id	sid	tid	token	lemma	pos
ejpam-5592	1	1	european	european	PROPN
ejpam-5592	1	2	journal	journal	PROPN
ejpam-5592	1	3	of	of	ADP
ejpam-5592	1	4	pure	pure	ADJ
ejpam-5592	1	5	and	and	CCONJ
ejpam-5592	1	6	applied	apply	VERB
ejpam-5592	1	7	mathematics	mathematic	NOUN
ejpam-5592	1	8	vol	vol	NOUN
ejpam-5592	1	9	.	.	PROPN
ejpam-5592	2	1	17	17	NUM
ejpam-5592	2	2	,	,	PUNCT
ejpam-5592	2	3	no	no	INTJ
ejpam-5592	2	4	.	.	NOUN
ejpam-5592	2	5	4	4	NUM
ejpam-5592	2	6	,	,	PUNCT
ejpam-5592	2	7	2024	2024	NUM
ejpam-5592	2	8	,	,	PUNCT
ejpam-5592	2	9	3687	3687	NUM
ejpam-5592	2	10	-	-	SYM
ejpam-5592	2	11	3707	3707	NUM
ejpam-5592	2	12	issn	issn	PROPN
ejpam-5592	2	13	1307	1307	NUM
ejpam-5592	2	14	-	-	SYM
ejpam-5592	2	15	5543	5543	NUM
ejpam-5592	2	16	–	–	PUNCT
ejpam-5592	2	17	ejpam.com	ejpam.com	X
ejpam-5592	2	18	published	publish	VERB
ejpam-5592	2	19	by	by	ADP
ejpam-5592	2	20	new	new	PROPN
ejpam-5592	2	21	york	york	PROPN
ejpam-5592	2	22	business	business	PROPN
ejpam-5592	2	23	global	global	ADJ
ejpam-5592	2	24	gronwall	gronwall	ADJ
ejpam-5592	2	25	-	-	PUNCT
ejpam-5592	2	26	type	type	NOUN
ejpam-5592	2	27	inequalities	inequality	NOUN
ejpam-5592	2	28	and	and	CCONJ
ejpam-5592	2	29	qualitative	qualitative	ADJ
ejpam-5592	2	30	studies	study	NOUN
ejpam-5592	2	31	on	on	ADP
ejpam-5592	2	32	higher	high	ADJ
ejpam-5592	2	33	-	-	PUNCT
ejpam-5592	2	34	variable	variable	ADJ
ejpam-5592	2	35	orders	order	NOUN
ejpam-5592	2	36	of	of	ADP
ejpam-5592	2	37	atangana	atangana	PROPN
ejpam-5592	2	38	-	-	PUNCT
ejpam-5592	2	39	baleanu	baleanu	ADJ
ejpam-5592	2	40	fractional	fractional	ADJ
ejpam-5592	2	41	operators	operator	NOUN
ejpam-5592	2	42	via	via	ADP
ejpam-5592	2	43	increasing	increase	VERB
ejpam-5592	2	44	functions	function	NOUN
ejpam-5592	2	45	hasanen	hasanen	PROPN
ejpam-5592	2	46	a.	a.	PROPN
ejpam-5592	2	47	hammad1,2,∗	hammad1,2,∗	PROPN
ejpam-5592	2	48	,	,	PUNCT
ejpam-5592	2	49	manuel	manuel	PROPN
ejpam-5592	2	50	de	de	X
ejpam-5592	2	51	la	la	X
ejpam-5592	2	52	sen3	sen3	PROPN
ejpam-5592	2	53	1	1	NUM
ejpam-5592	2	54	department	department	NOUN
ejpam-5592	2	55	of	of	ADP
ejpam-5592	2	56	mathematics	mathematic	NOUN
ejpam-5592	2	57	,	,	PUNCT
ejpam-5592	2	58	college	college	NOUN
ejpam-5592	2	59	of	of	ADP
ejpam-5592	2	60	science	science	NOUN
ejpam-5592	2	61	,	,	PUNCT
ejpam-5592	2	62	qassim	qassim	PROPN
ejpam-5592	2	63	university	university	PROPN
ejpam-5592	2	64	,	,	PUNCT
ejpam-5592	2	65	buraydah	buraydah	NOUN
ejpam-5592	2	66	51452	51452	NUM
ejpam-5592	2	67	,	,	PUNCT
ejpam-5592	2	68	saudi	saudi	PROPN
ejpam-5592	2	69	arabia	arabia	PROPN
ejpam-5592	2	70	2	2	NUM
ejpam-5592	2	71	department	department	NOUN
ejpam-5592	2	72	of	of	ADP
ejpam-5592	2	73	mathematics	mathematic	NOUN
ejpam-5592	2	74	,	,	PUNCT
ejpam-5592	2	75	faculty	faculty	NOUN
ejpam-5592	2	76	of	of	ADP
ejpam-5592	2	77	science	science	NOUN
ejpam-5592	2	78	,	,	PUNCT
ejpam-5592	2	79	sohag	sohag	NOUN
ejpam-5592	2	80	university	university	NOUN
ejpam-5592	2	81	,	,	PUNCT
ejpam-5592	2	82	sohag	sohag	NOUN
ejpam-5592	2	83	82524	82524	NUM
ejpam-5592	2	84	,	,	PUNCT
ejpam-5592	2	85	egypt	egypt	PROPN
ejpam-5592	2	86	3	3	NUM
ejpam-5592	2	87	institute	institute	PROPN
ejpam-5592	2	88	of	of	ADP
ejpam-5592	2	89	research	research	NOUN
ejpam-5592	2	90	and	and	CCONJ
ejpam-5592	2	91	development	development	NOUN
ejpam-5592	2	92	of	of	ADP
ejpam-5592	2	93	processes	process	NOUN
ejpam-5592	2	94	,	,	PUNCT
ejpam-5592	2	95	department	department	NOUN
ejpam-5592	2	96	of	of	ADP
ejpam-5592	2	97	electricity	electricity	NOUN
ejpam-5592	2	98	and	and	CCONJ
ejpam-5592	2	99	electronics	electronic	NOUN
ejpam-5592	2	100	,	,	PUNCT
ejpam-5592	2	101	faculty	faculty	NOUN
ejpam-5592	2	102	of	of	ADP
ejpam-5592	2	103	science	science	NOUN
ejpam-5592	2	104	and	and	CCONJ
ejpam-5592	2	105	technology	technology	NOUN
ejpam-5592	2	106	,	,	PUNCT
ejpam-5592	2	107	univesity	univesity	NOUN
ejpam-5592	2	108	of	of	ADP
ejpam-5592	2	109	the	the	DET
ejpam-5592	2	110	basque	basque	ADJ
ejpam-5592	2	111	country	country	NOUN
ejpam-5592	2	112	,	,	PUNCT
ejpam-5592	2	113	48940	48940	NUM
ejpam-5592	2	114	-	-	SYM
ejpam-5592	2	115	leioa	leioa	ADJ
ejpam-5592	2	116	(	(	PUNCT
ejpam-5592	2	117	bizkaia	bizkaia	PROPN
ejpam-5592	2	118	)	)	PUNCT
ejpam-5592	2	119	,	,	PUNCT
ejpam-5592	2	120	spain	spain	PROPN
ejpam-5592	2	121	abstract	abstract	NOUN
ejpam-5592	2	122	.	.	PUNCT
ejpam-5592	3	1	this	this	DET
ejpam-5592	3	2	paper	paper	NOUN
ejpam-5592	3	3	introduces	introduce	VERB
ejpam-5592	3	4	a	a	DET
ejpam-5592	3	5	novel	novel	ADJ
ejpam-5592	3	6	extension	extension	NOUN
ejpam-5592	3	7	of	of	ADP
ejpam-5592	3	8	caputo	caputo	PROPN
ejpam-5592	3	9	-	-	PUNCT
ejpam-5592	3	10	atangana	atangana	PROPN
ejpam-5592	3	11	-	-	PUNCT
ejpam-5592	3	12	baleanu	baleanu	PROPN
ejpam-5592	3	13	and	and	CCONJ
ejpam-5592	3	14	riemannatangana	riemannatangana	ADJ
ejpam-5592	3	15	-	-	PUNCT
ejpam-5592	3	16	baleanu	baleanu	ADJ
ejpam-5592	3	17	fractional	fractional	ADJ
ejpam-5592	3	18	derivatives	derivative	NOUN
ejpam-5592	3	19	from	from	ADP
ejpam-5592	3	20	constant	constant	ADJ
ejpam-5592	3	21	to	to	ADP
ejpam-5592	3	22	increasing	increase	VERB
ejpam-5592	3	23	variable	variable	ADJ
ejpam-5592	3	24	order	order	NOUN
ejpam-5592	3	25	.	.	PUNCT
ejpam-5592	4	1	we	we	PRON
ejpam-5592	4	2	generalize	generalize	VERB
ejpam-5592	4	3	the	the	DET
ejpam-5592	4	4	fractional	fractional	ADJ
ejpam-5592	4	5	order	order	NOUN
ejpam-5592	4	6	from	from	ADP
ejpam-5592	4	7	a	a	DET
ejpam-5592	4	8	fixed	fix	VERB
ejpam-5592	4	9	value	value	NOUN
ejpam-5592	4	10	in	in	ADP
ejpam-5592	4	11	(	(	PUNCT
ejpam-5592	4	12	0	0	NUM
ejpam-5592	4	13	,	,	PUNCT
ejpam-5592	4	14	1	1	NUM
ejpam-5592	4	15	]	]	PUNCT
ejpam-5592	4	16	to	to	ADP
ejpam-5592	4	17	a	a	DET
ejpam-5592	4	18	time	time	NOUN
ejpam-5592	4	19	-	-	PUNCT
ejpam-5592	4	20	dependent	dependent	ADJ
ejpam-5592	4	21	function	function	NOUN
ejpam-5592	4	22	in	in	ADP
ejpam-5592	4	23	(	(	PUNCT
ejpam-5592	4	24	k	k	X
ejpam-5592	4	25	,	,	PUNCT
ejpam-5592	4	26	k	k	PROPN
ejpam-5592	4	27	+	+	PROPN
ejpam-5592	4	28	1	1	NUM
ejpam-5592	4	29	]	]	PUNCT
ejpam-5592	4	30	,	,	PUNCT
ejpam-5592	4	31	where	where	SCONJ
ejpam-5592	4	32	k	k	PROPN
ejpam-5592	4	33	≥	≥	PROPN
ejpam-5592	4	34	0	0	NUM
ejpam-5592	4	35	.	.	PUNCT
ejpam-5592	5	1	the	the	DET
ejpam-5592	5	2	corresponding	corresponding	ADJ
ejpam-5592	5	3	atangana	atangana	PROPN
ejpam-5592	5	4	-	-	PUNCT
ejpam-5592	5	5	baleanu	baleanu	ADJ
ejpam-5592	5	6	fractional	fractional	ADJ
ejpam-5592	5	7	integral	integral	NOUN
ejpam-5592	5	8	is	be	AUX
ejpam-5592	5	9	also	also	ADV
ejpam-5592	5	10	extended	extend	VERB
ejpam-5592	5	11	.	.	PUNCT
ejpam-5592	6	1	key	key	ADJ
ejpam-5592	6	2	properties	property	NOUN
ejpam-5592	6	3	of	of	ADP
ejpam-5592	6	4	these	these	DET
ejpam-5592	6	5	new	new	ADJ
ejpam-5592	6	6	definitions	definition	NOUN
ejpam-5592	6	7	are	be	AUX
ejpam-5592	6	8	explored	explore	VERB
ejpam-5592	6	9	,	,	PUNCT
ejpam-5592	6	10	including	include	VERB
ejpam-5592	6	11	a	a	DET
ejpam-5592	6	12	generalized	generalized	ADJ
ejpam-5592	6	13	gronwall	gronwall	ADJ
ejpam-5592	6	14	inequality	inequality	NOUN
ejpam-5592	6	15	.	.	PUNCT
ejpam-5592	7	1	we	we	PRON
ejpam-5592	7	2	then	then	ADV
ejpam-5592	7	3	delve	delve	VERB
ejpam-5592	7	4	into	into	ADP
ejpam-5592	7	5	the	the	DET
ejpam-5592	7	6	analysis	analysis	NOUN
ejpam-5592	7	7	of	of	ADP
ejpam-5592	7	8	higher	high	ADJ
ejpam-5592	7	9	-	-	PUNCT
ejpam-5592	7	10	variable	variable	NOUN
ejpam-5592	7	11	initial	initial	ADJ
ejpam-5592	7	12	fractional	fractional	ADJ
ejpam-5592	7	13	differential	differential	NOUN
ejpam-5592	7	14	equations	equation	NOUN
ejpam-5592	7	15	using	use	VERB
ejpam-5592	7	16	the	the	DET
ejpam-5592	7	17	caputo	caputo	NOUN
ejpam-5592	7	18	-	-	PUNCT
ejpam-5592	7	19	atanganabaleanu	atanganabaleanu	NOUN
ejpam-5592	7	20	operator	operator	NOUN
ejpam-5592	7	21	with	with	ADP
ejpam-5592	7	22	an	an	DET
ejpam-5592	7	23	increasing	increase	VERB
ejpam-5592	7	24	function	function	NOUN
ejpam-5592	7	25	,	,	PUNCT
ejpam-5592	7	26	establishing	establish	VERB
ejpam-5592	7	27	existence	existence	NOUN
ejpam-5592	7	28	and	and	CCONJ
ejpam-5592	7	29	uniqueness	uniqueness	NOUN
ejpam-5592	7	30	results	result	NOUN
ejpam-5592	7	31	via	via	ADP
ejpam-5592	7	32	picard	picard	PROPN
ejpam-5592	7	33	’s	’s	PART
ejpam-5592	7	34	iterative	iterative	NOUN
ejpam-5592	7	35	method	method	NOUN
ejpam-5592	7	36	.	.	PUNCT
ejpam-5592	8	1	the	the	DET
ejpam-5592	8	2	findings	finding	NOUN
ejpam-5592	8	3	presented	present	VERB
ejpam-5592	8	4	in	in	ADP
ejpam-5592	8	5	this	this	DET
ejpam-5592	8	6	work	work	NOUN
ejpam-5592	8	7	are	be	AUX
ejpam-5592	8	8	expected	expect	VERB
ejpam-5592	8	9	to	to	PART
ejpam-5592	8	10	stimulate	stimulate	VERB
ejpam-5592	8	11	further	further	ADJ
ejpam-5592	8	12	research	research	NOUN
ejpam-5592	8	13	on	on	ADP
ejpam-5592	8	14	inequalities	inequality	NOUN
ejpam-5592	8	15	and	and	CCONJ
ejpam-5592	8	16	fractional	fractional	ADJ
ejpam-5592	8	17	differential	differential	ADJ
ejpam-5592	8	18	equations	equation	NOUN
ejpam-5592	8	19	related	relate	VERB
ejpam-5592	8	20	to	to	ADP
ejpam-5592	8	21	atangana	atangana	PROPN
ejpam-5592	8	22	-	-	PUNCT
ejpam-5592	8	23	baleanu	baleanu	ADJ
ejpam-5592	8	24	fractional	fractional	ADJ
ejpam-5592	8	25	calculus	calculus	NOUN
ejpam-5592	8	26	with	with	ADP
ejpam-5592	8	27	respect	respect	NOUN
ejpam-5592	8	28	to	to	ADP
ejpam-5592	8	29	increasing	increase	VERB
ejpam-5592	8	30	functions	function	NOUN
ejpam-5592	8	31	.	.	PUNCT
ejpam-5592	9	1	concrete	concrete	ADJ
ejpam-5592	9	2	examples	example	NOUN
ejpam-5592	9	3	are	be	AUX
ejpam-5592	9	4	provided	provide	VERB
ejpam-5592	9	5	to	to	PART
ejpam-5592	9	6	illustrate	illustrate	VERB
ejpam-5592	9	7	the	the	DET
ejpam-5592	9	8	practical	practical	ADJ
ejpam-5592	9	9	applications	application	NOUN
ejpam-5592	9	10	of	of	ADP
ejpam-5592	9	11	our	our	PRON
ejpam-5592	9	12	results	result	NOUN
ejpam-5592	9	13	.	.	PUNCT
ejpam-5592	10	1	2020	2020	NUM
ejpam-5592	10	2	mathematics	mathematic	NOUN
ejpam-5592	10	3	subject	subject	NOUN
ejpam-5592	10	4	classifications	classification	NOUN
ejpam-5592	10	5	:	:	PUNCT
ejpam-5592	10	6	74h10	74h10	NUM
ejpam-5592	10	7	,	,	PUNCT
ejpam-5592	10	8	54h25	54h25	NUM
ejpam-5592	10	9	,	,	PUNCT
ejpam-5592	10	10	34a08	34a08	NUM
ejpam-5592	10	11	,	,	PUNCT
ejpam-5592	10	12	34a12	34a12	NUM
ejpam-5592	10	13	key	key	ADJ
ejpam-5592	10	14	words	word	NOUN
ejpam-5592	10	15	and	and	CCONJ
ejpam-5592	10	16	phrases	phrase	NOUN
ejpam-5592	10	17	:	:	PUNCT
ejpam-5592	10	18	fractional	fractional	ADJ
ejpam-5592	10	19	derivatives	derivative	NOUN
ejpam-5592	10	20	,	,	PUNCT
ejpam-5592	10	21	variable	variable	ADJ
ejpam-5592	10	22	order	order	NOUN
ejpam-5592	10	23	derivatives	derivative	NOUN
ejpam-5592	10	24	,	,	PUNCT
ejpam-5592	10	25	fixed	fix	VERB
ejpam-5592	10	26	point	point	NOUN
ejpam-5592	10	27	techniques	technique	NOUN
ejpam-5592	10	28	,	,	PUNCT
ejpam-5592	10	29	existence	existence	NOUN
ejpam-5592	10	30	results	result	NOUN
ejpam-5592	10	31	,	,	PUNCT
ejpam-5592	10	32	differential	differential	ADJ
ejpam-5592	10	33	equations	equation	NOUN
ejpam-5592	10	34	1	1	NUM
ejpam-5592	10	35	.	.	PUNCT
ejpam-5592	10	36	introduction	introduction	NOUN
ejpam-5592	10	37	for	for	ADP
ejpam-5592	10	38	a	a	DET
ejpam-5592	10	39	better	well	ADJ
ejpam-5592	10	40	explanation	explanation	NOUN
ejpam-5592	10	41	of	of	ADP
ejpam-5592	10	42	chaotic	chaotic	ADJ
ejpam-5592	10	43	complex	complex	ADJ
ejpam-5592	10	44	systems	system	NOUN
ejpam-5592	10	45	,	,	PUNCT
ejpam-5592	10	46	fractional	fractional	ADJ
ejpam-5592	10	47	calculus	calculus	NOUN
ejpam-5592	10	48	has	have	AUX
ejpam-5592	10	49	drawn	draw	VERB
ejpam-5592	10	50	the	the	DET
ejpam-5592	10	51	attention	attention	NOUN
ejpam-5592	10	52	of	of	ADP
ejpam-5592	10	53	numerous	numerous	ADJ
ejpam-5592	10	54	authors	author	NOUN
ejpam-5592	10	55	in	in	ADP
ejpam-5592	10	56	a	a	DET
ejpam-5592	10	57	variety	variety	NOUN
ejpam-5592	10	58	of	of	ADP
ejpam-5592	10	59	fields	field	NOUN
ejpam-5592	10	60	over	over	ADP
ejpam-5592	10	61	the	the	DET
ejpam-5592	10	62	past	past	ADJ
ejpam-5592	10	63	three	three	NUM
ejpam-5592	10	64	decades	decade	NOUN
ejpam-5592	10	65	.	.	PUNCT
ejpam-5592	11	1	these	these	DET
ejpam-5592	11	2	fields	field	NOUN
ejpam-5592	11	3	have	have	VERB
ejpam-5592	11	4	many	many	ADJ
ejpam-5592	11	5	applications	application	NOUN
ejpam-5592	11	6	in	in	ADP
ejpam-5592	11	7	qualitative	qualitative	ADJ
ejpam-5592	11	8	theories	theory	NOUN
ejpam-5592	11	9	,	,	PUNCT
ejpam-5592	11	10	electrical	electrical	ADJ
ejpam-5592	11	11	networks	network	NOUN
ejpam-5592	11	12	,	,	PUNCT
ejpam-5592	11	13	etc	etc	X
ejpam-5592	11	14	.	.	X
ejpam-5592	11	15	for	for	ADP
ejpam-5592	11	16	more	more	ADJ
ejpam-5592	11	17	information	information	NOUN
ejpam-5592	11	18	,	,	PUNCT
ejpam-5592	11	19	see	see	VERB
ejpam-5592	11	20	[	[	X
ejpam-5592	11	21	16	16	NUM
ejpam-5592	11	22	,	,	PUNCT
ejpam-5592	11	23	18	18	NUM
ejpam-5592	11	24	,	,	PUNCT
ejpam-5592	11	25	22	22	NUM
ejpam-5592	11	26	]	]	PUNCT
ejpam-5592	11	27	.	.	PUNCT
ejpam-5592	12	1	the	the	DET
ejpam-5592	12	2	reason	reason	NOUN
ejpam-5592	12	3	why	why	SCONJ
ejpam-5592	12	4	this	this	DET
ejpam-5592	12	5	trend	trend	NOUN
ejpam-5592	12	6	has	have	VERB
ejpam-5592	12	7	so	so	ADV
ejpam-5592	12	8	many	many	ADJ
ejpam-5592	12	9	readers	reader	NOUN
ejpam-5592	12	10	is	be	AUX
ejpam-5592	12	11	that	that	SCONJ
ejpam-5592	12	12	the	the	DET
ejpam-5592	12	13	fractional	fractional	ADJ
ejpam-5592	12	14	differentiation	differentiation	NOUN
ejpam-5592	12	15	of	of	ADP
ejpam-5592	12	16	the	the	DET
ejpam-5592	12	17	function	function	NOUN
ejpam-5592	12	18	produces	produce	VERB
ejpam-5592	12	19	its	its	PRON
ejpam-5592	12	20	complete	complete	ADJ
ejpam-5592	12	21	spectrum	spectrum	NOUN
ejpam-5592	12	22	which	which	PRON
ejpam-5592	12	23	includes	include	VERB
ejpam-5592	12	24	∗corresponding	∗corresponde	VERB
ejpam-5592	12	25	author	author	NOUN
ejpam-5592	12	26	.	.	PUNCT
ejpam-5592	13	1	doi	doi	NOUN
ejpam-5592	13	2	:	:	PUNCT
ejpam-5592	13	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5592	https://doi.org/10.29020/nybg.ejpam.v17i4.5592	PRON
ejpam-5592	13	4	email	email	NOUN
ejpam-5592	13	5	addresses	address	NOUN
ejpam-5592	13	6	:	:	PUNCT
ejpam-5592	13	7	h.abdelwareth@qu.edu.sa	h.abdelwareth@qu.edu.sa	PROPN
ejpam-5592	13	8	(	(	PUNCT
ejpam-5592	13	9	h.a	h.a	PROPN
ejpam-5592	13	10	.	.	PROPN
ejpam-5592	13	11	hammad	hammad	PROPN
ejpam-5592	13	12	)	)	PUNCT
ejpam-5592	13	13	,	,	PUNCT
ejpam-5592	13	14	manuel.delasen@ehu.eus	manuel.delasen@ehu.eus	PROPN
ejpam-5592	13	15	(	(	PUNCT
ejpam-5592	13	16	m.	m.	NOUN
ejpam-5592	13	17	de	de	X
ejpam-5592	13	18	la	la	X
ejpam-5592	13	19	sen	sen	PROPN
ejpam-5592	13	20	)	)	PUNCT
ejpam-5592	13	21	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5592	13	22	3687	3687	NUM
ejpam-5592	13	23	copyright	copyright	NOUN
ejpam-5592	13	24	:	:	PUNCT
ejpam-5592	13	25	©	©	PROPN
ejpam-5592	13	26	2024	2024	NUM
ejpam-5592	13	27	the	the	DET
ejpam-5592	13	28	author(s	author(s	NOUN
ejpam-5592	13	29	)	)	PUNCT
ejpam-5592	13	30	.	.	PUNCT
ejpam-5592	14	1	(	(	PUNCT
ejpam-5592	14	2	cc	cc	NOUN
ejpam-5592	14	3	by	by	ADP
ejpam-5592	14	4	-	-	PUNCT
ejpam-5592	14	5	nc	nc	PROPN
ejpam-5592	14	6	4.0	4.0	NUM
ejpam-5592	14	7	)	)	PUNCT
ejpam-5592	14	8	h.a	h.a	PROPN
ejpam-5592	14	9	.	.	PROPN
ejpam-5592	14	10	hammad	hammad	PROPN
ejpam-5592	14	11	,	,	PUNCT
ejpam-5592	14	12	m.	m.	PROPN
ejpam-5592	14	13	de	de	X
ejpam-5592	14	14	la	la	PROPN
ejpam-5592	14	15	sen	sen	PROPN
ejpam-5592	14	16	/	/	SYM
ejpam-5592	14	17	eur	eur	PROPN
ejpam-5592	14	18	.	.	PUNCT
ejpam-5592	15	1	j.	j.	PROPN
ejpam-5592	15	2	pure	pure	PROPN
ejpam-5592	15	3	appl	appl	PROPN
ejpam-5592	15	4	.	.	PROPN
ejpam-5592	15	5	math	math	PROPN
ejpam-5592	15	6	,	,	PUNCT
ejpam-5592	15	7	17	17	NUM
ejpam-5592	15	8	(	(	PUNCT
ejpam-5592	15	9	4	4	NUM
ejpam-5592	15	10	)	)	PUNCT
ejpam-5592	15	11	(	(	PUNCT
ejpam-5592	15	12	2024	2024	NUM
ejpam-5592	15	13	)	)	PUNCT
ejpam-5592	15	14	,	,	PUNCT
ejpam-5592	15	15	3687	3687	NUM
ejpam-5592	15	16	-	-	SYM
ejpam-5592	15	17	3707	3707	NUM
ejpam-5592	15	18	3688	3688	NUM
ejpam-5592	15	19	the	the	DET
ejpam-5592	15	20	corresponding	corresponding	ADJ
ejpam-5592	15	21	integer	integer	NOUN
ejpam-5592	15	22	-	-	PUNCT
ejpam-5592	15	23	order	order	NOUN
ejpam-5592	15	24	counterpart	counterpart	NOUN
ejpam-5592	15	25	as	as	ADP
ejpam-5592	15	26	a	a	DET
ejpam-5592	15	27	special	special	ADJ
ejpam-5592	15	28	case	case	NOUN
ejpam-5592	15	29	.	.	PUNCT
ejpam-5592	16	1	in	in	ADP
ejpam-5592	16	2	addition	addition	NOUN
ejpam-5592	16	3	,	,	PUNCT
ejpam-5592	16	4	the	the	DET
ejpam-5592	16	5	use	use	NOUN
ejpam-5592	16	6	of	of	ADP
ejpam-5592	16	7	these	these	DET
ejpam-5592	16	8	equations	equation	NOUN
ejpam-5592	16	9	and	and	CCONJ
ejpam-5592	16	10	formulas	formula	NOUN
ejpam-5592	16	11	in	in	ADP
ejpam-5592	16	12	its	its	PRON
ejpam-5592	16	13	mathematical	mathematical	ADJ
ejpam-5592	16	14	models	model	NOUN
ejpam-5592	16	15	contributes	contribute	VERB
ejpam-5592	16	16	fundamentally	fundamentally	ADV
ejpam-5592	16	17	to	to	ADP
ejpam-5592	16	18	real	real	ADJ
ejpam-5592	16	19	-	-	PUNCT
ejpam-5592	16	20	world	world	NOUN
ejpam-5592	16	21	applications	application	NOUN
ejpam-5592	16	22	because	because	SCONJ
ejpam-5592	16	23	it	it	PRON
ejpam-5592	16	24	generates	generate	VERB
ejpam-5592	16	25	full	full	ADJ
ejpam-5592	16	26	dynamics	dynamic	NOUN
ejpam-5592	16	27	of	of	ADP
ejpam-5592	16	28	the	the	DET
ejpam-5592	16	29	topic	topic	NOUN
ejpam-5592	16	30	under	under	ADP
ejpam-5592	16	31	study	study	NOUN
ejpam-5592	16	32	and	and	CCONJ
ejpam-5592	16	33	benefits	benefit	NOUN
ejpam-5592	16	34	from	from	ADP
ejpam-5592	16	35	higher	high	ADJ
ejpam-5592	16	36	degrees	degree	NOUN
ejpam-5592	16	37	of	of	ADP
ejpam-5592	16	38	freedom	freedom	NOUN
ejpam-5592	16	39	.	.	PUNCT
ejpam-5592	17	1	regarding	regard	VERB
ejpam-5592	17	2	applications	application	NOUN
ejpam-5592	17	3	of	of	ADP
ejpam-5592	17	4	viscoelasticity	viscoelasticity	NOUN
ejpam-5592	17	5	,	,	PUNCT
ejpam-5592	17	6	physics	physics	NOUN
ejpam-5592	17	7	,	,	PUNCT
ejpam-5592	17	8	and	and	CCONJ
ejpam-5592	17	9	dynamics	dynamic	NOUN
ejpam-5592	17	10	,	,	PUNCT
ejpam-5592	17	11	reputable	reputable	ADJ
ejpam-5592	17	12	results	result	NOUN
ejpam-5592	17	13	can	can	AUX
ejpam-5592	17	14	be	be	AUX
ejpam-5592	17	15	found	find	VERB
ejpam-5592	17	16	in	in	ADP
ejpam-5592	17	17	[	[	X
ejpam-5592	17	18	1	1	NUM
ejpam-5592	17	19	,	,	PUNCT
ejpam-5592	17	20	7	7	NUM
ejpam-5592	17	21	,	,	PUNCT
ejpam-5592	17	22	13	13	NUM
ejpam-5592	17	23	,	,	PUNCT
ejpam-5592	17	24	21	21	NUM
ejpam-5592	17	25	]	]	PUNCT
ejpam-5592	17	26	.	.	PUNCT
ejpam-5592	18	1	some	some	DET
ejpam-5592	18	2	scientists	scientist	NOUN
ejpam-5592	18	3	and	and	CCONJ
ejpam-5592	18	4	engineers	engineer	NOUN
ejpam-5592	18	5	have	have	AUX
ejpam-5592	18	6	adapted	adapt	VERB
ejpam-5592	18	7	fractional	fractional	ADJ
ejpam-5592	18	8	calculus	calculus	NOUN
ejpam-5592	18	9	to	to	PART
ejpam-5592	18	10	singular	singular	NOUN
ejpam-5592	18	11	and	and	CCONJ
ejpam-5592	18	12	nonsingular	nonsingular	ADJ
ejpam-5592	18	13	kernels	kernel	NOUN
ejpam-5592	18	14	in	in	ADP
ejpam-5592	18	15	order	order	NOUN
ejpam-5592	18	16	to	to	PART
ejpam-5592	18	17	recognize	recognize	VERB
ejpam-5592	18	18	and	and	CCONJ
ejpam-5592	18	19	explain	explain	VERB
ejpam-5592	18	20	the	the	DET
ejpam-5592	18	21	genuine	genuine	ADJ
ejpam-5592	18	22	phenomena	phenomenon	NOUN
ejpam-5592	18	23	in	in	ADP
ejpam-5592	18	24	their	their	PRON
ejpam-5592	18	25	respective	respective	ADJ
ejpam-5592	18	26	domains	domain	NOUN
ejpam-5592	18	27	.	.	PUNCT
ejpam-5592	19	1	a	a	DET
ejpam-5592	19	2	novel	novel	ADJ
ejpam-5592	19	3	definition	definition	NOUN
ejpam-5592	19	4	of	of	ADP
ejpam-5592	19	5	a	a	DET
ejpam-5592	19	6	fractional	fractional	ADJ
ejpam-5592	19	7	operator	operator	NOUN
ejpam-5592	19	8	with	with	ADP
ejpam-5592	19	9	an	an	DET
ejpam-5592	19	10	exponential	exponential	ADJ
ejpam-5592	19	11	kernel	kernel	NOUN
ejpam-5592	19	12	was	be	AUX
ejpam-5592	19	13	studied	study	VERB
ejpam-5592	19	14	by	by	ADP
ejpam-5592	19	15	caputo	caputo	PROPN
ejpam-5592	19	16	and	and	CCONJ
ejpam-5592	19	17	fabrizio	fabrizio	PROPN
ejpam-5592	19	18	[	[	X
ejpam-5592	19	19	8	8	NUM
ejpam-5592	19	20	]	]	PUNCT
ejpam-5592	19	21	.	.	PUNCT
ejpam-5592	20	1	the	the	DET
ejpam-5592	20	2	atangana	atangana	PROPN
ejpam-5592	20	3	-	-	PUNCT
ejpam-5592	20	4	baleanu	baleanu	PROPN
ejpam-5592	20	5	(	(	PUNCT
ejpam-5592	20	6	ab	ab	NOUN
ejpam-5592	20	7	)	)	PUNCT
ejpam-5592	20	8	fractional	fractional	ADJ
ejpam-5592	20	9	operator	operator	NOUN
ejpam-5592	20	10	was	be	AUX
ejpam-5592	20	11	introduced	introduce	VERB
ejpam-5592	20	12	by	by	ADP
ejpam-5592	20	13	atangana	atangana	NOUN
ejpam-5592	20	14	and	and	CCONJ
ejpam-5592	20	15	baleanu	baleanu	NOUN
ejpam-5592	21	1	[	[	X
ejpam-5592	21	2	5	5	NUM
ejpam-5592	21	3	]	]	PUNCT
ejpam-5592	21	4	and	and	CCONJ
ejpam-5592	21	5	has	have	VERB
ejpam-5592	21	6	a	a	DET
ejpam-5592	21	7	fresh	fresh	ADJ
ejpam-5592	21	8	and	and	CCONJ
ejpam-5592	21	9	intriguing	intriguing	ADJ
ejpam-5592	21	10	definition	definition	NOUN
ejpam-5592	21	11	of	of	ADP
ejpam-5592	21	12	a	a	DET
ejpam-5592	21	13	mittag	mittag	ADJ
ejpam-5592	21	14	-	-	PUNCT
ejpam-5592	21	15	leffler	leffler	NOUN
ejpam-5592	21	16	(	(	PUNCT
ejpam-5592	21	17	ml	ml	NOUN
ejpam-5592	21	18	)	)	PUNCT
ejpam-5592	21	19	kernel	kernel	NOUN
ejpam-5592	21	20	.	.	PUNCT
ejpam-5592	22	1	the	the	DET
ejpam-5592	22	2	ab	ab	PROPN
ejpam-5592	22	3	fractional	fractional	ADJ
ejpam-5592	22	4	operator	operator	NOUN
ejpam-5592	22	5	was	be	AUX
ejpam-5592	22	6	extended	extend	VERB
ejpam-5592	22	7	to	to	ADP
ejpam-5592	22	8	higher	high	ADJ
ejpam-5592	22	9	arbitrary	arbitrary	ADJ
ejpam-5592	22	10	orders	order	NOUN
ejpam-5592	22	11	by	by	ADP
ejpam-5592	22	12	abdeljawad	abdeljawad	NOUN
ejpam-5592	22	13	[	[	X
ejpam-5592	22	14	2	2	NUM
ejpam-5592	22	15	]	]	PUNCT
ejpam-5592	22	16	.	.	PUNCT
ejpam-5592	23	1	following	follow	VERB
ejpam-5592	23	2	that	that	PRON
ejpam-5592	23	3	,	,	PUNCT
ejpam-5592	23	4	a	a	DET
ejpam-5592	23	5	number	number	NOUN
ejpam-5592	23	6	of	of	ADP
ejpam-5592	23	7	researchers	researcher	NOUN
ejpam-5592	23	8	examined	examine	VERB
ejpam-5592	23	9	the	the	DET
ejpam-5592	23	10	qualitative	qualitative	ADJ
ejpam-5592	23	11	characteristics	characteristic	NOUN
ejpam-5592	23	12	and	and	CCONJ
ejpam-5592	23	13	approximate	approximate	ADJ
ejpam-5592	23	14	solutions	solution	NOUN
ejpam-5592	23	15	of	of	ADP
ejpam-5592	23	16	fractional	fractional	ADJ
ejpam-5592	23	17	differential	differential	ADJ
ejpam-5592	23	18	equations	equation	NOUN
ejpam-5592	23	19	(	(	PUNCT
ejpam-5592	23	20	fdes	fde	NOUN
ejpam-5592	23	21	)	)	PUNCT
ejpam-5592	23	22	utilizing	utilize	VERB
ejpam-5592	23	23	atangana	atangana	PROPN
ejpam-5592	23	24	-	-	PUNCT
ejpam-5592	23	25	baleanu	baleanu	PROPN
ejpam-5592	23	26	-	-	PUNCT
ejpam-5592	23	27	caputo	caputo	PROPN
ejpam-5592	23	28	(	(	PUNCT
ejpam-5592	23	29	abc	abc	PROPN
ejpam-5592	23	30	)	)	PUNCT
ejpam-5592	23	31	fractional	fractional	ADJ
ejpam-5592	23	32	operators	operator	NOUN
ejpam-5592	23	33	,	,	PUNCT
ejpam-5592	23	34	caputo	caputo	PROPN
ejpam-5592	23	35	-	-	PUNCT
ejpam-5592	23	36	fabrizio	fabrizio	PROPN
ejpam-5592	23	37	derivatives	derivative	NOUN
ejpam-5592	23	38	,	,	PUNCT
ejpam-5592	23	39	and	and	CCONJ
ejpam-5592	23	40	others	other	NOUN
ejpam-5592	23	41	applied	apply	VERB
ejpam-5592	23	42	the	the	DET
ejpam-5592	23	43	technique	technique	NOUN
ejpam-5592	23	44	of	of	ADP
ejpam-5592	23	45	fp	fp	PROPN
ejpam-5592	23	46	theory	theory	NOUN
ejpam-5592	23	47	to	to	PART
ejpam-5592	23	48	find	find	VERB
ejpam-5592	23	49	the	the	DET
ejpam-5592	23	50	existence	existence	NOUN
ejpam-5592	23	51	solutions	solution	NOUN
ejpam-5592	23	52	to	to	ADP
ejpam-5592	23	53	theses	thesis	NOUN
ejpam-5592	23	54	operators	operator	NOUN
ejpam-5592	23	55	;	;	PUNCT
ejpam-5592	23	56	for	for	ADP
ejpam-5592	23	57	more	more	ADJ
ejpam-5592	23	58	information	information	NOUN
ejpam-5592	23	59	,	,	PUNCT
ejpam-5592	23	60	see	see	VERB
ejpam-5592	23	61	[	[	X
ejpam-5592	23	62	6	6	NUM
ejpam-5592	23	63	,	,	PUNCT
ejpam-5592	23	64	9	9	NUM
ejpam-5592	23	65	,	,	PUNCT
ejpam-5592	23	66	10	10	NUM
ejpam-5592	23	67	,	,	PUNCT
ejpam-5592	23	68	12	12	NUM
ejpam-5592	23	69	,	,	PUNCT
ejpam-5592	23	70	14	14	NUM
ejpam-5592	23	71	,	,	PUNCT
ejpam-5592	23	72	15	15	NUM
ejpam-5592	23	73	,	,	PUNCT
ejpam-5592	23	74	23–26	23–26	NUM
ejpam-5592	23	75	,	,	PUNCT
ejpam-5592	23	76	28	28	NUM
ejpam-5592	23	77	]	]	PUNCT
ejpam-5592	23	78	.	.	PUNCT
ejpam-5592	24	1	recently	recently	ADV
ejpam-5592	24	2	,	,	PUNCT
ejpam-5592	24	3	a	a	DET
ejpam-5592	24	4	fractional	fractional	ADJ
ejpam-5592	24	5	derivative	derivative	NOUN
ejpam-5592	24	6	of	of	ADP
ejpam-5592	24	7	a	a	DET
ejpam-5592	24	8	function	function	NOUN
ejpam-5592	24	9	with	with	ADP
ejpam-5592	24	10	respect	respect	NOUN
ejpam-5592	24	11	to	to	ADP
ejpam-5592	24	12	(	(	PUNCT
ejpam-5592	24	13	w.r.t	w.r.t	NOUN
ejpam-5592	24	14	.	.	PUNCT
ejpam-5592	24	15	)	)	PUNCT
ejpam-5592	25	1	another	another	DET
ejpam-5592	25	2	function	function	NOUN
ejpam-5592	25	3	with	with	ADP
ejpam-5592	25	4	a	a	DET
ejpam-5592	25	5	ml	ml	ADJ
ejpam-5592	25	6	kernel	kernel	PROPN
ejpam-5592	25	7	was	be	AUX
ejpam-5592	25	8	proposed	propose	VERB
ejpam-5592	25	9	by	by	ADP
ejpam-5592	25	10	fernandez	fernandez	PROPN
ejpam-5592	25	11	and	and	CCONJ
ejpam-5592	25	12	baleanu	baleanu	NOUN
ejpam-5592	26	1	[	[	X
ejpam-5592	26	2	11	11	NUM
ejpam-5592	26	3	]	]	PUNCT
ejpam-5592	26	4	,	,	PUNCT
ejpam-5592	26	5	and	and	CCONJ
ejpam-5592	26	6	it	it	PRON
ejpam-5592	26	7	is	be	AUX
ejpam-5592	26	8	actually	actually	ADV
ejpam-5592	26	9	thought	think	VERB
ejpam-5592	26	10	of	of	ADP
ejpam-5592	26	11	as	as	ADP
ejpam-5592	26	12	a	a	DET
ejpam-5592	26	13	generalized	generalized	ADJ
ejpam-5592	26	14	ab	ab	ADJ
ejpam-5592	26	15	fractional	fractional	ADJ
ejpam-5592	26	16	operator	operator	NOUN
ejpam-5592	26	17	.	.	PUNCT
ejpam-5592	27	1	by	by	ADP
ejpam-5592	27	2	establishing	establish	VERB
ejpam-5592	27	3	the	the	DET
ejpam-5592	27	4	appropriate	appropriate	ADJ
ejpam-5592	27	5	ab	ab	ADJ
ejpam-5592	27	6	-	-	PUNCT
ejpam-5592	27	7	fractional	fractional	ADJ
ejpam-5592	27	8	integral	integral	NOUN
ejpam-5592	27	9	of	of	ADP
ejpam-5592	27	10	a	a	DET
ejpam-5592	27	11	function	function	NOUN
ejpam-5592	27	12	w.r.t	w.r.t	NOUN
ejpam-5592	27	13	.	.	PUNCT
ejpam-5592	28	1	another	another	DET
ejpam-5592	28	2	function	function	NOUN
ejpam-5592	28	3	,	,	PUNCT
ejpam-5592	28	4	authors	author	NOUN
ejpam-5592	28	5	[	[	X
ejpam-5592	28	6	20	20	NUM
ejpam-5592	28	7	]	]	PUNCT
ejpam-5592	28	8	established	establish	VERB
ejpam-5592	28	9	a	a	DET
ejpam-5592	28	10	link	link	NOUN
ejpam-5592	28	11	between	between	ADP
ejpam-5592	28	12	the	the	DET
ejpam-5592	28	13	ab	ab	PROPN
ejpam-5592	28	14	fractional	fractional	ADJ
ejpam-5592	28	15	operator	operator	NOUN
ejpam-5592	28	16	and	and	CCONJ
ejpam-5592	28	17	the	the	DET
ejpam-5592	28	18	riemann	riemann	PROPN
ejpam-5592	28	19	-	-	PUNCT
ejpam-5592	28	20	liouville	liouville	PROPN
ejpam-5592	28	21	(	(	PUNCT
ejpam-5592	28	22	rl	rl	NOUN
ejpam-5592	28	23	)	)	PUNCT
ejpam-5592	28	24	fractional	fractional	ADJ
ejpam-5592	28	25	integral	integral	ADJ
ejpam-5592	28	26	w.r.t	w.r.t	NOUN
ejpam-5592	28	27	.	.	PUNCT
ejpam-5592	29	1	another	another	DET
ejpam-5592	29	2	function	function	NOUN
ejpam-5592	29	3	.	.	PUNCT
ejpam-5592	30	1	following	follow	VERB
ejpam-5592	30	2	that	that	PRON
ejpam-5592	30	3	,	,	PUNCT
ejpam-5592	30	4	kashuri	kashuri	PROPN
ejpam-5592	30	5	[	[	X
ejpam-5592	30	6	17	17	NUM
ejpam-5592	30	7	]	]	PUNCT
ejpam-5592	30	8	introduced	introduce	VERB
ejpam-5592	30	9	a	a	DET
ejpam-5592	30	10	fractional	fractional	ADJ
ejpam-5592	30	11	integral	integral	ADJ
ejpam-5592	30	12	operator	operator	NOUN
ejpam-5592	30	13	known	know	VERB
ejpam-5592	30	14	as	as	ADP
ejpam-5592	30	15	the	the	DET
ejpam-5592	30	16	atangana	atangana	PROPN
ejpam-5592	30	17	-	-	PUNCT
ejpam-5592	30	18	baleanu	baleanu	PROPN
ejpam-5592	30	19	-	-	PUNCT
ejpam-5592	30	20	kashuri	kashuri	NOUN
ejpam-5592	30	21	(	(	PUNCT
ejpam-5592	30	22	abk	abk	PROPN
ejpam-5592	30	23	)	)	PUNCT
ejpam-5592	30	24	fractional	fractional	ADJ
ejpam-5592	30	25	integral	integral	ADJ
ejpam-5592	30	26	.	.	PUNCT
ejpam-5592	31	1	inspired	inspire	VERB
ejpam-5592	31	2	of	of	ADP
ejpam-5592	31	3	the	the	DET
ejpam-5592	31	4	above	above	ADJ
ejpam-5592	31	5	works	work	NOUN
ejpam-5592	31	6	,	,	PUNCT
ejpam-5592	31	7	in	in	ADP
ejpam-5592	31	8	this	this	DET
ejpam-5592	31	9	article	article	NOUN
ejpam-5592	31	10	,	,	PUNCT
ejpam-5592	31	11	we	we	PRON
ejpam-5592	31	12	increase	increase	VERB
ejpam-5592	31	13	the	the	DET
ejpam-5592	31	14	fractional	fractional	ADJ
ejpam-5592	31	15	derivatives	derivative	NOUN
ejpam-5592	31	16	of	of	ADP
ejpam-5592	31	17	abc	abc	PROPN
ejpam-5592	31	18	and	and	CCONJ
ejpam-5592	31	19	rab	rab	PROPN
ejpam-5592	31	20	with	with	ADP
ejpam-5592	31	21	respect	respect	NOUN
ejpam-5592	31	22	to	to	ADP
ejpam-5592	31	23	an	an	DET
ejpam-5592	31	24	increasing	increase	VERB
ejpam-5592	31	25	function	function	NOUN
ejpam-5592	31	26	from	from	ADP
ejpam-5592	31	27	a	a	DET
ejpam-5592	31	28	fractional	fractional	ADJ
ejpam-5592	31	29	order	order	NOUN
ejpam-5592	31	30	ϖ	ϖ	X
ejpam-5592	31	31	∈	∈	PROPN
ejpam-5592	31	32	(	(	PUNCT
ejpam-5592	31	33	0	0	NUM
ejpam-5592	31	34	,	,	PUNCT
ejpam-5592	31	35	1	1	NUM
ejpam-5592	31	36	]	]	PUNCT
ejpam-5592	31	37	to	to	ADP
ejpam-5592	31	38	an	an	DET
ejpam-5592	31	39	arbitrary	arbitrary	ADJ
ejpam-5592	31	40	variable	variable	ADJ
ejpam-5592	31	41	order	order	NOUN
ejpam-5592	31	42	ϖ(τ	ϖ(τ	NOUN
ejpam-5592	31	43	)	)	PUNCT
ejpam-5592	31	44	∈	∈	PROPN
ejpam-5592	31	45	(	(	PUNCT
ejpam-5592	31	46	k	k	NOUN
ejpam-5592	31	47	,	,	PUNCT
ejpam-5592	31	48	k+	k+	NOUN
ejpam-5592	31	49	1	1	NUM
ejpam-5592	31	50	]	]	PUNCT
ejpam-5592	31	51	,	,	PUNCT
ejpam-5592	31	52	k	k	X
ejpam-5592	31	53	≥	≥	PROPN
ejpam-5592	31	54	0	0	NUM
ejpam-5592	31	55	.	.	PUNCT
ejpam-5592	32	1	several	several	ADJ
ejpam-5592	32	2	characteristics	characteristic	NOUN
ejpam-5592	32	3	and	and	CCONJ
ejpam-5592	32	4	uses	use	NOUN
ejpam-5592	32	5	of	of	ADP
ejpam-5592	32	6	these	these	DET
ejpam-5592	32	7	concepts	concept	NOUN
ejpam-5592	32	8	are	be	AUX
ejpam-5592	32	9	also	also	ADV
ejpam-5592	32	10	studied	study	VERB
ejpam-5592	32	11	.	.	PUNCT
ejpam-5592	33	1	further	far	ADV
ejpam-5592	33	2	,	,	PUNCT
ejpam-5592	33	3	in	in	ADP
ejpam-5592	33	4	the	the	DET
ejpam-5592	33	5	framework	framework	NOUN
ejpam-5592	33	6	of	of	ADP
ejpam-5592	33	7	the	the	DET
ejpam-5592	33	8	ab	ab	PROPN
ejpam-5592	33	9	fractional	fractional	ADJ
ejpam-5592	33	10	integrals	integral	NOUN
ejpam-5592	33	11	,	,	PUNCT
ejpam-5592	33	12	a	a	DET
ejpam-5592	33	13	brand	brand	NOUN
ejpam-5592	33	14	-	-	PUNCT
ejpam-5592	33	15	new	new	ADJ
ejpam-5592	33	16	generalized	generalized	ADJ
ejpam-5592	33	17	gronwall	gronwall	ADJ
ejpam-5592	33	18	inequality	inequality	NOUN
ejpam-5592	33	19	is	be	AUX
ejpam-5592	33	20	also	also	ADV
ejpam-5592	33	21	demonstrated	demonstrate	VERB
ejpam-5592	33	22	.	.	PUNCT
ejpam-5592	34	1	moreover	moreover	ADV
ejpam-5592	34	2	,	,	PUNCT
ejpam-5592	34	3	picard	picard	PROPN
ejpam-5592	34	4	’s	’s	PART
ejpam-5592	34	5	iterative	iterative	NOUN
ejpam-5592	34	6	approach	approach	NOUN
ejpam-5592	34	7	is	be	AUX
ejpam-5592	34	8	used	use	VERB
ejpam-5592	34	9	to	to	PART
ejpam-5592	34	10	establish	establish	VERB
ejpam-5592	34	11	the	the	DET
ejpam-5592	34	12	existence	existence	NOUN
ejpam-5592	34	13	and	and	CCONJ
ejpam-5592	34	14	uniqueness	uniqueness	NOUN
ejpam-5592	34	15	results	result	NOUN
ejpam-5592	34	16	of	of	ADP
ejpam-5592	34	17	a	a	DET
ejpam-5592	34	18	highervariable	highervariable	ADJ
ejpam-5592	34	19	order	order	NOUN
ejpam-5592	34	20	abc	abc	PROPN
ejpam-5592	34	21	fractional	fractional	ADJ
ejpam-5592	34	22	issue	issue	NOUN
ejpam-5592	34	23	under	under	ADP
ejpam-5592	34	24	initial	initial	ADJ
ejpam-5592	34	25	boundary	boundary	ADJ
ejpam-5592	34	26	constraints	constraint	NOUN
ejpam-5592	34	27	our	our	PRON
ejpam-5592	34	28	paper	paper	NOUN
ejpam-5592	34	29	extends	extend	VERB
ejpam-5592	34	30	and	and	CCONJ
ejpam-5592	34	31	generalizes	generalize	VERB
ejpam-5592	34	32	the	the	DET
ejpam-5592	34	33	results	result	NOUN
ejpam-5592	34	34	of	of	ADP
ejpam-5592	34	35	[	[	X
ejpam-5592	34	36	3	3	NUM
ejpam-5592	34	37	]	]	PUNCT
ejpam-5592	34	38	.	.	PUNCT
ejpam-5592	35	1	finally	finally	ADV
ejpam-5592	35	2	,	,	PUNCT
ejpam-5592	35	3	illustrative	illustrative	ADJ
ejpam-5592	35	4	examples	example	NOUN
ejpam-5592	35	5	are	be	AUX
ejpam-5592	35	6	provided	provide	VERB
ejpam-5592	35	7	to	to	PART
ejpam-5592	35	8	support	support	VERB
ejpam-5592	35	9	our	our	PRON
ejpam-5592	35	10	results	result	NOUN
ejpam-5592	35	11	.	.	PUNCT
ejpam-5592	36	1	2	2	X
ejpam-5592	36	2	.	.	X
ejpam-5592	36	3	preliminaries	preliminary	NOUN
ejpam-5592	36	4	this	this	DET
ejpam-5592	36	5	part	part	NOUN
ejpam-5592	36	6	is	be	AUX
ejpam-5592	36	7	devoted	devote	VERB
ejpam-5592	36	8	to	to	PART
ejpam-5592	36	9	present	present	VERB
ejpam-5592	36	10	some	some	DET
ejpam-5592	36	11	crucial	crucial	ADJ
ejpam-5592	36	12	foundational	foundational	ADJ
ejpam-5592	36	13	material	material	NOUN
ejpam-5592	36	14	for	for	ADP
ejpam-5592	36	15	fractional	fractional	ADJ
ejpam-5592	36	16	calculus	calculus	NOUN
ejpam-5592	36	17	.	.	PUNCT
ejpam-5592	37	1	let	let	VERB
ejpam-5592	37	2	us	we	PRON
ejpam-5592	37	3	denote	denote	VERB
ejpam-5592	37	4	by	by	ADP
ejpam-5592	37	5	ck(ℑ,r	ck(ℑ,r	PROPN
ejpam-5592	37	6	)	)	PUNCT
ejpam-5592	37	7	the	the	DET
ejpam-5592	37	8	bs	bs	NOUN
ejpam-5592	37	9	of	of	ADP
ejpam-5592	37	10	all	all	DET
ejpam-5592	37	11	the	the	DET
ejpam-5592	37	12	kth	kth	NOUN
ejpam-5592	37	13	continuously	continuously	ADV
ejpam-5592	37	14	differentiable	differentiable	VERB
ejpam-5592	37	15	functions	function	NOUN
ejpam-5592	37	16	κ	κ	PROPN
ejpam-5592	37	17	equipped	equip	VERB
ejpam-5592	37	18	with	with	ADP
ejpam-5592	37	19	usual	usual	ADJ
ejpam-5592	37	20	norm	norm	NOUN
ejpam-5592	37	21	∥κ∥	∥κ∥	NOUN
ejpam-5592	38	1	=	=	SYM
ejpam-5592	38	2	sup	sup	NOUN
ejpam-5592	38	3	{	{	PUNCT
ejpam-5592	38	4	|κ(r)|	|κ(r)|	NOUN
ejpam-5592	38	5	:	:	PUNCT
ejpam-5592	38	6	r	r	NOUN
ejpam-5592	38	7	∈	∈	PROPN
ejpam-5592	38	8	ℑ	ℑ	NOUN
ejpam-5592	38	9	=	=	PUNCT
ejpam-5592	39	1	[	[	X
ejpam-5592	39	2	κ	κ	X
ejpam-5592	39	3	,	,	PUNCT
ejpam-5592	39	4	ϱ	ϱ	ADP
ejpam-5592	39	5	]	]	PUNCT
ejpam-5592	39	6	}	}	PUNCT
ejpam-5592	39	7	.	.	PUNCT
ejpam-5592	40	1	definition	definition	NOUN
ejpam-5592	40	2	1	1	NUM
ejpam-5592	40	3	.	.	PUNCT
ejpam-5592	41	1	[	[	X
ejpam-5592	41	2	4	4	X
ejpam-5592	41	3	]	]	PUNCT
ejpam-5592	41	4	let	let	VERB
ejpam-5592	41	5	ψ	ψ	X
ejpam-5592	41	6	:	:	PUNCT
ejpam-5592	41	7	ℑ	ℑ	NOUN
ejpam-5592	41	8	→	→	SYM
ejpam-5592	41	9	r	r	NOUN
ejpam-5592	41	10	be	be	AUX
ejpam-5592	41	11	an	an	DET
ejpam-5592	41	12	increasing	increase	VERB
ejpam-5592	41	13	and	and	CCONJ
ejpam-5592	41	14	differentiable	differentiable	ADJ
ejpam-5592	41	15	function	function	NOUN
ejpam-5592	41	16	.	.	PUNCT
ejpam-5592	42	1	for	for	ADP
ejpam-5592	42	2	the	the	DET
ejpam-5592	42	3	integrable	integrable	ADJ
ejpam-5592	42	4	function	function	NOUN
ejpam-5592	42	5	ξ	ξ	PROPN
ejpam-5592	42	6	:	:	PUNCT
ejpam-5592	42	7	ℑ	ℑ	PROPN
ejpam-5592	42	8	→	→	SYM
ejpam-5592	42	9	r	r	NOUN
ejpam-5592	42	10	,	,	PUNCT
ejpam-5592	42	11	the	the	DET
ejpam-5592	42	12	ϖth	ϖth	NOUN
ejpam-5592	42	13	left	leave	VERB
ejpam-5592	42	14	-	-	PUNCT
ejpam-5592	42	15	sided	side	VERB
ejpam-5592	42	16	ψ−rl	ψ−rl	NOUN
ejpam-5592	42	17	fractional	fractional	ADJ
ejpam-5592	42	18	integral	integral	ADJ
ejpam-5592	42	19	w.r.t	w.r.t	NOUN
ejpam-5592	42	20	.	.	PUNCT
ejpam-5592	43	1	another	another	DET
ejpam-5592	43	2	h.a	h.a	PROPN
ejpam-5592	43	3	.	.	PROPN
ejpam-5592	43	4	hammad	hammad	PROPN
ejpam-5592	43	5	,	,	PUNCT
ejpam-5592	43	6	m.	m.	PROPN
ejpam-5592	43	7	de	de	X
ejpam-5592	43	8	la	la	PROPN
ejpam-5592	43	9	sen	sen	PROPN
ejpam-5592	43	10	/	/	SYM
ejpam-5592	43	11	eur	eur	PROPN
ejpam-5592	43	12	.	.	PUNCT
ejpam-5592	44	1	j.	j.	PROPN
ejpam-5592	44	2	pure	pure	PROPN
ejpam-5592	44	3	appl	appl	PROPN
ejpam-5592	44	4	.	.	PROPN
ejpam-5592	44	5	math	math	PROPN
ejpam-5592	44	6	,	,	PUNCT
ejpam-5592	44	7	17	17	NUM
ejpam-5592	44	8	(	(	PUNCT
ejpam-5592	44	9	4	4	NUM
ejpam-5592	44	10	)	)	PUNCT
ejpam-5592	44	11	(	(	PUNCT
ejpam-5592	44	12	2024	2024	NUM
ejpam-5592	44	13	)	)	PUNCT
ejpam-5592	44	14	,	,	PUNCT
ejpam-5592	44	15	3687	3687	NUM
ejpam-5592	44	16	-	-	SYM
ejpam-5592	44	17	3707	3707	NUM
ejpam-5592	44	18	3689	3689	NUM
ejpam-5592	44	19	function	function	NOUN
ejpam-5592	44	20	ψ(z	ψ(z	PROPN
ejpam-5592	44	21	)	)	PUNCT
ejpam-5592	44	22	,	,	PUNCT
ejpam-5592	44	23	is	be	AUX
ejpam-5592	44	24	described	describe	VERB
ejpam-5592	44	25	as	as	ADP
ejpam-5592	44	26	rlℜϖ,ψκ	rlℜϖ,ψκ	NOUN
ejpam-5592	44	27	ξ	ξ	X
ejpam-5592	44	28	(	(	PUNCT
ejpam-5592	44	29	z	z	NOUN
ejpam-5592	44	30	)	)	PUNCT
ejpam-5592	44	31	=	=	SYM
ejpam-5592	44	32	1	1	NUM
ejpam-5592	44	33	γ	γ	X
ejpam-5592	44	34	(	(	PUNCT
ejpam-5592	44	35	ϖ	ϖ	NOUN
ejpam-5592	44	36	)	)	PUNCT
ejpam-5592	44	37	z∫	z∫	NOUN
ejpam-5592	44	38	κ	κ	NOUN
ejpam-5592	44	39	(	(	PUNCT
ejpam-5592	44	40	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	44	41	ψ(r))ψ′(r)ξ	ψ(r))ψ′(r)ξ	PROPN
ejpam-5592	44	42	(	(	PUNCT
ejpam-5592	44	43	r	r	NOUN
ejpam-5592	44	44	)	)	PUNCT
ejpam-5592	44	45	dr	dr	NOUN
ejpam-5592	44	46	,	,	PUNCT
ejpam-5592	44	47	for	for	ADP
ejpam-5592	44	48	all	all	DET
ejpam-5592	44	49	z	z	NOUN
ejpam-5592	44	50	∈	∈	NOUN
ejpam-5592	44	51	ℑ	ℑ	NOUN
ejpam-5592	44	52	=	=	PUNCT
ejpam-5592	45	1	[	[	X
ejpam-5592	45	2	κ	κ	X
ejpam-5592	45	3	,	,	PUNCT
ejpam-5592	45	4	ϱ	ϱ	ADP
ejpam-5592	45	5	]	]	PUNCT
ejpam-5592	45	6	,	,	PUNCT
ejpam-5592	45	7	where	where	SCONJ
ejpam-5592	45	8	γ	γ	X
ejpam-5592	45	9	(	(	PUNCT
ejpam-5592	45	10	ϖ	ϖ	NOUN
ejpam-5592	45	11	)	)	PUNCT
ejpam-5592	45	12	=	=	SYM
ejpam-5592	45	13	∞∫	∞∫	NOUN
ejpam-5592	45	14	0	0	NUM
ejpam-5592	45	15	e−rrϖ−1dr	e−rrϖ−1dr	NOUN
ejpam-5592	45	16	,	,	PUNCT
ejpam-5592	45	17	ϖ	ϖ	INTJ
ejpam-5592	45	18	>	>	X
ejpam-5592	45	19	0	0	X
ejpam-5592	45	20	.	.	PUNCT
ejpam-5592	46	1	definition	definition	NOUN
ejpam-5592	46	2	2	2	NUM
ejpam-5592	46	3	.	.	PUNCT
ejpam-5592	47	1	[	[	X
ejpam-5592	47	2	5	5	NUM
ejpam-5592	47	3	]	]	PUNCT
ejpam-5592	47	4	for	for	ADP
ejpam-5592	47	5	the	the	DET
ejpam-5592	47	6	function	function	NOUN
ejpam-5592	47	7	ξ	ξ	PROPN
ejpam-5592	47	8	∈	∈	PROPN
ejpam-5592	47	9	h1(κ	h1(κ	PROPN
ejpam-5592	47	10	,	,	PUNCT
ejpam-5592	47	11	ϱ	ϱ	NOUN
ejpam-5592	47	12	)	)	PUNCT
ejpam-5592	47	13	and	and	CCONJ
ejpam-5592	47	14	ϖ	ϖ	PROPN
ejpam-5592	47	15	∈	∈	PROPN
ejpam-5592	47	16	(	(	PUNCT
ejpam-5592	47	17	0	0	NUM
ejpam-5592	47	18	,	,	PUNCT
ejpam-5592	47	19	1	1	NUM
ejpam-5592	47	20	]	]	PUNCT
ejpam-5592	47	21	,	,	PUNCT
ejpam-5592	47	22	the	the	DET
ejpam-5592	47	23	ϖth	ϖth	NOUN
ejpam-5592	47	24	left	leave	VERB
ejpam-5592	47	25	-	-	PUNCT
ejpam-5592	47	26	sided	sided	ADJ
ejpam-5592	47	27	rl	rl	X
ejpam-5592	47	28	-	-	PUNCT
ejpam-5592	47	29	ab	ab	NOUN
ejpam-5592	47	30	fractional	fractional	ADJ
ejpam-5592	47	31	derivative	derivative	NOUN
ejpam-5592	47	32	is	be	AUX
ejpam-5592	47	33	defined	define	VERB
ejpam-5592	47	34	by	by	ADP
ejpam-5592	47	35	(	(	PUNCT
ejpam-5592	47	36	rlabdϖ	rlabdϖ	PROPN
ejpam-5592	47	37	κ	κ	PROPN
ejpam-5592	47	38	ξ	ξ	PROPN
ejpam-5592	47	39	)	)	PUNCT
ejpam-5592	47	40	z	z	NOUN
ejpam-5592	47	41	=	=	PUNCT
ejpam-5592	47	42	λ(ϖ	λ(ϖ	NOUN
ejpam-5592	47	43	)	)	PUNCT
ejpam-5592	47	44	1−ϖ	1−ϖ	NUM
ejpam-5592	48	1	d	d	NUM
ejpam-5592	48	2	dz	dz	PROPN
ejpam-5592	48	3	z∫	z∫	PROPN
ejpam-5592	48	4	κ	κ	NOUN
ejpam-5592	48	5	lϖ	lϖ	NOUN
ejpam-5592	48	6	(	(	PUNCT
ejpam-5592	48	7	−ϖ	−ϖ	NOUN
ejpam-5592	48	8	1−ϖ	1−ϖ	NUM
ejpam-5592	48	9	(	(	PUNCT
ejpam-5592	48	10	z	z	NOUN
ejpam-5592	48	11	−	−	PROPN
ejpam-5592	48	12	r)ϖ	r)ϖ	NOUN
ejpam-5592	48	13	)	)	PUNCT
ejpam-5592	49	1	ξ	ξ	X
ejpam-5592	49	2	(	(	PUNCT
ejpam-5592	49	3	r	r	NOUN
ejpam-5592	49	4	)	)	PUNCT
ejpam-5592	49	5	dr	dr	PROPN
ejpam-5592	49	6	,	,	PUNCT
ejpam-5592	49	7	z	z	PROPN
ejpam-5592	49	8	∈	∈	PROPN
ejpam-5592	49	9	ℑ	ℑ	PROPN
ejpam-5592	49	10	,	,	PUNCT
ejpam-5592	49	11	where	where	SCONJ
ejpam-5592	49	12	λ(ϖ	λ(ϖ	NOUN
ejpam-5592	49	13	)	)	PUNCT
ejpam-5592	49	14	is	be	AUX
ejpam-5592	49	15	the	the	DET
ejpam-5592	49	16	normalization	normalization	NOUN
ejpam-5592	49	17	function	function	NOUN
ejpam-5592	49	18	with	with	ADP
ejpam-5592	49	19	λ(0	λ(0	PROPN
ejpam-5592	49	20	)	)	PUNCT
ejpam-5592	49	21	=	=	PUNCT
ejpam-5592	50	1	λ(1	λ(1	PROPN
ejpam-5592	50	2	)	)	PUNCT
ejpam-5592	50	3	=	=	SYM
ejpam-5592	50	4	1	1	NUM
ejpam-5592	50	5	,	,	PUNCT
ejpam-5592	50	6	and	and	CCONJ
ejpam-5592	50	7	lϖ	lϖ	VERB
ejpam-5592	50	8	is	be	AUX
ejpam-5592	50	9	the	the	DET
ejpam-5592	50	10	ml	ml	X
ejpam-5592	50	11	function	function	NOUN
ejpam-5592	50	12	given	give	VERB
ejpam-5592	50	13	by	by	ADP
ejpam-5592	50	14	lϖ(s	lϖ(	NOUN
ejpam-5592	50	15	)	)	PUNCT
ejpam-5592	50	16	=	=	NOUN
ejpam-5592	51	1	∞∑	∞∑	NUM
ejpam-5592	51	2	j=0	j=0	PROPN
ejpam-5592	51	3	sj	sj	PROPN
ejpam-5592	51	4	γ	γ	X
ejpam-5592	51	5	(	(	PUNCT
ejpam-5592	51	6	1	1	NUM
ejpam-5592	51	7	+	+	NOUN
ejpam-5592	51	8	ϖj	ϖj	NOUN
ejpam-5592	51	9	)	)	PUNCT
ejpam-5592	51	10	,	,	PUNCT
ejpam-5592	51	11	re(ϖ	re(ϖ	X
ejpam-5592	51	12	)	)	PUNCT
ejpam-5592	51	13	>	>	X
ejpam-5592	51	14	0	0	NUM
ejpam-5592	51	15	,	,	PUNCT
ejpam-5592	51	16	s	s	PROPN
ejpam-5592	51	17	∈	∈	PROPN
ejpam-5592	51	18	c.	c.	NOUN
ejpam-5592	51	19	definition	definition	NOUN
ejpam-5592	51	20	3	3	NUM
ejpam-5592	51	21	.	.	PUNCT
ejpam-5592	52	1	[	[	X
ejpam-5592	52	2	5	5	NUM
ejpam-5592	52	3	]	]	PUNCT
ejpam-5592	52	4	for	for	ADP
ejpam-5592	52	5	the	the	DET
ejpam-5592	52	6	function	function	NOUN
ejpam-5592	52	7	ξ	ξ	PROPN
ejpam-5592	52	8	∈	∈	PROPN
ejpam-5592	52	9	h1(κ	h1(κ	PROPN
ejpam-5592	52	10	,	,	PUNCT
ejpam-5592	52	11	ϱ	ϱ	NOUN
ejpam-5592	52	12	)	)	PUNCT
ejpam-5592	52	13	and	and	CCONJ
ejpam-5592	52	14	ϖ	ϖ	PROPN
ejpam-5592	52	15	∈	∈	PROPN
ejpam-5592	52	16	(	(	PUNCT
ejpam-5592	52	17	0	0	NUM
ejpam-5592	52	18	,	,	PUNCT
ejpam-5592	52	19	1	1	NUM
ejpam-5592	52	20	]	]	PUNCT
ejpam-5592	52	21	,	,	PUNCT
ejpam-5592	52	22	the	the	DET
ejpam-5592	52	23	ϖth	ϖth	NOUN
ejpam-5592	52	24	left	leave	VERB
ejpam-5592	52	25	-	-	PUNCT
ejpam-5592	52	26	sided	side	VERB
ejpam-5592	52	27	abc	abc	PROPN
ejpam-5592	52	28	fractional	fractional	PROPN
ejpam-5592	52	29	derivative	derivative	NOUN
ejpam-5592	52	30	is	be	AUX
ejpam-5592	52	31	proposed	propose	VERB
ejpam-5592	52	32	by	by	ADP
ejpam-5592	52	33	(	(	PUNCT
ejpam-5592	52	34	cabdϖ	cabdϖ	NOUN
ejpam-5592	52	35	κ	κ	PROPN
ejpam-5592	52	36	ξ	ξ	PROPN
ejpam-5592	52	37	)	)	PUNCT
ejpam-5592	52	38	z	z	NOUN
ejpam-5592	52	39	=	=	PUNCT
ejpam-5592	52	40	λ(ϖ	λ(ϖ	NOUN
ejpam-5592	52	41	)	)	PUNCT
ejpam-5592	52	42	1−ϖ	1−ϖ	NUM
ejpam-5592	52	43	z∫	z∫	NOUN
ejpam-5592	52	44	κ	κ	NOUN
ejpam-5592	52	45	lϖ	lϖ	NOUN
ejpam-5592	52	46	(	(	PUNCT
ejpam-5592	52	47	−ϖ	−ϖ	NOUN
ejpam-5592	52	48	1−ϖ	1−ϖ	NUM
ejpam-5592	52	49	(	(	PUNCT
ejpam-5592	52	50	z	z	NOUN
ejpam-5592	52	51	−	−	PROPN
ejpam-5592	52	52	r)ϖ	r)ϖ	ADJ
ejpam-5592	52	53	)	)	PUNCT
ejpam-5592	52	54	ξ′	ξ′	NOUN
ejpam-5592	52	55	(	(	PUNCT
ejpam-5592	52	56	r	r	NOUN
ejpam-5592	52	57	)	)	PUNCT
ejpam-5592	52	58	dr	dr	PROPN
ejpam-5592	52	59	,	,	PUNCT
ejpam-5592	52	60	z	z	NOUN
ejpam-5592	52	61	∈	∈	PROPN
ejpam-5592	52	62	ℑ.	ℑ.	NOUN
ejpam-5592	52	63	definition	definition	NOUN
ejpam-5592	52	64	4	4	NUM
ejpam-5592	52	65	.	.	PUNCT
ejpam-5592	53	1	[	[	X
ejpam-5592	53	2	5	5	NUM
ejpam-5592	53	3	]	]	PUNCT
ejpam-5592	53	4	for	for	ADP
ejpam-5592	53	5	the	the	DET
ejpam-5592	53	6	function	function	NOUN
ejpam-5592	53	7	ξ	ξ	PROPN
ejpam-5592	53	8	∈	∈	PROPN
ejpam-5592	53	9	h1(κ	h1(κ	PROPN
ejpam-5592	53	10	,	,	PUNCT
ejpam-5592	53	11	ϱ	ϱ	NOUN
ejpam-5592	53	12	)	)	PUNCT
ejpam-5592	53	13	and	and	CCONJ
ejpam-5592	53	14	ϖ	ϖ	PROPN
ejpam-5592	53	15	∈	∈	PROPN
ejpam-5592	53	16	(	(	PUNCT
ejpam-5592	53	17	0	0	NUM
ejpam-5592	53	18	,	,	PUNCT
ejpam-5592	53	19	1	1	NUM
ejpam-5592	53	20	]	]	PUNCT
ejpam-5592	53	21	,	,	PUNCT
ejpam-5592	53	22	the	the	DET
ejpam-5592	53	23	ϖth	ϖth	NOUN
ejpam-5592	53	24	left	leave	VERB
ejpam-5592	53	25	-	-	PUNCT
ejpam-5592	53	26	sided	sided	ADJ
ejpam-5592	53	27	rl	rl	X
ejpam-5592	53	28	-	-	PUNCT
ejpam-5592	53	29	ab	ab	ADJ
ejpam-5592	53	30	fractional	fractional	ADJ
ejpam-5592	53	31	integral	integral	NOUN
ejpam-5592	53	32	is	be	AUX
ejpam-5592	53	33	formed	form	VERB
ejpam-5592	53	34	as	as	ADP
ejpam-5592	53	35	(	(	PUNCT
ejpam-5592	53	36	rlabℜϖκ	rlabℜϖκ	ADP
ejpam-5592	53	37	ξ	ξ	X
ejpam-5592	53	38	)	)	PUNCT
ejpam-5592	53	39	z	z	NOUN
ejpam-5592	53	40	=	=	SYM
ejpam-5592	53	41	1−ϖ	1−ϖ	NUM
ejpam-5592	53	42	λ(ϖ	λ(ϖ	NOUN
ejpam-5592	53	43	)	)	PUNCT
ejpam-5592	53	44	ξ(z	ξ(z	PROPN
ejpam-5592	53	45	)	)	PUNCT
ejpam-5592	53	46	+	+	NUM
ejpam-5592	53	47	ϖ	ϖ	X
ejpam-5592	53	48	λ(ϖ	λ(ϖ	NOUN
ejpam-5592	53	49	)	)	PUNCT
ejpam-5592	53	50	rl	rl	ADP
ejpam-5592	53	51	ℜϖκ	ℜϖκ	PROPN
ejpam-5592	53	52	ξ	ξ	PROPN
ejpam-5592	53	53	(	(	PUNCT
ejpam-5592	53	54	z	z	NOUN
ejpam-5592	53	55	)	)	PUNCT
ejpam-5592	53	56	,	,	PUNCT
ejpam-5592	53	57	z	z	NOUN
ejpam-5592	53	58	∈	∈	PROPN
ejpam-5592	53	59	ℑ.	ℑ.	NOUN
ejpam-5592	53	60	definition	definition	NOUN
ejpam-5592	53	61	5	5	NUM
ejpam-5592	53	62	.	.	PUNCT
ejpam-5592	54	1	[	[	X
ejpam-5592	54	2	17	17	NUM
ejpam-5592	54	3	]	]	PUNCT
ejpam-5592	54	4	for	for	ADP
ejpam-5592	54	5	the	the	DET
ejpam-5592	54	6	function	function	NOUN
ejpam-5592	54	7	ξ	ξ	PROPN
ejpam-5592	54	8	∈	∈	PROPN
ejpam-5592	54	9	hq	hq	NOUN
ejpam-5592	54	10	t	t	PROPN
ejpam-5592	54	11	(	(	PUNCT
ejpam-5592	54	12	κ	κ	NOUN
ejpam-5592	54	13	,	,	PUNCT
ejpam-5592	54	14	ϱ	ϱ	NOUN
ejpam-5592	54	15	)	)	PUNCT
ejpam-5592	54	16	,	,	PUNCT
ejpam-5592	54	17	(	(	PUNCT
ejpam-5592	54	18	where	where	SCONJ
ejpam-5592	54	19	1	1	NUM
ejpam-5592	54	20	≤	≤	NOUN
ejpam-5592	54	21	q	q	NOUN
ejpam-5592	54	22	<	<	X
ejpam-5592	54	23	∞	∞	PROPN
ejpam-5592	54	24	,	,	PUNCT
ejpam-5592	54	25	t	t	PROPN
ejpam-5592	54	26	∈	∈	PROPN
ejpam-5592	54	27	r	r	NOUN
ejpam-5592	54	28	)	)	PUNCT
ejpam-5592	54	29	,	,	PUNCT
ejpam-5592	54	30	and	and	CCONJ
ejpam-5592	54	31	ϖ	ϖ	X
ejpam-5592	54	32	∈	∈	PROPN
ejpam-5592	54	33	(	(	PUNCT
ejpam-5592	54	34	0	0	NUM
ejpam-5592	54	35	,	,	PUNCT
ejpam-5592	54	36	1	1	NUM
ejpam-5592	54	37	]	]	PUNCT
ejpam-5592	54	38	,	,	PUNCT
ejpam-5592	54	39	the	the	DET
ejpam-5592	54	40	ϖth	ϖth	NOUN
ejpam-5592	54	41	left	leave	VERB
ejpam-5592	54	42	-	-	PUNCT
ejpam-5592	54	43	sided	side	VERB
ejpam-5592	54	44	kab	kab	PROPN
ejpam-5592	54	45	fractional	fractional	PROPN
ejpam-5592	54	46	integral	integral	ADJ
ejpam-5592	54	47	is	be	AUX
ejpam-5592	54	48	written	write	VERB
ejpam-5592	54	49	as	as	ADP
ejpam-5592	54	50	(	(	PUNCT
ejpam-5592	54	51	kab	kab	PROPN
ejpam-5592	54	52	κ	κ	X
ejpam-5592	54	53	ℜϖ,ηξ	ℜϖ,ηξ	PROPN
ejpam-5592	54	54	)	)	PUNCT
ejpam-5592	54	55	z	z	X
ejpam-5592	54	56	=	=	SYM
ejpam-5592	54	57	1−ϖ	1−ϖ	NUM
ejpam-5592	54	58	λ(ϖ	λ(ϖ	NOUN
ejpam-5592	54	59	)	)	PUNCT
ejpam-5592	54	60	ξ(z	ξ(z	PROPN
ejpam-5592	54	61	)	)	PUNCT
ejpam-5592	54	62	+	+	NUM
ejpam-5592	54	63	ϖ	ϖ	X
ejpam-5592	54	64	λ(ϖ	λ(ϖ	NOUN
ejpam-5592	54	65	)	)	PUNCT
ejpam-5592	55	1	1	1	NUM
ejpam-5592	55	2	γ	γ	X
ejpam-5592	55	3	(	(	PUNCT
ejpam-5592	55	4	ϖ	ϖ	NOUN
ejpam-5592	55	5	)	)	PUNCT
ejpam-5592	55	6	z∫	z∫	NOUN
ejpam-5592	55	7	κ	κ	X
ejpam-5592	55	8	rη−1	rη−1	PROPN
ejpam-5592	55	9	(	(	PUNCT
ejpam-5592	55	10	zη	zη	AUX
ejpam-5592	55	11	−	−	VERB
ejpam-5592	55	12	rη	rη	NOUN
ejpam-5592	55	13	η	η	NOUN
ejpam-5592	55	14	)	)	PUNCT
ejpam-5592	55	15	ϖ−1	ϖ−1	PROPN
ejpam-5592	55	16	ξ	ξ	PROPN
ejpam-5592	55	17	(	(	PUNCT
ejpam-5592	55	18	r	r	NOUN
ejpam-5592	55	19	)	)	PUNCT
ejpam-5592	55	20	dr	dr	PROPN
ejpam-5592	55	21	,	,	PUNCT
ejpam-5592	55	22	z	z	PROPN
ejpam-5592	55	23	∈	∈	PROPN
ejpam-5592	55	24	ℑ	ℑ	PROPN
ejpam-5592	55	25	,	,	PUNCT
ejpam-5592	55	26	η	η	PROPN
ejpam-5592	55	27	>	>	X
ejpam-5592	55	28	0	0	PROPN
ejpam-5592	55	29	.	.	PUNCT
ejpam-5592	55	30	definition	definition	NOUN
ejpam-5592	55	31	6	6	NUM
ejpam-5592	55	32	.	.	PUNCT
ejpam-5592	56	1	[	[	X
ejpam-5592	56	2	8	8	NUM
ejpam-5592	56	3	]	]	PUNCT
ejpam-5592	56	4	assume	assume	VERB
ejpam-5592	56	5	that	that	SCONJ
ejpam-5592	56	6	ϖ	ϖ	X
ejpam-5592	56	7	∈	∈	PROPN
ejpam-5592	56	8	(	(	PUNCT
ejpam-5592	56	9	0	0	NUM
ejpam-5592	56	10	,	,	PUNCT
ejpam-5592	56	11	1	1	NUM
ejpam-5592	56	12	]	]	PUNCT
ejpam-5592	56	13	.	.	PUNCT
ejpam-5592	57	1	for	for	ADP
ejpam-5592	57	2	the	the	DET
ejpam-5592	57	3	function	function	NOUN
ejpam-5592	57	4	ξ	ξ	PROPN
ejpam-5592	57	5	∈	∈	PROPN
ejpam-5592	57	6	h1(κ	h1(κ	PROPN
ejpam-5592	57	7	,	,	PUNCT
ejpam-5592	57	8	ϱ	ϱ	NOUN
ejpam-5592	57	9	)	)	PUNCT
ejpam-5592	57	10	,	,	PUNCT
ejpam-5592	57	11	the	the	DET
ejpam-5592	57	12	ϖth	ϖth	NOUN
ejpam-5592	57	13	left	leave	VERB
ejpam-5592	57	14	-	-	PUNCT
ejpam-5592	57	15	sided	side	VERB
ejpam-5592	57	16	ψ−rl	ψ−rl	PROPN
ejpam-5592	57	17	-	-	PUNCT
ejpam-5592	57	18	ab	ab	NOUN
ejpam-5592	57	19	fractional	fractional	ADJ
ejpam-5592	57	20	derivative	derivative	NOUN
ejpam-5592	57	21	under	under	ADP
ejpam-5592	57	22	an	an	DET
ejpam-5592	57	23	increasing	increase	VERB
ejpam-5592	57	24	differentiable	differentiable	ADJ
ejpam-5592	57	25	function	function	NOUN
ejpam-5592	57	26	ψ	ψ	NOUN
ejpam-5592	57	27	:	:	PUNCT
ejpam-5592	57	28	ℑ	ℑ	NOUN
ejpam-5592	57	29	→	→	SYM
ejpam-5592	57	30	r	r	NOUN
ejpam-5592	57	31	with	with	ADP
ejpam-5592	57	32	ψ′(z	ψ′(z	NOUN
ejpam-5592	57	33	)	)	PUNCT
ejpam-5592	57	34	̸=	̸=	PROPN
ejpam-5592	57	35	0	0	NUM
ejpam-5592	57	36	,	,	PUNCT
ejpam-5592	57	37	for	for	ADP
ejpam-5592	57	38	all	all	DET
ejpam-5592	57	39	z	z	NOUN
ejpam-5592	57	40	∈	∈	NOUN
ejpam-5592	57	41	ℑ	ℑ	PROPN
ejpam-5592	57	42	is	be	AUX
ejpam-5592	57	43	given	give	VERB
ejpam-5592	57	44	by	by	ADP
ejpam-5592	57	45	(	(	PUNCT
ejpam-5592	57	46	rlabdϖ,ψ	rlabdϖ,ψ	PROPN
ejpam-5592	57	47	κ	κ	NOUN
ejpam-5592	57	48	ξ	ξ	PROPN
ejpam-5592	57	49	)	)	PUNCT
ejpam-5592	57	50	(	(	PUNCT
ejpam-5592	57	51	z	z	X
ejpam-5592	57	52	)	)	PUNCT
ejpam-5592	57	53	=	=	PUNCT
ejpam-5592	57	54	λ(ϖ	λ(ϖ	NOUN
ejpam-5592	57	55	)	)	PUNCT
ejpam-5592	57	56	(	(	PUNCT
ejpam-5592	57	57	1−ϖ)ψ′(z	1−ϖ)ψ′(z	X
ejpam-5592	57	58	)	)	PUNCT
ejpam-5592	57	59	d	d	X
ejpam-5592	57	60	dz	dz	PROPN
ejpam-5592	57	61	z∫	z∫	PROPN
ejpam-5592	57	62	κ	κ	NOUN
ejpam-5592	57	63	ψ′(r	ψ′(r	PROPN
ejpam-5592	57	64	)	)	PUNCT
ejpam-5592	57	65	(	(	PUNCT
ejpam-5592	57	66	−ϖ	−ϖ	NOUN
ejpam-5592	57	67	1−ϖ	1−ϖ	NUM
ejpam-5592	57	68	(	(	PUNCT
ejpam-5592	57	69	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	57	70	ψ(r))ϖ	ψ(r))ϖ	PROPN
ejpam-5592	57	71	)	)	PUNCT
ejpam-5592	57	72	ξ	ξ	PROPN
ejpam-5592	57	73	(	(	PUNCT
ejpam-5592	57	74	r	r	NOUN
ejpam-5592	57	75	)	)	PUNCT
ejpam-5592	57	76	dr	dr	PROPN
ejpam-5592	57	77	,	,	PUNCT
ejpam-5592	57	78	z	z	PROPN
ejpam-5592	57	79	∈	∈	PROPN
ejpam-5592	57	80	ℑ.	ℑ.	PROPN
ejpam-5592	57	81	h.a	h.a	PROPN
ejpam-5592	57	82	.	.	PROPN
ejpam-5592	57	83	hammad	hammad	PROPN
ejpam-5592	57	84	,	,	PUNCT
ejpam-5592	57	85	m.	m.	PROPN
ejpam-5592	57	86	de	de	X
ejpam-5592	57	87	la	la	PROPN
ejpam-5592	57	88	sen	sen	PROPN
ejpam-5592	57	89	/	/	SYM
ejpam-5592	57	90	eur	eur	PROPN
ejpam-5592	57	91	.	.	PUNCT
ejpam-5592	58	1	j.	j.	PROPN
ejpam-5592	58	2	pure	pure	PROPN
ejpam-5592	58	3	appl	appl	PROPN
ejpam-5592	58	4	.	.	PROPN
ejpam-5592	58	5	math	math	PROPN
ejpam-5592	58	6	,	,	PUNCT
ejpam-5592	58	7	17	17	NUM
ejpam-5592	58	8	(	(	PUNCT
ejpam-5592	58	9	4	4	NUM
ejpam-5592	58	10	)	)	PUNCT
ejpam-5592	58	11	(	(	PUNCT
ejpam-5592	58	12	2024	2024	NUM
ejpam-5592	58	13	)	)	PUNCT
ejpam-5592	58	14	,	,	PUNCT
ejpam-5592	58	15	3687	3687	NUM
ejpam-5592	58	16	-	-	SYM
ejpam-5592	58	17	3707	3707	NUM
ejpam-5592	58	18	3690	3690	NUM
ejpam-5592	58	19	definition	definition	NOUN
ejpam-5592	58	20	7	7	NUM
ejpam-5592	58	21	.	.	PUNCT
ejpam-5592	59	1	[	[	X
ejpam-5592	59	2	8	8	NUM
ejpam-5592	59	3	]	]	PUNCT
ejpam-5592	59	4	assume	assume	VERB
ejpam-5592	59	5	that	that	SCONJ
ejpam-5592	59	6	ϖ	ϖ	X
ejpam-5592	59	7	∈	∈	PROPN
ejpam-5592	59	8	(	(	PUNCT
ejpam-5592	59	9	0	0	NUM
ejpam-5592	59	10	,	,	PUNCT
ejpam-5592	59	11	1	1	NUM
ejpam-5592	59	12	]	]	PUNCT
ejpam-5592	59	13	.	.	PUNCT
ejpam-5592	60	1	for	for	ADP
ejpam-5592	60	2	the	the	DET
ejpam-5592	60	3	function	function	NOUN
ejpam-5592	60	4	ξ	ξ	PROPN
ejpam-5592	60	5	∈	∈	PROPN
ejpam-5592	60	6	h1(κ	h1(κ	PROPN
ejpam-5592	60	7	,	,	PUNCT
ejpam-5592	60	8	ϱ	ϱ	NOUN
ejpam-5592	60	9	)	)	PUNCT
ejpam-5592	60	10	,	,	PUNCT
ejpam-5592	60	11	the	the	DET
ejpam-5592	60	12	ϖth	ϖth	NOUN
ejpam-5592	60	13	leftsided	leftside	VERB
ejpam-5592	60	14	ψ−abc	ψ−abc	NOUN
ejpam-5592	60	15	fractional	fractional	ADJ
ejpam-5592	60	16	derivative	derivative	NOUN
ejpam-5592	60	17	under	under	ADP
ejpam-5592	60	18	an	an	DET
ejpam-5592	60	19	increasing	increase	VERB
ejpam-5592	60	20	differentiable	differentiable	ADJ
ejpam-5592	60	21	function	function	NOUN
ejpam-5592	60	22	ψ	ψ	NOUN
ejpam-5592	60	23	:	:	PUNCT
ejpam-5592	60	24	ℑ	ℑ	NOUN
ejpam-5592	60	25	→	→	SYM
ejpam-5592	60	26	r	r	NOUN
ejpam-5592	60	27	with	with	ADP
ejpam-5592	60	28	ψ′(z	ψ′(z	NOUN
ejpam-5592	60	29	)	)	PUNCT
ejpam-5592	60	30	̸=	̸=	PROPN
ejpam-5592	60	31	0	0	NUM
ejpam-5592	60	32	,	,	PUNCT
ejpam-5592	60	33	for	for	ADP
ejpam-5592	60	34	all	all	DET
ejpam-5592	60	35	z	z	NOUN
ejpam-5592	60	36	∈	∈	NOUN
ejpam-5592	60	37	ℑ	ℑ	NOUN
ejpam-5592	60	38	is	be	AUX
ejpam-5592	60	39	defined	define	VERB
ejpam-5592	60	40	by	by	ADP
ejpam-5592	60	41	(	(	PUNCT
ejpam-5592	60	42	cabdϖ,ψ	cabdϖ,ψ	X
ejpam-5592	60	43	κ	κ	NOUN
ejpam-5592	60	44	ξ	ξ	NOUN
ejpam-5592	60	45	)	)	PUNCT
ejpam-5592	61	1	(	(	PUNCT
ejpam-5592	61	2	z	z	X
ejpam-5592	61	3	)	)	PUNCT
ejpam-5592	61	4	=	=	PUNCT
ejpam-5592	61	5	λ(ϖ	λ(ϖ	NOUN
ejpam-5592	61	6	)	)	PUNCT
ejpam-5592	61	7	(	(	PUNCT
ejpam-5592	61	8	1−ϖ	1−ϖ	NUM
ejpam-5592	61	9	)	)	PUNCT
ejpam-5592	61	10	z∫	z∫	NOUN
ejpam-5592	61	11	κ	κ	X
ejpam-5592	61	12	ψ′(r)lϖ	ψ′(r)lϖ	PROPN
ejpam-5592	61	13	(	(	PUNCT
ejpam-5592	61	14	−ϖ	−ϖ	NOUN
ejpam-5592	61	15	1−ϖ	1−ϖ	NUM
ejpam-5592	61	16	(	(	PUNCT
ejpam-5592	61	17	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	61	18	ψ(r))ϖ	ψ(r))ϖ	PRON
ejpam-5592	61	19	)	)	PUNCT
ejpam-5592	61	20	ξ′ψ	ξ′ψ	NOUN
ejpam-5592	61	21	(	(	PUNCT
ejpam-5592	61	22	r	r	NOUN
ejpam-5592	61	23	)	)	PUNCT
ejpam-5592	61	24	dr	dr	PROPN
ejpam-5592	61	25	,	,	PUNCT
ejpam-5592	61	26	z	z	PROPN
ejpam-5592	61	27	∈	∈	PROPN
ejpam-5592	61	28	ℑ	ℑ	PROPN
ejpam-5592	61	29	,	,	PUNCT
ejpam-5592	61	30	where	where	SCONJ
ejpam-5592	61	31	ξ′ψ	ξ′ψ	NOUN
ejpam-5592	61	32	(	(	PUNCT
ejpam-5592	61	33	r	r	NOUN
ejpam-5592	61	34	)	)	PUNCT
ejpam-5592	61	35	=	=	SYM
ejpam-5592	61	36	ξ′(z	ξ′(z	PROPN
ejpam-5592	61	37	)	)	PUNCT
ejpam-5592	61	38	ψ′(z	ψ′(z	NOUN
ejpam-5592	61	39	)	)	PUNCT
ejpam-5592	61	40	.	.	PUNCT
ejpam-5592	62	1	definition	definition	NOUN
ejpam-5592	62	2	8	8	NUM
ejpam-5592	62	3	.	.	PUNCT
ejpam-5592	63	1	[	[	X
ejpam-5592	63	2	20	20	NUM
ejpam-5592	63	3	]	]	PUNCT
ejpam-5592	63	4	assume	assume	VERB
ejpam-5592	63	5	that	that	SCONJ
ejpam-5592	63	6	ϖ	ϖ	X
ejpam-5592	63	7	∈	∈	PROPN
ejpam-5592	63	8	(	(	PUNCT
ejpam-5592	63	9	0	0	NUM
ejpam-5592	63	10	,	,	PUNCT
ejpam-5592	63	11	1	1	NUM
ejpam-5592	63	12	]	]	PUNCT
ejpam-5592	63	13	.	.	PUNCT
ejpam-5592	64	1	for	for	ADP
ejpam-5592	64	2	the	the	DET
ejpam-5592	64	3	function	function	NOUN
ejpam-5592	64	4	ξ	ξ	PROPN
ejpam-5592	64	5	∈	∈	PROPN
ejpam-5592	64	6	h1(κ	h1(κ	PROPN
ejpam-5592	64	7	,	,	PUNCT
ejpam-5592	64	8	ϱ	ϱ	NOUN
ejpam-5592	64	9	)	)	PUNCT
ejpam-5592	64	10	,	,	PUNCT
ejpam-5592	64	11	the	the	DET
ejpam-5592	64	12	ϖth	ϖth	NOUN
ejpam-5592	64	13	leftsided	leftside	VERB
ejpam-5592	64	14	ψ−rl	ψ−rl	PROPN
ejpam-5592	64	15	-	-	PUNCT
ejpam-5592	64	16	ab	ab	NOUN
ejpam-5592	64	17	fractional	fractional	ADJ
ejpam-5592	64	18	integral	integral	ADJ
ejpam-5592	64	19	under	under	ADP
ejpam-5592	64	20	an	an	DET
ejpam-5592	64	21	increasing	increase	VERB
ejpam-5592	64	22	differentiable	differentiable	ADJ
ejpam-5592	64	23	function	function	NOUN
ejpam-5592	64	24	ψ	ψ	NOUN
ejpam-5592	64	25	:	:	PUNCT
ejpam-5592	64	26	ℑ	ℑ	NOUN
ejpam-5592	64	27	→	→	SYM
ejpam-5592	64	28	r	r	NOUN
ejpam-5592	64	29	with	with	ADP
ejpam-5592	64	30	ψ′(z	ψ′(z	NOUN
ejpam-5592	64	31	)	)	PUNCT
ejpam-5592	64	32	̸=	̸=	PROPN
ejpam-5592	64	33	0	0	NUM
ejpam-5592	64	34	,	,	PUNCT
ejpam-5592	64	35	for	for	ADP
ejpam-5592	64	36	all	all	DET
ejpam-5592	64	37	z	z	NOUN
ejpam-5592	64	38	∈	∈	NOUN
ejpam-5592	64	39	ℑ	ℑ	PROPN
ejpam-5592	64	40	is	be	AUX
ejpam-5592	64	41	described	describe	VERB
ejpam-5592	64	42	as	as	ADP
ejpam-5592	64	43	(	(	PUNCT
ejpam-5592	64	44	rlabℜϖ,ψκ	rlabℜϖ,ψκ	PROPN
ejpam-5592	64	45	ξ	ξ	PROPN
ejpam-5592	64	46	)	)	PUNCT
ejpam-5592	64	47	(	(	PUNCT
ejpam-5592	64	48	z	z	NOUN
ejpam-5592	64	49	)	)	PUNCT
ejpam-5592	64	50	=	=	SYM
ejpam-5592	64	51	1−ϖ	1−ϖ	NUM
ejpam-5592	64	52	λ(ϖ	λ(ϖ	NOUN
ejpam-5592	64	53	)	)	PUNCT
ejpam-5592	64	54	ξ(z	ξ(z	PROPN
ejpam-5592	64	55	)	)	PUNCT
ejpam-5592	65	1	+	+	NUM
ejpam-5592	65	2	ϖ	ϖ	X
ejpam-5592	65	3	λ(ϖ	λ(ϖ	NOUN
ejpam-5592	65	4	)	)	PUNCT
ejpam-5592	65	5	(	(	PUNCT
ejpam-5592	65	6	rlℜϖ,ψκ	rlℜϖ,ψκ	NOUN
ejpam-5592	65	7	ξ	ξ	NOUN
ejpam-5592	65	8	)	)	PUNCT
ejpam-5592	65	9	(	(	PUNCT
ejpam-5592	65	10	z	z	NOUN
ejpam-5592	65	11	)	)	PUNCT
ejpam-5592	65	12	,	,	PUNCT
ejpam-5592	65	13	z	z	NOUN
ejpam-5592	65	14	∈	∈	PROPN
ejpam-5592	65	15	ℑ.	ℑ.	NOUN
ejpam-5592	65	16	remark	remark	NOUN
ejpam-5592	65	17	1	1	NUM
ejpam-5592	65	18	.	.	PUNCT
ejpam-5592	66	1	it	it	PRON
ejpam-5592	66	2	should	should	AUX
ejpam-5592	66	3	be	be	AUX
ejpam-5592	66	4	noted	note	VERB
ejpam-5592	66	5	that	that	SCONJ
ejpam-5592	66	6	(	(	PUNCT
ejpam-5592	66	7	i	i	NOUN
ejpam-5592	66	8	)	)	PUNCT
ejpam-5592	66	9	definitions	definition	NOUN
ejpam-5592	66	10	6	6	NUM
ejpam-5592	66	11	,	,	PUNCT
ejpam-5592	66	12	7	7	NUM
ejpam-5592	66	13	and	and	CCONJ
ejpam-5592	66	14	8	8	NUM
ejpam-5592	66	15	reduce	reduce	VERB
ejpam-5592	66	16	to	to	ADP
ejpam-5592	66	17	definitions	definition	NOUN
ejpam-5592	66	18	2	2	NUM
ejpam-5592	66	19	,	,	PUNCT
ejpam-5592	66	20	3	3	NUM
ejpam-5592	66	21	and	and	CCONJ
ejpam-5592	66	22	4	4	NUM
ejpam-5592	66	23	,	,	PUNCT
ejpam-5592	66	24	respectively	respectively	ADV
ejpam-5592	66	25	,	,	PUNCT
ejpam-5592	66	26	by	by	ADP
ejpam-5592	66	27	taking	take	VERB
ejpam-5592	66	28	ψ(z	ψ(z	NOUN
ejpam-5592	66	29	)	)	PUNCT
ejpam-5592	67	1	=	=	SYM
ejpam-5592	67	2	z.	z.	PROPN
ejpam-5592	67	3	(	(	PUNCT
ejpam-5592	67	4	ii	ii	PROPN
ejpam-5592	67	5	)	)	PUNCT
ejpam-5592	67	6	definition	definition	NOUN
ejpam-5592	67	7	8	8	NUM
ejpam-5592	67	8	follows	follow	VERB
ejpam-5592	67	9	immediately	immediately	ADV
ejpam-5592	67	10	from	from	ADP
ejpam-5592	67	11	definition	definition	NOUN
ejpam-5592	67	12	5	5	NUM
ejpam-5592	67	13	,	,	PUNCT
ejpam-5592	67	14	by	by	ADP
ejpam-5592	67	15	considering	consider	VERB
ejpam-5592	67	16	ψ(z	ψ(z	NOUN
ejpam-5592	67	17	)	)	PUNCT
ejpam-5592	67	18	=	=	PUNCT
ejpam-5592	67	19	zη	zη	PROPN
ejpam-5592	67	20	η	η	PROPN
ejpam-5592	67	21	.	.	PUNCT
ejpam-5592	68	1	lemma	lemma	PROPN
ejpam-5592	68	2	1	1	NUM
ejpam-5592	68	3	.	.	PUNCT
ejpam-5592	69	1	[	[	X
ejpam-5592	69	2	4	4	X
ejpam-5592	69	3	]	]	PUNCT
ejpam-5592	69	4	assume	assume	VERB
ejpam-5592	69	5	that	that	SCONJ
ejpam-5592	69	6	ϖ	ϖ	NOUN
ejpam-5592	69	7	,	,	PUNCT
ejpam-5592	69	8	ν	ν	X
ejpam-5592	69	9	>	>	X
ejpam-5592	69	10	0	0	PUNCT
ejpam-5592	69	11	and	and	CCONJ
ejpam-5592	69	12	ξ	ξ	X
ejpam-5592	69	13	:	:	PUNCT
ejpam-5592	69	14	ℑ	ℑ	PROPN
ejpam-5592	69	15	→	→	SYM
ejpam-5592	69	16	r.	r.	PROPN
ejpam-5592	69	17	then	then	ADV
ejpam-5592	69	18	(	(	PUNCT
ejpam-5592	69	19	1	1	X
ejpam-5592	69	20	)	)	PUNCT
ejpam-5592	69	21	rlℜϖ,ψκ	rlℜϖ,ψκ	NOUN
ejpam-5592	69	22	(	(	PUNCT
ejpam-5592	69	23	ξ	ξ	X
ejpam-5592	69	24	(	(	PUNCT
ejpam-5592	69	25	z)−	z)−	PROPN
ejpam-5592	69	26	ξ	ξ	PROPN
ejpam-5592	69	27	(	(	PUNCT
ejpam-5592	69	28	κ))ν−1	κ))ν−1	PROPN
ejpam-5592	69	29	=	=	SYM
ejpam-5592	69	30	γ(ν	γ(ν	PROPN
ejpam-5592	69	31	)	)	PUNCT
ejpam-5592	69	32	γ(ϖ+ν	γ(ϖ+ν	X
ejpam-5592	69	33	)	)	PUNCT
ejpam-5592	69	34	(	(	PUNCT
ejpam-5592	69	35	ξ	ξ	X
ejpam-5592	69	36	(	(	PUNCT
ejpam-5592	69	37	z)−	z)−	PROPN
ejpam-5592	69	38	ξ	ξ	PROPN
ejpam-5592	69	39	(	(	PUNCT
ejpam-5592	69	40	κ))ϖ+ν−1	κ))ϖ+ν−1	ADJ
ejpam-5592	69	41	;	;	PUNCT
ejpam-5592	69	42	(	(	PUNCT
ejpam-5592	69	43	2	2	X
ejpam-5592	69	44	)	)	PUNCT
ejpam-5592	69	45	rlℜϖ,ψκ	rlℜϖ,ψκ	NOUN
ejpam-5592	69	46	rlℜν	rlℜν	NOUN
ejpam-5592	69	47	,	,	PUNCT
ejpam-5592	69	48	ψκ	ψκ	PROPN
ejpam-5592	69	49	ξ	ξ	X
ejpam-5592	69	50	(	(	PUNCT
ejpam-5592	69	51	z	z	NOUN
ejpam-5592	69	52	)	)	PUNCT
ejpam-5592	69	53	=	=	VERB
ejpam-5592	69	54	rl	rl	ADP
ejpam-5592	69	55	ℜϖ+ν	ℜϖ+ν	PROPN
ejpam-5592	69	56	,	,	PUNCT
ejpam-5592	69	57	ψ	ψ	X
ejpam-5592	69	58	κ	κ	X
ejpam-5592	69	59	ξ	ξ	PROPN
ejpam-5592	69	60	(	(	PUNCT
ejpam-5592	69	61	z	z	NOUN
ejpam-5592	69	62	)	)	PUNCT
ejpam-5592	69	63	;	;	PUNCT
ejpam-5592	69	64	(	(	PUNCT
ejpam-5592	69	65	3	3	X
ejpam-5592	69	66	)	)	PUNCT
ejpam-5592	69	67	(	(	PUNCT
ejpam-5592	69	68	(	(	PUNCT
ejpam-5592	69	69	1	1	NUM
ejpam-5592	69	70	ψ(z	ψ(z	NOUN
ejpam-5592	69	71	)	)	PUNCT
ejpam-5592	69	72	d	d	X
ejpam-5592	69	73	dz	dz	X
ejpam-5592	69	74	)	)	PUNCT
ejpam-5592	69	75	k	k	PROPN
ejpam-5592	69	76	rlℜk	rlℜk	PROPN
ejpam-5592	69	77	,	,	PUNCT
ejpam-5592	69	78	ψκ	ψκ	PROPN
ejpam-5592	69	79	ξ	ξ	X
ejpam-5592	69	80	)	)	PUNCT
ejpam-5592	69	81	(	(	PUNCT
ejpam-5592	69	82	z	z	NOUN
ejpam-5592	69	83	)	)	PUNCT
ejpam-5592	69	84	=	=	SYM
ejpam-5592	69	85	ξ	ξ	X
ejpam-5592	69	86	(	(	PUNCT
ejpam-5592	69	87	z	z	NOUN
ejpam-5592	69	88	)	)	PUNCT
ejpam-5592	69	89	,	,	PUNCT
ejpam-5592	69	90	k	k	PROPN
ejpam-5592	69	91	∈	∈	PROPN
ejpam-5592	69	92	n.	n.	PROPN
ejpam-5592	69	93	lemma	lemma	PROPN
ejpam-5592	69	94	2	2	NUM
ejpam-5592	69	95	.	.	PUNCT
ejpam-5592	70	1	[	[	X
ejpam-5592	70	2	20	20	NUM
ejpam-5592	70	3	]	]	PUNCT
ejpam-5592	70	4	for	for	ADP
ejpam-5592	70	5	ϖ	ϖ	PRON
ejpam-5592	70	6	∈	∈	PROPN
ejpam-5592	70	7	(	(	PUNCT
ejpam-5592	70	8	0	0	NUM
ejpam-5592	70	9	,	,	PUNCT
ejpam-5592	70	10	1	1	NUM
ejpam-5592	70	11	]	]	PUNCT
ejpam-5592	70	12	and	and	CCONJ
ejpam-5592	70	13	ξ	ξ	X
ejpam-5592	70	14	:	:	PUNCT
ejpam-5592	70	15	ℑ	ℑ	PROPN
ejpam-5592	70	16	→	→	SYM
ejpam-5592	70	17	r	r	NOUN
ejpam-5592	70	18	,	,	PUNCT
ejpam-5592	70	19	the	the	DET
ejpam-5592	70	20	relations	relation	NOUN
ejpam-5592	70	21	below	below	ADV
ejpam-5592	70	22	are	be	AUX
ejpam-5592	70	23	satisfied	satisfied	ADJ
ejpam-5592	70	24	:	:	PUNCT
ejpam-5592	70	25	(	(	PUNCT
ejpam-5592	70	26	i	i	NOUN
ejpam-5592	70	27	)	)	PUNCT
ejpam-5592	70	28	(	(	PUNCT
ejpam-5592	71	1	rlabℜϖκ	rlabℜϖκ	ADP
ejpam-5592	71	2	rlabdϖ,ψ	rlabdϖ,ψ	PROPN
ejpam-5592	71	3	κ	κ	NOUN
ejpam-5592	71	4	ξ	ξ	NOUN
ejpam-5592	71	5	)	)	PUNCT
ejpam-5592	71	6	(	(	PUNCT
ejpam-5592	71	7	z	z	NOUN
ejpam-5592	71	8	)	)	PUNCT
ejpam-5592	71	9	=	=	SYM
ejpam-5592	71	10	ξ	ξ	X
ejpam-5592	71	11	(	(	PUNCT
ejpam-5592	71	12	z	z	NOUN
ejpam-5592	71	13	)	)	PUNCT
ejpam-5592	71	14	;	;	PUNCT
ejpam-5592	71	15	(	(	PUNCT
ejpam-5592	71	16	ii	ii	NOUN
ejpam-5592	71	17	)	)	PUNCT
ejpam-5592	71	18	(	(	PUNCT
ejpam-5592	71	19	rlabdϖ,ψ	rlabdϖ,ψ	PROPN
ejpam-5592	71	20	κ	κ	NOUN
ejpam-5592	71	21	rlabℜϖκ	rlabℜϖκ	SYM
ejpam-5592	71	22	ξ	ξ	NOUN
ejpam-5592	71	23	)	)	PUNCT
ejpam-5592	71	24	(	(	PUNCT
ejpam-5592	71	25	z	z	NOUN
ejpam-5592	71	26	)	)	PUNCT
ejpam-5592	71	27	=	=	SYM
ejpam-5592	71	28	ξ	ξ	X
ejpam-5592	71	29	(	(	PUNCT
ejpam-5592	71	30	z	z	NOUN
ejpam-5592	71	31	)	)	PUNCT
ejpam-5592	71	32	.	.	PUNCT
ejpam-5592	72	1	definition	definition	NOUN
ejpam-5592	72	2	9	9	NUM
ejpam-5592	72	3	.	.	PUNCT
ejpam-5592	73	1	[	[	X
ejpam-5592	73	2	22	22	NUM
ejpam-5592	73	3	]	]	PUNCT
ejpam-5592	73	4	for	for	ADP
ejpam-5592	73	5	the	the	DET
ejpam-5592	73	6	function	function	NOUN
ejpam-5592	73	7	ξ	ξ	X
ejpam-5592	73	8	∈	∈	PROPN
ejpam-5592	73	9	l([0	l([0	VERB
ejpam-5592	73	10	,	,	PUNCT
ejpam-5592	73	11	t	t	NOUN
ejpam-5592	73	12	]	]	PUNCT
ejpam-5592	73	13	)	)	PUNCT
ejpam-5592	73	14	,	,	PUNCT
ejpam-5592	73	15	(	(	PUNCT
ejpam-5592	73	16	a	a	X
ejpam-5592	73	17	)	)	PUNCT
ejpam-5592	73	18	the	the	DET
ejpam-5592	73	19	variable	variable	ADJ
ejpam-5592	73	20	order	order	NOUN
ejpam-5592	73	21	of	of	ADP
ejpam-5592	73	22	the	the	DET
ejpam-5592	73	23	rl	rl	PROPN
ejpam-5592	73	24	fractional	fractional	ADJ
ejpam-5592	73	25	integral	integral	ADJ
ejpam-5592	73	26	is	be	AUX
ejpam-5592	73	27	remembered	remember	VERB
ejpam-5592	73	28	as	as	ADP
ejpam-5592	73	29	ℜϖ(z	ℜϖ(z	NOUN
ejpam-5592	73	30	)	)	PUNCT
ejpam-5592	74	1	+0	+0	ADP
ejpam-5592	74	2	ξ(z	ξ(z	NOUN
ejpam-5592	74	3	)	)	PUNCT
ejpam-5592	74	4	=	=	SYM
ejpam-5592	74	5	1	1	NUM
ejpam-5592	74	6	γ(ϖ(z	γ(ϖ(z	PROPN
ejpam-5592	74	7	)	)	PUNCT
ejpam-5592	74	8	)	)	PUNCT
ejpam-5592	75	1	∫	∫	PROPN
ejpam-5592	76	1	z	z	NOUN
ejpam-5592	76	2	0	0	NUM
ejpam-5592	77	1	(	(	PUNCT
ejpam-5592	77	2	z	z	NOUN
ejpam-5592	77	3	−	−	PROPN
ejpam-5592	77	4	r)ϖ(r)−1ξ(r)dr	r)ϖ(r)−1ξ(r)dr	NOUN
ejpam-5592	77	5	;	;	PUNCT
ejpam-5592	77	6	(	(	PUNCT
ejpam-5592	77	7	b	b	X
ejpam-5592	77	8	)	)	PUNCT
ejpam-5592	77	9	the	the	DET
ejpam-5592	77	10	variable	variable	ADJ
ejpam-5592	77	11	order	order	NOUN
ejpam-5592	77	12	of	of	ADP
ejpam-5592	77	13	the	the	DET
ejpam-5592	77	14	caputo	caputo	PROPN
ejpam-5592	77	15	fractional	fractional	PROPN
ejpam-5592	77	16	derivative	derivative	NOUN
ejpam-5592	77	17	is	be	AUX
ejpam-5592	77	18	given	give	VERB
ejpam-5592	77	19	by	by	ADP
ejpam-5592	77	20	cd	cd	PROPN
ejpam-5592	77	21	ϖ(z	ϖ(z	PROPN
ejpam-5592	77	22	)	)	PUNCT
ejpam-5592	77	23	0	0	NUM
ejpam-5592	78	1	ξ(z	ξ(z	NOUN
ejpam-5592	78	2	)	)	PUNCT
ejpam-5592	78	3	=	=	SYM
ejpam-5592	78	4	1	1	NUM
ejpam-5592	78	5	γ(k	γ(k	PROPN
ejpam-5592	78	6	−ϖ(z	−ϖ(z	NOUN
ejpam-5592	78	7	)	)	PUNCT
ejpam-5592	78	8	)	)	PUNCT
ejpam-5592	79	1	∫	∫	PROPN
ejpam-5592	80	1	z	z	NOUN
ejpam-5592	80	2	0	0	NUM
ejpam-5592	81	1	(	(	PUNCT
ejpam-5592	81	2	z	z	NOUN
ejpam-5592	81	3	−	−	PROPN
ejpam-5592	81	4	r)k−ϖ(r)−1ξ(k)(r)dr	r)k−ϖ(r)−1ξ(k)(r)dr	NOUN
ejpam-5592	81	5	.	.	PUNCT
ejpam-5592	82	1	where	where	SCONJ
ejpam-5592	82	2	ϖ	ϖ	INTJ
ejpam-5592	82	3	:	:	PUNCT
ejpam-5592	83	1	[	[	X
ejpam-5592	83	2	0	0	NUM
ejpam-5592	83	3	,	,	PUNCT
ejpam-5592	83	4	t	t	NOUN
ejpam-5592	83	5	]	]	PUNCT
ejpam-5592	83	6	→	→	SYM
ejpam-5592	83	7	(	(	PUNCT
ejpam-5592	83	8	0	0	NUM
ejpam-5592	83	9	,	,	PUNCT
ejpam-5592	83	10	1	1	NUM
ejpam-5592	83	11	]	]	PUNCT
ejpam-5592	83	12	,	,	PUNCT
ejpam-5592	83	13	t	t	PROPN
ejpam-5592	83	14	>	>	X
ejpam-5592	83	15	0	0	PUNCT
ejpam-5592	83	16	is	be	AUX
ejpam-5592	83	17	a	a	DET
ejpam-5592	83	18	continuous	continuous	ADJ
ejpam-5592	83	19	function	function	NOUN
ejpam-5592	83	20	.	.	PUNCT
ejpam-5592	84	1	h.a	h.a	PROPN
ejpam-5592	84	2	.	.	PROPN
ejpam-5592	84	3	hammad	hammad	PROPN
ejpam-5592	84	4	,	,	PUNCT
ejpam-5592	84	5	m.	m.	PROPN
ejpam-5592	84	6	de	de	X
ejpam-5592	84	7	la	la	PROPN
ejpam-5592	84	8	sen	sen	PROPN
ejpam-5592	84	9	/	/	SYM
ejpam-5592	84	10	eur	eur	PROPN
ejpam-5592	84	11	.	.	PUNCT
ejpam-5592	85	1	j.	j.	PROPN
ejpam-5592	85	2	pure	pure	PROPN
ejpam-5592	85	3	appl	appl	PROPN
ejpam-5592	85	4	.	.	PROPN
ejpam-5592	85	5	math	math	PROPN
ejpam-5592	85	6	,	,	PUNCT
ejpam-5592	85	7	17	17	NUM
ejpam-5592	85	8	(	(	PUNCT
ejpam-5592	85	9	4	4	NUM
ejpam-5592	85	10	)	)	PUNCT
ejpam-5592	85	11	(	(	PUNCT
ejpam-5592	85	12	2024	2024	NUM
ejpam-5592	85	13	)	)	PUNCT
ejpam-5592	85	14	,	,	PUNCT
ejpam-5592	85	15	3687	3687	NUM
ejpam-5592	85	16	-	-	SYM
ejpam-5592	85	17	3707	3707	NUM
ejpam-5592	85	18	3691	3691	NUM
ejpam-5592	85	19	3	3	NUM
ejpam-5592	85	20	.	.	PUNCT
ejpam-5592	86	1	derivatives	derivative	NOUN
ejpam-5592	86	2	of	of	ADP
ejpam-5592	86	3	higher	high	ADJ
ejpam-5592	86	4	-	-	PUNCT
ejpam-5592	86	5	variable	variable	ADJ
ejpam-5592	86	6	orders	order	NOUN
ejpam-5592	86	7	in	in	ADP
ejpam-5592	86	8	this	this	DET
ejpam-5592	86	9	section	section	NOUN
ejpam-5592	86	10	,	,	PUNCT
ejpam-5592	86	11	we	we	PRON
ejpam-5592	86	12	consider	consider	VERB
ejpam-5592	86	13	ψ	ψ	X
ejpam-5592	86	14	:	:	PUNCT
ejpam-5592	86	15	ℑ	ℑ	PROPN
ejpam-5592	86	16	→	→	SYM
ejpam-5592	86	17	r	r	NOUN
ejpam-5592	86	18	to	to	PART
ejpam-5592	86	19	be	be	AUX
ejpam-5592	86	20	an	an	DET
ejpam-5592	86	21	increasing	increase	VERB
ejpam-5592	86	22	function	function	NOUN
ejpam-5592	86	23	with	with	ADP
ejpam-5592	86	24	ψ′(z	ψ′(z	NOUN
ejpam-5592	86	25	)	)	PUNCT
ejpam-5592	86	26	̸=	̸=	PROPN
ejpam-5592	86	27	0	0	NUM
ejpam-5592	86	28	to	to	PART
ejpam-5592	86	29	investigate	investigate	VERB
ejpam-5592	86	30	the	the	DET
ejpam-5592	86	31	definitions	definition	NOUN
ejpam-5592	86	32	of	of	ADP
ejpam-5592	86	33	higher	high	ADJ
ejpam-5592	86	34	-	-	PUNCT
ejpam-5592	86	35	variables	variable	NOUN
ejpam-5592	86	36	order	order	NOUN
ejpam-5592	86	37	fractional	fractional	ADJ
ejpam-5592	86	38	derivatives	derivative	NOUN
ejpam-5592	86	39	and	and	CCONJ
ejpam-5592	86	40	integrals	integral	NOUN
ejpam-5592	86	41	within	within	ADP
ejpam-5592	86	42	the	the	DET
ejpam-5592	86	43	ab	ab	PROPN
ejpam-5592	86	44	framework	framework	NOUN
ejpam-5592	86	45	with	with	ADP
ejpam-5592	86	46	regard	regard	NOUN
ejpam-5592	86	47	to	to	ADP
ejpam-5592	86	48	a	a	DET
ejpam-5592	86	49	function	function	NOUN
ejpam-5592	86	50	ψ	ψ	NOUN
ejpam-5592	86	51	.	.	NOUN
ejpam-5592	86	52	consider	consider	VERB
ejpam-5592	86	53	a	a	DET
ejpam-5592	86	54	partition	partition	NOUN
ejpam-5592	86	55	of	of	ADP
ejpam-5592	86	56	ℑ	ℑ	NOUN
ejpam-5592	86	57	=	=	PUNCT
ejpam-5592	87	1	[	[	X
ejpam-5592	87	2	κ	κ	X
ejpam-5592	87	3	,	,	PUNCT
ejpam-5592	87	4	ϱ	ϱ	VERB
ejpam-5592	87	5	]	]	PUNCT
ejpam-5592	87	6	as	as	ADP
ejpam-5592	87	7	{	{	PUNCT
ejpam-5592	87	8	ℑ1	ℑ1	NOUN
ejpam-5592	87	9	=	=	PUNCT
ejpam-5592	88	1	[	[	X
ejpam-5592	88	2	κ	κ	NOUN
ejpam-5592	88	3	,	,	PUNCT
ejpam-5592	88	4	τ1	τ1	PROPN
ejpam-5592	88	5	]	]	PUNCT
ejpam-5592	88	6	,	,	PUNCT
ejpam-5592	88	7	ℑ2	ℑ2	PROPN
ejpam-5592	88	8	=	=	SYM
ejpam-5592	88	9	(	(	PUNCT
ejpam-5592	88	10	τ1	τ1	NOUN
ejpam-5592	88	11	,	,	PUNCT
ejpam-5592	88	12	τ2	τ2	PROPN
ejpam-5592	88	13	]	]	PUNCT
ejpam-5592	88	14	,	,	PUNCT
ejpam-5592	88	15	ℑ3	ℑ3	X
ejpam-5592	88	16	=	=	SYM
ejpam-5592	88	17	(	(	PUNCT
ejpam-5592	88	18	τ2	τ2	PROPN
ejpam-5592	88	19	,	,	PUNCT
ejpam-5592	88	20	τ3	τ3	NOUN
ejpam-5592	88	21	]	]	X
ejpam-5592	88	22	,	,	PUNCT
ejpam-5592	88	23	·	·	PUNCT
ejpam-5592	88	24	·	·	PUNCT
ejpam-5592	88	25	·	·	PUNCT
ejpam-5592	88	26	,	,	PUNCT
ejpam-5592	89	1	ℑk	ℑk	ADV
ejpam-5592	89	2	=	=	SYM
ejpam-5592	89	3	(	(	PUNCT
ejpam-5592	89	4	τk−1	τk−1	PROPN
ejpam-5592	89	5	,	,	PUNCT
ejpam-5592	89	6	ϱ	ϱ	ADP
ejpam-5592	89	7	]	]	PUNCT
ejpam-5592	89	8	}	}	PUNCT
ejpam-5592	89	9	,	,	PUNCT
ejpam-5592	89	10	and	and	CCONJ
ejpam-5592	89	11	assume	assume	VERB
ejpam-5592	89	12	that	that	SCONJ
ejpam-5592	89	13	ϖ	ϖ	X
ejpam-5592	89	14	:	:	PUNCT
ejpam-5592	89	15	ℑ	ℑ	PROPN
ejpam-5592	89	16	→	→	SYM
ejpam-5592	89	17	(	(	PUNCT
ejpam-5592	89	18	k	k	X
ejpam-5592	89	19	,	,	PUNCT
ejpam-5592	89	20	k	k	PROPN
ejpam-5592	90	1	+	+	PROPN
ejpam-5592	90	2	1	1	X
ejpam-5592	90	3	]	]	PUNCT
ejpam-5592	90	4	is	be	AUX
ejpam-5592	90	5	a	a	DET
ejpam-5592	90	6	piecewise	piecewise	NOUN
ejpam-5592	90	7	function	function	NOUN
ejpam-5592	90	8	such	such	ADJ
ejpam-5592	90	9	that	that	DET
ejpam-5592	90	10	ϖ(τ	ϖ(τ	PROPN
ejpam-5592	90	11	)	)	PUNCT
ejpam-5592	91	1	=	=	PRON
ejpam-5592	91	2	k∑	k∑	VERB
ejpam-5592	91	3	u=1	u=1	X
ejpam-5592	92	1	ϖu(τ)iu(τ	ϖu(τ)iu(τ	NOUN
ejpam-5592	92	2	)	)	PUNCT
ejpam-5592	92	3	=	=	SYM
ejpam-5592	93	1			PROPN
ejpam-5592	93	2	ϖ1	ϖ1	VERB
ejpam-5592	93	3	,	,	PUNCT
ejpam-5592	93	4	if	if	SCONJ
ejpam-5592	93	5	τ	τ	PROPN
ejpam-5592	93	6	∈	∈	PROPN
ejpam-5592	93	7	ℑ1	ℑ1	NOUN
ejpam-5592	93	8	ϖ2	ϖ2	NOUN
ejpam-5592	93	9	,	,	PUNCT
ejpam-5592	93	10	if	if	SCONJ
ejpam-5592	93	11	τ	τ	PROPN
ejpam-5592	93	12	∈	∈	PROPN
ejpam-5592	93	13	ℑ2	ℑ2	NOUN
ejpam-5592	93	14	...	...	PUNCT
ejpam-5592	94	1	ϖk	ϖk	INTJ
ejpam-5592	94	2	,	,	PUNCT
ejpam-5592	94	3	if	if	SCONJ
ejpam-5592	94	4	τ	τ	PROPN
ejpam-5592	94	5	∈	∈	PROPN
ejpam-5592	95	1	ℑk	ℑk	PROPN
ejpam-5592	95	2	,	,	PUNCT
ejpam-5592	95	3	where	where	SCONJ
ejpam-5592	95	4	iu	iu	ADV
ejpam-5592	95	5	is	be	AUX
ejpam-5592	95	6	the	the	DET
ejpam-5592	95	7	indicator	indicator	NOUN
ejpam-5592	95	8	function	function	NOUN
ejpam-5592	95	9	of	of	ADP
ejpam-5592	95	10	ℑu	ℑu	PROPN
ejpam-5592	95	11	=	=	SYM
ejpam-5592	95	12	(	(	PUNCT
ejpam-5592	95	13	τu−1	τu−1	PROPN
ejpam-5592	95	14	,	,	PUNCT
ejpam-5592	95	15	τk	τk	ADP
ejpam-5592	95	16	]	]	PUNCT
ejpam-5592	95	17	and	and	CCONJ
ejpam-5592	95	18	k	k	X
ejpam-5592	95	19	<	<	X
ejpam-5592	95	20	ϖu	ϖu	X
ejpam-5592	95	21	<	<	X
ejpam-5592	95	22	k	k	PROPN
ejpam-5592	95	23	+	+	CCONJ
ejpam-5592	95	24	1	1	NUM
ejpam-5592	95	25	are	be	AUX
ejpam-5592	95	26	constants	constant	NOUN
ejpam-5592	95	27	with	with	ADP
ejpam-5592	95	28	u	u	NOUN
ejpam-5592	95	29	=	=	SYM
ejpam-5592	95	30	1	1	NUM
ejpam-5592	95	31	,	,	PUNCT
ejpam-5592	95	32	2	2	NUM
ejpam-5592	95	33	,	,	PUNCT
ejpam-5592	95	34	·	·	PUNCT
ejpam-5592	95	35	·	·	PUNCT
ejpam-5592	95	36	·	·	PUNCT
ejpam-5592	95	37	,	,	PUNCT
ejpam-5592	95	38	k	k	X
ejpam-5592	95	39	,	,	PUNCT
ejpam-5592	95	40	such	such	ADJ
ejpam-5592	95	41	that	that	SCONJ
ejpam-5592	95	42	τ0	τ0	NOUN
ejpam-5592	95	43	=	=	PUNCT
ejpam-5592	95	44	κ	κ	NOUN
ejpam-5592	95	45	and	and	CCONJ
ejpam-5592	95	46	τk	τk	ADP
ejpam-5592	95	47	=	=	PUNCT
ejpam-5592	95	48	ϱ	ϱ	NOUN
ejpam-5592	95	49	and	and	CCONJ
ejpam-5592	95	50	iu(τ	iu(τ	NUM
ejpam-5592	95	51	)	)	PUNCT
ejpam-5592	96	1	=	=	PRON
ejpam-5592	96	2	{	{	PUNCT
ejpam-5592	96	3	1	1	NUM
ejpam-5592	96	4	for	for	ADP
ejpam-5592	96	5	τ	τ	PROPN
ejpam-5592	96	6	∈	∈	PROPN
ejpam-5592	96	7	ℑu	ℑu	PROPN
ejpam-5592	96	8	,	,	PUNCT
ejpam-5592	96	9	0	0	NUM
ejpam-5592	96	10	otherwise	otherwise	ADV
ejpam-5592	96	11	.	.	PUNCT
ejpam-5592	97	1	assume	assume	VERB
ejpam-5592	97	2	that	that	SCONJ
ejpam-5592	97	3	ck(ℑu	ck(ℑu	NOUN
ejpam-5592	97	4	,	,	PUNCT
ejpam-5592	97	5	r	r	NOUN
ejpam-5592	97	6	)	)	PUNCT
ejpam-5592	97	7	refers	refer	VERB
ejpam-5592	97	8	to	to	ADP
ejpam-5592	97	9	the	the	DET
ejpam-5592	97	10	space	space	NOUN
ejpam-5592	97	11	of	of	ADP
ejpam-5592	97	12	all	all	PRON
ejpam-5592	97	13	kth	kth	NOUN
ejpam-5592	97	14	continuously	continuously	ADV
ejpam-5592	97	15	differentiable	differentiable	VERB
ejpam-5592	97	16	functions	function	NOUN
ejpam-5592	97	17	ξ	ξ	PROPN
ejpam-5592	97	18	.	.	PUNCT
ejpam-5592	98	1	clearly	clearly	ADV
ejpam-5592	98	2	,	,	PUNCT
ejpam-5592	98	3	it	it	PRON
ejpam-5592	98	4	is	be	AUX
ejpam-5592	98	5	a	a	DET
ejpam-5592	98	6	banach	banach	NOUN
ejpam-5592	98	7	space	space	NOUN
ejpam-5592	98	8	under	under	ADP
ejpam-5592	98	9	the	the	DET
ejpam-5592	98	10	norm	norm	NOUN
ejpam-5592	98	11	∥ξ∥	∥ξ∥	NOUN
ejpam-5592	98	12	=	=	SYM
ejpam-5592	98	13	sup	sup	NOUN
ejpam-5592	98	14	{	{	PUNCT
ejpam-5592	98	15	|ξ	|ξ	PROPN
ejpam-5592	98	16	(	(	PUNCT
ejpam-5592	98	17	z)|	z)|	INTJ
ejpam-5592	98	18	:	:	PUNCT
ejpam-5592	98	19	z	z	PROPN
ejpam-5592	98	20	∈	∈	PROPN
ejpam-5592	98	21	ℑ	ℑ	PROPN
ejpam-5592	98	22	=	=	PUNCT
ejpam-5592	99	1	[	[	X
ejpam-5592	99	2	κ	κ	X
ejpam-5592	99	3	,	,	PUNCT
ejpam-5592	99	4	ϱ	ϱ	ADP
ejpam-5592	99	5	]	]	PUNCT
ejpam-5592	99	6	}	}	PUNCT
ejpam-5592	99	7	.	.	PUNCT
ejpam-5592	100	1	here	here	ADV
ejpam-5592	100	2	,	,	PUNCT
ejpam-5592	100	3	we	we	PRON
ejpam-5592	100	4	shall	shall	AUX
ejpam-5592	100	5	write	write	VERB
ejpam-5592	100	6	for	for	ADP
ejpam-5592	100	7	simplicity	simplicity	NOUN
ejpam-5592	100	8	ϖu(τ	ϖu(τ	NUM
ejpam-5592	100	9	)	)	PUNCT
ejpam-5592	100	10	=	=	SYM
ejpam-5592	100	11	ϖu	ϖu	PROPN
ejpam-5592	100	12	and	and	CCONJ
ejpam-5592	100	13	θu(τ	θu(τ	NUM
ejpam-5592	100	14	)	)	PUNCT
ejpam-5592	101	1	=	=	NUM
ejpam-5592	101	2	θu	θu	NOUN
ejpam-5592	101	3	for	for	ADP
ejpam-5592	101	4	all	all	PRON
ejpam-5592	101	5	τ	τ	PROPN
ejpam-5592	101	6	∈	∈	PROPN
ejpam-5592	101	7	ℑu	ℑu	PROPN
ejpam-5592	101	8	.	.	PUNCT
ejpam-5592	101	9	definition	definition	NOUN
ejpam-5592	101	10	10	10	NUM
ejpam-5592	101	11	.	.	PUNCT
ejpam-5592	102	1	let	let	VERB
ejpam-5592	102	2	ϖu	ϖu	PRON
ejpam-5592	102	3	∈	∈	PROPN
ejpam-5592	102	4	(	(	PUNCT
ejpam-5592	102	5	k	k	NOUN
ejpam-5592	102	6	,	,	PUNCT
ejpam-5592	102	7	k	k	PROPN
ejpam-5592	103	1	+	+	PROPN
ejpam-5592	103	2	1	1	X
ejpam-5592	103	3	]	]	PUNCT
ejpam-5592	103	4	and	and	CCONJ
ejpam-5592	103	5	θu	θu	X
ejpam-5592	103	6	=	=	PUNCT
ejpam-5592	103	7	ϖu	ϖu	PROPN
ejpam-5592	104	1	−	−	PROPN
ejpam-5592	104	2	k	k	PROPN
ejpam-5592	104	3	,	,	PUNCT
ejpam-5592	104	4	for	for	ADP
ejpam-5592	104	5	k	k	PROPN
ejpam-5592	104	6	≥	≥	PROPN
ejpam-5592	104	7	0	0	NUM
ejpam-5592	104	8	,	,	PUNCT
ejpam-5592	104	9	u	u	NOUN
ejpam-5592	104	10	≥	≥	PROPN
ejpam-5592	104	11	1	1	NUM
ejpam-5592	104	12	.	.	PUNCT
ejpam-5592	105	1	for	for	ADP
ejpam-5592	105	2	the	the	DET
ejpam-5592	105	3	function	function	NOUN
ejpam-5592	105	4	℘	℘	PROPN
ejpam-5592	105	5	∈	∈	PROPN
ejpam-5592	105	6	h1(κ	h1(κ	PROPN
ejpam-5592	105	7	,	,	PUNCT
ejpam-5592	105	8	ϱ	ϱ	NOUN
ejpam-5592	105	9	)	)	PUNCT
ejpam-5592	105	10	,	,	PUNCT
ejpam-5592	105	11	the	the	DET
ejpam-5592	105	12	ϖuth	ϖuth	NOUN
ejpam-5592	105	13	left	left	ADJ
ejpam-5592	105	14	-	-	PUNCT
ejpam-5592	105	15	sided	side	VERB
ejpam-5592	105	16	ψ−rl	ψ−rl	PROPN
ejpam-5592	105	17	-	-	PUNCT
ejpam-5592	105	18	ab	ab	NOUN
ejpam-5592	105	19	fractional	fractional	ADJ
ejpam-5592	105	20	derivative	derivative	NOUN
ejpam-5592	105	21	under	under	ADP
ejpam-5592	105	22	the	the	DET
ejpam-5592	105	23	function	function	NOUN
ejpam-5592	105	24	ψ	ψ	X
ejpam-5592	105	25	with	with	ADP
ejpam-5592	105	26	ψ′(z	ψ′(z	NOUN
ejpam-5592	105	27	)	)	PUNCT
ejpam-5592	105	28	̸=	̸=	PROPN
ejpam-5592	105	29	0	0	NUM
ejpam-5592	105	30	,	,	PUNCT
ejpam-5592	105	31	for	for	ADP
ejpam-5592	105	32	all	all	DET
ejpam-5592	105	33	z	z	NOUN
ejpam-5592	105	34	∈	∈	NOUN
ejpam-5592	105	35	ℑ	ℑ	NOUN
ejpam-5592	105	36	is	be	AUX
ejpam-5592	105	37	defined	define	VERB
ejpam-5592	105	38	by	by	ADP
ejpam-5592	105	39	(	(	PUNCT
ejpam-5592	105	40	rlabdϖu	rlabdϖu	PROPN
ejpam-5592	105	41	,	,	PUNCT
ejpam-5592	105	42	ψ	ψ	VERB
ejpam-5592	105	43	κ	κ	PRON
ejpam-5592	105	44	℘	℘	PROPN
ejpam-5592	105	45	)	)	PUNCT
ejpam-5592	106	1	(	(	PUNCT
ejpam-5592	106	2	z	z	X
ejpam-5592	106	3	)	)	PUNCT
ejpam-5592	106	4	=	=	SYM
ejpam-5592	107	1	(	(	PUNCT
ejpam-5592	107	2	1	1	NUM
ejpam-5592	107	3	ψ′(z	ψ′(z	NOUN
ejpam-5592	107	4	)	)	PUNCT
ejpam-5592	107	5	d	d	X
ejpam-5592	107	6	dz	dz	PROPN
ejpam-5592	107	7	)	)	PUNCT
ejpam-5592	108	1	k	k	PROPN
ejpam-5592	108	2	(	(	PUNCT
ejpam-5592	108	3	rlabdθu	rlabdθu	NOUN
ejpam-5592	108	4	,	,	PUNCT
ejpam-5592	108	5	ψ	ψ	X
ejpam-5592	108	6	κ	κ	X
ejpam-5592	108	7	℘(z	℘(z	NOUN
ejpam-5592	108	8	)	)	PUNCT
ejpam-5592	108	9	)	)	PUNCT
ejpam-5592	109	1	=	=	PUNCT
ejpam-5592	109	2	(	(	PUNCT
ejpam-5592	109	3	1	1	NUM
ejpam-5592	109	4	ψ′(z	ψ′(z	NOUN
ejpam-5592	109	5	)	)	PUNCT
ejpam-5592	109	6	d	d	X
ejpam-5592	109	7	dz	dz	X
ejpam-5592	109	8	)	)	PUNCT
ejpam-5592	110	1	k	k	PROPN
ejpam-5592	110	2	λ(θu	λ(θu	NOUN
ejpam-5592	110	3	)	)	PUNCT
ejpam-5592	110	4	(	(	PUNCT
ejpam-5592	110	5	1−	1−	NUM
ejpam-5592	110	6	θu)ψ′(z	θu)ψ′(z	NOUN
ejpam-5592	110	7	)	)	PUNCT
ejpam-5592	110	8	d	d	X
ejpam-5592	110	9	dz	dz	PROPN
ejpam-5592	110	10	z∫	z∫	PROPN
ejpam-5592	110	11	κ	κ	PRON
ejpam-5592	110	12	ψ′(r)lθu	ψ′(r)lθu	NOUN
ejpam-5592	110	13	(	(	PUNCT
ejpam-5592	110	14	−θu	−θu	NOUN
ejpam-5592	110	15	1−	1−	NUM
ejpam-5592	110	16	θu	θu	NOUN
ejpam-5592	110	17	(	(	PUNCT
ejpam-5592	110	18	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	110	19	ψ(r))θu	ψ(r))θu	NOUN
ejpam-5592	110	20	)	)	PUNCT
ejpam-5592	110	21	℘	℘	PROPN
ejpam-5592	110	22	(	(	PUNCT
ejpam-5592	110	23	r	r	NOUN
ejpam-5592	110	24	)	)	PUNCT
ejpam-5592	110	25	dr	dr	NOUN
ejpam-5592	110	26	=	=	SYM
ejpam-5592	110	27	(	(	PUNCT
ejpam-5592	110	28	1	1	NUM
ejpam-5592	110	29	ψ′(z	ψ′(z	NOUN
ejpam-5592	110	30	)	)	PUNCT
ejpam-5592	110	31	d	d	X
ejpam-5592	110	32	dz	dz	X
ejpam-5592	110	33	)	)	PUNCT
ejpam-5592	110	34	k+1	k+1	PART
ejpam-5592	111	1	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	111	2	−	−	PROPN
ejpam-5592	111	3	k	k	X
ejpam-5592	111	4	)	)	PUNCT
ejpam-5592	111	5	(	(	PUNCT
ejpam-5592	111	6	k	k	PROPN
ejpam-5592	111	7	+	+	NUM
ejpam-5592	111	8	1−ϖu)ψ′(z	1−ϖu)ψ′(z	X
ejpam-5592	111	9	)	)	PUNCT
ejpam-5592	111	10	×	×	PROPN
ejpam-5592	111	11	z∫	z∫	PROPN
ejpam-5592	111	12	κ	κ	NOUN
ejpam-5592	111	13	ψ′(r)lϖu−k	ψ′(r)lϖu−k	NOUN
ejpam-5592	111	14	(	(	PUNCT
ejpam-5592	111	15	−	−	PROPN
ejpam-5592	111	16	(	(	PUNCT
ejpam-5592	111	17	ϖu	ϖu	PROPN
ejpam-5592	111	18	−	−	PROPN
ejpam-5592	111	19	k	k	NOUN
ejpam-5592	111	20	)	)	PUNCT
ejpam-5592	111	21	k	k	PROPN
ejpam-5592	112	1	+	+	PROPN
ejpam-5592	112	2	1−ϖu	1−ϖu	NUM
ejpam-5592	112	3	(	(	PUNCT
ejpam-5592	112	4	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	112	5	ψ(r))ϖu−k	ψ(r))ϖu−k	NOUN
ejpam-5592	112	6	)	)	PUNCT
ejpam-5592	112	7	℘	℘	PROPN
ejpam-5592	112	8	(	(	PUNCT
ejpam-5592	112	9	r	r	NOUN
ejpam-5592	112	10	)	)	PUNCT
ejpam-5592	112	11	dr	dr	PROPN
ejpam-5592	112	12	.	.	PROPN
ejpam-5592	112	13	h.a	h.a	PROPN
ejpam-5592	112	14	.	.	PROPN
ejpam-5592	112	15	hammad	hammad	PROPN
ejpam-5592	112	16	,	,	PUNCT
ejpam-5592	112	17	m.	m.	PROPN
ejpam-5592	112	18	de	de	X
ejpam-5592	112	19	la	la	PROPN
ejpam-5592	112	20	sen	sen	PROPN
ejpam-5592	112	21	/	/	SYM
ejpam-5592	112	22	eur	eur	PROPN
ejpam-5592	112	23	.	.	PUNCT
ejpam-5592	113	1	j.	j.	PROPN
ejpam-5592	113	2	pure	pure	PROPN
ejpam-5592	113	3	appl	appl	PROPN
ejpam-5592	113	4	.	.	PROPN
ejpam-5592	113	5	math	math	PROPN
ejpam-5592	113	6	,	,	PUNCT
ejpam-5592	113	7	17	17	NUM
ejpam-5592	113	8	(	(	PUNCT
ejpam-5592	113	9	4	4	NUM
ejpam-5592	113	10	)	)	PUNCT
ejpam-5592	113	11	(	(	PUNCT
ejpam-5592	113	12	2024	2024	NUM
ejpam-5592	113	13	)	)	PUNCT
ejpam-5592	113	14	,	,	PUNCT
ejpam-5592	113	15	3687	3687	NUM
ejpam-5592	113	16	-	-	SYM
ejpam-5592	113	17	3707	3707	NUM
ejpam-5592	113	18	3692	3692	NUM
ejpam-5592	113	19	definition	definition	NOUN
ejpam-5592	113	20	11	11	NUM
ejpam-5592	113	21	.	.	PUNCT
ejpam-5592	114	1	let	let	VERB
ejpam-5592	114	2	ϖu	ϖu	VERB
ejpam-5592	114	3	∈	∈	PROPN
ejpam-5592	114	4	(	(	PUNCT
ejpam-5592	114	5	k	k	NOUN
ejpam-5592	114	6	,	,	PUNCT
ejpam-5592	114	7	k	k	PROPN
ejpam-5592	115	1	+	+	PROPN
ejpam-5592	115	2	1	1	X
ejpam-5592	115	3	]	]	PUNCT
ejpam-5592	115	4	and	and	CCONJ
ejpam-5592	115	5	θu	θu	X
ejpam-5592	115	6	=	=	PUNCT
ejpam-5592	115	7	ϖu	ϖu	PROPN
ejpam-5592	116	1	−	−	PROPN
ejpam-5592	116	2	k	k	PROPN
ejpam-5592	116	3	,	,	PUNCT
ejpam-5592	116	4	for	for	ADP
ejpam-5592	116	5	k	k	PROPN
ejpam-5592	116	6	≥	≥	PROPN
ejpam-5592	116	7	0	0	NUM
ejpam-5592	116	8	,	,	PUNCT
ejpam-5592	116	9	u	u	NOUN
ejpam-5592	116	10	≥	≥	PROPN
ejpam-5592	116	11	1	1	NUM
ejpam-5592	116	12	.	.	PUNCT
ejpam-5592	117	1	for	for	ADP
ejpam-5592	117	2	the	the	DET
ejpam-5592	117	3	function	function	NOUN
ejpam-5592	117	4	℘(k	℘(k	NOUN
ejpam-5592	117	5	)	)	PUNCT
ejpam-5592	117	6	∈	∈	PROPN
ejpam-5592	118	1	h1(κ	h1(κ	PROPN
ejpam-5592	118	2	,	,	PUNCT
ejpam-5592	118	3	ϱ	ϱ	NOUN
ejpam-5592	118	4	)	)	PUNCT
ejpam-5592	118	5	,	,	PUNCT
ejpam-5592	118	6	the	the	DET
ejpam-5592	118	7	ϖuth	ϖuth	NOUN
ejpam-5592	118	8	left	left	ADJ
ejpam-5592	118	9	-	-	PUNCT
ejpam-5592	118	10	sided	sided	ADJ
ejpam-5592	118	11	ψ−abc	ψ−abc	NOUN
ejpam-5592	118	12	fractional	fractional	ADJ
ejpam-5592	118	13	derivative	derivative	NOUN
ejpam-5592	118	14	under	under	ADP
ejpam-5592	118	15	the	the	DET
ejpam-5592	118	16	function	function	NOUN
ejpam-5592	118	17	ψ	ψ	X
ejpam-5592	118	18	with	with	ADP
ejpam-5592	118	19	ψ′(z	ψ′(z	NOUN
ejpam-5592	118	20	)	)	PUNCT
ejpam-5592	118	21	̸=	̸=	PROPN
ejpam-5592	118	22	0	0	NUM
ejpam-5592	118	23	,	,	PUNCT
ejpam-5592	118	24	for	for	ADP
ejpam-5592	118	25	all	all	DET
ejpam-5592	118	26	z	z	NOUN
ejpam-5592	118	27	∈	∈	NOUN
ejpam-5592	118	28	ℑ	ℑ	PROPN
ejpam-5592	118	29	is	be	AUX
ejpam-5592	118	30	described	describe	VERB
ejpam-5592	118	31	as	as	ADP
ejpam-5592	118	32	(	(	PUNCT
ejpam-5592	118	33	cabdϖu	cabdϖu	PROPN
ejpam-5592	118	34	,	,	PUNCT
ejpam-5592	118	35	ψ	ψ	VERB
ejpam-5592	118	36	κ	κ	PRON
ejpam-5592	118	37	℘	℘	PROPN
ejpam-5592	118	38	)	)	PUNCT
ejpam-5592	118	39	(	(	PUNCT
ejpam-5592	118	40	z	z	X
ejpam-5592	118	41	)	)	PUNCT
ejpam-5592	118	42	=	=	SYM
ejpam-5592	118	43	(	(	PUNCT
ejpam-5592	118	44	cabdθu	cabdθu	X
ejpam-5592	118	45	,	,	PUNCT
ejpam-5592	118	46	ψ	ψ	VERB
ejpam-5592	119	1	κ	κ	PRON
ejpam-5592	119	2	℘	℘	PROPN
ejpam-5592	119	3	(	(	PUNCT
ejpam-5592	119	4	k	k	NOUN
ejpam-5592	119	5	)	)	PUNCT
ejpam-5592	119	6	ψ	ψ	NOUN
ejpam-5592	119	7	)	)	PUNCT
ejpam-5592	119	8	(	(	PUNCT
ejpam-5592	119	9	z	z	NOUN
ejpam-5592	119	10	)	)	PUNCT
ejpam-5592	119	11	=	=	SYM
ejpam-5592	119	12	λ(θu	λ(θu	NOUN
ejpam-5592	119	13	)	)	PUNCT
ejpam-5592	119	14	(	(	PUNCT
ejpam-5592	119	15	1−	1−	NUM
ejpam-5592	119	16	θu	θu	NOUN
ejpam-5592	119	17	)	)	PUNCT
ejpam-5592	119	18	z∫	z∫	PROPN
ejpam-5592	119	19	κ	κ	ADP
ejpam-5592	119	20	ψ′(r)lθu	ψ′(r)lθu	NOUN
ejpam-5592	119	21	(	(	PUNCT
ejpam-5592	119	22	−θu	−θu	NOUN
ejpam-5592	119	23	1−	1−	NUM
ejpam-5592	119	24	θu	θu	NOUN
ejpam-5592	119	25	(	(	PUNCT
ejpam-5592	119	26	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	119	27	ψ(r))θu	ψ(r))θu	NOUN
ejpam-5592	119	28	)	)	PUNCT
ejpam-5592	119	29	℘	℘	PROPN
ejpam-5592	119	30	(	(	PUNCT
ejpam-5592	119	31	k+1	k+1	NOUN
ejpam-5592	119	32	)	)	PUNCT
ejpam-5592	119	33	ψ	ψ	NOUN
ejpam-5592	119	34	(	(	PUNCT
ejpam-5592	119	35	r	r	NOUN
ejpam-5592	119	36	)	)	PUNCT
ejpam-5592	119	37	dr	dr	NOUN
ejpam-5592	119	38	=	=	PUNCT
ejpam-5592	119	39	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	119	40	−	−	PROPN
ejpam-5592	119	41	k	k	X
ejpam-5592	119	42	)	)	PUNCT
ejpam-5592	119	43	(	(	PUNCT
ejpam-5592	119	44	k	k	PROPN
ejpam-5592	119	45	+	+	SYM
ejpam-5592	119	46	1−ϖu	1−ϖu	NUM
ejpam-5592	119	47	)	)	PUNCT
ejpam-5592	119	48	×	×	PROPN
ejpam-5592	119	49	z∫	z∫	PROPN
ejpam-5592	119	50	κ	κ	NOUN
ejpam-5592	119	51	ψ′(r)lϖu−k	ψ′(r)lϖu−k	NOUN
ejpam-5592	119	52	(	(	PUNCT
ejpam-5592	119	53	−	−	PROPN
ejpam-5592	119	54	(	(	PUNCT
ejpam-5592	119	55	ϖu	ϖu	PROPN
ejpam-5592	119	56	−	−	PROPN
ejpam-5592	119	57	k	k	NOUN
ejpam-5592	119	58	)	)	PUNCT
ejpam-5592	119	59	k	k	PROPN
ejpam-5592	120	1	+	+	PROPN
ejpam-5592	120	2	1−ϖu	1−ϖu	NUM
ejpam-5592	120	3	(	(	PUNCT
ejpam-5592	120	4	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	120	5	ψ(r))ϖu−k	ψ(r))ϖu−k	NOUN
ejpam-5592	120	6	)	)	PUNCT
ejpam-5592	120	7	℘	℘	PROPN
ejpam-5592	120	8	(	(	PUNCT
ejpam-5592	120	9	k+1	k+1	NOUN
ejpam-5592	120	10	)	)	PUNCT
ejpam-5592	120	11	ψ	ψ	NOUN
ejpam-5592	120	12	(	(	PUNCT
ejpam-5592	120	13	r	r	NOUN
ejpam-5592	120	14	)	)	PUNCT
ejpam-5592	120	15	dr	dr	NOUN
ejpam-5592	120	16	,	,	PUNCT
ejpam-5592	120	17	where	where	SCONJ
ejpam-5592	120	18	℘	℘	PROPN
ejpam-5592	120	19	(	(	PUNCT
ejpam-5592	120	20	k	k	NOUN
ejpam-5592	120	21	)	)	PUNCT
ejpam-5592	120	22	ψ	ψ	X
ejpam-5592	120	23	(	(	PUNCT
ejpam-5592	120	24	z	z	NOUN
ejpam-5592	120	25	)	)	PUNCT
ejpam-5592	120	26	=	=	SYM
ejpam-5592	120	27	(	(	PUNCT
ejpam-5592	120	28	1	1	NUM
ejpam-5592	120	29	ψ′(z	ψ′(z	NOUN
ejpam-5592	120	30	)	)	PUNCT
ejpam-5592	120	31	d	d	X
ejpam-5592	120	32	dz	dz	X
ejpam-5592	120	33	)	)	PUNCT
ejpam-5592	120	34	k	k	PROPN
ejpam-5592	120	35	℘(z	℘(z	PROPN
ejpam-5592	120	36	)	)	PUNCT
ejpam-5592	120	37	and	and	CCONJ
ejpam-5592	120	38	℘	℘	PROPN
ejpam-5592	120	39	(	(	PUNCT
ejpam-5592	120	40	0	0	NUM
ejpam-5592	120	41	)	)	PUNCT
ejpam-5592	120	42	ψ	ψ	X
ejpam-5592	120	43	(	(	PUNCT
ejpam-5592	120	44	z	z	NOUN
ejpam-5592	120	45	)	)	PUNCT
ejpam-5592	120	46	=	=	SYM
ejpam-5592	120	47	℘(z	℘(z	ADJ
ejpam-5592	120	48	)	)	PUNCT
ejpam-5592	120	49	.	.	PUNCT
ejpam-5592	121	1	if	if	SCONJ
ejpam-5592	121	2	ϖu	ϖu	PROPN
ejpam-5592	121	3	=	=	SYM
ejpam-5592	121	4	n	n	CCONJ
ejpam-5592	121	5	∈	∈	PROPN
ejpam-5592	121	6	n	n	CCONJ
ejpam-5592	121	7	,	,	PUNCT
ejpam-5592	121	8	then	then	ADV
ejpam-5592	121	9	(	(	PUNCT
ejpam-5592	121	10	cabdϖu	cabdϖu	PROPN
ejpam-5592	121	11	,	,	PUNCT
ejpam-5592	121	12	ψ	ψ	VERB
ejpam-5592	121	13	κ	κ	PRON
ejpam-5592	121	14	℘	℘	PROPN
ejpam-5592	121	15	)	)	PUNCT
ejpam-5592	121	16	(	(	PUNCT
ejpam-5592	121	17	z	z	NOUN
ejpam-5592	121	18	)	)	PUNCT
ejpam-5592	121	19	=	=	PUNCT
ejpam-5592	121	20	℘	℘	PROPN
ejpam-5592	121	21	(	(	PUNCT
ejpam-5592	121	22	n	n	CCONJ
ejpam-5592	121	23	)	)	PUNCT
ejpam-5592	121	24	ψ	ψ	X
ejpam-5592	121	25	(	(	PUNCT
ejpam-5592	121	26	z	z	NOUN
ejpam-5592	121	27	)	)	PUNCT
ejpam-5592	121	28	.	.	PUNCT
ejpam-5592	122	1	definition	definition	NOUN
ejpam-5592	122	2	12	12	NUM
ejpam-5592	122	3	.	.	PUNCT
ejpam-5592	123	1	let	let	VERB
ejpam-5592	123	2	ϖu	ϖu	VERB
ejpam-5592	123	3	∈	∈	PROPN
ejpam-5592	123	4	(	(	PUNCT
ejpam-5592	123	5	k	k	NOUN
ejpam-5592	123	6	,	,	PUNCT
ejpam-5592	123	7	k	k	PROPN
ejpam-5592	124	1	+	+	PROPN
ejpam-5592	124	2	1	1	X
ejpam-5592	124	3	]	]	PUNCT
ejpam-5592	124	4	and	and	CCONJ
ejpam-5592	124	5	θu	θu	X
ejpam-5592	124	6	=	=	PUNCT
ejpam-5592	124	7	ϖu	ϖu	PROPN
ejpam-5592	125	1	−	−	PROPN
ejpam-5592	125	2	k	k	PROPN
ejpam-5592	125	3	,	,	PUNCT
ejpam-5592	125	4	for	for	ADP
ejpam-5592	125	5	k	k	PROPN
ejpam-5592	125	6	≥	≥	PROPN
ejpam-5592	125	7	0	0	NUM
ejpam-5592	125	8	,	,	PUNCT
ejpam-5592	125	9	u	u	NOUN
ejpam-5592	125	10	≥	≥	PROPN
ejpam-5592	125	11	1	1	NUM
ejpam-5592	125	12	.	.	PUNCT
ejpam-5592	126	1	for	for	ADP
ejpam-5592	126	2	the	the	DET
ejpam-5592	126	3	function	function	NOUN
ejpam-5592	126	4	℘	℘	PROPN
ejpam-5592	126	5	∈	∈	PROPN
ejpam-5592	126	6	h1(κ	h1(κ	PROPN
ejpam-5592	126	7	,	,	PUNCT
ejpam-5592	126	8	ϱ	ϱ	NOUN
ejpam-5592	126	9	)	)	PUNCT
ejpam-5592	126	10	,	,	PUNCT
ejpam-5592	126	11	the	the	DET
ejpam-5592	126	12	ϖuth	ϖuth	NOUN
ejpam-5592	126	13	left	left	ADJ
ejpam-5592	126	14	-	-	PUNCT
ejpam-5592	126	15	sided	side	VERB
ejpam-5592	126	16	ψ−rl	ψ−rl	PROPN
ejpam-5592	126	17	-	-	PUNCT
ejpam-5592	126	18	ab	ab	NOUN
ejpam-5592	126	19	fractional	fractional	ADJ
ejpam-5592	126	20	integral	integral	ADJ
ejpam-5592	126	21	under	under	ADP
ejpam-5592	126	22	the	the	DET
ejpam-5592	126	23	function	function	NOUN
ejpam-5592	126	24	ψ	ψ	X
ejpam-5592	126	25	with	with	ADP
ejpam-5592	126	26	ψ′(z	ψ′(z	NOUN
ejpam-5592	126	27	)	)	PUNCT
ejpam-5592	126	28	̸=	̸=	PROPN
ejpam-5592	126	29	0	0	NUM
ejpam-5592	126	30	,	,	PUNCT
ejpam-5592	126	31	for	for	ADP
ejpam-5592	126	32	all	all	DET
ejpam-5592	126	33	z	z	NOUN
ejpam-5592	126	34	∈	∈	NOUN
ejpam-5592	126	35	ℑ	ℑ	NOUN
ejpam-5592	126	36	is	be	AUX
ejpam-5592	126	37	defined	define	VERB
ejpam-5592	126	38	by	by	ADP
ejpam-5592	126	39	(	(	PUNCT
ejpam-5592	126	40	rlabℜϖu	rlabℜϖu	PROPN
ejpam-5592	126	41	,	,	PUNCT
ejpam-5592	126	42	ψκ	ψκ	VERB
ejpam-5592	126	43	℘	℘	PROPN
ejpam-5592	126	44	)	)	PUNCT
ejpam-5592	126	45	(	(	PUNCT
ejpam-5592	126	46	z	z	X
ejpam-5592	126	47	)	)	PUNCT
ejpam-5592	126	48	=	=	SYM
ejpam-5592	126	49	(	(	PUNCT
ejpam-5592	126	50	rlℜk	rlℜk	PROPN
ejpam-5592	126	51	,	,	PUNCT
ejpam-5592	127	1	ψκ	ψκ	VERB
ejpam-5592	127	2	abℜθu	abℜθu	ADJ
ejpam-5592	127	3	,	,	PUNCT
ejpam-5592	127	4	ψκ	ψκ	PROPN
ejpam-5592	127	5	℘	℘	PROPN
ejpam-5592	127	6	)	)	PUNCT
ejpam-5592	127	7	(	(	PUNCT
ejpam-5592	127	8	z	z	X
ejpam-5592	127	9	)	)	PUNCT
ejpam-5592	127	10	=	=	SYM
ejpam-5592	128	1	(	(	PUNCT
ejpam-5592	128	2	abℜθu	abℜθu	PROPN
ejpam-5592	128	3	,	,	PUNCT
ejpam-5592	128	4	ψκ	ψκ	PROPN
ejpam-5592	128	5	rlℜk	rlℜk	PROPN
ejpam-5592	128	6	,	,	PUNCT
ejpam-5592	128	7	ψκ	ψκ	VERB
ejpam-5592	128	8	℘	℘	PROPN
ejpam-5592	128	9	)	)	PUNCT
ejpam-5592	128	10	(	(	PUNCT
ejpam-5592	128	11	z	z	X
ejpam-5592	128	12	)	)	PUNCT
ejpam-5592	128	13	=	=	SYM
ejpam-5592	129	1	k	k	X
ejpam-5592	130	1	+	+	CCONJ
ejpam-5592	130	2	1−ϖu	1−ϖu	NUM
ejpam-5592	130	3	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	130	4	−	−	PROPN
ejpam-5592	130	5	k	k	X
ejpam-5592	130	6	)	)	PUNCT
ejpam-5592	130	7	rl	rl	ADP
ejpam-5592	130	8	ℜk	ℜk	NOUN
ejpam-5592	130	9	,	,	PUNCT
ejpam-5592	130	10	ψκ	ψκ	VERB
ejpam-5592	130	11	℘	℘	PROPN
ejpam-5592	130	12	(	(	PUNCT
ejpam-5592	130	13	z	z	NOUN
ejpam-5592	130	14	)	)	PUNCT
ejpam-5592	131	1	+	+	CCONJ
ejpam-5592	131	2	ϖu	ϖu	PRON
ejpam-5592	131	3	−	−	NOUN
ejpam-5592	131	4	k	k	PROPN
ejpam-5592	131	5	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	131	6	−	−	PROPN
ejpam-5592	131	7	k	k	X
ejpam-5592	131	8	)	)	PUNCT
ejpam-5592	131	9	rl	rl	ADP
ejpam-5592	131	10	ℜϖu	ℜϖu	PROPN
ejpam-5592	131	11	,	,	PUNCT
ejpam-5592	131	12	ψκ	ψκ	PROPN
ejpam-5592	131	13	℘	℘	PROPN
ejpam-5592	131	14	(	(	PUNCT
ejpam-5592	131	15	z	z	NOUN
ejpam-5592	131	16	)	)	PUNCT
ejpam-5592	131	17	,	,	PUNCT
ejpam-5592	131	18	where	where	SCONJ
ejpam-5592	131	19	ℜk	ℜk	NOUN
ejpam-5592	131	20	,	,	PUNCT
ejpam-5592	131	21	ψκ	ψκ	VERB
ejpam-5592	131	22	takes	take	VERB
ejpam-5592	131	23	the	the	DET
ejpam-5592	131	24	form	form	NOUN
ejpam-5592	131	25	ℜk	ℜk	PROPN
ejpam-5592	131	26	,	,	PUNCT
ejpam-5592	131	27	ψκ	ψκ	VERB
ejpam-5592	131	28	℘	℘	PROPN
ejpam-5592	131	29	(	(	PUNCT
ejpam-5592	131	30	z	z	NOUN
ejpam-5592	131	31	)	)	PUNCT
ejpam-5592	131	32	=	=	SYM
ejpam-5592	131	33	1	1	NUM
ejpam-5592	131	34	γ	γ	X
ejpam-5592	131	35	(	(	PUNCT
ejpam-5592	131	36	k	k	NOUN
ejpam-5592	131	37	)	)	PUNCT
ejpam-5592	131	38	z∫	z∫	NOUN
ejpam-5592	131	39	κ	κ	NOUN
ejpam-5592	131	40	ψ′(r	ψ′(r	PROPN
ejpam-5592	131	41	)	)	PUNCT
ejpam-5592	131	42	(	(	PUNCT
ejpam-5592	131	43	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	131	44	ψ(r))k−1	ψ(r))k−1	NUM
ejpam-5592	131	45	ξ	ξ	PROPN
ejpam-5592	131	46	(	(	PUNCT
ejpam-5592	131	47	r	r	NOUN
ejpam-5592	131	48	)	)	PUNCT
ejpam-5592	131	49	dr	dr	PROPN
ejpam-5592	131	50	.	.	PROPN
ejpam-5592	131	51	remark	remark	PROPN
ejpam-5592	131	52	2	2	NUM
ejpam-5592	131	53	.	.	PUNCT
ejpam-5592	131	54	for	for	ADP
ejpam-5592	131	55	u	u	PROPN
ejpam-5592	131	56	≥	≥	NUM
ejpam-5592	131	57	1	1	NUM
ejpam-5592	131	58	,	,	PUNCT
ejpam-5592	131	59	it	it	PRON
ejpam-5592	131	60	is	be	AUX
ejpam-5592	131	61	clear	clear	ADJ
ejpam-5592	131	62	that	that	SCONJ
ejpam-5592	131	63	(	(	PUNCT
ejpam-5592	131	64	i	i	NOUN
ejpam-5592	131	65	)	)	PUNCT
ejpam-5592	131	66	if	if	SCONJ
ejpam-5592	131	67	we	we	PRON
ejpam-5592	131	68	take	take	VERB
ejpam-5592	131	69	ϖu	ϖu	NOUN
ejpam-5592	131	70	=	=	PUNCT
ejpam-5592	131	71	ϖ	ϖ	X
ejpam-5592	131	72	∈	∈	PROPN
ejpam-5592	131	73	(	(	PUNCT
ejpam-5592	131	74	0	0	NUM
ejpam-5592	131	75	,	,	PUNCT
ejpam-5592	131	76	1	1	NUM
ejpam-5592	131	77	]	]	PUNCT
ejpam-5592	131	78	in	in	ADP
ejpam-5592	131	79	definitions	definition	NOUN
ejpam-5592	131	80	10	10	NUM
ejpam-5592	131	81	,	,	PUNCT
ejpam-5592	131	82	11	11	NUM
ejpam-5592	131	83	and	and	CCONJ
ejpam-5592	131	84	12	12	NUM
ejpam-5592	131	85	,	,	PUNCT
ejpam-5592	131	86	then	then	ADV
ejpam-5592	131	87	we	we	PRON
ejpam-5592	131	88	have	have	VERB
ejpam-5592	131	89	definitions	definition	NOUN
ejpam-5592	131	90	6	6	NUM
ejpam-5592	131	91	,	,	PUNCT
ejpam-5592	131	92	7	7	NUM
ejpam-5592	131	93	and	and	CCONJ
ejpam-5592	131	94	8	8	NUM
ejpam-5592	131	95	,	,	PUNCT
ejpam-5592	131	96	respectively	respectively	ADV
ejpam-5592	131	97	.	.	PUNCT
ejpam-5592	132	1	(	(	PUNCT
ejpam-5592	132	2	ii	ii	NOUN
ejpam-5592	132	3	)	)	PUNCT
ejpam-5592	132	4	if	if	SCONJ
ejpam-5592	132	5	we	we	PRON
ejpam-5592	132	6	put	put	VERB
ejpam-5592	132	7	ϖu	ϖu	NOUN
ejpam-5592	132	8	=	=	PUNCT
ejpam-5592	132	9	ϖ	ϖ	PROPN
ejpam-5592	132	10	=	=	SYM
ejpam-5592	132	11	k	k	PROPN
ejpam-5592	133	1	+	+	NOUN
ejpam-5592	133	2	1	1	NUM
ejpam-5592	133	3	,	,	PUNCT
ejpam-5592	133	4	then	then	ADV
ejpam-5592	133	5	ϖu	ϖu	PROPN
ejpam-5592	133	6	=	=	SYM
ejpam-5592	133	7	1	1	NUM
ejpam-5592	133	8	and	and	CCONJ
ejpam-5592	133	9	hence	hence	ADV
ejpam-5592	133	10	the	the	DET
ejpam-5592	133	11	following	follow	VERB
ejpam-5592	133	12	is	be	AUX
ejpam-5592	133	13	true	true	ADJ
ejpam-5592	133	14	for	for	ADP
ejpam-5592	133	15	our	our	PRON
ejpam-5592	133	16	generalization	generalization	NOUN
ejpam-5592	133	17	to	to	ADP
ejpam-5592	133	18	the	the	DET
ejpam-5592	133	19	higher	high	ADJ
ejpam-5592	133	20	-	-	PUNCT
ejpam-5592	133	21	variable	variable	ADJ
ejpam-5592	133	22	order	order	NOUN
ejpam-5592	133	23	cases	case	NOUN
ejpam-5592	133	24	:(	:(	PUNCT
ejpam-5592	133	25	rlabdϖu	rlabdϖu	NOUN
ejpam-5592	133	26	,	,	PUNCT
ejpam-5592	133	27	ψ	ψ	VERB
ejpam-5592	133	28	κ	κ	PRON
ejpam-5592	133	29	℘	℘	PROPN
ejpam-5592	133	30	)	)	PUNCT
ejpam-5592	133	31	(	(	PUNCT
ejpam-5592	133	32	z	z	X
ejpam-5592	133	33	)	)	PUNCT
ejpam-5592	133	34	=	=	SYM
ejpam-5592	133	35	(	(	PUNCT
ejpam-5592	133	36	1	1	NUM
ejpam-5592	133	37	ψ′(z	ψ′(z	NOUN
ejpam-5592	133	38	)	)	PUNCT
ejpam-5592	133	39	d	d	X
ejpam-5592	133	40	dz	dz	PROPN
ejpam-5592	134	1	)	)	PUNCT
ejpam-5592	134	2	k	k	PROPN
ejpam-5592	134	3	(	(	PUNCT
ejpam-5592	134	4	rlabd1,ψ	rlabd1,ψ	NOUN
ejpam-5592	134	5	κ	κ	X
ejpam-5592	134	6	℘(z	℘(z	NOUN
ejpam-5592	134	7	)	)	PUNCT
ejpam-5592	134	8	)	)	PUNCT
ejpam-5592	135	1	=	=	PUNCT
ejpam-5592	135	2	℘	℘	PROPN
ejpam-5592	135	3	(	(	PUNCT
ejpam-5592	135	4	k+1	k+1	NOUN
ejpam-5592	135	5	)	)	PUNCT
ejpam-5592	135	6	ψ	ψ	X
ejpam-5592	135	7	(	(	PUNCT
ejpam-5592	135	8	z	z	NOUN
ejpam-5592	135	9	)	)	PUNCT
ejpam-5592	135	10	,	,	PUNCT
ejpam-5592	135	11	(	(	PUNCT
ejpam-5592	135	12	cabdϖu	cabdϖu	PROPN
ejpam-5592	135	13	,	,	PUNCT
ejpam-5592	135	14	ψ	ψ	X
ejpam-5592	135	15	κ	κ	PRON
ejpam-5592	135	16	℘	℘	PROPN
ejpam-5592	135	17	)	)	PUNCT
ejpam-5592	135	18	(	(	PUNCT
ejpam-5592	135	19	z	z	X
ejpam-5592	135	20	)	)	PUNCT
ejpam-5592	135	21	=	=	SYM
ejpam-5592	136	1	(	(	PUNCT
ejpam-5592	136	2	cabd1,ψ	cabd1,ψ	X
ejpam-5592	136	3	κ	κ	PROPN
ejpam-5592	136	4	℘	℘	PROPN
ejpam-5592	136	5	(	(	PUNCT
ejpam-5592	136	6	k	k	NOUN
ejpam-5592	136	7	)	)	PUNCT
ejpam-5592	136	8	ψ	ψ	NOUN
ejpam-5592	136	9	)	)	PUNCT
ejpam-5592	136	10	(	(	PUNCT
ejpam-5592	136	11	z	z	X
ejpam-5592	136	12	)	)	PUNCT
ejpam-5592	136	13	=	=	PUNCT
ejpam-5592	136	14	℘	℘	PROPN
ejpam-5592	136	15	(	(	PUNCT
ejpam-5592	136	16	k+1	k+1	NOUN
ejpam-5592	136	17	)	)	PUNCT
ejpam-5592	136	18	ψ	ψ	X
ejpam-5592	136	19	(	(	PUNCT
ejpam-5592	136	20	z	z	NOUN
ejpam-5592	136	21	)	)	PUNCT
ejpam-5592	136	22	,	,	PUNCT
ejpam-5592	136	23	(	(	PUNCT
ejpam-5592	136	24	rlabℜϖu	rlabℜϖu	NOUN
ejpam-5592	136	25	,	,	PUNCT
ejpam-5592	136	26	ψκ	ψκ	VERB
ejpam-5592	136	27	℘	℘	PROPN
ejpam-5592	136	28	)	)	PUNCT
ejpam-5592	136	29	(	(	PUNCT
ejpam-5592	136	30	z	z	X
ejpam-5592	136	31	)	)	PUNCT
ejpam-5592	136	32	=	=	SYM
ejpam-5592	136	33	(	(	PUNCT
ejpam-5592	136	34	rlℜk	rlℜk	PROPN
ejpam-5592	136	35	,	,	PUNCT
ejpam-5592	136	36	ψκ	ψκ	VERB
ejpam-5592	136	37	abℜ1,ψ	abℜ1,ψ	X
ejpam-5592	136	38	κ	κ	PROPN
ejpam-5592	136	39	℘	℘	PROPN
ejpam-5592	136	40	)	)	PUNCT
ejpam-5592	136	41	(	(	PUNCT
ejpam-5592	136	42	z	z	X
ejpam-5592	136	43	)	)	PUNCT
ejpam-5592	136	44	=	=	SYM
ejpam-5592	137	1	(	(	PUNCT
ejpam-5592	137	2	rlℜk+1,ψ	rlℜk+1,ψ	X
ejpam-5592	137	3	κ	κ	NOUN
ejpam-5592	137	4	℘	℘	PROPN
ejpam-5592	137	5	)	)	PUNCT
ejpam-5592	137	6	(	(	PUNCT
ejpam-5592	137	7	z	z	NOUN
ejpam-5592	137	8	)	)	PUNCT
ejpam-5592	137	9	.	.	PUNCT
ejpam-5592	138	1	h.a	h.a	PROPN
ejpam-5592	138	2	.	.	PROPN
ejpam-5592	138	3	hammad	hammad	PROPN
ejpam-5592	138	4	,	,	PUNCT
ejpam-5592	138	5	m.	m.	PROPN
ejpam-5592	138	6	de	de	X
ejpam-5592	138	7	la	la	PROPN
ejpam-5592	138	8	sen	sen	PROPN
ejpam-5592	138	9	/	/	SYM
ejpam-5592	138	10	eur	eur	PROPN
ejpam-5592	138	11	.	.	PUNCT
ejpam-5592	139	1	j.	j.	PROPN
ejpam-5592	139	2	pure	pure	PROPN
ejpam-5592	139	3	appl	appl	PROPN
ejpam-5592	139	4	.	.	PROPN
ejpam-5592	139	5	math	math	PROPN
ejpam-5592	139	6	,	,	PUNCT
ejpam-5592	139	7	17	17	NUM
ejpam-5592	139	8	(	(	PUNCT
ejpam-5592	139	9	4	4	NUM
ejpam-5592	139	10	)	)	PUNCT
ejpam-5592	139	11	(	(	PUNCT
ejpam-5592	139	12	2024	2024	NUM
ejpam-5592	139	13	)	)	PUNCT
ejpam-5592	139	14	,	,	PUNCT
ejpam-5592	139	15	3687	3687	NUM
ejpam-5592	139	16	-	-	SYM
ejpam-5592	139	17	3707	3707	NUM
ejpam-5592	139	18	3693	3693	NUM
ejpam-5592	139	19	lemma	lemma	PROPN
ejpam-5592	139	20	3	3	X
ejpam-5592	139	21	.	.	X
ejpam-5592	140	1	for	for	ADP
ejpam-5592	140	2	ϖu	ϖu	NOUN
ejpam-5592	140	3	=	=	PUNCT
ejpam-5592	140	4	ϖ	ϖ	X
ejpam-5592	140	5	∈	∈	PROPN
ejpam-5592	140	6	(	(	PUNCT
ejpam-5592	140	7	0	0	NUM
ejpam-5592	140	8	,	,	PUNCT
ejpam-5592	140	9	1	1	NUM
ejpam-5592	140	10	]	]	PUNCT
ejpam-5592	140	11	,	,	PUNCT
ejpam-5592	140	12	u	u	NOUN
ejpam-5592	140	13	≥	≥	NOUN
ejpam-5592	140	14	1	1	NUM
ejpam-5592	140	15	,	,	PUNCT
ejpam-5592	140	16	the	the	DET
ejpam-5592	140	17	equations	equation	NOUN
ejpam-5592	140	18	below	below	ADP
ejpam-5592	140	19	hold	hold	NOUN
ejpam-5592	140	20	(	(	PUNCT
ejpam-5592	140	21	i	i	NOUN
ejpam-5592	140	22	)	)	PUNCT
ejpam-5592	140	23	(	(	PUNCT
ejpam-5592	140	24	rlabℜϖ,ψκ	rlabℜϖ,ψκ	X
ejpam-5592	140	25	cabdϖ,ψ	cabdϖ,ψ	X
ejpam-5592	140	26	κ	κ	NOUN
ejpam-5592	140	27	℘	℘	PROPN
ejpam-5592	140	28	)	)	PUNCT
ejpam-5592	140	29	(	(	PUNCT
ejpam-5592	140	30	z	z	X
ejpam-5592	140	31	)	)	PUNCT
ejpam-5592	140	32	=	=	SYM
ejpam-5592	140	33	℘(z)−	℘(z)−	PROPN
ejpam-5592	140	34	℘(κ	℘(κ	NOUN
ejpam-5592	140	35	)	)	PUNCT
ejpam-5592	140	36	.	.	PUNCT
ejpam-5592	141	1	(	(	PUNCT
ejpam-5592	141	2	ii	ii	NOUN
ejpam-5592	141	3	)	)	PUNCT
ejpam-5592	141	4	(	(	PUNCT
ejpam-5592	141	5	cabdϖ,ψ	cabdϖ,ψ	X
ejpam-5592	141	6	κ	κ	PRON
ejpam-5592	141	7	rlabℜϖ,ψκ	rlabℜϖ,ψκ	PROPN
ejpam-5592	141	8	℘	℘	PROPN
ejpam-5592	141	9	)	)	PUNCT
ejpam-5592	141	10	(	(	PUNCT
ejpam-5592	141	11	z	z	X
ejpam-5592	141	12	)	)	PUNCT
ejpam-5592	141	13	=	=	SYM
ejpam-5592	142	1	℘(z)−	℘(z)−	PROPN
ejpam-5592	142	2	℘(κ)lϖ	℘(κ)lϖ	PROPN
ejpam-5592	142	3	(	(	PUNCT
ejpam-5592	142	4	−ϖ	−ϖ	NOUN
ejpam-5592	142	5	1−ϖ	1−ϖ	NUM
ejpam-5592	142	6	(	(	PUNCT
ejpam-5592	142	7	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	142	8	ψ(κ))ϖ	ψ(κ))ϖ	PART
ejpam-5592	142	9	)	)	PUNCT
ejpam-5592	142	10	.	.	PUNCT
ejpam-5592	143	1	proof	proof	NOUN
ejpam-5592	143	2	.	.	PUNCT
ejpam-5592	144	1	(	(	PUNCT
ejpam-5592	144	2	i	i	NOUN
ejpam-5592	144	3	)	)	PUNCT
ejpam-5592	144	4	utilizing	utilize	VERB
ejpam-5592	144	5	definitions	definition	NOUN
ejpam-5592	144	6	7	7	NUM
ejpam-5592	144	7	and	and	CCONJ
ejpam-5592	144	8	8	8	NUM
ejpam-5592	144	9	,	,	PUNCT
ejpam-5592	144	10	we	we	PRON
ejpam-5592	144	11	get	get	VERB
ejpam-5592	144	12	(	(	PUNCT
ejpam-5592	144	13	rlabℜϖ,ψκ	rlabℜϖ,ψκ	X
ejpam-5592	144	14	cabdϖ,ψ	cabdϖ,ψ	X
ejpam-5592	144	15	κ	κ	NOUN
ejpam-5592	144	16	℘	℘	PROPN
ejpam-5592	144	17	)	)	PUNCT
ejpam-5592	144	18	(	(	PUNCT
ejpam-5592	144	19	z	z	X
ejpam-5592	144	20	)	)	PUNCT
ejpam-5592	144	21	=	=	PUNCT
ejpam-5592	144	22	λ(ϖ	λ(ϖ	NOUN
ejpam-5592	144	23	)	)	PUNCT
ejpam-5592	144	24	(	(	PUNCT
ejpam-5592	144	25	1−ϖ	1−ϖ	NUM
ejpam-5592	144	26	)	)	PUNCT
ejpam-5592	144	27	(	(	PUNCT
ejpam-5592	144	28	cabdϖ,ψ	cabdϖ,ψ	X
ejpam-5592	144	29	κ	κ	NOUN
ejpam-5592	144	30	℘	℘	PROPN
ejpam-5592	144	31	)	)	PUNCT
ejpam-5592	144	32	(	(	PUNCT
ejpam-5592	144	33	z	z	NOUN
ejpam-5592	144	34	)	)	PUNCT
ejpam-5592	145	1	+	+	CCONJ
ejpam-5592	145	2	ϖ	ϖ	X
ejpam-5592	145	3	λ(ϖ	λ(ϖ	NOUN
ejpam-5592	145	4	)	)	PUNCT
ejpam-5592	145	5	(	(	PUNCT
ejpam-5592	145	6	rlℜϖ,ψκ	rlℜϖ,ψκ	X
ejpam-5592	145	7	cabdϖ,ψ	cabdϖ,ψ	X
ejpam-5592	145	8	κ	κ	NOUN
ejpam-5592	145	9	℘	℘	PROPN
ejpam-5592	145	10	)	)	PUNCT
ejpam-5592	145	11	(	(	PUNCT
ejpam-5592	145	12	z	z	X
ejpam-5592	145	13	)	)	PUNCT
ejpam-5592	145	14	=	=	SYM
ejpam-5592	146	1	∞∑	∞∑	NUM
ejpam-5592	146	2	j=0	j=0	PROPN
ejpam-5592	146	3	(	(	PUNCT
ejpam-5592	146	4	−ϖ	−ϖ	NOUN
ejpam-5592	146	5	1−ϖ	1−ϖ	NUM
ejpam-5592	146	6	)	)	PUNCT
ejpam-5592	146	7	j	j	PROPN
ejpam-5592	146	8	z∫	z∫	PROPN
ejpam-5592	146	9	κ	κ	PRON
ejpam-5592	146	10	ψ′(r	ψ′(r	PROPN
ejpam-5592	146	11	)	)	PUNCT
ejpam-5592	146	12	(	(	PUNCT
ejpam-5592	146	13	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	146	14	ψ(r	ψ(r	PROPN
ejpam-5592	146	15	)	)	PUNCT
ejpam-5592	147	1	γ(1	γ(1	PROPN
ejpam-5592	147	2	+	+	CCONJ
ejpam-5592	147	3	jϖ	jϖ	PROPN
ejpam-5592	147	4	)	)	PUNCT
ejpam-5592	147	5	)	)	PUNCT
ejpam-5592	148	1	jϖ	jϖ	ADP
ejpam-5592	148	2	℘′	℘′	PROPN
ejpam-5592	148	3	ψ	ψ	X
ejpam-5592	148	4	(	(	PUNCT
ejpam-5592	148	5	r	r	NOUN
ejpam-5592	148	6	)	)	PUNCT
ejpam-5592	148	7	dr	dr	NOUN
ejpam-5592	148	8	+	+	PROPN
ejpam-5592	148	9	ϖ	ϖ	PROPN
ejpam-5592	148	10	1−ϖ	1−ϖ	NUM
ejpam-5592	148	11	rl	rl	NOUN
ejpam-5592	148	12	ℜϖ,ψκ	ℜϖ,ψκ	NOUN
ejpam-5592	149	1	∞∑	∞∑	NUM
ejpam-5592	149	2	j=0	j=0	PROPN
ejpam-5592	149	3	(	(	PUNCT
ejpam-5592	149	4	−ϖ	−ϖ	NOUN
ejpam-5592	149	5	1−ϖ	1−ϖ	NUM
ejpam-5592	149	6	)	)	PUNCT
ejpam-5592	149	7	j	j	PROPN
ejpam-5592	149	8	z∫	z∫	PROPN
ejpam-5592	149	9	κ	κ	NOUN
ejpam-5592	149	10	ψ′(r	ψ′(r	PROPN
ejpam-5592	149	11	)	)	PUNCT
ejpam-5592	150	1	[	[	X
ejpam-5592	150	2	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	150	3	ψ(r	ψ(r	PROPN
ejpam-5592	150	4	)	)	PUNCT
ejpam-5592	150	5	]	]	PUNCT
ejpam-5592	151	1	γ(1	γ(1	PROPN
ejpam-5592	151	2	+	+	CCONJ
ejpam-5592	151	3	jϖ	jϖ	VERB
ejpam-5592	151	4	)	)	PUNCT
ejpam-5592	151	5	jϖ	jϖ	ADP
ejpam-5592	151	6	℘′	℘′	PROPN
ejpam-5592	151	7	ψ	ψ	X
ejpam-5592	151	8	(	(	PUNCT
ejpam-5592	151	9	r	r	NOUN
ejpam-5592	151	10	)	)	PUNCT
ejpam-5592	151	11	dr	dr	NOUN
ejpam-5592	151	12	=	=	PROPN
ejpam-5592	151	13	∞∑	∞∑	PROPN
ejpam-5592	151	14	j=0	j=0	PROPN
ejpam-5592	151	15	(	(	PUNCT
ejpam-5592	151	16	−ϖ	−ϖ	NOUN
ejpam-5592	151	17	1−ϖ	1−ϖ	NUM
ejpam-5592	151	18	)	)	PUNCT
ejpam-5592	152	1	j	j	PROPN
ejpam-5592	152	2	rlℜjϖ+1,ψ	rlℜjϖ+1,ψ	PROPN
ejpam-5592	152	3	κ	κ	PROPN
ejpam-5592	152	4	℘′(z	℘′(z	NOUN
ejpam-5592	152	5	)	)	PUNCT
ejpam-5592	152	6	ψ′(z	ψ′(z	PUNCT
ejpam-5592	152	7	)	)	PUNCT
ejpam-5592	153	1	+	+	CCONJ
ejpam-5592	153	2	ϖ	ϖ	X
ejpam-5592	153	3	1−ϖ	1−ϖ	NUM
ejpam-5592	153	4	rl	rl	NOUN
ejpam-5592	153	5	ℜϖ,ψκ	ℜϖ,ψκ	NOUN
ejpam-5592	153	6	∞∑	∞∑	NUM
ejpam-5592	153	7	j=0	j=0	PROPN
ejpam-5592	153	8	(	(	PUNCT
ejpam-5592	153	9	−ϖ	−ϖ	NOUN
ejpam-5592	153	10	1−ϖ	1−ϖ	NUM
ejpam-5592	153	11	)	)	PUNCT
ejpam-5592	153	12	j	j	PROPN
ejpam-5592	153	13	rlℜjϖ+1,ψ	rlℜjϖ+1,ψ	PROPN
ejpam-5592	153	14	κ	κ	PROPN
ejpam-5592	153	15	℘′(z	℘′(z	NOUN
ejpam-5592	153	16	)	)	PUNCT
ejpam-5592	153	17	ψ′(z	ψ′(z	NOUN
ejpam-5592	153	18	)	)	PUNCT
ejpam-5592	154	1	=	=	PUNCT
ejpam-5592	155	1	∞∑	∞∑	NUM
ejpam-5592	155	2	j=0	j=0	PROPN
ejpam-5592	155	3	(	(	PUNCT
ejpam-5592	155	4	−ϖ	−ϖ	NOUN
ejpam-5592	155	5	1−ϖ	1−ϖ	NUM
ejpam-5592	155	6	)	)	PUNCT
ejpam-5592	156	1	j	j	PROPN
ejpam-5592	156	2	rlℜjϖ+1,ψ	rlℜjϖ+1,ψ	PROPN
ejpam-5592	156	3	κ	κ	PROPN
ejpam-5592	156	4	℘′(z	℘′(z	NOUN
ejpam-5592	156	5	)	)	PUNCT
ejpam-5592	156	6	ψ′(z	ψ′(z	NOUN
ejpam-5592	156	7	)	)	PUNCT
ejpam-5592	157	1	−	−	PROPN
ejpam-5592	157	2	∞∑	∞∑	NUM
ejpam-5592	157	3	j=0	j=0	PROPN
ejpam-5592	157	4	(	(	PUNCT
ejpam-5592	157	5	−ϖ	−ϖ	NOUN
ejpam-5592	157	6	1−ϖ	1−ϖ	NUM
ejpam-5592	157	7	)	)	PUNCT
ejpam-5592	158	1	j+1	j+1	ADV
ejpam-5592	158	2	rlℜjϖ+ϖ+1,ψ	rlℜjϖ+ϖ+1,ψ	VERB
ejpam-5592	158	3	κ	κ	NOUN
ejpam-5592	158	4	℘′(z	℘′(z	NOUN
ejpam-5592	158	5	)	)	PUNCT
ejpam-5592	158	6	ψ′(z	ψ′(z	PUNCT
ejpam-5592	158	7	)	)	PUNCT
ejpam-5592	159	1	=	=	PUNCT
ejpam-5592	160	1	rlℜ1,ψ	rlℜ1,ψ	PROPN
ejpam-5592	160	2	κ	κ	NOUN
ejpam-5592	160	3	℘′(z	℘′(z	NOUN
ejpam-5592	160	4	)	)	PUNCT
ejpam-5592	160	5	ψ′(z	ψ′(z	PUNCT
ejpam-5592	160	6	)	)	PUNCT
ejpam-5592	161	1	=	=	PUNCT
ejpam-5592	161	2	z∫	z∫	NUM
ejpam-5592	161	3	κ	κ	NOUN
ejpam-5592	161	4	℘′(r)dr	℘′(r)dr	PROPN
ejpam-5592	161	5	=	=	SYM
ejpam-5592	161	6	℘(z)−	℘(z)−	PROPN
ejpam-5592	161	7	℘(κ	℘(κ	NOUN
ejpam-5592	161	8	)	)	PUNCT
ejpam-5592	161	9	.	.	PUNCT
ejpam-5592	162	1	(	(	PUNCT
ejpam-5592	162	2	ii	ii	NOUN
ejpam-5592	162	3	)	)	PUNCT
ejpam-5592	162	4	again	again	ADV
ejpam-5592	162	5	,	,	PUNCT
ejpam-5592	162	6	utilizing	utilize	VERB
ejpam-5592	162	7	definitions	definition	NOUN
ejpam-5592	162	8	7	7	NUM
ejpam-5592	162	9	,	,	PUNCT
ejpam-5592	162	10	8	8	NUM
ejpam-5592	162	11	and	and	CCONJ
ejpam-5592	162	12	the	the	DET
ejpam-5592	162	13	identity	identity	NOUN
ejpam-5592	162	14	rlℜµ+1,ψ	rlℜµ+1,ψ	NOUN
ejpam-5592	162	15	κ	κ	PROPN
ejpam-5592	162	16	(	(	PUNCT
ejpam-5592	162	17	1	1	NUM
ejpam-5592	162	18	ψ′(z	ψ′(z	NOUN
ejpam-5592	162	19	)	)	PUNCT
ejpam-5592	162	20	d	d	X
ejpam-5592	162	21	dz	dz	X
ejpam-5592	162	22	)	)	PUNCT
ejpam-5592	162	23	℘(z	℘(z	ADJ
ejpam-5592	162	24	)	)	PUNCT
ejpam-5592	162	25	=	=	PRON
ejpam-5592	162	26	rl	rl	PART
ejpam-5592	162	27	ℜµ,ψκ	ℜµ,ψκ	NOUN
ejpam-5592	162	28	℘(z)−	℘(z)−	PROPN
ejpam-5592	162	29	℘(κ	℘(κ	PROPN
ejpam-5592	162	30	)	)	PUNCT
ejpam-5592	162	31	(	(	PUNCT
ejpam-5592	162	32	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	162	33	ψ(κ))µ	ψ(κ))µ	PROPN
ejpam-5592	162	34	γ(1	γ(1	PROPN
ejpam-5592	162	35	+	+	CCONJ
ejpam-5592	162	36	µ	µ	X
ejpam-5592	162	37	)	)	PUNCT
ejpam-5592	162	38	,	,	PUNCT
ejpam-5592	162	39	re(µ	re(µ	X
ejpam-5592	162	40	)	)	PUNCT
ejpam-5592	162	41	>	>	X
ejpam-5592	162	42	0	0	NUM
ejpam-5592	162	43	,	,	PUNCT
ejpam-5592	162	44	one	one	PRON
ejpam-5592	162	45	has	have	VERB
ejpam-5592	162	46	(	(	PUNCT
ejpam-5592	162	47	cabdϖ,ψ	cabdϖ,ψ	X
ejpam-5592	162	48	κ	κ	PRON
ejpam-5592	162	49	rlabℜϖ,ψκ	rlabℜϖ,ψκ	PROPN
ejpam-5592	162	50	℘	℘	PROPN
ejpam-5592	162	51	)	)	PUNCT
ejpam-5592	162	52	(	(	PUNCT
ejpam-5592	162	53	z	z	NOUN
ejpam-5592	162	54	)	)	PUNCT
ejpam-5592	162	55	=	=	NOUN
ejpam-5592	162	56	cabdϖ,ψ	cabdϖ,ψ	NUM
ejpam-5592	162	57	κ	κ	NOUN
ejpam-5592	162	58	(	(	PUNCT
ejpam-5592	162	59	1−ϖ	1−ϖ	NUM
ejpam-5592	162	60	λ(ϖ	λ(ϖ	NOUN
ejpam-5592	162	61	)	)	PUNCT
ejpam-5592	162	62	℘(z	℘(z	NOUN
ejpam-5592	162	63	)	)	PUNCT
ejpam-5592	163	1	+	+	CCONJ
ejpam-5592	163	2	ϖ	ϖ	X
ejpam-5592	163	3	λ(ϖ	λ(ϖ	NOUN
ejpam-5592	163	4	)	)	PUNCT
ejpam-5592	163	5	(	(	PUNCT
ejpam-5592	163	6	rlℜϖ,ψκ	rlℜϖ,ψκ	NOUN
ejpam-5592	163	7	℘	℘	PROPN
ejpam-5592	163	8	)	)	PUNCT
ejpam-5592	163	9	(	(	PUNCT
ejpam-5592	163	10	z	z	NOUN
ejpam-5592	163	11	)	)	PUNCT
ejpam-5592	163	12	)	)	PUNCT
ejpam-5592	164	1	=	=	SYM
ejpam-5592	164	2	1−ϖ	1−ϖ	NUM
ejpam-5592	164	3	λ(ϖ	λ(ϖ	NOUN
ejpam-5592	164	4	)	)	PUNCT
ejpam-5592	164	5	(	(	PUNCT
ejpam-5592	164	6	cabdϖ,ψ	cabdϖ,ψ	X
ejpam-5592	164	7	κ	κ	NOUN
ejpam-5592	164	8	℘	℘	PROPN
ejpam-5592	164	9	)	)	PUNCT
ejpam-5592	164	10	(	(	PUNCT
ejpam-5592	164	11	z	z	NOUN
ejpam-5592	164	12	)	)	PUNCT
ejpam-5592	164	13	+	+	CCONJ
ejpam-5592	164	14	ϖ	ϖ	X
ejpam-5592	164	15	λ(ϖ	λ(ϖ	NOUN
ejpam-5592	164	16	)	)	PUNCT
ejpam-5592	164	17	cab	cab	NOUN
ejpam-5592	164	18	dϖ,ψ	dϖ,ψ	NOUN
ejpam-5592	164	19	κ	κ	PROPN
ejpam-5592	164	20	(	(	PUNCT
ejpam-5592	164	21	rlℜϖ,ψκ	rlℜϖ,ψκ	NOUN
ejpam-5592	164	22	℘	℘	PROPN
ejpam-5592	164	23	)	)	PUNCT
ejpam-5592	164	24	(	(	PUNCT
ejpam-5592	164	25	z	z	X
ejpam-5592	164	26	)	)	PUNCT
ejpam-5592	164	27	=	=	SYM
ejpam-5592	165	1	∞∑	∞∑	NUM
ejpam-5592	165	2	j=0	j=0	PROPN
ejpam-5592	165	3	(	(	PUNCT
ejpam-5592	165	4	−ϖ	−ϖ	NOUN
ejpam-5592	165	5	1−ϖ	1−ϖ	NUM
ejpam-5592	165	6	)	)	PUNCT
ejpam-5592	166	1	j	j	PROPN
ejpam-5592	166	2	rlℜjϖ+1,ψ	rlℜjϖ+1,ψ	PROPN
ejpam-5592	166	3	κ	κ	PROPN
ejpam-5592	166	4	(	(	PUNCT
ejpam-5592	166	5	1	1	NUM
ejpam-5592	166	6	ψ′(z	ψ′(z	NOUN
ejpam-5592	166	7	)	)	PUNCT
ejpam-5592	166	8	d	d	X
ejpam-5592	166	9	dz	dz	X
ejpam-5592	166	10	)	)	PUNCT
ejpam-5592	166	11	℘(z	℘(z	ADJ
ejpam-5592	166	12	)	)	PUNCT
ejpam-5592	166	13	h.a	h.a	PROPN
ejpam-5592	166	14	.	.	PROPN
ejpam-5592	166	15	hammad	hammad	PROPN
ejpam-5592	166	16	,	,	PUNCT
ejpam-5592	166	17	m.	m.	PROPN
ejpam-5592	166	18	de	de	X
ejpam-5592	166	19	la	la	PROPN
ejpam-5592	166	20	sen	sen	PROPN
ejpam-5592	166	21	/	/	SYM
ejpam-5592	166	22	eur	eur	PROPN
ejpam-5592	166	23	.	.	PUNCT
ejpam-5592	167	1	j.	j.	PROPN
ejpam-5592	167	2	pure	pure	PROPN
ejpam-5592	167	3	appl	appl	PROPN
ejpam-5592	167	4	.	.	PROPN
ejpam-5592	167	5	math	math	PROPN
ejpam-5592	167	6	,	,	PUNCT
ejpam-5592	167	7	17	17	NUM
ejpam-5592	167	8	(	(	PUNCT
ejpam-5592	167	9	4	4	NUM
ejpam-5592	167	10	)	)	PUNCT
ejpam-5592	167	11	(	(	PUNCT
ejpam-5592	167	12	2024	2024	NUM
ejpam-5592	167	13	)	)	PUNCT
ejpam-5592	167	14	,	,	PUNCT
ejpam-5592	167	15	3687	3687	NUM
ejpam-5592	167	16	-	-	SYM
ejpam-5592	167	17	3707	3707	NUM
ejpam-5592	167	18	3694	3694	NUM
ejpam-5592	167	19	+	+	CCONJ
ejpam-5592	167	20	ϖ	ϖ	X
ejpam-5592	167	21	1−ϖ	1−ϖ	NUM
ejpam-5592	167	22	∞∑	∞∑	NUM
ejpam-5592	167	23	j=0	j=0	PROPN
ejpam-5592	167	24	(	(	PUNCT
ejpam-5592	167	25	−ϖ	−ϖ	NOUN
ejpam-5592	167	26	1−ϖ	1−ϖ	NUM
ejpam-5592	167	27	)	)	PUNCT
ejpam-5592	168	1	j	j	PROPN
ejpam-5592	168	2	rlℜjϖ+1,ψ	rlℜjϖ+1,ψ	PROPN
ejpam-5592	168	3	κ	κ	PROPN
ejpam-5592	168	4	(	(	PUNCT
ejpam-5592	168	5	1	1	NUM
ejpam-5592	168	6	ψ′(z	ψ′(z	NOUN
ejpam-5592	168	7	)	)	PUNCT
ejpam-5592	168	8	d	d	X
ejpam-5592	168	9	dz	dz	PROPN
ejpam-5592	168	10	)	)	PUNCT
ejpam-5592	168	11	(	(	PUNCT
ejpam-5592	168	12	rlℜϖ,ψκ	rlℜϖ,ψκ	NOUN
ejpam-5592	168	13	℘	℘	PROPN
ejpam-5592	168	14	)	)	PUNCT
ejpam-5592	168	15	(	(	PUNCT
ejpam-5592	168	16	z	z	X
ejpam-5592	168	17	)	)	PUNCT
ejpam-5592	168	18	=	=	SYM
ejpam-5592	169	1	∞∑	∞∑	NUM
ejpam-5592	169	2	j=0	j=0	PROPN
ejpam-5592	169	3	(	(	PUNCT
ejpam-5592	169	4	−ϖ	−ϖ	NOUN
ejpam-5592	169	5	1−ϖ	1−ϖ	NUM
ejpam-5592	169	6	)	)	PUNCT
ejpam-5592	169	7	j	j	PROPN
ejpam-5592	169	8	{	{	PUNCT
ejpam-5592	169	9	rlℜjϖ,ψκ	rlℜjϖ,ψκ	PROPN
ejpam-5592	169	10	℘(z)−	℘(z)−	PROPN
ejpam-5592	169	11	℘(κ	℘(κ	NOUN
ejpam-5592	169	12	)	)	PUNCT
ejpam-5592	170	1	[	[	X
ejpam-5592	170	2	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	170	3	ψ(κ	ψ(κ	PROPN
ejpam-5592	170	4	)	)	PUNCT
ejpam-5592	170	5	]	]	PUNCT
ejpam-5592	171	1	γ(1	γ(1	PROPN
ejpam-5592	171	2	+	+	CCONJ
ejpam-5592	171	3	jϖ	jϖ	VERB
ejpam-5592	171	4	)	)	PUNCT
ejpam-5592	171	5	jϖ	jϖ	VERB
ejpam-5592	171	6	}	}	PUNCT
ejpam-5592	171	7	−	−	PROPN
ejpam-5592	171	8	∞∑	∞∑	NUM
ejpam-5592	171	9	j=0	j=0	PROPN
ejpam-5592	171	10	(	(	PUNCT
ejpam-5592	171	11	−ϖ	−ϖ	NOUN
ejpam-5592	171	12	1−ϖ	1−ϖ	NUM
ejpam-5592	171	13	)	)	PUNCT
ejpam-5592	172	1	j+1	j+1	ADV
ejpam-5592	172	2	rlℜjϖ+ϖ,ψ	rlℜjϖ+ϖ,ψ	ADP
ejpam-5592	172	3	κ	κ	NOUN
ejpam-5592	172	4	℘(z	℘(z	NOUN
ejpam-5592	172	5	)	)	PUNCT
ejpam-5592	172	6	=	=	SYM
ejpam-5592	173	1	℘(z)−	℘(z)−	PROPN
ejpam-5592	173	2	∞∑	∞∑	NUM
ejpam-5592	173	3	j=0	j=0	PROPN
ejpam-5592	173	4	(	(	PUNCT
ejpam-5592	173	5	−ϖ	−ϖ	NOUN
ejpam-5592	173	6	1−ϖ	1−ϖ	NUM
ejpam-5592	173	7	)	)	PUNCT
ejpam-5592	173	8	j	j	PROPN
ejpam-5592	173	9	℘(κ	℘(κ	PROPN
ejpam-5592	173	10	)	)	PUNCT
ejpam-5592	174	1	[	[	X
ejpam-5592	174	2	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	174	3	ψ(κ	ψ(κ	PROPN
ejpam-5592	174	4	)	)	PUNCT
ejpam-5592	174	5	]	]	PUNCT
ejpam-5592	175	1	γ(1	γ(1	PROPN
ejpam-5592	175	2	+	+	CCONJ
ejpam-5592	175	3	jϖ	jϖ	VERB
ejpam-5592	175	4	)	)	PUNCT
ejpam-5592	175	5	jϖ	jϖ	VERB
ejpam-5592	175	6	=	=	SYM
ejpam-5592	175	7	℘(z)−	℘(z)−	PROPN
ejpam-5592	175	8	℘(κ)lϖ	℘(κ)lϖ	PROPN
ejpam-5592	175	9	(	(	PUNCT
ejpam-5592	175	10	−ϖ	−ϖ	NOUN
ejpam-5592	175	11	1−ϖ	1−ϖ	NUM
ejpam-5592	175	12	(	(	PUNCT
ejpam-5592	175	13	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	175	14	ψ(κ))ϖ	ψ(κ))ϖ	PART
ejpam-5592	175	15	)	)	PUNCT
ejpam-5592	175	16	.	.	PUNCT
ejpam-5592	176	1	lemma	lemma	PROPN
ejpam-5592	176	2	4	4	X
ejpam-5592	176	3	.	.	PUNCT
ejpam-5592	176	4	assume	assume	VERB
ejpam-5592	176	5	that	that	SCONJ
ejpam-5592	176	6	℘	℘	PROPN
ejpam-5592	176	7	∈	∈	NOUN
ejpam-5592	176	8	ck[ℑu	ck[ℑu	NOUN
ejpam-5592	176	9	,	,	PUNCT
ejpam-5592	176	10	r	r	NOUN
ejpam-5592	176	11	]	]	PUNCT
ejpam-5592	176	12	and	and	CCONJ
ejpam-5592	176	13	ψ	ψ	X
ejpam-5592	176	14	∈	∈	NOUN
ejpam-5592	176	15	ck[ℑu	ck[ℑu	NOUN
ejpam-5592	176	16	,	,	PUNCT
ejpam-5592	176	17	r+	r+	X
ejpam-5592	176	18	]	]	PUNCT
ejpam-5592	176	19	.	.	PUNCT
ejpam-5592	177	1	for	for	ADP
ejpam-5592	177	2	ϖu	ϖu	PROPN
ejpam-5592	177	3	∈	∈	PROPN
ejpam-5592	177	4	(	(	PUNCT
ejpam-5592	177	5	k	k	NOUN
ejpam-5592	177	6	,	,	PUNCT
ejpam-5592	177	7	k	k	PROPN
ejpam-5592	177	8	+	+	PROPN
ejpam-5592	177	9	1	1	X
ejpam-5592	177	10	]	]	PUNCT
ejpam-5592	177	11	and	and	CCONJ
ejpam-5592	177	12	θu	θu	X
ejpam-5592	177	13	=	=	PUNCT
ejpam-5592	177	14	ϖu	ϖu	PROPN
ejpam-5592	177	15	−	−	PROPN
ejpam-5592	177	16	k	k	PROPN
ejpam-5592	177	17	,	,	PUNCT
ejpam-5592	177	18	for	for	ADP
ejpam-5592	177	19	k	k	PROPN
ejpam-5592	177	20	≥	≥	PROPN
ejpam-5592	177	21	0	0	NUM
ejpam-5592	177	22	,	,	PUNCT
ejpam-5592	177	23	u	u	NOUN
ejpam-5592	177	24	≥	≥	NOUN
ejpam-5592	177	25	1	1	NUM
ejpam-5592	177	26	and	and	CCONJ
ejpam-5592	177	27	all	all	DET
ejpam-5592	177	28	τ	τ	PROPN
ejpam-5592	177	29	∈	∈	PROPN
ejpam-5592	177	30	ℑu	ℑu	PROPN
ejpam-5592	177	31	,	,	PUNCT
ejpam-5592	177	32	the	the	DET
ejpam-5592	177	33	following	follow	VERB
ejpam-5592	177	34	equations	equation	NOUN
ejpam-5592	177	35	are	be	AUX
ejpam-5592	177	36	true	true	ADJ
ejpam-5592	177	37	:	:	PUNCT
ejpam-5592	177	38	(	(	PUNCT
ejpam-5592	177	39	i	i	NOUN
ejpam-5592	177	40	)	)	PUNCT
ejpam-5592	177	41	(	(	PUNCT
ejpam-5592	177	42	rlabdϖu	rlabdϖu	PROPN
ejpam-5592	177	43	,	,	PUNCT
ejpam-5592	177	44	ψ	ψ	X
ejpam-5592	177	45	κ	κ	NOUN
ejpam-5592	177	46	rlabℜϖu	rlabℜϖu	PROPN
ejpam-5592	177	47	,	,	PUNCT
ejpam-5592	177	48	ψκ	ψκ	PROPN
ejpam-5592	177	49	℘	℘	PROPN
ejpam-5592	177	50	)	)	PUNCT
ejpam-5592	177	51	(	(	PUNCT
ejpam-5592	177	52	z	z	X
ejpam-5592	177	53	)	)	PUNCT
ejpam-5592	177	54	=	=	SYM
ejpam-5592	177	55	℘(z	℘(z	ADJ
ejpam-5592	177	56	)	)	PUNCT
ejpam-5592	177	57	.	.	PUNCT
ejpam-5592	178	1	(	(	PUNCT
ejpam-5592	178	2	ii	ii	NOUN
ejpam-5592	178	3	)	)	PUNCT
ejpam-5592	178	4	(	(	PUNCT
ejpam-5592	178	5	rlabℜϖu	rlabℜϖu	PROPN
ejpam-5592	178	6	,	,	PUNCT
ejpam-5592	178	7	ψκ	ψκ	VERB
ejpam-5592	178	8	rlabdϖu	rlabdϖu	ADJ
ejpam-5592	178	9	,	,	PUNCT
ejpam-5592	178	10	ψ	ψ	VERB
ejpam-5592	178	11	κ	κ	PRON
ejpam-5592	178	12	℘	℘	PROPN
ejpam-5592	178	13	)	)	PUNCT
ejpam-5592	178	14	(	(	PUNCT
ejpam-5592	178	15	z	z	X
ejpam-5592	178	16	)	)	PUNCT
ejpam-5592	178	17	=	=	SYM
ejpam-5592	178	18	℘(z	℘(z	ADJ
ejpam-5592	178	19	)	)	PUNCT
ejpam-5592	178	20	.	.	PUNCT
ejpam-5592	179	1	(	(	PUNCT
ejpam-5592	179	2	iii	iii	X
ejpam-5592	179	3	)	)	PUNCT
ejpam-5592	179	4	(	(	PUNCT
ejpam-5592	179	5	cabdϖu	cabdϖu	PROPN
ejpam-5592	179	6	,	,	PUNCT
ejpam-5592	179	7	ψ	ψ	X
ejpam-5592	179	8	κ	κ	NOUN
ejpam-5592	179	9	rlabℜϖu	rlabℜϖu	PROPN
ejpam-5592	179	10	,	,	PUNCT
ejpam-5592	179	11	ψκ	ψκ	PROPN
ejpam-5592	179	12	℘	℘	PROPN
ejpam-5592	179	13	)	)	PUNCT
ejpam-5592	179	14	(	(	PUNCT
ejpam-5592	179	15	z	z	X
ejpam-5592	179	16	)	)	PUNCT
ejpam-5592	179	17	=	=	SYM
ejpam-5592	180	1	℘(z)−℘(κ)lϖu−k	℘(z)−℘(κ)lϖu−k	PROPN
ejpam-5592	180	2	(	(	PUNCT
ejpam-5592	180	3	−(ϖu−k	−(ϖu−k	NOUN
ejpam-5592	180	4	)	)	PUNCT
ejpam-5592	180	5	1−(ϖu−k)(ψ(z)−	1−(ϖu−k)(ψ(z)−	NUM
ejpam-5592	180	6	ψ(κ))ϖu−k	ψ(κ))ϖu−k	NOUN
ejpam-5592	180	7	)	)	PUNCT
ejpam-5592	180	8	.	.	PUNCT
ejpam-5592	181	1	(	(	PUNCT
ejpam-5592	181	2	iv	iv	X
ejpam-5592	181	3	)	)	PUNCT
ejpam-5592	181	4	(	(	PUNCT
ejpam-5592	181	5	rlabℜϖu	rlabℜϖu	PROPN
ejpam-5592	181	6	,	,	PUNCT
ejpam-5592	181	7	ψκ	ψκ	PROPN
ejpam-5592	181	8	cabdϖu	cabdϖu	PROPN
ejpam-5592	181	9	,	,	PUNCT
ejpam-5592	181	10	ψ	ψ	VERB
ejpam-5592	181	11	κ	κ	PRON
ejpam-5592	181	12	℘	℘	PROPN
ejpam-5592	181	13	)	)	PUNCT
ejpam-5592	181	14	(	(	PUNCT
ejpam-5592	181	15	z	z	X
ejpam-5592	181	16	)	)	PUNCT
ejpam-5592	181	17	=	=	SYM
ejpam-5592	182	1	℘(z)−	℘(z)−	PROPN
ejpam-5592	182	2	k∑	k∑	VERB
ejpam-5592	182	3	m=0	m=0	PROPN
ejpam-5592	182	4	℘	℘	PROPN
ejpam-5592	182	5	(	(	PUNCT
ejpam-5592	182	6	m	m	NOUN
ejpam-5592	182	7	)	)	PUNCT
ejpam-5592	182	8	ψ	ψ	X
ejpam-5592	182	9	(	(	PUNCT
ejpam-5592	182	10	κ	κ	NOUN
ejpam-5592	182	11	)	)	PUNCT
ejpam-5592	182	12	m	m	PROPN
ejpam-5592	182	13	!	!	PUNCT
ejpam-5592	183	1	(	(	PUNCT
ejpam-5592	183	2	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	183	3	ψ(κ))m	ψ(κ))m	PROPN
ejpam-5592	183	4	.	.	PUNCT
ejpam-5592	184	1	proof	proof	NOUN
ejpam-5592	184	2	.	.	PUNCT
ejpam-5592	185	1	(	(	PUNCT
ejpam-5592	185	2	i	i	NOUN
ejpam-5592	185	3	)	)	PUNCT
ejpam-5592	185	4	in	in	ADP
ejpam-5592	185	5	light	light	NOUN
ejpam-5592	185	6	of	of	ADP
ejpam-5592	185	7	definitions	definition	NOUN
ejpam-5592	185	8	10	10	NUM
ejpam-5592	185	9	and	and	CCONJ
ejpam-5592	185	10	12	12	NUM
ejpam-5592	185	11	and	and	CCONJ
ejpam-5592	185	12	using	use	VERB
ejpam-5592	185	13	lemmas	lemmas	PROPN
ejpam-5592	185	14	1	1	NUM
ejpam-5592	185	15	and	and	CCONJ
ejpam-5592	185	16	2	2	NUM
ejpam-5592	185	17	,	,	PUNCT
ejpam-5592	185	18	for	for	ADP
ejpam-5592	185	19	u	u	PRON
ejpam-5592	185	20	≥	≥	NUM
ejpam-5592	185	21	1	1	NUM
ejpam-5592	185	22	,	,	PUNCT
ejpam-5592	185	23	we	we	PRON
ejpam-5592	185	24	can	can	AUX
ejpam-5592	185	25	write	write	VERB
ejpam-5592	185	26	(	(	PUNCT
ejpam-5592	185	27	rlabdϖu	rlabdϖu	ADJ
ejpam-5592	185	28	,	,	PUNCT
ejpam-5592	185	29	ψ	ψ	X
ejpam-5592	185	30	κ	κ	NOUN
ejpam-5592	185	31	rlabℜϖu	rlabℜϖu	PROPN
ejpam-5592	185	32	,	,	PUNCT
ejpam-5592	185	33	ψκ	ψκ	PROPN
ejpam-5592	185	34	℘	℘	PROPN
ejpam-5592	185	35	)	)	PUNCT
ejpam-5592	185	36	(	(	PUNCT
ejpam-5592	185	37	z	z	X
ejpam-5592	185	38	)	)	PUNCT
ejpam-5592	185	39	=	=	SYM
ejpam-5592	186	1	(	(	PUNCT
ejpam-5592	186	2	(	(	PUNCT
ejpam-5592	186	3	1	1	NUM
ejpam-5592	186	4	ψ(z	ψ(z	NOUN
ejpam-5592	186	5	)	)	PUNCT
ejpam-5592	186	6	d	d	X
ejpam-5592	186	7	dz	dz	X
ejpam-5592	186	8	)	)	PUNCT
ejpam-5592	186	9	k	k	NOUN
ejpam-5592	186	10	rlabdθu	rlabdθu	NOUN
ejpam-5592	186	11	,	,	PUNCT
ejpam-5592	186	12	ψ	ψ	X
ejpam-5592	186	13	κ	κ	PROPN
ejpam-5592	186	14	rlabℜθu	rlabℜθu	PROPN
ejpam-5592	186	15	,	,	PUNCT
ejpam-5592	186	16	ψκ	ψκ	PROPN
ejpam-5592	186	17	rlℜk	rlℜk	PROPN
ejpam-5592	186	18	,	,	PUNCT
ejpam-5592	186	19	ψκ	ψκ	VERB
ejpam-5592	186	20	℘	℘	PROPN
ejpam-5592	186	21	)	)	PUNCT
ejpam-5592	186	22	(	(	PUNCT
ejpam-5592	186	23	z	z	X
ejpam-5592	186	24	)	)	PUNCT
ejpam-5592	186	25	=	=	SYM
ejpam-5592	186	26	(	(	PUNCT
ejpam-5592	186	27	(	(	PUNCT
ejpam-5592	186	28	1	1	NUM
ejpam-5592	186	29	ψ(z	ψ(z	NOUN
ejpam-5592	186	30	)	)	PUNCT
ejpam-5592	186	31	d	d	X
ejpam-5592	186	32	dz	dz	X
ejpam-5592	186	33	)	)	PUNCT
ejpam-5592	186	34	k	k	PROPN
ejpam-5592	186	35	rlℜk	rlℜk	PROPN
ejpam-5592	186	36	,	,	PUNCT
ejpam-5592	186	37	ψκ	ψκ	VERB
ejpam-5592	186	38	℘	℘	PROPN
ejpam-5592	186	39	)	)	PUNCT
ejpam-5592	186	40	(	(	PUNCT
ejpam-5592	186	41	z	z	X
ejpam-5592	186	42	)	)	PUNCT
ejpam-5592	186	43	=	=	SYM
ejpam-5592	186	44	℘(z	℘(z	ADJ
ejpam-5592	186	45	)	)	PUNCT
ejpam-5592	186	46	.	.	PUNCT
ejpam-5592	187	1	(	(	PUNCT
ejpam-5592	187	2	ii	ii	NOUN
ejpam-5592	187	3	)	)	PUNCT
ejpam-5592	187	4	according	accord	VERB
ejpam-5592	187	5	to	to	ADP
ejpam-5592	187	6	definitions	definition	NOUN
ejpam-5592	187	7	10	10	NUM
ejpam-5592	187	8	and	and	CCONJ
ejpam-5592	187	9	12	12	NUM
ejpam-5592	187	10	,	,	PUNCT
ejpam-5592	187	11	for	for	ADP
ejpam-5592	187	12	u	u	PRON
ejpam-5592	187	13	≥	≥	NUM
ejpam-5592	187	14	1	1	NUM
ejpam-5592	187	15	,	,	PUNCT
ejpam-5592	187	16	we	we	PRON
ejpam-5592	187	17	have	have	VERB
ejpam-5592	187	18	(	(	PUNCT
ejpam-5592	187	19	rlabℜϖu	rlabℜϖu	NOUN
ejpam-5592	187	20	,	,	PUNCT
ejpam-5592	187	21	ψκ	ψκ	VERB
ejpam-5592	187	22	rlabdϖu	rlabdϖu	ADJ
ejpam-5592	187	23	,	,	PUNCT
ejpam-5592	187	24	ψ	ψ	VERB
ejpam-5592	187	25	κ	κ	PRON
ejpam-5592	187	26	℘	℘	PROPN
ejpam-5592	187	27	)	)	PUNCT
ejpam-5592	187	28	(	(	PUNCT
ejpam-5592	187	29	z	z	X
ejpam-5592	187	30	)	)	PUNCT
ejpam-5592	187	31	=	=	SYM
ejpam-5592	188	1	k	k	X
ejpam-5592	189	1	+	+	CCONJ
ejpam-5592	189	2	1−ϖu	1−ϖu	NUM
ejpam-5592	189	3	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	189	4	−	−	PROPN
ejpam-5592	189	5	k	k	X
ejpam-5592	189	6	)	)	PUNCT
ejpam-5592	189	7	rl	rl	ADP
ejpam-5592	189	8	ℜk	ℜk	PROPN
ejpam-5592	189	9	,	,	PUNCT
ejpam-5592	189	10	ψκ	ψκ	PROPN
ejpam-5592	189	11	(	(	PUNCT
ejpam-5592	189	12	rlabdϖu	rlabdϖu	PROPN
ejpam-5592	189	13	,	,	PUNCT
ejpam-5592	189	14	ψ	ψ	VERB
ejpam-5592	189	15	κ	κ	PRON
ejpam-5592	189	16	℘	℘	PROPN
ejpam-5592	189	17	(	(	PUNCT
ejpam-5592	189	18	z	z	NOUN
ejpam-5592	189	19	)	)	PUNCT
ejpam-5592	189	20	)	)	PUNCT
ejpam-5592	190	1	+	+	CCONJ
ejpam-5592	190	2	ϖu	ϖu	PRON
ejpam-5592	190	3	−	−	NOUN
ejpam-5592	190	4	k	k	PROPN
ejpam-5592	190	5	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	190	6	−	−	PROPN
ejpam-5592	190	7	k	k	X
ejpam-5592	190	8	)	)	PUNCT
ejpam-5592	190	9	rl	rl	ADP
ejpam-5592	190	10	ℜϖu	ℜϖu	PROPN
ejpam-5592	190	11	,	,	PUNCT
ejpam-5592	190	12	ψκ	ψκ	PROPN
ejpam-5592	190	13	(	(	PUNCT
ejpam-5592	190	14	rlabdϖu	rlabdϖu	PROPN
ejpam-5592	190	15	,	,	PUNCT
ejpam-5592	190	16	ψ	ψ	VERB
ejpam-5592	190	17	κ	κ	PRON
ejpam-5592	190	18	℘	℘	PROPN
ejpam-5592	190	19	(	(	PUNCT
ejpam-5592	190	20	z	z	NOUN
ejpam-5592	190	21	)	)	PUNCT
ejpam-5592	190	22	)	)	PUNCT
ejpam-5592	191	1	=	=	PUNCT
ejpam-5592	192	1	ℜk	ℜk	ADJ
ejpam-5592	192	2	,	,	PUNCT
ejpam-5592	192	3	ψκ	ψκ	INTJ
ejpam-5592	192	4	(	(	PUNCT
ejpam-5592	192	5	1	1	NUM
ejpam-5592	192	6	ψ′(z	ψ′(z	NOUN
ejpam-5592	192	7	)	)	PUNCT
ejpam-5592	192	8	d	d	X
ejpam-5592	192	9	dz	dz	PROPN
ejpam-5592	192	10	)	)	PUNCT
ejpam-5592	192	11	k+1	k+1	PROPN
ejpam-5592	192	12	∞∑	∞∑	NUM
ejpam-5592	192	13	j=0	j=0	PROPN
ejpam-5592	192	14	(	(	PUNCT
ejpam-5592	192	15	−(ϖu	−(ϖu	NOUN
ejpam-5592	192	16	−	−	PROPN
ejpam-5592	193	1	k	k	NOUN
ejpam-5592	193	2	)	)	PUNCT
ejpam-5592	193	3	k	k	PROPN
ejpam-5592	194	1	+	+	CCONJ
ejpam-5592	194	2	1−ϖu	1−ϖu	NUM
ejpam-5592	194	3	)	)	PUNCT
ejpam-5592	194	4	j	j	PROPN
ejpam-5592	194	5	z∫	z∫	PROPN
ejpam-5592	194	6	κ	κ	PRON
ejpam-5592	194	7	ψ′(r	ψ′(r	PROPN
ejpam-5592	194	8	)	)	PUNCT
ejpam-5592	194	9	(	(	PUNCT
ejpam-5592	194	10	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	194	11	ψ(r	ψ(r	PROPN
ejpam-5592	194	12	)	)	PUNCT
ejpam-5592	195	1	γ(1	γ(1	PROPN
ejpam-5592	196	1	+	+	NUM
ejpam-5592	196	2	j	j	PROPN
ejpam-5592	196	3	(	(	PUNCT
ejpam-5592	196	4	ϖu	ϖu	PROPN
ejpam-5592	196	5	−	−	PROPN
ejpam-5592	196	6	k	k	NOUN
ejpam-5592	196	7	)	)	PUNCT
ejpam-5592	196	8	)	)	PUNCT
ejpam-5592	196	9	)	)	PUNCT
ejpam-5592	196	10	j(ϖu−k	j(ϖu−k	NOUN
ejpam-5592	196	11	)	)	PUNCT
ejpam-5592	196	12	℘	℘	PROPN
ejpam-5592	196	13	(	(	PUNCT
ejpam-5592	196	14	r	r	NOUN
ejpam-5592	196	15	)	)	PUNCT
ejpam-5592	196	16	dr	dr	NOUN
ejpam-5592	196	17	+	+	CCONJ
ejpam-5592	196	18	(	(	PUNCT
ejpam-5592	196	19	ϖu	ϖu	PROPN
ejpam-5592	196	20	−	−	PROPN
ejpam-5592	196	21	k	k	NOUN
ejpam-5592	196	22	)	)	PUNCT
ejpam-5592	196	23	(	(	PUNCT
ejpam-5592	196	24	k	k	PROPN
ejpam-5592	196	25	+	+	SYM
ejpam-5592	196	26	1−ϖu	1−ϖu	NUM
ejpam-5592	196	27	)	)	PUNCT
ejpam-5592	196	28	rl	rl	ADP
ejpam-5592	196	29	ℜϖu	ℜϖu	PROPN
ejpam-5592	196	30	,	,	PUNCT
ejpam-5592	196	31	ψκ	ψκ	PROPN
ejpam-5592	196	32	(	(	PUNCT
ejpam-5592	196	33	1	1	NUM
ejpam-5592	196	34	ψ′(z	ψ′(z	NOUN
ejpam-5592	196	35	)	)	PUNCT
ejpam-5592	196	36	d	d	X
ejpam-5592	196	37	dz	dz	PROPN
ejpam-5592	196	38	)	)	PUNCT
ejpam-5592	196	39	k+1	k+1	PROPN
ejpam-5592	196	40	∞∑	∞∑	NUM
ejpam-5592	196	41	j=0	j=0	PROPN
ejpam-5592	196	42	(	(	PUNCT
ejpam-5592	196	43	−(ϖu	−(ϖu	NOUN
ejpam-5592	196	44	−	−	PROPN
ejpam-5592	197	1	k	k	NOUN
ejpam-5592	197	2	)	)	PUNCT
ejpam-5592	197	3	k	k	PROPN
ejpam-5592	198	1	+	+	CCONJ
ejpam-5592	198	2	1−ϖu	1−ϖu	NUM
ejpam-5592	198	3	)	)	PUNCT
ejpam-5592	198	4	j	j	PROPN
ejpam-5592	198	5	h.a	h.a	PROPN
ejpam-5592	198	6	.	.	PROPN
ejpam-5592	198	7	hammad	hammad	PROPN
ejpam-5592	198	8	,	,	PUNCT
ejpam-5592	198	9	m.	m.	PROPN
ejpam-5592	198	10	de	de	X
ejpam-5592	198	11	la	la	PROPN
ejpam-5592	198	12	sen	sen	PROPN
ejpam-5592	198	13	/	/	SYM
ejpam-5592	198	14	eur	eur	PROPN
ejpam-5592	198	15	.	.	PUNCT
ejpam-5592	199	1	j.	j.	PROPN
ejpam-5592	199	2	pure	pure	PROPN
ejpam-5592	199	3	appl	appl	PROPN
ejpam-5592	199	4	.	.	PROPN
ejpam-5592	199	5	math	math	PROPN
ejpam-5592	199	6	,	,	PUNCT
ejpam-5592	199	7	17	17	NUM
ejpam-5592	199	8	(	(	PUNCT
ejpam-5592	199	9	4	4	NUM
ejpam-5592	199	10	)	)	PUNCT
ejpam-5592	199	11	(	(	PUNCT
ejpam-5592	199	12	2024	2024	NUM
ejpam-5592	199	13	)	)	PUNCT
ejpam-5592	199	14	,	,	PUNCT
ejpam-5592	199	15	3687	3687	NUM
ejpam-5592	199	16	-	-	SYM
ejpam-5592	199	17	3707	3707	NUM
ejpam-5592	199	18	3695	3695	NUM
ejpam-5592	199	19	×	×	NOUN
ejpam-5592	199	20	z∫	z∫	NOUN
ejpam-5592	199	21	κ	κ	NOUN
ejpam-5592	199	22	ψ′(r	ψ′(r	PROPN
ejpam-5592	199	23	)	)	PUNCT
ejpam-5592	199	24	(	(	PUNCT
ejpam-5592	199	25	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	199	26	ψ(r	ψ(r	PROPN
ejpam-5592	199	27	)	)	PUNCT
ejpam-5592	200	1	γ(1	γ(1	PROPN
ejpam-5592	201	1	+	+	NUM
ejpam-5592	201	2	j	j	PROPN
ejpam-5592	201	3	(	(	PUNCT
ejpam-5592	201	4	ϖu	ϖu	PROPN
ejpam-5592	201	5	−	−	PROPN
ejpam-5592	201	6	k	k	NOUN
ejpam-5592	201	7	)	)	PUNCT
ejpam-5592	201	8	)	)	PUNCT
ejpam-5592	201	9	)	)	PUNCT
ejpam-5592	201	10	j(ϖu−k	j(ϖu−k	NOUN
ejpam-5592	201	11	)	)	PUNCT
ejpam-5592	201	12	℘	℘	PROPN
ejpam-5592	201	13	(	(	PUNCT
ejpam-5592	201	14	r	r	NOUN
ejpam-5592	201	15	)	)	PUNCT
ejpam-5592	201	16	dr	dr	PROPN
ejpam-5592	201	17	,	,	PUNCT
ejpam-5592	201	18	which	which	PRON
ejpam-5592	201	19	implies	imply	VERB
ejpam-5592	201	20	that	that	SCONJ
ejpam-5592	201	21	(	(	PUNCT
ejpam-5592	201	22	rlabℜϖu	rlabℜϖu	NOUN
ejpam-5592	201	23	,	,	PUNCT
ejpam-5592	201	24	ψκ	ψκ	VERB
ejpam-5592	201	25	rlabdϖu	rlabdϖu	ADJ
ejpam-5592	201	26	,	,	PUNCT
ejpam-5592	201	27	ψ	ψ	VERB
ejpam-5592	201	28	κ	κ	PRON
ejpam-5592	201	29	℘	℘	PROPN
ejpam-5592	201	30	)	)	PUNCT
ejpam-5592	201	31	(	(	PUNCT
ejpam-5592	201	32	z	z	X
ejpam-5592	201	33	)	)	PUNCT
ejpam-5592	201	34	=	=	SYM
ejpam-5592	202	1	∞∑	∞∑	NUM
ejpam-5592	202	2	j=0	j=0	PROPN
ejpam-5592	202	3	(	(	PUNCT
ejpam-5592	202	4	−(ϖu	−(ϖu	NOUN
ejpam-5592	202	5	−	−	PROPN
ejpam-5592	202	6	k	k	NOUN
ejpam-5592	202	7	)	)	PUNCT
ejpam-5592	202	8	k	k	PROPN
ejpam-5592	203	1	+	+	CCONJ
ejpam-5592	203	2	1−ϖu	1−ϖu	NUM
ejpam-5592	203	3	)	)	PUNCT
ejpam-5592	204	1	j	j	PROPN
ejpam-5592	205	1	ℜk	ℜk	PROPN
ejpam-5592	205	2	,	,	PUNCT
ejpam-5592	205	3	ψκ	ψκ	PROPN
ejpam-5592	205	4	(	(	PUNCT
ejpam-5592	205	5	1	1	NUM
ejpam-5592	205	6	ψ′(z	ψ′(z	NOUN
ejpam-5592	205	7	)	)	PUNCT
ejpam-5592	205	8	d	d	X
ejpam-5592	205	9	dz	dz	PROPN
ejpam-5592	205	10	)	)	PUNCT
ejpam-5592	205	11	k+1	k+1	PART
ejpam-5592	205	12	rlℜj(ϖu−k)+1,ψ	rlℜj(ϖu−k)+1,ψ	NOUN
ejpam-5592	205	13	κ	κ	PRON
ejpam-5592	205	14	℘	℘	PROPN
ejpam-5592	205	15	(	(	PUNCT
ejpam-5592	205	16	z	z	NOUN
ejpam-5592	205	17	)	)	PUNCT
ejpam-5592	205	18	−	−	PROPN
ejpam-5592	206	1	∞∑	∞∑	NUM
ejpam-5592	206	2	j=0	j=0	PROPN
ejpam-5592	206	3	(	(	PUNCT
ejpam-5592	206	4	−(ϖu	−(ϖu	NOUN
ejpam-5592	206	5	−	−	PROPN
ejpam-5592	206	6	k	k	NOUN
ejpam-5592	206	7	)	)	PUNCT
ejpam-5592	206	8	k	k	PROPN
ejpam-5592	207	1	+	+	CCONJ
ejpam-5592	207	2	1−ϖu	1−ϖu	NUM
ejpam-5592	207	3	)	)	PUNCT
ejpam-5592	208	1	j+1	j+1	PROPN
ejpam-5592	208	2	ℜϖu	ℜϖu	PROPN
ejpam-5592	208	3	,	,	PUNCT
ejpam-5592	208	4	ψκ	ψκ	PROPN
ejpam-5592	208	5	(	(	PUNCT
ejpam-5592	208	6	1	1	NUM
ejpam-5592	208	7	ψ′(z	ψ′(z	NOUN
ejpam-5592	208	8	)	)	PUNCT
ejpam-5592	208	9	d	d	X
ejpam-5592	208	10	dz	dz	PROPN
ejpam-5592	208	11	)	)	PUNCT
ejpam-5592	208	12	k+1	k+1	PART
ejpam-5592	208	13	rlℜj(ϖu−k)+1,ψ	rlℜj(ϖu−k)+1,ψ	NOUN
ejpam-5592	208	14	κ	κ	PRON
ejpam-5592	208	15	℘	℘	PROPN
ejpam-5592	208	16	(	(	PUNCT
ejpam-5592	208	17	z	z	NOUN
ejpam-5592	208	18	)	)	PUNCT
ejpam-5592	208	19	=	=	SYM
ejpam-5592	209	1	∞∑	∞∑	NUM
ejpam-5592	209	2	j=0	j=0	PROPN
ejpam-5592	209	3	(	(	PUNCT
ejpam-5592	209	4	−(ϖu	−(ϖu	NOUN
ejpam-5592	209	5	−	−	PROPN
ejpam-5592	209	6	k	k	NOUN
ejpam-5592	209	7	)	)	PUNCT
ejpam-5592	209	8	k	k	PROPN
ejpam-5592	210	1	+	+	CCONJ
ejpam-5592	210	2	1−ϖu	1−ϖu	NUM
ejpam-5592	210	3	)	)	PUNCT
ejpam-5592	211	1	j	j	PROPN
ejpam-5592	211	2	rlℜj(ϖu−k)+1,ψ	rlℜj(ϖu−k)+1,ψ	PROPN
ejpam-5592	211	3	κ	κ	ADP
ejpam-5592	211	4	℘	℘	PROPN
ejpam-5592	211	5	(	(	PUNCT
ejpam-5592	211	6	z	z	NOUN
ejpam-5592	211	7	)	)	PUNCT
ejpam-5592	211	8	−	−	PROPN
ejpam-5592	212	1	∞∑	∞∑	NUM
ejpam-5592	212	2	j=0	j=0	PROPN
ejpam-5592	212	3	(	(	PUNCT
ejpam-5592	212	4	−(ϖu	−(ϖu	NOUN
ejpam-5592	212	5	−	−	PROPN
ejpam-5592	212	6	k	k	NOUN
ejpam-5592	212	7	)	)	PUNCT
ejpam-5592	212	8	k	k	PROPN
ejpam-5592	213	1	+	+	CCONJ
ejpam-5592	213	2	1−ϖu	1−ϖu	NUM
ejpam-5592	213	3	)	)	PUNCT
ejpam-5592	214	1	j+1	j+1	SYM
ejpam-5592	214	2	rlℜj(ϖu−k)+(ϖu−k),ψ	rlℜj(ϖu−k)+(ϖu−k),ψ	NOUN
ejpam-5592	214	3	κ	κ	ADP
ejpam-5592	214	4	℘	℘	PROPN
ejpam-5592	214	5	(	(	PUNCT
ejpam-5592	214	6	z	z	NOUN
ejpam-5592	214	7	)	)	PUNCT
ejpam-5592	214	8	=	=	SYM
ejpam-5592	214	9	℘(z	℘(z	ADJ
ejpam-5592	214	10	)	)	PUNCT
ejpam-5592	214	11	.	.	PUNCT
ejpam-5592	215	1	(	(	PUNCT
ejpam-5592	215	2	iii	iii	X
ejpam-5592	215	3	)	)	PUNCT
ejpam-5592	215	4	using	use	VERB
ejpam-5592	215	5	definitions	definition	NOUN
ejpam-5592	215	6	10	10	NUM
ejpam-5592	215	7	,	,	PUNCT
ejpam-5592	215	8	12	12	NUM
ejpam-5592	215	9	,	,	PUNCT
ejpam-5592	215	10	lemmas	lemma	NOUN
ejpam-5592	215	11	1	1	NUM
ejpam-5592	215	12	and	and	CCONJ
ejpam-5592	215	13	3	3	NUM
ejpam-5592	215	14	,	,	PUNCT
ejpam-5592	215	15	for	for	ADP
ejpam-5592	215	16	u	u	PRON
ejpam-5592	215	17	≥	≥	NUM
ejpam-5592	215	18	1	1	NUM
ejpam-5592	215	19	,	,	PUNCT
ejpam-5592	215	20	one	one	PRON
ejpam-5592	215	21	has	have	VERB
ejpam-5592	215	22	(	(	PUNCT
ejpam-5592	215	23	cabdϖu	cabdϖu	PROPN
ejpam-5592	215	24	,	,	PUNCT
ejpam-5592	215	25	ψ	ψ	X
ejpam-5592	215	26	κ	κ	NOUN
ejpam-5592	215	27	rlabℜϖu	rlabℜϖu	PROPN
ejpam-5592	215	28	,	,	PUNCT
ejpam-5592	215	29	ψκ	ψκ	PROPN
ejpam-5592	215	30	℘	℘	PROPN
ejpam-5592	215	31	)	)	PUNCT
ejpam-5592	215	32	(	(	PUNCT
ejpam-5592	215	33	z	z	X
ejpam-5592	215	34	)	)	PUNCT
ejpam-5592	215	35	=	=	SYM
ejpam-5592	215	36	(	(	PUNCT
ejpam-5592	215	37	cabdθu	cabdθu	X
ejpam-5592	215	38	,	,	PUNCT
ejpam-5592	215	39	ψ	ψ	X
ejpam-5592	215	40	κ	κ	X
ejpam-5592	215	41	(	(	PUNCT
ejpam-5592	215	42	1	1	NUM
ejpam-5592	215	43	ψ(z	ψ(z	NOUN
ejpam-5592	215	44	)	)	PUNCT
ejpam-5592	215	45	d	d	X
ejpam-5592	215	46	dz	dz	X
ejpam-5592	215	47	)	)	PUNCT
ejpam-5592	215	48	k	k	PROPN
ejpam-5592	215	49	rlℜk	rlℜk	PROPN
ejpam-5592	215	50	,	,	PUNCT
ejpam-5592	215	51	ψκ	ψκ	VERB
ejpam-5592	215	52	rlabℜθu	rlabℜθu	PROPN
ejpam-5592	215	53	,	,	PUNCT
ejpam-5592	215	54	ψκ	ψκ	VERB
ejpam-5592	215	55	℘	℘	PROPN
ejpam-5592	215	56	)	)	PUNCT
ejpam-5592	215	57	(	(	PUNCT
ejpam-5592	215	58	z	z	X
ejpam-5592	215	59	)	)	PUNCT
ejpam-5592	215	60	=	=	SYM
ejpam-5592	215	61	(	(	PUNCT
ejpam-5592	215	62	cabdθu	cabdθu	X
ejpam-5592	215	63	,	,	PUNCT
ejpam-5592	215	64	ψ	ψ	X
ejpam-5592	215	65	κ	κ	PROPN
ejpam-5592	215	66	rlabℜθu	rlabℜθu	PROPN
ejpam-5592	215	67	,	,	PUNCT
ejpam-5592	215	68	ψκ	ψκ	VERB
ejpam-5592	215	69	℘	℘	PROPN
ejpam-5592	215	70	)	)	PUNCT
ejpam-5592	215	71	(	(	PUNCT
ejpam-5592	215	72	z	z	X
ejpam-5592	215	73	)	)	PUNCT
ejpam-5592	215	74	=	=	SYM
ejpam-5592	216	1	℘(z)−	℘(z)−	PROPN
ejpam-5592	216	2	℘(κ)lθu	℘(κ)lθu	X
ejpam-5592	216	3	(	(	PUNCT
ejpam-5592	216	4	−θu	−θu	NOUN
ejpam-5592	216	5	1−	1−	NUM
ejpam-5592	216	6	θu	θu	NOUN
ejpam-5592	216	7	(	(	PUNCT
ejpam-5592	216	8	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	216	9	ψ(κ))θu	ψ(κ))θu	NOUN
ejpam-5592	216	10	)	)	PUNCT
ejpam-5592	216	11	=	=	SYM
ejpam-5592	216	12	℘(z)−	℘(z)−	PROPN
ejpam-5592	216	13	℘(κ)lϖu−k	℘(κ)lϖu−k	PROPN
ejpam-5592	216	14	(	(	PUNCT
ejpam-5592	216	15	−(ϖu	−(ϖu	PROPN
ejpam-5592	216	16	−	−	PROPN
ejpam-5592	216	17	k	k	NOUN
ejpam-5592	216	18	)	)	PUNCT
ejpam-5592	216	19	1−	1−	NUM
ejpam-5592	216	20	(	(	PUNCT
ejpam-5592	216	21	ϖu	ϖu	PROPN
ejpam-5592	216	22	−	−	PROPN
ejpam-5592	216	23	k	k	NOUN
ejpam-5592	216	24	)	)	PUNCT
ejpam-5592	216	25	(	(	PUNCT
ejpam-5592	216	26	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	216	27	ψ(κ))ϖu−k	ψ(κ))ϖu−k	NOUN
ejpam-5592	216	28	)	)	PUNCT
ejpam-5592	216	29	.	.	PUNCT
ejpam-5592	217	1	(	(	PUNCT
ejpam-5592	217	2	iv	iv	X
ejpam-5592	217	3	)	)	PUNCT
ejpam-5592	217	4	based	base	VERB
ejpam-5592	217	5	on	on	ADP
ejpam-5592	217	6	definitions	definition	NOUN
ejpam-5592	217	7	10	10	NUM
ejpam-5592	217	8	,	,	PUNCT
ejpam-5592	217	9	12	12	NUM
ejpam-5592	217	10	and	and	CCONJ
ejpam-5592	217	11	lemma	lemma	PROPN
ejpam-5592	217	12	3	3	NUM
ejpam-5592	217	13	,	,	PUNCT
ejpam-5592	217	14	for	for	ADP
ejpam-5592	217	15	u	u	PRON
ejpam-5592	217	16	≥	≥	NUM
ejpam-5592	217	17	1	1	NUM
ejpam-5592	217	18	,	,	PUNCT
ejpam-5592	217	19	we	we	PRON
ejpam-5592	217	20	get	get	VERB
ejpam-5592	217	21	(	(	PUNCT
ejpam-5592	217	22	rlabℜϖu	rlabℜϖu	PROPN
ejpam-5592	217	23	,	,	PUNCT
ejpam-5592	217	24	ψκ	ψκ	PROPN
ejpam-5592	217	25	cabdϖu	cabdϖu	PROPN
ejpam-5592	217	26	,	,	PUNCT
ejpam-5592	217	27	ψ	ψ	VERB
ejpam-5592	217	28	κ	κ	PRON
ejpam-5592	217	29	℘	℘	PROPN
ejpam-5592	217	30	)	)	PUNCT
ejpam-5592	218	1	(	(	PUNCT
ejpam-5592	218	2	z	z	X
ejpam-5592	218	3	)	)	PUNCT
ejpam-5592	218	4	=	=	SYM
ejpam-5592	218	5	(	(	PUNCT
ejpam-5592	218	6	rlℜk	rlℜk	PROPN
ejpam-5592	218	7	,	,	PUNCT
ejpam-5592	218	8	ψκ	ψκ	VERB
ejpam-5592	218	9	rlabℜθu	rlabℜθu	PROPN
ejpam-5592	218	10	,	,	PUNCT
ejpam-5592	218	11	ψκ	ψκ	VERB
ejpam-5592	218	12	cabdθu	cabdθu	NOUN
ejpam-5592	218	13	,	,	PUNCT
ejpam-5592	218	14	ψ	ψ	VERB
ejpam-5592	218	15	κ	κ	PRON
ejpam-5592	218	16	℘	℘	PROPN
ejpam-5592	218	17	(	(	PUNCT
ejpam-5592	218	18	k	k	NOUN
ejpam-5592	218	19	)	)	PUNCT
ejpam-5592	218	20	ψ	ψ	NOUN
ejpam-5592	218	21	)	)	PUNCT
ejpam-5592	218	22	(	(	PUNCT
ejpam-5592	218	23	z	z	X
ejpam-5592	218	24	)	)	PUNCT
ejpam-5592	219	1	=	=	NOUN
ejpam-5592	219	2	rl	rl	ADP
ejpam-5592	219	3	ℜk	ℜk	NOUN
ejpam-5592	219	4	,	,	PUNCT
ejpam-5592	219	5	ψκ	ψκ	INTJ
ejpam-5592	219	6	(	(	PUNCT
ejpam-5592	219	7	℘	℘	PROPN
ejpam-5592	219	8	(	(	PUNCT
ejpam-5592	219	9	k	k	NOUN
ejpam-5592	219	10	)	)	PUNCT
ejpam-5592	219	11	ψ	ψ	X
ejpam-5592	219	12	(	(	PUNCT
ejpam-5592	219	13	z)−	z)−	PROPN
ejpam-5592	219	14	℘	℘	PROPN
ejpam-5592	219	15	(	(	PUNCT
ejpam-5592	219	16	k	k	NOUN
ejpam-5592	219	17	)	)	PUNCT
ejpam-5592	219	18	ψ	ψ	X
ejpam-5592	219	19	(	(	PUNCT
ejpam-5592	219	20	κ	κ	NOUN
ejpam-5592	219	21	)	)	PUNCT
ejpam-5592	219	22	)	)	PUNCT
ejpam-5592	220	1	=	=	SYM
ejpam-5592	220	2	℘(z)−	℘(z)−	PROPN
ejpam-5592	220	3	k−1∑	k−1∑	PROPN
ejpam-5592	220	4	m=0	m=0	PROPN
ejpam-5592	220	5	℘	℘	PROPN
ejpam-5592	220	6	(	(	PUNCT
ejpam-5592	220	7	m	m	NOUN
ejpam-5592	220	8	)	)	PUNCT
ejpam-5592	220	9	ψ	ψ	X
ejpam-5592	220	10	(	(	PUNCT
ejpam-5592	220	11	κ	κ	NOUN
ejpam-5592	220	12	)	)	PUNCT
ejpam-5592	220	13	m	m	PROPN
ejpam-5592	220	14	!	!	PUNCT
ejpam-5592	221	1	(	(	PUNCT
ejpam-5592	221	2	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	221	3	ψ(r))m	ψ(r))m	PROPN
ejpam-5592	221	4	−	−	PROPN
ejpam-5592	221	5	℘	℘	PROPN
ejpam-5592	221	6	(	(	PUNCT
ejpam-5592	221	7	k	k	NOUN
ejpam-5592	221	8	)	)	PUNCT
ejpam-5592	221	9	ψ	ψ	X
ejpam-5592	221	10	(	(	PUNCT
ejpam-5592	221	11	κ	κ	NOUN
ejpam-5592	221	12	)	)	PUNCT
ejpam-5592	221	13	k	k	NOUN
ejpam-5592	221	14	!	!	PUNCT
ejpam-5592	222	1	(	(	PUNCT
ejpam-5592	222	2	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	222	3	ψ(r))k	ψ(r))k	X
ejpam-5592	222	4	=	=	SYM
ejpam-5592	222	5	℘(z)−	℘(z)−	PROPN
ejpam-5592	222	6	k∑	k∑	ADJ
ejpam-5592	222	7	m=0	m=0	PROPN
ejpam-5592	222	8	℘	℘	PROPN
ejpam-5592	222	9	(	(	PUNCT
ejpam-5592	222	10	m	m	NOUN
ejpam-5592	222	11	)	)	PUNCT
ejpam-5592	222	12	ψ	ψ	X
ejpam-5592	222	13	(	(	PUNCT
ejpam-5592	222	14	κ	κ	NOUN
ejpam-5592	222	15	)	)	PUNCT
ejpam-5592	222	16	m	m	PROPN
ejpam-5592	222	17	!	!	PUNCT
ejpam-5592	223	1	(	(	PUNCT
ejpam-5592	223	2	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	223	3	ψ(κ))m	ψ(κ))m	PROPN
ejpam-5592	223	4	.	.	PUNCT
ejpam-5592	224	1	h.a	h.a	PROPN
ejpam-5592	224	2	.	.	PROPN
ejpam-5592	224	3	hammad	hammad	PROPN
ejpam-5592	224	4	,	,	PUNCT
ejpam-5592	224	5	m.	m.	PROPN
ejpam-5592	224	6	de	de	X
ejpam-5592	224	7	la	la	PROPN
ejpam-5592	224	8	sen	sen	PROPN
ejpam-5592	224	9	/	/	SYM
ejpam-5592	224	10	eur	eur	PROPN
ejpam-5592	224	11	.	.	PUNCT
ejpam-5592	225	1	j.	j.	PROPN
ejpam-5592	225	2	pure	pure	PROPN
ejpam-5592	225	3	appl	appl	PROPN
ejpam-5592	225	4	.	.	PROPN
ejpam-5592	225	5	math	math	PROPN
ejpam-5592	225	6	,	,	PUNCT
ejpam-5592	225	7	17	17	NUM
ejpam-5592	225	8	(	(	PUNCT
ejpam-5592	225	9	4	4	NUM
ejpam-5592	225	10	)	)	PUNCT
ejpam-5592	225	11	(	(	PUNCT
ejpam-5592	225	12	2024	2024	NUM
ejpam-5592	225	13	)	)	PUNCT
ejpam-5592	225	14	,	,	PUNCT
ejpam-5592	225	15	3687	3687	NUM
ejpam-5592	225	16	-	-	SYM
ejpam-5592	225	17	3707	3707	NUM
ejpam-5592	225	18	3696	3696	NUM
ejpam-5592	225	19	lemma	lemma	PROPN
ejpam-5592	225	20	5	5	NUM
ejpam-5592	225	21	.	.	PUNCT
ejpam-5592	225	22	assume	assume	VERB
ejpam-5592	225	23	that	that	SCONJ
ejpam-5592	225	24	℘	℘	PROPN
ejpam-5592	225	25	∈	∈	PROPN
ejpam-5592	225	26	ck(ℑu	ck(ℑu	PROPN
ejpam-5592	225	27	,	,	PUNCT
ejpam-5592	225	28	r	r	NOUN
ejpam-5592	225	29	)	)	PUNCT
ejpam-5592	225	30	and	and	CCONJ
ejpam-5592	225	31	ψ	ψ	X
ejpam-5592	225	32	∈	∈	PROPN
ejpam-5592	225	33	ck(ℑu	ck(ℑu	PROPN
ejpam-5592	225	34	,	,	PUNCT
ejpam-5592	225	35	r+	r+	PUNCT
ejpam-5592	225	36	)	)	PUNCT
ejpam-5592	225	37	with	with	ADP
ejpam-5592	225	38	ψ′(z	ψ′(z	NOUN
ejpam-5592	225	39	)	)	PUNCT
ejpam-5592	225	40	̸=	̸=	PROPN
ejpam-5592	225	41	0	0	NUM
ejpam-5592	225	42	.	.	PUNCT
ejpam-5592	226	1	for	for	ADP
ejpam-5592	226	2	ϖu	ϖu	PROPN
ejpam-5592	226	3	∈	∈	PROPN
ejpam-5592	226	4	(	(	PUNCT
ejpam-5592	226	5	k	k	NOUN
ejpam-5592	226	6	,	,	PUNCT
ejpam-5592	226	7	k+1	k+1	X
ejpam-5592	226	8	]	]	X
ejpam-5592	226	9	,	,	PUNCT
ejpam-5592	226	10	θu	θu	X
ejpam-5592	226	11	=	=	SYM
ejpam-5592	226	12	ϖu−k	ϖu−k	ADJ
ejpam-5592	226	13	,	,	PUNCT
ejpam-5592	226	14	λ	λ	X
ejpam-5592	226	15	≥	≥	NOUN
ejpam-5592	226	16	k+1	k+1	X
ejpam-5592	226	17	and	and	CCONJ
ejpam-5592	226	18	ζ	ζ	NOUN
ejpam-5592	226	19	≥	≥	NOUN
ejpam-5592	226	20	0	0	NUM
ejpam-5592	226	21	,	,	PUNCT
ejpam-5592	226	22	for	for	ADP
ejpam-5592	226	23	k	k	PROPN
ejpam-5592	226	24	≥	≥	PROPN
ejpam-5592	226	25	0	0	NUM
ejpam-5592	226	26	,	,	PUNCT
ejpam-5592	226	27	u	u	NOUN
ejpam-5592	226	28	≥	≥	NOUN
ejpam-5592	226	29	1	1	NUM
ejpam-5592	226	30	,	,	PUNCT
ejpam-5592	226	31	the	the	DET
ejpam-5592	226	32	relations	relation	NOUN
ejpam-5592	226	33	below	below	ADV
ejpam-5592	226	34	are	be	AUX
ejpam-5592	226	35	true	true	ADJ
ejpam-5592	226	36	:	:	PUNCT
ejpam-5592	226	37	(	(	PUNCT
ejpam-5592	226	38	i	i	NOUN
ejpam-5592	226	39	)	)	PUNCT
ejpam-5592	227	1	rlabℜϖu	rlabℜϖu	VERB
ejpam-5592	227	2	,	,	PUNCT
ejpam-5592	227	3	ψκ	ψκ	INTJ
ejpam-5592	227	4	(	(	PUNCT
ejpam-5592	227	5	℘	℘	PROPN
ejpam-5592	227	6	(	(	PUNCT
ejpam-5592	227	7	z)−	z)−	PROPN
ejpam-5592	227	8	℘	℘	PROPN
ejpam-5592	227	9	(	(	PUNCT
ejpam-5592	227	10	κ))ζ	κ))ζ	NOUN
ejpam-5592	227	11	=	=	SYM
ejpam-5592	227	12	(	(	PUNCT
ejpam-5592	227	13	k+1−ϖu)γ(1+ζ)(℘(z)−℘(κ))ζ+k	k+1−ϖu)γ(1+ζ)(℘(z)−℘(κ))ζ+k	PROPN
ejpam-5592	227	14	λ(ϖu−k)γ(1+ζ+k	λ(ϖu−k)γ(1+ζ+k	PROPN
ejpam-5592	227	15	)	)	PUNCT
ejpam-5592	227	16	+	+	CCONJ
ejpam-5592	227	17	(	(	PUNCT
ejpam-5592	227	18	ϖu−k)γ(1+ζ)(℘(z)−℘(κ))ζ+ϖu	ϖu−k)γ(1+ζ)(℘(z)−℘(κ))ζ+ϖu	NOUN
ejpam-5592	227	19	λ(ϖu−k)γ(1+ζ+k	λ(ϖu−k)γ(1+ζ+k	NOUN
ejpam-5592	227	20	)	)	PUNCT
ejpam-5592	227	21	.	.	PUNCT
ejpam-5592	228	1	(	(	PUNCT
ejpam-5592	228	2	ii	ii	NOUN
ejpam-5592	228	3	)	)	PUNCT
ejpam-5592	228	4	cabdϖu	cabdϖu	NOUN
ejpam-5592	228	5	,	,	PUNCT
ejpam-5592	228	6	ψ	ψ	X
ejpam-5592	228	7	κ	κ	X
ejpam-5592	228	8	(	(	PUNCT
ejpam-5592	228	9	℘	℘	PROPN
ejpam-5592	228	10	(	(	PUNCT
ejpam-5592	228	11	z)−	z)−	PROPN
ejpam-5592	228	12	℘	℘	PROPN
ejpam-5592	228	13	(	(	PUNCT
ejpam-5592	228	14	κ))λ	κ))λ	NOUN
ejpam-5592	228	15	=	=	SYM
ejpam-5592	228	16	λ(ϖu−k	λ(ϖu−k	NOUN
ejpam-5592	228	17	)	)	PUNCT
ejpam-5592	228	18	k+1−ϖu	k+1−ϖu	PROPN
ejpam-5592	229	1	∞∑	∞∑	NUM
ejpam-5592	229	2	j=0	j=0	PROPN
ejpam-5592	229	3	(	(	PUNCT
ejpam-5592	229	4	−(ϖu−k	−(ϖu−k	NOUN
ejpam-5592	229	5	)	)	PUNCT
ejpam-5592	229	6	k+1−ϖu	k+1−ϖu	PROPN
ejpam-5592	229	7	)	)	PUNCT
ejpam-5592	229	8	j	j	PROPN
ejpam-5592	229	9	γ(1+λ)(℘(z)−℘(κ))j(ϖu−k)+λ−k	γ(1+λ)(℘(z)−℘(κ))j(ϖu−k)+λ−k	PROPN
ejpam-5592	229	10	γ(j(ϖu−k)+λ−k+1	γ(j(ϖu−k)+λ−k+1	NUM
ejpam-5592	229	11	)	)	PUNCT
ejpam-5592	229	12	.	.	PUNCT
ejpam-5592	230	1	(	(	PUNCT
ejpam-5592	230	2	iii	iii	X
ejpam-5592	230	3	)	)	PUNCT
ejpam-5592	230	4	cabdϖu	cabdϖu	NOUN
ejpam-5592	230	5	,	,	PUNCT
ejpam-5592	230	6	ψ	ψ	X
ejpam-5592	230	7	κ	κ	X
ejpam-5592	230	8	(	(	PUNCT
ejpam-5592	230	9	℘	℘	PROPN
ejpam-5592	230	10	(	(	PUNCT
ejpam-5592	230	11	z)−	z)−	PROPN
ejpam-5592	230	12	℘	℘	PROPN
ejpam-5592	230	13	(	(	PUNCT
ejpam-5592	230	14	κ))σ	κ))σ	NOUN
ejpam-5592	230	15	=	=	SYM
ejpam-5592	230	16	0	0	NUM
ejpam-5592	230	17	,	,	PUNCT
ejpam-5592	230	18	σ	σ	NOUN
ejpam-5592	230	19	=	=	SYM
ejpam-5592	230	20	0	0	NUM
ejpam-5592	230	21	,	,	PUNCT
ejpam-5592	230	22	1	1	NUM
ejpam-5592	230	23	,	,	PUNCT
ejpam-5592	230	24	...	...	PUNCT
ejpam-5592	230	25	,	,	PUNCT
ejpam-5592	230	26	k.	k.	PROPN
ejpam-5592	230	27	(	(	PUNCT
ejpam-5592	230	28	iv	iv	X
ejpam-5592	230	29	)	)	PUNCT
ejpam-5592	230	30	(	(	PUNCT
ejpam-5592	230	31	rlabℜϖu	rlabℜϖu	PROPN
ejpam-5592	230	32	,	,	PUNCT
ejpam-5592	230	33	ψκ	ψκ	PROPN
ejpam-5592	230	34	1	1	NUM
ejpam-5592	230	35	)	)	PUNCT
ejpam-5592	230	36	(	(	PUNCT
ejpam-5592	230	37	z	z	X
ejpam-5592	230	38	)	)	PUNCT
ejpam-5592	230	39	=	=	SYM
ejpam-5592	230	40	(	(	PUNCT
ejpam-5592	230	41	k+1−ϖu)(℘(z)−℘(κ))k	k+1−ϖu)(℘(z)−℘(κ))k	PROPN
ejpam-5592	230	42	λ(ϖu−k)γ(k+1	λ(ϖu−k)γ(k+1	PROPN
ejpam-5592	230	43	)	)	PUNCT
ejpam-5592	231	1	+	+	CCONJ
ejpam-5592	231	2	(	(	PUNCT
ejpam-5592	231	3	ϖu−k)(℘(z)−℘(κ))ϖu	ϖu−k)(℘(z)−℘(κ))ϖu	NOUN
ejpam-5592	231	4	λ(ϖu−k)γ(1+k	λ(ϖu−k)γ(1+k	NOUN
ejpam-5592	231	5	)	)	PUNCT
ejpam-5592	231	6	.	.	PUNCT
ejpam-5592	232	1	(	(	PUNCT
ejpam-5592	232	2	v	v	NOUN
ejpam-5592	232	3	)	)	PUNCT
ejpam-5592	232	4	(	(	PUNCT
ejpam-5592	232	5	cabdϖu	cabdϖu	PROPN
ejpam-5592	232	6	,	,	PUNCT
ejpam-5592	232	7	ψ	ψ	X
ejpam-5592	232	8	κ	κ	PROPN
ejpam-5592	232	9	1	1	NUM
ejpam-5592	232	10	)	)	PUNCT
ejpam-5592	232	11	(	(	PUNCT
ejpam-5592	232	12	z	z	X
ejpam-5592	232	13	)	)	PUNCT
ejpam-5592	232	14	=	=	SYM
ejpam-5592	233	1	0	0	X
ejpam-5592	233	2	.	.	PUNCT
ejpam-5592	233	3	proof	proof	NOUN
ejpam-5592	233	4	.	.	PUNCT
ejpam-5592	234	1	(	(	PUNCT
ejpam-5592	234	2	i	i	NOUN
ejpam-5592	234	3	)	)	PUNCT
ejpam-5592	234	4	using	use	VERB
ejpam-5592	234	5	definition	definition	NOUN
ejpam-5592	234	6	12	12	NUM
ejpam-5592	234	7	and	and	CCONJ
ejpam-5592	234	8	lemma	lemma	PROPN
ejpam-5592	234	9	3	3	NUM
ejpam-5592	234	10	,	,	PUNCT
ejpam-5592	234	11	for	for	ADP
ejpam-5592	234	12	u	u	PRON
ejpam-5592	234	13	≥	≥	NUM
ejpam-5592	234	14	1	1	NUM
ejpam-5592	234	15	,	,	PUNCT
ejpam-5592	234	16	we	we	PRON
ejpam-5592	234	17	have	have	AUX
ejpam-5592	234	18	rlabℜϖu	rlabℜϖu	NOUN
ejpam-5592	234	19	,	,	PUNCT
ejpam-5592	234	20	ψκ	ψκ	INTJ
ejpam-5592	234	21	(	(	PUNCT
ejpam-5592	234	22	℘	℘	PROPN
ejpam-5592	234	23	(	(	PUNCT
ejpam-5592	234	24	z)−	z)−	PROPN
ejpam-5592	234	25	℘	℘	PROPN
ejpam-5592	234	26	(	(	PUNCT
ejpam-5592	234	27	κ))ζ	κ))ζ	NOUN
ejpam-5592	234	28	=	=	PUNCT
ejpam-5592	234	29	k	k	PROPN
ejpam-5592	235	1	+	+	CCONJ
ejpam-5592	235	2	1−ϖu	1−ϖu	NUM
ejpam-5592	235	3	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	235	4	−	−	PROPN
ejpam-5592	235	5	k	k	X
ejpam-5592	235	6	)	)	PUNCT
ejpam-5592	235	7	rl	rl	ADP
ejpam-5592	235	8	ℜk	ℜk	PROPN
ejpam-5592	235	9	,	,	PUNCT
ejpam-5592	235	10	ψκ	ψκ	INTJ
ejpam-5592	235	11	(	(	PUNCT
ejpam-5592	235	12	℘	℘	PROPN
ejpam-5592	235	13	(	(	PUNCT
ejpam-5592	235	14	z)−	z)−	NOUN
ejpam-5592	235	15	℘	℘	PROPN
ejpam-5592	235	16	(	(	PUNCT
ejpam-5592	235	17	κ))ζ	κ))ζ	NOUN
ejpam-5592	235	18	+	+	CCONJ
ejpam-5592	235	19	ϖu	ϖu	PROPN
ejpam-5592	235	20	−	−	NOUN
ejpam-5592	235	21	k	k	PROPN
ejpam-5592	235	22	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	235	23	−	−	PROPN
ejpam-5592	235	24	k	k	X
ejpam-5592	235	25	)	)	PUNCT
ejpam-5592	235	26	rl	rl	ADP
ejpam-5592	235	27	ℜϖu	ℜϖu	PROPN
ejpam-5592	235	28	,	,	PUNCT
ejpam-5592	235	29	ψκ	ψκ	PROPN
ejpam-5592	235	30	(	(	PUNCT
ejpam-5592	235	31	℘	℘	PROPN
ejpam-5592	235	32	(	(	PUNCT
ejpam-5592	235	33	z)−	z)−	PROPN
ejpam-5592	235	34	℘	℘	PROPN
ejpam-5592	235	35	(	(	PUNCT
ejpam-5592	235	36	κ))ζ	κ))ζ	NOUN
ejpam-5592	235	37	=	=	PUNCT
ejpam-5592	235	38	k	k	PROPN
ejpam-5592	236	1	+	+	CCONJ
ejpam-5592	236	2	1−ϖu	1−ϖu	NUM
ejpam-5592	237	1	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	237	2	−	−	PROPN
ejpam-5592	237	3	k	k	X
ejpam-5592	237	4	)	)	PUNCT
ejpam-5592	237	5	γ(1	γ(1	PROPN
ejpam-5592	238	1	+	+	CCONJ
ejpam-5592	238	2	ζ	ζ	NOUN
ejpam-5592	238	3	)	)	PUNCT
ejpam-5592	238	4	γ(1	γ(1	PROPN
ejpam-5592	239	1	+	+	CCONJ
ejpam-5592	239	2	ζ	ζ	NOUN
ejpam-5592	239	3	+	+	CCONJ
ejpam-5592	239	4	k	k	NOUN
ejpam-5592	239	5	)	)	PUNCT
ejpam-5592	239	6	(	(	PUNCT
ejpam-5592	239	7	℘	℘	PROPN
ejpam-5592	239	8	(	(	PUNCT
ejpam-5592	239	9	z)−	z)−	NOUN
ejpam-5592	239	10	℘	℘	PROPN
ejpam-5592	239	11	(	(	PUNCT
ejpam-5592	239	12	κ))ζ+k	κ))ζ+k	PROPN
ejpam-5592	239	13	+	+	CCONJ
ejpam-5592	239	14	ϖu	ϖu	PROPN
ejpam-5592	239	15	−	−	NOUN
ejpam-5592	239	16	k	k	PROPN
ejpam-5592	239	17	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	239	18	−	−	PROPN
ejpam-5592	239	19	k	k	X
ejpam-5592	239	20	)	)	PUNCT
ejpam-5592	239	21	γ(1	γ(1	PROPN
ejpam-5592	240	1	+	+	CCONJ
ejpam-5592	240	2	ζ	ζ	NOUN
ejpam-5592	240	3	)	)	PUNCT
ejpam-5592	240	4	γ(1	γ(1	PROPN
ejpam-5592	241	1	+	+	CCONJ
ejpam-5592	241	2	ζ	ζ	NOUN
ejpam-5592	241	3	+	+	CCONJ
ejpam-5592	241	4	k	k	NOUN
ejpam-5592	241	5	)	)	PUNCT
ejpam-5592	241	6	(	(	PUNCT
ejpam-5592	241	7	℘	℘	PROPN
ejpam-5592	241	8	(	(	PUNCT
ejpam-5592	241	9	z)−	z)−	NOUN
ejpam-5592	241	10	℘	℘	PROPN
ejpam-5592	241	11	(	(	PUNCT
ejpam-5592	241	12	κ))ζ+ϖu	κ))ζ+ϖu	NOUN
ejpam-5592	241	13	.	.	PUNCT
ejpam-5592	241	14	(	(	PUNCT
ejpam-5592	241	15	ii	ii	NOUN
ejpam-5592	241	16	)	)	PUNCT
ejpam-5592	241	17	from	from	ADP
ejpam-5592	241	18	definitions	definition	NOUN
ejpam-5592	241	19	3	3	NUM
ejpam-5592	241	20	,	,	PUNCT
ejpam-5592	241	21	11	11	NUM
ejpam-5592	241	22	and	and	CCONJ
ejpam-5592	241	23	lemma	lemma	PROPN
ejpam-5592	241	24	3	3	NUM
ejpam-5592	241	25	,	,	PUNCT
ejpam-5592	241	26	it	it	PRON
ejpam-5592	241	27	follows	follow	VERB
ejpam-5592	241	28	that	that	SCONJ
ejpam-5592	241	29	for	for	SCONJ
ejpam-5592	241	30	u	u	PROPN
ejpam-5592	241	31	≥	≥	NUM
ejpam-5592	241	32	1	1	NUM
ejpam-5592	241	33	,	,	PUNCT
ejpam-5592	241	34	cabdϖu	cabdϖu	NOUN
ejpam-5592	241	35	,	,	PUNCT
ejpam-5592	241	36	ψ	ψ	X
ejpam-5592	241	37	κ	κ	X
ejpam-5592	241	38	(	(	PUNCT
ejpam-5592	241	39	℘	℘	PROPN
ejpam-5592	241	40	(	(	PUNCT
ejpam-5592	241	41	z)−	z)−	PROPN
ejpam-5592	241	42	℘	℘	PROPN
ejpam-5592	241	43	(	(	PUNCT
ejpam-5592	241	44	κ))λ	κ))λ	NOUN
ejpam-5592	241	45	=	=	SYM
ejpam-5592	241	46	cabdθu	cabdθu	NOUN
ejpam-5592	241	47	,	,	PUNCT
ejpam-5592	241	48	ψ	ψ	X
ejpam-5592	241	49	κ	κ	X
ejpam-5592	241	50	(	(	PUNCT
ejpam-5592	241	51	1	1	NUM
ejpam-5592	241	52	ψ′(z	ψ′(z	NOUN
ejpam-5592	241	53	)	)	PUNCT
ejpam-5592	241	54	d	d	X
ejpam-5592	241	55	dz	dz	PROPN
ejpam-5592	241	56	)	)	PUNCT
ejpam-5592	241	57	k	k	PROPN
ejpam-5592	241	58	(	(	PUNCT
ejpam-5592	241	59	℘	℘	PROPN
ejpam-5592	241	60	(	(	PUNCT
ejpam-5592	241	61	z)−	z)−	PROPN
ejpam-5592	241	62	℘	℘	PROPN
ejpam-5592	241	63	(	(	PUNCT
ejpam-5592	241	64	κ))λ	κ))λ	NOUN
ejpam-5592	241	65	=	=	SYM
ejpam-5592	241	66	cabdθu	cabdθu	NOUN
ejpam-5592	241	67	,	,	PUNCT
ejpam-5592	241	68	ψ	ψ	NOUN
ejpam-5592	241	69	κ	κ	X
ejpam-5592	242	1	γ(1	γ(1	PROPN
ejpam-5592	242	2	+	+	NUM
ejpam-5592	242	3	λ	λ	NOUN
ejpam-5592	242	4	)	)	PUNCT
ejpam-5592	242	5	γ(λ−	γ(λ−	PROPN
ejpam-5592	242	6	k	k	NOUN
ejpam-5592	242	7	+	+	PROPN
ejpam-5592	242	8	1	1	X
ejpam-5592	242	9	)	)	PUNCT
ejpam-5592	242	10	(	(	PUNCT
ejpam-5592	242	11	℘	℘	PROPN
ejpam-5592	242	12	(	(	PUNCT
ejpam-5592	242	13	z)−	z)−	PROPN
ejpam-5592	242	14	℘	℘	PROPN
ejpam-5592	242	15	(	(	PUNCT
ejpam-5592	242	16	κ))λ−k	κ))λ−k	PROPN
ejpam-5592	242	17	=	=	SYM
ejpam-5592	242	18	λ(θu	λ(θu	NOUN
ejpam-5592	242	19	)	)	PUNCT
ejpam-5592	242	20	1−	1−	NUM
ejpam-5592	242	21	θu	θu	ADP
ejpam-5592	242	22	z∫	z∫	PROPN
ejpam-5592	242	23	κ	κ	NOUN
ejpam-5592	242	24	ψ′(r	ψ′(r	NOUN
ejpam-5592	242	25	)	)	PUNCT
ejpam-5592	242	26	∞∑	∞∑	PROPN
ejpam-5592	242	27	j=0	j=0	PROPN
ejpam-5592	242	28	(	(	PUNCT
ejpam-5592	242	29	−θu	−θu	NOUN
ejpam-5592	242	30	1−	1−	NUM
ejpam-5592	242	31	θu	θu	NOUN
ejpam-5592	242	32	)	)	PUNCT
ejpam-5592	242	33	j	j	PROPN
ejpam-5592	242	34	γ(1	γ(1	PROPN
ejpam-5592	242	35	+	+	NUM
ejpam-5592	242	36	λ	λ	NOUN
ejpam-5592	242	37	)	)	PUNCT
ejpam-5592	242	38	(	(	PUNCT
ejpam-5592	242	39	℘	℘	PROPN
ejpam-5592	242	40	(	(	PUNCT
ejpam-5592	242	41	r)−	r)−	PROPN
ejpam-5592	242	42	℘	℘	PROPN
ejpam-5592	242	43	(	(	PUNCT
ejpam-5592	242	44	κ))λ−(k+1	κ))λ−(k+1	PROPN
ejpam-5592	242	45	)	)	PUNCT
ejpam-5592	242	46	γ(λ−	γ(λ−	NOUN
ejpam-5592	242	47	k)γ(jθu	k)γ(jθu	PROPN
ejpam-5592	242	48	+	+	NOUN
ejpam-5592	242	49	1	1	NUM
ejpam-5592	242	50	)	)	PUNCT
ejpam-5592	242	51	(	(	PUNCT
ejpam-5592	242	52	℘	℘	PROPN
ejpam-5592	242	53	(	(	PUNCT
ejpam-5592	242	54	z)−	z)−	NOUN
ejpam-5592	242	55	℘	℘	PROPN
ejpam-5592	242	56	(	(	PUNCT
ejpam-5592	242	57	r))jθu	r))jθu	PROPN
ejpam-5592	242	58	dr	dr	PROPN
ejpam-5592	242	59	=	=	PROPN
ejpam-5592	242	60	γ(1	γ(1	PROPN
ejpam-5592	242	61	+	+	NUM
ejpam-5592	242	62	λ)λ(θu	λ)λ(θu	NUM
ejpam-5592	242	63	)	)	PUNCT
ejpam-5592	242	64	γ(λ−	γ(λ−	PROPN
ejpam-5592	242	65	k	k	NOUN
ejpam-5592	242	66	)	)	PUNCT
ejpam-5592	242	67	(	(	PUNCT
ejpam-5592	242	68	1−	1−	NUM
ejpam-5592	242	69	θu	θu	NOUN
ejpam-5592	242	70	)	)	PUNCT
ejpam-5592	242	71	∞∑	∞∑	NUM
ejpam-5592	242	72	j=0	j=0	PROPN
ejpam-5592	242	73	(	(	PUNCT
ejpam-5592	242	74	−θu	−θu	NOUN
ejpam-5592	242	75	1−	1−	NUM
ejpam-5592	242	76	θu	θu	NOUN
ejpam-5592	242	77	)	)	PUNCT
ejpam-5592	243	1	j	j	PROPN
ejpam-5592	243	2	rlℜjθu+1,ψ	rlℜjθu+1,ψ	PROPN
ejpam-5592	243	3	κ	κ	X
ejpam-5592	243	4	(	(	PUNCT
ejpam-5592	243	5	℘	℘	PROPN
ejpam-5592	243	6	(	(	PUNCT
ejpam-5592	243	7	z)−	z)−	PROPN
ejpam-5592	243	8	℘	℘	PROPN
ejpam-5592	243	9	(	(	PUNCT
ejpam-5592	243	10	κ))λ−(k+1	κ))λ−(k+1	PROPN
ejpam-5592	243	11	)	)	PUNCT
ejpam-5592	243	12	=	=	SYM
ejpam-5592	243	13	λ(θu	λ(θu	NOUN
ejpam-5592	243	14	)	)	PUNCT
ejpam-5592	243	15	1−	1−	NUM
ejpam-5592	243	16	θu	θu	ADP
ejpam-5592	243	17	∞∑	∞∑	NUM
ejpam-5592	243	18	j=0	j=0	PROPN
ejpam-5592	243	19	(	(	PUNCT
ejpam-5592	243	20	−θu	−θu	NOUN
ejpam-5592	243	21	1−	1−	NUM
ejpam-5592	243	22	θu	θu	NOUN
ejpam-5592	243	23	)	)	PUNCT
ejpam-5592	243	24	j	j	PROPN
ejpam-5592	243	25	γ(1	γ(1	PROPN
ejpam-5592	243	26	+	+	NUM
ejpam-5592	243	27	λ	λ	NOUN
ejpam-5592	243	28	)	)	PUNCT
ejpam-5592	243	29	γ(jθu	γ(jθu	PROPN
ejpam-5592	244	1	+	+	CCONJ
ejpam-5592	244	2	λ−	λ−	PROPN
ejpam-5592	244	3	k	k	PROPN
ejpam-5592	245	1	+	+	PROPN
ejpam-5592	245	2	1	1	X
ejpam-5592	245	3	)	)	PUNCT
ejpam-5592	245	4	(	(	PUNCT
ejpam-5592	245	5	℘	℘	PROPN
ejpam-5592	245	6	(	(	PUNCT
ejpam-5592	245	7	z)−	z)−	PROPN
ejpam-5592	245	8	℘	℘	PROPN
ejpam-5592	245	9	(	(	PUNCT
ejpam-5592	245	10	κ))jθu+λ−k	κ))jθu+λ−k	NOUN
ejpam-5592	245	11	=	=	PUNCT
ejpam-5592	246	1	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	246	2	−	−	PROPN
ejpam-5592	246	3	k	k	X
ejpam-5592	246	4	)	)	PUNCT
ejpam-5592	246	5	k	k	PROPN
ejpam-5592	247	1	+	+	PUNCT
ejpam-5592	247	2	1−ϖu	1−ϖu	NUM
ejpam-5592	247	3	∞∑	∞∑	NUM
ejpam-5592	247	4	j=0	j=0	PROPN
ejpam-5592	247	5	(	(	PUNCT
ejpam-5592	247	6	−(ϖu	−(ϖu	NOUN
ejpam-5592	247	7	−	−	PROPN
ejpam-5592	248	1	k	k	NOUN
ejpam-5592	248	2	)	)	PUNCT
ejpam-5592	248	3	k	k	PROPN
ejpam-5592	249	1	+	+	CCONJ
ejpam-5592	249	2	1−ϖu	1−ϖu	NUM
ejpam-5592	249	3	)	)	PUNCT
ejpam-5592	249	4	j	j	PROPN
ejpam-5592	249	5	γ(1	γ(1	PROPN
ejpam-5592	249	6	+	+	NUM
ejpam-5592	249	7	λ	λ	NOUN
ejpam-5592	249	8	)	)	PUNCT
ejpam-5592	249	9	(	(	PUNCT
ejpam-5592	249	10	℘	℘	PROPN
ejpam-5592	249	11	(	(	PUNCT
ejpam-5592	249	12	z)−	z)−	PROPN
ejpam-5592	249	13	℘	℘	PROPN
ejpam-5592	249	14	(	(	PUNCT
ejpam-5592	249	15	κ))j(ϖu−k)+λ−k	κ))j(ϖu−k)+λ−k	X
ejpam-5592	249	16	γ(j(ϖu	γ(j(ϖu	X
ejpam-5592	249	17	−	−	PROPN
ejpam-5592	249	18	k	k	NOUN
ejpam-5592	249	19	)	)	PUNCT
ejpam-5592	250	1	+	+	CCONJ
ejpam-5592	250	2	λ−	λ−	PROPN
ejpam-5592	250	3	k	k	PROPN
ejpam-5592	251	1	+	+	PROPN
ejpam-5592	251	2	1	1	NUM
ejpam-5592	251	3	)	)	PUNCT
ejpam-5592	251	4	.	.	PUNCT
ejpam-5592	252	1	h.a	h.a	PROPN
ejpam-5592	252	2	.	.	PROPN
ejpam-5592	252	3	hammad	hammad	PROPN
ejpam-5592	252	4	,	,	PUNCT
ejpam-5592	252	5	m.	m.	PROPN
ejpam-5592	252	6	de	de	X
ejpam-5592	252	7	la	la	PROPN
ejpam-5592	252	8	sen	sen	PROPN
ejpam-5592	252	9	/	/	SYM
ejpam-5592	252	10	eur	eur	PROPN
ejpam-5592	252	11	.	.	PUNCT
ejpam-5592	253	1	j.	j.	PROPN
ejpam-5592	253	2	pure	pure	PROPN
ejpam-5592	253	3	appl	appl	PROPN
ejpam-5592	253	4	.	.	PROPN
ejpam-5592	253	5	math	math	PROPN
ejpam-5592	253	6	,	,	PUNCT
ejpam-5592	253	7	17	17	NUM
ejpam-5592	253	8	(	(	PUNCT
ejpam-5592	253	9	4	4	NUM
ejpam-5592	253	10	)	)	PUNCT
ejpam-5592	253	11	(	(	PUNCT
ejpam-5592	253	12	2024	2024	NUM
ejpam-5592	253	13	)	)	PUNCT
ejpam-5592	253	14	,	,	PUNCT
ejpam-5592	253	15	3687	3687	NUM
ejpam-5592	253	16	-	-	SYM
ejpam-5592	253	17	3707	3707	NUM
ejpam-5592	253	18	3697	3697	NUM
ejpam-5592	253	19	(	(	PUNCT
ejpam-5592	253	20	iii	iii	NOUN
ejpam-5592	253	21	)	)	PUNCT
ejpam-5592	253	22	from	from	ADP
ejpam-5592	253	23	definitions	definition	NOUN
ejpam-5592	253	24	7	7	NUM
ejpam-5592	253	25	and	and	CCONJ
ejpam-5592	253	26	11	11	NUM
ejpam-5592	253	27	,	,	PUNCT
ejpam-5592	253	28	one	one	PRON
ejpam-5592	253	29	has	have	AUX
ejpam-5592	253	30	cabdϖu	cabdϖu	NOUN
ejpam-5592	253	31	,	,	PUNCT
ejpam-5592	253	32	ψ	ψ	X
ejpam-5592	253	33	κ	κ	X
ejpam-5592	253	34	(	(	PUNCT
ejpam-5592	253	35	℘	℘	PROPN
ejpam-5592	253	36	(	(	PUNCT
ejpam-5592	253	37	z)−	z)−	PROPN
ejpam-5592	253	38	℘	℘	PROPN
ejpam-5592	253	39	(	(	PUNCT
ejpam-5592	253	40	κ))σ	κ))σ	NOUN
ejpam-5592	253	41	=	=	SYM
ejpam-5592	253	42	cabdθu	cabdθu	NOUN
ejpam-5592	253	43	,	,	PUNCT
ejpam-5592	253	44	ψ	ψ	X
ejpam-5592	253	45	κ	κ	X
ejpam-5592	253	46	(	(	PUNCT
ejpam-5592	253	47	1	1	NUM
ejpam-5592	253	48	ψ′(z	ψ′(z	NOUN
ejpam-5592	253	49	)	)	PUNCT
ejpam-5592	253	50	d	d	X
ejpam-5592	253	51	dz	dz	PROPN
ejpam-5592	253	52	)	)	PUNCT
ejpam-5592	253	53	k	k	PROPN
ejpam-5592	253	54	(	(	PUNCT
ejpam-5592	253	55	℘	℘	PROPN
ejpam-5592	253	56	(	(	PUNCT
ejpam-5592	253	57	z)−	z)−	PROPN
ejpam-5592	253	58	℘	℘	PROPN
ejpam-5592	253	59	(	(	PUNCT
ejpam-5592	253	60	κ))σ	κ))σ	NOUN
ejpam-5592	253	61	=	=	SYM
ejpam-5592	253	62	cabdθu	cabdθu	NOUN
ejpam-5592	253	63	,	,	PUNCT
ejpam-5592	253	64	ψ	ψ	NOUN
ejpam-5592	253	65	κ	κ	X
ejpam-5592	253	66	γ(1	γ(1	PROPN
ejpam-5592	253	67	+	+	CCONJ
ejpam-5592	253	68	σ	σ	PROPN
ejpam-5592	253	69	)	)	PUNCT
ejpam-5592	253	70	γ(λ−	γ(λ−	PROPN
ejpam-5592	253	71	σ	σ	NOUN
ejpam-5592	253	72	+	+	PROPN
ejpam-5592	253	73	1	1	NUM
ejpam-5592	253	74	)	)	PUNCT
ejpam-5592	253	75	(	(	PUNCT
ejpam-5592	253	76	℘	℘	PROPN
ejpam-5592	253	77	(	(	PUNCT
ejpam-5592	253	78	z)−	z)−	NOUN
ejpam-5592	253	79	℘	℘	PROPN
ejpam-5592	253	80	(	(	PUNCT
ejpam-5592	253	81	κ))σ−k	κ))σ−k	NOUN
ejpam-5592	253	82	=	=	SYM
ejpam-5592	253	83	λ(θu	λ(θu	NOUN
ejpam-5592	253	84	)	)	PUNCT
ejpam-5592	253	85	1−	1−	NUM
ejpam-5592	253	86	θu	θu	ADP
ejpam-5592	253	87	z∫	z∫	NOUN
ejpam-5592	253	88	κ	κ	NOUN
ejpam-5592	253	89	lθu	lθu	NOUN
ejpam-5592	253	90	(	(	PUNCT
ejpam-5592	253	91	−θu	−θu	NOUN
ejpam-5592	253	92	1−	1−	NUM
ejpam-5592	253	93	θu	θu	NOUN
ejpam-5592	253	94	(	(	PUNCT
ejpam-5592	253	95	℘	℘	PROPN
ejpam-5592	253	96	(	(	PUNCT
ejpam-5592	253	97	z)−	z)−	NOUN
ejpam-5592	253	98	℘	℘	PROPN
ejpam-5592	253	99	(	(	PUNCT
ejpam-5592	253	100	r))θu	r))θu	PROPN
ejpam-5592	253	101	)	)	PUNCT
ejpam-5592	254	1	γ(1	γ(1	PROPN
ejpam-5592	254	2	+	+	NUM
ejpam-5592	254	3	σ	σ	PROPN
ejpam-5592	254	4	)	)	PUNCT
ejpam-5592	254	5	γ(λ−	γ(λ−	PROPN
ejpam-5592	254	6	σ	σ	NOUN
ejpam-5592	254	7	+	+	PROPN
ejpam-5592	254	8	1	1	NUM
ejpam-5592	254	9	)	)	PUNCT
ejpam-5592	254	10	(	(	PUNCT
ejpam-5592	254	11	℘	℘	PROPN
ejpam-5592	254	12	(	(	PUNCT
ejpam-5592	254	13	r)−	r)−	PROPN
ejpam-5592	254	14	℘	℘	PROPN
ejpam-5592	254	15	(	(	PUNCT
ejpam-5592	254	16	κ))σ−k	κ))σ−k	NOUN
ejpam-5592	254	17	dr	dr	PROPN
ejpam-5592	254	18	=	=	NOUN
ejpam-5592	254	19	0	0	PROPN
ejpam-5592	254	20	.	.	PUNCT
ejpam-5592	255	1	taking	take	VERB
ejpam-5592	255	2	ζ	ζ	NOUN
ejpam-5592	255	3	=	=	SYM
ejpam-5592	255	4	σ	σ	NOUN
ejpam-5592	255	5	=	=	NOUN
ejpam-5592	255	6	0	0	NUM
ejpam-5592	255	7	in	in	ADP
ejpam-5592	255	8	portions	portion	NOUN
ejpam-5592	255	9	(	(	PUNCT
ejpam-5592	255	10	i	i	NOUN
ejpam-5592	255	11	)	)	PUNCT
ejpam-5592	255	12	and	and	CCONJ
ejpam-5592	255	13	(	(	PUNCT
ejpam-5592	255	14	iii	iii	NOUN
ejpam-5592	255	15	)	)	PUNCT
ejpam-5592	255	16	,	,	PUNCT
ejpam-5592	255	17	we	we	PRON
ejpam-5592	255	18	conclude	conclude	VERB
ejpam-5592	255	19	(	(	PUNCT
ejpam-5592	255	20	iv	iv	X
ejpam-5592	255	21	)	)	PUNCT
ejpam-5592	255	22	and	and	CCONJ
ejpam-5592	255	23	(	(	PUNCT
ejpam-5592	255	24	v	v	NOUN
ejpam-5592	255	25	)	)	PUNCT
ejpam-5592	255	26	,	,	PUNCT
ejpam-5592	255	27	respectively	respectively	ADV
ejpam-5592	255	28	.	.	PUNCT
ejpam-5592	256	1	4	4	X
ejpam-5592	256	2	.	.	X
ejpam-5592	256	3	generalizing	generalize	VERB
ejpam-5592	256	4	gronwall	gronwall	ADJ
ejpam-5592	256	5	’s	’s	PART
ejpam-5592	256	6	inequality	inequality	NOUN
ejpam-5592	256	7	this	this	DET
ejpam-5592	256	8	part	part	NOUN
ejpam-5592	256	9	will	will	AUX
ejpam-5592	256	10	begin	begin	VERB
ejpam-5592	256	11	with	with	ADP
ejpam-5592	256	12	the	the	DET
ejpam-5592	256	13	following	follow	VERB
ejpam-5592	256	14	generalization	generalization	NOUN
ejpam-5592	256	15	of	of	ADP
ejpam-5592	256	16	gronwall	gronwall	PROPN
ejpam-5592	256	17	’s	’s	PART
ejpam-5592	256	18	inequality	inequality	NOUN
ejpam-5592	256	19	.	.	PUNCT
ejpam-5592	257	1	lemma	lemma	PROPN
ejpam-5592	257	2	6	6	NUM
ejpam-5592	257	3	.	.	PUNCT
ejpam-5592	258	1	[	[	X
ejpam-5592	258	2	27	27	NUM
ejpam-5592	258	3	]	]	PUNCT
ejpam-5592	258	4	assume	assume	VERB
ejpam-5592	258	5	that	that	SCONJ
ejpam-5592	258	6	the	the	DET
ejpam-5592	258	7	function	function	NOUN
ejpam-5592	258	8	ψ	ψ	X
ejpam-5592	258	9	∈	∈	PROPN
ejpam-5592	258	10	c1(ℑu	c1(ℑu	PROPN
ejpam-5592	258	11	,	,	PUNCT
ejpam-5592	258	12	r+	r+	X
ejpam-5592	258	13	)	)	PUNCT
ejpam-5592	258	14	is	be	AUX
ejpam-5592	258	15	increasing	increase	VERB
ejpam-5592	258	16	with	with	ADP
ejpam-5592	258	17	ψ′(z	ψ′(z	NOUN
ejpam-5592	258	18	)	)	PUNCT
ejpam-5592	258	19	̸=	̸=	PROPN
ejpam-5592	258	20	0	0	NUM
ejpam-5592	258	21	,	,	PUNCT
ejpam-5592	258	22	for	for	ADP
ejpam-5592	258	23	each	each	DET
ejpam-5592	258	24	z	z	NOUN
ejpam-5592	258	25	∈	∈	PROPN
ejpam-5592	258	26	ℑ	ℑ	PROPN
ejpam-5592	258	27	and	and	CCONJ
ejpam-5592	258	28	ϖ	ϖ	X
ejpam-5592	258	29	>	>	X
ejpam-5592	258	30	0	0	X
ejpam-5592	258	31	.	.	PUNCT
ejpam-5592	259	1	let	let	VERB
ejpam-5592	259	2	ℓ(z	ℓ(z	PROPN
ejpam-5592	259	3	)	)	PUNCT
ejpam-5592	260	1	be	be	AUX
ejpam-5592	260	2	a	a	DET
ejpam-5592	260	3	nonnegative	nonnegative	ADJ
ejpam-5592	260	4	and	and	CCONJ
ejpam-5592	260	5	nondecreasing	nondecreasing	ADJ
ejpam-5592	260	6	function	function	NOUN
ejpam-5592	260	7	(	(	PUNCT
ejpam-5592	260	8	nnf	nnf	NOUN
ejpam-5592	260	9	,	,	PUNCT
ejpam-5592	260	10	for	for	ADP
ejpam-5592	260	11	abbreviate	abbreviate	NOUN
ejpam-5592	260	12	)	)	PUNCT
ejpam-5592	260	13	,	,	PUNCT
ejpam-5592	260	14	ℏ(z	ℏ(z	NOUN
ejpam-5592	260	15	)	)	PUNCT
ejpam-5592	260	16	be	be	VERB
ejpam-5592	260	17	a	a	DET
ejpam-5592	260	18	nonnegative	nonnegative	ADJ
ejpam-5592	260	19	function	function	NOUN
ejpam-5592	260	20	locally	locally	ADV
ejpam-5592	260	21	integrable	integrable	ADJ
ejpam-5592	260	22	(	(	PUNCT
ejpam-5592	260	23	nfli	nfli	NOUN
ejpam-5592	260	24	,	,	PUNCT
ejpam-5592	260	25	for	for	ADP
ejpam-5592	260	26	short	short	ADJ
ejpam-5592	260	27	)	)	PUNCT
ejpam-5592	260	28	on	on	ADP
ejpam-5592	260	29	ℑ	ℑ	PROPN
ejpam-5592	260	30	and	and	CCONJ
ejpam-5592	260	31	ϱ	ϱ	NOUN
ejpam-5592	260	32	be	be	AUX
ejpam-5592	260	33	a	a	DET
ejpam-5592	260	34	nfli	nfli	NOUN
ejpam-5592	260	35	on	on	ADP
ejpam-5592	260	36	ℑ.	ℑ.	PROPN
ejpam-5592	260	37	if	if	SCONJ
ejpam-5592	260	38	the	the	DET
ejpam-5592	260	39	inequality	inequality	NOUN
ejpam-5592	260	40	ϱ	ϱ	ADP
ejpam-5592	260	41	(	(	PUNCT
ejpam-5592	260	42	z	z	NOUN
ejpam-5592	260	43	)	)	PUNCT
ejpam-5592	260	44	≤	≤	NOUN
ejpam-5592	260	45	ℏ(z	ℏ(z	NOUN
ejpam-5592	260	46	)	)	PUNCT
ejpam-5592	260	47	+	+	NUM
ejpam-5592	260	48	ℓ(z	ℓ(z	NOUN
ejpam-5592	260	49	)	)	PUNCT
ejpam-5592	260	50	z∫	z∫	PROPN
ejpam-5592	260	51	κ	κ	PRON
ejpam-5592	260	52	lθuψ	lθuψ	NOUN
ejpam-5592	260	53	′(r	′(r	ADV
ejpam-5592	260	54	)	)	PUNCT
ejpam-5592	260	55	(	(	PUNCT
ejpam-5592	260	56	ψ	ψ	X
ejpam-5592	260	57	(	(	PUNCT
ejpam-5592	260	58	z)−	z)−	PROPN
ejpam-5592	260	59	ψ	ψ	X
ejpam-5592	260	60	(	(	PUNCT
ejpam-5592	260	61	r))ϖ−1	r))ϖ−1	PROPN
ejpam-5592	260	62	ϱ	ϱ	PROPN
ejpam-5592	260	63	(	(	PUNCT
ejpam-5592	260	64	r	r	NOUN
ejpam-5592	260	65	)	)	PUNCT
ejpam-5592	260	66	dr	dr	PROPN
ejpam-5592	260	67	,	,	PUNCT
ejpam-5592	260	68	z	z	PROPN
ejpam-5592	260	69	∈	∈	PROPN
ejpam-5592	260	70	ℑ	ℑ	PROPN
ejpam-5592	260	71	holds	hold	VERB
ejpam-5592	260	72	,	,	PUNCT
ejpam-5592	260	73	then	then	ADV
ejpam-5592	260	74	ϱ	ϱ	PROPN
ejpam-5592	260	75	(	(	PUNCT
ejpam-5592	260	76	z	z	NOUN
ejpam-5592	260	77	)	)	PUNCT
ejpam-5592	260	78	≤	≤	NOUN
ejpam-5592	260	79	ℏ(z	ℏ(z	NOUN
ejpam-5592	260	80	)	)	PUNCT
ejpam-5592	261	1	+	+	SYM
ejpam-5592	261	2	z∫	z∫	NOUN
ejpam-5592	261	3	κ	κ	ADP
ejpam-5592	261	4	∞∑	∞∑	NUM
ejpam-5592	261	5	j=1	j=1	NOUN
ejpam-5592	262	1	[	[	X
ejpam-5592	262	2	ℓ(z)γ(ϖ)]j	ℓ(z)γ(ϖ)]j	PROPN
ejpam-5592	262	3	γ(jϖ	γ(jϖ	PROPN
ejpam-5592	262	4	)	)	PUNCT
ejpam-5592	262	5	ψ′(r	ψ′(r	PROPN
ejpam-5592	262	6	)	)	PUNCT
ejpam-5592	262	7	(	(	PUNCT
ejpam-5592	262	8	ψ	ψ	X
ejpam-5592	262	9	(	(	PUNCT
ejpam-5592	262	10	z)−	z)−	PROPN
ejpam-5592	262	11	ψ	ψ	NOUN
ejpam-5592	262	12	(	(	PUNCT
ejpam-5592	262	13	r))jϖ−1	r))jϖ−1	NOUN
ejpam-5592	262	14	ℏ	ℏ	PROPN
ejpam-5592	262	15	(	(	PUNCT
ejpam-5592	262	16	r	r	NOUN
ejpam-5592	262	17	)	)	PUNCT
ejpam-5592	262	18	dr	dr	NOUN
ejpam-5592	262	19	,	,	PUNCT
ejpam-5592	262	20	for	for	ADP
ejpam-5592	262	21	every	every	DET
ejpam-5592	262	22	z	z	PROPN
ejpam-5592	262	23	∈	∈	PROPN
ejpam-5592	262	24	ℑ.	ℑ.	PROPN
ejpam-5592	262	25	lemma	lemma	PROPN
ejpam-5592	262	26	7	7	NUM
ejpam-5592	262	27	.	.	PUNCT
ejpam-5592	263	1	[	[	X
ejpam-5592	263	2	27	27	NUM
ejpam-5592	263	3	]	]	PUNCT
ejpam-5592	263	4	assume	assume	VERB
ejpam-5592	263	5	that	that	SCONJ
ejpam-5592	263	6	all	all	DET
ejpam-5592	263	7	requirements	requirement	NOUN
ejpam-5592	263	8	of	of	ADP
ejpam-5592	263	9	lemma	lemma	PROPN
ejpam-5592	263	10	6	6	NUM
ejpam-5592	263	11	are	be	AUX
ejpam-5592	263	12	true	true	ADJ
ejpam-5592	263	13	,	,	PUNCT
ejpam-5592	263	14	if	if	SCONJ
ejpam-5592	263	15	the	the	DET
ejpam-5592	263	16	function	function	NOUN
ejpam-5592	263	17	ℏ(z	ℏ(z	NOUN
ejpam-5592	263	18	)	)	PUNCT
ejpam-5592	263	19	is	be	AUX
ejpam-5592	263	20	nondecreasing	nondecrease	VERB
ejpam-5592	263	21	on	on	ADP
ejpam-5592	263	22	ℑ	ℑ	PROPN
ejpam-5592	263	23	,	,	PUNCT
ejpam-5592	263	24	one	one	PRON
ejpam-5592	263	25	has	have	VERB
ejpam-5592	263	26	ϱ	ϱ	X
ejpam-5592	263	27	(	(	PUNCT
ejpam-5592	263	28	z	z	NOUN
ejpam-5592	263	29	)	)	PUNCT
ejpam-5592	263	30	≤	≤	NOUN
ejpam-5592	263	31	ℏ(z)lϖ	ℏ(z)lϖ	ADP
ejpam-5592	263	32	[	[	X
ejpam-5592	263	33	ℓ(z)γ(ϖ	ℓ(z)γ(ϖ	X
ejpam-5592	263	34	)	)	PUNCT
ejpam-5592	263	35	(	(	PUNCT
ejpam-5592	263	36	ψ	ψ	X
ejpam-5592	263	37	(	(	PUNCT
ejpam-5592	263	38	z)−	z)−	PROPN
ejpam-5592	263	39	ψ	ψ	PROPN
ejpam-5592	263	40	(	(	PUNCT
ejpam-5592	263	41	κ))ϖ	κ))ϖ	NOUN
ejpam-5592	263	42	]	]	PUNCT
ejpam-5592	263	43	,	,	PUNCT
ejpam-5592	263	44	z	z	NOUN
ejpam-5592	263	45	∈	∈	PROPN
ejpam-5592	263	46	ℑ.	ℑ.	NOUN
ejpam-5592	263	47	in	in	ADP
ejpam-5592	263	48	this	this	DET
ejpam-5592	263	49	role	role	NOUN
ejpam-5592	263	50	,	,	PUNCT
ejpam-5592	263	51	we	we	PRON
ejpam-5592	263	52	will	will	AUX
ejpam-5592	263	53	present	present	VERB
ejpam-5592	263	54	a	a	DET
ejpam-5592	263	55	novel	novel	ADJ
ejpam-5592	263	56	gronwall	gronwall	ADJ
ejpam-5592	263	57	inequality	inequality	NOUN
ejpam-5592	263	58	within	within	ADP
ejpam-5592	263	59	the	the	DET
ejpam-5592	263	60	context	context	NOUN
ejpam-5592	263	61	of	of	ADP
ejpam-5592	263	62	the	the	DET
ejpam-5592	263	63	ψ	ψ	X
ejpam-5592	263	64	−rl−ab	−rl−ab	NUM
ejpam-5592	263	65	fractional	fractional	ADJ
ejpam-5592	263	66	operator	operator	NOUN
ejpam-5592	263	67	.	.	PUNCT
ejpam-5592	264	1	h.a	h.a	PROPN
ejpam-5592	264	2	.	.	PROPN
ejpam-5592	264	3	hammad	hammad	PROPN
ejpam-5592	264	4	,	,	PUNCT
ejpam-5592	264	5	m.	m.	PROPN
ejpam-5592	264	6	de	de	X
ejpam-5592	264	7	la	la	PROPN
ejpam-5592	264	8	sen	sen	PROPN
ejpam-5592	264	9	/	/	SYM
ejpam-5592	264	10	eur	eur	PROPN
ejpam-5592	264	11	.	.	PUNCT
ejpam-5592	265	1	j.	j.	PROPN
ejpam-5592	265	2	pure	pure	PROPN
ejpam-5592	265	3	appl	appl	PROPN
ejpam-5592	265	4	.	.	PROPN
ejpam-5592	265	5	math	math	PROPN
ejpam-5592	265	6	,	,	PUNCT
ejpam-5592	265	7	17	17	NUM
ejpam-5592	265	8	(	(	PUNCT
ejpam-5592	265	9	4	4	NUM
ejpam-5592	265	10	)	)	PUNCT
ejpam-5592	265	11	(	(	PUNCT
ejpam-5592	265	12	2024	2024	NUM
ejpam-5592	265	13	)	)	PUNCT
ejpam-5592	265	14	,	,	PUNCT
ejpam-5592	265	15	3687	3687	NUM
ejpam-5592	265	16	-	-	SYM
ejpam-5592	265	17	3707	3707	NUM
ejpam-5592	265	18	3698	3698	NUM
ejpam-5592	265	19	lemma	lemma	PROPN
ejpam-5592	265	20	8	8	NUM
ejpam-5592	265	21	.	.	PUNCT
ejpam-5592	265	22	suppose	suppose	VERB
ejpam-5592	265	23	that	that	SCONJ
ejpam-5592	265	24	the	the	DET
ejpam-5592	265	25	function	function	NOUN
ejpam-5592	265	26	ψ	ψ	X
ejpam-5592	265	27	∈	∈	PROPN
ejpam-5592	265	28	c1(ℑu	c1(ℑu	PROPN
ejpam-5592	265	29	,	,	PUNCT
ejpam-5592	265	30	r+	r+	X
ejpam-5592	265	31	)	)	PUNCT
ejpam-5592	265	32	is	be	AUX
ejpam-5592	265	33	increasing	increase	VERB
ejpam-5592	265	34	with	with	ADP
ejpam-5592	265	35	ψ′(z	ψ′(z	NOUN
ejpam-5592	265	36	)	)	PUNCT
ejpam-5592	265	37	̸=	̸=	PROPN
ejpam-5592	265	38	0	0	NUM
ejpam-5592	265	39	,	,	PUNCT
ejpam-5592	265	40	for	for	ADP
ejpam-5592	265	41	each	each	DET
ejpam-5592	265	42	z	z	NOUN
ejpam-5592	265	43	∈	∈	PROPN
ejpam-5592	265	44	ℑ	ℑ	PROPN
ejpam-5592	265	45	and	and	CCONJ
ejpam-5592	265	46	ϖu	ϖu	NOUN
ejpam-5592	265	47	=	=	PUNCT
ejpam-5592	265	48	ϖ	ϖ	X
ejpam-5592	265	49	∈	∈	PROPN
ejpam-5592	265	50	(	(	PUNCT
ejpam-5592	265	51	0	0	NUM
ejpam-5592	265	52	,	,	PUNCT
ejpam-5592	265	53	1	1	NUM
ejpam-5592	265	54	]	]	PUNCT
ejpam-5592	265	55	,	,	PUNCT
ejpam-5592	265	56	for	for	ADP
ejpam-5592	265	57	u	u	PRON
ejpam-5592	265	58	≥	≥	NUM
ejpam-5592	265	59	1	1	NUM
ejpam-5592	265	60	.	.	PUNCT
ejpam-5592	265	61	assume	assume	VERB
ejpam-5592	265	62	that	that	SCONJ
ejpam-5592	265	63	θ(z	θ(z	NOUN
ejpam-5592	265	64	)	)	PUNCT
ejpam-5592	265	65	=	=	SYM
ejpam-5592	265	66	u(z)λ(ϖ	u(z)λ(ϖ	NOUN
ejpam-5592	265	67	)	)	PUNCT
ejpam-5592	265	68	λ(ϖ)−(1−ϖ)g(z	λ(ϖ)−(1−ϖ)g(z	PROPN
ejpam-5592	265	69	)	)	PUNCT
ejpam-5592	265	70	is	be	AUX
ejpam-5592	265	71	a	a	DET
ejpam-5592	265	72	nfli	nfli	NOUN
ejpam-5592	265	73	on	on	ADP
ejpam-5592	265	74	ℑ	ℑ	PROPN
ejpam-5592	265	75	,	,	PUNCT
ejpam-5592	265	76	ξ(z	ξ(z	PROPN
ejpam-5592	265	77	)	)	PUNCT
ejpam-5592	265	78	=	=	SYM
ejpam-5592	265	79	ϖg(z	ϖg(z	NOUN
ejpam-5592	265	80	)	)	PUNCT
ejpam-5592	265	81	λ(ϖ)−(1−ϖ)g(z	λ(ϖ)−(1−ϖ)g(z	PROPN
ejpam-5592	265	82	)	)	PUNCT
ejpam-5592	265	83	is	be	AUX
ejpam-5592	265	84	a	a	DET
ejpam-5592	265	85	nnf	nnf	NOUN
ejpam-5592	265	86	and	and	CCONJ
ejpam-5592	265	87	ϱ	ϱ	NOUN
ejpam-5592	265	88	is	be	AUX
ejpam-5592	265	89	a	a	DET
ejpam-5592	265	90	nfli	nfli	NOUN
ejpam-5592	265	91	on	on	ADP
ejpam-5592	265	92	ℑ	ℑ	PROPN
ejpam-5592	265	93	,	,	PUNCT
ejpam-5592	265	94	such	such	ADJ
ejpam-5592	265	95	that	that	SCONJ
ejpam-5592	265	96	ϱ	ϱ	PROPN
ejpam-5592	265	97	(	(	PUNCT
ejpam-5592	265	98	z	z	NOUN
ejpam-5592	265	99	)	)	PUNCT
ejpam-5592	265	100	≤	≤	NOUN
ejpam-5592	265	101	u(z	u(z	NOUN
ejpam-5592	265	102	)	)	PUNCT
ejpam-5592	266	1	+	+	VERB
ejpam-5592	266	2	g(z)rlabℜϖ,ψκ	g(z)rlabℜϖ,ψκ	ADJ
ejpam-5592	266	3	ϱ	ϱ	ADP
ejpam-5592	266	4	(	(	PUNCT
ejpam-5592	266	5	z	z	NOUN
ejpam-5592	266	6	)	)	PUNCT
ejpam-5592	266	7	,	,	PUNCT
ejpam-5592	266	8	z	z	NOUN
ejpam-5592	266	9	∈	∈	PROPN
ejpam-5592	266	10	ℑ.	ℑ.	NOUN
ejpam-5592	266	11	(	(	PUNCT
ejpam-5592	266	12	1	1	NUM
ejpam-5592	266	13	)	)	PUNCT
ejpam-5592	266	14	then	then	ADV
ejpam-5592	266	15	,	,	PUNCT
ejpam-5592	266	16	for	for	ADP
ejpam-5592	266	17	each	each	DET
ejpam-5592	266	18	z	z	PROPN
ejpam-5592	266	19	∈	∈	PROPN
ejpam-5592	266	20	ℑ	ℑ	PROPN
ejpam-5592	266	21	,	,	PUNCT
ejpam-5592	266	22	we	we	PRON
ejpam-5592	266	23	have	have	VERB
ejpam-5592	266	24	ϱ	ϱ	X
ejpam-5592	266	25	(	(	PUNCT
ejpam-5592	266	26	z	z	NOUN
ejpam-5592	266	27	)	)	PUNCT
ejpam-5592	266	28	≤	≤	NUM
ejpam-5592	266	29	θ(z	θ(z	NOUN
ejpam-5592	266	30	)	)	PUNCT
ejpam-5592	267	1	+	+	SYM
ejpam-5592	267	2	z∫	z∫	NOUN
ejpam-5592	267	3	κ	κ	ADP
ejpam-5592	267	4	∞∑	∞∑	NUM
ejpam-5592	267	5	j=1	j=1	NOUN
ejpam-5592	268	1	[	[	X
ejpam-5592	268	2	ξ(z))]j	ξ(z))]j	PROPN
ejpam-5592	268	3	γ(jϖ	γ(jϖ	PROPN
ejpam-5592	268	4	)	)	PUNCT
ejpam-5592	268	5	ψ′(r	ψ′(r	PROPN
ejpam-5592	268	6	)	)	PUNCT
ejpam-5592	268	7	(	(	PUNCT
ejpam-5592	268	8	ψ	ψ	X
ejpam-5592	268	9	(	(	PUNCT
ejpam-5592	268	10	z)−	z)−	PROPN
ejpam-5592	268	11	ψ	ψ	PROPN
ejpam-5592	268	12	(	(	PUNCT
ejpam-5592	268	13	r))jϖ−1θ(r	r))jϖ−1θ(r	NOUN
ejpam-5592	268	14	)	)	PUNCT
ejpam-5592	268	15	dr	dr	PROPN
ejpam-5592	268	16	.	.	PROPN
ejpam-5592	268	17	proof	proof	NOUN
ejpam-5592	268	18	.	.	PUNCT
ejpam-5592	269	1	utilizing	utilize	VERB
ejpam-5592	269	2	(	(	PUNCT
ejpam-5592	269	3	1	1	NUM
ejpam-5592	269	4	)	)	PUNCT
ejpam-5592	269	5	,	,	PUNCT
ejpam-5592	269	6	definitions	definition	NOUN
ejpam-5592	269	7	1	1	NUM
ejpam-5592	269	8	and	and	CCONJ
ejpam-5592	269	9	8	8	NUM
ejpam-5592	269	10	,	,	PUNCT
ejpam-5592	269	11	one	one	PRON
ejpam-5592	269	12	has	have	VERB
ejpam-5592	269	13	ϱ	ϱ	X
ejpam-5592	269	14	(	(	PUNCT
ejpam-5592	269	15	z	z	NOUN
ejpam-5592	269	16	)	)	PUNCT
ejpam-5592	269	17	≤	≤	NUM
ejpam-5592	269	18	u(z	u(z	NOUN
ejpam-5592	269	19	)	)	PUNCT
ejpam-5592	270	1	+	+	NOUN
ejpam-5592	270	2	g(z	g(z	ADJ
ejpam-5592	270	3	)	)	PUNCT
ejpam-5592	270	4	(	(	PUNCT
ejpam-5592	270	5	rlabℜϖ,ψκ	rlabℜϖ,ψκ	PROPN
ejpam-5592	270	6	ϱ	ϱ	PROPN
ejpam-5592	270	7	)	)	PUNCT
ejpam-5592	270	8	(	(	PUNCT
ejpam-5592	270	9	z	z	NOUN
ejpam-5592	270	10	)	)	PUNCT
ejpam-5592	270	11	≤	≤	NUM
ejpam-5592	270	12	u(z	u(z	NOUN
ejpam-5592	270	13	)	)	PUNCT
ejpam-5592	271	1	+	+	ADJ
ejpam-5592	271	2	g(z	g(z	ADJ
ejpam-5592	271	3	)	)	PUNCT
ejpam-5592	271	4	1−ϖ	1−ϖ	NOUN
ejpam-5592	271	5	λ(ϖ	λ(ϖ	NOUN
ejpam-5592	271	6	)	)	PUNCT
ejpam-5592	271	7	ϱ(z	ϱ(z	NOUN
ejpam-5592	271	8	)	)	PUNCT
ejpam-5592	272	1	+	+	CCONJ
ejpam-5592	272	2	ϖ	ϖ	X
ejpam-5592	272	3	λ(ϖ	λ(ϖ	NOUN
ejpam-5592	272	4	)	)	PUNCT
ejpam-5592	272	5	1	1	NUM
ejpam-5592	272	6	γ	γ	X
ejpam-5592	272	7	(	(	PUNCT
ejpam-5592	272	8	ϖ	ϖ	NOUN
ejpam-5592	272	9	)	)	PUNCT
ejpam-5592	272	10	z∫	z∫	NOUN
ejpam-5592	272	11	κ	κ	NOUN
ejpam-5592	272	12	(	(	PUNCT
ejpam-5592	272	13	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	272	14	ψ(r))ω−1	ψ(r))ω−1	NUM
ejpam-5592	272	15	ψ′(r)ϱ	ψ′(r)ϱ	PROPN
ejpam-5592	272	16	(	(	PUNCT
ejpam-5592	272	17	r	r	NOUN
ejpam-5592	272	18	)	)	PUNCT
ejpam-5592	272	19	dr	dr	NOUN
ejpam-5592	272	20			NOUN
ejpam-5592	272	21	.	.	PUNCT
ejpam-5592	273	1	therefore	therefore	ADV
ejpam-5592	273	2	,	,	PUNCT
ejpam-5592	273	3	ϱ	ϱ	PROPN
ejpam-5592	273	4	(	(	PUNCT
ejpam-5592	273	5	z	z	NOUN
ejpam-5592	273	6	)	)	PUNCT
ejpam-5592	273	7	≤	≤	NOUN
ejpam-5592	273	8	u(z)λ(ϖ	u(z)λ(ϖ	NOUN
ejpam-5592	273	9	)	)	PUNCT
ejpam-5592	273	10	λ(ϖ)−	λ(ϖ)−	PROPN
ejpam-5592	273	11	(	(	PUNCT
ejpam-5592	273	12	1−ϖ)g(z	1−ϖ)g(z	NUM
ejpam-5592	273	13	)	)	PUNCT
ejpam-5592	273	14	+	+	CCONJ
ejpam-5592	273	15	ϖg(z	ϖg(z	X
ejpam-5592	273	16	)	)	PUNCT
ejpam-5592	273	17	λ(ϖ)−	λ(ϖ)−	PROPN
ejpam-5592	273	18	(	(	PUNCT
ejpam-5592	273	19	1−ϖ)g(z	1−ϖ)g(z	NUM
ejpam-5592	273	20	)	)	PUNCT
ejpam-5592	273	21	1	1	NUM
ejpam-5592	273	22	γ	γ	X
ejpam-5592	273	23	(	(	PUNCT
ejpam-5592	273	24	ϖ	ϖ	NOUN
ejpam-5592	273	25	)	)	PUNCT
ejpam-5592	273	26	z∫	z∫	NOUN
ejpam-5592	273	27	κ	κ	NOUN
ejpam-5592	273	28	(	(	PUNCT
ejpam-5592	273	29	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	273	30	ψ(r))ϖ−1	ψ(r))ϖ−1	NUM
ejpam-5592	273	31	ψ′(r)ϱ	ψ′(r)ϱ	PROPN
ejpam-5592	273	32	(	(	PUNCT
ejpam-5592	273	33	r	r	NOUN
ejpam-5592	273	34	)	)	PUNCT
ejpam-5592	273	35	dr	dr	PROPN
ejpam-5592	273	36	lemma	lemma	PROPN
ejpam-5592	273	37	6	6	NUM
ejpam-5592	273	38	allows	allow	VERB
ejpam-5592	273	39	us	we	PRON
ejpam-5592	273	40	to	to	PART
ejpam-5592	273	41	obtain	obtain	VERB
ejpam-5592	273	42	ϱ	ϱ	ADP
ejpam-5592	273	43	(	(	PUNCT
ejpam-5592	273	44	z	z	NOUN
ejpam-5592	273	45	)	)	PUNCT
ejpam-5592	273	46	≤	≤	NOUN
ejpam-5592	273	47	u(z)λ(ϖ	u(z)λ(ϖ	NOUN
ejpam-5592	273	48	)	)	PUNCT
ejpam-5592	273	49	λ(ϖ)−	λ(ϖ)−	PROPN
ejpam-5592	273	50	(	(	PUNCT
ejpam-5592	273	51	1−ϖ)g(z	1−ϖ)g(z	NUM
ejpam-5592	273	52	)	)	PUNCT
ejpam-5592	273	53	+	+	NOUN
ejpam-5592	273	54	z∫	z∫	NOUN
ejpam-5592	273	55	κ	κ	ADP
ejpam-5592	273	56	∞∑	∞∑	NUM
ejpam-5592	273	57	j=1	j=1	ADJ
ejpam-5592	273	58	1	1	NUM
ejpam-5592	273	59	γ(jϖ	γ(jϖ	PROPN
ejpam-5592	273	60	)	)	PUNCT
ejpam-5592	273	61	(	(	PUNCT
ejpam-5592	273	62	ϖg(z	ϖg(z	PROPN
ejpam-5592	273	63	)	)	PUNCT
ejpam-5592	273	64	λ(ϖ)−	λ(ϖ)−	PROPN
ejpam-5592	273	65	(	(	PUNCT
ejpam-5592	273	66	1−ϖ)g(z	1−ϖ)g(z	NUM
ejpam-5592	273	67	)	)	PUNCT
ejpam-5592	273	68	)	)	PUNCT
ejpam-5592	274	1	j	j	PROPN
ejpam-5592	274	2	u(r)λ(ϖ	u(r)λ(ϖ	NOUN
ejpam-5592	274	3	)	)	PUNCT
ejpam-5592	274	4	(	(	PUNCT
ejpam-5592	274	5	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	274	6	ψ(r))jϖ−1	ψ(r))jϖ−1	PROPN
ejpam-5592	274	7	ψ′(r	ψ′(r	PROPN
ejpam-5592	274	8	)	)	PUNCT
ejpam-5592	274	9	λ(ϖ)−	λ(ϖ)−	PROPN
ejpam-5592	274	10	(	(	PUNCT
ejpam-5592	274	11	1−ϖ)g(z	1−ϖ)g(z	X
ejpam-5592	274	12	)	)	PUNCT
ejpam-5592	274	13	dr	dr	PROPN
ejpam-5592	274	14	≤	≤	PROPN
ejpam-5592	274	15	θ(z	θ(z	NOUN
ejpam-5592	274	16	)	)	PUNCT
ejpam-5592	274	17	+	+	SYM
ejpam-5592	274	18	z∫	z∫	NOUN
ejpam-5592	274	19	κ	κ	ADP
ejpam-5592	274	20	∞∑	∞∑	NUM
ejpam-5592	274	21	j=1	j=1	NOUN
ejpam-5592	275	1	[	[	X
ejpam-5592	275	2	ξ(z))]j	ξ(z))]j	PROPN
ejpam-5592	275	3	γ(jϖ	γ(jϖ	PROPN
ejpam-5592	275	4	)	)	PUNCT
ejpam-5592	275	5	ψ′(r	ψ′(r	PROPN
ejpam-5592	275	6	)	)	PUNCT
ejpam-5592	275	7	(	(	PUNCT
ejpam-5592	275	8	ψ	ψ	X
ejpam-5592	275	9	(	(	PUNCT
ejpam-5592	275	10	z)−	z)−	PROPN
ejpam-5592	275	11	ψ	ψ	PROPN
ejpam-5592	275	12	(	(	PUNCT
ejpam-5592	275	13	r))jϖ−1θ(r	r))jϖ−1θ(r	NOUN
ejpam-5592	275	14	)	)	PUNCT
ejpam-5592	275	15	dr	dr	PROPN
ejpam-5592	275	16	.	.	PROPN
ejpam-5592	275	17	corollary	corollary	PROPN
ejpam-5592	275	18	1	1	NUM
ejpam-5592	275	19	.	.	PUNCT
ejpam-5592	276	1	in	in	ADP
ejpam-5592	276	2	light	light	NOUN
ejpam-5592	276	3	of	of	ADP
ejpam-5592	276	4	assumptions	assumption	NOUN
ejpam-5592	276	5	of	of	ADP
ejpam-5592	276	6	lemma	lemma	PROPN
ejpam-5592	276	7	8	8	NUM
ejpam-5592	276	8	,	,	PUNCT
ejpam-5592	276	9	if	if	SCONJ
ejpam-5592	276	10	the	the	DET
ejpam-5592	276	11	function	function	NOUN
ejpam-5592	276	12	θ(z	θ(z	NOUN
ejpam-5592	276	13	)	)	PUNCT
ejpam-5592	276	14	is	be	AUX
ejpam-5592	276	15	nondecreasing	nondecrease	VERB
ejpam-5592	276	16	on	on	ADP
ejpam-5592	276	17	ℑ	ℑ	PROPN
ejpam-5592	276	18	,	,	PUNCT
ejpam-5592	276	19	then	then	ADV
ejpam-5592	276	20	,	,	PUNCT
ejpam-5592	276	21	we	we	PRON
ejpam-5592	276	22	get	get	VERB
ejpam-5592	276	23	ϱ	ϱ	ADP
ejpam-5592	276	24	(	(	PUNCT
ejpam-5592	276	25	z	z	NOUN
ejpam-5592	276	26	)	)	PUNCT
ejpam-5592	276	27	≤	≤	NOUN
ejpam-5592	276	28	θ(z)lϖ	θ(z)lϖ	CCONJ
ejpam-5592	276	29	[	[	X
ejpam-5592	276	30	ξ(z	ξ(z	PROPN
ejpam-5592	276	31	)	)	PUNCT
ejpam-5592	276	32	(	(	PUNCT
ejpam-5592	276	33	ψ	ψ	X
ejpam-5592	276	34	(	(	PUNCT
ejpam-5592	276	35	z)−	z)−	PROPN
ejpam-5592	276	36	ψ	ψ	PROPN
ejpam-5592	276	37	(	(	PUNCT
ejpam-5592	276	38	κ))ϖ	κ))ϖ	NOUN
ejpam-5592	276	39	]	]	PUNCT
ejpam-5592	276	40	,	,	PUNCT
ejpam-5592	276	41	z	z	NOUN
ejpam-5592	276	42	∈	∈	PROPN
ejpam-5592	276	43	ℑ.	ℑ.	PROPN
ejpam-5592	276	44	h.a	h.a	PROPN
ejpam-5592	276	45	.	.	PROPN
ejpam-5592	276	46	hammad	hammad	PROPN
ejpam-5592	276	47	,	,	PUNCT
ejpam-5592	276	48	m.	m.	PROPN
ejpam-5592	276	49	de	de	X
ejpam-5592	276	50	la	la	PROPN
ejpam-5592	276	51	sen	sen	PROPN
ejpam-5592	276	52	/	/	SYM
ejpam-5592	276	53	eur	eur	PROPN
ejpam-5592	276	54	.	.	PUNCT
ejpam-5592	277	1	j.	j.	PROPN
ejpam-5592	277	2	pure	pure	PROPN
ejpam-5592	277	3	appl	appl	PROPN
ejpam-5592	277	4	.	.	PROPN
ejpam-5592	277	5	math	math	PROPN
ejpam-5592	277	6	,	,	PUNCT
ejpam-5592	277	7	17	17	NUM
ejpam-5592	277	8	(	(	PUNCT
ejpam-5592	277	9	4	4	NUM
ejpam-5592	277	10	)	)	PUNCT
ejpam-5592	277	11	(	(	PUNCT
ejpam-5592	277	12	2024	2024	NUM
ejpam-5592	277	13	)	)	PUNCT
ejpam-5592	277	14	,	,	PUNCT
ejpam-5592	277	15	3687	3687	NUM
ejpam-5592	277	16	-	-	SYM
ejpam-5592	277	17	3707	3707	NUM
ejpam-5592	277	18	3699	3699	NUM
ejpam-5592	277	19	proof	proof	NOUN
ejpam-5592	277	20	.	.	PUNCT
ejpam-5592	278	1	based	base	VERB
ejpam-5592	278	2	on	on	ADP
ejpam-5592	278	3	lemma	lemma	PROPN
ejpam-5592	278	4	8	8	NUM
ejpam-5592	278	5	,	,	PUNCT
ejpam-5592	278	6	one	one	PRON
ejpam-5592	278	7	can	can	AUX
ejpam-5592	278	8	write	write	VERB
ejpam-5592	278	9	ϱ	ϱ	PROPN
ejpam-5592	278	10	(	(	PUNCT
ejpam-5592	278	11	z	z	NOUN
ejpam-5592	278	12	)	)	PUNCT
ejpam-5592	278	13	≤	≤	NOUN
ejpam-5592	278	14	u(z)λ(ϖ	u(z)λ(ϖ	NOUN
ejpam-5592	278	15	)	)	PUNCT
ejpam-5592	278	16	λ(ϖ)−	λ(ϖ)−	PROPN
ejpam-5592	278	17	(	(	PUNCT
ejpam-5592	278	18	1−ϖ)g(z	1−ϖ)g(z	NUM
ejpam-5592	278	19	)	)	PUNCT
ejpam-5592	278	20	lϖ	lϖ	NOUN
ejpam-5592	278	21	(	(	PUNCT
ejpam-5592	278	22	ϖg(z	ϖg(z	PROPN
ejpam-5592	278	23	)	)	PUNCT
ejpam-5592	278	24	(	(	PUNCT
ejpam-5592	278	25	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	278	26	ψ(r))ϖ	ψ(r))ϖ	PROPN
ejpam-5592	278	27	λ(ϖ)−	λ(ϖ)−	PROPN
ejpam-5592	278	28	(	(	PUNCT
ejpam-5592	278	29	1−ϖ)g(z	1−ϖ)g(z	NUM
ejpam-5592	278	30	)	)	PUNCT
ejpam-5592	278	31	)	)	PUNCT
ejpam-5592	279	1	≤	≤	PUNCT
ejpam-5592	279	2	θ(z)lϖ	θ(z)lϖ	CCONJ
ejpam-5592	279	3	[	[	X
ejpam-5592	279	4	ξ(z	ξ(z	PROPN
ejpam-5592	279	5	)	)	PUNCT
ejpam-5592	279	6	(	(	PUNCT
ejpam-5592	279	7	ψ	ψ	X
ejpam-5592	279	8	(	(	PUNCT
ejpam-5592	279	9	z)−	z)−	PROPN
ejpam-5592	279	10	ψ	ψ	PROPN
ejpam-5592	279	11	(	(	PUNCT
ejpam-5592	279	12	κ))ϖ	κ))ϖ	NOUN
ejpam-5592	279	13	]	]	PUNCT
ejpam-5592	279	14	.	.	PUNCT
ejpam-5592	280	1	a	a	DET
ejpam-5592	280	2	novel	novel	ADJ
ejpam-5592	280	3	gronwall	gronwall	ADJ
ejpam-5592	280	4	inequality	inequality	NOUN
ejpam-5592	280	5	in	in	ADP
ejpam-5592	280	6	the	the	DET
ejpam-5592	280	7	context	context	NOUN
ejpam-5592	280	8	of	of	ADP
ejpam-5592	280	9	the	the	DET
ejpam-5592	280	10	ψ−kab	ψ−kab	ADJ
ejpam-5592	280	11	fractional	fractional	ADJ
ejpam-5592	280	12	operator	operator	NOUN
ejpam-5592	280	13	will	will	AUX
ejpam-5592	280	14	be	be	AUX
ejpam-5592	280	15	concluded	conclude	VERB
ejpam-5592	280	16	here	here	ADV
ejpam-5592	280	17	.	.	PUNCT
ejpam-5592	281	1	corollary	corollary	ADJ
ejpam-5592	281	2	2	2	NUM
ejpam-5592	281	3	.	.	PUNCT
ejpam-5592	282	1	let	let	VERB
ejpam-5592	282	2	ϖu	ϖu	VERB
ejpam-5592	282	3	=	=	PUNCT
ejpam-5592	282	4	ϖ	ϖ	X
ejpam-5592	282	5	>	>	X
ejpam-5592	282	6	0	0	NUM
ejpam-5592	282	7	,	,	PUNCT
ejpam-5592	282	8	for	for	ADP
ejpam-5592	282	9	u	u	PRON
ejpam-5592	282	10	≥	≥	NUM
ejpam-5592	282	11	1	1	NUM
ejpam-5592	282	12	.	.	PUNCT
ejpam-5592	282	13	assume	assume	VERB
ejpam-5592	282	14	that	that	SCONJ
ejpam-5592	282	15	θ(z	θ(z	NOUN
ejpam-5592	282	16	)	)	PUNCT
ejpam-5592	282	17	=	=	SYM
ejpam-5592	282	18	u(z)λ(ϖ	u(z)λ(ϖ	NOUN
ejpam-5592	282	19	)	)	PUNCT
ejpam-5592	282	20	λ(ϖ)−(1−ϖ)g(z	λ(ϖ)−(1−ϖ)g(z	PROPN
ejpam-5592	282	21	)	)	PUNCT
ejpam-5592	282	22	is	be	AUX
ejpam-5592	282	23	a	a	DET
ejpam-5592	282	24	nfli	nfli	NOUN
ejpam-5592	282	25	on	on	ADP
ejpam-5592	282	26	ℑ	ℑ	PROPN
ejpam-5592	282	27	,	,	PUNCT
ejpam-5592	282	28	ξ(z	ξ(z	PROPN
ejpam-5592	282	29	)	)	PUNCT
ejpam-5592	282	30	=	=	SYM
ejpam-5592	282	31	ϖg(z	ϖg(z	NOUN
ejpam-5592	282	32	)	)	PUNCT
ejpam-5592	282	33	λ(ϖ)−(1−ϖ)g(z	λ(ϖ)−(1−ϖ)g(z	PROPN
ejpam-5592	282	34	)	)	PUNCT
ejpam-5592	282	35	is	be	AUX
ejpam-5592	282	36	a	a	DET
ejpam-5592	282	37	nnf	nnf	NOUN
ejpam-5592	282	38	and	and	CCONJ
ejpam-5592	282	39	ϱ	ϱ	NOUN
ejpam-5592	282	40	is	be	AUX
ejpam-5592	282	41	a	a	DET
ejpam-5592	282	42	nfli	nfli	NOUN
ejpam-5592	282	43	on	on	ADP
ejpam-5592	282	44	ℑ	ℑ	PROPN
ejpam-5592	282	45	,	,	PUNCT
ejpam-5592	282	46	such	such	ADJ
ejpam-5592	282	47	that	that	SCONJ
ejpam-5592	282	48	ϱ	ϱ	PROPN
ejpam-5592	282	49	(	(	PUNCT
ejpam-5592	282	50	z	z	NOUN
ejpam-5592	282	51	)	)	PUNCT
ejpam-5592	282	52	≤	≤	NOUN
ejpam-5592	282	53	u(z	u(z	NOUN
ejpam-5592	282	54	)	)	PUNCT
ejpam-5592	283	1	+	+	ADP
ejpam-5592	283	2	g(z)kabℜϖ,ηκ	g(z)kabℜϖ,ηκ	X
ejpam-5592	283	3	ϱ	ϱ	X
ejpam-5592	283	4	(	(	PUNCT
ejpam-5592	283	5	z	z	NOUN
ejpam-5592	283	6	)	)	PUNCT
ejpam-5592	283	7	,	,	PUNCT
ejpam-5592	283	8	z	z	PROPN
ejpam-5592	283	9	∈	∈	PROPN
ejpam-5592	283	10	ℑ	ℑ	PROPN
ejpam-5592	283	11	,	,	PUNCT
ejpam-5592	283	12	then	then	ADV
ejpam-5592	283	13	,	,	PUNCT
ejpam-5592	283	14	for	for	ADP
ejpam-5592	283	15	each	each	DET
ejpam-5592	283	16	z	z	PROPN
ejpam-5592	283	17	∈	∈	PROPN
ejpam-5592	283	18	ℑ	ℑ	PROPN
ejpam-5592	283	19	,	,	PUNCT
ejpam-5592	283	20	we	we	PRON
ejpam-5592	283	21	get	get	VERB
ejpam-5592	283	22	ϱ	ϱ	ADP
ejpam-5592	283	23	(	(	PUNCT
ejpam-5592	283	24	z	z	NOUN
ejpam-5592	283	25	)	)	PUNCT
ejpam-5592	283	26	≤	≤	NUM
ejpam-5592	283	27	θ(z	θ(z	NOUN
ejpam-5592	283	28	)	)	PUNCT
ejpam-5592	284	1	+	+	SYM
ejpam-5592	285	1	z∫	z∫	NOUN
ejpam-5592	285	2	κ	κ	ADP
ejpam-5592	285	3	∞∑	∞∑	NUM
ejpam-5592	285	4	j=1	j=1	NOUN
ejpam-5592	285	5	η1−jϖrη−1	η1−jϖrη−1	PRON
ejpam-5592	286	1	[	[	X
ejpam-5592	286	2	ξ(z))]j	ξ(z))]j	PROPN
ejpam-5592	286	3	γ(jϖ	γ(jϖ	PROPN
ejpam-5592	286	4	)	)	PUNCT
ejpam-5592	286	5	(	(	PUNCT
ejpam-5592	286	6	zη	zη	NOUN
ejpam-5592	286	7	−	−	NOUN
ejpam-5592	286	8	rη)jϖ−1θ(r	rη)jϖ−1θ(r	NOUN
ejpam-5592	286	9	)	)	PUNCT
ejpam-5592	286	10	dr	dr	PROPN
ejpam-5592	286	11	.	.	PROPN
ejpam-5592	286	12	proof	proof	PROPN
ejpam-5592	286	13	.	.	PUNCT
ejpam-5592	287	1	the	the	DET
ejpam-5592	287	2	proof	proof	NOUN
ejpam-5592	287	3	follows	follow	VERB
ejpam-5592	287	4	immediately	immediately	ADV
ejpam-5592	287	5	by	by	ADP
ejpam-5592	287	6	taking	take	VERB
ejpam-5592	287	7	ψ(z	ψ(z	NOUN
ejpam-5592	287	8	)	)	PUNCT
ejpam-5592	287	9	=	=	PUNCT
ejpam-5592	287	10	zη	zη	PROPN
ejpam-5592	287	11	η	η	PROPN
ejpam-5592	287	12	in	in	ADP
ejpam-5592	287	13	lemma	lemma	PROPN
ejpam-5592	287	14	8	8	NUM
ejpam-5592	287	15	.	.	PUNCT
ejpam-5592	287	16	corollary	corollary	ADJ
ejpam-5592	287	17	3	3	NUM
ejpam-5592	287	18	.	.	PUNCT
ejpam-5592	287	19	via	via	ADP
ejpam-5592	287	20	the	the	DET
ejpam-5592	287	21	assumptions	assumption	NOUN
ejpam-5592	287	22	of	of	ADP
ejpam-5592	287	23	corollary	corollary	ADJ
ejpam-5592	287	24	2	2	NUM
ejpam-5592	287	25	,	,	PUNCT
ejpam-5592	287	26	if	if	SCONJ
ejpam-5592	287	27	the	the	DET
ejpam-5592	287	28	function	function	NOUN
ejpam-5592	287	29	θ(z	θ(z	NOUN
ejpam-5592	287	30	)	)	PUNCT
ejpam-5592	287	31	is	be	AUX
ejpam-5592	287	32	nondecreasing	nondecrease	VERB
ejpam-5592	287	33	on	on	ADP
ejpam-5592	287	34	ℑ	ℑ	PROPN
ejpam-5592	287	35	,	,	PUNCT
ejpam-5592	287	36	then	then	ADV
ejpam-5592	287	37	,	,	PUNCT
ejpam-5592	287	38	we	we	PRON
ejpam-5592	287	39	get	get	VERB
ejpam-5592	287	40	ϱ	ϱ	ADP
ejpam-5592	287	41	(	(	PUNCT
ejpam-5592	287	42	z	z	NOUN
ejpam-5592	287	43	)	)	PUNCT
ejpam-5592	287	44	≤	≤	NOUN
ejpam-5592	287	45	θ(z)lϖ	θ(z)lϖ	ADP
ejpam-5592	287	46	[	[	PUNCT
ejpam-5592	287	47	ξ(z	ξ(z	PROPN
ejpam-5592	287	48	)	)	PUNCT
ejpam-5592	287	49	(	(	PUNCT
ejpam-5592	287	50	zη	zη	AUX
ejpam-5592	287	51	−	−	VERB
ejpam-5592	287	52	rη	rη	NOUN
ejpam-5592	287	53	η	η	PROPN
ejpam-5592	287	54	)	)	PUNCT
ejpam-5592	287	55	ϖ	ϖ	PROPN
ejpam-5592	287	56	]	]	X
ejpam-5592	287	57	,	,	PUNCT
ejpam-5592	287	58	z	z	NOUN
ejpam-5592	287	59	∈	∈	NOUN
ejpam-5592	287	60	ℑ.	ℑ.	NOUN
ejpam-5592	287	61	proof	proof	NOUN
ejpam-5592	287	62	.	.	PUNCT
ejpam-5592	288	1	taking	take	VERB
ejpam-5592	288	2	ψ(z	ψ(z	NOUN
ejpam-5592	288	3	)	)	PUNCT
ejpam-5592	288	4	=	=	PUNCT
ejpam-5592	288	5	zη	zη	ADP
ejpam-5592	288	6	η	η	PROPN
ejpam-5592	288	7	in	in	ADP
ejpam-5592	288	8	corollary	corollary	ADJ
ejpam-5592	288	9	1	1	NUM
ejpam-5592	288	10	,	,	PUNCT
ejpam-5592	288	11	we	we	PRON
ejpam-5592	288	12	get	get	VERB
ejpam-5592	288	13	the	the	DET
ejpam-5592	288	14	proof	proof	NOUN
ejpam-5592	288	15	.	.	PUNCT
ejpam-5592	289	1	5	5	X
ejpam-5592	289	2	.	.	X
ejpam-5592	289	3	solving	solve	VERB
ejpam-5592	289	4	a	a	DET
ejpam-5592	289	5	fractional	fractional	ADJ
ejpam-5592	289	6	differential	differential	NOUN
ejpam-5592	289	7	equation	equation	NOUN
ejpam-5592	289	8	this	this	DET
ejpam-5592	289	9	part	part	NOUN
ejpam-5592	289	10	is	be	AUX
ejpam-5592	289	11	devoted	devote	VERB
ejpam-5592	289	12	to	to	ADP
ejpam-5592	289	13	presenting	present	VERB
ejpam-5592	289	14	the	the	DET
ejpam-5592	289	15	existence	existence	NOUN
ejpam-5592	289	16	and	and	CCONJ
ejpam-5592	289	17	uniqueness	uniqueness	NOUN
ejpam-5592	289	18	of	of	ADP
ejpam-5592	289	19	solution	solution	NOUN
ejpam-5592	289	20	to	to	ADP
ejpam-5592	289	21	the	the	DET
ejpam-5592	289	22	initial	initial	ADJ
ejpam-5592	289	23	fde	fde	PROPN
ejpam-5592	289	24	below	below	ADV
ejpam-5592	289	25	:	:	PUNCT
ejpam-5592	289	26	{	{	PUNCT
ejpam-5592	289	27	cabdϖu	cabdϖu	PROPN
ejpam-5592	289	28	,	,	PUNCT
ejpam-5592	289	29	ψ	ψ	X
ejpam-5592	289	30	κ	κ	X
ejpam-5592	289	31	ϱ(z	ϱ(z	PROPN
ejpam-5592	289	32	)	)	PUNCT
ejpam-5592	289	33	=	=	SYM
ejpam-5592	289	34	ϕ(z	ϕ(z	NOUN
ejpam-5592	289	35	,	,	PUNCT
ejpam-5592	289	36	ϱ(z	ϱ(z	PROPN
ejpam-5592	289	37	)	)	PUNCT
ejpam-5592	289	38	)	)	PUNCT
ejpam-5592	289	39	,	,	PUNCT
ejpam-5592	289	40	z	z	PROPN
ejpam-5592	289	41	∈	∈	PROPN
ejpam-5592	289	42	ℑ	ℑ	PROPN
ejpam-5592	289	43	,	,	PUNCT
ejpam-5592	289	44	u	u	NOUN
ejpam-5592	289	45	≥	≥	NOUN
ejpam-5592	289	46	1	1	NUM
ejpam-5592	289	47	,	,	PUNCT
ejpam-5592	289	48	ϱ	ϱ	PROPN
ejpam-5592	289	49	(	(	PUNCT
ejpam-5592	289	50	i	i	NOUN
ejpam-5592	289	51	)	)	PUNCT
ejpam-5592	289	52	ψ	ψ	PROPN
ejpam-5592	289	53	(	(	PUNCT
ejpam-5592	289	54	κ	κ	NOUN
ejpam-5592	289	55	)	)	PUNCT
ejpam-5592	289	56	=	=	SYM
ejpam-5592	289	57	γi	γi	NOUN
ejpam-5592	289	58	,	,	PUNCT
ejpam-5592	289	59	i	i	NOUN
ejpam-5592	289	60	=	=	NOUN
ejpam-5592	289	61	0	0	NUM
ejpam-5592	289	62	,	,	PUNCT
ejpam-5592	289	63	1	1	NUM
ejpam-5592	289	64	,	,	PUNCT
ejpam-5592	289	65	...	...	PUNCT
ejpam-5592	289	66	,	,	PUNCT
ejpam-5592	289	67	k	k	NOUN
ejpam-5592	289	68	,	,	PUNCT
ejpam-5592	289	69	(	(	PUNCT
ejpam-5592	289	70	2	2	X
ejpam-5592	289	71	)	)	PUNCT
ejpam-5592	289	72	where	where	SCONJ
ejpam-5592	289	73	cabdϖu	cabdϖu	PROPN
ejpam-5592	289	74	,	,	PUNCT
ejpam-5592	289	75	ψ	ψ	X
ejpam-5592	289	76	κ	κ	NOUN
ejpam-5592	289	77	is	be	AUX
ejpam-5592	289	78	the	the	DET
ejpam-5592	289	79	ϖuth	ϖuth	NOUN
ejpam-5592	289	80	left	left	ADJ
ejpam-5592	289	81	-	-	PUNCT
ejpam-5592	289	82	sided	sided	ADJ
ejpam-5592	289	83	ψ−abc	ψ−abc	NOUN
ejpam-5592	289	84	fractional	fractional	ADJ
ejpam-5592	289	85	derivative	derivative	ADJ
ejpam-5592	289	86	such	such	ADJ
ejpam-5592	289	87	that	that	SCONJ
ejpam-5592	289	88	ϖu	ϖu	PROPN
ejpam-5592	289	89	∈	∈	PROPN
ejpam-5592	289	90	(	(	PUNCT
ejpam-5592	289	91	k	k	NOUN
ejpam-5592	289	92	,	,	PUNCT
ejpam-5592	289	93	k+1	k+1	X
ejpam-5592	289	94	]	]	X
ejpam-5592	289	95	,	,	PUNCT
ejpam-5592	289	96	γi	γi	X
ejpam-5592	289	97	∈	∈	PROPN
ejpam-5592	289	98	r	r	NOUN
ejpam-5592	289	99	(	(	PUNCT
ejpam-5592	289	100	i	i	PRON
ejpam-5592	289	101	≥	≥	NOUN
ejpam-5592	289	102	0	0	NUM
ejpam-5592	289	103	)	)	PUNCT
ejpam-5592	289	104	are	be	AUX
ejpam-5592	289	105	constants	constant	NOUN
ejpam-5592	289	106	,	,	PUNCT
ejpam-5592	289	107	ϕ	ϕ	NOUN
ejpam-5592	289	108	:	:	PUNCT
ejpam-5592	289	109	ℑ×r	ℑ×r	PROPN
ejpam-5592	289	110	→	→	SYM
ejpam-5592	289	111	r	r	NOUN
ejpam-5592	289	112	is	be	AUX
ejpam-5592	289	113	a	a	DET
ejpam-5592	289	114	continuous	continuous	ADJ
ejpam-5592	289	115	function	function	NOUN
ejpam-5592	289	116	,	,	PUNCT
ejpam-5592	289	117	ψ	ψ	X
ejpam-5592	289	118	:	:	PUNCT
ejpam-5592	289	119	ℑ	ℑ	NOUN
ejpam-5592	289	120	→	→	SYM
ejpam-5592	289	121	r	r	NOUN
ejpam-5592	289	122	is	be	AUX
ejpam-5592	289	123	an	an	DET
ejpam-5592	289	124	increasing	increase	VERB
ejpam-5592	289	125	function	function	NOUN
ejpam-5592	289	126	with	with	ADP
ejpam-5592	289	127	ψ′(z	ψ′(z	NOUN
ejpam-5592	289	128	)	)	PUNCT
ejpam-5592	289	129	∈	∈	PROPN
ejpam-5592	289	130	ck(ℑu	ck(ℑu	PROPN
ejpam-5592	289	131	,	,	PUNCT
ejpam-5592	289	132	r+	r+	PUNCT
ejpam-5592	289	133	)	)	PUNCT
ejpam-5592	289	134	and	and	CCONJ
ejpam-5592	289	135	ψ′(z	ψ′(z	NOUN
ejpam-5592	289	136	)	)	PUNCT
ejpam-5592	289	137	̸=	̸=	PROPN
ejpam-5592	289	138	0	0	NUM
ejpam-5592	289	139	,	,	PUNCT
ejpam-5592	289	140	for	for	ADP
ejpam-5592	289	141	all	all	DET
ejpam-5592	289	142	z	z	NOUN
ejpam-5592	289	143	∈	∈	PROPN
ejpam-5592	289	144	ℑ	ℑ	PROPN
ejpam-5592	289	145	and	and	CCONJ
ejpam-5592	289	146	ϱ(z	ϱ(z	PROPN
ejpam-5592	289	147	)	)	PUNCT
ejpam-5592	289	148	∈	∈	PROPN
ejpam-5592	289	149	ck(ℑu	ck(ℑu	PROPN
ejpam-5592	289	150	,	,	PUNCT
ejpam-5592	289	151	r	r	NOUN
ejpam-5592	289	152	)	)	PUNCT
ejpam-5592	289	153	is	be	AUX
ejpam-5592	289	154	a	a	DET
ejpam-5592	289	155	recognized	recognize	VERB
ejpam-5592	289	156	function	function	NOUN
ejpam-5592	289	157	in	in	ADP
ejpam-5592	289	158	which	which	PRON
ejpam-5592	289	159	ϱ	ϱ	PROPN
ejpam-5592	289	160	(	(	PUNCT
ejpam-5592	289	161	i	i	NOUN
ejpam-5592	289	162	)	)	PUNCT
ejpam-5592	289	163	ψ	ψ	PROPN
ejpam-5592	289	164	(	(	PUNCT
ejpam-5592	289	165	z	z	NOUN
ejpam-5592	289	166	)	)	PUNCT
ejpam-5592	289	167	=	=	SYM
ejpam-5592	289	168	(	(	PUNCT
ejpam-5592	289	169	1	1	NUM
ejpam-5592	289	170	ψ′(z	ψ′(z	NOUN
ejpam-5592	289	171	)	)	PUNCT
ejpam-5592	289	172	d	d	X
ejpam-5592	289	173	dz	dz	PROPN
ejpam-5592	289	174	)	)	PUNCT
ejpam-5592	289	175	i	i	PROPN
ejpam-5592	289	176	ϱ(z	ϱ(z	NOUN
ejpam-5592	289	177	)	)	PUNCT
ejpam-5592	289	178	such	such	ADJ
ejpam-5592	289	179	that	that	SCONJ
ejpam-5592	289	180	ϱ	ϱ	PROPN
ejpam-5592	289	181	(	(	PUNCT
ejpam-5592	289	182	0	0	NUM
ejpam-5592	289	183	)	)	PUNCT
ejpam-5592	289	184	ψ	ψ	X
ejpam-5592	289	185	(	(	PUNCT
ejpam-5592	289	186	z	z	NOUN
ejpam-5592	289	187	)	)	PUNCT
ejpam-5592	289	188	=	=	SYM
ejpam-5592	289	189	ϱ(z	ϱ(z	NOUN
ejpam-5592	289	190	)	)	PUNCT
ejpam-5592	289	191	.	.	PUNCT
ejpam-5592	290	1	h.a	h.a	PROPN
ejpam-5592	290	2	.	.	PROPN
ejpam-5592	290	3	hammad	hammad	PROPN
ejpam-5592	290	4	,	,	PUNCT
ejpam-5592	290	5	m.	m.	PROPN
ejpam-5592	290	6	de	de	X
ejpam-5592	290	7	la	la	PROPN
ejpam-5592	290	8	sen	sen	PROPN
ejpam-5592	290	9	/	/	SYM
ejpam-5592	290	10	eur	eur	PROPN
ejpam-5592	290	11	.	.	PUNCT
ejpam-5592	291	1	j.	j.	PROPN
ejpam-5592	291	2	pure	pure	PROPN
ejpam-5592	291	3	appl	appl	PROPN
ejpam-5592	291	4	.	.	PROPN
ejpam-5592	291	5	math	math	PROPN
ejpam-5592	291	6	,	,	PUNCT
ejpam-5592	291	7	17	17	NUM
ejpam-5592	291	8	(	(	PUNCT
ejpam-5592	291	9	4	4	NUM
ejpam-5592	291	10	)	)	PUNCT
ejpam-5592	291	11	(	(	PUNCT
ejpam-5592	291	12	2024	2024	NUM
ejpam-5592	291	13	)	)	PUNCT
ejpam-5592	291	14	,	,	PUNCT
ejpam-5592	291	15	3687	3687	NUM
ejpam-5592	291	16	-	-	SYM
ejpam-5592	291	17	3707	3707	NUM
ejpam-5592	291	18	3700	3700	NUM
ejpam-5592	291	19	in	in	ADP
ejpam-5592	291	20	fact	fact	NOUN
ejpam-5592	291	21	,	,	PUNCT
ejpam-5592	291	22	by	by	ADP
ejpam-5592	291	23	utilizing	utilize	VERB
ejpam-5592	291	24	lemma	lemma	PROPN
ejpam-5592	291	25	4	4	NUM
ejpam-5592	291	26	in	in	ADP
ejpam-5592	291	27	conjunction	conjunction	NOUN
ejpam-5592	291	28	with	with	ADP
ejpam-5592	291	29	the	the	DET
ejpam-5592	291	30	initial	initial	ADJ
ejpam-5592	291	31	fde	fde	NOUN
ejpam-5592	291	32	(	(	PUNCT
ejpam-5592	291	33	2	2	NUM
ejpam-5592	291	34	)	)	PUNCT
ejpam-5592	291	35	and	and	CCONJ
ejpam-5592	291	36	the	the	DET
ejpam-5592	291	37	ϖuth	ϖuth	NOUN
ejpam-5592	291	38	left	leave	VERB
ejpam-5592	291	39	-	-	PUNCT
ejpam-5592	291	40	sided	sided	ADJ
ejpam-5592	291	41	ψ	ψ	X
ejpam-5592	291	42	–	–	PUNCT
ejpam-5592	291	43	rl	rl	ADP
ejpam-5592	291	44	-	-	PUNCT
ejpam-5592	291	45	ab	ab	NOUN
ejpam-5592	291	46	fractional	fractional	ADJ
ejpam-5592	291	47	integral	integral	ADJ
ejpam-5592	291	48	operator	operator	NOUN
ejpam-5592	291	49	on	on	ADP
ejpam-5592	291	50	both	both	DET
ejpam-5592	291	51	sides	side	NOUN
ejpam-5592	291	52	of	of	ADP
ejpam-5592	291	53	(	(	PUNCT
ejpam-5592	291	54	2	2	NUM
ejpam-5592	291	55	)	)	PUNCT
ejpam-5592	291	56	,	,	PUNCT
ejpam-5592	291	57	we	we	PRON
ejpam-5592	291	58	get	get	VERB
ejpam-5592	291	59	ϱ	ϱ	ADP
ejpam-5592	291	60	(	(	PUNCT
ejpam-5592	291	61	z	z	NOUN
ejpam-5592	291	62	)	)	PUNCT
ejpam-5592	291	63	=	=	SYM
ejpam-5592	292	1	k∑	k∑	PROPN
ejpam-5592	292	2	i=0	i=0	PROPN
ejpam-5592	292	3	γi	γi	X
ejpam-5592	292	4	i	i	PRON
ejpam-5592	292	5	!	!	PUNCT
ejpam-5592	293	1	(	(	PUNCT
ejpam-5592	293	2	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	293	3	ψ(κ))i	ψ(κ))i	PROPN
ejpam-5592	293	4	+	+	PROPN
ejpam-5592	293	5	rlab	rlab	NOUN
ejpam-5592	293	6	ℜϖu	ℜϖu	PROPN
ejpam-5592	293	7	,	,	PUNCT
ejpam-5592	293	8	ψκ	ψκ	VERB
ejpam-5592	293	9	ϕ(z	ϕ(z	PROPN
ejpam-5592	293	10	,	,	PUNCT
ejpam-5592	293	11	ϱ(z	ϱ(z	PROPN
ejpam-5592	293	12	)	)	PUNCT
ejpam-5592	293	13	)	)	PUNCT
ejpam-5592	293	14	.	.	PUNCT
ejpam-5592	294	1	(	(	PUNCT
ejpam-5592	294	2	3	3	X
ejpam-5592	294	3	)	)	PUNCT
ejpam-5592	294	4	now	now	ADV
ejpam-5592	294	5	,	,	PUNCT
ejpam-5592	294	6	we	we	PRON
ejpam-5592	294	7	shall	shall	AUX
ejpam-5592	294	8	apply	apply	VERB
ejpam-5592	294	9	picard	picard	PROPN
ejpam-5592	294	10	’s	’s	PART
ejpam-5592	294	11	iterative	iterative	NOUN
ejpam-5592	294	12	technique	technique	NOUN
ejpam-5592	294	13	[	[	X
ejpam-5592	294	14	19	19	NUM
ejpam-5592	294	15	]	]	PUNCT
ejpam-5592	294	16	to	to	PART
ejpam-5592	294	17	demonstrate	demonstrate	VERB
ejpam-5592	294	18	the	the	DET
ejpam-5592	294	19	existence	existence	NOUN
ejpam-5592	294	20	and	and	CCONJ
ejpam-5592	294	21	uniqueness	uniqueness	NOUN
ejpam-5592	294	22	of	of	ADP
ejpam-5592	294	23	the	the	DET
ejpam-5592	294	24	solution	solution	NOUN
ejpam-5592	294	25	to	to	ADP
ejpam-5592	294	26	problem	problem	NOUN
ejpam-5592	294	27	(	(	PUNCT
ejpam-5592	294	28	2	2	NUM
ejpam-5592	294	29	)	)	PUNCT
ejpam-5592	294	30	.	.	PUNCT
ejpam-5592	295	1	theorem	theorem	NOUN
ejpam-5592	295	2	1	1	NUM
ejpam-5592	295	3	.	.	PUNCT
ejpam-5592	295	4	assume	assume	VERB
ejpam-5592	295	5	that	that	SCONJ
ejpam-5592	295	6	the	the	DET
ejpam-5592	295	7	assertions	assertion	NOUN
ejpam-5592	295	8	below	below	ADP
ejpam-5592	295	9	hold	hold	NOUN
ejpam-5592	295	10	:	:	PUNCT
ejpam-5592	295	11	(	(	PUNCT
ejpam-5592	295	12	i	i	NOUN
ejpam-5592	295	13	)	)	PUNCT
ejpam-5592	295	14	there	there	PRON
ejpam-5592	295	15	exists	exist	VERB
ejpam-5592	295	16	a	a	DET
ejpam-5592	295	17	constant	constant	ADJ
ejpam-5592	295	18	t	t	NOUN
ejpam-5592	295	19	>	>	X
ejpam-5592	295	20	0	0	NUM
ejpam-5592	295	21	such	such	ADJ
ejpam-5592	295	22	that	that	DET
ejpam-5592	295	23	sup	sup	NOUN
ejpam-5592	295	24	z∈ℑ	z∈ℑ	NUM
ejpam-5592	295	25	|ϕ(z	|ϕ(z	PROPN
ejpam-5592	295	26	,	,	PUNCT
ejpam-5592	295	27	ϱ0(z))|	ϱ0(z))|	PROPN
ejpam-5592	295	28	≤	≤	PROPN
ejpam-5592	295	29	t	t	PROPN
ejpam-5592	295	30	,	,	PUNCT
ejpam-5592	295	31	(	(	PUNCT
ejpam-5592	295	32	ii	ii	NOUN
ejpam-5592	295	33	)	)	PUNCT
ejpam-5592	295	34	there	there	PRON
ejpam-5592	295	35	exists	exist	VERB
ejpam-5592	295	36	a	a	DET
ejpam-5592	295	37	constant	constant	ADJ
ejpam-5592	295	38	p	p	X
ejpam-5592	295	39	>	>	X
ejpam-5592	295	40	0	0	NUM
ejpam-5592	295	41	such	such	ADJ
ejpam-5592	295	42	that	that	SCONJ
ejpam-5592	295	43	|ϕ(z	|ϕ(z	PROPN
ejpam-5592	295	44	,	,	PUNCT
ejpam-5592	295	45	ϱ1)−	ϱ1)−	NOUN
ejpam-5592	295	46	ϕ(z	ϕ(z	NOUN
ejpam-5592	295	47	,	,	PUNCT
ejpam-5592	296	1	ϱ2)|	ϱ2)|	NOUN
ejpam-5592	296	2	≤	≤	NUM
ejpam-5592	296	3	p	p	NOUN
ejpam-5592	296	4	|ϱ1	|ϱ1	NUM
ejpam-5592	296	5	−	−	PROPN
ejpam-5592	296	6	ϱ2|	ϱ2|	PROPN
ejpam-5592	296	7	,	,	PUNCT
ejpam-5592	296	8	for	for	ADP
ejpam-5592	296	9	all	all	DET
ejpam-5592	296	10	z	z	NOUN
ejpam-5592	296	11	∈	∈	PROPN
ejpam-5592	296	12	ℑ	ℑ	PROPN
ejpam-5592	296	13	,	,	PUNCT
ejpam-5592	296	14	ϱ1	ϱ1	NOUN
ejpam-5592	296	15	,	,	PUNCT
ejpam-5592	296	16	ϱ2	ϱ2	PROPN
ejpam-5592	296	17	∈	∈	PROPN
ejpam-5592	296	18	ck(ℑu	ck(ℑu	PROPN
ejpam-5592	296	19	,	,	PUNCT
ejpam-5592	296	20	r	r	NOUN
ejpam-5592	296	21	)	)	PUNCT
ejpam-5592	296	22	.	.	PUNCT
ejpam-5592	297	1	(	(	PUNCT
ejpam-5592	297	2	iii	iii	X
ejpam-5592	297	3	)	)	PUNCT
ejpam-5592	297	4	we	we	PRON
ejpam-5592	297	5	have	have	VERB
ejpam-5592	297	6	the	the	DET
ejpam-5592	297	7	inequality	inequality	NOUN
ejpam-5592	297	8	p	p	NOUN
ejpam-5592	297	9	(	(	PUNCT
ejpam-5592	297	10	(	(	PUNCT
ejpam-5592	297	11	k	k	X
ejpam-5592	297	12	+	+	NOUN
ejpam-5592	297	13	1−ϖu	1−ϖu	NUM
ejpam-5592	297	14	)	)	PUNCT
ejpam-5592	297	15	(	(	PUNCT
ejpam-5592	297	16	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	297	17	ψ(κ))k	ψ(κ))k	PROPN
ejpam-5592	297	18	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	297	19	−	−	PROPN
ejpam-5592	297	20	k)γ(k	k)γ(k	NOUN
ejpam-5592	297	21	+	+	CCONJ
ejpam-5592	297	22	1	1	NUM
ejpam-5592	297	23	)	)	PUNCT
ejpam-5592	297	24	+	+	CCONJ
ejpam-5592	297	25	(	(	PUNCT
ejpam-5592	297	26	ϖu	ϖu	PROPN
ejpam-5592	297	27	−	−	PROPN
ejpam-5592	297	28	k	k	NOUN
ejpam-5592	297	29	)	)	PUNCT
ejpam-5592	297	30	(	(	PUNCT
ejpam-5592	297	31	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	297	32	ψ(κ))ϖu	ψ(κ))ϖu	NOUN
ejpam-5592	297	33	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	297	34	−	−	PROPN
ejpam-5592	297	35	k)γ(ϖu	k)γ(ϖu	PUNCT
ejpam-5592	297	36	+	+	NOUN
ejpam-5592	297	37	1	1	NUM
ejpam-5592	297	38	)	)	PUNCT
ejpam-5592	297	39	)	)	PUNCT
ejpam-5592	297	40	<	<	X
ejpam-5592	298	1	1	1	X
ejpam-5592	298	2	.	.	PUNCT
ejpam-5592	298	3	(	(	PUNCT
ejpam-5592	298	4	4	4	NUM
ejpam-5592	298	5	)	)	PUNCT
ejpam-5592	298	6	then	then	ADV
ejpam-5592	298	7	,	,	PUNCT
ejpam-5592	298	8	the	the	DET
ejpam-5592	298	9	problem	problem	NOUN
ejpam-5592	298	10	(	(	PUNCT
ejpam-5592	298	11	2	2	X
ejpam-5592	298	12	)	)	PUNCT
ejpam-5592	298	13	has	have	VERB
ejpam-5592	298	14	a	a	DET
ejpam-5592	298	15	unique	unique	ADJ
ejpam-5592	298	16	solution	solution	NOUN
ejpam-5592	298	17	on	on	ADP
ejpam-5592	298	18	ℑ.	ℑ.	NOUN
ejpam-5592	298	19	proof	proof	NOUN
ejpam-5592	298	20	.	.	PUNCT
ejpam-5592	299	1	it	it	PRON
ejpam-5592	299	2	is	be	AUX
ejpam-5592	299	3	evident	evident	ADJ
ejpam-5592	299	4	that	that	SCONJ
ejpam-5592	299	5	the	the	DET
ejpam-5592	299	6	solution	solution	NOUN
ejpam-5592	299	7	to	to	ADP
ejpam-5592	299	8	system	system	NOUN
ejpam-5592	299	9	(	(	PUNCT
ejpam-5592	299	10	2	2	NUM
ejpam-5592	299	11	)	)	PUNCT
ejpam-5592	299	12	is	be	AUX
ejpam-5592	299	13	the	the	DET
ejpam-5592	299	14	same	same	ADJ
ejpam-5592	299	15	as	as	ADP
ejpam-5592	299	16	the	the	DET
ejpam-5592	299	17	solution	solution	NOUN
ejpam-5592	299	18	to	to	ADP
ejpam-5592	299	19	the	the	DET
ejpam-5592	299	20	fie	fie	NOUN
ejpam-5592	299	21	(	(	PUNCT
ejpam-5592	299	22	3	3	NUM
ejpam-5592	299	23	)	)	PUNCT
ejpam-5592	299	24	.	.	PUNCT
ejpam-5592	300	1	set	set	VERB
ejpam-5592	300	2	ϱ0	ϱ0	NOUN
ejpam-5592	300	3	(	(	PUNCT
ejpam-5592	300	4	z	z	NOUN
ejpam-5592	300	5	)	)	PUNCT
ejpam-5592	300	6	=	=	SYM
ejpam-5592	301	1	k∑	k∑	PROPN
ejpam-5592	301	2	i=0	i=0	PROPN
ejpam-5592	301	3	γi	γi	X
ejpam-5592	301	4	i	i	PRON
ejpam-5592	301	5	!	!	PUNCT
ejpam-5592	302	1	(	(	PUNCT
ejpam-5592	302	2	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	302	3	ψ(κ))i	ψ(κ))i	PROPN
ejpam-5592	302	4	,	,	PUNCT
ejpam-5592	302	5	(	(	PUNCT
ejpam-5592	302	6	5	5	NUM
ejpam-5592	302	7	)	)	PUNCT
ejpam-5592	302	8	and	and	CCONJ
ejpam-5592	302	9	ϱs	ϱs	NOUN
ejpam-5592	302	10	(	(	PUNCT
ejpam-5592	302	11	z	z	NOUN
ejpam-5592	302	12	)	)	PUNCT
ejpam-5592	302	13	=	=	SYM
ejpam-5592	303	1	k∑	k∑	PROPN
ejpam-5592	303	2	i=0	i=0	PROPN
ejpam-5592	303	3	γi	γi	X
ejpam-5592	303	4	i	i	PRON
ejpam-5592	303	5	!	!	PUNCT
ejpam-5592	304	1	(	(	PUNCT
ejpam-5592	304	2	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	304	3	ψ(κ))i	ψ(κ))i	PROPN
ejpam-5592	304	4	+	+	PROPN
ejpam-5592	304	5	rlab	rlab	NOUN
ejpam-5592	304	6	ℜϖu	ℜϖu	PROPN
ejpam-5592	304	7	,	,	PUNCT
ejpam-5592	304	8	ψκ	ψκ	VERB
ejpam-5592	304	9	ϕ(z	ϕ(z	PROPN
ejpam-5592	304	10	,	,	PUNCT
ejpam-5592	304	11	ϱs−1(z	ϱs−1(z	NOUN
ejpam-5592	304	12	)	)	PUNCT
ejpam-5592	304	13	)	)	PUNCT
ejpam-5592	304	14	,	,	PUNCT
ejpam-5592	304	15	s	s	PROPN
ejpam-5592	304	16	∈	∈	PROPN
ejpam-5592	304	17	n.	n.	NOUN
ejpam-5592	304	18	(	(	PUNCT
ejpam-5592	304	19	6	6	NUM
ejpam-5592	304	20	)	)	PUNCT
ejpam-5592	304	21	clearly	clearly	ADV
ejpam-5592	304	22	,	,	PUNCT
ejpam-5592	304	23	the	the	DET
ejpam-5592	304	24	series	series	NOUN
ejpam-5592	304	25	ϱ0	ϱ0	NOUN
ejpam-5592	304	26	(	(	PUNCT
ejpam-5592	304	27	z	z	NOUN
ejpam-5592	304	28	)	)	PUNCT
ejpam-5592	304	29	+	+	CCONJ
ejpam-5592	304	30	∞∑	∞∑	NUM
ejpam-5592	304	31	m=0	m=0	PROPN
ejpam-5592	304	32	(	(	PUNCT
ejpam-5592	304	33	ϱm	ϱm	ADP
ejpam-5592	304	34	−	−	PRON
ejpam-5592	304	35	ϱm−1	ϱm−1	NOUN
ejpam-5592	304	36	)	)	PUNCT
ejpam-5592	304	37	has	have	VERB
ejpam-5592	304	38	a	a	DET
ejpam-5592	304	39	partial	partial	ADJ
ejpam-5592	304	40	sum	sum	NOUN
ejpam-5592	304	41	ϱs	ϱs	NOUN
ejpam-5592	304	42	(	(	PUNCT
ejpam-5592	304	43	z	z	NOUN
ejpam-5592	304	44	)	)	PUNCT
ejpam-5592	304	45	=	=	SYM
ejpam-5592	304	46	ϱ0	ϱ0	NOUN
ejpam-5592	304	47	(	(	PUNCT
ejpam-5592	304	48	z	z	NOUN
ejpam-5592	304	49	)	)	PUNCT
ejpam-5592	305	1	+	+	CCONJ
ejpam-5592	305	2	s∑	s∑	PROPN
ejpam-5592	305	3	m=0	m=0	PROPN
ejpam-5592	305	4	(	(	PUNCT
ejpam-5592	305	5	ϱm	ϱm	ADP
ejpam-5592	305	6	−	−	PRON
ejpam-5592	305	7	ϱm−1	ϱm−1	NOUN
ejpam-5592	305	8	)	)	PUNCT
ejpam-5592	305	9	.	.	PUNCT
ejpam-5592	306	1	we	we	PRON
ejpam-5592	306	2	want	want	VERB
ejpam-5592	306	3	to	to	PART
ejpam-5592	306	4	show	show	VERB
ejpam-5592	306	5	that	that	SCONJ
ejpam-5592	306	6	the	the	DET
ejpam-5592	306	7	sequence	sequence	NOUN
ejpam-5592	306	8	{	{	PUNCT
ejpam-5592	306	9	ϱs	ϱs	X
ejpam-5592	306	10	(	(	PUNCT
ejpam-5592	306	11	z	z	NOUN
ejpam-5592	306	12	)	)	PUNCT
ejpam-5592	306	13	}	}	PUNCT
ejpam-5592	306	14	converges	converge	VERB
ejpam-5592	306	15	to	to	ADP
ejpam-5592	306	16	ϱ	ϱ	PROPN
ejpam-5592	306	17	(	(	PUNCT
ejpam-5592	306	18	z	z	NOUN
ejpam-5592	306	19	)	)	PUNCT
ejpam-5592	306	20	.	.	PUNCT
ejpam-5592	307	1	by	by	ADP
ejpam-5592	307	2	a	a	DET
ejpam-5592	307	3	mathematical	mathematical	ADJ
ejpam-5592	307	4	induction	induction	NOUN
ejpam-5592	307	5	,	,	PUNCT
ejpam-5592	307	6	for	for	ADP
ejpam-5592	307	7	all	all	DET
ejpam-5592	307	8	z	z	NOUN
ejpam-5592	307	9	∈	∈	PROPN
ejpam-5592	308	1	[	[	X
ejpam-5592	308	2	κ	κ	NOUN
ejpam-5592	308	3	,	,	PUNCT
ejpam-5592	308	4	υ	υ	PROPN
ejpam-5592	308	5	]	]	X
ejpam-5592	308	6	,	,	PUNCT
ejpam-5592	308	7	we	we	PRON
ejpam-5592	308	8	can	can	AUX
ejpam-5592	308	9	write	write	VERB
ejpam-5592	308	10	∥ϱs	∥ϱ	NOUN
ejpam-5592	308	11	(	(	PUNCT
ejpam-5592	308	12	z)−	z)−	PROPN
ejpam-5592	308	13	ϱs−1	ϱs−1	PROPN
ejpam-5592	308	14	(	(	PUNCT
ejpam-5592	308	15	z)∥	z)∥	NUM
ejpam-5592	308	16	h.a	h.a	PROPN
ejpam-5592	308	17	.	.	PROPN
ejpam-5592	308	18	hammad	hammad	PROPN
ejpam-5592	308	19	,	,	PUNCT
ejpam-5592	308	20	m.	m.	PROPN
ejpam-5592	308	21	de	de	X
ejpam-5592	308	22	la	la	PROPN
ejpam-5592	308	23	sen	sen	PROPN
ejpam-5592	308	24	/	/	SYM
ejpam-5592	308	25	eur	eur	PROPN
ejpam-5592	308	26	.	.	PUNCT
ejpam-5592	309	1	j.	j.	PROPN
ejpam-5592	309	2	pure	pure	PROPN
ejpam-5592	309	3	appl	appl	PROPN
ejpam-5592	309	4	.	.	PROPN
ejpam-5592	309	5	math	math	PROPN
ejpam-5592	309	6	,	,	PUNCT
ejpam-5592	309	7	17	17	NUM
ejpam-5592	309	8	(	(	PUNCT
ejpam-5592	309	9	4	4	NUM
ejpam-5592	309	10	)	)	PUNCT
ejpam-5592	309	11	(	(	PUNCT
ejpam-5592	309	12	2024	2024	NUM
ejpam-5592	309	13	)	)	PUNCT
ejpam-5592	309	14	,	,	PUNCT
ejpam-5592	309	15	3687	3687	NUM
ejpam-5592	309	16	-	-	SYM
ejpam-5592	309	17	3707	3707	NUM
ejpam-5592	309	18	3701	3701	NUM
ejpam-5592	309	19	≤	≤	NOUN
ejpam-5592	309	20	tp	tp	ADP
ejpam-5592	309	21	s−1	s−1	PROPN
ejpam-5592	309	22	(	(	PUNCT
ejpam-5592	309	23	(	(	PUNCT
ejpam-5592	309	24	k	k	X
ejpam-5592	309	25	+	+	NOUN
ejpam-5592	309	26	1−ϖu	1−ϖu	NUM
ejpam-5592	309	27	)	)	PUNCT
ejpam-5592	309	28	(	(	PUNCT
ejpam-5592	309	29	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	309	30	ψ(κ))k	ψ(κ))k	PROPN
ejpam-5592	309	31	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	309	32	−	−	PROPN
ejpam-5592	309	33	k)γ(k	k)γ(k	NOUN
ejpam-5592	309	34	+	+	CCONJ
ejpam-5592	309	35	1	1	NUM
ejpam-5592	309	36	)	)	PUNCT
ejpam-5592	309	37	+	+	CCONJ
ejpam-5592	309	38	(	(	PUNCT
ejpam-5592	309	39	ϖu	ϖu	PROPN
ejpam-5592	309	40	−	−	PROPN
ejpam-5592	309	41	k	k	NOUN
ejpam-5592	309	42	)	)	PUNCT
ejpam-5592	309	43	(	(	PUNCT
ejpam-5592	309	44	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	309	45	ψ(κ))ϖu	ψ(κ))ϖu	NOUN
ejpam-5592	309	46	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	309	47	−	−	PROPN
ejpam-5592	309	48	k)γ(ϖu	k)γ(ϖu	PUNCT
ejpam-5592	309	49	+	+	NOUN
ejpam-5592	309	50	1	1	NUM
ejpam-5592	309	51	)	)	PUNCT
ejpam-5592	309	52	)	)	PUNCT
ejpam-5592	310	1	s	s	X
ejpam-5592	310	2	,	,	PUNCT
ejpam-5592	310	3	s	s	PROPN
ejpam-5592	310	4	∈	∈	PROPN
ejpam-5592	310	5	n.(7	n.(7	PROPN
ejpam-5592	310	6	)	)	PUNCT
ejpam-5592	310	7	based	base	VERB
ejpam-5592	310	8	on	on	ADP
ejpam-5592	310	9	(	(	PUNCT
ejpam-5592	310	10	5	5	NUM
ejpam-5592	310	11	)	)	PUNCT
ejpam-5592	310	12	and	and	CCONJ
ejpam-5592	310	13	(	(	PUNCT
ejpam-5592	310	14	6	6	NUM
ejpam-5592	310	15	)	)	PUNCT
ejpam-5592	310	16	and	and	CCONJ
ejpam-5592	310	17	lemma	lemma	PROPN
ejpam-5592	310	18	5	5	NUM
ejpam-5592	310	19	(	(	PUNCT
ejpam-5592	310	20	iv	iv	NUM
ejpam-5592	310	21	)	)	PUNCT
ejpam-5592	310	22	,	,	PUNCT
ejpam-5592	310	23	one	one	NUM
ejpam-5592	310	24	has	have	VERB
ejpam-5592	310	25	∥ϱ1	∥ϱ1	VERB
ejpam-5592	310	26	−	−	PROPN
ejpam-5592	310	27	ϱ0∥	ϱ0∥	ADJ
ejpam-5592	310	28	=	=	SYM
ejpam-5592	310	29	sup	sup	NOUN
ejpam-5592	310	30	z∈ℑ	z∈ℑ	NUM
ejpam-5592	310	31	∣∣∣rlabℜϖu	∣∣∣rlabℜϖu	NUM
ejpam-5592	310	32	,	,	PUNCT
ejpam-5592	310	33	ψκ	ψκ	PART
ejpam-5592	310	34	ϕ(z	ϕ(z	PROPN
ejpam-5592	310	35	,	,	PUNCT
ejpam-5592	310	36	ϱ0(z	ϱ0(z	NOUN
ejpam-5592	310	37	)	)	PUNCT
ejpam-5592	310	38	)	)	PUNCT
ejpam-5592	310	39	∣∣∣	∣∣∣	NOUN
ejpam-5592	310	40	≤	≤	PROPN
ejpam-5592	310	41	t	t	NOUN
ejpam-5592	310	42	(	(	PUNCT
ejpam-5592	310	43	(	(	PUNCT
ejpam-5592	310	44	k	k	X
ejpam-5592	310	45	+	+	NOUN
ejpam-5592	310	46	1−ϖu	1−ϖu	NUM
ejpam-5592	310	47	)	)	PUNCT
ejpam-5592	310	48	(	(	PUNCT
ejpam-5592	310	49	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	310	50	ψ(κ))k	ψ(κ))k	PROPN
ejpam-5592	310	51	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	310	52	−	−	PROPN
ejpam-5592	310	53	k)γ(k	k)γ(k	NOUN
ejpam-5592	310	54	+	+	CCONJ
ejpam-5592	310	55	1	1	NUM
ejpam-5592	310	56	)	)	PUNCT
ejpam-5592	310	57	+	+	CCONJ
ejpam-5592	310	58	(	(	PUNCT
ejpam-5592	310	59	ϖu	ϖu	PROPN
ejpam-5592	310	60	−	−	PROPN
ejpam-5592	310	61	k	k	NOUN
ejpam-5592	310	62	)	)	PUNCT
ejpam-5592	310	63	(	(	PUNCT
ejpam-5592	310	64	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	310	65	ψ(κ))ϖu	ψ(κ))ϖu	NOUN
ejpam-5592	310	66	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	310	67	−	−	PROPN
ejpam-5592	310	68	k)γ(ϖu	k)γ(ϖu	PUNCT
ejpam-5592	310	69	+	+	NOUN
ejpam-5592	310	70	1	1	NUM
ejpam-5592	310	71	)	)	PUNCT
ejpam-5592	310	72	)	)	PUNCT
ejpam-5592	310	73	.	.	PUNCT
ejpam-5592	311	1	hence	hence	ADV
ejpam-5592	311	2	,	,	PUNCT
ejpam-5592	311	3	for	for	ADP
ejpam-5592	311	4	s	s	NOUN
ejpam-5592	311	5	=	=	SYM
ejpam-5592	311	6	1	1	NUM
ejpam-5592	311	7	,	,	PUNCT
ejpam-5592	311	8	the	the	DET
ejpam-5592	311	9	inequality	inequality	NOUN
ejpam-5592	311	10	(	(	PUNCT
ejpam-5592	311	11	7	7	NUM
ejpam-5592	311	12	)	)	PUNCT
ejpam-5592	311	13	is	be	AUX
ejpam-5592	311	14	true	true	ADJ
ejpam-5592	311	15	.	.	PUNCT
ejpam-5592	312	1	after	after	ADP
ejpam-5592	312	2	that	that	PRON
ejpam-5592	312	3	,	,	PUNCT
ejpam-5592	312	4	consider	consider	VERB
ejpam-5592	312	5	the	the	DET
ejpam-5592	312	6	inequality	inequality	NOUN
ejpam-5592	312	7	(	(	PUNCT
ejpam-5592	312	8	7	7	NUM
ejpam-5592	312	9	)	)	PUNCT
ejpam-5592	312	10	is	be	AUX
ejpam-5592	312	11	satisfied	satisfied	ADJ
ejpam-5592	312	12	when	when	SCONJ
ejpam-5592	312	13	s	s	AUX
ejpam-5592	312	14	=	=	VERB
ejpam-5592	312	15	n.	n.	PROPN
ejpam-5592	312	16	therefore	therefore	ADV
ejpam-5592	312	17	,	,	PUNCT
ejpam-5592	312	18	∥ϱn+1	∥ϱn+1	VERB
ejpam-5592	312	19	−	−	PROPN
ejpam-5592	312	20	ϱn∥	ϱn∥	NOUN
ejpam-5592	312	21	=	=	SYM
ejpam-5592	312	22	sup	sup	NOUN
ejpam-5592	312	23	z∈ℑ	z∈ℑ	NUM
ejpam-5592	312	24	∣∣∣rlabℜϖu	∣∣∣rlabℜϖu	NUM
ejpam-5592	312	25	,	,	PUNCT
ejpam-5592	312	26	ψκ	ψκ	PART
ejpam-5592	312	27	ϕ(z	ϕ(z	NOUN
ejpam-5592	312	28	,	,	PUNCT
ejpam-5592	312	29	ϱn(z))−rlab	ϱn(z))−rlab	PROPN
ejpam-5592	312	30	ℜϖu	ℜϖu	PROPN
ejpam-5592	312	31	,	,	PUNCT
ejpam-5592	312	32	ψκ	ψκ	VERB
ejpam-5592	312	33	ϕ(z	ϕ(z	PROPN
ejpam-5592	312	34	,	,	PUNCT
ejpam-5592	312	35	ϱn−1(z	ϱn−1(z	PROPN
ejpam-5592	312	36	)	)	PUNCT
ejpam-5592	312	37	)	)	PUNCT
ejpam-5592	312	38	∣∣∣	∣∣∣	NOUN
ejpam-5592	313	1	=	=	PUNCT
ejpam-5592	313	2	sup	sup	NOUN
ejpam-5592	313	3	z∈ℑ	z∈ℑ	NUM
ejpam-5592	313	4	∣∣∣rlabℜϖu	∣∣∣rlabℜϖu	NOUN
ejpam-5592	313	5	,	,	PUNCT
ejpam-5592	313	6	ψκ	ψκ	VERB
ejpam-5592	314	1	[	[	X
ejpam-5592	314	2	ϕ(z	ϕ(z	PROPN
ejpam-5592	314	3	,	,	PUNCT
ejpam-5592	314	4	ϱn(z))−	ϱn(z))−	ADJ
ejpam-5592	314	5	ϕ(z	ϕ(z	NOUN
ejpam-5592	314	6	,	,	PUNCT
ejpam-5592	314	7	ϱn−1(z	ϱn−1(z	PROPN
ejpam-5592	314	8	)	)	PUNCT
ejpam-5592	314	9	)	)	PUNCT
ejpam-5592	314	10	]	]	PUNCT
ejpam-5592	314	11	∣∣∣	∣∣∣	NOUN
ejpam-5592	314	12	≤	≤	NUM
ejpam-5592	314	13	rlabℜϖu	rlabℜϖu	NOUN
ejpam-5592	314	14	,	,	PUNCT
ejpam-5592	314	15	ψκ	ψκ	INTJ
ejpam-5592	314	16	(	(	PUNCT
ejpam-5592	314	17	p	p	NOUN
ejpam-5592	314	18	∥ϱn(z)−	∥ϱn(z)−	ADJ
ejpam-5592	314	19	ϱn−1(z)∥	ϱn−1(z)∥	PROPN
ejpam-5592	314	20	)	)	PUNCT
ejpam-5592	314	21	≤	≤	NUM
ejpam-5592	314	22	rlabℜϖu	rlabℜϖu	NOUN
ejpam-5592	314	23	,	,	PUNCT
ejpam-5592	314	24	ψκ	ψκ	INTJ
ejpam-5592	314	25	(	(	PUNCT
ejpam-5592	314	26	tpn	tpn	PROPN
ejpam-5592	314	27	(	(	PUNCT
ejpam-5592	314	28	(	(	PUNCT
ejpam-5592	314	29	k	k	X
ejpam-5592	314	30	+	+	NOUN
ejpam-5592	314	31	1−ϖu	1−ϖu	NUM
ejpam-5592	314	32	)	)	PUNCT
ejpam-5592	314	33	(	(	PUNCT
ejpam-5592	314	34	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	314	35	ψ(κ))k	ψ(κ))k	PROPN
ejpam-5592	314	36	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	314	37	−	−	PROPN
ejpam-5592	314	38	k)γ(k	k)γ(k	NOUN
ejpam-5592	314	39	+	+	CCONJ
ejpam-5592	314	40	1	1	NUM
ejpam-5592	314	41	)	)	PUNCT
ejpam-5592	314	42	+	+	CCONJ
ejpam-5592	314	43	(	(	PUNCT
ejpam-5592	314	44	ϖu	ϖu	PROPN
ejpam-5592	314	45	−	−	PROPN
ejpam-5592	314	46	k	k	NOUN
ejpam-5592	314	47	)	)	PUNCT
ejpam-5592	314	48	(	(	PUNCT
ejpam-5592	314	49	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	314	50	ψ(κ))ϖu	ψ(κ))ϖu	NOUN
ejpam-5592	314	51	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	314	52	−	−	PROPN
ejpam-5592	314	53	k)γ(ϖu	k)γ(ϖu	PUNCT
ejpam-5592	314	54	+	+	NOUN
ejpam-5592	314	55	1	1	NUM
ejpam-5592	314	56	)	)	PUNCT
ejpam-5592	314	57	)	)	PUNCT
ejpam-5592	314	58	n	n	CCONJ
ejpam-5592	314	59	)	)	PUNCT
ejpam-5592	314	60	≤	≤	NOUN
ejpam-5592	314	61	tp	tp	PART
ejpam-5592	314	62	(	(	PUNCT
ejpam-5592	314	63	s+1)−1	s+1)−1	X
ejpam-5592	314	64	(	(	PUNCT
ejpam-5592	314	65	(	(	PUNCT
ejpam-5592	314	66	k	k	X
ejpam-5592	314	67	+	+	NOUN
ejpam-5592	314	68	1−ϖu	1−ϖu	NUM
ejpam-5592	314	69	)	)	PUNCT
ejpam-5592	314	70	(	(	PUNCT
ejpam-5592	314	71	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	314	72	ψ(κ))k	ψ(κ))k	PROPN
ejpam-5592	314	73	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	314	74	−	−	PROPN
ejpam-5592	314	75	k)γ(k	k)γ(k	NOUN
ejpam-5592	314	76	+	+	CCONJ
ejpam-5592	314	77	1	1	NUM
ejpam-5592	314	78	)	)	PUNCT
ejpam-5592	314	79	+	+	CCONJ
ejpam-5592	314	80	(	(	PUNCT
ejpam-5592	314	81	ϖu	ϖu	PROPN
ejpam-5592	314	82	−	−	PROPN
ejpam-5592	314	83	k	k	NOUN
ejpam-5592	314	84	)	)	PUNCT
ejpam-5592	314	85	(	(	PUNCT
ejpam-5592	314	86	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	314	87	ψ(κ))ϖu	ψ(κ))ϖu	NOUN
ejpam-5592	314	88	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	314	89	−	−	PROPN
ejpam-5592	314	90	k)γ(ϖu	k)γ(ϖu	PUNCT
ejpam-5592	314	91	+	+	NOUN
ejpam-5592	314	92	1	1	NUM
ejpam-5592	314	93	)	)	PUNCT
ejpam-5592	314	94	)	)	PUNCT
ejpam-5592	315	1	n+1	n+1	X
ejpam-5592	315	2	.	.	PUNCT
ejpam-5592	316	1	hence	hence	ADV
ejpam-5592	316	2	,	,	PUNCT
ejpam-5592	316	3	the	the	DET
ejpam-5592	316	4	inequality	inequality	NOUN
ejpam-5592	316	5	(	(	PUNCT
ejpam-5592	316	6	7	7	NUM
ejpam-5592	316	7	)	)	PUNCT
ejpam-5592	316	8	is	be	AUX
ejpam-5592	316	9	fulfilled	fulfil	VERB
ejpam-5592	316	10	for	for	ADP
ejpam-5592	316	11	s	s	NOUN
ejpam-5592	316	12	=	=	SYM
ejpam-5592	316	13	n	n	PROPN
ejpam-5592	316	14	+	+	NOUN
ejpam-5592	316	15	1	1	NUM
ejpam-5592	316	16	.	.	X
ejpam-5592	316	17	then	then	ADV
ejpam-5592	316	18	inequality	inequality	NOUN
ejpam-5592	316	19	(	(	PUNCT
ejpam-5592	316	20	7	7	NUM
ejpam-5592	316	21	)	)	PUNCT
ejpam-5592	316	22	is	be	AUX
ejpam-5592	316	23	true	true	ADJ
ejpam-5592	316	24	for	for	ADP
ejpam-5592	316	25	every	every	DET
ejpam-5592	316	26	s	s	PART
ejpam-5592	316	27	∈	∈	PROPN
ejpam-5592	316	28	n	n	NOUN
ejpam-5592	316	29	and	and	CCONJ
ejpam-5592	316	30	all	all	DET
ejpam-5592	316	31	z	z	NOUN
ejpam-5592	316	32	∈	∈	PROPN
ejpam-5592	317	1	[	[	X
ejpam-5592	317	2	κ	κ	NOUN
ejpam-5592	317	3	,	,	PUNCT
ejpam-5592	317	4	υ	υ	NOUN
ejpam-5592	317	5	]	]	X
ejpam-5592	317	6	.	.	PUNCT
ejpam-5592	318	1	thus	thus	ADV
ejpam-5592	318	2	,	,	PUNCT
ejpam-5592	318	3	one	one	PRON
ejpam-5592	318	4	can	can	AUX
ejpam-5592	318	5	write	write	VERB
ejpam-5592	318	6	∞∑	∞∑	NUM
ejpam-5592	318	7	s=1	s=1	X
ejpam-5592	318	8	∥ϱs	∥ϱs	ADV
ejpam-5592	318	9	(	(	PUNCT
ejpam-5592	318	10	z)−	z)−	PROPN
ejpam-5592	318	11	ϱs−1	ϱs−1	PROPN
ejpam-5592	318	12	(	(	PUNCT
ejpam-5592	318	13	z)∥	z)∥	NUM
ejpam-5592	318	14	≤	≤	NOUN
ejpam-5592	319	1	∞∑	∞∑	NUM
ejpam-5592	319	2	s=1	s=1	PUNCT
ejpam-5592	319	3	tp	tp	ADP
ejpam-5592	319	4	s−1	s−1	PROPN
ejpam-5592	319	5	(	(	PUNCT
ejpam-5592	319	6	(	(	PUNCT
ejpam-5592	319	7	k	k	X
ejpam-5592	319	8	+	+	NOUN
ejpam-5592	319	9	1−ϖu	1−ϖu	NUM
ejpam-5592	319	10	)	)	PUNCT
ejpam-5592	319	11	(	(	PUNCT
ejpam-5592	319	12	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	319	13	ψ(κ))k	ψ(κ))k	PROPN
ejpam-5592	319	14	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	319	15	−	−	PROPN
ejpam-5592	319	16	k)γ(k	k)γ(k	NOUN
ejpam-5592	319	17	+	+	CCONJ
ejpam-5592	319	18	1	1	NUM
ejpam-5592	319	19	)	)	PUNCT
ejpam-5592	319	20	+	+	CCONJ
ejpam-5592	319	21	(	(	PUNCT
ejpam-5592	319	22	ϖu	ϖu	PROPN
ejpam-5592	319	23	−	−	PROPN
ejpam-5592	319	24	k	k	NOUN
ejpam-5592	319	25	)	)	PUNCT
ejpam-5592	319	26	(	(	PUNCT
ejpam-5592	319	27	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	319	28	ψ(κ))ϖu	ψ(κ))ϖu	NOUN
ejpam-5592	319	29	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	319	30	−	−	PROPN
ejpam-5592	319	31	k)γ(ϖu	k)γ(ϖu	PUNCT
ejpam-5592	319	32	+	+	NOUN
ejpam-5592	319	33	1	1	NUM
ejpam-5592	319	34	)	)	PUNCT
ejpam-5592	319	35	)	)	PUNCT
ejpam-5592	319	36	s	s	X
ejpam-5592	319	37	.	.	PUNCT
ejpam-5592	320	1	the	the	DET
ejpam-5592	320	2	series	series	NOUN
ejpam-5592	320	3	on	on	ADP
ejpam-5592	320	4	the	the	DET
ejpam-5592	320	5	right	right	ADJ
ejpam-5592	320	6	side	side	NOUN
ejpam-5592	320	7	of	of	ADP
ejpam-5592	320	8	the	the	DET
ejpam-5592	320	9	aforementioned	aforementioned	ADJ
ejpam-5592	320	10	inequality	inequality	NOUN
ejpam-5592	320	11	is	be	AUX
ejpam-5592	320	12	convergent	convergent	ADJ
ejpam-5592	320	13	as	as	ADP
ejpam-5592	320	14	a	a	DET
ejpam-5592	320	15	result	result	NOUN
ejpam-5592	320	16	of	of	ADP
ejpam-5592	320	17	assumption	assumption	NOUN
ejpam-5592	320	18	(	(	PUNCT
ejpam-5592	320	19	4	4	NUM
ejpam-5592	320	20	)	)	PUNCT
ejpam-5592	320	21	,	,	PUNCT
ejpam-5592	320	22	and	and	CCONJ
ejpam-5592	320	23	so	so	ADV
ejpam-5592	320	24	∞∑	∞∑	NUM
ejpam-5592	320	25	s=1	s=1	NOUN
ejpam-5592	320	26	∥ϱs	∥ϱs	NOUN
ejpam-5592	320	27	−	−	NOUN
ejpam-5592	320	28	ϱs−1∥	ϱs−1∥	NOUN
ejpam-5592	320	29	is	be	AUX
ejpam-5592	320	30	also	also	ADV
ejpam-5592	320	31	convergent	convergent	ADJ
ejpam-5592	320	32	that	that	PRON
ejpam-5592	320	33	shows	show	VERB
ejpam-5592	320	34	that	that	SCONJ
ejpam-5592	320	35	ϱ0	ϱ0	NOUN
ejpam-5592	320	36	+	+	X
ejpam-5592	320	37	∞∑	∞∑	NUM
ejpam-5592	321	1	s=1	s=1	AUX
ejpam-5592	321	2	∥ϱs	∥ϱs	NOUN
ejpam-5592	321	3	−	−	PRON
ejpam-5592	321	4	ϱs−1∥	ϱs−1∥	NOUN
ejpam-5592	321	5	converges	converge	VERB
ejpam-5592	321	6	.	.	PUNCT
ejpam-5592	322	1	put	put	VERB
ejpam-5592	322	2	ϱ	ϱ	NOUN
ejpam-5592	322	3	=	=	X
ejpam-5592	322	4	ϱ0	ϱ0	NOUN
ejpam-5592	322	5	+	+	CCONJ
ejpam-5592	322	6	∞∑	∞∑	NUM
ejpam-5592	322	7	s=1	s=1	X
ejpam-5592	322	8	∥ϱs	∥ϱs	NOUN
ejpam-5592	322	9	−	−	PROPN
ejpam-5592	322	10	ϱs−1∥	ϱs−1∥	NOUN
ejpam-5592	322	11	,	,	PUNCT
ejpam-5592	322	12	it	it	PRON
ejpam-5592	322	13	follows	follow	VERB
ejpam-5592	322	14	that	that	SCONJ
ejpam-5592	322	15	∥ϱs	∥ϱs	NOUN
ejpam-5592	322	16	−	−	PROPN
ejpam-5592	322	17	ϱ∥	ϱ∥	NOUN
ejpam-5592	322	18	→	→	SYM
ejpam-5592	322	19	0	0	NUM
ejpam-5592	322	20	,	,	PUNCT
ejpam-5592	322	21	as	as	SCONJ
ejpam-5592	322	22	s→	s→	PROPN
ejpam-5592	322	23	∞.	∞.	PROPN
ejpam-5592	322	24	(	(	PUNCT
ejpam-5592	322	25	8)	8)	NUM
ejpam-5592	322	26	this	this	PRON
ejpam-5592	322	27	indicates	indicate	VERB
ejpam-5592	322	28	that	that	SCONJ
ejpam-5592	322	29	the	the	DET
ejpam-5592	322	30	solution	solution	NOUN
ejpam-5592	322	31	to	to	ADP
ejpam-5592	322	32	problem	problem	NOUN
ejpam-5592	322	33	(	(	PUNCT
ejpam-5592	322	34	2	2	X
ejpam-5592	322	35	)	)	PUNCT
ejpam-5592	322	36	exists	exist	VERB
ejpam-5592	322	37	.	.	PUNCT
ejpam-5592	323	1	from	from	ADP
ejpam-5592	323	2	(	(	PUNCT
ejpam-5592	323	3	8)	8)	NUM
ejpam-5592	323	4	,	,	PUNCT
ejpam-5592	323	5	we	we	PRON
ejpam-5592	323	6	get	get	VERB
ejpam-5592	323	7	∥ϕ	∥ϕ	PROPN
ejpam-5592	323	8	(	(	PUNCT
ejpam-5592	323	9	.	.	PUNCT
ejpam-5592	323	10	,	,	PUNCT
ejpam-5592	323	11	ϱs−1(.))−	ϱs−1(.))−	ADP
ejpam-5592	323	12	ϕ	ϕ	NOUN
ejpam-5592	323	13	(	(	PUNCT
ejpam-5592	323	14	.	.	PUNCT
ejpam-5592	323	15	,	,	PUNCT
ejpam-5592	323	16	ϱ(.))∥	ϱ(.))∥	VERB
ejpam-5592	323	17	≤	≤	ADJ
ejpam-5592	323	18	p	p	NOUN
ejpam-5592	323	19	|ϱs−1	|ϱs−1	X
ejpam-5592	323	20	−	−	PROPN
ejpam-5592	323	21	ϱ|	ϱ|	PROPN
ejpam-5592	323	22	→	→	SYM
ejpam-5592	323	23	0	0	NUM
ejpam-5592	323	24	,	,	PUNCT
ejpam-5592	323	25	as	as	ADP
ejpam-5592	323	26	s→	s→	PROPN
ejpam-5592	323	27	∞.	∞.	PROPN
ejpam-5592	323	28	h.a	h.a	PROPN
ejpam-5592	323	29	.	.	PROPN
ejpam-5592	323	30	hammad	hammad	PROPN
ejpam-5592	323	31	,	,	PUNCT
ejpam-5592	323	32	m.	m.	PROPN
ejpam-5592	323	33	de	de	X
ejpam-5592	323	34	la	la	PROPN
ejpam-5592	323	35	sen	sen	PROPN
ejpam-5592	323	36	/	/	SYM
ejpam-5592	323	37	eur	eur	PROPN
ejpam-5592	323	38	.	.	PUNCT
ejpam-5592	324	1	j.	j.	PROPN
ejpam-5592	324	2	pure	pure	PROPN
ejpam-5592	324	3	appl	appl	PROPN
ejpam-5592	324	4	.	.	PROPN
ejpam-5592	324	5	math	math	PROPN
ejpam-5592	324	6	,	,	PUNCT
ejpam-5592	324	7	17	17	NUM
ejpam-5592	324	8	(	(	PUNCT
ejpam-5592	324	9	4	4	NUM
ejpam-5592	324	10	)	)	PUNCT
ejpam-5592	324	11	(	(	PUNCT
ejpam-5592	324	12	2024	2024	NUM
ejpam-5592	324	13	)	)	PUNCT
ejpam-5592	324	14	,	,	PUNCT
ejpam-5592	324	15	3687	3687	NUM
ejpam-5592	324	16	-	-	SYM
ejpam-5592	324	17	3707	3707	NUM
ejpam-5592	324	18	3702	3702	NUM
ejpam-5592	324	19	thus	thus	ADV
ejpam-5592	324	20	,	,	PUNCT
ejpam-5592	324	21	lim	lim	PROPN
ejpam-5592	324	22	s→∞	s→∞	PROPN
ejpam-5592	324	23	ϕ(z	ϕ(z	PROPN
ejpam-5592	324	24	,	,	PUNCT
ejpam-5592	324	25	ϱs−1(z	ϱs−1(z	NOUN
ejpam-5592	324	26	)	)	PUNCT
ejpam-5592	324	27	)	)	PUNCT
ejpam-5592	325	1	=	=	SYM
ejpam-5592	325	2	ϕ(z	ϕ(z	NOUN
ejpam-5592	325	3	,	,	PUNCT
ejpam-5592	325	4	ϱ(z	ϱ(z	PROPN
ejpam-5592	325	5	)	)	PUNCT
ejpam-5592	325	6	)	)	PUNCT
ejpam-5592	325	7	.	.	PUNCT
ejpam-5592	326	1	(	(	PUNCT
ejpam-5592	326	2	9	9	X
ejpam-5592	326	3	)	)	PUNCT
ejpam-5592	326	4	as	as	ADP
ejpam-5592	326	5	s→	s→	NOUN
ejpam-5592	326	6	∞	∞	PROPN
ejpam-5592	326	7	in	in	ADP
ejpam-5592	326	8	(	(	PUNCT
ejpam-5592	326	9	6	6	NUM
ejpam-5592	326	10	)	)	PUNCT
ejpam-5592	326	11	and	and	CCONJ
ejpam-5592	326	12	applying	apply	VERB
ejpam-5592	326	13	(	(	PUNCT
ejpam-5592	326	14	9	9	NUM
ejpam-5592	326	15	)	)	PUNCT
ejpam-5592	326	16	,	,	PUNCT
ejpam-5592	326	17	we	we	PRON
ejpam-5592	326	18	have	have	VERB
ejpam-5592	326	19	ϱ	ϱ	X
ejpam-5592	326	20	(	(	PUNCT
ejpam-5592	326	21	z	z	NOUN
ejpam-5592	326	22	)	)	PUNCT
ejpam-5592	326	23	=	=	SYM
ejpam-5592	326	24	k∑	k∑	PROPN
ejpam-5592	327	1	i=0	i=0	PROPN
ejpam-5592	327	2	γi	γi	X
ejpam-5592	328	1	i	i	PRON
ejpam-5592	328	2	!	!	PUNCT
ejpam-5592	329	1	(	(	PUNCT
ejpam-5592	329	2	ψ(z)−	ψ(z)−	PROPN
ejpam-5592	329	3	ψ(κ))i	ψ(κ))i	PROPN
ejpam-5592	329	4	+	+	PROPN
ejpam-5592	329	5	rlab	rlab	NOUN
ejpam-5592	329	6	ℜϖu	ℜϖu	PROPN
ejpam-5592	329	7	,	,	PUNCT
ejpam-5592	329	8	ψκ	ψκ	VERB
ejpam-5592	329	9	ϕ(z	ϕ(z	PROPN
ejpam-5592	329	10	,	,	PUNCT
ejpam-5592	329	11	ϱ(z	ϱ(z	PROPN
ejpam-5592	329	12	)	)	PUNCT
ejpam-5592	329	13	)	)	PUNCT
ejpam-5592	329	14	,	,	PUNCT
ejpam-5592	329	15	which	which	PRON
ejpam-5592	329	16	is	be	AUX
ejpam-5592	329	17	a	a	DET
ejpam-5592	329	18	solution	solution	NOUN
ejpam-5592	329	19	of	of	ADP
ejpam-5592	329	20	the	the	DET
ejpam-5592	329	21	initial	initial	ADJ
ejpam-5592	329	22	fde	fde	NOUN
ejpam-5592	329	23	(	(	PUNCT
ejpam-5592	329	24	2	2	NUM
ejpam-5592	329	25	)	)	PUNCT
ejpam-5592	329	26	.	.	PUNCT
ejpam-5592	330	1	finally	finally	ADV
ejpam-5592	330	2	,	,	PUNCT
ejpam-5592	330	3	for	for	ADP
ejpam-5592	330	4	the	the	DET
ejpam-5592	330	5	uniqueness	uniqueness	NOUN
ejpam-5592	330	6	,	,	PUNCT
ejpam-5592	330	7	assume	assume	VERB
ejpam-5592	330	8	that	that	SCONJ
ejpam-5592	330	9	ϱ̂	ϱ̂	NUM
ejpam-5592	330	10	is	be	AUX
ejpam-5592	330	11	another	another	DET
ejpam-5592	330	12	solution	solution	NOUN
ejpam-5592	330	13	to	to	ADP
ejpam-5592	330	14	problem	problem	NOUN
ejpam-5592	330	15	(	(	PUNCT
ejpam-5592	330	16	2	2	NUM
ejpam-5592	330	17	)	)	PUNCT
ejpam-5592	330	18	.	.	PUNCT
ejpam-5592	331	1	thus	thus	ADV
ejpam-5592	331	2	,	,	PUNCT
ejpam-5592	331	3	we	we	PRON
ejpam-5592	331	4	get	get	VERB
ejpam-5592	331	5	∥ϱ−	∥ϱ−	PRON
ejpam-5592	331	6	ϱ̂∥	ϱ̂∥	NOUN
ejpam-5592	331	7	=	=	SYM
ejpam-5592	331	8	sup	sup	NOUN
ejpam-5592	331	9	z∈ℑ	z∈ℑ	NUM
ejpam-5592	331	10	∣∣∣rlabℜϖu	∣∣∣rlabℜϖu	NUM
ejpam-5592	331	11	,	,	PUNCT
ejpam-5592	331	12	ψκ	ψκ	PART
ejpam-5592	331	13	ϕ(z	ϕ(z	NOUN
ejpam-5592	331	14	,	,	PUNCT
ejpam-5592	331	15	ϱ(z))−rlab	ϱ(z))−rlab	VERB
ejpam-5592	332	1	ℜϖu	ℜϖu	PROPN
ejpam-5592	332	2	,	,	PUNCT
ejpam-5592	332	3	ψκ	ψκ	VERB
ejpam-5592	332	4	ϕ(z	ϕ(z	NOUN
ejpam-5592	332	5	,	,	PUNCT
ejpam-5592	332	6	ϱ̂(z	ϱ̂(z	NOUN
ejpam-5592	332	7	)	)	PUNCT
ejpam-5592	332	8	)	)	PUNCT
ejpam-5592	332	9	∣∣∣	∣∣∣	NOUN
ejpam-5592	332	10	=	=	SYM
ejpam-5592	332	11	sup	sup	NOUN
ejpam-5592	332	12	z∈ℑ	z∈ℑ	NUM
ejpam-5592	332	13	∣∣∣rlabℜϖu	∣∣∣rlabℜϖu	NOUN
ejpam-5592	332	14	,	,	PUNCT
ejpam-5592	332	15	ψκ	ψκ	VERB
ejpam-5592	333	1	[	[	X
ejpam-5592	333	2	ϕ(z	ϕ(z	PROPN
ejpam-5592	333	3	,	,	PUNCT
ejpam-5592	333	4	ϱ(z))−	ϱ(z))−	ADJ
ejpam-5592	333	5	ϕ(z	ϕ(z	NOUN
ejpam-5592	333	6	,	,	PUNCT
ejpam-5592	333	7	ϱ̂(z	ϱ̂(z	NOUN
ejpam-5592	333	8	)	)	PUNCT
ejpam-5592	333	9	)	)	PUNCT
ejpam-5592	333	10	]	]	PUNCT
ejpam-5592	333	11	∣∣∣	∣∣∣	NOUN
ejpam-5592	333	12	≤	≤	NUM
ejpam-5592	333	13	rlabℜϖu	rlabℜϖu	NOUN
ejpam-5592	333	14	,	,	PUNCT
ejpam-5592	333	15	ψκ	ψκ	INTJ
ejpam-5592	333	16	(	(	PUNCT
ejpam-5592	333	17	p	p	NOUN
ejpam-5592	333	18	∥ϱ(z)−	∥ϱ(z)−	PUNCT
ejpam-5592	333	19	ϱ̂(z)∥	ϱ̂(z)∥	PROPN
ejpam-5592	333	20	)	)	PUNCT
ejpam-5592	333	21	≤	≤	NOUN
ejpam-5592	333	22	p	p	NOUN
ejpam-5592	333	23	(	(	PUNCT
ejpam-5592	333	24	(	(	PUNCT
ejpam-5592	333	25	k	k	X
ejpam-5592	333	26	+	+	NOUN
ejpam-5592	333	27	1−ϖu	1−ϖu	NUM
ejpam-5592	333	28	)	)	PUNCT
ejpam-5592	333	29	(	(	PUNCT
ejpam-5592	333	30	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	333	31	ψ(κ))k	ψ(κ))k	PROPN
ejpam-5592	333	32	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	333	33	−	−	PROPN
ejpam-5592	333	34	k)γ(k	k)γ(k	NOUN
ejpam-5592	333	35	+	+	CCONJ
ejpam-5592	333	36	1	1	NUM
ejpam-5592	333	37	)	)	PUNCT
ejpam-5592	333	38	+	+	CCONJ
ejpam-5592	333	39	(	(	PUNCT
ejpam-5592	333	40	ϖu	ϖu	PROPN
ejpam-5592	333	41	−	−	PROPN
ejpam-5592	333	42	k	k	NOUN
ejpam-5592	333	43	)	)	PUNCT
ejpam-5592	333	44	(	(	PUNCT
ejpam-5592	333	45	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	333	46	ψ(κ))ϖu	ψ(κ))ϖu	NOUN
ejpam-5592	333	47	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	333	48	−	−	PROPN
ejpam-5592	333	49	k)γ(ϖu	k)γ(ϖu	PUNCT
ejpam-5592	333	50	+	+	NOUN
ejpam-5592	333	51	1	1	NUM
ejpam-5592	333	52	)	)	PUNCT
ejpam-5592	333	53	)	)	PUNCT
ejpam-5592	334	1	∥ϱ−	∥ϱ−	PROPN
ejpam-5592	334	2	ϱ̂∥	ϱ̂∥	NOUN
ejpam-5592	334	3	.	.	PUNCT
ejpam-5592	335	1	in	in	ADP
ejpam-5592	335	2	light	light	NOUN
ejpam-5592	335	3	of	of	ADP
ejpam-5592	335	4	(	(	PUNCT
ejpam-5592	335	5	4	4	NUM
ejpam-5592	335	6	)	)	PUNCT
ejpam-5592	335	7	,	,	PUNCT
ejpam-5592	335	8	we	we	PRON
ejpam-5592	335	9	conclude	conclude	VERB
ejpam-5592	335	10	that	that	SCONJ
ejpam-5592	335	11	∥ϱ−	∥ϱ−	PROPN
ejpam-5592	335	12	ϱ̂∥	ϱ̂∥	NOUN
ejpam-5592	335	13	,	,	PUNCT
ejpam-5592	335	14	that	that	ADV
ejpam-5592	335	15	is	is	ADV
ejpam-5592	335	16	,	,	PUNCT
ejpam-5592	335	17	ϱ(z	ϱ(z	PROPN
ejpam-5592	335	18	)	)	PUNCT
ejpam-5592	335	19	=	=	PUNCT
ejpam-5592	335	20	ϱ̂(z	ϱ̂(z	NUM
ejpam-5592	335	21	)	)	PUNCT
ejpam-5592	335	22	.	.	PUNCT
ejpam-5592	336	1	this	this	PRON
ejpam-5592	336	2	completes	complete	VERB
ejpam-5592	336	3	the	the	DET
ejpam-5592	336	4	proof	proof	NOUN
ejpam-5592	336	5	.	.	PUNCT
ejpam-5592	337	1	6	6	X
ejpam-5592	337	2	.	.	X
ejpam-5592	337	3	supportive	supportive	ADJ
ejpam-5592	337	4	examples	example	NOUN
ejpam-5592	337	5	in	in	ADP
ejpam-5592	337	6	this	this	DET
ejpam-5592	337	7	part	part	NOUN
ejpam-5592	337	8	,	,	PUNCT
ejpam-5592	337	9	we	we	PRON
ejpam-5592	337	10	support	support	VERB
ejpam-5592	337	11	our	our	PRON
ejpam-5592	337	12	results	result	NOUN
ejpam-5592	337	13	by	by	ADP
ejpam-5592	337	14	the	the	DET
ejpam-5592	337	15	following	following	ADJ
ejpam-5592	337	16	examples	example	NOUN
ejpam-5592	337	17	:	:	PUNCT
ejpam-5592	337	18	example	example	NOUN
ejpam-5592	337	19	1	1	X
ejpam-5592	337	20	.	.	X
ejpam-5592	337	21	consider	consider	VERB
ejpam-5592	337	22	the	the	DET
ejpam-5592	337	23	following	following	ADJ
ejpam-5592	337	24	initial	initial	ADJ
ejpam-5592	337	25	fde	fde	NOUN
ejpam-5592	337	26	:	:	PUNCT
ejpam-5592	337	27	{	{	PUNCT
ejpam-5592	337	28	cabdϖu	cabdϖu	PROPN
ejpam-5592	337	29	,	,	PUNCT
ejpam-5592	337	30	ψ	ψ	PROPN
ejpam-5592	337	31	1	1	NUM
ejpam-5592	337	32	ϱ(z	ϱ(z	NOUN
ejpam-5592	337	33	)	)	PUNCT
ejpam-5592	337	34	=	=	SYM
ejpam-5592	337	35	cos	cos	PROPN
ejpam-5592	337	36	(	(	PUNCT
ejpam-5592	337	37	z2	z2	PROPN
ejpam-5592	337	38	)	)	PUNCT
ejpam-5592	337	39	−	−	PROPN
ejpam-5592	337	40	ϱ(z	ϱ(z	NOUN
ejpam-5592	337	41	)	)	PUNCT
ejpam-5592	337	42	1	1	NUM
ejpam-5592	337	43	4	4	NUM
ejpam-5592	337	44	−ϱ(z	−ϱ(z	NOUN
ejpam-5592	337	45	)	)	PUNCT
ejpam-5592	337	46	,	,	PUNCT
ejpam-5592	337	47	z	z	NOUN
ejpam-5592	337	48	∈	∈	PROPN
ejpam-5592	338	1	[	[	X
ejpam-5592	338	2	1	1	NUM
ejpam-5592	338	3	,	,	PUNCT
ejpam-5592	338	4	3	3	NUM
ejpam-5592	338	5	]	]	PUNCT
ejpam-5592	338	6	,	,	PUNCT
ejpam-5592	338	7	ϱ(1	ϱ(1	NOUN
ejpam-5592	338	8	)	)	PUNCT
ejpam-5592	338	9	=	=	SYM
ejpam-5592	338	10	1	1	NUM
ejpam-5592	338	11	,	,	PUNCT
ejpam-5592	338	12	ϱ′ψ(1	ϱ′ψ(1	NUM
ejpam-5592	338	13	)	)	PUNCT
ejpam-5592	338	14	=	=	SYM
ejpam-5592	338	15	1	1	NUM
ejpam-5592	338	16	,	,	PUNCT
ejpam-5592	338	17	(	(	PUNCT
ejpam-5592	338	18	10	10	NUM
ejpam-5592	338	19	)	)	PUNCT
ejpam-5592	338	20	where	where	SCONJ
ejpam-5592	338	21	ψ(z	ψ(z	NOUN
ejpam-5592	338	22	)	)	PUNCT
ejpam-5592	338	23	=	=	PUNCT
ejpam-5592	338	24	ln(z	ln(z	X
ejpam-5592	338	25	)	)	PUNCT
ejpam-5592	338	26	and	and	CCONJ
ejpam-5592	338	27	ϖu(τ	ϖu(τ	NUM
ejpam-5592	338	28	)	)	PUNCT
ejpam-5592	338	29	=	=	NOUN
ejpam-5592	338	30	{	{	PUNCT
ejpam-5592	338	31	0.98	0.98	NUM
ejpam-5592	338	32	,	,	PUNCT
ejpam-5592	338	33	τ	τ	PROPN
ejpam-5592	338	34	∈	∈	PROPN
ejpam-5592	339	1	[	[	X
ejpam-5592	339	2	1	1	NUM
ejpam-5592	339	3	,	,	PUNCT
ejpam-5592	339	4	2	2	NUM
ejpam-5592	339	5	]	]	PUNCT
ejpam-5592	339	6	,	,	PUNCT
ejpam-5592	339	7	1.21	1.21	NUM
ejpam-5592	339	8	,	,	PUNCT
ejpam-5592	339	9	τ	τ	PROPN
ejpam-5592	339	10	∈	∈	PROPN
ejpam-5592	339	11	(	(	PUNCT
ejpam-5592	339	12	2	2	NUM
ejpam-5592	339	13	,	,	PUNCT
ejpam-5592	339	14	3	3	NUM
ejpam-5592	339	15	]	]	PUNCT
ejpam-5592	339	16	,	,	PUNCT
ejpam-5592	339	17	for	for	ADP
ejpam-5592	339	18	u	u	PRON
ejpam-5592	339	19	≥	≥	NUM
ejpam-5592	339	20	1	1	NUM
ejpam-5592	339	21	.	.	PUNCT
ejpam-5592	340	1	the	the	DET
ejpam-5592	340	2	requirements	requirement	NOUN
ejpam-5592	340	3	of	of	ADP
ejpam-5592	340	4	theorem	theorem	NOUN
ejpam-5592	340	5	1	1	NUM
ejpam-5592	340	6	shall	shall	AUX
ejpam-5592	340	7	be	be	AUX
ejpam-5592	340	8	examined	examine	VERB
ejpam-5592	340	9	as	as	SCONJ
ejpam-5592	340	10	follows	follow	VERB
ejpam-5592	340	11	:	:	PUNCT
ejpam-5592	340	12	|ϕ(z	|ϕ(z	NOUN
ejpam-5592	340	13	,	,	PUNCT
ejpam-5592	340	14	ϱ1)−	ϱ1)−	NOUN
ejpam-5592	340	15	ϕ(z	ϕ(z	NOUN
ejpam-5592	340	16	,	,	PUNCT
ejpam-5592	340	17	ϱ2)|	ϱ2)|	NOUN
ejpam-5592	340	18	=	=	SYM
ejpam-5592	340	19	∣∣∣∣∣cos	∣∣∣∣∣cos	X
ejpam-5592	340	20	(	(	PUNCT
ejpam-5592	340	21	z2)−	z2)−	PROPN
ejpam-5592	340	22	ϱ1(z	ϱ1(z	PROPN
ejpam-5592	340	23	)	)	PUNCT
ejpam-5592	340	24	1	1	NUM
ejpam-5592	340	25	4	4	NUM
ejpam-5592	340	26	−	−	NOUN
ejpam-5592	340	27	ϱ1(z	ϱ1(z	NUM
ejpam-5592	340	28	)	)	PUNCT
ejpam-5592	340	29	−	−	PROPN
ejpam-5592	340	30	cos	cos	PROPN
ejpam-5592	340	31	(	(	PUNCT
ejpam-5592	340	32	z2	z2	PROPN
ejpam-5592	340	33	)	)	PUNCT
ejpam-5592	341	1	+	+	CCONJ
ejpam-5592	341	2	ϱ2(z	ϱ2(z	X
ejpam-5592	341	3	)	)	PUNCT
ejpam-5592	341	4	1	1	NUM
ejpam-5592	341	5	4	4	NUM
ejpam-5592	341	6	−	−	PROPN
ejpam-5592	341	7	ϱ(z	ϱ(z	NOUN
ejpam-5592	341	8	)	)	PUNCT
ejpam-5592	341	9	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5592	341	10	=	=	SYM
ejpam-5592	342	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5592	342	2	ϱ1(z	ϱ1(z	PROPN
ejpam-5592	342	3	)	)	PUNCT
ejpam-5592	342	4	1	1	NUM
ejpam-5592	342	5	4	4	NUM
ejpam-5592	342	6	−	−	NOUN
ejpam-5592	342	7	ϱ1(z	ϱ1(z	NUM
ejpam-5592	342	8	)	)	PUNCT
ejpam-5592	342	9	−	−	NOUN
ejpam-5592	342	10	ϱ2(z	ϱ2(z	NOUN
ejpam-5592	342	11	)	)	PUNCT
ejpam-5592	342	12	1	1	NUM
ejpam-5592	342	13	4	4	NUM
ejpam-5592	342	14	−	−	PROPN
ejpam-5592	342	15	ϱ(z	ϱ(z	PROPN
ejpam-5592	342	16	)	)	PUNCT
ejpam-5592	342	17	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5592	343	1	≤	≤	ADV
ejpam-5592	343	2	1	1	NUM
ejpam-5592	343	3	4	4	NUM
ejpam-5592	343	4	|ϱ1(z)−	|ϱ1(z)−	NOUN
ejpam-5592	343	5	ϱ2(z)|	ϱ2(z)|	NOUN
ejpam-5592	343	6	.	.	PUNCT
ejpam-5592	344	1	then	then	ADV
ejpam-5592	344	2	,	,	PUNCT
ejpam-5592	344	3	p	p	NOUN
ejpam-5592	344	4	=	=	NOUN
ejpam-5592	344	5	1	1	NUM
ejpam-5592	344	6	4	4	NUM
ejpam-5592	344	7	>	>	SYM
ejpam-5592	344	8	0	0	NUM
ejpam-5592	344	9	.	.	PUNCT
ejpam-5592	345	1	if	if	SCONJ
ejpam-5592	345	2	we	we	PRON
ejpam-5592	345	3	take	take	VERB
ejpam-5592	345	4	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	345	5	−	−	PROPN
ejpam-5592	345	6	k	k	X
ejpam-5592	345	7	)	)	PUNCT
ejpam-5592	345	8	=	=	SYM
ejpam-5592	345	9	1	1	NUM
ejpam-5592	345	10	,	,	PUNCT
ejpam-5592	345	11	then	then	ADV
ejpam-5592	345	12	,	,	PUNCT
ejpam-5592	345	13	we	we	PRON
ejpam-5592	345	14	have	have	VERB
ejpam-5592	345	15	the	the	DET
ejpam-5592	345	16	following	follow	VERB
ejpam-5592	345	17	cases	case	NOUN
ejpam-5592	345	18	:	:	PUNCT
ejpam-5592	345	19	h.a	h.a	PROPN
ejpam-5592	345	20	.	.	PROPN
ejpam-5592	345	21	hammad	hammad	PROPN
ejpam-5592	345	22	,	,	PUNCT
ejpam-5592	345	23	m.	m.	PROPN
ejpam-5592	345	24	de	de	X
ejpam-5592	345	25	la	la	PROPN
ejpam-5592	345	26	sen	sen	PROPN
ejpam-5592	345	27	/	/	SYM
ejpam-5592	345	28	eur	eur	PROPN
ejpam-5592	345	29	.	.	PUNCT
ejpam-5592	346	1	j.	j.	PROPN
ejpam-5592	346	2	pure	pure	PROPN
ejpam-5592	346	3	appl	appl	PROPN
ejpam-5592	346	4	.	.	PROPN
ejpam-5592	346	5	math	math	PROPN
ejpam-5592	346	6	,	,	PUNCT
ejpam-5592	346	7	17	17	NUM
ejpam-5592	346	8	(	(	PUNCT
ejpam-5592	346	9	4	4	NUM
ejpam-5592	346	10	)	)	PUNCT
ejpam-5592	346	11	(	(	PUNCT
ejpam-5592	346	12	2024	2024	NUM
ejpam-5592	346	13	)	)	PUNCT
ejpam-5592	346	14	,	,	PUNCT
ejpam-5592	346	15	3687	3687	NUM
ejpam-5592	346	16	-	-	SYM
ejpam-5592	346	17	3707	3707	NUM
ejpam-5592	346	18	3703	3703	NUM
ejpam-5592	346	19	(	(	PUNCT
ejpam-5592	346	20	a	a	X
ejpam-5592	346	21	)	)	PUNCT
ejpam-5592	346	22	if	if	SCONJ
ejpam-5592	346	23	τ	τ	PROPN
ejpam-5592	346	24	∈	∈	PROPN
ejpam-5592	347	1	[	[	X
ejpam-5592	347	2	1	1	NUM
ejpam-5592	347	3	,	,	PUNCT
ejpam-5592	347	4	2	2	NUM
ejpam-5592	347	5	]	]	PUNCT
ejpam-5592	347	6	,	,	PUNCT
ejpam-5592	347	7	one	one	PRON
ejpam-5592	347	8	has	have	VERB
ejpam-5592	347	9	k	k	NOUN
ejpam-5592	347	10	=	=	SYM
ejpam-5592	347	11	1	1	NUM
ejpam-5592	347	12	,	,	PUNCT
ejpam-5592	347	13	and	and	CCONJ
ejpam-5592	347	14	p	p	X
ejpam-5592	347	15	(	(	PUNCT
ejpam-5592	347	16	(	(	PUNCT
ejpam-5592	347	17	k	k	X
ejpam-5592	347	18	+	+	NOUN
ejpam-5592	347	19	1−ϖu	1−ϖu	NUM
ejpam-5592	347	20	)	)	PUNCT
ejpam-5592	347	21	(	(	PUNCT
ejpam-5592	347	22	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	347	23	ψ(κ))k	ψ(κ))k	PROPN
ejpam-5592	347	24	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	347	25	−	−	PROPN
ejpam-5592	347	26	k)γ(k	k)γ(k	NOUN
ejpam-5592	347	27	+	+	CCONJ
ejpam-5592	347	28	1	1	NUM
ejpam-5592	347	29	)	)	PUNCT
ejpam-5592	347	30	+	+	CCONJ
ejpam-5592	347	31	(	(	PUNCT
ejpam-5592	347	32	ϖu	ϖu	PROPN
ejpam-5592	347	33	−	−	PROPN
ejpam-5592	347	34	k	k	NOUN
ejpam-5592	347	35	)	)	PUNCT
ejpam-5592	347	36	(	(	PUNCT
ejpam-5592	347	37	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	347	38	ψ(κ))ϖu	ψ(κ))ϖu	NOUN
ejpam-5592	347	39	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	347	40	−	−	PROPN
ejpam-5592	347	41	k)γ(ϖu	k)γ(ϖu	PUNCT
ejpam-5592	347	42	+	+	NOUN
ejpam-5592	347	43	1	1	NUM
ejpam-5592	347	44	)	)	PUNCT
ejpam-5592	347	45	)	)	PUNCT
ejpam-5592	348	1	≈	≈	PROPN
ejpam-5592	348	2	0.171925	0.171925	NUM
ejpam-5592	348	3	<	<	X
ejpam-5592	348	4	1	1	NUM
ejpam-5592	348	5	.	.	PUNCT
ejpam-5592	348	6	(	(	PUNCT
ejpam-5592	348	7	b	b	X
ejpam-5592	348	8	)	)	PUNCT
ejpam-5592	348	9	if	if	SCONJ
ejpam-5592	348	10	τ	τ	PROPN
ejpam-5592	348	11	∈	∈	PROPN
ejpam-5592	348	12	(	(	PUNCT
ejpam-5592	348	13	2	2	NUM
ejpam-5592	348	14	,	,	PUNCT
ejpam-5592	348	15	3	3	NUM
ejpam-5592	348	16	]	]	PUNCT
ejpam-5592	348	17	,	,	PUNCT
ejpam-5592	348	18	we	we	PRON
ejpam-5592	348	19	have	have	VERB
ejpam-5592	348	20	k	k	NOUN
ejpam-5592	348	21	=	=	SYM
ejpam-5592	348	22	3	3	NUM
ejpam-5592	348	23	,	,	PUNCT
ejpam-5592	348	24	and	and	CCONJ
ejpam-5592	348	25	p	p	X
ejpam-5592	348	26	(	(	PUNCT
ejpam-5592	348	27	(	(	PUNCT
ejpam-5592	348	28	k	k	X
ejpam-5592	348	29	+	+	NOUN
ejpam-5592	348	30	1−ϖu	1−ϖu	NUM
ejpam-5592	348	31	)	)	PUNCT
ejpam-5592	348	32	(	(	PUNCT
ejpam-5592	348	33	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	348	34	ψ(κ))k	ψ(κ))k	PROPN
ejpam-5592	348	35	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	348	36	−	−	PROPN
ejpam-5592	348	37	k)γ(k	k)γ(k	NOUN
ejpam-5592	348	38	+	+	CCONJ
ejpam-5592	348	39	1	1	NUM
ejpam-5592	348	40	)	)	PUNCT
ejpam-5592	348	41	+	+	CCONJ
ejpam-5592	348	42	(	(	PUNCT
ejpam-5592	348	43	ϖu	ϖu	PROPN
ejpam-5592	348	44	−	−	PROPN
ejpam-5592	348	45	k	k	NOUN
ejpam-5592	348	46	)	)	PUNCT
ejpam-5592	348	47	(	(	PUNCT
ejpam-5592	348	48	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	348	49	ψ(κ))ϖu	ψ(κ))ϖu	NOUN
ejpam-5592	348	50	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	348	51	−	−	PROPN
ejpam-5592	348	52	k)γ(ϖu	k)γ(ϖu	PUNCT
ejpam-5592	348	53	+	+	NOUN
ejpam-5592	348	54	1	1	NUM
ejpam-5592	348	55	)	)	PUNCT
ejpam-5592	348	56	)	)	PUNCT
ejpam-5592	349	1	≈	≈	PROPN
ejpam-5592	349	2	0.568509	0.568509	NUM
ejpam-5592	349	3	<	<	X
ejpam-5592	349	4	1	1	NUM
ejpam-5592	349	5	.	.	PUNCT
ejpam-5592	349	6	therefore	therefore	ADV
ejpam-5592	349	7	,	,	PUNCT
ejpam-5592	349	8	all	all	DET
ejpam-5592	349	9	axioms	axiom	NOUN
ejpam-5592	349	10	of	of	ADP
ejpam-5592	349	11	theorem	theorem	ADJ
ejpam-5592	349	12	1	1	NUM
ejpam-5592	349	13	are	be	AUX
ejpam-5592	349	14	fulfilled	fulfil	VERB
ejpam-5592	349	15	.	.	PUNCT
ejpam-5592	350	1	hence	hence	ADV
ejpam-5592	350	2	,	,	PUNCT
ejpam-5592	350	3	there	there	PRON
ejpam-5592	350	4	exists	exist	VERB
ejpam-5592	350	5	a	a	DET
ejpam-5592	350	6	unique	unique	ADJ
ejpam-5592	350	7	solution	solution	NOUN
ejpam-5592	350	8	to	to	ADP
ejpam-5592	350	9	problem	problem	NOUN
ejpam-5592	350	10	(	(	PUNCT
ejpam-5592	350	11	10	10	NUM
ejpam-5592	350	12	)	)	PUNCT
ejpam-5592	350	13	.	.	PUNCT
ejpam-5592	351	1	example	example	NOUN
ejpam-5592	352	1	2	2	NUM
ejpam-5592	352	2	.	.	X
ejpam-5592	352	3	consider	consider	VERB
ejpam-5592	352	4	the	the	DET
ejpam-5592	352	5	following	following	ADJ
ejpam-5592	352	6	initial	initial	ADJ
ejpam-5592	352	7	fde	fde	NOUN
ejpam-5592	352	8	:	:	PUNCT
ejpam-5592	352	9	{	{	PUNCT
ejpam-5592	352	10	cabdϖu	cabdϖu	PROPN
ejpam-5592	352	11	,	,	PUNCT
ejpam-5592	352	12	ψ	ψ	PROPN
ejpam-5592	352	13	0	0	PUNCT
ejpam-5592	352	14	ϱ(z	ϱ(z	NOUN
ejpam-5592	352	15	)	)	PUNCT
ejpam-5592	352	16	=	=	PUNCT
ejpam-5592	352	17	z3	z3	PROPN
ejpam-5592	352	18	−	−	PROPN
ejpam-5592	352	19	ϱ(z	ϱ(z	PROPN
ejpam-5592	352	20	)	)	PUNCT
ejpam-5592	352	21	,	,	PUNCT
ejpam-5592	352	22	z	z	NOUN
ejpam-5592	352	23	∈	∈	PROPN
ejpam-5592	353	1	[	[	X
ejpam-5592	353	2	0	0	NUM
ejpam-5592	353	3	,	,	PUNCT
ejpam-5592	353	4	2	2	NUM
ejpam-5592	353	5	]	]	PUNCT
ejpam-5592	353	6	,	,	PUNCT
ejpam-5592	353	7	ϱ(0	ϱ(0	PROPN
ejpam-5592	353	8	)	)	PUNCT
ejpam-5592	353	9	=	=	SYM
ejpam-5592	353	10	0	0	NUM
ejpam-5592	353	11	,	,	PUNCT
ejpam-5592	353	12	ϱ′ψ(0	ϱ′ψ(0	NUM
ejpam-5592	353	13	)	)	PUNCT
ejpam-5592	353	14	=	=	SYM
ejpam-5592	353	15	0	0	NUM
ejpam-5592	353	16	,	,	PUNCT
ejpam-5592	353	17	ϱ	ϱ	ADP
ejpam-5592	353	18	′′	′′	PROPN
ejpam-5592	353	19	ψ(0	ψ(0	PROPN
ejpam-5592	353	20	)	)	PUNCT
ejpam-5592	353	21	=	=	SYM
ejpam-5592	353	22	2	2	NUM
ejpam-5592	353	23	(	(	PUNCT
ejpam-5592	353	24	11	11	NUM
ejpam-5592	353	25	)	)	PUNCT
ejpam-5592	353	26	where	where	SCONJ
ejpam-5592	353	27	ψ(z	ψ(z	NOUN
ejpam-5592	353	28	)	)	PUNCT
ejpam-5592	353	29	=	=	SYM
ejpam-5592	353	30	z	z	NOUN
ejpam-5592	353	31	and	and	CCONJ
ejpam-5592	353	32	ϖu(τ	ϖu(τ	NUM
ejpam-5592	353	33	)	)	PUNCT
ejpam-5592	353	34	=	=	PRON
ejpam-5592	353	35	{	{	PUNCT
ejpam-5592	353	36	0.2	0.2	NUM
ejpam-5592	353	37	,	,	PUNCT
ejpam-5592	353	38	τ	τ	PROPN
ejpam-5592	353	39	∈	∈	PROPN
ejpam-5592	353	40	[	[	X
ejpam-5592	353	41	12	12	NUM
ejpam-5592	353	42	,	,	PUNCT
ejpam-5592	353	43	1	1	NUM
ejpam-5592	353	44	]	]	PUNCT
ejpam-5592	353	45	,	,	PUNCT
ejpam-5592	353	46	0.4	0.4	NUM
ejpam-5592	353	47	,	,	PUNCT
ejpam-5592	353	48	τ	τ	PROPN
ejpam-5592	353	49	∈	∈	PROPN
ejpam-5592	353	50	(	(	PUNCT
ejpam-5592	353	51	1	1	NUM
ejpam-5592	353	52	,	,	PUNCT
ejpam-5592	353	53	2	2	NUM
ejpam-5592	353	54	]	]	PUNCT
ejpam-5592	353	55	,	,	PUNCT
ejpam-5592	353	56	for	for	ADP
ejpam-5592	353	57	u	u	PRON
ejpam-5592	353	58	≥	≥	NUM
ejpam-5592	353	59	1	1	NUM
ejpam-5592	353	60	.	.	PUNCT
ejpam-5592	353	61	assume	assume	VERB
ejpam-5592	353	62	that	that	SCONJ
ejpam-5592	353	63	problem	problem	NOUN
ejpam-5592	353	64	(	(	PUNCT
ejpam-5592	353	65	11	11	NUM
ejpam-5592	353	66	)	)	PUNCT
ejpam-5592	353	67	has	have	VERB
ejpam-5592	353	68	an	an	DET
ejpam-5592	353	69	exact	exact	ADJ
ejpam-5592	353	70	solution	solution	NOUN
ejpam-5592	353	71	ϱ(z	ϱ(z	PROPN
ejpam-5592	353	72	)	)	PUNCT
ejpam-5592	353	73	=	=	SYM
ejpam-5592	353	74	z3	z3	PROPN
ejpam-5592	353	75	.	.	PUNCT
ejpam-5592	354	1	the	the	DET
ejpam-5592	354	2	conditions	condition	NOUN
ejpam-5592	354	3	of	of	ADP
ejpam-5592	354	4	theorem	theorem	NOUN
ejpam-5592	354	5	1	1	NUM
ejpam-5592	354	6	shall	shall	AUX
ejpam-5592	354	7	be	be	AUX
ejpam-5592	354	8	checked	check	VERB
ejpam-5592	354	9	as	as	SCONJ
ejpam-5592	354	10	follows	follow	VERB
ejpam-5592	354	11	:	:	PUNCT
ejpam-5592	354	12	|ϕ(z	|ϕ(z	NOUN
ejpam-5592	354	13	,	,	PUNCT
ejpam-5592	354	14	ϱ1)−	ϱ1)−	NOUN
ejpam-5592	354	15	ϕ(z	ϕ(z	NOUN
ejpam-5592	354	16	,	,	PUNCT
ejpam-5592	354	17	ϱ2)|	ϱ2)|	NOUN
ejpam-5592	354	18	=	=	PUNCT
ejpam-5592	354	19	∣∣z3	∣∣z3	NOUN
ejpam-5592	354	20	−	−	NOUN
ejpam-5592	354	21	ϱ1(z)−	ϱ1(z)−	X
ejpam-5592	354	22	z3	z3	PROPN
ejpam-5592	354	23	+	+	CCONJ
ejpam-5592	354	24	ϱ2(z	ϱ2(z	NOUN
ejpam-5592	354	25	)	)	PUNCT
ejpam-5592	355	1	∣∣	∣∣	NUM
ejpam-5592	355	2	≤	≤	X
ejpam-5592	355	3	|ϱ1(z)−	|ϱ1(z)−	VERB
ejpam-5592	355	4	ϱ2(z)|	ϱ2(z)|	NOUN
ejpam-5592	355	5	.	.	PUNCT
ejpam-5592	356	1	then	then	ADV
ejpam-5592	356	2	,	,	PUNCT
ejpam-5592	356	3	p	p	X
ejpam-5592	356	4	=	=	NOUN
ejpam-5592	356	5	1	1	NUM
ejpam-5592	356	6	>	>	X
ejpam-5592	356	7	0	0	X
ejpam-5592	356	8	.	.	PUNCT
ejpam-5592	357	1	if	if	SCONJ
ejpam-5592	357	2	we	we	PRON
ejpam-5592	357	3	take	take	VERB
ejpam-5592	357	4	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	357	5	−	−	PROPN
ejpam-5592	357	6	k	k	X
ejpam-5592	357	7	)	)	PUNCT
ejpam-5592	357	8	=	=	SYM
ejpam-5592	357	9	1	1	NUM
ejpam-5592	357	10	,	,	PUNCT
ejpam-5592	357	11	then	then	ADV
ejpam-5592	357	12	,	,	PUNCT
ejpam-5592	357	13	we	we	PRON
ejpam-5592	357	14	have	have	VERB
ejpam-5592	357	15	the	the	DET
ejpam-5592	357	16	following	follow	VERB
ejpam-5592	357	17	cases	case	NOUN
ejpam-5592	357	18	:	:	PUNCT
ejpam-5592	357	19	(	(	PUNCT
ejpam-5592	357	20	a	a	X
ejpam-5592	357	21	)	)	PUNCT
ejpam-5592	357	22	if	if	SCONJ
ejpam-5592	357	23	τ	τ	PROPN
ejpam-5592	357	24	∈	∈	PROPN
ejpam-5592	357	25	[	[	X
ejpam-5592	357	26	12	12	NUM
ejpam-5592	357	27	,	,	PUNCT
ejpam-5592	357	28	1	1	NUM
ejpam-5592	357	29	]	]	PUNCT
ejpam-5592	357	30	,	,	PUNCT
ejpam-5592	357	31	one	one	PRON
ejpam-5592	357	32	has	have	AUX
ejpam-5592	357	33	k	k	NOUN
ejpam-5592	357	34	=	=	SYM
ejpam-5592	357	35	1	1	NUM
ejpam-5592	357	36	,	,	PUNCT
ejpam-5592	357	37	and	and	CCONJ
ejpam-5592	357	38	p	p	X
ejpam-5592	357	39	(	(	PUNCT
ejpam-5592	357	40	(	(	PUNCT
ejpam-5592	357	41	k	k	X
ejpam-5592	357	42	+	+	NOUN
ejpam-5592	357	43	1−ϖu	1−ϖu	NUM
ejpam-5592	357	44	)	)	PUNCT
ejpam-5592	357	45	(	(	PUNCT
ejpam-5592	357	46	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	357	47	ψ(κ))k	ψ(κ))k	PROPN
ejpam-5592	357	48	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	357	49	−	−	PROPN
ejpam-5592	357	50	k)γ(k	k)γ(k	NOUN
ejpam-5592	357	51	+	+	CCONJ
ejpam-5592	357	52	1	1	NUM
ejpam-5592	357	53	)	)	PUNCT
ejpam-5592	357	54	+	+	CCONJ
ejpam-5592	358	1	(	(	PUNCT
ejpam-5592	358	2	ϖu	ϖu	PROPN
ejpam-5592	358	3	−	−	PROPN
ejpam-5592	358	4	k	k	NOUN
ejpam-5592	358	5	)	)	PUNCT
ejpam-5592	358	6	(	(	PUNCT
ejpam-5592	358	7	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	358	8	ψ(κ))ϖu	ψ(κ))ϖu	NOUN
ejpam-5592	358	9	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	358	10	−	−	PROPN
ejpam-5592	358	11	k)γ(ϖu	k)γ(ϖu	PUNCT
ejpam-5592	358	12	+	+	NOUN
ejpam-5592	358	13	1	1	NUM
ejpam-5592	358	14	)	)	PUNCT
ejpam-5592	358	15	)	)	PUNCT
ejpam-5592	359	1	≈	≈	PROPN
ejpam-5592	359	2	0.645318	0.645318	NUM
ejpam-5592	359	3	<	<	X
ejpam-5592	359	4	1	1	NUM
ejpam-5592	359	5	.	.	PUNCT
ejpam-5592	359	6	example	example	NOUN
ejpam-5592	360	1	3	3	X
ejpam-5592	360	2	.	.	PUNCT
ejpam-5592	361	1	if	if	SCONJ
ejpam-5592	361	2	τ	τ	PROPN
ejpam-5592	361	3	∈	∈	PROPN
ejpam-5592	361	4	(	(	PUNCT
ejpam-5592	361	5	1	1	NUM
ejpam-5592	361	6	,	,	PUNCT
ejpam-5592	361	7	2	2	NUM
ejpam-5592	361	8	]	]	PUNCT
ejpam-5592	361	9	,	,	PUNCT
ejpam-5592	361	10	we	we	PRON
ejpam-5592	361	11	have	have	VERB
ejpam-5592	361	12	k	k	NOUN
ejpam-5592	361	13	=	=	SYM
ejpam-5592	361	14	2	2	NUM
ejpam-5592	361	15	,	,	PUNCT
ejpam-5592	361	16	and	and	CCONJ
ejpam-5592	361	17	p	p	X
ejpam-5592	361	18	(	(	PUNCT
ejpam-5592	361	19	(	(	PUNCT
ejpam-5592	361	20	k	k	X
ejpam-5592	361	21	+	+	NOUN
ejpam-5592	361	22	1−ϖu	1−ϖu	NUM
ejpam-5592	361	23	)	)	PUNCT
ejpam-5592	361	24	(	(	PUNCT
ejpam-5592	361	25	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	361	26	ψ(κ))k	ψ(κ))k	PROPN
ejpam-5592	361	27	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	361	28	−	−	PROPN
ejpam-5592	361	29	k)γ(k	k)γ(k	NOUN
ejpam-5592	361	30	+	+	CCONJ
ejpam-5592	361	31	1	1	NUM
ejpam-5592	361	32	)	)	PUNCT
ejpam-5592	361	33	+	+	CCONJ
ejpam-5592	361	34	(	(	PUNCT
ejpam-5592	361	35	ϖu	ϖu	PROPN
ejpam-5592	361	36	−	−	PROPN
ejpam-5592	361	37	k	k	NOUN
ejpam-5592	361	38	)	)	PUNCT
ejpam-5592	361	39	(	(	PUNCT
ejpam-5592	361	40	ψ(υ)−	ψ(υ)−	NOUN
ejpam-5592	361	41	ψ(κ))ϖu	ψ(κ))ϖu	NOUN
ejpam-5592	361	42	λ(ϖu	λ(ϖu	ADJ
ejpam-5592	361	43	−	−	PROPN
ejpam-5592	361	44	k)γ(ϖu	k)γ(ϖu	PUNCT
ejpam-5592	361	45	+	+	NOUN
ejpam-5592	361	46	1	1	NUM
ejpam-5592	361	47	)	)	PUNCT
ejpam-5592	361	48	)	)	PUNCT
ejpam-5592	362	1	≈	≈	ADP
ejpam-5592	362	2	0.735214	0.735214	NUM
ejpam-5592	362	3	<	<	X
ejpam-5592	362	4	1	1	NUM
ejpam-5592	362	5	.	.	PUNCT
ejpam-5592	363	1	hence	hence	ADV
ejpam-5592	363	2	,	,	PUNCT
ejpam-5592	363	3	all	all	DET
ejpam-5592	363	4	assumptions	assumption	NOUN
ejpam-5592	363	5	of	of	ADP
ejpam-5592	363	6	theorem	theorem	ADJ
ejpam-5592	363	7	1	1	NUM
ejpam-5592	363	8	are	be	AUX
ejpam-5592	363	9	fulfilled	fulfil	VERB
ejpam-5592	363	10	.	.	PUNCT
ejpam-5592	364	1	therefore	therefore	ADV
ejpam-5592	364	2	,	,	PUNCT
ejpam-5592	364	3	the	the	DET
ejpam-5592	364	4	problem	problem	NOUN
ejpam-5592	364	5	(	(	PUNCT
ejpam-5592	364	6	11	11	NUM
ejpam-5592	364	7	)	)	PUNCT
ejpam-5592	364	8	possesses	possess	VERB
ejpam-5592	364	9	a	a	DET
ejpam-5592	364	10	unique	unique	ADJ
ejpam-5592	364	11	solution	solution	NOUN
ejpam-5592	364	12	.	.	PUNCT
ejpam-5592	365	1	next	next	ADJ
ejpam-5592	365	2	,	,	PUNCT
ejpam-5592	365	3	using	use	VERB
ejpam-5592	365	4	picard	picard	PROPN
ejpam-5592	365	5	’s	’s	PART
ejpam-5592	365	6	iterative	iterative	NOUN
ejpam-5592	365	7	method	method	NOUN
ejpam-5592	365	8	,	,	PUNCT
ejpam-5592	365	9	we	we	PRON
ejpam-5592	365	10	will	will	AUX
ejpam-5592	365	11	compute	compute	VERB
ejpam-5592	365	12	the	the	DET
ejpam-5592	365	13	solution	solution	NOUN
ejpam-5592	365	14	of	of	ADP
ejpam-5592	365	15	system	system	NOUN
ejpam-5592	365	16	(	(	PUNCT
ejpam-5592	365	17	11	11	NUM
ejpam-5592	365	18	)	)	PUNCT
ejpam-5592	365	19	as	as	SCONJ
ejpam-5592	365	20	follows	follow	VERB
ejpam-5592	365	21	:	:	PUNCT
ejpam-5592	366	1	ϱs	ϱs	NOUN
ejpam-5592	366	2	(	(	PUNCT
ejpam-5592	366	3	z	z	NOUN
ejpam-5592	366	4	)	)	PUNCT
ejpam-5592	366	5	=	=	SYM
ejpam-5592	366	6	ϱ0	ϱ0	NOUN
ejpam-5592	366	7	(	(	PUNCT
ejpam-5592	366	8	z	z	NOUN
ejpam-5592	366	9	)	)	PUNCT
ejpam-5592	366	10	+	+	CCONJ
ejpam-5592	367	1	cab	cab	NOUN
ejpam-5592	367	2	dϖu	dϖu	NOUN
ejpam-5592	367	3	,	,	PUNCT
ejpam-5592	367	4	ψ	ψ	X
ejpam-5592	367	5	0	0	PUNCT
ejpam-5592	367	6	(	(	PUNCT
ejpam-5592	367	7	z3	z3	NOUN
ejpam-5592	367	8	−	−	PROPN
ejpam-5592	367	9	ϱs−1(z	ϱs−1(z	PROPN
ejpam-5592	367	10	)	)	PUNCT
ejpam-5592	367	11	)	)	PUNCT
ejpam-5592	367	12	,	,	PUNCT
ejpam-5592	367	13	ϱ0	ϱ0	NOUN
ejpam-5592	367	14	(	(	PUNCT
ejpam-5592	367	15	z	z	NOUN
ejpam-5592	367	16	)	)	PUNCT
ejpam-5592	367	17	=	=	SYM
ejpam-5592	367	18	z3	z3	PROPN
ejpam-5592	367	19	.	.	PUNCT
ejpam-5592	368	1	h.a	h.a	PROPN
ejpam-5592	368	2	.	.	PROPN
ejpam-5592	368	3	hammad	hammad	PROPN
ejpam-5592	368	4	,	,	PUNCT
ejpam-5592	368	5	m.	m.	PROPN
ejpam-5592	368	6	de	de	X
ejpam-5592	368	7	la	la	PROPN
ejpam-5592	368	8	sen	sen	PROPN
ejpam-5592	368	9	/	/	SYM
ejpam-5592	368	10	eur	eur	PROPN
ejpam-5592	368	11	.	.	PUNCT
ejpam-5592	369	1	j.	j.	PROPN
ejpam-5592	369	2	pure	pure	PROPN
ejpam-5592	369	3	appl	appl	PROPN
ejpam-5592	369	4	.	.	PROPN
ejpam-5592	369	5	math	math	PROPN
ejpam-5592	369	6	,	,	PUNCT
ejpam-5592	369	7	17	17	NUM
ejpam-5592	369	8	(	(	PUNCT
ejpam-5592	369	9	4	4	NUM
ejpam-5592	369	10	)	)	PUNCT
ejpam-5592	369	11	(	(	PUNCT
ejpam-5592	369	12	2024	2024	NUM
ejpam-5592	369	13	)	)	PUNCT
ejpam-5592	369	14	,	,	PUNCT
ejpam-5592	369	15	3687	3687	NUM
ejpam-5592	369	16	-	-	SYM
ejpam-5592	369	17	3707	3707	NUM
ejpam-5592	369	18	3704	3704	NUM
ejpam-5592	369	19	then	then	ADV
ejpam-5592	369	20	ϱ1	ϱ1	PROPN
ejpam-5592	369	21	(	(	PUNCT
ejpam-5592	369	22	z	z	NOUN
ejpam-5592	369	23	)	)	PUNCT
ejpam-5592	369	24	=	=	SYM
ejpam-5592	370	1	z3	z3	PROPN
ejpam-5592	370	2	+	+	CCONJ
ejpam-5592	370	3	cabdϖu	cabdϖu	PROPN
ejpam-5592	370	4	,	,	PUNCT
ejpam-5592	370	5	ψ	ψ	X
ejpam-5592	370	6	0	0	PUNCT
ejpam-5592	370	7	(	(	PUNCT
ejpam-5592	370	8	z3	z3	PROPN
ejpam-5592	370	9	−	−	PROPN
ejpam-5592	370	10	ϱ0(z	ϱ0(z	PROPN
ejpam-5592	370	11	)	)	PUNCT
ejpam-5592	370	12	)	)	PUNCT
ejpam-5592	371	1	=	=	SYM
ejpam-5592	371	2	z3	z3	PROPN
ejpam-5592	371	3	,	,	PUNCT
ejpam-5592	371	4	ϱ2	ϱ2	PROPN
ejpam-5592	371	5	(	(	PUNCT
ejpam-5592	371	6	z	z	NOUN
ejpam-5592	371	7	)	)	PUNCT
ejpam-5592	371	8	=	=	SYM
ejpam-5592	371	9	z3	z3	PROPN
ejpam-5592	371	10	+	+	CCONJ
ejpam-5592	371	11	cabdϖu	cabdϖu	PROPN
ejpam-5592	371	12	,	,	PUNCT
ejpam-5592	371	13	ψ	ψ	X
ejpam-5592	371	14	0	0	PUNCT
ejpam-5592	372	1	(	(	PUNCT
ejpam-5592	372	2	z3	z3	NOUN
ejpam-5592	372	3	−	−	PROPN
ejpam-5592	372	4	ϱ1(z	ϱ1(z	PROPN
ejpam-5592	372	5	)	)	PUNCT
ejpam-5592	372	6	)	)	PUNCT
ejpam-5592	373	1	=	=	SYM
ejpam-5592	373	2	z3	z3	PROPN
ejpam-5592	373	3	,	,	PUNCT
ejpam-5592	373	4	ϱ3	ϱ3	PROPN
ejpam-5592	373	5	(	(	PUNCT
ejpam-5592	373	6	z	z	NOUN
ejpam-5592	373	7	)	)	PUNCT
ejpam-5592	373	8	=	=	SYM
ejpam-5592	373	9	z3	z3	PROPN
ejpam-5592	373	10	,	,	PUNCT
ejpam-5592	373	11	...	...	PUNCT
ejpam-5592	373	12	ϱk	ϱk	NOUN
ejpam-5592	373	13	(	(	PUNCT
ejpam-5592	373	14	z	z	NOUN
ejpam-5592	373	15	)	)	PUNCT
ejpam-5592	373	16	=	=	SYM
ejpam-5592	373	17	z3	z3	PROPN
ejpam-5592	373	18	.	.	PUNCT
ejpam-5592	374	1	this	this	PRON
ejpam-5592	374	2	corresponds	correspond	VERB
ejpam-5592	374	3	to	to	ADP
ejpam-5592	374	4	the	the	DET
ejpam-5592	374	5	exact	exact	ADJ
ejpam-5592	374	6	solution	solution	NOUN
ejpam-5592	374	7	.	.	PUNCT
ejpam-5592	375	1	7	7	X
ejpam-5592	375	2	.	.	X
ejpam-5592	375	3	conclusion	conclusion	NOUN
ejpam-5592	375	4	and	and	CCONJ
ejpam-5592	375	5	open	open	ADJ
ejpam-5592	375	6	problems	problem	NOUN
ejpam-5592	375	7	this	this	DET
ejpam-5592	375	8	paper	paper	NOUN
ejpam-5592	375	9	delves	delve	VERB
ejpam-5592	375	10	into	into	ADP
ejpam-5592	375	11	the	the	DET
ejpam-5592	375	12	application	application	NOUN
ejpam-5592	375	13	of	of	ADP
ejpam-5592	375	14	ab	ab	PROPN
ejpam-5592	375	15	fractional	fractional	PROPN
ejpam-5592	375	16	operators	operator	NOUN
ejpam-5592	375	17	with	with	ADP
ejpam-5592	375	18	higher	high	ADJ
ejpam-5592	375	19	-	-	PUNCT
ejpam-5592	375	20	variable	variable	ADJ
ejpam-5592	375	21	orders	order	NOUN
ejpam-5592	375	22	using	use	VERB
ejpam-5592	375	23	increasing	increase	VERB
ejpam-5592	375	24	functions	function	NOUN
ejpam-5592	375	25	.	.	PUNCT
ejpam-5592	376	1	we	we	PRON
ejpam-5592	376	2	explore	explore	VERB
ejpam-5592	376	3	the	the	DET
ejpam-5592	376	4	qualitative	qualitative	ADJ
ejpam-5592	376	5	properties	property	NOUN
ejpam-5592	376	6	of	of	ADP
ejpam-5592	376	7	these	these	DET
ejpam-5592	376	8	operators	operator	NOUN
ejpam-5592	376	9	and	and	CCONJ
ejpam-5592	376	10	demonstrate	demonstrate	VERB
ejpam-5592	376	11	the	the	DET
ejpam-5592	376	12	existence	existence	NOUN
ejpam-5592	376	13	of	of	ADP
ejpam-5592	376	14	a	a	DET
ejpam-5592	376	15	unique	unique	ADJ
ejpam-5592	376	16	solution	solution	NOUN
ejpam-5592	376	17	for	for	ADP
ejpam-5592	376	18	an	an	DET
ejpam-5592	376	19	initial	initial	ADJ
ejpam-5592	376	20	fde	fde	NOUN
ejpam-5592	376	21	using	use	VERB
ejpam-5592	376	22	picard	picard	PROPN
ejpam-5592	376	23	’s	’s	PART
ejpam-5592	376	24	iteration	iteration	NOUN
ejpam-5592	376	25	method	method	NOUN
ejpam-5592	376	26	.	.	PUNCT
ejpam-5592	377	1	our	our	PRON
ejpam-5592	377	2	findings	finding	NOUN
ejpam-5592	377	3	are	be	AUX
ejpam-5592	377	4	supported	support	VERB
ejpam-5592	377	5	by	by	ADP
ejpam-5592	377	6	two	two	NUM
ejpam-5592	377	7	illustrative	illustrative	ADJ
ejpam-5592	377	8	examples	example	NOUN
ejpam-5592	377	9	.	.	PUNCT
ejpam-5592	378	1	we	we	PRON
ejpam-5592	378	2	also	also	ADV
ejpam-5592	378	3	introduce	introduce	VERB
ejpam-5592	378	4	a	a	DET
ejpam-5592	378	5	generalized	generalized	ADJ
ejpam-5592	378	6	gronwall	gronwall	ADJ
ejpam-5592	378	7	inequality	inequality	NOUN
ejpam-5592	378	8	within	within	ADP
ejpam-5592	378	9	the	the	DET
ejpam-5592	378	10	framework	framework	NOUN
ejpam-5592	378	11	of	of	ADP
ejpam-5592	378	12	ab	ab	PROPN
ejpam-5592	378	13	fractional	fractional	ADJ
ejpam-5592	378	14	integrals	integral	NOUN
ejpam-5592	378	15	.	.	PUNCT
ejpam-5592	379	1	this	this	DET
ejpam-5592	379	2	study	study	NOUN
ejpam-5592	379	3	contributes	contribute	VERB
ejpam-5592	379	4	to	to	ADP
ejpam-5592	379	5	the	the	DET
ejpam-5592	379	6	advancement	advancement	NOUN
ejpam-5592	379	7	of	of	ADP
ejpam-5592	379	8	fractional	fractional	ADJ
ejpam-5592	379	9	calculus	calculus	NOUN
ejpam-5592	379	10	and	and	CCONJ
ejpam-5592	379	11	its	its	PRON
ejpam-5592	379	12	potential	potential	ADJ
ejpam-5592	379	13	applications	application	NOUN
ejpam-5592	379	14	.	.	PUNCT
ejpam-5592	380	1	future	future	ADJ
ejpam-5592	380	2	research	research	NOUN
ejpam-5592	380	3	will	will	AUX
ejpam-5592	380	4	focus	focus	VERB
ejpam-5592	380	5	on	on	ADP
ejpam-5592	380	6	applying	apply	VERB
ejpam-5592	380	7	these	these	DET
ejpam-5592	380	8	extended	extend	VERB
ejpam-5592	380	9	operators	operator	NOUN
ejpam-5592	380	10	to	to	ADP
ejpam-5592	380	11	real	real	ADJ
ejpam-5592	380	12	-	-	PUNCT
ejpam-5592	380	13	world	world	NOUN
ejpam-5592	380	14	dynamic	dynamic	ADJ
ejpam-5592	380	15	systems	system	NOUN
ejpam-5592	380	16	,	,	PUNCT
ejpam-5592	380	17	investigating	investigate	VERB
ejpam-5592	380	18	new	new	ADJ
ejpam-5592	380	19	properties	property	NOUN
ejpam-5592	380	20	and	and	CCONJ
ejpam-5592	380	21	inequalities	inequality	NOUN
ejpam-5592	380	22	associated	associate	VERB
ejpam-5592	380	23	with	with	ADP
ejpam-5592	380	24	them	they	PRON
ejpam-5592	380	25	,	,	PUNCT
ejpam-5592	380	26	and	and	CCONJ
ejpam-5592	380	27	exploring	explore	VERB
ejpam-5592	380	28	the	the	DET
ejpam-5592	380	29	corresponding	corresponding	ADJ
ejpam-5592	380	30	right	right	ADV
ejpam-5592	380	31	-	-	PUNCT
ejpam-5592	380	32	sided	sided	ADJ
ejpam-5592	380	33	fractional	fractional	ADJ
ejpam-5592	380	34	operators	operator	NOUN
ejpam-5592	380	35	for	for	ADP
ejpam-5592	380	36	rl	rl	NOUN
ejpam-5592	380	37	-	-	PUNCT
ejpam-5592	380	38	ab	ab	PROPN
ejpam-5592	380	39	,	,	PUNCT
ejpam-5592	380	40	abc	abc	PROPN
ejpam-5592	380	41	,	,	PUNCT
ejpam-5592	380	42	and	and	CCONJ
ejpam-5592	380	43	kab	kab	PROPN
ejpam-5592	380	44	.	.	PROPN
ejpam-5592	381	1	8	8	NUM
ejpam-5592	381	2	.	.	X
ejpam-5592	381	3	abbreviations	abbreviation	NOUN
ejpam-5592	381	4	ab→atangana	ab→atangana	PROPN
ejpam-5592	381	5	-	-	PUNCT
ejpam-5592	381	6	baleanu	baleanu	NOUN
ejpam-5592	381	7	ml→mittag	ml→mittag	NOUN
ejpam-5592	381	8	-	-	PUNCT
ejpam-5592	381	9	leffler	leffler	NOUN
ejpam-5592	381	10	fde→fractional	fde→fractional	ADJ
ejpam-5592	381	11	differential	differential	NOUN
ejpam-5592	381	12	equations	equation	NOUN
ejpam-5592	381	13	abc→atangana	abc→atangana	PROPN
ejpam-5592	381	14	-	-	PUNCT
ejpam-5592	381	15	baleanu	baleanu	PROPN
ejpam-5592	381	16	-	-	PUNCT
ejpam-5592	381	17	caputo	caputo	NOUN
ejpam-5592	381	18	w.r.t.→with	w.r.t.→with	ADJ
ejpam-5592	381	19	respect	respect	NOUN
ejpam-5592	381	20	to	to	ADP
ejpam-5592	381	21	rl→riemann	rl→riemann	NOUN
ejpam-5592	381	22	-	-	PUNCT
ejpam-5592	381	23	liouville	liouville	VERB
ejpam-5592	381	24	abk→atangana	abk→atangana	PROPN
ejpam-5592	381	25	-	-	PUNCT
ejpam-5592	381	26	baleanu	baleanu	ADJ
ejpam-5592	381	27	-	-	PUNCT
ejpam-5592	381	28	kashuri	kashuri	ADJ
ejpam-5592	381	29	rab→riemann	rab→riemann	PROPN
ejpam-5592	381	30	-	-	PUNCT
ejpam-5592	381	31	atangana	atangana	PROPN
ejpam-5592	381	32	-	-	PUNCT
ejpam-5592	381	33	baleanu	baleanu	ADJ
ejpam-5592	381	34	rl	rl	NOUN
ejpam-5592	381	35	-	-	PUNCT
ejpam-5592	381	36	ab→riemann	ab→riemann	NOUN
ejpam-5592	381	37	-	-	PUNCT
ejpam-5592	381	38	liouville	liouville	NOUN
ejpam-5592	381	39	-	-	PUNCT
ejpam-5592	381	40	tangana	tangana	NOUN
ejpam-5592	381	41	-	-	PUNCT
ejpam-5592	381	42	baleanu	baleanu	NOUN
ejpam-5592	381	43	nnf→nonnegative	nnf→nonnegative	NOUN
ejpam-5592	381	44	and	and	CCONJ
ejpam-5592	381	45	nondecreasing	nondecreasing	ADJ
ejpam-5592	381	46	function	function	NOUN
ejpam-5592	381	47	nfli→nonnegative	nfli→nonnegative	ADJ
ejpam-5592	381	48	function	function	NOUN
ejpam-5592	382	1	locally	locally	ADV
ejpam-5592	382	2	integrable	integrable	ADJ
ejpam-5592	382	3	fie→fractional	fie→fractional	ADJ
ejpam-5592	382	4	integral	integral	ADJ
ejpam-5592	382	5	equation	equation	NOUN
ejpam-5592	382	6	conflicts	conflict	NOUN
ejpam-5592	382	7	of	of	ADP
ejpam-5592	382	8	interest	interest	NOUN
ejpam-5592	382	9	the	the	DET
ejpam-5592	382	10	authors	author	NOUN
ejpam-5592	382	11	declare	declare	VERB
ejpam-5592	382	12	that	that	SCONJ
ejpam-5592	382	13	they	they	PRON
ejpam-5592	382	14	have	have	VERB
ejpam-5592	382	15	no	no	DET
ejpam-5592	382	16	conflicts	conflict	NOUN
ejpam-5592	382	17	of	of	ADP
ejpam-5592	382	18	interest	interest	NOUN
ejpam-5592	382	19	.	.	PUNCT
ejpam-5592	383	1	references	reference	NOUN
ejpam-5592	383	2	3705	3705	NUM
ejpam-5592	383	3	author	author	NOUN
ejpam-5592	383	4	’s	’s	PART
ejpam-5592	383	5	contributions	contribution	NOUN
ejpam-5592	383	6	all	all	DET
ejpam-5592	383	7	authors	author	NOUN
ejpam-5592	383	8	contributed	contribute	VERB
ejpam-5592	383	9	equally	equally	ADV
ejpam-5592	383	10	and	and	CCONJ
ejpam-5592	383	11	significantly	significantly	ADV
ejpam-5592	383	12	in	in	ADP
ejpam-5592	383	13	writing	write	VERB
ejpam-5592	383	14	this	this	DET
ejpam-5592	383	15	article	article	NOUN
ejpam-5592	383	16	.	.	PUNCT
ejpam-5592	384	1	funding	fund	VERB
ejpam-5592	384	2	this	this	DET
ejpam-5592	384	3	work	work	NOUN
ejpam-5592	384	4	was	be	AUX
ejpam-5592	384	5	supported	support	VERB
ejpam-5592	384	6	in	in	ADP
ejpam-5592	384	7	part	part	NOUN
ejpam-5592	384	8	by	by	ADP
ejpam-5592	384	9	the	the	DET
ejpam-5592	384	10	basque	basque	ADJ
ejpam-5592	384	11	government	government	NOUN
ejpam-5592	384	12	under	under	AUX
ejpam-5592	384	13	grant	grant	VERB
ejpam-5592	384	14	it1555	it1555	NOUN
ejpam-5592	384	15	-	-	PUNCT
ejpam-5592	384	16	22	22	NUM
ejpam-5592	384	17	.	.	PUNCT
ejpam-5592	385	1	acknowledgments	acknowledgment	NOUN
ejpam-5592	385	2	the	the	DET
ejpam-5592	385	3	authors	author	NOUN
ejpam-5592	385	4	thank	thank	VERB
ejpam-5592	385	5	the	the	DET
ejpam-5592	385	6	basque	basque	ADJ
ejpam-5592	385	7	government	government	NOUN
ejpam-5592	385	8	for	for	ADP
ejpam-5592	385	9	grant	grant	VERB
ejpam-5592	385	10	it1555	it1555	NOUN
ejpam-5592	385	11	-	-	PUNCT
ejpam-5592	385	12	22	22	NUM
ejpam-5592	385	13	and	and	CCONJ
ejpam-5592	385	14	to	to	ADP
ejpam-5592	385	15	miciu	miciu	NOUN
ejpam-5592	385	16	/	/	SYM
ejpam-5592	385	17	aei/	aei/	PROPN
ejpam-5592	385	18	10.13039/501100011033	10.13039/501100011033	NUM
ejpam-5592	385	19	and	and	CCONJ
ejpam-5592	385	20	erdf	erdf	PROPN
ejpam-5592	385	21	/	/	SYM
ejpam-5592	385	22	e	e	NOUN
ejpam-5592	385	23	for	for	ADP
ejpam-5592	385	24	grants	grant	NOUN
ejpam-5592	385	25	pid2021	pid2021	NOUN
ejpam-5592	385	26	-	-	PUNCT
ejpam-5592	385	27	123543ob	123543ob	VERB
ejpam-5592	385	28	-	-	PUNCT
ejpam-5592	385	29	c21	c21	NOUN
ejpam-5592	385	30	and	and	CCONJ
ejpam-5592	385	31	pid2021123543ob	pid2021123543ob	NOUN
ejpam-5592	385	32	-	-	PUNCT
ejpam-5592	385	33	c22	c22	NOUN
ejpam-5592	385	34	.	.	PUNCT
ejpam-5592	386	1	references	reference	NOUN
ejpam-5592	386	2	[	[	X
ejpam-5592	386	3	1	1	NUM
ejpam-5592	386	4	]	]	X
ejpam-5592	386	5	s	s	VERB
ejpam-5592	386	6	abbas	abbas	NOUN
ejpam-5592	386	7	,	,	PUNCT
ejpam-5592	386	8	m	m	NOUN
ejpam-5592	386	9	benchohra	benchohra	NOUN
ejpam-5592	386	10	,	,	PUNCT
ejpam-5592	386	11	and	and	CCONJ
ejpam-5592	386	12	g	g	PROPN
ejpam-5592	386	13	m	m	PROPN
ejpam-5592	386	14	n’guérékata	n’guérékata	NOUN
ejpam-5592	386	15	.	.	PUNCT
ejpam-5592	387	1	topics	topic	NOUN
ejpam-5592	387	2	in	in	ADP
ejpam-5592	387	3	fractional	fractional	ADJ
ejpam-5592	387	4	differential	differential	ADJ
ejpam-5592	387	5	equations	equation	NOUN
ejpam-5592	387	6	.	.	PUNCT
ejpam-5592	388	1	springer	springer	NOUN
ejpam-5592	388	2	,	,	PUNCT
ejpam-5592	388	3	berlin	berlin	PROPN
ejpam-5592	388	4	,	,	PUNCT
ejpam-5592	388	5	2012	2012	NUM
ejpam-5592	388	6	.	.	PUNCT
ejpam-5592	389	1	[	[	X
ejpam-5592	389	2	2	2	NUM
ejpam-5592	389	3	]	]	PUNCT
ejpam-5592	389	4	t	t	NOUN
ejpam-5592	389	5	abdeljawad	abdeljawad	NOUN
ejpam-5592	389	6	.	.	PUNCT
ejpam-5592	390	1	a	a	DET
ejpam-5592	390	2	lyapunov	lyapunov	ADJ
ejpam-5592	390	3	type	type	NOUN
ejpam-5592	390	4	inequality	inequality	NOUN
ejpam-5592	390	5	for	for	ADP
ejpam-5592	390	6	fractional	fractional	ADJ
ejpam-5592	390	7	operators	operator	NOUN
ejpam-5592	390	8	with	with	ADP
ejpam-5592	390	9	nonsingular	nonsingular	ADJ
ejpam-5592	390	10	mittag	mittag	ADJ
ejpam-5592	390	11	-	-	PUNCT
ejpam-5592	390	12	leffler	leffler	NOUN
ejpam-5592	390	13	kernel	kernel	NOUN
ejpam-5592	390	14	.	.	PUNCT
ejpam-5592	391	1	j.	j.	PROPN
ejpam-5592	391	2	inequal	inequal	PROPN
ejpam-5592	391	3	.	.	PUNCT
ejpam-5592	392	1	appl	appl	PROPN
ejpam-5592	392	2	.	.	PROPN
ejpam-5592	392	3	,	,	PUNCT
ejpam-5592	392	4	130:1–11	130:1–11	NUM
ejpam-5592	392	5	,	,	PUNCT
ejpam-5592	392	6	2017	2017	NUM
ejpam-5592	392	7	.	.	PUNCT
ejpam-5592	393	1	[	[	X
ejpam-5592	393	2	3	3	X
ejpam-5592	393	3	]	]	X
ejpam-5592	393	4	t.	t.	NOUN
ejpam-5592	393	5	abdeljawad	abdeljawad	NOUN
ejpam-5592	393	6	,	,	PUNCT
ejpam-5592	393	7	s.	s.	PROPN
ejpam-5592	393	8	t.	t.	PROPN
ejpam-5592	393	9	m.	m.	PROPN
ejpam-5592	393	10	thabet	thabet	PROPN
ejpam-5592	393	11	,	,	PUNCT
ejpam-5592	393	12	i.	i.	PROPN
ejpam-5592	393	13	kedim	kedim	PROPN
ejpam-5592	393	14	,	,	PUNCT
ejpam-5592	393	15	m.	m.	NOUN
ejpam-5592	393	16	i.	i.	PROPN
ejpam-5592	393	17	ayari	ayari	PROPN
ejpam-5592	393	18	,	,	PUNCT
ejpam-5592	393	19	and	and	CCONJ
ejpam-5592	393	20	a.	a.	PROPN
ejpam-5592	393	21	khan	khan	PROPN
ejpam-5592	393	22	.	.	PUNCT
ejpam-5592	394	1	a	a	DET
ejpam-5592	394	2	higher	high	ADJ
ejpam-5592	394	3	-	-	PUNCT
ejpam-5592	394	4	order	order	NOUN
ejpam-5592	394	5	extension	extension	NOUN
ejpam-5592	394	6	of	of	ADP
ejpam-5592	394	7	atangana	atangana	PROPN
ejpam-5592	394	8	–	–	PUNCT
ejpam-5592	394	9	baleanu	baleanu	ADJ
ejpam-5592	394	10	fractional	fractional	ADJ
ejpam-5592	394	11	operators	operator	NOUN
ejpam-5592	394	12	with	with	ADP
ejpam-5592	394	13	respect	respect	NOUN
ejpam-5592	394	14	to	to	ADP
ejpam-5592	394	15	another	another	DET
ejpam-5592	394	16	function	function	NOUN
ejpam-5592	394	17	and	and	CCONJ
ejpam-5592	394	18	a	a	DET
ejpam-5592	394	19	gronwall	gronwall	ADJ
ejpam-5592	394	20	-	-	PUNCT
ejpam-5592	394	21	type	type	NOUN
ejpam-5592	394	22	inequality	inequality	NOUN
ejpam-5592	394	23	.	.	PUNCT
ejpam-5592	395	1	boundary	boundary	ADJ
ejpam-5592	395	2	value	value	NOUN
ejpam-5592	395	3	problems	problem	NOUN
ejpam-5592	395	4	,	,	PUNCT
ejpam-5592	395	5	2023:49	2023:49	NUM
ejpam-5592	395	6	,	,	PUNCT
ejpam-5592	395	7	2023	2023	NUM
ejpam-5592	395	8	.	.	PUNCT
ejpam-5592	396	1	[	[	X
ejpam-5592	396	2	4	4	NUM
ejpam-5592	396	3	]	]	X
ejpam-5592	396	4	r	r	PROPN
ejpam-5592	396	5	almeida	almeida	PROPN
ejpam-5592	396	6	,	,	PUNCT
ejpam-5592	396	7	a	a	DET
ejpam-5592	396	8	b	b	X
ejpam-5592	396	9	malinowska	malinowska	NOUN
ejpam-5592	396	10	,	,	PUNCT
ejpam-5592	396	11	and	and	CCONJ
ejpam-5592	396	12	m	m	PROPN
ejpam-5592	396	13	t	t	PROPN
ejpam-5592	396	14	t	t	PROPN
ejpam-5592	396	15	monteiro	monteiro	PROPN
ejpam-5592	396	16	.	.	PUNCT
ejpam-5592	397	1	fractional	fractional	ADJ
ejpam-5592	397	2	differential	differential	ADJ
ejpam-5592	397	3	equations	equation	NOUN
ejpam-5592	397	4	with	with	ADP
ejpam-5592	397	5	a	a	DET
ejpam-5592	397	6	caputo	caputo	PROPN
ejpam-5592	397	7	derivative	derivative	NOUN
ejpam-5592	397	8	with	with	ADP
ejpam-5592	397	9	respect	respect	NOUN
ejpam-5592	397	10	to	to	ADP
ejpam-5592	397	11	a	a	DET
ejpam-5592	397	12	kernel	kernel	NOUN
ejpam-5592	397	13	function	function	NOUN
ejpam-5592	397	14	and	and	CCONJ
ejpam-5592	397	15	their	their	PRON
ejpam-5592	397	16	applications	application	NOUN
ejpam-5592	397	17	.	.	PUNCT
ejpam-5592	398	1	math	math	NOUN
ejpam-5592	398	2	.	.	PUNCT
ejpam-5592	399	1	methods	method	NOUN
ejpam-5592	399	2	appl	appl	PROPN
ejpam-5592	399	3	.	.	PUNCT
ejpam-5592	400	1	sci	sci	PROPN
ejpam-5592	400	2	.	.	PROPN
ejpam-5592	400	3	,	,	PUNCT
ejpam-5592	400	4	41(1):336–352	41(1):336–352	PROPN
ejpam-5592	400	5	,	,	PUNCT
ejpam-5592	400	6	2018	2018	NUM
ejpam-5592	400	7	.	.	PUNCT
ejpam-5592	401	1	[	[	X
ejpam-5592	401	2	5	5	NUM
ejpam-5592	401	3	]	]	PUNCT
ejpam-5592	401	4	a	a	DET
ejpam-5592	401	5	atangana	atangana	NOUN
ejpam-5592	401	6	and	and	CCONJ
ejpam-5592	401	7	d	d	NOUN
ejpam-5592	401	8	baleanu	baleanu	NOUN
ejpam-5592	401	9	.	.	PUNCT
ejpam-5592	402	1	new	new	ADJ
ejpam-5592	402	2	fractional	fractional	ADJ
ejpam-5592	402	3	derivatives	derivative	NOUN
ejpam-5592	402	4	with	with	ADP
ejpam-5592	402	5	non	non	ADJ
ejpam-5592	402	6	-	-	ADJ
ejpam-5592	402	7	local	local	ADJ
ejpam-5592	402	8	and	and	CCONJ
ejpam-5592	402	9	nonsingular	nonsingular	ADJ
ejpam-5592	402	10	kernel	kernel	PROPN
ejpam-5592	402	11	:	:	PUNCT
ejpam-5592	402	12	theory	theory	NOUN
ejpam-5592	402	13	and	and	CCONJ
ejpam-5592	402	14	application	application	NOUN
ejpam-5592	402	15	to	to	PART
ejpam-5592	402	16	heat	heat	NOUN
ejpam-5592	402	17	transfer	transfer	NOUN
ejpam-5592	402	18	model	model	NOUN
ejpam-5592	402	19	.	.	PUNCT
ejpam-5592	403	1	therm	therm	PROPN
ejpam-5592	403	2	.	.	PUNCT
ejpam-5592	404	1	sci	sci	PROPN
ejpam-5592	404	2	.	.	PROPN
ejpam-5592	404	3	,	,	PUNCT
ejpam-5592	404	4	20(2):763–769	20(2):763–769	PROPN
ejpam-5592	404	5	,	,	PUNCT
ejpam-5592	404	6	2016	2016	NUM
ejpam-5592	404	7	.	.	PUNCT
ejpam-5592	405	1	[	[	X
ejpam-5592	405	2	6	6	NUM
ejpam-5592	405	3	]	]	PUNCT
ejpam-5592	405	4	m	m	VERB
ejpam-5592	405	5	i	i	PRON
ejpam-5592	405	6	ayari	ayari	PROPN
ejpam-5592	405	7	and	and	CCONJ
ejpam-5592	405	8	s	s	PROPN
ejpam-5592	405	9	t	t	PROPN
ejpam-5592	405	10	m	m	PROPN
ejpam-5592	405	11	thabet	thabet	ADJ
ejpam-5592	405	12	.	.	PUNCT
ejpam-5592	406	1	qualitative	qualitative	ADJ
ejpam-5592	406	2	properties	property	NOUN
ejpam-5592	406	3	and	and	CCONJ
ejpam-5592	406	4	approximate	approximate	ADJ
ejpam-5592	406	5	solutions	solution	NOUN
ejpam-5592	406	6	of	of	ADP
ejpam-5592	406	7	thermostat	thermostat	ADJ
ejpam-5592	406	8	fractional	fractional	ADJ
ejpam-5592	406	9	dynamics	dynamic	NOUN
ejpam-5592	406	10	system	system	NOUN
ejpam-5592	406	11	via	via	ADP
ejpam-5592	406	12	a	a	DET
ejpam-5592	406	13	nonsingular	nonsingular	ADJ
ejpam-5592	406	14	kernel	kernel	NOUN
ejpam-5592	406	15	operator	operator	NOUN
ejpam-5592	406	16	.	.	PUNCT
ejpam-5592	407	1	arab	arab	PROPN
ejpam-5592	407	2	j.	j.	PROPN
ejpam-5592	407	3	math	math	PROPN
ejpam-5592	407	4	.	.	PUNCT
ejpam-5592	408	1	sci	sci	PROPN
ejpam-5592	408	2	.	.	PROPN
ejpam-5592	408	3	,	,	PUNCT
ejpam-5592	408	4	https://doi.org/10.1108/ajms-06-2022-0147	https://doi.org/10.1108/ajms-06-2022-0147	PROPN
ejpam-5592	408	5	,	,	PUNCT
ejpam-5592	408	6	2023	2023	NUM
ejpam-5592	408	7	.	.	PUNCT
ejpam-5592	409	1	[	[	X
ejpam-5592	409	2	7	7	X
ejpam-5592	409	3	]	]	PUNCT
ejpam-5592	409	4	m	m	AUX
ejpam-5592	409	5	dalir	dalir	ADJ
ejpam-5592	409	6	and	and	CCONJ
ejpam-5592	409	7	m	m	ADJ
ejpam-5592	409	8	bashour	bashour	NOUN
ejpam-5592	409	9	.	.	PUNCT
ejpam-5592	410	1	applications	application	NOUN
ejpam-5592	410	2	of	of	ADP
ejpam-5592	410	3	fractional	fractional	ADJ
ejpam-5592	410	4	calculus	calculus	NOUN
ejpam-5592	410	5	.	.	PUNCT
ejpam-5592	411	1	math	math	NOUN
ejpam-5592	411	2	.	.	PUNCT
ejpam-5592	412	1	sci	sci	PROPN
ejpam-5592	412	2	.	.	PROPN
ejpam-5592	412	3	,	,	PUNCT
ejpam-5592	412	4	4(21):1021	4(21):1021	NUM
ejpam-5592	412	5	–	–	PUNCT
ejpam-5592	412	6	1032	1032	NUM
ejpam-5592	412	7	,	,	PUNCT
ejpam-5592	412	8	2010	2010	NUM
ejpam-5592	412	9	.	.	PUNCT
ejpam-5592	413	1	[	[	X
ejpam-5592	413	2	8	8	NUM
ejpam-5592	413	3	]	]	PUNCT
ejpam-5592	413	4	a	a	DET
ejpam-5592	413	5	fernandez	fernandez	NOUN
ejpam-5592	413	6	and	and	CCONJ
ejpam-5592	413	7	d	d	NOUN
ejpam-5592	413	8	baleanu	baleanu	NOUN
ejpam-5592	413	9	.	.	PUNCT
ejpam-5592	414	1	differintegration	differintegration	NOUN
ejpam-5592	414	2	with	with	ADP
ejpam-5592	414	3	respect	respect	NOUN
ejpam-5592	414	4	to	to	ADP
ejpam-5592	414	5	functions	function	NOUN
ejpam-5592	414	6	in	in	ADP
ejpam-5592	414	7	fractional	fractional	ADJ
ejpam-5592	414	8	models	model	NOUN
ejpam-5592	414	9	involving	involve	VERB
ejpam-5592	414	10	mittag	mittag	ADJ
ejpam-5592	414	11	-	-	PUNCT
ejpam-5592	414	12	leffler	leffler	NOUN
ejpam-5592	414	13	functions	function	NOUN
ejpam-5592	414	14	.	.	PUNCT
ejpam-5592	415	1	in	in	ADP
ejpam-5592	415	2	https://doi.org/10.2139/ssrn.3275746	https://doi.org/10.2139/ssrn.3275746	NOUN
ejpam-5592	415	3	,	,	PUNCT
ejpam-5592	415	4	editor	editor	NOUN
ejpam-5592	415	5	,	,	PUNCT
ejpam-5592	415	6	in	in	ADP
ejpam-5592	415	7	proceedings	proceeding	NOUN
ejpam-5592	415	8	of	of	ADP
ejpam-5592	415	9	international	international	ADJ
ejpam-5592	415	10	conference	conference	NOUN
ejpam-5592	415	11	on	on	ADP
ejpam-5592	415	12	fractional	fractional	ADJ
ejpam-5592	415	13	differentiation	differentiation	NOUN
ejpam-5592	415	14	and	and	CCONJ
ejpam-5592	415	15	its	its	PRON
ejpam-5592	415	16	applications	application	NOUN
ejpam-5592	415	17	(	(	PUNCT
ejpam-5592	415	18	icfda	icfda	PROPN
ejpam-5592	415	19	)	)	PUNCT
ejpam-5592	415	20	.	.	PUNCT
ejpam-5592	416	1	,	,	PUNCT
ejpam-5592	417	1	2018	2018	NUM
ejpam-5592	417	2	.	.	PUNCT
ejpam-5592	418	1	references	reference	NOUN
ejpam-5592	418	2	3706	3706	NUM
ejpam-5592	419	1	[	[	X
ejpam-5592	419	2	9	9	NUM
ejpam-5592	419	3	]	]	PUNCT
ejpam-5592	419	4	h	h	NOUN
ejpam-5592	419	5	a	a	DET
ejpam-5592	419	6	hammad	hammad	PROPN
ejpam-5592	419	7	,	,	PUNCT
ejpam-5592	419	8	h	h	PROPN
ejpam-5592	419	9	aydi	aydi	ADJ
ejpam-5592	419	10	,	,	PUNCT
ejpam-5592	419	11	h.	h.	PROPN
ejpam-5592	419	12	işık	işık	PROPN
ejpam-5592	419	13	,	,	PUNCT
ejpam-5592	419	14	and	and	CCONJ
ejpam-5592	419	15	m	m	PROPN
ejpam-5592	419	16	de	de	X
ejpam-5592	419	17	la	la	X
ejpam-5592	419	18	sen	sen	PROPN
ejpam-5592	419	19	.	.	PROPN
ejpam-5592	419	20	stability	stability	PROPN
ejpam-5592	419	21	and	and	CCONJ
ejpam-5592	419	22	controllability	controllability	NOUN
ejpam-5592	419	23	study	study	NOUN
ejpam-5592	419	24	for	for	ADP
ejpam-5592	419	25	mixed	mixed	ADJ
ejpam-5592	419	26	integral	integral	ADJ
ejpam-5592	419	27	fractional	fractional	ADJ
ejpam-5592	419	28	delay	delay	NOUN
ejpam-5592	419	29	dynamic	dynamic	ADJ
ejpam-5592	419	30	systems	system	NOUN
ejpam-5592	419	31	endowed	endow	VERB
ejpam-5592	419	32	with	with	ADP
ejpam-5592	419	33	impulsive	impulsive	ADJ
ejpam-5592	419	34	effects	effect	NOUN
ejpam-5592	419	35	on	on	ADP
ejpam-5592	419	36	time	time	NOUN
ejpam-5592	419	37	scales	scale	NOUN
ejpam-5592	419	38	.	.	PUNCT
ejpam-5592	420	1	aims	aim	VERB
ejpam-5592	420	2	math	math	NOUN
ejpam-5592	420	3	.	.	PUNCT
ejpam-5592	420	4	,	,	PUNCT
ejpam-5592	420	5	8(3):6913–6941	8(3):6913–6941	PROPN
ejpam-5592	420	6	,	,	PUNCT
ejpam-5592	420	7	2023	2023	NUM
ejpam-5592	420	8	.	.	PUNCT
ejpam-5592	421	1	[	[	X
ejpam-5592	421	2	10	10	NUM
ejpam-5592	421	3	]	]	X
ejpam-5592	421	4	h	h	NOUN
ejpam-5592	421	5	a	a	DET
ejpam-5592	421	6	hammad	hammad	PROPN
ejpam-5592	421	7	,	,	PUNCT
ejpam-5592	421	8	h	h	NOUN
ejpam-5592	421	9	aydi	aydi	ADJ
ejpam-5592	421	10	,	,	PUNCT
ejpam-5592	421	11	and	and	CCONJ
ejpam-5592	421	12	m	m	AUX
ejpam-5592	421	13	zayed	zayed	ADJ
ejpam-5592	421	14	.	.	PUNCT
ejpam-5592	422	1	on	on	ADP
ejpam-5592	422	2	the	the	DET
ejpam-5592	422	3	qualitative	qualitative	ADJ
ejpam-5592	422	4	evaluation	evaluation	NOUN
ejpam-5592	422	5	of	of	ADP
ejpam-5592	422	6	the	the	DET
ejpam-5592	422	7	variableorder	variableorder	NOUN
ejpam-5592	422	8	coupled	couple	VERB
ejpam-5592	422	9	boundary	boundary	ADJ
ejpam-5592	422	10	value	value	NOUN
ejpam-5592	422	11	problems	problem	NOUN
ejpam-5592	422	12	with	with	ADP
ejpam-5592	422	13	a	a	DET
ejpam-5592	422	14	fractional	fractional	ADJ
ejpam-5592	422	15	delay	delay	NOUN
ejpam-5592	422	16	.	.	PUNCT
ejpam-5592	423	1	j.	j.	PROPN
ejpam-5592	423	2	inequal	inequal	PROPN
ejpam-5592	423	3	.	.	PUNCT
ejpam-5592	424	1	appl	appl	PROPN
ejpam-5592	424	2	.	.	PROPN
ejpam-5592	424	3	,	,	PUNCT
ejpam-5592	424	4	2023:105	2023:105	NOUN
ejpam-5592	424	5	,	,	PUNCT
ejpam-5592	424	6	2023	2023	NUM
ejpam-5592	424	7	.	.	PUNCT
ejpam-5592	425	1	[	[	X
ejpam-5592	425	2	11	11	NUM
ejpam-5592	425	3	]	]	X
ejpam-5592	425	4	h	h	NOUN
ejpam-5592	425	5	a	a	DET
ejpam-5592	425	6	hammad	hammad	PROPN
ejpam-5592	425	7	and	and	CCONJ
ejpam-5592	425	8	m	m	PROPN
ejpam-5592	425	9	de	de	X
ejpam-5592	425	10	la	la	PROPN
ejpam-5592	425	11	sen	sen	PROPN
ejpam-5592	425	12	.	.	PROPN
ejpam-5592	425	13	solutions	solution	NOUN
ejpam-5592	425	14	of	of	ADP
ejpam-5592	425	15	fractional	fractional	ADJ
ejpam-5592	425	16	differential	differential	ADJ
ejpam-5592	425	17	type	type	NOUN
ejpam-5592	425	18	equations	equation	NOUN
ejpam-5592	425	19	by	by	ADP
ejpam-5592	425	20	fixed	fix	VERB
ejpam-5592	425	21	point	point	NOUN
ejpam-5592	425	22	techniques	technique	NOUN
ejpam-5592	425	23	for	for	ADP
ejpam-5592	425	24	multivalued	multivalued	ADJ
ejpam-5592	425	25	contractions	contraction	NOUN
ejpam-5592	425	26	.	.	PUNCT
ejpam-5592	426	1	complexity	complexity	NOUN
ejpam-5592	426	2	.	.	PUNCT
ejpam-5592	426	3	,	,	PUNCT
ejpam-5592	426	4	2021:5730853	2021:5730853	NOUN
ejpam-5592	426	5	,	,	PUNCT
ejpam-5592	426	6	2021	2021	NUM
ejpam-5592	426	7	.	.	PUNCT
ejpam-5592	427	1	[	[	X
ejpam-5592	427	2	12	12	NUM
ejpam-5592	427	3	]	]	X
ejpam-5592	427	4	h	h	NOUN
ejpam-5592	427	5	a	a	DET
ejpam-5592	427	6	hammad	hammad	PROPN
ejpam-5592	427	7	and	and	CCONJ
ejpam-5592	427	8	m	m	PROPN
ejpam-5592	427	9	de	de	X
ejpam-5592	427	10	la	la	PROPN
ejpam-5592	427	11	sen	sen	PROPN
ejpam-5592	427	12	.	.	PROPN
ejpam-5592	427	13	stability	stability	PROPN
ejpam-5592	427	14	and	and	CCONJ
ejpam-5592	427	15	controllability	controllability	NOUN
ejpam-5592	427	16	study	study	NOUN
ejpam-5592	427	17	for	for	ADP
ejpam-5592	427	18	mixed	mixed	ADJ
ejpam-5592	427	19	integral	integral	ADJ
ejpam-5592	427	20	fractional	fractional	ADJ
ejpam-5592	427	21	delay	delay	NOUN
ejpam-5592	427	22	dynamic	dynamic	ADJ
ejpam-5592	427	23	systems	system	NOUN
ejpam-5592	427	24	endowed	endow	VERB
ejpam-5592	427	25	with	with	ADP
ejpam-5592	427	26	impulsive	impulsive	ADJ
ejpam-5592	427	27	effects	effect	NOUN
ejpam-5592	427	28	on	on	ADP
ejpam-5592	427	29	time	time	NOUN
ejpam-5592	427	30	scales	scale	NOUN
ejpam-5592	427	31	.	.	PUNCT
ejpam-5592	428	1	fractal	fractal	ADJ
ejpam-5592	428	2	fract	fract	PROPN
ejpam-5592	428	3	.	.	PUNCT
ejpam-5592	428	4	,	,	PUNCT
ejpam-5592	428	5	7:92	7:92	NUM
ejpam-5592	428	6	,	,	PUNCT
ejpam-5592	428	7	2023	2023	NUM
ejpam-5592	428	8	.	.	PUNCT
ejpam-5592	429	1	[	[	X
ejpam-5592	429	2	13	13	NUM
ejpam-5592	429	3	]	]	SYM
ejpam-5592	429	4	h	h	NOUN
ejpam-5592	429	5	a	a	DET
ejpam-5592	429	6	hammad	hammad	PROPN
ejpam-5592	429	7	,	,	PUNCT
ejpam-5592	429	8	m	m	PROPN
ejpam-5592	429	9	de	de	X
ejpam-5592	429	10	la	la	X
ejpam-5592	429	11	sen	sen	PROPN
ejpam-5592	429	12	,	,	PUNCT
ejpam-5592	429	13	and	and	CCONJ
ejpam-5592	429	14	h	h	NOUN
ejpam-5592	429	15	aydi	aydi	VERB
ejpam-5592	429	16	.	.	PUNCT
ejpam-5592	430	1	generalized	generalize	VERB
ejpam-5592	430	2	dynamic	dynamic	ADJ
ejpam-5592	430	3	process	process	NOUN
ejpam-5592	430	4	for	for	ADP
ejpam-5592	430	5	an	an	DET
ejpam-5592	430	6	extended	extend	VERB
ejpam-5592	430	7	multivalued	multivalue	VERB
ejpam-5592	430	8	fcontraction	fcontraction	NOUN
ejpam-5592	430	9	in	in	ADP
ejpam-5592	430	10	metric	metric	ADJ
ejpam-5592	430	11	-	-	PUNCT
ejpam-5592	430	12	like	like	ADJ
ejpam-5592	430	13	spaces	space	NOUN
ejpam-5592	430	14	with	with	ADP
ejpam-5592	430	15	applications	application	NOUN
ejpam-5592	430	16	.	.	PUNCT
ejpam-5592	431	1	alexandria	alexandria	PROPN
ejpam-5592	431	2	engineering	engineering	PROPN
ejpam-5592	431	3	journal	journal	PROPN
ejpam-5592	431	4	,	,	PUNCT
ejpam-5592	431	5	59(5):3817–3825	59(5):3817–3825	NUM
ejpam-5592	431	6	,	,	PUNCT
ejpam-5592	431	7	2020	2020	NUM
ejpam-5592	431	8	.	.	PUNCT
ejpam-5592	432	1	[	[	X
ejpam-5592	432	2	14	14	NUM
ejpam-5592	432	3	]	]	X
ejpam-5592	432	4	h	h	NOUN
ejpam-5592	432	5	a	a	DET
ejpam-5592	432	6	hammad	hammad	PROPN
ejpam-5592	432	7	,	,	PUNCT
ejpam-5592	432	8	r	r	NOUN
ejpam-5592	432	9	a	a	DET
ejpam-5592	432	10	rashwan	rashwan	NOUN
ejpam-5592	432	11	,	,	PUNCT
ejpam-5592	432	12	a	a	DET
ejpam-5592	432	13	nafea	nafea	ADJ
ejpam-5592	432	14	,	,	PUNCT
ejpam-5592	432	15	m	m	PROPN
ejpam-5592	432	16	e	e	NOUN
ejpam-5592	432	17	samei	samei	NOUN
ejpam-5592	432	18	,	,	PUNCT
ejpam-5592	432	19	and	and	CCONJ
ejpam-5592	432	20	m	m	PROPN
ejpam-5592	432	21	de	de	X
ejpam-5592	432	22	la	la	X
ejpam-5592	432	23	sen	sen	PROPN
ejpam-5592	432	24	.	.	PROPN
ejpam-5592	432	25	stability	stability	NOUN
ejpam-5592	432	26	and	and	CCONJ
ejpam-5592	432	27	existence	existence	NOUN
ejpam-5592	432	28	of	of	ADP
ejpam-5592	432	29	solutions	solution	NOUN
ejpam-5592	432	30	for	for	ADP
ejpam-5592	432	31	a	a	DET
ejpam-5592	432	32	tripled	triple	VERB
ejpam-5592	432	33	problem	problem	NOUN
ejpam-5592	432	34	of	of	ADP
ejpam-5592	432	35	fractional	fractional	ADJ
ejpam-5592	432	36	hybrid	hybrid	ADJ
ejpam-5592	432	37	delay	delay	NOUN
ejpam-5592	432	38	differential	differential	ADJ
ejpam-5592	432	39	equations	equation	NOUN
ejpam-5592	432	40	.	.	PUNCT
ejpam-5592	433	1	symmetry	symmetry	PROPN
ejpam-5592	433	2	.	.	PUNCT
ejpam-5592	433	3	,	,	PUNCT
ejpam-5592	433	4	14:2579	14:2579	NUM
ejpam-5592	433	5	,	,	PUNCT
ejpam-5592	433	6	2022	2022	NUM
ejpam-5592	433	7	.	.	PUNCT
ejpam-5592	434	1	[	[	X
ejpam-5592	434	2	15	15	NUM
ejpam-5592	434	3	]	]	X
ejpam-5592	434	4	h	h	NOUN
ejpam-5592	434	5	a	a	DET
ejpam-5592	434	6	hammad	hammad	PROPN
ejpam-5592	434	7	,	,	PUNCT
ejpam-5592	434	8	r	r	NOUN
ejpam-5592	434	9	a	a	DET
ejpam-5592	434	10	rashwan	rashwan	NOUN
ejpam-5592	434	11	,	,	PUNCT
ejpam-5592	434	12	a	a	DET
ejpam-5592	434	13	nafea	nafea	ADJ
ejpam-5592	434	14	,	,	PUNCT
ejpam-5592	434	15	m	m	PROPN
ejpam-5592	434	16	e	e	NOUN
ejpam-5592	434	17	samei	samei	NOUN
ejpam-5592	434	18	,	,	PUNCT
ejpam-5592	434	19	and	and	CCONJ
ejpam-5592	434	20	s	s	VERB
ejpam-5592	434	21	noeiaghdam	noeiaghdam	NOUN
ejpam-5592	434	22	.	.	PUNCT
ejpam-5592	435	1	stability	stability	NOUN
ejpam-5592	435	2	analysis	analysis	NOUN
ejpam-5592	435	3	for	for	ADP
ejpam-5592	435	4	a	a	DET
ejpam-5592	435	5	tripled	triple	VERB
ejpam-5592	435	6	system	system	NOUN
ejpam-5592	435	7	of	of	ADP
ejpam-5592	435	8	fractional	fractional	ADJ
ejpam-5592	435	9	pantograph	pantograph	NOUN
ejpam-5592	435	10	differential	differential	NOUN
ejpam-5592	435	11	equations	equation	NOUN
ejpam-5592	435	12	with	with	ADP
ejpam-5592	435	13	nonlocal	nonlocal	ADJ
ejpam-5592	435	14	conditions	condition	NOUN
ejpam-5592	435	15	.	.	PUNCT
ejpam-5592	436	1	j.	j.	PROPN
ejpam-5592	436	2	vib	vib	PROPN
ejpam-5592	436	3	.	.	PUNCT
ejpam-5592	436	4	control	control	PROPN
ejpam-5592	436	5	.	.	PUNCT
ejpam-5592	436	6	,	,	PUNCT
ejpam-5592	436	7	30(3	30(3	X
ejpam-5592	436	8	-	-	PUNCT
ejpam-5592	436	9	4)):632–647	4)):632–647	NOUN
ejpam-5592	436	10	,	,	PUNCT
ejpam-5592	436	11	2024	2024	NUM
ejpam-5592	436	12	.	.	PUNCT
ejpam-5592	437	1	[	[	X
ejpam-5592	437	2	16	16	NUM
ejpam-5592	437	3	]	]	X
ejpam-5592	437	4	r	r	NOUN
ejpam-5592	437	5	hilfer	hilfer	NOUN
ejpam-5592	437	6	.	.	PUNCT
ejpam-5592	438	1	applications	application	NOUN
ejpam-5592	438	2	of	of	ADP
ejpam-5592	438	3	fractional	fractional	ADJ
ejpam-5592	438	4	calculus	calculus	NOUN
ejpam-5592	438	5	in	in	ADP
ejpam-5592	438	6	physics	physics	PROPN
ejpam-5592	438	7	.	.	PUNCT
ejpam-5592	439	1	singapore	singapore	PROPN
ejpam-5592	439	2	,	,	PUNCT
ejpam-5592	439	3	world	world	NOUN
ejpam-5592	439	4	scientific	scientific	NOUN
ejpam-5592	439	5	,	,	PUNCT
ejpam-5592	439	6	2000	2000	NUM
ejpam-5592	439	7	.	.	PUNCT
ejpam-5592	440	1	[	[	X
ejpam-5592	440	2	17	17	NUM
ejpam-5592	440	3	]	]	PUNCT
ejpam-5592	440	4	a	a	DET
ejpam-5592	440	5	kashuri	kashuri	X
ejpam-5592	440	6	.	.	PUNCT
ejpam-5592	441	1	hermite	hermite	PROPN
ejpam-5592	441	2	-	-	PUNCT
ejpam-5592	441	3	hadamard	hadamard	ADJ
ejpam-5592	441	4	type	type	NOUN
ejpam-5592	441	5	inequalities	inequality	NOUN
ejpam-5592	441	6	for	for	ADP
ejpam-5592	441	7	the	the	DET
ejpam-5592	441	8	abk	abk	PROPN
ejpam-5592	441	9	-	-	PUNCT
ejpam-5592	441	10	fractional	fractional	ADJ
ejpam-5592	441	11	integrals	integral	NOUN
ejpam-5592	441	12	.	.	PUNCT
ejpam-5592	442	1	j.	j.	PROPN
ejpam-5592	442	2	comput	comput	PROPN
ejpam-5592	442	3	.	.	PUNCT
ejpam-5592	443	1	anal	anal	PROPN
ejpam-5592	443	2	.	.	PUNCT
ejpam-5592	443	3	appl	appl	PROPN
ejpam-5592	443	4	.	.	PROPN
ejpam-5592	443	5	,	,	PUNCT
ejpam-5592	443	6	29:309–326	29:309–326	PROPN
ejpam-5592	443	7	,	,	PUNCT
ejpam-5592	443	8	2021	2021	NUM
ejpam-5592	443	9	.	.	PUNCT
ejpam-5592	444	1	[	[	X
ejpam-5592	444	2	18	18	NUM
ejpam-5592	444	3	]	]	PUNCT
ejpam-5592	444	4	a	a	DET
ejpam-5592	444	5	a	a	DET
ejpam-5592	444	6	kilbas	kilbas	NOUN
ejpam-5592	444	7	,	,	PUNCT
ejpam-5592	444	8	h	h	PROPN
ejpam-5592	444	9	m	m	PROPN
ejpam-5592	444	10	srivastava	srivastava	PROPN
ejpam-5592	444	11	,	,	PUNCT
ejpam-5592	444	12	and	and	CCONJ
ejpam-5592	444	13	j	j	PROPN
ejpam-5592	444	14	j	j	PROPN
ejpam-5592	444	15	trujillo	trujillo	PROPN
ejpam-5592	444	16	.	.	PUNCT
ejpam-5592	444	17	theory	theory	NOUN
ejpam-5592	444	18	and	and	CCONJ
ejpam-5592	444	19	applications	application	NOUN
ejpam-5592	444	20	of	of	ADP
ejpam-5592	444	21	fractional	fractional	ADJ
ejpam-5592	444	22	differential	differential	ADJ
ejpam-5592	444	23	equations	equation	NOUN
ejpam-5592	444	24	.	.	PUNCT
ejpam-5592	445	1	north	north	NOUN
ejpam-5592	445	2	-	-	PUNCT
ejpam-5592	445	3	holland	holland	PROPN
ejpam-5592	445	4	mathematics	mathematics	PROPN
ejpam-5592	445	5	studies	study	NOUN
ejpam-5592	445	6	.	.	PUNCT
ejpam-5592	446	1	elsevier	elsevier	PROPN
ejpam-5592	446	2	,	,	PUNCT
ejpam-5592	446	3	amsterdam	amsterdam	PROPN
ejpam-5592	446	4	,	,	PUNCT
ejpam-5592	446	5	2006	2006	NUM
ejpam-5592	446	6	.	.	PUNCT
ejpam-5592	447	1	[	[	X
ejpam-5592	447	2	19	19	NUM
ejpam-5592	447	3	]	]	X
ejpam-5592	447	4	r	r	NOUN
ejpam-5592	447	5	lyons	lyon	NOUN
ejpam-5592	447	6	,	,	PUNCT
ejpam-5592	447	7	a	a	DET
ejpam-5592	447	8	vatsala	vatsala	NOUN
ejpam-5592	447	9	,	,	PUNCT
ejpam-5592	447	10	and	and	CCONJ
ejpam-5592	447	11	r	r	NOUN
ejpam-5592	447	12	chiquet	chiquet	NOUN
ejpam-5592	447	13	.	.	PUNCT
ejpam-5592	448	1	picard	picard	PROPN
ejpam-5592	448	2	’s	’s	PART
ejpam-5592	448	3	iterative	iterative	NOUN
ejpam-5592	448	4	method	method	NOUN
ejpam-5592	448	5	for	for	ADP
ejpam-5592	448	6	caputo	caputo	PROPN
ejpam-5592	448	7	fractional	fractional	PROPN
ejpam-5592	448	8	differential	differential	ADJ
ejpam-5592	448	9	equations	equation	NOUN
ejpam-5592	448	10	with	with	ADP
ejpam-5592	448	11	numerical	numerical	ADJ
ejpam-5592	448	12	results	result	NOUN
ejpam-5592	448	13	.	.	PUNCT
ejpam-5592	449	1	mathematics	mathematic	NOUN
ejpam-5592	449	2	.	.	PUNCT
ejpam-5592	449	3	,	,	PUNCT
ejpam-5592	449	4	5(4):65	5(4):65	NUM
ejpam-5592	449	5	,	,	PUNCT
ejpam-5592	449	6	2017	2017	NUM
ejpam-5592	449	7	.	.	PUNCT
ejpam-5592	450	1	[	[	X
ejpam-5592	450	2	20	20	NUM
ejpam-5592	450	3	]	]	X
ejpam-5592	450	4	p	p	X
ejpam-5592	450	5	o	o	X
ejpam-5592	450	6	mohammed	mohammed	PROPN
ejpam-5592	450	7	and	and	CCONJ
ejpam-5592	450	8	t	t	PROPN
ejpam-5592	450	9	abdeljawad	abdeljawad	NOUN
ejpam-5592	450	10	.	.	PUNCT
ejpam-5592	451	1	integral	integral	ADJ
ejpam-5592	451	2	inequalities	inequality	NOUN
ejpam-5592	451	3	for	for	ADP
ejpam-5592	451	4	a	a	DET
ejpam-5592	451	5	fractional	fractional	ADJ
ejpam-5592	451	6	operator	operator	NOUN
ejpam-5592	451	7	of	of	ADP
ejpam-5592	451	8	a	a	DET
ejpam-5592	451	9	function	function	NOUN
ejpam-5592	451	10	with	with	ADP
ejpam-5592	451	11	respect	respect	NOUN
ejpam-5592	451	12	to	to	ADP
ejpam-5592	451	13	another	another	DET
ejpam-5592	451	14	function	function	NOUN
ejpam-5592	451	15	with	with	ADP
ejpam-5592	451	16	nonsingular	nonsingular	ADJ
ejpam-5592	451	17	kernel	kernel	PROPN
ejpam-5592	451	18	.	.	PUNCT
ejpam-5592	452	1	adv	adv	PROPN
ejpam-5592	452	2	.	.	PROPN
ejpam-5592	452	3	differ	differ	VERB
ejpam-5592	452	4	.	.	PUNCT
ejpam-5592	453	1	equ	equ	PROPN
ejpam-5592	453	2	.	.	PROPN
ejpam-5592	453	3	,	,	PUNCT
ejpam-5592	453	4	2020:363	2020:363	NOUN
ejpam-5592	453	5	,	,	PUNCT
ejpam-5592	453	6	2020	2020	NUM
ejpam-5592	453	7	.	.	PUNCT
ejpam-5592	454	1	[	[	X
ejpam-5592	454	2	21	21	NUM
ejpam-5592	454	3	]	]	X
ejpam-5592	454	4	m	m	VERB
ejpam-5592	454	5	rahimy	rahimy	ADJ
ejpam-5592	454	6	.	.	PUNCT
ejpam-5592	455	1	applications	application	NOUN
ejpam-5592	455	2	of	of	ADP
ejpam-5592	455	3	fractional	fractional	ADJ
ejpam-5592	455	4	differential	differential	ADJ
ejpam-5592	455	5	equations	equation	NOUN
ejpam-5592	455	6	.	.	PUNCT
ejpam-5592	456	1	appl	appl	PROPN
ejpam-5592	456	2	.	.	PROPN
ejpam-5592	456	3	math	math	PROPN
ejpam-5592	456	4	.	.	PUNCT
ejpam-5592	457	1	sci	sci	PROPN
ejpam-5592	457	2	.	.	PROPN
ejpam-5592	457	3	,	,	PUNCT
ejpam-5592	457	4	4(50):2453–2461	4(50):2453–2461	NUM
ejpam-5592	457	5	,	,	PUNCT
ejpam-5592	457	6	2010	2010	NUM
ejpam-5592	457	7	.	.	PUNCT
ejpam-5592	458	1	references	reference	NOUN
ejpam-5592	458	2	3707	3707	NUM
ejpam-5592	459	1	[	[	X
ejpam-5592	459	2	22	22	NUM
ejpam-5592	459	3	]	]	SYM
ejpam-5592	459	4	s	s	PART
ejpam-5592	459	5	k	k	PROPN
ejpam-5592	459	6	samko	samko	PROPN
ejpam-5592	459	7	,	,	PUNCT
ejpam-5592	459	8	a	a	DET
ejpam-5592	459	9	a	a	DET
ejpam-5592	459	10	kilbas	kilbas	NOUN
ejpam-5592	459	11	,	,	PUNCT
ejpam-5592	459	12	and	and	CCONJ
ejpam-5592	459	13	o	o	PROPN
ejpam-5592	459	14	i.	i.	PROPN
ejpam-5592	459	15	marichev	marichev	PROPN
ejpam-5592	459	16	.	.	PUNCT
ejpam-5592	460	1	fractional	fractional	ADJ
ejpam-5592	460	2	integrals	integral	NOUN
ejpam-5592	460	3	and	and	CCONJ
ejpam-5592	460	4	derivatives	derivative	NOUN
ejpam-5592	460	5	:	:	PUNCT
ejpam-5592	460	6	theory	theory	NOUN
ejpam-5592	460	7	and	and	CCONJ
ejpam-5592	460	8	applications	application	NOUN
ejpam-5592	460	9	.	.	PUNCT
ejpam-5592	461	1	gordon	gordon	PROPN
ejpam-5592	461	2	and	and	CCONJ
ejpam-5592	461	3	breach	breach	VERB
ejpam-5592	461	4	science	science	NOUN
ejpam-5592	461	5	,	,	PUNCT
ejpam-5592	461	6	switzerland	switzerland	PROPN
ejpam-5592	461	7	,	,	PUNCT
ejpam-5592	461	8	1993	1993	NUM
ejpam-5592	461	9	.	.	PUNCT
ejpam-5592	462	1	[	[	X
ejpam-5592	462	2	23	23	NUM
ejpam-5592	462	3	]	]	X
ejpam-5592	462	4	k	k	PROPN
ejpam-5592	462	5	shah	shah	PROPN
ejpam-5592	462	6	,	,	PUNCT
ejpam-5592	462	7	t	t	PROPN
ejpam-5592	462	8	abdeljawad	abdeljawad	NOUN
ejpam-5592	462	9	,	,	PUNCT
ejpam-5592	462	10	m	m	PROPN
ejpam-5592	462	11	b	b	NOUN
ejpam-5592	462	12	jeelani	jeelani	ADJ
ejpam-5592	462	13	,	,	PUNCT
ejpam-5592	462	14	and	and	CCONJ
ejpam-5592	462	15	m	m	VERB
ejpam-5592	462	16	a	a	DET
ejpam-5592	462	17	alqudah	alqudah	NOUN
ejpam-5592	462	18	.	.	PUNCT
ejpam-5592	463	1	spectral	spectral	ADJ
ejpam-5592	463	2	analysis	analysis	NOUN
ejpam-5592	463	3	of	of	ADP
ejpam-5592	463	4	variableorder	variableorder	NOUN
ejpam-5592	463	5	multi	multi	ADJ
ejpam-5592	463	6	-	-	ADJ
ejpam-5592	463	7	terms	term	NOUN
ejpam-5592	463	8	fractional	fractional	ADJ
ejpam-5592	463	9	differential	differential	ADJ
ejpam-5592	463	10	equations	equation	NOUN
ejpam-5592	463	11	.	.	PUNCT
ejpam-5592	464	1	open	open	ADJ
ejpam-5592	464	2	phy	phy	PROPN
ejpam-5592	464	3	.	.	PROPN
ejpam-5592	464	4	,	,	PUNCT
ejpam-5592	464	5	21(1):20230136	21(1):20230136	NUM
ejpam-5592	464	6	,	,	PUNCT
ejpam-5592	464	7	2023	2023	NUM
ejpam-5592	464	8	.	.	PUNCT
ejpam-5592	465	1	[	[	X
ejpam-5592	465	2	24	24	NUM
ejpam-5592	465	3	]	]	X
ejpam-5592	465	4	k	k	PROPN
ejpam-5592	465	5	shah	shah	PROPN
ejpam-5592	465	6	,	,	PUNCT
ejpam-5592	465	7	g	g	PROPN
ejpam-5592	465	8	ali	ali	PROPN
ejpam-5592	465	9	,	,	PUNCT
ejpam-5592	465	10	k	k	PROPN
ejpam-5592	465	11	j	j	PROPN
ejpam-5592	465	12	ansari	ansari	PROPN
ejpam-5592	465	13	,	,	PUNCT
ejpam-5592	465	14	m	m	VERB
ejpam-5592	465	15	meganathan	meganathan	ADJ
ejpam-5592	465	16	,	,	PUNCT
ejpam-5592	465	17	and	and	CCONJ
ejpam-5592	465	18	b	b	X
ejpam-5592	465	19	abdalla	abdalla	PROPN
ejpam-5592	465	20	.	.	PUNCT
ejpam-5592	466	1	on	on	ADP
ejpam-5592	466	2	qualitative	qualitative	ADJ
ejpam-5592	466	3	analysis	analysis	NOUN
ejpam-5592	466	4	of	of	ADP
ejpam-5592	466	5	boundary	boundary	ADJ
ejpam-5592	466	6	value	value	NOUN
ejpam-5592	466	7	problem	problem	NOUN
ejpam-5592	466	8	of	of	ADP
ejpam-5592	466	9	variable	variable	ADJ
ejpam-5592	466	10	order	order	NOUN
ejpam-5592	466	11	fractional	fractional	ADJ
ejpam-5592	466	12	delay	delay	NOUN
ejpam-5592	466	13	differential	differential	ADJ
ejpam-5592	466	14	equations	equation	NOUN
ejpam-5592	466	15	.	.	PUNCT
ejpam-5592	467	1	bound	bind	VERB
ejpam-5592	467	2	.	.	PUNCT
ejpam-5592	468	1	value	value	PROPN
ejpam-5592	468	2	probl	probl	PROPN
ejpam-5592	468	3	.	.	PUNCT
ejpam-5592	468	4	,	,	PUNCT
ejpam-5592	468	5	1023:55	1023:55	NUM
ejpam-5592	468	6	,	,	PUNCT
ejpam-5592	468	7	2023	2023	NUM
ejpam-5592	468	8	.	.	PUNCT
ejpam-5592	469	1	[	[	X
ejpam-5592	469	2	25	25	NUM
ejpam-5592	469	3	]	]	X
ejpam-5592	469	4	k	k	PROPN
ejpam-5592	469	5	shah	shah	PROPN
ejpam-5592	469	6	,	,	PUNCT
ejpam-5592	469	7	h	h	PROPN
ejpam-5592	469	8	naz	naz	PROPN
ejpam-5592	469	9	,	,	PUNCT
ejpam-5592	469	10	m	m	VERB
ejpam-5592	469	11	sarwar	sarwar	ADJ
ejpam-5592	469	12	,	,	PUNCT
ejpam-5592	469	13	and	and	CCONJ
ejpam-5592	469	14	t	t	PROPN
ejpam-5592	469	15	abdeljawad	abdeljawad	NOUN
ejpam-5592	469	16	.	.	PUNCT
ejpam-5592	470	1	on	on	ADP
ejpam-5592	470	2	spectral	spectral	ADJ
ejpam-5592	470	3	numerical	numerical	ADJ
ejpam-5592	470	4	method	method	NOUN
ejpam-5592	470	5	for	for	ADP
ejpam-5592	470	6	variable	variable	ADJ
ejpam-5592	470	7	-	-	PUNCT
ejpam-5592	470	8	order	order	NOUN
ejpam-5592	470	9	partial	partial	ADJ
ejpam-5592	470	10	differential	differential	NOUN
ejpam-5592	470	11	equations	equation	NOUN
ejpam-5592	470	12	.	.	PUNCT
ejpam-5592	471	1	aims	aim	VERB
ejpam-5592	471	2	math	math	NOUN
ejpam-5592	471	3	.	.	PUNCT
ejpam-5592	471	4	,	,	PUNCT
ejpam-5592	472	1	7(6):10422–10438	7(6):10422–10438	NUM
ejpam-5592	472	2	,	,	PUNCT
ejpam-5592	472	3	2022	2022	NUM
ejpam-5592	472	4	.	.	PUNCT
ejpam-5592	473	1	[	[	X
ejpam-5592	473	2	26	26	NUM
ejpam-5592	473	3	]	]	X
ejpam-5592	473	4	m	m	VERB
ejpam-5592	473	5	sher	sher	PROPN
ejpam-5592	473	6	,	,	PUNCT
ejpam-5592	473	7	k	k	PROPN
ejpam-5592	473	8	shah	shah	PROPN
ejpam-5592	473	9	,	,	PUNCT
ejpam-5592	473	10	and	and	CCONJ
ejpam-5592	473	11	j	j	PROPN
ejpam-5592	473	12	rassias	rassias	PROPN
ejpam-5592	473	13	.	.	PUNCT
ejpam-5592	474	1	on	on	ADP
ejpam-5592	474	2	qualitative	qualitative	ADJ
ejpam-5592	474	3	theory	theory	NOUN
ejpam-5592	474	4	of	of	ADP
ejpam-5592	474	5	fractional	fractional	ADJ
ejpam-5592	474	6	order	order	NOUN
ejpam-5592	474	7	delay	delay	NOUN
ejpam-5592	474	8	evolution	evolution	NOUN
ejpam-5592	474	9	equation	equation	NOUN
ejpam-5592	474	10	via	via	ADP
ejpam-5592	474	11	the	the	DET
ejpam-5592	474	12	prior	prior	ADJ
ejpam-5592	474	13	estimate	estimate	NOUN
ejpam-5592	474	14	method	method	NOUN
ejpam-5592	474	15	.	.	PUNCT
ejpam-5592	475	1	math	math	NOUN
ejpam-5592	475	2	.	.	PUNCT
ejpam-5592	476	1	methods	method	NOUN
ejpam-5592	476	2	appl	appl	PROPN
ejpam-5592	476	3	.	.	PUNCT
ejpam-5592	477	1	sci	sci	PROPN
ejpam-5592	477	2	.	.	PROPN
ejpam-5592	477	3	,	,	PUNCT
ejpam-5592	477	4	43(10):6464	43(10):6464	NUM
ejpam-5592	477	5	–	–	PUNCT
ejpam-5592	477	6	6475	6475	NUM
ejpam-5592	477	7	,	,	PUNCT
ejpam-5592	477	8	2020	2020	NUM
ejpam-5592	477	9	.	.	PUNCT
ejpam-5592	478	1	[	[	X
ejpam-5592	478	2	27	27	NUM
ejpam-5592	478	3	]	]	X
ejpam-5592	478	4	j	j	PROPN
ejpam-5592	478	5	v	v	PROPN
ejpam-5592	478	6	c	c	PROPN
ejpam-5592	478	7	sousa	sousa	PROPN
ejpam-5592	478	8	and	and	CCONJ
ejpam-5592	478	9	e	e	PROPN
ejpam-5592	478	10	c	c	PROPN
ejpam-5592	478	11	oliveira	oliveira	PROPN
ejpam-5592	478	12	.	.	PUNCT
ejpam-5592	479	1	a	a	DET
ejpam-5592	479	2	gronwall	gronwall	ADJ
ejpam-5592	479	3	inequality	inequality	NOUN
ejpam-5592	479	4	and	and	CCONJ
ejpam-5592	479	5	the	the	DET
ejpam-5592	479	6	cauchy	cauchy	NOUN
ejpam-5592	479	7	-	-	PUNCT
ejpam-5592	479	8	type	type	NOUN
ejpam-5592	479	9	problem	problem	NOUN
ejpam-5592	479	10	by	by	ADP
ejpam-5592	479	11	means	mean	NOUN
ejpam-5592	479	12	of	of	ADP
ejpam-5592	479	13	ψ−hilfer	ψ−hilfer	NOUN
ejpam-5592	479	14	operators	operator	NOUN
ejpam-5592	479	15	.	.	PUNCT
ejpam-5592	480	1	differ	differ	VERB
ejpam-5592	480	2	.	.	PUNCT
ejpam-5592	481	1	equ	equ	PROPN
ejpam-5592	481	2	.	.	PUNCT
ejpam-5592	481	3	appl	appl	PROPN
ejpam-5592	481	4	.	.	PROPN
ejpam-5592	481	5	,	,	PUNCT
ejpam-5592	481	6	11:87–106	11:87–106	NUM
ejpam-5592	481	7	,	,	PUNCT
ejpam-5592	481	8	2019	2019	NUM
ejpam-5592	481	9	.	.	PUNCT
ejpam-5592	482	1	[	[	X
ejpam-5592	482	2	28	28	NUM
ejpam-5592	482	3	]	]	SYM
ejpam-5592	482	4	v	v	ADP
ejpam-5592	482	5	stojiljković.	stojiljković.	PROPN
ejpam-5592	482	6	hermite	hermite	ADJ
ejpam-5592	482	7	hadamard	hadamard	ADJ
ejpam-5592	482	8	type	type	NOUN
ejpam-5592	482	9	inequalities	inequality	NOUN
ejpam-5592	482	10	involving	involve	VERB
ejpam-5592	482	11	(	(	PUNCT
ejpam-5592	482	12	k−	k−	NOUN
ejpam-5592	482	13	p	p	NOUN
ejpam-5592	482	14	)	)	PUNCT
ejpam-5592	482	15	fractional	fractional	ADJ
ejpam-5592	482	16	operator	operator	NOUN
ejpam-5592	482	17	with	with	ADP
ejpam-5592	482	18	(	(	PUNCT
ejpam-5592	482	19	α	α	NOUN
ejpam-5592	482	20	,	,	PUNCT
ejpam-5592	482	21	h−m)−	h−m)−	NOUN
ejpam-5592	482	22	p	p	NOUN
ejpam-5592	482	23	convexity	convexity	NOUN
ejpam-5592	482	24	.	.	PUNCT
ejpam-5592	483	1	eur	eur	PROPN
ejpam-5592	483	2	.	.	PUNCT
ejpam-5592	484	1	j.	j.	PROPN
ejpam-5592	484	2	pure	pure	PROPN
ejpam-5592	484	3	appl	appl	PROPN
ejpam-5592	484	4	.	.	PUNCT
ejpam-5592	484	5	math	math	PROPN
ejpam-5592	484	6	.	.	PUNCT
ejpam-5592	484	7	,	,	PUNCT
ejpam-5592	484	8	1616):503–522	1616):503–522	NUM
ejpam-5592	484	9	,	,	PUNCT
ejpam-5592	484	10	2023	2023	NUM
ejpam-5592	484	11	.	.	PUNCT