	PUNCT
ejpam-4559	37	4	4	4	NUM
ejpam-4559	37	5	]	]	PUNCT
ejpam-4559	37	6	.	.	PUNCT
ejpam-4559	38	1	we	we	PRON
ejpam-4559	38	2	may	may	AUX
ejpam-4559	38	3	point	point	VERB
ejpam-4559	38	4	interested	interested	ADJ
ejpam-4559	38	5	readers	reader	NOUN
ejpam-4559	38	6	to	to	ADP
ejpam-4559	38	7	recent	recent	ADJ
ejpam-4559	38	8	advances	advance	NOUN
ejpam-4559	38	9	in	in	ADP
ejpam-4559	38	10	the	the	DET
ejpam-4559	38	11	class	class	NOUN
ejpam-4559	38	12	of	of	ADP
ejpam-4559	38	13	bounded	bounded	ADJ
ejpam-4559	38	14	turning	turning	NOUN
ejpam-4559	38	15	functions	function	NOUN
ejpam-4559	38	16	connected	connect	VERB
ejpam-4559	38	17	to	to	ADP
ejpam-4559	38	18	a	a	DET
ejpam-4559	38	19	three	three	NUM
ejpam-4559	38	20	-	-	PUNCT
ejpam-4559	38	21	leaf	leaf	NOUN
ejpam-4559	38	22	-	-	PUNCT
ejpam-4559	38	23	shaped	shape	VERB
ejpam-4559	38	24	domain	domain	NOUN
ejpam-4559	38	25	and	and	CCONJ
ejpam-4559	38	26	bernoulli	bernoulli	PROPN
ejpam-4559	38	27	’s	’s	PART
ejpam-4559	38	28	lemniscate	lemniscate	PROPN
ejpam-4559	38	29	as	as	ADV
ejpam-4559	38	30	well	well	ADV
ejpam-4559	38	31	as	as	ADP
ejpam-4559	38	32	their	their	PRON
ejpam-4559	38	33	coefficient	coefficient	NOUN
ejpam-4559	38	34	problems	problem	NOUN
ejpam-4559	38	35	like	like	ADP
ejpam-4559	38	36	the	the	DET
ejpam-4559	38	37	hankel	hankel	NOUN
ejpam-4559	38	38	determinant	determinant	ADJ
ejpam-4559	38	39	,	,	PUNCT
ejpam-4559	38	40	logarithmic	logarithmic	ADJ
ejpam-4559	38	41	coefficients	coefficient	NOUN
ejpam-4559	38	42	,	,	PUNCT
ejpam-4559	38	43	and	and	CCONJ
ejpam-4559	38	44	the	the	DET
ejpam-4559	38	45	hankel	hankel	NOUN
ejpam-4559	38	46	determinant	determinant	ADJ
ejpam-4559	38	47	with	with	ADP
ejpam-4559	38	48	logarithmic	logarithmic	ADJ
ejpam-4559	38	49	coefficients	coefficient	NOUN
ejpam-4559	38	50	,	,	PUNCT
ejpam-4559	38	51	which	which	PRON
ejpam-4559	38	52	point	point	VERB
ejpam-4559	38	53	in	in	ADP
ejpam-4559	38	54	a	a	DET
ejpam-4559	38	55	different	different	ADJ
ejpam-4559	38	56	direction	direction	NOUN
ejpam-4559	38	57	than	than	ADP
ejpam-4559	38	58	the	the	DET
ejpam-4559	38	59	current	current	ADJ
ejpam-4559	38	60	study	study	NOUN
ejpam-4559	38	61	,	,	PUNCT
ejpam-4559	38	62	see	see	VERB
ejpam-4559	38	63	[	[	X
ejpam-4559	38	64	16	16	NUM
ejpam-4559	38	65	,	,	PUNCT
ejpam-4559	38	66	23	23	NUM
ejpam-4559	38	67	]	]	PUNCT
ejpam-4559	38	68	.	.	PUNCT
ejpam-4559	39	1	finding	find	VERB
ejpam-4559	39	2	estimates	estimate	NOUN
ejpam-4559	39	3	on	on	ADP
ejpam-4559	39	4	the	the	DET
ejpam-4559	39	5	functional	functional	ADJ
ejpam-4559	39	6	involving	involve	VERB
ejpam-4559	39	7	coefficients	coefficient	NOUN
ejpam-4559	39	8	of	of	ADP
ejpam-4559	39	9	f	f	PROPN
ejpam-4559	39	10	(	(	PUNCT
ejpam-4559	39	11	z	z	NOUN
ejpam-4559	39	12	)	)	PUNCT
ejpam-4559	39	13	∈	∈	PROPN
ejpam-4559	39	14	a	a	PRON
ejpam-4559	39	15	has	have	AUX
ejpam-4559	39	16	been	be	AUX
ejpam-4559	39	17	a	a	DET
ejpam-4559	39	18	major	major	ADJ
ejpam-4559	39	19	research	research	NOUN
ejpam-4559	39	20	area	area	NOUN
ejpam-4559	39	21	in	in	ADP
ejpam-4559	39	22	geometric	geometric	ADJ
ejpam-4559	39	23	function	function	NOUN
ejpam-4559	39	24	theory	theory	NOUN
ejpam-4559	39	25	since	since	SCONJ
ejpam-4559	39	26	the	the	DET
ejpam-4559	39	27	development	development	NOUN
ejpam-4559	39	28	of	of	ADP
ejpam-4559	39	29	the	the	DET
ejpam-4559	39	30	bieberbach	bieberbach	NOUN
ejpam-4559	39	31	conjecture	conjecture	NOUN
ejpam-4559	39	32	.	.	PUNCT
ejpam-4559	40	1	toeplitz	toeplitz	NOUN
ejpam-4559	40	2	determinant	determinant	ADJ
ejpam-4559	40	3	,	,	PUNCT
ejpam-4559	40	4	for	for	ADP
ejpam-4559	40	5	example	example	NOUN
ejpam-4559	40	6	,	,	PUNCT
ejpam-4559	40	7	whose	whose	DET
ejpam-4559	40	8	elements	element	NOUN
ejpam-4559	40	9	are	be	AUX
ejpam-4559	40	10	the	the	DET
ejpam-4559	40	11	coefficients	coefficient	NOUN
ejpam-4559	40	12	of	of	ADP
ejpam-4559	40	13	f	f	PROPN
ejpam-4559	40	14	(	(	PUNCT
ejpam-4559	40	15	z	z	NOUN
ejpam-4559	40	16	)	)	PUNCT
ejpam-4559	40	17	∈	∈	PROPN
ejpam-4559	40	18	a	a	PRON
ejpam-4559	40	19	has	have	AUX
ejpam-4559	40	20	been	be	AUX
ejpam-4559	40	21	appealing	appeal	VERB
ejpam-4559	40	22	to	to	ADP
ejpam-4559	40	23	many	many	ADJ
ejpam-4559	40	24	researchers	researcher	NOUN
ejpam-4559	40	25	because	because	SCONJ
ejpam-4559	40	26	it	it	PRON
ejpam-4559	40	27	is	be	AUX
ejpam-4559	40	28	related	relate	VERB
ejpam-4559	40	29	to	to	ADP
ejpam-4559	40	30	the	the	DET
ejpam-4559	40	31	coefficient	coefficient	NOUN
ejpam-4559	40	32	problems	problem	NOUN
ejpam-4559	40	33	.	.	PUNCT
ejpam-4559	41	1	toeplitz	toeplitz	NOUN
ejpam-4559	41	2	determinant	determinant	ADJ
ejpam-4559	41	3	appeared	appear	VERB
ejpam-4559	41	4	in	in	ADP
ejpam-4559	41	5	all	all	DET
ejpam-4559	41	6	branches	branch	NOUN
ejpam-4559	41	7	of	of	ADP
ejpam-4559	41	8	pure	pure	ADJ
ejpam-4559	41	9	and	and	CCONJ
ejpam-4559	41	10	applied	applied	ADJ
ejpam-4559	41	11	mathematics	mathematic	NOUN
ejpam-4559	41	12	,	,	PUNCT
ejpam-4559	41	13	statistics	statistic	NOUN
ejpam-4559	41	14	and	and	CCONJ
ejpam-4559	41	15	probability	probability	NOUN
ejpam-4559	41	16	,	,	PUNCT
ejpam-4559	41	17	image	image	NOUN
ejpam-4559	41	18	processing	processing	NOUN
ejpam-4559	41	19	,	,	PUNCT
ejpam-4559	41	20	quantum	quantum	NOUN
ejpam-4559	41	21	mechanics	mechanic	NOUN
ejpam-4559	41	22	,	,	PUNCT
ejpam-4559	41	23	queuing	queue	VERB
ejpam-4559	41	24	networks	network	NOUN
ejpam-4559	41	25	,	,	PUNCT
ejpam-4559	41	26	signal	signal	ADJ
ejpam-4559	41	27	processing	processing	NOUN
ejpam-4559	41	28	,	,	PUNCT
ejpam-4559	41	29	and	and	CCONJ
ejpam-4559	41	30	time	time	NOUN
ejpam-4559	41	31	series	series	NOUN
ejpam-4559	41	32	analysis	analysis	NOUN
ejpam-4559	41	33	(	(	PUNCT
ejpam-4559	41	34	see	see	VERB
ejpam-4559	41	35	ye	ye	PRON
ejpam-4559	41	36	and	and	CCONJ
ejpam-4559	41	37	lim	lim	PROPN
ejpam-4559	42	1	[	[	X
ejpam-4559	42	2	24	24	NUM
ejpam-4559	42	3	]	]	PUNCT
ejpam-4559	42	4	and	and	CCONJ
ejpam-4559	42	5	references	reference	NOUN
ejpam-4559	42	6	therein	therein	ADV
ejpam-4559	42	7	)	)	PUNCT
ejpam-4559	42	8	.	.	PUNCT
ejpam-4559	43	1	here	here	ADV
ejpam-4559	43	2	we	we	PRON
ejpam-4559	43	3	consider	consider	VERB
ejpam-4559	43	4	the	the	DET
ejpam-4559	43	5	symmetric	symmetric	ADJ
ejpam-4559	43	6	toeplitz	toeplitz	NOUN
ejpam-4559	43	7	determinant	determinant	ADJ
ejpam-4559	43	8	and	and	CCONJ
ejpam-4559	43	9	it	it	PRON
ejpam-4559	43	10	is	be	AUX
ejpam-4559	43	11	defined	define	VERB
ejpam-4559	43	12	by	by	ADP
ejpam-4559	43	13	[	[	X
ejpam-4559	43	14	21	21	NUM
ejpam-4559	43	15	]	]	PUNCT
ejpam-4559	43	16	tq	tq	X
ejpam-4559	43	17	(	(	PUNCT
ejpam-4559	43	18	n	n	CCONJ
ejpam-4559	43	19	)	)	PUNCT
ejpam-4559	44	1	=	=	SYM
ejpam-4559	44	2	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-4559	44	3	an	an	DET
ejpam-4559	44	4	an+1	an+1	NOUN
ejpam-4559	44	5	...	...	PUNCT
ejpam-4559	45	1	an+q−1	an+q−1	PRON
ejpam-4559	45	2	an+1	an+1	VERB
ejpam-4559	45	3	an	an	PRON
ejpam-4559	45	4	...	...	PUNCT
ejpam-4559	45	5	an+q−2	an+q−2	NOUN
ejpam-4559	45	6	·	·	PUNCT
ejpam-4559	45	7	·	·	PUNCT
ejpam-4559	45	8	·	·	PUNCT
ejpam-4559	45	9	·	·	PUNCT
ejpam-4559	45	10	·	·	PUNCT
ejpam-4559	45	11	·	·	PUNCT
ejpam-4559	45	12	...	...	PUNCT
ejpam-4559	45	13	·	·	PUNCT
ejpam-4559	45	14	·	·	PUNCT
ejpam-4559	45	15	·	·	PUNCT
ejpam-4559	46	1	an+q−1	an+q−1	PRON
ejpam-4559	46	2	an+q−2	an+q−2	VERB
ejpam-4559	46	3	...	...	PUNCT
ejpam-4559	46	4	an	an	DET
ejpam-4559	46	5	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-4559	46	6	,	,	PUNCT
ejpam-4559	46	7	a1	a1	NOUN
ejpam-4559	46	8	=	=	SYM
ejpam-4559	46	9	1	1	X
ejpam-4559	46	10	.	.	PUNCT
ejpam-4559	47	1	the	the	DET
ejpam-4559	47	2	estimates	estimate	NOUN
ejpam-4559	47	3	of	of	ADP
ejpam-4559	47	4	the	the	DET
ejpam-4559	47	5	toeplitz	toeplitz	NOUN
ejpam-4559	47	6	determinant	determinant	ADJ
ejpam-4559	47	7	were	be	AUX
ejpam-4559	47	8	obtained	obtain	VERB
ejpam-4559	47	9	for	for	ADP
ejpam-4559	47	10	different	different	ADJ
ejpam-4559	47	11	classes	class	NOUN
ejpam-4559	47	12	of	of	ADP
ejpam-4559	47	13	univalent	univalent	ADJ
ejpam-4559	47	14	functions	function	NOUN
ejpam-4559	47	15	.	.	PUNCT
ejpam-4559	48	1	for	for	ADP
ejpam-4559	48	2	instance	instance	NOUN
ejpam-4559	48	3	,	,	PUNCT
ejpam-4559	48	4	ali	ali	PROPN
ejpam-4559	48	5	et	et	PROPN
ejpam-4559	48	6	al	al	PROPN
ejpam-4559	48	7	.	.	PUNCT
ejpam-4559	49	1	[	[	X
ejpam-4559	49	2	2	2	NUM
ejpam-4559	49	3	]	]	PUNCT
ejpam-4559	49	4	studied	study	VERB
ejpam-4559	49	5	toeplitz	toeplitz	NOUN
ejpam-4559	49	6	matrices	matrix	NOUN
ejpam-4559	49	7	whose	whose	DET
ejpam-4559	49	8	elements	element	NOUN
ejpam-4559	49	9	are	be	AUX
ejpam-4559	49	10	the	the	DET
ejpam-4559	49	11	coefficients	coefficient	NOUN
ejpam-4559	49	12	of	of	ADP
ejpam-4559	49	13	bounded	bounded	ADJ
ejpam-4559	49	14	turning	turning	NOUN
ejpam-4559	49	15	,	,	PUNCT
ejpam-4559	49	16	starlike	starlike	NOUN
ejpam-4559	49	17	,	,	PUNCT
ejpam-4559	49	18	close	close	NOUN
ejpam-4559	49	19	-	-	PUNCT
ejpam-4559	49	20	to	to	ADP
ejpam-4559	49	21	-	-	PUNCT
ejpam-4559	49	22	convex	convex	NOUN
ejpam-4559	49	23	,	,	PUNCT
ejpam-4559	49	24	and	and	CCONJ
ejpam-4559	49	25	univalent	univalent	ADJ
ejpam-4559	49	26	functions	function	NOUN
ejpam-4559	49	27	,	,	PUNCT
ejpam-4559	49	28	radhika	radhika	PROPN
ejpam-4559	49	29	et	et	PROPN
ejpam-4559	49	30	al	al	PROPN
ejpam-4559	49	31	.	.	PUNCT
ejpam-4559	50	1	[	[	X
ejpam-4559	50	2	12	12	NUM
ejpam-4559	50	3	]	]	PUNCT
ejpam-4559	50	4	obtained	obtain	VERB
ejpam-4559	50	5	sharp	sharp	ADJ
ejpam-4559	50	6	bounds	bound	NOUN
ejpam-4559	50	7	for	for	ADP
ejpam-4559	50	8	toeplitz	toeplitz	NOUN
ejpam-4559	50	9	determinants	determinant	NOUN
ejpam-4559	50	10	for	for	ADP
ejpam-4559	50	11	the	the	DET
ejpam-4559	50	12	class	class	NOUN
ejpam-4559	50	13	of	of	ADP
ejpam-4559	50	14	bounded	bounded	ADJ
ejpam-4559	50	15	turning	turning	NOUN
ejpam-4559	50	16	functions	function	NOUN
ejpam-4559	50	17	,	,	PUNCT
ejpam-4559	50	18	zhang	zhang	PROPN
ejpam-4559	50	19	et	et	PROPN
ejpam-4559	50	20	al	al	PROPN
ejpam-4559	50	21	.	.	PUNCT
ejpam-4559	51	1	[	[	X
ejpam-4559	51	2	25	25	NUM
ejpam-4559	51	3	]	]	PUNCT
ejpam-4559	51	4	considered	consider	VERB
ejpam-4559	51	5	toeplitz	toeplitz	NOUN
ejpam-4559	51	6	determinants	determinant	NOUN
ejpam-4559	51	7	of	of	ADP
ejpam-4559	51	8	starlike	starlike	NOUN
ejpam-4559	51	9	functions	function	NOUN
ejpam-4559	51	10	connected	connect	VERB
ejpam-4559	51	11	with	with	ADP
ejpam-4559	51	12	the	the	DET
ejpam-4559	51	13	sine	sine	ADJ
ejpam-4559	51	14	function	function	NOUN
ejpam-4559	51	15	,	,	PUNCT
ejpam-4559	51	16	and	and	CCONJ
ejpam-4559	51	17	zulfiqar	zulfiqar	VERB
ejpam-4559	51	18	et	et	PROPN
ejpam-4559	51	19	al	al	PROPN
ejpam-4559	51	20	.	.	PUNCT
ejpam-4559	52	1	[	[	X
ejpam-4559	52	2	26	26	NUM
ejpam-4559	52	3	]	]	PUNCT
ejpam-4559	52	4	investigated	investigate	VERB
ejpam-4559	52	5	the	the	DET
ejpam-4559	52	6	fourth	fourth	ADJ
ejpam-4559	52	7	-	-	PUNCT
ejpam-4559	52	8	order	order	NOUN
ejpam-4559	52	9	toeplitz	toeplitz	NOUN
ejpam-4559	52	10	determinant	determinant	ADJ
ejpam-4559	52	11	for	for	ADP
ejpam-4559	52	12	convex	convex	NOUN
ejpam-4559	52	13	functions	function	NOUN
ejpam-4559	52	14	connected	connect	VERB
ejpam-4559	52	15	with	with	ADP
ejpam-4559	52	16	the	the	DET
ejpam-4559	52	17	sine	sine	ADJ
ejpam-4559	52	18	function	function	NOUN
ejpam-4559	52	19	.	.	PUNCT
ejpam-4559	53	1	much	much	ADJ
ejpam-4559	53	2	of	of	ADP
ejpam-4559	53	3	the	the	DET
ejpam-4559	53	4	recent	recent	ADJ
ejpam-4559	53	5	history	history	NOUN
ejpam-4559	53	6	of	of	ADP
ejpam-4559	53	7	the	the	DET
ejpam-4559	53	8	development	development	NOUN
ejpam-4559	53	9	of	of	ADP
ejpam-4559	53	10	this	this	DET
ejpam-4559	53	11	problem	problem	NOUN
ejpam-4559	53	12	can	can	AUX
ejpam-4559	53	13	also	also	ADV
ejpam-4559	53	14	be	be	AUX
ejpam-4559	53	15	found	find	VERB
ejpam-4559	53	16	in	in	ADP
ejpam-4559	53	17	[	[	X
ejpam-4559	53	18	1	1	NUM
ejpam-4559	53	19	,	,	PUNCT
ejpam-4559	53	20	5	5	NUM
ejpam-4559	53	21	,	,	PUNCT
ejpam-4559	53	22	11	11	NUM
ejpam-4559	53	23	,	,	PUNCT
ejpam-4559	53	24	13–15	13–15	NUM
ejpam-4559	53	25	,	,	PUNCT
ejpam-4559	53	26	18	18	NUM
ejpam-4559	53	27	–	–	SYM
ejpam-4559	53	28	20	20	NUM
ejpam-4559	53	29	,	,	PUNCT
ejpam-4559	53	30	22	22	NUM
ejpam-4559	53	31	]	]	PUNCT
ejpam-4559	53	32	.	.	PUNCT
ejpam-4559	54	1	thus	thus	ADV
ejpam-4559	54	2	,	,	PUNCT
ejpam-4559	54	3	inspired	inspire	VERB
ejpam-4559	54	4	by	by	ADP
ejpam-4559	54	5	these	these	DET
ejpam-4559	54	6	works	work	NOUN
ejpam-4559	54	7	,	,	PUNCT
ejpam-4559	54	8	in	in	ADP
ejpam-4559	54	9	this	this	DET
ejpam-4559	54	10	paper	paper	NOUN
ejpam-4559	54	11	,	,	PUNCT
ejpam-4559	54	12	we	we	PRON
ejpam-4559	54	13	aim	aim	VERB
ejpam-4559	54	14	to	to	PART
ejpam-4559	54	15	investigate	investigate	VERB
ejpam-4559	54	16	the	the	DET
ejpam-4559	54	17	upper	upper	ADJ
ejpam-4559	54	18	n.	n.	PROPN
ejpam-4559	54	19	h.	h.	PROPN
ejpam-4559	54	20	a.	a.	PROPN
ejpam-4559	54	21	a.	a.	PROPN
ejpam-4559	54	22	wahid	wahid	PROPN
ejpam-4559	54	23	et	et	PROPN
ejpam-4559	54	24	al	al	PROPN
ejpam-4559	54	25	.	.	PUNCT
ejpam-4559	54	26	/	/	SYM
ejpam-4559	54	27	eur	eur	PROPN
ejpam-4559	54	28	.	.	PUNCT
ejpam-4559	55	1	j.	j.	PROPN
ejpam-4559	55	2	pure	pure	PROPN
ejpam-4559	55	3	appl	appl	PROPN
ejpam-4559	55	4	.	.	PROPN
ejpam-4559	55	5	math	math	PROPN
ejpam-4559	55	6	,	,	PUNCT
ejpam-4559	55	7	15	15	NUM
ejpam-4559	55	8	(	(	PUNCT
ejpam-4559	55	9	4	4	NUM
ejpam-4559	55	10	)	)	PUNCT
ejpam-4559	55	11	(	(	PUNCT
ejpam-4559	55	12	2022	2022	NUM
ejpam-4559	55	13	)	)	PUNCT
ejpam-4559	55	14	,	,	PUNCT
ejpam-4559	55	15	1937	1937	NUM
ejpam-4559	55	16	-	-	SYM
ejpam-4559	55	17	1947	1947	NUM
ejpam-4559	55	18	1939	1939	NUM
ejpam-4559	55	19	bounds	bound	NOUN
ejpam-4559	55	20	of	of	ADP
ejpam-4559	55	21	the	the	DET
ejpam-4559	55	22	second	second	ADJ
ejpam-4559	55	23	,	,	PUNCT
ejpam-4559	55	24	third	third	ADJ
ejpam-4559	55	25	,	,	PUNCT
ejpam-4559	55	26	and	and	CCONJ
ejpam-4559	55	27	fourth	fourth	ADJ
ejpam-4559	55	28	-	-	PUNCT
ejpam-4559	55	29	order	order	NOUN
ejpam-4559	55	30	toeplitz	toeplitz	NOUN
ejpam-4559	55	31	determinants	determinant	NOUN
ejpam-4559	55	32	for	for	ADP
ejpam-4559	55	33	functions	function	NOUN
ejpam-4559	55	34	of	of	ADP
ejpam-4559	55	35	the	the	DET
ejpam-4559	55	36	class	class	NOUN
ejpam-4559	55	37	g	g	PROPN
ejpam-4559	55	38	(	(	PUNCT
ejpam-4559	55	39	α	α	PROPN
ejpam-4559	55	40	,	,	PUNCT
ejpam-4559	55	41	δ	δ	PROPN
ejpam-4559	55	42	)	)	PUNCT
ejpam-4559	55	43	.	.	PUNCT
ejpam-4559	56	1	in	in	ADP
ejpam-4559	56	2	particular	particular	ADJ
ejpam-4559	56	3	,	,	PUNCT
ejpam-4559	56	4	we	we	PRON
ejpam-4559	56	5	find	find	VERB
ejpam-4559	56	6	the	the	DET
ejpam-4559	56	7	bounds	bound	NOUN
ejpam-4559	56	8	for	for	ADP
ejpam-4559	56	9	the	the	DET
ejpam-4559	56	10	following	follow	VERB
ejpam-4559	56	11	determinants	determinant	NOUN
ejpam-4559	56	12	:	:	PUNCT
ejpam-4559	56	13	t2	t2	NOUN
ejpam-4559	56	14	(	(	PUNCT
ejpam-4559	56	15	n	n	CCONJ
ejpam-4559	56	16	)	)	PUNCT
ejpam-4559	56	17	=	=	SYM
ejpam-4559	56	18	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4559	56	19	an	an	DET
ejpam-4559	56	20	an+1	an+1	NOUN
ejpam-4559	56	21	an+1	an+1	NOUN
ejpam-4559	56	22	an	an	DET
ejpam-4559	56	23	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4559	56	24	,	,	PUNCT
ejpam-4559	56	25	n	n	CCONJ
ejpam-4559	56	26	⩾	⩾	NOUN
ejpam-4559	56	27	2	2	NUM
ejpam-4559	56	28	,	,	PUNCT
ejpam-4559	56	29	(	(	PUNCT
ejpam-4559	56	30	3	3	X
ejpam-4559	56	31	)	)	PUNCT
ejpam-4559	56	32	t3	t3	NOUN
ejpam-4559	56	33	(	(	PUNCT
ejpam-4559	56	34	1	1	NUM
ejpam-4559	56	35	)	)	PUNCT
ejpam-4559	56	36	=	=	SYM
ejpam-4559	56	37	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4559	56	38	1	1	NUM
ejpam-4559	56	39	a2	a2	PROPN
ejpam-4559	56	40	a3	a3	PROPN
ejpam-4559	56	41	a2	a2	PROPN
ejpam-4559	56	42	1	1	NUM
ejpam-4559	56	43	a2	a2	PROPN
ejpam-4559	56	44	a3	a3	NOUN
ejpam-4559	56	45	a2	a2	PROPN
ejpam-4559	56	46	1	1	NUM
ejpam-4559	56	47	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-4559	56	48	,	,	PUNCT
ejpam-4559	56	49	(	(	PUNCT
ejpam-4559	56	50	4	4	X
ejpam-4559	56	51	)	)	PUNCT
ejpam-4559	56	52	t3	t3	NOUN
ejpam-4559	56	53	(	(	PUNCT
ejpam-4559	56	54	2	2	NUM
ejpam-4559	56	55	)	)	PUNCT
ejpam-4559	56	56	=	=	SYM
ejpam-4559	56	57	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-4559	56	58	a2	a2	PROPN
ejpam-4559	56	59	a3	a3	PROPN
ejpam-4559	56	60	a4	a4	PROPN
ejpam-4559	56	61	a3	a3	NOUN
ejpam-4559	56	62	a2	a2	PROPN
ejpam-4559	56	63	a3	a3	PROPN
ejpam-4559	56	64	a4	a4	PROPN
ejpam-4559	56	65	a2	a2	PROPN
ejpam-4559	56	66	a2	a2	PROPN
ejpam-4559	56	67	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-4559	56	68	,	,	PUNCT
ejpam-4559	56	69	(	(	PUNCT
ejpam-4559	56	70	5	5	X
ejpam-4559	56	71	)	)	PUNCT
ejpam-4559	56	72	t3	t3	NOUN
ejpam-4559	56	73	(	(	PUNCT
ejpam-4559	56	74	3	3	NUM
ejpam-4559	56	75	)	)	PUNCT
ejpam-4559	56	76	=	=	SYM
ejpam-4559	56	77	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-4559	56	78	a3	a3	NOUN
ejpam-4559	56	79	a4	a4	PROPN
ejpam-4559	56	80	a5	a5	NOUN
ejpam-4559	56	81	a4	a4	PROPN
ejpam-4559	56	82	a3	a3	NOUN
ejpam-4559	56	83	a4	a4	NOUN
ejpam-4559	56	84	a5	a5	NOUN
ejpam-4559	56	85	a4	a4	PROPN
ejpam-4559	56	86	a3	a3	NOUN
ejpam-4559	56	87	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-4559	56	88	,	,	PUNCT
ejpam-4559	56	89	(	(	PUNCT
ejpam-4559	56	90	6	6	NUM
ejpam-4559	56	91	)	)	PUNCT
ejpam-4559	56	92	and	and	CCONJ
ejpam-4559	56	93	t4	t4	PROPN
ejpam-4559	56	94	(	(	PUNCT
ejpam-4559	56	95	1	1	NUM
ejpam-4559	56	96	)	)	PUNCT
ejpam-4559	56	97	=	=	PUNCT
ejpam-4559	56	98	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ejpam-4559	56	99	1	1	NUM
ejpam-4559	56	100	a2	a2	PROPN
ejpam-4559	56	101	a3	a3	PROPN
ejpam-4559	56	102	a4	a4	PROPN
ejpam-4559	56	103	a2	a2	PROPN
ejpam-4559	56	104	1	1	NUM
ejpam-4559	56	105	a4	a4	NOUN
ejpam-4559	56	106	a3	a3	NOUN
ejpam-4559	56	107	a3	a3	NOUN
ejpam-4559	56	108	a4	a4	PROPN
ejpam-4559	56	109	1	1	NUM
ejpam-4559	56	110	a2	a2	PROPN
ejpam-4559	56	111	a4	a4	PROPN
ejpam-4559	56	112	a3	a3	NOUN
ejpam-4559	56	113	a2	a2	PROPN
ejpam-4559	56	114	1	1	NUM
ejpam-4559	56	115	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ejpam-4559	56	116	,	,	PUNCT
ejpam-4559	56	117	(	(	PUNCT
ejpam-4559	56	118	7	7	X
ejpam-4559	56	119	)	)	PUNCT
ejpam-4559	56	120	where	where	SCONJ
ejpam-4559	56	121	the	the	DET
ejpam-4559	56	122	elements	element	NOUN
ejpam-4559	56	123	are	be	AUX
ejpam-4559	56	124	the	the	DET
ejpam-4559	56	125	coefficients	coefficient	NOUN
ejpam-4559	56	126	of	of	ADP
ejpam-4559	56	127	the	the	DET
ejpam-4559	56	128	functions	function	NOUN
ejpam-4559	56	129	f	f	X
ejpam-4559	56	130	(	(	PUNCT
ejpam-4559	56	131	z	z	NOUN
ejpam-4559	56	132	)	)	PUNCT
ejpam-4559	56	133	of	of	ADP
ejpam-4559	56	134	the	the	DET
ejpam-4559	56	135	form	form	NOUN
ejpam-4559	56	136	(	(	PUNCT
ejpam-4559	56	137	1	1	NUM
ejpam-4559	56	138	)	)	PUNCT
ejpam-4559	56	139	in	in	ADP
ejpam-4559	56	140	g	g	PROPN
ejpam-4559	56	141	(	(	PUNCT
ejpam-4559	56	142	α	α	PROPN
ejpam-4559	56	143	,	,	PUNCT
ejpam-4559	56	144	δ	δ	PROPN
ejpam-4559	56	145	)	)	PUNCT
ejpam-4559	56	146	.	.	PUNCT
ejpam-4559	57	1	besides	besides	ADV
ejpam-4559	57	2	,	,	PUNCT
ejpam-4559	57	3	we	we	PRON
ejpam-4559	57	4	point	point	VERB
ejpam-4559	57	5	out	out	ADP
ejpam-4559	57	6	several	several	ADJ
ejpam-4559	57	7	special	special	ADJ
ejpam-4559	57	8	cases	case	NOUN
ejpam-4559	57	9	and	and	CCONJ
ejpam-4559	57	10	the	the	DET
ejpam-4559	57	11	consequences	consequence	NOUN
ejpam-4559	57	12	of	of	ADP
ejpam-4559	57	13	our	our	PRON
ejpam-4559	57	14	results	result	NOUN
ejpam-4559	57	15	.	.	PUNCT
ejpam-4559	58	1	we	we	PRON
ejpam-4559	58	2	shall	shall	AUX
ejpam-4559	58	3	need	need	VERB
ejpam-4559	58	4	the	the	DET
ejpam-4559	58	5	following	follow	VERB
ejpam-4559	58	6	lemmas	lemma	NOUN
ejpam-4559	58	7	in	in	ADP
ejpam-4559	58	8	order	order	NOUN
ejpam-4559	58	9	to	to	PART
ejpam-4559	58	10	prove	prove	VERB
ejpam-4559	58	11	our	our	PRON
ejpam-4559	58	12	main	main	ADJ
ejpam-4559	58	13	results	result	NOUN
ejpam-4559	58	14	.	.	PUNCT
ejpam-4559	59	1	lemma	lemma	PROPN
ejpam-4559	59	2	1	1	NUM
ejpam-4559	59	3	.	.	PUNCT
ejpam-4559	60	1	(	(	PUNCT
ejpam-4559	60	2	[	[	X
ejpam-4559	60	3	6	6	NUM
ejpam-4559	60	4	]	]	PUNCT
ejpam-4559	60	5	)	)	PUNCT
ejpam-4559	60	6	let	let	VERB
ejpam-4559	60	7	p	p	NOUN
ejpam-4559	60	8	(	(	PUNCT
ejpam-4559	60	9	z	z	NOUN
ejpam-4559	60	10	)	)	PUNCT
ejpam-4559	60	11	∈	∈	PROPN
ejpam-4559	60	12	p	p	NOUN
ejpam-4559	60	13	of	of	ADP
ejpam-4559	60	14	the	the	DET
ejpam-4559	60	15	form	form	NOUN
ejpam-4559	60	16	p	p	X
ejpam-4559	60	17	(	(	PUNCT
ejpam-4559	60	18	z	z	NOUN
ejpam-4559	60	19	)	)	PUNCT
ejpam-4559	60	20	=	=	SYM
ejpam-4559	60	21	1	1	NUM
ejpam-4559	60	22	+	+	CCONJ
ejpam-4559	60	23	∞∑	∞∑	NUM
ejpam-4559	60	24	n=1	n=1	PROPN
ejpam-4559	60	25	pnz	pnz	PROPN
ejpam-4559	60	26	n.	n.	NOUN
ejpam-4559	60	27	then	then	ADV
ejpam-4559	60	28	|pn|	|pn|	ADJ
ejpam-4559	60	29	⩽	⩽	NOUN
ejpam-4559	60	30	2	2	NUM
ejpam-4559	60	31	,	,	PUNCT
ejpam-4559	60	32	n	n	CCONJ
ejpam-4559	60	33	⩾	⩾	NOUN
ejpam-4559	60	34	1	1	NUM
ejpam-4559	60	35	.	.	PUNCT
ejpam-4559	61	1	the	the	DET
ejpam-4559	61	2	inequality	inequality	NOUN
ejpam-4559	61	3	is	be	AUX
ejpam-4559	61	4	sharp	sharp	ADJ
ejpam-4559	61	5	for	for	ADP
ejpam-4559	61	6	the	the	DET
ejpam-4559	61	7	function	function	NOUN
ejpam-4559	61	8	p	p	NOUN
ejpam-4559	61	9	(	(	PUNCT
ejpam-4559	61	10	z	z	NOUN
ejpam-4559	61	11	)	)	PUNCT
ejpam-4559	61	12	=	=	SYM
ejpam-4559	62	1	1+z	1+z	NUM
ejpam-4559	62	2	1−z	1−z	NUM
ejpam-4559	62	3	.	.	PUNCT
ejpam-4559	63	1	lemma	lemma	PROPN
ejpam-4559	63	2	2	2	NUM
ejpam-4559	63	3	.	.	PUNCT
ejpam-4559	64	1	(	(	PUNCT
ejpam-4559	64	2	[	[	X
ejpam-4559	64	3	7	7	NUM
ejpam-4559	64	4	]	]	PUNCT
ejpam-4559	64	5	)	)	PUNCT
ejpam-4559	64	6	let	let	VERB
ejpam-4559	64	7	p	p	NOUN
ejpam-4559	64	8	(	(	PUNCT
ejpam-4559	64	9	z	z	NOUN
ejpam-4559	64	10	)	)	PUNCT
ejpam-4559	64	11	∈	∈	PROPN
ejpam-4559	64	12	p	p	NOUN
ejpam-4559	64	13	of	of	ADP
ejpam-4559	64	14	the	the	DET
ejpam-4559	64	15	form	form	NOUN
ejpam-4559	64	16	p	p	X
ejpam-4559	64	17	(	(	PUNCT
ejpam-4559	64	18	z	z	NOUN
ejpam-4559	64	19	)	)	PUNCT
ejpam-4559	64	20	=	=	SYM
ejpam-4559	65	1	1	1	NUM
ejpam-4559	65	2	+	+	CCONJ
ejpam-4559	65	3	∞∑	∞∑	NUM
ejpam-4559	65	4	n=1	n=1	ADJ
ejpam-4559	65	5	pnz	pnz	NOUN
ejpam-4559	65	6	n	n	ADJ
ejpam-4559	65	7	and	and	CCONJ
ejpam-4559	65	8	µ	µ	PROPN
ejpam-4559	65	9	∈	∈	PROPN
ejpam-4559	65	10	c.	c.	NOUN
ejpam-4559	65	11	then	then	ADV
ejpam-4559	65	12	|pn	|pn	X
ejpam-4559	65	13	−	−	PROPN
ejpam-4559	65	14	µpkpn−k|	µpkpn−k|	PROPN
ejpam-4559	65	15	⩽	⩽	NOUN
ejpam-4559	65	16	2max	2max	NUM
ejpam-4559	65	17	{	{	PUNCT
ejpam-4559	65	18	1	1	NUM
ejpam-4559	65	19	,	,	PUNCT
ejpam-4559	65	20	|2µ−	|2µ−	NOUN
ejpam-4559	65	21	1|	1|	NUM
ejpam-4559	65	22	}	}	PUNCT
ejpam-4559	65	23	,	,	PUNCT
ejpam-4559	65	24	1	1	NUM
ejpam-4559	65	25	⩽	⩽	NOUN
ejpam-4559	65	26	k	k	PROPN
ejpam-4559	65	27	⩽	⩽	ADJ
ejpam-4559	65	28	n−	n−	PROPN
ejpam-4559	65	29	1	1	NUM
ejpam-4559	65	30	.	.	PUNCT
ejpam-4559	66	1	if	if	SCONJ
ejpam-4559	66	2	|2µ−	|2µ−	NOUN
ejpam-4559	66	3	1|	1|	NUM
ejpam-4559	66	4	⩾	⩾	NOUN
ejpam-4559	66	5	1	1	NUM
ejpam-4559	66	6	,	,	PUNCT
ejpam-4559	66	7	then	then	ADV
ejpam-4559	66	8	the	the	DET
ejpam-4559	66	9	inequality	inequality	NOUN
ejpam-4559	66	10	is	be	AUX
ejpam-4559	66	11	sharp	sharp	ADJ
ejpam-4559	66	12	for	for	ADP
ejpam-4559	66	13	the	the	DET
ejpam-4559	66	14	function	function	NOUN
ejpam-4559	66	15	p	p	NOUN
ejpam-4559	66	16	(	(	PUNCT
ejpam-4559	66	17	z	z	NOUN
ejpam-4559	66	18	)	)	PUNCT
ejpam-4559	67	1	=	=	SYM
ejpam-4559	67	2	1+z	1+z	NUM
ejpam-4559	67	3	1−z	1−z	NUM
ejpam-4559	67	4	or	or	CCONJ
ejpam-4559	67	5	its	its	PRON
ejpam-4559	67	6	rotations	rotation	NOUN
ejpam-4559	67	7	.	.	PUNCT
ejpam-4559	68	1	if	if	SCONJ
ejpam-4559	68	2	|2µ−	|2µ−	NOUN
ejpam-4559	68	3	1|	1|	X
ejpam-4559	68	4	<	<	X
ejpam-4559	68	5	1	1	NUM
ejpam-4559	68	6	,	,	PUNCT
ejpam-4559	68	7	then	then	ADV
ejpam-4559	68	8	the	the	DET
ejpam-4559	68	9	inequality	inequality	NOUN
ejpam-4559	68	10	is	be	AUX
ejpam-4559	68	11	sharp	sharp	ADJ
ejpam-4559	68	12	for	for	ADP
ejpam-4559	68	13	the	the	DET
ejpam-4559	68	14	function	function	NOUN
ejpam-4559	68	15	p	p	NOUN
ejpam-4559	68	16	(	(	PUNCT
ejpam-4559	68	17	z	z	NOUN
ejpam-4559	68	18	)	)	PUNCT
ejpam-4559	68	19	=	=	PUNCT
ejpam-4559	69	1	1+zn	1+zn	NUM
ejpam-4559	69	2	1−zn	1−zn	NUM
ejpam-4559	69	3	or	or	CCONJ
ejpam-4559	69	4	its	its	PRON
ejpam-4559	69	5	rotations	rotation	NOUN
ejpam-4559	69	6	.	.	PUNCT
ejpam-4559	70	1	2	2	X
ejpam-4559	70	2	.	.	X
ejpam-4559	70	3	main	main	ADJ
ejpam-4559	70	4	results	result	NOUN
ejpam-4559	70	5	in	in	ADP
ejpam-4559	70	6	this	this	DET
ejpam-4559	70	7	section	section	NOUN
ejpam-4559	70	8	,	,	PUNCT
ejpam-4559	70	9	we	we	PRON
ejpam-4559	70	10	state	state	VERB
ejpam-4559	70	11	and	and	CCONJ
ejpam-4559	70	12	prove	prove	VERB
ejpam-4559	70	13	the	the	DET
ejpam-4559	70	14	main	main	ADJ
ejpam-4559	70	15	results	result	NOUN
ejpam-4559	70	16	of	of	ADP
ejpam-4559	70	17	our	our	PRON
ejpam-4559	70	18	present	present	ADJ
ejpam-4559	70	19	investigation	investigation	NOUN
ejpam-4559	70	20	.	.	PUNCT
ejpam-4559	71	1	n.	n.	PROPN
ejpam-4559	71	2	h.	h.	PROPN
ejpam-4559	71	3	a.	a.	PROPN
ejpam-4559	71	4	a.	a.	PROPN
ejpam-4559	71	5	wahid	wahid	PROPN
ejpam-4559	71	6	et	et	PROPN
ejpam-4559	71	7	al	al	PROPN
ejpam-4559	71	8	.	.	PUNCT
ejpam-4559	71	9	/	/	SYM
ejpam-4559	71	10	eur	eur	PROPN
ejpam-4559	71	11	.	.	PUNCT
ejpam-4559	72	1	j.	j.	PROPN
ejpam-4559	72	2	pure	pure	PROPN
ejpam-4559	72	3	appl	appl	PROPN
ejpam-4559	72	4	.	.	PROPN
ejpam-4559	72	5	math	math	PROPN
ejpam-4559	72	6	,	,	PUNCT
ejpam-4559	72	7	15	15	NUM
ejpam-4559	72	8	(	(	PUNCT
ejpam-4559	72	9	4	4	NUM
ejpam-4559	72	10	)	)	PUNCT
ejpam-4559	72	11	(	(	PUNCT
ejpam-4559	72	12	2022	2022	NUM
ejpam-4559	72	13	)	)	PUNCT
ejpam-4559	72	14	,	,	PUNCT
ejpam-4559	72	15	1937	1937	NUM
ejpam-4559	72	16	-	-	SYM
ejpam-4559	72	17	1947	1947	NUM
ejpam-4559	72	18	1940	1940	NUM
ejpam-4559	72	19	theorem	theorem	NOUN
ejpam-4559	72	20	1	1	NUM
ejpam-4559	72	21	.	.	PUNCT
ejpam-4559	73	1	let	let	VERB
ejpam-4559	73	2	f	f	PROPN
ejpam-4559	73	3	(	(	PUNCT
ejpam-4559	73	4	z	z	X
ejpam-4559	73	5	)	)	PUNCT
ejpam-4559	73	6	∈	∈	PROPN
ejpam-4559	73	7	g	g	PROPN
ejpam-4559	73	8	(	(	PUNCT
ejpam-4559	73	9	α	α	PROPN
ejpam-4559	73	10	,	,	PUNCT
ejpam-4559	73	11	δ	δ	PROPN
ejpam-4559	73	12	)	)	PUNCT
ejpam-4559	73	13	be	be	VERB
ejpam-4559	73	14	of	of	ADP
ejpam-4559	73	15	the	the	DET
ejpam-4559	73	16	form	form	NOUN
ejpam-4559	73	17	(	(	PUNCT
ejpam-4559	73	18	1	1	NUM
ejpam-4559	73	19	)	)	PUNCT
ejpam-4559	73	20	.	.	PUNCT
ejpam-4559	74	1	then	then	ADV
ejpam-4559	74	2	|t2	|t2	PROPN
ejpam-4559	74	3	(	(	PUNCT
ejpam-4559	74	4	n)|	n)|	PROPN
ejpam-4559	74	5	⩽	⩽	NOUN
ejpam-4559	74	6	4tαδ	4tαδ	NUM
ejpam-4559	74	7	2	2	NUM
ejpam-4559	74	8	[	[	PUNCT
ejpam-4559	74	9	1	1	NUM
ejpam-4559	74	10	n2	n2	NOUN
ejpam-4559	74	11	+	+	CCONJ
ejpam-4559	74	12	1	1	NUM
ejpam-4559	74	13	(	(	PUNCT
ejpam-4559	74	14	n	n	X
ejpam-4559	74	15	+	+	X
ejpam-4559	74	16	1)2	1)2	NUM
ejpam-4559	74	17	]	]	PUNCT
ejpam-4559	74	18	,	,	PUNCT
ejpam-4559	74	19	where	where	SCONJ
ejpam-4559	74	20	tαδ	tαδ	NOUN
ejpam-4559	74	21	=	=	SYM
ejpam-4559	74	22	cosα−	cosα−	PROPN
ejpam-4559	74	23	δ	δ	PROPN
ejpam-4559	74	24	.	.	PUNCT
ejpam-4559	75	1	the	the	DET
ejpam-4559	75	2	inequality	inequality	NOUN
ejpam-4559	75	3	is	be	AUX
ejpam-4559	75	4	sharp	sharp	ADJ
ejpam-4559	75	5	.	.	PUNCT
ejpam-4559	76	1	proof	proof	NOUN
ejpam-4559	76	2	.	.	PUNCT
ejpam-4559	77	1	let	let	VERB
ejpam-4559	77	2	a	a	DET
ejpam-4559	77	3	function	function	NOUN
ejpam-4559	77	4	f	f	X
ejpam-4559	77	5	(	(	PUNCT
ejpam-4559	77	6	z	z	NOUN
ejpam-4559	77	7	)	)	PUNCT
ejpam-4559	77	8	∈	∈	PROPN
ejpam-4559	77	9	g	g	PROPN
ejpam-4559	77	10	(	(	PUNCT
ejpam-4559	77	11	α	α	PROPN
ejpam-4559	77	12	,	,	PUNCT
ejpam-4559	77	13	δ	δ	PROPN
ejpam-4559	77	14	)	)	PUNCT
ejpam-4559	77	15	given	give	VERB
ejpam-4559	77	16	by	by	ADP
ejpam-4559	77	17	(	(	PUNCT
ejpam-4559	77	18	1	1	NUM
ejpam-4559	77	19	)	)	PUNCT
ejpam-4559	77	20	.	.	PUNCT
ejpam-4559	78	1	then	then	ADV
ejpam-4559	78	2	there	there	PRON
ejpam-4559	78	3	exists	exist	VERB
ejpam-4559	78	4	a	a	DET
ejpam-4559	78	5	function	function	NOUN
ejpam-4559	78	6	p	p	X
ejpam-4559	78	7	(	(	PUNCT
ejpam-4559	78	8	z	z	NOUN
ejpam-4559	78	9	)	)	PUNCT
ejpam-4559	78	10	∈	∈	PROPN
ejpam-4559	78	11	p	p	NOUN
ejpam-4559	78	12	of	of	ADP
ejpam-4559	78	13	the	the	DET
ejpam-4559	78	14	form	form	NOUN
ejpam-4559	78	15	(	(	PUNCT
ejpam-4559	78	16	2	2	NUM
ejpam-4559	78	17	)	)	PUNCT
ejpam-4559	78	18	such	such	ADJ
ejpam-4559	78	19	that	that	SCONJ
ejpam-4559	78	20	[	[	X
ejpam-4559	78	21	10	10	NUM
ejpam-4559	78	22	]	]	PUNCT
ejpam-4559	78	23	eiαf	eiαf	NOUN
ejpam-4559	78	24	′	′	NUM
ejpam-4559	78	25	(	(	PUNCT
ejpam-4559	78	26	z	z	NOUN
ejpam-4559	78	27	)	)	PUNCT
ejpam-4559	78	28	−	−	PROPN
ejpam-4559	79	1	i	i	PRON
ejpam-4559	79	2	sinα−	sinα−	VERB
ejpam-4559	79	3	δ	δ	PROPN
ejpam-4559	79	4	tαδ	tαδ	VERB
ejpam-4559	80	1	=	=	SYM
ejpam-4559	80	2	p	p	X
ejpam-4559	80	3	(	(	PUNCT
ejpam-4559	80	4	z	z	NOUN
ejpam-4559	80	5	)	)	PUNCT
ejpam-4559	80	6	,	,	PUNCT
ejpam-4559	80	7	(	(	PUNCT
ejpam-4559	80	8	8)	8)	NUM
ejpam-4559	80	9	where	where	SCONJ
ejpam-4559	80	10	tαδ	tαδ	NOUN
ejpam-4559	80	11	=	=	SYM
ejpam-4559	80	12	cosα−	cosα−	PROPN
ejpam-4559	80	13	δ	δ	PROPN
ejpam-4559	80	14	.	.	PUNCT
ejpam-4559	81	1	rearranging	rearrange	VERB
ejpam-4559	81	2	(	(	PUNCT
ejpam-4559	81	3	8)	8)	NUM
ejpam-4559	81	4	and	and	CCONJ
ejpam-4559	81	5	hence	hence	ADV
ejpam-4559	81	6	using	use	VERB
ejpam-4559	81	7	the	the	DET
ejpam-4559	81	8	series	series	NOUN
ejpam-4559	81	9	representations	representation	NOUN
ejpam-4559	81	10	for	for	ADP
ejpam-4559	81	11	f	f	PROPN
ejpam-4559	81	12	′	′	NUM
ejpam-4559	81	13	(	(	PUNCT
ejpam-4559	81	14	z	z	NOUN
ejpam-4559	81	15	)	)	PUNCT
ejpam-4559	81	16	and	and	CCONJ
ejpam-4559	81	17	p	p	X
ejpam-4559	81	18	(	(	PUNCT
ejpam-4559	81	19	z	z	NOUN
ejpam-4559	81	20	)	)	PUNCT
ejpam-4559	81	21	,	,	PUNCT
ejpam-4559	81	22	we	we	PRON
ejpam-4559	81	23	get	get	VERB
ejpam-4559	81	24	1	1	NUM
ejpam-4559	81	25	+	+	NOUN
ejpam-4559	81	26	2a2z+3a3z	2a2z+3a3z	NUM
ejpam-4559	81	27	2	2	NUM
ejpam-4559	81	28	+	+	NOUN
ejpam-4559	81	29	4a4z	4a4z	ADJ
ejpam-4559	81	30	3	3	NUM
ejpam-4559	81	31	+	+	NUM
ejpam-4559	81	32	·	·	PUNCT
ejpam-4559	81	33	·	·	PUNCT
ejpam-4559	81	34	·	·	PUNCT
ejpam-4559	82	1	=	=	SYM
ejpam-4559	82	2	e−iα	e−iα	NOUN
ejpam-4559	82	3	[	[	PUNCT
ejpam-4559	82	4	tαδ	tαδ	X
ejpam-4559	82	5	(	(	PUNCT
ejpam-4559	82	6	1	1	NUM
ejpam-4559	82	7	+	+	NUM
ejpam-4559	82	8	p1z	p1z	NOUN
ejpam-4559	82	9	+	+	CCONJ
ejpam-4559	82	10	p2z	p2z	PROPN
ejpam-4559	82	11	2	2	NUM
ejpam-4559	82	12	+	+	CCONJ
ejpam-4559	82	13	p3z	p3z	ADJ
ejpam-4559	82	14	3	3	NUM
ejpam-4559	82	15	+	+	CCONJ
ejpam-4559	82	16	·	·	PUNCT
ejpam-4559	82	17	·	·	PUNCT
ejpam-4559	82	18	·	·	PUNCT
ejpam-4559	82	19	)	)	PUNCT
ejpam-4559	83	1	+	+	CCONJ
ejpam-4559	83	2	i	i	PRON
ejpam-4559	83	3	sinα	sinα	VERB
ejpam-4559	83	4	+	+	CCONJ
ejpam-4559	83	5	δ	δ	X
ejpam-4559	83	6	]	]	PUNCT
ejpam-4559	83	7	.	.	PUNCT
ejpam-4559	84	1	(	(	PUNCT
ejpam-4559	84	2	9	9	X
ejpam-4559	84	3	)	)	PUNCT
ejpam-4559	84	4	equating	equate	VERB
ejpam-4559	84	5	the	the	DET
ejpam-4559	84	6	coefficients	coefficient	NOUN
ejpam-4559	84	7	of	of	ADP
ejpam-4559	84	8	like	like	ADP
ejpam-4559	84	9	powers	power	NOUN
ejpam-4559	84	10	of	of	ADP
ejpam-4559	84	11	zn	zn	PROPN
ejpam-4559	84	12	,	,	PUNCT
ejpam-4559	84	13	n	n	CCONJ
ejpam-4559	84	14	⩾	⩾	PROPN
ejpam-4559	84	15	1	1	NUM
ejpam-4559	84	16	yields	yield	NOUN
ejpam-4559	84	17	an	an	DET
ejpam-4559	84	18	=	=	X
ejpam-4559	84	19	tαδe	tαδe	NOUN
ejpam-4559	84	20	−iαpn−1	−iαpn−1	NOUN
ejpam-4559	84	21	n	n	NOUN
ejpam-4559	84	22	,	,	PUNCT
ejpam-4559	84	23	n	n	CCONJ
ejpam-4559	84	24	⩾	⩾	NOUN
ejpam-4559	84	25	2	2	NUM
ejpam-4559	84	26	.	.	PUNCT
ejpam-4559	85	1	(	(	PUNCT
ejpam-4559	85	2	10	10	NUM
ejpam-4559	85	3	)	)	PUNCT
ejpam-4559	85	4	then	then	ADV
ejpam-4559	85	5	,	,	PUNCT
ejpam-4559	85	6	applying	apply	VERB
ejpam-4559	85	7	lemma	lemma	PROPN
ejpam-4559	85	8	1	1	NUM
ejpam-4559	85	9	,	,	PUNCT
ejpam-4559	85	10	we	we	PRON
ejpam-4559	85	11	get	get	VERB
ejpam-4559	85	12	|an|	|an|	NOUN
ejpam-4559	85	13	=	=	PRON
ejpam-4559	85	14	tαδ	tαδ	VERB
ejpam-4559	85	15	|pn−1|	|pn−1|	PROPN
ejpam-4559	85	16	n	n	PRON
ejpam-4559	85	17	⩽	⩽	NOUN
ejpam-4559	85	18	2tαδ	2tαδ	NUM
ejpam-4559	85	19	n	n	NOUN
ejpam-4559	85	20	(	(	PUNCT
ejpam-4559	85	21	11	11	NUM
ejpam-4559	85	22	)	)	PUNCT
ejpam-4559	85	23	and	and	CCONJ
ejpam-4559	85	24	so	so	ADV
ejpam-4559	85	25	|an+1|	|an+1|	PROPN
ejpam-4559	85	26	=	=	PUNCT
ejpam-4559	85	27	tαδ	tαδ	VERB
ejpam-4559	85	28	|pn|	|pn|	NUM
ejpam-4559	85	29	n	n	NOUN
ejpam-4559	85	30	+	+	CCONJ
ejpam-4559	85	31	1	1	NUM
ejpam-4559	85	32	⩽	⩽	NOUN
ejpam-4559	85	33	2tαδ	2tαδ	NUM
ejpam-4559	85	34	n	n	NOUN
ejpam-4559	85	35	+	+	X
ejpam-4559	85	36	1	1	NUM
ejpam-4559	85	37	.	.	PUNCT
ejpam-4559	86	1	(	(	PUNCT
ejpam-4559	86	2	12	12	NUM
ejpam-4559	86	3	)	)	PUNCT
ejpam-4559	86	4	clearly	clearly	ADV
ejpam-4559	86	5	from	from	ADP
ejpam-4559	86	6	(	(	PUNCT
ejpam-4559	86	7	3	3	X
ejpam-4559	86	8	)	)	PUNCT
ejpam-4559	86	9	leads	lead	VERB
ejpam-4559	86	10	to	to	ADP
ejpam-4559	86	11	|t2	|t2	PROPN
ejpam-4559	86	12	(	(	PUNCT
ejpam-4559	86	13	n)|	n)|	NOUN
ejpam-4559	86	14	=	=	SYM
ejpam-4559	86	15	∣∣an2	∣∣an2	NOUN
ejpam-4559	87	1	−	−	NOUN
ejpam-4559	87	2	an+1	an+1	NOUN
ejpam-4559	87	3	2	2	NUM
ejpam-4559	87	4	∣∣	∣∣	NUM
ejpam-4559	87	5	⩽	⩽	ADJ
ejpam-4559	87	6	∣∣an2∣∣	∣∣an2∣∣	PART
ejpam-4559	87	7	+	+	CCONJ
ejpam-4559	87	8	∣∣an+1	∣∣an+1	NUM
ejpam-4559	87	9	2	2	NUM
ejpam-4559	87	10	∣∣	∣∣	X
ejpam-4559	87	11	.	.	PUNCT
ejpam-4559	88	1	(	(	PUNCT
ejpam-4559	88	2	13	13	NUM
ejpam-4559	88	3	)	)	PUNCT
ejpam-4559	88	4	thus	thus	ADV
ejpam-4559	88	5	,	,	PUNCT
ejpam-4559	88	6	making	make	VERB
ejpam-4559	88	7	use	use	NOUN
ejpam-4559	88	8	of	of	ADP
ejpam-4559	88	9	(	(	PUNCT
ejpam-4559	88	10	11	11	NUM
ejpam-4559	88	11	)	)	PUNCT
ejpam-4559	88	12	and	and	CCONJ
ejpam-4559	88	13	(	(	PUNCT
ejpam-4559	88	14	12	12	NUM
ejpam-4559	88	15	)	)	PUNCT
ejpam-4559	88	16	gives	give	VERB
ejpam-4559	88	17	the	the	DET
ejpam-4559	88	18	desired	desire	VERB
ejpam-4559	88	19	inequality	inequality	NOUN
ejpam-4559	88	20	.	.	PUNCT
ejpam-4559	89	1	the	the	DET
ejpam-4559	89	2	inequality	inequality	NOUN
ejpam-4559	89	3	is	be	AUX
ejpam-4559	89	4	sharp	sharp	ADJ
ejpam-4559	89	5	for	for	SCONJ
ejpam-4559	89	6	the	the	DET
ejpam-4559	89	7	function	function	NOUN
ejpam-4559	89	8	eiαf	eiαf	NOUN
ejpam-4559	89	9	′(z)−i	′(z)−i	PROPN
ejpam-4559	89	10	sinα−δ	sinα−δ	VERB
ejpam-4559	89	11	tαδ	tαδ	VERB
ejpam-4559	89	12	=	=	SYM
ejpam-4559	89	13	1+iz	1+iz	PROPN
ejpam-4559	89	14	1−iz	1−iz	NUM
ejpam-4559	89	15	.	.	PUNCT
ejpam-4559	90	1	theorem	theorem	NOUN
ejpam-4559	90	2	2	2	NUM
ejpam-4559	90	3	.	.	PUNCT
ejpam-4559	91	1	let	let	VERB
ejpam-4559	91	2	f	f	PROPN
ejpam-4559	91	3	(	(	PUNCT
ejpam-4559	91	4	z	z	X
ejpam-4559	91	5	)	)	PUNCT
ejpam-4559	91	6	∈	∈	PROPN
ejpam-4559	91	7	g	g	PROPN
ejpam-4559	91	8	(	(	PUNCT
ejpam-4559	91	9	α	α	PROPN
ejpam-4559	91	10	,	,	PUNCT
ejpam-4559	91	11	δ	δ	PROPN
ejpam-4559	91	12	)	)	PUNCT
ejpam-4559	91	13	be	be	VERB
ejpam-4559	91	14	of	of	ADP
ejpam-4559	91	15	the	the	DET
ejpam-4559	91	16	form	form	NOUN
ejpam-4559	91	17	(	(	PUNCT
ejpam-4559	91	18	1	1	NUM
ejpam-4559	91	19	)	)	PUNCT
ejpam-4559	91	20	.	.	PUNCT
ejpam-4559	92	1	then	then	ADV
ejpam-4559	92	2	|t3	|t3	PROPN
ejpam-4559	92	3	(	(	PUNCT
ejpam-4559	92	4	1)|	1)|	NUM
ejpam-4559	92	5	⩽	⩽	NOUN
ejpam-4559	92	6	1	1	NUM
ejpam-4559	92	7	9	9	NUM
ejpam-4559	92	8	(	(	PUNCT
ejpam-4559	92	9	9	9	NUM
ejpam-4559	92	10	+	+	NUM
ejpam-4559	92	11	18tαδ	18tαδ	NOUN
ejpam-4559	92	12	2	2	NUM
ejpam-4559	92	13	+	+	CCONJ
ejpam-4559	92	14	4tαδ	4tαδ	NUM
ejpam-4559	92	15	2	2	NUM
ejpam-4559	92	16	√	√	NUM
ejpam-4559	92	17	9tαδ2	9tαδ2	NUM
ejpam-4559	92	18	−	−	PROPN
ejpam-4559	92	19	6tαδ	6tαδ	NUM
ejpam-4559	92	20	cosα	cosα	NOUN
ejpam-4559	92	21	+	+	NOUN
ejpam-4559	92	22	1	1	NUM
ejpam-4559	92	23	)	)	PUNCT
ejpam-4559	92	24	,	,	PUNCT
ejpam-4559	92	25	where	where	SCONJ
ejpam-4559	92	26	tαδ	tαδ	NOUN
ejpam-4559	92	27	=	=	SYM
ejpam-4559	92	28	cosα−	cosα−	PROPN
ejpam-4559	92	29	δ	δ	PROPN
ejpam-4559	92	30	.	.	PUNCT
ejpam-4559	93	1	the	the	DET
ejpam-4559	93	2	inequality	inequality	NOUN
ejpam-4559	93	3	is	be	AUX
ejpam-4559	93	4	sharp	sharp	ADJ
ejpam-4559	93	5	.	.	PUNCT
ejpam-4559	94	1	n.	n.	PROPN
ejpam-4559	94	2	h.	h.	PROPN
ejpam-4559	94	3	a.	a.	PROPN
ejpam-4559	94	4	a.	a.	PROPN
ejpam-4559	94	5	wahid	wahid	PROPN
ejpam-4559	94	6	et	et	PROPN
ejpam-4559	94	7	al	al	PROPN
ejpam-4559	94	8	.	.	PUNCT
ejpam-4559	94	9	/	/	SYM
ejpam-4559	94	10	eur	eur	PROPN
ejpam-4559	94	11	.	.	PUNCT
ejpam-4559	95	1	j.	j.	PROPN
ejpam-4559	95	2	pure	pure	PROPN
ejpam-4559	95	3	appl	appl	PROPN
ejpam-4559	95	4	.	.	PROPN
ejpam-4559	95	5	math	math	PROPN
ejpam-4559	95	6	,	,	PUNCT
ejpam-4559	95	7	15	15	NUM
ejpam-4559	95	8	(	(	PUNCT
ejpam-4559	95	9	4	4	NUM
ejpam-4559	95	10	)	)	PUNCT
ejpam-4559	95	11	(	(	PUNCT
ejpam-4559	95	12	2022	2022	NUM
ejpam-4559	95	13	)	)	PUNCT
ejpam-4559	95	14	,	,	PUNCT
ejpam-4559	95	15	1937	1937	NUM
ejpam-4559	95	16	-	-	SYM
ejpam-4559	95	17	1947	1947	NUM
ejpam-4559	95	18	1941	1941	NUM
ejpam-4559	95	19	proof	proof	NOUN
ejpam-4559	95	20	.	.	PUNCT
ejpam-4559	96	1	by	by	ADP
ejpam-4559	96	2	making	make	VERB
ejpam-4559	96	3	use	use	NOUN
ejpam-4559	96	4	of	of	ADP
ejpam-4559	96	5	(	(	PUNCT
ejpam-4559	96	6	10	10	NUM
ejpam-4559	96	7	)	)	PUNCT
ejpam-4559	96	8	for	for	ADP
ejpam-4559	96	9	n	n	NOUN
ejpam-4559	96	10	=	=	SYM
ejpam-4559	96	11	2	2	NUM
ejpam-4559	96	12	,	,	PUNCT
ejpam-4559	96	13	3	3	NUM
ejpam-4559	96	14	,	,	PUNCT
ejpam-4559	96	15	from	from	ADP
ejpam-4559	96	16	(	(	PUNCT
ejpam-4559	96	17	4	4	NUM
ejpam-4559	96	18	)	)	PUNCT
ejpam-4559	96	19	,	,	PUNCT
ejpam-4559	96	20	we	we	PRON
ejpam-4559	96	21	obtain	obtain	VERB
ejpam-4559	96	22	t3	t3	NOUN
ejpam-4559	96	23	(	(	PUNCT
ejpam-4559	96	24	1	1	NUM
ejpam-4559	96	25	)	)	PUNCT
ejpam-4559	96	26	=	=	SYM
ejpam-4559	97	1	1	1	NUM
ejpam-4559	97	2	−	−	NUM
ejpam-4559	97	3	2a2	2a2	NUM
ejpam-4559	97	4	2	2	NUM
ejpam-4559	97	5	+	+	NUM
ejpam-4559	97	6	2a2	2a2	NUM
ejpam-4559	97	7	2a3	2a3	NUM
ejpam-4559	97	8	−	−	PROPN
ejpam-4559	97	9	a3	a3	NOUN
ejpam-4559	97	10	2	2	NUM
ejpam-4559	97	11	=	=	SYM
ejpam-4559	97	12	1	1	NUM
ejpam-4559	97	13	−	−	NOUN
ejpam-4559	97	14	2	2	NUM
ejpam-4559	97	15	(	(	PUNCT
ejpam-4559	97	16	tαδe	tαδe	NOUN
ejpam-4559	97	17	−iαp1	−iαp1	PROPN
ejpam-4559	97	18	2	2	NUM
ejpam-4559	97	19	)	)	SYM
ejpam-4559	97	20	2	2	NUM
ejpam-4559	97	21	+	+	NUM
ejpam-4559	97	22	2	2	NUM
ejpam-4559	97	23	(	(	PUNCT
ejpam-4559	97	24	tαδe	tαδe	NOUN
ejpam-4559	97	25	−iαp1	−iαp1	PROPN
ejpam-4559	97	26	2	2	NUM
ejpam-4559	97	27	)	)	PUNCT
ejpam-4559	97	28	2	2	NUM
ejpam-4559	97	29	(	(	PUNCT
ejpam-4559	97	30	tαδe	tαδe	NOUN
ejpam-4559	97	31	−iαp2	−iαp2	NOUN
ejpam-4559	97	32	3	3	NUM
ejpam-4559	97	33	)	)	PUNCT
ejpam-4559	97	34	−	−	PROPN
ejpam-4559	98	1	(	(	PUNCT
ejpam-4559	98	2	tαδe	tαδe	NOUN
ejpam-4559	98	3	−iαp2	−iαp2	NOUN
ejpam-4559	98	4	3	3	NUM
ejpam-4559	98	5	)	)	SYM
ejpam-4559	98	6	2	2	NUM
ejpam-4559	98	7	=	=	SYM
ejpam-4559	98	8	1	1	NUM
ejpam-4559	98	9	18	18	NUM
ejpam-4559	98	10	(	(	PUNCT
ejpam-4559	98	11	18	18	NUM
ejpam-4559	98	12	−	−	PROPN
ejpam-4559	98	13	9tαδ	9tαδ	NUM
ejpam-4559	98	14	2e−2iαp1	2e−2iαp1	NOUN
ejpam-4559	98	15	2	2	NUM
ejpam-4559	98	16	−	−	NOUN
ejpam-4559	99	1	2tαδ	2tαδ	NUM
ejpam-4559	99	2	2e−2iαp2	2e−2iαp2	NOUN
ejpam-4559	99	3	2	2	NUM
ejpam-4559	99	4	+	+	CCONJ
ejpam-4559	99	5	3tαδ	3tαδ	NUM
ejpam-4559	99	6	3e−3iαp1	3e−3iαp1	PROPN
ejpam-4559	99	7	2p2	2p2	NUM
ejpam-4559	99	8	)	)	PUNCT
ejpam-4559	99	9	.	.	PUNCT
ejpam-4559	100	1	(	(	PUNCT
ejpam-4559	100	2	14	14	NUM
ejpam-4559	100	3	)	)	PUNCT
ejpam-4559	100	4	further	far	ADV
ejpam-4559	100	5	,	,	PUNCT
ejpam-4559	100	6	we	we	PRON
ejpam-4559	100	7	can	can	AUX
ejpam-4559	100	8	rearrange	rearrange	VERB
ejpam-4559	100	9	(	(	PUNCT
ejpam-4559	100	10	14	14	NUM
ejpam-4559	100	11	)	)	PUNCT
ejpam-4559	100	12	as	as	ADP
ejpam-4559	100	13	|t3	|t3	PROPN
ejpam-4559	100	14	(	(	PUNCT
ejpam-4559	100	15	1)|	1)|	NUM
ejpam-4559	100	16	=	=	SYM
ejpam-4559	100	17	1	1	NUM
ejpam-4559	100	18	18	18	NUM
ejpam-4559	100	19	∣∣18	∣∣18	NUM
ejpam-4559	100	20	−	−	PROPN
ejpam-4559	100	21	9tαδ	9tαδ	NUM
ejpam-4559	100	22	2e−2iαp1	2e−2iαp1	NOUN
ejpam-4559	100	23	2	2	NUM
ejpam-4559	100	24	−	−	PROPN
ejpam-4559	100	25	2tαδ	2tαδ	NUM
ejpam-4559	100	26	2e−2iαp2	2e−2iαp2	NOUN
ejpam-4559	100	27	(	(	PUNCT
ejpam-4559	100	28	p2	p2	PROPN
ejpam-4559	100	29	−	−	PROPN
ejpam-4559	100	30	µp1	µp1	NOUN
ejpam-4559	100	31	2	2	NUM
ejpam-4559	100	32	)	)	PUNCT
ejpam-4559	100	33	∣∣	∣∣	X
ejpam-4559	100	34	,	,	PUNCT
ejpam-4559	100	35	(	(	PUNCT
ejpam-4559	100	36	15	15	NUM
ejpam-4559	100	37	)	)	PUNCT
ejpam-4559	100	38	where	where	SCONJ
ejpam-4559	100	39	µ	µ	X
ejpam-4559	100	40	=	=	SYM
ejpam-4559	100	41	3tαδe	3tαδe	NUM
ejpam-4559	100	42	−iα	−iα	NOUN
ejpam-4559	100	43	2	2	NUM
ejpam-4559	100	44	.	.	PUNCT
ejpam-4559	101	1	thus	thus	ADV
ejpam-4559	101	2	,	,	PUNCT
ejpam-4559	101	3	by	by	ADP
ejpam-4559	101	4	the	the	DET
ejpam-4559	101	5	triangle	triangle	NOUN
ejpam-4559	101	6	inequality	inequality	NOUN
ejpam-4559	101	7	along	along	ADP
ejpam-4559	101	8	with	with	ADP
ejpam-4559	101	9	lemma	lemma	PROPN
ejpam-4559	101	10	1	1	NUM
ejpam-4559	101	11	and	and	CCONJ
ejpam-4559	101	12	lemma	lemma	PROPN
ejpam-4559	101	13	2	2	NUM
ejpam-4559	101	14	,	,	PUNCT
ejpam-4559	101	15	we	we	PRON
ejpam-4559	101	16	get	get	VERB
ejpam-4559	101	17	|t3	|t3	PROPN
ejpam-4559	101	18	(	(	PUNCT
ejpam-4559	101	19	1)|	1)|	NUM
ejpam-4559	101	20	⩽	⩽	NOUN
ejpam-4559	101	21	1	1	NUM
ejpam-4559	101	22	9	9	NUM
ejpam-4559	101	23	(	(	PUNCT
ejpam-4559	101	24	9	9	NUM
ejpam-4559	101	25	+	+	NUM
ejpam-4559	101	26	18tαδ	18tαδ	NOUN
ejpam-4559	101	27	2	2	NUM
ejpam-4559	101	28	+	+	CCONJ
ejpam-4559	101	29	4tαδ	4tαδ	NUM
ejpam-4559	101	30	2	2	NUM
ejpam-4559	101	31	√	√	NUM
ejpam-4559	101	32	9tαδ2	9tαδ2	NUM
ejpam-4559	101	33	−	−	PROPN
ejpam-4559	101	34	6tαδ	6tαδ	NUM
ejpam-4559	101	35	cosα	cosα	NOUN
ejpam-4559	101	36	+	+	NOUN
ejpam-4559	101	37	1	1	NUM
ejpam-4559	101	38	)	)	PUNCT
ejpam-4559	101	39	.	.	PUNCT
ejpam-4559	102	1	(	(	PUNCT
ejpam-4559	102	2	16	16	NUM
ejpam-4559	102	3	)	)	PUNCT
ejpam-4559	102	4	this	this	DET
ejpam-4559	102	5	inequality	inequality	NOUN
ejpam-4559	102	6	is	be	AUX
ejpam-4559	102	7	sharp	sharp	ADJ
ejpam-4559	102	8	for	for	SCONJ
ejpam-4559	102	9	the	the	DET
ejpam-4559	102	10	function	function	NOUN
ejpam-4559	102	11	eiαf	eiαf	NOUN
ejpam-4559	102	12	′(z)−i	′(z)−i	PROPN
ejpam-4559	102	13	sinα−δ	sinα−δ	VERB
ejpam-4559	102	14	tαδ	tαδ	VERB
ejpam-4559	102	15	=	=	SYM
ejpam-4559	102	16	1+iz	1+iz	PROPN
ejpam-4559	102	17	1−iz	1−iz	NUM
ejpam-4559	102	18	.	.	PUNCT
ejpam-4559	103	1	theorem	theorem	NOUN
ejpam-4559	103	2	3	3	X
ejpam-4559	103	3	.	.	PUNCT
ejpam-4559	104	1	let	let	VERB
ejpam-4559	104	2	f	f	PROPN
ejpam-4559	104	3	(	(	PUNCT
ejpam-4559	104	4	z	z	X
ejpam-4559	104	5	)	)	PUNCT
ejpam-4559	104	6	∈	∈	PROPN
ejpam-4559	104	7	g	g	PROPN
ejpam-4559	104	8	(	(	PUNCT
ejpam-4559	104	9	α	α	PROPN
ejpam-4559	104	10	,	,	PUNCT
ejpam-4559	104	11	δ	δ	PROPN
ejpam-4559	104	12	)	)	PUNCT
ejpam-4559	104	13	be	be	VERB
ejpam-4559	104	14	of	of	ADP
ejpam-4559	104	15	the	the	DET
ejpam-4559	104	16	form	form	NOUN
ejpam-4559	104	17	(	(	PUNCT
ejpam-4559	104	18	1	1	NUM
ejpam-4559	104	19	)	)	PUNCT
ejpam-4559	104	20	.	.	PUNCT
ejpam-4559	105	1	then	then	ADV
ejpam-4559	105	2	|t3	|t3	PROPN
ejpam-4559	105	3	(	(	PUNCT
ejpam-4559	105	4	2)|	2)|	NUM
ejpam-4559	105	5	⩽	⩽	ADJ
ejpam-4559	105	6	7tαδ	7tαδ	PROPN
ejpam-4559	105	7	3	3	NUM
ejpam-4559	105	8	3	3	NUM
ejpam-4559	105	9	,	,	PUNCT
ejpam-4559	105	10	where	where	SCONJ
ejpam-4559	105	11	tαδ	tαδ	NOUN
ejpam-4559	105	12	=	=	SYM
ejpam-4559	105	13	cosα−	cosα−	PROPN
ejpam-4559	105	14	δ	δ	PROPN
ejpam-4559	105	15	.	.	PUNCT
ejpam-4559	106	1	proof	proof	NOUN
ejpam-4559	106	2	.	.	PUNCT
ejpam-4559	107	1	using	use	VERB
ejpam-4559	107	2	(	(	PUNCT
ejpam-4559	107	3	10	10	NUM
ejpam-4559	107	4	)	)	PUNCT
ejpam-4559	107	5	for	for	ADP
ejpam-4559	107	6	n	n	NOUN
ejpam-4559	107	7	=	=	SYM
ejpam-4559	107	8	2	2	NUM
ejpam-4559	107	9	,	,	PUNCT
ejpam-4559	107	10	3	3	NUM
ejpam-4559	107	11	,	,	PUNCT
ejpam-4559	107	12	4	4	NUM
ejpam-4559	107	13	,	,	PUNCT
ejpam-4559	107	14	from	from	ADP
ejpam-4559	107	15	(	(	PUNCT
ejpam-4559	107	16	5	5	NUM
ejpam-4559	107	17	)	)	PUNCT
ejpam-4559	107	18	,	,	PUNCT
ejpam-4559	107	19	it	it	PRON
ejpam-4559	107	20	follows	follow	VERB
ejpam-4559	107	21	that	that	SCONJ
ejpam-4559	107	22	t3	t3	PROPN
ejpam-4559	107	23	(	(	PUNCT
ejpam-4559	107	24	2	2	NUM
ejpam-4559	107	25	)	)	PUNCT
ejpam-4559	107	26	=	=	SYM
ejpam-4559	107	27	a2	a2	PROPN
ejpam-4559	107	28	3	3	NUM
ejpam-4559	107	29	−	−	NOUN
ejpam-4559	107	30	2a2a3	2a2a3	NUM
ejpam-4559	107	31	2	2	NUM
ejpam-4559	108	1	+	+	CCONJ
ejpam-4559	108	2	2a3	2a3	NUM
ejpam-4559	108	3	2a4	2a4	NUM
ejpam-4559	108	4	−	−	NOUN
ejpam-4559	108	5	a2a4	a2a4	SYM
ejpam-4559	108	6	2	2	NUM
ejpam-4559	108	7	=	=	SYM
ejpam-4559	108	8	(	(	PUNCT
ejpam-4559	108	9	tαδe	tαδe	NOUN
ejpam-4559	108	10	−iαp1	−iαp1	PROPN
ejpam-4559	108	11	2	2	NUM
ejpam-4559	108	12	)	)	SYM
ejpam-4559	108	13	3	3	NUM
ejpam-4559	108	14	−	−	NOUN
ejpam-4559	108	15	2	2	NUM
ejpam-4559	108	16	(	(	PUNCT
ejpam-4559	108	17	tαδe	tαδe	NOUN
ejpam-4559	108	18	−iαp1	−iαp1	PROPN
ejpam-4559	108	19	2	2	NUM
ejpam-4559	108	20	)	)	PUNCT
ejpam-4559	108	21	(	(	PUNCT
ejpam-4559	108	22	tαδe	tαδe	NOUN
ejpam-4559	108	23	−iαp2	−iαp2	NOUN
ejpam-4559	108	24	3	3	NUM
ejpam-4559	108	25	)	)	SYM
ejpam-4559	108	26	2	2	NUM
ejpam-4559	108	27	+	+	NUM
ejpam-4559	108	28	2	2	NUM
ejpam-4559	108	29	(	(	PUNCT
ejpam-4559	108	30	tαδe	tαδe	NOUN
ejpam-4559	108	31	−iαp2	−iαp2	NOUN
ejpam-4559	108	32	3	3	NUM
ejpam-4559	108	33	)	)	PUNCT
ejpam-4559	108	34	2	2	NUM
ejpam-4559	108	35	(	(	PUNCT
ejpam-4559	108	36	tαδe	tαδe	NOUN
ejpam-4559	108	37	−iαp3	−iαp3	NOUN
ejpam-4559	108	38	4	4	X
ejpam-4559	108	39	)	)	PUNCT
ejpam-4559	108	40	−	−	PROPN
ejpam-4559	109	1	(	(	PUNCT
ejpam-4559	109	2	tαδe	tαδe	NOUN
ejpam-4559	109	3	−iαp1	−iαp1	PROPN
ejpam-4559	109	4	2	2	NUM
ejpam-4559	109	5	)	)	PUNCT
ejpam-4559	109	6	(	(	PUNCT
ejpam-4559	109	7	tαδe	tαδe	NOUN
ejpam-4559	109	8	−iαp3	−iαp3	NOUN
ejpam-4559	109	9	4	4	NUM
ejpam-4559	109	10	)	)	SYM
ejpam-4559	109	11	2	2	NUM
ejpam-4559	109	12	=	=	PRON
ejpam-4559	109	13	tαδ	tαδ	VERB
ejpam-4559	109	14	3e−3iα	3e−3iα	NOUN
ejpam-4559	109	15	288	288	NUM
ejpam-4559	109	16	(	(	PUNCT
ejpam-4559	109	17	36p1	36p1	NUM
ejpam-4559	109	18	3	3	NUM
ejpam-4559	109	19	−	−	NOUN
ejpam-4559	109	20	32p1p2	32p1p2	ADJ
ejpam-4559	109	21	2	2	NUM
ejpam-4559	110	1	+	+	SYM
ejpam-4559	110	2	16p2	16p2	NUM
ejpam-4559	110	3	2p3	2p3	NUM
ejpam-4559	110	4	−	−	NOUN
ejpam-4559	110	5	9p1p3	9p1p3	NUM
ejpam-4559	110	6	2	2	NUM
ejpam-4559	110	7	)	)	PUNCT
ejpam-4559	110	8	.	.	PUNCT
ejpam-4559	111	1	(	(	PUNCT
ejpam-4559	111	2	17	17	NUM
ejpam-4559	111	3	)	)	PUNCT
ejpam-4559	111	4	rearranging	rearrange	VERB
ejpam-4559	111	5	the	the	DET
ejpam-4559	111	6	terms	term	NOUN
ejpam-4559	111	7	in	in	ADP
ejpam-4559	111	8	(	(	PUNCT
ejpam-4559	111	9	17	17	NUM
ejpam-4559	111	10	)	)	PUNCT
ejpam-4559	111	11	and	and	CCONJ
ejpam-4559	111	12	hence	hence	ADV
ejpam-4559	111	13	applying	apply	VERB
ejpam-4559	111	14	the	the	DET
ejpam-4559	111	15	triangle	triangle	NOUN
ejpam-4559	111	16	inequality	inequality	NOUN
ejpam-4559	111	17	,	,	PUNCT
ejpam-4559	111	18	then	then	ADV
ejpam-4559	111	19	we	we	PRON
ejpam-4559	111	20	can	can	AUX
ejpam-4559	111	21	rewrite	rewrite	VERB
ejpam-4559	111	22	it	it	PRON
ejpam-4559	111	23	as	as	ADP
ejpam-4559	111	24	|t3	|t3	PROPN
ejpam-4559	111	25	(	(	PUNCT
ejpam-4559	111	26	2)|	2)|	NUM
ejpam-4559	111	27	⩽	⩽	NOUN
ejpam-4559	111	28	tαδ	tαδ	VERB
ejpam-4559	111	29	3	3	NUM
ejpam-4559	111	30	288	288	NUM
ejpam-4559	111	31	[	[	PUNCT
ejpam-4559	111	32	36|p1|3	36|p1|3	NUM
ejpam-4559	111	33	+	+	SYM
ejpam-4559	111	34	32	32	NUM
ejpam-4559	111	35	|p1|	|p1|	ADV
ejpam-4559	111	36	|p2|2	|p2|2	PUNCT
ejpam-4559	112	1	+	+	CCONJ
ejpam-4559	112	2	16	16	NUM
ejpam-4559	112	3	|p3|	|p3|	NOUN
ejpam-4559	112	4	∣∣p4	∣∣p4	NOUN
ejpam-4559	112	5	−	−	PROPN
ejpam-4559	112	6	η1p2	η1p2	PROPN
ejpam-4559	112	7	2	2	NUM
ejpam-4559	112	8	∣∣	∣∣	NUM
ejpam-4559	112	9	+	+	CCONJ
ejpam-4559	112	10	16	16	NUM
ejpam-4559	112	11	|p3|	|p3|	NOUN
ejpam-4559	112	12	|p4	|p4	NOUN
ejpam-4559	112	13	−	−	NOUN
ejpam-4559	112	14	η2p1p3|	η2p1p3|	NOUN
ejpam-4559	112	15	]	]	PUNCT
ejpam-4559	112	16	,	,	PUNCT
ejpam-4559	112	17	(	(	PUNCT
ejpam-4559	112	18	18	18	NUM
ejpam-4559	112	19	)	)	PUNCT
ejpam-4559	112	20	where	where	SCONJ
ejpam-4559	112	21	η1	η1	NOUN
ejpam-4559	112	22	=	=	SYM
ejpam-4559	112	23	1	1	NUM
ejpam-4559	112	24	and	and	CCONJ
ejpam-4559	112	25	η2	η2	ADJ
ejpam-4559	112	26	=	=	SYM
ejpam-4559	112	27	9	9	NUM
ejpam-4559	112	28	16	16	NUM
ejpam-4559	112	29	.	.	PUNCT
ejpam-4559	113	1	further	far	ADV
ejpam-4559	113	2	,	,	PUNCT
ejpam-4559	113	3	by	by	ADP
ejpam-4559	113	4	implementing	implement	VERB
ejpam-4559	113	5	lemma	lemma	PROPN
ejpam-4559	113	6	1	1	NUM
ejpam-4559	113	7	and	and	CCONJ
ejpam-4559	113	8	lemma	lemma	PROPN
ejpam-4559	113	9	2	2	NUM
ejpam-4559	113	10	,	,	PUNCT
ejpam-4559	113	11	thus	thus	ADV
ejpam-4559	113	12	we	we	PRON
ejpam-4559	113	13	obtain	obtain	VERB
ejpam-4559	113	14	|t3	|t3	PROPN
ejpam-4559	113	15	(	(	PUNCT
ejpam-4559	113	16	2)|	2)|	NUM
ejpam-4559	113	17	⩽	⩽	ADJ
ejpam-4559	113	18	7tαδ	7tαδ	PROPN
ejpam-4559	113	19	3	3	NUM
ejpam-4559	113	20	3	3	NUM
ejpam-4559	113	21	.	.	PUNCT
ejpam-4559	114	1	this	this	PRON
ejpam-4559	114	2	concludes	conclude	VERB
ejpam-4559	114	3	the	the	DET
ejpam-4559	114	4	proof	proof	NOUN
ejpam-4559	114	5	.	.	PUNCT
ejpam-4559	115	1	n.	n.	PROPN
ejpam-4559	115	2	h.	h.	PROPN
ejpam-4559	115	3	a.	a.	PROPN
ejpam-4559	115	4	a.	a.	PROPN
ejpam-4559	115	5	wahid	wahid	PROPN
ejpam-4559	115	6	et	et	PROPN
ejpam-4559	115	7	al	al	PROPN
ejpam-4559	115	8	.	.	PUNCT
ejpam-4559	115	9	/	/	SYM
ejpam-4559	115	10	eur	eur	PROPN
ejpam-4559	115	11	.	.	PUNCT
ejpam-4559	116	1	j.	j.	PROPN
ejpam-4559	116	2	pure	pure	PROPN
ejpam-4559	116	3	appl	appl	PROPN
ejpam-4559	116	4	.	.	PROPN
ejpam-4559	116	5	math	math	PROPN
ejpam-4559	116	6	,	,	PUNCT
ejpam-4559	116	7	15	15	NUM
ejpam-4559	116	8	(	(	PUNCT
ejpam-4559	116	9	4	4	NUM
ejpam-4559	116	10	)	)	PUNCT
ejpam-4559	116	11	(	(	PUNCT
ejpam-4559	116	12	2022	2022	NUM
ejpam-4559	116	13	)	)	PUNCT
ejpam-4559	116	14	,	,	PUNCT
ejpam-4559	116	15	1937	1937	NUM
ejpam-4559	116	16	-	-	SYM
ejpam-4559	116	17	1947	1947	NUM
ejpam-4559	116	18	1942	1942	NUM
ejpam-4559	116	19	theorem	theorem	VERB
ejpam-4559	116	20	4	4	NUM
ejpam-4559	116	21	.	.	PUNCT
ejpam-4559	117	1	let	let	VERB
ejpam-4559	117	2	f	f	PROPN
ejpam-4559	117	3	(	(	PUNCT
ejpam-4559	117	4	z	z	X
ejpam-4559	117	5	)	)	PUNCT
ejpam-4559	117	6	∈	∈	PROPN
ejpam-4559	117	7	g	g	PROPN
ejpam-4559	117	8	(	(	PUNCT
ejpam-4559	117	9	α	α	PROPN
ejpam-4559	117	10	,	,	PUNCT
ejpam-4559	117	11	δ	δ	PROPN
ejpam-4559	117	12	)	)	PUNCT
ejpam-4559	117	13	be	be	VERB
ejpam-4559	117	14	of	of	ADP
ejpam-4559	117	15	the	the	DET
ejpam-4559	117	16	form	form	NOUN
ejpam-4559	117	17	(	(	PUNCT
ejpam-4559	117	18	1	1	NUM
ejpam-4559	117	19	)	)	PUNCT
ejpam-4559	117	20	.	.	PUNCT
ejpam-4559	118	1	then	then	ADV
ejpam-4559	118	2	|t3	|t3	PROPN
ejpam-4559	118	3	(	(	PUNCT
ejpam-4559	118	4	3)|	3)|	NUM
ejpam-4559	118	5	⩽	⩽	NOUN
ejpam-4559	118	6	112tαδ	112tαδ	NUM
ejpam-4559	118	7	3	3	NUM
ejpam-4559	118	8	135	135	NUM
ejpam-4559	118	9	,	,	PUNCT
ejpam-4559	118	10	where	where	SCONJ
ejpam-4559	118	11	tαδ	tαδ	NOUN
ejpam-4559	118	12	=	=	SYM
ejpam-4559	118	13	cosα−	cosα−	PROPN
ejpam-4559	118	14	δ	δ	PROPN
ejpam-4559	118	15	.	.	PUNCT
ejpam-4559	119	1	proof	proof	NOUN
ejpam-4559	119	2	.	.	PUNCT
ejpam-4559	120	1	using	use	VERB
ejpam-4559	120	2	the	the	DET
ejpam-4559	120	3	values	value	NOUN
ejpam-4559	120	4	of	of	ADP
ejpam-4559	120	5	a3	a3	NOUN
ejpam-4559	120	6	,	,	PUNCT
ejpam-4559	120	7	a4	a4	NOUN
ejpam-4559	120	8	,	,	PUNCT
ejpam-4559	120	9	and	and	CCONJ
ejpam-4559	120	10	a5	a5	VERB
ejpam-4559	120	11	from	from	ADP
ejpam-4559	120	12	(	(	PUNCT
ejpam-4559	120	13	10	10	NUM
ejpam-4559	120	14	)	)	PUNCT
ejpam-4559	120	15	and	and	CCONJ
ejpam-4559	120	16	in	in	ADP
ejpam-4559	120	17	view	view	NOUN
ejpam-4559	120	18	of	of	ADP
ejpam-4559	120	19	(	(	PUNCT
ejpam-4559	120	20	6	6	NUM
ejpam-4559	120	21	)	)	PUNCT
ejpam-4559	120	22	,	,	PUNCT
ejpam-4559	120	23	it	it	PRON
ejpam-4559	120	24	can	can	AUX
ejpam-4559	120	25	be	be	AUX
ejpam-4559	120	26	seen	see	VERB
ejpam-4559	120	27	that	that	SCONJ
ejpam-4559	120	28	t3	t3	PROPN
ejpam-4559	120	29	(	(	PUNCT
ejpam-4559	120	30	3	3	NUM
ejpam-4559	120	31	)	)	PUNCT
ejpam-4559	120	32	=	=	NOUN
ejpam-4559	120	33	a3	a3	VERB
ejpam-4559	120	34	3	3	NUM
ejpam-4559	120	35	−	−	NOUN
ejpam-4559	120	36	2a3a4	2a3a4	NUM
ejpam-4559	120	37	2	2	NUM
ejpam-4559	120	38	+	+	NUM
ejpam-4559	120	39	2a4	2a4	NUM
ejpam-4559	120	40	2a5	2a5	NUM
ejpam-4559	120	41	−	−	NOUN
ejpam-4559	120	42	a3a5	a3a5	SYM
ejpam-4559	120	43	2	2	NUM
ejpam-4559	120	44	=	=	SYM
ejpam-4559	120	45	(	(	PUNCT
ejpam-4559	120	46	tαδe	tαδe	NOUN
ejpam-4559	120	47	−iαp2	−iαp2	NOUN
ejpam-4559	120	48	3	3	NUM
ejpam-4559	120	49	)	)	SYM
ejpam-4559	120	50	3	3	NUM
ejpam-4559	120	51	−	−	NOUN
ejpam-4559	120	52	2	2	NUM
ejpam-4559	120	53	(	(	PUNCT
ejpam-4559	120	54	tαδe	tαδe	NOUN
ejpam-4559	120	55	−iαp2	−iαp2	NOUN
ejpam-4559	120	56	3	3	NUM
ejpam-4559	120	57	)	)	PUNCT
ejpam-4559	120	58	(	(	PUNCT
ejpam-4559	120	59	tαδe	tαδe	NOUN
ejpam-4559	120	60	−iαp3	−iαp3	NOUN
ejpam-4559	120	61	4	4	NUM
ejpam-4559	120	62	)	)	SYM
ejpam-4559	120	63	2	2	NUM
ejpam-4559	121	1	+	+	NUM
ejpam-4559	121	2	2	2	NUM
ejpam-4559	121	3	(	(	PUNCT
ejpam-4559	121	4	tαδe	tαδe	NOUN
ejpam-4559	121	5	−iαp3	−iαp3	NOUN
ejpam-4559	121	6	4	4	NUM
ejpam-4559	121	7	)	)	SYM
ejpam-4559	121	8	2	2	NUM
ejpam-4559	121	9	(	(	PUNCT
ejpam-4559	121	10	tαδe	tαδe	NOUN
ejpam-4559	121	11	−iαp4	−iαp4	NOUN
ejpam-4559	121	12	5	5	NUM
ejpam-4559	121	13	)	)	PUNCT
ejpam-4559	121	14	−	−	PROPN
ejpam-4559	122	1	(	(	PUNCT
ejpam-4559	122	2	tαδe	tαδe	NOUN
ejpam-4559	122	3	−iαp2	−iαp2	NOUN
ejpam-4559	122	4	3	3	NUM
ejpam-4559	122	5	)	)	PUNCT
ejpam-4559	122	6	(	(	PUNCT
ejpam-4559	122	7	tαδe	tαδe	NOUN
ejpam-4559	122	8	−iαp4	−iαp4	NOUN
ejpam-4559	122	9	5	5	NUM
ejpam-4559	122	10	)	)	SYM
ejpam-4559	122	11	2	2	NUM
ejpam-4559	122	12	=	=	PRON
ejpam-4559	122	13	tαδ	tαδ	VERB
ejpam-4559	122	14	3e−3iα	3e−3iα	NUM
ejpam-4559	122	15	5400	5400	NUM
ejpam-4559	122	16	(	(	PUNCT
ejpam-4559	122	17	200p2	200p2	NUM
ejpam-4559	122	18	3	3	NUM
ejpam-4559	122	19	−	−	NOUN
ejpam-4559	122	20	225p2p3	225p2p3	NUM
ejpam-4559	122	21	2	2	NUM
ejpam-4559	122	22	+	+	NUM
ejpam-4559	122	23	135p3	135p3	NUM
ejpam-4559	122	24	2p4	2p4	NUM
ejpam-4559	122	25	−	−	PROPN
ejpam-4559	122	26	72p2p4	72p2p4	NOUN
ejpam-4559	122	27	2	2	NUM
ejpam-4559	122	28	)	)	PUNCT
ejpam-4559	122	29	.	.	PUNCT
ejpam-4559	123	1	(	(	PUNCT
ejpam-4559	123	2	19	19	NUM
ejpam-4559	123	3	)	)	PUNCT
ejpam-4559	123	4	after	after	ADP
ejpam-4559	123	5	rearranging	rearrange	VERB
ejpam-4559	123	6	the	the	DET
ejpam-4559	123	7	terms	term	NOUN
ejpam-4559	123	8	and	and	CCONJ
ejpam-4559	123	9	using	use	VERB
ejpam-4559	123	10	triangular	triangular	NOUN
ejpam-4559	123	11	inequalities	inequality	NOUN
ejpam-4559	123	12	,	,	PUNCT
ejpam-4559	123	13	(	(	PUNCT
ejpam-4559	123	14	19	19	NUM
ejpam-4559	123	15	)	)	PUNCT
ejpam-4559	123	16	yields	yield	NOUN
ejpam-4559	123	17	|t3	|t3	PROPN
ejpam-4559	123	18	(	(	PUNCT
ejpam-4559	123	19	3)|	3)|	NUM
ejpam-4559	123	20	⩽	⩽	NOUN
ejpam-4559	123	21	tαδ	tαδ	VERB
ejpam-4559	123	22	3	3	NUM
ejpam-4559	123	23	5400	5400	NUM
ejpam-4559	123	24	[	[	PUNCT
ejpam-4559	123	25	200|p2|3	200|p2|3	NUM
ejpam-4559	123	26	+	+	CCONJ
ejpam-4559	123	27	225	225	NUM
ejpam-4559	123	28	|p2|	|p2|	NOUN
ejpam-4559	123	29	|p3|2	|p3|2	ADP
ejpam-4559	123	30	+	+	CCONJ
ejpam-4559	123	31	135	135	NUM
ejpam-4559	123	32	|p4|	|p4|	NOUN
ejpam-4559	123	33	∣∣p6	∣∣p6	NOUN
ejpam-4559	123	34	−	−	PROPN
ejpam-4559	123	35	η1p3	η1p3	X
ejpam-4559	123	36	2	2	NUM
ejpam-4559	123	37	∣∣	∣∣	NUM
ejpam-4559	123	38	+	+	CCONJ
ejpam-4559	123	39	135	135	NUM
ejpam-4559	123	40	|p4|	|p4|	NOUN
ejpam-4559	123	41	|p6	|p6	NOUN
ejpam-4559	123	42	−	−	PROPN
ejpam-4559	123	43	νp2p4|	νp2p4|	X
ejpam-4559	123	44	]	]	X
ejpam-4559	123	45	,	,	PUNCT
ejpam-4559	123	46	(	(	PUNCT
ejpam-4559	123	47	20	20	NUM
ejpam-4559	123	48	)	)	PUNCT
ejpam-4559	123	49	where	where	SCONJ
ejpam-4559	123	50	η1	η1	X
ejpam-4559	123	51	=	=	SYM
ejpam-4559	123	52	1	1	NUM
ejpam-4559	123	53	and	and	CCONJ
ejpam-4559	123	54	ν	ν	X
ejpam-4559	123	55	=	=	SYM
ejpam-4559	123	56	72	72	NUM
ejpam-4559	123	57	135	135	NUM
ejpam-4559	123	58	.	.	PUNCT
ejpam-4559	124	1	finally	finally	ADV
ejpam-4559	124	2	,	,	PUNCT
ejpam-4559	124	3	by	by	ADP
ejpam-4559	124	4	applying	apply	VERB
ejpam-4559	124	5	lemma	lemma	PROPN
ejpam-4559	124	6	1	1	NUM
ejpam-4559	124	7	and	and	CCONJ
ejpam-4559	124	8	lemma	lemma	PROPN
ejpam-4559	124	9	2	2	NUM
ejpam-4559	124	10	,	,	PUNCT
ejpam-4559	124	11	we	we	PRON
ejpam-4559	124	12	get	get	VERB
ejpam-4559	124	13	|t3	|t3	PROPN
ejpam-4559	124	14	(	(	PUNCT
ejpam-4559	124	15	3)|	3)|	NUM
ejpam-4559	124	16	⩽	⩽	NOUN
ejpam-4559	124	17	112tαδ	112tαδ	NUM
ejpam-4559	124	18	3	3	NUM
ejpam-4559	124	19	135	135	NUM
ejpam-4559	124	20	.	.	PUNCT
ejpam-4559	125	1	this	this	PRON
ejpam-4559	125	2	completes	complete	VERB
ejpam-4559	125	3	the	the	DET
ejpam-4559	125	4	proof	proof	NOUN
ejpam-4559	125	5	.	.	PUNCT
ejpam-4559	126	1	theorem	theorem	ADJ
ejpam-4559	126	2	5	5	NUM
ejpam-4559	126	3	.	.	PUNCT
ejpam-4559	127	1	let	let	VERB
ejpam-4559	127	2	f	f	PROPN
ejpam-4559	127	3	(	(	PUNCT
ejpam-4559	127	4	z	z	X
ejpam-4559	127	5	)	)	PUNCT
ejpam-4559	127	6	∈	∈	PROPN
ejpam-4559	127	7	g	g	PROPN
ejpam-4559	127	8	(	(	PUNCT
ejpam-4559	127	9	α	α	PROPN
ejpam-4559	127	10	,	,	PUNCT
ejpam-4559	127	11	δ	δ	PROPN
ejpam-4559	127	12	)	)	PUNCT
ejpam-4559	127	13	be	be	VERB
ejpam-4559	127	14	of	of	ADP
ejpam-4559	127	15	the	the	DET
ejpam-4559	127	16	form	form	NOUN
ejpam-4559	127	17	(	(	PUNCT
ejpam-4559	127	18	1	1	NUM
ejpam-4559	127	19	)	)	PUNCT
ejpam-4559	127	20	.	.	PUNCT
ejpam-4559	128	1	then	then	ADV
ejpam-4559	128	2	|t4	|t4	PROPN
ejpam-4559	128	3	(	(	PUNCT
ejpam-4559	128	4	1)|	1)|	NUM
ejpam-4559	128	5	⩽	⩽	ADJ
ejpam-4559	128	6	1	1	NUM
ejpam-4559	128	7	1296	1296	NUM
ejpam-4559	128	8	(	(	PUNCT
ejpam-4559	128	9	1296	1296	NUM
ejpam-4559	128	10	+	+	CCONJ
ejpam-4559	128	11	4392tαδ	4392tαδ	NUM
ejpam-4559	128	12	2	2	NUM
ejpam-4559	128	13	+	+	CCONJ
ejpam-4559	128	14	3456tαδ	3456tαδ	NUM
ejpam-4559	128	15	3	3	NUM
ejpam-4559	128	16	+	+	CCONJ
ejpam-4559	128	17	1921tαδ	1921tαδ	NUM
ejpam-4559	128	18	4	4	NUM
ejpam-4559	128	19	)	)	PUNCT
ejpam-4559	128	20	,	,	PUNCT
ejpam-4559	128	21	where	where	SCONJ
ejpam-4559	128	22	tαδ	tαδ	NOUN
ejpam-4559	128	23	=	=	SYM
ejpam-4559	128	24	cosα−	cosα−	PROPN
ejpam-4559	128	25	δ	δ	PROPN
ejpam-4559	128	26	.	.	PUNCT
ejpam-4559	129	1	n.	n.	PROPN
ejpam-4559	129	2	h.	h.	PROPN
ejpam-4559	129	3	a.	a.	PROPN
ejpam-4559	129	4	a.	a.	PROPN
ejpam-4559	129	5	wahid	wahid	PROPN
ejpam-4559	129	6	et	et	PROPN
ejpam-4559	129	7	al	al	PROPN
ejpam-4559	129	8	.	.	PUNCT
ejpam-4559	129	9	/	/	SYM
ejpam-4559	129	10	eur	eur	PROPN
ejpam-4559	129	11	.	.	PUNCT
ejpam-4559	130	1	j.	j.	PROPN
ejpam-4559	130	2	pure	pure	PROPN
ejpam-4559	130	3	appl	appl	PROPN
ejpam-4559	130	4	.	.	PROPN
ejpam-4559	130	5	math	math	PROPN
ejpam-4559	130	6	,	,	PUNCT
ejpam-4559	130	7	15	15	NUM
ejpam-4559	130	8	(	(	PUNCT
ejpam-4559	130	9	4	4	NUM
ejpam-4559	130	10	)	)	PUNCT
ejpam-4559	130	11	(	(	PUNCT
ejpam-4559	130	12	2022	2022	NUM
ejpam-4559	130	13	)	)	PUNCT
ejpam-4559	130	14	,	,	PUNCT
ejpam-4559	130	15	1937	1937	NUM
ejpam-4559	130	16	-	-	SYM
ejpam-4559	130	17	1947	1947	NUM
ejpam-4559	130	18	1943	1943	NUM
ejpam-4559	130	19	proof	proof	NOUN
ejpam-4559	130	20	.	.	PUNCT
ejpam-4559	131	1	from	from	ADP
ejpam-4559	131	2	the	the	DET
ejpam-4559	131	3	expansion	expansion	NOUN
ejpam-4559	131	4	of	of	ADP
ejpam-4559	131	5	(	(	PUNCT
ejpam-4559	131	6	7	7	NUM
ejpam-4559	131	7	)	)	PUNCT
ejpam-4559	131	8	and	and	CCONJ
ejpam-4559	131	9	using	use	VERB
ejpam-4559	131	10	the	the	DET
ejpam-4559	131	11	values	value	NOUN
ejpam-4559	131	12	of	of	ADP
ejpam-4559	131	13	a2	a2	PROPN
ejpam-4559	131	14	,	,	PUNCT
ejpam-4559	131	15	a3	a3	NOUN
ejpam-4559	131	16	,	,	PUNCT
ejpam-4559	131	17	and	and	CCONJ
ejpam-4559	131	18	a4	a4	NOUN
ejpam-4559	131	19	from	from	ADP
ejpam-4559	131	20	(	(	PUNCT
ejpam-4559	131	21	10	10	NUM
ejpam-4559	131	22	)	)	PUNCT
ejpam-4559	131	23	,	,	PUNCT
ejpam-4559	131	24	we	we	PRON
ejpam-4559	131	25	get	get	VERB
ejpam-4559	131	26	t4	t4	PROPN
ejpam-4559	131	27	(	(	PUNCT
ejpam-4559	131	28	1	1	NUM
ejpam-4559	131	29	)	)	PUNCT
ejpam-4559	131	30	=	=	SYM
ejpam-4559	132	1	1	1	NUM
ejpam-4559	132	2	−	−	NUM
ejpam-4559	132	3	2a2	2a2	NUM
ejpam-4559	132	4	2	2	NUM
ejpam-4559	132	5	+	+	NUM
ejpam-4559	132	6	a2	a2	PROPN
ejpam-4559	132	7	4	4	NUM
ejpam-4559	132	8	−	−	NOUN
ejpam-4559	132	9	2a3	2a3	NUM
ejpam-4559	132	10	2	2	NUM
ejpam-4559	132	11	+	+	NUM
ejpam-4559	132	12	a3	a3	VERB
ejpam-4559	132	13	4	4	NUM
ejpam-4559	132	14	−	−	NOUN
ejpam-4559	132	15	2a4	2a4	NUM
ejpam-4559	132	16	2	2	NUM
ejpam-4559	132	17	+	+	NUM
ejpam-4559	132	18	a4	a4	NOUN
ejpam-4559	132	19	4	4	NUM
ejpam-4559	132	20	−	−	NOUN
ejpam-4559	132	21	2a2	2a2	NUM
ejpam-4559	132	22	2a3	2a3	NUM
ejpam-4559	132	23	2	2	NUM
ejpam-4559	132	24	−	−	NUM
ejpam-4559	132	25	2a2	2a2	NUM
ejpam-4559	132	26	2a4	2a4	NUM
ejpam-4559	132	27	2	2	NUM
ejpam-4559	132	28	−2a3	−2a3	NUM
ejpam-4559	132	29	2a4	2a4	NUM
ejpam-4559	132	30	2	2	NUM
ejpam-4559	132	31	+	+	CCONJ
ejpam-4559	132	32	8a2a3a4	8a2a3a4	NUM
ejpam-4559	132	33	=	=	SYM
ejpam-4559	132	34	1	1	NUM
ejpam-4559	132	35	−	−	NUM
ejpam-4559	132	36	2	2	NUM
ejpam-4559	132	37	(	(	PUNCT
ejpam-4559	132	38	tαδe	tαδe	NOUN
ejpam-4559	132	39	−iαp1	−iαp1	PROPN
ejpam-4559	132	40	2	2	NUM
ejpam-4559	132	41	)	)	SYM
ejpam-4559	132	42	2	2	NUM
ejpam-4559	133	1	+	+	CCONJ
ejpam-4559	133	2	(	(	PUNCT
ejpam-4559	133	3	tαδe	tαδe	NOUN
ejpam-4559	133	4	−iαp1	−iαp1	PROPN
ejpam-4559	133	5	2	2	NUM
ejpam-4559	133	6	)	)	SYM
ejpam-4559	133	7	4	4	NUM
ejpam-4559	133	8	−	−	NOUN
ejpam-4559	133	9	2	2	NUM
ejpam-4559	133	10	(	(	PUNCT
ejpam-4559	133	11	tαδe	tαδe	NOUN
ejpam-4559	133	12	−iαp2	−iαp2	NOUN
ejpam-4559	133	13	3	3	NUM
ejpam-4559	133	14	)	)	SYM
ejpam-4559	133	15	2	2	NUM
ejpam-4559	133	16	+	+	CCONJ
ejpam-4559	133	17	(	(	PUNCT
ejpam-4559	133	18	tαδe	tαδe	NOUN
ejpam-4559	133	19	−iαp2	−iαp2	NOUN
ejpam-4559	133	20	3	3	NUM
ejpam-4559	133	21	)	)	SYM
ejpam-4559	133	22	4	4	NUM
ejpam-4559	133	23	−2	−2	NOUN
ejpam-4559	133	24	(	(	PUNCT
ejpam-4559	133	25	tαδe	tαδe	NOUN
ejpam-4559	133	26	−iαp3	−iαp3	NOUN
ejpam-4559	133	27	4	4	NUM
ejpam-4559	133	28	)	)	SYM
ejpam-4559	133	29	2	2	NUM
ejpam-4559	133	30	+	+	CCONJ
ejpam-4559	133	31	(	(	PUNCT
ejpam-4559	133	32	tαδe	tαδe	NOUN
ejpam-4559	133	33	−iαp3	−iαp3	NOUN
ejpam-4559	133	34	4	4	NUM
ejpam-4559	133	35	)	)	SYM
ejpam-4559	133	36	4	4	NUM
ejpam-4559	133	37	−	−	NOUN
ejpam-4559	133	38	2	2	NUM
ejpam-4559	133	39	(	(	PUNCT
ejpam-4559	133	40	tαδe	tαδe	NOUN
ejpam-4559	133	41	−iαp1	−iαp1	PROPN
ejpam-4559	133	42	2	2	NUM
ejpam-4559	133	43	)	)	PUNCT
ejpam-4559	133	44	2	2	NUM
ejpam-4559	133	45	(	(	PUNCT
ejpam-4559	133	46	tαδe	tαδe	NOUN
ejpam-4559	133	47	−iαp2	−iαp2	NOUN
ejpam-4559	133	48	3	3	NUM
ejpam-4559	133	49	)	)	SYM
ejpam-4559	133	50	2	2	NUM
ejpam-4559	133	51	−2	−2	NOUN
ejpam-4559	133	52	(	(	PUNCT
ejpam-4559	133	53	tαδe	tαδe	NOUN
ejpam-4559	133	54	−iαp1	−iαp1	PROPN
ejpam-4559	133	55	2	2	NUM
ejpam-4559	133	56	)	)	PUNCT
ejpam-4559	133	57	2	2	NUM
ejpam-4559	133	58	(	(	PUNCT
ejpam-4559	133	59	tαδe	tαδe	NOUN
ejpam-4559	133	60	−iαp3	−iαp3	NOUN
ejpam-4559	133	61	4	4	NUM
ejpam-4559	133	62	)	)	SYM
ejpam-4559	133	63	2	2	NUM
ejpam-4559	133	64	−	−	NOUN
ejpam-4559	133	65	2	2	NUM
ejpam-4559	133	66	(	(	PUNCT
ejpam-4559	133	67	tαδe	tαδe	NOUN
ejpam-4559	133	68	−iαp2	−iαp2	NOUN
ejpam-4559	133	69	3	3	NUM
ejpam-4559	133	70	)	)	PUNCT
ejpam-4559	133	71	2	2	NUM
ejpam-4559	133	72	(	(	PUNCT
ejpam-4559	133	73	tαδe	tαδe	NOUN
ejpam-4559	133	74	−iαp3	−iαp3	NOUN
ejpam-4559	133	75	4	4	NUM
ejpam-4559	133	76	)	)	SYM
ejpam-4559	133	77	2	2	NUM
ejpam-4559	133	78	+8	+8	NOUN
ejpam-4559	133	79	(	(	PUNCT
ejpam-4559	133	80	tαδe	tαδe	NOUN
ejpam-4559	133	81	−iαp1	−iαp1	PROPN
ejpam-4559	133	82	2	2	NUM
ejpam-4559	133	83	)	)	PUNCT
ejpam-4559	133	84	(	(	PUNCT
ejpam-4559	133	85	tαδe	tαδe	NOUN
ejpam-4559	133	86	−iαp2	−iαp2	NOUN
ejpam-4559	133	87	3	3	NUM
ejpam-4559	133	88	)	)	PUNCT
ejpam-4559	133	89	(	(	PUNCT
ejpam-4559	133	90	tαδe	tαδe	NOUN
ejpam-4559	133	91	−iαp3	−iαp3	NOUN
ejpam-4559	133	92	4	4	X
ejpam-4559	133	93	)	)	PUNCT
ejpam-4559	133	94	=	=	SYM
ejpam-4559	133	95	1	1	NUM
ejpam-4559	133	96	20736	20736	NUM
ejpam-4559	133	97	(	(	PUNCT
ejpam-4559	133	98	20736	20736	NUM
ejpam-4559	133	99	−	−	ADP
ejpam-4559	133	100	10368tαδ	10368tαδ	NUM
ejpam-4559	133	101	2e−2iαp1	2e−2iαp1	NOUN
ejpam-4559	133	102	2	2	NUM
ejpam-4559	133	103	+	+	CCONJ
ejpam-4559	133	104	1296tαδ	1296tαδ	NUM
ejpam-4559	133	105	4e−4iαp1	4e−4iαp1	NOUN
ejpam-4559	133	106	4	4	NUM
ejpam-4559	133	107	−	−	NOUN
ejpam-4559	133	108	4608tαδ	4608tαδ	NUM
ejpam-4559	133	109	2e−2iαp2	2e−2iαp2	NOUN
ejpam-4559	133	110	2	2	NUM
ejpam-4559	133	111	+256tαδ	+256tαδ	NOUN
ejpam-4559	133	112	4e−4iαp2	4e−4iαp2	ADJ
ejpam-4559	133	113	4	4	NUM
ejpam-4559	133	114	−	−	NOUN
ejpam-4559	133	115	2592tαδ	2592tαδ	NUM
ejpam-4559	133	116	2e−2iαp3	2e−2iαp3	NUM
ejpam-4559	133	117	2	2	NUM
ejpam-4559	133	118	+	+	CCONJ
ejpam-4559	133	119	81tαδ	81tαδ	NUM
ejpam-4559	133	120	4e−4iαp3	4e−4iαp3	NOUN
ejpam-4559	133	121	4	4	NUM
ejpam-4559	133	122	−	−	NUM
ejpam-4559	133	123	1152tαδ	1152tαδ	NUM
ejpam-4559	133	124	4e−4iαp1	4e−4iαp1	PROPN
ejpam-4559	133	125	2p2	2p2	NUM
ejpam-4559	133	126	2	2	NUM
ejpam-4559	133	127	−648tαδ	−648tαδ	PROPN
ejpam-4559	133	128	4e−4iαp1	4e−4iαp1	NOUN
ejpam-4559	133	129	2p3	2p3	NUM
ejpam-4559	133	130	2	2	NUM
ejpam-4559	133	131	−	−	NOUN
ejpam-4559	133	132	288tαδ	288tαδ	NUM
ejpam-4559	133	133	4e−4iαp2	4e−4iαp2	NOUN
ejpam-4559	133	134	2p3	2p3	NUM
ejpam-4559	133	135	2	2	NUM
ejpam-4559	133	136	+	+	CCONJ
ejpam-4559	133	137	6912tαδ	6912tαδ	PROPN
ejpam-4559	133	138	3e−3iαp1p2p3	3e−3iαp1p2p3	NUM
ejpam-4559	133	139	)	)	PUNCT
ejpam-4559	133	140	.	.	PUNCT
ejpam-4559	134	1	(	(	PUNCT
ejpam-4559	134	2	21	21	NUM
ejpam-4559	134	3	)	)	PUNCT
ejpam-4559	134	4	rearranging	rearrange	VERB
ejpam-4559	134	5	the	the	DET
ejpam-4559	134	6	terms	term	NOUN
ejpam-4559	134	7	in	in	ADP
ejpam-4559	134	8	(	(	PUNCT
ejpam-4559	134	9	21	21	NUM
ejpam-4559	134	10	)	)	PUNCT
ejpam-4559	134	11	and	and	CCONJ
ejpam-4559	134	12	applying	apply	VERB
ejpam-4559	134	13	the	the	DET
ejpam-4559	134	14	triangle	triangle	NOUN
ejpam-4559	134	15	inequality	inequality	NOUN
ejpam-4559	134	16	,	,	PUNCT
ejpam-4559	134	17	as	as	ADV
ejpam-4559	134	18	well	well	ADV
ejpam-4559	134	19	as	as	ADP
ejpam-4559	134	20	some	some	DET
ejpam-4559	134	21	calculations	calculation	NOUN
ejpam-4559	134	22	,	,	PUNCT
ejpam-4559	134	23	we	we	PRON
ejpam-4559	134	24	can	can	AUX
ejpam-4559	134	25	rewrite	rewrite	VERB
ejpam-4559	134	26	it	it	PRON
ejpam-4559	134	27	in	in	ADP
ejpam-4559	134	28	the	the	DET
ejpam-4559	134	29	following	follow	VERB
ejpam-4559	134	30	expression	expression	NOUN
ejpam-4559	134	31	:	:	PUNCT
ejpam-4559	134	32	|t4	|t4	NOUN
ejpam-4559	134	33	(	(	PUNCT
ejpam-4559	134	34	1)|	1)|	NUM
ejpam-4559	134	35	⩽	⩽	ADJ
ejpam-4559	134	36	1	1	NUM
ejpam-4559	134	37	20736	20736	NUM
ejpam-4559	134	38	[	[	PUNCT
ejpam-4559	134	39	20736	20736	NUM
ejpam-4559	134	40	+	+	CCONJ
ejpam-4559	134	41	10368tαδ	10368tαδ	NUM
ejpam-4559	134	42	2|p1|2	2|p1|2	NUM
ejpam-4559	134	43	+	+	NUM
ejpam-4559	134	44	256tαδ	256tαδ	NUM
ejpam-4559	134	45	4|p2|4	4|p2|4	NUM
ejpam-4559	135	1	+	+	CCONJ
ejpam-4559	135	2	81tαδ	81tαδ	NOUN
ejpam-4559	135	3	4|p3|4	4|p3|4	NUM
ejpam-4559	135	4	+	+	CCONJ
ejpam-4559	135	5	2592tαδ	2592tαδ	NUM
ejpam-4559	135	6	2|p3|2	2|p3|2	NUM
ejpam-4559	135	7	+648tαδ	+648tαδ	VERB
ejpam-4559	135	8	4|p1|2|p3|2	4|p1|2|p3|2	NOUN
ejpam-4559	135	9	+	+	CCONJ
ejpam-4559	135	10	288tαδ	288tαδ	NUM
ejpam-4559	135	11	4|p2|2|p3|2	4|p2|2|p3|2	NOUN
ejpam-4559	135	12	+	+	CCONJ
ejpam-4559	135	13	1296tαδ	1296tαδ	NUM
ejpam-4559	135	14	4|p1|2	4|p1|2	NUM
ejpam-4559	136	1	∣∣p2	∣∣p2	ADJ
ejpam-4559	136	2	−	−	NOUN
ejpam-4559	136	3	η1p1	η1p1	PUNCT
ejpam-4559	136	4	2	2	NUM
ejpam-4559	136	5	∣∣	∣∣	NUM
ejpam-4559	136	6	+4608tαδ	+4608tαδ	X
ejpam-4559	136	7	2	2	NUM
ejpam-4559	136	8	|p2|	|p2|	NOUN
ejpam-4559	136	9	∣∣p2	∣∣p2	PROPN
ejpam-4559	136	10	−	−	PROPN
ejpam-4559	136	11	υ1p1	υ1p1	PUNCT
ejpam-4559	136	12	2	2	NUM
ejpam-4559	136	13	∣∣	∣∣	NUM
ejpam-4559	136	14	+	+	CCONJ
ejpam-4559	136	15	6912tαδ	6912tαδ	NOUN
ejpam-4559	136	16	3	3	NUM
ejpam-4559	136	17	|p1|	|p1|	PROPN
ejpam-4559	136	18	|p2|	|p2|	PROPN
ejpam-4559	136	19	|p3	|p3	PROPN
ejpam-4559	136	20	−	−	PROPN
ejpam-4559	136	21	υ2p1p2|	υ2p1p2|	PROPN
ejpam-4559	136	22	]	]	PUNCT
ejpam-4559	136	23	,	,	PUNCT
ejpam-4559	136	24	(	(	PUNCT
ejpam-4559	136	25	22	22	NUM
ejpam-4559	136	26	)	)	PUNCT
ejpam-4559	136	27	where	where	SCONJ
ejpam-4559	136	28	η1	η1	NOUN
ejpam-4559	136	29	=	=	SYM
ejpam-4559	136	30	1	1	NUM
ejpam-4559	136	31	,	,	PUNCT
ejpam-4559	136	32	υ1	υ1	NOUN
ejpam-4559	136	33	=	=	PROPN
ejpam-4559	136	34	9tαδ	9tαδ	PROPN
ejpam-4559	136	35	2e−2iα	2e−2iα	NUM
ejpam-4559	136	36	32	32	NUM
ejpam-4559	136	37	,	,	PUNCT
ejpam-4559	136	38	and	and	CCONJ
ejpam-4559	136	39	υ2	υ2	NOUN
ejpam-4559	136	40	=	=	SYM
ejpam-4559	136	41	tαδe	tαδe	PROPN
ejpam-4559	136	42	−iα	−iα	VERB
ejpam-4559	136	43	6	6	NUM
ejpam-4559	136	44	.	.	PUNCT
ejpam-4559	137	1	now	now	ADV
ejpam-4559	137	2	,	,	PUNCT
ejpam-4559	137	3	with	with	ADP
ejpam-4559	137	4	the	the	DET
ejpam-4559	137	5	help	help	NOUN
ejpam-4559	137	6	of	of	ADP
ejpam-4559	137	7	lemma	lemma	PROPN
ejpam-4559	137	8	1	1	NUM
ejpam-4559	137	9	and	and	CCONJ
ejpam-4559	137	10	lemma	lemma	PROPN
ejpam-4559	137	11	2	2	NUM
ejpam-4559	137	12	,	,	PUNCT
ejpam-4559	137	13	we	we	PRON
ejpam-4559	137	14	obtain	obtain	VERB
ejpam-4559	137	15	|t4	|t4	NOUN
ejpam-4559	137	16	(	(	PUNCT
ejpam-4559	137	17	1)|	1)|	NUM
ejpam-4559	137	18	⩽	⩽	ADJ
ejpam-4559	137	19	1	1	NUM
ejpam-4559	137	20	1296	1296	NUM
ejpam-4559	137	21	(	(	PUNCT
ejpam-4559	137	22	1296	1296	NUM
ejpam-4559	137	23	+	+	CCONJ
ejpam-4559	137	24	4392tαδ	4392tαδ	NUM
ejpam-4559	137	25	2	2	NUM
ejpam-4559	137	26	+	+	CCONJ
ejpam-4559	137	27	3456tαδ	3456tαδ	NUM
ejpam-4559	137	28	3	3	NUM
ejpam-4559	137	29	+	+	CCONJ
ejpam-4559	137	30	1921tαδ	1921tαδ	NUM
ejpam-4559	137	31	4	4	NUM
ejpam-4559	137	32	)	)	PUNCT
ejpam-4559	137	33	.	.	PUNCT
ejpam-4559	138	1	thus	thus	ADV
ejpam-4559	138	2	,	,	PUNCT
ejpam-4559	138	3	this	this	PRON
ejpam-4559	138	4	completes	complete	VERB
ejpam-4559	138	5	the	the	DET
ejpam-4559	138	6	proof	proof	NOUN
ejpam-4559	138	7	.	.	PUNCT
ejpam-4559	139	1	3	3	X
ejpam-4559	139	2	.	.	X
ejpam-4559	139	3	corollaries	corollary	NOUN
ejpam-4559	139	4	and	and	CCONJ
ejpam-4559	139	5	consequences	consequence	NOUN
ejpam-4559	139	6	in	in	ADP
ejpam-4559	139	7	this	this	DET
ejpam-4559	139	8	section	section	NOUN
ejpam-4559	139	9	,	,	PUNCT
ejpam-4559	139	10	we	we	PRON
ejpam-4559	139	11	shall	shall	AUX
ejpam-4559	139	12	give	give	VERB
ejpam-4559	139	13	the	the	DET
ejpam-4559	139	14	consequences	consequence	NOUN
ejpam-4559	139	15	of	of	ADP
ejpam-4559	139	16	our	our	PRON
ejpam-4559	139	17	main	main	ADJ
ejpam-4559	139	18	results	result	NOUN
ejpam-4559	139	19	.	.	PUNCT
ejpam-4559	140	1	for	for	ADP
ejpam-4559	140	2	α	α	NOUN
ejpam-4559	140	3	=	=	SYM
ejpam-4559	140	4	0	0	PROPN
ejpam-4559	140	5	and	and	CCONJ
ejpam-4559	140	6	δ	δ	PROPN
ejpam-4559	140	7	=	=	SYM
ejpam-4559	140	8	0	0	NUM
ejpam-4559	140	9	in	in	ADP
ejpam-4559	140	10	theorem	theorem	ADJ
ejpam-4559	140	11	1	1	NUM
ejpam-4559	140	12	,	,	PUNCT
ejpam-4559	140	13	theorem	theorem	ADJ
ejpam-4559	140	14	2	2	NUM
ejpam-4559	140	15	,	,	PUNCT
ejpam-4559	140	16	theorem	theorem	ADJ
ejpam-4559	140	17	3	3	NUM
ejpam-4559	140	18	,	,	PUNCT
ejpam-4559	140	19	theorem	theorem	VERB
ejpam-4559	140	20	4	4	NUM
ejpam-4559	140	21	,	,	PUNCT
ejpam-4559	140	22	and	and	CCONJ
ejpam-4559	140	23	theorem	theorem	VERB
ejpam-4559	140	24	5	5	NUM
ejpam-4559	140	25	,	,	PUNCT
ejpam-4559	140	26	we	we	PRON
ejpam-4559	140	27	get	get	VERB
ejpam-4559	140	28	the	the	DET
ejpam-4559	140	29	estimates	estimate	NOUN
ejpam-4559	140	30	for	for	ADP
ejpam-4559	140	31	the	the	DET
ejpam-4559	140	32	class	class	PROPN
ejpam-4559	140	33	r.	r.	PROPN
ejpam-4559	140	34	corollary	corollary	NOUN
ejpam-4559	141	1	1	1	NUM
ejpam-4559	141	2	.	.	PUNCT
ejpam-4559	142	1	let	let	VERB
ejpam-4559	142	2	f	f	PROPN
ejpam-4559	142	3	(	(	PUNCT
ejpam-4559	142	4	z	z	X
ejpam-4559	142	5	)	)	PUNCT
ejpam-4559	142	6	∈	∈	PROPN
ejpam-4559	142	7	r.	r.	PROPN
ejpam-4559	142	8	then	then	ADV
ejpam-4559	142	9	n.	n.	PROPN
ejpam-4559	142	10	h.	h.	PROPN
ejpam-4559	142	11	a.	a.	PROPN
ejpam-4559	142	12	a.	a.	PROPN
ejpam-4559	142	13	wahid	wahid	PROPN
ejpam-4559	142	14	et	et	PROPN
ejpam-4559	143	1	al	al	PROPN
ejpam-4559	143	2	.	.	PUNCT
ejpam-4559	143	3	/	/	SYM
ejpam-4559	143	4	eur	eur	PROPN
ejpam-4559	143	5	.	.	PUNCT
ejpam-4559	144	1	j.	j.	PROPN
ejpam-4559	144	2	pure	pure	PROPN
ejpam-4559	144	3	appl	appl	PROPN
ejpam-4559	144	4	.	.	PROPN
ejpam-4559	144	5	math	math	PROPN
ejpam-4559	144	6	,	,	PUNCT
ejpam-4559	144	7	15	15	NUM
ejpam-4559	144	8	(	(	PUNCT
ejpam-4559	144	9	4	4	NUM
ejpam-4559	144	10	)	)	PUNCT
ejpam-4559	144	11	(	(	PUNCT
ejpam-4559	144	12	2022	2022	NUM
ejpam-4559	144	13	)	)	PUNCT
ejpam-4559	144	14	,	,	PUNCT
ejpam-4559	144	15	1937	1937	NUM
ejpam-4559	144	16	-	-	SYM
ejpam-4559	144	17	1947	1947	NUM
ejpam-4559	144	18	1944	1944	NUM
ejpam-4559	144	19	(	(	PUNCT
ejpam-4559	144	20	i	i	NOUN
ejpam-4559	144	21	)	)	PUNCT
ejpam-4559	144	22	|t2	|t2	PROPN
ejpam-4559	144	23	(	(	PUNCT
ejpam-4559	144	24	n)|	n)|	PROPN
ejpam-4559	144	25	⩽	⩽	PROPN
ejpam-4559	144	26	4	4	NUM
ejpam-4559	144	27	[	[	SYM
ejpam-4559	144	28	1	1	NUM
ejpam-4559	144	29	n2	n2	NOUN
ejpam-4559	144	30	+	+	CCONJ
ejpam-4559	144	31	1	1	NUM
ejpam-4559	144	32	(	(	PUNCT
ejpam-4559	144	33	n+1)2	n+1)2	PROPN
ejpam-4559	144	34	]	]	PUNCT
ejpam-4559	144	35	.	.	PUNCT
ejpam-4559	145	1	(	(	PUNCT
ejpam-4559	145	2	ii	ii	X
ejpam-4559	145	3	)	)	PUNCT
ejpam-4559	145	4	|t3	|t3	NOUN
ejpam-4559	145	5	(	(	PUNCT
ejpam-4559	145	6	1)|	1)|	NUM
ejpam-4559	145	7	⩽	⩽	NOUN
ejpam-4559	145	8	35	35	NUM
ejpam-4559	145	9	9	9	NUM
ejpam-4559	145	10	.	.	PUNCT
ejpam-4559	146	1	(	(	PUNCT
ejpam-4559	146	2	iii	iii	X
ejpam-4559	146	3	)	)	PUNCT
ejpam-4559	146	4	|t3	|t3	NOUN
ejpam-4559	146	5	(	(	PUNCT
ejpam-4559	146	6	2)|	2)|	NUM
ejpam-4559	146	7	⩽	⩽	ADJ
ejpam-4559	146	8	7	7	NUM
ejpam-4559	146	9	3	3	NUM
ejpam-4559	146	10	.	.	PUNCT
ejpam-4559	147	1	(	(	PUNCT
ejpam-4559	147	2	iv	iv	X
ejpam-4559	147	3	)	)	PUNCT
ejpam-4559	147	4	|t3	|t3	NOUN
ejpam-4559	147	5	(	(	PUNCT
ejpam-4559	147	6	3)|	3)|	NUM
ejpam-4559	147	7	⩽	⩽	NOUN
ejpam-4559	147	8	112	112	NUM
ejpam-4559	147	9	135	135	NUM
ejpam-4559	147	10	.	.	PUNCT
ejpam-4559	148	1	(	(	PUNCT
ejpam-4559	148	2	v	v	NOUN
ejpam-4559	148	3	)	)	PUNCT
ejpam-4559	148	4	|t4	|t4	NOUN
ejpam-4559	148	5	(	(	PUNCT
ejpam-4559	148	6	1)|	1)|	NUM
ejpam-4559	148	7	⩽	⩽	NOUN
ejpam-4559	148	8	11065	11065	NUM
ejpam-4559	148	9	1296	1296	NUM
ejpam-4559	148	10	.	.	PUNCT
ejpam-4559	149	1	for	for	ADP
ejpam-4559	149	2	α	α	NOUN
ejpam-4559	149	3	=	=	SYM
ejpam-4559	149	4	0	0	NUM
ejpam-4559	149	5	in	in	ADP
ejpam-4559	149	6	theorem	theorem	ADJ
ejpam-4559	149	7	1	1	NUM
ejpam-4559	149	8	,	,	PUNCT
ejpam-4559	149	9	theorem	theorem	ADJ
ejpam-4559	149	10	2	2	NUM
ejpam-4559	149	11	,	,	PUNCT
ejpam-4559	149	12	theorem	theorem	ADJ
ejpam-4559	149	13	3	3	NUM
ejpam-4559	149	14	,	,	PUNCT
ejpam-4559	149	15	theorem	theorem	VERB
ejpam-4559	149	16	4	4	NUM
ejpam-4559	149	17	,	,	PUNCT
ejpam-4559	149	18	and	and	CCONJ
ejpam-4559	149	19	theorem	theorem	VERB
ejpam-4559	149	20	5	5	NUM
ejpam-4559	149	21	,	,	PUNCT
ejpam-4559	149	22	we	we	PRON
ejpam-4559	149	23	obtain	obtain	VERB
ejpam-4559	149	24	the	the	DET
ejpam-4559	149	25	estimates	estimate	NOUN
ejpam-4559	149	26	for	for	ADP
ejpam-4559	149	27	the	the	DET
ejpam-4559	149	28	class	class	NOUN
ejpam-4559	149	29	r	r	NOUN
ejpam-4559	149	30	(	(	PUNCT
ejpam-4559	149	31	δ	δ	PROPN
ejpam-4559	149	32	)	)	PUNCT
ejpam-4559	149	33	.	.	PUNCT
ejpam-4559	150	1	corollary	corollary	ADJ
ejpam-4559	150	2	2	2	NUM
ejpam-4559	150	3	.	.	PUNCT
ejpam-4559	151	1	let	let	VERB
ejpam-4559	151	2	f	f	PROPN
ejpam-4559	151	3	(	(	PUNCT
ejpam-4559	151	4	z	z	NOUN
ejpam-4559	151	5	)	)	PUNCT
ejpam-4559	151	6	∈	∈	PROPN
ejpam-4559	151	7	r	r	NOUN
ejpam-4559	151	8	(	(	PUNCT
ejpam-4559	151	9	δ	δ	PROPN
ejpam-4559	151	10	)	)	PUNCT
ejpam-4559	151	11	.	.	PUNCT
ejpam-4559	152	1	then	then	ADV
ejpam-4559	152	2	(	(	PUNCT
ejpam-4559	152	3	i	i	NOUN
ejpam-4559	152	4	)	)	PUNCT
ejpam-4559	152	5	|t2	|t2	PROPN
ejpam-4559	152	6	(	(	PUNCT
ejpam-4559	152	7	n)|	n)|	PROPN
ejpam-4559	152	8	⩽	⩽	PROPN
ejpam-4559	152	9	4(1	4(1	PROPN
ejpam-4559	153	1	−	−	PROPN
ejpam-4559	153	2	δ)2	δ)2	PROPN
ejpam-4559	153	3	[	[	PUNCT
ejpam-4559	153	4	1	1	NUM
ejpam-4559	153	5	n2	n2	NOUN
ejpam-4559	153	6	+	+	CCONJ
ejpam-4559	153	7	1	1	NUM
ejpam-4559	153	8	(	(	PUNCT
ejpam-4559	153	9	n+1)2	n+1)2	PROPN
ejpam-4559	153	10	]	]	PUNCT
ejpam-4559	153	11	.	.	PUNCT
ejpam-4559	154	1	(	(	PUNCT
ejpam-4559	154	2	ii	ii	X
ejpam-4559	154	3	)	)	PUNCT
ejpam-4559	154	4	|t3	|t3	NOUN
ejpam-4559	154	5	(	(	PUNCT
ejpam-4559	154	6	1)|	1)|	NUM
ejpam-4559	154	7	⩽	⩽	NOUN
ejpam-4559	154	8	1	1	NUM
ejpam-4559	154	9	9	9	NUM
ejpam-4559	154	10	(	(	PUNCT
ejpam-4559	154	11	9	9	NUM
ejpam-4559	154	12	+	+	NUM
ejpam-4559	154	13	18(1	18(1	NOUN
ejpam-4559	154	14	−	−	ADP
ejpam-4559	154	15	δ)2	δ)2	PROPN
ejpam-4559	154	16	+	+	NUM
ejpam-4559	154	17	4(1	4(1	NUM
ejpam-4559	154	18	−	−	PRON
ejpam-4559	154	19	δ)2	δ)2	NOUN
ejpam-4559	154	20	(	(	PUNCT
ejpam-4559	154	21	3δ	3δ	NOUN
ejpam-4559	154	22	−	−	NOUN
ejpam-4559	154	23	2	2	NUM
ejpam-4559	154	24	)	)	PUNCT
ejpam-4559	154	25	)	)	PUNCT
ejpam-4559	154	26	.	.	PUNCT
ejpam-4559	155	1	(	(	PUNCT
ejpam-4559	155	2	iii	iii	X
ejpam-4559	155	3	)	)	PUNCT
ejpam-4559	155	4	|t3	|t3	NOUN
ejpam-4559	155	5	(	(	PUNCT
ejpam-4559	155	6	2)|	2)|	NUM
ejpam-4559	155	7	⩽	⩽	ADJ
ejpam-4559	155	8	7(1−δ)3	7(1−δ)3	NUM
ejpam-4559	155	9	3	3	NUM
ejpam-4559	155	10	.	.	PUNCT
ejpam-4559	156	1	(	(	PUNCT
ejpam-4559	156	2	iv	iv	X
ejpam-4559	156	3	)	)	PUNCT
ejpam-4559	156	4	|t3	|t3	NOUN
ejpam-4559	156	5	(	(	PUNCT
ejpam-4559	156	6	3)|	3)|	NUM
ejpam-4559	156	7	⩽	⩽	NOUN
ejpam-4559	156	8	112(1−δ)3	112(1−δ)3	NUM
ejpam-4559	156	9	135	135	NUM
ejpam-4559	156	10	.	.	PUNCT
ejpam-4559	157	1	(	(	PUNCT
ejpam-4559	157	2	v	v	NOUN
ejpam-4559	157	3	)	)	PUNCT
ejpam-4559	157	4	|t4	|t4	NOUN
ejpam-4559	157	5	(	(	PUNCT
ejpam-4559	157	6	1)|	1)|	NUM
ejpam-4559	157	7	⩽	⩽	ADJ
ejpam-4559	157	8	1	1	NUM
ejpam-4559	157	9	1296	1296	NUM
ejpam-4559	157	10	(	(	PUNCT
ejpam-4559	157	11	1296	1296	NUM
ejpam-4559	157	12	+	+	NUM
ejpam-4559	157	13	4392(1	4392(1	NUM
ejpam-4559	157	14	−	−	NOUN
ejpam-4559	157	15	δ)2	δ)2	NOUN
ejpam-4559	158	1	+	+	CCONJ
ejpam-4559	158	2	3456(1	3456(1	NUM
ejpam-4559	158	3	−	−	NOUN
ejpam-4559	158	4	δ)3	δ)3	NOUN
ejpam-4559	158	5	+	+	CCONJ
ejpam-4559	158	6	1921(1	1921(1	NUM
ejpam-4559	158	7	−	−	NOUN
ejpam-4559	158	8	δ)4	δ)4	NOUN
ejpam-4559	158	9	)	)	PUNCT
ejpam-4559	158	10	.	.	PUNCT
ejpam-4559	159	1	by	by	ADP
ejpam-4559	159	2	choosing	choose	VERB
ejpam-4559	159	3	δ	δ	PROPN
ejpam-4559	159	4	=	=	SYM
ejpam-4559	159	5	0	0	NUM
ejpam-4559	159	6	in	in	ADP
ejpam-4559	159	7	theorem	theorem	ADJ
ejpam-4559	159	8	1	1	NUM
ejpam-4559	159	9	,	,	PUNCT
ejpam-4559	159	10	theorem	theorem	ADJ
ejpam-4559	159	11	2	2	NUM
ejpam-4559	159	12	,	,	PUNCT
ejpam-4559	159	13	theorem	theorem	ADJ
ejpam-4559	159	14	3	3	NUM
ejpam-4559	159	15	,	,	PUNCT
ejpam-4559	159	16	theorem	theorem	VERB
ejpam-4559	159	17	4	4	NUM
ejpam-4559	159	18	,	,	PUNCT
ejpam-4559	159	19	and	and	CCONJ
ejpam-4559	159	20	theorem	theorem	VERB
ejpam-4559	159	21	5	5	NUM
ejpam-4559	159	22	,	,	PUNCT
ejpam-4559	159	23	we	we	PRON
ejpam-4559	159	24	obtain	obtain	VERB
ejpam-4559	159	25	the	the	DET
ejpam-4559	159	26	estimates	estimate	NOUN
ejpam-4559	159	27	for	for	ADP
ejpam-4559	159	28	the	the	DET
ejpam-4559	159	29	class	class	NOUN
ejpam-4559	159	30	r	r	NOUN
ejpam-4559	159	31	(	(	PUNCT
ejpam-4559	159	32	α	α	NOUN
ejpam-4559	159	33	)	)	PUNCT
ejpam-4559	159	34	.	.	PUNCT
ejpam-4559	160	1	corollary	corollary	ADJ
ejpam-4559	160	2	3	3	X
ejpam-4559	160	3	.	.	PUNCT
ejpam-4559	161	1	let	let	VERB
ejpam-4559	161	2	f	f	PROPN
ejpam-4559	161	3	(	(	PUNCT
ejpam-4559	161	4	z	z	NOUN
ejpam-4559	161	5	)	)	PUNCT
ejpam-4559	161	6	∈	∈	PROPN
ejpam-4559	161	7	r	r	NOUN
ejpam-4559	161	8	(	(	PUNCT
ejpam-4559	161	9	α	α	NOUN
ejpam-4559	161	10	)	)	PUNCT
ejpam-4559	161	11	.	.	PUNCT
ejpam-4559	162	1	then	then	ADV
ejpam-4559	162	2	(	(	PUNCT
ejpam-4559	162	3	i	i	NOUN
ejpam-4559	162	4	)	)	PUNCT
ejpam-4559	162	5	|t2	|t2	PROPN
ejpam-4559	162	6	(	(	PUNCT
ejpam-4559	162	7	n)|	n)|	PROPN
ejpam-4559	162	8	⩽	⩽	PROPN
ejpam-4559	162	9	4cos2α	4cos2α	NUM
ejpam-4559	162	10	[	[	PUNCT
ejpam-4559	162	11	1	1	NUM
ejpam-4559	162	12	n2	n2	NOUN
ejpam-4559	162	13	+	+	CCONJ
ejpam-4559	162	14	1	1	NUM
ejpam-4559	162	15	(	(	PUNCT
ejpam-4559	162	16	n+1)2	n+1)2	PROPN
ejpam-4559	162	17	]	]	PUNCT
ejpam-4559	162	18	.	.	PUNCT
ejpam-4559	163	1	(	(	PUNCT
ejpam-4559	163	2	ii	ii	X
ejpam-4559	163	3	)	)	PUNCT
ejpam-4559	163	4	|t3	|t3	NOUN
ejpam-4559	163	5	(	(	PUNCT
ejpam-4559	163	6	1)|	1)|	NUM
ejpam-4559	163	7	⩽	⩽	NOUN
ejpam-4559	163	8	1	1	NUM
ejpam-4559	163	9	9	9	NUM
ejpam-4559	163	10	(	(	PUNCT
ejpam-4559	163	11	9	9	NUM
ejpam-4559	163	12	+	+	NUM
ejpam-4559	163	13	18cos2α	18cos2α	NUM
ejpam-4559	163	14	+	+	CCONJ
ejpam-4559	163	15	4cos2α	4cos2α	NUM
ejpam-4559	163	16	√	√	NOUN
ejpam-4559	163	17	3cos2α	3cos2α	NUM
ejpam-4559	163	18	+	+	CCONJ
ejpam-4559	163	19	1	1	NUM
ejpam-4559	163	20	)	)	PUNCT
ejpam-4559	163	21	.	.	PUNCT
ejpam-4559	164	1	(	(	PUNCT
ejpam-4559	164	2	iii	iii	X
ejpam-4559	164	3	)	)	PUNCT
ejpam-4559	164	4	|t3	|t3	NOUN
ejpam-4559	164	5	(	(	PUNCT
ejpam-4559	164	6	2)|	2)|	NUM
ejpam-4559	164	7	⩽	⩽	ADJ
ejpam-4559	164	8	7	7	NUM
ejpam-4559	164	9	cosα3	cosα3	NOUN
ejpam-4559	164	10	3	3	NUM
ejpam-4559	164	11	.	.	PUNCT
ejpam-4559	165	1	(	(	PUNCT
ejpam-4559	165	2	iv	iv	X
ejpam-4559	165	3	)	)	PUNCT
ejpam-4559	165	4	|t3	|t3	NOUN
ejpam-4559	165	5	(	(	PUNCT
ejpam-4559	165	6	3)|	3)|	NUM
ejpam-4559	165	7	⩽	⩽	NOUN
ejpam-4559	165	8	112cos3α	112cos3α	NUM
ejpam-4559	165	9	135	135	NUM
ejpam-4559	165	10	.	.	PUNCT
ejpam-4559	166	1	(	(	PUNCT
ejpam-4559	166	2	v	v	NOUN
ejpam-4559	166	3	)	)	PUNCT
ejpam-4559	166	4	|t4	|t4	NOUN
ejpam-4559	166	5	(	(	PUNCT
ejpam-4559	166	6	1)|	1)|	NUM
ejpam-4559	166	7	⩽	⩽	ADJ
ejpam-4559	166	8	1	1	NUM
ejpam-4559	166	9	1296	1296	NUM
ejpam-4559	166	10	(	(	PUNCT
ejpam-4559	166	11	1296	1296	NUM
ejpam-4559	166	12	+	+	CCONJ
ejpam-4559	166	13	4392cos2α	4392cos2α	PRON
ejpam-4559	167	1	+	+	NOUN
ejpam-4559	167	2	3456cos3α	3456cos3α	NUM
ejpam-4559	167	3	+	+	CCONJ
ejpam-4559	167	4	1921cos4α	1921cos4α	NUM
ejpam-4559	167	5	)	)	PUNCT
ejpam-4559	167	6	.	.	PUNCT
ejpam-4559	168	1	we	we	PRON
ejpam-4559	168	2	remark	remark	VERB
ejpam-4559	168	3	that	that	SCONJ
ejpam-4559	168	4	the	the	DET
ejpam-4559	168	5	inequalities	inequality	NOUN
ejpam-4559	168	6	in	in	ADP
ejpam-4559	168	7	corollary	corollary	ADJ
ejpam-4559	168	8	1(i	1(i	NUM
ejpam-4559	168	9	)	)	PUNCT
ejpam-4559	168	10	,	,	PUNCT
ejpam-4559	168	11	corollary	corollary	ADJ
ejpam-4559	168	12	1(ii	1(ii	NUM
ejpam-4559	168	13	)	)	PUNCT
ejpam-4559	168	14	,	,	PUNCT
ejpam-4559	168	15	and	and	CCONJ
ejpam-4559	168	16	corollary	corollary	ADJ
ejpam-4559	168	17	1(iii	1(iii	NUM
ejpam-4559	168	18	)	)	PUNCT
ejpam-4559	168	19	coincide	coincide	NOUN
ejpam-4559	168	20	with	with	ADP
ejpam-4559	168	21	the	the	DET
ejpam-4559	168	22	results	result	NOUN
ejpam-4559	168	23	of	of	ADP
ejpam-4559	168	24	ali	ali	PROPN
ejpam-4559	168	25	et	et	PROPN
ejpam-4559	168	26	al	al	PROPN
ejpam-4559	168	27	.	.	PUNCT
ejpam-4559	169	1	[	[	X
ejpam-4559	169	2	2	2	NUM
ejpam-4559	169	3	]	]	PUNCT
ejpam-4559	169	4	.	.	PUNCT
ejpam-4559	170	1	it	it	PRON
ejpam-4559	170	2	is	be	AUX
ejpam-4559	170	3	also	also	ADV
ejpam-4559	170	4	shown	show	VERB
ejpam-4559	170	5	in	in	ADP
ejpam-4559	170	6	[	[	X
ejpam-4559	170	7	2	2	X
ejpam-4559	170	8	]	]	PUNCT
ejpam-4559	170	9	that	that	SCONJ
ejpam-4559	170	10	the	the	DET
ejpam-4559	170	11	results	result	NOUN
ejpam-4559	170	12	in	in	ADP
ejpam-4559	170	13	corollary	corollary	ADJ
ejpam-4559	170	14	1(i	1(i	NUM
ejpam-4559	170	15	)	)	PUNCT
ejpam-4559	170	16	and	and	CCONJ
ejpam-4559	170	17	corollary	corollary	ADJ
ejpam-4559	170	18	1(ii	1(ii	NUM
ejpam-4559	170	19	)	)	PUNCT
ejpam-4559	170	20	were	be	AUX
ejpam-4559	170	21	sharp	sharp	ADJ
ejpam-4559	170	22	.	.	PUNCT
ejpam-4559	171	1	in	in	ADP
ejpam-4559	171	2	the	the	DET
ejpam-4559	171	3	existing	exist	VERB
ejpam-4559	171	4	literature	literature	NOUN
ejpam-4559	171	5	,	,	PUNCT
ejpam-4559	171	6	no	no	DET
ejpam-4559	171	7	bounds	bound	NOUN
ejpam-4559	171	8	for	for	ADP
ejpam-4559	171	9	|t2	|t2	PROPN
ejpam-4559	171	10	(	(	PUNCT
ejpam-4559	171	11	n)|	n)|	PROPN
ejpam-4559	171	12	,	,	PUNCT
ejpam-4559	171	13	n	n	CCONJ
ejpam-4559	171	14	⩾	⩾	NOUN
ejpam-4559	171	15	2	2	NUM
ejpam-4559	171	16	,	,	PUNCT
ejpam-4559	171	17	|t3	|t3	PROPN
ejpam-4559	171	18	(	(	PUNCT
ejpam-4559	171	19	n)|	n)|	NOUN
ejpam-4559	171	20	,	,	PUNCT
ejpam-4559	171	21	n	n	NOUN
ejpam-4559	171	22	=	=	SYM
ejpam-4559	171	23	1	1	NUM
ejpam-4559	171	24	,	,	PUNCT
ejpam-4559	171	25	2	2	NUM
ejpam-4559	171	26	,	,	PUNCT
ejpam-4559	171	27	3	3	NUM
ejpam-4559	171	28	,	,	PUNCT
ejpam-4559	171	29	and	and	CCONJ
ejpam-4559	171	30	|t4	|t4	NOUN
ejpam-4559	171	31	(	(	PUNCT
ejpam-4559	171	32	1)|	1)|	NUM
ejpam-4559	171	33	for	for	ADP
ejpam-4559	171	34	the	the	DET
ejpam-4559	171	35	classes	class	NOUN
ejpam-4559	171	36	g	g	PROPN
ejpam-4559	171	37	(	(	PUNCT
ejpam-4559	171	38	α	α	PROPN
ejpam-4559	171	39	,	,	PUNCT
ejpam-4559	171	40	δ	δ	PROPN
ejpam-4559	171	41	)	)	PUNCT
ejpam-4559	171	42	,	,	PUNCT
ejpam-4559	171	43	r	r	NOUN
ejpam-4559	171	44	(	(	PUNCT
ejpam-4559	171	45	δ	δ	PROPN
ejpam-4559	171	46	)	)	PUNCT
ejpam-4559	171	47	,	,	PUNCT
ejpam-4559	171	48	and	and	CCONJ
ejpam-4559	171	49	r	r	NOUN
ejpam-4559	171	50	(	(	PUNCT
ejpam-4559	171	51	α	α	NOUN
ejpam-4559	171	52	)	)	PUNCT
ejpam-4559	171	53	were	be	AUX
ejpam-4559	171	54	obtained	obtain	VERB
ejpam-4559	171	55	.	.	PUNCT
ejpam-4559	172	1	additionally	additionally	ADV
ejpam-4559	172	2	,	,	PUNCT
ejpam-4559	172	3	the	the	DET
ejpam-4559	172	4	results	result	NOUN
ejpam-4559	172	5	on	on	ADP
ejpam-4559	172	6	|t3	|t3	PROPN
ejpam-4559	172	7	(	(	PUNCT
ejpam-4559	172	8	3)|	3)|	NUM
ejpam-4559	172	9	and	and	CCONJ
ejpam-4559	172	10	|t4	|t4	PROPN
ejpam-4559	172	11	(	(	PUNCT
ejpam-4559	172	12	1)|	1)|	NUM
ejpam-4559	172	13	for	for	ADP
ejpam-4559	172	14	functions	function	NOUN
ejpam-4559	172	15	in	in	ADP
ejpam-4559	172	16	the	the	DET
ejpam-4559	172	17	class	class	NOUN
ejpam-4559	172	18	r	r	NOUN
ejpam-4559	172	19	had	have	AUX
ejpam-4559	172	20	never	never	ADV
ejpam-4559	172	21	been	be	AUX
ejpam-4559	172	22	studied	study	VERB
ejpam-4559	172	23	before	before	ADV
ejpam-4559	172	24	.	.	PUNCT
ejpam-4559	173	1	references	reference	NOUN
ejpam-4559	173	2	1945	1945	NUM
ejpam-4559	173	3	4	4	NUM
ejpam-4559	173	4	.	.	PUNCT
ejpam-4559	173	5	conclusions	conclusion	NOUN
ejpam-4559	173	6	in	in	ADP
ejpam-4559	173	7	the	the	DET
ejpam-4559	173	8	present	present	ADJ
ejpam-4559	173	9	paper	paper	NOUN
ejpam-4559	173	10	,	,	PUNCT
ejpam-4559	173	11	we	we	PRON
ejpam-4559	173	12	have	have	AUX
ejpam-4559	173	13	considered	consider	VERB
ejpam-4559	173	14	the	the	DET
ejpam-4559	173	15	toeplitz	toeplitz	NOUN
ejpam-4559	173	16	determinants	determinant	NOUN
ejpam-4559	173	17	whose	whose	DET
ejpam-4559	173	18	elements	element	NOUN
ejpam-4559	173	19	are	be	AUX
ejpam-4559	173	20	coefficients	coefficient	NOUN
ejpam-4559	173	21	of	of	ADP
ejpam-4559	173	22	univalent	univalent	ADJ
ejpam-4559	173	23	functions	function	NOUN
ejpam-4559	173	24	.	.	PUNCT
ejpam-4559	174	1	we	we	PRON
ejpam-4559	174	2	have	have	AUX
ejpam-4559	174	3	obtained	obtain	VERB
ejpam-4559	174	4	the	the	DET
ejpam-4559	174	5	upper	upper	ADJ
ejpam-4559	174	6	bounds	bound	NOUN
ejpam-4559	174	7	of	of	ADP
ejpam-4559	174	8	|t2	|t2	PROPN
ejpam-4559	174	9	(	(	PUNCT
ejpam-4559	174	10	n)|	n)|	PROPN
ejpam-4559	174	11	,	,	PUNCT
ejpam-4559	174	12	n	n	CCONJ
ejpam-4559	174	13	⩾	⩾	NOUN
ejpam-4559	174	14	2	2	NUM
ejpam-4559	174	15	,	,	PUNCT
ejpam-4559	174	16	|t3	|t3	PROPN
ejpam-4559	174	17	(	(	PUNCT
ejpam-4559	174	18	n)|	n)|	NOUN
ejpam-4559	174	19	,	,	PUNCT
ejpam-4559	174	20	n	n	NOUN
ejpam-4559	174	21	=	=	SYM
ejpam-4559	174	22	1	1	NUM
ejpam-4559	174	23	,	,	PUNCT
ejpam-4559	174	24	2	2	NUM
ejpam-4559	174	25	,	,	PUNCT
ejpam-4559	174	26	3	3	NUM
ejpam-4559	174	27	,	,	PUNCT
ejpam-4559	174	28	and	and	CCONJ
ejpam-4559	174	29	|t4	|t4	NOUN
ejpam-4559	174	30	(	(	PUNCT
ejpam-4559	174	31	1)|	1)|	NUM
ejpam-4559	174	32	not	not	PART
ejpam-4559	174	33	only	only	ADV
ejpam-4559	174	34	for	for	ADP
ejpam-4559	174	35	functions	function	NOUN
ejpam-4559	174	36	of	of	ADP
ejpam-4559	174	37	the	the	DET
ejpam-4559	174	38	class	class	NOUN
ejpam-4559	174	39	g	g	PROPN
ejpam-4559	174	40	(	(	PUNCT
ejpam-4559	174	41	α	α	PROPN
ejpam-4559	174	42	,	,	PUNCT
ejpam-4559	174	43	δ	δ	PROPN
ejpam-4559	174	44	)	)	PUNCT
ejpam-4559	174	45	,	,	PUNCT
ejpam-4559	174	46	but	but	CCONJ
ejpam-4559	174	47	also	also	ADV
ejpam-4559	174	48	for	for	ADP
ejpam-4559	174	49	some	some	DET
ejpam-4559	174	50	classes	class	NOUN
ejpam-4559	174	51	of	of	ADP
ejpam-4559	174	52	functions	function	NOUN
ejpam-4559	174	53	with	with	ADP
ejpam-4559	174	54	bounded	bounded	ADJ
ejpam-4559	174	55	turning	turn	VERB
ejpam-4559	174	56	namely	namely	ADV
ejpam-4559	174	57	r	r	NOUN
ejpam-4559	174	58	,	,	PUNCT
ejpam-4559	174	59	r	r	NOUN
ejpam-4559	174	60	(	(	PUNCT
ejpam-4559	174	61	δ	δ	PROPN
ejpam-4559	174	62	)	)	PUNCT
ejpam-4559	174	63	,	,	PUNCT
ejpam-4559	174	64	and	and	CCONJ
ejpam-4559	174	65	r	r	NOUN
ejpam-4559	174	66	(	(	PUNCT
ejpam-4559	174	67	α	α	NOUN
ejpam-4559	174	68	)	)	PUNCT
ejpam-4559	174	69	.	.	PUNCT
ejpam-4559	175	1	some	some	DET
ejpam-4559	175	2	results	result	NOUN
ejpam-4559	175	3	obtained	obtain	VERB
ejpam-4559	175	4	are	be	AUX
ejpam-4559	175	5	reduced	reduce	VERB
ejpam-4559	175	6	to	to	ADP
ejpam-4559	175	7	the	the	DET
ejpam-4559	175	8	estimates	estimate	NOUN
ejpam-4559	175	9	proven	prove	VERB
ejpam-4559	175	10	in	in	ADP
ejpam-4559	175	11	[	[	X
ejpam-4559	175	12	2	2	NUM
ejpam-4559	175	13	]	]	PUNCT
ejpam-4559	175	14	for	for	ADP
ejpam-4559	175	15	specific	specific	ADJ
ejpam-4559	175	16	choices	choice	NOUN
ejpam-4559	175	17	of	of	ADP
ejpam-4559	175	18	parameters	parameter	NOUN
ejpam-4559	175	19	α	α	PROPN
ejpam-4559	175	20	and	and	CCONJ
ejpam-4559	175	21	δ	δ	PROPN
ejpam-4559	175	22	.	.	PUNCT
ejpam-4559	176	1	for	for	ADP
ejpam-4559	176	2	the	the	DET
ejpam-4559	176	3	class	class	NOUN
ejpam-4559	176	4	g	g	PROPN
ejpam-4559	176	5	(	(	PUNCT
ejpam-4559	176	6	α	α	PROPN
ejpam-4559	176	7	,	,	PUNCT
ejpam-4559	176	8	δ	δ	PROPN
ejpam-4559	176	9	)	)	PUNCT
ejpam-4559	176	10	,	,	PUNCT
ejpam-4559	176	11	we	we	PRON
ejpam-4559	176	12	have	have	AUX
ejpam-4559	176	13	determined	determine	VERB
ejpam-4559	176	14	the	the	DET
ejpam-4559	176	15	sharp	sharp	ADJ
ejpam-4559	176	16	estimates	estimate	NOUN
ejpam-4559	176	17	for	for	ADP
ejpam-4559	176	18	|t2	|t2	PROPN
ejpam-4559	176	19	(	(	PUNCT
ejpam-4559	176	20	n)|	n)|	PROPN
ejpam-4559	176	21	,	,	PUNCT
ejpam-4559	176	22	n	n	CCONJ
ejpam-4559	176	23	⩾	⩾	PROPN
ejpam-4559	176	24	2	2	NUM
ejpam-4559	176	25	and	and	CCONJ
ejpam-4559	176	26	|t3	|t3	PROPN
ejpam-4559	176	27	(	(	PUNCT
ejpam-4559	176	28	1)|	1)|	NUM
ejpam-4559	176	29	.	.	PUNCT
ejpam-4559	177	1	the	the	DET
ejpam-4559	177	2	results	result	NOUN
ejpam-4559	177	3	obtained	obtain	VERB
ejpam-4559	177	4	perhaps	perhaps	ADV
ejpam-4559	177	5	give	give	VERB
ejpam-4559	177	6	an	an	DET
ejpam-4559	177	7	opportunity	opportunity	NOUN
ejpam-4559	177	8	for	for	SCONJ
ejpam-4559	177	9	researchers	researcher	NOUN
ejpam-4559	177	10	to	to	PART
ejpam-4559	177	11	further	far	ADV
ejpam-4559	177	12	investigate	investigate	VERB
ejpam-4559	177	13	inequalities	inequality	NOUN
ejpam-4559	177	14	problems	problem	NOUN
ejpam-4559	177	15	for	for	ADP
ejpam-4559	177	16	functions	function	NOUN
ejpam-4559	177	17	of	of	ADP
ejpam-4559	177	18	the	the	DET
ejpam-4559	177	19	class	class	NOUN
ejpam-4559	177	20	g	g	PROPN
ejpam-4559	177	21	(	(	PUNCT
ejpam-4559	177	22	α	α	PROPN
ejpam-4559	177	23	,	,	PUNCT
ejpam-4559	177	24	δ	δ	PROPN
ejpam-4559	177	25	)	)	PUNCT
ejpam-4559	177	26	as	as	ADV
ejpam-4559	177	27	well	well	ADV
ejpam-4559	177	28	as	as	ADP
ejpam-4559	177	29	other	other	ADJ
ejpam-4559	177	30	subclasses	subclass	NOUN
ejpam-4559	177	31	of	of	ADP
ejpam-4559	177	32	s.	s.	PROPN
ejpam-4559	177	33	acknowledgements	acknowledgement	VERB
ejpam-4559	177	34	the	the	DET
ejpam-4559	177	35	authors	author	NOUN
ejpam-4559	177	36	truly	truly	ADV
ejpam-4559	177	37	appreciate	appreciate	VERB
ejpam-4559	177	38	the	the	DET
ejpam-4559	177	39	referees	referee	NOUN
ejpam-4559	177	40	’	’	PART
ejpam-4559	177	41	insightful	insightful	ADJ
ejpam-4559	177	42	comments	comment	NOUN
ejpam-4559	177	43	.	.	PUNCT
ejpam-4559	178	1	a	a	DET
ejpam-4559	178	2	special	special	ADJ
ejpam-4559	178	3	thanks	thank	NOUN
ejpam-4559	178	4	to	to	ADP
ejpam-4559	178	5	universiti	universiti	PROPN
ejpam-4559	178	6	teknologi	teknologi	PROPN
ejpam-4559	178	7	mara	mara	PROPN
ejpam-4559	178	8	for	for	ADP
ejpam-4559	178	9	supporting	support	VERB
ejpam-4559	178	10	the	the	DET
ejpam-4559	178	11	publication	publication	NOUN
ejpam-4559	178	12	of	of	ADP
ejpam-4559	178	13	this	this	DET
ejpam-4559	178	14	paper	paper	NOUN
ejpam-4559	178	15	.	.	PUNCT
ejpam-4559	179	1	references	reference	NOUN
ejpam-4559	179	2	[	[	X
ejpam-4559	179	3	1	1	X
ejpam-4559	179	4	]	]	X
ejpam-4559	179	5	saba	saba	PROPN
ejpam-4559	179	6	n	n	PROPN
ejpam-4559	179	7	al	al	PROPN
ejpam-4559	179	8	-	-	PUNCT
ejpam-4559	179	9	khafaji	khafaji	PROPN
ejpam-4559	179	10	,	,	PUNCT
ejpam-4559	179	11	ali	ali	PROPN
ejpam-4559	179	12	al	al	PROPN
ejpam-4559	179	13	-	-	PUNCT
ejpam-4559	179	14	fayadh	fayadh	PROPN
ejpam-4559	179	15	,	,	PUNCT
ejpam-4559	179	16	ahmed	ahmed	PROPN
ejpam-4559	179	17	hadi	hadi	PROPN
ejpam-4559	179	18	hussain	hussain	PROPN
ejpam-4559	179	19	,	,	PUNCT
ejpam-4559	179	20	and	and	CCONJ
ejpam-4559	179	21	sameer	sameer	PROPN
ejpam-4559	179	22	annon	annon	PROPN
ejpam-4559	179	23	abbas	abbas	PROPN
ejpam-4559	179	24	.	.	PUNCT
ejpam-4559	180	1	toeplitz	toeplitz	NOUN
ejpam-4559	180	2	determinant	determinant	ADJ
ejpam-4559	180	3	whose	whose	DET
ejpam-4559	180	4	its	its	PRON
ejpam-4559	180	5	entries	entry	NOUN
ejpam-4559	180	6	are	be	AUX
ejpam-4559	180	7	the	the	DET
ejpam-4559	180	8	coefficients	coefficient	NOUN
ejpam-4559	180	9	for	for	ADP
ejpam-4559	180	10	class	class	NOUN
ejpam-4559	180	11	of	of	ADP
ejpam-4559	180	12	non	non	ADJ
ejpam-4559	180	13	-	-	ADJ
ejpam-4559	180	14	bazilević	bazilević	ADJ
ejpam-4559	180	15	functions	function	NOUN
ejpam-4559	180	16	.	.	PUNCT
ejpam-4559	181	1	in	in	ADP
ejpam-4559	181	2	journal	journal	PROPN
ejpam-4559	181	3	of	of	ADP
ejpam-4559	181	4	physics	physics	PROPN
ejpam-4559	181	5	:	:	PUNCT
ejpam-4559	181	6	conference	conference	NOUN
ejpam-4559	181	7	series	series	NOUN
ejpam-4559	181	8	,	,	PUNCT
ejpam-4559	181	9	volume	volume	NOUN
ejpam-4559	181	10	1660	1660	NUM
ejpam-4559	181	11	,	,	PUNCT
ejpam-4559	181	12	page	page	NOUN
ejpam-4559	181	13	012091	012091	NUM
ejpam-4559	181	14	.	.	PUNCT
ejpam-4559	182	1	iop	iop	PROPN
ejpam-4559	182	2	publishing	publishing	NOUN
ejpam-4559	182	3	,	,	PUNCT
ejpam-4559	182	4	2020	2020	NUM
ejpam-4559	182	5	.	.	PUNCT
ejpam-4559	183	1	[	[	X
ejpam-4559	183	2	2	2	X
ejpam-4559	183	3	]	]	X
ejpam-4559	183	4	md	md	PROPN
ejpam-4559	183	5	firoz	firoz	PROPN
ejpam-4559	183	6	ali	ali	PROPN
ejpam-4559	183	7	,	,	PUNCT
ejpam-4559	183	8	dk	dk	PROPN
ejpam-4559	183	9	thomas	thomas	PROPN
ejpam-4559	183	10	,	,	PUNCT
ejpam-4559	183	11	and	and	CCONJ
ejpam-4559	183	12	a	a	DET
ejpam-4559	183	13	vasudevarao	vasudevarao	NOUN
ejpam-4559	183	14	.	.	PUNCT
ejpam-4559	184	1	toeplitz	toeplitz	NOUN
ejpam-4559	184	2	determinants	determinant	NOUN
ejpam-4559	184	3	whose	whose	DET
ejpam-4559	184	4	elements	element	NOUN
ejpam-4559	184	5	are	be	AUX
ejpam-4559	184	6	the	the	DET
ejpam-4559	184	7	coefficients	coefficient	NOUN
ejpam-4559	184	8	of	of	ADP
ejpam-4559	184	9	analytic	analytic	ADJ
ejpam-4559	184	10	and	and	CCONJ
ejpam-4559	184	11	univalent	univalent	ADJ
ejpam-4559	184	12	functions	function	NOUN
ejpam-4559	184	13	.	.	PUNCT
ejpam-4559	185	1	bulletin	bulletin	NOUN
ejpam-4559	185	2	of	of	ADP
ejpam-4559	185	3	the	the	DET
ejpam-4559	185	4	australian	australian	ADJ
ejpam-4559	185	5	mathematical	mathematical	ADJ
ejpam-4559	185	6	society	society	NOUN
ejpam-4559	185	7	,	,	PUNCT
ejpam-4559	185	8	97(2):253–264	97(2):253–264	NOUN
ejpam-4559	185	9	,	,	PUNCT
ejpam-4559	185	10	2018	2018	NUM
ejpam-4559	185	11	.	.	PUNCT
ejpam-4559	186	1	[	[	X
ejpam-4559	186	2	3	3	X
ejpam-4559	186	3	]	]	X
ejpam-4559	186	4	muhammad	muhammad	PROPN
ejpam-4559	186	5	arif	arif	PROPN
ejpam-4559	186	6	,	,	PUNCT
ejpam-4559	186	7	mohsan	mohsan	PROPN
ejpam-4559	186	8	raza	raza	PROPN
ejpam-4559	186	9	,	,	PUNCT
ejpam-4559	186	10	inayat	inayat	PROPN
ejpam-4559	186	11	ullah	ullah	PROPN
ejpam-4559	186	12	,	,	PUNCT
ejpam-4559	186	13	and	and	CCONJ
ejpam-4559	186	14	pawel	pawel	PROPN
ejpam-4559	186	15	zaprawa	zaprawa	PROPN
ejpam-4559	186	16	.	.	PUNCT
ejpam-4559	187	1	hankel	hankel	NOUN
ejpam-4559	187	2	determinants	determinant	NOUN
ejpam-4559	187	3	of	of	ADP
ejpam-4559	187	4	order	order	NOUN
ejpam-4559	187	5	four	four	NUM
ejpam-4559	187	6	for	for	ADP
ejpam-4559	187	7	a	a	DET
ejpam-4559	187	8	set	set	NOUN
ejpam-4559	187	9	of	of	ADP
ejpam-4559	187	10	functions	function	NOUN
ejpam-4559	187	11	with	with	ADP
ejpam-4559	187	12	bounded	bounded	ADJ
ejpam-4559	187	13	turning	turning	NOUN
ejpam-4559	187	14	of	of	ADP
ejpam-4559	187	15	order	order	NOUN
ejpam-4559	187	16	α	α	NOUN
ejpam-4559	187	17	.	.	PUNCT
ejpam-4559	188	1	lithuanian	lithuanian	PROPN
ejpam-4559	188	2	mathematical	mathematical	ADJ
ejpam-4559	188	3	journal	journal	PROPN
ejpam-4559	188	4	,	,	PUNCT
ejpam-4559	188	5	62(2):135–145	62(2):135–145	PROPN
ejpam-4559	188	6	,	,	PUNCT
ejpam-4559	188	7	2022	2022	NUM
ejpam-4559	188	8	.	.	PUNCT
ejpam-4559	189	1	[	[	X
ejpam-4559	189	2	4	4	X
ejpam-4559	189	3	]	]	X
ejpam-4559	189	4	muhammad	muhammad	PROPN
ejpam-4559	189	5	arif	arif	PROPN
ejpam-4559	189	6	,	,	PUNCT
ejpam-4559	189	7	inayat	inayat	PROPN
ejpam-4559	189	8	ullah	ullah	PROPN
ejpam-4559	189	9	,	,	PUNCT
ejpam-4559	189	10	mohsan	mohsan	PROPN
ejpam-4559	189	11	raza	raza	PROPN
ejpam-4559	189	12	,	,	PUNCT
ejpam-4559	189	13	and	and	CCONJ
ejpam-4559	189	14	pawe	pawe	PROPN
ejpam-4559	189	15	l	l	PROPN
ejpam-4559	189	16	zaprawa	zaprawa	PROPN
ejpam-4559	189	17	.	.	PUNCT
ejpam-4559	190	1	investigation	investigation	NOUN
ejpam-4559	190	2	of	of	ADP
ejpam-4559	190	3	the	the	DET
ejpam-4559	190	4	fifth	fifth	ADJ
ejpam-4559	190	5	hankel	hankel	NOUN
ejpam-4559	190	6	determinant	determinant	ADJ
ejpam-4559	190	7	for	for	ADP
ejpam-4559	190	8	a	a	DET
ejpam-4559	190	9	family	family	NOUN
ejpam-4559	190	10	of	of	ADP
ejpam-4559	190	11	functions	function	NOUN
ejpam-4559	190	12	with	with	ADP
ejpam-4559	190	13	bounded	bounded	ADJ
ejpam-4559	190	14	turnings	turning	NOUN
ejpam-4559	190	15	.	.	PUNCT
ejpam-4559	191	1	mathematica	mathematica	PROPN
ejpam-4559	191	2	slovaca	slovaca	PROPN
ejpam-4559	191	3	,	,	PUNCT
ejpam-4559	191	4	70(2):319–328	70(2):319–328	PROPN
ejpam-4559	191	5	,	,	PUNCT
ejpam-4559	191	6	2020	2020	NUM
ejpam-4559	191	7	.	.	PUNCT
ejpam-4559	192	1	[	[	X
ejpam-4559	192	2	5	5	NUM
ejpam-4559	192	3	]	]	PUNCT
ejpam-4559	192	4	luminiţa	luminiţa	PROPN
ejpam-4559	192	5	-	-	PUNCT
ejpam-4559	192	6	ioana	ioana	PROPN
ejpam-4559	192	7	cot̂ırlă	cot̂ırlă	PROPN
ejpam-4559	192	8	and	and	CCONJ
ejpam-4559	192	9	abbas	abbas	PROPN
ejpam-4559	192	10	kareem	kareem	PROPN
ejpam-4559	192	11	wanas	wanas	PROPN
ejpam-4559	192	12	.	.	PUNCT
ejpam-4559	193	1	symmetric	symmetric	ADJ
ejpam-4559	193	2	toeplitz	toeplitz	NOUN
ejpam-4559	193	3	matrices	matrix	NOUN
ejpam-4559	193	4	for	for	ADP
ejpam-4559	193	5	a	a	DET
ejpam-4559	193	6	new	new	ADJ
ejpam-4559	193	7	family	family	NOUN
ejpam-4559	193	8	of	of	ADP
ejpam-4559	193	9	prestarlike	prestarlike	ADJ
ejpam-4559	193	10	functions	function	NOUN
ejpam-4559	193	11	.	.	PUNCT
ejpam-4559	194	1	symmetry	symmetry	NOUN
ejpam-4559	194	2	,	,	PUNCT
ejpam-4559	194	3	14(7):1413	14(7):1413	NUM
ejpam-4559	194	4	,	,	PUNCT
ejpam-4559	194	5	2022	2022	NUM
ejpam-4559	194	6	.	.	PUNCT
ejpam-4559	195	1	[	[	X
ejpam-4559	195	2	6	6	NUM
ejpam-4559	195	3	]	]	PUNCT
ejpam-4559	195	4	pl	pl	PROPN
ejpam-4559	195	5	duren	duren	PROPN
ejpam-4559	195	6	.	.	PUNCT
ejpam-4559	195	7	univalent	univalent	ADJ
ejpam-4559	195	8	functions	function	NOUN
ejpam-4559	195	9	,	,	PUNCT
ejpam-4559	195	10	vol	vol	NOUN
ejpam-4559	195	11	.	.	PUNCT
ejpam-4559	195	12	259	259	NUM
ejpam-4559	195	13	,	,	PUNCT
ejpam-4559	195	14	1983	1983	NUM
ejpam-4559	195	15	.	.	PUNCT
ejpam-4559	196	1	[	[	X
ejpam-4559	196	2	7	7	NUM
ejpam-4559	196	3	]	]	X
ejpam-4559	196	4	iason	iason	NOUN
ejpam-4559	196	5	efraimidis	efraimidis	NOUN
ejpam-4559	196	6	.	.	PUNCT
ejpam-4559	197	1	a	a	DET
ejpam-4559	197	2	generalization	generalization	NOUN
ejpam-4559	197	3	of	of	ADP
ejpam-4559	197	4	livingston	livingston	PROPN
ejpam-4559	197	5	’s	’s	PART
ejpam-4559	197	6	coefficient	coefficient	NOUN
ejpam-4559	197	7	inequalities	inequality	NOUN
ejpam-4559	197	8	for	for	ADP
ejpam-4559	197	9	functions	function	NOUN
ejpam-4559	197	10	with	with	ADP
ejpam-4559	197	11	positive	positive	ADJ
ejpam-4559	197	12	real	real	ADJ
ejpam-4559	197	13	part	part	NOUN
ejpam-4559	197	14	.	.	PUNCT
ejpam-4559	198	1	journal	journal	PROPN
ejpam-4559	198	2	of	of	ADP
ejpam-4559	198	3	mathematical	mathematical	ADJ
ejpam-4559	198	4	analysis	analysis	NOUN
ejpam-4559	198	5	and	and	CCONJ
ejpam-4559	198	6	applications	application	NOUN
ejpam-4559	198	7	,	,	PUNCT
ejpam-4559	198	8	435(1):369–379	435(1):369–379	PROPN
ejpam-4559	198	9	,	,	PUNCT
ejpam-4559	198	10	2016	2016	NUM
ejpam-4559	198	11	.	.	PUNCT
ejpam-4559	199	1	references	reference	NOUN
ejpam-4559	199	2	1946	1946	NUM
ejpam-4559	199	3	[	[	X
ejpam-4559	199	4	8	8	NUM
ejpam-4559	199	5	]	]	X
ejpam-4559	199	6	rm	rm	PROPN
ejpam-4559	199	7	goel	goel	PROPN
ejpam-4559	199	8	and	and	CCONJ
ejpam-4559	199	9	beant	beant	VERB
ejpam-4559	199	10	singh	singh	PROPN
ejpam-4559	199	11	mehrok	mehrok	PROPN
ejpam-4559	199	12	.	.	PUNCT
ejpam-4559	200	1	a	a	DET
ejpam-4559	200	2	subclass	subclass	NOUN
ejpam-4559	200	3	of	of	ADP
ejpam-4559	200	4	univalent	univalent	ADJ
ejpam-4559	200	5	functions	function	NOUN
ejpam-4559	200	6	.	.	PUNCT
ejpam-4559	201	1	journal	journal	NOUN
ejpam-4559	201	2	of	of	ADP
ejpam-4559	201	3	the	the	DET
ejpam-4559	201	4	australian	australian	ADJ
ejpam-4559	201	5	mathematical	mathematical	ADJ
ejpam-4559	201	6	society	society	NOUN
ejpam-4559	201	7	,	,	PUNCT
ejpam-4559	201	8	35(1):1–17	35(1):1–17	NUM
ejpam-4559	201	9	,	,	PUNCT
ejpam-4559	201	10	1983	1983	NUM
ejpam-4559	201	11	.	.	PUNCT
ejpam-4559	202	1	[	[	X
ejpam-4559	202	2	9	9	NUM
ejpam-4559	202	3	]	]	PUNCT
ejpam-4559	202	4	thomas	thomas	PROPN
ejpam-4559	202	5	h	h	PROPN
ejpam-4559	202	6	macgregor	macgregor	PROPN
ejpam-4559	202	7	.	.	PUNCT
ejpam-4559	202	8	functions	function	NOUN
ejpam-4559	202	9	whose	whose	DET
ejpam-4559	202	10	derivative	derivative	NOUN
ejpam-4559	202	11	has	have	VERB
ejpam-4559	202	12	a	a	DET
ejpam-4559	202	13	positive	positive	ADJ
ejpam-4559	202	14	real	real	ADJ
ejpam-4559	202	15	part	part	NOUN
ejpam-4559	202	16	.	.	PUNCT
ejpam-4559	203	1	transactions	transaction	NOUN
ejpam-4559	203	2	of	of	ADP
ejpam-4559	203	3	the	the	DET
ejpam-4559	203	4	american	american	PROPN
ejpam-4559	203	5	mathematical	mathematical	PROPN
ejpam-4559	203	6	society	society	NOUN
ejpam-4559	203	7	,	,	PUNCT
ejpam-4559	203	8	104(3):532–537	104(3):532–537	NUM
ejpam-4559	203	9	,	,	PUNCT
ejpam-4559	203	10	1962	1962	NUM
ejpam-4559	203	11	.	.	PUNCT
ejpam-4559	204	1	[	[	X
ejpam-4559	204	2	10	10	NUM
ejpam-4559	204	3	]	]	X
ejpam-4559	204	4	daud	daud	PROPN
ejpam-4559	204	5	mohamad	mohamad	PROPN
ejpam-4559	204	6	.	.	PUNCT
ejpam-4559	205	1	on	on	ADP
ejpam-4559	205	2	a	a	DET
ejpam-4559	205	3	class	class	NOUN
ejpam-4559	205	4	of	of	ADP
ejpam-4559	205	5	functions	function	NOUN
ejpam-4559	205	6	whose	whose	DET
ejpam-4559	205	7	derivatives	derivative	NOUN
ejpam-4559	205	8	map	map	VERB
ejpam-4559	205	9	the	the	DET
ejpam-4559	205	10	unit	unit	NOUN
ejpam-4559	205	11	disc	disc	VERB
ejpam-4559	205	12	into	into	ADP
ejpam-4559	205	13	a	a	DET
ejpam-4559	205	14	half	half	ADJ
ejpam-4559	205	15	plane	plane	NOUN
ejpam-4559	205	16	.	.	PUNCT
ejpam-4559	206	1	bulletin	bulletin	NOUN
ejpam-4559	206	2	of	of	ADP
ejpam-4559	206	3	the	the	DET
ejpam-4559	206	4	malaysian	malaysian	PROPN
ejpam-4559	206	5	mathematical	mathematical	PROPN
ejpam-4559	206	6	sciences	sciences	PROPN
ejpam-4559	206	7	society	society	NOUN
ejpam-4559	206	8	,	,	PUNCT
ejpam-4559	206	9	23(2	23(2	NOUN
ejpam-4559	206	10	)	)	PUNCT
ejpam-4559	206	11	,	,	PUNCT
ejpam-4559	206	12	2000	2000	NUM
ejpam-4559	206	13	.	.	PUNCT
ejpam-4559	207	1	[	[	X
ejpam-4559	207	2	11	11	NUM
ejpam-4559	207	3	]	]	PUNCT
ejpam-4559	207	4	daud	daud	PROPN
ejpam-4559	207	5	mohamad	mohamad	PROPN
ejpam-4559	207	6	and	and	CCONJ
ejpam-4559	207	7	nur	nur	VERB
ejpam-4559	207	8	hazwani	hazwani	PROPN
ejpam-4559	207	9	aqilah	aqilah	PROPN
ejpam-4559	207	10	abdul	abdul	PROPN
ejpam-4559	207	11	wahid	wahid	PROPN
ejpam-4559	207	12	.	.	PUNCT
ejpam-4559	208	1	bounds	bound	VERB
ejpam-4559	208	2	on	on	ADP
ejpam-4559	208	3	toeplitz	toeplitz	NOUN
ejpam-4559	208	4	determinant	determinant	ADJ
ejpam-4559	208	5	for	for	ADP
ejpam-4559	208	6	starlike	starlike	NOUN
ejpam-4559	208	7	functions	function	NOUN
ejpam-4559	208	8	with	with	ADP
ejpam-4559	208	9	respect	respect	NOUN
ejpam-4559	208	10	to	to	ADP
ejpam-4559	208	11	conjugate	conjugate	ADJ
ejpam-4559	208	12	points	point	NOUN
ejpam-4559	208	13	.	.	PUNCT
ejpam-4559	209	1	international	international	ADJ
ejpam-4559	209	2	journal	journal	NOUN
ejpam-4559	209	3	of	of	ADP
ejpam-4559	209	4	analysis	analysis	NOUN
ejpam-4559	209	5	and	and	CCONJ
ejpam-4559	209	6	applications	application	NOUN
ejpam-4559	209	7	,	,	PUNCT
ejpam-4559	209	8	19(3):477–493	19(3):477–493	NUM
ejpam-4559	209	9	,	,	PUNCT
ejpam-4559	209	10	2021	2021	NUM
ejpam-4559	209	11	.	.	PUNCT
ejpam-4559	210	1	[	[	X
ejpam-4559	210	2	12	12	NUM
ejpam-4559	210	3	]	]	SYM
ejpam-4559	210	4	v	v	X
ejpam-4559	210	5	radhika	radhika	X
ejpam-4559	210	6	,	,	PUNCT
ejpam-4559	210	7	s	s	VERB
ejpam-4559	210	8	sivasubramanian	sivasubramanian	ADJ
ejpam-4559	210	9	,	,	PUNCT
ejpam-4559	210	10	g	g	PROPN
ejpam-4559	210	11	murugusundaramoorthy	murugusundaramoorthy	ADJ
ejpam-4559	210	12	,	,	PUNCT
ejpam-4559	210	13	jay	jay	NOUN
ejpam-4559	210	14	m	m	VERB
ejpam-4559	210	15	jahangiri	jahangiri	ADV
ejpam-4559	210	16	,	,	PUNCT
ejpam-4559	210	17	et	et	PROPN
ejpam-4559	210	18	al	al	PROPN
ejpam-4559	210	19	.	.	PUNCT
ejpam-4559	211	1	toeplitz	toeplitz	NOUN
ejpam-4559	211	2	matrices	matrix	NOUN
ejpam-4559	211	3	whose	whose	DET
ejpam-4559	211	4	elements	element	NOUN
ejpam-4559	211	5	are	be	AUX
ejpam-4559	211	6	the	the	DET
ejpam-4559	211	7	coefficients	coefficient	NOUN
ejpam-4559	211	8	of	of	ADP
ejpam-4559	211	9	functions	function	NOUN
ejpam-4559	211	10	with	with	ADP
ejpam-4559	211	11	bounded	bounded	ADJ
ejpam-4559	211	12	boundary	boundary	ADJ
ejpam-4559	211	13	rotation	rotation	NOUN
ejpam-4559	211	14	.	.	PUNCT
ejpam-4559	212	1	j.	j.	PROPN
ejpam-4559	212	2	complex	complex	PROPN
ejpam-4559	212	3	anal	anal	PROPN
ejpam-4559	212	4	,	,	PUNCT
ejpam-4559	212	5	4960704(4	4960704(4	NUM
ejpam-4559	212	6	)	)	PUNCT
ejpam-4559	212	7	,	,	PUNCT
ejpam-4559	212	8	2016	2016	NUM
ejpam-4559	212	9	.	.	PUNCT
ejpam-4559	213	1	[	[	X
ejpam-4559	213	2	13	13	NUM
ejpam-4559	213	3	]	]	PUNCT
ejpam-4559	213	4	varadharajan	varadharajan	PROPN
ejpam-4559	213	5	radhika	radhika	PROPN
ejpam-4559	213	6	,	,	PUNCT
ejpam-4559	213	7	jay	jay	PROPN
ejpam-4559	213	8	m	m	VERB
ejpam-4559	213	9	jahangiri	jahangiri	ADV
ejpam-4559	213	10	,	,	PUNCT
ejpam-4559	213	11	srikandan	srikandan	PROPN
ejpam-4559	213	12	sivasubramanian	sivasubramanian	PROPN
ejpam-4559	213	13	,	,	PUNCT
ejpam-4559	213	14	and	and	CCONJ
ejpam-4559	213	15	gangadharan	gangadharan	NOUN
ejpam-4559	213	16	murugusundaramoorthy	murugusundaramoorthy	ADJ
ejpam-4559	213	17	.	.	PUNCT
ejpam-4559	214	1	toeplitz	toeplitz	NOUN
ejpam-4559	214	2	matrices	matrix	NOUN
ejpam-4559	214	3	whose	whose	DET
ejpam-4559	214	4	elements	element	NOUN
ejpam-4559	214	5	are	be	AUX
ejpam-4559	214	6	coefficients	coefficient	NOUN
ejpam-4559	214	7	of	of	ADP
ejpam-4559	214	8	bazilevič	bazilevič	NOUN
ejpam-4559	214	9	functions	function	NOUN
ejpam-4559	214	10	.	.	PUNCT
ejpam-4559	215	1	open	open	ADJ
ejpam-4559	215	2	mathematics	mathematic	NOUN
ejpam-4559	215	3	,	,	PUNCT
ejpam-4559	215	4	16(1):1161–1169	16(1):1161–1169	NUM
ejpam-4559	215	5	,	,	PUNCT
ejpam-4559	215	6	2018	2018	NUM
ejpam-4559	215	7	.	.	PUNCT
ejpam-4559	216	1	[	[	X
ejpam-4559	216	2	14	14	NUM
ejpam-4559	216	3	]	]	X
ejpam-4559	216	4	c	c	PROPN
ejpam-4559	216	5	ramachandran	ramachandran	PROPN
ejpam-4559	216	6	and	and	CCONJ
ejpam-4559	216	7	s	s	PROPN
ejpam-4559	216	8	annamalai	annamalai	PROPN
ejpam-4559	216	9	.	.	PUNCT
ejpam-4559	217	1	on	on	ADP
ejpam-4559	217	2	hankel	hankel	NOUN
ejpam-4559	217	3	and	and	CCONJ
ejpam-4559	217	4	toeplitz	toeplitz	NOUN
ejpam-4559	217	5	determinants	determinant	NOUN
ejpam-4559	217	6	for	for	ADP
ejpam-4559	217	7	some	some	DET
ejpam-4559	217	8	special	special	ADJ
ejpam-4559	217	9	class	class	NOUN
ejpam-4559	217	10	of	of	ADP
ejpam-4559	217	11	analytic	analytic	ADJ
ejpam-4559	217	12	functions	function	NOUN
ejpam-4559	217	13	involving	involve	VERB
ejpam-4559	217	14	conical	conical	ADJ
ejpam-4559	217	15	domains	domain	NOUN
ejpam-4559	217	16	defined	define	VERB
ejpam-4559	217	17	by	by	ADP
ejpam-4559	217	18	subordination	subordination	NOUN
ejpam-4559	217	19	.	.	PUNCT
ejpam-4559	218	1	internat	internat	PROPN
ejpam-4559	218	2	.	.	PUNCT
ejpam-4559	219	1	j.	j.	PROPN
ejpam-4559	219	2	engrg	engrg	PROPN
ejpam-4559	219	3	.	.	PUNCT
ejpam-4559	220	1	res	re	NOUN
ejpam-4559	220	2	.	.	PUNCT
ejpam-4559	221	1	technol	technol	NOUN
ejpam-4559	221	2	,	,	PUNCT
ejpam-4559	221	3	5:553–561	5:553–561	NUM
ejpam-4559	221	4	,	,	PUNCT
ejpam-4559	221	5	2016	2016	NUM
ejpam-4559	221	6	.	.	PUNCT
ejpam-4559	222	1	[	[	X
ejpam-4559	222	2	15	15	NUM
ejpam-4559	222	3	]	]	X
ejpam-4559	222	4	c	c	PROPN
ejpam-4559	222	5	ramachandran	ramachandran	PROPN
ejpam-4559	222	6	and	and	CCONJ
ejpam-4559	222	7	d	d	PROPN
ejpam-4559	222	8	kavitha	kavitha	PROPN
ejpam-4559	222	9	.	.	PUNCT
ejpam-4559	223	1	toeplitz	toeplitz	PROPN
ejpam-4559	223	2	determinant	determinant	ADJ
ejpam-4559	223	3	for	for	ADP
ejpam-4559	223	4	some	some	DET
ejpam-4559	223	5	subclasses	subclass	NOUN
ejpam-4559	223	6	of	of	ADP
ejpam-4559	223	7	analytic	analytic	ADJ
ejpam-4559	223	8	functions	function	NOUN
ejpam-4559	223	9	.	.	PUNCT
ejpam-4559	224	1	global	global	ADJ
ejpam-4559	224	2	journal	journal	PROPN
ejpam-4559	224	3	of	of	ADP
ejpam-4559	224	4	pure	pure	ADJ
ejpam-4559	224	5	and	and	CCONJ
ejpam-4559	224	6	applied	applied	ADJ
ejpam-4559	224	7	mathematics	mathematic	NOUN
ejpam-4559	224	8	,	,	PUNCT
ejpam-4559	224	9	13(2):785–793	13(2):785–793	NUM
ejpam-4559	224	10	,	,	PUNCT
ejpam-4559	224	11	2017	2017	NUM
ejpam-4559	224	12	.	.	PUNCT
ejpam-4559	225	1	[	[	X
ejpam-4559	225	2	16	16	NUM
ejpam-4559	225	3	]	]	X
ejpam-4559	225	4	lei	lei	PROPN
ejpam-4559	225	5	shi	shi	PROPN
ejpam-4559	225	6	,	,	PUNCT
ejpam-4559	225	7	muhammad	muhammad	PROPN
ejpam-4559	225	8	arif	arif	PROPN
ejpam-4559	225	9	,	,	PUNCT
ejpam-4559	225	10	mohsan	mohsan	PROPN
ejpam-4559	225	11	raza	raza	PROPN
ejpam-4559	225	12	,	,	PUNCT
ejpam-4559	225	13	and	and	CCONJ
ejpam-4559	225	14	muhammad	muhammad	PROPN
ejpam-4559	225	15	abbas	abbas	PROPN
ejpam-4559	225	16	.	.	PUNCT
ejpam-4559	226	1	hankel	hankel	PROPN
ejpam-4559	226	2	determinant	determinant	ADJ
ejpam-4559	226	3	containing	contain	VERB
ejpam-4559	226	4	logarithmic	logarithmic	ADJ
ejpam-4559	226	5	coefficients	coefficient	NOUN
ejpam-4559	226	6	for	for	ADP
ejpam-4559	226	7	bounded	bounded	ADJ
ejpam-4559	226	8	turning	turning	NOUN
ejpam-4559	226	9	functions	function	NOUN
ejpam-4559	226	10	connected	connect	VERB
ejpam-4559	226	11	to	to	ADP
ejpam-4559	226	12	a	a	DET
ejpam-4559	226	13	threeleaf	threeleaf	NOUN
ejpam-4559	226	14	-	-	PUNCT
ejpam-4559	226	15	shaped	shape	VERB
ejpam-4559	226	16	domain	domain	NOUN
ejpam-4559	226	17	.	.	PUNCT
ejpam-4559	227	1	mathematics	mathematic	NOUN
ejpam-4559	227	2	,	,	PUNCT
ejpam-4559	227	3	10(16):2924	10(16):2924	NUM
ejpam-4559	227	4	,	,	PUNCT
ejpam-4559	227	5	2022	2022	NUM
ejpam-4559	227	6	.	.	PUNCT
ejpam-4559	228	1	[	[	X
ejpam-4559	228	2	17	17	NUM
ejpam-4559	228	3	]	]	PUNCT
ejpam-4559	228	4	herb	herb	NOUN
ejpam-4559	228	5	silverman	silverman	NOUN
ejpam-4559	228	6	and	and	CCONJ
ejpam-4559	228	7	em	em	PRON
ejpam-4559	228	8	silvia	silvia	PROPN
ejpam-4559	228	9	.	.	PUNCT
ejpam-4559	229	1	on	on	ADP
ejpam-4559	229	2	α	α	NOUN
ejpam-4559	229	3	-	-	PUNCT
ejpam-4559	229	4	close	close	VERB
ejpam-4559	229	5	-	-	PUNCT
ejpam-4559	229	6	to	to	ADP
ejpam-4559	229	7	-	-	PUNCT
ejpam-4559	229	8	convex	convex	NOUN
ejpam-4559	229	9	functions	function	NOUN
ejpam-4559	229	10	.	.	PUNCT
ejpam-4559	230	1	publ	publ	NOUN
ejpam-4559	230	2	.	.	PUNCT
ejpam-4559	231	1	math	math	NOUN
ejpam-4559	231	2	.	.	PUNCT
ejpam-4559	232	1	debrecen	debrecen	PROPN
ejpam-4559	232	2	,	,	PUNCT
ejpam-4559	232	3	49(3	49(3	PROPN
ejpam-4559	232	4	-	-	PUNCT
ejpam-4559	232	5	4):305–316	4):305–316	NUM
ejpam-4559	232	6	,	,	PUNCT
ejpam-4559	232	7	1996	1996	NUM
ejpam-4559	232	8	.	.	PUNCT
ejpam-4559	233	1	[	[	X
ejpam-4559	233	2	18	18	NUM
ejpam-4559	233	3	]	]	X
ejpam-4559	233	4	s	s	VERB
ejpam-4559	233	5	sivasubramanian	sivasubramanian	ADJ
ejpam-4559	233	6	,	,	PUNCT
ejpam-4559	233	7	m	m	AUX
ejpam-4559	233	8	govindaraj	govindaraj	ADJ
ejpam-4559	233	9	,	,	PUNCT
ejpam-4559	233	10	and	and	CCONJ
ejpam-4559	233	11	g	g	PROPN
ejpam-4559	233	12	murugusundaramoorthy	murugusundaramoorthy	ADJ
ejpam-4559	233	13	.	.	PUNCT
ejpam-4559	234	1	toeplitz	toeplitz	NOUN
ejpam-4559	234	2	matrices	matrix	NOUN
ejpam-4559	234	3	whose	whose	DET
ejpam-4559	234	4	elements	element	NOUN
ejpam-4559	234	5	are	be	AUX
ejpam-4559	234	6	the	the	DET
ejpam-4559	234	7	coefficients	coefficient	NOUN
ejpam-4559	234	8	of	of	ADP
ejpam-4559	234	9	analytic	analytic	ADJ
ejpam-4559	234	10	functions	function	NOUN
ejpam-4559	234	11	belonging	belong	VERB
ejpam-4559	234	12	to	to	ADP
ejpam-4559	234	13	certain	certain	ADJ
ejpam-4559	234	14	conic	conic	ADJ
ejpam-4559	234	15	domains	domain	NOUN
ejpam-4559	234	16	.	.	PUNCT
ejpam-4559	235	1	int	int	NOUN
ejpam-4559	235	2	.	.	PUNCT
ejpam-4559	236	1	j.	j.	PROPN
ejpam-4559	236	2	pure	pure	PROPN
ejpam-4559	236	3	appl	appl	PROPN
ejpam-4559	236	4	.	.	PROPN
ejpam-4559	236	5	math	math	PROPN
ejpam-4559	236	6	,	,	PUNCT
ejpam-4559	236	7	109(10):39–49	109(10):39–49	NUM
ejpam-4559	236	8	,	,	PUNCT
ejpam-4559	236	9	2016	2016	NUM
ejpam-4559	236	10	.	.	PUNCT
ejpam-4559	237	1	[	[	X
ejpam-4559	237	2	19	19	NUM
ejpam-4559	237	3	]	]	X
ejpam-4559	237	4	hari	hari	PROPN
ejpam-4559	237	5	m	m	PROPN
ejpam-4559	237	6	srivastava	srivastava	PROPN
ejpam-4559	237	7	,	,	PUNCT
ejpam-4559	237	8	qazi	qazi	PROPN
ejpam-4559	237	9	zahoor	zahoor	PROPN
ejpam-4559	237	10	ahmad	ahmad	PROPN
ejpam-4559	237	11	,	,	PUNCT
ejpam-4559	237	12	nasir	nasir	PROPN
ejpam-4559	237	13	khan	khan	PROPN
ejpam-4559	237	14	,	,	PUNCT
ejpam-4559	237	15	nazar	nazar	PROPN
ejpam-4559	237	16	khan	khan	PROPN
ejpam-4559	237	17	,	,	PUNCT
ejpam-4559	237	18	and	and	CCONJ
ejpam-4559	237	19	bilal	bilal	PROPN
ejpam-4559	237	20	khan	khan	PROPN
ejpam-4559	237	21	.	.	PUNCT
ejpam-4559	238	1	hankel	hankel	NOUN
ejpam-4559	238	2	and	and	CCONJ
ejpam-4559	238	3	toeplitz	toeplitz	NOUN
ejpam-4559	238	4	determinants	determinant	NOUN
ejpam-4559	238	5	for	for	ADP
ejpam-4559	238	6	a	a	DET
ejpam-4559	238	7	subclass	subclass	NOUN
ejpam-4559	238	8	of	of	ADP
ejpam-4559	238	9	q	q	ADJ
ejpam-4559	238	10	-	-	PUNCT
ejpam-4559	238	11	starlike	starlike	NOUN
ejpam-4559	238	12	functions	function	NOUN
ejpam-4559	238	13	associated	associate	VERB
ejpam-4559	238	14	with	with	ADP
ejpam-4559	238	15	a	a	DET
ejpam-4559	238	16	general	general	ADJ
ejpam-4559	238	17	conic	conic	ADJ
ejpam-4559	238	18	domain	domain	NOUN
ejpam-4559	238	19	.	.	PUNCT
ejpam-4559	239	1	mathematics	mathematic	NOUN
ejpam-4559	239	2	,	,	PUNCT
ejpam-4559	239	3	7(2):181	7(2):181	NUM
ejpam-4559	239	4	,	,	PUNCT
ejpam-4559	239	5	2019	2019	NUM
ejpam-4559	239	6	.	.	PUNCT
ejpam-4559	240	1	[	[	X
ejpam-4559	240	2	20	20	NUM
ejpam-4559	240	3	]	]	PUNCT
ejpam-4559	240	4	huo	huo	PROPN
ejpam-4559	240	5	tang	tang	PROPN
ejpam-4559	240	6	,	,	PUNCT
ejpam-4559	240	7	shahid	shahid	PROPN
ejpam-4559	240	8	khan	khan	PROPN
ejpam-4559	240	9	,	,	PUNCT
ejpam-4559	240	10	saqib	saqib	PROPN
ejpam-4559	240	11	hussain	hussain	PROPN
ejpam-4559	240	12	,	,	PUNCT
ejpam-4559	240	13	and	and	CCONJ
ejpam-4559	240	14	nasir	nasir	PROPN
ejpam-4559	240	15	khan	khan	PROPN
ejpam-4559	240	16	.	.	PUNCT
ejpam-4559	241	1	hankel	hankel	NOUN
ejpam-4559	241	2	and	and	CCONJ
ejpam-4559	241	3	toeplitz	toeplitz	NOUN
ejpam-4559	241	4	determinant	determinant	ADJ
ejpam-4559	241	5	for	for	ADP
ejpam-4559	241	6	a	a	DET
ejpam-4559	241	7	subclass	subclass	NOUN
ejpam-4559	241	8	of	of	ADP
ejpam-4559	241	9	multivalent	multivalent	ADJ
ejpam-4559	241	10	q	q	ADJ
ejpam-4559	241	11	-	-	PUNCT
ejpam-4559	241	12	starlike	starlike	ADJ
ejpam-4559	241	13	functions	function	NOUN
ejpam-4559	241	14	of	of	ADP
ejpam-4559	241	15	order	order	NOUN
ejpam-4559	241	16	α	α	X
ejpam-4559	241	17	.	.	PUNCT
ejpam-4559	241	18	aims	aim	VERB
ejpam-4559	241	19	math	math	NOUN
ejpam-4559	241	20	,	,	PUNCT
ejpam-4559	241	21	6:5421–5439	6:5421–5439	NOUN
ejpam-4559	241	22	,	,	PUNCT
ejpam-4559	241	23	2021	2021	NUM
ejpam-4559	241	24	.	.	PUNCT
ejpam-4559	242	1	references	reference	NOUN
ejpam-4559	242	2	1947	1947	NUM
ejpam-4559	242	3	[	[	X
ejpam-4559	242	4	21	21	NUM
ejpam-4559	242	5	]	]	X
ejpam-4559	242	6	dk	dk	PROPN
ejpam-4559	242	7	thomas	thomas	PROPN
ejpam-4559	242	8	and	and	CCONJ
ejpam-4559	242	9	s	s	PROPN
ejpam-4559	242	10	abdul	abdul	PROPN
ejpam-4559	242	11	halim	halim	PROPN
ejpam-4559	242	12	.	.	PUNCT
ejpam-4559	243	1	retracted	retracted	ADJ
ejpam-4559	243	2	article	article	NOUN
ejpam-4559	243	3	:	:	PUNCT
ejpam-4559	243	4	toeplitz	toeplitz	NOUN
ejpam-4559	243	5	matrices	matrix	NOUN
ejpam-4559	243	6	whose	whose	DET
ejpam-4559	243	7	elements	element	NOUN
ejpam-4559	243	8	are	be	AUX
ejpam-4559	243	9	the	the	DET
ejpam-4559	243	10	coefficients	coefficient	NOUN
ejpam-4559	243	11	of	of	ADP
ejpam-4559	243	12	starlike	starlike	NOUN
ejpam-4559	243	13	and	and	CCONJ
ejpam-4559	243	14	close	close	NOUN
ejpam-4559	243	15	-	-	PUNCT
ejpam-4559	243	16	to	to	ADP
ejpam-4559	243	17	-	-	PUNCT
ejpam-4559	243	18	convex	convex	NOUN
ejpam-4559	243	19	functions	function	NOUN
ejpam-4559	243	20	.	.	PUNCT
ejpam-4559	244	1	bulletin	bulletin	NOUN
ejpam-4559	244	2	of	of	ADP
ejpam-4559	244	3	the	the	DET
ejpam-4559	244	4	malaysian	malaysian	PROPN
ejpam-4559	244	5	mathematical	mathematical	PROPN
ejpam-4559	244	6	sciences	sciences	PROPN
ejpam-4559	244	7	society	society	NOUN
ejpam-4559	244	8	,	,	PUNCT
ejpam-4559	244	9	40(4):1781–1790	40(4):1781–1790	NOUN
ejpam-4559	244	10	,	,	PUNCT
ejpam-4559	244	11	2017	2017	NUM
ejpam-4559	244	12	.	.	PUNCT
ejpam-4559	245	1	[	[	X
ejpam-4559	245	2	22	22	NUM
ejpam-4559	245	3	]	]	PUNCT
ejpam-4559	245	4	nur	nur	PROPN
ejpam-4559	245	5	hazwani	hazwani	PROPN
ejpam-4559	245	6	aqilah	aqilah	PROPN
ejpam-4559	245	7	abdul	abdul	PROPN
ejpam-4559	245	8	wahid	wahid	PROPN
ejpam-4559	245	9	and	and	CCONJ
ejpam-4559	245	10	daud	daud	PROPN
ejpam-4559	245	11	mohamad	mohamad	PROPN
ejpam-4559	245	12	.	.	PUNCT
ejpam-4559	246	1	toeplitz	toeplitz	NOUN
ejpam-4559	246	2	determinant	determinant	ADJ
ejpam-4559	246	3	for	for	ADP
ejpam-4559	246	4	a	a	DET
ejpam-4559	246	5	subclass	subclass	NOUN
ejpam-4559	246	6	of	of	ADP
ejpam-4559	246	7	tilted	tilted	ADJ
ejpam-4559	246	8	starlike	starlike	NOUN
ejpam-4559	246	9	functions	function	NOUN
ejpam-4559	246	10	with	with	ADP
ejpam-4559	246	11	respect	respect	NOUN
ejpam-4559	246	12	to	to	ADP
ejpam-4559	246	13	conjugate	conjugate	ADJ
ejpam-4559	246	14	points	point	NOUN
ejpam-4559	246	15	.	.	PUNCT
ejpam-4559	247	1	sains	sain	NOUN
ejpam-4559	247	2	malaysiana	malaysiana	PROPN
ejpam-4559	247	3	,	,	PUNCT
ejpam-4559	247	4	50(12):3745–3751	50(12):3745–3751	NUM
ejpam-4559	247	5	,	,	PUNCT
ejpam-4559	247	6	2021	2021	NUM
ejpam-4559	247	7	.	.	PUNCT
ejpam-4559	248	1	[	[	X
ejpam-4559	248	2	23	23	NUM
ejpam-4559	248	3	]	]	X
ejpam-4559	248	4	zhi	zhi	PROPN
ejpam-4559	248	5	-	-	PUNCT
ejpam-4559	248	6	gang	gang	PROPN
ejpam-4559	248	7	wang	wang	PROPN
ejpam-4559	248	8	,	,	PUNCT
ejpam-4559	248	9	mohsan	mohsan	PROPN
ejpam-4559	248	10	raza	raza	PROPN
ejpam-4559	248	11	,	,	PUNCT
ejpam-4559	248	12	muhammad	muhammad	PROPN
ejpam-4559	248	13	arif	arif	PROPN
ejpam-4559	248	14	,	,	PUNCT
ejpam-4559	248	15	and	and	CCONJ
ejpam-4559	248	16	khurshid	khurshid	PROPN
ejpam-4559	248	17	ahmad	ahmad	PROPN
ejpam-4559	248	18	.	.	PUNCT
ejpam-4559	249	1	on	on	ADP
ejpam-4559	249	2	the	the	DET
ejpam-4559	249	3	third	third	ADJ
ejpam-4559	249	4	and	and	CCONJ
ejpam-4559	249	5	fourth	fourth	ADJ
ejpam-4559	249	6	hankel	hankel	NOUN
ejpam-4559	249	7	determinants	determinant	VERB
ejpam-4559	249	8	for	for	ADP
ejpam-4559	249	9	a	a	DET
ejpam-4559	249	10	subclass	subclass	NOUN
ejpam-4559	249	11	of	of	ADP
ejpam-4559	249	12	analytic	analytic	ADJ
ejpam-4559	249	13	functions	function	NOUN
ejpam-4559	249	14	.	.	PUNCT
ejpam-4559	250	1	bulletin	bulletin	NOUN
ejpam-4559	250	2	of	of	ADP
ejpam-4559	250	3	the	the	DET
ejpam-4559	250	4	malaysian	malaysian	PROPN
ejpam-4559	250	5	mathematical	mathematical	PROPN
ejpam-4559	250	6	sciences	sciences	PROPN
ejpam-4559	250	7	society	society	NOUN
ejpam-4559	250	8	,	,	PUNCT
ejpam-4559	250	9	45(1):323–359	45(1):323–359	PROPN
ejpam-4559	250	10	,	,	PUNCT
ejpam-4559	250	11	2022	2022	NUM
ejpam-4559	250	12	.	.	PUNCT
ejpam-4559	251	1	[	[	X
ejpam-4559	251	2	24	24	NUM
ejpam-4559	251	3	]	]	X
ejpam-4559	251	4	ke	ke	NOUN
ejpam-4559	251	5	ye	ye	PROPN
ejpam-4559	251	6	and	and	CCONJ
ejpam-4559	251	7	lek	lek	PROPN
ejpam-4559	251	8	-	-	PUNCT
ejpam-4559	251	9	heng	heng	PROPN
ejpam-4559	251	10	lim	lim	PROPN
ejpam-4559	251	11	.	.	PUNCT
ejpam-4559	252	1	every	every	DET
ejpam-4559	252	2	matrix	matrix	NOUN
ejpam-4559	252	3	is	be	AUX
ejpam-4559	252	4	a	a	DET
ejpam-4559	252	5	product	product	NOUN
ejpam-4559	252	6	of	of	ADP
ejpam-4559	252	7	toeplitz	toeplitz	NOUN
ejpam-4559	252	8	matrices	matrix	NOUN
ejpam-4559	252	9	.	.	PUNCT
ejpam-4559	253	1	foundations	foundation	NOUN
ejpam-4559	253	2	of	of	ADP
ejpam-4559	253	3	computational	computational	ADJ
ejpam-4559	253	4	mathematics	mathematic	NOUN
ejpam-4559	253	5	,	,	PUNCT
ejpam-4559	253	6	16(3):577–598	16(3):577–598	NUM
ejpam-4559	253	7	,	,	PUNCT
ejpam-4559	253	8	2016	2016	NUM
ejpam-4559	253	9	.	.	PUNCT
ejpam-4559	254	1	[	[	X
ejpam-4559	254	2	25	25	NUM
ejpam-4559	254	3	]	]	X
ejpam-4559	254	4	hai	hai	PROPN
ejpam-4559	254	5	-	-	PUNCT
ejpam-4559	254	6	yan	yan	PROPN
ejpam-4559	254	7	zhang	zhang	PROPN
ejpam-4559	254	8	,	,	PUNCT
ejpam-4559	254	9	rekha	rekha	PROPN
ejpam-4559	254	10	srivastava	srivastava	PROPN
ejpam-4559	254	11	,	,	PUNCT
ejpam-4559	254	12	and	and	CCONJ
ejpam-4559	254	13	huo	huo	PROPN
ejpam-4559	254	14	tang	tang	PROPN
ejpam-4559	254	15	.	.	PUNCT
ejpam-4559	255	1	third	third	ADJ
ejpam-4559	255	2	-	-	PUNCT
ejpam-4559	255	3	order	order	NOUN
ejpam-4559	255	4	hankel	hankel	NOUN
ejpam-4559	255	5	and	and	CCONJ
ejpam-4559	255	6	toeplitz	toeplitz	NOUN
ejpam-4559	255	7	determinants	determinant	NOUN
ejpam-4559	255	8	for	for	ADP
ejpam-4559	255	9	starlike	starlike	NOUN
ejpam-4559	255	10	functions	function	NOUN
ejpam-4559	255	11	connected	connect	VERB
ejpam-4559	255	12	with	with	ADP
ejpam-4559	255	13	the	the	DET
ejpam-4559	255	14	sine	sine	ADJ
ejpam-4559	255	15	function	function	NOUN
ejpam-4559	255	16	.	.	PUNCT
ejpam-4559	256	1	mathematics	mathematic	NOUN
ejpam-4559	256	2	,	,	PUNCT
ejpam-4559	256	3	7(5):404	7(5):404	NUM
ejpam-4559	256	4	,	,	PUNCT
ejpam-4559	256	5	2019	2019	NUM
ejpam-4559	256	6	.	.	PUNCT
ejpam-4559	257	1	[	[	X
ejpam-4559	257	2	26	26	NUM
ejpam-4559	257	3	]	]	X
ejpam-4559	257	4	farah	farah	PROPN
ejpam-4559	257	5	zulfiqar	zulfiqar	PROPN
ejpam-4559	257	6	,	,	PUNCT
ejpam-4559	257	7	sarfraz	sarfraz	PROPN
ejpam-4559	257	8	nawaz	nawaz	PROPN
ejpam-4559	257	9	malik	malik	PROPN
ejpam-4559	257	10	,	,	PUNCT
ejpam-4559	257	11	mohsan	mohsan	PROPN
ejpam-4559	257	12	raza	raza	PROPN
ejpam-4559	257	13	,	,	PUNCT
ejpam-4559	257	14	md	md	PROPN
ejpam-4559	257	15	ali	ali	PROPN
ejpam-4559	257	16	,	,	PUNCT
ejpam-4559	257	17	et	et	PROPN
ejpam-4559	257	18	al	al	PROPN
ejpam-4559	257	19	.	.	PUNCT
ejpam-4559	258	1	fourth	fourth	ADJ
ejpam-4559	258	2	-	-	PUNCT
ejpam-4559	258	3	order	order	NOUN
ejpam-4559	258	4	hankel	hankel	NOUN
ejpam-4559	258	5	determinants	determinant	NOUN
ejpam-4559	258	6	and	and	CCONJ
ejpam-4559	258	7	toeplitz	toeplitz	NOUN
ejpam-4559	258	8	determinants	determinant	NOUN
ejpam-4559	258	9	for	for	ADP
ejpam-4559	258	10	convex	convex	NOUN
ejpam-4559	258	11	functions	function	NOUN
ejpam-4559	258	12	connected	connect	VERB
ejpam-4559	258	13	with	with	ADP
ejpam-4559	258	14	sine	sine	ADJ
ejpam-4559	258	15	functions	function	NOUN
ejpam-4559	258	16	.	.	PUNCT
ejpam-4559	259	1	journal	journal	NOUN
ejpam-4559	259	2	of	of	ADP
ejpam-4559	259	3	mathematics	mathematic	NOUN
ejpam-4559	259	4	,	,	PUNCT
ejpam-4559	259	5	2022	2022	NUM
ejpam-4559	259	6	,	,	PUNCT
ejpam-4559	259	7	2022	2022	NUM
ejpam-4559	259	8	.	.	PUNCT