id	sid	tid	token	lemma	pos
ejpam-5374	1	1	european	european	PROPN
ejpam-5374	1	2	journal	journal	PROPN
ejpam-5374	1	3	of	of	ADP
ejpam-5374	1	4	pure	pure	ADJ
ejpam-5374	1	5	and	and	CCONJ
ejpam-5374	1	6	applied	apply	VERB
ejpam-5374	1	7	mathematics	mathematic	NOUN
ejpam-5374	1	8	vol	vol	NOUN
ejpam-5374	1	9	.	.	PROPN
ejpam-5374	2	1	17	17	NUM
ejpam-5374	2	2	,	,	PUNCT
ejpam-5374	2	3	no	no	INTJ
ejpam-5374	2	4	.	.	NOUN
ejpam-5374	2	5	4	4	NUM
ejpam-5374	2	6	,	,	PUNCT
ejpam-5374	2	7	2024	2024	NUM
ejpam-5374	2	8	,	,	PUNCT
ejpam-5374	2	9	2738	2738	NUM
ejpam-5374	2	10	-	-	SYM
ejpam-5374	2	11	2752	2752	NUM
ejpam-5374	2	12	issn	issn	PROPN
ejpam-5374	2	13	1307	1307	NUM
ejpam-5374	2	14	-	-	SYM
ejpam-5374	2	15	5543	5543	NUM
ejpam-5374	2	16	–	–	PUNCT
ejpam-5374	2	17	ejpam.com	ejpam.com	X
ejpam-5374	2	18	published	publish	VERB
ejpam-5374	2	19	by	by	ADP
ejpam-5374	2	20	new	new	PROPN
ejpam-5374	2	21	york	york	PROPN
ejpam-5374	2	22	business	business	PROPN
ejpam-5374	2	23	global	global	ADJ
ejpam-5374	2	24	bounds	bound	NOUN
ejpam-5374	2	25	for	for	ADP
ejpam-5374	2	26	certain	certain	ADJ
ejpam-5374	2	27	determinants	determinant	NOUN
ejpam-5374	2	28	of	of	ADP
ejpam-5374	2	29	logarithmic	logarithmic	ADJ
ejpam-5374	2	30	coefficients	coefficient	NOUN
ejpam-5374	2	31	for	for	ADP
ejpam-5374	2	32	the	the	DET
ejpam-5374	2	33	class	class	NOUN
ejpam-5374	2	34	of	of	ADP
ejpam-5374	2	35	functions	function	NOUN
ejpam-5374	2	36	with	with	ADP
ejpam-5374	2	37	bounded	bounded	ADJ
ejpam-5374	2	38	turning	turn	VERB
ejpam-5374	2	39	nur	nur	PROPN
ejpam-5374	2	40	hazwani	hazwani	PROPN
ejpam-5374	2	41	aqilah	aqilah	PROPN
ejpam-5374	2	42	abdul	abdul	PROPN
ejpam-5374	2	43	wahid1,∗	wahid1,∗	PROPN
ejpam-5374	2	44	,	,	PUNCT
ejpam-5374	2	45	ilya	ilya	PROPN
ejpam-5374	2	46	qursiah	qursiah	PROPN
ejpam-5374	2	47	amirnuddin1	amirnuddin1	PROPN
ejpam-5374	2	48	,	,	PUNCT
ejpam-5374	2	49	nurul	nurul	NOUN
ejpam-5374	2	50	izzah	izzah	NOUN
ejpam-5374	2	51	mohammad	mohammad	PROPN
ejpam-5374	2	52	azmi1	azmi1	PROPN
ejpam-5374	2	53	1	1	NUM
ejpam-5374	2	54	school	school	NOUN
ejpam-5374	2	55	of	of	ADP
ejpam-5374	2	56	mathematical	mathematical	ADJ
ejpam-5374	2	57	sciences	science	NOUN
ejpam-5374	2	58	,	,	PUNCT
ejpam-5374	2	59	college	college	NOUN
ejpam-5374	2	60	of	of	ADP
ejpam-5374	2	61	computing	computing	NOUN
ejpam-5374	2	62	,	,	PUNCT
ejpam-5374	2	63	informatics	informatic	NOUN
ejpam-5374	2	64	and	and	CCONJ
ejpam-5374	2	65	mathematics	mathematic	NOUN
ejpam-5374	2	66	,	,	PUNCT
ejpam-5374	2	67	universiti	universiti	PROPN
ejpam-5374	2	68	teknologi	teknologi	PROPN
ejpam-5374	2	69	mara	mara	PROPN
ejpam-5374	2	70	,	,	PUNCT
ejpam-5374	2	71	40450	40450	NUM
ejpam-5374	2	72	shah	shah	PROPN
ejpam-5374	2	73	alam	alam	PROPN
ejpam-5374	2	74	,	,	PUNCT
ejpam-5374	2	75	selangor	selangor	PROPN
ejpam-5374	2	76	,	,	PUNCT
ejpam-5374	2	77	malaysia	malaysia	PROPN
ejpam-5374	2	78	abstract	abstract	NOUN
ejpam-5374	2	79	.	.	PUNCT
ejpam-5374	3	1	this	this	DET
ejpam-5374	3	2	paper	paper	NOUN
ejpam-5374	3	3	aims	aim	VERB
ejpam-5374	3	4	to	to	PART
ejpam-5374	3	5	estimate	estimate	VERB
ejpam-5374	3	6	the	the	DET
ejpam-5374	3	7	logarithmic	logarithmic	ADJ
ejpam-5374	3	8	coefficients	coefficient	NOUN
ejpam-5374	3	9	for	for	ADP
ejpam-5374	3	10	the	the	DET
ejpam-5374	3	11	class	class	NOUN
ejpam-5374	3	12	of	of	ADP
ejpam-5374	3	13	functions	function	NOUN
ejpam-5374	3	14	with	with	ADP
ejpam-5374	3	15	bounded	bounded	ADJ
ejpam-5374	3	16	turning	turning	NOUN
ejpam-5374	3	17	.	.	PUNCT
ejpam-5374	4	1	hence	hence	ADV
ejpam-5374	4	2	,	,	PUNCT
ejpam-5374	4	3	the	the	DET
ejpam-5374	4	4	upper	upper	ADJ
ejpam-5374	4	5	bounds	bound	NOUN
ejpam-5374	4	6	of	of	ADP
ejpam-5374	4	7	the	the	DET
ejpam-5374	4	8	second	second	ADJ
ejpam-5374	4	9	-	-	PUNCT
ejpam-5374	4	10	order	order	NOUN
ejpam-5374	4	11	for	for	ADP
ejpam-5374	4	12	three	three	NUM
ejpam-5374	4	13	types	type	NOUN
ejpam-5374	4	14	of	of	ADP
ejpam-5374	4	15	determinants	determinant	NOUN
ejpam-5374	4	16	(	(	PUNCT
ejpam-5374	4	17	hankel	hankel	NOUN
ejpam-5374	4	18	,	,	PUNCT
ejpam-5374	4	19	toeplitz	toeplitz	NOUN
ejpam-5374	4	20	,	,	PUNCT
ejpam-5374	4	21	and	and	CCONJ
ejpam-5374	4	22	vandermonde	vandermonde	NOUN
ejpam-5374	4	23	)	)	PUNCT
ejpam-5374	4	24	whose	whose	DET
ejpam-5374	4	25	entries	entry	NOUN
ejpam-5374	4	26	are	be	AUX
ejpam-5374	4	27	logarithmic	logarithmic	ADJ
ejpam-5374	4	28	coefficients	coefficient	NOUN
ejpam-5374	4	29	for	for	ADP
ejpam-5374	4	30	this	this	DET
ejpam-5374	4	31	class	class	NOUN
ejpam-5374	4	32	of	of	ADP
ejpam-5374	4	33	functions	function	NOUN
ejpam-5374	4	34	are	be	AUX
ejpam-5374	4	35	obtained	obtain	VERB
ejpam-5374	4	36	.	.	PUNCT
ejpam-5374	5	1	some	some	DET
ejpam-5374	5	2	interesting	interesting	ADJ
ejpam-5374	5	3	consequences	consequence	NOUN
ejpam-5374	5	4	of	of	ADP
ejpam-5374	5	5	these	these	DET
ejpam-5374	5	6	results	result	NOUN
ejpam-5374	5	7	are	be	AUX
ejpam-5374	5	8	also	also	ADV
ejpam-5374	5	9	highlighted	highlight	VERB
ejpam-5374	5	10	,	,	PUNCT
ejpam-5374	5	11	offering	offer	VERB
ejpam-5374	5	12	new	new	ADJ
ejpam-5374	5	13	findings	finding	NOUN
ejpam-5374	5	14	within	within	ADP
ejpam-5374	5	15	the	the	DET
ejpam-5374	5	16	class	class	NOUN
ejpam-5374	5	17	of	of	ADP
ejpam-5374	5	18	functions	function	NOUN
ejpam-5374	5	19	with	with	ADP
ejpam-5374	5	20	bounded	bounded	ADJ
ejpam-5374	5	21	turning	turning	NOUN
ejpam-5374	5	22	.	.	PUNCT
ejpam-5374	6	1	2020	2020	NUM
ejpam-5374	6	2	mathematics	mathematic	NOUN
ejpam-5374	6	3	subject	subject	NOUN
ejpam-5374	6	4	classifications	classification	NOUN
ejpam-5374	6	5	:	:	PUNCT
ejpam-5374	6	6	30c45	30c45	NUM
ejpam-5374	6	7	,	,	PUNCT
ejpam-5374	6	8	30c50	30c50	DET
ejpam-5374	6	9	key	key	ADJ
ejpam-5374	6	10	words	word	NOUN
ejpam-5374	6	11	and	and	CCONJ
ejpam-5374	6	12	phrases	phrase	NOUN
ejpam-5374	6	13	:	:	PUNCT
ejpam-5374	6	14	univalent	univalent	ADJ
ejpam-5374	6	15	functions	function	NOUN
ejpam-5374	6	16	,	,	PUNCT
ejpam-5374	6	17	bounded	bound	VERB
ejpam-5374	6	18	turning	turning	NOUN
ejpam-5374	6	19	functions	function	NOUN
ejpam-5374	6	20	,	,	PUNCT
ejpam-5374	6	21	logarithmic	logarithmic	ADJ
ejpam-5374	6	22	coefficients	coefficient	NOUN
ejpam-5374	6	23	,	,	PUNCT
ejpam-5374	6	24	hankel	hankel	NOUN
ejpam-5374	6	25	determinant	determinant	ADJ
ejpam-5374	6	26	,	,	PUNCT
ejpam-5374	6	27	toeplitz	toeplitz	NOUN
ejpam-5374	6	28	determinant	determinant	ADJ
ejpam-5374	6	29	,	,	PUNCT
ejpam-5374	6	30	vandermonde	vandermonde	VERB
ejpam-5374	6	31	determinant	determinant	ADJ
ejpam-5374	6	32	1	1	NUM
ejpam-5374	6	33	.	.	PUNCT
ejpam-5374	7	1	introduction	introduction	NOUN
ejpam-5374	7	2	let	let	VERB
ejpam-5374	7	3	a	a	DET
ejpam-5374	7	4	denote	denote	NOUN
ejpam-5374	7	5	the	the	DET
ejpam-5374	7	6	class	class	NOUN
ejpam-5374	7	7	of	of	ADP
ejpam-5374	7	8	all	all	DET
ejpam-5374	7	9	functions	function	NOUN
ejpam-5374	7	10	f	f	X
ejpam-5374	7	11	(	(	PUNCT
ejpam-5374	7	12	z	z	NOUN
ejpam-5374	7	13	)	)	PUNCT
ejpam-5374	7	14	of	of	ADP
ejpam-5374	7	15	the	the	DET
ejpam-5374	7	16	form	form	NOUN
ejpam-5374	7	17	f	f	X
ejpam-5374	7	18	(	(	PUNCT
ejpam-5374	7	19	z	z	NOUN
ejpam-5374	7	20	)	)	PUNCT
ejpam-5374	7	21	=	=	SYM
ejpam-5374	8	1	z	z	NOUN
ejpam-5374	9	1	+	+	NOUN
ejpam-5374	9	2	∞∑	∞∑	NUM
ejpam-5374	9	3	n=2	n=2	ADV
ejpam-5374	9	4	anz	anz	NOUN
ejpam-5374	9	5	n	n	CCONJ
ejpam-5374	9	6	,	,	PUNCT
ejpam-5374	9	7	(	(	PUNCT
ejpam-5374	9	8	1	1	X
ejpam-5374	9	9	)	)	PUNCT
ejpam-5374	9	10	which	which	PRON
ejpam-5374	9	11	are	be	AUX
ejpam-5374	9	12	analytic	analytic	ADJ
ejpam-5374	9	13	in	in	ADP
ejpam-5374	9	14	the	the	DET
ejpam-5374	9	15	open	open	ADJ
ejpam-5374	9	16	unit	unit	NOUN
ejpam-5374	9	17	disk	disk	NOUN
ejpam-5374	9	18	e	e	NOUN
ejpam-5374	9	19	=	=	PUNCT
ejpam-5374	9	20	{	{	PUNCT
ejpam-5374	9	21	z	z	NOUN
ejpam-5374	9	22	∈	∈	PROPN
ejpam-5374	9	23	c	c	NOUN
ejpam-5374	9	24	:	:	PUNCT
ejpam-5374	9	25	|z|	|z|	NOUN
ejpam-5374	9	26	<	<	X
ejpam-5374	9	27	1	1	NUM
ejpam-5374	9	28	}	}	PUNCT
ejpam-5374	9	29	.	.	PUNCT
ejpam-5374	10	1	we	we	PRON
ejpam-5374	10	2	denote	denote	VERB
ejpam-5374	10	3	by	by	ADP
ejpam-5374	10	4	s	s	PRON
ejpam-5374	10	5	the	the	DET
ejpam-5374	10	6	subclass	subclass	NOUN
ejpam-5374	10	7	of	of	ADP
ejpam-5374	10	8	a	a	DET
ejpam-5374	10	9	consisting	consisting	NOUN
ejpam-5374	10	10	of	of	ADP
ejpam-5374	10	11	univalent	univalent	ADJ
ejpam-5374	10	12	functions	function	NOUN
ejpam-5374	10	13	in	in	ADP
ejpam-5374	10	14	e.	e.	PROPN
ejpam-5374	10	15	a	a	DET
ejpam-5374	10	16	typical	typical	ADJ
ejpam-5374	10	17	problem	problem	NOUN
ejpam-5374	10	18	in	in	ADP
ejpam-5374	10	19	geometric	geometric	ADJ
ejpam-5374	10	20	function	function	NOUN
ejpam-5374	10	21	theory	theory	NOUN
ejpam-5374	10	22	is	be	AUX
ejpam-5374	10	23	to	to	PART
ejpam-5374	10	24	study	study	VERB
ejpam-5374	10	25	a	a	DET
ejpam-5374	10	26	functional	functional	ADJ
ejpam-5374	10	27	consisting	consisting	NOUN
ejpam-5374	10	28	of	of	ADP
ejpam-5374	10	29	combinations	combination	NOUN
ejpam-5374	10	30	of	of	ADP
ejpam-5374	10	31	the	the	DET
ejpam-5374	10	32	taylor	taylor	PROPN
ejpam-5374	10	33	coefficients	coefficient	VERB
ejpam-5374	10	34	an	an	PRON
ejpam-5374	10	35	,	,	PUNCT
ejpam-5374	10	36	n	n	X
ejpam-5374	10	37	≥	≥	NOUN
ejpam-5374	10	38	2	2	NUM
ejpam-5374	10	39	for	for	ADP
ejpam-5374	10	40	the	the	DET
ejpam-5374	10	41	subclass	subclass	NOUN
ejpam-5374	10	42	of	of	ADP
ejpam-5374	10	43	univalent	univalent	ADJ
ejpam-5374	10	44	functions	function	NOUN
ejpam-5374	10	45	such	such	ADJ
ejpam-5374	10	46	as	as	ADP
ejpam-5374	10	47	hankel	hankel	NOUN
ejpam-5374	10	48	and	and	CCONJ
ejpam-5374	10	49	toeplitz	toeplitz	NOUN
ejpam-5374	10	50	determinants	determinant	NOUN
ejpam-5374	10	51	,	,	PUNCT
ejpam-5374	10	52	but	but	CCONJ
ejpam-5374	10	53	this	this	PRON
ejpam-5374	10	54	is	be	AUX
ejpam-5374	10	55	not	not	PART
ejpam-5374	10	56	limited	limit	VERB
ejpam-5374	10	57	to	to	ADP
ejpam-5374	10	58	this	this	PRON
ejpam-5374	10	59	.	.	PUNCT
ejpam-5374	11	1	the	the	DET
ejpam-5374	11	2	unknown	unknown	ADJ
ejpam-5374	11	3	upper	upper	ADJ
ejpam-5374	11	4	bounds	bound	NOUN
ejpam-5374	11	5	of	of	ADP
ejpam-5374	11	6	these	these	DET
ejpam-5374	11	7	determinants	determinant	NOUN
ejpam-5374	11	8	for	for	ADP
ejpam-5374	11	9	the	the	DET
ejpam-5374	11	10	class	class	NOUN
ejpam-5374	11	11	of	of	ADP
ejpam-5374	11	12	univalent	univalent	ADJ
ejpam-5374	11	13	functions	function	NOUN
ejpam-5374	11	14	have	have	AUX
ejpam-5374	11	15	attracted	attract	VERB
ejpam-5374	11	16	researchers	researcher	NOUN
ejpam-5374	11	17	,	,	PUNCT
ejpam-5374	11	18	making	make	VERB
ejpam-5374	11	19	this	this	PRON
ejpam-5374	11	20	an	an	DET
ejpam-5374	11	21	open	open	ADJ
ejpam-5374	11	22	and	and	CCONJ
ejpam-5374	11	23	intriguing	intriguing	ADJ
ejpam-5374	11	24	topic	topic	NOUN
ejpam-5374	11	25	for	for	ADP
ejpam-5374	11	26	further	further	ADJ
ejpam-5374	11	27	study	study	NOUN
ejpam-5374	11	28	.	.	PUNCT
ejpam-5374	12	1	the	the	DET
ejpam-5374	12	2	hankel	hankel	NOUN
ejpam-5374	12	3	∗corresponding	∗corresponde	VERB
ejpam-5374	12	4	author	author	NOUN
ejpam-5374	12	5	.	.	PUNCT
ejpam-5374	13	1	doi	doi	NOUN
ejpam-5374	13	2	:	:	PUNCT
ejpam-5374	13	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5374	https://doi.org/10.29020/nybg.ejpam.v17i4.5374	VERB
ejpam-5374	13	4	email	email	NOUN
ejpam-5374	13	5	addresses	address	NOUN
ejpam-5374	13	6	:	:	PUNCT
ejpam-5374	13	7	hazwaniaqilah@uitm.edu.my	hazwaniaqilah@uitm.edu.my	PROPN
ejpam-5374	13	8	(	(	PUNCT
ejpam-5374	13	9	n.	n.	PROPN
ejpam-5374	13	10	h.	h.	PROPN
ejpam-5374	13	11	a.	a.	PROPN
ejpam-5374	13	12	a.	a.	PROPN
ejpam-5374	13	13	wahid	wahid	PROPN
ejpam-5374	13	14	)	)	PUNCT
ejpam-5374	13	15	,	,	PUNCT
ejpam-5374	13	16	ilyaqursiah17@gmail.com	ilyaqursiah17@gmail.com	PROPN
ejpam-5374	13	17	(	(	PUNCT
ejpam-5374	13	18	i.	i.	PROPN
ejpam-5374	13	19	q.	q.	PROPN
ejpam-5374	13	20	amirnuddin	amirnuddin	PROPN
ejpam-5374	13	21	)	)	PUNCT
ejpam-5374	13	22	,	,	PUNCT
ejpam-5374	13	23	izzah.nurul63.ni@gmail.com	izzah.nurul63.ni@gmail.com	X
ejpam-5374	13	24	(	(	PUNCT
ejpam-5374	13	25	n.	n.	PROPN
ejpam-5374	13	26	i.	i.	PROPN
ejpam-5374	13	27	m.	m.	PROPN
ejpam-5374	13	28	azmi	azmi	PROPN
ejpam-5374	13	29	)	)	PUNCT
ejpam-5374	13	30	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5374	14	1	2738	2738	NUM
ejpam-5374	14	2	copyright	copyright	NOUN
ejpam-5374	14	3	:	:	PUNCT
ejpam-5374	14	4	©	©	PROPN
ejpam-5374	14	5	2024	2024	NUM
ejpam-5374	14	6	the	the	DET
ejpam-5374	14	7	author(s	author(s	NOUN
ejpam-5374	14	8	)	)	PUNCT
ejpam-5374	14	9	.	.	PUNCT
ejpam-5374	15	1	(	(	PUNCT
ejpam-5374	15	2	cc	cc	NOUN
ejpam-5374	15	3	by	by	ADP
ejpam-5374	15	4	-	-	PUNCT
ejpam-5374	15	5	nc	nc	PROPN
ejpam-5374	15	6	4.0	4.0	NUM
ejpam-5374	15	7	)	)	PUNCT
ejpam-5374	15	8	n.h.a.a	n.h.a.a	PROPN
ejpam-5374	15	9	.	.	PROPN
ejpam-5374	15	10	wahid	wahid	PROPN
ejpam-5374	15	11	,	,	PUNCT
ejpam-5374	15	12	i.q	i.q	PROPN
ejpam-5374	15	13	.	.	PROPN
ejpam-5374	15	14	amirnuddin	amirnuddin	PROPN
ejpam-5374	15	15	,	,	PUNCT
ejpam-5374	15	16	n.i.m	n.i.m	NOUN
ejpam-5374	15	17	.	.	PUNCT
ejpam-5374	16	1	azmi	azmi	PROPN
ejpam-5374	16	2	/	/	SYM
ejpam-5374	16	3	eur	eur	PROPN
ejpam-5374	16	4	.	.	PUNCT
ejpam-5374	17	1	j.	j.	PROPN
ejpam-5374	17	2	pure	pure	PROPN
ejpam-5374	17	3	appl	appl	PROPN
ejpam-5374	17	4	.	.	PROPN
ejpam-5374	17	5	math	math	PROPN
ejpam-5374	17	6	,	,	PUNCT
ejpam-5374	17	7	17	17	NUM
ejpam-5374	17	8	(	(	PUNCT
ejpam-5374	17	9	4	4	NUM
ejpam-5374	17	10	)	)	PUNCT
ejpam-5374	17	11	(	(	PUNCT
ejpam-5374	17	12	2024	2024	NUM
ejpam-5374	17	13	)	)	PUNCT
ejpam-5374	17	14	,	,	PUNCT
ejpam-5374	17	15	2738	2738	NUM
ejpam-5374	17	16	-	-	SYM
ejpam-5374	17	17	2752	2752	NUM
ejpam-5374	17	18	2739	2739	NUM
ejpam-5374	17	19	determinant	determinant	ADJ
ejpam-5374	17	20	is	be	AUX
ejpam-5374	17	21	an	an	DET
ejpam-5374	17	22	extremely	extremely	ADV
ejpam-5374	17	23	useful	useful	ADJ
ejpam-5374	17	24	tool	tool	NOUN
ejpam-5374	17	25	in	in	ADP
ejpam-5374	17	26	the	the	DET
ejpam-5374	17	27	study	study	NOUN
ejpam-5374	17	28	of	of	ADP
ejpam-5374	17	29	singularities	singularity	NOUN
ejpam-5374	17	30	.	.	PUNCT
ejpam-5374	18	1	this	this	PRON
ejpam-5374	18	2	is	be	AUX
ejpam-5374	18	3	particularly	particularly	ADV
ejpam-5374	18	4	important	important	ADJ
ejpam-5374	18	5	when	when	SCONJ
ejpam-5374	18	6	analyzing	analyze	VERB
ejpam-5374	18	7	power	power	NOUN
ejpam-5374	18	8	series	series	NOUN
ejpam-5374	18	9	with	with	ADP
ejpam-5374	18	10	integral	integral	ADJ
ejpam-5374	18	11	coefficients	coefficient	NOUN
ejpam-5374	18	12	[	[	X
ejpam-5374	18	13	6	6	NUM
ejpam-5374	18	14	,	,	PUNCT
ejpam-5374	18	15	9	9	NUM
ejpam-5374	18	16	]	]	PUNCT
ejpam-5374	18	17	.	.	PUNCT
ejpam-5374	19	1	meanwhile	meanwhile	ADV
ejpam-5374	19	2	,	,	PUNCT
ejpam-5374	19	3	the	the	DET
ejpam-5374	19	4	toeplitz	toeplitz	NOUN
ejpam-5374	19	5	determinant	determinant	ADJ
ejpam-5374	19	6	has	have	VERB
ejpam-5374	19	7	a	a	DET
ejpam-5374	19	8	variety	variety	NOUN
ejpam-5374	19	9	of	of	ADP
ejpam-5374	19	10	applications	application	NOUN
ejpam-5374	19	11	in	in	ADP
ejpam-5374	19	12	both	both	CCONJ
ejpam-5374	19	13	pure	pure	ADJ
ejpam-5374	19	14	and	and	CCONJ
ejpam-5374	19	15	applied	applied	ADJ
ejpam-5374	19	16	mathematics	mathematic	NOUN
ejpam-5374	19	17	,	,	PUNCT
ejpam-5374	19	18	statistics	statistic	NOUN
ejpam-5374	19	19	,	,	PUNCT
ejpam-5374	19	20	and	and	CCONJ
ejpam-5374	19	21	probability	probability	NOUN
ejpam-5374	19	22	;	;	PUNCT
ejpam-5374	19	23	for	for	ADP
ejpam-5374	19	24	example	example	NOUN
ejpam-5374	19	25	,	,	PUNCT
ejpam-5374	19	26	it	it	PRON
ejpam-5374	19	27	is	be	AUX
ejpam-5374	19	28	used	use	VERB
ejpam-5374	19	29	in	in	ADP
ejpam-5374	19	30	algebra	algebra	NOUN
ejpam-5374	19	31	,	,	PUNCT
ejpam-5374	19	32	quantum	quantum	NOUN
ejpam-5374	19	33	mechanics	mechanic	NOUN
ejpam-5374	19	34	,	,	PUNCT
ejpam-5374	19	35	queuing	queue	VERB
ejpam-5374	19	36	networks	network	NOUN
ejpam-5374	19	37	,	,	PUNCT
ejpam-5374	19	38	signal	signal	ADJ
ejpam-5374	19	39	processing	processing	NOUN
ejpam-5374	19	40	,	,	PUNCT
ejpam-5374	19	41	partial	partial	ADJ
ejpam-5374	19	42	differential	differential	NOUN
ejpam-5374	19	43	equations	equation	NOUN
ejpam-5374	19	44	,	,	PUNCT
ejpam-5374	19	45	and	and	CCONJ
ejpam-5374	19	46	time	time	NOUN
ejpam-5374	19	47	series	series	PROPN
ejpam-5374	19	48	analysis	analysis	NOUN
ejpam-5374	19	49	[	[	X
ejpam-5374	19	50	49	49	NUM
ejpam-5374	19	51	]	]	PUNCT
ejpam-5374	19	52	.	.	PUNCT
ejpam-5374	20	1	pommerenke	pommerenke	PROPN
ejpam-5374	20	2	[	[	X
ejpam-5374	20	3	38	38	NUM
ejpam-5374	20	4	,	,	PUNCT
ejpam-5374	20	5	39	39	NUM
ejpam-5374	20	6	]	]	PUNCT
ejpam-5374	20	7	and	and	CCONJ
ejpam-5374	20	8	ali	ali	PROPN
ejpam-5374	20	9	et	et	PROPN
ejpam-5374	20	10	al	al	PROPN
ejpam-5374	20	11	.	.	PUNCT
ejpam-5374	21	1	[	[	X
ejpam-5374	21	2	7	7	X
ejpam-5374	21	3	]	]	PUNCT
ejpam-5374	21	4	defined	define	VERB
ejpam-5374	21	5	the	the	DET
ejpam-5374	21	6	hankel	hankel	NOUN
ejpam-5374	21	7	determinant	determinant	ADJ
ejpam-5374	21	8	hq	hq	NOUN
ejpam-5374	21	9	,	,	PUNCT
ejpam-5374	21	10	n	n	PROPN
ejpam-5374	21	11	(	(	PUNCT
ejpam-5374	21	12	f	f	X
ejpam-5374	21	13	)	)	PUNCT
ejpam-5374	21	14	and	and	CCONJ
ejpam-5374	21	15	toeplitz	toeplitz	NOUN
ejpam-5374	21	16	determinant	determinant	ADJ
ejpam-5374	21	17	tq	tq	ADP
ejpam-5374	21	18	,	,	PUNCT
ejpam-5374	21	19	n	n	PROPN
ejpam-5374	21	20	(	(	PUNCT
ejpam-5374	21	21	f	f	X
ejpam-5374	21	22	)	)	PUNCT
ejpam-5374	21	23	,	,	PUNCT
ejpam-5374	21	24	n	n	CCONJ
ejpam-5374	21	25	,	,	PUNCT
ejpam-5374	21	26	q	q	X
ejpam-5374	21	27	≥	≥	NOUN
ejpam-5374	21	28	1	1	NUM
ejpam-5374	21	29	,	,	PUNCT
ejpam-5374	21	30	whose	whose	DET
ejpam-5374	21	31	elements	element	NOUN
ejpam-5374	21	32	are	be	AUX
ejpam-5374	21	33	taylor	taylor	PROPN
ejpam-5374	21	34	coefficients	coefficient	NOUN
ejpam-5374	21	35	an	an	PRON
ejpam-5374	21	36	,	,	PUNCT
ejpam-5374	21	37	n	n	X
ejpam-5374	21	38	≥	≥	NOUN
ejpam-5374	21	39	2	2	NUM
ejpam-5374	21	40	for	for	ADP
ejpam-5374	21	41	functions	function	NOUN
ejpam-5374	21	42	f	f	X
ejpam-5374	21	43	(	(	PUNCT
ejpam-5374	21	44	z	z	NOUN
ejpam-5374	21	45	)	)	PUNCT
ejpam-5374	21	46	∈	∈	PROPN
ejpam-5374	21	47	a	a	PRON
ejpam-5374	21	48	,	,	PUNCT
ejpam-5374	21	49	respectively	respectively	ADV
ejpam-5374	21	50	,	,	PUNCT
ejpam-5374	21	51	as	as	SCONJ
ejpam-5374	21	52	follows	follow	VERB
ejpam-5374	21	53	:	:	PUNCT
ejpam-5374	21	54	hq	hq	NOUN
ejpam-5374	21	55	,	,	PUNCT
ejpam-5374	21	56	n	n	PROPN
ejpam-5374	21	57	(	(	PUNCT
ejpam-5374	21	58	f	f	X
ejpam-5374	21	59	)	)	PUNCT
ejpam-5374	22	1	=	=	SYM
ejpam-5374	22	2	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5374	22	3	an	an	DET
ejpam-5374	22	4	an+1	an+1	NOUN
ejpam-5374	22	5	·	·	PUNCT
ejpam-5374	22	6	·	·	PUNCT
ejpam-5374	22	7	·	·	PUNCT
ejpam-5374	23	1	an+q−1	an+q−1	PRON
ejpam-5374	23	2	an+1	an+1	VERB
ejpam-5374	23	3	an+2	an+2	X
ejpam-5374	23	4	·	·	PUNCT
ejpam-5374	23	5	·	·	PUNCT
ejpam-5374	23	6	·	·	PUNCT
ejpam-5374	23	7	an+q	an+q	PROPN
ejpam-5374	23	8	...	...	PUNCT
ejpam-5374	23	9	...	...	PUNCT
ejpam-5374	23	10	.	.	PUNCT
ejpam-5374	23	11	.	.	PUNCT
ejpam-5374	23	12	.	.	PUNCT
ejpam-5374	23	13	...	...	PUNCT
ejpam-5374	24	1	an+q−1	an+q−1	PRON
ejpam-5374	24	2	an+q	an+q	PROPN
ejpam-5374	24	3	·	·	PUNCT
ejpam-5374	24	4	·	·	PUNCT
ejpam-5374	24	5	·	·	PUNCT
ejpam-5374	24	6	an+2q−2	an+2q−2	X
ejpam-5374	24	7	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5374	24	8	,	,	PUNCT
ejpam-5374	24	9	a1	a1	NOUN
ejpam-5374	24	10	=	=	SYM
ejpam-5374	24	11	1	1	NUM
ejpam-5374	24	12	(	(	PUNCT
ejpam-5374	24	13	2	2	NUM
ejpam-5374	24	14	)	)	PUNCT
ejpam-5374	24	15	and	and	CCONJ
ejpam-5374	24	16	tq	tq	ADP
ejpam-5374	24	17	,	,	PUNCT
ejpam-5374	24	18	n	n	PROPN
ejpam-5374	24	19	(	(	PUNCT
ejpam-5374	24	20	f	f	X
ejpam-5374	24	21	)	)	PUNCT
ejpam-5374	24	22	=	=	SYM
ejpam-5374	24	23	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5374	24	24	an	an	DET
ejpam-5374	24	25	an+1	an+1	NOUN
ejpam-5374	24	26	...	...	PUNCT
ejpam-5374	25	1	an+q−1	an+q−1	PRON
ejpam-5374	25	2	an+1	an+1	VERB
ejpam-5374	25	3	an	an	PRON
ejpam-5374	25	4	...	...	PUNCT
ejpam-5374	25	5	an+q−2	an+q−2	NOUN
ejpam-5374	25	6	·	·	PUNCT
ejpam-5374	25	7	·	·	PUNCT
ejpam-5374	25	8	·	·	PUNCT
ejpam-5374	25	9	·	·	PUNCT
ejpam-5374	25	10	·	·	PUNCT
ejpam-5374	25	11	·	·	PUNCT
ejpam-5374	25	12	...	...	PUNCT
ejpam-5374	25	13	·	·	PUNCT
ejpam-5374	25	14	·	·	PUNCT
ejpam-5374	25	15	·	·	PUNCT
ejpam-5374	26	1	an+q−1	an+q−1	PRON
ejpam-5374	26	2	an+q−2	an+q−2	VERB
ejpam-5374	26	3	...	...	PUNCT
ejpam-5374	26	4	an	an	DET
ejpam-5374	26	5	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5374	26	6	.	.	PUNCT
ejpam-5374	27	1	(	(	PUNCT
ejpam-5374	27	2	3	3	X
ejpam-5374	27	3	)	)	PUNCT
ejpam-5374	27	4	a	a	DET
ejpam-5374	27	5	recent	recent	ADJ
ejpam-5374	27	6	work	work	NOUN
ejpam-5374	27	7	delves	delf	NOUN
ejpam-5374	27	8	into	into	ADP
ejpam-5374	27	9	the	the	DET
ejpam-5374	27	10	interesting	interesting	ADJ
ejpam-5374	27	11	world	world	NOUN
ejpam-5374	27	12	of	of	ADP
ejpam-5374	27	13	hankel	hankel	NOUN
ejpam-5374	27	14	and	and	CCONJ
ejpam-5374	27	15	toeplitz	toeplitz	NOUN
ejpam-5374	27	16	determinants	determinant	NOUN
ejpam-5374	27	17	in	in	ADP
ejpam-5374	27	18	the	the	DET
ejpam-5374	27	19	context	context	NOUN
ejpam-5374	27	20	of	of	ADP
ejpam-5374	27	21	considering	consider	VERB
ejpam-5374	27	22	logarithmic	logarithmic	ADJ
ejpam-5374	27	23	coefficients	coefficient	NOUN
ejpam-5374	27	24	as	as	ADP
ejpam-5374	27	25	the	the	DET
ejpam-5374	27	26	entries	entry	NOUN
ejpam-5374	27	27	.	.	PUNCT
ejpam-5374	28	1	this	this	DET
ejpam-5374	28	2	idea	idea	NOUN
ejpam-5374	28	3	generalizes	generalize	VERB
ejpam-5374	28	4	the	the	DET
ejpam-5374	28	5	traditional	traditional	ADJ
ejpam-5374	28	6	concept	concept	NOUN
ejpam-5374	28	7	of	of	ADP
ejpam-5374	28	8	both	both	DET
ejpam-5374	28	9	determinants	determinant	NOUN
ejpam-5374	28	10	(	(	PUNCT
ejpam-5374	28	11	2	2	NUM
ejpam-5374	28	12	)	)	PUNCT
ejpam-5374	28	13	and	and	CCONJ
ejpam-5374	28	14	(	(	PUNCT
ejpam-5374	28	15	3	3	X
ejpam-5374	28	16	)	)	PUNCT
ejpam-5374	28	17	by	by	ADP
ejpam-5374	28	18	replacing	replace	VERB
ejpam-5374	28	19	their	their	PRON
ejpam-5374	28	20	entries	entry	NOUN
ejpam-5374	28	21	with	with	ADP
ejpam-5374	28	22	the	the	DET
ejpam-5374	28	23	logarithmic	logarithmic	ADJ
ejpam-5374	28	24	coefficients	coefficient	NOUN
ejpam-5374	28	25	of	of	ADP
ejpam-5374	28	26	f	f	PROPN
ejpam-5374	28	27	(	(	PUNCT
ejpam-5374	28	28	z	z	NOUN
ejpam-5374	28	29	)	)	PUNCT
ejpam-5374	28	30	∈	∈	PROPN
ejpam-5374	28	31	a.	a.	NOUN
ejpam-5374	28	32	kowalczyk	kowalczyk	NOUN
ejpam-5374	28	33	and	and	CCONJ
ejpam-5374	28	34	lecko	lecko	NOUN
ejpam-5374	28	35	[	[	X
ejpam-5374	28	36	22	22	NUM
ejpam-5374	28	37	,	,	PUNCT
ejpam-5374	28	38	23	23	NUM
ejpam-5374	28	39	]	]	PUNCT
ejpam-5374	28	40	,	,	PUNCT
ejpam-5374	28	41	as	as	ADV
ejpam-5374	28	42	well	well	ADV
ejpam-5374	28	43	as	as	ADP
ejpam-5374	28	44	giri	giri	PROPN
ejpam-5374	28	45	,	,	PUNCT
ejpam-5374	28	46	kumar	kumar	PROPN
ejpam-5374	28	47	,	,	PUNCT
ejpam-5374	28	48	and	and	CCONJ
ejpam-5374	28	49	mohamad	mohamad	PROPN
ejpam-5374	28	50	et	et	PROPN
ejpam-5374	28	51	al	al	PROPN
ejpam-5374	28	52	.	.	PUNCT
ejpam-5374	29	1	[	[	X
ejpam-5374	29	2	15	15	NUM
ejpam-5374	29	3	,	,	PUNCT
ejpam-5374	29	4	35	35	NUM
ejpam-5374	29	5	]	]	PUNCT
ejpam-5374	29	6	,	,	PUNCT
ejpam-5374	29	7	introduced	introduce	VERB
ejpam-5374	29	8	the	the	DET
ejpam-5374	29	9	hankel	hankel	NOUN
ejpam-5374	29	10	and	and	CCONJ
ejpam-5374	29	11	toeplitz	toeplitz	NOUN
ejpam-5374	29	12	determinants	determinant	NOUN
ejpam-5374	29	13	of	of	ADP
ejpam-5374	29	14	logarithmic	logarithmic	ADJ
ejpam-5374	29	15	coefficients	coefficient	NOUN
ejpam-5374	29	16	γn	γn	ADP
ejpam-5374	29	17	,	,	PUNCT
ejpam-5374	29	18	n	n	CCONJ
ejpam-5374	29	19	⩾	⩾	PROPN
ejpam-5374	29	20	1	1	NUM
ejpam-5374	29	21	for	for	ADP
ejpam-5374	29	22	functions	function	NOUN
ejpam-5374	29	23	f	f	X
ejpam-5374	29	24	(	(	PUNCT
ejpam-5374	29	25	z	z	NOUN
ejpam-5374	29	26	)	)	PUNCT
ejpam-5374	29	27	∈	∈	PROPN
ejpam-5374	29	28	a	a	PRON
ejpam-5374	29	29	,	,	PUNCT
ejpam-5374	29	30	respectively	respectively	ADV
ejpam-5374	29	31	,	,	PUNCT
ejpam-5374	29	32	as	as	SCONJ
ejpam-5374	29	33	follows	follow	VERB
ejpam-5374	29	34	:	:	PUNCT
ejpam-5374	29	35	hq	hq	NOUN
ejpam-5374	29	36	,	,	PUNCT
ejpam-5374	29	37	n	n	CCONJ
ejpam-5374	29	38	(	(	PUNCT
ejpam-5374	29	39	γf	γf	ADJ
ejpam-5374	29	40	)	)	PUNCT
ejpam-5374	29	41	=	=	PUNCT
ejpam-5374	30	1	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5374	30	2	γn	γn	X
ejpam-5374	30	3	γn+1	γn+1	NUM
ejpam-5374	31	1	...	...	PUNCT
ejpam-5374	31	2	γn+q−1	γn+q−1	PROPN
ejpam-5374	31	3	γn+1	γn+1	ADP
ejpam-5374	31	4	γn+2	γn+2	NUM
ejpam-5374	31	5	...	...	PUNCT
ejpam-5374	32	1	γn+q	γn+q	PROPN
ejpam-5374	32	2	·	·	PUNCT
ejpam-5374	32	3	·	·	PUNCT
ejpam-5374	32	4	·	·	PUNCT
ejpam-5374	32	5	·	·	PUNCT
ejpam-5374	32	6	·	·	PUNCT
ejpam-5374	32	7	·	·	PUNCT
ejpam-5374	32	8	...	...	PUNCT
ejpam-5374	32	9	·	·	PUNCT
ejpam-5374	33	1	·	·	PUNCT
ejpam-5374	33	2	·	·	PUNCT
ejpam-5374	33	3	γn+q−1	γn+q−1	PROPN
ejpam-5374	33	4	γn+q	γn+q	PROPN
ejpam-5374	33	5	...	...	PUNCT
ejpam-5374	34	1	γn+2q−2	γn+2q−2	PROPN
ejpam-5374	34	2	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5374	34	3	,	,	PUNCT
ejpam-5374	34	4	(	(	PUNCT
ejpam-5374	34	5	4	4	NUM
ejpam-5374	34	6	)	)	PUNCT
ejpam-5374	34	7	and	and	CCONJ
ejpam-5374	34	8	tq	tq	ADV
ejpam-5374	34	9	,	,	PUNCT
ejpam-5374	34	10	n	n	CCONJ
ejpam-5374	34	11	(	(	PUNCT
ejpam-5374	34	12	γf	γf	ADJ
ejpam-5374	34	13	)	)	PUNCT
ejpam-5374	34	14	=	=	PUNCT
ejpam-5374	34	15	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5374	34	16	γn	γn	X
ejpam-5374	34	17	γn+1	γn+1	NUM
ejpam-5374	34	18	...	...	PUNCT
ejpam-5374	35	1	γn+q−1	γn+q−1	PROPN
ejpam-5374	35	2	γn+1	γn+1	NUM
ejpam-5374	35	3	γn	γn	NOUN
ejpam-5374	35	4	...	...	PUNCT
ejpam-5374	36	1	γn+q−2	γn+q−2	X
ejpam-5374	36	2	·	·	PUNCT
ejpam-5374	36	3	·	·	PUNCT
ejpam-5374	36	4	·	·	PUNCT
ejpam-5374	36	5	·	·	PUNCT
ejpam-5374	36	6	·	·	PUNCT
ejpam-5374	36	7	·	·	PUNCT
ejpam-5374	36	8	...	...	PUNCT
ejpam-5374	36	9	·	·	PUNCT
ejpam-5374	36	10	·	·	PUNCT
ejpam-5374	36	11	·	·	PUNCT
ejpam-5374	37	1	γn+q−1	γn+q−1	PROPN
ejpam-5374	37	2	γn+q−2	γn+q−2	PROPN
ejpam-5374	37	3	...	...	PUNCT
ejpam-5374	37	4	γn	γn	X
ejpam-5374	37	5	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5374	37	6	.	.	PUNCT
ejpam-5374	38	1	(	(	PUNCT
ejpam-5374	38	2	5	5	X
ejpam-5374	38	3	)	)	PUNCT
ejpam-5374	38	4	the	the	DET
ejpam-5374	38	5	logarithmic	logarithmic	ADJ
ejpam-5374	38	6	coefficients	coefficient	NOUN
ejpam-5374	38	7	γn	γn	ADP
ejpam-5374	38	8	,	,	PUNCT
ejpam-5374	38	9	n	n	CCONJ
ejpam-5374	38	10	⩾	⩾	PROPN
ejpam-5374	38	11	1	1	NUM
ejpam-5374	38	12	of	of	ADP
ejpam-5374	38	13	f	f	PROPN
ejpam-5374	38	14	(	(	PUNCT
ejpam-5374	38	15	z	z	NOUN
ejpam-5374	38	16	)	)	PUNCT
ejpam-5374	38	17	∈	∈	PROPN
ejpam-5374	38	18	a	a	PRON
ejpam-5374	38	19	are	be	AUX
ejpam-5374	38	20	defined	define	VERB
ejpam-5374	38	21	by	by	ADP
ejpam-5374	38	22	log	log	PROPN
ejpam-5374	38	23	f	f	PROPN
ejpam-5374	38	24	(	(	PUNCT
ejpam-5374	38	25	z	z	NOUN
ejpam-5374	38	26	)	)	PUNCT
ejpam-5374	38	27	z	z	NOUN
ejpam-5374	38	28	=	=	SYM
ejpam-5374	38	29	2	2	NUM
ejpam-5374	38	30	∞∑	∞∑	NUM
ejpam-5374	38	31	n=1	n=1	NUM
ejpam-5374	38	32	γnz	γnz	VERB
ejpam-5374	38	33	n.	n.	NOUN
ejpam-5374	38	34	(	(	PUNCT
ejpam-5374	38	35	6	6	NUM
ejpam-5374	38	36	)	)	PUNCT
ejpam-5374	38	37	differentiating	differentiate	VERB
ejpam-5374	38	38	(	(	PUNCT
ejpam-5374	38	39	6	6	NUM
ejpam-5374	38	40	)	)	PUNCT
ejpam-5374	38	41	and	and	CCONJ
ejpam-5374	38	42	equating	equate	VERB
ejpam-5374	38	43	coefficients	coefficient	NOUN
ejpam-5374	38	44	of	of	ADP
ejpam-5374	38	45	zn	zn	PROPN
ejpam-5374	38	46	provides	provide	VERB
ejpam-5374	38	47	the	the	DET
ejpam-5374	38	48	logarithmic	logarithmic	ADJ
ejpam-5374	38	49	coefficients	coefficient	NOUN
ejpam-5374	38	50	in	in	ADP
ejpam-5374	38	51	terms	term	NOUN
ejpam-5374	38	52	of	of	ADP
ejpam-5374	38	53	taylor	taylor	PROPN
ejpam-5374	38	54	coefficients	coefficient	NOUN
ejpam-5374	38	55	for	for	ADP
ejpam-5374	38	56	f	f	PROPN
ejpam-5374	38	57	(	(	PUNCT
ejpam-5374	38	58	z	z	NOUN
ejpam-5374	38	59	)	)	PUNCT
ejpam-5374	38	60	∈	∈	PROPN
ejpam-5374	38	61	a	a	PRON
ejpam-5374	38	62	,	,	PUNCT
ejpam-5374	38	63	which	which	PRON
ejpam-5374	38	64	specifically	specifically	ADV
ejpam-5374	38	65	,	,	PUNCT
ejpam-5374	38	66	for	for	ADP
ejpam-5374	38	67	n	n	NOUN
ejpam-5374	38	68	=	=	SYM
ejpam-5374	38	69	1	1	NUM
ejpam-5374	38	70	,	,	PUNCT
ejpam-5374	38	71	2	2	NUM
ejpam-5374	38	72	,	,	PUNCT
ejpam-5374	38	73	3	3	NUM
ejpam-5374	38	74	,	,	PUNCT
ejpam-5374	38	75	4	4	NUM
ejpam-5374	38	76	:	:	PUNCT
ejpam-5374	38	77	γ1	γ1	NOUN
ejpam-5374	38	78	=	=	NOUN
ejpam-5374	38	79	1	1	NUM
ejpam-5374	38	80	2	2	NUM
ejpam-5374	38	81	a2	a2	NOUN
ejpam-5374	38	82	,	,	PUNCT
ejpam-5374	38	83	(	(	PUNCT
ejpam-5374	38	84	7	7	X
ejpam-5374	38	85	)	)	PUNCT
ejpam-5374	38	86	n.h.a.a	n.h.a.a	PROPN
ejpam-5374	38	87	.	.	PROPN
ejpam-5374	38	88	wahid	wahid	PROPN
ejpam-5374	38	89	,	,	PUNCT
ejpam-5374	38	90	i.q	i.q	PROPN
ejpam-5374	38	91	.	.	PROPN
ejpam-5374	38	92	amirnuddin	amirnuddin	PROPN
ejpam-5374	38	93	,	,	PUNCT
ejpam-5374	38	94	n.i.m	n.i.m	NOUN
ejpam-5374	38	95	.	.	PUNCT
ejpam-5374	39	1	azmi	azmi	PROPN
ejpam-5374	39	2	/	/	SYM
ejpam-5374	39	3	eur	eur	PROPN
ejpam-5374	39	4	.	.	PUNCT
ejpam-5374	40	1	j.	j.	PROPN
ejpam-5374	40	2	pure	pure	PROPN
ejpam-5374	40	3	appl	appl	PROPN
ejpam-5374	40	4	.	.	PROPN
ejpam-5374	40	5	math	math	PROPN
ejpam-5374	40	6	,	,	PUNCT
ejpam-5374	40	7	17	17	NUM
ejpam-5374	40	8	(	(	PUNCT
ejpam-5374	40	9	4	4	NUM
ejpam-5374	40	10	)	)	PUNCT
ejpam-5374	40	11	(	(	PUNCT
ejpam-5374	40	12	2024	2024	NUM
ejpam-5374	40	13	)	)	PUNCT
ejpam-5374	40	14	,	,	PUNCT
ejpam-5374	40	15	2738	2738	NUM
ejpam-5374	40	16	-	-	SYM
ejpam-5374	40	17	2752	2752	NUM
ejpam-5374	40	18	2740	2740	NUM
ejpam-5374	40	19	γ2	γ2	NOUN
ejpam-5374	40	20	=	=	SYM
ejpam-5374	40	21	1	1	NUM
ejpam-5374	40	22	2	2	NUM
ejpam-5374	40	23	(	(	PUNCT
ejpam-5374	40	24	a3	a3	NOUN
ejpam-5374	40	25	−	−	NOUN
ejpam-5374	40	26	1	1	NUM
ejpam-5374	40	27	2	2	NUM
ejpam-5374	40	28	a2	a2	PROPN
ejpam-5374	40	29	2	2	NUM
ejpam-5374	40	30	)	)	PUNCT
ejpam-5374	40	31	,	,	PUNCT
ejpam-5374	40	32	(	(	PUNCT
ejpam-5374	40	33	8)	8)	NUM
ejpam-5374	40	34	γ3	γ3	NOUN
ejpam-5374	40	35	=	=	NOUN
ejpam-5374	40	36	1	1	NUM
ejpam-5374	40	37	2	2	NUM
ejpam-5374	40	38	(	(	PUNCT
ejpam-5374	40	39	a4	a4	NOUN
ejpam-5374	40	40	−	−	NOUN
ejpam-5374	41	1	a2a3	a2a3	NOUN
ejpam-5374	41	2	+	+	NUM
ejpam-5374	41	3	1	1	NUM
ejpam-5374	41	4	3	3	NUM
ejpam-5374	41	5	a2	a2	PROPN
ejpam-5374	41	6	3	3	NUM
ejpam-5374	41	7	)	)	PUNCT
ejpam-5374	41	8	,	,	PUNCT
ejpam-5374	41	9	(	(	PUNCT
ejpam-5374	41	10	9	9	NUM
ejpam-5374	41	11	)	)	PUNCT
ejpam-5374	41	12	and	and	CCONJ
ejpam-5374	42	1	γ4	γ4	NOUN
ejpam-5374	42	2	=	=	SYM
ejpam-5374	42	3	1	1	NUM
ejpam-5374	42	4	2	2	NUM
ejpam-5374	42	5	(	(	PUNCT
ejpam-5374	42	6	a5	a5	NOUN
ejpam-5374	42	7	−	−	PROPN
ejpam-5374	42	8	a2a4	a2a4	PROPN
ejpam-5374	42	9	+	+	NUM
ejpam-5374	42	10	a2	a2	PROPN
ejpam-5374	42	11	2a3	2a3	NUM
ejpam-5374	42	12	−	−	NOUN
ejpam-5374	42	13	1	1	NUM
ejpam-5374	42	14	2	2	NUM
ejpam-5374	42	15	a3	a3	NOUN
ejpam-5374	42	16	2	2	NUM
ejpam-5374	42	17	−	−	NOUN
ejpam-5374	42	18	1	1	NUM
ejpam-5374	42	19	4	4	NUM
ejpam-5374	42	20	a2	a2	PROPN
ejpam-5374	42	21	4	4	NUM
ejpam-5374	42	22	)	)	PUNCT
ejpam-5374	42	23	.	.	PUNCT
ejpam-5374	43	1	(	(	PUNCT
ejpam-5374	43	2	10	10	NUM
ejpam-5374	43	3	)	)	PUNCT
ejpam-5374	43	4	milin	milin	NOUN
ejpam-5374	44	1	[	[	X
ejpam-5374	44	2	31–33	31–33	NUM
ejpam-5374	44	3	]	]	PUNCT
ejpam-5374	44	4	highlighted	highlight	VERB
ejpam-5374	44	5	the	the	DET
ejpam-5374	44	6	importance	importance	NOUN
ejpam-5374	44	7	of	of	ADP
ejpam-5374	44	8	logarithmic	logarithmic	ADJ
ejpam-5374	44	9	coefficients	coefficient	NOUN
ejpam-5374	44	10	for	for	ADP
ejpam-5374	44	11	estimating	estimate	VERB
ejpam-5374	44	12	the	the	DET
ejpam-5374	44	13	taylor	taylor	PROPN
ejpam-5374	44	14	coefficients	coefficient	NOUN
ejpam-5374	44	15	of	of	ADP
ejpam-5374	44	16	univalent	univalent	ADJ
ejpam-5374	44	17	functions	function	NOUN
ejpam-5374	44	18	.	.	PUNCT
ejpam-5374	45	1	subsequently	subsequently	ADV
ejpam-5374	45	2	,	,	PUNCT
ejpam-5374	45	3	this	this	PRON
ejpam-5374	45	4	led	lead	VERB
ejpam-5374	45	5	to	to	ADP
ejpam-5374	45	6	de	de	X
ejpam-5374	45	7	branges	brange	NOUN
ejpam-5374	45	8	[	[	X
ejpam-5374	45	9	4	4	X
ejpam-5374	45	10	]	]	PUNCT
ejpam-5374	45	11	establishing	establish	VERB
ejpam-5374	45	12	the	the	DET
ejpam-5374	45	13	bieberbach	bieberbach	NOUN
ejpam-5374	45	14	conjecture	conjecture	NOUN
ejpam-5374	45	15	.	.	PUNCT
ejpam-5374	46	1	logarithmic	logarithmic	ADJ
ejpam-5374	46	2	coefficients	coefficient	NOUN
ejpam-5374	46	3	also	also	ADV
ejpam-5374	46	4	play	play	VERB
ejpam-5374	46	5	a	a	DET
ejpam-5374	46	6	significant	significant	ADJ
ejpam-5374	46	7	role	role	NOUN
ejpam-5374	46	8	in	in	ADP
ejpam-5374	46	9	conformal	conformal	ADJ
ejpam-5374	46	10	mapping	mapping	NOUN
ejpam-5374	46	11	,	,	PUNCT
ejpam-5374	46	12	which	which	PRON
ejpam-5374	46	13	helped	help	VERB
ejpam-5374	46	14	kayumov	kayumov	ADJ
ejpam-5374	46	15	[	[	X
ejpam-5374	46	16	20	20	NUM
ejpam-5374	46	17	]	]	PUNCT
ejpam-5374	46	18	solve	solve	PROPN
ejpam-5374	46	19	brennan	brennan	PROPN
ejpam-5374	46	20	’s	’s	PART
ejpam-5374	46	21	conjecture	conjecture	NOUN
ejpam-5374	46	22	.	.	PUNCT
ejpam-5374	47	1	since	since	SCONJ
ejpam-5374	47	2	then	then	ADV
ejpam-5374	47	3	,	,	PUNCT
ejpam-5374	47	4	numerous	numerous	ADJ
ejpam-5374	47	5	studies	study	NOUN
ejpam-5374	47	6	on	on	ADP
ejpam-5374	47	7	logarithmic	logarithmic	ADJ
ejpam-5374	47	8	coefficients	coefficient	NOUN
ejpam-5374	47	9	have	have	AUX
ejpam-5374	47	10	continued	continue	VERB
ejpam-5374	47	11	,	,	PUNCT
ejpam-5374	47	12	with	with	ADP
ejpam-5374	47	13	examples	example	NOUN
ejpam-5374	47	14	found	find	VERB
ejpam-5374	47	15	in	in	ADP
ejpam-5374	47	16	[	[	X
ejpam-5374	47	17	3	3	NUM
ejpam-5374	47	18	,	,	PUNCT
ejpam-5374	47	19	12	12	NUM
ejpam-5374	47	20	,	,	PUNCT
ejpam-5374	47	21	14	14	NUM
ejpam-5374	47	22	,	,	PUNCT
ejpam-5374	47	23	42	42	NUM
ejpam-5374	47	24	]	]	PUNCT
ejpam-5374	47	25	.	.	PUNCT
ejpam-5374	48	1	on	on	ADP
ejpam-5374	48	2	the	the	DET
ejpam-5374	48	3	other	other	ADJ
ejpam-5374	48	4	hand	hand	NOUN
ejpam-5374	48	5	,	,	PUNCT
ejpam-5374	48	6	vijayalakshmi	vijayalakshmi	NOUN
ejpam-5374	48	7	et	et	PROPN
ejpam-5374	48	8	al	al	PROPN
ejpam-5374	48	9	.	.	PUNCT
ejpam-5374	49	1	[	[	X
ejpam-5374	49	2	44	44	NUM
ejpam-5374	49	3	]	]	PUNCT
ejpam-5374	49	4	introduced	introduce	VERB
ejpam-5374	49	5	the	the	DET
ejpam-5374	49	6	vandermonde	vandermonde	NOUN
ejpam-5374	49	7	determinant	determinant	ADJ
ejpam-5374	49	8	vq	vq	NOUN
ejpam-5374	49	9	,	,	PUNCT
ejpam-5374	49	10	n	n	PROPN
ejpam-5374	49	11	(	(	PUNCT
ejpam-5374	49	12	f	f	X
ejpam-5374	49	13	)	)	PUNCT
ejpam-5374	49	14	,	,	PUNCT
ejpam-5374	49	15	where	where	SCONJ
ejpam-5374	49	16	n	n	CCONJ
ejpam-5374	49	17	,	,	PUNCT
ejpam-5374	49	18	q	q	X
ejpam-5374	49	19	≥	≥	NOUN
ejpam-5374	49	20	1	1	NUM
ejpam-5374	49	21	and	and	CCONJ
ejpam-5374	49	22	an	an	PRON
ejpam-5374	49	23	,	,	PUNCT
ejpam-5374	49	24	n	n	PRON
ejpam-5374	49	25	≥	≥	NOUN
ejpam-5374	49	26	2	2	NUM
ejpam-5374	49	27	are	be	AUX
ejpam-5374	49	28	the	the	DET
ejpam-5374	49	29	coefficients	coefficient	NOUN
ejpam-5374	49	30	of	of	ADP
ejpam-5374	49	31	the	the	DET
ejpam-5374	49	32	taylor	taylor	PROPN
ejpam-5374	49	33	series	series	PROPN
ejpam-5374	49	34	in	in	ADP
ejpam-5374	49	35	(	(	PUNCT
ejpam-5374	49	36	1	1	NUM
ejpam-5374	49	37	):	):	PUNCT
ejpam-5374	49	38	vq	vq	NOUN
ejpam-5374	49	39	,	,	PUNCT
ejpam-5374	49	40	n	n	PROPN
ejpam-5374	49	41	(	(	PUNCT
ejpam-5374	49	42	f	f	X
ejpam-5374	49	43	)	)	PUNCT
ejpam-5374	49	44	=	=	SYM
ejpam-5374	49	45	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5374	49	46	1	1	NUM
ejpam-5374	49	47	1	1	NUM
ejpam-5374	49	48	...	...	SYM
ejpam-5374	49	49	1	1	NUM
ejpam-5374	49	50	an	an	DET
ejpam-5374	49	51	an+1	an+1	NOUN
ejpam-5374	49	52	...	...	PUNCT
ejpam-5374	50	1	an+q−1	an+q−1	PRON
ejpam-5374	50	2	·	·	PUNCT
ejpam-5374	50	3	·	·	PUNCT
ejpam-5374	50	4	·	·	PUNCT
ejpam-5374	50	5	·	·	PUNCT
ejpam-5374	50	6	·	·	PUNCT
ejpam-5374	50	7	·	·	PUNCT
ejpam-5374	50	8	...	...	PUNCT
ejpam-5374	50	9	·	·	PUNCT
ejpam-5374	50	10	·	·	PUNCT
ejpam-5374	50	11	·	·	PUNCT
ejpam-5374	51	1	an	an	DET
ejpam-5374	51	2	q−1	q−1	PROPN
ejpam-5374	51	3	an+1	an+1	AUX
ejpam-5374	51	4	q−1	q−1	NOUN
ejpam-5374	51	5	...	...	PUNCT
ejpam-5374	52	1	an+q−1	an+q−1	PRON
ejpam-5374	52	2	q−1	q−1	PROPN
ejpam-5374	52	3	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5374	52	4	,	,	PUNCT
ejpam-5374	52	5	a1	a1	NOUN
ejpam-5374	52	6	=	=	SYM
ejpam-5374	52	7	1	1	X
ejpam-5374	52	8	.	.	PUNCT
ejpam-5374	52	9	(	(	PUNCT
ejpam-5374	52	10	11	11	NUM
ejpam-5374	52	11	)	)	PUNCT
ejpam-5374	52	12	this	this	DET
ejpam-5374	52	13	determinant	determinant	ADJ
ejpam-5374	52	14	has	have	VERB
ejpam-5374	52	15	many	many	ADJ
ejpam-5374	52	16	applications	application	NOUN
ejpam-5374	52	17	in	in	ADP
ejpam-5374	52	18	a	a	DET
ejpam-5374	52	19	variety	variety	NOUN
ejpam-5374	52	20	of	of	ADP
ejpam-5374	52	21	domains	domain	NOUN
ejpam-5374	52	22	.	.	PUNCT
ejpam-5374	53	1	for	for	ADP
ejpam-5374	53	2	example	example	NOUN
ejpam-5374	53	3	,	,	PUNCT
ejpam-5374	53	4	it	it	PRON
ejpam-5374	53	5	is	be	AUX
ejpam-5374	53	6	used	use	VERB
ejpam-5374	53	7	in	in	ADP
ejpam-5374	53	8	digital	digital	ADJ
ejpam-5374	53	9	signal	signal	NOUN
ejpam-5374	53	10	processing	processing	NOUN
ejpam-5374	53	11	to	to	PART
ejpam-5374	53	12	compute	compute	VERB
ejpam-5374	53	13	the	the	DET
ejpam-5374	53	14	discrete	discrete	ADJ
ejpam-5374	53	15	fourier	fourier	NOUN
ejpam-5374	53	16	transform	transform	NOUN
ejpam-5374	53	17	(	(	PUNCT
ejpam-5374	53	18	dft	dft	NOUN
ejpam-5374	53	19	)	)	PUNCT
ejpam-5374	53	20	and	and	CCONJ
ejpam-5374	53	21	the	the	DET
ejpam-5374	53	22	inverse	inverse	NOUN
ejpam-5374	53	23	discrete	discrete	NOUN
ejpam-5374	53	24	fourier	fourier	NOUN
ejpam-5374	53	25	transform	transform	NOUN
ejpam-5374	53	26	(	(	PUNCT
ejpam-5374	53	27	idft	idft	NOUN
ejpam-5374	53	28	)	)	PUNCT
ejpam-5374	53	29	,	,	PUNCT
ejpam-5374	53	30	and	and	CCONJ
ejpam-5374	53	31	it	it	PRON
ejpam-5374	53	32	also	also	ADV
ejpam-5374	53	33	plays	play	VERB
ejpam-5374	53	34	an	an	DET
ejpam-5374	53	35	important	important	ADJ
ejpam-5374	53	36	part	part	NOUN
ejpam-5374	53	37	in	in	ADP
ejpam-5374	53	38	approximation	approximation	NOUN
ejpam-5374	53	39	problems	problem	NOUN
ejpam-5374	53	40	[	[	X
ejpam-5374	53	41	44	44	NUM
ejpam-5374	53	42	]	]	PUNCT
ejpam-5374	53	43	.	.	PUNCT
ejpam-5374	54	1	the	the	DET
ejpam-5374	54	2	vandermonde	vandermonde	NOUN
ejpam-5374	54	3	determinant	determinant	ADJ
ejpam-5374	54	4	,	,	PUNCT
ejpam-5374	54	5	often	often	ADV
ejpam-5374	54	6	known	know	VERB
ejpam-5374	54	7	as	as	ADP
ejpam-5374	54	8	a	a	DET
ejpam-5374	54	9	discriminant	discriminant	NOUN
ejpam-5374	54	10	,	,	PUNCT
ejpam-5374	54	11	is	be	AUX
ejpam-5374	54	12	also	also	ADV
ejpam-5374	54	13	an	an	DET
ejpam-5374	54	14	important	important	ADJ
ejpam-5374	54	15	tool	tool	NOUN
ejpam-5374	54	16	in	in	ADP
ejpam-5374	54	17	linear	linear	PROPN
ejpam-5374	54	18	algebra	algebra	NOUN
ejpam-5374	54	19	;	;	PUNCT
ejpam-5374	54	20	refer	refer	VERB
ejpam-5374	54	21	to	to	ADP
ejpam-5374	54	22	[	[	X
ejpam-5374	54	23	26	26	NUM
ejpam-5374	54	24	]	]	PUNCT
ejpam-5374	54	25	and	and	CCONJ
ejpam-5374	54	26	the	the	DET
ejpam-5374	54	27	references	reference	NOUN
ejpam-5374	54	28	therein	therein	ADV
ejpam-5374	54	29	for	for	ADP
ejpam-5374	54	30	details	detail	NOUN
ejpam-5374	54	31	.	.	PUNCT
ejpam-5374	55	1	therefore	therefore	ADV
ejpam-5374	55	2	,	,	PUNCT
ejpam-5374	55	3	following	follow	VERB
ejpam-5374	55	4	the	the	DET
ejpam-5374	55	5	generalization	generalization	NOUN
ejpam-5374	55	6	of	of	ADP
ejpam-5374	55	7	the	the	DET
ejpam-5374	55	8	hankel	hankel	NOUN
ejpam-5374	55	9	and	and	CCONJ
ejpam-5374	55	10	toeplitz	toeplitz	NOUN
ejpam-5374	55	11	determinants	determinant	NOUN
ejpam-5374	55	12	in	in	ADP
ejpam-5374	55	13	(	(	PUNCT
ejpam-5374	55	14	2	2	NUM
ejpam-5374	55	15	)	)	PUNCT
ejpam-5374	55	16	and	and	CCONJ
ejpam-5374	55	17	(	(	PUNCT
ejpam-5374	55	18	3	3	NUM
ejpam-5374	55	19	)	)	PUNCT
ejpam-5374	55	20	,	,	PUNCT
ejpam-5374	55	21	where	where	SCONJ
ejpam-5374	55	22	their	their	PRON
ejpam-5374	55	23	entries	entry	NOUN
ejpam-5374	55	24	are	be	AUX
ejpam-5374	55	25	replaced	replace	VERB
ejpam-5374	55	26	by	by	ADP
ejpam-5374	55	27	logarithmic	logarithmic	ADJ
ejpam-5374	55	28	coefficients	coefficient	NOUN
ejpam-5374	55	29	,	,	PUNCT
ejpam-5374	55	30	and	and	CCONJ
ejpam-5374	55	31	acknowledging	acknowledge	VERB
ejpam-5374	55	32	the	the	DET
ejpam-5374	55	33	significance	significance	NOUN
ejpam-5374	55	34	of	of	ADP
ejpam-5374	55	35	both	both	CCONJ
ejpam-5374	55	36	the	the	DET
ejpam-5374	55	37	vandermonde	vandermonde	ADJ
ejpam-5374	55	38	determinant	determinant	ADJ
ejpam-5374	55	39	and	and	CCONJ
ejpam-5374	55	40	logarithmic	logarithmic	ADJ
ejpam-5374	55	41	coefficients	coefficient	NOUN
ejpam-5374	55	42	,	,	PUNCT
ejpam-5374	55	43	we	we	PRON
ejpam-5374	55	44	now	now	ADV
ejpam-5374	55	45	define	define	VERB
ejpam-5374	55	46	the	the	DET
ejpam-5374	55	47	vandermonde	vandermonde	NOUN
ejpam-5374	55	48	determinant	determinant	ADJ
ejpam-5374	55	49	of	of	ADP
ejpam-5374	55	50	logarithmic	logarithmic	ADJ
ejpam-5374	55	51	coefficients	coefficient	NOUN
ejpam-5374	55	52	for	for	ADP
ejpam-5374	55	53	functions	function	NOUN
ejpam-5374	55	54	f	f	X
ejpam-5374	55	55	(	(	PUNCT
ejpam-5374	55	56	z	z	NOUN
ejpam-5374	55	57	)	)	PUNCT
ejpam-5374	55	58	∈	∈	PROPN
ejpam-5374	55	59	a	a	DET
ejpam-5374	55	60	as	as	SCONJ
ejpam-5374	55	61	follows	follow	VERB
ejpam-5374	55	62	:	:	PUNCT
ejpam-5374	55	63	vq	vq	NOUN
ejpam-5374	55	64	,	,	PUNCT
ejpam-5374	55	65	n	n	CCONJ
ejpam-5374	55	66	(	(	PUNCT
ejpam-5374	55	67	γf	γf	ADJ
ejpam-5374	55	68	)	)	PUNCT
ejpam-5374	55	69	=	=	PUNCT
ejpam-5374	56	1	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5374	56	2	1	1	NUM
ejpam-5374	56	3	1	1	NUM
ejpam-5374	56	4	...	...	SYM
ejpam-5374	56	5	1	1	NUM
ejpam-5374	56	6	γn	γn	NOUN
ejpam-5374	56	7	γn+1	γn+1	NUM
ejpam-5374	56	8	...	...	PUNCT
ejpam-5374	57	1	γn+q−1	γn+q−1	PROPN
ejpam-5374	57	2	·	·	PUNCT
ejpam-5374	57	3	·	·	PUNCT
ejpam-5374	57	4	·	·	PUNCT
ejpam-5374	57	5	·	·	PUNCT
ejpam-5374	57	6	·	·	PUNCT
ejpam-5374	57	7	·	·	PUNCT
ejpam-5374	57	8	...	...	PUNCT
ejpam-5374	57	9	·	·	PUNCT
ejpam-5374	57	10	·	·	PUNCT
ejpam-5374	57	11	·	·	PUNCT
ejpam-5374	58	1	γn	γn	NUM
ejpam-5374	58	2	q−1	q−1	PROPN
ejpam-5374	58	3	γn+1	γn+1	NUM
ejpam-5374	58	4	q−1	q−1	PROPN
ejpam-5374	58	5	...	...	PUNCT
ejpam-5374	59	1	γn+q−1	γn+q−1	PROPN
ejpam-5374	59	2	q−1	q−1	PROPN
ejpam-5374	59	3	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-5374	59	4	.	.	PUNCT
ejpam-5374	60	1	(	(	PUNCT
ejpam-5374	60	2	12	12	NUM
ejpam-5374	60	3	)	)	PUNCT
ejpam-5374	60	4	consequently	consequently	ADV
ejpam-5374	60	5	,	,	PUNCT
ejpam-5374	60	6	if	if	SCONJ
ejpam-5374	60	7	q	q	NOUN
ejpam-5374	60	8	=	=	SYM
ejpam-5374	60	9	2	2	NUM
ejpam-5374	60	10	and	and	CCONJ
ejpam-5374	60	11	n	n	NOUN
ejpam-5374	60	12	=	=	SYM
ejpam-5374	60	13	2	2	NUM
ejpam-5374	60	14	,	,	PUNCT
ejpam-5374	60	15	then	then	ADV
ejpam-5374	60	16	from	from	ADP
ejpam-5374	60	17	(	(	PUNCT
ejpam-5374	60	18	4	4	NUM
ejpam-5374	60	19	)	)	PUNCT
ejpam-5374	60	20	,	,	PUNCT
ejpam-5374	60	21	(	(	PUNCT
ejpam-5374	60	22	5	5	NUM
ejpam-5374	60	23	)	)	PUNCT
ejpam-5374	60	24	,	,	PUNCT
ejpam-5374	60	25	and	and	CCONJ
ejpam-5374	60	26	(	(	PUNCT
ejpam-5374	60	27	12	12	NUM
ejpam-5374	60	28	)	)	PUNCT
ejpam-5374	60	29	,	,	PUNCT
ejpam-5374	60	30	respectively	respectively	ADV
ejpam-5374	60	31	,	,	PUNCT
ejpam-5374	60	32	yield	yield	VERB
ejpam-5374	60	33	the	the	DET
ejpam-5374	60	34	second	second	ADJ
ejpam-5374	60	35	-	-	PUNCT
ejpam-5374	60	36	order	order	NOUN
ejpam-5374	60	37	of	of	ADP
ejpam-5374	60	38	three	three	NUM
ejpam-5374	60	39	types	type	NOUN
ejpam-5374	60	40	of	of	ADP
ejpam-5374	60	41	determinants	determinant	NOUN
ejpam-5374	60	42	,	,	PUNCT
ejpam-5374	60	43	namely	namely	ADV
ejpam-5374	60	44	hankel	hankel	NOUN
ejpam-5374	60	45	,	,	PUNCT
ejpam-5374	60	46	toeplitz	toeplitz	NOUN
ejpam-5374	60	47	,	,	PUNCT
ejpam-5374	60	48	and	and	CCONJ
ejpam-5374	60	49	vandermonde	vandermonde	NOUN
ejpam-5374	60	50	,	,	PUNCT
ejpam-5374	60	51	as	as	SCONJ
ejpam-5374	60	52	follows	follow	VERB
ejpam-5374	60	53	:	:	PUNCT
ejpam-5374	60	54	h2,2	h2,2	PROPN
ejpam-5374	60	55	(	(	PUNCT
ejpam-5374	60	56	γf	γf	ADJ
ejpam-5374	60	57	)	)	PUNCT
ejpam-5374	61	1	=	=	PUNCT
ejpam-5374	61	2	γ2γ4	γ2γ4	PUNCT
ejpam-5374	61	3	−	−	PROPN
ejpam-5374	61	4	γ3	γ3	NOUN
ejpam-5374	61	5	2	2	NUM
ejpam-5374	61	6	,	,	PUNCT
ejpam-5374	61	7	(	(	PUNCT
ejpam-5374	61	8	13	13	NUM
ejpam-5374	61	9	)	)	PUNCT
ejpam-5374	61	10	t2,2	t2,2	NOUN
ejpam-5374	61	11	(	(	PUNCT
ejpam-5374	61	12	γf	γf	PROPN
ejpam-5374	61	13	)	)	PUNCT
ejpam-5374	61	14	=	=	SYM
ejpam-5374	62	1	γ2	γ2	ADJ
ejpam-5374	62	2	2	2	NUM
ejpam-5374	62	3	−	−	PROPN
ejpam-5374	62	4	γ3	γ3	NOUN
ejpam-5374	62	5	2	2	NUM
ejpam-5374	62	6	,	,	PUNCT
ejpam-5374	62	7	(	(	PUNCT
ejpam-5374	62	8	14	14	NUM
ejpam-5374	62	9	)	)	PUNCT
ejpam-5374	62	10	n.h.a.a	n.h.a.a	PROPN
ejpam-5374	62	11	.	.	PROPN
ejpam-5374	62	12	wahid	wahid	PROPN
ejpam-5374	62	13	,	,	PUNCT
ejpam-5374	62	14	i.q	i.q	PROPN
ejpam-5374	62	15	.	.	PROPN
ejpam-5374	62	16	amirnuddin	amirnuddin	PROPN
ejpam-5374	62	17	,	,	PUNCT
ejpam-5374	62	18	n.i.m	n.i.m	NOUN
ejpam-5374	62	19	.	.	PUNCT
ejpam-5374	63	1	azmi	azmi	PROPN
ejpam-5374	63	2	/	/	SYM
ejpam-5374	63	3	eur	eur	PROPN
ejpam-5374	63	4	.	.	PUNCT
ejpam-5374	64	1	j.	j.	PROPN
ejpam-5374	64	2	pure	pure	PROPN
ejpam-5374	64	3	appl	appl	PROPN
ejpam-5374	64	4	.	.	PROPN
ejpam-5374	64	5	math	math	PROPN
ejpam-5374	64	6	,	,	PUNCT
ejpam-5374	64	7	17	17	NUM
ejpam-5374	64	8	(	(	PUNCT
ejpam-5374	64	9	4	4	NUM
ejpam-5374	64	10	)	)	PUNCT
ejpam-5374	64	11	(	(	PUNCT
ejpam-5374	64	12	2024	2024	NUM
ejpam-5374	64	13	)	)	PUNCT
ejpam-5374	64	14	,	,	PUNCT
ejpam-5374	64	15	2738	2738	NUM
ejpam-5374	64	16	-	-	SYM
ejpam-5374	64	17	2752	2752	NUM
ejpam-5374	64	18	2741	2741	NUM
ejpam-5374	64	19	and	and	CCONJ
ejpam-5374	64	20	v2,2	v2,2	PROPN
ejpam-5374	64	21	(	(	PUNCT
ejpam-5374	64	22	γf	γf	PROPN
ejpam-5374	64	23	)	)	PUNCT
ejpam-5374	64	24	=	=	SYM
ejpam-5374	64	25	γ3	γ3	NOUN
ejpam-5374	64	26	−	−	PROPN
ejpam-5374	64	27	γ2	γ2	PROPN
ejpam-5374	64	28	.	.	PUNCT
ejpam-5374	65	1	(	(	PUNCT
ejpam-5374	65	2	15	15	NUM
ejpam-5374	65	3	)	)	PUNCT
ejpam-5374	65	4	in	in	ADP
ejpam-5374	65	5	[	[	X
ejpam-5374	65	6	2	2	NUM
ejpam-5374	65	7	,	,	PUNCT
ejpam-5374	65	8	5	5	NUM
ejpam-5374	65	9	,	,	PUNCT
ejpam-5374	65	10	8	8	NUM
ejpam-5374	65	11	,	,	PUNCT
ejpam-5374	65	12	24	24	NUM
ejpam-5374	65	13	,	,	PUNCT
ejpam-5374	65	14	28	28	NUM
ejpam-5374	65	15	,	,	PUNCT
ejpam-5374	65	16	43	43	NUM
ejpam-5374	65	17	,	,	PUNCT
ejpam-5374	65	18	46	46	NUM
ejpam-5374	65	19	,	,	PUNCT
ejpam-5374	65	20	48	48	NUM
ejpam-5374	65	21	]	]	PUNCT
ejpam-5374	65	22	,	,	PUNCT
ejpam-5374	65	23	sharp	sharp	ADJ
ejpam-5374	65	24	bounds	bound	NOUN
ejpam-5374	65	25	for	for	ADP
ejpam-5374	65	26	the	the	DET
ejpam-5374	65	27	hankel	hankel	NOUN
ejpam-5374	65	28	determinant	determinant	ADJ
ejpam-5374	65	29	of	of	ADP
ejpam-5374	65	30	logarithmic	logarithmic	ADJ
ejpam-5374	65	31	coefficients	coefficient	NOUN
ejpam-5374	65	32	were	be	AUX
ejpam-5374	65	33	recently	recently	ADV
ejpam-5374	65	34	established	establish	VERB
ejpam-5374	65	35	for	for	ADP
ejpam-5374	65	36	several	several	ADJ
ejpam-5374	65	37	subclasses	subclass	NOUN
ejpam-5374	65	38	of	of	ADP
ejpam-5374	65	39	univalent	univalent	ADJ
ejpam-5374	65	40	functions	function	NOUN
ejpam-5374	65	41	.	.	PUNCT
ejpam-5374	66	1	works	work	VERB
ejpam-5374	66	2	by	by	ADP
ejpam-5374	66	3	[	[	X
ejpam-5374	66	4	1	1	NUM
ejpam-5374	66	5	,	,	PUNCT
ejpam-5374	66	6	35	35	NUM
ejpam-5374	66	7	]	]	PUNCT
ejpam-5374	66	8	also	also	ADV
ejpam-5374	66	9	investigated	investigate	VERB
ejpam-5374	66	10	both	both	DET
ejpam-5374	66	11	hankel	hankel	NOUN
ejpam-5374	66	12	and	and	CCONJ
ejpam-5374	66	13	toeplitz	toeplitz	NOUN
ejpam-5374	66	14	determinants	determinant	NOUN
ejpam-5374	66	15	with	with	ADP
ejpam-5374	66	16	logarithmic	logarithmic	ADJ
ejpam-5374	66	17	coefficients	coefficient	NOUN
ejpam-5374	66	18	as	as	ADP
ejpam-5374	66	19	entries	entry	NOUN
ejpam-5374	66	20	,	,	PUNCT
ejpam-5374	66	21	specifically	specifically	ADV
ejpam-5374	66	22	for	for	ADP
ejpam-5374	66	23	the	the	DET
ejpam-5374	66	24	subclass	subclass	NOUN
ejpam-5374	66	25	of	of	ADP
ejpam-5374	66	26	starlike	starlike	NOUN
ejpam-5374	66	27	functions	function	NOUN
ejpam-5374	66	28	with	with	ADP
ejpam-5374	66	29	respect	respect	NOUN
ejpam-5374	66	30	to	to	ADP
ejpam-5374	66	31	other	other	ADJ
ejpam-5374	66	32	points	point	NOUN
ejpam-5374	66	33	.	.	PUNCT
ejpam-5374	67	1	while	while	SCONJ
ejpam-5374	67	2	there	there	PRON
ejpam-5374	67	3	has	have	AUX
ejpam-5374	67	4	been	be	AUX
ejpam-5374	67	5	limited	limit	VERB
ejpam-5374	67	6	study	study	NOUN
ejpam-5374	67	7	on	on	ADP
ejpam-5374	67	8	toeplitz	toeplitz	NOUN
ejpam-5374	67	9	determinants	determinant	NOUN
ejpam-5374	67	10	in	in	ADP
ejpam-5374	67	11	this	this	DET
ejpam-5374	67	12	context	context	NOUN
ejpam-5374	67	13	,	,	PUNCT
ejpam-5374	67	14	it	it	PRON
ejpam-5374	67	15	is	be	AUX
ejpam-5374	67	16	important	important	ADJ
ejpam-5374	67	17	to	to	PART
ejpam-5374	67	18	note	note	VERB
ejpam-5374	67	19	that	that	SCONJ
ejpam-5374	67	20	,	,	PUNCT
ejpam-5374	67	21	in	in	ADP
ejpam-5374	67	22	general	general	ADJ
ejpam-5374	67	23	,	,	PUNCT
ejpam-5374	67	24	the	the	DET
ejpam-5374	67	25	upper	upper	ADJ
ejpam-5374	67	26	bounds	bound	NOUN
ejpam-5374	67	27	for	for	ADP
ejpam-5374	67	28	both	both	CCONJ
ejpam-5374	67	29	hankel	hankel	NOUN
ejpam-5374	67	30	and	and	CCONJ
ejpam-5374	67	31	toeplitz	toeplitz	NOUN
ejpam-5374	67	32	determinants	determinant	NOUN
ejpam-5374	67	33	remain	remain	VERB
ejpam-5374	67	34	unknown	unknown	ADJ
ejpam-5374	67	35	for	for	ADP
ejpam-5374	67	36	classes	class	NOUN
ejpam-5374	67	37	of	of	ADP
ejpam-5374	67	38	functions	function	NOUN
ejpam-5374	67	39	.	.	PUNCT
ejpam-5374	68	1	in	in	ADP
ejpam-5374	68	2	fact	fact	NOUN
ejpam-5374	68	3	,	,	PUNCT
ejpam-5374	68	4	to	to	ADP
ejpam-5374	68	5	the	the	DET
ejpam-5374	68	6	best	good	ADJ
ejpam-5374	68	7	of	of	ADP
ejpam-5374	68	8	our	our	PRON
ejpam-5374	68	9	knowledge	knowledge	NOUN
ejpam-5374	68	10	,	,	PUNCT
ejpam-5374	68	11	no	no	DET
ejpam-5374	68	12	one	one	NOUN
ejpam-5374	68	13	has	have	AUX
ejpam-5374	68	14	yet	yet	ADV
ejpam-5374	68	15	studied	study	VERB
ejpam-5374	68	16	the	the	DET
ejpam-5374	68	17	vandermonde	vandermonde	NOUN
ejpam-5374	68	18	determinant	determinant	ADJ
ejpam-5374	68	19	of	of	ADP
ejpam-5374	68	20	logarithmic	logarithmic	ADJ
ejpam-5374	68	21	coefficients	coefficient	NOUN
ejpam-5374	68	22	.	.	PUNCT
ejpam-5374	69	1	thus	thus	ADV
ejpam-5374	69	2	,	,	PUNCT
ejpam-5374	69	3	motivated	motivate	VERB
ejpam-5374	69	4	by	by	ADP
ejpam-5374	69	5	the	the	DET
ejpam-5374	69	6	previous	previous	ADJ
ejpam-5374	69	7	studies	study	NOUN
ejpam-5374	69	8	,	,	PUNCT
ejpam-5374	69	9	in	in	ADP
ejpam-5374	69	10	this	this	DET
ejpam-5374	69	11	paper	paper	NOUN
ejpam-5374	69	12	,	,	PUNCT
ejpam-5374	69	13	we	we	PRON
ejpam-5374	69	14	aim	aim	VERB
ejpam-5374	69	15	to	to	PART
ejpam-5374	69	16	estimate	estimate	VERB
ejpam-5374	69	17	the	the	DET
ejpam-5374	69	18	upper	upper	ADJ
ejpam-5374	69	19	bounds	bound	NOUN
ejpam-5374	69	20	of	of	ADP
ejpam-5374	69	21	the	the	DET
ejpam-5374	69	22	logarithmic	logarithmic	ADJ
ejpam-5374	69	23	coefficients	coefficient	NOUN
ejpam-5374	69	24	|γn|	|γn|	PROPN
ejpam-5374	69	25	,	,	PUNCT
ejpam-5374	69	26	specifically	specifically	ADV
ejpam-5374	69	27	for	for	ADP
ejpam-5374	69	28	n	n	NOUN
ejpam-5374	69	29	=	=	SYM
ejpam-5374	69	30	1	1	NUM
ejpam-5374	69	31	,	,	PUNCT
ejpam-5374	69	32	2	2	NUM
ejpam-5374	69	33	,	,	PUNCT
ejpam-5374	69	34	3	3	NUM
ejpam-5374	69	35	,	,	PUNCT
ejpam-5374	69	36	4	4	NUM
ejpam-5374	69	37	.	.	PUNCT
ejpam-5374	70	1	hence	hence	ADV
ejpam-5374	70	2	,	,	PUNCT
ejpam-5374	70	3	we	we	PRON
ejpam-5374	70	4	focus	focus	VERB
ejpam-5374	70	5	on	on	ADP
ejpam-5374	70	6	estimating	estimate	VERB
ejpam-5374	70	7	the	the	DET
ejpam-5374	70	8	upper	upper	ADJ
ejpam-5374	70	9	bounds	bound	NOUN
ejpam-5374	70	10	of	of	ADP
ejpam-5374	70	11	the	the	DET
ejpam-5374	70	12	second	second	ADJ
ejpam-5374	70	13	-	-	PUNCT
ejpam-5374	70	14	order	order	NOUN
ejpam-5374	70	15	hankel	hankel	NOUN
ejpam-5374	70	16	,	,	PUNCT
ejpam-5374	70	17	toeplitz	toeplitz	NOUN
ejpam-5374	70	18	,	,	PUNCT
ejpam-5374	70	19	and	and	CCONJ
ejpam-5374	70	20	vandermonde	vandermonde	VERB
ejpam-5374	70	21	determinants	determinant	NOUN
ejpam-5374	70	22	whose	whose	DET
ejpam-5374	70	23	entries	entry	NOUN
ejpam-5374	70	24	are	be	AUX
ejpam-5374	70	25	logarithmic	logarithmic	ADJ
ejpam-5374	70	26	coefficients	coefficient	NOUN
ejpam-5374	70	27	,	,	PUNCT
ejpam-5374	70	28	as	as	SCONJ
ejpam-5374	70	29	given	give	VERB
ejpam-5374	70	30	in	in	ADP
ejpam-5374	70	31	(	(	PUNCT
ejpam-5374	70	32	7)-(10	7)-(10	NOUN
ejpam-5374	70	33	)	)	PUNCT
ejpam-5374	70	34	,	,	PUNCT
ejpam-5374	70	35	for	for	ADP
ejpam-5374	70	36	functions	function	NOUN
ejpam-5374	70	37	belonging	belong	VERB
ejpam-5374	70	38	to	to	ADP
ejpam-5374	70	39	the	the	DET
ejpam-5374	70	40	following	follow	VERB
ejpam-5374	70	41	class	class	NOUN
ejpam-5374	70	42	of	of	ADP
ejpam-5374	70	43	bounded	bounded	ADJ
ejpam-5374	70	44	turning	turning	NOUN
ejpam-5374	70	45	functions	function	NOUN
ejpam-5374	70	46	:	:	PUNCT
ejpam-5374	70	47	definition	definition	NOUN
ejpam-5374	70	48	1	1	NUM
ejpam-5374	70	49	.	.	PUNCT
ejpam-5374	71	1	a	a	DET
ejpam-5374	71	2	function	function	NOUN
ejpam-5374	71	3	f	f	X
ejpam-5374	71	4	(	(	PUNCT
ejpam-5374	71	5	z	z	NOUN
ejpam-5374	71	6	)	)	PUNCT
ejpam-5374	71	7	given	give	VERB
ejpam-5374	71	8	by	by	ADP
ejpam-5374	71	9	(	(	PUNCT
ejpam-5374	71	10	1	1	NUM
ejpam-5374	71	11	)	)	PUNCT
ejpam-5374	71	12	is	be	AUX
ejpam-5374	71	13	said	say	VERB
ejpam-5374	71	14	to	to	PART
ejpam-5374	71	15	be	be	AUX
ejpam-5374	71	16	in	in	ADP
ejpam-5374	71	17	the	the	DET
ejpam-5374	71	18	class	class	NOUN
ejpam-5374	71	19	g	g	NOUN
ejpam-5374	71	20	(	(	PUNCT
ejpam-5374	71	21	α	α	PROPN
ejpam-5374	71	22	,	,	PUNCT
ejpam-5374	71	23	δ	δ	PROPN
ejpam-5374	71	24	)	)	PUNCT
ejpam-5374	71	25	if	if	SCONJ
ejpam-5374	71	26	the	the	DET
ejpam-5374	71	27	following	follow	VERB
ejpam-5374	71	28	condition	condition	NOUN
ejpam-5374	71	29	is	be	AUX
ejpam-5374	71	30	satisfied	satisfied	ADJ
ejpam-5374	71	31	:	:	PUNCT
ejpam-5374	71	32	re	re	X
ejpam-5374	71	33	(	(	PUNCT
ejpam-5374	71	34	eiαf	eiαf	NOUN
ejpam-5374	71	35	′	′	NUM
ejpam-5374	71	36	(	(	PUNCT
ejpam-5374	71	37	z	z	NOUN
ejpam-5374	71	38	)	)	PUNCT
ejpam-5374	71	39	)	)	PUNCT
ejpam-5374	71	40	>	>	PUNCT
ejpam-5374	72	1	δ	δ	PROPN
ejpam-5374	72	2	,	,	PUNCT
ejpam-5374	72	3	z	z	NOUN
ejpam-5374	72	4	∈	∈	PROPN
ejpam-5374	72	5	e	e	NOUN
ejpam-5374	72	6	,	,	PUNCT
ejpam-5374	72	7	where	where	SCONJ
ejpam-5374	72	8	|α|	|α|	PROPN
ejpam-5374	72	9	<	<	X
ejpam-5374	72	10	π	π	PROPN
ejpam-5374	72	11	,	,	PUNCT
ejpam-5374	72	12	0	0	NUM
ejpam-5374	72	13	⩽	⩽	PROPN
ejpam-5374	72	14	δ	δ	PROPN
ejpam-5374	72	15	<	<	X
ejpam-5374	72	16	1	1	NUM
ejpam-5374	72	17	,	,	PUNCT
ejpam-5374	72	18	and	and	CCONJ
ejpam-5374	72	19	cosα	cosα	NOUN
ejpam-5374	72	20	>	>	X
ejpam-5374	72	21	δ	δ	PROPN
ejpam-5374	72	22	.	.	PUNCT
ejpam-5374	73	1	this	this	DET
ejpam-5374	73	2	class	class	NOUN
ejpam-5374	73	3	was	be	AUX
ejpam-5374	73	4	introduced	introduce	VERB
ejpam-5374	73	5	by	by	ADP
ejpam-5374	73	6	mohamad	mohamad	PROPN
ejpam-5374	73	7	[	[	X
ejpam-5374	73	8	34	34	NUM
ejpam-5374	73	9	]	]	PUNCT
ejpam-5374	73	10	.	.	PUNCT
ejpam-5374	74	1	remark	remark	PROPN
ejpam-5374	74	2	1	1	NUM
ejpam-5374	74	3	.	.	PUNCT
ejpam-5374	74	4	selecting	select	VERB
ejpam-5374	74	5	specific	specific	ADJ
ejpam-5374	74	6	values	value	NOUN
ejpam-5374	74	7	for	for	ADP
ejpam-5374	74	8	the	the	DET
ejpam-5374	74	9	parameters	parameter	NOUN
ejpam-5374	74	10	α	α	PROPN
ejpam-5374	74	11	and	and	CCONJ
ejpam-5374	74	12	δ	δ	PROPN
ejpam-5374	74	13	in	in	ADP
ejpam-5374	74	14	the	the	DET
ejpam-5374	74	15	class	class	NOUN
ejpam-5374	74	16	g	g	PROPN
ejpam-5374	74	17	(	(	PUNCT
ejpam-5374	74	18	α	α	PROPN
ejpam-5374	74	19	,	,	PUNCT
ejpam-5374	74	20	δ	δ	PROPN
ejpam-5374	74	21	)	)	PUNCT
ejpam-5374	74	22	yields	yield	VERB
ejpam-5374	74	23	the	the	DET
ejpam-5374	74	24	following	follow	VERB
ejpam-5374	74	25	classes	class	NOUN
ejpam-5374	74	26	:	:	PUNCT
ejpam-5374	74	27	(	(	PUNCT
ejpam-5374	74	28	i	i	NOUN
ejpam-5374	74	29	)	)	PUNCT
ejpam-5374	74	30	if	if	SCONJ
ejpam-5374	74	31	we	we	PRON
ejpam-5374	74	32	choose	choose	VERB
ejpam-5374	74	33	α	α	X
ejpam-5374	74	34	=	=	PUNCT
ejpam-5374	74	35	δ	δ	X
ejpam-5374	74	36	=	=	SYM
ejpam-5374	74	37	0	0	PROPN
ejpam-5374	74	38	,	,	PUNCT
ejpam-5374	74	39	then	then	ADV
ejpam-5374	74	40	g	g	PROPN
ejpam-5374	74	41	(	(	PUNCT
ejpam-5374	74	42	α	α	PROPN
ejpam-5374	74	43	,	,	PUNCT
ejpam-5374	74	44	δ	δ	NOUN
ejpam-5374	74	45	)	)	PUNCT
ejpam-5374	74	46	reduces	reduce	VERB
ejpam-5374	74	47	to	to	ADP
ejpam-5374	74	48	r	r	NOUN
ejpam-5374	74	49	which	which	PRON
ejpam-5374	74	50	satisfies	satisfy	VERB
ejpam-5374	74	51	re	re	VERB
ejpam-5374	74	52	f	f	PROPN
ejpam-5374	74	53	′	′	NUM
ejpam-5374	75	1	(	(	PUNCT
ejpam-5374	75	2	z	z	NOUN
ejpam-5374	75	3	)	)	PUNCT
ejpam-5374	75	4	>	>	X
ejpam-5374	76	1	0	0	X
ejpam-5374	76	2	.	.	PUNCT
ejpam-5374	77	1	the	the	DET
ejpam-5374	77	2	functions	function	NOUN
ejpam-5374	77	3	from	from	ADP
ejpam-5374	77	4	r	r	NOUN
ejpam-5374	77	5	are	be	AUX
ejpam-5374	77	6	said	say	VERB
ejpam-5374	77	7	to	to	PART
ejpam-5374	77	8	be	be	AUX
ejpam-5374	77	9	of	of	ADP
ejpam-5374	77	10	bounded	bounded	ADJ
ejpam-5374	77	11	turning	turning	NOUN
ejpam-5374	77	12	.	.	PUNCT
ejpam-5374	78	1	(	(	PUNCT
ejpam-5374	78	2	ii	ii	NOUN
ejpam-5374	78	3	)	)	PUNCT
ejpam-5374	78	4	if	if	SCONJ
ejpam-5374	78	5	we	we	PRON
ejpam-5374	78	6	choose	choose	VERB
ejpam-5374	78	7	α	α	NOUN
ejpam-5374	78	8	=	=	SYM
ejpam-5374	78	9	0	0	NUM
ejpam-5374	78	10	,	,	PUNCT
ejpam-5374	78	11	then	then	ADV
ejpam-5374	78	12	g	g	PROPN
ejpam-5374	78	13	(	(	PUNCT
ejpam-5374	78	14	α	α	PROPN
ejpam-5374	78	15	,	,	PUNCT
ejpam-5374	78	16	δ	δ	NOUN
ejpam-5374	78	17	)	)	PUNCT
ejpam-5374	78	18	reduces	reduce	VERB
ejpam-5374	78	19	to	to	ADP
ejpam-5374	78	20	r	r	NOUN
ejpam-5374	78	21	(	(	PUNCT
ejpam-5374	78	22	δ	δ	PROPN
ejpam-5374	78	23	)	)	PUNCT
ejpam-5374	78	24	which	which	PRON
ejpam-5374	78	25	satisfies	satisfy	VERB
ejpam-5374	78	26	re	re	VERB
ejpam-5374	78	27	(	(	PUNCT
ejpam-5374	78	28	f	f	NOUN
ejpam-5374	78	29	′	′	NUM
ejpam-5374	78	30	(	(	PUNCT
ejpam-5374	78	31	z	z	NOUN
ejpam-5374	78	32	)	)	PUNCT
ejpam-5374	78	33	)	)	PUNCT
ejpam-5374	79	1	>	>	PUNCT
ejpam-5374	79	2	δ	δ	PROPN
ejpam-5374	79	3	.	.	PUNCT
ejpam-5374	80	1	the	the	DET
ejpam-5374	80	2	class	class	NOUN
ejpam-5374	80	3	r	r	NOUN
ejpam-5374	80	4	(	(	PUNCT
ejpam-5374	80	5	δ	δ	NOUN
ejpam-5374	80	6	)	)	PUNCT
ejpam-5374	80	7	is	be	AUX
ejpam-5374	80	8	called	call	VERB
ejpam-5374	80	9	the	the	DET
ejpam-5374	80	10	class	class	NOUN
ejpam-5374	80	11	of	of	ADP
ejpam-5374	80	12	bounded	bounded	ADJ
ejpam-5374	80	13	turning	turning	NOUN
ejpam-5374	80	14	functions	function	NOUN
ejpam-5374	80	15	of	of	ADP
ejpam-5374	80	16	order	order	NOUN
ejpam-5374	80	17	δ	δ	PROPN
ejpam-5374	80	18	.	.	PUNCT
ejpam-5374	81	1	(	(	PUNCT
ejpam-5374	81	2	iii	iii	X
ejpam-5374	81	3	)	)	PUNCT
ejpam-5374	81	4	if	if	SCONJ
ejpam-5374	81	5	we	we	PRON
ejpam-5374	81	6	choose	choose	VERB
ejpam-5374	81	7	δ	δ	X
ejpam-5374	81	8	=	=	SYM
ejpam-5374	81	9	0	0	PROPN
ejpam-5374	81	10	,	,	PUNCT
ejpam-5374	81	11	then	then	ADV
ejpam-5374	81	12	g	g	PROPN
ejpam-5374	81	13	(	(	PUNCT
ejpam-5374	81	14	α	α	PROPN
ejpam-5374	81	15	,	,	PUNCT
ejpam-5374	81	16	δ	δ	NOUN
ejpam-5374	81	17	)	)	PUNCT
ejpam-5374	81	18	reduces	reduce	VERB
ejpam-5374	81	19	to	to	ADP
ejpam-5374	81	20	r	r	NOUN
ejpam-5374	81	21	(	(	PUNCT
ejpam-5374	81	22	α	α	NOUN
ejpam-5374	81	23	)	)	PUNCT
ejpam-5374	81	24	which	which	PRON
ejpam-5374	81	25	satisfies	satisfy	VERB
ejpam-5374	81	26	re	re	VERB
ejpam-5374	81	27	(	(	PUNCT
ejpam-5374	81	28	eiαf	eiαf	NOUN
ejpam-5374	81	29	′	′	NUM
ejpam-5374	82	1	(	(	PUNCT
ejpam-5374	82	2	z	z	NOUN
ejpam-5374	82	3	)	)	PUNCT
ejpam-5374	82	4	)	)	PUNCT
ejpam-5374	83	1	>	>	X
ejpam-5374	83	2	0	0	X
ejpam-5374	83	3	.	.	X
ejpam-5374	83	4	pioneering	pioneer	VERB
ejpam-5374	83	5	researchers	researcher	NOUN
ejpam-5374	83	6	like	like	ADP
ejpam-5374	83	7	goel	goel	PROPN
ejpam-5374	83	8	and	and	CCONJ
ejpam-5374	83	9	mehrok	mehrok	ADJ
ejpam-5374	84	1	[	[	X
ejpam-5374	84	2	16	16	NUM
ejpam-5374	84	3	]	]	PUNCT
ejpam-5374	84	4	,	,	PUNCT
ejpam-5374	84	5	macgregor	macgregor	PROPN
ejpam-5374	85	1	[	[	X
ejpam-5374	85	2	30	30	NUM
ejpam-5374	85	3	]	]	PUNCT
ejpam-5374	85	4	,	,	PUNCT
ejpam-5374	85	5	noshiro	noshiro	VERB
ejpam-5374	86	1	[	[	X
ejpam-5374	86	2	37	37	NUM
ejpam-5374	86	3	]	]	PUNCT
ejpam-5374	86	4	,	,	PUNCT
ejpam-5374	86	5	silverman	silverman	NOUN
ejpam-5374	86	6	and	and	CCONJ
ejpam-5374	86	7	silvia	silvia	PROPN
ejpam-5374	86	8	[	[	X
ejpam-5374	86	9	45	45	NUM
ejpam-5374	86	10	]	]	PUNCT
ejpam-5374	86	11	,	,	PUNCT
ejpam-5374	86	12	and	and	CCONJ
ejpam-5374	86	13	warschawski	warschawski	VERB
ejpam-5374	86	14	[	[	X
ejpam-5374	86	15	47	47	NUM
ejpam-5374	86	16	]	]	PUNCT
ejpam-5374	86	17	were	be	AUX
ejpam-5374	86	18	among	among	ADP
ejpam-5374	86	19	those	those	PRON
ejpam-5374	86	20	who	who	PRON
ejpam-5374	86	21	explored	explore	VERB
ejpam-5374	86	22	the	the	DET
ejpam-5374	86	23	classes	class	NOUN
ejpam-5374	86	24	r	r	NOUN
ejpam-5374	86	25	,	,	PUNCT
ejpam-5374	86	26	r	r	NOUN
ejpam-5374	86	27	(	(	PUNCT
ejpam-5374	86	28	δ	δ	PROPN
ejpam-5374	86	29	)	)	PUNCT
ejpam-5374	86	30	,	,	PUNCT
ejpam-5374	86	31	and	and	CCONJ
ejpam-5374	86	32	r	r	NOUN
ejpam-5374	86	33	(	(	PUNCT
ejpam-5374	86	34	α	α	NOUN
ejpam-5374	86	35	)	)	PUNCT
ejpam-5374	86	36	,	,	PUNCT
ejpam-5374	86	37	and	and	CCONJ
ejpam-5374	86	38	further	further	ADJ
ejpam-5374	86	39	investigation	investigation	NOUN
ejpam-5374	86	40	into	into	ADP
ejpam-5374	86	41	the	the	DET
ejpam-5374	86	42	class	class	NOUN
ejpam-5374	86	43	of	of	ADP
ejpam-5374	86	44	bounded	bound	VERB
ejpam-5374	86	45	turning	turning	NOUN
ejpam-5374	86	46	functions	function	NOUN
ejpam-5374	86	47	has	have	AUX
ejpam-5374	86	48	also	also	ADV
ejpam-5374	86	49	been	be	AUX
ejpam-5374	86	50	extensively	extensively	ADV
ejpam-5374	86	51	studied	study	VERB
ejpam-5374	86	52	by	by	ADP
ejpam-5374	86	53	other	other	ADJ
ejpam-5374	86	54	researchers	researcher	NOUN
ejpam-5374	86	55	,	,	PUNCT
ejpam-5374	86	56	see	see	VERB
ejpam-5374	86	57	,	,	PUNCT
ejpam-5374	86	58	for	for	ADP
ejpam-5374	86	59	example	example	NOUN
ejpam-5374	86	60	,	,	PUNCT
ejpam-5374	86	61	[	[	X
ejpam-5374	86	62	13	13	NUM
ejpam-5374	86	63	,	,	PUNCT
ejpam-5374	86	64	18	18	NUM
ejpam-5374	86	65	,	,	PUNCT
ejpam-5374	86	66	19	19	NUM
ejpam-5374	86	67	,	,	PUNCT
ejpam-5374	86	68	21	21	NUM
ejpam-5374	86	69	,	,	PUNCT
ejpam-5374	86	70	25	25	NUM
ejpam-5374	86	71	,	,	PUNCT
ejpam-5374	86	72	27	27	NUM
ejpam-5374	86	73	,	,	PUNCT
ejpam-5374	86	74	36	36	NUM
ejpam-5374	86	75	,	,	PUNCT
ejpam-5374	86	76	40	40	NUM
ejpam-5374	86	77	]	]	PUNCT
ejpam-5374	86	78	,	,	PUNCT
ejpam-5374	86	79	suggesting	suggest	VERB
ejpam-5374	86	80	different	different	ADJ
ejpam-5374	86	81	directions	direction	NOUN
ejpam-5374	86	82	than	than	ADP
ejpam-5374	86	83	the	the	DET
ejpam-5374	86	84	current	current	ADJ
ejpam-5374	86	85	study	study	NOUN
ejpam-5374	86	86	.	.	PUNCT
ejpam-5374	87	1	n.h.a.a	n.h.a.a	PROPN
ejpam-5374	87	2	.	.	PROPN
ejpam-5374	87	3	wahid	wahid	PROPN
ejpam-5374	87	4	,	,	PUNCT
ejpam-5374	87	5	i.q	i.q	PROPN
ejpam-5374	87	6	.	.	PROPN
ejpam-5374	87	7	amirnuddin	amirnuddin	PROPN
ejpam-5374	87	8	,	,	PUNCT
ejpam-5374	87	9	n.i.m	n.i.m	NOUN
ejpam-5374	87	10	.	.	PUNCT
ejpam-5374	88	1	azmi	azmi	PROPN
ejpam-5374	88	2	/	/	SYM
ejpam-5374	88	3	eur	eur	PROPN
ejpam-5374	88	4	.	.	PUNCT
ejpam-5374	89	1	j.	j.	PROPN
ejpam-5374	89	2	pure	pure	PROPN
ejpam-5374	89	3	appl	appl	PROPN
ejpam-5374	89	4	.	.	PROPN
ejpam-5374	89	5	math	math	PROPN
ejpam-5374	89	6	,	,	PUNCT
ejpam-5374	89	7	17	17	NUM
ejpam-5374	89	8	(	(	PUNCT
ejpam-5374	89	9	4	4	NUM
ejpam-5374	89	10	)	)	PUNCT
ejpam-5374	89	11	(	(	PUNCT
ejpam-5374	89	12	2024	2024	NUM
ejpam-5374	89	13	)	)	PUNCT
ejpam-5374	89	14	,	,	PUNCT
ejpam-5374	89	15	2738	2738	NUM
ejpam-5374	89	16	-	-	SYM
ejpam-5374	89	17	2752	2752	NUM
ejpam-5374	89	18	2742	2742	NUM
ejpam-5374	89	19	2	2	NUM
ejpam-5374	89	20	.	.	PUNCT
ejpam-5374	89	21	preliminary	preliminary	ADJ
ejpam-5374	89	22	results	result	NOUN
ejpam-5374	89	23	let	let	VERB
ejpam-5374	89	24	p	p	PRON
ejpam-5374	89	25	denote	denote	VERB
ejpam-5374	89	26	the	the	DET
ejpam-5374	89	27	class	class	NOUN
ejpam-5374	89	28	of	of	ADP
ejpam-5374	89	29	positive	positive	ADJ
ejpam-5374	89	30	real	real	ADJ
ejpam-5374	89	31	part	part	NOUN
ejpam-5374	89	32	functions	function	NOUN
ejpam-5374	89	33	p	p	X
ejpam-5374	89	34	(	(	PUNCT
ejpam-5374	89	35	z	z	NOUN
ejpam-5374	89	36	)	)	PUNCT
ejpam-5374	89	37	,	,	PUNCT
ejpam-5374	89	38	also	also	ADV
ejpam-5374	89	39	known	know	VERB
ejpam-5374	89	40	as	as	ADP
ejpam-5374	89	41	carathéodory	carathéodory	NOUN
ejpam-5374	89	42	functions	function	NOUN
ejpam-5374	89	43	,	,	PUNCT
ejpam-5374	89	44	of	of	ADP
ejpam-5374	89	45	the	the	DET
ejpam-5374	89	46	form	form	NOUN
ejpam-5374	89	47	p	p	X
ejpam-5374	89	48	(	(	PUNCT
ejpam-5374	89	49	z	z	NOUN
ejpam-5374	89	50	)	)	PUNCT
ejpam-5374	89	51	=	=	SYM
ejpam-5374	90	1	1	1	NUM
ejpam-5374	90	2	+	+	CCONJ
ejpam-5374	90	3	∞∑	∞∑	NUM
ejpam-5374	90	4	n=1	n=1	PROPN
ejpam-5374	90	5	pnz	pnz	NOUN
ejpam-5374	90	6	n	n	CCONJ
ejpam-5374	90	7	,	,	PUNCT
ejpam-5374	90	8	(	(	PUNCT
ejpam-5374	90	9	16	16	NUM
ejpam-5374	90	10	)	)	PUNCT
ejpam-5374	90	11	which	which	PRON
ejpam-5374	90	12	satisfy	satisfy	VERB
ejpam-5374	90	13	re	re	ADP
ejpam-5374	90	14	p	p	PROPN
ejpam-5374	90	15	(	(	PUNCT
ejpam-5374	90	16	z	z	NOUN
ejpam-5374	90	17	)	)	PUNCT
ejpam-5374	90	18	>	>	X
ejpam-5374	90	19	0	0	PUNCT
ejpam-5374	91	1	for	for	SCONJ
ejpam-5374	91	2	z	z	PROPN
ejpam-5374	91	3	∈	∈	PROPN
ejpam-5374	91	4	e.	e.	PROPN
ejpam-5374	91	5	to	to	PART
ejpam-5374	91	6	verify	verify	VERB
ejpam-5374	91	7	our	our	PRON
ejpam-5374	91	8	main	main	ADJ
ejpam-5374	91	9	findings	finding	NOUN
ejpam-5374	91	10	,	,	PUNCT
ejpam-5374	91	11	we	we	PRON
ejpam-5374	91	12	require	require	VERB
ejpam-5374	91	13	a	a	DET
ejpam-5374	91	14	few	few	ADJ
ejpam-5374	91	15	sharp	sharp	ADJ
ejpam-5374	91	16	estimates	estimate	NOUN
ejpam-5374	91	17	in	in	ADP
ejpam-5374	91	18	the	the	DET
ejpam-5374	91	19	form	form	NOUN
ejpam-5374	91	20	of	of	ADP
ejpam-5374	91	21	lemmas	lemmas	ADJ
ejpam-5374	91	22	valid	valid	NOUN
ejpam-5374	91	23	for	for	ADP
ejpam-5374	91	24	functions	function	NOUN
ejpam-5374	91	25	with	with	ADP
ejpam-5374	91	26	a	a	DET
ejpam-5374	91	27	positive	positive	ADJ
ejpam-5374	91	28	real	real	ADJ
ejpam-5374	91	29	part	part	NOUN
ejpam-5374	91	30	,	,	PUNCT
ejpam-5374	91	31	as	as	SCONJ
ejpam-5374	91	32	follows	follow	VERB
ejpam-5374	91	33	:	:	PUNCT
ejpam-5374	91	34	lemma	lemma	PROPN
ejpam-5374	91	35	1	1	NUM
ejpam-5374	91	36	.	.	PUNCT
ejpam-5374	92	1	(	(	PUNCT
ejpam-5374	92	2	[	[	X
ejpam-5374	92	3	10	10	NUM
ejpam-5374	92	4	]	]	PUNCT
ejpam-5374	92	5	)	)	PUNCT
ejpam-5374	92	6	for	for	ADP
ejpam-5374	92	7	a	a	DET
ejpam-5374	92	8	function	function	NOUN
ejpam-5374	92	9	p	p	NOUN
ejpam-5374	92	10	(	(	PUNCT
ejpam-5374	92	11	z	z	NOUN
ejpam-5374	92	12	)	)	PUNCT
ejpam-5374	92	13	∈	∈	PROPN
ejpam-5374	92	14	p	p	NOUN
ejpam-5374	92	15	of	of	ADP
ejpam-5374	92	16	the	the	DET
ejpam-5374	92	17	form	form	NOUN
ejpam-5374	92	18	(	(	PUNCT
ejpam-5374	92	19	16	16	NUM
ejpam-5374	92	20	)	)	PUNCT
ejpam-5374	92	21	,	,	PUNCT
ejpam-5374	92	22	the	the	DET
ejpam-5374	92	23	sharp	sharp	ADJ
ejpam-5374	92	24	inequality	inequality	NOUN
ejpam-5374	92	25	|pn|	|pn|	ADJ
ejpam-5374	92	26	⩽	⩽	ADJ
ejpam-5374	92	27	2	2	NUM
ejpam-5374	92	28	holds	hold	VERB
ejpam-5374	92	29	for	for	ADP
ejpam-5374	92	30	each	each	DET
ejpam-5374	92	31	n	n	CCONJ
ejpam-5374	92	32	⩾	⩾	NOUN
ejpam-5374	92	33	1	1	X
ejpam-5374	92	34	.	.	X
ejpam-5374	93	1	equality	equality	NOUN
ejpam-5374	93	2	holds	hold	VERB
ejpam-5374	93	3	for	for	ADP
ejpam-5374	93	4	the	the	DET
ejpam-5374	93	5	function	function	NOUN
ejpam-5374	93	6	p	p	NOUN
ejpam-5374	93	7	(	(	PUNCT
ejpam-5374	93	8	z	z	NOUN
ejpam-5374	93	9	)	)	PUNCT
ejpam-5374	93	10	=	=	SYM
ejpam-5374	94	1	1+z	1+z	NUM
ejpam-5374	94	2	1−z	1−z	NUM
ejpam-5374	94	3	.	.	PUNCT
ejpam-5374	95	1	lemma	lemma	PROPN
ejpam-5374	95	2	2	2	NUM
ejpam-5374	95	3	.	.	PUNCT
ejpam-5374	96	1	(	(	PUNCT
ejpam-5374	96	2	[	[	X
ejpam-5374	96	3	11	11	NUM
ejpam-5374	96	4	]	]	PUNCT
ejpam-5374	96	5	)	)	PUNCT
ejpam-5374	96	6	let	let	VERB
ejpam-5374	96	7	p	p	NOUN
ejpam-5374	96	8	(	(	PUNCT
ejpam-5374	96	9	z	z	NOUN
ejpam-5374	96	10	)	)	PUNCT
ejpam-5374	96	11	∈	∈	PROPN
ejpam-5374	96	12	p	p	NOUN
ejpam-5374	96	13	be	be	AUX
ejpam-5374	96	14	a	a	DET
ejpam-5374	96	15	function	function	NOUN
ejpam-5374	96	16	of	of	ADP
ejpam-5374	96	17	the	the	DET
ejpam-5374	96	18	form	form	NOUN
ejpam-5374	96	19	(	(	PUNCT
ejpam-5374	96	20	16	16	NUM
ejpam-5374	96	21	)	)	PUNCT
ejpam-5374	96	22	and	and	CCONJ
ejpam-5374	96	23	µ	µ	PROPN
ejpam-5374	96	24	∈	∈	PROPN
ejpam-5374	96	25	c.	c.	NOUN
ejpam-5374	97	1	then	then	ADV
ejpam-5374	97	2	|pn	|pn	X
ejpam-5374	97	3	−	−	PROPN
ejpam-5374	97	4	µpkpn−k|	µpkpn−k|	PROPN
ejpam-5374	97	5	⩽	⩽	NOUN
ejpam-5374	97	6	2max	2max	NUM
ejpam-5374	97	7	{	{	PUNCT
ejpam-5374	97	8	1	1	NUM
ejpam-5374	97	9	,	,	PUNCT
ejpam-5374	97	10	|2µ−	|2µ−	NOUN
ejpam-5374	97	11	1|	1|	NUM
ejpam-5374	97	12	}	}	PUNCT
ejpam-5374	97	13	,	,	PUNCT
ejpam-5374	97	14	1	1	NUM
ejpam-5374	97	15	⩽	⩽	NOUN
ejpam-5374	97	16	k	k	PROPN
ejpam-5374	97	17	⩽	⩽	ADJ
ejpam-5374	97	18	n−	n−	PROPN
ejpam-5374	97	19	1	1	NUM
ejpam-5374	97	20	.	.	PUNCT
ejpam-5374	98	1	if	if	SCONJ
ejpam-5374	98	2	|2µ−	|2µ−	NOUN
ejpam-5374	98	3	1|	1|	NUM
ejpam-5374	98	4	⩾	⩾	NOUN
ejpam-5374	98	5	1	1	NUM
ejpam-5374	98	6	,	,	PUNCT
ejpam-5374	98	7	then	then	ADV
ejpam-5374	98	8	the	the	DET
ejpam-5374	98	9	inequality	inequality	NOUN
ejpam-5374	98	10	is	be	AUX
ejpam-5374	98	11	sharp	sharp	ADJ
ejpam-5374	98	12	for	for	ADP
ejpam-5374	98	13	the	the	DET
ejpam-5374	98	14	function	function	NOUN
ejpam-5374	98	15	p	p	NOUN
ejpam-5374	98	16	(	(	PUNCT
ejpam-5374	98	17	z	z	NOUN
ejpam-5374	98	18	)	)	PUNCT
ejpam-5374	99	1	=	=	SYM
ejpam-5374	99	2	1+z	1+z	NUM
ejpam-5374	99	3	1−z	1−z	NUM
ejpam-5374	99	4	or	or	CCONJ
ejpam-5374	99	5	its	its	PRON
ejpam-5374	99	6	rotations	rotation	NOUN
ejpam-5374	99	7	.	.	PUNCT
ejpam-5374	100	1	if	if	SCONJ
ejpam-5374	100	2	|2µ−	|2µ−	NOUN
ejpam-5374	100	3	1|	1|	X
ejpam-5374	100	4	<	<	X
ejpam-5374	100	5	1	1	NUM
ejpam-5374	100	6	,	,	PUNCT
ejpam-5374	100	7	then	then	ADV
ejpam-5374	100	8	the	the	DET
ejpam-5374	100	9	inequality	inequality	NOUN
ejpam-5374	100	10	is	be	AUX
ejpam-5374	100	11	sharp	sharp	ADJ
ejpam-5374	100	12	for	for	ADP
ejpam-5374	100	13	the	the	DET
ejpam-5374	100	14	function	function	NOUN
ejpam-5374	100	15	p	p	NOUN
ejpam-5374	100	16	(	(	PUNCT
ejpam-5374	100	17	z	z	NOUN
ejpam-5374	100	18	)	)	PUNCT
ejpam-5374	100	19	=	=	PUNCT
ejpam-5374	101	1	1+zn	1+zn	NUM
ejpam-5374	101	2	1−zn	1−zn	NUM
ejpam-5374	101	3	or	or	CCONJ
ejpam-5374	101	4	its	its	PRON
ejpam-5374	101	5	rotations	rotation	NOUN
ejpam-5374	101	6	.	.	PUNCT
ejpam-5374	102	1	3	3	X
ejpam-5374	102	2	.	.	X
ejpam-5374	102	3	main	main	ADJ
ejpam-5374	102	4	results	result	NOUN
ejpam-5374	102	5	this	this	DET
ejpam-5374	102	6	section	section	NOUN
ejpam-5374	102	7	presents	present	VERB
ejpam-5374	102	8	the	the	DET
ejpam-5374	102	9	proof	proof	NOUN
ejpam-5374	102	10	of	of	ADP
ejpam-5374	102	11	our	our	PRON
ejpam-5374	102	12	main	main	ADJ
ejpam-5374	102	13	findings	finding	NOUN
ejpam-5374	102	14	,	,	PUNCT
ejpam-5374	102	15	primarily	primarily	ADV
ejpam-5374	102	16	focusing	focus	VERB
ejpam-5374	102	17	on	on	ADP
ejpam-5374	102	18	the	the	DET
ejpam-5374	102	19	upper	upper	ADJ
ejpam-5374	102	20	bounds	bound	NOUN
ejpam-5374	102	21	of	of	ADP
ejpam-5374	102	22	logarithmic	logarithmic	ADJ
ejpam-5374	102	23	coefficients	coefficient	NOUN
ejpam-5374	102	24	and	and	CCONJ
ejpam-5374	102	25	three	three	NUM
ejpam-5374	102	26	types	type	NOUN
ejpam-5374	102	27	of	of	ADP
ejpam-5374	102	28	determinants	determinant	NOUN
ejpam-5374	102	29	(	(	PUNCT
ejpam-5374	102	30	hankel	hankel	NOUN
ejpam-5374	102	31	,	,	PUNCT
ejpam-5374	102	32	toeplitz	toeplitz	NOUN
ejpam-5374	102	33	,	,	PUNCT
ejpam-5374	102	34	and	and	CCONJ
ejpam-5374	102	35	vandermonde	vandermonde	NOUN
ejpam-5374	102	36	)	)	PUNCT
ejpam-5374	102	37	for	for	ADP
ejpam-5374	102	38	the	the	DET
ejpam-5374	102	39	class	class	NOUN
ejpam-5374	102	40	g	g	PROPN
ejpam-5374	102	41	(	(	PUNCT
ejpam-5374	102	42	α	α	PROPN
ejpam-5374	102	43	,	,	PUNCT
ejpam-5374	102	44	δ	δ	PROPN
ejpam-5374	102	45	)	)	PUNCT
ejpam-5374	102	46	.	.	PUNCT
ejpam-5374	103	1	3.1	3.1	NUM
ejpam-5374	103	2	.	.	PUNCT
ejpam-5374	104	1	logarithmic	logarithmic	ADJ
ejpam-5374	104	2	coefficients	coefficient	NOUN
ejpam-5374	104	3	for	for	ADP
ejpam-5374	104	4	g(α	g(α	PROPN
ejpam-5374	104	5	,	,	PUNCT
ejpam-5374	104	6	δ	δ	PROPN
ejpam-5374	104	7	)	)	PUNCT
ejpam-5374	104	8	we	we	PRON
ejpam-5374	104	9	now	now	ADV
ejpam-5374	104	10	estimate	estimate	VERB
ejpam-5374	104	11	the	the	DET
ejpam-5374	104	12	upper	upper	ADJ
ejpam-5374	104	13	bounds	bound	NOUN
ejpam-5374	104	14	of	of	ADP
ejpam-5374	104	15	the	the	DET
ejpam-5374	104	16	logarithmic	logarithmic	ADJ
ejpam-5374	104	17	coefficients	coefficient	NOUN
ejpam-5374	104	18	for	for	ADP
ejpam-5374	104	19	functions	function	NOUN
ejpam-5374	104	20	belonging	belong	VERB
ejpam-5374	104	21	to	to	ADP
ejpam-5374	104	22	g	g	PROPN
ejpam-5374	104	23	(	(	PUNCT
ejpam-5374	104	24	α	α	PROPN
ejpam-5374	104	25	,	,	PUNCT
ejpam-5374	104	26	δ	δ	PROPN
ejpam-5374	104	27	)	)	PUNCT
ejpam-5374	104	28	.	.	PUNCT
ejpam-5374	105	1	theorem	theorem	NOUN
ejpam-5374	105	2	1	1	NUM
ejpam-5374	105	3	.	.	PUNCT
ejpam-5374	106	1	if	if	SCONJ
ejpam-5374	106	2	f	f	PROPN
ejpam-5374	106	3	(	(	PUNCT
ejpam-5374	106	4	z	z	NOUN
ejpam-5374	106	5	)	)	PUNCT
ejpam-5374	106	6	=	=	SYM
ejpam-5374	106	7	z	z	NOUN
ejpam-5374	107	1	+	+	NOUN
ejpam-5374	107	2	∞∑	∞∑	NUM
ejpam-5374	107	3	n=2	n=2	CCONJ
ejpam-5374	107	4	anz	anz	NOUN
ejpam-5374	107	5	n	n	ADP
ejpam-5374	107	6	∈	∈	PROPN
ejpam-5374	107	7	g	g	PROPN
ejpam-5374	107	8	(	(	PUNCT
ejpam-5374	107	9	α	α	PROPN
ejpam-5374	107	10	,	,	PUNCT
ejpam-5374	107	11	δ	δ	PROPN
ejpam-5374	107	12	)	)	PUNCT
ejpam-5374	107	13	,	,	PUNCT
ejpam-5374	107	14	then	then	ADV
ejpam-5374	107	15	|γ1|	|γ1|	PROPN
ejpam-5374	107	16	≤	≤	PROPN
ejpam-5374	107	17	tαδ	tαδ	VERB
ejpam-5374	107	18	2	2	NUM
ejpam-5374	107	19	,	,	PUNCT
ejpam-5374	107	20	|γ2|	|γ2|	VERB
ejpam-5374	107	21	≤	≤	NUM
ejpam-5374	107	22	tαδ	tαδ	VERB
ejpam-5374	107	23	3	3	NUM
ejpam-5374	107	24	,	,	PUNCT
ejpam-5374	107	25	|γ3|	|γ3|	ADJ
ejpam-5374	107	26	≤	≤	NUM
ejpam-5374	107	27	tαδ	tαδ	VERB
ejpam-5374	107	28	4	4	NUM
ejpam-5374	107	29	+	+	CCONJ
ejpam-5374	107	30	tαδ	tαδ	PRON
ejpam-5374	107	31	3	3	NUM
ejpam-5374	107	32	6	6	NUM
ejpam-5374	107	33	,	,	PUNCT
ejpam-5374	107	34	and	and	CCONJ
ejpam-5374	107	35	|γ4|	|γ4|	NOUN
ejpam-5374	107	36	≤	≤	NOUN
ejpam-5374	107	37	tαδ	tαδ	VERB
ejpam-5374	107	38	5	5	NUM
ejpam-5374	107	39	+	+	CCONJ
ejpam-5374	107	40	tαδ	tαδ	PRON
ejpam-5374	107	41	2	2	NUM
ejpam-5374	107	42	4	4	NUM
ejpam-5374	107	43	+	+	CCONJ
ejpam-5374	107	44	tαδ	tαδ	PRON
ejpam-5374	107	45	4	4	NUM
ejpam-5374	107	46	8	8	NUM
ejpam-5374	107	47	,	,	PUNCT
ejpam-5374	107	48	where	where	SCONJ
ejpam-5374	107	49	tαδ	tαδ	NOUN
ejpam-5374	107	50	=	=	SYM
ejpam-5374	107	51	cosα−	cosα−	PROPN
ejpam-5374	107	52	δ	δ	PROPN
ejpam-5374	107	53	.	.	PUNCT
ejpam-5374	108	1	n.h.a.a	n.h.a.a	PROPN
ejpam-5374	108	2	.	.	PROPN
ejpam-5374	108	3	wahid	wahid	PROPN
ejpam-5374	108	4	,	,	PUNCT
ejpam-5374	108	5	i.q	i.q	PROPN
ejpam-5374	108	6	.	.	PROPN
ejpam-5374	108	7	amirnuddin	amirnuddin	PROPN
ejpam-5374	108	8	,	,	PUNCT
ejpam-5374	108	9	n.i.m	n.i.m	NOUN
ejpam-5374	108	10	.	.	PUNCT
ejpam-5374	109	1	azmi	azmi	PROPN
ejpam-5374	109	2	/	/	SYM
ejpam-5374	109	3	eur	eur	PROPN
ejpam-5374	109	4	.	.	PUNCT
ejpam-5374	110	1	j.	j.	PROPN
ejpam-5374	110	2	pure	pure	PROPN
ejpam-5374	110	3	appl	appl	PROPN
ejpam-5374	110	4	.	.	PROPN
ejpam-5374	110	5	math	math	PROPN
ejpam-5374	110	6	,	,	PUNCT
ejpam-5374	110	7	17	17	NUM
ejpam-5374	110	8	(	(	PUNCT
ejpam-5374	110	9	4	4	NUM
ejpam-5374	110	10	)	)	PUNCT
ejpam-5374	110	11	(	(	PUNCT
ejpam-5374	110	12	2024	2024	NUM
ejpam-5374	110	13	)	)	PUNCT
ejpam-5374	110	14	,	,	PUNCT
ejpam-5374	110	15	2738	2738	NUM
ejpam-5374	110	16	-	-	SYM
ejpam-5374	110	17	2752	2752	NUM
ejpam-5374	110	18	2743	2743	NUM
ejpam-5374	110	19	proof	proof	NOUN
ejpam-5374	110	20	.	.	PUNCT
ejpam-5374	111	1	let	let	VERB
ejpam-5374	111	2	a	a	DET
ejpam-5374	111	3	function	function	NOUN
ejpam-5374	111	4	f	f	X
ejpam-5374	111	5	(	(	PUNCT
ejpam-5374	111	6	z	z	NOUN
ejpam-5374	111	7	)	)	PUNCT
ejpam-5374	111	8	∈	∈	PROPN
ejpam-5374	111	9	g	g	PROPN
ejpam-5374	111	10	(	(	PUNCT
ejpam-5374	111	11	α	α	PROPN
ejpam-5374	111	12	,	,	PUNCT
ejpam-5374	111	13	δ	δ	PROPN
ejpam-5374	111	14	)	)	PUNCT
ejpam-5374	111	15	given	give	VERB
ejpam-5374	111	16	by	by	ADP
ejpam-5374	111	17	(	(	PUNCT
ejpam-5374	111	18	1	1	NUM
ejpam-5374	111	19	)	)	PUNCT
ejpam-5374	111	20	.	.	PUNCT
ejpam-5374	112	1	then	then	ADV
ejpam-5374	112	2	there	there	PRON
ejpam-5374	112	3	exists	exist	VERB
ejpam-5374	112	4	a	a	DET
ejpam-5374	112	5	function	function	NOUN
ejpam-5374	112	6	p	p	X
ejpam-5374	112	7	(	(	PUNCT
ejpam-5374	112	8	z	z	NOUN
ejpam-5374	112	9	)	)	PUNCT
ejpam-5374	112	10	∈	∈	PROPN
ejpam-5374	112	11	p	p	NOUN
ejpam-5374	112	12	such	such	ADJ
ejpam-5374	112	13	that	that	SCONJ
ejpam-5374	112	14	[	[	X
ejpam-5374	112	15	34	34	NUM
ejpam-5374	112	16	]	]	PUNCT
ejpam-5374	112	17	eiαf	eiαf	NOUN
ejpam-5374	112	18	′	′	NUM
ejpam-5374	113	1	(	(	PUNCT
ejpam-5374	113	2	z)−	z)−	NOUN
ejpam-5374	113	3	i	i	PRON
ejpam-5374	113	4	sinα−	sinα−	VERB
ejpam-5374	113	5	δ	δ	PROPN
ejpam-5374	113	6	tαδ	tαδ	VERB
ejpam-5374	113	7	=	=	SYM
ejpam-5374	113	8	p(z	p(z	PROPN
ejpam-5374	113	9	)	)	PUNCT
ejpam-5374	113	10	,	,	PUNCT
ejpam-5374	113	11	where	where	SCONJ
ejpam-5374	113	12	tαδ	tαδ	NOUN
ejpam-5374	113	13	=	=	SYM
ejpam-5374	113	14	cosα−	cosα−	PROPN
ejpam-5374	113	15	δ	δ	PROPN
ejpam-5374	113	16	,	,	PUNCT
ejpam-5374	113	17	p	p	X
ejpam-5374	113	18	(	(	PUNCT
ejpam-5374	113	19	z	z	NOUN
ejpam-5374	113	20	)	)	PUNCT
ejpam-5374	113	21	=	=	SYM
ejpam-5374	113	22	1	1	NUM
ejpam-5374	113	23	+	+	CCONJ
ejpam-5374	113	24	∞∑	∞∑	NUM
ejpam-5374	113	25	n=1	n=1	PROPN
ejpam-5374	113	26	pnz	pnz	NOUN
ejpam-5374	113	27	n	n	CCONJ
ejpam-5374	113	28	,	,	PUNCT
ejpam-5374	113	29	and	and	CCONJ
ejpam-5374	113	30	f	f	PROPN
ejpam-5374	113	31	′	′	NUM
ejpam-5374	114	1	(	(	PUNCT
ejpam-5374	114	2	z	z	NOUN
ejpam-5374	114	3	)	)	PUNCT
ejpam-5374	114	4	=	=	SYM
ejpam-5374	114	5	1	1	NUM
ejpam-5374	114	6	+	+	NUM
ejpam-5374	114	7	n	n	CCONJ
ejpam-5374	114	8	∞∑	∞∑	NUM
ejpam-5374	114	9	n=2	n=2	ADV
ejpam-5374	114	10	anz	anz	PROPN
ejpam-5374	114	11	n−1	n−1	PROPN
ejpam-5374	114	12	.	.	PUNCT
ejpam-5374	115	1	moreover	moreover	ADV
ejpam-5374	115	2	,	,	PUNCT
ejpam-5374	115	3	it	it	PRON
ejpam-5374	115	4	can	can	AUX
ejpam-5374	115	5	be	be	AUX
ejpam-5374	115	6	observed	observe	VERB
ejpam-5374	115	7	that	that	SCONJ
ejpam-5374	115	8	an	an	DET
ejpam-5374	115	9	=	=	ADJ
ejpam-5374	115	10	tαδe	tαδe	NOUN
ejpam-5374	115	11	−iαpn−1	−iαpn−1	NOUN
ejpam-5374	115	12	n	n	NOUN
ejpam-5374	115	13	,	,	PUNCT
ejpam-5374	115	14	n	n	CCONJ
ejpam-5374	115	15	⩾	⩾	NOUN
ejpam-5374	115	16	2	2	NUM
ejpam-5374	115	17	,	,	PUNCT
ejpam-5374	115	18	(	(	PUNCT
ejpam-5374	115	19	17	17	NUM
ejpam-5374	115	20	)	)	PUNCT
ejpam-5374	115	21	and	and	CCONJ
ejpam-5374	115	22	specifically	specifically	ADV
ejpam-5374	115	23	,	,	PUNCT
ejpam-5374	115	24	for	for	ADP
ejpam-5374	115	25	n	n	NOUN
ejpam-5374	115	26	=	=	SYM
ejpam-5374	115	27	2	2	NUM
ejpam-5374	115	28	,	,	PUNCT
ejpam-5374	115	29	3	3	NUM
ejpam-5374	115	30	,	,	PUNCT
ejpam-5374	115	31	4	4	NUM
ejpam-5374	115	32	,	,	PUNCT
ejpam-5374	115	33	5	5	NUM
ejpam-5374	115	34	,	,	PUNCT
ejpam-5374	115	35	we	we	PRON
ejpam-5374	115	36	get	get	VERB
ejpam-5374	115	37	a2	a2	NOUN
ejpam-5374	115	38	=	=	SYM
ejpam-5374	116	1	tαδe	tαδe	NOUN
ejpam-5374	116	2	−iαp1	−iαp1	PROPN
ejpam-5374	116	3	2	2	NUM
ejpam-5374	116	4	,	,	PUNCT
ejpam-5374	116	5	a3	a3	NOUN
ejpam-5374	116	6	=	=	SYM
ejpam-5374	116	7	tαδe	tαδe	NOUN
ejpam-5374	116	8	−iαp2	−iαp2	NOUN
ejpam-5374	116	9	3	3	NUM
ejpam-5374	116	10	,	,	PUNCT
ejpam-5374	116	11	a4	a4	NOUN
ejpam-5374	116	12	=	=	SYM
ejpam-5374	116	13	tαδe	tαδe	NOUN
ejpam-5374	116	14	−iαp3	−iαp3	NOUN
ejpam-5374	116	15	4	4	NUM
ejpam-5374	116	16	,	,	PUNCT
ejpam-5374	116	17	a5	a5	PROPN
ejpam-5374	116	18	=	=	SYM
ejpam-5374	116	19	tαδe	tαδe	ADJ
ejpam-5374	116	20	−iαp4	−iαp4	NOUN
ejpam-5374	116	21	5	5	NUM
ejpam-5374	116	22	.	.	PUNCT
ejpam-5374	117	1			NOUN
ejpam-5374	117	2	(	(	PUNCT
ejpam-5374	117	3	18	18	NUM
ejpam-5374	117	4	)	)	PUNCT
ejpam-5374	117	5	substituting	substituting	NOUN
ejpam-5374	117	6	(	(	PUNCT
ejpam-5374	117	7	18	18	NUM
ejpam-5374	117	8	)	)	PUNCT
ejpam-5374	117	9	into	into	ADP
ejpam-5374	117	10	(	(	PUNCT
ejpam-5374	117	11	7)-(10	7)-(10	NOUN
ejpam-5374	117	12	)	)	PUNCT
ejpam-5374	117	13	yields	yield	NOUN
ejpam-5374	117	14	γ1	γ1	NOUN
ejpam-5374	117	15	=	=	SYM
ejpam-5374	117	16	tαδe	tαδe	NOUN
ejpam-5374	117	17	−iαp1	−iαp1	PROPN
ejpam-5374	117	18	4	4	NUM
ejpam-5374	117	19	,	,	PUNCT
ejpam-5374	117	20	(	(	PUNCT
ejpam-5374	117	21	19	19	NUM
ejpam-5374	117	22	)	)	PUNCT
ejpam-5374	117	23	γ2	γ2	NOUN
ejpam-5374	117	24	=	=	SYM
ejpam-5374	117	25	tαδe	tαδe	PROPN
ejpam-5374	117	26	−iα	−iα	VERB
ejpam-5374	117	27	48	48	NUM
ejpam-5374	117	28	(	(	PUNCT
ejpam-5374	117	29	8p2	8p2	NUM
ejpam-5374	117	30	−	−	PROPN
ejpam-5374	117	31	3tαδe	3tαδe	NUM
ejpam-5374	117	32	−iαp21	−iαp21	VERB
ejpam-5374	117	33	)	)	PUNCT
ejpam-5374	117	34	,	,	PUNCT
ejpam-5374	117	35	(	(	PUNCT
ejpam-5374	117	36	20	20	X
ejpam-5374	117	37	)	)	PUNCT
ejpam-5374	117	38	γ3	γ3	NOUN
ejpam-5374	117	39	=	=	SYM
ejpam-5374	117	40	tαδe	tαδe	PROPN
ejpam-5374	117	41	−iα	−iα	VERB
ejpam-5374	117	42	48	48	NUM
ejpam-5374	117	43	(	(	PUNCT
ejpam-5374	117	44	6p3	6p3	NUM
ejpam-5374	117	45	−	−	NOUN
ejpam-5374	118	1	4tαδe	4tαδe	NUM
ejpam-5374	118	2	−iαp1p2	−iαp1p2	NOUN
ejpam-5374	118	3	+	+	CCONJ
ejpam-5374	118	4	tαδ	tαδ	PRON
ejpam-5374	118	5	2e−2iαp31	2e−2iαp31	PROPN
ejpam-5374	118	6	)	)	PUNCT
ejpam-5374	118	7	,	,	PUNCT
ejpam-5374	118	8	(	(	PUNCT
ejpam-5374	118	9	21	21	NUM
ejpam-5374	118	10	)	)	PUNCT
ejpam-5374	118	11	and	and	CCONJ
ejpam-5374	118	12	γ4	γ4	NOUN
ejpam-5374	118	13	=	=	SYM
ejpam-5374	118	14	tαδe	tαδe	NOUN
ejpam-5374	118	15	−iαp4	−iαp4	NOUN
ejpam-5374	118	16	10	10	NUM
ejpam-5374	118	17	−	−	NOUN
ejpam-5374	118	18	tαδ	tαδ	VERB
ejpam-5374	118	19	2e−2iαp22	2e−2iαp22	NUM
ejpam-5374	118	20	36	36	NUM
ejpam-5374	118	21	−	−	NOUN
ejpam-5374	118	22	tαδ	tαδ	VERB
ejpam-5374	118	23	2e−2iαp1p3	2e−2iαp1p3	NUM
ejpam-5374	118	24	16	16	NUM
ejpam-5374	118	25	+	+	CCONJ
ejpam-5374	118	26	tαδ	tαδ	PRON
ejpam-5374	118	27	3e−3iαp21p2	3e−3iαp21p2	NUM
ejpam-5374	118	28	24	24	NUM
ejpam-5374	118	29	−	−	NOUN
ejpam-5374	118	30	tαδ	tαδ	VERB
ejpam-5374	118	31	4e−4iαp41	4e−4iαp41	PROPN
ejpam-5374	118	32	128	128	NUM
ejpam-5374	118	33	.	.	PUNCT
ejpam-5374	119	1	(	(	PUNCT
ejpam-5374	119	2	22	22	NUM
ejpam-5374	119	3	)	)	PUNCT
ejpam-5374	119	4	hence	hence	ADV
ejpam-5374	119	5	,	,	PUNCT
ejpam-5374	119	6	we	we	PRON
ejpam-5374	119	7	can	can	AUX
ejpam-5374	119	8	express	express	VERB
ejpam-5374	119	9	(	(	PUNCT
ejpam-5374	119	10	19)-(22	19)-(22	NUM
ejpam-5374	119	11	)	)	PUNCT
ejpam-5374	119	12	as	as	SCONJ
ejpam-5374	119	13	follows	follow	VERB
ejpam-5374	119	14	:	:	PUNCT
ejpam-5374	119	15	|γ1	|γ1	VERB
ejpam-5374	119	16	|	|	ADV
ejpam-5374	119	17	=	=	PUNCT
ejpam-5374	119	18	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5374	119	19	tαδe−iαp1	tαδe−iαp1	NUM
ejpam-5374	119	20	4	4	NUM
ejpam-5374	119	21	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5374	119	22	,	,	PUNCT
ejpam-5374	119	23	(	(	PUNCT
ejpam-5374	119	24	23	23	NUM
ejpam-5374	119	25	)	)	PUNCT
ejpam-5374	119	26	|γ2|	|γ2|	NOUN
ejpam-5374	119	27	=	=	PUNCT
ejpam-5374	119	28	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5374	119	29	tαδe−iα	tαδe−iα	NUM
ejpam-5374	119	30	48	48	NUM
ejpam-5374	119	31	(	(	PUNCT
ejpam-5374	119	32	8	8	NUM
ejpam-5374	119	33	(	(	PUNCT
ejpam-5374	119	34	p2	p2	PROPN
ejpam-5374	119	35	−	−	PROPN
ejpam-5374	119	36	3tαδe	3tαδe	NUM
ejpam-5374	119	37	−iα	−iα	NOUN
ejpam-5374	119	38	8	8	NUM
ejpam-5374	119	39	p21	p21	NOUN
ejpam-5374	119	40	)	)	PUNCT
ejpam-5374	119	41	)	)	PUNCT
ejpam-5374	120	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5374	120	2	,	,	PUNCT
ejpam-5374	120	3	(	(	PUNCT
ejpam-5374	120	4	24	24	NUM
ejpam-5374	120	5	)	)	PUNCT
ejpam-5374	120	6	|γ3|	|γ3|	NOUN
ejpam-5374	120	7	=	=	PUNCT
ejpam-5374	120	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5374	120	9	tαδe−iα	tαδe−iα	NUM
ejpam-5374	120	10	48	48	NUM
ejpam-5374	120	11	(	(	PUNCT
ejpam-5374	120	12	6	6	NUM
ejpam-5374	120	13	(	(	PUNCT
ejpam-5374	120	14	p3	p3	NOUN
ejpam-5374	120	15	−	−	PROPN
ejpam-5374	121	1	2tαδe	2tαδe	NUM
ejpam-5374	121	2	−iα	−iα	NOUN
ejpam-5374	121	3	3	3	NUM
ejpam-5374	121	4	p1p2	p1p2	NOUN
ejpam-5374	121	5	)	)	PUNCT
ejpam-5374	122	1	+	+	CCONJ
ejpam-5374	122	2	tαδ	tαδ	PRON
ejpam-5374	122	3	2e−2iαp31	2e−2iαp31	PROPN
ejpam-5374	122	4	)	)	PUNCT
ejpam-5374	122	5	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5374	122	6	,	,	PUNCT
ejpam-5374	122	7	(	(	PUNCT
ejpam-5374	122	8	25	25	NUM
ejpam-5374	122	9	)	)	PUNCT
ejpam-5374	122	10	n.h.a.a	n.h.a.a	PROPN
ejpam-5374	122	11	.	.	PROPN
ejpam-5374	122	12	wahid	wahid	PROPN
ejpam-5374	122	13	,	,	PUNCT
ejpam-5374	122	14	i.q	i.q	PROPN
ejpam-5374	122	15	.	.	PROPN
ejpam-5374	122	16	amirnuddin	amirnuddin	PROPN
ejpam-5374	122	17	,	,	PUNCT
ejpam-5374	122	18	n.i.m	n.i.m	NOUN
ejpam-5374	122	19	.	.	PUNCT
ejpam-5374	123	1	azmi	azmi	PROPN
ejpam-5374	123	2	/	/	SYM
ejpam-5374	123	3	eur	eur	PROPN
ejpam-5374	123	4	.	.	PUNCT
ejpam-5374	124	1	j.	j.	PROPN
ejpam-5374	124	2	pure	pure	PROPN
ejpam-5374	124	3	appl	appl	PROPN
ejpam-5374	124	4	.	.	PROPN
ejpam-5374	124	5	math	math	PROPN
ejpam-5374	124	6	,	,	PUNCT
ejpam-5374	124	7	17	17	NUM
ejpam-5374	124	8	(	(	PUNCT
ejpam-5374	124	9	4	4	NUM
ejpam-5374	124	10	)	)	PUNCT
ejpam-5374	124	11	(	(	PUNCT
ejpam-5374	124	12	2024	2024	NUM
ejpam-5374	124	13	)	)	PUNCT
ejpam-5374	124	14	,	,	PUNCT
ejpam-5374	124	15	2738	2738	NUM
ejpam-5374	124	16	-	-	SYM
ejpam-5374	124	17	2752	2752	NUM
ejpam-5374	124	18	2744	2744	NUM
ejpam-5374	124	19	|γ4|	|γ4|	NOUN
ejpam-5374	124	20	=	=	PUNCT
ejpam-5374	125	1	∣∣∣∣tαδe−iα	∣∣∣∣tαδe−iα	PRON
ejpam-5374	125	2	(	(	PUNCT
ejpam-5374	125	3	−	−	PROPN
ejpam-5374	125	4	1	1	NUM
ejpam-5374	125	5	10	10	NUM
ejpam-5374	125	6	(	(	PUNCT
ejpam-5374	125	7	p4	p4	ADJ
ejpam-5374	125	8	−	−	PROPN
ejpam-5374	125	9	10tαδe	10tαδe	NUM
ejpam-5374	125	10	−iα	−iα	NUM
ejpam-5374	125	11	36	36	NUM
ejpam-5374	125	12	p22	p22	NOUN
ejpam-5374	125	13	)	)	PUNCT
ejpam-5374	126	1	+	+	CCONJ
ejpam-5374	126	2	tαδe	tαδe	PROPN
ejpam-5374	126	3	−iαp1	−iαp1	PROPN
ejpam-5374	126	4	16	16	NUM
ejpam-5374	126	5	(	(	PUNCT
ejpam-5374	126	6	p3	p3	PROPN
ejpam-5374	126	7	−	−	PROPN
ejpam-5374	126	8	2tαδe	2tαδe	NUM
ejpam-5374	126	9	−iα	−iα	NOUN
ejpam-5374	126	10	3	3	NUM
ejpam-5374	126	11	p1p2	p1p2	NOUN
ejpam-5374	126	12	)	)	PUNCT
ejpam-5374	127	1	+	+	CCONJ
ejpam-5374	127	2	tαδ	tαδ	VERB
ejpam-5374	127	3	3e−3iαp41	3e−3iαp41	NUM
ejpam-5374	127	4	128	128	NUM
ejpam-5374	127	5	)	)	PUNCT
ejpam-5374	127	6	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5374	127	7	.	.	PUNCT
ejpam-5374	128	1	(	(	PUNCT
ejpam-5374	128	2	26	26	NUM
ejpam-5374	128	3	)	)	PUNCT
ejpam-5374	128	4	applying	apply	VERB
ejpam-5374	128	5	lemma	lemma	PROPN
ejpam-5374	128	6	2	2	NUM
ejpam-5374	128	7	,	,	PUNCT
ejpam-5374	128	8	it	it	PRON
ejpam-5374	128	9	can	can	AUX
ejpam-5374	128	10	be	be	AUX
ejpam-5374	128	11	observed	observe	VERB
ejpam-5374	128	12	that∣∣∣p2	that∣∣∣p2	NOUN
ejpam-5374	128	13	−	−	PROPN
ejpam-5374	128	14	3tαδe	3tαδe	NUM
ejpam-5374	128	15	−iα	−iα	NOUN
ejpam-5374	128	16	8	8	NUM
ejpam-5374	128	17	p21	p21	NOUN
ejpam-5374	128	18	∣∣∣	∣∣∣	NOUN
ejpam-5374	128	19	≤	≤	PROPN
ejpam-5374	128	20	2max	2max	NUM
ejpam-5374	128	21	{	{	PUNCT
ejpam-5374	128	22	1	1	NUM
ejpam-5374	128	23	,	,	PUNCT
ejpam-5374	128	24	∣∣∣3tαδe	∣∣∣3tαδe	NOUN
ejpam-5374	128	25	−iα−4	−iα−4	VERB
ejpam-5374	128	26	4	4	NUM
ejpam-5374	128	27	∣∣∣	∣∣∣	ADJ
ejpam-5374	128	28	}	}	PUNCT
ejpam-5374	128	29	=	=	SYM
ejpam-5374	128	30	2	2	NUM
ejpam-5374	128	31	,	,	PUNCT
ejpam-5374	128	32	∣∣∣p3	∣∣∣p3	PROPN
ejpam-5374	128	33	−	−	PROPN
ejpam-5374	128	34	2tαδe	2tαδe	NUM
ejpam-5374	128	35	−iα	−iα	NOUN
ejpam-5374	128	36	3	3	NUM
ejpam-5374	128	37	p1p2	p1p2	ADV
ejpam-5374	128	38	∣∣∣	∣∣∣	ADJ
ejpam-5374	128	39	≤	≤	ADJ
ejpam-5374	128	40	2max	2max	NUM
ejpam-5374	128	41	{	{	PUNCT
ejpam-5374	128	42	1	1	NUM
ejpam-5374	128	43	,	,	PUNCT
ejpam-5374	128	44	∣∣∣4tαδe	∣∣∣4tαδe	ADP
ejpam-5374	128	45	−iα−3	−iα−3	X
ejpam-5374	128	46	3	3	NUM
ejpam-5374	128	47	∣∣∣	∣∣∣	ADJ
ejpam-5374	128	48	}	}	PUNCT
ejpam-5374	128	49	=	=	SYM
ejpam-5374	128	50	2	2	NUM
ejpam-5374	128	51	,	,	PUNCT
ejpam-5374	128	52	∣∣∣p4	∣∣∣p4	VERB
ejpam-5374	128	53	−	−	PROPN
ejpam-5374	128	54	10tαδe	10tαδe	NUM
ejpam-5374	128	55	−iα	−iα	NUM
ejpam-5374	128	56	36	36	NUM
ejpam-5374	128	57	p22	p22	NOUN
ejpam-5374	128	58	∣∣∣	∣∣∣	ADJ
ejpam-5374	128	59	≤	≤	NOUN
ejpam-5374	128	60	2max	2max	NUM
ejpam-5374	128	61	{	{	PUNCT
ejpam-5374	128	62	1	1	NUM
ejpam-5374	128	63	,	,	PUNCT
ejpam-5374	128	64	∣∣∣5tαδe	∣∣∣5tαδe	NOUN
ejpam-5374	128	65	−iα−9	−iα−9	ADP
ejpam-5374	128	66	9	9	NUM
ejpam-5374	128	67	∣∣∣	∣∣∣	ADJ
ejpam-5374	128	68	}	}	PUNCT
ejpam-5374	128	69	=	=	SYM
ejpam-5374	128	70	2	2	NUM
ejpam-5374	128	71	,	,	PUNCT
ejpam-5374	128	72	∣∣∣p3	∣∣∣p3	PROPN
ejpam-5374	128	73	−	−	PROPN
ejpam-5374	128	74	2tαδe	2tαδe	NUM
ejpam-5374	128	75	−iα	−iα	NOUN
ejpam-5374	128	76	3	3	NUM
ejpam-5374	128	77	p1p2	p1p2	ADV
ejpam-5374	128	78	∣∣∣	∣∣∣	ADJ
ejpam-5374	128	79	≤	≤	ADJ
ejpam-5374	128	80	2max	2max	NUM
ejpam-5374	128	81	{	{	PUNCT
ejpam-5374	128	82	1	1	NUM
ejpam-5374	128	83	,	,	PUNCT
ejpam-5374	128	84	∣∣∣4tαδe	∣∣∣4tαδe	ADP
ejpam-5374	128	85	−iα−3	−iα−3	X
ejpam-5374	128	86	3	3	NUM
ejpam-5374	128	87	∣∣∣	∣∣∣	ADJ
ejpam-5374	128	88	}	}	PUNCT
ejpam-5374	128	89	=	=	SYM
ejpam-5374	128	90	2	2	X
ejpam-5374	128	91	.	.	PUNCT
ejpam-5374	128	92			ADJ
ejpam-5374	128	93	(	(	PUNCT
ejpam-5374	128	94	27	27	NUM
ejpam-5374	128	95	)	)	PUNCT
ejpam-5374	128	96	thus	thus	ADV
ejpam-5374	128	97	,	,	PUNCT
ejpam-5374	128	98	the	the	DET
ejpam-5374	128	99	upper	upper	ADJ
ejpam-5374	128	100	bounds	bound	NOUN
ejpam-5374	128	101	of	of	ADP
ejpam-5374	128	102	|γ1|	|γ1|	NOUN
ejpam-5374	128	103	and	and	CCONJ
ejpam-5374	128	104	|γ2|	|γ2|	PROPN
ejpam-5374	128	105	result	result	NOUN
ejpam-5374	128	106	from	from	ADP
ejpam-5374	128	107	applying	apply	VERB
ejpam-5374	128	108	lemma	lemma	PROPN
ejpam-5374	128	109	1	1	NUM
ejpam-5374	128	110	and	and	CCONJ
ejpam-5374	128	111	lemma	lemma	PROPN
ejpam-5374	128	112	2	2	NUM
ejpam-5374	128	113	,	,	PUNCT
ejpam-5374	128	114	respectively	respectively	ADV
ejpam-5374	128	115	.	.	PUNCT
ejpam-5374	129	1	meanwhile	meanwhile	ADV
ejpam-5374	129	2	,	,	PUNCT
ejpam-5374	129	3	the	the	DET
ejpam-5374	129	4	upper	upper	ADJ
ejpam-5374	129	5	bounds	bound	NOUN
ejpam-5374	129	6	of	of	ADP
ejpam-5374	129	7	|γ3|	|γ3|	NOUN
ejpam-5374	129	8	and	and	CCONJ
ejpam-5374	129	9	|γ4|	|γ4|	NOUN
ejpam-5374	129	10	result	result	NOUN
ejpam-5374	129	11	from	from	ADP
ejpam-5374	129	12	using	use	VERB
ejpam-5374	129	13	both	both	CCONJ
ejpam-5374	129	14	lemma	lemma	PROPN
ejpam-5374	129	15	1	1	NUM
ejpam-5374	129	16	and	and	CCONJ
ejpam-5374	129	17	lemma	lemma	PROPN
ejpam-5374	129	18	2	2	NUM
ejpam-5374	129	19	,	,	PUNCT
ejpam-5374	129	20	as	as	ADV
ejpam-5374	129	21	well	well	ADV
ejpam-5374	129	22	as	as	ADP
ejpam-5374	129	23	triangle	triangle	NOUN
ejpam-5374	129	24	inequality	inequality	NOUN
ejpam-5374	129	25	.	.	PUNCT
ejpam-5374	130	1	this	this	PRON
ejpam-5374	130	2	completes	complete	VERB
ejpam-5374	130	3	the	the	DET
ejpam-5374	130	4	proof	proof	NOUN
ejpam-5374	130	5	of	of	ADP
ejpam-5374	130	6	theorem	theorem	NOUN
ejpam-5374	130	7	1	1	NUM
ejpam-5374	130	8	.	.	NOUN
ejpam-5374	130	9	3.2	3.2	NUM
ejpam-5374	130	10	.	.	PUNCT
ejpam-5374	131	1	second	second	ADJ
ejpam-5374	131	2	-	-	PUNCT
ejpam-5374	131	3	order	order	NOUN
ejpam-5374	131	4	hankel	hankel	NOUN
ejpam-5374	131	5	determinant	determinant	ADJ
ejpam-5374	131	6	of	of	ADP
ejpam-5374	131	7	logarithmic	logarithmic	ADJ
ejpam-5374	131	8	coefficients	coefficient	NOUN
ejpam-5374	131	9	for	for	ADP
ejpam-5374	131	10	g(α	g(α	PROPN
ejpam-5374	131	11	,	,	PUNCT
ejpam-5374	131	12	δ	δ	PROPN
ejpam-5374	131	13	)	)	PUNCT
ejpam-5374	131	14	now	now	ADV
ejpam-5374	131	15	,	,	PUNCT
ejpam-5374	131	16	in	in	ADP
ejpam-5374	131	17	this	this	DET
ejpam-5374	131	18	subsection	subsection	NOUN
ejpam-5374	131	19	,	,	PUNCT
ejpam-5374	131	20	using	use	VERB
ejpam-5374	131	21	the	the	DET
ejpam-5374	131	22	results	result	NOUN
ejpam-5374	131	23	from	from	ADP
ejpam-5374	131	24	theorem	theorem	ADJ
ejpam-5374	131	25	1	1	NUM
ejpam-5374	131	26	,	,	PUNCT
ejpam-5374	131	27	we	we	PRON
ejpam-5374	131	28	estimate	estimate	VERB
ejpam-5374	131	29	the	the	DET
ejpam-5374	131	30	upper	upper	ADJ
ejpam-5374	131	31	bound	bound	NOUN
ejpam-5374	131	32	of	of	ADP
ejpam-5374	131	33	the	the	DET
ejpam-5374	131	34	second	second	ADJ
ejpam-5374	131	35	-	-	PUNCT
ejpam-5374	131	36	order	order	NOUN
ejpam-5374	131	37	hankel	hankel	NOUN
ejpam-5374	131	38	determinant	determinant	ADJ
ejpam-5374	131	39	of	of	ADP
ejpam-5374	131	40	logarithmic	logarithmic	ADJ
ejpam-5374	131	41	coefficients	coefficient	NOUN
ejpam-5374	131	42	,	,	PUNCT
ejpam-5374	131	43	specifically	specifically	ADV
ejpam-5374	131	44	for	for	ADP
ejpam-5374	131	45	n	n	NOUN
ejpam-5374	131	46	=	=	SYM
ejpam-5374	131	47	2	2	NUM
ejpam-5374	131	48	and	and	CCONJ
ejpam-5374	131	49	q	q	NOUN
ejpam-5374	131	50	=	=	NOUN
ejpam-5374	131	51	2	2	NUM
ejpam-5374	131	52	,	,	PUNCT
ejpam-5374	131	53	for	for	ADP
ejpam-5374	131	54	functions	function	NOUN
ejpam-5374	131	55	belonging	belong	VERB
ejpam-5374	131	56	to	to	ADP
ejpam-5374	131	57	g	g	PROPN
ejpam-5374	131	58	(	(	PUNCT
ejpam-5374	131	59	α	α	PROPN
ejpam-5374	131	60	,	,	PUNCT
ejpam-5374	131	61	δ	δ	PROPN
ejpam-5374	131	62	)	)	PUNCT
ejpam-5374	131	63	.	.	PUNCT
ejpam-5374	132	1	theorem	theorem	NOUN
ejpam-5374	132	2	2	2	NUM
ejpam-5374	132	3	.	.	PUNCT
ejpam-5374	133	1	if	if	SCONJ
ejpam-5374	133	2	f	f	PROPN
ejpam-5374	133	3	(	(	PUNCT
ejpam-5374	133	4	z	z	NOUN
ejpam-5374	133	5	)	)	PUNCT
ejpam-5374	133	6	=	=	SYM
ejpam-5374	133	7	z	z	NOUN
ejpam-5374	134	1	+	+	NOUN
ejpam-5374	134	2	∞∑	∞∑	NUM
ejpam-5374	134	3	n=2	n=2	CCONJ
ejpam-5374	134	4	anz	anz	NOUN
ejpam-5374	134	5	n	n	ADP
ejpam-5374	134	6	∈	∈	PROPN
ejpam-5374	134	7	g	g	PROPN
ejpam-5374	134	8	(	(	PUNCT
ejpam-5374	134	9	α	α	PROPN
ejpam-5374	134	10	,	,	PUNCT
ejpam-5374	134	11	δ	δ	PROPN
ejpam-5374	134	12	)	)	PUNCT
ejpam-5374	134	13	,	,	PUNCT
ejpam-5374	134	14	then	then	ADV
ejpam-5374	134	15	|h2,2	|h2,2	VERB
ejpam-5374	134	16	(	(	PUNCT
ejpam-5374	134	17	γf	γf	PROPN
ejpam-5374	134	18	)	)	PUNCT
ejpam-5374	134	19	|	|	ADV
ejpam-5374	134	20	≤	≤	NUM
ejpam-5374	134	21	tαδ	tαδ	VERB
ejpam-5374	134	22	2	2	NUM
ejpam-5374	134	23	2160	2160	NUM
ejpam-5374	134	24	(	(	PUNCT
ejpam-5374	134	25	36	36	NUM
ejpam-5374	134	26	∣∣5tαδe−iα	∣∣5tαδe−iα	ADJ
ejpam-5374	134	27	+	+	NUM
ejpam-5374	134	28	4	4	NUM
ejpam-5374	134	29	∣∣+	∣∣+	NOUN
ejpam-5374	134	30	9tαδ	9tαδ	NUM
ejpam-5374	134	31	∣∣5tαδe−iα	∣∣5tαδe−iα	PRON
ejpam-5374	134	32	+	+	NUM
ejpam-5374	134	33	12	12	NUM
ejpam-5374	134	34	∣∣+	∣∣+	PROPN
ejpam-5374	134	35	30tαδ	30tαδ	PROPN
ejpam-5374	134	36	3	3	NUM
ejpam-5374	134	37	+	+	NOUN
ejpam-5374	134	38	80tαδ	80tαδ	NOUN
ejpam-5374	134	39	+	+	CCONJ
ejpam-5374	134	40	135	135	NUM
ejpam-5374	134	41	)	)	PUNCT
ejpam-5374	134	42	,	,	PUNCT
ejpam-5374	134	43	where	where	SCONJ
ejpam-5374	134	44	tαδ	tαδ	NOUN
ejpam-5374	134	45	=	=	SYM
ejpam-5374	134	46	cosα−	cosα−	PROPN
ejpam-5374	134	47	δ	δ	PROPN
ejpam-5374	134	48	.	.	PUNCT
ejpam-5374	135	1	proof	proof	NOUN
ejpam-5374	135	2	.	.	PUNCT
ejpam-5374	136	1	using	use	VERB
ejpam-5374	136	2	(	(	PUNCT
ejpam-5374	136	3	8)–(10	8)–(10	NUM
ejpam-5374	136	4	)	)	PUNCT
ejpam-5374	136	5	,	,	PUNCT
ejpam-5374	136	6	we	we	PRON
ejpam-5374	136	7	can	can	AUX
ejpam-5374	136	8	establish	establish	VERB
ejpam-5374	136	9	γ3	γ3	NOUN
ejpam-5374	136	10	2	2	NUM
ejpam-5374	136	11	=	=	PUNCT
ejpam-5374	136	12	tαδ	tαδ	VERB
ejpam-5374	136	13	2e−2iα	2e−2iα	PROPN
ejpam-5374	136	14	2304	2304	NUM
ejpam-5374	136	15	(	(	PUNCT
ejpam-5374	136	16	6p3	6p3	NUM
ejpam-5374	136	17	−	−	PROPN
ejpam-5374	136	18	4tαδe	4tαδe	NUM
ejpam-5374	136	19	−iαp1p2	−iαp1p2	NOUN
ejpam-5374	136	20	+	+	CCONJ
ejpam-5374	136	21	tαδ	tαδ	PRON
ejpam-5374	136	22	2e−2iαp31	2e−2iαp31	NUM
ejpam-5374	136	23	)	)	PUNCT
ejpam-5374	136	24	2	2	NUM
ejpam-5374	136	25	=	=	PUNCT
ejpam-5374	136	26	tαδ	tαδ	VERB
ejpam-5374	136	27	2e−2iα	2e−2iα	PROPN
ejpam-5374	136	28	2304	2304	NUM
ejpam-5374	136	29	(	(	PUNCT
ejpam-5374	136	30	36p23	36p23	NUM
ejpam-5374	137	1	−	−	NOUN
ejpam-5374	137	2	48tαδe	48tαδe	NUM
ejpam-5374	137	3	−iαp1p2p3	−iαp1p2p3	PROPN
ejpam-5374	138	1	+	+	CCONJ
ejpam-5374	138	2	16tαδ	16tαδ	X
ejpam-5374	139	1	2e−2iαp21p	2e−2iαp21p	NUM
ejpam-5374	139	2	2	2	NUM
ejpam-5374	139	3	2	2	NUM
ejpam-5374	139	4	+12tαδ	+12tαδ	NUM
ejpam-5374	139	5	2e−2iαp31p3	2e−2iαp31p3	NUM
ejpam-5374	139	6	−	−	NOUN
ejpam-5374	139	7	8tαδ	8tαδ	NUM
ejpam-5374	139	8	3e−3iαp41p2	3e−3iαp41p2	NUM
ejpam-5374	139	9	+	+	CCONJ
ejpam-5374	139	10	tαδ	tαδ	VERB
ejpam-5374	139	11	4e−4iαp61	4e−4iαp61	NUM
ejpam-5374	139	12	)	)	PUNCT
ejpam-5374	139	13	and	and	CCONJ
ejpam-5374	139	14	γ2γ4	γ2γ4	X
ejpam-5374	139	15	=	=	PRON
ejpam-5374	139	16	tαδ	tαδ	VERB
ejpam-5374	139	17	2e−2iα(8p2−	2e−2iα(8p2−	NOUN
ejpam-5374	139	18	3tαδp	3tαδp	NUM
ejpam-5374	139	19	2	2	NUM
ejpam-5374	139	20	1e	1e	PROPN
ejpam-5374	139	21	−iα	−iα	PROPN
ejpam-5374	139	22	)	)	PUNCT
ejpam-5374	139	23	48	48	NUM
ejpam-5374	139	24	(	(	PUNCT
ejpam-5374	139	25	p4	p4	ADJ
ejpam-5374	139	26	10	10	NUM
ejpam-5374	139	27	−	−	NOUN
ejpam-5374	139	28	tαδp	tαδp	NOUN
ejpam-5374	139	29	2	2	NUM
ejpam-5374	139	30	2e	2e	NOUN
ejpam-5374	139	31	−iα	−iα	NOUN
ejpam-5374	139	32	36	36	NUM
ejpam-5374	139	33	−	−	NOUN
ejpam-5374	139	34	tαδp1p3e	tαδp1p3e	PUNCT
ejpam-5374	139	35	−iα	−iα	NOUN
ejpam-5374	139	36	16	16	NUM
ejpam-5374	139	37	+	+	CCONJ
ejpam-5374	139	38	tαδ	tαδ	VERB
ejpam-5374	139	39	2p21p2e	2p21p2e	ADJ
ejpam-5374	139	40	−2iα	−2iα	NUM
ejpam-5374	139	41	24	24	NUM
ejpam-5374	139	42	−	−	NOUN
ejpam-5374	139	43	tαδ	tαδ	VERB
ejpam-5374	139	44	3p41e	3p41e	PRON
ejpam-5374	139	45	−3iα	−3iα	X
ejpam-5374	139	46	128	128	NUM
ejpam-5374	139	47	)	)	PUNCT
ejpam-5374	139	48	=	=	PUNCT
ejpam-5374	139	49	tαδ	tαδ	VERB
ejpam-5374	139	50	2e−2iα	2e−2iα	NUM
ejpam-5374	139	51	2304	2304	NUM
ejpam-5374	139	52	(	(	PUNCT
ejpam-5374	139	53	192p2p4	192p2p4	NUM
ejpam-5374	139	54	5	5	NUM
ejpam-5374	139	55	−	−	PROPN
ejpam-5374	139	56	32tαδe	32tαδe	NUM
ejpam-5374	139	57	−iαp32	−iαp32	NOUN
ejpam-5374	139	58	3	3	NUM
ejpam-5374	139	59	−	−	PROPN
ejpam-5374	140	1	24tαδe	24tαδe	NUM
ejpam-5374	141	1	−iαp1p2p3	−iαp1p2p3	PROPN
ejpam-5374	142	1	+	+	CCONJ
ejpam-5374	142	2	20tαδ	20tαδ	NUM
ejpam-5374	142	3	2e−2iαp21p	2e−2iαp21p	NUM
ejpam-5374	142	4	2	2	NUM
ejpam-5374	142	5	2	2	NUM
ejpam-5374	142	6	−	−	PROPN
ejpam-5374	142	7	9tαδ	9tαδ	NUM
ejpam-5374	142	8	3e−3iαp41p2	3e−3iαp41p2	NUM
ejpam-5374	143	1	−	−	NOUN
ejpam-5374	143	2	72tαδe	72tαδe	NUM
ejpam-5374	144	1	−iαp21p4	−iαp21p4	NOUN
ejpam-5374	144	2	5	5	NUM
ejpam-5374	145	1	+	+	CCONJ
ejpam-5374	145	2	9tαδ	9tαδ	NUM
ejpam-5374	145	3	2e−2iαp31p3	2e−2iαp31p3	NUM
ejpam-5374	145	4	+	+	CCONJ
ejpam-5374	145	5	9tαδ	9tαδ	NUM
ejpam-5374	145	6	4e−4iαp61	4e−4iαp61	NUM
ejpam-5374	145	7	8	8	NUM
ejpam-5374	145	8	)	)	PUNCT
ejpam-5374	145	9	.	.	PUNCT
ejpam-5374	146	1	n.h.a.a	n.h.a.a	PROPN
ejpam-5374	146	2	.	.	PROPN
ejpam-5374	146	3	wahid	wahid	PROPN
ejpam-5374	146	4	,	,	PUNCT
ejpam-5374	146	5	i.q	i.q	PROPN
ejpam-5374	146	6	.	.	PROPN
ejpam-5374	146	7	amirnuddin	amirnuddin	PROPN
ejpam-5374	146	8	,	,	PUNCT
ejpam-5374	146	9	n.i.m	n.i.m	NOUN
ejpam-5374	146	10	.	.	PUNCT
ejpam-5374	147	1	azmi	azmi	PROPN
ejpam-5374	147	2	/	/	SYM
ejpam-5374	147	3	eur	eur	PROPN
ejpam-5374	147	4	.	.	PUNCT
ejpam-5374	148	1	j.	j.	PROPN
ejpam-5374	148	2	pure	pure	PROPN
ejpam-5374	148	3	appl	appl	PROPN
ejpam-5374	148	4	.	.	PROPN
ejpam-5374	148	5	math	math	PROPN
ejpam-5374	148	6	,	,	PUNCT
ejpam-5374	148	7	17	17	NUM
ejpam-5374	148	8	(	(	PUNCT
ejpam-5374	148	9	4	4	NUM
ejpam-5374	148	10	)	)	PUNCT
ejpam-5374	148	11	(	(	PUNCT
ejpam-5374	148	12	2024	2024	NUM
ejpam-5374	148	13	)	)	PUNCT
ejpam-5374	148	14	,	,	PUNCT
ejpam-5374	148	15	2738	2738	NUM
ejpam-5374	148	16	-	-	SYM
ejpam-5374	148	17	2752	2752	NUM
ejpam-5374	148	18	2745	2745	NUM
ejpam-5374	148	19	therefore	therefore	ADV
ejpam-5374	148	20	,	,	PUNCT
ejpam-5374	148	21	we	we	PRON
ejpam-5374	148	22	have	have	AUX
ejpam-5374	148	23	h2,2	h2,2	PROPN
ejpam-5374	148	24	(	(	PUNCT
ejpam-5374	148	25	γf	γf	ADJ
ejpam-5374	148	26	)	)	PUNCT
ejpam-5374	149	1	=	=	PUNCT
ejpam-5374	149	2	tαδ	tαδ	VERB
ejpam-5374	149	3	2e−2iα	2e−2iα	NUM
ejpam-5374	149	4	2304	2304	NUM
ejpam-5374	149	5	(	(	PUNCT
ejpam-5374	149	6	192p2p4	192p2p4	NUM
ejpam-5374	149	7	5	5	NUM
ejpam-5374	149	8	+	+	NUM
ejpam-5374	149	9	24tαδe	24tαδe	NUM
ejpam-5374	149	10	−iαp1p2p3	−iαp1p2p3	NUM
ejpam-5374	150	1	−	−	PROPN
ejpam-5374	150	2	32tαδe	32tαδe	NUM
ejpam-5374	150	3	−iαp32	−iαp32	NOUN
ejpam-5374	150	4	3	3	NUM
ejpam-5374	150	5	+	+	CCONJ
ejpam-5374	150	6	4tαδ	4tαδ	NUM
ejpam-5374	150	7	2e−2iαp21p2	2e−2iαp21p2	NUM
ejpam-5374	150	8	2	2	NUM
ejpam-5374	150	9	−	−	NOUN
ejpam-5374	150	10	36p23	36p23	NUM
ejpam-5374	150	11	−72tαδe	−72tαδe	NOUN
ejpam-5374	151	1	−iαp21p4	−iαp21p4	NOUN
ejpam-5374	151	2	5	5	NUM
ejpam-5374	151	3	−	−	PROPN
ejpam-5374	151	4	3tαδ	3tαδ	NUM
ejpam-5374	152	1	2e−2iαp31p3	2e−2iαp31p3	NUM
ejpam-5374	152	2	−	−	PROPN
ejpam-5374	152	3	tαδ	tαδ	VERB
ejpam-5374	152	4	3e−3iαp41p2	3e−3iαp41p2	NUM
ejpam-5374	152	5	+	+	CCONJ
ejpam-5374	152	6	tαδ	tαδ	VERB
ejpam-5374	152	7	4e−4iαp61	4e−4iαp61	ADJ
ejpam-5374	152	8	8	8	NUM
ejpam-5374	152	9	)	)	PUNCT
ejpam-5374	152	10	.	.	PUNCT
ejpam-5374	153	1	(	(	PUNCT
ejpam-5374	153	2	28	28	X
ejpam-5374	153	3	)	)	PUNCT
ejpam-5374	153	4	taking	take	VERB
ejpam-5374	153	5	the	the	DET
ejpam-5374	153	6	modulus	modulus	NOUN
ejpam-5374	153	7	of	of	ADP
ejpam-5374	153	8	both	both	DET
ejpam-5374	153	9	sides	side	NOUN
ejpam-5374	153	10	of	of	ADP
ejpam-5374	153	11	equation	equation	NOUN
ejpam-5374	153	12	(	(	PUNCT
ejpam-5374	153	13	28	28	NUM
ejpam-5374	153	14	)	)	PUNCT
ejpam-5374	153	15	and	and	CCONJ
ejpam-5374	153	16	rearranging	rearrange	VERB
ejpam-5374	153	17	the	the	DET
ejpam-5374	153	18	terms	term	NOUN
ejpam-5374	153	19	according	accord	VERB
ejpam-5374	153	20	to	to	ADP
ejpam-5374	153	21	lemma	lemma	PROPN
ejpam-5374	153	22	2	2	NUM
ejpam-5374	153	23	,	,	PUNCT
ejpam-5374	153	24	we	we	PRON
ejpam-5374	153	25	obtain	obtain	VERB
ejpam-5374	153	26	|h2,2	|h2,2	NOUN
ejpam-5374	153	27	(	(	PUNCT
ejpam-5374	153	28	γf	γf	NOUN
ejpam-5374	153	29	)	)	PUNCT
ejpam-5374	154	1	|	|	ADV
ejpam-5374	154	2	=	=	PUNCT
ejpam-5374	154	3	tαδ	tαδ	VERB
ejpam-5374	154	4	2	2	NUM
ejpam-5374	154	5	2304	2304	NUM
ejpam-5374	154	6	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5374	154	7	−192p2	−192p2	ADP
ejpam-5374	154	8	5	5	NUM
ejpam-5374	154	9	(	(	PUNCT
ejpam-5374	154	10	p4	p4	ADJ
ejpam-5374	154	11	−	−	NOUN
ejpam-5374	154	12	ν∗p1p3	ν∗p1p3	NOUN
ejpam-5374	154	13	)	)	PUNCT
ejpam-5374	154	14	+	+	CCONJ
ejpam-5374	154	15	32tαδe	32tαδe	PRON
ejpam-5374	154	16	−iαp22	−iαp22	NOUN
ejpam-5374	154	17	3	3	NUM
ejpam-5374	154	18	(	(	PUNCT
ejpam-5374	154	19	p2	p2	X
ejpam-5374	154	20	−	−	PROPN
ejpam-5374	154	21	ν∗∗p21	ν∗∗p21	PROPN
ejpam-5374	154	22	)	)	PUNCT
ejpam-5374	155	1	+	+	CCONJ
ejpam-5374	155	2	36p23	36p23	NUM
ejpam-5374	155	3	+	+	NUM
ejpam-5374	155	4	72tαδe	72tαδe	NOUN
ejpam-5374	155	5	−iαp21	−iαp21	VERB
ejpam-5374	155	6	5	5	NUM
ejpam-5374	155	7	(	(	PUNCT
ejpam-5374	155	8	p4	p4	ADJ
ejpam-5374	155	9	−	−	PROPN
ejpam-5374	155	10	ν∗∗∗p1p3	ν∗∗∗p1p3	NUM
ejpam-5374	155	11	)	)	PUNCT
ejpam-5374	155	12	+	+	CCONJ
ejpam-5374	155	13	tαδ	tαδ	PRON
ejpam-5374	155	14	3e−3iαp41	3e−3iαp41	NUM
ejpam-5374	155	15	(	(	PUNCT
ejpam-5374	155	16	p2	p2	PROPN
ejpam-5374	155	17	−	−	PROPN
ejpam-5374	155	18	ν∗∗∗∗p21	ν∗∗∗∗p21	PROPN
ejpam-5374	155	19	)	)	PUNCT
ejpam-5374	155	20	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5374	155	21	,	,	PUNCT
ejpam-5374	155	22	(	(	PUNCT
ejpam-5374	155	23	29	29	NUM
ejpam-5374	155	24	)	)	PUNCT
ejpam-5374	155	25	where	where	SCONJ
ejpam-5374	155	26	ν∗	ν∗	NOUN
ejpam-5374	155	27	=	=	PUNCT
ejpam-5374	155	28	−5tαδe	−5tαδe	NOUN
ejpam-5374	155	29	−iα	−iα	NOUN
ejpam-5374	155	30	8	8	NUM
ejpam-5374	155	31	,	,	PUNCT
ejpam-5374	155	32	ν∗∗	ν∗∗	PROPN
ejpam-5374	155	33	=	=	SYM
ejpam-5374	155	34	3tαδe	3tαδe	NUM
ejpam-5374	155	35	−iα	−iα	NUM
ejpam-5374	155	36	8	8	NUM
ejpam-5374	155	37	,	,	PUNCT
ejpam-5374	155	38	ν∗∗∗	ν∗∗∗	NOUN
ejpam-5374	156	1	=	=	PUNCT
ejpam-5374	157	1	−5tαδe	−5tαδe	PROPN
ejpam-5374	157	2	−iα	−iα	NOUN
ejpam-5374	157	3	24	24	NUM
ejpam-5374	157	4	,	,	PUNCT
ejpam-5374	157	5	and	and	CCONJ
ejpam-5374	157	6	ν∗∗∗∗	ν∗∗∗∗	PROPN
ejpam-5374	157	7	=	=	SYM
ejpam-5374	157	8	tαδe	tαδe	PROPN
ejpam-5374	157	9	−iα	−iα	NOUN
ejpam-5374	157	10	8	8	NUM
ejpam-5374	157	11	.	.	PUNCT
ejpam-5374	158	1	we	we	PRON
ejpam-5374	158	2	see	see	VERB
ejpam-5374	158	3	that	that	DET
ejpam-5374	158	4	|p4	|p4	ADJ
ejpam-5374	158	5	−	−	NUM
ejpam-5374	158	6	ν∗p1p3|	ν∗p1p3|	ADJ
ejpam-5374	158	7	≤	≤	NUM
ejpam-5374	158	8	∣∣∣5tαδe	∣∣∣5tαδe	NOUN
ejpam-5374	158	9	−iα+4	−iα+4	NOUN
ejpam-5374	158	10	2	2	NUM
ejpam-5374	158	11	∣∣∣	∣∣∣	NOUN
ejpam-5374	158	12	,	,	PUNCT
ejpam-5374	158	13	∣∣p2	∣∣p2	PROPN
ejpam-5374	158	14	−	−	PROPN
ejpam-5374	158	15	ν∗∗p21	ν∗∗p21	X
ejpam-5374	158	16	∣∣	∣∣	X
ejpam-5374	158	17	≤	≤	ADV
ejpam-5374	158	18	2	2	NUM
ejpam-5374	158	19	,	,	PUNCT
ejpam-5374	158	20	|p4	|p4	ADJ
ejpam-5374	158	21	−	−	PROPN
ejpam-5374	158	22	ν∗∗∗p1p3|	ν∗∗∗p1p3|	ADV
ejpam-5374	158	23	≤	≤	NUM
ejpam-5374	158	24	∣∣∣5tαδe	∣∣∣5tαδe	NOUN
ejpam-5374	158	25	−iα+12	−iα+12	PROPN
ejpam-5374	158	26	6	6	NUM
ejpam-5374	158	27	∣∣∣	∣∣∣	NOUN
ejpam-5374	158	28	,	,	PUNCT
ejpam-5374	158	29	∣∣p2	∣∣p2	PROPN
ejpam-5374	158	30	−	−	X
ejpam-5374	158	31	ν∗∗∗∗p21	ν∗∗∗∗p21	PRON
ejpam-5374	158	32	∣∣	∣∣	VERB
ejpam-5374	158	33	≤	≤	ADV
ejpam-5374	158	34	2	2	NUM
ejpam-5374	158	35	.	.	X
ejpam-5374	159	1			NOUN
ejpam-5374	159	2	(	(	PUNCT
ejpam-5374	159	3	30	30	NUM
ejpam-5374	159	4	)	)	PUNCT
ejpam-5374	159	5	thus	thus	ADV
ejpam-5374	159	6	,	,	PUNCT
ejpam-5374	159	7	from	from	ADP
ejpam-5374	159	8	(	(	PUNCT
ejpam-5374	159	9	29	29	NUM
ejpam-5374	159	10	)	)	PUNCT
ejpam-5374	159	11	,	,	PUNCT
ejpam-5374	159	12	considering	consider	VERB
ejpam-5374	159	13	the	the	DET
ejpam-5374	159	14	triangle	triangle	NOUN
ejpam-5374	159	15	inequality	inequality	NOUN
ejpam-5374	159	16	,	,	PUNCT
ejpam-5374	159	17	lemma	lemma	PROPN
ejpam-5374	159	18	1	1	NUM
ejpam-5374	159	19	,	,	PUNCT
ejpam-5374	159	20	and	and	CCONJ
ejpam-5374	159	21	(	(	PUNCT
ejpam-5374	159	22	30	30	NUM
ejpam-5374	159	23	)	)	PUNCT
ejpam-5374	159	24	,	,	PUNCT
ejpam-5374	159	25	we	we	PRON
ejpam-5374	159	26	obtain	obtain	VERB
ejpam-5374	159	27	the	the	DET
ejpam-5374	159	28	desired	desire	VERB
ejpam-5374	159	29	inequality	inequality	NOUN
ejpam-5374	159	30	.	.	PUNCT
ejpam-5374	160	1	this	this	PRON
ejpam-5374	160	2	concludes	conclude	VERB
ejpam-5374	160	3	the	the	DET
ejpam-5374	160	4	proof	proof	NOUN
ejpam-5374	160	5	of	of	ADP
ejpam-5374	160	6	theorem	theorem	ADJ
ejpam-5374	160	7	2	2	NUM
ejpam-5374	160	8	.	.	NOUN
ejpam-5374	160	9	3.3	3.3	NUM
ejpam-5374	160	10	.	.	PUNCT
ejpam-5374	161	1	second	second	ADJ
ejpam-5374	161	2	-	-	PUNCT
ejpam-5374	161	3	order	order	NOUN
ejpam-5374	161	4	toeplitz	toeplitz	NOUN
ejpam-5374	161	5	determinant	determinant	ADJ
ejpam-5374	161	6	of	of	ADP
ejpam-5374	161	7	logarithmic	logarithmic	ADJ
ejpam-5374	161	8	coefficients	coefficient	NOUN
ejpam-5374	161	9	for	for	ADP
ejpam-5374	161	10	g(α	g(α	PROPN
ejpam-5374	161	11	,	,	PUNCT
ejpam-5374	161	12	δ	δ	PROPN
ejpam-5374	161	13	)	)	PUNCT
ejpam-5374	161	14	in	in	ADP
ejpam-5374	161	15	this	this	DET
ejpam-5374	161	16	subsection	subsection	NOUN
ejpam-5374	161	17	,	,	PUNCT
ejpam-5374	161	18	using	use	VERB
ejpam-5374	161	19	the	the	DET
ejpam-5374	161	20	results	result	NOUN
ejpam-5374	161	21	from	from	ADP
ejpam-5374	161	22	theorem	theorem	ADJ
ejpam-5374	161	23	1	1	NUM
ejpam-5374	161	24	,	,	PUNCT
ejpam-5374	161	25	we	we	PRON
ejpam-5374	161	26	determine	determine	VERB
ejpam-5374	161	27	the	the	DET
ejpam-5374	161	28	upper	upper	ADJ
ejpam-5374	161	29	bound	bound	NOUN
ejpam-5374	161	30	of	of	ADP
ejpam-5374	161	31	the	the	DET
ejpam-5374	161	32	second	second	ADJ
ejpam-5374	161	33	-	-	PUNCT
ejpam-5374	161	34	order	order	NOUN
ejpam-5374	161	35	toeplitz	toeplitz	NOUN
ejpam-5374	161	36	determinant	determinant	ADJ
ejpam-5374	161	37	of	of	ADP
ejpam-5374	161	38	logarithmic	logarithmic	ADJ
ejpam-5374	161	39	coefficients	coefficient	NOUN
ejpam-5374	161	40	,	,	PUNCT
ejpam-5374	161	41	specifically	specifically	ADV
ejpam-5374	161	42	for	for	ADP
ejpam-5374	161	43	n	n	NOUN
ejpam-5374	161	44	=	=	SYM
ejpam-5374	161	45	2	2	NUM
ejpam-5374	161	46	and	and	CCONJ
ejpam-5374	161	47	q	q	NOUN
ejpam-5374	161	48	=	=	NOUN
ejpam-5374	161	49	2	2	NUM
ejpam-5374	161	50	,	,	PUNCT
ejpam-5374	161	51	for	for	ADP
ejpam-5374	161	52	functions	function	NOUN
ejpam-5374	161	53	belonging	belong	VERB
ejpam-5374	161	54	to	to	ADP
ejpam-5374	161	55	g	g	PROPN
ejpam-5374	161	56	(	(	PUNCT
ejpam-5374	161	57	α	α	PROPN
ejpam-5374	161	58	,	,	PUNCT
ejpam-5374	161	59	δ	δ	PROPN
ejpam-5374	161	60	)	)	PUNCT
ejpam-5374	161	61	.	.	PUNCT
ejpam-5374	162	1	theorem	theorem	NOUN
ejpam-5374	162	2	3	3	NUM
ejpam-5374	162	3	.	.	PUNCT
ejpam-5374	163	1	if	if	SCONJ
ejpam-5374	163	2	f	f	PROPN
ejpam-5374	163	3	(	(	PUNCT
ejpam-5374	163	4	z	z	NOUN
ejpam-5374	163	5	)	)	PUNCT
ejpam-5374	163	6	=	=	SYM
ejpam-5374	163	7	z	z	NOUN
ejpam-5374	164	1	+	+	NOUN
ejpam-5374	164	2	∞∑	∞∑	NUM
ejpam-5374	164	3	n=2	n=2	CCONJ
ejpam-5374	164	4	anz	anz	NOUN
ejpam-5374	164	5	n	n	ADP
ejpam-5374	164	6	∈	∈	PROPN
ejpam-5374	164	7	g	g	PROPN
ejpam-5374	164	8	(	(	PUNCT
ejpam-5374	164	9	α	α	PROPN
ejpam-5374	164	10	,	,	PUNCT
ejpam-5374	164	11	δ	δ	PROPN
ejpam-5374	164	12	)	)	PUNCT
ejpam-5374	164	13	,	,	PUNCT
ejpam-5374	164	14	then	then	ADV
ejpam-5374	164	15	|t2,2	|t2,2	NOUN
ejpam-5374	164	16	(	(	PUNCT
ejpam-5374	164	17	γf	γf	PROPN
ejpam-5374	164	18	)	)	PUNCT
ejpam-5374	164	19	|	|	ADV
ejpam-5374	164	20	≤	≤	NUM
ejpam-5374	164	21	tαδ	tαδ	VERB
ejpam-5374	164	22	2	2	NUM
ejpam-5374	164	23	144	144	NUM
ejpam-5374	164	24	(	(	PUNCT
ejpam-5374	164	25	16	16	NUM
ejpam-5374	164	26	+	+	CCONJ
ejpam-5374	164	27	37tαδ	37tαδ	NOUN
ejpam-5374	164	28	2	2	NUM
ejpam-5374	164	29	+	+	SYM
ejpam-5374	164	30	4	4	NUM
ejpam-5374	164	31	tαδ	tαδ	VERB
ejpam-5374	164	32	4	4	NUM
ejpam-5374	164	33	+	+	SYM
ejpam-5374	164	34	3	3	NUM
ejpam-5374	164	35	∣∣8tαδe−iα	∣∣8tαδe−iα	ADV
ejpam-5374	164	36	−	−	NUM
ejpam-5374	164	37	3	3	NUM
ejpam-5374	164	38	∣∣	∣∣	NOUN
ejpam-5374	164	39	)	)	PUNCT
ejpam-5374	164	40	,	,	PUNCT
ejpam-5374	164	41	where	where	SCONJ
ejpam-5374	164	42	tαδ	tαδ	NOUN
ejpam-5374	164	43	=	=	SYM
ejpam-5374	164	44	cosα−	cosα−	PROPN
ejpam-5374	164	45	δ	δ	PROPN
ejpam-5374	164	46	.	.	PUNCT
ejpam-5374	165	1	proof	proof	NOUN
ejpam-5374	165	2	.	.	PUNCT
ejpam-5374	166	1	in	in	ADP
ejpam-5374	166	2	light	light	NOUN
ejpam-5374	166	3	of	of	ADP
ejpam-5374	166	4	(	(	PUNCT
ejpam-5374	166	5	8)	8)	NUM
ejpam-5374	166	6	and	and	CCONJ
ejpam-5374	166	7	(	(	PUNCT
ejpam-5374	166	8	9	9	X
ejpam-5374	166	9	)	)	PUNCT
ejpam-5374	166	10	give	give	VERB
ejpam-5374	166	11	γ2	γ2	NOUN
ejpam-5374	166	12	2	2	NUM
ejpam-5374	166	13	=	=	SYM
ejpam-5374	166	14	1	1	NUM
ejpam-5374	166	15	2304	2304	NUM
ejpam-5374	166	16	(	(	PUNCT
ejpam-5374	166	17	8tαδe	8tαδe	NUM
ejpam-5374	166	18	−iαp2	−iαp2	NOUN
ejpam-5374	166	19	−	−	ADP
ejpam-5374	166	20	3tαδ	3tαδ	NUM
ejpam-5374	166	21	2e−2iαp21	2e−2iαp21	PROPN
ejpam-5374	166	22	)	)	PUNCT
ejpam-5374	166	23	2	2	NUM
ejpam-5374	166	24	=	=	PUNCT
ejpam-5374	166	25	tαδ	tαδ	VERB
ejpam-5374	166	26	2e−2iα	2e−2iα	PROPN
ejpam-5374	166	27	2304	2304	NUM
ejpam-5374	166	28	(	(	PUNCT
ejpam-5374	166	29	64p22	64p22	NUM
ejpam-5374	166	30	−	−	NOUN
ejpam-5374	166	31	48tαδe	48tαδe	NUM
ejpam-5374	167	1	−iαp21p2	−iαp21p2	PROPN
ejpam-5374	167	2	+	+	CCONJ
ejpam-5374	167	3	9tαδ	9tαδ	NUM
ejpam-5374	167	4	2e−2iαp41	2e−2iαp41	NOUN
ejpam-5374	167	5	)	)	PUNCT
ejpam-5374	168	1	n.h.a.a	n.h.a.a	PROPN
ejpam-5374	168	2	.	.	PROPN
ejpam-5374	168	3	wahid	wahid	PROPN
ejpam-5374	168	4	,	,	PUNCT
ejpam-5374	168	5	i.q	i.q	PROPN
ejpam-5374	168	6	.	.	PROPN
ejpam-5374	168	7	amirnuddin	amirnuddin	PROPN
ejpam-5374	168	8	,	,	PUNCT
ejpam-5374	168	9	n.i.m	n.i.m	NOUN
ejpam-5374	168	10	.	.	PUNCT
ejpam-5374	169	1	azmi	azmi	PROPN
ejpam-5374	169	2	/	/	SYM
ejpam-5374	169	3	eur	eur	PROPN
ejpam-5374	169	4	.	.	PUNCT
ejpam-5374	170	1	j.	j.	PROPN
ejpam-5374	170	2	pure	pure	PROPN
ejpam-5374	170	3	appl	appl	PROPN
ejpam-5374	170	4	.	.	PROPN
ejpam-5374	170	5	math	math	PROPN
ejpam-5374	170	6	,	,	PUNCT
ejpam-5374	170	7	17	17	NUM
ejpam-5374	170	8	(	(	PUNCT
ejpam-5374	170	9	4	4	NUM
ejpam-5374	170	10	)	)	PUNCT
ejpam-5374	170	11	(	(	PUNCT
ejpam-5374	170	12	2024	2024	NUM
ejpam-5374	170	13	)	)	PUNCT
ejpam-5374	170	14	,	,	PUNCT
ejpam-5374	170	15	2738	2738	NUM
ejpam-5374	170	16	-	-	SYM
ejpam-5374	170	17	2752	2752	NUM
ejpam-5374	170	18	2746	2746	NUM
ejpam-5374	170	19	and	and	CCONJ
ejpam-5374	170	20	γ3	γ3	NOUN
ejpam-5374	170	21	2	2	NUM
ejpam-5374	170	22	=	=	SYM
ejpam-5374	170	23	1	1	NUM
ejpam-5374	170	24	2304	2304	NUM
ejpam-5374	170	25	(	(	PUNCT
ejpam-5374	170	26	6tαδp3e	6tαδp3e	NUM
ejpam-5374	170	27	−iα	−iα	ADV
ejpam-5374	170	28	−	−	NOUN
ejpam-5374	170	29	4tαδ	4tαδ	NUM
ejpam-5374	170	30	2p1p2e	2p1p2e	NUM
ejpam-5374	170	31	−2iα	−2iα	NOUN
ejpam-5374	170	32	+	+	CCONJ
ejpam-5374	170	33	tαδ	tαδ	PRON
ejpam-5374	170	34	3p31e	3p31e	NUM
ejpam-5374	170	35	−3iα	−3iα	PROPN
ejpam-5374	170	36	)	)	PUNCT
ejpam-5374	170	37	2	2	X
ejpam-5374	170	38	=	=	PUNCT
ejpam-5374	170	39	tαδ	tαδ	VERB
ejpam-5374	170	40	2e−2iα	2e−2iα	PROPN
ejpam-5374	170	41	2304	2304	NUM
ejpam-5374	170	42	(	(	PUNCT
ejpam-5374	170	43	36p23	36p23	NUM
ejpam-5374	170	44	−	−	PROPN
ejpam-5374	170	45	48tαδp1p2p3e	48tαδp1p2p3e	NUM
ejpam-5374	170	46	−iα	−iα	NOUN
ejpam-5374	170	47	+	+	NUM
ejpam-5374	170	48	12tαδ	12tαδ	ADJ
ejpam-5374	170	49	2p31p3e	2p31p3e	NOUN
ejpam-5374	170	50	−2iα	−2iα	PUNCT
ejpam-5374	170	51	+16tαδ	+16tαδ	ADV
ejpam-5374	170	52	2p21p	2p21p	NUM
ejpam-5374	170	53	2	2	NUM
ejpam-5374	170	54	2e	2e	NOUN
ejpam-5374	170	55	−2iα	−2iα	ADV
ejpam-5374	170	56	−	−	PROPN
ejpam-5374	170	57	8tαδ	8tαδ	NUM
ejpam-5374	170	58	3p41p2e	3p41p2e	PROPN
ejpam-5374	170	59	−3iα	−3iα	PROPN
ejpam-5374	171	1	+	+	CCONJ
ejpam-5374	171	2	tαδ	tαδ	PRON
ejpam-5374	171	3	4p61e	4p61e	X
ejpam-5374	171	4	−4iα	−4iα	PROPN
ejpam-5374	171	5	)	)	PUNCT
ejpam-5374	171	6	.	.	PUNCT
ejpam-5374	172	1	therefore	therefore	ADV
ejpam-5374	172	2	,	,	PUNCT
ejpam-5374	172	3	we	we	PRON
ejpam-5374	172	4	obtain	obtain	VERB
ejpam-5374	172	5	t2,2	t2,2	PROPN
ejpam-5374	172	6	(	(	PUNCT
ejpam-5374	172	7	γf	γf	PROPN
ejpam-5374	172	8	)	)	PUNCT
ejpam-5374	172	9	=	=	PUNCT
ejpam-5374	172	10	tαδ	tαδ	VERB
ejpam-5374	172	11	2e−2iα	2e−2iα	NUM
ejpam-5374	172	12	2304	2304	NUM
ejpam-5374	172	13	(	(	PUNCT
ejpam-5374	172	14	64p22	64p22	NUM
ejpam-5374	172	15	−	−	NOUN
ejpam-5374	172	16	48tαδe	48tαδe	NUM
ejpam-5374	173	1	−iαp21p2	−iαp21p2	PROPN
ejpam-5374	173	2	−	−	PROPN
ejpam-5374	173	3	36p23	36p23	NUM
ejpam-5374	174	1	+	+	CCONJ
ejpam-5374	175	1	48tαδe	48tαδe	NUM
ejpam-5374	175	2	−iαp1p2p3	−iαp1p2p3	NUM
ejpam-5374	176	1	+	+	CCONJ
ejpam-5374	176	2	9tαδ	9tαδ	NUM
ejpam-5374	176	3	2e−2iαp41	2e−2iαp41	NUM
ejpam-5374	176	4	−	−	NOUN
ejpam-5374	176	5	12tαδ	12tαδ	NOUN
ejpam-5374	177	1	2e−2iαp31p3	2e−2iαp31p3	NUM
ejpam-5374	178	1	+	+	CCONJ
ejpam-5374	178	2	8tαδ	8tαδ	PROPN
ejpam-5374	178	3	3e−3iαp41p2	3e−3iαp41p2	NUM
ejpam-5374	178	4	−	−	NOUN
ejpam-5374	178	5	16tαδ	16tαδ	NOUN
ejpam-5374	178	6	2e−2iαp21p	2e−2iαp21p	NUM
ejpam-5374	178	7	2	2	NUM
ejpam-5374	178	8	2	2	NUM
ejpam-5374	178	9	−	−	NOUN
ejpam-5374	178	10	tαδ	tαδ	VERB
ejpam-5374	178	11	4e−4iαp61	4e−4iαp61	PROPN
ejpam-5374	178	12	)	)	PUNCT
ejpam-5374	178	13	,	,	PUNCT
ejpam-5374	178	14	(	(	PUNCT
ejpam-5374	178	15	31	31	NUM
ejpam-5374	178	16	)	)	PUNCT
ejpam-5374	178	17	and	and	CCONJ
ejpam-5374	178	18	we	we	PRON
ejpam-5374	178	19	can	can	AUX
ejpam-5374	178	20	express	express	VERB
ejpam-5374	178	21	(	(	PUNCT
ejpam-5374	178	22	31	31	NUM
ejpam-5374	178	23	)	)	PUNCT
ejpam-5374	178	24	as	as	SCONJ
ejpam-5374	178	25	follows	follow	VERB
ejpam-5374	178	26	:	:	PUNCT
ejpam-5374	178	27	|t2,2	|t2,2	NOUN
ejpam-5374	178	28	(	(	PUNCT
ejpam-5374	178	29	γf	γf	PROPN
ejpam-5374	178	30	)	)	PUNCT
ejpam-5374	179	1	|	|	ADV
ejpam-5374	179	2	=	=	PUNCT
ejpam-5374	179	3	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5374	179	4	tαδ2e−2iα	tαδ2e−2iα	NOUN
ejpam-5374	179	5	2304	2304	NUM
ejpam-5374	179	6	(	(	PUNCT
ejpam-5374	179	7	−64p2	−64p2	X
ejpam-5374	179	8	(	(	PUNCT
ejpam-5374	179	9	p2	p2	PROPN
ejpam-5374	179	10	−	−	PROPN
ejpam-5374	179	11	κ∗p21	κ∗p21	NOUN
ejpam-5374	179	12	)	)	PUNCT
ejpam-5374	180	1	+	+	CCONJ
ejpam-5374	180	2	12tαδ	12tαδ	ADJ
ejpam-5374	180	3	2e−2iαp31	2e−2iαp31	NUM
ejpam-5374	180	4	(	(	PUNCT
ejpam-5374	180	5	p3	p3	PROPN
ejpam-5374	180	6	−	−	PROPN
ejpam-5374	180	7	κ∗∗p1p2)−	κ∗∗p1p2)−	ADJ
ejpam-5374	180	8	9tαδ	9tαδ	NUM
ejpam-5374	180	9	2e−2iαp41	2e−2iαp41	NUM
ejpam-5374	180	10	+36p3	+36p3	X
ejpam-5374	180	11	(	(	PUNCT
ejpam-5374	180	12	p3	p3	PROPN
ejpam-5374	180	13	−	−	PROPN
ejpam-5374	180	14	κ∗∗∗p1p2	κ∗∗∗p1p2	NOUN
ejpam-5374	180	15	)	)	PUNCT
ejpam-5374	180	16	+	+	NUM
ejpam-5374	180	17	16tαδ	16tαδ	X
ejpam-5374	180	18	2e−2iαp21p	2e−2iαp21p	NUM
ejpam-5374	180	19	2	2	NUM
ejpam-5374	180	20	2	2	NUM
ejpam-5374	180	21	+	+	CCONJ
ejpam-5374	180	22	tαδ	tαδ	VERB
ejpam-5374	180	23	4e−4iαp61	4e−4iαp61	ADJ
ejpam-5374	180	24	)	)	PUNCT
ejpam-5374	180	25	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5374	180	26	,	,	PUNCT
ejpam-5374	180	27	(	(	PUNCT
ejpam-5374	180	28	32	32	NUM
ejpam-5374	180	29	)	)	PUNCT
ejpam-5374	180	30	where	where	SCONJ
ejpam-5374	180	31	κ∗	κ∗	NOUN
ejpam-5374	180	32	=	=	SYM
ejpam-5374	181	1	48tαδe	48tαδe	PROPN
ejpam-5374	181	2	−iα	−iα	PROPN
ejpam-5374	181	3	64	64	NUM
ejpam-5374	181	4	,	,	PUNCT
ejpam-5374	181	5	κ∗∗	κ∗∗	X
ejpam-5374	181	6	=	=	SYM
ejpam-5374	181	7	8tαδe	8tαδe	NUM
ejpam-5374	181	8	−iα	−iα	PROPN
ejpam-5374	181	9	12	12	NUM
ejpam-5374	181	10	,	,	PUNCT
ejpam-5374	181	11	and	and	CCONJ
ejpam-5374	181	12	κ∗∗∗	κ∗∗∗	PROPN
ejpam-5374	181	13	=	=	SYM
ejpam-5374	182	1	48tαδe	48tαδe	PROPN
ejpam-5374	182	2	−iα	−iα	PROPN
ejpam-5374	182	3	36	36	NUM
ejpam-5374	182	4	.	.	PUNCT
ejpam-5374	183	1	according	accord	VERB
ejpam-5374	183	2	to	to	ADP
ejpam-5374	183	3	lemma	lemma	PROPN
ejpam-5374	183	4	2	2	NUM
ejpam-5374	183	5	,	,	PUNCT
ejpam-5374	183	6	we	we	PRON
ejpam-5374	183	7	can	can	AUX
ejpam-5374	183	8	conclude	conclude	VERB
ejpam-5374	183	9	that∣∣p2	that∣∣p2	PROPN
ejpam-5374	183	10	−	−	PROPN
ejpam-5374	183	11	κ∗p21	κ∗p21	NOUN
ejpam-5374	183	12	∣∣	∣∣	X
ejpam-5374	183	13	≤	≤	PROPN
ejpam-5374	183	14	2max	2max	NUM
ejpam-5374	183	15	{	{	PUNCT
ejpam-5374	183	16	1	1	NUM
ejpam-5374	183	17	,	,	PUNCT
ejpam-5374	183	18	∣∣∣3tαδe	∣∣∣3tαδe	ADJ
ejpam-5374	183	19	−iα−2	−iα−2	X
ejpam-5374	183	20	2	2	NUM
ejpam-5374	183	21	∣∣∣	∣∣∣	ADJ
ejpam-5374	183	22	}	}	PUNCT
ejpam-5374	183	23	=	=	SYM
ejpam-5374	183	24	2	2	NUM
ejpam-5374	183	25	,	,	PUNCT
ejpam-5374	183	26	|p3	|p3	VERB
ejpam-5374	183	27	−	−	PROPN
ejpam-5374	183	28	κ∗∗p1p2|	κ∗∗p1p2|	PROPN
ejpam-5374	183	29	≤	≤	NOUN
ejpam-5374	183	30	2max	2max	NUM
ejpam-5374	183	31	{	{	PUNCT
ejpam-5374	183	32	1	1	NUM
ejpam-5374	183	33	,	,	PUNCT
ejpam-5374	183	34	∣∣∣4tαδe	∣∣∣4tαδe	ADP
ejpam-5374	183	35	−iα−3	−iα−3	X
ejpam-5374	183	36	3	3	NUM
ejpam-5374	183	37	∣∣∣	∣∣∣	ADJ
ejpam-5374	183	38	}	}	PUNCT
ejpam-5374	183	39	=	=	SYM
ejpam-5374	183	40	2	2	NUM
ejpam-5374	183	41	,	,	PUNCT
ejpam-5374	183	42	|p3	|p3	PROPN
ejpam-5374	184	1	−	−	PROPN
ejpam-5374	185	1	κ∗∗∗p1p2|	κ∗∗∗p1p2|	PROPN
ejpam-5374	185	2	≤	≤	NOUN
ejpam-5374	185	3	2max	2max	NUM
ejpam-5374	185	4	{	{	PUNCT
ejpam-5374	185	5	1	1	NUM
ejpam-5374	185	6	,	,	PUNCT
ejpam-5374	185	7	∣∣∣8tαδe	∣∣∣8tαδe	ADP
ejpam-5374	185	8	−iα−3	−iα−3	X
ejpam-5374	185	9	3	3	NUM
ejpam-5374	185	10	∣∣∣	∣∣∣	ADJ
ejpam-5374	185	11	}	}	PUNCT
ejpam-5374	185	12	=	=	SYM
ejpam-5374	185	13	2	2	NUM
ejpam-5374	185	14	∣∣∣8tαδe	∣∣∣8tαδe	ADP
ejpam-5374	185	15	−iα−3	−iα−3	X
ejpam-5374	185	16	3	3	NUM
ejpam-5374	185	17	∣∣∣	∣∣∣	NOUN
ejpam-5374	185	18	.	.	PUNCT
ejpam-5374	186	1			NOUN
ejpam-5374	186	2	(	(	PUNCT
ejpam-5374	186	3	33	33	NUM
ejpam-5374	186	4	)	)	PUNCT
ejpam-5374	186	5	using	use	VERB
ejpam-5374	186	6	lemma	lemma	PROPN
ejpam-5374	186	7	1	1	NUM
ejpam-5374	186	8	,	,	PUNCT
ejpam-5374	186	9	(	(	PUNCT
ejpam-5374	186	10	33	33	NUM
ejpam-5374	186	11	)	)	PUNCT
ejpam-5374	186	12	,	,	PUNCT
ejpam-5374	186	13	and	and	CCONJ
ejpam-5374	186	14	the	the	DET
ejpam-5374	186	15	triangle	triangle	NOUN
ejpam-5374	186	16	inequality	inequality	NOUN
ejpam-5374	186	17	,	,	PUNCT
ejpam-5374	186	18	we	we	PRON
ejpam-5374	186	19	obtain	obtain	VERB
ejpam-5374	186	20	the	the	DET
ejpam-5374	186	21	desired	desire	VERB
ejpam-5374	186	22	bound	bind	VERB
ejpam-5374	186	23	from	from	ADP
ejpam-5374	186	24	(	(	PUNCT
ejpam-5374	186	25	32	32	NUM
ejpam-5374	186	26	)	)	PUNCT
ejpam-5374	186	27	.	.	PUNCT
ejpam-5374	187	1	this	this	PRON
ejpam-5374	187	2	concludes	conclude	VERB
ejpam-5374	187	3	the	the	DET
ejpam-5374	187	4	proof	proof	NOUN
ejpam-5374	187	5	of	of	ADP
ejpam-5374	187	6	theorem	theorem	ADJ
ejpam-5374	187	7	3	3	NUM
ejpam-5374	187	8	.	.	NOUN
ejpam-5374	187	9	3.4	3.4	NUM
ejpam-5374	187	10	.	.	PUNCT
ejpam-5374	188	1	second	second	ADJ
ejpam-5374	188	2	-	-	PUNCT
ejpam-5374	188	3	order	order	NOUN
ejpam-5374	188	4	vandermonde	vandermonde	NOUN
ejpam-5374	188	5	determinant	determinant	ADJ
ejpam-5374	188	6	of	of	ADP
ejpam-5374	188	7	logarithmic	logarithmic	ADJ
ejpam-5374	188	8	coefficients	coefficient	NOUN
ejpam-5374	188	9	for	for	ADP
ejpam-5374	188	10	g(α	g(α	PROPN
ejpam-5374	188	11	,	,	PUNCT
ejpam-5374	188	12	δ	δ	PROPN
ejpam-5374	188	13	)	)	PUNCT
ejpam-5374	188	14	in	in	ADP
ejpam-5374	188	15	this	this	DET
ejpam-5374	188	16	subsection	subsection	NOUN
ejpam-5374	188	17	,	,	PUNCT
ejpam-5374	188	18	we	we	PRON
ejpam-5374	188	19	obtain	obtain	VERB
ejpam-5374	188	20	the	the	DET
ejpam-5374	188	21	upper	upper	ADJ
ejpam-5374	188	22	bound	bind	VERB
ejpam-5374	188	23	of	of	ADP
ejpam-5374	188	24	the	the	DET
ejpam-5374	188	25	second	second	ADJ
ejpam-5374	188	26	-	-	PUNCT
ejpam-5374	188	27	order	order	NOUN
ejpam-5374	188	28	vandermonde	vandermonde	NOUN
ejpam-5374	188	29	determinant	determinant	ADJ
ejpam-5374	188	30	of	of	ADP
ejpam-5374	188	31	logarithmic	logarithmic	ADJ
ejpam-5374	188	32	coefficients	coefficient	NOUN
ejpam-5374	188	33	,	,	PUNCT
ejpam-5374	188	34	specifically	specifically	ADV
ejpam-5374	188	35	for	for	ADP
ejpam-5374	188	36	n	n	NOUN
ejpam-5374	188	37	=	=	SYM
ejpam-5374	188	38	2	2	NUM
ejpam-5374	188	39	and	and	CCONJ
ejpam-5374	188	40	q	q	NOUN
ejpam-5374	188	41	=	=	NOUN
ejpam-5374	188	42	2	2	NUM
ejpam-5374	188	43	,	,	PUNCT
ejpam-5374	188	44	for	for	ADP
ejpam-5374	188	45	functions	function	NOUN
ejpam-5374	188	46	belonging	belong	VERB
ejpam-5374	188	47	to	to	ADP
ejpam-5374	188	48	g	g	PROPN
ejpam-5374	188	49	(	(	PUNCT
ejpam-5374	188	50	α	α	PROPN
ejpam-5374	188	51	,	,	PUNCT
ejpam-5374	188	52	δ	δ	PROPN
ejpam-5374	188	53	)	)	PUNCT
ejpam-5374	188	54	.	.	PUNCT
ejpam-5374	189	1	theorem	theorem	ADJ
ejpam-5374	189	2	4	4	NUM
ejpam-5374	189	3	.	.	PUNCT
ejpam-5374	190	1	if	if	SCONJ
ejpam-5374	190	2	f	f	PROPN
ejpam-5374	190	3	(	(	PUNCT
ejpam-5374	190	4	z	z	NOUN
ejpam-5374	190	5	)	)	PUNCT
ejpam-5374	190	6	=	=	SYM
ejpam-5374	190	7	z	z	NOUN
ejpam-5374	191	1	+	+	NOUN
ejpam-5374	191	2	∞∑	∞∑	NUM
ejpam-5374	191	3	n=2	n=2	CCONJ
ejpam-5374	191	4	anz	anz	NOUN
ejpam-5374	191	5	n	n	ADP
ejpam-5374	191	6	∈	∈	PROPN
ejpam-5374	191	7	g	g	PROPN
ejpam-5374	191	8	(	(	PUNCT
ejpam-5374	191	9	α	α	PROPN
ejpam-5374	191	10	,	,	PUNCT
ejpam-5374	191	11	δ	δ	PROPN
ejpam-5374	191	12	)	)	PUNCT
ejpam-5374	191	13	,	,	PUNCT
ejpam-5374	191	14	then	then	ADV
ejpam-5374	191	15	|v2,2	|v2,2	PROPN
ejpam-5374	191	16	(	(	PUNCT
ejpam-5374	191	17	γf	γf	PROPN
ejpam-5374	191	18	)	)	PUNCT
ejpam-5374	191	19	|	|	ADV
ejpam-5374	191	20	≤	≤	NUM
ejpam-5374	191	21	tαδ	tαδ	NOUN
ejpam-5374	191	22	(	(	PUNCT
ejpam-5374	191	23	7	7	NUM
ejpam-5374	191	24	+	+	CCONJ
ejpam-5374	191	25	2tαδ	2tαδ	NUM
ejpam-5374	191	26	2	2	NUM
ejpam-5374	191	27	)	)	PUNCT
ejpam-5374	191	28	12	12	NUM
ejpam-5374	191	29	,	,	PUNCT
ejpam-5374	191	30	where	where	SCONJ
ejpam-5374	191	31	tαδ	tαδ	NOUN
ejpam-5374	191	32	=	=	SYM
ejpam-5374	191	33	cosα−	cosα−	PROPN
ejpam-5374	191	34	δ	δ	PROPN
ejpam-5374	191	35	.	.	PUNCT
ejpam-5374	192	1	proof	proof	NOUN
ejpam-5374	192	2	.	.	PUNCT
ejpam-5374	193	1	through	through	ADP
ejpam-5374	193	2	(	(	PUNCT
ejpam-5374	193	3	8)	8)	NUM
ejpam-5374	193	4	and	and	CCONJ
ejpam-5374	193	5	(	(	PUNCT
ejpam-5374	193	6	9	9	NUM
ejpam-5374	193	7	)	)	PUNCT
ejpam-5374	193	8	yield	yield	NOUN
ejpam-5374	193	9	v2,2	v2,2	PROPN
ejpam-5374	193	10	(	(	PUNCT
ejpam-5374	193	11	γf	γf	PROPN
ejpam-5374	193	12	)	)	PUNCT
ejpam-5374	193	13	=	=	SYM
ejpam-5374	194	1	tαδe	tαδe	NOUN
ejpam-5374	194	2	−iα	−iα	VERB
ejpam-5374	194	3	48	48	NUM
ejpam-5374	194	4	(	(	PUNCT
ejpam-5374	194	5	6p3	6p3	NUM
ejpam-5374	194	6	−	−	NOUN
ejpam-5374	194	7	4tαδe	4tαδe	NUM
ejpam-5374	194	8	−iαp1p2	−iαp1p2	NOUN
ejpam-5374	194	9	+	+	CCONJ
ejpam-5374	194	10	tαδ	tαδ	PRON
ejpam-5374	194	11	2e−2iαp31	2e−2iαp31	PROPN
ejpam-5374	195	1	−	−	ADP
ejpam-5374	195	2	8p2	8p2	NUM
ejpam-5374	195	3	+	+	CCONJ
ejpam-5374	195	4	3tαδe	3tαδe	NUM
ejpam-5374	195	5	−iαp21	−iαp21	VERB
ejpam-5374	195	6	)	)	PUNCT
ejpam-5374	195	7	.	.	PUNCT
ejpam-5374	196	1	(	(	PUNCT
ejpam-5374	196	2	34	34	X
ejpam-5374	196	3	)	)	PUNCT
ejpam-5374	196	4	n.h.a.a	n.h.a.a	PROPN
ejpam-5374	196	5	.	.	PROPN
ejpam-5374	196	6	wahid	wahid	PROPN
ejpam-5374	196	7	,	,	PUNCT
ejpam-5374	196	8	i.q	i.q	PROPN
ejpam-5374	196	9	.	.	PROPN
ejpam-5374	196	10	amirnuddin	amirnuddin	PROPN
ejpam-5374	196	11	,	,	PUNCT
ejpam-5374	196	12	n.i.m	n.i.m	NOUN
ejpam-5374	196	13	.	.	PUNCT
ejpam-5374	197	1	azmi	azmi	PROPN
ejpam-5374	197	2	/	/	SYM
ejpam-5374	197	3	eur	eur	PROPN
ejpam-5374	197	4	.	.	PUNCT
ejpam-5374	198	1	j.	j.	PROPN
ejpam-5374	198	2	pure	pure	PROPN
ejpam-5374	198	3	appl	appl	PROPN
ejpam-5374	198	4	.	.	PROPN
ejpam-5374	198	5	math	math	PROPN
ejpam-5374	198	6	,	,	PUNCT
ejpam-5374	198	7	17	17	NUM
ejpam-5374	198	8	(	(	PUNCT
ejpam-5374	198	9	4	4	NUM
ejpam-5374	198	10	)	)	PUNCT
ejpam-5374	198	11	(	(	PUNCT
ejpam-5374	198	12	2024	2024	NUM
ejpam-5374	198	13	)	)	PUNCT
ejpam-5374	198	14	,	,	PUNCT
ejpam-5374	198	15	2738	2738	NUM
ejpam-5374	198	16	-	-	SYM
ejpam-5374	198	17	2752	2752	NUM
ejpam-5374	198	18	2747	2747	NUM
ejpam-5374	198	19	by	by	ADP
ejpam-5374	198	20	rearranging	rearrange	VERB
ejpam-5374	198	21	the	the	DET
ejpam-5374	198	22	terms	term	NOUN
ejpam-5374	198	23	in	in	ADP
ejpam-5374	198	24	(	(	PUNCT
ejpam-5374	198	25	34	34	NUM
ejpam-5374	198	26	)	)	PUNCT
ejpam-5374	198	27	according	accord	VERB
ejpam-5374	198	28	to	to	ADP
ejpam-5374	198	29	lemma	lemma	PROPN
ejpam-5374	198	30	2	2	NUM
ejpam-5374	198	31	,	,	PUNCT
ejpam-5374	198	32	we	we	PRON
ejpam-5374	198	33	obtain	obtain	VERB
ejpam-5374	198	34	|v2,2	|v2,2	NOUN
ejpam-5374	198	35	(	(	PUNCT
ejpam-5374	198	36	γf	γf	ADJ
ejpam-5374	198	37	)	)	PUNCT
ejpam-5374	198	38	|	|	NOUN
ejpam-5374	199	1	=	=	PUNCT
ejpam-5374	199	2	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5374	199	3	tαδe−iα	tαδe−iα	NUM
ejpam-5374	199	4	48	48	NUM
ejpam-5374	199	5	(	(	PUNCT
ejpam-5374	199	6	6	6	NUM
ejpam-5374	199	7	(	(	PUNCT
ejpam-5374	199	8	p3	p3	PROPN
ejpam-5374	199	9	−	−	PROPN
ejpam-5374	199	10	η∗p1p2)−	η∗p1p2)−	PROPN
ejpam-5374	199	11	8	8	NUM
ejpam-5374	199	12	(	(	PUNCT
ejpam-5374	199	13	p2	p2	PROPN
ejpam-5374	199	14	−	−	PROPN
ejpam-5374	199	15	η∗∗p21	η∗∗p21	PROPN
ejpam-5374	199	16	)	)	PUNCT
ejpam-5374	199	17	+	+	CCONJ
ejpam-5374	199	18	tαδ	tαδ	PRON
ejpam-5374	199	19	2e−2iαp31	2e−2iαp31	PROPN
ejpam-5374	199	20	)	)	PUNCT
ejpam-5374	199	21	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5374	199	22	,	,	PUNCT
ejpam-5374	199	23	(	(	PUNCT
ejpam-5374	199	24	35	35	NUM
ejpam-5374	199	25	)	)	PUNCT
ejpam-5374	199	26	where	where	SCONJ
ejpam-5374	199	27	η∗	η∗	NOUN
ejpam-5374	199	28	=	=	PUNCT
ejpam-5374	200	1	4tαδe	4tαδe	PROPN
ejpam-5374	200	2	−iα	−iα	NUM
ejpam-5374	200	3	6	6	NUM
ejpam-5374	200	4	and	and	CCONJ
ejpam-5374	200	5	η∗∗	η∗∗	ADV
ejpam-5374	200	6	=	=	SYM
ejpam-5374	200	7	3tαδe	3tαδe	NUM
ejpam-5374	200	8	−iα	−iα	NOUN
ejpam-5374	200	9	8	8	NUM
ejpam-5374	200	10	.	.	PUNCT
ejpam-5374	201	1	furthermore	furthermore	ADV
ejpam-5374	201	2	,	,	PUNCT
ejpam-5374	201	3	we	we	PRON
ejpam-5374	201	4	discover	discover	VERB
ejpam-5374	201	5	that	that	SCONJ
ejpam-5374	201	6	|p3	|p3	PROPN
ejpam-5374	201	7	−	−	PROPN
ejpam-5374	201	8	η∗p1p2|	η∗p1p2|	PROPN
ejpam-5374	201	9	≤	≤	ADV
ejpam-5374	201	10	2max	2max	NUM
ejpam-5374	201	11	{	{	PUNCT
ejpam-5374	201	12	1	1	NUM
ejpam-5374	201	13	,	,	PUNCT
ejpam-5374	201	14	∣∣∣4tαδe	∣∣∣4tαδe	ADP
ejpam-5374	201	15	−iα−3	−iα−3	X
ejpam-5374	201	16	3	3	NUM
ejpam-5374	201	17	∣∣∣	∣∣∣	ADJ
ejpam-5374	201	18	}	}	PUNCT
ejpam-5374	201	19	=	=	SYM
ejpam-5374	201	20	2	2	NUM
ejpam-5374	201	21	,	,	PUNCT
ejpam-5374	201	22	∣∣p2	∣∣p2	PROPN
ejpam-5374	201	23	−	−	NOUN
ejpam-5374	201	24	η∗∗p21	η∗∗p21	ADJ
ejpam-5374	201	25	∣∣	∣∣	ADJ
ejpam-5374	201	26	≤	≤	PROPN
ejpam-5374	201	27	2max	2max	NUM
ejpam-5374	201	28	{	{	PUNCT
ejpam-5374	201	29	1	1	NUM
ejpam-5374	201	30	,	,	PUNCT
ejpam-5374	201	31	∣∣∣3tαδe	∣∣∣3tαδe	NOUN
ejpam-5374	201	32	−iα−4	−iα−4	VERB
ejpam-5374	201	33	4	4	NUM
ejpam-5374	201	34	∣∣∣	∣∣∣	ADJ
ejpam-5374	201	35	}	}	PUNCT
ejpam-5374	201	36	=	=	SYM
ejpam-5374	201	37	2	2	X
ejpam-5374	201	38	.	.	X
ejpam-5374	202	1			NOUN
ejpam-5374	202	2	(	(	PUNCT
ejpam-5374	202	3	36	36	NUM
ejpam-5374	202	4	)	)	PUNCT
ejpam-5374	202	5	by	by	ADP
ejpam-5374	202	6	implementing	implement	VERB
ejpam-5374	202	7	lemma	lemma	PROPN
ejpam-5374	202	8	1	1	NUM
ejpam-5374	202	9	and	and	CCONJ
ejpam-5374	202	10	(	(	PUNCT
ejpam-5374	202	11	36	36	NUM
ejpam-5374	202	12	)	)	PUNCT
ejpam-5374	202	13	into	into	ADP
ejpam-5374	202	14	(	(	PUNCT
ejpam-5374	202	15	35	35	NUM
ejpam-5374	202	16	)	)	PUNCT
ejpam-5374	202	17	,	,	PUNCT
ejpam-5374	202	18	as	as	ADV
ejpam-5374	202	19	well	well	ADV
ejpam-5374	202	20	as	as	ADP
ejpam-5374	202	21	applying	apply	VERB
ejpam-5374	202	22	the	the	DET
ejpam-5374	202	23	triangle	triangle	NOUN
ejpam-5374	202	24	inequality	inequality	NOUN
ejpam-5374	202	25	,	,	PUNCT
ejpam-5374	202	26	we	we	PRON
ejpam-5374	202	27	achieve	achieve	VERB
ejpam-5374	202	28	the	the	DET
ejpam-5374	202	29	desired	desire	VERB
ejpam-5374	202	30	bound	bind	VERB
ejpam-5374	202	31	.	.	PUNCT
ejpam-5374	203	1	this	this	PRON
ejpam-5374	203	2	completes	complete	VERB
ejpam-5374	203	3	the	the	DET
ejpam-5374	203	4	proof	proof	NOUN
ejpam-5374	203	5	of	of	ADP
ejpam-5374	203	6	theorem	theorem	ADJ
ejpam-5374	203	7	4	4	NUM
ejpam-5374	203	8	.	.	NOUN
ejpam-5374	203	9	4	4	NUM
ejpam-5374	203	10	.	.	NOUN
ejpam-5374	203	11	consequences	consequence	NOUN
ejpam-5374	203	12	and	and	CCONJ
ejpam-5374	203	13	corollaries	corollary	NOUN
ejpam-5374	203	14	since	since	SCONJ
ejpam-5374	203	15	g	g	PROPN
ejpam-5374	203	16	(	(	PUNCT
ejpam-5374	203	17	α	α	PROPN
ejpam-5374	203	18	,	,	PUNCT
ejpam-5374	203	19	δ	δ	NOUN
ejpam-5374	203	20	)	)	PUNCT
ejpam-5374	203	21	generalizes	generalize	VERB
ejpam-5374	203	22	r	r	NOUN
ejpam-5374	203	23	,	,	PUNCT
ejpam-5374	203	24	r	r	NOUN
ejpam-5374	203	25	(	(	PUNCT
ejpam-5374	203	26	δ	δ	PROPN
ejpam-5374	203	27	)	)	PUNCT
ejpam-5374	203	28	,	,	PUNCT
ejpam-5374	203	29	and	and	CCONJ
ejpam-5374	203	30	r	r	NOUN
ejpam-5374	203	31	(	(	PUNCT
ejpam-5374	203	32	α	α	NOUN
ejpam-5374	203	33	)	)	PUNCT
ejpam-5374	203	34	,	,	PUNCT
ejpam-5374	203	35	several	several	ADJ
ejpam-5374	203	36	new	new	ADJ
ejpam-5374	203	37	consequences	consequence	NOUN
ejpam-5374	203	38	of	of	ADP
ejpam-5374	203	39	theorems	theorem	NOUN
ejpam-5374	203	40	1	1	NUM
ejpam-5374	203	41	-	-	SYM
ejpam-5374	203	42	4	4	NUM
ejpam-5374	203	43	are	be	AUX
ejpam-5374	203	44	highlighted	highlight	VERB
ejpam-5374	203	45	out	out	ADP
ejpam-5374	203	46	for	for	ADP
ejpam-5374	203	47	specific	specific	ADJ
ejpam-5374	203	48	choices	choice	NOUN
ejpam-5374	203	49	of	of	ADP
ejpam-5374	203	50	α	α	NOUN
ejpam-5374	203	51	and	and	CCONJ
ejpam-5374	203	52	δ	δ	PROPN
ejpam-5374	203	53	as	as	SCONJ
ejpam-5374	203	54	follows	follow	VERB
ejpam-5374	203	55	:	:	PUNCT
ejpam-5374	203	56	substituting	substitute	VERB
ejpam-5374	203	57	α	α	NOUN
ejpam-5374	203	58	=	=	SYM
ejpam-5374	203	59	0	0	NUM
ejpam-5374	203	60	and	and	CCONJ
ejpam-5374	203	61	δ	δ	PROPN
ejpam-5374	203	62	=	=	NOUN
ejpam-5374	203	63	0	0	NUM
ejpam-5374	203	64	in	in	ADP
ejpam-5374	203	65	theorems	theorem	NOUN
ejpam-5374	203	66	1	1	NUM
ejpam-5374	203	67	-	-	SYM
ejpam-5374	203	68	4	4	NUM
ejpam-5374	203	69	,	,	PUNCT
ejpam-5374	203	70	we	we	PRON
ejpam-5374	203	71	get	get	VERB
ejpam-5374	203	72	the	the	DET
ejpam-5374	203	73	estimates	estimate	NOUN
ejpam-5374	203	74	bounds	bound	VERB
ejpam-5374	203	75	for	for	ADP
ejpam-5374	203	76	the	the	DET
ejpam-5374	203	77	class	class	PROPN
ejpam-5374	203	78	r.	r.	PROPN
ejpam-5374	203	79	corollary	corollary	NOUN
ejpam-5374	203	80	1	1	NUM
ejpam-5374	203	81	.	.	PUNCT
ejpam-5374	203	82	for	for	ADP
ejpam-5374	203	83	any	any	DET
ejpam-5374	203	84	function	function	NOUN
ejpam-5374	203	85	f	f	PROPN
ejpam-5374	203	86	(	(	PUNCT
ejpam-5374	203	87	z	z	NOUN
ejpam-5374	203	88	)	)	PUNCT
ejpam-5374	203	89	given	give	VERB
ejpam-5374	203	90	by	by	ADP
ejpam-5374	203	91	(	(	PUNCT
ejpam-5374	203	92	1	1	NUM
ejpam-5374	203	93	)	)	PUNCT
ejpam-5374	203	94	for	for	ADP
ejpam-5374	203	95	the	the	DET
ejpam-5374	203	96	class	class	NOUN
ejpam-5374	203	97	g	g	PROPN
ejpam-5374	203	98	(	(	PUNCT
ejpam-5374	203	99	0	0	NUM
ejpam-5374	203	100	,	,	PUNCT
ejpam-5374	203	101	0	0	NUM
ejpam-5374	203	102	)	)	PUNCT
ejpam-5374	203	103	≡	≡	PROPN
ejpam-5374	203	104	r	r	NOUN
ejpam-5374	203	105	,	,	PUNCT
ejpam-5374	203	106	then	then	ADV
ejpam-5374	203	107	(	(	PUNCT
ejpam-5374	203	108	i	i	NOUN
ejpam-5374	203	109	)	)	PUNCT
ejpam-5374	203	110	|γ1|	|γ1|	NOUN
ejpam-5374	203	111	≤	≤	NUM
ejpam-5374	203	112	1	1	NUM
ejpam-5374	203	113	2	2	NUM
ejpam-5374	203	114	,	,	PUNCT
ejpam-5374	203	115	|γ2|	|γ2|	VERB
ejpam-5374	203	116	≤	≤	NUM
ejpam-5374	203	117	1	1	NUM
ejpam-5374	203	118	3	3	NUM
ejpam-5374	203	119	,	,	PUNCT
ejpam-5374	203	120	|γ3|	|γ3|	ADJ
ejpam-5374	203	121	≤	≤	NUM
ejpam-5374	203	122	5	5	NUM
ejpam-5374	203	123	12	12	NUM
ejpam-5374	203	124	,	,	PUNCT
ejpam-5374	203	125	|γ4|	|γ4|	NOUN
ejpam-5374	203	126	≤	≤	NUM
ejpam-5374	203	127	23	23	NUM
ejpam-5374	203	128	40	40	NUM
ejpam-5374	203	129	(	(	PUNCT
ejpam-5374	203	130	ii	ii	NOUN
ejpam-5374	203	131	)	)	PUNCT
ejpam-5374	203	132	|h2,2	|h2,2	NOUN
ejpam-5374	203	133	(	(	PUNCT
ejpam-5374	203	134	γf	γf	NOUN
ejpam-5374	203	135	)	)	PUNCT
ejpam-5374	203	136	|	|	ADV
ejpam-5374	203	137	≤	≤	NUM
ejpam-5374	203	138	301	301	NUM
ejpam-5374	203	139	432	432	NUM
ejpam-5374	203	140	(	(	PUNCT
ejpam-5374	203	141	iii	iii	NOUN
ejpam-5374	203	142	)	)	PUNCT
ejpam-5374	203	143	|t2,2	|t2,2	NOUN
ejpam-5374	203	144	(	(	PUNCT
ejpam-5374	203	145	γf	γf	PROPN
ejpam-5374	203	146	)	)	PUNCT
ejpam-5374	204	1	|	|	ADV
ejpam-5374	204	2	≤	≤	NUM
ejpam-5374	204	3	1	1	NUM
ejpam-5374	204	4	2	2	NUM
ejpam-5374	204	5	(	(	PUNCT
ejpam-5374	204	6	iv	iv	X
ejpam-5374	204	7	)	)	PUNCT
ejpam-5374	204	8	|v2,2	|v2,2	NOUN
ejpam-5374	204	9	(	(	PUNCT
ejpam-5374	204	10	γf	γf	PROPN
ejpam-5374	204	11	)	)	PUNCT
ejpam-5374	204	12	|	|	ADV
ejpam-5374	204	13	≤	≤	NUM
ejpam-5374	204	14	3	3	NUM
ejpam-5374	204	15	4	4	NUM
ejpam-5374	204	16	if	if	SCONJ
ejpam-5374	204	17	we	we	PRON
ejpam-5374	204	18	consider	consider	VERB
ejpam-5374	204	19	α	α	NOUN
ejpam-5374	204	20	=	=	NOUN
ejpam-5374	204	21	0	0	NUM
ejpam-5374	204	22	in	in	ADP
ejpam-5374	204	23	theorems	theorem	NOUN
ejpam-5374	204	24	1	1	NUM
ejpam-5374	204	25	-	-	SYM
ejpam-5374	204	26	4	4	NUM
ejpam-5374	204	27	,	,	PUNCT
ejpam-5374	204	28	we	we	PRON
ejpam-5374	204	29	obtain	obtain	VERB
ejpam-5374	204	30	the	the	DET
ejpam-5374	204	31	estimates	estimate	NOUN
ejpam-5374	204	32	bounds	bound	VERB
ejpam-5374	204	33	for	for	ADP
ejpam-5374	204	34	the	the	DET
ejpam-5374	204	35	class	class	NOUN
ejpam-5374	204	36	r	r	NOUN
ejpam-5374	204	37	(	(	PUNCT
ejpam-5374	204	38	δ	δ	PROPN
ejpam-5374	204	39	)	)	PUNCT
ejpam-5374	204	40	.	.	PUNCT
ejpam-5374	205	1	corollary	corollary	ADJ
ejpam-5374	205	2	2	2	NUM
ejpam-5374	205	3	.	.	PUNCT
ejpam-5374	206	1	for	for	ADP
ejpam-5374	206	2	any	any	DET
ejpam-5374	206	3	function	function	NOUN
ejpam-5374	206	4	f	f	PROPN
ejpam-5374	206	5	(	(	PUNCT
ejpam-5374	206	6	z	z	NOUN
ejpam-5374	206	7	)	)	PUNCT
ejpam-5374	206	8	given	give	VERB
ejpam-5374	206	9	by	by	ADP
ejpam-5374	206	10	(	(	PUNCT
ejpam-5374	206	11	1	1	NUM
ejpam-5374	206	12	)	)	PUNCT
ejpam-5374	206	13	for	for	ADP
ejpam-5374	206	14	the	the	DET
ejpam-5374	206	15	class	class	NOUN
ejpam-5374	206	16	g	g	PROPN
ejpam-5374	206	17	(	(	PUNCT
ejpam-5374	206	18	0	0	NUM
ejpam-5374	206	19	,	,	PUNCT
ejpam-5374	206	20	δ	δ	PROPN
ejpam-5374	206	21	)	)	PUNCT
ejpam-5374	206	22	≡	≡	PROPN
ejpam-5374	206	23	r	r	PROPN
ejpam-5374	206	24	(	(	PUNCT
ejpam-5374	206	25	δ	δ	PROPN
ejpam-5374	206	26	)	)	PUNCT
ejpam-5374	206	27	,	,	PUNCT
ejpam-5374	206	28	then	then	ADV
ejpam-5374	206	29	(	(	PUNCT
ejpam-5374	206	30	i	i	NOUN
ejpam-5374	206	31	)	)	PUNCT
ejpam-5374	206	32	|γ1|	|γ1|	PROPN
ejpam-5374	206	33	≤	≤	NUM
ejpam-5374	207	1	1−δ	1−δ	NUM
ejpam-5374	207	2	2	2	NUM
ejpam-5374	207	3	,	,	PUNCT
ejpam-5374	207	4	|γ2|	|γ2|	VERB
ejpam-5374	207	5	≤	≤	ADJ
ejpam-5374	207	6	1−δ	1−δ	NUM
ejpam-5374	207	7	3	3	NUM
ejpam-5374	207	8	,	,	PUNCT
ejpam-5374	207	9	|γ3|	|γ3|	ADP
ejpam-5374	207	10	≤	≤	NUM
ejpam-5374	207	11	1−δ	1−δ	NUM
ejpam-5374	207	12	4	4	NUM
ejpam-5374	208	1	+	+	CCONJ
ejpam-5374	208	2	(	(	PUNCT
ejpam-5374	208	3	1−δ)3	1−δ)3	NUM
ejpam-5374	208	4	6	6	NUM
ejpam-5374	208	5	,	,	PUNCT
ejpam-5374	208	6	|γ4|	|γ4|	NOUN
ejpam-5374	208	7	≤	≤	NOUN
ejpam-5374	208	8	1−δ	1−δ	NUM
ejpam-5374	208	9	5	5	NUM
ejpam-5374	209	1	+	+	CCONJ
ejpam-5374	209	2	(	(	PUNCT
ejpam-5374	209	3	1−δ)2	1−δ)2	NUM
ejpam-5374	209	4	4	4	NUM
ejpam-5374	209	5	+	+	CCONJ
ejpam-5374	209	6	(	(	PUNCT
ejpam-5374	209	7	1−δ)4	1−δ)4	NUM
ejpam-5374	209	8	8	8	NUM
ejpam-5374	209	9	(	(	PUNCT
ejpam-5374	209	10	ii	ii	NOUN
ejpam-5374	209	11	)	)	PUNCT
ejpam-5374	209	12	|h2,2	|h2,2	NOUN
ejpam-5374	209	13	(	(	PUNCT
ejpam-5374	209	14	γf	γf	NOUN
ejpam-5374	209	15	)	)	PUNCT
ejpam-5374	209	16	|	|	ADV
ejpam-5374	209	17	≤	≤	NUM
ejpam-5374	209	18	(	(	PUNCT
ejpam-5374	209	19	1−δ)2	1−δ)2	NUM
ejpam-5374	209	20	2160	2160	NUM
ejpam-5374	209	21	(	(	PUNCT
ejpam-5374	209	22	36	36	NUM
ejpam-5374	209	23	|5	|5	NUM
ejpam-5374	209	24	(	(	PUNCT
ejpam-5374	209	25	1−	1−	NUM
ejpam-5374	209	26	δ	δ	NOUN
ejpam-5374	209	27	)	)	PUNCT
ejpam-5374	210	1	+	+	NUM
ejpam-5374	210	2	4|+	4|+	NUM
ejpam-5374	210	3	9	9	NUM
ejpam-5374	210	4	(	(	PUNCT
ejpam-5374	210	5	1−	1−	NUM
ejpam-5374	210	6	δ	δ	PROPN
ejpam-5374	210	7	)	)	PUNCT
ejpam-5374	210	8	|5	|5	X
ejpam-5374	210	9	(	(	PUNCT
ejpam-5374	210	10	1−	1−	NUM
ejpam-5374	210	11	δ	δ	NOUN
ejpam-5374	210	12	)	)	PUNCT
ejpam-5374	211	1	+	+	CCONJ
ejpam-5374	211	2	12|	12|	NUM
ejpam-5374	211	3	+30(1−	+30(1−	ADJ
ejpam-5374	211	4	δ)3	δ)3	NOUN
ejpam-5374	211	5	+	+	CCONJ
ejpam-5374	211	6	80	80	NUM
ejpam-5374	211	7	(	(	PUNCT
ejpam-5374	211	8	1−	1−	NUM
ejpam-5374	211	9	δ	δ	PROPN
ejpam-5374	211	10	)	)	PUNCT
ejpam-5374	212	1	+	+	CCONJ
ejpam-5374	212	2	135	135	NUM
ejpam-5374	212	3	)	)	PUNCT
ejpam-5374	212	4	(	(	PUNCT
ejpam-5374	212	5	iii	iii	X
ejpam-5374	212	6	)	)	PUNCT
ejpam-5374	212	7	|t2,2	|t2,2	NOUN
ejpam-5374	212	8	(	(	PUNCT
ejpam-5374	212	9	γf	γf	PROPN
ejpam-5374	212	10	)	)	PUNCT
ejpam-5374	212	11	|	|	ADV
ejpam-5374	212	12	≤	≤	NUM
ejpam-5374	212	13	(	(	PUNCT
ejpam-5374	212	14	1−δ)2	1−δ)2	NUM
ejpam-5374	212	15	144	144	NUM
ejpam-5374	212	16	(	(	PUNCT
ejpam-5374	212	17	16	16	NUM
ejpam-5374	212	18	+	+	SYM
ejpam-5374	212	19	37(1−	37(1−	NUM
ejpam-5374	212	20	δ)2	δ)2	NOUN
ejpam-5374	212	21	+	+	X
ejpam-5374	212	22	4	4	NUM
ejpam-5374	212	23	(	(	PUNCT
ejpam-5374	212	24	1−	1−	NUM
ejpam-5374	212	25	δ)4	δ)4	NOUN
ejpam-5374	212	26	+	+	CCONJ
ejpam-5374	212	27	3	3	NUM
ejpam-5374	212	28	|8	|8	NOUN
ejpam-5374	212	29	(	(	PUNCT
ejpam-5374	212	30	1−	1−	NUM
ejpam-5374	212	31	δ)−	δ)−	PROPN
ejpam-5374	212	32	3|	3|	NUM
ejpam-5374	212	33	)	)	PUNCT
ejpam-5374	212	34	(	(	PUNCT
ejpam-5374	212	35	iv	iv	X
ejpam-5374	212	36	)	)	PUNCT
ejpam-5374	212	37	|v2,2	|v2,2	NOUN
ejpam-5374	212	38	(	(	PUNCT
ejpam-5374	212	39	γf	γf	PROPN
ejpam-5374	212	40	)	)	PUNCT
ejpam-5374	212	41	|	|	ADV
ejpam-5374	212	42	≤	≤	NUM
ejpam-5374	212	43	(	(	PUNCT
ejpam-5374	212	44	1−δ)(7	1−δ)(7	ADJ
ejpam-5374	212	45	+	+	NOUN
ejpam-5374	212	46	2(1−δ)2	2(1−δ)2	NUM
ejpam-5374	212	47	)	)	PUNCT
ejpam-5374	212	48	12	12	NUM
ejpam-5374	212	49	references	reference	NOUN
ejpam-5374	212	50	2748	2748	NUM
ejpam-5374	212	51	putting	put	VERB
ejpam-5374	212	52	δ	δ	NOUN
ejpam-5374	212	53	=	=	PUNCT
ejpam-5374	212	54	0	0	NUM
ejpam-5374	212	55	in	in	ADP
ejpam-5374	212	56	theorems	theorem	NOUN
ejpam-5374	212	57	1	1	NUM
ejpam-5374	212	58	-	-	SYM
ejpam-5374	212	59	4	4	NUM
ejpam-5374	212	60	,	,	PUNCT
ejpam-5374	212	61	we	we	PRON
ejpam-5374	212	62	have	have	VERB
ejpam-5374	212	63	the	the	DET
ejpam-5374	212	64	following	follow	VERB
ejpam-5374	212	65	results	result	NOUN
ejpam-5374	212	66	for	for	ADP
ejpam-5374	212	67	the	the	DET
ejpam-5374	212	68	class	class	NOUN
ejpam-5374	212	69	r	r	NOUN
ejpam-5374	212	70	(	(	PUNCT
ejpam-5374	212	71	α	α	NOUN
ejpam-5374	212	72	)	)	PUNCT
ejpam-5374	212	73	.	.	PUNCT
ejpam-5374	213	1	corollary	corollary	ADJ
ejpam-5374	213	2	3	3	NUM
ejpam-5374	213	3	.	.	PUNCT
ejpam-5374	214	1	for	for	ADP
ejpam-5374	214	2	any	any	DET
ejpam-5374	214	3	function	function	NOUN
ejpam-5374	214	4	f	f	PROPN
ejpam-5374	214	5	(	(	PUNCT
ejpam-5374	214	6	z	z	NOUN
ejpam-5374	214	7	)	)	PUNCT
ejpam-5374	214	8	given	give	VERB
ejpam-5374	214	9	by	by	ADP
ejpam-5374	214	10	(	(	PUNCT
ejpam-5374	214	11	1	1	NUM
ejpam-5374	214	12	)	)	PUNCT
ejpam-5374	214	13	for	for	ADP
ejpam-5374	214	14	the	the	DET
ejpam-5374	214	15	class	class	NOUN
ejpam-5374	214	16	g	g	PROPN
ejpam-5374	214	17	(	(	PUNCT
ejpam-5374	214	18	α	α	NOUN
ejpam-5374	214	19	,	,	PUNCT
ejpam-5374	214	20	0	0	NUM
ejpam-5374	214	21	)	)	PUNCT
ejpam-5374	214	22	≡	≡	PROPN
ejpam-5374	214	23	r	r	NOUN
ejpam-5374	214	24	(	(	PUNCT
ejpam-5374	214	25	α	α	NOUN
ejpam-5374	214	26	)	)	PUNCT
ejpam-5374	214	27	,	,	PUNCT
ejpam-5374	214	28	then	then	ADV
ejpam-5374	214	29	(	(	PUNCT
ejpam-5374	214	30	i	i	NOUN
ejpam-5374	214	31	)	)	PUNCT
ejpam-5374	214	32	|γ1|	|γ1|	PROPN
ejpam-5374	214	33	≤	≤	NUM
ejpam-5374	214	34	cosα	cosα	NOUN
ejpam-5374	214	35	2	2	NUM
ejpam-5374	214	36	,	,	PUNCT
ejpam-5374	214	37	|γ2|	|γ2|	VERB
ejpam-5374	214	38	≤	≤	ADJ
ejpam-5374	214	39	cosα	cosα	NOUN
ejpam-5374	214	40	3	3	NUM
ejpam-5374	214	41	,	,	PUNCT
ejpam-5374	214	42	|γ3|	|γ3|	ADP
ejpam-5374	214	43	≤	≤	NUM
ejpam-5374	214	44	cosα	cosα	NOUN
ejpam-5374	214	45	4	4	NUM
ejpam-5374	214	46	+	+	CCONJ
ejpam-5374	214	47	cos3α	cos3α	PROPN
ejpam-5374	214	48	6	6	NUM
ejpam-5374	214	49	,	,	PUNCT
ejpam-5374	214	50	|γ4|	|γ4|	NOUN
ejpam-5374	214	51	≤	≤	PUNCT
ejpam-5374	214	52	cosα	cosα	NOUN
ejpam-5374	214	53	5	5	NUM
ejpam-5374	214	54	+	+	CCONJ
ejpam-5374	214	55	cos2α	cos2α	NOUN
ejpam-5374	214	56	4	4	NUM
ejpam-5374	214	57	+	+	CCONJ
ejpam-5374	214	58	cos4α	cos4α	PROPN
ejpam-5374	214	59	8	8	NUM
ejpam-5374	214	60	(	(	PUNCT
ejpam-5374	214	61	ii	ii	NOUN
ejpam-5374	214	62	)	)	PUNCT
ejpam-5374	214	63	|h2,2	|h2,2	NOUN
ejpam-5374	214	64	(	(	PUNCT
ejpam-5374	214	65	γf	γf	NOUN
ejpam-5374	214	66	)	)	PUNCT
ejpam-5374	214	67	|	|	ADV
ejpam-5374	214	68	≤	≤	NUM
ejpam-5374	214	69	cos2α	cos2α	NOUN
ejpam-5374	215	1	2160	2160	NUM
ejpam-5374	215	2	(	(	PUNCT
ejpam-5374	215	3	36	36	NUM
ejpam-5374	215	4	∣∣5e−iα	∣∣5e−iα	PROPN
ejpam-5374	215	5	cosα+	cosα+	SYM
ejpam-5374	215	6	4	4	NUM
ejpam-5374	215	7	∣∣+	∣∣+	PROPN
ejpam-5374	215	8	9	9	NUM
ejpam-5374	215	9	cosα	cosα	NOUN
ejpam-5374	215	10	∣∣5e−iα	∣∣5e−iα	PROPN
ejpam-5374	215	11	cosα+	cosα+	X
ejpam-5374	215	12	12	12	NUM
ejpam-5374	215	13	∣∣	∣∣	NUM
ejpam-5374	215	14	+30cos3α+	+30cos3α+	NOUN
ejpam-5374	215	15	80	80	NUM
ejpam-5374	215	16	cosα+	cosα+	NOUN
ejpam-5374	215	17	135	135	NUM
ejpam-5374	215	18	)	)	PUNCT
ejpam-5374	215	19	(	(	PUNCT
ejpam-5374	215	20	iii	iii	X
ejpam-5374	215	21	)	)	PUNCT
ejpam-5374	215	22	|t2,2	|t2,2	NOUN
ejpam-5374	215	23	(	(	PUNCT
ejpam-5374	215	24	γf	γf	PROPN
ejpam-5374	215	25	)	)	PUNCT
ejpam-5374	215	26	|	|	ADV
ejpam-5374	215	27	≤	≤	NUM
ejpam-5374	215	28	cos2α	cos2α	NOUN
ejpam-5374	216	1	144	144	NUM
ejpam-5374	216	2	(	(	PUNCT
ejpam-5374	216	3	16	16	NUM
ejpam-5374	216	4	+	+	CCONJ
ejpam-5374	216	5	37cos2α+	37cos2α+	NUM
ejpam-5374	216	6	4	4	NUM
ejpam-5374	216	7	cos4α+	cos4α+	NOUN
ejpam-5374	216	8	3	3	NUM
ejpam-5374	216	9	∣∣8e−iα	∣∣8e−iα	ADV
ejpam-5374	216	10	cosα−	cosα−	NOUN
ejpam-5374	216	11	3	3	NUM
ejpam-5374	216	12	∣∣	∣∣	NOUN
ejpam-5374	216	13	)	)	PUNCT
ejpam-5374	216	14	(	(	PUNCT
ejpam-5374	216	15	iv	iv	X
ejpam-5374	216	16	)	)	PUNCT
ejpam-5374	216	17	|v2,2	|v2,2	NOUN
ejpam-5374	216	18	(	(	PUNCT
ejpam-5374	216	19	γf	γf	PROPN
ejpam-5374	216	20	)	)	PUNCT
ejpam-5374	216	21	|	|	ADV
ejpam-5374	216	22	≤	≤	NUM
ejpam-5374	216	23	cosα(7	cosα(7	PROPN
ejpam-5374	216	24	+	+	PROPN
ejpam-5374	216	25	2cos2α	2cos2α	NUM
ejpam-5374	216	26	)	)	PUNCT
ejpam-5374	216	27	12	12	NUM
ejpam-5374	216	28	5	5	NUM
ejpam-5374	216	29	.	.	PUNCT
ejpam-5374	216	30	conclusion	conclusion	NOUN
ejpam-5374	216	31	in	in	ADP
ejpam-5374	216	32	this	this	DET
ejpam-5374	216	33	paper	paper	NOUN
ejpam-5374	216	34	,	,	PUNCT
ejpam-5374	216	35	we	we	PRON
ejpam-5374	216	36	have	have	AUX
ejpam-5374	216	37	obtained	obtain	VERB
ejpam-5374	216	38	the	the	DET
ejpam-5374	216	39	estimates	estimate	NOUN
ejpam-5374	216	40	on	on	ADP
ejpam-5374	216	41	logarithmic	logarithmic	ADJ
ejpam-5374	216	42	coefficients	coefficient	NOUN
ejpam-5374	216	43	|γn|	|γn|	PROPN
ejpam-5374	216	44	,	,	PUNCT
ejpam-5374	216	45	n	n	NOUN
ejpam-5374	216	46	=	=	SYM
ejpam-5374	216	47	1	1	NUM
ejpam-5374	216	48	,	,	PUNCT
ejpam-5374	216	49	2	2	NUM
ejpam-5374	216	50	,	,	PUNCT
ejpam-5374	216	51	3	3	NUM
ejpam-5374	216	52	,	,	PUNCT
ejpam-5374	216	53	4	4	NUM
ejpam-5374	216	54	,	,	PUNCT
ejpam-5374	216	55	thereby	thereby	ADV
ejpam-5374	216	56	extending	extend	VERB
ejpam-5374	216	57	the	the	DET
ejpam-5374	216	58	properties	property	NOUN
ejpam-5374	216	59	of	of	ADP
ejpam-5374	216	60	g(α	g(α	PROPN
ejpam-5374	216	61	,	,	PUNCT
ejpam-5374	216	62	δ	δ	PROPN
ejpam-5374	216	63	)	)	PUNCT
ejpam-5374	216	64	,	,	PUNCT
ejpam-5374	216	65	r	r	NOUN
ejpam-5374	216	66	,	,	PUNCT
ejpam-5374	216	67	r	r	NOUN
ejpam-5374	216	68	(	(	PUNCT
ejpam-5374	216	69	δ	δ	PROPN
ejpam-5374	216	70	)	)	PUNCT
ejpam-5374	216	71	,	,	PUNCT
ejpam-5374	216	72	and	and	CCONJ
ejpam-5374	216	73	r	r	NOUN
ejpam-5374	216	74	(	(	PUNCT
ejpam-5374	216	75	α	α	NOUN
ejpam-5374	216	76	)	)	PUNCT
ejpam-5374	216	77	.	.	PUNCT
ejpam-5374	217	1	recent	recent	ADJ
ejpam-5374	217	2	research	research	NOUN
ejpam-5374	217	3	has	have	AUX
ejpam-5374	217	4	sparked	spark	VERB
ejpam-5374	217	5	considerable	considerable	ADJ
ejpam-5374	217	6	interest	interest	NOUN
ejpam-5374	217	7	in	in	ADP
ejpam-5374	217	8	logarithmic	logarithmic	ADJ
ejpam-5374	217	9	coefficients	coefficient	NOUN
ejpam-5374	217	10	and	and	CCONJ
ejpam-5374	217	11	the	the	DET
ejpam-5374	217	12	hankel	hankel	NOUN
ejpam-5374	217	13	,	,	PUNCT
ejpam-5374	217	14	toeplitz	toeplitz	NOUN
ejpam-5374	217	15	,	,	PUNCT
ejpam-5374	217	16	and	and	CCONJ
ejpam-5374	217	17	vandermonde	vandermonde	ADJ
ejpam-5374	217	18	determinants	determinant	NOUN
ejpam-5374	217	19	.	.	PUNCT
ejpam-5374	218	1	this	this	PRON
ejpam-5374	218	2	has	have	AUX
ejpam-5374	218	3	inspired	inspire	VERB
ejpam-5374	218	4	us	we	PRON
ejpam-5374	218	5	to	to	PART
ejpam-5374	218	6	define	define	VERB
ejpam-5374	218	7	the	the	DET
ejpam-5374	218	8	vandermonde	vandermonde	NOUN
ejpam-5374	218	9	determinant	determinant	ADJ
ejpam-5374	218	10	of	of	ADP
ejpam-5374	218	11	logarithmic	logarithmic	ADJ
ejpam-5374	218	12	coefficients	coefficient	NOUN
ejpam-5374	218	13	for	for	ADP
ejpam-5374	218	14	functions	function	NOUN
ejpam-5374	218	15	f	f	X
ejpam-5374	218	16	(	(	PUNCT
ejpam-5374	218	17	z	z	NOUN
ejpam-5374	218	18	)	)	PUNCT
ejpam-5374	218	19	∈	∈	PROPN
ejpam-5374	218	20	a.	a.	NOUN
ejpam-5374	218	21	as	as	ADP
ejpam-5374	218	22	a	a	DET
ejpam-5374	218	23	result	result	NOUN
ejpam-5374	218	24	of	of	ADP
ejpam-5374	218	25	determining	determine	VERB
ejpam-5374	218	26	the	the	DET
ejpam-5374	218	27	logarithmic	logarithmic	ADJ
ejpam-5374	218	28	coefficients	coefficient	NOUN
ejpam-5374	218	29	,	,	PUNCT
ejpam-5374	218	30	we	we	PRON
ejpam-5374	218	31	have	have	AUX
ejpam-5374	218	32	established	establish	VERB
ejpam-5374	218	33	the	the	DET
ejpam-5374	218	34	upper	upper	ADJ
ejpam-5374	218	35	bounds	bound	NOUN
ejpam-5374	218	36	for	for	ADP
ejpam-5374	218	37	three	three	NUM
ejpam-5374	218	38	types	type	NOUN
ejpam-5374	218	39	of	of	ADP
ejpam-5374	218	40	determinants	determinant	NOUN
ejpam-5374	218	41	:	:	PUNCT
ejpam-5374	218	42	|h2,2	|h2,2	NOUN
ejpam-5374	218	43	(	(	PUNCT
ejpam-5374	218	44	γf	γf	ADJ
ejpam-5374	218	45	)	)	PUNCT
ejpam-5374	218	46	|	|	ADV
ejpam-5374	218	47	,	,	PUNCT
ejpam-5374	218	48	|t2,2	|t2,2	NOUN
ejpam-5374	218	49	(	(	PUNCT
ejpam-5374	218	50	γf	γf	PROPN
ejpam-5374	218	51	)	)	PUNCT
ejpam-5374	218	52	|	|	ADV
ejpam-5374	218	53	,	,	PUNCT
ejpam-5374	218	54	and	and	CCONJ
ejpam-5374	218	55	|v2,2	|v2,2	NOUN
ejpam-5374	218	56	(	(	PUNCT
ejpam-5374	218	57	γf	γf	PROPN
ejpam-5374	218	58	)	)	PUNCT
ejpam-5374	218	59	|	|	ADV
ejpam-5374	218	60	,	,	PUNCT
ejpam-5374	218	61	where	where	SCONJ
ejpam-5374	218	62	the	the	DET
ejpam-5374	218	63	logarithmic	logarithmic	ADJ
ejpam-5374	218	64	coefficients	coefficient	NOUN
ejpam-5374	218	65	are	be	AUX
ejpam-5374	218	66	considered	consider	VERB
ejpam-5374	218	67	as	as	ADP
ejpam-5374	218	68	the	the	DET
ejpam-5374	218	69	entries	entry	NOUN
ejpam-5374	218	70	,	,	PUNCT
ejpam-5374	218	71	for	for	ADP
ejpam-5374	218	72	functions	function	NOUN
ejpam-5374	218	73	from	from	ADP
ejpam-5374	218	74	g(α	g(α	PROPN
ejpam-5374	218	75	,	,	PUNCT
ejpam-5374	218	76	δ	δ	PROPN
ejpam-5374	218	77	)	)	PUNCT
ejpam-5374	218	78	,	,	PUNCT
ejpam-5374	218	79	as	as	ADV
ejpam-5374	218	80	well	well	ADV
ejpam-5374	218	81	as	as	ADP
ejpam-5374	218	82	r	r	NOUN
ejpam-5374	218	83	,	,	PUNCT
ejpam-5374	218	84	r	r	NOUN
ejpam-5374	218	85	(	(	PUNCT
ejpam-5374	218	86	δ	δ	PROPN
ejpam-5374	218	87	)	)	PUNCT
ejpam-5374	218	88	,	,	PUNCT
ejpam-5374	218	89	and	and	CCONJ
ejpam-5374	218	90	r	r	NOUN
ejpam-5374	218	91	(	(	PUNCT
ejpam-5374	218	92	α	α	NOUN
ejpam-5374	218	93	)	)	PUNCT
ejpam-5374	218	94	.	.	PUNCT
ejpam-5374	219	1	the	the	DET
ejpam-5374	219	2	lemmas	lemma	NOUN
ejpam-5374	219	3	from	from	ADP
ejpam-5374	219	4	the	the	DET
ejpam-5374	219	5	preliminary	preliminary	ADJ
ejpam-5374	219	6	section	section	NOUN
ejpam-5374	219	7	have	have	AUX
ejpam-5374	219	8	proven	prove	VERB
ejpam-5374	219	9	invaluable	invaluable	ADJ
ejpam-5374	219	10	in	in	ADP
ejpam-5374	219	11	establishing	establish	VERB
ejpam-5374	219	12	upper	upper	ADJ
ejpam-5374	219	13	bounds	bound	NOUN
ejpam-5374	219	14	for	for	ADP
ejpam-5374	219	15	three	three	NUM
ejpam-5374	219	16	types	type	NOUN
ejpam-5374	219	17	of	of	ADP
ejpam-5374	219	18	determinants	determinant	NOUN
ejpam-5374	219	19	of	of	ADP
ejpam-5374	219	20	logarithmic	logarithmic	ADJ
ejpam-5374	219	21	coefficients	coefficient	NOUN
ejpam-5374	219	22	.	.	PUNCT
ejpam-5374	220	1	the	the	DET
ejpam-5374	220	2	findings	finding	NOUN
ejpam-5374	220	3	in	in	ADP
ejpam-5374	220	4	this	this	DET
ejpam-5374	220	5	paper	paper	NOUN
ejpam-5374	220	6	could	could	AUX
ejpam-5374	220	7	inspire	inspire	VERB
ejpam-5374	220	8	further	further	ADJ
ejpam-5374	220	9	research	research	NOUN
ejpam-5374	220	10	into	into	ADP
ejpam-5374	220	11	determining	determine	VERB
ejpam-5374	220	12	upper	upper	ADJ
ejpam-5374	220	13	bounds	bound	NOUN
ejpam-5374	220	14	for	for	ADP
ejpam-5374	220	15	hankel	hankel	NOUN
ejpam-5374	220	16	,	,	PUNCT
ejpam-5374	220	17	toeplitz	toeplitz	NOUN
ejpam-5374	220	18	,	,	PUNCT
ejpam-5374	220	19	and	and	CCONJ
ejpam-5374	220	20	vandermonde	vandermonde	VERB
ejpam-5374	220	21	determinants	determinant	NOUN
ejpam-5374	220	22	with	with	ADP
ejpam-5374	220	23	logarithmic	logarithmic	ADJ
ejpam-5374	220	24	coefficients	coefficient	NOUN
ejpam-5374	220	25	as	as	ADP
ejpam-5374	220	26	entries	entry	NOUN
ejpam-5374	220	27	,	,	PUNCT
ejpam-5374	220	28	particularly	particularly	ADV
ejpam-5374	220	29	within	within	ADP
ejpam-5374	220	30	other	other	ADJ
ejpam-5374	220	31	subclasses	subclass	NOUN
ejpam-5374	220	32	of	of	ADP
ejpam-5374	220	33	univalent	univalent	ADJ
ejpam-5374	220	34	functions	function	NOUN
ejpam-5374	220	35	,	,	PUNCT
ejpam-5374	220	36	while	while	SCONJ
ejpam-5374	220	37	considering	consider	VERB
ejpam-5374	220	38	the	the	DET
ejpam-5374	220	39	inverse	inverse	NOUN
ejpam-5374	220	40	functions	function	NOUN
ejpam-5374	220	41	for	for	ADP
ejpam-5374	220	42	g(α	g(α	PROPN
ejpam-5374	220	43	,	,	PUNCT
ejpam-5374	220	44	δ	δ	PROPN
ejpam-5374	220	45	)	)	PUNCT
ejpam-5374	220	46	.	.	PUNCT
ejpam-5374	221	1	additionally	additionally	ADV
ejpam-5374	221	2	,	,	PUNCT
ejpam-5374	221	3	for	for	ADP
ejpam-5374	221	4	new	new	ADJ
ejpam-5374	221	5	insights	insight	NOUN
ejpam-5374	221	6	,	,	PUNCT
ejpam-5374	221	7	one	one	PRON
ejpam-5374	221	8	might	might	AUX
ejpam-5374	221	9	refer	refer	VERB
ejpam-5374	221	10	to	to	ADP
ejpam-5374	221	11	[	[	X
ejpam-5374	221	12	41	41	NUM
ejpam-5374	221	13	]	]	PUNCT
ejpam-5374	221	14	for	for	ADP
ejpam-5374	221	15	other	other	ADJ
ejpam-5374	221	16	coefficient	coefficient	NOUN
ejpam-5374	221	17	-	-	PUNCT
ejpam-5374	221	18	related	relate	VERB
ejpam-5374	221	19	problems	problem	NOUN
ejpam-5374	221	20	in	in	ADP
ejpam-5374	221	21	logarithmic	logarithmic	ADJ
ejpam-5374	221	22	functions	function	NOUN
ejpam-5374	221	23	such	such	ADJ
ejpam-5374	221	24	as	as	ADP
ejpam-5374	221	25	fekete	fekete	PROPN
ejpam-5374	221	26	szegö	szegö	PROPN
ejpam-5374	221	27	inequality	inequality	NOUN
ejpam-5374	221	28	;	;	PUNCT
ejpam-5374	221	29	however	however	ADV
ejpam-5374	221	30	,	,	PUNCT
ejpam-5374	221	31	consider	consider	VERB
ejpam-5374	221	32	subclasses	subclass	NOUN
ejpam-5374	221	33	of	of	ADP
ejpam-5374	221	34	bi	bi	ADJ
ejpam-5374	221	35	-	-	ADJ
ejpam-5374	221	36	univalent	univalent	ADJ
ejpam-5374	221	37	functions	function	NOUN
ejpam-5374	221	38	,	,	PUNCT
ejpam-5374	221	39	which	which	PRON
ejpam-5374	221	40	could	could	AUX
ejpam-5374	221	41	expand	expand	VERB
ejpam-5374	221	42	upon	upon	SCONJ
ejpam-5374	221	43	,	,	PUNCT
ejpam-5374	221	44	for	for	ADP
ejpam-5374	221	45	example	example	NOUN
ejpam-5374	221	46	,	,	PUNCT
ejpam-5374	221	47	the	the	DET
ejpam-5374	221	48	works	work	NOUN
ejpam-5374	221	49	of	of	ADP
ejpam-5374	221	50	[	[	X
ejpam-5374	221	51	17	17	NUM
ejpam-5374	221	52	,	,	PUNCT
ejpam-5374	221	53	29	29	NUM
ejpam-5374	221	54	]	]	PUNCT
ejpam-5374	221	55	.	.	PUNCT
ejpam-5374	222	1	acknowledgements	acknowledgement	VERB
ejpam-5374	222	2	the	the	DET
ejpam-5374	222	3	authors	author	NOUN
ejpam-5374	222	4	deeply	deeply	ADV
ejpam-5374	222	5	appreciate	appreciate	VERB
ejpam-5374	222	6	the	the	DET
ejpam-5374	222	7	referees	referee	NOUN
ejpam-5374	222	8	’	’	PART
ejpam-5374	222	9	thoughtful	thoughtful	ADJ
ejpam-5374	222	10	comments	comment	NOUN
ejpam-5374	222	11	and	and	CCONJ
ejpam-5374	222	12	extend	extend	VERB
ejpam-5374	222	13	their	their	PRON
ejpam-5374	222	14	heartfelt	heartfelt	ADJ
ejpam-5374	222	15	thanks	thank	NOUN
ejpam-5374	222	16	to	to	ADP
ejpam-5374	222	17	universiti	universiti	PROPN
ejpam-5374	222	18	teknologi	teknologi	PROPN
ejpam-5374	222	19	mara	mara	PROPN
ejpam-5374	222	20	for	for	ADP
ejpam-5374	222	21	supporting	support	VERB
ejpam-5374	222	22	the	the	DET
ejpam-5374	222	23	publication	publication	NOUN
ejpam-5374	222	24	of	of	ADP
ejpam-5374	222	25	this	this	DET
ejpam-5374	222	26	paper	paper	NOUN
ejpam-5374	222	27	.	.	PUNCT
ejpam-5374	223	1	this	this	DET
ejpam-5374	223	2	work	work	NOUN
ejpam-5374	223	3	is	be	AUX
ejpam-5374	223	4	dedicated	dedicate	VERB
ejpam-5374	223	5	to	to	PART
ejpam-5374	223	6	prof	prof	PROPN
ejpam-5374	223	7	.	.	PUNCT
ejpam-5374	224	1	dr	dr	PROPN
ejpam-5374	224	2	.	.	PROPN
ejpam-5374	224	3	daud	daud	PROPN
ejpam-5374	224	4	mohamad	mohamad	PROPN
ejpam-5374	224	5	upon	upon	SCONJ
ejpam-5374	224	6	his	his	PRON
ejpam-5374	224	7	retirement	retirement	NOUN
ejpam-5374	224	8	after	after	ADP
ejpam-5374	224	9	his	his	PRON
ejpam-5374	224	10	distinguished	distinguished	ADJ
ejpam-5374	224	11	service	service	NOUN
ejpam-5374	224	12	at	at	ADP
ejpam-5374	224	13	universiti	universiti	PROPN
ejpam-5374	224	14	teknologi	teknologi	PROPN
ejpam-5374	224	15	mara	mara	PROPN
ejpam-5374	224	16	,	,	PUNCT
ejpam-5374	224	17	in	in	ADP
ejpam-5374	224	18	recognition	recognition	NOUN
ejpam-5374	224	19	of	of	ADP
ejpam-5374	224	20	his	his	PRON
ejpam-5374	224	21	pioneering	pioneer	VERB
ejpam-5374	224	22	role	role	NOUN
ejpam-5374	224	23	in	in	ADP
ejpam-5374	224	24	introducing	introduce	VERB
ejpam-5374	224	25	the	the	DET
ejpam-5374	224	26	class	class	NOUN
ejpam-5374	224	27	of	of	ADP
ejpam-5374	224	28	functions	function	NOUN
ejpam-5374	224	29	with	with	ADP
ejpam-5374	224	30	bounded	bounded	ADJ
ejpam-5374	224	31	turning	turning	NOUN
ejpam-5374	224	32	and	and	CCONJ
ejpam-5374	224	33	tilted	tilted	ADJ
ejpam-5374	224	34	factors	factor	NOUN
ejpam-5374	224	35	.	.	PUNCT
ejpam-5374	225	1	references	reference	NOUN
ejpam-5374	225	2	[	[	X
ejpam-5374	225	3	1	1	NUM
ejpam-5374	225	4	]	]	PUNCT
ejpam-5374	225	5	n	n	NOUN
ejpam-5374	225	6	h	h	NOUN
ejpam-5374	225	7	a	a	DET
ejpam-5374	225	8	a	a	DET
ejpam-5374	225	9	wahid	wahid	NOUN
ejpam-5374	225	10	,	,	PUNCT
ejpam-5374	225	11	a	a	DET
ejpam-5374	225	12	tumiran	tumiran	NOUN
ejpam-5374	225	13	and	and	CCONJ
ejpam-5374	225	14	t	t	PROPN
ejpam-5374	225	15	g	g	PROPN
ejpam-5374	225	16	shaba	shaba	PROPN
ejpam-5374	225	17	.	.	PUNCT
ejpam-5374	226	1	hankel	hankel	NOUN
ejpam-5374	226	2	and	and	CCONJ
ejpam-5374	226	3	toeplitz	toeplitz	NOUN
ejpam-5374	226	4	determinants	determinant	NOUN
ejpam-5374	226	5	of	of	ADP
ejpam-5374	226	6	logarithmic	logarithmic	ADJ
ejpam-5374	226	7	coefficients	coefficient	NOUN
ejpam-5374	226	8	of	of	ADP
ejpam-5374	226	9	inverse	inverse	NOUN
ejpam-5374	226	10	functions	function	NOUN
ejpam-5374	226	11	for	for	ADP
ejpam-5374	226	12	the	the	DET
ejpam-5374	226	13	subclass	subclass	NOUN
ejpam-5374	226	14	of	of	ADP
ejpam-5374	226	15	starlike	starlike	NOUN
ejpam-5374	226	16	functions	function	NOUN
ejpam-5374	226	17	references	reference	NOUN
ejpam-5374	226	18	2749	2749	NUM
ejpam-5374	226	19	with	with	ADP
ejpam-5374	226	20	respect	respect	NOUN
ejpam-5374	226	21	to	to	ADP
ejpam-5374	226	22	symmetric	symmetric	ADJ
ejpam-5374	226	23	conjugate	conjugate	ADJ
ejpam-5374	226	24	points	point	NOUN
ejpam-5374	226	25	.	.	PUNCT
ejpam-5374	227	1	european	european	ADJ
ejpam-5374	227	2	journal	journal	PROPN
ejpam-5374	227	3	of	of	ADP
ejpam-5374	227	4	pure	pure	ADJ
ejpam-5374	227	5	and	and	CCONJ
ejpam-5374	227	6	applied	applied	ADJ
ejpam-5374	227	7	mathematics	mathematic	NOUN
ejpam-5374	227	8	,	,	PUNCT
ejpam-5374	227	9	13(3):1818–1830	13(3):1818–1830	NUM
ejpam-5374	227	10	,	,	PUNCT
ejpam-5374	227	11	2024	2024	NUM
ejpam-5374	227	12	.	.	PUNCT
ejpam-5374	228	1	[	[	X
ejpam-5374	228	2	2	2	NUM
ejpam-5374	228	3	]	]	SYM
ejpam-5374	228	4	v	v	ADP
ejpam-5374	228	5	allu	allu	NOUN
ejpam-5374	228	6	and	and	CCONJ
ejpam-5374	228	7	v	v	ADP
ejpam-5374	228	8	arora	arora	PROPN
ejpam-5374	228	9	.	.	PUNCT
ejpam-5374	229	1	second	second	ADJ
ejpam-5374	229	2	hankel	hankel	NOUN
ejpam-5374	229	3	determinant	determinant	ADJ
ejpam-5374	229	4	of	of	ADP
ejpam-5374	229	5	logarithmic	logarithmic	ADJ
ejpam-5374	229	6	coefficients	coefficient	NOUN
ejpam-5374	229	7	of	of	ADP
ejpam-5374	229	8	certain	certain	ADJ
ejpam-5374	229	9	analytic	analytic	ADJ
ejpam-5374	229	10	functions	function	NOUN
ejpam-5374	229	11	.	.	PUNCT
ejpam-5374	230	1	rocky	rocky	ADJ
ejpam-5374	230	2	mountain	mountain	PROPN
ejpam-5374	230	3	journal	journal	NOUN
ejpam-5374	230	4	of	of	ADP
ejpam-5374	230	5	mathematics	mathematic	NOUN
ejpam-5374	230	6	,	,	PUNCT
ejpam-5374	230	7	54(2):343–359	54(2):343–359	ADV
ejpam-5374	230	8	,	,	PUNCT
ejpam-5374	230	9	2024	2024	NUM
ejpam-5374	230	10	.	.	PUNCT
ejpam-5374	231	1	[	[	X
ejpam-5374	231	2	3	3	X
ejpam-5374	231	3	]	]	PUNCT
ejpam-5374	231	4	v	v	NOUN
ejpam-5374	231	5	v	v	NOUN
ejpam-5374	231	6	andreev	andreev	NOUN
ejpam-5374	231	7	and	and	CCONJ
ejpam-5374	231	8	p	p	NOUN
ejpam-5374	231	9	l	l	PROPN
ejpam-5374	231	10	duren	duren	PROPN
ejpam-5374	231	11	.	.	PROPN
ejpam-5374	232	1	inequalities	inequality	NOUN
ejpam-5374	232	2	for	for	ADP
ejpam-5374	232	3	logarithmic	logarithmic	ADJ
ejpam-5374	232	4	coefficients	coefficient	NOUN
ejpam-5374	232	5	of	of	ADP
ejpam-5374	232	6	univalent	univalent	ADJ
ejpam-5374	232	7	functions	function	NOUN
ejpam-5374	232	8	and	and	CCONJ
ejpam-5374	232	9	their	their	PRON
ejpam-5374	232	10	derivatives	derivative	NOUN
ejpam-5374	232	11	.	.	PUNCT
ejpam-5374	233	1	indiana	indiana	PROPN
ejpam-5374	233	2	university	university	PROPN
ejpam-5374	233	3	mathematics	mathematics	PROPN
ejpam-5374	233	4	journal	journal	NOUN
ejpam-5374	233	5	,	,	PUNCT
ejpam-5374	233	6	37(4):721	37(4):721	NUM
ejpam-5374	233	7	–	–	PUNCT
ejpam-5374	233	8	733	733	NUM
ejpam-5374	233	9	,	,	PUNCT
ejpam-5374	233	10	1988	1988	NUM
ejpam-5374	233	11	.	.	PUNCT
ejpam-5374	234	1	[	[	X
ejpam-5374	234	2	4	4	NUM
ejpam-5374	234	3	]	]	X
ejpam-5374	234	4	l	l	X
ejpam-5374	234	5	de	de	X
ejpam-5374	234	6	branges	brange	NOUN
ejpam-5374	234	7	.	.	PUNCT
ejpam-5374	235	1	a	a	DET
ejpam-5374	235	2	proof	proof	NOUN
ejpam-5374	235	3	of	of	ADP
ejpam-5374	235	4	the	the	DET
ejpam-5374	235	5	bieberbach	bieberbach	NOUN
ejpam-5374	235	6	conjecture	conjecture	NOUN
ejpam-5374	235	7	.	.	PUNCT
ejpam-5374	236	1	acta	acta	PROPN
ejpam-5374	236	2	mathematica	mathematica	PROPN
ejpam-5374	236	3	,	,	PUNCT
ejpam-5374	236	4	154(1):137	154(1):137	NUM
ejpam-5374	236	5	–	–	PUNCT
ejpam-5374	236	6	152	152	NUM
ejpam-5374	236	7	,	,	PUNCT
ejpam-5374	236	8	1985	1985	NUM
ejpam-5374	236	9	.	.	PUNCT
ejpam-5374	237	1	[	[	X
ejpam-5374	237	2	5	5	NUM
ejpam-5374	237	3	]	]	PUNCT
ejpam-5374	237	4	s	s	PART
ejpam-5374	237	5	bulut	bulut	NOUN
ejpam-5374	237	6	.	.	PUNCT
ejpam-5374	238	1	sharp	sharp	ADJ
ejpam-5374	238	2	bounds	bound	NOUN
ejpam-5374	238	3	for	for	ADP
ejpam-5374	238	4	the	the	DET
ejpam-5374	238	5	second	second	ADJ
ejpam-5374	238	6	hankel	hankel	NOUN
ejpam-5374	238	7	determinant	determinant	ADJ
ejpam-5374	238	8	of	of	ADP
ejpam-5374	238	9	logarithmic	logarithmic	ADJ
ejpam-5374	238	10	coefficients	coefficient	NOUN
ejpam-5374	238	11	for	for	ADP
ejpam-5374	238	12	parabolic	parabolic	ADJ
ejpam-5374	238	13	starlike	starlike	NOUN
ejpam-5374	238	14	and	and	CCONJ
ejpam-5374	238	15	uniformly	uniformly	ADV
ejpam-5374	238	16	convex	convex	NOUN
ejpam-5374	238	17	functions	function	NOUN
ejpam-5374	238	18	of	of	ADP
ejpam-5374	238	19	order	order	NOUN
ejpam-5374	238	20	alpha	alpha	NOUN
ejpam-5374	238	21	.	.	PUNCT
ejpam-5374	239	1	khayyam	khayyam	PROPN
ejpam-5374	239	2	journal	journal	PROPN
ejpam-5374	239	3	of	of	ADP
ejpam-5374	239	4	mathematics	mathematic	NOUN
ejpam-5374	239	5	,	,	PUNCT
ejpam-5374	239	6	10(1):51–69	10(1):51–69	NUM
ejpam-5374	239	7	,	,	PUNCT
ejpam-5374	239	8	2024	2024	NUM
ejpam-5374	239	9	.	.	PUNCT
ejpam-5374	240	1	[	[	X
ejpam-5374	240	2	6	6	NUM
ejpam-5374	240	3	]	]	PUNCT
ejpam-5374	240	4	d	d	X
ejpam-5374	240	5	g	g	PROPN
ejpam-5374	240	6	cantor	cantor	PROPN
ejpam-5374	240	7	.	.	PUNCT
ejpam-5374	241	1	power	power	NOUN
ejpam-5374	241	2	series	series	PROPN
ejpam-5374	241	3	with	with	ADP
ejpam-5374	241	4	integral	integral	ADJ
ejpam-5374	241	5	coefficients	coefficient	NOUN
ejpam-5374	241	6	.	.	PUNCT
ejpam-5374	242	1	bulletin	bulletin	NOUN
ejpam-5374	242	2	of	of	ADP
ejpam-5374	242	3	the	the	DET
ejpam-5374	242	4	american	american	PROPN
ejpam-5374	242	5	mathematical	mathematical	PROPN
ejpam-5374	242	6	society	society	NOUN
ejpam-5374	242	7	,	,	PUNCT
ejpam-5374	242	8	69:362–366	69:362–366	PROPN
ejpam-5374	242	9	,	,	PUNCT
ejpam-5374	242	10	1963	1963	NUM
ejpam-5374	242	11	.	.	PUNCT
ejpam-5374	243	1	[	[	X
ejpam-5374	243	2	7	7	X
ejpam-5374	243	3	]	]	X
ejpam-5374	243	4	m	m	PROPN
ejpam-5374	243	5	f	f	PROPN
ejpam-5374	243	6	ali	ali	PROPN
ejpam-5374	243	7	,	,	PUNCT
ejpam-5374	243	8	d	d	PROPN
ejpam-5374	243	9	k	k	PROPN
ejpam-5374	243	10	thomas	thomas	PROPN
ejpam-5374	243	11	,	,	PUNCT
ejpam-5374	243	12	and	and	CCONJ
ejpam-5374	243	13	a	a	DET
ejpam-5374	243	14	vasudevarao	vasudevarao	NOUN
ejpam-5374	243	15	.	.	PUNCT
ejpam-5374	244	1	toeplitz	toeplitz	NOUN
ejpam-5374	244	2	determinants	determinant	NOUN
ejpam-5374	244	3	whose	whose	DET
ejpam-5374	244	4	elements	element	NOUN
ejpam-5374	244	5	are	be	AUX
ejpam-5374	244	6	the	the	DET
ejpam-5374	244	7	coefficients	coefficient	NOUN
ejpam-5374	244	8	of	of	ADP
ejpam-5374	244	9	analytic	analytic	ADJ
ejpam-5374	244	10	and	and	CCONJ
ejpam-5374	244	11	univalent	univalent	ADJ
ejpam-5374	244	12	functions	function	NOUN
ejpam-5374	244	13	.	.	PUNCT
ejpam-5374	245	1	bulletin	bulletin	NOUN
ejpam-5374	245	2	of	of	ADP
ejpam-5374	245	3	the	the	DET
ejpam-5374	245	4	australian	australian	ADJ
ejpam-5374	245	5	mathematical	mathematical	ADJ
ejpam-5374	245	6	society	society	NOUN
ejpam-5374	245	7	,	,	PUNCT
ejpam-5374	245	8	97:253–264	97:253–264	NUM
ejpam-5374	245	9	,	,	PUNCT
ejpam-5374	245	10	2018	2018	NUM
ejpam-5374	245	11	.	.	PUNCT
ejpam-5374	246	1	[	[	X
ejpam-5374	246	2	8	8	NUM
ejpam-5374	246	3	]	]	X
ejpam-5374	246	4	s	s	X
ejpam-5374	246	5	cik	cik	PROPN
ejpam-5374	246	6	soh	soh	PROPN
ejpam-5374	246	7	,	,	PUNCT
ejpam-5374	246	8	d	d	PROPN
ejpam-5374	246	9	mohamad	mohamad	PROPN
ejpam-5374	246	10	,	,	PUNCT
ejpam-5374	246	11	and	and	CCONJ
ejpam-5374	246	12	h	h	NOUN
ejpam-5374	246	13	dzubaidi	dzubaidi	PROPN
ejpam-5374	246	14	.	.	PUNCT
ejpam-5374	247	1	coefficient	coefficient	ADJ
ejpam-5374	247	2	estimate	estimate	NOUN
ejpam-5374	247	3	of	of	ADP
ejpam-5374	247	4	the	the	DET
ejpam-5374	247	5	second	second	ADJ
ejpam-5374	247	6	hankel	hankel	NOUN
ejpam-5374	247	7	determinant	determinant	ADJ
ejpam-5374	247	8	of	of	ADP
ejpam-5374	247	9	logarithmic	logarithmic	ADJ
ejpam-5374	247	10	coefficients	coefficient	NOUN
ejpam-5374	247	11	for	for	ADP
ejpam-5374	247	12	the	the	DET
ejpam-5374	247	13	subclass	subclass	NOUN
ejpam-5374	247	14	of	of	ADP
ejpam-5374	247	15	close	close	NOUN
ejpam-5374	247	16	-	-	PUNCT
ejpam-5374	247	17	to	to	ADP
ejpam-5374	247	18	-	-	PUNCT
ejpam-5374	247	19	convex	convex	NOUN
ejpam-5374	247	20	function	function	NOUN
ejpam-5374	247	21	.	.	PUNCT
ejpam-5374	248	1	twms	twms	PROPN
ejpam-5374	248	2	journal	journal	PROPN
ejpam-5374	248	3	of	of	ADP
ejpam-5374	248	4	applied	apply	VERB
ejpam-5374	248	5	and	and	CCONJ
ejpam-5374	248	6	engineering	engineering	NOUN
ejpam-5374	248	7	mathematics	mathematic	NOUN
ejpam-5374	248	8	,	,	PUNCT
ejpam-5374	248	9	24(2):563–570	24(2):563–570	NUM
ejpam-5374	248	10	,	,	PUNCT
ejpam-5374	248	11	2024	2024	NUM
ejpam-5374	248	12	.	.	PUNCT
ejpam-5374	249	1	[	[	X
ejpam-5374	249	2	9	9	NUM
ejpam-5374	249	3	]	]	X
ejpam-5374	249	4	p	p	NOUN
ejpam-5374	249	5	dienes	diene	NOUN
ejpam-5374	249	6	.	.	PUNCT
ejpam-5374	250	1	the	the	DET
ejpam-5374	250	2	taylor	taylor	PROPN
ejpam-5374	250	3	series	series	PROPN
ejpam-5374	250	4	:	:	PUNCT
ejpam-5374	250	5	an	an	DET
ejpam-5374	250	6	introduction	introduction	NOUN
ejpam-5374	250	7	to	to	ADP
ejpam-5374	250	8	the	the	DET
ejpam-5374	250	9	theory	theory	NOUN
ejpam-5374	250	10	of	of	ADP
ejpam-5374	250	11	functions	function	NOUN
ejpam-5374	250	12	of	of	ADP
ejpam-5374	250	13	a	a	DET
ejpam-5374	250	14	complex	complex	ADJ
ejpam-5374	250	15	variable	variable	NOUN
ejpam-5374	250	16	.	.	PUNCT
ejpam-5374	251	1	new	new	PROPN
ejpam-5374	251	2	york	york	PROPN
ejpam-5374	251	3	-	-	PUNCT
ejpam-5374	251	4	dover	dover	PROPN
ejpam-5374	251	5	publishing	publishing	PROPN
ejpam-5374	251	6	company	company	NOUN
ejpam-5374	251	7	,	,	PUNCT
ejpam-5374	251	8	mineola	mineola	PROPN
ejpam-5374	251	9	,	,	PUNCT
ejpam-5374	251	10	ny	ny	PROPN
ejpam-5374	251	11	,	,	PUNCT
ejpam-5374	251	12	usa	usa	PROPN
ejpam-5374	251	13	,	,	PUNCT
ejpam-5374	251	14	1957	1957	NUM
ejpam-5374	251	15	.	.	PUNCT
ejpam-5374	252	1	[	[	X
ejpam-5374	252	2	10	10	NUM
ejpam-5374	252	3	]	]	X
ejpam-5374	252	4	p	p	X
ejpam-5374	252	5	l	l	PROPN
ejpam-5374	252	6	duren	duren	PROPN
ejpam-5374	252	7	.	.	PUNCT
ejpam-5374	253	1	univalent	univalent	ADJ
ejpam-5374	253	2	functions	function	NOUN
ejpam-5374	253	3	vol	vol	NOUN
ejpam-5374	253	4	.	.	PUNCT
ejpam-5374	254	1	259	259	NUM
ejpam-5374	254	2	.	.	X
ejpam-5374	254	3	springer	springer	NOUN
ejpam-5374	254	4	-	-	PUNCT
ejpam-5374	254	5	verlag	verlag	PROPN
ejpam-5374	254	6	.	.	PROPN
ejpam-5374	254	7	,	,	PUNCT
ejpam-5374	254	8	new	new	PROPN
ejpam-5374	254	9	york	york	PROPN
ejpam-5374	254	10	,	,	PUNCT
ejpam-5374	254	11	berlin	berlin	PROPN
ejpam-5374	254	12	,	,	PUNCT
ejpam-5374	254	13	heidelberg	heidelberg	PROPN
ejpam-5374	254	14	,	,	PUNCT
ejpam-5374	254	15	tokyo	tokyo	PROPN
ejpam-5374	254	16	,	,	PUNCT
ejpam-5374	254	17	1983	1983	NUM
ejpam-5374	254	18	.	.	PUNCT
ejpam-5374	255	1	[	[	X
ejpam-5374	255	2	11	11	NUM
ejpam-5374	255	3	]	]	X
ejpam-5374	255	4	i	i	PRON
ejpam-5374	255	5	efraimidis	efraimidi	VERB
ejpam-5374	255	6	.	.	PUNCT
ejpam-5374	256	1	a	a	DET
ejpam-5374	256	2	generalization	generalization	NOUN
ejpam-5374	256	3	of	of	ADP
ejpam-5374	256	4	livingston	livingston	PROPN
ejpam-5374	256	5	’s	’s	PART
ejpam-5374	256	6	coefficient	coefficient	NOUN
ejpam-5374	256	7	inequalities	inequality	NOUN
ejpam-5374	256	8	for	for	ADP
ejpam-5374	256	9	functions	function	NOUN
ejpam-5374	256	10	with	with	ADP
ejpam-5374	256	11	positive	positive	ADJ
ejpam-5374	256	12	real	real	ADJ
ejpam-5374	256	13	part	part	NOUN
ejpam-5374	256	14	.	.	PUNCT
ejpam-5374	257	1	journal	journal	PROPN
ejpam-5374	257	2	of	of	ADP
ejpam-5374	257	3	mathematical	mathematical	ADJ
ejpam-5374	257	4	analysis	analysis	NOUN
ejpam-5374	257	5	and	and	CCONJ
ejpam-5374	257	6	applications	application	NOUN
ejpam-5374	257	7	,	,	PUNCT
ejpam-5374	257	8	435(1):369	435(1):369	NUM
ejpam-5374	257	9	–	–	PUNCT
ejpam-5374	257	10	379	379	NUM
ejpam-5374	257	11	,	,	PUNCT
ejpam-5374	257	12	2016	2016	NUM
ejpam-5374	257	13	.	.	PUNCT
ejpam-5374	258	1	[	[	X
ejpam-5374	258	2	12	12	NUM
ejpam-5374	258	3	]	]	X
ejpam-5374	258	4	m	m	VERB
ejpam-5374	258	5	m	m	VERB
ejpam-5374	258	6	elhosh	elhosh	ADJ
ejpam-5374	258	7	.	.	PUNCT
ejpam-5374	259	1	on	on	ADP
ejpam-5374	259	2	the	the	DET
ejpam-5374	259	3	logarithmic	logarithmic	ADJ
ejpam-5374	259	4	coefficients	coefficient	NOUN
ejpam-5374	259	5	of	of	ADP
ejpam-5374	259	6	close	close	NOUN
ejpam-5374	259	7	-	-	PUNCT
ejpam-5374	259	8	to	to	ADP
ejpam-5374	259	9	-	-	PUNCT
ejpam-5374	259	10	convex	convex	NOUN
ejpam-5374	259	11	functions	function	NOUN
ejpam-5374	259	12	.	.	PUNCT
ejpam-5374	260	1	journal	journal	NOUN
ejpam-5374	260	2	of	of	ADP
ejpam-5374	260	3	the	the	DET
ejpam-5374	260	4	australian	australian	ADJ
ejpam-5374	260	5	mathematical	mathematical	ADJ
ejpam-5374	260	6	society	society	NOUN
ejpam-5374	260	7	,	,	PUNCT
ejpam-5374	260	8	60(1):1–6	60(1):1–6	NOUN
ejpam-5374	260	9	,	,	PUNCT
ejpam-5374	260	10	1996	1996	NUM
ejpam-5374	260	11	.	.	PUNCT
ejpam-5374	261	1	[	[	X
ejpam-5374	261	2	13	13	NUM
ejpam-5374	261	3	]	]	SYM
ejpam-5374	261	4	h	h	NOUN
ejpam-5374	261	5	tang	tang	PROPN
ejpam-5374	261	6	,	,	PUNCT
ejpam-5374	261	7	z	z	PROPN
ejpam-5374	261	8	mujahid	mujahid	PROPN
ejpam-5374	261	9	,	,	PUNCT
ejpam-5374	261	10	n	n	PRON
ejpam-5374	261	11	khan	khan	PROPN
ejpam-5374	261	12	,	,	PUNCT
ejpam-5374	261	13	f	f	PROPN
ejpam-5374	261	14	tchier	tchier	NOUN
ejpam-5374	261	15	,	,	PUNCT
ejpam-5374	261	16	and	and	CCONJ
ejpam-5374	261	17	m	m	PROPN
ejpam-5374	261	18	k	k	PROPN
ejpam-5374	261	19	ghaffar	ghaffar	PROPN
ejpam-5374	261	20	khan	khan	PROPN
ejpam-5374	261	21	.	.	PUNCT
ejpam-5374	262	1	generalized	generalize	VERB
ejpam-5374	262	2	bounded	bounded	ADJ
ejpam-5374	262	3	turning	turning	NOUN
ejpam-5374	262	4	functions	function	NOUN
ejpam-5374	262	5	connected	connect	VERB
ejpam-5374	262	6	with	with	ADP
ejpam-5374	262	7	gregory	gregory	PROPN
ejpam-5374	262	8	coefficients	coefficient	NOUN
ejpam-5374	262	9	.	.	PUNCT
ejpam-5374	263	1	axioms	axiom	NOUN
ejpam-5374	263	2	,	,	PUNCT
ejpam-5374	263	3	13(6):359	13(6):359	NUM
ejpam-5374	263	4	,	,	PUNCT
ejpam-5374	263	5	2024	2024	NUM
ejpam-5374	263	6	.	.	PUNCT
ejpam-5374	264	1	[	[	X
ejpam-5374	264	2	14	14	NUM
ejpam-5374	264	3	]	]	X
ejpam-5374	264	4	d	d	X
ejpam-5374	264	5	girela	girela	NOUN
ejpam-5374	264	6	.	.	PUNCT
ejpam-5374	265	1	logarithmic	logarithmic	ADJ
ejpam-5374	265	2	coefficients	coefficient	NOUN
ejpam-5374	265	3	of	of	ADP
ejpam-5374	265	4	univalent	univalent	ADJ
ejpam-5374	265	5	functions	function	NOUN
ejpam-5374	265	6	.	.	PUNCT
ejpam-5374	266	1	annales	annales	PROPN
ejpam-5374	266	2	fennici	fennici	PROPN
ejpam-5374	266	3	mathematici	mathematici	PROPN
ejpam-5374	266	4	,	,	PUNCT
ejpam-5374	266	5	25(2):337–350	25(2):337–350	PROPN
ejpam-5374	266	6	,	,	PUNCT
ejpam-5374	266	7	2000	2000	NUM
ejpam-5374	266	8	.	.	PUNCT
ejpam-5374	267	1	references	reference	NOUN
ejpam-5374	267	2	2750	2750	NUM
ejpam-5374	268	1	[	[	X
ejpam-5374	268	2	15	15	NUM
ejpam-5374	268	3	]	]	X
ejpam-5374	268	4	s	s	X
ejpam-5374	268	5	giri	giri	PROPN
ejpam-5374	268	6	and	and	CCONJ
ejpam-5374	268	7	s	s	NOUN
ejpam-5374	268	8	s	s	PROPN
ejpam-5374	268	9	kumar	kumar	PROPN
ejpam-5374	268	10	.	.	PUNCT
ejpam-5374	269	1	toeplitz	toeplitz	NOUN
ejpam-5374	269	2	determinants	determinant	NOUN
ejpam-5374	269	3	of	of	ADP
ejpam-5374	269	4	logarithmic	logarithmic	ADJ
ejpam-5374	269	5	coefficients	coefficient	NOUN
ejpam-5374	269	6	for	for	ADP
ejpam-5374	269	7	starlike	starlike	NOUN
ejpam-5374	269	8	and	and	CCONJ
ejpam-5374	269	9	convex	convex	NOUN
ejpam-5374	269	10	functions	function	NOUN
ejpam-5374	269	11	.	.	PUNCT
ejpam-5374	270	1	arxiv	arxiv	PROPN
ejpam-5374	270	2	preprint	preprint	PROPN
ejpam-5374	270	3	arxiv:2303.14712	arxiv:2303.14712	NOUN
ejpam-5374	270	4	,	,	PUNCT
ejpam-5374	270	5	2023	2023	NUM
ejpam-5374	270	6	.	.	PUNCT
ejpam-5374	271	1	[	[	X
ejpam-5374	271	2	16	16	NUM
ejpam-5374	271	3	]	]	X
ejpam-5374	271	4	r	r	NOUN
ejpam-5374	271	5	m	m	VERB
ejpam-5374	271	6	goel	goel	PROPN
ejpam-5374	271	7	and	and	CCONJ
ejpam-5374	271	8	b	b	NOUN
ejpam-5374	271	9	s	s	X
ejpam-5374	271	10	mehrok	mehrok	NOUN
ejpam-5374	271	11	.	.	PUNCT
ejpam-5374	272	1	a	a	DET
ejpam-5374	272	2	subclass	subclass	NOUN
ejpam-5374	272	3	of	of	ADP
ejpam-5374	272	4	univalent	univalent	ADJ
ejpam-5374	272	5	functions	function	NOUN
ejpam-5374	272	6	.	.	PUNCT
ejpam-5374	273	1	journal	journal	NOUN
ejpam-5374	273	2	of	of	ADP
ejpam-5374	273	3	the	the	DET
ejpam-5374	273	4	australian	australian	ADJ
ejpam-5374	273	5	mathematical	mathematical	ADJ
ejpam-5374	273	6	society	society	NOUN
ejpam-5374	273	7	,	,	PUNCT
ejpam-5374	273	8	35(1):1–17	35(1):1–17	NUM
ejpam-5374	273	9	,	,	PUNCT
ejpam-5374	273	10	1983	1983	NUM
ejpam-5374	273	11	.	.	PUNCT
ejpam-5374	274	1	[	[	X
ejpam-5374	274	2	17	17	NUM
ejpam-5374	274	3	]	]	PUNCT
ejpam-5374	274	4	a	a	DET
ejpam-5374	274	5	hussen	hussen	NOUN
ejpam-5374	274	6	and	and	CCONJ
ejpam-5374	274	7	a.	a.	NOUN
ejpam-5374	274	8	zeyani	zeyani	PROPN
ejpam-5374	274	9	.	.	PUNCT
ejpam-5374	275	1	coefficients	coefficient	NOUN
ejpam-5374	275	2	and	and	CCONJ
ejpam-5374	275	3	fekete	fekete	PROPN
ejpam-5374	275	4	–	–	PUNCT
ejpam-5374	275	5	szegö	szegö	ADJ
ejpam-5374	275	6	functional	functional	ADJ
ejpam-5374	275	7	estimations	estimation	NOUN
ejpam-5374	275	8	of	of	ADP
ejpam-5374	275	9	biunivalent	biunivalent	NOUN
ejpam-5374	275	10	subclasses	subclass	NOUN
ejpam-5374	275	11	based	base	VERB
ejpam-5374	275	12	on	on	ADP
ejpam-5374	275	13	gegenbauer	gegenbauer	NOUN
ejpam-5374	275	14	polynomials	polynomial	NOUN
ejpam-5374	275	15	.	.	PUNCT
ejpam-5374	276	1	mathematics	mathematic	NOUN
ejpam-5374	276	2	,	,	PUNCT
ejpam-5374	276	3	11(13):2852	11(13):2852	NUM
ejpam-5374	276	4	,	,	PUNCT
ejpam-5374	276	5	2023	2023	NUM
ejpam-5374	276	6	.	.	PUNCT
ejpam-5374	277	1	[	[	X
ejpam-5374	277	2	18	18	NUM
ejpam-5374	277	3	]	]	X
ejpam-5374	277	4	m	m	PROPN
ejpam-5374	277	5	arif	arif	PROPN
ejpam-5374	277	6	,	,	PUNCT
ejpam-5374	277	7	m	m	PROPN
ejpam-5374	277	8	raza	raza	NOUN
ejpam-5374	277	9	,	,	PUNCT
ejpam-5374	277	10	i	i	PRON
ejpam-5374	277	11	ullah	ullah	PROPN
ejpam-5374	277	12	,	,	PUNCT
ejpam-5374	277	13	and	and	CCONJ
ejpam-5374	277	14	p	p	PROPN
ejpam-5374	277	15	zaprawa	zaprawa	PROPN
ejpam-5374	277	16	.	.	PUNCT
ejpam-5374	278	1	hankel	hankel	NOUN
ejpam-5374	278	2	determinants	determinant	NOUN
ejpam-5374	278	3	of	of	ADP
ejpam-5374	278	4	order	order	NOUN
ejpam-5374	278	5	four	four	NUM
ejpam-5374	278	6	for	for	ADP
ejpam-5374	278	7	a	a	DET
ejpam-5374	278	8	set	set	NOUN
ejpam-5374	278	9	of	of	ADP
ejpam-5374	278	10	functions	function	NOUN
ejpam-5374	278	11	with	with	ADP
ejpam-5374	278	12	bounded	bounded	ADJ
ejpam-5374	278	13	turning	turning	NOUN
ejpam-5374	278	14	of	of	ADP
ejpam-5374	278	15	order	order	NOUN
ejpam-5374	278	16	α	α	NOUN
ejpam-5374	278	17	.	.	PUNCT
ejpam-5374	279	1	lithuanian	lithuanian	PROPN
ejpam-5374	279	2	mathematical	mathematical	ADJ
ejpam-5374	279	3	journal	journal	PROPN
ejpam-5374	279	4	,	,	PUNCT
ejpam-5374	279	5	62(2):135–145	62(2):135–145	PROPN
ejpam-5374	279	6	,	,	PUNCT
ejpam-5374	279	7	2022	2022	NUM
ejpam-5374	279	8	.	.	PUNCT
ejpam-5374	280	1	[	[	X
ejpam-5374	280	2	19	19	NUM
ejpam-5374	280	3	]	]	X
ejpam-5374	280	4	m	m	VERB
ejpam-5374	280	5	g	g	PROPN
ejpam-5374	280	6	khan	khan	PROPN
ejpam-5374	280	7	,	,	PUNCT
ejpam-5374	280	8	w	w	PROPN
ejpam-5374	280	9	k	k	PROPN
ejpam-5374	280	10	mashwani	mashwani	PROPN
ejpam-5374	280	11	,	,	PUNCT
ejpam-5374	280	12	j	j	PROPN
ejpam-5374	280	13	s	s	X
ejpam-5374	280	14	ro	ro	PROPN
ejpam-5374	280	15	,	,	PUNCT
ejpam-5374	280	16	and	and	CCONJ
ejpam-5374	280	17	b	b	X
ejpam-5374	280	18	ahmad	ahmad	PROPN
ejpam-5374	280	19	.	.	PUNCT
ejpam-5374	281	1	problems	problem	NOUN
ejpam-5374	281	2	concerning	concern	VERB
ejpam-5374	281	3	sharp	sharp	ADJ
ejpam-5374	281	4	coefficient	coefficient	NOUN
ejpam-5374	281	5	functionals	functional	NOUN
ejpam-5374	281	6	of	of	ADP
ejpam-5374	281	7	bounded	bounded	ADJ
ejpam-5374	281	8	turning	turning	NOUN
ejpam-5374	281	9	functions	function	NOUN
ejpam-5374	281	10	.	.	PUNCT
ejpam-5374	282	1	aims	aim	VERB
ejpam-5374	282	2	mathematics	mathematic	NOUN
ejpam-5374	282	3	,	,	PUNCT
ejpam-5374	282	4	8(11):27396	8(11):27396	NUM
ejpam-5374	282	5	–	–	PUNCT
ejpam-5374	282	6	27413	27413	NUM
ejpam-5374	282	7	,	,	PUNCT
ejpam-5374	282	8	2023	2023	NUM
ejpam-5374	282	9	.	.	PUNCT
ejpam-5374	283	1	[	[	X
ejpam-5374	283	2	20	20	NUM
ejpam-5374	283	3	]	]	X
ejpam-5374	284	1	i	i	PRON
ejpam-5374	284	2	p	p	NOUN
ejpam-5374	284	3	kayumov	kayumov	ADJ
ejpam-5374	284	4	.	.	PUNCT
ejpam-5374	285	1	on	on	ADP
ejpam-5374	285	2	brennan	brennan	PROPN
ejpam-5374	285	3	’s	’s	PART
ejpam-5374	285	4	conjecture	conjecture	NOUN
ejpam-5374	285	5	for	for	ADP
ejpam-5374	285	6	a	a	DET
ejpam-5374	285	7	special	special	ADJ
ejpam-5374	285	8	class	class	NOUN
ejpam-5374	285	9	of	of	ADP
ejpam-5374	285	10	functions	function	NOUN
ejpam-5374	285	11	.	.	PUNCT
ejpam-5374	286	1	mathematical	mathematical	ADJ
ejpam-5374	286	2	notes	note	NOUN
ejpam-5374	286	3	,	,	PUNCT
ejpam-5374	286	4	78:498–502	78:498–502	PROPN
ejpam-5374	286	5	,	,	PUNCT
ejpam-5374	286	6	2005	2005	NUM
ejpam-5374	286	7	.	.	PUNCT
ejpam-5374	287	1	[	[	X
ejpam-5374	287	2	21	21	NUM
ejpam-5374	287	3	]	]	SYM
ejpam-5374	287	4	b	b	X
ejpam-5374	287	5	kowalczyk	kowalczyk	NOUN
ejpam-5374	287	6	and	and	CCONJ
ejpam-5374	287	7	a	a	DET
ejpam-5374	287	8	lecko	lecko	NOUN
ejpam-5374	287	9	.	.	PUNCT
ejpam-5374	288	1	the	the	DET
ejpam-5374	288	2	sharp	sharp	ADJ
ejpam-5374	288	3	bound	bind	VERB
ejpam-5374	288	4	of	of	ADP
ejpam-5374	288	5	the	the	DET
ejpam-5374	288	6	third	third	ADJ
ejpam-5374	288	7	hankel	hankel	NOUN
ejpam-5374	288	8	determinant	determinant	ADJ
ejpam-5374	288	9	for	for	ADP
ejpam-5374	288	10	functions	function	NOUN
ejpam-5374	288	11	of	of	ADP
ejpam-5374	288	12	bounded	bounded	ADJ
ejpam-5374	288	13	turning	turning	NOUN
ejpam-5374	288	14	.	.	PUNCT
ejpam-5374	289	1	boletin	boletin	PROPN
ejpam-5374	289	2	de	de	X
ejpam-5374	289	3	la	la	PROPN
ejpam-5374	289	4	sociedad	sociedad	PROPN
ejpam-5374	289	5	matematica	matematica	PROPN
ejpam-5374	289	6	mexicana	mexicana	PROPN
ejpam-5374	289	7	,	,	PUNCT
ejpam-5374	289	8	27:1–13	27:1–13	NUM
ejpam-5374	289	9	,	,	PUNCT
ejpam-5374	289	10	2021	2021	NUM
ejpam-5374	289	11	.	.	PUNCT
ejpam-5374	290	1	[	[	X
ejpam-5374	290	2	22	22	NUM
ejpam-5374	290	3	]	]	SYM
ejpam-5374	290	4	b	b	X
ejpam-5374	290	5	kowalczyk	kowalczyk	NOUN
ejpam-5374	290	6	and	and	CCONJ
ejpam-5374	290	7	a	a	DET
ejpam-5374	290	8	lecko	lecko	NOUN
ejpam-5374	290	9	.	.	PUNCT
ejpam-5374	291	1	second	second	ADJ
ejpam-5374	291	2	hankel	hankel	NOUN
ejpam-5374	291	3	determinant	determinant	ADJ
ejpam-5374	291	4	of	of	ADP
ejpam-5374	291	5	logarithmic	logarithmic	ADJ
ejpam-5374	291	6	coefficients	coefficient	NOUN
ejpam-5374	291	7	of	of	ADP
ejpam-5374	291	8	convex	convex	NOUN
ejpam-5374	291	9	and	and	CCONJ
ejpam-5374	291	10	starlike	starlike	NOUN
ejpam-5374	291	11	functions	function	NOUN
ejpam-5374	291	12	.	.	PUNCT
ejpam-5374	292	1	bulletin	bulletin	NOUN
ejpam-5374	292	2	of	of	ADP
ejpam-5374	292	3	the	the	DET
ejpam-5374	292	4	australian	australian	ADJ
ejpam-5374	292	5	mathematical	mathematical	ADJ
ejpam-5374	292	6	society	society	NOUN
ejpam-5374	292	7	,	,	PUNCT
ejpam-5374	292	8	105(3):458–467	105(3):458–467	NUM
ejpam-5374	292	9	,	,	PUNCT
ejpam-5374	292	10	2022	2022	NUM
ejpam-5374	292	11	.	.	PUNCT
ejpam-5374	293	1	[	[	X
ejpam-5374	293	2	23	23	NUM
ejpam-5374	293	3	]	]	SYM
ejpam-5374	293	4	b	b	X
ejpam-5374	293	5	kowalczyk	kowalczyk	NOUN
ejpam-5374	293	6	and	and	CCONJ
ejpam-5374	293	7	a	a	DET
ejpam-5374	293	8	lecko	lecko	NOUN
ejpam-5374	293	9	.	.	PUNCT
ejpam-5374	294	1	second	second	ADJ
ejpam-5374	294	2	hankel	hankel	NOUN
ejpam-5374	294	3	determinant	determinant	ADJ
ejpam-5374	294	4	of	of	ADP
ejpam-5374	294	5	logarithmic	logarithmic	ADJ
ejpam-5374	294	6	coefficients	coefficient	NOUN
ejpam-5374	294	7	of	of	ADP
ejpam-5374	294	8	convex	convex	NOUN
ejpam-5374	294	9	and	and	CCONJ
ejpam-5374	294	10	starlike	starlike	NOUN
ejpam-5374	294	11	functions	function	NOUN
ejpam-5374	294	12	of	of	ADP
ejpam-5374	294	13	order	order	NOUN
ejpam-5374	294	14	alpha	alpha	NOUN
ejpam-5374	294	15	.	.	PUNCT
ejpam-5374	295	1	bulletin	bulletin	NOUN
ejpam-5374	295	2	of	of	ADP
ejpam-5374	295	3	the	the	DET
ejpam-5374	295	4	malaysian	malaysian	PROPN
ejpam-5374	295	5	mathematical	mathematical	PROPN
ejpam-5374	295	6	sciences	sciences	PROPN
ejpam-5374	295	7	society	society	NOUN
ejpam-5374	295	8	,	,	PUNCT
ejpam-5374	295	9	45(2	45(2	NOUN
ejpam-5374	295	10	)	)	PUNCT
ejpam-5374	295	11	,	,	PUNCT
ejpam-5374	295	12	2022	2022	NUM
ejpam-5374	295	13	.	.	PUNCT
ejpam-5374	296	1	[	[	X
ejpam-5374	296	2	24	24	NUM
ejpam-5374	296	3	]	]	SYM
ejpam-5374	296	4	b	b	X
ejpam-5374	296	5	kowalczyk	kowalczyk	NOUN
ejpam-5374	296	6	and	and	CCONJ
ejpam-5374	296	7	a	a	DET
ejpam-5374	296	8	lecko	lecko	NOUN
ejpam-5374	296	9	.	.	PUNCT
ejpam-5374	297	1	the	the	DET
ejpam-5374	297	2	second	second	ADJ
ejpam-5374	297	3	hankel	hankel	NOUN
ejpam-5374	297	4	determinant	determinant	ADJ
ejpam-5374	297	5	of	of	ADP
ejpam-5374	297	6	the	the	DET
ejpam-5374	297	7	logarithmic	logarithmic	ADJ
ejpam-5374	297	8	coefficients	coefficient	NOUN
ejpam-5374	297	9	of	of	ADP
ejpam-5374	297	10	strongly	strongly	ADV
ejpam-5374	297	11	starlike	starlike	NOUN
ejpam-5374	297	12	and	and	CCONJ
ejpam-5374	297	13	strongly	strongly	ADV
ejpam-5374	297	14	convex	convex	ADJ
ejpam-5374	297	15	functions	function	NOUN
ejpam-5374	297	16	.	.	PUNCT
ejpam-5374	298	1	revista	revista	PROPN
ejpam-5374	298	2	de	de	X
ejpam-5374	298	3	la	la	PROPN
ejpam-5374	298	4	real	real	PROPN
ejpam-5374	298	5	academia	academia	PROPN
ejpam-5374	298	6	de	de	PROPN
ejpam-5374	298	7	ciencias	ciencias	PROPN
ejpam-5374	298	8	exactas	exacta	NOUN
ejpam-5374	298	9	,	,	PUNCT
ejpam-5374	298	10	fisicas	fisicas	PROPN
ejpam-5374	298	11	y	y	PROPN
ejpam-5374	298	12	naturales	naturales	PROPN
ejpam-5374	298	13	.	.	PUNCT
ejpam-5374	299	1	serie	serie	PROPN
ejpam-5374	299	2	a.	a.	PROPN
ejpam-5374	299	3	matematicas	matematicas	PROPN
ejpam-5374	299	4	,	,	PUNCT
ejpam-5374	299	5	117(2):91	117(2):91	NUM
ejpam-5374	299	6	,	,	PUNCT
ejpam-5374	299	7	2023	2023	NUM
ejpam-5374	299	8	.	.	PUNCT
ejpam-5374	300	1	[	[	X
ejpam-5374	300	2	25	25	NUM
ejpam-5374	300	3	]	]	PUNCT
ejpam-5374	300	4	a	a	DET
ejpam-5374	300	5	lecko	lecko	NOUN
ejpam-5374	300	6	and	and	CCONJ
ejpam-5374	300	7	b	b	PROPN
ejpam-5374	300	8	śmiarowska	śmiarowska	PROPN
ejpam-5374	300	9	.	.	PUNCT
ejpam-5374	301	1	the	the	DET
ejpam-5374	301	2	second	second	ADJ
ejpam-5374	301	3	hankel	hankel	NOUN
ejpam-5374	301	4	determinant	determinant	ADJ
ejpam-5374	301	5	for	for	ADP
ejpam-5374	301	6	logarithmic	logarithmic	ADJ
ejpam-5374	301	7	coefficients	coefficient	NOUN
ejpam-5374	301	8	of	of	ADP
ejpam-5374	301	9	inverse	inverse	NOUN
ejpam-5374	301	10	functions	function	NOUN
ejpam-5374	301	11	of	of	ADP
ejpam-5374	301	12	bounded	bounded	ADJ
ejpam-5374	301	13	turning	turning	NOUN
ejpam-5374	301	14	of	of	ADP
ejpam-5374	301	15	a	a	DET
ejpam-5374	301	16	given	give	VERB
ejpam-5374	301	17	order	order	NOUN
ejpam-5374	301	18	.	.	PUNCT
ejpam-5374	302	1	bolet́ın	bolet́ın	ADJ
ejpam-5374	302	2	de	de	X
ejpam-5374	302	3	la	la	PROPN
ejpam-5374	302	4	sociedad	sociedad	PROPN
ejpam-5374	302	5	matemática	matemática	PROPN
ejpam-5374	302	6	mexicana	mexicana	PROPN
ejpam-5374	302	7	,	,	PUNCT
ejpam-5374	302	8	30(2):51	30(2):51	PROPN
ejpam-5374	302	9	,	,	PUNCT
ejpam-5374	302	10	2024	2024	NUM
ejpam-5374	302	11	.	.	PUNCT
ejpam-5374	303	1	[	[	X
ejpam-5374	303	2	26	26	NUM
ejpam-5374	303	3	]	]	X
ejpam-5374	303	4	y	y	PROPN
ejpam-5374	303	5	li	li	PROPN
ejpam-5374	303	6	and	and	CCONJ
ejpam-5374	303	7	x	x	ADJ
ejpam-5374	303	8	ding	ding	NOUN
ejpam-5374	303	9	.	.	PUNCT
ejpam-5374	304	1	vandermonde	vandermonde	ADJ
ejpam-5374	304	2	determinant	determinant	ADJ
ejpam-5374	304	3	and	and	CCONJ
ejpam-5374	304	4	its	its	PRON
ejpam-5374	304	5	applications	application	NOUN
ejpam-5374	304	6	.	.	PUNCT
ejpam-5374	305	1	journal	journal	NOUN
ejpam-5374	305	2	of	of	ADP
ejpam-5374	305	3	education	education	NOUN
ejpam-5374	305	4	and	and	CCONJ
ejpam-5374	305	5	culture	culture	NOUN
ejpam-5374	305	6	studies	study	NOUN
ejpam-5374	305	7	,	,	PUNCT
ejpam-5374	305	8	7(4):16–24	7(4):16–24	NUM
ejpam-5374	305	9	,	,	PUNCT
ejpam-5374	305	10	2023	2023	NUM
ejpam-5374	305	11	.	.	PUNCT
ejpam-5374	306	1	[	[	X
ejpam-5374	306	2	27	27	NUM
ejpam-5374	306	3	]	]	X
ejpam-5374	306	4	o	o	PROPN
ejpam-5374	306	5	m	m	NOUN
ejpam-5374	306	6	barukab	barukab	PROPN
ejpam-5374	306	7	,	,	PUNCT
ejpam-5374	306	8	m	m	PROPN
ejpam-5374	306	9	arif	arif	PROPN
ejpam-5374	306	10	,	,	PUNCT
ejpam-5374	306	11	m	m	NOUN
ejpam-5374	306	12	abbas	abbas	NOUN
ejpam-5374	306	13	,	,	PUNCT
ejpam-5374	306	14	and	and	CCONJ
ejpam-5374	306	15	s	s	VERB
ejpam-5374	306	16	a	a	DET
ejpam-5374	306	17	khan	khan	PROPN
ejpam-5374	306	18	.	.	PUNCT
ejpam-5374	307	1	sharp	sharp	ADJ
ejpam-5374	307	2	bounds	bound	NOUN
ejpam-5374	307	3	of	of	ADP
ejpam-5374	307	4	the	the	DET
ejpam-5374	307	5	coefficient	coefficient	NOUN
ejpam-5374	307	6	results	result	VERB
ejpam-5374	307	7	for	for	ADP
ejpam-5374	307	8	the	the	DET
ejpam-5374	307	9	family	family	NOUN
ejpam-5374	307	10	of	of	ADP
ejpam-5374	307	11	bounded	bound	VERB
ejpam-5374	307	12	turning	turning	NOUN
ejpam-5374	307	13	functions	function	NOUN
ejpam-5374	307	14	associated	associate	VERB
ejpam-5374	307	15	with	with	ADP
ejpam-5374	307	16	a	a	DET
ejpam-5374	307	17	petal	petal	ADJ
ejpam-5374	307	18	-	-	PUNCT
ejpam-5374	307	19	shaped	shape	VERB
ejpam-5374	307	20	domain	domain	NOUN
ejpam-5374	307	21	.	.	PUNCT
ejpam-5374	308	1	journal	journal	NOUN
ejpam-5374	308	2	of	of	ADP
ejpam-5374	308	3	function	function	NOUN
ejpam-5374	308	4	spaces	space	NOUN
ejpam-5374	308	5	,	,	PUNCT
ejpam-5374	308	6	2021(1):5535629	2021(1):5535629	NOUN
ejpam-5374	308	7	,	,	PUNCT
ejpam-5374	308	8	2021	2021	NUM
ejpam-5374	308	9	.	.	PUNCT
ejpam-5374	309	1	references	reference	NOUN
ejpam-5374	309	2	2751	2751	NUM
ejpam-5374	310	1	[	[	X
ejpam-5374	310	2	28	28	NUM
ejpam-5374	310	3	]	]	X
ejpam-5374	310	4	p	p	PROPN
ejpam-5374	310	5	sunthrayuth	sunthrayuth	NOUN
ejpam-5374	310	6	,	,	PUNCT
ejpam-5374	310	7	i	i	PRON
ejpam-5374	310	8	aldawish	aldawish	VERB
ejpam-5374	310	9	,	,	PUNCT
ejpam-5374	310	10	m	m	PROPN
ejpam-5374	310	11	arif	arif	PROPN
ejpam-5374	310	12	,	,	PUNCT
ejpam-5374	310	13	m	m	NOUN
ejpam-5374	310	14	abbas	abbas	NOUN
ejpam-5374	310	15	,	,	PUNCT
ejpam-5374	310	16	and	and	CCONJ
ejpam-5374	310	17	s	s	VERB
ejpam-5374	310	18	el	el	PROPN
ejpam-5374	310	19	-	-	PUNCT
ejpam-5374	310	20	deeb	deeb	PROPN
ejpam-5374	310	21	.	.	PUNCT
ejpam-5374	311	1	estimation	estimation	NOUN
ejpam-5374	311	2	of	of	ADP
ejpam-5374	311	3	the	the	DET
ejpam-5374	311	4	second	second	ADJ
ejpam-5374	311	5	-	-	PUNCT
ejpam-5374	311	6	order	order	NOUN
ejpam-5374	311	7	hankel	hankel	NOUN
ejpam-5374	311	8	determinant	determinant	ADJ
ejpam-5374	311	9	of	of	ADP
ejpam-5374	311	10	logarithmic	logarithmic	ADJ
ejpam-5374	311	11	coefficients	coefficient	NOUN
ejpam-5374	311	12	for	for	ADP
ejpam-5374	311	13	two	two	NUM
ejpam-5374	311	14	subclasses	subclass	NOUN
ejpam-5374	311	15	of	of	ADP
ejpam-5374	311	16	starlike	starlike	NOUN
ejpam-5374	311	17	functions	function	NOUN
ejpam-5374	311	18	.	.	PUNCT
ejpam-5374	312	1	symmetry	symmetry	NOUN
ejpam-5374	312	2	,	,	PUNCT
ejpam-5374	312	3	14(10):2039	14(10):2039	NUM
ejpam-5374	312	4	,	,	PUNCT
ejpam-5374	312	5	2022	2022	NUM
ejpam-5374	312	6	.	.	PUNCT
ejpam-5374	313	1	[	[	X
ejpam-5374	313	2	29	29	NUM
ejpam-5374	313	3	]	]	X
ejpam-5374	313	4	a	a	DET
ejpam-5374	313	5	hussen	hussen	NOUN
ejpam-5374	313	6	,	,	PUNCT
ejpam-5374	313	7	m	m	PROPN
ejpam-5374	313	8	s	s	PROPN
ejpam-5374	313	9	madi	madi	NOUN
ejpam-5374	313	10	,	,	PUNCT
ejpam-5374	313	11	and	and	CCONJ
ejpam-5374	313	12	a	a	DET
ejpam-5374	313	13	m	m	NOUN
ejpam-5374	313	14	abominjil	abominjil	NOUN
ejpam-5374	313	15	.	.	PUNCT
ejpam-5374	314	1	bounding	bound	VERB
ejpam-5374	314	2	coefficients	coefficient	NOUN
ejpam-5374	314	3	for	for	ADP
ejpam-5374	314	4	certain	certain	ADJ
ejpam-5374	314	5	subclasses	subclass	NOUN
ejpam-5374	314	6	of	of	ADP
ejpam-5374	314	7	bi	bi	ADJ
ejpam-5374	314	8	-	-	ADJ
ejpam-5374	314	9	univalent	univalent	ADJ
ejpam-5374	314	10	functions	function	NOUN
ejpam-5374	314	11	related	relate	VERB
ejpam-5374	314	12	to	to	ADP
ejpam-5374	314	13	lucas	lucas	NOUN
ejpam-5374	314	14	-	-	PUNCT
ejpam-5374	314	15	balancing	balance	VERB
ejpam-5374	314	16	polynomials	polynomial	NOUN
ejpam-5374	314	17	.	.	PUNCT
ejpam-5374	315	1	aims	aim	VERB
ejpam-5374	315	2	mathematics	mathematic	NOUN
ejpam-5374	315	3	,	,	PUNCT
ejpam-5374	315	4	9(7):18034–18047	9(7):18034–18047	NUM
ejpam-5374	315	5	,	,	PUNCT
ejpam-5374	315	6	2024	2024	NUM
ejpam-5374	315	7	.	.	PUNCT
ejpam-5374	316	1	[	[	X
ejpam-5374	316	2	30	30	NUM
ejpam-5374	316	3	]	]	X
ejpam-5374	316	4	t	t	PROPN
ejpam-5374	316	5	h	h	PROPN
ejpam-5374	316	6	macgregor	macgregor	PROPN
ejpam-5374	316	7	.	.	PUNCT
ejpam-5374	317	1	functions	function	NOUN
ejpam-5374	317	2	whose	whose	DET
ejpam-5374	317	3	derivative	derivative	NOUN
ejpam-5374	317	4	has	have	VERB
ejpam-5374	317	5	a	a	DET
ejpam-5374	317	6	positive	positive	ADJ
ejpam-5374	317	7	real	real	ADJ
ejpam-5374	317	8	part	part	NOUN
ejpam-5374	317	9	.	.	PUNCT
ejpam-5374	318	1	transactions	transaction	NOUN
ejpam-5374	318	2	of	of	ADP
ejpam-5374	318	3	the	the	DET
ejpam-5374	318	4	american	american	PROPN
ejpam-5374	318	5	mathematical	mathematical	PROPN
ejpam-5374	318	6	society	society	NOUN
ejpam-5374	318	7	,	,	PUNCT
ejpam-5374	318	8	104(3):532–537	104(3):532–537	NUM
ejpam-5374	318	9	,	,	PUNCT
ejpam-5374	318	10	1962	1962	NUM
ejpam-5374	318	11	.	.	PUNCT
ejpam-5374	319	1	[	[	X
ejpam-5374	319	2	31	31	NUM
ejpam-5374	319	3	]	]	X
ejpam-5374	320	1	i	i	PRON
ejpam-5374	320	2	m	m	VERB
ejpam-5374	320	3	milin	milin	PROPN
ejpam-5374	320	4	.	.	PUNCT
ejpam-5374	321	1	univalent	univalent	ADJ
ejpam-5374	321	2	functions	function	NOUN
ejpam-5374	321	3	and	and	CCONJ
ejpam-5374	321	4	orthonormal	orthonormal	ADJ
ejpam-5374	321	5	systems	system	NOUN
ejpam-5374	321	6	,	,	PUNCT
ejpam-5374	321	7	volume	volume	NOUN
ejpam-5374	321	8	49	49	NUM
ejpam-5374	321	9	.	.	PUNCT
ejpam-5374	322	1	american	american	PROPN
ejpam-5374	322	2	mathematical	mathematical	PROPN
ejpam-5374	322	3	society	society	NOUN
ejpam-5374	322	4	,	,	PUNCT
ejpam-5374	322	5	1977	1977	NUM
ejpam-5374	322	6	.	.	PUNCT
ejpam-5374	323	1	[	[	X
ejpam-5374	323	2	32	32	NUM
ejpam-5374	323	3	]	]	X
ejpam-5374	324	1	i	i	PRON
ejpam-5374	324	2	m	m	VERB
ejpam-5374	324	3	milin	milin	PROPN
ejpam-5374	324	4	.	.	PUNCT
ejpam-5374	325	1	on	on	ADP
ejpam-5374	325	2	a	a	DET
ejpam-5374	325	3	property	property	NOUN
ejpam-5374	325	4	of	of	ADP
ejpam-5374	325	5	the	the	DET
ejpam-5374	325	6	logarithmic	logarithmic	ADJ
ejpam-5374	325	7	coefficients	coefficient	NOUN
ejpam-5374	325	8	of	of	ADP
ejpam-5374	325	9	univalent	univalent	ADJ
ejpam-5374	325	10	functions	function	NOUN
ejpam-5374	325	11	.	.	PUNCT
ejpam-5374	326	1	metric	metric	ADJ
ejpam-5374	326	2	questions	question	NOUN
ejpam-5374	326	3	in	in	ADP
ejpam-5374	326	4	the	the	DET
ejpam-5374	326	5	theory	theory	NOUN
ejpam-5374	326	6	of	of	ADP
ejpam-5374	326	7	functions	function	NOUN
ejpam-5374	326	8	,	,	PUNCT
ejpam-5374	326	9	pages	page	NOUN
ejpam-5374	326	10	86–90	86–90	NUM
ejpam-5374	326	11	,	,	PUNCT
ejpam-5374	326	12	1980	1980	NUM
ejpam-5374	326	13	.	.	PUNCT
ejpam-5374	327	1	[	[	X
ejpam-5374	327	2	33	33	NUM
ejpam-5374	327	3	]	]	X
ejpam-5374	327	4	i	i	PRON
ejpam-5374	327	5	m	m	VERB
ejpam-5374	327	6	milin	milin	PROPN
ejpam-5374	327	7	.	.	PUNCT
ejpam-5374	328	1	on	on	ADP
ejpam-5374	328	2	one	one	NUM
ejpam-5374	328	3	conjecture	conjecture	NOUN
ejpam-5374	328	4	for	for	ADP
ejpam-5374	328	5	the	the	DET
ejpam-5374	328	6	logarithhmic	logarithhmic	ADJ
ejpam-5374	328	7	coefficients	coefficient	NOUN
ejpam-5374	328	8	of	of	ADP
ejpam-5374	328	9	univalent	univalent	ADJ
ejpam-5374	328	10	functions	function	NOUN
ejpam-5374	328	11	.	.	PUNCT
ejpam-5374	329	1	zapiski	zapiski	PROPN
ejpam-5374	329	2	nauchnykh	nauchnykh	PROPN
ejpam-5374	329	3	seminarov	seminarov	PROPN
ejpam-5374	329	4	pomi	pomi	NOUN
ejpam-5374	329	5	,	,	PUNCT
ejpam-5374	329	6	125:135–143	125:135–143	NUM
ejpam-5374	329	7	,	,	PUNCT
ejpam-5374	329	8	1983	1983	NUM
ejpam-5374	329	9	.	.	PUNCT
ejpam-5374	330	1	[	[	X
ejpam-5374	330	2	34	34	NUM
ejpam-5374	330	3	]	]	X
ejpam-5374	330	4	d	d	X
ejpam-5374	330	5	mohamad	mohamad	PROPN
ejpam-5374	330	6	.	.	PUNCT
ejpam-5374	331	1	on	on	ADP
ejpam-5374	331	2	a	a	DET
ejpam-5374	331	3	class	class	NOUN
ejpam-5374	331	4	of	of	ADP
ejpam-5374	331	5	functions	function	NOUN
ejpam-5374	331	6	whose	whose	DET
ejpam-5374	331	7	derivatives	derivative	NOUN
ejpam-5374	331	8	map	map	VERB
ejpam-5374	331	9	the	the	DET
ejpam-5374	331	10	unit	unit	NOUN
ejpam-5374	331	11	disc	disc	VERB
ejpam-5374	331	12	into	into	ADP
ejpam-5374	331	13	a	a	DET
ejpam-5374	331	14	half	half	ADJ
ejpam-5374	331	15	plane	plane	NOUN
ejpam-5374	331	16	.	.	PUNCT
ejpam-5374	332	1	bulletin	bulletin	NOUN
ejpam-5374	332	2	of	of	ADP
ejpam-5374	332	3	the	the	DET
ejpam-5374	332	4	malaysian	malaysian	PROPN
ejpam-5374	332	5	mathematical	mathematical	PROPN
ejpam-5374	332	6	sciences	sciences	PROPN
ejpam-5374	332	7	society	society	NOUN
ejpam-5374	332	8	,	,	PUNCT
ejpam-5374	332	9	23(2	23(2	NOUN
ejpam-5374	332	10	)	)	PUNCT
ejpam-5374	332	11	,	,	PUNCT
ejpam-5374	332	12	2000	2000	NUM
ejpam-5374	332	13	.	.	PUNCT
ejpam-5374	333	1	[	[	X
ejpam-5374	333	2	35	35	NUM
ejpam-5374	333	3	]	]	X
ejpam-5374	333	4	d	d	X
ejpam-5374	333	5	mohamad	mohamad	PROPN
ejpam-5374	333	6	,	,	PUNCT
ejpam-5374	333	7	n	n	PRON
ejpam-5374	333	8	h	h	NOUN
ejpam-5374	333	9	a	a	DET
ejpam-5374	333	10	a	a	DET
ejpam-5374	333	11	wahid	wahid	NOUN
ejpam-5374	333	12	,	,	PUNCT
ejpam-5374	333	13	and	and	CCONJ
ejpam-5374	333	14	n	n	CCONJ
ejpam-5374	333	15	n	n	PRON
ejpam-5374	333	16	hasni	hasni	NOUN
ejpam-5374	333	17	.	.	PUNCT
ejpam-5374	334	1	coefficient	coefficient	NOUN
ejpam-5374	334	2	problems	problem	NOUN
ejpam-5374	334	3	for	for	ADP
ejpam-5374	334	4	star	star	NOUN
ejpam-5374	334	5	-	-	PUNCT
ejpam-5374	334	6	like	like	ADJ
ejpam-5374	334	7	functions	function	NOUN
ejpam-5374	334	8	with	with	ADP
ejpam-5374	334	9	respect	respect	NOUN
ejpam-5374	334	10	to	to	ADP
ejpam-5374	334	11	symmetric	symmetric	ADJ
ejpam-5374	334	12	conjugate	conjugate	ADJ
ejpam-5374	334	13	points	point	NOUN
ejpam-5374	334	14	connected	connect	VERB
ejpam-5374	334	15	to	to	ADP
ejpam-5374	334	16	the	the	DET
ejpam-5374	334	17	sine	sine	ADJ
ejpam-5374	334	18	function	function	NOUN
ejpam-5374	334	19	.	.	PUNCT
ejpam-5374	335	1	european	european	ADJ
ejpam-5374	335	2	journal	journal	PROPN
ejpam-5374	335	3	of	of	ADP
ejpam-5374	335	4	pure	pure	ADJ
ejpam-5374	335	5	and	and	CCONJ
ejpam-5374	335	6	applied	applied	ADJ
ejpam-5374	335	7	mathematics	mathematic	NOUN
ejpam-5374	335	8	,	,	PUNCT
ejpam-5374	335	9	16(2):1167–1179	16(2):1167–1179	NUM
ejpam-5374	335	10	,	,	PUNCT
ejpam-5374	335	11	2023	2023	NUM
ejpam-5374	335	12	.	.	PUNCT
ejpam-5374	336	1	[	[	X
ejpam-5374	336	2	36	36	NUM
ejpam-5374	336	3	]	]	PUNCT
ejpam-5374	336	4	n	n	PRON
ejpam-5374	336	5	h	h	NOUN
ejpam-5374	336	6	a	a	DET
ejpam-5374	336	7	a	a	DET
ejpam-5374	336	8	wahid	wahid	NOUN
ejpam-5374	336	9	,	,	PUNCT
ejpam-5374	336	10	d	d	PROPN
ejpam-5374	336	11	mohamad	mohamad	X
ejpam-5374	336	12	,	,	PUNCT
ejpam-5374	336	13	n	n	PRON
ejpam-5374	336	14	m	m	PROPN
ejpam-5374	336	15	kamarozzaman	kamarozzaman	NOUN
ejpam-5374	336	16	,	,	PUNCT
ejpam-5374	336	17	and	and	CCONJ
ejpam-5374	336	18	a	a	DET
ejpam-5374	336	19	a	a	DET
ejpam-5374	336	20	shahminan	shahminan	NOUN
ejpam-5374	336	21	.	.	PUNCT
ejpam-5374	337	1	toeplitz	toeplitz	NOUN
ejpam-5374	337	2	determinants	determinant	NOUN
ejpam-5374	337	3	for	for	ADP
ejpam-5374	337	4	the	the	DET
ejpam-5374	337	5	class	class	NOUN
ejpam-5374	337	6	of	of	ADP
ejpam-5374	337	7	functions	function	NOUN
ejpam-5374	337	8	with	with	ADP
ejpam-5374	337	9	bounded	bounded	ADJ
ejpam-5374	337	10	turning	turning	NOUN
ejpam-5374	337	11	.	.	PUNCT
ejpam-5374	338	1	european	european	PROPN
ejpam-5374	338	2	journal	journal	PROPN
ejpam-5374	338	3	of	of	ADP
ejpam-5374	338	4	pure	pure	ADJ
ejpam-5374	338	5	and	and	CCONJ
ejpam-5374	338	6	applied	applied	ADJ
ejpam-5374	338	7	mathematics	mathematic	NOUN
ejpam-5374	338	8	,	,	PUNCT
ejpam-5374	338	9	15(4):1937–1947	15(4):1937–1947	NUM
ejpam-5374	338	10	,	,	PUNCT
ejpam-5374	338	11	2022	2022	NUM
ejpam-5374	338	12	.	.	PUNCT
ejpam-5374	339	1	[	[	X
ejpam-5374	339	2	37	37	NUM
ejpam-5374	339	3	]	]	X
ejpam-5374	339	4	k	k	X
ejpam-5374	339	5	noshiro	noshiro	PROPN
ejpam-5374	339	6	.	.	PUNCT
ejpam-5374	340	1	on	on	ADP
ejpam-5374	340	2	the	the	DET
ejpam-5374	340	3	theory	theory	NOUN
ejpam-5374	340	4	of	of	ADP
ejpam-5374	340	5	schlicht	schlicht	NOUN
ejpam-5374	340	6	functions	function	NOUN
ejpam-5374	340	7	.	.	PUNCT
ejpam-5374	341	1	journal	journal	NOUN
ejpam-5374	341	2	of	of	ADP
ejpam-5374	341	3	faculty	faculty	NOUN
ejpam-5374	341	4	of	of	ADP
ejpam-5374	341	5	science	science	NOUN
ejpam-5374	341	6	,	,	PUNCT
ejpam-5374	341	7	hokkaido	hokkaido	PROPN
ejpam-5374	341	8	imperial	imperial	PROPN
ejpam-5374	341	9	university	university	PROPN
ejpam-5374	341	10	.	.	PUNCT
ejpam-5374	342	1	series	series	PROPN
ejpam-5374	342	2	i.	i.	PROPN
ejpam-5374	342	3	mathematics	mathematics	PROPN
ejpam-5374	342	4	,	,	PUNCT
ejpam-5374	342	5	2:129–155	2:129–155	NOUN
ejpam-5374	342	6	,	,	PUNCT
ejpam-5374	342	7	1934	1934	NUM
ejpam-5374	342	8	.	.	PUNCT
ejpam-5374	343	1	[	[	X
ejpam-5374	343	2	38	38	NUM
ejpam-5374	343	3	]	]	PUNCT
ejpam-5374	343	4	c	c	NOUN
ejpam-5374	343	5	pommerenke	pommerenke	NOUN
ejpam-5374	343	6	.	.	PUNCT
ejpam-5374	344	1	on	on	ADP
ejpam-5374	344	2	the	the	DET
ejpam-5374	344	3	coefficients	coefficient	NOUN
ejpam-5374	344	4	and	and	CCONJ
ejpam-5374	344	5	hankel	hankel	NOUN
ejpam-5374	344	6	determinants	determinant	NOUN
ejpam-5374	344	7	of	of	ADP
ejpam-5374	344	8	univalent	univalent	ADJ
ejpam-5374	344	9	functions	function	NOUN
ejpam-5374	344	10	.	.	PUNCT
ejpam-5374	345	1	journal	journal	NOUN
ejpam-5374	345	2	of	of	ADP
ejpam-5374	345	3	the	the	DET
ejpam-5374	345	4	london	london	PROPN
ejpam-5374	345	5	mathematical	mathematical	ADJ
ejpam-5374	345	6	society	society	NOUN
ejpam-5374	345	7	,	,	PUNCT
ejpam-5374	345	8	1(1):111–122	1(1):111–122	NUM
ejpam-5374	345	9	,	,	PUNCT
ejpam-5374	345	10	1966	1966	NUM
ejpam-5374	345	11	.	.	PUNCT
ejpam-5374	346	1	[	[	X
ejpam-5374	346	2	39	39	NUM
ejpam-5374	346	3	]	]	PUNCT
ejpam-5374	346	4	c	c	NOUN
ejpam-5374	346	5	pommerenke	pommerenke	NOUN
ejpam-5374	346	6	.	.	PUNCT
ejpam-5374	347	1	on	on	ADP
ejpam-5374	347	2	the	the	DET
ejpam-5374	347	3	hankel	hankel	NOUN
ejpam-5374	347	4	determinants	determinant	NOUN
ejpam-5374	347	5	of	of	ADP
ejpam-5374	347	6	univalent	univalent	ADJ
ejpam-5374	347	7	functions	function	NOUN
ejpam-5374	347	8	.	.	PUNCT
ejpam-5374	347	9	mathematika	mathematika	NOUN
ejpam-5374	347	10	,	,	PUNCT
ejpam-5374	347	11	14(1):108–112	14(1):108–112	PROPN
ejpam-5374	347	12	,	,	PUNCT
ejpam-5374	347	13	1967	1967	NUM
ejpam-5374	347	14	.	.	PUNCT
ejpam-5374	348	1	[	[	X
ejpam-5374	348	2	40	40	NUM
ejpam-5374	348	3	]	]	X
ejpam-5374	348	4	m	m	VERB
ejpam-5374	348	5	g	g	PROPN
ejpam-5374	348	6	khan	khan	PROPN
ejpam-5374	348	7	,	,	PUNCT
ejpam-5374	348	8	b	b	PROPN
ejpam-5374	348	9	ahmad	ahmad	PROPN
ejpam-5374	348	10	,	,	PUNCT
ejpam-5374	348	11	j	j	PROPN
ejpam-5374	348	12	sokol	sokol	PROPN
ejpam-5374	348	13	,	,	PUNCT
ejpam-5374	348	14	z	z	PROPN
ejpam-5374	348	15	muhammad	muhammad	PROPN
ejpam-5374	348	16	,	,	PUNCT
ejpam-5374	348	17	w	w	PROPN
ejpam-5374	348	18	k	k	PROPN
ejpam-5374	348	19	mashwani	mashwani	PROPN
ejpam-5374	348	20	,	,	PUNCT
ejpam-5374	348	21	r	r	NOUN
ejpam-5374	348	22	chinram	chinram	NOUN
ejpam-5374	348	23	,	,	PUNCT
ejpam-5374	348	24	and	and	CCONJ
ejpam-5374	348	25	p	p	NOUN
ejpam-5374	348	26	petchkaew	petchkaew	NOUN
ejpam-5374	348	27	.	.	PUNCT
ejpam-5374	349	1	coefficient	coefficient	NOUN
ejpam-5374	349	2	problems	problem	NOUN
ejpam-5374	349	3	in	in	ADP
ejpam-5374	349	4	a	a	DET
ejpam-5374	349	5	class	class	NOUN
ejpam-5374	349	6	of	of	ADP
ejpam-5374	349	7	functions	function	NOUN
ejpam-5374	349	8	with	with	ADP
ejpam-5374	349	9	bounded	bounded	ADJ
ejpam-5374	349	10	turning	turning	NOUN
ejpam-5374	349	11	associated	associate	VERB
ejpam-5374	349	12	with	with	ADP
ejpam-5374	349	13	sine	sine	ADJ
ejpam-5374	349	14	function	function	NOUN
ejpam-5374	349	15	.	.	PUNCT
ejpam-5374	350	1	european	european	ADJ
ejpam-5374	350	2	journal	journal	PROPN
ejpam-5374	350	3	of	of	ADP
ejpam-5374	350	4	pure	pure	ADJ
ejpam-5374	350	5	and	and	CCONJ
ejpam-5374	350	6	applied	applied	ADJ
ejpam-5374	350	7	mathematics	mathematic	NOUN
ejpam-5374	350	8	,	,	PUNCT
ejpam-5374	350	9	14(1):53–64	14(1):53–64	NUM
ejpam-5374	350	10	,	,	PUNCT
ejpam-5374	350	11	2021	2021	NUM
ejpam-5374	350	12	.	.	PUNCT
ejpam-5374	351	1	[	[	X
ejpam-5374	351	2	41	41	NUM
ejpam-5374	351	3	]	]	PUNCT
ejpam-5374	351	4	a	a	DET
ejpam-5374	351	5	s	s	NOUN
ejpam-5374	351	6	alshehry	alshehry	NOUN
ejpam-5374	351	7	,	,	PUNCT
ejpam-5374	351	8	r	r	NOUN
ejpam-5374	351	9	shah	shah	NOUN
ejpam-5374	351	10	,	,	PUNCT
ejpam-5374	351	11	and	and	CCONJ
ejpam-5374	351	12	a	a	DET
ejpam-5374	351	13	bariq	bariq	NOUN
ejpam-5374	351	14	.	.	PUNCT
ejpam-5374	352	1	the	the	DET
ejpam-5374	352	2	second	second	ADJ
ejpam-5374	352	3	hankel	hankel	NOUN
ejpam-5374	352	4	determinant	determinant	ADJ
ejpam-5374	352	5	of	of	ADP
ejpam-5374	352	6	logarithmic	logarithmic	ADJ
ejpam-5374	352	7	coefficients	coefficient	NOUN
ejpam-5374	352	8	for	for	ADP
ejpam-5374	352	9	starlike	starlike	NOUN
ejpam-5374	352	10	and	and	CCONJ
ejpam-5374	352	11	convex	convex	NOUN
ejpam-5374	352	12	functions	function	NOUN
ejpam-5374	352	13	involving	involve	VERB
ejpam-5374	352	14	four	four	NUM
ejpam-5374	352	15	-	-	PUNCT
ejpam-5374	352	16	leaf	leaf	NOUN
ejpam-5374	352	17	-	-	PUNCT
ejpam-5374	352	18	shaped	shape	VERB
ejpam-5374	352	19	domain	domain	NOUN
ejpam-5374	352	20	.	.	PUNCT
ejpam-5374	353	1	journal	journal	NOUN
ejpam-5374	353	2	of	of	ADP
ejpam-5374	353	3	function	function	NOUN
ejpam-5374	353	4	spaces	space	NOUN
ejpam-5374	353	5	,	,	PUNCT
ejpam-5374	353	6	2022(1):2621811	2022(1):2621811	NUM
ejpam-5374	353	7	,	,	PUNCT
ejpam-5374	353	8	2022	2022	NUM
ejpam-5374	353	9	.	.	PUNCT
ejpam-5374	354	1	references	reference	NOUN
ejpam-5374	354	2	2752	2752	NUM
ejpam-5374	354	3	[	[	X
ejpam-5374	354	4	42	42	NUM
ejpam-5374	354	5	]	]	X
ejpam-5374	354	6	o	o	X
ejpam-5374	354	7	roth	roth	PROPN
ejpam-5374	354	8	.	.	PUNCT
ejpam-5374	355	1	a	a	DET
ejpam-5374	355	2	sharp	sharp	ADJ
ejpam-5374	355	3	inequality	inequality	NOUN
ejpam-5374	355	4	for	for	ADP
ejpam-5374	355	5	the	the	DET
ejpam-5374	355	6	logarithmic	logarithmic	ADJ
ejpam-5374	355	7	coefficients	coefficient	NOUN
ejpam-5374	355	8	of	of	ADP
ejpam-5374	355	9	univalent	univalent	ADJ
ejpam-5374	355	10	functions	function	NOUN
ejpam-5374	355	11	.	.	PUNCT
ejpam-5374	356	1	proceedings	proceeding	NOUN
ejpam-5374	356	2	of	of	ADP
ejpam-5374	356	3	the	the	DET
ejpam-5374	356	4	american	american	PROPN
ejpam-5374	356	5	mathematical	mathematical	PROPN
ejpam-5374	356	6	society	society	NOUN
ejpam-5374	356	7	,	,	PUNCT
ejpam-5374	356	8	135(7):2051–2054	135(7):2051–2054	NUM
ejpam-5374	356	9	,	,	PUNCT
ejpam-5374	356	10	2007	2007	NUM
ejpam-5374	356	11	.	.	PUNCT
ejpam-5374	357	1	[	[	X
ejpam-5374	357	2	43	43	NUM
ejpam-5374	357	3	]	]	X
ejpam-5374	357	4	b	b	X
ejpam-5374	357	5	khan	khan	PROPN
ejpam-5374	357	6	,	,	PUNCT
ejpam-5374	357	7	i	i	PRON
ejpam-5374	357	8	aldawish	aldawish	VERB
ejpam-5374	357	9	,	,	PUNCT
ejpam-5374	357	10	s	s	PART
ejpam-5374	357	11	araci	araci	NOUN
ejpam-5374	357	12	,	,	PUNCT
ejpam-5374	357	13	and	and	CCONJ
ejpam-5374	357	14	m	m	PROPN
ejpam-5374	357	15	g	g	PROPN
ejpam-5374	357	16	khan	khan	PROPN
ejpam-5374	357	17	.	.	PUNCT
ejpam-5374	358	1	third	third	ADJ
ejpam-5374	358	2	hankel	hankel	NOUN
ejpam-5374	358	3	determinant	determinant	ADJ
ejpam-5374	358	4	for	for	ADP
ejpam-5374	358	5	the	the	DET
ejpam-5374	358	6	logarithmic	logarithmic	ADJ
ejpam-5374	358	7	coefficients	coefficient	NOUN
ejpam-5374	358	8	of	of	ADP
ejpam-5374	358	9	starlike	starlike	NOUN
ejpam-5374	358	10	functions	function	NOUN
ejpam-5374	358	11	associated	associate	VERB
ejpam-5374	358	12	with	with	ADP
ejpam-5374	358	13	sine	sine	ADJ
ejpam-5374	358	14	function	function	NOUN
ejpam-5374	358	15	.	.	PUNCT
ejpam-5374	359	1	fractal	fractal	ADJ
ejpam-5374	359	2	and	and	CCONJ
ejpam-5374	359	3	fractional	fractional	ADJ
ejpam-5374	359	4	,	,	PUNCT
ejpam-5374	359	5	6(5):261	6(5):261	NUM
ejpam-5374	359	6	,	,	PUNCT
ejpam-5374	359	7	2022	2022	NUM
ejpam-5374	359	8	.	.	PUNCT
ejpam-5374	360	1	[	[	X
ejpam-5374	360	2	44	44	NUM
ejpam-5374	360	3	]	]	SYM
ejpam-5374	360	4	s	s	X
ejpam-5374	360	5	p	p	NOUN
ejpam-5374	360	6	vijayalakshmi	vijayalakshmi	NOUN
ejpam-5374	360	7	,	,	PUNCT
ejpam-5374	360	8	s	s	NOUN
ejpam-5374	360	9	bulut	bulut	NOUN
ejpam-5374	360	10	,	,	PUNCT
ejpam-5374	360	11	and	and	CCONJ
ejpam-5374	360	12	t	t	PROPN
ejpam-5374	360	13	v	v	PROPN
ejpam-5374	360	14	sudharsan	sudharsan	NOUN
ejpam-5374	360	15	.	.	PUNCT
ejpam-5374	361	1	vandermonde	vandermonde	VERB
ejpam-5374	361	2	determinant	determinant	ADJ
ejpam-5374	361	3	for	for	ADP
ejpam-5374	361	4	a	a	DET
ejpam-5374	361	5	certain	certain	ADJ
ejpam-5374	361	6	sakaguchi	sakaguchi	ADJ
ejpam-5374	361	7	type	type	NOUN
ejpam-5374	361	8	function	function	NOUN
ejpam-5374	361	9	in	in	ADP
ejpam-5374	361	10	limaçon	limaçon	NOUN
ejpam-5374	361	11	domain	domain	NOUN
ejpam-5374	361	12	.	.	PUNCT
ejpam-5374	362	1	asian	asian	ADJ
ejpam-5374	362	2	-	-	PUNCT
ejpam-5374	362	3	european	european	ADJ
ejpam-5374	362	4	journal	journal	NOUN
ejpam-5374	362	5	of	of	ADP
ejpam-5374	362	6	mathematics	mathematic	NOUN
ejpam-5374	362	7	,	,	PUNCT
ejpam-5374	362	8	15(12):2250212	15(12):2250212	NUM
ejpam-5374	362	9	,	,	PUNCT
ejpam-5374	362	10	2022	2022	NUM
ejpam-5374	362	11	.	.	PUNCT
ejpam-5374	363	1	[	[	X
ejpam-5374	363	2	45	45	NUM
ejpam-5374	363	3	]	]	PUNCT
ejpam-5374	363	4	h	h	NOUN
ejpam-5374	363	5	silverman	silverman	NOUN
ejpam-5374	363	6	and	and	CCONJ
ejpam-5374	363	7	e	e	NOUN
ejpam-5374	363	8	m	m	PROPN
ejpam-5374	363	9	silvia	silvia	PROPN
ejpam-5374	363	10	.	.	PUNCT
ejpam-5374	364	1	on	on	ADP
ejpam-5374	364	2	α	α	NOUN
ejpam-5374	364	3	-	-	PUNCT
ejpam-5374	364	4	close	close	VERB
ejpam-5374	364	5	-	-	PUNCT
ejpam-5374	364	6	to	to	ADP
ejpam-5374	364	7	-	-	PUNCT
ejpam-5374	364	8	convex	convex	NOUN
ejpam-5374	364	9	functions	function	NOUN
ejpam-5374	364	10	.	.	PUNCT
ejpam-5374	365	1	publicationes	publicatione	NOUN
ejpam-5374	365	2	mathematicae	mathematicae	PROPN
ejpam-5374	365	3	debrecen	debrecen	PROPN
ejpam-5374	365	4	,	,	PUNCT
ejpam-5374	365	5	49(3	49(3	PROPN
ejpam-5374	365	6	-	-	PUNCT
ejpam-5374	365	7	4):305–316	4):305–316	NUM
ejpam-5374	365	8	,	,	PUNCT
ejpam-5374	365	9	1996	1996	NUM
ejpam-5374	365	10	.	.	PUNCT
ejpam-5374	366	1	[	[	X
ejpam-5374	366	2	46	46	NUM
ejpam-5374	366	3	]	]	SYM
ejpam-5374	366	4	v	v	ADP
ejpam-5374	366	5	allu	allu	NOUN
ejpam-5374	366	6	,	,	PUNCT
ejpam-5374	366	7	v	v	X
ejpam-5374	366	8	arora	arora	PROPN
ejpam-5374	366	9	,	,	PUNCT
ejpam-5374	366	10	and	and	CCONJ
ejpam-5374	366	11	a	a	DET
ejpam-5374	366	12	shaji	shaji	NOUN
ejpam-5374	366	13	.	.	PUNCT
ejpam-5374	367	1	on	on	ADP
ejpam-5374	367	2	the	the	DET
ejpam-5374	367	3	second	second	ADJ
ejpam-5374	367	4	hankel	hankel	NOUN
ejpam-5374	367	5	determinant	determinant	ADJ
ejpam-5374	367	6	of	of	ADP
ejpam-5374	367	7	logarithmic	logarithmic	ADJ
ejpam-5374	367	8	coefficients	coefficient	NOUN
ejpam-5374	367	9	for	for	ADP
ejpam-5374	367	10	certain	certain	ADJ
ejpam-5374	367	11	univalent	univalent	ADJ
ejpam-5374	367	12	functions	function	NOUN
ejpam-5374	367	13	.	.	PUNCT
ejpam-5374	368	1	mediterranean	mediterranean	PROPN
ejpam-5374	368	2	journal	journal	PROPN
ejpam-5374	368	3	of	of	ADP
ejpam-5374	368	4	mathematics	mathematic	NOUN
ejpam-5374	368	5	,	,	PUNCT
ejpam-5374	368	6	20(2):81	20(2):81	NUM
ejpam-5374	368	7	,	,	PUNCT
ejpam-5374	368	8	2023	2023	NUM
ejpam-5374	368	9	.	.	PUNCT
ejpam-5374	369	1	[	[	X
ejpam-5374	369	2	47	47	NUM
ejpam-5374	369	3	]	]	SYM
ejpam-5374	369	4	s	s	PART
ejpam-5374	369	5	e	e	NOUN
ejpam-5374	369	6	warschawski	warschawski	NOUN
ejpam-5374	369	7	.	.	PUNCT
ejpam-5374	370	1	on	on	ADP
ejpam-5374	370	2	the	the	DET
ejpam-5374	370	3	higher	high	ADJ
ejpam-5374	370	4	derivatives	derivative	NOUN
ejpam-5374	370	5	at	at	ADP
ejpam-5374	370	6	the	the	DET
ejpam-5374	370	7	boundary	boundary	NOUN
ejpam-5374	370	8	in	in	ADP
ejpam-5374	370	9	conformal	conformal	ADJ
ejpam-5374	370	10	mapping	mapping	NOUN
ejpam-5374	370	11	.	.	PUNCT
ejpam-5374	371	1	transactions	transaction	NOUN
ejpam-5374	371	2	of	of	ADP
ejpam-5374	371	3	the	the	DET
ejpam-5374	371	4	american	american	PROPN
ejpam-5374	371	5	mathematical	mathematical	PROPN
ejpam-5374	371	6	society	society	NOUN
ejpam-5374	371	7	,	,	PUNCT
ejpam-5374	371	8	38:310–340	38:310–340	NUM
ejpam-5374	371	9	,	,	PUNCT
ejpam-5374	371	10	1935	1935	NUM
ejpam-5374	371	11	.	.	PUNCT
ejpam-5374	372	1	[	[	X
ejpam-5374	372	2	48	48	NUM
ejpam-5374	372	3	]	]	X
ejpam-5374	372	4	p	p	PRON
ejpam-5374	372	5	sunthrayuth	sunthrayuth	NOUN
ejpam-5374	372	6	,	,	PUNCT
ejpam-5374	372	7	n	n	PROPN
ejpam-5374	372	8	iqbal	iqbal	PROPN
ejpam-5374	372	9	,	,	PUNCT
ejpam-5374	372	10	m	m	PROPN
ejpam-5374	372	11	naeem	naeem	PROPN
ejpam-5374	372	12	,	,	PUNCT
ejpam-5374	372	13	y	y	PROPN
ejpam-5374	372	14	jawarneh	jawarneh	NOUN
ejpam-5374	372	15	,	,	PUNCT
ejpam-5374	372	16	and	and	CCONJ
ejpam-5374	372	17	s	s	X
ejpam-5374	372	18	k	k	NOUN
ejpam-5374	372	19	samura	samura	NOUN
ejpam-5374	372	20	.	.	PUNCT
ejpam-5374	373	1	the	the	DET
ejpam-5374	373	2	sharp	sharp	ADJ
ejpam-5374	373	3	upper	upper	ADJ
ejpam-5374	373	4	bounds	bound	NOUN
ejpam-5374	373	5	of	of	ADP
ejpam-5374	373	6	the	the	DET
ejpam-5374	373	7	hankel	hankel	NOUN
ejpam-5374	373	8	determinant	determinant	ADJ
ejpam-5374	373	9	on	on	ADP
ejpam-5374	373	10	logarithmic	logarithmic	ADJ
ejpam-5374	373	11	coefficients	coefficient	NOUN
ejpam-5374	373	12	for	for	ADP
ejpam-5374	373	13	certain	certain	ADJ
ejpam-5374	373	14	analytic	analytic	ADJ
ejpam-5374	373	15	functions	function	NOUN
ejpam-5374	373	16	connected	connect	VERB
ejpam-5374	373	17	with	with	ADP
ejpam-5374	373	18	eight	eight	NUM
ejpam-5374	373	19	-	-	PUNCT
ejpam-5374	373	20	shaped	shape	VERB
ejpam-5374	373	21	domains	domain	NOUN
ejpam-5374	373	22	.	.	PUNCT
ejpam-5374	374	1	journal	journal	NOUN
ejpam-5374	374	2	of	of	ADP
ejpam-5374	374	3	function	function	NOUN
ejpam-5374	374	4	spaces	space	NOUN
ejpam-5374	374	5	,	,	PUNCT
ejpam-5374	374	6	2022(1):2229960	2022(1):2229960	NUM
ejpam-5374	374	7	,	,	PUNCT
ejpam-5374	374	8	2022	2022	NUM
ejpam-5374	374	9	.	.	PUNCT
ejpam-5374	375	1	[	[	X
ejpam-5374	375	2	49	49	NUM
ejpam-5374	375	3	]	]	X
ejpam-5374	375	4	k	k	PROPN
ejpam-5374	375	5	ye	ye	NOUN
ejpam-5374	375	6	and	and	CCONJ
ejpam-5374	375	7	l	l	PROPN
ejpam-5374	375	8	h	h	PROPN
ejpam-5374	375	9	lim	lim	PROPN
ejpam-5374	375	10	.	.	PUNCT
ejpam-5374	376	1	every	every	DET
ejpam-5374	376	2	matrix	matrix	NOUN
ejpam-5374	376	3	is	be	AUX
ejpam-5374	376	4	a	a	DET
ejpam-5374	376	5	product	product	NOUN
ejpam-5374	376	6	of	of	ADP
ejpam-5374	376	7	toeplitz	toeplitz	NOUN
ejpam-5374	376	8	matrices	matrix	NOUN
ejpam-5374	376	9	.	.	PUNCT
ejpam-5374	377	1	foundations	foundation	NOUN
ejpam-5374	377	2	of	of	ADP
ejpam-5374	377	3	computational	computational	ADJ
ejpam-5374	377	4	mathematics	mathematic	NOUN
ejpam-5374	377	5	,	,	PUNCT
ejpam-5374	377	6	16(3):577–598	16(3):577–598	NUM
ejpam-5374	377	7	,	,	PUNCT
ejpam-5374	377	8	2016	2016	NUM
ejpam-5374	377	9	.	.	PUNCT