id	sid	tid	token	lemma	pos
ma-77	1	1	2022	2022	NUM
ma-77	1	2	ada	ada	PROPN
ma-77	1	3	academica	academica	PROPN
ma-77	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-77	1	5	.	.	PUNCT
ma-77	2	1	j.	j.	PROPN
ma-77	2	2	math	math	PROPN
ma-77	2	3	.	.	PUNCT
ma-77	3	1	anal	anal	ADJ
ma-77	3	2	.	.	PUNCT
ma-77	3	3	2	2	NUM
ma-77	3	4	(	(	PUNCT
ma-77	3	5	2022	2022	NUM
ma-77	3	6	)	)	PUNCT
ma-77	3	7	12doi	12doi	NUM
ma-77	3	8	:	:	PUNCT
ma-77	3	9	10.28924	10.28924	NUM
ma-77	3	10	/	/	SYM
ma-77	3	11	ada	ada	PROPN
ma-77	3	12	/	/	SYM
ma-77	3	13	ma.2.12	ma.2.12	VERB
ma-77	3	14	some	some	DET
ma-77	3	15	investigations	investigation	NOUN
ma-77	3	16	on	on	ADP
ma-77	3	17	a	a	DET
ma-77	3	18	class	class	NOUN
ma-77	3	19	of	of	ADP
ma-77	3	20	analytic	analytic	ADJ
ma-77	3	21	and	and	CCONJ
ma-77	3	22	univalent	univalent	ADJ
ma-77	3	23	functions	function	NOUN
ma-77	3	24	involving	involve	VERB
ma-77	3	25	q	q	ADJ
ma-77	3	26	-	-	PUNCT
ma-77	3	27	differentiation	differentiation	NOUN
ma-77	3	28	ayotunde	ayotunde	NOUN
ma-77	3	29	olajide	olajide	PROPN
ma-77	3	30	lasode∗	lasode∗	NOUN
ma-77	3	31	,	,	PUNCT
ma-77	3	32	timothy	timothy	PROPN
ma-77	3	33	oloyede	oloyede	PROPN
ma-77	3	34	opoola	opoola	PROPN
ma-77	3	35	department	department	PROPN
ma-77	3	36	of	of	ADP
ma-77	3	37	mathematics	mathematic	NOUN
ma-77	3	38	,	,	PUNCT
ma-77	3	39	faculty	faculty	NOUN
ma-77	3	40	of	of	ADP
ma-77	3	41	physical	physical	ADJ
ma-77	3	42	sciences	science	NOUN
ma-77	3	43	,	,	PUNCT
ma-77	3	44	university	university	NOUN
ma-77	3	45	of	of	ADP
ma-77	3	46	ilorin	ilorin	PROPN
ma-77	3	47	,	,	PUNCT
ma-77	3	48	ilorin	ilorin	PROPN
ma-77	3	49	,	,	PUNCT
ma-77	3	50	nigeria	nigeria	PROPN
ma-77	3	51	lasode_ayo@yahoo.com	lasode_ayo@yahoo.com	PROPN
ma-77	3	52	,	,	PUNCT
ma-77	3	53	opoola.to@unilorin.edu.ng	opoola.to@unilorin.edu.ng	ADV
ma-77	3	54	∗correspondence	∗correspondence	NOUN
ma-77	3	55	:	:	PUNCT
ma-77	4	1	lasode_ayo@yahoo.com	lasode_ayo@yahoo.com	X
ma-77	5	1	abstract	abstract	ADJ
ma-77	5	2	.	.	PUNCT
ma-77	6	1	we	we	PRON
ma-77	6	2	use	use	VERB
ma-77	6	3	the	the	DET
ma-77	6	4	concept	concept	NOUN
ma-77	6	5	of	of	ADP
ma-77	6	6	q	q	NOUN
ma-77	6	7	-	-	PUNCT
ma-77	6	8	differentiation	differentiation	NOUN
ma-77	6	9	to	to	PART
ma-77	6	10	define	define	VERB
ma-77	6	11	a	a	DET
ma-77	6	12	class	class	NOUN
ma-77	6	13	eq(β	eq(β	X
ma-77	6	14	,	,	PUNCT
ma-77	6	15	δ	δ	PROPN
ma-77	6	16	)	)	PUNCT
ma-77	6	17	of	of	ADP
ma-77	6	18	analytic	analytic	ADJ
ma-77	6	19	and	and	CCONJ
ma-77	6	20	univalentfunctions	univalentfunction	NOUN
ma-77	6	21	.	.	PUNCT
ma-77	7	1	the	the	DET
ma-77	7	2	investigations	investigation	NOUN
ma-77	7	3	thereafter	thereafter	ADV
ma-77	7	4	includes	include	VERB
ma-77	7	5	coefficient	coefficient	NOUN
ma-77	7	6	estimates	estimate	NOUN
ma-77	7	7	,	,	PUNCT
ma-77	7	8	inclusion	inclusion	NOUN
ma-77	7	9	property	property	NOUN
ma-77	7	10	and	and	CCONJ
ma-77	7	11	someconditions	somecondition	NOUN
ma-77	7	12	for	for	ADP
ma-77	7	13	membership	membership	NOUN
ma-77	7	14	of	of	ADP
ma-77	7	15	some	some	DET
ma-77	7	16	analytic	analytic	ADJ
ma-77	7	17	functions	function	NOUN
ma-77	7	18	to	to	PART
ma-77	7	19	be	be	AUX
ma-77	7	20	in	in	ADP
ma-77	7	21	the	the	DET
ma-77	7	22	class	class	NOUN
ma-77	7	23	eq(β	eq(β	X
ma-77	7	24	,	,	PUNCT
ma-77	7	25	δ	δ	PROPN
ma-77	7	26	)	)	PUNCT
ma-77	7	27	.	.	PUNCT
ma-77	8	1	our	our	PRON
ma-77	8	2	results	result	NOUN
ma-77	8	3	generalizesome	generalizesome	VERB
ma-77	8	4	known	known	ADJ
ma-77	8	5	and	and	CCONJ
ma-77	8	6	new	new	ADJ
ma-77	8	7	ones	one	NOUN
ma-77	8	8	.	.	PUNCT
ma-77	9	1	1	1	X
ma-77	9	2	.	.	X
ma-77	9	3	introduction	introduction	NOUN
ma-77	9	4	and	and	CCONJ
ma-77	9	5	definitions	definition	NOUN
ma-77	9	6	we	we	PRON
ma-77	9	7	let	let	VERB
ma-77	9	8	ud	ud	INTJ
ma-77	9	9	=	=	PUNCT
ma-77	9	10	{	{	PUNCT
ma-77	9	11	z	z	NOUN
ma-77	9	12	:	:	PUNCT
ma-77	10	1	z	z	X
ma-77	10	2	∈	∈	PROPN
ma-77	11	1	c	c	X
ma-77	11	2	,	,	PUNCT
ma-77	11	3	|z	|z	PROPN
ma-77	12	1	|	|	ADV
ma-77	12	2	<	<	X
ma-77	12	3	1	1	NUM
ma-77	12	4	}	}	PUNCT
ma-77	12	5	represent	represent	VERB
ma-77	12	6	the	the	DET
ma-77	12	7	unit	unit	NOUN
ma-77	12	8	disk	disk	NOUN
ma-77	12	9	and	and	CCONJ
ma-77	12	10	a	a	DET
ma-77	12	11	represent	represent	NOUN
ma-77	12	12	the	the	DET
ma-77	12	13	class	class	NOUN
ma-77	12	14	ofnormalized	ofnormalize	VERB
ma-77	12	15	analytic	analytic	ADJ
ma-77	12	16	functions	function	NOUN
ma-77	12	17	of	of	ADP
ma-77	12	18	the	the	DET
ma-77	12	19	form	form	NOUN
ma-77	13	1	f	f	X
ma-77	13	2	(	(	PUNCT
ma-77	13	3	z	z	NOUN
ma-77	13	4	)	)	PUNCT
ma-77	13	5	=	=	SYM
ma-77	13	6	z	z	NOUN
ma-77	14	1	+	+	NOUN
ma-77	14	2	∞∑	∞∑	PROPN
ma-77	14	3	m=2	m=2	NUM
ma-77	14	4	amz	amz	PROPN
ma-77	14	5	m	m	PROPN
ma-77	14	6	,	,	PUNCT
ma-77	14	7	z	z	PROPN
ma-77	14	8	∈	∈	PROPN
ma-77	14	9	ud	ud	INTJ
ma-77	14	10	(	(	PUNCT
ma-77	14	11	1	1	NUM
ma-77	14	12	)	)	PUNCT
ma-77	15	1	where	where	SCONJ
ma-77	15	2	f	f	PROPN
ma-77	15	3	(	(	PUNCT
ma-77	15	4	0	0	NUM
ma-77	15	5	)	)	PUNCT
ma-77	15	6	=	=	SYM
ma-77	15	7	0	0	PUNCT
ma-77	15	8	=	=	SYM
ma-77	15	9	f	f	PROPN
ma-77	15	10	′(0	′(0	PROPN
ma-77	15	11	)	)	PUNCT
ma-77	16	1	−	−	PROPN
ma-77	16	2	1	1	X
ma-77	16	3	.	.	PUNCT
ma-77	17	1	also	also	ADV
ma-77	17	2	,	,	PUNCT
ma-77	17	3	let	let	VERB
ma-77	17	4	s	s	PRON
ma-77	17	5	represent	represent	VERB
ma-77	17	6	a	a	DET
ma-77	17	7	subset	subset	NOUN
ma-77	17	8	of	of	ADP
ma-77	17	9	a	a	DET
ma-77	17	10	containing	contain	VERB
ma-77	17	11	functions	function	NOUN
ma-77	17	12	univalentin	univalentin	NOUN
ma-77	17	13	ud	ud	PROPN
ma-77	17	14	.	.	PUNCT
ma-77	18	1	a	a	DET
ma-77	18	2	function	function	NOUN
ma-77	18	3	f	f	PROPN
ma-77	18	4	in	in	ADP
ma-77	18	5	s	s	PROPN
ma-77	18	6	is	be	AUX
ma-77	18	7	a	a	DET
ma-77	18	8	member	member	NOUN
ma-77	18	9	of	of	ADP
ma-77	18	10	class	class	PROPN
ma-77	18	11	bt	bt	PROPN
ma-77	18	12	(	(	PUNCT
ma-77	18	13	δ	δ	PROPN
ma-77	18	14	)	)	PUNCT
ma-77	18	15	of	of	ADP
ma-77	18	16	bounded	bounded	ADJ
ma-77	18	17	turning	turning	NOUN
ma-77	18	18	functions	function	NOUN
ma-77	18	19	of	of	ADP
ma-77	18	20	order	order	NOUN
ma-77	18	21	δ	δ	NOUN
ma-77	18	22	if	if	SCONJ
ma-77	18	23	itsatisfies	itsatisfie	NOUN
ma-77	18	24	the	the	DET
ma-77	18	25	geometric	geometric	ADJ
ma-77	18	26	condition	condition	NOUN
ma-77	18	27	ref	ref	NOUN
ma-77	18	28	′(z	′(z	NOUN
ma-77	18	29	)	)	PUNCT
ma-77	18	30	>	>	X
ma-77	19	1	δ	δ	X
ma-77	19	2	∈	∈	PROPN
ma-77	20	1	[	[	X
ma-77	20	2	0	0	NUM
ma-77	20	3	,	,	PUNCT
ma-77	20	4	1	1	NUM
ma-77	20	5	)	)	PUNCT
ma-77	21	1	,	,	PUNCT
ma-77	21	2	z	z	NOUN
ma-77	21	3	∈	∈	PROPN
ma-77	21	4	ud	ud	INTJ
ma-77	21	5	.	.	PUNCT
ma-77	22	1	let	let	VERB
ma-77	22	2	bt	bt	NOUN
ma-77	22	3	(	(	PUNCT
ma-77	22	4	0	0	NUM
ma-77	22	5	)	)	PUNCT
ma-77	22	6	=	=	VERB
ma-77	22	7	bt	bt	PROPN
ma-77	22	8	represent	represent	VERB
ma-77	22	9	the	the	DET
ma-77	22	10	class	class	NOUN
ma-77	22	11	of	of	ADP
ma-77	22	12	bounded	bounded	ADJ
ma-77	22	13	turning	turning	NOUN
ma-77	22	14	functions	function	NOUN
ma-77	22	15	.	.	PUNCT
ma-77	23	1	it	it	PRON
ma-77	23	2	is	be	AUX
ma-77	23	3	known	know	VERB
ma-77	23	4	(	(	PUNCT
ma-77	23	5	see	see	VERB
ma-77	23	6	[	[	X
ma-77	23	7	1	1	NUM
ma-77	23	8	]	]	PUNCT
ma-77	23	9	)	)	PUNCT
ma-77	23	10	that	that	SCONJ
ma-77	23	11	f	f	PROPN
ma-77	23	12	∈	∈	PROPN
ma-77	23	13	btare	btare	VERB
ma-77	23	14	univalent	univalent	ADJ
ma-77	23	15	functions	function	NOUN
ma-77	23	16	.	.	PUNCT
ma-77	24	1	also	also	ADV
ma-77	24	2	,	,	PUNCT
ma-77	24	3	a	a	DET
ma-77	24	4	function	function	NOUN
ma-77	24	5	f	f	NOUN
ma-77	24	6	in	in	ADP
ma-77	24	7	s	s	PROPN
ma-77	24	8	is	be	AUX
ma-77	24	9	a	a	DET
ma-77	24	10	member	member	NOUN
ma-77	24	11	of	of	ADP
ma-77	24	12	class	class	NOUN
ma-77	24	13	cv(δ	cv(δ	NOUN
ma-77	24	14	)	)	PUNCT
ma-77	24	15	of	of	ADP
ma-77	24	16	convex	convex	NOUN
ma-77	24	17	functions	function	NOUN
ma-77	24	18	oforder	oforder	VERB
ma-77	24	19	δ	δ	PROPN
ma-77	24	20	if	if	SCONJ
ma-77	24	21	it	it	PRON
ma-77	24	22	satisfies	satisfy	VERB
ma-77	24	23	the	the	DET
ma-77	24	24	geometric	geometric	ADJ
ma-77	24	25	condition	condition	NOUN
ma-77	24	26	re	re	ADP
ma-77	24	27	(	(	PUNCT
ma-77	24	28	z	z	NOUN
ma-77	24	29	f	f	PROPN
ma-77	24	30	′′(z	′′(z	PROPN
ma-77	24	31	)	)	PUNCT
ma-77	24	32	f	f	PROPN
ma-77	24	33	′(z	′(z	NOUN
ma-77	24	34	)	)	PUNCT
ma-77	25	1	+	+	CCONJ
ma-77	25	2	1	1	X
ma-77	25	3	)	)	PUNCT
ma-77	25	4	>	>	X
ma-77	26	1	δ	δ	PROPN
ma-77	26	2	∈	∈	PROPN
ma-77	27	1	[	[	X
ma-77	27	2	0	0	NUM
ma-77	27	3	,	,	PUNCT
ma-77	27	4	1	1	NUM
ma-77	27	5	)	)	PUNCT
ma-77	27	6	,	,	PUNCT
ma-77	27	7	z	z	NOUN
ma-77	27	8	∈	∈	PROPN
ma-77	27	9	ud	ud	INTJ
ma-77	27	10	.	.	PUNCT
ma-77	28	1	let	let	VERB
ma-77	28	2	cv(0	cv(0	NOUN
ma-77	28	3	)	)	PUNCT
ma-77	28	4	=	=	SYM
ma-77	29	1	cv	cv	PROPN
ma-77	29	2	represent	represent	VERB
ma-77	29	3	the	the	DET
ma-77	29	4	class	class	NOUN
ma-77	29	5	of	of	ADP
ma-77	29	6	convex	convex	VERB
ma-77	29	7	functions.the	functions.the	DET
ma-77	29	8	importance	importance	NOUN
ma-77	29	9	of	of	ADP
ma-77	29	10	operators	operator	NOUN
ma-77	29	11	in	in	ADP
ma-77	29	12	geometric	geometric	ADJ
ma-77	29	13	function	function	NOUN
ma-77	29	14	theory	theory	NOUN
ma-77	29	15	can	can	AUX
ma-77	29	16	not	not	PART
ma-77	29	17	be	be	AUX
ma-77	29	18	underrated	underrate	VERB
ma-77	29	19	.	.	PUNCT
ma-77	30	1	for	for	ADP
ma-77	30	2	instancesee	instancesee	NOUN
ma-77	30	3	[	[	X
ma-77	30	4	2	2	NUM
ma-77	30	5	,	,	PUNCT
ma-77	30	6	13,15	13,15	NUM
ma-77	30	7	]	]	PUNCT
ma-77	30	8	for	for	ADP
ma-77	30	9	some	some	DET
ma-77	30	10	known	know	VERB
ma-77	30	11	ones.in	ones.in	NOUN
ma-77	30	12	1908	1908	NUM
ma-77	30	13	,	,	PUNCT
ma-77	30	14	jackson	jackson	PROPN
ma-77	31	1	[	[	X
ma-77	31	2	7	7	NUM
ma-77	31	3	]	]	PUNCT
ma-77	31	4	(	(	PUNCT
ma-77	31	5	see	see	VERB
ma-77	31	6	also	also	ADV
ma-77	31	7	[	[	X
ma-77	31	8	3	3	NUM
ma-77	31	9	,	,	PUNCT
ma-77	31	10	4	4	NUM
ma-77	31	11	,	,	PUNCT
ma-77	31	12	8–11	8–11	NOUN
ma-77	31	13	]	]	PUNCT
ma-77	31	14	)	)	PUNCT
ma-77	31	15	initiated	initiate	VERB
ma-77	31	16	the	the	DET
ma-77	31	17	concept	concept	NOUN
ma-77	31	18	of	of	ADP
ma-77	31	19	q	q	NOUN
ma-77	31	20	-	-	NOUN
ma-77	31	21	calculus	calculus	NOUN
ma-77	31	22	as	as	SCONJ
ma-77	31	23	follows	follow	VERB
ma-77	31	24	.	.	PUNCT
ma-77	32	1	received	receive	VERB
ma-77	32	2	:	:	PUNCT
ma-77	32	3	21	21	NUM
ma-77	32	4	jan	jan	PROPN
ma-77	32	5	2022	2022	NUM
ma-77	32	6	.	.	PUNCT
ma-77	33	1	key	key	ADJ
ma-77	33	2	words	word	NOUN
ma-77	33	3	and	and	CCONJ
ma-77	33	4	phrases	phrase	NOUN
ma-77	33	5	.	.	PUNCT
ma-77	34	1	analytic	analytic	ADJ
ma-77	34	2	functions	function	NOUN
ma-77	34	3	;	;	PUNCT
ma-77	34	4	carathéodory	carathéodory	ADJ
ma-77	34	5	functions	function	NOUN
ma-77	34	6	;	;	PUNCT
ma-77	34	7	univalent	univalent	ADJ
ma-77	34	8	functions	function	NOUN
ma-77	34	9	;	;	PUNCT
ma-77	34	10	bounded	bound	VERB
ma-77	34	11	turning	turn	VERB
ma-77	34	12	function;coefficient	function;coefficient	PROPN
ma-77	34	13	bound	bind	VERB
ma-77	34	14	;	;	PUNCT
ma-77	34	15	inclusion	inclusion	NOUN
ma-77	34	16	property	property	NOUN
ma-77	34	17	and	and	CCONJ
ma-77	34	18	q	q	NOUN
ma-77	34	19	-	-	NOUN
ma-77	34	20	calculus	calculus	NOUN
ma-77	34	21	.	.	PUNCT
ma-77	35	1	1	1	NUM
ma-77	35	2	https://adac.ee	https://adac.ee	PROPN
ma-77	35	3	https://doi.org/10.28924/ada/ma.2.12	https://doi.org/10.28924/ada/ma.2.12	NUM
ma-77	35	4	https://orcid.org/0000-0002-2657-7698	https://orcid.org/0000-0002-2657-7698	PROPN
ma-77	35	5	eur	eur	NOUN
ma-77	35	6	.	.	PUNCT
ma-77	36	1	j.	j.	PROPN
ma-77	36	2	math	math	PROPN
ma-77	36	3	.	.	PUNCT
ma-77	37	1	anal	anal	PROPN
ma-77	37	2	.	.	PUNCT
ma-77	38	1	10.28924	10.28924	NUM
ma-77	38	2	/	/	SYM
ma-77	38	3	ada	ada	PROPN
ma-77	38	4	/	/	SYM
ma-77	38	5	ma.2.12	ma.2.12	ADJ
ma-77	38	6	2	2	NUM
ma-77	38	7	definition	definition	NOUN
ma-77	38	8	1.1	1.1	NUM
ma-77	38	9	.	.	PUNCT
ma-77	39	1	for	for	ADP
ma-77	39	2	q	q	PROPN
ma-77	39	3	∈	∈	PROPN
ma-77	39	4	(	(	PUNCT
ma-77	39	5	0	0	NUM
ma-77	39	6	,	,	PUNCT
ma-77	39	7	1	1	NUM
ma-77	39	8	)	)	PUNCT
ma-77	39	9	,	,	PUNCT
ma-77	39	10	the	the	DET
ma-77	39	11	q	q	NOUN
ma-77	39	12	-	-	PUNCT
ma-77	39	13	differentiation	differentiation	NOUN
ma-77	39	14	of	of	ADP
ma-77	39	15	function	function	NOUN
ma-77	39	16	f	f	PROPN
ma-77	39	17	∈	∈	PROPN
ma-77	39	18	a	a	PRON
ma-77	39	19	is	be	AUX
ma-77	39	20	defined	define	VERB
ma-77	39	21	by	by	ADP
ma-77	39	22	dqf	dqf	NOUN
ma-77	39	23	(	(	PUNCT
ma-77	39	24	0	0	NUM
ma-77	39	25	)	)	PUNCT
ma-77	39	26	=	=	PUNCT
ma-77	40	1	f	f	PROPN
ma-77	40	2	′(0	′(0	NOUN
ma-77	40	3	)	)	PUNCT
ma-77	40	4	,	,	PUNCT
ma-77	40	5	dqf	dqf	NOUN
ma-77	40	6	(	(	PUNCT
ma-77	40	7	z	z	NOUN
ma-77	40	8	)	)	PUNCT
ma-77	40	9	=	=	SYM
ma-77	40	10	f	f	X
ma-77	40	11	(	(	PUNCT
ma-77	40	12	z)−	z)−	PROPN
ma-77	40	13	f	f	PROPN
ma-77	40	14	(	(	PUNCT
ma-77	40	15	qz	qz	PROPN
ma-77	40	16	)	)	PUNCT
ma-77	40	17	z(1−	z(1−	PROPN
ma-77	40	18	q	q	NOUN
ma-77	40	19	)	)	PUNCT
ma-77	40	20	(	(	PUNCT
ma-77	40	21	z	z	NOUN
ma-77	40	22	6=	6=	NUM
ma-77	40	23	0	0	NUM
ma-77	40	24	)	)	PUNCT
ma-77	40	25	and	and	CCONJ
ma-77	40	26	d2qf	d2qf	X
ma-77	40	27	(	(	PUNCT
ma-77	40	28	z	z	NOUN
ma-77	40	29	)	)	PUNCT
ma-77	40	30	=	=	VERB
ma-77	41	1	dq(dqf	dq(dqf	NOUN
ma-77	41	2	(	(	PUNCT
ma-77	41	3	z	z	NOUN
ma-77	41	4	)	)	PUNCT
ma-77	41	5	)	)	PUNCT
ma-77	41	6	.	.	PUNCT
ma-77	42	1	(	(	PUNCT
ma-77	42	2	2	2	X
ma-77	42	3	)	)	PUNCT
ma-77	42	4	obviously	obviously	ADV
ma-77	42	5	,	,	PUNCT
ma-77	42	6	applying	apply	VERB
ma-77	42	7	(	(	PUNCT
ma-77	42	8	2	2	NUM
ma-77	42	9	)	)	PUNCT
ma-77	42	10	in	in	ADP
ma-77	42	11	(	(	PUNCT
ma-77	42	12	1	1	X
ma-77	42	13	)	)	PUNCT
ma-77	42	14	gives	give	VERB
ma-77	42	15	us	we	PRON
ma-77	42	16	dqf	dqf	NOUN
ma-77	42	17	(	(	PUNCT
ma-77	42	18	z	z	NOUN
ma-77	42	19	)	)	PUNCT
ma-77	42	20	=	=	SYM
ma-77	43	1	1	1	NUM
ma-77	43	2	+	+	NUM
ma-77	43	3	∞∑	∞∑	NUM
ma-77	43	4	m=2	m=2	PROPN
ma-77	44	1	[	[	X
ma-77	44	2	m]qamz	m]qamz	X
ma-77	44	3	m−1	m−1	PROPN
ma-77	44	4	and	and	CCONJ
ma-77	44	5	zd2qf	zd2qf	NUM
ma-77	44	6	(	(	PUNCT
ma-77	44	7	z	z	NOUN
ma-77	44	8	)	)	PUNCT
ma-77	44	9	=	=	PUNCT
ma-77	45	1	∞∑	∞∑	NUM
ma-77	45	2	m=2	m=2	PROPN
ma-77	46	1	[	[	X
ma-77	46	2	m	m	NOUN
ma-77	46	3	−	−	PROPN
ma-77	46	4	1]q[m]qamzm−1	1]q[m]qamzm−1	NUM
ma-77	46	5	(	(	PUNCT
ma-77	46	6	3	3	NUM
ma-77	46	7	)	)	PUNCT
ma-77	46	8	where	where	SCONJ
ma-77	46	9	[	[	X
ma-77	46	10	m]q	m]q	X
ma-77	46	11	=	=	SYM
ma-77	46	12	1−qm	1−qm	NUM
ma-77	46	13	1−q	1−q	NUM
ma-77	46	14	and	and	CCONJ
ma-77	46	15	lim	lim	PROPN
ma-77	46	16	q↑1	q↑1	PROPN
ma-77	47	1	[	[	X
ma-77	47	2	m]q	m]q	NOUN
ma-77	47	3	=	=	SYM
ma-77	47	4	m.for	m.for	ADP
ma-77	47	5	example	example	NOUN
ma-77	47	6	if	if	SCONJ
ma-77	47	7	f	f	PROPN
ma-77	47	8	(	(	PUNCT
ma-77	47	9	z	z	NOUN
ma-77	47	10	)	)	PUNCT
ma-77	47	11	=	=	SYM
ma-77	47	12	zm	zm	PROPN
ma-77	47	13	,	,	PUNCT
ma-77	47	14	then	then	ADV
ma-77	47	15	by	by	ADP
ma-77	47	16	using	use	VERB
ma-77	47	17	(	(	PUNCT
ma-77	47	18	2	2	NUM
ma-77	47	19	)	)	PUNCT
ma-77	47	20	,	,	PUNCT
ma-77	47	21	dqf	dqf	NOUN
ma-77	47	22	(	(	PUNCT
ma-77	47	23	z	z	NOUN
ma-77	47	24	)	)	PUNCT
ma-77	47	25	=	=	SYM
ma-77	47	26	dq(zm	dq(zm	NOUN
ma-77	47	27	)	)	PUNCT
ma-77	47	28	=	=	SYM
ma-77	48	1	1−	1−	NUM
ma-77	48	2	qm	qm	PROPN
ma-77	48	3	1−	1−	NUM
ma-77	48	4	q	q	PROPN
ma-77	49	1	z	z	X
ma-77	49	2	m−1	m−1	PROPN
ma-77	49	3	=	=	PUNCT
ma-77	50	1	[	[	PUNCT
ma-77	50	2	m]qz	m]qz	ADP
ma-77	50	3	m−1	m−1	PROPN
ma-77	51	1	and	and	CCONJ
ma-77	51	2	observe	observe	VERB
ma-77	51	3	that	that	SCONJ
ma-77	51	4	lim	lim	PROPN
ma-77	51	5	q↑1	q↑1	PROPN
ma-77	51	6	dqf	dqf	NOUN
ma-77	51	7	(	(	PUNCT
ma-77	51	8	z	z	NOUN
ma-77	51	9	)	)	PUNCT
ma-77	52	1	=	=	SYM
ma-77	52	2	lim	lim	PROPN
ma-77	52	3	q↑1	q↑1	PROPN
ma-77	52	4	(	(	PUNCT
ma-77	52	5	[	[	X
ma-77	52	6	m]qz	m]qz	PROPN
ma-77	52	7	m−1	m−1	PROPN
ma-77	52	8	)	)	PUNCT
ma-77	53	1	=	=	PUNCT
ma-77	54	1	mzm−1	mzm−1	NOUN
ma-77	54	2	=	=	PUNCT
ma-77	54	3	f	f	PROPN
ma-77	54	4	′(z	′(z	NOUN
ma-77	54	5	)	)	PUNCT
ma-77	54	6	where	where	SCONJ
ma-77	54	7	f	f	PROPN
ma-77	54	8	′(z	′(z	VERB
ma-77	54	9	)	)	PUNCT
ma-77	54	10	is	be	AUX
ma-77	54	11	the	the	DET
ma-77	54	12	classical	classical	ADJ
ma-77	54	13	differentiation.in	differentiation.in	NUM
ma-77	54	14	this	this	DET
ma-77	54	15	work	work	NOUN
ma-77	54	16	,	,	PUNCT
ma-77	54	17	the	the	DET
ma-77	54	18	q	q	ADJ
ma-77	54	19	-	-	PUNCT
ma-77	54	20	differential	differential	ADJ
ma-77	54	21	operator	operator	NOUN
ma-77	54	22	was	be	AUX
ma-77	54	23	used	use	VERB
ma-77	54	24	to	to	PART
ma-77	54	25	define	define	VERB
ma-77	54	26	a	a	DET
ma-77	54	27	class	class	NOUN
ma-77	54	28	of	of	ADP
ma-77	54	29	analytic	analytic	ADJ
ma-77	54	30	functions	function	NOUN
ma-77	54	31	andgeneralize	andgeneralize	VERB
ma-77	54	32	some	some	DET
ma-77	54	33	results	result	NOUN
ma-77	54	34	.	.	PUNCT
ma-77	55	1	2	2	X
ma-77	55	2	.	.	X
ma-77	55	3	relevant	relevant	ADJ
ma-77	55	4	lemmas	lemma	NOUN
ma-77	55	5	we	we	PRON
ma-77	55	6	represent	represent	VERB
ma-77	55	7	by	by	ADP
ma-77	55	8	p	p	PRON
ma-77	55	9	the	the	DET
ma-77	55	10	well	well	ADV
ma-77	55	11	-	-	PUNCT
ma-77	55	12	known	know	VERB
ma-77	55	13	class	class	NOUN
ma-77	55	14	of	of	ADP
ma-77	55	15	analytic	analytic	ADJ
ma-77	55	16	functions	function	NOUN
ma-77	55	17	of	of	ADP
ma-77	55	18	the	the	DET
ma-77	55	19	form	form	NOUN
ma-77	55	20	p(z	p(z	NOUN
ma-77	55	21	)	)	PUNCT
ma-77	55	22	=	=	SYM
ma-77	56	1	1	1	NUM
ma-77	56	2	+	+	NUM
ma-77	56	3	∞∑	∞∑	PROPN
ma-77	56	4	m=1	m=1	PROPN
ma-77	56	5	cmz	cmz	ADV
ma-77	56	6	m	m	NOUN
ma-77	56	7	,	,	PUNCT
ma-77	56	8	re	re	VERB
ma-77	56	9	p(z	p(z	NOUN
ma-77	56	10	)	)	PUNCT
ma-77	56	11	>	>	X
ma-77	57	1	0	0	NUM
ma-77	57	2	,	,	PUNCT
ma-77	57	3	z	z	NOUN
ma-77	57	4	∈	∈	PROPN
ma-77	57	5	ud	ud	INTJ
ma-77	57	6	(	(	PUNCT
ma-77	57	7	4	4	NUM
ma-77	57	8	)	)	PUNCT
ma-77	57	9	and	and	CCONJ
ma-77	57	10	by	by	ADP
ma-77	57	11	p(δ	p(δ	NOUN
ma-77	57	12	)	)	PUNCT
ma-77	57	13	⊆	⊆	NUM
ma-77	57	14	p(0	p(0	NOUN
ma-77	57	15	)	)	PUNCT
ma-77	57	16	=	=	VERB
ma-77	58	1	p	p	X
ma-77	58	2	the	the	DET
ma-77	58	3	class	class	NOUN
ma-77	58	4	whose	whose	DET
ma-77	58	5	members	member	NOUN
ma-77	58	6	are	be	AUX
ma-77	58	7	of	of	ADP
ma-77	58	8	the	the	DET
ma-77	58	9	form	form	NOUN
ma-77	58	10	pδ(z	pδ(z	NOUN
ma-77	58	11	)	)	PUNCT
ma-77	58	12	=	=	SYM
ma-77	59	1	1	1	NUM
ma-77	59	2	+	+	NUM
ma-77	59	3	∞∑	∞∑	PROPN
ma-77	59	4	m=1	m=1	X
ma-77	59	5	(	(	PUNCT
ma-77	59	6	1−	1−	NUM
ma-77	59	7	δ)cmzm	δ)cmzm	NOUN
ma-77	59	8	,	,	PUNCT
ma-77	59	9	re	re	VERB
ma-77	59	10	p(z	p(z	NOUN
ma-77	59	11	)	)	PUNCT
ma-77	59	12	>	>	PUNCT
ma-77	60	1	δ	δ	X
ma-77	60	2	∈	∈	PROPN
ma-77	61	1	[	[	X
ma-77	61	2	0	0	NUM
ma-77	61	3	,	,	PUNCT
ma-77	61	4	1	1	NUM
ma-77	61	5	)	)	PUNCT
ma-77	61	6	,	,	PUNCT
ma-77	61	7	z	z	NOUN
ma-77	61	8	∈	∈	PROPN
ma-77	61	9	ud	ud	INTJ
ma-77	61	10	.	.	PUNCT
ma-77	62	1	(	(	PUNCT
ma-77	62	2	5	5	X
ma-77	62	3	)	)	PUNCT
ma-77	62	4	the	the	DET
ma-77	62	5	following	follow	VERB
ma-77	62	6	lemmas	lemmas	PROPN
ma-77	62	7	shall	shall	AUX
ma-77	62	8	be	be	AUX
ma-77	62	9	required	require	VERB
ma-77	62	10	to	to	PART
ma-77	62	11	proof	proof	VERB
ma-77	62	12	our	our	PRON
ma-77	62	13	results	result	NOUN
ma-77	62	14	.	.	PUNCT
ma-77	63	1	lemma	lemma	PROPN
ma-77	63	2	2.1	2.1	NUM
ma-77	63	3	(	(	PUNCT
ma-77	63	4	[	[	X
ma-77	63	5	14	14	NUM
ma-77	63	6	]	]	NUM
ma-77	63	7	)	)	PUNCT
ma-77	63	8	.	.	PUNCT
ma-77	64	1	let	let	VERB
ma-77	64	2	g(z	g(z	ADJ
ma-77	64	3	)	)	PUNCT
ma-77	64	4	=	=	PUNCT
ma-77	65	1	∞∑	∞∑	NUM
ma-77	65	2	m=1	m=1	PROPN
ma-77	65	3	amz	amz	PROPN
ma-77	65	4	m	m	NUM
ma-77	65	5	≺	≺	NOUN
ma-77	65	6	g(z	g(z	PROPN
ma-77	65	7	)	)	PUNCT
ma-77	65	8	=	=	PUNCT
ma-77	66	1	∞∑	∞∑	PRON
ma-77	66	2	m=1	m=1	NUM
ma-77	66	3	bmz	bmz	NOUN
ma-77	66	4	m	m	NOUN
ma-77	66	5	,	,	PUNCT
ma-77	66	6	z	z	NOUN
ma-77	66	7	∈	∈	PROPN
ma-77	66	8	ud	ud	INTJ
ma-77	66	9	where	where	SCONJ
ma-77	66	10	g(z	g(z	ADJ
ma-77	66	11	)	)	PUNCT
ma-77	66	12	is	be	AUX
ma-77	66	13	univalent	univalent	ADJ
ma-77	66	14	in	in	ADP
ma-77	66	15	ud	ud	INTJ
ma-77	66	16	and	and	CCONJ
ma-77	66	17	g(ud	g(ud	NOUN
ma-77	66	18	)	)	PUNCT
ma-77	66	19	is	be	AUX
ma-77	66	20	a	a	DET
ma-77	66	21	convex	convex	ADJ
ma-77	66	22	domain	domain	NOUN
ma-77	66	23	,	,	PUNCT
ma-77	66	24	then	then	ADV
ma-77	66	25	|am|	|am|	VERB
ma-77	66	26	≤	≤	ADJ
ma-77	66	27	|b1|	|b1|	NOUN
ma-77	66	28	,	,	PUNCT
ma-77	66	29	m	m	PROPN
ma-77	66	30	∈	∈	NOUN
ma-77	66	31	n.	n.	NOUN
ma-77	66	32	equality	equality	NOUN
ma-77	66	33	holds	hold	VERB
ma-77	66	34	for	for	ADP
ma-77	66	35	the	the	DET
ma-77	66	36	function	function	NOUN
ma-77	66	37	g(z	g(z	PROPN
ma-77	66	38	)	)	PUNCT
ma-77	66	39	=	=	SYM
ma-77	66	40	g(τzm	g(τzm	NOUN
ma-77	66	41	)	)	PUNCT
ma-77	66	42	,	,	PUNCT
ma-77	66	43	|τ	|τ	ADJ
ma-77	66	44	|	|	NOUN
ma-77	66	45	=	=	NOUN
ma-77	66	46	1	1	X
ma-77	66	47	.	.	PUNCT
ma-77	67	1	the	the	DET
ma-77	67	2	lemmas	lemma	NOUN
ma-77	67	3	that	that	PRON
ma-77	67	4	follow	follow	NOUN
ma-77	67	5	are	be	AUX
ma-77	67	6	the	the	DET
ma-77	67	7	q	q	ADJ
ma-77	67	8	-	-	ADJ
ma-77	67	9	analogous	analogous	ADJ
ma-77	67	10	versions	version	NOUN
ma-77	67	11	of	of	ADP
ma-77	67	12	the	the	DET
ma-77	67	13	original	original	ADJ
ma-77	67	14	ones	one	NOUN
ma-77	67	15	as	as	SCONJ
ma-77	67	16	referenced	reference	VERB
ma-77	67	17	.	.	PUNCT
ma-77	68	1	lemma	lemma	PROPN
ma-77	68	2	2.2	2.2	NUM
ma-77	68	3	(	(	PUNCT
ma-77	68	4	[	[	X
ma-77	68	5	6	6	NUM
ma-77	68	6	]	]	PUNCT
ma-77	68	7	)	)	PUNCT
ma-77	68	8	.	.	PUNCT
ma-77	69	1	let	let	AUX
ma-77	69	2	p(z	p(z	VERB
ma-77	69	3	)	)	PUNCT
ma-77	69	4	be	be	AUX
ma-77	69	5	analytic	analytic	ADJ
ma-77	69	6	in	in	ADP
ma-77	69	7	ud	ud	INTJ
ma-77	69	8	such	such	ADJ
ma-77	69	9	that	that	DET
ma-77	69	10	p(0	p(0	NOUN
ma-77	69	11	)	)	PUNCT
ma-77	69	12	=	=	SYM
ma-77	70	1	1	1	X
ma-77	70	2	.	.	X
ma-77	71	1	if	if	SCONJ
ma-77	71	2	re	re	X
ma-77	71	3	(	(	PUNCT
ma-77	71	4	zdq(p(z	zdq(p(z	NOUN
ma-77	71	5	)	)	PUNCT
ma-77	71	6	)	)	PUNCT
ma-77	72	1	p(z	p(z	CCONJ
ma-77	72	2	)	)	PUNCT
ma-77	73	1	+	+	CCONJ
ma-77	73	2	1	1	X
ma-77	73	3	)	)	PUNCT
ma-77	73	4	>	>	X
ma-77	74	1	3δ	3δ	NUM
ma-77	74	2	−	−	NOUN
ma-77	74	3	1	1	NUM
ma-77	74	4	2δ	2δ	NUM
ma-77	74	5	,	,	PUNCT
ma-77	74	6	z	z	PROPN
ma-77	74	7	∈	∈	PROPN
ma-77	74	8	ud	ud	ADP
ma-77	74	9	,	,	PUNCT
ma-77	74	10	then	then	ADV
ma-77	74	11	for	for	ADP
ma-77	74	12	α	α	NOUN
ma-77	74	13	=	=	SYM
ma-77	74	14	(	(	PUNCT
ma-77	74	15	δ	δ	PROPN
ma-77	74	16	−	−	PROPN
ma-77	74	17	1)/δ	1)/δ	PROPN
ma-77	74	18	(	(	PUNCT
ma-77	74	19	δ	δ	PROPN
ma-77	74	20	∈	∈	PROPN
ma-77	75	1	[	[	X
ma-77	75	2	1/2	1/2	NUM
ma-77	75	3	,	,	PUNCT
ma-77	75	4	1	1	NUM
ma-77	75	5	)	)	PUNCT
ma-77	75	6	)	)	PUNCT
ma-77	75	7	,	,	PUNCT
ma-77	75	8	re	re	VERB
ma-77	75	9	p(z	p(z	VERB
ma-77	75	10	)	)	PUNCT
ma-77	75	11	>	>	X
ma-77	76	1	2α	2α	NOUN
ma-77	76	2	.	.	PUNCT
ma-77	77	1	the	the	DET
ma-77	77	2	constant	constant	ADJ
ma-77	77	3	2α	2α	NOUN
ma-77	77	4	is	be	AUX
ma-77	77	5	the	the	DET
ma-77	77	6	best	good	ADJ
ma-77	77	7	possible	possible	ADJ
ma-77	77	8	.	.	PUNCT
ma-77	78	1	lemma	lemma	PROPN
ma-77	78	2	2.3	2.3	NUM
ma-77	78	3	(	(	PUNCT
ma-77	78	4	[	[	X
ma-77	78	5	5	5	NUM
ma-77	78	6	]	]	PUNCT
ma-77	78	7	)	)	PUNCT
ma-77	78	8	.	.	PUNCT
ma-77	79	1	let	let	VERB
ma-77	79	2	u	u	PRON
ma-77	79	3	=	=	PUNCT
ma-77	79	4	u1+u2i	u1+u2i	NUM
ma-77	79	5	and	and	CCONJ
ma-77	79	6	v	v	NOUN
ma-77	79	7	=	=	SYM
ma-77	79	8	v1+v2i	v1+v2i	X
ma-77	80	1	such	such	ADJ
ma-77	80	2	that	that	SCONJ
ma-77	80	3	γ(u	γ(u	PROPN
ma-77	80	4	,	,	PUNCT
ma-77	80	5	v	v	NOUN
ma-77	80	6	)	)	PUNCT
ma-77	80	7	:	:	PUNCT
ma-77	80	8	c2	c2	PROPN
ma-77	80	9	−→	−→	NOUN
ma-77	80	10	c	c	PROPN
ma-77	80	11	is	be	AUX
ma-77	80	12	a	a	DET
ma-77	80	13	complex	complex	ADV
ma-77	80	14	-	-	PUNCT
ma-77	80	15	valued	value	VERB
ma-77	80	16	function	function	NOUN
ma-77	80	17	such	such	ADJ
ma-77	80	18	that	that	SCONJ
ma-77	80	19	https://doi.org/10.28924/ada/ma.2.12	https://doi.org/10.28924/ada/ma.2.12	PROPN
ma-77	80	20	eur	eur	NOUN
ma-77	80	21	.	.	PUNCT
ma-77	81	1	j.	j.	PROPN
ma-77	81	2	math	math	PROPN
ma-77	81	3	.	.	PUNCT
ma-77	82	1	anal	anal	PROPN
ma-77	82	2	.	.	PUNCT
ma-77	83	1	10.28924	10.28924	NUM
ma-77	83	2	/	/	SYM
ma-77	83	3	ada	ada	PROPN
ma-77	83	4	/	/	SYM
ma-77	83	5	ma.2.12	ma.2.12	NOUN
ma-77	83	6	3(1	3(1	NUM
ma-77	83	7	)	)	PUNCT
ma-77	83	8	γ(u	γ(u	PROPN
ma-77	83	9	,	,	PUNCT
ma-77	83	10	v	v	NOUN
ma-77	83	11	)	)	PUNCT
ma-77	83	12	is	be	AUX
ma-77	83	13	continuous	continuous	ADJ
ma-77	83	14	in	in	ADP
ma-77	83	15	π	π	PROPN
ma-77	83	16	⊂	⊂	PROPN
ma-77	83	17	c2,(2	c2,(2	PROPN
ma-77	83	18	)	)	PUNCT
ma-77	83	19	(	(	PUNCT
ma-77	83	20	1	1	NUM
ma-77	83	21	,	,	PUNCT
ma-77	83	22	0	0	NUM
ma-77	83	23	)	)	PUNCT
ma-77	83	24	∈	∈	PROPN
ma-77	83	25	π	π	NOUN
ma-77	83	26	and	and	CCONJ
ma-77	83	27	re(γ(1	re(γ(1	NOUN
ma-77	83	28	,	,	PUNCT
ma-77	83	29	0	0	NUM
ma-77	83	30	)	)	PUNCT
ma-77	83	31	)	)	PUNCT
ma-77	83	32	>	>	SYM
ma-77	83	33	0	0	PUNCT
ma-77	84	1	and(3	and(3	NOUN
ma-77	84	2	)	)	PUNCT
ma-77	85	1	re(γ(ξ	re(γ(ξ	NOUN
ma-77	86	1	+	+	CCONJ
ma-77	86	2	(	(	PUNCT
ma-77	86	3	1−	1−	NUM
ma-77	86	4	ξ)u2i	ξ)u2i	NUM
ma-77	86	5	,	,	PUNCT
ma-77	86	6	v1	v1	NOUN
ma-77	86	7	)	)	PUNCT
ma-77	86	8	)	)	PUNCT
ma-77	87	1	≤	≤	NUM
ma-77	87	2	ξ	ξ	X
ma-77	87	3	(	(	PUNCT
ma-77	87	4	0	0	NUM
ma-77	87	5	≤	≤	NOUN
ma-77	87	6	ξ	ξ	X
ma-77	87	7	<	<	X
ma-77	87	8	1	1	NUM
ma-77	87	9	)	)	PUNCT
ma-77	87	10	)	)	PUNCT
ma-77	87	11	if	if	SCONJ
ma-77	87	12	(	(	PUNCT
ma-77	87	13	ξ	ξ	X
ma-77	87	14	+	+	PUNCT
ma-77	87	15	(	(	PUNCT
ma-77	87	16	1−	1−	NUM
ma-77	87	17	ξ)u2i	ξ)u2i	NUM
ma-77	87	18	,	,	PUNCT
ma-77	87	19	v1	v1	NOUN
ma-77	87	20	)	)	PUNCT
ma-77	87	21	∈	∈	PROPN
ma-77	87	22	π	π	NOUN
ma-77	87	23	and	and	CCONJ
ma-77	87	24	v1	v1	VERB
ma-77	87	25	≤	≤	NUM
ma-77	87	26	−12(1−ξ)(1+u	−12(1−ξ)(1+u	ADV
ma-77	87	27	2	2	NUM
ma-77	87	28	2	2	NUM
ma-77	87	29	)	)	PUNCT
ma-77	87	30	and	and	CCONJ
ma-77	87	31	re(γ(ξ+(1−ξ)u2i	re(γ(ξ+(1−ξ)u2i	PROPN
ma-77	87	32	,	,	PUNCT
ma-77	87	33	v1	v1	NOUN
ma-77	87	34	)	)	PUNCT
ma-77	87	35	)	)	PUNCT
ma-77	87	36	≥	≥	X
ma-77	88	1	ξ	ξ	X
ma-77	88	2	(	(	PUNCT
ma-77	88	3	ξ	ξ	X
ma-77	88	4	>	>	X
ma-77	88	5	1	1	NUM
ma-77	88	6	)	)	PUNCT
ma-77	88	7	if	if	SCONJ
ma-77	88	8	(	(	PUNCT
ma-77	88	9	ξ+(1−ξ)u2i	ξ+(1−ξ)u2i	ADJ
ma-77	88	10	,	,	PUNCT
ma-77	88	11	v1	v1	NOUN
ma-77	88	12	)	)	PUNCT
ma-77	88	13	∈	∈	PROPN
ma-77	88	14	π	π	NOUN
ma-77	88	15	and	and	CCONJ
ma-77	88	16	v1	v1	VERB
ma-77	88	17	≥	≥	NOUN
ma-77	88	18	1	1	NUM
ma-77	88	19	2(1−	2(1−	NUM
ma-77	88	20	ξ)(1	ξ)(1	NUM
ma-77	89	1	+	+	CCONJ
ma-77	89	2	u	u	NOUN
ma-77	89	3	2	2	NUM
ma-77	89	4	2	2	NUM
ma-77	89	5	)	)	PUNCT
ma-77	89	6	.	.	PUNCT
ma-77	90	1	if	if	SCONJ
ma-77	90	2	p(z	p(z	NOUN
ma-77	90	3	)	)	PUNCT
ma-77	90	4	∈	∈	PROPN
ma-77	90	5	p	p	NOUN
ma-77	90	6	for	for	ADP
ma-77	90	7	(	(	PUNCT
ma-77	90	8	p(z	p(z	NOUN
ma-77	90	9	)	)	PUNCT
ma-77	90	10	,	,	PUNCT
ma-77	90	11	zdqp(z	zdqp(z	NOUN
ma-77	90	12	)	)	PUNCT
ma-77	90	13	)	)	PUNCT
ma-77	91	1	∈	∈	PROPN
ma-77	91	2	π	π	NOUN
ma-77	91	3	and	and	CCONJ
ma-77	91	4	re(γ(p(z	re(γ(p(z	ADJ
ma-77	91	5	)	)	PUNCT
ma-77	91	6	,	,	PUNCT
ma-77	91	7	zdqp(z	zdqp(z	NOUN
ma-77	91	8	)	)	PUNCT
ma-77	91	9	)	)	PUNCT
ma-77	91	10	)	)	PUNCT
ma-77	92	1	>	>	PUNCT
ma-77	92	2	ξ	ξ	X
ma-77	92	3	,	,	PUNCT
ma-77	92	4	z	z	PROPN
ma-77	92	5	∈	∈	PROPN
ma-77	92	6	ud	ud	INTJ
ma-77	92	7	,	,	PUNCT
ma-77	92	8	then	then	ADV
ma-77	92	9	rep(z	rep(z	PROPN
ma-77	92	10	)	)	PUNCT
ma-77	92	11	>	>	X
ma-77	93	1	ξ	ξ	X
ma-77	93	2	in	in	ADP
ma-77	93	3	ud	ud	PROPN
ma-77	93	4	.	.	PROPN
ma-77	94	1	3	3	NUM
ma-77	94	2	.	.	X
ma-77	94	3	main	main	ADJ
ma-77	94	4	results	result	NOUN
ma-77	94	5	the	the	DET
ma-77	94	6	definition	definition	NOUN
ma-77	94	7	of	of	ADP
ma-77	94	8	the	the	DET
ma-77	94	9	investigated	investigate	VERB
ma-77	94	10	class	class	NOUN
ma-77	94	11	is	be	AUX
ma-77	94	12	as	as	SCONJ
ma-77	94	13	follows.a	follows.a	NOUN
ma-77	94	14	function	function	NOUN
ma-77	94	15	f	f	PROPN
ma-77	94	16	(	(	PUNCT
ma-77	94	17	z	z	NOUN
ma-77	94	18	)	)	PUNCT
ma-77	94	19	∈	∈	PROPN
ma-77	94	20	a	a	PRON
ma-77	94	21	is	be	AUX
ma-77	94	22	a	a	DET
ma-77	94	23	member	member	NOUN
ma-77	94	24	of	of	ADP
ma-77	94	25	the	the	DET
ma-77	94	26	class	class	NOUN
ma-77	94	27	eq(β	eq(β	X
ma-77	94	28	,	,	PUNCT
ma-77	94	29	δ	δ	PROPN
ma-77	94	30	)	)	PUNCT
ma-77	94	31	if	if	SCONJ
ma-77	94	32	the	the	DET
ma-77	94	33	condition	condition	NOUN
ma-77	94	34	re	re	VERB
ma-77	94	35	(	(	PUNCT
ma-77	94	36	dqf	dqf	NOUN
ma-77	94	37	(	(	PUNCT
ma-77	94	38	z	z	NOUN
ma-77	94	39	)	)	PUNCT
ma-77	95	1	+	+	CCONJ
ma-77	95	2	1	1	NUM
ma-77	95	3	+	+	NUM
ma-77	95	4	e	e	NOUN
ma-77	95	5	iβ	iβ	ADP
ma-77	95	6	2	2	NUM
ma-77	95	7	zd2qf	zd2qf	NUM
ma-77	95	8	(	(	PUNCT
ma-77	95	9	z	z	NOUN
ma-77	95	10	)	)	PUNCT
ma-77	95	11	)	)	PUNCT
ma-77	95	12	>	>	PUNCT
ma-77	95	13	δ	δ	PROPN
ma-77	95	14	,	,	PUNCT
ma-77	95	15	δ	δ	PROPN
ma-77	95	16	∈	∈	PROPN
ma-77	96	1	[	[	X
ma-77	96	2	0	0	NUM
ma-77	96	3	,	,	PUNCT
ma-77	96	4	1	1	NUM
ma-77	96	5	)	)	PUNCT
ma-77	96	6	,	,	PUNCT
ma-77	96	7	β	β	X
ma-77	96	8	∈	∈	PROPN
ma-77	96	9	(	(	PUNCT
ma-77	96	10	−π	−π	PROPN
ma-77	96	11	,	,	PUNCT
ma-77	96	12	π	π	PROPN
ma-77	96	13	]	]	X
ma-77	96	14	,	,	PUNCT
ma-77	96	15	z	z	PROPN
ma-77	96	16	∈	∈	PROPN
ma-77	96	17	ud	ud	INTJ
ma-77	96	18	(	(	PUNCT
ma-77	96	19	6	6	NUM
ma-77	96	20	)	)	PUNCT
ma-77	96	21	holds.when	holds.when	ADP
ma-77	96	22	parameters	parameter	NOUN
ma-77	96	23	in	in	ADP
ma-77	96	24	(	(	PUNCT
ma-77	96	25	6	6	NUM
ma-77	96	26	)	)	PUNCT
ma-77	96	27	are	be	AUX
ma-77	96	28	varied	varied	ADJ
ma-77	96	29	,	,	PUNCT
ma-77	96	30	the	the	DET
ma-77	96	31	class	class	NOUN
ma-77	96	32	eq(β	eq(β	X
ma-77	96	33	,	,	PUNCT
ma-77	96	34	δ	δ	PROPN
ma-77	96	35	)	)	PUNCT
ma-77	96	36	reduces	reduce	VERB
ma-77	96	37	to	to	ADP
ma-77	96	38	some	some	DET
ma-77	96	39	well	well	ADV
ma-77	96	40	-	-	PUNCT
ma-77	96	41	known	know	VERB
ma-77	96	42	classes	class	NOUN
ma-77	96	43	ofanalytic	ofanalytic	ADJ
ma-77	96	44	functions	function	NOUN
ma-77	96	45	that	that	PRON
ma-77	96	46	have	have	AUX
ma-77	96	47	been	be	AUX
ma-77	96	48	studied	study	VERB
ma-77	96	49	by	by	ADP
ma-77	96	50	some	some	DET
ma-77	96	51	authors	author	NOUN
ma-77	96	52	.	.	PUNCT
ma-77	97	1	these	these	PRON
ma-77	97	2	are	be	AUX
ma-77	97	3	cited	cite	VERB
ma-77	97	4	in	in	ADP
ma-77	97	5	our	our	PRON
ma-77	97	6	corollaries	corollary	NOUN
ma-77	97	7	andremarks.the	andremarks.the	DET
ma-77	97	8	following	follow	VERB
ma-77	97	9	are	be	AUX
ma-77	97	10	the	the	DET
ma-77	97	11	proved	prove	VERB
ma-77	97	12	results	result	NOUN
ma-77	97	13	.	.	PUNCT
ma-77	98	1	theorem	theorem	VERB
ma-77	98	2	3.1	3.1	NUM
ma-77	98	3	.	.	PUNCT
ma-77	99	1	let	let	VERB
ma-77	99	2	β	β	X
ma-77	99	3	∈	∈	PROPN
ma-77	99	4	(	(	PUNCT
ma-77	99	5	−π	−π	PROPN
ma-77	99	6	,	,	PUNCT
ma-77	99	7	π	π	X
ma-77	99	8	]	]	PUNCT
ma-77	99	9	and	and	CCONJ
ma-77	99	10	δ	δ	PROPN
ma-77	99	11	∈	∈	PROPN
ma-77	100	1	[	[	X
ma-77	100	2	0	0	NUM
ma-77	100	3	,	,	PUNCT
ma-77	100	4	1	1	NUM
ma-77	100	5	)	)	PUNCT
ma-77	100	6	,	,	PUNCT
ma-77	100	7	if	if	SCONJ
ma-77	100	8	condition	condition	NOUN
ma-77	100	9	(	(	PUNCT
ma-77	100	10	6	6	NUM
ma-77	100	11	)	)	PUNCT
ma-77	100	12	holds	hold	VERB
ma-77	100	13	,	,	PUNCT
ma-77	100	14	then	then	ADV
ma-77	100	15	eq(β	eq(β	X
ma-77	100	16	,	,	PUNCT
ma-77	100	17	δ	δ	PROPN
ma-77	100	18	)	)	PUNCT
ma-77	101	1	⊂	⊂	PROPN
ma-77	101	2	bt	bt	PROPN
ma-77	101	3	q(δ	q(δ	NOUN
ma-77	101	4	)	)	PUNCT
ma-77	101	5	.	.	PUNCT
ma-77	102	1	bt	bt	NOUN
ma-77	102	2	q(δ	q(δ	NOUN
ma-77	102	3	)	)	PUNCT
ma-77	102	4	is	be	AUX
ma-77	102	5	the	the	DET
ma-77	102	6	class	class	NOUN
ma-77	102	7	of	of	ADP
ma-77	102	8	q	q	NOUN
ma-77	102	9	-	-	PUNCT
ma-77	102	10	bounded	bounded	ADJ
ma-77	102	11	turning	turning	NOUN
ma-77	102	12	function	function	NOUN
ma-77	102	13	of	of	ADP
ma-77	102	14	order	order	NOUN
ma-77	102	15	δ	δ	PROPN
ma-77	102	16	.	.	PUNCT
ma-77	102	17	proof	proof	NOUN
ma-77	102	18	.	.	PUNCT
ma-77	103	1	let	let	VERB
ma-77	103	2	p(z	p(z	VERB
ma-77	103	3	)	)	PUNCT
ma-77	103	4	=	=	PUNCT
ma-77	103	5	dqf	dqf	NOUN
ma-77	103	6	(	(	PUNCT
ma-77	103	7	z	z	NOUN
ma-77	103	8	)	)	PUNCT
ma-77	103	9	so	so	SCONJ
ma-77	103	10	that	that	PRON
ma-77	103	11	dqp(z	dqp(z	NOUN
ma-77	103	12	)	)	PUNCT
ma-77	103	13	=	=	SYM
ma-77	103	14	d2qf	d2qf	X
ma-77	103	15	(	(	PUNCT
ma-77	103	16	z	z	NOUN
ma-77	103	17	)	)	PUNCT
ma-77	103	18	and	and	CCONJ
ma-77	103	19	for	for	ADP
ma-77	103	20	κ	κ	NOUN
ma-77	103	21	=	=	PUNCT
ma-77	103	22	(	(	PUNCT
ma-77	104	1	1	1	NUM
ma-77	104	2	+	+	NUM
ma-77	104	3	e	e	NOUN
ma-77	104	4	iβ)/2	iβ)/2	NOUN
ma-77	104	5	,	,	PUNCT
ma-77	104	6	then	then	ADV
ma-77	104	7	(	(	PUNCT
ma-77	104	8	6	6	X
ma-77	104	9	)	)	PUNCT
ma-77	104	10	can	can	AUX
ma-77	104	11	beexpressed	beexpresse	VERB
ma-77	104	12	as	as	ADP
ma-77	104	13	re(p(z	re(p(z	ADJ
ma-77	104	14	)	)	PUNCT
ma-77	104	15	+	+	CCONJ
ma-77	104	16	κzdqp(z	κzdqp(z	NOUN
ma-77	104	17	)	)	PUNCT
ma-77	104	18	)	)	PUNCT
ma-77	104	19	>	>	X
ma-77	105	1	δ	δ	PROPN
ma-77	105	2	.	.	PUNCT
ma-77	106	1	(	(	PUNCT
ma-77	106	2	7	7	X
ma-77	106	3	)	)	PUNCT
ma-77	106	4	in	in	ADP
ma-77	106	5	view	view	NOUN
ma-77	106	6	of	of	ADP
ma-77	106	7	the	the	DET
ma-77	106	8	conditions	condition	NOUN
ma-77	106	9	in	in	ADP
ma-77	106	10	lemma	lemma	PROPN
ma-77	106	11	2.3	2.3	NUM
ma-77	106	12	and	and	CCONJ
ma-77	106	13	for	for	ADP
ma-77	106	14	p(z	p(z	NOUN
ma-77	106	15	)	)	PUNCT
ma-77	106	16	in	in	ADP
ma-77	106	17	(	(	PUNCT
ma-77	106	18	7	7	NUM
ma-77	106	19	)	)	PUNCT
ma-77	106	20	,	,	PUNCT
ma-77	106	21	we	we	PRON
ma-77	106	22	define	define	VERB
ma-77	106	23	the	the	DET
ma-77	106	24	function	function	NOUN
ma-77	106	25	γ(u	γ(u	NOUN
ma-77	106	26	,	,	PUNCT
ma-77	106	27	ν	ν	NOUN
ma-77	106	28	)	)	PUNCT
ma-77	106	29	=	=	SYM
ma-77	106	30	u	u	NOUN
ma-77	107	1	+	+	X
ma-77	107	2	κν	κν	ADV
ma-77	107	3	on	on	ADP
ma-77	107	4	the	the	DET
ma-77	107	5	domain	domain	NOUN
ma-77	107	6	π	π	PROPN
ma-77	107	7	of	of	ADP
ma-77	107	8	c2	c2	PROPN
ma-77	107	9	,	,	PUNCT
ma-77	107	10	then(i	then(i	PROPN
ma-77	107	11	)	)	PUNCT
ma-77	107	12	clearly	clearly	ADV
ma-77	107	13	,	,	PUNCT
ma-77	107	14	γ(u	γ(u	PROPN
ma-77	107	15	,	,	PUNCT
ma-77	107	16	ν	ν	NOUN
ma-77	107	17	)	)	PUNCT
ma-77	107	18	satisfies	satisfy	VERB
ma-77	107	19	the	the	DET
ma-77	107	20	condition	condition	NOUN
ma-77	107	21	(	(	PUNCT
ma-77	107	22	1	1	NUM
ma-77	107	23	)	)	PUNCT
ma-77	107	24	in	in	ADP
ma-77	107	25	lemma	lemma	PROPN
ma-77	107	26	2.3,(ii	2.3,(ii	NUM
ma-77	107	27	)	)	PUNCT
ma-77	107	28	for	for	ADP
ma-77	107	29	(	(	PUNCT
ma-77	107	30	1	1	NUM
ma-77	107	31	,	,	PUNCT
ma-77	107	32	0	0	NUM
ma-77	107	33	)	)	PUNCT
ma-77	107	34	∈	∈	PROPN
ma-77	107	35	π	π	PROPN
ma-77	107	36	,	,	PUNCT
ma-77	107	37	γ(1	γ(1	PROPN
ma-77	107	38	,	,	PUNCT
ma-77	107	39	0	0	NUM
ma-77	107	40	)	)	PUNCT
ma-77	107	41	=	=	SYM
ma-77	108	1	1	1	NUM
ma-77	108	2	=	=	NOUN
ma-77	108	3	⇒	⇒	NOUN
ma-77	108	4	re(γ(1	re(γ(1	NOUN
ma-77	108	5	,	,	PUNCT
ma-77	108	6	0	0	NUM
ma-77	108	7	)	)	PUNCT
ma-77	108	8	)	)	PUNCT
ma-77	109	1	>	>	SYM
ma-77	109	2	0	0	NUM
ma-77	109	3	and(iii	and(iii	NOUN
ma-77	109	4	)	)	PUNCT
ma-77	110	1	γ(δ	γ(δ	PROPN
ma-77	110	2	+	+	CCONJ
ma-77	110	3	(	(	PUNCT
ma-77	110	4	1−	1−	NUM
ma-77	110	5	δ)u2i	δ)u2i	NOUN
ma-77	110	6	,	,	PUNCT
ma-77	110	7	ν1	ν1	NOUN
ma-77	110	8	)	)	PUNCT
ma-77	110	9	=	=	SYM
ma-77	110	10	δ	δ	PROPN
ma-77	110	11	+	+	CCONJ
ma-77	110	12	1+cos	1+cos	NUM
ma-77	110	13	δ2	δ2	VERB
ma-77	110	14	ν1	ν1	NOUN
ma-77	110	15	+	+	CCONJ
ma-77	110	16	(	(	PUNCT
ma-77	110	17	(	(	PUNCT
ma-77	110	18	1−	1−	NUM
ma-77	110	19	δ)u2	δ)u2	PROPN
ma-77	110	20	+	+	CCONJ
ma-77	110	21	sin	sin	NOUN
ma-77	110	22	δ2	δ2	VERB
ma-77	110	23	ν1	ν1	NOUN
ma-77	110	24	)	)	PUNCT
ma-77	111	1	i	i	PRON
ma-77	111	2	,	,	PUNCT
ma-77	111	3	thus	thus	ADV
ma-77	111	4	,	,	PUNCT
ma-77	111	5	re(γ(δ	re(γ(δ	X
ma-77	111	6	+	+	CCONJ
ma-77	111	7	(	(	PUNCT
ma-77	111	8	1−	1−	NUM
ma-77	111	9	δ)u2i	δ)u2i	NOUN
ma-77	111	10	,	,	PUNCT
ma-77	111	11	ν1	ν1	NOUN
ma-77	111	12	)	)	PUNCT
ma-77	111	13	)	)	PUNCT
ma-77	112	1	=	=	PUNCT
ma-77	112	2	δ	δ	PROPN
ma-77	112	3	+	+	CCONJ
ma-77	112	4	1	1	NUM
ma-77	112	5	+	+	NUM
ma-77	112	6	cosβ	cosβ	NOUN
ma-77	112	7	2	2	NUM
ma-77	112	8	ν1	ν1	NOUN
ma-77	112	9	≤	≤	NUM
ma-77	112	10	δ	δ	PROPN
ma-77	112	11	for	for	ADP
ma-77	112	12	ν1	ν1	NOUN
ma-77	112	13	≤	≤	NOUN
ma-77	112	14	−12(1−	−12(1−	PROPN
ma-77	112	15	δ)(1	δ)(1	X
ma-77	112	16	+	+	CCONJ
ma-77	112	17	u22	u22	NOUN
ma-77	112	18	)	)	PUNCT
ma-77	112	19	.	.	PUNCT
ma-77	113	1	https://doi.org/10.28924/ada/ma.2.12	https://doi.org/10.28924/ada/ma.2.12	PROPN
ma-77	113	2	eur	eur	PROPN
ma-77	113	3	.	.	PUNCT
ma-77	114	1	j.	j.	PROPN
ma-77	114	2	math	math	PROPN
ma-77	114	3	.	.	PUNCT
ma-77	115	1	anal	anal	PROPN
ma-77	115	2	.	.	PUNCT
ma-77	116	1	10.28924	10.28924	NUM
ma-77	116	2	/	/	SYM
ma-77	116	3	ada	ada	PROPN
ma-77	116	4	/	/	SYM
ma-77	116	5	ma.2.12	ma.2.12	NOUN
ma-77	116	6	4now	4now	PROPN
ma-77	116	7	since	since	SCONJ
ma-77	116	8	γ(u	γ(u	PROPN
ma-77	116	9	,	,	PUNCT
ma-77	116	10	ν	ν	NOUN
ma-77	116	11	)	)	PUNCT
ma-77	116	12	satisfies	satisfie	NOUN
ma-77	116	13	all	all	DET
ma-77	116	14	the	the	DET
ma-77	116	15	conditions	condition	NOUN
ma-77	116	16	(	(	PUNCT
ma-77	116	17	1−	1−	NUM
ma-77	116	18	3	3	NUM
ma-77	116	19	)	)	PUNCT
ma-77	116	20	in	in	ADP
ma-77	116	21	lemma	lemma	PROPN
ma-77	116	22	2.3	2.3	NUM
ma-77	116	23	,	,	PUNCT
ma-77	116	24	then	then	ADV
ma-77	116	25	it	it	PRON
ma-77	116	26	implies	imply	VERB
ma-77	116	27	that	that	SCONJ
ma-77	116	28	rep(z	rep(z	NOUN
ma-77	116	29	)	)	PUNCT
ma-77	117	1	=	=	SYM
ma-77	117	2	re(dqf	re(dqf	NOUN
ma-77	117	3	(	(	PUNCT
ma-77	117	4	z	z	NOUN
ma-77	117	5	)	)	PUNCT
ma-77	117	6	)	)	PUNCT
ma-77	117	7	>	>	PUNCT
ma-77	118	1	δ	δ	PROPN
ma-77	118	2	,	,	PUNCT
ma-77	118	3	z	z	PROPN
ma-77	118	4	∈	∈	PROPN
ma-77	118	5	ud	ud	INTJ
ma-77	118	6	hence	hence	ADV
ma-77	118	7	the	the	DET
ma-77	118	8	proof	proof	NOUN
ma-77	118	9	is	be	AUX
ma-77	118	10	complete	complete	ADJ
ma-77	118	11	.	.	PUNCT
ma-77	119	1	�	�	PROPN
ma-77	119	2	corollary	corollary	ADJ
ma-77	119	3	3.2	3.2	NUM
ma-77	119	4	(	(	PUNCT
ma-77	119	5	[	[	X
ma-77	119	6	1	1	NUM
ma-77	119	7	]	]	PUNCT
ma-77	119	8	)	)	PUNCT
ma-77	119	9	.	.	PUNCT
ma-77	120	1	since	since	SCONJ
ma-77	120	2	class	class	NOUN
ma-77	120	3	bt	bt	NOUN
ma-77	120	4	q(δ	q(δ	NOUN
ma-77	120	5	)	)	PUNCT
ma-77	120	6	is	be	AUX
ma-77	120	7	well	well	ADV
ma-77	120	8	-	-	PUNCT
ma-77	120	9	known	know	VERB
ma-77	120	10	to	to	PART
ma-77	120	11	consist	consist	VERB
ma-77	120	12	of	of	ADP
ma-77	120	13	univalent	univalent	ADJ
ma-77	120	14	functions	function	NOUN
ma-77	120	15	,	,	PUNCT
ma-77	120	16	then	then	ADV
ma-77	120	17	eq(β	eq(β	X
ma-77	120	18	,	,	PUNCT
ma-77	120	19	δ	δ	PROPN
ma-77	120	20	)	)	PUNCT
ma-77	120	21	⊂	⊂	PROPN
ma-77	120	22	bt	bt	PROPN
ma-77	120	23	q(δ	q(δ	NOUN
ma-77	120	24	)	)	PUNCT
ma-77	120	25	consists	consist	VERB
ma-77	120	26	of	of	ADP
ma-77	120	27	univalent	univalent	ADJ
ma-77	120	28	functions	function	NOUN
ma-77	120	29	.	.	PUNCT
ma-77	121	1	corollary	corollary	ADJ
ma-77	121	2	3.3	3.3	NUM
ma-77	121	3	.	.	PUNCT
ma-77	122	1	lim	lim	PROPN
ma-77	122	2	q↑1	q↑1	PROPN
ma-77	122	3	eq(β	eq(β	NOUN
ma-77	122	4	,	,	PUNCT
ma-77	122	5	δ	δ	PROPN
ma-77	122	6	)	)	PUNCT
ma-77	122	7	⊂	⊂	PROPN
ma-77	122	8	bt	bt	PROPN
ma-77	122	9	(	(	PUNCT
ma-77	122	10	δ	δ	PROPN
ma-77	122	11	)	)	PUNCT
ma-77	122	12	,	,	PUNCT
ma-77	122	13	z	z	PROPN
ma-77	122	14	∈	∈	PROPN
ma-77	122	15	ud	ud	INTJ
ma-77	122	16	.	.	PUNCT
ma-77	122	17	theorem	theorem	VERB
ma-77	122	18	3.4	3.4	NUM
ma-77	122	19	.	.	PUNCT
ma-77	123	1	if	if	SCONJ
ma-77	123	2	f	f	PROPN
ma-77	123	3	∈	∈	PROPN
ma-77	123	4	a	a	PRON
ma-77	123	5	is	be	AUX
ma-77	123	6	such	such	ADJ
ma-77	123	7	that	that	SCONJ
ma-77	123	8	re	re	ADP
ma-77	123	9	(	(	PUNCT
ma-77	123	10	zdq(dqf	zdq(dqf	X
ma-77	123	11	(	(	PUNCT
ma-77	123	12	z	z	NOUN
ma-77	123	13	)	)	PUNCT
ma-77	124	1	+	+	CCONJ
ma-77	124	2	κzd2qf	κzd2qf	X
ma-77	124	3	(	(	PUNCT
ma-77	124	4	z	z	NOUN
ma-77	124	5	)	)	PUNCT
ma-77	124	6	)	)	PUNCT
ma-77	124	7	dqf	dqf	NOUN
ma-77	124	8	(	(	PUNCT
ma-77	124	9	z	z	NOUN
ma-77	124	10	)	)	PUNCT
ma-77	125	1	+	+	CCONJ
ma-77	125	2	κzd2qf	κzd2qf	X
ma-77	125	3	(	(	PUNCT
ma-77	125	4	z	z	NOUN
ma-77	125	5	)	)	PUNCT
ma-77	125	6	)	)	PUNCT
ma-77	125	7	>	>	PUNCT
ma-77	126	1	δ	δ	X
ma-77	127	1	−	−	NOUN
ma-77	127	2	1	1	NUM
ma-77	127	3	2δ	2δ	NOUN
ma-77	127	4	,	,	PUNCT
ma-77	127	5	(	(	PUNCT
ma-77	127	6	8)	8)	NUM
ma-77	127	7	then	then	ADV
ma-77	127	8	re(dqf	re(dqf	VERB
ma-77	127	9	(	(	PUNCT
ma-77	127	10	z	z	NOUN
ma-77	127	11	)	)	PUNCT
ma-77	128	1	+	+	CCONJ
ma-77	128	2	κzd2qf	κzd2qf	X
ma-77	128	3	(	(	PUNCT
ma-77	128	4	z	z	NOUN
ma-77	128	5	)	)	PUNCT
ma-77	128	6	)	)	PUNCT
ma-77	128	7	>	>	X
ma-77	129	1	2(δ−1)/δ	2(δ−1)/δ	NUM
ma-77	129	2	,	,	PUNCT
ma-77	129	3	δ	δ	PROPN
ma-77	129	4	∈	∈	PROPN
ma-77	130	1	[	[	X
ma-77	130	2	1/2	1/2	NUM
ma-77	130	3	,	,	PUNCT
ma-77	130	4	1	1	NUM
ma-77	130	5	)	)	PUNCT
ma-77	130	6	,	,	PUNCT
ma-77	130	7	z	z	NOUN
ma-77	130	8	∈	∈	PROPN
ma-77	130	9	ud	ud	INTJ
ma-77	130	10	and	and	CCONJ
ma-77	130	11	κ	κ	X
ma-77	130	12	=	=	PUNCT
ma-77	130	13	(	(	PUNCT
ma-77	130	14	1	1	NUM
ma-77	130	15	+	+	NUM
ma-77	130	16	e	e	NOUN
ma-77	130	17	iβ)/2	iβ)/2	NOUN
ma-77	130	18	.	.	PUNCT
ma-77	131	1	proof	proof	NOUN
ma-77	131	2	.	.	PUNCT
ma-77	132	1	from	from	ADP
ma-77	132	2	(	(	PUNCT
ma-77	132	3	6	6	NUM
ma-77	132	4	)	)	PUNCT
ma-77	132	5	,	,	PUNCT
ma-77	132	6	let	let	VERB
ma-77	132	7	p(z	p(z	VERB
ma-77	132	8	)	)	PUNCT
ma-77	133	1	=	=	PUNCT
ma-77	133	2	dqf	dqf	NOUN
ma-77	133	3	(	(	PUNCT
ma-77	133	4	z	z	NOUN
ma-77	133	5	)	)	PUNCT
ma-77	133	6	+	+	CCONJ
ma-77	133	7	κzd2qf	κzd2qf	X
ma-77	133	8	(	(	PUNCT
ma-77	133	9	z	z	NOUN
ma-77	133	10	)	)	PUNCT
ma-77	133	11	,	,	PUNCT
ma-77	133	12	then	then	ADV
ma-77	133	13	by	by	ADP
ma-77	133	14	logarithmic	logarithmic	ADJ
ma-77	133	15	q	q	NOUN
ma-77	133	16	-	-	PUNCT
ma-77	133	17	differentiation	differentiation	NOUN
ma-77	133	18	we	we	PRON
ma-77	133	19	obtain	obtain	VERB
ma-77	133	20	zdqp(z	zdqp(z	NOUN
ma-77	133	21	)	)	PUNCT
ma-77	133	22	p(z	p(z	PROPN
ma-77	133	23	)	)	PUNCT
ma-77	134	1	+	+	CCONJ
ma-77	134	2	1	1	NUM
ma-77	134	3	=	=	NOUN
ma-77	134	4	zdq(dqf	zdq(dqf	NOUN
ma-77	134	5	(	(	PUNCT
ma-77	134	6	z	z	NOUN
ma-77	134	7	)	)	PUNCT
ma-77	134	8	+	+	CCONJ
ma-77	134	9	κzd2qf	κzd2qf	X
ma-77	134	10	(	(	PUNCT
ma-77	134	11	z	z	NOUN
ma-77	134	12	)	)	PUNCT
ma-77	134	13	)	)	PUNCT
ma-77	134	14	dqf	dqf	NOUN
ma-77	134	15	(	(	PUNCT
ma-77	134	16	z	z	NOUN
ma-77	134	17	)	)	PUNCT
ma-77	135	1	+	+	CCONJ
ma-77	135	2	κzd2qf	κzd2qf	X
ma-77	135	3	(	(	PUNCT
ma-77	135	4	z	z	NOUN
ma-77	135	5	)	)	PUNCT
ma-77	135	6	+	+	NOUN
ma-77	135	7	1	1	X
ma-77	135	8	.	.	PUNCT
ma-77	135	9	now	now	ADV
ma-77	135	10	applying	apply	VERB
ma-77	135	11	lemma	lemma	PROPN
ma-77	135	12	2.2	2.2	NUM
ma-77	135	13	gives	give	NOUN
ma-77	135	14	re	re	PROPN
ma-77	135	15	(	(	PUNCT
ma-77	135	16	zdqp(z	zdqp(z	NOUN
ma-77	135	17	)	)	PUNCT
ma-77	135	18	p(z	p(z	PROPN
ma-77	135	19	)	)	PUNCT
ma-77	136	1	+	+	CCONJ
ma-77	136	2	1	1	X
ma-77	136	3	)	)	PUNCT
ma-77	136	4	=	=	SYM
ma-77	136	5	re	re	X
ma-77	136	6	(	(	PUNCT
ma-77	136	7	zdq(dqf	zdq(dqf	X
ma-77	136	8	(	(	PUNCT
ma-77	136	9	z	z	NOUN
ma-77	136	10	)	)	PUNCT
ma-77	136	11	+	+	CCONJ
ma-77	136	12	κzd2qf	κzd2qf	X
ma-77	136	13	(	(	PUNCT
ma-77	136	14	z	z	NOUN
ma-77	136	15	)	)	PUNCT
ma-77	136	16	)	)	PUNCT
ma-77	136	17	dqf	dqf	NOUN
ma-77	136	18	(	(	PUNCT
ma-77	136	19	z	z	NOUN
ma-77	136	20	)	)	PUNCT
ma-77	137	1	+	+	CCONJ
ma-77	137	2	κzd2qf	κzd2qf	X
ma-77	137	3	(	(	PUNCT
ma-77	137	4	z	z	NOUN
ma-77	137	5	)	)	PUNCT
ma-77	137	6	+	+	CCONJ
ma-77	138	1	1	1	X
ma-77	138	2	)	)	PUNCT
ma-77	138	3	>	>	X
ma-77	138	4	3δ	3δ	NUM
ma-77	138	5	−	−	NUM
ma-77	138	6	1	1	NUM
ma-77	138	7	2δ	2δ	NOUN
ma-77	138	8	implies	imply	VERB
ma-77	138	9	that	that	SCONJ
ma-77	139	1	re	re	VERB
ma-77	139	2	(	(	PUNCT
ma-77	139	3	zdq(dqf	zdq(dqf	X
ma-77	139	4	(	(	PUNCT
ma-77	139	5	z	z	NOUN
ma-77	139	6	)	)	PUNCT
ma-77	139	7	+	+	CCONJ
ma-77	139	8	κzd2qf	κzd2qf	X
ma-77	139	9	(	(	PUNCT
ma-77	139	10	z	z	NOUN
ma-77	139	11	)	)	PUNCT
ma-77	139	12	)	)	PUNCT
ma-77	139	13	dqf	dqf	NOUN
ma-77	139	14	(	(	PUNCT
ma-77	139	15	z	z	NOUN
ma-77	139	16	)	)	PUNCT
ma-77	140	1	+	+	CCONJ
ma-77	140	2	κzd2qf	κzd2qf	X
ma-77	140	3	(	(	PUNCT
ma-77	140	4	z	z	NOUN
ma-77	140	5	)	)	PUNCT
ma-77	140	6	)	)	PUNCT
ma-77	140	7	>	>	PUNCT
ma-77	141	1	δ	δ	X
ma-77	142	1	−	−	NOUN
ma-77	142	2	1	1	NUM
ma-77	142	3	2δ	2δ	NUM
ma-77	142	4	and	and	CCONJ
ma-77	142	5	by	by	ADP
ma-77	142	6	the	the	DET
ma-77	142	7	same	same	ADJ
ma-77	142	8	lemma	lemma	PROPN
ma-77	142	9	2.2	2.2	NUM
ma-77	142	10	the	the	DET
ma-77	142	11	proof	proof	NOUN
ma-77	142	12	in	in	ADP
ma-77	142	13	complete	complete	ADJ
ma-77	142	14	.	.	PUNCT
ma-77	143	1	�	�	PROPN
ma-77	143	2	corollary	corollary	ADJ
ma-77	143	3	3.5	3.5	NUM
ma-77	143	4	.	.	PUNCT
ma-77	144	1	if	if	SCONJ
ma-77	144	2	f	f	PROPN
ma-77	144	3	∈	∈	PROPN
ma-77	144	4	a	a	DET
ma-77	144	5	satisfies	satisfie	NOUN
ma-77	144	6	condition	condition	NOUN
ma-77	144	7	(	(	PUNCT
ma-77	144	8	8)	8)	NUM
ma-77	144	9	,	,	PUNCT
ma-77	144	10	then	then	ADV
ma-77	144	11	f	f	PROPN
ma-77	144	12	∈	∈	PROPN
ma-77	144	13	eq(β	eq(β	X
ma-77	144	14	,	,	PUNCT
ma-77	144	15	2(δ−1)/δ	2(δ−1)/δ	NUM
ma-77	144	16	)	)	PUNCT
ma-77	144	17	.	.	PUNCT
ma-77	145	1	corollary	corollary	ADJ
ma-77	145	2	3.6	3.6	NUM
ma-77	145	3	.	.	PUNCT
ma-77	146	1	if	if	SCONJ
ma-77	146	2	f	f	PROPN
ma-77	146	3	∈	∈	PROPN
ma-77	146	4	lim	lim	PROPN
ma-77	146	5	q↑1	q↑1	PROPN
ma-77	146	6	eq(β	eq(β	NOUN
ma-77	146	7	,	,	PUNCT
ma-77	146	8	1/2	1/2	NUM
ma-77	146	9	)	)	PUNCT
ma-77	146	10	is	be	AUX
ma-77	146	11	such	such	ADJ
ma-77	146	12	that	that	SCONJ
ma-77	146	13	re	re	ADP
ma-77	146	14	(	(	PUNCT
ma-77	146	15	z(1	z(1	PROPN
ma-77	146	16	+	+	CCONJ
ma-77	146	17	κ)f	κ)f	ADJ
ma-77	146	18	′′(z	′′(z	NOUN
ma-77	146	19	)	)	PUNCT
ma-77	147	1	+	+	CCONJ
ma-77	147	2	κz2f	κz2f	PROPN
ma-77	147	3	′′′(z	′′′(z	PROPN
ma-77	147	4	)	)	PUNCT
ma-77	147	5	f	f	PROPN
ma-77	147	6	′(z	′(z	NOUN
ma-77	147	7	)	)	PUNCT
ma-77	147	8	+	+	CCONJ
ma-77	147	9	κzf	κzf	PROPN
ma-77	147	10	′′(z	′′(z	NOUN
ma-77	147	11	)	)	PUNCT
ma-77	147	12	)	)	PUNCT
ma-77	147	13	>	>	PUNCT
ma-77	148	1	−	−	NUM
ma-77	148	2	1	1	NUM
ma-77	148	3	2	2	NUM
ma-77	148	4	,	,	PUNCT
ma-77	148	5	then	then	ADV
ma-77	148	6	re(f	re(f	PUNCT
ma-77	148	7	′(z	′(z	NOUN
ma-77	148	8	)	)	PUNCT
ma-77	149	1	+	+	CCONJ
ma-77	149	2	κzf	κzf	NOUN
ma-77	149	3	′′(z	′′(z	NOUN
ma-77	149	4	)	)	PUNCT
ma-77	149	5	)	)	PUNCT
ma-77	150	1	>	>	PUNCT
ma-77	150	2	1/2	1/2	NUM
ma-77	150	3	,	,	PUNCT
ma-77	150	4	z	z	PROPN
ma-77	150	5	∈	∈	PROPN
ma-77	150	6	ud	ud	INTJ
ma-77	150	7	.	.	PUNCT
ma-77	151	1	https://doi.org/10.28924/ada/ma.2.12	https://doi.org/10.28924/ada/ma.2.12	PROPN
ma-77	151	2	eur	eur	PROPN
ma-77	151	3	.	.	PUNCT
ma-77	152	1	j.	j.	PROPN
ma-77	152	2	math	math	PROPN
ma-77	152	3	.	.	PUNCT
ma-77	153	1	anal	anal	PROPN
ma-77	153	2	.	.	PUNCT
ma-77	154	1	10.28924	10.28924	NUM
ma-77	154	2	/	/	SYM
ma-77	154	3	ada	ada	PROPN
ma-77	154	4	/	/	SYM
ma-77	154	5	ma.2.12	ma.2.12	ADJ
ma-77	154	6	5	5	NUM
ma-77	154	7	corollary	corollary	NOUN
ma-77	154	8	3.7	3.7	NUM
ma-77	154	9	.	.	PUNCT
ma-77	155	1	if	if	SCONJ
ma-77	155	2	f	f	PROPN
ma-77	155	3	∈	∈	PROPN
ma-77	155	4	eq(π	eq(π	NOUN
ma-77	155	5	,	,	PUNCT
ma-77	155	6	1/2	1/2	NUM
ma-77	155	7	)	)	PUNCT
ma-77	155	8	is	be	AUX
ma-77	155	9	such	such	ADJ
ma-77	155	10	that	that	SCONJ
ma-77	155	11	re	re	ADP
ma-77	155	12	(	(	PUNCT
ma-77	155	13	zdq(dqf	zdq(dqf	X
ma-77	155	14	(	(	PUNCT
ma-77	155	15	z	z	NOUN
ma-77	155	16	)	)	PUNCT
ma-77	155	17	)	)	PUNCT
ma-77	155	18	dqf	dqf	NOUN
ma-77	155	19	(	(	PUNCT
ma-77	155	20	z	z	NOUN
ma-77	155	21	)	)	PUNCT
ma-77	155	22	)	)	PUNCT
ma-77	155	23	>	>	PUNCT
ma-77	156	1	−	−	NUM
ma-77	156	2	1	1	NUM
ma-77	156	3	2	2	NUM
ma-77	156	4	,	,	PUNCT
ma-77	156	5	(	(	PUNCT
ma-77	156	6	9	9	NUM
ma-77	156	7	)	)	PUNCT
ma-77	156	8	then	then	ADV
ma-77	156	9	re(dqf	re(dqf	VERB
ma-77	156	10	(	(	PUNCT
ma-77	156	11	z	z	NOUN
ma-77	156	12	)	)	PUNCT
ma-77	156	13	)	)	PUNCT
ma-77	156	14	>	>	PUNCT
ma-77	156	15	1	1	NUM
ma-77	156	16	2	2	NUM
ma-77	156	17	.	.	PUNCT
ma-77	157	1	this	this	PRON
ma-77	157	2	means	mean	VERB
ma-77	157	3	that	that	SCONJ
ma-77	157	4	if	if	SCONJ
ma-77	157	5	condition	condition	NOUN
ma-77	157	6	(	(	PUNCT
ma-77	157	7	9	9	NUM
ma-77	157	8	)	)	PUNCT
ma-77	157	9	holds	hold	VERB
ma-77	157	10	,	,	PUNCT
ma-77	157	11	then	then	ADV
ma-77	157	12	f	f	PROPN
ma-77	157	13	is	be	AUX
ma-77	157	14	a	a	DET
ma-77	157	15	q	q	ADJ
ma-77	157	16	-	-	PUNCT
ma-77	157	17	bounded	bounded	ADJ
ma-77	157	18	turning	turning	NOUN
ma-77	157	19	function	function	NOUN
ma-77	157	20	of	of	ADP
ma-77	157	21	order	order	NOUN
ma-77	157	22	1/2	1/2	NUM
ma-77	157	23	.	.	PUNCT
ma-77	158	1	now	now	ADV
ma-77	158	2	if	if	SCONJ
ma-77	158	3	q	q	PROPN
ma-77	158	4	↑	↑	PROPN
ma-77	158	5	1	1	NUM
ma-77	158	6	,	,	PUNCT
ma-77	158	7	then	then	ADV
ma-77	158	8	re	re	X
ma-77	158	9	(	(	PUNCT
ma-77	158	10	zf	zf	PROPN
ma-77	158	11	′′(z	′′(z	PROPN
ma-77	158	12	)	)	PUNCT
ma-77	158	13	f	f	PROPN
ma-77	158	14	′(z	′(z	NOUN
ma-77	158	15	)	)	PUNCT
ma-77	158	16	)	)	PUNCT
ma-77	158	17	>	>	PUNCT
ma-77	159	1	−	−	NUM
ma-77	159	2	1	1	NUM
ma-77	159	3	2	2	NUM
ma-77	159	4	,	,	PUNCT
ma-77	159	5	(	(	PUNCT
ma-77	159	6	10	10	NUM
ma-77	159	7	)	)	PUNCT
ma-77	159	8	implies	imply	VERB
ma-77	159	9	re(f	re(f	NOUN
ma-77	159	10	′(z	′(z	NOUN
ma-77	159	11	)	)	PUNCT
ma-77	159	12	)	)	PUNCT
ma-77	159	13	>	>	PUNCT
ma-77	160	1	1	1	NUM
ma-77	160	2	2	2	NUM
ma-77	160	3	z	z	NOUN
ma-77	160	4	∈	∈	PRON
ma-77	160	5	ud	ud	INTJ
ma-77	160	6	.	.	PUNCT
ma-77	161	1	this	this	PRON
ma-77	161	2	means	mean	VERB
ma-77	161	3	that	that	SCONJ
ma-77	161	4	if	if	SCONJ
ma-77	161	5	condition	condition	NOUN
ma-77	161	6	(	(	PUNCT
ma-77	161	7	10	10	NUM
ma-77	161	8	)	)	PUNCT
ma-77	161	9	holds	hold	VERB
ma-77	161	10	,	,	PUNCT
ma-77	161	11	then	then	ADV
ma-77	161	12	f	f	PROPN
ma-77	161	13	is	be	AUX
ma-77	161	14	a	a	DET
ma-77	161	15	bounded	bounded	ADJ
ma-77	161	16	turning	turn	VERB
ma-77	161	17	function	function	NOUN
ma-77	161	18	of	of	ADP
ma-77	161	19	order	order	NOUN
ma-77	161	20	1/2	1/2	NUM
ma-77	161	21	.	.	PUNCT
ma-77	162	1	corollary	corollary	ADJ
ma-77	162	2	3.8	3.8	NUM
ma-77	162	3	.	.	PUNCT
ma-77	163	1	if	if	SCONJ
ma-77	163	2	f	f	PROPN
ma-77	163	3	∈	∈	PROPN
ma-77	163	4	eq(0	eq(0	PROPN
ma-77	163	5	,	,	PUNCT
ma-77	163	6	1/2	1/2	NUM
ma-77	163	7	)	)	PUNCT
ma-77	163	8	is	be	AUX
ma-77	163	9	such	such	ADJ
ma-77	163	10	that	that	SCONJ
ma-77	163	11	re	re	ADP
ma-77	163	12	(	(	PUNCT
ma-77	163	13	zdq(dqf	zdq(dqf	X
ma-77	163	14	(	(	PUNCT
ma-77	163	15	z	z	NOUN
ma-77	163	16	)	)	PUNCT
ma-77	163	17	+	+	CCONJ
ma-77	163	18	zd2qf	zd2qf	NUM
ma-77	163	19	(	(	PUNCT
ma-77	163	20	z	z	NOUN
ma-77	163	21	)	)	PUNCT
ma-77	163	22	)	)	PUNCT
ma-77	163	23	dqf	dqf	NOUN
ma-77	163	24	(	(	PUNCT
ma-77	163	25	z	z	NOUN
ma-77	163	26	)	)	PUNCT
ma-77	164	1	+	+	CCONJ
ma-77	164	2	zd2qf	zd2qf	NUM
ma-77	164	3	(	(	PUNCT
ma-77	164	4	z	z	NOUN
ma-77	164	5	)	)	PUNCT
ma-77	164	6	)	)	PUNCT
ma-77	164	7	>	>	PUNCT
ma-77	165	1	−	−	NUM
ma-77	165	2	1	1	NUM
ma-77	165	3	2	2	NUM
ma-77	165	4	,	,	PUNCT
ma-77	165	5	(	(	PUNCT
ma-77	165	6	11	11	NUM
ma-77	165	7	)	)	PUNCT
ma-77	165	8	then	then	ADV
ma-77	165	9	re(dqf	re(dqf	VERB
ma-77	165	10	(	(	PUNCT
ma-77	165	11	z	z	NOUN
ma-77	165	12	)	)	PUNCT
ma-77	166	1	+	+	CCONJ
ma-77	166	2	zd2qf	zd2qf	NUM
ma-77	166	3	(	(	PUNCT
ma-77	166	4	z	z	NOUN
ma-77	166	5	)	)	PUNCT
ma-77	166	6	)	)	PUNCT
ma-77	166	7	>	>	PUNCT
ma-77	167	1	1	1	NUM
ma-77	167	2	2	2	NUM
ma-77	167	3	and	and	CCONJ
ma-77	167	4	if	if	SCONJ
ma-77	167	5	q	q	PROPN
ma-77	167	6	↑	↑	PROPN
ma-77	167	7	1	1	NUM
ma-77	167	8	,	,	PUNCT
ma-77	167	9	re	re	ADP
ma-77	167	10	(	(	PUNCT
ma-77	167	11	2zf	2zf	ADJ
ma-77	167	12	′′(z	′′(z	NOUN
ma-77	167	13	)	)	PUNCT
ma-77	168	1	+	+	CCONJ
ma-77	168	2	z2f	z2f	PROPN
ma-77	168	3	′′′(z	′′′(z	PROPN
ma-77	168	4	)	)	PUNCT
ma-77	168	5	f	f	PROPN
ma-77	168	6	′(z	′(z	NOUN
ma-77	168	7	)	)	PUNCT
ma-77	169	1	+	+	CCONJ
ma-77	169	2	zf	zf	PROPN
ma-77	169	3	′′(z	′′(z	PROPN
ma-77	169	4	)	)	PUNCT
ma-77	169	5	)	)	PUNCT
ma-77	169	6	>	>	PUNCT
ma-77	170	1	−	−	NUM
ma-77	170	2	1	1	NUM
ma-77	170	3	2	2	NUM
ma-77	170	4	implies	imply	VERB
ma-77	170	5	that	that	SCONJ
ma-77	170	6	re(f	re(f	NOUN
ma-77	170	7	′(z	′(z	NOUN
ma-77	170	8	)	)	PUNCT
ma-77	171	1	+	+	CCONJ
ma-77	171	2	zf	zf	PROPN
ma-77	171	3	′′(z	′′(z	PROPN
ma-77	171	4	)	)	PUNCT
ma-77	171	5	)	)	PUNCT
ma-77	172	1	>	>	PUNCT
ma-77	172	2	1/2	1/2	NUM
ma-77	172	3	,	,	PUNCT
ma-77	172	4	z	z	PROPN
ma-77	172	5	∈	∈	PROPN
ma-77	172	6	ud	ud	INTJ
ma-77	172	7	.	.	PUNCT
ma-77	172	8	theorem	theorem	VERB
ma-77	172	9	3.9	3.9	NUM
ma-77	172	10	.	.	PUNCT
ma-77	173	1	let	let	VERB
ma-77	173	2	β	β	X
ma-77	173	3	∈	∈	PROPN
ma-77	173	4	(	(	PUNCT
ma-77	173	5	−π	−π	PROPN
ma-77	173	6	,	,	PUNCT
ma-77	173	7	π	π	X
ma-77	173	8	]	]	PUNCT
ma-77	173	9	and	and	CCONJ
ma-77	173	10	δ	δ	PROPN
ma-77	173	11	∈	∈	PROPN
ma-77	174	1	[	[	X
ma-77	174	2	0	0	NUM
ma-77	174	3	,	,	PUNCT
ma-77	174	4	1	1	NUM
ma-77	174	5	)	)	PUNCT
ma-77	174	6	,	,	PUNCT
ma-77	174	7	then	then	ADV
ma-77	174	8	the	the	DET
ma-77	174	9	function	function	NOUN
ma-77	174	10	f	f	X
ma-77	174	11	(	(	PUNCT
ma-77	174	12	z	z	NOUN
ma-77	174	13	)	)	PUNCT
ma-77	174	14	=	=	SYM
ma-77	175	1	z	z	NOUN
ma-77	176	1	+	+	CCONJ
ma-77	176	2	amz	amz	PROPN
ma-77	176	3	m	m	PROPN
ma-77	176	4	∈	∈	PROPN
ma-77	176	5	eq(β	eq(β	X
ma-77	176	6	,	,	PUNCT
ma-77	176	7	δ	δ	PROPN
ma-77	176	8	)	)	PUNCT
ma-77	176	9	,	,	PUNCT
ma-77	176	10	m	m	VERB
ma-77	176	11	=	=	X
ma-77	176	12	{	{	PUNCT
ma-77	176	13	2	2	NUM
ma-77	176	14	,	,	PUNCT
ma-77	176	15	3	3	NUM
ma-77	176	16	,	,	PUNCT
ma-77	176	17	.	.	PUNCT
ma-77	176	18	.	.	PUNCT
ma-77	176	19	.	.	PUNCT
ma-77	177	1	}	}	PUNCT
ma-77	177	2	(	(	PUNCT
ma-77	177	3	12	12	NUM
ma-77	177	4	)	)	PUNCT
ma-77	177	5	if	if	SCONJ
ma-77	177	6	|am|	|am|	NOUN
ma-77	177	7	≤	≤	NOUN
ma-77	177	8	2	2	NUM
ma-77	178	1	[	[	X
ma-77	178	2	m]q	m]q	X
ma-77	178	3	{	{	PUNCT
ma-77	178	4	|xm|	|xm|	PROPN
ma-77	178	5	−	−	PROPN
ma-77	178	6	(	(	PUNCT
ma-77	178	7	(	(	PUNCT
ma-77	178	8	2	2	NUM
ma-77	178	9	+	+	CCONJ
ma-77	179	1	[	[	X
ma-77	179	2	m	m	NOUN
ma-77	179	3	−	−	NOUN
ma-77	179	4	1]q	1]q	NUM
ma-77	179	5	)	)	PUNCT
ma-77	179	6	cos	cos	ADP
ma-77	179	7	θ	θ	PROPN
ma-77	180	1	+	+	PUNCT
ma-77	181	1	[	[	X
ma-77	181	2	m	m	VERB
ma-77	181	3	−	−	PROPN
ma-77	181	4	1]q	1]q	NUM
ma-77	181	5	cos(β	cos(β	PROPN
ma-77	181	6	+	+	NUM
ma-77	181	7	θ0	θ0	NOUN
ma-77	181	8	)	)	PUNCT
ma-77	181	9	)	)	PUNCT
ma-77	181	10	}	}	PUNCT
ma-77	181	11	(	(	PUNCT
ma-77	181	12	13	13	NUM
ma-77	181	13	)	)	PUNCT
ma-77	181	14	where	where	SCONJ
ma-77	181	15	xm	xm	PROPN
ma-77	182	1	=	=	SYM
ma-77	182	2	2	2	NUM
ma-77	183	1	+	+	CCONJ
ma-77	184	1	[	[	X
ma-77	184	2	m	m	NOUN
ma-77	184	3	−	−	NOUN
ma-77	184	4	1]q(1	1]q(1	NOUN
ma-77	184	5	+	+	CCONJ
ma-77	184	6	e	e	NOUN
ma-77	184	7	iβ	iβ	ADP
ma-77	184	8	)	)	PUNCT
ma-77	184	9	|xm|	|xm|	PROPN
ma-77	184	10	=	=	SYM
ma-77	184	11	√	√	NUM
ma-77	184	12	2	2	NUM
ma-77	184	13	{	{	PUNCT
ma-77	184	14	2	2	NUM
ma-77	184	15	+	+	CCONJ
ma-77	185	1	[	[	X
ma-77	185	2	m	m	NOUN
ma-77	185	3	−	−	NOUN
ma-77	185	4	1]q(2	1]q(2	NUM
ma-77	186	1	+	+	CCONJ
ma-77	187	1	[	[	X
ma-77	187	2	m	m	VERB
ma-77	187	3	−	−	NUM
ma-77	187	4	1]q)(1	1]q)(1	PROPN
ma-77	187	5	+	+	CCONJ
ma-77	187	6	cosβ	cosβ	NOUN
ma-77	187	7	)	)	PUNCT
ma-77	187	8	}	}	PUNCT
ma-77	187	9	≥	≥	NOUN
ma-77	187	10	2	2	NUM
ma-77	187	11			NOUN
ma-77	187	12	(	(	PUNCT
ma-77	187	13	14	14	NUM
ma-77	187	14	)	)	PUNCT
ma-77	187	15	and	and	CCONJ
ma-77	187	16	θ0	θ0	PROPN
ma-77	187	17	attains	attain	VERB
ma-77	187	18	minimum	minimum	ADJ
ma-77	187	19	at	at	ADP
ma-77	187	20	θ0	θ0	PROPN
ma-77	187	21	=	=	PROPN
ma-77	187	22	π	π	PROPN
ma-77	187	23	+	+	CCONJ
ma-77	187	24	arctan	arctan	PROPN
ma-77	187	25	(	(	PUNCT
ma-77	187	26	−[m	−[m	NOUN
ma-77	187	27	−	−	PROPN
ma-77	187	28	1]q	1]q	NUM
ma-77	187	29	sinβ	sinβ	NOUN
ma-77	187	30	2	2	NUM
ma-77	188	1	+	+	CCONJ
ma-77	189	1	[	[	X
ma-77	189	2	m	m	NOUN
ma-77	189	3	−	−	PROPN
ma-77	189	4	1]q(1	1]q(1	NUM
ma-77	189	5	+	+	NUM
ma-77	189	6	cosβ	cosβ	NOUN
ma-77	189	7	)	)	PUNCT
ma-77	189	8	)	)	PUNCT
ma-77	189	9	.	.	PUNCT
ma-77	190	1	(	(	PUNCT
ma-77	190	2	15	15	X
ma-77	190	3	)	)	PUNCT
ma-77	190	4	https://doi.org/10.28924/ada/ma.2.12	https://doi.org/10.28924/ada/ma.2.12	PROPN
ma-77	190	5	eur	eur	NOUN
ma-77	190	6	.	.	PUNCT
ma-77	191	1	j.	j.	PROPN
ma-77	191	2	math	math	PROPN
ma-77	191	3	.	.	PUNCT
ma-77	192	1	anal	anal	PROPN
ma-77	192	2	.	.	PUNCT
ma-77	193	1	10.28924	10.28924	NUM
ma-77	193	2	/	/	SYM
ma-77	193	3	ada	ada	PROPN
ma-77	193	4	/	/	SYM
ma-77	193	5	ma.2.12	ma.2.12	ADJ
ma-77	193	6	6	6	NUM
ma-77	193	7	proof	proof	NOUN
ma-77	193	8	.	.	PUNCT
ma-77	194	1	firstly	firstly	ADV
ma-77	194	2	,	,	PUNCT
ma-77	194	3	applying	apply	VERB
ma-77	194	4	(	(	PUNCT
ma-77	194	5	2	2	NUM
ma-77	194	6	)	)	PUNCT
ma-77	194	7	in	in	ADP
ma-77	194	8	(	(	PUNCT
ma-77	194	9	12	12	NUM
ma-77	194	10	)	)	PUNCT
ma-77	194	11	gives	give	VERB
ma-77	194	12	dqf	dqf	NOUN
ma-77	194	13	(	(	PUNCT
ma-77	194	14	z	z	NOUN
ma-77	194	15	)	)	PUNCT
ma-77	194	16	=	=	SYM
ma-77	195	1	1	1	NUM
ma-77	196	1	+	+	CCONJ
ma-77	196	2	[	[	X
ma-77	196	3	m]qamzm−1	m]qamzm−1	PROPN
ma-77	196	4	zd2qf	zd2qf	NUM
ma-77	196	5	(	(	PUNCT
ma-77	196	6	z	z	NOUN
ma-77	196	7	)	)	PUNCT
ma-77	196	8	=	=	PUNCT
ma-77	197	1	[	[	X
ma-77	197	2	m	m	NOUN
ma-77	197	3	−	−	PROPN
ma-77	197	4	1]q[m]qamzm−1	1]q[m]qamzm−1	NUM
ma-77	197	5	}	}	PUNCT
ma-77	197	6	.	.	PUNCT
ma-77	198	1	(	(	PUNCT
ma-77	198	2	16	16	X
ma-77	198	3	)	)	PUNCT
ma-77	198	4	note	note	NOUN
ma-77	198	5	that	that	SCONJ
ma-77	198	6	it	it	PRON
ma-77	198	7	suffices	suffice	VERB
ma-77	198	8	to	to	PART
ma-77	198	9	study	study	VERB
ma-77	198	10	the	the	DET
ma-77	198	11	condition	condition	NOUN
ma-77	199	1	that	that	SCONJ
ma-77	199	2	for	for	ADP
ma-77	199	3	|z	|z	PROPN
ma-77	199	4	|	|	ADV
ma-77	199	5	=	=	SYM
ma-77	199	6	1,∣∣∣∣dqf	1,∣∣∣∣dqf	NUM
ma-77	199	7	(	(	PUNCT
ma-77	199	8	z	z	NOUN
ma-77	199	9	)	)	PUNCT
ma-77	199	10	+	+	CCONJ
ma-77	199	11	1	1	NUM
ma-77	199	12	+	+	NUM
ma-77	199	13	e	e	VERB
ma-77	199	14	iβ2	iβ2	PROPN
ma-77	199	15	zd2qf	zd2qf	NUM
ma-77	199	16	(	(	PUNCT
ma-77	199	17	z)−	z)−	PROPN
ma-77	199	18	1	1	NUM
ma-77	199	19	∣∣∣∣	∣∣∣∣	NOUN
ma-77	199	20	<	<	X
ma-77	199	21	re	re	X
ma-77	199	22	{	{	PUNCT
ma-77	199	23	dqf	dqf	NOUN
ma-77	199	24	(	(	PUNCT
ma-77	199	25	z	z	NOUN
ma-77	199	26	)	)	PUNCT
ma-77	199	27	+	+	CCONJ
ma-77	199	28	1	1	NUM
ma-77	199	29	+	+	NUM
ma-77	199	30	e	e	VERB
ma-77	199	31	iβ2	iβ2	PROPN
ma-77	199	32	zd2qf	zd2qf	NUM
ma-77	199	33	(	(	PUNCT
ma-77	199	34	z	z	NOUN
ma-77	199	35	)	)	PUNCT
ma-77	199	36	}	}	PUNCT
ma-77	199	37	(	(	PUNCT
ma-77	199	38	17	17	NUM
ma-77	199	39	)	)	PUNCT
ma-77	200	1	so	so	SCONJ
ma-77	200	2	that	that	SCONJ
ma-77	200	3	by	by	ADP
ma-77	200	4	putting	put	VERB
ma-77	200	5	(	(	PUNCT
ma-77	200	6	16	16	NUM
ma-77	200	7	)	)	PUNCT
ma-77	200	8	into	into	ADP
ma-77	200	9	(	(	PUNCT
ma-77	200	10	17	17	NUM
ma-77	200	11	)	)	PUNCT
ma-77	200	12	we	we	PRON
ma-77	200	13	obtain∣∣∣∣[m]qamzm−1	obtain∣∣∣∣[m]qamzm−1	PROPN
ma-77	200	14	+	+	CCONJ
ma-77	200	15	12[m	12[m	NUM
ma-77	200	16	−	−	NOUN
ma-77	200	17	1]q[m]q(1	1]q[m]q(1	NUM
ma-77	200	18	+	+	CCONJ
ma-77	200	19	e	e	PROPN
ma-77	200	20	iβ)amzm−1	iβ)amzm−1	PROPN
ma-77	200	21	∣∣∣∣	∣∣∣∣	PROPN
ma-77	200	22	<	<	X
ma-77	200	23	re	re	X
ma-77	200	24	{	{	PUNCT
ma-77	200	25	1	1	NUM
ma-77	201	1	+	+	CCONJ
ma-77	201	2	[	[	X
ma-77	201	3	m]qamz	m]qamz	X
ma-77	201	4	m−1	m−1	PROPN
ma-77	201	5	+	+	CCONJ
ma-77	201	6	1	1	NUM
ma-77	201	7	2	2	NUM
ma-77	202	1	[	[	X
ma-77	202	2	m	m	NOUN
ma-77	202	3	−	−	NUM
ma-77	203	1	1]q[m]q(1	1]q[m]q(1	NUM
ma-77	203	2	+	+	CCONJ
ma-77	203	3	e	e	X
ma-77	203	4	iβ)amzm−1	iβ)amzm−1	PROPN
ma-77	203	5	}	}	PUNCT
ma-77	203	6	.	.	PUNCT
ma-77	204	1	now	now	ADV
ma-77	204	2	letting	let	VERB
ma-77	204	3	|am|	|am|	NOUN
ma-77	204	4	=	=	NOUN
ma-77	204	5	r	r	NOUN
ma-77	204	6	,	,	PUNCT
ma-77	204	7	amzm−1	amzm−1	X
ma-77	204	8	=	=	PUNCT
ma-77	204	9	re	re	AUX
ma-77	204	10	iθ	iθ	NOUN
ma-77	204	11	and	and	CCONJ
ma-77	204	12	using	use	VERB
ma-77	204	13	(	(	PUNCT
ma-77	204	14	14	14	NUM
ma-77	204	15	)	)	PUNCT
ma-77	204	16	we	we	PRON
ma-77	204	17	obtain∣∣∣∣12[m]qre	obtain∣∣∣∣12[m]qre	NUM
ma-77	204	18	iθxm	iθxm	NOUN
ma-77	204	19	∣∣∣∣	∣∣∣∣	NOUN
ma-77	204	20	≤	≤	NUM
ma-77	204	21	re	re	ADP
ma-77	204	22	{	{	PUNCT
ma-77	204	23	1	1	NUM
ma-77	205	1	+	+	CCONJ
ma-77	205	2	[	[	NOUN
ma-77	205	3	m]qre	m]qre	NOUN
ma-77	205	4	iθ	iθ	VERB
ma-77	205	5	+	+	NOUN
ma-77	205	6	12[m	12[m	NUM
ma-77	205	7	−	−	NOUN
ma-77	205	8	1]q[m]q(1	1]q[m]q(1	NUM
ma-77	206	1	+	+	CCONJ
ma-77	206	2	e	e	NOUN
ma-77	206	3	iβ)re	iβ)re	VERB
ma-77	206	4	iθ	iθ	NOUN
ma-77	206	5	}	}	PUNCT
ma-77	206	6	(	(	PUNCT
ma-77	206	7	18	18	NUM
ma-77	206	8	)	)	PUNCT
ma-77	206	9	so	so	SCONJ
ma-77	206	10	that	that	SCONJ
ma-77	206	11	1	1	NUM
ma-77	206	12	2	2	NUM
ma-77	206	13	[	[	PUNCT
ma-77	206	14	m]qr	m]qr	NOUN
ma-77	206	15	|xm|	|xm|	NOUN
ma-77	206	16	≤	≤	NOUN
ma-77	206	17	re	re	VERB
ma-77	206	18	f	f	PROPN
ma-77	206	19	(	(	PUNCT
ma-77	206	20	19)where	19)where	NUM
ma-77	206	21	f	f	X
ma-77	206	22	=	=	SYM
ma-77	206	23	1	1	NUM
ma-77	206	24	+	+	CCONJ
ma-77	207	1	[	[	X
ma-77	207	2	m]qre	m]qre	NOUN
ma-77	207	3	iθ	iθ	VERB
ma-77	207	4	+	+	NOUN
ma-77	207	5	1	1	NUM
ma-77	207	6	2	2	NUM
ma-77	208	1	[	[	X
ma-77	208	2	m	m	NOUN
ma-77	208	3	−	−	NUM
ma-77	208	4	1]q[m]q(1	1]q[m]q(1	NUM
ma-77	208	5	+	+	CCONJ
ma-77	208	6	e	e	NOUN
ma-77	208	7	iβ)re	iβ)re	X
ma-77	208	8	iθin	iθin	NOUN
ma-77	208	9	(	(	PUNCT
ma-77	208	10	18	18	NUM
ma-77	208	11	)	)	PUNCT
ma-77	208	12	.	.	PUNCT
ma-77	209	1	further	further	ADJ
ma-77	209	2	simplification	simplification	NOUN
ma-77	209	3	gives	give	VERB
ma-77	209	4	f	f	PROPN
ma-77	209	5	=	=	SYM
ma-77	209	6	1	1	NUM
ma-77	209	7	+	+	CCONJ
ma-77	210	1	[	[	X
ma-77	210	2	m]qr	m]qr	NOUN
ma-77	210	3	cos	cos	NOUN
ma-77	210	4	θ	θ	PROPN
ma-77	210	5	+	+	NOUN
ma-77	210	6	1	1	NUM
ma-77	210	7	2	2	NUM
ma-77	211	1	[	[	X
ma-77	211	2	m	m	NOUN
ma-77	211	3	−	−	PROPN
ma-77	211	4	1]q[m]qr	1]q[m]qr	NUM
ma-77	211	5	cos	cos	PROPN
ma-77	211	6	θ	θ	PROPN
ma-77	212	1	+	+	NOUN
ma-77	212	2	1	1	NUM
ma-77	212	3	2	2	NUM
ma-77	213	1	[	[	X
ma-77	213	2	m	m	NOUN
ma-77	213	3	−	−	X
ma-77	213	4	1]q[m]qr	1]q[m]qr	NUM
ma-77	213	5	cos(β	cos(β	NOUN
ma-77	213	6	+	+	NUM
ma-77	213	7	θ	θ	NOUN
ma-77	213	8	)	)	PUNCT
ma-77	213	9	+	+	NUM
ma-77	213	10	im(f	im(f	NOUN
ma-77	213	11	)	)	PUNCT
ma-77	214	1	so	so	SCONJ
ma-77	214	2	that	that	SCONJ
ma-77	214	3	re	re	VERB
ma-77	214	4	f	f	NOUN
ma-77	214	5	=	=	SYM
ma-77	214	6	1	1	NUM
ma-77	214	7	+	+	CCONJ
ma-77	214	8	1	1	NUM
ma-77	214	9	2	2	NUM
ma-77	214	10	[	[	X
ma-77	214	11	m]qr{2	m]qr{2	X
ma-77	214	12	cos	cos	PROPN
ma-77	214	13	θ	θ	PROPN
ma-77	214	14	+	+	PUNCT
ma-77	215	1	[	[	X
ma-77	215	2	m	m	VERB
ma-77	215	3	−	−	X
ma-77	215	4	1]q	1]q	NUM
ma-77	215	5	cos	cos	PROPN
ma-77	215	6	θ	θ	PROPN
ma-77	215	7	+	+	PUNCT
ma-77	216	1	[	[	X
ma-77	216	2	m	m	VERB
ma-77	216	3	−	−	PROPN
ma-77	216	4	1]q	1]q	NUM
ma-77	216	5	cos(β	cos(β	PROPN
ma-77	216	6	+	+	CCONJ
ma-77	216	7	θ	θ	NOUN
ma-77	216	8	)	)	PUNCT
ma-77	216	9	}	}	PUNCT
ma-77	216	10	=	=	SYM
ma-77	216	11	ψ	ψ	X
ma-77	216	12	.	.	PUNCT
ma-77	217	1	(	(	PUNCT
ma-77	217	2	20)now	20)now	NUM
ma-77	217	3	(	(	PUNCT
ma-77	217	4	19	19	NUM
ma-77	217	5	)	)	PUNCT
ma-77	217	6	becomes	become	VERB
ma-77	217	7	1	1	NUM
ma-77	217	8	2	2	NUM
ma-77	217	9	[	[	X
ma-77	217	10	m]qr	m]qr	NOUN
ma-77	217	11	|xm|	|xm|	NOUN
ma-77	217	12	≤	≤	NUM
ma-77	217	13	1	1	NUM
ma-77	217	14	+	+	CCONJ
ma-77	217	15	1	1	NUM
ma-77	217	16	2	2	NUM
ma-77	218	1	[	[	X
ma-77	218	2	m]qr{(2	m]qr{(2	X
ma-77	218	3	+	+	PROPN
ma-77	219	1	[	[	X
ma-77	219	2	m	m	VERB
ma-77	219	3	−	−	NOUN
ma-77	219	4	1]q	1]q	NUM
ma-77	219	5	)	)	PUNCT
ma-77	219	6	cos	cos	ADP
ma-77	219	7	θ	θ	PROPN
ma-77	220	1	+	+	PUNCT
ma-77	221	1	[	[	X
ma-77	221	2	m	m	VERB
ma-77	221	3	−	−	PROPN
ma-77	221	4	1]q	1]q	NUM
ma-77	221	5	cos(β	cos(β	PROPN
ma-77	221	6	+	+	CCONJ
ma-77	221	7	θ	θ	NOUN
ma-77	221	8	)	)	PUNCT
ma-77	221	9	}	}	PUNCT
ma-77	221	10	and	and	CCONJ
ma-77	221	11	by	by	ADP
ma-77	221	12	simplification	simplification	NOUN
ma-77	221	13	we	we	PRON
ma-77	221	14	obtain	obtain	VERB
ma-77	221	15	(	(	PUNCT
ma-77	221	16	13).to	13).to	NOUN
ma-77	221	17	know	know	VERB
ma-77	221	18	the	the	DET
ma-77	221	19	values	value	NOUN
ma-77	221	20	of	of	ADP
ma-77	221	21	θ	θ	PROPN
ma-77	221	22	where	where	SCONJ
ma-77	221	23	(	(	PUNCT
ma-77	221	24	20	20	NUM
ma-77	221	25	)	)	PUNCT
ma-77	221	26	attains	attain	VERB
ma-77	221	27	minimum	minimum	ADJ
ma-77	221	28	implies	imply	VERB
ma-77	221	29	that	that	PRON
ma-77	221	30	∂ψ	∂ψ	VERB
ma-77	222	1	∂θ	∂θ	NOUN
ma-77	223	1	=	=	PUNCT
ma-77	224	1	−	−	NOUN
ma-77	224	2	r	r	NOUN
ma-77	225	1	[	[	X
ma-77	225	2	m]q	m]q	NOUN
ma-77	225	3	2	2	NUM
ma-77	225	4	{	{	PUNCT
ma-77	225	5	(	(	PUNCT
ma-77	225	6	2	2	NUM
ma-77	225	7	+	+	CCONJ
ma-77	226	1	[	[	X
ma-77	226	2	m	m	NOUN
ma-77	226	3	−	−	NOUN
ma-77	226	4	1]q	1]q	NUM
ma-77	226	5	)	)	PUNCT
ma-77	226	6	sin	sin	NOUN
ma-77	226	7	θ	θ	NOUN
ma-77	227	1	+	+	PUNCT
ma-77	228	1	[	[	X
ma-77	228	2	m	m	VERB
ma-77	228	3	−	−	X
ma-77	228	4	1]q	1]q	NUM
ma-77	228	5	sin(β	sin(β	PROPN
ma-77	228	6	+	+	NUM
ma-77	228	7	θ	θ	NOUN
ma-77	228	8	)	)	PUNCT
ma-77	228	9	}	}	PUNCT
ma-77	228	10	implies	imply	VERB
ma-77	228	11	that	that	SCONJ
ma-77	228	12	(	(	PUNCT
ma-77	228	13	2	2	NUM
ma-77	228	14	+	+	CCONJ
ma-77	229	1	[	[	X
ma-77	229	2	m	m	NOUN
ma-77	229	3	−	−	NOUN
ma-77	229	4	1]q	1]q	NUM
ma-77	229	5	)	)	PUNCT
ma-77	229	6	sin	sin	NOUN
ma-77	229	7	θ	θ	NOUN
ma-77	230	1	+	+	PUNCT
ma-77	231	1	[	[	X
ma-77	231	2	m	m	VERB
ma-77	231	3	−	−	X
ma-77	231	4	1]q	1]q	NUM
ma-77	231	5	sin(β	sin(β	PROPN
ma-77	231	6	+	+	NUM
ma-77	231	7	θ	θ	NOUN
ma-77	231	8	)	)	PUNCT
ma-77	231	9	=	=	SYM
ma-77	231	10	0so	0so	VERB
ma-77	231	11	that	that	SCONJ
ma-77	231	12	tan	tan	PROPN
ma-77	231	13	θ	θ	NOUN
ma-77	231	14	=	=	PUNCT
ma-77	231	15	−[m	−[m	PROPN
ma-77	231	16	−	−	PROPN
ma-77	231	17	1]q	1]q	NUM
ma-77	231	18	sinβ	sinβ	NOUN
ma-77	231	19	2	2	NUM
ma-77	232	1	+	+	CCONJ
ma-77	233	1	[	[	X
ma-77	233	2	m	m	NOUN
ma-77	233	3	−	−	NOUN
ma-77	233	4	1]q(1	1]q(1	NUM
ma-77	233	5	+	+	CCONJ
ma-77	233	6	cosβ)which	cosβ)which	PROPN
ma-77	233	7	simplifies	simplifie	NOUN
ma-77	233	8	to	to	ADP
ma-77	233	9	(	(	PUNCT
ma-77	233	10	15	15	NUM
ma-77	233	11	)	)	PUNCT
ma-77	233	12	.	.	PUNCT
ma-77	234	1	�	�	PROPN
ma-77	234	2	https://doi.org/10.28924/ada/ma.2.12	https://doi.org/10.28924/ada/ma.2.12	PROPN
ma-77	234	3	eur	eur	PROPN
ma-77	234	4	.	.	PUNCT
ma-77	235	1	j.	j.	PROPN
ma-77	235	2	math	math	PROPN
ma-77	235	3	.	.	PUNCT
ma-77	236	1	anal	anal	PROPN
ma-77	236	2	.	.	PUNCT
ma-77	237	1	10.28924	10.28924	NUM
ma-77	237	2	/	/	SYM
ma-77	237	3	ada	ada	PROPN
ma-77	237	4	/	/	SYM
ma-77	237	5	ma.2.12	ma.2.12	X
ma-77	237	6	7	7	NUM
ma-77	237	7	corollary	corollary	NOUN
ma-77	237	8	3.10	3.10	NUM
ma-77	237	9	.	.	PUNCT
ma-77	238	1	let	let	VERB
ma-77	238	2	f	f	PROPN
ma-77	238	3	(	(	PUNCT
ma-77	238	4	z	z	NOUN
ma-77	238	5	)	)	PUNCT
ma-77	238	6	=	=	SYM
ma-77	239	1	z	z	NOUN
ma-77	239	2	+	+	NUM
ma-77	239	3	amzm	amzm	PROPN
ma-77	239	4	∈	∈	PROPN
ma-77	239	5	eq(0	eq(0	PROPN
ma-77	239	6	,	,	PUNCT
ma-77	239	7	δ	δ	PROPN
ma-77	239	8	)	)	PUNCT
ma-77	239	9	and	and	CCONJ
ma-77	239	10	m	m	PROPN
ma-77	239	11	=	=	X
ma-77	239	12	{	{	PUNCT
ma-77	239	13	2	2	NUM
ma-77	239	14	,	,	PUNCT
ma-77	239	15	3	3	NUM
ma-77	239	16	,	,	PUNCT
ma-77	239	17	.	.	PUNCT
ma-77	239	18	.	.	PUNCT
ma-77	239	19	.	.	PUNCT
ma-77	240	1	}	}	PUNCT
ma-77	240	2	,	,	PUNCT
ma-77	240	3	then	then	ADV
ma-77	240	4	|am|	|am|	VERB
ma-77	240	5	≤	≤	NOUN
ma-77	240	6	1	1	NUM
ma-77	241	1	[	[	X
ma-77	241	2	m]q	m]q	X
ma-77	241	3	{	{	PUNCT
ma-77	241	4	√	√	NOUN
ma-77	241	5	1	1	NUM
ma-77	241	6	+	+	NUM
ma-77	241	7	2[m	2[m	NUM
ma-77	241	8	−	−	SYM
ma-77	241	9	1]q	1]q	NUM
ma-77	241	10	+	+	PUNCT
ma-77	242	1	[	[	X
ma-77	242	2	m	m	VERB
ma-77	242	3	−	−	PROPN
ma-77	242	4	1]2q	1]2q	NUM
ma-77	242	5	+	+	CCONJ
ma-77	242	6	1	1	NUM
ma-77	242	7	+	+	CCONJ
ma-77	242	8	[	[	X
ma-77	242	9	m	m	VERB
ma-77	242	10	−	−	PROPN
ma-77	242	11	1]q	1]q	NUM
ma-77	242	12	}	}	PUNCT
ma-77	242	13	and	and	CCONJ
ma-77	242	14	if	if	SCONJ
ma-77	242	15	q	q	PROPN
ma-77	242	16	↑	↑	PROPN
ma-77	242	17	1	1	NUM
ma-77	242	18	,	,	PUNCT
ma-77	242	19	then	then	ADV
ma-77	242	20	|am|	|am|	VERB
ma-77	242	21	≤	≤	NUM
ma-77	242	22	1	1	NUM
ma-77	242	23	2m2	2m2	NUM
ma-77	242	24	.	.	PUNCT
ma-77	243	1	corollary	corollary	ADJ
ma-77	243	2	3.11	3.11	NUM
ma-77	243	3	.	.	PUNCT
ma-77	244	1	let	let	VERB
ma-77	244	2	f	f	PROPN
ma-77	244	3	(	(	PUNCT
ma-77	244	4	z	z	NOUN
ma-77	244	5	)	)	PUNCT
ma-77	244	6	=	=	SYM
ma-77	245	1	z	z	NOUN
ma-77	245	2	+	+	NUM
ma-77	245	3	amzm	amzm	ADJ
ma-77	245	4	∈	∈	PROPN
ma-77	245	5	eq(π	eq(π	X
ma-77	245	6	,	,	PUNCT
ma-77	245	7	δ	δ	PROPN
ma-77	245	8	)	)	PUNCT
ma-77	245	9	and	and	CCONJ
ma-77	245	10	m	m	PROPN
ma-77	245	11	=	=	X
ma-77	245	12	{	{	PUNCT
ma-77	245	13	2	2	NUM
ma-77	245	14	,	,	PUNCT
ma-77	245	15	3	3	NUM
ma-77	245	16	,	,	PUNCT
ma-77	245	17	.	.	PUNCT
ma-77	245	18	.	.	PUNCT
ma-77	245	19	.	.	PUNCT
ma-77	246	1	}	}	PUNCT
ma-77	246	2	,	,	PUNCT
ma-77	246	3	then	then	ADV
ma-77	246	4	|am|	|am|	NOUN
ma-77	246	5	5	5	NUM
ma-77	246	6	1	1	NUM
ma-77	246	7	2[m]q	2[m]q	NUM
ma-77	246	8	and	and	CCONJ
ma-77	246	9	if	if	SCONJ
ma-77	246	10	q	q	PROPN
ma-77	246	11	↑	↑	PROPN
ma-77	246	12	1	1	NUM
ma-77	246	13	,	,	PUNCT
ma-77	246	14	then	then	ADV
ma-77	246	15	|am|	|am|	VERB
ma-77	246	16	≤	≤	NUM
ma-77	246	17	1	1	NUM
ma-77	246	18	2	2	NUM
ma-77	246	19	m	m	NOUN
ma-77	246	20	.	.	PUNCT
ma-77	247	1	remark	remark	PROPN
ma-77	247	2	3.12	3.12	NUM
ma-77	247	3	.	.	PUNCT
ma-77	248	1	let	let	VERB
ma-77	248	2	q	q	PROPN
ma-77	248	3	↑	↑	PROPN
ma-77	248	4	1	1	NUM
ma-77	248	5	,	,	PUNCT
ma-77	248	6	then	then	ADV
ma-77	248	7	theorem	theorem	VERB
ma-77	248	8	3.9	3.9	NUM
ma-77	248	9	becomes	become	VERB
ma-77	248	10	the	the	DET
ma-77	248	11	result	result	NOUN
ma-77	248	12	in	in	ADP
ma-77	248	13	[	[	X
ma-77	248	14	18	18	NUM
ma-77	248	15	]	]	PUNCT
ma-77	248	16	.	.	PUNCT
ma-77	249	1	theorem	theorem	ADJ
ma-77	249	2	3.13	3.13	NUM
ma-77	249	3	(	(	PUNCT
ma-77	249	4	coefficient	coefficient	NOUN
ma-77	249	5	estimates	estimate	NOUN
ma-77	249	6	)	)	PUNCT
ma-77	249	7	.	.	PUNCT
ma-77	250	1	let	let	VERB
ma-77	250	2	β	β	X
ma-77	250	3	∈	∈	PROPN
ma-77	250	4	(	(	PUNCT
ma-77	250	5	−π	−π	PROPN
ma-77	250	6	,	,	PUNCT
ma-77	250	7	π	π	PROPN
ma-77	250	8	]	]	X
ma-77	250	9	,	,	PUNCT
ma-77	250	10	δ	δ	PROPN
ma-77	250	11	∈	∈	PROPN
ma-77	251	1	[	[	X
ma-77	251	2	0	0	NUM
ma-77	251	3	,	,	PUNCT
ma-77	251	4	1	1	NUM
ma-77	251	5	)	)	PUNCT
ma-77	251	6	and	and	CCONJ
ma-77	251	7	let	let	VERB
ma-77	251	8	g(z	g(z	ADJ
ma-77	251	9	)	)	PUNCT
ma-77	251	10	=	=	SYM
ma-77	252	1	1	1	NUM
ma-77	252	2	+	+	CCONJ
ma-77	252	3	b1z	b1z	PROPN
ma-77	252	4	+	+	CCONJ
ma-77	252	5	b2z	b2z	NOUN
ma-77	252	6	2	2	NUM
ma-77	252	7	+	+	CCONJ
ma-77	252	8	·	·	PUNCT
ma-77	252	9	·	·	PUNCT
ma-77	252	10	·	·	PUNCT
ma-77	252	11	∈	∈	PROPN
ma-77	252	12	cv(δ	cv(δ	NOUN
ma-77	252	13	)	)	PUNCT
ma-77	252	14	.	.	PUNCT
ma-77	253	1	if	if	SCONJ
ma-77	253	2	f	f	PROPN
ma-77	253	3	∈	∈	PROPN
ma-77	253	4	a	a	PRON
ma-77	253	5	belongs	belong	VERB
ma-77	253	6	to	to	ADP
ma-77	253	7	eq(β	eq(β	ADJ
ma-77	253	8	,	,	PUNCT
ma-77	253	9	δ	δ	PROPN
ma-77	253	10	)	)	PUNCT
ma-77	253	11	,	,	PUNCT
ma-77	253	12	then	then	ADV
ma-77	253	13	|am|	|am|	VERB
ma-77	253	14	≤	≤	NOUN
ma-77	253	15	2(1−	2(1−	NUM
ma-77	253	16	δ)|b1|	δ)|b1|	NOUN
ma-77	253	17	[	[	X
ma-77	253	18	m]q|xm|	m]q|xm|	X
ma-77	253	19	,	,	PUNCT
ma-77	253	20	m	m	VERB
ma-77	253	21	=	=	X
ma-77	253	22	{	{	PUNCT
ma-77	253	23	2	2	NUM
ma-77	253	24	,	,	PUNCT
ma-77	253	25	3	3	NUM
ma-77	253	26	,	,	PUNCT
ma-77	253	27	.	.	PUNCT
ma-77	253	28	.	.	PUNCT
ma-77	254	1	.	.	PUNCT
ma-77	254	2	}	}	PUNCT
ma-77	255	1	(	(	PUNCT
ma-77	255	2	21	21	NUM
ma-77	255	3	)	)	PUNCT
ma-77	255	4	where	where	SCONJ
ma-77	255	5	|xm|	|xm|	PROPN
ma-77	255	6	is	be	AUX
ma-77	255	7	defined	define	VERB
ma-77	255	8	in	in	ADP
ma-77	255	9	(	(	PUNCT
ma-77	255	10	14	14	NUM
ma-77	255	11	)	)	PUNCT
ma-77	255	12	.	.	PUNCT
ma-77	256	1	proof	proof	NOUN
ma-77	256	2	.	.	PUNCT
ma-77	257	1	let	let	VERB
ma-77	257	2	f	f	PROPN
ma-77	257	3	(	(	PUNCT
ma-77	257	4	z	z	X
ma-77	257	5	)	)	PUNCT
ma-77	257	6	∈	∈	PROPN
ma-77	257	7	eq(β	eq(β	X
ma-77	257	8	,	,	PUNCT
ma-77	257	9	δ	δ	PROPN
ma-77	257	10	)	)	PUNCT
ma-77	257	11	,	,	PUNCT
ma-77	257	12	therefore	therefore	ADV
ma-77	257	13	from	from	ADP
ma-77	257	14	(	(	PUNCT
ma-77	257	15	6	6	NUM
ma-77	257	16	)	)	PUNCT
ma-77	257	17	and	and	CCONJ
ma-77	257	18	using	use	VERB
ma-77	257	19	(	(	PUNCT
ma-77	257	20	5	5	NUM
ma-77	257	21	)	)	PUNCT
ma-77	257	22	,	,	PUNCT
ma-77	257	23	dqf	dqf	NOUN
ma-77	257	24	(	(	PUNCT
ma-77	257	25	z	z	NOUN
ma-77	257	26	)	)	PUNCT
ma-77	257	27	+	+	CCONJ
ma-77	257	28	1	1	NUM
ma-77	257	29	+	+	NUM
ma-77	257	30	e	e	NOUN
ma-77	257	31	iβ	iβ	ADP
ma-77	257	32	2	2	NUM
ma-77	257	33	zd2qf	zd2qf	NUM
ma-77	257	34	(	(	PUNCT
ma-77	257	35	z	z	NOUN
ma-77	257	36	)	)	PUNCT
ma-77	257	37	=	=	SYM
ma-77	257	38	δ	δ	PROPN
ma-77	257	39	+	+	PUNCT
ma-77	257	40	(	(	PUNCT
ma-77	257	41	1−	1−	NUM
ma-77	257	42	δ)p(z	δ)p(z	NOUN
ma-77	257	43	)	)	PUNCT
ma-77	257	44	,	,	PUNCT
ma-77	257	45	z	z	PROPN
ma-77	257	46	∈	∈	PROPN
ma-77	257	47	ud	ud	INTJ
ma-77	257	48	.	.	PUNCT
ma-77	258	1	(	(	PUNCT
ma-77	258	2	22	22	NUM
ma-77	258	3	)	)	PUNCT
ma-77	258	4	now	now	ADV
ma-77	258	5	putting	put	VERB
ma-77	258	6	(	(	PUNCT
ma-77	258	7	3	3	NUM
ma-77	258	8	)	)	PUNCT
ma-77	258	9	and	and	CCONJ
ma-77	258	10	(	(	PUNCT
ma-77	258	11	4	4	NUM
ma-77	258	12	)	)	PUNCT
ma-77	258	13	into	into	ADP
ma-77	258	14	(	(	PUNCT
ma-77	258	15	22	22	NUM
ma-77	258	16	)	)	PUNCT
ma-77	258	17	and	and	CCONJ
ma-77	258	18	simplifying	simplifying	NOUN
ma-77	258	19	gives	give	VERB
ma-77	258	20	1	1	NUM
ma-77	258	21	+	+	CCONJ
ma-77	258	22	∞∑	∞∑	PROPN
ma-77	258	23	m=2	m=2	PROPN
ma-77	258	24	{	{	PUNCT
ma-77	259	1	1	1	NUM
ma-77	259	2	+	+	CCONJ
ma-77	260	1	[	[	X
ma-77	260	2	m	m	VERB
ma-77	260	3	−	−	PROPN
ma-77	260	4	1]q	1]q	NUM
ma-77	260	5	(	(	PUNCT
ma-77	260	6	1	1	NUM
ma-77	260	7	+	+	NUM
ma-77	260	8	e	e	NOUN
ma-77	260	9	iβ	iβ	ADP
ma-77	260	10	2	2	NUM
ma-77	260	11	)	)	PUNCT
ma-77	260	12	}	}	PUNCT
ma-77	261	1	[	[	X
ma-77	261	2	m]qamz	m]qamz	X
ma-77	261	3	m−1	m−1	PROPN
ma-77	261	4	=	=	PUNCT
ma-77	261	5	1	1	NUM
ma-77	261	6	+	+	NUM
ma-77	261	7	∞∑	∞∑	NUM
ma-77	261	8	m=2	m=2	PROPN
ma-77	261	9	(	(	PUNCT
ma-77	261	10	1−	1−	NUM
ma-77	261	11	δ)cm−1zm−1	δ)cm−1zm−1	NOUN
ma-77	261	12	which	which	PRON
ma-77	261	13	implies	imply	VERB
ma-77	261	14	that	that	SCONJ
ma-77	261	15	{	{	PUNCT
ma-77	261	16	2	2	NUM
ma-77	261	17	+	+	SYM
ma-77	262	1	[	[	X
ma-77	262	2	m	m	NOUN
ma-77	262	3	−	−	NOUN
ma-77	262	4	1]q(1	1]q(1	NOUN
ma-77	262	5	+	+	CCONJ
ma-77	262	6	e	e	NOUN
ma-77	262	7	iβ	iβ	NOUN
ma-77	262	8	)	)	PUNCT
ma-77	262	9	}	}	PUNCT
ma-77	263	1	[	[	X
ma-77	263	2	m]q	m]q	X
ma-77	263	3	2	2	NUM
ma-77	263	4	am	am	NOUN
ma-77	263	5	=	=	PUNCT
ma-77	263	6	(	(	PUNCT
ma-77	263	7	1−	1−	NUM
ma-77	263	8	δ)cm−1	δ)cm−1	NOUN
ma-77	263	9	,	,	PUNCT
ma-77	263	10	m	m	VERB
ma-77	263	11	=	=	X
ma-77	263	12	{	{	PUNCT
ma-77	263	13	2	2	NUM
ma-77	263	14	,	,	PUNCT
ma-77	263	15	3	3	NUM
ma-77	263	16	,	,	PUNCT
ma-77	263	17	.	.	PUNCT
ma-77	263	18	.	.	PUNCT
ma-77	263	19	.	.	PUNCT
ma-77	263	20	}	}	PUNCT
ma-77	264	1	where	where	SCONJ
ma-77	264	2	by	by	ADP
ma-77	264	3	applying	apply	VERB
ma-77	264	4	(	(	PUNCT
ma-77	264	5	14	14	NUM
ma-77	264	6	)	)	PUNCT
ma-77	264	7	we	we	PRON
ma-77	264	8	obtain	obtain	VERB
ma-77	264	9	xm	xm	PUNCT
ma-77	265	1	[	[	X
ma-77	265	2	m]q	m]q	X
ma-77	265	3	2(1−	2(1−	X
ma-77	265	4	δ)am	δ)am	PROPN
ma-77	265	5	=	=	SYM
ma-77	265	6	cm−1	cm−1	PROPN
ma-77	265	7	,	,	PUNCT
ma-77	265	8	m	m	VERB
ma-77	265	9	=	=	PUNCT
ma-77	265	10	{	{	PUNCT
ma-77	265	11	2	2	NUM
ma-77	265	12	,	,	PUNCT
ma-77	265	13	3	3	NUM
ma-77	265	14	,	,	PUNCT
ma-77	265	15	.	.	PUNCT
ma-77	265	16	.	.	PUNCT
ma-77	265	17	.	.	PUNCT
ma-77	265	18	}	}	PUNCT
ma-77	265	19	.	.	PUNCT
ma-77	266	1	(	(	PUNCT
ma-77	266	2	23	23	NUM
ma-77	266	3	)	)	PUNCT
ma-77	266	4	since	since	SCONJ
ma-77	266	5	g(ud	g(ud	NOUN
ma-77	266	6	)	)	PUNCT
ma-77	266	7	is	be	AUX
ma-77	266	8	a	a	DET
ma-77	266	9	convex	convex	ADJ
ma-77	266	10	domain	domain	NOUN
ma-77	266	11	,	,	PUNCT
ma-77	266	12	then	then	ADV
ma-77	266	13	from	from	ADP
ma-77	266	14	lemma	lemma	PROPN
ma-77	266	15	2.1	2.1	NUM
ma-77	266	16	,	,	PUNCT
ma-77	266	17	(	(	PUNCT
ma-77	266	18	23	23	NUM
ma-77	266	19	)	)	PUNCT
ma-77	266	20	becomes∣∣∣∣xm	becomes∣∣∣∣xm	PROPN
ma-77	266	21	[	[	X
ma-77	266	22	m]q	m]q	NOUN
ma-77	266	23	2(1−	2(1−	X
ma-77	266	24	δ)am	δ)am	PROPN
ma-77	266	25	∣∣∣∣	∣∣∣∣	NOUN
ma-77	266	26	=	=	SYM
ma-77	266	27	|cm−1|	|cm−1|	PROPN
ma-77	266	28	≤	≤	NOUN
ma-77	266	29	|b1|	|b1|	NOUN
ma-77	266	30	and	and	CCONJ
ma-77	266	31	simplifying	simplify	VERB
ma-77	266	32	further	far	ADV
ma-77	266	33	we	we	PRON
ma-77	266	34	obtain	obtain	VERB
ma-77	266	35	(	(	PUNCT
ma-77	266	36	21	21	NUM
ma-77	266	37	)	)	PUNCT
ma-77	266	38	.	.	PUNCT
ma-77	267	1	�	�	PROPN
ma-77	267	2	https://doi.org/10.28924/ada/ma.2.12	https://doi.org/10.28924/ada/ma.2.12	PROPN
ma-77	267	3	eur	eur	PROPN
ma-77	267	4	.	.	PUNCT
ma-77	268	1	j.	j.	PROPN
ma-77	268	2	math	math	PROPN
ma-77	268	3	.	.	PUNCT
ma-77	269	1	anal	anal	PROPN
ma-77	269	2	.	.	PUNCT
ma-77	270	1	10.28924	10.28924	NUM
ma-77	270	2	/	/	SYM
ma-77	270	3	ada	ada	PROPN
ma-77	270	4	/	/	SYM
ma-77	270	5	ma.2.12	ma.2.12	ADJ
ma-77	270	6	8	8	NUM
ma-77	270	7	corollary	corollary	NOUN
ma-77	270	8	3.14	3.14	NUM
ma-77	270	9	.	.	PUNCT
ma-77	271	1	let	let	VERB
ma-77	271	2	f	f	PROPN
ma-77	271	3	(	(	PUNCT
ma-77	271	4	z	z	NOUN
ma-77	271	5	)	)	PUNCT
ma-77	271	6	∈	∈	PROPN
ma-77	271	7	eq(0	eq(0	PROPN
ma-77	271	8	,	,	PUNCT
ma-77	271	9	δ	δ	PROPN
ma-77	271	10	)	)	PUNCT
ma-77	271	11	,	,	PUNCT
ma-77	271	12	then	then	ADV
ma-77	271	13	|am|	|am|	VERB
ma-77	271	14	≤	≤	NOUN
ma-77	271	15	(	(	PUNCT
ma-77	271	16	1−	1−	NUM
ma-77	271	17	δ)|b1|√	δ)|b1|√	PROPN
ma-77	271	18	1	1	NUM
ma-77	272	1	+	+	NUM
ma-77	272	2	2[m	2[m	NUM
ma-77	272	3	−	−	SYM
ma-77	272	4	1]q	1]q	NUM
ma-77	272	5	+	+	PUNCT
ma-77	273	1	[	[	X
ma-77	273	2	m	m	VERB
ma-77	273	3	−	−	PROPN
ma-77	273	4	1]2q	1]2q	NUM
ma-77	273	5	and	and	CCONJ
ma-77	273	6	if	if	SCONJ
ma-77	273	7	q	q	PROPN
ma-77	273	8	↑	↑	PROPN
ma-77	273	9	1	1	NUM
ma-77	273	10	,	,	PUNCT
ma-77	273	11	then	then	ADV
ma-77	273	12	|am|	|am|	VERB
ma-77	273	13	≤	≤	NOUN
ma-77	273	14	(	(	PUNCT
ma-77	273	15	1−	1−	NUM
ma-77	273	16	δ)|b1|	δ)|b1|	PROPN
ma-77	273	17	m	m	PROPN
ma-77	273	18	,	,	PUNCT
ma-77	273	19	m	m	VERB
ma-77	273	20	=	=	PUNCT
ma-77	273	21	{	{	PUNCT
ma-77	273	22	2	2	NUM
ma-77	273	23	,	,	PUNCT
ma-77	273	24	3	3	NUM
ma-77	273	25	,	,	PUNCT
ma-77	273	26	.	.	PUNCT
ma-77	273	27	.	.	PUNCT
ma-77	274	1	.	.	PUNCT
ma-77	274	2	}	}	PUNCT
ma-77	274	3	.	.	PUNCT
ma-77	275	1	corollary	corollary	ADJ
ma-77	275	2	3.15	3.15	NUM
ma-77	275	3	.	.	PUNCT
ma-77	276	1	let	let	VERB
ma-77	276	2	f	f	PROPN
ma-77	276	3	∈	∈	PROPN
ma-77	276	4	eq(π	eq(π	X
ma-77	276	5	,	,	PUNCT
ma-77	276	6	δ	δ	PROPN
ma-77	276	7	)	)	PUNCT
ma-77	276	8	,	,	PUNCT
ma-77	276	9	then	then	ADV
ma-77	276	10	|am|	|am|	VERB
ma-77	276	11	≤	≤	NOUN
ma-77	276	12	(	(	PUNCT
ma-77	276	13	1−	1−	NUM
ma-77	276	14	δ)|b1|	δ)|b1|	NOUN
ma-77	276	15	[	[	X
ma-77	276	16	m]q	m]q	NOUN
ma-77	276	17	and	and	CCONJ
ma-77	276	18	if	if	SCONJ
ma-77	276	19	q	q	PROPN
ma-77	276	20	↑	↑	PROPN
ma-77	276	21	1	1	NUM
ma-77	276	22	,	,	PUNCT
ma-77	276	23	then	then	ADV
ma-77	276	24	|am|	|am|	VERB
ma-77	276	25	≤	≤	NOUN
ma-77	276	26	(	(	PUNCT
ma-77	276	27	1−	1−	NUM
ma-77	276	28	δ)|b1|	δ)|b1|	PROPN
ma-77	276	29	m	m	PROPN
ma-77	276	30	,	,	PUNCT
ma-77	276	31	m	m	VERB
ma-77	276	32	=	=	PUNCT
ma-77	276	33	{	{	PUNCT
ma-77	276	34	2	2	NUM
ma-77	276	35	,	,	PUNCT
ma-77	276	36	3	3	NUM
ma-77	276	37	,	,	PUNCT
ma-77	276	38	.	.	PUNCT
ma-77	276	39	.	.	PUNCT
ma-77	277	1	.	.	PUNCT
ma-77	277	2	}	}	PUNCT
ma-77	277	3	remark	remark	VERB
ma-77	277	4	3.16	3.16	NUM
ma-77	277	5	.	.	PUNCT
ma-77	278	1	let	let	VERB
ma-77	278	2	p(z	p(z	NOUN
ma-77	278	3	)	)	PUNCT
ma-77	278	4	∈	∈	PROPN
ma-77	278	5	p	p	NOUN
ma-77	278	6	and	and	CCONJ
ma-77	278	7	φ(z	φ(z	PROPN
ma-77	278	8	)	)	PUNCT
ma-77	278	9	=	=	SYM
ma-77	279	1	1	1	NUM
ma-77	279	2	+	+	NUM
ma-77	279	3	2	2	NUM
ma-77	279	4	π2	π2	NOUN
ma-77	279	5	(	(	PUNCT
ma-77	279	6	ln	ln	NOUN
ma-77	279	7	1	1	NUM
ma-77	279	8	+	+	NUM
ma-77	279	9	√	√	PROPN
ma-77	279	10	z	z	NOUN
ma-77	279	11	1−	1−	NUM
ma-77	279	12	√	√	PROPN
ma-77	279	13	z	z	NOUN
ma-77	279	14	)	)	PUNCT
ma-77	279	15	2	2	X
ma-77	279	16	.	.	X
ma-77	280	1	if	if	SCONJ
ma-77	280	2	q	q	PROPN
ma-77	280	3	↑	↑	PROPN
ma-77	280	4	1,(1	1,(1	NUM
ma-77	280	5	)	)	PUNCT
ma-77	280	6	β	β	X
ma-77	280	7	=	=	SYM
ma-77	280	8	π	π	PROPN
ma-77	280	9	and	and	CCONJ
ma-77	280	10	g(z	g(z	PROPN
ma-77	280	11	)	)	PUNCT
ma-77	280	12	=	=	SYM
ma-77	280	13	p(z	p(z	NOUN
ma-77	280	14	)	)	PUNCT
ma-77	280	15	,	,	PUNCT
ma-77	280	16	then	then	ADV
ma-77	280	17	theorem	theorem	VERB
ma-77	280	18	3.13	3.13	NUM
ma-77	280	19	becomes	become	VERB
ma-77	280	20	the	the	DET
ma-77	280	21	result	result	NOUN
ma-77	280	22	in	in	ADP
ma-77	280	23	[	[	X
ma-77	280	24	12].(2	12].(2	NUM
ma-77	280	25	)	)	PUNCT
ma-77	280	26	and	and	CCONJ
ma-77	280	27	g(z	g(z	PROPN
ma-77	280	28	)	)	PUNCT
ma-77	280	29	=	=	SYM
ma-77	280	30	p(z	p(z	NOUN
ma-77	280	31	)	)	PUNCT
ma-77	280	32	,	,	PUNCT
ma-77	280	33	then	then	ADV
ma-77	280	34	theorem	theorem	VERB
ma-77	280	35	3.13	3.13	NUM
ma-77	280	36	becomes	become	VERB
ma-77	280	37	the	the	DET
ma-77	280	38	result	result	NOUN
ma-77	280	39	in	in	ADP
ma-77	280	40	[	[	X
ma-77	280	41	16].(3	16].(3	NUM
ma-77	280	42	)	)	PUNCT
ma-77	280	43	and	and	CCONJ
ma-77	280	44	g(z	g(z	PROPN
ma-77	280	45	)	)	PUNCT
ma-77	280	46	=	=	SYM
ma-77	280	47	φ(z	φ(z	NOUN
ma-77	280	48	)	)	PUNCT
ma-77	280	49	,	,	PUNCT
ma-77	280	50	then	then	ADV
ma-77	280	51	theorem	theorem	VERB
ma-77	280	52	3.13	3.13	NUM
ma-77	280	53	becomes	become	VERB
ma-77	280	54	the	the	DET
ma-77	280	55	result	result	NOUN
ma-77	280	56	in	in	ADP
ma-77	280	57	[	[	X
ma-77	280	58	18].(4	18].(4	NUM
ma-77	280	59	)	)	PUNCT
ma-77	280	60	and	and	CCONJ
ma-77	280	61	β	β	X
ma-77	280	62	=	=	SYM
ma-77	280	63	0	0	PROPN
ma-77	280	64	,	,	PUNCT
ma-77	280	65	then	then	ADV
ma-77	280	66	theorem	theorem	VERB
ma-77	280	67	3.13	3.13	NUM
ma-77	280	68	becomes	become	VERB
ma-77	280	69	the	the	DET
ma-77	280	70	result	result	NOUN
ma-77	280	71	in	in	ADP
ma-77	280	72	[	[	X
ma-77	280	73	17	17	NUM
ma-77	280	74	]	]	PUNCT
ma-77	280	75	.	.	PUNCT
ma-77	281	1	acknowledgment	acknowledgment	NOUN
ma-77	281	2	.	.	PUNCT
ma-77	282	1	the	the	DET
ma-77	282	2	authors	author	NOUN
ma-77	282	3	would	would	AUX
ma-77	282	4	like	like	VERB
ma-77	282	5	to	to	PART
ma-77	282	6	thank	thank	VERB
ma-77	282	7	the	the	DET
ma-77	282	8	referees	referee	NOUN
ma-77	282	9	for	for	ADP
ma-77	282	10	their	their	PRON
ma-77	282	11	careful	careful	ADJ
ma-77	282	12	reading	reading	NOUN
ma-77	282	13	of	of	ADP
ma-77	282	14	thismanuscript	thismanuscript	NOUN
ma-77	282	15	and	and	CCONJ
ma-77	282	16	their	their	PRON
ma-77	282	17	valuable	valuable	ADJ
ma-77	282	18	suggestions	suggestion	NOUN
ma-77	282	19	.	.	PUNCT
ma-77	283	1	references	reference	NOUN
ma-77	283	2	[	[	X
ma-77	283	3	1	1	X
ma-77	283	4	]	]	X
ma-77	283	5	j.w	j.w	PROPN
ma-77	283	6	.	.	PROPN
ma-77	283	7	alexander	alexander	PROPN
ma-77	283	8	,	,	PUNCT
ma-77	283	9	functions	function	NOUN
ma-77	283	10	which	which	PRON
ma-77	283	11	map	map	VERB
ma-77	283	12	the	the	DET
ma-77	283	13	interior	interior	NOUN
ma-77	283	14	of	of	ADP
ma-77	283	15	the	the	DET
ma-77	283	16	unit	unit	NOUN
ma-77	283	17	circle	circle	NOUN
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ma-77	283	20	regions	region	NOUN
ma-77	283	21	,	,	PUNCT
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ma-77	283	23	.	.	PROPN
ma-77	283	24	math	math	PROPN
ma-77	283	25	.	.	PUNCT
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ma-77	284	3	.	.	PROPN
ma-77	285	1	17(1915	17(1915	NUM
ma-77	285	2	)	)	PUNCT
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ma-77	285	4	.	.	PUNCT
ma-77	286	1	https://doi.org/10.2307/2007212.[2	https://doi.org/10.2307/2007212.[2	PROPN
ma-77	286	2	]	]	X
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ma-77	286	6	-	-	PUNCT
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ma-77	286	8	,	,	PUNCT
ma-77	286	9	on	on	ADP
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ma-77	286	11	functions	function	NOUN
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ma-77	286	13	by	by	ADP
ma-77	286	14	a	a	DET
ma-77	286	15	generalized	generalize	VERB
ma-77	286	16	differential	differential	NOUN
ma-77	286	17	operator	operator	NOUN
ma-77	286	18	,	,	PUNCT
ma-77	286	19	intern	intern	NOUN
ma-77	286	20	.	.	PUNCT
ma-77	287	1	j.	j.	PROPN
ma-77	287	2	math	math	PROPN
ma-77	287	3	.	.	PUNCT
ma-77	288	1	math	math	NOUN
ma-77	288	2	.	.	PUNCT
ma-77	289	1	sci.27	sci.27	PROPN
ma-77	289	2	(	(	PUNCT
ma-77	289	3	2004	2004	NUM
ma-77	289	4	)	)	PUNCT
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ma-77	289	6	.	.	PUNCT
ma-77	290	1	https://doi.org/10.1155/s0161171204108090.[3	https://doi.org/10.1155/s0161171204108090.[3	NOUN
ma-77	290	2	]	]	X
ma-77	290	3	m.h	m.h	PROPN
ma-77	290	4	.	.	PROPN
ma-77	290	5	annaby	annaby	PROPN
ma-77	290	6	,	,	PUNCT
ma-77	290	7	z.s	z.s	PROPN
ma-77	290	8	.	.	PROPN
ma-77	290	9	mansour	mansour	PROPN
ma-77	290	10	,	,	PUNCT
ma-77	290	11	q	q	ADJ
ma-77	290	12	-	-	PUNCT
ma-77	290	13	fractional	fractional	ADJ
ma-77	290	14	calculus	calculus	NOUN
ma-77	290	15	and	and	CCONJ
ma-77	290	16	equations	equation	NOUN
ma-77	290	17	,	,	PUNCT
ma-77	290	18	springer	springer	NOUN
ma-77	290	19	-	-	PUNCT
ma-77	290	20	verlag	verlag	PROPN
ma-77	290	21	inc	inc	PROPN
ma-77	290	22	.	.	PROPN
ma-77	290	23	,	,	PUNCT
ma-77	290	24	new	new	PROPN
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ma-77	290	26	,	,	PUNCT
ma-77	290	27	2012	2012	NUM
ma-77	290	28	.	.	PUNCT
ma-77	291	1	https	https	NOUN
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ma-77	291	3	//doi.org/10.1007/978	//doi.org/10.1007/978	NUM
ma-77	291	4	-	-	PUNCT
ma-77	291	5	3	3	NUM
ma-77	291	6	-	-	PUNCT
ma-77	291	7	642	642	NUM
ma-77	291	8	-	-	PUNCT
ma-77	291	9	30898	30898	NUM
ma-77	291	10	-	-	SYM
ma-77	291	11	7.[4	7.[4	NOUN
ma-77	291	12	]	]	X
ma-77	291	13	a.	a.	NOUN
ma-77	291	14	aral	aral	PROPN
ma-77	291	15	,	,	PUNCT
ma-77	291	16	v.	v.	PROPN
ma-77	291	17	gupta	gupta	PROPN
ma-77	291	18	,	,	PUNCT
ma-77	291	19	r.p	r.p	PROPN
ma-77	291	20	.	.	PROPN
ma-77	291	21	agarwal	agarwal	PROPN
ma-77	291	22	,	,	PUNCT
ma-77	291	23	applications	application	NOUN
ma-77	291	24	of	of	ADP
ma-77	291	25	q	q	NOUN
ma-77	291	26	-	-	NOUN
ma-77	291	27	calculus	calculus	NOUN
ma-77	291	28	in	in	ADP
ma-77	291	29	operator	operator	NOUN
ma-77	291	30	theory	theory	NOUN
ma-77	291	31	,	,	PUNCT
ma-77	291	32	springer	springer	NOUN
ma-77	291	33	-	-	PUNCT
ma-77	291	34	verlag	verlag	PROPN
ma-77	291	35	inc	inc	PROPN
ma-77	291	36	.	.	PROPN
ma-77	291	37	,	,	PUNCT
ma-77	291	38	new	new	PROPN
ma-77	291	39	york,2013	york,2013	PROPN
ma-77	291	40	.	.	PROPN
ma-77	291	41	https://doi.org/10.1007/978-1-4614-6946-9_1.[5	https://doi.org/10.1007/978-1-4614-6946-9_1.[5	PROPN
ma-77	291	42	]	]	X
ma-77	291	43	k.o	k.o	PROPN
ma-77	291	44	.	.	PROPN
ma-77	291	45	babalola	babalola	PROPN
ma-77	291	46	,	,	PUNCT
ma-77	291	47	t.o	t.o	PROPN
ma-77	291	48	.	.	PROPN
ma-77	291	49	opoola	opoola	PROPN
ma-77	291	50	,	,	PUNCT
ma-77	291	51	iterated	iterate	VERB
ma-77	291	52	integral	integral	ADJ
ma-77	291	53	transforms	transform	NOUN
ma-77	291	54	of	of	ADP
ma-77	291	55	carathéodory	carathéodory	ADJ
ma-77	291	56	functions	function	NOUN
ma-77	291	57	and	and	CCONJ
ma-77	291	58	their	their	PRON
ma-77	291	59	application	application	NOUN
ma-77	291	60	to	to	PART
ma-77	291	61	analyticand	analyticand	VERB
ma-77	291	62	univalent	univalent	ADJ
ma-77	291	63	functions	function	NOUN
ma-77	291	64	,	,	PUNCT
ma-77	291	65	tamkang	tamkang	PROPN
ma-77	291	66	j.	j.	PROPN
ma-77	291	67	math	math	PROPN
ma-77	291	68	.	.	PUNCT
ma-77	292	1	135	135	NUM
ma-77	292	2	(	(	PUNCT
ma-77	292	3	2006	2006	NUM
ma-77	292	4	)	)	PUNCT
ma-77	293	1	429–446	429–446	NUM
ma-77	293	2	.	.	PUNCT
ma-77	294	1	https://doi.org/10.5556/j.tkjm.37.2006.149.[6	https://doi.org/10.5556/j.tkjm.37.2006.149.[6	NOUN
ma-77	294	2	]	]	PUNCT
ma-77	294	3	k.o	k.o	PROPN
ma-77	294	4	.	.	PROPN
ma-77	294	5	babalola	babalola	PROPN
ma-77	294	6	,	,	PUNCT
ma-77	294	7	λ	λ	NOUN
ma-77	294	8	-	-	PUNCT
ma-77	294	9	pseudo	pseudo	ADJ
ma-77	294	10	-	-	ADJ
ma-77	294	11	starlike	starlike	ADJ
ma-77	294	12	functions	function	NOUN
ma-77	294	13	,	,	PUNCT
ma-77	294	14	j.	j.	PROPN
ma-77	294	15	class	class	PROPN
ma-77	294	16	.	.	PUNCT
ma-77	295	1	anal	anal	PROPN
ma-77	295	2	.	.	PUNCT
ma-77	296	1	3	3	NUM
ma-77	296	2	(	(	PUNCT
ma-77	296	3	2013	2013	NUM
ma-77	296	4	)	)	PUNCT
ma-77	296	5	137–147	137–147	NUM
ma-77	296	6	.	.	PUNCT
ma-77	297	1	https://doi.org/10.7153/	https://doi.org/10.7153/	PROPN
ma-77	297	2	jca-03	jca-03	PROPN
ma-77	297	3	-	-	PUNCT
ma-77	297	4	12.[7	12.[7	NUM
ma-77	297	5	]	]	X
ma-77	297	6	f.h	f.h	PROPN
ma-77	297	7	.	.	PROPN
ma-77	297	8	jackson	jackson	PROPN
ma-77	297	9	,	,	PUNCT
ma-77	297	10	on	on	ADP
ma-77	297	11	q	q	NOUN
ma-77	297	12	-	-	PUNCT
ma-77	297	13	functions	function	NOUN
ma-77	297	14	and	and	CCONJ
ma-77	297	15	a	a	DET
ma-77	297	16	certain	certain	ADJ
ma-77	297	17	difference	difference	NOUN
ma-77	297	18	operator	operator	NOUN
ma-77	297	19	,	,	PUNCT
ma-77	297	20	trans	trans	PROPN
ma-77	297	21	.	.	PROPN
ma-77	297	22	roy	roy	PROPN
ma-77	297	23	.	.	PROPN
ma-77	297	24	soc	soc	PROPN
ma-77	297	25	.	.	PUNCT
ma-77	298	1	edinb	edinb	PROPN
ma-77	298	2	.	.	PUNCT
ma-77	299	1	46	46	NUM
ma-77	299	2	(	(	PUNCT
ma-77	299	3	1908	1908	NUM
ma-77	299	4	)	)	PUNCT
ma-77	299	5	253–281	253–281	NUM
ma-77	299	6	.	.	PUNCT
ma-77	299	7	https	https	NOUN
ma-77	299	8	:	:	PUNCT
ma-77	299	9	//doi.org/10.1017	//doi.org/10.1017	X
ma-77	299	10	/	/	SYM
ma-77	299	11	s0080456800002751.[8	s0080456800002751.[8	NUM
ma-77	299	12	]	]	X
ma-77	299	13	f.h	f.h	PROPN
ma-77	299	14	.	.	PROPN
ma-77	299	15	jackson	jackson	PROPN
ma-77	299	16	,	,	PUNCT
ma-77	299	17	on	on	ADP
ma-77	299	18	q	q	NOUN
ma-77	299	19	-	-	PUNCT
ma-77	299	20	difference	difference	NOUN
ma-77	299	21	,	,	PUNCT
ma-77	299	22	amer	amer	PROPN
ma-77	299	23	.	.	PUNCT
ma-77	300	1	j.	j.	PROPN
ma-77	300	2	math	math	PROPN
ma-77	300	3	.	.	PUNCT
ma-77	301	1	32	32	NUM
ma-77	301	2	(	(	PUNCT
ma-77	301	3	1910	1910	NUM
ma-77	301	4	)	)	PUNCT
ma-77	301	5	305–314	305–314	NUM
ma-77	301	6	.	.	PUNCT
ma-77	302	1	https://doi.org/10.2307/2370183.[9	https://doi.org/10.2307/2370183.[9	X
ma-77	302	2	]	]	X
ma-77	302	3	v.	v.	X
ma-77	302	4	kac	kac	PROPN
ma-77	302	5	,	,	PUNCT
ma-77	302	6	p.	p.	PROPN
ma-77	302	7	cheung	cheung	PROPN
ma-77	302	8	,	,	PUNCT
ma-77	302	9	quantum	quantum	NOUN
ma-77	302	10	calculus	calculus	NOUN
ma-77	302	11	,	,	PUNCT
ma-77	302	12	springer	springer	NOUN
ma-77	302	13	-	-	PUNCT
ma-77	302	14	verlag	verlag	PROPN
ma-77	302	15	inc	inc	PROPN
ma-77	302	16	.	.	PROPN
ma-77	302	17	,	,	PUNCT
ma-77	302	18	new	new	PROPN
ma-77	302	19	york	york	PROPN
ma-77	302	20	,	,	PUNCT
ma-77	302	21	2002	2002	NUM
ma-77	302	22	.	.	PUNCT
ma-77	303	1	https://doi.org/10.1007/	https://doi.org/10.1007/	PROPN
ma-77	303	2	978	978	NUM
ma-77	303	3	-	-	SYM
ma-77	303	4	1	1	NUM
ma-77	303	5	-	-	PUNCT
ma-77	303	6	4613	4613	NUM
ma-77	303	7	-	-	PUNCT
ma-77	303	8	0071	0071	NUM
ma-77	303	9	-	-	PUNCT
ma-77	303	10	7	7	NUM
ma-77	303	11	.	.	PUNCT
ma-77	304	1	https://doi.org/10.28924/ada/ma.2.12	https://doi.org/10.28924/ada/ma.2.12	NUM
ma-77	304	2	https://doi.org/10.2307/2007212	https://doi.org/10.2307/2007212	NOUN
ma-77	304	3	https://doi.org/10.1155/s0161171204108090	https://doi.org/10.1155/s0161171204108090	NUM
ma-77	304	4	https://doi.org/10.1007/978-3-642-30898-7	https://doi.org/10.1007/978-3-642-30898-7	PROPN
ma-77	304	5	https://doi.org/10.1007/978-3-642-30898-7	https://doi.org/10.1007/978-3-642-30898-7	PROPN
ma-77	304	6	https://doi.org/10.1007/978-1-4614-6946-9_1	https://doi.org/10.1007/978-1-4614-6946-9_1	NOUN
ma-77	304	7	https://doi.org/10.5556/j.tkjm.37.2006.149	https://doi.org/10.5556/j.tkjm.37.2006.149	VERB
ma-77	304	8	https://doi.org/10.7153/jca-03-12	https://doi.org/10.7153/jca-03-12	NOUN
ma-77	304	9	https://doi.org/10.7153/jca-03-12	https://doi.org/10.7153/jca-03-12	NOUN
ma-77	304	10	https://doi.org/10.1017/s0080456800002751	https://doi.org/10.1017/s0080456800002751	CCONJ
ma-77	304	11	https://doi.org/10.1017/s0080456800002751	https://doi.org/10.1017/s0080456800002751	NUM
ma-77	304	12	https://doi.org/10.2307/2370183	https://doi.org/10.2307/2370183	NOUN
ma-77	305	1	https://doi.org/10.1007/978-1-4613-0071-7	https://doi.org/10.1007/978-1-4613-0071-7	PROPN
ma-77	305	2	https://doi.org/10.1007/978-1-4613-0071-7	https://doi.org/10.1007/978-1-4613-0071-7	PROPN
ma-77	305	3	eur	eur	PROPN
ma-77	305	4	.	.	PUNCT
ma-77	306	1	j.	j.	PROPN
ma-77	306	2	math	math	PROPN
ma-77	306	3	.	.	PUNCT
ma-77	307	1	anal	anal	PROPN
ma-77	307	2	.	.	PUNCT
ma-77	308	1	10.28924	10.28924	NUM
ma-77	308	2	/	/	SYM
ma-77	308	3	ada	ada	PROPN
ma-77	308	4	/	/	SYM
ma-77	308	5	ma.2.12	ma.2.12	NOUN
ma-77	308	6	9	9	NUM
ma-77	309	1	[	[	SYM
ma-77	309	2	10	10	NUM
ma-77	309	3	]	]	X
ma-77	309	4	a.o	a.o	PROPN
ma-77	309	5	.	.	PROPN
ma-77	309	6	lasode	lasode	PROPN
ma-77	309	7	,	,	PUNCT
ma-77	309	8	t.o	t.o	PROPN
ma-77	309	9	.	.	PROPN
ma-77	309	10	opoola	opoola	PROPN
ma-77	309	11	,	,	PUNCT
ma-77	309	12	fekete	fekete	NOUN
ma-77	309	13	-	-	PUNCT
ma-77	309	14	szegö	szegö	ADJ
ma-77	309	15	estimates	estimate	NOUN
ma-77	309	16	and	and	CCONJ
ma-77	309	17	second	second	ADJ
ma-77	309	18	hankel	hankel	NOUN
ma-77	309	19	determinant	determinant	ADJ
ma-77	309	20	for	for	ADP
ma-77	309	21	a	a	DET
ma-77	309	22	generalized	generalize	VERB
ma-77	309	23	subfamily	subfamily	ADV
ma-77	309	24	ofanalytic	ofanalytic	ADJ
ma-77	309	25	functions	function	NOUN
ma-77	309	26	defined	define	VERB
ma-77	309	27	by	by	ADP
ma-77	309	28	q	q	ADJ
ma-77	309	29	-	-	PUNCT
ma-77	309	30	differential	differential	ADJ
ma-77	309	31	operator	operator	NOUN
ma-77	309	32	,	,	PUNCT
ma-77	309	33	gulf	gulf	PROPN
ma-77	309	34	j.	j.	PROPN
ma-77	309	35	math	math	PROPN
ma-77	309	36	.	.	PUNCT
ma-77	310	1	11	11	NUM
ma-77	310	2	(	(	PUNCT
ma-77	310	3	2021	2021	NUM
ma-77	310	4	)	)	PUNCT
ma-77	311	1	36–43	36–43	NUM
ma-77	311	2	.	.	PUNCT
ma-77	312	1	https://gjom.org/index	https://gjom.org/index	PROPN
ma-77	312	2	.	.	PUNCT
ma-77	312	3	php	php	PROPN
ma-77	312	4	/	/	SYM
ma-77	312	5	gjom	gjom	NOUN
ma-77	312	6	/	/	SYM
ma-77	312	7	article	article	NOUN
ma-77	312	8	/	/	SYM
ma-77	312	9	view/583.[11	view/583.[11	PROPN
ma-77	312	10	]	]	X
ma-77	312	11	a.o	a.o	PROPN
ma-77	312	12	.	.	PROPN
ma-77	312	13	lasode	lasode	PROPN
ma-77	312	14	,	,	PUNCT
ma-77	312	15	t.o	t.o	PROPN
ma-77	312	16	.	.	PROPN
ma-77	312	17	opoola	opoola	PROPN
ma-77	312	18	,	,	PUNCT
ma-77	312	19	on	on	ADP
ma-77	312	20	a	a	DET
ma-77	312	21	generalized	generalized	ADJ
ma-77	312	22	class	class	NOUN
ma-77	312	23	of	of	ADP
ma-77	312	24	bi	bi	ADJ
ma-77	312	25	-	-	ADJ
ma-77	312	26	univalent	univalent	ADJ
ma-77	312	27	functions	function	NOUN
ma-77	312	28	defined	define	VERB
ma-77	312	29	by	by	ADP
ma-77	312	30	subordination	subordination	NOUN
ma-77	312	31	and	and	CCONJ
ma-77	312	32	q	q	NOUN
ma-77	312	33	-	-	NOUN
ma-77	312	34	derivativeoperator	derivativeoperator	NOUN
ma-77	312	35	,	,	PUNCT
ma-77	312	36	open	open	ADJ
ma-77	312	37	j.	j.	PROPN
ma-77	312	38	math	math	PROPN
ma-77	312	39	.	.	PUNCT
ma-77	313	1	anal	anal	ADJ
ma-77	313	2	.	.	PUNCT
ma-77	314	1	5	5	NUM
ma-77	314	2	(	(	PUNCT
ma-77	314	3	2021	2021	NUM
ma-77	314	4	)	)	PUNCT
ma-77	314	5	46–52	46–52	NUM
ma-77	314	6	.	.	PUNCT
ma-77	315	1	https://doi.org/10.30538/psrp-oma2021.0092.[12	https://doi.org/10.30538/psrp-oma2021.0092.[12	PROPN
ma-77	315	2	]	]	X
ma-77	315	3	t.h	t.h	PROPN
ma-77	315	4	.	.	PROPN
ma-77	315	5	macgregor	macgregor	PROPN
ma-77	315	6	,	,	PUNCT
ma-77	315	7	functions	function	VERB
ma-77	315	8	whose	whose	DET
ma-77	315	9	derivative	derivative	NOUN
ma-77	315	10	has	have	VERB
ma-77	315	11	a	a	DET
ma-77	315	12	positive	positive	ADJ
ma-77	315	13	real	real	ADJ
ma-77	315	14	part	part	NOUN
ma-77	315	15	,	,	PUNCT
ma-77	315	16	trans	trans	PROPN
ma-77	315	17	.	.	PROPN
ma-77	316	1	amer	amer	PROPN
ma-77	316	2	.	.	PUNCT
ma-77	316	3	math	math	PROPN
ma-77	316	4	.	.	PUNCT
ma-77	317	1	soc	soc	PROPN
ma-77	317	2	.	.	PUNCT
ma-77	318	1	104	104	NUM
ma-77	318	2	(	(	PUNCT
ma-77	318	3	1962	1962	NUM
ma-77	318	4	)	)	PUNCT
ma-77	318	5	532–537	532–537	NUM
ma-77	318	6	.	.	PUNCT
ma-77	319	1	https://doi.org/10.1090/s0002-9947-1962-0140674-7.[13	https://doi.org/10.1090/s0002-9947-1962-0140674-7.[13	PROPN
ma-77	319	2	]	]	PUNCT
ma-77	319	3	t.o	t.o	PROPN
ma-77	319	4	.	.	PROPN
ma-77	319	5	opoola	opoola	PROPN
ma-77	319	6	,	,	PUNCT
ma-77	319	7	on	on	ADP
ma-77	319	8	a	a	DET
ma-77	319	9	subclass	subclass	NOUN
ma-77	319	10	of	of	ADP
ma-77	319	11	univalent	univalent	ADJ
ma-77	319	12	functions	function	NOUN
ma-77	319	13	defined	define	VERB
ma-77	319	14	by	by	ADP
ma-77	319	15	a	a	DET
ma-77	319	16	generalised	generalise	VERB
ma-77	319	17	differential	differential	NOUN
ma-77	319	18	operator	operator	NOUN
ma-77	319	19	,	,	PUNCT
ma-77	319	20	int	int	NOUN
ma-77	319	21	.	.	PUNCT
ma-77	320	1	j.	j.	PROPN
ma-77	320	2	math	math	PROPN
ma-77	320	3	.	.	PUNCT
ma-77	321	1	anal.11	anal.11	PROPN
ma-77	321	2	(	(	PUNCT
ma-77	321	3	2017	2017	NUM
ma-77	321	4	)	)	PUNCT
ma-77	321	5	869–876	869–876	NUM
ma-77	321	6	.	.	PUNCT
ma-77	322	1	https://doi.org/10.12988/ijma.2017.7232.[14	https://doi.org/10.12988/ijma.2017.7232.[14	PROPN
ma-77	322	2	]	]	PUNCT
ma-77	323	1	w.	w.	PROPN
ma-77	323	2	rogosinski	rogosinski	PROPN
ma-77	323	3	,	,	PUNCT
ma-77	323	4	on	on	ADP
ma-77	323	5	the	the	DET
ma-77	323	6	coefficients	coefficient	NOUN
ma-77	323	7	of	of	ADP
ma-77	323	8	subordinate	subordinate	ADJ
ma-77	323	9	functions	function	NOUN
ma-77	323	10	,	,	PUNCT
ma-77	323	11	proc	proc	NOUN
ma-77	323	12	.	.	PUNCT
ma-77	324	1	lond	lond	PROPN
ma-77	324	2	.	.	PUNCT
ma-77	325	1	math	math	NOUN
ma-77	325	2	.	.	PUNCT
ma-77	326	1	soc	soc	PROPN
ma-77	326	2	.	.	PUNCT
ma-77	327	1	48	48	NUM
ma-77	327	2	(	(	PUNCT
ma-77	327	3	1945	1945	NUM
ma-77	327	4	)	)	PUNCT
ma-77	327	5	48–82	48–82	NUM
ma-77	327	6	.	.	PUNCT
ma-77	328	1	https	https	NOUN
ma-77	328	2	:	:	PUNCT
ma-77	329	1	//doi.org/10.112	//doi.org/10.112	PROPN
ma-77	329	2	/	/	SYM
ma-77	329	3	plms	plms	PROPN
ma-77	329	4	/	/	SYM
ma-77	329	5	s2	s2	PROPN
ma-77	329	6	-	-	PUNCT
ma-77	329	7	48.1.48.[15	48.1.48.[15	PROPN
ma-77	329	8	]	]	X
ma-77	329	9	g.s	g.s	PROPN
ma-77	329	10	.	.	PROPN
ma-77	329	11	sǎlǎgean	sǎlǎgean	PROPN
ma-77	329	12	,	,	PUNCT
ma-77	329	13	subclasses	subclass	NOUN
ma-77	329	14	of	of	ADP
ma-77	329	15	univalent	univalent	ADJ
ma-77	329	16	functions	function	NOUN
ma-77	329	17	,	,	PUNCT
ma-77	329	18	lect	lect	PROPN
ma-77	329	19	.	.	PUNCT
ma-77	330	1	notes	note	VERB
ma-77	330	2	math	math	PROPN
ma-77	330	3	.	.	PUNCT
ma-77	331	1	1013	1013	NUM
ma-77	331	2	(	(	PUNCT
ma-77	331	3	1983	1983	NUM
ma-77	331	4	)	)	PUNCT
ma-77	332	1	362–372	362–372	NUM
ma-77	332	2	.	.	PUNCT
ma-77	333	1	https://doi.org/10	https://doi.org/10	PROPN
ma-77	333	2	.	.	PUNCT
ma-77	334	1	1007	1007	NUM
ma-77	334	2	/	/	SYM
ma-77	334	3	bfb0066543.[16	bfb0066543.[16	NOUN
ma-77	334	4	]	]	X
ma-77	334	5	h.	h.	PROPN
ma-77	334	6	silverman	silverman	PROPN
ma-77	334	7	,	,	PUNCT
ma-77	334	8	e.m	e.m	PROPN
ma-77	334	9	.	.	PROPN
ma-77	334	10	silvia	silvia	PROPN
ma-77	334	11	,	,	PUNCT
ma-77	334	12	characterizations	characterization	NOUN
ma-77	334	13	for	for	ADP
ma-77	334	14	subclasses	subclass	NOUN
ma-77	334	15	of	of	ADP
ma-77	334	16	univalent	univalent	ADJ
ma-77	334	17	functions	function	NOUN
ma-77	334	18	,	,	PUNCT
ma-77	334	19	sci	sci	PROPN
ma-77	334	20	.	.	PROPN
ma-77	334	21	math	math	PROPN
ma-77	334	22	.	.	PUNCT
ma-77	335	1	jpn	jpn	PROPN
ma-77	335	2	.	.	PROPN
ma-77	336	1	50	50	NUM
ma-77	336	2	(	(	PUNCT
ma-77	336	3	1999	1999	NUM
ma-77	336	4	)	)	PUNCT
ma-77	337	1	103–109	103–109	NUM
ma-77	337	2	.	.	PUNCT
ma-77	338	1	https://www.jams.jp/notice/mj/50-1.html.[17	https://www.jams.jp/notice/mj/50-1.html.[17	PROPN
ma-77	338	2	]	]	X
ma-77	338	3	h.m	h.m	PROPN
ma-77	338	4	.	.	PROPN
ma-77	338	5	srivastava	srivastava	PROPN
ma-77	338	6	,	,	PUNCT
ma-77	338	7	d.	d.	PROPN
ma-77	338	8	rǎducanu	rǎducanu	PROPN
ma-77	338	9	,	,	PUNCT
ma-77	338	10	p.	p.	NOUN
ma-77	338	11	zaprawa	zaprawa	PROPN
ma-77	338	12	,	,	PUNCT
ma-77	338	13	a	a	DET
ma-77	338	14	certain	certain	ADJ
ma-77	338	15	subclass	subclass	NOUN
ma-77	338	16	of	of	ADP
ma-77	338	17	analytic	analytic	ADJ
ma-77	338	18	functions	function	NOUN
ma-77	338	19	defined	define	VERB
ma-77	338	20	by	by	ADP
ma-77	338	21	means	mean	NOUN
ma-77	338	22	of	of	ADP
ma-77	338	23	differentialsubordination	differentialsubordination	NOUN
ma-77	338	24	,	,	PUNCT
ma-77	338	25	fac	fac	PROPN
ma-77	338	26	.	.	PUNCT
ma-77	339	1	sci	sci	PROPN
ma-77	339	2	.	.	PUNCT
ma-77	339	3	math	math	PROPN
ma-77	339	4	.	.	PUNCT
ma-77	340	1	univ	univ	PROPN
ma-77	340	2	.	.	PUNCT
ma-77	341	1	niš	niš	PROPN
ma-77	341	2	,	,	PUNCT
ma-77	341	3	serbia	serbia	PROPN
ma-77	341	4	30	30	NUM
ma-77	341	5	(	(	PUNCT
ma-77	341	6	2016	2016	NUM
ma-77	341	7	)	)	PUNCT
ma-77	341	8	3743–3757	3743–3757	NOUN
ma-77	341	9	.	.	PUNCT
ma-77	342	1	https://doi.org/10.2298/fil1614743s.[18	https://doi.org/10.2298/fil1614743s.[18	NOUN
ma-77	342	2	]	]	X
ma-77	342	3	l.	l.	PROPN
ma-77	342	4	trojnar	trojnar	PROPN
ma-77	342	5	-	-	PUNCT
ma-77	342	6	spelina	spelina	NOUN
ma-77	342	7	,	,	PUNCT
ma-77	342	8	characterizations	characterization	NOUN
ma-77	342	9	of	of	ADP
ma-77	342	10	subclasses	subclass	NOUN
ma-77	342	11	of	of	ADP
ma-77	342	12	univalent	univalent	ADJ
ma-77	342	13	functions	function	NOUN
ma-77	342	14	,	,	PUNCT
ma-77	342	15	demonstr	demonstr	NOUN
ma-77	342	16	.	.	PUNCT
ma-77	342	17	math	math	NOUN
ma-77	342	18	.	.	PUNCT
ma-77	343	1	38	38	NUM
ma-77	343	2	(	(	PUNCT
ma-77	343	3	2005	2005	NUM
ma-77	343	4	)	)	PUNCT
ma-77	343	5	35–42	35–42	NUM
ma-77	343	6	.	.	PUNCT
ma-77	343	7	https	https	NOUN
ma-77	343	8	:	:	PUNCT
ma-77	343	9	//doi.org/10.1515	//doi.org/10.1515	NOUN
ma-77	343	10	/	/	SYM
ma-77	343	11	dema-2005	dema-2005	NOUN
ma-77	343	12	-	-	PUNCT
ma-77	343	13	0106	0106	NUM
ma-77	343	14	.	.	PUNCT
ma-77	344	1	https://doi.org/10.28924/ada/ma.2.12	https://doi.org/10.28924/ada/ma.2.12	NUM
ma-77	344	2	https://gjom.org/index.php/gjom/article/view/583	https://gjom.org/index.php/gjom/article/view/583	PROPN
ma-77	344	3	https://gjom.org/index.php/gjom/article/view/583	https://gjom.org/index.php/gjom/article/view/583	NOUN
ma-77	344	4	https://doi.org/10.30538/psrp-oma2021.0092	https://doi.org/10.30538/psrp-oma2021.0092	X
ma-77	344	5	https://doi.org/10.1090/s0002-9947-1962-0140674-7	https://doi.org/10.1090/s0002-9947-1962-0140674-7	X
ma-77	344	6	https://doi.org/10.12988/ijma.2017.7232	https://doi.org/10.12988/ijma.2017.7232	PROPN
ma-77	344	7	https://doi.org/10.112/plms/s2-48.1.48	https://doi.org/10.112/plms/s2-48.1.48	VERB
ma-77	344	8	https://doi.org/10.112/plms/s2-48.1.48	https://doi.org/10.112/plms/s2-48.1.48	PROPN
ma-77	344	9	https://doi.org/10.1007/bfb0066543	https://doi.org/10.1007/bfb0066543	PROPN
ma-77	344	10	https://doi.org/10.1007/bfb0066543	https://doi.org/10.1007/bfb0066543	PROPN
ma-77	344	11	https://www.jams.jp/notice/mj/50-1.html	https://www.jams.jp/notice/mj/50-1.html	PROPN
ma-77	344	12	https://doi.org/10.2298/fil1614743s	https://doi.org/10.2298/fil1614743s	PROPN
ma-77	345	1	https://doi.org/10.1515/dema-2005-0106	https://doi.org/10.1515/dema-2005-0106	PROPN
ma-77	345	2	https://doi.org/10.1515/dema-2005-0106	https://doi.org/10.1515/dema-2005-0106	PROPN
ma-77	345	3	1	1	NUM
ma-77	345	4	.	.	PUNCT
ma-77	346	1	introduction	introduction	NOUN
ma-77	346	2	and	and	CCONJ
ma-77	346	3	definitions	definition	NOUN
ma-77	346	4	2	2	NUM
ma-77	346	5	.	.	PUNCT
ma-77	346	6	relevant	relevant	ADJ
ma-77	346	7	lemmas	lemmas	PROPN
ma-77	346	8	3	3	NUM
ma-77	346	9	.	.	PUNCT
ma-77	346	10	main	main	ADJ
ma-77	346	11	results	result	NOUN
ma-77	346	12	references	reference	NOUN