id	sid	tid	token	lemma	pos
ejpam-6633	1	1	european	european	PROPN
ejpam-6633	1	2	journal	journal	PROPN
ejpam-6633	1	3	of	of	ADP
ejpam-6633	1	4	pure	pure	ADJ
ejpam-6633	1	5	and	and	CCONJ
ejpam-6633	1	6	applied	applied	ADJ
ejpam-6633	1	7	mathematics	mathematic	NOUN
ejpam-6633	1	8	2025	2025	NUM
ejpam-6633	1	9	,	,	PUNCT
ejpam-6633	1	10	vol	vol	NOUN
ejpam-6633	1	11	.	.	PROPN
ejpam-6633	1	12	18	18	NUM
ejpam-6633	1	13	,	,	PUNCT
ejpam-6633	1	14	issue	issue	NOUN
ejpam-6633	1	15	3	3	NUM
ejpam-6633	1	16	,	,	PUNCT
ejpam-6633	1	17	article	article	NOUN
ejpam-6633	1	18	number	number	NOUN
ejpam-6633	1	19	6633	6633	NUM
ejpam-6633	1	20	issn	issn	PROPN
ejpam-6633	1	21	1307	1307	NUM
ejpam-6633	1	22	-	-	SYM
ejpam-6633	1	23	5543	5543	NUM
ejpam-6633	1	24	–	–	PUNCT
ejpam-6633	1	25	ejpam.com	ejpam.com	X
ejpam-6633	1	26	published	publish	VERB
ejpam-6633	1	27	by	by	ADP
ejpam-6633	1	28	new	new	PROPN
ejpam-6633	1	29	york	york	PROPN
ejpam-6633	1	30	business	business	PROPN
ejpam-6633	2	1	global	global	PROPN
ejpam-6633	2	2	a	a	DET
ejpam-6633	2	3	boundary	boundary	ADJ
ejpam-6633	2	4	-	-	PUNCT
ejpam-6633	2	5	value	value	NOUN
ejpam-6633	2	6	problem	problem	NOUN
ejpam-6633	2	7	with	with	ADP
ejpam-6633	2	8	caputo	caputo	PROPN
ejpam-6633	2	9	-	-	PUNCT
ejpam-6633	2	10	hadamard	hadamard	ADJ
ejpam-6633	2	11	fractional	fractional	ADJ
ejpam-6633	2	12	derivative	derivative	NOUN
ejpam-6633	2	13	:	:	PUNCT
ejpam-6633	2	14	analysis	analysis	NOUN
ejpam-6633	2	15	and	and	CCONJ
ejpam-6633	2	16	numerical	numerical	ADJ
ejpam-6633	2	17	solution	solution	NOUN
ejpam-6633	2	18	afrah	afrah	PROPN
ejpam-6633	2	19	sadiq	sadiq	PROPN
ejpam-6633	2	20	hasan1,∗	hasan1,∗	PROPN
ejpam-6633	2	21	,	,	PUNCT
ejpam-6633	2	22	shayma	shayma	PROPN
ejpam-6633	2	23	adil	adil	PROPN
ejpam-6633	2	24	murad1	murad1	PROPN
ejpam-6633	2	25	1	1	NUM
ejpam-6633	2	26	department	department	NOUN
ejpam-6633	2	27	of	of	ADP
ejpam-6633	2	28	mathematics	mathematic	NOUN
ejpam-6633	2	29	,	,	PUNCT
ejpam-6633	2	30	college	college	NOUN
ejpam-6633	2	31	of	of	ADP
ejpam-6633	2	32	science	science	NOUN
ejpam-6633	2	33	,	,	PUNCT
ejpam-6633	2	34	university	university	NOUN
ejpam-6633	2	35	of	of	ADP
ejpam-6633	2	36	duhok	duhok	NOUN
ejpam-6633	2	37	,	,	PUNCT
ejpam-6633	2	38	duhok	duhok	NOUN
ejpam-6633	2	39	,	,	PUNCT
ejpam-6633	2	40	iraq	iraq	PROPN
ejpam-6633	2	41	abstract	abstract	NOUN
ejpam-6633	2	42	.	.	PUNCT
ejpam-6633	3	1	we	we	PRON
ejpam-6633	3	2	investigate	investigate	VERB
ejpam-6633	3	3	a	a	DET
ejpam-6633	3	4	boundary	boundary	ADJ
ejpam-6633	3	5	-	-	PUNCT
ejpam-6633	3	6	value	value	NOUN
ejpam-6633	3	7	problem	problem	NOUN
ejpam-6633	3	8	governed	govern	VERB
ejpam-6633	3	9	by	by	ADP
ejpam-6633	3	10	a	a	DET
ejpam-6633	3	11	fractional	fractional	ADJ
ejpam-6633	3	12	differential	differential	NOUN
ejpam-6633	3	13	equation	equation	NOUN
ejpam-6633	3	14	,	,	PUNCT
ejpam-6633	3	15	which	which	PRON
ejpam-6633	3	16	is	be	AUX
ejpam-6633	3	17	non	non	ADJ
ejpam-6633	3	18	-	-	ADJ
ejpam-6633	3	19	linear	linear	ADJ
ejpam-6633	3	20	.	.	PUNCT
ejpam-6633	4	1	the	the	DET
ejpam-6633	4	2	fractional	fractional	ADJ
ejpam-6633	4	3	derivative	derivative	NOUN
ejpam-6633	4	4	is	be	AUX
ejpam-6633	4	5	the	the	DET
ejpam-6633	4	6	combined	combined	ADJ
ejpam-6633	4	7	caputo	caputo	PROPN
ejpam-6633	4	8	-	-	PUNCT
ejpam-6633	4	9	hadamard	hadamard	ADJ
ejpam-6633	4	10	fractional	fractional	ADJ
ejpam-6633	4	11	derivative	derivative	NOUN
ejpam-6633	4	12	.	.	PUNCT
ejpam-6633	5	1	we	we	PRON
ejpam-6633	5	2	establish	establish	VERB
ejpam-6633	5	3	the	the	DET
ejpam-6633	5	4	required	require	VERB
ejpam-6633	5	5	conditions	condition	NOUN
ejpam-6633	5	6	for	for	ADP
ejpam-6633	5	7	the	the	DET
ejpam-6633	5	8	existence	existence	NOUN
ejpam-6633	5	9	and	and	CCONJ
ejpam-6633	5	10	uniqueness	uniqueness	NOUN
ejpam-6633	5	11	of	of	ADP
ejpam-6633	5	12	solutions	solution	NOUN
ejpam-6633	5	13	,	,	PUNCT
ejpam-6633	5	14	utilising	utilise	VERB
ejpam-6633	5	15	the	the	DET
ejpam-6633	5	16	two	two	NUM
ejpam-6633	5	17	standard	standard	ADJ
ejpam-6633	5	18	fixed	fix	VERB
ejpam-6633	5	19	-	-	PUNCT
ejpam-6633	5	20	point	point	NOUN
ejpam-6633	5	21	theorems	theorem	NOUN
ejpam-6633	5	22	,	,	PUNCT
ejpam-6633	5	23	banach	banach	ADV
ejpam-6633	5	24	fixed	fix	VERB
ejpam-6633	5	25	-	-	PUNCT
ejpam-6633	5	26	point	point	NOUN
ejpam-6633	5	27	and	and	CCONJ
ejpam-6633	5	28	sadovskii	sadovskii	VERB
ejpam-6633	5	29	fixed	fix	VERB
ejpam-6633	5	30	-	-	PUNCT
ejpam-6633	5	31	point	point	NOUN
ejpam-6633	5	32	.	.	PUNCT
ejpam-6633	6	1	furthermore	furthermore	ADV
ejpam-6633	6	2	,	,	PUNCT
ejpam-6633	6	3	we	we	PRON
ejpam-6633	6	4	address	address	VERB
ejpam-6633	6	5	and	and	CCONJ
ejpam-6633	6	6	analyse	analyse	VERB
ejpam-6633	6	7	the	the	DET
ejpam-6633	6	8	problem	problem	NOUN
ejpam-6633	6	9	’s	’s	PART
ejpam-6633	6	10	stability	stability	NOUN
ejpam-6633	6	11	through	through	ADP
ejpam-6633	6	12	demanding	demand	VERB
ejpam-6633	6	13	conditions	condition	NOUN
ejpam-6633	6	14	using	use	VERB
ejpam-6633	6	15	the	the	DET
ejpam-6633	6	16	ulam	ulam	NOUN
ejpam-6633	6	17	-	-	PUNCT
ejpam-6633	6	18	hyers	hyer	NOUN
ejpam-6633	6	19	and	and	CCONJ
ejpam-6633	6	20	ulam	ulam	NOUN
ejpam-6633	6	21	-	-	PUNCT
ejpam-6633	6	22	hyers	hyer	NOUN
ejpam-6633	6	23	-	-	PUNCT
ejpam-6633	6	24	rassias	rassias	PROPN
ejpam-6633	6	25	stability	stability	NOUN
ejpam-6633	6	26	methods	method	NOUN
ejpam-6633	6	27	.	.	PUNCT
ejpam-6633	7	1	to	to	PART
ejpam-6633	7	2	illustrate	illustrate	VERB
ejpam-6633	7	3	the	the	DET
ejpam-6633	7	4	theoretical	theoretical	ADJ
ejpam-6633	7	5	results	result	NOUN
ejpam-6633	7	6	,	,	PUNCT
ejpam-6633	7	7	we	we	PRON
ejpam-6633	7	8	present	present	VERB
ejpam-6633	7	9	an	an	DET
ejpam-6633	7	10	example	example	NOUN
ejpam-6633	7	11	that	that	PRON
ejpam-6633	7	12	validates	validate	VERB
ejpam-6633	7	13	the	the	DET
ejpam-6633	7	14	existence	existence	NOUN
ejpam-6633	7	15	,	,	PUNCT
ejpam-6633	7	16	uniqueness	uniqueness	NOUN
ejpam-6633	7	17	,	,	PUNCT
ejpam-6633	7	18	and	and	CCONJ
ejpam-6633	7	19	stability	stability	NOUN
ejpam-6633	7	20	criteria	criterion	NOUN
ejpam-6633	7	21	.	.	PUNCT
ejpam-6633	8	1	the	the	DET
ejpam-6633	8	2	analytical	analytical	ADJ
ejpam-6633	8	3	solution	solution	NOUN
ejpam-6633	8	4	obtained	obtain	VERB
ejpam-6633	8	5	from	from	ADP
ejpam-6633	8	6	the	the	DET
ejpam-6633	8	7	problem	problem	NOUN
ejpam-6633	8	8	is	be	AUX
ejpam-6633	8	9	discretised	discretise	VERB
ejpam-6633	8	10	with	with	ADP
ejpam-6633	8	11	fractional	fractional	ADJ
ejpam-6633	8	12	rectangular	rectangular	ADJ
ejpam-6633	8	13	,	,	PUNCT
ejpam-6633	8	14	lln,1	lln,1	NOUN
ejpam-6633	8	15	interpolation	interpolation	NOUN
ejpam-6633	8	16	on	on	ADP
ejpam-6633	8	17	a	a	DET
ejpam-6633	8	18	non	non	ADJ
ejpam-6633	8	19	-	-	ADJ
ejpam-6633	8	20	uniform	uniform	ADJ
ejpam-6633	8	21	mesh	mesh	NOUN
ejpam-6633	8	22	.	.	PUNCT
ejpam-6633	9	1	the	the	DET
ejpam-6633	9	2	resulting	result	VERB
ejpam-6633	9	3	system	system	NOUN
ejpam-6633	9	4	of	of	ADP
ejpam-6633	9	5	non	non	ADJ
ejpam-6633	9	6	-	-	ADJ
ejpam-6633	9	7	linear	linear	ADJ
ejpam-6633	9	8	equations	equation	NOUN
ejpam-6633	9	9	is	be	AUX
ejpam-6633	9	10	solved	solve	VERB
ejpam-6633	9	11	using	use	VERB
ejpam-6633	9	12	the	the	DET
ejpam-6633	9	13	newtonraphson	newtonraphson	NOUN
ejpam-6633	9	14	method	method	NOUN
ejpam-6633	9	15	,	,	PUNCT
ejpam-6633	9	16	incorporating	incorporate	VERB
ejpam-6633	9	17	the	the	DET
ejpam-6633	9	18	jacobian	jacobian	ADJ
ejpam-6633	9	19	matrix	matrix	NOUN
ejpam-6633	9	20	to	to	ADP
ejpam-6633	9	21	couple	couple	NOUN
ejpam-6633	9	22	η(t	η(t	NOUN
ejpam-6633	9	23	)	)	PUNCT
ejpam-6633	9	24	and	and	CCONJ
ejpam-6633	9	25	θ(t	θ(t	PROPN
ejpam-6633	9	26	,	,	PUNCT
ejpam-6633	9	27	η(t	η(t	NOUN
ejpam-6633	9	28	)	)	PUNCT
ejpam-6633	9	29	)	)	PUNCT
ejpam-6633	9	30	non	non	ADJ
ejpam-6633	9	31	-	-	ADJ
ejpam-6633	9	32	linearly	linearly	ADV
ejpam-6633	9	33	.	.	PUNCT
ejpam-6633	10	1	the	the	DET
ejpam-6633	10	2	stability	stability	NOUN
ejpam-6633	10	3	and	and	CCONJ
ejpam-6633	10	4	reliability	reliability	NOUN
ejpam-6633	10	5	of	of	ADP
ejpam-6633	10	6	the	the	DET
ejpam-6633	10	7	suggested	suggest	VERB
ejpam-6633	10	8	numerical	numerical	PROPN
ejpam-6633	10	9	approach	approach	NOUN
ejpam-6633	10	10	are	be	AUX
ejpam-6633	10	11	examined	examine	VERB
ejpam-6633	10	12	through	through	ADP
ejpam-6633	10	13	illustrative	illustrative	ADJ
ejpam-6633	10	14	examples	example	NOUN
ejpam-6633	10	15	.	.	PUNCT
ejpam-6633	11	1	2020	2020	NUM
ejpam-6633	11	2	mathematics	mathematic	NOUN
ejpam-6633	11	3	subject	subject	NOUN
ejpam-6633	11	4	classifications	classification	NOUN
ejpam-6633	11	5	:	:	PUNCT
ejpam-6633	11	6	34a08	34a08	NUM
ejpam-6633	11	7	,	,	PUNCT
ejpam-6633	11	8	34k37	34k37	NUM
ejpam-6633	11	9	,	,	PUNCT
ejpam-6633	11	10	34a12	34a12	NUM
ejpam-6633	11	11	,	,	PUNCT
ejpam-6633	11	12	34dxx	34dxx	NOUN
ejpam-6633	11	13	,	,	PUNCT
ejpam-6633	11	14	65lxx	65lxx	NOUN
ejpam-6633	11	15	key	key	ADJ
ejpam-6633	11	16	words	word	NOUN
ejpam-6633	11	17	and	and	CCONJ
ejpam-6633	11	18	phrases	phrase	NOUN
ejpam-6633	11	19	:	:	PUNCT
ejpam-6633	11	20	lane	lane	NOUN
ejpam-6633	11	21	-	-	PUNCT
ejpam-6633	11	22	emden	emden	ADJ
ejpam-6633	11	23	fractional	fractional	ADJ
ejpam-6633	11	24	differential	differential	NOUN
ejpam-6633	11	25	equation	equation	NOUN
ejpam-6633	11	26	,	,	PUNCT
ejpam-6633	11	27	existance	existance	NOUN
ejpam-6633	11	28	,	,	PUNCT
ejpam-6633	11	29	uniqueness	uniqueness	NOUN
ejpam-6633	11	30	,	,	PUNCT
ejpam-6633	11	31	stability	stability	NOUN
ejpam-6633	11	32	,	,	PUNCT
ejpam-6633	11	33	numerical	numerical	ADJ
ejpam-6633	11	34	solution	solution	NOUN
ejpam-6633	11	35	1	1	NUM
ejpam-6633	11	36	.	.	PUNCT
ejpam-6633	12	1	introduction	introduction	NOUN
ejpam-6633	12	2	it	it	PRON
ejpam-6633	12	3	is	be	AUX
ejpam-6633	12	4	an	an	DET
ejpam-6633	12	5	indisputable	indisputable	ADJ
ejpam-6633	12	6	fact	fact	NOUN
ejpam-6633	12	7	that	that	SCONJ
ejpam-6633	12	8	fractional	fractional	ADJ
ejpam-6633	12	9	differential	differential	ADJ
ejpam-6633	12	10	equations	equation	NOUN
ejpam-6633	12	11	(	(	PUNCT
ejpam-6633	12	12	fdes	fde	NOUN
ejpam-6633	12	13	)	)	PUNCT
ejpam-6633	12	14	are	be	AUX
ejpam-6633	12	15	crucial	crucial	ADJ
ejpam-6633	12	16	for	for	ADP
ejpam-6633	12	17	modeling	model	VERB
ejpam-6633	12	18	complex	complex	ADJ
ejpam-6633	12	19	systems	system	NOUN
ejpam-6633	12	20	where	where	SCONJ
ejpam-6633	12	21	traditional	traditional	ADJ
ejpam-6633	12	22	integer	integer	NOUN
ejpam-6633	12	23	-	-	PUNCT
ejpam-6633	12	24	order	order	NOUN
ejpam-6633	12	25	equations	equation	NOUN
ejpam-6633	12	26	fall	fall	VERB
ejpam-6633	12	27	short	short	ADJ
ejpam-6633	12	28	,	,	PUNCT
ejpam-6633	12	29	see	see	VERB
ejpam-6633	12	30	[	[	X
ejpam-6633	12	31	1	1	NUM
ejpam-6633	12	32	,	,	PUNCT
ejpam-6633	12	33	2	2	NUM
ejpam-6633	12	34	]	]	PUNCT
ejpam-6633	12	35	.	.	PUNCT
ejpam-6633	13	1	they	they	PRON
ejpam-6633	13	2	offer	offer	VERB
ejpam-6633	13	3	a	a	DET
ejpam-6633	13	4	more	more	ADV
ejpam-6633	13	5	flexible	flexible	ADJ
ejpam-6633	13	6	and	and	CCONJ
ejpam-6633	13	7	accurate	accurate	ADJ
ejpam-6633	13	8	framework	framework	NOUN
ejpam-6633	13	9	for	for	ADP
ejpam-6633	13	10	governing	govern	VERB
ejpam-6633	13	11	processes	process	NOUN
ejpam-6633	13	12	with	with	ADP
ejpam-6633	13	13	nonlocal	nonlocal	ADJ
ejpam-6633	13	14	behaviors	behavior	NOUN
ejpam-6633	13	15	and	and	CCONJ
ejpam-6633	13	16	irregular	irregular	ADJ
ejpam-6633	13	17	dynamics	dynamic	NOUN
ejpam-6633	13	18	.	.	PUNCT
ejpam-6633	14	1	this	this	PRON
ejpam-6633	14	2	makes	make	VERB
ejpam-6633	14	3	fdes	fde	NOUN
ejpam-6633	14	4	valuable	valuable	ADJ
ejpam-6633	14	5	across	across	ADP
ejpam-6633	14	6	various	various	ADJ
ejpam-6633	14	7	fields	field	NOUN
ejpam-6633	14	8	,	,	PUNCT
ejpam-6633	14	9	including	include	VERB
ejpam-6633	14	10	physics	physics	NOUN
ejpam-6633	14	11	,	,	PUNCT
ejpam-6633	14	12	biology	biology	NOUN
ejpam-6633	14	13	,	,	PUNCT
ejpam-6633	14	14	engineering	engineering	NOUN
ejpam-6633	14	15	,	,	PUNCT
ejpam-6633	14	16	and	and	CCONJ
ejpam-6633	14	17	finance	finance	NOUN
ejpam-6633	14	18	,	,	PUNCT
ejpam-6633	14	19	where	where	SCONJ
ejpam-6633	14	20	systems	system	NOUN
ejpam-6633	14	21	exhibit	exhibit	VERB
ejpam-6633	14	22	non	non	ADJ
ejpam-6633	14	23	-	-	ADJ
ejpam-6633	14	24	linear	linear	ADJ
ejpam-6633	14	25	and	and	CCONJ
ejpam-6633	14	26	complex	complex	ADJ
ejpam-6633	14	27	characteristics	characteristic	NOUN
ejpam-6633	14	28	.	.	PUNCT
ejpam-6633	15	1	the	the	DET
ejpam-6633	15	2	ability	ability	NOUN
ejpam-6633	15	3	of	of	ADP
ejpam-6633	15	4	fdes	fde	NOUN
ejpam-6633	15	5	to	to	PART
ejpam-6633	15	6	capture	capture	VERB
ejpam-6633	15	7	a	a	DET
ejpam-6633	15	8	wider	wide	ADJ
ejpam-6633	15	9	range	range	NOUN
ejpam-6633	15	10	of	of	ADP
ejpam-6633	15	11	phenomena	phenomenon	NOUN
ejpam-6633	15	12	makes	make	VERB
ejpam-6633	15	13	them	they	PRON
ejpam-6633	15	14	an	an	DET
ejpam-6633	15	15	essential	essential	ADJ
ejpam-6633	15	16	tool	tool	NOUN
ejpam-6633	15	17	for	for	ADP
ejpam-6633	15	18	advancing	advance	VERB
ejpam-6633	15	19	our	our	PRON
ejpam-6633	15	20	understanding	understanding	NOUN
ejpam-6633	15	21	of	of	ADP
ejpam-6633	15	22	intricate	intricate	ADJ
ejpam-6633	15	23	real	real	ADJ
ejpam-6633	15	24	-	-	PUNCT
ejpam-6633	15	25	world	world	NOUN
ejpam-6633	15	26	problems	problem	NOUN
ejpam-6633	15	27	.	.	PUNCT
ejpam-6633	16	1	see	see	VERB
ejpam-6633	16	2	[	[	X
ejpam-6633	16	3	3–8	3–8	X
ejpam-6633	16	4	]	]	X
ejpam-6633	16	5	and	and	CCONJ
ejpam-6633	16	6	references	reference	NOUN
ejpam-6633	16	7	therein	therein	ADV
ejpam-6633	16	8	.	.	PUNCT
ejpam-6633	17	1	∗corresponding	∗corresponde	VERB
ejpam-6633	17	2	author	author	NOUN
ejpam-6633	17	3	.	.	PUNCT
ejpam-6633	18	1	doi	doi	NOUN
ejpam-6633	18	2	:	:	PUNCT
ejpam-6633	18	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6633	https://doi.org/10.29020/nybg.ejpam.v18i3.6633	NUM
ejpam-6633	18	4	email	email	NOUN
ejpam-6633	18	5	addresses	address	NOUN
ejpam-6633	18	6	:	:	PUNCT
ejpam-6633	18	7	afrah.hasan@uod.ac	afrah.hasan@uod.ac	NOUN
ejpam-6633	18	8	(	(	PUNCT
ejpam-6633	18	9	a.	a.	PROPN
ejpam-6633	18	10	s.	s.	PROPN
ejpam-6633	18	11	hasan	hasan	PROPN
ejpam-6633	18	12	)	)	PUNCT
ejpam-6633	18	13	,	,	PUNCT
ejpam-6633	18	14	shayma.murad@uod.ac	shayma.murad@uod.ac	PROPN
ejpam-6633	18	15	(	(	PUNCT
ejpam-6633	18	16	s.	s.	PROPN
ejpam-6633	18	17	a.	a.	PROPN
ejpam-6633	18	18	murad	murad	PROPN
ejpam-6633	18	19	)	)	PUNCT
ejpam-6633	18	20	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6633	19	1	1	1	NUM
ejpam-6633	19	2	copyright	copyright	NOUN
ejpam-6633	19	3	:	:	PUNCT
ejpam-6633	19	4	©	©	PROPN
ejpam-6633	19	5	2025	2025	NUM
ejpam-6633	19	6	the	the	DET
ejpam-6633	19	7	author(s	author(s	NOUN
ejpam-6633	19	8	)	)	PUNCT
ejpam-6633	19	9	.	.	PUNCT
ejpam-6633	20	1	(	(	PUNCT
ejpam-6633	20	2	cc	cc	NOUN
ejpam-6633	20	3	by	by	ADP
ejpam-6633	20	4	-	-	PUNCT
ejpam-6633	20	5	nc	nc	PROPN
ejpam-6633	20	6	4.0	4.0	NUM
ejpam-6633	20	7	)	)	PUNCT
ejpam-6633	20	8	a.	a.	PROPN
ejpam-6633	20	9	s.	s.	PROPN
ejpam-6633	20	10	hasan	hasan	PROPN
ejpam-6633	20	11	,	,	PUNCT
ejpam-6633	20	12	s.	s.	PROPN
ejpam-6633	20	13	a.	a.	PROPN
ejpam-6633	20	14	murad	murad	PROPN
ejpam-6633	20	15	/	/	SYM
ejpam-6633	20	16	eur	eur	PROPN
ejpam-6633	20	17	.	.	PUNCT
ejpam-6633	21	1	j.	j.	PROPN
ejpam-6633	21	2	pure	pure	PROPN
ejpam-6633	21	3	appl	appl	PROPN
ejpam-6633	21	4	.	.	PROPN
ejpam-6633	21	5	math	math	PROPN
ejpam-6633	21	6	,	,	PUNCT
ejpam-6633	21	7	18	18	NUM
ejpam-6633	21	8	(	(	PUNCT
ejpam-6633	21	9	3	3	NUM
ejpam-6633	21	10	)	)	PUNCT
ejpam-6633	21	11	(	(	PUNCT
ejpam-6633	21	12	2025	2025	NUM
ejpam-6633	21	13	)	)	PUNCT
ejpam-6633	21	14	,	,	PUNCT
ejpam-6633	21	15	6633	6633	NUM
ejpam-6633	21	16	2	2	NUM
ejpam-6633	21	17	of	of	ADP
ejpam-6633	21	18	24	24	NUM
ejpam-6633	21	19	the	the	DET
ejpam-6633	21	20	classical	classical	ADJ
ejpam-6633	21	21	lane	lane	NOUN
ejpam-6633	21	22	-	-	PUNCT
ejpam-6633	21	23	emden	emden	NOUN
ejpam-6633	21	24	equation	equation	NOUN
ejpam-6633	21	25	,	,	PUNCT
ejpam-6633	21	26	rooted	root	VERB
ejpam-6633	21	27	in	in	ADP
ejpam-6633	21	28	astrophysics	astrophysic	NOUN
ejpam-6633	21	29	,	,	PUNCT
ejpam-6633	21	30	was	be	AUX
ejpam-6633	21	31	pioneered	pioneer	VERB
ejpam-6633	21	32	by	by	ADP
ejpam-6633	21	33	[	[	X
ejpam-6633	21	34	9	9	NUM
ejpam-6633	21	35	]	]	PUNCT
ejpam-6633	21	36	and	and	CCONJ
ejpam-6633	21	37	[	[	X
ejpam-6633	21	38	10	10	NUM
ejpam-6633	21	39	]	]	PUNCT
ejpam-6633	21	40	to	to	PART
ejpam-6633	21	41	model	model	VERB
ejpam-6633	21	42	the	the	DET
ejpam-6633	21	43	equilibrium	equilibrium	NOUN
ejpam-6633	21	44	of	of	ADP
ejpam-6633	21	45	self	self	NOUN
ejpam-6633	21	46	-	-	PUNCT
ejpam-6633	21	47	gravitating	gravitate	VERB
ejpam-6633	21	48	polytropic	polytropic	ADJ
ejpam-6633	21	49	gas	gas	NOUN
ejpam-6633	21	50	spheres	sphere	NOUN
ejpam-6633	21	51	.	.	PUNCT
ejpam-6633	22	1	its	its	PRON
ejpam-6633	22	2	dimensionless	dimensionless	NOUN
ejpam-6633	22	3	form	form	NOUN
ejpam-6633	22	4	,	,	PUNCT
ejpam-6633	22	5	η′′(t	η′′(t	NOUN
ejpam-6633	22	6	)	)	PUNCT
ejpam-6633	22	7	+	+	NUM
ejpam-6633	22	8	µ	µ	PROPN
ejpam-6633	22	9	t	t	NOUN
ejpam-6633	22	10	η′(t	η′(t	PROPN
ejpam-6633	22	11	)	)	PUNCT
ejpam-6633	23	1	=	=	SYM
ejpam-6633	23	2	−ηn	−ηn	PROPN
ejpam-6633	23	3	,	,	PUNCT
ejpam-6633	23	4	0	0	PUNCT
ejpam-6633	23	5	<	<	X
ejpam-6633	23	6	t	t	X
ejpam-6633	23	7	≤	≤	NUM
ejpam-6633	23	8	1	1	NUM
ejpam-6633	23	9	,	,	PUNCT
ejpam-6633	23	10	µ	µ	X
ejpam-6633	23	11	>	>	X
ejpam-6633	23	12	0	0	NUM
ejpam-6633	23	13	,	,	PUNCT
ejpam-6633	23	14	(	(	PUNCT
ejpam-6633	23	15	1	1	X
ejpam-6633	23	16	)	)	PUNCT
ejpam-6633	23	17	governs	govern	VERB
ejpam-6633	23	18	density	density	NOUN
ejpam-6633	23	19	profiles	profile	NOUN
ejpam-6633	23	20	in	in	ADP
ejpam-6633	23	21	stars	star	NOUN
ejpam-6633	23	22	,	,	PUNCT
ejpam-6633	23	23	where	where	SCONJ
ejpam-6633	23	24	η(t	η(t	NOUN
ejpam-6633	23	25	)	)	PUNCT
ejpam-6633	23	26	represents	represent	VERB
ejpam-6633	23	27	scaled	scale	VERB
ejpam-6633	23	28	density	density	NOUN
ejpam-6633	23	29	and	and	CCONJ
ejpam-6633	23	30	n	n	NOUN
ejpam-6633	23	31	is	be	AUX
ejpam-6633	23	32	the	the	DET
ejpam-6633	23	33	polytropic	polytropic	ADJ
ejpam-6633	23	34	index	index	NOUN
ejpam-6633	23	35	[	[	X
ejpam-6633	23	36	11	11	NUM
ejpam-6633	23	37	]	]	PUNCT
ejpam-6633	23	38	.	.	PUNCT
ejpam-6633	24	1	chandrasekhar	chandrasekhar	PROPN
ejpam-6633	24	2	’s	’s	PART
ejpam-6633	24	3	seminal	seminal	ADJ
ejpam-6633	24	4	work	work	NOUN
ejpam-6633	24	5	formalized	formalize	VERB
ejpam-6633	24	6	its	its	PRON
ejpam-6633	24	7	role	role	NOUN
ejpam-6633	24	8	in	in	ADP
ejpam-6633	24	9	stellar	stellar	ADJ
ejpam-6633	24	10	structure	structure	NOUN
ejpam-6633	24	11	theory	theory	NOUN
ejpam-6633	24	12	,	,	PUNCT
ejpam-6633	24	13	linking	link	VERB
ejpam-6633	24	14	solutions	solution	NOUN
ejpam-6633	24	15	(	(	PUNCT
ejpam-6633	24	16	polytropes	polytrope	NOUN
ejpam-6633	24	17	)	)	PUNCT
ejpam-6633	24	18	to	to	ADP
ejpam-6633	24	19	configurations	configuration	NOUN
ejpam-6633	24	20	of	of	ADP
ejpam-6633	24	21	stars	star	NOUN
ejpam-6633	24	22	and	and	CCONJ
ejpam-6633	24	23	gaseous	gaseous	ADJ
ejpam-6633	24	24	planets	planet	NOUN
ejpam-6633	24	25	.	.	PUNCT
ejpam-6633	25	1	prialnik	prialnik	VERB
ejpam-6633	25	2	in	in	ADP
ejpam-6633	25	3	his	his	PRON
ejpam-6633	25	4	book	book	NOUN
ejpam-6633	26	1	[	[	X
ejpam-6633	26	2	12	12	NUM
ejpam-6633	26	3	]	]	PUNCT
ejpam-6633	26	4	further	far	ADV
ejpam-6633	26	5	contextualized	contextualize	VERB
ejpam-6633	26	6	its	its	PRON
ejpam-6633	26	7	applications	application	NOUN
ejpam-6633	26	8	in	in	ADP
ejpam-6633	26	9	stellar	stellar	ADJ
ejpam-6633	26	10	evolution	evolution	NOUN
ejpam-6633	26	11	,	,	PUNCT
ejpam-6633	26	12	particularly	particularly	ADV
ejpam-6633	26	13	in	in	ADP
ejpam-6633	26	14	modeling	model	VERB
ejpam-6633	26	15	pre	pre	ADJ
ejpam-6633	26	16	-	-	ADJ
ejpam-6633	26	17	main	main	ADJ
ejpam-6633	26	18	-	-	PUNCT
ejpam-6633	26	19	sequence	sequence	NOUN
ejpam-6633	26	20	stars	star	NOUN
ejpam-6633	26	21	and	and	CCONJ
ejpam-6633	26	22	degenerate	degenerate	ADJ
ejpam-6633	26	23	cores	core	NOUN
ejpam-6633	26	24	.	.	PUNCT
ejpam-6633	27	1	beyond	beyond	ADP
ejpam-6633	27	2	astrophysics	astrophysic	NOUN
ejpam-6633	27	3	,	,	PUNCT
ejpam-6633	27	4	the	the	DET
ejpam-6633	27	5	equation	equation	NOUN
ejpam-6633	27	6	’s	’s	PART
ejpam-6633	27	7	singular	singular	ADJ
ejpam-6633	27	8	term	term	NOUN
ejpam-6633	27	9	t−1	t−1	PROPN
ejpam-6633	27	10	and	and	CCONJ
ejpam-6633	27	11	nonlinearity	nonlinearity	NOUN
ejpam-6633	27	12	ηn	ηn	VERB
ejpam-6633	27	13	inspired	inspire	VERB
ejpam-6633	27	14	adaptations	adaptation	NOUN
ejpam-6633	27	15	in	in	ADP
ejpam-6633	27	16	plasma	plasma	NOUN
ejpam-6633	27	17	physics	physics	NOUN
ejpam-6633	27	18	and	and	CCONJ
ejpam-6633	27	19	radiative	radiative	ADJ
ejpam-6633	27	20	cooling	cooling	NOUN
ejpam-6633	27	21	.	.	PUNCT
ejpam-6633	28	1	the	the	DET
ejpam-6633	28	2	lane	lane	NOUN
ejpam-6633	28	3	-	-	PUNCT
ejpam-6633	28	4	emden	emden	ADJ
ejpam-6633	28	5	fractional	fractional	ADJ
ejpam-6633	28	6	differential	differential	ADJ
ejpam-6633	28	7	equation	equation	NOUN
ejpam-6633	28	8	(	(	PUNCT
ejpam-6633	28	9	lefde	lefde	NOUN
ejpam-6633	28	10	)	)	PUNCT
ejpam-6633	28	11	emerged	emerge	VERB
ejpam-6633	28	12	as	as	ADP
ejpam-6633	28	13	a	a	DET
ejpam-6633	28	14	modern	modern	ADJ
ejpam-6633	28	15	extension	extension	NOUN
ejpam-6633	28	16	,	,	PUNCT
ejpam-6633	28	17	replacing	replace	VERB
ejpam-6633	28	18	integer	integer	NOUN
ejpam-6633	28	19	derivatives	derivative	NOUN
ejpam-6633	28	20	with	with	ADP
ejpam-6633	28	21	fractional	fractional	ADJ
ejpam-6633	28	22	operators	operator	NOUN
ejpam-6633	28	23	to	to	PART
ejpam-6633	28	24	incorporate	incorporate	VERB
ejpam-6633	28	25	memory	memory	NOUN
ejpam-6633	28	26	effects	effect	NOUN
ejpam-6633	28	27	and	and	CCONJ
ejpam-6633	28	28	anomalous	anomalous	ADJ
ejpam-6633	28	29	transport	transport	NOUN
ejpam-6633	28	30	.	.	PUNCT
ejpam-6633	29	1	a	a	DET
ejpam-6633	29	2	generalized	generalized	ADJ
ejpam-6633	29	3	form	form	NOUN
ejpam-6633	29	4	,	,	PUNCT
ejpam-6633	29	5	dβ+αη(t	dβ+αη(t	PROPN
ejpam-6633	29	6	)	)	PUNCT
ejpam-6633	30	1	+	+	NUM
ejpam-6633	30	2	µ	µ	X
ejpam-6633	30	3	t	t	NOUN
ejpam-6633	30	4	dαη(t	dαη(t	PROPN
ejpam-6633	30	5	)	)	PUNCT
ejpam-6633	30	6	=	=	SYM
ejpam-6633	30	7	θ(t	θ(t	PROPN
ejpam-6633	30	8	,	,	PUNCT
ejpam-6633	30	9	η(t	η(t	NOUN
ejpam-6633	30	10	)	)	PUNCT
ejpam-6633	30	11	)	)	PUNCT
ejpam-6633	30	12	,	,	PUNCT
ejpam-6633	30	13	0	0	NUM
ejpam-6633	30	14	<	<	X
ejpam-6633	30	15	α	α	X
ejpam-6633	30	16	,	,	PUNCT
ejpam-6633	30	17	β	β	X
ejpam-6633	30	18	<	<	X
ejpam-6633	30	19	1	1	NUM
ejpam-6633	30	20	,	,	PUNCT
ejpam-6633	30	21	(	(	PUNCT
ejpam-6633	30	22	2	2	X
ejpam-6633	30	23	)	)	PUNCT
ejpam-6633	30	24	addresses	address	NOUN
ejpam-6633	30	25	non	non	ADJ
ejpam-6633	30	26	-	-	ADJ
ejpam-6633	30	27	local	local	ADJ
ejpam-6633	30	28	dynamics	dynamic	NOUN
ejpam-6633	30	29	in	in	ADP
ejpam-6633	30	30	systems	system	NOUN
ejpam-6633	30	31	like	like	ADP
ejpam-6633	30	32	viscoelastic	viscoelastic	NOUN
ejpam-6633	30	33	collapsing	collapse	VERB
ejpam-6633	30	34	clouds	cloud	NOUN
ejpam-6633	30	35	or	or	CCONJ
ejpam-6633	30	36	turbulent	turbulent	ADJ
ejpam-6633	30	37	plasmas	plasma	NOUN
ejpam-6633	30	38	.	.	PUNCT
ejpam-6633	31	1	dβ+α	dβ+α	NOUN
ejpam-6633	31	2	and	and	CCONJ
ejpam-6633	31	3	dα	dα	NOUN
ejpam-6633	31	4	are	be	AUX
ejpam-6633	31	5	the	the	DET
ejpam-6633	31	6	fractional	fractional	ADJ
ejpam-6633	31	7	derivatives	derivative	NOUN
ejpam-6633	31	8	of	of	ADP
ejpam-6633	31	9	order	order	NOUN
ejpam-6633	31	10	β	β	NOUN
ejpam-6633	31	11	+	+	X
ejpam-6633	31	12	α	α	NOUN
ejpam-6633	31	13	and	and	CCONJ
ejpam-6633	31	14	α	α	NOUN
ejpam-6633	31	15	,	,	PUNCT
ejpam-6633	31	16	respectively	respectively	ADV
ejpam-6633	31	17	.	.	PUNCT
ejpam-6633	32	1	while	while	SCONJ
ejpam-6633	32	2	[	[	X
ejpam-6633	32	3	11	11	NUM
ejpam-6633	32	4	]	]	PUNCT
ejpam-6633	32	5	,	,	PUNCT
ejpam-6633	32	6	[	[	X
ejpam-6633	32	7	13	13	NUM
ejpam-6633	32	8	]	]	PUNCT
ejpam-6633	32	9	and	and	CCONJ
ejpam-6633	32	10	[	[	X
ejpam-6633	32	11	12	12	NUM
ejpam-6633	32	12	]	]	PUNCT
ejpam-6633	32	13	focus	focus	NOUN
ejpam-6633	32	14	on	on	ADP
ejpam-6633	32	15	classical	classical	ADJ
ejpam-6633	32	16	theory	theory	NOUN
ejpam-6633	32	17	,	,	PUNCT
ejpam-6633	32	18	recent	recent	ADJ
ejpam-6633	32	19	studies	study	NOUN
ejpam-6633	32	20	leverage	leverage	VERB
ejpam-6633	32	21	fractional	fractional	ADJ
ejpam-6633	32	22	calculus	calculus	NOUN
ejpam-6633	32	23	to	to	PART
ejpam-6633	32	24	resolve	resolve	VERB
ejpam-6633	32	25	discrepancies	discrepancy	NOUN
ejpam-6633	32	26	in	in	ADP
ejpam-6633	32	27	observational	observational	ADJ
ejpam-6633	32	28	data	datum	NOUN
ejpam-6633	32	29	,	,	PUNCT
ejpam-6633	32	30	such	such	ADJ
ejpam-6633	32	31	as	as	ADP
ejpam-6633	32	32	non	non	ADJ
ejpam-6633	32	33	-	-	ADJ
ejpam-6633	32	34	isothermal	isothermal	ADJ
ejpam-6633	32	35	collapse	collapse	NOUN
ejpam-6633	32	36	in	in	ADP
ejpam-6633	32	37	molecular	molecular	ADJ
ejpam-6633	32	38	clouds	cloud	NOUN
ejpam-6633	32	39	.	.	PUNCT
ejpam-6633	33	1	this	this	DET
ejpam-6633	33	2	fractional	fractional	ADJ
ejpam-6633	33	3	framework	framework	NOUN
ejpam-6633	33	4	retains	retain	VERB
ejpam-6633	33	5	the	the	DET
ejpam-6633	33	6	singular	singular	ADJ
ejpam-6633	33	7	coefficient	coefficient	NOUN
ejpam-6633	33	8	t−1	t−1	PROPN
ejpam-6633	33	9	but	but	CCONJ
ejpam-6633	33	10	introduces	introduce	VERB
ejpam-6633	33	11	flexibility	flexibility	NOUN
ejpam-6633	33	12	in	in	ADP
ejpam-6633	33	13	modeling	model	VERB
ejpam-6633	33	14	multi	multi	ADJ
ejpam-6633	33	15	-	-	ADJ
ejpam-6633	33	16	scale	scale	ADJ
ejpam-6633	33	17	phenomena	phenomenon	NOUN
ejpam-6633	33	18	,	,	PUNCT
ejpam-6633	33	19	bridging	bridge	VERB
ejpam-6633	33	20	gaps	gap	NOUN
ejpam-6633	33	21	between	between	ADP
ejpam-6633	33	22	classical	classical	ADJ
ejpam-6633	33	23	polytropic	polytropic	NOUN
ejpam-6633	33	24	assumptions	assumption	NOUN
ejpam-6633	33	25	and	and	CCONJ
ejpam-6633	33	26	complex	complex	ADJ
ejpam-6633	33	27	astrophysical	astrophysical	ADJ
ejpam-6633	33	28	systems	system	NOUN
ejpam-6633	33	29	.	.	PUNCT
ejpam-6633	34	1	lately	lately	ADV
ejpam-6633	34	2	,	,	PUNCT
ejpam-6633	34	3	the	the	DET
ejpam-6633	34	4	study	study	NOUN
ejpam-6633	34	5	of	of	ADP
ejpam-6633	34	6	initial	initial	ADJ
ejpam-6633	34	7	and	and	CCONJ
ejpam-6633	34	8	boundary	boundary	ADJ
ejpam-6633	34	9	-	-	PUNCT
ejpam-6633	34	10	value	value	NOUN
ejpam-6633	34	11	problems	problem	NOUN
ejpam-6633	34	12	that	that	PRON
ejpam-6633	34	13	are	be	AUX
ejpam-6633	34	14	governed	govern	VERB
ejpam-6633	34	15	by	by	ADP
ejpam-6633	34	16	lefde	lefde	NOUN
ejpam-6633	34	17	has	have	AUX
ejpam-6633	34	18	garnered	garner	VERB
ejpam-6633	34	19	substantial	substantial	ADJ
ejpam-6633	34	20	attention	attention	NOUN
ejpam-6633	34	21	from	from	ADP
ejpam-6633	34	22	many	many	ADJ
ejpam-6633	34	23	researchers	researcher	NOUN
ejpam-6633	34	24	.	.	PUNCT
ejpam-6633	35	1	ibrahim	ibrahim	PROPN
ejpam-6633	35	2	in	in	ADP
ejpam-6633	35	3	[	[	X
ejpam-6633	35	4	14	14	NUM
ejpam-6633	35	5	]	]	PUNCT
ejpam-6633	35	6	studied	study	VERB
ejpam-6633	35	7	the	the	DET
ejpam-6633	35	8	existence	existence	NOUN
ejpam-6633	35	9	of	of	ADP
ejpam-6633	35	10	the	the	DET
ejpam-6633	35	11	non	non	ADJ
ejpam-6633	35	12	-	-	ADJ
ejpam-6633	35	13	linear	linear	ADJ
ejpam-6633	35	14	lefde	lefde	NOUN
ejpam-6633	35	15	dβ	dβ	ADP
ejpam-6633	35	16	(	(	PUNCT
ejpam-6633	35	17	dα	dα	NOUN
ejpam-6633	35	18	+	+	X
ejpam-6633	35	19	µ	µ	X
ejpam-6633	35	20	t	t	NOUN
ejpam-6633	35	21	)	)	PUNCT
ejpam-6633	35	22	η(t	η(t	NOUN
ejpam-6633	35	23	)	)	PUNCT
ejpam-6633	35	24	=	=	SYM
ejpam-6633	35	25	θ(t	θ(t	PROPN
ejpam-6633	35	26	,	,	PUNCT
ejpam-6633	35	27	η(t	η(t	NOUN
ejpam-6633	35	28	)	)	PUNCT
ejpam-6633	35	29	)	)	PUNCT
ejpam-6633	35	30	,	,	PUNCT
ejpam-6633	35	31	(	(	PUNCT
ejpam-6633	35	32	3	3	X
ejpam-6633	35	33	)	)	PUNCT
ejpam-6633	35	34	for	for	ADP
ejpam-6633	35	35	0	0	NUM
ejpam-6633	35	36	<	<	X
ejpam-6633	35	37	α	α	PROPN
ejpam-6633	35	38	,	,	PUNCT
ejpam-6633	35	39	β	β	X
ejpam-6633	35	40	≤	≤	NUM
ejpam-6633	35	41	1	1	NUM
ejpam-6633	35	42	,	,	PUNCT
ejpam-6633	35	43	0	0	NUM
ejpam-6633	35	44	<	<	X
ejpam-6633	35	45	t	t	X
ejpam-6633	35	46	≤	≤	NUM
ejpam-6633	35	47	1	1	NUM
ejpam-6633	35	48	,	,	PUNCT
ejpam-6633	35	49	subject	subject	ADJ
ejpam-6633	35	50	to	to	ADP
ejpam-6633	35	51	the	the	DET
ejpam-6633	35	52	boundary	boundary	ADJ
ejpam-6633	35	53	conditions	condition	NOUN
ejpam-6633	35	54	η(0	η(0	PROPN
ejpam-6633	35	55	)	)	PUNCT
ejpam-6633	35	56	=	=	SYM
ejpam-6633	36	1	η(t1	η(t1	NOUN
ejpam-6633	36	2	)	)	PUNCT
ejpam-6633	36	3	=	=	SYM
ejpam-6633	36	4	η(1	η(1	PROPN
ejpam-6633	36	5	)	)	PUNCT
ejpam-6633	36	6	=	=	SYM
ejpam-6633	36	7	0	0	NUM
ejpam-6633	37	1	for	for	ADP
ejpam-6633	37	2	some	some	DET
ejpam-6633	37	3	t1	t1	NOUN
ejpam-6633	37	4	∈	∈	PROPN
ejpam-6633	37	5	(	(	PUNCT
ejpam-6633	37	6	0	0	NUM
ejpam-6633	37	7	,	,	PUNCT
ejpam-6633	37	8	1	1	NUM
ejpam-6633	37	9	)	)	PUNCT
ejpam-6633	37	10	.	.	PUNCT
ejpam-6633	38	1	the	the	DET
ejpam-6633	38	2	same	same	ADJ
ejpam-6633	38	3	author	author	NOUN
ejpam-6633	38	4	in	in	ADP
ejpam-6633	38	5	[	[	X
ejpam-6633	38	6	15	15	NUM
ejpam-6633	38	7	]	]	PUNCT
ejpam-6633	38	8	studied	study	VERB
ejpam-6633	38	9	the	the	DET
ejpam-6633	38	10	stability	stability	NOUN
ejpam-6633	38	11	of	of	ADP
ejpam-6633	38	12	the	the	DET
ejpam-6633	38	13	linear	linear	ADJ
ejpam-6633	38	14	lefde	lefde	NOUN
ejpam-6633	38	15	dβ	dβ	ADP
ejpam-6633	38	16	(	(	PUNCT
ejpam-6633	38	17	dα	dα	NOUN
ejpam-6633	38	18	+	+	X
ejpam-6633	38	19	µ	µ	X
ejpam-6633	38	20	t	t	NOUN
ejpam-6633	38	21	)	)	PUNCT
ejpam-6633	38	22	η(t	η(t	NOUN
ejpam-6633	38	23	)	)	PUNCT
ejpam-6633	38	24	=	=	PUNCT
ejpam-6633	38	25	θ(t	θ(t	PROPN
ejpam-6633	38	26	)	)	PUNCT
ejpam-6633	38	27	,	,	PUNCT
ejpam-6633	38	28	(	(	PUNCT
ejpam-6633	38	29	4	4	X
ejpam-6633	38	30	)	)	PUNCT
ejpam-6633	38	31	for	for	ADP
ejpam-6633	38	32	0	0	NUM
ejpam-6633	38	33	<	<	X
ejpam-6633	38	34	α	α	PROPN
ejpam-6633	38	35	,	,	PUNCT
ejpam-6633	38	36	β	β	X
ejpam-6633	38	37	≤	≤	NUM
ejpam-6633	38	38	1	1	NUM
ejpam-6633	38	39	,	,	PUNCT
ejpam-6633	38	40	0	0	NUM
ejpam-6633	38	41	<	<	X
ejpam-6633	38	42	t	t	X
ejpam-6633	38	43	≤	≤	NUM
ejpam-6633	38	44	1	1	NUM
ejpam-6633	38	45	,	,	PUNCT
ejpam-6633	38	46	with	with	ADP
ejpam-6633	38	47	boundary	boundary	ADJ
ejpam-6633	38	48	conditions	condition	NOUN
ejpam-6633	38	49	η(0	η(0	PROPN
ejpam-6633	38	50	)	)	PUNCT
ejpam-6633	39	1	=	=	SYM
ejpam-6633	39	2	l1	l1	PROPN
ejpam-6633	39	3	and	and	CCONJ
ejpam-6633	39	4	η(1	η(1	PROPN
ejpam-6633	39	5	)	)	PUNCT
ejpam-6633	39	6	=	=	SYM
ejpam-6633	39	7	l2	l2	NOUN
ejpam-6633	39	8	,	,	PUNCT
ejpam-6633	39	9	where	where	SCONJ
ejpam-6633	39	10	l1	l1	PROPN
ejpam-6633	39	11	and	and	CCONJ
ejpam-6633	39	12	l2	l2	NOUN
ejpam-6633	39	13	are	be	AUX
ejpam-6633	39	14	constants	constant	NOUN
ejpam-6633	39	15	.	.	PUNCT
ejpam-6633	40	1	in	in	ADP
ejpam-6633	40	2	[	[	X
ejpam-6633	40	3	16	16	NUM
ejpam-6633	40	4	]	]	PUNCT
ejpam-6633	40	5	the	the	DET
ejpam-6633	40	6	authors	author	NOUN
ejpam-6633	40	7	used	use	VERB
ejpam-6633	40	8	a	a	DET
ejpam-6633	40	9	combination	combination	NOUN
ejpam-6633	40	10	of	of	ADP
ejpam-6633	40	11	chebyshev	chebyshev	NOUN
ejpam-6633	40	12	wavelets	wavelet	NOUN
ejpam-6633	40	13	and	and	CCONJ
ejpam-6633	40	14	a	a	DET
ejpam-6633	40	15	finite	finite	ADJ
ejpam-6633	40	16	difference	difference	NOUN
ejpam-6633	40	17	approaches	approach	NOUN
ejpam-6633	40	18	to	to	PART
ejpam-6633	40	19	numerically	numerically	ADV
ejpam-6633	40	20	solve	solve	VERB
ejpam-6633	40	21	the	the	DET
ejpam-6633	40	22	lefde	lefde	NOUN
ejpam-6633	40	23	dαη(t	dαη(t	PROPN
ejpam-6633	40	24	)	)	PUNCT
ejpam-6633	41	1	+	+	NUM
ejpam-6633	41	2	µ	µ	PRON
ejpam-6633	41	3	tα−β	tα−β	NOUN
ejpam-6633	41	4	dβη(t	dβη(t	PROPN
ejpam-6633	41	5	)	)	PUNCT
ejpam-6633	41	6	=	=	SYM
ejpam-6633	41	7	θ(t	θ(t	PROPN
ejpam-6633	41	8	,	,	PUNCT
ejpam-6633	41	9	η(t	η(t	NOUN
ejpam-6633	41	10	)	)	PUNCT
ejpam-6633	41	11	)	)	PUNCT
ejpam-6633	41	12	,	,	PUNCT
ejpam-6633	41	13	(	(	PUNCT
ejpam-6633	41	14	5	5	X
ejpam-6633	41	15	)	)	PUNCT
ejpam-6633	41	16	for	for	ADP
ejpam-6633	41	17	1	1	NUM
ejpam-6633	41	18	<	<	X
ejpam-6633	41	19	α	α	PROPN
ejpam-6633	41	20	≤	≤	ADJ
ejpam-6633	41	21	2	2	NUM
ejpam-6633	41	22	,	,	PUNCT
ejpam-6633	41	23	0	0	PUNCT
ejpam-6633	41	24	<	<	X
ejpam-6633	41	25	β	β	X
ejpam-6633	41	26	≤	≤	NUM
ejpam-6633	41	27	1	1	NUM
ejpam-6633	41	28	,	,	PUNCT
ejpam-6633	41	29	0	0	NUM
ejpam-6633	41	30	<	<	X
ejpam-6633	41	31	t	t	X
ejpam-6633	41	32	≤	≤	NUM
ejpam-6633	41	33	1	1	NUM
ejpam-6633	41	34	,	,	PUNCT
ejpam-6633	41	35	subject	subject	ADJ
ejpam-6633	41	36	to	to	ADP
ejpam-6633	41	37	the	the	DET
ejpam-6633	41	38	initial	initial	ADJ
ejpam-6633	41	39	or	or	CCONJ
ejpam-6633	41	40	boundary	boundary	ADJ
ejpam-6633	41	41	conditions	condition	NOUN
ejpam-6633	41	42	.	.	PUNCT
ejpam-6633	42	1	in	in	ADP
ejpam-6633	42	2	a	a	DET
ejpam-6633	42	3	study	study	NOUN
ejpam-6633	42	4	by	by	ADP
ejpam-6633	42	5	[	[	X
ejpam-6633	42	6	17	17	NUM
ejpam-6633	42	7	]	]	PUNCT
ejpam-6633	42	8	,	,	PUNCT
ejpam-6633	42	9	they	they	PRON
ejpam-6633	42	10	considered	consider	VERB
ejpam-6633	42	11	the	the	DET
ejpam-6633	42	12	lefde	lefde	NOUN
ejpam-6633	42	13	in	in	ADP
ejpam-6633	42	14	an	an	DET
ejpam-6633	42	15	n	n	ADV
ejpam-6633	42	16	-	-	PUNCT
ejpam-6633	42	17	dimensional	dimensional	ADJ
ejpam-6633	42	18	system	system	NOUN
ejpam-6633	42	19	where	where	SCONJ
ejpam-6633	42	20	each	each	DET
ejpam-6633	42	21	equation	equation	NOUN
ejpam-6633	42	22	a.	a.	PROPN
ejpam-6633	42	23	s.	s.	PROPN
ejpam-6633	42	24	hasan	hasan	PROPN
ejpam-6633	42	25	,	,	PUNCT
ejpam-6633	42	26	s.	s.	PROPN
ejpam-6633	42	27	a.	a.	PROPN
ejpam-6633	42	28	murad	murad	PROPN
ejpam-6633	42	29	/	/	SYM
ejpam-6633	42	30	eur	eur	PROPN
ejpam-6633	42	31	.	.	PUNCT
ejpam-6633	43	1	j.	j.	PROPN
ejpam-6633	43	2	pure	pure	PROPN
ejpam-6633	43	3	appl	appl	PROPN
ejpam-6633	43	4	.	.	PROPN
ejpam-6633	43	5	math	math	PROPN
ejpam-6633	43	6	,	,	PUNCT
ejpam-6633	43	7	18	18	NUM
ejpam-6633	43	8	(	(	PUNCT
ejpam-6633	43	9	3	3	NUM
ejpam-6633	43	10	)	)	PUNCT
ejpam-6633	43	11	(	(	PUNCT
ejpam-6633	43	12	2025	2025	NUM
ejpam-6633	43	13	)	)	PUNCT
ejpam-6633	43	14	,	,	PUNCT
ejpam-6633	43	15	6633	6633	NUM
ejpam-6633	43	16	3	3	NUM
ejpam-6633	43	17	of	of	ADP
ejpam-6633	43	18	24	24	NUM
ejpam-6633	43	19	consists	consist	NOUN
ejpam-6633	43	20	of	of	ADP
ejpam-6633	43	21	two	two	NUM
ejpam-6633	43	22	arbitrary	arbitrary	ADJ
ejpam-6633	43	23	differential	differential	ADJ
ejpam-6633	43	24	orders	order	NOUN
ejpam-6633	43	25	in	in	ADP
ejpam-6633	43	26	terms	term	NOUN
ejpam-6633	43	27	of	of	ADP
ejpam-6633	43	28	caputo	caputo	PROPN
ejpam-6633	43	29	fractional	fractional	PROPN
ejpam-6633	43	30	derivative	derivative	PROPN
ejpam-6633	43	31	.	.	PUNCT
ejpam-6633	44	1	they	they	PRON
ejpam-6633	44	2	proved	prove	VERB
ejpam-6633	44	3	the	the	DET
ejpam-6633	44	4	existence	existence	NOUN
ejpam-6633	44	5	and	and	CCONJ
ejpam-6633	44	6	uniqueness	uniqueness	NOUN
ejpam-6633	44	7	using	use	VERB
ejpam-6633	44	8	krasnoselskii	krasnoselskii	PROPN
ejpam-6633	44	9	and	and	CCONJ
ejpam-6633	44	10	banach	banach	ADV
ejpam-6633	44	11	’s	’s	ADV
ejpam-6633	44	12	fixed	fix	VERB
ejpam-6633	44	13	point	point	NOUN
ejpam-6633	44	14	theorems	theorem	NOUN
ejpam-6633	44	15	and	and	CCONJ
ejpam-6633	44	16	they	they	PRON
ejpam-6633	44	17	showed	show	VERB
ejpam-6633	44	18	that	that	SCONJ
ejpam-6633	44	19	the	the	DET
ejpam-6633	44	20	system	system	NOUN
ejpam-6633	44	21	is	be	AUX
ejpam-6633	44	22	both	both	DET
ejpam-6633	44	23	ulam	ulam	X
ejpam-6633	44	24	–	–	PUNCT
ejpam-6633	44	25	hyers	hyer	NOUN
ejpam-6633	44	26	and	and	CCONJ
ejpam-6633	44	27	ulam	ulam	NOUN
ejpam-6633	44	28	-	-	PUNCT
ejpam-6633	44	29	hyers	hyer	NOUN
ejpam-6633	44	30	-	-	PUNCT
ejpam-6633	44	31	rassias	rassia	NOUN
ejpam-6633	44	32	stable	stable	ADJ
ejpam-6633	44	33	according	accord	VERB
ejpam-6633	44	34	to	to	ADP
ejpam-6633	44	35	the	the	DET
ejpam-6633	44	36	proposed	propose	VERB
ejpam-6633	44	37	conditions	condition	NOUN
ejpam-6633	44	38	.	.	PUNCT
ejpam-6633	45	1	the	the	DET
ejpam-6633	45	2	existence	existence	NOUN
ejpam-6633	45	3	and	and	CCONJ
ejpam-6633	45	4	stability	stability	NOUN
ejpam-6633	45	5	of	of	ADP
ejpam-6633	45	6	lefde	lefde	NOUN
ejpam-6633	45	7	has	have	AUX
ejpam-6633	45	8	been	be	AUX
ejpam-6633	45	9	studied	study	VERB
ejpam-6633	45	10	by	by	ADP
ejpam-6633	45	11	[	[	X
ejpam-6633	45	12	18	18	NUM
ejpam-6633	45	13	]	]	PUNCT
ejpam-6633	45	14	using	use	VERB
ejpam-6633	45	15	advanced	advanced	ADJ
ejpam-6633	45	16	monotonicity	monotonicity	NOUN
ejpam-6633	45	17	,	,	PUNCT
ejpam-6633	45	18	concentration	concentration	NOUN
ejpam-6633	45	19	-	-	PUNCT
ejpam-6633	45	20	compactness	compactness	NOUN
ejpam-6633	45	21	,	,	PUNCT
ejpam-6633	45	22	and	and	CCONJ
ejpam-6633	45	23	sobolevtype	sobolevtype	NOUN
ejpam-6633	45	24	inequalities	inequality	NOUN
ejpam-6633	45	25	techniques	technique	NOUN
ejpam-6633	45	26	.	.	PUNCT
ejpam-6633	46	1	in	in	ADP
ejpam-6633	46	2	[	[	X
ejpam-6633	46	3	19	19	NUM
ejpam-6633	46	4	]	]	PUNCT
ejpam-6633	46	5	,	,	PUNCT
ejpam-6633	46	6	the	the	DET
ejpam-6633	46	7	author	author	NOUN
ejpam-6633	46	8	presents	present	VERB
ejpam-6633	46	9	a	a	DET
ejpam-6633	46	10	modern	modern	ADJ
ejpam-6633	46	11	analytical	analytical	ADJ
ejpam-6633	46	12	method	method	NOUN
ejpam-6633	46	13	for	for	ADP
ejpam-6633	46	14	solving	solve	VERB
ejpam-6633	46	15	nonlinear	nonlinear	ADJ
ejpam-6633	46	16	singular	singular	ADJ
ejpam-6633	46	17	type	type	NOUN
ejpam-6633	46	18	of	of	ADP
ejpam-6633	46	19	lefde	lefde	NOUN
ejpam-6633	46	20	with	with	ADP
ejpam-6633	46	21	liouville	liouville	NOUN
ejpam-6633	46	22	–	–	PUNCT
ejpam-6633	46	23	caputo	caputo	NOUN
ejpam-6633	46	24	derivatives	derivative	NOUN
ejpam-6633	46	25	,	,	PUNCT
ejpam-6633	46	26	focusing	focus	VERB
ejpam-6633	46	27	on	on	ADP
ejpam-6633	46	28	the	the	DET
ejpam-6633	46	29	conditions	condition	NOUN
ejpam-6633	46	30	that	that	PRON
ejpam-6633	46	31	are	be	AUX
ejpam-6633	46	32	proving	prove	VERB
ejpam-6633	46	33	the	the	DET
ejpam-6633	46	34	existence	existence	NOUN
ejpam-6633	46	35	and	and	CCONJ
ejpam-6633	46	36	uniqueness	uniqueness	NOUN
ejpam-6633	46	37	of	of	ADP
ejpam-6633	46	38	solutions	solution	NOUN
ejpam-6633	46	39	.	.	PUNCT
ejpam-6633	47	1	the	the	DET
ejpam-6633	47	2	author	author	NOUN
ejpam-6633	47	3	combines	combine	VERB
ejpam-6633	47	4	techniques	technique	NOUN
ejpam-6633	47	5	in	in	ADP
ejpam-6633	47	6	fractional	fractional	ADJ
ejpam-6633	47	7	calculus	calculus	NOUN
ejpam-6633	47	8	alongside	alongside	ADV
ejpam-6633	47	9	with	with	ADP
ejpam-6633	47	10	advanced	advanced	ADJ
ejpam-6633	47	11	analytical	analytical	ADJ
ejpam-6633	47	12	methods	method	NOUN
ejpam-6633	47	13	to	to	PART
ejpam-6633	47	14	establish	establish	VERB
ejpam-6633	47	15	the	the	DET
ejpam-6633	47	16	conditions	condition	NOUN
ejpam-6633	47	17	under	under	ADP
ejpam-6633	47	18	which	which	PRON
ejpam-6633	47	19	these	these	DET
ejpam-6633	47	20	solutions	solution	NOUN
ejpam-6633	47	21	exist	exist	VERB
ejpam-6633	47	22	and	and	CCONJ
ejpam-6633	47	23	are	be	AUX
ejpam-6633	47	24	unique	unique	ADJ
ejpam-6633	47	25	.	.	PUNCT
ejpam-6633	48	1	the	the	DET
ejpam-6633	48	2	stability	stability	NOUN
ejpam-6633	48	3	of	of	ADP
ejpam-6633	48	4	solutions	solution	NOUN
ejpam-6633	48	5	for	for	ADP
ejpam-6633	48	6	two	two	NUM
ejpam-6633	48	7	classes	class	NOUN
ejpam-6633	48	8	of	of	ADP
ejpam-6633	48	9	lefde	lefde	NOUN
ejpam-6633	48	10	has	have	AUX
ejpam-6633	48	11	been	be	AUX
ejpam-6633	48	12	studied	study	VERB
ejpam-6633	48	13	by	by	ADP
ejpam-6633	48	14	[	[	X
ejpam-6633	48	15	20	20	NUM
ejpam-6633	48	16	]	]	PUNCT
ejpam-6633	48	17	thought	think	VERB
ejpam-6633	48	18	lyapunov	lyapunov	NOUN
ejpam-6633	48	19	’s	’s	PART
ejpam-6633	48	20	direct	direct	ADJ
ejpam-6633	48	21	method	method	NOUN
ejpam-6633	48	22	while	while	SCONJ
ejpam-6633	48	23	the	the	DET
ejpam-6633	48	24	existence	existence	NOUN
ejpam-6633	48	25	and	and	CCONJ
ejpam-6633	48	26	uniqueness	uniqueness	NOUN
ejpam-6633	48	27	of	of	ADP
ejpam-6633	48	28	solutions	solution	NOUN
ejpam-6633	48	29	are	be	AUX
ejpam-6633	48	30	demonstrated	demonstrate	VERB
ejpam-6633	48	31	using	use	VERB
ejpam-6633	48	32	banach	banach	NOUN
ejpam-6633	48	33	’s	’s	PART
ejpam-6633	48	34	fixed	fix	VERB
ejpam-6633	48	35	-	-	PUNCT
ejpam-6633	48	36	point	point	NOUN
ejpam-6633	48	37	theory	theory	NOUN
ejpam-6633	48	38	.	.	PUNCT
ejpam-6633	49	1	the	the	DET
ejpam-6633	49	2	solution	solution	NOUN
ejpam-6633	49	3	of	of	ADP
ejpam-6633	49	4	lefde	lefde	NOUN
ejpam-6633	49	5	analytically	analytically	ADV
ejpam-6633	49	6	studied	study	VERB
ejpam-6633	49	7	by	by	ADP
ejpam-6633	49	8	[	[	X
ejpam-6633	49	9	21	21	NUM
ejpam-6633	49	10	]	]	PUNCT
ejpam-6633	49	11	using	use	VERB
ejpam-6633	49	12	the	the	DET
ejpam-6633	49	13	techniques	technique	NOUN
ejpam-6633	49	14	of	of	ADP
ejpam-6633	49	15	power	power	NOUN
ejpam-6633	49	16	series	series	PROPN
ejpam-6633	49	17	approaches	approach	NOUN
ejpam-6633	49	18	.	.	PUNCT
ejpam-6633	50	1	most	most	ADV
ejpam-6633	50	2	recently	recently	ADV
ejpam-6633	50	3	,	,	PUNCT
ejpam-6633	50	4	[	[	X
ejpam-6633	50	5	22	22	NUM
ejpam-6633	50	6	]	]	PUNCT
ejpam-6633	50	7	explored	explore	VERB
ejpam-6633	50	8	the	the	DET
ejpam-6633	50	9	lefde	lefde	NOUN
ejpam-6633	50	10	with	with	ADP
ejpam-6633	50	11	caputo	caputo	PROPN
ejpam-6633	50	12	derivatives	derivative	NOUN
ejpam-6633	50	13	.	.	PUNCT
ejpam-6633	51	1	the	the	DET
ejpam-6633	51	2	author	author	NOUN
ejpam-6633	51	3	managed	manage	VERB
ejpam-6633	51	4	to	to	PART
ejpam-6633	51	5	study	study	VERB
ejpam-6633	51	6	the	the	DET
ejpam-6633	51	7	existence	existence	NOUN
ejpam-6633	51	8	and	and	CCONJ
ejpam-6633	51	9	uniqueness	uniqueness	NOUN
ejpam-6633	51	10	of	of	ADP
ejpam-6633	51	11	mild	mild	ADJ
ejpam-6633	51	12	solutions	solution	NOUN
ejpam-6633	51	13	undergoing	undergo	VERB
ejpam-6633	51	14	the	the	DET
ejpam-6633	51	15	bielecki	bielecki	ADJ
ejpam-6633	51	16	-	-	PUNCT
ejpam-6633	51	17	type	type	NOUN
ejpam-6633	51	18	norm	norm	NOUN
ejpam-6633	51	19	.	.	PUNCT
ejpam-6633	52	1	in	in	ADP
ejpam-6633	52	2	addition	addition	NOUN
ejpam-6633	52	3	,	,	PUNCT
ejpam-6633	52	4	the	the	DET
ejpam-6633	52	5	author	author	NOUN
ejpam-6633	52	6	manifested	manifest	VERB
ejpam-6633	52	7	that	that	SCONJ
ejpam-6633	52	8	,	,	PUNCT
ejpam-6633	52	9	the	the	DET
ejpam-6633	52	10	mild	mild	ADJ
ejpam-6633	52	11	solution	solution	NOUN
ejpam-6633	52	12	is	be	AUX
ejpam-6633	52	13	ulam	ulam	NOUN
ejpam-6633	52	14	-	-	PUNCT
ejpam-6633	52	15	hyres	hyre	NOUN
ejpam-6633	52	16	type	type	NOUN
ejpam-6633	52	17	stable	stable	ADJ
ejpam-6633	52	18	.	.	PUNCT
ejpam-6633	53	1	motivated	motivate	VERB
ejpam-6633	53	2	by	by	ADP
ejpam-6633	53	3	the	the	DET
ejpam-6633	53	4	above	above	ADJ
ejpam-6633	53	5	studies	study	NOUN
ejpam-6633	53	6	,	,	PUNCT
ejpam-6633	53	7	we	we	PRON
ejpam-6633	53	8	examine	examine	VERB
ejpam-6633	53	9	the	the	DET
ejpam-6633	53	10	existence	existence	NOUN
ejpam-6633	53	11	,	,	PUNCT
ejpam-6633	53	12	uniqueness	uniqueness	NOUN
ejpam-6633	53	13	,	,	PUNCT
ejpam-6633	53	14	and	and	CCONJ
ejpam-6633	53	15	stability	stability	NOUN
ejpam-6633	53	16	of	of	ADP
ejpam-6633	53	17	the	the	DET
ejpam-6633	53	18	fractional	fractional	ADJ
ejpam-6633	53	19	lane	lane	NOUN
ejpam-6633	53	20	-	-	PUNCT
ejpam-6633	53	21	emden	emden	NOUN
ejpam-6633	53	22	boundary	boundary	ADJ
ejpam-6633	53	23	-	-	PUNCT
ejpam-6633	53	24	value	value	NOUN
ejpam-6633	53	25	problem	problem	NOUN
ejpam-6633	53	26	.	.	PUNCT
ejpam-6633	54	1	we	we	PRON
ejpam-6633	54	2	consider	consider	VERB
ejpam-6633	54	3	the	the	DET
ejpam-6633	54	4	nonlinear	nonlinear	ADJ
ejpam-6633	54	5	laneemden	laneemden	ADJ
ejpam-6633	54	6	equation	equation	NOUN
ejpam-6633	54	7	with	with	ADP
ejpam-6633	54	8	multiple	multiple	ADJ
ejpam-6633	54	9	fractional	fractional	ADJ
ejpam-6633	54	10	derivatives	derivative	NOUN
ejpam-6633	54	11	:	:	PUNCT
ejpam-6633	54	12	chd	chd	PROPN
ejpam-6633	54	13	β	β	X
ejpam-6633	54	14	(	(	PUNCT
ejpam-6633	54	15	chd	chd	PROPN
ejpam-6633	54	16	α	α	PROPN
ejpam-6633	54	17	+	+	X
ejpam-6633	54	18	µ	µ	PROPN
ejpam-6633	54	19	t	t	NOUN
ejpam-6633	54	20	)	)	PUNCT
ejpam-6633	54	21	η(t	η(t	NOUN
ejpam-6633	54	22	)	)	PUNCT
ejpam-6633	54	23	=	=	SYM
ejpam-6633	54	24	θ(t	θ(t	PROPN
ejpam-6633	54	25	,	,	PUNCT
ejpam-6633	54	26	η(t	η(t	NOUN
ejpam-6633	54	27	)	)	PUNCT
ejpam-6633	54	28	)	)	PUNCT
ejpam-6633	54	29	,	,	PUNCT
ejpam-6633	54	30	(	(	PUNCT
ejpam-6633	54	31	6	6	X
ejpam-6633	54	32	)	)	PUNCT
ejpam-6633	54	33	supplemented	supplement	VERB
ejpam-6633	54	34	with	with	ADP
ejpam-6633	54	35	boundary	boundary	ADJ
ejpam-6633	54	36	conditions	condition	NOUN
ejpam-6633	54	37	:	:	PUNCT
ejpam-6633	54	38	η(a	η(a	VERB
ejpam-6633	54	39	)	)	PUNCT
ejpam-6633	54	40	=	=	SYM
ejpam-6633	54	41	ξ1	ξ1	NOUN
ejpam-6633	54	42	,	,	PUNCT
ejpam-6633	54	43	(	(	PUNCT
ejpam-6633	54	44	7	7	X
ejpam-6633	54	45	)	)	PUNCT
ejpam-6633	54	46	η(1	η(1	NOUN
ejpam-6633	54	47	)	)	PUNCT
ejpam-6633	54	48	=	=	SYM
ejpam-6633	54	49	ξ2	ξ2	NOUN
ejpam-6633	54	50	,	,	PUNCT
ejpam-6633	54	51	(	(	PUNCT
ejpam-6633	54	52	8)	8)	NUM
ejpam-6633	54	53	where	where	SCONJ
ejpam-6633	54	54	µ	µ	NOUN
ejpam-6633	54	55	,	,	PUNCT
ejpam-6633	54	56	ξ1	ξ1	NOUN
ejpam-6633	54	57	,	,	PUNCT
ejpam-6633	54	58	ξ2	ξ2	NOUN
ejpam-6633	54	59	∈	∈	PROPN
ejpam-6633	54	60	r	r	NOUN
ejpam-6633	54	61	,	,	PUNCT
ejpam-6633	54	62	t	t	PROPN
ejpam-6633	54	63	∈	∈	PROPN
ejpam-6633	55	1	[	[	X
ejpam-6633	55	2	a	a	X
ejpam-6633	55	3	,	,	PUNCT
ejpam-6633	55	4	1	1	NUM
ejpam-6633	55	5	]	]	PUNCT
ejpam-6633	55	6	and	and	CCONJ
ejpam-6633	55	7	0	0	NUM
ejpam-6633	55	8	<	<	X
ejpam-6633	55	9	a	a	DET
ejpam-6633	55	10	<	<	X
ejpam-6633	55	11	1	1	NUM
ejpam-6633	55	12	.	.	PUNCT
ejpam-6633	56	1	in	in	ADP
ejpam-6633	56	2	equation	equation	NOUN
ejpam-6633	56	3	(	(	PUNCT
ejpam-6633	56	4	6	6	NUM
ejpam-6633	56	5	)	)	PUNCT
ejpam-6633	56	6	,	,	PUNCT
ejpam-6633	56	7	α	α	PROPN
ejpam-6633	56	8	and	and	CCONJ
ejpam-6633	56	9	β	β	X
ejpam-6633	56	10	are	be	AUX
ejpam-6633	56	11	positive	positive	ADJ
ejpam-6633	56	12	noninteger	noninteger	NOUN
ejpam-6633	56	13	numbers	number	NOUN
ejpam-6633	56	14	less	less	ADJ
ejpam-6633	56	15	than	than	ADP
ejpam-6633	56	16	one	one	NUM
ejpam-6633	56	17	;	;	PUNCT
ejpam-6633	56	18	we	we	PRON
ejpam-6633	56	19	obtain	obtain	VERB
ejpam-6633	56	20	the	the	DET
ejpam-6633	56	21	classical	classical	ADJ
ejpam-6633	56	22	lane	lane	NOUN
ejpam-6633	56	23	-	-	PUNCT
ejpam-6633	56	24	emden	emden	NOUN
ejpam-6633	56	25	equation	equation	NOUN
ejpam-6633	56	26	for	for	ADP
ejpam-6633	56	27	α	α	NOUN
ejpam-6633	56	28	=	=	SYM
ejpam-6633	56	29	β	β	X
ejpam-6633	56	30	=	=	SYM
ejpam-6633	56	31	1	1	X
ejpam-6633	56	32	.	.	PUNCT
ejpam-6633	57	1	the	the	DET
ejpam-6633	57	2	two	two	NUM
ejpam-6633	57	3	functions	function	NOUN
ejpam-6633	57	4	η(t	η(t	NOUN
ejpam-6633	57	5	)	)	PUNCT
ejpam-6633	57	6	and	and	CCONJ
ejpam-6633	57	7	θ(t	θ(t	PROPN
ejpam-6633	57	8	,	,	PUNCT
ejpam-6633	57	9	η(t	η(t	NOUN
ejpam-6633	57	10	)	)	PUNCT
ejpam-6633	57	11	)	)	PUNCT
ejpam-6633	57	12	belong	belong	VERB
ejpam-6633	57	13	to	to	ADP
ejpam-6633	57	14	the	the	DET
ejpam-6633	57	15	set	set	NOUN
ejpam-6633	57	16	of	of	ADP
ejpam-6633	57	17	all	all	DET
ejpam-6633	57	18	continuous	continuous	ADJ
ejpam-6633	57	19	function	function	NOUN
ejpam-6633	57	20	on	on	ADP
ejpam-6633	57	21	[	[	X
ejpam-6633	57	22	a	a	X
ejpam-6633	57	23	,	,	PUNCT
ejpam-6633	57	24	1	1	NUM
ejpam-6633	57	25	]	]	PUNCT
ejpam-6633	57	26	,	,	PUNCT
ejpam-6633	57	27	i.e.	i.e.	X
ejpam-6633	57	28	η(t	η(t	NOUN
ejpam-6633	57	29	)	)	PUNCT
ejpam-6633	57	30	,	,	PUNCT
ejpam-6633	57	31	θ(t	θ(t	PROPN
ejpam-6633	57	32	,	,	PUNCT
ejpam-6633	57	33	η(t	η(t	NOUN
ejpam-6633	57	34	)	)	PUNCT
ejpam-6633	57	35	)	)	PUNCT
ejpam-6633	58	1	∈	∈	PROPN
ejpam-6633	58	2	c	c	NOUN
ejpam-6633	58	3	(	(	PUNCT
ejpam-6633	58	4	[	[	X
ejpam-6633	58	5	a	a	X
ejpam-6633	58	6	,	,	PUNCT
ejpam-6633	58	7	1	1	NUM
ejpam-6633	58	8	]	]	PUNCT
ejpam-6633	58	9	,	,	PUNCT
ejpam-6633	58	10	r	r	NOUN
ejpam-6633	58	11	)	)	PUNCT
ejpam-6633	58	12	.	.	PUNCT
ejpam-6633	59	1	here	here	ADV
ejpam-6633	59	2	chd	chd	PROPN
ejpam-6633	59	3	β	β	PROPN
ejpam-6633	59	4	represents	represent	VERB
ejpam-6633	59	5	the	the	DET
ejpam-6633	59	6	caputo	caputo	PROPN
ejpam-6633	59	7	-	-	PUNCT
ejpam-6633	59	8	hadamard	hadamard	ADJ
ejpam-6633	59	9	fractional	fractional	ADJ
ejpam-6633	59	10	derivative	derivative	NOUN
ejpam-6633	59	11	of	of	ADP
ejpam-6633	59	12	order	order	NOUN
ejpam-6633	59	13	β	β	PUNCT
ejpam-6633	59	14	as	as	SCONJ
ejpam-6633	59	15	stated	state	VERB
ejpam-6633	59	16	in	in	ADP
ejpam-6633	59	17	definition	definition	NOUN
ejpam-6633	59	18	3	3	NUM
ejpam-6633	59	19	.	.	PUNCT
ejpam-6633	60	1	we	we	PRON
ejpam-6633	60	2	study	study	VERB
ejpam-6633	60	3	the	the	DET
ejpam-6633	60	4	existence	existence	NOUN
ejpam-6633	60	5	,	,	PUNCT
ejpam-6633	60	6	uniqueness	uniqueness	NOUN
ejpam-6633	60	7	,	,	PUNCT
ejpam-6633	60	8	and	and	CCONJ
ejpam-6633	60	9	stability	stability	NOUN
ejpam-6633	60	10	of	of	ADP
ejpam-6633	60	11	the	the	DET
ejpam-6633	60	12	problem	problem	NOUN
ejpam-6633	60	13	(	(	PUNCT
ejpam-6633	60	14	6	6	NUM
ejpam-6633	60	15	-	-	SYM
ejpam-6633	60	16	8)	8)	NUM
ejpam-6633	60	17	on	on	ADP
ejpam-6633	60	18	the	the	DET
ejpam-6633	60	19	interval	interval	NOUN
ejpam-6633	60	20	[	[	X
ejpam-6633	60	21	a	a	X
ejpam-6633	60	22	,	,	PUNCT
ejpam-6633	60	23	1	1	NUM
ejpam-6633	60	24	]	]	PUNCT
ejpam-6633	60	25	such	such	ADJ
ejpam-6633	60	26	that	that	SCONJ
ejpam-6633	60	27	1	1	NUM
ejpam-6633	60	28	/	/	SYM
ejpam-6633	60	29	a	a	PRON
ejpam-6633	60	30	is	be	AUX
ejpam-6633	60	31	finite	finite	ADJ
ejpam-6633	60	32	.	.	PUNCT
ejpam-6633	61	1	in	in	ADP
ejpam-6633	61	2	addition	addition	NOUN
ejpam-6633	61	3	,	,	PUNCT
ejpam-6633	61	4	we	we	PRON
ejpam-6633	61	5	assemble	assemble	VERB
ejpam-6633	61	6	a	a	DET
ejpam-6633	61	7	numerical	numerical	ADJ
ejpam-6633	61	8	scheme	scheme	NOUN
ejpam-6633	61	9	,	,	PUNCT
ejpam-6633	61	10	by	by	ADP
ejpam-6633	61	11	applying	apply	VERB
ejpam-6633	61	12	the	the	DET
ejpam-6633	61	13	fractional	fractional	ADJ
ejpam-6633	61	14	rectangular	rectangular	ADJ
ejpam-6633	61	15	,	,	PUNCT
ejpam-6633	61	16	lln,1	lln,1	NOUN
ejpam-6633	61	17	interpolation	interpolation	NOUN
ejpam-6633	61	18	on	on	ADP
ejpam-6633	61	19	a	a	DET
ejpam-6633	61	20	logarithmic	logarithmic	ADJ
ejpam-6633	61	21	grid	grid	NOUN
ejpam-6633	61	22	to	to	PART
ejpam-6633	61	23	approximate	approximate	VERB
ejpam-6633	61	24	the	the	DET
ejpam-6633	61	25	derived	derive	VERB
ejpam-6633	61	26	analytical	analytical	ADJ
ejpam-6633	61	27	solution	solution	NOUN
ejpam-6633	61	28	(	(	PUNCT
ejpam-6633	61	29	18	18	NUM
ejpam-6633	61	30	)	)	PUNCT
ejpam-6633	61	31	.	.	PUNCT
ejpam-6633	62	1	the	the	DET
ejpam-6633	62	2	resulting	result	VERB
ejpam-6633	62	3	system	system	NOUN
ejpam-6633	62	4	of	of	ADP
ejpam-6633	62	5	nonlinear	nonlinear	ADJ
ejpam-6633	62	6	equation	equation	NOUN
ejpam-6633	62	7	solved	solve	VERB
ejpam-6633	62	8	by	by	ADP
ejpam-6633	62	9	the	the	DET
ejpam-6633	62	10	newton	newton	PROPN
ejpam-6633	62	11	-	-	PUNCT
ejpam-6633	62	12	raphson	raphson	PROPN
ejpam-6633	62	13	method	method	NOUN
ejpam-6633	62	14	using	use	VERB
ejpam-6633	62	15	the	the	DET
ejpam-6633	62	16	jacobian	jacobian	ADJ
ejpam-6633	62	17	matrix	matrix	NOUN
ejpam-6633	62	18	to	to	PART
ejpam-6633	62	19	handle	handle	VERB
ejpam-6633	62	20	the	the	DET
ejpam-6633	62	21	non	non	ADJ
ejpam-6633	62	22	-	-	ADJ
ejpam-6633	62	23	linear	linear	ADJ
ejpam-6633	62	24	coupling	coupling	NOUN
ejpam-6633	62	25	between	between	ADP
ejpam-6633	62	26	η(t	η(t	NOUN
ejpam-6633	62	27	)	)	PUNCT
ejpam-6633	62	28	and	and	CCONJ
ejpam-6633	62	29	θ(t	θ(t	PROPN
ejpam-6633	62	30	,	,	PUNCT
ejpam-6633	62	31	η(t	η(t	NOUN
ejpam-6633	62	32	)	)	PUNCT
ejpam-6633	62	33	)	)	PUNCT
ejpam-6633	62	34	.	.	PUNCT
ejpam-6633	63	1	numerical	numerical	ADJ
ejpam-6633	63	2	approaches	approach	NOUN
ejpam-6633	63	3	to	to	PART
ejpam-6633	63	4	solve	solve	VERB
ejpam-6633	63	5	caputo	caputo	PROPN
ejpam-6633	63	6	-	-	PUNCT
ejpam-6633	63	7	hadamard	hadamard	ADJ
ejpam-6633	63	8	fractional	fractional	ADJ
ejpam-6633	63	9	differential	differential	NOUN
ejpam-6633	63	10	equations	equation	NOUN
ejpam-6633	63	11	are	be	AUX
ejpam-6633	63	12	complicated	complicate	VERB
ejpam-6633	63	13	due	due	ADP
ejpam-6633	63	14	to	to	ADP
ejpam-6633	63	15	the	the	DET
ejpam-6633	63	16	logarithmic	logarithmic	ADJ
ejpam-6633	63	17	kernel	kernel	NOUN
ejpam-6633	63	18	,	,	PUNCT
ejpam-6633	63	19	which	which	PRON
ejpam-6633	63	20	is	be	AUX
ejpam-6633	63	21	weakly	weakly	ADV
ejpam-6633	63	22	singular	singular	ADJ
ejpam-6633	63	23	.	.	PUNCT
ejpam-6633	64	1	recently	recently	ADV
ejpam-6633	64	2	,	,	PUNCT
ejpam-6633	64	3	some	some	DET
ejpam-6633	64	4	researchers	researcher	NOUN
ejpam-6633	64	5	are	be	AUX
ejpam-6633	64	6	investigating	investigate	VERB
ejpam-6633	64	7	the	the	DET
ejpam-6633	64	8	numerical	numerical	ADJ
ejpam-6633	64	9	schemes	scheme	NOUN
ejpam-6633	64	10	that	that	PRON
ejpam-6633	64	11	can	can	AUX
ejpam-6633	64	12	be	be	AUX
ejpam-6633	64	13	considered	consider	VERB
ejpam-6633	64	14	.	.	PUNCT
ejpam-6633	65	1	in	in	ADP
ejpam-6633	65	2	a	a	DET
ejpam-6633	65	3	study	study	NOUN
ejpam-6633	65	4	a.	a.	PROPN
ejpam-6633	65	5	s.	s.	PROPN
ejpam-6633	65	6	hasan	hasan	PROPN
ejpam-6633	65	7	,	,	PUNCT
ejpam-6633	65	8	s.	s.	PROPN
ejpam-6633	65	9	a.	a.	PROPN
ejpam-6633	65	10	murad	murad	PROPN
ejpam-6633	65	11	/	/	SYM
ejpam-6633	65	12	eur	eur	PROPN
ejpam-6633	65	13	.	.	PUNCT
ejpam-6633	66	1	j.	j.	PROPN
ejpam-6633	66	2	pure	pure	PROPN
ejpam-6633	66	3	appl	appl	PROPN
ejpam-6633	66	4	.	.	PROPN
ejpam-6633	66	5	math	math	PROPN
ejpam-6633	66	6	,	,	PUNCT
ejpam-6633	66	7	18	18	NUM
ejpam-6633	66	8	(	(	PUNCT
ejpam-6633	66	9	3	3	NUM
ejpam-6633	66	10	)	)	PUNCT
ejpam-6633	66	11	(	(	PUNCT
ejpam-6633	66	12	2025	2025	NUM
ejpam-6633	66	13	)	)	PUNCT
ejpam-6633	66	14	,	,	PUNCT
ejpam-6633	66	15	6633	6633	NUM
ejpam-6633	66	16	4	4	NUM
ejpam-6633	66	17	of	of	ADP
ejpam-6633	66	18	24	24	NUM
ejpam-6633	66	19	by	by	ADP
ejpam-6633	66	20	[	[	X
ejpam-6633	66	21	23	23	NUM
ejpam-6633	66	22	]	]	PUNCT
ejpam-6633	67	1	,	,	PUNCT
ejpam-6633	67	2	they	they	PRON
ejpam-6633	67	3	examined	examine	VERB
ejpam-6633	67	4	finite	finite	ADJ
ejpam-6633	67	5	difference	difference	NOUN
ejpam-6633	67	6	methods	method	NOUN
ejpam-6633	67	7	for	for	ADP
ejpam-6633	67	8	caputo	caputo	PROPN
ejpam-6633	67	9	-	-	PUNCT
ejpam-6633	67	10	hadamard	hadamard	ADJ
ejpam-6633	67	11	derivative	derivative	ADJ
ejpam-6633	67	12	fractional	fractional	ADJ
ejpam-6633	67	13	differential	differential	NOUN
ejpam-6633	67	14	equations	equation	NOUN
ejpam-6633	67	15	.	.	PUNCT
ejpam-6633	68	1	in	in	ADP
ejpam-6633	68	2	their	their	PRON
ejpam-6633	68	3	study	study	NOUN
ejpam-6633	68	4	,	,	PUNCT
ejpam-6633	68	5	the	the	DET
ejpam-6633	68	6	analogous	analogous	ADJ
ejpam-6633	68	7	volterra	volterra	NOUN
ejpam-6633	68	8	integral	integral	ADJ
ejpam-6633	68	9	equations	equation	NOUN
ejpam-6633	68	10	were	be	AUX
ejpam-6633	68	11	approximated	approximate	VERB
ejpam-6633	68	12	via	via	ADP
ejpam-6633	68	13	fractional	fractional	ADJ
ejpam-6633	68	14	rectangle	rectangle	NOUN
ejpam-6633	68	15	,	,	PUNCT
ejpam-6633	68	16	llog,1	llog,1	NOUN
ejpam-6633	68	17	interpolation	interpolation	NOUN
ejpam-6633	68	18	when	when	SCONJ
ejpam-6633	68	19	they	they	PRON
ejpam-6633	68	20	used	use	VERB
ejpam-6633	68	21	the	the	DET
ejpam-6633	68	22	modified	modify	VERB
ejpam-6633	68	23	predictor	predictor	NOUN
ejpam-6633	68	24	–	–	PUNCT
ejpam-6633	68	25	corrector	corrector	NOUN
ejpam-6633	68	26	for	for	ADP
ejpam-6633	68	27	caputo	caputo	PROPN
ejpam-6633	68	28	-	-	PUNCT
ejpam-6633	68	29	hadamard	hadamard	ADJ
ejpam-6633	68	30	fractional	fractional	ADJ
ejpam-6633	68	31	differential	differential	NOUN
ejpam-6633	68	32	equations	equation	NOUN
ejpam-6633	68	33	.	.	PUNCT
ejpam-6633	69	1	[	[	X
ejpam-6633	69	2	24	24	NUM
ejpam-6633	69	3	]	]	PUNCT
ejpam-6633	69	4	used	use	VERB
ejpam-6633	69	5	the	the	DET
ejpam-6633	69	6	local	local	ADJ
ejpam-6633	69	7	discontinuous	discontinuous	ADJ
ejpam-6633	69	8	galerkin	galerkin	ADJ
ejpam-6633	69	9	method	method	NOUN
ejpam-6633	69	10	to	to	PART
ejpam-6633	69	11	solve	solve	VERB
ejpam-6633	69	12	boundary	boundary	ADJ
ejpam-6633	69	13	-	-	PUNCT
ejpam-6633	69	14	value	value	NOUN
ejpam-6633	69	15	problems	problem	NOUN
ejpam-6633	69	16	with	with	ADP
ejpam-6633	69	17	the	the	DET
ejpam-6633	69	18	caputohadamard	caputohadamard	ADJ
ejpam-6633	69	19	fractional	fractional	ADJ
ejpam-6633	69	20	derivative	derivative	NOUN
ejpam-6633	69	21	.	.	PUNCT
ejpam-6633	70	1	furthermore	furthermore	ADV
ejpam-6633	70	2	,	,	PUNCT
ejpam-6633	70	3	[	[	X
ejpam-6633	70	4	25	25	NUM
ejpam-6633	70	5	]	]	PUNCT
ejpam-6633	70	6	numerically	numerically	ADV
ejpam-6633	70	7	solved	solve	VERB
ejpam-6633	70	8	caputo	caputo	PROPN
ejpam-6633	70	9	–	–	PUNCT
ejpam-6633	70	10	hadamard	hadamard	ADJ
ejpam-6633	70	11	fractional	fractional	ADJ
ejpam-6633	70	12	differential	differential	ADJ
ejpam-6633	70	13	equations	equation	NOUN
ejpam-6633	70	14	with	with	ADP
ejpam-6633	70	15	the	the	DET
ejpam-6633	70	16	graded	grade	VERB
ejpam-6633	70	17	meshes	mesh	NOUN
ejpam-6633	70	18	.	.	PUNCT
ejpam-6633	71	1	the	the	DET
ejpam-6633	71	2	organization	organization	NOUN
ejpam-6633	71	3	of	of	ADP
ejpam-6633	71	4	this	this	DET
ejpam-6633	71	5	paper	paper	NOUN
ejpam-6633	71	6	is	be	AUX
ejpam-6633	71	7	as	as	SCONJ
ejpam-6633	71	8	follows	follow	VERB
ejpam-6633	71	9	:	:	PUNCT
ejpam-6633	71	10	section	section	NOUN
ejpam-6633	71	11	2	2	NUM
ejpam-6633	71	12	presents	present	VERB
ejpam-6633	71	13	the	the	DET
ejpam-6633	71	14	essential	essential	ADJ
ejpam-6633	71	15	definitions	definition	NOUN
ejpam-6633	71	16	,	,	PUNCT
ejpam-6633	71	17	theorems	theorem	NOUN
ejpam-6633	71	18	,	,	PUNCT
ejpam-6633	71	19	remarks	remark	NOUN
ejpam-6633	71	20	,	,	PUNCT
ejpam-6633	71	21	and	and	CCONJ
ejpam-6633	71	22	lemmas	lemma	VERB
ejpam-6633	71	23	that	that	PRON
ejpam-6633	71	24	support	support	VERB
ejpam-6633	71	25	our	our	PRON
ejpam-6633	71	26	current	current	ADJ
ejpam-6633	71	27	investigation	investigation	NOUN
ejpam-6633	71	28	.	.	PUNCT
ejpam-6633	72	1	section	section	NOUN
ejpam-6633	72	2	3	3	NUM
ejpam-6633	72	3	addresses	address	NOUN
ejpam-6633	72	4	the	the	DET
ejpam-6633	72	5	existence	existence	NOUN
ejpam-6633	72	6	and	and	CCONJ
ejpam-6633	72	7	uniqueness	uniqueness	NOUN
ejpam-6633	72	8	of	of	ADP
ejpam-6633	72	9	the	the	DET
ejpam-6633	72	10	solution	solution	NOUN
ejpam-6633	72	11	for	for	ADP
ejpam-6633	72	12	the	the	DET
ejpam-6633	72	13	problem	problem	NOUN
ejpam-6633	72	14	(	(	PUNCT
ejpam-6633	72	15	6	6	NUM
ejpam-6633	72	16	-	-	SYM
ejpam-6633	72	17	8)	8)	NUM
ejpam-6633	72	18	.	.	PUNCT
ejpam-6633	73	1	section	section	NOUN
ejpam-6633	73	2	4	4	NUM
ejpam-6633	73	3	examines	examine	VERB
ejpam-6633	73	4	the	the	DET
ejpam-6633	73	5	ulam	ulam	NOUN
ejpam-6633	73	6	-	-	PUNCT
ejpam-6633	73	7	hyers	hyer	NOUN
ejpam-6633	73	8	and	and	CCONJ
ejpam-6633	73	9	ulam	ulam	NOUN
ejpam-6633	73	10	-	-	PUNCT
ejpam-6633	73	11	hyers	hyer	NOUN
ejpam-6633	73	12	-	-	PUNCT
ejpam-6633	73	13	rassias	rassias	PROPN
ejpam-6633	73	14	stability	stability	NOUN
ejpam-6633	73	15	results	result	NOUN
ejpam-6633	73	16	,	,	PUNCT
ejpam-6633	73	17	whilst	whilst	SCONJ
ejpam-6633	73	18	section	section	NOUN
ejpam-6633	73	19	5	5	NUM
ejpam-6633	73	20	presents	present	VERB
ejpam-6633	73	21	the	the	DET
ejpam-6633	73	22	numerical	numerical	ADJ
ejpam-6633	73	23	scheme	scheme	NOUN
ejpam-6633	73	24	using	use	VERB
ejpam-6633	73	25	newton	newton	PROPN
ejpam-6633	73	26	-	-	PUNCT
ejpam-6633	73	27	raphson	raphson	PROPN
ejpam-6633	73	28	method	method	NOUN
ejpam-6633	73	29	to	to	PART
ejpam-6633	73	30	solve	solve	VERB
ejpam-6633	73	31	the	the	DET
ejpam-6633	73	32	caputo	caputo	PROPN
ejpam-6633	73	33	-	-	PUNCT
ejpam-6633	73	34	hadamard	hadamard	ADJ
ejpam-6633	73	35	fractional	fractional	ADJ
ejpam-6633	73	36	problem	problem	NOUN
ejpam-6633	73	37	.	.	PUNCT
ejpam-6633	74	1	examples	example	NOUN
ejpam-6633	74	2	along	along	ADP
ejpam-6633	74	3	with	with	ADP
ejpam-6633	74	4	relevant	relevant	ADJ
ejpam-6633	74	5	graphs	graph	NOUN
ejpam-6633	74	6	are	be	AUX
ejpam-6633	74	7	presented	present	VERB
ejpam-6633	74	8	in	in	ADP
ejpam-6633	74	9	sections	section	NOUN
ejpam-6633	74	10	4	4	NUM
ejpam-6633	74	11	-	-	SYM
ejpam-6633	74	12	5	5	NUM
ejpam-6633	74	13	.	.	NOUN
ejpam-6633	74	14	2	2	NUM
ejpam-6633	74	15	.	.	X
ejpam-6633	74	16	preliminaries	preliminary	NOUN
ejpam-6633	74	17	this	this	DET
ejpam-6633	74	18	section	section	NOUN
ejpam-6633	74	19	presents	present	VERB
ejpam-6633	74	20	key	key	ADJ
ejpam-6633	74	21	definitions	definition	NOUN
ejpam-6633	74	22	,	,	PUNCT
ejpam-6633	74	23	lemmas	lemmas	ADJ
ejpam-6633	74	24	,	,	PUNCT
ejpam-6633	74	25	and	and	CCONJ
ejpam-6633	74	26	remarks	remark	NOUN
ejpam-6633	74	27	that	that	PRON
ejpam-6633	74	28	form	form	VERB
ejpam-6633	74	29	the	the	DET
ejpam-6633	74	30	foundational	foundational	ADJ
ejpam-6633	74	31	concepts	concept	NOUN
ejpam-6633	74	32	for	for	ADP
ejpam-6633	74	33	this	this	DET
ejpam-6633	74	34	study	study	NOUN
ejpam-6633	74	35	and	and	CCONJ
ejpam-6633	74	36	will	will	AUX
ejpam-6633	74	37	be	be	AUX
ejpam-6633	74	38	referenced	reference	VERB
ejpam-6633	74	39	and	and	CCONJ
ejpam-6633	74	40	served	serve	VERB
ejpam-6633	74	41	as	as	ADP
ejpam-6633	74	42	the	the	DET
ejpam-6633	74	43	groundwork	groundwork	NOUN
ejpam-6633	74	44	for	for	ADP
ejpam-6633	74	45	the	the	DET
ejpam-6633	74	46	analysis	analysis	NOUN
ejpam-6633	74	47	and	and	CCONJ
ejpam-6633	74	48	discussions	discussion	NOUN
ejpam-6633	74	49	in	in	ADP
ejpam-6633	74	50	this	this	DET
ejpam-6633	74	51	study	study	NOUN
ejpam-6633	74	52	.	.	PUNCT
ejpam-6633	75	1	definition	definition	NOUN
ejpam-6633	75	2	1	1	NUM
ejpam-6633	75	3	.	.	PUNCT
ejpam-6633	76	1	[	[	X
ejpam-6633	76	2	7	7	X
ejpam-6633	76	3	]	]	PUNCT
ejpam-6633	76	4	for	for	ADP
ejpam-6633	76	5	a	a	DET
ejpam-6633	76	6	given	give	VERB
ejpam-6633	76	7	function	function	NOUN
ejpam-6633	76	8	η(t	η(t	NOUN
ejpam-6633	76	9	)	)	PUNCT
ejpam-6633	76	10	,	,	PUNCT
ejpam-6633	76	11	the	the	DET
ejpam-6633	76	12	left	left	ADV
ejpam-6633	76	13	-	-	PUNCT
ejpam-6633	76	14	sided	sided	ADJ
ejpam-6633	76	15	fractional	fractional	ADJ
ejpam-6633	76	16	integral	integral	ADJ
ejpam-6633	76	17	of	of	ADP
ejpam-6633	76	18	order	order	NOUN
ejpam-6633	76	19	β	β	X
ejpam-6633	76	20	>	>	X
ejpam-6633	76	21	0	0	NUM
ejpam-6633	76	22	of	of	ADP
ejpam-6633	76	23	hadamard	hadamard	ADJ
ejpam-6633	76	24	type	type	NOUN
ejpam-6633	76	25	is	be	AUX
ejpam-6633	76	26	defined	define	VERB
ejpam-6633	76	27	as	as	ADP
ejpam-6633	76	28	hi	hi	INTJ
ejpam-6633	76	29	β	β	X
ejpam-6633	76	30	a	a	DET
ejpam-6633	76	31	η(t	η(t	NOUN
ejpam-6633	76	32	)	)	PUNCT
ejpam-6633	76	33	=	=	SYM
ejpam-6633	76	34	1	1	NUM
ejpam-6633	76	35	γ(β	γ(β	PROPN
ejpam-6633	76	36	)	)	PUNCT
ejpam-6633	77	1	∫	∫	PROPN
ejpam-6633	77	2	t	t	PROPN
ejpam-6633	77	3	a	a	X
ejpam-6633	77	4	(	(	PUNCT
ejpam-6633	77	5	ln	ln	X
ejpam-6633	77	6	(	(	PUNCT
ejpam-6633	77	7	t	t	PROPN
ejpam-6633	77	8	τ	τ	PROPN
ejpam-6633	77	9	)	)	PUNCT
ejpam-6633	77	10	)	)	PUNCT
ejpam-6633	77	11	β−1	β−1	PUNCT
ejpam-6633	77	12	η(τ	η(τ	PROPN
ejpam-6633	77	13	)	)	PUNCT
ejpam-6633	77	14	τ	τ	PROPN
ejpam-6633	77	15	dτ	dτ	PROPN
ejpam-6633	77	16	,	,	PUNCT
ejpam-6633	77	17	(	(	PUNCT
ejpam-6633	77	18	9	9	NUM
ejpam-6633	77	19	)	)	PUNCT
ejpam-6633	77	20	where	where	SCONJ
ejpam-6633	77	21	γ	γ	X
ejpam-6633	77	22	(	(	PUNCT
ejpam-6633	77	23	·	·	PUNCT
ejpam-6633	77	24	)	)	PUNCT
ejpam-6633	77	25	refers	refer	VERB
ejpam-6633	77	26	to	to	ADP
ejpam-6633	77	27	the	the	DET
ejpam-6633	77	28	euler	euler	NOUN
ejpam-6633	77	29	gamma	gamma	PROPN
ejpam-6633	77	30	function	function	PROPN
ejpam-6633	77	31	.	.	PUNCT
ejpam-6633	78	1	definition	definition	NOUN
ejpam-6633	78	2	2	2	NUM
ejpam-6633	78	3	.	.	PUNCT
ejpam-6633	79	1	[	[	X
ejpam-6633	79	2	7	7	X
ejpam-6633	79	3	]	]	PUNCT
ejpam-6633	79	4	for	for	ADP
ejpam-6633	79	5	a	a	DET
ejpam-6633	79	6	given	give	VERB
ejpam-6633	79	7	function	function	NOUN
ejpam-6633	79	8	η(t	η(t	NOUN
ejpam-6633	79	9	)	)	PUNCT
ejpam-6633	79	10	,	,	PUNCT
ejpam-6633	79	11	the	the	DET
ejpam-6633	79	12	left	left	ADV
ejpam-6633	79	13	-	-	PUNCT
ejpam-6633	79	14	sided	side	VERB
ejpam-6633	79	15	fractional	fractional	ADJ
ejpam-6633	79	16	derivative	derivative	NOUN
ejpam-6633	79	17	of	of	ADP
ejpam-6633	79	18	order	order	NOUN
ejpam-6633	79	19	β	β	X
ejpam-6633	79	20	>	>	X
ejpam-6633	79	21	0	0	PUNCT
ejpam-6633	80	1	(	(	PUNCT
ejpam-6633	80	2	n−	n−	NOUN
ejpam-6633	80	3	1	1	NUM
ejpam-6633	80	4	<	<	X
ejpam-6633	80	5	β	β	X
ejpam-6633	80	6	<	<	X
ejpam-6633	80	7	n	n	PRON
ejpam-6633	80	8	∈	∈	PROPN
ejpam-6633	80	9	n	n	CCONJ
ejpam-6633	80	10	)	)	PUNCT
ejpam-6633	80	11	of	of	ADP
ejpam-6633	80	12	hadamard	hadamard	ADJ
ejpam-6633	80	13	type	type	NOUN
ejpam-6633	80	14	is	be	AUX
ejpam-6633	80	15	defined	define	VERB
ejpam-6633	80	16	as	as	ADP
ejpam-6633	80	17	hd	hd	PROPN
ejpam-6633	80	18	β	β	X
ejpam-6633	80	19	aη(t	aη(t	NOUN
ejpam-6633	80	20	)	)	PUNCT
ejpam-6633	81	1	=	=	SYM
ejpam-6633	81	2	1	1	NUM
ejpam-6633	81	3	γ(n−	γ(n−	PROPN
ejpam-6633	81	4	β	β	NOUN
ejpam-6633	81	5	)	)	PUNCT
ejpam-6633	81	6	δn	δn	PROPN
ejpam-6633	81	7	∫	∫	PROPN
ejpam-6633	81	8	t	t	PROPN
ejpam-6633	81	9	a	a	X
ejpam-6633	81	10	(	(	PUNCT
ejpam-6633	81	11	ln	ln	X
ejpam-6633	81	12	(	(	PUNCT
ejpam-6633	81	13	t	t	PROPN
ejpam-6633	81	14	τ	τ	PROPN
ejpam-6633	81	15	)	)	PUNCT
ejpam-6633	81	16	)	)	PUNCT
ejpam-6633	82	1	n−β−1	n−β−1	ADP
ejpam-6633	82	2	η(τ	η(τ	PROPN
ejpam-6633	82	3	)	)	PUNCT
ejpam-6633	82	4	τ	τ	PROPN
ejpam-6633	82	5	dτ	dτ	PROPN
ejpam-6633	82	6	,	,	PUNCT
ejpam-6633	82	7	(	(	PUNCT
ejpam-6633	82	8	10	10	NUM
ejpam-6633	82	9	)	)	PUNCT
ejpam-6633	82	10	where	where	SCONJ
ejpam-6633	82	11	δn	δn	NOUN
ejpam-6633	82	12	=	=	SYM
ejpam-6633	82	13	(	(	PUNCT
ejpam-6633	82	14	t	t	PROPN
ejpam-6633	82	15	ddt	ddt	PROPN
ejpam-6633	82	16	)	)	PUNCT
ejpam-6633	82	17	n	n	CCONJ
ejpam-6633	82	18	.	.	PUNCT
ejpam-6633	83	1	with	with	ADP
ejpam-6633	83	2	changing	change	VERB
ejpam-6633	83	3	the	the	DET
ejpam-6633	83	4	order	order	NOUN
ejpam-6633	83	5	of	of	ADP
ejpam-6633	83	6	integration	integration	NOUN
ejpam-6633	83	7	and	and	CCONJ
ejpam-6633	83	8	derivative	derivative	NOUN
ejpam-6633	83	9	in	in	ADP
ejpam-6633	83	10	(	(	PUNCT
ejpam-6633	83	11	10	10	NUM
ejpam-6633	83	12	)	)	PUNCT
ejpam-6633	83	13	we	we	PRON
ejpam-6633	83	14	arrive	arrive	VERB
ejpam-6633	83	15	at	at	ADP
ejpam-6633	83	16	the	the	DET
ejpam-6633	83	17	following	following	NOUN
ejpam-6633	83	18	.	.	PUNCT
ejpam-6633	84	1	definition	definition	NOUN
ejpam-6633	84	2	3	3	NUM
ejpam-6633	84	3	.	.	PUNCT
ejpam-6633	85	1	[	[	X
ejpam-6633	85	2	26	26	NUM
ejpam-6633	85	3	]	]	PUNCT
ejpam-6633	85	4	if	if	SCONJ
ejpam-6633	85	5	η(t	η(t	NOUN
ejpam-6633	85	6	)	)	PUNCT
ejpam-6633	85	7	belongs	belong	VERB
ejpam-6633	85	8	to	to	ADP
ejpam-6633	85	9	c([a	c([a	PROPN
ejpam-6633	85	10	,	,	PUNCT
ejpam-6633	85	11	1],r	1],r	NUM
ejpam-6633	85	12	)	)	PUNCT
ejpam-6633	85	13	,	,	PUNCT
ejpam-6633	85	14	then	then	ADV
ejpam-6633	85	15	,	,	PUNCT
ejpam-6633	85	16	the	the	DET
ejpam-6633	85	17	left	left	ADV
ejpam-6633	85	18	-	-	PUNCT
ejpam-6633	85	19	sided	side	VERB
ejpam-6633	85	20	fractional	fractional	ADJ
ejpam-6633	85	21	derivative	derivative	NOUN
ejpam-6633	85	22	of	of	ADP
ejpam-6633	85	23	order	order	NOUN
ejpam-6633	85	24	β	β	X
ejpam-6633	85	25	>	>	X
ejpam-6633	85	26	0	0	NUM
ejpam-6633	85	27	of	of	ADP
ejpam-6633	85	28	caputo	caputo	PROPN
ejpam-6633	85	29	-	-	PUNCT
ejpam-6633	85	30	hadamard	hadamard	ADJ
ejpam-6633	85	31	type	type	NOUN
ejpam-6633	85	32	is	be	AUX
ejpam-6633	85	33	defined	define	VERB
ejpam-6633	85	34	as	as	ADP
ejpam-6633	85	35	chd	chd	PROPN
ejpam-6633	85	36	β	β	PROPN
ejpam-6633	85	37	aη(t	aη(t	PUNCT
ejpam-6633	85	38	)	)	PUNCT
ejpam-6633	86	1	=	=	SYM
ejpam-6633	86	2	1	1	NUM
ejpam-6633	86	3	γ(n−	γ(n−	PROPN
ejpam-6633	86	4	β	β	NOUN
ejpam-6633	86	5	)	)	PUNCT
ejpam-6633	86	6	∫	∫	PROPN
ejpam-6633	86	7	t	t	PROPN
ejpam-6633	86	8	a	a	X
ejpam-6633	86	9	(	(	PUNCT
ejpam-6633	86	10	ln	ln	X
ejpam-6633	86	11	(	(	PUNCT
ejpam-6633	86	12	t	t	PROPN
ejpam-6633	86	13	τ	τ	PROPN
ejpam-6633	86	14	)	)	PUNCT
ejpam-6633	86	15	)	)	PUNCT
ejpam-6633	86	16	n−β−1	n−β−1	X
ejpam-6633	86	17	δnη(τ	δnη(τ	VERB
ejpam-6633	86	18	)	)	PUNCT
ejpam-6633	86	19	dτ	dτ	NOUN
ejpam-6633	86	20	τ	τ	PROPN
ejpam-6633	86	21	,	,	PUNCT
ejpam-6633	86	22	(	(	PUNCT
ejpam-6633	86	23	11	11	NUM
ejpam-6633	86	24	)	)	PUNCT
ejpam-6633	86	25	where	where	SCONJ
ejpam-6633	86	26	δn	δn	NOUN
ejpam-6633	86	27	=	=	SYM
ejpam-6633	86	28	(	(	PUNCT
ejpam-6633	86	29	τ	τ	PROPN
ejpam-6633	86	30	d	d	PROPN
ejpam-6633	86	31	dτ	dτ	PROPN
ejpam-6633	86	32	)	)	PUNCT
ejpam-6633	86	33	n	n	NOUN
ejpam-6633	86	34	and	and	CCONJ
ejpam-6633	86	35	n−	n−	NOUN
ejpam-6633	86	36	1	1	NUM
ejpam-6633	86	37	<	<	X
ejpam-6633	86	38	β	β	X
ejpam-6633	86	39	<	<	X
ejpam-6633	86	40	n.	n.	PROPN
ejpam-6633	86	41	a.	a.	PROPN
ejpam-6633	86	42	s.	s.	PROPN
ejpam-6633	86	43	hasan	hasan	PROPN
ejpam-6633	86	44	,	,	PUNCT
ejpam-6633	86	45	s.	s.	PROPN
ejpam-6633	86	46	a.	a.	PROPN
ejpam-6633	86	47	murad	murad	PROPN
ejpam-6633	86	48	/	/	SYM
ejpam-6633	86	49	eur	eur	PROPN
ejpam-6633	86	50	.	.	PUNCT
ejpam-6633	87	1	j.	j.	PROPN
ejpam-6633	87	2	pure	pure	PROPN
ejpam-6633	87	3	appl	appl	PROPN
ejpam-6633	87	4	.	.	PROPN
ejpam-6633	87	5	math	math	PROPN
ejpam-6633	87	6	,	,	PUNCT
ejpam-6633	87	7	18	18	NUM
ejpam-6633	87	8	(	(	PUNCT
ejpam-6633	87	9	3	3	NUM
ejpam-6633	87	10	)	)	PUNCT
ejpam-6633	87	11	(	(	PUNCT
ejpam-6633	87	12	2025	2025	NUM
ejpam-6633	87	13	)	)	PUNCT
ejpam-6633	87	14	,	,	PUNCT
ejpam-6633	87	15	6633	6633	NUM
ejpam-6633	87	16	5	5	NUM
ejpam-6633	87	17	of	of	ADP
ejpam-6633	87	18	24	24	NUM
ejpam-6633	87	19	lemma	lemma	PROPN
ejpam-6633	87	20	1	1	NUM
ejpam-6633	87	21	.	.	PUNCT
ejpam-6633	88	1	[	[	X
ejpam-6633	88	2	27	27	NUM
ejpam-6633	88	3	]	]	PUNCT
ejpam-6633	88	4	for	for	ADP
ejpam-6633	88	5	a	a	DET
ejpam-6633	88	6	given	give	VERB
ejpam-6633	88	7	function	function	NOUN
ejpam-6633	88	8	η(t	η(t	NOUN
ejpam-6633	88	9	)	)	PUNCT
ejpam-6633	88	10	,	,	PUNCT
ejpam-6633	88	11	if	if	SCONJ
ejpam-6633	88	12	β	β	X
ejpam-6633	88	13	>	>	X
ejpam-6633	88	14	0	0	PUNCT
ejpam-6633	88	15	(	(	PUNCT
ejpam-6633	88	16	n−	n−	NOUN
ejpam-6633	88	17	1	1	NUM
ejpam-6633	88	18	<	<	X
ejpam-6633	88	19	β	β	X
ejpam-6633	88	20	<	<	X
ejpam-6633	88	21	n	n	CCONJ
ejpam-6633	88	22	)	)	PUNCT
ejpam-6633	88	23	where	where	SCONJ
ejpam-6633	88	24	n	n	PRON
ejpam-6633	88	25	is	be	AUX
ejpam-6633	88	26	an	an	DET
ejpam-6633	88	27	integer	integer	NOUN
ejpam-6633	88	28	greater	great	ADJ
ejpam-6633	88	29	than	than	ADP
ejpam-6633	88	30	0	0	NUM
ejpam-6633	88	31	,	,	PUNCT
ejpam-6633	88	32	then	then	ADV
ejpam-6633	88	33	,	,	PUNCT
ejpam-6633	88	34	the	the	DET
ejpam-6633	88	35	hadamard	hadamard	ADJ
ejpam-6633	88	36	integral	integral	ADJ
ejpam-6633	88	37	operates	operate	NOUN
ejpam-6633	88	38	on	on	ADP
ejpam-6633	88	39	the	the	DET
ejpam-6633	88	40	caputo	caputo	PROPN
ejpam-6633	88	41	-	-	PUNCT
ejpam-6633	88	42	hadamard	hadamard	ADJ
ejpam-6633	88	43	derivatives	derivative	NOUN
ejpam-6633	88	44	as	as	ADP
ejpam-6633	88	45	hi	hi	INTJ
ejpam-6633	88	46	β	β	X
ejpam-6633	88	47	a+	a+	X
ejpam-6633	88	48	chd	chd	PROPN
ejpam-6633	88	49	β	β	X
ejpam-6633	88	50	a+	a+	X
ejpam-6633	88	51	η(t	η(t	NOUN
ejpam-6633	88	52	)	)	PUNCT
ejpam-6633	88	53	=	=	SYM
ejpam-6633	88	54	η(t	η(t	NOUN
ejpam-6633	88	55	)	)	PUNCT
ejpam-6633	89	1	+	+	CCONJ
ejpam-6633	89	2	c0	c0	PROPN
ejpam-6633	89	3	+	+	CCONJ
ejpam-6633	89	4	c1	c1	PROPN
ejpam-6633	89	5	ln	ln	PROPN
ejpam-6633	89	6	(	(	PUNCT
ejpam-6633	89	7	t	t	PROPN
ejpam-6633	89	8	a	a	PRON
ejpam-6633	89	9	)	)	PUNCT
ejpam-6633	89	10	+	+	CCONJ
ejpam-6633	89	11	c2	c2	PROPN
ejpam-6633	89	12	(	(	PUNCT
ejpam-6633	89	13	ln	ln	PROPN
ejpam-6633	89	14	(	(	PUNCT
ejpam-6633	89	15	t	t	PROPN
ejpam-6633	89	16	a	a	PRON
ejpam-6633	89	17	)	)	PUNCT
ejpam-6633	89	18	)	)	PUNCT
ejpam-6633	89	19	2	2	NUM
ejpam-6633	89	20	+	+	CCONJ
ejpam-6633	89	21	·	·	PUNCT
ejpam-6633	89	22	·	·	PUNCT
ejpam-6633	89	23	·	·	PUNCT
ejpam-6633	89	24	+	+	NUM
ejpam-6633	89	25	cn−1	cn−1	PROPN
ejpam-6633	89	26	(	(	PUNCT
ejpam-6633	89	27	ln	ln	X
ejpam-6633	89	28	(	(	PUNCT
ejpam-6633	89	29	t	t	PROPN
ejpam-6633	89	30	a	a	PRON
ejpam-6633	89	31	)	)	PUNCT
ejpam-6633	89	32	)	)	PUNCT
ejpam-6633	89	33	n−1	n−1	PROPN
ejpam-6633	89	34	,	,	PUNCT
ejpam-6633	89	35	(	(	PUNCT
ejpam-6633	89	36	12	12	NUM
ejpam-6633	89	37	)	)	PUNCT
ejpam-6633	89	38	where	where	SCONJ
ejpam-6633	89	39	ci	ci	NOUN
ejpam-6633	89	40	=	=	SYM
ejpam-6633	89	41	δiη(a	δiη(a	PROPN
ejpam-6633	89	42	)	)	PUNCT
ejpam-6633	89	43	i	i	PRON
ejpam-6633	89	44	!	!	PUNCT
ejpam-6633	89	45	,	,	PUNCT
ejpam-6633	89	46	i	i	PRON
ejpam-6633	89	47	=	=	NOUN
ejpam-6633	89	48	0	0	NUM
ejpam-6633	89	49	,	,	PUNCT
ejpam-6633	89	50	1	1	NUM
ejpam-6633	89	51	,	,	PUNCT
ejpam-6633	89	52	.	.	PUNCT
ejpam-6633	89	53	.	.	PUNCT
ejpam-6633	89	54	.	.	PUNCT
ejpam-6633	90	1	,	,	PUNCT
ejpam-6633	90	2	n−	n−	NOUN
ejpam-6633	90	3	1	1	NUM
ejpam-6633	90	4	,	,	PUNCT
ejpam-6633	90	5	are	be	AUX
ejpam-6633	90	6	constants	constant	NOUN
ejpam-6633	90	7	.	.	PUNCT
ejpam-6633	91	1	lemma	lemma	PROPN
ejpam-6633	91	2	2	2	NUM
ejpam-6633	91	3	.	.	PUNCT
ejpam-6633	92	1	[	[	X
ejpam-6633	92	2	27	27	NUM
ejpam-6633	92	3	]	]	PUNCT
ejpam-6633	92	4	for	for	ADP
ejpam-6633	92	5	β	β	X
ejpam-6633	92	6	>	>	X
ejpam-6633	92	7	0	0	PUNCT
ejpam-6633	92	8	and	and	CCONJ
ejpam-6633	92	9	α	α	X
ejpam-6633	92	10	>	>	X
ejpam-6633	92	11	0	0	NUM
ejpam-6633	92	12	,	,	PUNCT
ejpam-6633	92	13	we	we	PRON
ejpam-6633	92	14	have	have	AUX
ejpam-6633	92	15	hi	hi	VERB
ejpam-6633	92	16	β	β	X
ejpam-6633	92	17	a+	a+	PUNCT
ejpam-6633	92	18	(	(	PUNCT
ejpam-6633	92	19	ln	ln	X
ejpam-6633	92	20	(	(	PUNCT
ejpam-6633	92	21	t	t	PROPN
ejpam-6633	92	22	a	a	PRON
ejpam-6633	92	23	)	)	PUNCT
ejpam-6633	92	24	)	)	PUNCT
ejpam-6633	93	1	α	α	X
ejpam-6633	93	2	=	=	PUNCT
ejpam-6633	93	3	γ(α+	γ(α+	DET
ejpam-6633	93	4	1	1	NUM
ejpam-6633	93	5	)	)	PUNCT
ejpam-6633	93	6	γ(α+	γ(α+	X
ejpam-6633	93	7	β	β	X
ejpam-6633	94	1	+	+	NOUN
ejpam-6633	94	2	1	1	NUM
ejpam-6633	94	3	)	)	PUNCT
ejpam-6633	94	4	(	(	PUNCT
ejpam-6633	94	5	ln	ln	X
ejpam-6633	94	6	(	(	PUNCT
ejpam-6633	94	7	t	t	PROPN
ejpam-6633	94	8	a	a	PRON
ejpam-6633	94	9	)	)	PUNCT
ejpam-6633	94	10	)	)	PUNCT
ejpam-6633	94	11	α+β	α+β	NUM
ejpam-6633	94	12	.	.	PUNCT
ejpam-6633	95	1	(	(	PUNCT
ejpam-6633	95	2	13	13	NUM
ejpam-6633	95	3	)	)	PUNCT
ejpam-6633	95	4	theorem	theorem	NOUN
ejpam-6633	95	5	1	1	NUM
ejpam-6633	95	6	.	.	PUNCT
ejpam-6633	96	1	[	[	X
ejpam-6633	96	2	3	3	X
ejpam-6633	96	3	]	]	X
ejpam-6633	96	4	let	let	VERB
ejpam-6633	96	5	ϕ1	ϕ1	NOUN
ejpam-6633	96	6	and	and	CCONJ
ejpam-6633	96	7	ϕ2	ϕ2	ADV
ejpam-6633	96	8	be	be	AUX
ejpam-6633	96	9	two	two	NUM
ejpam-6633	96	10	opertors	opertor	NOUN
ejpam-6633	96	11	such	such	ADJ
ejpam-6633	96	12	that	that	SCONJ
ejpam-6633	96	13	their	their	PRON
ejpam-6633	96	14	combined	combine	VERB
ejpam-6633	96	15	mapping	mapping	NOUN
ejpam-6633	96	16	ϕ1+ϕ2	ϕ1+ϕ2	PROPN
ejpam-6633	96	17	forms	form	VERB
ejpam-6633	96	18	a	a	DET
ejpam-6633	96	19	k∗set	k∗set	NOUN
ejpam-6633	96	20	-	-	PUNCT
ejpam-6633	96	21	contraction	contraction	NOUN
ejpam-6633	96	22	for	for	ADP
ejpam-6633	96	23	0	0	NUM
ejpam-6633	96	24	≤	≤	NOUN
ejpam-6633	96	25	k∗	k∗	NOUN
ejpam-6633	96	26	<	<	X
ejpam-6633	96	27	1	1	X
ejpam-6633	96	28	.	.	PUNCT
ejpam-6633	97	1	this	this	DET
ejpam-6633	97	2	map	map	NOUN
ejpam-6633	97	3	is	be	AUX
ejpam-6633	97	4	also	also	ADV
ejpam-6633	97	5	condensing	condense	VERB
ejpam-6633	97	6	if	if	SCONJ
ejpam-6633	97	7	the	the	DET
ejpam-6633	97	8	following	follow	VERB
ejpam-6633	97	9	conditions	condition	NOUN
ejpam-6633	97	10	are	be	AUX
ejpam-6633	97	11	satisfied	satisfied	ADJ
ejpam-6633	97	12	:	:	PUNCT
ejpam-6633	97	13	iϕ1	iϕ1	NOUN
ejpam-6633	97	14	,	,	PUNCT
ejpam-6633	97	15	ϕ2	ϕ2	ADV
ejpam-6633	97	16	:	:	PUNCT
ejpam-6633	97	17	b	b	X
ejpam-6633	97	18	⊆	⊆	NUM
ejpam-6633	97	19	q	q	NOUN
ejpam-6633	97	20	→	→	PUNCT
ejpam-6633	97	21	q	q	X
ejpam-6633	97	22	are	be	AUX
ejpam-6633	97	23	operators	operator	NOUN
ejpam-6633	97	24	on	on	ADP
ejpam-6633	97	25	the	the	DET
ejpam-6633	97	26	banach	banach	NOUN
ejpam-6633	97	27	space	space	NOUN
ejpam-6633	97	28	q	q	PROPN
ejpam-6633	98	1	where	where	SCONJ
ejpam-6633	98	2	q	q	NOUN
ejpam-6633	98	3	=	=	SYM
ejpam-6633	98	4	c([a	c([a	NOUN
ejpam-6633	98	5	,	,	PUNCT
ejpam-6633	98	6	1],r	1],r	NUM
ejpam-6633	98	7	)	)	PUNCT
ejpam-6633	98	8	.	.	PUNCT
ejpam-6633	99	1	iiϕ1	iiϕ1	PROPN
ejpam-6633	99	2	is	be	AUX
ejpam-6633	99	3	k∗-contractive	k∗-contractive	ADJ
ejpam-6633	99	4	,	,	PUNCT
ejpam-6633	99	5	that	that	ADV
ejpam-6633	99	6	is	is	ADV
ejpam-6633	99	7	,	,	PUNCT
ejpam-6633	99	8	∥ϕ1(x	∥ϕ1(x	NUM
ejpam-6633	99	9	)	)	PUNCT
ejpam-6633	100	1	−	−	PROPN
ejpam-6633	100	2	ϕ1(y)∥	ϕ1(y)∥	NOUN
ejpam-6633	100	3	≤	≤	NUM
ejpam-6633	100	4	k∗∥x	k∗∥x	NOUN
ejpam-6633	100	5	−	−	PROPN
ejpam-6633	100	6	y∥	y∥	NOUN
ejpam-6633	100	7	for	for	ADP
ejpam-6633	100	8	all	all	DET
ejpam-6633	100	9	x	x	PUNCT
ejpam-6633	100	10	and	and	CCONJ
ejpam-6633	100	11	y	y	PROPN
ejpam-6633	100	12	in	in	ADP
ejpam-6633	100	13	the	the	DET
ejpam-6633	100	14	domain	domain	NOUN
ejpam-6633	100	15	and	and	CCONJ
ejpam-6633	100	16	fixed	fix	VERB
ejpam-6633	100	17	k∗	k∗	PROPN
ejpam-6633	100	18	∈	∈	PROPN
ejpam-6633	101	1	[	[	X
ejpam-6633	101	2	0	0	NUM
ejpam-6633	101	3	,	,	PUNCT
ejpam-6633	101	4	1	1	NUM
ejpam-6633	101	5	)	)	PUNCT
ejpam-6633	101	6	.	.	PUNCT
ejpam-6633	102	1	iiiϕ2	iiiϕ2	NOUN
ejpam-6633	102	2	is	be	AUX
ejpam-6633	102	3	compact	compact	ADJ
ejpam-6633	102	4	.	.	PUNCT
ejpam-6633	103	1	theorem	theorem	NOUN
ejpam-6633	103	2	2	2	NUM
ejpam-6633	103	3	.	.	PUNCT
ejpam-6633	104	1	[	[	X
ejpam-6633	104	2	3	3	NUM
ejpam-6633	104	3	]	]	PUNCT
ejpam-6633	104	4	(	(	PUNCT
ejpam-6633	104	5	sadovskii	sadovskii	VERB
ejpam-6633	104	6	fixed	fix	VERB
ejpam-6633	104	7	point	point	NOUN
ejpam-6633	104	8	theorem	theorem	VERB
ejpam-6633	104	9	)	)	PUNCT
ejpam-6633	104	10	for	for	ADP
ejpam-6633	104	11	a	a	DET
ejpam-6633	104	12	subset	subset	NOUN
ejpam-6633	104	13	b	b	NOUN
ejpam-6633	104	14	of	of	ADP
ejpam-6633	104	15	a	a	DET
ejpam-6633	104	16	banach	banach	NOUN
ejpam-6633	104	17	space	space	NOUN
ejpam-6633	104	18	q	q	NOUN
ejpam-6633	104	19	which	which	PRON
ejpam-6633	104	20	is	be	AUX
ejpam-6633	104	21	convex	convex	PROPN
ejpam-6633	104	22	,	,	PUNCT
ejpam-6633	104	23	bounded	bound	VERB
ejpam-6633	104	24	,	,	PUNCT
ejpam-6633	104	25	and	and	CCONJ
ejpam-6633	104	26	closed	close	VERB
ejpam-6633	104	27	the	the	DET
ejpam-6633	104	28	condensing	condense	VERB
ejpam-6633	104	29	map	map	NOUN
ejpam-6633	104	30	ϕ	ϕ	NOUN
ejpam-6633	104	31	:	:	PUNCT
ejpam-6633	104	32	b	b	X
ejpam-6633	104	33	→	→	SYM
ejpam-6633	104	34	b	b	PROPN
ejpam-6633	104	35	has	have	VERB
ejpam-6633	104	36	a	a	DET
ejpam-6633	104	37	fixed	fix	VERB
ejpam-6633	104	38	point	point	NOUN
ejpam-6633	104	39	.	.	PUNCT
ejpam-6633	105	1	theorem	theorem	NOUN
ejpam-6633	105	2	3	3	NUM
ejpam-6633	105	3	.	.	PUNCT
ejpam-6633	106	1	[	[	X
ejpam-6633	106	2	28	28	NUM
ejpam-6633	106	3	]	]	X
ejpam-6633	106	4	(	(	PUNCT
ejpam-6633	106	5	banach	banach	ADV
ejpam-6633	106	6	fixed	fix	VERB
ejpam-6633	106	7	point	point	NOUN
ejpam-6633	106	8	theorem	theorem	ADJ
ejpam-6633	106	9	)	)	PUNCT
ejpam-6633	106	10	.	.	PUNCT
ejpam-6633	107	1	for	for	ADP
ejpam-6633	107	2	a	a	DET
ejpam-6633	107	3	continuous	continuous	ADJ
ejpam-6633	107	4	operator	operator	NOUN
ejpam-6633	107	5	ϕ	ϕ	NOUN
ejpam-6633	107	6	:	:	PUNCT
ejpam-6633	107	7	b	b	X
ejpam-6633	107	8	→	→	SYM
ejpam-6633	107	9	b	b	NOUN
ejpam-6633	107	10	which	which	PRON
ejpam-6633	107	11	is	be	AUX
ejpam-6633	107	12	k∗-contractive	k∗-contractive	ADJ
ejpam-6633	107	13	there	there	PRON
ejpam-6633	107	14	is	be	VERB
ejpam-6633	107	15	a	a	DET
ejpam-6633	107	16	unique	unique	ADJ
ejpam-6633	107	17	fixed	fix	VERB
ejpam-6633	107	18	point	point	NOUN
ejpam-6633	107	19	.	.	PUNCT
ejpam-6633	108	1	definition	definition	NOUN
ejpam-6633	108	2	4	4	NUM
ejpam-6633	108	3	.	.	PUNCT
ejpam-6633	109	1	[	[	X
ejpam-6633	109	2	29	29	NUM
ejpam-6633	109	3	]	]	PUNCT
ejpam-6633	109	4	the	the	DET
ejpam-6633	109	5	boundary	boundary	ADJ
ejpam-6633	109	6	-	-	PUNCT
ejpam-6633	109	7	value	value	NOUN
ejpam-6633	109	8	problem	problem	NOUN
ejpam-6633	109	9	(	(	PUNCT
ejpam-6633	109	10	6	6	NUM
ejpam-6633	109	11	-	-	SYM
ejpam-6633	109	12	8)	8)	NUM
ejpam-6633	109	13	is	be	AUX
ejpam-6633	109	14	ulam	ulam	NOUN
ejpam-6633	109	15	-	-	PUNCT
ejpam-6633	109	16	hyers	hyer	NOUN
ejpam-6633	109	17	stable	stable	ADJ
ejpam-6633	109	18	if	if	SCONJ
ejpam-6633	109	19	there	there	PRON
ejpam-6633	109	20	exists	exist	VERB
ejpam-6633	109	21	a	a	DET
ejpam-6633	109	22	real	real	ADV
ejpam-6633	109	23	constant	constant	ADJ
ejpam-6633	109	24	ch	ch	NOUN
ejpam-6633	109	25	>	>	X
ejpam-6633	109	26	0	0	NUM
ejpam-6633	109	27	such	such	ADJ
ejpam-6633	109	28	that	that	PRON
ejpam-6633	109	29	for	for	ADP
ejpam-6633	109	30	any	any	DET
ejpam-6633	109	31	ϵ	ϵ	X
ejpam-6633	109	32	>	>	X
ejpam-6633	109	33	0	0	NUM
ejpam-6633	109	34	,	,	PUNCT
ejpam-6633	109	35	and	and	CCONJ
ejpam-6633	109	36	for	for	ADP
ejpam-6633	109	37	every	every	DET
ejpam-6633	109	38	solution	solution	NOUN
ejpam-6633	109	39	η(t	η(t	NOUN
ejpam-6633	109	40	)	)	PUNCT
ejpam-6633	109	41	∈	∈	PROPN
ejpam-6633	109	42	q	q	NOUN
ejpam-6633	109	43	of	of	ADP
ejpam-6633	109	44	the	the	DET
ejpam-6633	109	45	inequality	inequality	NOUN
ejpam-6633	109	46	∣∣∣chdβ	∣∣∣chdβ	PROPN
ejpam-6633	109	47	(	(	PUNCT
ejpam-6633	109	48	chd	chd	PROPN
ejpam-6633	109	49	α	α	PROPN
ejpam-6633	109	50	+	+	X
ejpam-6633	109	51	µ	µ	PROPN
ejpam-6633	109	52	t	t	NOUN
ejpam-6633	109	53	)	)	PUNCT
ejpam-6633	109	54	η(t)−	η(t)−	PROPN
ejpam-6633	109	55	θ(t	θ(t	PROPN
ejpam-6633	109	56	,	,	PUNCT
ejpam-6633	109	57	η(t	η(t	NOUN
ejpam-6633	109	58	)	)	PUNCT
ejpam-6633	109	59	)	)	PUNCT
ejpam-6633	109	60	∣∣∣	∣∣∣	ADP
ejpam-6633	109	61	≤	≤	NUM
ejpam-6633	109	62	ϵ	ϵ	NOUN
ejpam-6633	109	63	,	,	PUNCT
ejpam-6633	109	64	(	(	PUNCT
ejpam-6633	109	65	14	14	NUM
ejpam-6633	109	66	)	)	PUNCT
ejpam-6633	109	67	there	there	PRON
ejpam-6633	109	68	exists	exist	VERB
ejpam-6633	109	69	a	a	DET
ejpam-6633	109	70	solution	solution	NOUN
ejpam-6633	109	71	z(t	z(t	NOUN
ejpam-6633	109	72	)	)	PUNCT
ejpam-6633	109	73	∈	∈	PROPN
ejpam-6633	109	74	q	q	NOUN
ejpam-6633	109	75	of	of	ADP
ejpam-6633	109	76	the	the	DET
ejpam-6633	109	77	problem	problem	NOUN
ejpam-6633	109	78	(	(	PUNCT
ejpam-6633	109	79	6	6	NUM
ejpam-6633	109	80	-	-	SYM
ejpam-6633	109	81	8)	8)	NUM
ejpam-6633	109	82	with	with	ADP
ejpam-6633	109	83	|η(t)−	|η(t)−	PROPN
ejpam-6633	109	84	z(t)|	z(t)|	PROPN
ejpam-6633	109	85	≤	≤	PROPN
ejpam-6633	109	86	chϵ	chϵ	ADV
ejpam-6633	109	87	,	,	PUNCT
ejpam-6633	109	88	(	(	PUNCT
ejpam-6633	109	89	15	15	NUM
ejpam-6633	109	90	)	)	PUNCT
ejpam-6633	109	91	for	for	ADP
ejpam-6633	109	92	all	all	DET
ejpam-6633	109	93	t	t	NOUN
ejpam-6633	109	94	∈	∈	PROPN
ejpam-6633	110	1	[	[	X
ejpam-6633	110	2	a	a	X
ejpam-6633	110	3	,	,	PUNCT
ejpam-6633	110	4	1	1	NUM
ejpam-6633	110	5	]	]	PUNCT
ejpam-6633	110	6	.	.	PUNCT
ejpam-6633	111	1	remark	remark	PROPN
ejpam-6633	111	2	1	1	NUM
ejpam-6633	111	3	.	.	PUNCT
ejpam-6633	112	1	[	[	X
ejpam-6633	112	2	30	30	NUM
ejpam-6633	112	3	]	]	PUNCT
ejpam-6633	113	1	a	a	DET
ejpam-6633	113	2	function	function	NOUN
ejpam-6633	113	3	η(t	η(t	NOUN
ejpam-6633	113	4	)	)	PUNCT
ejpam-6633	113	5	∈	∈	PROPN
ejpam-6633	113	6	q	q	NOUN
ejpam-6633	113	7	is	be	AUX
ejpam-6633	113	8	a	a	DET
ejpam-6633	113	9	solution	solution	NOUN
ejpam-6633	113	10	of	of	ADP
ejpam-6633	113	11	the	the	DET
ejpam-6633	113	12	inequality	inequality	NOUN
ejpam-6633	113	13	(	(	PUNCT
ejpam-6633	113	14	14	14	NUM
ejpam-6633	113	15	)	)	PUNCT
ejpam-6633	113	16	if	if	SCONJ
ejpam-6633	113	17	and	and	CCONJ
ejpam-6633	113	18	only	only	ADV
ejpam-6633	113	19	if	if	SCONJ
ejpam-6633	113	20	there	there	PRON
ejpam-6633	113	21	exists	exist	VERB
ejpam-6633	113	22	a	a	DET
ejpam-6633	113	23	function	function	NOUN
ejpam-6633	113	24	g(t	g(t	PROPN
ejpam-6633	113	25	)	)	PUNCT
ejpam-6633	113	26	∈	∈	PROPN
ejpam-6633	113	27	q	q	X
ejpam-6633	113	28	(	(	PUNCT
ejpam-6633	113	29	which	which	PRON
ejpam-6633	113	30	is	be	AUX
ejpam-6633	113	31	dependent	dependent	ADJ
ejpam-6633	113	32	on	on	ADP
ejpam-6633	113	33	η	η	PROPN
ejpam-6633	113	34	)	)	PUNCT
ejpam-6633	113	35	,	,	PUNCT
ejpam-6633	113	36	such	such	ADJ
ejpam-6633	113	37	that	that	SCONJ
ejpam-6633	113	38	:	:	PUNCT
ejpam-6633	113	39	(	(	PUNCT
ejpam-6633	113	40	i	i	NOUN
ejpam-6633	113	41	)	)	PUNCT
ejpam-6633	114	1	|g(t)|	|g(t)|	ADV
ejpam-6633	114	2	≤	≤	PUNCT
ejpam-6633	114	3	ϵ	ϵ	X
ejpam-6633	114	4	for	for	ADP
ejpam-6633	114	5	all	all	DET
ejpam-6633	114	6	t	t	NOUN
ejpam-6633	114	7	∈	∈	PROPN
ejpam-6633	115	1	[	[	X
ejpam-6633	115	2	a	a	X
ejpam-6633	115	3	,	,	PUNCT
ejpam-6633	115	4	1	1	NUM
ejpam-6633	115	5	]	]	PUNCT
ejpam-6633	115	6	,	,	PUNCT
ejpam-6633	115	7	a.	a.	PROPN
ejpam-6633	115	8	s.	s.	PROPN
ejpam-6633	115	9	hasan	hasan	PROPN
ejpam-6633	115	10	,	,	PUNCT
ejpam-6633	115	11	s.	s.	PROPN
ejpam-6633	115	12	a.	a.	PROPN
ejpam-6633	115	13	murad	murad	PROPN
ejpam-6633	115	14	/	/	SYM
ejpam-6633	115	15	eur	eur	PROPN
ejpam-6633	115	16	.	.	PUNCT
ejpam-6633	116	1	j.	j.	PROPN
ejpam-6633	116	2	pure	pure	PROPN
ejpam-6633	116	3	appl	appl	PROPN
ejpam-6633	116	4	.	.	PROPN
ejpam-6633	116	5	math	math	PROPN
ejpam-6633	116	6	,	,	PUNCT
ejpam-6633	116	7	18	18	NUM
ejpam-6633	116	8	(	(	PUNCT
ejpam-6633	116	9	3	3	NUM
ejpam-6633	116	10	)	)	PUNCT
ejpam-6633	116	11	(	(	PUNCT
ejpam-6633	116	12	2025	2025	NUM
ejpam-6633	116	13	)	)	PUNCT
ejpam-6633	116	14	,	,	PUNCT
ejpam-6633	116	15	6633	6633	NUM
ejpam-6633	116	16	6	6	NUM
ejpam-6633	116	17	of	of	ADP
ejpam-6633	116	18	24	24	NUM
ejpam-6633	116	19	(	(	PUNCT
ejpam-6633	116	20	ii	ii	NOUN
ejpam-6633	116	21	)	)	PUNCT
ejpam-6633	116	22	chd	chd	PROPN
ejpam-6633	116	23	β	β	PROPN
ejpam-6633	116	24	(	(	PUNCT
ejpam-6633	116	25	chd	chd	PROPN
ejpam-6633	116	26	α	α	PROPN
ejpam-6633	116	27	+	+	X
ejpam-6633	116	28	µ	µ	PROPN
ejpam-6633	116	29	t	t	NOUN
ejpam-6633	116	30	)	)	PUNCT
ejpam-6633	116	31	η(t	η(t	NOUN
ejpam-6633	116	32	)	)	PUNCT
ejpam-6633	116	33	=	=	SYM
ejpam-6633	116	34	θ(t	θ(t	PROPN
ejpam-6633	116	35	,	,	PUNCT
ejpam-6633	116	36	η(t	η(t	NOUN
ejpam-6633	116	37	)	)	PUNCT
ejpam-6633	116	38	)	)	PUNCT
ejpam-6633	117	1	+	+	CCONJ
ejpam-6633	117	2	g(t	g(t	PROPN
ejpam-6633	117	3	)	)	PUNCT
ejpam-6633	117	4	.	.	PUNCT
ejpam-6633	118	1	definition	definition	NOUN
ejpam-6633	118	2	5	5	NUM
ejpam-6633	118	3	.	.	PUNCT
ejpam-6633	119	1	[	[	X
ejpam-6633	119	2	29	29	NUM
ejpam-6633	119	3	]	]	PUNCT
ejpam-6633	119	4	the	the	DET
ejpam-6633	119	5	boundary	boundary	ADJ
ejpam-6633	119	6	-	-	PUNCT
ejpam-6633	119	7	value	value	NOUN
ejpam-6633	119	8	problem	problem	NOUN
ejpam-6633	119	9	(	(	PUNCT
ejpam-6633	119	10	6	6	NUM
ejpam-6633	119	11	-	-	SYM
ejpam-6633	119	12	8)	8)	NUM
ejpam-6633	119	13	has	have	VERB
ejpam-6633	119	14	the	the	DET
ejpam-6633	119	15	stability	stability	NOUN
ejpam-6633	119	16	of	of	ADP
ejpam-6633	119	17	the	the	DET
ejpam-6633	119	18	type	type	NOUN
ejpam-6633	119	19	ulamhyers	ulamhyer	NOUN
ejpam-6633	119	20	-	-	PUNCT
ejpam-6633	119	21	rassiass	rassiass	NOUN
ejpam-6633	119	22	if	if	SCONJ
ejpam-6633	119	23	there	there	PRON
ejpam-6633	119	24	exists	exist	VERB
ejpam-6633	119	25	a	a	DET
ejpam-6633	119	26	real	real	ADV
ejpam-6633	119	27	constant	constant	ADJ
ejpam-6633	119	28	cλ	cλ	INTJ
ejpam-6633	119	29	>	>	X
ejpam-6633	119	30	0	0	NUM
ejpam-6633	119	31	such	such	ADJ
ejpam-6633	119	32	that	that	PRON
ejpam-6633	119	33	for	for	ADP
ejpam-6633	119	34	any	any	DET
ejpam-6633	119	35	ϵ	ϵ	X
ejpam-6633	119	36	>	>	X
ejpam-6633	119	37	0	0	NUM
ejpam-6633	119	38	,	,	PUNCT
ejpam-6633	119	39	and	and	CCONJ
ejpam-6633	119	40	for	for	ADP
ejpam-6633	119	41	every	every	DET
ejpam-6633	119	42	solution	solution	NOUN
ejpam-6633	119	43	η(t	η(t	NOUN
ejpam-6633	119	44	)	)	PUNCT
ejpam-6633	119	45	∈	∈	PROPN
ejpam-6633	119	46	q	q	NOUN
ejpam-6633	119	47	of	of	ADP
ejpam-6633	119	48	the	the	DET
ejpam-6633	119	49	inequality∣∣∣chdβ	inequality∣∣∣chdβ	PROPN
ejpam-6633	119	50	(	(	PUNCT
ejpam-6633	119	51	chd	chd	PROPN
ejpam-6633	119	52	α	α	PROPN
ejpam-6633	119	53	+	+	X
ejpam-6633	119	54	µ	µ	PROPN
ejpam-6633	119	55	t	t	NOUN
ejpam-6633	119	56	)	)	PUNCT
ejpam-6633	119	57	η(t)−	η(t)−	PROPN
ejpam-6633	119	58	θ(t	θ(t	PROPN
ejpam-6633	119	59	,	,	PUNCT
ejpam-6633	119	60	η(t	η(t	NOUN
ejpam-6633	119	61	)	)	PUNCT
ejpam-6633	119	62	)	)	PUNCT
ejpam-6633	119	63	∣∣∣	∣∣∣	ADP
ejpam-6633	119	64	≤	≤	NUM
ejpam-6633	119	65	ϵψ(t	ϵψ(t	NUM
ejpam-6633	119	66	)	)	PUNCT
ejpam-6633	119	67	,	,	PUNCT
ejpam-6633	119	68	(	(	PUNCT
ejpam-6633	119	69	16	16	NUM
ejpam-6633	119	70	)	)	PUNCT
ejpam-6633	119	71	where	where	SCONJ
ejpam-6633	119	72	ψ(t	ψ(t	PROPN
ejpam-6633	119	73	)	)	PUNCT
ejpam-6633	119	74	∈	∈	PROPN
ejpam-6633	119	75	q	q	NOUN
ejpam-6633	119	76	is	be	AUX
ejpam-6633	119	77	the	the	DET
ejpam-6633	119	78	control	control	NOUN
ejpam-6633	119	79	function	function	NOUN
ejpam-6633	119	80	,	,	PUNCT
ejpam-6633	119	81	positive	positive	ADJ
ejpam-6633	119	82	and	and	CCONJ
ejpam-6633	119	83	non	non	ADJ
ejpam-6633	119	84	-	-	ADJ
ejpam-6633	119	85	decreasing	decrease	VERB
ejpam-6633	119	86	,	,	PUNCT
ejpam-6633	119	87	there	there	PRON
ejpam-6633	119	88	exists	exist	VERB
ejpam-6633	119	89	a	a	DET
ejpam-6633	119	90	solution	solution	NOUN
ejpam-6633	119	91	z(t	z(t	NOUN
ejpam-6633	119	92	)	)	PUNCT
ejpam-6633	119	93	∈	∈	PROPN
ejpam-6633	119	94	q	q	NOUN
ejpam-6633	119	95	of	of	ADP
ejpam-6633	119	96	the	the	DET
ejpam-6633	119	97	problem	problem	NOUN
ejpam-6633	119	98	(	(	PUNCT
ejpam-6633	119	99	6	6	NUM
ejpam-6633	119	100	-	-	SYM
ejpam-6633	119	101	8)	8)	NUM
ejpam-6633	119	102	with	with	ADP
ejpam-6633	119	103	|η(t)−	|η(t)−	PROPN
ejpam-6633	119	104	z(t)|	z(t)|	PROPN
ejpam-6633	119	105	≤	≤	NUM
ejpam-6633	119	106	cλϵψ(t	cλϵψ(t	NOUN
ejpam-6633	119	107	)	)	PUNCT
ejpam-6633	119	108	,	,	PUNCT
ejpam-6633	119	109	(	(	PUNCT
ejpam-6633	119	110	17	17	NUM
ejpam-6633	119	111	)	)	PUNCT
ejpam-6633	119	112	for	for	ADP
ejpam-6633	119	113	all	all	DET
ejpam-6633	119	114	t	t	NOUN
ejpam-6633	119	115	∈	∈	PROPN
ejpam-6633	120	1	[	[	X
ejpam-6633	120	2	a	a	X
ejpam-6633	120	3	,	,	PUNCT
ejpam-6633	120	4	1	1	NUM
ejpam-6633	120	5	]	]	PUNCT
ejpam-6633	120	6	.	.	PUNCT
ejpam-6633	121	1	remark	remark	PROPN
ejpam-6633	121	2	2	2	NUM
ejpam-6633	121	3	.	.	PUNCT
ejpam-6633	122	1	[	[	X
ejpam-6633	122	2	30	30	NUM
ejpam-6633	122	3	]	]	PUNCT
ejpam-6633	123	1	a	a	DET
ejpam-6633	123	2	function	function	NOUN
ejpam-6633	123	3	η(t	η(t	NOUN
ejpam-6633	123	4	)	)	PUNCT
ejpam-6633	123	5	∈	∈	PROPN
ejpam-6633	123	6	q	q	NOUN
ejpam-6633	123	7	is	be	AUX
ejpam-6633	123	8	a	a	DET
ejpam-6633	123	9	solution	solution	NOUN
ejpam-6633	123	10	of	of	ADP
ejpam-6633	123	11	the	the	DET
ejpam-6633	123	12	inequality	inequality	NOUN
ejpam-6633	123	13	(	(	PUNCT
ejpam-6633	123	14	16	16	NUM
ejpam-6633	123	15	)	)	PUNCT
ejpam-6633	123	16	if	if	SCONJ
ejpam-6633	123	17	and	and	CCONJ
ejpam-6633	123	18	only	only	ADV
ejpam-6633	123	19	if	if	SCONJ
ejpam-6633	123	20	there	there	PRON
ejpam-6633	123	21	exists	exist	VERB
ejpam-6633	123	22	a	a	DET
ejpam-6633	123	23	function	function	NOUN
ejpam-6633	123	24	g(t	g(t	PROPN
ejpam-6633	123	25	)	)	PUNCT
ejpam-6633	123	26	∈	∈	PROPN
ejpam-6633	123	27	q	q	X
ejpam-6633	123	28	(	(	PUNCT
ejpam-6633	123	29	which	which	PRON
ejpam-6633	123	30	is	be	AUX
ejpam-6633	123	31	dependent	dependent	ADJ
ejpam-6633	123	32	on	on	ADP
ejpam-6633	123	33	η	η	PROPN
ejpam-6633	123	34	)	)	PUNCT
ejpam-6633	123	35	,	,	PUNCT
ejpam-6633	123	36	such	such	ADJ
ejpam-6633	123	37	that	that	SCONJ
ejpam-6633	123	38	:	:	PUNCT
ejpam-6633	123	39	(	(	PUNCT
ejpam-6633	123	40	i	i	NOUN
ejpam-6633	123	41	)	)	PUNCT
ejpam-6633	124	1	|g(t)|	|g(t)|	ADV
ejpam-6633	124	2	≤	≤	NOUN
ejpam-6633	124	3	ϵψ(t	ϵψ(t	NUM
ejpam-6633	124	4	)	)	PUNCT
ejpam-6633	124	5	for	for	ADP
ejpam-6633	124	6	all	all	DET
ejpam-6633	124	7	t	t	NOUN
ejpam-6633	124	8	∈	∈	PROPN
ejpam-6633	125	1	[	[	X
ejpam-6633	125	2	a	a	X
ejpam-6633	125	3	,	,	PUNCT
ejpam-6633	125	4	1	1	NUM
ejpam-6633	125	5	]	]	PUNCT
ejpam-6633	125	6	,	,	PUNCT
ejpam-6633	125	7	(	(	PUNCT
ejpam-6633	125	8	ii	ii	NOUN
ejpam-6633	125	9	)	)	PUNCT
ejpam-6633	125	10	chd	chd	PROPN
ejpam-6633	125	11	β	β	PROPN
ejpam-6633	125	12	(	(	PUNCT
ejpam-6633	125	13	chd	chd	PROPN
ejpam-6633	125	14	α	α	PROPN
ejpam-6633	125	15	+	+	X
ejpam-6633	125	16	µ	µ	PROPN
ejpam-6633	125	17	t	t	NOUN
ejpam-6633	125	18	)	)	PUNCT
ejpam-6633	125	19	η(t	η(t	NOUN
ejpam-6633	125	20	)	)	PUNCT
ejpam-6633	126	1	=	=	SYM
ejpam-6633	126	2	θ(t	θ(t	PROPN
ejpam-6633	126	3	,	,	PUNCT
ejpam-6633	126	4	η(t	η(t	NOUN
ejpam-6633	126	5	)	)	PUNCT
ejpam-6633	126	6	)	)	PUNCT
ejpam-6633	127	1	+	+	CCONJ
ejpam-6633	127	2	g(t	g(t	PROPN
ejpam-6633	127	3	)	)	PUNCT
ejpam-6633	127	4	.	.	PUNCT
ejpam-6633	128	1	lemma	lemma	PROPN
ejpam-6633	128	2	3	3	X
ejpam-6633	128	3	.	.	PUNCT
ejpam-6633	129	1	the	the	DET
ejpam-6633	129	2	solution	solution	NOUN
ejpam-6633	129	3	of	of	ADP
ejpam-6633	129	4	the	the	DET
ejpam-6633	129	5	boundary	boundary	ADJ
ejpam-6633	129	6	-	-	PUNCT
ejpam-6633	129	7	value	value	NOUN
ejpam-6633	129	8	problem	problem	NOUN
ejpam-6633	129	9	(	(	PUNCT
ejpam-6633	129	10	6	6	NUM
ejpam-6633	129	11	-	-	SYM
ejpam-6633	129	12	8)	8)	NUM
ejpam-6633	129	13	is	be	AUX
ejpam-6633	129	14	a	a	DET
ejpam-6633	129	15	function	function	NOUN
ejpam-6633	129	16	η(t	η(t	NOUN
ejpam-6633	129	17	)	)	PUNCT
ejpam-6633	129	18	that	that	PRON
ejpam-6633	129	19	belongs	belong	VERB
ejpam-6633	129	20	to	to	ADP
ejpam-6633	129	21	c([a	c([a	PROPN
ejpam-6633	129	22	,	,	PUNCT
ejpam-6633	129	23	1],r	1],r	NUM
ejpam-6633	129	24	)	)	PUNCT
ejpam-6633	129	25	which	which	PRON
ejpam-6633	129	26	takes	take	VERB
ejpam-6633	129	27	the	the	DET
ejpam-6633	129	28	following	follow	VERB
ejpam-6633	129	29	form	form	NOUN
ejpam-6633	129	30	:	:	PUNCT
ejpam-6633	129	31	η(t	η(t	NOUN
ejpam-6633	129	32	)	)	PUNCT
ejpam-6633	129	33	=	=	SYM
ejpam-6633	130	1	1	1	NUM
ejpam-6633	130	2	γ(β	γ(β	PROPN
ejpam-6633	130	3	+	+	NUM
ejpam-6633	130	4	α	α	X
ejpam-6633	130	5	)	)	PUNCT
ejpam-6633	130	6	∫	∫	PROPN
ejpam-6633	130	7	t	t	PROPN
ejpam-6633	130	8	a	a	X
ejpam-6633	130	9	(	(	PUNCT
ejpam-6633	130	10	ln	ln	X
ejpam-6633	130	11	(	(	PUNCT
ejpam-6633	130	12	t	t	PROPN
ejpam-6633	130	13	τ	τ	PROPN
ejpam-6633	130	14	)	)	PUNCT
ejpam-6633	130	15	)	)	PUNCT
ejpam-6633	131	1	β+α−1	β+α−1	PUNCT
ejpam-6633	132	1	θ(τ	θ(τ	PROPN
ejpam-6633	132	2	,	,	PUNCT
ejpam-6633	132	3	η(τ	η(τ	PROPN
ejpam-6633	132	4	)	)	PUNCT
ejpam-6633	132	5	)	)	PUNCT
ejpam-6633	133	1	τ	τ	PROPN
ejpam-6633	133	2	dτ	dτ	NOUN
ejpam-6633	133	3	−	−	PROPN
ejpam-6633	133	4	µ	µ	PROPN
ejpam-6633	133	5	γ(α	γ(α	NOUN
ejpam-6633	133	6	)	)	PUNCT
ejpam-6633	134	1	∫	∫	PROPN
ejpam-6633	134	2	t	t	PROPN
ejpam-6633	134	3	a	a	X
ejpam-6633	134	4	(	(	PUNCT
ejpam-6633	134	5	ln	ln	X
ejpam-6633	134	6	(	(	PUNCT
ejpam-6633	134	7	t	t	PROPN
ejpam-6633	134	8	τ	τ	PROPN
ejpam-6633	134	9	)	)	PUNCT
ejpam-6633	134	10	)	)	PUNCT
ejpam-6633	134	11	α−1	α−1	PROPN
ejpam-6633	134	12	η(τ	η(τ	PROPN
ejpam-6633	134	13	)	)	PUNCT
ejpam-6633	134	14	τ2	τ2	PROPN
ejpam-6633	134	15	dτ	dτ	NOUN
ejpam-6633	135	1	−	−	PROPN
ejpam-6633	136	1	(	(	PUNCT
ejpam-6633	136	2	ln	ln	X
ejpam-6633	136	3	(	(	PUNCT
ejpam-6633	136	4	t	t	PROPN
ejpam-6633	136	5	a	a	PRON
ejpam-6633	136	6	)	)	PUNCT
ejpam-6633	136	7	)	)	PUNCT
ejpam-6633	137	1	α	α	NOUN
ejpam-6633	137	2	bγ(β	bγ(β	X
ejpam-6633	137	3	+	+	X
ejpam-6633	137	4	α	α	X
ejpam-6633	137	5	)	)	PUNCT
ejpam-6633	137	6	∫	∫	PROPN
ejpam-6633	137	7	1	1	NUM
ejpam-6633	137	8	a	a	PRON
ejpam-6633	137	9	(	(	PUNCT
ejpam-6633	137	10	ln	ln	NOUN
ejpam-6633	137	11	(	(	PUNCT
ejpam-6633	137	12	1	1	NUM
ejpam-6633	137	13	τ	τ	PROPN
ejpam-6633	137	14	)	)	PUNCT
ejpam-6633	137	15	)	)	PUNCT
ejpam-6633	137	16	β+α−1	β+α−1	PROPN
ejpam-6633	138	1	θ(τ	θ(τ	PROPN
ejpam-6633	138	2	,	,	PUNCT
ejpam-6633	138	3	η(τ	η(τ	PROPN
ejpam-6633	138	4	)	)	PUNCT
ejpam-6633	138	5	)	)	PUNCT
ejpam-6633	139	1	τ	τ	PROPN
ejpam-6633	139	2	dτ	dτ	PROPN
ejpam-6633	140	1	+	+	X
ejpam-6633	140	2	µ	µ	X
ejpam-6633	140	3	(	(	PUNCT
ejpam-6633	140	4	ln	ln	X
ejpam-6633	140	5	(	(	PUNCT
ejpam-6633	140	6	t	t	PROPN
ejpam-6633	140	7	a	a	PRON
ejpam-6633	140	8	)	)	PUNCT
ejpam-6633	140	9	)	)	PUNCT
ejpam-6633	140	10	α	α	PROPN
ejpam-6633	140	11	bγ(α	bγ(α	PROPN
ejpam-6633	140	12	)	)	PUNCT
ejpam-6633	140	13	∫	∫	PROPN
ejpam-6633	141	1	1	1	NUM
ejpam-6633	141	2	a	a	DET
ejpam-6633	141	3	(	(	PUNCT
ejpam-6633	141	4	ln	ln	NOUN
ejpam-6633	141	5	(	(	PUNCT
ejpam-6633	141	6	1	1	NUM
ejpam-6633	141	7	τ	τ	PROPN
ejpam-6633	141	8	)	)	PUNCT
ejpam-6633	141	9	)	)	PUNCT
ejpam-6633	141	10	α−1	α−1	PROPN
ejpam-6633	141	11	η(τ	η(τ	PROPN
ejpam-6633	141	12	)	)	PUNCT
ejpam-6633	141	13	τ2	τ2	PROPN
ejpam-6633	141	14	dτ	dτ	PROPN
ejpam-6633	141	15	+	+	NOUN
ejpam-6633	141	16	φ(t	φ(t	PROPN
ejpam-6633	141	17	)	)	PUNCT
ejpam-6633	141	18	,	,	PUNCT
ejpam-6633	141	19	(	(	PUNCT
ejpam-6633	141	20	18	18	NUM
ejpam-6633	141	21	)	)	PUNCT
ejpam-6633	141	22	where	where	SCONJ
ejpam-6633	141	23	φ(t	φ(t	NOUN
ejpam-6633	141	24	)	)	PUNCT
ejpam-6633	141	25	=	=	SYM
ejpam-6633	141	26	ξ1	ξ1	NOUN
ejpam-6633	141	27	+	+	CCONJ
ejpam-6633	141	28	1	1	NUM
ejpam-6633	141	29	b	b	X
ejpam-6633	141	30	(	(	PUNCT
ejpam-6633	141	31	ξ2	ξ2	NOUN
ejpam-6633	141	32	−	−	PROPN
ejpam-6633	141	33	ξ1	ξ1	NOUN
ejpam-6633	141	34	)	)	PUNCT
ejpam-6633	141	35	(	(	PUNCT
ejpam-6633	141	36	ln	ln	X
ejpam-6633	141	37	(	(	PUNCT
ejpam-6633	141	38	t	t	PROPN
ejpam-6633	141	39	a	a	PRON
ejpam-6633	141	40	)	)	PUNCT
ejpam-6633	141	41	)	)	PUNCT
ejpam-6633	142	1	α	α	PROPN
ejpam-6633	142	2	and	and	CCONJ
ejpam-6633	142	3	b	b	X
ejpam-6633	142	4	=	=	PRON
ejpam-6633	142	5	(	(	PUNCT
ejpam-6633	142	6	ln	ln	X
ejpam-6633	142	7	(	(	PUNCT
ejpam-6633	142	8	1	1	NUM
ejpam-6633	142	9	a	a	NOUN
ejpam-6633	142	10	)	)	PUNCT
ejpam-6633	142	11	)	)	PUNCT
ejpam-6633	142	12	α	α	NOUN
ejpam-6633	142	13	.	.	PUNCT
ejpam-6633	143	1	proof	proof	NOUN
ejpam-6633	143	2	by	by	ADP
ejpam-6633	143	3	implementing	implement	VERB
ejpam-6633	143	4	the	the	DET
ejpam-6633	143	5	fractional	fractional	ADJ
ejpam-6633	143	6	hadamard	hadamard	ADJ
ejpam-6633	143	7	integral	integral	ADJ
ejpam-6633	143	8	operator	operator	NOUN
ejpam-6633	143	9	of	of	ADP
ejpam-6633	143	10	order	order	NOUN
ejpam-6633	143	11	β	β	X
ejpam-6633	143	12	,	,	PUNCT
ejpam-6633	143	13	h	h	PROPN
ejpam-6633	143	14	a	a	X
ejpam-6633	143	15	i	i	NOUN
ejpam-6633	143	16	β	β	NOUN
ejpam-6633	143	17	,	,	PUNCT
ejpam-6633	143	18	given	give	VERB
ejpam-6633	143	19	by	by	ADP
ejpam-6633	143	20	definition	definition	NOUN
ejpam-6633	143	21	1	1	NUM
ejpam-6633	143	22	on	on	ADP
ejpam-6633	143	23	both	both	DET
ejpam-6633	143	24	sides	side	NOUN
ejpam-6633	143	25	of	of	ADP
ejpam-6633	143	26	(	(	PUNCT
ejpam-6633	143	27	6	6	NUM
ejpam-6633	143	28	)	)	PUNCT
ejpam-6633	143	29	and	and	CCONJ
ejpam-6633	143	30	following	follow	VERB
ejpam-6633	143	31	lemma	lemma	PROPN
ejpam-6633	143	32	1	1	NUM
ejpam-6633	143	33	and	and	CCONJ
ejpam-6633	143	34	definition	definition	NOUN
ejpam-6633	143	35	1	1	NUM
ejpam-6633	143	36	we	we	PRON
ejpam-6633	143	37	arrive	arrive	VERB
ejpam-6633	143	38	at	at	ADP
ejpam-6633	143	39	dαη(t	dαη(t	NOUN
ejpam-6633	143	40	)	)	PUNCT
ejpam-6633	143	41	=	=	PUNCT
ejpam-6633	143	42	1	1	NUM
ejpam-6633	143	43	γ(β	γ(β	PROPN
ejpam-6633	143	44	)	)	PUNCT
ejpam-6633	144	1	∫	∫	PROPN
ejpam-6633	144	2	t	t	PROPN
ejpam-6633	144	3	a	a	X
ejpam-6633	144	4	(	(	PUNCT
ejpam-6633	144	5	ln	ln	X
ejpam-6633	144	6	(	(	PUNCT
ejpam-6633	144	7	t	t	PROPN
ejpam-6633	144	8	τ	τ	PROPN
ejpam-6633	144	9	)	)	PUNCT
ejpam-6633	144	10	)	)	PUNCT
ejpam-6633	144	11	β−1	β−1	PUNCT
ejpam-6633	145	1	θ(τ	θ(τ	PROPN
ejpam-6633	145	2	,	,	PUNCT
ejpam-6633	145	3	η(τ	η(τ	PROPN
ejpam-6633	145	4	)	)	PUNCT
ejpam-6633	145	5	)	)	PUNCT
ejpam-6633	146	1	τ	τ	PROPN
ejpam-6633	146	2	dτ	dτ	NOUN
ejpam-6633	146	3	−	−	PROPN
ejpam-6633	146	4	µ	µ	PROPN
ejpam-6633	146	5	t	t	NOUN
ejpam-6633	146	6	η(t	η(t	NOUN
ejpam-6633	146	7	)	)	PUNCT
ejpam-6633	147	1	+	+	CCONJ
ejpam-6633	147	2	c̄	c̄	ADJ
ejpam-6633	147	3	,	,	PUNCT
ejpam-6633	147	4	(	(	PUNCT
ejpam-6633	147	5	19	19	NUM
ejpam-6633	147	6	)	)	PUNCT
ejpam-6633	147	7	where	where	SCONJ
ejpam-6633	147	8	c̄	c̄	PROPN
ejpam-6633	147	9	is	be	AUX
ejpam-6633	147	10	a	a	DET
ejpam-6633	147	11	constant	constant	ADJ
ejpam-6633	147	12	to	to	PART
ejpam-6633	147	13	be	be	AUX
ejpam-6633	147	14	determined	determine	VERB
ejpam-6633	147	15	.	.	PUNCT
ejpam-6633	148	1	next	next	ADV
ejpam-6633	148	2	,	,	PUNCT
ejpam-6633	148	3	we	we	PRON
ejpam-6633	148	4	operate	operate	VERB
ejpam-6633	148	5	both	both	DET
ejpam-6633	148	6	sides	side	NOUN
ejpam-6633	148	7	of	of	ADP
ejpam-6633	148	8	(	(	PUNCT
ejpam-6633	148	9	19	19	NUM
ejpam-6633	148	10	)	)	PUNCT
ejpam-6633	148	11	by	by	ADP
ejpam-6633	148	12	the	the	DET
ejpam-6633	148	13	fractional	fractional	ADJ
ejpam-6633	148	14	hadamard	hadamard	ADJ
ejpam-6633	148	15	integral	integral	ADJ
ejpam-6633	148	16	operator	operator	NOUN
ejpam-6633	148	17	of	of	ADP
ejpam-6633	148	18	order	order	NOUN
ejpam-6633	148	19	α	α	NOUN
ejpam-6633	148	20	,	,	PUNCT
ejpam-6633	148	21	h	h	PROPN
ejpam-6633	149	1	a	a	X
ejpam-6633	149	2	i	i	NOUN
ejpam-6633	149	3	α	α	NOUN
ejpam-6633	149	4	,	,	PUNCT
ejpam-6633	149	5	through	through	ADP
ejpam-6633	149	6	lemma	lemma	PROPN
ejpam-6633	149	7	1	1	NUM
ejpam-6633	149	8	,	,	PUNCT
ejpam-6633	149	9	to	to	PART
ejpam-6633	149	10	provide	provide	VERB
ejpam-6633	149	11	the	the	DET
ejpam-6633	149	12	following	follow	VERB
ejpam-6633	149	13	general	general	ADJ
ejpam-6633	149	14	solution	solution	NOUN
ejpam-6633	149	15	a.	a.	PROPN
ejpam-6633	149	16	s.	s.	PROPN
ejpam-6633	149	17	hasan	hasan	PROPN
ejpam-6633	149	18	,	,	PUNCT
ejpam-6633	149	19	s.	s.	PROPN
ejpam-6633	149	20	a.	a.	PROPN
ejpam-6633	149	21	murad	murad	PROPN
ejpam-6633	149	22	/	/	SYM
ejpam-6633	149	23	eur	eur	PROPN
ejpam-6633	149	24	.	.	PUNCT
ejpam-6633	150	1	j.	j.	PROPN
ejpam-6633	150	2	pure	pure	PROPN
ejpam-6633	150	3	appl	appl	PROPN
ejpam-6633	150	4	.	.	PROPN
ejpam-6633	150	5	math	math	PROPN
ejpam-6633	150	6	,	,	PUNCT
ejpam-6633	150	7	18	18	NUM
ejpam-6633	150	8	(	(	PUNCT
ejpam-6633	150	9	3	3	NUM
ejpam-6633	150	10	)	)	PUNCT
ejpam-6633	150	11	(	(	PUNCT
ejpam-6633	150	12	2025	2025	NUM
ejpam-6633	150	13	)	)	PUNCT
ejpam-6633	150	14	,	,	PUNCT
ejpam-6633	150	15	6633	6633	NUM
ejpam-6633	150	16	7	7	NUM
ejpam-6633	150	17	of	of	ADP
ejpam-6633	150	18	24	24	NUM
ejpam-6633	150	19	η(t	η(t	NOUN
ejpam-6633	150	20	)	)	PUNCT
ejpam-6633	151	1	+	+	PUNCT
ejpam-6633	152	1	c	c	NOUN
ejpam-6633	152	2	=	=	SYM
ejpam-6633	152	3	1	1	NUM
ejpam-6633	152	4	γ(β	γ(β	PROPN
ejpam-6633	152	5	+	+	NUM
ejpam-6633	152	6	α	α	X
ejpam-6633	152	7	)	)	PUNCT
ejpam-6633	152	8	∫	∫	PROPN
ejpam-6633	152	9	t	t	PROPN
ejpam-6633	152	10	a	a	X
ejpam-6633	152	11	(	(	PUNCT
ejpam-6633	152	12	ln	ln	X
ejpam-6633	152	13	(	(	PUNCT
ejpam-6633	152	14	t	t	PROPN
ejpam-6633	152	15	τ	τ	PROPN
ejpam-6633	152	16	)	)	PUNCT
ejpam-6633	152	17	)	)	PUNCT
ejpam-6633	153	1	β+α−1	β+α−1	PUNCT
ejpam-6633	154	1	θ(τ	θ(τ	PROPN
ejpam-6633	154	2	,	,	PUNCT
ejpam-6633	154	3	η(τ	η(τ	PROPN
ejpam-6633	154	4	)	)	PUNCT
ejpam-6633	154	5	)	)	PUNCT
ejpam-6633	155	1	τ	τ	PROPN
ejpam-6633	155	2	dτ	dτ	NOUN
ejpam-6633	155	3	−	−	PROPN
ejpam-6633	155	4	µ	µ	PROPN
ejpam-6633	155	5	γ(α	γ(α	NOUN
ejpam-6633	155	6	)	)	PUNCT
ejpam-6633	156	1	∫	∫	PROPN
ejpam-6633	156	2	t	t	PROPN
ejpam-6633	156	3	a	a	X
ejpam-6633	156	4	(	(	PUNCT
ejpam-6633	156	5	ln	ln	X
ejpam-6633	156	6	(	(	PUNCT
ejpam-6633	156	7	t	t	PROPN
ejpam-6633	156	8	τ	τ	PROPN
ejpam-6633	156	9	)	)	PUNCT
ejpam-6633	156	10	)	)	PUNCT
ejpam-6633	156	11	α−1	α−1	PROPN
ejpam-6633	156	12	η(τ	η(τ	PROPN
ejpam-6633	156	13	)	)	PUNCT
ejpam-6633	156	14	τ2	τ2	PROPN
ejpam-6633	156	15	dτ	dτ	NOUN
ejpam-6633	156	16	+	+	CCONJ
ejpam-6633	156	17	c̄	c̄	ADJ
ejpam-6633	156	18	γ(α+	γ(α+	DET
ejpam-6633	156	19	1	1	NUM
ejpam-6633	156	20	)	)	PUNCT
ejpam-6633	156	21	(	(	PUNCT
ejpam-6633	156	22	ln	ln	X
ejpam-6633	156	23	(	(	PUNCT
ejpam-6633	156	24	t	t	PROPN
ejpam-6633	156	25	a	a	PRON
ejpam-6633	156	26	)	)	PUNCT
ejpam-6633	156	27	)	)	PUNCT
ejpam-6633	157	1	α	α	PROPN
ejpam-6633	157	2	.	.	PUNCT
ejpam-6633	158	1	(	(	PUNCT
ejpam-6633	158	2	20	20	NUM
ejpam-6633	158	3	)	)	PUNCT
ejpam-6633	158	4	with	with	ADP
ejpam-6633	158	5	applying	apply	VERB
ejpam-6633	158	6	the	the	DET
ejpam-6633	158	7	two	two	NUM
ejpam-6633	158	8	boundary	boundary	ADJ
ejpam-6633	158	9	conditions	condition	NOUN
ejpam-6633	158	10	(	(	PUNCT
ejpam-6633	158	11	7	7	NUM
ejpam-6633	158	12	-	-	SYM
ejpam-6633	158	13	8)	8)	NUM
ejpam-6633	158	14	on	on	ADP
ejpam-6633	158	15	equation	equation	NOUN
ejpam-6633	158	16	(	(	PUNCT
ejpam-6633	158	17	20	20	NUM
ejpam-6633	158	18	)	)	PUNCT
ejpam-6633	158	19	we	we	PRON
ejpam-6633	158	20	obtain	obtain	VERB
ejpam-6633	158	21	c	c	NOUN
ejpam-6633	158	22	=	=	SYM
ejpam-6633	158	23	−ξ1	−ξ1	PROPN
ejpam-6633	158	24	and	and	CCONJ
ejpam-6633	158	25	c̄	c̄	ADJ
ejpam-6633	158	26	=	=	PUNCT
ejpam-6633	158	27	ξ2γ(α+	ξ2γ(α+	NOUN
ejpam-6633	158	28	1	1	NUM
ejpam-6633	158	29	)	)	PUNCT
ejpam-6633	158	30	b	b	NOUN
ejpam-6633	159	1	−	−	NOUN
ejpam-6633	159	2	ξ1γ(α+	ξ1γ(α+	NUM
ejpam-6633	159	3	1	1	NUM
ejpam-6633	159	4	)	)	PUNCT
ejpam-6633	159	5	b	b	NOUN
ejpam-6633	159	6	−	−	NOUN
ejpam-6633	159	7	γ(α+	γ(α+	DET
ejpam-6633	159	8	1	1	NUM
ejpam-6633	159	9	)	)	PUNCT
ejpam-6633	159	10	bγ(β	bγ(β	PUNCT
ejpam-6633	160	1	+	+	CCONJ
ejpam-6633	160	2	α	α	X
ejpam-6633	160	3	)	)	PUNCT
ejpam-6633	160	4	∫	∫	PROPN
ejpam-6633	160	5	1	1	NUM
ejpam-6633	160	6	a	a	PRON
ejpam-6633	160	7	(	(	PUNCT
ejpam-6633	160	8	ln	ln	NOUN
ejpam-6633	160	9	(	(	PUNCT
ejpam-6633	160	10	1	1	NUM
ejpam-6633	160	11	τ	τ	PROPN
ejpam-6633	160	12	)	)	PUNCT
ejpam-6633	160	13	)	)	PUNCT
ejpam-6633	161	1	β+α−1	β+α−1	PROPN
ejpam-6633	162	1	θ(τ	θ(τ	PROPN
ejpam-6633	162	2	,	,	PUNCT
ejpam-6633	162	3	η(τ	η(τ	PROPN
ejpam-6633	162	4	)	)	PUNCT
ejpam-6633	162	5	)	)	PUNCT
ejpam-6633	163	1	τ	τ	PROPN
ejpam-6633	163	2	dτ	dτ	NOUN
ejpam-6633	164	1	+	+	CCONJ
ejpam-6633	164	2	αµ	αµ	PROPN
ejpam-6633	164	3	b	b	SYM
ejpam-6633	164	4	∫	∫	PROPN
ejpam-6633	164	5	1	1	NUM
ejpam-6633	164	6	a	a	DET
ejpam-6633	164	7	(	(	PUNCT
ejpam-6633	164	8	ln	ln	NOUN
ejpam-6633	164	9	(	(	PUNCT
ejpam-6633	164	10	1	1	NUM
ejpam-6633	164	11	τ	τ	PROPN
ejpam-6633	164	12	)	)	PUNCT
ejpam-6633	164	13	)	)	PUNCT
ejpam-6633	164	14	α−1	α−1	PROPN
ejpam-6633	164	15	η(τ	η(τ	PROPN
ejpam-6633	164	16	)	)	PUNCT
ejpam-6633	164	17	τ2	τ2	PROPN
ejpam-6633	164	18	dτ	dτ	PROPN
ejpam-6633	164	19	.	.	PROPN
ejpam-6633	164	20	(	(	PUNCT
ejpam-6633	164	21	21	21	NUM
ejpam-6633	164	22	)	)	PUNCT
ejpam-6633	164	23	after	after	ADP
ejpam-6633	164	24	plugging	plug	VERB
ejpam-6633	164	25	in	in	ADP
ejpam-6633	164	26	the	the	DET
ejpam-6633	164	27	known	know	VERB
ejpam-6633	164	28	values	value	NOUN
ejpam-6633	164	29	of	of	ADP
ejpam-6633	164	30	c̄	c̄	PROPN
ejpam-6633	164	31	and	and	CCONJ
ejpam-6633	164	32	c	c	NOUN
ejpam-6633	164	33	into	into	ADP
ejpam-6633	164	34	(	(	PUNCT
ejpam-6633	164	35	20	20	NUM
ejpam-6633	164	36	)	)	PUNCT
ejpam-6633	164	37	,	,	PUNCT
ejpam-6633	164	38	it	it	PRON
ejpam-6633	164	39	turns	turn	VERB
ejpam-6633	164	40	out	out	ADP
ejpam-6633	164	41	that	that	SCONJ
ejpam-6633	164	42	the	the	DET
ejpam-6633	164	43	solution	solution	NOUN
ejpam-6633	164	44	to	to	ADP
ejpam-6633	164	45	the	the	DET
ejpam-6633	164	46	boundary	boundary	ADJ
ejpam-6633	164	47	-	-	PUNCT
ejpam-6633	164	48	value	value	NOUN
ejpam-6633	164	49	problem	problem	NOUN
ejpam-6633	164	50	(	(	PUNCT
ejpam-6633	164	51	6	6	NUM
ejpam-6633	164	52	-	-	SYM
ejpam-6633	164	53	8)	8)	NUM
ejpam-6633	164	54	is	be	AUX
ejpam-6633	164	55	given	give	VERB
ejpam-6633	164	56	by	by	ADP
ejpam-6633	164	57	(	(	PUNCT
ejpam-6633	164	58	18	18	NUM
ejpam-6633	164	59	)	)	PUNCT
ejpam-6633	164	60	.	.	PUNCT
ejpam-6633	165	1	through	through	ADP
ejpam-6633	165	2	direct	direct	ADJ
ejpam-6633	165	3	computation	computation	NOUN
ejpam-6633	165	4	,	,	PUNCT
ejpam-6633	165	5	the	the	DET
ejpam-6633	165	6	converse	converse	NOUN
ejpam-6633	165	7	is	be	AUX
ejpam-6633	165	8	obtained	obtain	VERB
ejpam-6633	165	9	.	.	PUNCT
ejpam-6633	166	1	the	the	DET
ejpam-6633	166	2	proof	proof	NOUN
ejpam-6633	166	3	for	for	ADP
ejpam-6633	166	4	lemma	lemma	PROPN
ejpam-6633	166	5	3	3	NUM
ejpam-6633	166	6	has	have	AUX
ejpam-6633	166	7	been	be	AUX
ejpam-6633	166	8	finalised	finalise	VERB
ejpam-6633	166	9	.	.	PUNCT
ejpam-6633	167	1	3	3	X
ejpam-6633	167	2	.	.	X
ejpam-6633	167	3	existence	existence	NOUN
ejpam-6633	167	4	and	and	CCONJ
ejpam-6633	167	5	uniqueness	uniqueness	NOUN
ejpam-6633	167	6	of	of	ADP
ejpam-6633	167	7	solution	solution	NOUN
ejpam-6633	167	8	in	in	ADP
ejpam-6633	167	9	this	this	DET
ejpam-6633	167	10	section	section	NOUN
ejpam-6633	167	11	,	,	PUNCT
ejpam-6633	167	12	first	first	ADV
ejpam-6633	167	13	we	we	PRON
ejpam-6633	167	14	apply	apply	VERB
ejpam-6633	167	15	the	the	DET
ejpam-6633	167	16	banach	banach	ADV
ejpam-6633	167	17	fixed	fix	VERB
ejpam-6633	167	18	point	point	NOUN
ejpam-6633	167	19	theorem	theorem	VERB
ejpam-6633	167	20	to	to	PART
ejpam-6633	167	21	show	show	VERB
ejpam-6633	167	22	the	the	DET
ejpam-6633	167	23	existence	existence	NOUN
ejpam-6633	167	24	and	and	CCONJ
ejpam-6633	167	25	uniqueness	uniqueness	NOUN
ejpam-6633	167	26	of	of	ADP
ejpam-6633	167	27	the	the	DET
ejpam-6633	167	28	boundary	boundary	ADJ
ejpam-6633	167	29	-	-	PUNCT
ejpam-6633	167	30	value	value	NOUN
ejpam-6633	167	31	problem	problem	NOUN
ejpam-6633	167	32	(	(	PUNCT
ejpam-6633	167	33	6	6	NUM
ejpam-6633	167	34	-	-	SYM
ejpam-6633	167	35	8)	8)	NUM
ejpam-6633	167	36	,	,	PUNCT
ejpam-6633	167	37	and	and	CCONJ
ejpam-6633	167	38	then	then	ADV
ejpam-6633	167	39	,	,	PUNCT
ejpam-6633	167	40	the	the	DET
ejpam-6633	167	41	sadovoskii	sadovoskii	ADJ
ejpam-6633	167	42	fixed	fix	VERB
ejpam-6633	167	43	point	point	NOUN
ejpam-6633	167	44	theorem	theorem	NOUN
ejpam-6633	167	45	for	for	ADP
ejpam-6633	167	46	the	the	DET
ejpam-6633	167	47	existence	existence	NOUN
ejpam-6633	167	48	of	of	ADP
ejpam-6633	167	49	the	the	DET
ejpam-6633	167	50	solution	solution	NOUN
ejpam-6633	167	51	to	to	ADP
ejpam-6633	167	52	our	our	PRON
ejpam-6633	167	53	problem	problem	NOUN
ejpam-6633	167	54	.	.	PUNCT
ejpam-6633	168	1	let	let	VERB
ejpam-6633	168	2	br	br	INTJ
ejpam-6633	168	3	=	=	PUNCT
ejpam-6633	168	4	{	{	PUNCT
ejpam-6633	168	5	η(t	η(t	NOUN
ejpam-6633	168	6	)	)	PUNCT
ejpam-6633	168	7	∈	∈	PROPN
ejpam-6633	168	8	q	q	NOUN
ejpam-6633	168	9	:	:	PUNCT
ejpam-6633	168	10	∥η∥	∥η∥	PROPN
ejpam-6633	168	11	≤	≤	ADV
ejpam-6633	169	1	r	r	AUX
ejpam-6633	169	2	}	}	PUNCT
ejpam-6633	169	3	be	be	AUX
ejpam-6633	169	4	a	a	DET
ejpam-6633	169	5	closed	closed	ADJ
ejpam-6633	169	6	,	,	PUNCT
ejpam-6633	169	7	bounded	bound	VERB
ejpam-6633	169	8	,	,	PUNCT
ejpam-6633	169	9	and	and	CCONJ
ejpam-6633	169	10	convex	convex	PROPN
ejpam-6633	169	11	subset	subset	NOUN
ejpam-6633	169	12	of	of	ADP
ejpam-6633	169	13	q	q	PROPN
ejpam-6633	169	14	=	=	SYM
ejpam-6633	169	15	c([a	c([a	PROPN
ejpam-6633	169	16	,	,	PUNCT
ejpam-6633	169	17	1],r	1],r	NUM
ejpam-6633	169	18	)	)	PUNCT
ejpam-6633	169	19	where	where	SCONJ
ejpam-6633	169	20	r	r	NOUN
ejpam-6633	169	21	is	be	AUX
ejpam-6633	169	22	a	a	DET
ejpam-6633	169	23	positive	positive	ADJ
ejpam-6633	169	24	constant	constant	ADJ
ejpam-6633	169	25	such	such	ADJ
ejpam-6633	169	26	that	that	SCONJ
ejpam-6633	169	27	r	r	NOUN
ejpam-6633	169	28	≥	≥	NOUN
ejpam-6633	169	29	2bω	2bω	ADJ
ejpam-6633	169	30	γ(β+α+1	γ(β+α+1	NOUN
ejpam-6633	169	31	)	)	PUNCT
ejpam-6633	169	32	(	(	PUNCT
ejpam-6633	169	33	ln	ln	NOUN
ejpam-6633	169	34	(	(	PUNCT
ejpam-6633	169	35	1	1	NUM
ejpam-6633	169	36	a	a	NOUN
ejpam-6633	169	37	)	)	PUNCT
ejpam-6633	169	38	)	)	PUNCT
ejpam-6633	169	39	β	β	PROPN
ejpam-6633	169	40	+	+	CCONJ
ejpam-6633	169	41	∥φ∥	∥φ∥	PROPN
ejpam-6633	169	42	1−	1−	NUM
ejpam-6633	169	43	2bµ	2bµ	ADJ
ejpam-6633	169	44	aγ(α+1	aγ(α+1	NOUN
ejpam-6633	169	45	)	)	PUNCT
ejpam-6633	169	46	,	,	PUNCT
ejpam-6633	169	47	2bµ	2bµ	NOUN
ejpam-6633	169	48	<	<	X
ejpam-6633	169	49	aγ(α+	aγ(α+	PROPN
ejpam-6633	169	50	1	1	NUM
ejpam-6633	169	51	)	)	PUNCT
ejpam-6633	169	52	.	.	PUNCT
ejpam-6633	170	1	(	(	PUNCT
ejpam-6633	170	2	22	22	NUM
ejpam-6633	170	3	)	)	PUNCT
ejpam-6633	170	4	here	here	ADV
ejpam-6633	170	5	q	q	X
ejpam-6633	170	6	is	be	AUX
ejpam-6633	170	7	a	a	DET
ejpam-6633	170	8	banach	banach	NOUN
ejpam-6633	170	9	space	space	NOUN
ejpam-6633	170	10	of	of	ADP
ejpam-6633	170	11	all	all	DET
ejpam-6633	170	12	continuous	continuous	ADJ
ejpam-6633	170	13	function	function	NOUN
ejpam-6633	170	14	from	from	ADP
ejpam-6633	170	15	[	[	X
ejpam-6633	170	16	a	a	X
ejpam-6633	170	17	,	,	PUNCT
ejpam-6633	170	18	1	1	NUM
ejpam-6633	170	19	]	]	PUNCT
ejpam-6633	170	20	to	to	ADP
ejpam-6633	170	21	r	r	NOUN
ejpam-6633	170	22	with	with	ADP
ejpam-6633	170	23	the	the	DET
ejpam-6633	170	24	norm	norm	NOUN
ejpam-6633	170	25	∥η∥	∥η∥	NOUN
ejpam-6633	170	26	=	=	SYM
ejpam-6633	170	27	sup	sup	PROPN
ejpam-6633	170	28	t	t	PROPN
ejpam-6633	170	29	{	{	PUNCT
ejpam-6633	170	30	|η(t)|	|η(t)|	PROPN
ejpam-6633	170	31	,	,	PUNCT
ejpam-6633	170	32	t	t	PROPN
ejpam-6633	170	33	∈	∈	PROPN
ejpam-6633	171	1	[	[	X
ejpam-6633	171	2	a	a	X
ejpam-6633	171	3	,	,	PUNCT
ejpam-6633	171	4	1	1	NUM
ejpam-6633	171	5	]	]	PUNCT
ejpam-6633	171	6	}	}	PUNCT
ejpam-6633	171	7	for	for	ADP
ejpam-6633	171	8	all	all	DET
ejpam-6633	171	9	η	η	PROPN
ejpam-6633	171	10	∈	∈	PROPN
ejpam-6633	171	11	q.	q.	NOUN
ejpam-6633	171	12	(	(	PUNCT
ejpam-6633	171	13	23	23	NUM
ejpam-6633	171	14	)	)	PUNCT
ejpam-6633	171	15	we	we	PRON
ejpam-6633	171	16	proceed	proceed	VERB
ejpam-6633	171	17	with	with	ADP
ejpam-6633	171	18	section	section	NOUN
ejpam-6633	171	19	3	3	NUM
ejpam-6633	171	20	under	under	ADP
ejpam-6633	171	21	the	the	DET
ejpam-6633	171	22	following	follow	VERB
ejpam-6633	171	23	two	two	NUM
ejpam-6633	171	24	assumptions	assumption	NOUN
ejpam-6633	171	25	,	,	PUNCT
ejpam-6633	171	26	namely	namely	ADV
ejpam-6633	171	27	h1	h1	NOUN
ejpam-6633	171	28	and	and	CCONJ
ejpam-6633	171	29	h2	h2	PROPN
ejpam-6633	171	30	,	,	PUNCT
ejpam-6633	171	31	which	which	DET
ejpam-6633	171	32	state	state	NOUN
ejpam-6633	171	33	:	:	PUNCT
ejpam-6633	171	34	h1	h1	PROPN
ejpam-6633	171	35	:	:	PUNCT
ejpam-6633	171	36	there	there	PRON
ejpam-6633	171	37	exists	exist	VERB
ejpam-6633	171	38	a	a	DET
ejpam-6633	171	39	constant	constant	ADJ
ejpam-6633	171	40	ω	ω	NOUN
ejpam-6633	171	41	>	>	X
ejpam-6633	171	42	0	0	PROPN
ejpam-6633	171	43	,	,	PUNCT
ejpam-6633	171	44	such	such	ADJ
ejpam-6633	171	45	that	that	DET
ejpam-6633	171	46	|θ(t	|θ(t	NOUN
ejpam-6633	171	47	,	,	PUNCT
ejpam-6633	171	48	η(t))|	η(t))|	PROPN
ejpam-6633	171	49	≤	≤	PROPN
ejpam-6633	171	50	ω	ω	PROPN
ejpam-6633	171	51	for	for	ADP
ejpam-6633	171	52	all	all	DET
ejpam-6633	171	53	t	t	NOUN
ejpam-6633	171	54	∈	∈	PROPN
ejpam-6633	172	1	[	[	X
ejpam-6633	172	2	a	a	X
ejpam-6633	172	3	,	,	PUNCT
ejpam-6633	172	4	1	1	NUM
ejpam-6633	172	5	]	]	PUNCT
ejpam-6633	172	6	and	and	CCONJ
ejpam-6633	172	7	η	η	PROPN
ejpam-6633	172	8	∈	∈	PROPN
ejpam-6633	172	9	q.	q.	PROPN
ejpam-6633	172	10	h2	h2	PROPN
ejpam-6633	172	11	:	:	PUNCT
ejpam-6633	172	12	there	there	PRON
ejpam-6633	172	13	exists	exist	VERB
ejpam-6633	172	14	a	a	DET
ejpam-6633	172	15	constant	constant	ADJ
ejpam-6633	172	16	k	k	X
ejpam-6633	172	17	>	>	X
ejpam-6633	172	18	0	0	PROPN
ejpam-6633	172	19	,	,	PUNCT
ejpam-6633	172	20	such	such	ADJ
ejpam-6633	172	21	that	that	DET
ejpam-6633	172	22	∥θ(t	∥θ(t	NOUN
ejpam-6633	172	23	,	,	PUNCT
ejpam-6633	172	24	η1	η1	NOUN
ejpam-6633	172	25	)	)	PUNCT
ejpam-6633	172	26	−	−	PROPN
ejpam-6633	172	27	θ(t	θ(t	PROPN
ejpam-6633	172	28	,	,	PUNCT
ejpam-6633	172	29	η2)∥	η2)∥	PROPN
ejpam-6633	172	30	≤	≤	X
ejpam-6633	172	31	k∥η1	k∥η1	PROPN
ejpam-6633	172	32	−	−	PROPN
ejpam-6633	172	33	η2∥	η2∥	PROPN
ejpam-6633	172	34	for	for	ADP
ejpam-6633	172	35	all	all	DET
ejpam-6633	172	36	t	t	NOUN
ejpam-6633	172	37	∈	∈	PROPN
ejpam-6633	173	1	[	[	X
ejpam-6633	173	2	a	a	X
ejpam-6633	173	3	,	,	PUNCT
ejpam-6633	173	4	1	1	NUM
ejpam-6633	173	5	]	]	PUNCT
ejpam-6633	173	6	and	and	CCONJ
ejpam-6633	173	7	η1	η1	NOUN
ejpam-6633	173	8	,	,	PUNCT
ejpam-6633	173	9	η2	η2	X
ejpam-6633	173	10	∈	∈	PROPN
ejpam-6633	173	11	q	q	X
ejpam-6633	173	12	if	if	SCONJ
ejpam-6633	173	13	:	:	PUNCT
ejpam-6633	173	14	0	0	NUM
ejpam-6633	173	15	<	<	X
ejpam-6633	173	16	k	k	X
ejpam-6633	173	17	γ(β	γ(β	PROPN
ejpam-6633	173	18	+	+	CCONJ
ejpam-6633	173	19	α+	α+	PUNCT
ejpam-6633	173	20	1	1	NUM
ejpam-6633	173	21	)	)	PUNCT
ejpam-6633	173	22	(	(	PUNCT
ejpam-6633	173	23	ln	ln	X
ejpam-6633	173	24	(	(	PUNCT
ejpam-6633	173	25	1	1	NUM
ejpam-6633	173	26	a	a	NOUN
ejpam-6633	173	27	)	)	PUNCT
ejpam-6633	173	28	)	)	PUNCT
ejpam-6633	173	29	β	β	PROPN
ejpam-6633	173	30	+	+	SYM
ejpam-6633	173	31	µ	µ	X
ejpam-6633	173	32	aγ(α+	aγ(α+	NOUN
ejpam-6633	173	33	1	1	NUM
ejpam-6633	173	34	)	)	PUNCT
ejpam-6633	173	35	<	<	X
ejpam-6633	173	36	1	1	NUM
ejpam-6633	173	37	2b	2b	NUM
ejpam-6633	173	38	.	.	PUNCT
ejpam-6633	174	1	we	we	PRON
ejpam-6633	174	2	initiate	initiate	VERB
ejpam-6633	174	3	by	by	ADP
ejpam-6633	174	4	calling	call	VERB
ejpam-6633	174	5	the	the	DET
ejpam-6633	174	6	operator	operator	NOUN
ejpam-6633	174	7	ϕ	ϕ	NOUN
ejpam-6633	174	8	:	:	PUNCT
ejpam-6633	174	9	q	q	PUNCT
ejpam-6633	174	10	−→	−→	NOUN
ejpam-6633	174	11	q	q	PUNCT
ejpam-6633	174	12	to	to	PART
ejpam-6633	174	13	be	be	AUX
ejpam-6633	174	14	set	set	VERB
ejpam-6633	174	15	as	as	ADP
ejpam-6633	174	16	:	:	PUNCT
ejpam-6633	174	17	ϕ	ϕ	X
ejpam-6633	174	18	(	(	PUNCT
ejpam-6633	174	19	η(t	η(t	NOUN
ejpam-6633	174	20	)	)	PUNCT
ejpam-6633	174	21	)	)	PUNCT
ejpam-6633	175	1	=	=	SYM
ejpam-6633	175	2	1	1	NUM
ejpam-6633	175	3	γ(β	γ(β	PROPN
ejpam-6633	175	4	+	+	NUM
ejpam-6633	175	5	α	α	X
ejpam-6633	175	6	)	)	PUNCT
ejpam-6633	175	7	∫	∫	PROPN
ejpam-6633	175	8	t	t	PROPN
ejpam-6633	175	9	a	a	X
ejpam-6633	175	10	(	(	PUNCT
ejpam-6633	175	11	ln	ln	X
ejpam-6633	175	12	(	(	PUNCT
ejpam-6633	175	13	t	t	PROPN
ejpam-6633	175	14	τ	τ	PROPN
ejpam-6633	175	15	)	)	PUNCT
ejpam-6633	175	16	)	)	PUNCT
ejpam-6633	176	1	β+α−1	β+α−1	PUNCT
ejpam-6633	177	1	θ(τ	θ(τ	PROPN
ejpam-6633	177	2	,	,	PUNCT
ejpam-6633	177	3	η(τ	η(τ	PROPN
ejpam-6633	177	4	)	)	PUNCT
ejpam-6633	177	5	)	)	PUNCT
ejpam-6633	178	1	τ	τ	PROPN
ejpam-6633	178	2	dτ	dτ	PROPN
ejpam-6633	178	3	a.	a.	PROPN
ejpam-6633	178	4	s.	s.	PROPN
ejpam-6633	178	5	hasan	hasan	PROPN
ejpam-6633	178	6	,	,	PUNCT
ejpam-6633	178	7	s.	s.	PROPN
ejpam-6633	178	8	a.	a.	PROPN
ejpam-6633	178	9	murad	murad	PROPN
ejpam-6633	178	10	/	/	SYM
ejpam-6633	178	11	eur	eur	PROPN
ejpam-6633	178	12	.	.	PUNCT
ejpam-6633	179	1	j.	j.	PROPN
ejpam-6633	179	2	pure	pure	PROPN
ejpam-6633	179	3	appl	appl	PROPN
ejpam-6633	179	4	.	.	PROPN
ejpam-6633	179	5	math	math	PROPN
ejpam-6633	179	6	,	,	PUNCT
ejpam-6633	179	7	18	18	NUM
ejpam-6633	179	8	(	(	PUNCT
ejpam-6633	179	9	3	3	NUM
ejpam-6633	179	10	)	)	PUNCT
ejpam-6633	179	11	(	(	PUNCT
ejpam-6633	179	12	2025	2025	NUM
ejpam-6633	179	13	)	)	PUNCT
ejpam-6633	179	14	,	,	PUNCT
ejpam-6633	179	15	6633	6633	NUM
ejpam-6633	179	16	8	8	NUM
ejpam-6633	179	17	of	of	ADP
ejpam-6633	179	18	24	24	NUM
ejpam-6633	179	19	−	−	PROPN
ejpam-6633	179	20	µ	µ	PRON
ejpam-6633	179	21	γ(α	γ(α	NOUN
ejpam-6633	179	22	)	)	PUNCT
ejpam-6633	180	1	∫	∫	PROPN
ejpam-6633	181	1	t	t	PROPN
ejpam-6633	181	2	a	a	X
ejpam-6633	181	3	(	(	PUNCT
ejpam-6633	181	4	ln	ln	X
ejpam-6633	181	5	(	(	PUNCT
ejpam-6633	181	6	t	t	PROPN
ejpam-6633	181	7	τ	τ	PROPN
ejpam-6633	181	8	)	)	PUNCT
ejpam-6633	181	9	)	)	PUNCT
ejpam-6633	181	10	α−1	α−1	PROPN
ejpam-6633	181	11	η(τ	η(τ	PROPN
ejpam-6633	181	12	)	)	PUNCT
ejpam-6633	181	13	τ2	τ2	PROPN
ejpam-6633	181	14	dτ	dτ	NOUN
ejpam-6633	181	15	−	−	PROPN
ejpam-6633	182	1	(	(	PUNCT
ejpam-6633	182	2	ln	ln	X
ejpam-6633	182	3	(	(	PUNCT
ejpam-6633	182	4	t	t	PROPN
ejpam-6633	182	5	a	a	PRON
ejpam-6633	182	6	)	)	PUNCT
ejpam-6633	182	7	)	)	PUNCT
ejpam-6633	183	1	α	α	NOUN
ejpam-6633	183	2	bγ(β	bγ(β	X
ejpam-6633	183	3	+	+	X
ejpam-6633	183	4	α	α	X
ejpam-6633	183	5	)	)	PUNCT
ejpam-6633	183	6	∫	∫	PROPN
ejpam-6633	183	7	1	1	NUM
ejpam-6633	183	8	a	a	PRON
ejpam-6633	183	9	(	(	PUNCT
ejpam-6633	183	10	ln	ln	NOUN
ejpam-6633	183	11	(	(	PUNCT
ejpam-6633	183	12	1	1	NUM
ejpam-6633	183	13	τ	τ	PROPN
ejpam-6633	183	14	)	)	PUNCT
ejpam-6633	183	15	)	)	PUNCT
ejpam-6633	183	16	β+α−1	β+α−1	PROPN
ejpam-6633	184	1	θ(τ	θ(τ	PROPN
ejpam-6633	184	2	,	,	PUNCT
ejpam-6633	184	3	η(τ	η(τ	PROPN
ejpam-6633	184	4	)	)	PUNCT
ejpam-6633	184	5	)	)	PUNCT
ejpam-6633	185	1	τ	τ	PROPN
ejpam-6633	185	2	dτ	dτ	PROPN
ejpam-6633	186	1	+	+	X
ejpam-6633	186	2	µ	µ	X
ejpam-6633	186	3	(	(	PUNCT
ejpam-6633	186	4	ln	ln	X
ejpam-6633	186	5	(	(	PUNCT
ejpam-6633	186	6	t	t	PROPN
ejpam-6633	186	7	a	a	PRON
ejpam-6633	186	8	)	)	PUNCT
ejpam-6633	186	9	)	)	PUNCT
ejpam-6633	186	10	α	α	PROPN
ejpam-6633	186	11	bγ(α	bγ(α	PROPN
ejpam-6633	186	12	)	)	PUNCT
ejpam-6633	186	13	∫	∫	PROPN
ejpam-6633	187	1	1	1	NUM
ejpam-6633	187	2	a	a	DET
ejpam-6633	187	3	(	(	PUNCT
ejpam-6633	187	4	ln	ln	NOUN
ejpam-6633	187	5	(	(	PUNCT
ejpam-6633	187	6	1	1	NUM
ejpam-6633	187	7	τ	τ	PROPN
ejpam-6633	187	8	)	)	PUNCT
ejpam-6633	187	9	)	)	PUNCT
ejpam-6633	187	10	α−1	α−1	PROPN
ejpam-6633	187	11	η(τ	η(τ	PROPN
ejpam-6633	187	12	)	)	PUNCT
ejpam-6633	187	13	τ2	τ2	PROPN
ejpam-6633	187	14	dτ	dτ	PROPN
ejpam-6633	187	15	+	+	PROPN
ejpam-6633	187	16	φ(t	φ(t	PROPN
ejpam-6633	187	17	)	)	PUNCT
ejpam-6633	187	18	,	,	PUNCT
ejpam-6633	187	19	t	t	PROPN
ejpam-6633	187	20	∈	∈	PROPN
ejpam-6633	188	1	[	[	X
ejpam-6633	188	2	a	a	X
ejpam-6633	188	3	,	,	PUNCT
ejpam-6633	188	4	1	1	NUM
ejpam-6633	188	5	]	]	PUNCT
ejpam-6633	188	6	.	.	PUNCT
ejpam-6633	189	1	(	(	PUNCT
ejpam-6633	189	2	24	24	NUM
ejpam-6633	189	3	)	)	PUNCT
ejpam-6633	189	4	it	it	PRON
ejpam-6633	189	5	has	have	VERB
ejpam-6633	189	6	to	to	PART
ejpam-6633	189	7	be	be	AUX
ejpam-6633	189	8	shown	show	VERB
ejpam-6633	189	9	that	that	SCONJ
ejpam-6633	189	10	ϕ	ϕ	NOUN
ejpam-6633	189	11	has	have	VERB
ejpam-6633	189	12	a	a	DET
ejpam-6633	189	13	fixed	fix	VERB
ejpam-6633	189	14	point	point	NOUN
ejpam-6633	189	15	.	.	PUNCT
ejpam-6633	190	1	the	the	DET
ejpam-6633	190	2	fixed	fix	VERB
ejpam-6633	190	3	point	point	NOUN
ejpam-6633	190	4	is	be	AUX
ejpam-6633	190	5	a	a	DET
ejpam-6633	190	6	solution	solution	NOUN
ejpam-6633	190	7	to	to	ADP
ejpam-6633	190	8	the	the	DET
ejpam-6633	190	9	boundaryvalue	boundaryvalue	NOUN
ejpam-6633	190	10	problem	problem	NOUN
ejpam-6633	190	11	(	(	PUNCT
ejpam-6633	190	12	6	6	NUM
ejpam-6633	190	13	-	-	SYM
ejpam-6633	190	14	8)	8)	NUM
ejpam-6633	190	15	.	.	PUNCT
ejpam-6633	191	1	we	we	PRON
ejpam-6633	191	2	have	have	VERB
ejpam-6633	191	3	to	to	PART
ejpam-6633	191	4	manifest	manifest	VERB
ejpam-6633	191	5	that	that	SCONJ
ejpam-6633	191	6	ϕ	ϕ	PROPN
ejpam-6633	191	7	(	(	PUNCT
ejpam-6633	191	8	br	br	NOUN
ejpam-6633	191	9	)	)	PUNCT
ejpam-6633	191	10	⊂	⊂	PROPN
ejpam-6633	191	11	br	br	PROPN
ejpam-6633	191	12	.	.	PUNCT
ejpam-6633	192	1	for	for	ADP
ejpam-6633	192	2	any	any	DET
ejpam-6633	192	3	η	η	PROPN
ejpam-6633	192	4	∈	∈	PROPN
ejpam-6633	192	5	br	br	NOUN
ejpam-6633	192	6	:	:	PUNCT
ejpam-6633	192	7	∥ϕ	∥ϕ	PROPN
ejpam-6633	192	8	(	(	PUNCT
ejpam-6633	192	9	η	η	NOUN
ejpam-6633	192	10	)	)	PUNCT
ejpam-6633	192	11	∥	∥	X
ejpam-6633	192	12	=	=	PUNCT
ejpam-6633	192	13	sup	sup	NOUN
ejpam-6633	192	14	t	t	PROPN
ejpam-6633	192	15	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6633	192	16	1	1	NUM
ejpam-6633	192	17	γ(β	γ(β	PROPN
ejpam-6633	192	18	+	+	NUM
ejpam-6633	192	19	α	α	X
ejpam-6633	192	20	)	)	PUNCT
ejpam-6633	192	21	∫	∫	PROPN
ejpam-6633	192	22	t	t	PROPN
ejpam-6633	192	23	a	a	X
ejpam-6633	192	24	(	(	PUNCT
ejpam-6633	192	25	ln	ln	X
ejpam-6633	192	26	(	(	PUNCT
ejpam-6633	192	27	t	t	PROPN
ejpam-6633	192	28	τ	τ	PROPN
ejpam-6633	192	29	)	)	PUNCT
ejpam-6633	192	30	)	)	PUNCT
ejpam-6633	193	1	β+α−1	β+α−1	PUNCT
ejpam-6633	194	1	θ(τ	θ(τ	PROPN
ejpam-6633	194	2	,	,	PUNCT
ejpam-6633	194	3	η(τ	η(τ	PROPN
ejpam-6633	194	4	)	)	PUNCT
ejpam-6633	194	5	)	)	PUNCT
ejpam-6633	195	1	τ	τ	PROPN
ejpam-6633	195	2	dτ	dτ	NOUN
ejpam-6633	195	3	−	−	PROPN
ejpam-6633	195	4	µ	µ	PROPN
ejpam-6633	195	5	γ(α	γ(α	NOUN
ejpam-6633	195	6	)	)	PUNCT
ejpam-6633	196	1	∫	∫	PROPN
ejpam-6633	196	2	t	t	PROPN
ejpam-6633	196	3	a	a	X
ejpam-6633	196	4	(	(	PUNCT
ejpam-6633	196	5	ln	ln	X
ejpam-6633	196	6	(	(	PUNCT
ejpam-6633	196	7	t	t	PROPN
ejpam-6633	196	8	τ	τ	PROPN
ejpam-6633	196	9	)	)	PUNCT
ejpam-6633	196	10	)	)	PUNCT
ejpam-6633	196	11	α−1	α−1	PROPN
ejpam-6633	196	12	η(τ	η(τ	PROPN
ejpam-6633	196	13	)	)	PUNCT
ejpam-6633	196	14	τ2	τ2	PROPN
ejpam-6633	196	15	dτ	dτ	NOUN
ejpam-6633	197	1	−	−	PROPN
ejpam-6633	198	1	(	(	PUNCT
ejpam-6633	198	2	ln	ln	X
ejpam-6633	198	3	(	(	PUNCT
ejpam-6633	198	4	t	t	PROPN
ejpam-6633	198	5	a	a	PRON
ejpam-6633	198	6	)	)	PUNCT
ejpam-6633	198	7	)	)	PUNCT
ejpam-6633	199	1	α	α	NOUN
ejpam-6633	199	2	bγ(β	bγ(β	X
ejpam-6633	199	3	+	+	X
ejpam-6633	199	4	α	α	X
ejpam-6633	199	5	)	)	PUNCT
ejpam-6633	199	6	∫	∫	PROPN
ejpam-6633	199	7	1	1	NUM
ejpam-6633	199	8	a	a	PRON
ejpam-6633	199	9	(	(	PUNCT
ejpam-6633	199	10	ln	ln	NOUN
ejpam-6633	199	11	(	(	PUNCT
ejpam-6633	199	12	1	1	NUM
ejpam-6633	199	13	τ	τ	PROPN
ejpam-6633	199	14	)	)	PUNCT
ejpam-6633	199	15	)	)	PUNCT
ejpam-6633	199	16	β+α−1	β+α−1	PROPN
ejpam-6633	200	1	θ(τ	θ(τ	PROPN
ejpam-6633	200	2	,	,	PUNCT
ejpam-6633	200	3	η(τ	η(τ	PROPN
ejpam-6633	200	4	)	)	PUNCT
ejpam-6633	200	5	)	)	PUNCT
ejpam-6633	201	1	τ	τ	PROPN
ejpam-6633	201	2	dτ	dτ	PROPN
ejpam-6633	202	1	+	+	X
ejpam-6633	202	2	µ	µ	X
ejpam-6633	202	3	(	(	PUNCT
ejpam-6633	202	4	ln	ln	X
ejpam-6633	202	5	(	(	PUNCT
ejpam-6633	202	6	t	t	PROPN
ejpam-6633	202	7	a	a	PRON
ejpam-6633	202	8	)	)	PUNCT
ejpam-6633	202	9	)	)	PUNCT
ejpam-6633	202	10	α	α	PROPN
ejpam-6633	202	11	bγ(α	bγ(α	PROPN
ejpam-6633	202	12	)	)	PUNCT
ejpam-6633	202	13	∫	∫	PROPN
ejpam-6633	203	1	1	1	NUM
ejpam-6633	203	2	a	a	DET
ejpam-6633	203	3	(	(	PUNCT
ejpam-6633	203	4	ln	ln	NOUN
ejpam-6633	203	5	(	(	PUNCT
ejpam-6633	203	6	1	1	NUM
ejpam-6633	203	7	τ	τ	PROPN
ejpam-6633	203	8	)	)	PUNCT
ejpam-6633	203	9	)	)	PUNCT
ejpam-6633	203	10	α−1	α−1	PROPN
ejpam-6633	203	11	η(τ	η(τ	PROPN
ejpam-6633	203	12	)	)	PUNCT
ejpam-6633	203	13	τ2	τ2	PROPN
ejpam-6633	203	14	dτ	dτ	PROPN
ejpam-6633	203	15	+	+	NOUN
ejpam-6633	203	16	φ(t	φ(t	PROPN
ejpam-6633	203	17	)	)	PUNCT
ejpam-6633	203	18	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6633	203	19	,	,	PUNCT
ejpam-6633	203	20	t	t	NOUN
ejpam-6633	203	21	∈	∈	PROPN
ejpam-6633	204	1	[	[	X
ejpam-6633	204	2	a	a	X
ejpam-6633	204	3	,	,	PUNCT
ejpam-6633	204	4	1	1	NUM
ejpam-6633	204	5	]	]	PUNCT
ejpam-6633	204	6	.	.	PUNCT
ejpam-6633	205	1	(	(	PUNCT
ejpam-6633	205	2	25	25	NUM
ejpam-6633	205	3	)	)	PUNCT
ejpam-6633	205	4	utilizing	utilize	VERB
ejpam-6633	205	5	the	the	DET
ejpam-6633	205	6	assumption	assumption	NOUN
ejpam-6633	205	7	h1	h1	NOUN
ejpam-6633	205	8	and	and	CCONJ
ejpam-6633	205	9	the	the	DET
ejpam-6633	205	10	condition	condition	NOUN
ejpam-6633	205	11	(	(	PUNCT
ejpam-6633	205	12	22	22	NUM
ejpam-6633	205	13	)	)	PUNCT
ejpam-6633	205	14	,	,	PUNCT
ejpam-6633	205	15	we	we	PRON
ejpam-6633	205	16	arrive	arrive	VERB
ejpam-6633	205	17	at	at	ADP
ejpam-6633	205	18	:	:	PUNCT
ejpam-6633	205	19	∥ϕ	∥ϕ	PROPN
ejpam-6633	205	20	(	(	PUNCT
ejpam-6633	205	21	η	η	NOUN
ejpam-6633	205	22	)	)	PUNCT
ejpam-6633	205	23	∥	∥	PUNCT
ejpam-6633	205	24	≤	≤	NUM
ejpam-6633	205	25	ωφ1	ωφ1	VERB
ejpam-6633	205	26	+	+	CCONJ
ejpam-6633	205	27	rφ2	rφ2	PROPN
ejpam-6633	205	28	+	+	CCONJ
ejpam-6633	205	29	∥φ∥	∥φ∥	X
ejpam-6633	205	30	≤	≤	ADJ
ejpam-6633	205	31	r	r	NOUN
ejpam-6633	205	32	,	,	PUNCT
ejpam-6633	205	33	(	(	PUNCT
ejpam-6633	205	34	26	26	NUM
ejpam-6633	205	35	)	)	PUNCT
ejpam-6633	205	36	where	where	SCONJ
ejpam-6633	205	37	φ1	φ1	NOUN
ejpam-6633	205	38	=	=	SYM
ejpam-6633	205	39	2b	2b	NUM
ejpam-6633	205	40	γ(β+α+1	γ(β+α+1	NOUN
ejpam-6633	205	41	)	)	PUNCT
ejpam-6633	205	42	(	(	PUNCT
ejpam-6633	205	43	ln	ln	NOUN
ejpam-6633	205	44	(	(	PUNCT
ejpam-6633	205	45	1	1	NUM
ejpam-6633	205	46	a	a	NOUN
ejpam-6633	205	47	)	)	PUNCT
ejpam-6633	205	48	)	)	PUNCT
ejpam-6633	205	49	β	β	PROPN
ejpam-6633	205	50	and	and	CCONJ
ejpam-6633	205	51	φ2	φ2	PROPN
ejpam-6633	205	52	=	=	SYM
ejpam-6633	205	53	2bµ	2bµ	ADJ
ejpam-6633	205	54	aγ(α+1	aγ(α+1	NOUN
ejpam-6633	205	55	)	)	PUNCT
ejpam-6633	205	56	,	,	PUNCT
ejpam-6633	205	57	and	and	CCONJ
ejpam-6633	205	58	inequality	inequality	NOUN
ejpam-6633	205	59	(	(	PUNCT
ejpam-6633	205	60	26	26	NUM
ejpam-6633	205	61	)	)	PUNCT
ejpam-6633	205	62	reveal	reveal	VERB
ejpam-6633	205	63	that	that	SCONJ
ejpam-6633	205	64	ϕ	ϕ	PROPN
ejpam-6633	205	65	(	(	PUNCT
ejpam-6633	205	66	br	br	NOUN
ejpam-6633	205	67	)	)	PUNCT
ejpam-6633	205	68	⊂	⊂	PROPN
ejpam-6633	205	69	br	br	PROPN
ejpam-6633	205	70	.	.	PUNCT
ejpam-6633	206	1	progressing	progress	VERB
ejpam-6633	206	2	from	from	ADP
ejpam-6633	206	3	the	the	DET
ejpam-6633	206	4	prior	prior	NOUN
ejpam-6633	206	5	,	,	PUNCT
ejpam-6633	206	6	we	we	PRON
ejpam-6633	206	7	now	now	ADV
ejpam-6633	206	8	prove	prove	VERB
ejpam-6633	206	9	the	the	DET
ejpam-6633	206	10	contraction	contraction	NOUN
ejpam-6633	206	11	requirement	requirement	NOUN
ejpam-6633	206	12	on	on	ADP
ejpam-6633	206	13	the	the	DET
ejpam-6633	206	14	mapping	mapping	NOUN
ejpam-6633	206	15	.	.	PUNCT
ejpam-6633	207	1	for	for	ADP
ejpam-6633	207	2	any	any	DET
ejpam-6633	207	3	two	two	NUM
ejpam-6633	207	4	functions	function	NOUN
ejpam-6633	207	5	η1	η1	NOUN
ejpam-6633	207	6	and	and	CCONJ
ejpam-6633	207	7	η2	η2	PROPN
ejpam-6633	207	8	in	in	ADP
ejpam-6633	207	9	br	br	PROPN
ejpam-6633	207	10	,	,	PUNCT
ejpam-6633	207	11	the	the	DET
ejpam-6633	207	12	norm	norm	NOUN
ejpam-6633	207	13	of	of	ADP
ejpam-6633	207	14	their	their	PRON
ejpam-6633	207	15	difference	difference	NOUN
ejpam-6633	207	16	follows	follow	VERB
ejpam-6633	207	17	:	:	PUNCT
ejpam-6633	208	1	∥ϕ	∥ϕ	PROPN
ejpam-6633	208	2	(	(	PUNCT
ejpam-6633	208	3	η2)−	η2)−	ADJ
ejpam-6633	208	4	ϕ	ϕ	X
ejpam-6633	208	5	(	(	PUNCT
ejpam-6633	208	6	η1)∥	η1)∥	X
ejpam-6633	208	7	=	=	SYM
ejpam-6633	208	8	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-6633	208	9	1	1	NUM
ejpam-6633	208	10	γ(β	γ(β	PROPN
ejpam-6633	208	11	+	+	NUM
ejpam-6633	208	12	α	α	X
ejpam-6633	208	13	)	)	PUNCT
ejpam-6633	208	14	∫	∫	PROPN
ejpam-6633	209	1	t	t	PROPN
ejpam-6633	209	2	a	a	X
ejpam-6633	209	3	(	(	PUNCT
ejpam-6633	209	4	ln	ln	X
ejpam-6633	209	5	(	(	PUNCT
ejpam-6633	209	6	t	t	PROPN
ejpam-6633	209	7	τ	τ	PROPN
ejpam-6633	209	8	)	)	PUNCT
ejpam-6633	209	9	)	)	PUNCT
ejpam-6633	209	10	β+α−1	β+α−1	NOUN
ejpam-6633	210	1	[	[	X
ejpam-6633	210	2	θ(τ	θ(τ	PROPN
ejpam-6633	210	3	,	,	PUNCT
ejpam-6633	210	4	η2(τ))−	η2(τ))−	VERB
ejpam-6633	210	5	θ(τ	θ(τ	PROPN
ejpam-6633	210	6	,	,	PUNCT
ejpam-6633	210	7	η1(τ	η1(τ	NOUN
ejpam-6633	210	8	)	)	PUNCT
ejpam-6633	210	9	)	)	PUNCT
ejpam-6633	210	10	]	]	PUNCT
ejpam-6633	210	11	dτ	dτ	X
ejpam-6633	210	12	τ	τ	PROPN
ejpam-6633	210	13	−	−	PROPN
ejpam-6633	210	14	µ	µ	X
ejpam-6633	210	15	γ(α	γ(α	NOUN
ejpam-6633	210	16	)	)	PUNCT
ejpam-6633	211	1	∫	∫	PROPN
ejpam-6633	211	2	t	t	PROPN
ejpam-6633	211	3	a	a	X
ejpam-6633	211	4	(	(	PUNCT
ejpam-6633	211	5	ln	ln	X
ejpam-6633	211	6	(	(	PUNCT
ejpam-6633	211	7	t	t	PROPN
ejpam-6633	211	8	τ	τ	PROPN
ejpam-6633	211	9	)	)	PUNCT
ejpam-6633	211	10	)	)	PUNCT
ejpam-6633	211	11	α−1	α−1	PROPN
ejpam-6633	212	1	[	[	X
ejpam-6633	212	2	η2(τ)−	η2(τ)−	PROPN
ejpam-6633	212	3	η1(τ	η1(τ	PROPN
ejpam-6633	212	4	)	)	PUNCT
ejpam-6633	212	5	]	]	PUNCT
ejpam-6633	212	6	dτ	dτ	NOUN
ejpam-6633	213	1	τ2	τ2	NOUN
ejpam-6633	213	2	−	−	PROPN
ejpam-6633	213	3	(	(	PUNCT
ejpam-6633	213	4	ln	ln	X
ejpam-6633	213	5	(	(	PUNCT
ejpam-6633	213	6	t	t	PROPN
ejpam-6633	213	7	a	a	PRON
ejpam-6633	213	8	)	)	PUNCT
ejpam-6633	213	9	)	)	PUNCT
ejpam-6633	213	10	α	α	NOUN
ejpam-6633	213	11	bγ(β	bγ(β	X
ejpam-6633	213	12	+	+	X
ejpam-6633	213	13	α	α	X
ejpam-6633	213	14	)	)	PUNCT
ejpam-6633	213	15	∫	∫	PROPN
ejpam-6633	213	16	1	1	NUM
ejpam-6633	213	17	a	a	PRON
ejpam-6633	213	18	(	(	PUNCT
ejpam-6633	213	19	ln	ln	NOUN
ejpam-6633	213	20	(	(	PUNCT
ejpam-6633	213	21	1	1	NUM
ejpam-6633	213	22	τ	τ	PROPN
ejpam-6633	213	23	)	)	PUNCT
ejpam-6633	213	24	)	)	PUNCT
ejpam-6633	213	25	β+α−1	β+α−1	NOUN
ejpam-6633	214	1	[	[	X
ejpam-6633	214	2	θ(τ	θ(τ	PROPN
ejpam-6633	214	3	,	,	PUNCT
ejpam-6633	214	4	η2(τ))−	η2(τ))−	VERB
ejpam-6633	214	5	θ(τ	θ(τ	PROPN
ejpam-6633	214	6	,	,	PUNCT
ejpam-6633	214	7	η1(τ	η1(τ	NOUN
ejpam-6633	214	8	)	)	PUNCT
ejpam-6633	214	9	)	)	PUNCT
ejpam-6633	214	10	]	]	PUNCT
ejpam-6633	214	11	dτ	dτ	X
ejpam-6633	214	12	τ	τ	PROPN
ejpam-6633	214	13	+	+	X
ejpam-6633	214	14	µ	µ	X
ejpam-6633	214	15	(	(	PUNCT
ejpam-6633	214	16	ln	ln	X
ejpam-6633	214	17	(	(	PUNCT
ejpam-6633	214	18	t	t	PROPN
ejpam-6633	214	19	a	a	PRON
ejpam-6633	214	20	)	)	PUNCT
ejpam-6633	214	21	)	)	PUNCT
ejpam-6633	214	22	α	α	PROPN
ejpam-6633	214	23	bγ(α	bγ(α	PROPN
ejpam-6633	214	24	)	)	PUNCT
ejpam-6633	214	25	∫	∫	PROPN
ejpam-6633	215	1	1	1	NUM
ejpam-6633	215	2	a	a	PRON
ejpam-6633	215	3	(	(	PUNCT
ejpam-6633	215	4	ln	ln	NOUN
ejpam-6633	215	5	(	(	PUNCT
ejpam-6633	215	6	1	1	NUM
ejpam-6633	215	7	τ	τ	PROPN
ejpam-6633	215	8	)	)	PUNCT
ejpam-6633	215	9	)	)	PUNCT
ejpam-6633	215	10	α−1	α−1	PROPN
ejpam-6633	216	1	[	[	X
ejpam-6633	216	2	η2(τ)−	η2(τ)−	PROPN
ejpam-6633	216	3	η1(τ	η1(τ	PROPN
ejpam-6633	216	4	)	)	PUNCT
ejpam-6633	216	5	]	]	PUNCT
ejpam-6633	216	6	dτ	dτ	PROPN
ejpam-6633	216	7	τ2	τ2	PROPN
ejpam-6633	216	8	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-6633	216	9	,	,	PUNCT
ejpam-6633	216	10	t	t	PROPN
ejpam-6633	216	11	∈	∈	PROPN
ejpam-6633	217	1	[	[	X
ejpam-6633	217	2	a	a	X
ejpam-6633	217	3	,	,	PUNCT
ejpam-6633	217	4	1	1	NUM
ejpam-6633	217	5	]	]	PUNCT
ejpam-6633	217	6	.	.	PUNCT
ejpam-6633	218	1	(	(	PUNCT
ejpam-6633	218	2	27	27	NUM
ejpam-6633	218	3	)	)	PUNCT
ejpam-6633	218	4	equation	equation	NOUN
ejpam-6633	218	5	(	(	PUNCT
ejpam-6633	218	6	27	27	NUM
ejpam-6633	218	7	)	)	PUNCT
ejpam-6633	218	8	follows	follow	VERB
ejpam-6633	218	9	:	:	PUNCT
ejpam-6633	218	10	∥ϕ	∥ϕ	PROPN
ejpam-6633	218	11	(	(	PUNCT
ejpam-6633	218	12	η2)−	η2)−	ADJ
ejpam-6633	218	13	ϕ	ϕ	X
ejpam-6633	218	14	(	(	PUNCT
ejpam-6633	218	15	η1)∥	η1)∥	PROPN
ejpam-6633	218	16	≤	≤	NUM
ejpam-6633	218	17	(	(	PUNCT
ejpam-6633	218	18	ln	ln	X
ejpam-6633	218	19	(	(	PUNCT
ejpam-6633	218	20	t	t	PROPN
ejpam-6633	218	21	a	a	PRON
ejpam-6633	218	22	)	)	PUNCT
ejpam-6633	218	23	)	)	PUNCT
ejpam-6633	218	24	α+β	α+β	PROPN
ejpam-6633	219	1	γ(β	γ(β	PROPN
ejpam-6633	219	2	+	+	CCONJ
ejpam-6633	219	3	α+	α+	PUNCT
ejpam-6633	219	4	1	1	NUM
ejpam-6633	219	5	)	)	PUNCT
ejpam-6633	219	6	∥θ2	∥θ2	NOUN
ejpam-6633	219	7	−	−	PROPN
ejpam-6633	219	8	θ1∥+	θ1∥+	PROPN
ejpam-6633	219	9	µ	µ	X
ejpam-6633	219	10	(	(	PUNCT
ejpam-6633	219	11	ln	ln	X
ejpam-6633	219	12	(	(	PUNCT
ejpam-6633	219	13	t	t	PROPN
ejpam-6633	219	14	a	a	PRON
ejpam-6633	219	15	)	)	PUNCT
ejpam-6633	219	16	)	)	PUNCT
ejpam-6633	220	1	α	α	PROPN
ejpam-6633	220	2	aγ(α+	aγ(α+	NOUN
ejpam-6633	220	3	1	1	NUM
ejpam-6633	220	4	)	)	PUNCT
ejpam-6633	220	5	∥η2	∥η2	NOUN
ejpam-6633	220	6	−	−	PROPN
ejpam-6633	220	7	η1∥	η1∥	PROPN
ejpam-6633	220	8	a.	a.	PROPN
ejpam-6633	220	9	s.	s.	PROPN
ejpam-6633	220	10	hasan	hasan	PROPN
ejpam-6633	220	11	,	,	PUNCT
ejpam-6633	220	12	s.	s.	PROPN
ejpam-6633	220	13	a.	a.	PROPN
ejpam-6633	220	14	murad	murad	PROPN
ejpam-6633	220	15	/	/	SYM
ejpam-6633	220	16	eur	eur	PROPN
ejpam-6633	220	17	.	.	PUNCT
ejpam-6633	221	1	j.	j.	PROPN
ejpam-6633	221	2	pure	pure	PROPN
ejpam-6633	221	3	appl	appl	PROPN
ejpam-6633	221	4	.	.	PROPN
ejpam-6633	221	5	math	math	PROPN
ejpam-6633	221	6	,	,	PUNCT
ejpam-6633	221	7	18	18	NUM
ejpam-6633	221	8	(	(	PUNCT
ejpam-6633	221	9	3	3	NUM
ejpam-6633	221	10	)	)	PUNCT
ejpam-6633	221	11	(	(	PUNCT
ejpam-6633	221	12	2025	2025	NUM
ejpam-6633	221	13	)	)	PUNCT
ejpam-6633	221	14	,	,	PUNCT
ejpam-6633	221	15	6633	6633	NUM
ejpam-6633	221	16	9	9	NUM
ejpam-6633	221	17	of	of	ADP
ejpam-6633	221	18	24	24	NUM
ejpam-6633	221	19	+	+	CCONJ
ejpam-6633	221	20	(	(	PUNCT
ejpam-6633	221	21	ln	ln	INTJ
ejpam-6633	221	22	(	(	PUNCT
ejpam-6633	221	23	t	t	PROPN
ejpam-6633	221	24	a	a	PRON
ejpam-6633	221	25	)	)	PUNCT
ejpam-6633	221	26	)	)	PUNCT
ejpam-6633	222	1	α	α	PROPN
ejpam-6633	222	2	(	(	PUNCT
ejpam-6633	222	3	ln	ln	NOUN
ejpam-6633	222	4	(	(	PUNCT
ejpam-6633	222	5	1	1	NUM
ejpam-6633	222	6	a	a	NOUN
ejpam-6633	222	7	)	)	PUNCT
ejpam-6633	222	8	)	)	PUNCT
ejpam-6633	222	9	α+β	α+β	NUM
ejpam-6633	222	10	bγ(β	bγ(β	PUNCT
ejpam-6633	222	11	+	+	CCONJ
ejpam-6633	222	12	α+	α+	PUNCT
ejpam-6633	222	13	1	1	X
ejpam-6633	222	14	)	)	PUNCT
ejpam-6633	222	15	∥θ2	∥θ2	NOUN
ejpam-6633	222	16	−	−	PROPN
ejpam-6633	222	17	θ1∥+	θ1∥+	PROPN
ejpam-6633	222	18	µ	µ	X
ejpam-6633	222	19	(	(	PUNCT
ejpam-6633	222	20	ln	ln	X
ejpam-6633	222	21	(	(	PUNCT
ejpam-6633	222	22	t	t	PROPN
ejpam-6633	222	23	a	a	PRON
ejpam-6633	222	24	)	)	PUNCT
ejpam-6633	222	25	)	)	PUNCT
ejpam-6633	223	1	α	α	PROPN
ejpam-6633	223	2	(	(	PUNCT
ejpam-6633	223	3	ln	ln	NOUN
ejpam-6633	223	4	(	(	PUNCT
ejpam-6633	223	5	1	1	NUM
ejpam-6633	223	6	a	a	NOUN
ejpam-6633	223	7	)	)	PUNCT
ejpam-6633	223	8	)	)	PUNCT
ejpam-6633	223	9	α	α	X
ejpam-6633	224	1	abγ(α+	abγ(α+	ADJ
ejpam-6633	224	2	1	1	NUM
ejpam-6633	224	3	)	)	PUNCT
ejpam-6633	224	4	∥η2	∥η2	NOUN
ejpam-6633	225	1	−	−	PROPN
ejpam-6633	225	2	η1∥	η1∥	PROPN
ejpam-6633	225	3	.	.	PUNCT
ejpam-6633	226	1	=	=	SYM
ejpam-6633	226	2	φ1	φ1	PROPN
ejpam-6633	226	3	∥θ2	∥θ2	NOUN
ejpam-6633	226	4	−	−	PROPN
ejpam-6633	226	5	θ1∥+	θ1∥+	PROPN
ejpam-6633	226	6	φ2	φ2	PROPN
ejpam-6633	226	7	∥η2	∥η2	VERB
ejpam-6633	227	1	−	−	PROPN
ejpam-6633	227	2	η1∥	η1∥	PROPN
ejpam-6633	227	3	,	,	PUNCT
ejpam-6633	227	4	(	(	PUNCT
ejpam-6633	227	5	28	28	NUM
ejpam-6633	227	6	)	)	PUNCT
ejpam-6633	227	7	using	use	VERB
ejpam-6633	227	8	assumption	assumption	NOUN
ejpam-6633	227	9	(	(	PUNCT
ejpam-6633	227	10	h2	h2	NOUN
ejpam-6633	227	11	)	)	PUNCT
ejpam-6633	227	12	,	,	PUNCT
ejpam-6633	227	13	(	(	PUNCT
ejpam-6633	227	14	28	28	NUM
ejpam-6633	227	15	)	)	PUNCT
ejpam-6633	227	16	arrives	arrive	VERB
ejpam-6633	227	17	at	at	ADP
ejpam-6633	227	18	:	:	PUNCT
ejpam-6633	227	19	∥ϕ	∥ϕ	PROPN
ejpam-6633	227	20	(	(	PUNCT
ejpam-6633	227	21	η2)−	η2)−	ADJ
ejpam-6633	227	22	ϕ	ϕ	X
ejpam-6633	227	23	(	(	PUNCT
ejpam-6633	227	24	η1)∥	η1)∥	PROPN
ejpam-6633	227	25	≤	≤	NUM
ejpam-6633	227	26	υ	υ	NOUN
ejpam-6633	227	27	∥η2	∥η2	NOUN
ejpam-6633	228	1	−	−	PROPN
ejpam-6633	228	2	η1∥	η1∥	NOUN
ejpam-6633	228	3	,	,	PUNCT
ejpam-6633	228	4	(	(	PUNCT
ejpam-6633	228	5	29	29	NUM
ejpam-6633	228	6	)	)	PUNCT
ejpam-6633	228	7	where	where	SCONJ
ejpam-6633	228	8	0	0	NUM
ejpam-6633	228	9	<	<	X
ejpam-6633	228	10	υ	υ	X
ejpam-6633	228	11	=	=	PUNCT
ejpam-6633	228	12	kφ1	kφ1	NOUN
ejpam-6633	228	13	+	+	CCONJ
ejpam-6633	228	14	φ2	φ2	PROPN
ejpam-6633	228	15	<	<	X
ejpam-6633	228	16	1	1	X
ejpam-6633	228	17	.	.	PUNCT
ejpam-6633	228	18	using	use	VERB
ejpam-6633	228	19	theorem	theorem	NOUN
ejpam-6633	228	20	3	3	NUM
ejpam-6633	228	21	,	,	PUNCT
ejpam-6633	228	22	we	we	PRON
ejpam-6633	228	23	can	can	AUX
ejpam-6633	228	24	show	show	VERB
ejpam-6633	228	25	that	that	SCONJ
ejpam-6633	228	26	the	the	DET
ejpam-6633	228	27	solution	solution	NOUN
ejpam-6633	228	28	to	to	ADP
ejpam-6633	228	29	the	the	DET
ejpam-6633	228	30	boundary	boundary	ADJ
ejpam-6633	228	31	-	-	PUNCT
ejpam-6633	228	32	value	value	NOUN
ejpam-6633	228	33	problem	problem	NOUN
ejpam-6633	228	34	(	(	PUNCT
ejpam-6633	228	35	6–8	6–8	X
ejpam-6633	228	36	)	)	PUNCT
ejpam-6633	228	37	is	be	AUX
ejpam-6633	228	38	unique	unique	ADJ
ejpam-6633	228	39	.	.	PUNCT
ejpam-6633	229	1	for	for	ADP
ejpam-6633	229	2	the	the	DET
ejpam-6633	229	3	existence	existence	NOUN
ejpam-6633	229	4	of	of	ADP
ejpam-6633	229	5	a	a	DET
ejpam-6633	229	6	solution	solution	NOUN
ejpam-6633	229	7	for	for	ADP
ejpam-6633	229	8	the	the	DET
ejpam-6633	229	9	boundaryvalue	boundaryvalue	NOUN
ejpam-6633	229	10	problem	problem	NOUN
ejpam-6633	229	11	(	(	PUNCT
ejpam-6633	229	12	6	6	NUM
ejpam-6633	229	13	-	-	SYM
ejpam-6633	229	14	8)	8)	NUM
ejpam-6633	229	15	,	,	PUNCT
ejpam-6633	229	16	we	we	PRON
ejpam-6633	229	17	apply	apply	VERB
ejpam-6633	229	18	the	the	DET
ejpam-6633	229	19	sadovoskii	sadovoskii	ADJ
ejpam-6633	229	20	fixed	fix	VERB
ejpam-6633	229	21	point	point	NOUN
ejpam-6633	229	22	theorem	theorem	VERB
ejpam-6633	229	23	.	.	PUNCT
ejpam-6633	230	1	we	we	PRON
ejpam-6633	230	2	consider	consider	VERB
ejpam-6633	230	3	the	the	DET
ejpam-6633	230	4	operator	operator	NOUN
ejpam-6633	230	5	to	to	PART
ejpam-6633	230	6	be	be	AUX
ejpam-6633	230	7	ϕ	ϕ	NOUN
ejpam-6633	230	8	,	,	PUNCT
ejpam-6633	230	9	as	as	SCONJ
ejpam-6633	230	10	it	it	PRON
ejpam-6633	230	11	is	be	AUX
ejpam-6633	230	12	defined	define	VERB
ejpam-6633	230	13	in	in	ADP
ejpam-6633	230	14	24	24	NUM
ejpam-6633	230	15	.	.	PUNCT
ejpam-6633	231	1	at	at	ADP
ejpam-6633	231	2	this	this	DET
ejpam-6633	231	3	point	point	NOUN
ejpam-6633	231	4	,	,	PUNCT
ejpam-6633	231	5	we	we	PRON
ejpam-6633	231	6	introduce	introduce	VERB
ejpam-6633	231	7	two	two	NUM
ejpam-6633	231	8	operators	operator	NOUN
ejpam-6633	231	9	called	call	VERB
ejpam-6633	231	10	ϕ1	ϕ1	NOUN
ejpam-6633	231	11	and	and	CCONJ
ejpam-6633	231	12	ϕ2	ϕ2	ADV
ejpam-6633	231	13	that	that	PRON
ejpam-6633	231	14	map	map	VERB
ejpam-6633	231	15	q	q	PUNCT
ejpam-6633	231	16	to	to	ADP
ejpam-6633	231	17	itself	itself	PRON
ejpam-6633	231	18	as	as	SCONJ
ejpam-6633	231	19	follows	follow	VERB
ejpam-6633	231	20	:	:	PUNCT
ejpam-6633	231	21	ϕ1	ϕ1	NOUN
ejpam-6633	231	22	(	(	PUNCT
ejpam-6633	231	23	η(t	η(t	NOUN
ejpam-6633	231	24	)	)	PUNCT
ejpam-6633	231	25	)	)	PUNCT
ejpam-6633	232	1	=	=	SYM
ejpam-6633	232	2	−	−	PROPN
ejpam-6633	232	3	µ	µ	PROPN
ejpam-6633	232	4	γ(α	γ(α	NOUN
ejpam-6633	232	5	)	)	PUNCT
ejpam-6633	233	1	∫	∫	PROPN
ejpam-6633	233	2	t	t	PROPN
ejpam-6633	233	3	a	a	X
ejpam-6633	233	4	(	(	PUNCT
ejpam-6633	233	5	ln	ln	X
ejpam-6633	233	6	(	(	PUNCT
ejpam-6633	233	7	t	t	PROPN
ejpam-6633	233	8	τ	τ	PROPN
ejpam-6633	233	9	)	)	PUNCT
ejpam-6633	233	10	)	)	PUNCT
ejpam-6633	233	11	α−1	α−1	PROPN
ejpam-6633	233	12	η(τ	η(τ	PROPN
ejpam-6633	233	13	)	)	PUNCT
ejpam-6633	233	14	τ2	τ2	PROPN
ejpam-6633	233	15	dτ	dτ	NOUN
ejpam-6633	233	16	+	+	X
ejpam-6633	233	17	µ	µ	X
ejpam-6633	233	18	(	(	PUNCT
ejpam-6633	233	19	ln	ln	X
ejpam-6633	233	20	(	(	PUNCT
ejpam-6633	233	21	t	t	PROPN
ejpam-6633	233	22	a	a	PRON
ejpam-6633	233	23	)	)	PUNCT
ejpam-6633	233	24	)	)	PUNCT
ejpam-6633	233	25	α	α	PROPN
ejpam-6633	233	26	bγ(α	bγ(α	PROPN
ejpam-6633	233	27	)	)	PUNCT
ejpam-6633	233	28	∫	∫	PROPN
ejpam-6633	234	1	1	1	NUM
ejpam-6633	234	2	a	a	DET
ejpam-6633	234	3	(	(	PUNCT
ejpam-6633	234	4	ln	ln	NOUN
ejpam-6633	234	5	(	(	PUNCT
ejpam-6633	234	6	1	1	NUM
ejpam-6633	234	7	τ	τ	PROPN
ejpam-6633	234	8	)	)	PUNCT
ejpam-6633	234	9	)	)	PUNCT
ejpam-6633	234	10	α−1	α−1	PROPN
ejpam-6633	234	11	η(τ	η(τ	PROPN
ejpam-6633	234	12	)	)	PUNCT
ejpam-6633	234	13	τ2	τ2	PROPN
ejpam-6633	234	14	dτ	dτ	PROPN
ejpam-6633	234	15	+	+	PROPN
ejpam-6633	234	16	φ(t	φ(t	PROPN
ejpam-6633	234	17	)	)	PUNCT
ejpam-6633	234	18	,	,	PUNCT
ejpam-6633	234	19	t	t	PROPN
ejpam-6633	234	20	∈	∈	PROPN
ejpam-6633	235	1	[	[	X
ejpam-6633	235	2	a	a	X
ejpam-6633	235	3	,	,	PUNCT
ejpam-6633	235	4	1	1	NUM
ejpam-6633	235	5	]	]	PUNCT
ejpam-6633	235	6	,	,	PUNCT
ejpam-6633	235	7	(	(	PUNCT
ejpam-6633	235	8	30	30	NUM
ejpam-6633	235	9	)	)	PUNCT
ejpam-6633	235	10	and	and	CCONJ
ejpam-6633	235	11	ϕ2	ϕ2	ADV
ejpam-6633	235	12	(	(	PUNCT
ejpam-6633	235	13	η(t	η(t	NOUN
ejpam-6633	235	14	)	)	PUNCT
ejpam-6633	235	15	)	)	PUNCT
ejpam-6633	236	1	=	=	SYM
ejpam-6633	236	2	1	1	NUM
ejpam-6633	236	3	γ(β	γ(β	PROPN
ejpam-6633	236	4	+	+	NUM
ejpam-6633	236	5	α	α	X
ejpam-6633	236	6	)	)	PUNCT
ejpam-6633	236	7	∫	∫	PROPN
ejpam-6633	236	8	t	t	PROPN
ejpam-6633	236	9	a	a	X
ejpam-6633	236	10	(	(	PUNCT
ejpam-6633	236	11	ln	ln	X
ejpam-6633	236	12	(	(	PUNCT
ejpam-6633	236	13	t	t	PROPN
ejpam-6633	236	14	τ	τ	PROPN
ejpam-6633	236	15	)	)	PUNCT
ejpam-6633	236	16	)	)	PUNCT
ejpam-6633	237	1	β+α−1	β+α−1	PUNCT
ejpam-6633	238	1	θ(τ	θ(τ	PROPN
ejpam-6633	238	2	,	,	PUNCT
ejpam-6633	238	3	η(τ	η(τ	PROPN
ejpam-6633	238	4	)	)	PUNCT
ejpam-6633	238	5	)	)	PUNCT
ejpam-6633	239	1	τ	τ	PROPN
ejpam-6633	239	2	dτ	dτ	INTJ
ejpam-6633	240	1	−	−	PROPN
ejpam-6633	240	2	(	(	PUNCT
ejpam-6633	240	3	ln	ln	X
ejpam-6633	240	4	(	(	PUNCT
ejpam-6633	240	5	t	t	PROPN
ejpam-6633	240	6	a	a	PRON
ejpam-6633	240	7	)	)	PUNCT
ejpam-6633	240	8	)	)	PUNCT
ejpam-6633	240	9	α	α	NOUN
ejpam-6633	240	10	bγ(β	bγ(β	X
ejpam-6633	240	11	+	+	X
ejpam-6633	240	12	α	α	X
ejpam-6633	240	13	)	)	PUNCT
ejpam-6633	240	14	∫	∫	PROPN
ejpam-6633	240	15	1	1	NUM
ejpam-6633	240	16	a	a	PRON
ejpam-6633	240	17	(	(	PUNCT
ejpam-6633	240	18	ln	ln	NOUN
ejpam-6633	240	19	(	(	PUNCT
ejpam-6633	240	20	1	1	NUM
ejpam-6633	240	21	τ	τ	PROPN
ejpam-6633	240	22	)	)	PUNCT
ejpam-6633	240	23	)	)	PUNCT
ejpam-6633	240	24	β+α−1	β+α−1	PROPN
ejpam-6633	241	1	θ(τ	θ(τ	PROPN
ejpam-6633	241	2	,	,	PUNCT
ejpam-6633	241	3	η(τ	η(τ	PROPN
ejpam-6633	241	4	)	)	PUNCT
ejpam-6633	241	5	)	)	PUNCT
ejpam-6633	242	1	τ	τ	PROPN
ejpam-6633	242	2	dτ	dτ	PROPN
ejpam-6633	242	3	,	,	PUNCT
ejpam-6633	242	4	t	t	PROPN
ejpam-6633	242	5	∈	∈	PROPN
ejpam-6633	243	1	[	[	X
ejpam-6633	243	2	a	a	X
ejpam-6633	243	3	,	,	PUNCT
ejpam-6633	243	4	1	1	NUM
ejpam-6633	243	5	]	]	PUNCT
ejpam-6633	243	6	,	,	PUNCT
ejpam-6633	243	7	(	(	PUNCT
ejpam-6633	243	8	31	31	NUM
ejpam-6633	243	9	)	)	PUNCT
ejpam-6633	243	10	respectively	respectively	ADV
ejpam-6633	243	11	.	.	PUNCT
ejpam-6633	244	1	instead	instead	ADV
ejpam-6633	244	2	of	of	ADP
ejpam-6633	244	3	seeking	seek	VERB
ejpam-6633	244	4	the	the	DET
ejpam-6633	244	5	existence	existence	NOUN
ejpam-6633	244	6	of	of	ADP
ejpam-6633	244	7	a	a	DET
ejpam-6633	244	8	fixed	fix	VERB
ejpam-6633	244	9	point	point	NOUN
ejpam-6633	244	10	for	for	ADP
ejpam-6633	244	11	the	the	DET
ejpam-6633	244	12	operator	operator	NOUN
ejpam-6633	244	13	ϕ	ϕ	X
ejpam-6633	244	14	(	(	PUNCT
ejpam-6633	244	15	η(t	η(t	NOUN
ejpam-6633	244	16	)	)	PUNCT
ejpam-6633	244	17	)	)	PUNCT
ejpam-6633	244	18	,	,	PUNCT
ejpam-6633	244	19	we	we	PRON
ejpam-6633	244	20	shall	shall	AUX
ejpam-6633	244	21	do	do	VERB
ejpam-6633	244	22	the	the	DET
ejpam-6633	244	23	same	same	ADJ
ejpam-6633	244	24	through	through	ADP
ejpam-6633	244	25	the	the	DET
ejpam-6633	244	26	sum	sum	NOUN
ejpam-6633	244	27	of	of	ADP
ejpam-6633	244	28	the	the	DET
ejpam-6633	244	29	two	two	NUM
ejpam-6633	244	30	previously	previously	ADV
ejpam-6633	244	31	defined	define	VERB
ejpam-6633	244	32	operators	operator	NOUN
ejpam-6633	244	33	in	in	ADP
ejpam-6633	244	34	(	(	PUNCT
ejpam-6633	244	35	30	30	NUM
ejpam-6633	244	36	-	-	SYM
ejpam-6633	244	37	31	31	NUM
ejpam-6633	244	38	)	)	PUNCT
ejpam-6633	244	39	.	.	PUNCT
ejpam-6633	245	1	we	we	PRON
ejpam-6633	245	2	will	will	AUX
ejpam-6633	245	3	use	use	VERB
ejpam-6633	245	4	theorem	theorem	NOUN
ejpam-6633	245	5	2	2	NUM
ejpam-6633	245	6	and	and	CCONJ
ejpam-6633	245	7	the	the	DET
ejpam-6633	245	8	contraction	contraction	NOUN
ejpam-6633	245	9	condition	condition	NOUN
ejpam-6633	245	10	0	0	NUM
ejpam-6633	245	11	≤	≤	NUM
ejpam-6633	245	12	µ(b	µ(b	NOUN
ejpam-6633	245	13	+	+	CCONJ
ejpam-6633	245	14	1)/(aγ(α	1)/(aγ(α	NUM
ejpam-6633	245	15	+	+	NOUN
ejpam-6633	245	16	1	1	NUM
ejpam-6633	245	17	)	)	PUNCT
ejpam-6633	245	18	)	)	PUNCT
ejpam-6633	246	1	<	<	X
ejpam-6633	246	2	1	1	NUM
ejpam-6633	246	3	to	to	PART
ejpam-6633	246	4	show	show	VERB
ejpam-6633	246	5	that	that	SCONJ
ejpam-6633	246	6	ϕ1	ϕ1	NOUN
ejpam-6633	246	7	+	+	CCONJ
ejpam-6633	246	8	ϕ2	ϕ2	ADV
ejpam-6633	246	9	has	have	VERB
ejpam-6633	246	10	a	a	DET
ejpam-6633	246	11	fixed	fix	VERB
ejpam-6633	246	12	point	point	NOUN
ejpam-6633	246	13	using	use	VERB
ejpam-6633	246	14	the	the	DET
ejpam-6633	246	15	steps	step	NOUN
ejpam-6633	246	16	below	below	ADV
ejpam-6633	246	17	.	.	PUNCT
ejpam-6633	247	1	step	step	NOUN
ejpam-6633	247	2	1	1	NUM
ejpam-6633	247	3	:	:	PUNCT
ejpam-6633	247	4	it	it	PRON
ejpam-6633	247	5	has	have	AUX
ejpam-6633	247	6	previously	previously	ADV
ejpam-6633	247	7	manifested	manifest	VERB
ejpam-6633	248	1	that	that	DET
ejpam-6633	248	2	ϕ	ϕ	NOUN
ejpam-6633	248	3	(	(	PUNCT
ejpam-6633	248	4	br	br	NOUN
ejpam-6633	248	5	)	)	PUNCT
ejpam-6633	248	6	⊂	⊂	PROPN
ejpam-6633	248	7	br	br	PROPN
ejpam-6633	248	8	.	.	PUNCT
ejpam-6633	248	9	step	step	NOUN
ejpam-6633	248	10	2	2	NUM
ejpam-6633	248	11	:	:	PUNCT
ejpam-6633	248	12	we	we	PRON
ejpam-6633	248	13	are	be	AUX
ejpam-6633	248	14	compelled	compel	VERB
ejpam-6633	248	15	to	to	PART
ejpam-6633	248	16	exhibit	exhibit	VERB
ejpam-6633	248	17	that	that	SCONJ
ejpam-6633	248	18	ϕ2	ϕ2	ADV
ejpam-6633	248	19	is	be	AUX
ejpam-6633	248	20	compact	compact	ADJ
ejpam-6633	248	21	.	.	PUNCT
ejpam-6633	249	1	for	for	ADP
ejpam-6633	249	2	any	any	DET
ejpam-6633	249	3	t1	t1	NOUN
ejpam-6633	249	4	,	,	PUNCT
ejpam-6633	249	5	t2	t2	PROPN
ejpam-6633	249	6	∈	∈	PROPN
ejpam-6633	250	1	[	[	X
ejpam-6633	250	2	a	a	X
ejpam-6633	250	3	,	,	PUNCT
ejpam-6633	250	4	1	1	NUM
ejpam-6633	250	5	]	]	PUNCT
ejpam-6633	250	6	with	with	ADP
ejpam-6633	250	7	t1	t1	NOUN
ejpam-6633	250	8	<	<	X
ejpam-6633	250	9	t2	t2	PROPN
ejpam-6633	250	10	and	and	CCONJ
ejpam-6633	250	11	for	for	ADP
ejpam-6633	250	12	any	any	DET
ejpam-6633	250	13	η(t	η(t	NOUN
ejpam-6633	250	14	)	)	PUNCT
ejpam-6633	250	15	∈	∈	NOUN
ejpam-6633	250	16	br	br	NOUN
ejpam-6633	250	17	we	we	PRON
ejpam-6633	250	18	have	have	VERB
ejpam-6633	250	19	:	:	PUNCT
ejpam-6633	251	1	|ϕ2(η(t2))−	|ϕ2(η(t2))−	PROPN
ejpam-6633	251	2	ϕ2(η(t1))|	ϕ2(η(t1))|	VERB
ejpam-6633	251	3	=	=	PUNCT
ejpam-6633	251	4	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-6633	251	5	1	1	NUM
ejpam-6633	251	6	γ(β	γ(β	PROPN
ejpam-6633	251	7	+	+	NUM
ejpam-6633	251	8	α	α	X
ejpam-6633	251	9	)	)	PUNCT
ejpam-6633	251	10	∫	∫	PROPN
ejpam-6633	251	11	t2	t2	PROPN
ejpam-6633	251	12	a	a	PRON
ejpam-6633	251	13	(	(	PUNCT
ejpam-6633	251	14	ln	ln	NOUN
ejpam-6633	251	15	(	(	PUNCT
ejpam-6633	251	16	t2	t2	PROPN
ejpam-6633	251	17	τ	τ	PROPN
ejpam-6633	251	18	)	)	PUNCT
ejpam-6633	251	19	)	)	PUNCT
ejpam-6633	252	1	β+α−1	β+α−1	PUNCT
ejpam-6633	253	1	θ(τ	θ(τ	PROPN
ejpam-6633	253	2	,	,	PUNCT
ejpam-6633	253	3	η(τ	η(τ	PROPN
ejpam-6633	253	4	)	)	PUNCT
ejpam-6633	253	5	)	)	PUNCT
ejpam-6633	254	1	τ	τ	PROPN
ejpam-6633	254	2	dτ	dτ	INTJ
ejpam-6633	255	1	−	−	PROPN
ejpam-6633	255	2	(	(	PUNCT
ejpam-6633	255	3	ln	ln	INTJ
ejpam-6633	255	4	(	(	PUNCT
ejpam-6633	255	5	t2	t2	PROPN
ejpam-6633	255	6	a	a	PRON
ejpam-6633	255	7	)	)	PUNCT
ejpam-6633	255	8	)	)	PUNCT
ejpam-6633	255	9	α	α	NOUN
ejpam-6633	255	10	bγ(β	bγ(β	X
ejpam-6633	255	11	+	+	X
ejpam-6633	255	12	α	α	X
ejpam-6633	255	13	)	)	PUNCT
ejpam-6633	255	14	∫	∫	PROPN
ejpam-6633	255	15	1	1	NUM
ejpam-6633	255	16	a	a	PRON
ejpam-6633	255	17	(	(	PUNCT
ejpam-6633	255	18	ln	ln	NOUN
ejpam-6633	255	19	(	(	PUNCT
ejpam-6633	255	20	1	1	NUM
ejpam-6633	255	21	τ	τ	PROPN
ejpam-6633	255	22	)	)	PUNCT
ejpam-6633	255	23	)	)	PUNCT
ejpam-6633	255	24	β+α−1	β+α−1	PROPN
ejpam-6633	256	1	θ(τ	θ(τ	PROPN
ejpam-6633	256	2	,	,	PUNCT
ejpam-6633	256	3	η(τ	η(τ	PROPN
ejpam-6633	256	4	)	)	PUNCT
ejpam-6633	256	5	)	)	PUNCT
ejpam-6633	257	1	τ	τ	PROPN
ejpam-6633	257	2	dτ	dτ	NOUN
ejpam-6633	257	3	−	−	PROPN
ejpam-6633	257	4	1	1	NUM
ejpam-6633	257	5	γ(β	γ(β	PROPN
ejpam-6633	257	6	+	+	NUM
ejpam-6633	257	7	α	α	X
ejpam-6633	257	8	)	)	PUNCT
ejpam-6633	257	9	∫	∫	PROPN
ejpam-6633	257	10	t1	t1	NOUN
ejpam-6633	258	1	a	a	PROPN
ejpam-6633	258	2	(	(	PUNCT
ejpam-6633	258	3	ln	ln	NOUN
ejpam-6633	258	4	(	(	PUNCT
ejpam-6633	258	5	t1	t1	NOUN
ejpam-6633	258	6	τ	τ	PROPN
ejpam-6633	258	7	)	)	PUNCT
ejpam-6633	258	8	)	)	PUNCT
ejpam-6633	258	9	β+α−1	β+α−1	PROPN
ejpam-6633	259	1	θ(τ	θ(τ	PROPN
ejpam-6633	259	2	,	,	PUNCT
ejpam-6633	259	3	η(τ	η(τ	PROPN
ejpam-6633	259	4	)	)	PUNCT
ejpam-6633	259	5	)	)	PUNCT
ejpam-6633	260	1	τ	τ	PROPN
ejpam-6633	260	2	dτ	dτ	NOUN
ejpam-6633	261	1	+	+	CCONJ
ejpam-6633	261	2	(	(	PUNCT
ejpam-6633	261	3	ln	ln	INTJ
ejpam-6633	261	4	(	(	PUNCT
ejpam-6633	261	5	t1	t1	PROPN
ejpam-6633	261	6	a	a	NOUN
ejpam-6633	261	7	)	)	PUNCT
ejpam-6633	261	8	)	)	PUNCT
ejpam-6633	261	9	α	α	NOUN
ejpam-6633	261	10	bγ(β	bγ(β	X
ejpam-6633	261	11	+	+	X
ejpam-6633	261	12	α	α	X
ejpam-6633	261	13	)	)	PUNCT
ejpam-6633	261	14	∫	∫	PROPN
ejpam-6633	261	15	1	1	NUM
ejpam-6633	261	16	a	a	PRON
ejpam-6633	261	17	(	(	PUNCT
ejpam-6633	261	18	ln	ln	NOUN
ejpam-6633	261	19	(	(	PUNCT
ejpam-6633	261	20	1	1	NUM
ejpam-6633	261	21	τ	τ	PROPN
ejpam-6633	261	22	)	)	PUNCT
ejpam-6633	261	23	)	)	PUNCT
ejpam-6633	261	24	β+α−1	β+α−1	PROPN
ejpam-6633	262	1	θ(τ	θ(τ	PROPN
ejpam-6633	262	2	,	,	PUNCT
ejpam-6633	262	3	η(τ	η(τ	PROPN
ejpam-6633	262	4	)	)	PUNCT
ejpam-6633	262	5	)	)	PUNCT
ejpam-6633	263	1	τ	τ	PROPN
ejpam-6633	263	2	dτ	dτ	NOUN
ejpam-6633	263	3	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6633	263	4	.	.	PUNCT
ejpam-6633	264	1	(	(	PUNCT
ejpam-6633	264	2	32	32	NUM
ejpam-6633	264	3	)	)	PUNCT
ejpam-6633	264	4	a.	a.	NOUN
ejpam-6633	264	5	s.	s.	PROPN
ejpam-6633	264	6	hasan	hasan	PROPN
ejpam-6633	264	7	,	,	PUNCT
ejpam-6633	264	8	s.	s.	PROPN
ejpam-6633	264	9	a.	a.	PROPN
ejpam-6633	264	10	murad	murad	PROPN
ejpam-6633	264	11	/	/	SYM
ejpam-6633	264	12	eur	eur	PROPN
ejpam-6633	264	13	.	.	PUNCT
ejpam-6633	265	1	j.	j.	PROPN
ejpam-6633	265	2	pure	pure	PROPN
ejpam-6633	265	3	appl	appl	PROPN
ejpam-6633	265	4	.	.	PROPN
ejpam-6633	265	5	math	math	PROPN
ejpam-6633	265	6	,	,	PUNCT
ejpam-6633	265	7	18	18	NUM
ejpam-6633	265	8	(	(	PUNCT
ejpam-6633	265	9	3	3	NUM
ejpam-6633	265	10	)	)	PUNCT
ejpam-6633	265	11	(	(	PUNCT
ejpam-6633	265	12	2025	2025	NUM
ejpam-6633	265	13	)	)	PUNCT
ejpam-6633	265	14	,	,	PUNCT
ejpam-6633	265	15	6633	6633	NUM
ejpam-6633	265	16	10	10	NUM
ejpam-6633	265	17	of	of	ADP
ejpam-6633	265	18	24	24	NUM
ejpam-6633	265	19	≤	≤	NUM
ejpam-6633	265	20	1	1	NUM
ejpam-6633	265	21	γ(β	γ(β	PROPN
ejpam-6633	265	22	+	+	NUM
ejpam-6633	265	23	α	α	X
ejpam-6633	265	24	)	)	PUNCT
ejpam-6633	265	25	∫	∫	PROPN
ejpam-6633	266	1	t1	t1	NOUN
ejpam-6633	266	2	a	a	PRON
ejpam-6633	266	3	[	[	X
ejpam-6633	266	4	(	(	PUNCT
ejpam-6633	266	5	ln	ln	INTJ
ejpam-6633	266	6	(	(	PUNCT
ejpam-6633	266	7	t2	t2	PROPN
ejpam-6633	266	8	τ	τ	PROPN
ejpam-6633	266	9	)	)	PUNCT
ejpam-6633	266	10	)	)	PUNCT
ejpam-6633	267	1	β+α−1	β+α−1	NOUN
ejpam-6633	267	2	−	−	PROPN
ejpam-6633	267	3	(	(	PUNCT
ejpam-6633	267	4	ln	ln	NOUN
ejpam-6633	267	5	(	(	PUNCT
ejpam-6633	267	6	t1	t1	NOUN
ejpam-6633	267	7	τ	τ	PROPN
ejpam-6633	267	8	)	)	PUNCT
ejpam-6633	267	9	)	)	PUNCT
ejpam-6633	268	1	β+α−1	β+α−1	SYM
ejpam-6633	268	2	]	]	X
ejpam-6633	269	1	|θ(τ	|θ(τ	NOUN
ejpam-6633	269	2	,	,	PUNCT
ejpam-6633	269	3	η(τ))|	η(τ))|	X
ejpam-6633	269	4	τ	τ	X
ejpam-6633	269	5	dτ	dτ	NOUN
ejpam-6633	269	6	+	+	CCONJ
ejpam-6633	269	7	1	1	NUM
ejpam-6633	269	8	γ(β	γ(β	PROPN
ejpam-6633	269	9	+	+	NUM
ejpam-6633	269	10	α	α	X
ejpam-6633	269	11	)	)	PUNCT
ejpam-6633	269	12	∫	∫	PROPN
ejpam-6633	269	13	t2	t2	PROPN
ejpam-6633	269	14	t1	t1	PROPN
ejpam-6633	269	15	(	(	PUNCT
ejpam-6633	269	16	ln	ln	PROPN
ejpam-6633	269	17	(	(	PUNCT
ejpam-6633	269	18	t2	t2	PROPN
ejpam-6633	269	19	τ	τ	PROPN
ejpam-6633	269	20	)	)	PUNCT
ejpam-6633	269	21	)	)	PUNCT
ejpam-6633	270	1	β+α−1	β+α−1	PROPN
ejpam-6633	270	2	|θ(τ	|θ(τ	PROPN
ejpam-6633	270	3	,	,	PUNCT
ejpam-6633	270	4	η(τ))|	η(τ))|	X
ejpam-6633	270	5	τ	τ	X
ejpam-6633	270	6	dτ	dτ	NOUN
ejpam-6633	270	7	+	+	ADP
ejpam-6633	270	8	1	1	NUM
ejpam-6633	270	9	bγ(β	bγ(β	PUNCT
ejpam-6633	270	10	+	+	CCONJ
ejpam-6633	270	11	α	α	X
ejpam-6633	270	12	)	)	PUNCT
ejpam-6633	270	13	∣∣∣∣(ln	∣∣∣∣(ln	NOUN
ejpam-6633	270	14	(	(	PUNCT
ejpam-6633	270	15	t1a	t1a	NUM
ejpam-6633	270	16	)	)	PUNCT
ejpam-6633	270	17	)	)	PUNCT
ejpam-6633	271	1	α	α	PRON
ejpam-6633	271	2	−	−	PROPN
ejpam-6633	272	1	(	(	PUNCT
ejpam-6633	272	2	ln	ln	INTJ
ejpam-6633	272	3	(	(	PUNCT
ejpam-6633	272	4	t2	t2	PROPN
ejpam-6633	272	5	a	a	PRON
ejpam-6633	272	6	)	)	PUNCT
ejpam-6633	272	7	)	)	PUNCT
ejpam-6633	272	8	α∣∣∣∣	α∣∣∣∣	ADJ
ejpam-6633	272	9	∫	∫	NOUN
ejpam-6633	272	10	1	1	NUM
ejpam-6633	272	11	a	a	PRON
ejpam-6633	272	12	(	(	PUNCT
ejpam-6633	272	13	ln	ln	NOUN
ejpam-6633	272	14	(	(	PUNCT
ejpam-6633	272	15	1	1	NUM
ejpam-6633	272	16	τ	τ	PROPN
ejpam-6633	272	17	)	)	PUNCT
ejpam-6633	272	18	)	)	PUNCT
ejpam-6633	273	1	β+α−1	β+α−1	PROPN
ejpam-6633	274	1	|θ(τ	|θ(τ	PROPN
ejpam-6633	274	2	,	,	PUNCT
ejpam-6633	274	3	η(τ))|	η(τ))|	X
ejpam-6633	274	4	τ	τ	X
ejpam-6633	274	5	dτ	dτ	NOUN
ejpam-6633	274	6	.	.	PROPN
ejpam-6633	274	7	(	(	PUNCT
ejpam-6633	274	8	33	33	NUM
ejpam-6633	274	9	)	)	PUNCT
ejpam-6633	274	10	it	it	PRON
ejpam-6633	274	11	is	be	AUX
ejpam-6633	274	12	shown	show	VERB
ejpam-6633	274	13	in	in	ADP
ejpam-6633	274	14	(	(	PUNCT
ejpam-6633	274	15	33	33	NUM
ejpam-6633	274	16	)	)	PUNCT
ejpam-6633	274	17	that	that	SCONJ
ejpam-6633	274	18	as	as	SCONJ
ejpam-6633	274	19	|t2	|t2	ADP
ejpam-6633	274	20	−	−	PROPN
ejpam-6633	275	1	t1|	t1|	NOUN
ejpam-6633	275	2	−→	−→	NOUN
ejpam-6633	275	3	0	0	NUM
ejpam-6633	276	1	we	we	PRON
ejpam-6633	276	2	have	have	VERB
ejpam-6633	276	3	|ϕ2(η(t2))−	|ϕ2(η(t2))−	PROPN
ejpam-6633	276	4	ϕ1(η(t1))|	ϕ1(η(t1))|	NOUN
ejpam-6633	276	5	−→	−→	NOUN
ejpam-6633	276	6	0	0	NUM
ejpam-6633	276	7	.	.	PUNCT
ejpam-6633	277	1	hence	hence	ADV
ejpam-6633	277	2	ϕ	ϕ	PROPN
ejpam-6633	277	3	is	be	AUX
ejpam-6633	277	4	equicontinuous	equicontinuous	ADJ
ejpam-6633	277	5	.	.	PUNCT
ejpam-6633	278	1	since	since	SCONJ
ejpam-6633	278	2	ϕ	ϕ	PROPN
ejpam-6633	278	3	(	(	PUNCT
ejpam-6633	278	4	br	br	NOUN
ejpam-6633	278	5	)	)	PUNCT
ejpam-6633	278	6	⊂	⊂	PROPN
ejpam-6633	278	7	br	br	PROPN
ejpam-6633	278	8	,	,	PUNCT
ejpam-6633	278	9	then	then	ADV
ejpam-6633	278	10	,	,	PUNCT
ejpam-6633	278	11	ϕ2	ϕ2	ADV
ejpam-6633	278	12	is	be	AUX
ejpam-6633	278	13	uniformly	uniformly	ADV
ejpam-6633	278	14	bounded	bound	VERB
ejpam-6633	278	15	.	.	PUNCT
ejpam-6633	279	1	as	as	ADP
ejpam-6633	279	2	a	a	DET
ejpam-6633	279	3	consequence	consequence	NOUN
ejpam-6633	279	4	of	of	ADP
ejpam-6633	279	5	the	the	DET
ejpam-6633	279	6	arzelà-ascoli	arzelà-ascoli	PUNCT
ejpam-6633	279	7	theorem	theorem	PROPN
ejpam-6633	279	8	,	,	PUNCT
ejpam-6633	279	9	ϕ2	ϕ2	ADV
ejpam-6633	279	10	(	(	PUNCT
ejpam-6633	279	11	br	br	NOUN
ejpam-6633	279	12	)	)	PUNCT
ejpam-6633	279	13	is	be	AUX
ejpam-6633	279	14	compact	compact	ADJ
ejpam-6633	279	15	.	.	PUNCT
ejpam-6633	280	1	step	step	NOUN
ejpam-6633	280	2	3	3	NUM
ejpam-6633	280	3	:	:	PUNCT
ejpam-6633	280	4	for	for	ADP
ejpam-6633	280	5	this	this	DET
ejpam-6633	280	6	part	part	NOUN
ejpam-6633	280	7	,	,	PUNCT
ejpam-6633	280	8	we	we	PRON
ejpam-6633	280	9	have	have	VERB
ejpam-6633	280	10	to	to	PART
ejpam-6633	280	11	demonstrate	demonstrate	VERB
ejpam-6633	280	12	that	that	SCONJ
ejpam-6633	280	13	ϕ1	ϕ1	NOUN
ejpam-6633	280	14	is	be	AUX
ejpam-6633	280	15	k∗-contractive	k∗-contractive	ADJ
ejpam-6633	280	16	.	.	PUNCT
ejpam-6633	281	1	for	for	ADP
ejpam-6633	281	2	any	any	DET
ejpam-6633	281	3	η1	η1	NOUN
ejpam-6633	281	4	and	and	CCONJ
ejpam-6633	281	5	η2	η2	PROPN
ejpam-6633	281	6	in	in	ADP
ejpam-6633	281	7	br	br	PROPN
ejpam-6633	281	8	,	,	PUNCT
ejpam-6633	281	9	we	we	PRON
ejpam-6633	281	10	have	have	VERB
ejpam-6633	281	11	:	:	PUNCT
ejpam-6633	281	12	∥ϕ1	∥ϕ1	X
ejpam-6633	281	13	(	(	PUNCT
ejpam-6633	281	14	η1)−	η1)−	PROPN
ejpam-6633	281	15	ϕ1	ϕ1	NOUN
ejpam-6633	281	16	(	(	PUNCT
ejpam-6633	282	1	η2)∥	η2)∥	NOUN
ejpam-6633	282	2	≤	≤	PROPN
ejpam-6633	282	3	sup	sup	PROPN
ejpam-6633	282	4	t	t	PROPN
ejpam-6633	282	5	{	{	PUNCT
ejpam-6633	282	6	µ	µ	X
ejpam-6633	282	7	γ(α	γ(α	NOUN
ejpam-6633	282	8	)	)	PUNCT
ejpam-6633	282	9	∫	∫	PROPN
ejpam-6633	282	10	t	t	PROPN
ejpam-6633	282	11	a	a	X
ejpam-6633	282	12	(	(	PUNCT
ejpam-6633	282	13	ln	ln	X
ejpam-6633	282	14	(	(	PUNCT
ejpam-6633	282	15	t	t	PROPN
ejpam-6633	282	16	τ	τ	PROPN
ejpam-6633	282	17	)	)	PUNCT
ejpam-6633	282	18	)	)	PUNCT
ejpam-6633	283	1	α−1	α−1	PROPN
ejpam-6633	283	2	|η1(τ)−	|η1(τ)−	NOUN
ejpam-6633	283	3	η2(τ)|	η2(τ)|	PROPN
ejpam-6633	283	4	τ2	τ2	PROPN
ejpam-6633	283	5	dτ	dτ	PROPN
ejpam-6633	283	6	+	+	X
ejpam-6633	283	7	µ	µ	X
ejpam-6633	283	8	(	(	PUNCT
ejpam-6633	283	9	ln	ln	X
ejpam-6633	283	10	(	(	PUNCT
ejpam-6633	283	11	t	t	PROPN
ejpam-6633	283	12	a	a	PRON
ejpam-6633	283	13	)	)	PUNCT
ejpam-6633	283	14	)	)	PUNCT
ejpam-6633	283	15	α	α	PROPN
ejpam-6633	283	16	bγ(α	bγ(α	PROPN
ejpam-6633	283	17	)	)	PUNCT
ejpam-6633	283	18	∫	∫	PROPN
ejpam-6633	284	1	1	1	NUM
ejpam-6633	284	2	a	a	PRON
ejpam-6633	284	3	(	(	PUNCT
ejpam-6633	284	4	ln	ln	NOUN
ejpam-6633	284	5	(	(	PUNCT
ejpam-6633	284	6	1	1	NUM
ejpam-6633	284	7	τ	τ	PROPN
ejpam-6633	284	8	)	)	PUNCT
ejpam-6633	284	9	)	)	PUNCT
ejpam-6633	285	1	α−1	α−1	PROPN
ejpam-6633	285	2	|η1(τ)−	|η1(τ)−	NOUN
ejpam-6633	285	3	η2(τ)|	η2(τ)|	PROPN
ejpam-6633	285	4	τ2	τ2	PROPN
ejpam-6633	285	5	dτ	dτ	PROPN
ejpam-6633	285	6	}	}	PUNCT
ejpam-6633	285	7	,	,	PUNCT
ejpam-6633	285	8	t	t	PROPN
ejpam-6633	285	9	∈	∈	PROPN
ejpam-6633	286	1	[	[	X
ejpam-6633	286	2	a	a	X
ejpam-6633	286	3	,	,	PUNCT
ejpam-6633	286	4	1	1	NUM
ejpam-6633	286	5	]	]	PUNCT
ejpam-6633	286	6	.	.	PUNCT
ejpam-6633	287	1	≤	≤	NUM
ejpam-6633	287	2	µb	µb	ADP
ejpam-6633	287	3	aγ(α+	aγ(α+	NOUN
ejpam-6633	287	4	1	1	NUM
ejpam-6633	287	5	)	)	PUNCT
ejpam-6633	287	6	∥η1	∥η1	ADP
ejpam-6633	287	7	−	−	PROPN
ejpam-6633	287	8	η2∥+	η2∥+	PROPN
ejpam-6633	287	9	µ	µ	PRON
ejpam-6633	287	10	aγ(α+	aγ(α+	NOUN
ejpam-6633	287	11	1	1	NUM
ejpam-6633	287	12	)	)	PUNCT
ejpam-6633	287	13	∥η1	∥η1	ADP
ejpam-6633	287	14	−	−	PROPN
ejpam-6633	287	15	η2∥	η2∥	PROPN
ejpam-6633	287	16	=	=	PUNCT
ejpam-6633	287	17	k∗	k∗	NOUN
ejpam-6633	287	18	∥η1	∥η1	ADV
ejpam-6633	287	19	−	−	PROPN
ejpam-6633	288	1	η2∥	η2∥	PROPN
ejpam-6633	288	2	.	.	PUNCT
ejpam-6633	289	1	(	(	PUNCT
ejpam-6633	289	2	34	34	NUM
ejpam-6633	289	3	)	)	PUNCT
ejpam-6633	289	4	where	where	SCONJ
ejpam-6633	289	5	k∗	k∗	NOUN
ejpam-6633	289	6	=	=	SYM
ejpam-6633	289	7	µ(b+1	µ(b+1	PROPN
ejpam-6633	289	8	)	)	PUNCT
ejpam-6633	289	9	aγ(α+1	aγ(α+1	NOUN
ejpam-6633	289	10	)	)	PUNCT
ejpam-6633	289	11	.	.	PUNCT
ejpam-6633	290	1	step	step	NOUN
ejpam-6633	290	2	4	4	NUM
ejpam-6633	290	3	:	:	PUNCT
ejpam-6633	290	4	in	in	ADP
ejpam-6633	290	5	the	the	DET
ejpam-6633	290	6	last	last	ADJ
ejpam-6633	290	7	part	part	NOUN
ejpam-6633	290	8	,	,	PUNCT
ejpam-6633	290	9	we	we	PRON
ejpam-6633	290	10	need	need	VERB
ejpam-6633	290	11	to	to	PART
ejpam-6633	290	12	show	show	VERB
ejpam-6633	290	13	that	that	SCONJ
ejpam-6633	290	14	ϕ	ϕ	PROPN
ejpam-6633	290	15	is	be	AUX
ejpam-6633	290	16	condensing	condense	VERB
ejpam-6633	290	17	.	.	PUNCT
ejpam-6633	291	1	since	since	SCONJ
ejpam-6633	291	2	ϕ1	ϕ1	PROPN
ejpam-6633	291	3	is	be	AUX
ejpam-6633	291	4	continuous	continuous	ADJ
ejpam-6633	291	5	and	and	CCONJ
ejpam-6633	291	6	k∗-contractive	k∗-contractive	ADJ
ejpam-6633	291	7	,	,	PUNCT
ejpam-6633	291	8	and	and	CCONJ
ejpam-6633	291	9	we	we	PRON
ejpam-6633	291	10	found	find	VERB
ejpam-6633	291	11	that	that	SCONJ
ejpam-6633	291	12	ϕ2	ϕ2	ADV
ejpam-6633	291	13	is	be	AUX
ejpam-6633	291	14	compact	compact	ADJ
ejpam-6633	291	15	,	,	PUNCT
ejpam-6633	291	16	therefore	therefore	ADV
ejpam-6633	291	17	,	,	PUNCT
ejpam-6633	291	18	by	by	ADP
ejpam-6633	291	19	theorem	theorem	NOUN
ejpam-6633	291	20	1	1	NUM
ejpam-6633	291	21	,	,	PUNCT
ejpam-6633	291	22	we	we	PRON
ejpam-6633	291	23	observe	observe	VERB
ejpam-6633	291	24	that	that	SCONJ
ejpam-6633	291	25	ϕ	ϕ	NOUN
ejpam-6633	291	26	=	=	X
ejpam-6633	291	27	ϕ1	ϕ1	NOUN
ejpam-6633	291	28	+	+	CCONJ
ejpam-6633	291	29	ϕ2	ϕ2	ADV
ejpam-6633	291	30	is	be	AUX
ejpam-6633	291	31	a	a	DET
ejpam-6633	291	32	condensing	condense	VERB
ejpam-6633	291	33	map	map	NOUN
ejpam-6633	291	34	on	on	ADP
ejpam-6633	291	35	br	br	PROPN
ejpam-6633	291	36	.	.	PUNCT
ejpam-6633	292	1	from	from	ADP
ejpam-6633	292	2	the	the	DET
ejpam-6633	292	3	above	above	ADJ
ejpam-6633	292	4	four	four	NUM
ejpam-6633	292	5	steps	step	NOUN
ejpam-6633	292	6	and	and	CCONJ
ejpam-6633	292	7	by	by	ADP
ejpam-6633	292	8	the	the	DET
ejpam-6633	292	9	sadovski	sadovski	PROPN
ejpam-6633	292	10	theorem	theorem	NOUN
ejpam-6633	292	11	2	2	NUM
ejpam-6633	292	12	,	,	PUNCT
ejpam-6633	292	13	we	we	PRON
ejpam-6633	292	14	arrive	arrive	VERB
ejpam-6633	292	15	at	at	ADP
ejpam-6633	292	16	the	the	DET
ejpam-6633	292	17	conclusion	conclusion	NOUN
ejpam-6633	292	18	that	that	SCONJ
ejpam-6633	292	19	the	the	DET
ejpam-6633	292	20	map	map	NOUN
ejpam-6633	292	21	ϕ	ϕ	NOUN
ejpam-6633	292	22	has	have	AUX
ejpam-6633	292	23	a	a	DET
ejpam-6633	292	24	fixed	fix	VERB
ejpam-6633	292	25	point	point	NOUN
ejpam-6633	292	26	.	.	PUNCT
ejpam-6633	293	1	4	4	X
ejpam-6633	293	2	.	.	X
ejpam-6633	293	3	stability	stability	NOUN
ejpam-6633	293	4	this	this	DET
ejpam-6633	293	5	section	section	NOUN
ejpam-6633	293	6	examines	examine	VERB
ejpam-6633	293	7	the	the	DET
ejpam-6633	293	8	stability	stability	NOUN
ejpam-6633	293	9	of	of	ADP
ejpam-6633	293	10	the	the	DET
ejpam-6633	293	11	boundary	boundary	ADJ
ejpam-6633	293	12	-	-	PUNCT
ejpam-6633	293	13	value	value	NOUN
ejpam-6633	293	14	problem	problem	NOUN
ejpam-6633	293	15	(	(	PUNCT
ejpam-6633	293	16	6	6	NUM
ejpam-6633	293	17	-	-	PUNCT
ejpam-6633	293	18	8)	8)	NUM
ejpam-6633	293	19	utilising	utilise	VERB
ejpam-6633	293	20	two	two	NUM
ejpam-6633	293	21	established	establish	VERB
ejpam-6633	293	22	definitions	definition	NOUN
ejpam-6633	293	23	of	of	ADP
ejpam-6633	293	24	stability	stability	NOUN
ejpam-6633	293	25	:	:	PUNCT
ejpam-6633	293	26	ulam	ulam	ADJ
ejpam-6633	293	27	-	-	PUNCT
ejpam-6633	293	28	heyrs	heyr	NOUN
ejpam-6633	293	29	stability	stability	NOUN
ejpam-6633	293	30	and	and	CCONJ
ejpam-6633	293	31	ulam	ulam	NOUN
ejpam-6633	293	32	-	-	PUNCT
ejpam-6633	293	33	heyrs	heyr	NOUN
ejpam-6633	293	34	-	-	PUNCT
ejpam-6633	293	35	rassias	rassias	PROPN
ejpam-6633	293	36	stability	stability	NOUN
ejpam-6633	293	37	.	.	PUNCT
ejpam-6633	294	1	theorem	theorem	ADJ
ejpam-6633	294	2	4	4	NUM
ejpam-6633	294	3	.	.	PUNCT
ejpam-6633	294	4	assume	assume	VERB
ejpam-6633	294	5	that	that	SCONJ
ejpam-6633	294	6	θ	θ	NOUN
ejpam-6633	294	7	:	:	PUNCT
ejpam-6633	295	1	[	[	X
ejpam-6633	295	2	a	a	X
ejpam-6633	295	3	,	,	PUNCT
ejpam-6633	295	4	1]×r	1]×r	NUM
ejpam-6633	295	5	−→	−→	NOUN
ejpam-6633	295	6	r	r	NOUN
ejpam-6633	295	7	is	be	AUX
ejpam-6633	295	8	a	a	DET
ejpam-6633	295	9	continuous	continuous	ADJ
ejpam-6633	295	10	function	function	NOUN
ejpam-6633	295	11	and	and	CCONJ
ejpam-6633	295	12	the	the	DET
ejpam-6633	295	13	assumption	assumption	NOUN
ejpam-6633	295	14	h2	h2	NOUN
ejpam-6633	295	15	holds	hold	VERB
ejpam-6633	295	16	.	.	PUNCT
ejpam-6633	296	1	then	then	ADV
ejpam-6633	296	2	,	,	PUNCT
ejpam-6633	296	3	the	the	DET
ejpam-6633	296	4	solution	solution	NOUN
ejpam-6633	296	5	of	of	ADP
ejpam-6633	296	6	the	the	DET
ejpam-6633	296	7	boundary	boundary	ADJ
ejpam-6633	296	8	-	-	PUNCT
ejpam-6633	296	9	value	value	NOUN
ejpam-6633	296	10	problem	problem	NOUN
ejpam-6633	296	11	(	(	PUNCT
ejpam-6633	296	12	6	6	NUM
ejpam-6633	296	13	-	-	SYM
ejpam-6633	296	14	8)	8)	NUM
ejpam-6633	296	15	is	be	AUX
ejpam-6633	296	16	ulam	ulam	NOUN
ejpam-6633	296	17	-	-	PUNCT
ejpam-6633	296	18	hyers	hyer	NOUN
ejpam-6633	296	19	stable	stable	ADJ
ejpam-6633	296	20	.	.	PUNCT
ejpam-6633	297	1	proof	proof	NOUN
ejpam-6633	297	2	:	:	PUNCT
ejpam-6633	297	3	let	let	VERB
ejpam-6633	297	4	η(t	η(t	NOUN
ejpam-6633	297	5	)	)	PUNCT
ejpam-6633	297	6	∈	∈	PROPN
ejpam-6633	297	7	c([a	c([a	PROPN
ejpam-6633	297	8	,	,	PUNCT
ejpam-6633	297	9	1],r	1],r	NUM
ejpam-6633	297	10	)	)	PUNCT
ejpam-6633	297	11	be	be	VERB
ejpam-6633	297	12	a	a	DET
ejpam-6633	297	13	solution	solution	NOUN
ejpam-6633	297	14	of	of	ADP
ejpam-6633	297	15	the	the	DET
ejpam-6633	297	16	inequality	inequality	NOUN
ejpam-6633	297	17	(	(	PUNCT
ejpam-6633	297	18	14	14	NUM
ejpam-6633	297	19	)	)	PUNCT
ejpam-6633	297	20	which	which	PRON
ejpam-6633	297	21	satisfies	satisfy	VERB
ejpam-6633	297	22	boundary	boundary	ADJ
ejpam-6633	297	23	conditions	condition	NOUN
ejpam-6633	297	24	(	(	PUNCT
ejpam-6633	297	25	7	7	NUM
ejpam-6633	297	26	-	-	SYM
ejpam-6633	297	27	8)	8)	NUM
ejpam-6633	297	28	.	.	PUNCT
ejpam-6633	298	1	through	through	ADP
ejpam-6633	298	2	remark	remark	NOUN
ejpam-6633	298	3	1	1	NUM
ejpam-6633	298	4	,	,	PUNCT
ejpam-6633	298	5	we	we	PRON
ejpam-6633	298	6	have	have	VERB
ejpam-6633	298	7	chd	chd	NOUN
ejpam-6633	298	8	β	β	PROPN
ejpam-6633	298	9	(	(	PUNCT
ejpam-6633	298	10	dα	dα	PROPN
ejpam-6633	298	11	+	+	CCONJ
ejpam-6633	298	12	µ	µ	X
ejpam-6633	298	13	t	t	NOUN
ejpam-6633	298	14	)	)	PUNCT
ejpam-6633	298	15	η(t	η(t	NOUN
ejpam-6633	298	16	)	)	PUNCT
ejpam-6633	298	17	=	=	SYM
ejpam-6633	298	18	θ(t	θ(t	PROPN
ejpam-6633	298	19	,	,	PUNCT
ejpam-6633	298	20	η(t	η(t	NOUN
ejpam-6633	298	21	)	)	PUNCT
ejpam-6633	298	22	)	)	PUNCT
ejpam-6633	299	1	+	+	CCONJ
ejpam-6633	299	2	g(t	g(t	PROPN
ejpam-6633	299	3	)	)	PUNCT
ejpam-6633	299	4	,	,	PUNCT
ejpam-6633	299	5	(	(	PUNCT
ejpam-6633	299	6	35	35	NUM
ejpam-6633	299	7	)	)	PUNCT
ejpam-6633	299	8	a.	a.	NOUN
ejpam-6633	299	9	s.	s.	PROPN
ejpam-6633	299	10	hasan	hasan	PROPN
ejpam-6633	299	11	,	,	PUNCT
ejpam-6633	299	12	s.	s.	PROPN
ejpam-6633	299	13	a.	a.	PROPN
ejpam-6633	299	14	murad	murad	PROPN
ejpam-6633	299	15	/	/	SYM
ejpam-6633	299	16	eur	eur	PROPN
ejpam-6633	299	17	.	.	PUNCT
ejpam-6633	300	1	j.	j.	PROPN
ejpam-6633	300	2	pure	pure	PROPN
ejpam-6633	300	3	appl	appl	PROPN
ejpam-6633	300	4	.	.	PROPN
ejpam-6633	300	5	math	math	PROPN
ejpam-6633	300	6	,	,	PUNCT
ejpam-6633	300	7	18	18	NUM
ejpam-6633	300	8	(	(	PUNCT
ejpam-6633	300	9	3	3	NUM
ejpam-6633	300	10	)	)	PUNCT
ejpam-6633	300	11	(	(	PUNCT
ejpam-6633	300	12	2025	2025	NUM
ejpam-6633	300	13	)	)	PUNCT
ejpam-6633	300	14	,	,	PUNCT
ejpam-6633	300	15	6633	6633	NUM
ejpam-6633	300	16	11	11	NUM
ejpam-6633	300	17	of	of	ADP
ejpam-6633	300	18	24	24	NUM
ejpam-6633	300	19	where	where	SCONJ
ejpam-6633	300	20	g(t	g(t	PROPN
ejpam-6633	300	21	)	)	PUNCT
ejpam-6633	300	22	possesses	possess	VERB
ejpam-6633	300	23	the	the	DET
ejpam-6633	300	24	same	same	ADJ
ejpam-6633	300	25	property	property	NOUN
ejpam-6633	300	26	mentioned	mention	VERB
ejpam-6633	300	27	in	in	ADP
ejpam-6633	300	28	remark	remark	NOUN
ejpam-6633	300	29	1	1	NUM
ejpam-6633	300	30	.	.	PUNCT
ejpam-6633	301	1	the	the	DET
ejpam-6633	301	2	solution	solution	NOUN
ejpam-6633	301	3	of	of	ADP
ejpam-6633	301	4	the	the	DET
ejpam-6633	301	5	perturbed	perturb	VERB
ejpam-6633	301	6	problem	problem	NOUN
ejpam-6633	301	7	(	(	PUNCT
ejpam-6633	301	8	35	35	NUM
ejpam-6633	301	9	)	)	PUNCT
ejpam-6633	301	10	supplemented	supplement	VERB
ejpam-6633	301	11	with	with	ADP
ejpam-6633	301	12	(	(	PUNCT
ejpam-6633	301	13	7	7	NUM
ejpam-6633	301	14	-	-	SYM
ejpam-6633	301	15	8)	8)	NUM
ejpam-6633	301	16	can	can	AUX
ejpam-6633	301	17	be	be	AUX
ejpam-6633	301	18	found	find	VERB
ejpam-6633	301	19	to	to	PART
ejpam-6633	301	20	be	be	AUX
ejpam-6633	301	21	:	:	PUNCT
ejpam-6633	301	22	η(t	η(t	NOUN
ejpam-6633	301	23	)	)	PUNCT
ejpam-6633	301	24	=	=	SYM
ejpam-6633	302	1	1	1	NUM
ejpam-6633	302	2	γ(β	γ(β	PROPN
ejpam-6633	302	3	+	+	NUM
ejpam-6633	302	4	α	α	X
ejpam-6633	302	5	)	)	PUNCT
ejpam-6633	302	6	∫	∫	PROPN
ejpam-6633	302	7	t	t	PROPN
ejpam-6633	302	8	a	a	X
ejpam-6633	302	9	(	(	PUNCT
ejpam-6633	302	10	ln	ln	X
ejpam-6633	302	11	(	(	PUNCT
ejpam-6633	302	12	t	t	PROPN
ejpam-6633	302	13	τ	τ	PROPN
ejpam-6633	302	14	)	)	PUNCT
ejpam-6633	302	15	)	)	PUNCT
ejpam-6633	303	1	β+α−1	β+α−1	PUNCT
ejpam-6633	304	1	θ(τ	θ(τ	PROPN
ejpam-6633	304	2	,	,	PUNCT
ejpam-6633	304	3	η(τ	η(τ	PROPN
ejpam-6633	304	4	)	)	PUNCT
ejpam-6633	304	5	)	)	PUNCT
ejpam-6633	305	1	τ	τ	PROPN
ejpam-6633	305	2	dτ	dτ	NOUN
ejpam-6633	305	3	−	−	PROPN
ejpam-6633	305	4	µ	µ	PROPN
ejpam-6633	305	5	γ(α	γ(α	NOUN
ejpam-6633	305	6	)	)	PUNCT
ejpam-6633	306	1	∫	∫	PROPN
ejpam-6633	306	2	t	t	PROPN
ejpam-6633	306	3	a	a	X
ejpam-6633	306	4	(	(	PUNCT
ejpam-6633	306	5	ln	ln	X
ejpam-6633	306	6	(	(	PUNCT
ejpam-6633	306	7	t	t	PROPN
ejpam-6633	306	8	τ	τ	PROPN
ejpam-6633	306	9	)	)	PUNCT
ejpam-6633	306	10	)	)	PUNCT
ejpam-6633	306	11	α−1	α−1	PROPN
ejpam-6633	306	12	η(τ	η(τ	PROPN
ejpam-6633	306	13	)	)	PUNCT
ejpam-6633	306	14	τ2	τ2	NOUN
ejpam-6633	306	15	dτ	dτ	NOUN
ejpam-6633	306	16	+	+	CCONJ
ejpam-6633	306	17	1	1	NUM
ejpam-6633	306	18	γ(β	γ(β	PROPN
ejpam-6633	306	19	+	+	NUM
ejpam-6633	306	20	α	α	X
ejpam-6633	306	21	)	)	PUNCT
ejpam-6633	306	22	∫	∫	PROPN
ejpam-6633	306	23	t	t	PROPN
ejpam-6633	306	24	a	a	X
ejpam-6633	306	25	(	(	PUNCT
ejpam-6633	306	26	ln	ln	X
ejpam-6633	306	27	(	(	PUNCT
ejpam-6633	306	28	t	t	PROPN
ejpam-6633	306	29	τ	τ	PROPN
ejpam-6633	306	30	)	)	PUNCT
ejpam-6633	306	31	)	)	PUNCT
ejpam-6633	306	32	β+α−1	β+α−1	NOUN
ejpam-6633	306	33	g(τ	g(τ	PROPN
ejpam-6633	306	34	)	)	PUNCT
ejpam-6633	306	35	τ	τ	PROPN
ejpam-6633	306	36	dτ	dτ	NOUN
ejpam-6633	306	37	−	−	PROPN
ejpam-6633	307	1	(	(	PUNCT
ejpam-6633	307	2	ln	ln	X
ejpam-6633	307	3	(	(	PUNCT
ejpam-6633	307	4	t	t	PROPN
ejpam-6633	307	5	a	a	PRON
ejpam-6633	307	6	)	)	PUNCT
ejpam-6633	307	7	)	)	PUNCT
ejpam-6633	308	1	α	α	NOUN
ejpam-6633	308	2	bγ(β	bγ(β	X
ejpam-6633	308	3	+	+	X
ejpam-6633	308	4	α	α	X
ejpam-6633	308	5	)	)	PUNCT
ejpam-6633	308	6	∫	∫	PROPN
ejpam-6633	308	7	1	1	NUM
ejpam-6633	308	8	a	a	PRON
ejpam-6633	308	9	(	(	PUNCT
ejpam-6633	308	10	ln	ln	NOUN
ejpam-6633	308	11	(	(	PUNCT
ejpam-6633	308	12	1	1	NUM
ejpam-6633	308	13	τ	τ	PROPN
ejpam-6633	308	14	)	)	PUNCT
ejpam-6633	308	15	)	)	PUNCT
ejpam-6633	308	16	β+α−1	β+α−1	PROPN
ejpam-6633	309	1	θ(τ	θ(τ	PROPN
ejpam-6633	309	2	,	,	PUNCT
ejpam-6633	309	3	η(τ	η(τ	PROPN
ejpam-6633	309	4	)	)	PUNCT
ejpam-6633	309	5	)	)	PUNCT
ejpam-6633	310	1	τ	τ	PROPN
ejpam-6633	310	2	dτ	dτ	PROPN
ejpam-6633	311	1	+	+	X
ejpam-6633	311	2	µ	µ	X
ejpam-6633	311	3	(	(	PUNCT
ejpam-6633	311	4	ln	ln	X
ejpam-6633	311	5	(	(	PUNCT
ejpam-6633	311	6	t	t	PROPN
ejpam-6633	311	7	a	a	PRON
ejpam-6633	311	8	)	)	PUNCT
ejpam-6633	311	9	)	)	PUNCT
ejpam-6633	311	10	α	α	PROPN
ejpam-6633	311	11	bγ(α	bγ(α	PROPN
ejpam-6633	311	12	)	)	PUNCT
ejpam-6633	311	13	∫	∫	PROPN
ejpam-6633	312	1	1	1	NUM
ejpam-6633	312	2	a	a	DET
ejpam-6633	312	3	(	(	PUNCT
ejpam-6633	312	4	ln	ln	NOUN
ejpam-6633	312	5	(	(	PUNCT
ejpam-6633	312	6	1	1	NUM
ejpam-6633	312	7	τ	τ	PROPN
ejpam-6633	312	8	)	)	PUNCT
ejpam-6633	312	9	)	)	PUNCT
ejpam-6633	312	10	α−1	α−1	PROPN
ejpam-6633	312	11	η(τ	η(τ	PROPN
ejpam-6633	312	12	)	)	PUNCT
ejpam-6633	312	13	τ2	τ2	PROPN
ejpam-6633	312	14	dτ	dτ	NOUN
ejpam-6633	312	15	−	−	PROPN
ejpam-6633	313	1	(	(	PUNCT
ejpam-6633	313	2	ln	ln	X
ejpam-6633	313	3	(	(	PUNCT
ejpam-6633	313	4	t	t	PROPN
ejpam-6633	313	5	a	a	PRON
ejpam-6633	313	6	)	)	PUNCT
ejpam-6633	313	7	)	)	PUNCT
ejpam-6633	314	1	α	α	NOUN
ejpam-6633	314	2	bγ(β	bγ(β	X
ejpam-6633	314	3	+	+	X
ejpam-6633	314	4	α	α	X
ejpam-6633	314	5	)	)	PUNCT
ejpam-6633	314	6	∫	∫	PROPN
ejpam-6633	314	7	1	1	NUM
ejpam-6633	314	8	a	a	PRON
ejpam-6633	314	9	(	(	PUNCT
ejpam-6633	314	10	ln	ln	NOUN
ejpam-6633	314	11	(	(	PUNCT
ejpam-6633	314	12	1	1	NUM
ejpam-6633	314	13	τ	τ	PROPN
ejpam-6633	314	14	)	)	PUNCT
ejpam-6633	314	15	)	)	PUNCT
ejpam-6633	314	16	β+α−1	β+α−1	NOUN
ejpam-6633	315	1	g(τ	g(τ	PROPN
ejpam-6633	315	2	)	)	PUNCT
ejpam-6633	315	3	τ	τ	PROPN
ejpam-6633	315	4	dτ	dτ	PROPN
ejpam-6633	315	5	+	+	PROPN
ejpam-6633	315	6	φ(t	φ(t	PROPN
ejpam-6633	315	7	)	)	PUNCT
ejpam-6633	315	8	,	,	PUNCT
ejpam-6633	315	9	(	(	PUNCT
ejpam-6633	315	10	36	36	NUM
ejpam-6633	315	11	)	)	PUNCT
ejpam-6633	315	12	where	where	SCONJ
ejpam-6633	315	13	(	(	PUNCT
ejpam-6633	315	14	36	36	NUM
ejpam-6633	315	15	)	)	PUNCT
ejpam-6633	315	16	satisfies	satisfy	VERB
ejpam-6633	315	17	the	the	DET
ejpam-6633	315	18	following	follow	VERB
ejpam-6633	315	19	inequality:∣∣∣∣∣η(t)−	inequality:∣∣∣∣∣η(t)−	PROPN
ejpam-6633	315	20	1	1	NUM
ejpam-6633	316	1	γ(β	γ(β	PROPN
ejpam-6633	316	2	+	+	NUM
ejpam-6633	316	3	α	α	X
ejpam-6633	316	4	)	)	PUNCT
ejpam-6633	316	5	∫	∫	PROPN
ejpam-6633	316	6	t	t	PROPN
ejpam-6633	316	7	a	a	X
ejpam-6633	316	8	(	(	PUNCT
ejpam-6633	316	9	ln	ln	X
ejpam-6633	316	10	(	(	PUNCT
ejpam-6633	316	11	t	t	PROPN
ejpam-6633	316	12	τ	τ	PROPN
ejpam-6633	316	13	)	)	PUNCT
ejpam-6633	316	14	)	)	PUNCT
ejpam-6633	317	1	β+α−1	β+α−1	PUNCT
ejpam-6633	318	1	θ(τ	θ(τ	PROPN
ejpam-6633	318	2	,	,	PUNCT
ejpam-6633	318	3	η(τ	η(τ	PROPN
ejpam-6633	318	4	)	)	PUNCT
ejpam-6633	318	5	)	)	PUNCT
ejpam-6633	319	1	τ	τ	PROPN
ejpam-6633	319	2	dτ	dτ	NOUN
ejpam-6633	319	3	+	+	PROPN
ejpam-6633	319	4	µ	µ	X
ejpam-6633	319	5	γ(α	γ(α	NOUN
ejpam-6633	319	6	)	)	PUNCT
ejpam-6633	320	1	∫	∫	PROPN
ejpam-6633	320	2	t	t	PROPN
ejpam-6633	320	3	a	a	X
ejpam-6633	320	4	(	(	PUNCT
ejpam-6633	320	5	ln	ln	X
ejpam-6633	320	6	(	(	PUNCT
ejpam-6633	320	7	t	t	PROPN
ejpam-6633	320	8	τ	τ	PROPN
ejpam-6633	320	9	)	)	PUNCT
ejpam-6633	320	10	)	)	PUNCT
ejpam-6633	320	11	α−1	α−1	PROPN
ejpam-6633	320	12	η(τ	η(τ	PROPN
ejpam-6633	320	13	)	)	PUNCT
ejpam-6633	320	14	τ2	τ2	NOUN
ejpam-6633	320	15	dτ	dτ	NOUN
ejpam-6633	320	16	+	+	CCONJ
ejpam-6633	320	17	(	(	PUNCT
ejpam-6633	320	18	ln	ln	INTJ
ejpam-6633	320	19	(	(	PUNCT
ejpam-6633	320	20	t	t	PROPN
ejpam-6633	320	21	a	a	PRON
ejpam-6633	320	22	)	)	PUNCT
ejpam-6633	320	23	)	)	PUNCT
ejpam-6633	320	24	α	α	NOUN
ejpam-6633	320	25	bγ(β	bγ(β	X
ejpam-6633	320	26	+	+	X
ejpam-6633	320	27	α	α	X
ejpam-6633	320	28	)	)	PUNCT
ejpam-6633	320	29	∫	∫	PROPN
ejpam-6633	320	30	1	1	NUM
ejpam-6633	321	1	a	a	PRON
ejpam-6633	321	2	(	(	PUNCT
ejpam-6633	321	3	ln	ln	NOUN
ejpam-6633	321	4	(	(	PUNCT
ejpam-6633	321	5	1	1	NUM
ejpam-6633	321	6	τ	τ	PROPN
ejpam-6633	321	7	)	)	PUNCT
ejpam-6633	321	8	)	)	PUNCT
ejpam-6633	321	9	β+α−1	β+α−1	PROPN
ejpam-6633	322	1	θ(τ	θ(τ	PROPN
ejpam-6633	322	2	,	,	PUNCT
ejpam-6633	322	3	η(τ	η(τ	PROPN
ejpam-6633	322	4	)	)	PUNCT
ejpam-6633	322	5	)	)	PUNCT
ejpam-6633	323	1	τ	τ	PROPN
ejpam-6633	323	2	dτ	dτ	NOUN
ejpam-6633	323	3	−	−	PROPN
ejpam-6633	323	4	µ	µ	X
ejpam-6633	323	5	(	(	PUNCT
ejpam-6633	323	6	ln	ln	X
ejpam-6633	323	7	(	(	PUNCT
ejpam-6633	323	8	t	t	PROPN
ejpam-6633	323	9	a	a	PRON
ejpam-6633	323	10	)	)	PUNCT
ejpam-6633	323	11	)	)	PUNCT
ejpam-6633	323	12	α	α	PROPN
ejpam-6633	323	13	bγ(α	bγ(α	PROPN
ejpam-6633	323	14	)	)	PUNCT
ejpam-6633	323	15	∫	∫	PROPN
ejpam-6633	324	1	1	1	NUM
ejpam-6633	324	2	a	a	PRON
ejpam-6633	324	3	(	(	PUNCT
ejpam-6633	324	4	ln	ln	NOUN
ejpam-6633	324	5	(	(	PUNCT
ejpam-6633	324	6	1	1	NUM
ejpam-6633	324	7	τ	τ	PROPN
ejpam-6633	324	8	)	)	PUNCT
ejpam-6633	324	9	)	)	PUNCT
ejpam-6633	324	10	α−1	α−1	PROPN
ejpam-6633	324	11	η(τ	η(τ	PROPN
ejpam-6633	324	12	)	)	PUNCT
ejpam-6633	324	13	τ2	τ2	PROPN
ejpam-6633	324	14	dτ	dτ	NOUN
ejpam-6633	324	15	−	−	PROPN
ejpam-6633	324	16	φ(t	φ(t	PROPN
ejpam-6633	324	17	)	)	PUNCT
ejpam-6633	325	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-6633	325	2	≤	≤	ADV
ejpam-6633	325	3	2	2	NUM
ejpam-6633	325	4	ϵ	ϵ	PART
ejpam-6633	325	5	b	b	PROPN
ejpam-6633	325	6	(	(	PUNCT
ejpam-6633	325	7	ln	ln	X
ejpam-6633	325	8	(	(	PUNCT
ejpam-6633	325	9	1	1	NUM
ejpam-6633	325	10	a	a	NOUN
ejpam-6633	325	11	)	)	PUNCT
ejpam-6633	325	12	)	)	PUNCT
ejpam-6633	325	13	β	β	PROPN
ejpam-6633	325	14	γ(β	γ(β	PROPN
ejpam-6633	326	1	+	+	PUNCT
ejpam-6633	326	2	α+	α+	PUNCT
ejpam-6633	326	3	1	1	NUM
ejpam-6633	326	4	)	)	PUNCT
ejpam-6633	326	5	,	,	PUNCT
ejpam-6633	326	6	(	(	PUNCT
ejpam-6633	326	7	37	37	NUM
ejpam-6633	326	8	)	)	PUNCT
ejpam-6633	326	9	for	for	ADP
ejpam-6633	326	10	all	all	DET
ejpam-6633	326	11	t	t	NOUN
ejpam-6633	326	12	∈	∈	PROPN
ejpam-6633	327	1	[	[	X
ejpam-6633	327	2	a	a	X
ejpam-6633	327	3	,	,	PUNCT
ejpam-6633	327	4	1	1	NUM
ejpam-6633	327	5	]	]	PUNCT
ejpam-6633	327	6	.	.	PUNCT
ejpam-6633	328	1	let	let	VERB
ejpam-6633	328	2	z(t	z(t	NOUN
ejpam-6633	328	3	)	)	PUNCT
ejpam-6633	328	4	be	be	AUX
ejpam-6633	328	5	the	the	DET
ejpam-6633	328	6	unique	unique	ADJ
ejpam-6633	328	7	solution	solution	NOUN
ejpam-6633	328	8	for	for	ADP
ejpam-6633	328	9	our	our	PRON
ejpam-6633	328	10	boundary	boundary	ADJ
ejpam-6633	328	11	-	-	PUNCT
ejpam-6633	328	12	value	value	NOUN
ejpam-6633	328	13	problem	problem	NOUN
ejpam-6633	328	14	(	(	PUNCT
ejpam-6633	328	15	6	6	NUM
ejpam-6633	328	16	-	-	SYM
ejpam-6633	328	17	8)	8)	NUM
ejpam-6633	328	18	.	.	PUNCT
ejpam-6633	329	1	the	the	DET
ejpam-6633	329	2	left	left	ADJ
ejpam-6633	329	3	side	side	NOUN
ejpam-6633	329	4	of	of	ADP
ejpam-6633	329	5	inequality	inequality	NOUN
ejpam-6633	329	6	(	(	PUNCT
ejpam-6633	329	7	15	15	NUM
ejpam-6633	329	8	)	)	PUNCT
ejpam-6633	329	9	conforms	conform	VERB
ejpam-6633	329	10	to	to	ADP
ejpam-6633	329	11	|η(t)−	|η(t)−	PROPN
ejpam-6633	329	12	z(t)|	z(t)|	PROPN
ejpam-6633	329	13	≤	≤	ADV
ejpam-6633	329	14	2	2	NUM
ejpam-6633	329	15	ϵ	ϵ	NOUN
ejpam-6633	329	16	(	(	PUNCT
ejpam-6633	329	17	ln	ln	X
ejpam-6633	329	18	(	(	PUNCT
ejpam-6633	329	19	1	1	NUM
ejpam-6633	329	20	a	a	NOUN
ejpam-6633	329	21	)	)	PUNCT
ejpam-6633	329	22	)	)	PUNCT
ejpam-6633	329	23	β+α	β+α	PUNCT
ejpam-6633	330	1	γ(β	γ(β	X
ejpam-6633	330	2	+	+	CCONJ
ejpam-6633	330	3	α+	α+	PUNCT
ejpam-6633	330	4	1	1	NUM
ejpam-6633	330	5	)	)	PUNCT
ejpam-6633	330	6	+	+	CCONJ
ejpam-6633	330	7	1	1	NUM
ejpam-6633	330	8	γ(β	γ(β	PROPN
ejpam-6633	330	9	+	+	NUM
ejpam-6633	330	10	α	α	X
ejpam-6633	330	11	)	)	PUNCT
ejpam-6633	330	12	∫	∫	PROPN
ejpam-6633	330	13	t	t	PROPN
ejpam-6633	331	1	a	a	X
ejpam-6633	331	2	(	(	PUNCT
ejpam-6633	331	3	ln	ln	X
ejpam-6633	331	4	(	(	PUNCT
ejpam-6633	331	5	t	t	PROPN
ejpam-6633	331	6	τ	τ	PROPN
ejpam-6633	331	7	)	)	PUNCT
ejpam-6633	331	8	)	)	PUNCT
ejpam-6633	331	9	β+α−1	β+α−1	PROPN
ejpam-6633	332	1	|θ(τ	|θ(τ	PROPN
ejpam-6633	332	2	,	,	PUNCT
ejpam-6633	332	3	η(τ))−	η(τ))−	VERB
ejpam-6633	332	4	θ(τ	θ(τ	PROPN
ejpam-6633	332	5	,	,	PUNCT
ejpam-6633	332	6	z(τ))|	z(τ))|	PROPN
ejpam-6633	332	7	dτ	dτ	X
ejpam-6633	332	8	τ	τ	PROPN
ejpam-6633	332	9	+	+	PROPN
ejpam-6633	332	10	µ	µ	X
ejpam-6633	332	11	γ(α	γ(α	NOUN
ejpam-6633	332	12	)	)	PUNCT
ejpam-6633	332	13	∫	∫	PROPN
ejpam-6633	333	1	t	t	PROPN
ejpam-6633	333	2	a	a	X
ejpam-6633	333	3	(	(	PUNCT
ejpam-6633	333	4	ln	ln	X
ejpam-6633	333	5	(	(	PUNCT
ejpam-6633	333	6	t	t	PROPN
ejpam-6633	333	7	τ	τ	PROPN
ejpam-6633	333	8	)	)	PUNCT
ejpam-6633	333	9	)	)	PUNCT
ejpam-6633	334	1	α−1	α−1	PROPN
ejpam-6633	334	2	|η(τ)−	|η(τ)−	NOUN
ejpam-6633	334	3	z(τ)|	z(τ)|	PROPN
ejpam-6633	334	4	dτ	dτ	NOUN
ejpam-6633	335	1	τ2	τ2	NOUN
ejpam-6633	335	2	+	+	CCONJ
ejpam-6633	335	3	(	(	PUNCT
ejpam-6633	335	4	ln	ln	X
ejpam-6633	335	5	(	(	PUNCT
ejpam-6633	335	6	t	t	PROPN
ejpam-6633	335	7	a	a	PRON
ejpam-6633	335	8	)	)	PUNCT
ejpam-6633	335	9	)	)	PUNCT
ejpam-6633	335	10	α	α	NOUN
ejpam-6633	335	11	bγ(β	bγ(β	X
ejpam-6633	335	12	+	+	X
ejpam-6633	335	13	α	α	X
ejpam-6633	335	14	)	)	PUNCT
ejpam-6633	335	15	∫	∫	PROPN
ejpam-6633	336	1	1	1	NUM
ejpam-6633	336	2	a	a	PRON
ejpam-6633	336	3	(	(	PUNCT
ejpam-6633	336	4	ln	ln	NOUN
ejpam-6633	336	5	(	(	PUNCT
ejpam-6633	336	6	1	1	NUM
ejpam-6633	336	7	τ	τ	PROPN
ejpam-6633	336	8	)	)	PUNCT
ejpam-6633	336	9	)	)	PUNCT
ejpam-6633	337	1	β+α−1	β+α−1	PROPN
ejpam-6633	338	1	|θ(τ	|θ(τ	PROPN
ejpam-6633	338	2	,	,	PUNCT
ejpam-6633	338	3	η(τ))−	η(τ))−	VERB
ejpam-6633	338	4	θ(τ	θ(τ	PROPN
ejpam-6633	338	5	,	,	PUNCT
ejpam-6633	338	6	z(τ))|	z(τ))|	PROPN
ejpam-6633	338	7	dτ	dτ	X
ejpam-6633	338	8	τ	τ	PROPN
ejpam-6633	338	9	+	+	X
ejpam-6633	338	10	µ	µ	X
ejpam-6633	338	11	(	(	PUNCT
ejpam-6633	338	12	ln	ln	X
ejpam-6633	338	13	(	(	PUNCT
ejpam-6633	338	14	t	t	PROPN
ejpam-6633	338	15	a	a	PRON
ejpam-6633	338	16	)	)	PUNCT
ejpam-6633	338	17	)	)	PUNCT
ejpam-6633	338	18	α	α	PROPN
ejpam-6633	338	19	bγ(α	bγ(α	PROPN
ejpam-6633	338	20	)	)	PUNCT
ejpam-6633	338	21	∫	∫	PROPN
ejpam-6633	338	22	1	1	NUM
ejpam-6633	338	23	a	a	PRON
ejpam-6633	338	24	(	(	PUNCT
ejpam-6633	338	25	ln	ln	NOUN
ejpam-6633	338	26	(	(	PUNCT
ejpam-6633	338	27	1	1	NUM
ejpam-6633	338	28	τ	τ	PROPN
ejpam-6633	338	29	)	)	PUNCT
ejpam-6633	338	30	)	)	PUNCT
ejpam-6633	338	31	α−1	α−1	PROPN
ejpam-6633	338	32	|η(τ)−	|η(τ)−	NOUN
ejpam-6633	338	33	z(τ)|	z(τ)|	PROPN
ejpam-6633	338	34	dτ	dτ	NOUN
ejpam-6633	338	35	τ2	τ2	PROPN
ejpam-6633	338	36	.	.	PUNCT
ejpam-6633	339	1	(	(	PUNCT
ejpam-6633	339	2	38	38	NUM
ejpam-6633	339	3	)	)	PUNCT
ejpam-6633	339	4	considering	consider	VERB
ejpam-6633	339	5	the	the	DET
ejpam-6633	339	6	lipchitz	lipchitz	PROPN
ejpam-6633	339	7	condition	condition	NOUN
ejpam-6633	339	8	h2	h2	PROPN
ejpam-6633	339	9	,	,	PUNCT
ejpam-6633	339	10	the	the	DET
ejpam-6633	339	11	inequality	inequality	NOUN
ejpam-6633	339	12	(	(	PUNCT
ejpam-6633	339	13	38	38	NUM
ejpam-6633	339	14	)	)	PUNCT
ejpam-6633	339	15	reads	read	VERB
ejpam-6633	339	16	a.	a.	PROPN
ejpam-6633	339	17	s.	s.	PROPN
ejpam-6633	339	18	hasan	hasan	PROPN
ejpam-6633	339	19	,	,	PUNCT
ejpam-6633	339	20	s.	s.	PROPN
ejpam-6633	339	21	a.	a.	PROPN
ejpam-6633	339	22	murad	murad	PROPN
ejpam-6633	339	23	/	/	SYM
ejpam-6633	339	24	eur	eur	PROPN
ejpam-6633	339	25	.	.	PUNCT
ejpam-6633	340	1	j.	j.	PROPN
ejpam-6633	340	2	pure	pure	PROPN
ejpam-6633	340	3	appl	appl	PROPN
ejpam-6633	340	4	.	.	PROPN
ejpam-6633	340	5	math	math	PROPN
ejpam-6633	340	6	,	,	PUNCT
ejpam-6633	340	7	18	18	NUM
ejpam-6633	340	8	(	(	PUNCT
ejpam-6633	340	9	3	3	NUM
ejpam-6633	340	10	)	)	PUNCT
ejpam-6633	340	11	(	(	PUNCT
ejpam-6633	340	12	2025	2025	NUM
ejpam-6633	340	13	)	)	PUNCT
ejpam-6633	340	14	,	,	PUNCT
ejpam-6633	340	15	6633	6633	NUM
ejpam-6633	340	16	12	12	NUM
ejpam-6633	340	17	of	of	ADP
ejpam-6633	340	18	24	24	NUM
ejpam-6633	340	19	|η(t)−	|η(t)−	PROPN
ejpam-6633	340	20	z(t)|	z(t)|	VERB
ejpam-6633	341	1	≤	≤	NUM
ejpam-6633	341	2	2bϵ	2bϵ	NOUN
ejpam-6633	342	1	(	(	PUNCT
ejpam-6633	342	2	ln	ln	NOUN
ejpam-6633	342	3	(	(	PUNCT
ejpam-6633	342	4	1	1	NUM
ejpam-6633	342	5	a	a	NOUN
ejpam-6633	342	6	)	)	PUNCT
ejpam-6633	342	7	)	)	PUNCT
ejpam-6633	342	8	β	β	PROPN
ejpam-6633	342	9	γ(β	γ(β	PROPN
ejpam-6633	343	1	+	+	PUNCT
ejpam-6633	344	1	α+	α+	PUNCT
ejpam-6633	344	2	1	1	NUM
ejpam-6633	344	3	)	)	PUNCT
ejpam-6633	344	4	+	+	CCONJ
ejpam-6633	344	5	(	(	PUNCT
ejpam-6633	344	6	kφ1	kφ1	NOUN
ejpam-6633	344	7	+	+	CCONJ
ejpam-6633	344	8	φ2	φ2	PROPN
ejpam-6633	344	9	)	)	PUNCT
ejpam-6633	344	10	|η(t)−	|η(t)−	PROPN
ejpam-6633	344	11	z(t)|	z(t)|	PROPN
ejpam-6633	344	12	,	,	PUNCT
ejpam-6633	344	13	(	(	PUNCT
ejpam-6633	344	14	39	39	NUM
ejpam-6633	344	15	)	)	PUNCT
ejpam-6633	344	16	and	and	CCONJ
ejpam-6633	344	17	by	by	ADP
ejpam-6633	344	18	rewriting	rewrite	VERB
ejpam-6633	344	19	inequality	inequality	NOUN
ejpam-6633	344	20	(	(	PUNCT
ejpam-6633	344	21	39	39	NUM
ejpam-6633	344	22	)	)	PUNCT
ejpam-6633	344	23	,	,	PUNCT
ejpam-6633	344	24	we	we	PRON
ejpam-6633	344	25	obtain	obtain	VERB
ejpam-6633	344	26	|η(t)−	|η(t)−	PROPN
ejpam-6633	344	27	z(t)|	z(t)|	PROPN
ejpam-6633	344	28	≤	≤	PROPN
ejpam-6633	344	29	chϵ	chϵ	ADV
ejpam-6633	344	30	,	,	PUNCT
ejpam-6633	344	31	(	(	PUNCT
ejpam-6633	344	32	40	40	NUM
ejpam-6633	344	33	)	)	PUNCT
ejpam-6633	344	34	where	where	SCONJ
ejpam-6633	344	35	ch	ch	NOUN
ejpam-6633	344	36	=	=	PROPN
ejpam-6633	344	37	φ1	φ1	PROPN
ejpam-6633	344	38	1−υ	1−υ	NUM
ejpam-6633	344	39	.	.	PUNCT
ejpam-6633	345	1	inequality	inequality	NOUN
ejpam-6633	345	2	(	(	PUNCT
ejpam-6633	345	3	40	40	NUM
ejpam-6633	345	4	)	)	PUNCT
ejpam-6633	345	5	via	via	ADP
ejpam-6633	345	6	definition	definition	NOUN
ejpam-6633	345	7	4	4	NUM
ejpam-6633	345	8	ensures	ensure	VERB
ejpam-6633	345	9	that	that	SCONJ
ejpam-6633	345	10	the	the	DET
ejpam-6633	345	11	boundary	boundary	ADJ
ejpam-6633	345	12	-	-	PUNCT
ejpam-6633	345	13	value	value	NOUN
ejpam-6633	345	14	problem	problem	NOUN
ejpam-6633	345	15	(	(	PUNCT
ejpam-6633	345	16	6	6	NUM
ejpam-6633	345	17	-	-	SYM
ejpam-6633	345	18	8)	8)	NUM
ejpam-6633	345	19	is	be	AUX
ejpam-6633	345	20	stable	stable	ADJ
ejpam-6633	345	21	of	of	ADP
ejpam-6633	345	22	type	type	NOUN
ejpam-6633	345	23	ulam	ulam	NOUN
ejpam-6633	345	24	-	-	PUNCT
ejpam-6633	345	25	hayrs	hayr	NOUN
ejpam-6633	345	26	.	.	PUNCT
ejpam-6633	346	1	to	to	PART
ejpam-6633	346	2	investigate	investigate	VERB
ejpam-6633	346	3	the	the	DET
ejpam-6633	346	4	ulam	ulam	NOUN
ejpam-6633	346	5	-	-	PUNCT
ejpam-6633	346	6	hayrs	hayr	NOUN
ejpam-6633	346	7	-	-	PUNCT
ejpam-6633	346	8	rassias	rassias	PROPN
ejpam-6633	346	9	type	type	NOUN
ejpam-6633	346	10	stability	stability	NOUN
ejpam-6633	346	11	,	,	PUNCT
ejpam-6633	346	12	we	we	PRON
ejpam-6633	346	13	imposed	impose	VERB
ejpam-6633	346	14	a	a	DET
ejpam-6633	346	15	new	new	ADJ
ejpam-6633	346	16	assumption	assumption	NOUN
ejpam-6633	346	17	on	on	ADP
ejpam-6633	346	18	the	the	DET
ejpam-6633	346	19	problem	problem	NOUN
ejpam-6633	346	20	(	(	PUNCT
ejpam-6633	346	21	6	6	NUM
ejpam-6633	346	22	-	-	SYM
ejpam-6633	346	23	8)	8)	NUM
ejpam-6633	346	24	.	.	PUNCT
ejpam-6633	347	1	h3	h3	NOUN
ejpam-6633	347	2	:	:	PUNCT
ejpam-6633	347	3	the	the	DET
ejpam-6633	347	4	control	control	NOUN
ejpam-6633	347	5	function	function	VERB
ejpam-6633	347	6	ψ(t	ψ(t	PROPN
ejpam-6633	347	7	)	)	PUNCT
ejpam-6633	347	8	in	in	ADP
ejpam-6633	347	9	definition	definition	NOUN
ejpam-6633	347	10	5	5	NUM
ejpam-6633	347	11	is	be	AUX
ejpam-6633	347	12	a	a	DET
ejpam-6633	347	13	positive	positive	ADJ
ejpam-6633	347	14	non	non	ADJ
ejpam-6633	347	15	-	-	ADJ
ejpam-6633	347	16	decreasing	decrease	VERB
ejpam-6633	347	17	function	function	NOUN
ejpam-6633	347	18	such	such	ADJ
ejpam-6633	347	19	that	that	PRON
ejpam-6633	347	20	:	:	PUNCT
ejpam-6633	347	21	h	h	NOUN
ejpam-6633	348	1	a	a	X
ejpam-6633	348	2	i	i	NOUN
ejpam-6633	348	3	α+βψ(t	α+βψ(t	PROPN
ejpam-6633	348	4	)	)	PUNCT
ejpam-6633	348	5	≤	≤	NOUN
ejpam-6633	348	6	λψ(t	λψ(t	NOUN
ejpam-6633	348	7	)	)	PUNCT
ejpam-6633	348	8	,	,	PUNCT
ejpam-6633	348	9	(	(	PUNCT
ejpam-6633	348	10	41	41	NUM
ejpam-6633	348	11	)	)	PUNCT
ejpam-6633	348	12	where	where	SCONJ
ejpam-6633	348	13	λ	λ	X
ejpam-6633	348	14	>	>	X
ejpam-6633	348	15	0	0	X
ejpam-6633	348	16	.	.	PUNCT
ejpam-6633	348	17	theorem	theorem	NOUN
ejpam-6633	348	18	5	5	NUM
ejpam-6633	348	19	.	.	PUNCT
ejpam-6633	348	20	assume	assume	VERB
ejpam-6633	348	21	that	that	SCONJ
ejpam-6633	348	22	θ	θ	NOUN
ejpam-6633	348	23	:	:	PUNCT
ejpam-6633	349	1	[	[	X
ejpam-6633	349	2	a	a	X
ejpam-6633	349	3	,	,	PUNCT
ejpam-6633	349	4	1]×r	1]×r	NUM
ejpam-6633	349	5	−→	−→	NOUN
ejpam-6633	349	6	r	r	NOUN
ejpam-6633	349	7	is	be	AUX
ejpam-6633	349	8	a	a	DET
ejpam-6633	349	9	continuous	continuous	ADJ
ejpam-6633	349	10	function	function	NOUN
ejpam-6633	349	11	and	and	CCONJ
ejpam-6633	349	12	both	both	DET
ejpam-6633	349	13	hypotheses	hypothese	VERB
ejpam-6633	349	14	h2	h2	NOUN
ejpam-6633	349	15	and	and	CCONJ
ejpam-6633	349	16	h3	h3	NOUN
ejpam-6633	349	17	hold	hold	VERB
ejpam-6633	349	18	.	.	PUNCT
ejpam-6633	350	1	then	then	ADV
ejpam-6633	350	2	,	,	PUNCT
ejpam-6633	350	3	the	the	DET
ejpam-6633	350	4	solution	solution	NOUN
ejpam-6633	350	5	of	of	ADP
ejpam-6633	350	6	the	the	DET
ejpam-6633	350	7	boundary	boundary	ADJ
ejpam-6633	350	8	-	-	PUNCT
ejpam-6633	350	9	value	value	NOUN
ejpam-6633	350	10	problem	problem	NOUN
ejpam-6633	350	11	(	(	PUNCT
ejpam-6633	350	12	6	6	NUM
ejpam-6633	350	13	-	-	SYM
ejpam-6633	350	14	8)	8)	NUM
ejpam-6633	350	15	is	be	AUX
ejpam-6633	350	16	ulam	ulam	NOUN
ejpam-6633	350	17	-	-	PUNCT
ejpam-6633	350	18	hyersrassias	hyersrassias	PROPN
ejpam-6633	350	19	type	type	NOUN
ejpam-6633	350	20	stable	stable	ADJ
ejpam-6633	350	21	.	.	PUNCT
ejpam-6633	351	1	proof	proof	NOUN
ejpam-6633	351	2	:	:	PUNCT
ejpam-6633	351	3	let	let	VERB
ejpam-6633	351	4	η(t	η(t	NOUN
ejpam-6633	351	5	)	)	PUNCT
ejpam-6633	351	6	∈	∈	PROPN
ejpam-6633	351	7	c([a	c([a	PROPN
ejpam-6633	351	8	,	,	PUNCT
ejpam-6633	351	9	1],r	1],r	NUM
ejpam-6633	351	10	)	)	PUNCT
ejpam-6633	351	11	be	be	VERB
ejpam-6633	351	12	a	a	DET
ejpam-6633	351	13	solution	solution	NOUN
ejpam-6633	351	14	of	of	ADP
ejpam-6633	351	15	the	the	DET
ejpam-6633	351	16	inequality	inequality	NOUN
ejpam-6633	351	17	(	(	PUNCT
ejpam-6633	351	18	16	16	NUM
ejpam-6633	351	19	)	)	PUNCT
ejpam-6633	351	20	which	which	PRON
ejpam-6633	351	21	satisfies	satisfy	VERB
ejpam-6633	351	22	boundary	boundary	ADJ
ejpam-6633	351	23	conditions	condition	NOUN
ejpam-6633	351	24	(	(	PUNCT
ejpam-6633	351	25	7	7	NUM
ejpam-6633	351	26	-	-	SYM
ejpam-6633	351	27	8)	8)	NUM
ejpam-6633	351	28	.	.	PUNCT
ejpam-6633	352	1	through	through	ADP
ejpam-6633	352	2	remark	remark	NOUN
ejpam-6633	352	3	2	2	NUM
ejpam-6633	352	4	,	,	PUNCT
ejpam-6633	352	5	we	we	PRON
ejpam-6633	352	6	obtain	obtain	VERB
ejpam-6633	352	7	the	the	DET
ejpam-6633	352	8	perturbed	perturb	VERB
ejpam-6633	352	9	problem	problem	NOUN
ejpam-6633	352	10	(	(	PUNCT
ejpam-6633	352	11	35	35	NUM
ejpam-6633	352	12	)	)	PUNCT
ejpam-6633	352	13	,	,	PUNCT
ejpam-6633	352	14	where	where	SCONJ
ejpam-6633	352	15	|g(t)|	|g(t)|	NOUN
ejpam-6633	352	16	is	be	AUX
ejpam-6633	352	17	bounded	bound	VERB
ejpam-6633	352	18	by	by	ADP
ejpam-6633	352	19	ϵψ(t	ϵψ(t	NOUN
ejpam-6633	352	20	)	)	PUNCT
ejpam-6633	352	21	as	as	SCONJ
ejpam-6633	352	22	stated	state	VERB
ejpam-6633	352	23	in	in	ADP
ejpam-6633	352	24	remark	remark	NOUN
ejpam-6633	352	25	2	2	NUM
ejpam-6633	352	26	,	,	PUNCT
ejpam-6633	352	27	and	and	CCONJ
ejpam-6633	352	28	ψ(t	ψ(t	PROPN
ejpam-6633	352	29	)	)	PUNCT
ejpam-6633	352	30	is	be	AUX
ejpam-6633	352	31	the	the	DET
ejpam-6633	352	32	control	control	NOUN
ejpam-6633	352	33	function	function	NOUN
ejpam-6633	352	34	that	that	PRON
ejpam-6633	352	35	fulfills	fulfill	VERB
ejpam-6633	352	36	assumption	assumption	NOUN
ejpam-6633	352	37	h3	h3	NOUN
ejpam-6633	352	38	.	.	PUNCT
ejpam-6633	353	1	thus	thus	ADV
ejpam-6633	353	2	we	we	PRON
ejpam-6633	353	3	have∣∣∣∣∣η(t)−	have∣∣∣∣∣η(t)−	PROPN
ejpam-6633	353	4	1	1	NUM
ejpam-6633	353	5	γ(β	γ(β	PROPN
ejpam-6633	353	6	+	+	NUM
ejpam-6633	353	7	α	α	X
ejpam-6633	353	8	)	)	PUNCT
ejpam-6633	353	9	∫	∫	PROPN
ejpam-6633	353	10	t	t	PROPN
ejpam-6633	353	11	a	a	X
ejpam-6633	353	12	(	(	PUNCT
ejpam-6633	353	13	ln	ln	X
ejpam-6633	353	14	(	(	PUNCT
ejpam-6633	353	15	t	t	PROPN
ejpam-6633	353	16	τ	τ	PROPN
ejpam-6633	353	17	)	)	PUNCT
ejpam-6633	353	18	)	)	PUNCT
ejpam-6633	354	1	β+α−1	β+α−1	PUNCT
ejpam-6633	355	1	θ(τ	θ(τ	PROPN
ejpam-6633	355	2	,	,	PUNCT
ejpam-6633	355	3	η(τ	η(τ	PROPN
ejpam-6633	355	4	)	)	PUNCT
ejpam-6633	355	5	)	)	PUNCT
ejpam-6633	356	1	τ	τ	PROPN
ejpam-6633	356	2	dτ	dτ	NOUN
ejpam-6633	356	3	+	+	PROPN
ejpam-6633	356	4	µ	µ	X
ejpam-6633	356	5	γ(α	γ(α	NOUN
ejpam-6633	356	6	)	)	PUNCT
ejpam-6633	357	1	∫	∫	PROPN
ejpam-6633	357	2	t	t	PROPN
ejpam-6633	357	3	a	a	X
ejpam-6633	357	4	(	(	PUNCT
ejpam-6633	357	5	ln	ln	X
ejpam-6633	357	6	(	(	PUNCT
ejpam-6633	357	7	t	t	PROPN
ejpam-6633	357	8	τ	τ	PROPN
ejpam-6633	357	9	)	)	PUNCT
ejpam-6633	357	10	)	)	PUNCT
ejpam-6633	357	11	α−1	α−1	PROPN
ejpam-6633	357	12	η(τ	η(τ	PROPN
ejpam-6633	357	13	)	)	PUNCT
ejpam-6633	357	14	τ2	τ2	NOUN
ejpam-6633	357	15	dτ	dτ	NOUN
ejpam-6633	357	16	+	+	CCONJ
ejpam-6633	357	17	(	(	PUNCT
ejpam-6633	357	18	ln	ln	INTJ
ejpam-6633	357	19	(	(	PUNCT
ejpam-6633	357	20	t	t	PROPN
ejpam-6633	357	21	a	a	PRON
ejpam-6633	357	22	)	)	PUNCT
ejpam-6633	357	23	)	)	PUNCT
ejpam-6633	357	24	α	α	NOUN
ejpam-6633	357	25	bγ(β	bγ(β	X
ejpam-6633	357	26	+	+	X
ejpam-6633	357	27	α	α	X
ejpam-6633	357	28	)	)	PUNCT
ejpam-6633	357	29	∫	∫	PROPN
ejpam-6633	357	30	1	1	NUM
ejpam-6633	358	1	a	a	PRON
ejpam-6633	358	2	(	(	PUNCT
ejpam-6633	358	3	ln	ln	NOUN
ejpam-6633	358	4	(	(	PUNCT
ejpam-6633	358	5	1	1	NUM
ejpam-6633	358	6	τ	τ	PROPN
ejpam-6633	358	7	)	)	PUNCT
ejpam-6633	358	8	)	)	PUNCT
ejpam-6633	358	9	β+α−1	β+α−1	PROPN
ejpam-6633	359	1	θ(τ	θ(τ	PROPN
ejpam-6633	359	2	,	,	PUNCT
ejpam-6633	359	3	η(τ	η(τ	PROPN
ejpam-6633	359	4	)	)	PUNCT
ejpam-6633	359	5	)	)	PUNCT
ejpam-6633	360	1	τ	τ	PROPN
ejpam-6633	360	2	dτ	dτ	NOUN
ejpam-6633	360	3	−	−	PROPN
ejpam-6633	360	4	µ	µ	X
ejpam-6633	360	5	(	(	PUNCT
ejpam-6633	360	6	ln	ln	X
ejpam-6633	360	7	(	(	PUNCT
ejpam-6633	360	8	t	t	PROPN
ejpam-6633	360	9	a	a	PRON
ejpam-6633	360	10	)	)	PUNCT
ejpam-6633	360	11	)	)	PUNCT
ejpam-6633	360	12	α	α	PROPN
ejpam-6633	360	13	bγ(α	bγ(α	PROPN
ejpam-6633	360	14	)	)	PUNCT
ejpam-6633	360	15	∫	∫	PROPN
ejpam-6633	361	1	1	1	NUM
ejpam-6633	361	2	a	a	PRON
ejpam-6633	361	3	(	(	PUNCT
ejpam-6633	361	4	ln	ln	NOUN
ejpam-6633	361	5	(	(	PUNCT
ejpam-6633	361	6	1	1	NUM
ejpam-6633	361	7	τ	τ	PROPN
ejpam-6633	361	8	)	)	PUNCT
ejpam-6633	361	9	)	)	PUNCT
ejpam-6633	361	10	α−1	α−1	PROPN
ejpam-6633	361	11	η(τ	η(τ	PROPN
ejpam-6633	361	12	)	)	PUNCT
ejpam-6633	361	13	τ2	τ2	PROPN
ejpam-6633	361	14	dτ	dτ	NOUN
ejpam-6633	361	15	−	−	PROPN
ejpam-6633	361	16	φ(t	φ(t	PROPN
ejpam-6633	361	17	)	)	PUNCT
ejpam-6633	362	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-6633	362	2	≤	≤	ADJ
ejpam-6633	362	3	2ϵλψ(t	2ϵλψ(t	NUM
ejpam-6633	362	4	)	)	PUNCT
ejpam-6633	362	5	,	,	PUNCT
ejpam-6633	362	6	(	(	PUNCT
ejpam-6633	362	7	42	42	NUM
ejpam-6633	362	8	)	)	PUNCT
ejpam-6633	362	9	for	for	ADP
ejpam-6633	362	10	all	all	DET
ejpam-6633	362	11	t	t	NOUN
ejpam-6633	362	12	∈	∈	PROPN
ejpam-6633	363	1	[	[	X
ejpam-6633	363	2	a	a	X
ejpam-6633	363	3	,	,	PUNCT
ejpam-6633	363	4	1	1	NUM
ejpam-6633	363	5	]	]	PUNCT
ejpam-6633	363	6	.	.	PUNCT
ejpam-6633	364	1	if	if	SCONJ
ejpam-6633	364	2	we	we	PRON
ejpam-6633	364	3	call	call	VERB
ejpam-6633	364	4	z(t	z(t	NOUN
ejpam-6633	364	5	)	)	PUNCT
ejpam-6633	364	6	the	the	DET
ejpam-6633	364	7	unique	unique	ADJ
ejpam-6633	364	8	solution	solution	NOUN
ejpam-6633	364	9	for	for	ADP
ejpam-6633	364	10	our	our	PRON
ejpam-6633	364	11	boundary	boundary	ADJ
ejpam-6633	364	12	-	-	PUNCT
ejpam-6633	364	13	value	value	NOUN
ejpam-6633	364	14	problem	problem	NOUN
ejpam-6633	364	15	(	(	PUNCT
ejpam-6633	364	16	6	6	NUM
ejpam-6633	364	17	-	-	SYM
ejpam-6633	364	18	8)	8)	NUM
ejpam-6633	364	19	,	,	PUNCT
ejpam-6633	364	20	then	then	ADV
ejpam-6633	364	21	,	,	PUNCT
ejpam-6633	364	22	the	the	DET
ejpam-6633	364	23	left	left	ADJ
ejpam-6633	364	24	side	side	NOUN
ejpam-6633	364	25	of	of	ADP
ejpam-6633	364	26	inequality	inequality	NOUN
ejpam-6633	364	27	(	(	PUNCT
ejpam-6633	364	28	17	17	NUM
ejpam-6633	364	29	)	)	PUNCT
ejpam-6633	364	30	conforms	conform	VERB
ejpam-6633	364	31	to	to	ADP
ejpam-6633	364	32	|η(t)−	|η(t)−	PROPN
ejpam-6633	364	33	z(t)|	z(t)|	VERB
ejpam-6633	364	34	≤	≤	ADJ
ejpam-6633	364	35	2ϵλψ(t	2ϵλψ(t	NUM
ejpam-6633	364	36	)	)	PUNCT
ejpam-6633	365	1	+	+	CCONJ
ejpam-6633	365	2	1	1	NUM
ejpam-6633	365	3	γ(β	γ(β	PROPN
ejpam-6633	365	4	+	+	NUM
ejpam-6633	365	5	α	α	X
ejpam-6633	365	6	)	)	PUNCT
ejpam-6633	365	7	∫	∫	PROPN
ejpam-6633	365	8	t	t	PROPN
ejpam-6633	365	9	a	a	X
ejpam-6633	365	10	(	(	PUNCT
ejpam-6633	365	11	ln	ln	X
ejpam-6633	365	12	(	(	PUNCT
ejpam-6633	365	13	t	t	PROPN
ejpam-6633	365	14	τ	τ	PROPN
ejpam-6633	365	15	)	)	PUNCT
ejpam-6633	365	16	)	)	PUNCT
ejpam-6633	366	1	β+α−1	β+α−1	PROPN
ejpam-6633	366	2	|θ(τ	|θ(τ	PROPN
ejpam-6633	366	3	,	,	PUNCT
ejpam-6633	366	4	η(τ))−	η(τ))−	VERB
ejpam-6633	366	5	θ(τ	θ(τ	PROPN
ejpam-6633	366	6	,	,	PUNCT
ejpam-6633	366	7	z(τ))|	z(τ))|	PROPN
ejpam-6633	366	8	dτ	dτ	X
ejpam-6633	366	9	τ	τ	PROPN
ejpam-6633	366	10	+	+	PROPN
ejpam-6633	366	11	µ	µ	X
ejpam-6633	366	12	γ(α	γ(α	NOUN
ejpam-6633	366	13	)	)	PUNCT
ejpam-6633	367	1	∫	∫	PROPN
ejpam-6633	367	2	t	t	PROPN
ejpam-6633	367	3	a	a	X
ejpam-6633	367	4	(	(	PUNCT
ejpam-6633	367	5	ln	ln	X
ejpam-6633	367	6	(	(	PUNCT
ejpam-6633	367	7	t	t	PROPN
ejpam-6633	367	8	τ	τ	PROPN
ejpam-6633	367	9	)	)	PUNCT
ejpam-6633	367	10	)	)	PUNCT
ejpam-6633	368	1	α−1	α−1	PROPN
ejpam-6633	368	2	|η(τ)−	|η(τ)−	NOUN
ejpam-6633	368	3	z(τ)|	z(τ)|	PROPN
ejpam-6633	368	4	dτ	dτ	NOUN
ejpam-6633	368	5	τ2	τ2	PROPN
ejpam-6633	368	6	a.	a.	PROPN
ejpam-6633	368	7	s.	s.	PROPN
ejpam-6633	368	8	hasan	hasan	PROPN
ejpam-6633	368	9	,	,	PUNCT
ejpam-6633	368	10	s.	s.	PROPN
ejpam-6633	368	11	a.	a.	PROPN
ejpam-6633	368	12	murad	murad	PROPN
ejpam-6633	368	13	/	/	SYM
ejpam-6633	368	14	eur	eur	PROPN
ejpam-6633	368	15	.	.	PUNCT
ejpam-6633	369	1	j.	j.	PROPN
ejpam-6633	369	2	pure	pure	PROPN
ejpam-6633	369	3	appl	appl	PROPN
ejpam-6633	369	4	.	.	PROPN
ejpam-6633	369	5	math	math	PROPN
ejpam-6633	369	6	,	,	PUNCT
ejpam-6633	369	7	18	18	NUM
ejpam-6633	369	8	(	(	PUNCT
ejpam-6633	369	9	3	3	NUM
ejpam-6633	369	10	)	)	PUNCT
ejpam-6633	369	11	(	(	PUNCT
ejpam-6633	369	12	2025	2025	NUM
ejpam-6633	369	13	)	)	PUNCT
ejpam-6633	369	14	,	,	PUNCT
ejpam-6633	369	15	6633	6633	NUM
ejpam-6633	369	16	13	13	NUM
ejpam-6633	369	17	of	of	ADP
ejpam-6633	369	18	24	24	NUM
ejpam-6633	369	19	+	+	CCONJ
ejpam-6633	369	20	(	(	PUNCT
ejpam-6633	369	21	ln	ln	INTJ
ejpam-6633	369	22	(	(	PUNCT
ejpam-6633	369	23	t	t	PROPN
ejpam-6633	369	24	a	a	PRON
ejpam-6633	369	25	)	)	PUNCT
ejpam-6633	369	26	)	)	PUNCT
ejpam-6633	369	27	α	α	NOUN
ejpam-6633	369	28	bγ(β	bγ(β	X
ejpam-6633	369	29	+	+	X
ejpam-6633	369	30	α	α	X
ejpam-6633	369	31	)	)	PUNCT
ejpam-6633	369	32	∫	∫	PROPN
ejpam-6633	369	33	1	1	NUM
ejpam-6633	369	34	a	a	PRON
ejpam-6633	369	35	(	(	PUNCT
ejpam-6633	369	36	ln	ln	NOUN
ejpam-6633	369	37	(	(	PUNCT
ejpam-6633	369	38	1	1	NUM
ejpam-6633	369	39	τ	τ	PROPN
ejpam-6633	369	40	)	)	PUNCT
ejpam-6633	369	41	)	)	PUNCT
ejpam-6633	370	1	β+α−1	β+α−1	PROPN
ejpam-6633	371	1	|θ(τ	|θ(τ	PROPN
ejpam-6633	371	2	,	,	PUNCT
ejpam-6633	371	3	η(τ))−	η(τ))−	VERB
ejpam-6633	371	4	θ(τ	θ(τ	PROPN
ejpam-6633	371	5	,	,	PUNCT
ejpam-6633	371	6	z(τ))|	z(τ))|	PROPN
ejpam-6633	371	7	dτ	dτ	X
ejpam-6633	371	8	τ	τ	PROPN
ejpam-6633	371	9	+	+	X
ejpam-6633	371	10	µ	µ	X
ejpam-6633	371	11	(	(	PUNCT
ejpam-6633	371	12	ln	ln	X
ejpam-6633	371	13	(	(	PUNCT
ejpam-6633	371	14	t	t	PROPN
ejpam-6633	371	15	a	a	PRON
ejpam-6633	371	16	)	)	PUNCT
ejpam-6633	371	17	)	)	PUNCT
ejpam-6633	371	18	α	α	PROPN
ejpam-6633	371	19	bγ(α	bγ(α	PROPN
ejpam-6633	371	20	)	)	PUNCT
ejpam-6633	371	21	∫	∫	PROPN
ejpam-6633	371	22	1	1	NUM
ejpam-6633	371	23	a	a	PRON
ejpam-6633	371	24	(	(	PUNCT
ejpam-6633	371	25	ln	ln	NOUN
ejpam-6633	371	26	(	(	PUNCT
ejpam-6633	371	27	1	1	NUM
ejpam-6633	371	28	τ	τ	PROPN
ejpam-6633	371	29	)	)	PUNCT
ejpam-6633	371	30	)	)	PUNCT
ejpam-6633	371	31	α−1	α−1	PROPN
ejpam-6633	371	32	|η(τ)−	|η(τ)−	NOUN
ejpam-6633	371	33	z(τ)|	z(τ)|	PROPN
ejpam-6633	371	34	dτ	dτ	NOUN
ejpam-6633	371	35	τ2	τ2	PROPN
ejpam-6633	371	36	.	.	PUNCT
ejpam-6633	372	1	(	(	PUNCT
ejpam-6633	372	2	43	43	NUM
ejpam-6633	372	3	)	)	PUNCT
ejpam-6633	372	4	considering	consider	VERB
ejpam-6633	372	5	the	the	DET
ejpam-6633	372	6	second	second	ADJ
ejpam-6633	372	7	assumption	assumption	NOUN
ejpam-6633	372	8	h2	h2	NOUN
ejpam-6633	372	9	,	,	PUNCT
ejpam-6633	372	10	the	the	DET
ejpam-6633	372	11	inequality	inequality	NOUN
ejpam-6633	372	12	(	(	PUNCT
ejpam-6633	372	13	43	43	NUM
ejpam-6633	372	14	)	)	PUNCT
ejpam-6633	372	15	reads	read	VERB
ejpam-6633	372	16	|η(t)−	|η(t)−	PROPN
ejpam-6633	372	17	z(t)|	z(t)|	VERB
ejpam-6633	372	18	≤	≤	ADJ
ejpam-6633	372	19	2ϵλψ(t	2ϵλψ(t	NUM
ejpam-6633	372	20	)	)	PUNCT
ejpam-6633	373	1	+	+	CCONJ
ejpam-6633	373	2	(	(	PUNCT
ejpam-6633	373	3	kφ1	kφ1	NOUN
ejpam-6633	373	4	+	+	CCONJ
ejpam-6633	373	5	φ2	φ2	PROPN
ejpam-6633	373	6	)	)	PUNCT
ejpam-6633	373	7	|η(t)−	|η(t)−	PROPN
ejpam-6633	373	8	z(t)|	z(t)|	PROPN
ejpam-6633	373	9	,	,	PUNCT
ejpam-6633	373	10	(	(	PUNCT
ejpam-6633	373	11	44	44	NUM
ejpam-6633	373	12	)	)	PUNCT
ejpam-6633	373	13	and	and	CCONJ
ejpam-6633	373	14	by	by	ADP
ejpam-6633	373	15	rewriting	rewrite	VERB
ejpam-6633	373	16	inequality	inequality	NOUN
ejpam-6633	373	17	(	(	PUNCT
ejpam-6633	373	18	44	44	NUM
ejpam-6633	373	19	)	)	PUNCT
ejpam-6633	373	20	,	,	PUNCT
ejpam-6633	373	21	we	we	PRON
ejpam-6633	373	22	obtain	obtain	VERB
ejpam-6633	373	23	|η(t)−	|η(t)−	PROPN
ejpam-6633	373	24	z(t)|	z(t)|	VERB
ejpam-6633	373	25	≤	≤	PROPN
ejpam-6633	374	1	ϵcλψ(t	ϵcλψ(t	X
ejpam-6633	374	2	)	)	PUNCT
ejpam-6633	374	3	,	,	PUNCT
ejpam-6633	374	4	(	(	PUNCT
ejpam-6633	374	5	45	45	NUM
ejpam-6633	374	6	)	)	PUNCT
ejpam-6633	374	7	where	where	SCONJ
ejpam-6633	374	8	cλ	cλ	PROPN
ejpam-6633	374	9	=	=	PUNCT
ejpam-6633	374	10	2λ	2λ	NOUN
ejpam-6633	374	11	(	(	PUNCT
ejpam-6633	374	12	1−υ	1−υ	NUM
ejpam-6633	374	13	)	)	PUNCT
ejpam-6633	374	14	.	.	PUNCT
ejpam-6633	375	1	inequality	inequality	NOUN
ejpam-6633	375	2	(	(	PUNCT
ejpam-6633	375	3	45	45	NUM
ejpam-6633	375	4	)	)	PUNCT
ejpam-6633	375	5	guarantees	guarantee	VERB
ejpam-6633	375	6	the	the	DET
ejpam-6633	375	7	stability	stability	NOUN
ejpam-6633	375	8	of	of	ADP
ejpam-6633	375	9	type	type	NOUN
ejpam-6633	375	10	ulam	ulam	PROPN
ejpam-6633	375	11	-	-	PUNCT
ejpam-6633	375	12	hyers	hyer	NOUN
ejpam-6633	375	13	-	-	PUNCT
ejpam-6633	375	14	rassias	rassia	NOUN
ejpam-6633	375	15	according	accord	VERB
ejpam-6633	375	16	to	to	ADP
ejpam-6633	375	17	definition	definition	NOUN
ejpam-6633	375	18	5	5	NUM
ejpam-6633	375	19	.	.	PUNCT
ejpam-6633	375	20	example	example	NOUN
ejpam-6633	375	21	1	1	NUM
ejpam-6633	375	22	:	:	PUNCT
ejpam-6633	375	23	consider	consider	VERB
ejpam-6633	375	24	the	the	DET
ejpam-6633	375	25	following	follow	VERB
ejpam-6633	375	26	multifractional	multifractional	ADJ
ejpam-6633	375	27	boundary	boundary	ADJ
ejpam-6633	375	28	-	-	PUNCT
ejpam-6633	375	29	value	value	NOUN
ejpam-6633	375	30	problem	problem	NOUN
ejpam-6633	375	31	:	:	PUNCT
ejpam-6633	375	32	chd	chd	PROPN
ejpam-6633	375	33	β	β	X
ejpam-6633	375	34	(	(	PUNCT
ejpam-6633	375	35	chd	chd	PROPN
ejpam-6633	375	36	α	α	PROPN
ejpam-6633	375	37	+	+	X
ejpam-6633	375	38	µ	µ	PROPN
ejpam-6633	375	39	t	t	NOUN
ejpam-6633	375	40	)	)	PUNCT
ejpam-6633	375	41	η(t	η(t	NOUN
ejpam-6633	375	42	)	)	PUNCT
ejpam-6633	376	1	=	=	SYM
ejpam-6633	376	2	|η(t)|	|η(t)|	PROPN
ejpam-6633	376	3	e−2	e−2	PROPN
ejpam-6633	376	4	t	t	PROPN
ejpam-6633	376	5	(	(	PUNCT
ejpam-6633	376	6	10	10	NUM
ejpam-6633	376	7	+	+	CCONJ
ejpam-6633	376	8	t2	t2	NOUN
ejpam-6633	376	9	)	)	PUNCT
ejpam-6633	376	10	(	(	PUNCT
ejpam-6633	376	11	1	1	NUM
ejpam-6633	376	12	+	+	CCONJ
ejpam-6633	376	13	η(t)2	η(t)2	PROPN
ejpam-6633	376	14	)	)	PUNCT
ejpam-6633	376	15	.	.	PUNCT
ejpam-6633	377	1	(	(	PUNCT
ejpam-6633	377	2	46	46	NUM
ejpam-6633	377	3	)	)	PUNCT
ejpam-6633	377	4	η(a	η(a	VERB
ejpam-6633	377	5	)	)	PUNCT
ejpam-6633	378	1	=	=	SYM
ejpam-6633	378	2	0	0	NUM
ejpam-6633	378	3	,	,	PUNCT
ejpam-6633	378	4	(	(	PUNCT
ejpam-6633	378	5	47	47	NUM
ejpam-6633	378	6	)	)	PUNCT
ejpam-6633	378	7	η(1	η(1	NOUN
ejpam-6633	378	8	)	)	PUNCT
ejpam-6633	378	9	=	=	NOUN
ejpam-6633	378	10	0.1	0.1	NUM
ejpam-6633	378	11	.	.	PUNCT
ejpam-6633	379	1	(	(	PUNCT
ejpam-6633	379	2	48	48	NUM
ejpam-6633	379	3	)	)	PUNCT
ejpam-6633	379	4	in	in	ADP
ejpam-6633	379	5	this	this	DET
ejpam-6633	379	6	problem	problem	NOUN
ejpam-6633	379	7	,	,	PUNCT
ejpam-6633	379	8	(	(	PUNCT
ejpam-6633	379	9	46	46	NUM
ejpam-6633	379	10	-	-	SYM
ejpam-6633	379	11	48	48	NUM
ejpam-6633	379	12	)	)	PUNCT
ejpam-6633	379	13	,	,	PUNCT
ejpam-6633	379	14	which	which	PRON
ejpam-6633	379	15	is	be	AUX
ejpam-6633	379	16	defined	define	VERB
ejpam-6633	379	17	on	on	ADP
ejpam-6633	379	18	[	[	X
ejpam-6633	379	19	a	a	X
ejpam-6633	379	20	,	,	PUNCT
ejpam-6633	379	21	1	1	NUM
ejpam-6633	379	22	]	]	PUNCT
ejpam-6633	379	23	where	where	SCONJ
ejpam-6633	379	24	0	0	PUNCT
ejpam-6633	379	25	<	<	X
ejpam-6633	379	26	a	a	DET
ejpam-6633	379	27	<	<	X
ejpam-6633	379	28	1	1	NUM
ejpam-6633	379	29	,	,	PUNCT
ejpam-6633	379	30	we	we	PRON
ejpam-6633	379	31	have	have	VERB
ejpam-6633	379	32	θ(t	θ(t	NOUN
ejpam-6633	379	33	,	,	PUNCT
ejpam-6633	379	34	η(t	η(t	NOUN
ejpam-6633	379	35	)	)	PUNCT
ejpam-6633	379	36	)	)	PUNCT
ejpam-6633	380	1	=	=	PUNCT
ejpam-6633	380	2	|η(t)|e−2	|η(t)|e−2	PROPN
ejpam-6633	380	3	t	t	PROPN
ejpam-6633	380	4	(	(	PUNCT
ejpam-6633	380	5	10+t2)(1+η2	10+t2)(1+η2	PROPN
ejpam-6633	380	6	)	)	PUNCT
ejpam-6633	380	7	which	which	PRON
ejpam-6633	380	8	satisfies	satisfy	VERB
ejpam-6633	380	9	both	both	DET
ejpam-6633	380	10	hypotheses	hypothesis	NOUN
ejpam-6633	380	11	h1	h1	ADJ
ejpam-6633	380	12	and	and	CCONJ
ejpam-6633	380	13	h2	h2	PROPN
ejpam-6633	380	14	with	with	ADP
ejpam-6633	380	15	ω	ω	PROPN
ejpam-6633	380	16	=	=	SYM
ejpam-6633	380	17	k	k	NOUN
ejpam-6633	380	18	=	=	PUNCT
ejpam-6633	380	19	e−2a	e−2a	PROPN
ejpam-6633	380	20	10+a2	10+a2	NOUN
ejpam-6633	380	21	,	,	PUNCT
ejpam-6633	380	22	i.e.	i.e.	X
ejpam-6633	380	23	:	:	PUNCT
ejpam-6633	380	24	|θ(t	|θ(t	NOUN
ejpam-6633	380	25	,	,	PUNCT
ejpam-6633	380	26	η(t))|	η(t))|	PROPN
ejpam-6633	380	27	≤	≤	PROPN
ejpam-6633	380	28	ω	ω	PROPN
ejpam-6633	380	29	=	=	PUNCT
ejpam-6633	380	30	e−2a	e−2a	NOUN
ejpam-6633	380	31	10	10	NUM
ejpam-6633	380	32	+	+	NUM
ejpam-6633	380	33	a2	a2	PROPN
ejpam-6633	380	34	,	,	PUNCT
ejpam-6633	380	35	(	(	PUNCT
ejpam-6633	380	36	49	49	NUM
ejpam-6633	380	37	)	)	PUNCT
ejpam-6633	380	38	and	and	CCONJ
ejpam-6633	380	39	∥θ(t	∥θ(t	PROPN
ejpam-6633	380	40	,	,	PUNCT
ejpam-6633	380	41	η1)−	η1)−	PROPN
ejpam-6633	380	42	θ(t	θ(t	PROPN
ejpam-6633	380	43	,	,	PUNCT
ejpam-6633	380	44	η2)∥	η2)∥	NOUN
ejpam-6633	380	45	≤	≤	ADV
ejpam-6633	380	46	e−2a	e−2a	X
ejpam-6633	380	47	10	10	NUM
ejpam-6633	380	48	+	+	NUM
ejpam-6633	380	49	a2	a2	NOUN
ejpam-6633	380	50	∥η1	∥η1	ADJ
ejpam-6633	380	51	−	−	PROPN
ejpam-6633	380	52	η2∥.	η2∥.	NOUN
ejpam-6633	380	53	(	(	PUNCT
ejpam-6633	380	54	50	50	NUM
ejpam-6633	380	55	)	)	PUNCT
ejpam-6633	380	56	hence	hence	ADV
ejpam-6633	380	57	by	by	ADP
ejpam-6633	380	58	banach	banach	NOUN
ejpam-6633	380	59	’s	’s	PART
ejpam-6633	380	60	fixed	fix	VERB
ejpam-6633	380	61	point	point	NOUN
ejpam-6633	380	62	theorem	theorem	VERB
ejpam-6633	380	63	there	there	PRON
ejpam-6633	380	64	exists	exist	VERB
ejpam-6633	380	65	a	a	DET
ejpam-6633	380	66	unique	unique	ADJ
ejpam-6633	380	67	solution	solution	NOUN
ejpam-6633	380	68	to	to	ADP
ejpam-6633	380	69	the	the	DET
ejpam-6633	380	70	problem	problem	NOUN
ejpam-6633	380	71	(	(	PUNCT
ejpam-6633	380	72	46	46	NUM
ejpam-6633	380	73	-	-	SYM
ejpam-6633	380	74	48	48	NUM
ejpam-6633	380	75	)	)	PUNCT
ejpam-6633	380	76	.	.	PUNCT
ejpam-6633	381	1	to	to	PART
ejpam-6633	381	2	analyze	analyze	VERB
ejpam-6633	381	3	the	the	DET
ejpam-6633	381	4	problem	problem	NOUN
ejpam-6633	381	5	(	(	PUNCT
ejpam-6633	381	6	46	46	NUM
ejpam-6633	381	7	-	-	SYM
ejpam-6633	381	8	48	48	NUM
ejpam-6633	381	9	)	)	PUNCT
ejpam-6633	381	10	,	,	PUNCT
ejpam-6633	381	11	we	we	PRON
ejpam-6633	381	12	set	set	VERB
ejpam-6633	381	13	the	the	DET
ejpam-6633	381	14	interval	interval	NOUN
ejpam-6633	381	15	[	[	X
ejpam-6633	381	16	a	a	X
ejpam-6633	381	17	,	,	PUNCT
ejpam-6633	381	18	1	1	NUM
ejpam-6633	381	19	]	]	PUNCT
ejpam-6633	381	20	with	with	ADP
ejpam-6633	381	21	a	a	DET
ejpam-6633	381	22	=	=	SYM
ejpam-6633	381	23	0.8	0.8	NUM
ejpam-6633	381	24	,	,	PUNCT
ejpam-6633	381	25	and	and	CCONJ
ejpam-6633	381	26	a	a	DET
ejpam-6633	381	27	=	=	SYM
ejpam-6633	381	28	0.9	0.9	NUM
ejpam-6633	381	29	,	,	PUNCT
ejpam-6633	381	30	which	which	PRON
ejpam-6633	381	31	read	read	VERB
ejpam-6633	381	32	k	k	PROPN
ejpam-6633	381	33	≈	≈	PROPN
ejpam-6633	381	34	0.01898	0.01898	NUM
ejpam-6633	381	35	,	,	PUNCT
ejpam-6633	381	36	and	and	CCONJ
ejpam-6633	381	37	k	k	PROPN
ejpam-6633	381	38	≈	≈	PROPN
ejpam-6633	381	39	0.01529	0.01529	NUM
ejpam-6633	381	40	,	,	PUNCT
ejpam-6633	381	41	respectively.also	respectively.also	ADV
ejpam-6633	381	42	,	,	PUNCT
ejpam-6633	381	43	we	we	PRON
ejpam-6633	381	44	set	set	VERB
ejpam-6633	381	45	µ	µ	NOUN
ejpam-6633	381	46	=	=	SYM
ejpam-6633	381	47	0.1	0.1	NUM
ejpam-6633	381	48	.	.	PUNCT
ejpam-6633	382	1	next	next	ADV
ejpam-6633	382	2	,	,	PUNCT
ejpam-6633	382	3	we	we	PRON
ejpam-6633	382	4	take	take	VERB
ejpam-6633	382	5	the	the	DET
ejpam-6633	382	6	values	value	NOUN
ejpam-6633	382	7	of	of	ADP
ejpam-6633	382	8	α	α	NOUN
ejpam-6633	382	9	and	and	CCONJ
ejpam-6633	382	10	β	β	X
ejpam-6633	382	11	to	to	PART
ejpam-6633	382	12	run	run	VERB
ejpam-6633	382	13	on	on	ADP
ejpam-6633	382	14	[	[	X
ejpam-6633	382	15	0.1	0.1	NUM
ejpam-6633	382	16	,	,	PUNCT
ejpam-6633	382	17	0.9	0.9	NUM
ejpam-6633	382	18	]	]	PUNCT
ejpam-6633	382	19	.	.	PUNCT
ejpam-6633	383	1	we	we	PRON
ejpam-6633	383	2	demonstrate	demonstrate	VERB
ejpam-6633	383	3	the	the	DET
ejpam-6633	383	4	proposed	propose	VERB
ejpam-6633	383	5	contraction	contraction	NOUN
ejpam-6633	383	6	condition	condition	NOUN
ejpam-6633	383	7	in	in	ADP
ejpam-6633	383	8	inequality	inequality	NOUN
ejpam-6633	383	9	(	(	PUNCT
ejpam-6633	383	10	29	29	NUM
ejpam-6633	383	11	)	)	PUNCT
ejpam-6633	383	12	,	,	PUNCT
ejpam-6633	383	13	υ	υ	NOUN
ejpam-6633	383	14	=	=	NOUN
ejpam-6633	383	15	kφ1	kφ1	PROPN
ejpam-6633	383	16	+	+	CCONJ
ejpam-6633	383	17	φ2	φ2	PROPN
ejpam-6633	383	18	,	,	PUNCT
ejpam-6633	383	19	which	which	PRON
ejpam-6633	383	20	depends	depend	VERB
ejpam-6633	383	21	on	on	ADP
ejpam-6633	383	22	α	α	PROPN
ejpam-6633	383	23	,	,	PUNCT
ejpam-6633	383	24	β	β	X
ejpam-6633	383	25	,	,	PUNCT
ejpam-6633	383	26	µ	µ	NOUN
ejpam-6633	383	27	,	,	PUNCT
ejpam-6633	383	28	and	and	CCONJ
ejpam-6633	383	29	a.	a.	NOUN
ejpam-6633	383	30	a.	a.	PROPN
ejpam-6633	383	31	s.	s.	PROPN
ejpam-6633	383	32	hasan	hasan	PROPN
ejpam-6633	383	33	,	,	PUNCT
ejpam-6633	383	34	s.	s.	PROPN
ejpam-6633	383	35	a.	a.	PROPN
ejpam-6633	383	36	murad	murad	PROPN
ejpam-6633	383	37	/	/	SYM
ejpam-6633	383	38	eur	eur	PROPN
ejpam-6633	383	39	.	.	PUNCT
ejpam-6633	384	1	j.	j.	PROPN
ejpam-6633	384	2	pure	pure	PROPN
ejpam-6633	384	3	appl	appl	PROPN
ejpam-6633	384	4	.	.	PROPN
ejpam-6633	384	5	math	math	PROPN
ejpam-6633	384	6	,	,	PUNCT
ejpam-6633	384	7	18	18	NUM
ejpam-6633	384	8	(	(	PUNCT
ejpam-6633	384	9	3	3	NUM
ejpam-6633	384	10	)	)	PUNCT
ejpam-6633	384	11	(	(	PUNCT
ejpam-6633	384	12	2025	2025	NUM
ejpam-6633	384	13	)	)	PUNCT
ejpam-6633	384	14	,	,	PUNCT
ejpam-6633	384	15	6633	6633	NUM
ejpam-6633	384	16	14	14	NUM
ejpam-6633	384	17	of	of	ADP
ejpam-6633	384	18	24	24	NUM
ejpam-6633	384	19	(	(	PUNCT
ejpam-6633	384	20	a	a	NOUN
ejpam-6633	384	21	)	)	PUNCT
ejpam-6633	384	22	(	(	PUNCT
ejpam-6633	384	23	b	b	X
ejpam-6633	384	24	)	)	PUNCT
ejpam-6633	384	25	figure	figure	NOUN
ejpam-6633	384	26	1	1	NUM
ejpam-6633	384	27	:	:	PUNCT
ejpam-6633	384	28	the	the	DET
ejpam-6633	384	29	range	range	NOUN
ejpam-6633	384	30	of	of	ADP
ejpam-6633	384	31	contraction	contraction	NOUN
ejpam-6633	384	32	parameter	parameter	NOUN
ejpam-6633	384	33	υ	υ	PROPN
ejpam-6633	384	34	,	,	PUNCT
ejpam-6633	384	35	with	with	ADP
ejpam-6633	384	36	µ	µ	NOUN
ejpam-6633	384	37	=	=	SYM
ejpam-6633	384	38	0.1	0.1	NUM
ejpam-6633	384	39	as	as	ADP
ejpam-6633	384	40	α	α	PROPN
ejpam-6633	384	41	and	and	CCONJ
ejpam-6633	384	42	β	β	X
ejpam-6633	384	43	move	move	VERB
ejpam-6633	384	44	from	from	ADP
ejpam-6633	384	45	0.1	0.1	NUM
ejpam-6633	384	46	to	to	ADP
ejpam-6633	384	47	0.9	0.9	NUM
ejpam-6633	384	48	for	for	ADP
ejpam-6633	384	49	the	the	DET
ejpam-6633	384	50	values	value	NOUN
ejpam-6633	384	51	of	of	ADP
ejpam-6633	384	52	a	a	DET
ejpam-6633	384	53	:	:	PUNCT
ejpam-6633	384	54	(	(	PUNCT
ejpam-6633	384	55	a	a	X
ejpam-6633	384	56	)	)	PUNCT
ejpam-6633	384	57	a	a	DET
ejpam-6633	384	58	=	=	NOUN
ejpam-6633	384	59	0.8	0.8	NUM
ejpam-6633	384	60	,	,	PUNCT
ejpam-6633	384	61	and	and	CCONJ
ejpam-6633	384	62	(	(	PUNCT
ejpam-6633	384	63	b	b	X
ejpam-6633	384	64	)	)	PUNCT
ejpam-6633	384	65	a	a	DET
ejpam-6633	384	66	=	=	NOUN
ejpam-6633	384	67	0.9	0.9	NUM
ejpam-6633	384	68	.	.	PUNCT
ejpam-6633	385	1	for	for	ADP
ejpam-6633	385	2	stability	stability	NOUN
ejpam-6633	385	3	,	,	PUNCT
ejpam-6633	385	4	we	we	PRON
ejpam-6633	385	5	assume	assume	VERB
ejpam-6633	385	6	that	that	SCONJ
ejpam-6633	385	7	η(t	η(t	NOUN
ejpam-6633	385	8	)	)	PUNCT
ejpam-6633	385	9	and	and	CCONJ
ejpam-6633	385	10	z(t	z(t	NOUN
ejpam-6633	385	11	)	)	PUNCT
ejpam-6633	385	12	are	be	AUX
ejpam-6633	385	13	the	the	DET
ejpam-6633	385	14	solutions	solution	NOUN
ejpam-6633	385	15	for	for	ADP
ejpam-6633	385	16	the	the	DET
ejpam-6633	385	17	perturbed	perturb	VERB
ejpam-6633	385	18	(	(	PUNCT
ejpam-6633	385	19	for	for	ADP
ejpam-6633	385	20	some	some	PRON
ejpam-6633	385	21	ϵ	ϵ	PROPN
ejpam-6633	385	22	>	>	X
ejpam-6633	385	23	0	0	NUM
ejpam-6633	385	24	)	)	PUNCT
ejpam-6633	385	25	and	and	CCONJ
ejpam-6633	385	26	unperturbed	unperturbed	ADJ
ejpam-6633	385	27	problem	problem	NOUN
ejpam-6633	385	28	(	(	PUNCT
ejpam-6633	385	29	46	46	NUM
ejpam-6633	385	30	-	-	SYM
ejpam-6633	385	31	48	48	NUM
ejpam-6633	385	32	)	)	PUNCT
ejpam-6633	385	33	,	,	PUNCT
ejpam-6633	385	34	respectively	respectively	ADV
ejpam-6633	385	35	.	.	PUNCT
ejpam-6633	386	1	hence	hence	ADV
ejpam-6633	386	2	,	,	PUNCT
ejpam-6633	386	3	η(t	η(t	NOUN
ejpam-6633	386	4	)	)	PUNCT
ejpam-6633	386	5	is	be	AUX
ejpam-6633	386	6	a	a	DET
ejpam-6633	386	7	solution	solution	NOUN
ejpam-6633	386	8	for	for	ADP
ejpam-6633	386	9	the	the	DET
ejpam-6633	386	10	inequality	inequality	NOUN
ejpam-6633	386	11	(	(	PUNCT
ejpam-6633	386	12	14	14	NUM
ejpam-6633	386	13	)	)	PUNCT
ejpam-6633	386	14	.	.	PUNCT
ejpam-6633	387	1	since	since	SCONJ
ejpam-6633	387	2	both	both	DET
ejpam-6633	387	3	hypotheses	hypothesis	NOUN
ejpam-6633	387	4	h1	h1	ADJ
ejpam-6633	387	5	and	and	CCONJ
ejpam-6633	387	6	h2	h2	NOUN
ejpam-6633	387	7	are	be	AUX
ejpam-6633	387	8	satisfied	satisfied	ADJ
ejpam-6633	387	9	through	through	ADP
ejpam-6633	387	10	(	(	PUNCT
ejpam-6633	387	11	49	49	NUM
ejpam-6633	387	12	-	-	SYM
ejpam-6633	387	13	50	50	NUM
ejpam-6633	387	14	)	)	PUNCT
ejpam-6633	387	15	,	,	PUNCT
ejpam-6633	387	16	then	then	ADV
ejpam-6633	387	17	,	,	PUNCT
ejpam-6633	387	18	by	by	ADP
ejpam-6633	387	19	theorem	theorem	NOUN
ejpam-6633	387	20	4	4	NUM
ejpam-6633	387	21	,	,	PUNCT
ejpam-6633	387	22	both	both	DET
ejpam-6633	387	23	η(t	η(t	NOUN
ejpam-6633	387	24	)	)	PUNCT
ejpam-6633	387	25	and	and	CCONJ
ejpam-6633	387	26	z(t	z(t	NOUN
ejpam-6633	387	27	)	)	PUNCT
ejpam-6633	387	28	satisfy	satisfy	NOUN
ejpam-6633	387	29	inequality	inequality	NOUN
ejpam-6633	387	30	(	(	PUNCT
ejpam-6633	387	31	15	15	NUM
ejpam-6633	387	32	)	)	PUNCT
ejpam-6633	387	33	,	,	PUNCT
ejpam-6633	387	34	and	and	CCONJ
ejpam-6633	387	35	consequently	consequently	ADV
ejpam-6633	387	36	the	the	DET
ejpam-6633	387	37	problem	problem	NOUN
ejpam-6633	387	38	(	(	PUNCT
ejpam-6633	387	39	46	46	NUM
ejpam-6633	387	40	-	-	SYM
ejpam-6633	387	41	48	48	NUM
ejpam-6633	387	42	)	)	PUNCT
ejpam-6633	387	43	is	be	AUX
ejpam-6633	387	44	ulam	ulam	NOUN
ejpam-6633	387	45	-	-	PUNCT
ejpam-6633	387	46	hyers	hyer	NOUN
ejpam-6633	387	47	stable	stable	ADJ
ejpam-6633	387	48	with	with	ADP
ejpam-6633	387	49	ch	ch	NOUN
ejpam-6633	387	50	=	=	SYM
ejpam-6633	387	51	φ1	φ1	PROPN
ejpam-6633	387	52	1−υ	1−υ	NUM
ejpam-6633	387	53	.	.	PUNCT
ejpam-6633	388	1	a.	a.	PROPN
ejpam-6633	388	2	s.	s.	PROPN
ejpam-6633	388	3	hasan	hasan	PROPN
ejpam-6633	388	4	,	,	PUNCT
ejpam-6633	388	5	s.	s.	PROPN
ejpam-6633	388	6	a.	a.	PROPN
ejpam-6633	388	7	murad	murad	PROPN
ejpam-6633	388	8	/	/	SYM
ejpam-6633	388	9	eur	eur	PROPN
ejpam-6633	388	10	.	.	PUNCT
ejpam-6633	389	1	j.	j.	PROPN
ejpam-6633	389	2	pure	pure	PROPN
ejpam-6633	389	3	appl	appl	PROPN
ejpam-6633	389	4	.	.	PROPN
ejpam-6633	389	5	math	math	PROPN
ejpam-6633	389	6	,	,	PUNCT
ejpam-6633	389	7	18	18	NUM
ejpam-6633	389	8	(	(	PUNCT
ejpam-6633	389	9	3	3	NUM
ejpam-6633	389	10	)	)	PUNCT
ejpam-6633	389	11	(	(	PUNCT
ejpam-6633	389	12	2025	2025	NUM
ejpam-6633	389	13	)	)	PUNCT
ejpam-6633	389	14	,	,	PUNCT
ejpam-6633	389	15	6633	6633	NUM
ejpam-6633	389	16	15	15	NUM
ejpam-6633	389	17	of	of	ADP
ejpam-6633	389	18	24	24	NUM
ejpam-6633	389	19	the	the	DET
ejpam-6633	389	20	last	last	ADJ
ejpam-6633	389	21	part	part	NOUN
ejpam-6633	389	22	is	be	AUX
ejpam-6633	389	23	to	to	PART
ejpam-6633	389	24	establish	establish	VERB
ejpam-6633	389	25	how	how	SCONJ
ejpam-6633	389	26	the	the	DET
ejpam-6633	389	27	problem	problem	NOUN
ejpam-6633	389	28	is	be	AUX
ejpam-6633	389	29	stable	stable	ADJ
ejpam-6633	389	30	by	by	ADP
ejpam-6633	389	31	the	the	DET
ejpam-6633	389	32	means	mean	NOUN
ejpam-6633	389	33	of	of	ADP
ejpam-6633	389	34	ulam	ulam	NOUN
ejpam-6633	389	35	-	-	PUNCT
ejpam-6633	389	36	hyersrassiass	hyersrassiass	NOUN
ejpam-6633	389	37	as	as	SCONJ
ejpam-6633	389	38	stated	state	VERB
ejpam-6633	389	39	in	in	ADP
ejpam-6633	389	40	definition	definition	NOUN
ejpam-6633	389	41	5	5	NUM
ejpam-6633	389	42	.	.	PUNCT
ejpam-6633	390	1	if	if	SCONJ
ejpam-6633	390	2	η(t	η(t	NOUN
ejpam-6633	390	3	)	)	PUNCT
ejpam-6633	390	4	is	be	AUX
ejpam-6633	390	5	a	a	DET
ejpam-6633	390	6	solution	solution	NOUN
ejpam-6633	390	7	to	to	ADP
ejpam-6633	390	8	the	the	DET
ejpam-6633	390	9	inequality	inequality	NOUN
ejpam-6633	390	10	(	(	PUNCT
ejpam-6633	390	11	16	16	NUM
ejpam-6633	390	12	)	)	PUNCT
ejpam-6633	390	13	for	for	ADP
ejpam-6633	390	14	some	some	DET
ejpam-6633	390	15	constant	constant	ADJ
ejpam-6633	390	16	ϵ	ϵ	X
ejpam-6633	390	17	>	>	X
ejpam-6633	390	18	0	0	PUNCT
ejpam-6633	390	19	and	and	CCONJ
ejpam-6633	390	20	the	the	DET
ejpam-6633	390	21	control	control	NOUN
ejpam-6633	390	22	function	function	NOUN
ejpam-6633	390	23	is	be	AUX
ejpam-6633	390	24	ψ(t	ψ(t	PROPN
ejpam-6633	390	25	)	)	PUNCT
ejpam-6633	391	1	=	=	SYM
ejpam-6633	391	2	ln	ln	NOUN
ejpam-6633	391	3	(	(	PUNCT
ejpam-6633	391	4	t	t	PROPN
ejpam-6633	391	5	a	a	PRON
ejpam-6633	391	6	)	)	PUNCT
ejpam-6633	391	7	,	,	PUNCT
ejpam-6633	391	8	for	for	ADP
ejpam-6633	391	9	t	t	PROPN
ejpam-6633	391	10	∈	∈	PROPN
ejpam-6633	392	1	[	[	X
ejpam-6633	392	2	a	a	X
ejpam-6633	392	3	,	,	PUNCT
ejpam-6633	392	4	1	1	NUM
ejpam-6633	392	5	]	]	PUNCT
ejpam-6633	392	6	,	,	PUNCT
ejpam-6633	392	7	then	then	ADV
ejpam-6633	392	8	,	,	PUNCT
ejpam-6633	392	9	ψ(t	ψ(t	PROPN
ejpam-6633	392	10	)	)	PUNCT
ejpam-6633	392	11	satisfies	satisfy	VERB
ejpam-6633	392	12	the	the	DET
ejpam-6633	392	13	hypothesis	hypothesis	NOUN
ejpam-6633	392	14	h3	h3	NOUN
ejpam-6633	392	15	.	.	PUNCT
ejpam-6633	393	1	in	in	ADP
ejpam-6633	393	2	other	other	ADJ
ejpam-6633	393	3	words	word	NOUN
ejpam-6633	393	4	,	,	PUNCT
ejpam-6633	393	5	h	h	NOUN
ejpam-6633	393	6	a	a	X
ejpam-6633	393	7	i	i	NOUN
ejpam-6633	393	8	α+βψ(t	α+βψ(t	VERB
ejpam-6633	393	9	)	)	PUNCT
ejpam-6633	393	10	=	=	SYM
ejpam-6633	393	11	h	h	NOUN
ejpam-6633	394	1	a	a	X
ejpam-6633	394	2	i	i	PRON
ejpam-6633	394	3	α+β	α+β	NUM
ejpam-6633	395	1	ln	ln	INTJ
ejpam-6633	396	1	(	(	PUNCT
ejpam-6633	396	2	t	t	PROPN
ejpam-6633	396	3	a	a	NOUN
ejpam-6633	396	4	)	)	PUNCT
ejpam-6633	396	5	(	(	PUNCT
ejpam-6633	396	6	51	51	NUM
ejpam-6633	396	7	)	)	PUNCT
ejpam-6633	396	8	=	=	SYM
ejpam-6633	396	9	γ(2	γ(2	PROPN
ejpam-6633	396	10	)	)	PUNCT
ejpam-6633	397	1	γ(β	γ(β	PROPN
ejpam-6633	398	1	+	+	CCONJ
ejpam-6633	398	2	α+	α+	PUNCT
ejpam-6633	398	3	2	2	NUM
ejpam-6633	398	4	)	)	PUNCT
ejpam-6633	398	5	(	(	PUNCT
ejpam-6633	398	6	ln	ln	X
ejpam-6633	398	7	(	(	PUNCT
ejpam-6633	398	8	t	t	PROPN
ejpam-6633	398	9	a	a	PRON
ejpam-6633	398	10	)	)	PUNCT
ejpam-6633	398	11	)	)	PUNCT
ejpam-6633	398	12	α+β+1	α+β+1	PROPN
ejpam-6633	398	13	=	=	NOUN
ejpam-6633	398	14	1	1	NUM
ejpam-6633	398	15	γ(β	γ(β	PROPN
ejpam-6633	398	16	+	+	CCONJ
ejpam-6633	398	17	α+	α+	PUNCT
ejpam-6633	398	18	2	2	NUM
ejpam-6633	398	19	)	)	PUNCT
ejpam-6633	398	20	(	(	PUNCT
ejpam-6633	398	21	ln	ln	X
ejpam-6633	398	22	(	(	PUNCT
ejpam-6633	398	23	t	t	PROPN
ejpam-6633	398	24	a	a	PRON
ejpam-6633	398	25	)	)	PUNCT
ejpam-6633	398	26	)	)	PUNCT
ejpam-6633	398	27	α+β	α+β	PROPN
ejpam-6633	399	1	ln	ln	INTJ
ejpam-6633	399	2	(	(	PUNCT
ejpam-6633	399	3	t	t	PROPN
ejpam-6633	399	4	a	a	PRON
ejpam-6633	399	5	)	)	PUNCT
ejpam-6633	399	6	≤	≤	NOUN
ejpam-6633	399	7	λψ(t	λψ(t	NOUN
ejpam-6633	399	8	)	)	PUNCT
ejpam-6633	399	9	,	,	PUNCT
ejpam-6633	399	10	where	where	SCONJ
ejpam-6633	399	11	λ	λ	X
ejpam-6633	399	12	=	=	VERB
ejpam-6633	399	13	γ	γ	X
ejpam-6633	399	14	γ(β+α+2	γ(β+α+2	NOUN
ejpam-6633	399	15	)	)	PUNCT
ejpam-6633	399	16	and	and	CCONJ
ejpam-6633	399	17	γ	γ	PROPN
ejpam-6633	399	18	represents	represent	VERB
ejpam-6633	399	19	the	the	DET
ejpam-6633	399	20	maximum	maximum	ADJ
ejpam-6633	399	21	value	value	NOUN
ejpam-6633	399	22	of	of	ADP
ejpam-6633	399	23	(	(	PUNCT
ejpam-6633	399	24	ln	ln	X
ejpam-6633	399	25	(	(	PUNCT
ejpam-6633	399	26	t	t	PROPN
ejpam-6633	399	27	a	a	PRON
ejpam-6633	399	28	)	)	PUNCT
ejpam-6633	399	29	)	)	PUNCT
ejpam-6633	399	30	α+β	α+β	PROPN
ejpam-6633	399	31	on	on	ADP
ejpam-6633	399	32	[	[	X
ejpam-6633	399	33	a	a	X
ejpam-6633	399	34	,	,	PUNCT
ejpam-6633	399	35	1	1	NUM
ejpam-6633	399	36	]	]	PUNCT
ejpam-6633	399	37	.	.	PUNCT
ejpam-6633	400	1	the	the	DET
ejpam-6633	400	2	value	value	NOUN
ejpam-6633	400	3	of	of	ADP
ejpam-6633	400	4	λ	λ	PROPN
ejpam-6633	400	5	depends	depend	VERB
ejpam-6633	400	6	on	on	ADP
ejpam-6633	400	7	three	three	NUM
ejpam-6633	400	8	parameters	parameter	NOUN
ejpam-6633	400	9	,	,	PUNCT
ejpam-6633	400	10	a	a	DET
ejpam-6633	400	11	,	,	PUNCT
ejpam-6633	400	12	α	α	NOUN
ejpam-6633	400	13	,	,	PUNCT
ejpam-6633	400	14	and	and	CCONJ
ejpam-6633	400	15	β	β	AUX
ejpam-6633	400	16	.	.	PUNCT
ejpam-6633	401	1	for	for	ADP
ejpam-6633	401	2	example	example	NOUN
ejpam-6633	401	3	,	,	PUNCT
ejpam-6633	401	4	for	for	ADP
ejpam-6633	401	5	a	a	DET
ejpam-6633	401	6	=	=	SYM
ejpam-6633	401	7	0.9	0.9	NUM
ejpam-6633	401	8	,	,	PUNCT
ejpam-6633	401	9	α	α	X
ejpam-6633	401	10	=	=	PUNCT
ejpam-6633	401	11	β	β	X
ejpam-6633	401	12	=	=	SYM
ejpam-6633	401	13	0.5	0.5	NUM
ejpam-6633	401	14	,	,	PUNCT
ejpam-6633	401	15	we	we	PRON
ejpam-6633	401	16	have	have	VERB
ejpam-6633	401	17	λ	λ	NOUN
ejpam-6633	401	18	=	=	SYM
ejpam-6633	401	19	0.05268	0.05268	NUM
ejpam-6633	401	20	.	.	PUNCT
ejpam-6633	402	1	consequently	consequently	ADV
ejpam-6633	402	2	,	,	PUNCT
ejpam-6633	402	3	by	by	ADP
ejpam-6633	402	4	theorem	theorem	NOUN
ejpam-6633	402	5	5	5	NUM
ejpam-6633	402	6	,	,	PUNCT
ejpam-6633	402	7	the	the	DET
ejpam-6633	402	8	problem	problem	NOUN
ejpam-6633	402	9	(	(	PUNCT
ejpam-6633	402	10	46	46	NUM
ejpam-6633	402	11	-	-	SYM
ejpam-6633	402	12	48	48	NUM
ejpam-6633	402	13	)	)	PUNCT
ejpam-6633	402	14	is	be	AUX
ejpam-6633	402	15	ulam	ulam	ADJ
ejpam-6633	402	16	-	-	PUNCT
ejpam-6633	402	17	hyersrassiass	hyersrassiass	NOUN
ejpam-6633	402	18	stable	stable	ADJ
ejpam-6633	402	19	as	as	ADP
ejpam-6633	402	20	the	the	DET
ejpam-6633	402	21	following	follow	VERB
ejpam-6633	402	22	inequality	inequality	NOUN
ejpam-6633	402	23	holds	hold	VERB
ejpam-6633	402	24	,	,	PUNCT
ejpam-6633	402	25	|η(t)−	|η(t)−	PROPN
ejpam-6633	402	26	z(t)|	z(t)|	VERB
ejpam-6633	402	27	≤	≤	PROPN
ejpam-6633	402	28	ϵcλψ(t	ϵcλψ(t	X
ejpam-6633	402	29	)	)	PUNCT
ejpam-6633	402	30	,	,	PUNCT
ejpam-6633	402	31	(	(	PUNCT
ejpam-6633	402	32	52	52	NUM
ejpam-6633	402	33	)	)	PUNCT
ejpam-6633	402	34	where	where	SCONJ
ejpam-6633	402	35	cλ	cλ	PROPN
ejpam-6633	402	36	=	=	SYM
ejpam-6633	402	37	2λ	2λ	PROPN
ejpam-6633	402	38	(	(	PUNCT
ejpam-6633	402	39	1−kφ1−φ2	1−kφ1−φ2	PROPN
ejpam-6633	402	40	)	)	PUNCT
ejpam-6633	402	41	.	.	PUNCT
ejpam-6633	403	1	both	both	DET
ejpam-6633	403	2	parameters	parameter	NOUN
ejpam-6633	403	3	,	,	PUNCT
ejpam-6633	403	4	ch	ch	PROPN
ejpam-6633	403	5	and	and	CCONJ
ejpam-6633	403	6	cλ	cλ	PROPN
ejpam-6633	403	7	are	be	AUX
ejpam-6633	403	8	depicted	depict	VERB
ejpam-6633	403	9	in	in	ADP
ejpam-6633	403	10	figure	figure	NOUN
ejpam-6633	403	11	2	2	NUM
ejpam-6633	403	12	for	for	ADP
ejpam-6633	403	13	both	both	CCONJ
ejpam-6633	403	14	a	a	DET
ejpam-6633	403	15	=	=	SYM
ejpam-6633	403	16	0.9	0.9	NUM
ejpam-6633	403	17	and	and	CCONJ
ejpam-6633	403	18	a	a	DET
ejpam-6633	403	19	=	=	NOUN
ejpam-6633	403	20	0.8	0.8	NUM
ejpam-6633	403	21	.	.	PUNCT
ejpam-6633	404	1	a.	a.	PROPN
ejpam-6633	404	2	s.	s.	PROPN
ejpam-6633	404	3	hasan	hasan	PROPN
ejpam-6633	404	4	,	,	PUNCT
ejpam-6633	404	5	s.	s.	PROPN
ejpam-6633	404	6	a.	a.	PROPN
ejpam-6633	404	7	murad	murad	PROPN
ejpam-6633	404	8	/	/	SYM
ejpam-6633	404	9	eur	eur	PROPN
ejpam-6633	404	10	.	.	PUNCT
ejpam-6633	405	1	j.	j.	PROPN
ejpam-6633	405	2	pure	pure	PROPN
ejpam-6633	405	3	appl	appl	PROPN
ejpam-6633	405	4	.	.	PROPN
ejpam-6633	405	5	math	math	PROPN
ejpam-6633	405	6	,	,	PUNCT
ejpam-6633	405	7	18	18	NUM
ejpam-6633	405	8	(	(	PUNCT
ejpam-6633	405	9	3	3	NUM
ejpam-6633	405	10	)	)	PUNCT
ejpam-6633	405	11	(	(	PUNCT
ejpam-6633	405	12	2025	2025	NUM
ejpam-6633	405	13	)	)	PUNCT
ejpam-6633	405	14	,	,	PUNCT
ejpam-6633	405	15	6633	6633	NUM
ejpam-6633	405	16	16	16	NUM
ejpam-6633	405	17	of	of	ADP
ejpam-6633	405	18	24	24	NUM
ejpam-6633	405	19	(	(	PUNCT
ejpam-6633	405	20	a	a	NOUN
ejpam-6633	405	21	)	)	PUNCT
ejpam-6633	405	22	(	(	PUNCT
ejpam-6633	405	23	b	b	X
ejpam-6633	405	24	)	)	PUNCT
ejpam-6633	405	25	figure	figure	NOUN
ejpam-6633	405	26	2	2	NUM
ejpam-6633	405	27	:	:	PUNCT
ejpam-6633	405	28	the	the	DET
ejpam-6633	405	29	range	range	NOUN
ejpam-6633	405	30	of	of	ADP
ejpam-6633	405	31	values	value	NOUN
ejpam-6633	405	32	of	of	ADP
ejpam-6633	405	33	ch	ch	NOUN
ejpam-6633	405	34	and	and	CCONJ
ejpam-6633	405	35	cλ	cλ	NOUN
ejpam-6633	405	36	as	as	ADP
ejpam-6633	405	37	both	both	DET
ejpam-6633	405	38	orders	order	NOUN
ejpam-6633	405	39	,	,	PUNCT
ejpam-6633	405	40	α	α	NOUN
ejpam-6633	405	41	and	and	CCONJ
ejpam-6633	405	42	β	β	NOUN
ejpam-6633	405	43	,	,	PUNCT
ejpam-6633	405	44	grow	grow	VERB
ejpam-6633	405	45	from	from	ADP
ejpam-6633	405	46	0.1	0.1	NUM
ejpam-6633	405	47	up	up	ADP
ejpam-6633	405	48	to	to	ADP
ejpam-6633	405	49	0.9	0.9	NUM
ejpam-6633	405	50	for	for	ADP
ejpam-6633	405	51	a	a	DET
ejpam-6633	405	52	=	=	SYM
ejpam-6633	405	53	0.9	0.9	NUM
ejpam-6633	405	54	(	(	PUNCT
ejpam-6633	405	55	left	leave	VERB
ejpam-6633	405	56	)	)	PUNCT
ejpam-6633	405	57	and	and	CCONJ
ejpam-6633	405	58	a	a	DET
ejpam-6633	405	59	=	=	SYM
ejpam-6633	405	60	0.8	0.8	NUM
ejpam-6633	405	61	(	(	PUNCT
ejpam-6633	405	62	right	right	NOUN
ejpam-6633	405	63	)	)	PUNCT
ejpam-6633	405	64	,	,	PUNCT
ejpam-6633	405	65	(	(	PUNCT
ejpam-6633	405	66	a	a	X
ejpam-6633	405	67	)	)	PUNCT
ejpam-6633	405	68	ch	ch	NOUN
ejpam-6633	405	69	,	,	PUNCT
ejpam-6633	405	70	and	and	CCONJ
ejpam-6633	405	71	(	(	PUNCT
ejpam-6633	405	72	b	b	X
ejpam-6633	405	73	)	)	PUNCT
ejpam-6633	405	74	cλ	cλ	NOUN
ejpam-6633	405	75	.	.	NOUN
ejpam-6633	405	76	5	5	NUM
ejpam-6633	405	77	.	.	X
ejpam-6633	405	78	numerical	numerical	ADJ
ejpam-6633	405	79	scheme	scheme	NOUN
ejpam-6633	405	80	in	in	ADP
ejpam-6633	405	81	this	this	DET
ejpam-6633	405	82	section	section	NOUN
ejpam-6633	405	83	we	we	PRON
ejpam-6633	405	84	introduce	introduce	VERB
ejpam-6633	405	85	a	a	DET
ejpam-6633	405	86	numerical	numerical	ADJ
ejpam-6633	405	87	scheme	scheme	NOUN
ejpam-6633	405	88	to	to	PART
ejpam-6633	405	89	approximately	approximately	ADV
ejpam-6633	405	90	solve	solve	VERB
ejpam-6633	405	91	the	the	DET
ejpam-6633	405	92	problem	problem	NOUN
ejpam-6633	405	93	(	(	PUNCT
ejpam-6633	405	94	6	6	NUM
ejpam-6633	405	95	-	-	SYM
ejpam-6633	405	96	8)	8)	NUM
ejpam-6633	405	97	through	through	ADP
ejpam-6633	405	98	the	the	DET
ejpam-6633	405	99	newton	newton	PROPN
ejpam-6633	405	100	-	-	PUNCT
ejpam-6633	405	101	raphson	raphson	NOUN
ejpam-6633	405	102	method	method	NOUN
ejpam-6633	405	103	.	.	PUNCT
ejpam-6633	406	1	we	we	PRON
ejpam-6633	406	2	apply	apply	VERB
ejpam-6633	406	3	the	the	DET
ejpam-6633	406	4	fractional	fractional	ADJ
ejpam-6633	406	5	rectangular	rectangular	ADJ
ejpam-6633	406	6	,	,	PUNCT
ejpam-6633	406	7	lln,1	lln,1	NOUN
ejpam-6633	406	8	,	,	PUNCT
ejpam-6633	406	9	interpolation	interpolation	NOUN
ejpam-6633	406	10	on	on	ADP
ejpam-6633	406	11	a	a	DET
ejpam-6633	406	12	logarithmic	logarithmic	ADJ
ejpam-6633	406	13	grid	grid	NOUN
ejpam-6633	406	14	to	to	PART
ejpam-6633	406	15	approximate	approximate	VERB
ejpam-6633	406	16	the	the	DET
ejpam-6633	406	17	derived	derive	VERB
ejpam-6633	406	18	analytical	analytical	ADJ
ejpam-6633	406	19	solution	solution	NOUN
ejpam-6633	406	20	(	(	PUNCT
ejpam-6633	406	21	18	18	NUM
ejpam-6633	406	22	)	)	PUNCT
ejpam-6633	406	23	.	.	PUNCT
ejpam-6633	407	1	a.	a.	PROPN
ejpam-6633	407	2	s.	s.	PROPN
ejpam-6633	407	3	hasan	hasan	PROPN
ejpam-6633	407	4	,	,	PUNCT
ejpam-6633	407	5	s.	s.	PROPN
ejpam-6633	407	6	a.	a.	PROPN
ejpam-6633	407	7	murad	murad	PROPN
ejpam-6633	407	8	/	/	SYM
ejpam-6633	407	9	eur	eur	PROPN
ejpam-6633	407	10	.	.	PUNCT
ejpam-6633	408	1	j.	j.	PROPN
ejpam-6633	408	2	pure	pure	PROPN
ejpam-6633	408	3	appl	appl	PROPN
ejpam-6633	408	4	.	.	PROPN
ejpam-6633	408	5	math	math	PROPN
ejpam-6633	408	6	,	,	PUNCT
ejpam-6633	408	7	18	18	NUM
ejpam-6633	408	8	(	(	PUNCT
ejpam-6633	408	9	3	3	NUM
ejpam-6633	408	10	)	)	PUNCT
ejpam-6633	408	11	(	(	PUNCT
ejpam-6633	408	12	2025	2025	NUM
ejpam-6633	408	13	)	)	PUNCT
ejpam-6633	408	14	,	,	PUNCT
ejpam-6633	408	15	6633	6633	NUM
ejpam-6633	408	16	17	17	NUM
ejpam-6633	408	17	of	of	ADP
ejpam-6633	408	18	24	24	NUM
ejpam-6633	408	19	this	this	DET
ejpam-6633	408	20	results	result	NOUN
ejpam-6633	408	21	in	in	ADP
ejpam-6633	408	22	a	a	DET
ejpam-6633	408	23	system	system	NOUN
ejpam-6633	408	24	of	of	ADP
ejpam-6633	408	25	non	non	ADJ
ejpam-6633	408	26	-	-	ADJ
ejpam-6633	408	27	linear	linear	ADJ
ejpam-6633	408	28	equations	equation	NOUN
ejpam-6633	408	29	which	which	PRON
ejpam-6633	408	30	will	will	AUX
ejpam-6633	408	31	be	be	AUX
ejpam-6633	408	32	solved	solve	VERB
ejpam-6633	408	33	by	by	ADP
ejpam-6633	408	34	the	the	DET
ejpam-6633	408	35	newtonraphson	newtonraphson	PROPN
ejpam-6633	408	36	method	method	NOUN
ejpam-6633	408	37	using	use	VERB
ejpam-6633	408	38	the	the	DET
ejpam-6633	408	39	jacobian	jacobian	ADJ
ejpam-6633	408	40	matrix	matrix	NOUN
ejpam-6633	408	41	to	to	PART
ejpam-6633	408	42	handle	handle	VERB
ejpam-6633	408	43	the	the	DET
ejpam-6633	408	44	non	non	ADJ
ejpam-6633	408	45	-	-	ADJ
ejpam-6633	408	46	linear	linear	ADJ
ejpam-6633	408	47	coupling	coupling	NOUN
ejpam-6633	408	48	between	between	ADP
ejpam-6633	408	49	η(t	η(t	NOUN
ejpam-6633	408	50	)	)	PUNCT
ejpam-6633	408	51	and	and	CCONJ
ejpam-6633	408	52	θ(t	θ(t	PROPN
ejpam-6633	408	53	,	,	PUNCT
ejpam-6633	408	54	η(t	η(t	NOUN
ejpam-6633	408	55	)	)	PUNCT
ejpam-6633	408	56	)	)	PUNCT
ejpam-6633	408	57	.	.	PUNCT
ejpam-6633	409	1	we	we	PRON
ejpam-6633	409	2	subdivide	subdivide	VERB
ejpam-6633	409	3	the	the	DET
ejpam-6633	409	4	domain	domain	NOUN
ejpam-6633	409	5	using	use	VERB
ejpam-6633	409	6	a	a	DET
ejpam-6633	409	7	non	non	ADJ
ejpam-6633	409	8	-	-	ADJ
ejpam-6633	409	9	uniform	uniform	ADJ
ejpam-6633	409	10	mesh	mesh	NOUN
ejpam-6633	409	11	on	on	ADP
ejpam-6633	409	12	[	[	X
ejpam-6633	409	13	a	a	X
ejpam-6633	409	14	,	,	PUNCT
ejpam-6633	409	15	1	1	NUM
ejpam-6633	409	16	]	]	PUNCT
ejpam-6633	409	17	,	,	PUNCT
ejpam-6633	409	18	b	b	X
ejpam-6633	409	19	=	=	SYM
ejpam-6633	409	20	{	{	PUNCT
ejpam-6633	409	21	t0	t0	PROPN
ejpam-6633	409	22	,	,	PUNCT
ejpam-6633	409	23	t1	t1	PROPN
ejpam-6633	409	24	,	,	PUNCT
ejpam-6633	409	25	·	·	PUNCT
ejpam-6633	409	26	·	·	PUNCT
ejpam-6633	409	27	·	·	PUNCT
ejpam-6633	409	28	,	,	PUNCT
ejpam-6633	409	29	tn	tn	PROPN
ejpam-6633	409	30	}	}	PUNCT
ejpam-6633	409	31	,	,	PUNCT
ejpam-6633	409	32	for	for	ADP
ejpam-6633	409	33	some	some	DET
ejpam-6633	409	34	positive	positive	ADJ
ejpam-6633	409	35	integer	integer	NOUN
ejpam-6633	409	36	n	n	CCONJ
ejpam-6633	409	37	where	where	SCONJ
ejpam-6633	409	38	t0	t0	X
ejpam-6633	409	39	=	=	PUNCT
ejpam-6633	409	40	a	a	PROPN
ejpam-6633	409	41	and	and	CCONJ
ejpam-6633	409	42	tn	tn	NOUN
ejpam-6633	409	43	=	=	SYM
ejpam-6633	409	44	1	1	X
ejpam-6633	409	45	.	.	PUNCT
ejpam-6633	410	1	the	the	DET
ejpam-6633	410	2	following	follow	VERB
ejpam-6633	410	3	formula	formula	NOUN
ejpam-6633	410	4	is	be	AUX
ejpam-6633	410	5	used	use	VERB
ejpam-6633	410	6	to	to	PART
ejpam-6633	410	7	generate	generate	VERB
ejpam-6633	410	8	the	the	DET
ejpam-6633	410	9	graded	grade	VERB
ejpam-6633	410	10	mesh	mesh	NOUN
ejpam-6633	410	11	:	:	PUNCT
ejpam-6633	410	12	ln(ti	ln(ti	NOUN
ejpam-6633	410	13	)	)	PUNCT
ejpam-6633	410	14	=	=	SYM
ejpam-6633	410	15	ln(t0	ln(t0	NOUN
ejpam-6633	410	16	)	)	PUNCT
ejpam-6633	411	1	+	+	CCONJ
ejpam-6633	411	2	∆	∆	PROPN
ejpam-6633	411	3	(	(	PUNCT
ejpam-6633	411	4	i	i	NOUN
ejpam-6633	411	5	n	n	PROPN
ejpam-6633	411	6	)	)	PUNCT
ejpam-6633	411	7	s	s	PART
ejpam-6633	411	8	,	,	PUNCT
ejpam-6633	411	9	(	(	PUNCT
ejpam-6633	411	10	53	53	NUM
ejpam-6633	411	11	)	)	PUNCT
ejpam-6633	411	12	where	where	SCONJ
ejpam-6633	411	13	∆	∆	VERB
ejpam-6633	411	14	=	=	SYM
ejpam-6633	411	15	ln(tn	ln(tn	PROPN
ejpam-6633	411	16	)	)	PUNCT
ejpam-6633	411	17	−	−	ADP
ejpam-6633	411	18	ln(t0	ln(t0	NOUN
ejpam-6633	411	19	)	)	PUNCT
ejpam-6633	411	20	,	,	PUNCT
ejpam-6633	411	21	for	for	ADP
ejpam-6633	411	22	the	the	DET
ejpam-6633	411	23	considered	consider	VERB
ejpam-6633	411	24	interval	interval	NOUN
ejpam-6633	411	25	we	we	PRON
ejpam-6633	411	26	have	have	VERB
ejpam-6633	411	27	∆	∆	PROPN
ejpam-6633	411	28	=	=	SYM
ejpam-6633	411	29	−ln(t0	−ln(t0	NUM
ejpam-6633	411	30	)	)	PUNCT
ejpam-6633	411	31	,	,	PUNCT
ejpam-6633	411	32	and	and	CCONJ
ejpam-6633	411	33	s	s	VERB
ejpam-6633	411	34	is	be	AUX
ejpam-6633	411	35	the	the	DET
ejpam-6633	411	36	mesh	mesh	NOUN
ejpam-6633	411	37	graded	grade	VERB
ejpam-6633	411	38	parameter	parameter	NOUN
ejpam-6633	411	39	which	which	PRON
ejpam-6633	411	40	is	be	AUX
ejpam-6633	411	41	sensitive	sensitive	ADJ
ejpam-6633	411	42	.	.	PUNCT
ejpam-6633	412	1	for	for	ADP
ejpam-6633	412	2	s	s	NOUN
ejpam-6633	412	3	=	=	SYM
ejpam-6633	412	4	1	1	NUM
ejpam-6633	412	5	we	we	PRON
ejpam-6633	412	6	obtain	obtain	VERB
ejpam-6633	412	7	the	the	DET
ejpam-6633	412	8	uniform	uniform	ADJ
ejpam-6633	412	9	mesh	mesh	NOUN
ejpam-6633	412	10	(	(	PUNCT
ejpam-6633	412	11	in	in	ADP
ejpam-6633	412	12	the	the	DET
ejpam-6633	412	13	logarithmic	logarithmic	ADJ
ejpam-6633	412	14	scale	scale	NOUN
ejpam-6633	412	15	)	)	PUNCT
ejpam-6633	412	16	,	,	PUNCT
ejpam-6633	412	17	while	while	SCONJ
ejpam-6633	412	18	for	for	SCONJ
ejpam-6633	412	19	optimized	optimize	VERB
ejpam-6633	412	20	s	s	X
ejpam-6633	412	21	>	>	X
ejpam-6633	412	22	1	1	NUM
ejpam-6633	412	23	,	,	PUNCT
ejpam-6633	412	24	both	both	CCONJ
ejpam-6633	412	25	the	the	DET
ejpam-6633	412	26	resolution	resolution	NOUN
ejpam-6633	412	27	of	of	ADP
ejpam-6633	412	28	the	the	DET
ejpam-6633	412	29	non	non	ADJ
ejpam-6633	412	30	-	-	ADJ
ejpam-6633	412	31	local	local	ADJ
ejpam-6633	412	32	effects	effect	NOUN
ejpam-6633	412	33	inherent	inherent	ADJ
ejpam-6633	412	34	to	to	PART
ejpam-6633	412	35	fractional	fractional	ADJ
ejpam-6633	412	36	derivatives	derivative	NOUN
ejpam-6633	412	37	and	and	CCONJ
ejpam-6633	412	38	the	the	DET
ejpam-6633	412	39	logarithmic	logarithmic	ADJ
ejpam-6633	412	40	kernel	kernel	NOUN
ejpam-6633	412	41	close	close	ADJ
ejpam-6633	412	42	to	to	ADP
ejpam-6633	412	43	t	t	NOUN
ejpam-6633	412	44	=	=	PUNCT
ejpam-6633	412	45	a	a	PRON
ejpam-6633	412	46	and	and	CCONJ
ejpam-6633	412	47	the	the	DET
ejpam-6633	412	48	convergence	convergence	NOUN
ejpam-6633	412	49	rate	rate	NOUN
ejpam-6633	412	50	are	be	AUX
ejpam-6633	412	51	improved	improve	VERB
ejpam-6633	412	52	.	.	PUNCT
ejpam-6633	413	1	for	for	ADP
ejpam-6633	413	2	i	i	PRON
ejpam-6633	413	3	=	=	SYM
ejpam-6633	413	4	0	0	NUM
ejpam-6633	413	5	,	,	PUNCT
ejpam-6633	413	6	formula	formula	NOUN
ejpam-6633	413	7	(	(	PUNCT
ejpam-6633	413	8	53	53	NUM
ejpam-6633	413	9	)	)	PUNCT
ejpam-6633	413	10	generates	generate	VERB
ejpam-6633	413	11	ln(t0	ln(t0	NOUN
ejpam-6633	413	12	)	)	PUNCT
ejpam-6633	413	13	and	and	CCONJ
ejpam-6633	413	14	for	for	ADP
ejpam-6633	413	15	i	i	PRON
ejpam-6633	413	16	=	=	SYM
ejpam-6633	413	17	n	n	PROPN
ejpam-6633	413	18	,	,	PUNCT
ejpam-6633	413	19	it	it	PRON
ejpam-6633	413	20	generates	generate	VERB
ejpam-6633	413	21	ln(tn	ln(tn	PROPN
ejpam-6633	413	22	)	)	PUNCT
ejpam-6633	413	23	.	.	PUNCT
ejpam-6633	414	1	the	the	DET
ejpam-6633	414	2	numerical	numerical	ADJ
ejpam-6633	414	3	solution	solution	NOUN
ejpam-6633	414	4	of	of	ADP
ejpam-6633	414	5	(	(	PUNCT
ejpam-6633	414	6	18	18	NUM
ejpam-6633	414	7	)	)	PUNCT
ejpam-6633	414	8	is	be	AUX
ejpam-6633	414	9	equivalent	equivalent	ADJ
ejpam-6633	414	10	to	to	ADP
ejpam-6633	414	11	solving	solve	VERB
ejpam-6633	414	12	the	the	DET
ejpam-6633	414	13	two	two	NUM
ejpam-6633	414	14	-	-	PUNCT
ejpam-6633	414	15	point	point	NOUN
ejpam-6633	414	16	fractional	fractional	ADJ
ejpam-6633	414	17	boundaryvalue	boundaryvalue	NOUN
ejpam-6633	414	18	problem	problem	NOUN
ejpam-6633	414	19	(	(	PUNCT
ejpam-6633	414	20	6	6	NUM
ejpam-6633	414	21	-	-	SYM
ejpam-6633	414	22	8)	8)	NUM
ejpam-6633	414	23	.	.	PUNCT
ejpam-6633	415	1	at	at	ADP
ejpam-6633	415	2	t	t	NOUN
ejpam-6633	415	3	=	=	PUNCT
ejpam-6633	415	4	tq	tq	ADP
ejpam-6633	415	5	,	,	PUNCT
ejpam-6633	415	6	(	(	PUNCT
ejpam-6633	415	7	0	0	NUM
ejpam-6633	415	8	≤	≤	PROPN
ejpam-6633	415	9	q	q	PROPN
ejpam-6633	415	10	≤	≤	NUM
ejpam-6633	415	11	n	n	CCONJ
ejpam-6633	415	12	)	)	PUNCT
ejpam-6633	415	13	,	,	PUNCT
ejpam-6633	415	14	tq	tq	ADP
ejpam-6633	415	15	∈	∈	PROPN
ejpam-6633	415	16	b	b	PROPN
ejpam-6633	415	17	,	,	PUNCT
ejpam-6633	415	18	denote	denote	VERB
ejpam-6633	415	19	ηq	ηq	ADP
ejpam-6633	415	20	≈	≈	PROPN
ejpam-6633	415	21	η(tq	η(tq	PROPN
ejpam-6633	415	22	)	)	PUNCT
ejpam-6633	415	23	,	,	PUNCT
ejpam-6633	415	24	we	we	PRON
ejpam-6633	415	25	have	have	VERB
ejpam-6633	415	26	:	:	PUNCT
ejpam-6633	415	27	ηq	ηq	VERB
ejpam-6633	415	28	=	=	SYM
ejpam-6633	415	29	1	1	NUM
ejpam-6633	415	30	γ(β	γ(β	PROPN
ejpam-6633	415	31	+	+	NUM
ejpam-6633	415	32	α	α	X
ejpam-6633	415	33	)	)	PUNCT
ejpam-6633	415	34	∫	∫	PROPN
ejpam-6633	416	1	tq	tq	INTJ
ejpam-6633	416	2	a	a	PRON
ejpam-6633	416	3	(	(	PUNCT
ejpam-6633	416	4	ln	ln	NOUN
ejpam-6633	416	5	(	(	PUNCT
ejpam-6633	416	6	tq	tq	INTJ
ejpam-6633	416	7	τ	τ	PROPN
ejpam-6633	416	8	)	)	PUNCT
ejpam-6633	416	9	)	)	PUNCT
ejpam-6633	416	10	β+α−1	β+α−1	PUNCT
ejpam-6633	417	1	θ(τ	θ(τ	PROPN
ejpam-6633	417	2	,	,	PUNCT
ejpam-6633	417	3	η(τ	η(τ	PROPN
ejpam-6633	417	4	)	)	PUNCT
ejpam-6633	417	5	)	)	PUNCT
ejpam-6633	418	1	τ	τ	PROPN
ejpam-6633	418	2	dτ	dτ	NOUN
ejpam-6633	418	3	−	−	PROPN
ejpam-6633	418	4	µ	µ	PROPN
ejpam-6633	418	5	γ(α	γ(α	NOUN
ejpam-6633	418	6	)	)	PUNCT
ejpam-6633	418	7	∫	∫	PROPN
ejpam-6633	419	1	tq	tq	INTJ
ejpam-6633	419	2	a	a	DET
ejpam-6633	419	3	(	(	PUNCT
ejpam-6633	419	4	ln	ln	NOUN
ejpam-6633	419	5	(	(	PUNCT
ejpam-6633	419	6	tq	tq	INTJ
ejpam-6633	419	7	τ	τ	PROPN
ejpam-6633	419	8	)	)	PUNCT
ejpam-6633	419	9	)	)	PUNCT
ejpam-6633	419	10	α−1	α−1	PROPN
ejpam-6633	419	11	η(τ	η(τ	PROPN
ejpam-6633	419	12	)	)	PUNCT
ejpam-6633	419	13	τ2	τ2	PROPN
ejpam-6633	419	14	dτ	dτ	NOUN
ejpam-6633	419	15	−	−	PROPN
ejpam-6633	420	1	(	(	PUNCT
ejpam-6633	420	2	ln	ln	INTJ
ejpam-6633	420	3	(	(	PUNCT
ejpam-6633	420	4	tq	tq	INTJ
ejpam-6633	420	5	a	a	PRON
ejpam-6633	420	6	)	)	PUNCT
ejpam-6633	420	7	)	)	PUNCT
ejpam-6633	420	8	α	α	NOUN
ejpam-6633	420	9	bγ(β	bγ(β	X
ejpam-6633	420	10	+	+	X
ejpam-6633	420	11	α	α	X
ejpam-6633	420	12	)	)	PUNCT
ejpam-6633	420	13	∫	∫	PROPN
ejpam-6633	420	14	1	1	NUM
ejpam-6633	420	15	a	a	PRON
ejpam-6633	420	16	(	(	PUNCT
ejpam-6633	420	17	ln	ln	NOUN
ejpam-6633	420	18	(	(	PUNCT
ejpam-6633	420	19	1	1	NUM
ejpam-6633	420	20	τ	τ	PROPN
ejpam-6633	420	21	)	)	PUNCT
ejpam-6633	420	22	)	)	PUNCT
ejpam-6633	421	1	β+α−1	β+α−1	PROPN
ejpam-6633	422	1	θ(τ	θ(τ	PROPN
ejpam-6633	422	2	,	,	PUNCT
ejpam-6633	422	3	η(τ	η(τ	PROPN
ejpam-6633	422	4	)	)	PUNCT
ejpam-6633	422	5	)	)	PUNCT
ejpam-6633	423	1	τ	τ	PROPN
ejpam-6633	423	2	dτ	dτ	PROPN
ejpam-6633	424	1	+	+	X
ejpam-6633	424	2	µ	µ	X
ejpam-6633	424	3	(	(	PUNCT
ejpam-6633	424	4	ln	ln	X
ejpam-6633	424	5	(	(	PUNCT
ejpam-6633	424	6	tq	tq	INTJ
ejpam-6633	424	7	a	a	PRON
ejpam-6633	424	8	)	)	PUNCT
ejpam-6633	424	9	)	)	PUNCT
ejpam-6633	424	10	α	α	PROPN
ejpam-6633	424	11	bγ(α	bγ(α	PROPN
ejpam-6633	424	12	)	)	PUNCT
ejpam-6633	424	13	∫	∫	PROPN
ejpam-6633	425	1	1	1	NUM
ejpam-6633	425	2	a	a	DET
ejpam-6633	425	3	(	(	PUNCT
ejpam-6633	425	4	ln	ln	NOUN
ejpam-6633	425	5	(	(	PUNCT
ejpam-6633	425	6	1	1	NUM
ejpam-6633	425	7	τ	τ	PROPN
ejpam-6633	425	8	)	)	PUNCT
ejpam-6633	425	9	)	)	PUNCT
ejpam-6633	425	10	α−1	α−1	PROPN
ejpam-6633	425	11	η(τ	η(τ	PROPN
ejpam-6633	425	12	)	)	PUNCT
ejpam-6633	425	13	τ2	τ2	PROPN
ejpam-6633	425	14	dτ	dτ	NOUN
ejpam-6633	425	15	+	+	NOUN
ejpam-6633	425	16	φq	φq	PROPN
ejpam-6633	425	17	,	,	PUNCT
ejpam-6633	425	18	(	(	PUNCT
ejpam-6633	425	19	54	54	NUM
ejpam-6633	425	20	)	)	PUNCT
ejpam-6633	425	21	where	where	SCONJ
ejpam-6633	425	22	φq	φq	ADP
ejpam-6633	425	23	=	=	PUNCT
ejpam-6633	425	24	φ(tq	φ(tq	NOUN
ejpam-6633	425	25	)	)	PUNCT
ejpam-6633	425	26	=	=	SYM
ejpam-6633	426	1	ξ1	ξ1	NOUN
ejpam-6633	426	2	+	+	CCONJ
ejpam-6633	426	3	1	1	NUM
ejpam-6633	426	4	b	b	X
ejpam-6633	426	5	(	(	PUNCT
ejpam-6633	426	6	ξ2	ξ2	NOUN
ejpam-6633	426	7	−	−	PROPN
ejpam-6633	426	8	ξ1	ξ1	NOUN
ejpam-6633	426	9	)	)	PUNCT
ejpam-6633	426	10	(	(	PUNCT
ejpam-6633	426	11	ln	ln	X
ejpam-6633	426	12	(	(	PUNCT
ejpam-6633	426	13	tq	tq	INTJ
ejpam-6633	426	14	a	a	PRON
ejpam-6633	426	15	)	)	PUNCT
ejpam-6633	426	16	)	)	PUNCT
ejpam-6633	426	17	α	α	PROPN
ejpam-6633	426	18	.	.	PUNCT
ejpam-6633	427	1	furthermore	furthermore	ADV
ejpam-6633	427	2	,	,	PUNCT
ejpam-6633	427	3	ηq	ηq	ADP
ejpam-6633	427	4	=	=	NOUN
ejpam-6633	427	5	1	1	NUM
ejpam-6633	427	6	γ(β	γ(β	PROPN
ejpam-6633	427	7	+	+	NUM
ejpam-6633	427	8	α	α	X
ejpam-6633	427	9	)	)	PUNCT
ejpam-6633	427	10	q∑	q∑	PROPN
ejpam-6633	428	1	i=1	i=1	PROPN
ejpam-6633	428	2	∫	∫	PROPN
ejpam-6633	428	3	ti	ti	PROPN
ejpam-6633	428	4	ti−1	ti−1	PROPN
ejpam-6633	428	5	(	(	PUNCT
ejpam-6633	428	6	ln	ln	X
ejpam-6633	428	7	(	(	PUNCT
ejpam-6633	428	8	tq	tq	INTJ
ejpam-6633	428	9	τ	τ	PROPN
ejpam-6633	428	10	)	)	PUNCT
ejpam-6633	428	11	)	)	PUNCT
ejpam-6633	429	1	β+α−1	β+α−1	PUNCT
ejpam-6633	429	2	θ(τ	θ(τ	PROPN
ejpam-6633	429	3	,	,	PUNCT
ejpam-6633	429	4	η(τ	η(τ	PROPN
ejpam-6633	429	5	)	)	PUNCT
ejpam-6633	429	6	)	)	PUNCT
ejpam-6633	429	7	dτ	dτ	NOUN
ejpam-6633	430	1	τ	τ	PROPN
ejpam-6633	430	2	−	−	PROPN
ejpam-6633	430	3	µ	µ	X
ejpam-6633	430	4	γ(α	γ(α	NOUN
ejpam-6633	430	5	)	)	PUNCT
ejpam-6633	431	1	q∑	q∑	PROPN
ejpam-6633	432	1	i=1	i=1	PROPN
ejpam-6633	432	2	∫	∫	PROPN
ejpam-6633	432	3	ti	ti	PROPN
ejpam-6633	432	4	ti−1	ti−1	PROPN
ejpam-6633	432	5	(	(	PUNCT
ejpam-6633	432	6	ln	ln	X
ejpam-6633	432	7	(	(	PUNCT
ejpam-6633	432	8	tq	tq	INTJ
ejpam-6633	432	9	τ	τ	PROPN
ejpam-6633	432	10	)	)	PUNCT
ejpam-6633	432	11	)	)	PUNCT
ejpam-6633	432	12	α−1	α−1	PROPN
ejpam-6633	432	13	η(τ	η(τ	PROPN
ejpam-6633	432	14	)	)	PUNCT
ejpam-6633	433	1	τ	τ	PROPN
ejpam-6633	433	2	dτ	dτ	NOUN
ejpam-6633	433	3	τ	τ	PROPN
ejpam-6633	433	4	+	+	CCONJ
ejpam-6633	433	5	f(tq	f(tq	PROPN
ejpam-6633	433	6	)	)	PUNCT
ejpam-6633	433	7	,	,	PUNCT
ejpam-6633	433	8	(	(	PUNCT
ejpam-6633	433	9	55	55	NUM
ejpam-6633	433	10	)	)	PUNCT
ejpam-6633	433	11	where	where	SCONJ
ejpam-6633	433	12	f(tq	f(tq	X
ejpam-6633	433	13	)	)	PUNCT
ejpam-6633	433	14	=	=	SYM
ejpam-6633	434	1	−	−	PROPN
ejpam-6633	434	2	(	(	PUNCT
ejpam-6633	434	3	ln	ln	INTJ
ejpam-6633	434	4	(	(	PUNCT
ejpam-6633	434	5	tq	tq	INTJ
ejpam-6633	434	6	a	a	PRON
ejpam-6633	434	7	)	)	PUNCT
ejpam-6633	434	8	)	)	PUNCT
ejpam-6633	434	9	α	α	NOUN
ejpam-6633	434	10	bγ(β	bγ(β	X
ejpam-6633	434	11	+	+	X
ejpam-6633	434	12	α	α	X
ejpam-6633	434	13	)	)	PUNCT
ejpam-6633	434	14	n∑	n∑	PROPN
ejpam-6633	435	1	i=1	i=1	PROPN
ejpam-6633	435	2	∫	∫	PROPN
ejpam-6633	435	3	ti	ti	PROPN
ejpam-6633	435	4	ti−1	ti−1	NOUN
ejpam-6633	435	5	(	(	PUNCT
ejpam-6633	435	6	ln	ln	NOUN
ejpam-6633	435	7	(	(	PUNCT
ejpam-6633	435	8	1	1	NUM
ejpam-6633	435	9	τ	τ	PROPN
ejpam-6633	435	10	)	)	PUNCT
ejpam-6633	435	11	)	)	PUNCT
ejpam-6633	436	1	β+α−1	β+α−1	PROPN
ejpam-6633	436	2	θ(τ	θ(τ	PROPN
ejpam-6633	436	3	,	,	PUNCT
ejpam-6633	436	4	η(τ	η(τ	PROPN
ejpam-6633	436	5	)	)	PUNCT
ejpam-6633	436	6	)	)	PUNCT
ejpam-6633	436	7	dτ	dτ	NOUN
ejpam-6633	437	1	τ	τ	PROPN
ejpam-6633	437	2	+	+	X
ejpam-6633	437	3	µ	µ	X
ejpam-6633	437	4	(	(	PUNCT
ejpam-6633	437	5	ln	ln	X
ejpam-6633	437	6	(	(	PUNCT
ejpam-6633	437	7	tq	tq	INTJ
ejpam-6633	437	8	a	a	PRON
ejpam-6633	437	9	)	)	PUNCT
ejpam-6633	437	10	)	)	PUNCT
ejpam-6633	437	11	α	α	PROPN
ejpam-6633	437	12	bγ(α	bγ(α	NUM
ejpam-6633	437	13	)	)	PUNCT
ejpam-6633	438	1	n∑	n∑	PROPN
ejpam-6633	439	1	i=1	i=1	PROPN
ejpam-6633	439	2	∫	∫	PROPN
ejpam-6633	439	3	ti	ti	PROPN
ejpam-6633	439	4	ti−1	ti−1	NOUN
ejpam-6633	439	5	(	(	PUNCT
ejpam-6633	439	6	ln	ln	NOUN
ejpam-6633	439	7	(	(	PUNCT
ejpam-6633	439	8	1	1	NUM
ejpam-6633	439	9	τ	τ	PROPN
ejpam-6633	439	10	)	)	PUNCT
ejpam-6633	439	11	)	)	PUNCT
ejpam-6633	439	12	α−1	α−1	PROPN
ejpam-6633	439	13	η(τ	η(τ	PROPN
ejpam-6633	439	14	)	)	PUNCT
ejpam-6633	440	1	τ	τ	PROPN
ejpam-6633	440	2	dτ	dτ	NOUN
ejpam-6633	440	3	τ	τ	PROPN
ejpam-6633	440	4	+	+	PROPN
ejpam-6633	440	5	φq	φq	PROPN
ejpam-6633	440	6	.	.	PUNCT
ejpam-6633	441	1	(	(	PUNCT
ejpam-6633	441	2	56	56	NUM
ejpam-6633	441	3	)	)	PUNCT
ejpam-6633	441	4	a.	a.	NOUN
ejpam-6633	441	5	s.	s.	PROPN
ejpam-6633	441	6	hasan	hasan	PROPN
ejpam-6633	441	7	,	,	PUNCT
ejpam-6633	441	8	s.	s.	PROPN
ejpam-6633	441	9	a.	a.	PROPN
ejpam-6633	441	10	murad	murad	PROPN
ejpam-6633	441	11	/	/	SYM
ejpam-6633	441	12	eur	eur	PROPN
ejpam-6633	441	13	.	.	PUNCT
ejpam-6633	442	1	j.	j.	PROPN
ejpam-6633	442	2	pure	pure	PROPN
ejpam-6633	442	3	appl	appl	PROPN
ejpam-6633	442	4	.	.	PROPN
ejpam-6633	442	5	math	math	PROPN
ejpam-6633	442	6	,	,	PUNCT
ejpam-6633	442	7	18	18	NUM
ejpam-6633	442	8	(	(	PUNCT
ejpam-6633	442	9	3	3	NUM
ejpam-6633	442	10	)	)	PUNCT
ejpam-6633	442	11	(	(	PUNCT
ejpam-6633	442	12	2025	2025	NUM
ejpam-6633	442	13	)	)	PUNCT
ejpam-6633	442	14	,	,	PUNCT
ejpam-6633	442	15	6633	6633	NUM
ejpam-6633	442	16	18	18	NUM
ejpam-6633	442	17	of	of	ADP
ejpam-6633	442	18	24	24	NUM
ejpam-6633	442	19	note	note	NOUN
ejpam-6633	442	20	that	that	SCONJ
ejpam-6633	442	21	,	,	PUNCT
ejpam-6633	442	22	the	the	DET
ejpam-6633	442	23	first	first	ADJ
ejpam-6633	442	24	sum	sum	NOUN
ejpam-6633	442	25	of	of	ADP
ejpam-6633	442	26	(	(	PUNCT
ejpam-6633	442	27	56	56	NUM
ejpam-6633	442	28	)	)	PUNCT
ejpam-6633	442	29	is	be	AUX
ejpam-6633	442	30	the	the	DET
ejpam-6633	442	31	same	same	ADJ
ejpam-6633	442	32	as	as	ADP
ejpam-6633	442	33	the	the	DET
ejpam-6633	442	34	first	first	ADJ
ejpam-6633	442	35	sum	sum	NOUN
ejpam-6633	442	36	of	of	ADP
ejpam-6633	442	37	(	(	PUNCT
ejpam-6633	442	38	55	55	NUM
ejpam-6633	442	39	)	)	PUNCT
ejpam-6633	442	40	,	,	PUNCT
ejpam-6633	442	41	for	for	ADP
ejpam-6633	442	42	q	q	NOUN
ejpam-6633	442	43	=	=	NOUN
ejpam-6633	442	44	n	n	PROPN
ejpam-6633	442	45	.	.	PUNCT
ejpam-6633	443	1	the	the	DET
ejpam-6633	443	2	same	same	ADJ
ejpam-6633	443	3	is	be	AUX
ejpam-6633	443	4	true	true	ADJ
ejpam-6633	443	5	for	for	ADP
ejpam-6633	443	6	the	the	DET
ejpam-6633	443	7	second	second	ADJ
ejpam-6633	443	8	sums	sum	NOUN
ejpam-6633	443	9	of	of	ADP
ejpam-6633	443	10	(	(	PUNCT
ejpam-6633	443	11	55	55	NUM
ejpam-6633	443	12	)	)	PUNCT
ejpam-6633	443	13	and	and	CCONJ
ejpam-6633	443	14	(	(	PUNCT
ejpam-6633	443	15	56	56	NUM
ejpam-6633	443	16	)	)	PUNCT
ejpam-6633	443	17	.	.	PUNCT
ejpam-6633	444	1	applying	apply	VERB
ejpam-6633	444	2	the	the	DET
ejpam-6633	444	3	fractional	fractional	ADJ
ejpam-6633	444	4	rectangular	rectangular	ADJ
ejpam-6633	444	5	,	,	PUNCT
ejpam-6633	444	6	lln,1	lln,1	NOUN
ejpam-6633	444	7	interpolation	interpolation	NOUN
ejpam-6633	444	8	to	to	PART
ejpam-6633	444	9	approximate	approximate	VERB
ejpam-6633	444	10	the	the	DET
ejpam-6633	444	11	nonlinear	nonlinear	ADJ
ejpam-6633	444	12	terms	term	NOUN
ejpam-6633	444	13	θ(τ	θ(τ	PROPN
ejpam-6633	444	14	,	,	PUNCT
ejpam-6633	444	15	η(τ	η(τ	PROPN
ejpam-6633	444	16	)	)	PUNCT
ejpam-6633	444	17	)	)	PUNCT
ejpam-6633	445	1	and	and	CCONJ
ejpam-6633	445	2	η(τ	η(τ	NUM
ejpam-6633	445	3	)	)	PUNCT
ejpam-6633	445	4	τ	τ	PROPN
ejpam-6633	445	5	,	,	PUNCT
ejpam-6633	445	6	that	that	PRON
ejpam-6633	445	7	is	be	AUX
ejpam-6633	445	8	θ(τ	θ(τ	PROPN
ejpam-6633	445	9	,	,	PUNCT
ejpam-6633	445	10	η(τ	η(τ	PROPN
ejpam-6633	445	11	)	)	PUNCT
ejpam-6633	445	12	)	)	PUNCT
ejpam-6633	446	1	≈	≈	PROPN
ejpam-6633	446	2	ln	ln	INTJ
ejpam-6633	446	3	(	(	PUNCT
ejpam-6633	446	4	τ	τ	X
ejpam-6633	446	5	ti	ti	NOUN
ejpam-6633	446	6	)	)	PUNCT
ejpam-6633	446	7	ln	ln	NOUN
ejpam-6633	446	8	(	(	PUNCT
ejpam-6633	446	9	ti−1	ti−1	NOUN
ejpam-6633	446	10	ti	ti	NOUN
ejpam-6633	446	11	)	)	PUNCT
ejpam-6633	446	12	θi−1	θi−1	PROPN
ejpam-6633	447	1	+	+	CCONJ
ejpam-6633	447	2	ln	ln	PROPN
ejpam-6633	447	3	(	(	PUNCT
ejpam-6633	447	4	τ	τ	PROPN
ejpam-6633	447	5	ti−1	ti−1	NOUN
ejpam-6633	447	6	)	)	PUNCT
ejpam-6633	447	7	ln	ln	NOUN
ejpam-6633	447	8	(	(	PUNCT
ejpam-6633	447	9	ti	ti	NOUN
ejpam-6633	447	10	ti−1	ti−1	NOUN
ejpam-6633	447	11	)	)	PUNCT
ejpam-6633	447	12	θi	θi	PROPN
ejpam-6633	447	13	,	,	PUNCT
ejpam-6633	447	14	(	(	PUNCT
ejpam-6633	447	15	57	57	NUM
ejpam-6633	447	16	)	)	PUNCT
ejpam-6633	447	17	η(τ	η(τ	PROPN
ejpam-6633	447	18	)	)	PUNCT
ejpam-6633	448	1	≈	≈	PROPN
ejpam-6633	448	2	ln	ln	INTJ
ejpam-6633	448	3	(	(	PUNCT
ejpam-6633	448	4	τ	τ	X
ejpam-6633	448	5	ti	ti	NOUN
ejpam-6633	448	6	)	)	PUNCT
ejpam-6633	448	7	ln	ln	NOUN
ejpam-6633	449	1	(	(	PUNCT
ejpam-6633	449	2	ti−1	ti−1	NOUN
ejpam-6633	449	3	ti	ti	NOUN
ejpam-6633	449	4	)	)	PUNCT
ejpam-6633	449	5	ηi−1	ηi−1	PROPN
ejpam-6633	450	1	+	+	PROPN
ejpam-6633	450	2	ln	ln	PROPN
ejpam-6633	450	3	(	(	PUNCT
ejpam-6633	450	4	τ	τ	PROPN
ejpam-6633	450	5	ti−1	ti−1	NOUN
ejpam-6633	450	6	)	)	PUNCT
ejpam-6633	450	7	ln	ln	NOUN
ejpam-6633	450	8	(	(	PUNCT
ejpam-6633	450	9	ti	ti	NOUN
ejpam-6633	450	10	ti−1	ti−1	NOUN
ejpam-6633	450	11	)	)	PUNCT
ejpam-6633	450	12	ηi	ηi	PROPN
ejpam-6633	450	13	,	,	PUNCT
ejpam-6633	450	14	(	(	PUNCT
ejpam-6633	450	15	58	58	NUM
ejpam-6633	450	16	)	)	PUNCT
ejpam-6633	450	17	where	where	SCONJ
ejpam-6633	450	18	θi	θi	X
ejpam-6633	450	19	=	=	PUNCT
ejpam-6633	450	20	θ(ti	θ(ti	NOUN
ejpam-6633	450	21	,	,	PUNCT
ejpam-6633	450	22	η(ti	η(ti	NOUN
ejpam-6633	450	23	)	)	PUNCT
ejpam-6633	450	24	)	)	PUNCT
ejpam-6633	451	1	and	and	CCONJ
ejpam-6633	451	2	ηi	ηi	NOUN
ejpam-6633	451	3	=	=	SYM
ejpam-6633	451	4	η(ti	η(ti	PROPN
ejpam-6633	451	5	)	)	PUNCT
ejpam-6633	451	6	.	.	PUNCT
ejpam-6633	452	1	now	now	ADV
ejpam-6633	452	2	,	,	PUNCT
ejpam-6633	452	3	in	in	ADP
ejpam-6633	452	4	conjunction	conjunction	NOUN
ejpam-6633	452	5	with	with	ADP
ejpam-6633	452	6	(	(	PUNCT
ejpam-6633	452	7	57	57	NUM
ejpam-6633	452	8	-	-	SYM
ejpam-6633	452	9	58	58	NUM
ejpam-6633	452	10	)	)	PUNCT
ejpam-6633	452	11	and	and	CCONJ
ejpam-6633	452	12	ηq	ηq	VERB
ejpam-6633	452	13	in	in	ADP
ejpam-6633	452	14	(	(	PUNCT
ejpam-6633	452	15	55	55	NUM
ejpam-6633	452	16	)	)	PUNCT
ejpam-6633	452	17	we	we	PRON
ejpam-6633	452	18	arrive	arrive	VERB
ejpam-6633	452	19	at	at	ADP
ejpam-6633	452	20	:	:	PUNCT
ejpam-6633	452	21	ηq	ηq	ADP
ejpam-6633	452	22	=	=	SYM
ejpam-6633	452	23	1	1	NUM
ejpam-6633	452	24	γ(β	γ(β	PROPN
ejpam-6633	452	25	+	+	NUM
ejpam-6633	452	26	α	α	X
ejpam-6633	452	27	)	)	PUNCT
ejpam-6633	452	28	q∑	q∑	PROPN
ejpam-6633	453	1	i=1	i=1	PROPN
ejpam-6633	453	2	∫	∫	PROPN
ejpam-6633	453	3	ti	ti	PROPN
ejpam-6633	453	4	ti−1	ti−1	PROPN
ejpam-6633	453	5	(	(	PUNCT
ejpam-6633	453	6	ln	ln	X
ejpam-6633	453	7	(	(	PUNCT
ejpam-6633	453	8	tq	tq	INTJ
ejpam-6633	453	9	τ	τ	PROPN
ejpam-6633	453	10	)	)	PUNCT
ejpam-6633	453	11	)	)	PUNCT
ejpam-6633	454	1	β+α−1	β+α−1	X
ejpam-6633	454	2			NOUN
ejpam-6633	454	3	ln	ln	X
ejpam-6633	454	4	(	(	PUNCT
ejpam-6633	454	5	τ	τ	X
ejpam-6633	454	6	ti	ti	NOUN
ejpam-6633	454	7	)	)	PUNCT
ejpam-6633	454	8	ln	ln	NOUN
ejpam-6633	455	1	(	(	PUNCT
ejpam-6633	455	2	ti−1	ti−1	NOUN
ejpam-6633	455	3	ti	ti	NOUN
ejpam-6633	455	4	)	)	PUNCT
ejpam-6633	455	5	θi−1	θi−1	PROPN
ejpam-6633	455	6	+	+	CCONJ
ejpam-6633	455	7	ln	ln	PROPN
ejpam-6633	455	8	(	(	PUNCT
ejpam-6633	455	9	τ	τ	PROPN
ejpam-6633	455	10	ti−1	ti−1	NOUN
ejpam-6633	455	11	)	)	PUNCT
ejpam-6633	455	12	ln	ln	NOUN
ejpam-6633	455	13	(	(	PUNCT
ejpam-6633	455	14	ti	ti	NOUN
ejpam-6633	455	15	ti−1	ti−1	NOUN
ejpam-6633	455	16	)	)	PUNCT
ejpam-6633	455	17	θi	θi	NOUN
ejpam-6633	455	18			NOUN
ejpam-6633	455	19	dτ	dτ	PROPN
ejpam-6633	455	20	τ	τ	PROPN
ejpam-6633	455	21	−	−	PROPN
ejpam-6633	455	22	µ	µ	X
ejpam-6633	455	23	γ(α	γ(α	NOUN
ejpam-6633	455	24	)	)	PUNCT
ejpam-6633	456	1	q∑	q∑	PROPN
ejpam-6633	457	1	i=1	i=1	PROPN
ejpam-6633	457	2	∫	∫	PROPN
ejpam-6633	457	3	ti	ti	PROPN
ejpam-6633	457	4	ti−1	ti−1	PROPN
ejpam-6633	457	5	(	(	PUNCT
ejpam-6633	457	6	ln	ln	X
ejpam-6633	457	7	(	(	PUNCT
ejpam-6633	457	8	tq	tq	INTJ
ejpam-6633	457	9	τ	τ	PROPN
ejpam-6633	457	10	)	)	PUNCT
ejpam-6633	457	11	)	)	PUNCT
ejpam-6633	458	1	α−1	α−1	PROPN
ejpam-6633	458	2			NOUN
ejpam-6633	458	3	ln	ln	INTJ
ejpam-6633	458	4	(	(	PUNCT
ejpam-6633	458	5	τ	τ	X
ejpam-6633	458	6	ti	ti	NOUN
ejpam-6633	458	7	)	)	PUNCT
ejpam-6633	458	8	ln	ln	NOUN
ejpam-6633	458	9	(	(	PUNCT
ejpam-6633	458	10	ti−1	ti−1	NOUN
ejpam-6633	458	11	ti	ti	NOUN
ejpam-6633	458	12	)	)	PUNCT
ejpam-6633	459	1	ηi−1	ηi−1	PROPN
ejpam-6633	459	2	+	+	PROPN
ejpam-6633	459	3	ln	ln	PROPN
ejpam-6633	459	4	(	(	PUNCT
ejpam-6633	459	5	τ	τ	PROPN
ejpam-6633	459	6	ti−1	ti−1	NOUN
ejpam-6633	459	7	)	)	PUNCT
ejpam-6633	459	8	ln	ln	NOUN
ejpam-6633	459	9	(	(	PUNCT
ejpam-6633	459	10	ti	ti	NOUN
ejpam-6633	459	11	ti−1	ti−1	NOUN
ejpam-6633	459	12	)	)	PUNCT
ejpam-6633	459	13	ηi	ηi	PROPN
ejpam-6633	459	14			NOUN
ejpam-6633	459	15	dτ	dτ	NOUN
ejpam-6633	459	16	τ2	τ2	NOUN
ejpam-6633	459	17	+	+	CCONJ
ejpam-6633	459	18	f(tq	f(tq	PROPN
ejpam-6633	459	19	)	)	PUNCT
ejpam-6633	459	20	=	=	SYM
ejpam-6633	460	1	1	1	NUM
ejpam-6633	460	2	γ(β	γ(β	PROPN
ejpam-6633	460	3	+	+	NUM
ejpam-6633	460	4	α	α	X
ejpam-6633	460	5	)	)	PUNCT
ejpam-6633	460	6	q∑	q∑	PROPN
ejpam-6633	461	1	i=1	i=1	PROPN
ejpam-6633	461	2			PROPN
ejpam-6633	461	3	θi−1	θi−1	PROPN
ejpam-6633	461	4	ln	ln	ADV
ejpam-6633	461	5	(	(	PUNCT
ejpam-6633	461	6	ti−1	ti−1	NOUN
ejpam-6633	461	7	ti	ti	NOUN
ejpam-6633	461	8	)	)	PUNCT
ejpam-6633	461	9	∫	∫	PROPN
ejpam-6633	461	10	ti	ti	PROPN
ejpam-6633	461	11	ti−1	ti−1	NOUN
ejpam-6633	461	12	(	(	PUNCT
ejpam-6633	461	13	ln	ln	X
ejpam-6633	461	14	(	(	PUNCT
ejpam-6633	461	15	tq	tq	INTJ
ejpam-6633	461	16	τ	τ	PROPN
ejpam-6633	461	17	)	)	PUNCT
ejpam-6633	461	18	)	)	PUNCT
ejpam-6633	462	1	β+α−1	β+α−1	NOUN
ejpam-6633	462	2	ln	ln	ADV
ejpam-6633	462	3	(	(	PUNCT
ejpam-6633	462	4	τ	τ	X
ejpam-6633	462	5	ti	ti	NOUN
ejpam-6633	462	6	)	)	PUNCT
ejpam-6633	462	7	dτ	dτ	NOUN
ejpam-6633	462	8	τ	τ	PROPN
ejpam-6633	463	1	+	+	NUM
ejpam-6633	463	2	θi	θi	ADP
ejpam-6633	463	3	ln	ln	NOUN
ejpam-6633	463	4	(	(	PUNCT
ejpam-6633	463	5	ti	ti	NOUN
ejpam-6633	463	6	ti−1	ti−1	NOUN
ejpam-6633	463	7	)	)	PUNCT
ejpam-6633	463	8	∫	∫	PROPN
ejpam-6633	463	9	ti	ti	PROPN
ejpam-6633	463	10	ti−1	ti−1	NOUN
ejpam-6633	463	11	(	(	PUNCT
ejpam-6633	463	12	ln	ln	X
ejpam-6633	463	13	(	(	PUNCT
ejpam-6633	463	14	tq	tq	INTJ
ejpam-6633	463	15	τ	τ	PROPN
ejpam-6633	463	16	)	)	PUNCT
ejpam-6633	463	17	)	)	PUNCT
ejpam-6633	464	1	β+α−1	β+α−1	NOUN
ejpam-6633	464	2	ln	ln	ADV
ejpam-6633	464	3	(	(	PUNCT
ejpam-6633	464	4	τ	τ	PROPN
ejpam-6633	464	5	ti−1	ti−1	NOUN
ejpam-6633	464	6	)	)	PUNCT
ejpam-6633	464	7	dτ	dτ	NOUN
ejpam-6633	464	8	τ	τ	PROPN
ejpam-6633	464	9			NOUN
ejpam-6633	464	10	−	−	PROPN
ejpam-6633	464	11	µ	µ	X
ejpam-6633	464	12	γ(α	γ(α	NOUN
ejpam-6633	464	13	)	)	PUNCT
ejpam-6633	465	1	q∑	q∑	PROPN
ejpam-6633	466	1	i=1	i=1	PROPN
ejpam-6633	466	2			NOUN
ejpam-6633	466	3	ηi−1	ηi−1	PROPN
ejpam-6633	466	4	ln	ln	NOUN
ejpam-6633	466	5	(	(	PUNCT
ejpam-6633	466	6	ti−1	ti−1	NOUN
ejpam-6633	466	7	ti	ti	NOUN
ejpam-6633	466	8	)	)	PUNCT
ejpam-6633	466	9	∫	∫	PROPN
ejpam-6633	466	10	ti	ti	PROPN
ejpam-6633	466	11	ti−1	ti−1	NOUN
ejpam-6633	466	12	(	(	PUNCT
ejpam-6633	466	13	ln	ln	X
ejpam-6633	466	14	(	(	PUNCT
ejpam-6633	466	15	tq	tq	INTJ
ejpam-6633	466	16	τ	τ	PROPN
ejpam-6633	466	17	)	)	PUNCT
ejpam-6633	466	18	)	)	PUNCT
ejpam-6633	467	1	α−1	α−1	PROPN
ejpam-6633	467	2	ln	ln	ADV
ejpam-6633	467	3	(	(	PUNCT
ejpam-6633	467	4	τ	τ	X
ejpam-6633	467	5	ti	ti	NOUN
ejpam-6633	467	6	)	)	PUNCT
ejpam-6633	467	7	dτ	dτ	NOUN
ejpam-6633	467	8	τ2	τ2	NOUN
ejpam-6633	467	9	+	+	PROPN
ejpam-6633	467	10	ηi	ηi	X
ejpam-6633	467	11	ln	ln	NOUN
ejpam-6633	467	12	(	(	PUNCT
ejpam-6633	467	13	ti	ti	NOUN
ejpam-6633	467	14	ti−1	ti−1	NOUN
ejpam-6633	467	15	)	)	PUNCT
ejpam-6633	467	16	∫	∫	PROPN
ejpam-6633	467	17	ti	ti	PROPN
ejpam-6633	467	18	ti−1	ti−1	NOUN
ejpam-6633	467	19	(	(	PUNCT
ejpam-6633	467	20	ln	ln	X
ejpam-6633	467	21	(	(	PUNCT
ejpam-6633	467	22	tq	tq	INTJ
ejpam-6633	467	23	τ	τ	PROPN
ejpam-6633	467	24	)	)	PUNCT
ejpam-6633	467	25	)	)	PUNCT
ejpam-6633	468	1	α−1	α−1	PROPN
ejpam-6633	468	2	ln	ln	ADV
ejpam-6633	468	3	(	(	PUNCT
ejpam-6633	468	4	τ	τ	PROPN
ejpam-6633	468	5	ti−1	ti−1	NOUN
ejpam-6633	468	6	)	)	PUNCT
ejpam-6633	468	7	dτ	dτ	NOUN
ejpam-6633	468	8	τ2	τ2	PROPN
ejpam-6633	468	9	+	+	PROPN
ejpam-6633	468	10	f(tq	f(tq	PROPN
ejpam-6633	468	11	)	)	PUNCT
ejpam-6633	468	12	,	,	PUNCT
ejpam-6633	468	13	(	(	PUNCT
ejpam-6633	468	14	59	59	NUM
ejpam-6633	468	15	)	)	PUNCT
ejpam-6633	468	16	proceeding	proceed	VERB
ejpam-6633	468	17	the	the	DET
ejpam-6633	468	18	integration	integration	NOUN
ejpam-6633	468	19	in	in	ADP
ejpam-6633	468	20	(	(	PUNCT
ejpam-6633	468	21	59	59	NUM
ejpam-6633	468	22	)	)	PUNCT
ejpam-6633	468	23	using	use	VERB
ejpam-6633	468	24	the	the	DET
ejpam-6633	468	25	change	change	NOUN
ejpam-6633	468	26	of	of	ADP
ejpam-6633	468	27	variables	variable	NOUN
ejpam-6633	468	28	tq	tq	ADP
ejpam-6633	469	1	=	=	PUNCT
ejpam-6633	469	2	τeu	τeu	NOUN
ejpam-6633	469	3	we	we	PRON
ejpam-6633	469	4	obtain	obtain	VERB
ejpam-6633	469	5	:	:	PUNCT
ejpam-6633	469	6	ηq	ηq	ADP
ejpam-6633	469	7	=	=	SYM
ejpam-6633	469	8	1	1	NUM
ejpam-6633	469	9	γ(β	γ(β	PROPN
ejpam-6633	469	10	+	+	NUM
ejpam-6633	469	11	α	α	X
ejpam-6633	469	12	)	)	PUNCT
ejpam-6633	469	13	q∑	q∑	PROPN
ejpam-6633	470	1	i=1	i=1	PROPN
ejpam-6633	470	2			PROPN
ejpam-6633	470	3	θi−1	θi−1	PROPN
ejpam-6633	470	4	ln	ln	ADV
ejpam-6633	470	5	(	(	PUNCT
ejpam-6633	470	6	ti−1	ti−1	NOUN
ejpam-6633	470	7	ti	ti	NOUN
ejpam-6633	470	8	)	)	PUNCT
ejpam-6633	471	1	ln	ln	NOUN
ejpam-6633	471	2	(	(	PUNCT
ejpam-6633	471	3	tq	tq	INTJ
ejpam-6633	471	4	ti	ti	NOUN
ejpam-6633	471	5	)	)	PUNCT
ejpam-6633	471	6	(	(	PUNCT
ejpam-6633	471	7	ln	ln	INTJ
ejpam-6633	471	8	tq	tq	ADV
ejpam-6633	471	9	ti−1	ti−1	NOUN
ejpam-6633	471	10	)	)	PUNCT
ejpam-6633	471	11	β+α	β+α	PUNCT
ejpam-6633	471	12	−	−	PROPN
ejpam-6633	472	1	(	(	PUNCT
ejpam-6633	472	2	ln	ln	INTJ
ejpam-6633	472	3	tq	tq	INTJ
ejpam-6633	472	4	ti	ti	NOUN
ejpam-6633	472	5	)	)	PUNCT
ejpam-6633	472	6	β+α	β+α	PUNCT
ejpam-6633	473	1	β	β	X
ejpam-6633	473	2	+	+	CCONJ
ejpam-6633	473	3	α	α	PROPN
ejpam-6633	473	4	−	−	PROPN
ejpam-6633	473	5	θi−1	θi−1	PROPN
ejpam-6633	473	6	ln	ln	ADV
ejpam-6633	473	7	(	(	PUNCT
ejpam-6633	473	8	ti−1	ti−1	NOUN
ejpam-6633	473	9	ti	ti	NOUN
ejpam-6633	473	10	)	)	PUNCT
ejpam-6633	473	11	(	(	PUNCT
ejpam-6633	473	12	ln	ln	INTJ
ejpam-6633	473	13	tq	tq	ADP
ejpam-6633	473	14	ti−1	ti−1	NOUN
ejpam-6633	473	15	)	)	PUNCT
ejpam-6633	473	16	β+α+1	β+α+1	NOUN
ejpam-6633	473	17	−	−	NOUN
ejpam-6633	474	1	(	(	PUNCT
ejpam-6633	474	2	ln	ln	INTJ
ejpam-6633	474	3	tq	tq	INTJ
ejpam-6633	474	4	ti	ti	NOUN
ejpam-6633	474	5	)	)	PUNCT
ejpam-6633	474	6	β+α+1	β+α+1	VERB
ejpam-6633	474	7	β	β	NOUN
ejpam-6633	475	1	+	+	CCONJ
ejpam-6633	475	2	α+	α+	PUNCT
ejpam-6633	475	3	1	1	NUM
ejpam-6633	475	4	a.	a.	PROPN
ejpam-6633	475	5	s.	s.	PROPN
ejpam-6633	475	6	hasan	hasan	PROPN
ejpam-6633	475	7	,	,	PUNCT
ejpam-6633	475	8	s.	s.	PROPN
ejpam-6633	475	9	a.	a.	PROPN
ejpam-6633	475	10	murad	murad	PROPN
ejpam-6633	475	11	/	/	SYM
ejpam-6633	475	12	eur	eur	PROPN
ejpam-6633	475	13	.	.	PUNCT
ejpam-6633	476	1	j.	j.	PROPN
ejpam-6633	476	2	pure	pure	PROPN
ejpam-6633	476	3	appl	appl	PROPN
ejpam-6633	476	4	.	.	PROPN
ejpam-6633	476	5	math	math	PROPN
ejpam-6633	476	6	,	,	PUNCT
ejpam-6633	476	7	18	18	NUM
ejpam-6633	476	8	(	(	PUNCT
ejpam-6633	476	9	3	3	NUM
ejpam-6633	476	10	)	)	PUNCT
ejpam-6633	476	11	(	(	PUNCT
ejpam-6633	476	12	2025	2025	NUM
ejpam-6633	476	13	)	)	PUNCT
ejpam-6633	476	14	,	,	PUNCT
ejpam-6633	476	15	6633	6633	NUM
ejpam-6633	476	16	19	19	NUM
ejpam-6633	476	17	of	of	ADP
ejpam-6633	476	18	24	24	NUM
ejpam-6633	476	19	+	+	CCONJ
ejpam-6633	476	20	θi	θi	ADP
ejpam-6633	476	21	ln	ln	NOUN
ejpam-6633	476	22	(	(	PUNCT
ejpam-6633	476	23	ti	ti	NOUN
ejpam-6633	476	24	ti−1	ti−1	NOUN
ejpam-6633	476	25	)	)	PUNCT
ejpam-6633	476	26	ln	ln	NOUN
ejpam-6633	477	1	(	(	PUNCT
ejpam-6633	477	2	tq	tq	ADV
ejpam-6633	477	3	ti−1	ti−1	NOUN
ejpam-6633	477	4	)	)	PUNCT
ejpam-6633	477	5	(	(	PUNCT
ejpam-6633	477	6	ln	ln	INTJ
ejpam-6633	477	7	tq	tq	ADV
ejpam-6633	477	8	ti−1	ti−1	NOUN
ejpam-6633	477	9	)	)	PUNCT
ejpam-6633	477	10	β+α	β+α	PUNCT
ejpam-6633	477	11	−	−	PROPN
ejpam-6633	478	1	(	(	PUNCT
ejpam-6633	478	2	ln	ln	INTJ
ejpam-6633	478	3	tq	tq	INTJ
ejpam-6633	478	4	ti	ti	NOUN
ejpam-6633	478	5	)	)	PUNCT
ejpam-6633	478	6	β+α	β+α	PUNCT
ejpam-6633	479	1	β	β	X
ejpam-6633	479	2	+	+	CCONJ
ejpam-6633	479	3	α	α	PROPN
ejpam-6633	479	4	−	−	PROPN
ejpam-6633	479	5	θi	θi	ADP
ejpam-6633	479	6	ln	ln	PROPN
ejpam-6633	479	7	(	(	PUNCT
ejpam-6633	479	8	ti	ti	NOUN
ejpam-6633	479	9	ti−1	ti−1	NOUN
ejpam-6633	479	10	)	)	PUNCT
ejpam-6633	479	11	(	(	PUNCT
ejpam-6633	479	12	ln	ln	INTJ
ejpam-6633	479	13	tq	tq	ADV
ejpam-6633	479	14	ti−1	ti−1	NOUN
ejpam-6633	479	15	)	)	PUNCT
ejpam-6633	479	16	β+α+1	β+α+1	NOUN
ejpam-6633	479	17	−	−	NOUN
ejpam-6633	480	1	(	(	PUNCT
ejpam-6633	480	2	ln	ln	INTJ
ejpam-6633	480	3	tq	tq	INTJ
ejpam-6633	480	4	ti	ti	NOUN
ejpam-6633	480	5	)	)	PUNCT
ejpam-6633	480	6	β+α+1	β+α+1	VERB
ejpam-6633	480	7	β	β	NOUN
ejpam-6633	481	1	+	+	CCONJ
ejpam-6633	481	2	α+	α+	PUNCT
ejpam-6633	481	3	1	1	NUM
ejpam-6633	481	4			NOUN
ejpam-6633	481	5	−	−	PROPN
ejpam-6633	481	6	µ	µ	X
ejpam-6633	481	7	γ(α	γ(α	NOUN
ejpam-6633	481	8	)	)	PUNCT
ejpam-6633	482	1	q∑	q∑	PROPN
ejpam-6633	483	1	i=1	i=1	PROPN
ejpam-6633	483	2			PROPN
ejpam-6633	483	3	(	(	PUNCT
ejpam-6633	483	4	−1)αηi−1	−1)αηi−1	X
ejpam-6633	483	5	tq	tq	ADP
ejpam-6633	483	6	ln	ln	PROPN
ejpam-6633	483	7	(	(	PUNCT
ejpam-6633	483	8	ti−1	ti−1	NOUN
ejpam-6633	483	9	ti	ti	NOUN
ejpam-6633	483	10	)	)	PUNCT
ejpam-6633	484	1	[	[	X
ejpam-6633	484	2	γ(α+	γ(α+	PRON
ejpam-6633	484	3	1,−	1,−	NUM
ejpam-6633	484	4	ln	ln	ADJ
ejpam-6633	484	5	(	(	PUNCT
ejpam-6633	484	6	tq	tq	ADV
ejpam-6633	484	7	ti−1	ti−1	NOUN
ejpam-6633	484	8	)	)	PUNCT
ejpam-6633	484	9	)	)	PUNCT
ejpam-6633	485	1	−	−	PROPN
ejpam-6633	485	2	γ	γ	X
ejpam-6633	485	3	(	(	PUNCT
ejpam-6633	485	4	α+	α+	PROPN
ejpam-6633	485	5	1,−	1,−	NUM
ejpam-6633	485	6	ln	ln	NOUN
ejpam-6633	485	7	(	(	PUNCT
ejpam-6633	485	8	tq	tq	ADV
ejpam-6633	485	9	ti	ti	NOUN
ejpam-6633	485	10	)	)	PUNCT
ejpam-6633	485	11	)	)	PUNCT
ejpam-6633	485	12	]	]	PUNCT
ejpam-6633	486	1	−(−1)α−1ηi−1	−(−1)α−1ηi−1	NOUN
ejpam-6633	487	1	tq	tq	INTJ
ejpam-6633	487	2	ln	ln	ADV
ejpam-6633	487	3	(	(	PUNCT
ejpam-6633	487	4	ti−1	ti−1	NOUN
ejpam-6633	487	5	ti	ti	NOUN
ejpam-6633	487	6	)	)	PUNCT
ejpam-6633	488	1	ln	ln	NOUN
ejpam-6633	488	2	(	(	PUNCT
ejpam-6633	488	3	tq	tq	ADV
ejpam-6633	488	4	ti−1	ti−1	NOUN
ejpam-6633	488	5	)	)	PUNCT
ejpam-6633	488	6	[	[	PUNCT
ejpam-6633	488	7	γ	γ	X
ejpam-6633	488	8	(	(	PUNCT
ejpam-6633	488	9	α,−	α,−	PROPN
ejpam-6633	488	10	ln	ln	NOUN
ejpam-6633	488	11	(	(	PUNCT
ejpam-6633	488	12	tq	tq	ADV
ejpam-6633	488	13	ti−1	ti−1	NOUN
ejpam-6633	488	14	)	)	PUNCT
ejpam-6633	488	15	)	)	PUNCT
ejpam-6633	489	1	−	−	PROPN
ejpam-6633	489	2	γ	γ	X
ejpam-6633	489	3	(	(	PUNCT
ejpam-6633	489	4	α,−	α,−	PROPN
ejpam-6633	489	5	ln	ln	NOUN
ejpam-6633	489	6	(	(	PUNCT
ejpam-6633	489	7	tq	tq	INTJ
ejpam-6633	489	8	ti	ti	NOUN
ejpam-6633	489	9	)	)	PUNCT
ejpam-6633	489	10	)	)	PUNCT
ejpam-6633	489	11	]	]	PUNCT
ejpam-6633	490	1	+	+	CCONJ
ejpam-6633	490	2	(	(	PUNCT
ejpam-6633	490	3	−1)α−1ηi	−1)α−1ηi	PRON
ejpam-6633	490	4	tq	tq	INTJ
ejpam-6633	490	5	ln	ln	ADJ
ejpam-6633	490	6	(	(	PUNCT
ejpam-6633	490	7	ti	ti	NOUN
ejpam-6633	490	8	ti−1	ti−1	NOUN
ejpam-6633	490	9	)	)	PUNCT
ejpam-6633	490	10	ln	ln	NOUN
ejpam-6633	490	11	(	(	PUNCT
ejpam-6633	490	12	tq	tq	INTJ
ejpam-6633	490	13	ti	ti	NOUN
ejpam-6633	490	14	)	)	PUNCT
ejpam-6633	490	15	[	[	PUNCT
ejpam-6633	490	16	γ	γ	X
ejpam-6633	490	17	(	(	PUNCT
ejpam-6633	490	18	α,−	α,−	PROPN
ejpam-6633	490	19	ln	ln	NOUN
ejpam-6633	490	20	(	(	PUNCT
ejpam-6633	490	21	tq	tq	ADV
ejpam-6633	490	22	ti−1	ti−1	NOUN
ejpam-6633	490	23	)	)	PUNCT
ejpam-6633	490	24	)	)	PUNCT
ejpam-6633	490	25	−	−	PROPN
ejpam-6633	491	1	γ	γ	X
ejpam-6633	491	2	(	(	PUNCT
ejpam-6633	491	3	α,−	α,−	PROPN
ejpam-6633	491	4	ln	ln	NOUN
ejpam-6633	491	5	(	(	PUNCT
ejpam-6633	491	6	tq	tq	INTJ
ejpam-6633	491	7	ti	ti	NOUN
ejpam-6633	491	8	)	)	PUNCT
ejpam-6633	491	9	)	)	PUNCT
ejpam-6633	491	10	]	]	PUNCT
ejpam-6633	492	1	−	−	PROPN
ejpam-6633	492	2	(	(	PUNCT
ejpam-6633	492	3	−1)αηi	−1)αηi	INTJ
ejpam-6633	492	4	tq	tq	INTJ
ejpam-6633	492	5	ln	ln	ADV
ejpam-6633	492	6	(	(	PUNCT
ejpam-6633	492	7	ti	ti	NOUN
ejpam-6633	492	8	ti−1	ti−1	NOUN
ejpam-6633	492	9	)	)	PUNCT
ejpam-6633	493	1	[	[	X
ejpam-6633	493	2	γ(α+	γ(α+	PRON
ejpam-6633	493	3	1,−	1,−	NUM
ejpam-6633	493	4	ln	ln	ADJ
ejpam-6633	493	5	(	(	PUNCT
ejpam-6633	493	6	tq	tq	ADV
ejpam-6633	493	7	ti−1	ti−1	NOUN
ejpam-6633	493	8	)	)	PUNCT
ejpam-6633	493	9	)	)	PUNCT
ejpam-6633	494	1	−	−	PROPN
ejpam-6633	494	2	γ	γ	X
ejpam-6633	494	3	(	(	PUNCT
ejpam-6633	494	4	α+	α+	PROPN
ejpam-6633	494	5	1,−	1,−	NUM
ejpam-6633	494	6	ln	ln	NOUN
ejpam-6633	494	7	(	(	PUNCT
ejpam-6633	494	8	tq	tq	INTJ
ejpam-6633	494	9	ti	ti	NOUN
ejpam-6633	494	10	)	)	PUNCT
ejpam-6633	494	11	)	)	PUNCT
ejpam-6633	494	12	]	]	PUNCT
ejpam-6633	494	13	]	]	PUNCT
ejpam-6633	494	14	,	,	PUNCT
ejpam-6633	494	15	(	(	PUNCT
ejpam-6633	494	16	60	60	NUM
ejpam-6633	494	17	)	)	PUNCT
ejpam-6633	494	18	where	where	SCONJ
ejpam-6633	494	19	γ	γ	X
ejpam-6633	494	20	(	(	PUNCT
ejpam-6633	494	21	.	.	PUNCT
ejpam-6633	494	22	,	,	PUNCT
ejpam-6633	494	23	.	.	PUNCT
ejpam-6633	494	24	)	)	PUNCT
ejpam-6633	494	25	is	be	AUX
ejpam-6633	494	26	the	the	DET
ejpam-6633	494	27	incomplete	incomplete	ADJ
ejpam-6633	494	28	gamma	gamma	NOUN
ejpam-6633	494	29	function	function	NOUN
ejpam-6633	494	30	.	.	PUNCT
ejpam-6633	495	1	rearranging	rearrange	VERB
ejpam-6633	495	2	(	(	PUNCT
ejpam-6633	495	3	60	60	NUM
ejpam-6633	495	4	)	)	PUNCT
ejpam-6633	495	5	ηq	ηq	PROPN
ejpam-6633	495	6	+	+	ADJ
ejpam-6633	495	7	µ	µ	X
ejpam-6633	495	8	γ(α	γ(α	NOUN
ejpam-6633	495	9	)	)	PUNCT
ejpam-6633	496	1	q∑	q∑	PROPN
ejpam-6633	496	2	i=1	i=1	X
ejpam-6633	497	1	[	[	X
ejpam-6633	497	2	νqiηi−1	νqiηi−1	PROPN
ejpam-6633	497	3	+	+	CCONJ
ejpam-6633	497	4	ν̄qiηi	ν̄qiηi	NOUN
ejpam-6633	497	5	]	]	X
ejpam-6633	497	6	=	=	SYM
ejpam-6633	497	7	1	1	NUM
ejpam-6633	497	8	γ(β	γ(β	PROPN
ejpam-6633	497	9	+	+	NUM
ejpam-6633	497	10	α	α	X
ejpam-6633	497	11	)	)	PUNCT
ejpam-6633	497	12	q∑	q∑	PROPN
ejpam-6633	497	13	i=1	i=1	X
ejpam-6633	498	1	[	[	X
ejpam-6633	498	2	ωqiθi−1	ωqiθi−1	NUM
ejpam-6633	498	3	+	+	NUM
ejpam-6633	498	4	ω̄qiθi	ω̄qiθi	NOUN
ejpam-6633	498	5	]	]	X
ejpam-6633	498	6	+	+	CCONJ
ejpam-6633	498	7	f(tq	f(tq	PROPN
ejpam-6633	498	8	)	)	PUNCT
ejpam-6633	498	9	,	,	PUNCT
ejpam-6633	498	10	(	(	PUNCT
ejpam-6633	498	11	61	61	NUM
ejpam-6633	498	12	)	)	PUNCT
ejpam-6633	498	13	where	where	SCONJ
ejpam-6633	498	14	νqi	νqi	NOUN
ejpam-6633	498	15	=	=	PUNCT
ejpam-6633	498	16	(	(	PUNCT
ejpam-6633	498	17	−1)α	−1)α	VERB
ejpam-6633	498	18	tq	tq	ADP
ejpam-6633	498	19	ln	ln	NOUN
ejpam-6633	498	20	(	(	PUNCT
ejpam-6633	498	21	ti−1	ti−1	NOUN
ejpam-6633	498	22	ti	ti	NOUN
ejpam-6633	498	23	)	)	PUNCT
ejpam-6633	499	1	[	[	X
ejpam-6633	499	2	γ(α+	γ(α+	PRON
ejpam-6633	499	3	1,−	1,−	NUM
ejpam-6633	499	4	ln	ln	ADJ
ejpam-6633	499	5	(	(	PUNCT
ejpam-6633	499	6	tq	tq	ADV
ejpam-6633	499	7	ti−1	ti−1	NOUN
ejpam-6633	499	8	)	)	PUNCT
ejpam-6633	499	9	)	)	PUNCT
ejpam-6633	500	1	−	−	PROPN
ejpam-6633	500	2	γ	γ	X
ejpam-6633	500	3	(	(	PUNCT
ejpam-6633	500	4	α+	α+	PROPN
ejpam-6633	500	5	1,−	1,−	NUM
ejpam-6633	500	6	ln	ln	NOUN
ejpam-6633	500	7	(	(	PUNCT
ejpam-6633	500	8	tq	tq	ADV
ejpam-6633	500	9	ti	ti	NOUN
ejpam-6633	500	10	)	)	PUNCT
ejpam-6633	500	11	)	)	PUNCT
ejpam-6633	500	12	]	]	PUNCT
ejpam-6633	501	1	−	−	PROPN
ejpam-6633	501	2	(	(	PUNCT
ejpam-6633	501	3	−1)α−1	−1)α−1	NOUN
ejpam-6633	501	4	tq	tq	INTJ
ejpam-6633	501	5	ln	ln	NOUN
ejpam-6633	501	6	(	(	PUNCT
ejpam-6633	501	7	ti−1	ti−1	NOUN
ejpam-6633	501	8	ti	ti	NOUN
ejpam-6633	501	9	)	)	PUNCT
ejpam-6633	501	10	ln	ln	NOUN
ejpam-6633	501	11	(	(	PUNCT
ejpam-6633	501	12	tq	tq	ADV
ejpam-6633	501	13	ti−1	ti−1	NOUN
ejpam-6633	501	14	)	)	PUNCT
ejpam-6633	501	15	[	[	PUNCT
ejpam-6633	501	16	γ	γ	X
ejpam-6633	501	17	(	(	PUNCT
ejpam-6633	501	18	α,−	α,−	PROPN
ejpam-6633	501	19	ln	ln	NOUN
ejpam-6633	501	20	(	(	PUNCT
ejpam-6633	501	21	tq	tq	ADV
ejpam-6633	501	22	ti−1	ti−1	NOUN
ejpam-6633	501	23	)	)	PUNCT
ejpam-6633	501	24	)	)	PUNCT
ejpam-6633	502	1	−	−	PROPN
ejpam-6633	502	2	γ	γ	X
ejpam-6633	502	3	(	(	PUNCT
ejpam-6633	502	4	α,−	α,−	PROPN
ejpam-6633	502	5	ln	ln	NOUN
ejpam-6633	502	6	(	(	PUNCT
ejpam-6633	502	7	tq	tq	INTJ
ejpam-6633	502	8	ti	ti	NOUN
ejpam-6633	502	9	)	)	PUNCT
ejpam-6633	502	10	)	)	PUNCT
ejpam-6633	502	11	]	]	PUNCT
ejpam-6633	502	12	,	,	PUNCT
ejpam-6633	502	13	ν̄qi	ν̄qi	PROPN
ejpam-6633	502	14	=	=	PUNCT
ejpam-6633	502	15	(	(	PUNCT
ejpam-6633	502	16	−1)α−1	−1)α−1	NOUN
ejpam-6633	502	17	tq	tq	INTJ
ejpam-6633	502	18	ln	ln	NOUN
ejpam-6633	502	19	(	(	PUNCT
ejpam-6633	502	20	ti	ti	NOUN
ejpam-6633	502	21	ti−1	ti−1	NOUN
ejpam-6633	502	22	)	)	PUNCT
ejpam-6633	502	23	ln	ln	NOUN
ejpam-6633	502	24	(	(	PUNCT
ejpam-6633	502	25	tq	tq	INTJ
ejpam-6633	502	26	ti	ti	NOUN
ejpam-6633	502	27	)	)	PUNCT
ejpam-6633	502	28	[	[	PUNCT
ejpam-6633	502	29	γ	γ	X
ejpam-6633	502	30	(	(	PUNCT
ejpam-6633	502	31	α,−	α,−	PROPN
ejpam-6633	502	32	ln	ln	NOUN
ejpam-6633	502	33	(	(	PUNCT
ejpam-6633	502	34	tq	tq	ADV
ejpam-6633	502	35	ti−1	ti−1	NOUN
ejpam-6633	502	36	)	)	PUNCT
ejpam-6633	502	37	)	)	PUNCT
ejpam-6633	502	38	−	−	PROPN
ejpam-6633	503	1	γ	γ	X
ejpam-6633	503	2	(	(	PUNCT
ejpam-6633	503	3	α,−	α,−	PROPN
ejpam-6633	503	4	ln	ln	NOUN
ejpam-6633	503	5	(	(	PUNCT
ejpam-6633	503	6	tq	tq	INTJ
ejpam-6633	503	7	ti	ti	NOUN
ejpam-6633	503	8	)	)	PUNCT
ejpam-6633	503	9	)	)	PUNCT
ejpam-6633	503	10	]	]	PUNCT
ejpam-6633	504	1	−	−	PROPN
ejpam-6633	504	2	(	(	PUNCT
ejpam-6633	504	3	−1)α	−1)α	VERB
ejpam-6633	504	4	tq	tq	ADP
ejpam-6633	504	5	ln	ln	PROPN
ejpam-6633	504	6	(	(	PUNCT
ejpam-6633	504	7	ti	ti	NOUN
ejpam-6633	504	8	ti−1	ti−1	NOUN
ejpam-6633	504	9	)	)	PUNCT
ejpam-6633	505	1	[	[	X
ejpam-6633	505	2	γ(α+	γ(α+	PRON
ejpam-6633	505	3	1,−	1,−	NUM
ejpam-6633	505	4	ln	ln	ADJ
ejpam-6633	505	5	(	(	PUNCT
ejpam-6633	505	6	tq	tq	ADV
ejpam-6633	505	7	ti−1	ti−1	NOUN
ejpam-6633	505	8	)	)	PUNCT
ejpam-6633	505	9	)	)	PUNCT
ejpam-6633	506	1	−	−	PROPN
ejpam-6633	506	2	γ	γ	X
ejpam-6633	506	3	(	(	PUNCT
ejpam-6633	506	4	α+	α+	PROPN
ejpam-6633	506	5	1,−	1,−	NUM
ejpam-6633	506	6	ln	ln	NOUN
ejpam-6633	506	7	(	(	PUNCT
ejpam-6633	506	8	tq	tq	ADV
ejpam-6633	506	9	ti	ti	NOUN
ejpam-6633	506	10	)	)	PUNCT
ejpam-6633	506	11	)	)	PUNCT
ejpam-6633	506	12	]	]	PUNCT
ejpam-6633	506	13	,	,	PUNCT
ejpam-6633	506	14	ωqi	ωqi	ADJ
ejpam-6633	506	15	=	=	SYM
ejpam-6633	506	16	ln	ln	ADJ
ejpam-6633	506	17	(	(	PUNCT
ejpam-6633	506	18	tq	tq	INTJ
ejpam-6633	506	19	ti	ti	NOUN
ejpam-6633	506	20	)	)	PUNCT
ejpam-6633	506	21	(	(	PUNCT
ejpam-6633	506	22	ln	ln	INTJ
ejpam-6633	506	23	tq	tq	ADV
ejpam-6633	506	24	ti−1	ti−1	NOUN
ejpam-6633	506	25	)	)	PUNCT
ejpam-6633	506	26	β+α	β+α	PUNCT
ejpam-6633	506	27	−	−	PROPN
ejpam-6633	506	28	(	(	PUNCT
ejpam-6633	506	29	ln	ln	INTJ
ejpam-6633	506	30	tq	tq	INTJ
ejpam-6633	506	31	ti	ti	NOUN
ejpam-6633	506	32	)	)	PUNCT
ejpam-6633	506	33	β+α	β+α	PUNCT
ejpam-6633	506	34	(	(	PUNCT
ejpam-6633	506	35	β	β	X
ejpam-6633	506	36	+	+	NOUN
ejpam-6633	506	37	α	α	X
ejpam-6633	506	38	)	)	PUNCT
ejpam-6633	506	39	ln	ln	NOUN
ejpam-6633	506	40	(	(	PUNCT
ejpam-6633	506	41	ti−1	ti−1	NOUN
ejpam-6633	506	42	ti	ti	NOUN
ejpam-6633	506	43	)	)	PUNCT
ejpam-6633	506	44	−	−	PROPN
ejpam-6633	507	1	(	(	PUNCT
ejpam-6633	507	2	ln	ln	INTJ
ejpam-6633	507	3	tq	tq	ADV
ejpam-6633	507	4	ti−1	ti−1	NOUN
ejpam-6633	507	5	)	)	PUNCT
ejpam-6633	507	6	β+α+1	β+α+1	NOUN
ejpam-6633	507	7	−	−	NOUN
ejpam-6633	508	1	(	(	PUNCT
ejpam-6633	508	2	ln	ln	INTJ
ejpam-6633	508	3	tq	tq	INTJ
ejpam-6633	508	4	ti	ti	NOUN
ejpam-6633	508	5	)	)	PUNCT
ejpam-6633	508	6	β+α+1	β+α+1	NOUN
ejpam-6633	508	7	(	(	PUNCT
ejpam-6633	508	8	β	β	X
ejpam-6633	508	9	+	+	X
ejpam-6633	508	10	α+	α+	PUNCT
ejpam-6633	508	11	1	1	X
ejpam-6633	508	12	)	)	PUNCT
ejpam-6633	508	13	ln	ln	NOUN
ejpam-6633	508	14	(	(	PUNCT
ejpam-6633	508	15	ti−1	ti−1	NOUN
ejpam-6633	508	16	ti	ti	NOUN
ejpam-6633	508	17	)	)	PUNCT
ejpam-6633	508	18	,	,	PUNCT
ejpam-6633	508	19	ω̄qi	ω̄qi	NOUN
ejpam-6633	508	20	=	=	PUNCT
ejpam-6633	509	1	ln	ln	ADJ
ejpam-6633	509	2	(	(	PUNCT
ejpam-6633	509	3	tq	tq	ADV
ejpam-6633	509	4	ti−1	ti−1	NOUN
ejpam-6633	509	5	)	)	PUNCT
ejpam-6633	509	6	(	(	PUNCT
ejpam-6633	509	7	ln	ln	INTJ
ejpam-6633	509	8	tq	tq	ADV
ejpam-6633	509	9	ti−1	ti−1	NOUN
ejpam-6633	509	10	)	)	PUNCT
ejpam-6633	509	11	β+α	β+α	PUNCT
ejpam-6633	509	12	−	−	PROPN
ejpam-6633	510	1	(	(	PUNCT
ejpam-6633	510	2	ln	ln	INTJ
ejpam-6633	510	3	tq	tq	INTJ
ejpam-6633	510	4	ti	ti	NOUN
ejpam-6633	510	5	)	)	PUNCT
ejpam-6633	510	6	β+α	β+α	PUNCT
ejpam-6633	510	7	(	(	PUNCT
ejpam-6633	510	8	β	β	X
ejpam-6633	510	9	+	+	NOUN
ejpam-6633	510	10	α	α	X
ejpam-6633	510	11	)	)	PUNCT
ejpam-6633	510	12	ln	ln	NOUN
ejpam-6633	510	13	(	(	PUNCT
ejpam-6633	510	14	ti	ti	NOUN
ejpam-6633	510	15	ti−1	ti−1	NOUN
ejpam-6633	510	16	)	)	PUNCT
ejpam-6633	510	17	−	−	PROPN
ejpam-6633	511	1	(	(	PUNCT
ejpam-6633	511	2	ln	ln	INTJ
ejpam-6633	511	3	tq	tq	ADV
ejpam-6633	511	4	ti−1	ti−1	NOUN
ejpam-6633	511	5	)	)	PUNCT
ejpam-6633	511	6	β+α+1	β+α+1	NOUN
ejpam-6633	511	7	−	−	NOUN
ejpam-6633	512	1	(	(	PUNCT
ejpam-6633	512	2	ln	ln	INTJ
ejpam-6633	512	3	tq	tq	INTJ
ejpam-6633	512	4	ti	ti	NOUN
ejpam-6633	512	5	)	)	PUNCT
ejpam-6633	512	6	β+α+1	β+α+1	NOUN
ejpam-6633	512	7	(	(	PUNCT
ejpam-6633	512	8	β	β	X
ejpam-6633	512	9	+	+	X
ejpam-6633	512	10	α+	α+	PUNCT
ejpam-6633	512	11	1	1	X
ejpam-6633	512	12	)	)	PUNCT
ejpam-6633	512	13	ln	ln	NOUN
ejpam-6633	512	14	(	(	PUNCT
ejpam-6633	512	15	ti	ti	NOUN
ejpam-6633	512	16	ti−1	ti−1	NOUN
ejpam-6633	512	17	)	)	PUNCT
ejpam-6633	512	18	.	.	PUNCT
ejpam-6633	513	1	(	(	PUNCT
ejpam-6633	513	2	62	62	NUM
ejpam-6633	513	3	)	)	PUNCT
ejpam-6633	513	4	a.	a.	NOUN
ejpam-6633	513	5	s.	s.	PROPN
ejpam-6633	513	6	hasan	hasan	PROPN
ejpam-6633	513	7	,	,	PUNCT
ejpam-6633	513	8	s.	s.	PROPN
ejpam-6633	513	9	a.	a.	PROPN
ejpam-6633	513	10	murad	murad	PROPN
ejpam-6633	513	11	/	/	SYM
ejpam-6633	513	12	eur	eur	PROPN
ejpam-6633	513	13	.	.	PUNCT
ejpam-6633	514	1	j.	j.	PROPN
ejpam-6633	514	2	pure	pure	PROPN
ejpam-6633	514	3	appl	appl	PROPN
ejpam-6633	514	4	.	.	PROPN
ejpam-6633	514	5	math	math	PROPN
ejpam-6633	514	6	,	,	PUNCT
ejpam-6633	514	7	18	18	NUM
ejpam-6633	514	8	(	(	PUNCT
ejpam-6633	514	9	3	3	NUM
ejpam-6633	514	10	)	)	PUNCT
ejpam-6633	514	11	(	(	PUNCT
ejpam-6633	514	12	2025	2025	NUM
ejpam-6633	514	13	)	)	PUNCT
ejpam-6633	514	14	,	,	PUNCT
ejpam-6633	514	15	6633	6633	NUM
ejpam-6633	514	16	20	20	NUM
ejpam-6633	514	17	of	of	ADP
ejpam-6633	514	18	24	24	NUM
ejpam-6633	514	19	based	base	VERB
ejpam-6633	514	20	on	on	ADP
ejpam-6633	514	21	the	the	DET
ejpam-6633	514	22	right	right	ADJ
ejpam-6633	514	23	-	-	PUNCT
ejpam-6633	514	24	hand	hand	NOUN
ejpam-6633	514	25	side	side	NOUN
ejpam-6633	514	26	of	of	ADP
ejpam-6633	514	27	(	(	PUNCT
ejpam-6633	514	28	61	61	NUM
ejpam-6633	514	29	)	)	PUNCT
ejpam-6633	515	1	,	,	PUNCT
ejpam-6633	515	2	we	we	PRON
ejpam-6633	515	3	introduce	introduce	VERB
ejpam-6633	515	4	the	the	DET
ejpam-6633	515	5	vector	vector	NOUN
ejpam-6633	515	6	h	h	NOUN
ejpam-6633	515	7	=	=	PUNCT
ejpam-6633	516	1	[	[	X
ejpam-6633	516	2	η0	η0	NOUN
ejpam-6633	516	3	,	,	PUNCT
ejpam-6633	516	4	η1	η1	NOUN
ejpam-6633	516	5	,	,	PUNCT
ejpam-6633	516	6	.	.	PUNCT
ejpam-6633	516	7	.	.	PUNCT
ejpam-6633	516	8	.	.	PUNCT
ejpam-6633	517	1	,	,	PUNCT
ejpam-6633	517	2	ηn	ηn	PROPN
ejpam-6633	517	3	]	]	X
ejpam-6633	517	4	t	t	PROPN
ejpam-6633	517	5	.	.	PUNCT
ejpam-6633	518	1	we	we	PRON
ejpam-6633	518	2	further	far	ADV
ejpam-6633	518	3	introduce	introduce	VERB
ejpam-6633	518	4	an	an	DET
ejpam-6633	518	5	(	(	PUNCT
ejpam-6633	518	6	n	n	NOUN
ejpam-6633	518	7	+	+	NOUN
ejpam-6633	518	8	1	1	NUM
ejpam-6633	518	9	)	)	PUNCT
ejpam-6633	518	10	×	×	NOUN
ejpam-6633	518	11	(	(	PUNCT
ejpam-6633	518	12	n	n	NOUN
ejpam-6633	518	13	+	+	CCONJ
ejpam-6633	518	14	1	1	NUM
ejpam-6633	518	15	)	)	PUNCT
ejpam-6633	518	16	matrix	matrix	NOUN
ejpam-6633	518	17	a.	a.	NOUN
ejpam-6633	518	18	the	the	DET
ejpam-6633	518	19	first	first	ADJ
ejpam-6633	518	20	and	and	CCONJ
ejpam-6633	518	21	last	last	ADJ
ejpam-6633	518	22	rows	row	NOUN
ejpam-6633	518	23	of	of	ADP
ejpam-6633	518	24	the	the	DET
ejpam-6633	518	25	matrix	matrix	NOUN
ejpam-6633	518	26	a	a	PRON
ejpam-6633	518	27	are	be	AUX
ejpam-6633	518	28	[	[	X
ejpam-6633	518	29	1	1	NUM
ejpam-6633	518	30	,	,	PUNCT
ejpam-6633	518	31	0	0	NUM
ejpam-6633	518	32	,	,	PUNCT
ejpam-6633	518	33	0	0	NUM
ejpam-6633	518	34	,	,	PUNCT
ejpam-6633	518	35	.	.	PUNCT
ejpam-6633	518	36	.	.	PUNCT
ejpam-6633	519	1	.	.	PUNCT
ejpam-6633	520	1	,	,	PUNCT
ejpam-6633	520	2	0	0	NUM
ejpam-6633	520	3	]	]	PUNCT
ejpam-6633	520	4	and	and	CCONJ
ejpam-6633	520	5	[	[	X
ejpam-6633	520	6	0	0	NUM
ejpam-6633	520	7	,	,	PUNCT
ejpam-6633	520	8	0	0	NUM
ejpam-6633	520	9	,	,	PUNCT
ejpam-6633	520	10	.	.	PUNCT
ejpam-6633	520	11	.	.	PUNCT
ejpam-6633	520	12	.	.	PUNCT
ejpam-6633	521	1	,	,	PUNCT
ejpam-6633	521	2	0	0	NUM
ejpam-6633	521	3	,	,	PUNCT
ejpam-6633	521	4	1	1	NUM
ejpam-6633	521	5	]	]	NUM
ejpam-6633	521	6	,	,	PUNCT
ejpam-6633	521	7	respectively	respectively	ADV
ejpam-6633	521	8	,	,	PUNCT
ejpam-6633	521	9	as	as	ADP
ejpam-6633	521	10	a	a	DET
ejpam-6633	521	11	result	result	NOUN
ejpam-6633	521	12	of	of	ADP
ejpam-6633	521	13	enforcing	enforce	VERB
ejpam-6633	521	14	the	the	DET
ejpam-6633	521	15	boundary	boundary	ADJ
ejpam-6633	521	16	conditions	condition	NOUN
ejpam-6633	521	17	(	(	PUNCT
ejpam-6633	521	18	7	7	NUM
ejpam-6633	521	19	)	)	PUNCT
ejpam-6633	521	20	and	and	CCONJ
ejpam-6633	521	21	(	(	PUNCT
ejpam-6633	521	22	8)	8)	NUM
ejpam-6633	521	23	on	on	ADP
ejpam-6633	521	24	η0	η0	NOUN
ejpam-6633	521	25	and	and	CCONJ
ejpam-6633	521	26	ηn	ηn	INTJ
ejpam-6633	521	27	,	,	PUNCT
ejpam-6633	521	28	respectively	respectively	ADV
ejpam-6633	521	29	.	.	PUNCT
ejpam-6633	522	1	the	the	DET
ejpam-6633	522	2	elements	element	NOUN
ejpam-6633	522	3	of	of	ADP
ejpam-6633	522	4	the	the	DET
ejpam-6633	522	5	interior	interior	ADJ
ejpam-6633	522	6	rows	row	NOUN
ejpam-6633	522	7	are	be	AUX
ejpam-6633	522	8	represented	represent	VERB
ejpam-6633	522	9	by	by	ADP
ejpam-6633	522	10	(	(	PUNCT
ejpam-6633	522	11	aqi	aqi	PROPN
ejpam-6633	522	12	)	)	PUNCT
ejpam-6633	522	13	n	n	CCONJ
ejpam-6633	522	14	i=1	i=1	PROPN
ejpam-6633	522	15	with	with	ADP
ejpam-6633	522	16	q	q	NOUN
ejpam-6633	522	17	=	=	SYM
ejpam-6633	522	18	2	2	NUM
ejpam-6633	522	19	,	,	PUNCT
ejpam-6633	522	20	.	.	PUNCT
ejpam-6633	522	21	.	.	PUNCT
ejpam-6633	523	1	.	.	PUNCT
ejpam-6633	524	1	,	,	PUNCT
ejpam-6633	525	1	n	n	CCONJ
ejpam-6633	525	2	−	−	PROPN
ejpam-6633	525	3	1	1	NUM
ejpam-6633	525	4	,	,	PUNCT
ejpam-6633	525	5	so	so	SCONJ
ejpam-6633	525	6	that	that	SCONJ
ejpam-6633	525	7	:	:	PUNCT
ejpam-6633	525	8	aqi	aqi	PROPN
ejpam-6633	525	9	=	=	PROPN
ejpam-6633	525	10	µ	µ	X
ejpam-6633	525	11	γ(α	γ(α	NOUN
ejpam-6633	525	12	)	)	PUNCT
ejpam-6633	525	13			NOUN
ejpam-6633	525	14	νqi	νqi	ADJ
ejpam-6633	525	15	;	;	PUNCT
ejpam-6633	525	16	i	i	PRON
ejpam-6633	525	17	=	=	NOUN
ejpam-6633	525	18	1	1	NUM
ejpam-6633	525	19	,	,	PUNCT
ejpam-6633	525	20	νqi	νqi	NOUN
ejpam-6633	525	21	+	+	CCONJ
ejpam-6633	525	22	ν̄qi	ν̄qi	NOUN
ejpam-6633	525	23	;	;	PUNCT
ejpam-6633	525	24	i	i	PRON
ejpam-6633	525	25	=	=	NOUN
ejpam-6633	525	26	2	2	NUM
ejpam-6633	525	27	,	,	PUNCT
ejpam-6633	525	28	3	3	NUM
ejpam-6633	525	29	,	,	PUNCT
ejpam-6633	525	30	.	.	PUNCT
ejpam-6633	525	31	.	.	PUNCT
ejpam-6633	525	32	.	.	PUNCT
ejpam-6633	526	1	,	,	PUNCT
ejpam-6633	526	2	q	q	X
ejpam-6633	527	1	−	−	PROPN
ejpam-6633	527	2	1	1	NUM
ejpam-6633	527	3	,	,	PUNCT
ejpam-6633	527	4	γ(α)µ−1	γ(α)µ−1	X
ejpam-6633	527	5	+	+	CCONJ
ejpam-6633	527	6	ν̄qi	ν̄qi	NOUN
ejpam-6633	527	7	;	;	PUNCT
ejpam-6633	527	8	i	i	PRON
ejpam-6633	527	9	=	=	SYM
ejpam-6633	527	10	q	q	X
ejpam-6633	527	11	,	,	PUNCT
ejpam-6633	527	12	0	0	NUM
ejpam-6633	527	13	;	;	PUNCT
ejpam-6633	527	14	q	q	X
ejpam-6633	527	15	<	<	X
ejpam-6633	527	16	i	i	PROPN
ejpam-6633	527	17	≤	≤	PROPN
ejpam-6633	527	18	n.	n.	NOUN
ejpam-6633	527	19	(	(	PUNCT
ejpam-6633	527	20	63	63	NUM
ejpam-6633	527	21	)	)	PUNCT
ejpam-6633	527	22	for	for	ADP
ejpam-6633	527	23	the	the	DET
ejpam-6633	527	24	left	left	ADJ
ejpam-6633	527	25	-	-	PUNCT
ejpam-6633	527	26	hand	hand	NOUN
ejpam-6633	527	27	side	side	NOUN
ejpam-6633	527	28	of	of	ADP
ejpam-6633	527	29	(	(	PUNCT
ejpam-6633	527	30	61	61	NUM
ejpam-6633	527	31	)	)	PUNCT
ejpam-6633	527	32	,	,	PUNCT
ejpam-6633	527	33	we	we	PRON
ejpam-6633	527	34	assemble	assemble	VERB
ejpam-6633	527	35	the	the	DET
ejpam-6633	527	36	vector	vector	NOUN
ejpam-6633	527	37	b	b	NOUN
ejpam-6633	527	38	=	=	PUNCT
ejpam-6633	528	1	[	[	X
ejpam-6633	528	2	b0	b0	NOUN
ejpam-6633	528	3	,	,	PUNCT
ejpam-6633	528	4	b1	b1	NOUN
ejpam-6633	528	5	,	,	PUNCT
ejpam-6633	528	6	.	.	PUNCT
ejpam-6633	528	7	.	.	PUNCT
ejpam-6633	528	8	.	.	PUNCT
ejpam-6633	529	1	,	,	PUNCT
ejpam-6633	530	1	bn	bn	X
ejpam-6633	530	2	]	]	X
ejpam-6633	530	3	t	t	NOUN
ejpam-6633	530	4	,	,	PUNCT
ejpam-6633	530	5	where	where	SCONJ
ejpam-6633	530	6	bq	bq	ADP
ejpam-6633	530	7	=	=	PUNCT
ejpam-6633	530	8			PROPN
ejpam-6633	530	9	ξ1	ξ1	NOUN
ejpam-6633	530	10	;	;	PUNCT
ejpam-6633	530	11	q	q	NOUN
ejpam-6633	530	12	=	=	SYM
ejpam-6633	530	13	0	0	NUM
ejpam-6633	530	14	,	,	PUNCT
ejpam-6633	530	15	1	1	NUM
ejpam-6633	530	16	γ(β+α	γ(β+α	NOUN
ejpam-6633	530	17	)	)	PUNCT
ejpam-6633	530	18	∑q	∑q	VERB
ejpam-6633	530	19	i=1	i=1	PUNCT
ejpam-6633	531	1	[	[	X
ejpam-6633	531	2	ωqiθi−1	ωqiθi−1	NUM
ejpam-6633	531	3	+	+	NUM
ejpam-6633	531	4	ω̄qiθi	ω̄qiθi	NOUN
ejpam-6633	531	5	]	]	X
ejpam-6633	531	6	+	+	CCONJ
ejpam-6633	531	7	f(tq	f(tq	PROPN
ejpam-6633	531	8	)	)	PUNCT
ejpam-6633	531	9	;	;	PUNCT
ejpam-6633	531	10	q	q	NOUN
ejpam-6633	532	1	=	=	SYM
ejpam-6633	532	2	1	1	NUM
ejpam-6633	532	3	,	,	PUNCT
ejpam-6633	532	4	2	2	NUM
ejpam-6633	532	5	,	,	PUNCT
ejpam-6633	532	6	.	.	PUNCT
ejpam-6633	532	7	.	.	PUNCT
ejpam-6633	533	1	.	.	PUNCT
ejpam-6633	534	1	,	,	PUNCT
ejpam-6633	534	2	n	n	CCONJ
ejpam-6633	534	3	−	−	PROPN
ejpam-6633	534	4	1	1	NUM
ejpam-6633	534	5	,	,	PUNCT
ejpam-6633	534	6	ξ2	ξ2	NOUN
ejpam-6633	534	7	;	;	PUNCT
ejpam-6633	534	8	q	q	X
ejpam-6633	534	9	=	=	PUNCT
ejpam-6633	534	10	n.	n.	NOUN
ejpam-6633	534	11	(	(	PUNCT
ejpam-6633	534	12	64	64	NUM
ejpam-6633	534	13	)	)	PUNCT
ejpam-6633	534	14	therefore	therefore	ADV
ejpam-6633	534	15	,	,	PUNCT
ejpam-6633	534	16	the	the	DET
ejpam-6633	534	17	two	two	NUM
ejpam-6633	534	18	-	-	PUNCT
ejpam-6633	534	19	point	point	NOUN
ejpam-6633	534	20	boundary	boundary	ADJ
ejpam-6633	534	21	-	-	PUNCT
ejpam-6633	534	22	value	value	NOUN
ejpam-6633	534	23	problem	problem	NOUN
ejpam-6633	534	24	(	(	PUNCT
ejpam-6633	534	25	6	6	NUM
ejpam-6633	534	26	-	-	SYM
ejpam-6633	534	27	8)	8)	NUM
ejpam-6633	534	28	numerically	numerically	ADV
ejpam-6633	534	29	will	will	AUX
ejpam-6633	534	30	be	be	AUX
ejpam-6633	534	31	solved	solve	VERB
ejpam-6633	534	32	by	by	ADP
ejpam-6633	534	33	implementing	implement	VERB
ejpam-6633	534	34	the	the	DET
ejpam-6633	534	35	newton	newton	PROPN
ejpam-6633	534	36	-	-	PUNCT
ejpam-6633	534	37	raphson	raphson	NOUN
ejpam-6633	534	38	iteration	iteration	NOUN
ejpam-6633	534	39	on	on	ADP
ejpam-6633	534	40	the	the	DET
ejpam-6633	534	41	non	non	ADJ
ejpam-6633	534	42	-	-	ADJ
ejpam-6633	534	43	linear	linear	ADJ
ejpam-6633	534	44	system	system	NOUN
ejpam-6633	534	45	:	:	PUNCT
ejpam-6633	534	46	ah	ah	INTJ
ejpam-6633	534	47	=	=	SYM
ejpam-6633	534	48	b.	b.	PROPN
ejpam-6633	534	49	(	(	PUNCT
ejpam-6633	534	50	65	65	NUM
ejpam-6633	534	51	)	)	PUNCT
ejpam-6633	534	52	we	we	PRON
ejpam-6633	534	53	rearrange	rearrange	VERB
ejpam-6633	534	54	the	the	DET
ejpam-6633	534	55	nonlinear	nonlinear	ADJ
ejpam-6633	534	56	system	system	NOUN
ejpam-6633	534	57	in	in	ADP
ejpam-6633	534	58	(	(	PUNCT
ejpam-6633	534	59	65	65	NUM
ejpam-6633	534	60	)	)	PUNCT
ejpam-6633	534	61	as	as	ADP
ejpam-6633	534	62	:	:	PUNCT
ejpam-6633	534	63	f(h	f(h	PROPN
ejpam-6633	534	64	)	)	PUNCT
ejpam-6633	535	1	=	=	PUNCT
ejpam-6633	535	2	ah−	ah−	PUNCT
ejpam-6633	536	1	b	b	X
ejpam-6633	536	2	=	=	SYM
ejpam-6633	536	3	0	0	PROPN
ejpam-6633	536	4	,	,	PUNCT
ejpam-6633	536	5	(	(	PUNCT
ejpam-6633	536	6	66	66	NUM
ejpam-6633	536	7	)	)	PUNCT
ejpam-6633	536	8	and	and	CCONJ
ejpam-6633	536	9	we	we	PRON
ejpam-6633	536	10	use	use	VERB
ejpam-6633	536	11	a	a	DET
ejpam-6633	536	12	matlab	matlab	PROPN
ejpam-6633	536	13	code	code	NOUN
ejpam-6633	536	14	to	to	PART
ejpam-6633	536	15	solve	solve	VERB
ejpam-6633	536	16	iteratively	iteratively	ADV
ejpam-6633	536	17	the	the	DET
ejpam-6633	536	18	following	following	NOUN
ejpam-6633	536	19	:	:	PUNCT
ejpam-6633	536	20	h(k+1	h(k+1	NUM
ejpam-6633	536	21	)	)	PUNCT
ejpam-6633	536	22	=	=	SYM
ejpam-6633	536	23	h(k	h(k	PROPN
ejpam-6633	536	24	)	)	PUNCT
ejpam-6633	536	25	−	−	PROPN
ejpam-6633	536	26	j(h(k	j(h(k	PROPN
ejpam-6633	536	27	)	)	PUNCT
ejpam-6633	536	28	)	)	PUNCT
ejpam-6633	536	29	−1	−1	NOUN
ejpam-6633	536	30	f(h(k	f(h(k	PROPN
ejpam-6633	536	31	)	)	PUNCT
ejpam-6633	536	32	)	)	PUNCT
ejpam-6633	536	33	.	.	PUNCT
ejpam-6633	537	1	(	(	PUNCT
ejpam-6633	537	2	67	67	NUM
ejpam-6633	537	3	)	)	PUNCT
ejpam-6633	537	4	here	here	ADV
ejpam-6633	537	5	,	,	PUNCT
ejpam-6633	537	6	j(h	j(h	PROPN
ejpam-6633	537	7	)	)	PUNCT
ejpam-6633	537	8	is	be	AUX
ejpam-6633	537	9	the	the	DET
ejpam-6633	537	10	jacobian	jacobian	ADJ
ejpam-6633	537	11	matrix	matrix	NOUN
ejpam-6633	537	12	with	with	ADP
ejpam-6633	537	13	entries	entry	NOUN
ejpam-6633	537	14	jpi	jpi	NOUN
ejpam-6633	537	15	=	=	SYM
ejpam-6633	538	1	api−	api−	PROPN
ejpam-6633	538	2	∂bq	∂bq	PROPN
ejpam-6633	538	3	∂ηi	∂ηi	PROPN
ejpam-6633	538	4	.	.	PUNCT
ejpam-6633	539	1	initially	initially	ADV
ejpam-6633	539	2	,	,	PUNCT
ejpam-6633	539	3	we	we	PRON
ejpam-6633	539	4	start	start	VERB
ejpam-6633	539	5	with	with	ADP
ejpam-6633	539	6	h(0	h(0	PROPN
ejpam-6633	539	7	)	)	PUNCT
ejpam-6633	539	8	,	,	PUNCT
ejpam-6633	539	9	which	which	PRON
ejpam-6633	539	10	is	be	AUX
ejpam-6633	539	11	generated	generate	VERB
ejpam-6633	539	12	by	by	ADP
ejpam-6633	539	13	applying	apply	VERB
ejpam-6633	539	14	the	the	DET
ejpam-6633	539	15	linear	linear	ADJ
ejpam-6633	539	16	interpolation	interpolation	NOUN
ejpam-6633	539	17	ηp	ηp	ADP
ejpam-6633	539	18	=	=	PUNCT
ejpam-6633	539	19	ξ1	ξ1	PROPN
ejpam-6633	539	20	+	+	CCONJ
ejpam-6633	539	21	(	(	PUNCT
ejpam-6633	539	22	tp	tp	AUX
ejpam-6633	539	23	−	−	PROPN
ejpam-6633	539	24	a)/(1−	a)/(1−	VERB
ejpam-6633	539	25	a)(ξ2	a)(ξ2	PROPN
ejpam-6633	539	26	−	−	PROPN
ejpam-6633	539	27	ξ1	ξ1	NOUN
ejpam-6633	539	28	)	)	PUNCT
ejpam-6633	539	29	using	use	VERB
ejpam-6633	539	30	the	the	DET
ejpam-6633	539	31	boundary	boundary	ADJ
ejpam-6633	539	32	conditions	condition	NOUN
ejpam-6633	539	33	(	(	PUNCT
ejpam-6633	539	34	7	7	NUM
ejpam-6633	539	35	)	)	PUNCT
ejpam-6633	539	36	and	and	CCONJ
ejpam-6633	539	37	(	(	PUNCT
ejpam-6633	539	38	8)	8)	NUM
ejpam-6633	539	39	.	.	PUNCT
ejpam-6633	540	1	then	then	ADV
ejpam-6633	540	2	,	,	PUNCT
ejpam-6633	540	3	from	from	ADP
ejpam-6633	540	4	(	(	PUNCT
ejpam-6633	540	5	67	67	NUM
ejpam-6633	540	6	)	)	PUNCT
ejpam-6633	540	7	we	we	PRON
ejpam-6633	540	8	obtain	obtain	VERB
ejpam-6633	540	9	h(1	h(1	PRON
ejpam-6633	540	10	)	)	PUNCT
ejpam-6633	540	11	and	and	CCONJ
ejpam-6633	540	12	so	so	ADV
ejpam-6633	540	13	on	on	ADV
ejpam-6633	540	14	.	.	PUNCT
ejpam-6633	541	1	the	the	DET
ejpam-6633	541	2	iteration	iteration	NOUN
ejpam-6633	541	3	stops	stop	VERB
ejpam-6633	541	4	when	when	SCONJ
ejpam-6633	541	5	we	we	PRON
ejpam-6633	541	6	achieve	achieve	VERB
ejpam-6633	541	7	the	the	DET
ejpam-6633	541	8	required	require	VERB
ejpam-6633	541	9	tolerance	tolerance	NOUN
ejpam-6633	541	10	.	.	PUNCT
ejpam-6633	542	1	in	in	ADP
ejpam-6633	542	2	the	the	DET
ejpam-6633	542	3	following	follow	VERB
ejpam-6633	542	4	examples	example	NOUN
ejpam-6633	542	5	we	we	PRON
ejpam-6633	542	6	set	set	VERB
ejpam-6633	542	7	s	s	PRON
ejpam-6633	542	8	to	to	ADP
ejpam-6633	542	9	2−β	2−β	NUM
ejpam-6633	542	10	β	β	X
ejpam-6633	542	11	(	(	PUNCT
ejpam-6633	542	12	see	see	VERB
ejpam-6633	542	13	[	[	X
ejpam-6633	542	14	31	31	NUM
ejpam-6633	542	15	]	]	PUNCT
ejpam-6633	542	16	)	)	PUNCT
ejpam-6633	542	17	.	.	PUNCT
ejpam-6633	543	1	example	example	NOUN
ejpam-6633	543	2	2	2	NUM
ejpam-6633	543	3	:	:	PUNCT
ejpam-6633	543	4	consider	consider	VERB
ejpam-6633	543	5	the	the	DET
ejpam-6633	543	6	following	follow	VERB
ejpam-6633	543	7	multifractional	multifractional	ADJ
ejpam-6633	543	8	boundary	boundary	ADJ
ejpam-6633	543	9	-	-	PUNCT
ejpam-6633	543	10	value	value	NOUN
ejpam-6633	543	11	problem	problem	NOUN
ejpam-6633	543	12	:	:	PUNCT
ejpam-6633	543	13	chd	chd	PROPN
ejpam-6633	543	14	β	β	X
ejpam-6633	543	15	(	(	PUNCT
ejpam-6633	543	16	chd	chd	PROPN
ejpam-6633	543	17	α	α	PROPN
ejpam-6633	543	18	+	+	X
ejpam-6633	543	19	µ	µ	PROPN
ejpam-6633	543	20	t	t	NOUN
ejpam-6633	543	21	)	)	PUNCT
ejpam-6633	543	22	η(t	η(t	NOUN
ejpam-6633	543	23	)	)	PUNCT
ejpam-6633	543	24	=	=	SYM
ejpam-6633	543	25	η(t	η(t	NOUN
ejpam-6633	543	26	)	)	PUNCT
ejpam-6633	543	27	t	t	NOUN
ejpam-6633	543	28	(	(	PUNCT
ejpam-6633	543	29	2	2	NUM
ejpam-6633	543	30	+	+	NUM
ejpam-6633	543	31	µ	µ	X
ejpam-6633	543	32	erf	erf	NOUN
ejpam-6633	543	33	(	(	PUNCT
ejpam-6633	543	34	√	√	NUM
ejpam-6633	543	35	ln	ln	PROPN
ejpam-6633	543	36	(	(	PUNCT
ejpam-6633	543	37	η(t	η(t	NOUN
ejpam-6633	543	38	)	)	PUNCT
ejpam-6633	543	39	at	at	ADP
ejpam-6633	543	40	)	)	PUNCT
ejpam-6633	543	41	)	)	PUNCT
ejpam-6633	543	42	)	)	PUNCT
ejpam-6633	543	43	,	,	PUNCT
ejpam-6633	543	44	(	(	PUNCT
ejpam-6633	543	45	68	68	NUM
ejpam-6633	543	46	)	)	PUNCT
ejpam-6633	543	47	η(a	η(a	ADJ
ejpam-6633	543	48	)	)	PUNCT
ejpam-6633	543	49	=	=	SYM
ejpam-6633	543	50	a2	a2	PROPN
ejpam-6633	543	51	,	,	PUNCT
ejpam-6633	543	52	(	(	PUNCT
ejpam-6633	543	53	69	69	NUM
ejpam-6633	543	54	)	)	PUNCT
ejpam-6633	543	55	η(1	η(1	NOUN
ejpam-6633	543	56	)	)	PUNCT
ejpam-6633	543	57	=	=	SYM
ejpam-6633	544	1	1	1	X
ejpam-6633	544	2	.	.	PUNCT
ejpam-6633	544	3	(	(	PUNCT
ejpam-6633	544	4	70	70	X
ejpam-6633	544	5	)	)	PUNCT
ejpam-6633	544	6	a.	a.	PROPN
ejpam-6633	544	7	s.	s.	PROPN
ejpam-6633	544	8	hasan	hasan	PROPN
ejpam-6633	544	9	,	,	PUNCT
ejpam-6633	544	10	s.	s.	PROPN
ejpam-6633	544	11	a.	a.	PROPN
ejpam-6633	544	12	murad	murad	PROPN
ejpam-6633	544	13	/	/	SYM
ejpam-6633	544	14	eur	eur	PROPN
ejpam-6633	544	15	.	.	PUNCT
ejpam-6633	545	1	j.	j.	PROPN
ejpam-6633	545	2	pure	pure	PROPN
ejpam-6633	545	3	appl	appl	PROPN
ejpam-6633	545	4	.	.	PROPN
ejpam-6633	545	5	math	math	PROPN
ejpam-6633	545	6	,	,	PUNCT
ejpam-6633	545	7	18	18	NUM
ejpam-6633	545	8	(	(	PUNCT
ejpam-6633	545	9	3	3	NUM
ejpam-6633	545	10	)	)	PUNCT
ejpam-6633	545	11	(	(	PUNCT
ejpam-6633	545	12	2025	2025	NUM
ejpam-6633	545	13	)	)	PUNCT
ejpam-6633	545	14	,	,	PUNCT
ejpam-6633	545	15	6633	6633	NUM
ejpam-6633	545	16	21	21	NUM
ejpam-6633	545	17	of	of	ADP
ejpam-6633	545	18	24	24	NUM
ejpam-6633	545	19	here	here	ADV
ejpam-6633	545	20	,	,	PUNCT
ejpam-6633	545	21	the	the	DET
ejpam-6633	545	22	non	non	ADJ
ejpam-6633	545	23	-	-	ADJ
ejpam-6633	545	24	linear	linear	ADJ
ejpam-6633	545	25	function	function	NOUN
ejpam-6633	545	26	θ(t	θ(t	PROPN
ejpam-6633	545	27	,	,	PUNCT
ejpam-6633	545	28	η(t	η(t	NOUN
ejpam-6633	545	29	)	)	PUNCT
ejpam-6633	545	30	)	)	PUNCT
ejpam-6633	546	1	=	=	SYM
ejpam-6633	546	2	η(t	η(t	NOUN
ejpam-6633	546	3	)	)	PUNCT
ejpam-6633	546	4	t	t	NOUN
ejpam-6633	546	5	(	(	PUNCT
ejpam-6633	546	6	2	2	NUM
ejpam-6633	546	7	+	+	NUM
ejpam-6633	546	8	µ	µ	X
ejpam-6633	546	9	erf	erf	NOUN
ejpam-6633	546	10	(	(	PUNCT
ejpam-6633	546	11	√	√	PROPN
ejpam-6633	546	12	ln	ln	ADJ
ejpam-6633	546	13	η(t	η(t	NOUN
ejpam-6633	546	14	)	)	PUNCT
ejpam-6633	546	15	at	at	ADP
ejpam-6633	546	16	)	)	PUNCT
ejpam-6633	546	17	)	)	PUNCT
ejpam-6633	546	18	,	,	PUNCT
ejpam-6633	546	19	where	where	SCONJ
ejpam-6633	546	20	erf	erf	NOUN
ejpam-6633	546	21	(	(	PUNCT
ejpam-6633	546	22	·	·	PUNCT
ejpam-6633	546	23	)	)	PUNCT
ejpam-6633	546	24	is	be	AUX
ejpam-6633	546	25	the	the	DET
ejpam-6633	546	26	error	error	NOUN
ejpam-6633	546	27	function	function	NOUN
ejpam-6633	546	28	.	.	PUNCT
ejpam-6633	547	1	for	for	ADP
ejpam-6633	547	2	α	α	NOUN
ejpam-6633	547	3	=	=	SYM
ejpam-6633	547	4	β	β	X
ejpam-6633	547	5	=	=	SYM
ejpam-6633	547	6	0.5	0.5	NUM
ejpam-6633	547	7	and	and	CCONJ
ejpam-6633	547	8	µ	µ	X
ejpam-6633	547	9	=	=	SYM
ejpam-6633	547	10	0.1	0.1	NUM
ejpam-6633	547	11	,	,	PUNCT
ejpam-6633	547	12	η(t	η(t	NOUN
ejpam-6633	547	13	)	)	PUNCT
ejpam-6633	547	14	=	=	SYM
ejpam-6633	547	15	t2	t2	PROPN
ejpam-6633	547	16	is	be	AUX
ejpam-6633	547	17	the	the	DET
ejpam-6633	547	18	exact	exact	ADJ
ejpam-6633	547	19	solution	solution	NOUN
ejpam-6633	547	20	for	for	ADP
ejpam-6633	547	21	the	the	DET
ejpam-6633	547	22	problem	problem	NOUN
ejpam-6633	547	23	(	(	PUNCT
ejpam-6633	547	24	68	68	NUM
ejpam-6633	547	25	-	-	SYM
ejpam-6633	547	26	70	70	NUM
ejpam-6633	547	27	)	)	PUNCT
ejpam-6633	547	28	.	.	PUNCT
ejpam-6633	548	1	the	the	DET
ejpam-6633	548	2	exact	exact	ADJ
ejpam-6633	548	3	solution	solution	NOUN
ejpam-6633	548	4	of	of	ADP
ejpam-6633	548	5	the	the	DET
ejpam-6633	548	6	problem	problem	NOUN
ejpam-6633	548	7	(	(	PUNCT
ejpam-6633	548	8	68	68	NUM
ejpam-6633	548	9	-	-	SYM
ejpam-6633	548	10	70	70	NUM
ejpam-6633	548	11	)	)	PUNCT
ejpam-6633	548	12	versus	versus	ADP
ejpam-6633	548	13	the	the	DET
ejpam-6633	548	14	numerical	numerical	ADJ
ejpam-6633	548	15	solution	solution	NOUN
ejpam-6633	548	16	is	be	AUX
ejpam-6633	548	17	depicted	depict	VERB
ejpam-6633	548	18	in	in	ADP
ejpam-6633	548	19	figures	figure	NOUN
ejpam-6633	548	20	(	(	PUNCT
ejpam-6633	548	21	3)a	3)a	PROPN
ejpam-6633	548	22	-	-	PUNCT
ejpam-6633	548	23	b.	b.	NOUN
ejpam-6633	548	24	both	both	DET
ejpam-6633	548	25	graphs	graph	NOUN
ejpam-6633	548	26	presented	present	VERB
ejpam-6633	548	27	with	with	ADP
ejpam-6633	548	28	n	n	NOUN
ejpam-6633	548	29	=	=	SYM
ejpam-6633	548	30	512	512	NUM
ejpam-6633	548	31	,	,	PUNCT
ejpam-6633	548	32	and	and	CCONJ
ejpam-6633	548	33	the	the	DET
ejpam-6633	548	34	convergence	convergence	NOUN
ejpam-6633	548	35	was	be	AUX
ejpam-6633	548	36	achieved	achieve	VERB
ejpam-6633	548	37	with	with	ADP
ejpam-6633	548	38	tolerance	tolerance	NOUN
ejpam-6633	548	39	1e-06	1e-06	NUM
ejpam-6633	548	40	at	at	ADP
ejpam-6633	548	41	the	the	DET
ejpam-6633	548	42	4th	4th	ADJ
ejpam-6633	548	43	iteration	iteration	NOUN
ejpam-6633	548	44	.	.	PUNCT
ejpam-6633	549	1	(	(	PUNCT
ejpam-6633	549	2	a	a	X
ejpam-6633	549	3	)	)	PUNCT
ejpam-6633	549	4	(	(	PUNCT
ejpam-6633	549	5	b	b	X
ejpam-6633	549	6	)	)	PUNCT
ejpam-6633	549	7	figure	figure	NOUN
ejpam-6633	549	8	3	3	NUM
ejpam-6633	549	9	:	:	PUNCT
ejpam-6633	549	10	exact	exact	ADJ
ejpam-6633	549	11	solution	solution	NOUN
ejpam-6633	549	12	,	,	PUNCT
ejpam-6633	549	13	η(t	η(t	NOUN
ejpam-6633	549	14	)	)	PUNCT
ejpam-6633	549	15	=	=	SYM
ejpam-6633	549	16	t2	t2	NOUN
ejpam-6633	549	17	,	,	PUNCT
ejpam-6633	549	18	(	(	PUNCT
ejpam-6633	549	19	solid	solid	ADJ
ejpam-6633	549	20	line	line	NOUN
ejpam-6633	549	21	)	)	PUNCT
ejpam-6633	549	22	versus	versus	ADP
ejpam-6633	549	23	numerical	numerical	ADJ
ejpam-6633	549	24	solution	solution	NOUN
ejpam-6633	549	25	(	(	PUNCT
ejpam-6633	549	26	dashed	dash	VERB
ejpam-6633	549	27	line	line	NOUN
ejpam-6633	549	28	)	)	PUNCT
ejpam-6633	549	29	for	for	ADP
ejpam-6633	549	30	the	the	DET
ejpam-6633	549	31	problem	problem	NOUN
ejpam-6633	549	32	(	(	PUNCT
ejpam-6633	549	33	68	68	NUM
ejpam-6633	549	34	-	-	SYM
ejpam-6633	549	35	70	70	NUM
ejpam-6633	549	36	)	)	PUNCT
ejpam-6633	549	37	,	,	PUNCT
ejpam-6633	549	38	with	with	ADP
ejpam-6633	549	39	µ	µ	NOUN
ejpam-6633	549	40	=	=	SYM
ejpam-6633	549	41	0.1	0.1	NUM
ejpam-6633	549	42	,	,	PUNCT
ejpam-6633	549	43	α	α	X
ejpam-6633	549	44	=	=	SYM
ejpam-6633	549	45	β	β	X
ejpam-6633	549	46	=	=	SYM
ejpam-6633	549	47	0.5	0.5	NUM
ejpam-6633	549	48	,	,	PUNCT
ejpam-6633	549	49	n	n	NOUN
ejpam-6633	549	50	=	=	SYM
ejpam-6633	549	51	512	512	NUM
ejpam-6633	549	52	,	,	PUNCT
ejpam-6633	549	53	(	(	PUNCT
ejpam-6633	549	54	a	a	X
ejpam-6633	549	55	)	)	PUNCT
ejpam-6633	549	56	a	a	DET
ejpam-6633	549	57	=	=	NOUN
ejpam-6633	549	58	0.9	0.9	NUM
ejpam-6633	549	59	,	,	PUNCT
ejpam-6633	549	60	and	and	CCONJ
ejpam-6633	549	61	(	(	PUNCT
ejpam-6633	549	62	b	b	X
ejpam-6633	549	63	)	)	PUNCT
ejpam-6633	549	64	a	a	DET
ejpam-6633	549	65	=	=	NOUN
ejpam-6633	549	66	0.8	0.8	NUM
ejpam-6633	549	67	.	.	PUNCT
ejpam-6633	550	1	the	the	DET
ejpam-6633	550	2	reduction	reduction	NOUN
ejpam-6633	550	3	of	of	ADP
ejpam-6633	550	4	the	the	DET
ejpam-6633	550	5	absolute	absolute	ADJ
ejpam-6633	550	6	error	error	NOUN
ejpam-6633	550	7	is	be	AUX
ejpam-6633	550	8	depicted	depict	VERB
ejpam-6633	550	9	in	in	ADP
ejpam-6633	550	10	figures	figure	NOUN
ejpam-6633	550	11	(	(	PUNCT
ejpam-6633	550	12	4)a	4)a	NUM
ejpam-6633	550	13	-	-	PUNCT
ejpam-6633	550	14	b	b	NOUN
ejpam-6633	550	15	,	,	PUNCT
ejpam-6633	550	16	which	which	PRON
ejpam-6633	550	17	is	be	AUX
ejpam-6633	550	18	of	of	ADP
ejpam-6633	550	19	order	order	NOUN
ejpam-6633	550	20	o(1e-03	o(1e-03	PROPN
ejpam-6633	550	21	)	)	PUNCT
ejpam-6633	550	22	,	,	PUNCT
ejpam-6633	550	23	as	as	ADP
ejpam-6633	550	24	the	the	DET
ejpam-6633	550	25	mesh	mesh	NOUN
ejpam-6633	550	26	increases	increase	NOUN
ejpam-6633	550	27	.	.	PUNCT
ejpam-6633	551	1	(	(	PUNCT
ejpam-6633	551	2	a	a	X
ejpam-6633	551	3	)	)	PUNCT
ejpam-6633	551	4	(	(	PUNCT
ejpam-6633	551	5	b	b	X
ejpam-6633	551	6	)	)	PUNCT
ejpam-6633	551	7	figure	figure	NOUN
ejpam-6633	551	8	4	4	NUM
ejpam-6633	551	9	:	:	PUNCT
ejpam-6633	551	10	absolute	absolute	ADJ
ejpam-6633	551	11	error	error	NOUN
ejpam-6633	551	12	for	for	ADP
ejpam-6633	551	13	the	the	DET
ejpam-6633	551	14	problem	problem	NOUN
ejpam-6633	551	15	(	(	PUNCT
ejpam-6633	551	16	68	68	NUM
ejpam-6633	551	17	-	-	SYM
ejpam-6633	551	18	70	70	NUM
ejpam-6633	551	19	)	)	PUNCT
ejpam-6633	551	20	as	as	ADP
ejpam-6633	551	21	the	the	DET
ejpam-6633	551	22	mesh	mesh	NOUN
ejpam-6633	551	23	number	number	NOUN
ejpam-6633	551	24	(	(	PUNCT
ejpam-6633	551	25	n	n	CCONJ
ejpam-6633	551	26	)	)	PUNCT
ejpam-6633	551	27	increases	increase	NOUN
ejpam-6633	551	28	:	:	PUNCT
ejpam-6633	551	29	(	(	PUNCT
ejpam-6633	551	30	a	a	X
ejpam-6633	551	31	)	)	PUNCT
ejpam-6633	551	32	for	for	ADP
ejpam-6633	551	33	a	a	DET
ejpam-6633	551	34	=	=	SYM
ejpam-6633	551	35	0.9	0.9	NUM
ejpam-6633	551	36	at	at	ADP
ejpam-6633	551	37	t	t	PROPN
ejpam-6633	551	38	=	=	SYM
ejpam-6633	551	39	0.92	0.92	NUM
ejpam-6633	551	40	,	,	PUNCT
ejpam-6633	551	41	and	and	CCONJ
ejpam-6633	551	42	(	(	PUNCT
ejpam-6633	551	43	b	b	NOUN
ejpam-6633	551	44	)	)	PUNCT
ejpam-6633	551	45	for	for	ADP
ejpam-6633	551	46	a	a	DET
ejpam-6633	551	47	=	=	SYM
ejpam-6633	551	48	0.8	0.8	NUM
ejpam-6633	551	49	at	at	ADP
ejpam-6633	551	50	t	t	PROPN
ejpam-6633	551	51	=	=	SYM
ejpam-6633	551	52	8.2	8.2	NUM
ejpam-6633	551	53	.	.	PUNCT
ejpam-6633	551	54	example	example	NOUN
ejpam-6633	552	1	3	3	NUM
ejpam-6633	552	2	:	:	PUNCT
ejpam-6633	552	3	consider	consider	VERB
ejpam-6633	552	4	the	the	DET
ejpam-6633	552	5	following	follow	VERB
ejpam-6633	552	6	multifractional	multifractional	ADJ
ejpam-6633	552	7	boundary	boundary	ADJ
ejpam-6633	552	8	-	-	PUNCT
ejpam-6633	552	9	value	value	NOUN
ejpam-6633	552	10	problem	problem	NOUN
ejpam-6633	552	11	:	:	PUNCT
ejpam-6633	552	12	chd	chd	PROPN
ejpam-6633	552	13	β	β	X
ejpam-6633	552	14	(	(	PUNCT
ejpam-6633	552	15	chd	chd	PROPN
ejpam-6633	552	16	α	α	PROPN
ejpam-6633	552	17	+	+	X
ejpam-6633	552	18	µ	µ	PROPN
ejpam-6633	552	19	t	t	NOUN
ejpam-6633	552	20	)	)	PUNCT
ejpam-6633	552	21	η(t	η(t	NOUN
ejpam-6633	552	22	)	)	PUNCT
ejpam-6633	552	23	=	=	SYM
ejpam-6633	552	24	η(t	η(t	NOUN
ejpam-6633	552	25	)	)	PUNCT
ejpam-6633	552	26	t	t	NOUN
ejpam-6633	553	1	+	+	CCONJ
ejpam-6633	553	2	2µ√	2µ√	NUM
ejpam-6633	553	3	πt	πt	ADP
ejpam-6633	553	4	√	√	NUM
ejpam-6633	553	5	η(t	η(t	NOUN
ejpam-6633	553	6	)	)	PUNCT
ejpam-6633	554	1	+	+	CCONJ
ejpam-6633	555	1	1	1	X
ejpam-6633	555	2	.	.	PUNCT
ejpam-6633	555	3	(	(	PUNCT
ejpam-6633	555	4	71	71	NUM
ejpam-6633	555	5	)	)	PUNCT
ejpam-6633	555	6	η(a	η(a	VERB
ejpam-6633	555	7	)	)	PUNCT
ejpam-6633	555	8	=	=	SYM
ejpam-6633	555	9	0	0	NUM
ejpam-6633	555	10	,	,	PUNCT
ejpam-6633	555	11	(	(	PUNCT
ejpam-6633	555	12	72	72	X
ejpam-6633	555	13	)	)	PUNCT
ejpam-6633	555	14	η(1	η(1	NOUN
ejpam-6633	555	15	)	)	PUNCT
ejpam-6633	555	16	=	=	SYM
ejpam-6633	555	17	ln	ln	NOUN
ejpam-6633	555	18	(	(	PUNCT
ejpam-6633	555	19	1	1	NUM
ejpam-6633	555	20	a	a	PRON
ejpam-6633	555	21	)	)	PUNCT
ejpam-6633	555	22	.	.	PUNCT
ejpam-6633	556	1	(	(	PUNCT
ejpam-6633	556	2	73	73	NUM
ejpam-6633	556	3	)	)	PUNCT
ejpam-6633	556	4	here	here	ADV
ejpam-6633	556	5	,	,	PUNCT
ejpam-6633	556	6	the	the	DET
ejpam-6633	556	7	non	non	ADJ
ejpam-6633	556	8	-	-	ADJ
ejpam-6633	556	9	linear	linear	ADJ
ejpam-6633	556	10	function	function	NOUN
ejpam-6633	556	11	θ(t	θ(t	PROPN
ejpam-6633	556	12	,	,	PUNCT
ejpam-6633	556	13	η(t	η(t	NOUN
ejpam-6633	556	14	)	)	PUNCT
ejpam-6633	556	15	)	)	PUNCT
ejpam-6633	557	1	=	=	SYM
ejpam-6633	557	2	η(t	η(t	NOUN
ejpam-6633	557	3	)	)	PUNCT
ejpam-6633	557	4	t	t	NOUN
ejpam-6633	558	1	+	+	CCONJ
ejpam-6633	558	2	2µ√	2µ√	NUM
ejpam-6633	558	3	πt	πt	ADP
ejpam-6633	558	4	√	√	NUM
ejpam-6633	558	5	η(t	η(t	NOUN
ejpam-6633	558	6	)	)	PUNCT
ejpam-6633	558	7	+	+	CCONJ
ejpam-6633	558	8	1	1	X
ejpam-6633	558	9	.	.	X
ejpam-6633	558	10	for	for	ADP
ejpam-6633	558	11	α	α	NOUN
ejpam-6633	558	12	=	=	SYM
ejpam-6633	558	13	β	β	X
ejpam-6633	558	14	=	=	SYM
ejpam-6633	558	15	0.5	0.5	NUM
ejpam-6633	558	16	and	and	CCONJ
ejpam-6633	558	17	µ	µ	X
ejpam-6633	558	18	=	=	SYM
ejpam-6633	558	19	0.1	0.1	NUM
ejpam-6633	558	20	,	,	PUNCT
ejpam-6633	558	21	the	the	DET
ejpam-6633	558	22	exact	exact	ADJ
ejpam-6633	558	23	solution	solution	NOUN
ejpam-6633	558	24	for	for	ADP
ejpam-6633	558	25	the	the	DET
ejpam-6633	558	26	problem	problem	NOUN
ejpam-6633	558	27	(	(	PUNCT
ejpam-6633	558	28	71	71	NUM
ejpam-6633	558	29	-	-	SYM
ejpam-6633	558	30	73	73	NUM
ejpam-6633	558	31	)	)	PUNCT
ejpam-6633	558	32	is	be	AUX
ejpam-6633	558	33	η(t	η(t	NOUN
ejpam-6633	558	34	)	)	PUNCT
ejpam-6633	559	1	=	=	SYM
ejpam-6633	559	2	t	t	NOUN
ejpam-6633	559	3	ln	ln	NOUN
ejpam-6633	560	1	(	(	PUNCT
ejpam-6633	560	2	t	t	PROPN
ejpam-6633	560	3	a	a	PRON
ejpam-6633	560	4	)	)	PUNCT
ejpam-6633	560	5	.	.	PUNCT
ejpam-6633	561	1	the	the	DET
ejpam-6633	561	2	exact	exact	ADJ
ejpam-6633	561	3	solution	solution	NOUN
ejpam-6633	561	4	a.	a.	PROPN
ejpam-6633	561	5	s.	s.	PROPN
ejpam-6633	561	6	hasan	hasan	PROPN
ejpam-6633	561	7	,	,	PUNCT
ejpam-6633	561	8	s.	s.	PROPN
ejpam-6633	561	9	a.	a.	PROPN
ejpam-6633	561	10	murad	murad	PROPN
ejpam-6633	561	11	/	/	SYM
ejpam-6633	561	12	eur	eur	PROPN
ejpam-6633	561	13	.	.	PUNCT
ejpam-6633	562	1	j.	j.	PROPN
ejpam-6633	562	2	pure	pure	PROPN
ejpam-6633	562	3	appl	appl	PROPN
ejpam-6633	562	4	.	.	PROPN
ejpam-6633	562	5	math	math	PROPN
ejpam-6633	562	6	,	,	PUNCT
ejpam-6633	562	7	18	18	NUM
ejpam-6633	562	8	(	(	PUNCT
ejpam-6633	562	9	3	3	NUM
ejpam-6633	562	10	)	)	PUNCT
ejpam-6633	562	11	(	(	PUNCT
ejpam-6633	562	12	2025	2025	NUM
ejpam-6633	562	13	)	)	PUNCT
ejpam-6633	562	14	,	,	PUNCT
ejpam-6633	562	15	6633	6633	NUM
ejpam-6633	562	16	22	22	NUM
ejpam-6633	562	17	of	of	ADP
ejpam-6633	562	18	24	24	NUM
ejpam-6633	562	19	of	of	ADP
ejpam-6633	562	20	the	the	DET
ejpam-6633	562	21	problem	problem	NOUN
ejpam-6633	562	22	(	(	PUNCT
ejpam-6633	562	23	71	71	NUM
ejpam-6633	562	24	-	-	SYM
ejpam-6633	562	25	73	73	NUM
ejpam-6633	562	26	)	)	PUNCT
ejpam-6633	562	27	versus	versus	ADP
ejpam-6633	562	28	the	the	DET
ejpam-6633	562	29	numerical	numerical	ADJ
ejpam-6633	562	30	solution	solution	NOUN
ejpam-6633	562	31	is	be	AUX
ejpam-6633	562	32	depicted	depict	VERB
ejpam-6633	562	33	in	in	ADP
ejpam-6633	562	34	figures	figure	NOUN
ejpam-6633	562	35	(	(	PUNCT
ejpam-6633	562	36	6)a	6)a	NOUN
ejpam-6633	562	37	-	-	PUNCT
ejpam-6633	562	38	b.	b.	NOUN
ejpam-6633	562	39	both	both	DET
ejpam-6633	562	40	graphs	graph	NOUN
ejpam-6633	562	41	presented	present	VERB
ejpam-6633	562	42	with	with	ADP
ejpam-6633	562	43	n	n	PROPN
ejpam-6633	562	44	=	=	SYM
ejpam-6633	562	45	128	128	NUM
ejpam-6633	562	46	,	,	PUNCT
ejpam-6633	562	47	and	and	CCONJ
ejpam-6633	562	48	the	the	DET
ejpam-6633	562	49	convergence	convergence	NOUN
ejpam-6633	562	50	achieved	achieve	VERB
ejpam-6633	562	51	with	with	ADP
ejpam-6633	562	52	tolerance	tolerance	NOUN
ejpam-6633	562	53	1e-06	1e-06	NOUN
ejpam-6633	562	54	at	at	ADP
ejpam-6633	562	55	the	the	DET
ejpam-6633	562	56	3rd	3rd	ADJ
ejpam-6633	562	57	iteration	iteration	NOUN
ejpam-6633	562	58	.	.	PUNCT
ejpam-6633	563	1	(	(	PUNCT
ejpam-6633	563	2	a	a	X
ejpam-6633	563	3	)	)	PUNCT
ejpam-6633	563	4	(	(	PUNCT
ejpam-6633	563	5	b	b	X
ejpam-6633	563	6	)	)	PUNCT
ejpam-6633	563	7	figure	figure	NOUN
ejpam-6633	563	8	5	5	NUM
ejpam-6633	563	9	:	:	PUNCT
ejpam-6633	563	10	absolute	absolute	ADJ
ejpam-6633	563	11	error	error	NOUN
ejpam-6633	563	12	for	for	ADP
ejpam-6633	563	13	the	the	DET
ejpam-6633	563	14	problem	problem	NOUN
ejpam-6633	563	15	(	(	PUNCT
ejpam-6633	563	16	68	68	NUM
ejpam-6633	563	17	-	-	SYM
ejpam-6633	563	18	70	70	NUM
ejpam-6633	563	19	)	)	PUNCT
ejpam-6633	563	20	as	as	ADP
ejpam-6633	563	21	the	the	DET
ejpam-6633	563	22	mesh	mesh	NOUN
ejpam-6633	563	23	number	number	NOUN
ejpam-6633	563	24	(	(	PUNCT
ejpam-6633	563	25	n	n	CCONJ
ejpam-6633	563	26	)	)	PUNCT
ejpam-6633	563	27	increases	increase	NOUN
ejpam-6633	563	28	,	,	PUNCT
ejpam-6633	563	29	(	(	PUNCT
ejpam-6633	563	30	a	a	X
ejpam-6633	563	31	)	)	PUNCT
ejpam-6633	563	32	for	for	ADP
ejpam-6633	563	33	a	a	DET
ejpam-6633	563	34	=	=	SYM
ejpam-6633	563	35	0.9	0.9	NUM
ejpam-6633	563	36	at	at	ADP
ejpam-6633	563	37	t	t	PROPN
ejpam-6633	563	38	=	=	SYM
ejpam-6633	563	39	0.92	0.92	NUM
ejpam-6633	563	40	,	,	PUNCT
ejpam-6633	563	41	and	and	CCONJ
ejpam-6633	563	42	(	(	PUNCT
ejpam-6633	563	43	b	b	NOUN
ejpam-6633	563	44	)	)	PUNCT
ejpam-6633	563	45	for	for	ADP
ejpam-6633	563	46	a	a	DET
ejpam-6633	563	47	=	=	SYM
ejpam-6633	563	48	0.8	0.8	NUM
ejpam-6633	563	49	at	at	ADP
ejpam-6633	563	50	t	t	PROPN
ejpam-6633	563	51	=	=	SYM
ejpam-6633	563	52	8.2	8.2	NUM
ejpam-6633	563	53	.	.	PUNCT
ejpam-6633	564	1	(	(	PUNCT
ejpam-6633	564	2	a	a	X
ejpam-6633	564	3	)	)	PUNCT
ejpam-6633	564	4	(	(	PUNCT
ejpam-6633	564	5	b	b	X
ejpam-6633	564	6	)	)	PUNCT
ejpam-6633	564	7	figure	figure	NOUN
ejpam-6633	564	8	6	6	NUM
ejpam-6633	564	9	:	:	PUNCT
ejpam-6633	564	10	exact	exact	ADJ
ejpam-6633	564	11	solution	solution	NOUN
ejpam-6633	564	12	(	(	PUNCT
ejpam-6633	564	13	solid	solid	ADJ
ejpam-6633	564	14	line	line	NOUN
ejpam-6633	564	15	)	)	PUNCT
ejpam-6633	564	16	versus	versus	ADP
ejpam-6633	564	17	numerical	numerical	ADJ
ejpam-6633	564	18	solution	solution	NOUN
ejpam-6633	564	19	(	(	PUNCT
ejpam-6633	564	20	dashed	dash	VERB
ejpam-6633	564	21	line	line	NOUN
ejpam-6633	564	22	)	)	PUNCT
ejpam-6633	564	23	for	for	ADP
ejpam-6633	564	24	the	the	DET
ejpam-6633	564	25	problem	problem	NOUN
ejpam-6633	564	26	(	(	PUNCT
ejpam-6633	564	27	71	71	NUM
ejpam-6633	564	28	-	-	SYM
ejpam-6633	564	29	73	73	NUM
ejpam-6633	564	30	)	)	PUNCT
ejpam-6633	564	31	,	,	PUNCT
ejpam-6633	564	32	with	with	ADP
ejpam-6633	564	33	µ	µ	NOUN
ejpam-6633	564	34	=	=	SYM
ejpam-6633	564	35	0.1	0.1	NUM
ejpam-6633	564	36	,	,	PUNCT
ejpam-6633	564	37	α	α	X
ejpam-6633	564	38	=	=	SYM
ejpam-6633	564	39	β	β	X
ejpam-6633	564	40	=	=	SYM
ejpam-6633	564	41	0.5	0.5	NUM
ejpam-6633	564	42	,	,	PUNCT
ejpam-6633	564	43	n	n	NOUN
ejpam-6633	564	44	=	=	SYM
ejpam-6633	564	45	128	128	NUM
ejpam-6633	564	46	,	,	PUNCT
ejpam-6633	564	47	(	(	PUNCT
ejpam-6633	564	48	a	a	X
ejpam-6633	564	49	)	)	PUNCT
ejpam-6633	564	50	a	a	DET
ejpam-6633	564	51	=	=	NOUN
ejpam-6633	564	52	0.9	0.9	NUM
ejpam-6633	564	53	,	,	PUNCT
ejpam-6633	564	54	and	and	CCONJ
ejpam-6633	564	55	(	(	PUNCT
ejpam-6633	564	56	b	b	X
ejpam-6633	564	57	)	)	PUNCT
ejpam-6633	564	58	a	a	DET
ejpam-6633	564	59	=	=	NOUN
ejpam-6633	564	60	0.8	0.8	NUM
ejpam-6633	564	61	.	.	PUNCT
ejpam-6633	565	1	the	the	DET
ejpam-6633	565	2	reduction	reduction	NOUN
ejpam-6633	565	3	of	of	ADP
ejpam-6633	565	4	absolute	absolute	ADJ
ejpam-6633	565	5	error	error	NOUN
ejpam-6633	565	6	is	be	AUX
ejpam-6633	565	7	depicted	depict	VERB
ejpam-6633	565	8	in	in	ADP
ejpam-6633	565	9	figures	figure	NOUN
ejpam-6633	565	10	(	(	PUNCT
ejpam-6633	565	11	5)a	5)a	NUM
ejpam-6633	565	12	-	-	SYM
ejpam-6633	565	13	b	b	NOUN
ejpam-6633	565	14	as	as	ADP
ejpam-6633	565	15	the	the	DET
ejpam-6633	565	16	mesh	mesh	NOUN
ejpam-6633	565	17	increases	increase	NOUN
ejpam-6633	565	18	.	.	PUNCT
ejpam-6633	566	1	for	for	ADP
ejpam-6633	566	2	a	a	DET
ejpam-6633	566	3	=	=	SYM
ejpam-6633	566	4	0.9	0.9	NUM
ejpam-6633	566	5	,	,	PUNCT
ejpam-6633	566	6	the	the	DET
ejpam-6633	566	7	absolute	absolute	ADJ
ejpam-6633	566	8	error	error	NOUN
ejpam-6633	566	9	is	be	AUX
ejpam-6633	566	10	of	of	ADP
ejpam-6633	566	11	order	order	NOUN
ejpam-6633	566	12	o(1e	o(1e	NOUN
ejpam-6633	566	13	−	−	NUM
ejpam-6633	566	14	04	04	NUM
ejpam-6633	566	15	)	)	PUNCT
ejpam-6633	566	16	and	and	CCONJ
ejpam-6633	566	17	it	it	PRON
ejpam-6633	566	18	is	be	AUX
ejpam-6633	566	19	of	of	ADP
ejpam-6633	566	20	order	order	NOUN
ejpam-6633	566	21	o(1e	o(1e	NOUN
ejpam-6633	566	22	−	−	NOUN
ejpam-6633	566	23	03	03	NUM
ejpam-6633	566	24	)	)	PUNCT
ejpam-6633	566	25	for	for	ADP
ejpam-6633	566	26	a	a	DET
ejpam-6633	566	27	=	=	SYM
ejpam-6633	566	28	0.8	0.8	NUM
ejpam-6633	566	29	.	.	PUNCT
ejpam-6633	567	1	a	a	DET
ejpam-6633	567	2	similar	similar	ADJ
ejpam-6633	567	3	behavior	behavior	NOUN
ejpam-6633	567	4	for	for	ADP
ejpam-6633	567	5	the	the	DET
ejpam-6633	567	6	absolute	absolute	ADJ
ejpam-6633	567	7	error	error	NOUN
ejpam-6633	567	8	was	be	AUX
ejpam-6633	567	9	observed	observe	VERB
ejpam-6633	567	10	for	for	ADP
ejpam-6633	567	11	the	the	DET
ejpam-6633	567	12	previous	previous	ADJ
ejpam-6633	567	13	example	example	NOUN
ejpam-6633	567	14	.	.	PUNCT
ejpam-6633	568	1	6	6	X
ejpam-6633	568	2	.	.	X
ejpam-6633	568	3	conclusion	conclusion	NOUN
ejpam-6633	568	4	this	this	DET
ejpam-6633	568	5	study	study	NOUN
ejpam-6633	568	6	has	have	AUX
ejpam-6633	568	7	provided	provide	VERB
ejpam-6633	568	8	a	a	DET
ejpam-6633	568	9	detailed	detailed	ADJ
ejpam-6633	568	10	examination	examination	NOUN
ejpam-6633	568	11	of	of	ADP
ejpam-6633	568	12	the	the	DET
ejpam-6633	568	13	boundary	boundary	ADJ
ejpam-6633	568	14	-	-	PUNCT
ejpam-6633	568	15	value	value	NOUN
ejpam-6633	568	16	problem	problem	NOUN
ejpam-6633	568	17	(	(	PUNCT
ejpam-6633	568	18	6	6	NUM
ejpam-6633	568	19	-	-	SYM
ejpam-6633	568	20	8)	8)	NUM
ejpam-6633	568	21	,	,	PUNCT
ejpam-6633	568	22	which	which	PRON
ejpam-6633	568	23	is	be	AUX
ejpam-6633	568	24	governed	govern	VERB
ejpam-6633	568	25	by	by	ADP
ejpam-6633	568	26	the	the	DET
ejpam-6633	568	27	lane	lane	NOUN
ejpam-6633	568	28	-	-	PUNCT
ejpam-6633	568	29	emden	emden	ADJ
ejpam-6633	568	30	fractional	fractional	ADJ
ejpam-6633	568	31	differential	differential	ADJ
ejpam-6633	568	32	equation	equation	NOUN
ejpam-6633	568	33	in	in	ADP
ejpam-6633	568	34	terms	term	NOUN
ejpam-6633	568	35	of	of	ADP
ejpam-6633	568	36	existence	existence	NOUN
ejpam-6633	568	37	,	,	PUNCT
ejpam-6633	568	38	uniqueness	uniqueness	NOUN
ejpam-6633	568	39	,	,	PUNCT
ejpam-6633	568	40	and	and	CCONJ
ejpam-6633	568	41	stability	stability	NOUN
ejpam-6633	568	42	.	.	PUNCT
ejpam-6633	569	1	the	the	DET
ejpam-6633	569	2	fractional	fractional	ADJ
ejpam-6633	569	3	derivative	derivative	NOUN
ejpam-6633	569	4	is	be	AUX
ejpam-6633	569	5	of	of	ADP
ejpam-6633	569	6	the	the	DET
ejpam-6633	569	7	caputo	caputo	PROPN
ejpam-6633	569	8	-	-	PUNCT
ejpam-6633	569	9	hadamard	hadamard	PROPN
ejpam-6633	569	10	type	type	NOUN
ejpam-6633	569	11	.	.	PUNCT
ejpam-6633	570	1	the	the	DET
ejpam-6633	570	2	banach	banach	NOUN
ejpam-6633	570	3	and	and	CCONJ
ejpam-6633	570	4	sodavoski	sodavoski	VERB
ejpam-6633	570	5	’s	’s	PART
ejpam-6633	570	6	fixed	fix	VERB
ejpam-6633	570	7	-	-	PUNCT
ejpam-6633	570	8	point	point	NOUN
ejpam-6633	570	9	theorems	theorem	NOUN
ejpam-6633	570	10	proved	prove	VERB
ejpam-6633	570	11	the	the	DET
ejpam-6633	570	12	existence	existence	NOUN
ejpam-6633	570	13	and	and	CCONJ
ejpam-6633	570	14	uniqueness	uniqueness	NOUN
ejpam-6633	570	15	of	of	ADP
ejpam-6633	570	16	the	the	DET
ejpam-6633	570	17	solution	solution	NOUN
ejpam-6633	570	18	.	.	PUNCT
ejpam-6633	571	1	the	the	DET
ejpam-6633	571	2	stability	stability	NOUN
ejpam-6633	571	3	of	of	ADP
ejpam-6633	571	4	the	the	DET
ejpam-6633	571	5	problem	problem	NOUN
ejpam-6633	571	6	of	of	ADP
ejpam-6633	571	7	type	type	NOUN
ejpam-6633	571	8	ulam	ulam	X
ejpam-6633	571	9	-	-	PUNCT
ejpam-6633	571	10	hyers	hyer	NOUN
ejpam-6633	571	11	and	and	CCONJ
ejpam-6633	571	12	ulam	ulam	NOUN
ejpam-6633	571	13	-	-	PUNCT
ejpam-6633	571	14	hyers	hyer	NOUN
ejpam-6633	571	15	-	-	PUNCT
ejpam-6633	571	16	rassiass	rassiass	NOUN
ejpam-6633	571	17	has	have	AUX
ejpam-6633	571	18	been	be	AUX
ejpam-6633	571	19	investigated	investigate	VERB
ejpam-6633	571	20	.	.	PUNCT
ejpam-6633	572	1	the	the	DET
ejpam-6633	572	2	existence	existence	NOUN
ejpam-6633	572	3	,	,	PUNCT
ejpam-6633	572	4	uniqueness	uniqueness	NOUN
ejpam-6633	572	5	,	,	PUNCT
ejpam-6633	572	6	and	and	CCONJ
ejpam-6633	572	7	stability	stability	NOUN
ejpam-6633	572	8	of	of	ADP
ejpam-6633	572	9	the	the	DET
ejpam-6633	572	10	solutions	solution	NOUN
ejpam-6633	572	11	are	be	AUX
ejpam-6633	572	12	demonstrated	demonstrate	VERB
ejpam-6633	572	13	with	with	ADP
ejpam-6633	572	14	an	an	DET
ejpam-6633	572	15	example	example	NOUN
ejpam-6633	572	16	in	in	ADP
ejpam-6633	572	17	section	section	NOUN
ejpam-6633	572	18	4	4	NUM
ejpam-6633	572	19	.	.	PUNCT
ejpam-6633	573	1	the	the	DET
ejpam-6633	573	2	derived	derive	VERB
ejpam-6633	573	3	analytical	analytical	ADJ
ejpam-6633	573	4	solution	solution	NOUN
ejpam-6633	573	5	to	to	ADP
ejpam-6633	573	6	the	the	DET
ejpam-6633	573	7	problem	problem	NOUN
ejpam-6633	573	8	is	be	AUX
ejpam-6633	573	9	discretised	discretise	VERB
ejpam-6633	573	10	on	on	ADP
ejpam-6633	573	11	a	a	DET
ejpam-6633	573	12	graded	grade	VERB
ejpam-6633	573	13	mesh	mesh	NOUN
ejpam-6633	573	14	using	use	VERB
ejpam-6633	573	15	the	the	DET
ejpam-6633	573	16	fractional	fractional	ADJ
ejpam-6633	573	17	rectangular	rectangular	ADJ
ejpam-6633	573	18	,	,	PUNCT
ejpam-6633	573	19	lln,1	lln,1	NOUN
ejpam-6633	573	20	interpolation	interpolation	NOUN
ejpam-6633	573	21	.	.	PUNCT
ejpam-6633	574	1	the	the	DET
ejpam-6633	574	2	a.	a.	NOUN
ejpam-6633	574	3	s.	s.	PROPN
ejpam-6633	574	4	hasan	hasan	PROPN
ejpam-6633	574	5	,	,	PUNCT
ejpam-6633	574	6	s.	s.	PROPN
ejpam-6633	574	7	a.	a.	PROPN
ejpam-6633	574	8	murad	murad	PROPN
ejpam-6633	574	9	/	/	SYM
ejpam-6633	574	10	eur	eur	PROPN
ejpam-6633	574	11	.	.	PUNCT
ejpam-6633	575	1	j.	j.	PROPN
ejpam-6633	575	2	pure	pure	PROPN
ejpam-6633	575	3	appl	appl	PROPN
ejpam-6633	575	4	.	.	PROPN
ejpam-6633	575	5	math	math	PROPN
ejpam-6633	575	6	,	,	PUNCT
ejpam-6633	575	7	18	18	NUM
ejpam-6633	575	8	(	(	PUNCT
ejpam-6633	575	9	3	3	NUM
ejpam-6633	575	10	)	)	PUNCT
ejpam-6633	575	11	(	(	PUNCT
ejpam-6633	575	12	2025	2025	NUM
ejpam-6633	575	13	)	)	PUNCT
ejpam-6633	575	14	,	,	PUNCT
ejpam-6633	575	15	6633	6633	NUM
ejpam-6633	575	16	23	23	NUM
ejpam-6633	575	17	of	of	ADP
ejpam-6633	575	18	24	24	NUM
ejpam-6633	575	19	resulting	result	VERB
ejpam-6633	575	20	set	set	NOUN
ejpam-6633	575	21	of	of	ADP
ejpam-6633	575	22	non	non	ADJ
ejpam-6633	575	23	-	-	ADJ
ejpam-6633	575	24	linear	linear	ADJ
ejpam-6633	575	25	equations	equation	NOUN
ejpam-6633	575	26	is	be	AUX
ejpam-6633	575	27	solved	solve	VERB
ejpam-6633	575	28	using	use	VERB
ejpam-6633	575	29	the	the	DET
ejpam-6633	575	30	newton	newton	PROPN
ejpam-6633	575	31	-	-	PUNCT
ejpam-6633	575	32	raphson	raphson	PROPN
ejpam-6633	575	33	method	method	NOUN
ejpam-6633	575	34	,	,	PUNCT
ejpam-6633	575	35	which	which	PRON
ejpam-6633	575	36	involves	involve	VERB
ejpam-6633	575	37	the	the	DET
ejpam-6633	575	38	jacobian	jacobian	ADJ
ejpam-6633	575	39	matrix	matrix	NOUN
ejpam-6633	575	40	to	to	PART
ejpam-6633	575	41	connect	connect	VERB
ejpam-6633	575	42	η(t	η(t	NOUN
ejpam-6633	575	43	)	)	PUNCT
ejpam-6633	575	44	and	and	CCONJ
ejpam-6633	575	45	θ(t	θ(t	PROPN
ejpam-6633	575	46	,	,	PUNCT
ejpam-6633	575	47	η(t	η(t	NOUN
ejpam-6633	575	48	)	)	PUNCT
ejpam-6633	575	49	)	)	PUNCT
ejpam-6633	575	50	in	in	ADP
ejpam-6633	575	51	a	a	DET
ejpam-6633	575	52	non	non	ADJ
ejpam-6633	575	53	-	-	ADJ
ejpam-6633	575	54	linear	linear	ADJ
ejpam-6633	575	55	way	way	NOUN
ejpam-6633	575	56	.	.	PUNCT
ejpam-6633	576	1	the	the	DET
ejpam-6633	576	2	stability	stability	NOUN
ejpam-6633	576	3	and	and	CCONJ
ejpam-6633	576	4	reliability	reliability	NOUN
ejpam-6633	576	5	of	of	ADP
ejpam-6633	576	6	the	the	DET
ejpam-6633	576	7	proposed	propose	VERB
ejpam-6633	576	8	numerical	numerical	ADJ
ejpam-6633	576	9	scheme	scheme	NOUN
ejpam-6633	576	10	were	be	AUX
ejpam-6633	576	11	studied	study	VERB
ejpam-6633	576	12	through	through	ADP
ejpam-6633	576	13	providing	provide	VERB
ejpam-6633	576	14	examples	example	NOUN
ejpam-6633	576	15	.	.	PUNCT
ejpam-6633	577	1	references	reference	NOUN
ejpam-6633	577	2	[	[	X
ejpam-6633	577	3	1	1	NUM
ejpam-6633	577	4	]	]	PUNCT
ejpam-6633	577	5	i.	i.	NOUN
ejpam-6633	577	6	podlubny	podlubny	PROPN
ejpam-6633	577	7	.	.	PUNCT
ejpam-6633	578	1	fractional	fractional	ADJ
ejpam-6633	578	2	differential	differential	ADJ
ejpam-6633	578	3	equations	equation	NOUN
ejpam-6633	578	4	:	:	PUNCT
ejpam-6633	578	5	an	an	DET
ejpam-6633	578	6	introduction	introduction	NOUN
ejpam-6633	578	7	to	to	ADP
ejpam-6633	578	8	fractional	fractional	ADJ
ejpam-6633	578	9	derivatives	derivative	NOUN
ejpam-6633	578	10	,	,	PUNCT
ejpam-6633	578	11	fractional	fractional	ADJ
ejpam-6633	578	12	differential	differential	ADJ
ejpam-6633	578	13	equations	equation	NOUN
ejpam-6633	578	14	,	,	PUNCT
ejpam-6633	578	15	to	to	ADP
ejpam-6633	578	16	methods	method	NOUN
ejpam-6633	578	17	of	of	ADP
ejpam-6633	578	18	their	their	PRON
ejpam-6633	578	19	solution	solution	NOUN
ejpam-6633	578	20	and	and	CCONJ
ejpam-6633	578	21	some	some	PRON
ejpam-6633	578	22	of	of	ADP
ejpam-6633	578	23	their	their	PRON
ejpam-6633	578	24	applications	application	NOUN
ejpam-6633	578	25	.	.	PUNCT
ejpam-6633	579	1	elsevier	elsevier	NOUN
ejpam-6633	579	2	,	,	PUNCT
ejpam-6633	579	3	1998	1998	NUM
ejpam-6633	579	4	.	.	PUNCT
ejpam-6633	580	1	[	[	X
ejpam-6633	580	2	2	2	X
ejpam-6633	580	3	]	]	X
ejpam-6633	580	4	y.	y.	PROPN
ejpam-6633	580	5	zhou	zhou	PROPN
ejpam-6633	580	6	.	.	PUNCT
ejpam-6633	581	1	basic	basic	ADJ
ejpam-6633	581	2	theory	theory	NOUN
ejpam-6633	581	3	of	of	ADP
ejpam-6633	581	4	fractional	fractional	ADJ
ejpam-6633	581	5	differential	differential	ADJ
ejpam-6633	581	6	equations	equation	NOUN
ejpam-6633	581	7	.	.	PUNCT
ejpam-6633	582	1	world	world	PROPN
ejpam-6633	582	2	scientific	scientific	ADJ
ejpam-6633	582	3	,	,	PUNCT
ejpam-6633	582	4	2023	2023	NUM
ejpam-6633	582	5	.	.	PUNCT
ejpam-6633	583	1	[	[	X
ejpam-6633	583	2	3	3	X
ejpam-6633	583	3	]	]	X
ejpam-6633	583	4	b.	b.	PROPN
ejpam-6633	583	5	ahmad	ahmad	PROPN
ejpam-6633	583	6	and	and	CCONJ
ejpam-6633	583	7	r.	r.	PROPN
ejpam-6633	583	8	p.	p.	PROPN
ejpam-6633	583	9	agarwal	agarwal	PROPN
ejpam-6633	583	10	.	.	PUNCT
ejpam-6633	584	1	some	some	DET
ejpam-6633	584	2	new	new	ADJ
ejpam-6633	584	3	versions	version	NOUN
ejpam-6633	584	4	of	of	ADP
ejpam-6633	584	5	fractional	fractional	ADJ
ejpam-6633	584	6	boundary	boundary	ADJ
ejpam-6633	584	7	value	value	NOUN
ejpam-6633	584	8	problems	problem	NOUN
ejpam-6633	584	9	with	with	ADP
ejpam-6633	584	10	slit	slit	ADJ
ejpam-6633	584	11	-	-	PUNCT
ejpam-6633	584	12	strips	strip	NOUN
ejpam-6633	584	13	conditions	condition	NOUN
ejpam-6633	584	14	.	.	PUNCT
ejpam-6633	585	1	boundary	boundary	ADJ
ejpam-6633	585	2	value	value	NOUN
ejpam-6633	585	3	problems	problem	NOUN
ejpam-6633	585	4	,	,	PUNCT
ejpam-6633	585	5	2014:1–12	2014:1–12	NUM
ejpam-6633	585	6	,	,	PUNCT
ejpam-6633	585	7	2014	2014	NUM
ejpam-6633	585	8	.	.	PUNCT
ejpam-6633	586	1	[	[	X
ejpam-6633	586	2	4	4	X
ejpam-6633	586	3	]	]	PUNCT
ejpam-6633	586	4	k.	k.	PROPN
ejpam-6633	586	5	diethelm	diethelm	PROPN
ejpam-6633	586	6	and	and	CCONJ
ejpam-6633	586	7	n.	n.	PROPN
ejpam-6633	586	8	j.	j.	PROPN
ejpam-6633	586	9	ford	ford	PROPN
ejpam-6633	586	10	.	.	PUNCT
ejpam-6633	587	1	analysis	analysis	NOUN
ejpam-6633	587	2	of	of	ADP
ejpam-6633	587	3	fractional	fractional	ADJ
ejpam-6633	587	4	differential	differential	ADJ
ejpam-6633	587	5	equations	equation	NOUN
ejpam-6633	587	6	.	.	PUNCT
ejpam-6633	588	1	journal	journal	PROPN
ejpam-6633	588	2	of	of	ADP
ejpam-6633	588	3	mathematical	mathematical	ADJ
ejpam-6633	588	4	analysis	analysis	NOUN
ejpam-6633	588	5	and	and	CCONJ
ejpam-6633	588	6	applications	application	NOUN
ejpam-6633	588	7	,	,	PUNCT
ejpam-6633	588	8	265(2):229–248	265(2):229–248	NUM
ejpam-6633	588	9	,	,	PUNCT
ejpam-6633	588	10	2002	2002	NUM
ejpam-6633	588	11	.	.	PUNCT
ejpam-6633	589	1	[	[	X
ejpam-6633	589	2	5	5	X
ejpam-6633	589	3	]	]	X
ejpam-6633	589	4	muhammad	muhammad	PROPN
ejpam-6633	589	5	farhan	farhan	PROPN
ejpam-6633	589	6	,	,	PUNCT
ejpam-6633	589	7	zahir	zahir	ADJ
ejpam-6633	589	8	shah	shah	NOUN
ejpam-6633	589	9	,	,	PUNCT
ejpam-6633	589	10	rashid	rashid	PROPN
ejpam-6633	589	11	jan	jan	PROPN
ejpam-6633	589	12	,	,	PUNCT
ejpam-6633	589	13	and	and	CCONJ
ejpam-6633	589	14	saeed	saeed	PROPN
ejpam-6633	589	15	islam	islam	PROPN
ejpam-6633	589	16	.	.	PUNCT
ejpam-6633	590	1	a	a	DET
ejpam-6633	590	2	fractional	fractional	ADJ
ejpam-6633	590	3	modeling	modeling	NOUN
ejpam-6633	590	4	approach	approach	NOUN
ejpam-6633	590	5	of	of	ADP
ejpam-6633	590	6	buruli	buruli	ADJ
ejpam-6633	590	7	ulcer	ulcer	NOUN
ejpam-6633	590	8	in	in	ADP
ejpam-6633	590	9	possum	possum	NOUN
ejpam-6633	590	10	mammals	mammal	NOUN
ejpam-6633	590	11	.	.	PUNCT
ejpam-6633	591	1	physica	physica	PROPN
ejpam-6633	591	2	scripta	scripta	PROPN
ejpam-6633	591	3	,	,	PUNCT
ejpam-6633	591	4	98(6):065219	98(6):065219	NUM
ejpam-6633	591	5	,	,	PUNCT
ejpam-6633	591	6	2023	2023	NUM
ejpam-6633	591	7	.	.	PUNCT
ejpam-6633	592	1	[	[	X
ejpam-6633	592	2	6	6	NUM
ejpam-6633	592	3	]	]	PUNCT
ejpam-6633	592	4	a.	a.	PROPN
ejpam-6633	592	5	s.	s.	PROPN
ejpam-6633	592	6	hasan	hasan	PROPN
ejpam-6633	592	7	.	.	PUNCT
ejpam-6633	593	1	numerical	numerical	ADJ
ejpam-6633	593	2	solution	solution	NOUN
ejpam-6633	593	3	of	of	ADP
ejpam-6633	593	4	the	the	DET
ejpam-6633	593	5	bagley	bagley	NOUN
ejpam-6633	593	6	-	-	PUNCT
ejpam-6633	593	7	torvik	torvik	NOUN
ejpam-6633	593	8	equation	equation	NOUN
ejpam-6633	593	9	using	use	VERB
ejpam-6633	593	10	the	the	DET
ejpam-6633	593	11	integer	integer	NOUN
ejpam-6633	593	12	-	-	PUNCT
ejpam-6633	593	13	order	order	NOUN
ejpam-6633	593	14	derivatives	derivative	NOUN
ejpam-6633	593	15	expansion	expansion	NOUN
ejpam-6633	593	16	.	.	PUNCT
ejpam-6633	594	1	science	science	PROPN
ejpam-6633	594	2	journal	journal	PROPN
ejpam-6633	594	3	of	of	ADP
ejpam-6633	594	4	university	university	PROPN
ejpam-6633	594	5	of	of	ADP
ejpam-6633	594	6	zakho	zakho	PROPN
ejpam-6633	594	7	,	,	PUNCT
ejpam-6633	594	8	6(2):64–69	6(2):64–69	NUM
ejpam-6633	594	9	,	,	PUNCT
ejpam-6633	594	10	2018	2018	NUM
ejpam-6633	594	11	.	.	PUNCT
ejpam-6633	595	1	[	[	X
ejpam-6633	595	2	7	7	X
ejpam-6633	595	3	]	]	PUNCT
ejpam-6633	595	4	a.	a.	NOUN
ejpam-6633	595	5	a.	a.	NOUN
ejpam-6633	595	6	kilbas	kilbas	PROPN
ejpam-6633	595	7	.	.	PUNCT
ejpam-6633	596	1	theory	theory	NOUN
ejpam-6633	596	2	and	and	CCONJ
ejpam-6633	596	3	applications	application	NOUN
ejpam-6633	596	4	of	of	ADP
ejpam-6633	596	5	fractional	fractional	ADJ
ejpam-6633	596	6	differential	differential	ADJ
ejpam-6633	596	7	equations	equation	NOUN
ejpam-6633	596	8	.	.	PUNCT
ejpam-6633	597	1	northholland	northholland	PROPN
ejpam-6633	597	2	mathematics	mathematics	PROPN
ejpam-6633	597	3	studies	study	NOUN
ejpam-6633	597	4	,	,	PUNCT
ejpam-6633	597	5	204	204	NUM
ejpam-6633	597	6	,	,	PUNCT
ejpam-6633	597	7	2006	2006	NUM
ejpam-6633	597	8	.	.	PUNCT
ejpam-6633	598	1	[	[	X
ejpam-6633	598	2	8	8	NUM
ejpam-6633	598	3	]	]	X
ejpam-6633	598	4	sh	sh	PROPN
ejpam-6633	598	5	.	.	PUNCT
ejpam-6633	598	6	a.	a.	PROPN
ejpam-6633	598	7	murad	murad	PROPN
ejpam-6633	598	8	,	,	PUNCT
ejpam-6633	598	9	h.	h.	PROPN
ejpam-6633	598	10	j.	j.	PROPN
ejpam-6633	598	11	zekri	zekri	PROPN
ejpam-6633	598	12	,	,	PUNCT
ejpam-6633	598	13	and	and	CCONJ
ejpam-6633	598	14	s.	s.	PROPN
ejpam-6633	598	15	hadid	hadid	PROPN
ejpam-6633	598	16	.	.	PUNCT
ejpam-6633	599	1	existence	existence	NOUN
ejpam-6633	599	2	and	and	CCONJ
ejpam-6633	599	3	uniqueness	uniqueness	NOUN
ejpam-6633	599	4	theorem	theorem	NOUN
ejpam-6633	599	5	of	of	ADP
ejpam-6633	599	6	fractional	fractional	ADJ
ejpam-6633	599	7	mixed	mixed	ADJ
ejpam-6633	599	8	volterra	volterra	NOUN
ejpam-6633	599	9	-	-	PUNCT
ejpam-6633	599	10	fredholm	fredholm	NOUN
ejpam-6633	599	11	integrodifferential	integrodifferential	ADJ
ejpam-6633	599	12	equation	equation	NOUN
ejpam-6633	599	13	with	with	ADP
ejpam-6633	599	14	integral	integral	ADJ
ejpam-6633	599	15	boundary	boundary	ADJ
ejpam-6633	599	16	conditions	condition	NOUN
ejpam-6633	599	17	.	.	PUNCT
ejpam-6633	600	1	international	international	ADJ
ejpam-6633	600	2	journal	journal	PROPN
ejpam-6633	600	3	of	of	ADP
ejpam-6633	600	4	differential	differential	ADJ
ejpam-6633	600	5	equations	equation	NOUN
ejpam-6633	600	6	,	,	PUNCT
ejpam-6633	600	7	2011(1):304570	2011(1):304570	NUM
ejpam-6633	600	8	,	,	PUNCT
ejpam-6633	600	9	2011	2011	NUM
ejpam-6633	600	10	.	.	PUNCT
ejpam-6633	601	1	[	[	X
ejpam-6633	601	2	9	9	NUM
ejpam-6633	601	3	]	]	X
ejpam-6633	601	4	h.	h.	PROPN
ejpam-6633	601	5	j.	j.	PROPN
ejpam-6633	601	6	lane	lane	PROPN
ejpam-6633	601	7	.	.	PUNCT
ejpam-6633	602	1	on	on	ADP
ejpam-6633	602	2	the	the	DET
ejpam-6633	602	3	theoretical	theoretical	ADJ
ejpam-6633	602	4	temperature	temperature	NOUN
ejpam-6633	602	5	of	of	ADP
ejpam-6633	602	6	the	the	DET
ejpam-6633	602	7	sun	sun	NOUN
ejpam-6633	602	8	,	,	PUNCT
ejpam-6633	602	9	under	under	ADP
ejpam-6633	602	10	the	the	DET
ejpam-6633	602	11	hypothesis	hypothesis	NOUN
ejpam-6633	602	12	of	of	ADP
ejpam-6633	602	13	a	a	DET
ejpam-6633	602	14	gaseous	gaseous	ADJ
ejpam-6633	602	15	mass	mass	NOUN
ejpam-6633	602	16	maintaining	maintain	VERB
ejpam-6633	602	17	its	its	PRON
ejpam-6633	602	18	volume	volume	NOUN
ejpam-6633	602	19	by	by	ADP
ejpam-6633	602	20	its	its	PRON
ejpam-6633	602	21	internal	internal	ADJ
ejpam-6633	602	22	heat	heat	NOUN
ejpam-6633	602	23	,	,	PUNCT
ejpam-6633	602	24	and	and	CCONJ
ejpam-6633	602	25	depending	depend	VERB
ejpam-6633	602	26	on	on	ADP
ejpam-6633	602	27	the	the	DET
ejpam-6633	602	28	laws	law	NOUN
ejpam-6633	602	29	of	of	ADP
ejpam-6633	602	30	gases	gas	NOUN
ejpam-6633	602	31	as	as	SCONJ
ejpam-6633	602	32	known	know	VERB
ejpam-6633	602	33	to	to	ADP
ejpam-6633	602	34	terrestrial	terrestrial	ADJ
ejpam-6633	602	35	experiment	experiment	NOUN
ejpam-6633	602	36	.	.	PUNCT
ejpam-6633	603	1	american	american	PROPN
ejpam-6633	603	2	journal	journal	PROPN
ejpam-6633	603	3	of	of	ADP
ejpam-6633	603	4	science	science	NOUN
ejpam-6633	603	5	,	,	PUNCT
ejpam-6633	603	6	2(148):57	2(148):57	NUM
ejpam-6633	603	7	–	–	PUNCT
ejpam-6633	603	8	74	74	NUM
ejpam-6633	603	9	,	,	PUNCT
ejpam-6633	603	10	1870	1870	NUM
ejpam-6633	603	11	.	.	PUNCT
ejpam-6633	604	1	[	[	X
ejpam-6633	604	2	10	10	NUM
ejpam-6633	604	3	]	]	X
ejpam-6633	604	4	r.	r.	PROPN
ejpam-6633	604	5	emden	emden	PROPN
ejpam-6633	604	6	.	.	PUNCT
ejpam-6633	605	1	gaskugeln	gaskugeln	NOUN
ejpam-6633	605	2	:	:	PUNCT
ejpam-6633	605	3	anwendungen	anwendungen	PROPN
ejpam-6633	605	4	der	der	NOUN
ejpam-6633	605	5	mechanischen	mechanischen	ADV
ejpam-6633	605	6	warmetheorie	warmetheorie	VERB
ejpam-6633	605	7	auf	auf	PROPN
ejpam-6633	605	8	kosmologische	kosmologische	PROPN
ejpam-6633	605	9	und	und	VERB
ejpam-6633	605	10	meteorologische	meteorologische	PROPN
ejpam-6633	605	11	probleme	probleme	NOUN
ejpam-6633	605	12	...	...	PUNCT
ejpam-6633	606	1	bg	bg	PROPN
ejpam-6633	606	2	teubner	teubner	NOUN
ejpam-6633	606	3	,	,	PUNCT
ejpam-6633	606	4	1907	1907	NUM
ejpam-6633	606	5	.	.	PUNCT
ejpam-6633	607	1	[	[	X
ejpam-6633	607	2	11	11	NUM
ejpam-6633	607	3	]	]	PUNCT
ejpam-6633	607	4	s.	s.	PROPN
ejpam-6633	607	5	chandrasekhar	chandrasekhar	PROPN
ejpam-6633	607	6	.	.	PUNCT
ejpam-6633	608	1	an	an	DET
ejpam-6633	608	2	introduction	introduction	NOUN
ejpam-6633	608	3	to	to	ADP
ejpam-6633	608	4	the	the	DET
ejpam-6633	608	5	study	study	NOUN
ejpam-6633	608	6	of	of	ADP
ejpam-6633	608	7	stellar	stellar	ADJ
ejpam-6633	608	8	structure	structure	NOUN
ejpam-6633	608	9	,	,	PUNCT
ejpam-6633	608	10	volume	volume	NOUN
ejpam-6633	608	11	2	2	NUM
ejpam-6633	608	12	.	.	PUNCT
ejpam-6633	609	1	courier	courier	NOUN
ejpam-6633	609	2	corporation	corporation	NOUN
ejpam-6633	609	3	,	,	PUNCT
ejpam-6633	609	4	1957	1957	NUM
ejpam-6633	609	5	.	.	PUNCT
ejpam-6633	610	1	[	[	X
ejpam-6633	610	2	12	12	NUM
ejpam-6633	610	3	]	]	X
ejpam-6633	610	4	dina	dina	PROPN
ejpam-6633	610	5	prialnik	prialnik	PROPN
ejpam-6633	610	6	.	.	PUNCT
ejpam-6633	611	1	an	an	DET
ejpam-6633	611	2	introduction	introduction	NOUN
ejpam-6633	611	3	to	to	ADP
ejpam-6633	611	4	the	the	DET
ejpam-6633	611	5	theory	theory	NOUN
ejpam-6633	611	6	of	of	ADP
ejpam-6633	611	7	stellar	stellar	ADJ
ejpam-6633	611	8	structure	structure	NOUN
ejpam-6633	611	9	and	and	CCONJ
ejpam-6633	611	10	evolution	evolution	NOUN
ejpam-6633	611	11	.	.	PUNCT
ejpam-6633	612	1	cambridge	cambridge	PROPN
ejpam-6633	612	2	university	university	PROPN
ejpam-6633	612	3	press	press	NOUN
ejpam-6633	612	4	,	,	PUNCT
ejpam-6633	612	5	2009	2009	NUM
ejpam-6633	612	6	.	.	PUNCT
ejpam-6633	613	1	[	[	X
ejpam-6633	613	2	13	13	NUM
ejpam-6633	613	3	]	]	X
ejpam-6633	613	4	d.	d.	PROPN
ejpam-6633	613	5	a.	a.	PROPN
ejpam-6633	613	6	frank	frank	PROPN
ejpam-6633	613	7	-	-	PUNCT
ejpam-6633	613	8	kamenetskii	kamenetskii	PROPN
ejpam-6633	613	9	.	.	PUNCT
ejpam-6633	613	10	diffusion	diffusion	NOUN
ejpam-6633	613	11	and	and	CCONJ
ejpam-6633	613	12	heat	heat	NOUN
ejpam-6633	613	13	exchange	exchange	NOUN
ejpam-6633	613	14	in	in	ADP
ejpam-6633	613	15	chemical	chemical	ADJ
ejpam-6633	613	16	kinetics	kinetic	NOUN
ejpam-6633	613	17	,	,	PUNCT
ejpam-6633	613	18	volume	volume	NOUN
ejpam-6633	613	19	2171	2171	NUM
ejpam-6633	613	20	.	.	PUNCT
ejpam-6633	614	1	princeton	princeton	PROPN
ejpam-6633	614	2	university	university	PROPN
ejpam-6633	614	3	press	press	NOUN
ejpam-6633	614	4	,	,	PUNCT
ejpam-6633	614	5	2015	2015	NUM
ejpam-6633	614	6	.	.	PUNCT
ejpam-6633	615	1	[	[	X
ejpam-6633	615	2	14	14	NUM
ejpam-6633	615	3	]	]	X
ejpam-6633	615	4	r.	r.	PROPN
ejpam-6633	615	5	w.	w.	PROPN
ejpam-6633	615	6	ibrahim	ibrahim	PROPN
ejpam-6633	615	7	.	.	PUNCT
ejpam-6633	616	1	existence	existence	NOUN
ejpam-6633	616	2	of	of	ADP
ejpam-6633	616	3	nonlinear	nonlinear	ADJ
ejpam-6633	616	4	lane	lane	NOUN
ejpam-6633	616	5	-	-	PUNCT
ejpam-6633	616	6	emden	emden	NOUN
ejpam-6633	616	7	equation	equation	NOUN
ejpam-6633	616	8	of	of	ADP
ejpam-6633	616	9	fractional	fractional	ADJ
ejpam-6633	616	10	order	order	NOUN
ejpam-6633	616	11	.	.	PUNCT
ejpam-6633	617	1	miskolc	miskolc	ADJ
ejpam-6633	617	2	mathematical	mathematical	ADJ
ejpam-6633	617	3	notes	note	NOUN
ejpam-6633	617	4	,	,	PUNCT
ejpam-6633	617	5	13(1):39–52	13(1):39–52	NUM
ejpam-6633	617	6	,	,	PUNCT
ejpam-6633	617	7	2012	2012	NUM
ejpam-6633	617	8	.	.	PUNCT
ejpam-6633	618	1	[	[	X
ejpam-6633	618	2	15	15	NUM
ejpam-6633	618	3	]	]	X
ejpam-6633	618	4	r.	r.	PROPN
ejpam-6633	618	5	w.	w.	PROPN
ejpam-6633	618	6	ibrahim	ibrahim	PROPN
ejpam-6633	618	7	.	.	PUNCT
ejpam-6633	619	1	stability	stability	NOUN
ejpam-6633	619	2	of	of	ADP
ejpam-6633	619	3	a	a	DET
ejpam-6633	619	4	fractional	fractional	ADJ
ejpam-6633	619	5	differential	differential	NOUN
ejpam-6633	619	6	equation	equation	NOUN
ejpam-6633	619	7	.	.	PUNCT
ejpam-6633	620	1	international	international	ADJ
ejpam-6633	620	2	journal	journal	PROPN
ejpam-6633	620	3	of	of	ADP
ejpam-6633	620	4	mathematical	mathematical	ADJ
ejpam-6633	620	5	and	and	CCONJ
ejpam-6633	620	6	computational	computational	ADJ
ejpam-6633	620	7	sciences	science	NOUN
ejpam-6633	620	8	,	,	PUNCT
ejpam-6633	620	9	7(3):300–305	7(3):300–305	NOUN
ejpam-6633	620	10	,	,	PUNCT
ejpam-6633	620	11	2013	2013	NUM
ejpam-6633	620	12	.	.	PUNCT
ejpam-6633	621	1	[	[	X
ejpam-6633	621	2	16	16	NUM
ejpam-6633	621	3	]	]	PUNCT
ejpam-6633	621	4	a.	a.	PROPN
ejpam-6633	621	5	k.	k.	PROPN
ejpam-6633	621	6	nasab	nasab	PROPN
ejpam-6633	621	7	,	,	PUNCT
ejpam-6633	621	8	z.	z.	PROPN
ejpam-6633	621	9	p.	p.	PROPN
ejpam-6633	621	10	atabakan	atabakan	PROPN
ejpam-6633	621	11	,	,	PUNCT
ejpam-6633	621	12	a.	a.	PROPN
ejpam-6633	621	13	i.	i.	PROPN
ejpam-6633	621	14	ismail	ismail	PROPN
ejpam-6633	621	15	,	,	PUNCT
ejpam-6633	621	16	and	and	CCONJ
ejpam-6633	621	17	r.	r.	PROPN
ejpam-6633	621	18	w.	w.	PROPN
ejpam-6633	621	19	ibrahim	ibrahim	PROPN
ejpam-6633	621	20	.	.	PUNCT
ejpam-6633	622	1	a	a	DET
ejpam-6633	622	2	numerical	numerical	ADJ
ejpam-6633	622	3	method	method	NOUN
ejpam-6633	622	4	for	for	ADP
ejpam-6633	622	5	solving	solve	VERB
ejpam-6633	622	6	singular	singular	ADJ
ejpam-6633	622	7	fractional	fractional	ADJ
ejpam-6633	622	8	lane	lane	PROPN
ejpam-6633	622	9	–	–	PUNCT
ejpam-6633	622	10	emden	emden	ADJ
ejpam-6633	622	11	type	type	NOUN
ejpam-6633	622	12	equations	equation	NOUN
ejpam-6633	622	13	.	.	PUNCT
ejpam-6633	623	1	journal	journal	PROPN
ejpam-6633	623	2	of	of	ADP
ejpam-6633	623	3	king	king	PROPN
ejpam-6633	623	4	saud	saud	PROPN
ejpam-6633	623	5	university	university	PROPN
ejpam-6633	623	6	-	-	PUNCT
ejpam-6633	623	7	science	science	NOUN
ejpam-6633	623	8	,	,	PUNCT
ejpam-6633	623	9	30(1):120–130	30(1):120–130	PROPN
ejpam-6633	623	10	,	,	PUNCT
ejpam-6633	623	11	2018	2018	NUM
ejpam-6633	623	12	.	.	PUNCT
ejpam-6633	624	1	a.	a.	PROPN
ejpam-6633	624	2	s.	s.	PROPN
ejpam-6633	624	3	hasan	hasan	PROPN
ejpam-6633	624	4	,	,	PUNCT
ejpam-6633	624	5	s.	s.	PROPN
ejpam-6633	624	6	a.	a.	PROPN
ejpam-6633	624	7	murad	murad	PROPN
ejpam-6633	624	8	/	/	SYM
ejpam-6633	624	9	eur	eur	PROPN
ejpam-6633	624	10	.	.	PUNCT
ejpam-6633	625	1	j.	j.	PROPN
ejpam-6633	625	2	pure	pure	PROPN
ejpam-6633	625	3	appl	appl	PROPN
ejpam-6633	625	4	.	.	PROPN
ejpam-6633	625	5	math	math	PROPN
ejpam-6633	625	6	,	,	PUNCT
ejpam-6633	625	7	18	18	NUM
ejpam-6633	625	8	(	(	PUNCT
ejpam-6633	625	9	3	3	NUM
ejpam-6633	625	10	)	)	PUNCT
ejpam-6633	625	11	(	(	PUNCT
ejpam-6633	625	12	2025	2025	NUM
ejpam-6633	625	13	)	)	PUNCT
ejpam-6633	625	14	,	,	PUNCT
ejpam-6633	625	15	6633	6633	NUM
ejpam-6633	625	16	24	24	NUM
ejpam-6633	625	17	of	of	ADP
ejpam-6633	625	18	24	24	NUM
ejpam-6633	625	19	[	[	X
ejpam-6633	625	20	17	17	NUM
ejpam-6633	625	21	]	]	PUNCT
ejpam-6633	625	22	a.	a.	NOUN
ejpam-6633	625	23	taieb	taieb	PROPN
ejpam-6633	625	24	and	and	CCONJ
ejpam-6633	625	25	z.	z.	PROPN
ejpam-6633	625	26	dahmani	dahmani	PROPN
ejpam-6633	625	27	.	.	PUNCT
ejpam-6633	626	1	the	the	DET
ejpam-6633	626	2	hight	hight	ADJ
ejpam-6633	626	3	order	order	NOUN
ejpam-6633	626	4	lane	lane	NOUN
ejpam-6633	626	5	-	-	PUNCT
ejpam-6633	626	6	emden	emden	ADJ
ejpam-6633	626	7	fractional	fractional	ADJ
ejpam-6633	626	8	differential	differential	NOUN
ejpam-6633	626	9	system	system	NOUN
ejpam-6633	626	10	:	:	PUNCT
ejpam-6633	626	11	existence	existence	NOUN
ejpam-6633	626	12	,	,	PUNCT
ejpam-6633	626	13	uniqueness	uniqueness	NOUN
ejpam-6633	626	14	and	and	CCONJ
ejpam-6633	626	15	ulam	ulam	PROPN
ejpam-6633	626	16	type	type	NOUN
ejpam-6633	626	17	stabilities	stability	NOUN
ejpam-6633	626	18	.	.	PUNCT
ejpam-6633	627	1	kragujevac	kragujevac	PROPN
ejpam-6633	627	2	journal	journal	PROPN
ejpam-6633	627	3	of	of	ADP
ejpam-6633	627	4	mathematics	mathematic	NOUN
ejpam-6633	627	5	,	,	PUNCT
ejpam-6633	627	6	40(2):238–259	40(2):238–259	PROPN
ejpam-6633	627	7	,	,	PUNCT
ejpam-6633	627	8	2016	2016	NUM
ejpam-6633	627	9	.	.	PUNCT
ejpam-6633	628	1	[	[	X
ejpam-6633	628	2	18	18	NUM
ejpam-6633	628	3	]	]	X
ejpam-6633	628	4	j.	j.	PROPN
ejpam-6633	628	5	dávila	dávila	PROPN
ejpam-6633	628	6	,	,	PUNCT
ejpam-6633	628	7	l.	l.	NOUN
ejpam-6633	628	8	dupaigne	dupaigne	PROPN
ejpam-6633	628	9	,	,	PUNCT
ejpam-6633	628	10	and	and	CCONJ
ejpam-6633	628	11	j.	j.	PROPN
ejpam-6633	628	12	wei	wei	PROPN
ejpam-6633	628	13	.	.	PUNCT
ejpam-6633	629	1	on	on	ADP
ejpam-6633	629	2	the	the	DET
ejpam-6633	629	3	fractional	fractional	ADJ
ejpam-6633	629	4	lane	lane	NOUN
ejpam-6633	629	5	-	-	PUNCT
ejpam-6633	629	6	emden	emden	NOUN
ejpam-6633	629	7	equation	equation	NOUN
ejpam-6633	629	8	.	.	PUNCT
ejpam-6633	630	1	transactions	transaction	NOUN
ejpam-6633	630	2	of	of	ADP
ejpam-6633	630	3	the	the	DET
ejpam-6633	630	4	american	american	PROPN
ejpam-6633	630	5	mathematical	mathematical	PROPN
ejpam-6633	630	6	society	society	NOUN
ejpam-6633	630	7	,	,	PUNCT
ejpam-6633	630	8	369(9):6087–6104	369(9):6087–6104	PROPN
ejpam-6633	630	9	,	,	PUNCT
ejpam-6633	630	10	2017	2017	NUM
ejpam-6633	630	11	.	.	PUNCT
ejpam-6633	631	1	[	[	X
ejpam-6633	631	2	19	19	NUM
ejpam-6633	631	3	]	]	PUNCT
ejpam-6633	631	4	m.	m.	PROPN
ejpam-6633	631	5	e.	e.	PROPN
ejpam-6633	631	6	omaba	omaba	PROPN
ejpam-6633	631	7	.	.	PUNCT
ejpam-6633	632	1	new	new	ADJ
ejpam-6633	632	2	analytical	analytical	ADJ
ejpam-6633	632	3	method	method	NOUN
ejpam-6633	632	4	of	of	ADP
ejpam-6633	632	5	solution	solution	NOUN
ejpam-6633	632	6	to	to	ADP
ejpam-6633	632	7	a	a	DET
ejpam-6633	632	8	nonlinear	nonlinear	ADJ
ejpam-6633	632	9	singular	singular	ADJ
ejpam-6633	632	10	fractional	fractional	PROPN
ejpam-6633	632	11	lane	lane	PROPN
ejpam-6633	632	12	–	–	PUNCT
ejpam-6633	632	13	emden	emden	ADJ
ejpam-6633	632	14	type	type	NOUN
ejpam-6633	632	15	equation	equation	NOUN
ejpam-6633	632	16	.	.	PUNCT
ejpam-6633	633	1	aims	aim	VERB
ejpam-6633	633	2	mathematics	mathematic	NOUN
ejpam-6633	633	3	,	,	PUNCT
ejpam-6633	633	4	7(10):19539–19552	7(10):19539–19552	NUM
ejpam-6633	633	5	,	,	PUNCT
ejpam-6633	633	6	2022	2022	NUM
ejpam-6633	633	7	.	.	PUNCT
ejpam-6633	634	1	[	[	X
ejpam-6633	634	2	20	20	NUM
ejpam-6633	634	3	]	]	X
ejpam-6633	634	4	y.	y.	NOUN
ejpam-6633	634	5	gouari	gouari	PROPN
ejpam-6633	634	6	and	and	CCONJ
ejpam-6633	634	7	z.	z.	PROPN
ejpam-6633	634	8	dahmani	dahmani	PROPN
ejpam-6633	634	9	.	.	PUNCT
ejpam-6633	635	1	stability	stability	NOUN
ejpam-6633	635	2	of	of	ADP
ejpam-6633	635	3	solutions	solution	NOUN
ejpam-6633	635	4	for	for	ADP
ejpam-6633	635	5	two	two	NUM
ejpam-6633	635	6	classes	class	NOUN
ejpam-6633	635	7	of	of	ADP
ejpam-6633	635	8	fractional	fractional	ADJ
ejpam-6633	635	9	differential	differential	ADJ
ejpam-6633	635	10	equations	equation	NOUN
ejpam-6633	635	11	of	of	ADP
ejpam-6633	635	12	lane	lane	NOUN
ejpam-6633	635	13	-	-	PUNCT
ejpam-6633	635	14	emden	emden	NOUN
ejpam-6633	635	15	type	type	NOUN
ejpam-6633	635	16	.	.	PUNCT
ejpam-6633	636	1	journal	journal	NOUN
ejpam-6633	636	2	of	of	ADP
ejpam-6633	636	3	interdisciplinary	interdisciplinary	ADJ
ejpam-6633	636	4	mathematics	mathematic	NOUN
ejpam-6633	636	5	,	,	PUNCT
ejpam-6633	636	6	24(8):2087–2099	24(8):2087–2099	NUM
ejpam-6633	636	7	,	,	PUNCT
ejpam-6633	636	8	2021	2021	NUM
ejpam-6633	636	9	.	.	PUNCT
ejpam-6633	637	1	[	[	X
ejpam-6633	637	2	21	21	NUM
ejpam-6633	637	3	]	]	X
ejpam-6633	637	4	r.	r.	PROPN
ejpam-6633	637	5	o.	o.	PROPN
ejpam-6633	637	6	awonusika	awonusika	PROPN
ejpam-6633	637	7	.	.	PUNCT
ejpam-6633	638	1	analytical	analytical	ADJ
ejpam-6633	638	2	solutions	solution	NOUN
ejpam-6633	638	3	of	of	ADP
ejpam-6633	638	4	a	a	DET
ejpam-6633	638	5	class	class	NOUN
ejpam-6633	638	6	of	of	ADP
ejpam-6633	638	7	fractional	fractional	ADJ
ejpam-6633	638	8	lane	lane	NOUN
ejpam-6633	638	9	–	–	PUNCT
ejpam-6633	638	10	emden	emden	ADJ
ejpam-6633	638	11	equation	equation	NOUN
ejpam-6633	638	12	:	:	PUNCT
ejpam-6633	638	13	a	a	DET
ejpam-6633	638	14	power	power	NOUN
ejpam-6633	638	15	series	series	NOUN
ejpam-6633	638	16	method	method	NOUN
ejpam-6633	638	17	.	.	PUNCT
ejpam-6633	639	1	international	international	ADJ
ejpam-6633	639	2	journal	journal	PROPN
ejpam-6633	639	3	of	of	ADP
ejpam-6633	639	4	applied	applied	ADJ
ejpam-6633	639	5	and	and	CCONJ
ejpam-6633	639	6	computational	computational	ADJ
ejpam-6633	639	7	mathematics	mathematic	NOUN
ejpam-6633	639	8	,	,	PUNCT
ejpam-6633	639	9	8(4):155	8(4):155	NUM
ejpam-6633	639	10	,	,	PUNCT
ejpam-6633	639	11	2022	2022	NUM
ejpam-6633	639	12	.	.	PUNCT
ejpam-6633	640	1	[	[	X
ejpam-6633	640	2	22	22	NUM
ejpam-6633	640	3	]	]	X
ejpam-6633	640	4	n.	n.	NOUN
ejpam-6633	640	5	m.	m.	NOUN
ejpam-6633	640	6	dien	dien	PROPN
ejpam-6633	640	7	.	.	PUNCT
ejpam-6633	641	1	solvability	solvability	NOUN
ejpam-6633	641	2	of	of	ADP
ejpam-6633	641	3	nonlinear	nonlinear	ADJ
ejpam-6633	641	4	fractional	fractional	ADJ
ejpam-6633	641	5	lane	lane	NOUN
ejpam-6633	641	6	–	–	PUNCT
ejpam-6633	641	7	emden	emden	ADJ
ejpam-6633	641	8	-	-	PUNCT
ejpam-6633	641	9	type	type	NOUN
ejpam-6633	641	10	delay	delay	NOUN
ejpam-6633	641	11	equations	equation	NOUN
ejpam-6633	641	12	with	with	ADP
ejpam-6633	641	13	time	time	NOUN
ejpam-6633	641	14	-	-	PUNCT
ejpam-6633	641	15	singular	singular	ADJ
ejpam-6633	641	16	coefficients	coefficient	NOUN
ejpam-6633	641	17	.	.	PUNCT
ejpam-6633	642	1	rocky	rocky	ADJ
ejpam-6633	642	2	mountain	mountain	PROPN
ejpam-6633	642	3	journal	journal	NOUN
ejpam-6633	642	4	of	of	ADP
ejpam-6633	642	5	mathematics	mathematic	NOUN
ejpam-6633	642	6	,	,	PUNCT
ejpam-6633	642	7	54(3):855–868	54(3):855–868	PROPN
ejpam-6633	642	8	,	,	PUNCT
ejpam-6633	642	9	2024	2024	NUM
ejpam-6633	642	10	.	.	PUNCT
ejpam-6633	643	1	[	[	X
ejpam-6633	643	2	23	23	NUM
ejpam-6633	643	3	]	]	PUNCT
ejpam-6633	643	4	m.	m.	NOUN
ejpam-6633	643	5	gohar	gohar	PROPN
ejpam-6633	643	6	,	,	PUNCT
ejpam-6633	643	7	c.	c.	PROPN
ejpam-6633	643	8	li	li	PROPN
ejpam-6633	643	9	,	,	PUNCT
ejpam-6633	643	10	and	and	CCONJ
ejpam-6633	643	11	z.	z.	PROPN
ejpam-6633	643	12	li	li	PROPN
ejpam-6633	643	13	.	.	PROPN
ejpam-6633	643	14	finite	finite	PROPN
ejpam-6633	643	15	difference	difference	NOUN
ejpam-6633	643	16	methods	method	NOUN
ejpam-6633	643	17	for	for	ADP
ejpam-6633	643	18	caputo	caputo	PROPN
ejpam-6633	643	19	–	–	PUNCT
ejpam-6633	643	20	hadamard	hadamard	ADJ
ejpam-6633	643	21	fractional	fractional	ADJ
ejpam-6633	643	22	differential	differential	ADJ
ejpam-6633	643	23	equations	equation	NOUN
ejpam-6633	643	24	.	.	PUNCT
ejpam-6633	644	1	mediterranean	mediterranean	PROPN
ejpam-6633	644	2	journal	journal	PROPN
ejpam-6633	644	3	of	of	ADP
ejpam-6633	644	4	mathematics	mathematics	PROPN
ejpam-6633	644	5	,	,	PUNCT
ejpam-6633	644	6	17(6):194	17(6):194	NUM
ejpam-6633	644	7	,	,	PUNCT
ejpam-6633	644	8	2020	2020	NUM
ejpam-6633	644	9	.	.	PUNCT
ejpam-6633	645	1	[	[	X
ejpam-6633	645	2	24	24	NUM
ejpam-6633	645	3	]	]	PUNCT
ejpam-6633	645	4	changpin	changpin	NOUN
ejpam-6633	645	5	li	li	PROPN
ejpam-6633	645	6	,	,	PUNCT
ejpam-6633	645	7	zhiqiang	zhiqiang	PROPN
ejpam-6633	645	8	li	li	PROPN
ejpam-6633	645	9	,	,	PUNCT
ejpam-6633	645	10	and	and	CCONJ
ejpam-6633	645	11	zhen	zhen	PROPN
ejpam-6633	645	12	wang	wang	PROPN
ejpam-6633	645	13	.	.	PUNCT
ejpam-6633	645	14	mathematical	mathematical	ADJ
ejpam-6633	645	15	analysis	analysis	NOUN
ejpam-6633	645	16	and	and	CCONJ
ejpam-6633	645	17	the	the	DET
ejpam-6633	645	18	local	local	ADJ
ejpam-6633	645	19	discontinuous	discontinuous	ADJ
ejpam-6633	645	20	galerkin	galerkin	ADJ
ejpam-6633	645	21	method	method	NOUN
ejpam-6633	645	22	for	for	ADP
ejpam-6633	645	23	caputo	caputo	PROPN
ejpam-6633	645	24	–	–	PUNCT
ejpam-6633	645	25	hadamard	hadamard	ADJ
ejpam-6633	645	26	fractional	fractional	ADJ
ejpam-6633	645	27	partial	partial	ADJ
ejpam-6633	645	28	differential	differential	NOUN
ejpam-6633	645	29	equation	equation	NOUN
ejpam-6633	645	30	.	.	PUNCT
ejpam-6633	646	1	journal	journal	NOUN
ejpam-6633	646	2	of	of	ADP
ejpam-6633	646	3	scientific	scientific	ADJ
ejpam-6633	646	4	computing	computing	NOUN
ejpam-6633	646	5	,	,	PUNCT
ejpam-6633	646	6	85:1–27	85:1–27	NUM
ejpam-6633	646	7	,	,	PUNCT
ejpam-6633	646	8	2020	2020	NUM
ejpam-6633	646	9	.	.	PUNCT
ejpam-6633	647	1	[	[	X
ejpam-6633	647	2	25	25	NUM
ejpam-6633	647	3	]	]	X
ejpam-6633	647	4	c.	c.	PROPN
ejpam-6633	647	5	w.	w.	PROPN
ejpam-6633	647	6	h.	h.	PROPN
ejpam-6633	647	7	green	green	PROPN
ejpam-6633	647	8	,	,	PUNCT
ejpam-6633	647	9	y.	y.	PROPN
ejpam-6633	647	10	liu	liu	PROPN
ejpam-6633	647	11	,	,	PUNCT
ejpam-6633	647	12	and	and	CCONJ
ejpam-6633	647	13	y.	y.	PROPN
ejpam-6633	647	14	yan	yan	PROPN
ejpam-6633	647	15	.	.	PUNCT
ejpam-6633	648	1	numerical	numerical	ADJ
ejpam-6633	648	2	methods	method	NOUN
ejpam-6633	648	3	for	for	ADP
ejpam-6633	648	4	caputo	caputo	PROPN
ejpam-6633	648	5	–	–	PUNCT
ejpam-6633	648	6	hadamard	hadamard	ADJ
ejpam-6633	648	7	fractional	fractional	ADJ
ejpam-6633	648	8	differential	differential	ADJ
ejpam-6633	648	9	equations	equation	NOUN
ejpam-6633	648	10	with	with	ADP
ejpam-6633	648	11	graded	grade	VERB
ejpam-6633	648	12	and	and	CCONJ
ejpam-6633	648	13	non	non	ADJ
ejpam-6633	648	14	-	-	ADJ
ejpam-6633	648	15	uniform	uniform	ADJ
ejpam-6633	648	16	meshes	mesh	NOUN
ejpam-6633	648	17	.	.	PUNCT
ejpam-6633	649	1	mathematics	mathematic	NOUN
ejpam-6633	649	2	,	,	PUNCT
ejpam-6633	649	3	9(21):2728	9(21):2728	NOUN
ejpam-6633	649	4	,	,	PUNCT
ejpam-6633	649	5	2021	2021	NUM
ejpam-6633	649	6	.	.	PUNCT
ejpam-6633	650	1	[	[	X
ejpam-6633	650	2	26	26	NUM
ejpam-6633	650	3	]	]	X
ejpam-6633	650	4	f.	f.	PROPN
ejpam-6633	650	5	jarad	jarad	PROPN
ejpam-6633	650	6	,	,	PUNCT
ejpam-6633	650	7	t.	t.	NOUN
ejpam-6633	650	8	abdeljawad	abdeljawad	NOUN
ejpam-6633	650	9	,	,	PUNCT
ejpam-6633	650	10	and	and	CCONJ
ejpam-6633	650	11	d.	d.	PROPN
ejpam-6633	650	12	baleanu	baleanu	PROPN
ejpam-6633	650	13	.	.	PUNCT
ejpam-6633	651	1	caputo	caputo	NOUN
ejpam-6633	651	2	-	-	PUNCT
ejpam-6633	651	3	type	type	NOUN
ejpam-6633	651	4	modification	modification	NOUN
ejpam-6633	651	5	of	of	ADP
ejpam-6633	651	6	the	the	DET
ejpam-6633	651	7	hadamard	hadamard	ADJ
ejpam-6633	651	8	fractional	fractional	ADJ
ejpam-6633	651	9	derivatives	derivative	NOUN
ejpam-6633	651	10	.	.	PUNCT
ejpam-6633	652	1	advances	advance	NOUN
ejpam-6633	652	2	in	in	ADP
ejpam-6633	652	3	difference	difference	NOUN
ejpam-6633	652	4	equations	equation	NOUN
ejpam-6633	652	5	,	,	PUNCT
ejpam-6633	652	6	2012:1–8	2012:1–8	NUM
ejpam-6633	652	7	,	,	PUNCT
ejpam-6633	652	8	2012	2012	NUM
ejpam-6633	652	9	.	.	PUNCT
ejpam-6633	653	1	[	[	X
ejpam-6633	653	2	27	27	NUM
ejpam-6633	653	3	]	]	X
ejpam-6633	653	4	sh	sh	PROPN
ejpam-6633	653	5	.	.	PROPN
ejpam-6633	653	6	aljoudi	aljoudi	PROPN
ejpam-6633	653	7	,	,	PUNCT
ejpam-6633	653	8	b.	b.	PROPN
ejpam-6633	653	9	ahmad	ahmad	PROPN
ejpam-6633	653	10	,	,	PUNCT
ejpam-6633	653	11	j.	j.	PROPN
ejpam-6633	653	12	j.	j.	PROPN
ejpam-6633	653	13	nieto	nieto	PROPN
ejpam-6633	653	14	,	,	PUNCT
ejpam-6633	653	15	and	and	CCONJ
ejpam-6633	653	16	a.	a.	NOUN
ejpam-6633	653	17	alsaedi	alsaedi	PROPN
ejpam-6633	653	18	.	.	PUNCT
ejpam-6633	654	1	a	a	DET
ejpam-6633	654	2	coupled	couple	VERB
ejpam-6633	654	3	system	system	NOUN
ejpam-6633	654	4	of	of	ADP
ejpam-6633	654	5	hadamard	hadamard	ADJ
ejpam-6633	654	6	type	type	NOUN
ejpam-6633	654	7	sequential	sequential	ADJ
ejpam-6633	654	8	fractional	fractional	ADJ
ejpam-6633	654	9	differential	differential	NOUN
ejpam-6633	654	10	equations	equation	NOUN
ejpam-6633	654	11	with	with	ADP
ejpam-6633	654	12	coupled	couple	VERB
ejpam-6633	654	13	strip	strip	NOUN
ejpam-6633	654	14	conditions	condition	NOUN
ejpam-6633	654	15	.	.	PUNCT
ejpam-6633	655	1	chaos	chaos	NOUN
ejpam-6633	655	2	,	,	PUNCT
ejpam-6633	655	3	solitons	soliton	NOUN
ejpam-6633	655	4	&	&	CCONJ
ejpam-6633	655	5	fractals	fractal	NOUN
ejpam-6633	655	6	,	,	PUNCT
ejpam-6633	655	7	91:39–46	91:39–46	NUM
ejpam-6633	655	8	,	,	PUNCT
ejpam-6633	655	9	2016	2016	NUM
ejpam-6633	655	10	.	.	PUNCT
ejpam-6633	656	1	[	[	X
ejpam-6633	656	2	28	28	NUM
ejpam-6633	656	3	]	]	X
ejpam-6633	656	4	s.	s.	PROPN
ejpam-6633	656	5	banach	banach	PROPN
ejpam-6633	656	6	.	.	PUNCT
ejpam-6633	657	1	sur	sur	PROPN
ejpam-6633	657	2	les	les	X
ejpam-6633	657	3	opérations	opération	NOUN
ejpam-6633	657	4	dans	dan	NOUN
ejpam-6633	657	5	les	les	X
ejpam-6633	657	6	ensembles	ensemble	NOUN
ejpam-6633	657	7	abstraits	abstrait	NOUN
ejpam-6633	657	8	et	et	PROPN
ejpam-6633	657	9	leur	leur	X
ejpam-6633	657	10	application	application	PROPN
ejpam-6633	657	11	aux	aux	PROPN
ejpam-6633	657	12	équations	équations	PROPN
ejpam-6633	657	13	intégrales	intégrale	NOUN
ejpam-6633	657	14	.	.	PUNCT
ejpam-6633	658	1	fundamenta	fundamenta	PROPN
ejpam-6633	658	2	mathematicae	mathematicae	PROPN
ejpam-6633	658	3	,	,	PUNCT
ejpam-6633	658	4	3(1):133–181	3(1):133–181	NUM
ejpam-6633	658	5	,	,	PUNCT
ejpam-6633	658	6	1922	1922	NUM
ejpam-6633	658	7	.	.	PUNCT
ejpam-6633	659	1	[	[	X
ejpam-6633	659	2	29	29	NUM
ejpam-6633	659	3	]	]	PUNCT
ejpam-6633	659	4	ioan	ioan	NOUN
ejpam-6633	659	5	a	a	DET
ejpam-6633	659	6	rus	rus	PROPN
ejpam-6633	659	7	.	.	PUNCT
ejpam-6633	660	1	ulam	ulam	PROPN
ejpam-6633	660	2	stability	stability	NOUN
ejpam-6633	660	3	of	of	ADP
ejpam-6633	660	4	ordinary	ordinary	ADJ
ejpam-6633	660	5	differential	differential	ADJ
ejpam-6633	660	6	equations	equation	NOUN
ejpam-6633	660	7	.	.	PUNCT
ejpam-6633	661	1	studia	studia	PROPN
ejpam-6633	661	2	universitatis	universitatis	PROPN
ejpam-6633	661	3	babeş-bolyai	babeş-bolyai	PROPN
ejpam-6633	661	4	,	,	PUNCT
ejpam-6633	661	5	mathematica	mathematica	PROPN
ejpam-6633	661	6	,	,	PUNCT
ejpam-6633	661	7	(	(	PUNCT
ejpam-6633	661	8	4	4	NUM
ejpam-6633	661	9	)	)	PUNCT
ejpam-6633	661	10	,	,	PUNCT
ejpam-6633	661	11	2009	2009	NUM
ejpam-6633	661	12	.	.	PUNCT
ejpam-6633	662	1	[	[	X
ejpam-6633	662	2	30	30	NUM
ejpam-6633	662	3	]	]	X
ejpam-6633	662	4	saleh	saleh	PROPN
ejpam-6633	662	5	s	s	PROPN
ejpam-6633	662	6	redhwan	redhwan	NOUN
ejpam-6633	662	7	,	,	PUNCT
ejpam-6633	662	8	sadikali	sadikali	VERB
ejpam-6633	662	9	l	l	NOUN
ejpam-6633	662	10	shaikh	shaikh	PROPN
ejpam-6633	662	11	,	,	PUNCT
ejpam-6633	662	12	mohammed	mohammed	PROPN
ejpam-6633	662	13	s	s	PROPN
ejpam-6633	662	14	abdo	abdo	PROPN
ejpam-6633	662	15	,	,	PUNCT
ejpam-6633	662	16	wasfi	wasfi	NOUN
ejpam-6633	662	17	shatanawi	shatanawi	ADJ
ejpam-6633	662	18	,	,	PUNCT
ejpam-6633	662	19	kamaleldin	kamaleldin	NOUN
ejpam-6633	662	20	abodayeh	abodayeh	NOUN
ejpam-6633	662	21	,	,	PUNCT
ejpam-6633	662	22	mohammed	mohammed	PROPN
ejpam-6633	662	23	a	a	DET
ejpam-6633	662	24	almalahi	almalahi	NOUN
ejpam-6633	662	25	,	,	PUNCT
ejpam-6633	662	26	and	and	CCONJ
ejpam-6633	662	27	tariq	tariq	PROPN
ejpam-6633	662	28	aljaaidi	aljaaidi	VERB
ejpam-6633	662	29	.	.	PUNCT
ejpam-6633	663	1	investigating	investigate	VERB
ejpam-6633	663	2	a	a	DET
ejpam-6633	663	3	generalized	generalized	ADJ
ejpam-6633	663	4	hilfer	hilfer	NOUN
ejpam-6633	663	5	-	-	PUNCT
ejpam-6633	663	6	type	type	NOUN
ejpam-6633	663	7	fractional	fractional	ADJ
ejpam-6633	663	8	differential	differential	NOUN
ejpam-6633	663	9	equation	equation	NOUN
ejpam-6633	663	10	with	with	ADP
ejpam-6633	663	11	two	two	NUM
ejpam-6633	663	12	-	-	PUNCT
ejpam-6633	663	13	point	point	NOUN
ejpam-6633	663	14	and	and	CCONJ
ejpam-6633	663	15	integral	integral	ADJ
ejpam-6633	663	16	boundary	boundary	ADJ
ejpam-6633	663	17	conditions	condition	NOUN
ejpam-6633	663	18	.	.	PUNCT
ejpam-6633	664	1	aims	aim	VERB
ejpam-6633	664	2	mathematics	mathematic	NOUN
ejpam-6633	664	3	,	,	PUNCT
ejpam-6633	664	4	7(2):1856–1872	7(2):1856–1872	PROPN
ejpam-6633	664	5	,	,	PUNCT
ejpam-6633	664	6	2022	2022	NUM
ejpam-6633	664	7	.	.	PUNCT
ejpam-6633	665	1	[	[	X
ejpam-6633	665	2	31	31	NUM
ejpam-6633	665	3	]	]	X
ejpam-6633	665	4	yi	yi	PROPN
ejpam-6633	665	5	yang	yang	PROPN
ejpam-6633	665	6	and	and	CCONJ
ejpam-6633	665	7	jin	jin	PROPN
ejpam-6633	665	8	huang	huang	PROPN
ejpam-6633	665	9	.	.	PROPN
ejpam-6633	666	1	double	double	ADJ
ejpam-6633	666	2	fast	fast	ADJ
ejpam-6633	666	3	algorithm	algorithm	NOUN
ejpam-6633	666	4	for	for	ADP
ejpam-6633	666	5	solving	solve	VERB
ejpam-6633	666	6	time	time	NOUN
ejpam-6633	666	7	-	-	PUNCT
ejpam-6633	666	8	space	space	NOUN
ejpam-6633	666	9	fractional	fractional	ADJ
ejpam-6633	666	10	diffusion	diffusion	NOUN
ejpam-6633	666	11	problems	problem	NOUN
ejpam-6633	666	12	with	with	ADP
ejpam-6633	666	13	spectral	spectral	ADJ
ejpam-6633	666	14	fractional	fractional	PROPN
ejpam-6633	666	15	laplacian	laplacian	PROPN
ejpam-6633	666	16	.	.	PUNCT
ejpam-6633	667	1	applied	apply	VERB
ejpam-6633	667	2	mathematics	mathematic	NOUN
ejpam-6633	667	3	and	and	CCONJ
ejpam-6633	667	4	computation	computation	NOUN
ejpam-6633	667	5	,	,	PUNCT
ejpam-6633	667	6	475:128715	475:128715	NOUN
ejpam-6633	667	7	,	,	PUNCT
ejpam-6633	667	8	2024	2024	NUM
ejpam-6633	667	9	.	.	PUNCT