id	sid	tid	token	lemma	pos
ejpam-5259	1	1	european	european	PROPN
ejpam-5259	1	2	journal	journal	PROPN
ejpam-5259	1	3	of	of	ADP
ejpam-5259	1	4	pure	pure	ADJ
ejpam-5259	1	5	and	and	CCONJ
ejpam-5259	1	6	applied	apply	VERB
ejpam-5259	1	7	mathematics	mathematic	NOUN
ejpam-5259	1	8	vol	vol	NOUN
ejpam-5259	1	9	.	.	PROPN
ejpam-5259	2	1	17	17	NUM
ejpam-5259	2	2	,	,	PUNCT
ejpam-5259	2	3	no	no	INTJ
ejpam-5259	2	4	.	.	NOUN
ejpam-5259	2	5	3	3	NUM
ejpam-5259	2	6	,	,	PUNCT
ejpam-5259	2	7	2024	2024	NUM
ejpam-5259	2	8	,	,	PUNCT
ejpam-5259	2	9	1894	1894	NUM
ejpam-5259	2	10	-	-	SYM
ejpam-5259	2	11	1907	1907	NUM
ejpam-5259	2	12	issn	issn	PROPN
ejpam-5259	2	13	1307	1307	NUM
ejpam-5259	2	14	-	-	SYM
ejpam-5259	2	15	5543	5543	NUM
ejpam-5259	2	16	–	–	PUNCT
ejpam-5259	2	17	ejpam.com	ejpam.com	X
ejpam-5259	2	18	published	publish	VERB
ejpam-5259	2	19	by	by	ADP
ejpam-5259	2	20	new	new	PROPN
ejpam-5259	2	21	york	york	PROPN
ejpam-5259	2	22	business	business	PROPN
ejpam-5259	2	23	global	global	PROPN
ejpam-5259	2	24	a	a	DET
ejpam-5259	2	25	specific	specific	ADJ
ejpam-5259	2	26	class	class	NOUN
ejpam-5259	2	27	of	of	ADP
ejpam-5259	2	28	harmonic	harmonic	ADJ
ejpam-5259	2	29	meromorphic	meromorphic	ADJ
ejpam-5259	2	30	functions	function	NOUN
ejpam-5259	2	31	associated	associate	VERB
ejpam-5259	2	32	with	with	ADP
ejpam-5259	2	33	the	the	DET
ejpam-5259	2	34	mittagleffler	mittagleffler	NOUN
ejpam-5259	2	35	transformation	transformation	NOUN
ejpam-5259	2	36	sarah	sarah	PROPN
ejpam-5259	2	37	ahmed1,2	ahmed1,2	PROPN
ejpam-5259	2	38	,	,	PUNCT
ejpam-5259	2	39	abdullah	abdullah	PROPN
ejpam-5259	2	40	alsoboh3,∗	alsoboh3,∗	PROPN
ejpam-5259	2	41	,	,	PUNCT
ejpam-5259	2	42	maslina	maslina	NOUN
ejpam-5259	2	43	darus2	darus2	PROPN
ejpam-5259	2	44	1	1	NUM
ejpam-5259	2	45	department	department	NOUN
ejpam-5259	2	46	of	of	ADP
ejpam-5259	2	47	mathematics	mathematic	NOUN
ejpam-5259	2	48	,	,	PUNCT
ejpam-5259	2	49	college	college	NOUN
ejpam-5259	2	50	of	of	ADP
ejpam-5259	2	51	education	education	NOUN
ejpam-5259	2	52	for	for	ADP
ejpam-5259	2	53	pure	pure	ADJ
ejpam-5259	2	54	science	science	NOUN
ejpam-5259	2	55	,	,	PUNCT
ejpam-5259	2	56	university	university	NOUN
ejpam-5259	2	57	of	of	ADP
ejpam-5259	2	58	kerbala	kerbala	PROPN
ejpam-5259	2	59	,	,	PUNCT
ejpam-5259	2	60	kerbala	kerbala	PROPN
ejpam-5259	2	61	,	,	PUNCT
ejpam-5259	2	62	iraq	iraq	PROPN
ejpam-5259	2	63	2	2	NUM
ejpam-5259	2	64	department	department	NOUN
ejpam-5259	2	65	of	of	ADP
ejpam-5259	2	66	mathematical	mathematical	ADJ
ejpam-5259	2	67	sciences	sciences	PROPN
ejpam-5259	2	68	,	,	PUNCT
ejpam-5259	2	69	universiti	universiti	PROPN
ejpam-5259	2	70	kebangsaan	kebangsaan	PROPN
ejpam-5259	2	71	malaysia	malaysia	PROPN
ejpam-5259	2	72	,	,	PUNCT
ejpam-5259	2	73	selangor	selangor	PROPN
ejpam-5259	2	74	,	,	PUNCT
ejpam-5259	2	75	malaysia	malaysia	PROPN
ejpam-5259	2	76	3	3	NUM
ejpam-5259	2	77	department	department	NOUN
ejpam-5259	2	78	of	of	ADP
ejpam-5259	2	79	mathematics	mathematic	NOUN
ejpam-5259	2	80	,	,	PUNCT
ejpam-5259	2	81	faculty	faculty	NOUN
ejpam-5259	2	82	of	of	ADP
ejpam-5259	2	83	science	science	NOUN
ejpam-5259	2	84	,	,	PUNCT
ejpam-5259	2	85	philadelphia	philadelphia	PROPN
ejpam-5259	2	86	university	university	PROPN
ejpam-5259	2	87	,	,	PUNCT
ejpam-5259	2	88	amman	amman	PROPN
ejpam-5259	2	89	,	,	PUNCT
ejpam-5259	2	90	jordan	jordan	PROPN
ejpam-5259	2	91	.	.	PUNCT
ejpam-5259	3	1	abstract	abstract	PROPN
ejpam-5259	3	2	.	.	PUNCT
ejpam-5259	4	1	this	this	DET
ejpam-5259	4	2	article	article	NOUN
ejpam-5259	4	3	uses	use	VERB
ejpam-5259	4	4	the	the	DET
ejpam-5259	4	5	mittag	mittag	ADJ
ejpam-5259	4	6	-	-	PUNCT
ejpam-5259	4	7	leffler	leffler	NOUN
ejpam-5259	4	8	transformation	transformation	NOUN
ejpam-5259	4	9	to	to	PART
ejpam-5259	4	10	explore	explore	VERB
ejpam-5259	4	11	a	a	DET
ejpam-5259	4	12	specific	specific	ADJ
ejpam-5259	4	13	category	category	NOUN
ejpam-5259	4	14	of	of	ADP
ejpam-5259	4	15	harmonic	harmonic	ADJ
ejpam-5259	4	16	meromorphic	meromorphic	ADJ
ejpam-5259	4	17	functions	function	NOUN
ejpam-5259	4	18	.	.	PUNCT
ejpam-5259	5	1	the	the	DET
ejpam-5259	5	2	mittag	mittag	ADJ
ejpam-5259	5	3	-	-	PUNCT
ejpam-5259	5	4	leffler	leffler	NOUN
ejpam-5259	5	5	transformation	transformation	NOUN
ejpam-5259	5	6	is	be	AUX
ejpam-5259	5	7	a	a	DET
ejpam-5259	5	8	crucial	crucial	ADJ
ejpam-5259	5	9	tool	tool	NOUN
ejpam-5259	5	10	for	for	ADP
ejpam-5259	5	11	analysing	analyse	VERB
ejpam-5259	5	12	meromorphic	meromorphic	ADJ
ejpam-5259	5	13	functions	function	NOUN
ejpam-5259	5	14	and	and	CCONJ
ejpam-5259	5	15	provides	provide	VERB
ejpam-5259	5	16	essential	essential	ADJ
ejpam-5259	5	17	properties	property	NOUN
ejpam-5259	5	18	and	and	CCONJ
ejpam-5259	5	19	insights	insight	NOUN
ejpam-5259	5	20	into	into	ADP
ejpam-5259	5	21	their	their	PRON
ejpam-5259	5	22	behavior	behavior	NOUN
ejpam-5259	5	23	.	.	PUNCT
ejpam-5259	6	1	the	the	DET
ejpam-5259	6	2	main	main	ADJ
ejpam-5259	6	3	focus	focus	NOUN
ejpam-5259	6	4	of	of	ADP
ejpam-5259	6	5	this	this	DET
ejpam-5259	6	6	study	study	NOUN
ejpam-5259	6	7	is	be	AUX
ejpam-5259	6	8	on	on	ADP
ejpam-5259	6	9	harmonic	harmonic	ADJ
ejpam-5259	6	10	meromorphic	meromorphic	ADJ
ejpam-5259	6	11	functions	function	NOUN
ejpam-5259	6	12	that	that	PRON
ejpam-5259	6	13	can	can	AUX
ejpam-5259	6	14	be	be	AUX
ejpam-5259	6	15	represented	represent	VERB
ejpam-5259	6	16	by	by	ADP
ejpam-5259	6	17	the	the	DET
ejpam-5259	6	18	mittagleffler	mittagleffler	NOUN
ejpam-5259	6	19	transformation	transformation	NOUN
ejpam-5259	6	20	.	.	PUNCT
ejpam-5259	7	1	furthermore	furthermore	ADV
ejpam-5259	7	2	,	,	PUNCT
ejpam-5259	7	3	this	this	DET
ejpam-5259	7	4	research	research	NOUN
ejpam-5259	7	5	introduces	introduce	VERB
ejpam-5259	7	6	an	an	DET
ejpam-5259	7	7	innovative	innovative	ADJ
ejpam-5259	7	8	derivative	derivative	ADJ
ejpam-5259	7	9	operator	operator	NOUN
ejpam-5259	7	10	that	that	PRON
ejpam-5259	7	11	incorporates	incorporate	VERB
ejpam-5259	7	12	this	this	DET
ejpam-5259	7	13	transformation	transformation	NOUN
ejpam-5259	7	14	into	into	ADP
ejpam-5259	7	15	the	the	DET
ejpam-5259	7	16	domain	domain	NOUN
ejpam-5259	7	17	of	of	ADP
ejpam-5259	7	18	harmonic	harmonic	ADJ
ejpam-5259	7	19	meromorphic	meromorphic	ADJ
ejpam-5259	7	20	functions	function	NOUN
ejpam-5259	7	21	.	.	PUNCT
ejpam-5259	8	1	the	the	DET
ejpam-5259	8	2	mittag	mittag	ADJ
ejpam-5259	8	3	-	-	PUNCT
ejpam-5259	8	4	leffler	leffler	NOUN
ejpam-5259	8	5	transformation	transformation	NOUN
ejpam-5259	8	6	is	be	AUX
ejpam-5259	8	7	widely	widely	ADV
ejpam-5259	8	8	recognised	recognise	VERB
ejpam-5259	8	9	as	as	ADP
ejpam-5259	8	10	a	a	DET
ejpam-5259	8	11	powerful	powerful	ADJ
ejpam-5259	8	12	technique	technique	NOUN
ejpam-5259	8	13	for	for	ADP
ejpam-5259	8	14	analysing	analyse	VERB
ejpam-5259	8	15	various	various	ADJ
ejpam-5259	8	16	mathematical	mathematical	ADJ
ejpam-5259	8	17	functions	function	NOUN
ejpam-5259	8	18	,	,	PUNCT
ejpam-5259	8	19	especially	especially	ADV
ejpam-5259	8	20	those	those	PRON
ejpam-5259	8	21	with	with	ADP
ejpam-5259	8	22	fractional	fractional	ADJ
ejpam-5259	8	23	order	order	NOUN
ejpam-5259	8	24	derivatives	derivative	NOUN
ejpam-5259	8	25	.	.	PUNCT
ejpam-5259	9	1	it	it	PRON
ejpam-5259	9	2	improves	improve	VERB
ejpam-5259	9	3	our	our	PRON
ejpam-5259	9	4	understanding	understanding	NOUN
ejpam-5259	9	5	of	of	ADP
ejpam-5259	9	6	harmonic	harmonic	ADJ
ejpam-5259	9	7	meromorphic	meromorphic	ADJ
ejpam-5259	9	8	functions	function	NOUN
ejpam-5259	9	9	and	and	CCONJ
ejpam-5259	9	10	their	their	PRON
ejpam-5259	9	11	inherent	inherent	ADJ
ejpam-5259	9	12	characteristics	characteristic	NOUN
ejpam-5259	9	13	.	.	PUNCT
ejpam-5259	10	1	the	the	DET
ejpam-5259	10	2	research	research	NOUN
ejpam-5259	10	3	findings	finding	NOUN
ejpam-5259	10	4	highlight	highlight	VERB
ejpam-5259	10	5	the	the	DET
ejpam-5259	10	6	effectiveness	effectiveness	NOUN
ejpam-5259	10	7	of	of	ADP
ejpam-5259	10	8	this	this	DET
ejpam-5259	10	9	new	new	ADJ
ejpam-5259	10	10	derivative	derivative	ADJ
ejpam-5259	10	11	operator	operator	NOUN
ejpam-5259	10	12	in	in	ADP
ejpam-5259	10	13	unraveling	unravel	VERB
ejpam-5259	10	14	the	the	DET
ejpam-5259	10	15	complexities	complexity	NOUN
ejpam-5259	10	16	of	of	ADP
ejpam-5259	10	17	these	these	DET
ejpam-5259	10	18	functions	function	NOUN
ejpam-5259	10	19	.	.	PUNCT
ejpam-5259	11	1	they	they	PRON
ejpam-5259	11	2	provide	provide	VERB
ejpam-5259	11	3	valuable	valuable	ADJ
ejpam-5259	11	4	insights	insight	NOUN
ejpam-5259	11	5	into	into	ADP
ejpam-5259	11	6	their	their	PRON
ejpam-5259	11	7	behavior	behavior	NOUN
ejpam-5259	11	8	and	and	CCONJ
ejpam-5259	11	9	fundamental	fundamental	ADJ
ejpam-5259	11	10	traits	trait	NOUN
ejpam-5259	11	11	.	.	PUNCT
ejpam-5259	12	1	additionally	additionally	ADV
ejpam-5259	12	2	,	,	PUNCT
ejpam-5259	12	3	the	the	DET
ejpam-5259	12	4	study	study	NOUN
ejpam-5259	12	5	offers	offer	VERB
ejpam-5259	12	6	coefficient	coefficient	NOUN
ejpam-5259	12	7	inequalities	inequality	NOUN
ejpam-5259	12	8	,	,	PUNCT
ejpam-5259	12	9	the	the	DET
ejpam-5259	12	10	distortion	distortion	NOUN
ejpam-5259	12	11	theorem	theorem	VERB
ejpam-5259	12	12	,	,	PUNCT
ejpam-5259	12	13	distortion	distortion	NOUN
ejpam-5259	12	14	bounds	bound	NOUN
ejpam-5259	12	15	,	,	PUNCT
ejpam-5259	12	16	extreme	extreme	ADJ
ejpam-5259	12	17	points	point	NOUN
ejpam-5259	12	18	,	,	PUNCT
ejpam-5259	12	19	convex	convex	ADJ
ejpam-5259	12	20	combinations	combination	NOUN
ejpam-5259	12	21	,	,	PUNCT
ejpam-5259	12	22	and	and	CCONJ
ejpam-5259	12	23	convolution	convolution	NOUN
ejpam-5259	12	24	analyses	analysis	NOUN
ejpam-5259	12	25	specifically	specifically	ADV
ejpam-5259	12	26	tailored	tailor	VERB
ejpam-5259	12	27	to	to	ADP
ejpam-5259	12	28	functions	function	NOUN
ejpam-5259	12	29	within	within	ADP
ejpam-5259	12	30	this	this	DET
ejpam-5259	12	31	particular	particular	ADJ
ejpam-5259	12	32	class	class	NOUN
ejpam-5259	12	33	.	.	PUNCT
ejpam-5259	13	1	2020	2020	NUM
ejpam-5259	13	2	mathematics	mathematic	NOUN
ejpam-5259	13	3	subject	subject	NOUN
ejpam-5259	13	4	classifications	classification	NOUN
ejpam-5259	13	5	:	:	PUNCT
ejpam-5259	13	6	30c41	30c41	NUM
ejpam-5259	13	7	,	,	PUNCT
ejpam-5259	13	8	30c50	30c50	DET
ejpam-5259	13	9	key	key	ADJ
ejpam-5259	13	10	words	word	NOUN
ejpam-5259	13	11	and	and	CCONJ
ejpam-5259	13	12	phrases	phrase	NOUN
ejpam-5259	13	13	:	:	PUNCT
ejpam-5259	13	14	analytic	analytic	ADJ
ejpam-5259	13	15	functions	function	NOUN
ejpam-5259	13	16	,	,	PUNCT
ejpam-5259	13	17	meromorphic	meromorphic	ADJ
ejpam-5259	13	18	functions	function	NOUN
ejpam-5259	13	19	,	,	PUNCT
ejpam-5259	13	20	starlike	starlike	NOUN
ejpam-5259	13	21	functions	function	NOUN
ejpam-5259	13	22	,	,	PUNCT
ejpam-5259	13	23	multiplier	multipli	ADJ
ejpam-5259	13	24	transformation	transformation	NOUN
ejpam-5259	13	25	,	,	PUNCT
ejpam-5259	13	26	mittag	mittag	ADJ
ejpam-5259	13	27	-	-	PUNCT
ejpam-5259	13	28	leffler	leffler	NOUN
ejpam-5259	13	29	function	function	NOUN
ejpam-5259	13	30	,	,	PUNCT
ejpam-5259	13	31	hadamard	hadamard	ADJ
ejpam-5259	13	32	products	product	NOUN
ejpam-5259	13	33	1	1	NUM
ejpam-5259	13	34	.	.	PUNCT
ejpam-5259	14	1	introduction	introduction	NOUN
ejpam-5259	14	2	we	we	PRON
ejpam-5259	14	3	begin	begin	VERB
ejpam-5259	14	4	by	by	ADP
ejpam-5259	14	5	considering	consider	VERB
ejpam-5259	14	6	the	the	DET
ejpam-5259	14	7	open	open	ADJ
ejpam-5259	14	8	unit	unit	NOUN
ejpam-5259	14	9	disk	disk	NOUN
ejpam-5259	14	10	in	in	ADP
ejpam-5259	14	11	the	the	DET
ejpam-5259	14	12	complex	complex	ADJ
ejpam-5259	14	13	plane	plane	NOUN
ejpam-5259	14	14	,	,	PUNCT
ejpam-5259	14	15	denoted	denote	VERB
ejpam-5259	14	16	by	by	ADP
ejpam-5259	14	17	♢	♢	PROPN
ejpam-5259	14	18	=	=	SYM
ejpam-5259	14	19	{	{	PUNCT
ejpam-5259	14	20	ς	ς	PROPN
ejpam-5259	14	21	∈	∈	PROPN
ejpam-5259	14	22	c	c	NOUN
ejpam-5259	14	23	:	:	PUNCT
ejpam-5259	14	24	|ς|	|ς|	PROPN
ejpam-5259	14	25	<	<	X
ejpam-5259	14	26	1	1	NUM
ejpam-5259	14	27	}	}	PUNCT
ejpam-5259	14	28	,	,	PUNCT
ejpam-5259	14	29	and	and	CCONJ
ejpam-5259	14	30	the	the	DET
ejpam-5259	14	31	class	class	NOUN
ejpam-5259	14	32	of	of	ADP
ejpam-5259	14	33	meromorphic	meromorphic	ADJ
ejpam-5259	14	34	functions	function	NOUN
ejpam-5259	14	35	σ	σ	NOUN
ejpam-5259	14	36	defined	define	VERB
ejpam-5259	14	37	as	as	SCONJ
ejpam-5259	14	38	follows	follow	VERB
ejpam-5259	14	39	:	:	PUNCT
ejpam-5259	14	40	∗corresponding	∗corresponde	VERB
ejpam-5259	14	41	author	author	NOUN
ejpam-5259	14	42	.	.	PUNCT
ejpam-5259	15	1	doi	doi	NOUN
ejpam-5259	15	2	:	:	PUNCT
ejpam-5259	15	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5259	https://doi.org/10.29020/nybg.ejpam.v17i3.5259	NOUN
ejpam-5259	15	4	email	email	NOUN
ejpam-5259	15	5	addresses	address	NOUN
ejpam-5259	15	6	:	:	PUNCT
ejpam-5259	15	7	p102354@siswa.ukm.edu.my	p102354@siswa.ukm.edu.my	PROPN
ejpam-5259	15	8	(	(	PUNCT
ejpam-5259	15	9	s.	s.	PROPN
ejpam-5259	15	10	ahmed	ahmed	PROPN
ejpam-5259	15	11	)	)	PUNCT
ejpam-5259	15	12	,	,	PUNCT
ejpam-5259	15	13	aalsoboh@philadelphia.edu.jo	aalsoboh@philadelphia.edu.jo	NOUN
ejpam-5259	15	14	(	(	PUNCT
ejpam-5259	15	15	a.	a.	NOUN
ejpam-5259	15	16	alsoboh	alsoboh	PROPN
ejpam-5259	15	17	)	)	PUNCT
ejpam-5259	15	18	,	,	PUNCT
ejpam-5259	15	19	maslina@ukm.edu.my	maslina@ukm.edu.my	X
ejpam-5259	15	20	(	(	PUNCT
ejpam-5259	15	21	m.	m.	NOUN
ejpam-5259	15	22	darus	darus	PROPN
ejpam-5259	15	23	)	)	PUNCT
ejpam-5259	15	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5259	15	25	1894	1894	NUM
ejpam-5259	16	1	©	©	ADP
ejpam-5259	16	2	2024	2024	NUM
ejpam-5259	16	3	ejpam	ejpam	NOUN
ejpam-5259	16	4	all	all	DET
ejpam-5259	16	5	rights	right	NOUN
ejpam-5259	16	6	reserved	reserve	VERB
ejpam-5259	16	7	.	.	PUNCT
ejpam-5259	17	1	s.	s.	PROPN
ejpam-5259	17	2	ahmed	ahmed	PROPN
ejpam-5259	17	3	,	,	PUNCT
ejpam-5259	17	4	a.	a.	PROPN
ejpam-5259	17	5	alsoboh	alsoboh	PROPN
ejpam-5259	17	6	,	,	PUNCT
ejpam-5259	17	7	m.	m.	NOUN
ejpam-5259	17	8	darus	darus	NOUN
ejpam-5259	17	9	/	/	SYM
ejpam-5259	17	10	eur	eur	PROPN
ejpam-5259	17	11	.	.	PUNCT
ejpam-5259	18	1	j.	j.	PROPN
ejpam-5259	18	2	pure	pure	PROPN
ejpam-5259	18	3	appl	appl	PROPN
ejpam-5259	18	4	.	.	PROPN
ejpam-5259	18	5	math	math	PROPN
ejpam-5259	18	6	,	,	PUNCT
ejpam-5259	18	7	17	17	NUM
ejpam-5259	18	8	(	(	PUNCT
ejpam-5259	18	9	3	3	NUM
ejpam-5259	18	10	)	)	PUNCT
ejpam-5259	18	11	(	(	PUNCT
ejpam-5259	18	12	2024	2024	NUM
ejpam-5259	18	13	)	)	PUNCT
ejpam-5259	18	14	,	,	PUNCT
ejpam-5259	18	15	1894	1894	NUM
ejpam-5259	18	16	-	-	SYM
ejpam-5259	18	17	1907	1907	NUM
ejpam-5259	18	18	1895	1895	NUM
ejpam-5259	18	19	f(ς	f(ς	PROPN
ejpam-5259	18	20	)	)	PUNCT
ejpam-5259	18	21	=	=	SYM
ejpam-5259	19	1	1	1	NUM
ejpam-5259	19	2	ς	ς	PROPN
ejpam-5259	19	3	+	+	NOUN
ejpam-5259	19	4	∞∑	∞∑	NUM
ejpam-5259	19	5	µ=1	µ=1	ADV
ejpam-5259	19	6	aµς	aµς	NOUN
ejpam-5259	19	7	µ	µ	NUM
ejpam-5259	19	8	,	,	PUNCT
ejpam-5259	19	9	aµ	aµ	PROPN
ejpam-5259	19	10	∈	∈	PROPN
ejpam-5259	19	11	c.	c.	PROPN
ejpam-5259	19	12	(	(	PUNCT
ejpam-5259	19	13	1	1	NUM
ejpam-5259	19	14	)	)	PUNCT
ejpam-5259	19	15	where	where	SCONJ
ejpam-5259	19	16	f	f	PROPN
ejpam-5259	19	17	is	be	AUX
ejpam-5259	19	18	analytic	analytic	ADJ
ejpam-5259	19	19	in	in	ADP
ejpam-5259	19	20	the	the	DET
ejpam-5259	19	21	punctured	puncture	VERB
ejpam-5259	19	22	open	open	ADJ
ejpam-5259	19	23	unit	unit	NOUN
ejpam-5259	19	24	disk	disk	NOUN
ejpam-5259	19	25	♢	♢	PROPN
ejpam-5259	19	26	∗	∗	NOUN
ejpam-5259	19	27	=	=	SYM
ejpam-5259	20	1	♢	♢	PROPN
ejpam-5259	20	2	\	\	PROPN
ejpam-5259	20	3	{	{	PUNCT
ejpam-5259	20	4	0	0	NUM
ejpam-5259	20	5	}	}	PUNCT
ejpam-5259	20	6	=	=	PRON
ejpam-5259	20	7	{	{	PUNCT
ejpam-5259	20	8	ς	ς	PROPN
ejpam-5259	20	9	∈	∈	PROPN
ejpam-5259	20	10	c	c	NOUN
ejpam-5259	20	11	:	:	PUNCT
ejpam-5259	20	12	0	0	PUNCT
ejpam-5259	20	13	<	<	X
ejpam-5259	20	14	|ς|	|ς|	X
ejpam-5259	20	15	<	<	X
ejpam-5259	20	16	1	1	NUM
ejpam-5259	20	17	}	}	PUNCT
ejpam-5259	20	18	.	.	PUNCT
ejpam-5259	21	1	the	the	DET
ejpam-5259	21	2	class	class	NOUN
ejpam-5259	21	3	σ	σ	PROPN
ejpam-5259	21	4	was	be	AUX
ejpam-5259	21	5	investigated	investigate	VERB
ejpam-5259	21	6	and	and	CCONJ
ejpam-5259	21	7	studied	study	VERB
ejpam-5259	21	8	by	by	ADP
ejpam-5259	21	9	clunie	clunie	NOUN
ejpam-5259	21	10	[	[	X
ejpam-5259	21	11	13	13	NUM
ejpam-5259	21	12	]	]	PUNCT
ejpam-5259	21	13	.	.	PUNCT
ejpam-5259	22	1	for	for	ADP
ejpam-5259	22	2	f	f	PROPN
ejpam-5259	22	3	∈	∈	PROPN
ejpam-5259	22	4	σ	σ	NOUN
ejpam-5259	22	5	of	of	ADP
ejpam-5259	22	6	the	the	DET
ejpam-5259	22	7	form	form	NOUN
ejpam-5259	22	8	(	(	PUNCT
ejpam-5259	22	9	1	1	NUM
ejpam-5259	22	10	)	)	PUNCT
ejpam-5259	22	11	and	and	CCONJ
ejpam-5259	22	12	g	g	PROPN
ejpam-5259	22	13	∈	∈	PROPN
ejpam-5259	22	14	σ	σ	NOUN
ejpam-5259	22	15	given	give	VERB
ejpam-5259	22	16	by	by	ADP
ejpam-5259	22	17	g(ς	g(ς	PROPN
ejpam-5259	22	18	)	)	PUNCT
ejpam-5259	22	19	=	=	PUNCT
ejpam-5259	22	20	1	1	NUM
ejpam-5259	22	21	ς	ς	PROPN
ejpam-5259	22	22	+	+	NOUN
ejpam-5259	22	23	∞∑	∞∑	NUM
ejpam-5259	22	24	µ=1	µ=1	SYM
ejpam-5259	22	25	bµς	bµς	PROPN
ejpam-5259	22	26	µ	µ	NUM
ejpam-5259	22	27	,	,	PUNCT
ejpam-5259	22	28	bµ	bµ	PROPN
ejpam-5259	22	29	∈	∈	PROPN
ejpam-5259	22	30	c	c	PROPN
ejpam-5259	22	31	.	.	PUNCT
ejpam-5259	23	1	the	the	DET
ejpam-5259	23	2	hadamard	hadamard	ADJ
ejpam-5259	23	3	product	product	NOUN
ejpam-5259	23	4	or	or	CCONJ
ejpam-5259	23	5	convolution	convolution	NOUN
ejpam-5259	23	6	of	of	ADP
ejpam-5259	23	7	f	f	PROPN
ejpam-5259	23	8	and	and	CCONJ
ejpam-5259	23	9	g	g	PROPN
ejpam-5259	23	10	is	be	AUX
ejpam-5259	23	11	defined	define	VERB
ejpam-5259	23	12	as	as	SCONJ
ejpam-5259	23	13	follows	follow	VERB
ejpam-5259	23	14	(	(	PUNCT
ejpam-5259	23	15	see	see	VERB
ejpam-5259	23	16	[	[	X
ejpam-5259	23	17	1	1	NUM
ejpam-5259	23	18	,	,	PUNCT
ejpam-5259	23	19	3	3	NUM
ejpam-5259	23	20	]	]	NUM
ejpam-5259	23	21	):	):	PUNCT
ejpam-5259	23	22	(	(	PUNCT
ejpam-5259	23	23	f	f	PROPN
ejpam-5259	23	24	∗	∗	PROPN
ejpam-5259	23	25	g)(ς	g)(ς	PROPN
ejpam-5259	23	26	)	)	PUNCT
ejpam-5259	24	1	=	=	PUNCT
ejpam-5259	24	2	(	(	PUNCT
ejpam-5259	24	3	g	g	NOUN
ejpam-5259	24	4	∗	∗	NOUN
ejpam-5259	24	5	f)(ς	f)(ς	PUNCT
ejpam-5259	24	6	)	)	PUNCT
ejpam-5259	24	7	=	=	SYM
ejpam-5259	25	1	1	1	NUM
ejpam-5259	25	2	ς	ς	PROPN
ejpam-5259	25	3	+	+	NOUN
ejpam-5259	25	4	∞∑	∞∑	NUM
ejpam-5259	25	5	µ=1	µ=1	ADV
ejpam-5259	25	6	aµbµς	aµbµς	ADJ
ejpam-5259	25	7	µ.	µ.	NOUN
ejpam-5259	25	8	the	the	DET
ejpam-5259	25	9	well	well	ADV
ejpam-5259	25	10	-	-	PUNCT
ejpam-5259	25	11	known	know	VERB
ejpam-5259	25	12	multiplier	multipli	ADJ
ejpam-5259	25	13	transformation	transformation	NOUN
ejpam-5259	25	14	operator	operator	NOUN
ejpam-5259	25	15	i1(r	i1(r	PROPN
ejpam-5259	25	16	,	,	PUNCT
ejpam-5259	25	17	λ	λ	PROPN
ejpam-5259	25	18	)	)	PUNCT
ejpam-5259	25	19	:	:	PUNCT
ejpam-5259	26	1	σ	σ	PROPN
ejpam-5259	26	2	→	→	PROPN
ejpam-5259	26	3	σ	σ	PROPN
ejpam-5259	26	4	has	have	AUX
ejpam-5259	26	5	been	be	AUX
ejpam-5259	26	6	studied	study	VERB
ejpam-5259	26	7	by	by	ADP
ejpam-5259	26	8	cho	cho	PROPN
ejpam-5259	26	9	and	and	CCONJ
ejpam-5259	26	10	srivastava	srivastava	PROPN
ejpam-5259	27	1	[	[	X
ejpam-5259	27	2	12	12	NUM
ejpam-5259	27	3	]	]	PUNCT
ejpam-5259	27	4	,	,	PUNCT
ejpam-5259	27	5	cho	cho	PROPN
ejpam-5259	27	6	and	and	CCONJ
ejpam-5259	27	7	kim	kim	PROPN
ejpam-5259	28	1	[	[	X
ejpam-5259	28	2	11	11	NUM
ejpam-5259	28	3	]	]	PUNCT
ejpam-5259	28	4	,	,	PUNCT
ejpam-5259	28	5	and	and	CCONJ
ejpam-5259	28	6	recently	recently	ADV
ejpam-5259	28	7	by	by	ADP
ejpam-5259	28	8	atshan	atshan	NOUN
ejpam-5259	28	9	and	and	CCONJ
ejpam-5259	28	10	joudah	joudah	PROPN
ejpam-5259	29	1	[	[	X
ejpam-5259	29	2	6	6	NUM
ejpam-5259	29	3	]	]	PUNCT
ejpam-5259	29	4	.	.	PUNCT
ejpam-5259	30	1	it	it	PRON
ejpam-5259	30	2	is	be	AUX
ejpam-5259	30	3	defined	define	VERB
ejpam-5259	30	4	as	as	SCONJ
ejpam-5259	30	5	follows	follow	VERB
ejpam-5259	30	6	:	:	PUNCT
ejpam-5259	30	7	i1(r	i1(r	NUM
ejpam-5259	30	8	,	,	PUNCT
ejpam-5259	30	9	λ)f(ς	λ)f(ς	PROPN
ejpam-5259	30	10	)	)	PUNCT
ejpam-5259	30	11	=	=	SYM
ejpam-5259	31	1	1	1	NUM
ejpam-5259	31	2	ς	ς	PROPN
ejpam-5259	31	3	+	+	NOUN
ejpam-5259	31	4	∞∑	∞∑	NUM
ejpam-5259	31	5	µ=1	µ=1	PUNCT
ejpam-5259	31	6	(	(	PUNCT
ejpam-5259	31	7	µ+	µ+	X
ejpam-5259	31	8	δ	δ	NOUN
ejpam-5259	31	9	1	1	NUM
ejpam-5259	31	10	+	+	CCONJ
ejpam-5259	31	11	δ	δ	NOUN
ejpam-5259	31	12	)	)	PUNCT
ejpam-5259	31	13	r	r	NOUN
ejpam-5259	31	14	aµς	aµς	NOUN
ejpam-5259	31	15	µ	µ	X
ejpam-5259	31	16	(	(	PUNCT
ejpam-5259	31	17	δ	δ	PROPN
ejpam-5259	31	18	≥	≥	NOUN
ejpam-5259	31	19	0	0	NUM
ejpam-5259	31	20	,	,	PUNCT
ejpam-5259	31	21	ς	ς	PROPN
ejpam-5259	31	22	∈	∈	PROPN
ejpam-5259	31	23	♢	♢	PROPN
ejpam-5259	31	24	∗	∗	PROPN
ejpam-5259	31	25	)	)	PUNCT
ejpam-5259	31	26	.	.	PUNCT
ejpam-5259	32	1	(	(	PUNCT
ejpam-5259	32	2	2	2	X
ejpam-5259	32	3	)	)	PUNCT
ejpam-5259	32	4	for	for	ADP
ejpam-5259	32	5	α	α	NOUN
ejpam-5259	32	6	,	,	PUNCT
ejpam-5259	32	7	η	η	PROPN
ejpam-5259	32	8	∈	∈	PROPN
ejpam-5259	32	9	c	c	PROPN
ejpam-5259	32	10	,	,	PUNCT
ejpam-5259	32	11	wiman	wiman	PROPN
ejpam-5259	32	12	[	[	X
ejpam-5259	32	13	23	23	NUM
ejpam-5259	32	14	]	]	PUNCT
ejpam-5259	32	15	introduced	introduce	VERB
ejpam-5259	32	16	the	the	DET
ejpam-5259	32	17	generalised	generalise	VERB
ejpam-5259	32	18	mittag	mittag	ADJ
ejpam-5259	32	19	–	–	PUNCT
ejpam-5259	32	20	leffler	leffler	NOUN
ejpam-5259	32	21	function	function	NOUN
ejpam-5259	32	22	eα	eα	NOUN
ejpam-5259	32	23	,	,	PUNCT
ejpam-5259	32	24	η(ς	η(ς	NOUN
ejpam-5259	32	25	)	)	PUNCT
ejpam-5259	32	26	which	which	PRON
ejpam-5259	32	27	is	be	AUX
ejpam-5259	32	28	given	give	VERB
ejpam-5259	32	29	by	by	ADP
ejpam-5259	32	30	:	:	PUNCT
ejpam-5259	32	31	eα(ς	eα(ς	NUM
ejpam-5259	32	32	)	)	PUNCT
ejpam-5259	33	1	=	=	PUNCT
ejpam-5259	34	1	∞∑	∞∑	NUM
ejpam-5259	34	2	µ=0	µ=0	NOUN
ejpam-5259	34	3	ςµ	ςµ	NOUN
ejpam-5259	34	4	γ(αµ+	γ(αµ+	NOUN
ejpam-5259	34	5	1	1	NUM
ejpam-5259	34	6	)	)	PUNCT
ejpam-5259	34	7	(	(	PUNCT
ejpam-5259	34	8	3	3	X
ejpam-5259	34	9	)	)	PUNCT
ejpam-5259	34	10	and	and	CCONJ
ejpam-5259	34	11	eα	eα	INTJ
ejpam-5259	34	12	,	,	PUNCT
ejpam-5259	34	13	η(ς	η(ς	NOUN
ejpam-5259	34	14	)	)	PUNCT
ejpam-5259	34	15	=	=	PUNCT
ejpam-5259	35	1	∞∑	∞∑	NUM
ejpam-5259	35	2	µ=0	µ=0	NOUN
ejpam-5259	35	3	ςµ	ςµ	NOUN
ejpam-5259	35	4	γ(αµ+	γ(αµ+	NOUN
ejpam-5259	35	5	η	η	PROPN
ejpam-5259	35	6	)	)	PUNCT
ejpam-5259	35	7	,	,	PUNCT
ejpam-5259	35	8	ℜe{α	ℜe{α	PROPN
ejpam-5259	35	9	,	,	PUNCT
ejpam-5259	35	10	η	η	NOUN
ejpam-5259	35	11	}	}	PUNCT
ejpam-5259	35	12	>	>	X
ejpam-5259	35	13	0	0	X
ejpam-5259	35	14	.	.	PUNCT
ejpam-5259	36	1	(	(	PUNCT
ejpam-5259	36	2	4	4	X
ejpam-5259	36	3	)	)	PUNCT
ejpam-5259	36	4	the	the	DET
ejpam-5259	36	5	function	function	NOUN
ejpam-5259	36	6	given	give	VERB
ejpam-5259	36	7	by	by	ADP
ejpam-5259	36	8	(	(	PUNCT
ejpam-5259	36	9	4	4	NUM
ejpam-5259	36	10	)	)	PUNCT
ejpam-5259	36	11	is	be	AUX
ejpam-5259	36	12	not	not	PART
ejpam-5259	36	13	within	within	ADP
ejpam-5259	36	14	the	the	DET
ejpam-5259	36	15	class	class	NOUN
ejpam-5259	36	16	σ	σ	PROPN
ejpam-5259	36	17	.	.	PROPN
ejpam-5259	36	18	based	base	VERB
ejpam-5259	36	19	on	on	ADP
ejpam-5259	36	20	this	this	PRON
ejpam-5259	36	21	,	,	PUNCT
ejpam-5259	36	22	the	the	DET
ejpam-5259	36	23	function	function	NOUN
ejpam-5259	36	24	is	be	AUX
ejpam-5259	36	25	then	then	ADV
ejpam-5259	36	26	normalised	normalise	VERB
ejpam-5259	36	27	as	as	SCONJ
ejpam-5259	36	28	follows	follow	VERB
ejpam-5259	36	29	[	[	X
ejpam-5259	36	30	14	14	NUM
ejpam-5259	36	31	]	]	SYM
ejpam-5259	36	32	:	:	PUNCT
ejpam-5259	36	33	ωα	ωα	X
ejpam-5259	36	34	,	,	PUNCT
ejpam-5259	36	35	η(ς	η(ς	NOUN
ejpam-5259	36	36	)	)	PUNCT
ejpam-5259	36	37	=	=	SYM
ejpam-5259	36	38	ς−1γ(η)eα	ς−1γ(η)eα	NOUN
ejpam-5259	36	39	,	,	PUNCT
ejpam-5259	36	40	η(ς	η(ς	NOUN
ejpam-5259	36	41	)	)	PUNCT
ejpam-5259	36	42	=	=	SYM
ejpam-5259	37	1	1	1	NUM
ejpam-5259	37	2	ς	ς	PROPN
ejpam-5259	37	3	+	+	NOUN
ejpam-5259	37	4	∞∑	∞∑	NUM
ejpam-5259	37	5	µ=1	µ=1	ADV
ejpam-5259	37	6	γ(η	γ(η	NOUN
ejpam-5259	37	7	)	)	PUNCT
ejpam-5259	37	8	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	37	9	1	1	NUM
ejpam-5259	37	10	)	)	PUNCT
ejpam-5259	37	11	+	+	NUM
ejpam-5259	37	12	η	η	PROPN
ejpam-5259	37	13	)	)	PUNCT
ejpam-5259	37	14	ςµ.	ςµ.	NOUN
ejpam-5259	37	15	(	(	PUNCT
ejpam-5259	37	16	5	5	NUM
ejpam-5259	37	17	)	)	PUNCT
ejpam-5259	37	18	in	in	ADP
ejpam-5259	37	19	recent	recent	ADJ
ejpam-5259	37	20	years	year	NOUN
ejpam-5259	37	21	,	,	PUNCT
ejpam-5259	37	22	there	there	PRON
ejpam-5259	37	23	has	have	AUX
ejpam-5259	37	24	been	be	AUX
ejpam-5259	37	25	a	a	DET
ejpam-5259	37	26	growing	grow	VERB
ejpam-5259	37	27	interest	interest	NOUN
ejpam-5259	37	28	in	in	ADP
ejpam-5259	37	29	mittag	mittag	ADJ
ejpam-5259	37	30	–	–	PUNCT
ejpam-5259	37	31	leffler	leffler	NOUN
ejpam-5259	37	32	-	-	PUNCT
ejpam-5259	37	33	type	type	NOUN
ejpam-5259	37	34	functions	function	NOUN
ejpam-5259	37	35	,	,	PUNCT
ejpam-5259	37	36	driven	drive	VERB
ejpam-5259	37	37	by	by	ADP
ejpam-5259	37	38	their	their	PRON
ejpam-5259	37	39	increasing	increase	VERB
ejpam-5259	37	40	range	range	NOUN
ejpam-5259	37	41	of	of	ADP
ejpam-5259	37	42	applications	application	NOUN
ejpam-5259	37	43	in	in	ADP
ejpam-5259	37	44	probability	probability	NOUN
ejpam-5259	37	45	,	,	PUNCT
ejpam-5259	37	46	applied	apply	VERB
ejpam-5259	37	47	problem	problem	NOUN
ejpam-5259	37	48	-	-	PUNCT
ejpam-5259	37	49	solving	solve	VERB
ejpam-5259	37	50	,	,	PUNCT
ejpam-5259	37	51	statistical	statistical	ADJ
ejpam-5259	37	52	analysis	analysis	NOUN
ejpam-5259	37	53	,	,	PUNCT
ejpam-5259	37	54	and	and	CCONJ
ejpam-5259	37	55	distribution	distribution	NOUN
ejpam-5259	37	56	theory	theory	NOUN
ejpam-5259	37	57	,	,	PUNCT
ejpam-5259	37	58	among	among	ADP
ejpam-5259	37	59	other	other	ADJ
ejpam-5259	37	60	domains	domain	NOUN
ejpam-5259	37	61	.	.	PUNCT
ejpam-5259	38	1	more	more	ADJ
ejpam-5259	38	2	information	information	NOUN
ejpam-5259	38	3	about	about	ADP
ejpam-5259	38	4	the	the	DET
ejpam-5259	38	5	utilization	utilization	NOUN
ejpam-5259	38	6	of	of	ADP
ejpam-5259	38	7	mittag	mittag	ADJ
ejpam-5259	38	8	–	–	PUNCT
ejpam-5259	38	9	leffler	leffler	NOUN
ejpam-5259	38	10	functions	function	NOUN
ejpam-5259	38	11	can	can	AUX
ejpam-5259	38	12	be	be	AUX
ejpam-5259	38	13	found	find	VERB
ejpam-5259	38	14	in	in	ADP
ejpam-5259	38	15	references	reference	NOUN
ejpam-5259	38	16	[	[	X
ejpam-5259	38	17	3	3	NUM
ejpam-5259	38	18	,	,	PUNCT
ejpam-5259	38	19	4	4	NUM
ejpam-5259	38	20	,	,	PUNCT
ejpam-5259	38	21	7	7	NUM
ejpam-5259	38	22	,	,	PUNCT
ejpam-5259	38	23	8	8	NUM
ejpam-5259	38	24	,	,	PUNCT
ejpam-5259	38	25	16	16	NUM
ejpam-5259	38	26	,	,	PUNCT
ejpam-5259	38	27	20	20	NUM
ejpam-5259	38	28	,	,	PUNCT
ejpam-5259	38	29	22	22	NUM
ejpam-5259	38	30	]	]	PUNCT
ejpam-5259	38	31	.	.	PUNCT
ejpam-5259	39	1	much	much	ADJ
ejpam-5259	39	2	of	of	ADP
ejpam-5259	39	3	our	our	PRON
ejpam-5259	39	4	research	research	NOUN
ejpam-5259	39	5	involving	involve	VERB
ejpam-5259	39	6	mittag	mittag	ADJ
ejpam-5259	39	7	–	–	PUNCT
ejpam-5259	39	8	leffler	leffler	NOUN
ejpam-5259	39	9	functions	function	NOUN
ejpam-5259	39	10	focuses	focus	VERB
ejpam-5259	39	11	on	on	ADP
ejpam-5259	39	12	aspects	aspect	NOUN
ejpam-5259	39	13	of	of	ADP
ejpam-5259	39	14	convexity	convexity	NOUN
ejpam-5259	39	15	,	,	PUNCT
ejpam-5259	39	16	close	close	NOUN
ejpam-5259	39	17	-	-	PUNCT
ejpam-5259	39	18	to	to	ADP
ejpam-5259	39	19	-	-	PUNCT
ejpam-5259	39	20	convexity	convexity	NOUN
ejpam-5259	39	21	,	,	PUNCT
ejpam-5259	39	22	and	and	CCONJ
ejpam-5259	39	23	starlikeness	starlikeness	NOUN
ejpam-5259	39	24	.	.	PUNCT
ejpam-5259	40	1	recent	recent	ADJ
ejpam-5259	40	2	studies	study	NOUN
ejpam-5259	40	3	on	on	ADP
ejpam-5259	40	4	the	the	DET
ejpam-5259	40	5	eα	eα	NOUN
ejpam-5259	40	6	,	,	PUNCT
ejpam-5259	40	7	η(ς	η(ς	NOUN
ejpam-5259	40	8	)	)	PUNCT
ejpam-5259	40	9	mittag	mittag	ADJ
ejpam-5259	40	10	–	–	PUNCT
ejpam-5259	40	11	leffler	leffler	NOUN
ejpam-5259	40	12	function	function	NOUN
ejpam-5259	40	13	s.	s.	PROPN
ejpam-5259	40	14	ahmed	ahmed	PROPN
ejpam-5259	40	15	,	,	PUNCT
ejpam-5259	40	16	a.	a.	PROPN
ejpam-5259	40	17	alsoboh	alsoboh	PROPN
ejpam-5259	40	18	,	,	PUNCT
ejpam-5259	40	19	m.	m.	NOUN
ejpam-5259	40	20	darus	darus	NOUN
ejpam-5259	40	21	/	/	SYM
ejpam-5259	40	22	eur	eur	PROPN
ejpam-5259	40	23	.	.	PUNCT
ejpam-5259	41	1	j.	j.	PROPN
ejpam-5259	41	2	pure	pure	PROPN
ejpam-5259	41	3	appl	appl	PROPN
ejpam-5259	41	4	.	.	PROPN
ejpam-5259	41	5	math	math	PROPN
ejpam-5259	41	6	,	,	PUNCT
ejpam-5259	41	7	17	17	NUM
ejpam-5259	41	8	(	(	PUNCT
ejpam-5259	41	9	3	3	NUM
ejpam-5259	41	10	)	)	PUNCT
ejpam-5259	41	11	(	(	PUNCT
ejpam-5259	41	12	2024	2024	NUM
ejpam-5259	41	13	)	)	PUNCT
ejpam-5259	41	14	,	,	PUNCT
ejpam-5259	41	15	1894	1894	NUM
ejpam-5259	41	16	-	-	SYM
ejpam-5259	41	17	1907	1907	NUM
ejpam-5259	41	18	1896	1896	NUM
ejpam-5259	41	19	can	can	AUX
ejpam-5259	41	20	be	be	AUX
ejpam-5259	41	21	found	find	VERB
ejpam-5259	41	22	in	in	ADP
ejpam-5259	41	23	[	[	X
ejpam-5259	41	24	9	9	NUM
ejpam-5259	41	25	]	]	PUNCT
ejpam-5259	41	26	.	.	PUNCT
ejpam-5259	42	1	additionally	additionally	ADV
ejpam-5259	42	2	,	,	PUNCT
ejpam-5259	42	3	[	[	X
ejpam-5259	42	4	21	21	NUM
ejpam-5259	42	5	]	]	PUNCT
ejpam-5259	42	6	has	have	AUX
ejpam-5259	42	7	presented	present	VERB
ejpam-5259	42	8	findings	finding	NOUN
ejpam-5259	42	9	related	relate	VERB
ejpam-5259	42	10	to	to	ADP
ejpam-5259	42	11	partial	partial	ADJ
ejpam-5259	42	12	sums	sum	NOUN
ejpam-5259	42	13	for	for	ADP
ejpam-5259	42	14	eα	eα	NOUN
ejpam-5259	42	15	,	,	PUNCT
ejpam-5259	42	16	η(ς	η(ς	NOUN
ejpam-5259	42	17	)	)	PUNCT
ejpam-5259	42	18	.	.	PUNCT
ejpam-5259	43	1	motivated	motivate	VERB
ejpam-5259	43	2	by	by	ADP
ejpam-5259	43	3	challab	challab	NOUN
ejpam-5259	43	4	and	and	CCONJ
ejpam-5259	43	5	darus	darus	NOUN
ejpam-5259	43	6	[	[	X
ejpam-5259	43	7	10	10	NUM
ejpam-5259	43	8	]	]	PUNCT
ejpam-5259	43	9	,	,	PUNCT
ejpam-5259	43	10	we	we	PRON
ejpam-5259	43	11	define	define	VERB
ejpam-5259	43	12	the	the	DET
ejpam-5259	43	13	linear	linear	ADJ
ejpam-5259	43	14	derivative	derivative	ADJ
ejpam-5259	43	15	operator	operator	NOUN
ejpam-5259	43	16	sα	sα	PROPN
ejpam-5259	43	17	η	η	PROPN
ejpam-5259	43	18	[	[	X
ejpam-5259	43	19	r	r	PROPN
ejpam-5259	43	20	,	,	PUNCT
ejpam-5259	43	21	δ	δ	PROPN
ejpam-5259	43	22	,	,	PUNCT
ejpam-5259	43	23	λ	λ	X
ejpam-5259	43	24	]	]	X
ejpam-5259	43	25	:	:	PUNCT
ejpam-5259	43	26	σ	σ	PROPN
ejpam-5259	43	27	→	→	SYM
ejpam-5259	43	28	σ	σ	PROPN
ejpam-5259	43	29	by	by	ADP
ejpam-5259	43	30	sα	sα	PROPN
ejpam-5259	43	31	η	η	PROPN
ejpam-5259	43	32	[	[	X
ejpam-5259	43	33	r	r	PROPN
ejpam-5259	43	34	,	,	PUNCT
ejpam-5259	43	35	δ	δ	PROPN
ejpam-5259	43	36	,	,	PUNCT
ejpam-5259	43	37	λ]f(ς	λ]f(ς	NOUN
ejpam-5259	43	38	)	)	PUNCT
ejpam-5259	43	39	=(	=(	NOUN
ejpam-5259	43	40	1−	1−	NUM
ejpam-5259	43	41	λ)(i1(r	λ)(i1(r	NOUN
ejpam-5259	43	42	,	,	PUNCT
ejpam-5259	43	43	δ)f(ς	δ)f(ς	ADJ
ejpam-5259	43	44	)	)	PUNCT
ejpam-5259	43	45	∗	∗	NOUN
ejpam-5259	43	46	ωα	ωα	PROPN
ejpam-5259	43	47	,	,	PUNCT
ejpam-5259	43	48	η(ς	η(ς	NOUN
ejpam-5259	43	49	)	)	PUNCT
ejpam-5259	43	50	+	+	X
ejpam-5259	44	1	λς((i1(r	λς((i1(r	NOUN
ejpam-5259	44	2	,	,	PUNCT
ejpam-5259	44	3	δ)f(ς	δ)f(ς	ADJ
ejpam-5259	44	4	)	)	PUNCT
ejpam-5259	44	5	∗	∗	NOUN
ejpam-5259	44	6	ωα	ωα	PROPN
ejpam-5259	44	7	,	,	PUNCT
ejpam-5259	44	8	η(ς	η(ς	NOUN
ejpam-5259	44	9	)	)	PUNCT
ejpam-5259	44	10	)	)	PUNCT
ejpam-5259	45	1	′	′	NUM
ejpam-5259	46	1	=	=	SYM
ejpam-5259	46	2	1	1	NUM
ejpam-5259	46	3	ς	ς	PROPN
ejpam-5259	46	4	+	+	NOUN
ejpam-5259	46	5	∞∑	∞∑	NUM
ejpam-5259	46	6	µ=1	µ=1	PROPN
ejpam-5259	46	7	γ(η)[1	γ(η)[1	X
ejpam-5259	47	1	+	+	PUNCT
ejpam-5259	47	2	λ(µ−	λ(µ−	VERB
ejpam-5259	47	3	1)]k	1)]k	NUM
ejpam-5259	47	4	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	47	5	1	1	NUM
ejpam-5259	47	6	)	)	PUNCT
ejpam-5259	47	7	+	+	NUM
ejpam-5259	47	8	η	η	X
ejpam-5259	47	9	)	)	PUNCT
ejpam-5259	47	10	(	(	PUNCT
ejpam-5259	47	11	µ+	µ+	X
ejpam-5259	47	12	δ	δ	PROPN
ejpam-5259	47	13	1	1	NUM
ejpam-5259	47	14	+	+	CCONJ
ejpam-5259	47	15	δ	δ	NOUN
ejpam-5259	47	16	)	)	PUNCT
ejpam-5259	47	17	r	r	NOUN
ejpam-5259	47	18	aµς	aµς	NOUN
ejpam-5259	47	19	µ	µ	NOUN
ejpam-5259	47	20	,	,	PUNCT
ejpam-5259	47	21	(	(	PUNCT
ejpam-5259	47	22	6	6	NUM
ejpam-5259	47	23	)	)	PUNCT
ejpam-5259	47	24	where	where	SCONJ
ejpam-5259	47	25	δ	δ	PROPN
ejpam-5259	47	26	≥	≥	NOUN
ejpam-5259	47	27	0	0	NUM
ejpam-5259	47	28	,	,	PUNCT
ejpam-5259	47	29	r	r	NOUN
ejpam-5259	47	30	∈	∈	PROPN
ejpam-5259	47	31	n	n	NOUN
ejpam-5259	47	32	,	,	PUNCT
ejpam-5259	47	33	0	0	NUM
ejpam-5259	47	34	≤	≤	NUM
ejpam-5259	47	35	λ	λ	X
ejpam-5259	47	36	≤	≤	NOUN
ejpam-5259	47	37	1	1	NUM
ejpam-5259	47	38	,	,	PUNCT
ejpam-5259	47	39	α	α	PROPN
ejpam-5259	47	40	,	,	PUNCT
ejpam-5259	47	41	η	η	PROPN
ejpam-5259	47	42	∈	∈	PROPN
ejpam-5259	47	43	c	c	PROPN
ejpam-5259	47	44	and	and	CCONJ
ejpam-5259	47	45	i1(r	i1(r	NOUN
ejpam-5259	47	46	,	,	PUNCT
ejpam-5259	47	47	λ)f(ς	λ)f(ς	PROPN
ejpam-5259	47	48	)	)	PUNCT
ejpam-5259	47	49	of	of	ADP
ejpam-5259	47	50	the	the	DET
ejpam-5259	47	51	form	form	NOUN
ejpam-5259	47	52	(	(	PUNCT
ejpam-5259	47	53	2	2	NUM
ejpam-5259	47	54	)	)	PUNCT
ejpam-5259	47	55	.	.	PUNCT
ejpam-5259	48	1	example	example	NOUN
ejpam-5259	49	1	1	1	NUM
ejpam-5259	49	2	.	.	PUNCT
ejpam-5259	50	1	if	if	SCONJ
ejpam-5259	50	2	r	r	NOUN
ejpam-5259	50	3	=	=	SYM
ejpam-5259	50	4	0	0	NUM
ejpam-5259	50	5	,	,	PUNCT
ejpam-5259	50	6	then	then	ADV
ejpam-5259	50	7	sα	sα	PROPN
ejpam-5259	50	8	η	η	PROPN
ejpam-5259	50	9	[	[	X
ejpam-5259	50	10	r	r	PROPN
ejpam-5259	50	11	,	,	PUNCT
ejpam-5259	50	12	δ	δ	PROPN
ejpam-5259	50	13	,	,	PUNCT
ejpam-5259	50	14	λ	λ	X
ejpam-5259	50	15	]	]	X
ejpam-5259	50	16	is	be	AUX
ejpam-5259	50	17	reduced	reduce	VERB
ejpam-5259	50	18	to	to	ADP
ejpam-5259	50	19	sα	sα	PROPN
ejpam-5259	50	20	η	η	PROPN
ejpam-5259	50	21	[	[	X
ejpam-5259	50	22	0	0	NUM
ejpam-5259	50	23	,	,	PUNCT
ejpam-5259	50	24	δ	δ	PROPN
ejpam-5259	50	25	,	,	PUNCT
ejpam-5259	50	26	λ]f(ς	λ]f(ς	NOUN
ejpam-5259	50	27	)	)	PUNCT
ejpam-5259	50	28	=	=	SYM
ejpam-5259	50	29	1	1	NUM
ejpam-5259	50	30	ς	ς	PROPN
ejpam-5259	50	31	+	+	NOUN
ejpam-5259	50	32	∞∑	∞∑	NUM
ejpam-5259	50	33	µ=1	µ=1	PROPN
ejpam-5259	50	34	γ(η)[1	γ(η)[1	X
ejpam-5259	50	35	+	+	PUNCT
ejpam-5259	50	36	λ(µ−	λ(µ−	VERB
ejpam-5259	50	37	1)]k	1)]k	NUM
ejpam-5259	50	38	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	50	39	1	1	NUM
ejpam-5259	50	40	)	)	PUNCT
ejpam-5259	50	41	+	+	NUM
ejpam-5259	50	42	η	η	NOUN
ejpam-5259	50	43	)	)	PUNCT
ejpam-5259	50	44	aµς	aµς	NOUN
ejpam-5259	50	45	µ	µ	NOUN
ejpam-5259	50	46	introduced	introduce	VERB
ejpam-5259	50	47	by	by	ADP
ejpam-5259	50	48	ghanim	ghanim	NOUN
ejpam-5259	50	49	and	and	CCONJ
ejpam-5259	50	50	al	al	PROPN
ejpam-5259	50	51	-	-	PUNCT
ejpam-5259	50	52	janaby	janaby	PROPN
ejpam-5259	51	1	[	[	X
ejpam-5259	51	2	15	15	NUM
ejpam-5259	51	3	]	]	PUNCT
ejpam-5259	51	4	.	.	PUNCT
ejpam-5259	51	5	example	example	NOUN
ejpam-5259	52	1	2	2	NUM
ejpam-5259	52	2	.	.	PUNCT
ejpam-5259	53	1	if	if	SCONJ
ejpam-5259	53	2	α	α	NUM
ejpam-5259	53	3	=	=	SYM
ejpam-5259	53	4	0	0	PROPN
ejpam-5259	53	5	,	,	PUNCT
ejpam-5259	53	6	then	then	ADV
ejpam-5259	53	7	sα	sα	PROPN
ejpam-5259	53	8	η	η	PROPN
ejpam-5259	53	9	[	[	X
ejpam-5259	53	10	r	r	PROPN
ejpam-5259	53	11	,	,	PUNCT
ejpam-5259	53	12	δ	δ	PROPN
ejpam-5259	53	13	,	,	PUNCT
ejpam-5259	53	14	λ	λ	X
ejpam-5259	53	15	]	]	X
ejpam-5259	53	16	is	be	AUX
ejpam-5259	53	17	reduced	reduce	VERB
ejpam-5259	53	18	to	to	ADP
ejpam-5259	53	19	s0	s0	PROPN
ejpam-5259	53	20	η	η	PROPN
ejpam-5259	53	21	[	[	X
ejpam-5259	53	22	r	r	PROPN
ejpam-5259	53	23	,	,	PUNCT
ejpam-5259	53	24	δ	δ	PROPN
ejpam-5259	53	25	,	,	PUNCT
ejpam-5259	53	26	λ]f(ς	λ]f(ς	NOUN
ejpam-5259	53	27	)	)	PUNCT
ejpam-5259	53	28	=	=	SYM
ejpam-5259	53	29	1	1	NUM
ejpam-5259	53	30	ς	ς	PROPN
ejpam-5259	53	31	+	+	NOUN
ejpam-5259	53	32	∞∑	∞∑	NUM
ejpam-5259	53	33	µ=1	µ=1	PUNCT
ejpam-5259	53	34	[	[	X
ejpam-5259	53	35	1	1	NUM
ejpam-5259	53	36	+	+	NUM
ejpam-5259	53	37	λ(µ−	λ(µ−	NOUN
ejpam-5259	53	38	1)]k	1)]k	NUM
ejpam-5259	53	39	(	(	PUNCT
ejpam-5259	53	40	µ+	µ+	X
ejpam-5259	53	41	δ	δ	PROPN
ejpam-5259	53	42	1	1	NUM
ejpam-5259	53	43	+	+	CCONJ
ejpam-5259	53	44	δ	δ	NOUN
ejpam-5259	53	45	)	)	PUNCT
ejpam-5259	53	46	r	r	NOUN
ejpam-5259	53	47	aµς	aµς	NOUN
ejpam-5259	53	48	µ	µ	PRON
ejpam-5259	53	49	example	example	NOUN
ejpam-5259	54	1	3	3	X
ejpam-5259	54	2	.	.	PUNCT
ejpam-5259	55	1	if	if	SCONJ
ejpam-5259	55	2	α	α	PROPN
ejpam-5259	55	3	=	=	NOUN
ejpam-5259	55	4	0	0	PROPN
ejpam-5259	55	5	and	and	CCONJ
ejpam-5259	55	6	k	k	X
ejpam-5259	55	7	=	=	SYM
ejpam-5259	55	8	0	0	PROPN
ejpam-5259	55	9	,	,	PUNCT
ejpam-5259	55	10	then	then	ADV
ejpam-5259	55	11	sα	sα	PROPN
ejpam-5259	55	12	η	η	PROPN
ejpam-5259	55	13	[	[	X
ejpam-5259	55	14	r	r	PROPN
ejpam-5259	55	15	,	,	PUNCT
ejpam-5259	55	16	δ	δ	PROPN
ejpam-5259	55	17	,	,	PUNCT
ejpam-5259	55	18	λ	λ	X
ejpam-5259	55	19	]	]	X
ejpam-5259	55	20	is	be	AUX
ejpam-5259	55	21	reduced	reduce	VERB
ejpam-5259	55	22	to	to	ADP
ejpam-5259	55	23	s0	s0	PROPN
ejpam-5259	55	24	η	η	PROPN
ejpam-5259	55	25	[	[	X
ejpam-5259	55	26	r	r	PROPN
ejpam-5259	55	27	,	,	PUNCT
ejpam-5259	55	28	δ	δ	PROPN
ejpam-5259	55	29	,	,	PUNCT
ejpam-5259	55	30	λ]f(ς	λ]f(ς	NOUN
ejpam-5259	55	31	)	)	PUNCT
ejpam-5259	55	32	=	=	SYM
ejpam-5259	55	33	1	1	NUM
ejpam-5259	55	34	ς	ς	PROPN
ejpam-5259	55	35	+	+	NOUN
ejpam-5259	55	36	∞∑	∞∑	NUM
ejpam-5259	55	37	µ=1	µ=1	PUNCT
ejpam-5259	55	38	(	(	PUNCT
ejpam-5259	55	39	µ+	µ+	X
ejpam-5259	55	40	δ	δ	NOUN
ejpam-5259	55	41	1	1	NUM
ejpam-5259	55	42	+	+	CCONJ
ejpam-5259	55	43	δ	δ	NOUN
ejpam-5259	55	44	)	)	PUNCT
ejpam-5259	55	45	r	r	NOUN
ejpam-5259	55	46	aµς	aµς	NOUN
ejpam-5259	55	47	µ	µ	NOUN
ejpam-5259	55	48	introduced	introduce	VERB
ejpam-5259	55	49	by	by	ADP
ejpam-5259	55	50	atshan	atshan	NOUN
ejpam-5259	55	51	and	and	CCONJ
ejpam-5259	55	52	joudah	joudah	PROPN
ejpam-5259	56	1	[	[	X
ejpam-5259	56	2	6	6	NUM
ejpam-5259	56	3	]	]	PUNCT
ejpam-5259	56	4	.	.	PUNCT
ejpam-5259	57	1	example	example	NOUN
ejpam-5259	58	1	4	4	NUM
ejpam-5259	58	2	.	.	PUNCT
ejpam-5259	59	1	if	if	SCONJ
ejpam-5259	59	2	α	α	NUM
ejpam-5259	59	3	=	=	SYM
ejpam-5259	59	4	0	0	NUM
ejpam-5259	59	5	,	,	PUNCT
ejpam-5259	59	6	r	r	NOUN
ejpam-5259	59	7	=	=	SYM
ejpam-5259	59	8	0	0	NUM
ejpam-5259	59	9	,	,	PUNCT
ejpam-5259	59	10	then	then	ADV
ejpam-5259	59	11	sα	sα	PROPN
ejpam-5259	59	12	η	η	PROPN
ejpam-5259	59	13	[	[	X
ejpam-5259	59	14	r	r	PROPN
ejpam-5259	59	15	,	,	PUNCT
ejpam-5259	59	16	δ	δ	PROPN
ejpam-5259	59	17	,	,	PUNCT
ejpam-5259	59	18	λ	λ	X
ejpam-5259	59	19	]	]	X
ejpam-5259	59	20	is	be	AUX
ejpam-5259	59	21	reduced	reduce	VERB
ejpam-5259	59	22	to	to	ADP
ejpam-5259	59	23	s0	s0	PROPN
ejpam-5259	59	24	η	η	PROPN
ejpam-5259	59	25	[	[	X
ejpam-5259	59	26	r	r	PROPN
ejpam-5259	59	27	,	,	PUNCT
ejpam-5259	59	28	δ	δ	PROPN
ejpam-5259	59	29	,	,	PUNCT
ejpam-5259	59	30	λ]f(ς	λ]f(ς	NOUN
ejpam-5259	59	31	)	)	PUNCT
ejpam-5259	59	32	=	=	SYM
ejpam-5259	59	33	1	1	NUM
ejpam-5259	59	34	ς	ς	PROPN
ejpam-5259	59	35	+	+	NOUN
ejpam-5259	59	36	∞∑	∞∑	NUM
ejpam-5259	59	37	µ=1	µ=1	PUNCT
ejpam-5259	59	38	[	[	X
ejpam-5259	59	39	1	1	NUM
ejpam-5259	59	40	+	+	PUNCT
ejpam-5259	59	41	λ(µ−	λ(µ−	VERB
ejpam-5259	59	42	1)]kaµς	1)]kaµς	PROPN
ejpam-5259	59	43	µ	µ	NOUN
ejpam-5259	59	44	introduced	introduce	VERB
ejpam-5259	59	45	by	by	ADP
ejpam-5259	59	46	challab	challab	NOUN
ejpam-5259	59	47	and	and	CCONJ
ejpam-5259	59	48	darus	darus	NOUN
ejpam-5259	59	49	[	[	X
ejpam-5259	59	50	10	10	NUM
ejpam-5259	59	51	]	]	PUNCT
ejpam-5259	59	52	.	.	PUNCT
ejpam-5259	60	1	for	for	ADP
ejpam-5259	60	2	ς	ς	PROPN
ejpam-5259	60	3	∈	∈	PROPN
ejpam-5259	60	4	♢	♢	PROPN
ejpam-5259	60	5	∗	∗	PROPN
ejpam-5259	60	6	=	=	SYM
ejpam-5259	60	7	♢	♢	NOUN
ejpam-5259	60	8	\{0	\{0	X
ejpam-5259	60	9	}	}	PUNCT
ejpam-5259	60	10	,	,	PUNCT
ejpam-5259	60	11	by	by	ADP
ejpam-5259	60	12	mh	mh	PROPN
ejpam-5259	60	13	,	,	PUNCT
ejpam-5259	60	14	we	we	PRON
ejpam-5259	60	15	denote	denote	VERB
ejpam-5259	60	16	the	the	DET
ejpam-5259	60	17	class	class	NOUN
ejpam-5259	60	18	of	of	ADP
ejpam-5259	60	19	harmonic	harmonic	ADJ
ejpam-5259	60	20	meromorphic	meromorphic	ADJ
ejpam-5259	60	21	functions	function	NOUN
ejpam-5259	60	22	of	of	ADP
ejpam-5259	60	23	the	the	DET
ejpam-5259	60	24	form	form	NOUN
ejpam-5259	60	25	f(ς	f(ς	PROPN
ejpam-5259	60	26	)	)	PUNCT
ejpam-5259	60	27	=	=	SYM
ejpam-5259	61	1	ℏ(ς	ℏ(ς	PROPN
ejpam-5259	61	2	)	)	PUNCT
ejpam-5259	61	3	+	+	CCONJ
ejpam-5259	61	4	g(ς	g(ς	PROPN
ejpam-5259	61	5	)	)	PUNCT
ejpam-5259	61	6	=	=	PUNCT
ejpam-5259	61	7	1	1	NUM
ejpam-5259	61	8	ς	ς	PROPN
ejpam-5259	61	9	+	+	NOUN
ejpam-5259	61	10	∞∑	∞∑	NUM
ejpam-5259	61	11	µ=1	µ=1	ADV
ejpam-5259	61	12	aµς	aµς	NOUN
ejpam-5259	61	13	µ	µ	NOUN
ejpam-5259	61	14	+	+	NOUN
ejpam-5259	61	15	∞∑	∞∑	NUM
ejpam-5259	61	16	µ=1	µ=1	ADV
ejpam-5259	61	17	bµςµ	bµςµ	ADJ
ejpam-5259	61	18	,	,	PUNCT
ejpam-5259	61	19	(	(	PUNCT
ejpam-5259	61	20	7	7	X
ejpam-5259	61	21	)	)	PUNCT
ejpam-5259	61	22	which	which	PRON
ejpam-5259	61	23	are	be	AUX
ejpam-5259	61	24	harmonic	harmonic	ADJ
ejpam-5259	61	25	in	in	ADP
ejpam-5259	61	26	the	the	DET
ejpam-5259	61	27	punctured	punctured	ADJ
ejpam-5259	61	28	unit	unit	NOUN
ejpam-5259	61	29	disk	disk	NOUN
ejpam-5259	61	30	♢	♢	NOUN
ejpam-5259	61	31	\{0	\{0	NOUN
ejpam-5259	61	32	}	}	PUNCT
ejpam-5259	61	33	,	,	PUNCT
ejpam-5259	61	34	where	where	SCONJ
ejpam-5259	61	35	h	h	NOUN
ejpam-5259	61	36	and	and	CCONJ
ejpam-5259	61	37	g	g	PROPN
ejpam-5259	61	38	are	be	AUX
ejpam-5259	61	39	analytic	analytic	ADJ
ejpam-5259	61	40	in	in	ADP
ejpam-5259	61	41	♢	♢	PROPN
ejpam-5259	61	42	∗and	∗and	PROPN
ejpam-5259	61	43	♢	♢	PROPN
ejpam-5259	61	44	,	,	PUNCT
ejpam-5259	61	45	respectively	respectively	ADV
ejpam-5259	61	46	,	,	PUNCT
ejpam-5259	61	47	and	and	CCONJ
ejpam-5259	61	48	ℏ	ℏ	PROPN
ejpam-5259	61	49	has	have	VERB
ejpam-5259	61	50	a	a	DET
ejpam-5259	61	51	simple	simple	ADJ
ejpam-5259	61	52	pole	pole	NOUN
ejpam-5259	61	53	at	at	ADP
ejpam-5259	61	54	the	the	DET
ejpam-5259	61	55	origin	origin	NOUN
ejpam-5259	61	56	with	with	ADP
ejpam-5259	61	57	residue	residue	NOUN
ejpam-5259	61	58	1	1	NUM
ejpam-5259	61	59	here	here	ADV
ejpam-5259	61	60	.	.	PUNCT
ejpam-5259	62	1	this	this	DET
ejpam-5259	62	2	class	class	NOUN
ejpam-5259	62	3	was	be	AUX
ejpam-5259	62	4	s.	s.	PROPN
ejpam-5259	62	5	ahmed	ahmed	PROPN
ejpam-5259	62	6	,	,	PUNCT
ejpam-5259	62	7	a.	a.	PROPN
ejpam-5259	62	8	alsoboh	alsoboh	PROPN
ejpam-5259	62	9	,	,	PUNCT
ejpam-5259	62	10	m.	m.	NOUN
ejpam-5259	62	11	darus	darus	NOUN
ejpam-5259	62	12	/	/	SYM
ejpam-5259	62	13	eur	eur	PROPN
ejpam-5259	62	14	.	.	PUNCT
ejpam-5259	63	1	j.	j.	PROPN
ejpam-5259	63	2	pure	pure	PROPN
ejpam-5259	63	3	appl	appl	PROPN
ejpam-5259	63	4	.	.	PROPN
ejpam-5259	63	5	math	math	PROPN
ejpam-5259	63	6	,	,	PUNCT
ejpam-5259	63	7	17	17	NUM
ejpam-5259	63	8	(	(	PUNCT
ejpam-5259	63	9	3	3	NUM
ejpam-5259	63	10	)	)	PUNCT
ejpam-5259	63	11	(	(	PUNCT
ejpam-5259	63	12	2024	2024	NUM
ejpam-5259	63	13	)	)	PUNCT
ejpam-5259	63	14	,	,	PUNCT
ejpam-5259	63	15	1894	1894	NUM
ejpam-5259	63	16	-	-	SYM
ejpam-5259	63	17	1907	1907	NUM
ejpam-5259	63	18	1897	1897	NUM
ejpam-5259	63	19	firstly	firstly	ADV
ejpam-5259	63	20	studied	study	VERB
ejpam-5259	63	21	by	by	ADP
ejpam-5259	63	22	jahangiri	jahangiri	PROPN
ejpam-5259	63	23	and	and	CCONJ
ejpam-5259	63	24	silverman	silverman	NOUN
ejpam-5259	63	25	[	[	X
ejpam-5259	63	26	19	19	NUM
ejpam-5259	63	27	]	]	PUNCT
ejpam-5259	63	28	,	,	PUNCT
ejpam-5259	63	29	followed	follow	VERB
ejpam-5259	63	30	by	by	ADP
ejpam-5259	63	31	jahangiri	jahangiri	PROPN
ejpam-5259	63	32	et	et	PROPN
ejpam-5259	63	33	al	al	PROPN
ejpam-5259	63	34	.	.	PUNCT
ejpam-5259	64	1	[	[	X
ejpam-5259	64	2	18	18	NUM
ejpam-5259	64	3	]	]	PUNCT
ejpam-5259	64	4	,	,	PUNCT
ejpam-5259	64	5	ahuja	ahuja	PROPN
ejpam-5259	64	6	and	and	CCONJ
ejpam-5259	64	7	jahangiri	jahangiri	PROPN
ejpam-5259	65	1	[	[	X
ejpam-5259	65	2	2	2	X
ejpam-5259	65	3	]	]	PUNCT
ejpam-5259	65	4	and	and	CCONJ
ejpam-5259	65	5	others	other	NOUN
ejpam-5259	65	6	.	.	PUNCT
ejpam-5259	66	1	we	we	PRON
ejpam-5259	66	2	further	far	ADV
ejpam-5259	66	3	denote	denote	VERB
ejpam-5259	66	4	by	by	ADP
ejpam-5259	66	5	the	the	DET
ejpam-5259	66	6	subclass	subclass	NOUN
ejpam-5259	66	7	mh	mh	PROPN
ejpam-5259	66	8	of	of	ADP
ejpam-5259	66	9	mh	mh	PROPN
ejpam-5259	66	10	consisting	consist	VERB
ejpam-5259	66	11	of	of	ADP
ejpam-5259	66	12	functions	function	NOUN
ejpam-5259	66	13	f	f	PROPN
ejpam-5259	66	14	of	of	ADP
ejpam-5259	66	15	the	the	DET
ejpam-5259	66	16	form	form	NOUN
ejpam-5259	66	17	f(ς	f(ς	PROPN
ejpam-5259	66	18	)	)	PUNCT
ejpam-5259	66	19	=	=	SYM
ejpam-5259	67	1	1	1	NUM
ejpam-5259	67	2	ς	ς	PROPN
ejpam-5259	67	3	+	+	NOUN
ejpam-5259	67	4	∞∑	∞∑	NUM
ejpam-5259	67	5	µ=1	µ=1	ADP
ejpam-5259	67	6	|aµ|ςµ	|aµ|ςµ	NOUN
ejpam-5259	67	7	+	+	PUNCT
ejpam-5259	67	8	∞∑	∞∑	NUM
ejpam-5259	67	9	µ=1	µ=1	ADV
ejpam-5259	67	10	|bµ|ςµ	|bµ|ςµ	PUNCT
ejpam-5259	67	11	,	,	PUNCT
ejpam-5259	67	12	(	(	PUNCT
ejpam-5259	67	13	z	z	PROPN
ejpam-5259	67	14	∈	∈	PROPN
ejpam-5259	67	15	♢	♢	NOUN
ejpam-5259	67	16	∗	∗	PROPN
ejpam-5259	67	17	)	)	PUNCT
ejpam-5259	67	18	.	.	PUNCT
ejpam-5259	68	1	(	(	PUNCT
ejpam-5259	68	2	8)	8)	NUM
ejpam-5259	68	3	the	the	DET
ejpam-5259	68	4	function	function	NOUN
ejpam-5259	68	5	f	f	PROPN
ejpam-5259	68	6	=	=	SYM
ejpam-5259	68	7	ℏ	ℏ	PROPN
ejpam-5259	68	8	+	+	CCONJ
ejpam-5259	68	9	g	g	NOUN
ejpam-5259	68	10	,	,	PUNCT
ejpam-5259	68	11	defined	define	VERB
ejpam-5259	68	12	by	by	ADP
ejpam-5259	68	13	the	the	DET
ejpam-5259	68	14	equation	equation	NOUN
ejpam-5259	68	15	(	(	PUNCT
ejpam-5259	68	16	7	7	NUM
ejpam-5259	68	17	)	)	PUNCT
ejpam-5259	68	18	,	,	PUNCT
ejpam-5259	68	19	can	can	AUX
ejpam-5259	68	20	be	be	AUX
ejpam-5259	68	21	classified	classify	VERB
ejpam-5259	68	22	as	as	ADP
ejpam-5259	68	23	a	a	DET
ejpam-5259	68	24	harmonic	harmonic	ADJ
ejpam-5259	68	25	meromorphic	meromorphic	ADJ
ejpam-5259	68	26	function	function	NOUN
ejpam-5259	68	27	that	that	PRON
ejpam-5259	68	28	is	be	AUX
ejpam-5259	68	29	locally	locally	ADV
ejpam-5259	68	30	univalent	univalent	ADJ
ejpam-5259	68	31	and	and	CCONJ
ejpam-5259	68	32	sense	sense	NOUN
ejpam-5259	68	33	-	-	PUNCT
ejpam-5259	68	34	preserving	preserve	VERB
ejpam-5259	68	35	in	in	ADP
ejpam-5259	68	36	the	the	DET
ejpam-5259	68	37	region	region	NOUN
ejpam-5259	68	38	♢	♢	PROPN
ejpam-5259	68	39	∗	∗	PROPN
ejpam-5259	68	40	if	if	SCONJ
ejpam-5259	68	41	and	and	CCONJ
ejpam-5259	68	42	only	only	ADV
ejpam-5259	68	43	if	if	SCONJ
ejpam-5259	68	44	∣∣∣∣g′	∣∣∣∣g′	X
ejpam-5259	68	45	(	(	PUNCT
ejpam-5259	68	46	ς)ℏ′	ς)ℏ′	PROPN
ejpam-5259	68	47	(	(	PUNCT
ejpam-5259	68	48	ς	ς	NOUN
ejpam-5259	68	49	)	)	PUNCT
ejpam-5259	68	50	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5259	68	51	<	<	X
ejpam-5259	68	52	1	1	NUM
ejpam-5259	68	53	.	.	PUNCT
ejpam-5259	69	1	the	the	DET
ejpam-5259	69	2	investigation	investigation	NOUN
ejpam-5259	69	3	of	of	ADP
ejpam-5259	69	4	harmonic	harmonic	ADJ
ejpam-5259	69	5	meromorphic	meromorphic	ADJ
ejpam-5259	69	6	functions	function	NOUN
ejpam-5259	69	7	within	within	ADP
ejpam-5259	69	8	this	this	DET
ejpam-5259	69	9	specific	specific	ADJ
ejpam-5259	69	10	context	context	NOUN
ejpam-5259	69	11	has	have	AUX
ejpam-5259	69	12	been	be	AUX
ejpam-5259	69	13	examined	examine	VERB
ejpam-5259	69	14	by	by	ADP
ejpam-5259	69	15	jahangiri	jahangiri	NOUN
ejpam-5259	69	16	and	and	CCONJ
ejpam-5259	69	17	silverman	silverman	NOUN
ejpam-5259	69	18	in	in	ADP
ejpam-5259	69	19	their	their	PRON
ejpam-5259	69	20	work	work	NOUN
ejpam-5259	69	21	[	[	X
ejpam-5259	69	22	19	19	NUM
ejpam-5259	69	23	]	]	PUNCT
ejpam-5259	69	24	.	.	PUNCT
ejpam-5259	70	1	a	a	DET
ejpam-5259	70	2	function	function	NOUN
ejpam-5259	70	3	f	f	PROPN
ejpam-5259	70	4	∈	∈	PROPN
ejpam-5259	70	5	mh	mh	PROPN
ejpam-5259	70	6	is	be	AUX
ejpam-5259	70	7	said	say	VERB
ejpam-5259	70	8	to	to	PART
ejpam-5259	70	9	be	be	AUX
ejpam-5259	70	10	in	in	ADP
ejpam-5259	70	11	the	the	DET
ejpam-5259	70	12	class	class	NOUN
ejpam-5259	70	13	ms∗	ms∗	NOUN
ejpam-5259	70	14	h	h	NOUN
ejpam-5259	70	15	of	of	ADP
ejpam-5259	70	16	meromorphically	meromorphically	ADV
ejpam-5259	70	17	harmonic	harmonic	ADJ
ejpam-5259	70	18	starlike	starlike	NOUN
ejpam-5259	70	19	functions	function	NOUN
ejpam-5259	70	20	in	in	ADP
ejpam-5259	70	21	♢	♢	PROPN
ejpam-5259	70	22	∗	∗	NOUN
ejpam-5259	70	23	,	,	PUNCT
ejpam-5259	70	24	if	if	SCONJ
ejpam-5259	70	25	it	it	PRON
ejpam-5259	70	26	satisfies	satisfy	VERB
ejpam-5259	70	27	the	the	DET
ejpam-5259	70	28	condition	condition	NOUN
ejpam-5259	70	29	ℜe	ℜe	ADP
ejpam-5259	70	30	{	{	PUNCT
ejpam-5259	70	31	ςℏ′	ςℏ′	NOUN
ejpam-5259	70	32	(	(	PUNCT
ejpam-5259	70	33	ς)−	ς)−	PROPN
ejpam-5259	70	34	ς	ς	X
ejpam-5259	70	35	g′(ς	g′(ς	PROPN
ejpam-5259	70	36	)	)	PUNCT
ejpam-5259	70	37	ℏ(ς	ℏ(ς	PROPN
ejpam-5259	70	38	)	)	PUNCT
ejpam-5259	71	1	+	+	CCONJ
ejpam-5259	71	2	g(ς	g(ς	PROPN
ejpam-5259	71	3	)	)	PUNCT
ejpam-5259	71	4	}	}	PUNCT
ejpam-5259	72	1	>	>	X
ejpam-5259	72	2	0	0	NUM
ejpam-5259	72	3	,	,	PUNCT
ejpam-5259	72	4	(	(	PUNCT
ejpam-5259	72	5	z	z	NOUN
ejpam-5259	72	6	∈	∈	PROPN
ejpam-5259	72	7	♢	♢	NOUN
ejpam-5259	72	8	∗	∗	PROPN
ejpam-5259	72	9	)	)	PUNCT
ejpam-5259	72	10	.	.	PUNCT
ejpam-5259	73	1	in	in	ADP
ejpam-5259	73	2	other	other	ADJ
ejpam-5259	73	3	hand	hand	NOUN
ejpam-5259	73	4	,	,	PUNCT
ejpam-5259	73	5	a	a	DET
ejpam-5259	73	6	function	function	NOUN
ejpam-5259	73	7	f	f	PROPN
ejpam-5259	73	8	∈	∈	PROPN
ejpam-5259	73	9	mh	mh	PROPN
ejpam-5259	73	10	is	be	AUX
ejpam-5259	73	11	said	say	VERB
ejpam-5259	73	12	to	to	PART
ejpam-5259	73	13	be	be	AUX
ejpam-5259	73	14	in	in	ADP
ejpam-5259	73	15	the	the	DET
ejpam-5259	73	16	class	class	NOUN
ejpam-5259	73	17	mch	mch	NOUN
ejpam-5259	73	18	of	of	ADP
ejpam-5259	73	19	meromorphically	meromorphically	ADV
ejpam-5259	73	20	harmonic	harmonic	VERB
ejpam-5259	73	21	convex	convex	NOUN
ejpam-5259	73	22	functions	function	NOUN
ejpam-5259	73	23	in	in	ADP
ejpam-5259	73	24	♢	♢	PROPN
ejpam-5259	73	25	∗	∗	NOUN
ejpam-5259	73	26	,	,	PUNCT
ejpam-5259	73	27	if	if	SCONJ
ejpam-5259	73	28	it	it	PRON
ejpam-5259	73	29	satisfies	satisfy	VERB
ejpam-5259	73	30	the	the	DET
ejpam-5259	73	31	condition	condition	NOUN
ejpam-5259	73	32	ℜe	ℜe	PROPN
ejpam-5259	73	33	{	{	PUNCT
ejpam-5259	73	34	ςℏ′′	ςℏ′′	PRON
ejpam-5259	73	35	(	(	PUNCT
ejpam-5259	73	36	ς	ς	NOUN
ejpam-5259	73	37	)	)	PUNCT
ejpam-5259	73	38	+	+	NUM
ejpam-5259	73	39	ℏ′	ℏ′	X
ejpam-5259	73	40	(	(	PUNCT
ejpam-5259	73	41	ς)−	ς)−	PROPN
ejpam-5259	73	42	ς	ς	PROPN
ejpam-5259	73	43	g′′(ς	g′′(ς	NOUN
ejpam-5259	73	44	)	)	PUNCT
ejpam-5259	73	45	+	+	CCONJ
ejpam-5259	73	46	g′(ς	g′(ς	X
ejpam-5259	73	47	)	)	PUNCT
ejpam-5259	73	48	ℏ′(ς	ℏ′(ς	PUNCT
ejpam-5259	73	49	)	)	PUNCT
ejpam-5259	74	1	+	+	CCONJ
ejpam-5259	74	2	g′(ς	g′(ς	X
ejpam-5259	74	3	)	)	PUNCT
ejpam-5259	74	4	}	}	PUNCT
ejpam-5259	74	5	>	>	X
ejpam-5259	74	6	0	0	NUM
ejpam-5259	74	7	,	,	PUNCT
ejpam-5259	74	8	(	(	PUNCT
ejpam-5259	74	9	z	z	NOUN
ejpam-5259	74	10	∈	∈	PROPN
ejpam-5259	74	11	♢	♢	NOUN
ejpam-5259	74	12	∗	∗	PROPN
ejpam-5259	74	13	)	)	PUNCT
ejpam-5259	74	14	.	.	PUNCT
ejpam-5259	75	1	the	the	DET
ejpam-5259	75	2	classes	class	NOUN
ejpam-5259	75	3	ms∗	ms∗	VERB
ejpam-5259	75	4	h	h	NOUN
ejpam-5259	75	5	and	and	CCONJ
ejpam-5259	75	6	mch	mch	PROPN
ejpam-5259	75	7	,	,	PUNCT
ejpam-5259	75	8	which	which	PRON
ejpam-5259	75	9	consist	consist	VERB
ejpam-5259	75	10	of	of	ADP
ejpam-5259	75	11	harmonic	harmonic	ADJ
ejpam-5259	75	12	meromorphic	meromorphic	ADJ
ejpam-5259	75	13	starlike	starlike	NOUN
ejpam-5259	75	14	functions	function	NOUN
ejpam-5259	75	15	and	and	CCONJ
ejpam-5259	75	16	harmonic	harmonic	VERB
ejpam-5259	75	17	meromorphic	meromorphic	ADJ
ejpam-5259	75	18	convex	convex	NOUN
ejpam-5259	75	19	functions	function	NOUN
ejpam-5259	75	20	,	,	PUNCT
ejpam-5259	75	21	have	have	AUX
ejpam-5259	75	22	been	be	AUX
ejpam-5259	75	23	the	the	DET
ejpam-5259	75	24	subject	subject	NOUN
ejpam-5259	75	25	of	of	ADP
ejpam-5259	75	26	study	study	NOUN
ejpam-5259	75	27	by	by	ADP
ejpam-5259	75	28	jahangiri	jahangiri	PROPN
ejpam-5259	75	29	and	and	CCONJ
ejpam-5259	75	30	silverman	silverman	NOUN
ejpam-5259	76	1	[	[	X
ejpam-5259	76	2	19	19	NUM
ejpam-5259	76	3	]	]	PUNCT
ejpam-5259	76	4	,	,	PUNCT
ejpam-5259	76	5	jahangiri	jahangiri	X
ejpam-5259	77	1	[	[	X
ejpam-5259	77	2	17	17	NUM
ejpam-5259	77	3	]	]	PUNCT
ejpam-5259	77	4	,	,	PUNCT
ejpam-5259	77	5	atshan	atshan	PROPN
ejpam-5259	77	6	and	and	CCONJ
ejpam-5259	77	7	joudah	joudah	PROPN
ejpam-5259	78	1	[	[	X
ejpam-5259	78	2	6	6	NUM
ejpam-5259	78	3	]	]	PUNCT
ejpam-5259	78	4	,	,	PUNCT
ejpam-5259	78	5	ghanem	ghanem	PROPN
ejpam-5259	78	6	and	and	CCONJ
ejpam-5259	78	7	al	al	PROPN
ejpam-5259	78	8	-	-	PUNCT
ejpam-5259	78	9	janaby	janaby	PROPN
ejpam-5259	79	1	[	[	X
ejpam-5259	79	2	15	15	NUM
ejpam-5259	79	3	]	]	PUNCT
ejpam-5259	79	4	,	,	PUNCT
ejpam-5259	79	5	elhaddad	elhaddad	ADJ
ejpam-5259	79	6	and	and	CCONJ
ejpam-5259	79	7	darus	darus	NOUN
ejpam-5259	79	8	[	[	X
ejpam-5259	79	9	14	14	NUM
ejpam-5259	79	10	]	]	PUNCT
ejpam-5259	79	11	and	and	CCONJ
ejpam-5259	79	12	alsoboh	alsoboh	PROPN
ejpam-5259	79	13	et	et	PROPN
ejpam-5259	79	14	al	al	PROPN
ejpam-5259	79	15	.	.	PUNCT
ejpam-5259	80	1	[	[	X
ejpam-5259	80	2	5	5	NUM
ejpam-5259	80	3	]	]	PUNCT
ejpam-5259	80	4	.	.	PUNCT
ejpam-5259	81	1	motivated	motivate	VERB
ejpam-5259	81	2	by	by	ADP
ejpam-5259	81	3	challab	challab	NOUN
ejpam-5259	81	4	and	and	CCONJ
ejpam-5259	81	5	darus	darus	NOUN
ejpam-5259	81	6	[	[	X
ejpam-5259	81	7	10	10	NUM
ejpam-5259	81	8	]	]	PUNCT
ejpam-5259	81	9	,	,	PUNCT
ejpam-5259	81	10	we	we	PRON
ejpam-5259	81	11	define	define	VERB
ejpam-5259	81	12	the	the	DET
ejpam-5259	81	13	linear	linear	ADJ
ejpam-5259	81	14	operator	operator	NOUN
ejpam-5259	81	15	for	for	ADP
ejpam-5259	81	16	the	the	DET
ejpam-5259	81	17	harmonic	harmonic	ADJ
ejpam-5259	81	18	meromorphic	meromorphic	ADJ
ejpam-5259	81	19	class	class	NOUN
ejpam-5259	81	20	of	of	ADP
ejpam-5259	81	21	functions	function	NOUN
ejpam-5259	81	22	f	f	PROPN
ejpam-5259	81	23	∈	∈	PROPN
ejpam-5259	81	24	mh	mh	PROPN
ejpam-5259	81	25	,	,	PUNCT
ejpam-5259	81	26	by	by	ADP
ejpam-5259	81	27	letting	let	VERB
ejpam-5259	81	28	k	k	PROPN
ejpam-5259	81	29	≥	≥	X
ejpam-5259	81	30	0	0	NUM
ejpam-5259	81	31	and	and	CCONJ
ejpam-5259	81	32	ik(sα	ik(sα	PROPN
ejpam-5259	81	33	η	η	PROPN
ejpam-5259	81	34	[	[	X
ejpam-5259	81	35	r	r	X
ejpam-5259	81	36	,	,	PUNCT
ejpam-5259	81	37	δ	δ	PROPN
ejpam-5259	81	38	,	,	PUNCT
ejpam-5259	81	39	λ])f(ς	λ])f(ς	ADJ
ejpam-5259	81	40	)	)	PUNCT
ejpam-5259	81	41	=	=	SYM
ejpam-5259	81	42	ik(sα	ik(sα	PROPN
ejpam-5259	81	43	η	η	PROPN
ejpam-5259	82	1	[	[	X
ejpam-5259	82	2	r	r	X
ejpam-5259	82	3	,	,	PUNCT
ejpam-5259	82	4	δ	δ	PROPN
ejpam-5259	82	5	,	,	PUNCT
ejpam-5259	82	6	λ])ℏ(ς	λ])ℏ(ς	ADJ
ejpam-5259	82	7	)	)	PUNCT
ejpam-5259	83	1	+	+	CCONJ
ejpam-5259	83	2	(	(	PUNCT
ejpam-5259	83	3	−1)kik(sα	−1)kik(sα	PROPN
ejpam-5259	83	4	η	η	PROPN
ejpam-5259	83	5	[	[	X
ejpam-5259	83	6	r	r	X
ejpam-5259	83	7	,	,	PUNCT
ejpam-5259	83	8	δ	δ	PROPN
ejpam-5259	83	9	,	,	PUNCT
ejpam-5259	83	10	λ])g(ς	λ])g(ς	PROPN
ejpam-5259	83	11	)	)	PUNCT
ejpam-5259	83	12	,	,	PUNCT
ejpam-5259	83	13	(	(	PUNCT
ejpam-5259	83	14	9	9	X
ejpam-5259	83	15	)	)	PUNCT
ejpam-5259	83	16	where	where	SCONJ
ejpam-5259	83	17	ik(sα	ik(sα	PROPN
ejpam-5259	83	18	η	η	PROPN
ejpam-5259	83	19	[	[	X
ejpam-5259	83	20	r	r	X
ejpam-5259	83	21	,	,	PUNCT
ejpam-5259	83	22	δ	δ	PROPN
ejpam-5259	83	23	,	,	PUNCT
ejpam-5259	83	24	λ])ℏ(ς	λ])ℏ(ς	ADJ
ejpam-5259	83	25	)	)	PUNCT
ejpam-5259	83	26	=	=	PUNCT
ejpam-5259	83	27	(	(	PUNCT
ejpam-5259	83	28	−1)k	−1)k	PROPN
ejpam-5259	83	29	ς	ς	PROPN
ejpam-5259	83	30	+	+	PROPN
ejpam-5259	83	31	∞∑	∞∑	NUM
ejpam-5259	83	32	µ=1	µ=1	PROPN
ejpam-5259	83	33	γ(η)[1	γ(η)[1	X
ejpam-5259	83	34	+	+	PUNCT
ejpam-5259	83	35	λ(µ−	λ(µ−	VERB
ejpam-5259	83	36	1)]k	1)]k	NUM
ejpam-5259	83	37	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	83	38	1	1	NUM
ejpam-5259	83	39	)	)	PUNCT
ejpam-5259	83	40	+	+	NUM
ejpam-5259	83	41	η	η	X
ejpam-5259	83	42	)	)	PUNCT
ejpam-5259	83	43	(	(	PUNCT
ejpam-5259	83	44	µ+	µ+	X
ejpam-5259	83	45	δ	δ	PROPN
ejpam-5259	83	46	1	1	NUM
ejpam-5259	83	47	+	+	CCONJ
ejpam-5259	83	48	δ	δ	NOUN
ejpam-5259	83	49	)	)	PUNCT
ejpam-5259	83	50	r	r	NOUN
ejpam-5259	83	51	aµς	aµς	NOUN
ejpam-5259	83	52	µ	µ	NOUN
ejpam-5259	83	53	,	,	PUNCT
ejpam-5259	83	54	(	(	PUNCT
ejpam-5259	83	55	10	10	NUM
ejpam-5259	83	56	)	)	PUNCT
ejpam-5259	83	57	and	and	CCONJ
ejpam-5259	83	58	ik(sα	ik(sα	PROPN
ejpam-5259	83	59	η	η	PROPN
ejpam-5259	84	1	[	[	X
ejpam-5259	84	2	r	r	X
ejpam-5259	84	3	,	,	PUNCT
ejpam-5259	84	4	δ	δ	PROPN
ejpam-5259	84	5	,	,	PUNCT
ejpam-5259	84	6	λ])g(ς	λ])g(ς	ADJ
ejpam-5259	84	7	)	)	PUNCT
ejpam-5259	84	8	=	=	PUNCT
ejpam-5259	85	1	∞∑	∞∑	PRON
ejpam-5259	85	2	µ=1	µ=1	SYM
ejpam-5259	85	3	γ(η)[1	γ(η)[1	X
ejpam-5259	85	4	+	+	PUNCT
ejpam-5259	85	5	λ(µ−	λ(µ−	VERB
ejpam-5259	85	6	1)]k	1)]k	NUM
ejpam-5259	85	7	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	85	8	1	1	NUM
ejpam-5259	85	9	)	)	PUNCT
ejpam-5259	85	10	+	+	NUM
ejpam-5259	85	11	η	η	X
ejpam-5259	85	12	)	)	PUNCT
ejpam-5259	85	13	(	(	PUNCT
ejpam-5259	85	14	µ+	µ+	X
ejpam-5259	85	15	δ	δ	PROPN
ejpam-5259	85	16	1	1	NUM
ejpam-5259	85	17	+	+	CCONJ
ejpam-5259	85	18	δ	δ	NOUN
ejpam-5259	85	19	)	)	PUNCT
ejpam-5259	85	20	r	r	NOUN
ejpam-5259	85	21	bµς	bµς	PROPN
ejpam-5259	85	22	µ.	µ.	NOUN
ejpam-5259	85	23	(	(	PUNCT
ejpam-5259	85	24	11	11	NUM
ejpam-5259	85	25	)	)	PUNCT
ejpam-5259	85	26	utilising	utilise	VERB
ejpam-5259	85	27	the	the	DET
ejpam-5259	85	28	operator	operator	NOUN
ejpam-5259	85	29	ik(sα	ik(sα	PROPN
ejpam-5259	85	30	η	η	PROPN
ejpam-5259	86	1	[	[	X
ejpam-5259	86	2	r	r	X
ejpam-5259	86	3	,	,	PUNCT
ejpam-5259	86	4	δ	δ	PROPN
ejpam-5259	86	5	,	,	PUNCT
ejpam-5259	86	6	λ	λ	PROPN
ejpam-5259	86	7	]	]	NOUN
ejpam-5259	86	8	)	)	PUNCT
ejpam-5259	86	9	,	,	PUNCT
ejpam-5259	86	10	we	we	PRON
ejpam-5259	86	11	introduce	introduce	VERB
ejpam-5259	86	12	a	a	DET
ejpam-5259	86	13	class	class	NOUN
ejpam-5259	86	14	of	of	ADP
ejpam-5259	86	15	generalised	generalise	VERB
ejpam-5259	86	16	harmonic	harmonic	NOUN
ejpam-5259	86	17	meromorphically	meromorphically	ADV
ejpam-5259	86	18	starlike	starlike	NOUN
ejpam-5259	86	19	functions	function	NOUN
ejpam-5259	86	20	within	within	ADP
ejpam-5259	86	21	the	the	DET
ejpam-5259	86	22	region	region	NOUN
ejpam-5259	86	23	♢	♢	PROPN
ejpam-5259	86	24	∗	∗	NOUN
ejpam-5259	86	25	through	through	ADP
ejpam-5259	86	26	the	the	DET
ejpam-5259	86	27	following	follow	VERB
ejpam-5259	86	28	definition	definition	NOUN
ejpam-5259	86	29	.	.	PUNCT
ejpam-5259	87	1	s.	s.	PROPN
ejpam-5259	87	2	ahmed	ahmed	PROPN
ejpam-5259	87	3	,	,	PUNCT
ejpam-5259	87	4	a.	a.	PROPN
ejpam-5259	87	5	alsoboh	alsoboh	PROPN
ejpam-5259	87	6	,	,	PUNCT
ejpam-5259	87	7	m.	m.	NOUN
ejpam-5259	87	8	darus	darus	NOUN
ejpam-5259	87	9	/	/	SYM
ejpam-5259	87	10	eur	eur	PROPN
ejpam-5259	87	11	.	.	PUNCT
ejpam-5259	88	1	j.	j.	PROPN
ejpam-5259	88	2	pure	pure	PROPN
ejpam-5259	88	3	appl	appl	PROPN
ejpam-5259	88	4	.	.	PROPN
ejpam-5259	88	5	math	math	PROPN
ejpam-5259	88	6	,	,	PUNCT
ejpam-5259	88	7	17	17	NUM
ejpam-5259	88	8	(	(	PUNCT
ejpam-5259	88	9	3	3	NUM
ejpam-5259	88	10	)	)	PUNCT
ejpam-5259	88	11	(	(	PUNCT
ejpam-5259	88	12	2024	2024	NUM
ejpam-5259	88	13	)	)	PUNCT
ejpam-5259	88	14	,	,	PUNCT
ejpam-5259	88	15	1894	1894	NUM
ejpam-5259	88	16	-	-	SYM
ejpam-5259	88	17	1907	1907	NUM
ejpam-5259	88	18	1898	1898	NUM
ejpam-5259	88	19	definition	definition	NOUN
ejpam-5259	88	20	1	1	NUM
ejpam-5259	88	21	.	.	PUNCT
ejpam-5259	89	1	for	for	ADP
ejpam-5259	89	2	0	0	NUM
ejpam-5259	89	3	≤	≤	NUM
ejpam-5259	89	4	γ	γ	X
ejpam-5259	89	5	<	<	X
ejpam-5259	89	6	1	1	NUM
ejpam-5259	89	7	,	,	PUNCT
ejpam-5259	89	8	the	the	DET
ejpam-5259	89	9	class	class	NOUN
ejpam-5259	89	10	mkh(k	mkh(k	PROPN
ejpam-5259	89	11	,	,	PUNCT
ejpam-5259	89	12	r	r	NOUN
ejpam-5259	89	13	,	,	PUNCT
ejpam-5259	89	14	α	α	PROPN
ejpam-5259	89	15	,	,	PUNCT
ejpam-5259	89	16	η	η	PROPN
ejpam-5259	89	17	,	,	PUNCT
ejpam-5259	89	18	δ	δ	PROPN
ejpam-5259	89	19	,	,	PUNCT
ejpam-5259	89	20	λ	λ	PROPN
ejpam-5259	89	21	,	,	PUNCT
ejpam-5259	89	22	γ	γ	NOUN
ejpam-5259	89	23	)	)	PUNCT
ejpam-5259	89	24	is	be	AUX
ejpam-5259	89	25	used	use	VERB
ejpam-5259	89	26	to	to	PART
ejpam-5259	89	27	denote	denote	VERB
ejpam-5259	89	28	harmonic	harmonic	ADJ
ejpam-5259	89	29	meromorphic	meromorphic	ADJ
ejpam-5259	89	30	functions	function	NOUN
ejpam-5259	89	31	f	f	PRON
ejpam-5259	89	32	defined	define	VERB
ejpam-5259	89	33	as	as	ADP
ejpam-5259	89	34	in	in	ADP
ejpam-5259	89	35	(	(	PUNCT
ejpam-5259	89	36	1	1	NUM
ejpam-5259	89	37	)	)	PUNCT
ejpam-5259	89	38	,	,	PUNCT
ejpam-5259	89	39	and	and	CCONJ
ejpam-5259	89	40	belonging	belong	VERB
ejpam-5259	89	41	to	to	ADP
ejpam-5259	89	42	this	this	DET
ejpam-5259	89	43	class	class	NOUN
ejpam-5259	89	44	is	be	AUX
ejpam-5259	89	45	upon	upon	SCONJ
ejpam-5259	89	46	the	the	DET
ejpam-5259	89	47	satisfaction	satisfaction	NOUN
ejpam-5259	89	48	of	of	ADP
ejpam-5259	89	49	the	the	DET
ejpam-5259	89	50	condition	condition	NOUN
ejpam-5259	89	51	:	:	PUNCT
ejpam-5259	90	1	re	re	X
ejpam-5259	90	2	{	{	PUNCT
ejpam-5259	90	3	−	−	PROPN
ejpam-5259	90	4	ς(ik(sα	ς(ik(sα	PROPN
ejpam-5259	90	5	η	η	PROPN
ejpam-5259	90	6	[	[	X
ejpam-5259	90	7	r	r	PROPN
ejpam-5259	90	8	,	,	PUNCT
ejpam-5259	90	9	δ	δ	PROPN
ejpam-5259	90	10	,	,	PUNCT
ejpam-5259	90	11	λ])ℏ(ς))′	λ])ℏ(ς))′	PROPN
ejpam-5259	90	12	−	−	PROPN
ejpam-5259	90	13	ς(ik(sα	ς(ik(sα	PROPN
ejpam-5259	90	14	η	η	PROPN
ejpam-5259	91	1	[	[	X
ejpam-5259	91	2	r	r	PROPN
ejpam-5259	91	3	,	,	PUNCT
ejpam-5259	91	4	δ	δ	PROPN
ejpam-5259	91	5	,	,	PUNCT
ejpam-5259	91	6	λ])g(ς	λ])g(ς	PROPN
ejpam-5259	91	7	)	)	PUNCT
ejpam-5259	91	8	)	)	PUNCT
ejpam-5259	92	1	′	′	NUM
ejpam-5259	93	1	ik(sα	ik(sα	PROPN
ejpam-5259	93	2	η	η	PROPN
ejpam-5259	94	1	[	[	X
ejpam-5259	94	2	r	r	X
ejpam-5259	94	3	,	,	PUNCT
ejpam-5259	94	4	δ	δ	PROPN
ejpam-5259	94	5	,	,	PUNCT
ejpam-5259	94	6	λ])ℏ(ς	λ])ℏ(ς	ADJ
ejpam-5259	94	7	)	)	PUNCT
ejpam-5259	94	8	+	+	CCONJ
ejpam-5259	94	9	ik(sα	ik(sα	PROPN
ejpam-5259	94	10	η	η	X
ejpam-5259	95	1	[	[	X
ejpam-5259	95	2	r	r	X
ejpam-5259	95	3	,	,	PUNCT
ejpam-5259	95	4	δ	δ	PROPN
ejpam-5259	95	5	,	,	PUNCT
ejpam-5259	95	6	λ])g(ς	λ])g(ς	PROPN
ejpam-5259	95	7	)	)	PUNCT
ejpam-5259	95	8	}	}	PUNCT
ejpam-5259	96	1	>	>	X
ejpam-5259	96	2	γ	γ	X
ejpam-5259	96	3	,	,	PUNCT
ejpam-5259	96	4	(	(	PUNCT
ejpam-5259	96	5	ς	ς	PROPN
ejpam-5259	96	6	∈	∈	PROPN
ejpam-5259	96	7	♢	♢	PROPN
ejpam-5259	96	8	∗	∗	PROPN
ejpam-5259	96	9	)	)	PUNCT
ejpam-5259	96	10	.	.	PUNCT
ejpam-5259	97	1	(	(	PUNCT
ejpam-5259	97	2	12	12	NUM
ejpam-5259	97	3	)	)	PUNCT
ejpam-5259	97	4	furthermore	furthermore	ADV
ejpam-5259	97	5	,	,	PUNCT
ejpam-5259	97	6	by	by	ADP
ejpam-5259	97	7	t	t	PROPN
ejpam-5259	97	8	mkh(k	mkh(k	PROPN
ejpam-5259	97	9	,	,	PUNCT
ejpam-5259	97	10	r	r	NOUN
ejpam-5259	97	11	,	,	PUNCT
ejpam-5259	97	12	α	α	PROPN
ejpam-5259	97	13	,	,	PUNCT
ejpam-5259	97	14	η	η	PROPN
ejpam-5259	97	15	,	,	PUNCT
ejpam-5259	97	16	δ	δ	PROPN
ejpam-5259	97	17	,	,	PUNCT
ejpam-5259	97	18	λ	λ	PROPN
ejpam-5259	97	19	,	,	PUNCT
ejpam-5259	97	20	γ	γ	PROPN
ejpam-5259	97	21	)	)	PUNCT
ejpam-5259	97	22	⊂	⊂	PROPN
ejpam-5259	97	23	mkh(k	mkh(k	PROPN
ejpam-5259	97	24	,	,	PUNCT
ejpam-5259	97	25	r	r	PROPN
ejpam-5259	97	26	,	,	PUNCT
ejpam-5259	97	27	α	α	PROPN
ejpam-5259	97	28	,	,	PUNCT
ejpam-5259	97	29	η	η	PROPN
ejpam-5259	97	30	,	,	PUNCT
ejpam-5259	97	31	δ	δ	PROPN
ejpam-5259	97	32	,	,	PUNCT
ejpam-5259	97	33	λ	λ	PROPN
ejpam-5259	97	34	,	,	PUNCT
ejpam-5259	97	35	γ	γ	NOUN
ejpam-5259	97	36	)	)	PUNCT
ejpam-5259	97	37	,	,	PUNCT
ejpam-5259	97	38	we	we	PRON
ejpam-5259	97	39	denote	denote	VERB
ejpam-5259	97	40	the	the	DET
ejpam-5259	97	41	subclass	subclass	NOUN
ejpam-5259	97	42	of	of	ADP
ejpam-5259	97	43	harmonic	harmonic	ADJ
ejpam-5259	97	44	meromorphic	meromorphic	ADJ
ejpam-5259	97	45	functions	function	NOUN
ejpam-5259	97	46	fk	fk	INTJ
ejpam-5259	97	47	=	=	PUNCT
ejpam-5259	97	48	ℏk	ℏk	ADP
ejpam-5259	97	49	+	+	CCONJ
ejpam-5259	97	50	gk(ς	gk(ς	NOUN
ejpam-5259	97	51	)	)	PUNCT
ejpam-5259	97	52	where	where	SCONJ
ejpam-5259	97	53	ℏk	ℏk	ADP
ejpam-5259	97	54	and	and	CCONJ
ejpam-5259	97	55	gk	gk	PROPN
ejpam-5259	97	56	of	of	ADP
ejpam-5259	97	57	the	the	DET
ejpam-5259	97	58	form	form	NOUN
ejpam-5259	97	59	ℏk(ς	ℏk(ς	PUNCT
ejpam-5259	97	60	)	)	PUNCT
ejpam-5259	97	61	=	=	SYM
ejpam-5259	97	62	(	(	PUNCT
ejpam-5259	97	63	−1)k	−1)k	PROPN
ejpam-5259	97	64	ς	ς	PROPN
ejpam-5259	98	1	+	+	PUNCT
ejpam-5259	98	2	∞∑	∞∑	NUM
ejpam-5259	98	3	µ=1	µ=1	ADP
ejpam-5259	98	4	|aµ|ςµ	|aµ|ςµ	NUM
ejpam-5259	98	5	and	and	CCONJ
ejpam-5259	98	6	gk(ς	gk(ς	NOUN
ejpam-5259	98	7	)	)	PUNCT
ejpam-5259	98	8	=	=	PUNCT
ejpam-5259	99	1	(	(	PUNCT
ejpam-5259	99	2	−1)k	−1)k	PROPN
ejpam-5259	99	3	∞∑	∞∑	NUM
ejpam-5259	99	4	µ=1	µ=1	ADV
ejpam-5259	99	5	|bµ|ςµ	|bµ|ςµ	PUNCT
ejpam-5259	99	6	,	,	PUNCT
ejpam-5259	99	7	(	(	PUNCT
ejpam-5259	99	8	z	z	PROPN
ejpam-5259	99	9	∈	∈	PROPN
ejpam-5259	99	10	♢	♢	NOUN
ejpam-5259	99	11	∗	∗	PROPN
ejpam-5259	99	12	)	)	PUNCT
ejpam-5259	99	13	.	.	PUNCT
ejpam-5259	100	1	(	(	PUNCT
ejpam-5259	100	2	13	13	NUM
ejpam-5259	100	3	)	)	SYM
ejpam-5259	100	4	2	2	NUM
ejpam-5259	100	5	.	.	PUNCT
ejpam-5259	100	6	coefficient	coefficient	NOUN
ejpam-5259	100	7	inequalities	inequality	NOUN
ejpam-5259	100	8	in	in	ADP
ejpam-5259	100	9	our	our	PRON
ejpam-5259	100	10	initial	initial	ADJ
ejpam-5259	100	11	theorem	theorem	NOUN
ejpam-5259	100	12	,	,	PUNCT
ejpam-5259	100	13	we	we	PRON
ejpam-5259	100	14	establish	establish	VERB
ejpam-5259	100	15	the	the	DET
ejpam-5259	100	16	sufficient	sufficient	ADJ
ejpam-5259	100	17	coefficient	coefficient	NOUN
ejpam-5259	100	18	bounds	bound	NOUN
ejpam-5259	100	19	applicable	applicable	ADJ
ejpam-5259	100	20	to	to	ADP
ejpam-5259	100	21	functions	function	VERB
ejpam-5259	100	22	f	f	PROPN
ejpam-5259	100	23	within	within	ADP
ejpam-5259	100	24	the	the	DET
ejpam-5259	100	25	class	class	NOUN
ejpam-5259	100	26	t	t	PROPN
ejpam-5259	100	27	mkh(k	mkh(k	PROPN
ejpam-5259	100	28	,	,	PUNCT
ejpam-5259	100	29	r	r	NOUN
ejpam-5259	100	30	,	,	PUNCT
ejpam-5259	100	31	α	α	PROPN
ejpam-5259	100	32	,	,	PUNCT
ejpam-5259	100	33	η	η	PROPN
ejpam-5259	100	34	,	,	PUNCT
ejpam-5259	100	35	δ	δ	PROPN
ejpam-5259	100	36	,	,	PUNCT
ejpam-5259	100	37	λ	λ	PROPN
ejpam-5259	100	38	,	,	PUNCT
ejpam-5259	100	39	γ	γ	NOUN
ejpam-5259	100	40	)	)	PUNCT
ejpam-5259	100	41	.	.	PUNCT
ejpam-5259	101	1	theorem	theorem	NOUN
ejpam-5259	101	2	1	1	NUM
ejpam-5259	101	3	.	.	PUNCT
ejpam-5259	102	1	for	for	ADP
ejpam-5259	102	2	0	0	NUM
ejpam-5259	102	3	≤	≤	NUM
ejpam-5259	102	4	γ	γ	X
ejpam-5259	102	5	<	<	X
ejpam-5259	102	6	1	1	NUM
ejpam-5259	102	7	,	,	PUNCT
ejpam-5259	102	8	consider	consider	VERB
ejpam-5259	102	9	the	the	DET
ejpam-5259	102	10	function	function	NOUN
ejpam-5259	102	11	f	f	PROPN
ejpam-5259	102	12	=	=	SYM
ejpam-5259	102	13	ℏ	ℏ	PROPN
ejpam-5259	102	14	+	+	CCONJ
ejpam-5259	102	15	g	g	NOUN
ejpam-5259	102	16	defined	define	VERB
ejpam-5259	102	17	by	by	ADP
ejpam-5259	102	18	(	(	PUNCT
ejpam-5259	102	19	7	7	NUM
ejpam-5259	102	20	)	)	PUNCT
ejpam-5259	102	21	,	,	PUNCT
ejpam-5259	102	22	subject	subject	ADJ
ejpam-5259	102	23	to	to	ADP
ejpam-5259	102	24	the	the	DET
ejpam-5259	102	25	condition	condition	NOUN
ejpam-5259	103	1	∞∑	∞∑	ADP
ejpam-5259	103	2	µ=1	µ=1	PUNCT
ejpam-5259	103	3	γ(η)[1	γ(η)[1	X
ejpam-5259	103	4	+	+	PUNCT
ejpam-5259	103	5	λ(µ−	λ(µ−	VERB
ejpam-5259	103	6	1)]k	1)]k	NUM
ejpam-5259	103	7	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	103	8	1	1	NUM
ejpam-5259	103	9	)	)	PUNCT
ejpam-5259	103	10	+	+	NUM
ejpam-5259	103	11	η	η	X
ejpam-5259	103	12	)	)	PUNCT
ejpam-5259	103	13	(	(	PUNCT
ejpam-5259	103	14	µ+	µ+	X
ejpam-5259	103	15	δ	δ	PROPN
ejpam-5259	103	16	1	1	NUM
ejpam-5259	103	17	+	+	CCONJ
ejpam-5259	103	18	δ	δ	NOUN
ejpam-5259	103	19	)	)	PUNCT
ejpam-5259	103	20	r	r	NOUN
ejpam-5259	103	21	[	[	PUNCT
ejpam-5259	103	22	(	(	PUNCT
ejpam-5259	103	23	µ+	µ+	X
ejpam-5259	103	24	γ	γ	NOUN
ejpam-5259	103	25	)	)	PUNCT
ejpam-5259	103	26	|aµ|+	|aµ|+	PROPN
ejpam-5259	103	27	(	(	PUNCT
ejpam-5259	103	28	µ−	µ−	PROPN
ejpam-5259	103	29	γ	γ	PROPN
ejpam-5259	103	30	)	)	PUNCT
ejpam-5259	103	31	|bµ|	|bµ|	NOUN
ejpam-5259	103	32	]	]	PUNCT
ejpam-5259	104	1	≤	≤	PROPN
ejpam-5259	104	2	1−	1−	NUM
ejpam-5259	104	3	γ	γ	X
ejpam-5259	104	4	,	,	PUNCT
ejpam-5259	104	5	where	where	SCONJ
ejpam-5259	104	6	µ	µ	X
ejpam-5259	104	7	∈	∈	NOUN
ejpam-5259	104	8	0	0	NUM
ejpam-5259	104	9	,	,	PUNCT
ejpam-5259	104	10	1	1	NUM
ejpam-5259	104	11	,	,	PUNCT
ejpam-5259	104	12	2	2	NUM
ejpam-5259	104	13	,	,	PUNCT
ejpam-5259	104	14	.	.	PUNCT
ejpam-5259	104	15	.	.	PUNCT
ejpam-5259	104	16	.	.	PUNCT
ejpam-5259	104	17	.	.	PUNCT
ejpam-5259	105	1	then	then	ADV
ejpam-5259	105	2	,	,	PUNCT
ejpam-5259	105	3	f	f	PROPN
ejpam-5259	105	4	is	be	AUX
ejpam-5259	105	5	harmonic	harmonic	ADJ
ejpam-5259	105	6	univalent	univalent	ADJ
ejpam-5259	105	7	and	and	CCONJ
ejpam-5259	105	8	sense	sense	NOUN
ejpam-5259	105	9	-	-	PUNCT
ejpam-5259	105	10	preserving	preserve	VERB
ejpam-5259	105	11	in	in	ADP
ejpam-5259	105	12	♢	♢	PROPN
ejpam-5259	105	13	∗	∗	NOUN
ejpam-5259	105	14	,	,	PUNCT
ejpam-5259	105	15	and	and	CCONJ
ejpam-5259	105	16	f	f	PROPN
ejpam-5259	105	17	∈	∈	PROPN
ejpam-5259	105	18	t	t	PROPN
ejpam-5259	105	19	mkh(k	mkh(k	PROPN
ejpam-5259	105	20	,	,	PUNCT
ejpam-5259	105	21	r	r	NOUN
ejpam-5259	105	22	,	,	PUNCT
ejpam-5259	105	23	α	α	PROPN
ejpam-5259	105	24	,	,	PUNCT
ejpam-5259	105	25	η	η	PROPN
ejpam-5259	105	26	,	,	PUNCT
ejpam-5259	105	27	δ	δ	PROPN
ejpam-5259	105	28	,	,	PUNCT
ejpam-5259	105	29	λ	λ	PROPN
ejpam-5259	105	30	,	,	PUNCT
ejpam-5259	105	31	γ	γ	NOUN
ejpam-5259	105	32	)	)	PUNCT
ejpam-5259	105	33	.	.	PUNCT
ejpam-5259	106	1	proof	proof	NOUN
ejpam-5259	106	2	.	.	PUNCT
ejpam-5259	107	1	consider	consider	VERB
ejpam-5259	107	2	the	the	DET
ejpam-5259	107	3	function	function	NOUN
ejpam-5259	107	4	f	f	PROPN
ejpam-5259	108	1	=	=	PUNCT
ejpam-5259	108	2	ℏ+	ℏ+	VERB
ejpam-5259	108	3	g	g	NOUN
ejpam-5259	108	4	as	as	SCONJ
ejpam-5259	108	5	defined	define	VERB
ejpam-5259	108	6	in	in	ADP
ejpam-5259	108	7	equation	equation	NOUN
ejpam-5259	108	8	(	(	PUNCT
ejpam-5259	108	9	7	7	NUM
ejpam-5259	108	10	)	)	PUNCT
ejpam-5259	108	11	,	,	PUNCT
ejpam-5259	108	12	which	which	PRON
ejpam-5259	108	13	satisfies	satisfy	VERB
ejpam-5259	108	14	the	the	DET
ejpam-5259	108	15	inequality	inequality	NOUN
ejpam-5259	108	16	given	give	VERB
ejpam-5259	108	17	in	in	ADP
ejpam-5259	108	18	equation	equation	NOUN
ejpam-5259	108	19	(	(	PUNCT
ejpam-5259	108	20	1	1	NUM
ejpam-5259	108	21	)	)	PUNCT
ejpam-5259	108	22	.	.	PUNCT
ejpam-5259	109	1	assuming	assume	VERB
ejpam-5259	109	2	that	that	SCONJ
ejpam-5259	109	3	0	0	NUM
ejpam-5259	109	4	<	<	X
ejpam-5259	109	5	|ς1|	|ς1|	PROPN
ejpam-5259	109	6	≤	≤	PROPN
ejpam-5259	109	7	|ς2|	|ς2|	VERB
ejpam-5259	109	8	<	<	X
ejpam-5259	109	9	1	1	NUM
ejpam-5259	109	10	,	,	PUNCT
ejpam-5259	109	11	we	we	PRON
ejpam-5259	109	12	can	can	AUX
ejpam-5259	109	13	conclude	conclude	VERB
ejpam-5259	109	14	that	that	PRON
ejpam-5259	109	15	∣∣f(ς1)−	∣∣f(ς1)−	PROPN
ejpam-5259	109	16	f(ς2	f(ς2	NOUN
ejpam-5259	109	17	)	)	PUNCT
ejpam-5259	109	18	∣∣	∣∣	NUM
ejpam-5259	109	19	≥	≥	X
ejpam-5259	109	20	|ς1	|ς1	PROPN
ejpam-5259	109	21	−	−	PROPN
ejpam-5259	109	22	ς2|	ς2|	NOUN
ejpam-5259	109	23	|ς1ς2|	|ς1ς2|	ADP
ejpam-5259	109	24	1−	1−	NOUN
ejpam-5259	109	25	|ς2|2	|ς2|2	PUNCT
ejpam-5259	109	26	∞∑	∞∑	NUM
ejpam-5259	109	27	µ=1	µ=1	SYM
ejpam-5259	109	28	(	(	PUNCT
ejpam-5259	109	29	|aµ|+	|aµ|+	PROPN
ejpam-5259	109	30	|bµ|	|bµ|	NOUN
ejpam-5259	109	31	)	)	PUNCT
ejpam-5259	109	32	|ς1µ	|ς1µ	NOUN
ejpam-5259	109	33	−	−	PROPN
ejpam-5259	109	34	ς2	ς2	PROPN
ejpam-5259	109	35	µ|	µ|	PROPN
ejpam-5259	109	36	|ς1	|ς1	NOUN
ejpam-5259	109	37	−	−	PROPN
ejpam-5259	109	38	ς2|	ς2|	NOUN
ejpam-5259	109	39			PROPN
ejpam-5259	109	40	≥	≥	NOUN
ejpam-5259	109	41	|ς1	|ς1	NOUN
ejpam-5259	109	42	−	−	PROPN
ejpam-5259	109	43	ς2|	ς2|	NOUN
ejpam-5259	109	44	|ς1ς2|	|ς1ς2|	ADP
ejpam-5259	109	45	1−	1−	NOUN
ejpam-5259	109	46	|ς2|2	|ς2|2	PUNCT
ejpam-5259	109	47	∞∑	∞∑	NUM
ejpam-5259	109	48	µ=1	µ=1	SYM
ejpam-5259	109	49	(	(	PUNCT
ejpam-5259	109	50	|aµ|+	|aµ|+	PROPN
ejpam-5259	109	51	|bµ|	|bµ|	NOUN
ejpam-5259	109	52	)	)	PUNCT
ejpam-5259	109	53	∣∣∣ςµ−1	∣∣∣ςµ−1	NOUN
ejpam-5259	109	54	1	1	NUM
ejpam-5259	109	55	+	+	CCONJ
ejpam-5259	109	56	·	·	PUNCT
ejpam-5259	109	57	·	·	PUNCT
ejpam-5259	109	58	·	·	PUNCT
ejpam-5259	110	1	+	+	NUM
ejpam-5259	110	2	ςµ−1	ςµ−1	NOUN
ejpam-5259	110	3	2	2	NUM
ejpam-5259	110	4	∣∣∣	∣∣∣	NOUN
ejpam-5259	110	5			PROPN
ejpam-5259	110	6	≥	≥	NOUN
ejpam-5259	110	7	|ς1	|ς1	NOUN
ejpam-5259	110	8	−	−	PROPN
ejpam-5259	110	9	ς2|	ς2|	NOUN
ejpam-5259	110	10	|ς1ς2|	|ς1ς2|	ADP
ejpam-5259	110	11	1−	1−	NOUN
ejpam-5259	110	12	|ς2|2	|ς2|2	X
ejpam-5259	110	13	∞∑	∞∑	NUM
ejpam-5259	110	14	µ=1	µ=1	PROPN
ejpam-5259	110	15	γ(η)[1	γ(η)[1	X
ejpam-5259	110	16	+	+	PUNCT
ejpam-5259	110	17	λ(µ−	λ(µ−	VERB
ejpam-5259	110	18	1)]k	1)]k	NUM
ejpam-5259	110	19	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	110	20	1	1	NUM
ejpam-5259	110	21	)	)	PUNCT
ejpam-5259	110	22	+	+	NUM
ejpam-5259	110	23	η	η	X
ejpam-5259	110	24	)	)	PUNCT
ejpam-5259	110	25	(	(	PUNCT
ejpam-5259	110	26	µ+	µ+	X
ejpam-5259	110	27	δ	δ	PROPN
ejpam-5259	110	28	1	1	NUM
ejpam-5259	110	29	+	+	NUM
ejpam-5259	110	30	δ	δ	NOUN
ejpam-5259	110	31	)	)	PUNCT
ejpam-5259	110	32	r	r	NOUN
ejpam-5259	110	33	µ(|aµ|+	µ(|aµ|+	PROPN
ejpam-5259	110	34	|bµ|	|bµ|	PROPN
ejpam-5259	110	35	)	)	PUNCT
ejpam-5259	111	1			PROPN
ejpam-5259	111	2	>	>	X
ejpam-5259	111	3	|ς1	|ς1	PROPN
ejpam-5259	111	4	−	−	PROPN
ejpam-5259	111	5	ς2|	ς2|	NOUN
ejpam-5259	111	6	(	(	PUNCT
ejpam-5259	111	7	1−	1−	NUM
ejpam-5259	111	8	∞∑	∞∑	NUM
ejpam-5259	111	9	µ=1	µ=1	PUNCT
ejpam-5259	111	10	γ(η)[1+λ(µ−1)]k	γ(η)[1+λ(µ−1)]k	X
ejpam-5259	111	11	γ(α(µ+1)+η	γ(α(µ+1)+η	NUM
ejpam-5259	111	12	)	)	PUNCT
ejpam-5259	112	1	(	(	PUNCT
ejpam-5259	112	2	µ+δ	µ+δ	NUM
ejpam-5259	112	3	1+δ	1+δ	NUM
ejpam-5259	112	4	)	)	PUNCT
ejpam-5259	112	5	r	r	NOUN
ejpam-5259	112	6	{	{	PUNCT
ejpam-5259	112	7	(	(	PUNCT
ejpam-5259	112	8	µ+γ	µ+γ	NUM
ejpam-5259	112	9	1−γ	1−γ	NUM
ejpam-5259	112	10	)	)	PUNCT
ejpam-5259	112	11	|aµ|+	|aµ|+	ADP
ejpam-5259	112	12	(	(	PUNCT
ejpam-5259	112	13	µ+γ	µ+γ	NUM
ejpam-5259	112	14	1−γ	1−γ	NUM
ejpam-5259	112	15	)	)	PUNCT
ejpam-5259	112	16	|bµ|	|bµ|	NOUN
ejpam-5259	112	17	}	}	PUNCT
ejpam-5259	112	18	)	)	PUNCT
ejpam-5259	112	19	.	.	PUNCT
ejpam-5259	113	1	s.	s.	PROPN
ejpam-5259	113	2	ahmed	ahmed	PROPN
ejpam-5259	113	3	,	,	PUNCT
ejpam-5259	113	4	a.	a.	PROPN
ejpam-5259	113	5	alsoboh	alsoboh	PROPN
ejpam-5259	113	6	,	,	PUNCT
ejpam-5259	113	7	m.	m.	NOUN
ejpam-5259	113	8	darus	darus	NOUN
ejpam-5259	113	9	/	/	SYM
ejpam-5259	113	10	eur	eur	PROPN
ejpam-5259	113	11	.	.	PUNCT
ejpam-5259	114	1	j.	j.	PROPN
ejpam-5259	114	2	pure	pure	PROPN
ejpam-5259	114	3	appl	appl	PROPN
ejpam-5259	114	4	.	.	PROPN
ejpam-5259	114	5	math	math	PROPN
ejpam-5259	114	6	,	,	PUNCT
ejpam-5259	114	7	17	17	NUM
ejpam-5259	114	8	(	(	PUNCT
ejpam-5259	114	9	3	3	NUM
ejpam-5259	114	10	)	)	PUNCT
ejpam-5259	114	11	(	(	PUNCT
ejpam-5259	114	12	2024	2024	NUM
ejpam-5259	114	13	)	)	PUNCT
ejpam-5259	114	14	,	,	PUNCT
ejpam-5259	114	15	1894	1894	NUM
ejpam-5259	114	16	-	-	SYM
ejpam-5259	114	17	1907	1907	NUM
ejpam-5259	114	18	1899	1899	NUM
ejpam-5259	114	19	by	by	ADP
ejpam-5259	114	20	utilising	utilise	VERB
ejpam-5259	114	21	condition	condition	NOUN
ejpam-5259	114	22	(	(	PUNCT
ejpam-5259	114	23	1	1	NUM
ejpam-5259	114	24	)	)	PUNCT
ejpam-5259	115	1	,	,	PUNCT
ejpam-5259	115	2	one	one	PRON
ejpam-5259	115	3	can	can	AUX
ejpam-5259	115	4	determine	determine	VERB
ejpam-5259	115	5	that	that	SCONJ
ejpam-5259	115	6	the	the	DET
ejpam-5259	115	7	last	last	ADJ
ejpam-5259	115	8	expression	expression	NOUN
ejpam-5259	115	9	is	be	AUX
ejpam-5259	115	10	non	non	ADJ
ejpam-5259	115	11	-	-	ADJ
ejpam-5259	115	12	negative	negative	ADJ
ejpam-5259	115	13	.	.	PUNCT
ejpam-5259	116	1	consequently	consequently	ADV
ejpam-5259	116	2	,	,	PUNCT
ejpam-5259	116	3	it	it	PRON
ejpam-5259	116	4	can	can	AUX
ejpam-5259	116	5	be	be	AUX
ejpam-5259	116	6	deduced	deduce	VERB
ejpam-5259	116	7	that	that	SCONJ
ejpam-5259	116	8	f	f	PROPN
ejpam-5259	116	9	is	be	AUX
ejpam-5259	116	10	univalent	univalent	ADJ
ejpam-5259	116	11	in	in	ADP
ejpam-5259	116	12	♢	♢	PROPN
ejpam-5259	116	13	∗.	∗.	PROPN
ejpam-5259	116	14	to	to	PART
ejpam-5259	116	15	establish	establish	VERB
ejpam-5259	116	16	that	that	SCONJ
ejpam-5259	116	17	f	f	PROPN
ejpam-5259	116	18	is	be	AUX
ejpam-5259	116	19	sensepreserving	sensepreserve	VERB
ejpam-5259	116	20	in	in	ADP
ejpam-5259	116	21	♢	♢	PROPN
ejpam-5259	116	22	∗	∗	PROPN
ejpam-5259	116	23	,	,	PUNCT
ejpam-5259	116	24	it	it	PRON
ejpam-5259	116	25	suffices	suffice	VERB
ejpam-5259	116	26	to	to	PART
ejpam-5259	116	27	demonstrate	demonstrate	VERB
ejpam-5259	116	28	that	that	SCONJ
ejpam-5259	116	29	|ℏ′(ς)|	|ℏ′(ς)|	ADV
ejpam-5259	116	30	>	>	X
ejpam-5259	116	31	|g′(ς)|	|g′(ς)|	NOUN
ejpam-5259	116	32	using	use	VERB
ejpam-5259	116	33	the	the	DET
ejpam-5259	116	34	ordinary	ordinary	ADJ
ejpam-5259	116	35	derivative	derivative	NOUN
ejpam-5259	116	36	.	.	PUNCT
ejpam-5259	117	1	for	for	ADP
ejpam-5259	117	2	0	0	NUM
ejpam-5259	117	3	<	<	X
ejpam-5259	117	4	|ς|	|ς|	PROPN
ejpam-5259	117	5	=	=	PUNCT
ejpam-5259	117	6	r	r	NOUN
ejpam-5259	117	7	<	<	X
ejpam-5259	117	8	1	1	NUM
ejpam-5259	117	9	,	,	PUNCT
ejpam-5259	117	10	this	this	PRON
ejpam-5259	117	11	can	can	AUX
ejpam-5259	117	12	be	be	AUX
ejpam-5259	117	13	inferred	infer	VERB
ejpam-5259	117	14	from	from	ADP
ejpam-5259	117	15	the	the	DET
ejpam-5259	117	16	utilization	utilization	NOUN
ejpam-5259	117	17	of	of	ADP
ejpam-5259	117	18	(	(	PUNCT
ejpam-5259	117	19	1	1	NUM
ejpam-5259	117	20	)	)	PUNCT
ejpam-5259	117	21	.	.	PUNCT
ejpam-5259	118	1	∣∣∣ℏ′	∣∣∣ℏ′	PROPN
ejpam-5259	118	2	(	(	PUNCT
ejpam-5259	118	3	ς	ς	NOUN
ejpam-5259	118	4	)	)	PUNCT
ejpam-5259	118	5	∣∣∣	∣∣∣	NOUN
ejpam-5259	118	6	=	=	PUNCT
ejpam-5259	118	7	∣∣∣∣∣∣−1	∣∣∣∣∣∣−1	PROPN
ejpam-5259	118	8	ς2	ς2	PROPN
ejpam-5259	118	9	+	+	CCONJ
ejpam-5259	118	10	∞∑	∞∑	NUM
ejpam-5259	118	11	µ=1	µ=1	PUNCT
ejpam-5259	118	12	µaµς	µaµς	VERB
ejpam-5259	118	13	µ−1	µ−1	PROPN
ejpam-5259	118	14	∣∣∣∣∣∣	∣∣∣∣∣∣	X
ejpam-5259	118	15	≥	≥	NOUN
ejpam-5259	118	16	∣∣∣∣∣∣−1	∣∣∣∣∣∣−1	PROPN
ejpam-5259	118	17	ς2	ς2	PROPN
ejpam-5259	118	18	+	+	CCONJ
ejpam-5259	118	19	∞∑	∞∑	NUM
ejpam-5259	118	20	µ=1	µ=1	ADJ
ejpam-5259	118	21	µγ(η)[1	µγ(η)[1	PRON
ejpam-5259	118	22	+	+	CCONJ
ejpam-5259	118	23	λ(µ−	λ(µ−	VERB
ejpam-5259	118	24	1)]k	1)]k	NUM
ejpam-5259	118	25	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	118	26	1	1	NUM
ejpam-5259	118	27	)	)	PUNCT
ejpam-5259	118	28	+	+	NUM
ejpam-5259	118	29	η	η	X
ejpam-5259	118	30	)	)	PUNCT
ejpam-5259	118	31	(	(	PUNCT
ejpam-5259	118	32	µ+	µ+	X
ejpam-5259	118	33	δ	δ	PROPN
ejpam-5259	118	34	1	1	NUM
ejpam-5259	118	35	+	+	CCONJ
ejpam-5259	118	36	δ	δ	NOUN
ejpam-5259	118	37	)	)	PUNCT
ejpam-5259	118	38	r	r	NOUN
ejpam-5259	118	39	aµς	aµς	NOUN
ejpam-5259	118	40	µ−1	µ−1	PROPN
ejpam-5259	118	41	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5259	118	42	≥	≥	NOUN
ejpam-5259	118	43	∣∣∣∣−1	∣∣∣∣−1	ADP
ejpam-5259	119	1	ς2	ς2	PROPN
ejpam-5259	119	2	∣∣∣∣−	∣∣∣∣−	PROPN
ejpam-5259	119	3	∞∑	∞∑	PRON
ejpam-5259	119	4	µ=1	µ=1	ADP
ejpam-5259	119	5	µγ(η)[1	µγ(η)[1	PRON
ejpam-5259	119	6	+	+	CCONJ
ejpam-5259	119	7	λ(µ−	λ(µ−	VERB
ejpam-5259	119	8	1)]k	1)]k	NUM
ejpam-5259	119	9	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	119	10	1	1	NUM
ejpam-5259	119	11	)	)	PUNCT
ejpam-5259	119	12	+	+	NUM
ejpam-5259	119	13	η	η	X
ejpam-5259	119	14	)	)	PUNCT
ejpam-5259	119	15	(	(	PUNCT
ejpam-5259	119	16	µ+	µ+	X
ejpam-5259	119	17	δ	δ	PROPN
ejpam-5259	119	18	1	1	NUM
ejpam-5259	119	19	+	+	CCONJ
ejpam-5259	119	20	δ	δ	NOUN
ejpam-5259	119	21	)	)	PUNCT
ejpam-5259	119	22	r	r	NOUN
ejpam-5259	119	23	|aµ||ς|µ−1	|aµ||ς|µ−1	X
ejpam-5259	119	24	≥	≥	NOUN
ejpam-5259	119	25	1	1	NUM
ejpam-5259	119	26	r	r	NOUN
ejpam-5259	119	27	2	2	NUM
ejpam-5259	119	28	−	−	PROPN
ejpam-5259	119	29	∞∑	∞∑	NUM
ejpam-5259	119	30	µ=1	µ=1	ADJ
ejpam-5259	119	31	µγ(η)[1	µγ(η)[1	PRON
ejpam-5259	119	32	+	+	CCONJ
ejpam-5259	119	33	λ(µ−	λ(µ−	VERB
ejpam-5259	119	34	1)]k	1)]k	NUM
ejpam-5259	119	35	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	119	36	1	1	NUM
ejpam-5259	119	37	)	)	PUNCT
ejpam-5259	119	38	+	+	NUM
ejpam-5259	119	39	η	η	X
ejpam-5259	119	40	)	)	PUNCT
ejpam-5259	119	41	(	(	PUNCT
ejpam-5259	119	42	µ+	µ+	X
ejpam-5259	119	43	δ	δ	PROPN
ejpam-5259	119	44	1	1	NUM
ejpam-5259	119	45	+	+	CCONJ
ejpam-5259	119	46	δ	δ	NOUN
ejpam-5259	119	47	)	)	PUNCT
ejpam-5259	119	48	r	r	PROPN
ejpam-5259	119	49	|aµ|rµ−1	|aµ|rµ−1	NUM
ejpam-5259	119	50	≥	≥	NOUN
ejpam-5259	119	51	1−	1−	NUM
ejpam-5259	119	52	∞∑	∞∑	NUM
ejpam-5259	119	53	µ=1	µ=1	ADP
ejpam-5259	119	54	µγ(η)[1	µγ(η)[1	PRON
ejpam-5259	119	55	+	+	CCONJ
ejpam-5259	119	56	λ(µ−	λ(µ−	VERB
ejpam-5259	119	57	1)]k	1)]k	NUM
ejpam-5259	119	58	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	119	59	1	1	NUM
ejpam-5259	119	60	)	)	PUNCT
ejpam-5259	119	61	+	+	NUM
ejpam-5259	119	62	η	η	X
ejpam-5259	119	63	)	)	PUNCT
ejpam-5259	119	64	(	(	PUNCT
ejpam-5259	119	65	µ+	µ+	X
ejpam-5259	119	66	δ	δ	PROPN
ejpam-5259	119	67	1	1	NUM
ejpam-5259	119	68	+	+	CCONJ
ejpam-5259	119	69	δ	δ	NOUN
ejpam-5259	119	70	)	)	PUNCT
ejpam-5259	120	1	r	r	NOUN
ejpam-5259	120	2	|aµ|	|aµ|	PROPN
ejpam-5259	120	3	≥	≥	NOUN
ejpam-5259	120	4	1−	1−	NUM
ejpam-5259	121	1	∞∑	∞∑	PRON
ejpam-5259	121	2	µ=1	µ=1	PROPN
ejpam-5259	121	3	γ(η)[1	γ(η)[1	X
ejpam-5259	121	4	+	+	PUNCT
ejpam-5259	121	5	λ(µ−	λ(µ−	VERB
ejpam-5259	121	6	1)]k	1)]k	NUM
ejpam-5259	121	7	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	121	8	1	1	NUM
ejpam-5259	121	9	)	)	PUNCT
ejpam-5259	121	10	+	+	NUM
ejpam-5259	121	11	η	η	X
ejpam-5259	121	12	)	)	PUNCT
ejpam-5259	121	13	(	(	PUNCT
ejpam-5259	121	14	µ+	µ+	X
ejpam-5259	121	15	δ	δ	PROPN
ejpam-5259	121	16	1	1	NUM
ejpam-5259	121	17	+	+	CCONJ
ejpam-5259	121	18	δ	δ	NOUN
ejpam-5259	121	19	)	)	PUNCT
ejpam-5259	121	20	r	r	NOUN
ejpam-5259	121	21	(	(	PUNCT
ejpam-5259	121	22	µ+	µ+	NOUN
ejpam-5259	121	23	γ	γ	PROPN
ejpam-5259	121	24	1−	1−	NUM
ejpam-5259	121	25	γ	γ	PROPN
ejpam-5259	121	26	)	)	PUNCT
ejpam-5259	121	27	|aµ|	|aµ|	NOUN
ejpam-5259	121	28	≥	≥	NUM
ejpam-5259	122	1	∞∑	∞∑	NUM
ejpam-5259	122	2	µ=1	µ=1	PUNCT
ejpam-5259	122	3	γ(η)[1	γ(η)[1	X
ejpam-5259	122	4	+	+	PUNCT
ejpam-5259	122	5	λ(µ−	λ(µ−	VERB
ejpam-5259	122	6	1)]k	1)]k	NUM
ejpam-5259	122	7	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	122	8	1	1	NUM
ejpam-5259	122	9	)	)	PUNCT
ejpam-5259	122	10	+	+	NUM
ejpam-5259	122	11	η	η	X
ejpam-5259	122	12	)	)	PUNCT
ejpam-5259	122	13	(	(	PUNCT
ejpam-5259	122	14	µ+	µ+	X
ejpam-5259	122	15	δ	δ	PROPN
ejpam-5259	122	16	1	1	NUM
ejpam-5259	122	17	+	+	CCONJ
ejpam-5259	122	18	δ	δ	NOUN
ejpam-5259	122	19	)	)	PUNCT
ejpam-5259	122	20	r	r	NOUN
ejpam-5259	122	21	(	(	PUNCT
ejpam-5259	122	22	µ−	µ−	PROPN
ejpam-5259	122	23	γ	γ	X
ejpam-5259	122	24	1−	1−	NUM
ejpam-5259	122	25	γ	γ	PROPN
ejpam-5259	122	26	)	)	PUNCT
ejpam-5259	122	27	|bµ|	|bµ|	PROPN
ejpam-5259	122	28	>	>	PUNCT
ejpam-5259	122	29	∣∣∣∣∣∣−1	∣∣∣∣∣∣−1	PROPN
ejpam-5259	122	30	ς2	ς2	PROPN
ejpam-5259	122	31	+	+	CCONJ
ejpam-5259	122	32	∞∑	∞∑	NUM
ejpam-5259	122	33	µ=1	µ=1	SYM
ejpam-5259	122	34	µ	µ	PRON
ejpam-5259	122	35	bµς	bµς	NOUN
ejpam-5259	122	36	µ−1	µ−1	PROPN
ejpam-5259	122	37	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-5259	122	38	≥	≥	PRON
ejpam-5259	122	39	∣∣∣g′	∣∣∣g′	PROPN
ejpam-5259	122	40	(	(	PUNCT
ejpam-5259	122	41	ς	ς	NOUN
ejpam-5259	122	42	)	)	PUNCT
ejpam-5259	122	43	∣∣∣.	∣∣∣.	NOUN
ejpam-5259	122	44	in	in	ADP
ejpam-5259	122	45	order	order	NOUN
ejpam-5259	122	46	to	to	PART
ejpam-5259	122	47	prove	prove	VERB
ejpam-5259	122	48	that	that	SCONJ
ejpam-5259	122	49	f	f	PROPN
ejpam-5259	122	50	∈	∈	PROPN
ejpam-5259	122	51	t	t	PROPN
ejpam-5259	122	52	mkh(k	mkh(k	PROPN
ejpam-5259	122	53	,	,	PUNCT
ejpam-5259	122	54	r	r	NOUN
ejpam-5259	122	55	,	,	PUNCT
ejpam-5259	122	56	α	α	PROPN
ejpam-5259	122	57	,	,	PUNCT
ejpam-5259	122	58	η	η	PROPN
ejpam-5259	122	59	,	,	PUNCT
ejpam-5259	122	60	δ	δ	PROPN
ejpam-5259	122	61	,	,	PUNCT
ejpam-5259	122	62	λ	λ	PROPN
ejpam-5259	122	63	,	,	PUNCT
ejpam-5259	122	64	γ	γ	NOUN
ejpam-5259	122	65	)	)	PUNCT
ejpam-5259	122	66	,	,	PUNCT
ejpam-5259	122	67	it	it	PRON
ejpam-5259	122	68	suffices	suffice	VERB
ejpam-5259	122	69	to	to	PART
ejpam-5259	122	70	show	show	VERB
ejpam-5259	122	71	that	that	SCONJ
ejpam-5259	122	72	re	re	VERB
ejpam-5259	122	73	−	−	NOUN
ejpam-5259	122	74	ς	ς	PROPN
ejpam-5259	122	75	(	(	PUNCT
ejpam-5259	122	76	ik(sα	ik(sα	PROPN
ejpam-5259	122	77	η	η	PROPN
ejpam-5259	123	1	[	[	X
ejpam-5259	123	2	r	r	X
ejpam-5259	123	3	,	,	PUNCT
ejpam-5259	123	4	δ	δ	PROPN
ejpam-5259	123	5	,	,	PUNCT
ejpam-5259	123	6	λ]ℏ(ς	λ]ℏ(ς	NOUN
ejpam-5259	123	7	)	)	PUNCT
ejpam-5259	123	8	)	)	PUNCT
ejpam-5259	123	9	)	)	PUNCT
ejpam-5259	124	1	′	′	NUM
ejpam-5259	125	1	−	−	NOUN
ejpam-5259	125	2	ς	ς	PROPN
ejpam-5259	125	3	(	(	PUNCT
ejpam-5259	125	4	ik(sα	ik(sα	PROPN
ejpam-5259	125	5	η	η	PROPN
ejpam-5259	125	6	[	[	X
ejpam-5259	125	7	r	r	X
ejpam-5259	125	8	,	,	PUNCT
ejpam-5259	125	9	δ	δ	PROPN
ejpam-5259	125	10	,	,	PUNCT
ejpam-5259	125	11	λ]g(ς	λ]g(ς	PROPN
ejpam-5259	125	12	)	)	PUNCT
ejpam-5259	125	13	)	)	PUNCT
ejpam-5259	125	14	′	′	NUM
ejpam-5259	126	1	ik	ik	PROPN
ejpam-5259	126	2	(	(	PUNCT
ejpam-5259	126	3	sα	sα	PROPN
ejpam-5259	126	4	η	η	PROPN
ejpam-5259	126	5	[	[	X
ejpam-5259	126	6	r	r	X
ejpam-5259	126	7	,	,	PUNCT
ejpam-5259	126	8	δ	δ	PROPN
ejpam-5259	126	9	,	,	PUNCT
ejpam-5259	126	10	λ]ℏ(ς	λ]ℏ(ς	NOUN
ejpam-5259	126	11	)	)	PUNCT
ejpam-5259	126	12	)	)	PUNCT
ejpam-5259	127	1	+	+	CCONJ
ejpam-5259	127	2	ik	ik	PROPN
ejpam-5259	127	3	(	(	PUNCT
ejpam-5259	127	4	sα	sα	PROPN
ejpam-5259	127	5	η	η	PROPN
ejpam-5259	127	6	[	[	X
ejpam-5259	127	7	r	r	PROPN
ejpam-5259	127	8	,	,	PUNCT
ejpam-5259	127	9	δ	δ	PROPN
ejpam-5259	127	10	,	,	PUNCT
ejpam-5259	127	11	λ]g(ς	λ]g(ς	PROPN
ejpam-5259	127	12	)	)	PUNCT
ejpam-5259	127	13	)	)	PUNCT
ejpam-5259	127	14	−	−	PROPN
ejpam-5259	128	1	γ	γ	X
ejpam-5259	128	2			PROPN
ejpam-5259	128	3	>	>	X
ejpam-5259	128	4	0	0	NUM
ejpam-5259	128	5	,	,	PUNCT
ejpam-5259	128	6	(	(	PUNCT
ejpam-5259	128	7	ς	ς	PROPN
ejpam-5259	128	8	∈	∈	PROPN
ejpam-5259	128	9	♢	♢	PROPN
ejpam-5259	128	10	∗	∗	PROPN
ejpam-5259	128	11	)	)	PUNCT
ejpam-5259	128	12	.	.	PUNCT
ejpam-5259	129	1	since	since	SCONJ
ejpam-5259	129	2	,	,	PUNCT
ejpam-5259	129	3	ℜe(ρ(ς	ℜe(ρ(ς	VERB
ejpam-5259	129	4	)	)	PUNCT
ejpam-5259	129	5	)	)	PUNCT
ejpam-5259	129	6	>	>	X
ejpam-5259	129	7	0	0	PUNCT
ejpam-5259	130	1	if	if	SCONJ
ejpam-5259	130	2	and	and	CCONJ
ejpam-5259	130	3	only	only	ADV
ejpam-5259	130	4	if	if	SCONJ
ejpam-5259	130	5	∣∣∣ρ(ς)−1	∣∣∣ρ(ς)−1	NOUN
ejpam-5259	130	6	ρ(ς)+1	ρ(ς)+1	PRON
ejpam-5259	130	7	∣∣∣	∣∣∣	NOUN
ejpam-5259	130	8	<	<	X
ejpam-5259	130	9	1	1	NUM
ejpam-5259	130	10	for	for	ADP
ejpam-5259	130	11	an	an	DET
ejpam-5259	130	12	analytic	analytic	ADJ
ejpam-5259	130	13	function	function	NOUN
ejpam-5259	130	14	ρ(ς	ρ(ς	NUM
ejpam-5259	130	15	)	)	PUNCT
ejpam-5259	130	16	=	=	SYM
ejpam-5259	130	17	1	1	NUM
ejpam-5259	130	18	+	+	CCONJ
ejpam-5259	130	19	c1ς	c1ς	ADJ
ejpam-5259	130	20	+	+	CCONJ
ejpam-5259	130	21	c2ς	c2ς	NOUN
ejpam-5259	130	22	2	2	NUM
ejpam-5259	130	23	+	+	CCONJ
ejpam-5259	130	24	.	.	PUNCT
ejpam-5259	130	25	.	.	PUNCT
ejpam-5259	131	1	.	.	PUNCT
ejpam-5259	132	1	.	.	PUNCT
ejpam-5259	133	1	we	we	PRON
ejpam-5259	133	2	let	let	VERB
ejpam-5259	133	3	m(ς	m(ς	NOUN
ejpam-5259	133	4	)	)	PUNCT
ejpam-5259	134	1	=	=	PRON
ejpam-5259	134	2	{	{	PUNCT
ejpam-5259	135	1	−ς(ik(sα	−ς(ik(sα	PROPN
ejpam-5259	135	2	η	η	PROPN
ejpam-5259	135	3	[	[	X
ejpam-5259	135	4	r	r	X
ejpam-5259	135	5	,	,	PUNCT
ejpam-5259	135	6	δ	δ	PROPN
ejpam-5259	135	7	,	,	PUNCT
ejpam-5259	135	8	λ]ℏ(ς	λ]ℏ(ς	NOUN
ejpam-5259	135	9	)	)	PUNCT
ejpam-5259	135	10	)	)	PUNCT
ejpam-5259	135	11	)	)	PUNCT
ejpam-5259	136	1	′	′	PUNCT
ejpam-5259	137	1	+	+	CCONJ
ejpam-5259	137	2	ς(ik(sα	ς(ik(sα	PROPN
ejpam-5259	137	3	η	η	PROPN
ejpam-5259	137	4	[	[	X
ejpam-5259	137	5	r	r	PROPN
ejpam-5259	137	6	,	,	PUNCT
ejpam-5259	137	7	δ	δ	PROPN
ejpam-5259	137	8	,	,	PUNCT
ejpam-5259	137	9	λ]g(ς	λ]g(ς	PROPN
ejpam-5259	137	10	)	)	PUNCT
ejpam-5259	137	11	)	)	PUNCT
ejpam-5259	138	1	′	′	NUM
ejpam-5259	139	1	−	−	PROPN
ejpam-5259	139	2	γik(sα	γik(sα	PROPN
ejpam-5259	139	3	η	η	PROPN
ejpam-5259	140	1	[	[	X
ejpam-5259	140	2	r	r	X
ejpam-5259	140	3	,	,	PUNCT
ejpam-5259	140	4	δ	δ	PROPN
ejpam-5259	140	5	,	,	PUNCT
ejpam-5259	140	6	λ]ℏ(ς	λ]ℏ(ς	NOUN
ejpam-5259	140	7	)	)	PUNCT
ejpam-5259	140	8	−γik(sα	−γik(sα	PROPN
ejpam-5259	140	9	η	η	NOUN
ejpam-5259	141	1	[	[	X
ejpam-5259	141	2	r	r	X
ejpam-5259	141	3	,	,	PUNCT
ejpam-5259	141	4	δ	δ	PROPN
ejpam-5259	141	5	,	,	PUNCT
ejpam-5259	141	6	λ]g(ς	λ]g(ς	PROPN
ejpam-5259	141	7	)	)	PUNCT
ejpam-5259	141	8	}	}	PUNCT
ejpam-5259	141	9	(	(	PUNCT
ejpam-5259	141	10	14	14	NUM
ejpam-5259	141	11	)	)	PUNCT
ejpam-5259	141	12	and	and	CCONJ
ejpam-5259	141	13	n(ς	n(ς	PROPN
ejpam-5259	141	14	)	)	PUNCT
ejpam-5259	142	1	=	=	SYM
ejpam-5259	142	2	ik(sα	ik(sα	PROPN
ejpam-5259	142	3	η	η	PROPN
ejpam-5259	143	1	[	[	X
ejpam-5259	143	2	r	r	X
ejpam-5259	143	3	,	,	PUNCT
ejpam-5259	143	4	δ	δ	PROPN
ejpam-5259	143	5	,	,	PUNCT
ejpam-5259	143	6	λ]ℏ(ς	λ]ℏ(ς	NOUN
ejpam-5259	143	7	)	)	PUNCT
ejpam-5259	143	8	+	+	NUM
ejpam-5259	143	9	ik(sα	ik(sα	PROPN
ejpam-5259	143	10	η	η	X
ejpam-5259	144	1	[	[	X
ejpam-5259	144	2	r	r	X
ejpam-5259	144	3	,	,	PUNCT
ejpam-5259	144	4	δ	δ	PROPN
ejpam-5259	144	5	,	,	PUNCT
ejpam-5259	144	6	λ]g(ς	λ]g(ς	PROPN
ejpam-5259	144	7	)	)	PUNCT
ejpam-5259	144	8	.	.	PUNCT
ejpam-5259	145	1	(	(	PUNCT
ejpam-5259	145	2	15	15	NUM
ejpam-5259	145	3	)	)	PUNCT
ejpam-5259	145	4	then	then	ADV
ejpam-5259	145	5	,	,	PUNCT
ejpam-5259	145	6	we	we	PRON
ejpam-5259	145	7	have	have	VERB
ejpam-5259	145	8	to	to	PART
ejpam-5259	145	9	show	show	VERB
ejpam-5259	145	10	that	that	SCONJ
ejpam-5259	145	11	ξ(ς	ξ(ς	VERB
ejpam-5259	145	12	)	)	PUNCT
ejpam-5259	145	13	=	=	SYM
ejpam-5259	145	14	|m(ς	|m(ς	NOUN
ejpam-5259	145	15	)	)	PUNCT
ejpam-5259	146	1	+	+	ADP
ejpam-5259	146	2	n(ς)|	n(ς)|	ADV
ejpam-5259	146	3	−	−	ADP
ejpam-5259	146	4	|m(ς)−n(ς)|	|m(ς)−n(ς)|	NOUN
ejpam-5259	146	5	>	>	ADP
ejpam-5259	146	6	0	0	NUM
ejpam-5259	146	7	.	.	PUNCT
ejpam-5259	147	1	(	(	PUNCT
ejpam-5259	147	2	16	16	NUM
ejpam-5259	147	3	)	)	PUNCT
ejpam-5259	147	4	s.	s.	PROPN
ejpam-5259	147	5	ahmed	ahmed	PROPN
ejpam-5259	147	6	,	,	PUNCT
ejpam-5259	147	7	a.	a.	PROPN
ejpam-5259	147	8	alsoboh	alsoboh	PROPN
ejpam-5259	147	9	,	,	PUNCT
ejpam-5259	147	10	m.	m.	NOUN
ejpam-5259	147	11	darus	darus	NOUN
ejpam-5259	147	12	/	/	SYM
ejpam-5259	147	13	eur	eur	PROPN
ejpam-5259	147	14	.	.	PUNCT
ejpam-5259	148	1	j.	j.	PROPN
ejpam-5259	148	2	pure	pure	PROPN
ejpam-5259	148	3	appl	appl	PROPN
ejpam-5259	148	4	.	.	PROPN
ejpam-5259	148	5	math	math	PROPN
ejpam-5259	148	6	,	,	PUNCT
ejpam-5259	148	7	17	17	NUM
ejpam-5259	148	8	(	(	PUNCT
ejpam-5259	148	9	3	3	NUM
ejpam-5259	148	10	)	)	PUNCT
ejpam-5259	148	11	(	(	PUNCT
ejpam-5259	148	12	2024	2024	NUM
ejpam-5259	148	13	)	)	PUNCT
ejpam-5259	148	14	,	,	PUNCT
ejpam-5259	148	15	1894	1894	NUM
ejpam-5259	148	16	-	-	SYM
ejpam-5259	148	17	1907	1907	NUM
ejpam-5259	148	18	1900	1900	NUM
ejpam-5259	148	19	now	now	ADV
ejpam-5259	148	20	,	,	PUNCT
ejpam-5259	148	21	by	by	ADP
ejpam-5259	148	22	substituting	substitute	VERB
ejpam-5259	148	23	equations	equation	NOUN
ejpam-5259	148	24	(	(	PUNCT
ejpam-5259	148	25	9	9	NUM
ejpam-5259	148	26	)	)	PUNCT
ejpam-5259	148	27	and	and	CCONJ
ejpam-5259	148	28	(	(	PUNCT
ejpam-5259	148	29	10	10	NUM
ejpam-5259	148	30	)	)	PUNCT
ejpam-5259	148	31	into	into	ADP
ejpam-5259	148	32	the	the	DET
ejpam-5259	148	33	left	left	ADJ
ejpam-5259	148	34	-	-	PUNCT
ejpam-5259	148	35	hand	hand	NOUN
ejpam-5259	148	36	side	side	NOUN
ejpam-5259	148	37	of	of	ADP
ejpam-5259	148	38	inequality	inequality	NOUN
ejpam-5259	148	39	(	(	PUNCT
ejpam-5259	148	40	16	16	NUM
ejpam-5259	148	41	)	)	PUNCT
ejpam-5259	148	42	,	,	PUNCT
ejpam-5259	148	43	we	we	PRON
ejpam-5259	148	44	obtain	obtain	VERB
ejpam-5259	148	45	ξ(ς	ξ(ς	NOUN
ejpam-5259	148	46	)	)	PUNCT
ejpam-5259	148	47	≥	≥	NOUN
ejpam-5259	148	48			NOUN
ejpam-5259	148	49	2−2γ	2−2γ	NUM
ejpam-5259	148	50	r	r	NOUN
ejpam-5259	148	51	−	−	PROPN
ejpam-5259	148	52	2	2	NUM
ejpam-5259	149	1	∞∑	∞∑	PRON
ejpam-5259	149	2	µ=1	µ=1	PUNCT
ejpam-5259	149	3	γ(η)[1+λ(µ−1)]k	γ(η)[1+λ(µ−1)]k	X
ejpam-5259	149	4	γ(α(µ+1)+η	γ(α(µ+1)+η	NUM
ejpam-5259	149	5	)	)	PUNCT
ejpam-5259	149	6	(	(	PUNCT
ejpam-5259	149	7	µ+δ	µ+δ	NUM
ejpam-5259	149	8	1+δ	1+δ	NUM
ejpam-5259	149	9	)	)	PUNCT
ejpam-5259	149	10	r	r	NOUN
ejpam-5259	149	11	(	(	PUNCT
ejpam-5259	149	12	µ+	µ+	NOUN
ejpam-5259	149	13	γ	γ	NOUN
ejpam-5259	149	14	)	)	PUNCT
ejpam-5259	149	15	|aµ|rµ	|aµ|rµ	ADJ
ejpam-5259	149	16	−2	−2	NOUN
ejpam-5259	149	17	∞∑	∞∑	NUM
ejpam-5259	149	18	µ=1	µ=1	PUNCT
ejpam-5259	149	19	γ(η)[1+λ(µ−1)]k	γ(η)[1+λ(µ−1)]k	X
ejpam-5259	149	20	γ(α(µ+1)+η	γ(α(µ+1)+η	NUM
ejpam-5259	149	21	)	)	PUNCT
ejpam-5259	149	22	(	(	PUNCT
ejpam-5259	149	23	µ+δ	µ+δ	NUM
ejpam-5259	149	24	1+δ	1+δ	NUM
ejpam-5259	149	25	)	)	PUNCT
ejpam-5259	149	26	r	r	NOUN
ejpam-5259	149	27	(	(	PUNCT
ejpam-5259	149	28	µ−	µ−	PROPN
ejpam-5259	149	29	γ	γ	PROPN
ejpam-5259	149	30	)	)	PUNCT
ejpam-5259	149	31	|bµ|rµ	|bµ|rµ	PUNCT
ejpam-5259	149	32			NOUN
ejpam-5259	149	33	≥	≥	NOUN
ejpam-5259	149	34	2(1−	2(1−	NUM
ejpam-5259	149	35	γ	γ	X
ejpam-5259	149	36	)	)	PUNCT
ejpam-5259	149	37			NOUN
ejpam-5259	149	38	1−	1−	NUM
ejpam-5259	149	39	∞∑	∞∑	PRON
ejpam-5259	149	40	µ=1	µ=1	PUNCT
ejpam-5259	149	41	γ(η)[1+λ(µ−1)]k	γ(η)[1+λ(µ−1)]k	X
ejpam-5259	149	42	γ(α(µ+1)+η	γ(α(µ+1)+η	NUM
ejpam-5259	149	43	)	)	PUNCT
ejpam-5259	149	44	(	(	PUNCT
ejpam-5259	149	45	µ+δ	µ+δ	NUM
ejpam-5259	149	46	1+δ	1+δ	NUM
ejpam-5259	149	47	)	)	PUNCT
ejpam-5259	149	48	r	r	NOUN
ejpam-5259	149	49	(	(	PUNCT
ejpam-5259	149	50	µ+γ	µ+γ	NUM
ejpam-5259	149	51	1−γ	1−γ	NUM
ejpam-5259	149	52	)	)	PUNCT
ejpam-5259	149	53	|aµ|rµ	|aµ|rµ	NOUN
ejpam-5259	149	54	−	−	ADP
ejpam-5259	149	55	∞∑	∞∑	NUM
ejpam-5259	149	56	µ=1	µ=1	PUNCT
ejpam-5259	149	57	γ(η)[1+λ(µ−1)]k	γ(η)[1+λ(µ−1)]k	X
ejpam-5259	149	58	γ(α(µ+1)+η	γ(α(µ+1)+η	NUM
ejpam-5259	149	59	)	)	PUNCT
ejpam-5259	149	60	(	(	PUNCT
ejpam-5259	149	61	µ+δ	µ+δ	NUM
ejpam-5259	149	62	1+δ	1+δ	NUM
ejpam-5259	149	63	)	)	PUNCT
ejpam-5259	149	64	r	r	NOUN
ejpam-5259	149	65	(	(	PUNCT
ejpam-5259	149	66	µ−γ	µ−γ	ADV
ejpam-5259	149	67	1−γ	1−γ	NUM
ejpam-5259	149	68	)	)	PUNCT
ejpam-5259	149	69	|bµ|rµ	|bµ|rµ	NOUN
ejpam-5259	149	70			NOUN
ejpam-5259	149	71	.	.	PUNCT
ejpam-5259	150	1	the	the	DET
ejpam-5259	150	2	positivity	positivity	NOUN
ejpam-5259	150	3	of	of	ADP
ejpam-5259	150	4	this	this	DET
ejpam-5259	150	5	expression	expression	NOUN
ejpam-5259	150	6	is	be	AUX
ejpam-5259	150	7	assured	assure	VERB
ejpam-5259	150	8	by	by	ADP
ejpam-5259	150	9	the	the	DET
ejpam-5259	150	10	fulfillment	fulfillment	NOUN
ejpam-5259	150	11	of	of	ADP
ejpam-5259	150	12	condition	condition	NOUN
ejpam-5259	150	13	(	(	PUNCT
ejpam-5259	150	14	1	1	NUM
ejpam-5259	150	15	)	)	PUNCT
ejpam-5259	150	16	,	,	PUNCT
ejpam-5259	150	17	thereby	thereby	ADV
ejpam-5259	150	18	concluding	conclude	VERB
ejpam-5259	150	19	the	the	DET
ejpam-5259	150	20	proof	proof	NOUN
ejpam-5259	150	21	.	.	PUNCT
ejpam-5259	151	1	in	in	ADP
ejpam-5259	151	2	the	the	DET
ejpam-5259	151	3	subsequent	subsequent	ADJ
ejpam-5259	151	4	theorem	theorem	NOUN
ejpam-5259	151	5	,	,	PUNCT
ejpam-5259	151	6	it	it	PRON
ejpam-5259	151	7	is	be	AUX
ejpam-5259	151	8	demonstrated	demonstrate	VERB
ejpam-5259	151	9	that	that	SCONJ
ejpam-5259	151	10	the	the	DET
ejpam-5259	151	11	condition	condition	NOUN
ejpam-5259	151	12	(	(	PUNCT
ejpam-5259	151	13	1	1	X
ejpam-5259	151	14	)	)	PUNCT
ejpam-5259	151	15	is	be	AUX
ejpam-5259	151	16	necessary	necessary	ADJ
ejpam-5259	151	17	for	for	ADP
ejpam-5259	151	18	the	the	DET
ejpam-5259	151	19	inclusion	inclusion	NOUN
ejpam-5259	151	20	of	of	ADP
ejpam-5259	151	21	f	f	PROPN
ejpam-5259	151	22	in	in	ADP
ejpam-5259	151	23	the	the	DET
ejpam-5259	151	24	class	class	NOUN
ejpam-5259	151	25	t	t	PROPN
ejpam-5259	151	26	mkh(k	mkh(k	PROPN
ejpam-5259	151	27	,	,	PUNCT
ejpam-5259	151	28	r	r	NOUN
ejpam-5259	151	29	,	,	PUNCT
ejpam-5259	151	30	α	α	PROPN
ejpam-5259	151	31	,	,	PUNCT
ejpam-5259	151	32	η	η	PROPN
ejpam-5259	151	33	,	,	PUNCT
ejpam-5259	151	34	δ	δ	PROPN
ejpam-5259	151	35	,	,	PUNCT
ejpam-5259	151	36	λ	λ	PROPN
ejpam-5259	151	37	,	,	PUNCT
ejpam-5259	151	38	γ	γ	NOUN
ejpam-5259	151	39	)	)	PUNCT
ejpam-5259	151	40	.	.	PUNCT
ejpam-5259	152	1	theorem	theorem	NOUN
ejpam-5259	152	2	2	2	NUM
ejpam-5259	152	3	.	.	X
ejpam-5259	153	1	let	let	VERB
ejpam-5259	153	2	(	(	PUNCT
ejpam-5259	153	3	0	0	NUM
ejpam-5259	153	4	≤	≤	NUM
ejpam-5259	153	5	γ	γ	X
ejpam-5259	153	6	<	<	X
ejpam-5259	153	7	1	1	NUM
ejpam-5259	153	8	)	)	PUNCT
ejpam-5259	153	9	and	and	CCONJ
ejpam-5259	153	10	fk	fk	INTJ
ejpam-5259	153	11	=	=	PUNCT
ejpam-5259	154	1	ℏk	ℏk	ADP
ejpam-5259	154	2	+	+	CCONJ
ejpam-5259	154	3	gk	gk	PROPN
ejpam-5259	154	4	∈	∈	PROPN
ejpam-5259	154	5	t	t	PROPN
ejpam-5259	154	6	mh	mh	PROPN
ejpam-5259	154	7	is	be	AUX
ejpam-5259	154	8	given	give	VERB
ejpam-5259	154	9	by	by	ADP
ejpam-5259	154	10	(	(	PUNCT
ejpam-5259	154	11	13	13	NUM
ejpam-5259	154	12	)	)	PUNCT
ejpam-5259	154	13	.	.	PUNCT
ejpam-5259	155	1	then	then	ADV
ejpam-5259	155	2	fk	fk	INTJ
ejpam-5259	155	3	∈	∈	PROPN
ejpam-5259	155	4	t	t	PROPN
ejpam-5259	155	5	mkh(k	mkh(k	PROPN
ejpam-5259	155	6	,	,	PUNCT
ejpam-5259	155	7	r	r	NOUN
ejpam-5259	155	8	,	,	PUNCT
ejpam-5259	155	9	α	α	PROPN
ejpam-5259	155	10	,	,	PUNCT
ejpam-5259	155	11	η	η	PROPN
ejpam-5259	155	12	,	,	PUNCT
ejpam-5259	155	13	δ	δ	PROPN
ejpam-5259	155	14	,	,	PUNCT
ejpam-5259	155	15	λ	λ	PROPN
ejpam-5259	155	16	,	,	PUNCT
ejpam-5259	155	17	γ	γ	NOUN
ejpam-5259	155	18	)	)	PUNCT
ejpam-5259	155	19	if	if	SCONJ
ejpam-5259	155	20	and	and	CCONJ
ejpam-5259	155	21	only	only	ADV
ejpam-5259	155	22	if	if	SCONJ
ejpam-5259	155	23	the	the	DET
ejpam-5259	155	24	inequality	inequality	NOUN
ejpam-5259	155	25	∞∑	∞∑	NUM
ejpam-5259	155	26	µ=1	µ=1	PUNCT
ejpam-5259	155	27	γ(η)[1	γ(η)[1	X
ejpam-5259	155	28	+	+	PUNCT
ejpam-5259	155	29	λ(µ−	λ(µ−	VERB
ejpam-5259	155	30	1)]k	1)]k	NUM
ejpam-5259	155	31	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	155	32	1	1	NUM
ejpam-5259	155	33	)	)	PUNCT
ejpam-5259	155	34	+	+	NUM
ejpam-5259	155	35	η	η	X
ejpam-5259	155	36	)	)	PUNCT
ejpam-5259	155	37	(	(	PUNCT
ejpam-5259	155	38	µ+	µ+	X
ejpam-5259	155	39	δ	δ	PROPN
ejpam-5259	155	40	1	1	NUM
ejpam-5259	155	41	+	+	CCONJ
ejpam-5259	155	42	δ	δ	NOUN
ejpam-5259	155	43	)	)	PUNCT
ejpam-5259	155	44	r	r	NOUN
ejpam-5259	155	45	[	[	PUNCT
ejpam-5259	155	46	(	(	PUNCT
ejpam-5259	155	47	µ+	µ+	X
ejpam-5259	155	48	γ	γ	NOUN
ejpam-5259	155	49	)	)	PUNCT
ejpam-5259	155	50	|aµ|+	|aµ|+	PROPN
ejpam-5259	155	51	(	(	PUNCT
ejpam-5259	155	52	µ−	µ−	PROPN
ejpam-5259	155	53	γ	γ	PROPN
ejpam-5259	155	54	)	)	PUNCT
ejpam-5259	155	55	|bµ|	|bµ|	NOUN
ejpam-5259	155	56	]	]	PUNCT
ejpam-5259	155	57	≤	≤	PROPN
ejpam-5259	155	58	1−	1−	NUM
ejpam-5259	155	59	γ	γ	X
ejpam-5259	155	60	,	,	PUNCT
ejpam-5259	155	61	is	be	AUX
ejpam-5259	155	62	satisfied	satisfied	ADJ
ejpam-5259	155	63	.	.	PUNCT
ejpam-5259	156	1	proof	proof	NOUN
ejpam-5259	156	2	.	.	PUNCT
ejpam-5259	157	1	considering	consider	VERB
ejpam-5259	157	2	theorem	theorem	NOUN
ejpam-5259	157	3	1	1	NUM
ejpam-5259	157	4	,	,	PUNCT
ejpam-5259	157	5	it	it	PRON
ejpam-5259	157	6	is	be	AUX
ejpam-5259	157	7	adequate	adequate	ADJ
ejpam-5259	157	8	to	to	PART
ejpam-5259	157	9	demonstrate	demonstrate	VERB
ejpam-5259	157	10	the	the	DET
ejpam-5259	157	11	validity	validity	NOUN
ejpam-5259	157	12	of	of	ADP
ejpam-5259	157	13	the	the	DET
ejpam-5259	157	14	”	"	PUNCT
ejpam-5259	157	15	if	if	SCONJ
ejpam-5259	157	16	”	"	PUNCT
ejpam-5259	157	17	part	part	NOUN
ejpam-5259	157	18	.	.	PUNCT
ejpam-5259	158	1	assume	assume	VERB
ejpam-5259	158	2	that	that	SCONJ
ejpam-5259	158	3	fk	fk	INTJ
ejpam-5259	158	4	∈	∈	PROPN
ejpam-5259	158	5	t	t	PROPN
ejpam-5259	158	6	mkh(k	mkh(k	PROPN
ejpam-5259	158	7	,	,	PUNCT
ejpam-5259	158	8	r	r	NOUN
ejpam-5259	158	9	,	,	PUNCT
ejpam-5259	158	10	α	α	PROPN
ejpam-5259	158	11	,	,	PUNCT
ejpam-5259	158	12	η	η	PROPN
ejpam-5259	158	13	,	,	PUNCT
ejpam-5259	158	14	δ	δ	PROPN
ejpam-5259	158	15	,	,	PUNCT
ejpam-5259	158	16	λ	λ	PROPN
ejpam-5259	158	17	,	,	PUNCT
ejpam-5259	158	18	γ	γ	NOUN
ejpam-5259	158	19	)	)	PUNCT
ejpam-5259	158	20	.	.	PUNCT
ejpam-5259	159	1	then	then	ADV
ejpam-5259	159	2	re	re	VERB
ejpam-5259	159	3	{	{	PUNCT
ejpam-5259	159	4	−	−	PROPN
ejpam-5259	159	5	ς(ik(sα	ς(ik(sα	PROPN
ejpam-5259	159	6	η	η	PROPN
ejpam-5259	159	7	[	[	X
ejpam-5259	159	8	r	r	X
ejpam-5259	159	9	,	,	PUNCT
ejpam-5259	159	10	δ	δ	PROPN
ejpam-5259	159	11	,	,	PUNCT
ejpam-5259	159	12	λ]ℏk(ς)))′	λ]ℏk(ς)))′	PROPN
ejpam-5259	159	13	−	−	PROPN
ejpam-5259	159	14	(	(	PUNCT
ejpam-5259	159	15	−1)kς(ik(sα	−1)kς(ik(sα	PROPN
ejpam-5259	159	16	η	η	PROPN
ejpam-5259	159	17	[	[	X
ejpam-5259	159	18	r	r	PROPN
ejpam-5259	159	19	,	,	PUNCT
ejpam-5259	159	20	δ	δ	PROPN
ejpam-5259	159	21	,	,	PUNCT
ejpam-5259	159	22	λ]gk(ς	λ]gk(ς	PROPN
ejpam-5259	159	23	)	)	PUNCT
ejpam-5259	159	24	)	)	PUNCT
ejpam-5259	159	25	)	)	PUNCT
ejpam-5259	160	1	′	′	NOUN
ejpam-5259	161	1	+	+	CCONJ
ejpam-5259	161	2	γik(sα	γik(sα	X
ejpam-5259	161	3	η	η	X
ejpam-5259	161	4	[	[	X
ejpam-5259	161	5	r	r	PROPN
ejpam-5259	161	6	,	,	PUNCT
ejpam-5259	161	7	δ	δ	PROPN
ejpam-5259	161	8	,	,	PUNCT
ejpam-5259	161	9	λ]ℏk(ς	λ]ℏk(ς	PROPN
ejpam-5259	161	10	)	)	PUNCT
ejpam-5259	161	11	+	+	CCONJ
ejpam-5259	161	12	(	(	PUNCT
ejpam-5259	161	13	−1)kγik(sα	−1)kγik(sα	NOUN
ejpam-5259	161	14	η	η	X
ejpam-5259	161	15	[	[	X
ejpam-5259	161	16	r	r	X
ejpam-5259	161	17	,	,	PUNCT
ejpam-5259	161	18	δ	δ	PROPN
ejpam-5259	161	19	,	,	PUNCT
ejpam-5259	161	20	λ]gk(ς	λ]gk(ς	PROPN
ejpam-5259	161	21	)	)	PUNCT
ejpam-5259	162	1	ik(sα	ik(sα	PROPN
ejpam-5259	162	2	η	η	PROPN
ejpam-5259	162	3	[	[	X
ejpam-5259	162	4	r	r	X
ejpam-5259	162	5	,	,	PUNCT
ejpam-5259	162	6	δ	δ	PROPN
ejpam-5259	162	7	,	,	PUNCT
ejpam-5259	162	8	λ]ℏk(ς	λ]ℏk(ς	PROPN
ejpam-5259	162	9	)	)	PUNCT
ejpam-5259	163	1	+	+	CCONJ
ejpam-5259	163	2	(	(	PUNCT
ejpam-5259	163	3	−1)kik(sα	−1)kik(sα	PROPN
ejpam-5259	163	4	η	η	PROPN
ejpam-5259	164	1	[	[	X
ejpam-5259	164	2	r	r	X
ejpam-5259	164	3	,	,	PUNCT
ejpam-5259	164	4	δ	δ	PROPN
ejpam-5259	164	5	,	,	PUNCT
ejpam-5259	164	6	λ]gk(ς	λ]gk(ς	PROPN
ejpam-5259	164	7	)	)	PUNCT
ejpam-5259	164	8	}	}	PUNCT
ejpam-5259	165	1	=	=	PUNCT
ejpam-5259	165	2	re	re	VERB
ejpam-5259	165	3			PROPN
ejpam-5259	165	4	1−γ	1−γ	NUM
ejpam-5259	165	5	ς	ς	PROPN
ejpam-5259	165	6	−	−	PROPN
ejpam-5259	165	7	(	(	PUNCT
ejpam-5259	165	8	∞∑	∞∑	NUM
ejpam-5259	165	9	µ=1	µ=1	PUNCT
ejpam-5259	165	10	γ(η)[1+λ(µ−1)]k	γ(η)[1+λ(µ−1)]k	X
ejpam-5259	165	11	γ(α(µ+1)+η	γ(α(µ+1)+η	NUM
ejpam-5259	165	12	)	)	PUNCT
ejpam-5259	165	13	(	(	PUNCT
ejpam-5259	165	14	µ+δ	µ+δ	NUM
ejpam-5259	165	15	1+δ	1+δ	NUM
ejpam-5259	165	16	)	)	PUNCT
ejpam-5259	165	17	r	r	NOUN
ejpam-5259	165	18	(	(	PUNCT
ejpam-5259	165	19	µ+	µ+	X
ejpam-5259	165	20	γ	γ	X
ejpam-5259	165	21	)	)	PUNCT
ejpam-5259	165	22	aµςµ	aµςµ	NOUN
ejpam-5259	165	23	+	+	CCONJ
ejpam-5259	165	24	∞∑	∞∑	NUM
ejpam-5259	165	25	µ=1	µ=1	PUNCT
ejpam-5259	165	26	γ(η)[1+λ(µ−1)]k	γ(η)[1+λ(µ−1)]k	X
ejpam-5259	165	27	γ(α(µ+1)+η	γ(α(µ+1)+η	NUM
ejpam-5259	165	28	)	)	PUNCT
ejpam-5259	165	29	(	(	PUNCT
ejpam-5259	165	30	µ+δ	µ+δ	NUM
ejpam-5259	165	31	1+δ	1+δ	NUM
ejpam-5259	165	32	)	)	PUNCT
ejpam-5259	166	1	r	r	NOUN
ejpam-5259	166	2	(	(	PUNCT
ejpam-5259	166	3	µ−	µ−	PROPN
ejpam-5259	166	4	γ	γ	PROPN
ejpam-5259	166	5	)	)	PUNCT
ejpam-5259	166	6	bµ	bµ	PROPN
ejpam-5259	166	7	ςµ	ςµ	NOUN
ejpam-5259	166	8	)	)	PUNCT
ejpam-5259	166	9	1	1	NUM
ejpam-5259	166	10	ς	ς	PROPN
ejpam-5259	166	11	+	+	PUNCT
ejpam-5259	166	12	∞∑	∞∑	NUM
ejpam-5259	166	13	µ=1	µ=1	PUNCT
ejpam-5259	166	14	γ(η)[1+λ(µ−1)]k	γ(η)[1+λ(µ−1)]k	X
ejpam-5259	166	15	γ(α(µ+1)+η	γ(α(µ+1)+η	NUM
ejpam-5259	166	16	)	)	PUNCT
ejpam-5259	166	17	(	(	PUNCT
ejpam-5259	166	18	µ+δ	µ+δ	NUM
ejpam-5259	166	19	1+δ	1+δ	NUM
ejpam-5259	166	20	)	)	PUNCT
ejpam-5259	166	21	r	r	NOUN
ejpam-5259	166	22	|aµ|ςµ	|aµ|ςµ	NUM
ejpam-5259	166	23	−	−	PROPN
ejpam-5259	166	24	∞∑	∞∑	PROPN
ejpam-5259	166	25	µ=1	µ=1	PUNCT
ejpam-5259	166	26	γ(η)[1+λ(µ−1)]k	γ(η)[1+λ(µ−1)]k	X
ejpam-5259	166	27	γ(α(µ+1)+η	γ(α(µ+1)+η	NUM
ejpam-5259	166	28	)	)	PUNCT
ejpam-5259	166	29	(	(	PUNCT
ejpam-5259	166	30	µ+δ	µ+δ	NUM
ejpam-5259	166	31	1+δ	1+δ	NUM
ejpam-5259	166	32	)	)	PUNCT
ejpam-5259	166	33	r	r	NOUN
ejpam-5259	166	34	|bµ|ςs	|bµ|ςs	NOUN
ejpam-5259	166	35			NOUN
ejpam-5259	166	36	>	>	X
ejpam-5259	166	37	0	0	NUM
ejpam-5259	166	38	.	.	PUNCT
ejpam-5259	167	1	(	(	PUNCT
ejpam-5259	167	2	17	17	NUM
ejpam-5259	167	3	)	)	PUNCT
ejpam-5259	167	4	the	the	DET
ejpam-5259	167	5	equation	equation	NOUN
ejpam-5259	167	6	(	(	PUNCT
ejpam-5259	167	7	17	17	NUM
ejpam-5259	167	8	)	)	PUNCT
ejpam-5259	167	9	must	must	AUX
ejpam-5259	167	10	be	be	AUX
ejpam-5259	167	11	satisfied	satisfied	ADJ
ejpam-5259	167	12	for	for	ADP
ejpam-5259	167	13	all	all	PRON
ejpam-5259	167	14	ς	ς	PROPN
ejpam-5259	167	15	∈	∈	PROPN
ejpam-5259	167	16	♢	♢	PROPN
ejpam-5259	167	17	∗.	∗.	PROPN
ejpam-5259	167	18	when	when	SCONJ
ejpam-5259	167	19	we	we	PRON
ejpam-5259	167	20	select	select	VERB
ejpam-5259	167	21	the	the	DET
ejpam-5259	167	22	value	value	NOUN
ejpam-5259	167	23	of	of	ADP
ejpam-5259	167	24	ς	ς	PROPN
ejpam-5259	167	25	on	on	ADP
ejpam-5259	167	26	the	the	DET
ejpam-5259	167	27	positive	positive	ADJ
ejpam-5259	167	28	real	real	ADJ
ejpam-5259	167	29	axis	axis	NOUN
ejpam-5259	167	30	,	,	PUNCT
ejpam-5259	167	31	with	with	ADP
ejpam-5259	167	32	0	0	NUM
ejpam-5259	167	33	<	<	X
ejpam-5259	167	34	ς	ς	PROPN
ejpam-5259	167	35	=	=	SYM
ejpam-5259	167	36	r	r	NOUN
ejpam-5259	167	37	<	<	X
ejpam-5259	167	38	1	1	NUM
ejpam-5259	167	39	,	,	PUNCT
ejpam-5259	167	40	we	we	PRON
ejpam-5259	167	41	obtain	obtain	PROPN
ejpam-5259	167	42	1−	1−	NUM
ejpam-5259	167	43	γ	γ	NOUN
ejpam-5259	167	44	−	−	PROPN
ejpam-5259	167	45	∞∑	∞∑	PROPN
ejpam-5259	167	46	µ=1	µ=1	PUNCT
ejpam-5259	167	47	γ(η)[1+λ(µ−1)]k	γ(η)[1+λ(µ−1)]k	X
ejpam-5259	167	48	γ(α(µ+1)+η	γ(α(µ+1)+η	NUM
ejpam-5259	167	49	)	)	PUNCT
ejpam-5259	168	1	(	(	PUNCT
ejpam-5259	168	2	µ+δ	µ+δ	NUM
ejpam-5259	168	3	1+δ	1+δ	NUM
ejpam-5259	168	4	)	)	PUNCT
ejpam-5259	168	5	r	r	NOUN
ejpam-5259	168	6	(	(	PUNCT
ejpam-5259	168	7	µ+	µ+	X
ejpam-5259	168	8	γ	γ	NOUN
ejpam-5259	168	9	)	)	PUNCT
ejpam-5259	168	10	|aµ|rµ+1	|aµ|rµ+1	NOUN
ejpam-5259	168	11	−	−	NOUN
ejpam-5259	168	12	∞∑	∞∑	PROPN
ejpam-5259	168	13	µ=1	µ=1	PUNCT
ejpam-5259	168	14	γ(η)[1+λ(µ−1)]k	γ(η)[1+λ(µ−1)]k	X
ejpam-5259	168	15	γ(α(µ+1)+η	γ(α(µ+1)+η	NUM
ejpam-5259	168	16	)	)	PUNCT
ejpam-5259	168	17	(	(	PUNCT
ejpam-5259	168	18	µ+δ	µ+δ	NUM
ejpam-5259	168	19	1+δ	1+δ	NUM
ejpam-5259	168	20	)	)	PUNCT
ejpam-5259	168	21	r	r	NOUN
ejpam-5259	168	22	(	(	PUNCT
ejpam-5259	168	23	µ+	µ+	X
ejpam-5259	168	24	γ	γ	NOUN
ejpam-5259	168	25	)	)	PUNCT
ejpam-5259	168	26	|bµ|(µ+	|bµ|(µ+	PROPN
ejpam-5259	168	27	γ)rµ+1	γ)rµ+1	NOUN
ejpam-5259	168	28			NOUN
ejpam-5259	168	29			PUNCT
ejpam-5259	168	30	1	1	NUM
ejpam-5259	168	31	+	+	CCONJ
ejpam-5259	168	32	∞∑	∞∑	NUM
ejpam-5259	168	33	µ=1	µ=1	PUNCT
ejpam-5259	168	34	[	[	X
ejpam-5259	168	35	1	1	NUM
ejpam-5259	168	36	+	+	NUM
ejpam-5259	168	37	(	(	PUNCT
ejpam-5259	168	38	µ−	µ−	PROPN
ejpam-5259	168	39	1)λ]k	1)λ]k	NUM
ejpam-5259	168	40	(	(	PUNCT
ejpam-5259	168	41	µ+δ	µ+δ	NUM
ejpam-5259	168	42	1+δ	1+δ	NUM
ejpam-5259	168	43	)	)	PUNCT
ejpam-5259	168	44	r	r	NOUN
ejpam-5259	168	45	ωµ+1(α	ωµ+1(α	PROPN
ejpam-5259	168	46	,	,	PUNCT
ejpam-5259	168	47	η)|aµ|rµ+1−	η)|aµ|rµ+1−	PROPN
ejpam-5259	168	48	∞∑	∞∑	PROPN
ejpam-5259	168	49	µ=1	µ=1	PROPN
ejpam-5259	168	50	[	[	X
ejpam-5259	168	51	1	1	NUM
ejpam-5259	168	52	+	+	NUM
ejpam-5259	168	53	(	(	PUNCT
ejpam-5259	168	54	µ−	µ−	PROPN
ejpam-5259	168	55	1)λ]k	1)λ]k	NUM
ejpam-5259	168	56	(	(	PUNCT
ejpam-5259	168	57	µ+δ	µ+δ	NUM
ejpam-5259	168	58	1+δ	1+δ	NUM
ejpam-5259	168	59	)	)	PUNCT
ejpam-5259	168	60	r	r	NOUN
ejpam-5259	168	61	ωµ+1(α	ωµ+1(α	PROPN
ejpam-5259	168	62	,	,	PUNCT
ejpam-5259	168	63	η)|bµ|rµ+1	η)|bµ|rµ+1	VERB
ejpam-5259	168	64			PROPN
ejpam-5259	168	65	>	>	X
ejpam-5259	168	66	γ	γ	X
ejpam-5259	168	67	.	.	PROPN
ejpam-5259	168	68	(	(	PUNCT
ejpam-5259	168	69	18	18	NUM
ejpam-5259	168	70	)	)	PUNCT
ejpam-5259	168	71	s.	s.	PROPN
ejpam-5259	168	72	ahmed	ahmed	PROPN
ejpam-5259	168	73	,	,	PUNCT
ejpam-5259	168	74	a.	a.	PROPN
ejpam-5259	168	75	alsoboh	alsoboh	PROPN
ejpam-5259	168	76	,	,	PUNCT
ejpam-5259	168	77	m.	m.	NOUN
ejpam-5259	168	78	darus	darus	NOUN
ejpam-5259	168	79	/	/	SYM
ejpam-5259	168	80	eur	eur	PROPN
ejpam-5259	168	81	.	.	PUNCT
ejpam-5259	169	1	j.	j.	PROPN
ejpam-5259	169	2	pure	pure	PROPN
ejpam-5259	169	3	appl	appl	PROPN
ejpam-5259	169	4	.	.	PROPN
ejpam-5259	169	5	math	math	PROPN
ejpam-5259	169	6	,	,	PUNCT
ejpam-5259	169	7	17	17	NUM
ejpam-5259	169	8	(	(	PUNCT
ejpam-5259	169	9	3	3	NUM
ejpam-5259	169	10	)	)	PUNCT
ejpam-5259	169	11	(	(	PUNCT
ejpam-5259	169	12	2024	2024	NUM
ejpam-5259	169	13	)	)	PUNCT
ejpam-5259	169	14	,	,	PUNCT
ejpam-5259	169	15	1894	1894	NUM
ejpam-5259	169	16	-	-	SYM
ejpam-5259	169	17	1907	1907	NUM
ejpam-5259	169	18	1901	1901	NUM
ejpam-5259	169	19	if	if	SCONJ
ejpam-5259	169	20	condition	condition	NOUN
ejpam-5259	169	21	(	(	PUNCT
ejpam-5259	169	22	2	2	X
ejpam-5259	169	23	)	)	PUNCT
ejpam-5259	169	24	is	be	AUX
ejpam-5259	169	25	not	not	PART
ejpam-5259	169	26	fulfilled	fulfil	VERB
ejpam-5259	169	27	,	,	PUNCT
ejpam-5259	169	28	then	then	ADV
ejpam-5259	169	29	as	as	ADP
ejpam-5259	169	30	r	r	NOUN
ejpam-5259	169	31	→	→	SYM
ejpam-5259	169	32	1−	1−	NUM
ejpam-5259	169	33	,	,	PUNCT
ejpam-5259	169	34	the	the	DET
ejpam-5259	169	35	numerator	numerator	NOUN
ejpam-5259	169	36	of	of	ADP
ejpam-5259	169	37	(	(	PUNCT
ejpam-5259	169	38	18	18	NUM
ejpam-5259	169	39	)	)	PUNCT
ejpam-5259	169	40	becomes	become	VERB
ejpam-5259	169	41	negative	negative	ADJ
ejpam-5259	169	42	.	.	PUNCT
ejpam-5259	170	1	as	as	ADP
ejpam-5259	170	2	a	a	DET
ejpam-5259	170	3	result	result	NOUN
ejpam-5259	170	4	,	,	PUNCT
ejpam-5259	170	5	there	there	PRON
ejpam-5259	170	6	exists	exist	VERB
ejpam-5259	170	7	a	a	DET
ejpam-5259	170	8	value	value	NOUN
ejpam-5259	170	9	ς0	ς0	NOUN
ejpam-5259	170	10	=	=	SYM
ejpam-5259	170	11	r0	r0	NOUN
ejpam-5259	170	12	within	within	ADP
ejpam-5259	170	13	the	the	DET
ejpam-5259	170	14	interval	interval	NOUN
ejpam-5259	170	15	(	(	PUNCT
ejpam-5259	170	16	0	0	NUM
ejpam-5259	170	17	,	,	PUNCT
ejpam-5259	170	18	1	1	NUM
ejpam-5259	170	19	)	)	PUNCT
ejpam-5259	170	20	such	such	ADJ
ejpam-5259	170	21	that	that	SCONJ
ejpam-5259	170	22	the	the	DET
ejpam-5259	170	23	left	left	ADJ
ejpam-5259	170	24	-	-	PUNCT
ejpam-5259	170	25	hand	hand	NOUN
ejpam-5259	170	26	side	side	NOUN
ejpam-5259	170	27	of	of	ADP
ejpam-5259	170	28	inequality	inequality	NOUN
ejpam-5259	170	29	(	(	PUNCT
ejpam-5259	170	30	18	18	NUM
ejpam-5259	170	31	)	)	PUNCT
ejpam-5259	170	32	is	be	AUX
ejpam-5259	170	33	negative	negative	ADJ
ejpam-5259	170	34	.	.	PUNCT
ejpam-5259	171	1	this	this	PRON
ejpam-5259	171	2	contradicts	contradict	VERB
ejpam-5259	171	3	the	the	DET
ejpam-5259	171	4	condition	condition	NOUN
ejpam-5259	171	5	stated	state	VERB
ejpam-5259	171	6	in	in	ADP
ejpam-5259	171	7	(	(	PUNCT
ejpam-5259	171	8	2	2	NUM
ejpam-5259	171	9	)	)	PUNCT
ejpam-5259	171	10	,	,	PUNCT
ejpam-5259	171	11	thus	thus	ADV
ejpam-5259	171	12	completing	complete	VERB
ejpam-5259	171	13	the	the	DET
ejpam-5259	171	14	proof	proof	NOUN
ejpam-5259	171	15	.	.	PUNCT
ejpam-5259	172	1	for	for	ADP
ejpam-5259	172	2	k	k	PROPN
ejpam-5259	172	3	=	=	SYM
ejpam-5259	172	4	0	0	NUM
ejpam-5259	172	5	in	in	ADP
ejpam-5259	172	6	theorem	theorem	NOUN
ejpam-5259	172	7	2	2	NUM
ejpam-5259	172	8	,	,	PUNCT
ejpam-5259	172	9	we	we	PRON
ejpam-5259	172	10	have	have	VERB
ejpam-5259	172	11	the	the	DET
ejpam-5259	172	12	following	follow	VERB
ejpam-5259	172	13	corollary	corollary	NOUN
ejpam-5259	172	14	.	.	PUNCT
ejpam-5259	173	1	corollary	corollary	ADJ
ejpam-5259	173	2	1	1	NUM
ejpam-5259	173	3	.	.	PUNCT
ejpam-5259	174	1	for	for	ADP
ejpam-5259	174	2	f	f	NOUN
ejpam-5259	174	3	=	=	SYM
ejpam-5259	174	4	h	h	PROPN
ejpam-5259	175	1	+	+	CCONJ
ejpam-5259	175	2	g	g	NOUN
ejpam-5259	175	3	of	of	ADP
ejpam-5259	175	4	the	the	DET
ejpam-5259	175	5	form	form	NOUN
ejpam-5259	175	6	(	(	PUNCT
ejpam-5259	175	7	7	7	NUM
ejpam-5259	175	8	)	)	PUNCT
ejpam-5259	175	9	.	.	PUNCT
ejpam-5259	176	1	then	then	ADV
ejpam-5259	176	2	,	,	PUNCT
ejpam-5259	176	3	f	f	PROPN
ejpam-5259	176	4	∈	∈	PROPN
ejpam-5259	176	5	mkh(0	mkh(0	NOUN
ejpam-5259	176	6	,	,	PUNCT
ejpam-5259	176	7	r	r	NOUN
ejpam-5259	176	8	,	,	PUNCT
ejpam-5259	176	9	α	α	PROPN
ejpam-5259	176	10	,	,	PUNCT
ejpam-5259	176	11	η	η	PROPN
ejpam-5259	176	12	,	,	PUNCT
ejpam-5259	176	13	δ	δ	PROPN
ejpam-5259	176	14	,	,	PUNCT
ejpam-5259	176	15	λ	λ	PROPN
ejpam-5259	176	16	,	,	PUNCT
ejpam-5259	176	17	γ	γ	NOUN
ejpam-5259	176	18	)	)	PUNCT
ejpam-5259	176	19	if	if	SCONJ
ejpam-5259	176	20	and	and	CCONJ
ejpam-5259	176	21	only	only	ADV
ejpam-5259	176	22	if	if	SCONJ
ejpam-5259	176	23	the	the	DET
ejpam-5259	176	24	inequality	inequality	NOUN
ejpam-5259	176	25	∞∑	∞∑	NUM
ejpam-5259	176	26	µ=1	µ=1	ADP
ejpam-5259	176	27	γ(η	γ(η	NOUN
ejpam-5259	176	28	)	)	PUNCT
ejpam-5259	176	29	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	176	30	1	1	NUM
ejpam-5259	176	31	)	)	PUNCT
ejpam-5259	176	32	+	+	NUM
ejpam-5259	176	33	η	η	X
ejpam-5259	176	34	)	)	PUNCT
ejpam-5259	176	35	(	(	PUNCT
ejpam-5259	176	36	µ+	µ+	X
ejpam-5259	176	37	δ	δ	PROPN
ejpam-5259	176	38	1	1	NUM
ejpam-5259	176	39	+	+	CCONJ
ejpam-5259	176	40	δ	δ	NOUN
ejpam-5259	176	41	)	)	PUNCT
ejpam-5259	176	42	r	r	NOUN
ejpam-5259	176	43	[	[	PUNCT
ejpam-5259	176	44	(	(	PUNCT
ejpam-5259	176	45	µ+	µ+	X
ejpam-5259	176	46	γ	γ	NOUN
ejpam-5259	176	47	)	)	PUNCT
ejpam-5259	176	48	|aµ|+	|aµ|+	PROPN
ejpam-5259	176	49	(	(	PUNCT
ejpam-5259	176	50	µ−	µ−	PROPN
ejpam-5259	176	51	γ	γ	PROPN
ejpam-5259	176	52	)	)	PUNCT
ejpam-5259	176	53	|bµ|	|bµ|	NOUN
ejpam-5259	176	54	]	]	PUNCT
ejpam-5259	176	55	≤	≤	PROPN
ejpam-5259	176	56	1−	1−	NUM
ejpam-5259	176	57	γ	γ	X
ejpam-5259	176	58	,	,	PUNCT
ejpam-5259	176	59	is	be	AUX
ejpam-5259	176	60	satisfied	satisfied	ADJ
ejpam-5259	176	61	.	.	PUNCT
ejpam-5259	177	1	corollary	corollary	ADJ
ejpam-5259	177	2	2	2	NUM
ejpam-5259	177	3	.	.	PUNCT
ejpam-5259	178	1	[	[	X
ejpam-5259	178	2	17	17	NUM
ejpam-5259	178	3	]	]	PUNCT
ejpam-5259	178	4	for	for	ADP
ejpam-5259	178	5	f	f	PROPN
ejpam-5259	178	6	=	=	SYM
ejpam-5259	178	7	h	h	PROPN
ejpam-5259	179	1	+	+	CCONJ
ejpam-5259	179	2	g	g	NOUN
ejpam-5259	179	3	of	of	ADP
ejpam-5259	179	4	the	the	DET
ejpam-5259	179	5	form	form	NOUN
ejpam-5259	179	6	(	(	PUNCT
ejpam-5259	179	7	7	7	NUM
ejpam-5259	179	8	)	)	PUNCT
ejpam-5259	179	9	.	.	PUNCT
ejpam-5259	180	1	then	then	ADV
ejpam-5259	180	2	,	,	PUNCT
ejpam-5259	180	3	f	f	PROPN
ejpam-5259	180	4	∈	∈	PROPN
ejpam-5259	180	5	mkh(0	mkh(0	NOUN
ejpam-5259	180	6	,	,	PUNCT
ejpam-5259	180	7	r	r	NOUN
ejpam-5259	180	8	,	,	PUNCT
ejpam-5259	180	9	α	α	PROPN
ejpam-5259	180	10	,	,	PUNCT
ejpam-5259	180	11	η	η	PROPN
ejpam-5259	180	12	,	,	PUNCT
ejpam-5259	180	13	δ	δ	PROPN
ejpam-5259	180	14	,	,	PUNCT
ejpam-5259	180	15	λ	λ	PROPN
ejpam-5259	180	16	,	,	PUNCT
ejpam-5259	180	17	γ	γ	NOUN
ejpam-5259	180	18	)	)	PUNCT
ejpam-5259	180	19	if	if	SCONJ
ejpam-5259	180	20	and	and	CCONJ
ejpam-5259	180	21	only	only	ADV
ejpam-5259	180	22	if	if	SCONJ
ejpam-5259	180	23	the	the	DET
ejpam-5259	180	24	inequality	inequality	NOUN
ejpam-5259	180	25	∞∑	∞∑	NUM
ejpam-5259	180	26	µ=1	µ=1	PUNCT
ejpam-5259	180	27	[	[	PUNCT
ejpam-5259	180	28	(	(	PUNCT
ejpam-5259	180	29	µ+	µ+	X
ejpam-5259	180	30	γ	γ	NOUN
ejpam-5259	180	31	)	)	PUNCT
ejpam-5259	180	32	|aµ|+	|aµ|+	PROPN
ejpam-5259	180	33	(	(	PUNCT
ejpam-5259	180	34	µ−	µ−	PROPN
ejpam-5259	180	35	γ	γ	PROPN
ejpam-5259	180	36	)	)	PUNCT
ejpam-5259	180	37	|bµ|	|bµ|	NOUN
ejpam-5259	180	38	]	]	PUNCT
ejpam-5259	180	39	≤	≤	PROPN
ejpam-5259	180	40	1−	1−	NUM
ejpam-5259	180	41	γ	γ	X
ejpam-5259	180	42	,	,	PUNCT
ejpam-5259	180	43	is	be	AUX
ejpam-5259	180	44	satisfied	satisfied	ADJ
ejpam-5259	180	45	.	.	PUNCT
ejpam-5259	181	1	the	the	DET
ejpam-5259	181	2	ensuing	ensue	VERB
ejpam-5259	181	3	theorem	theorem	NOUN
ejpam-5259	181	4	establishes	establish	VERB
ejpam-5259	181	5	a	a	DET
ejpam-5259	181	6	growth	growth	NOUN
ejpam-5259	181	7	property	property	NOUN
ejpam-5259	181	8	for	for	ADP
ejpam-5259	181	9	the	the	DET
ejpam-5259	181	10	class	class	NOUN
ejpam-5259	181	11	t	t	PROPN
ejpam-5259	181	12	mkh(k	mkh(k	PROPN
ejpam-5259	181	13	,	,	PUNCT
ejpam-5259	181	14	r	r	NOUN
ejpam-5259	181	15	,	,	PUNCT
ejpam-5259	181	16	α	α	PROPN
ejpam-5259	181	17	,	,	PUNCT
ejpam-5259	181	18	η	η	PROPN
ejpam-5259	181	19	,	,	PUNCT
ejpam-5259	181	20	δ	δ	PROPN
ejpam-5259	181	21	,	,	PUNCT
ejpam-5259	181	22	λ	λ	PROPN
ejpam-5259	181	23	,	,	PUNCT
ejpam-5259	181	24	γ	γ	NOUN
ejpam-5259	181	25	)	)	PUNCT
ejpam-5259	181	26	.	.	PUNCT
ejpam-5259	182	1	theorem	theorem	NOUN
ejpam-5259	182	2	3	3	X
ejpam-5259	182	3	.	.	PUNCT
ejpam-5259	183	1	let	let	VERB
ejpam-5259	183	2	fk(ς	fk(ς	NOUN
ejpam-5259	183	3	)	)	PUNCT
ejpam-5259	183	4	=	=	SYM
ejpam-5259	183	5	ℏk(ς	ℏk(ς	X
ejpam-5259	183	6	)	)	PUNCT
ejpam-5259	183	7	+	+	CCONJ
ejpam-5259	183	8	gk(ς	gk(ς	X
ejpam-5259	183	9	)	)	PUNCT
ejpam-5259	183	10	∈	∈	PROPN
ejpam-5259	183	11	t	t	PROPN
ejpam-5259	183	12	mkh(k	mkh(k	PROPN
ejpam-5259	183	13	,	,	PUNCT
ejpam-5259	183	14	r	r	NOUN
ejpam-5259	183	15	,	,	PUNCT
ejpam-5259	183	16	α	α	PROPN
ejpam-5259	183	17	,	,	PUNCT
ejpam-5259	183	18	η	η	PROPN
ejpam-5259	183	19	,	,	PUNCT
ejpam-5259	183	20	δ	δ	PROPN
ejpam-5259	183	21	,	,	PUNCT
ejpam-5259	183	22	λ	λ	PROPN
ejpam-5259	183	23	,	,	PUNCT
ejpam-5259	183	24	γ	γ	NOUN
ejpam-5259	183	25	)	)	PUNCT
ejpam-5259	183	26	of	of	ADP
ejpam-5259	183	27	the	the	DET
ejpam-5259	183	28	form	form	NOUN
ejpam-5259	183	29	(	(	PUNCT
ejpam-5259	183	30	13	13	NUM
ejpam-5259	183	31	)	)	PUNCT
ejpam-5259	183	32	,	,	PUNCT
ejpam-5259	183	33	then	then	ADV
ejpam-5259	183	34	we	we	PRON
ejpam-5259	183	35	have	have	VERB
ejpam-5259	183	36	for	for	ADP
ejpam-5259	183	37	|z|	|z|	NOUN
ejpam-5259	183	38	=	=	SYM
ejpam-5259	184	1	r	r	NOUN
ejpam-5259	184	2	<	<	X
ejpam-5259	184	3	1	1	NUM
ejpam-5259	184	4	:	:	SYM
ejpam-5259	184	5	1	1	NUM
ejpam-5259	184	6	r	r	NOUN
ejpam-5259	184	7	−	−	PROPN
ejpam-5259	184	8	γ(3α+	γ(3α+	NOUN
ejpam-5259	184	9	η)(1−	η)(1−	PROPN
ejpam-5259	184	10	γ)r2	γ)r2	PROPN
ejpam-5259	184	11	γ(η)(1	γ(η)(1	PROPN
ejpam-5259	184	12	+	+	CCONJ
ejpam-5259	184	13	λ)k	λ)k	X
ejpam-5259	184	14	(	(	PUNCT
ejpam-5259	184	15	2−	2−	NUM
ejpam-5259	184	16	γ	γ	NOUN
ejpam-5259	184	17	)	)	PUNCT
ejpam-5259	184	18	(	(	PUNCT
ejpam-5259	184	19	2+δ	2+δ	NUM
ejpam-5259	184	20	1+δ	1+δ	NUM
ejpam-5259	184	21	)	)	PUNCT
ejpam-5259	185	1	r	r	NOUN
ejpam-5259	185	2	≤	≤	NOUN
ejpam-5259	185	3	|fk(ς)|	|fk(ς)|	NOUN
ejpam-5259	185	4	≤	≤	NUM
ejpam-5259	185	5	1	1	NUM
ejpam-5259	185	6	r	r	NOUN
ejpam-5259	185	7	+	+	NOUN
ejpam-5259	185	8	γ(3α+	γ(3α+	NOUN
ejpam-5259	185	9	η)(1−	η)(1−	ADP
ejpam-5259	185	10	γ)r2	γ)r2	PROPN
ejpam-5259	185	11	γ(η)(1	γ(η)(1	PROPN
ejpam-5259	186	1	+	+	CCONJ
ejpam-5259	186	2	λ)k	λ)k	X
ejpam-5259	186	3	(	(	PUNCT
ejpam-5259	187	1	2−	2−	NUM
ejpam-5259	187	2	γ	γ	NOUN
ejpam-5259	187	3	)	)	PUNCT
ejpam-5259	187	4	(	(	PUNCT
ejpam-5259	187	5	2+δ	2+δ	NUM
ejpam-5259	187	6	1+δ	1+δ	NUM
ejpam-5259	187	7	)	)	PUNCT
ejpam-5259	188	1	r	r	NOUN
ejpam-5259	188	2	.	.	PUNCT
ejpam-5259	189	1	proof	proof	NOUN
ejpam-5259	189	2	.	.	PUNCT
ejpam-5259	190	1	taking	take	VERB
ejpam-5259	190	2	the	the	DET
ejpam-5259	190	3	absolute	absolute	ADJ
ejpam-5259	190	4	value	value	NOUN
ejpam-5259	190	5	for	for	ADP
ejpam-5259	190	6	fk(ς	fk(ς	NOUN
ejpam-5259	190	7	)	)	PUNCT
ejpam-5259	190	8	given	give	VERB
ejpam-5259	190	9	by	by	ADP
ejpam-5259	190	10	(	(	PUNCT
ejpam-5259	190	11	13	13	NUM
ejpam-5259	190	12	)	)	PUNCT
ejpam-5259	190	13	,	,	PUNCT
ejpam-5259	190	14	we	we	PRON
ejpam-5259	190	15	have	have	VERB
ejpam-5259	190	16	|fk(ς)|	|fk(ς)|	NOUN
ejpam-5259	190	17	=	=	SYM
ejpam-5259	190	18	∣∣∣∣∣∣(−1)k	∣∣∣∣∣∣(−1)k	ADJ
ejpam-5259	190	19	ς	ς	PROPN
ejpam-5259	190	20	+	+	PUNCT
ejpam-5259	190	21	∞∑	∞∑	NUM
ejpam-5259	190	22	µ=1	µ=1	ADV
ejpam-5259	190	23	aµς	aµς	NOUN
ejpam-5259	190	24	µ	µ	AUX
ejpam-5259	190	25	+	+	CCONJ
ejpam-5259	190	26	(	(	PUNCT
ejpam-5259	190	27	−1)k	−1)k	PROPN
ejpam-5259	190	28	∞∑	∞∑	NUM
ejpam-5259	190	29	µ=1	µ=1	PUNCT
ejpam-5259	190	30	bµςµ	bµςµ	ADJ
ejpam-5259	190	31	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5259	190	32	≤	≤	ADV
ejpam-5259	190	33	1	1	NUM
ejpam-5259	190	34	r	r	NOUN
ejpam-5259	190	35	+	+	NOUN
ejpam-5259	191	1	∞∑	∞∑	PROPN
ejpam-5259	191	2	µ=1	µ=1	PROPN
ejpam-5259	191	3	(	(	PUNCT
ejpam-5259	191	4	|aµ|+	|aµ|+	ADP
ejpam-5259	191	5	|bk|)rµ	|bk|)rµ	PROPN
ejpam-5259	191	6	≤	≤	NOUN
ejpam-5259	191	7	1	1	NUM
ejpam-5259	191	8	r	r	NOUN
ejpam-5259	191	9	+	+	NOUN
ejpam-5259	191	10	∞∑	∞∑	PROPN
ejpam-5259	191	11	µ=1	µ=1	SYM
ejpam-5259	191	12	(	(	PUNCT
ejpam-5259	191	13	|aµ|+	|aµ|+	ADP
ejpam-5259	191	14	|bk|)r	|bk|)r	SYM
ejpam-5259	191	15	≤	≤	NUM
ejpam-5259	191	16	1	1	NUM
ejpam-5259	191	17	r	r	NOUN
ejpam-5259	191	18	+	+	NOUN
ejpam-5259	191	19	γ(3α+η)(1−γ	γ(3α+η)(1−γ	NOUN
ejpam-5259	191	20	)	)	PUNCT
ejpam-5259	191	21	γ(η)(1+λ)k	γ(η)(1+λ)k	PROPN
ejpam-5259	191	22	(	(	PUNCT
ejpam-5259	191	23	2+δ	2+δ	NUM
ejpam-5259	191	24	1+δ	1+δ	NUM
ejpam-5259	191	25	)	)	PUNCT
ejpam-5259	192	1	r	r	NOUN
ejpam-5259	192	2	(	(	PUNCT
ejpam-5259	192	3	2−γ	2−γ	NUM
ejpam-5259	192	4	)	)	PUNCT
ejpam-5259	192	5	{	{	PUNCT
ejpam-5259	192	6	∞∑	∞∑	NUM
ejpam-5259	192	7	µ=1	µ=1	PUNCT
ejpam-5259	192	8	γ(η)[1+λ(µ−1)]k	γ(η)[1+λ(µ−1)]k	X
ejpam-5259	192	9	γ(α(µ+1)+η	γ(α(µ+1)+η	NUM
ejpam-5259	192	10	)	)	PUNCT
ejpam-5259	192	11	(	(	PUNCT
ejpam-5259	192	12	µ+δ	µ+δ	NUM
ejpam-5259	192	13	1+δ	1+δ	NUM
ejpam-5259	192	14	)	)	PUNCT
ejpam-5259	192	15	r	r	NOUN
ejpam-5259	192	16	[	[	PUNCT
ejpam-5259	192	17	µ+γ	µ+γ	NUM
ejpam-5259	192	18	1−γ	1−γ	NUM
ejpam-5259	192	19	|aµ|+	|aµ|+	ADV
ejpam-5259	192	20	µ−γ	µ−γ	ADV
ejpam-5259	192	21	1−γ	1−γ	NUM
ejpam-5259	192	22	|bµ|	|bµ|	NOUN
ejpam-5259	192	23	]	]	PUNCT
ejpam-5259	192	24	}	}	PUNCT
ejpam-5259	192	25	r	r	NOUN
ejpam-5259	192	26	≤	≤	NUM
ejpam-5259	192	27	1	1	NUM
ejpam-5259	192	28	r	r	NOUN
ejpam-5259	192	29	+	+	NOUN
ejpam-5259	192	30	γ(3α+	γ(3α+	NOUN
ejpam-5259	192	31	η)(1−	η)(1−	PROPN
ejpam-5259	192	32	γ	γ	NOUN
ejpam-5259	192	33	)	)	PUNCT
ejpam-5259	192	34	γ(η)(1	γ(η)(1	NOUN
ejpam-5259	193	1	+	+	CCONJ
ejpam-5259	193	2	λ)k	λ)k	X
ejpam-5259	193	3	(	(	PUNCT
ejpam-5259	193	4	2−	2−	NUM
ejpam-5259	193	5	γ	γ	NOUN
ejpam-5259	193	6	)	)	PUNCT
ejpam-5259	193	7	(	(	PUNCT
ejpam-5259	193	8	2+δ	2+δ	NUM
ejpam-5259	193	9	1+δ	1+δ	NUM
ejpam-5259	193	10	)	)	PUNCT
ejpam-5259	194	1	r	r	NOUN
ejpam-5259	194	2	.	.	PUNCT
ejpam-5259	195	1	the	the	DET
ejpam-5259	195	2	second	second	ADJ
ejpam-5259	195	3	inequality	inequality	NOUN
ejpam-5259	195	4	,	,	PUNCT
ejpam-5259	195	5	is	be	AUX
ejpam-5259	195	6	the	the	DET
ejpam-5259	195	7	same	same	ADJ
ejpam-5259	195	8	of	of	ADP
ejpam-5259	195	9	first	first	ADJ
ejpam-5259	195	10	inequality	inequality	NOUN
ejpam-5259	195	11	,	,	PUNCT
ejpam-5259	195	12	so	so	SCONJ
ejpam-5259	195	13	the	the	DET
ejpam-5259	195	14	proof	proof	NOUN
ejpam-5259	195	15	is	be	AUX
ejpam-5259	195	16	omitted	omit	VERB
ejpam-5259	195	17	.	.	PUNCT
ejpam-5259	196	1	this	this	PRON
ejpam-5259	196	2	proves	prove	VERB
ejpam-5259	196	3	the	the	DET
ejpam-5259	196	4	required	require	VERB
ejpam-5259	196	5	result	result	NOUN
ejpam-5259	196	6	.	.	PUNCT
ejpam-5259	197	1	s.	s.	PROPN
ejpam-5259	197	2	ahmed	ahmed	PROPN
ejpam-5259	197	3	,	,	PUNCT
ejpam-5259	197	4	a.	a.	PROPN
ejpam-5259	197	5	alsoboh	alsoboh	PROPN
ejpam-5259	197	6	,	,	PUNCT
ejpam-5259	197	7	m.	m.	NOUN
ejpam-5259	197	8	darus	darus	NOUN
ejpam-5259	197	9	/	/	SYM
ejpam-5259	197	10	eur	eur	PROPN
ejpam-5259	197	11	.	.	PUNCT
ejpam-5259	198	1	j.	j.	PROPN
ejpam-5259	198	2	pure	pure	PROPN
ejpam-5259	198	3	appl	appl	PROPN
ejpam-5259	198	4	.	.	PROPN
ejpam-5259	198	5	math	math	PROPN
ejpam-5259	198	6	,	,	PUNCT
ejpam-5259	198	7	17	17	NUM
ejpam-5259	198	8	(	(	PUNCT
ejpam-5259	198	9	3	3	NUM
ejpam-5259	198	10	)	)	PUNCT
ejpam-5259	198	11	(	(	PUNCT
ejpam-5259	198	12	2024	2024	NUM
ejpam-5259	198	13	)	)	PUNCT
ejpam-5259	198	14	,	,	PUNCT
ejpam-5259	198	15	1894	1894	NUM
ejpam-5259	198	16	-	-	SYM
ejpam-5259	198	17	1907	1907	NUM
ejpam-5259	198	18	1902	1902	NUM
ejpam-5259	198	19	3	3	X
ejpam-5259	198	20	.	.	PUNCT
ejpam-5259	198	21	extreme	extreme	ADJ
ejpam-5259	198	22	points	point	NOUN
ejpam-5259	198	23	subsequently	subsequently	ADV
ejpam-5259	198	24	,	,	PUNCT
ejpam-5259	198	25	we	we	PRON
ejpam-5259	198	26	identify	identify	VERB
ejpam-5259	198	27	the	the	DET
ejpam-5259	198	28	extreme	extreme	ADJ
ejpam-5259	198	29	points	point	NOUN
ejpam-5259	198	30	of	of	ADP
ejpam-5259	198	31	the	the	DET
ejpam-5259	198	32	closed	closed	ADJ
ejpam-5259	198	33	convex	convex	ADJ
ejpam-5259	198	34	hulls	hull	NOUN
ejpam-5259	198	35	of	of	ADP
ejpam-5259	198	36	the	the	DET
ejpam-5259	198	37	class	class	NOUN
ejpam-5259	198	38	t	t	PROPN
ejpam-5259	198	39	mkh(k	mkh(k	PROPN
ejpam-5259	198	40	,	,	PUNCT
ejpam-5259	198	41	r	r	NOUN
ejpam-5259	198	42	,	,	PUNCT
ejpam-5259	198	43	α	α	PROPN
ejpam-5259	198	44	,	,	PUNCT
ejpam-5259	198	45	η	η	PROPN
ejpam-5259	198	46	,	,	PUNCT
ejpam-5259	198	47	δ	δ	PROPN
ejpam-5259	198	48	,	,	PUNCT
ejpam-5259	198	49	λ	λ	PROPN
ejpam-5259	198	50	,	,	PUNCT
ejpam-5259	198	51	γ	γ	NOUN
ejpam-5259	198	52	)	)	PUNCT
ejpam-5259	198	53	,	,	PUNCT
ejpam-5259	198	54	designated	designate	VERB
ejpam-5259	198	55	as	as	ADP
ejpam-5259	198	56	clcot	clcot	PROPN
ejpam-5259	198	57	mkh	mkh	PROPN
ejpam-5259	198	58	.	.	PUNCT
ejpam-5259	199	1	theorem	theorem	VERB
ejpam-5259	199	2	4	4	NUM
ejpam-5259	199	3	.	.	PUNCT
ejpam-5259	199	4	consider	consider	VERB
ejpam-5259	199	5	a	a	DET
ejpam-5259	199	6	function	function	NOUN
ejpam-5259	199	7	fk	fk	INTJ
ejpam-5259	199	8	=	=	PUNCT
ejpam-5259	200	1	ℏk	ℏk	ADP
ejpam-5259	200	2	+	+	CCONJ
ejpam-5259	200	3	gk	gk	PROPN
ejpam-5259	200	4	in	in	ADP
ejpam-5259	200	5	the	the	DET
ejpam-5259	200	6	form	form	NOUN
ejpam-5259	200	7	(	(	PUNCT
ejpam-5259	200	8	13	13	NUM
ejpam-5259	200	9	)	)	PUNCT
ejpam-5259	200	10	.	.	PUNCT
ejpam-5259	201	1	then	then	ADV
ejpam-5259	201	2	,	,	PUNCT
ejpam-5259	201	3	f	f	PROPN
ejpam-5259	201	4	∈	∈	PROPN
ejpam-5259	201	5	clcot	clcot	PROPN
ejpam-5259	201	6	mkh	mkh	PROPN
ejpam-5259	201	7	if	if	SCONJ
ejpam-5259	201	8	and	and	CCONJ
ejpam-5259	201	9	only	only	ADV
ejpam-5259	201	10	if	if	SCONJ
ejpam-5259	201	11	fk,µ(ς	fk,µ(ς	NUM
ejpam-5259	201	12	)	)	PUNCT
ejpam-5259	201	13	can	can	AUX
ejpam-5259	201	14	be	be	AUX
ejpam-5259	201	15	represented	represent	VERB
ejpam-5259	201	16	as	as	ADP
ejpam-5259	201	17	fk(ς	fk(ς	NOUN
ejpam-5259	201	18	)	)	PUNCT
ejpam-5259	201	19	=	=	SYM
ejpam-5259	202	1	∞∑	∞∑	PRON
ejpam-5259	202	2	µ=1	µ=1	ADV
ejpam-5259	202	3	ϱµℏk,µ(ς	ϱµℏk,µ(ς	NOUN
ejpam-5259	202	4	)	)	PUNCT
ejpam-5259	202	5	+	+	CCONJ
ejpam-5259	202	6	ψµgk,µ(ς	ψµgk,µ(ς	NOUN
ejpam-5259	202	7	)	)	PUNCT
ejpam-5259	202	8	,	,	PUNCT
ejpam-5259	202	9	where	where	SCONJ
ejpam-5259	202	10	ℏk,0(ς	ℏk,0(ς	NOUN
ejpam-5259	202	11	)	)	PUNCT
ejpam-5259	202	12	=	=	PUNCT
ejpam-5259	202	13	(	(	PUNCT
ejpam-5259	202	14	−1)k	−1)k	PROPN
ejpam-5259	202	15	ς	ς	PROPN
ejpam-5259	202	16	,	,	PUNCT
ejpam-5259	202	17	ℏk,µ(ς	ℏk,µ(ς	NUM
ejpam-5259	202	18	)	)	PUNCT
ejpam-5259	202	19	=	=	PUNCT
ejpam-5259	203	1	(	(	PUNCT
ejpam-5259	203	2	−1)k	−1)k	PROPN
ejpam-5259	203	3	ς	ς	PROPN
ejpam-5259	203	4	+	+	PROPN
ejpam-5259	203	5	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	203	6	1	1	NUM
ejpam-5259	203	7	)	)	PUNCT
ejpam-5259	203	8	+	+	CCONJ
ejpam-5259	203	9	η)(1	η)(1	NUM
ejpam-5259	204	1	+	+	CCONJ
ejpam-5259	204	2	δ)r(1−	δ)r(1−	PROPN
ejpam-5259	204	3	γ	γ	NOUN
ejpam-5259	204	4	)	)	PUNCT
ejpam-5259	204	5	γ(η)[1	γ(η)[1	NOUN
ejpam-5259	205	1	+	+	PUNCT
ejpam-5259	205	2	λ(µ−	λ(µ−	X
ejpam-5259	205	3	1)]k(µ+	1)]k(µ+	PROPN
ejpam-5259	205	4	δ)r(µ+	δ)r(µ+	PROPN
ejpam-5259	205	5	γ	γ	PROPN
ejpam-5259	205	6	)	)	PUNCT
ejpam-5259	205	7	ςµ	ςµ	NOUN
ejpam-5259	205	8	,	,	PUNCT
ejpam-5259	205	9	and	and	CCONJ
ejpam-5259	205	10	gk,0(ς	gk,0(ς	NOUN
ejpam-5259	205	11	)	)	PUNCT
ejpam-5259	205	12	=	=	PUNCT
ejpam-5259	206	1	(	(	PUNCT
ejpam-5259	206	2	−1)k	−1)k	PROPN
ejpam-5259	206	3	ς	ς	PROPN
ejpam-5259	206	4	,	,	PUNCT
ejpam-5259	206	5	gk,µ(ς	gk,µ(ς	ADJ
ejpam-5259	206	6	)	)	PUNCT
ejpam-5259	206	7	=	=	PUNCT
ejpam-5259	207	1	(	(	PUNCT
ejpam-5259	207	2	−1)k	−1)k	PROPN
ejpam-5259	207	3	ς	ς	PROPN
ejpam-5259	207	4	+	+	PROPN
ejpam-5259	207	5	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	207	6	1	1	NUM
ejpam-5259	207	7	)	)	PUNCT
ejpam-5259	207	8	+	+	CCONJ
ejpam-5259	207	9	η)(1	η)(1	NUM
ejpam-5259	208	1	+	+	CCONJ
ejpam-5259	208	2	δ)r(1−	δ)r(1−	PROPN
ejpam-5259	208	3	γ	γ	NOUN
ejpam-5259	208	4	)	)	PUNCT
ejpam-5259	208	5	γ(η)[1	γ(η)[1	NOUN
ejpam-5259	209	1	+	+	PUNCT
ejpam-5259	209	2	λ(µ−	λ(µ−	X
ejpam-5259	209	3	1)]k(µ+	1)]k(µ+	PROPN
ejpam-5259	209	4	δ)r(µ−	δ)r(µ−	NOUN
ejpam-5259	209	5	γ	γ	NOUN
ejpam-5259	209	6	)	)	PUNCT
ejpam-5259	209	7	ςµ	ςµ	NOUN
ejpam-5259	209	8	where	where	SCONJ
ejpam-5259	209	9	ϱµ	ϱµ	PROPN
ejpam-5259	209	10	≥	≥	NUM
ejpam-5259	209	11	0	0	NUM
ejpam-5259	209	12	,	,	PUNCT
ejpam-5259	209	13	ψµ	ψµ	ADP
ejpam-5259	209	14	≥	≥	NOUN
ejpam-5259	209	15	0	0	NUM
ejpam-5259	209	16	,	,	PUNCT
ejpam-5259	209	17	µ	µ	X
ejpam-5259	209	18	=	=	SYM
ejpam-5259	209	19	1	1	NUM
ejpam-5259	209	20	,	,	PUNCT
ejpam-5259	209	21	2	2	NUM
ejpam-5259	209	22	,	,	PUNCT
ejpam-5259	209	23	.	.	PUNCT
ejpam-5259	209	24	.	.	PUNCT
ejpam-5259	210	1	.	.	PUNCT
ejpam-5259	211	1	and	and	CCONJ
ejpam-5259	211	2	∞∑	∞∑	PRON
ejpam-5259	211	3	µ=0	µ=0	PROPN
ejpam-5259	211	4	(	(	PUNCT
ejpam-5259	211	5	ϱµ+ψµ	ϱµ+ψµ	NOUN
ejpam-5259	211	6	)	)	PUNCT
ejpam-5259	211	7	=	=	SYM
ejpam-5259	211	8	1	1	X
ejpam-5259	211	9	.	.	PUNCT
ejpam-5259	212	1	the	the	DET
ejpam-5259	212	2	extreme	extreme	ADJ
ejpam-5259	212	3	points	point	NOUN
ejpam-5259	212	4	of	of	ADP
ejpam-5259	212	5	the	the	DET
ejpam-5259	212	6	class	class	NOUN
ejpam-5259	212	7	t	t	PROPN
ejpam-5259	212	8	mkh(k	mkh(k	PROPN
ejpam-5259	212	9	,	,	PUNCT
ejpam-5259	212	10	r	r	NOUN
ejpam-5259	212	11	,	,	PUNCT
ejpam-5259	212	12	α	α	PROPN
ejpam-5259	212	13	,	,	PUNCT
ejpam-5259	212	14	η	η	PROPN
ejpam-5259	212	15	,	,	PUNCT
ejpam-5259	212	16	δ	δ	PROPN
ejpam-5259	212	17	,	,	PUNCT
ejpam-5259	212	18	λ	λ	PROPN
ejpam-5259	212	19	,	,	PUNCT
ejpam-5259	212	20	γ	γ	NOUN
ejpam-5259	212	21	)	)	PUNCT
ejpam-5259	212	22	are	be	AUX
ejpam-5259	212	23	{	{	PUNCT
ejpam-5259	212	24	ℏk,µ	ℏk,µ	NOUN
ejpam-5259	212	25	}	}	PUNCT
ejpam-5259	212	26	and	and	CCONJ
ejpam-5259	212	27	{	{	PUNCT
ejpam-5259	212	28	gk,µ	gk,µ	NOUN
ejpam-5259	212	29	}	}	PUNCT
ejpam-5259	212	30	.	.	PUNCT
ejpam-5259	213	1	proof	proof	NOUN
ejpam-5259	213	2	.	.	PUNCT
ejpam-5259	214	1	for	for	ADP
ejpam-5259	214	2	f(ς	f(ς	PROPN
ejpam-5259	214	3	)	)	PUNCT
ejpam-5259	214	4	=	=	PUNCT
ejpam-5259	215	1	∞∑	∞∑	NUM
ejpam-5259	215	2	µ=0	µ=0	NOUN
ejpam-5259	215	3	(	(	PUNCT
ejpam-5259	215	4	ϱµhk,µ	ϱµhk,µ	PROPN
ejpam-5259	215	5	+	+	CCONJ
ejpam-5259	215	6	ψµgk,µ	ψµgk,µ	PROPN
ejpam-5259	215	7	)	)	PUNCT
ejpam-5259	215	8	where	where	SCONJ
ejpam-5259	215	9	∞∑	∞∑	NUM
ejpam-5259	215	10	µ=0	µ=0	PROPN
ejpam-5259	215	11	(	(	PUNCT
ejpam-5259	215	12	ϱµ	ϱµ	PROPN
ejpam-5259	215	13	+	+	CCONJ
ejpam-5259	215	14	ψµ	ψµ	NOUN
ejpam-5259	215	15	)	)	PUNCT
ejpam-5259	215	16	=	=	SYM
ejpam-5259	215	17	1	1	NUM
ejpam-5259	215	18	,	,	PUNCT
ejpam-5259	215	19	we	we	PRON
ejpam-5259	215	20	have	have	VERB
ejpam-5259	215	21	fk(ς	fk(ς	NOUN
ejpam-5259	215	22	)	)	PUNCT
ejpam-5259	215	23	=	=	SYM
ejpam-5259	215	24	ϱ0ℏ0,µ	ϱ0ℏ0,µ	NOUN
ejpam-5259	215	25	+	+	CCONJ
ejpam-5259	215	26	ψ0g0,n	ψ0g0,n	ADJ
ejpam-5259	215	27	+	+	CCONJ
ejpam-5259	215	28	∞∑	∞∑	NUM
ejpam-5259	215	29	µ=1	µ=1	SYM
ejpam-5259	215	30	(	(	PUNCT
ejpam-5259	215	31	ϱµℏk,µ	ϱµℏk,µ	PROPN
ejpam-5259	215	32	+	+	NUM
ejpam-5259	215	33	ψµgk,µ	ψµgk,µ	PROPN
ejpam-5259	215	34	)	)	PUNCT
ejpam-5259	216	1	=	=	PUNCT
ejpam-5259	217	1	∞∑	∞∑	NUM
ejpam-5259	217	2	µ=0	µ=0	NOUN
ejpam-5259	217	3	(	(	PUNCT
ejpam-5259	217	4	−1)k(ϱµ+ψµ	−1)k(ϱµ+ψµ	VERB
ejpam-5259	217	5	)	)	PUNCT
ejpam-5259	217	6	ς	ς	PROPN
ejpam-5259	218	1	+	+	VERB
ejpam-5259	218	2	∞∑	∞∑	NUM
ejpam-5259	218	3	µ=1	µ=1	SYM
ejpam-5259	218	4	ϱµ	ϱµ	PROPN
ejpam-5259	218	5	(	(	PUNCT
ejpam-5259	218	6	γ(α(µ+1)+η)(1+δ)r(1−γ	γ(α(µ+1)+η)(1+δ)r(1−γ	NUM
ejpam-5259	218	7	)	)	PUNCT
ejpam-5259	218	8	γ(η)[1+λ(µ−1)]k(µ+δ)r(µ+γ	γ(η)[1+λ(µ−1)]k(µ+δ)r(µ+γ	PROPN
ejpam-5259	218	9	)	)	PUNCT
ejpam-5259	218	10	)	)	PUNCT
ejpam-5259	219	1	ςµ	ςµ	VERB
ejpam-5259	220	1	+	+	ADJ
ejpam-5259	220	2	(	(	PUNCT
ejpam-5259	220	3	−1)k	−1)k	PROPN
ejpam-5259	220	4	∞∑	∞∑	NUM
ejpam-5259	220	5	µ=1	µ=1	PUNCT
ejpam-5259	220	6	ψµ	ψµ	ADV
ejpam-5259	220	7	(	(	PUNCT
ejpam-5259	220	8	γ(α(µ+1)+η)(1+δ)r(1−γ	γ(α(µ+1)+η)(1+δ)r(1−γ	NUM
ejpam-5259	220	9	)	)	PUNCT
ejpam-5259	220	10	γ(η)[1+λ(µ−1)]k(µ+δ)r(µ−γ	γ(η)[1+λ(µ−1)]k(µ+δ)r(µ−γ	ADV
ejpam-5259	220	11	)	)	PUNCT
ejpam-5259	220	12	)	)	PUNCT
ejpam-5259	221	1	ςµ	ςµ	NOUN
ejpam-5259	221	2	=	=	SYM
ejpam-5259	221	3	(	(	PUNCT
ejpam-5259	221	4	−1)k	−1)k	PROPN
ejpam-5259	221	5	ς	ς	PROPN
ejpam-5259	222	1	+	+	PROPN
ejpam-5259	222	2	∞∑	∞∑	NUM
ejpam-5259	222	3	µ=1	µ=1	ADV
ejpam-5259	222	4	(	(	PUNCT
ejpam-5259	222	5	γ(α(µ+1)+η)(1+δ)r(1−γ	γ(α(µ+1)+η)(1+δ)r(1−γ	NUM
ejpam-5259	222	6	)	)	PUNCT
ejpam-5259	222	7	γ(η)[1+λ(µ−1)]k(µ+δ)r(µ+γ	γ(η)[1+λ(µ−1)]k(µ+δ)r(µ+γ	PROPN
ejpam-5259	222	8	)	)	PUNCT
ejpam-5259	222	9	)	)	PUNCT
ejpam-5259	223	1	ϱµς	ϱµς	VERB
ejpam-5259	223	2	µ	µ	ADJ
ejpam-5259	223	3	+	+	PROPN
ejpam-5259	223	4	(	(	PUNCT
ejpam-5259	223	5	−1)k	−1)k	PROPN
ejpam-5259	223	6	∞∑	∞∑	NUM
ejpam-5259	223	7	µ=1	µ=1	ADV
ejpam-5259	223	8	(	(	PUNCT
ejpam-5259	223	9	γ(α(µ+1)+η)(1+δ)r(1−γ	γ(α(µ+1)+η)(1+δ)r(1−γ	NUM
ejpam-5259	223	10	)	)	PUNCT
ejpam-5259	223	11	γ(η)[1+λ(µ−1)]k(µ+δ)r(µ−γ	γ(η)[1+λ(µ−1)]k(µ+δ)r(µ−γ	ADV
ejpam-5259	223	12	)	)	PUNCT
ejpam-5259	223	13	)	)	PUNCT
ejpam-5259	224	1	ψµς	ψµς	PROPN
ejpam-5259	224	2	µ.	µ.	PROPN
ejpam-5259	224	3	this	this	PRON
ejpam-5259	224	4	belong	belong	VERB
ejpam-5259	224	5	to	to	ADP
ejpam-5259	224	6	t	t	PROPN
ejpam-5259	224	7	mkh(k	mkh(k	PROPN
ejpam-5259	224	8	,	,	PUNCT
ejpam-5259	224	9	r	r	NOUN
ejpam-5259	224	10	,	,	PUNCT
ejpam-5259	224	11	α	α	PROPN
ejpam-5259	224	12	,	,	PUNCT
ejpam-5259	224	13	η	η	PROPN
ejpam-5259	224	14	,	,	PUNCT
ejpam-5259	224	15	δ	δ	PROPN
ejpam-5259	224	16	,	,	PUNCT
ejpam-5259	224	17	λ	λ	PROPN
ejpam-5259	224	18	,	,	PUNCT
ejpam-5259	224	19	γ	γ	NOUN
ejpam-5259	224	20	)	)	PUNCT
ejpam-5259	224	21	because	because	SCONJ
ejpam-5259	224	22	∞∑	∞∑	NUM
ejpam-5259	224	23	µ=1	µ=1	PROPN
ejpam-5259	224	24	γ(η)[1	γ(η)[1	X
ejpam-5259	225	1	+	+	CCONJ
ejpam-5259	225	2	λ(µ−	λ(µ−	X
ejpam-5259	225	3	1)]k(µ+	1)]k(µ+	PROPN
ejpam-5259	225	4	δ)r(µ+	δ)r(µ+	PROPN
ejpam-5259	225	5	γ	γ	PROPN
ejpam-5259	225	6	)	)	PUNCT
ejpam-5259	225	7	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	225	8	1	1	NUM
ejpam-5259	225	9	)	)	PUNCT
ejpam-5259	225	10	+	+	CCONJ
ejpam-5259	225	11	η)(1	η)(1	NUM
ejpam-5259	226	1	+	+	SYM
ejpam-5259	226	2	δ)r	δ)r	X
ejpam-5259	226	3	(	(	PUNCT
ejpam-5259	226	4	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	226	5	1	1	NUM
ejpam-5259	226	6	)	)	PUNCT
ejpam-5259	226	7	+	+	CCONJ
ejpam-5259	226	8	η)(1	η)(1	NUM
ejpam-5259	226	9	+	+	CCONJ
ejpam-5259	226	10	δ)r(1−	δ)r(1−	PROPN
ejpam-5259	226	11	γ	γ	NOUN
ejpam-5259	226	12	)	)	PUNCT
ejpam-5259	226	13	γ(η)[1	γ(η)[1	NOUN
ejpam-5259	227	1	+	+	PUNCT
ejpam-5259	227	2	λ(µ−	λ(µ−	X
ejpam-5259	227	3	1)]k(µ+	1)]k(µ+	PROPN
ejpam-5259	227	4	δ)r(µ+	δ)r(µ+	PROPN
ejpam-5259	227	5	γ	γ	PROPN
ejpam-5259	227	6	)	)	PUNCT
ejpam-5259	227	7	)	)	PUNCT
ejpam-5259	227	8	ϱµ	ϱµ	VERB
ejpam-5259	227	9	∞∑	∞∑	NUM
ejpam-5259	227	10	µ=1	µ=1	PROPN
ejpam-5259	228	1	γ(η)[1	γ(η)[1	X
ejpam-5259	229	1	+	+	PUNCT
ejpam-5259	229	2	λ(µ−	λ(µ−	X
ejpam-5259	229	3	1)]k(µ+	1)]k(µ+	PROPN
ejpam-5259	229	4	δ)r(µ−	δ)r(µ−	NOUN
ejpam-5259	229	5	γ	γ	X
ejpam-5259	229	6	)	)	PUNCT
ejpam-5259	229	7	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	229	8	1	1	NUM
ejpam-5259	229	9	)	)	PUNCT
ejpam-5259	229	10	+	+	CCONJ
ejpam-5259	229	11	η)(1	η)(1	NUM
ejpam-5259	230	1	+	+	SYM
ejpam-5259	230	2	δ)r	δ)r	X
ejpam-5259	230	3	(	(	PUNCT
ejpam-5259	230	4	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	230	5	1	1	NUM
ejpam-5259	230	6	)	)	PUNCT
ejpam-5259	230	7	+	+	CCONJ
ejpam-5259	230	8	η)(1	η)(1	NUM
ejpam-5259	230	9	+	+	CCONJ
ejpam-5259	230	10	δ)r(1−	δ)r(1−	PROPN
ejpam-5259	230	11	γ	γ	NOUN
ejpam-5259	230	12	)	)	PUNCT
ejpam-5259	230	13	γ(η)[1	γ(η)[1	NOUN
ejpam-5259	231	1	+	+	PUNCT
ejpam-5259	231	2	λ(µ−	λ(µ−	X
ejpam-5259	231	3	1)]k(µ+	1)]k(µ+	PROPN
ejpam-5259	231	4	δ)r(µ−	δ)r(µ−	NOUN
ejpam-5259	231	5	γ	γ	NOUN
ejpam-5259	231	6	)	)	PUNCT
ejpam-5259	231	7	)	)	PUNCT
ejpam-5259	232	1	ψµ	ψµ	ADP
ejpam-5259	232	2	s.	s.	PROPN
ejpam-5259	232	3	ahmed	ahmed	PROPN
ejpam-5259	232	4	,	,	PUNCT
ejpam-5259	232	5	a.	a.	PROPN
ejpam-5259	232	6	alsoboh	alsoboh	PROPN
ejpam-5259	232	7	,	,	PUNCT
ejpam-5259	232	8	m.	m.	NOUN
ejpam-5259	232	9	darus	darus	NOUN
ejpam-5259	232	10	/	/	SYM
ejpam-5259	232	11	eur	eur	PROPN
ejpam-5259	232	12	.	.	PUNCT
ejpam-5259	233	1	j.	j.	PROPN
ejpam-5259	233	2	pure	pure	PROPN
ejpam-5259	233	3	appl	appl	PROPN
ejpam-5259	233	4	.	.	PROPN
ejpam-5259	233	5	math	math	PROPN
ejpam-5259	233	6	,	,	PUNCT
ejpam-5259	233	7	17	17	NUM
ejpam-5259	233	8	(	(	PUNCT
ejpam-5259	233	9	3	3	NUM
ejpam-5259	233	10	)	)	PUNCT
ejpam-5259	233	11	(	(	PUNCT
ejpam-5259	233	12	2024	2024	NUM
ejpam-5259	233	13	)	)	PUNCT
ejpam-5259	233	14	,	,	PUNCT
ejpam-5259	233	15	1894	1894	NUM
ejpam-5259	233	16	-	-	SYM
ejpam-5259	233	17	1907	1907	NUM
ejpam-5259	233	18	1903	1903	NUM
ejpam-5259	233	19	=	=	PUNCT
ejpam-5259	234	1	∞∑	∞∑	NUM
ejpam-5259	234	2	µ=1	µ=1	SYM
ejpam-5259	234	3	(	(	PUNCT
ejpam-5259	234	4	1−	1−	NUM
ejpam-5259	234	5	γ)ϱµ	γ)ϱµ	PROPN
ejpam-5259	234	6	+	+	CCONJ
ejpam-5259	234	7	(	(	PUNCT
ejpam-5259	234	8	1−	1−	NUM
ejpam-5259	234	9	γ)ψµ	γ)ψµ	PROPN
ejpam-5259	234	10	=	=	SYM
ejpam-5259	234	11	(	(	PUNCT
ejpam-5259	234	12	1−	1−	NUM
ejpam-5259	234	13	γ	γ	NOUN
ejpam-5259	234	14	)	)	PUNCT
ejpam-5259	234	15	∞∑	∞∑	PROPN
ejpam-5259	234	16	µ=1	µ=1	PROPN
ejpam-5259	234	17	(	(	PUNCT
ejpam-5259	234	18	ϱµ	ϱµ	PROPN
ejpam-5259	234	19	+	+	CCONJ
ejpam-5259	234	20	ψµ	ψµ	NOUN
ejpam-5259	234	21	)	)	PUNCT
ejpam-5259	234	22	=	=	SYM
ejpam-5259	234	23	(	(	PUNCT
ejpam-5259	234	24	1−	1−	NUM
ejpam-5259	234	25	γ)(1−	γ)(1−	PROPN
ejpam-5259	234	26	ϱ0	ϱ0	NOUN
ejpam-5259	234	27	−	−	PROPN
ejpam-5259	234	28	ψ0	ψ0	ADJ
ejpam-5259	234	29	)	)	PUNCT
ejpam-5259	234	30	≤	≤	NOUN
ejpam-5259	234	31	1−	1−	NUM
ejpam-5259	234	32	γ	γ	NOUN
ejpam-5259	234	33	.	.	PUNCT
ejpam-5259	234	34	conversely	conversely	ADV
ejpam-5259	234	35	,	,	PUNCT
ejpam-5259	234	36	suppose	suppose	VERB
ejpam-5259	234	37	that	that	SCONJ
ejpam-5259	234	38	f	f	PROPN
ejpam-5259	234	39	∈	∈	PROPN
ejpam-5259	234	40	clcot	clcot	NOUN
ejpam-5259	234	41	mkh(k	mkh(k	PROPN
ejpam-5259	234	42	,	,	PUNCT
ejpam-5259	234	43	r	r	PROPN
ejpam-5259	234	44	,	,	PUNCT
ejpam-5259	234	45	α	α	PROPN
ejpam-5259	234	46	,	,	PUNCT
ejpam-5259	234	47	η	η	PROPN
ejpam-5259	234	48	,	,	PUNCT
ejpam-5259	234	49	δ	δ	PROPN
ejpam-5259	234	50	,	,	PUNCT
ejpam-5259	234	51	λ	λ	PROPN
ejpam-5259	234	52	,	,	PUNCT
ejpam-5259	234	53	γ	γ	NOUN
ejpam-5259	234	54	)	)	PUNCT
ejpam-5259	234	55	.	.	PUNCT
ejpam-5259	235	1	for	for	ADP
ejpam-5259	235	2	µ	µ	NOUN
ejpam-5259	235	3	=	=	SYM
ejpam-5259	235	4	1	1	NUM
ejpam-5259	235	5	,	,	PUNCT
ejpam-5259	235	6	2	2	NUM
ejpam-5259	235	7	,	,	PUNCT
ejpam-5259	235	8	3	3	NUM
ejpam-5259	235	9	,	,	PUNCT
ejpam-5259	235	10	.	.	PUNCT
ejpam-5259	235	11	.	.	PUNCT
ejpam-5259	235	12	.	.	PUNCT
ejpam-5259	236	1	,	,	PUNCT
ejpam-5259	236	2	set	set	VERB
ejpam-5259	236	3	ϱµ	ϱµ	NOUN
ejpam-5259	236	4	=	=	PUNCT
ejpam-5259	237	1	γ(η)[1	γ(η)[1	PROPN
ejpam-5259	238	1	+	+	CCONJ
ejpam-5259	238	2	λ(µ−	λ(µ−	X
ejpam-5259	238	3	1)]k(µ+	1)]k(µ+	PROPN
ejpam-5259	238	4	δ)r(µ+	δ)r(µ+	PROPN
ejpam-5259	238	5	γ	γ	PROPN
ejpam-5259	238	6	)	)	PUNCT
ejpam-5259	238	7	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	238	8	1	1	NUM
ejpam-5259	238	9	)	)	PUNCT
ejpam-5259	239	1	+	+	CCONJ
ejpam-5259	239	2	η)(1	η)(1	NUM
ejpam-5259	240	1	+	+	CCONJ
ejpam-5259	240	2	δ)r(1−	δ)r(1−	PROPN
ejpam-5259	240	3	γ	γ	NOUN
ejpam-5259	240	4	)	)	PUNCT
ejpam-5259	240	5	|aµ|	|aµ|	NOUN
ejpam-5259	240	6	,	,	PUNCT
ejpam-5259	240	7	(	(	PUNCT
ejpam-5259	240	8	0	0	NUM
ejpam-5259	240	9	≤	≤	NUM
ejpam-5259	240	10	ϱµ	ϱµ	NOUN
ejpam-5259	240	11	≤	≤	NUM
ejpam-5259	240	12	1	1	NUM
ejpam-5259	240	13	)	)	PUNCT
ejpam-5259	240	14	ψµ	ψµ	NOUN
ejpam-5259	240	15	=	=	PUNCT
ejpam-5259	240	16	γ(η)[1	γ(η)[1	NOUN
ejpam-5259	241	1	+	+	PUNCT
ejpam-5259	241	2	λ(µ−	λ(µ−	X
ejpam-5259	241	3	1)]k(µ+	1)]k(µ+	PROPN
ejpam-5259	241	4	δ)r(µ−	δ)r(µ−	NOUN
ejpam-5259	241	5	γ	γ	X
ejpam-5259	241	6	)	)	PUNCT
ejpam-5259	241	7	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	241	8	1	1	NUM
ejpam-5259	241	9	)	)	PUNCT
ejpam-5259	241	10	+	+	CCONJ
ejpam-5259	241	11	η)(1	η)(1	NUM
ejpam-5259	242	1	+	+	CCONJ
ejpam-5259	242	2	δ)r(1−	δ)r(1−	PROPN
ejpam-5259	242	3	γ	γ	X
ejpam-5259	242	4	)	)	PUNCT
ejpam-5259	242	5	|bµ|	|bµ|	PROPN
ejpam-5259	242	6	,	,	PUNCT
ejpam-5259	242	7	(	(	PUNCT
ejpam-5259	242	8	0	0	NUM
ejpam-5259	242	9	≤	≤	NUM
ejpam-5259	242	10	ψµ	ψµ	NOUN
ejpam-5259	242	11	≤	≤	NUM
ejpam-5259	242	12	1	1	NUM
ejpam-5259	242	13	)	)	PUNCT
ejpam-5259	242	14	and	and	CCONJ
ejpam-5259	242	15	ϱ0	ϱ0	VERB
ejpam-5259	242	16	+	+	CCONJ
ejpam-5259	242	17	ψ0	ψ0	ADJ
ejpam-5259	242	18	=	=	X
ejpam-5259	242	19	1−	1−	NUM
ejpam-5259	243	1	∞∑	∞∑	NUM
ejpam-5259	243	2	µ=1	µ=1	SYM
ejpam-5259	243	3	ϱµ	ϱµ	NOUN
ejpam-5259	243	4	−	−	PROPN
ejpam-5259	243	5	∞∑	∞∑	NUM
ejpam-5259	243	6	µ=1	µ=1	PUNCT
ejpam-5259	243	7	ψµ	ψµ	NOUN
ejpam-5259	243	8	..	..	PUNCT
ejpam-5259	243	9	therefore	therefore	ADV
ejpam-5259	243	10	,	,	PUNCT
ejpam-5259	243	11	fk	fk	INTJ
ejpam-5259	243	12	can	can	AUX
ejpam-5259	243	13	be	be	AUX
ejpam-5259	243	14	written	write	VERB
ejpam-5259	243	15	as	as	ADP
ejpam-5259	243	16	fk(ς	fk(ς	NOUN
ejpam-5259	243	17	)	)	PUNCT
ejpam-5259	243	18	=	=	SYM
ejpam-5259	244	1	(	(	PUNCT
ejpam-5259	244	2	−1)k	−1)k	PROPN
ejpam-5259	244	3	ς	ς	PROPN
ejpam-5259	244	4	+	+	PUNCT
ejpam-5259	244	5	∞∑	∞∑	NUM
ejpam-5259	244	6	µ=1	µ=1	ADP
ejpam-5259	244	7	|aµ|ςµ	|aµ|ςµ	PROPN
ejpam-5259	244	8	+	+	CCONJ
ejpam-5259	244	9	(	(	PUNCT
ejpam-5259	244	10	−1)k	−1)k	PROPN
ejpam-5259	244	11	∞∑	∞∑	NUM
ejpam-5259	244	12	µ=1	µ=1	PUNCT
ejpam-5259	244	13	|bµ|ςµ	|bµ|ςµ	PUNCT
ejpam-5259	244	14	=	=	SYM
ejpam-5259	244	15	(	(	PUNCT
ejpam-5259	244	16	−1)k	−1)k	PROPN
ejpam-5259	244	17	ς	ς	PROPN
ejpam-5259	244	18	+	+	CCONJ
ejpam-5259	244	19	∞∑	∞∑	NUM
ejpam-5259	244	20	µ=1	µ=1	PUNCT
ejpam-5259	244	21	(	(	PUNCT
ejpam-5259	244	22	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	244	23	1	1	NUM
ejpam-5259	244	24	)	)	PUNCT
ejpam-5259	244	25	+	+	CCONJ
ejpam-5259	244	26	η)(1	η)(1	NUM
ejpam-5259	245	1	+	+	CCONJ
ejpam-5259	245	2	δ)r(1−	δ)r(1−	PROPN
ejpam-5259	245	3	γ	γ	NOUN
ejpam-5259	245	4	)	)	PUNCT
ejpam-5259	245	5	γ(η)[1	γ(η)[1	NOUN
ejpam-5259	246	1	+	+	PUNCT
ejpam-5259	246	2	λ(µ−	λ(µ−	X
ejpam-5259	246	3	1)]k(µ+	1)]k(µ+	PROPN
ejpam-5259	246	4	δ)r(µ+	δ)r(µ+	PROPN
ejpam-5259	246	5	γ	γ	PROPN
ejpam-5259	246	6	)	)	PUNCT
ejpam-5259	246	7	)	)	PUNCT
ejpam-5259	246	8	ϱµς	ϱµς	VERB
ejpam-5259	246	9	µ	µ	PROPN
ejpam-5259	246	10	+	+	CCONJ
ejpam-5259	246	11	(	(	PUNCT
ejpam-5259	246	12	−1)k	−1)k	PROPN
ejpam-5259	246	13	∞∑	∞∑	NUM
ejpam-5259	246	14	µ=1	µ=1	PUNCT
ejpam-5259	246	15	(	(	PUNCT
ejpam-5259	246	16	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	246	17	1	1	NUM
ejpam-5259	246	18	)	)	PUNCT
ejpam-5259	247	1	+	+	CCONJ
ejpam-5259	247	2	η)(1	η)(1	NUM
ejpam-5259	248	1	+	+	CCONJ
ejpam-5259	248	2	δ)r(1−	δ)r(1−	PROPN
ejpam-5259	248	3	γ	γ	NOUN
ejpam-5259	248	4	)	)	PUNCT
ejpam-5259	248	5	γ(η)[1	γ(η)[1	NOUN
ejpam-5259	249	1	+	+	PUNCT
ejpam-5259	249	2	λ(µ−	λ(µ−	X
ejpam-5259	249	3	1)]k(µ+	1)]k(µ+	PROPN
ejpam-5259	249	4	δ)r(µ−	δ)r(µ−	NOUN
ejpam-5259	249	5	γ	γ	NOUN
ejpam-5259	249	6	)	)	PUNCT
ejpam-5259	249	7	)	)	PUNCT
ejpam-5259	250	1	ψµς	ψµς	PROPN
ejpam-5259	250	2	µ	µ	X
ejpam-5259	250	3	=	=	PUNCT
ejpam-5259	250	4	ϱ0	ϱ0	NOUN
ejpam-5259	250	5	+	+	CCONJ
ejpam-5259	250	6	ψ0	ψ0	ADJ
ejpam-5259	250	7	ς	ς	NOUN
ejpam-5259	250	8	+	+	NOUN
ejpam-5259	250	9	∞∑	∞∑	NUM
ejpam-5259	250	10	µ=1	µ=1	PROPN
ejpam-5259	250	11	(	(	PUNCT
ejpam-5259	250	12	hk	hk	PROPN
ejpam-5259	250	13	,	,	PUNCT
ejpam-5259	250	14	n(ς)−	n(ς)−	PROPN
ejpam-5259	250	15	(	(	PUNCT
ejpam-5259	250	16	−1)k	−1)k	PROPN
ejpam-5259	250	17	ς	ς	PROPN
ejpam-5259	250	18	)	)	PUNCT
ejpam-5259	250	19	ϱµ	ϱµ	NOUN
ejpam-5259	250	20	+	+	CCONJ
ejpam-5259	250	21	∞∑	∞∑	NUM
ejpam-5259	250	22	µ=1	µ=1	PROPN
ejpam-5259	250	23	(	(	PUNCT
ejpam-5259	250	24	gk	gk	PROPN
ejpam-5259	250	25	,	,	PUNCT
ejpam-5259	250	26	n(ς)−	n(ς)−	PROPN
ejpam-5259	250	27	(	(	PUNCT
ejpam-5259	250	28	−1)k	−1)k	PROPN
ejpam-5259	250	29	ς	ς	PROPN
ejpam-5259	250	30	)	)	PUNCT
ejpam-5259	250	31	ψµ	ψµ	ADP
ejpam-5259	250	32	=	=	NOUN
ejpam-5259	251	1	∞∑	∞∑	NUM
ejpam-5259	251	2	µ=0	µ=0	NOUN
ejpam-5259	251	3	(	(	PUNCT
ejpam-5259	251	4	ϱµℏk,µ	ϱµℏk,µ	PROPN
ejpam-5259	251	5	+	+	NUM
ejpam-5259	251	6	ψµgk,µ	ψµgk,µ	PROPN
ejpam-5259	251	7	)	)	PUNCT
ejpam-5259	251	8	.	.	PUNCT
ejpam-5259	252	1	4	4	X
ejpam-5259	252	2	.	.	X
ejpam-5259	252	3	convex	convex	NOUN
ejpam-5259	252	4	combination	combination	NOUN
ejpam-5259	252	5	and	and	CCONJ
ejpam-5259	252	6	convolution	convolution	NOUN
ejpam-5259	252	7	subsequently	subsequently	ADV
ejpam-5259	252	8	,	,	PUNCT
ejpam-5259	252	9	we	we	PRON
ejpam-5259	252	10	can	can	AUX
ejpam-5259	252	11	establish	establish	VERB
ejpam-5259	252	12	that	that	SCONJ
ejpam-5259	252	13	the	the	DET
ejpam-5259	252	14	class	class	NOUN
ejpam-5259	252	15	t	t	PROPN
ejpam-5259	252	16	mkh(k	mkh(k	PROPN
ejpam-5259	252	17	,	,	PUNCT
ejpam-5259	252	18	r	r	NOUN
ejpam-5259	252	19	,	,	PUNCT
ejpam-5259	252	20	α	α	PROPN
ejpam-5259	252	21	,	,	PUNCT
ejpam-5259	252	22	η	η	PROPN
ejpam-5259	252	23	,	,	PUNCT
ejpam-5259	252	24	δ	δ	PROPN
ejpam-5259	252	25	,	,	PUNCT
ejpam-5259	252	26	λ	λ	PROPN
ejpam-5259	252	27	,	,	PUNCT
ejpam-5259	252	28	γ	γ	NOUN
ejpam-5259	252	29	)	)	PUNCT
ejpam-5259	252	30	exhibits	exhibit	VERB
ejpam-5259	252	31	closure	closure	NOUN
ejpam-5259	252	32	properties	property	NOUN
ejpam-5259	252	33	in	in	ADP
ejpam-5259	252	34	relation	relation	NOUN
ejpam-5259	252	35	to	to	ADP
ejpam-5259	252	36	both	both	CCONJ
ejpam-5259	252	37	convolution	convolution	NOUN
ejpam-5259	252	38	and	and	CCONJ
ejpam-5259	252	39	convex	convex	NOUN
ejpam-5259	252	40	combination	combination	NOUN
ejpam-5259	252	41	.	.	PUNCT
ejpam-5259	253	1	theorem	theorem	NOUN
ejpam-5259	253	2	5	5	NUM
ejpam-5259	253	3	.	.	PUNCT
ejpam-5259	254	1	for	for	ADP
ejpam-5259	254	2	0	0	NUM
ejpam-5259	254	3	≤	≤	NOUN
ejpam-5259	254	4	β	β	NOUN
ejpam-5259	254	5	≤	≤	NUM
ejpam-5259	254	6	γ	γ	X
ejpam-5259	254	7	<	<	X
ejpam-5259	254	8	1	1	NUM
ejpam-5259	254	9	.	.	PUNCT
ejpam-5259	254	10	let	let	VERB
ejpam-5259	254	11	fk(ς	fk(ς	NOUN
ejpam-5259	254	12	)	)	PUNCT
ejpam-5259	254	13	∈	∈	PROPN
ejpam-5259	254	14	t	t	PROPN
ejpam-5259	254	15	mkh(k	mkh(k	PROPN
ejpam-5259	254	16	,	,	PUNCT
ejpam-5259	254	17	r	r	NOUN
ejpam-5259	254	18	,	,	PUNCT
ejpam-5259	254	19	α	α	PROPN
ejpam-5259	254	20	,	,	PUNCT
ejpam-5259	254	21	η	η	PROPN
ejpam-5259	254	22	,	,	PUNCT
ejpam-5259	254	23	δ	δ	PROPN
ejpam-5259	254	24	,	,	PUNCT
ejpam-5259	254	25	λ	λ	PROPN
ejpam-5259	254	26	,	,	PUNCT
ejpam-5259	254	27	γ	γ	NOUN
ejpam-5259	254	28	)	)	PUNCT
ejpam-5259	254	29	and	and	CCONJ
ejpam-5259	254	30	ξk(ς	ξk(ς	NOUN
ejpam-5259	254	31	)	)	PUNCT
ejpam-5259	254	32	∈	∈	PROPN
ejpam-5259	254	33	t	t	PROPN
ejpam-5259	254	34	mhmkh(k	mhmkh(k	PROPN
ejpam-5259	254	35	,	,	PUNCT
ejpam-5259	254	36	r	r	PROPN
ejpam-5259	254	37	,	,	PUNCT
ejpam-5259	254	38	α	α	PROPN
ejpam-5259	254	39	,	,	PUNCT
ejpam-5259	254	40	η	η	PROPN
ejpam-5259	254	41	,	,	PUNCT
ejpam-5259	254	42	δ	δ	PROPN
ejpam-5259	254	43	,	,	PUNCT
ejpam-5259	254	44	λ	λ	PROPN
ejpam-5259	254	45	,	,	PUNCT
ejpam-5259	254	46	β	β	X
ejpam-5259	254	47	,	,	PUNCT
ejpam-5259	254	48	n	n	CCONJ
ejpam-5259	254	49	)	)	PUNCT
ejpam-5259	254	50	,	,	PUNCT
ejpam-5259	254	51	then	then	ADV
ejpam-5259	254	52	(	(	PUNCT
ejpam-5259	254	53	fk	fk	INTJ
ejpam-5259	254	54	∗	∗	X
ejpam-5259	254	55	ξk)(ς	ξk)(ς	PROPN
ejpam-5259	254	56	)	)	PUNCT
ejpam-5259	254	57	∈	∈	PROPN
ejpam-5259	254	58	t	t	PROPN
ejpam-5259	254	59	mkh(k	mkh(k	PROPN
ejpam-5259	254	60	,	,	PUNCT
ejpam-5259	254	61	r	r	NOUN
ejpam-5259	254	62	,	,	PUNCT
ejpam-5259	254	63	α	α	PROPN
ejpam-5259	254	64	,	,	PUNCT
ejpam-5259	254	65	η	η	PROPN
ejpam-5259	254	66	,	,	PUNCT
ejpam-5259	254	67	δ	δ	PROPN
ejpam-5259	254	68	,	,	PUNCT
ejpam-5259	254	69	λ	λ	PROPN
ejpam-5259	254	70	,	,	PUNCT
ejpam-5259	254	71	γ	γ	NOUN
ejpam-5259	254	72	)	)	PUNCT
ejpam-5259	254	73	⊆	⊆	NUM
ejpam-5259	254	74	t	t	PROPN
ejpam-5259	254	75	mkh(k	mkh(k	PROPN
ejpam-5259	254	76	,	,	PUNCT
ejpam-5259	254	77	r	r	NOUN
ejpam-5259	254	78	,	,	PUNCT
ejpam-5259	254	79	α	α	PROPN
ejpam-5259	254	80	,	,	PUNCT
ejpam-5259	254	81	η	η	PROPN
ejpam-5259	254	82	,	,	PUNCT
ejpam-5259	254	83	δ	δ	PROPN
ejpam-5259	254	84	,	,	PUNCT
ejpam-5259	254	85	λ	λ	PROPN
ejpam-5259	254	86	,	,	PUNCT
ejpam-5259	254	87	β	β	NOUN
ejpam-5259	254	88	)	)	PUNCT
ejpam-5259	254	89	.	.	PUNCT
ejpam-5259	255	1	proof	proof	NOUN
ejpam-5259	255	2	.	.	PUNCT
ejpam-5259	256	1	the	the	DET
ejpam-5259	256	2	convolution	convolution	NOUN
ejpam-5259	256	3	,	,	PUNCT
ejpam-5259	256	4	or	or	CCONJ
ejpam-5259	256	5	the	the	DET
ejpam-5259	256	6	hadamard	hadamard	ADJ
ejpam-5259	256	7	product	product	NOUN
ejpam-5259	256	8	,	,	PUNCT
ejpam-5259	256	9	of	of	ADP
ejpam-5259	256	10	fk(ς	fk(ς	NOUN
ejpam-5259	256	11	)	)	PUNCT
ejpam-5259	256	12	and	and	CCONJ
ejpam-5259	256	13	ξk(ς	ξk(ς	NOUN
ejpam-5259	256	14	)	)	PUNCT
ejpam-5259	256	15	is	be	AUX
ejpam-5259	256	16	expressed	express	VERB
ejpam-5259	256	17	as	as	ADP
ejpam-5259	256	18	(	(	PUNCT
ejpam-5259	256	19	fk	fk	INTJ
ejpam-5259	256	20	∗	∗	NOUN
ejpam-5259	256	21	βk)(ς	βk)(ς	PROPN
ejpam-5259	256	22	)	)	PUNCT
ejpam-5259	257	1	=	=	PRON
ejpam-5259	257	2	(	(	PUNCT
ejpam-5259	257	3	−1)k	−1)k	PROPN
ejpam-5259	257	4	ς	ς	PROPN
ejpam-5259	257	5	+	+	PROPN
ejpam-5259	257	6	∞∑	∞∑	NUM
ejpam-5259	257	7	µ=1	µ=1	X
ejpam-5259	257	8	|aµ||cµ|ςµ	|aµ||cµ|ςµ	PROPN
ejpam-5259	257	9	+	+	CCONJ
ejpam-5259	257	10	(	(	PUNCT
ejpam-5259	257	11	−1)k	−1)k	PROPN
ejpam-5259	257	12	∞∑	∞∑	NUM
ejpam-5259	257	13	µ=1	µ=1	PROPN
ejpam-5259	257	14	|bµ||dµ|ςµ.	|bµ||dµ|ςµ.	PRON
ejpam-5259	257	15	s.	s.	PROPN
ejpam-5259	257	16	ahmed	ahmed	PROPN
ejpam-5259	257	17	,	,	PUNCT
ejpam-5259	257	18	a.	a.	PROPN
ejpam-5259	257	19	alsoboh	alsoboh	PROPN
ejpam-5259	257	20	,	,	PUNCT
ejpam-5259	257	21	m.	m.	NOUN
ejpam-5259	257	22	darus	darus	NOUN
ejpam-5259	257	23	/	/	SYM
ejpam-5259	257	24	eur	eur	PROPN
ejpam-5259	257	25	.	.	PUNCT
ejpam-5259	258	1	j.	j.	PROPN
ejpam-5259	258	2	pure	pure	PROPN
ejpam-5259	258	3	appl	appl	PROPN
ejpam-5259	258	4	.	.	PROPN
ejpam-5259	258	5	math	math	PROPN
ejpam-5259	258	6	,	,	PUNCT
ejpam-5259	258	7	17	17	NUM
ejpam-5259	258	8	(	(	PUNCT
ejpam-5259	258	9	3	3	NUM
ejpam-5259	258	10	)	)	PUNCT
ejpam-5259	258	11	(	(	PUNCT
ejpam-5259	258	12	2024	2024	NUM
ejpam-5259	258	13	)	)	PUNCT
ejpam-5259	258	14	,	,	PUNCT
ejpam-5259	258	15	1894	1894	NUM
ejpam-5259	258	16	-	-	SYM
ejpam-5259	258	17	1907	1907	NUM
ejpam-5259	258	18	1904	1904	NUM
ejpam-5259	258	19	we	we	PRON
ejpam-5259	258	20	want	want	VERB
ejpam-5259	258	21	to	to	PART
ejpam-5259	258	22	show	show	VERB
ejpam-5259	258	23	that	that	SCONJ
ejpam-5259	258	24	the	the	DET
ejpam-5259	258	25	coefficients	coefficient	NOUN
ejpam-5259	258	26	of	of	ADP
ejpam-5259	258	27	fk	fk	INTJ
ejpam-5259	258	28	∗	∗	NOUN
ejpam-5259	258	29	ξk	ξk	ADP
ejpam-5259	258	30	satisfy	satisfy	NOUN
ejpam-5259	258	31	condition	condition	NOUN
ejpam-5259	258	32	(	(	PUNCT
ejpam-5259	258	33	2	2	NUM
ejpam-5259	258	34	)	)	PUNCT
ejpam-5259	258	35	.	.	PUNCT
ejpam-5259	259	1	for	for	ADP
ejpam-5259	259	2	ξk(ς	ξk(ς	NOUN
ejpam-5259	259	3	)	)	PUNCT
ejpam-5259	259	4	∈	∈	PROPN
ejpam-5259	259	5	t	t	PROPN
ejpam-5259	259	6	mkh(k	mkh(k	PROPN
ejpam-5259	259	7	,	,	PUNCT
ejpam-5259	259	8	r	r	NOUN
ejpam-5259	259	9	,	,	PUNCT
ejpam-5259	259	10	α	α	PROPN
ejpam-5259	259	11	,	,	PUNCT
ejpam-5259	259	12	η	η	PROPN
ejpam-5259	259	13	,	,	PUNCT
ejpam-5259	259	14	δ	δ	PROPN
ejpam-5259	259	15	,	,	PUNCT
ejpam-5259	259	16	λ	λ	PROPN
ejpam-5259	259	17	,	,	PUNCT
ejpam-5259	259	18	β	β	NOUN
ejpam-5259	259	19	)	)	PUNCT
ejpam-5259	259	20	,	,	PUNCT
ejpam-5259	259	21	we	we	PRON
ejpam-5259	259	22	note	note	VERB
ejpam-5259	259	23	that	that	SCONJ
ejpam-5259	259	24	|cµ|	|cµ|	PROPN
ejpam-5259	259	25	≤	≤	NOUN
ejpam-5259	259	26	1	1	NUM
ejpam-5259	259	27	and	and	CCONJ
ejpam-5259	259	28	|dµ|	|dµ|	ADJ
ejpam-5259	259	29	≤	≤	NUM
ejpam-5259	259	30	1	1	NUM
ejpam-5259	259	31	,	,	PUNCT
ejpam-5259	259	32	∞∑	∞∑	NUM
ejpam-5259	259	33	µ=1	µ=1	PUNCT
ejpam-5259	259	34	γ(η)[1	γ(η)[1	X
ejpam-5259	260	1	+	+	CCONJ
ejpam-5259	260	2	λ(µ−	λ(µ−	X
ejpam-5259	260	3	1)]k(µ+	1)]k(µ+	PROPN
ejpam-5259	260	4	δ)r(µ+	δ)r(µ+	PROPN
ejpam-5259	260	5	β	β	X
ejpam-5259	260	6	)	)	PUNCT
ejpam-5259	260	7	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	260	8	1	1	NUM
ejpam-5259	260	9	)	)	PUNCT
ejpam-5259	260	10	+	+	CCONJ
ejpam-5259	260	11	η)(1	η)(1	NUM
ejpam-5259	261	1	+	+	CCONJ
ejpam-5259	261	2	δ)r(1−	δ)r(1−	PROPN
ejpam-5259	261	3	β	β	NOUN
ejpam-5259	261	4	)	)	PUNCT
ejpam-5259	261	5	|aµ||cµ|+	|aµ||cµ|+	PROPN
ejpam-5259	262	1	∞∑	∞∑	NUM
ejpam-5259	262	2	µ=1	µ=1	PUNCT
ejpam-5259	262	3	γ(η)[1	γ(η)[1	X
ejpam-5259	262	4	+	+	CCONJ
ejpam-5259	262	5	λ(µ−	λ(µ−	X
ejpam-5259	262	6	1)]k(µ+	1)]k(µ+	PROPN
ejpam-5259	262	7	δ)r(µ−	δ)r(µ−	NOUN
ejpam-5259	262	8	β	β	X
ejpam-5259	262	9	)	)	PUNCT
ejpam-5259	262	10	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	262	11	1	1	NUM
ejpam-5259	262	12	)	)	PUNCT
ejpam-5259	262	13	+	+	CCONJ
ejpam-5259	262	14	η)(1	η)(1	NUM
ejpam-5259	262	15	+	+	CCONJ
ejpam-5259	262	16	δ)r(1−	δ)r(1−	ADJ
ejpam-5259	262	17	β	β	NOUN
ejpam-5259	262	18	)	)	PUNCT
ejpam-5259	262	19	|bµ||dµ|	|bµ||dµ|	NOUN
ejpam-5259	262	20	≤	≤	NOUN
ejpam-5259	263	1	∞∑	∞∑	PRON
ejpam-5259	263	2	µ=1	µ=1	PROPN
ejpam-5259	263	3	γ(η)[1	γ(η)[1	X
ejpam-5259	263	4	+	+	CCONJ
ejpam-5259	263	5	λ(µ−	λ(µ−	X
ejpam-5259	263	6	1)]k(µ+	1)]k(µ+	PROPN
ejpam-5259	263	7	δ)r(µ+	δ)r(µ+	PROPN
ejpam-5259	263	8	β	β	X
ejpam-5259	263	9	)	)	PUNCT
ejpam-5259	263	10	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	263	11	1	1	NUM
ejpam-5259	263	12	)	)	PUNCT
ejpam-5259	263	13	+	+	CCONJ
ejpam-5259	263	14	η)(1	η)(1	NUM
ejpam-5259	263	15	+	+	CCONJ
ejpam-5259	263	16	δ)r(1−	δ)r(1−	PROPN
ejpam-5259	263	17	β	β	NOUN
ejpam-5259	263	18	)	)	PUNCT
ejpam-5259	263	19	|aµ|+	|aµ|+	ADP
ejpam-5259	263	20	∞∑	∞∑	NUM
ejpam-5259	263	21	µ=1	µ=1	PROPN
ejpam-5259	263	22	γ(η)[1	γ(η)[1	X
ejpam-5259	263	23	+	+	PUNCT
ejpam-5259	263	24	λ(µ−	λ(µ−	X
ejpam-5259	263	25	1)]k(µ+	1)]k(µ+	PROPN
ejpam-5259	263	26	δ)r(µ−	δ)r(µ−	NOUN
ejpam-5259	263	27	β	β	X
ejpam-5259	263	28	)	)	PUNCT
ejpam-5259	263	29	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	263	30	1	1	NUM
ejpam-5259	263	31	)	)	PUNCT
ejpam-5259	263	32	+	+	CCONJ
ejpam-5259	263	33	η)(1	η)(1	NUM
ejpam-5259	264	1	+	+	CCONJ
ejpam-5259	264	2	δ)r(1−	δ)r(1−	ADJ
ejpam-5259	264	3	β	β	NOUN
ejpam-5259	264	4	)	)	PUNCT
ejpam-5259	264	5	|bµ|	|bµ|	VERB
ejpam-5259	264	6	≤	≤	NOUN
ejpam-5259	265	1	∞∑	∞∑	NUM
ejpam-5259	265	2	µ=1	µ=1	PROPN
ejpam-5259	265	3	γ(η)[1	γ(η)[1	X
ejpam-5259	265	4	+	+	CCONJ
ejpam-5259	265	5	λ(µ−	λ(µ−	X
ejpam-5259	265	6	1)]k(µ+	1)]k(µ+	PROPN
ejpam-5259	265	7	δ)r(µ+	δ)r(µ+	PROPN
ejpam-5259	265	8	γ	γ	PROPN
ejpam-5259	265	9	)	)	PUNCT
ejpam-5259	265	10	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	265	11	1	1	NUM
ejpam-5259	265	12	)	)	PUNCT
ejpam-5259	265	13	+	+	CCONJ
ejpam-5259	265	14	η)(1	η)(1	NUM
ejpam-5259	265	15	+	+	CCONJ
ejpam-5259	265	16	δ)r(1−	δ)r(1−	PROPN
ejpam-5259	265	17	γ	γ	NOUN
ejpam-5259	265	18	)	)	PUNCT
ejpam-5259	265	19	|aµ|+	|aµ|+	ADP
ejpam-5259	265	20	∞∑	∞∑	NUM
ejpam-5259	265	21	µ=1	µ=1	PROPN
ejpam-5259	265	22	γ(η)[1	γ(η)[1	X
ejpam-5259	265	23	+	+	PUNCT
ejpam-5259	265	24	λ(µ−	λ(µ−	X
ejpam-5259	265	25	1)]k(µ+	1)]k(µ+	PROPN
ejpam-5259	265	26	δ)r(µ−	δ)r(µ−	NOUN
ejpam-5259	265	27	γ	γ	X
ejpam-5259	265	28	)	)	PUNCT
ejpam-5259	265	29	γ(α(µ+	γ(α(µ+	PROPN
ejpam-5259	265	30	1	1	NUM
ejpam-5259	265	31	)	)	PUNCT
ejpam-5259	265	32	+	+	CCONJ
ejpam-5259	265	33	η)(1	η)(1	NUM
ejpam-5259	265	34	+	+	CCONJ
ejpam-5259	265	35	δ)r(1−	δ)r(1−	PROPN
ejpam-5259	265	36	γ	γ	NOUN
ejpam-5259	265	37	)	)	PUNCT
ejpam-5259	265	38	|bµ|	|bµ|	NOUN
ejpam-5259	265	39	≤	≤	NUM
ejpam-5259	265	40	1	1	NUM
ejpam-5259	265	41	,	,	PUNCT
ejpam-5259	265	42	since	since	SCONJ
ejpam-5259	265	43	fk(ς	fk(ς	NOUN
ejpam-5259	265	44	)	)	PUNCT
ejpam-5259	265	45	∈	∈	PROPN
ejpam-5259	265	46	t	t	PROPN
ejpam-5259	265	47	mkh(k	mkh(k	PROPN
ejpam-5259	265	48	,	,	PUNCT
ejpam-5259	265	49	r	r	NOUN
ejpam-5259	265	50	,	,	PUNCT
ejpam-5259	265	51	α	α	PROPN
ejpam-5259	265	52	,	,	PUNCT
ejpam-5259	265	53	η	η	PROPN
ejpam-5259	265	54	,	,	PUNCT
ejpam-5259	265	55	δ	δ	PROPN
ejpam-5259	265	56	,	,	PUNCT
ejpam-5259	265	57	λ	λ	PROPN
ejpam-5259	265	58	,	,	PUNCT
ejpam-5259	265	59	γ	γ	NOUN
ejpam-5259	265	60	)	)	PUNCT
ejpam-5259	265	61	and	and	CCONJ
ejpam-5259	265	62	0	0	NUM
ejpam-5259	265	63	≤	≤	NUM
ejpam-5259	265	64	β	β	NOUN
ejpam-5259	265	65	≤	≤	NUM
ejpam-5259	265	66	γ	γ	X
ejpam-5259	265	67	<	<	X
ejpam-5259	265	68	1	1	NUM
ejpam-5259	265	69	.	.	PUNCT
ejpam-5259	266	1	therefore	therefore	ADV
ejpam-5259	266	2	,	,	PUNCT
ejpam-5259	266	3	(	(	PUNCT
ejpam-5259	266	4	f	f	PROPN
ejpam-5259	266	5	∗	∗	X
ejpam-5259	266	6	ξ)(ς	ξ)(ς	PROPN
ejpam-5259	266	7	)	)	PUNCT
ejpam-5259	266	8	∈	∈	PROPN
ejpam-5259	266	9	t	t	PROPN
ejpam-5259	266	10	mkh(k	mkh(k	PROPN
ejpam-5259	266	11	,	,	PUNCT
ejpam-5259	266	12	r	r	NOUN
ejpam-5259	266	13	,	,	PUNCT
ejpam-5259	266	14	α	α	PROPN
ejpam-5259	266	15	,	,	PUNCT
ejpam-5259	266	16	η	η	PROPN
ejpam-5259	266	17	,	,	PUNCT
ejpam-5259	266	18	δ	δ	PROPN
ejpam-5259	266	19	,	,	PUNCT
ejpam-5259	266	20	λ	λ	PROPN
ejpam-5259	266	21	,	,	PUNCT
ejpam-5259	266	22	γ	γ	NOUN
ejpam-5259	266	23	)	)	PUNCT
ejpam-5259	266	24	⊆	⊆	NUM
ejpam-5259	266	25	t	t	PROPN
ejpam-5259	266	26	mkh(k	mkh(k	PROPN
ejpam-5259	266	27	,	,	PUNCT
ejpam-5259	266	28	r	r	NOUN
ejpam-5259	266	29	,	,	PUNCT
ejpam-5259	266	30	α	α	PROPN
ejpam-5259	266	31	,	,	PUNCT
ejpam-5259	266	32	η	η	PROPN
ejpam-5259	266	33	,	,	PUNCT
ejpam-5259	266	34	δ	δ	PROPN
ejpam-5259	266	35	,	,	PUNCT
ejpam-5259	266	36	λ	λ	PROPN
ejpam-5259	266	37	,	,	PUNCT
ejpam-5259	266	38	β	β	NOUN
ejpam-5259	266	39	)	)	PUNCT
ejpam-5259	266	40	.	.	PUNCT
ejpam-5259	267	1	theorem	theorem	ADJ
ejpam-5259	267	2	6	6	NUM
ejpam-5259	267	3	.	.	PUNCT
ejpam-5259	268	1	let	let	VERB
ejpam-5259	268	2	fm	fm	PROPN
ejpam-5259	268	3	,	,	PUNCT
ejpam-5259	268	4	k	k	PROPN
ejpam-5259	268	5	defined	define	VERB
ejpam-5259	268	6	as	as	ADP
ejpam-5259	268	7	fm	fm	PROPN
ejpam-5259	268	8	,	,	PUNCT
ejpam-5259	268	9	k	k	PROPN
ejpam-5259	269	1	=	=	PUNCT
ejpam-5259	270	1	(	(	PUNCT
ejpam-5259	270	2	−1)k	−1)k	PROPN
ejpam-5259	270	3	ς	ς	PROPN
ejpam-5259	270	4	+	+	PUNCT
ejpam-5259	271	1	∞∑	∞∑	NUM
ejpam-5259	271	2	µ=1	µ=1	PUNCT
ejpam-5259	271	3	|aµ,m|ςµ	|aµ,m|ςµ	PROPN
ejpam-5259	271	4	+	+	CCONJ
ejpam-5259	271	5	(	(	PUNCT
ejpam-5259	271	6	−1)k	−1)k	PROPN
ejpam-5259	271	7	∞∑	∞∑	NUM
ejpam-5259	271	8	µ=1	µ=1	ADV
ejpam-5259	271	9	|bµ,m|ςµ	|bµ,m|ςµ	PROPN
ejpam-5259	271	10	be	be	VERB
ejpam-5259	271	11	in	in	ADP
ejpam-5259	271	12	class	class	NOUN
ejpam-5259	271	13	t	t	PROPN
ejpam-5259	271	14	mkh(k	mkh(k	PROPN
ejpam-5259	271	15	,	,	PUNCT
ejpam-5259	271	16	r	r	NOUN
ejpam-5259	271	17	,	,	PUNCT
ejpam-5259	271	18	α	α	PROPN
ejpam-5259	271	19	,	,	PUNCT
ejpam-5259	271	20	η	η	PROPN
ejpam-5259	271	21	,	,	PUNCT
ejpam-5259	271	22	δ	δ	PROPN
ejpam-5259	271	23	,	,	PUNCT
ejpam-5259	271	24	λ	λ	PROPN
ejpam-5259	271	25	,	,	PUNCT
ejpam-5259	271	26	γ	γ	NOUN
ejpam-5259	271	27	)	)	PUNCT
ejpam-5259	271	28	for	for	ADP
ejpam-5259	271	29	every	every	DET
ejpam-5259	271	30	m	m	NOUN
ejpam-5259	271	31	=	=	NOUN
ejpam-5259	271	32	1	1	NUM
ejpam-5259	271	33	,	,	PUNCT
ejpam-5259	271	34	2	2	NUM
ejpam-5259	271	35	,	,	PUNCT
ejpam-5259	271	36	...	...	PUNCT
ejpam-5259	271	37	,	,	PUNCT
ejpam-5259	271	38	l	l	NOUN
ejpam-5259	271	39	,	,	PUNCT
ejpam-5259	271	40	then	then	ADV
ejpam-5259	271	41	the	the	DET
ejpam-5259	271	42	function	function	NOUN
ejpam-5259	271	43	ℑm(ς	ℑm(ς	NOUN
ejpam-5259	271	44	)	)	PUNCT
ejpam-5259	271	45	=	=	PUNCT
ejpam-5259	272	1	l∑	l∑	PROPN
ejpam-5259	272	2	m=1	m=1	X
ejpam-5259	272	3	cmfm	cmfm	ADJ
ejpam-5259	272	4	,	,	PUNCT
ejpam-5259	272	5	k(ς	k(ς	PROPN
ejpam-5259	272	6	)	)	PUNCT
ejpam-5259	272	7	,	,	PUNCT
ejpam-5259	272	8	(	(	PUNCT
ejpam-5259	272	9	0	0	NUM
ejpam-5259	272	10	≤	≤	NUM
ejpam-5259	272	11	cm	cm	NOUN
ejpam-5259	272	12	≤	≤	NUM
ejpam-5259	272	13	1	1	NUM
ejpam-5259	272	14	)	)	PUNCT
ejpam-5259	272	15	,	,	PUNCT
ejpam-5259	272	16	(	(	PUNCT
ejpam-5259	272	17	19	19	NUM
ejpam-5259	272	18	)	)	PUNCT
ejpam-5259	272	19	are	be	AUX
ejpam-5259	272	20	also	also	ADV
ejpam-5259	272	21	in	in	ADP
ejpam-5259	272	22	the	the	DET
ejpam-5259	272	23	class	class	NOUN
ejpam-5259	272	24	t	t	PROPN
ejpam-5259	272	25	mkh(k	mkh(k	PROPN
ejpam-5259	272	26	,	,	PUNCT
ejpam-5259	272	27	r	r	NOUN
ejpam-5259	272	28	,	,	PUNCT
ejpam-5259	272	29	α	α	PROPN
ejpam-5259	272	30	,	,	PUNCT
ejpam-5259	272	31	η	η	PROPN
ejpam-5259	272	32	,	,	PUNCT
ejpam-5259	272	33	δ	δ	PROPN
ejpam-5259	272	34	,	,	PUNCT
ejpam-5259	272	35	λ	λ	PROPN
ejpam-5259	272	36	,	,	PUNCT
ejpam-5259	272	37	γ	γ	NOUN
ejpam-5259	272	38	)	)	PUNCT
ejpam-5259	272	39	,	,	PUNCT
ejpam-5259	272	40	where	where	SCONJ
ejpam-5259	272	41	l∑	l∑	X
ejpam-5259	272	42	m=1	m=1	X
ejpam-5259	272	43	cm	cm	NOUN
ejpam-5259	272	44	=	=	SYM
ejpam-5259	272	45	1	1	NUM
ejpam-5259	272	46	.	.	PUNCT
ejpam-5259	273	1	proof	proof	NOUN
ejpam-5259	273	2	.	.	PUNCT
ejpam-5259	274	1	according	accord	VERB
ejpam-5259	274	2	to	to	ADP
ejpam-5259	274	3	the	the	DET
ejpam-5259	274	4	definition	definition	NOUN
ejpam-5259	274	5	of	of	ADP
ejpam-5259	274	6	ℑm(ς	ℑm(ς	NOUN
ejpam-5259	274	7	)	)	PUNCT
ejpam-5259	274	8	given	give	VERB
ejpam-5259	274	9	by	by	ADP
ejpam-5259	274	10	(	(	PUNCT
ejpam-5259	274	11	19	19	NUM
ejpam-5259	274	12	)	)	PUNCT
ejpam-5259	274	13	,	,	PUNCT
ejpam-5259	274	14	we	we	PRON
ejpam-5259	274	15	can	can	AUX
ejpam-5259	274	16	write	write	VERB
ejpam-5259	274	17	ℑm(ς	ℑm(ς	NOUN
ejpam-5259	274	18	)	)	PUNCT
ejpam-5259	274	19	=	=	PUNCT
ejpam-5259	274	20	(	(	PUNCT
ejpam-5259	274	21	−1)k	−1)k	PROPN
ejpam-5259	274	22	ς	ς	PROPN
ejpam-5259	275	1	+	+	CCONJ
ejpam-5259	275	2	∞∑	∞∑	NUM
ejpam-5259	275	3	µ=1	µ=1	PUNCT
ejpam-5259	275	4	(	(	PUNCT
ejpam-5259	275	5	l∑	l∑	PROPN
ejpam-5259	275	6	m=1	m=1	PROPN
ejpam-5259	275	7	cm|aµ,m|	cm|aµ,m|	NOUN
ejpam-5259	275	8	)	)	PUNCT
ejpam-5259	275	9	ςµ	ςµ	NOUN
ejpam-5259	276	1	+	+	CCONJ
ejpam-5259	276	2	(	(	PUNCT
ejpam-5259	276	3	−1)k	−1)k	PROPN
ejpam-5259	276	4	∞∑	∞∑	NUM
ejpam-5259	276	5	µ=1	µ=1	ADV
ejpam-5259	276	6	(	(	PUNCT
ejpam-5259	276	7	l∑	l∑	X
ejpam-5259	276	8	m=1	m=1	X
ejpam-5259	276	9	cm|bµ,m|	cm|bµ,m|	NOUN
ejpam-5259	276	10	)	)	PUNCT
ejpam-5259	276	11	ςµ.	ςµ.	NOUN
ejpam-5259	276	12	furthermore	furthermore	ADV
ejpam-5259	276	13	,	,	PUNCT
ejpam-5259	276	14	for	for	ADP
ejpam-5259	276	15	every	every	DET
ejpam-5259	276	16	m	m	NOUN
ejpam-5259	276	17	=	=	NOUN
ejpam-5259	276	18	1	1	NUM
ejpam-5259	276	19	,	,	PUNCT
ejpam-5259	276	20	2	2	NUM
ejpam-5259	276	21	,	,	PUNCT
ejpam-5259	276	22	·	·	PUNCT
ejpam-5259	276	23	·	·	PUNCT
ejpam-5259	276	24	·	·	PUNCT
ejpam-5259	276	25	,	,	PUNCT
ejpam-5259	276	26	l	l	NOUN
ejpam-5259	276	27	,	,	PUNCT
ejpam-5259	276	28	we	we	PRON
ejpam-5259	276	29	have	have	AUX
ejpam-5259	276	30	fm	fm	PROPN
ejpam-5259	276	31	,	,	PUNCT
ejpam-5259	276	32	k	k	PROPN
ejpam-5259	276	33	∈	∈	PROPN
ejpam-5259	276	34	t	t	PROPN
ejpam-5259	276	35	mkh(k	mkh(k	PROPN
ejpam-5259	276	36	,	,	PUNCT
ejpam-5259	276	37	r	r	NOUN
ejpam-5259	276	38	,	,	PUNCT
ejpam-5259	276	39	α	α	PROPN
ejpam-5259	276	40	,	,	PUNCT
ejpam-5259	276	41	η	η	PROPN
ejpam-5259	276	42	,	,	PUNCT
ejpam-5259	276	43	δ	δ	PROPN
ejpam-5259	276	44	,	,	PUNCT
ejpam-5259	276	45	λ	λ	PROPN
ejpam-5259	276	46	,	,	PUNCT
ejpam-5259	276	47	γ	γ	NOUN
ejpam-5259	276	48	)	)	PUNCT
ejpam-5259	276	49	.	.	PUNCT
ejpam-5259	277	1	then	then	ADV
ejpam-5259	277	2	,	,	PUNCT
ejpam-5259	277	3	by	by	ADP
ejpam-5259	277	4	(	(	PUNCT
ejpam-5259	277	5	2	2	NUM
ejpam-5259	277	6	)	)	PUNCT
ejpam-5259	277	7	,	,	PUNCT
ejpam-5259	277	8	we	we	PRON
ejpam-5259	277	9	have	have	VERB
ejpam-5259	277	10	i	i	PRON
ejpam-5259	277	11	=	=	SYM
ejpam-5259	277	12			PROPN
ejpam-5259	277	13	∞∑	∞∑	NUM
ejpam-5259	277	14	µ=1	µ=1	PUNCT
ejpam-5259	277	15	(	(	PUNCT
ejpam-5259	277	16	γ(η)[1+λ(µ−1)]k(µ+δ)r(µ+γ	γ(η)[1+λ(µ−1)]k(µ+δ)r(µ+γ	PROPN
ejpam-5259	277	17	)	)	PUNCT
ejpam-5259	277	18	γ(α(µ+1)+η)(1+δ)r	γ(α(µ+1)+η)(1+δ)r	PROPN
ejpam-5259	277	19	)	)	PUNCT
ejpam-5259	277	20	{	{	PUNCT
ejpam-5259	277	21	l∑	l∑	PROPN
ejpam-5259	277	22	m=1	m=1	X
ejpam-5259	277	23	cµ|aµ,m|	cµ|aµ,m|	NOUN
ejpam-5259	277	24	}	}	PUNCT
ejpam-5259	278	1	+	+	CCONJ
ejpam-5259	278	2	∞∑	∞∑	NUM
ejpam-5259	278	3	µ=1	µ=1	ADV
ejpam-5259	278	4	(	(	PUNCT
ejpam-5259	278	5	γ(η)[1+λ(µ−1)]k(µ+δ)r(µ−γ	γ(η)[1+λ(µ−1)]k(µ+δ)r(µ−γ	ADV
ejpam-5259	278	6	)	)	PUNCT
ejpam-5259	278	7	γ(α(µ+1)+η)(1+δ)r	γ(α(µ+1)+η)(1+δ)r	PROPN
ejpam-5259	278	8	)	)	PUNCT
ejpam-5259	278	9	{	{	PUNCT
ejpam-5259	278	10	l∑	l∑	X
ejpam-5259	278	11	m=1	m=1	PRON
ejpam-5259	278	12	cm|bµ,m|	cm|bµ,m|	ADJ
ejpam-5259	278	13	}	}	PUNCT
ejpam-5259	278	14			NOUN
ejpam-5259	279	1	=	=	PUNCT
ejpam-5259	279	2	l∑	l∑	X
ejpam-5259	280	1	m=1	m=1	X
ejpam-5259	280	2	cm	cm	NOUN
ejpam-5259	280	3	{	{	PUNCT
ejpam-5259	280	4	∞∑	∞∑	NUM
ejpam-5259	280	5	µ=1	µ=1	ADV
ejpam-5259	280	6	(	(	PUNCT
ejpam-5259	280	7	γ(η)[1+λ(µ−1)]k(µ+δ)r(µ+γ	γ(η)[1+λ(µ−1)]k(µ+δ)r(µ+γ	PROPN
ejpam-5259	280	8	)	)	PUNCT
ejpam-5259	280	9	γ(α(µ+1)+η)(1+δ)r	γ(α(µ+1)+η)(1+δ)r	PROPN
ejpam-5259	280	10	)	)	PUNCT
ejpam-5259	281	1	|aµ,m|+	|aµ,m|+	X
ejpam-5259	282	1	∞∑	∞∑	PRON
ejpam-5259	282	2	µ=1	µ=1	ADV
ejpam-5259	282	3	(	(	PUNCT
ejpam-5259	282	4	γ(η)[1+λ(µ−1)]k(µ+δ)r(µ−γ	γ(η)[1+λ(µ−1)]k(µ+δ)r(µ−γ	ADV
ejpam-5259	282	5	)	)	PUNCT
ejpam-5259	282	6	γ(α(µ+1)+η)(1+δ)r	γ(α(µ+1)+η)(1+δ)r	PROPN
ejpam-5259	282	7	)	)	PUNCT
ejpam-5259	282	8	|bµ,m|	|bµ,m|	PROPN
ejpam-5259	282	9	}	}	PUNCT
ejpam-5259	282	10	≤	≤	NOUN
ejpam-5259	282	11	l∑	l∑	PUNCT
ejpam-5259	283	1	m=1	m=1	X
ejpam-5259	283	2	cm(1−	cm(1−	VERB
ejpam-5259	283	3	γ	γ	X
ejpam-5259	283	4	)	)	PUNCT
ejpam-5259	283	5	≤	≤	NOUN
ejpam-5259	283	6	1−	1−	NUM
ejpam-5259	283	7	γ	γ	X
ejpam-5259	283	8	.	.	PROPN
ejpam-5259	283	9	therefore	therefore	ADV
ejpam-5259	283	10	,	,	PUNCT
ejpam-5259	283	11	ℑm(ς	ℑm(ς	NOUN
ejpam-5259	283	12	)	)	PUNCT
ejpam-5259	283	13	∈	∈	PROPN
ejpam-5259	283	14	t	t	PROPN
ejpam-5259	283	15	mkh(k	mkh(k	PROPN
ejpam-5259	283	16	,	,	PUNCT
ejpam-5259	283	17	r	r	NOUN
ejpam-5259	283	18	,	,	PUNCT
ejpam-5259	283	19	α	α	PROPN
ejpam-5259	283	20	,	,	PUNCT
ejpam-5259	283	21	η	η	PROPN
ejpam-5259	283	22	,	,	PUNCT
ejpam-5259	283	23	δ	δ	PROPN
ejpam-5259	283	24	,	,	PUNCT
ejpam-5259	283	25	λ	λ	PROPN
ejpam-5259	283	26	,	,	PUNCT
ejpam-5259	283	27	γ	γ	NOUN
ejpam-5259	283	28	)	)	PUNCT
ejpam-5259	283	29	.	.	PUNCT
ejpam-5259	284	1	corollary	corollary	ADJ
ejpam-5259	284	2	3	3	NUM
ejpam-5259	284	3	.	.	PUNCT
ejpam-5259	285	1	the	the	DET
ejpam-5259	285	2	class	class	NOUN
ejpam-5259	285	3	t	t	PROPN
ejpam-5259	285	4	mkh(k	mkh(k	PROPN
ejpam-5259	285	5	,	,	PUNCT
ejpam-5259	285	6	r	r	NOUN
ejpam-5259	285	7	,	,	PUNCT
ejpam-5259	285	8	α	α	PROPN
ejpam-5259	285	9	,	,	PUNCT
ejpam-5259	285	10	η	η	PROPN
ejpam-5259	285	11	,	,	PUNCT
ejpam-5259	285	12	δ	δ	PROPN
ejpam-5259	285	13	,	,	PUNCT
ejpam-5259	285	14	λ	λ	PROPN
ejpam-5259	285	15	,	,	PUNCT
ejpam-5259	285	16	γ	γ	NOUN
ejpam-5259	285	17	)	)	PUNCT
ejpam-5259	285	18	is	be	AUX
ejpam-5259	285	19	closed	close	VERB
ejpam-5259	285	20	under	under	ADP
ejpam-5259	285	21	convex	convex	ADJ
ejpam-5259	285	22	combination	combination	NOUN
ejpam-5259	285	23	.	.	PUNCT
ejpam-5259	286	1	references	reference	NOUN
ejpam-5259	286	2	1905	1905	NUM
ejpam-5259	286	3	conclusion	conclusion	NOUN
ejpam-5259	286	4	in	in	ADP
ejpam-5259	286	5	the	the	DET
ejpam-5259	286	6	current	current	ADJ
ejpam-5259	286	7	study	study	NOUN
ejpam-5259	286	8	,	,	PUNCT
ejpam-5259	286	9	we	we	PRON
ejpam-5259	286	10	have	have	AUX
ejpam-5259	286	11	introduced	introduce	VERB
ejpam-5259	286	12	and	and	CCONJ
ejpam-5259	286	13	examined	examine	VERB
ejpam-5259	286	14	the	the	DET
ejpam-5259	286	15	coefficient	coefficient	NOUN
ejpam-5259	286	16	issues	issue	NOUN
ejpam-5259	286	17	related	relate	VERB
ejpam-5259	286	18	to	to	ADP
ejpam-5259	286	19	each	each	PRON
ejpam-5259	286	20	of	of	ADP
ejpam-5259	286	21	class	class	NOUN
ejpam-5259	286	22	mkh(k	mkh(k	PROPN
ejpam-5259	286	23	,	,	PUNCT
ejpam-5259	286	24	r	r	NOUN
ejpam-5259	286	25	,	,	PUNCT
ejpam-5259	286	26	α	α	PROPN
ejpam-5259	286	27	,	,	PUNCT
ejpam-5259	286	28	η	η	PROPN
ejpam-5259	286	29	,	,	PUNCT
ejpam-5259	286	30	δ	δ	PROPN
ejpam-5259	286	31	,	,	PUNCT
ejpam-5259	286	32	λ	λ	PROPN
ejpam-5259	286	33	,	,	PUNCT
ejpam-5259	286	34	γ	γ	NOUN
ejpam-5259	286	35	)	)	PUNCT
ejpam-5259	286	36	,	,	PUNCT
ejpam-5259	286	37	which	which	PRON
ejpam-5259	286	38	consists	consist	VERB
ejpam-5259	286	39	of	of	ADP
ejpam-5259	286	40	harmonic	harmonic	ADJ
ejpam-5259	286	41	meromorphic	meromorphic	ADJ
ejpam-5259	286	42	starlike	starlike	NOUN
ejpam-5259	286	43	functions	function	NOUN
ejpam-5259	286	44	.	.	PUNCT
ejpam-5259	287	1	this	this	DET
ejpam-5259	287	2	class	class	NOUN
ejpam-5259	287	3	is	be	AUX
ejpam-5259	287	4	utilised	utilise	VERB
ejpam-5259	287	5	to	to	PART
ejpam-5259	287	6	describe	describe	VERB
ejpam-5259	287	7	a	a	DET
ejpam-5259	287	8	derivative	derivative	ADJ
ejpam-5259	287	9	operator	operator	NOUN
ejpam-5259	287	10	that	that	PRON
ejpam-5259	287	11	incorporates	incorporate	VERB
ejpam-5259	287	12	the	the	DET
ejpam-5259	287	13	mittag	mittag	ADJ
ejpam-5259	287	14	-	-	PUNCT
ejpam-5259	287	15	leffler	leffler	NOUN
ejpam-5259	287	16	function	function	NOUN
ejpam-5259	287	17	as	as	ADP
ejpam-5259	287	18	a	a	DET
ejpam-5259	287	19	multiplier	multipli	ADJ
ejpam-5259	287	20	transformation	transformation	NOUN
ejpam-5259	287	21	.	.	PUNCT
ejpam-5259	288	1	this	this	DET
ejpam-5259	288	2	study	study	NOUN
ejpam-5259	288	3	derives	derive	VERB
ejpam-5259	288	4	coefficient	coefficient	NOUN
ejpam-5259	288	5	inequalities	inequality	NOUN
ejpam-5259	288	6	,	,	PUNCT
ejpam-5259	288	7	the	the	DET
ejpam-5259	288	8	distortion	distortion	NOUN
ejpam-5259	288	9	theorem	theorem	VERB
ejpam-5259	288	10	,	,	PUNCT
ejpam-5259	288	11	distortion	distortion	NOUN
ejpam-5259	288	12	bounds	bound	NOUN
ejpam-5259	288	13	,	,	PUNCT
ejpam-5259	288	14	extreme	extreme	ADJ
ejpam-5259	288	15	points	point	NOUN
ejpam-5259	288	16	,	,	PUNCT
ejpam-5259	288	17	convex	convex	NOUN
ejpam-5259	288	18	combination	combination	NOUN
ejpam-5259	288	19	,	,	PUNCT
ejpam-5259	288	20	and	and	CCONJ
ejpam-5259	288	21	convolution	convolution	NOUN
ejpam-5259	288	22	for	for	ADP
ejpam-5259	288	23	functions	function	NOUN
ejpam-5259	288	24	inside	inside	ADP
ejpam-5259	288	25	this	this	DET
ejpam-5259	288	26	particular	particular	ADJ
ejpam-5259	288	27	class	class	NOUN
ejpam-5259	288	28	.	.	PUNCT
ejpam-5259	289	1	the	the	DET
ejpam-5259	289	2	results	result	NOUN
ejpam-5259	289	3	obtained	obtain	VERB
ejpam-5259	289	4	in	in	ADP
ejpam-5259	289	5	this	this	DET
ejpam-5259	289	6	article	article	NOUN
ejpam-5259	289	7	can	can	AUX
ejpam-5259	289	8	be	be	AUX
ejpam-5259	289	9	generalised	generalise	VERB
ejpam-5259	289	10	in	in	ADP
ejpam-5259	289	11	the	the	DET
ejpam-5259	289	12	future	future	NOUN
ejpam-5259	289	13	using	use	VERB
ejpam-5259	289	14	quantum	quantum	ADJ
ejpam-5259	289	15	calculus	calculus	NOUN
ejpam-5259	289	16	and	and	CCONJ
ejpam-5259	289	17	other	other	ADJ
ejpam-5259	289	18	q	q	NOUN
ejpam-5259	289	19	-	-	PUNCT
ejpam-5259	289	20	analogues	analogue	NOUN
ejpam-5259	289	21	of	of	ADP
ejpam-5259	289	22	the	the	DET
ejpam-5259	289	23	fractional	fractional	ADJ
ejpam-5259	289	24	derivative	derivative	ADJ
ejpam-5259	289	25	operator	operator	NOUN
ejpam-5259	289	26	.	.	PUNCT
ejpam-5259	290	1	acknowledgements	acknowledgement	NOUN
ejpam-5259	290	2	the	the	DET
ejpam-5259	290	3	second	second	ADJ
ejpam-5259	290	4	author	author	NOUN
ejpam-5259	290	5	express	express	VERB
ejpam-5259	290	6	their	their	PRON
ejpam-5259	290	7	gratitude	gratitude	NOUN
ejpam-5259	290	8	to	to	ADP
ejpam-5259	290	9	philadelphia	philadelphia	PROPN
ejpam-5259	290	10	university	university	PROPN
ejpam-5259	290	11	-	-	PUNCT
ejpam-5259	290	12	jordan	jordan	PROPN
ejpam-5259	290	13	supporting	support	VERB
ejpam-5259	290	14	this	this	DET
ejpam-5259	290	15	work	work	NOUN
ejpam-5259	290	16	,	,	PUNCT
ejpam-5259	290	17	emphasising	emphasise	VERB
ejpam-5259	290	18	non	non	ADJ
ejpam-5259	290	19	-	-	ADJ
ejpam-5259	290	20	financial	financial	ADJ
ejpam-5259	290	21	support	support	NOUN
ejpam-5259	290	22	in	in	ADP
ejpam-5259	290	23	providing	provide	VERB
ejpam-5259	290	24	necessary	necessary	ADJ
ejpam-5259	290	25	resources	resource	NOUN
ejpam-5259	290	26	.	.	PUNCT
ejpam-5259	291	1	references	reference	NOUN
ejpam-5259	291	2	[	[	X
ejpam-5259	291	3	1	1	NUM
ejpam-5259	291	4	]	]	X
ejpam-5259	291	5	sarah	sarah	PROPN
ejpam-5259	291	6	ahmed	ahmed	PROPN
ejpam-5259	291	7	,	,	PUNCT
ejpam-5259	291	8	maslina	maslina	NOUN
ejpam-5259	291	9	darus	darus	NOUN
ejpam-5259	291	10	,	,	PUNCT
ejpam-5259	291	11	and	and	CCONJ
ejpam-5259	291	12	georgia	georgia	PROPN
ejpam-5259	291	13	irina	irina	PROPN
ejpam-5259	291	14	oros	oros	PROPN
ejpam-5259	291	15	.	.	PUNCT
ejpam-5259	292	1	subordination	subordination	NOUN
ejpam-5259	292	2	results	result	VERB
ejpam-5259	292	3	for	for	ADP
ejpam-5259	292	4	the	the	DET
ejpam-5259	292	5	second	second	ADJ
ejpam-5259	292	6	-	-	PUNCT
ejpam-5259	292	7	order	order	NOUN
ejpam-5259	292	8	differential	differential	ADJ
ejpam-5259	292	9	polynomials	polynomial	NOUN
ejpam-5259	292	10	of	of	ADP
ejpam-5259	292	11	meromorphic	meromorphic	ADJ
ejpam-5259	292	12	functions	function	NOUN
ejpam-5259	292	13	.	.	PUNCT
ejpam-5259	293	1	symmetry	symmetry	NOUN
ejpam-5259	293	2	,	,	PUNCT
ejpam-5259	293	3	14(12):2587	14(12):2587	NUM
ejpam-5259	293	4	,	,	PUNCT
ejpam-5259	293	5	2022	2022	NUM
ejpam-5259	293	6	.	.	PUNCT
ejpam-5259	294	1	[	[	X
ejpam-5259	294	2	2	2	X
ejpam-5259	294	3	]	]	PUNCT
ejpam-5259	294	4	om	om	PROPN
ejpam-5259	294	5	p	p	PROPN
ejpam-5259	294	6	ahuja	ahuja	PROPN
ejpam-5259	294	7	and	and	CCONJ
ejpam-5259	294	8	jay	jay	PROPN
ejpam-5259	294	9	m	m	PROPN
ejpam-5259	294	10	jahangiri	jahangiri	ADV
ejpam-5259	294	11	.	.	PUNCT
ejpam-5259	295	1	certain	certain	ADJ
ejpam-5259	295	2	meromorphic	meromorphic	ADJ
ejpam-5259	295	3	harmonic	harmonic	ADJ
ejpam-5259	295	4	functions	function	NOUN
ejpam-5259	295	5	.	.	PUNCT
ejpam-5259	296	1	bulletin	bulletin	NOUN
ejpam-5259	296	2	of	of	ADP
ejpam-5259	296	3	the	the	DET
ejpam-5259	296	4	malaysian	malaysian	PROPN
ejpam-5259	296	5	mathematical	mathematical	PROPN
ejpam-5259	296	6	sciences	sciences	PROPN
ejpam-5259	296	7	society	society	NOUN
ejpam-5259	296	8	,	,	PUNCT
ejpam-5259	296	9	25(1	25(1	NUM
ejpam-5259	296	10	)	)	PUNCT
ejpam-5259	296	11	,	,	PUNCT
ejpam-5259	296	12	2002	2002	NUM
ejpam-5259	296	13	.	.	PUNCT
ejpam-5259	297	1	[	[	X
ejpam-5259	297	2	3	3	X
ejpam-5259	297	3	]	]	X
ejpam-5259	297	4	abdullah	abdullah	PROPN
ejpam-5259	297	5	alsoboh	alsoboh	PROPN
ejpam-5259	297	6	,	,	PUNCT
ejpam-5259	297	7	ala	ala	PROPN
ejpam-5259	297	8	amourah	amourah	PROPN
ejpam-5259	297	9	,	,	PUNCT
ejpam-5259	297	10	maslina	maslina	NOUN
ejpam-5259	297	11	darus	darus	NOUN
ejpam-5259	297	12	,	,	PUNCT
ejpam-5259	297	13	and	and	CCONJ
ejpam-5259	297	14	carla	carla	PROPN
ejpam-5259	297	15	amoi	amoi	AUX
ejpam-5259	297	16	rudder	rudder	VERB
ejpam-5259	297	17	.	.	PUNCT
ejpam-5259	298	1	studying	study	VERB
ejpam-5259	298	2	the	the	DET
ejpam-5259	298	3	harmonic	harmonic	ADJ
ejpam-5259	298	4	functions	function	NOUN
ejpam-5259	298	5	associated	associate	VERB
ejpam-5259	298	6	with	with	ADP
ejpam-5259	298	7	quantum	quantum	NOUN
ejpam-5259	298	8	calculus	calculus	NOUN
ejpam-5259	298	9	.	.	PUNCT
ejpam-5259	299	1	mathematics	mathematic	NOUN
ejpam-5259	299	2	,	,	PUNCT
ejpam-5259	299	3	11(10):2220	11(10):2220	NUM
ejpam-5259	299	4	,	,	PUNCT
ejpam-5259	299	5	2023	2023	NUM
ejpam-5259	299	6	.	.	PUNCT
ejpam-5259	300	1	[	[	X
ejpam-5259	300	2	4	4	X
ejpam-5259	300	3	]	]	X
ejpam-5259	300	4	abdullah	abdullah	PROPN
ejpam-5259	300	5	alsoboh	alsoboh	NOUN
ejpam-5259	300	6	and	and	CCONJ
ejpam-5259	300	7	maslina	maslina	PROPN
ejpam-5259	300	8	darus	darus	PROPN
ejpam-5259	300	9	.	.	PUNCT
ejpam-5259	301	1	a	a	DET
ejpam-5259	301	2	q	q	ADJ
ejpam-5259	301	3	-	-	PUNCT
ejpam-5259	301	4	starlike	starlike	ADJ
ejpam-5259	301	5	class	class	NOUN
ejpam-5259	301	6	of	of	ADP
ejpam-5259	301	7	harmonic	harmonic	ADJ
ejpam-5259	301	8	meromorphic	meromorphic	ADJ
ejpam-5259	301	9	functions	function	NOUN
ejpam-5259	301	10	defined	define	VERB
ejpam-5259	301	11	by	by	ADP
ejpam-5259	301	12	q	q	ADJ
ejpam-5259	301	13	-	-	ADJ
ejpam-5259	301	14	derivative	derivative	ADJ
ejpam-5259	301	15	operator	operator	NOUN
ejpam-5259	301	16	.	.	PUNCT
ejpam-5259	302	1	in	in	ADP
ejpam-5259	302	2	mathematics	mathematic	NOUN
ejpam-5259	302	3	and	and	CCONJ
ejpam-5259	302	4	computation	computation	NOUN
ejpam-5259	302	5	,	,	PUNCT
ejpam-5259	302	6	pages	page	NOUN
ejpam-5259	302	7	257–269	257–269	NUM
ejpam-5259	302	8	,	,	PUNCT
ejpam-5259	302	9	singapore	singapore	PROPN
ejpam-5259	302	10	,	,	PUNCT
ejpam-5259	302	11	2023	2023	NUM
ejpam-5259	302	12	.	.	PUNCT
ejpam-5259	302	13	springer	springer	NOUN
ejpam-5259	302	14	nature	nature	PROPN
ejpam-5259	302	15	singapore	singapore	PROPN
ejpam-5259	302	16	.	.	PUNCT
ejpam-5259	303	1	[	[	X
ejpam-5259	303	2	5	5	X
ejpam-5259	303	3	]	]	X
ejpam-5259	303	4	abdullah	abdullah	PROPN
ejpam-5259	303	5	alsoboh	alsoboh	PROPN
ejpam-5259	303	6	,	,	PUNCT
ejpam-5259	303	7	maslina	maslina	NOUN
ejpam-5259	303	8	darus	darus	PROPN
ejpam-5259	303	9	,	,	PUNCT
ejpam-5259	303	10	ala	ala	PROPN
ejpam-5259	303	11	amourah	amourah	PROPN
ejpam-5259	303	12	,	,	PUNCT
ejpam-5259	303	13	and	and	CCONJ
ejpam-5259	303	14	waggas	waggas	NOUN
ejpam-5259	303	15	galib	galib	PROPN
ejpam-5259	303	16	atshan	atshan	PROPN
ejpam-5259	303	17	.	.	PUNCT
ejpam-5259	304	1	a	a	DET
ejpam-5259	304	2	certain	certain	ADJ
ejpam-5259	304	3	subclass	subclass	NOUN
ejpam-5259	304	4	of	of	ADP
ejpam-5259	304	5	harmonic	harmonic	ADJ
ejpam-5259	304	6	meromorphic	meromorphic	ADJ
ejpam-5259	304	7	functions	function	NOUN
ejpam-5259	304	8	with	with	ADP
ejpam-5259	304	9	respect	respect	NOUN
ejpam-5259	304	10	to	to	ADP
ejpam-5259	304	11	k	k	ADJ
ejpam-5259	304	12	-	-	ADJ
ejpam-5259	304	13	symmetric	symmetric	ADJ
ejpam-5259	304	14	points	point	NOUN
ejpam-5259	304	15	.	.	PUNCT
ejpam-5259	305	1	int	int	NOUN
ejpam-5259	305	2	.	.	PUNCT
ejpam-5259	306	1	j.	j.	PROPN
ejpam-5259	306	2	open	open	PROPN
ejpam-5259	306	3	problems	problem	NOUN
ejpam-5259	306	4	complex	complex	ADJ
ejpam-5259	306	5	analysis	analysis	NOUN
ejpam-5259	306	6	,	,	PUNCT
ejpam-5259	306	7	15(1	15(1	NUM
ejpam-5259	306	8	)	)	PUNCT
ejpam-5259	306	9	,	,	PUNCT
ejpam-5259	306	10	2023	2023	NUM
ejpam-5259	306	11	.	.	PUNCT
ejpam-5259	307	1	[	[	X
ejpam-5259	307	2	6	6	NUM
ejpam-5259	307	3	]	]	PUNCT
ejpam-5259	307	4	waggas	waggas	NOUN
ejpam-5259	307	5	galib	galib	NOUN
ejpam-5259	307	6	atshan	atshan	PROPN
ejpam-5259	307	7	and	and	CCONJ
ejpam-5259	307	8	ahmed	ahmed	PROPN
ejpam-5259	307	9	sallal	sallal	PROPN
ejpam-5259	307	10	joudah	joudah	PROPN
ejpam-5259	307	11	.	.	PUNCT
ejpam-5259	308	1	subclass	subclass	NOUN
ejpam-5259	308	2	of	of	ADP
ejpam-5259	308	3	meromorphic	meromorphic	ADJ
ejpam-5259	308	4	univalent	univalent	ADJ
ejpam-5259	308	5	functions	function	NOUN
ejpam-5259	308	6	defined	define	VERB
ejpam-5259	308	7	by	by	ADP
ejpam-5259	308	8	hadamard	hadamard	ADJ
ejpam-5259	308	9	product	product	NOUN
ejpam-5259	308	10	with	with	ADP
ejpam-5259	308	11	multiplier	multipli	ADJ
ejpam-5259	308	12	transformation	transformation	NOUN
ejpam-5259	308	13	.	.	PUNCT
ejpam-5259	309	1	in	in	ADP
ejpam-5259	309	2	international	international	PROPN
ejpam-5259	309	3	mathematical	mathematical	ADJ
ejpam-5259	309	4	forum	forum	PROPN
ejpam-5259	309	5	,	,	PUNCT
ejpam-5259	309	6	volume	volume	NOUN
ejpam-5259	309	7	6	6	NUM
ejpam-5259	309	8	,	,	PUNCT
ejpam-5259	309	9	pages	page	NOUN
ejpam-5259	309	10	2279–2292	2279–2292	NUM
ejpam-5259	309	11	,	,	PUNCT
ejpam-5259	309	12	2011	2011	NUM
ejpam-5259	309	13	.	.	PUNCT
ejpam-5259	310	1	[	[	X
ejpam-5259	310	2	7	7	X
ejpam-5259	310	3	]	]	X
ejpam-5259	310	4	adel	adel	PROPN
ejpam-5259	310	5	a	a	DET
ejpam-5259	310	6	attiya	attiya	PROPN
ejpam-5259	310	7	.	.	PUNCT
ejpam-5259	311	1	some	some	DET
ejpam-5259	311	2	applications	application	NOUN
ejpam-5259	311	3	of	of	ADP
ejpam-5259	311	4	mittag	mittag	ADJ
ejpam-5259	311	5	-	-	PUNCT
ejpam-5259	311	6	leffler	leffler	NOUN
ejpam-5259	311	7	function	function	NOUN
ejpam-5259	311	8	in	in	ADP
ejpam-5259	311	9	the	the	DET
ejpam-5259	311	10	unit	unit	NOUN
ejpam-5259	311	11	disk	disk	NOUN
ejpam-5259	311	12	.	.	PUNCT
ejpam-5259	312	1	filomat	filomat	PROPN
ejpam-5259	312	2	,	,	PUNCT
ejpam-5259	312	3	30(7):2075–2081	30(7):2075–2081	NUM
ejpam-5259	312	4	,	,	PUNCT
ejpam-5259	312	5	2016	2016	NUM
ejpam-5259	312	6	.	.	PUNCT
ejpam-5259	313	1	references	reference	NOUN
ejpam-5259	313	2	1906	1906	NUM
ejpam-5259	313	3	[	[	X
ejpam-5259	313	4	8	8	NUM
ejpam-5259	313	5	]	]	X
ejpam-5259	313	6	d	d	NOUN
ejpam-5259	313	7	bansal	bansal	NOUN
ejpam-5259	313	8	and	and	CCONJ
ejpam-5259	313	9	jk	jk	PROPN
ejpam-5259	313	10	prajapat	prajapat	PROPN
ejpam-5259	313	11	.	.	PUNCT
ejpam-5259	314	1	certain	certain	ADJ
ejpam-5259	314	2	geometric	geometric	ADJ
ejpam-5259	314	3	properties	property	NOUN
ejpam-5259	314	4	of	of	ADP
ejpam-5259	314	5	the	the	DET
ejpam-5259	314	6	mittag	mittag	ADJ
ejpam-5259	314	7	-	-	PUNCT
ejpam-5259	314	8	leffler	leffler	NOUN
ejpam-5259	314	9	functions	function	NOUN
ejpam-5259	314	10	.	.	PUNCT
ejpam-5259	315	1	complex	complex	ADJ
ejpam-5259	315	2	variables	variable	NOUN
ejpam-5259	315	3	and	and	CCONJ
ejpam-5259	315	4	elliptic	elliptic	ADJ
ejpam-5259	315	5	equations	equation	NOUN
ejpam-5259	315	6	,	,	PUNCT
ejpam-5259	315	7	61(3):338–350	61(3):338–350	NUM
ejpam-5259	315	8	,	,	PUNCT
ejpam-5259	315	9	2016	2016	NUM
ejpam-5259	315	10	.	.	PUNCT
ejpam-5259	316	1	[	[	X
ejpam-5259	316	2	9	9	X
ejpam-5259	316	3	]	]	X
ejpam-5259	316	4	khalid	khalid	PROPN
ejpam-5259	316	5	challab	challab	PROPN
ejpam-5259	316	6	and	and	CCONJ
ejpam-5259	316	7	maslina	maslina	PROPN
ejpam-5259	316	8	darus	darus	NOUN
ejpam-5259	316	9	.	.	PUNCT
ejpam-5259	317	1	on	on	ADP
ejpam-5259	317	2	certain	certain	ADJ
ejpam-5259	317	3	class	class	NOUN
ejpam-5259	317	4	of	of	ADP
ejpam-5259	317	5	meromorphic	meromorphic	ADJ
ejpam-5259	317	6	harmonic	harmonic	ADJ
ejpam-5259	317	7	concave	concave	NOUN
ejpam-5259	317	8	functions	function	NOUN
ejpam-5259	317	9	defined	define	VERB
ejpam-5259	317	10	by	by	ADP
ejpam-5259	317	11	salagean	salagean	ADJ
ejpam-5259	317	12	operator	operator	NOUN
ejpam-5259	317	13	.	.	PUNCT
ejpam-5259	317	14	journal	journal	PROPN
ejpam-5259	317	15	of	of	ADP
ejpam-5259	317	16	quality	quality	NOUN
ejpam-5259	317	17	measurement	measurement	NOUN
ejpam-5259	317	18	and	and	CCONJ
ejpam-5259	317	19	analysis	analysis	NOUN
ejpam-5259	317	20	(	(	PUNCT
ejpam-5259	317	21	jqma	jqma	ADV
ejpam-5259	317	22	)	)	PUNCT
ejpam-5259	317	23	,	,	PUNCT
ejpam-5259	317	24	11(1):49–60	11(1):49–60	NUM
ejpam-5259	317	25	,	,	PUNCT
ejpam-5259	317	26	2015	2015	NUM
ejpam-5259	317	27	.	.	PUNCT
ejpam-5259	318	1	[	[	X
ejpam-5259	318	2	10	10	NUM
ejpam-5259	318	3	]	]	X
ejpam-5259	318	4	khalid	khalid	PROPN
ejpam-5259	318	5	challab	challab	PROPN
ejpam-5259	318	6	and	and	CCONJ
ejpam-5259	318	7	maslina	maslina	PROPN
ejpam-5259	318	8	darus	darus	NOUN
ejpam-5259	318	9	.	.	PUNCT
ejpam-5259	319	1	on	on	ADP
ejpam-5259	319	2	certain	certain	ADJ
ejpam-5259	319	3	classes	class	NOUN
ejpam-5259	319	4	of	of	ADP
ejpam-5259	319	5	meromorphic	meromorphic	ADJ
ejpam-5259	319	6	harmonic	harmonic	ADJ
ejpam-5259	319	7	concave	concave	NOUN
ejpam-5259	319	8	functions	function	NOUN
ejpam-5259	319	9	defined	define	VERB
ejpam-5259	319	10	by	by	ADP
ejpam-5259	319	11	al	al	PROPN
ejpam-5259	319	12	-	-	PUNCT
ejpam-5259	319	13	oboudi	oboudi	ADJ
ejpam-5259	319	14	operator	operator	NOUN
ejpam-5259	319	15	.	.	PUNCT
ejpam-5259	320	1	journal	journal	PROPN
ejpam-5259	320	2	of	of	ADP
ejpam-5259	320	3	quality	quality	NOUN
ejpam-5259	320	4	measurement	measurement	NOUN
ejpam-5259	320	5	and	and	CCONJ
ejpam-5259	320	6	analysis	analysis	NOUN
ejpam-5259	320	7	(	(	PUNCT
ejpam-5259	320	8	jqma	jqma	ADV
ejpam-5259	320	9	)	)	PUNCT
ejpam-5259	320	10	,	,	PUNCT
ejpam-5259	320	11	12(1	12(1	NUM
ejpam-5259	320	12	-	-	PUNCT
ejpam-5259	320	13	2):53–65	2):53–65	NUM
ejpam-5259	320	14	,	,	PUNCT
ejpam-5259	320	15	2016	2016	NUM
ejpam-5259	320	16	.	.	PUNCT
ejpam-5259	321	1	[	[	X
ejpam-5259	321	2	11	11	NUM
ejpam-5259	321	3	]	]	PUNCT
ejpam-5259	321	4	nak	nak	PROPN
ejpam-5259	321	5	eun	eun	PROPN
ejpam-5259	321	6	cho	cho	PROPN
ejpam-5259	321	7	and	and	CCONJ
ejpam-5259	321	8	tae	tae	PROPN
ejpam-5259	321	9	hwa	hwa	PROPN
ejpam-5259	321	10	kim	kim	PROPN
ejpam-5259	321	11	.	.	PUNCT
ejpam-5259	322	1	multiplier	multipli	ADJ
ejpam-5259	322	2	transformations	transformation	NOUN
ejpam-5259	322	3	and	and	CCONJ
ejpam-5259	322	4	strongly	strongly	ADV
ejpam-5259	322	5	close	close	ADJ
ejpam-5259	322	6	-	-	PUNCT
ejpam-5259	322	7	toconvex	toconvex	NOUN
ejpam-5259	322	8	functions	function	NOUN
ejpam-5259	322	9	.	.	PUNCT
ejpam-5259	323	1	bulletin	bulletin	NOUN
ejpam-5259	323	2	of	of	ADP
ejpam-5259	323	3	the	the	DET
ejpam-5259	323	4	korean	korean	PROPN
ejpam-5259	323	5	mathematical	mathematical	ADJ
ejpam-5259	323	6	society	society	NOUN
ejpam-5259	323	7	,	,	PUNCT
ejpam-5259	323	8	40(3):399–410	40(3):399–410	PROPN
ejpam-5259	323	9	,	,	PUNCT
ejpam-5259	323	10	2003	2003	NUM
ejpam-5259	323	11	.	.	PUNCT
ejpam-5259	324	1	[	[	X
ejpam-5259	324	2	12	12	NUM
ejpam-5259	324	3	]	]	PUNCT
ejpam-5259	324	4	ne	ne	PROPN
ejpam-5259	324	5	cho	cho	PROPN
ejpam-5259	324	6	and	and	CCONJ
ejpam-5259	324	7	hm	hm	INTJ
ejpam-5259	324	8	srivastava	srivastava	PROPN
ejpam-5259	324	9	.	.	PUNCT
ejpam-5259	325	1	argument	argument	NOUN
ejpam-5259	325	2	estimates	estimate	NOUN
ejpam-5259	325	3	of	of	ADP
ejpam-5259	325	4	certain	certain	ADJ
ejpam-5259	325	5	analytic	analytic	ADJ
ejpam-5259	325	6	functions	function	NOUN
ejpam-5259	325	7	defined	define	VERB
ejpam-5259	325	8	by	by	ADP
ejpam-5259	325	9	a	a	DET
ejpam-5259	325	10	class	class	NOUN
ejpam-5259	325	11	of	of	ADP
ejpam-5259	325	12	multiplier	multipli	ADJ
ejpam-5259	325	13	transformations	transformation	NOUN
ejpam-5259	325	14	.	.	PUNCT
ejpam-5259	326	1	mathematical	mathematical	ADJ
ejpam-5259	326	2	and	and	CCONJ
ejpam-5259	326	3	computer	computer	NOUN
ejpam-5259	326	4	modelling	modelling	NOUN
ejpam-5259	326	5	,	,	PUNCT
ejpam-5259	326	6	37(12):39–49	37(12):39–49	NUM
ejpam-5259	326	7	,	,	PUNCT
ejpam-5259	326	8	2003	2003	NUM
ejpam-5259	326	9	.	.	PUNCT
ejpam-5259	327	1	[	[	X
ejpam-5259	327	2	13	13	NUM
ejpam-5259	327	3	]	]	X
ejpam-5259	327	4	j	j	PROPN
ejpam-5259	327	5	clunie	clunie	PROPN
ejpam-5259	327	6	.	.	PUNCT
ejpam-5259	328	1	on	on	ADP
ejpam-5259	328	2	meromorphic	meromorphic	ADJ
ejpam-5259	328	3	schlicht	schlicht	NOUN
ejpam-5259	328	4	functions	function	NOUN
ejpam-5259	328	5	.	.	PUNCT
ejpam-5259	329	1	journal	journal	NOUN
ejpam-5259	329	2	of	of	ADP
ejpam-5259	329	3	the	the	DET
ejpam-5259	329	4	london	london	PROPN
ejpam-5259	329	5	mathematical	mathematical	ADJ
ejpam-5259	329	6	society	society	NOUN
ejpam-5259	329	7	,	,	PUNCT
ejpam-5259	329	8	1(2):215–216	1(2):215–216	NUM
ejpam-5259	329	9	,	,	PUNCT
ejpam-5259	329	10	1959	1959	NUM
ejpam-5259	329	11	.	.	PUNCT
ejpam-5259	330	1	[	[	X
ejpam-5259	330	2	14	14	NUM
ejpam-5259	330	3	]	]	X
ejpam-5259	330	4	suhila	suhila	NOUN
ejpam-5259	330	5	elhaddad	elhaddad	NOUN
ejpam-5259	330	6	and	and	CCONJ
ejpam-5259	330	7	maslina	maslina	PROPN
ejpam-5259	330	8	darus	darus	NOUN
ejpam-5259	330	9	.	.	PUNCT
ejpam-5259	331	1	on	on	ADP
ejpam-5259	331	2	meromorphic	meromorphic	ADJ
ejpam-5259	331	3	functions	function	NOUN
ejpam-5259	331	4	defined	define	VERB
ejpam-5259	331	5	by	by	ADP
ejpam-5259	331	6	a	a	DET
ejpam-5259	331	7	new	new	ADJ
ejpam-5259	331	8	operator	operator	NOUN
ejpam-5259	331	9	containing	contain	VERB
ejpam-5259	331	10	the	the	DET
ejpam-5259	331	11	mittag	mittag	ADJ
ejpam-5259	331	12	–	–	PUNCT
ejpam-5259	331	13	leffler	leffler	NOUN
ejpam-5259	331	14	function	function	NOUN
ejpam-5259	331	15	.	.	PUNCT
ejpam-5259	332	1	symmetry	symmetry	NOUN
ejpam-5259	332	2	,	,	PUNCT
ejpam-5259	332	3	11(2):210	11(2):210	PROPN
ejpam-5259	332	4	,	,	PUNCT
ejpam-5259	332	5	2019	2019	NUM
ejpam-5259	332	6	.	.	PUNCT
ejpam-5259	333	1	[	[	X
ejpam-5259	333	2	15	15	NUM
ejpam-5259	333	3	]	]	X
ejpam-5259	333	4	f	f	PROPN
ejpam-5259	333	5	ghanim	ghanim	NOUN
ejpam-5259	333	6	and	and	CCONJ
ejpam-5259	333	7	hiba	hiba	PROPN
ejpam-5259	333	8	f	f	PROPN
ejpam-5259	333	9	al	al	PROPN
ejpam-5259	333	10	-	-	PUNCT
ejpam-5259	333	11	janaby	janaby	PROPN
ejpam-5259	333	12	.	.	PUNCT
ejpam-5259	334	1	inclusion	inclusion	NOUN
ejpam-5259	334	2	and	and	CCONJ
ejpam-5259	334	3	convolution	convolution	NOUN
ejpam-5259	334	4	features	feature	NOUN
ejpam-5259	334	5	of	of	ADP
ejpam-5259	334	6	univalent	univalent	ADJ
ejpam-5259	334	7	meromorphic	meromorphic	ADJ
ejpam-5259	334	8	functions	function	NOUN
ejpam-5259	334	9	correlating	correlate	VERB
ejpam-5259	334	10	with	with	ADP
ejpam-5259	334	11	mittag	mittag	ADJ
ejpam-5259	334	12	-	-	PUNCT
ejpam-5259	334	13	leffler	leffler	NOUN
ejpam-5259	334	14	function	function	NOUN
ejpam-5259	334	15	.	.	PUNCT
ejpam-5259	335	1	filomat	filomat	NOUN
ejpam-5259	335	2	,	,	PUNCT
ejpam-5259	335	3	34(7):2141	34(7):2141	NUM
ejpam-5259	335	4	–	–	PUNCT
ejpam-5259	335	5	2150	2150	NUM
ejpam-5259	335	6	,	,	PUNCT
ejpam-5259	335	7	2020	2020	NUM
ejpam-5259	335	8	.	.	PUNCT
ejpam-5259	336	1	[	[	X
ejpam-5259	336	2	16	16	NUM
ejpam-5259	336	3	]	]	X
ejpam-5259	336	4	indranil	indranil	PROPN
ejpam-5259	336	5	sen	sen	PROPN
ejpam-5259	336	6	gupta	gupta	PROPN
ejpam-5259	336	7	and	and	CCONJ
ejpam-5259	336	8	lokenath	lokenath	NOUN
ejpam-5259	336	9	debnath	debnath	NOUN
ejpam-5259	336	10	.	.	PUNCT
ejpam-5259	337	1	some	some	DET
ejpam-5259	337	2	properties	property	NOUN
ejpam-5259	337	3	of	of	ADP
ejpam-5259	337	4	the	the	DET
ejpam-5259	337	5	mittag	mittag	ADJ
ejpam-5259	337	6	-	-	PUNCT
ejpam-5259	337	7	leffler	leffler	NOUN
ejpam-5259	337	8	functions	function	NOUN
ejpam-5259	337	9	.	.	PUNCT
ejpam-5259	338	1	integral	integral	ADJ
ejpam-5259	338	2	transforms	transform	NOUN
ejpam-5259	338	3	and	and	CCONJ
ejpam-5259	338	4	special	special	ADJ
ejpam-5259	338	5	functions	function	NOUN
ejpam-5259	338	6	,	,	PUNCT
ejpam-5259	338	7	18(5):329–336	18(5):329–336	PROPN
ejpam-5259	338	8	,	,	PUNCT
ejpam-5259	338	9	2007	2007	NUM
ejpam-5259	338	10	.	.	PUNCT
ejpam-5259	339	1	[	[	X
ejpam-5259	339	2	17	17	NUM
ejpam-5259	339	3	]	]	PUNCT
ejpam-5259	339	4	jay	jay	PROPN
ejpam-5259	339	5	jahangiri	jahangiri	PROPN
ejpam-5259	339	6	et	et	PROPN
ejpam-5259	339	7	al	al	PROPN
ejpam-5259	339	8	.	.	PROPN
ejpam-5259	339	9	harmonic	harmonic	VERB
ejpam-5259	339	10	meromorphic	meromorphic	ADJ
ejpam-5259	339	11	starlike	starlike	NOUN
ejpam-5259	339	12	functions	function	NOUN
ejpam-5259	339	13	.	.	PUNCT
ejpam-5259	340	1	bulletin	bulletin	NOUN
ejpam-5259	340	2	of	of	ADP
ejpam-5259	340	3	the	the	DET
ejpam-5259	340	4	korean	korean	PROPN
ejpam-5259	340	5	mathematical	mathematical	ADJ
ejpam-5259	340	6	society	society	NOUN
ejpam-5259	340	7	,	,	PUNCT
ejpam-5259	340	8	37(2):291–301	37(2):291–301	NUM
ejpam-5259	340	9	,	,	PUNCT
ejpam-5259	340	10	2000	2000	NUM
ejpam-5259	340	11	.	.	PUNCT
ejpam-5259	341	1	[	[	X
ejpam-5259	341	2	18	18	NUM
ejpam-5259	341	3	]	]	PUNCT
ejpam-5259	341	4	jay	jay	PROPN
ejpam-5259	341	5	m	m	VERB
ejpam-5259	341	6	jahangiri	jahangiri	ADV
ejpam-5259	341	7	,	,	PUNCT
ejpam-5259	341	8	g	g	PROPN
ejpam-5259	341	9	murugusundaramoorthy	murugusundaramoorthy	ADJ
ejpam-5259	341	10	,	,	PUNCT
ejpam-5259	341	11	and	and	CCONJ
ejpam-5259	341	12	k	k	PROPN
ejpam-5259	341	13	vijaya	vijaya	PROPN
ejpam-5259	341	14	.	.	PUNCT
ejpam-5259	342	1	salagean	salagean	ADJ
ejpam-5259	342	2	-	-	PUNCT
ejpam-5259	342	3	type	type	NOUN
ejpam-5259	342	4	harmonic	harmonic	ADJ
ejpam-5259	342	5	univalent	univalent	ADJ
ejpam-5259	342	6	functions	function	NOUN
ejpam-5259	342	7	.	.	PUNCT
ejpam-5259	343	1	southwest	southwest	PROPN
ejpam-5259	343	2	journal	journal	PROPN
ejpam-5259	343	3	of	of	ADP
ejpam-5259	343	4	pure	pure	ADJ
ejpam-5259	343	5	and	and	CCONJ
ejpam-5259	343	6	applied	applied	ADJ
ejpam-5259	343	7	mathematics	mathematic	NOUN
ejpam-5259	344	1	[	[	X
ejpam-5259	344	2	electronic	electronic	ADJ
ejpam-5259	344	3	only	only	ADV
ejpam-5259	344	4	]	]	PUNCT
ejpam-5259	344	5	,	,	PUNCT
ejpam-5259	344	6	2002:77–82	2002:77–82	NOUN
ejpam-5259	344	7	,	,	PUNCT
ejpam-5259	344	8	2002	2002	NUM
ejpam-5259	344	9	.	.	PUNCT
ejpam-5259	345	1	[	[	X
ejpam-5259	345	2	19	19	NUM
ejpam-5259	345	3	]	]	PUNCT
ejpam-5259	345	4	jay	jay	PROPN
ejpam-5259	345	5	m.	m.	NOUN
ejpam-5259	345	6	jahangiri	jahangiri	PROPN
ejpam-5259	345	7	and	and	CCONJ
ejpam-5259	345	8	herb	herb	PROPN
ejpam-5259	345	9	silverman	silverman	PROPN
ejpam-5259	345	10	.	.	PUNCT
ejpam-5259	346	1	meromorphic	meromorphic	ADJ
ejpam-5259	346	2	univalent	univalent	ADJ
ejpam-5259	346	3	harmonic	harmonic	ADJ
ejpam-5259	346	4	functions	function	NOUN
ejpam-5259	346	5	with	with	ADP
ejpam-5259	346	6	negative	negative	ADJ
ejpam-5259	346	7	coefficients	coefficient	NOUN
ejpam-5259	346	8	.	.	PUNCT
ejpam-5259	347	1	bulletin	bulletin	NOUN
ejpam-5259	347	2	of	of	ADP
ejpam-5259	347	3	the	the	DET
ejpam-5259	347	4	korean	korean	PROPN
ejpam-5259	347	5	mathematical	mathematical	ADJ
ejpam-5259	347	6	society	society	NOUN
ejpam-5259	347	7	,	,	PUNCT
ejpam-5259	347	8	36(4):763	36(4):763	NUM
ejpam-5259	347	9	–	–	PUNCT
ejpam-5259	347	10	770	770	NUM
ejpam-5259	347	11	,	,	PUNCT
ejpam-5259	347	12	1999	1999	NUM
ejpam-5259	347	13	.	.	PUNCT
ejpam-5259	348	1	[	[	X
ejpam-5259	348	2	20	20	NUM
ejpam-5259	348	3	]	]	X
ejpam-5259	348	4	gustave	gustave	ADJ
ejpam-5259	348	5	mittag	mittag	ADJ
ejpam-5259	348	6	-	-	PUNCT
ejpam-5259	348	7	leffler	leffler	NOUN
ejpam-5259	348	8	.	.	PUNCT
ejpam-5259	349	1	sur	sur	PROPN
ejpam-5259	349	2	la	la	PROPN
ejpam-5259	349	3	représentation	représentation	PROPN
ejpam-5259	349	4	analytique	analytique	ADJ
ejpam-5259	349	5	d’une	d’une	X
ejpam-5259	349	6	branche	branche	PROPN
ejpam-5259	349	7	uniforme	uniforme	PROPN
ejpam-5259	349	8	d’une	d’une	CCONJ
ejpam-5259	349	9	fonction	fonction	NOUN
ejpam-5259	349	10	monogène	monogène	ADJ
ejpam-5259	349	11	:	:	PUNCT
ejpam-5259	349	12	cinquième	cinquième	PROPN
ejpam-5259	349	13	note	note	PROPN
ejpam-5259	349	14	.	.	PUNCT
ejpam-5259	350	1	acta	acta	PROPN
ejpam-5259	350	2	mathematica	mathematica	PROPN
ejpam-5259	350	3	,	,	PUNCT
ejpam-5259	350	4	29(1):101–181	29(1):101–181	PROPN
ejpam-5259	350	5	,	,	PUNCT
ejpam-5259	350	6	1905	1905	NUM
ejpam-5259	350	7	.	.	PUNCT
ejpam-5259	351	1	[	[	X
ejpam-5259	351	2	21	21	NUM
ejpam-5259	351	3	]	]	X
ejpam-5259	351	4	ms	ms	PROPN
ejpam-5259	351	5	rehman	rehman	PROPN
ejpam-5259	351	6	,	,	PUNCT
ejpam-5259	351	7	qazi	qazi	PROPN
ejpam-5259	351	8	zahoor	zahoor	PROPN
ejpam-5259	351	9	ahmad	ahmad	PROPN
ejpam-5259	351	10	,	,	PUNCT
ejpam-5259	351	11	hari	hari	PROPN
ejpam-5259	351	12	m	m	PROPN
ejpam-5259	351	13	srivastava	srivastava	PROPN
ejpam-5259	351	14	,	,	PUNCT
ejpam-5259	351	15	bilal	bilal	PROPN
ejpam-5259	351	16	khan	khan	PROPN
ejpam-5259	351	17	,	,	PUNCT
ejpam-5259	351	18	and	and	CCONJ
ejpam-5259	351	19	nazar	nazar	PROPN
ejpam-5259	351	20	khan	khan	PROPN
ejpam-5259	351	21	.	.	PUNCT
ejpam-5259	352	1	partial	partial	ADJ
ejpam-5259	352	2	sums	sum	NOUN
ejpam-5259	352	3	of	of	ADP
ejpam-5259	352	4	generalized	generalized	ADJ
ejpam-5259	352	5	q	q	ADJ
ejpam-5259	352	6	-	-	ADJ
ejpam-5259	352	7	mittag	mittag	ADJ
ejpam-5259	352	8	-	-	PUNCT
ejpam-5259	352	9	leffler	leffler	NOUN
ejpam-5259	352	10	functions	function	NOUN
ejpam-5259	352	11	.	.	PUNCT
ejpam-5259	353	1	aims	aim	VERB
ejpam-5259	353	2	math	math	NOUN
ejpam-5259	353	3	,	,	PUNCT
ejpam-5259	353	4	5(1):408–420	5(1):408–420	NUM
ejpam-5259	353	5	,	,	PUNCT
ejpam-5259	353	6	2019	2019	NUM
ejpam-5259	353	7	.	.	PUNCT
ejpam-5259	354	1	references	reference	NOUN
ejpam-5259	354	2	1907	1907	NUM
ejpam-5259	355	1	[	[	X
ejpam-5259	355	2	22	22	NUM
ejpam-5259	355	3	]	]	X
ejpam-5259	355	4	hari	hari	PROPN
ejpam-5259	355	5	m	m	PROPN
ejpam-5259	355	6	srivastava	srivastava	PROPN
ejpam-5259	355	7	and	and	CCONJ
ejpam-5259	355	8	živorad	živorad	PROPN
ejpam-5259	355	9	tomovski	tomovski	NOUN
ejpam-5259	355	10	.	.	PUNCT
ejpam-5259	356	1	fractional	fractional	ADJ
ejpam-5259	356	2	calculus	calculus	NOUN
ejpam-5259	356	3	with	with	ADP
ejpam-5259	356	4	an	an	DET
ejpam-5259	356	5	integral	integral	ADJ
ejpam-5259	356	6	operator	operator	NOUN
ejpam-5259	356	7	containing	contain	VERB
ejpam-5259	356	8	a	a	DET
ejpam-5259	356	9	generalized	generalize	VERB
ejpam-5259	356	10	mittag	mittag	ADJ
ejpam-5259	356	11	–	–	PUNCT
ejpam-5259	356	12	leffler	leffler	NOUN
ejpam-5259	356	13	function	function	NOUN
ejpam-5259	356	14	in	in	ADP
ejpam-5259	356	15	the	the	DET
ejpam-5259	356	16	kernel	kernel	NOUN
ejpam-5259	356	17	.	.	PUNCT
ejpam-5259	357	1	applied	apply	VERB
ejpam-5259	357	2	mathematics	mathematic	NOUN
ejpam-5259	357	3	and	and	CCONJ
ejpam-5259	357	4	computation	computation	NOUN
ejpam-5259	357	5	,	,	PUNCT
ejpam-5259	357	6	211(1):198–210	211(1):198–210	NUM
ejpam-5259	357	7	,	,	PUNCT
ejpam-5259	357	8	2009	2009	NUM
ejpam-5259	357	9	.	.	PUNCT
ejpam-5259	358	1	[	[	X
ejpam-5259	358	2	23	23	NUM
ejpam-5259	358	3	]	]	PUNCT
ejpam-5259	358	4	adders	adder	NOUN
ejpam-5259	358	5	wiman	wiman	PROPN
ejpam-5259	358	6	.	.	PUNCT
ejpam-5259	359	1	über	über	PROPN
ejpam-5259	359	2	den	den	NOUN
ejpam-5259	359	3	fundamentalsatz	fundamentalsatz	NOUN
ejpam-5259	359	4	in	in	ADP
ejpam-5259	359	5	der	der	PROPN
ejpam-5259	359	6	teorie	teorie	PROPN
ejpam-5259	359	7	der	der	NOUN
ejpam-5259	359	8	funktionen	funktionen	PROPN
ejpam-5259	359	9	ea(x	ea(x	NOUN
ejpam-5259	359	10	)	)	PUNCT
ejpam-5259	359	11	.	.	PUNCT
ejpam-5259	360	1	acta	acta	PROPN
ejpam-5259	360	2	mathematica	mathematica	PROPN
ejpam-5259	360	3	,	,	PUNCT
ejpam-5259	360	4	29:191–201	29:191–201	NUM
ejpam-5259	360	5	,	,	PUNCT
ejpam-5259	360	6	1905	1905	NUM
ejpam-5259	360	7	.	.	PUNCT