id	sid	tid	token	lemma	pos
cana-2210	1	1	communications	communication	NOUN
cana-2210	1	2	on	on	ADP
cana-2210	1	3	applied	apply	VERB
cana-2210	1	4	nonlinear	nonlinear	ADJ
cana-2210	1	5	analysis	analysis	NOUN
cana-2210	1	6	issn	issn	NOUN
cana-2210	1	7	:	:	PUNCT
cana-2210	1	8	1074	1074	NUM
cana-2210	1	9	-	-	PUNCT
cana-2210	1	10	133x	133x	NUM
cana-2210	1	11	vol	vol	NOUN
cana-2210	1	12	32	32	NUM
cana-2210	1	13	no	no	NOUN
cana-2210	1	14	.	.	PUNCT
cana-2210	2	1	1s	1s	NUM
cana-2210	2	2	(	(	PUNCT
cana-2210	2	3	2025	2025	NUM
cana-2210	2	4	)	)	PUNCT
cana-2210	2	5	461	461	NUM
cana-2210	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2210	2	7	a	a	DET
cana-2210	2	8	new	new	ADJ
cana-2210	2	9	subclass	subclass	NOUN
cana-2210	2	10	of	of	ADP
cana-2210	2	11	univalent	univalent	ADJ
cana-2210	2	12	functions	function	NOUN
cana-2210	2	13	defined	define	VERB
cana-2210	2	14	by	by	ADP
cana-2210	2	15	raducanu	raducanu	NOUN
cana-2210	2	16	-	-	PUNCT
cana-2210	2	17	orhan	orhan	PROPN
cana-2210	2	18	linear	linear	PROPN
cana-2210	2	19	differential	differential	NOUN
cana-2210	2	20	operator	operator	NOUN
cana-2210	2	21	thirucheran	thirucheran	VERB
cana-2210	2	22	m1	m1	PROPN
cana-2210	2	23	,	,	PUNCT
cana-2210	2	24	saravanan	saravanan	PROPN
cana-2210	2	25	k2	k2	PROPN
cana-2210	2	26	,	,	PUNCT
cana-2210	2	27	stalin	stalin	PROPN
cana-2210	2	28	t3	t3	PROPN
cana-2210	2	29	,	,	PUNCT
cana-2210	2	30	and	and	CCONJ
cana-2210	2	31	brotto	brotto	ADJ
cana-2210	2	32	manoj	manoj	PROPN
cana-2210	2	33	a4	a4	PROPN
cana-2210	2	34	1department	1department	NUM
cana-2210	2	35	of	of	ADP
cana-2210	2	36	mathematics	mathematic	NOUN
cana-2210	2	37	,	,	PUNCT
cana-2210	2	38	l	l	PROPN
cana-2210	2	39	n	n	PRON
cana-2210	2	40	government	government	NOUN
cana-2210	2	41	college	college	NOUN
cana-2210	2	42	,	,	PUNCT
cana-2210	2	43	ponneri	ponneri	NOUN
cana-2210	2	44	,	,	PUNCT
cana-2210	2	45	chennai	chennai	NOUN
cana-2210	2	46	,	,	PUNCT
cana-2210	2	47	601	601	NUM
cana-2210	2	48	204	204	NUM
cana-2210	2	49	,	,	PUNCT
cana-2210	2	50	india	india	PROPN
cana-2210	2	51	.	.	PUNCT
cana-2210	3	1	drthirucheran@gmail.com	drthirucheran@gmail.com	X
cana-2210	4	1	2department	2department	NUM
cana-2210	4	2	of	of	ADP
cana-2210	4	3	mathematics	mathematic	NOUN
cana-2210	4	4	,	,	PUNCT
cana-2210	4	5	dr	dr	PROPN
cana-2210	4	6	ambedkar	ambedkar	PROPN
cana-2210	4	7	government	government	PROPN
cana-2210	4	8	arts	arts	PROPN
cana-2210	4	9	college	college	PROPN
cana-2210	4	10	,	,	PUNCT
cana-2210	4	11	chennai	chennai	PROPN
cana-2210	4	12	,	,	PUNCT
cana-2210	4	13	600	600	NUM
cana-2210	4	14	039	039	NUM
cana-2210	4	15	,	,	PUNCT
cana-2210	4	16	india	india	PROPN
cana-2210	4	17	.	.	PUNCT
cana-2210	5	1	saravanandagac@gmail.com	saravanandagac@gmail.com	X
cana-2210	6	1	3department	3department	NUM
cana-2210	6	2	of	of	ADP
cana-2210	6	3	mathematics	mathematic	NOUN
cana-2210	6	4	,	,	PUNCT
cana-2210	6	5	vel	vel	PROPN
cana-2210	6	6	tech	tech	PROPN
cana-2210	6	7	rangarajan	rangarajan	PROPN
cana-2210	6	8	dr	dr	PROPN
cana-2210	6	9	sagunthala	sagunthala	PROPN
cana-2210	6	10	r	r	PROPN
cana-2210	6	11	&	&	CCONJ
cana-2210	6	12	dinstitute	dinstitute	VERB
cana-2210	6	13	of	of	ADP
cana-2210	6	14	science	science	NOUN
cana-2210	6	15	and	and	CCONJ
cana-2210	6	16	technology	technology	NOUN
cana-2210	6	17	,	,	PUNCT
cana-2210	6	18	chennai	chennai	PROPN
cana-2210	6	19	,	,	PUNCT
cana-2210	6	20	600	600	NUM
cana-2210	6	21	062	062	NUM
cana-2210	6	22	,	,	PUNCT
cana-2210	6	23	india	india	PROPN
cana-2210	6	24	.	.	PUNCT
cana-2210	6	25	drstalint@veltech.edu.in	drstalint@veltech.edu.in	PROPN
cana-2210	6	26	4department	4department	NUM
cana-2210	6	27	of	of	ADP
cana-2210	6	28	advanced	advanced	ADJ
cana-2210	6	29	computer	computer	NOUN
cana-2210	6	30	science	science	NOUN
cana-2210	6	31	and	and	CCONJ
cana-2210	6	32	engineering	engineering	NOUN
cana-2210	6	33	,	,	PUNCT
cana-2210	6	34	vignan	vignan	NOUN
cana-2210	6	35	’s	’s	PART
cana-2210	6	36	foundation	foundation	PROPN
cana-2210	6	37	for	for	ADP
cana-2210	6	38	science	science	NOUN
cana-2210	6	39	,	,	PUNCT
cana-2210	6	40	technology	technology	NOUN
cana-2210	6	41	&	&	CCONJ
cana-2210	6	42	research	research	NOUN
cana-2210	6	43	,	,	PUNCT
cana-2210	6	44	guntur(dist)-522213	guntur(dist)-522213	PROPN
cana-2210	6	45	,	,	PUNCT
cana-2210	6	46	andhra	andhra	PROPN
cana-2210	6	47	pradesh	pradesh	PROPN
cana-2210	6	48	,	,	PUNCT
cana-2210	6	49	india	india	PROPN
cana-2210	6	50	.	.	PUNCT
cana-2210	7	1	brittomanoj@gmail.com	brittomanoj@gmail.com	X
cana-2210	7	2	article	article	NOUN
cana-2210	7	3	history	history	NOUN
cana-2210	7	4	:	:	PUNCT
cana-2210	7	5	received	receive	VERB
cana-2210	7	6	:	:	PUNCT
cana-2210	7	7	23	23	NUM
cana-2210	7	8	-	-	SYM
cana-2210	7	9	08	08	NUM
cana-2210	7	10	-	-	PUNCT
cana-2210	7	11	2024	2024	NUM
cana-2210	7	12	revised	revise	VERB
cana-2210	7	13	:	:	PUNCT
cana-2210	7	14	06	06	NUM
cana-2210	7	15	-	-	SYM
cana-2210	7	16	10	10	NUM
cana-2210	7	17	-	-	PUNCT
cana-2210	7	18	2024	2024	NUM
cana-2210	7	19	accepted	accept	VERB
cana-2210	7	20	:	:	PUNCT
cana-2210	7	21	25	25	NUM
cana-2210	7	22	-	-	SYM
cana-2210	7	23	10	10	NUM
cana-2210	7	24	-	-	PUNCT
cana-2210	7	25	2024	2024	NUM
cana-2210	7	26	abstract	abstract	NOUN
cana-2210	7	27	:	:	PUNCT
cana-2210	7	28	the	the	DET
cana-2210	7	29	univalent	univalent	ADJ
cana-2210	7	30	function	function	NOUN
cana-2210	7	31	is	be	AUX
cana-2210	7	32	incredibly	incredibly	ADV
cana-2210	7	33	exciting	exciting	ADJ
cana-2210	7	34	,	,	PUNCT
cana-2210	7	35	as	as	SCONJ
cana-2210	7	36	evidenced	evidence	VERB
cana-2210	7	37	by	by	ADP
cana-2210	7	38	the	the	DET
cana-2210	7	39	large	large	ADJ
cana-2210	7	40	number	number	NOUN
cana-2210	7	41	of	of	ADP
cana-2210	7	42	new	new	ADJ
cana-2210	7	43	studies	study	NOUN
cana-2210	7	44	that	that	PRON
cana-2210	7	45	have	have	AUX
cana-2210	7	46	been	be	AUX
cana-2210	7	47	written	write	VERB
cana-2210	7	48	about	about	ADP
cana-2210	7	49	it	it	PRON
cana-2210	7	50	recently	recently	ADV
cana-2210	7	51	.	.	PUNCT
cana-2210	8	1	as	as	ADP
cana-2210	8	2	injective	injective	ADJ
cana-2210	8	3	analytic	analytic	ADJ
cana-2210	8	4	functions	function	NOUN
cana-2210	8	5	,	,	PUNCT
cana-2210	8	6	univalent	univalent	ADJ
cana-2210	8	7	functions	function	NOUN
cana-2210	8	8	do	do	AUX
cana-2210	8	9	not	not	PART
cana-2210	8	10	take	take	VERB
cana-2210	8	11	the	the	DET
cana-2210	8	12	same	same	ADJ
cana-2210	8	13	value	value	NOUN
cana-2210	8	14	at	at	ADP
cana-2210	8	15	different	different	ADJ
cana-2210	8	16	points	point	NOUN
cana-2210	8	17	inside	inside	ADP
cana-2210	8	18	their	their	PRON
cana-2210	8	19	domain	domain	NOUN
cana-2210	8	20	.	.	PUNCT
cana-2210	9	1	univalent	univalent	ADJ
cana-2210	9	2	functions	function	NOUN
cana-2210	9	3	are	be	AUX
cana-2210	9	4	widely	widely	ADV
cana-2210	9	5	used	use	VERB
cana-2210	9	6	in	in	ADP
cana-2210	9	7	several	several	ADJ
cana-2210	9	8	branches	branch	NOUN
cana-2210	9	9	of	of	ADP
cana-2210	9	10	mathematics	mathematic	NOUN
cana-2210	9	11	,	,	PUNCT
cana-2210	9	12	physics	physics	NOUN
cana-2210	9	13	,	,	PUNCT
cana-2210	9	14	and	and	CCONJ
cana-2210	9	15	engineering	engineering	NOUN
cana-2210	9	16	and	and	CCONJ
cana-2210	9	17	are	be	AUX
cana-2210	9	18	particularly	particularly	ADV
cana-2210	9	19	significant	significant	ADJ
cana-2210	9	20	in	in	ADP
cana-2210	9	21	complicated	complicated	ADJ
cana-2210	9	22	analysis	analysis	NOUN
cana-2210	9	23	.	.	PUNCT
cana-2210	10	1	operators	operator	NOUN
cana-2210	10	2	of	of	ADP
cana-2210	10	3	normalized	normalize	VERB
cana-2210	10	4	analytic	analytic	ADJ
cana-2210	10	5	functions	function	NOUN
cana-2210	10	6	are	be	AUX
cana-2210	10	7	in	in	ADP
cana-2210	10	8	considerable	considerable	ADJ
cana-2210	10	9	demand	demand	NOUN
cana-2210	10	10	these	these	DET
cana-2210	10	11	days	day	NOUN
cana-2210	10	12	,	,	PUNCT
cana-2210	10	13	especially	especially	ADV
cana-2210	10	14	differential	differential	ADJ
cana-2210	10	15	and	and	CCONJ
cana-2210	10	16	integral	integral	ADJ
cana-2210	10	17	operators	operator	NOUN
cana-2210	10	18	.	.	PUNCT
cana-2210	11	1	there	there	PRON
cana-2210	11	2	are	be	VERB
cana-2210	11	3	many	many	ADJ
cana-2210	11	4	mathematical	mathematical	ADJ
cana-2210	11	5	and	and	CCONJ
cana-2210	11	6	scientific	scientific	ADJ
cana-2210	11	7	applications	application	NOUN
cana-2210	11	8	for	for	ADP
cana-2210	11	9	operators	operator	NOUN
cana-2210	11	10	.	.	PUNCT
cana-2210	12	1	these	these	DET
cana-2210	12	2	operators	operator	NOUN
cana-2210	12	3	,	,	PUNCT
cana-2210	12	4	which	which	PRON
cana-2210	12	5	are	be	AUX
cana-2210	12	6	also	also	ADV
cana-2210	12	7	employed	employ	VERB
cana-2210	12	8	to	to	PART
cana-2210	12	9	explain	explain	VERB
cana-2210	12	10	a	a	DET
cana-2210	12	11	wide	wide	ADJ
cana-2210	12	12	range	range	NOUN
cana-2210	12	13	of	of	ADP
cana-2210	12	14	physical	physical	ADJ
cana-2210	12	15	processes	process	NOUN
cana-2210	12	16	,	,	PUNCT
cana-2210	12	17	can	can	AUX
cana-2210	12	18	be	be	AUX
cana-2210	12	19	utilized	utilize	VERB
cana-2210	12	20	to	to	PART
cana-2210	12	21	solve	solve	VERB
cana-2210	12	22	differential	differential	ADJ
cana-2210	12	23	equations	equation	NOUN
cana-2210	12	24	.	.	PUNCT
cana-2210	13	1	a	a	DET
cana-2210	13	2	significant	significant	ADJ
cana-2210	13	3	amount	amount	NOUN
cana-2210	13	4	of	of	ADP
cana-2210	13	5	material	material	NOUN
cana-2210	13	6	has	have	AUX
cana-2210	13	7	been	be	AUX
cana-2210	13	8	studied	study	VERB
cana-2210	13	9	and	and	CCONJ
cana-2210	13	10	debated	debate	VERB
cana-2210	13	11	by	by	ADP
cana-2210	13	12	numerous	numerous	ADJ
cana-2210	13	13	researchers	researcher	NOUN
cana-2210	13	14	for	for	ADP
cana-2210	13	15	the	the	DET
cana-2210	13	16	operators	operator	NOUN
cana-2210	13	17	.	.	PUNCT
cana-2210	14	1	in	in	ADP
cana-2210	14	2	this	this	DET
cana-2210	14	3	study	study	NOUN
cana-2210	14	4	,	,	PUNCT
cana-2210	14	5	the	the	DET
cana-2210	14	6	raducanu	raducanu	NOUN
cana-2210	14	7	-	-	PUNCT
cana-2210	14	8	orhan	orhan	PROPN
cana-2210	14	9	differential	differential	NOUN
cana-2210	14	10	operator	operator	NOUN
cana-2210	14	11	defines	define	VERB
cana-2210	14	12	the	the	DET
cana-2210	14	13	new	new	ADJ
cana-2210	14	14	subclass	subclass	NOUN
cana-2210	14	15	of	of	ADP
cana-2210	14	16	univalent	univalent	ADJ
cana-2210	14	17	functions	function	NOUN
cana-2210	14	18	.	.	PUNCT
cana-2210	15	1	furthermore	furthermore	ADV
cana-2210	15	2	,	,	PUNCT
cana-2210	15	3	the	the	DET
cana-2210	15	4	subclass	subclass	NOUN
cana-2210	15	5	’s	’s	PART
cana-2210	15	6	fekte	fekte	PROPN
cana-2210	15	7	-	-	PUNCT
cana-2210	15	8	szego	szego	NOUN
cana-2210	15	9	inequality	inequality	NOUN
cana-2210	15	10	,	,	PUNCT
cana-2210	15	11	extreme	extreme	ADJ
cana-2210	15	12	points	point	NOUN
cana-2210	15	13	,	,	PUNCT
cana-2210	15	14	integral	integral	ADJ
cana-2210	15	15	means	mean	NOUN
cana-2210	15	16	of	of	ADP
cana-2210	15	17	inequalities	inequality	NOUN
cana-2210	15	18	,	,	PUNCT
cana-2210	15	19	and	and	CCONJ
cana-2210	15	20	coefficient	coefficient	NOUN
cana-2210	15	21	inequality	inequality	NOUN
cana-2210	15	22	have	have	AUX
cana-2210	15	23	been	be	AUX
cana-2210	15	24	determined	determine	VERB
cana-2210	15	25	.	.	PUNCT
cana-2210	16	1	keywords	keyword	NOUN
cana-2210	16	2	:	:	PUNCT
cana-2210	16	3	univalent	univalent	ADJ
cana-2210	16	4	functions	function	NOUN
cana-2210	16	5	,	,	PUNCT
cana-2210	16	6	differential	differential	NOUN
cana-2210	16	7	operator	operator	NOUN
cana-2210	16	8	,	,	PUNCT
cana-2210	16	9	subordination	subordination	NOUN
cana-2210	16	10	,	,	PUNCT
cana-2210	16	11	coefficient	coefficient	NOUN
cana-2210	16	12	inequality	inequality	NOUN
cana-2210	16	13	.	.	PUNCT
cana-2210	17	1	1	1	X
cana-2210	17	2	.	.	X
cana-2210	17	3	introduction	introduction	NOUN
cana-2210	17	4	a	a	DET
cana-2210	17	5	univalent	univalent	ADJ
cana-2210	17	6	analytic	analytic	ADJ
cana-2210	17	7	function	function	NOUN
cana-2210	17	8	in	in	ADP
cana-2210	17	9	the	the	DET
cana-2210	17	10	complex	complex	ADJ
cana-2210	17	11	plane	plane	NOUN
cana-2210	17	12	is	be	AUX
cana-2210	17	13	a	a	DET
cana-2210	17	14	one	one	NUM
cana-2210	17	15	-	-	PUNCT
cana-2210	17	16	to	to	ADP
cana-2210	17	17	-	-	PUNCT
cana-2210	17	18	one	one	NUM
cana-2210	17	19	function	function	NOUN
cana-2210	17	20	that	that	PRON
cana-2210	17	21	is	be	AUX
cana-2210	17	22	also	also	ADV
cana-2210	17	23	referred	refer	VERB
cana-2210	17	24	to	to	ADP
cana-2210	17	25	as	as	ADP
cana-2210	17	26	a	a	DET
cana-2210	17	27	univalent	univalent	ADJ
cana-2210	17	28	function	function	NOUN
cana-2210	17	29	.	.	PUNCT
cana-2210	18	1	in	in	ADP
cana-2210	18	2	many	many	ADJ
cana-2210	18	3	branches	branch	NOUN
cana-2210	18	4	of	of	ADP
cana-2210	18	5	mathematics	mathematic	NOUN
cana-2210	18	6	,	,	PUNCT
cana-2210	18	7	such	such	ADJ
cana-2210	18	8	as	as	ADP
cana-2210	18	9	differential	differential	ADJ
cana-2210	18	10	equations	equation	NOUN
cana-2210	18	11	and	and	CCONJ
cana-2210	18	12	complex	complex	ADJ
cana-2210	18	13	analysis	analysis	NOUN
cana-2210	18	14	,	,	PUNCT
cana-2210	18	15	uniform	uniform	ADJ
cana-2210	18	16	functions	function	NOUN
cana-2210	18	17	play	play	VERB
cana-2210	18	18	a	a	DET
cana-2210	18	19	significant	significant	ADJ
cana-2210	18	20	role	role	NOUN
cana-2210	18	21	because	because	SCONJ
cana-2210	18	22	of	of	ADP
cana-2210	18	23	their	their	PRON
cana-2210	18	24	unique	unique	ADJ
cana-2210	18	25	characteristics	characteristic	NOUN
cana-2210	18	26	and	and	CCONJ
cana-2210	18	27	uses	use	NOUN
cana-2210	18	28	.	.	PUNCT
cana-2210	19	1	for	for	SCONJ
cana-2210	19	2	ex	ex	PRON
cana-2210	19	3	ample	ample	ADJ
cana-2210	19	4	,	,	PUNCT
cana-2210	19	5	univalent	univalent	ADJ
cana-2210	19	6	functions	function	NOUN
cana-2210	19	7	can	can	AUX
cana-2210	19	8	be	be	AUX
cana-2210	19	9	used	use	VERB
cana-2210	19	10	to	to	PART
cana-2210	19	11	express	express	VERB
cana-2210	19	12	conformal	conformal	ADJ
cana-2210	19	13	mappings	mapping	NOUN
cana-2210	19	14	,	,	PUNCT
cana-2210	19	15	which	which	PRON
cana-2210	19	16	maintain	maintain	VERB
cana-2210	19	17	angles	angle	NOUN
cana-2210	19	18	locally	locally	ADV
cana-2210	19	19	;	;	PUNCT
cana-2210	19	20	they	they	PRON
cana-2210	19	21	are	be	AUX
cana-2210	19	22	particularly	particularly	ADV
cana-2210	19	23	relevant	relevant	ADJ
cana-2210	19	24	in	in	ADP
cana-2210	19	25	complex	complex	ADJ
cana-2210	19	26	analysis	analysis	NOUN
cana-2210	19	27	.	.	PUNCT
cana-2210	20	1	the	the	DET
cana-2210	20	2	detailed	detailed	ADJ
cana-2210	20	3	study	study	NOUN
cana-2210	20	4	for	for	ADP
cana-2210	20	5	the	the	DET
cana-2210	20	6	class	class	NOUN
cana-2210	20	7	of	of	ADP
cana-2210	20	8	univalent	univalent	ADJ
cana-2210	20	9	functions	function	NOUN
cana-2210	20	10	is	be	AUX
cana-2210	20	11	more	more	ADV
cana-2210	20	12	important	important	ADJ
cana-2210	20	13	because	because	SCONJ
cana-2210	20	14	it	it	PRON
cana-2210	20	15	has	have	VERB
cana-2210	20	16	links	link	NOUN
cana-2210	20	17	to	to	ADP
cana-2210	20	18	many	many	ADJ
cana-2210	20	19	other	other	ADJ
cana-2210	20	20	areas	area	NOUN
cana-2210	20	21	,	,	PUNCT
cana-2210	20	22	including	include	VERB
cana-2210	20	23	the	the	DET
cana-2210	20	24	theory	theory	NOUN
cana-2210	20	25	of	of	ADP
cana-2210	20	26	special	special	ADJ
cana-2210	20	27	functions	function	NOUN
cana-2210	20	28	,	,	PUNCT
cana-2210	20	29	geo	geo	PROPN
cana-2210	20	30	metric	metric	ADJ
cana-2210	20	31	function	function	PROPN
cana-2210	20	32	theory	theory	NOUN
cana-2210	20	33	,	,	PUNCT
cana-2210	20	34	and	and	CCONJ
cana-2210	20	35	conformal	conformal	ADJ
cana-2210	20	36	mapping	mapping	NOUN
cana-2210	20	37	.	.	PUNCT
cana-2210	21	1	to	to	PART
cana-2210	21	2	gain	gain	VERB
cana-2210	21	3	a	a	DET
cana-2210	21	4	better	well	ADJ
cana-2210	21	5	understanding	understanding	NOUN
cana-2210	21	6	of	of	ADP
cana-2210	21	7	these	these	DET
cana-2210	21	8	functions	function	NOUN
cana-2210	21	9	’	'	PUNCT
cana-2210	21	10	behaviour	behaviour	NOUN
cana-2210	21	11	and	and	CCONJ
cana-2210	21	12	applicability	applicability	NOUN
cana-2210	21	13	in	in	ADP
cana-2210	21	14	other	other	ADJ
cana-2210	21	15	mathematical	mathematical	ADJ
cana-2210	21	16	domains	domain	NOUN
cana-2210	21	17	,	,	PUNCT
cana-2210	21	18	researchers	researcher	NOUN
cana-2210	21	19	frequently	frequently	ADV
cana-2210	21	20	look	look	VERB
cana-2210	21	21	at	at	ADP
cana-2210	21	22	aspects	aspect	NOUN
cana-2210	21	23	of	of	ADP
cana-2210	21	24	these	these	DET
cana-2210	21	25	functions	function	NOUN
cana-2210	21	26	such	such	ADJ
cana-2210	21	27	growth	growth	NOUN
cana-2210	21	28	requirements	requirement	NOUN
cana-2210	21	29	,	,	PUNCT
cana-2210	21	30	distortion	distortion	NOUN
cana-2210	21	31	theorems	theorem	NOUN
cana-2210	21	32	,	,	PUNCT
cana-2210	21	33	and	and	CCONJ
cana-2210	21	34	coefficient	coefficient	NOUN
cana-2210	21	35	bounds	bound	NOUN
cana-2210	21	36	.	.	PUNCT
cana-2210	22	1	in	in	ADP
cana-2210	22	2	recent	recent	ADJ
cana-2210	22	3	years	year	NOUN
cana-2210	22	4	,	,	PUNCT
cana-2210	22	5	researchers	researcher	NOUN
cana-2210	22	6	have	have	AUX
cana-2210	22	7	become	become	VERB
cana-2210	22	8	popular	popular	ADJ
cana-2210	22	9	for	for	ADP
cana-2210	22	10	defining	define	VERB
cana-2210	22	11	a	a	DET
cana-2210	22	12	new	new	ADJ
cana-2210	22	13	subclass	subclass	NOUN
cana-2210	22	14	of	of	ADP
cana-2210	22	15	univalent	univalent	ADJ
cana-2210	22	16	analytic	analytic	ADJ
cana-2210	22	17	functions	function	NOUN
cana-2210	22	18	linked	link	VERB
cana-2210	22	19	with	with	ADP
cana-2210	22	20	some	some	DET
cana-2210	22	21	differential	differential	ADJ
cana-2210	22	22	operators	operator	NOUN
cana-2210	22	23	[	[	X
cana-2210	22	24	17	17	NUM
cana-2210	22	25	,	,	PUNCT
cana-2210	22	26	9	9	NUM
cana-2210	22	27	,	,	PUNCT
cana-2210	22	28	3	3	NUM
cana-2210	22	29	,	,	PUNCT
cana-2210	22	30	21	21	NUM
cana-2210	22	31	,	,	PUNCT
cana-2210	22	32	23	23	NUM
cana-2210	22	33	,	,	PUNCT
cana-2210	22	34	24	24	NUM
cana-2210	22	35	]	]	PUNCT
cana-2210	22	36	.	.	PUNCT
cana-2210	23	1	because	because	SCONJ
cana-2210	23	2	it	it	PRON
cana-2210	23	3	has	have	VERB
cana-2210	23	4	many	many	ADJ
cana-2210	23	5	applications	application	NOUN
cana-2210	23	6	in	in	ADP
cana-2210	23	7	mathematics	mathematic	NOUN
cana-2210	23	8	,	,	PUNCT
cana-2210	23	9	physics	physics	NOUN
cana-2210	23	10	,	,	PUNCT
cana-2210	23	11	and	and	CCONJ
cana-2210	23	12	engineering	engineering	NOUN
cana-2210	23	13	.	.	PUNCT
cana-2210	24	1	the	the	DET
cana-2210	24	2	core	core	NOUN
cana-2210	24	3	challenges	challenge	NOUN
cana-2210	24	4	in	in	ADP
cana-2210	24	5	the	the	DET
cana-2210	24	6	theory	theory	NOUN
cana-2210	24	7	of	of	ADP
cana-2210	24	8	univalent	univalent	ADJ
cana-2210	24	9	functions	function	NOUN
cana-2210	24	10	are	be	AUX
cana-2210	24	11	comprehending	comprehend	VERB
cana-2210	24	12	limit	limit	NOUN
cana-2210	24	13	correspondence	correspondence	NOUN
cana-2210	24	14	in	in	ADP
cana-2210	24	15	conformal	conformal	ADJ
cana-2210	24	16	mapping	mapping	NOUN
cana-2210	24	17	,	,	PUNCT
cana-2210	24	18	figuring	figure	VERB
cana-2210	24	19	out	out	ADP
cana-2210	24	20	univalent	univalent	ADJ
cana-2210	24	21	mailto:drthirucheran@gmail.com	mailto:drthirucheran@gmail.com	PROPN
cana-2210	24	22	mailto:drstalint@veltech.edu.in	mailto:drstalint@veltech.edu.in	NOUN
cana-2210	24	23	mailto:brittomanoj@gmail.com	mailto:brittomanoj@gmail.com	NOUN
cana-2210	24	24	communications	communication	NOUN
cana-2210	24	25	on	on	ADP
cana-2210	24	26	applied	apply	VERB
cana-2210	24	27	nonlinear	nonlinear	ADJ
cana-2210	24	28	analysis	analysis	NOUN
cana-2210	24	29	issn	issn	NOUN
cana-2210	24	30	:	:	PUNCT
cana-2210	24	31	1074	1074	NUM
cana-2210	24	32	-	-	PUNCT
cana-2210	24	33	133x	133x	NUM
cana-2210	24	34	vol	vol	NOUN
cana-2210	24	35	32	32	NUM
cana-2210	24	36	no	no	NOUN
cana-2210	24	37	.	.	PUNCT
cana-2210	25	1	1s	1s	NUM
cana-2210	25	2	(	(	PUNCT
cana-2210	25	3	2025	2025	NUM
cana-2210	25	4	)	)	PUNCT
cana-2210	25	5	462	462	NUM
cana-2210	25	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2210	25	7	requirements	requirement	NOUN
cana-2210	25	8	and	and	CCONJ
cana-2210	25	9	addressing	address	VERB
cana-2210	25	10	numerous	numerous	ADJ
cana-2210	25	11	functional	functional	ADJ
cana-2210	25	12	theory	theory	NOUN
cana-2210	25	13	extreme	extreme	ADJ
cana-2210	25	14	problems	problem	NOUN
cana-2210	25	15	.	.	PUNCT
cana-2210	26	1	more	more	ADV
cana-2210	26	2	precisely	precisely	ADV
cana-2210	26	3	defining	define	VERB
cana-2210	26	4	limits	limit	NOUN
cana-2210	26	5	on	on	ADP
cana-2210	26	6	a	a	DET
cana-2210	26	7	range	range	NOUN
cana-2210	26	8	of	of	ADP
cana-2210	26	9	values	value	NOUN
cana-2210	26	10	for	for	ADP
cana-2210	26	11	various	various	ADJ
cana-2210	26	12	functions	function	NOUN
cana-2210	26	13	in	in	ADP
cana-2210	26	14	class	class	NOUN
cana-2210	26	15	.	.	PUNCT
cana-2210	27	1	the	the	DET
cana-2210	27	2	area	area	NOUN
cana-2210	27	3	principle	principle	NOUN
cana-2210	27	4	was	be	AUX
cana-2210	27	5	used	use	VERB
cana-2210	27	6	to	to	PART
cana-2210	27	7	generate	generate	VERB
cana-2210	27	8	the	the	DET
cana-2210	27	9	first	first	ADJ
cana-2210	27	10	significant	significant	ADJ
cana-2210	27	11	findings	finding	NOUN
cana-2210	27	12	in	in	ADP
cana-2210	27	13	the	the	DET
cana-2210	27	14	theory	theory	NOUN
cana-2210	27	15	of	of	ADP
cana-2210	27	16	univalent	univalent	ADJ
cana-2210	27	17	functions	function	NOUN
cana-2210	27	18	.	.	PUNCT
cana-2210	28	1	bieberbach	bieberbach	NOUN
cana-2210	29	1	[	[	X
cana-2210	29	2	4	4	X
cana-2210	29	3	]	]	PUNCT
cana-2210	29	4	found	find	VERB
cana-2210	29	5	exact	exact	ADJ
cana-2210	29	6	upper	upper	ADJ
cana-2210	29	7	and	and	CCONJ
cana-2210	29	8	lower	low	ADJ
cana-2210	29	9	bounds	bound	NOUN
cana-2210	29	10	for	for	ADP
cana-2210	29	11	|𝑓(𝜁)|	|𝑓(𝜁)|	NOUN
cana-2210	29	12	and	and	CCONJ
cana-2210	29	13	|𝑓	|𝑓	NOUN
cana-2210	29	14	′(𝜁)|	′(𝜁)|	X
cana-2210	29	15	for	for	ADP
cana-2210	29	16	𝑓	𝑓	DET
cana-2210	29	17	∈	∈	PROPN
cana-2210	29	18	𝑆	𝑆	PROPN
cana-2210	29	19	,	,	PUNCT
cana-2210	29	20	given	give	VERB
cana-2210	29	21	|𝑎2|	|𝑎2|	NOUN
cana-2210	29	22	≤	≤	ADJ
cana-2210	29	23	2	2	NUM
cana-2210	29	24	and	and	CCONJ
cana-2210	29	25	hypothesized	hypothesize	VERB
cana-2210	29	26	that	that	SCONJ
cana-2210	29	27	|𝑎𝑛|	|𝑎𝑛|	DET
cana-2210	29	28	≤	≤	PUNCT
cana-2210	29	29	𝑛	𝑛	PRON
cana-2210	29	30	with	with	ADP
cana-2210	29	31	the	the	DET
cana-2210	29	32	help	help	NOUN
cana-2210	29	33	of	of	ADP
cana-2210	29	34	the	the	DET
cana-2210	29	35	outer	outer	ADJ
cana-2210	29	36	area	area	NOUN
cana-2210	29	37	theorem	theorem	NOUN
cana-2210	29	38	(	(	PUNCT
cana-2210	29	39	1916	1916	NUM
cana-2210	29	40	)	)	PUNCT
cana-2210	29	41	.	.	PUNCT
cana-2210	30	1	additionally	additionally	ADV
cana-2210	30	2	,	,	PUNCT
cana-2210	30	3	he	he	PRON
cana-2210	30	4	determined	determine	VERB
cana-2210	30	5	the	the	DET
cana-2210	30	6	koebe	koebe	NOUN
cana-2210	30	7	[	[	X
cana-2210	30	8	11	11	NUM
cana-2210	30	9	]	]	X
cana-2210	30	10	constant	constant	PROPN
cana-2210	30	11	’s	’s	PART
cana-2210	30	12	precise	precise	ADJ
cana-2210	30	13	value	value	NOUN
cana-2210	30	14	.	.	PUNCT
cana-2210	31	1	for	for	ADP
cana-2210	31	2	a	a	DET
cana-2210	31	3	long	long	ADJ
cana-2210	31	4	time	time	NOUN
cana-2210	31	5	,	,	PUNCT
cana-2210	31	6	mathematicians	mathematician	NOUN
cana-2210	31	7	have	have	AUX
cana-2210	31	8	been	be	AUX
cana-2210	31	9	challenged	challenge	VERB
cana-2210	31	10	by	by	ADP
cana-2210	31	11	this	this	DET
cana-2210	31	12	conjecture	conjecture	NOUN
cana-2210	31	13	.	.	PUNCT
cana-2210	32	1	louis	louis	X
cana-2210	32	2	de	de	X
cana-2210	32	3	branges	brange	NOUN
cana-2210	32	4	[	[	X
cana-2210	32	5	6	6	NUM
cana-2210	32	6	]	]	PUNCT
cana-2210	32	7	found	find	VERB
cana-2210	32	8	a	a	DET
cana-2210	32	9	solution	solution	NOUN
cana-2210	32	10	to	to	ADP
cana-2210	32	11	the	the	DET
cana-2210	32	12	conjecture	conjecture	NOUN
cana-2210	32	13	|𝑎𝑛|	|𝑎𝑛|	ADV
cana-2210	32	14	≤	≤	NUM
cana-2210	32	15	𝑛	𝑛	NOUN
cana-2210	32	16	,	,	PUNCT
cana-2210	32	17	(	(	PUNCT
cana-2210	32	18	𝑛	𝑛	NOUN
cana-2210	32	19	=	=	SYM
cana-2210	32	20	2,3	2,3	NUM
cana-2210	32	21	,	,	PUNCT
cana-2210	32	22	…	…	PUNCT
cana-2210	32	23	.	.	PUNCT
cana-2210	32	24	)	)	PUNCT
cana-2210	32	25	in	in	ADP
cana-2210	32	26	1984	1984	NUM
cana-2210	32	27	.	.	PUNCT
cana-2210	33	1	following	follow	VERB
cana-2210	33	2	loewner	loewner	NOUN
cana-2210	33	3	[	[	X
cana-2210	33	4	12	12	NUM
cana-2210	33	5	]	]	SYM
cana-2210	33	6	’s	’s	AUX
cana-2210	33	7	1923	1923	NUM
cana-2210	33	8	proof	proof	NOUN
cana-2210	33	9	of	of	ADP
cana-2210	33	10	|𝑎3|	|𝑎3|	NOUN
cana-2210	33	11	≤	≤	ADJ
cana-2210	33	12	3	3	NUM
cana-2210	33	13	,	,	PUNCT
cana-2210	33	14	fekete	fekete	NOUN
cana-2210	33	15	-	-	PUNCT
cana-2210	33	16	szego	szego	NOUN
cana-2210	33	17	[	[	X
cana-2210	33	18	7	7	NUM
cana-2210	33	19	]	]	SYM
cana-2210	33	20	astounded	astounded	ADJ
cana-2210	33	21	mathematicians	mathematician	NOUN
cana-2210	33	22	with	with	ADP
cana-2210	33	23	the	the	DET
cana-2210	33	24	troublesome	troublesome	ADJ
cana-2210	33	25	inequality	inequality	NOUN
cana-2210	33	26	|𝑎3	|𝑎3	VERB
cana-2210	33	27	−	−	PROPN
cana-2210	33	28	µ𝑎2	µ𝑎2	PROPN
cana-2210	33	29	2|	2|	NUM
cana-2210	33	30	≤	≤	ADV
cana-2210	33	31	1	1	NUM
cana-2210	34	1	+	+	NUM
cana-2210	34	2	2𝑒	2𝑒	NUM
cana-2210	34	3	(	(	PUNCT
cana-2210	34	4	−2µ	−2µ	PROPN
cana-2210	34	5	1−µ	1−µ	NUM
cana-2210	34	6	)	)	PUNCT
cana-2210	34	7	,	,	PUNCT
cana-2210	34	8	0	0	NUM
cana-2210	34	9	≤	≤	NUM
cana-2210	34	10	µ	µ	X
cana-2210	34	11	≤	≤	NOUN
cana-2210	34	12	1	1	NUM
cana-2210	34	13	.	.	PUNCT
cana-2210	35	1	by	by	ADP
cana-2210	35	2	then	then	ADV
cana-2210	35	3	,	,	PUNCT
cana-2210	35	4	univalent	univalent	ADJ
cana-2210	35	5	function	function	NOUN
cana-2210	35	6	theory	theory	NOUN
cana-2210	35	7	had	have	AUX
cana-2210	35	8	acquired	acquire	VERB
cana-2210	35	9	its	its	PRON
cana-2210	35	10	own	own	ADJ
cana-2210	35	11	name	name	NOUN
cana-2210	35	12	.	.	PUNCT
cana-2210	36	1	a	a	DET
cana-2210	36	2	univalent	univalent	ADJ
cana-2210	36	3	function	function	NOUN
cana-2210	36	4	that	that	PRON
cana-2210	36	5	is	be	AUX
cana-2210	36	6	analytic	analytic	ADJ
cana-2210	36	7	in	in	ADP
cana-2210	36	8	a	a	DET
cana-2210	36	9	domain	domain	NOUN
cana-2210	36	10	and	and	CCONJ
cana-2210	36	11	is	be	AUX
cana-2210	36	12	also	also	ADV
cana-2210	36	13	referred	refer	VERB
cana-2210	36	14	to	to	ADP
cana-2210	36	15	as	as	ADP
cana-2210	36	16	a	a	DET
cana-2210	36	17	one	one	NUM
cana-2210	36	18	-	-	PUNCT
cana-2210	36	19	to	to	ADP
cana-2210	36	20	-	-	PUNCT
cana-2210	36	21	one	one	NUM
cana-2210	36	22	or	or	CCONJ
cana-2210	36	23	injective	injective	ADJ
cana-2210	36	24	function	function	NOUN
cana-2210	36	25	in	in	ADP
cana-2210	36	26	complex	complex	ADJ
cana-2210	36	27	analysis	analysis	NOUN
cana-2210	36	28	is	be	AUX
cana-2210	36	29	said	say	VERB
cana-2210	36	30	to	to	PART
cana-2210	36	31	be	be	AUX
cana-2210	36	32	conformal	conformal	ADJ
cana-2210	36	33	.	.	PUNCT
cana-2210	37	1	locally	locally	ADV
cana-2210	37	2	,	,	PUNCT
cana-2210	37	3	angles	angle	NOUN
cana-2210	37	4	are	be	AUX
cana-2210	37	5	preserved	preserve	VERB
cana-2210	37	6	by	by	ADP
cana-2210	37	7	conformal	conformal	ADJ
cana-2210	37	8	mappings	mapping	NOUN
cana-2210	37	9	.	.	PUNCT
cana-2210	38	1	formally	formally	ADV
cana-2210	38	2	speaking	speak	VERB
cana-2210	38	3	,	,	PUNCT
cana-2210	38	4	if	if	SCONJ
cana-2210	38	5	a	a	DET
cana-2210	38	6	function	function	NOUN
cana-2210	38	7	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	38	8	)	)	PUNCT
cana-2210	38	9	that	that	PRON
cana-2210	38	10	is	be	AUX
cana-2210	38	11	defined	define	VERB
cana-2210	38	12	on	on	ADP
cana-2210	38	13	a	a	DET
cana-2210	38	14	domain	domain	NOUN
cana-2210	38	15	𝐷	𝐷	PROPN
cana-2210	38	16	⊂	⊂	PROPN
cana-2210	38	17	𝐶	𝐶	PROPN
cana-2210	38	18	maintains	maintain	VERB
cana-2210	38	19	angles	angle	NOUN
cana-2210	38	20	between	between	ADP
cana-2210	38	21	curves	curve	NOUN
cana-2210	38	22	that	that	PRON
cana-2210	38	23	pass	pass	VERB
cana-2210	38	24	through	through	ADP
cana-2210	38	25	𝜁	𝜁	PROPN
cana-2210	38	26	,	,	PUNCT
cana-2210	38	27	then	then	ADV
cana-2210	38	28	𝜁	𝜁	PROPN
cana-2210	38	29	∈	∈	PROPN
cana-2210	38	30	𝐷	𝐷	PROPN
cana-2210	38	31	is	be	AUX
cana-2210	38	32	conformal	conformal	ADJ
cana-2210	38	33	at	at	ADP
cana-2210	38	34	that	that	DET
cana-2210	38	35	point	point	NOUN
cana-2210	38	36	.	.	PUNCT
cana-2210	39	1	a	a	DET
cana-2210	39	2	function	function	NOUN
cana-2210	39	3	is	be	AUX
cana-2210	39	4	conformal	conformal	ADJ
cana-2210	39	5	in	in	ADP
cana-2210	39	6	a	a	DET
cana-2210	39	7	domain	domain	NOUN
cana-2210	39	8	𝐷	𝐷	NOUN
cana-2210	39	9	if	if	SCONJ
cana-2210	39	10	it	it	PRON
cana-2210	39	11	is	be	AUX
cana-2210	39	12	both	both	CCONJ
cana-2210	39	13	univalent	univalent	ADJ
cana-2210	39	14	(	(	PUNCT
cana-2210	39	15	injective	injective	ADJ
cana-2210	39	16	)	)	PUNCT
cana-2210	39	17	and	and	CCONJ
cana-2210	39	18	analytic	analytic	ADJ
cana-2210	39	19	in	in	ADP
cana-2210	39	20	𝐷.	𝐷.	PROPN
cana-2210	39	21	in	in	ADP
cana-2210	39	22	line	line	NOUN
cana-2210	39	23	with	with	ADP
cana-2210	39	24	conformal	conformal	ADJ
cana-2210	39	25	maps	map	NOUN
cana-2210	39	26	in	in	ADP
cana-2210	39	27	complex	complex	ADJ
cana-2210	39	28	analysis	analysis	NOUN
cana-2210	39	29	,	,	PUNCT
cana-2210	39	30	this	this	PRON
cana-2210	39	31	indicates	indicate	VERB
cana-2210	39	32	that	that	SCONJ
cana-2210	39	33	the	the	DET
cana-2210	39	34	mapping	mapping	NOUN
cana-2210	39	35	maintains	maintain	VERB
cana-2210	39	36	the	the	DET
cana-2210	39	37	local	local	ADJ
cana-2210	39	38	structure	structure	NOUN
cana-2210	39	39	of	of	ADP
cana-2210	39	40	the	the	DET
cana-2210	39	41	domain	domain	NOUN
cana-2210	39	42	locally	locally	ADV
cana-2210	39	43	by	by	ADP
cana-2210	39	44	not	not	PART
cana-2210	39	45	distorting	distort	VERB
cana-2210	39	46	the	the	DET
cana-2210	39	47	angles	angle	NOUN
cana-2210	39	48	between	between	ADP
cana-2210	39	49	curves	curve	NOUN
cana-2210	39	50	.	.	PUNCT
cana-2210	40	1	despite	despite	SCONJ
cana-2210	40	2	of	of	ADP
cana-2210	40	3	many	many	ADJ
cana-2210	40	4	practical	practical	ADJ
cana-2210	40	5	uses	use	NOUN
cana-2210	40	6	,	,	PUNCT
cana-2210	40	7	conformal	conformal	ADJ
cana-2210	40	8	mapping	mapping	NOUN
cana-2210	40	9	is	be	AUX
cana-2210	40	10	an	an	DET
cana-2210	40	11	essential	essential	ADJ
cana-2210	40	12	technique	technique	NOUN
cana-2210	40	13	in	in	ADP
cana-2210	40	14	complex	complex	ADJ
cana-2210	40	15	analysis	analysis	NOUN
cana-2210	40	16	.	.	PUNCT
cana-2210	41	1	if	if	SCONJ
cana-2210	41	2	the	the	DET
cana-2210	41	3	function	function	NOUN
cana-2210	41	4	is	be	AUX
cana-2210	41	5	harmonic	harmonic	ADJ
cana-2210	41	6	that	that	PRON
cana-2210	41	7	is	be	AUX
cana-2210	41	8	,	,	PUNCT
cana-2210	41	9	it	it	PRON
cana-2210	41	10	satisfies	satisfy	VERB
cana-2210	41	11	𝛻2𝑓	𝛻2𝑓	PROPN
cana-2210	41	12	=	=	SYM
cana-2210	41	13	0	0	NUM
cana-2210	42	1	according	accord	VERB
cana-2210	42	2	to	to	ADP
cana-2210	42	3	laplace	laplace	NOUN
cana-2210	42	4	then	then	ADV
cana-2210	42	5	the	the	DET
cana-2210	42	6	conformal	conformal	ADJ
cana-2210	42	7	mapping	mapping	NOUN
cana-2210	42	8	transformation	transformation	NOUN
cana-2210	42	9	of	of	ADP
cana-2210	42	10	such	such	ADJ
cana-2210	42	11	functions	function	NOUN
cana-2210	42	12	is	be	AUX
cana-2210	42	13	likewise	likewise	ADV
cana-2210	42	14	harmonic	harmonic	ADJ
cana-2210	42	15	.	.	PUNCT
cana-2210	43	1	as	as	ADP
cana-2210	43	2	a	a	DET
cana-2210	43	3	result	result	NOUN
cana-2210	43	4	,	,	PUNCT
cana-2210	43	5	any	any	DET
cana-2210	43	6	field	field	NOUN
cana-2210	43	7	whose	whose	DET
cana-2210	43	8	equations	equation	NOUN
cana-2210	43	9	can	can	AUX
cana-2210	43	10	be	be	AUX
cana-2210	43	11	represented	represent	VERB
cana-2210	43	12	by	by	ADP
cana-2210	43	13	a	a	DET
cana-2210	43	14	potential	potential	ADJ
cana-2210	43	15	function	function	NOUN
cana-2210	43	16	can	can	AUX
cana-2210	43	17	be	be	AUX
cana-2210	43	18	solved	solve	VERB
cana-2210	43	19	using	use	VERB
cana-2210	43	20	conformal	conformal	ADJ
cana-2210	43	21	mapping	mapping	NOUN
cana-2210	43	22	.	.	PUNCT
cana-2210	44	1	laplace	laplace	PROPN
cana-2210	44	2	’s	’s	PART
cana-2210	44	3	equation	equation	NOUN
cana-2210	44	4	𝜙𝑥𝑥	𝜙𝑥𝑥	NOUN
cana-2210	45	1	+	+	CCONJ
cana-2210	45	2	𝜙𝑦𝑦	𝜙𝑦𝑦	NOUN
cana-2210	45	3	=	=	SYM
cana-2210	45	4	0	0	PUNCT
cana-2210	45	5	can	can	AUX
cana-2210	45	6	be	be	AUX
cana-2210	45	7	used	use	VERB
cana-2210	45	8	to	to	PART
cana-2210	45	9	formulate	formulate	VERB
cana-2210	45	10	various	various	ADJ
cana-2210	45	11	mathematical	mathematical	ADJ
cana-2210	45	12	issues	issue	NOUN
cana-2210	45	13	related	relate	VERB
cana-2210	45	14	to	to	ADP
cana-2210	45	15	the	the	DET
cana-2210	45	16	motion	motion	NOUN
cana-2210	45	17	of	of	ADP
cana-2210	45	18	fluids	fluid	NOUN
cana-2210	45	19	,	,	PUNCT
cana-2210	45	20	the	the	DET
cana-2210	45	21	field	field	NOUN
cana-2210	45	22	of	of	ADP
cana-2210	45	23	electrostatic	electrostatic	ADJ
cana-2210	45	24	,	,	PUNCT
cana-2210	45	25	heat	heat	NOUN
cana-2210	45	26	transfer	transfer	NOUN
cana-2210	45	27	,	,	PUNCT
cana-2210	45	28	and	and	CCONJ
cana-2210	45	29	many	many	ADJ
cana-2210	45	30	other	other	ADJ
cana-2210	45	31	physical	physical	ADJ
cana-2210	45	32	circumstances	circumstance	NOUN
cana-2210	45	33	in	in	ADP
cana-2210	45	34	a	a	DET
cana-2210	45	35	certain	certain	ADJ
cana-2210	45	36	region	region	NOUN
cana-2210	45	37	𝐷	𝐷	PROPN
cana-2210	45	38	of	of	ADP
cana-2210	45	39	the	the	DET
cana-2210	45	40	complex	complex	ADJ
cana-2210	45	41	plane	plane	NOUN
cana-2210	45	42	.	.	PUNCT
cana-2210	46	1	for	for	ADP
cana-2210	46	2	exam	exam	PROPN
cana-2210	46	3	ple	ple	PROPN
cana-2210	46	4	,	,	PUNCT
cana-2210	46	5	it	it	PRON
cana-2210	46	6	can	can	AUX
cana-2210	46	7	be	be	AUX
cana-2210	46	8	used	use	VERB
cana-2210	46	9	to	to	PART
cana-2210	46	10	apply	apply	VERB
cana-2210	46	11	in	in	ADP
cana-2210	46	12	scattering	scatter	VERB
cana-2210	46	13	and	and	CCONJ
cana-2210	46	14	diffraction	diffraction	NOUN
cana-2210	46	15	problems	problem	NOUN
cana-2210	46	16	,	,	PUNCT
cana-2210	46	17	brain	brain	NOUN
cana-2210	46	18	surface	surface	NOUN
cana-2210	46	19	mapping	mapping	NOUN
cana-2210	46	20	problem	problem	NOUN
cana-2210	46	21	,	,	PUNCT
cana-2210	46	22	and	and	CCONJ
cana-2210	46	23	the	the	DET
cana-2210	46	24	electrostatic	electrostatic	ADJ
cana-2210	46	25	potential	potential	ADJ
cana-2210	46	26	problems	problem	NOUN
cana-2210	46	27	in	in	ADP
cana-2210	46	28	the	the	DET
cana-2210	46	29	shaded	shaded	ADJ
cana-2210	46	30	region	region	NOUN
cana-2210	46	31	of	of	ADP
cana-2210	46	32	the	the	DET
cana-2210	46	33	𝜁	𝜁	PROPN
cana-2210	46	34	plane	plane	NOUN
cana-2210	46	35	[	[	X
cana-2210	46	36	31	31	NUM
cana-2210	46	37	,	,	PUNCT
cana-2210	46	38	32	32	NUM
cana-2210	46	39	]	]	PUNCT
cana-2210	46	40	.	.	PUNCT
cana-2210	47	1	it	it	PRON
cana-2210	47	2	can	can	AUX
cana-2210	47	3	also	also	ADV
cana-2210	47	4	be	be	AUX
cana-2210	47	5	used	use	VERB
cana-2210	47	6	in	in	ADP
cana-2210	47	7	stealth	stealth	ADJ
cana-2210	47	8	technology	technology	NOUN
cana-2210	47	9	.	.	PUNCT
cana-2210	48	1	although	although	SCONJ
cana-2210	48	2	the	the	DET
cana-2210	48	3	concept	concept	NOUN
cana-2210	48	4	of	of	ADP
cana-2210	48	5	conformal	conformal	ADJ
cana-2210	48	6	mapping	mapping	NOUN
cana-2210	48	7	is	be	AUX
cana-2210	48	8	not	not	PART
cana-2210	48	9	directly	directly	ADV
cana-2210	48	10	used	use	VERB
cana-2210	48	11	in	in	ADP
cana-2210	48	12	stealth	stealth	ADJ
cana-2210	48	13	technology	technology	NOUN
cana-2210	48	14	,	,	PUNCT
cana-2210	48	15	the	the	DET
cana-2210	48	16	development	development	NOUN
cana-2210	48	17	of	of	ADP
cana-2210	48	18	effective	effective	ADJ
cana-2210	48	19	stealth	stealth	ADJ
cana-2210	48	20	technologies	technology	NOUN
cana-2210	48	21	greatly	greatly	ADV
cana-2210	48	22	benefits	benefit	VERB
cana-2210	48	23	from	from	ADP
cana-2210	48	24	an	an	DET
cana-2210	48	25	un	un	PROPN
cana-2210	48	26	derstanding	derstanding	NOUN
cana-2210	48	27	of	of	ADP
cana-2210	48	28	shape	shape	NOUN
cana-2210	48	29	optimisation	optimisation	NOUN
cana-2210	48	30	,	,	PUNCT
cana-2210	48	31	material	material	NOUN
cana-2210	48	32	science	science	NOUN
cana-2210	48	33	,	,	PUNCT
cana-2210	48	34	and	and	CCONJ
cana-2210	48	35	electromagnetic	electromagnetic	ADJ
cana-2210	48	36	wave	wave	NOUN
cana-2210	48	37	behaviour	behaviour	NOUN
cana-2210	49	1	[	[	X
cana-2210	49	2	1	1	NUM
cana-2210	49	3	]	]	PUNCT
cana-2210	49	4	.	.	PUNCT
cana-2210	50	1	further	far	ADV
cana-2210	50	2	,	,	PUNCT
cana-2210	50	3	the	the	DET
cana-2210	50	4	univalent	univalent	ADJ
cana-2210	50	5	function	function	NOUN
cana-2210	50	6	help	help	NOUN
cana-2210	50	7	to	to	PART
cana-2210	50	8	analysis	analysis	VERB
cana-2210	50	9	the	the	DET
cana-2210	50	10	frequency	frequency	NOUN
cana-2210	50	11	analysis	analysis	NOUN
cana-2210	50	12	problem	problem	NOUN
cana-2210	50	13	[	[	X
cana-2210	50	14	16	16	NUM
cana-2210	50	15	]	]	PUNCT
cana-2210	50	16	.	.	PUNCT
cana-2210	51	1	recent	recent	ADJ
cana-2210	51	2	years	year	NOUN
cana-2210	51	3	,	,	PUNCT
cana-2210	51	4	the	the	DET
cana-2210	51	5	new	new	ADJ
cana-2210	51	6	subclasses	subclass	NOUN
cana-2210	51	7	defined	define	VERB
cana-2210	51	8	by	by	ADP
cana-2210	51	9	using	use	VERB
cana-2210	51	10	the	the	DET
cana-2210	51	11	linear	linear	ADJ
cana-2210	51	12	differential	differential	NOUN
cana-2210	51	13	operators	operator	NOUN
cana-2210	51	14	.	.	PUNCT
cana-2210	52	1	the	the	DET
cana-2210	52	2	differential	differential	ADJ
cana-2210	52	3	operator	operator	NOUN
cana-2210	52	4	was	be	AUX
cana-2210	52	5	first	first	ADV
cana-2210	52	6	introduced	introduce	VERB
cana-2210	52	7	by	by	ADP
cana-2210	52	8	ruscheweyh	ruscheweyh	NOUN
cana-2210	52	9	[	[	X
cana-2210	52	10	19	19	NUM
cana-2210	52	11	]	]	PUNCT
cana-2210	52	12	in	in	ADP
cana-2210	52	13	1975	1975	NUM
cana-2210	52	14	,	,	PUNCT
cana-2210	52	15	which	which	PRON
cana-2210	52	16	is	be	AUX
cana-2210	52	17	cleared	clear	VERB
cana-2210	52	18	the	the	DET
cana-2210	52	19	path	path	NOUN
cana-2210	52	20	.	.	PUNCT
cana-2210	53	1	salagean	salagean	ADJ
cana-2210	53	2	[	[	X
cana-2210	53	3	20	20	NUM
cana-2210	53	4	]	]	PUNCT
cana-2210	53	5	followed	follow	VERB
cana-2210	53	6	in	in	ADP
cana-2210	53	7	1983	1983	NUM
cana-2210	53	8	with	with	ADP
cana-2210	53	9	an	an	DET
cana-2210	53	10	additional	additional	ADJ
cana-2210	53	11	variation	variation	NOUN
cana-2210	53	12	of	of	ADP
cana-2210	53	13	differential	differential	ADJ
cana-2210	53	14	and	and	CCONJ
cana-2210	53	15	integral	integral	ADJ
cana-2210	53	16	operators	operator	NOUN
cana-2210	53	17	.	.	PUNCT
cana-2210	54	1	many	many	ADJ
cana-2210	54	2	scholars	scholar	NOUN
cana-2210	54	3	have	have	AUX
cana-2210	54	4	examined	examine	VERB
cana-2210	54	5	and	and	CCONJ
cana-2210	54	6	debated	debate	VERB
cana-2210	54	7	a	a	DET
cana-2210	54	8	wide	wide	ADJ
cana-2210	54	9	range	range	NOUN
cana-2210	54	10	of	of	ADP
cana-2210	54	11	properties	property	NOUN
cana-2210	54	12	related	relate	VERB
cana-2210	54	13	to	to	ADP
cana-2210	54	14	these	these	DET
cana-2210	54	15	two	two	NUM
cana-2210	54	16	operators	operator	NOUN
cana-2210	54	17	.	.	PUNCT
cana-2210	55	1	al	al	PROPN
cana-2210	55	2	-	-	PUNCT
cana-2210	55	3	oboudi	oboudi	NOUN
cana-2210	55	4	[	[	X
cana-2210	55	5	2	2	X
cana-2210	55	6	]	]	PUNCT
cana-2210	55	7	generalized	generalize	VERB
cana-2210	55	8	the	the	DET
cana-2210	55	9	salagean	salagean	ADJ
cana-2210	55	10	operator	operator	NOUN
cana-2210	55	11	in	in	ADP
cana-2210	55	12	2004	2004	NUM
cana-2210	55	13	.	.	PUNCT
cana-2210	56	1	in	in	ADP
cana-2210	56	2	2010	2010	NUM
cana-2210	56	3	,	,	PUNCT
cana-2210	56	4	raducanu	raducanu	NOUN
cana-2210	56	5	and	and	CCONJ
cana-2210	56	6	orhan	orhan	PROPN
cana-2210	56	7	[	[	X
cana-2210	56	8	15	15	NUM
cana-2210	56	9	]	]	X
cana-2210	56	10	generalized	generalize	VERB
cana-2210	56	11	the	the	DET
cana-2210	56	12	aloboudi	aloboudi	PROPN
cana-2210	56	13	differential	differential	NOUN
cana-2210	56	14	operator	operator	NOUN
cana-2210	56	15	.	.	PUNCT
cana-2210	57	1	in	in	ADP
cana-2210	57	2	this	this	DET
cana-2210	57	3	study	study	NOUN
cana-2210	57	4	we	we	PRON
cana-2210	57	5	define	define	VERB
cana-2210	57	6	two	two	NUM
cana-2210	57	7	new	new	ADJ
cana-2210	57	8	subclasses	subclass	NOUN
cana-2210	57	9	,	,	PUNCT
cana-2210	57	10	which	which	PRON
cana-2210	57	11	is	be	AUX
cana-2210	57	12	defined	define	VERB
cana-2210	57	13	by	by	ADP
cana-2210	57	14	the	the	DET
cana-2210	57	15	raducanu	raducanu	PROPN
cana-2210	57	16	-	-	PUNCT
cana-2210	57	17	orhan	orhan	PROPN
cana-2210	57	18	differential	differential	ADJ
cana-2210	57	19	operator	operator	NOUN
cana-2210	57	20	.	.	PUNCT
cana-2210	58	1	also	also	ADV
cana-2210	58	2	,	,	PUNCT
cana-2210	58	3	we	we	PRON
cana-2210	58	4	have	have	AUX
cana-2210	58	5	discussed	discuss	VERB
cana-2210	58	6	some	some	DET
cana-2210	58	7	properties	property	NOUN
cana-2210	58	8	of	of	ADP
cana-2210	58	9	these	these	DET
cana-2210	58	10	subclasses	subclass	NOUN
cana-2210	58	11	.	.	PUNCT
cana-2210	59	1	let	let	VERB
cana-2210	59	2	𝐴	𝐴	PROPN
cana-2210	59	3	be	be	AUX
cana-2210	59	4	the	the	DET
cana-2210	59	5	class	class	NOUN
cana-2210	59	6	of	of	ADP
cana-2210	59	7	univalent	univalent	ADJ
cana-2210	59	8	functions	function	NOUN
cana-2210	59	9	consists	consist	VERB
cana-2210	59	10	of	of	ADP
cana-2210	59	11	the	the	DET
cana-2210	59	12	form	form	NOUN
cana-2210	59	13	communications	communication	NOUN
cana-2210	59	14	on	on	ADP
cana-2210	59	15	applied	apply	VERB
cana-2210	59	16	nonlinear	nonlinear	ADJ
cana-2210	59	17	analysis	analysis	NOUN
cana-2210	59	18	issn	issn	NOUN
cana-2210	59	19	:	:	PUNCT
cana-2210	59	20	1074	1074	NUM
cana-2210	59	21	-	-	PUNCT
cana-2210	59	22	133x	133x	NUM
cana-2210	59	23	vol	vol	NOUN
cana-2210	59	24	32	32	NUM
cana-2210	59	25	no	no	NOUN
cana-2210	59	26	.	.	PUNCT
cana-2210	60	1	1s	1s	NUM
cana-2210	60	2	(	(	PUNCT
cana-2210	60	3	2025	2025	NUM
cana-2210	60	4	)	)	PUNCT
cana-2210	60	5	463	463	NUM
cana-2210	60	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2210	60	7	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	60	8	)	)	PUNCT
cana-2210	60	9	=	=	SYM
cana-2210	61	1	𝜁	𝜁	PROPN
cana-2210	61	2	+	+	CCONJ
cana-2210	61	3	∑	∑	PUNCT
cana-2210	61	4	𝑎𝑙	𝑎𝑙	NOUN
cana-2210	61	5	∞	∞	PROPN
cana-2210	61	6	𝑙=2	𝑙=2	PROPN
cana-2210	61	7	𝜁𝑙	𝜁𝑙	NOUN
cana-2210	61	8	,	,	PUNCT
cana-2210	61	9	𝜁	𝜁	PROPN
cana-2210	61	10	∈	∈	PROPN
cana-2210	61	11	𝑈	𝑈	PROPN
cana-2210	61	12	∶=	∶=	NUM
cana-2210	61	13	{	{	PUNCT
cana-2210	61	14	𝜁	𝜁	PROPN
cana-2210	61	15	∈	∈	PROPN
cana-2210	61	16	𝐶	𝐶	PROPN
cana-2210	61	17	∶	∶	NOUN
cana-2210	61	18	|𝜁|	|𝜁|	NOUN
cana-2210	61	19	<	<	X
cana-2210	61	20	1	1	NUM
cana-2210	61	21	}	}	PUNCT
cana-2210	61	22	,	,	PUNCT
cana-2210	61	23	(	(	PUNCT
cana-2210	61	24	1	1	X
cana-2210	61	25	)	)	PUNCT
cana-2210	61	26	which	which	PRON
cana-2210	61	27	is	be	AUX
cana-2210	61	28	analytic	analytic	ADJ
cana-2210	61	29	in	in	ADP
cana-2210	61	30	the	the	DET
cana-2210	61	31	unit	unit	NOUN
cana-2210	61	32	disk	disk	NOUN
cana-2210	61	33	u.	u.	NOUN
cana-2210	61	34	for	for	ADP
cana-2210	61	35	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	61	36	)	)	PUNCT
cana-2210	61	37	∈	∈	PROPN
cana-2210	61	38	𝐴	𝐴	PROPN
cana-2210	61	39	,	,	PUNCT
cana-2210	61	40	the	the	DET
cana-2210	61	41	raducanu	raducanu	NOUN
cana-2210	61	42	-	-	PUNCT
cana-2210	61	43	orhan	orhan	NOUN
cana-2210	61	44	[	[	X
cana-2210	61	45	15	15	NUM
cana-2210	61	46	]	]	X
cana-2210	61	47	differential	differential	NOUN
cana-2210	61	48	operator	operator	NOUN
cana-2210	61	49	is	be	AUX
cana-2210	61	50	defined	define	VERB
cana-2210	61	51	as	as	ADP
cana-2210	61	52	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	61	53	𝑛	𝑛	DET
cana-2210	61	54	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	61	55	)	)	PUNCT
cana-2210	61	56	.	.	PUNCT
cana-2210	62	1	𝑅𝜌,µ	𝑅𝜌,µ	NOUN
cana-2210	62	2	0	0	NUM
cana-2210	63	1	=	=	PUNCT
cana-2210	63	2	𝑓	𝑓	PROPN
cana-2210	63	3	=	=	PUNCT
cana-2210	63	4	𝜁	𝜁	PROPN
cana-2210	63	5	+	+	NOUN
cana-2210	63	6	∑	∑	PUNCT
cana-2210	63	7	𝑎𝑙	𝑎𝑙	NOUN
cana-2210	63	8	∞	∞	PROPN
cana-2210	63	9	𝑙=2	𝑙=2	PROPN
cana-2210	63	10	𝜁𝑙	𝜁𝑙	NOUN
cana-2210	63	11	,	,	PUNCT
cana-2210	63	12	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	63	13	1	1	NUM
cana-2210	63	14	=	=	SYM
cana-2210	63	15	(	(	PUNCT
cana-2210	63	16	1	1	NUM
cana-2210	63	17	−	−	NOUN
cana-2210	63	18	𝜌	𝜌	X
cana-2210	63	19	+	+	X
cana-2210	63	20	𝜇)𝑓(𝜁	𝜇)𝑓(𝜁	NOUN
cana-2210	63	21	)	)	PUNCT
cana-2210	63	22	+	+	CCONJ
cana-2210	63	23	(	(	PUNCT
cana-2210	63	24	𝜌	𝜌	X
cana-2210	63	25	−	−	PROPN
cana-2210	63	26	𝜇)𝑓	𝜇)𝑓	X
cana-2210	63	27	′(𝜁	′(𝜁	NUM
cana-2210	63	28	)	)	PUNCT
cana-2210	64	1	+	+	CCONJ
cana-2210	64	2	(	(	PUNCT
cana-2210	64	3	𝜌𝜇)𝜁2𝑓	𝜌𝜇)𝜁2𝑓	ADJ
cana-2210	64	4	′′(𝜁	′′(𝜁	NOUN
cana-2210	64	5	)	)	PUNCT
cana-2210	64	6	=	=	SYM
cana-2210	65	1	𝜁	𝜁	PROPN
cana-2210	65	2	+	+	CCONJ
cana-2210	65	3	∑[1	∑[1	NUM
cana-2210	65	4	+	+	SYM
cana-2210	65	5	(	(	PUNCT
cana-2210	65	6	𝑙	𝑙	PRON
cana-2210	65	7	−	−	PROPN
cana-2210	65	8	1)(𝑙𝜌𝜇	1)(𝑙𝜌𝜇	NUM
cana-2210	65	9	+	+	CCONJ
cana-2210	65	10	𝜌	𝜌	ADP
cana-2210	65	11	−	−	NUM
cana-2210	65	12	𝜇)]𝑎𝑙	𝜇)]𝑎𝑙	NUM
cana-2210	65	13	∞	∞	NUM
cana-2210	65	14	𝑙=2	𝑙=2	PROPN
cana-2210	65	15	𝜁𝑙	𝜁𝑙	NOUN
cana-2210	65	16	,	,	PUNCT
cana-2210	65	17	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	65	18	2	2	NUM
cana-2210	65	19	=	=	SYM
cana-2210	65	20	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	65	21	1	1	NUM
cana-2210	65	22	(	(	PUNCT
cana-2210	65	23	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	65	24	1	1	NUM
cana-2210	65	25	)	)	PUNCT
cana-2210	65	26	similarly	similarly	ADV
cana-2210	65	27	,	,	PUNCT
cana-2210	65	28	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	65	29	𝑛	𝑛	NOUN
cana-2210	65	30	=	=	SYM
cana-2210	65	31	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	65	32	1	1	NUM
cana-2210	65	33	(	(	PUNCT
cana-2210	65	34	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	65	35	𝑛−1	𝑛−1	PROPN
cana-2210	65	36	)	)	PUNCT
cana-2210	66	1	=	=	SYM
cana-2210	66	2	𝜁	𝜁	PROPN
cana-2210	66	3	+	+	CCONJ
cana-2210	66	4	∑[1	∑[1	NUM
cana-2210	66	5	+	+	SYM
cana-2210	66	6	(	(	PUNCT
cana-2210	66	7	𝑙	𝑙	PRON
cana-2210	66	8	−	−	PROPN
cana-2210	66	9	1)(𝑙𝜌𝜇	1)(𝑙𝜌𝜇	NUM
cana-2210	66	10	+	+	CCONJ
cana-2210	66	11	𝜌	𝜌	ADP
cana-2210	66	12	−	−	PROPN
cana-2210	66	13	𝜇)]𝑛𝑎𝑙	𝜇)]𝑛𝑎𝑙	NOUN
cana-2210	66	14	∞	∞	NUM
cana-2210	66	15	𝑙=2	𝑙=2	PROPN
cana-2210	66	16	𝜁𝑙	𝜁𝑙	NOUN
cana-2210	66	17	.	.	PUNCT
cana-2210	67	1	(	(	PUNCT
cana-2210	67	2	2	2	X
cana-2210	67	3	)	)	PUNCT
cana-2210	67	4	where	where	SCONJ
cana-2210	67	5	𝑛	𝑛	DET
cana-2210	67	6	∈	∈	PROPN
cana-2210	67	7	𝑁0	𝑁0	VERB
cana-2210	67	8	=	=	PUNCT
cana-2210	67	9	𝑁	𝑁	NOUN
cana-2210	67	10	∪	∪	ADJ
cana-2210	67	11	0	0	NUM
cana-2210	67	12	,	,	PUNCT
cana-2210	67	13	𝑁	𝑁	PROPN
cana-2210	67	14	=	=	SYM
cana-2210	67	15	{	{	PUNCT
cana-2210	67	16	1,2,3	1,2,3	NUM
cana-2210	67	17	,	,	PUNCT
cana-2210	67	18	…	…	PUNCT
cana-2210	67	19	}	}	PUNCT
cana-2210	67	20	,	,	PUNCT
cana-2210	67	21	𝜇	𝜇	ADP
cana-2210	67	22	,	,	PUNCT
cana-2210	67	23	𝜌	𝜌	X
cana-2210	67	24	≥	≥	NOUN
cana-2210	67	25	0	0	NUM
cana-2210	67	26	,	,	PUNCT
cana-2210	67	27	𝜁	𝜁	PROPN
cana-2210	67	28	∈	∈	PROPN
cana-2210	67	29	𝑈.	𝑈.	PROPN
cana-2210	67	30	remark	remark	NOUN
cana-2210	67	31	.	.	PUNCT
cana-2210	68	1	𝑅𝜌,0	𝑅𝜌,0	NOUN
cana-2210	68	2	𝑛	𝑛	NOUN
cana-2210	68	3	=	=	PUNCT
cana-2210	68	4	𝐷𝑛	𝐷𝑛	NOUN
cana-2210	68	5	yields	yield	NOUN
cana-2210	68	6	the	the	DET
cana-2210	68	7	al	al	PROPN
cana-2210	68	8	-	-	PUNCT
cana-2210	68	9	oboudi	oboudi	ADJ
cana-2210	68	10	differential	differential	NOUN
cana-2210	68	11	operator	operator	NOUN
cana-2210	68	12	[	[	X
cana-2210	68	13	2	2	NUM
cana-2210	68	14	]	]	PUNCT
cana-2210	68	15	,	,	PUNCT
cana-2210	68	16	𝑅1,0	𝑅1,0	ADJ
cana-2210	69	1	𝑛	𝑛	PROPN
cana-2210	69	2	=	=	NOUN
cana-2210	69	3	𝐷𝑛	𝐷𝑛	NOUN
cana-2210	69	4	gives	give	VERB
cana-2210	69	5	salagean	salagean	ADJ
cana-2210	69	6	differential	differential	NOUN
cana-2210	69	7	operator	operator	NOUN
cana-2210	69	8	[	[	X
cana-2210	69	9	20	20	NUM
cana-2210	69	10	]	]	PUNCT
cana-2210	69	11	.	.	PUNCT
cana-2210	70	1	2	2	X
cana-2210	70	2	.	.	X
cana-2210	70	3	the	the	DET
cana-2210	70	4	subclass	subclass	NOUN
cana-2210	70	5	𝑺𝒃,𝝉,𝝆,µ	𝑺𝒃,𝝉,𝝆,µ	PROPN
cana-2210	70	6	𝒎,𝒏	𝒎,𝒏	PROPN
cana-2210	70	7	(	(	PUNCT
cana-2210	70	8	𝜸	𝜸	NOUN
cana-2210	70	9	)	)	PUNCT
cana-2210	70	10	definition	definition	NOUN
cana-2210	70	11	2.1	2.1	NUM
cana-2210	70	12	let	let	VERB
cana-2210	70	13	𝑆𝑏,𝜏,𝜌,µ	𝑆𝑏,𝜏,𝜌,µ	PROPN
cana-2210	70	14	𝑚,𝑛	𝑚,𝑛	VERB
cana-2210	70	15	(	(	PUNCT
cana-2210	70	16	𝛾	𝛾	NOUN
cana-2210	70	17	)	)	PUNCT
cana-2210	70	18	denote	denote	VERB
cana-2210	70	19	the	the	DET
cana-2210	70	20	subclass	subclass	NOUN
cana-2210	70	21	of	of	ADP
cana-2210	70	22	𝐴	𝐴	PROPN
cana-2210	70	23	consisting	consist	VERB
cana-2210	70	24	of	of	ADP
cana-2210	70	25	function	function	NOUN
cana-2210	70	26	𝑓	𝑓	PRON
cana-2210	70	27	which	which	PRON
cana-2210	70	28	satisfies	satisfy	VERB
cana-2210	70	29	the	the	DET
cana-2210	70	30	inequality	inequality	NOUN
cana-2210	70	31	𝑅𝑒	𝑅𝑒	PROPN
cana-2210	70	32	(	(	PUNCT
cana-2210	70	33	1	1	NUM
cana-2210	70	34	+	+	SYM
cana-2210	70	35	1	1	NUM
cana-2210	70	36	𝑏	𝑏	NOUN
cana-2210	70	37	(	(	PUNCT
cana-2210	70	38	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	70	39	𝑚	𝑚	X
cana-2210	70	40	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	70	41	)	)	PUNCT
cana-2210	70	42	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	70	43	𝑛	𝑛	DET
cana-2210	70	44	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	70	45	)	)	PUNCT
cana-2210	70	46	−	−	PROPN
cana-2210	70	47	1	1	NUM
cana-2210	70	48	)	)	PUNCT
cana-2210	70	49	)	)	PUNCT
cana-2210	70	50	>	>	X
cana-2210	71	1	𝜏	𝜏	X
cana-2210	71	2	|	|	ADV
cana-2210	71	3	𝑅𝜌,µ	𝑅𝜌,µ	X
cana-2210	71	4	𝑚	𝑚	X
cana-2210	71	5	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	71	6	)	)	PUNCT
cana-2210	71	7	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	71	8	𝑛	𝑛	DET
cana-2210	71	9	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	71	10	)	)	PUNCT
cana-2210	71	11	−	−	PROPN
cana-2210	71	12	1|	1|	NUM
cana-2210	72	1	+	+	CCONJ
cana-2210	72	2	𝛾.	𝛾.	ADJ
cana-2210	72	3	(	(	PUNCT
cana-2210	72	4	3	3	NUM
cana-2210	72	5	)	)	PUNCT
cana-2210	72	6	for	for	ADP
cana-2210	72	7	some	some	DET
cana-2210	72	8	𝑏	𝑏	PRON
cana-2210	72	9	∈	∈	PROPN
cana-2210	72	10	𝐶	𝐶	PROPN
cana-2210	72	11	−	−	PROPN
cana-2210	72	12	{	{	PUNCT
cana-2210	72	13	0	0	NUM
cana-2210	72	14	}	}	PUNCT
cana-2210	72	15	,	,	PUNCT
cana-2210	72	16	𝑚	𝑚	PROPN
cana-2210	72	17	∈	∈	PROPN
cana-2210	72	18	𝑁	𝑁	PROPN
cana-2210	72	19	,	,	PUNCT
cana-2210	72	20	𝑛	𝑛	DET
cana-2210	72	21	∈	∈	PROPN
cana-2210	72	22	𝑁0	𝑁0	VERB
cana-2210	72	23	,	,	PUNCT
cana-2210	72	24	𝜏	𝜏	NOUN
cana-2210	72	25	,	,	PUNCT
cana-2210	72	26	𝜌,µ	𝜌,µ	PRON
cana-2210	72	27	≥	≥	NOUN
cana-2210	72	28	0,0	0,0	NOUN
cana-2210	72	29	≤	≤	NUM
cana-2210	72	30	𝛾	𝛾	ADP
cana-2210	72	31	<	<	X
cana-2210	72	32	1	1	NUM
cana-2210	72	33	and	and	CCONJ
cana-2210	72	34	all	all	DET
cana-2210	72	35	𝜁	𝜁	PRON
cana-2210	72	36	∈	∈	PROPN
cana-2210	72	37	𝑈.	𝑈.	PROPN
cana-2210	72	38	for	for	ADP
cana-2210	72	39	suitable	suitable	ADJ
cana-2210	72	40	choices	choice	NOUN
cana-2210	72	41	of	of	ADP
cana-2210	72	42	the	the	DET
cana-2210	72	43	parameters	parameter	NOUN
cana-2210	72	44	of	of	ADP
cana-2210	72	45	the	the	PRON
cana-2210	72	46	of	of	ADP
cana-2210	72	47	𝑆𝑏,𝜏,𝜌,µ	𝑆𝑏,𝜏,𝜌,µ	PROPN
cana-2210	72	48	𝑚,𝑛	𝑚,𝑛	NOUN
cana-2210	72	49	(	(	PUNCT
cana-2210	72	50	𝛾	𝛾	NOUN
cana-2210	72	51	)	)	PUNCT
cana-2210	72	52	provides	provide	VERB
cana-2210	72	53	several	several	ADJ
cana-2210	72	54	well	well	ADV
cana-2210	72	55	-	-	PUNCT
cana-2210	72	56	known	know	VERB
cana-2210	72	57	subclasses	subclass	NOUN
cana-2210	72	58	.	.	PUNCT
cana-2210	73	1	remark	remark	VERB
cana-2210	73	2	2.2	2.2	NUM
cana-2210	73	3	𝑆𝑏,0,0,𝜌	𝑆𝑏,0,0,𝜌	ADV
cana-2210	73	4	𝑚,𝑛	𝑚,𝑛	NOUN
cana-2210	73	5	(	(	PUNCT
cana-2210	73	6	𝛾	𝛾	NOUN
cana-2210	73	7	)	)	PUNCT
cana-2210	73	8	=	=	SYM
cana-2210	73	9	𝑆(𝑚	𝑆(𝑚	PROPN
cana-2210	73	10	,	,	PUNCT
cana-2210	73	11	𝑛	𝑛	PROPN
cana-2210	73	12	,	,	PUNCT
cana-2210	73	13	𝛾	𝛾	NOUN
cana-2210	73	14	,	,	PUNCT
cana-2210	73	15	𝜏	𝜏	NOUN
cana-2210	73	16	,	,	PUNCT
cana-2210	73	17	𝜌	𝜌	X
cana-2210	73	18	,	,	PUNCT
cana-2210	73	19	𝑏	𝑏	NOUN
cana-2210	73	20	,	,	PUNCT
cana-2210	73	21	𝑙	𝑙	NUM
cana-2210	73	22	)	)	PUNCT
cana-2210	73	23	studied	study	VERB
cana-2210	73	24	by	by	ADP
cana-2210	73	25	stalin	stalin	PROPN
cana-2210	73	26	and	and	CCONJ
cana-2210	73	27	thiruchran	thiruchran	ADV
cana-2210	74	1	[	[	X
cana-2210	74	2	30	30	NUM
cana-2210	74	3	]	]	PUNCT
cana-2210	74	4	.	.	PUNCT
cana-2210	75	1	𝑆1,0,0,1	𝑆1,0,0,1	NOUN
cana-2210	75	2	𝑚,𝑛	𝑚,𝑛	PROPN
cana-2210	75	3	(	(	PUNCT
cana-2210	75	4	𝛾	𝛾	NOUN
cana-2210	75	5	)	)	PUNCT
cana-2210	75	6	=	=	SYM
cana-2210	75	7	𝐾𝑚,𝑛(𝛾	𝐾𝑚,𝑛(𝛾	ADV
cana-2210	75	8	)	)	PUNCT
cana-2210	75	9	studied	study	VERB
cana-2210	75	10	by	by	ADP
cana-2210	75	11	sumer	sumer	PROPN
cana-2210	75	12	eker	eker	PROPN
cana-2210	75	13	and	and	CCONJ
cana-2210	75	14	owa	owa	PROPN
cana-2210	75	15	[	[	X
cana-2210	75	16	26	26	NUM
cana-2210	75	17	]	]	PUNCT
cana-2210	75	18	.	.	PUNCT
cana-2210	76	1	𝑆1,0,0,𝜌	𝑆1,0,0,𝜌	NOUN
cana-2210	76	2	𝑚,𝑛	𝑚,𝑛	NOUN
cana-2210	76	3	(	(	PUNCT
cana-2210	76	4	𝛾	𝛾	NOUN
cana-2210	76	5	)	)	PUNCT
cana-2210	76	6	=	=	SYM
cana-2210	76	7	𝑆𝑚,𝑛,𝜌(𝛾	𝑆𝑚,𝑛,𝜌(𝛾	NOUN
cana-2210	76	8	)	)	PUNCT
cana-2210	76	9	studied	study	VERB
cana-2210	76	10	by	by	ADP
cana-2210	76	11	sumer	sumer	PROPN
cana-2210	76	12	eker	eker	PROPN
cana-2210	76	13	and	and	CCONJ
cana-2210	76	14	ozlem	ozlem	ADJ
cana-2210	76	15	guney	guney	NOUN
cana-2210	76	16	[	[	X
cana-2210	76	17	27	27	NUM
cana-2210	76	18	]	]	PUNCT
cana-2210	76	19	.	.	PUNCT
cana-2210	77	1	𝑆1,0,0,1	𝑆1,0,0,1	NOUN
cana-2210	77	2	𝑛+1,𝑛	𝑛+1,𝑛	PROPN
cana-2210	77	3	(	(	PUNCT
cana-2210	77	4	𝛾	𝛾	NOUN
cana-2210	77	5	)	)	PUNCT
cana-2210	77	6	=	=	SYM
cana-2210	77	7	𝑆𝑛(𝛾	𝑆𝑛(𝛾	NOUN
cana-2210	77	8	)	)	PUNCT
cana-2210	77	9	studied	study	VERB
cana-2210	77	10	by	by	ADP
cana-2210	77	11	kadioglu	kadioglu	NOUN
cana-2210	77	12	[	[	X
cana-2210	77	13	10	10	NUM
cana-2210	77	14	]	]	PUNCT
cana-2210	77	15	.	.	PUNCT
cana-2210	78	1	theorem	theorem	NOUN
cana-2210	78	2	2.3	2.3	NUM
cana-2210	78	3	let	let	VERB
cana-2210	78	4	𝑓	𝑓	DET
cana-2210	78	5	∈	∈	PROPN
cana-2210	78	6	𝐴	𝐴	PROPN
cana-2210	78	7	satisfies	satisfy	VERB
cana-2210	78	8	communications	communication	NOUN
cana-2210	78	9	on	on	ADP
cana-2210	78	10	applied	apply	VERB
cana-2210	78	11	nonlinear	nonlinear	ADJ
cana-2210	78	12	analysis	analysis	NOUN
cana-2210	78	13	issn	issn	NOUN
cana-2210	78	14	:	:	PUNCT
cana-2210	78	15	1074	1074	NUM
cana-2210	78	16	-	-	PUNCT
cana-2210	78	17	133x	133x	NUM
cana-2210	78	18	vol	vol	NOUN
cana-2210	78	19	32	32	NUM
cana-2210	78	20	no	no	NOUN
cana-2210	78	21	.	.	PUNCT
cana-2210	79	1	1s	1s	NUM
cana-2210	79	2	(	(	PUNCT
cana-2210	79	3	2025	2025	NUM
cana-2210	79	4	)	)	PUNCT
cana-2210	79	5	464	464	NUM
cana-2210	79	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2210	79	7	∑	∑	PUNCT
cana-2210	79	8	𝜙(𝛾	𝜙(𝛾	PROPN
cana-2210	79	9	,	,	PUNCT
cana-2210	79	10	𝜏)|𝑎𝑙|	𝜏)|𝑎𝑙|	DET
cana-2210	79	11	≤	≤	NOUN
cana-2210	79	12	2(1	2(1	NUM
cana-2210	79	13	−	−	PROPN
cana-2210	80	1	𝛾)|𝑏|	𝛾)|𝑏|	PROPN
cana-2210	80	2	.	.	PUNCT
cana-2210	81	1	(	(	PUNCT
cana-2210	81	2	4	4	X
cana-2210	81	3	)	)	PUNCT
cana-2210	81	4	∞	∞	NUM
cana-2210	82	1	𝑙=2	𝑙=2	PROPN
cana-2210	82	2	for	for	ADP
cana-2210	82	3	some	some	DET
cana-2210	82	4	𝑏	𝑏	PRON
cana-2210	82	5	∈	∈	PROPN
cana-2210	82	6	𝐶	𝐶	PROPN
cana-2210	82	7	−	−	PROPN
cana-2210	82	8	{	{	PUNCT
cana-2210	82	9	0	0	NUM
cana-2210	82	10	}	}	PUNCT
cana-2210	82	11	,	,	PUNCT
cana-2210	82	12	𝑚	𝑚	PROPN
cana-2210	82	13	∈	∈	PROPN
cana-2210	82	14	𝑁	𝑁	PROPN
cana-2210	82	15	,	,	PUNCT
cana-2210	82	16	𝑛	𝑛	DET
cana-2210	82	17	∈	∈	PROPN
cana-2210	82	18	𝑁0	𝑁0	VERB
cana-2210	82	19	,	,	PUNCT
cana-2210	82	20	𝜏	𝜏	NOUN
cana-2210	82	21	,	,	PUNCT
cana-2210	82	22	𝜌,µ	𝜌,µ	PRON
cana-2210	82	23	≥	≥	NOUN
cana-2210	82	24	0	0	NUM
cana-2210	82	25	,	,	PUNCT
cana-2210	82	26	0	0	NUM
cana-2210	82	27	≤	≤	NOUN
cana-2210	82	28	𝛾	𝛾	ADP
cana-2210	82	29	<	<	X
cana-2210	82	30	1	1	NUM
cana-2210	82	31	and	and	CCONJ
cana-2210	82	32	all	all	DET
cana-2210	82	33	𝜁	𝜁	PROPN
cana-2210	82	34	∈	∈	PROPN
cana-2210	82	35	𝑈	𝑈	PROPN
cana-2210	82	36	,	,	PUNCT
cana-2210	82	37	then	then	ADV
cana-2210	82	38	𝑓	𝑓	DET
cana-2210	82	39	∈	∈	PROPN
cana-2210	82	40	𝑆𝑏,𝜏,𝜌,µ	𝑆𝑏,𝜏,𝜌,µ	PROPN
cana-2210	82	41	𝑚,𝑛	𝑚,𝑛	NOUN
cana-2210	82	42	(	(	PUNCT
cana-2210	82	43	𝛾	𝛾	NOUN
cana-2210	82	44	)	)	PUNCT
cana-2210	82	45	,	,	PUNCT
cana-2210	82	46	where	where	SCONJ
cana-2210	82	47	𝜙(𝛾	𝜙(𝛾	NOUN
cana-2210	82	48	,	,	PUNCT
cana-2210	82	49	𝜏	𝜏	NOUN
cana-2210	82	50	)	)	PUNCT
cana-2210	82	51	=	=	PUNCT
cana-2210	83	1	|(1	|(1	PROPN
cana-2210	83	2	+	+	X
cana-2210	83	3	(	(	PUNCT
cana-2210	83	4	𝑙	𝑙	PRON
cana-2210	83	5	−	−	PROPN
cana-2210	83	6	1)(𝑙𝜌µ	1)(𝑙𝜌µ	NOUN
cana-2210	83	7	+	+	CCONJ
cana-2210	83	8	𝜌	𝜌	ADP
cana-2210	83	9	−	−	PROPN
cana-2210	83	10	µ))𝑚	µ))𝑚	PROPN
cana-2210	83	11	−	−	PROPN
cana-2210	84	1	(	(	PUNCT
cana-2210	84	2	1	1	NUM
cana-2210	84	3	+	+	NUM
cana-2210	84	4	𝛾𝑏)(1	𝛾𝑏)(1	PRON
cana-2210	85	1	+	+	CCONJ
cana-2210	85	2	(	(	PUNCT
cana-2210	85	3	𝑙	𝑙	PRON
cana-2210	85	4	−	−	PROPN
cana-2210	85	5	1)(𝑙𝜌µ	1)(𝑙𝜌µ	NOUN
cana-2210	85	6	+	+	CCONJ
cana-2210	85	7	𝜌	𝜌	X
cana-2210	85	8	−	−	PROPN
cana-2210	85	9	µ))𝑛|	µ))𝑛|	PROPN
cana-2210	86	1	+	+	NOUN
cana-2210	86	2	(	(	PUNCT
cana-2210	86	3	1	1	NUM
cana-2210	86	4	+	+	CCONJ
cana-2210	86	5	(	(	PUNCT
cana-2210	86	6	𝑙	𝑙	PRON
cana-2210	86	7	−	−	PROPN
cana-2210	86	8	1)(𝑙𝜌µ	1)(𝑙𝜌µ	NOUN
cana-2210	86	9	+	+	CCONJ
cana-2210	86	10	𝜌	𝜌	ADP
cana-2210	86	11	−	−	X
cana-2210	86	12	µ))𝑚	µ))𝑚	NOUN
cana-2210	86	13	+	+	CCONJ
cana-2210	86	14	(	(	PUNCT
cana-2210	86	15	(	(	PUNCT
cana-2210	86	16	2	2	NUM
cana-2210	86	17	−	−	NOUN
cana-2210	86	18	𝛾)𝑏	𝛾)𝑏	NOUN
cana-2210	86	19	−	−	PROPN
cana-2210	86	20	1)(1	1)(1	NUM
cana-2210	86	21	+	+	CCONJ
cana-2210	86	22	(	(	PUNCT
cana-2210	86	23	𝑙	𝑙	PRON
cana-2210	86	24	−	−	PROPN
cana-2210	86	25	1)(𝑙𝜌µ	1)(𝑙𝜌µ	NOUN
cana-2210	86	26	+	+	CCONJ
cana-2210	86	27	𝜌	𝜌	ADP
cana-2210	86	28	−	−	PROPN
cana-2210	86	29	µ))𝑛	µ))𝑛	NOUN
cana-2210	86	30	+2𝑏𝜏|(1	+2𝑏𝜏|(1	PROPN
cana-2210	86	31	+	+	CCONJ
cana-2210	86	32	(	(	PUNCT
cana-2210	86	33	𝑙	𝑙	PRON
cana-2210	86	34	−	−	PROPN
cana-2210	86	35	1)(𝑙𝜌µ	1)(𝑙𝜌µ	NOUN
cana-2210	86	36	+	+	CCONJ
cana-2210	86	37	𝜌	𝜌	ADP
cana-2210	86	38	−	−	PROPN
cana-2210	86	39	µ))𝑚	µ))𝑚	PROPN
cana-2210	86	40	−	−	PROPN
cana-2210	87	1	(	(	PUNCT
cana-2210	87	2	1	1	NUM
cana-2210	87	3	+	+	CCONJ
cana-2210	87	4	(	(	PUNCT
cana-2210	87	5	𝑙	𝑙	PRON
cana-2210	87	6	−	−	PROPN
cana-2210	87	7	1)(𝑙𝜌µ	1)(𝑙𝜌µ	NOUN
cana-2210	87	8	+	+	CCONJ
cana-2210	87	9	𝜌	𝜌	X
cana-2210	87	10	−	−	PROPN
cana-2210	87	11	µ))𝑛|	µ))𝑛|	PROPN
cana-2210	87	12	.	.	PUNCT
cana-2210	88	1	proof	proof	NOUN
cana-2210	88	2	.	.	PUNCT
cana-2210	89	1	suppose	suppose	VERB
cana-2210	89	2	that	that	SCONJ
cana-2210	89	3	∑	∑	ADP
cana-2210	89	4	𝜙(𝛾	𝜙(𝛾	NOUN
cana-2210	89	5	,	,	PUNCT
cana-2210	89	6	𝜏)|𝑎𝑙|	𝜏)|𝑎𝑙|	PRON
cana-2210	89	7	≤	≤	NUM
cana-2210	89	8	2(1	2(1	NUM
cana-2210	89	9	−	−	NOUN
cana-2210	89	10	𝛾)|𝑏|∞	𝛾)|𝑏|∞	NUM
cana-2210	90	1	𝑙=2	𝑙=2	PROPN
cana-2210	90	2	is	be	AUX
cana-2210	90	3	true	true	ADJ
cana-2210	90	4	.	.	PUNCT
cana-2210	91	1	for	for	ADP
cana-2210	91	2	some	some	DET
cana-2210	91	3	𝑏	𝑏	PRON
cana-2210	91	4	∈	∈	PROPN
cana-2210	91	5	𝐶	𝐶	PROPN
cana-2210	91	6	−	−	PROPN
cana-2210	91	7	{	{	PUNCT
cana-2210	91	8	0	0	NUM
cana-2210	91	9	}	}	PUNCT
cana-2210	91	10	,	,	PUNCT
cana-2210	91	11	𝑚	𝑚	PROPN
cana-2210	91	12	∈	∈	PROPN
cana-2210	91	13	𝑁	𝑁	PROPN
cana-2210	91	14	,	,	PUNCT
cana-2210	91	15	𝑛	𝑛	DET
cana-2210	91	16	∈	∈	PROPN
cana-2210	91	17	𝑁0	𝑁0	VERB
cana-2210	91	18	,	,	PUNCT
cana-2210	91	19	𝜏	𝜏	NOUN
cana-2210	91	20	,	,	PUNCT
cana-2210	91	21	𝜌,µ	𝜌,µ	PRON
cana-2210	91	22	≥	≥	NOUN
cana-2210	91	23	0	0	NUM
cana-2210	91	24	,	,	PUNCT
cana-2210	91	25	0	0	NUM
cana-2210	91	26	≤	≤	NOUN
cana-2210	91	27	𝛾	𝛾	ADP
cana-2210	91	28	<	<	X
cana-2210	91	29	1	1	NUM
cana-2210	91	30	and	and	CCONJ
cana-2210	91	31	all	all	DET
cana-2210	91	32	𝜁	𝜁	PROPN
cana-2210	91	33	∈	∈	PROPN
cana-2210	91	34	𝑈	𝑈	PROPN
cana-2210	91	35	,	,	PUNCT
cana-2210	91	36	then	then	ADV
cana-2210	91	37	it	it	PRON
cana-2210	91	38	is	be	AUX
cana-2210	91	39	sufficient	sufficient	ADJ
cana-2210	91	40	to	to	PART
cana-2210	91	41	prove	prove	VERB
cana-2210	91	42	that	that	SCONJ
cana-2210	91	43	|	|	ADV
cana-2210	91	44	𝐹(𝜁)−1	𝐹(𝜁)−1	NUM
cana-2210	91	45	𝐹(𝜁)+1	𝐹(𝜁)+1	NOUN
cana-2210	92	1	|	|	ADV
cana-2210	92	2	<	<	X
cana-2210	92	3	1	1	X
cana-2210	92	4	.	.	X
cana-2210	92	5	for	for	ADP
cana-2210	92	6	𝑓	𝑓	DET
cana-2210	92	7	∈	∈	PROPN
cana-2210	92	8	𝐴	𝐴	PROPN
cana-2210	92	9	,	,	PUNCT
cana-2210	92	10	then	then	ADV
cana-2210	92	11	define	define	VERB
cana-2210	92	12	the	the	DET
cana-2210	92	13	function	function	NOUN
cana-2210	92	14	𝐹	𝐹	PROPN
cana-2210	92	15	by	by	ADP
cana-2210	92	16	𝐹(𝜁	𝐹(𝜁	NOUN
cana-2210	92	17	)	)	PUNCT
cana-2210	92	18	=	=	SYM
cana-2210	93	1	1	1	NUM
cana-2210	93	2	+	+	SYM
cana-2210	93	3	1	1	NUM
cana-2210	93	4	𝑏	𝑏	NOUN
cana-2210	93	5	(	(	PUNCT
cana-2210	93	6	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	93	7	𝑚	𝑚	X
cana-2210	93	8	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	93	9	)	)	PUNCT
cana-2210	93	10	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	93	11	𝑛	𝑛	DET
cana-2210	93	12	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	93	13	)	)	PUNCT
cana-2210	93	14	−	−	PROPN
cana-2210	93	15	1	1	NUM
cana-2210	93	16	)	)	PUNCT
cana-2210	93	17	−	−	NOUN
cana-2210	93	18	𝜏	𝜏	PROPN
cana-2210	93	19	|	|	ADV
cana-2210	93	20	𝑅𝜌,µ	𝑅𝜌,µ	NOUN
cana-2210	93	21	𝑚	𝑚	X
cana-2210	93	22	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	93	23	)	)	PUNCT
cana-2210	93	24	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	93	25	𝑛	𝑛	DET
cana-2210	93	26	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	93	27	)	)	PUNCT
cana-2210	93	28	−	−	PROPN
cana-2210	93	29	1|	1|	NUM
cana-2210	93	30	−	−	NOUN
cana-2210	93	31	𝛾	𝛾	NOUN
cana-2210	93	32	𝐹(𝜁	𝐹(𝜁	NOUN
cana-2210	93	33	)	)	PUNCT
cana-2210	93	34	−	−	PROPN
cana-2210	93	35	1	1	NUM
cana-2210	93	36	=	=	PUNCT
cana-2210	93	37	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	93	38	𝑚	𝑚	X
cana-2210	93	39	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	93	40	)	)	PUNCT
cana-2210	93	41	−	−	PROPN
cana-2210	93	42	(	(	PUNCT
cana-2210	93	43	1	1	NUM
cana-2210	93	44	+	+	CCONJ
cana-2210	93	45	𝛾𝑏)𝑅𝜌,µ	𝛾𝑏)𝑅𝜌,µ	X
cana-2210	93	46	𝑛	𝑛	X
cana-2210	93	47	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	93	48	)	)	PUNCT
cana-2210	93	49	−	−	NOUN
cana-2210	93	50	𝑏𝜏|𝑅𝜌,µ	𝑏𝜏|𝑅𝜌,µ	NOUN
cana-2210	93	51	𝑚	𝑚	X
cana-2210	93	52	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	93	53	)	)	PUNCT
cana-2210	93	54	−	−	PROPN
cana-2210	94	1	𝑅𝜌,µ	𝑅𝜌,µ	INTJ
cana-2210	94	2	𝑛	𝑛	PRON
cana-2210	94	3	𝑓(𝜁)|	𝑓(𝜁)|	PROPN
cana-2210	94	4	𝑏𝑅𝜌,µ	𝑏𝑅𝜌,µ	NUM
cana-2210	94	5	𝑛	𝑛	DET
cana-2210	94	6	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	94	7	)	)	PUNCT
cana-2210	94	8	and	and	CCONJ
cana-2210	94	9	𝐹(𝜁	𝐹(𝜁	NUM
cana-2210	94	10	)	)	PUNCT
cana-2210	94	11	−	−	PROPN
cana-2210	94	12	1	1	NUM
cana-2210	94	13	=	=	PUNCT
cana-2210	94	14	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	94	15	𝑚	𝑚	X
cana-2210	94	16	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	94	17	)	)	PUNCT
cana-2210	94	18	−	−	PROPN
cana-2210	95	1	(	(	PUNCT
cana-2210	95	2	1	1	NUM
cana-2210	95	3	+	+	CCONJ
cana-2210	95	4	(	(	PUNCT
cana-2210	95	5	𝛾	𝛾	NOUN
cana-2210	95	6	−	−	PRON
cana-2210	95	7	2)𝑏)𝑅𝜌,µ	2)𝑏)𝑅𝜌,µ	NUM
cana-2210	95	8	𝑛	𝑛	X
cana-2210	95	9	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	95	10	)	)	PUNCT
cana-2210	95	11	−	−	NOUN
cana-2210	95	12	𝑏𝜏|𝑅𝜌,µ	𝑏𝜏|𝑅𝜌,µ	NOUN
cana-2210	95	13	𝑚	𝑚	X
cana-2210	95	14	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	95	15	)	)	PUNCT
cana-2210	95	16	−	−	PROPN
cana-2210	96	1	𝑅𝜌,µ	𝑅𝜌,µ	INTJ
cana-2210	96	2	𝑛	𝑛	PRON
cana-2210	96	3	𝑓(𝜁)|	𝑓(𝜁)|	PROPN
cana-2210	96	4	𝑏𝑅𝜌,µ	𝑏𝑅𝜌,µ	NUM
cana-2210	96	5	𝑛	𝑛	DET
cana-2210	96	6	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	96	7	)	)	PUNCT
cana-2210	96	8	therefore	therefore	ADV
cana-2210	96	9	,	,	PUNCT
cana-2210	96	10	|	|	ADV
cana-2210	96	11	𝐹(𝜁	𝐹(𝜁	NUM
cana-2210	96	12	)	)	PUNCT
cana-2210	96	13	−	−	PROPN
cana-2210	96	14	1	1	NUM
cana-2210	96	15	𝐹(𝜁	𝐹(𝜁	NOUN
cana-2210	96	16	)	)	PUNCT
cana-2210	96	17	+	+	CCONJ
cana-2210	96	18	1	1	NUM
cana-2210	96	19	|	|	NOUN
cana-2210	96	20	=	=	SYM
cana-2210	97	1	|	|	ADV
cana-2210	97	2	𝑅𝜌,µ	𝑅𝜌,µ	X
cana-2210	97	3	𝑚	𝑚	X
cana-2210	97	4	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	97	5	)	)	PUNCT
cana-2210	97	6	−	−	PROPN
cana-2210	98	1	(	(	PUNCT
cana-2210	98	2	1	1	NUM
cana-2210	98	3	+	+	CCONJ
cana-2210	98	4	𝛾𝑏)𝑅𝜌,µ	𝛾𝑏)𝑅𝜌,µ	X
cana-2210	98	5	𝑛	𝑛	X
cana-2210	98	6	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	98	7	)	)	PUNCT
cana-2210	98	8	−	−	NOUN
cana-2210	98	9	𝑏𝜏|𝑅𝜌,µ	𝑏𝜏|𝑅𝜌,µ	NOUN
cana-2210	98	10	𝑚	𝑚	X
cana-2210	98	11	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	98	12	)	)	PUNCT
cana-2210	98	13	−	−	PROPN
cana-2210	99	1	𝑅𝜌,µ	𝑅𝜌,µ	INTJ
cana-2210	99	2	𝑛	𝑛	PRON
cana-2210	99	3	𝑓(𝜁)|	𝑓(𝜁)|	NOUN
cana-2210	99	4	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	99	5	𝑚	𝑚	X
cana-2210	99	6	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	99	7	)	)	PUNCT
cana-2210	99	8	−	−	PROPN
cana-2210	100	1	(	(	PUNCT
cana-2210	100	2	1	1	NUM
cana-2210	100	3	+	+	CCONJ
cana-2210	100	4	(	(	PUNCT
cana-2210	100	5	𝛾	𝛾	NOUN
cana-2210	100	6	−	−	PRON
cana-2210	100	7	2)𝑏)𝑅𝜌,µ	2)𝑏)𝑅𝜌,µ	NUM
cana-2210	100	8	𝑛	𝑛	X
cana-2210	100	9	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	100	10	)	)	PUNCT
cana-2210	100	11	−	−	NOUN
cana-2210	100	12	𝑏𝜏|𝑅𝜌,µ	𝑏𝜏|𝑅𝜌,µ	NOUN
cana-2210	100	13	𝑚	𝑚	X
cana-2210	100	14	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	100	15	)	)	PUNCT
cana-2210	100	16	−	−	PROPN
cana-2210	101	1	𝑅𝜌,µ	𝑅𝜌,µ	INTJ
cana-2210	101	2	𝑛	𝑛	PRON
cana-2210	101	3	𝑓(𝜁)|	𝑓(𝜁)|	NOUN
cana-2210	101	4	|	|	ADV
cana-2210	101	5	<	<	X
cana-2210	101	6	1	1	NUM
cana-2210	101	7	.	.	NUM
cana-2210	101	8	⟹	⟹	NUM
cana-2210	102	1	∑	∑	PUNCT
cana-2210	102	2	{	{	PUNCT
cana-2210	102	3	|(1	|(1	PROPN
cana-2210	102	4	+	+	X
cana-2210	102	5	(	(	PUNCT
cana-2210	102	6	𝑙	𝑙	PRON
cana-2210	102	7	−	−	PROPN
cana-2210	102	8	1)(𝑙𝜌µ	1)(𝑙𝜌µ	NOUN
cana-2210	102	9	+	+	CCONJ
cana-2210	102	10	𝜌	𝜌	ADP
cana-2210	102	11	−	−	PROPN
cana-2210	102	12	µ))𝑚	µ))𝑚	PROPN
cana-2210	102	13	−	−	PROPN
cana-2210	103	1	(	(	PUNCT
cana-2210	103	2	1	1	NUM
cana-2210	103	3	+	+	NUM
cana-2210	103	4	𝛾𝑏)(1	𝛾𝑏)(1	PRON
cana-2210	104	1	+	+	CCONJ
cana-2210	104	2	(	(	PUNCT
cana-2210	104	3	𝑙	𝑙	PRON
cana-2210	104	4	−	−	PROPN
cana-2210	104	5	1)(𝑙𝜌µ	1)(𝑙𝜌µ	NOUN
cana-2210	104	6	+	+	CCONJ
cana-2210	104	7	𝜌	𝜌	X
cana-2210	104	8	−	−	PROPN
cana-2210	104	9	µ))𝑛|	µ))𝑛|	PROPN
cana-2210	105	1	+	+	NOUN
cana-2210	105	2	(	(	PUNCT
cana-2210	105	3	1	1	NUM
cana-2210	105	4	+	+	CCONJ
cana-2210	105	5	(	(	PUNCT
cana-2210	105	6	𝑙	𝑙	PRON
cana-2210	105	7	−	−	PROPN
cana-2210	105	8	1)(𝑙𝜌µ	1)(𝑙𝜌µ	NOUN
cana-2210	105	9	+	+	CCONJ
cana-2210	105	10	𝜌	𝜌	ADP
cana-2210	105	11	−	−	X
cana-2210	105	12	µ))𝑚	µ))𝑚	NOUN
cana-2210	105	13	+	+	CCONJ
cana-2210	105	14	(	(	PUNCT
cana-2210	105	15	(	(	PUNCT
cana-2210	105	16	2	2	NUM
cana-2210	105	17	−	−	NOUN
cana-2210	105	18	𝛾)𝑏	𝛾)𝑏	NOUN
cana-2210	105	19	−	−	PROPN
cana-2210	105	20	1)(1	1)(1	NUM
cana-2210	105	21	+	+	CCONJ
cana-2210	105	22	(	(	PUNCT
cana-2210	105	23	𝑙	𝑙	PRON
cana-2210	105	24	−	−	PROPN
cana-2210	105	25	1)(𝑙𝜌µ	1)(𝑙𝜌µ	NOUN
cana-2210	105	26	+	+	CCONJ
cana-2210	105	27	𝜌	𝜌	ADP
cana-2210	105	28	−	−	PROPN
cana-2210	105	29	µ))𝑛	µ))𝑛	NOUN
cana-2210	105	30	+2𝑏𝜏|(1	+2𝑏𝜏|(1	PROPN
cana-2210	105	31	+	+	CCONJ
cana-2210	105	32	(	(	PUNCT
cana-2210	105	33	𝑙	𝑙	PRON
cana-2210	105	34	−	−	PROPN
cana-2210	105	35	1)(𝑙𝜌µ	1)(𝑙𝜌µ	NOUN
cana-2210	105	36	+	+	CCONJ
cana-2210	105	37	𝜌	𝜌	ADP
cana-2210	105	38	−	−	PROPN
cana-2210	105	39	µ))𝑚	µ))𝑚	PROPN
cana-2210	105	40	−	−	PROPN
cana-2210	106	1	(	(	PUNCT
cana-2210	106	2	1	1	NUM
cana-2210	106	3	+	+	CCONJ
cana-2210	106	4	(	(	PUNCT
cana-2210	106	5	𝑙	𝑙	PRON
cana-2210	106	6	−	−	PROPN
cana-2210	106	7	1)(𝑙𝜌µ	1)(𝑙𝜌µ	NOUN
cana-2210	106	8	+	+	CCONJ
cana-2210	106	9	𝜌	𝜌	X
cana-2210	106	10	−	−	PROPN
cana-2210	106	11	µ))𝑛|	µ))𝑛|	PROPN
cana-2210	106	12	}	}	PUNCT
cana-2210	106	13	∞	∞	PROPN
cana-2210	107	1	𝑙=2	𝑙=2	PROPN
cana-2210	107	2	|𝑎𝑙|	|𝑎𝑙|	PROPN
cana-2210	107	3	≤	≤	NOUN
cana-2210	107	4	2(1	2(1	NUM
cana-2210	108	1	−	−	PROPN
cana-2210	109	1	𝛾)|𝑏|	𝛾)|𝑏|	PROPN
cana-2210	109	2	.	.	PUNCT
cana-2210	110	1	∴	∴	PROPN
cana-2210	110	2	∑	∑	PUNCT
cana-2210	110	3	𝜙(𝛾	𝜙(𝛾	PROPN
cana-2210	110	4	,	,	PUNCT
cana-2210	110	5	𝜏)|𝑎𝑙|	𝜏)|𝑎𝑙|	DET
cana-2210	110	6	≤	≤	NOUN
cana-2210	110	7	2(1	2(1	NUM
cana-2210	110	8	−	−	PROPN
cana-2210	111	1	𝛾)|𝑏|	𝛾)|𝑏|	PROPN
cana-2210	111	2	.	.	PUNCT
cana-2210	112	1	∞	∞	PROPN
cana-2210	113	1	𝑙=2	𝑙=2	PROPN
cana-2210	113	2	hence	hence	ADV
cana-2210	113	3	,	,	PUNCT
cana-2210	113	4	equation	equation	NOUN
cana-2210	113	5	(	(	PUNCT
cana-2210	113	6	4	4	X
cana-2210	113	7	)	)	PUNCT
cana-2210	113	8	holds	hold	VERB
cana-2210	113	9	.	.	PUNCT
cana-2210	114	1	put	put	VERB
cana-2210	114	2	𝜏	𝜏	NOUN
cana-2210	114	3	=	=	SYM
cana-2210	114	4	0	0	NUM
cana-2210	114	5	and	and	CCONJ
cana-2210	114	6	µ	µ	X
cana-2210	114	7	=	=	SYM
cana-2210	114	8	0	0	NUM
cana-2210	114	9	in	in	ADP
cana-2210	114	10	𝑆𝑏,𝜏,𝜌,µ	𝑆𝑏,𝜏,𝜌,µ	PROPN
cana-2210	114	11	𝑚,𝑛	𝑚,𝑛	X
cana-2210	114	12	(	(	PUNCT
cana-2210	114	13	𝛾	𝛾	NOUN
cana-2210	114	14	)	)	PUNCT
cana-2210	114	15	then	then	ADV
cana-2210	114	16	this	this	DET
cana-2210	114	17	class	class	NOUN
cana-2210	114	18	reduces	reduce	VERB
cana-2210	114	19	as	as	ADP
cana-2210	114	20	𝑆(𝑚	𝑆(𝑚	NOUN
cana-2210	114	21	,	,	PUNCT
cana-2210	114	22	𝑛	𝑛	PROPN
cana-2210	114	23	,	,	PUNCT
cana-2210	114	24	𝛾	𝛾	NOUN
cana-2210	114	25	,	,	PUNCT
cana-2210	114	26	𝜏	𝜏	NOUN
cana-2210	114	27	,	,	PUNCT
cana-2210	114	28	𝜌	𝜌	X
cana-2210	114	29	,	,	PUNCT
cana-2210	114	30	𝑏	𝑏	NOUN
cana-2210	114	31	)	)	PUNCT
cana-2210	114	32	,	,	PUNCT
cana-2210	114	33	which	which	PRON
cana-2210	114	34	was	be	AUX
cana-2210	114	35	studied	study	VERB
cana-2210	114	36	by	by	ADP
cana-2210	114	37	thirucheran	thirucheran	ADJ
cana-2210	114	38	and	and	CCONJ
cana-2210	114	39	stalin	stalin	PROPN
cana-2210	115	1	[	[	X
cana-2210	115	2	30	30	NUM
cana-2210	115	3	]	]	PUNCT
cana-2210	115	4	.	.	PUNCT
cana-2210	116	1	corollary	corollary	ADJ
cana-2210	116	2	2.4	2.4	NUM
cana-2210	116	3	let	let	VERB
cana-2210	116	4	𝑓	𝑓	DET
cana-2210	116	5	∈	∈	PROPN
cana-2210	116	6	𝐴	𝐴	PROPN
cana-2210	116	7	satisfies	satisfy	VERB
cana-2210	116	8	∑	∑	PUNCT
cana-2210	116	9	𝜙(𝑚	𝜙(𝑚	PROPN
cana-2210	116	10	,	,	PUNCT
cana-2210	116	11	𝑛	𝑛	PROPN
cana-2210	116	12	,	,	PUNCT
cana-2210	116	13	𝛾	𝛾	NOUN
cana-2210	116	14	,	,	PUNCT
cana-2210	116	15	𝜏	𝜏	NOUN
cana-2210	116	16	,	,	PUNCT
cana-2210	116	17	𝜌	𝜌	X
cana-2210	116	18	,	,	PUNCT
cana-2210	116	19	𝑏	𝑏	NOUN
cana-2210	116	20	,	,	PUNCT
cana-2210	116	21	𝑙	𝑙	NUM
cana-2210	116	22	)	)	PUNCT
cana-2210	116	23	∞	∞	PROPN
cana-2210	117	1	𝑙=2	𝑙=2	PROPN
cana-2210	117	2	|𝑎𝑙|	|𝑎𝑙|	VERB
cana-2210	117	3	≤	≤	NOUN
cana-2210	117	4	2(1	2(1	NUM
cana-2210	118	1	−	−	NOUN
cana-2210	118	2	𝛾)𝑏.	𝛾)𝑏.	X
cana-2210	118	3	for	for	ADP
cana-2210	118	4	some	some	DET
cana-2210	118	5	(	(	PUNCT
cana-2210	118	6	0	0	NUM
cana-2210	118	7	≤	≤	NOUN
cana-2210	118	8	𝛾	𝛾	ADP
cana-2210	118	9	<	<	X
cana-2210	118	10	1	1	NUM
cana-2210	118	11	)	)	PUNCT
cana-2210	118	12	,	,	PUNCT
cana-2210	118	13	𝜏	𝜏	PRON
cana-2210	118	14	≥	≥	NOUN
cana-2210	118	15	0	0	NUM
cana-2210	118	16	,	,	PUNCT
cana-2210	118	17	𝑚	𝑚	PROPN
cana-2210	118	18	∈	∈	PROPN
cana-2210	118	19	𝑁	𝑁	PROPN
cana-2210	118	20	,	,	PUNCT
cana-2210	118	21	𝑛	𝑛	DET
cana-2210	118	22	∈	∈	PROPN
cana-2210	118	23	𝑁0	𝑁0	VERB
cana-2210	118	24	,	,	PUNCT
cana-2210	118	25	𝜌(𝜌	𝜌(𝜌	PROPN
cana-2210	118	26	≥	≥	NOUN
cana-2210	118	27	0	0	NUM
cana-2210	118	28	)	)	PUNCT
cana-2210	118	29	,	,	PUNCT
cana-2210	118	30	and	and	CCONJ
cana-2210	118	31	all	all	DET
cana-2210	118	32	𝜁	𝜁	PROPN
cana-2210	118	33	∈	∈	PROPN
cana-2210	118	34	𝑈	𝑈	PROPN
cana-2210	118	35	,	,	PUNCT
cana-2210	118	36	then	then	ADV
cana-2210	118	37	𝑓	𝑓	PRON
cana-2210	118	38	∈	∈	PROPN
cana-2210	118	39	𝑆(𝑚	𝑆(𝑚	SYM
cana-2210	118	40	,	,	PUNCT
cana-2210	118	41	𝑛	𝑛	PROPN
cana-2210	118	42	,	,	PUNCT
cana-2210	118	43	𝛾	𝛾	NOUN
cana-2210	118	44	,	,	PUNCT
cana-2210	118	45	𝜏	𝜏	NOUN
cana-2210	118	46	,	,	PUNCT
cana-2210	118	47	𝜌	𝜌	X
cana-2210	118	48	,	,	PUNCT
cana-2210	118	49	𝑏	𝑏	NOUN
cana-2210	118	50	)	)	PUNCT
cana-2210	118	51	,	,	PUNCT
cana-2210	118	52	communications	communication	NOUN
cana-2210	118	53	on	on	ADP
cana-2210	118	54	applied	apply	VERB
cana-2210	118	55	nonlinear	nonlinear	ADJ
cana-2210	118	56	analysis	analysis	NOUN
cana-2210	118	57	issn	issn	NOUN
cana-2210	118	58	:	:	PUNCT
cana-2210	118	59	1074	1074	NUM
cana-2210	118	60	-	-	PUNCT
cana-2210	118	61	133x	133x	NUM
cana-2210	118	62	vol	vol	NOUN
cana-2210	118	63	32	32	NUM
cana-2210	118	64	no	no	NOUN
cana-2210	118	65	.	.	PUNCT
cana-2210	119	1	1s	1s	NUM
cana-2210	119	2	(	(	PUNCT
cana-2210	119	3	2025	2025	NUM
cana-2210	119	4	)	)	PUNCT
cana-2210	119	5	465	465	NUM
cana-2210	119	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2210	120	1	where	where	SCONJ
cana-2210	120	2	𝜙(𝑚	𝜙(𝑚	PROPN
cana-2210	120	3	,	,	PUNCT
cana-2210	120	4	𝑛	𝑛	PROPN
cana-2210	120	5	,	,	PUNCT
cana-2210	120	6	𝛾	𝛾	NOUN
cana-2210	120	7	,	,	PUNCT
cana-2210	120	8	𝜏	𝜏	NOUN
cana-2210	120	9	,	,	PUNCT
cana-2210	120	10	𝜌	𝜌	X
cana-2210	120	11	,	,	PUNCT
cana-2210	120	12	𝑏	𝑏	NOUN
cana-2210	120	13	,	,	PUNCT
cana-2210	120	14	𝑙	𝑙	NUM
cana-2210	120	15	)	)	PUNCT
cana-2210	120	16	=	=	PUNCT
cana-2210	120	17	|(1	|(1	PROPN
cana-2210	120	18	+	+	X
cana-2210	120	19	(	(	PUNCT
cana-2210	120	20	𝑙	𝑙	X
cana-2210	120	21	–	–	PUNCT
cana-2210	120	22	1)𝜌)𝑚	1)𝜌)𝑚	NUM
cana-2210	120	23	−	−	PROPN
cana-2210	120	24	(	(	PUNCT
cana-2210	120	25	1	1	NUM
cana-2210	120	26	+	+	NUM
cana-2210	120	27	𝛾𝑏)(1	𝛾𝑏)(1	PRON
cana-2210	120	28	+	+	CCONJ
cana-2210	120	29	(	(	PUNCT
cana-2210	120	30	𝑙	𝑙	PRON
cana-2210	120	31	−	−	NUM
cana-2210	120	32	1)𝜌)𝑛|	1)𝜌)𝑛|	NUM
cana-2210	120	33	+	+	ADJ
cana-2210	120	34	(	(	PUNCT
cana-2210	120	35	1	1	NUM
cana-2210	120	36	+	+	CCONJ
cana-2210	120	37	(	(	PUNCT
cana-2210	120	38	𝑙	𝑙	X
cana-2210	120	39	−	−	X
cana-2210	120	40	1)𝜌)𝑚	1)𝜌)𝑚	PROPN
cana-2210	120	41	+	+	CCONJ
cana-2210	120	42	(	(	PUNCT
cana-2210	120	43	(	(	PUNCT
cana-2210	120	44	2	2	NUM
cana-2210	120	45	−	−	NOUN
cana-2210	120	46	𝛾)𝑏	𝛾)𝑏	NOUN
cana-2210	120	47	−	−	PROPN
cana-2210	120	48	1)(1	1)(1	NUM
cana-2210	120	49	+	+	CCONJ
cana-2210	120	50	(	(	PUNCT
cana-2210	120	51	𝑙	𝑙	X
cana-2210	120	52	−	−	PROPN
cana-2210	120	53	1)𝜌)𝑛	1)𝜌)𝑛	NOUN
cana-2210	121	1	+2𝑏𝜏	+2𝑏𝜏	PUNCT
cana-2210	121	2	|(1	|(1	PROPN
cana-2210	121	3	+	+	CCONJ
cana-2210	121	4	(	(	PUNCT
cana-2210	121	5	𝑙	𝑙	X
cana-2210	121	6	−	−	PROPN
cana-2210	121	7	1)𝜌)𝑚	1)𝜌)𝑚	NUM
cana-2210	121	8	−	−	PROPN
cana-2210	121	9	(	(	PUNCT
cana-2210	121	10	1	1	NUM
cana-2210	121	11	+	+	CCONJ
cana-2210	121	12	(	(	PUNCT
cana-2210	121	13	𝑙	𝑙	PROPN
cana-2210	121	14	−	−	PROPN
cana-2210	121	15	1)𝜌)𝑛|	1)𝜌)𝑛|	NUM
cana-2210	121	16	.	.	PUNCT
cana-2210	122	1	if	if	SCONJ
cana-2210	122	2	𝑏	𝑏	PROPN
cana-2210	122	3	=	=	SYM
cana-2210	122	4	1	1	NUM
cana-2210	122	5	and	and	CCONJ
cana-2210	122	6	𝜏	𝜏	NOUN
cana-2210	122	7	=	=	SYM
cana-2210	122	8	0	0	NUM
cana-2210	122	9	,	,	PUNCT
cana-2210	122	10	then	then	ADV
cana-2210	122	11	the	the	DET
cana-2210	122	12	class	class	NOUN
cana-2210	122	13	𝑆𝑏,𝜏,𝜌,µ	𝑆𝑏,𝜏,𝜌,µ	PROPN
cana-2210	122	14	𝑚,𝑛	𝑚,𝑛	NOUN
cana-2210	122	15	(	(	PUNCT
cana-2210	122	16	𝛾	𝛾	NOUN
cana-2210	122	17	)	)	PUNCT
cana-2210	122	18	reduces	reduce	VERB
cana-2210	122	19	to	to	PART
cana-2210	122	20	𝑅𝑒	𝑅𝑒	PROPN
cana-2210	122	21	(	(	PUNCT
cana-2210	122	22	𝑅𝜌	𝑅𝜌	PROPN
cana-2210	122	23	𝑚𝑓(𝜁	𝑚𝑓(𝜁	NUM
cana-2210	122	24	)	)	PUNCT
cana-2210	122	25	𝑅𝜌	𝑅𝜌	PROPN
cana-2210	122	26	𝑚𝑓(𝜁	𝑚𝑓(𝜁	NUM
cana-2210	122	27	)	)	PUNCT
cana-2210	122	28	)	)	PUNCT
cana-2210	122	29	>	>	X
cana-2210	123	1	𝛾	𝛾	X
cana-2210	123	2	which	which	PRON
cana-2210	123	3	analogues	analogue	VERB
cana-2210	123	4	to	to	ADP
cana-2210	123	5	the	the	DET
cana-2210	123	6	class	class	NOUN
cana-2210	123	7	𝑆𝑚,𝑛,𝜌(𝛾	𝑆𝑚,𝑛,𝜌(𝛾	NOUN
cana-2210	123	8	)	)	PUNCT
cana-2210	123	9	introduced	introduce	VERB
cana-2210	123	10	by	by	ADP
cana-2210	123	11	sevtap	sevtap	NOUN
cana-2210	123	12	sumer	sumer	PROPN
cana-2210	123	13	eker	eker	PROPN
cana-2210	123	14	and	and	CCONJ
cana-2210	123	15	ozlem	ozlem	NOUN
cana-2210	123	16	guney[27	guney[27	NOUN
cana-2210	123	17	]	]	PUNCT
cana-2210	123	18	.	.	PUNCT
cana-2210	124	1	corollary	corollary	ADJ
cana-2210	124	2	2.5	2.5	NUM
cana-2210	124	3	let	let	VERB
cana-2210	124	4	𝑓	𝑓	DET
cana-2210	124	5	∈	∈	PROPN
cana-2210	124	6	𝐴	𝐴	PROPN
cana-2210	124	7	satisfies	satisfy	VERB
cana-2210	124	8	the	the	DET
cana-2210	124	9	inequality	inequality	NOUN
cana-2210	124	10	∑	∑	PUNCT
cana-2210	124	11	𝜙(𝛾	𝜙(𝛾	PROPN
cana-2210	124	12	,	,	PUNCT
cana-2210	124	13	𝑚	𝑚	PROPN
cana-2210	124	14	,	,	PUNCT
cana-2210	124	15	𝑛	𝑛	PROPN
cana-2210	124	16	,	,	PUNCT
cana-2210	124	17	𝜌	𝜌	X
cana-2210	124	18	,	,	PUNCT
cana-2210	124	19	𝑙)∞	𝑙)∞	PROPN
cana-2210	124	20	𝑙=2	𝑙=2	PROPN
cana-2210	124	21	|𝑎𝑙|	|𝑎𝑙|	VERB
cana-2210	124	22	≤	≤	NOUN
cana-2210	124	23	2(1	2(1	NUM
cana-2210	124	24	–	–	PUNCT
cana-2210	124	25	𝛾	𝛾	NOUN
cana-2210	124	26	)	)	PUNCT
cana-2210	124	27	,	,	PUNCT
cana-2210	124	28	for	for	ADP
cana-2210	124	29	some	some	DET
cana-2210	124	30	𝑏	𝑏	PRON
cana-2210	124	31	∈	∈	PROPN
cana-2210	124	32	𝐶	𝐶	PROPN
cana-2210	124	33	−	−	PROPN
cana-2210	124	34	{	{	PUNCT
cana-2210	124	35	0	0	NUM
cana-2210	124	36	}	}	PUNCT
cana-2210	124	37	,	,	PUNCT
cana-2210	124	38	𝑚	𝑚	PROPN
cana-2210	124	39	∈	∈	PROPN
cana-2210	124	40	𝑁	𝑁	PROPN
cana-2210	124	41	,	,	PUNCT
cana-2210	124	42	𝑛	𝑛	DET
cana-2210	124	43	∈	∈	PROPN
cana-2210	124	44	𝑁0	𝑁0	VERB
cana-2210	124	45	,	,	PUNCT
cana-2210	124	46	𝜌,µ	𝜌,µ	DET
cana-2210	124	47	≥	≥	NOUN
cana-2210	124	48	0,0	0,0	NOUN
cana-2210	124	49	≤	≤	NUM
cana-2210	124	50	𝛾	𝛾	ADP
cana-2210	124	51	<	<	X
cana-2210	124	52	1	1	NUM
cana-2210	124	53	,	,	PUNCT
cana-2210	124	54	then	then	ADV
cana-2210	124	55	𝑓	𝑓	DET
cana-2210	124	56	∈	∈	PROPN
cana-2210	124	57	𝑆𝑚,𝑛,𝜌(𝛾	𝑆𝑚,𝑛,𝜌(𝛾	NOUN
cana-2210	124	58	)	)	PUNCT
cana-2210	124	59	,	,	PUNCT
cana-2210	124	60	where	where	SCONJ
cana-2210	124	61	𝜙(𝛾	𝜙(𝛾	NOUN
cana-2210	124	62	,	,	PUNCT
cana-2210	124	63	𝑚	𝑚	PROPN
cana-2210	124	64	,	,	PUNCT
cana-2210	124	65	𝑛	𝑛	PROPN
cana-2210	124	66	,	,	PUNCT
cana-2210	124	67	𝜌	𝜌	X
cana-2210	124	68	,	,	PUNCT
cana-2210	124	69	𝑙	𝑙	NUM
cana-2210	124	70	)	)	PUNCT
cana-2210	124	71	=	=	PUNCT
cana-2210	125	1	|(1	|(1	PROPN
cana-2210	125	2	+	+	X
cana-2210	125	3	(	(	PUNCT
cana-2210	125	4	𝑙	𝑙	PROPN
cana-2210	125	5	−	−	PROPN
cana-2210	125	6	1)𝜌)𝑚	1)𝜌)𝑚	NUM
cana-2210	125	7	−	−	PROPN
cana-2210	125	8	(	(	PUNCT
cana-2210	125	9	1	1	NUM
cana-2210	125	10	+	+	NUM
cana-2210	125	11	𝛾)(1	𝛾)(1	X
cana-2210	126	1	+	+	CCONJ
cana-2210	126	2	(	(	PUNCT
cana-2210	126	3	𝑙	𝑙	PRON
cana-2210	126	4	−	−	NUM
cana-2210	126	5	1)𝜌)𝑛|	1)𝜌)𝑛|	NUM
cana-2210	127	1	+	+	ADJ
cana-2210	127	2	(	(	PUNCT
cana-2210	127	3	1	1	NUM
cana-2210	127	4	+	+	CCONJ
cana-2210	127	5	(	(	PUNCT
cana-2210	127	6	𝑙	𝑙	X
cana-2210	127	7	−	−	X
cana-2210	127	8	1)𝜌)𝑚	1)𝜌)𝑚	PROPN
cana-2210	128	1	+	+	CCONJ
cana-2210	128	2	(	(	PUNCT
cana-2210	128	3	1	1	NUM
cana-2210	128	4	−	−	NOUN
cana-2210	128	5	𝛾)(1	𝛾)(1	X
cana-2210	129	1	+	+	CCONJ
cana-2210	129	2	(	(	PUNCT
cana-2210	129	3	𝑙	𝑙	X
cana-2210	129	4	−	−	PROPN
cana-2210	130	1	1)𝜌)𝑛	1)𝜌)𝑛	INTJ
cana-2210	131	1	if	if	SCONJ
cana-2210	131	2	𝑏	𝑏	PROPN
cana-2210	131	3	=	=	SYM
cana-2210	131	4	1	1	NUM
cana-2210	131	5	,	,	PUNCT
cana-2210	131	6	𝜏	𝜏	NOUN
cana-2210	131	7	=	=	SYM
cana-2210	131	8	0	0	NUM
cana-2210	131	9	and	and	CCONJ
cana-2210	131	10	𝜌	𝜌	X
cana-2210	131	11	=	=	SYM
cana-2210	131	12	1	1	NUM
cana-2210	131	13	,	,	PUNCT
cana-2210	131	14	then	then	ADV
cana-2210	131	15	the	the	DET
cana-2210	131	16	class	class	NOUN
cana-2210	131	17	𝑆𝑏,𝜏,𝜌,µ	𝑆𝑏,𝜏,𝜌,µ	PROPN
cana-2210	131	18	𝑚,𝑛	𝑚,𝑛	NOUN
cana-2210	131	19	(	(	PUNCT
cana-2210	131	20	𝛾	𝛾	NOUN
cana-2210	131	21	)	)	PUNCT
cana-2210	131	22	given	give	VERB
cana-2210	131	23	the	the	DET
cana-2210	131	24	class	class	NOUN
cana-2210	131	25	𝑆𝑚,𝑛(𝛾	𝑆𝑚,𝑛(𝛾	ADJ
cana-2210	131	26	)	)	PUNCT
cana-2210	131	27	,	,	PUNCT
cana-2210	131	28	which	which	PRON
cana-2210	131	29	is	be	AUX
cana-2210	131	30	discussed	discuss	VERB
cana-2210	131	31	by	by	ADP
cana-2210	131	32	sevtap	sevtap	NOUN
cana-2210	131	33	sumer	sumer	PROPN
cana-2210	131	34	eker	eker	PROPN
cana-2210	131	35	and	and	CCONJ
cana-2210	131	36	owa	owa	PROPN
cana-2210	131	37	[	[	X
cana-2210	131	38	26	26	NUM
cana-2210	131	39	]	]	PUNCT
cana-2210	131	40	.	.	PUNCT
cana-2210	132	1	corollary	corollary	ADJ
cana-2210	132	2	2.6	2.6	NUM
cana-2210	132	3	let	let	VERB
cana-2210	132	4	𝑓	𝑓	DET
cana-2210	132	5	∈	∈	PROPN
cana-2210	132	6	𝐴	𝐴	PROPN
cana-2210	132	7	satisfies	satisfy	VERB
cana-2210	132	8	∑	∑	PUNCT
cana-2210	132	9	𝜙(𝛾	𝜙(𝛾	NOUN
cana-2210	132	10	,	,	PUNCT
cana-2210	132	11	𝑚	𝑚	PROPN
cana-2210	132	12	,	,	PUNCT
cana-2210	132	13	𝑛	𝑛	NOUN
cana-2210	132	14	,	,	PUNCT
cana-2210	132	15	𝑙)∞	𝑙)∞	PROPN
cana-2210	132	16	𝑙=2	𝑙=2	PROPN
cana-2210	132	17	|𝑎𝑙|	|𝑎𝑙|	VERB
cana-2210	132	18	≤	≤	NOUN
cana-2210	132	19	2(1	2(1	NUM
cana-2210	133	1	−	−	NOUN
cana-2210	133	2	𝛾	𝛾	NOUN
cana-2210	133	3	)	)	PUNCT
cana-2210	133	4	,	,	PUNCT
cana-2210	133	5	for	for	ADP
cana-2210	133	6	some	some	DET
cana-2210	133	7	𝛾(0	𝛾(0	NOUN
cana-2210	133	8	≤	≤	NOUN
cana-2210	133	9	𝛾	𝛾	ADP
cana-2210	133	10	<	<	X
cana-2210	133	11	1	1	NUM
cana-2210	133	12	)	)	PUNCT
cana-2210	133	13	,	,	PUNCT
cana-2210	133	14	𝑚	𝑚	PROPN
cana-2210	133	15	∈	∈	PROPN
cana-2210	133	16	𝑁	𝑁	PROPN
cana-2210	133	17	,	,	PUNCT
cana-2210	133	18	𝑛	𝑛	DET
cana-2210	133	19	∈	∈	PROPN
cana-2210	133	20	𝑁0	𝑁0	VERB
cana-2210	133	21	,	,	PUNCT
cana-2210	133	22	then	then	ADV
cana-2210	133	23	𝑓	𝑓	DET
cana-2210	133	24	∈	∈	NOUN
cana-2210	133	25	𝑆𝑚,𝑛(𝛾	𝑆𝑚,𝑛(𝛾	NOUN
cana-2210	133	26	)	)	PUNCT
cana-2210	133	27	,	,	PUNCT
cana-2210	133	28	where	where	SCONJ
cana-2210	133	29	𝜙(𝛾	𝜙(𝛾	NOUN
cana-2210	133	30	,	,	PUNCT
cana-2210	133	31	𝑚	𝑚	PROPN
cana-2210	133	32	,	,	PUNCT
cana-2210	133	33	𝑛	𝑛	PROPN
cana-2210	133	34	,	,	PUNCT
cana-2210	133	35	𝑙	𝑙	NUM
cana-2210	133	36	)	)	PUNCT
cana-2210	133	37	=	=	SYM
cana-2210	133	38	|(𝑙)𝑚	|(𝑙)𝑚	NOUN
cana-2210	134	1	−	−	NOUN
cana-2210	134	2	(	(	PUNCT
cana-2210	134	3	1	1	NUM
cana-2210	134	4	+	+	NUM
cana-2210	134	5	𝛾)(𝑙)𝑛|	𝛾)(𝑙)𝑛|	NOUN
cana-2210	134	6	+	+	CCONJ
cana-2210	134	7	(	(	PUNCT
cana-2210	134	8	𝑙)𝑚	𝑙)𝑚	X
cana-2210	134	9	+	+	CCONJ
cana-2210	134	10	(	(	PUNCT
cana-2210	134	11	1	1	NUM
cana-2210	134	12	−	−	NOUN
cana-2210	134	13	𝛾)(𝑙)𝑛.	𝛾)(𝑙)𝑛.	ADV
cana-2210	134	14	we	we	PRON
cana-2210	134	15	define	define	VERB
cana-2210	134	16	the	the	DET
cana-2210	134	17	subclass	subclass	ADJ
cana-2210	134	18	𝑆𝑏,𝜏,𝜌,µ	𝑆𝑏,𝜏,𝜌,µ	NUM
cana-2210	134	19	𝑚,𝑛	𝑚,𝑛	NOUN
cana-2210	134	20	(	(	PUNCT
cana-2210	134	21	𝛾)̃	𝛾)̃	PROPN
cana-2210	134	22	⊂	⊂	PUNCT
cana-2210	134	23	𝑆𝑏,𝜏,𝜌,µ	𝑆𝑏,𝜏,𝜌,µ	NOUN
cana-2210	134	24	𝑚,𝑛	𝑚,𝑛	X
cana-2210	134	25	(	(	PUNCT
cana-2210	134	26	𝛾	𝛾	NOUN
cana-2210	134	27	)	)	PUNCT
cana-2210	134	28	,	,	PUNCT
cana-2210	134	29	and	and	CCONJ
cana-2210	134	30	determine	determine	VERB
cana-2210	134	31	the	the	DET
cana-2210	134	32	extreme	extreme	ADJ
cana-2210	134	33	points	point	NOUN
cana-2210	134	34	of	of	ADP
cana-2210	134	35	the	the	DET
cana-2210	134	36	subclass	subclass	NOUN
cana-2210	134	37	for	for	ADP
cana-2210	134	38	the	the	DET
cana-2210	134	39	subclass	subclass	ADJ
cana-2210	134	40	𝑆𝑏,𝜏,𝜌,µ	𝑆𝑏,𝜏,𝜌,µ	PROPN
cana-2210	134	41	𝑚,𝑛	𝑚,𝑛	NOUN
cana-2210	134	42	(	(	PUNCT
cana-2210	134	43	𝛾)̃	𝛾)̃	PROPN
cana-2210	134	44	.	.	PUNCT
cana-2210	135	1	theorem	theorem	ADJ
cana-2210	135	2	2.7	2.7	NUM
cana-2210	135	3	let	let	VERB
cana-2210	135	4	𝑓1(𝜁	𝑓1(𝜁	NOUN
cana-2210	135	5	)	)	PUNCT
cana-2210	135	6	=	=	SYM
cana-2210	135	7	𝜁	𝜁	PROPN
cana-2210	135	8	,	,	PUNCT
cana-2210	135	9	and	and	CCONJ
cana-2210	135	10	𝑓𝑙(𝜁	𝑓𝑙(𝜁	NUM
cana-2210	135	11	)	)	PUNCT
cana-2210	135	12	=	=	SYM
cana-2210	136	1	𝜁	𝜁	PROPN
cana-2210	136	2	+	+	CCONJ
cana-2210	136	3	∑	∑	PROPN
cana-2210	136	4	𝜂𝑙	𝜂𝑙	PROPN
cana-2210	136	5	2(1−𝛾)𝑏	2(1−𝛾)𝑏	NUM
cana-2210	136	6	𝜙(𝛾,𝜏	𝜙(𝛾,𝜏	NOUN
cana-2210	136	7	)	)	PUNCT
cana-2210	136	8	𝜁𝑙	𝜁𝑙	NOUN
cana-2210	136	9	,	,	PUNCT
cana-2210	136	10	(	(	PUNCT
cana-2210	136	11	𝑙	𝑙	X
cana-2210	136	12	=	=	PUNCT
cana-2210	136	13	2,3,4	2,3,4	NUM
cana-2210	136	14	,	,	PUNCT
cana-2210	136	15	…	…	PUNCT
cana-2210	136	16	)	)	PUNCT
cana-2210	136	17	,	,	PUNCT
cana-2210	136	18	∞	∞	PROPN
cana-2210	137	1	𝑙=2	𝑙=2	PROPN
cana-2210	137	2	then	then	ADV
cana-2210	137	3	𝑓	𝑓	DET
cana-2210	137	4	∈	∈	PROPN
cana-2210	137	5	𝑆𝑏,𝜏,𝜌,µ	𝑆𝑏,𝜏,𝜌,µ	PROPN
cana-2210	137	6	𝑚,𝑛	𝑚,𝑛	NOUN
cana-2210	137	7	(	(	PUNCT
cana-2210	137	8	𝛾)̃	𝛾)̃	PUNCT
cana-2210	137	9	if	if	SCONJ
cana-2210	137	10	it	it	PRON
cana-2210	137	11	is	be	AUX
cana-2210	137	12	able	able	ADJ
cana-2210	137	13	to	to	PART
cana-2210	137	14	represented	represent	VERB
cana-2210	137	15	as	as	ADP
cana-2210	137	16	𝑓	𝑓	PROPN
cana-2210	137	17	=	=	SYM
cana-2210	137	18	∑	∑	PUNCT
cana-2210	137	19	𝜂𝑙𝑓𝑙(𝜁	𝜂𝑙𝑓𝑙(𝜁	PROPN
cana-2210	137	20	)	)	PUNCT
cana-2210	137	21	,	,	PUNCT
cana-2210	137	22	𝜂𝑙	𝜂𝑙	ADP
cana-2210	137	23	>	>	X
cana-2210	137	24	0	0	PUNCT
cana-2210	137	25	∞	∞	NUM
cana-2210	137	26	𝑙=1	𝑙=1	PUNCT
cana-2210	137	27	and	and	CCONJ
cana-2210	137	28	∑	∑	ADV
cana-2210	137	29	𝜂𝑙	𝜂𝑙	PROPN
cana-2210	137	30	=	=	SYM
cana-2210	137	31	1.∞	1.∞	NOUN
cana-2210	137	32	𝑙=1	𝑙=1	ADJ
cana-2210	137	33	proof	proof	NOUN
cana-2210	137	34	.	.	PUNCT
cana-2210	137	35	suppose	suppose	VERB
cana-2210	137	36	that	that	SCONJ
cana-2210	137	37	𝑓	𝑓	PROPN
cana-2210	137	38	=	=	SYM
cana-2210	137	39	∑	∑	PUNCT
cana-2210	137	40	𝜂𝑙𝑓𝑙(𝜁	𝜂𝑙𝑓𝑙(𝜁	PROPN
cana-2210	137	41	)	)	PUNCT
cana-2210	137	42	∞	∞	PROPN
cana-2210	137	43	𝑙=1	𝑙=1	PUNCT
cana-2210	138	1	=	=	PUNCT
cana-2210	138	2	𝜁	𝜁	PROPN
cana-2210	138	3	+	+	CCONJ
cana-2210	138	4	∑	∑	PROPN
cana-2210	138	5	𝜂𝑙	𝜂𝑙	ADJ
cana-2210	138	6	2(1	2(1	NUM
cana-2210	138	7	−	−	NOUN
cana-2210	138	8	𝛾)𝑏	𝛾)𝑏	PUNCT
cana-2210	138	9	𝜙(𝛾	𝜙(𝛾	NOUN
cana-2210	138	10	,	,	PUNCT
cana-2210	138	11	𝜏	𝜏	NOUN
cana-2210	138	12	)	)	PUNCT
cana-2210	138	13	𝜁𝑙	𝜁𝑙	NOUN
cana-2210	138	14	∞	∞	NUM
cana-2210	138	15	𝑙=2	𝑙=2	PUNCT
cana-2210	138	16	=	=	SYM
cana-2210	139	1	2(1	2(1	NUM
cana-2210	139	2	−	−	NOUN
cana-2210	139	3	𝛾)𝑏	𝛾)𝑏	PUNCT
cana-2210	139	4	∑	∑	PUNCT
cana-2210	139	5	𝜂𝑙	𝜂𝑙	ADP
cana-2210	139	6	∞	∞	NUM
cana-2210	139	7	𝑙=2	𝑙=2	PUNCT
cana-2210	139	8	=	=	SYM
cana-2210	140	1	2(1	2(1	NUM
cana-2210	140	2	−	−	NOUN
cana-2210	141	1	𝛾)𝑏(1	𝛾)𝑏(1	PROPN
cana-2210	141	2	−	−	PROPN
cana-2210	141	3	𝜂1	𝜂1	PROPN
cana-2210	141	4	)	)	PUNCT
cana-2210	141	5	communications	communication	NOUN
cana-2210	141	6	on	on	ADP
cana-2210	141	7	applied	apply	VERB
cana-2210	141	8	nonlinear	nonlinear	ADJ
cana-2210	141	9	analysis	analysis	NOUN
cana-2210	141	10	issn	issn	NOUN
cana-2210	141	11	:	:	PUNCT
cana-2210	141	12	1074	1074	NUM
cana-2210	141	13	-	-	PUNCT
cana-2210	141	14	133x	133x	NUM
cana-2210	141	15	vol	vol	NOUN
cana-2210	141	16	32	32	NUM
cana-2210	141	17	no	no	NOUN
cana-2210	141	18	.	.	PUNCT
cana-2210	142	1	1s	1s	NUM
cana-2210	142	2	(	(	PUNCT
cana-2210	142	3	2025	2025	NUM
cana-2210	142	4	)	)	PUNCT
cana-2210	142	5	466	466	NUM
cana-2210	143	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2210	143	2	<	<	X
cana-2210	143	3	2(1	2(1	NUM
cana-2210	144	1	−	−	X
cana-2210	144	2	𝛾)𝑏.	𝛾)𝑏.	X
cana-2210	144	3	which	which	PRON
cana-2210	144	4	shows	show	VERB
cana-2210	144	5	that	that	SCONJ
cana-2210	144	6	𝑓	𝑓	DET
cana-2210	144	7	∈	∈	PROPN
cana-2210	144	8	𝑆𝑏,𝜏,𝜌,µ	𝑆𝑏,𝜏,𝜌,µ	PROPN
cana-2210	144	9	𝑚,𝑛	𝑚,𝑛	NOUN
cana-2210	144	10	(	(	PUNCT
cana-2210	144	11	𝛾)̃	𝛾)̃	PROPN
cana-2210	144	12	.	.	PUNCT
cana-2210	145	1	conversely	conversely	ADV
cana-2210	145	2	,	,	PUNCT
cana-2210	145	3	suppose	suppose	VERB
cana-2210	145	4	that	that	SCONJ
cana-2210	145	5	𝑓	𝑓	DET
cana-2210	145	6	∈	∈	PROPN
cana-2210	145	7	𝑆𝑏,𝜏,𝜌,µ	𝑆𝑏,𝜏,𝜌,µ	PROPN
cana-2210	145	8	𝑚,𝑛	𝑚,𝑛	NOUN
cana-2210	145	9	(	(	PUNCT
cana-2210	145	10	𝛾	𝛾	NOUN
cana-2210	145	11	)	)	PUNCT
cana-2210	145	12	since	since	ADV
cana-2210	145	13	,	,	PUNCT
cana-2210	145	14	𝑎𝑙	𝑎𝑙	ADJ
cana-2210	145	15	≤	≤	NUM
cana-2210	145	16	2(1−𝛾)𝑏	2(1−𝛾)𝑏	NUM
cana-2210	145	17	𝜙(𝛾,𝜏	𝜙(𝛾,𝜏	NOUN
cana-2210	145	18	)	)	PUNCT
cana-2210	145	19	let	let	VERB
cana-2210	145	20	𝜂𝑙	𝜂𝑙	ADP
cana-2210	145	21	≤	≤	ADJ
cana-2210	145	22	𝜙(𝛾	𝜙(𝛾	NOUN
cana-2210	145	23	,	,	PUNCT
cana-2210	145	24	𝜏	𝜏	NOUN
cana-2210	145	25	)	)	PUNCT
cana-2210	145	26	2(1	2(1	NUM
cana-2210	145	27	−	−	NOUN
cana-2210	145	28	𝛾)𝑏	𝛾)𝑏	ADJ
cana-2210	145	29	𝑎𝑙	𝑎𝑙	NOUN
cana-2210	145	30	and	and	CCONJ
cana-2210	145	31	𝜂1	𝜂1	NOUN
cana-2210	145	32	=	=	NOUN
cana-2210	145	33	1	1	NUM
cana-2210	145	34	−	−	NOUN
cana-2210	145	35	∑	∑	NOUN
cana-2210	145	36	𝜂𝑙	𝜂𝑙	INTJ
cana-2210	145	37	,	,	PUNCT
cana-2210	145	38	∞	∞	PROPN
cana-2210	145	39	𝑙=2	𝑙=2	PROPN
cana-2210	145	40	then	then	ADV
cana-2210	145	41	we	we	PRON
cana-2210	145	42	obtain	obtain	VERB
cana-2210	145	43	𝑓	𝑓	PRON
cana-2210	145	44	=	=	PUNCT
cana-2210	145	45	∑	∑	PUNCT
cana-2210	145	46	𝜂𝑙𝑓𝑙(𝜁)∞	𝜂𝑙𝑓𝑙(𝜁)∞	NOUN
cana-2210	145	47	𝑙=1	𝑙=1	PUNCT
cana-2210	145	48	.	.	PUNCT
cana-2210	146	1	let	let	VERB
cana-2210	146	2	µ	µ	X
cana-2210	146	3	=	=	SYM
cana-2210	146	4	0	0	NUM
cana-2210	146	5	,	,	PUNCT
cana-2210	146	6	then	then	ADV
cana-2210	146	7	the	the	DET
cana-2210	146	8	class	class	NOUN
cana-2210	146	9	𝑆𝑏,𝜏,𝜌,µ	𝑆𝑏,𝜏,𝜌,µ	PROPN
cana-2210	146	10	𝑚,𝑛	𝑚,𝑛	NOUN
cana-2210	146	11	(	(	PUNCT
cana-2210	146	12	𝛾	𝛾	NOUN
cana-2210	146	13	)	)	PUNCT
cana-2210	146	14	reduces	reduce	VERB
cana-2210	146	15	and	and	CCONJ
cana-2210	146	16	analogues	analogue	NOUN
cana-2210	146	17	to	to	ADP
cana-2210	146	18	the	the	DET
cana-2210	146	19	class	class	NOUN
cana-2210	146	20	,	,	PUNCT
cana-2210	146	21	which	which	PRON
cana-2210	146	22	is	be	AUX
cana-2210	146	23	examined	examine	VERB
cana-2210	146	24	by	by	ADP
cana-2210	146	25	thirucheran	thirucheran	ADJ
cana-2210	146	26	and	and	CCONJ
cana-2210	146	27	stalin	stalin	PROPN
cana-2210	147	1	[	[	X
cana-2210	147	2	30	30	NUM
cana-2210	147	3	]	]	PUNCT
cana-2210	147	4	.	.	PUNCT
cana-2210	148	1	corollary	corollary	ADJ
cana-2210	148	2	2.8	2.8	NUM
cana-2210	148	3	let	let	VERB
cana-2210	148	4	𝑓1(𝜁	𝑓1(𝜁	NOUN
cana-2210	148	5	)	)	PUNCT
cana-2210	148	6	=	=	SYM
cana-2210	148	7	𝜁	𝜁	PROPN
cana-2210	148	8	,	,	PUNCT
cana-2210	148	9	and	and	CCONJ
cana-2210	148	10	𝑓𝑙(𝜁	𝑓𝑙(𝜁	NUM
cana-2210	148	11	)	)	PUNCT
cana-2210	148	12	=	=	SYM
cana-2210	149	1	𝜁	𝜁	PROPN
cana-2210	149	2	+	+	CCONJ
cana-2210	149	3	∑	∑	PROPN
cana-2210	149	4	𝜂𝑙	𝜂𝑙	PROPN
cana-2210	149	5	2(1−𝛾)𝑏	2(1−𝛾)𝑏	NUM
cana-2210	149	6	𝜙(𝑚,𝑛,𝛾,𝜏,𝜌,𝑏,𝑙	𝜙(𝑚,𝑛,𝛾,𝜏,𝜌,𝑏,𝑙	NOUN
cana-2210	149	7	)	)	PUNCT
cana-2210	149	8	𝜁𝑙	𝜁𝑙	NOUN
cana-2210	149	9	,	,	PUNCT
cana-2210	149	10	(	(	PUNCT
cana-2210	149	11	𝑙	𝑙	X
cana-2210	149	12	=	=	PUNCT
cana-2210	149	13	2,3,4	2,3,4	NUM
cana-2210	149	14	,	,	PUNCT
cana-2210	149	15	…	…	PUNCT
cana-2210	149	16	)	)	PUNCT
cana-2210	149	17	,	,	PUNCT
cana-2210	149	18	∞	∞	PROPN
cana-2210	150	1	𝑙=2	𝑙=2	PROPN
cana-2210	150	2	then	then	ADV
cana-2210	150	3	𝑓	𝑓	DET
cana-2210	150	4	∈	∈	NOUN
cana-2210	150	5	𝑆𝑏,𝜏,𝜌	𝑆𝑏,𝜏,𝜌	PROPN
cana-2210	150	6	𝑚,𝑛	𝑚,𝑛	NOUN
cana-2210	150	7	(	(	PUNCT
cana-2210	150	8	𝛾)̃	𝛾)̃	PROPN
cana-2210	150	9	if	if	SCONJ
cana-2210	150	10	it	it	PRON
cana-2210	150	11	is	be	AUX
cana-2210	150	12	able	able	ADJ
cana-2210	150	13	to	to	PART
cana-2210	150	14	represented	represent	VERB
cana-2210	150	15	as	as	ADP
cana-2210	150	16	𝑓	𝑓	PROPN
cana-2210	150	17	=	=	SYM
cana-2210	150	18	∑	∑	PUNCT
cana-2210	150	19	𝜂𝑙𝑓𝑙(𝜁	𝜂𝑙𝑓𝑙(𝜁	PROPN
cana-2210	150	20	)	)	PUNCT
cana-2210	150	21	,	,	PUNCT
cana-2210	150	22	𝜂𝑙	𝜂𝑙	ADP
cana-2210	150	23	>	>	X
cana-2210	150	24	0	0	PUNCT
cana-2210	150	25	∞	∞	NUM
cana-2210	150	26	𝑙=1	𝑙=1	PUNCT
cana-2210	150	27	and	and	CCONJ
cana-2210	150	28	∑	∑	ADV
cana-2210	150	29	𝜂𝑙	𝜂𝑙	PROPN
cana-2210	150	30	=	=	PUNCT
cana-2210	150	31	1.∞	1.∞	NUM
cana-2210	150	32	𝑙=1	𝑙=1	NOUN
cana-2210	150	33	if	if	SCONJ
cana-2210	150	34	𝑏	𝑏	PROPN
cana-2210	150	35	=	=	SYM
cana-2210	150	36	1	1	NUM
cana-2210	150	37	and	and	CCONJ
cana-2210	150	38	𝜏	𝜏	NOUN
cana-2210	150	39	=	=	SYM
cana-2210	150	40	0	0	NUM
cana-2210	150	41	,	,	PUNCT
cana-2210	150	42	we	we	PRON
cana-2210	150	43	get	get	VERB
cana-2210	150	44	the	the	DET
cana-2210	150	45	result	result	NOUN
cana-2210	150	46	of	of	ADP
cana-2210	150	47	the	the	DET
cana-2210	150	48	class	class	NOUN
cana-2210	150	49	𝑆𝑚,𝑛,𝜌(𝛾	𝑆𝑚,𝑛,𝜌(𝛾	NOUN
cana-2210	150	50	)	)	PUNCT
cana-2210	150	51	introduced	introduce	VERB
cana-2210	150	52	by	by	ADP
cana-2210	150	53	sevtap	sevtap	NOUN
cana-2210	150	54	sumer	sumer	PROPN
cana-2210	150	55	eker	eker	PROPN
cana-2210	150	56	and	and	CCONJ
cana-2210	150	57	ozlem	ozlem	ADJ
cana-2210	150	58	guney	guney	NOUN
cana-2210	150	59	[	[	X
cana-2210	150	60	27	27	NUM
cana-2210	150	61	]	]	PUNCT
cana-2210	150	62	.	.	PUNCT
cana-2210	151	1	corollary	corollary	ADJ
cana-2210	151	2	2.9	2.9	NUM
cana-2210	151	3	let	let	VERB
cana-2210	151	4	𝑓1(𝜁	𝑓1(𝜁	PRON
cana-2210	151	5	)	)	PUNCT
cana-2210	151	6	=	=	SYM
cana-2210	151	7	𝜁	𝜁	PROPN
cana-2210	151	8	,	,	PUNCT
cana-2210	151	9	and	and	CCONJ
cana-2210	151	10	𝑓𝑙(𝜁	𝑓𝑙(𝜁	NUM
cana-2210	151	11	)	)	PUNCT
cana-2210	151	12	=	=	SYM
cana-2210	152	1	𝜁	𝜁	PROPN
cana-2210	152	2	+	+	CCONJ
cana-2210	152	3	∑	∑	PROPN
cana-2210	152	4	𝜂𝑙	𝜂𝑙	PROPN
cana-2210	152	5	2(1−𝛾)𝑏	2(1−𝛾)𝑏	NUM
cana-2210	152	6	𝜙(𝛾,𝑚,𝑛,𝜌,𝑙	𝜙(𝛾,𝑚,𝑛,𝜌,𝑙	ADJ
cana-2210	152	7	)	)	PUNCT
cana-2210	152	8	𝜁𝑙	𝜁𝑙	NOUN
cana-2210	152	9	,	,	PUNCT
cana-2210	152	10	(	(	PUNCT
cana-2210	152	11	𝑙	𝑙	X
cana-2210	152	12	=	=	PUNCT
cana-2210	152	13	2,3,4	2,3,4	NUM
cana-2210	152	14	,	,	PUNCT
cana-2210	152	15	…	…	PUNCT
cana-2210	152	16	)	)	PUNCT
cana-2210	152	17	,	,	PUNCT
cana-2210	152	18	∞	∞	PROPN
cana-2210	153	1	𝑙=2	𝑙=2	PROPN
cana-2210	153	2	then	then	ADV
cana-2210	153	3	𝑓	𝑓	PROPN
cana-2210	153	4	∈	∈	PROPN
cana-2210	153	5	�	�	PROPN
cana-2210	153	6	̃	̃	PROPN
cana-2210	153	7	�	�	PROPN
cana-2210	153	8	𝑚,𝑛,𝜌	𝑚,𝑛,𝜌	NOUN
cana-2210	153	9	if	if	SCONJ
cana-2210	153	10	it	it	PRON
cana-2210	153	11	is	be	AUX
cana-2210	153	12	able	able	ADJ
cana-2210	153	13	to	to	PART
cana-2210	153	14	represented	represent	VERB
cana-2210	153	15	as	as	ADP
cana-2210	153	16	𝑓	𝑓	PROPN
cana-2210	153	17	=	=	SYM
cana-2210	153	18	∑	∑	PUNCT
cana-2210	153	19	𝜂𝑙𝑓𝑙(𝜁	𝜂𝑙𝑓𝑙(𝜁	PROPN
cana-2210	153	20	)	)	PUNCT
cana-2210	153	21	,	,	PUNCT
cana-2210	153	22	𝜂𝑙	𝜂𝑙	ADP
cana-2210	153	23	>	>	X
cana-2210	153	24	0	0	PUNCT
cana-2210	153	25	∞	∞	NUM
cana-2210	153	26	𝑙=1	𝑙=1	PUNCT
cana-2210	153	27	and	and	CCONJ
cana-2210	153	28	∑	∑	ADV
cana-2210	153	29	𝜂𝑙	𝜂𝑙	ADJ
cana-2210	153	30	=	=	SYM
cana-2210	153	31	1.∞	1.∞	NOUN
cana-2210	153	32	𝑙=1	𝑙=1	ADJ
cana-2210	153	33	theorem	theorem	VERB
cana-2210	153	34	2.10	2.10	NUM
cana-2210	153	35	let	let	VERB
cana-2210	153	36	𝑓	𝑓	DET
cana-2210	153	37	∈	∈	PROPN
cana-2210	153	38	𝑆𝑏,𝜏,𝜌,µ	𝑆𝑏,𝜏,𝜌,µ	PROPN
cana-2210	153	39	𝑚,𝑛	𝑚,𝑛	NOUN
cana-2210	153	40	(	(	PUNCT
cana-2210	153	41	𝛾	𝛾	NOUN
cana-2210	153	42	)	)	PUNCT
cana-2210	153	43	and	and	CCONJ
cana-2210	153	44	suppose	suppose	VERB
cana-2210	153	45	that	that	SCONJ
cana-2210	153	46	𝑓	𝑓	PROPN
cana-2210	153	47	is	be	AUX
cana-2210	153	48	defined	define	VERB
cana-2210	153	49	by	by	ADP
cana-2210	153	50	𝜁	𝜁	PROPN
cana-2210	153	51	+	+	CCONJ
cana-2210	153	52	2(1	2(1	NUM
cana-2210	153	53	−	−	ADP
cana-2210	153	54	𝛾)𝑏𝜀𝑙	𝛾)𝑏𝜀𝑙	PROPN
cana-2210	153	55	𝜙(𝛾	𝜙(𝛾	PROPN
cana-2210	153	56	,	,	PUNCT
cana-2210	153	57	𝜏	𝜏	NOUN
cana-2210	153	58	)	)	PUNCT
cana-2210	153	59	𝜁𝑙	𝜁𝑙	NOUN
cana-2210	153	60	,	,	PUNCT
cana-2210	153	61	(	(	PUNCT
cana-2210	153	62	𝑙	𝑙	X
cana-2210	153	63	=	=	PUNCT
cana-2210	153	64	2,3,4	2,3,4	NUM
cana-2210	153	65	,	,	PUNCT
cana-2210	153	66	…	…	PUNCT
cana-2210	153	67	)	)	PUNCT
cana-2210	153	68	,	,	PUNCT
cana-2210	153	69	|𝜀𝑙|	|𝜀𝑙|	PROPN
cana-2210	153	70	=	=	SYM
cana-2210	153	71	1	1	X
cana-2210	153	72	.	.	PUNCT
cana-2210	154	1	if	if	SCONJ
cana-2210	154	2	an	an	DET
cana-2210	154	3	analytic	analytic	ADJ
cana-2210	154	4	function	function	NOUN
cana-2210	154	5	is	be	AUX
cana-2210	154	6	present	present	ADJ
cana-2210	154	7	𝑤(𝜁	𝑤(𝜁	VERB
cana-2210	154	8	)	)	PUNCT
cana-2210	154	9	given	give	VERB
cana-2210	154	10	by	by	ADP
cana-2210	154	11	{	{	PUNCT
cana-2210	154	12	𝑤(𝜁)}𝑙−1	𝑤(𝜁)}𝑙−1	NUM
cana-2210	154	13	=	=	SYM
cana-2210	154	14	𝜙(𝛾	𝜙(𝛾	NOUN
cana-2210	154	15	,	,	PUNCT
cana-2210	154	16	𝜏	𝜏	NOUN
cana-2210	154	17	)	)	PUNCT
cana-2210	154	18	2(1	2(1	NUM
cana-2210	154	19	−	−	NOUN
cana-2210	154	20	𝛾)𝑏𝜀𝑙	𝛾)𝑏𝜀𝑙	PROPN
cana-2210	154	21	∑	∑	PUNCT
cana-2210	154	22	𝑎𝑙𝜁	𝑎𝑙𝜁	PROPN
cana-2210	154	23	𝑙−1	𝑙−1	PROPN
cana-2210	154	24	,	,	PUNCT
cana-2210	154	25	(	(	PUNCT
cana-2210	154	26	𝜁	𝜁	PROPN
cana-2210	154	27	=	=	SYM
cana-2210	154	28	𝑟𝑒𝑖𝜃	𝑟𝑒𝑖𝜃	NOUN
cana-2210	154	29	,	,	PUNCT
cana-2210	154	30	0	0	PUNCT
cana-2210	154	31	<	<	X
cana-2210	154	32	𝑟	𝑟	X
cana-2210	154	33	<	<	X
cana-2210	154	34	1	1	NUM
cana-2210	154	35	)	)	PUNCT
cana-2210	154	36	,	,	PUNCT
cana-2210	154	37	∞	∞	PROPN
cana-2210	154	38	𝑙=2	𝑙=2	PROPN
cana-2210	154	39	communications	communication	NOUN
cana-2210	154	40	on	on	ADP
cana-2210	154	41	applied	apply	VERB
cana-2210	154	42	nonlinear	nonlinear	ADJ
cana-2210	154	43	analysis	analysis	NOUN
cana-2210	154	44	issn	issn	NOUN
cana-2210	154	45	:	:	PUNCT
cana-2210	154	46	1074	1074	NUM
cana-2210	154	47	-	-	PUNCT
cana-2210	154	48	133x	133x	NUM
cana-2210	154	49	vol	vol	NOUN
cana-2210	154	50	32	32	NUM
cana-2210	154	51	no	no	NOUN
cana-2210	154	52	.	.	PUNCT
cana-2210	155	1	1s	1s	NUM
cana-2210	155	2	(	(	PUNCT
cana-2210	155	3	2025	2025	NUM
cana-2210	155	4	)	)	PUNCT
cana-2210	155	5	467	467	NUM
cana-2210	155	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2210	155	7	then	then	ADV
cana-2210	155	8	∫	∫	PROPN
cana-2210	155	9	|𝑓(𝑟𝑒𝑖𝜃)|	|𝑓(𝑟𝑒𝑖𝜃)|	PROPN
cana-2210	155	10	𝜇	𝜇	ADP
cana-2210	155	11	𝑑𝜃	𝑑𝜃	PROPN
cana-2210	155	12	≤	≤	NUM
cana-2210	155	13	∫	∫	PROPN
cana-2210	155	14	|1	|1	X
cana-2210	156	1	+	+	NUM
cana-2210	156	2	2(1	2(1	NUM
cana-2210	156	3	−	−	NOUN
cana-2210	156	4	𝛾)𝑏𝜀𝑙	𝛾)𝑏𝜀𝑙	PROPN
cana-2210	156	5	𝜙(𝛾	𝜙(𝛾	PROPN
cana-2210	156	6	,	,	PUNCT
cana-2210	156	7	𝜏	𝜏	NOUN
cana-2210	156	8	)	)	PUNCT
cana-2210	156	9	𝜁𝑙−1|	𝜁𝑙−1|	X
cana-2210	156	10	𝜇	𝜇	X
cana-2210	156	11	𝑑𝜃.	𝑑𝜃.	X
cana-2210	156	12	2𝜋	2𝜋	NOUN
cana-2210	156	13	0	0	NUM
cana-2210	156	14	2𝜋	2𝜋	NOUN
cana-2210	156	15	0	0	NUM
cana-2210	156	16	proof	proof	NOUN
cana-2210	156	17	.	.	PUNCT
cana-2210	157	1	we	we	PRON
cana-2210	157	2	show	show	VERB
cana-2210	157	3	that	that	SCONJ
cana-2210	157	4	∫	∫	PROPN
cana-2210	157	5	|1	|1	X
cana-2210	158	1	+	+	CCONJ
cana-2210	158	2	∑	∑	PUNCT
cana-2210	158	3	𝑎𝑙	𝑎𝑙	PROPN
cana-2210	158	4	∞	∞	PROPN
cana-2210	158	5	𝑙=2	𝑙=2	PROPN
cana-2210	158	6	𝜁𝑙−1|	𝜁𝑙−1|	ADP
cana-2210	158	7	𝜇	𝜇	ADP
cana-2210	158	8	𝑑𝜃	𝑑𝜃	PROPN
cana-2210	158	9	≤	≤	NUM
cana-2210	158	10	∫	∫	PROPN
cana-2210	158	11	|1	|1	X
cana-2210	159	1	+	+	NUM
cana-2210	159	2	2(1	2(1	NUM
cana-2210	159	3	−	−	NOUN
cana-2210	159	4	𝛾)𝑏𝜀𝑙	𝛾)𝑏𝜀𝑙	PROPN
cana-2210	159	5	𝜙(𝛾	𝜙(𝛾	PROPN
cana-2210	159	6	,	,	PUNCT
cana-2210	159	7	𝜏	𝜏	NOUN
cana-2210	159	8	)	)	PUNCT
cana-2210	159	9	𝜁𝑙−1|	𝜁𝑙−1|	X
cana-2210	159	10	𝜇	𝜇	X
cana-2210	159	11	𝑑𝜃.	𝑑𝜃.	X
cana-2210	159	12	2𝜋	2𝜋	NOUN
cana-2210	159	13	0	0	NUM
cana-2210	159	14	2𝜋	2𝜋	NOUN
cana-2210	159	15	0	0	NUM
cana-2210	159	16	by	by	ADP
cana-2210	159	17	the	the	DET
cana-2210	159	18	help	help	NOUN
cana-2210	159	19	of	of	ADP
cana-2210	159	20	little	little	ADJ
cana-2210	159	21	wood	wood	NOUN
cana-2210	159	22	subordination	subordination	NOUN
cana-2210	159	23	theorem	theorem	VERB
cana-2210	159	24	[	[	PUNCT
cana-2210	159	25	13	13	NUM
cana-2210	159	26	]	]	PUNCT
cana-2210	159	27	,	,	PUNCT
cana-2210	159	28	it	it	PRON
cana-2210	159	29	is	be	AUX
cana-2210	159	30	sufficient	sufficient	ADJ
cana-2210	159	31	to	to	PART
cana-2210	159	32	show	show	VERB
cana-2210	159	33	that	that	SCONJ
cana-2210	159	34	1	1	NUM
cana-2210	159	35	+	+	CCONJ
cana-2210	159	36	∑	∑	PUNCT
cana-2210	159	37	𝑎𝑙	𝑎𝑙	NOUN
cana-2210	159	38	∞	∞	PROPN
cana-2210	159	39	𝑙=2	𝑙=2	PROPN
cana-2210	160	1	𝜁𝑙−1	𝜁𝑙−1	PROPN
cana-2210	160	2	≺	≺	VERB
cana-2210	160	3	1	1	NUM
cana-2210	160	4	+	+	NUM
cana-2210	160	5	2(1	2(1	NUM
cana-2210	160	6	−	−	ADP
cana-2210	160	7	𝛾)𝑏𝜀𝑙	𝛾)𝑏𝜀𝑙	PROPN
cana-2210	160	8	𝜙(𝛾	𝜙(𝛾	PROPN
cana-2210	160	9	,	,	PUNCT
cana-2210	160	10	𝜏	𝜏	NOUN
cana-2210	160	11	)	)	PUNCT
cana-2210	160	12	𝜁𝑙−1	𝜁𝑙−1	PROPN
cana-2210	160	13	.	.	PUNCT
cana-2210	161	1	let	let	VERB
cana-2210	161	2	1	1	NUM
cana-2210	161	3	+	+	CCONJ
cana-2210	161	4	∑	∑	PUNCT
cana-2210	161	5	𝑎𝑙	𝑎𝑙	NOUN
cana-2210	161	6	∞	∞	PROPN
cana-2210	161	7	𝑙=2	𝑙=2	PROPN
cana-2210	162	1	𝜁𝑙−1	𝜁𝑙−1	NOUN
cana-2210	162	2	=	=	PUNCT
cana-2210	162	3	1	1	NUM
cana-2210	162	4	+	+	NUM
cana-2210	162	5	2(1	2(1	NUM
cana-2210	162	6	−	−	ADP
cana-2210	162	7	𝛾)𝑏𝜀𝑙	𝛾)𝑏𝜀𝑙	PROPN
cana-2210	162	8	𝜙(𝛾	𝜙(𝛾	PROPN
cana-2210	162	9	,	,	PUNCT
cana-2210	162	10	𝜏	𝜏	NOUN
cana-2210	162	11	)	)	PUNCT
cana-2210	162	12	(	(	PUNCT
cana-2210	162	13	𝑤(𝜁))𝑙−1	𝑤(𝜁))𝑙−1	X
cana-2210	162	14	.	.	PUNCT
cana-2210	163	1	∴	∴	NOUN
cana-2210	163	2	(	(	PUNCT
cana-2210	163	3	𝑤(𝜁))𝑙−1	𝑤(𝜁))𝑙−1	NUM
cana-2210	163	4	=	=	SYM
cana-2210	163	5	𝜙(𝛾	𝜙(𝛾	NOUN
cana-2210	163	6	,	,	PUNCT
cana-2210	163	7	𝜏	𝜏	NOUN
cana-2210	163	8	)	)	PUNCT
cana-2210	163	9	2(1	2(1	NUM
cana-2210	163	10	−	−	NOUN
cana-2210	163	11	𝛾)𝑏𝜀𝑙	𝛾)𝑏𝜀𝑙	PROPN
cana-2210	163	12	∑	∑	PUNCT
cana-2210	163	13	𝑎𝑙𝜁	𝑎𝑙𝜁	PROPN
cana-2210	163	14	𝑙−1	𝑙−1	PROPN
cana-2210	163	15	.	.	PUNCT
cana-2210	164	1	∞	∞	PROPN
cana-2210	164	2	𝑙=2	𝑙=2	PROPN
cana-2210	164	3	which	which	PRON
cana-2210	164	4	readily	readily	ADV
cana-2210	164	5	yields	yield	VERB
cana-2210	164	6	𝑤(0	𝑤(0	NOUN
cana-2210	164	7	)	)	PUNCT
cana-2210	165	1	=	=	SYM
cana-2210	165	2	0	0	X
cana-2210	165	3	.	.	PUNCT
cana-2210	166	1	further	far	ADV
cana-2210	166	2	,	,	PUNCT
cana-2210	166	3	we	we	PRON
cana-2210	166	4	prove	prove	VERB
cana-2210	166	5	that	that	SCONJ
cana-2210	166	6	the	the	DET
cana-2210	166	7	analytic	analytic	ADJ
cana-2210	166	8	function	function	NOUN
cana-2210	166	9	𝑤(𝜁	𝑤(𝜁	NOUN
cana-2210	166	10	)	)	PUNCT
cana-2210	166	11	satisfies	satisfie	NOUN
cana-2210	166	12	|𝑤(𝜁	|𝑤(𝜁	NOUN
cana-2210	166	13	)	)	PUNCT
cana-2210	166	14	|	|	ADV
cana-2210	166	15	<	<	X
cana-2210	166	16	1	1	NUM
cana-2210	166	17	using	use	VERB
cana-2210	166	18	schwarz	schwarz	PROPN
cana-2210	166	19	lemma	lemma	PROPN
cana-2210	166	20	.	.	PUNCT
cana-2210	167	1	we	we	PRON
cana-2210	167	2	know	know	VERB
cana-2210	167	3	that	that	PRON
cana-2210	167	4	|(𝑤(𝜁))𝑙−1|	|(𝑤(𝜁))𝑙−1|	PROPN
cana-2210	167	5	=	=	PUNCT
cana-2210	168	1	|	|	ADV
cana-2210	168	2	𝜙(𝛾	𝜙(𝛾	NOUN
cana-2210	168	3	,	,	PUNCT
cana-2210	168	4	𝜏	𝜏	NOUN
cana-2210	168	5	)	)	PUNCT
cana-2210	168	6	2(1	2(1	NUM
cana-2210	168	7	−	−	ADP
cana-2210	168	8	𝛾)𝑏𝜀𝑙	𝛾)𝑏𝜀𝑙	PROPN
cana-2210	168	9	∑	∑	PROPN
cana-2210	168	10	𝑎𝑙𝜁𝑙−1	𝑎𝑙𝜁𝑙−1	PROPN
cana-2210	168	11	.	.	PUNCT
cana-2210	169	1	∞	∞	PROPN
cana-2210	169	2	𝑙=2	𝑙=2	PROPN
cana-2210	170	1	|	|	ADV
cana-2210	170	2	≤	≤	NUM
cana-2210	170	3	|𝜁|	|𝜁|	NOUN
cana-2210	170	4	<	<	X
cana-2210	170	5	1	1	X
cana-2210	170	6	.	.	PUNCT
cana-2210	170	7	let	let	VERB
cana-2210	170	8	µ	µ	X
cana-2210	170	9	=	=	SYM
cana-2210	170	10	0	0	NUM
cana-2210	170	11	,	,	PUNCT
cana-2210	170	12	then	then	ADV
cana-2210	170	13	the	the	DET
cana-2210	170	14	class	class	NOUN
cana-2210	170	15	𝑆𝑏,𝜏,𝜌,µ	𝑆𝑏,𝜏,𝜌,µ	PROPN
cana-2210	170	16	𝑚,𝑛	𝑚,𝑛	NOUN
cana-2210	170	17	(	(	PUNCT
cana-2210	170	18	𝛾	𝛾	NOUN
cana-2210	170	19	)	)	PUNCT
cana-2210	170	20	reduces	reduce	VERB
cana-2210	170	21	and	and	CCONJ
cana-2210	170	22	analogues	analogue	NOUN
cana-2210	170	23	to	to	ADP
cana-2210	170	24	the	the	DET
cana-2210	170	25	class	class	NOUN
cana-2210	170	26	,	,	PUNCT
cana-2210	170	27	which	which	PRON
cana-2210	170	28	is	be	AUX
cana-2210	170	29	examined	examine	VERB
cana-2210	170	30	by	by	ADP
cana-2210	170	31	thirucheran	thirucheran	ADJ
cana-2210	170	32	and	and	CCONJ
cana-2210	170	33	stalin	stalin	PROPN
cana-2210	171	1	[	[	X
cana-2210	171	2	30	30	NUM
cana-2210	171	3	]	]	PUNCT
cana-2210	171	4	.	.	PUNCT
cana-2210	172	1	corollary	corollary	ADJ
cana-2210	172	2	2.11	2.11	NUM
cana-2210	172	3	let	let	VERB
cana-2210	172	4	𝑓	𝑓	PRON
cana-2210	172	5	∈	∈	PROPN
cana-2210	172	6	𝑆(𝑚	𝑆(𝑚	SYM
cana-2210	172	7	,	,	PUNCT
cana-2210	172	8	𝑛	𝑛	PROPN
cana-2210	172	9	,	,	PUNCT
cana-2210	172	10	𝛾	𝛾	NOUN
cana-2210	172	11	,	,	PUNCT
cana-2210	172	12	𝜏	𝜏	NOUN
cana-2210	172	13	,	,	PUNCT
cana-2210	172	14	𝜌	𝜌	X
cana-2210	172	15	,	,	PUNCT
cana-2210	172	16	𝑏	𝑏	NOUN
cana-2210	172	17	)	)	PUNCT
cana-2210	172	18	and	and	CCONJ
cana-2210	172	19	suppose	suppose	VERB
cana-2210	172	20	that	that	SCONJ
cana-2210	172	21	𝑓	𝑓	PROPN
cana-2210	172	22	is	be	AUX
cana-2210	172	23	defined	define	VERB
cana-2210	172	24	by	by	ADP
cana-2210	172	25	𝜁	𝜁	PROPN
cana-2210	172	26	+	+	CCONJ
cana-2210	172	27	2(1	2(1	NUM
cana-2210	172	28	−	−	ADP
cana-2210	172	29	𝛾)𝑏𝜀𝑙	𝛾)𝑏𝜀𝑙	PROPN
cana-2210	172	30	𝜙(𝑚	𝜙(𝑚	PROPN
cana-2210	172	31	,	,	PUNCT
cana-2210	172	32	𝑛	𝑛	PROPN
cana-2210	172	33	,	,	PUNCT
cana-2210	172	34	𝛾	𝛾	NOUN
cana-2210	172	35	,	,	PUNCT
cana-2210	172	36	𝜏	𝜏	NOUN
cana-2210	172	37	,	,	PUNCT
cana-2210	172	38	𝜌	𝜌	X
cana-2210	172	39	,	,	PUNCT
cana-2210	172	40	𝑏	𝑏	NOUN
cana-2210	172	41	,	,	PUNCT
cana-2210	172	42	𝑙	𝑙	NUM
cana-2210	172	43	)	)	PUNCT
cana-2210	172	44	𝜁𝑙	𝜁𝑙	NOUN
cana-2210	172	45	,	,	PUNCT
cana-2210	172	46	(	(	PUNCT
cana-2210	172	47	𝑙	𝑙	X
cana-2210	172	48	=	=	PUNCT
cana-2210	172	49	2,3,4	2,3,4	NUM
cana-2210	172	50	,	,	PUNCT
cana-2210	172	51	…	…	PUNCT
cana-2210	172	52	)	)	PUNCT
cana-2210	172	53	,	,	PUNCT
cana-2210	172	54	|𝜀𝑙|	|𝜀𝑙|	PROPN
cana-2210	172	55	=	=	SYM
cana-2210	172	56	1	1	X
cana-2210	172	57	.	.	PUNCT
cana-2210	173	1	if	if	SCONJ
cana-2210	173	2	an	an	DET
cana-2210	173	3	analytic	analytic	ADJ
cana-2210	173	4	function	function	NOUN
cana-2210	173	5	is	be	AUX
cana-2210	173	6	present	present	ADJ
cana-2210	173	7	𝑤(𝜁	𝑤(𝜁	VERB
cana-2210	173	8	)	)	PUNCT
cana-2210	173	9	given	give	VERB
cana-2210	173	10	by	by	ADP
cana-2210	173	11	{	{	PUNCT
cana-2210	173	12	𝑤(𝜁)}𝑙−1	𝑤(𝜁)}𝑙−1	NUM
cana-2210	173	13	=	=	PROPN
cana-2210	173	14	𝜙(𝑚	𝜙(𝑚	PROPN
cana-2210	173	15	,	,	PUNCT
cana-2210	173	16	𝑛	𝑛	PROPN
cana-2210	173	17	,	,	PUNCT
cana-2210	173	18	𝛾	𝛾	NOUN
cana-2210	173	19	,	,	PUNCT
cana-2210	173	20	𝜏	𝜏	NOUN
cana-2210	173	21	,	,	PUNCT
cana-2210	173	22	𝜌	𝜌	X
cana-2210	173	23	,	,	PUNCT
cana-2210	173	24	𝑏	𝑏	NOUN
cana-2210	173	25	,	,	PUNCT
cana-2210	173	26	𝑙	𝑙	NUM
cana-2210	173	27	)	)	PUNCT
cana-2210	173	28	2(1	2(1	NUM
cana-2210	173	29	−	−	NOUN
cana-2210	173	30	𝛾)𝑏𝜀𝑙	𝛾)𝑏𝜀𝑙	PROPN
cana-2210	173	31	∑	∑	PUNCT
cana-2210	173	32	𝑎𝑙𝜁	𝑎𝑙𝜁	PROPN
cana-2210	173	33	𝑙−1	𝑙−1	PROPN
cana-2210	173	34	,	,	PUNCT
cana-2210	173	35	(	(	PUNCT
cana-2210	173	36	𝜁	𝜁	PROPN
cana-2210	173	37	=	=	SYM
cana-2210	173	38	𝑟𝑒𝑖𝜃	𝑟𝑒𝑖𝜃	NOUN
cana-2210	173	39	,	,	PUNCT
cana-2210	173	40	0	0	PUNCT
cana-2210	173	41	<	<	X
cana-2210	173	42	𝑟	𝑟	X
cana-2210	173	43	<	<	X
cana-2210	173	44	1	1	NUM
cana-2210	173	45	)	)	PUNCT
cana-2210	173	46	,	,	PUNCT
cana-2210	173	47	∞	∞	PROPN
cana-2210	173	48	𝑙=2	𝑙=2	PROPN
cana-2210	173	49	communications	communication	NOUN
cana-2210	173	50	on	on	ADP
cana-2210	173	51	applied	apply	VERB
cana-2210	173	52	nonlinear	nonlinear	ADJ
cana-2210	173	53	analysis	analysis	NOUN
cana-2210	173	54	issn	issn	NOUN
cana-2210	173	55	:	:	PUNCT
cana-2210	173	56	1074	1074	NUM
cana-2210	173	57	-	-	PUNCT
cana-2210	173	58	133x	133x	NUM
cana-2210	173	59	vol	vol	NOUN
cana-2210	173	60	32	32	NUM
cana-2210	173	61	no	no	NOUN
cana-2210	173	62	.	.	PUNCT
cana-2210	174	1	1s	1s	NUM
cana-2210	174	2	(	(	PUNCT
cana-2210	174	3	2025	2025	NUM
cana-2210	174	4	)	)	PUNCT
cana-2210	174	5	468	468	NUM
cana-2210	174	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2210	174	7	then	then	ADV
cana-2210	174	8	∫	∫	PROPN
cana-2210	174	9	|𝑓(𝑟𝑒𝑖𝜃)|	|𝑓(𝑟𝑒𝑖𝜃)|	PROPN
cana-2210	174	10	𝜇	𝜇	ADP
cana-2210	174	11	𝑑𝜃	𝑑𝜃	PROPN
cana-2210	174	12	≤	≤	NUM
cana-2210	174	13	∫	∫	NOUN
cana-2210	174	14	|𝑔(𝑟𝑒𝑖𝜃)|	|𝑔(𝑟𝑒𝑖𝜃)|	PROPN
cana-2210	174	15	𝜇	𝜇	ADP
cana-2210	174	16	𝑑𝜃	𝑑𝜃	PROPN
cana-2210	174	17	,	,	PUNCT
cana-2210	174	18	𝜇	𝜇	X
cana-2210	174	19	>	>	X
cana-2210	174	20	0	0	NUM
cana-2210	174	21	.	.	PUNCT
cana-2210	175	1	2𝜋	2𝜋	NOUN
cana-2210	175	2	0	0	NUM
cana-2210	176	1	2𝜋	2𝜋	NOUN
cana-2210	176	2	0	0	NUM
cana-2210	177	1	3	3	X
cana-2210	177	2	.	.	PUNCT
cana-2210	178	1	the	the	DET
cana-2210	178	2	fekete	fekete	PROPN
cana-2210	178	3	-	-	PUNCT
cana-2210	178	4	szego	szego	NOUN
cana-2210	178	5	inequality	inequality	NOUN
cana-2210	178	6	for	for	ADP
cana-2210	178	7	the	the	DET
cana-2210	178	8	subclass	subclass	NOUN
cana-2210	178	9	𝑺𝒃,𝝉,𝝆,µ	𝑺𝒃,𝝉,𝝆,µ	PROPN
cana-2210	178	10	𝒎,𝒏	𝒎,𝒏	PROPN
cana-2210	178	11	(	(	PUNCT
cana-2210	178	12	𝜸	𝜸	NOUN
cana-2210	178	13	)	)	PUNCT
cana-2210	178	14	in	in	ADP
cana-2210	178	15	1933	1933	NUM
cana-2210	178	16	,	,	PUNCT
cana-2210	178	17	fekete	fekete	NOUN
cana-2210	178	18	-	-	PUNCT
cana-2210	178	19	szego	szego	NOUN
cana-2210	178	20	[	[	X
cana-2210	178	21	7	7	NUM
cana-2210	178	22	]	]	PUNCT
cana-2210	178	23	obtained	obtain	VERB
cana-2210	178	24	the	the	DET
cana-2210	178	25	maximum	maximum	ADJ
cana-2210	178	26	value	value	NOUN
cana-2210	178	27	of	of	ADP
cana-2210	178	28	|𝑎3	|𝑎3	VERB
cana-2210	178	29	−	−	PROPN
cana-2210	178	30	µ𝑎2	µ𝑎2	PROPN
cana-2210	178	31	2|	2|	PROPN
cana-2210	178	32	as	as	ADP
cana-2210	178	33	a	a	DET
cana-2210	178	34	function	function	NOUN
cana-2210	178	35	of	of	ADP
cana-2210	178	36	the	the	DET
cana-2210	178	37	real	real	ADJ
cana-2210	178	38	parameter	parameter	NOUN
cana-2210	178	39	µ	µ	NOUN
cana-2210	178	40	,	,	PUNCT
cana-2210	178	41	for	for	ADP
cana-2210	178	42	the	the	DET
cana-2210	178	43	function	function	NOUN
cana-2210	178	44	of	of	ADP
cana-2210	178	45	class	class	NOUN
cana-2210	178	46	𝐴.	𝐴.	PROPN
cana-2210	178	47	since	since	SCONJ
cana-2210	178	48	then	then	ADV
cana-2210	178	49	,	,	PUNCT
cana-2210	178	50	the	the	DET
cana-2210	178	51	various	various	ADJ
cana-2210	178	52	authors	author	NOUN
cana-2210	178	53	were	be	AUX
cana-2210	178	54	investigated	investigate	VERB
cana-2210	178	55	and	and	CCONJ
cana-2210	178	56	obtained	obtain	VERB
cana-2210	178	57	the	the	DET
cana-2210	178	58	fekete	fekete	PROPN
cana-2210	178	59	-	-	PUNCT
cana-2210	178	60	szego	szego	NOUN
cana-2210	178	61	inequalities	inequality	NOUN
cana-2210	178	62	for	for	ADP
cana-2210	178	63	different	different	ADJ
cana-2210	178	64	subclasses	subclass	NOUN
cana-2210	178	65	of	of	ADP
cana-2210	178	66	the	the	DET
cana-2210	178	67	class	class	NOUN
cana-2210	178	68	𝐴	𝐴	PROPN
cana-2210	179	1	[	[	X
cana-2210	179	2	5	5	NUM
cana-2210	179	3	]	]	PUNCT
cana-2210	179	4	[	[	X
cana-2210	179	5	7],[8],[18],[22],[25	7],[8],[18],[22],[25	NOUN
cana-2210	179	6	]	]	X
cana-2210	179	7	,	,	PUNCT
cana-2210	179	8	[	[	X
cana-2210	179	9	28	28	NUM
cana-2210	179	10	]	]	PUNCT
cana-2210	179	11	,	,	PUNCT
cana-2210	179	12	[	[	X
cana-2210	179	13	29	29	NUM
cana-2210	179	14	]	]	PUNCT
cana-2210	179	15	.	.	PUNCT
cana-2210	180	1	in	in	ADP
cana-2210	180	2	this	this	DET
cana-2210	180	3	article	article	NOUN
cana-2210	180	4	,	,	PUNCT
cana-2210	180	5	we	we	PRON
cana-2210	180	6	introduced	introduce	VERB
cana-2210	180	7	two	two	NUM
cana-2210	180	8	new	new	ADJ
cana-2210	180	9	subclasses	subclass	NOUN
cana-2210	180	10	of	of	ADP
cana-2210	180	11	univalent	univalent	ADJ
cana-2210	180	12	functions	function	NOUN
cana-2210	180	13	which	which	PRON
cana-2210	180	14	are	be	AUX
cana-2210	180	15	defined	define	VERB
cana-2210	180	16	by	by	ADP
cana-2210	180	17	using	use	VERB
cana-2210	180	18	raducanu	raducanu	NOUN
cana-2210	180	19	-	-	PUNCT
cana-2210	180	20	ohran	ohran	NOUN
cana-2210	180	21	differential	differential	ADJ
cana-2210	180	22	operator	operator	NOUN
cana-2210	180	23	in	in	ADP
cana-2210	180	24	the	the	DET
cana-2210	180	25	open	open	ADJ
cana-2210	180	26	unit	unit	NOUN
cana-2210	180	27	disc	disc	NOUN
cana-2210	180	28	.	.	PUNCT
cana-2210	181	1	for	for	ADP
cana-2210	181	2	these	these	DET
cana-2210	181	3	subclasses	subclass	NOUN
cana-2210	181	4	,	,	PUNCT
cana-2210	181	5	we	we	PRON
cana-2210	181	6	obtain	obtain	VERB
cana-2210	181	7	the	the	DET
cana-2210	181	8	fekete	fekete	PROPN
cana-2210	181	9	-	-	PUNCT
cana-2210	181	10	szego	szego	NOUN
cana-2210	181	11	inequality	inequality	NOUN
cana-2210	181	12	|𝑎3	|𝑎3	VERB
cana-2210	181	13	−	−	PROPN
cana-2210	181	14	µ𝑎2	µ𝑎2	PROPN
cana-2210	181	15	2|	2|	NUM
cana-2210	181	16	.	.	PUNCT
cana-2210	182	1	if	if	SCONJ
cana-2210	182	2	replacing	replace	VERB
cana-2210	182	3	special	special	ADJ
cana-2210	182	4	values	value	NOUN
cana-2210	182	5	for	for	ADP
cana-2210	182	6	the	the	DET
cana-2210	182	7	subclass	subclass	NOUN
cana-2210	182	8	,	,	PUNCT
cana-2210	182	9	we	we	PRON
cana-2210	182	10	obtained	obtain	VERB
cana-2210	182	11	several	several	ADJ
cana-2210	182	12	well	well	ADV
cana-2210	182	13	-	-	PUNCT
cana-2210	182	14	known	know	VERB
cana-2210	182	15	subclasses	subclass	NOUN
cana-2210	182	16	.	.	PUNCT
cana-2210	183	1	remark	remark	VERB
cana-2210	183	2	𝑆1,0,0,1	𝑆1,0,0,1	NOUN
cana-2210	183	3	1,0	1,0	NUM
cana-2210	183	4	(	(	PUNCT
cana-2210	183	5	𝛾	𝛾	NOUN
cana-2210	183	6	)	)	PUNCT
cana-2210	183	7	=	=	SYM
cana-2210	183	8	𝑆∗(𝛾	𝑆∗(𝛾	PRON
cana-2210	183	9	)	)	PUNCT
cana-2210	183	10	studied	study	VERB
cana-2210	183	11	by	by	ADP
cana-2210	183	12	ma	ma	PROPN
cana-2210	183	13	and	and	CCONJ
cana-2210	183	14	minda	minda	PROPN
cana-2210	184	1	[	[	X
cana-2210	184	2	14	14	NUM
cana-2210	184	3	]	]	PUNCT
cana-2210	184	4	.	.	PUNCT
cana-2210	185	1	𝑆𝑏,0,0,1	𝑆𝑏,0,0,1	NOUN
cana-2210	185	2	1,0	1,0	NUM
cana-2210	185	3	(	(	PUNCT
cana-2210	185	4	𝛾	𝛾	NOUN
cana-2210	185	5	)	)	PUNCT
cana-2210	185	6	=	=	SYM
cana-2210	186	1	𝑆𝑏	𝑆𝑏	PROPN
cana-2210	186	2	∗(𝛾	∗(𝛾	PROPN
cana-2210	186	3	)	)	PUNCT
cana-2210	186	4	studied	study	VERB
cana-2210	186	5	by	by	ADP
cana-2210	186	6	ravichandran	ravichandran	NOUN
cana-2210	186	7	et.al	et.al	PROPN
cana-2210	186	8	.	.	PUNCT
cana-2210	187	1	[	[	X
cana-2210	187	2	18	18	NUM
cana-2210	187	3	]	]	PUNCT
cana-2210	187	4	.	.	PUNCT
cana-2210	188	1	𝑆𝑏,0,0,𝜌	𝑆𝑏,0,0,𝜌	ADP
cana-2210	188	2	2,0	2,0	NUM
cana-2210	188	3	(	(	PUNCT
cana-2210	188	4	𝛾	𝛾	NOUN
cana-2210	188	5	)	)	PUNCT
cana-2210	188	6	=	=	SYM
cana-2210	188	7	𝑀𝑎,𝑏(𝜙	𝑀𝑎,𝑏(𝜙	NOUN
cana-2210	188	8	)	)	PUNCT
cana-2210	188	9	studied	study	VERB
cana-2210	188	10	by	by	ADP
cana-2210	188	11	suchitra	suchitra	PROPN
cana-2210	188	12	et.al	et.al	PROPN
cana-2210	188	13	.	.	PUNCT
cana-2210	189	1	[	[	X
cana-2210	189	2	25	25	NUM
cana-2210	189	3	]	]	PUNCT
cana-2210	189	4	.	.	PUNCT
cana-2210	190	1	𝑆𝑏,0,0,𝜌	𝑆𝑏,0,0,𝜌	ADP
cana-2210	190	2	2,1	2,1	NUM
cana-2210	190	3	(	(	PUNCT
cana-2210	190	4	𝛾	𝛾	NOUN
cana-2210	190	5	)	)	PUNCT
cana-2210	190	6	=	=	VERB
cana-2210	191	1	𝑀𝛾(𝜙)studied	𝑀𝛾(𝜙)studie	VERB
cana-2210	191	2	by	by	ADP
cana-2210	191	3	shanmugam	shanmugam	NOUN
cana-2210	191	4	and	and	CCONJ
cana-2210	191	5	sivasubramanian	sivasubramanian	ADJ
cana-2210	192	1	[	[	X
cana-2210	192	2	22	22	NUM
cana-2210	192	3	]	]	PUNCT
cana-2210	192	4	.	.	PUNCT
cana-2210	193	1	lemma	lemma	PROPN
cana-2210	193	2	3.2	3.2	NUM
cana-2210	193	3	if	if	SCONJ
cana-2210	193	4	𝑃(𝜁	𝑃(𝜁	NUM
cana-2210	193	5	)	)	PUNCT
cana-2210	193	6	=	=	SYM
cana-2210	193	7	1	1	NUM
cana-2210	193	8	+	+	NUM
cana-2210	193	9	𝑐1𝜁	𝑐1𝜁	X
cana-2210	194	1	+	+	CCONJ
cana-2210	194	2	𝑐2𝜁2	𝑐2𝜁2	NOUN
cana-2210	194	3	+	+	CCONJ
cana-2210	194	4	𝑐3𝜁3	𝑐3𝜁3	X
cana-2210	194	5	+	+	CCONJ
cana-2210	194	6	⋯	⋯	NOUN
cana-2210	194	7	is	be	AUX
cana-2210	194	8	a	a	DET
cana-2210	194	9	function	function	NOUN
cana-2210	194	10	with	with	ADP
cana-2210	194	11	positive	positive	ADJ
cana-2210	194	12	real	real	ADJ
cana-2210	194	13	part	part	NOUN
cana-2210	194	14	in	in	ADP
cana-2210	194	15	𝑈	𝑈	PROPN
cana-2210	194	16	and	and	CCONJ
cana-2210	194	17	µ	µ	PROPN
cana-2210	194	18	is	be	AUX
cana-2210	194	19	a	a	DET
cana-2210	194	20	complex	complex	ADJ
cana-2210	194	21	number	number	NOUN
cana-2210	194	22	,	,	PUNCT
cana-2210	194	23	then	then	ADV
cana-2210	194	24	|𝑐2	|𝑐2	VERB
cana-2210	194	25	−	−	NOUN
cana-2210	194	26	µ𝑐1	µ𝑐1	INTJ
cana-2210	194	27	2|	2|	NUM
cana-2210	194	28	≤	≤	ADV
cana-2210	194	29	2	2	NUM
cana-2210	194	30	𝑀𝑎𝑥{1	𝑀𝑎𝑥{1	NUM
cana-2210	194	31	,	,	PUNCT
cana-2210	194	32	|2µ	|2µ	ADP
cana-2210	194	33	−	−	PROPN
cana-2210	194	34	1|	1|	NUM
cana-2210	194	35	}	}	PUNCT
cana-2210	194	36	.	.	PUNCT
cana-2210	195	1	the	the	DET
cana-2210	195	2	result	result	NOUN
cana-2210	195	3	is	be	AUX
cana-2210	195	4	sharp	sharp	ADJ
cana-2210	195	5	for	for	SCONJ
cana-2210	195	6	the	the	DET
cana-2210	195	7	function	function	NOUN
cana-2210	195	8	is	be	AUX
cana-2210	195	9	given	give	VERB
cana-2210	195	10	by	by	ADP
cana-2210	195	11	𝑃(𝜁	𝑃(𝜁	NUM
cana-2210	195	12	)	)	PUNCT
cana-2210	195	13	=	=	SYM
cana-2210	195	14	1+𝜁2	1+𝜁2	NUM
cana-2210	195	15	1−𝜁2	1−𝜁2	NUM
cana-2210	195	16	and	and	CCONJ
cana-2210	195	17	𝑃(𝜁	𝑃(𝜁	X
cana-2210	195	18	)	)	PUNCT
cana-2210	195	19	=	=	NUM
cana-2210	195	20	1+𝜁	1+𝜁	NUM
cana-2210	195	21	1−𝜁	1−𝜁	NUM
cana-2210	195	22	.	.	PUNCT
cana-2210	196	1	theorem	theorem	VERB
cana-2210	196	2	3.3	3.3	NUM
cana-2210	196	3	let	let	VERB
cana-2210	196	4	𝜙(𝜁	𝜙(𝜁	PROPN
cana-2210	196	5	)	)	PUNCT
cana-2210	196	6	=	=	SYM
cana-2210	196	7	1	1	NUM
cana-2210	197	1	+	+	CCONJ
cana-2210	197	2	𝐵1𝜁	𝐵1𝜁	ADJ
cana-2210	197	3	+	+	CCONJ
cana-2210	197	4	𝐵2𝜁2	𝐵2𝜁2	NOUN
cana-2210	197	5	+	+	CCONJ
cana-2210	197	6	𝐵3𝜁3	𝐵3𝜁3	NOUN
cana-2210	197	7	+	+	CCONJ
cana-2210	197	8	⋯	⋯	PROPN
cana-2210	197	9	,	,	PUNCT
cana-2210	197	10	with	with	ADP
cana-2210	197	11	𝐵1	𝐵1	NOUN
cana-2210	197	12	=	=	SYM
cana-2210	197	13	0	0	X
cana-2210	197	14	.	.	PUNCT
cana-2210	198	1	if	if	SCONJ
cana-2210	198	2	𝑓	𝑓	DET
cana-2210	198	3	∈	∈	PROPN
cana-2210	198	4	𝑆𝑏,𝜏,𝜌,µ	𝑆𝑏,𝜏,𝜌,µ	PROPN
cana-2210	198	5	𝑚,𝑛	𝑚,𝑛	NOUN
cana-2210	198	6	(	(	PUNCT
cana-2210	198	7	𝛾	𝛾	NOUN
cana-2210	198	8	)	)	PUNCT
cana-2210	198	9	satisfies	satisfy	VERB
cana-2210	198	10	the	the	DET
cana-2210	198	11	inequality	inequality	NOUN
cana-2210	198	12	𝑅𝑒	𝑅𝑒	PROPN
cana-2210	198	13	(	(	PUNCT
cana-2210	198	14	1	1	NUM
cana-2210	198	15	+	+	SYM
cana-2210	198	16	1	1	NUM
cana-2210	198	17	𝑏	𝑏	NOUN
cana-2210	198	18	(	(	PUNCT
cana-2210	198	19	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	198	20	𝑚	𝑚	X
cana-2210	198	21	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	198	22	)	)	PUNCT
cana-2210	198	23	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	198	24	𝑛	𝑛	DET
cana-2210	198	25	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	198	26	)	)	PUNCT
cana-2210	198	27	−	−	PROPN
cana-2210	198	28	1	1	NUM
cana-2210	198	29	)	)	PUNCT
cana-2210	198	30	)	)	PUNCT
cana-2210	199	1	−	−	NOUN
cana-2210	199	2	𝜏	𝜏	PRON
cana-2210	199	3	|	|	ADV
cana-2210	199	4	𝑅𝜌,µ	𝑅𝜌,µ	NOUN
cana-2210	199	5	𝑚	𝑚	X
cana-2210	199	6	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	199	7	)	)	PUNCT
cana-2210	199	8	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	199	9	𝑛	𝑛	DET
cana-2210	199	10	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	199	11	)	)	PUNCT
cana-2210	199	12	−	−	PROPN
cana-2210	199	13	1|	1|	NUM
cana-2210	199	14	≺	≺	NOUN
cana-2210	199	15	𝜙(𝜁	𝜙(𝜁	PROPN
cana-2210	199	16	)	)	PUNCT
cana-2210	199	17	.	.	PUNCT
cana-2210	200	1	then	then	ADV
cana-2210	200	2	|𝑎3	|𝑎3	VERB
cana-2210	200	3	−	−	PROPN
cana-2210	200	4	µ𝑎2	µ𝑎2	PROPN
cana-2210	200	5	2|	2|	NOUN
cana-2210	200	6	≤	≤	NOUN
cana-2210	200	7	𝐵1|𝑏	𝐵1|𝑏	PUNCT
cana-2210	200	8	|	|	ADV
cana-2210	200	9	𝑌2−𝑏𝜏|𝑌2|	𝑌2−𝑏𝜏|𝑌2|	NOUN
cana-2210	200	10	max	max	PROPN
cana-2210	200	11	{	{	PUNCT
cana-2210	200	12	1	1	NUM
cana-2210	200	13	,	,	PUNCT
cana-2210	200	14	|	|	ADV
cana-2210	200	15	𝐵2	𝐵2	NOUN
cana-2210	200	16	𝐵1	𝐵1	NOUN
cana-2210	201	1	+	+	CCONJ
cana-2210	201	2	[	[	PUNCT
cana-2210	201	3	[	[	X
cana-2210	201	4	𝑌3−𝑏𝜏|𝑌3|]−µ[[𝑌2]−𝑏𝜏|𝑌2|	𝑌3−𝑏𝜏|𝑌3|]−µ[[𝑌2]−𝑏𝜏|𝑌2|	X
cana-2210	201	5	]	]	X
cana-2210	202	1	[	[	X
cana-2210	202	2	𝑌1−𝑏𝜏[𝑌1]]2	𝑌1−𝑏𝜏[𝑌1]]2	X
cana-2210	202	3	]	]	PUNCT
cana-2210	202	4	𝑏𝐵1|	𝑏𝐵1|	VERB
cana-2210	202	5	}	}	PUNCT
cana-2210	202	6	,	,	PUNCT
cana-2210	202	7	(	(	PUNCT
cana-2210	202	8	5	5	X
cana-2210	202	9	)	)	PUNCT
cana-2210	202	10	where	where	SCONJ
cana-2210	202	11	𝑌1	𝑌1	NOUN
cana-2210	202	12	=	=	SYM
cana-2210	202	13	(	(	PUNCT
cana-2210	202	14	(	(	PUNCT
cana-2210	202	15	1	1	NUM
cana-2210	202	16	+	+	CCONJ
cana-2210	202	17	(	(	PUNCT
cana-2210	202	18	𝜌	𝜌	X
cana-2210	202	19	−	−	PROPN
cana-2210	202	20	µ	µ	X
cana-2210	202	21	+	+	NUM
cana-2210	202	22	2𝜌µ)))𝑚	2𝜌µ)))𝑚	NUM
cana-2210	202	23	−	−	NOUN
cana-2210	202	24	(	(	PUNCT
cana-2210	202	25	(	(	PUNCT
cana-2210	202	26	1	1	NUM
cana-2210	202	27	+	+	CCONJ
cana-2210	202	28	(	(	PUNCT
cana-2210	202	29	𝜌	𝜌	X
cana-2210	202	30	−	−	PROPN
cana-2210	202	31	µ	µ	X
cana-2210	202	32	+	+	X
cana-2210	202	33	2𝜌µ)))𝑛	2𝜌µ)))𝑛	NUM
cana-2210	202	34	,	,	PUNCT
cana-2210	202	35	𝑌2	𝑌2	NOUN
cana-2210	202	36	=	=	SYM
cana-2210	202	37	(	(	PUNCT
cana-2210	202	38	(	(	PUNCT
cana-2210	202	39	1	1	NUM
cana-2210	202	40	+	+	NUM
cana-2210	202	41	2(𝜌	2(𝜌	NUM
cana-2210	202	42	−	−	NOUN
cana-2210	202	43	µ	µ	X
cana-2210	202	44	+	+	CCONJ
cana-2210	202	45	3𝜌µ)))𝑚	3𝜌µ)))𝑚	NUM
cana-2210	202	46	−	−	NOUN
cana-2210	202	47	(	(	PUNCT
cana-2210	202	48	(	(	PUNCT
cana-2210	202	49	1	1	NUM
cana-2210	202	50	+	+	NUM
cana-2210	202	51	2(𝜌	2(𝜌	NUM
cana-2210	202	52	−	−	PROPN
cana-2210	202	53	µ	µ	X
cana-2210	202	54	+	+	X
cana-2210	202	55	3𝜌µ)))𝑛	3𝜌µ)))𝑛	NUM
cana-2210	202	56	and	and	CCONJ
cana-2210	202	57	communications	communication	NOUN
cana-2210	202	58	on	on	ADP
cana-2210	202	59	applied	apply	VERB
cana-2210	202	60	nonlinear	nonlinear	ADJ
cana-2210	202	61	analysis	analysis	NOUN
cana-2210	202	62	issn	issn	NOUN
cana-2210	202	63	:	:	PUNCT
cana-2210	202	64	1074	1074	NUM
cana-2210	202	65	-	-	PUNCT
cana-2210	202	66	133x	133x	NUM
cana-2210	202	67	vol	vol	NOUN
cana-2210	202	68	32	32	NUM
cana-2210	202	69	no	no	NOUN
cana-2210	202	70	.	.	PUNCT
cana-2210	203	1	1s	1s	NUM
cana-2210	203	2	(	(	PUNCT
cana-2210	203	3	2025	2025	NUM
cana-2210	203	4	)	)	PUNCT
cana-2210	203	5	469	469	NUM
cana-2210	203	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2210	203	7	𝑌3	𝑌3	PROPN
cana-2210	203	8	=	=	SYM
cana-2210	203	9	(	(	PUNCT
cana-2210	203	10	(	(	PUNCT
cana-2210	203	11	1	1	NUM
cana-2210	203	12	+	+	CCONJ
cana-2210	203	13	(	(	PUNCT
cana-2210	203	14	𝜌	𝜌	X
cana-2210	203	15	−	−	PROPN
cana-2210	203	16	µ	µ	X
cana-2210	203	17	+	+	CCONJ
cana-2210	203	18	2𝜌µ)))𝑚+𝑛	2𝜌µ)))𝑚+𝑛	NUM
cana-2210	203	19	−	−	PROPN
cana-2210	203	20	(	(	PUNCT
cana-2210	203	21	(	(	PUNCT
cana-2210	203	22	1	1	NUM
cana-2210	203	23	+	+	CCONJ
cana-2210	203	24	(	(	PUNCT
cana-2210	203	25	𝜌	𝜌	X
cana-2210	203	26	−	−	PROPN
cana-2210	203	27	µ	µ	X
cana-2210	203	28	+	+	CCONJ
cana-2210	203	29	2𝜌µ)))2𝑛.	2𝜌µ)))2𝑛.	NUM
cana-2210	203	30	then	then	ADV
cana-2210	203	31	the	the	DET
cana-2210	203	32	result	result	NOUN
cana-2210	203	33	is	be	AUX
cana-2210	203	34	sharp	sharp	ADJ
cana-2210	203	35	.	.	PUNCT
cana-2210	204	1	proof	proof	NOUN
cana-2210	204	2	.	.	PUNCT
cana-2210	205	1	if	if	SCONJ
cana-2210	205	2	𝑓	𝑓	DET
cana-2210	205	3	∈	∈	PROPN
cana-2210	205	4	𝑆𝑏,𝜏,𝜌,µ	𝑆𝑏,𝜏,𝜌,µ	PROPN
cana-2210	205	5	𝑚,𝑛	𝑚,𝑛	NOUN
cana-2210	205	6	(	(	PUNCT
cana-2210	205	7	𝛾	𝛾	NOUN
cana-2210	205	8	)	)	PUNCT
cana-2210	205	9	,	,	PUNCT
cana-2210	205	10	then	then	ADV
cana-2210	205	11	there	there	PRON
cana-2210	205	12	is	be	VERB
cana-2210	205	13	a	a	DET
cana-2210	205	14	schwarz	schwarz	NOUN
cana-2210	205	15	function	function	NOUN
cana-2210	205	16	𝑤(𝜁	𝑤(𝜁	PROPN
cana-2210	205	17	)	)	PUNCT
cana-2210	205	18	,	,	PUNCT
cana-2210	205	19	analytic	analytic	NOUN
cana-2210	205	20	in	in	ADP
cana-2210	205	21	𝑈	𝑈	PROPN
cana-2210	205	22	with	with	ADP
cana-2210	205	23	𝑤(0	𝑤(0	NOUN
cana-2210	205	24	)	)	PUNCT
cana-2210	205	25	=	=	SYM
cana-2210	205	26	0	0	NUM
cana-2210	205	27	and	and	CCONJ
cana-2210	205	28	|𝑤(𝜁)|	|𝑤(𝜁)|	PROPN
cana-2210	205	29	<	<	X
cana-2210	205	30	1	1	NUM
cana-2210	205	31	in	in	ADP
cana-2210	205	32	such	such	ADJ
cana-2210	205	33	that	that	SCONJ
cana-2210	205	34	1	1	NUM
cana-2210	205	35	+	+	SYM
cana-2210	205	36	1	1	NUM
cana-2210	205	37	𝑏	𝑏	NOUN
cana-2210	205	38	(	(	PUNCT
cana-2210	205	39	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	205	40	𝑚	𝑚	X
cana-2210	205	41	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	205	42	)	)	PUNCT
cana-2210	205	43	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	205	44	𝑛	𝑛	DET
cana-2210	205	45	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	205	46	)	)	PUNCT
cana-2210	205	47	−	−	PROPN
cana-2210	205	48	1	1	NUM
cana-2210	205	49	)	)	PUNCT
cana-2210	205	50	−	−	NOUN
cana-2210	205	51	𝜏	𝜏	PROPN
cana-2210	205	52	|	|	ADV
cana-2210	205	53	𝑅𝜌,µ	𝑅𝜌,µ	NOUN
cana-2210	205	54	𝑚	𝑚	X
cana-2210	205	55	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	205	56	)	)	PUNCT
cana-2210	205	57	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	205	58	𝑛	𝑛	DET
cana-2210	205	59	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	205	60	)	)	PUNCT
cana-2210	205	61	−	−	PROPN
cana-2210	205	62	1|	1|	NUM
cana-2210	205	63	≺	≺	NOUN
cana-2210	205	64	𝜙(𝑤(𝜁	𝜙(𝑤(𝜁	ADJ
cana-2210	205	65	)	)	PUNCT
cana-2210	205	66	)	)	PUNCT
cana-2210	205	67	.	.	PUNCT
cana-2210	206	1	define	define	VERB
cana-2210	206	2	𝑃(𝜁	𝑃(𝜁	X
cana-2210	206	3	)	)	PUNCT
cana-2210	206	4	by	by	ADP
cana-2210	206	5	𝑃(𝜁	𝑃(𝜁	X
cana-2210	206	6	)	)	PUNCT
cana-2210	206	7	=	=	SYM
cana-2210	206	8	1+𝑤(𝜁	1+𝑤(𝜁	X
cana-2210	206	9	)	)	PUNCT
cana-2210	206	10	1−𝑤(𝜁	1−𝑤(𝜁	NUM
cana-2210	206	11	)	)	PUNCT
cana-2210	206	12	=	=	SYM
cana-2210	207	1	1	1	NUM
cana-2210	207	2	+	+	NUM
cana-2210	207	3	𝑐1𝜁	𝑐1𝜁	X
cana-2210	207	4	+	+	CCONJ
cana-2210	207	5	𝑐2𝜁2	𝑐2𝜁2	NOUN
cana-2210	207	6	+	+	CCONJ
cana-2210	207	7	𝑐3𝜁3	𝑐3𝜁3	X
cana-2210	207	8	+	+	X
cana-2210	207	9	⋯	⋯	NOUN
cana-2210	207	10	since	since	SCONJ
cana-2210	207	11	𝑤(𝜁	𝑤(𝜁	NUM
cana-2210	207	12	)	)	PUNCT
cana-2210	207	13	is	be	AUX
cana-2210	207	14	a	a	DET
cana-2210	207	15	schwarz	schwarz	PROPN
cana-2210	207	16	function	function	NOUN
cana-2210	207	17	,	,	PUNCT
cana-2210	207	18	it	it	PRON
cana-2210	207	19	is	be	AUX
cana-2210	207	20	clear	clear	ADJ
cana-2210	207	21	that	that	SCONJ
cana-2210	207	22	𝑅𝑒𝑃(𝜁	𝑅𝑒𝑃(𝜁	NUM
cana-2210	207	23	)	)	PUNCT
cana-2210	207	24	>	>	X
cana-2210	207	25	0	0	NUM
cana-2210	207	26	and	and	CCONJ
cana-2210	207	27	𝑃(0	𝑃(0	NUM
cana-2210	207	28	)	)	PUNCT
cana-2210	207	29	=	=	SYM
cana-2210	207	30	1	1	X
cana-2210	207	31	.	.	X
cana-2210	208	1	∴	∴	PROPN
cana-2210	208	2	𝜙(𝜁	𝜙(𝜁	PROPN
cana-2210	208	3	)	)	PUNCT
cana-2210	209	1	=	=	SYM
cana-2210	209	2	𝜙	𝜙	PROPN
cana-2210	209	3	(	(	PUNCT
cana-2210	209	4	𝑃(𝜁)−1	𝑃(𝜁)−1	PROPN
cana-2210	209	5	𝑃(𝜁)+1	𝑃(𝜁)+1	NOUN
cana-2210	209	6	)	)	PUNCT
cana-2210	209	7	=	=	SYM
cana-2210	210	1	1	1	NUM
cana-2210	210	2	+	+	CCONJ
cana-2210	210	3	𝐵1𝑐1	𝐵1𝑐1	ADJ
cana-2210	210	4	2	2	NUM
cana-2210	210	5	𝜁	𝜁	NOUN
cana-2210	210	6	+	+	X
cana-2210	210	7	[	[	PUNCT
cana-2210	210	8	𝐵1	𝐵1	NOUN
cana-2210	210	9	2	2	NUM
cana-2210	210	10	(	(	PUNCT
cana-2210	210	11	𝑐2	𝑐2	NOUN
cana-2210	210	12	−	−	NOUN
cana-2210	210	13	𝑐1	𝑐1	NOUN
cana-2210	210	14	2	2	NUM
cana-2210	210	15	2	2	NUM
cana-2210	210	16	)	)	PUNCT
cana-2210	210	17	+	+	CCONJ
cana-2210	210	18	𝐵2𝑐1	𝐵2𝑐1	ADJ
cana-2210	210	19	2	2	NUM
cana-2210	210	20	4	4	NUM
cana-2210	210	21	]	]	PUNCT
cana-2210	210	22	𝜁2	𝜁2	NOUN
cana-2210	210	23	+	+	PROPN
cana-2210	210	24	.	.	PUNCT
cana-2210	210	25	...	...	PUNCT
cana-2210	211	1	now	now	ADV
cana-2210	211	2	,	,	PUNCT
cana-2210	211	3	1	1	NUM
cana-2210	211	4	+	+	SYM
cana-2210	211	5	1	1	NUM
cana-2210	211	6	𝑏	𝑏	NOUN
cana-2210	211	7	(	(	PUNCT
cana-2210	211	8	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	211	9	𝑚	𝑚	X
cana-2210	211	10	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	211	11	)	)	PUNCT
cana-2210	211	12	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	211	13	𝑛	𝑛	DET
cana-2210	211	14	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	211	15	)	)	PUNCT
cana-2210	211	16	−	−	PROPN
cana-2210	211	17	1	1	NUM
cana-2210	211	18	)	)	PUNCT
cana-2210	211	19	−	−	NOUN
cana-2210	211	20	𝜏	𝜏	PROPN
cana-2210	211	21	|	|	ADV
cana-2210	211	22	𝑅𝜌,µ	𝑅𝜌,µ	NOUN
cana-2210	211	23	𝑚	𝑚	X
cana-2210	211	24	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	211	25	)	)	PUNCT
cana-2210	211	26	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	211	27	𝑛	𝑛	DET
cana-2210	211	28	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	211	29	)	)	PUNCT
cana-2210	211	30	−	−	PROPN
cana-2210	211	31	1|	1|	NUM
cana-2210	212	1	=	=	SYM
cana-2210	212	2	1	1	NUM
cana-2210	212	3	+	+	CCONJ
cana-2210	212	4	𝐵1𝑐1	𝐵1𝑐1	ADJ
cana-2210	212	5	2	2	NUM
cana-2210	212	6	𝜁	𝜁	NOUN
cana-2210	212	7	+	+	X
cana-2210	212	8	[	[	PUNCT
cana-2210	212	9	𝐵1	𝐵1	NOUN
cana-2210	212	10	2	2	NUM
cana-2210	212	11	(	(	PUNCT
cana-2210	212	12	𝑐2	𝑐2	NOUN
cana-2210	212	13	−	−	NOUN
cana-2210	212	14	𝑐1	𝑐1	NOUN
cana-2210	212	15	2	2	NUM
cana-2210	212	16	2	2	NUM
cana-2210	212	17	)	)	PUNCT
cana-2210	213	1	+	+	CCONJ
cana-2210	213	2	𝐵2𝑐1	𝐵2𝑐1	ADJ
cana-2210	213	3	2	2	NUM
cana-2210	213	4	4	4	NUM
cana-2210	213	5	]	]	PUNCT
cana-2210	213	6	𝜁2	𝜁2	NOUN
cana-2210	213	7	+	+	CCONJ
cana-2210	213	8	⋯	⋯	PROPN
cana-2210	213	9	∴	∴	PROPN
cana-2210	213	10	𝑎2	𝑎2	NOUN
cana-2210	213	11	=	=	SYM
cana-2210	213	12	𝑏𝐵1𝑐1	𝑏𝐵1𝑐1	NOUN
cana-2210	213	13	2[𝑌1	2[𝑌1	NUM
cana-2210	213	14	−	−	NOUN
cana-2210	213	15	𝑏𝜏|𝑌1|	𝑏𝜏|𝑌1|	PROPN
cana-2210	213	16	]	]	X
cana-2210	213	17	and	and	CCONJ
cana-2210	213	18	𝑎3	𝑎3	PROPN
cana-2210	213	19	=	=	SYM
cana-2210	213	20	𝑏𝐵1𝑐2	𝑏𝐵1𝑐2	PROPN
cana-2210	213	21	2[𝑌2	2[𝑌2	PROPN
cana-2210	213	22	−	−	NOUN
cana-2210	213	23	𝑏𝜏|𝑌2|	𝑏𝜏|𝑌2|	ADP
cana-2210	213	24	]	]	X
cana-2210	213	25	+	+	CCONJ
cana-2210	213	26	𝑏𝐵1𝑐1	𝑏𝐵1𝑐1	NOUN
cana-2210	213	27	2	2	NUM
cana-2210	213	28	4[𝑌2	4[𝑌2	NUM
cana-2210	213	29	−	−	NOUN
cana-2210	213	30	𝑏𝜏|𝑌2|	𝑏𝜏|𝑌2|	ADP
cana-2210	213	31	]	]	PUNCT
cana-2210	213	32	[	[	PUNCT
cana-2210	213	33	[	[	X
cana-2210	213	34	𝑌1	𝑌1	NOUN
cana-2210	213	35	−	−	PROPN
cana-2210	214	1	𝑏𝜏|𝑌1|]𝑏𝐵1	𝑏𝜏|𝑌1|]𝑏𝐵1	PROPN
cana-2210	215	1	[	[	X
cana-2210	215	2	𝑌1	𝑌1	NOUN
cana-2210	215	3	−	−	PROPN
cana-2210	215	4	𝑏𝜏|𝑌1|]2	𝑏𝜏|𝑌1|]2	NOUN
cana-2210	215	5	−	−	PROPN
cana-2210	216	1	(	(	PUNCT
cana-2210	216	2	1	1	NUM
cana-2210	216	3	−	−	PRON
cana-2210	216	4	𝐵2	𝐵2	NOUN
cana-2210	216	5	𝐵1	𝐵1	NOUN
cana-2210	216	6	)	)	PUNCT
cana-2210	216	7	]	]	PUNCT
cana-2210	217	1	∴	∴	PROPN
cana-2210	217	2	𝑎3	𝑎3	PROPN
cana-2210	217	3	−	−	PROPN
cana-2210	217	4	µ𝑎2	µ𝑎2	PROPN
cana-2210	217	5	2	2	NUM
cana-2210	217	6	=	=	SYM
cana-2210	217	7	𝑏𝐵1	𝑏𝐵1	PROPN
cana-2210	217	8	2[𝑌2	2[𝑌2	PROPN
cana-2210	217	9	−	−	NOUN
cana-2210	217	10	𝑏𝜏|𝑌2|	𝑏𝜏|𝑌2|	ADP
cana-2210	217	11	]	]	PUNCT
cana-2210	217	12	{	{	PUNCT
cana-2210	217	13	𝑐2	𝑐2	NOUN
cana-2210	217	14	−	−	NOUN
cana-2210	217	15	𝑣𝑐1	𝑣𝑐1	ADJ
cana-2210	217	16	2	2	NUM
cana-2210	217	17	}	}	PUNCT
cana-2210	217	18	,	,	PUNCT
cana-2210	217	19	where	where	SCONJ
cana-2210	217	20	𝑣	𝑣	ADP
cana-2210	217	21	=	=	SYM
cana-2210	217	22	1	1	NUM
cana-2210	217	23	2	2	NUM
cana-2210	217	24	(	(	PUNCT
cana-2210	217	25	1	1	NUM
cana-2210	217	26	−	−	PRON
cana-2210	217	27	𝐵2	𝐵2	NOUN
cana-2210	217	28	𝐵1	𝐵1	NOUN
cana-2210	217	29	+	+	CCONJ
cana-2210	217	30	𝜇𝑏𝐵1[𝑌2−𝑏𝜏|𝑌2|	𝜇𝑏𝐵1[𝑌2−𝑏𝜏|𝑌2|	NOUN
cana-2210	217	31	]	]	X
cana-2210	218	1	[	[	X
cana-2210	218	2	𝑌1−𝑏𝜏|𝑌1|]2	𝑌1−𝑏𝜏|𝑌1|]2	X
cana-2210	218	3	−	−	PROPN
cana-2210	218	4	𝑏𝐵1[𝑌3−𝑏𝜏|𝑌3|	𝑏𝐵1[𝑌3−𝑏𝜏|𝑌3|	PROPN
cana-2210	218	5	]	]	X
cana-2210	219	1	[	[	X
cana-2210	219	2	𝑌1−𝑏𝜏|𝑌1|]2	𝑌1−𝑏𝜏|𝑌1|]2	NOUN
cana-2210	219	3	)	)	PUNCT
cana-2210	219	4	.	.	PUNCT
cana-2210	220	1	hence	hence	ADV
cana-2210	220	2	,	,	PUNCT
cana-2210	220	3	|𝑎3	|𝑎3	VERB
cana-2210	220	4	−	−	PROPN
cana-2210	220	5	µ𝑎2	µ𝑎2	PROPN
cana-2210	220	6	2|	2|	NOUN
cana-2210	220	7	≤	≤	ADJ
cana-2210	220	8	𝐵1|𝑏	𝐵1|𝑏	NOUN
cana-2210	220	9	|	|	ADV
cana-2210	220	10	𝑌2	𝑌2	NOUN
cana-2210	220	11	−	−	PROPN
cana-2210	221	1	𝑏𝜏|𝑌2|	𝑏𝜏|𝑌2|	ADP
cana-2210	221	2	max	max	PROPN
cana-2210	221	3	{	{	PUNCT
cana-2210	221	4	1	1	NUM
cana-2210	221	5	,	,	PUNCT
cana-2210	221	6	|	|	ADV
cana-2210	221	7	𝐵2	𝐵2	NOUN
cana-2210	221	8	𝐵1	𝐵1	NOUN
cana-2210	222	1	+	+	CCONJ
cana-2210	222	2	[	[	PUNCT
cana-2210	222	3	[	[	X
cana-2210	222	4	𝑌3	𝑌3	X
cana-2210	222	5	−	−	PROPN
cana-2210	222	6	𝑏𝜏|𝑌3|	𝑏𝜏|𝑌3|	PROPN
cana-2210	222	7	]	]	PUNCT
cana-2210	222	8	−	−	PROPN
cana-2210	222	9	µ[[𝑌2	µ[[𝑌2	X
cana-2210	222	10	]	]	X
cana-2210	222	11	−	−	PROPN
cana-2210	222	12	𝑏𝜏|𝑌2|	𝑏𝜏|𝑌2|	ADP
cana-2210	222	13	]	]	X
cana-2210	223	1	[	[	X
cana-2210	223	2	𝑌1	𝑌1	NOUN
cana-2210	223	3	−	−	PROPN
cana-2210	223	4	𝑏𝜏[𝑌1]]2	𝑏𝜏[𝑌1]]2	NOUN
cana-2210	223	5	]	]	PUNCT
cana-2210	223	6	𝑏𝐵1|	𝑏𝐵1|	VERB
cana-2210	223	7	}	}	PUNCT
cana-2210	223	8	.	.	PUNCT
cana-2210	224	1	therefore	therefore	ADV
cana-2210	224	2	,	,	PUNCT
cana-2210	224	3	the	the	DET
cana-2210	224	4	result	result	NOUN
cana-2210	224	5	(	(	PUNCT
cana-2210	224	6	22	22	NUM
cana-2210	224	7	)	)	PUNCT
cana-2210	224	8	is	be	AUX
cana-2210	224	9	sharp	sharp	ADJ
cana-2210	224	10	for	for	ADP
cana-2210	224	11	the	the	DET
cana-2210	224	12	function	function	NOUN
cana-2210	224	13	defined	define	VERB
cana-2210	224	14	by	by	ADP
cana-2210	224	15	1	1	NUM
cana-2210	224	16	+	+	SYM
cana-2210	224	17	1	1	NUM
cana-2210	224	18	𝑏	𝑏	NOUN
cana-2210	224	19	(	(	PUNCT
cana-2210	224	20	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	224	21	𝑚	𝑚	X
cana-2210	224	22	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	224	23	)	)	PUNCT
cana-2210	224	24	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	224	25	𝑛	𝑛	DET
cana-2210	224	26	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	224	27	)	)	PUNCT
cana-2210	224	28	−	−	PROPN
cana-2210	224	29	1	1	NUM
cana-2210	224	30	)	)	PUNCT
cana-2210	224	31	−	−	NOUN
cana-2210	224	32	𝜏	𝜏	PROPN
cana-2210	224	33	|	|	ADV
cana-2210	224	34	𝑅𝜌,µ	𝑅𝜌,µ	NOUN
cana-2210	224	35	𝑚	𝑚	X
cana-2210	224	36	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	224	37	)	)	PUNCT
cana-2210	224	38	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	224	39	𝑛	𝑛	DET
cana-2210	224	40	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	224	41	)	)	PUNCT
cana-2210	224	42	−	−	PROPN
cana-2210	224	43	1|	1|	NUM
cana-2210	224	44	=	=	SYM
cana-2210	224	45	𝜙(𝜁2	𝜙(𝜁2	NOUN
cana-2210	224	46	)	)	PUNCT
cana-2210	224	47	and	and	CCONJ
cana-2210	224	48	1	1	NUM
cana-2210	224	49	+	+	SYM
cana-2210	224	50	1	1	NUM
cana-2210	224	51	𝑏	𝑏	NOUN
cana-2210	224	52	(	(	PUNCT
cana-2210	224	53	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	224	54	𝑚	𝑚	X
cana-2210	224	55	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	224	56	)	)	PUNCT
cana-2210	224	57	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	224	58	𝑛	𝑛	DET
cana-2210	224	59	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	224	60	)	)	PUNCT
cana-2210	224	61	−	−	PROPN
cana-2210	224	62	1	1	NUM
cana-2210	224	63	)	)	PUNCT
cana-2210	224	64	−	−	NOUN
cana-2210	224	65	𝜏	𝜏	PROPN
cana-2210	224	66	|	|	ADV
cana-2210	224	67	𝑅𝜌,µ	𝑅𝜌,µ	NOUN
cana-2210	224	68	𝑚	𝑚	X
cana-2210	224	69	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	224	70	)	)	PUNCT
cana-2210	224	71	𝑅𝜌,µ	𝑅𝜌,µ	PROPN
cana-2210	224	72	𝑛	𝑛	DET
cana-2210	224	73	𝑓(𝜁	𝑓(𝜁	NOUN
cana-2210	224	74	)	)	PUNCT
cana-2210	224	75	−	−	PROPN
cana-2210	224	76	1|	1|	NUM
cana-2210	224	77	=	=	SYM
cana-2210	224	78	𝜙(𝜁	𝜙(𝜁	PROPN
cana-2210	224	79	)	)	PUNCT
cana-2210	224	80	.	.	PUNCT
cana-2210	225	1	communications	communication	NOUN
cana-2210	225	2	on	on	ADP
cana-2210	225	3	applied	apply	VERB
cana-2210	225	4	nonlinear	nonlinear	ADJ
cana-2210	225	5	analysis	analysis	NOUN
cana-2210	225	6	issn	issn	NOUN
cana-2210	225	7	:	:	PUNCT
cana-2210	225	8	1074	1074	NUM
cana-2210	225	9	-	-	PUNCT
cana-2210	225	10	133x	133x	NUM
cana-2210	225	11	vol	vol	NOUN
cana-2210	225	12	32	32	NUM
cana-2210	225	13	no	no	NOUN
cana-2210	225	14	.	.	PUNCT
cana-2210	226	1	1s	1s	NUM
cana-2210	226	2	(	(	PUNCT
cana-2210	226	3	2025	2025	NUM
cana-2210	226	4	)	)	PUNCT
cana-2210	226	5	470	470	NUM
cana-2210	226	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2210	226	7	4	4	NUM
cana-2210	226	8	.	.	PUNCT
cana-2210	226	9	conclusion	conclusion	NOUN
cana-2210	226	10	this	this	DET
cana-2210	226	11	present	present	ADJ
cana-2210	226	12	work	work	NOUN
cana-2210	226	13	,	,	PUNCT
cana-2210	226	14	we	we	PRON
cana-2210	226	15	got	get	VERB
cana-2210	226	16	some	some	DET
cana-2210	226	17	results	result	NOUN
cana-2210	226	18	that	that	PRON
cana-2210	226	19	were	be	AUX
cana-2210	226	20	obtained	obtain	VERB
cana-2210	226	21	from	from	ADP
cana-2210	226	22	the	the	DET
cana-2210	226	23	new	new	ADJ
cana-2210	226	24	sub	sub	NOUN
cana-2210	226	25	class	class	NOUN
cana-2210	226	26	of	of	ADP
cana-2210	226	27	normalized	normalize	VERB
cana-2210	226	28	analytic	analytic	ADJ
cana-2210	226	29	univalent	univalent	ADJ
cana-2210	226	30	function	function	NOUN
cana-2210	226	31	.	.	PUNCT
cana-2210	227	1	we	we	PRON
cana-2210	227	2	also	also	ADV
cana-2210	227	3	acquired	acquire	VERB
cana-2210	227	4	and	and	CCONJ
cana-2210	227	5	examined	examine	VERB
cana-2210	227	6	a	a	DET
cana-2210	227	7	few	few	ADJ
cana-2210	227	8	fundamental	fundamental	ADJ
cana-2210	227	9	characteristics	characteristic	NOUN
cana-2210	227	10	of	of	ADP
cana-2210	227	11	univalent	univalent	ADJ
cana-2210	227	12	functions	function	NOUN
cana-2210	227	13	,	,	PUNCT
cana-2210	227	14	comparing	compare	VERB
cana-2210	227	15	them	they	PRON
cana-2210	227	16	to	to	ADP
cana-2210	227	17	earlier	early	ADJ
cana-2210	227	18	findings	finding	NOUN
cana-2210	227	19	.	.	PUNCT
cana-2210	228	1	also	also	ADV
cana-2210	228	2	,	,	PUNCT
cana-2210	228	3	sharp	sharp	ADJ
cana-2210	228	4	boundaries	boundary	NOUN
cana-2210	228	5	were	be	AUX
cana-2210	228	6	obtained	obtain	VERB
cana-2210	228	7	for	for	ADP
cana-2210	228	8	the	the	DET
cana-2210	228	9	subclass	subclass	NOUN
cana-2210	228	10	.	.	PUNCT
cana-2210	229	1	the	the	DET
cana-2210	229	2	researchers	researcher	NOUN
cana-2210	229	3	are	be	AUX
cana-2210	229	4	motivated	motivated	ADJ
cana-2210	229	5	to	to	PART
cana-2210	229	6	improve	improve	VERB
cana-2210	229	7	the	the	DET
cana-2210	229	8	findings	finding	NOUN
cana-2210	229	9	of	of	ADP
cana-2210	229	10	this	this	DET
cana-2210	229	11	subclass	subclass	NOUN
cana-2210	229	12	in	in	ADP
cana-2210	229	13	future	future	NOUN
cana-2210	229	14	by	by	ADP
cana-2210	229	15	using	use	VERB
cana-2210	229	16	biunivalent	biunivalent	NOUN
cana-2210	229	17	,	,	PUNCT
cana-2210	229	18	multivalent	multivalent	NOUN
cana-2210	229	19	,	,	PUNCT
cana-2210	229	20	q	q	NOUN
cana-2210	229	21	-	-	PUNCT
cana-2210	229	22	analoque	analoque	ADJ
cana-2210	229	23	,	,	PUNCT
cana-2210	229	24	and	and	CCONJ
cana-2210	229	25	meromorpihic	meromorpihic	ADJ
cana-2210	229	26	functions	function	NOUN
cana-2210	229	27	with	with	ADP
cana-2210	229	28	positive	positive	ADJ
cana-2210	229	29	and	and	CCONJ
cana-2210	229	30	negative	negative	ADJ
cana-2210	229	31	coefficients	coefficient	NOUN
cana-2210	229	32	.	.	PUNCT
cana-2210	230	1	acknowledgment	acknowledgment	NOUN
cana-2210	230	2	the	the	DET
cana-2210	230	3	authors	author	NOUN
cana-2210	230	4	sincerely	sincerely	ADV
cana-2210	230	5	thank	thank	VERB
cana-2210	230	6	the	the	DET
cana-2210	230	7	reviewers	reviewer	NOUN
cana-2210	230	8	for	for	ADP
cana-2210	230	9	their	their	PRON
cana-2210	230	10	helpful	helpful	ADJ
cana-2210	230	11	remarks	remark	NOUN
cana-2210	230	12	,	,	PUNCT
cana-2210	230	13	that	that	PRON
cana-2210	230	14	helped	help	VERB
cana-2210	230	15	in	in	ADP
cana-2210	230	16	the	the	DET
cana-2210	230	17	success	success	NOUN
cana-2210	230	18	of	of	ADP
cana-2210	230	19	this	this	DET
cana-2210	230	20	article	article	NOUN
cana-2210	230	21	.	.	PUNCT
cana-2210	231	1	references	reference	NOUN
cana-2210	231	2	[	[	X
cana-2210	231	3	1	1	NUM
cana-2210	231	4	]	]	X
cana-2210	231	5	al	al	PROPN
cana-2210	231	6	-	-	PUNCT
cana-2210	231	7	ameedee	ameedee	PROPN
cana-2210	231	8	,	,	PUNCT
cana-2210	231	9	sarah	sarah	PROPN
cana-2210	231	10	a.	a.	PROPN
cana-2210	231	11	al	al	PROPN
cana-2210	231	12	-	-	PUNCT
cana-2210	231	13	ameedee	ameedee	PROPN
cana-2210	231	14	,	,	PUNCT
cana-2210	231	15	al	al	PROPN
cana-2210	231	16	-	-	PUNCT
cana-2210	231	17	hakeem	hakeem	PROPN
cana-2210	231	18	,	,	PUNCT
cana-2210	231	19	mohammed	mohammed	PROPN
cana-2210	231	20	baqer	baqer	PROPN
cana-2210	231	21	hashim	hashim	PROPN
cana-2210	231	22	&	&	CCONJ
cana-2210	231	23	alghafil	alghafil	PROPN
cana-2210	231	24	,	,	PUNCT
cana-2210	231	25	ali	ali	PROPN
cana-2210	231	26	kadhim	kadhim	PROPN
cana-2210	231	27	hussein	hussein	PROPN
cana-2210	231	28	,	,	PUNCT
cana-2210	231	29	fekete	fekete	PROPN
cana-2210	231	30	-	-	PUNCT
cana-2210	231	31	szego	szego	NOUN
cana-2210	231	32	inequalities	inequality	NOUN
cana-2210	231	33	for	for	ADP
cana-2210	231	34	higher	high	ADJ
cana-2210	231	35	-	-	PUNCT
cana-2210	231	36	order	order	NOUN
cana-2210	231	37	derivatives	derivative	NOUN
cana-2210	231	38	of	of	ADP
cana-2210	231	39	multivalent	multivalent	ADJ
cana-2210	231	40	analytic	analytic	ADJ
cana-2210	231	41	function	function	NOUN
cana-2210	231	42	with	with	ADP
cana-2210	231	43	application	application	NOUN
cana-2210	231	44	to	to	ADP
cana-2210	231	45	stealth	stealth	ADJ
cana-2210	231	46	combat	combat	NOUN
cana-2210	231	47	aircraft	aircraft	NOUN
cana-2210	231	48	,	,	PUNCT
cana-2210	231	49	journal	journal	NOUN
cana-2210	231	50	of	of	ADP
cana-2210	231	51	interdisciplinary	interdisciplinary	ADJ
cana-2210	231	52	mathematics	mathematic	NOUN
cana-2210	231	53	,	,	PUNCT
cana-2210	231	54	(	(	PUNCT
cana-2210	231	55	2024	2024	NUM
cana-2210	231	56	)	)	PUNCT
cana-2210	231	57	,	,	PUNCT
cana-2210	231	58	1–7	1–7	X
cana-2210	231	59	.	.	PUNCT
cana-2210	232	1	[	[	X
cana-2210	232	2	2	2	NUM
cana-2210	232	3	]	]	X
cana-2210	232	4	al	al	PROPN
cana-2210	232	5	-	-	PUNCT
cana-2210	232	6	oboudi	oboudi	NOUN
cana-2210	232	7	f.m	f.m	PROPN
cana-2210	232	8	,	,	PUNCT
cana-2210	232	9	on	on	ADP
cana-2210	232	10	univalent	univalent	ADJ
cana-2210	232	11	functions	function	NOUN
cana-2210	232	12	defined	define	VERB
cana-2210	232	13	by	by	ADP
cana-2210	232	14	a	a	DET
cana-2210	232	15	generalized	generalize	VERB
cana-2210	232	16	salagean	salagean	ADJ
cana-2210	232	17	operator	operator	NOUN
cana-2210	232	18	,	,	PUNCT
cana-2210	232	19	international	international	ADJ
cana-2210	232	20	journal	journal	NOUN
cana-2210	232	21	of	of	ADP
cana-2210	232	22	mathematics	mathematics	PROPN
cana-2210	232	23	and	and	CCONJ
cana-2210	232	24	mathematical	mathematical	ADJ
cana-2210	232	25	sciences	science	NOUN
cana-2210	232	26	,	,	PUNCT
cana-2210	232	27	2004(27	2004(27	NUM
cana-2210	232	28	)	)	PUNCT
cana-2210	232	29	,	,	PUNCT
cana-2210	232	30	(	(	PUNCT
cana-2210	232	31	2004	2004	NUM
cana-2210	232	32	)	)	PUNCT
cana-2210	232	33	,	,	PUNCT
cana-2210	232	34	1429–1436	1429–1436	NUM
cana-2210	232	35	.	.	PUNCT
cana-2210	233	1	[	[	X
cana-2210	233	2	3	3	NUM
cana-2210	233	3	]	]	X
cana-2210	233	4	amourah	amourah	PROPN
cana-2210	233	5	,	,	PUNCT
cana-2210	233	6	a.	a.	NOUN
cana-2210	233	7	a.	a.	PROPN
cana-2210	233	8	,	,	PUNCT
cana-2210	233	9	and	and	CCONJ
cana-2210	233	10	feras	feras	PROPN
cana-2210	233	11	yousef	yousef	PROPN
cana-2210	233	12	,	,	PUNCT
cana-2210	233	13	some	some	DET
cana-2210	233	14	properties	property	NOUN
cana-2210	233	15	of	of	ADP
cana-2210	233	16	a	a	DET
cana-2210	233	17	class	class	NOUN
cana-2210	233	18	of	of	ADP
cana-2210	233	19	analytic	analytic	ADJ
cana-2210	233	20	functions	function	NOUN
cana-2210	233	21	involving	involve	VERB
cana-2210	233	22	a	a	DET
cana-2210	233	23	new	new	ADJ
cana-2210	233	24	generalized	generalize	VERB
cana-2210	233	25	differential	differential	NOUN
cana-2210	233	26	opera	opera	NOUN
cana-2210	233	27	tor	tor	NOUN
cana-2210	233	28	,	,	PUNCT
cana-2210	233	29	bol	bol	NOUN
cana-2210	233	30	.	.	PUNCT
cana-2210	234	1	soc	soc	PROPN
cana-2210	234	2	.	.	PUNCT
cana-2210	235	1	paran	paran	PROPN
cana-2210	235	2	.	.	PUNCT
cana-2210	236	1	mat	mat	PROPN
cana-2210	236	2	.	.	PROPN
cana-2210	236	3	,	,	PUNCT
cana-2210	236	4	38(6	38(6	NOUN
cana-2210	236	5	)	)	PUNCT
cana-2210	236	6	,	,	PUNCT
cana-2210	236	7	(	(	PUNCT
cana-2210	236	8	2020	2020	NUM
cana-2210	236	9	)	)	PUNCT
cana-2210	236	10	,	,	PUNCT
cana-2210	236	11	33–42	33–42	NUM
cana-2210	236	12	.	.	PUNCT
cana-2210	237	1	[	[	X
cana-2210	237	2	4	4	NUM
cana-2210	237	3	]	]	PUNCT
cana-2210	237	4	bieberbach	bieberbach	NOUN
cana-2210	237	5	,	,	PUNCT
cana-2210	237	6	uber	uber	ADJ
cana-2210	237	7	einige	einige	PROPN
cana-2210	237	8	extremal	extremal	ADJ
cana-2210	237	9	problem	problem	NOUN
cana-2210	237	10	in	in	ADP
cana-2210	237	11	gebiete	gebiete	ADJ
cana-2210	237	12	der	der	NOUN
cana-2210	237	13	kon	kon	PROPN
cana-2210	237	14	formenabbdildung	formenabbdildung	PROPN
cana-2210	237	15	,	,	PUNCT
cana-2210	237	16	math	math	NOUN
cana-2210	237	17	.	.	PUNCT
cana-2210	238	1	ann	ann	PROPN
cana-2210	238	2	.	.	PROPN
cana-2210	238	3	,	,	PUNCT
cana-2210	238	4	77	77	NUM
cana-2210	238	5	,	,	PUNCT
cana-2210	238	6	(	(	PUNCT
cana-2210	238	7	1916	1916	NUM
cana-2210	238	8	)	)	PUNCT
cana-2210	238	9	,	,	PUNCT
cana-2210	238	10	153	153	NUM
cana-2210	238	11	–	–	PUNCT
cana-2210	238	12	172	172	NUM
cana-2210	238	13	.	.	PUNCT
cana-2210	239	1	[	[	X
cana-2210	239	2	5	5	NUM
cana-2210	239	3	]	]	PUNCT
cana-2210	239	4	choi	choi	PROPN
cana-2210	239	5	j.h	j.h	PROPN
cana-2210	239	6	,	,	PUNCT
cana-2210	239	7	y.ch.kim	y.ch.kim	PROPN
cana-2210	239	8	,	,	PUNCT
cana-2210	239	9	t.sugawa	t.sugawa	PROPN
cana-2210	239	10	,	,	PUNCT
cana-2210	239	11	a	a	DET
cana-2210	239	12	general	general	ADJ
cana-2210	239	13	approach	approach	NOUN
cana-2210	239	14	to	to	ADP
cana-2210	239	15	the	the	DET
cana-2210	239	16	fekete	fekete	PROPN
cana-2210	239	17	-	-	PUNCT
cana-2210	239	18	szego	szego	NOUN
cana-2210	239	19	problem	problem	NOUN
cana-2210	239	20	,	,	PUNCT
cana-2210	239	21	j.	j.	PROPN
cana-2210	239	22	math	math	PROPN
cana-2210	239	23	.	.	PUNCT
cana-2210	239	24	soc	soc	PROPN
cana-2210	239	25	.	.	PUNCT
cana-2210	240	1	japon	japon	PROPN
cana-2210	240	2	.	.	PROPN
cana-2210	240	3	,	,	PUNCT
cana-2210	240	4	3(59	3(59	NUM
cana-2210	240	5	)	)	PUNCT
cana-2210	240	6	,	,	PUNCT
cana-2210	240	7	(	(	PUNCT
cana-2210	240	8	2007	2007	NUM
cana-2210	240	9	)	)	PUNCT
cana-2210	240	10	,	,	PUNCT
cana-2210	240	11	707	707	NUM
cana-2210	240	12	-	-	SYM
cana-2210	240	13	727	727	NUM
cana-2210	240	14	.	.	PUNCT
cana-2210	241	1	[	[	X
cana-2210	241	2	6	6	NUM
cana-2210	241	3	]	]	SYM
cana-2210	241	4	de	de	X
cana-2210	241	5	branges	brange	NOUN
cana-2210	241	6	l	l	NOUN
cana-2210	241	7	,	,	PUNCT
cana-2210	241	8	a	a	DET
cana-2210	241	9	proof	proof	NOUN
cana-2210	241	10	of	of	ADP
cana-2210	241	11	the	the	DET
cana-2210	241	12	bieberbach	bieberbach	NOUN
cana-2210	241	13	conjecture	conjecture	NOUN
cana-2210	241	14	,	,	PUNCT
cana-2210	241	15	acta	acta	PROPN
cana-2210	241	16	math	math	PROPN
cana-2210	241	17	.	.	PUNCT
cana-2210	241	18	,	,	PUNCT
cana-2210	241	19	154	154	NUM
cana-2210	241	20	,	,	PUNCT
cana-2210	241	21	(	(	PUNCT
cana-2210	241	22	1984	1984	NUM
cana-2210	241	23	)	)	PUNCT
cana-2210	241	24	,	,	PUNCT
cana-2210	241	25	137–152	137–152	NUM
cana-2210	241	26	.	.	PUNCT
cana-2210	242	1	[	[	X
cana-2210	242	2	7	7	X
cana-2210	242	3	]	]	X
cana-2210	242	4	fekete	fekete	PROPN
cana-2210	242	5	m	m	PROPN
cana-2210	242	6	,	,	PUNCT
cana-2210	242	7	g.szego	g.szego	PROPN
cana-2210	242	8	,	,	PUNCT
cana-2210	242	9	eine	eine	PROPN
cana-2210	242	10	bemerkung	bemerkung	PROPN
cana-2210	242	11	uber	uber	PROPN
cana-2210	242	12	ungrade	ungrade	PROPN
cana-2210	242	13	schlichte	schlichte	VERB
cana-2210	242	14	functionen	functionen	PROPN
cana-2210	242	15	,	,	PUNCT
cana-2210	242	16	j.lond	j.lond	NOUN
cana-2210	242	17	.	.	PUNCT
cana-2210	242	18	math	math	NOUN
cana-2210	242	19	.	.	PUNCT
cana-2210	243	1	soc	soc	PROPN
cana-2210	243	2	.	.	PUNCT
cana-2210	243	3	,	,	PUNCT
cana-2210	243	4	8	8	NUM
cana-2210	243	5	,	,	PUNCT
cana-2210	243	6	(	(	PUNCT
cana-2210	243	7	1933	1933	NUM
cana-2210	243	8	)	)	PUNCT
cana-2210	243	9	,	,	PUNCT
cana-2210	243	10	85–89	85–89	NUM
cana-2210	243	11	.	.	PUNCT
cana-2210	244	1	[	[	X
cana-2210	244	2	8	8	NUM
cana-2210	244	3	]	]	X
cana-2210	244	4	grenander	grenander	NOUN
cana-2210	244	5	u	u	PROPN
cana-2210	244	6	,	,	PUNCT
cana-2210	244	7	g.	g.	PROPN
cana-2210	244	8	szego	szego	PROPN
cana-2210	244	9	,	,	PUNCT
cana-2210	244	10	toeplitz	toeplitz	NOUN
cana-2210	244	11	forms	form	NOUN
cana-2210	244	12	and	and	CCONJ
cana-2210	244	13	their	their	PRON
cana-2210	244	14	applications	application	NOUN
cana-2210	244	15	,	,	PUNCT
cana-2210	244	16	univ	univ	PROPN
cana-2210	244	17	.	.	PROPN
cana-2210	244	18	of	of	ADP
cana-2210	244	19	california	california	PROPN
cana-2210	244	20	press	press	PROPN
cana-2210	244	21	,	,	PUNCT
cana-2210	244	22	berkeley	berkeley	PROPN
cana-2210	244	23	,	,	PUNCT
cana-2210	244	24	los	los	PROPN
cana-2210	244	25	angeles	angeles	PROPN
cana-2210	244	26	,	,	PUNCT
cana-2210	244	27	(	(	PUNCT
cana-2210	244	28	1958	1958	NUM
cana-2210	244	29	)	)	PUNCT
cana-2210	244	30	.	.	PUNCT
cana-2210	245	1	[	[	X
cana-2210	245	2	9	9	NUM
cana-2210	245	3	]	]	SYM
cana-2210	245	4	hadi	hadi	PROPN
cana-2210	245	5	,	,	PUNCT
cana-2210	245	6	sarem	sarem	PROPN
cana-2210	245	7	h.	h.	PROPN
cana-2210	245	8	,	,	PUNCT
cana-2210	245	9	maslina	maslina	NOUN
cana-2210	245	10	darus	darus	NOUN
cana-2210	245	11	,	,	PUNCT
cana-2210	245	12	and	and	CCONJ
cana-2210	245	13	jung	jung	PROPN
cana-2210	245	14	rye	rye	PROPN
cana-2210	245	15	lee	lee	PROPN
cana-2210	245	16	.	.	PROPN
cana-2210	245	17	,	,	PUNCT
cana-2210	245	18	some	some	DET
cana-2210	245	19	geo	geo	PROPN
cana-2210	245	20	metric	metric	ADJ
cana-2210	245	21	properties	property	NOUN
cana-2210	245	22	of	of	ADP
cana-2210	245	23	multivalent	multivalent	NOUN
cana-2210	245	24	functions	function	NOUN
cana-2210	245	25	associated	associate	VERB
cana-2210	245	26	with	with	ADP
cana-2210	245	27	a	a	DET
cana-2210	245	28	new	new	ADJ
cana-2210	245	29	generalized	generalized	ADJ
cana-2210	245	30	q	q	ADJ
cana-2210	245	31	-	-	ADJ
cana-2210	245	32	mittag	mittag	ADJ
cana-2210	245	33	-	-	PUNCT
cana-2210	245	34	leffler	leffler	NOUN
cana-2210	245	35	function	function	NOUN
cana-2210	245	36	,	,	PUNCT
cana-2210	245	37	aims	aim	VERB
cana-2210	245	38	mathematics	mathematics	NOUN
cana-2210	245	39	7.7	7.7	NUM
cana-2210	245	40	,	,	PUNCT
cana-2210	245	41	(	(	PUNCT
cana-2210	245	42	2022	2022	NUM
cana-2210	245	43	)	)	PUNCT
cana-2210	245	44	,	,	PUNCT
cana-2210	245	45	11772–11783	11772–11783	NUM
cana-2210	245	46	.	.	PUNCT
cana-2210	246	1	[	[	X
cana-2210	246	2	10	10	NUM
cana-2210	246	3	]	]	X
cana-2210	246	4	kadioglu	kadioglu	PROPN
cana-2210	246	5	e	e	PROPN
cana-2210	246	6	,	,	PUNCT
cana-2210	246	7	on	on	ADP
cana-2210	246	8	subclass	subclass	NOUN
cana-2210	246	9	of	of	ADP
cana-2210	246	10	univalent	univalent	ADJ
cana-2210	246	11	functions	function	NOUN
cana-2210	246	12	with	with	ADP
cana-2210	246	13	negative	negative	ADJ
cana-2210	246	14	co	co	NOUN
cana-2210	246	15	efficients	efficients	PROPN
cana-2210	246	16	,	,	PUNCT
cana-2210	246	17	appl	appl	PROPN
cana-2210	246	18	.	.	PROPN
cana-2210	246	19	math	math	PROPN
cana-2210	246	20	.	.	PUNCT
cana-2210	247	1	computation	computation	NOUN
cana-2210	247	2	,	,	PUNCT
cana-2210	247	3	146(2	146(2	NUM
cana-2210	247	4	-	-	SYM
cana-2210	247	5	3	3	NUM
cana-2210	247	6	)	)	PUNCT
cana-2210	247	7	,	,	PUNCT
cana-2210	247	8	(	(	PUNCT
cana-2210	247	9	2003	2003	NUM
cana-2210	247	10	)	)	PUNCT
cana-2210	247	11	,	,	PUNCT
cana-2210	247	12	351–358	351–358	NUM
cana-2210	247	13	.	.	PUNCT
cana-2210	248	1	[	[	X
cana-2210	248	2	11	11	NUM
cana-2210	248	3	]	]	PUNCT
cana-2210	248	4	koebe	koebe	NOUN
cana-2210	248	5	p	p	NOUN
cana-2210	248	6	,	,	PUNCT
cana-2210	248	7	uber	uber	ADJ
cana-2210	248	8	die	die	VERB
cana-2210	248	9	uniformisierung	uniformisierung	PROPN
cana-2210	248	10	beliebiger	beliebiger	PROPN
cana-2210	248	11	analytis	analytis	PROPN
cana-2210	248	12	cherkueven	cherkueven	PROPN
cana-2210	248	13	,	,	PUNCT
cana-2210	248	14	nachr.koniglichen.ges	nachr.koniglichen.ge	NOUN
cana-2210	248	15	.wissenschaft	.wissenschaft	VERB
cana-2210	248	16	.	.	PUNCT
cana-2210	249	1	gottinger	gottinger	ADP
cana-2210	249	2	math	math	PROPN
cana-2210	249	3	phys.klasse	phys.klasse	PROPN
cana-2210	249	4	,	,	PUNCT
cana-2210	249	5	(	(	PUNCT
cana-2210	249	6	1907	1907	NUM
cana-2210	249	7	)	)	PUNCT
cana-2210	249	8	,	,	PUNCT
cana-2210	249	9	191–210	191–210	NUM
cana-2210	249	10	.	.	PUNCT
cana-2210	250	1	[	[	X
cana-2210	250	2	12	12	NUM
cana-2210	250	3	]	]	PUNCT
cana-2210	250	4	loewner	loewner	NOUN
cana-2210	250	5	.	.	PUNCT
cana-2210	251	1	c.	c.	PROPN
cana-2210	251	2	and	and	CCONJ
cana-2210	251	3	netanyahu.e	netanyahu.e	PROPN
cana-2210	251	4	.	.	PROPN
cana-2210	251	5	,	,	PUNCT
cana-2210	251	6	untersuchungen	untersuchungen	PROPN
cana-2210	251	7	uber	uber	PROPN
cana-2210	251	8	schlichte	schlichte	VERB
cana-2210	251	9	konforme	konforme	PROPN
cana-2210	251	10	abbildungen	abbildungen	PROPN
cana-2210	251	11	des	des	PROPN
cana-2210	251	12	einheitskreises	einheitskreise	NOUN
cana-2210	251	13	,	,	PUNCT
cana-2210	251	14	i.	i.	PROPN
cana-2210	251	15	math	math	PROPN
cana-2210	251	16	.	.	PUNCT
cana-2210	252	1	ann	ann	PROPN
cana-2210	252	2	.	.	PROPN
cana-2210	252	3	,	,	PUNCT
cana-2210	252	4	89	89	NUM
cana-2210	252	5	,	,	PUNCT
cana-2210	252	6	(	(	PUNCT
cana-2210	252	7	1923	1923	NUM
cana-2210	252	8	)	)	PUNCT
cana-2210	252	9	,	,	PUNCT
cana-2210	252	10	103–121	103–121	NUM
cana-2210	252	11	.	.	PUNCT
cana-2210	253	1	[	[	X
cana-2210	253	2	13	13	NUM
cana-2210	253	3	]	]	X
cana-2210	253	4	littlewood	littlewood	PROPN
cana-2210	253	5	j.e	j.e	PROPN
cana-2210	253	6	,	,	PUNCT
cana-2210	253	7	on	on	ADP
cana-2210	253	8	inequalities	inequality	NOUN
cana-2210	253	9	in	in	ADP
cana-2210	253	10	the	the	DET
cana-2210	253	11	theory	theory	NOUN
cana-2210	253	12	of	of	ADP
cana-2210	253	13	functions	function	NOUN
cana-2210	253	14	,	,	PUNCT
cana-2210	253	15	pro	pro	ADJ
cana-2210	253	16	ceedings	ceeding	NOUN
cana-2210	253	17	of	of	ADP
cana-2210	253	18	society	society	NOUN
cana-2210	253	19	,	,	PUNCT
cana-2210	253	20	bf23(1	bf23(1	NOUN
cana-2210	253	21	)	)	PUNCT
cana-2210	253	22	,	,	PUNCT
cana-2210	253	23	(	(	PUNCT
cana-2210	253	24	1925	1925	NUM
cana-2210	253	25	)	)	PUNCT
cana-2210	253	26	,	,	PUNCT
cana-2210	253	27	481–519	481–519	NUM
cana-2210	253	28	.	.	PUNCT
cana-2210	254	1	[	[	X
cana-2210	254	2	14	14	NUM
cana-2210	254	3	]	]	X
cana-2210	254	4	ma	ma	PROPN
cana-2210	254	5	w.	w.	PROPN
cana-2210	254	6	and	and	CCONJ
cana-2210	254	7	d.	d.	PROPN
cana-2210	254	8	minda	minda	PROPN
cana-2210	254	9	,	,	PUNCT
cana-2210	254	10	a	a	DET
cana-2210	254	11	unified	unified	ADJ
cana-2210	254	12	treatment	treatment	NOUN
cana-2210	254	13	of	of	ADP
cana-2210	254	14	some	some	DET
cana-2210	254	15	special	special	ADJ
cana-2210	254	16	classes	class	NOUN
cana-2210	254	17	of	of	ADP
cana-2210	254	18	some	some	DET
cana-2210	254	19	special	special	ADJ
cana-2210	254	20	classes	class	NOUN
cana-2210	254	21	of	of	ADP
cana-2210	254	22	univalent	univalent	ADJ
cana-2210	254	23	functions	function	NOUN
cana-2210	254	24	,	,	PUNCT
cana-2210	254	25	in	in	ADP
cana-2210	254	26	:	:	PUNCT
cana-2210	254	27	z.	z.	PROPN
cana-2210	254	28	li	li	PROPN
cana-2210	254	29	.	.	PUNCT
cana-2210	255	1	ren	ren	PROPN
cana-2210	255	2	.	.	PUNCT
cana-2210	256	1	l.	l.	PROPN
cana-2210	256	2	lang	lang	PROPN
cana-2210	256	3	,	,	PUNCT
cana-2210	256	4	s.	s.	PROPN
cana-2210	256	5	zhang	zhang	PROPN
cana-2210	256	6	(	(	PUNCT
cana-2210	256	7	eds	eds	PROPN
cana-2210	256	8	.	.	PUNCT
cana-2210	256	9	)	)	PUNCT
cana-2210	256	10	,	,	PUNCT
cana-2210	256	11	proceedings	proceeding	NOUN
cana-2210	256	12	of	of	ADP
cana-2210	256	13	of	of	ADP
cana-2210	256	14	the	the	DET
cana-2210	256	15	conference	conference	NOUN
cana-2210	256	16	on	on	ADP
cana-2210	256	17	com	com	NOUN
cana-2210	256	18	plex	plex	NOUN
cana-2210	256	19	analysis	analysis	NOUN
cana-2210	256	20	,	,	PUNCT
cana-2210	256	21	j.	j.	PROPN
cana-2210	256	22	inequal	inequal	PROPN
cana-2210	256	23	.	.	PUNCT
cana-2210	257	1	pure	pure	ADJ
cana-2210	257	2	appl	appl	PROPN
cana-2210	257	3	.	.	PUNCT
cana-2210	257	4	math	math	PROPN
cana-2210	257	5	.	.	PUNCT
cana-2210	257	6	,	,	PUNCT
cana-2210	257	7	6(3	6(3	NUM
cana-2210	257	8	)	)	PUNCT
cana-2210	257	9	,	,	PUNCT
cana-2210	257	10	(	(	PUNCT
cana-2210	257	11	2005	2005	NUM
cana-2210	257	12	)	)	PUNCT
cana-2210	257	13	,	,	PUNCT
cana-2210	257	14	1–15	1–15	NUM
cana-2210	257	15	.	.	PUNCT
cana-2210	258	1	[	[	X
cana-2210	258	2	15	15	NUM
cana-2210	258	3	]	]	X
cana-2210	258	4	raducanu	raducanu	PROPN
cana-2210	258	5	d.	d.	PROPN
cana-2210	258	6	and	and	CCONJ
cana-2210	258	7	orhan	orhan	PROPN
cana-2210	258	8	h.	h.	PROPN
cana-2210	258	9	,	,	PUNCT
cana-2210	258	10	subclasses	subclass	NOUN
cana-2210	258	11	of	of	ADP
cana-2210	258	12	analytic	analytic	ADJ
cana-2210	258	13	functions	function	NOUN
cana-2210	258	14	defined	define	VERB
cana-2210	258	15	by	by	ADP
cana-2210	258	16	a	a	DET
cana-2210	258	17	generalized	generalize	VERB
cana-2210	258	18	differential	differential	NOUN
cana-2210	258	19	operator	operator	NOUN
cana-2210	258	20	,	,	PUNCT
cana-2210	258	21	int	int	NOUN
cana-2210	258	22	.	.	PUNCT
cana-2210	259	1	journal	journal	PROPN
cana-2210	259	2	of	of	ADP
cana-2210	259	3	math	math	NOUN
cana-2210	259	4	.	.	PUNCT
cana-2210	260	1	analysis	analysis	NOUN
cana-2210	260	2	,	,	PUNCT
cana-2210	260	3	4(1	4(1	NOUN
cana-2210	260	4	)	)	PUNCT
cana-2210	260	5	,	,	PUNCT
cana-2210	260	6	(	(	PUNCT
cana-2210	260	7	2010	2010	NUM
cana-2210	260	8	)	)	PUNCT
cana-2210	260	9	,	,	PUNCT
cana-2210	260	10	1–15	1–15	NUM
cana-2210	260	11	.	.	PUNCT
cana-2210	261	1	[	[	X
cana-2210	261	2	16	16	NUM
cana-2210	261	3	]	]	X
cana-2210	261	4	ragnhild	ragnhild	NOUN
cana-2210	261	5	johanne	johanne	PROPN
cana-2210	261	6	rensaa	rensaa	PROPN
cana-2210	261	7	,	,	PUNCT
cana-2210	261	8	univalent	univalent	ADJ
cana-2210	261	9	functions	function	NOUN
cana-2210	261	10	and	and	CCONJ
cana-2210	261	11	frequency	frequency	NOUN
cana-2210	261	12	analysis	analysis	NOUN
cana-2210	261	13	,	,	PUNCT
cana-2210	261	14	rocky	rocky	ADJ
cana-2210	261	15	mountain	mountain	NOUN
cana-2210	261	16	journal	journal	NOUN
cana-2210	261	17	of	of	ADP
cana-2210	261	18	mathematics	mathematic	NOUN
cana-2210	261	19	,	,	PUNCT
cana-2210	261	20	33(2	33(2	NUM
cana-2210	261	21	,	,	PUNCT
cana-2210	261	22	(	(	PUNCT
cana-2210	261	23	2003	2003	NUM
cana-2210	261	24	)	)	PUNCT
cana-2210	261	25	,	,	PUNCT
cana-2210	261	26	742–758	742–758	NUM
cana-2210	261	27	.	.	PUNCT
cana-2210	262	1	[	[	X
cana-2210	262	2	17	17	NUM
cana-2210	262	3	]	]	X
cana-2210	262	4	rashid	rashid	PROPN
cana-2210	262	5	,	,	PUNCT
cana-2210	262	6	amal	amal	PROPN
cana-2210	262	7	madhi	madhi	PROPN
cana-2210	262	8	,	,	PUNCT
cana-2210	262	9	abdul	abdul	PROPN
cana-2210	262	10	rahman	rahman	PROPN
cana-2210	262	11	s.	s.	PROPN
cana-2210	262	12	juma	juma	PROPN
cana-2210	262	13	,	,	PUNCT
cana-2210	262	14	and	and	CCONJ
cana-2210	262	15	sibel	sibel	PROPN
cana-2210	262	16	yalcın	yalcın	NOUN
cana-2210	262	17	.	.	PUNCT
cana-2210	262	18	,	,	PUNCT
cana-2210	262	19	subordination	subordination	NOUN
cana-2210	262	20	properties	property	NOUN
cana-2210	262	21	for	for	ADP
cana-2210	262	22	classes	class	NOUN
cana-2210	262	23	of	of	ADP
cana-2210	262	24	analytic	analytic	ADJ
cana-2210	262	25	univalent	univalent	ADJ
cana-2210	262	26	involving	involve	VERB
cana-2210	262	27	linear	linear	ADJ
cana-2210	262	28	operator	operator	NOUN
cana-2210	262	29	,	,	PUNCT
cana-2210	262	30	kyungpook	kyungpook	PROPN
cana-2210	262	31	mathematical	mathematical	ADJ
cana-2210	262	32	journal	journal	NOUN
cana-2210	262	33	,	,	PUNCT
cana-2210	262	34	63.2	63.2	NUM
cana-2210	262	35	,	,	PUNCT
cana-2210	262	36	(	(	PUNCT
cana-2210	262	37	2023	2023	NUM
cana-2210	262	38	)	)	PUNCT
cana-2210	262	39	,	,	PUNCT
cana-2210	262	40	225–234	225–234	NUM
cana-2210	262	41	.	.	PUNCT
cana-2210	263	1	[	[	X
cana-2210	263	2	18	18	NUM
cana-2210	263	3	]	]	PUNCT
cana-2210	263	4	ravichandran	ravichandran	NOUN
cana-2210	263	5	v	v	NOUN
cana-2210	263	6	,	,	PUNCT
cana-2210	263	7	netinbolcal	netinbolcal	ADJ
cana-2210	263	8	,	,	PUNCT
cana-2210	263	9	yasar	yasar	PROPN
cana-2210	263	10	polatoglu	polatoglu	PROPN
cana-2210	263	11	and	and	CCONJ
cana-2210	263	12	a.	a.	NOUN
cana-2210	263	13	sen	sen	PROPN
cana-2210	263	14	,	,	PUNCT
cana-2210	263	15	certain	certain	ADJ
cana-2210	263	16	subclasses	subclass	NOUN
cana-2210	263	17	of	of	ADP
cana-2210	263	18	starlike	starlike	NOUN
cana-2210	263	19	and	and	CCONJ
cana-2210	263	20	convex	convex	NOUN
cana-2210	263	21	functions	function	NOUN
cana-2210	263	22	of	of	ADP
cana-2210	263	23	complex	complex	ADJ
cana-2210	263	24	order	order	NOUN
cana-2210	263	25	,	,	PUNCT
cana-2210	263	26	hacettepe	hacettepe	ADJ
cana-2210	263	27	journal	journal	NOUN
cana-2210	263	28	of	of	ADP
cana-2210	263	29	mathematics	mathematic	NOUN
cana-2210	263	30	and	and	CCONJ
cana-2210	263	31	statistics	statistic	NOUN
cana-2210	263	32	,	,	PUNCT
cana-2210	263	33	34	34	NUM
cana-2210	263	34	,	,	PUNCT
cana-2210	263	35	(	(	PUNCT
cana-2210	263	36	2005	2005	NUM
cana-2210	263	37	)	)	PUNCT
cana-2210	263	38	,	,	PUNCT
cana-2210	263	39	9	9	NUM
cana-2210	263	40	-	-	SYM
cana-2210	263	41	15	15	NUM
cana-2210	263	42	.	.	PUNCT
cana-2210	264	1	communications	communication	NOUN
cana-2210	264	2	on	on	ADP
cana-2210	264	3	applied	apply	VERB
cana-2210	264	4	nonlinear	nonlinear	ADJ
cana-2210	264	5	analysis	analysis	NOUN
cana-2210	264	6	issn	issn	NOUN
cana-2210	264	7	:	:	PUNCT
cana-2210	264	8	1074	1074	NUM
cana-2210	264	9	-	-	PUNCT
cana-2210	264	10	133x	133x	NUM
cana-2210	264	11	vol	vol	NOUN
cana-2210	264	12	32	32	NUM
cana-2210	264	13	no	no	NOUN
cana-2210	264	14	.	.	PUNCT
cana-2210	265	1	1s	1s	NUM
cana-2210	265	2	(	(	PUNCT
cana-2210	265	3	2025	2025	NUM
cana-2210	265	4	)	)	PUNCT
cana-2210	265	5	471	471	NUM
cana-2210	265	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2210	266	1	[	[	X
cana-2210	266	2	19	19	NUM
cana-2210	266	3	]	]	X
cana-2210	266	4	ruscheweyh	ruscheweyh	NOUN
cana-2210	266	5	.	.	PUNCT
cana-2210	267	1	s	s	X
cana-2210	267	2	,	,	PUNCT
cana-2210	267	3	new	new	ADJ
cana-2210	267	4	criteria	criterion	NOUN
cana-2210	267	5	for	for	ADP
cana-2210	267	6	univalent	univalent	ADJ
cana-2210	267	7	functions	function	NOUN
cana-2210	267	8	,	,	PUNCT
cana-2210	267	9	proc	proc	NOUN
cana-2210	267	10	.	.	PUNCT
cana-2210	268	1	amer	amer	PROPN
cana-2210	268	2	.	.	PUNCT
cana-2210	268	3	math	math	PROPN
cana-2210	268	4	.	.	PUNCT
cana-2210	269	1	soc	soc	PROPN
cana-2210	269	2	.	.	PUNCT
cana-2210	269	3	,	,	PUNCT
cana-2210	269	4	49	49	NUM
cana-2210	269	5	,	,	PUNCT
cana-2210	269	6	(	(	PUNCT
cana-2210	269	7	1975	1975	NUM
cana-2210	269	8	)	)	PUNCT
cana-2210	269	9	,	,	PUNCT
cana-2210	269	10	109	109	NUM
cana-2210	269	11	-	-	SYM
cana-2210	269	12	115	115	NUM
cana-2210	269	13	.	.	PUNCT
cana-2210	270	1	[	[	X
cana-2210	270	2	20	20	NUM
cana-2210	270	3	]	]	PUNCT
cana-2210	270	4	salagean	salagean	PROPN
cana-2210	270	5	g	g	NOUN
cana-2210	270	6	,	,	PUNCT
cana-2210	270	7	subclasses	subclass	NOUN
cana-2210	270	8	of	of	ADP
cana-2210	270	9	univalent	univalent	ADJ
cana-2210	270	10	functions	function	NOUN
cana-2210	270	11	,	,	PUNCT
cana-2210	270	12	lecture	lecture	NOUN
cana-2210	270	13	notes	note	NOUN
cana-2210	270	14	in	in	ADP
cana-2210	270	15	maths	math	NOUN
cana-2210	270	16	,	,	PUNCT
cana-2210	270	17	springer	springer	NOUN
cana-2210	270	18	-	-	PUNCT
cana-2210	270	19	verlag	verlag	PROPN
cana-2210	270	20	,	,	PUNCT
cana-2210	270	21	berlin	berlin	PROPN
cana-2210	270	22	,	,	PUNCT
cana-2210	270	23	1013	1013	NUM
cana-2210	270	24	,	,	PUNCT
cana-2210	270	25	(	(	PUNCT
cana-2210	270	26	1983	1983	NUM
cana-2210	270	27	)	)	PUNCT
cana-2210	270	28	,	,	PUNCT
cana-2210	270	29	362	362	NUM
cana-2210	270	30	–	–	PUNCT
cana-2210	270	31	372	372	NUM
cana-2210	270	32	.	.	PUNCT
cana-2210	271	1	[	[	X
cana-2210	271	2	21	21	NUM
cana-2210	271	3	]	]	PUNCT
cana-2210	271	4	shams	sham	NOUN
cana-2210	271	5	s.	s.	PROPN
cana-2210	271	6	,	,	PUNCT
cana-2210	271	7	kulkarni	kulkarni	PROPN
cana-2210	271	8	s.r	s.r	PROPN
cana-2210	271	9	.	.	PROPN
cana-2210	271	10	and	and	CCONJ
cana-2210	271	11	jahangiri	jahangiri	PROPN
cana-2210	271	12	j.m	j.m	PROPN
cana-2210	271	13	.	.	PROPN
cana-2210	271	14	,	,	PUNCT
cana-2210	271	15	classes	class	NOUN
cana-2210	271	16	of	of	ADP
cana-2210	271	17	uniformly	uniformly	ADJ
cana-2210	271	18	starlike	starlike	NOUN
cana-2210	271	19	and	and	CCONJ
cana-2210	271	20	convex	convex	NOUN
cana-2210	271	21	functions	function	NOUN
cana-2210	271	22	,	,	PUNCT
cana-2210	271	23	international	international	ADJ
cana-2210	271	24	journal	journal	NOUN
cana-2210	271	25	of	of	ADP
cana-2210	271	26	mathe	mathe	PROPN
cana-2210	271	27	matics	matics	PROPN
cana-2210	271	28	and	and	CCONJ
cana-2210	271	29	mathematical	mathematical	ADJ
cana-2210	271	30	sciences	science	NOUN
cana-2210	271	31	,	,	PUNCT
cana-2210	271	32	2004(55	2004(55	NUM
cana-2210	271	33	)	)	PUNCT
cana-2210	271	34	,	,	PUNCT
cana-2210	271	35	(	(	PUNCT
cana-2210	271	36	2004	2004	NUM
cana-2210	271	37	)	)	PUNCT
cana-2210	271	38	,	,	PUNCT
cana-2210	271	39	2959–2961	2959–2961	NUM
cana-2210	271	40	.	.	PUNCT
cana-2210	272	1	[	[	X
cana-2210	272	2	22	22	NUM
cana-2210	272	3	]	]	X
cana-2210	272	4	shanmugam	shanmugam	NOUN
cana-2210	272	5	t.	t.	PROPN
cana-2210	272	6	and	and	CCONJ
cana-2210	272	7	s.	s.	PROPN
cana-2210	272	8	sivasubramanian	sivasubramanian	PROPN
cana-2210	272	9	,	,	PUNCT
cana-2210	272	10	on	on	ADP
cana-2210	272	11	a	a	DET
cana-2210	272	12	fekete	fekete	NOUN
cana-2210	272	13	-	-	PUNCT
cana-2210	272	14	szego	szego	NOUN
cana-2210	272	15	prob	prob	NOUN
cana-2210	272	16	lem	lem	PROPN
cana-2210	272	17	for	for	ADP
cana-2210	272	18	some	some	DET
cana-2210	272	19	subclasses	subclass	NOUN
cana-2210	272	20	of	of	ADP
cana-2210	272	21	analytic	analytic	ADJ
cana-2210	272	22	functions	function	NOUN
cana-2210	272	23	,	,	PUNCT
cana-2210	272	24	j.	j.	PROPN
cana-2210	272	25	ineql	ineql	PROPN
cana-2210	272	26	.	.	PUNCT
cana-2210	273	1	pure	pure	ADJ
cana-2210	273	2	and	and	CCONJ
cana-2210	273	3	appl	appl	PROPN
cana-2210	273	4	.	.	PROPN
cana-2210	273	5	math	math	PROPN
cana-2210	273	6	.	.	PUNCT
cana-2210	273	7	,	,	PUNCT
cana-2210	273	8	6(3	6(3	NUM
cana-2210	273	9	)	)	PUNCT
cana-2210	273	10	,	,	PUNCT
cana-2210	273	11	(	(	PUNCT
cana-2210	273	12	2005	2005	NUM
cana-2210	273	13	)	)	PUNCT
cana-2210	273	14	,	,	PUNCT
cana-2210	273	15	1–15	1–15	NUM
cana-2210	273	16	.	.	PUNCT
cana-2210	274	1	[	[	X
cana-2210	274	2	23	23	NUM
cana-2210	274	3	]	]	X
cana-2210	274	4	srivastava	srivastava	PROPN
cana-2210	274	5	h.m	h.m	PROPN
cana-2210	274	6	,	,	PUNCT
cana-2210	274	7	mishra	mishra	PROPN
cana-2210	274	8	a.k	a.k	PROPN
cana-2210	274	9	.	.	PROPN
cana-2210	274	10	,	,	PUNCT
cana-2210	274	11	applications	application	NOUN
cana-2210	274	12	of	of	ADP
cana-2210	274	13	fractional	fractional	ADJ
cana-2210	274	14	calculus	calculus	NOUN
cana-2210	274	15	to	to	PART
cana-2210	274	16	parabolic	parabolic	VERB
cana-2210	274	17	starlike	starlike	NOUN
cana-2210	274	18	and	and	CCONJ
cana-2210	274	19	uniform	uniform	ADJ
cana-2210	274	20	convex	convex	NOUN
cana-2210	274	21	functions	function	NOUN
cana-2210	274	22	,	,	PUNCT
cana-2210	274	23	comp	comp	NOUN
cana-2210	274	24	.	.	PUNCT
cana-2210	274	25	math	math	NOUN
cana-2210	274	26	.	.	PUNCT
cana-2210	274	27	,	,	PUNCT
cana-2210	274	28	39	39	NUM
cana-2210	274	29	,	,	PUNCT
cana-2210	274	30	(	(	PUNCT
cana-2210	274	31	2000	2000	NUM
cana-2210	274	32	)	)	PUNCT
cana-2210	274	33	,	,	PUNCT
cana-2210	274	34	57–69	57–69	X
cana-2210	274	35	.	.	PUNCT
cana-2210	275	1	[	[	X
cana-2210	275	2	24	24	NUM
cana-2210	275	3	]	]	X
cana-2210	275	4	srivastava	srivastava	PROPN
cana-2210	275	5	h.m	h.m	PROPN
cana-2210	275	6	,	,	PUNCT
cana-2210	275	7	mishra	mishra	PROPN
cana-2210	275	8	a.k	a.k	PROPN
cana-2210	275	9	.	.	PROPN
cana-2210	275	10	,	,	PUNCT
cana-2210	275	11	das	das	PROPN
cana-2210	275	12	m.k	m.k	PROPN
cana-2210	275	13	.	.	PROPN
cana-2210	275	14	,	,	PUNCT
cana-2210	275	15	a	a	DET
cana-2210	275	16	nested	nested	ADJ
cana-2210	275	17	class	class	NOUN
cana-2210	275	18	of	of	ADP
cana-2210	275	19	an	an	DET
cana-2210	275	20	alytic	alytic	ADJ
cana-2210	275	21	functions	function	NOUN
cana-2210	275	22	defined	define	VERB
cana-2210	275	23	by	by	ADP
cana-2210	275	24	fractional	fractional	ADJ
cana-2210	275	25	calculus	calculus	NOUN
cana-2210	275	26	,	,	PUNCT
cana-2210	275	27	commun	commun	PROPN
cana-2210	275	28	.	.	PUNCT
cana-2210	275	29	appl	appl	PROPN
cana-2210	275	30	.	.	PUNCT
cana-2210	276	1	anal	anal	PROPN
cana-2210	276	2	.	.	PROPN
cana-2210	276	3	,	,	PUNCT
cana-2210	276	4	2(3	2(3	NUM
cana-2210	276	5	)	)	PUNCT
cana-2210	276	6	,	,	PUNCT
cana-2210	276	7	(	(	PUNCT
cana-2210	276	8	1998	1998	NUM
cana-2210	276	9	)	)	PUNCT
cana-2210	276	10	,	,	PUNCT
cana-2210	276	11	321–332	321–332	NUM
cana-2210	276	12	.	.	PUNCT
cana-2210	277	1	[	[	X
cana-2210	277	2	25	25	NUM
cana-2210	277	3	]	]	X
cana-2210	277	4	suchitra	suchitra	PROPN
cana-2210	277	5	k.	k.	PROPN
cana-2210	277	6	,	,	PUNCT
cana-2210	277	7	adolf	adolf	PROPN
cana-2210	277	8	stephen	stephen	PROPN
cana-2210	277	9	b.	b.	PROPN
cana-2210	277	10	,	,	PUNCT
cana-2210	277	11	and	and	CCONJ
cana-2210	277	12	sivssubramanian	sivssubramanian	PROPN
cana-2210	277	13	s.	s.	PROPN
cana-2210	277	14	,	,	PUNCT
cana-2210	277	15	a	a	DET
cana-2210	277	16	co	co	X
cana-2210	277	17	efficient	efficient	ADJ
cana-2210	277	18	inequality	inequality	NOUN
cana-2210	277	19	for	for	ADP
cana-2210	277	20	certain	certain	ADJ
cana-2210	277	21	classes	class	NOUN
cana-2210	277	22	of	of	ADP
cana-2210	277	23	analytic	analytic	ADJ
cana-2210	277	24	function	function	NOUN
cana-2210	277	25	of	of	ADP
cana-2210	277	26	com	com	NOUN
cana-2210	277	27	plex	plex	NOUN
cana-2210	277	28	order	order	NOUN
cana-2210	277	29	,	,	PUNCT
cana-2210	277	30	j.	j.	PROPN
cana-2210	277	31	in	in	PROPN
cana-2210	277	32	.	.	PUNCT
cana-2210	278	1	pure	pure	ADJ
cana-2210	278	2	.	.	PUNCT
cana-2210	279	1	appl	appl	PROPN
cana-2210	279	2	.	.	PROPN
cana-2210	279	3	math	math	PROPN
cana-2210	279	4	.	.	PUNCT
cana-2210	279	5	,	,	PUNCT
cana-2210	279	6	7(4	7(4	NUM
cana-2210	279	7	)	)	PUNCT
cana-2210	279	8	,	,	PUNCT
cana-2210	279	9	(	(	PUNCT
cana-2210	279	10	2006	2006	NUM
cana-2210	279	11	)	)	PUNCT
cana-2210	279	12	,	,	PUNCT
cana-2210	279	13	art	art	NOUN
cana-2210	279	14	145	145	NUM
cana-2210	279	15	.	.	PUNCT
cana-2210	280	1	[	[	X
cana-2210	280	2	26	26	NUM
cana-2210	280	3	]	]	PUNCT
cana-2210	280	4	sumer	sumer	PROPN
cana-2210	280	5	s.	s.	PROPN
cana-2210	280	6	eker	eker	PROPN
cana-2210	280	7	and	and	CCONJ
cana-2210	280	8	owa	owa	PROPN
cana-2210	280	9	s.	s.	PROPN
cana-2210	280	10	,	,	PUNCT
cana-2210	280	11	new	new	ADJ
cana-2210	280	12	applications	application	NOUN
cana-2210	280	13	of	of	ADP
cana-2210	280	14	classes	class	NOUN
cana-2210	280	15	of	of	ADP
cana-2210	280	16	an	an	DET
cana-2210	280	17	alytic	alytic	ADJ
cana-2210	280	18	functions	function	NOUN
cana-2210	280	19	involving	involve	VERB
cana-2210	280	20	the	the	DET
cana-2210	280	21	salagean	salagean	ADJ
cana-2210	280	22	operator	operator	NOUN
cana-2210	280	23	,	,	PUNCT
cana-2210	280	24	in	in	ADP
cana-2210	280	25	proceedings	proceeding	NOUN
cana-2210	280	26	of	of	ADP
cana-2210	280	27	the	the	DET
cana-2210	280	28	international	international	ADJ
cana-2210	280	29	symposium	symposium	NOUN
cana-2210	280	30	on	on	ADP
cana-2210	280	31	complex	complex	ADJ
cana-2210	280	32	function	function	NOUN
cana-2210	280	33	theory	theory	NOUN
cana-2210	280	34	and	and	CCONJ
cana-2210	280	35	applications	application	NOUN
cana-2210	280	36	,	,	PUNCT
cana-2210	280	37	transilvania	transilvania	PROPN
cana-2210	280	38	university	university	PROPN
cana-2210	280	39	of	of	ADP
cana-2210	280	40	printing	printing	NOUN
cana-2210	280	41	house	house	PROPN
cana-2210	280	42	,	,	PUNCT
cana-2210	280	43	brasov	brasov	NOUN
cana-2210	280	44	,	,	PUNCT
cana-2210	280	45	romania	romania	PROPN
cana-2210	280	46	,	,	PUNCT
cana-2210	280	47	(	(	PUNCT
cana-2210	280	48	2006	2006	NUM
cana-2210	280	49	)	)	PUNCT
cana-2210	280	50	,	,	PUNCT
cana-2210	280	51	21–34	21–34	NUM
cana-2210	280	52	.	.	PUNCT
cana-2210	281	1	[	[	X
cana-2210	281	2	27	27	NUM
cana-2210	281	3	]	]	X
cana-2210	281	4	sumer	sumer	PROPN
cana-2210	281	5	s.	s.	PROPN
cana-2210	281	6	eker	eker	PROPN
cana-2210	281	7	and	and	CCONJ
cana-2210	281	8	ozlem	ozlem	PROPN
cana-2210	281	9	guney	guney	PROPN
cana-2210	281	10	h.	h.	PROPN
cana-2210	281	11	,	,	PUNCT
cana-2210	281	12	a	a	DET
cana-2210	281	13	new	new	ADJ
cana-2210	281	14	subclass	subclass	NOUN
cana-2210	281	15	of	of	ADP
cana-2210	281	16	analytic	analytic	ADJ
cana-2210	281	17	functions	function	NOUN
cana-2210	281	18	of	of	ADP
cana-2210	281	19	differential	differential	ADJ
cana-2210	281	20	operator	operator	NOUN
cana-2210	281	21	,	,	PUNCT
cana-2210	281	22	journal	journal	NOUN
cana-2210	281	23	of	of	ADP
cana-2210	281	24	inequality	inequality	NOUN
cana-2210	281	25	and	and	CCONJ
cana-2210	281	26	ap	ap	PROPN
cana-2210	281	27	plications	plication	NOUN
cana-2210	281	28	,	,	PUNCT
cana-2210	281	29	2008	2008	NUM
cana-2210	281	30	,	,	PUNCT
cana-2210	281	31	(	(	PUNCT
cana-2210	281	32	2008	2008	NUM
cana-2210	281	33	)	)	PUNCT
cana-2210	281	34	.	.	PUNCT
cana-2210	282	1	[	[	X
cana-2210	282	2	28	28	NUM
cana-2210	282	3	]	]	X
cana-2210	282	4	thirucheran	thirucheran	ADJ
cana-2210	282	5	m.	m.	NOUN
cana-2210	282	6	and	and	CCONJ
cana-2210	282	7	stalin	stalin	PROPN
cana-2210	282	8	t.	t.	PROPN
cana-2210	282	9	,	,	PUNCT
cana-2210	282	10	fekete	fekete	PROPN
cana-2210	282	11	-	-	PUNCT
cana-2210	282	12	szego	szego	NOUN
cana-2210	282	13	inequality	inequality	NOUN
cana-2210	282	14	for	for	ADP
cana-2210	282	15	the	the	DET
cana-2210	282	16	new	new	ADJ
cana-2210	282	17	subclasses	subclass	NOUN
cana-2210	282	18	of	of	ADP
cana-2210	282	19	univalent	univalent	ADJ
cana-2210	282	20	function	function	NOUN
cana-2210	282	21	defined	define	VERB
cana-2210	282	22	by	by	ADP
cana-2210	282	23	linear	linear	PROPN
cana-2210	282	24	operators	operator	NOUN
cana-2210	282	25	,	,	PUNCT
cana-2210	282	26	journal	journal	NOUN
cana-2210	282	27	of	of	ADP
cana-2210	282	28	computer	computer	NOUN
cana-2210	282	29	and	and	CCONJ
cana-2210	282	30	mathematical	mathematical	ADJ
cana-2210	282	31	sciences	science	NOUN
cana-2210	282	32	,	,	PUNCT
cana-2210	282	33	9(8	9(8	NUM
cana-2210	282	34	)	)	PUNCT
cana-2210	282	35	,	,	PUNCT
cana-2210	282	36	(	(	PUNCT
cana-2210	282	37	2018	2018	NUM
cana-2210	282	38	)	)	PUNCT
cana-2210	282	39	,	,	PUNCT
cana-2210	282	40	921–930	921–930	NUM
cana-2210	282	41	.	.	PUNCT
cana-2210	283	1	[	[	X
cana-2210	283	2	29	29	NUM
cana-2210	283	3	]	]	X
cana-2210	283	4	thirucheran	thirucheran	ADJ
cana-2210	283	5	m.	m.	NOUN
cana-2210	283	6	and	and	CCONJ
cana-2210	283	7	stalin	stalin	PROPN
cana-2210	283	8	t.	t.	PROPN
cana-2210	283	9	,	,	PUNCT
cana-2210	283	10	obtain	obtain	VERB
cana-2210	283	11	fekete	fekete	NOUN
cana-2210	283	12	-	-	PUNCT
cana-2210	283	13	szego	szego	NOUN
cana-2210	283	14	inequality	inequality	NOUN
cana-2210	283	15	of	of	ADP
cana-2210	283	16	the	the	DET
cana-2210	283	17	new	new	ADJ
cana-2210	283	18	subclass	subclass	NOUN
cana-2210	283	19	defined	define	VERB
cana-2210	283	20	by	by	ADP
cana-2210	283	21	al	al	PROPN
cana-2210	283	22	-	-	PUNCT
cana-2210	283	23	oboudi	oboudi	ADJ
cana-2210	283	24	operator	operator	NOUN
cana-2210	283	25	,	,	PUNCT
cana-2210	283	26	mathematical	mathematical	ADJ
cana-2210	283	27	sciences	sciences	PROPN
cana-2210	283	28	international	international	ADJ
cana-2210	283	29	research	research	PROPN
cana-2210	283	30	journal	journal	NOUN
cana-2210	283	31	,	,	PUNCT
cana-2210	283	32	7	7	NUM
cana-2210	283	33	,	,	PUNCT
cana-2210	283	34	(	(	PUNCT
cana-2210	283	35	2018	2018	NUM
cana-2210	283	36	)	)	PUNCT
cana-2210	283	37	,	,	PUNCT
cana-2210	283	38	131	131	NUM
cana-2210	283	39	-	-	SYM
cana-2210	283	40	137	137	NUM
cana-2210	283	41	.	.	PUNCT
cana-2210	284	1	[	[	X
cana-2210	284	2	30	30	NUM
cana-2210	284	3	]	]	X
cana-2210	284	4	thirucheran	thirucheran	ADJ
cana-2210	284	5	m.	m.	NOUN
cana-2210	284	6	and	and	CCONJ
cana-2210	284	7	stalin	stalin	PROPN
cana-2210	284	8	t.	t.	PROPN
cana-2210	284	9	,	,	PUNCT
cana-2210	284	10	on	on	ADP
cana-2210	284	11	a	a	DET
cana-2210	284	12	new	new	ADJ
cana-2210	284	13	subclass	subclass	NOUN
cana-2210	284	14	of	of	ADP
cana-2210	284	15	analytic	analytic	ADJ
cana-2210	284	16	functions	function	NOUN
cana-2210	284	17	defined	define	VERB
cana-2210	284	18	by	by	ADP
cana-2210	284	19	using	use	VERB
cana-2210	284	20	generalized	generalized	ADJ
cana-2210	284	21	al	al	PROPN
cana-2210	284	22	-	-	PUNCT
cana-2210	284	23	oboudi	oboudi	ADJ
cana-2210	284	24	differential	differential	ADJ
cana-2210	284	25	oper	oper	NOUN
cana-2210	284	26	ator	ator	NOUN
cana-2210	284	27	,	,	PUNCT
cana-2210	284	28	journal	journal	NOUN
cana-2210	284	29	of	of	ADP
cana-2210	284	30	global	global	ADJ
cana-2210	284	31	research	research	NOUN
cana-2210	284	32	in	in	ADP
cana-2210	284	33	mathematical	mathematical	ADJ
cana-2210	284	34	archives	archive	NOUN
cana-2210	284	35	,	,	PUNCT
cana-2210	284	36	5(5	5(5	NUM
cana-2210	284	37	)	)	PUNCT
cana-2210	284	38	,	,	PUNCT
cana-2210	284	39	(	(	PUNCT
cana-2210	284	40	2018	2018	NUM
cana-2210	284	41	)	)	PUNCT
cana-2210	284	42	,	,	PUNCT
cana-2210	284	43	33–40	33–40	X
cana-2210	284	44	.	.	PUNCT
cana-2210	285	1	[	[	X
cana-2210	285	2	31	31	NUM
cana-2210	285	3	]	]	X
cana-2210	285	4	xianfeng	xianfeng	PROPN
cana-2210	285	5	gu	gu	PROPN
cana-2210	285	6	,	,	PUNCT
cana-2210	285	7	yalin	yalin	PROPN
cana-2210	285	8	wang	wang	PROPN
cana-2210	285	9	*	*	PROPN
cana-2210	285	10	,	,	PUNCT
cana-2210	285	11	tony	tony	PROPN
cana-2210	285	12	f.	f.	PROPN
cana-2210	285	13	chan	chan	PROPN
cana-2210	285	14	,	,	PUNCT
cana-2210	285	15	paul	paul	PROPN
cana-2210	285	16	m.	m.	PROPN
cana-2210	285	17	thompson	thompson	PROPN
cana-2210	285	18	,	,	PUNCT
cana-2210	285	19	and	and	CCONJ
cana-2210	285	20	shing	she	VERB
cana-2210	285	21	-	-	PUNCT
cana-2210	285	22	tung	tung	VERB
cana-2210	285	23	yau	yau	PROPN
cana-2210	285	24	,	,	PUNCT
cana-2210	285	25	genus	genus	NOUN
cana-2210	285	26	zero	zero	NUM
cana-2210	285	27	surface	surface	NOUN
cana-2210	285	28	conformal	conformal	NOUN
cana-2210	285	29	mapping	mapping	NOUN
cana-2210	285	30	and	and	CCONJ
cana-2210	285	31	its	its	PRON
cana-2210	285	32	application	application	NOUN
cana-2210	285	33	to	to	PART
cana-2210	285	34	brain	brain	NOUN
cana-2210	285	35	surface	surface	NOUN
cana-2210	285	36	mapping	mapping	NOUN
cana-2210	285	37	,	,	PUNCT
cana-2210	285	38	ieee	ieee	NOUN
cana-2210	285	39	transaction	transaction	NOUN
cana-2210	285	40	on	on	ADP
cana-2210	285	41	medical	medical	ADJ
cana-2210	285	42	imaging	imaging	NOUN
cana-2210	285	43	,	,	PUNCT
cana-2210	285	44	23(8),(2004	23(8),(2004	NUM
cana-2210	285	45	)	)	PUNCT
cana-2210	285	46	,	,	PUNCT
cana-2210	285	47	949	949	NUM
cana-2210	285	48	–	–	PUNCT
cana-2210	285	49	958	958	NUM
cana-2210	285	50	.	.	PUNCT
cana-2210	286	1	[	[	X
cana-2210	286	2	32	32	NUM
cana-2210	286	3	]	]	PUNCT
cana-2210	286	4	xianfeng	xianfeng	PROPN
cana-2210	286	5	gu	gu	PROPN
cana-2210	286	6	,	,	PUNCT
cana-2210	286	7	yalin	yalin	PROPN
cana-2210	286	8	wang	wang	PROPN
cana-2210	286	9	*	*	PROPN
cana-2210	286	10	,	,	PUNCT
cana-2210	286	11	tony	tony	PROPN
cana-2210	286	12	f.	f.	PROPN
cana-2210	286	13	chan	chan	PROPN
cana-2210	286	14	,	,	PUNCT
cana-2210	286	15	paul	paul	PROPN
cana-2210	286	16	m.	m.	PROPN
cana-2210	286	17	thompson	thompson	PROPN
cana-2210	286	18	,	,	PUNCT
cana-2210	286	19	and	and	CCONJ
cana-2210	286	20	shing	she	VERB
cana-2210	286	21	-	-	PUNCT
cana-2210	286	22	tung	tung	VERB
cana-2210	286	23	yau	yau	PROPN
cana-2210	286	24	,	,	PUNCT
cana-2210	286	25	genus	genus	NOUN
cana-2210	286	26	zero	zero	NUM
cana-2210	286	27	surface	surface	NOUN
cana-2210	286	28	conformal	conformal	NOUN
cana-2210	286	29	mapping	mapping	NOUN
cana-2210	286	30	and	and	CCONJ
cana-2210	286	31	its	its	PRON
cana-2210	286	32	application	application	NOUN
cana-2210	286	33	to	to	PART
cana-2210	286	34	brain	brain	NOUN
cana-2210	286	35	surface	surface	NOUN
cana-2210	286	36	mapping	mapping	NOUN
cana-2210	286	37	,	,	PUNCT
cana-2210	286	38	ieee	ieee	NOUN
cana-2210	286	39	transactions	transaction	NOUN
cana-2210	286	40	on	on	ADP
cana-2210	286	41	medical	medical	ADJ
cana-2210	286	42	imaging	imaging	NOUN
cana-2210	286	43	,	,	PUNCT
cana-2210	286	44	23(8	23(8	NOUN
cana-2210	286	45	)	)	PUNCT
cana-2210	286	46	,	,	PUNCT
cana-2210	286	47	(	(	PUNCT
cana-2210	286	48	2004	2004	NUM
cana-2210	286	49	)	)	PUNCT
cana-2210	286	50	,	,	PUNCT
cana-2210	286	51	949	949	NUM
cana-2210	286	52	-	-	SYM
cana-2210	286	53	958	958	NUM
cana-2210	286	54	.	.	PUNCT