id	sid	tid	token	lemma	pos
ejpam-5455	1	1	european	european	PROPN
ejpam-5455	1	2	journal	journal	PROPN
ejpam-5455	1	3	of	of	ADP
ejpam-5455	1	4	pure	pure	ADJ
ejpam-5455	1	5	and	and	CCONJ
ejpam-5455	1	6	applied	apply	VERB
ejpam-5455	1	7	mathematics	mathematic	NOUN
ejpam-5455	1	8	vol	vol	NOUN
ejpam-5455	1	9	.	.	PROPN
ejpam-5455	2	1	17	17	NUM
ejpam-5455	2	2	,	,	PUNCT
ejpam-5455	2	3	no	no	INTJ
ejpam-5455	2	4	.	.	NOUN
ejpam-5455	2	5	4	4	NUM
ejpam-5455	2	6	,	,	PUNCT
ejpam-5455	2	7	2024	2024	NUM
ejpam-5455	2	8	,	,	PUNCT
ejpam-5455	2	9	4071	4071	NUM
ejpam-5455	2	10	-	-	SYM
ejpam-5455	2	11	4092	4092	NUM
ejpam-5455	2	12	issn	issn	PROPN
ejpam-5455	2	13	1307	1307	NUM
ejpam-5455	2	14	-	-	SYM
ejpam-5455	2	15	5543	5543	NUM
ejpam-5455	2	16	–	–	PUNCT
ejpam-5455	3	1	ejpam.com	ejpam.com	X
ejpam-5455	3	2	published	publish	VERB
ejpam-5455	3	3	by	by	ADP
ejpam-5455	3	4	new	new	PROPN
ejpam-5455	3	5	york	york	PROPN
ejpam-5455	3	6	business	business	PROPN
ejpam-5455	3	7	global	global	PROPN
ejpam-5455	3	8	on	on	ADP
ejpam-5455	3	9	a	a	DET
ejpam-5455	3	10	hybrid	hybrid	ADJ
ejpam-5455	3	11	class	class	NOUN
ejpam-5455	3	12	of	of	ADP
ejpam-5455	3	13	p	p	NOUN
ejpam-5455	3	14	-	-	PUNCT
ejpam-5455	3	15	laplacian	laplacian	ADJ
ejpam-5455	3	16	initial	initial	ADJ
ejpam-5455	3	17	value	value	NOUN
ejpam-5455	3	18	problems	problem	NOUN
ejpam-5455	3	19	with	with	ADP
ejpam-5455	3	20	modified	modified	ADJ
ejpam-5455	3	21	mittag	mittag	ADJ
ejpam-5455	3	22	-	-	PUNCT
ejpam-5455	3	23	leffler	leffler	NOUN
ejpam-5455	3	24	kernel	kernel	PROPN
ejpam-5455	3	25	sowmiya	sowmiya	PROPN
ejpam-5455	3	26	ramasamy1	ramasamy1	PROPN
ejpam-5455	3	27	,	,	PUNCT
ejpam-5455	3	28	kavitha	kavitha	PROPN
ejpam-5455	3	29	velusamy1	velusamy1	PROPN
ejpam-5455	3	30	,	,	PUNCT
ejpam-5455	3	31	dumitru	dumitru	PROPN
ejpam-5455	3	32	baleanu2	baleanu2	PROPN
ejpam-5455	3	33	,	,	PUNCT
ejpam-5455	3	34	mallika	mallika	PROPN
ejpam-5455	3	35	arjunan	arjunan	PROPN
ejpam-5455	3	36	mani3,∗	mani3,∗	PROPN
ejpam-5455	3	37	1	1	NUM
ejpam-5455	3	38	department	department	NOUN
ejpam-5455	3	39	of	of	ADP
ejpam-5455	3	40	mathematics	mathematic	NOUN
ejpam-5455	3	41	,	,	PUNCT
ejpam-5455	3	42	school	school	NOUN
ejpam-5455	3	43	of	of	ADP
ejpam-5455	3	44	sciences	science	NOUN
ejpam-5455	3	45	,	,	PUNCT
ejpam-5455	3	46	arts	art	NOUN
ejpam-5455	3	47	media	medium	NOUN
ejpam-5455	3	48	&	&	CCONJ
ejpam-5455	3	49	management	management	PROPN
ejpam-5455	3	50	,	,	PUNCT
ejpam-5455	3	51	karunya	karunya	PROPN
ejpam-5455	3	52	institute	institute	PROPN
ejpam-5455	3	53	of	of	ADP
ejpam-5455	3	54	technology	technology	PROPN
ejpam-5455	3	55	and	and	CCONJ
ejpam-5455	3	56	sciences	sciences	PROPN
ejpam-5455	3	57	,	,	PUNCT
ejpam-5455	3	58	karunya	karunya	NOUN
ejpam-5455	3	59	nagar	nagar	NOUN
ejpam-5455	3	60	,	,	PUNCT
ejpam-5455	3	61	coimbatore-641114	coimbatore-641114	NOUN
ejpam-5455	3	62	,	,	PUNCT
ejpam-5455	3	63	tamil	tamil	PROPN
ejpam-5455	3	64	nadu	nadu	PROPN
ejpam-5455	3	65	,	,	PUNCT
ejpam-5455	3	66	india	india	PROPN
ejpam-5455	3	67	2	2	NUM
ejpam-5455	3	68	department	department	NOUN
ejpam-5455	3	69	of	of	ADP
ejpam-5455	3	70	computer	computer	NOUN
ejpam-5455	3	71	science	science	NOUN
ejpam-5455	3	72	and	and	CCONJ
ejpam-5455	3	73	mathematics	mathematic	NOUN
ejpam-5455	3	74	,	,	PUNCT
ejpam-5455	3	75	labanese	labanese	PROPN
ejpam-5455	3	76	american	american	PROPN
ejpam-5455	3	77	university	university	PROPN
ejpam-5455	3	78	,	,	PUNCT
ejpam-5455	3	79	beirut	beirut	PROPN
ejpam-5455	3	80	,	,	PUNCT
ejpam-5455	3	81	lebanon	lebanon	PROPN
ejpam-5455	3	82	3	3	NUM
ejpam-5455	3	83	department	department	PROPN
ejpam-5455	3	84	of	of	ADP
ejpam-5455	3	85	mathematics	mathematic	NOUN
ejpam-5455	3	86	,	,	PUNCT
ejpam-5455	3	87	school	school	NOUN
ejpam-5455	3	88	of	of	ADP
ejpam-5455	3	89	arts	art	NOUN
ejpam-5455	3	90	,	,	PUNCT
ejpam-5455	3	91	sciences	science	NOUN
ejpam-5455	3	92	,	,	PUNCT
ejpam-5455	3	93	humanities	humanity	NOUN
ejpam-5455	3	94	and	and	CCONJ
ejpam-5455	3	95	education	education	NOUN
ejpam-5455	3	96	,	,	PUNCT
ejpam-5455	3	97	sastra	sastra	PROPN
ejpam-5455	3	98	deemed	deem	VERB
ejpam-5455	3	99	to	to	PART
ejpam-5455	3	100	be	be	AUX
ejpam-5455	3	101	university	university	NOUN
ejpam-5455	3	102	,	,	PUNCT
ejpam-5455	3	103	thanjavur-613401	thanjavur-613401	NOUN
ejpam-5455	3	104	,	,	PUNCT
ejpam-5455	3	105	tamil	tamil	PROPN
ejpam-5455	3	106	nadu	nadu	NOUN
ejpam-5455	3	107	,	,	PUNCT
ejpam-5455	3	108	india	india	PROPN
ejpam-5455	3	109	abstract	abstract	NOUN
ejpam-5455	3	110	.	.	PUNCT
ejpam-5455	4	1	in	in	ADP
ejpam-5455	4	2	this	this	DET
ejpam-5455	4	3	work	work	NOUN
ejpam-5455	4	4	,	,	PUNCT
ejpam-5455	4	5	we	we	PRON
ejpam-5455	4	6	establish	establish	VERB
ejpam-5455	4	7	key	key	ADJ
ejpam-5455	4	8	results	result	NOUN
ejpam-5455	4	9	on	on	ADP
ejpam-5455	4	10	the	the	DET
ejpam-5455	4	11	existence	existence	NOUN
ejpam-5455	4	12	theory	theory	NOUN
ejpam-5455	4	13	for	for	ADP
ejpam-5455	4	14	a	a	DET
ejpam-5455	4	15	category	category	NOUN
ejpam-5455	4	16	of	of	ADP
ejpam-5455	4	17	initial	initial	ADJ
ejpam-5455	4	18	value	value	NOUN
ejpam-5455	4	19	problems	problem	NOUN
ejpam-5455	4	20	(	(	PUNCT
ejpam-5455	4	21	ivps	ivps	PROPN
ejpam-5455	4	22	)	)	PUNCT
ejpam-5455	4	23	involving	involve	VERB
ejpam-5455	4	24	hybrid	hybrid	ADJ
ejpam-5455	4	25	fractional	fractional	ADJ
ejpam-5455	4	26	integro	integro	ADJ
ejpam-5455	4	27	-	-	PUNCT
ejpam-5455	4	28	differential	differential	NOUN
ejpam-5455	4	29	equations	equation	NOUN
ejpam-5455	4	30	(	(	PUNCT
ejpam-5455	4	31	hfides	hfide	NOUN
ejpam-5455	4	32	)	)	PUNCT
ejpam-5455	4	33	with	with	ADP
ejpam-5455	4	34	a	a	DET
ejpam-5455	4	35	p	p	ADJ
ejpam-5455	4	36	-	-	PUNCT
ejpam-5455	4	37	laplacian	laplacian	ADJ
ejpam-5455	4	38	operator	operator	NOUN
ejpam-5455	4	39	,	,	PUNCT
ejpam-5455	4	40	utilizing	utilize	VERB
ejpam-5455	4	41	the	the	DET
ejpam-5455	4	42	modified	modify	VERB
ejpam-5455	4	43	mittag	mittag	ADJ
ejpam-5455	4	44	-	-	PUNCT
ejpam-5455	4	45	leffler	leffler	NOUN
ejpam-5455	4	46	kernel	kernel	NOUN
ejpam-5455	4	47	.	.	PUNCT
ejpam-5455	5	1	by	by	ADP
ejpam-5455	5	2	employing	employ	VERB
ejpam-5455	5	3	krasnoselskii	krasnoselskii	PROPN
ejpam-5455	5	4	and	and	CCONJ
ejpam-5455	5	5	banach	banach	ADV
ejpam-5455	5	6	fixed	fix	VERB
ejpam-5455	5	7	point	point	NOUN
ejpam-5455	5	8	theorems	theorem	NOUN
ejpam-5455	5	9	(	(	PUNCT
ejpam-5455	5	10	fpts	fpt	NOUN
ejpam-5455	5	11	)	)	PUNCT
ejpam-5455	5	12	,	,	PUNCT
ejpam-5455	5	13	we	we	PRON
ejpam-5455	5	14	determine	determine	VERB
ejpam-5455	5	15	the	the	DET
ejpam-5455	5	16	conditions	condition	NOUN
ejpam-5455	5	17	required	require	VERB
ejpam-5455	5	18	for	for	ADP
ejpam-5455	5	19	the	the	DET
ejpam-5455	5	20	existence	existence	NOUN
ejpam-5455	5	21	of	of	ADP
ejpam-5455	5	22	solutions	solution	NOUN
ejpam-5455	5	23	.	.	PUNCT
ejpam-5455	6	1	additionally	additionally	ADV
ejpam-5455	6	2	,	,	PUNCT
ejpam-5455	6	3	we	we	PRON
ejpam-5455	6	4	examine	examine	VERB
ejpam-5455	6	5	the	the	DET
ejpam-5455	6	6	hyers	hyers	PROPN
ejpam-5455	6	7	-	-	PUNCT
ejpam-5455	6	8	ulam	ulam	INTJ
ejpam-5455	6	9	(	(	PUNCT
ejpam-5455	6	10	h	h	NOUN
ejpam-5455	6	11	-	-	PUNCT
ejpam-5455	6	12	u	u	NOUN
ejpam-5455	6	13	)	)	PUNCT
ejpam-5455	6	14	stability	stability	NOUN
ejpam-5455	6	15	of	of	ADP
ejpam-5455	6	16	the	the	DET
ejpam-5455	6	17	problem	problem	NOUN
ejpam-5455	6	18	.	.	PUNCT
ejpam-5455	7	1	lastly	lastly	ADV
ejpam-5455	7	2	,	,	PUNCT
ejpam-5455	7	3	we	we	PRON
ejpam-5455	7	4	present	present	VERB
ejpam-5455	7	5	an	an	DET
ejpam-5455	7	6	example	example	NOUN
ejpam-5455	7	7	to	to	PART
ejpam-5455	7	8	confirm	confirm	VERB
ejpam-5455	7	9	our	our	PRON
ejpam-5455	7	10	theoretical	theoretical	ADJ
ejpam-5455	7	11	results	result	NOUN
ejpam-5455	7	12	.	.	PUNCT
ejpam-5455	8	1	2020	2020	NUM
ejpam-5455	8	2	mathematics	mathematic	NOUN
ejpam-5455	8	3	subject	subject	NOUN
ejpam-5455	8	4	classifications	classification	NOUN
ejpam-5455	8	5	:	:	PUNCT
ejpam-5455	8	6	26a33	26a33	NUM
ejpam-5455	8	7	,	,	PUNCT
ejpam-5455	8	8	34a08	34a08	NUM
ejpam-5455	8	9	,	,	PUNCT
ejpam-5455	8	10	34d20	34d20	NUM
ejpam-5455	8	11	key	key	ADJ
ejpam-5455	8	12	words	word	NOUN
ejpam-5455	8	13	and	and	CCONJ
ejpam-5455	8	14	phrases	phrase	NOUN
ejpam-5455	8	15	:	:	PUNCT
ejpam-5455	8	16	fractional	fractional	ADJ
ejpam-5455	8	17	-	-	PUNCT
ejpam-5455	8	18	order	order	NOUN
ejpam-5455	8	19	,	,	PUNCT
ejpam-5455	8	20	mabc	mabc	ADJ
ejpam-5455	8	21	fractional	fractional	ADJ
ejpam-5455	8	22	derivative	derivative	NOUN
ejpam-5455	8	23	,	,	PUNCT
ejpam-5455	8	24	existence	existence	NOUN
ejpam-5455	8	25	and	and	CCONJ
ejpam-5455	8	26	uniqueness	uniqueness	NOUN
ejpam-5455	8	27	,	,	PUNCT
ejpam-5455	8	28	stability	stability	NOUN
ejpam-5455	8	29	,	,	PUNCT
ejpam-5455	8	30	fpts	fpt	NOUN
ejpam-5455	8	31	1	1	NUM
ejpam-5455	8	32	.	.	PUNCT
ejpam-5455	9	1	introduction	introduction	NOUN
ejpam-5455	9	2	this	this	DET
ejpam-5455	9	3	paper	paper	NOUN
ejpam-5455	9	4	addresses	address	VERB
ejpam-5455	9	5	the	the	DET
ejpam-5455	9	6	existence	existence	NOUN
ejpam-5455	9	7	of	of	ADP
ejpam-5455	9	8	solutions	solution	NOUN
ejpam-5455	9	9	for	for	ADP
ejpam-5455	9	10	a	a	DET
ejpam-5455	9	11	hybrid	hybrid	ADJ
ejpam-5455	9	12	class	class	NOUN
ejpam-5455	9	13	of	of	ADP
ejpam-5455	9	14	mabc	mabc	NOUN
ejpam-5455	9	15	-	-	PUNCT
ejpam-5455	9	16	hfides	hfide	NOUN
ejpam-5455	9	17	with	with	ADP
ejpam-5455	9	18	a	a	DET
ejpam-5455	9	19	p	p	ADJ
ejpam-5455	9	20	-	-	PUNCT
ejpam-5455	9	21	laplacian	laplacian	ADJ
ejpam-5455	9	22	operator	operator	NOUN
ejpam-5455	9	23	given	give	VERB
ejpam-5455	9	24	by	by	ADP
ejpam-5455	9	25	the	the	DET
ejpam-5455	9	26	abstract	abstract	ADJ
ejpam-5455	9	27	form	form	NOUN
ejpam-5455	9	28	:	:	PUNCT
ejpam-5455	9	29	cdβ	cdβ	PROPN
ejpam-5455	9	30	ψp	ψp	NOUN
ejpam-5455	9	31	mabcdρ	mabcdρ	NOUN
ejpam-5455	9	32	0	0	PUNCT
ejpam-5455	10	1	+	+	NUM
ejpam-5455	10	2			PROPN
ejpam-5455	10	3	w(7)−	w(7)−	PROPN
ejpam-5455	10	4	h(7	h(7	PROPN
ejpam-5455	10	5	,	,	PUNCT
ejpam-5455	10	6	w(7	w(7	NOUN
ejpam-5455	10	7	)	)	PUNCT
ejpam-5455	10	8	)	)	PUNCT
ejpam-5455	11	1	q(7	q(7	CCONJ
ejpam-5455	11	2	)	)	PUNCT
ejpam-5455	11	3	+	+	CCONJ
ejpam-5455	11	4	1	1	NUM
ejpam-5455	11	5	γ(γ	γ(γ	NOUN
ejpam-5455	11	6	)	)	PUNCT
ejpam-5455	11	7	∫	∫	PROPN
ejpam-5455	11	8	7	7	NUM
ejpam-5455	11	9	0	0	NUM
ejpam-5455	11	10	(	(	PUNCT
ejpam-5455	11	11	7	7	NUM
ejpam-5455	11	12	−	−	NOUN
ejpam-5455	11	13	σ)γ−1f(σ	σ)γ−1f(σ	NOUN
ejpam-5455	11	14	,	,	PUNCT
ejpam-5455	11	15	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	11	16			NOUN
ejpam-5455	11	17			NOUN
ejpam-5455	11	18			NOUN
ejpam-5455	11	19	=	=	SYM
ejpam-5455	11	20	g(7	g(7	PROPN
ejpam-5455	11	21	,	,	PUNCT
ejpam-5455	11	22	w(7	w(7	PROPN
ejpam-5455	11	23	)	)	PUNCT
ejpam-5455	11	24	)	)	PUNCT
ejpam-5455	11	25	,	,	PUNCT
ejpam-5455	11	26	w(0	w(0	PROPN
ejpam-5455	11	27	)	)	PUNCT
ejpam-5455	12	1	=	=	SYM
ejpam-5455	12	2	h(0	h(0	PROPN
ejpam-5455	12	3	,	,	PUNCT
ejpam-5455	12	4	w(0	w(0	PROPN
ejpam-5455	12	5	)	)	PUNCT
ejpam-5455	12	6	)	)	PUNCT
ejpam-5455	13	1	+	+	PUNCT
ejpam-5455	13	2	q(0)abiρ0+θ	q(0)abiρ0+θ	ADJ
ejpam-5455	13	3	,	,	PUNCT
ejpam-5455	13	4	(	(	PUNCT
ejpam-5455	13	5	1	1	X
ejpam-5455	13	6	)	)	PUNCT
ejpam-5455	13	7	∗corresponding	∗corresponde	VERB
ejpam-5455	13	8	author	author	NOUN
ejpam-5455	13	9	.	.	PUNCT
ejpam-5455	14	1	doi	doi	NOUN
ejpam-5455	14	2	:	:	PUNCT
ejpam-5455	14	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5455	https://doi.org/10.29020/nybg.ejpam.v17i4.5455	NUM
ejpam-5455	14	4	email	email	NOUN
ejpam-5455	14	5	addresses	address	NOUN
ejpam-5455	14	6	:	:	PUNCT
ejpam-5455	14	7	sowmiyar@karunya.edu.in	sowmiyar@karunya.edu.in	X
ejpam-5455	14	8	(	(	PUNCT
ejpam-5455	14	9	r.	r.	PROPN
ejpam-5455	14	10	sowmiya	sowmiya	PROPN
ejpam-5455	14	11	)	)	PUNCT
ejpam-5455	14	12	,	,	PUNCT
ejpam-5455	14	13	kavi	kavi	PROPN
ejpam-5455	14	14	velubagyam@yahoo.co.in	velubagyam@yahoo.co.in	PROPN
ejpam-5455	14	15	(	(	PUNCT
ejpam-5455	14	16	v.	v.	PROPN
ejpam-5455	14	17	kavitha	kavitha	PROPN
ejpam-5455	14	18	)	)	PUNCT
ejpam-5455	14	19	,	,	PUNCT
ejpam-5455	14	20	dumitru.baleanu@lau.edu.lb	dumitru.baleanu@lau.edu.lb	PROPN
ejpam-5455	14	21	(	(	PUNCT
ejpam-5455	14	22	d.	d.	PROPN
ejpam-5455	14	23	baleanu	baleanu	PROPN
ejpam-5455	14	24	)	)	PUNCT
ejpam-5455	14	25	,	,	PUNCT
ejpam-5455	14	26	arjunphd07@yahoo.co.in	arjunphd07@yahoo.co.in	ADV
ejpam-5455	14	27	(	(	PUNCT
ejpam-5455	14	28	m.	m.	NOUN
ejpam-5455	14	29	m.	m.	PROPN
ejpam-5455	14	30	arjunan	arjunan	PROPN
ejpam-5455	14	31	)	)	PUNCT
ejpam-5455	14	32	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5455	15	1	4071	4071	NUM
ejpam-5455	15	2	copyright	copyright	NOUN
ejpam-5455	15	3	:	:	PUNCT
ejpam-5455	15	4	©	©	PROPN
ejpam-5455	15	5	2024	2024	NUM
ejpam-5455	15	6	the	the	DET
ejpam-5455	15	7	author(s	author(s	NOUN
ejpam-5455	15	8	)	)	PUNCT
ejpam-5455	15	9	.	.	PUNCT
ejpam-5455	16	1	(	(	PUNCT
ejpam-5455	16	2	cc	cc	NOUN
ejpam-5455	16	3	by	by	ADP
ejpam-5455	16	4	-	-	PUNCT
ejpam-5455	16	5	nc	nc	PROPN
ejpam-5455	16	6	4.0	4.0	NUM
ejpam-5455	16	7	)	)	PUNCT
ejpam-5455	16	8	m.	m.	NOUN
ejpam-5455	16	9	m.	m.	NOUN
ejpam-5455	16	10	arjunan	arjunan	PROPN
ejpam-5455	16	11	/	/	SYM
ejpam-5455	16	12	eur	eur	PROPN
ejpam-5455	16	13	.	.	PUNCT
ejpam-5455	17	1	j.	j.	PROPN
ejpam-5455	17	2	pure	pure	PROPN
ejpam-5455	17	3	appl	appl	PROPN
ejpam-5455	17	4	.	.	PROPN
ejpam-5455	17	5	math	math	PROPN
ejpam-5455	17	6	,	,	PUNCT
ejpam-5455	17	7	17	17	NUM
ejpam-5455	17	8	(	(	PUNCT
ejpam-5455	17	9	4	4	NUM
ejpam-5455	17	10	)	)	PUNCT
ejpam-5455	17	11	(	(	PUNCT
ejpam-5455	17	12	2024	2024	NUM
ejpam-5455	17	13	)	)	PUNCT
ejpam-5455	17	14	,	,	PUNCT
ejpam-5455	17	15	4071	4071	NUM
ejpam-5455	17	16	-	-	SYM
ejpam-5455	17	17	4092	4092	NUM
ejpam-5455	17	18	4072	4072	NUM
ejpam-5455	18	1	where	where	SCONJ
ejpam-5455	18	2	ρ	ρ	NOUN
ejpam-5455	18	3	,	,	PUNCT
ejpam-5455	18	4	β	β	X
ejpam-5455	18	5	,	,	PUNCT
ejpam-5455	18	6	γ	γ	PROPN
ejpam-5455	18	7	∈	∈	PROPN
ejpam-5455	18	8	(	(	PUNCT
ejpam-5455	18	9	0	0	NUM
ejpam-5455	18	10	,	,	PUNCT
ejpam-5455	18	11	1	1	NUM
ejpam-5455	18	12	)	)	PUNCT
ejpam-5455	18	13	and	and	CCONJ
ejpam-5455	18	14	mabcdρ	mabcdρ	VERB
ejpam-5455	18	15	0	0	PUNCT
ejpam-5455	18	16	+	+	NUM
ejpam-5455	18	17	represents	represent	VERB
ejpam-5455	18	18	the	the	DET
ejpam-5455	18	19	mabc	mabc	PROPN
ejpam-5455	18	20	derivative	derivative	NOUN
ejpam-5455	18	21	,	,	PUNCT
ejpam-5455	18	22	abiρ0	abiρ0	PROPN
ejpam-5455	18	23	+	+	X
ejpam-5455	18	24	is	be	AUX
ejpam-5455	18	25	the	the	DET
ejpam-5455	18	26	atangana	atangana	PROPN
ejpam-5455	18	27	-	-	PUNCT
ejpam-5455	18	28	baleanu	baleanu	ADJ
ejpam-5455	18	29	fractional	fractional	ADJ
ejpam-5455	18	30	integral	integral	ADJ
ejpam-5455	18	31	,	,	PUNCT
ejpam-5455	18	32	cdβ	cdβ	NOUN
ejpam-5455	18	33	signifies	signify	VERB
ejpam-5455	18	34	the	the	DET
ejpam-5455	18	35	caputo	caputo	PROPN
ejpam-5455	18	36	fractional	fractional	PROPN
ejpam-5455	18	37	derivative	derivative	PROPN
ejpam-5455	18	38	,	,	PUNCT
ejpam-5455	18	39	ψp	ψp	NOUN
ejpam-5455	18	40	,	,	PUNCT
ejpam-5455	18	41	p	p	X
ejpam-5455	18	42	>	>	X
ejpam-5455	18	43	1	1	NUM
ejpam-5455	18	44	is	be	AUX
ejpam-5455	18	45	a	a	DET
ejpam-5455	18	46	p	p	ADJ
ejpam-5455	18	47	-	-	PUNCT
ejpam-5455	18	48	laplacian	laplacian	ADJ
ejpam-5455	18	49	operator	operator	NOUN
ejpam-5455	18	50	,	,	PUNCT
ejpam-5455	18	51	θ	θ	PROPN
ejpam-5455	18	52	∈	∈	PROPN
ejpam-5455	18	53	r	r	NOUN
ejpam-5455	18	54	,	,	PUNCT
ejpam-5455	18	55	q	q	NOUN
ejpam-5455	18	56	:	:	PUNCT
ejpam-5455	18	57	ω	ω	PROPN
ejpam-5455	18	58	→	→	SYM
ejpam-5455	18	59	r	r	NOUN
ejpam-5455	18	60	,	,	PUNCT
ejpam-5455	18	61	where	where	SCONJ
ejpam-5455	18	62	ω	ω	NOUN
ejpam-5455	18	63	=	=	PUNCT
ejpam-5455	19	1	[	[	X
ejpam-5455	19	2	0	0	NUM
ejpam-5455	19	3	,	,	PUNCT
ejpam-5455	19	4	z	z	NOUN
ejpam-5455	19	5	]	]	X
ejpam-5455	19	6	,	,	PUNCT
ejpam-5455	19	7	f	f	X
ejpam-5455	19	8	,	,	PUNCT
ejpam-5455	19	9	g	g	PROPN
ejpam-5455	19	10	,	,	PUNCT
ejpam-5455	19	11	h	h	NOUN
ejpam-5455	19	12	∈	∈	PROPN
ejpam-5455	19	13	c(ω×	c(ω×	X
ejpam-5455	19	14	r	r	NOUN
ejpam-5455	19	15	,	,	PUNCT
ejpam-5455	19	16	r	r	NOUN
ejpam-5455	19	17	)	)	PUNCT
ejpam-5455	19	18	with	with	ADP
ejpam-5455	19	19	q(7	q(7	PROPN
ejpam-5455	19	20	)	)	PUNCT
ejpam-5455	19	21	+	+	NUM
ejpam-5455	19	22	iγ0+f(7	iγ0+f(7	NOUN
ejpam-5455	19	23	,	,	PUNCT
ejpam-5455	19	24	w(7	w(7	PROPN
ejpam-5455	19	25	)	)	PUNCT
ejpam-5455	19	26	)	)	PUNCT
ejpam-5455	20	1	̸=	̸=	PROPN
ejpam-5455	20	2	0	0	NUM
ejpam-5455	20	3	.	.	PUNCT
ejpam-5455	21	1	fractional	fractional	ADJ
ejpam-5455	21	2	differential	differential	ADJ
ejpam-5455	21	3	equations	equation	NOUN
ejpam-5455	21	4	extend	extend	VERB
ejpam-5455	21	5	traditional	traditional	ADJ
ejpam-5455	21	6	differential	differential	ADJ
ejpam-5455	21	7	equations	equation	NOUN
ejpam-5455	21	8	by	by	ADP
ejpam-5455	21	9	incorporating	incorporate	VERB
ejpam-5455	21	10	derivatives	derivative	NOUN
ejpam-5455	21	11	of	of	ADP
ejpam-5455	21	12	non	non	ADJ
ejpam-5455	21	13	-	-	ADJ
ejpam-5455	21	14	integer	integer	ADJ
ejpam-5455	21	15	orders	order	NOUN
ejpam-5455	21	16	.	.	PUNCT
ejpam-5455	22	1	this	this	DET
ejpam-5455	22	2	extension	extension	NOUN
ejpam-5455	22	3	allows	allow	VERB
ejpam-5455	22	4	for	for	ADP
ejpam-5455	22	5	the	the	DET
ejpam-5455	22	6	modeling	modeling	NOUN
ejpam-5455	22	7	of	of	ADP
ejpam-5455	22	8	processes	process	NOUN
ejpam-5455	22	9	that	that	PRON
ejpam-5455	22	10	involve	involve	VERB
ejpam-5455	22	11	complex	complex	ADJ
ejpam-5455	22	12	dynamics	dynamic	NOUN
ejpam-5455	22	13	,	,	PUNCT
ejpam-5455	22	14	such	such	ADJ
ejpam-5455	22	15	as	as	ADP
ejpam-5455	22	16	systems	system	NOUN
ejpam-5455	22	17	with	with	ADP
ejpam-5455	22	18	memory	memory	NOUN
ejpam-5455	22	19	and	and	CCONJ
ejpam-5455	22	20	hereditary	hereditary	ADJ
ejpam-5455	22	21	characteristics	characteristic	NOUN
ejpam-5455	22	22	.	.	PUNCT
ejpam-5455	23	1	unlike	unlike	ADP
ejpam-5455	23	2	standard	standard	ADJ
ejpam-5455	23	3	derivatives	derivative	NOUN
ejpam-5455	23	4	,	,	PUNCT
ejpam-5455	23	5	which	which	PRON
ejpam-5455	23	6	are	be	AUX
ejpam-5455	23	7	local	local	ADJ
ejpam-5455	23	8	operators	operator	NOUN
ejpam-5455	23	9	,	,	PUNCT
ejpam-5455	23	10	fractional	fractional	ADJ
ejpam-5455	23	11	derivatives	derivative	NOUN
ejpam-5455	23	12	consider	consider	VERB
ejpam-5455	23	13	the	the	DET
ejpam-5455	23	14	entire	entire	ADJ
ejpam-5455	23	15	history	history	NOUN
ejpam-5455	23	16	of	of	ADP
ejpam-5455	23	17	the	the	DET
ejpam-5455	23	18	function	function	NOUN
ejpam-5455	23	19	,	,	PUNCT
ejpam-5455	23	20	making	make	VERB
ejpam-5455	23	21	them	they	PRON
ejpam-5455	23	22	ideal	ideal	ADJ
ejpam-5455	23	23	for	for	ADP
ejpam-5455	23	24	modeling	model	VERB
ejpam-5455	23	25	phenomena	phenomenon	NOUN
ejpam-5455	23	26	where	where	SCONJ
ejpam-5455	23	27	past	past	ADJ
ejpam-5455	23	28	states	state	NOUN
ejpam-5455	23	29	influence	influence	VERB
ejpam-5455	23	30	the	the	DET
ejpam-5455	23	31	present	present	ADJ
ejpam-5455	23	32	and	and	CCONJ
ejpam-5455	23	33	future	future	ADJ
ejpam-5455	23	34	behavior	behavior	NOUN
ejpam-5455	23	35	.	.	PUNCT
ejpam-5455	24	1	this	this	DET
ejpam-5455	24	2	non	non	ADJ
ejpam-5455	24	3	-	-	ADJ
ejpam-5455	24	4	local	local	ADJ
ejpam-5455	24	5	nature	nature	NOUN
ejpam-5455	24	6	of	of	ADP
ejpam-5455	24	7	fractional	fractional	ADJ
ejpam-5455	24	8	derivatives	derivative	NOUN
ejpam-5455	24	9	has	have	AUX
ejpam-5455	24	10	made	make	VERB
ejpam-5455	24	11	them	they	PRON
ejpam-5455	24	12	increasingly	increasingly	ADV
ejpam-5455	24	13	popular	popular	ADJ
ejpam-5455	24	14	in	in	ADP
ejpam-5455	24	15	various	various	ADJ
ejpam-5455	24	16	scientific	scientific	ADJ
ejpam-5455	24	17	and	and	CCONJ
ejpam-5455	24	18	engineering	engineering	NOUN
ejpam-5455	24	19	disciplines	discipline	NOUN
ejpam-5455	24	20	,	,	PUNCT
ejpam-5455	24	21	where	where	SCONJ
ejpam-5455	24	22	they	they	PRON
ejpam-5455	24	23	offer	offer	VERB
ejpam-5455	24	24	a	a	DET
ejpam-5455	24	25	more	more	ADV
ejpam-5455	24	26	nuanced	nuanced	ADJ
ejpam-5455	24	27	understanding	understanding	NOUN
ejpam-5455	24	28	of	of	ADP
ejpam-5455	24	29	systems	system	NOUN
ejpam-5455	24	30	exhibiting	exhibit	VERB
ejpam-5455	24	31	non	non	ADJ
ejpam-5455	24	32	-	-	ADJ
ejpam-5455	24	33	traditional	traditional	ADJ
ejpam-5455	24	34	dynamics	dynamic	NOUN
ejpam-5455	24	35	[	[	X
ejpam-5455	24	36	6	6	NUM
ejpam-5455	24	37	,	,	PUNCT
ejpam-5455	24	38	9	9	NUM
ejpam-5455	24	39	,	,	PUNCT
ejpam-5455	24	40	15	15	NUM
ejpam-5455	24	41	,	,	PUNCT
ejpam-5455	24	42	22	22	NUM
ejpam-5455	24	43	,	,	PUNCT
ejpam-5455	24	44	26	26	NUM
ejpam-5455	24	45	]	]	PUNCT
ejpam-5455	24	46	.	.	PUNCT
ejpam-5455	25	1	the	the	DET
ejpam-5455	25	2	use	use	NOUN
ejpam-5455	25	3	of	of	ADP
ejpam-5455	25	4	fractional	fractional	ADJ
ejpam-5455	25	5	differential	differential	ADJ
ejpam-5455	25	6	equations	equation	NOUN
ejpam-5455	25	7	has	have	AUX
ejpam-5455	25	8	become	become	VERB
ejpam-5455	25	9	widespread	widespread	ADJ
ejpam-5455	25	10	across	across	ADP
ejpam-5455	25	11	different	different	ADJ
ejpam-5455	25	12	fields	field	NOUN
ejpam-5455	25	13	due	due	ADP
ejpam-5455	25	14	to	to	ADP
ejpam-5455	25	15	their	their	PRON
ejpam-5455	25	16	ability	ability	NOUN
ejpam-5455	25	17	to	to	PART
ejpam-5455	25	18	model	model	VERB
ejpam-5455	25	19	processes	process	NOUN
ejpam-5455	25	20	more	more	ADV
ejpam-5455	25	21	accurately	accurately	ADV
ejpam-5455	25	22	than	than	ADP
ejpam-5455	25	23	traditional	traditional	ADJ
ejpam-5455	25	24	differential	differential	ADJ
ejpam-5455	25	25	equations	equation	NOUN
ejpam-5455	25	26	.	.	PUNCT
ejpam-5455	26	1	in	in	ADP
ejpam-5455	26	2	physics	physics	PROPN
ejpam-5455	26	3	,	,	PUNCT
ejpam-5455	26	4	they	they	PRON
ejpam-5455	26	5	are	be	AUX
ejpam-5455	26	6	used	use	VERB
ejpam-5455	26	7	to	to	PART
ejpam-5455	26	8	describe	describe	VERB
ejpam-5455	26	9	anomalous	anomalous	ADJ
ejpam-5455	26	10	diffusion	diffusion	NOUN
ejpam-5455	26	11	processes	process	NOUN
ejpam-5455	26	12	,	,	PUNCT
ejpam-5455	26	13	where	where	SCONJ
ejpam-5455	26	14	the	the	DET
ejpam-5455	26	15	movement	movement	NOUN
ejpam-5455	26	16	of	of	ADP
ejpam-5455	26	17	particles	particle	NOUN
ejpam-5455	26	18	does	do	AUX
ejpam-5455	26	19	not	not	PART
ejpam-5455	26	20	follow	follow	VERB
ejpam-5455	26	21	the	the	DET
ejpam-5455	26	22	standard	standard	ADJ
ejpam-5455	26	23	pattern	pattern	NOUN
ejpam-5455	26	24	seen	see	VERB
ejpam-5455	26	25	in	in	ADP
ejpam-5455	26	26	classical	classical	ADJ
ejpam-5455	26	27	diffusion	diffusion	NOUN
ejpam-5455	27	1	[	[	X
ejpam-5455	27	2	24	24	NUM
ejpam-5455	27	3	]	]	PUNCT
ejpam-5455	27	4	.	.	PUNCT
ejpam-5455	28	1	in	in	ADP
ejpam-5455	28	2	biology	biology	NOUN
ejpam-5455	28	3	,	,	PUNCT
ejpam-5455	28	4	fractional	fractional	ADJ
ejpam-5455	28	5	differential	differential	NOUN
ejpam-5455	28	6	equations	equation	NOUN
ejpam-5455	28	7	help	help	VERB
ejpam-5455	28	8	model	model	VERB
ejpam-5455	28	9	complex	complex	ADJ
ejpam-5455	28	10	biological	biological	ADJ
ejpam-5455	28	11	processes	process	NOUN
ejpam-5455	28	12	,	,	PUNCT
ejpam-5455	28	13	such	such	ADJ
ejpam-5455	28	14	as	as	ADP
ejpam-5455	28	15	the	the	DET
ejpam-5455	28	16	diffusion	diffusion	NOUN
ejpam-5455	28	17	of	of	ADP
ejpam-5455	28	18	substances	substance	NOUN
ejpam-5455	28	19	across	across	ADP
ejpam-5455	28	20	cellular	cellular	ADJ
ejpam-5455	28	21	membranes	membrane	NOUN
ejpam-5455	28	22	and	and	CCONJ
ejpam-5455	28	23	the	the	DET
ejpam-5455	28	24	dynamics	dynamic	NOUN
ejpam-5455	28	25	of	of	ADP
ejpam-5455	28	26	cell	cell	NOUN
ejpam-5455	28	27	potentials	potential	VERB
ejpam-5455	29	1	[	[	X
ejpam-5455	29	2	19–21	19–21	NUM
ejpam-5455	29	3	]	]	PUNCT
ejpam-5455	29	4	.	.	PUNCT
ejpam-5455	30	1	in	in	ADP
ejpam-5455	30	2	engineering	engineering	NOUN
ejpam-5455	30	3	,	,	PUNCT
ejpam-5455	30	4	these	these	DET
ejpam-5455	30	5	equations	equation	NOUN
ejpam-5455	30	6	are	be	AUX
ejpam-5455	30	7	crucial	crucial	ADJ
ejpam-5455	30	8	for	for	ADP
ejpam-5455	30	9	modeling	model	VERB
ejpam-5455	30	10	materials	material	NOUN
ejpam-5455	30	11	with	with	ADP
ejpam-5455	30	12	viscoelastic	viscoelastic	ADJ
ejpam-5455	30	13	properties	property	NOUN
ejpam-5455	30	14	,	,	PUNCT
ejpam-5455	30	15	where	where	SCONJ
ejpam-5455	30	16	the	the	DET
ejpam-5455	30	17	relationship	relationship	NOUN
ejpam-5455	30	18	between	between	ADP
ejpam-5455	30	19	stress	stress	NOUN
ejpam-5455	30	20	and	and	CCONJ
ejpam-5455	30	21	strain	strain	NOUN
ejpam-5455	30	22	is	be	AUX
ejpam-5455	30	23	not	not	PART
ejpam-5455	30	24	instantaneous	instantaneous	ADJ
ejpam-5455	30	25	but	but	CCONJ
ejpam-5455	30	26	depends	depend	VERB
ejpam-5455	30	27	on	on	ADP
ejpam-5455	30	28	the	the	DET
ejpam-5455	30	29	material	material	NOUN
ejpam-5455	30	30	’s	’s	PART
ejpam-5455	30	31	history	history	NOUN
ejpam-5455	31	1	[	[	X
ejpam-5455	31	2	27	27	NUM
ejpam-5455	31	3	]	]	PUNCT
ejpam-5455	31	4	.	.	PUNCT
ejpam-5455	32	1	in	in	ADP
ejpam-5455	32	2	finance	finance	NOUN
ejpam-5455	32	3	,	,	PUNCT
ejpam-5455	32	4	fractional	fractional	ADJ
ejpam-5455	32	5	models	model	NOUN
ejpam-5455	32	6	are	be	AUX
ejpam-5455	32	7	employed	employ	VERB
ejpam-5455	32	8	to	to	PART
ejpam-5455	32	9	capture	capture	VERB
ejpam-5455	32	10	memory	memory	NOUN
ejpam-5455	32	11	effects	effect	NOUN
ejpam-5455	32	12	in	in	ADP
ejpam-5455	32	13	stock	stock	NOUN
ejpam-5455	32	14	prices	price	NOUN
ejpam-5455	32	15	and	and	CCONJ
ejpam-5455	32	16	to	to	PART
ejpam-5455	32	17	model	model	VERB
ejpam-5455	32	18	the	the	DET
ejpam-5455	32	19	dynamics	dynamic	NOUN
ejpam-5455	32	20	of	of	ADP
ejpam-5455	32	21	financial	financial	ADJ
ejpam-5455	32	22	instruments	instrument	NOUN
ejpam-5455	32	23	over	over	ADP
ejpam-5455	32	24	time	time	NOUN
ejpam-5455	32	25	.	.	PUNCT
ejpam-5455	33	1	these	these	DET
ejpam-5455	33	2	applications	application	NOUN
ejpam-5455	33	3	highlight	highlight	VERB
ejpam-5455	33	4	the	the	DET
ejpam-5455	33	5	versatility	versatility	NOUN
ejpam-5455	33	6	and	and	CCONJ
ejpam-5455	33	7	effectiveness	effectiveness	NOUN
ejpam-5455	33	8	of	of	ADP
ejpam-5455	33	9	fractional	fractional	ADJ
ejpam-5455	33	10	differential	differential	ADJ
ejpam-5455	33	11	equations	equation	NOUN
ejpam-5455	33	12	in	in	ADP
ejpam-5455	33	13	providing	provide	VERB
ejpam-5455	33	14	deeper	deep	ADJ
ejpam-5455	33	15	insights	insight	NOUN
ejpam-5455	33	16	into	into	ADP
ejpam-5455	33	17	various	various	ADJ
ejpam-5455	33	18	complex	complex	ADJ
ejpam-5455	33	19	systems	system	NOUN
ejpam-5455	33	20	.	.	PUNCT
ejpam-5455	34	1	the	the	DET
ejpam-5455	34	2	realm	realm	NOUN
ejpam-5455	34	3	of	of	ADP
ejpam-5455	34	4	fractional	fractional	ADJ
ejpam-5455	34	5	calculus	calculus	NOUN
ejpam-5455	34	6	has	have	AUX
ejpam-5455	34	7	expanded	expand	VERB
ejpam-5455	34	8	remarkably	remarkably	ADV
ejpam-5455	34	9	with	with	ADP
ejpam-5455	34	10	the	the	DET
ejpam-5455	34	11	introduction	introduction	NOUN
ejpam-5455	34	12	of	of	ADP
ejpam-5455	34	13	various	various	ADJ
ejpam-5455	34	14	fractional	fractional	ADJ
ejpam-5455	34	15	derivative	derivative	ADJ
ejpam-5455	34	16	definitions	definition	NOUN
ejpam-5455	34	17	,	,	PUNCT
ejpam-5455	34	18	each	each	PRON
ejpam-5455	34	19	bringing	bring	VERB
ejpam-5455	34	20	its	its	PRON
ejpam-5455	34	21	own	own	ADJ
ejpam-5455	34	22	advantages	advantage	NOUN
ejpam-5455	34	23	and	and	CCONJ
ejpam-5455	34	24	specific	specific	ADJ
ejpam-5455	34	25	uses	use	NOUN
ejpam-5455	34	26	.	.	PUNCT
ejpam-5455	35	1	among	among	ADP
ejpam-5455	35	2	the	the	DET
ejpam-5455	35	3	pioneering	pioneering	ADJ
ejpam-5455	35	4	contributions	contribution	NOUN
ejpam-5455	35	5	is	be	AUX
ejpam-5455	35	6	the	the	DET
ejpam-5455	35	7	caputo	caputo	PROPN
ejpam-5455	35	8	derivative	derivative	NOUN
ejpam-5455	35	9	,	,	PUNCT
ejpam-5455	35	10	introduced	introduce	VERB
ejpam-5455	35	11	by	by	ADP
ejpam-5455	35	12	michele	michele	PROPN
ejpam-5455	35	13	caputo	caputo	PROPN
ejpam-5455	36	1	[	[	X
ejpam-5455	36	2	7	7	X
ejpam-5455	36	3	]	]	PUNCT
ejpam-5455	36	4	in	in	ADP
ejpam-5455	36	5	1967	1967	NUM
ejpam-5455	36	6	,	,	PUNCT
ejpam-5455	36	7	which	which	PRON
ejpam-5455	36	8	has	have	AUX
ejpam-5455	36	9	gained	gain	VERB
ejpam-5455	36	10	widespread	widespread	ADJ
ejpam-5455	36	11	recognition	recognition	NOUN
ejpam-5455	36	12	for	for	ADP
ejpam-5455	36	13	its	its	PRON
ejpam-5455	36	14	practical	practical	ADJ
ejpam-5455	36	15	utility	utility	NOUN
ejpam-5455	36	16	.	.	PUNCT
ejpam-5455	37	1	despite	despite	SCONJ
ejpam-5455	37	2	its	its	PRON
ejpam-5455	37	3	widespread	widespread	ADJ
ejpam-5455	37	4	adoption	adoption	NOUN
ejpam-5455	37	5	,	,	PUNCT
ejpam-5455	37	6	the	the	DET
ejpam-5455	37	7	caputo	caputo	PROPN
ejpam-5455	37	8	derivative	derivative	PROPN
ejpam-5455	37	9	’s	’s	PART
ejpam-5455	37	10	reliance	reliance	NOUN
ejpam-5455	37	11	on	on	ADP
ejpam-5455	37	12	a	a	DET
ejpam-5455	37	13	single	single	ADJ
ejpam-5455	37	14	kernel	kernel	NOUN
ejpam-5455	37	15	presents	present	VERB
ejpam-5455	37	16	certain	certain	ADJ
ejpam-5455	37	17	constraints	constraint	NOUN
ejpam-5455	37	18	,	,	PUNCT
ejpam-5455	37	19	particularly	particularly	ADV
ejpam-5455	37	20	when	when	SCONJ
ejpam-5455	37	21	modeling	model	VERB
ejpam-5455	37	22	diverse	diverse	ADJ
ejpam-5455	37	23	phenomena	phenomenon	NOUN
ejpam-5455	37	24	.	.	PUNCT
ejpam-5455	38	1	to	to	PART
ejpam-5455	38	2	overcome	overcome	VERB
ejpam-5455	38	3	these	these	DET
ejpam-5455	38	4	limitations	limitation	NOUN
ejpam-5455	38	5	,	,	PUNCT
ejpam-5455	38	6	caputo	caputo	PROPN
ejpam-5455	38	7	and	and	CCONJ
ejpam-5455	38	8	fabrizio	fabrizio	PROPN
ejpam-5455	39	1	[	[	X
ejpam-5455	39	2	8	8	NUM
ejpam-5455	39	3	]	]	PUNCT
ejpam-5455	39	4	proposed	propose	VERB
ejpam-5455	39	5	a	a	DET
ejpam-5455	39	6	new	new	ADJ
ejpam-5455	39	7	approach	approach	NOUN
ejpam-5455	39	8	by	by	ADP
ejpam-5455	39	9	introducing	introduce	VERB
ejpam-5455	39	10	a	a	DET
ejpam-5455	39	11	non	non	ADJ
ejpam-5455	39	12	-	-	ADJ
ejpam-5455	39	13	singular	singular	ADJ
ejpam-5455	39	14	derivative	derivative	NOUN
ejpam-5455	39	15	based	base	VERB
ejpam-5455	39	16	on	on	ADP
ejpam-5455	39	17	the	the	DET
ejpam-5455	39	18	exponential	exponential	ADJ
ejpam-5455	39	19	function	function	NOUN
ejpam-5455	39	20	.	.	PUNCT
ejpam-5455	40	1	this	this	DET
ejpam-5455	40	2	innovation	innovation	NOUN
ejpam-5455	40	3	effectively	effectively	ADV
ejpam-5455	40	4	addresses	address	VERB
ejpam-5455	40	5	the	the	DET
ejpam-5455	40	6	issue	issue	NOUN
ejpam-5455	40	7	of	of	ADP
ejpam-5455	40	8	singularity	singularity	NOUN
ejpam-5455	40	9	,	,	PUNCT
ejpam-5455	40	10	although	although	SCONJ
ejpam-5455	40	11	it	it	PRON
ejpam-5455	40	12	encounters	encounter	VERB
ejpam-5455	40	13	difficulties	difficulty	NOUN
ejpam-5455	40	14	when	when	SCONJ
ejpam-5455	40	15	applied	apply	VERB
ejpam-5455	40	16	to	to	ADP
ejpam-5455	40	17	systems	system	NOUN
ejpam-5455	40	18	that	that	PRON
ejpam-5455	40	19	do	do	AUX
ejpam-5455	40	20	not	not	PART
ejpam-5455	40	21	naturally	naturally	ADV
ejpam-5455	40	22	follow	follow	VERB
ejpam-5455	40	23	exponential	exponential	ADJ
ejpam-5455	40	24	patterns	pattern	NOUN
ejpam-5455	40	25	.	.	PUNCT
ejpam-5455	41	1	seeking	seek	VERB
ejpam-5455	41	2	to	to	PART
ejpam-5455	41	3	further	far	ADV
ejpam-5455	41	4	expand	expand	VERB
ejpam-5455	41	5	the	the	DET
ejpam-5455	41	6	modeling	modeling	NOUN
ejpam-5455	41	7	potential	potential	NOUN
ejpam-5455	41	8	of	of	ADP
ejpam-5455	41	9	fractional	fractional	ADJ
ejpam-5455	41	10	derivatives	derivative	NOUN
ejpam-5455	41	11	,	,	PUNCT
ejpam-5455	41	12	atangana	atangana	NOUN
ejpam-5455	41	13	and	and	CCONJ
ejpam-5455	41	14	baleanu	baleanu	NOUN
ejpam-5455	41	15	[	[	X
ejpam-5455	41	16	4	4	NUM
ejpam-5455	41	17	]	]	PUNCT
ejpam-5455	41	18	introduced	introduce	VERB
ejpam-5455	41	19	a	a	DET
ejpam-5455	41	20	derivative	derivative	NOUN
ejpam-5455	41	21	based	base	VERB
ejpam-5455	41	22	on	on	ADP
ejpam-5455	41	23	the	the	DET
ejpam-5455	41	24	extended	extended	ADJ
ejpam-5455	41	25	mittag	mittag	ADJ
ejpam-5455	41	26	-	-	PUNCT
ejpam-5455	41	27	leffler	leffler	NOUN
ejpam-5455	41	28	function	function	NOUN
ejpam-5455	41	29	.	.	PUNCT
ejpam-5455	42	1	this	this	DET
ejpam-5455	42	2	derivative	derivative	NOUN
ejpam-5455	42	3	allows	allow	VERB
ejpam-5455	42	4	for	for	ADP
ejpam-5455	42	5	a	a	DET
ejpam-5455	42	6	more	more	ADV
ejpam-5455	42	7	flexible	flexible	ADJ
ejpam-5455	42	8	description	description	NOUN
ejpam-5455	42	9	of	of	ADP
ejpam-5455	42	10	non	non	ADJ
ejpam-5455	42	11	-	-	ADJ
ejpam-5455	42	12	local	local	ADJ
ejpam-5455	42	13	and	and	CCONJ
ejpam-5455	42	14	non	non	ADJ
ejpam-5455	42	15	-	-	ADJ
ejpam-5455	42	16	singular	singular	ADJ
ejpam-5455	42	17	kernels	kernel	NOUN
ejpam-5455	42	18	,	,	PUNCT
ejpam-5455	42	19	thereby	thereby	ADV
ejpam-5455	42	20	extending	extend	VERB
ejpam-5455	42	21	the	the	DET
ejpam-5455	42	22	range	range	NOUN
ejpam-5455	42	23	of	of	ADP
ejpam-5455	42	24	phenomena	phenomenon	NOUN
ejpam-5455	42	25	that	that	PRON
ejpam-5455	42	26	can	can	AUX
ejpam-5455	42	27	be	be	AUX
ejpam-5455	42	28	accurately	accurately	ADV
ejpam-5455	42	29	represented	represent	VERB
ejpam-5455	42	30	.	.	PUNCT
ejpam-5455	43	1	building	build	VERB
ejpam-5455	43	2	on	on	ADP
ejpam-5455	43	3	these	these	DET
ejpam-5455	43	4	significant	significant	ADJ
ejpam-5455	43	5	developments	development	NOUN
ejpam-5455	43	6	,	,	PUNCT
ejpam-5455	43	7	refai	refai	NOUN
ejpam-5455	43	8	and	and	CCONJ
ejpam-5455	43	9	baleanu	baleanu	NOUN
ejpam-5455	43	10	recently	recently	ADV
ejpam-5455	43	11	introduced	introduce	VERB
ejpam-5455	43	12	the	the	DET
ejpam-5455	43	13	mabc	mabc	NOUN
ejpam-5455	43	14	-	-	PUNCT
ejpam-5455	43	15	derivative	derivative	NOUN
ejpam-5455	43	16	,	,	PUNCT
ejpam-5455	43	17	a	a	DET
ejpam-5455	43	18	novel	novel	ADJ
ejpam-5455	43	19	operator	operator	NOUN
ejpam-5455	43	20	that	that	PRON
ejpam-5455	43	21	merges	merge	VERB
ejpam-5455	43	22	the	the	DET
ejpam-5455	43	23	strengths	strength	NOUN
ejpam-5455	43	24	of	of	ADP
ejpam-5455	43	25	both	both	CCONJ
ejpam-5455	43	26	the	the	DET
ejpam-5455	43	27	caputo	caputo	PROPN
ejpam-5455	43	28	and	and	CCONJ
ejpam-5455	43	29	atangana	atangana	PROPN
ejpam-5455	43	30	-	-	PUNCT
ejpam-5455	43	31	baleanu	baleanu	ADJ
ejpam-5455	43	32	derivatives	derivative	NOUN
ejpam-5455	43	33	[	[	X
ejpam-5455	43	34	2	2	NUM
ejpam-5455	43	35	]	]	PUNCT
ejpam-5455	43	36	.	.	PUNCT
ejpam-5455	44	1	this	this	DET
ejpam-5455	44	2	new	new	ADJ
ejpam-5455	44	3	tool	tool	NOUN
ejpam-5455	44	4	offers	offer	VERB
ejpam-5455	44	5	a	a	DET
ejpam-5455	44	6	robust	robust	ADJ
ejpam-5455	44	7	solution	solution	NOUN
ejpam-5455	44	8	for	for	ADP
ejpam-5455	44	9	tackling	tackle	VERB
ejpam-5455	44	10	complex	complex	ADJ
ejpam-5455	44	11	problems	problem	NOUN
ejpam-5455	44	12	that	that	PRON
ejpam-5455	44	13	were	be	AUX
ejpam-5455	44	14	previously	previously	ADV
ejpam-5455	44	15	challenging	challenge	VERB
ejpam-5455	44	16	to	to	PART
ejpam-5455	44	17	address	address	VERB
ejpam-5455	44	18	with	with	ADP
ejpam-5455	44	19	existing	exist	VERB
ejpam-5455	44	20	methodologies	methodology	NOUN
ejpam-5455	44	21	,	,	PUNCT
ejpam-5455	44	22	marking	mark	VERB
ejpam-5455	44	23	a	a	DET
ejpam-5455	44	24	substantial	substantial	ADJ
ejpam-5455	44	25	m.	m.	NOUN
ejpam-5455	44	26	m.	m.	NOUN
ejpam-5455	44	27	arjunan	arjunan	PROPN
ejpam-5455	44	28	/	/	SYM
ejpam-5455	44	29	eur	eur	PROPN
ejpam-5455	44	30	.	.	PUNCT
ejpam-5455	45	1	j.	j.	PROPN
ejpam-5455	45	2	pure	pure	PROPN
ejpam-5455	45	3	appl	appl	PROPN
ejpam-5455	45	4	.	.	PROPN
ejpam-5455	45	5	math	math	PROPN
ejpam-5455	45	6	,	,	PUNCT
ejpam-5455	45	7	17	17	NUM
ejpam-5455	45	8	(	(	PUNCT
ejpam-5455	45	9	4	4	NUM
ejpam-5455	45	10	)	)	PUNCT
ejpam-5455	45	11	(	(	PUNCT
ejpam-5455	45	12	2024	2024	NUM
ejpam-5455	45	13	)	)	PUNCT
ejpam-5455	45	14	,	,	PUNCT
ejpam-5455	45	15	4071	4071	NUM
ejpam-5455	45	16	-	-	SYM
ejpam-5455	45	17	4092	4092	NUM
ejpam-5455	45	18	4073	4073	NUM
ejpam-5455	45	19	advancement	advancement	NOUN
ejpam-5455	45	20	in	in	ADP
ejpam-5455	45	21	the	the	DET
ejpam-5455	45	22	field	field	NOUN
ejpam-5455	45	23	of	of	ADP
ejpam-5455	45	24	fractional	fractional	ADJ
ejpam-5455	45	25	calculus	calculus	NOUN
ejpam-5455	45	26	.	.	PUNCT
ejpam-5455	46	1	initial	initial	ADJ
ejpam-5455	46	2	value	value	NOUN
ejpam-5455	46	3	problems	problem	NOUN
ejpam-5455	46	4	(	(	PUNCT
ejpam-5455	46	5	ivps	ivps	PROPN
ejpam-5455	46	6	)	)	PUNCT
ejpam-5455	46	7	play	play	VERB
ejpam-5455	46	8	a	a	DET
ejpam-5455	46	9	pivotal	pivotal	ADJ
ejpam-5455	46	10	role	role	NOUN
ejpam-5455	46	11	in	in	ADP
ejpam-5455	46	12	the	the	DET
ejpam-5455	46	13	mathematical	mathematical	ADJ
ejpam-5455	46	14	modeling	modeling	NOUN
ejpam-5455	46	15	of	of	ADP
ejpam-5455	46	16	real	real	ADJ
ejpam-5455	46	17	-	-	PUNCT
ejpam-5455	46	18	world	world	NOUN
ejpam-5455	46	19	systems	system	NOUN
ejpam-5455	46	20	,	,	PUNCT
ejpam-5455	46	21	where	where	SCONJ
ejpam-5455	46	22	the	the	DET
ejpam-5455	46	23	state	state	NOUN
ejpam-5455	46	24	of	of	ADP
ejpam-5455	46	25	a	a	DET
ejpam-5455	46	26	system	system	NOUN
ejpam-5455	46	27	at	at	ADP
ejpam-5455	46	28	a	a	DET
ejpam-5455	46	29	given	give	VERB
ejpam-5455	46	30	initial	initial	ADJ
ejpam-5455	46	31	time	time	NOUN
ejpam-5455	46	32	dictates	dictate	VERB
ejpam-5455	46	33	its	its	PRON
ejpam-5455	46	34	future	future	ADJ
ejpam-5455	46	35	behavior	behavior	NOUN
ejpam-5455	46	36	.	.	PUNCT
ejpam-5455	47	1	in	in	ADP
ejpam-5455	47	2	the	the	DET
ejpam-5455	47	3	context	context	NOUN
ejpam-5455	47	4	of	of	ADP
ejpam-5455	47	5	p	p	NOUN
ejpam-5455	47	6	-	-	PUNCT
ejpam-5455	47	7	laplacian	laplacian	ADJ
ejpam-5455	47	8	equations	equation	NOUN
ejpam-5455	47	9	,	,	PUNCT
ejpam-5455	47	10	ivps	ivps	PROPN
ejpam-5455	47	11	involve	involve	VERB
ejpam-5455	47	12	determining	determine	VERB
ejpam-5455	47	13	the	the	DET
ejpam-5455	47	14	evolution	evolution	NOUN
ejpam-5455	47	15	of	of	ADP
ejpam-5455	47	16	a	a	DET
ejpam-5455	47	17	system	system	NOUN
ejpam-5455	47	18	governed	govern	VERB
ejpam-5455	47	19	by	by	ADP
ejpam-5455	47	20	a	a	DET
ejpam-5455	47	21	nonlinear	nonlinear	ADJ
ejpam-5455	47	22	differential	differential	ADJ
ejpam-5455	47	23	operator	operator	NOUN
ejpam-5455	47	24	.	.	PUNCT
ejpam-5455	48	1	the	the	DET
ejpam-5455	48	2	analysis	analysis	NOUN
ejpam-5455	48	3	of	of	ADP
ejpam-5455	48	4	ivps	ivps	PROPN
ejpam-5455	48	5	for	for	ADP
ejpam-5455	48	6	plaplacian	plaplacian	ADJ
ejpam-5455	48	7	equations	equation	NOUN
ejpam-5455	48	8	is	be	AUX
ejpam-5455	48	9	particularly	particularly	ADV
ejpam-5455	48	10	challenging	challenging	ADJ
ejpam-5455	48	11	due	due	ADJ
ejpam-5455	48	12	to	to	ADP
ejpam-5455	48	13	the	the	DET
ejpam-5455	48	14	nonlinearity	nonlinearity	NOUN
ejpam-5455	48	15	of	of	ADP
ejpam-5455	48	16	the	the	DET
ejpam-5455	48	17	operator	operator	NOUN
ejpam-5455	48	18	,	,	PUNCT
ejpam-5455	48	19	which	which	PRON
ejpam-5455	48	20	can	can	AUX
ejpam-5455	48	21	lead	lead	VERB
ejpam-5455	48	22	to	to	ADP
ejpam-5455	48	23	complex	complex	ADJ
ejpam-5455	48	24	dynamics	dynamic	NOUN
ejpam-5455	48	25	,	,	PUNCT
ejpam-5455	48	26	including	include	VERB
ejpam-5455	48	27	the	the	DET
ejpam-5455	48	28	existence	existence	NOUN
ejpam-5455	48	29	of	of	ADP
ejpam-5455	48	30	multiple	multiple	ADJ
ejpam-5455	48	31	solutions	solution	NOUN
ejpam-5455	48	32	,	,	PUNCT
ejpam-5455	48	33	bifurcations	bifurcation	NOUN
ejpam-5455	48	34	,	,	PUNCT
ejpam-5455	48	35	and	and	CCONJ
ejpam-5455	48	36	sensitivity	sensitivity	NOUN
ejpam-5455	48	37	to	to	ADP
ejpam-5455	48	38	initial	initial	ADJ
ejpam-5455	48	39	conditions	condition	NOUN
ejpam-5455	48	40	.	.	PUNCT
ejpam-5455	49	1	understanding	understand	VERB
ejpam-5455	49	2	these	these	DET
ejpam-5455	49	3	aspects	aspect	NOUN
ejpam-5455	49	4	is	be	AUX
ejpam-5455	49	5	crucial	crucial	ADJ
ejpam-5455	49	6	for	for	ADP
ejpam-5455	49	7	accurately	accurately	ADV
ejpam-5455	49	8	predicting	predict	VERB
ejpam-5455	49	9	the	the	DET
ejpam-5455	49	10	behavior	behavior	NOUN
ejpam-5455	49	11	of	of	ADP
ejpam-5455	49	12	the	the	DET
ejpam-5455	49	13	modeled	model	VERB
ejpam-5455	49	14	systems	system	NOUN
ejpam-5455	49	15	,	,	PUNCT
ejpam-5455	49	16	whether	whether	SCONJ
ejpam-5455	49	17	they	they	PRON
ejpam-5455	49	18	pertain	pertain	VERB
ejpam-5455	49	19	to	to	ADP
ejpam-5455	49	20	physical	physical	ADJ
ejpam-5455	49	21	processes	process	NOUN
ejpam-5455	49	22	,	,	PUNCT
ejpam-5455	49	23	biological	biological	ADJ
ejpam-5455	49	24	systems	system	NOUN
ejpam-5455	49	25	,	,	PUNCT
ejpam-5455	49	26	or	or	CCONJ
ejpam-5455	49	27	engineering	engineering	NOUN
ejpam-5455	49	28	applications	application	NOUN
ejpam-5455	49	29	.	.	PUNCT
ejpam-5455	50	1	in	in	ADP
ejpam-5455	50	2	recent	recent	ADJ
ejpam-5455	50	3	times	time	NOUN
ejpam-5455	50	4	,	,	PUNCT
ejpam-5455	50	5	a	a	DET
ejpam-5455	50	6	novel	novel	ADJ
ejpam-5455	50	7	category	category	NOUN
ejpam-5455	50	8	known	know	VERB
ejpam-5455	50	9	as	as	ADP
ejpam-5455	50	10	hybrid	hybrid	ADJ
ejpam-5455	50	11	boundary	boundary	ADJ
ejpam-5455	50	12	value	value	NOUN
ejpam-5455	50	13	problems	problem	NOUN
ejpam-5455	50	14	has	have	AUX
ejpam-5455	50	15	gained	gain	VERB
ejpam-5455	50	16	prominence	prominence	NOUN
ejpam-5455	50	17	,	,	PUNCT
ejpam-5455	50	18	integrating	integrate	VERB
ejpam-5455	50	19	aspects	aspect	NOUN
ejpam-5455	50	20	from	from	ADP
ejpam-5455	50	21	both	both	CCONJ
ejpam-5455	50	22	linear	linear	ADJ
ejpam-5455	50	23	and	and	CCONJ
ejpam-5455	50	24	nonlinear	nonlinear	ADJ
ejpam-5455	50	25	theories	theory	NOUN
ejpam-5455	50	26	.	.	PUNCT
ejpam-5455	51	1	this	this	DET
ejpam-5455	51	2	hybrid	hybrid	ADJ
ejpam-5455	51	3	approach	approach	NOUN
ejpam-5455	51	4	facilitates	facilitate	VERB
ejpam-5455	51	5	a	a	DET
ejpam-5455	51	6	more	more	ADV
ejpam-5455	51	7	thorough	thorough	ADJ
ejpam-5455	51	8	comprehension	comprehension	NOUN
ejpam-5455	51	9	of	of	ADP
ejpam-5455	51	10	intricate	intricate	ADJ
ejpam-5455	51	11	systems	system	NOUN
ejpam-5455	51	12	,	,	PUNCT
ejpam-5455	51	13	where	where	SCONJ
ejpam-5455	51	14	conventional	conventional	ADJ
ejpam-5455	51	15	methods	method	NOUN
ejpam-5455	51	16	might	might	AUX
ejpam-5455	51	17	be	be	AUX
ejpam-5455	51	18	inadequate	inadequate	ADJ
ejpam-5455	51	19	.	.	PUNCT
ejpam-5455	52	1	a	a	DET
ejpam-5455	52	2	notable	notable	ADJ
ejpam-5455	52	3	contribution	contribution	NOUN
ejpam-5455	52	4	to	to	ADP
ejpam-5455	52	5	this	this	DET
ejpam-5455	52	6	field	field	NOUN
ejpam-5455	52	7	is	be	AUX
ejpam-5455	52	8	the	the	DET
ejpam-5455	52	9	research	research	NOUN
ejpam-5455	52	10	conducted	conduct	VERB
ejpam-5455	52	11	by	by	ADP
ejpam-5455	52	12	dhage	dhage	NOUN
ejpam-5455	52	13	[	[	X
ejpam-5455	52	14	10	10	NUM
ejpam-5455	52	15	,	,	PUNCT
ejpam-5455	52	16	13	13	NUM
ejpam-5455	52	17	]	]	PUNCT
ejpam-5455	52	18	,	,	PUNCT
ejpam-5455	52	19	which	which	PRON
ejpam-5455	52	20	highlights	highlight	VERB
ejpam-5455	52	21	the	the	DET
ejpam-5455	52	22	significance	significance	NOUN
ejpam-5455	52	23	of	of	ADP
ejpam-5455	52	24	hybrid	hybrid	ADJ
ejpam-5455	52	25	differential	differential	ADJ
ejpam-5455	52	26	equations	equation	NOUN
ejpam-5455	52	27	(	(	PUNCT
ejpam-5455	52	28	hdes	hde	NOUN
ejpam-5455	52	29	)	)	PUNCT
ejpam-5455	52	30	in	in	ADP
ejpam-5455	52	31	the	the	DET
ejpam-5455	52	32	analysis	analysis	NOUN
ejpam-5455	52	33	of	of	ADP
ejpam-5455	52	34	dynamical	dynamical	ADJ
ejpam-5455	52	35	systems	system	NOUN
ejpam-5455	52	36	.	.	PUNCT
ejpam-5455	53	1	dhage	dhage	NOUN
ejpam-5455	53	2	meticulously	meticulously	ADV
ejpam-5455	53	3	categorized	categorize	VERB
ejpam-5455	53	4	hdes	hde	NOUN
ejpam-5455	53	5	based	base	VERB
ejpam-5455	53	6	on	on	ADP
ejpam-5455	53	7	different	different	ADJ
ejpam-5455	53	8	types	type	NOUN
ejpam-5455	53	9	of	of	ADP
ejpam-5455	53	10	perturbations	perturbation	NOUN
ejpam-5455	53	11	,	,	PUNCT
ejpam-5455	53	12	emphasizing	emphasize	VERB
ejpam-5455	53	13	their	their	PRON
ejpam-5455	53	14	importance	importance	NOUN
ejpam-5455	53	15	in	in	ADP
ejpam-5455	53	16	refining	refining	NOUN
ejpam-5455	53	17	perturbation	perturbation	NOUN
ejpam-5455	53	18	techniques	technique	NOUN
ejpam-5455	53	19	within	within	ADP
ejpam-5455	53	20	the	the	DET
ejpam-5455	53	21	expansive	expansive	ADJ
ejpam-5455	53	22	domain	domain	NOUN
ejpam-5455	53	23	of	of	ADP
ejpam-5455	53	24	differential	differential	ADJ
ejpam-5455	53	25	and	and	CCONJ
ejpam-5455	53	26	integral	integral	ADJ
ejpam-5455	53	27	equations	equation	NOUN
ejpam-5455	53	28	.	.	PUNCT
ejpam-5455	54	1	his	his	PRON
ejpam-5455	54	2	work	work	NOUN
ejpam-5455	54	3	underscores	underscore	VERB
ejpam-5455	54	4	the	the	DET
ejpam-5455	54	5	potential	potential	NOUN
ejpam-5455	54	6	of	of	ADP
ejpam-5455	54	7	hdes	hde	NOUN
ejpam-5455	54	8	to	to	PART
ejpam-5455	54	9	provide	provide	VERB
ejpam-5455	54	10	deeper	deep	ADJ
ejpam-5455	54	11	insights	insight	NOUN
ejpam-5455	54	12	and	and	CCONJ
ejpam-5455	54	13	more	more	ADV
ejpam-5455	54	14	robust	robust	ADJ
ejpam-5455	54	15	solutions	solution	NOUN
ejpam-5455	54	16	to	to	ADP
ejpam-5455	54	17	complex	complex	ADJ
ejpam-5455	54	18	mathematical	mathematical	ADJ
ejpam-5455	54	19	problems	problem	NOUN
ejpam-5455	54	20	.	.	PUNCT
ejpam-5455	55	1	following	follow	VERB
ejpam-5455	55	2	dhage	dhage	NOUN
ejpam-5455	55	3	’s	’s	PART
ejpam-5455	55	4	pioneering	pioneer	VERB
ejpam-5455	55	5	contributions	contribution	NOUN
ejpam-5455	55	6	,	,	PUNCT
ejpam-5455	55	7	numerous	numerous	ADJ
ejpam-5455	55	8	researchers	researcher	NOUN
ejpam-5455	55	9	in	in	ADP
ejpam-5455	55	10	mathematics	mathematic	NOUN
ejpam-5455	55	11	and	and	CCONJ
ejpam-5455	55	12	related	related	ADJ
ejpam-5455	55	13	disciplines	discipline	NOUN
ejpam-5455	55	14	have	have	AUX
ejpam-5455	55	15	focused	focus	VERB
ejpam-5455	55	16	on	on	ADP
ejpam-5455	55	17	exploring	explore	VERB
ejpam-5455	55	18	various	various	ADJ
ejpam-5455	55	19	hybrid	hybrid	ADJ
ejpam-5455	55	20	differential	differential	ADJ
ejpam-5455	55	21	equations	equation	NOUN
ejpam-5455	55	22	(	(	PUNCT
ejpam-5455	55	23	hdes	hde	NOUN
ejpam-5455	55	24	)	)	PUNCT
ejpam-5455	55	25	.	.	PUNCT
ejpam-5455	56	1	a	a	DET
ejpam-5455	56	2	key	key	ADJ
ejpam-5455	56	3	discovery	discovery	NOUN
ejpam-5455	56	4	from	from	ADP
ejpam-5455	56	5	this	this	DET
ejpam-5455	56	6	extensive	extensive	ADJ
ejpam-5455	56	7	research	research	NOUN
ejpam-5455	56	8	is	be	AUX
ejpam-5455	56	9	that	that	SCONJ
ejpam-5455	56	10	fractional	fractional	ADJ
ejpam-5455	56	11	-	-	PUNCT
ejpam-5455	56	12	order	order	NOUN
ejpam-5455	56	13	hybrid	hybrid	ADJ
ejpam-5455	56	14	differential	differential	ADJ
ejpam-5455	56	15	equations	equation	NOUN
ejpam-5455	56	16	(	(	PUNCT
ejpam-5455	56	17	fhdes	fhde	NOUN
ejpam-5455	56	18	)	)	PUNCT
ejpam-5455	56	19	offer	offer	VERB
ejpam-5455	56	20	a	a	DET
ejpam-5455	56	21	more	more	ADV
ejpam-5455	56	22	detailed	detailed	ADJ
ejpam-5455	56	23	representation	representation	NOUN
ejpam-5455	56	24	of	of	ADP
ejpam-5455	56	25	hereditary	hereditary	ADJ
ejpam-5455	56	26	and	and	CCONJ
ejpam-5455	56	27	memory	memory	NOUN
ejpam-5455	56	28	effects	effect	NOUN
ejpam-5455	56	29	,	,	PUNCT
ejpam-5455	56	30	particularly	particularly	ADV
ejpam-5455	56	31	in	in	ADP
ejpam-5455	56	32	fields	field	NOUN
ejpam-5455	56	33	such	such	ADJ
ejpam-5455	56	34	as	as	ADP
ejpam-5455	56	35	biology	biology	NOUN
ejpam-5455	56	36	,	,	PUNCT
ejpam-5455	56	37	chemistry	chemistry	NOUN
ejpam-5455	56	38	,	,	PUNCT
ejpam-5455	56	39	and	and	CCONJ
ejpam-5455	56	40	physics	physics	NOUN
ejpam-5455	56	41	.	.	PUNCT
ejpam-5455	57	1	this	this	DET
ejpam-5455	57	2	enhanced	enhance	VERB
ejpam-5455	57	3	capability	capability	NOUN
ejpam-5455	57	4	allows	allow	VERB
ejpam-5455	57	5	fhdes	fhde	NOUN
ejpam-5455	57	6	to	to	PART
ejpam-5455	57	7	outperform	outperform	VERB
ejpam-5455	57	8	traditional	traditional	ADJ
ejpam-5455	57	9	integer	integer	NOUN
ejpam-5455	57	10	-	-	PUNCT
ejpam-5455	57	11	order	order	NOUN
ejpam-5455	57	12	hdes	hde	NOUN
ejpam-5455	57	13	,	,	PUNCT
ejpam-5455	57	14	capturing	capture	VERB
ejpam-5455	57	15	the	the	DET
ejpam-5455	57	16	interest	interest	NOUN
ejpam-5455	57	17	of	of	ADP
ejpam-5455	57	18	many	many	ADJ
ejpam-5455	57	19	scholars	scholar	NOUN
ejpam-5455	57	20	and	and	CCONJ
ejpam-5455	57	21	prompting	prompt	VERB
ejpam-5455	57	22	deeper	deep	ADJ
ejpam-5455	57	23	investigations	investigation	NOUN
ejpam-5455	57	24	into	into	ADP
ejpam-5455	57	25	their	their	PRON
ejpam-5455	57	26	properties	property	NOUN
ejpam-5455	57	27	.	.	PUNCT
ejpam-5455	58	1	building	build	VERB
ejpam-5455	58	2	on	on	ADP
ejpam-5455	58	3	the	the	DET
ejpam-5455	58	4	foundational	foundational	ADJ
ejpam-5455	58	5	work	work	NOUN
ejpam-5455	58	6	of	of	ADP
ejpam-5455	58	7	dhage	dhage	NOUN
ejpam-5455	58	8	et	et	PROPN
ejpam-5455	58	9	al	al	PROPN
ejpam-5455	58	10	.	.	PUNCT
ejpam-5455	59	1	[	[	X
ejpam-5455	59	2	11	11	NUM
ejpam-5455	59	3	,	,	PUNCT
ejpam-5455	59	4	12	12	NUM
ejpam-5455	59	5	]	]	PUNCT
ejpam-5455	59	6	,	,	PUNCT
ejpam-5455	59	7	who	who	PRON
ejpam-5455	59	8	explored	explore	VERB
ejpam-5455	59	9	the	the	DET
ejpam-5455	59	10	conditions	condition	NOUN
ejpam-5455	59	11	for	for	ADP
ejpam-5455	59	12	the	the	DET
ejpam-5455	59	13	existence	existence	NOUN
ejpam-5455	59	14	and	and	CCONJ
ejpam-5455	59	15	uniqueness	uniqueness	NOUN
ejpam-5455	59	16	of	of	ADP
ejpam-5455	59	17	solutions	solution	NOUN
ejpam-5455	59	18	in	in	ADP
ejpam-5455	59	19	fhdes	fhde	NOUN
ejpam-5455	59	20	,	,	PUNCT
ejpam-5455	59	21	baleanu	baleanu	NOUN
ejpam-5455	59	22	et	et	PROPN
ejpam-5455	59	23	al	al	PROPN
ejpam-5455	59	24	.	.	PUNCT
ejpam-5455	60	1	[	[	X
ejpam-5455	60	2	5	5	NUM
ejpam-5455	60	3	]	]	PUNCT
ejpam-5455	60	4	integrated	integrate	VERB
ejpam-5455	60	5	caputo	caputo	PROPN
ejpam-5455	60	6	fractional	fractional	ADJ
ejpam-5455	60	7	derivatives	derivative	NOUN
ejpam-5455	60	8	within	within	ADP
ejpam-5455	60	9	a	a	DET
ejpam-5455	60	10	hybrid	hybrid	ADJ
ejpam-5455	60	11	framework	framework	NOUN
ejpam-5455	60	12	.	.	PUNCT
ejpam-5455	61	1	their	their	PRON
ejpam-5455	61	2	study	study	NOUN
ejpam-5455	61	3	of	of	ADP
ejpam-5455	61	4	a	a	DET
ejpam-5455	61	5	thermostat	thermostat	NOUN
ejpam-5455	61	6	model	model	NOUN
ejpam-5455	61	7	demonstrated	demonstrate	VERB
ejpam-5455	61	8	the	the	DET
ejpam-5455	61	9	effectiveness	effectiveness	NOUN
ejpam-5455	61	10	of	of	ADP
ejpam-5455	61	11	this	this	DET
ejpam-5455	61	12	approach	approach	NOUN
ejpam-5455	61	13	in	in	ADP
ejpam-5455	61	14	revealing	reveal	VERB
ejpam-5455	61	15	complex	complex	ADJ
ejpam-5455	61	16	dynamical	dynamical	ADJ
ejpam-5455	61	17	behaviors	behavior	NOUN
ejpam-5455	61	18	.	.	PUNCT
ejpam-5455	62	1	the	the	DET
ejpam-5455	62	2	exploration	exploration	NOUN
ejpam-5455	62	3	of	of	ADP
ejpam-5455	62	4	fhdes	fhde	NOUN
ejpam-5455	62	5	has	have	AUX
ejpam-5455	62	6	since	since	SCONJ
ejpam-5455	62	7	led	lead	VERB
ejpam-5455	62	8	to	to	ADP
ejpam-5455	62	9	a	a	DET
ejpam-5455	62	10	wealth	wealth	NOUN
ejpam-5455	62	11	of	of	ADP
ejpam-5455	62	12	contributions	contribution	NOUN
ejpam-5455	62	13	,	,	PUNCT
ejpam-5455	62	14	with	with	ADP
ejpam-5455	62	15	researchers	researcher	NOUN
ejpam-5455	62	16	examining	examine	VERB
ejpam-5455	62	17	various	various	ADJ
ejpam-5455	62	18	derivatives	derivative	NOUN
ejpam-5455	62	19	such	such	ADJ
ejpam-5455	62	20	as	as	ADP
ejpam-5455	62	21	the	the	DET
ejpam-5455	62	22	hadamard	hadamard	ADJ
ejpam-5455	62	23	derivative	derivative	NOUN
ejpam-5455	63	1	[	[	X
ejpam-5455	63	2	1	1	NUM
ejpam-5455	63	3	]	]	PUNCT
ejpam-5455	63	4	,	,	PUNCT
ejpam-5455	63	5	the	the	DET
ejpam-5455	63	6	riemann	riemann	PROPN
ejpam-5455	63	7	derivative	derivative	NOUN
ejpam-5455	64	1	[	[	X
ejpam-5455	64	2	32	32	NUM
ejpam-5455	64	3	]	]	PUNCT
ejpam-5455	64	4	,	,	PUNCT
ejpam-5455	64	5	the	the	DET
ejpam-5455	64	6	hilfer	hilfer	NOUN
ejpam-5455	64	7	derivative	derivative	NOUN
ejpam-5455	64	8	[	[	X
ejpam-5455	64	9	30	30	NUM
ejpam-5455	64	10	]	]	PUNCT
ejpam-5455	64	11	,	,	PUNCT
ejpam-5455	64	12	and	and	CCONJ
ejpam-5455	64	13	the	the	DET
ejpam-5455	64	14	abc	abc	PROPN
ejpam-5455	64	15	derivative	derivative	NOUN
ejpam-5455	65	1	[	[	X
ejpam-5455	65	2	3	3	NUM
ejpam-5455	65	3	,	,	PUNCT
ejpam-5455	65	4	18	18	NUM
ejpam-5455	65	5	,	,	PUNCT
ejpam-5455	65	6	20	20	NUM
ejpam-5455	65	7	,	,	PUNCT
ejpam-5455	65	8	28	28	NUM
ejpam-5455	65	9	,	,	PUNCT
ejpam-5455	65	10	29	29	NUM
ejpam-5455	65	11	,	,	PUNCT
ejpam-5455	65	12	31	31	NUM
ejpam-5455	65	13	]	]	PUNCT
ejpam-5455	65	14	.	.	PUNCT
ejpam-5455	66	1	additionally	additionally	ADV
ejpam-5455	66	2	,	,	PUNCT
ejpam-5455	66	3	innovative	innovative	ADJ
ejpam-5455	66	4	formulations	formulation	NOUN
ejpam-5455	66	5	like	like	ADP
ejpam-5455	66	6	the	the	DET
ejpam-5455	66	7	mabc	mabc	PROPN
ejpam-5455	66	8	derivative	derivative	NOUN
ejpam-5455	66	9	have	have	AUX
ejpam-5455	66	10	been	be	AUX
ejpam-5455	66	11	proposed	propose	VERB
ejpam-5455	66	12	[	[	X
ejpam-5455	66	13	19	19	NUM
ejpam-5455	66	14	,	,	PUNCT
ejpam-5455	66	15	21	21	NUM
ejpam-5455	66	16	]	]	PUNCT
ejpam-5455	66	17	,	,	PUNCT
ejpam-5455	66	18	further	far	ADV
ejpam-5455	66	19	broadening	broaden	VERB
ejpam-5455	66	20	the	the	DET
ejpam-5455	66	21	scope	scope	NOUN
ejpam-5455	66	22	of	of	ADP
ejpam-5455	66	23	fractional	fractional	ADJ
ejpam-5455	66	24	calculus	calculus	NOUN
ejpam-5455	66	25	in	in	ADP
ejpam-5455	66	26	the	the	DET
ejpam-5455	66	27	context	context	NOUN
ejpam-5455	66	28	of	of	ADP
ejpam-5455	66	29	hdes	hde	NOUN
ejpam-5455	66	30	.	.	PUNCT
ejpam-5455	67	1	despite	despite	SCONJ
ejpam-5455	67	2	the	the	DET
ejpam-5455	67	3	growing	grow	VERB
ejpam-5455	67	4	interest	interest	NOUN
ejpam-5455	67	5	in	in	ADP
ejpam-5455	67	6	fractional	fractional	ADJ
ejpam-5455	67	7	calculus	calculus	NOUN
ejpam-5455	67	8	,	,	PUNCT
ejpam-5455	67	9	the	the	DET
ejpam-5455	67	10	application	application	NOUN
ejpam-5455	67	11	of	of	ADP
ejpam-5455	67	12	the	the	DET
ejpam-5455	67	13	mabc	mabc	ADJ
ejpam-5455	67	14	fractional	fractional	ADJ
ejpam-5455	67	15	derivative	derivative	NOUN
ejpam-5455	67	16	in	in	ADP
ejpam-5455	67	17	fhdes	fhde	NOUN
ejpam-5455	67	18	involving	involve	VERB
ejpam-5455	67	19	the	the	DET
ejpam-5455	67	20	p	p	PROPN
ejpam-5455	67	21	-	-	PUNCT
ejpam-5455	67	22	laplacian	laplacian	ADJ
ejpam-5455	67	23	operator	operator	NOUN
ejpam-5455	67	24	with	with	ADP
ejpam-5455	67	25	ivps	ivps	PROPN
ejpam-5455	67	26	remains	remain	VERB
ejpam-5455	67	27	largely	largely	ADV
ejpam-5455	67	28	unexplored	unexplored	ADJ
ejpam-5455	67	29	in	in	ADP
ejpam-5455	67	30	the	the	DET
ejpam-5455	67	31	current	current	ADJ
ejpam-5455	67	32	literature	literature	NOUN
ejpam-5455	67	33	.	.	PUNCT
ejpam-5455	68	1	this	this	DET
ejpam-5455	68	2	intriguing	intriguing	ADJ
ejpam-5455	68	3	gap	gap	NOUN
ejpam-5455	68	4	presents	present	VERB
ejpam-5455	68	5	a	a	DET
ejpam-5455	68	6	unique	unique	ADJ
ejpam-5455	68	7	opportunity	opportunity	NOUN
ejpam-5455	68	8	for	for	ADP
ejpam-5455	68	9	further	further	ADJ
ejpam-5455	68	10	investigation	investigation	NOUN
ejpam-5455	68	11	and	and	CCONJ
ejpam-5455	68	12	serves	serve	VERB
ejpam-5455	68	13	as	as	ADP
ejpam-5455	68	14	the	the	DET
ejpam-5455	68	15	primary	primary	ADJ
ejpam-5455	68	16	motivation	motivation	NOUN
ejpam-5455	68	17	for	for	ADP
ejpam-5455	68	18	this	this	DET
ejpam-5455	68	19	work	work	NOUN
ejpam-5455	68	20	.	.	PUNCT
ejpam-5455	69	1	this	this	DET
ejpam-5455	69	2	work	work	NOUN
ejpam-5455	69	3	makes	make	VERB
ejpam-5455	69	4	the	the	DET
ejpam-5455	69	5	following	follow	VERB
ejpam-5455	69	6	key	key	ADJ
ejpam-5455	69	7	contributions	contribution	NOUN
ejpam-5455	69	8	to	to	ADP
ejpam-5455	69	9	the	the	DET
ejpam-5455	69	10	field	field	NOUN
ejpam-5455	69	11	.	.	PUNCT
ejpam-5455	70	1	(	(	PUNCT
ejpam-5455	70	2	i	i	NOUN
ejpam-5455	70	3	)	)	PUNCT
ejpam-5455	70	4	this	this	DET
ejpam-5455	70	5	research	research	NOUN
ejpam-5455	70	6	represents	represent	VERB
ejpam-5455	70	7	the	the	DET
ejpam-5455	70	8	first	first	ADJ
ejpam-5455	70	9	known	know	VERB
ejpam-5455	70	10	attempt	attempt	NOUN
ejpam-5455	70	11	to	to	PART
ejpam-5455	70	12	address	address	VERB
ejpam-5455	70	13	mabc	mabc	NOUN
ejpam-5455	70	14	-	-	PUNCT
ejpam-5455	70	15	hfides	hfide	NOUN
ejpam-5455	70	16	in	in	ADP
ejpam-5455	70	17	conjunction	conjunction	NOUN
ejpam-5455	70	18	with	with	ADP
ejpam-5455	70	19	the	the	DET
ejpam-5455	70	20	p	p	ADJ
ejpam-5455	70	21	-	-	PUNCT
ejpam-5455	70	22	laplacian	laplacian	ADJ
ejpam-5455	70	23	operator	operator	NOUN
ejpam-5455	70	24	for	for	ADP
ejpam-5455	70	25	the	the	DET
ejpam-5455	70	26	system	system	NOUN
ejpam-5455	70	27	described	describe	VERB
ejpam-5455	70	28	in	in	ADP
ejpam-5455	70	29	(	(	PUNCT
ejpam-5455	70	30	1	1	NUM
ejpam-5455	70	31	)	)	PUNCT
ejpam-5455	70	32	.	.	PUNCT
ejpam-5455	71	1	it	it	PRON
ejpam-5455	71	2	thoroughly	thoroughly	ADV
ejpam-5455	71	3	examines	examine	VERB
ejpam-5455	71	4	the	the	DET
ejpam-5455	71	5	existence	existence	NOUN
ejpam-5455	71	6	,	,	PUNCT
ejpam-5455	71	7	uniqueness	uniqueness	NOUN
ejpam-5455	71	8	,	,	PUNCT
ejpam-5455	71	9	and	and	CCONJ
ejpam-5455	71	10	stability	stability	NOUN
ejpam-5455	71	11	of	of	ADP
ejpam-5455	71	12	the	the	DET
ejpam-5455	71	13	proposed	propose	VERB
ejpam-5455	71	14	system	system	NOUN
ejpam-5455	71	15	.	.	PUNCT
ejpam-5455	72	1	m.	m.	NOUN
ejpam-5455	72	2	m.	m.	PROPN
ejpam-5455	72	3	arjunan	arjunan	PROPN
ejpam-5455	72	4	/	/	SYM
ejpam-5455	72	5	eur	eur	PROPN
ejpam-5455	72	6	.	.	PUNCT
ejpam-5455	73	1	j.	j.	PROPN
ejpam-5455	73	2	pure	pure	PROPN
ejpam-5455	73	3	appl	appl	PROPN
ejpam-5455	73	4	.	.	PROPN
ejpam-5455	73	5	math	math	PROPN
ejpam-5455	73	6	,	,	PUNCT
ejpam-5455	73	7	17	17	NUM
ejpam-5455	73	8	(	(	PUNCT
ejpam-5455	73	9	4	4	NUM
ejpam-5455	73	10	)	)	PUNCT
ejpam-5455	73	11	(	(	PUNCT
ejpam-5455	73	12	2024	2024	NUM
ejpam-5455	73	13	)	)	PUNCT
ejpam-5455	73	14	,	,	PUNCT
ejpam-5455	73	15	4071	4071	NUM
ejpam-5455	73	16	-	-	SYM
ejpam-5455	73	17	4092	4092	NUM
ejpam-5455	73	18	4074	4074	NUM
ejpam-5455	73	19	(	(	PUNCT
ejpam-5455	73	20	ii	ii	NOUN
ejpam-5455	73	21	)	)	PUNCT
ejpam-5455	73	22	by	by	ADP
ejpam-5455	73	23	utilizing	utilize	VERB
ejpam-5455	73	24	the	the	DET
ejpam-5455	73	25	properties	property	NOUN
ejpam-5455	73	26	of	of	ADP
ejpam-5455	73	27	the	the	DET
ejpam-5455	73	28	mabc	mabc	PROPN
ejpam-5455	73	29	derivative	derivative	NOUN
ejpam-5455	74	1	,	,	PUNCT
ejpam-5455	74	2	we	we	PRON
ejpam-5455	74	3	have	have	AUX
ejpam-5455	74	4	derived	derive	VERB
ejpam-5455	74	5	the	the	DET
ejpam-5455	74	6	solution	solution	NOUN
ejpam-5455	74	7	for	for	ADP
ejpam-5455	74	8	the	the	DET
ejpam-5455	74	9	system	system	NOUN
ejpam-5455	74	10	outlined	outline	VERB
ejpam-5455	74	11	in	in	ADP
ejpam-5455	74	12	(	(	PUNCT
ejpam-5455	74	13	1	1	NUM
ejpam-5455	74	14	)	)	PUNCT
ejpam-5455	74	15	,	,	PUNCT
ejpam-5455	74	16	as	as	SCONJ
ejpam-5455	74	17	detailed	detailed	ADJ
ejpam-5455	74	18	in	in	ADP
ejpam-5455	74	19	lemma	lemma	PROPN
ejpam-5455	74	20	2	2	NUM
ejpam-5455	74	21	.	.	PUNCT
ejpam-5455	74	22	(	(	PUNCT
ejpam-5455	74	23	iv	iv	X
ejpam-5455	74	24	)	)	PUNCT
ejpam-5455	74	25	expanding	expand	VERB
ejpam-5455	74	26	upon	upon	SCONJ
ejpam-5455	74	27	the	the	DET
ejpam-5455	74	28	seminal	seminal	ADJ
ejpam-5455	74	29	contributions	contribution	NOUN
ejpam-5455	74	30	of	of	ADP
ejpam-5455	74	31	previous	previous	ADJ
ejpam-5455	74	32	research	research	NOUN
ejpam-5455	74	33	[	[	X
ejpam-5455	74	34	17	17	NUM
ejpam-5455	74	35	,	,	PUNCT
ejpam-5455	74	36	20	20	NUM
ejpam-5455	74	37	,	,	PUNCT
ejpam-5455	74	38	21	21	NUM
ejpam-5455	74	39	,	,	PUNCT
ejpam-5455	74	40	31	31	NUM
ejpam-5455	74	41	]	]	PUNCT
ejpam-5455	74	42	,	,	PUNCT
ejpam-5455	74	43	this	this	DET
ejpam-5455	74	44	study	study	NOUN
ejpam-5455	74	45	offers	offer	VERB
ejpam-5455	74	46	novel	novel	ADJ
ejpam-5455	74	47	insights	insight	NOUN
ejpam-5455	74	48	and	and	CCONJ
ejpam-5455	74	49	significantly	significantly	ADV
ejpam-5455	74	50	extends	extend	VERB
ejpam-5455	74	51	the	the	DET
ejpam-5455	74	52	applicability	applicability	NOUN
ejpam-5455	74	53	of	of	ADP
ejpam-5455	74	54	prior	prior	ADJ
ejpam-5455	74	55	findings	finding	NOUN
ejpam-5455	74	56	.	.	PUNCT
ejpam-5455	75	1	this	this	DET
ejpam-5455	75	2	paper	paper	NOUN
ejpam-5455	75	3	is	be	AUX
ejpam-5455	75	4	organized	organize	VERB
ejpam-5455	75	5	in	in	ADP
ejpam-5455	75	6	a	a	DET
ejpam-5455	75	7	carefully	carefully	ADV
ejpam-5455	75	8	structured	structure	VERB
ejpam-5455	75	9	way	way	NOUN
ejpam-5455	75	10	.	.	PUNCT
ejpam-5455	76	1	section	section	NOUN
ejpam-5455	76	2	2	2	NUM
ejpam-5455	76	3	establishes	establish	VERB
ejpam-5455	76	4	the	the	DET
ejpam-5455	76	5	necessary	necessary	ADJ
ejpam-5455	76	6	foundation	foundation	NOUN
ejpam-5455	76	7	by	by	ADP
ejpam-5455	76	8	providing	provide	VERB
ejpam-5455	76	9	the	the	DET
ejpam-5455	76	10	reader	reader	NOUN
ejpam-5455	76	11	with	with	ADP
ejpam-5455	76	12	essential	essential	ADJ
ejpam-5455	76	13	background	background	NOUN
ejpam-5455	76	14	information	information	NOUN
ejpam-5455	76	15	.	.	PUNCT
ejpam-5455	77	1	this	this	PRON
ejpam-5455	77	2	includes	include	VERB
ejpam-5455	77	3	the	the	DET
ejpam-5455	77	4	definition	definition	NOUN
ejpam-5455	77	5	of	of	ADP
ejpam-5455	77	6	the	the	DET
ejpam-5455	77	7	mabc	mabc	ADJ
ejpam-5455	77	8	fractional	fractional	ADJ
ejpam-5455	77	9	derivative	derivative	ADJ
ejpam-5455	77	10	,	,	PUNCT
ejpam-5455	77	11	relevant	relevant	ADJ
ejpam-5455	77	12	results	result	NOUN
ejpam-5455	77	13	,	,	PUNCT
ejpam-5455	77	14	and	and	CCONJ
ejpam-5455	77	15	the	the	DET
ejpam-5455	77	16	fundamental	fundamental	ADJ
ejpam-5455	77	17	concept	concept	NOUN
ejpam-5455	77	18	of	of	ADP
ejpam-5455	77	19	fixed	fix	VERB
ejpam-5455	77	20	-	-	PUNCT
ejpam-5455	77	21	point	point	NOUN
ejpam-5455	77	22	theory	theory	NOUN
ejpam-5455	77	23	that	that	PRON
ejpam-5455	77	24	underpins	underpin	VERB
ejpam-5455	77	25	our	our	PRON
ejpam-5455	77	26	analysis	analysis	NOUN
ejpam-5455	77	27	.	.	PUNCT
ejpam-5455	78	1	section	section	NOUN
ejpam-5455	78	2	3	3	NUM
ejpam-5455	78	3	addresses	address	NOUN
ejpam-5455	78	4	the	the	DET
ejpam-5455	78	5	core	core	ADJ
ejpam-5455	78	6	issues	issue	NOUN
ejpam-5455	78	7	of	of	ADP
ejpam-5455	78	8	existence	existence	NOUN
ejpam-5455	78	9	and	and	CCONJ
ejpam-5455	78	10	uniqueness	uniqueness	NOUN
ejpam-5455	78	11	of	of	ADP
ejpam-5455	78	12	solutions	solution	NOUN
ejpam-5455	78	13	for	for	ADP
ejpam-5455	78	14	system	system	NOUN
ejpam-5455	78	15	(	(	PUNCT
ejpam-5455	78	16	1	1	NUM
ejpam-5455	78	17	)	)	PUNCT
ejpam-5455	78	18	.	.	PUNCT
ejpam-5455	79	1	we	we	PRON
ejpam-5455	79	2	effectively	effectively	ADV
ejpam-5455	79	3	utilize	utilize	VERB
ejpam-5455	79	4	both	both	DET
ejpam-5455	79	5	the	the	DET
ejpam-5455	79	6	banach	banach	NOUN
ejpam-5455	79	7	and	and	CCONJ
ejpam-5455	79	8	krasnoselskii	krasnoselskii	PROPN
ejpam-5455	79	9	fpts	fpt	NOUN
ejpam-5455	79	10	to	to	PART
ejpam-5455	79	11	accomplish	accomplish	VERB
ejpam-5455	79	12	these	these	DET
ejpam-5455	79	13	objectives	objective	NOUN
ejpam-5455	79	14	.	.	PUNCT
ejpam-5455	80	1	to	to	PART
ejpam-5455	80	2	deepen	deepen	VERB
ejpam-5455	80	3	our	our	PRON
ejpam-5455	80	4	understanding	understanding	NOUN
ejpam-5455	80	5	,	,	PUNCT
ejpam-5455	80	6	section	section	NOUN
ejpam-5455	80	7	4	4	NUM
ejpam-5455	80	8	thoroughly	thoroughly	ADV
ejpam-5455	80	9	examines	examine	VERB
ejpam-5455	80	10	the	the	DET
ejpam-5455	80	11	stability	stability	NOUN
ejpam-5455	80	12	properties	property	NOUN
ejpam-5455	80	13	of	of	ADP
ejpam-5455	80	14	the	the	DET
ejpam-5455	80	15	system	system	NOUN
ejpam-5455	80	16	,	,	PUNCT
ejpam-5455	80	17	highlighting	highlight	VERB
ejpam-5455	80	18	its	its	PRON
ejpam-5455	80	19	behavior	behavior	NOUN
ejpam-5455	80	20	in	in	ADP
ejpam-5455	80	21	response	response	NOUN
ejpam-5455	80	22	to	to	ADP
ejpam-5455	80	23	perturbations	perturbation	NOUN
ejpam-5455	80	24	.	.	PUNCT
ejpam-5455	81	1	finally	finally	ADV
ejpam-5455	81	2	,	,	PUNCT
ejpam-5455	81	3	section	section	NOUN
ejpam-5455	81	4	5	5	NUM
ejpam-5455	81	5	offers	offer	VERB
ejpam-5455	81	6	a	a	DET
ejpam-5455	81	7	numerical	numerical	ADJ
ejpam-5455	81	8	example	example	NOUN
ejpam-5455	81	9	to	to	PART
ejpam-5455	81	10	demonstrate	demonstrate	VERB
ejpam-5455	81	11	the	the	DET
ejpam-5455	81	12	application	application	NOUN
ejpam-5455	81	13	and	and	CCONJ
ejpam-5455	81	14	importance	importance	NOUN
ejpam-5455	81	15	of	of	ADP
ejpam-5455	81	16	our	our	PRON
ejpam-5455	81	17	main	main	ADJ
ejpam-5455	81	18	findings	finding	NOUN
ejpam-5455	81	19	.	.	PUNCT
ejpam-5455	82	1	2	2	X
ejpam-5455	82	2	.	.	NUM
ejpam-5455	82	3	preliminaries	preliminary	NOUN
ejpam-5455	82	4	and	and	CCONJ
ejpam-5455	82	5	hypotheses	hypothesis	NOUN
ejpam-5455	82	6	in	in	ADP
ejpam-5455	82	7	this	this	DET
ejpam-5455	82	8	section	section	NOUN
ejpam-5455	82	9	,	,	PUNCT
ejpam-5455	82	10	we	we	PRON
ejpam-5455	82	11	provide	provide	VERB
ejpam-5455	82	12	a	a	DET
ejpam-5455	82	13	comprehensive	comprehensive	ADJ
ejpam-5455	82	14	overview	overview	NOUN
ejpam-5455	82	15	of	of	ADP
ejpam-5455	82	16	the	the	DET
ejpam-5455	82	17	caputo	caputo	NOUN
ejpam-5455	82	18	-	-	PUNCT
ejpam-5455	82	19	type	type	NOUN
ejpam-5455	82	20	mittag	mittag	ADJ
ejpam-5455	82	21	-	-	PUNCT
ejpam-5455	82	22	leffler	leffler	NOUN
ejpam-5455	82	23	fractional	fractional	ADJ
ejpam-5455	82	24	derivative	derivative	ADJ
ejpam-5455	82	25	(	(	PUNCT
ejpam-5455	82	26	cmlfd	cmlfd	NOUN
ejpam-5455	82	27	)	)	PUNCT
ejpam-5455	82	28	and	and	CCONJ
ejpam-5455	82	29	integral	integral	ADJ
ejpam-5455	82	30	operator	operator	NOUN
ejpam-5455	82	31	and	and	CCONJ
ejpam-5455	82	32	several	several	ADJ
ejpam-5455	82	33	fundamental	fundamental	ADJ
ejpam-5455	82	34	properties	property	NOUN
ejpam-5455	82	35	.	.	PUNCT
ejpam-5455	83	1	definition	definition	NOUN
ejpam-5455	83	2	1	1	NUM
ejpam-5455	83	3	.	.	PUNCT
ejpam-5455	84	1	[	[	X
ejpam-5455	84	2	4	4	X
ejpam-5455	84	3	]	]	PUNCT
ejpam-5455	84	4	let	let	VERB
ejpam-5455	84	5	0	0	NUM
ejpam-5455	84	6	<	<	X
ejpam-5455	84	7	ρ	ρ	X
ejpam-5455	84	8	<	<	X
ejpam-5455	84	9	1	1	NUM
ejpam-5455	84	10	and	and	CCONJ
ejpam-5455	84	11	y	y	PROPN
ejpam-5455	84	12	∈	∈	PROPN
ejpam-5455	84	13	h1(0	h1(0	PROPN
ejpam-5455	84	14	,	,	PUNCT
ejpam-5455	84	15	z	z	PROPN
ejpam-5455	84	16	)	)	PUNCT
ejpam-5455	84	17	,	,	PUNCT
ejpam-5455	84	18	where	where	SCONJ
ejpam-5455	84	19	z	z	NOUN
ejpam-5455	84	20	>	>	X
ejpam-5455	84	21	0	0	PROPN
ejpam-5455	84	22	,	,	PUNCT
ejpam-5455	84	23	the	the	DET
ejpam-5455	84	24	cmlfd	cmlfd	NOUN
ejpam-5455	84	25	of	of	ADP
ejpam-5455	84	26	order	order	NOUN
ejpam-5455	84	27	ρ	ρ	PROPN
ejpam-5455	84	28	of	of	ADP
ejpam-5455	84	29	y	y	PROPN
ejpam-5455	84	30	is	be	AUX
ejpam-5455	84	31	defined	define	VERB
ejpam-5455	84	32	as(abcdρ	as(abcdρ	NOUN
ejpam-5455	84	33	0+y	0+y	NUM
ejpam-5455	84	34	)	)	PUNCT
ejpam-5455	84	35	(	(	PUNCT
ejpam-5455	84	36	7	7	X
ejpam-5455	84	37	)	)	PUNCT
ejpam-5455	84	38	=	=	SYM
ejpam-5455	84	39	b(ρ	b(ρ	PROPN
ejpam-5455	84	40	)	)	PUNCT
ejpam-5455	84	41	1−	1−	NUM
ejpam-5455	84	42	ρ	ρ	NUM
ejpam-5455	84	43	∫	∫	PROPN
ejpam-5455	84	44	7	7	NUM
ejpam-5455	84	45	0	0	NUM
ejpam-5455	84	46	eρ	eρ	PROPN
ejpam-5455	84	47	(	(	PUNCT
ejpam-5455	84	48	−µρ(7	−µρ(7	X
ejpam-5455	84	49	−	−	NOUN
ejpam-5455	84	50	σ)ρ	σ)ρ	NOUN
ejpam-5455	84	51	)	)	PUNCT
ejpam-5455	84	52	y′(σ)dσ	y′(σ)dσ	NOUN
ejpam-5455	84	53	,	,	PUNCT
ejpam-5455	84	54	0	0	PUNCT
ejpam-5455	84	55	<	<	X
ejpam-5455	84	56	7	7	NUM
ejpam-5455	84	57	<	<	X
ejpam-5455	84	58	z	z	NOUN
ejpam-5455	84	59	(	(	PUNCT
ejpam-5455	84	60	2	2	NUM
ejpam-5455	84	61	)	)	PUNCT
ejpam-5455	84	62	where	where	SCONJ
ejpam-5455	84	63	µρ	µρ	ADV
ejpam-5455	84	64	=	=	SYM
ejpam-5455	84	65	ρ	ρ	PROPN
ejpam-5455	84	66	1−	1−	NUM
ejpam-5455	84	67	ρ	ρ	NOUN
ejpam-5455	84	68	,	,	PUNCT
ejpam-5455	84	69	b(ρ	b(ρ	PROPN
ejpam-5455	84	70	)	)	PUNCT
ejpam-5455	84	71	=	=	SYM
ejpam-5455	85	1	1	1	NUM
ejpam-5455	85	2	−	−	PROPN
ejpam-5455	85	3	ρ	ρ	PROPN
ejpam-5455	85	4	+	+	PROPN
ejpam-5455	85	5	ρ	ρ	PROPN
ejpam-5455	85	6	γ(ρ	γ(ρ	PROPN
ejpam-5455	85	7	)	)	PUNCT
ejpam-5455	85	8	is	be	AUX
ejpam-5455	85	9	a	a	DET
ejpam-5455	85	10	normalization	normalization	NOUN
ejpam-5455	85	11	function	function	NOUN
ejpam-5455	85	12	satisfying	satisfy	VERB
ejpam-5455	85	13	b(0	b(0	NOUN
ejpam-5455	85	14	)	)	PUNCT
ejpam-5455	85	15	=	=	SYM
ejpam-5455	85	16	b(1	b(1	PROPN
ejpam-5455	85	17	)	)	PUNCT
ejpam-5455	85	18	=	=	NOUN
ejpam-5455	86	1	1	1	X
ejpam-5455	86	2	.	.	PUNCT
ejpam-5455	86	3	let	let	VERB
ejpam-5455	86	4	eρ	eρ	PART
ejpam-5455	86	5	denote	denote	VERB
ejpam-5455	86	6	the	the	DET
ejpam-5455	86	7	ml	ml	X
ejpam-5455	86	8	function	function	NOUN
ejpam-5455	86	9	,	,	PUNCT
ejpam-5455	86	10	defined	define	VERB
ejpam-5455	86	11	by	by	ADP
ejpam-5455	86	12	eρ(z	eρ(z	ADJ
ejpam-5455	86	13	)	)	PUNCT
ejpam-5455	86	14	=	=	PUNCT
ejpam-5455	87	1	∞∑	∞∑	NUM
ejpam-5455	87	2	k=0	k=0	PROPN
ejpam-5455	87	3	zk	zk	ADP
ejpam-5455	87	4	γ(ρk	γ(ρk	PROPN
ejpam-5455	87	5	+	+	CCONJ
ejpam-5455	87	6	1	1	NUM
ejpam-5455	87	7	)	)	PUNCT
ejpam-5455	87	8	,	,	PUNCT
ejpam-5455	87	9	ρ	ρ	PROPN
ejpam-5455	87	10	>	>	X
ejpam-5455	87	11	0	0	NUM
ejpam-5455	87	12	,	,	PUNCT
ejpam-5455	87	13	z	z	PROPN
ejpam-5455	87	14	∈	∈	PROPN
ejpam-5455	87	15	c	c	PROPN
ejpam-5455	87	16	h1(0	h1(0	PROPN
ejpam-5455	87	17	,	,	PUNCT
ejpam-5455	87	18	z	z	NOUN
ejpam-5455	87	19	)	)	PUNCT
ejpam-5455	87	20	=	=	PRON
ejpam-5455	87	21	{	{	PUNCT
ejpam-5455	87	22	v	v	NUM
ejpam-5455	87	23	∈	∈	PROPN
ejpam-5455	87	24	l2(0	l2(0	NOUN
ejpam-5455	87	25	,	,	PUNCT
ejpam-5455	87	26	z	z	NOUN
ejpam-5455	87	27	)	)	PUNCT
ejpam-5455	87	28	|	|	ADV
ejpam-5455	87	29	v′	v′	PROPN
ejpam-5455	87	30	∈	∈	PROPN
ejpam-5455	87	31	l2(0	l2(0	NOUN
ejpam-5455	87	32	,	,	PUNCT
ejpam-5455	87	33	z	z	NOUN
ejpam-5455	87	34	)	)	PUNCT
ejpam-5455	87	35	}	}	PUNCT
ejpam-5455	87	36	.	.	PUNCT
ejpam-5455	88	1	additionally	additionally	ADV
ejpam-5455	88	2	,	,	PUNCT
ejpam-5455	88	3	lm	lm	PROPN
ejpam-5455	88	4	denotes	denote	VERB
ejpam-5455	88	5	the	the	DET
ejpam-5455	88	6	space	space	NOUN
ejpam-5455	88	7	of	of	ADP
ejpam-5455	88	8	functions	function	NOUN
ejpam-5455	88	9	for	for	ADP
ejpam-5455	88	10	which	which	PRON
ejpam-5455	88	11	the	the	DET
ejpam-5455	88	12	m	m	NOUN
ejpam-5455	88	13	-	-	PUNCT
ejpam-5455	88	14	th	th	VERB
ejpam-5455	88	15	power	power	NOUN
ejpam-5455	88	16	of	of	ADP
ejpam-5455	88	17	their	their	PRON
ejpam-5455	88	18	absolute	absolute	ADJ
ejpam-5455	88	19	value	value	NOUN
ejpam-5455	88	20	is	be	AUX
ejpam-5455	88	21	lebesgue	lebesgue	NOUN
ejpam-5455	88	22	integrable	integrable	ADJ
ejpam-5455	88	23	.	.	PUNCT
ejpam-5455	89	1	definition	definition	NOUN
ejpam-5455	89	2	2	2	NUM
ejpam-5455	89	3	.	.	PUNCT
ejpam-5455	90	1	[	[	X
ejpam-5455	90	2	4	4	X
ejpam-5455	90	3	]	]	PUNCT
ejpam-5455	90	4	let	let	VERB
ejpam-5455	90	5	0	0	NUM
ejpam-5455	90	6	<	<	X
ejpam-5455	90	7	ρ	ρ	X
ejpam-5455	90	8	<	<	X
ejpam-5455	90	9	1	1	NUM
ejpam-5455	90	10	and	and	CCONJ
ejpam-5455	90	11	y	y	PROPN
ejpam-5455	90	12	∈	∈	PROPN
ejpam-5455	90	13	l1(0	l1(0	PROPN
ejpam-5455	90	14	,	,	PUNCT
ejpam-5455	90	15	z	z	PROPN
ejpam-5455	90	16	)	)	PUNCT
ejpam-5455	90	17	,	,	PUNCT
ejpam-5455	90	18	where	where	SCONJ
ejpam-5455	90	19	z	z	NOUN
ejpam-5455	90	20	>	>	X
ejpam-5455	90	21	0	0	PROPN
ejpam-5455	90	22	,	,	PUNCT
ejpam-5455	90	23	the	the	DET
ejpam-5455	90	24	fractional	fractional	ADJ
ejpam-5455	90	25	integral	integral	ADJ
ejpam-5455	90	26	associated	associate	VERB
ejpam-5455	90	27	with	with	ADP
ejpam-5455	90	28	the	the	DET
ejpam-5455	90	29	above	above	ADJ
ejpam-5455	90	30	cmlfd	cmlfd	NOUN
ejpam-5455	90	31	of	of	ADP
ejpam-5455	90	32	order	order	NOUN
ejpam-5455	90	33	ρ	ρ	PROPN
ejpam-5455	90	34	of	of	ADP
ejpam-5455	90	35	y	y	PROPN
ejpam-5455	90	36	is	be	AUX
ejpam-5455	90	37	described	describe	VERB
ejpam-5455	90	38	as:(abiρ0+y	as:(abiρ0+y	PROPN
ejpam-5455	90	39	)	)	PUNCT
ejpam-5455	90	40	(	(	PUNCT
ejpam-5455	90	41	7	7	X
ejpam-5455	90	42	)	)	PUNCT
ejpam-5455	90	43	=	=	SYM
ejpam-5455	90	44	1−	1−	NUM
ejpam-5455	90	45	ρ	ρ	NUM
ejpam-5455	90	46	b(ρ	b(ρ	PROPN
ejpam-5455	90	47	)	)	PUNCT
ejpam-5455	90	48	y(7	y(7	PROPN
ejpam-5455	90	49	)	)	PUNCT
ejpam-5455	91	1	+	+	CCONJ
ejpam-5455	91	2	ρ	ρ	PROPN
ejpam-5455	91	3	b(ρ	b(ρ	PROPN
ejpam-5455	91	4	)	)	PUNCT
ejpam-5455	91	5	(	(	PUNCT
ejpam-5455	91	6	rliρ0+y	rliρ0+y	PUNCT
ejpam-5455	91	7	)	)	PUNCT
ejpam-5455	91	8	(	(	PUNCT
ejpam-5455	91	9	7	7	NUM
ejpam-5455	91	10	)	)	PUNCT
ejpam-5455	91	11	,	,	PUNCT
ejpam-5455	91	12	0	0	PUNCT
ejpam-5455	92	1	<	<	X
ejpam-5455	92	2	7	7	NUM
ejpam-5455	92	3	<	<	X
ejpam-5455	92	4	z	z	X
ejpam-5455	92	5	(	(	PUNCT
ejpam-5455	92	6	3	3	NUM
ejpam-5455	92	7	)	)	PUNCT
ejpam-5455	92	8	where	where	SCONJ
ejpam-5455	92	9	rliρ0	rliρ0	PROPN
ejpam-5455	92	10	+	+	CCONJ
ejpam-5455	92	11	denotes	denote	VERB
ejpam-5455	92	12	the	the	DET
ejpam-5455	92	13	riemann	riemann	PROPN
ejpam-5455	92	14	-	-	PUNCT
ejpam-5455	92	15	liouville	liouville	VERB
ejpam-5455	92	16	fractional	fractional	ADJ
ejpam-5455	92	17	integral	integral	ADJ
ejpam-5455	92	18	operator	operator	NOUN
ejpam-5455	92	19	,	,	PUNCT
ejpam-5455	92	20	given	give	VERB
ejpam-5455	92	21	by	by	ADP
ejpam-5455	92	22	:	:	PUNCT
ejpam-5455	92	23	rliρ0+y(7	rliρ0+y(7	ADJ
ejpam-5455	92	24	)	)	PUNCT
ejpam-5455	93	1	=	=	SYM
ejpam-5455	93	2	1	1	NUM
ejpam-5455	93	3	γ(ρ	γ(ρ	PROPN
ejpam-5455	93	4	)	)	PUNCT
ejpam-5455	93	5	∫	∫	PROPN
ejpam-5455	94	1	7	7	NUM
ejpam-5455	94	2	0	0	NUM
ejpam-5455	94	3	(	(	PUNCT
ejpam-5455	94	4	7	7	NUM
ejpam-5455	94	5	−	−	NOUN
ejpam-5455	94	6	σ)ρ−1y(σ)dσ	σ)ρ−1y(σ)dσ	NOUN
ejpam-5455	94	7	,	,	PUNCT
ejpam-5455	94	8	7	7	NUM
ejpam-5455	94	9	>	>	SYM
ejpam-5455	94	10	0	0	NUM
ejpam-5455	94	11	.	.	PUNCT
ejpam-5455	95	1	(	(	PUNCT
ejpam-5455	95	2	4	4	X
ejpam-5455	95	3	)	)	PUNCT
ejpam-5455	95	4	m.	m.	NOUN
ejpam-5455	95	5	m.	m.	NOUN
ejpam-5455	95	6	arjunan	arjunan	PROPN
ejpam-5455	95	7	/	/	SYM
ejpam-5455	95	8	eur	eur	PROPN
ejpam-5455	95	9	.	.	PUNCT
ejpam-5455	96	1	j.	j.	PROPN
ejpam-5455	96	2	pure	pure	PROPN
ejpam-5455	96	3	appl	appl	PROPN
ejpam-5455	96	4	.	.	PROPN
ejpam-5455	96	5	math	math	PROPN
ejpam-5455	96	6	,	,	PUNCT
ejpam-5455	96	7	17	17	NUM
ejpam-5455	96	8	(	(	PUNCT
ejpam-5455	96	9	4	4	NUM
ejpam-5455	96	10	)	)	PUNCT
ejpam-5455	96	11	(	(	PUNCT
ejpam-5455	96	12	2024	2024	NUM
ejpam-5455	96	13	)	)	PUNCT
ejpam-5455	96	14	,	,	PUNCT
ejpam-5455	96	15	4071	4071	NUM
ejpam-5455	96	16	-	-	SYM
ejpam-5455	96	17	4092	4092	NUM
ejpam-5455	96	18	4075	4075	NUM
ejpam-5455	96	19	remark	remark	NOUN
ejpam-5455	96	20	1	1	NUM
ejpam-5455	96	21	.	.	PUNCT
ejpam-5455	97	1	in	in	ADP
ejpam-5455	97	2	(	(	PUNCT
ejpam-5455	97	3	2	2	NUM
ejpam-5455	97	4	)	)	PUNCT
ejpam-5455	97	5	,	,	PUNCT
ejpam-5455	97	6	the	the	DET
ejpam-5455	97	7	kernel	kernel	PROPN
ejpam-5455	97	8	eρ	eρ	PROPN
ejpam-5455	97	9	(	(	PUNCT
ejpam-5455	97	10	−µρ(7	−µρ(7	X
ejpam-5455	97	11	−	−	PROPN
ejpam-5455	97	12	σ)ρ	σ)ρ	NOUN
ejpam-5455	97	13	)	)	PUNCT
ejpam-5455	97	14	is	be	AUX
ejpam-5455	97	15	non	non	ADJ
ejpam-5455	97	16	-	-	ADJ
ejpam-5455	97	17	singular	singular	ADJ
ejpam-5455	97	18	.	.	PUNCT
ejpam-5455	98	1	since	since	SCONJ
ejpam-5455	98	2	eρ	eρ	PROPN
ejpam-5455	98	3	(	(	PUNCT
ejpam-5455	98	4	−µρ(7	−µρ(7	X
ejpam-5455	98	5	−	−	NOUN
ejpam-5455	98	6	σ)ρ	σ)ρ	NOUN
ejpam-5455	98	7	)	)	PUNCT
ejpam-5455	98	8	=	=	SYM
ejpam-5455	98	9	eρ	eρ	PROPN
ejpam-5455	98	10	(	(	PUNCT
ejpam-5455	98	11	−	−	PROPN
ejpam-5455	98	12	ρ	ρ	PROPN
ejpam-5455	98	13	1−	1−	NUM
ejpam-5455	98	14	ρ	ρ	NOUN
ejpam-5455	98	15	(	(	PUNCT
ejpam-5455	98	16	7	7	NUM
ejpam-5455	98	17	−	−	NOUN
ejpam-5455	98	18	σ)ρ	σ)ρ	NOUN
ejpam-5455	98	19	)	)	PUNCT
ejpam-5455	98	20	.	.	PUNCT
ejpam-5455	99	1	as	as	ADP
ejpam-5455	99	2	7	7	NUM
ejpam-5455	99	3	approaches	approach	NOUN
ejpam-5455	99	4	σ	σ	PROPN
ejpam-5455	99	5	,	,	PUNCT
ejpam-5455	99	6	the	the	DET
ejpam-5455	99	7	term	term	NOUN
ejpam-5455	99	8	(	(	PUNCT
ejpam-5455	99	9	7	7	NUM
ejpam-5455	99	10	−	−	NOUN
ejpam-5455	99	11	σ)ρ	σ)ρ	NOUN
ejpam-5455	99	12	approaches	approach	VERB
ejpam-5455	99	13	0	0	NUM
ejpam-5455	99	14	.	.	PUNCT
ejpam-5455	100	1	thus	thus	ADV
ejpam-5455	100	2	,	,	PUNCT
ejpam-5455	100	3	we	we	PRON
ejpam-5455	100	4	have	have	VERB
ejpam-5455	100	5	eρ	eρ	NOUN
ejpam-5455	100	6	(	(	PUNCT
ejpam-5455	100	7	−µρ(7	−µρ(7	X
ejpam-5455	100	8	−	−	NOUN
ejpam-5455	100	9	σ)ρ	σ)ρ	NOUN
ejpam-5455	100	10	)	)	PUNCT
ejpam-5455	100	11	=	=	SYM
ejpam-5455	100	12	eρ(0	eρ(0	NOUN
ejpam-5455	100	13	)	)	PUNCT
ejpam-5455	100	14	=	=	SYM
ejpam-5455	101	1	1	1	X
ejpam-5455	101	2	.	.	X
ejpam-5455	101	3	from	from	ADP
ejpam-5455	101	4	this	this	PRON
ejpam-5455	101	5	,	,	PUNCT
ejpam-5455	101	6	we	we	PRON
ejpam-5455	101	7	observe	observe	VERB
ejpam-5455	101	8	that	that	SCONJ
ejpam-5455	101	9	(	(	PUNCT
ejpam-5455	101	10	abcdρ	abcdρ	NOUN
ejpam-5455	101	11	0+y	0+y	NUM
ejpam-5455	101	12	)	)	PUNCT
ejpam-5455	101	13	(	(	PUNCT
ejpam-5455	101	14	0	0	NUM
ejpam-5455	101	15	)	)	PUNCT
ejpam-5455	101	16	=	=	SYM
ejpam-5455	101	17	0	0	NUM
ejpam-5455	101	18	,	,	PUNCT
ejpam-5455	101	19	if	if	SCONJ
ejpam-5455	101	20	y	y	PROPN
ejpam-5455	101	21	∈	∈	PROPN
ejpam-5455	101	22	h1(0	h1(0	PROPN
ejpam-5455	101	23	,	,	PUNCT
ejpam-5455	101	24	z	z	PROPN
ejpam-5455	101	25	)	)	PUNCT
ejpam-5455	101	26	.	.	PUNCT
ejpam-5455	102	1	the	the	DET
ejpam-5455	102	2	aforementioned	aforementioned	ADJ
ejpam-5455	102	3	operators	operator	NOUN
ejpam-5455	102	4	serve	serve	VERB
ejpam-5455	102	5	as	as	ADP
ejpam-5455	102	6	fundamental	fundamental	ADJ
ejpam-5455	102	7	tools	tool	NOUN
ejpam-5455	102	8	in	in	ADP
ejpam-5455	102	9	establishing	establish	VERB
ejpam-5455	102	10	various	various	ADJ
ejpam-5455	102	11	theoretical	theoretical	ADJ
ejpam-5455	102	12	underpinnings	underpinning	NOUN
ejpam-5455	102	13	.	.	PUNCT
ejpam-5455	103	1	the	the	DET
ejpam-5455	103	2	efficacy	efficacy	NOUN
ejpam-5455	103	3	of	of	ADP
ejpam-5455	103	4	these	these	DET
ejpam-5455	103	5	operators	operator	NOUN
ejpam-5455	103	6	in	in	ADP
ejpam-5455	103	7	practical	practical	ADJ
ejpam-5455	103	8	applications	application	NOUN
ejpam-5455	103	9	is	be	AUX
ejpam-5455	103	10	significantly	significantly	ADV
ejpam-5455	103	11	influenced	influence	VERB
ejpam-5455	103	12	by	by	ADP
ejpam-5455	103	13	the	the	DET
ejpam-5455	103	14	underlying	underlie	VERB
ejpam-5455	103	15	function	function	NOUN
ejpam-5455	103	16	spaces	space	NOUN
ejpam-5455	103	17	,	,	PUNCT
ejpam-5455	103	18	as	as	SCONJ
ejpam-5455	103	19	elucidated	elucidate	VERB
ejpam-5455	103	20	by	by	ADP
ejpam-5455	103	21	al	al	PROPN
ejpam-5455	103	22	-	-	PUNCT
ejpam-5455	103	23	refai	refai	PROPN
ejpam-5455	103	24	et	et	PROPN
ejpam-5455	103	25	al	al	PROPN
ejpam-5455	103	26	.	.	PUNCT
ejpam-5455	104	1	in	in	ADP
ejpam-5455	104	2	[	[	X
ejpam-5455	104	3	2	2	NUM
ejpam-5455	104	4	]	]	PUNCT
ejpam-5455	104	5	.	.	PUNCT
ejpam-5455	105	1	for	for	ADP
ejpam-5455	105	2	instance	instance	NOUN
ejpam-5455	105	3	,	,	PUNCT
ejpam-5455	105	4	we	we	PRON
ejpam-5455	105	5	fix	fix	VERB
ejpam-5455	105	6	y(7	y(7	PROPN
ejpam-5455	105	7	)	)	PUNCT
ejpam-5455	105	8	∈	∈	PROPN
ejpam-5455	105	9	h1(0	h1(0	PROPN
ejpam-5455	105	10	,	,	PUNCT
ejpam-5455	105	11	z	z	PROPN
ejpam-5455	105	12	)	)	PUNCT
ejpam-5455	105	13	then	then	ADV
ejpam-5455	105	14	the	the	DET
ejpam-5455	105	15	system	system	NOUN
ejpam-5455	105	16	(	(	PUNCT
ejpam-5455	105	17	abcdρ	abcdρ	NOUN
ejpam-5455	105	18	0+y	0+y	NUM
ejpam-5455	105	19	)	)	PUNCT
ejpam-5455	105	20	(	(	PUNCT
ejpam-5455	105	21	7	7	X
ejpam-5455	105	22	)	)	PUNCT
ejpam-5455	105	23	−	−	NOUN
ejpam-5455	106	1	ωy(7	ωy(7	NOUN
ejpam-5455	106	2	)	)	PUNCT
ejpam-5455	106	3	=	=	SYM
ejpam-5455	106	4	0	0	NUM
ejpam-5455	106	5	,	,	PUNCT
ejpam-5455	106	6	ω	ω	PROPN
ejpam-5455	106	7	∈	∈	PROPN
ejpam-5455	106	8	r	r	NOUN
ejpam-5455	106	9	,	,	PUNCT
ejpam-5455	106	10	has	have	VERB
ejpam-5455	106	11	only	only	ADV
ejpam-5455	106	12	the	the	DET
ejpam-5455	106	13	trivial	trivial	ADJ
ejpam-5455	106	14	solution	solution	NOUN
ejpam-5455	106	15	y(7	y(7	PROPN
ejpam-5455	106	16	)	)	PUNCT
ejpam-5455	106	17	=	=	PUNCT
ejpam-5455	107	1	0	0	X
ejpam-5455	107	2	.	.	PUNCT
ejpam-5455	108	1	however	however	ADV
ejpam-5455	108	2	,	,	PUNCT
ejpam-5455	108	3	in	in	ADP
ejpam-5455	108	4	this	this	DET
ejpam-5455	108	5	context	context	NOUN
ejpam-5455	108	6	,	,	PUNCT
ejpam-5455	108	7	the	the	DET
ejpam-5455	108	8	space	space	NOUN
ejpam-5455	108	9	is	be	AUX
ejpam-5455	108	10	restrictive	restrictive	ADJ
ejpam-5455	108	11	for	for	ADP
ejpam-5455	108	12	the	the	DET
ejpam-5455	108	13	caputo	caputo	PROPN
ejpam-5455	108	14	derivative	derivative	NOUN
ejpam-5455	108	15	.	.	PUNCT
ejpam-5455	109	1	if	if	SCONJ
ejpam-5455	109	2	we	we	PRON
ejpam-5455	109	3	fix	fix	VERB
ejpam-5455	109	4	the	the	DET
ejpam-5455	109	5	space	space	NOUN
ejpam-5455	109	6	χ(y	χ(y	NOUN
ejpam-5455	109	7	)	)	PUNCT
ejpam-5455	110	1	=	=	PRON
ejpam-5455	110	2	{	{	PUNCT
ejpam-5455	110	3	y	y	NOUN
ejpam-5455	110	4	:	:	PUNCT
ejpam-5455	110	5	y′	y′	X
ejpam-5455	110	6	∈	∈	PROPN
ejpam-5455	111	1	l1[0	l1[0	PROPN
ejpam-5455	111	2	,	,	PUNCT
ejpam-5455	111	3	1	1	NUM
ejpam-5455	111	4	]	]	PUNCT
ejpam-5455	111	5	}	}	PUNCT
ejpam-5455	111	6	,	,	PUNCT
ejpam-5455	111	7	then	then	ADV
ejpam-5455	111	8	the	the	DET
ejpam-5455	111	9	following	follow	VERB
ejpam-5455	111	10	system	system	NOUN
ejpam-5455	111	11	(	(	PUNCT
ejpam-5455	111	12	abcdρ	abcdρ	NOUN
ejpam-5455	111	13	0+y	0+y	NUM
ejpam-5455	111	14	)	)	PUNCT
ejpam-5455	111	15	(	(	PUNCT
ejpam-5455	111	16	7	7	X
ejpam-5455	111	17	)	)	PUNCT
ejpam-5455	111	18	=	=	PRON
ejpam-5455	111	19	{	{	PUNCT
ejpam-5455	111	20	ωy(7	ωy(7	NOUN
ejpam-5455	111	21	)	)	PUNCT
ejpam-5455	111	22	,	,	PUNCT
ejpam-5455	111	23	7	7	NUM
ejpam-5455	111	24	∈	∈	NOUN
ejpam-5455	111	25	(	(	PUNCT
ejpam-5455	111	26	0	0	NUM
ejpam-5455	111	27	,	,	PUNCT
ejpam-5455	111	28	z	z	NOUN
ejpam-5455	111	29	)	)	PUNCT
ejpam-5455	111	30	;	;	PUNCT
ejpam-5455	111	31	y0	y0	NOUN
ejpam-5455	111	32	,	,	PUNCT
ejpam-5455	111	33	7	7	NUM
ejpam-5455	111	34	=	=	SYM
ejpam-5455	111	35	0	0	NUM
ejpam-5455	111	36	with	with	ADP
ejpam-5455	111	37	0	0	NUM
ejpam-5455	111	38	<	<	X
ejpam-5455	111	39	ρ	ρ	X
ejpam-5455	111	40	<	<	X
ejpam-5455	111	41	1	1	NUM
ejpam-5455	111	42	,	,	PUNCT
ejpam-5455	111	43	we	we	PRON
ejpam-5455	111	44	have	have	VERB
ejpam-5455	111	45	the	the	DET
ejpam-5455	111	46	solution	solution	NOUN
ejpam-5455	111	47	y(7	y(7	PROPN
ejpam-5455	111	48	)	)	PUNCT
ejpam-5455	111	49	=	=	SYM
ejpam-5455	111	50	y0eρ,1(−ω7ρ	y0eρ,1(−ω7ρ	NUM
ejpam-5455	111	51	)	)	PUNCT
ejpam-5455	111	52	,	,	PUNCT
ejpam-5455	111	53	where	where	SCONJ
ejpam-5455	111	54	eρ,1(z	eρ,1(z	VERB
ejpam-5455	111	55	)	)	PUNCT
ejpam-5455	111	56	=	=	NOUN
ejpam-5455	112	1	∞∑	∞∑	NUM
ejpam-5455	112	2	k=0	k=0	PROPN
ejpam-5455	112	3	zk	zk	ADP
ejpam-5455	112	4	γ(ρk	γ(ρk	PROPN
ejpam-5455	112	5	+	+	CCONJ
ejpam-5455	112	6	1	1	NUM
ejpam-5455	112	7	)	)	PUNCT
ejpam-5455	112	8	.	.	PUNCT
ejpam-5455	113	1	this	this	PRON
ejpam-5455	113	2	demonstrates	demonstrate	VERB
ejpam-5455	113	3	the	the	DET
ejpam-5455	113	4	significant	significant	ADJ
ejpam-5455	113	5	impact	impact	NOUN
ejpam-5455	113	6	of	of	ADP
ejpam-5455	113	7	space	space	NOUN
ejpam-5455	113	8	.	.	PUNCT
ejpam-5455	114	1	to	to	PART
ejpam-5455	114	2	address	address	VERB
ejpam-5455	114	3	this	this	DET
ejpam-5455	114	4	challenge	challenge	NOUN
ejpam-5455	114	5	,	,	PUNCT
ejpam-5455	114	6	al	al	PROPN
ejpam-5455	114	7	-	-	PUNCT
ejpam-5455	114	8	refai	refai	PROPN
ejpam-5455	114	9	et	et	PROPN
ejpam-5455	114	10	al	al	PROPN
ejpam-5455	114	11	.	.	PUNCT
ejpam-5455	115	1	[	[	X
ejpam-5455	115	2	2	2	NUM
ejpam-5455	115	3	]	]	PUNCT
ejpam-5455	115	4	published	publish	VERB
ejpam-5455	115	5	a	a	DET
ejpam-5455	115	6	research	research	NOUN
ejpam-5455	115	7	work	work	NOUN
ejpam-5455	115	8	in	in	ADP
ejpam-5455	115	9	which	which	PRON
ejpam-5455	115	10	a	a	DET
ejpam-5455	115	11	larger	large	ADJ
ejpam-5455	115	12	space	space	NOUN
ejpam-5455	115	13	is	be	AUX
ejpam-5455	115	14	selected	select	VERB
ejpam-5455	115	15	to	to	PART
ejpam-5455	115	16	eliminate	eliminate	VERB
ejpam-5455	115	17	the	the	DET
ejpam-5455	115	18	need	need	NOUN
ejpam-5455	115	19	for	for	ADP
ejpam-5455	115	20	additional	additional	ADJ
ejpam-5455	115	21	conditions	condition	NOUN
ejpam-5455	115	22	.	.	PUNCT
ejpam-5455	116	1	following	follow	VERB
ejpam-5455	116	2	[	[	X
ejpam-5455	116	3	2	2	NUM
ejpam-5455	116	4	]	]	PUNCT
ejpam-5455	116	5	,	,	PUNCT
ejpam-5455	116	6	we	we	PRON
ejpam-5455	116	7	presents	present	VERB
ejpam-5455	116	8	a	a	DET
ejpam-5455	116	9	mabc	mabc	ADJ
ejpam-5455	116	10	fractional	fractional	ADJ
ejpam-5455	116	11	derivative	derivative	ADJ
ejpam-5455	116	12	operator	operator	NOUN
ejpam-5455	116	13	,	,	PUNCT
ejpam-5455	116	14	which	which	PRON
ejpam-5455	116	15	is	be	AUX
ejpam-5455	116	16	applicable	applicable	ADJ
ejpam-5455	116	17	in	in	ADP
ejpam-5455	116	18	a	a	DET
ejpam-5455	116	19	broader	broad	ADJ
ejpam-5455	116	20	functional	functional	ADJ
ejpam-5455	116	21	space	space	NOUN
ejpam-5455	116	22	to	to	PART
ejpam-5455	116	23	address	address	VERB
ejpam-5455	116	24	the	the	DET
ejpam-5455	116	25	initialization	initialization	NOUN
ejpam-5455	116	26	problem	problem	NOUN
ejpam-5455	116	27	effectively	effectively	ADV
ejpam-5455	116	28	.	.	PUNCT
ejpam-5455	117	1	definition	definition	NOUN
ejpam-5455	117	2	3	3	NUM
ejpam-5455	117	3	.	.	PUNCT
ejpam-5455	118	1	[	[	X
ejpam-5455	118	2	2	2	NUM
ejpam-5455	118	3	,	,	PUNCT
ejpam-5455	118	4	25	25	NUM
ejpam-5455	118	5	]	]	PUNCT
ejpam-5455	118	6	let	let	VERB
ejpam-5455	118	7	y	y	PROPN
ejpam-5455	118	8	∈	∈	PROPN
ejpam-5455	118	9	l1(0	l1(0	PROPN
ejpam-5455	118	10	,	,	PUNCT
ejpam-5455	118	11	z	z	PROPN
ejpam-5455	118	12	)	)	PUNCT
ejpam-5455	118	13	,	,	PUNCT
ejpam-5455	118	14	z	z	NOUN
ejpam-5455	118	15	>	>	X
ejpam-5455	118	16	0	0	NUM
ejpam-5455	119	1	and	and	CCONJ
ejpam-5455	119	2	ρ	ρ	PROPN
ejpam-5455	119	3	∈	∈	PROPN
ejpam-5455	119	4	(	(	PUNCT
ejpam-5455	119	5	0	0	NUM
ejpam-5455	119	6	,	,	PUNCT
ejpam-5455	119	7	1	1	NUM
ejpam-5455	119	8	)	)	PUNCT
ejpam-5455	119	9	,	,	PUNCT
ejpam-5455	119	10	the	the	DET
ejpam-5455	119	11	mabc	mabc	PROPN
ejpam-5455	119	12	derivative	derivative	NOUN
ejpam-5455	119	13	is	be	AUX
ejpam-5455	119	14	described	describe	VERB
ejpam-5455	119	15	by	by	ADP
ejpam-5455	119	16	(	(	PUNCT
ejpam-5455	119	17	mabcdρ	mabcdρ	PROPN
ejpam-5455	119	18	0+y	0+y	NUM
ejpam-5455	119	19	)	)	PUNCT
ejpam-5455	119	20	(	(	PUNCT
ejpam-5455	119	21	7	7	X
ejpam-5455	119	22	)	)	PUNCT
ejpam-5455	119	23	=	=	SYM
ejpam-5455	119	24	b(ρ	b(ρ	PROPN
ejpam-5455	119	25	)	)	PUNCT
ejpam-5455	119	26	1−	1−	NUM
ejpam-5455	119	27	ρ	ρ	NOUN
ejpam-5455	120	1	[	[	X
ejpam-5455	120	2	y(7)−	y(7)−	X
ejpam-5455	120	3	eρ	eρ	PROPN
ejpam-5455	120	4	(	(	PUNCT
ejpam-5455	120	5	−µρ7ρ	−µρ7ρ	PROPN
ejpam-5455	120	6	)	)	PUNCT
ejpam-5455	120	7	y(0	y(0	PROPN
ejpam-5455	120	8	)	)	PUNCT
ejpam-5455	120	9	−µρ	−µρ	PROPN
ejpam-5455	120	10	∫	∫	PROPN
ejpam-5455	120	11	7	7	NUM
ejpam-5455	120	12	0	0	NUM
ejpam-5455	120	13	(	(	PUNCT
ejpam-5455	120	14	7	7	NUM
ejpam-5455	120	15	−	−	PROPN
ejpam-5455	120	16	σ)ρ−1eρ	σ)ρ−1eρ	PROPN
ejpam-5455	120	17	,	,	PUNCT
ejpam-5455	120	18	ρ	ρ	PROPN
ejpam-5455	120	19	(	(	PUNCT
ejpam-5455	120	20	−µρ(7	−µρ(7	X
ejpam-5455	120	21	−	−	NOUN
ejpam-5455	120	22	σ)ρ	σ)ρ	NOUN
ejpam-5455	120	23	)	)	PUNCT
ejpam-5455	120	24	y(σ)dσ	y(σ)dσ	NOUN
ejpam-5455	120	25	]	]	PUNCT
ejpam-5455	120	26	,	,	PUNCT
ejpam-5455	120	27	0	0	PUNCT
ejpam-5455	120	28	<	<	X
ejpam-5455	120	29	7	7	NUM
ejpam-5455	120	30	<	<	X
ejpam-5455	120	31	z	z	X
ejpam-5455	120	32	(	(	PUNCT
ejpam-5455	120	33	5	5	NUM
ejpam-5455	120	34	)	)	PUNCT
ejpam-5455	120	35	where	where	SCONJ
ejpam-5455	120	36	µρ	µρ	ADV
ejpam-5455	120	37	=	=	SYM
ejpam-5455	120	38	ρ	ρ	PROPN
ejpam-5455	120	39	1−	1−	NUM
ejpam-5455	120	40	ρ	ρ	NOUN
ejpam-5455	120	41	,	,	PUNCT
ejpam-5455	120	42	the	the	DET
ejpam-5455	120	43	normalized	normalize	VERB
ejpam-5455	120	44	function	function	NOUN
ejpam-5455	120	45	b(ρ	b(ρ	PROPN
ejpam-5455	120	46	)	)	PUNCT
ejpam-5455	120	47	satisfies	satisfy	VERB
ejpam-5455	120	48	the	the	DET
ejpam-5455	120	49	property	property	NOUN
ejpam-5455	120	50	b(0	b(0	NOUN
ejpam-5455	120	51	)	)	PUNCT
ejpam-5455	120	52	=	=	SYM
ejpam-5455	120	53	b(1	b(1	PROPN
ejpam-5455	120	54	)	)	PUNCT
ejpam-5455	120	55	=	=	NOUN
ejpam-5455	120	56	1	1	NUM
ejpam-5455	120	57	and	and	CCONJ
ejpam-5455	120	58	eρ	eρ	PROPN
ejpam-5455	120	59	,	,	PUNCT
ejpam-5455	120	60	ρ	ρ	PROPN
ejpam-5455	120	61	is	be	AUX
ejpam-5455	120	62	the	the	DET
ejpam-5455	120	63	two	two	NUM
ejpam-5455	120	64	-	-	PUNCT
ejpam-5455	120	65	parameters	parameter	NOUN
ejpam-5455	120	66	m	m	NOUN
ejpam-5455	120	67	-	-	ADJ
ejpam-5455	120	68	l	l	NOUN
ejpam-5455	120	69	function	function	NOUN
ejpam-5455	120	70	.	.	PUNCT
ejpam-5455	121	1	m.	m.	NOUN
ejpam-5455	121	2	m.	m.	PROPN
ejpam-5455	121	3	arjunan	arjunan	PROPN
ejpam-5455	121	4	/	/	SYM
ejpam-5455	121	5	eur	eur	PROPN
ejpam-5455	121	6	.	.	PUNCT
ejpam-5455	122	1	j.	j.	PROPN
ejpam-5455	122	2	pure	pure	PROPN
ejpam-5455	122	3	appl	appl	PROPN
ejpam-5455	122	4	.	.	PROPN
ejpam-5455	122	5	math	math	PROPN
ejpam-5455	122	6	,	,	PUNCT
ejpam-5455	122	7	17	17	NUM
ejpam-5455	122	8	(	(	PUNCT
ejpam-5455	122	9	4	4	NUM
ejpam-5455	122	10	)	)	PUNCT
ejpam-5455	122	11	(	(	PUNCT
ejpam-5455	122	12	2024	2024	NUM
ejpam-5455	122	13	)	)	PUNCT
ejpam-5455	122	14	,	,	PUNCT
ejpam-5455	122	15	4071	4071	NUM
ejpam-5455	122	16	-	-	SYM
ejpam-5455	122	17	4092	4092	NUM
ejpam-5455	122	18	4076	4076	NUM
ejpam-5455	122	19	we	we	PRON
ejpam-5455	122	20	see	see	VERB
ejpam-5455	122	21	that	that	SCONJ
ejpam-5455	122	22	definitions	definition	NOUN
ejpam-5455	122	23	1	1	NUM
ejpam-5455	122	24	and	and	CCONJ
ejpam-5455	122	25	3	3	NUM
ejpam-5455	122	26	are	be	AUX
ejpam-5455	122	27	the	the	DET
ejpam-5455	122	28	same	same	ADJ
ejpam-5455	122	29	in	in	ADP
ejpam-5455	122	30	the	the	DET
ejpam-5455	122	31	space	space	NOUN
ejpam-5455	122	32	h1(0	h1(0	PROPN
ejpam-5455	122	33	,	,	PUNCT
ejpam-5455	122	34	z	z	PROPN
ejpam-5455	122	35	)	)	PUNCT
ejpam-5455	122	36	⊆	⊆	NUM
ejpam-5455	122	37	l1(0	l1(0	PROPN
ejpam-5455	122	38	,	,	PUNCT
ejpam-5455	122	39	z	z	NOUN
ejpam-5455	122	40	)	)	PUNCT
ejpam-5455	122	41	.	.	PUNCT
ejpam-5455	123	1	however	however	ADV
ejpam-5455	123	2	,	,	PUNCT
ejpam-5455	123	3	if	if	SCONJ
ejpam-5455	123	4	y	y	PROPN
ejpam-5455	123	5	∈	∈	PROPN
ejpam-5455	123	6	l1(0	l1(0	PROPN
ejpam-5455	123	7	,	,	PUNCT
ejpam-5455	123	8	z	z	PROPN
ejpam-5455	123	9	)	)	PUNCT
ejpam-5455	123	10	,	,	PUNCT
ejpam-5455	123	11	it	it	PRON
ejpam-5455	123	12	is	be	AUX
ejpam-5455	123	13	not	not	PART
ejpam-5455	123	14	guaranteed	guarantee	VERB
ejpam-5455	123	15	that	that	SCONJ
ejpam-5455	123	16	(	(	PUNCT
ejpam-5455	123	17	mabcdρ	mabcdρ	PROPN
ejpam-5455	123	18	0+y	0+y	NUM
ejpam-5455	123	19	)	)	PUNCT
ejpam-5455	123	20	(	(	PUNCT
ejpam-5455	123	21	0	0	NUM
ejpam-5455	123	22	)	)	PUNCT
ejpam-5455	123	23	=	=	NOUN
ejpam-5455	124	1	0	0	X
ejpam-5455	124	2	.	.	PUNCT
ejpam-5455	124	3	to	to	PART
ejpam-5455	124	4	support	support	VERB
ejpam-5455	124	5	this	this	DET
ejpam-5455	124	6	result	result	NOUN
ejpam-5455	124	7	,	,	PUNCT
ejpam-5455	124	8	we	we	PRON
ejpam-5455	124	9	have	have	VERB
ejpam-5455	124	10	the	the	DET
ejpam-5455	124	11	following	follow	VERB
ejpam-5455	124	12	example	example	NOUN
ejpam-5455	124	13	:	:	PUNCT
ejpam-5455	124	14	example	example	NOUN
ejpam-5455	124	15	1	1	X
ejpam-5455	124	16	.	.	X
ejpam-5455	124	17	consider	consider	VERB
ejpam-5455	124	18	u(7	u(7	PRON
ejpam-5455	124	19	)	)	PUNCT
ejpam-5455	124	20	=	=	PRON
ejpam-5455	124	21	{	{	PUNCT
ejpam-5455	124	22	7−	7−	NUM
ejpam-5455	124	23	3	3	NUM
ejpam-5455	124	24	4	4	NUM
ejpam-5455	124	25	,	,	PUNCT
ejpam-5455	125	1	7	7	NUM
ejpam-5455	125	2	̸=	̸=	PROPN
ejpam-5455	125	3	0	0	NUM
ejpam-5455	125	4	b	b	NOUN
ejpam-5455	125	5	,	,	PUNCT
ejpam-5455	125	6	7	7	NUM
ejpam-5455	125	7	=	=	SYM
ejpam-5455	125	8	0	0	NUM
ejpam-5455	125	9	where	where	SCONJ
ejpam-5455	125	10	b	b	X
ejpam-5455	125	11	∈	∈	PROPN
ejpam-5455	125	12	r	r	NOUN
ejpam-5455	125	13	and	and	CCONJ
ejpam-5455	125	14	u	u	PROPN
ejpam-5455	125	15	∈	∈	PROPN
ejpam-5455	125	16	l1(0	l1(0	PROPN
ejpam-5455	125	17	,	,	PUNCT
ejpam-5455	125	18	z	z	NOUN
ejpam-5455	125	19	)	)	PUNCT
ejpam-5455	125	20	.	.	PUNCT
ejpam-5455	126	1	for	for	ADP
ejpam-5455	126	2	b(ρ	b(ρ	PROPN
ejpam-5455	126	3	)	)	PUNCT
ejpam-5455	126	4	=	=	SYM
ejpam-5455	127	1	1	1	NUM
ejpam-5455	127	2	−	−	PROPN
ejpam-5455	127	3	ρ	ρ	PROPN
ejpam-5455	127	4	+	+	PROPN
ejpam-5455	127	5	ρ	ρ	PROPN
ejpam-5455	127	6	γ(ρ	γ(ρ	PROPN
ejpam-5455	127	7	)	)	PUNCT
ejpam-5455	127	8	and	and	CCONJ
ejpam-5455	127	9	µρ	µρ	ADV
ejpam-5455	127	10	=	=	SYM
ejpam-5455	127	11	ρ	ρ	PROPN
ejpam-5455	127	12	1−	1−	NUM
ejpam-5455	127	13	ρ	ρ	NOUN
ejpam-5455	127	14	,	,	PUNCT
ejpam-5455	127	15	the	the	DET
ejpam-5455	127	16	modified	modified	ADJ
ejpam-5455	127	17	atangana	atangana	PROPN
ejpam-5455	127	18	-	-	PUNCT
ejpam-5455	127	19	baleanu	baleanu	PROPN
ejpam-5455	127	20	derivative	derivative	NOUN
ejpam-5455	127	21	in	in	ADP
ejpam-5455	127	22	caputo	caputo	PROPN
ejpam-5455	127	23	sense	sense	NOUN
ejpam-5455	127	24	is	be	AUX
ejpam-5455	127	25	:	:	PUNCT
ejpam-5455	127	26	(	(	PUNCT
ejpam-5455	127	27	mabcdρ	mabcdρ	PROPN
ejpam-5455	127	28	0+u	0+u	NUM
ejpam-5455	127	29	)	)	PUNCT
ejpam-5455	127	30	(	(	PUNCT
ejpam-5455	127	31	7	7	X
ejpam-5455	127	32	)	)	PUNCT
ejpam-5455	127	33	=	=	SYM
ejpam-5455	127	34	b(ρ	b(ρ	PROPN
ejpam-5455	127	35	)	)	PUNCT
ejpam-5455	127	36	1−	1−	NUM
ejpam-5455	127	37	ρ	ρ	NOUN
ejpam-5455	127	38	[	[	PUNCT
ejpam-5455	127	39	u(7)−	u(7)−	NOUN
ejpam-5455	127	40	eρ	eρ	NOUN
ejpam-5455	127	41	(	(	PUNCT
ejpam-5455	127	42	−µρ7ρ)u(0	−µρ7ρ)u(0	NOUN
ejpam-5455	127	43	)	)	PUNCT
ejpam-5455	127	44	−	−	PROPN
ejpam-5455	127	45	µρ	µρ	ADV
ejpam-5455	127	46	∫	∫	PROPN
ejpam-5455	127	47	7	7	NUM
ejpam-5455	127	48	0	0	NUM
ejpam-5455	127	49	(	(	PUNCT
ejpam-5455	127	50	7	7	NUM
ejpam-5455	127	51	−	−	PROPN
ejpam-5455	127	52	σ)ρ−1eρ	σ)ρ−1eρ	PROPN
ejpam-5455	127	53	,	,	PUNCT
ejpam-5455	127	54	ρ	ρ	PROPN
ejpam-5455	127	55	(	(	PUNCT
ejpam-5455	127	56	−µρ(7	−µρ(7	X
ejpam-5455	127	57	−	−	PROPN
ejpam-5455	127	58	σ)ρ)u(σ	σ)ρ)u(σ	NUM
ejpam-5455	127	59	)	)	PUNCT
ejpam-5455	127	60	dσ	dσ	VERB
ejpam-5455	127	61	]	]	PUNCT
ejpam-5455	127	62	.	.	PUNCT
ejpam-5455	128	1	if	if	SCONJ
ejpam-5455	128	2	ρ	ρ	PROPN
ejpam-5455	128	3	=	=	SYM
ejpam-5455	128	4	3	3	NUM
ejpam-5455	128	5	4	4	NUM
ejpam-5455	128	6	,	,	PUNCT
ejpam-5455	128	7	then	then	ADV
ejpam-5455	128	8	above	above	ADP
ejpam-5455	128	9	expression	expression	NOUN
ejpam-5455	128	10	becomes	become	VERB
ejpam-5455	128	11	(	(	PUNCT
ejpam-5455	128	12	mabcd	mabcd	NOUN
ejpam-5455	128	13	3	3	NUM
ejpam-5455	128	14	4	4	NUM
ejpam-5455	128	15	0+u	0+u	NUM
ejpam-5455	128	16	)	)	PUNCT
ejpam-5455	129	1	(	(	PUNCT
ejpam-5455	129	2	7	7	X
ejpam-5455	129	3	)	)	PUNCT
ejpam-5455	129	4	=	=	SYM
ejpam-5455	129	5	3.25	3.25	NUM
ejpam-5455	129	6	[	[	PUNCT
ejpam-5455	129	7	u(7)−	u(7)−	NOUN
ejpam-5455	129	8	e	e	NOUN
ejpam-5455	129	9	3	3	NUM
ejpam-5455	129	10	4	4	NUM
ejpam-5455	129	11	(	(	PUNCT
ejpam-5455	129	12	−37	−37	NOUN
ejpam-5455	129	13	3	3	NUM
ejpam-5455	129	14	4	4	NUM
ejpam-5455	129	15	)	)	PUNCT
ejpam-5455	129	16	u(0	u(0	NOUN
ejpam-5455	129	17	)	)	PUNCT
ejpam-5455	129	18	−	−	PROPN
ejpam-5455	129	19	3	3	NUM
ejpam-5455	129	20	∫	∫	NOUN
ejpam-5455	129	21	7	7	NUM
ejpam-5455	129	22	0	0	NUM
ejpam-5455	129	23	(	(	PUNCT
ejpam-5455	129	24	7	7	NUM
ejpam-5455	129	25	−	−	PROPN
ejpam-5455	129	26	σ)−	σ)−	PROPN
ejpam-5455	129	27	1	1	NUM
ejpam-5455	129	28	4e	4e	NOUN
ejpam-5455	129	29	3	3	NUM
ejpam-5455	129	30	4	4	NUM
ejpam-5455	129	31	,	,	PUNCT
ejpam-5455	129	32	3	3	NUM
ejpam-5455	129	33	4	4	NUM
ejpam-5455	129	34	(	(	PUNCT
ejpam-5455	129	35	−3(7	−3(7	ADJ
ejpam-5455	129	36	−	−	PROPN
ejpam-5455	129	37	σ	σ	PROPN
ejpam-5455	129	38	)	)	PUNCT
ejpam-5455	129	39	3	3	NUM
ejpam-5455	129	40	4	4	NUM
ejpam-5455	129	41	)	)	PUNCT
ejpam-5455	129	42	u(σ	u(σ	PROPN
ejpam-5455	129	43	)	)	PUNCT
ejpam-5455	130	1	dσ	dσ	X
ejpam-5455	130	2	]	]	PUNCT
ejpam-5455	130	3	.	.	PUNCT
ejpam-5455	131	1	(	(	PUNCT
ejpam-5455	131	2	6	6	NUM
ejpam-5455	131	3	)	)	PUNCT
ejpam-5455	131	4	for	for	ADP
ejpam-5455	131	5	7	7	NUM
ejpam-5455	131	6	̸=	̸=	PROPN
ejpam-5455	131	7	0	0	NUM
ejpam-5455	131	8	:	:	PUNCT
ejpam-5455	131	9	u(7	u(7	SYM
ejpam-5455	131	10	)	)	PUNCT
ejpam-5455	131	11	=	=	PUNCT
ejpam-5455	131	12	7−	7−	NUM
ejpam-5455	131	13	3	3	NUM
ejpam-5455	131	14	4	4	NUM
ejpam-5455	131	15	.	.	PUNCT
ejpam-5455	132	1	for	for	ADP
ejpam-5455	132	2	7	7	NUM
ejpam-5455	132	3	=	=	SYM
ejpam-5455	132	4	0	0	NUM
ejpam-5455	132	5	:	:	PUNCT
ejpam-5455	132	6	u(0	u(0	NOUN
ejpam-5455	132	7	)	)	PUNCT
ejpam-5455	132	8	=	=	SYM
ejpam-5455	132	9	b.	b.	PROPN
ejpam-5455	132	10	since	since	SCONJ
ejpam-5455	132	11	∫	∫	PROPN
ejpam-5455	132	12	7	7	NUM
ejpam-5455	132	13	0	0	NUM
ejpam-5455	132	14	(	(	PUNCT
ejpam-5455	132	15	7	7	NUM
ejpam-5455	132	16	−	−	PROPN
ejpam-5455	132	17	σ)−	σ)−	PROPN
ejpam-5455	132	18	1	1	NUM
ejpam-5455	132	19	4e	4e	NOUN
ejpam-5455	132	20	3	3	NUM
ejpam-5455	132	21	4	4	NUM
ejpam-5455	132	22	,	,	PUNCT
ejpam-5455	132	23	3	3	NUM
ejpam-5455	132	24	4	4	NUM
ejpam-5455	132	25	(	(	PUNCT
ejpam-5455	132	26	−3(7	−3(7	ADJ
ejpam-5455	132	27	−	−	PROPN
ejpam-5455	132	28	σ	σ	PROPN
ejpam-5455	132	29	)	)	PUNCT
ejpam-5455	132	30	3	3	NUM
ejpam-5455	132	31	4	4	NUM
ejpam-5455	132	32	)	)	PUNCT
ejpam-5455	132	33	σ−	σ−	NOUN
ejpam-5455	132	34	3	3	NUM
ejpam-5455	132	35	4dσ	4dσ	NOUN
ejpam-5455	132	36	=	=	SYM
ejpam-5455	132	37	γ	γ	X
ejpam-5455	132	38	(	(	PUNCT
ejpam-5455	132	39	1	1	NUM
ejpam-5455	132	40	4	4	NUM
ejpam-5455	132	41	)	)	PUNCT
ejpam-5455	132	42	e	e	NOUN
ejpam-5455	132	43	3	3	NUM
ejpam-5455	132	44	4	4	NUM
ejpam-5455	132	45	(	(	PUNCT
ejpam-5455	132	46	−37	−37	NOUN
ejpam-5455	132	47	3	3	NUM
ejpam-5455	132	48	4	4	NUM
ejpam-5455	132	49	)	)	PUNCT
ejpam-5455	132	50	using	use	VERB
ejpam-5455	132	51	the	the	DET
ejpam-5455	132	52	fact	fact	NOUN
ejpam-5455	132	53	that∫	that∫	NOUN
ejpam-5455	132	54	7	7	NUM
ejpam-5455	132	55	0	0	NUM
ejpam-5455	132	56	(	(	PUNCT
ejpam-5455	132	57	7	7	NUM
ejpam-5455	132	58	−	−	PROPN
ejpam-5455	132	59	σ)ρ−1eρ	σ)ρ−1eρ	PROPN
ejpam-5455	132	60	,	,	PUNCT
ejpam-5455	132	61	ρ	ρ	PROPN
ejpam-5455	132	62	(	(	PUNCT
ejpam-5455	132	63	−µρ(7	−µρ(7	SYM
ejpam-5455	132	64	−	−	PROPN
ejpam-5455	132	65	σ)ρ)σ−ρdσ	σ)ρ)σ−ρdσ	NOUN
ejpam-5455	132	66	=	=	SYM
ejpam-5455	132	67	γ(1−	γ(1−	PROPN
ejpam-5455	132	68	ρ)eρ	ρ)eρ	PROPN
ejpam-5455	132	69	(	(	PUNCT
ejpam-5455	132	70	−µρ7ρ	−µρ7ρ	PROPN
ejpam-5455	132	71	)	)	PUNCT
ejpam-5455	132	72	.	.	PUNCT
ejpam-5455	133	1	thus	thus	ADV
ejpam-5455	133	2	(	(	PUNCT
ejpam-5455	133	3	6	6	X
ejpam-5455	133	4	)	)	PUNCT
ejpam-5455	133	5	becomes	become	VERB
ejpam-5455	133	6	(	(	PUNCT
ejpam-5455	133	7	mabcd	mabcd	PROPN
ejpam-5455	133	8	3	3	NUM
ejpam-5455	133	9	4	4	NUM
ejpam-5455	133	10	0+u	0+u	NUM
ejpam-5455	133	11	)	)	PUNCT
ejpam-5455	134	1	(	(	PUNCT
ejpam-5455	134	2	7	7	X
ejpam-5455	134	3	)	)	PUNCT
ejpam-5455	134	4	=	=	SYM
ejpam-5455	134	5	3.25	3.25	NUM
ejpam-5455	134	6	[	[	PUNCT
ejpam-5455	134	7	7−	7−	NUM
ejpam-5455	134	8	3	3	NUM
ejpam-5455	134	9	4	4	NUM
ejpam-5455	134	10	−	−	NOUN
ejpam-5455	134	11	e	e	NOUN
ejpam-5455	134	12	3	3	NUM
ejpam-5455	134	13	4	4	NUM
ejpam-5455	134	14	(	(	PUNCT
ejpam-5455	134	15	−37	−37	NOUN
ejpam-5455	134	16	3	3	NUM
ejpam-5455	134	17	4	4	NUM
ejpam-5455	134	18	)	)	PUNCT
ejpam-5455	134	19	b	b	NOUN
ejpam-5455	134	20	−	−	ADP
ejpam-5455	134	21	3γ	3γ	NUM
ejpam-5455	134	22	(	(	PUNCT
ejpam-5455	134	23	1	1	NUM
ejpam-5455	134	24	4	4	NUM
ejpam-5455	134	25	)	)	PUNCT
ejpam-5455	134	26	e	e	NOUN
ejpam-5455	134	27	3	3	NUM
ejpam-5455	134	28	4	4	NUM
ejpam-5455	134	29	(	(	PUNCT
ejpam-5455	134	30	−37	−37	NOUN
ejpam-5455	134	31	3	3	NUM
ejpam-5455	134	32	4	4	NUM
ejpam-5455	134	33	)	)	PUNCT
ejpam-5455	134	34	]	]	PUNCT
ejpam-5455	134	35	.	.	PUNCT
ejpam-5455	135	1	consequently	consequently	ADV
ejpam-5455	135	2	mabcd	mabcd	VERB
ejpam-5455	135	3	3	3	NUM
ejpam-5455	135	4	4	4	NUM
ejpam-5455	135	5	0+u(0	0+u(0	NOUN
ejpam-5455	135	6	)	)	PUNCT
ejpam-5455	136	1	=	=	PUNCT
ejpam-5455	136	2	−9.75γ	−9.75γ	NOUN
ejpam-5455	136	3	(	(	PUNCT
ejpam-5455	136	4	1	1	NUM
ejpam-5455	136	5	4	4	NUM
ejpam-5455	136	6	)	)	PUNCT
ejpam-5455	136	7	̸=	̸=	PROPN
ejpam-5455	136	8	0	0	NUM
ejpam-5455	136	9	.	.	PUNCT
ejpam-5455	136	10	m.	m.	NOUN
ejpam-5455	136	11	m.	m.	PROPN
ejpam-5455	136	12	arjunan	arjunan	PROPN
ejpam-5455	136	13	/	/	SYM
ejpam-5455	136	14	eur	eur	PROPN
ejpam-5455	136	15	.	.	PUNCT
ejpam-5455	137	1	j.	j.	PROPN
ejpam-5455	137	2	pure	pure	PROPN
ejpam-5455	137	3	appl	appl	PROPN
ejpam-5455	137	4	.	.	PROPN
ejpam-5455	137	5	math	math	PROPN
ejpam-5455	137	6	,	,	PUNCT
ejpam-5455	137	7	17	17	NUM
ejpam-5455	137	8	(	(	PUNCT
ejpam-5455	137	9	4	4	NUM
ejpam-5455	137	10	)	)	PUNCT
ejpam-5455	137	11	(	(	PUNCT
ejpam-5455	137	12	2024	2024	NUM
ejpam-5455	137	13	)	)	PUNCT
ejpam-5455	137	14	,	,	PUNCT
ejpam-5455	137	15	4071	4071	NUM
ejpam-5455	137	16	-	-	SYM
ejpam-5455	137	17	4092	4092	NUM
ejpam-5455	137	18	4077	4077	NUM
ejpam-5455	137	19	remark	remark	NOUN
ejpam-5455	137	20	2	2	NUM
ejpam-5455	137	21	.	.	PUNCT
ejpam-5455	138	1	in	in	ADP
ejpam-5455	138	2	the	the	DET
ejpam-5455	138	3	preceding	precede	VERB
ejpam-5455	138	4	illustration	illustration	NOUN
ejpam-5455	138	5	,	,	PUNCT
ejpam-5455	138	6	it	it	PRON
ejpam-5455	138	7	is	be	AUX
ejpam-5455	138	8	observed	observe	VERB
ejpam-5455	138	9	that	that	SCONJ
ejpam-5455	138	10	the	the	DET
ejpam-5455	138	11	fractional	fractional	ADJ
ejpam-5455	138	12	derivative	derivative	ADJ
ejpam-5455	138	13	mabcd	mabcd	NOUN
ejpam-5455	138	14	3	3	NUM
ejpam-5455	138	15	4	4	NUM
ejpam-5455	138	16	0+u(0	0+u(0	NOUN
ejpam-5455	138	17	)	)	PUNCT
ejpam-5455	138	18	̸=	̸=	NOUN
ejpam-5455	138	19	0	0	NUM
ejpam-5455	138	20	at	at	ADP
ejpam-5455	138	21	the	the	DET
ejpam-5455	138	22	point	point	NOUN
ejpam-5455	138	23	7	7	NUM
ejpam-5455	138	24	=	=	SYM
ejpam-5455	138	25	0	0	NUM
ejpam-5455	138	26	.	.	PUNCT
ejpam-5455	139	1	finally	finally	ADV
ejpam-5455	139	2	,	,	PUNCT
ejpam-5455	139	3	we	we	PRON
ejpam-5455	139	4	recall	recall	VERB
ejpam-5455	139	5	the	the	DET
ejpam-5455	139	6	well	well	ADV
ejpam-5455	139	7	-	-	PUNCT
ejpam-5455	139	8	known	know	VERB
ejpam-5455	139	9	related	relate	VERB
ejpam-5455	139	10	to	to	ADP
ejpam-5455	139	11	caputo	caputo	PROPN
ejpam-5455	139	12	fractional	fractional	PROPN
ejpam-5455	139	13	derivative	derivative	PROPN
ejpam-5455	139	14	and	and	CCONJ
ejpam-5455	139	15	the	the	DET
ejpam-5455	139	16	properties	property	NOUN
ejpam-5455	139	17	of	of	ADP
ejpam-5455	139	18	the	the	DET
ejpam-5455	139	19	p	p	ADJ
ejpam-5455	139	20	-	-	PUNCT
ejpam-5455	139	21	laplacian	laplacian	ADJ
ejpam-5455	139	22	operator	operator	NOUN
ejpam-5455	139	23	.	.	PUNCT
ejpam-5455	140	1	definition	definition	NOUN
ejpam-5455	140	2	4	4	NUM
ejpam-5455	140	3	.	.	PUNCT
ejpam-5455	141	1	[	[	X
ejpam-5455	141	2	6	6	NUM
ejpam-5455	141	3	,	,	PUNCT
ejpam-5455	141	4	26	26	NUM
ejpam-5455	141	5	]	]	PUNCT
ejpam-5455	141	6	for	for	ADP
ejpam-5455	141	7	any	any	DET
ejpam-5455	141	8	ρ	ρ	NOUN
ejpam-5455	141	9	>	>	X
ejpam-5455	141	10	0	0	PUNCT
ejpam-5455	141	11	and	and	CCONJ
ejpam-5455	141	12	u	u	PROPN
ejpam-5455	141	13	∈	∈	PROPN
ejpam-5455	141	14	c(0	c(0	PROPN
ejpam-5455	141	15	,	,	PUNCT
ejpam-5455	141	16	t	t	NOUN
ejpam-5455	141	17	)	)	PUNCT
ejpam-5455	141	18	∩	∩	PROPN
ejpam-5455	141	19	l(0	l(0	PROPN
ejpam-5455	141	20	,	,	PUNCT
ejpam-5455	141	21	z	z	NOUN
ejpam-5455	141	22	)	)	PUNCT
ejpam-5455	141	23	,	,	PUNCT
ejpam-5455	141	24	we	we	PRON
ejpam-5455	141	25	have	have	AUX
ejpam-5455	141	26	iρ0+d	iρ0+d	VERB
ejpam-5455	141	27	ρ	ρ	PROPN
ejpam-5455	141	28	0+u(7	0+u(7	NOUN
ejpam-5455	141	29	)	)	PUNCT
ejpam-5455	141	30	=	=	SYM
ejpam-5455	142	1	u(7	u(7	X
ejpam-5455	142	2	)	)	PUNCT
ejpam-5455	143	1	+	+	CCONJ
ejpam-5455	143	2	c0	c0	NOUN
ejpam-5455	143	3	+	+	CCONJ
ejpam-5455	143	4	c17	c17	NOUN
ejpam-5455	143	5	+	+	X
ejpam-5455	143	6	.	.	PUNCT
ejpam-5455	143	7	.	.	PUNCT
ejpam-5455	144	1	.+	.+	NOUN
ejpam-5455	144	2	cn−17n−1	cn−17n−1	PROPN
ejpam-5455	144	3	,	,	PUNCT
ejpam-5455	144	4	fore	fore	NOUN
ejpam-5455	144	5	some	some	DET
ejpam-5455	144	6	ci	ci	NOUN
ejpam-5455	144	7	∈	∈	PROPN
ejpam-5455	144	8	r	r	NOUN
ejpam-5455	144	9	,	,	PUNCT
ejpam-5455	144	10	i	i	NOUN
ejpam-5455	144	11	=	=	NOUN
ejpam-5455	144	12	1	1	NUM
ejpam-5455	144	13	,	,	PUNCT
ejpam-5455	144	14	2	2	NUM
ejpam-5455	144	15	,	,	PUNCT
ejpam-5455	144	16	.	.	PUNCT
ejpam-5455	144	17	.	.	PUNCT
ejpam-5455	145	1	.	.	PUNCT
ejpam-5455	146	1	,	,	PUNCT
ejpam-5455	147	1	n	n	CCONJ
ejpam-5455	147	2	−	−	PROPN
ejpam-5455	148	1	1	1	NUM
ejpam-5455	148	2	.	.	PUNCT
ejpam-5455	148	3	where	where	SCONJ
ejpam-5455	148	4	n	n	NOUN
ejpam-5455	148	5	=	=	SYM
ejpam-5455	149	1	[	[	X
ejpam-5455	149	2	ρ	ρ	X
ejpam-5455	149	3	]	]	X
ejpam-5455	149	4	+	+	NOUN
ejpam-5455	149	5	1	1	X
ejpam-5455	149	6	.	.	X
ejpam-5455	149	7	in	in	ADP
ejpam-5455	149	8	particular	particular	ADJ
ejpam-5455	149	9	,	,	PUNCT
ejpam-5455	149	10	when	when	SCONJ
ejpam-5455	149	11	ρ	ρ	PROPN
ejpam-5455	149	12	∈	∈	PROPN
ejpam-5455	149	13	(	(	PUNCT
ejpam-5455	149	14	0	0	NUM
ejpam-5455	149	15	,	,	PUNCT
ejpam-5455	149	16	1	1	NUM
ejpam-5455	149	17	)	)	PUNCT
ejpam-5455	149	18	,	,	PUNCT
ejpam-5455	149	19	iρ0+d	iρ0+d	PROPN
ejpam-5455	149	20	ρ	ρ	PROPN
ejpam-5455	149	21	0+u(7	0+u(7	PROPN
ejpam-5455	149	22	)	)	PUNCT
ejpam-5455	149	23	=	=	SYM
ejpam-5455	150	1	u(7	u(7	X
ejpam-5455	150	2	)	)	PUNCT
ejpam-5455	151	1	+	+	CCONJ
ejpam-5455	151	2	c0	c0	NOUN
ejpam-5455	151	3	.	.	PUNCT
ejpam-5455	152	1	definition	definition	NOUN
ejpam-5455	152	2	5	5	NUM
ejpam-5455	152	3	.	.	PUNCT
ejpam-5455	153	1	[	[	X
ejpam-5455	153	2	23	23	NUM
ejpam-5455	153	3	]	]	PUNCT
ejpam-5455	153	4	the	the	DET
ejpam-5455	153	5	p	p	PROPN
ejpam-5455	153	6	-	-	PUNCT
ejpam-5455	153	7	laplacian	laplacian	ADJ
ejpam-5455	153	8	operator	operator	NOUN
ejpam-5455	153	9	is	be	AUX
ejpam-5455	153	10	given	give	VERB
ejpam-5455	153	11	by	by	ADP
ejpam-5455	153	12	ψp(ū	ψp(ū	PROPN
ejpam-5455	153	13	)	)	PUNCT
ejpam-5455	153	14	=	=	SYM
ejpam-5455	153	15	|ū|p−2ū	|ū|p−2ū	NOUN
ejpam-5455	154	1	=	=	SYM
ejpam-5455	154	2	ūp−1	ūp−1	NOUN
ejpam-5455	154	3	,	,	PUNCT
ejpam-5455	154	4	ū	ū	NOUN
ejpam-5455	154	5	≥	≥	NUM
ejpam-5455	154	6	0	0	NUM
ejpam-5455	154	7	,	,	PUNCT
ejpam-5455	154	8	p	p	X
ejpam-5455	154	9	>	>	X
ejpam-5455	154	10	1	1	NUM
ejpam-5455	154	11	,	,	PUNCT
ejpam-5455	154	12	(	(	PUNCT
ejpam-5455	154	13	7	7	X
ejpam-5455	154	14	)	)	PUNCT
ejpam-5455	154	15	at	at	ADP
ejpam-5455	154	16	which	which	PRON
ejpam-5455	154	17	ψ−1	ψ−1	PROPN
ejpam-5455	154	18	p	p	X
ejpam-5455	154	19	=	=	PUNCT
ejpam-5455	154	20	ψq	ψq	X
ejpam-5455	154	21	where	where	SCONJ
ejpam-5455	154	22	1	1	NUM
ejpam-5455	154	23	p	p	NOUN
ejpam-5455	154	24	+	+	NOUN
ejpam-5455	154	25	1	1	NUM
ejpam-5455	154	26	q	q	NOUN
ejpam-5455	154	27	=	=	ADJ
ejpam-5455	154	28	1	1	X
ejpam-5455	154	29	.	.	PUNCT
ejpam-5455	154	30	lemma	lemma	PROPN
ejpam-5455	154	31	1	1	NUM
ejpam-5455	154	32	.	.	PUNCT
ejpam-5455	155	1	[	[	X
ejpam-5455	155	2	23	23	NUM
ejpam-5455	155	3	]	]	PUNCT
ejpam-5455	155	4	assume	assume	VERB
ejpam-5455	155	5	that	that	SCONJ
ejpam-5455	155	6	ψp(ū	ψp(ū	PRON
ejpam-5455	155	7	)	)	PUNCT
ejpam-5455	155	8	,	,	PUNCT
ejpam-5455	155	9	p	p	NOUN
ejpam-5455	155	10	≥	≥	NOUN
ejpam-5455	155	11	2	2	NUM
ejpam-5455	155	12	,	,	PUNCT
ejpam-5455	155	13	be	be	AUX
ejpam-5455	155	14	p	p	ADJ
ejpam-5455	155	15	-	-	PUNCT
ejpam-5455	155	16	laplacian	laplacian	ADJ
ejpam-5455	155	17	operator	operator	NOUN
ejpam-5455	155	18	and	and	CCONJ
ejpam-5455	155	19	|ū|	|ū|	NOUN
ejpam-5455	155	20	,	,	PUNCT
ejpam-5455	155	21	|v̄|	|v̄|	PROPN
ejpam-5455	155	22	≤	≤	NUM
ejpam-5455	155	23	m	m	NOUN
ejpam-5455	155	24	,	,	PUNCT
ejpam-5455	155	25	then	then	ADV
ejpam-5455	155	26	|ψp(ū)−ψp(v̄)|	|ψp(ū)−ψp(v̄)|	PROPN
ejpam-5455	155	27	≤	≤	NOUN
ejpam-5455	155	28	(	(	PUNCT
ejpam-5455	155	29	p−	p−	NOUN
ejpam-5455	155	30	1)mp−2|ū−	1)mp−2|ū−	NOUN
ejpam-5455	155	31	v̄|	v̄|	PROPN
ejpam-5455	155	32	.	.	PUNCT
ejpam-5455	156	1	(	(	PUNCT
ejpam-5455	156	2	8)	8)	NUM
ejpam-5455	156	3	definition	definition	NOUN
ejpam-5455	156	4	6	6	NUM
ejpam-5455	156	5	.	.	PUNCT
ejpam-5455	157	1	a	a	DET
ejpam-5455	157	2	function	function	NOUN
ejpam-5455	157	3	w	w	PROPN
ejpam-5455	157	4	∈	∈	PROPN
ejpam-5455	157	5	ac(ω	ac(ω	X
ejpam-5455	157	6	,	,	PUNCT
ejpam-5455	157	7	r	r	NOUN
ejpam-5455	157	8	)	)	PUNCT
ejpam-5455	157	9	is	be	AUX
ejpam-5455	157	10	called	call	VERB
ejpam-5455	157	11	a	a	DET
ejpam-5455	157	12	solution	solution	NOUN
ejpam-5455	157	13	of	of	ADP
ejpam-5455	157	14	the	the	DET
ejpam-5455	157	15	system	system	NOUN
ejpam-5455	157	16	(	(	PUNCT
ejpam-5455	157	17	1	1	X
ejpam-5455	157	18	)	)	PUNCT
ejpam-5455	157	19	if	if	SCONJ
ejpam-5455	157	20	function	function	VERB
ejpam-5455	157	21	g	g	PROPN
ejpam-5455	157	22	∈	∈	PROPN
ejpam-5455	157	23	l1(ω	l1(ω	PROPN
ejpam-5455	157	24	,	,	PUNCT
ejpam-5455	157	25	r	r	NOUN
ejpam-5455	157	26	)	)	PUNCT
ejpam-5455	157	27	,	,	PUNCT
ejpam-5455	157	28	and	and	CCONJ
ejpam-5455	157	29	w	w	PROPN
ejpam-5455	157	30	fulfills	fulfills	PROPN
ejpam-5455	157	31	(	(	PUNCT
ejpam-5455	157	32	1	1	NUM
ejpam-5455	157	33	)	)	PUNCT
ejpam-5455	157	34	.	.	PUNCT
ejpam-5455	158	1	lemma	lemma	PROPN
ejpam-5455	158	2	2	2	X
ejpam-5455	158	3	.	.	PUNCT
ejpam-5455	159	1	let	let	VERB
ejpam-5455	159	2	0	0	NUM
ejpam-5455	159	3	<	<	X
ejpam-5455	159	4	ρ	ρ	X
ejpam-5455	159	5	<	<	X
ejpam-5455	159	6	1	1	NUM
ejpam-5455	159	7	and	and	CCONJ
ejpam-5455	159	8	g	g	PROPN
ejpam-5455	159	9	∈	∈	PROPN
ejpam-5455	159	10	l1(0	l1(0	PROPN
ejpam-5455	159	11	,	,	PUNCT
ejpam-5455	159	12	z	z	NOUN
ejpam-5455	159	13	)	)	PUNCT
ejpam-5455	159	14	.	.	PUNCT
ejpam-5455	160	1	then	then	ADV
ejpam-5455	160	2	,	,	PUNCT
ejpam-5455	160	3	the	the	DET
ejpam-5455	160	4	solution	solution	NOUN
ejpam-5455	160	5	w	w	PROPN
ejpam-5455	160	6	∈	∈	PROPN
ejpam-5455	160	7	ac(ω	ac(ω	X
ejpam-5455	160	8	,	,	PUNCT
ejpam-5455	160	9	r	r	NOUN
ejpam-5455	160	10	)	)	PUNCT
ejpam-5455	160	11	of	of	ADP
ejpam-5455	160	12	the	the	DET
ejpam-5455	160	13	system	system	NOUN
ejpam-5455	160	14	(	(	PUNCT
ejpam-5455	160	15	1	1	X
ejpam-5455	160	16	)	)	PUNCT
ejpam-5455	160	17	iff	iff	NOUN
ejpam-5455	160	18	it	it	PRON
ejpam-5455	160	19	is	be	AUX
ejpam-5455	160	20	a	a	DET
ejpam-5455	160	21	solution	solution	NOUN
ejpam-5455	160	22	to	to	ADP
ejpam-5455	160	23	the	the	DET
ejpam-5455	160	24	subsequent	subsequent	ADJ
ejpam-5455	160	25	integral	integral	ADJ
ejpam-5455	160	26	equation	equation	NOUN
ejpam-5455	160	27	:	:	PUNCT
ejpam-5455	160	28	w(7	w(7	X
ejpam-5455	160	29	)	)	PUNCT
ejpam-5455	160	30	=	=	PRON
ejpam-5455	160	31	(	(	PUNCT
ejpam-5455	160	32	q(7	q(7	PROPN
ejpam-5455	160	33	)	)	PUNCT
ejpam-5455	161	1	+	+	CCONJ
ejpam-5455	161	2	1	1	NUM
ejpam-5455	161	3	γ(γ	γ(γ	NOUN
ejpam-5455	161	4	)	)	PUNCT
ejpam-5455	161	5	∫	∫	PROPN
ejpam-5455	161	6	7	7	NUM
ejpam-5455	161	7	0	0	NUM
ejpam-5455	161	8	(	(	PUNCT
ejpam-5455	161	9	7	7	NUM
ejpam-5455	161	10	−	−	NOUN
ejpam-5455	161	11	σ)γ−1f(σ	σ)γ−1f(σ	NOUN
ejpam-5455	161	12	,	,	PUNCT
ejpam-5455	161	13	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	161	14	)	)	PUNCT
ejpam-5455	161	15	(	(	PUNCT
ejpam-5455	161	16	×	×	NOUN
ejpam-5455	161	17	)	)	PUNCT
ejpam-5455	161	18	[	[	PUNCT
ejpam-5455	161	19	abiρ0+(θ	abiρ0+(θ	NOUN
ejpam-5455	161	20	)	)	PUNCT
ejpam-5455	162	1	+	+	CCONJ
ejpam-5455	162	2	1−	1−	NUM
ejpam-5455	162	3	ρ	ρ	NUM
ejpam-5455	162	4	b(ρ	b(ρ	PROPN
ejpam-5455	162	5	)	)	PUNCT
ejpam-5455	162	6	ψq	ψq	PROPN
ejpam-5455	162	7	(	(	PUNCT
ejpam-5455	162	8	1	1	NUM
ejpam-5455	162	9	γ(β	γ(β	PROPN
ejpam-5455	162	10	)	)	PUNCT
ejpam-5455	162	11	∫	∫	PROPN
ejpam-5455	163	1	7	7	NUM
ejpam-5455	163	2	0	0	NUM
ejpam-5455	163	3	(	(	PUNCT
ejpam-5455	163	4	7	7	NUM
ejpam-5455	163	5	−	−	NOUN
ejpam-5455	163	6	σ)β−1g(σ	σ)β−1g(σ	NOUN
ejpam-5455	163	7	,	,	PUNCT
ejpam-5455	163	8	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	163	9	)	)	PUNCT
ejpam-5455	164	1	+	+	CCONJ
ejpam-5455	164	2	ρ	ρ	PROPN
ejpam-5455	164	3	b(ρ)γ(ρ	b(ρ)γ(ρ	NOUN
ejpam-5455	164	4	)	)	PUNCT
ejpam-5455	164	5	∫	∫	PROPN
ejpam-5455	165	1	7	7	NUM
ejpam-5455	165	2	0	0	NUM
ejpam-5455	165	3	(	(	PUNCT
ejpam-5455	165	4	7	7	NUM
ejpam-5455	165	5	−	−	NOUN
ejpam-5455	165	6	σ)ρ−1	σ)ρ−1	NOUN
ejpam-5455	165	7	(	(	PUNCT
ejpam-5455	165	8	ψq	ψq	X
ejpam-5455	165	9	(	(	PUNCT
ejpam-5455	165	10	1	1	NUM
ejpam-5455	165	11	γ(β	γ(β	PROPN
ejpam-5455	165	12	)	)	PUNCT
ejpam-5455	165	13	∫	∫	PROPN
ejpam-5455	166	1	σ	σ	PROPN
ejpam-5455	166	2	0	0	NUM
ejpam-5455	166	3	(	(	PUNCT
ejpam-5455	166	4	σ	σ	NOUN
ejpam-5455	166	5	−	−	PROPN
ejpam-5455	166	6	τ)β−1g(τ	τ)β−1g(τ	PUNCT
ejpam-5455	166	7	,	,	PUNCT
ejpam-5455	166	8	w(τ))dτ	w(τ))dτ	PROPN
ejpam-5455	166	9	)	)	PUNCT
ejpam-5455	166	10	)	)	PUNCT
ejpam-5455	166	11	dσ	dσ	VERB
ejpam-5455	166	12	]	]	PUNCT
ejpam-5455	166	13	+	+	CCONJ
ejpam-5455	166	14	h(7	h(7	PROPN
ejpam-5455	166	15	,	,	PUNCT
ejpam-5455	166	16	w(7	w(7	PROPN
ejpam-5455	166	17	)	)	PUNCT
ejpam-5455	166	18	)	)	PUNCT
ejpam-5455	166	19	.	.	PUNCT
ejpam-5455	167	1	(	(	PUNCT
ejpam-5455	167	2	9	9	X
ejpam-5455	167	3	)	)	PUNCT
ejpam-5455	167	4	proof	proof	NOUN
ejpam-5455	167	5	.	.	PUNCT
ejpam-5455	168	1	since	since	SCONJ
ejpam-5455	168	2	cdβ	cdβ	PROPN
ejpam-5455	168	3	(	(	PUNCT
ejpam-5455	168	4	ψp	ψp	X
ejpam-5455	168	5	(	(	PUNCT
ejpam-5455	168	6	mabcdρ	mabcdρ	PROPN
ejpam-5455	168	7	0	0	PUNCT
ejpam-5455	168	8	+	+	CCONJ
ejpam-5455	168	9	(	(	PUNCT
ejpam-5455	168	10	w(7)−	w(7)−	PROPN
ejpam-5455	168	11	h(7	h(7	PROPN
ejpam-5455	168	12	,	,	PUNCT
ejpam-5455	168	13	w(7	w(7	NOUN
ejpam-5455	168	14	)	)	PUNCT
ejpam-5455	168	15	)	)	PUNCT
ejpam-5455	168	16	q(7	q(7	PROPN
ejpam-5455	168	17	)	)	PUNCT
ejpam-5455	168	18	+	+	NUM
ejpam-5455	168	19	iγ0+f(7	iγ0+f(7	NOUN
ejpam-5455	168	20	,	,	PUNCT
ejpam-5455	168	21	w(7	w(7	PROPN
ejpam-5455	168	22	)	)	PUNCT
ejpam-5455	168	23	)	)	PUNCT
ejpam-5455	168	24	)	)	PUNCT
ejpam-5455	168	25	)	)	PUNCT
ejpam-5455	168	26	)	)	PUNCT
ejpam-5455	169	1	=	=	SYM
ejpam-5455	169	2	g(7	g(7	PROPN
ejpam-5455	169	3	,	,	PUNCT
ejpam-5455	169	4	w(7	w(7	PROPN
ejpam-5455	169	5	)	)	PUNCT
ejpam-5455	169	6	)	)	PUNCT
ejpam-5455	169	7	.	.	PUNCT
ejpam-5455	170	1	taking	take	VERB
ejpam-5455	170	2	iβ0	iβ0	NOUN
ejpam-5455	170	3	+	+	X
ejpam-5455	170	4	on	on	ADP
ejpam-5455	170	5	both	both	DET
ejpam-5455	170	6	sides	side	NOUN
ejpam-5455	170	7	of	of	ADP
ejpam-5455	170	8	the	the	DET
ejpam-5455	170	9	above	above	ADJ
ejpam-5455	170	10	equation	equation	NOUN
ejpam-5455	170	11	,	,	PUNCT
ejpam-5455	170	12	we	we	PRON
ejpam-5455	170	13	have	have	VERB
ejpam-5455	170	14	ψp	ψp	VERB
ejpam-5455	170	15	(	(	PUNCT
ejpam-5455	170	16	mabcdρ	mabcdρ	PROPN
ejpam-5455	170	17	0	0	PUNCT
ejpam-5455	171	1	+	+	CCONJ
ejpam-5455	171	2	(	(	PUNCT
ejpam-5455	171	3	w(7)−	w(7)−	PROPN
ejpam-5455	171	4	h(7	h(7	PROPN
ejpam-5455	171	5	,	,	PUNCT
ejpam-5455	171	6	w(7	w(7	NOUN
ejpam-5455	171	7	)	)	PUNCT
ejpam-5455	171	8	)	)	PUNCT
ejpam-5455	172	1	q(7	q(7	PROPN
ejpam-5455	172	2	)	)	PUNCT
ejpam-5455	172	3	+	+	NUM
ejpam-5455	172	4	iγ0+f(7	iγ0+f(7	NOUN
ejpam-5455	172	5	,	,	PUNCT
ejpam-5455	172	6	w(7	w(7	PROPN
ejpam-5455	172	7	)	)	PUNCT
ejpam-5455	172	8	)	)	PUNCT
ejpam-5455	172	9	)	)	PUNCT
ejpam-5455	172	10	)	)	PUNCT
ejpam-5455	173	1	=	=	SYM
ejpam-5455	173	2	iβ0+g(7	iβ0+g(7	PROPN
ejpam-5455	173	3	,	,	PUNCT
ejpam-5455	173	4	w(7	w(7	PROPN
ejpam-5455	173	5	)	)	PUNCT
ejpam-5455	173	6	)	)	PUNCT
ejpam-5455	174	1	+	+	CCONJ
ejpam-5455	174	2	c0	c0	NOUN
ejpam-5455	174	3	,	,	PUNCT
ejpam-5455	174	4	m.	m.	NOUN
ejpam-5455	174	5	m.	m.	NOUN
ejpam-5455	174	6	arjunan	arjunan	PROPN
ejpam-5455	174	7	/	/	SYM
ejpam-5455	174	8	eur	eur	PROPN
ejpam-5455	174	9	.	.	PUNCT
ejpam-5455	175	1	j.	j.	PROPN
ejpam-5455	175	2	pure	pure	PROPN
ejpam-5455	175	3	appl	appl	PROPN
ejpam-5455	175	4	.	.	PROPN
ejpam-5455	175	5	math	math	PROPN
ejpam-5455	175	6	,	,	PUNCT
ejpam-5455	175	7	17	17	NUM
ejpam-5455	175	8	(	(	PUNCT
ejpam-5455	175	9	4	4	NUM
ejpam-5455	175	10	)	)	PUNCT
ejpam-5455	175	11	(	(	PUNCT
ejpam-5455	175	12	2024	2024	NUM
ejpam-5455	175	13	)	)	PUNCT
ejpam-5455	175	14	,	,	PUNCT
ejpam-5455	175	15	4071	4071	NUM
ejpam-5455	175	16	-	-	SYM
ejpam-5455	175	17	4092	4092	NUM
ejpam-5455	175	18	4078	4078	NUM
ejpam-5455	175	19	for	for	ADP
ejpam-5455	175	20	some	some	DET
ejpam-5455	175	21	c0	c0	PROPN
ejpam-5455	175	22	∈	∈	PROPN
ejpam-5455	175	23	r.	r.	PROPN
ejpam-5455	175	24	at	at	ADP
ejpam-5455	175	25	7	7	NUM
ejpam-5455	175	26	=	=	SYM
ejpam-5455	175	27	0	0	NUM
ejpam-5455	175	28	,	,	PUNCT
ejpam-5455	175	29	we	we	PRON
ejpam-5455	175	30	have	have	AUX
ejpam-5455	175	31	ψp	ψp	VERB
ejpam-5455	175	32	(	(	PUNCT
ejpam-5455	175	33	mabcdρ	mabcdρ	PROPN
ejpam-5455	175	34	0	0	PUNCT
ejpam-5455	176	1	+	+	CCONJ
ejpam-5455	177	1	(	(	PUNCT
ejpam-5455	177	2	w(0)−	w(0)−	PROPN
ejpam-5455	177	3	h(0	h(0	PROPN
ejpam-5455	177	4	,	,	PUNCT
ejpam-5455	177	5	w(0	w(0	PROPN
ejpam-5455	177	6	)	)	PUNCT
ejpam-5455	177	7	)	)	PUNCT
ejpam-5455	178	1	q(0	q(0	NOUN
ejpam-5455	178	2	)	)	PUNCT
ejpam-5455	178	3	)	)	PUNCT
ejpam-5455	178	4	)	)	PUNCT
ejpam-5455	179	1	=	=	SYM
ejpam-5455	179	2	c0	c0	NOUN
ejpam-5455	179	3	.	.	PUNCT
ejpam-5455	180	1	that	that	PRON
ejpam-5455	180	2	is	is	ADV
ejpam-5455	180	3	ψp	ψp	NOUN
ejpam-5455	180	4	(	(	PUNCT
ejpam-5455	180	5	mabcdρ	mabcdρ	PROPN
ejpam-5455	180	6	0	0	PUNCT
ejpam-5455	181	1	+	+	CCONJ
ejpam-5455	181	2	(	(	PUNCT
ejpam-5455	181	3	w(7)−	w(7)−	PROPN
ejpam-5455	181	4	h(7	h(7	PROPN
ejpam-5455	181	5	,	,	PUNCT
ejpam-5455	181	6	w(7	w(7	NOUN
ejpam-5455	181	7	)	)	PUNCT
ejpam-5455	181	8	)	)	PUNCT
ejpam-5455	182	1	q(7	q(7	PROPN
ejpam-5455	182	2	)	)	PUNCT
ejpam-5455	182	3	+	+	NUM
ejpam-5455	182	4	iγ0+f(7	iγ0+f(7	NOUN
ejpam-5455	182	5	,	,	PUNCT
ejpam-5455	182	6	w(7	w(7	PROPN
ejpam-5455	182	7	)	)	PUNCT
ejpam-5455	182	8	)	)	PUNCT
ejpam-5455	182	9	)	)	PUNCT
ejpam-5455	182	10	)	)	PUNCT
ejpam-5455	182	11	−ψp	−ψp	PROPN
ejpam-5455	182	12	(	(	PUNCT
ejpam-5455	182	13	mabcdρ	mabcdρ	PROPN
ejpam-5455	182	14	0	0	PUNCT
ejpam-5455	182	15	+	+	CCONJ
ejpam-5455	182	16	(	(	PUNCT
ejpam-5455	182	17	w(0)−	w(0)−	PROPN
ejpam-5455	182	18	h(0	h(0	PROPN
ejpam-5455	182	19	,	,	PUNCT
ejpam-5455	182	20	w(0	w(0	PROPN
ejpam-5455	182	21	)	)	PUNCT
ejpam-5455	182	22	)	)	PUNCT
ejpam-5455	183	1	q(0	q(0	NOUN
ejpam-5455	183	2	)	)	PUNCT
ejpam-5455	183	3	)	)	PUNCT
ejpam-5455	183	4	)	)	PUNCT
ejpam-5455	184	1	=	=	SYM
ejpam-5455	184	2	iβ0+g(7	iβ0+g(7	PROPN
ejpam-5455	184	3	,	,	PUNCT
ejpam-5455	184	4	w(7	w(7	PROPN
ejpam-5455	184	5	)	)	PUNCT
ejpam-5455	184	6	)	)	PUNCT
ejpam-5455	184	7	.	.	PUNCT
ejpam-5455	185	1	by	by	ADP
ejpam-5455	185	2	the	the	DET
ejpam-5455	185	3	properties	property	NOUN
ejpam-5455	185	4	of	of	ADP
ejpam-5455	185	5	p	p	NOUN
ejpam-5455	185	6	-	-	PUNCT
ejpam-5455	185	7	laplacian	laplacian	ADJ
ejpam-5455	185	8	operator	operator	NOUN
ejpam-5455	185	9	,	,	PUNCT
ejpam-5455	185	10	we	we	PRON
ejpam-5455	185	11	have	have	VERB
ejpam-5455	185	12	mabcdρ	mabcdρ	VERB
ejpam-5455	185	13	0	0	PUNCT
ejpam-5455	186	1	+	+	CCONJ
ejpam-5455	186	2	(	(	PUNCT
ejpam-5455	186	3	w(7)−	w(7)−	PROPN
ejpam-5455	186	4	h(7	h(7	PROPN
ejpam-5455	186	5	,	,	PUNCT
ejpam-5455	186	6	w(7	w(7	NOUN
ejpam-5455	186	7	)	)	PUNCT
ejpam-5455	186	8	)	)	PUNCT
ejpam-5455	187	1	q(7	q(7	PROPN
ejpam-5455	187	2	)	)	PUNCT
ejpam-5455	187	3	+	+	NUM
ejpam-5455	187	4	iγ0+f(7	iγ0+f(7	NOUN
ejpam-5455	187	5	,	,	PUNCT
ejpam-5455	187	6	w(7	w(7	PROPN
ejpam-5455	187	7	)	)	PUNCT
ejpam-5455	187	8	)	)	PUNCT
ejpam-5455	187	9	)	)	PUNCT
ejpam-5455	188	1	−mabc	−mabc	X
ejpam-5455	188	2	dρ	dρ	VERB
ejpam-5455	188	3	0	0	PUNCT
ejpam-5455	189	1	+	+	CCONJ
ejpam-5455	189	2	(	(	PUNCT
ejpam-5455	189	3	w(0)−	w(0)−	PROPN
ejpam-5455	189	4	h(0	h(0	PROPN
ejpam-5455	189	5	,	,	PUNCT
ejpam-5455	189	6	w(0	w(0	PROPN
ejpam-5455	189	7	)	)	PUNCT
ejpam-5455	189	8	)	)	PUNCT
ejpam-5455	190	1	q(0	q(0	NOUN
ejpam-5455	190	2	)	)	PUNCT
ejpam-5455	190	3	)	)	PUNCT
ejpam-5455	191	1	=	=	PUNCT
ejpam-5455	191	2	ψq	ψq	PROPN
ejpam-5455	191	3	(	(	PUNCT
ejpam-5455	191	4	iβ0+g(7	iβ0+g(7	NOUN
ejpam-5455	191	5	,	,	PUNCT
ejpam-5455	191	6	w(7	w(7	PROPN
ejpam-5455	191	7	)	)	PUNCT
ejpam-5455	191	8	)	)	PUNCT
ejpam-5455	191	9	)	)	PUNCT
ejpam-5455	191	10	.	.	PUNCT
ejpam-5455	192	1	taking	take	VERB
ejpam-5455	192	2	abiρ0	abiρ0	NOUN
ejpam-5455	192	3	+	+	X
ejpam-5455	192	4	on	on	ADP
ejpam-5455	192	5	both	both	DET
ejpam-5455	192	6	sides	side	NOUN
ejpam-5455	192	7	of	of	ADP
ejpam-5455	192	8	the	the	DET
ejpam-5455	192	9	above	above	ADJ
ejpam-5455	192	10	equation	equation	NOUN
ejpam-5455	192	11	,	,	PUNCT
ejpam-5455	192	12	we	we	PRON
ejpam-5455	192	13	have	have	VERB
ejpam-5455	192	14	w(7)−	w(7)−	NOUN
ejpam-5455	192	15	h(7	h(7	NOUN
ejpam-5455	192	16	,	,	PUNCT
ejpam-5455	192	17	w(7	w(7	NOUN
ejpam-5455	192	18	)	)	PUNCT
ejpam-5455	192	19	)	)	PUNCT
ejpam-5455	193	1	q(7	q(7	PROPN
ejpam-5455	193	2	)	)	PUNCT
ejpam-5455	193	3	+	+	NUM
ejpam-5455	193	4	iγ0+f(7	iγ0+f(7	NOUN
ejpam-5455	193	5	,	,	PUNCT
ejpam-5455	193	6	w(7	w(7	PROPN
ejpam-5455	193	7	)	)	PUNCT
ejpam-5455	193	8	)	)	PUNCT
ejpam-5455	194	1	−	−	PROPN
ejpam-5455	194	2	w(0)−	w(0)−	NOUN
ejpam-5455	194	3	h(0	h(0	PROPN
ejpam-5455	194	4	,	,	PUNCT
ejpam-5455	194	5	w(0	w(0	PROPN
ejpam-5455	194	6	)	)	PUNCT
ejpam-5455	194	7	)	)	PUNCT
ejpam-5455	195	1	q(0	q(0	NOUN
ejpam-5455	195	2	)	)	PUNCT
ejpam-5455	195	3	=	=	PUNCT
ejpam-5455	196	1	abiρ0	abiρ0	PROPN
ejpam-5455	196	2	+	+	CCONJ
ejpam-5455	196	3	(	(	PUNCT
ejpam-5455	196	4	ψq	ψq	PROPN
ejpam-5455	196	5	(	(	PUNCT
ejpam-5455	196	6	iβ0+g(7	iβ0+g(7	NOUN
ejpam-5455	196	7	,	,	PUNCT
ejpam-5455	196	8	w(7	w(7	PROPN
ejpam-5455	196	9	)	)	PUNCT
ejpam-5455	196	10	)	)	PUNCT
ejpam-5455	196	11	)	)	PUNCT
ejpam-5455	196	12	)	)	PUNCT
ejpam-5455	197	1	by	by	ADP
ejpam-5455	197	2	using	use	VERB
ejpam-5455	197	3	the	the	DET
ejpam-5455	197	4	fact	fact	NOUN
ejpam-5455	197	5	that	that	SCONJ
ejpam-5455	197	6	(	(	PUNCT
ejpam-5455	197	7	abiρ0	abiρ0	PROPN
ejpam-5455	197	8	+	+	CCONJ
ejpam-5455	197	9	mabcdρ	mabcdρ	PROPN
ejpam-5455	197	10	0+w	0+w	NUM
ejpam-5455	197	11	)	)	PUNCT
ejpam-5455	197	12	(	(	PUNCT
ejpam-5455	197	13	7	7	X
ejpam-5455	197	14	)	)	PUNCT
ejpam-5455	197	15	=	=	SYM
ejpam-5455	197	16	w(7)−	w(7)−	PROPN
ejpam-5455	197	17	w(0	w(0	PROPN
ejpam-5455	197	18	)	)	PUNCT
ejpam-5455	197	19	.	.	PUNCT
ejpam-5455	198	1	thus	thus	ADV
ejpam-5455	198	2	w(7	w(7	ADV
ejpam-5455	198	3	)	)	PUNCT
ejpam-5455	198	4	=	=	PRON
ejpam-5455	198	5	(	(	PUNCT
ejpam-5455	198	6	q(7	q(7	PROPN
ejpam-5455	198	7	)	)	PUNCT
ejpam-5455	198	8	+	+	NUM
ejpam-5455	198	9	iγ0+f(7	iγ0+f(7	NOUN
ejpam-5455	198	10	,	,	PUNCT
ejpam-5455	198	11	w(7	w(7	PROPN
ejpam-5455	198	12	)	)	PUNCT
ejpam-5455	198	13	)	)	PUNCT
ejpam-5455	198	14	)	)	PUNCT
ejpam-5455	199	1	(	(	PUNCT
ejpam-5455	199	2	abiρ0+(θ	abiρ0+(θ	PROPN
ejpam-5455	199	3	)	)	PUNCT
ejpam-5455	200	1	+	+	CCONJ
ejpam-5455	200	2	abiρ0	abiρ0	NUM
ejpam-5455	200	3	+	+	SYM
ejpam-5455	200	4	(	(	PUNCT
ejpam-5455	200	5	ψq	ψq	PROPN
ejpam-5455	200	6	(	(	PUNCT
ejpam-5455	200	7	iβ0+g(7	iβ0+g(7	NOUN
ejpam-5455	200	8	,	,	PUNCT
ejpam-5455	200	9	w(7	w(7	PROPN
ejpam-5455	200	10	)	)	PUNCT
ejpam-5455	200	11	)	)	PUNCT
ejpam-5455	200	12	)	)	PUNCT
ejpam-5455	200	13	)	)	PUNCT
ejpam-5455	200	14	)	)	PUNCT
ejpam-5455	201	1	+	+	CCONJ
ejpam-5455	201	2	h(7	h(7	PROPN
ejpam-5455	201	3	,	,	PUNCT
ejpam-5455	201	4	w(7	w(7	PROPN
ejpam-5455	201	5	)	)	PUNCT
ejpam-5455	201	6	)	)	PUNCT
ejpam-5455	201	7	or	or	CCONJ
ejpam-5455	201	8	equivalently	equivalently	ADV
ejpam-5455	201	9	w(7	w(7	ADJ
ejpam-5455	201	10	)	)	PUNCT
ejpam-5455	201	11	=	=	PUNCT
ejpam-5455	201	12	(	(	PUNCT
ejpam-5455	201	13	q(7	q(7	PROPN
ejpam-5455	201	14	)	)	PUNCT
ejpam-5455	201	15	+	+	CCONJ
ejpam-5455	201	16	1	1	NUM
ejpam-5455	201	17	γ(γ	γ(γ	NOUN
ejpam-5455	201	18	)	)	PUNCT
ejpam-5455	201	19	∫	∫	PROPN
ejpam-5455	201	20	7	7	NUM
ejpam-5455	201	21	0	0	NUM
ejpam-5455	201	22	(	(	PUNCT
ejpam-5455	201	23	7	7	NUM
ejpam-5455	201	24	−	−	NOUN
ejpam-5455	201	25	σ)γ−1f(σ	σ)γ−1f(σ	NOUN
ejpam-5455	201	26	,	,	PUNCT
ejpam-5455	201	27	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	201	28	)	)	PUNCT
ejpam-5455	201	29	(	(	PUNCT
ejpam-5455	201	30	×	×	NOUN
ejpam-5455	201	31	)	)	PUNCT
ejpam-5455	201	32	[	[	PUNCT
ejpam-5455	201	33	abiρ0+(θ	abiρ0+(θ	NOUN
ejpam-5455	201	34	)	)	PUNCT
ejpam-5455	202	1	+	+	CCONJ
ejpam-5455	202	2	1−	1−	NUM
ejpam-5455	202	3	ρ	ρ	NUM
ejpam-5455	202	4	b(ρ	b(ρ	PROPN
ejpam-5455	202	5	)	)	PUNCT
ejpam-5455	202	6	ψq	ψq	PROPN
ejpam-5455	202	7	(	(	PUNCT
ejpam-5455	202	8	1	1	NUM
ejpam-5455	202	9	γ(β	γ(β	PROPN
ejpam-5455	202	10	)	)	PUNCT
ejpam-5455	202	11	∫	∫	PROPN
ejpam-5455	203	1	7	7	NUM
ejpam-5455	203	2	0	0	NUM
ejpam-5455	203	3	(	(	PUNCT
ejpam-5455	203	4	7	7	NUM
ejpam-5455	203	5	−	−	NOUN
ejpam-5455	203	6	σ)β−1g(σ	σ)β−1g(σ	NOUN
ejpam-5455	203	7	,	,	PUNCT
ejpam-5455	203	8	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	203	9	)	)	PUNCT
ejpam-5455	204	1	+	+	CCONJ
ejpam-5455	204	2	ρ	ρ	PROPN
ejpam-5455	204	3	b(ρ)γ(ρ	b(ρ)γ(ρ	NOUN
ejpam-5455	204	4	)	)	PUNCT
ejpam-5455	204	5	∫	∫	PROPN
ejpam-5455	205	1	7	7	NUM
ejpam-5455	205	2	0	0	NUM
ejpam-5455	205	3	(	(	PUNCT
ejpam-5455	205	4	7	7	NUM
ejpam-5455	205	5	−	−	NOUN
ejpam-5455	205	6	σ)ρ−1	σ)ρ−1	NOUN
ejpam-5455	205	7	(	(	PUNCT
ejpam-5455	205	8	ψq	ψq	X
ejpam-5455	205	9	(	(	PUNCT
ejpam-5455	205	10	1	1	NUM
ejpam-5455	205	11	γ(β	γ(β	PROPN
ejpam-5455	205	12	)	)	PUNCT
ejpam-5455	205	13	∫	∫	PROPN
ejpam-5455	206	1	σ	σ	PROPN
ejpam-5455	206	2	0	0	NUM
ejpam-5455	206	3	(	(	PUNCT
ejpam-5455	206	4	σ	σ	NOUN
ejpam-5455	206	5	−	−	PROPN
ejpam-5455	206	6	τ)β−1g(τ	τ)β−1g(τ	PUNCT
ejpam-5455	206	7	,	,	PUNCT
ejpam-5455	206	8	w(τ))dτ	w(τ))dτ	PROPN
ejpam-5455	206	9	)	)	PUNCT
ejpam-5455	206	10	)	)	PUNCT
ejpam-5455	206	11	dσ	dσ	VERB
ejpam-5455	206	12	]	]	PUNCT
ejpam-5455	206	13	+	+	CCONJ
ejpam-5455	206	14	h(7	h(7	PROPN
ejpam-5455	206	15	,	,	PUNCT
ejpam-5455	206	16	w(7	w(7	PROPN
ejpam-5455	206	17	)	)	PUNCT
ejpam-5455	206	18	)	)	PUNCT
ejpam-5455	206	19	.	.	PUNCT
ejpam-5455	207	1	(	(	PUNCT
ejpam-5455	207	2	10	10	NUM
ejpam-5455	207	3	)	)	PUNCT
ejpam-5455	207	4	conversely	conversely	ADV
ejpam-5455	207	5	,	,	PUNCT
ejpam-5455	207	6	we	we	PRON
ejpam-5455	207	7	have	have	VERB
ejpam-5455	207	8	w(7)−	w(7)−	NOUN
ejpam-5455	207	9	h(7	h(7	NOUN
ejpam-5455	207	10	,	,	PUNCT
ejpam-5455	207	11	w(7	w(7	NOUN
ejpam-5455	207	12	)	)	PUNCT
ejpam-5455	207	13	)	)	PUNCT
ejpam-5455	208	1	q(7	q(7	PROPN
ejpam-5455	208	2	)	)	PUNCT
ejpam-5455	208	3	+	+	NUM
ejpam-5455	208	4	iγ0+f(7	iγ0+f(7	NOUN
ejpam-5455	208	5	,	,	PUNCT
ejpam-5455	208	6	w(7	w(7	PROPN
ejpam-5455	208	7	)	)	PUNCT
ejpam-5455	208	8	)	)	PUNCT
ejpam-5455	209	1	=	=	SYM
ejpam-5455	209	2	abiρ0+(θ	abiρ0+(θ	NOUN
ejpam-5455	209	3	)	)	PUNCT
ejpam-5455	210	1	+	+	CCONJ
ejpam-5455	210	2	abiρ0	abiρ0	NUM
ejpam-5455	210	3	+	+	SYM
ejpam-5455	210	4	(	(	PUNCT
ejpam-5455	210	5	ψq	ψq	X
ejpam-5455	210	6	(	(	PUNCT
ejpam-5455	210	7	iβ0+(g(7	iβ0+(g(7	PROPN
ejpam-5455	210	8	,	,	PUNCT
ejpam-5455	210	9	w(7	w(7	PROPN
ejpam-5455	210	10	)	)	PUNCT
ejpam-5455	210	11	)	)	PUNCT
ejpam-5455	210	12	)	)	PUNCT
ejpam-5455	210	13	)	)	PUNCT
ejpam-5455	210	14	)	)	PUNCT
ejpam-5455	210	15	.	.	PUNCT
ejpam-5455	211	1	taking	take	VERB
ejpam-5455	211	2	mabcdρ	mabcdρ	PROPN
ejpam-5455	211	3	0	0	PUNCT
ejpam-5455	211	4	+	+	NUM
ejpam-5455	211	5	derivative	derivative	NOUN
ejpam-5455	211	6	on	on	ADP
ejpam-5455	211	7	both	both	DET
ejpam-5455	211	8	sides	side	NOUN
ejpam-5455	211	9	of	of	ADP
ejpam-5455	211	10	the	the	DET
ejpam-5455	211	11	above	above	ADJ
ejpam-5455	211	12	equation	equation	NOUN
ejpam-5455	211	13	,	,	PUNCT
ejpam-5455	211	14	we	we	PRON
ejpam-5455	211	15	have	have	VERB
ejpam-5455	211	16	mabcdρ	mabcdρ	VERB
ejpam-5455	211	17	0	0	PUNCT
ejpam-5455	212	1	+	+	CCONJ
ejpam-5455	212	2	(	(	PUNCT
ejpam-5455	212	3	w(7)−	w(7)−	PROPN
ejpam-5455	212	4	h(7	h(7	PROPN
ejpam-5455	212	5	,	,	PUNCT
ejpam-5455	212	6	w(7	w(7	NOUN
ejpam-5455	212	7	)	)	PUNCT
ejpam-5455	212	8	)	)	PUNCT
ejpam-5455	213	1	q(7	q(7	PROPN
ejpam-5455	213	2	)	)	PUNCT
ejpam-5455	213	3	+	+	NUM
ejpam-5455	213	4	iγ0+f(7	iγ0+f(7	NOUN
ejpam-5455	213	5	,	,	PUNCT
ejpam-5455	213	6	w(7	w(7	PROPN
ejpam-5455	213	7	)	)	PUNCT
ejpam-5455	213	8	)	)	PUNCT
ejpam-5455	213	9	)	)	PUNCT
ejpam-5455	213	10	m.	m.	NOUN
ejpam-5455	213	11	m.	m.	NOUN
ejpam-5455	213	12	arjunan	arjunan	PROPN
ejpam-5455	213	13	/	/	SYM
ejpam-5455	213	14	eur	eur	PROPN
ejpam-5455	213	15	.	.	PUNCT
ejpam-5455	214	1	j.	j.	PROPN
ejpam-5455	214	2	pure	pure	PROPN
ejpam-5455	214	3	appl	appl	PROPN
ejpam-5455	214	4	.	.	PROPN
ejpam-5455	214	5	math	math	PROPN
ejpam-5455	214	6	,	,	PUNCT
ejpam-5455	214	7	17	17	NUM
ejpam-5455	214	8	(	(	PUNCT
ejpam-5455	214	9	4	4	NUM
ejpam-5455	214	10	)	)	PUNCT
ejpam-5455	214	11	(	(	PUNCT
ejpam-5455	214	12	2024	2024	NUM
ejpam-5455	214	13	)	)	PUNCT
ejpam-5455	214	14	,	,	PUNCT
ejpam-5455	214	15	4071	4071	NUM
ejpam-5455	214	16	-	-	SYM
ejpam-5455	214	17	4092	4092	NUM
ejpam-5455	214	18	4079	4079	NUM
ejpam-5455	214	19	=	=	NUM
ejpam-5455	214	20	mabc	mabc	NOUN
ejpam-5455	214	21	dρ	dρ	VERB
ejpam-5455	214	22	0	0	NUM
ejpam-5455	215	1	+	+	CCONJ
ejpam-5455	215	2	(	(	PUNCT
ejpam-5455	215	3	abiρ0+(θ	abiρ0+(θ	NOUN
ejpam-5455	215	4	)	)	PUNCT
ejpam-5455	216	1	+	+	CCONJ
ejpam-5455	216	2	abiρ0	abiρ0	NUM
ejpam-5455	216	3	+	+	SYM
ejpam-5455	216	4	(	(	PUNCT
ejpam-5455	216	5	ψq	ψq	PROPN
ejpam-5455	216	6	(	(	PUNCT
ejpam-5455	216	7	iβ0+g(7	iβ0+g(7	NOUN
ejpam-5455	216	8	,	,	PUNCT
ejpam-5455	216	9	w(7	w(7	PROPN
ejpam-5455	216	10	)	)	PUNCT
ejpam-5455	216	11	)	)	PUNCT
ejpam-5455	216	12	)	)	PUNCT
ejpam-5455	216	13	)	)	PUNCT
ejpam-5455	216	14	)	)	PUNCT
ejpam-5455	217	1	=	=	PRON
ejpam-5455	217	2	θ+	θ+	NOUN
ejpam-5455	217	3	(	(	PUNCT
ejpam-5455	217	4	ψq	ψq	PROPN
ejpam-5455	217	5	(	(	PUNCT
ejpam-5455	217	6	iβ0+g(7	iβ0+g(7	NOUN
ejpam-5455	217	7	,	,	PUNCT
ejpam-5455	217	8	w(7	w(7	PROPN
ejpam-5455	217	9	)	)	PUNCT
ejpam-5455	217	10	)	)	PUNCT
ejpam-5455	217	11	)	)	PUNCT
ejpam-5455	217	12	)	)	PUNCT
ejpam-5455	217	13	by	by	ADP
ejpam-5455	217	14	utilizing	utilize	VERB
ejpam-5455	217	15	the	the	DET
ejpam-5455	217	16	fact	fact	NOUN
ejpam-5455	217	17	that	that	SCONJ
ejpam-5455	217	18	(	(	PUNCT
ejpam-5455	217	19	mabcdρ	mabcdρ	PROPN
ejpam-5455	217	20	0	0	PUNCT
ejpam-5455	217	21	+	+	CCONJ
ejpam-5455	217	22	(	(	PUNCT
ejpam-5455	217	23	abiρ0+w	abiρ0+w	NOUN
ejpam-5455	217	24	)	)	PUNCT
ejpam-5455	217	25	)	)	PUNCT
ejpam-5455	217	26	(	(	PUNCT
ejpam-5455	217	27	7	7	X
ejpam-5455	217	28	)	)	PUNCT
ejpam-5455	217	29	=	=	SYM
ejpam-5455	217	30	w(7	w(7	PROPN
ejpam-5455	217	31	)	)	PUNCT
ejpam-5455	217	32	.	.	PUNCT
ejpam-5455	218	1	taking	take	VERB
ejpam-5455	218	2	p	p	NOUN
ejpam-5455	218	3	-	-	PUNCT
ejpam-5455	218	4	laplacian	laplacian	ADJ
ejpam-5455	218	5	operator	operator	NOUN
ejpam-5455	218	6	on	on	ADP
ejpam-5455	218	7	both	both	DET
ejpam-5455	218	8	sides	side	NOUN
ejpam-5455	218	9	,	,	PUNCT
ejpam-5455	218	10	we	we	PRON
ejpam-5455	218	11	have	have	VERB
ejpam-5455	218	12	ψp	ψp	VERB
ejpam-5455	218	13	(	(	PUNCT
ejpam-5455	218	14	mabcdρ	mabcdρ	PROPN
ejpam-5455	218	15	0	0	PUNCT
ejpam-5455	219	1	+	+	CCONJ
ejpam-5455	219	2	(	(	PUNCT
ejpam-5455	219	3	w(7)−	w(7)−	PROPN
ejpam-5455	219	4	h(7	h(7	PROPN
ejpam-5455	219	5	,	,	PUNCT
ejpam-5455	219	6	w(7	w(7	NOUN
ejpam-5455	219	7	)	)	PUNCT
ejpam-5455	219	8	)	)	PUNCT
ejpam-5455	220	1	q(7	q(7	PROPN
ejpam-5455	220	2	)	)	PUNCT
ejpam-5455	220	3	+	+	NUM
ejpam-5455	220	4	iγ0+f(7	iγ0+f(7	NOUN
ejpam-5455	220	5	,	,	PUNCT
ejpam-5455	220	6	w(7	w(7	PROPN
ejpam-5455	220	7	)	)	PUNCT
ejpam-5455	220	8	)	)	PUNCT
ejpam-5455	220	9	)	)	PUNCT
ejpam-5455	220	10	)	)	PUNCT
ejpam-5455	221	1	=	=	PRON
ejpam-5455	221	2	ψp(θ	ψp(θ	PUNCT
ejpam-5455	221	3	)	)	PUNCT
ejpam-5455	222	1	+	+	CCONJ
ejpam-5455	222	2	iβ0+g(7	iβ0+g(7	NOUN
ejpam-5455	222	3	,	,	PUNCT
ejpam-5455	222	4	w(7	w(7	PROPN
ejpam-5455	222	5	)	)	PUNCT
ejpam-5455	222	6	)	)	PUNCT
ejpam-5455	222	7	.	.	PUNCT
ejpam-5455	223	1	taking	take	VERB
ejpam-5455	223	2	cdβ	cdβ	NOUN
ejpam-5455	223	3	on	on	ADP
ejpam-5455	223	4	both	both	DET
ejpam-5455	223	5	sides	side	NOUN
ejpam-5455	223	6	,	,	PUNCT
ejpam-5455	223	7	we	we	PRON
ejpam-5455	223	8	get	get	VERB
ejpam-5455	223	9	cdβ	cdβ	NOUN
ejpam-5455	223	10	(	(	PUNCT
ejpam-5455	223	11	ψp	ψp	X
ejpam-5455	223	12	(	(	PUNCT
ejpam-5455	223	13	mabcdρ	mabcdρ	PROPN
ejpam-5455	223	14	0	0	PUNCT
ejpam-5455	223	15	+	+	CCONJ
ejpam-5455	223	16	(	(	PUNCT
ejpam-5455	223	17	w(7)−	w(7)−	PROPN
ejpam-5455	223	18	h(7	h(7	PROPN
ejpam-5455	223	19	,	,	PUNCT
ejpam-5455	223	20	w(7	w(7	NOUN
ejpam-5455	223	21	)	)	PUNCT
ejpam-5455	223	22	)	)	PUNCT
ejpam-5455	224	1	q(7	q(7	PROPN
ejpam-5455	224	2	)	)	PUNCT
ejpam-5455	224	3	+	+	NUM
ejpam-5455	224	4	iγ0+f(7	iγ0+f(7	NOUN
ejpam-5455	224	5	,	,	PUNCT
ejpam-5455	224	6	w(7	w(7	PROPN
ejpam-5455	224	7	)	)	PUNCT
ejpam-5455	224	8	)	)	PUNCT
ejpam-5455	224	9	)	)	PUNCT
ejpam-5455	224	10	)	)	PUNCT
ejpam-5455	224	11	)	)	PUNCT
ejpam-5455	225	1	=	=	SYM
ejpam-5455	225	2	g(7	g(7	PROPN
ejpam-5455	225	3	,	,	PUNCT
ejpam-5455	225	4	w(7	w(7	PROPN
ejpam-5455	225	5	)	)	PUNCT
ejpam-5455	225	6	)	)	PUNCT
ejpam-5455	225	7	by	by	ADP
ejpam-5455	225	8	utilizing	utilize	VERB
ejpam-5455	225	9	the	the	DET
ejpam-5455	225	10	fact	fact	NOUN
ejpam-5455	225	11	that	that	SCONJ
ejpam-5455	225	12	cdβiβ0+w(7	cdβiβ0+w(7	ADV
ejpam-5455	225	13	)	)	PUNCT
ejpam-5455	225	14	=	=	SYM
ejpam-5455	225	15	w(7	w(7	X
ejpam-5455	225	16	)	)	PUNCT
ejpam-5455	225	17	and	and	CCONJ
ejpam-5455	225	18	further	further	ADJ
ejpam-5455	225	19	w(0	w(0	PROPN
ejpam-5455	225	20	)	)	PUNCT
ejpam-5455	225	21	=	=	SYM
ejpam-5455	226	1	h(0	h(0	PROPN
ejpam-5455	226	2	,	,	PUNCT
ejpam-5455	226	3	w(0))+q(0)abiρ0+θ	w(0))+q(0)abiρ0+θ	PROPN
ejpam-5455	226	4	.	.	PUNCT
ejpam-5455	226	5	describe	describe	VERB
ejpam-5455	226	6	the	the	DET
ejpam-5455	226	7	operator	operator	NOUN
ejpam-5455	226	8	φ	φ	NOUN
ejpam-5455	226	9	:	:	PUNCT
ejpam-5455	226	10	ac(ω	ac(ω	ADV
ejpam-5455	226	11	,	,	PUNCT
ejpam-5455	226	12	r	r	NOUN
ejpam-5455	226	13	)	)	PUNCT
ejpam-5455	226	14	→	→	SYM
ejpam-5455	226	15	ac(ω	ac(ω	ADV
ejpam-5455	226	16	,	,	PUNCT
ejpam-5455	226	17	r	r	NOUN
ejpam-5455	226	18	)	)	PUNCT
ejpam-5455	226	19	by	by	ADP
ejpam-5455	226	20	(	(	PUNCT
ejpam-5455	226	21	φw)(7	φw)(7	NUM
ejpam-5455	226	22	)	)	PUNCT
ejpam-5455	226	23	=	=	PRON
ejpam-5455	226	24	(	(	PUNCT
ejpam-5455	226	25	q(7	q(7	PROPN
ejpam-5455	226	26	)	)	PUNCT
ejpam-5455	226	27	+	+	CCONJ
ejpam-5455	226	28	1	1	NUM
ejpam-5455	226	29	γ(γ	γ(γ	NOUN
ejpam-5455	226	30	)	)	PUNCT
ejpam-5455	226	31	∫	∫	PROPN
ejpam-5455	226	32	7	7	NUM
ejpam-5455	226	33	0	0	NUM
ejpam-5455	226	34	(	(	PUNCT
ejpam-5455	226	35	7	7	NUM
ejpam-5455	226	36	−	−	NOUN
ejpam-5455	226	37	σ)γ−1f(σ	σ)γ−1f(σ	NOUN
ejpam-5455	226	38	,	,	PUNCT
ejpam-5455	226	39	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	226	40	)	)	PUNCT
ejpam-5455	226	41	(	(	PUNCT
ejpam-5455	226	42	×	×	NOUN
ejpam-5455	226	43	)	)	PUNCT
ejpam-5455	226	44	[	[	PUNCT
ejpam-5455	226	45	abiρ0+(θ	abiρ0+(θ	NOUN
ejpam-5455	226	46	)	)	PUNCT
ejpam-5455	227	1	+	+	CCONJ
ejpam-5455	227	2	1−	1−	NUM
ejpam-5455	227	3	ρ	ρ	NUM
ejpam-5455	227	4	b(ρ	b(ρ	PROPN
ejpam-5455	227	5	)	)	PUNCT
ejpam-5455	227	6	ψq	ψq	PROPN
ejpam-5455	227	7	(	(	PUNCT
ejpam-5455	227	8	1	1	NUM
ejpam-5455	227	9	γ(β	γ(β	PROPN
ejpam-5455	227	10	)	)	PUNCT
ejpam-5455	227	11	∫	∫	PROPN
ejpam-5455	228	1	7	7	NUM
ejpam-5455	228	2	0	0	NUM
ejpam-5455	228	3	(	(	PUNCT
ejpam-5455	228	4	7	7	NUM
ejpam-5455	228	5	−	−	NOUN
ejpam-5455	228	6	σ)β−1g(σ	σ)β−1g(σ	NOUN
ejpam-5455	228	7	,	,	PUNCT
ejpam-5455	228	8	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	228	9	)	)	PUNCT
ejpam-5455	229	1	+	+	CCONJ
ejpam-5455	229	2	ρ	ρ	PROPN
ejpam-5455	229	3	b(ρ)γ(ρ	b(ρ)γ(ρ	NOUN
ejpam-5455	229	4	)	)	PUNCT
ejpam-5455	229	5	∫	∫	PROPN
ejpam-5455	230	1	7	7	NUM
ejpam-5455	230	2	0	0	NUM
ejpam-5455	230	3	(	(	PUNCT
ejpam-5455	230	4	7	7	NUM
ejpam-5455	230	5	−	−	NOUN
ejpam-5455	230	6	σ)ρ−1	σ)ρ−1	NOUN
ejpam-5455	230	7	(	(	PUNCT
ejpam-5455	230	8	ψq	ψq	X
ejpam-5455	230	9	(	(	PUNCT
ejpam-5455	230	10	1	1	NUM
ejpam-5455	230	11	γ(β	γ(β	PROPN
ejpam-5455	230	12	)	)	PUNCT
ejpam-5455	230	13	∫	∫	PROPN
ejpam-5455	231	1	σ	σ	PROPN
ejpam-5455	231	2	0	0	NUM
ejpam-5455	231	3	(	(	PUNCT
ejpam-5455	231	4	σ	σ	NOUN
ejpam-5455	231	5	−	−	PROPN
ejpam-5455	231	6	τ)β−1g(τ	τ)β−1g(τ	PUNCT
ejpam-5455	231	7	,	,	PUNCT
ejpam-5455	231	8	w(τ))dτ	w(τ))dτ	PROPN
ejpam-5455	231	9	)	)	PUNCT
ejpam-5455	231	10	)	)	PUNCT
ejpam-5455	231	11	dσ	dσ	VERB
ejpam-5455	231	12	]	]	PUNCT
ejpam-5455	231	13	+	+	CCONJ
ejpam-5455	231	14	h(7	h(7	PROPN
ejpam-5455	231	15	,	,	PUNCT
ejpam-5455	231	16	w(7	w(7	PROPN
ejpam-5455	231	17	)	)	PUNCT
ejpam-5455	231	18	)	)	PUNCT
ejpam-5455	231	19	.	.	PUNCT
ejpam-5455	232	1	(	(	PUNCT
ejpam-5455	232	2	11	11	NUM
ejpam-5455	232	3	)	)	PUNCT
ejpam-5455	232	4	according	accord	VERB
ejpam-5455	232	5	to	to	ADP
ejpam-5455	232	6	equation	equation	NOUN
ejpam-5455	232	7	(	(	PUNCT
ejpam-5455	232	8	11	11	NUM
ejpam-5455	232	9	)	)	PUNCT
ejpam-5455	232	10	,	,	PUNCT
ejpam-5455	232	11	each	each	DET
ejpam-5455	232	12	fixed	fix	VERB
ejpam-5455	232	13	point	point	NOUN
ejpam-5455	232	14	of	of	ADP
ejpam-5455	232	15	the	the	DET
ejpam-5455	232	16	operator	operator	NOUN
ejpam-5455	232	17	φ	φ	PROPN
ejpam-5455	232	18	is	be	AUX
ejpam-5455	232	19	associated	associate	VERB
ejpam-5455	232	20	with	with	ADP
ejpam-5455	232	21	the	the	DET
ejpam-5455	232	22	desired	desire	VERB
ejpam-5455	232	23	solution	solution	NOUN
ejpam-5455	232	24	of	of	ADP
ejpam-5455	232	25	the	the	DET
ejpam-5455	232	26	system	system	NOUN
ejpam-5455	232	27	(	(	PUNCT
ejpam-5455	232	28	1	1	NUM
ejpam-5455	232	29	)	)	PUNCT
ejpam-5455	232	30	.	.	PUNCT
ejpam-5455	233	1	note	note	VERB
ejpam-5455	233	2	2.1	2.1	NUM
ejpam-5455	233	3	.	.	PUNCT
ejpam-5455	234	1	for	for	ADP
ejpam-5455	234	2	our	our	PRON
ejpam-5455	234	3	convenience	convenience	NOUN
ejpam-5455	234	4	,	,	PUNCT
ejpam-5455	234	5	we	we	PRON
ejpam-5455	234	6	split	split	VERB
ejpam-5455	234	7	the	the	DET
ejpam-5455	234	8	operator	operator	NOUN
ejpam-5455	234	9	(	(	PUNCT
ejpam-5455	234	10	11	11	NUM
ejpam-5455	234	11	)	)	PUNCT
ejpam-5455	234	12	as	as	ADP
ejpam-5455	234	13	:	:	PUNCT
ejpam-5455	234	14	(	(	PUNCT
ejpam-5455	234	15	φw)(7	φw)(7	NUM
ejpam-5455	234	16	)	)	PUNCT
ejpam-5455	234	17	=	=	SYM
ejpam-5455	234	18	(	(	PUNCT
ejpam-5455	234	19	aw)(7	aw)(7	NOUN
ejpam-5455	234	20	)	)	PUNCT
ejpam-5455	234	21	+	+	CCONJ
ejpam-5455	234	22	(	(	PUNCT
ejpam-5455	234	23	bw)(7	bw)(7	NOUN
ejpam-5455	234	24	)	)	PUNCT
ejpam-5455	234	25	,	,	PUNCT
ejpam-5455	234	26	7	7	NUM
ejpam-5455	234	27	∈	∈	NOUN
ejpam-5455	234	28	ω	ω	NOUN
ejpam-5455	234	29	,	,	PUNCT
ejpam-5455	234	30	where	where	SCONJ
ejpam-5455	234	31	(	(	PUNCT
ejpam-5455	234	32	aw)(7	aw)(7	NOUN
ejpam-5455	234	33	)	)	PUNCT
ejpam-5455	234	34	=	=	PUNCT
ejpam-5455	234	35	(	(	PUNCT
ejpam-5455	234	36	q(7	q(7	PROPN
ejpam-5455	234	37	)	)	PUNCT
ejpam-5455	234	38	+	+	CCONJ
ejpam-5455	234	39	1	1	NUM
ejpam-5455	234	40	γ(γ	γ(γ	NOUN
ejpam-5455	234	41	)	)	PUNCT
ejpam-5455	234	42	∫	∫	PROPN
ejpam-5455	235	1	7	7	NUM
ejpam-5455	235	2	0	0	NUM
ejpam-5455	235	3	(	(	PUNCT
ejpam-5455	235	4	7	7	NUM
ejpam-5455	235	5	−	−	NOUN
ejpam-5455	235	6	σ)γ−1f(σ	σ)γ−1f(σ	NOUN
ejpam-5455	235	7	,	,	PUNCT
ejpam-5455	235	8	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	235	9	)	)	PUNCT
ejpam-5455	235	10	(	(	PUNCT
ejpam-5455	235	11	×	×	NOUN
ejpam-5455	235	12	)	)	PUNCT
ejpam-5455	235	13	[	[	PUNCT
ejpam-5455	235	14	abiρ0+(θ	abiρ0+(θ	NOUN
ejpam-5455	235	15	)	)	PUNCT
ejpam-5455	235	16	+	+	CCONJ
ejpam-5455	235	17	1−	1−	NUM
ejpam-5455	235	18	ρ	ρ	NUM
ejpam-5455	235	19	b(ρ	b(ρ	PROPN
ejpam-5455	235	20	)	)	PUNCT
ejpam-5455	235	21	ψq	ψq	PROPN
ejpam-5455	235	22	(	(	PUNCT
ejpam-5455	235	23	1	1	NUM
ejpam-5455	235	24	γ(β	γ(β	PROPN
ejpam-5455	235	25	)	)	PUNCT
ejpam-5455	235	26	∫	∫	PROPN
ejpam-5455	236	1	7	7	NUM
ejpam-5455	236	2	0	0	NUM
ejpam-5455	236	3	(	(	PUNCT
ejpam-5455	236	4	7	7	NUM
ejpam-5455	236	5	−	−	NOUN
ejpam-5455	236	6	σ)β−1g(σ	σ)β−1g(σ	NOUN
ejpam-5455	236	7	,	,	PUNCT
ejpam-5455	236	8	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	236	9	)	)	PUNCT
ejpam-5455	237	1	+	+	CCONJ
ejpam-5455	237	2	ρ	ρ	PROPN
ejpam-5455	237	3	b(ρ)γ(ρ	b(ρ)γ(ρ	NOUN
ejpam-5455	237	4	)	)	PUNCT
ejpam-5455	237	5	∫	∫	PROPN
ejpam-5455	238	1	7	7	NUM
ejpam-5455	238	2	0	0	NUM
ejpam-5455	238	3	(	(	PUNCT
ejpam-5455	238	4	7	7	NUM
ejpam-5455	238	5	−	−	NOUN
ejpam-5455	238	6	σ)ρ−1	σ)ρ−1	NOUN
ejpam-5455	238	7	(	(	PUNCT
ejpam-5455	238	8	ψq	ψq	X
ejpam-5455	238	9	(	(	PUNCT
ejpam-5455	238	10	1	1	NUM
ejpam-5455	238	11	γ(β	γ(β	PROPN
ejpam-5455	238	12	)	)	PUNCT
ejpam-5455	238	13	∫	∫	PROPN
ejpam-5455	239	1	σ	σ	PROPN
ejpam-5455	239	2	0	0	NUM
ejpam-5455	239	3	(	(	PUNCT
ejpam-5455	239	4	σ	σ	NOUN
ejpam-5455	239	5	−	−	PROPN
ejpam-5455	239	6	τ)β−1g(τ	τ)β−1g(τ	PUNCT
ejpam-5455	239	7	,	,	PUNCT
ejpam-5455	239	8	w(τ))dτ	w(τ))dτ	PROPN
ejpam-5455	239	9	)	)	PUNCT
ejpam-5455	239	10	)	)	PUNCT
ejpam-5455	239	11	dσ	dσ	VERB
ejpam-5455	239	12	]	]	PUNCT
ejpam-5455	239	13	,	,	PUNCT
ejpam-5455	239	14	(	(	PUNCT
ejpam-5455	239	15	12	12	NUM
ejpam-5455	239	16	)	)	PUNCT
ejpam-5455	239	17	m.	m.	NOUN
ejpam-5455	239	18	m.	m.	NOUN
ejpam-5455	239	19	arjunan	arjunan	PROPN
ejpam-5455	239	20	/	/	SYM
ejpam-5455	239	21	eur	eur	PROPN
ejpam-5455	239	22	.	.	PUNCT
ejpam-5455	240	1	j.	j.	PROPN
ejpam-5455	240	2	pure	pure	PROPN
ejpam-5455	240	3	appl	appl	PROPN
ejpam-5455	240	4	.	.	PROPN
ejpam-5455	240	5	math	math	PROPN
ejpam-5455	240	6	,	,	PUNCT
ejpam-5455	240	7	17	17	NUM
ejpam-5455	240	8	(	(	PUNCT
ejpam-5455	240	9	4	4	NUM
ejpam-5455	240	10	)	)	PUNCT
ejpam-5455	240	11	(	(	PUNCT
ejpam-5455	240	12	2024	2024	NUM
ejpam-5455	240	13	)	)	PUNCT
ejpam-5455	240	14	,	,	PUNCT
ejpam-5455	240	15	4071	4071	NUM
ejpam-5455	240	16	-	-	SYM
ejpam-5455	240	17	4092	4092	NUM
ejpam-5455	240	18	4080	4080	NUM
ejpam-5455	240	19	and	and	CCONJ
ejpam-5455	240	20	(	(	PUNCT
ejpam-5455	240	21	bw)(7	bw)(7	NOUN
ejpam-5455	240	22	)	)	PUNCT
ejpam-5455	240	23	=	=	SYM
ejpam-5455	241	1	h(7	h(7	PROPN
ejpam-5455	241	2	,	,	PUNCT
ejpam-5455	241	3	w(7	w(7	PROPN
ejpam-5455	241	4	)	)	PUNCT
ejpam-5455	241	5	)	)	PUNCT
ejpam-5455	241	6	,	,	PUNCT
ejpam-5455	241	7	7	7	NUM
ejpam-5455	241	8	∈	∈	PROPN
ejpam-5455	241	9	ω	ω	NOUN
ejpam-5455	241	10	.	.	PUNCT
ejpam-5455	241	11	(	(	PUNCT
ejpam-5455	241	12	13	13	NUM
ejpam-5455	241	13	)	)	PUNCT
ejpam-5455	241	14	now	now	ADV
ejpam-5455	241	15	|(aw)(7)−	|(aw)(7)−	VERB
ejpam-5455	241	16	(	(	PUNCT
ejpam-5455	241	17	aw)(7)|	aw)(7)|	PROPN
ejpam-5455	241	18	=	=	SYM
ejpam-5455	241	19	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5455	241	20	(	(	PUNCT
ejpam-5455	241	21	q(7	q(7	PROPN
ejpam-5455	241	22	)	)	PUNCT
ejpam-5455	241	23	+	+	CCONJ
ejpam-5455	241	24	1	1	NUM
ejpam-5455	241	25	γ(γ	γ(γ	NOUN
ejpam-5455	241	26	)	)	PUNCT
ejpam-5455	241	27	∫	∫	PROPN
ejpam-5455	241	28	7	7	NUM
ejpam-5455	241	29	0	0	NUM
ejpam-5455	241	30	(	(	PUNCT
ejpam-5455	241	31	7	7	NUM
ejpam-5455	241	32	−	−	NOUN
ejpam-5455	241	33	σ)γ−1f(σ	σ)γ−1f(σ	NOUN
ejpam-5455	241	34	,	,	PUNCT
ejpam-5455	241	35	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	241	36	)	)	PUNCT
ejpam-5455	241	37	(	(	PUNCT
ejpam-5455	241	38	×	×	NOUN
ejpam-5455	241	39	)	)	PUNCT
ejpam-5455	241	40	[	[	PUNCT
ejpam-5455	241	41	abiρ0+(θ	abiρ0+(θ	NOUN
ejpam-5455	241	42	)	)	PUNCT
ejpam-5455	241	43	+	+	CCONJ
ejpam-5455	241	44	1−	1−	NUM
ejpam-5455	241	45	ρ	ρ	NUM
ejpam-5455	241	46	b(ρ	b(ρ	PROPN
ejpam-5455	241	47	)	)	PUNCT
ejpam-5455	241	48	ψq	ψq	PROPN
ejpam-5455	241	49	(	(	PUNCT
ejpam-5455	241	50	1	1	NUM
ejpam-5455	241	51	γ(β	γ(β	PROPN
ejpam-5455	241	52	)	)	PUNCT
ejpam-5455	241	53	∫	∫	PROPN
ejpam-5455	241	54	7	7	NUM
ejpam-5455	241	55	0	0	NUM
ejpam-5455	241	56	(	(	PUNCT
ejpam-5455	241	57	7	7	NUM
ejpam-5455	241	58	−	−	NOUN
ejpam-5455	241	59	σ)β−1g(σ	σ)β−1g(σ	NOUN
ejpam-5455	241	60	,	,	PUNCT
ejpam-5455	241	61	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	241	62	)	)	PUNCT
ejpam-5455	241	63	+	+	CCONJ
ejpam-5455	241	64	ρ	ρ	PROPN
ejpam-5455	241	65	b(ρ)γ(ρ	b(ρ)γ(ρ	NOUN
ejpam-5455	241	66	)	)	PUNCT
ejpam-5455	241	67	∫	∫	PROPN
ejpam-5455	241	68	7	7	NUM
ejpam-5455	241	69	0	0	NUM
ejpam-5455	241	70	(	(	PUNCT
ejpam-5455	241	71	7	7	NUM
ejpam-5455	241	72	−	−	NOUN
ejpam-5455	241	73	σ)ρ−1	σ)ρ−1	NOUN
ejpam-5455	241	74	(	(	PUNCT
ejpam-5455	241	75	ψq	ψq	X
ejpam-5455	241	76	(	(	PUNCT
ejpam-5455	241	77	1	1	NUM
ejpam-5455	241	78	γ(β	γ(β	PROPN
ejpam-5455	241	79	)	)	PUNCT
ejpam-5455	241	80	∫	∫	PROPN
ejpam-5455	242	1	σ	σ	PROPN
ejpam-5455	242	2	0	0	NUM
ejpam-5455	242	3	(	(	PUNCT
ejpam-5455	242	4	σ	σ	NOUN
ejpam-5455	242	5	−	−	PROPN
ejpam-5455	242	6	τ)β−1g(τ	τ)β−1g(τ	PUNCT
ejpam-5455	242	7	,	,	PUNCT
ejpam-5455	242	8	w(τ))dτ	w(τ))dτ	PROPN
ejpam-5455	242	9	)	)	PUNCT
ejpam-5455	242	10	)	)	PUNCT
ejpam-5455	242	11	dσ	dσ	VERB
ejpam-5455	242	12	]	]	PUNCT
ejpam-5455	242	13	−	−	PROPN
ejpam-5455	242	14	(	(	PUNCT
ejpam-5455	242	15	q(7	q(7	PROPN
ejpam-5455	242	16	)	)	PUNCT
ejpam-5455	242	17	+	+	CCONJ
ejpam-5455	242	18	1	1	NUM
ejpam-5455	242	19	γ(γ	γ(γ	NOUN
ejpam-5455	242	20	)	)	PUNCT
ejpam-5455	242	21	∫	∫	PROPN
ejpam-5455	243	1	7	7	NUM
ejpam-5455	243	2	0	0	NUM
ejpam-5455	243	3	(	(	PUNCT
ejpam-5455	243	4	7	7	NUM
ejpam-5455	243	5	−	−	NOUN
ejpam-5455	243	6	σ)γ−1f(σ	σ)γ−1f(σ	NOUN
ejpam-5455	243	7	,	,	PUNCT
ejpam-5455	243	8	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	243	9	)	)	PUNCT
ejpam-5455	243	10	(	(	PUNCT
ejpam-5455	243	11	×	×	NOUN
ejpam-5455	243	12	)	)	PUNCT
ejpam-5455	243	13	[	[	PUNCT
ejpam-5455	243	14	abiρ0+(θ	abiρ0+(θ	NOUN
ejpam-5455	243	15	)	)	PUNCT
ejpam-5455	243	16	+	+	CCONJ
ejpam-5455	243	17	1−	1−	NUM
ejpam-5455	243	18	ρ	ρ	NUM
ejpam-5455	243	19	b(ρ	b(ρ	PROPN
ejpam-5455	243	20	)	)	PUNCT
ejpam-5455	243	21	ψq	ψq	PROPN
ejpam-5455	243	22	(	(	PUNCT
ejpam-5455	243	23	1	1	NUM
ejpam-5455	243	24	γ(β	γ(β	PROPN
ejpam-5455	243	25	)	)	PUNCT
ejpam-5455	243	26	∫	∫	PROPN
ejpam-5455	244	1	7	7	NUM
ejpam-5455	244	2	0	0	NUM
ejpam-5455	244	3	(	(	PUNCT
ejpam-5455	244	4	7	7	NUM
ejpam-5455	244	5	−	−	NOUN
ejpam-5455	244	6	σ)β−1g(σ	σ)β−1g(σ	NOUN
ejpam-5455	244	7	,	,	PUNCT
ejpam-5455	244	8	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	244	9	)	)	PUNCT
ejpam-5455	245	1	+	+	CCONJ
ejpam-5455	245	2	ρ	ρ	PROPN
ejpam-5455	245	3	b(ρ)γ(ρ	b(ρ)γ(ρ	NOUN
ejpam-5455	245	4	)	)	PUNCT
ejpam-5455	245	5	∫	∫	PROPN
ejpam-5455	246	1	7	7	NUM
ejpam-5455	246	2	0	0	NUM
ejpam-5455	246	3	(	(	PUNCT
ejpam-5455	246	4	7	7	NUM
ejpam-5455	246	5	−	−	NOUN
ejpam-5455	246	6	σ)ρ−1	σ)ρ−1	NOUN
ejpam-5455	246	7	(	(	PUNCT
ejpam-5455	246	8	ψq	ψq	X
ejpam-5455	246	9	(	(	PUNCT
ejpam-5455	246	10	1	1	NUM
ejpam-5455	246	11	γ(β	γ(β	PROPN
ejpam-5455	246	12	)	)	PUNCT
ejpam-5455	246	13	∫	∫	PROPN
ejpam-5455	247	1	σ	σ	PROPN
ejpam-5455	247	2	0	0	NUM
ejpam-5455	247	3	(	(	PUNCT
ejpam-5455	247	4	σ	σ	NOUN
ejpam-5455	247	5	−	−	PROPN
ejpam-5455	247	6	τ)β−1g(τ	τ)β−1g(τ	PUNCT
ejpam-5455	247	7	,	,	PUNCT
ejpam-5455	247	8	w(τ))dτ	w(τ))dτ	PROPN
ejpam-5455	247	9	)	)	PUNCT
ejpam-5455	247	10	)	)	PUNCT
ejpam-5455	247	11	dσ	dσ	VERB
ejpam-5455	247	12	]	]	PUNCT
ejpam-5455	247	13	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5455	247	14	we	we	PRON
ejpam-5455	247	15	denote	denote	VERB
ejpam-5455	247	16	aw	aw	INTJ
ejpam-5455	247	17	=	=	X
ejpam-5455	247	18	(	(	PUNCT
ejpam-5455	247	19	q(7	q(7	PROPN
ejpam-5455	247	20	)	)	PUNCT
ejpam-5455	247	21	+	+	CCONJ
ejpam-5455	247	22	1	1	NUM
ejpam-5455	247	23	γ(γ	γ(γ	NOUN
ejpam-5455	247	24	)	)	PUNCT
ejpam-5455	247	25	∫	∫	PROPN
ejpam-5455	247	26	7	7	NUM
ejpam-5455	247	27	0	0	NUM
ejpam-5455	247	28	(	(	PUNCT
ejpam-5455	247	29	7	7	NUM
ejpam-5455	247	30	−	−	NOUN
ejpam-5455	247	31	σ)γ−1f(σ	σ)γ−1f(σ	NOUN
ejpam-5455	247	32	,	,	PUNCT
ejpam-5455	247	33	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	247	34	)	)	PUNCT
ejpam-5455	247	35	bw	bw	PROPN
ejpam-5455	247	36	=	=	SYM
ejpam-5455	247	37	abiρ0+(θ	abiρ0+(θ	PROPN
ejpam-5455	247	38	)	)	PUNCT
ejpam-5455	248	1	+	+	CCONJ
ejpam-5455	248	2	1−	1−	NUM
ejpam-5455	248	3	ρ	ρ	NUM
ejpam-5455	248	4	b(ρ	b(ρ	PROPN
ejpam-5455	248	5	)	)	PUNCT
ejpam-5455	248	6	ψq	ψq	PROPN
ejpam-5455	248	7	(	(	PUNCT
ejpam-5455	248	8	1	1	NUM
ejpam-5455	248	9	γ(β	γ(β	PROPN
ejpam-5455	248	10	)	)	PUNCT
ejpam-5455	248	11	∫	∫	PROPN
ejpam-5455	249	1	7	7	NUM
ejpam-5455	249	2	0	0	NUM
ejpam-5455	249	3	(	(	PUNCT
ejpam-5455	249	4	7	7	NUM
ejpam-5455	249	5	−	−	NOUN
ejpam-5455	249	6	σ)β−1g(σ	σ)β−1g(σ	NOUN
ejpam-5455	249	7	,	,	PUNCT
ejpam-5455	249	8	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	249	9	)	)	PUNCT
ejpam-5455	250	1	+	+	CCONJ
ejpam-5455	250	2	ρ	ρ	PROPN
ejpam-5455	250	3	b(ρ)γ(ρ	b(ρ)γ(ρ	NOUN
ejpam-5455	250	4	)	)	PUNCT
ejpam-5455	250	5	∫	∫	PROPN
ejpam-5455	251	1	7	7	NUM
ejpam-5455	251	2	0	0	NUM
ejpam-5455	251	3	(	(	PUNCT
ejpam-5455	251	4	7	7	NUM
ejpam-5455	251	5	−	−	NOUN
ejpam-5455	251	6	σ)ρ−1	σ)ρ−1	NOUN
ejpam-5455	251	7	(	(	PUNCT
ejpam-5455	251	8	ψq	ψq	X
ejpam-5455	251	9	(	(	PUNCT
ejpam-5455	251	10	1	1	NUM
ejpam-5455	251	11	γ(β	γ(β	PROPN
ejpam-5455	251	12	)	)	PUNCT
ejpam-5455	251	13	∫	∫	PROPN
ejpam-5455	252	1	σ	σ	PROPN
ejpam-5455	252	2	0	0	NUM
ejpam-5455	252	3	(	(	PUNCT
ejpam-5455	252	4	σ	σ	NOUN
ejpam-5455	252	5	−	−	PROPN
ejpam-5455	252	6	τ)β−1g(τ	τ)β−1g(τ	PUNCT
ejpam-5455	252	7	,	,	PUNCT
ejpam-5455	252	8	w(τ))dτ	w(τ))dτ	PROPN
ejpam-5455	252	9	)	)	PUNCT
ejpam-5455	252	10	)	)	PUNCT
ejpam-5455	252	11	dσ	dσ	VERB
ejpam-5455	252	12	;	;	PUNCT
ejpam-5455	252	13	aw	aw	INTJ
ejpam-5455	252	14	=	=	SYM
ejpam-5455	252	15	(	(	PUNCT
ejpam-5455	252	16	q(7	q(7	PROPN
ejpam-5455	252	17	)	)	PUNCT
ejpam-5455	252	18	+	+	CCONJ
ejpam-5455	252	19	1	1	NUM
ejpam-5455	252	20	γ(γ	γ(γ	NOUN
ejpam-5455	252	21	)	)	PUNCT
ejpam-5455	252	22	∫	∫	PROPN
ejpam-5455	253	1	7	7	NUM
ejpam-5455	253	2	0	0	NUM
ejpam-5455	253	3	(	(	PUNCT
ejpam-5455	253	4	7	7	NUM
ejpam-5455	253	5	−	−	NOUN
ejpam-5455	253	6	σ)γ−1f(σ	σ)γ−1f(σ	NOUN
ejpam-5455	253	7	,	,	PUNCT
ejpam-5455	253	8	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	253	9	)	)	PUNCT
ejpam-5455	253	10	bw	bw	PROPN
ejpam-5455	253	11	=	=	SYM
ejpam-5455	253	12	abiρ0+(θ	abiρ0+(θ	PROPN
ejpam-5455	253	13	)	)	PUNCT
ejpam-5455	254	1	+	+	CCONJ
ejpam-5455	254	2	1−	1−	NUM
ejpam-5455	254	3	ρ	ρ	NUM
ejpam-5455	254	4	b(ρ	b(ρ	PROPN
ejpam-5455	254	5	)	)	PUNCT
ejpam-5455	254	6	ψq	ψq	PROPN
ejpam-5455	254	7	(	(	PUNCT
ejpam-5455	254	8	1	1	NUM
ejpam-5455	254	9	γ(β	γ(β	PROPN
ejpam-5455	254	10	)	)	PUNCT
ejpam-5455	254	11	∫	∫	PROPN
ejpam-5455	255	1	7	7	NUM
ejpam-5455	255	2	0	0	NUM
ejpam-5455	255	3	(	(	PUNCT
ejpam-5455	255	4	7	7	NUM
ejpam-5455	255	5	−	−	NOUN
ejpam-5455	255	6	σ)β−1g(σ	σ)β−1g(σ	NOUN
ejpam-5455	255	7	,	,	PUNCT
ejpam-5455	255	8	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	255	9	)	)	PUNCT
ejpam-5455	256	1	+	+	CCONJ
ejpam-5455	256	2	ρ	ρ	PROPN
ejpam-5455	256	3	b(ρ)γ(ρ	b(ρ)γ(ρ	NOUN
ejpam-5455	256	4	)	)	PUNCT
ejpam-5455	256	5	∫	∫	PROPN
ejpam-5455	257	1	7	7	NUM
ejpam-5455	257	2	0	0	NUM
ejpam-5455	257	3	(	(	PUNCT
ejpam-5455	257	4	7	7	NUM
ejpam-5455	257	5	−	−	NOUN
ejpam-5455	257	6	σ)ρ−1	σ)ρ−1	NOUN
ejpam-5455	257	7	(	(	PUNCT
ejpam-5455	257	8	ψq	ψq	X
ejpam-5455	257	9	(	(	PUNCT
ejpam-5455	257	10	1	1	NUM
ejpam-5455	257	11	γ(β	γ(β	PROPN
ejpam-5455	257	12	)	)	PUNCT
ejpam-5455	257	13	∫	∫	PROPN
ejpam-5455	258	1	σ	σ	PROPN
ejpam-5455	258	2	0	0	NUM
ejpam-5455	258	3	(	(	PUNCT
ejpam-5455	258	4	σ	σ	NOUN
ejpam-5455	258	5	−	−	PROPN
ejpam-5455	258	6	τ)β−1g(τ	τ)β−1g(τ	PUNCT
ejpam-5455	258	7	,	,	PUNCT
ejpam-5455	258	8	w(τ))dτ	w(τ))dτ	PROPN
ejpam-5455	258	9	)	)	PUNCT
ejpam-5455	258	10	)	)	PUNCT
ejpam-5455	259	1	dσ	dσ	PROPN
ejpam-5455	259	2	.	.	PUNCT
ejpam-5455	260	1	the	the	DET
ejpam-5455	260	2	right	right	ADJ
ejpam-5455	260	3	side	side	NOUN
ejpam-5455	260	4	of	of	ADP
ejpam-5455	260	5	the	the	DET
ejpam-5455	260	6	above	above	ADJ
ejpam-5455	260	7	expression	expression	NOUN
ejpam-5455	260	8	can	can	AUX
ejpam-5455	260	9	be	be	AUX
ejpam-5455	260	10	written	write	VERB
ejpam-5455	260	11	as	as	ADP
ejpam-5455	260	12	|awbw	|awbw	PRON
ejpam-5455	260	13	−	−	PROPN
ejpam-5455	260	14	awbw|	awbw|	ADV
ejpam-5455	260	15	.	.	PUNCT
ejpam-5455	261	1	using	use	VERB
ejpam-5455	261	2	the	the	DET
ejpam-5455	261	3	property	property	NOUN
ejpam-5455	261	4	of	of	ADP
ejpam-5455	261	5	absolute	absolute	ADJ
ejpam-5455	261	6	values	value	NOUN
ejpam-5455	261	7	for	for	ADP
ejpam-5455	261	8	products	product	NOUN
ejpam-5455	261	9	,	,	PUNCT
ejpam-5455	261	10	we	we	PRON
ejpam-5455	261	11	can	can	AUX
ejpam-5455	261	12	express	express	VERB
ejpam-5455	261	13	this	this	PRON
ejpam-5455	261	14	as	as	ADP
ejpam-5455	261	15	:	:	PUNCT
ejpam-5455	261	16	|awbw	|awbw	X
ejpam-5455	261	17	−awbw|	−awbw|	VERB
ejpam-5455	262	1	=	=	PUNCT
ejpam-5455	262	2	|awbw	|awbw	PRON
ejpam-5455	262	3	−awbw	−awbw	VERB
ejpam-5455	263	1	+	+	ADJ
ejpam-5455	263	2	awbw	awbw	ADJ
ejpam-5455	263	3	−awbw|	−awbw|	PUNCT
ejpam-5455	263	4	≤	≤	NUM
ejpam-5455	263	5	|aw(bw	|aw(bw	NOUN
ejpam-5455	263	6	−bw	−bw	NOUN
ejpam-5455	263	7	)	)	PUNCT
ejpam-5455	264	1	+	+	ADP
ejpam-5455	264	2	bw(aw	bw(aw	PROPN
ejpam-5455	264	3	−aw)|	−aw)|	PROPN
ejpam-5455	264	4	m.	m.	NOUN
ejpam-5455	264	5	m.	m.	NOUN
ejpam-5455	264	6	arjunan	arjunan	PROPN
ejpam-5455	264	7	/	/	SYM
ejpam-5455	264	8	eur	eur	PROPN
ejpam-5455	264	9	.	.	PUNCT
ejpam-5455	265	1	j.	j.	PROPN
ejpam-5455	265	2	pure	pure	PROPN
ejpam-5455	265	3	appl	appl	PROPN
ejpam-5455	265	4	.	.	PROPN
ejpam-5455	265	5	math	math	PROPN
ejpam-5455	265	6	,	,	PUNCT
ejpam-5455	265	7	17	17	NUM
ejpam-5455	265	8	(	(	PUNCT
ejpam-5455	265	9	4	4	NUM
ejpam-5455	265	10	)	)	PUNCT
ejpam-5455	265	11	(	(	PUNCT
ejpam-5455	265	12	2024	2024	NUM
ejpam-5455	265	13	)	)	PUNCT
ejpam-5455	265	14	,	,	PUNCT
ejpam-5455	265	15	4071	4071	NUM
ejpam-5455	265	16	-	-	SYM
ejpam-5455	265	17	4092	4092	NUM
ejpam-5455	265	18	4081	4081	NUM
ejpam-5455	265	19	≤	≤	NOUN
ejpam-5455	266	1	|aw||bw	|aw||bw	PROPN
ejpam-5455	266	2	−bw|+	−bw|+	PROPN
ejpam-5455	266	3	|bw||aw	|bw||aw	ADJ
ejpam-5455	266	4	−aw|	−aw|	PROPN
ejpam-5455	266	5	.	.	PUNCT
ejpam-5455	267	1	(	(	PUNCT
ejpam-5455	267	2	14	14	NUM
ejpam-5455	267	3	)	)	PUNCT
ejpam-5455	267	4	now	now	ADV
ejpam-5455	267	5	|bw	|bw	X
ejpam-5455	267	6	−bw|	−bw|	PROPN
ejpam-5455	267	7	≤	≤	PROPN
ejpam-5455	267	8	∣∣∣∣∣abiρ0+(θ	∣∣∣∣∣abiρ0+(θ	PROPN
ejpam-5455	267	9	)	)	PUNCT
ejpam-5455	267	10	+	+	CCONJ
ejpam-5455	267	11	1−	1−	NUM
ejpam-5455	267	12	ρ	ρ	NUM
ejpam-5455	267	13	b(ρ	b(ρ	PROPN
ejpam-5455	267	14	)	)	PUNCT
ejpam-5455	267	15	ψq	ψq	PROPN
ejpam-5455	267	16	(	(	PUNCT
ejpam-5455	267	17	1	1	NUM
ejpam-5455	267	18	γ(β	γ(β	PROPN
ejpam-5455	267	19	)	)	PUNCT
ejpam-5455	267	20	∫	∫	PROPN
ejpam-5455	267	21	7	7	NUM
ejpam-5455	267	22	0	0	NUM
ejpam-5455	267	23	(	(	PUNCT
ejpam-5455	267	24	7	7	NUM
ejpam-5455	267	25	−	−	NOUN
ejpam-5455	267	26	σ)β−1g(σ	σ)β−1g(σ	NOUN
ejpam-5455	267	27	,	,	PUNCT
ejpam-5455	267	28	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	267	29	)	)	PUNCT
ejpam-5455	267	30	+	+	CCONJ
ejpam-5455	267	31	ρ	ρ	PROPN
ejpam-5455	267	32	b(ρ)γ(ρ	b(ρ)γ(ρ	NOUN
ejpam-5455	267	33	)	)	PUNCT
ejpam-5455	267	34	∫	∫	PROPN
ejpam-5455	267	35	7	7	NUM
ejpam-5455	267	36	0	0	NUM
ejpam-5455	267	37	(	(	PUNCT
ejpam-5455	267	38	7	7	NUM
ejpam-5455	267	39	−	−	NOUN
ejpam-5455	267	40	σ)ρ−1	σ)ρ−1	NOUN
ejpam-5455	267	41	(	(	PUNCT
ejpam-5455	267	42	ψq	ψq	X
ejpam-5455	267	43	(	(	PUNCT
ejpam-5455	267	44	1	1	NUM
ejpam-5455	267	45	γ(β	γ(β	PROPN
ejpam-5455	267	46	)	)	PUNCT
ejpam-5455	267	47	∫	∫	PROPN
ejpam-5455	268	1	σ	σ	PROPN
ejpam-5455	268	2	0	0	NUM
ejpam-5455	268	3	(	(	PUNCT
ejpam-5455	268	4	σ	σ	NOUN
ejpam-5455	268	5	−	−	PROPN
ejpam-5455	268	6	τ)β−1g(τ	τ)β−1g(τ	PUNCT
ejpam-5455	268	7	,	,	PUNCT
ejpam-5455	268	8	w(τ))dτ	w(τ))dτ	PROPN
ejpam-5455	268	9	)	)	PUNCT
ejpam-5455	268	10	)	)	PUNCT
ejpam-5455	268	11	dσ	dσ	VERB
ejpam-5455	268	12	−	−	PROPN
ejpam-5455	268	13	abiρ0+(θ)−	abiρ0+(θ)−	PROPN
ejpam-5455	268	14	1−	1−	NUM
ejpam-5455	268	15	ρ	ρ	PROPN
ejpam-5455	268	16	b(ρ	b(ρ	PROPN
ejpam-5455	268	17	)	)	PUNCT
ejpam-5455	268	18	ψq	ψq	PROPN
ejpam-5455	268	19	(	(	PUNCT
ejpam-5455	268	20	1	1	NUM
ejpam-5455	268	21	γ(β	γ(β	PROPN
ejpam-5455	268	22	)	)	PUNCT
ejpam-5455	268	23	∫	∫	PROPN
ejpam-5455	268	24	7	7	NUM
ejpam-5455	268	25	0	0	NUM
ejpam-5455	268	26	(	(	PUNCT
ejpam-5455	268	27	7	7	NUM
ejpam-5455	268	28	−	−	NOUN
ejpam-5455	268	29	σ)β−1g(σ	σ)β−1g(σ	ADP
ejpam-5455	268	30	,	,	PUNCT
ejpam-5455	268	31	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	268	32	)	)	PUNCT
ejpam-5455	268	33	−	−	PROPN
ejpam-5455	268	34	ρ	ρ	NUM
ejpam-5455	268	35	b(ρ)γ(ρ	b(ρ)γ(ρ	PROPN
ejpam-5455	268	36	)	)	PUNCT
ejpam-5455	268	37	∫	∫	PROPN
ejpam-5455	268	38	7	7	NUM
ejpam-5455	268	39	0	0	NUM
ejpam-5455	268	40	(	(	PUNCT
ejpam-5455	268	41	7	7	NUM
ejpam-5455	268	42	−	−	NOUN
ejpam-5455	268	43	σ)ρ−1	σ)ρ−1	NOUN
ejpam-5455	268	44	(	(	PUNCT
ejpam-5455	268	45	ψq	ψq	X
ejpam-5455	268	46	(	(	PUNCT
ejpam-5455	268	47	1	1	NUM
ejpam-5455	268	48	γ(β	γ(β	PROPN
ejpam-5455	268	49	)	)	PUNCT
ejpam-5455	268	50	∫	∫	PROPN
ejpam-5455	269	1	σ	σ	PROPN
ejpam-5455	269	2	0	0	NUM
ejpam-5455	269	3	(	(	PUNCT
ejpam-5455	269	4	σ	σ	NOUN
ejpam-5455	269	5	−	−	PROPN
ejpam-5455	269	6	τ)β−1g(τ	τ)β−1g(τ	PUNCT
ejpam-5455	269	7	,	,	PUNCT
ejpam-5455	269	8	w(τ))dτ	w(τ))dτ	PROPN
ejpam-5455	269	9	)	)	PUNCT
ejpam-5455	269	10	)	)	PUNCT
ejpam-5455	269	11	dσ	dσ	VERB
ejpam-5455	269	12	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5455	269	13	≤	≤	PROPN
ejpam-5455	269	14	1−	1−	NUM
ejpam-5455	269	15	ρ	ρ	NUM
ejpam-5455	269	16	b(ρ	b(ρ	PROPN
ejpam-5455	269	17	)	)	PUNCT
ejpam-5455	269	18	{	{	PUNCT
ejpam-5455	269	19	∣∣∣∣∣ψq	∣∣∣∣∣ψq	NOUN
ejpam-5455	269	20	(	(	PUNCT
ejpam-5455	269	21	1	1	NUM
ejpam-5455	269	22	γ(β	γ(β	PROPN
ejpam-5455	269	23	)	)	PUNCT
ejpam-5455	269	24	∫	∫	PROPN
ejpam-5455	269	25	7	7	NUM
ejpam-5455	269	26	0	0	NUM
ejpam-5455	269	27	(	(	PUNCT
ejpam-5455	269	28	7	7	NUM
ejpam-5455	269	29	−	−	NOUN
ejpam-5455	269	30	σ)β−1g(σ	σ)β−1g(σ	NOUN
ejpam-5455	269	31	,	,	PUNCT
ejpam-5455	269	32	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	269	33	)	)	PUNCT
ejpam-5455	269	34	−ψq	−ψq	NOUN
ejpam-5455	269	35	(	(	PUNCT
ejpam-5455	269	36	1	1	NUM
ejpam-5455	269	37	γ(β	γ(β	PROPN
ejpam-5455	269	38	)	)	PUNCT
ejpam-5455	269	39	∫	∫	PROPN
ejpam-5455	269	40	7	7	NUM
ejpam-5455	269	41	0	0	NUM
ejpam-5455	269	42	(	(	PUNCT
ejpam-5455	269	43	7	7	NUM
ejpam-5455	269	44	−	−	NOUN
ejpam-5455	269	45	σ)β−1g(σ	σ)β−1g(σ	ADP
ejpam-5455	269	46	,	,	PUNCT
ejpam-5455	269	47	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	269	48	)	)	PUNCT
ejpam-5455	269	49	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5455	269	50	}	}	PUNCT
ejpam-5455	270	1	+	+	NUM
ejpam-5455	270	2	ρ	ρ	PROPN
ejpam-5455	270	3	b(ρ)γ(ρ	b(ρ)γ(ρ	NOUN
ejpam-5455	270	4	)	)	PUNCT
ejpam-5455	270	5	∫	∫	PROPN
ejpam-5455	271	1	7	7	NUM
ejpam-5455	271	2	0	0	NUM
ejpam-5455	271	3	(	(	PUNCT
ejpam-5455	271	4	7	7	NUM
ejpam-5455	271	5	−	−	NOUN
ejpam-5455	271	6	σ)ρ−1	σ)ρ−1	NOUN
ejpam-5455	271	7	∣∣∣∣∣ψq	∣∣∣∣∣ψq	NOUN
ejpam-5455	271	8	(	(	PUNCT
ejpam-5455	271	9	1	1	NUM
ejpam-5455	271	10	γ(β	γ(β	PROPN
ejpam-5455	271	11	)	)	PUNCT
ejpam-5455	271	12	∫	∫	PROPN
ejpam-5455	272	1	σ	σ	PROPN
ejpam-5455	272	2	0	0	NUM
ejpam-5455	272	3	(	(	PUNCT
ejpam-5455	272	4	σ	σ	NOUN
ejpam-5455	272	5	−	−	PROPN
ejpam-5455	272	6	τ)β−1g(τ	τ)β−1g(τ	PUNCT
ejpam-5455	272	7	,	,	PUNCT
ejpam-5455	272	8	w(τ))dτ	w(τ))dτ	PROPN
ejpam-5455	272	9	)	)	PUNCT
ejpam-5455	272	10	−ψq	−ψq	NOUN
ejpam-5455	272	11	(	(	PUNCT
ejpam-5455	272	12	1	1	NUM
ejpam-5455	272	13	γ(β	γ(β	PROPN
ejpam-5455	272	14	)	)	PUNCT
ejpam-5455	272	15	∫	∫	PROPN
ejpam-5455	273	1	σ	σ	PROPN
ejpam-5455	273	2	0	0	NUM
ejpam-5455	273	3	(	(	PUNCT
ejpam-5455	273	4	σ	σ	NOUN
ejpam-5455	273	5	−	−	PROPN
ejpam-5455	273	6	τ)β−1g(τ	τ)β−1g(τ	PUNCT
ejpam-5455	273	7	,	,	PUNCT
ejpam-5455	273	8	w(τ))dτ	w(τ))dτ	NOUN
ejpam-5455	273	9	)	)	PUNCT
ejpam-5455	273	10	∣∣∣∣∣dσ	∣∣∣∣∣dσ	NOUN
ejpam-5455	273	11	,	,	PUNCT
ejpam-5455	273	12	(	(	PUNCT
ejpam-5455	273	13	15	15	NUM
ejpam-5455	273	14	)	)	PUNCT
ejpam-5455	273	15	and	and	CCONJ
ejpam-5455	273	16	|aw	|aw	NUM
ejpam-5455	273	17	−aw|	−aw|	NOUN
ejpam-5455	273	18	≤	≤	NUM
ejpam-5455	273	19	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5455	273	20	(	(	PUNCT
ejpam-5455	273	21	q(7	q(7	PROPN
ejpam-5455	273	22	)	)	PUNCT
ejpam-5455	273	23	+	+	CCONJ
ejpam-5455	273	24	1	1	NUM
ejpam-5455	273	25	γ(γ	γ(γ	NOUN
ejpam-5455	273	26	)	)	PUNCT
ejpam-5455	273	27	∫	∫	PROPN
ejpam-5455	274	1	7	7	NUM
ejpam-5455	274	2	0	0	NUM
ejpam-5455	274	3	(	(	PUNCT
ejpam-5455	274	4	7	7	NUM
ejpam-5455	274	5	−	−	NOUN
ejpam-5455	274	6	σ)γ−1f(σ	σ)γ−1f(σ	NOUN
ejpam-5455	274	7	,	,	PUNCT
ejpam-5455	274	8	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	274	9	)	)	PUNCT
ejpam-5455	274	10	−	−	PROPN
ejpam-5455	274	11	(	(	PUNCT
ejpam-5455	274	12	q(7	q(7	PROPN
ejpam-5455	274	13	)	)	PUNCT
ejpam-5455	274	14	+	+	CCONJ
ejpam-5455	274	15	1	1	NUM
ejpam-5455	274	16	γ(γ	γ(γ	NOUN
ejpam-5455	274	17	)	)	PUNCT
ejpam-5455	274	18	∫	∫	PROPN
ejpam-5455	274	19	7	7	NUM
ejpam-5455	274	20	0	0	NUM
ejpam-5455	274	21	(	(	PUNCT
ejpam-5455	274	22	7	7	NUM
ejpam-5455	274	23	−	−	NOUN
ejpam-5455	274	24	σ)γ−1f(σ	σ)γ−1f(σ	NOUN
ejpam-5455	274	25	,	,	PUNCT
ejpam-5455	274	26	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	274	27	)	)	PUNCT
ejpam-5455	274	28	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5455	274	29	≤	≤	PROPN
ejpam-5455	274	30	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5455	274	31	1	1	NUM
ejpam-5455	274	32	γ(γ	γ(γ	NOUN
ejpam-5455	274	33	)	)	PUNCT
ejpam-5455	274	34	∫	∫	PROPN
ejpam-5455	275	1	7	7	NUM
ejpam-5455	275	2	0	0	NUM
ejpam-5455	275	3	(	(	PUNCT
ejpam-5455	275	4	7	7	NUM
ejpam-5455	275	5	−	−	NOUN
ejpam-5455	275	6	σ)γ−1[f(σ	σ)γ−1[f(σ	NOUN
ejpam-5455	275	7	,	,	PUNCT
ejpam-5455	275	8	w(σ))−	w(σ))−	NOUN
ejpam-5455	275	9	f(s	f(	NOUN
ejpam-5455	275	10	,	,	PUNCT
ejpam-5455	275	11	w(s))]dσ	w(s))]dσ	PROPN
ejpam-5455	275	12	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5455	275	13	.	.	PUNCT
ejpam-5455	276	1	(	(	PUNCT
ejpam-5455	276	2	16	16	NUM
ejpam-5455	276	3	)	)	PUNCT
ejpam-5455	276	4	we	we	PRON
ejpam-5455	276	5	will	will	AUX
ejpam-5455	276	6	now	now	ADV
ejpam-5455	276	7	outline	outline	VERB
ejpam-5455	276	8	the	the	DET
ejpam-5455	276	9	following	following	ADJ
ejpam-5455	276	10	assumptions	assumption	NOUN
ejpam-5455	276	11	:	:	PUNCT
ejpam-5455	276	12	(	(	PUNCT
ejpam-5455	276	13	a1	a1	NOUN
ejpam-5455	276	14	)	)	PUNCT
ejpam-5455	276	15	for	for	ADP
ejpam-5455	276	16	positive	positive	ADJ
ejpam-5455	276	17	constants	constant	NOUN
ejpam-5455	276	18	lf	lf	ADP
ejpam-5455	276	19	,	,	PUNCT
ejpam-5455	276	20	lg	lg	PROPN
ejpam-5455	276	21	,	,	PUNCT
ejpam-5455	276	22	lh	lh	PROPN
ejpam-5455	276	23	>	>	X
ejpam-5455	276	24	0	0	PROPN
ejpam-5455	276	25	,	,	PUNCT
ejpam-5455	276	26	it	it	PRON
ejpam-5455	276	27	holds	hold	VERB
ejpam-5455	276	28	that	that	SCONJ
ejpam-5455	276	29	for	for	ADP
ejpam-5455	276	30	any	any	DET
ejpam-5455	276	31	elements	element	NOUN
ejpam-5455	276	32	w	w	ADP
ejpam-5455	276	33	,	,	PUNCT
ejpam-5455	276	34	w1	w1	NOUN
ejpam-5455	276	35	,	,	PUNCT
ejpam-5455	276	36	w	w	PROPN
ejpam-5455	276	37	,	,	PUNCT
ejpam-5455	276	38	w1	w1	PROPN
ejpam-5455	276	39	∈	∈	PROPN
ejpam-5455	276	40	ac(ω	ac(ω	ADV
ejpam-5455	276	41	)	)	PUNCT
ejpam-5455	276	42	|f(7	|f(7	ADV
ejpam-5455	276	43	,	,	PUNCT
ejpam-5455	276	44	w(7))−	w(7))−	NOUN
ejpam-5455	276	45	f(7	f(7	NOUN
ejpam-5455	276	46	,	,	PUNCT
ejpam-5455	276	47	w(7))|	w(7))|	NOUN
ejpam-5455	276	48	≤	≤	PROPN
ejpam-5455	276	49	lf	lf	ADP
ejpam-5455	276	50	|w(7)−	|w(7)−	PROPN
ejpam-5455	276	51	w(7)|	w(7)|	PROPN
ejpam-5455	276	52	,	,	PUNCT
ejpam-5455	276	53	|g(7	|g(7	NOUN
ejpam-5455	276	54	,	,	PUNCT
ejpam-5455	276	55	w(7))−	w(7))−	PROPN
ejpam-5455	276	56	g(7	g(7	PROPN
ejpam-5455	276	57	,	,	PUNCT
ejpam-5455	276	58	w(7))|	w(7))|	NOUN
ejpam-5455	276	59	≤	≤	PROPN
ejpam-5455	276	60	lg|w(7)−	lg|w(7)−	NUM
ejpam-5455	276	61	w(7)|	w(7)|	PROPN
ejpam-5455	276	62	,	,	PUNCT
ejpam-5455	276	63	and	and	CCONJ
ejpam-5455	276	64	|h(7	|h(7	NUM
ejpam-5455	276	65	,	,	PUNCT
ejpam-5455	276	66	w(7))−	w(7))−	PROPN
ejpam-5455	276	67	h(7	h(7	PROPN
ejpam-5455	276	68	,	,	PUNCT
ejpam-5455	276	69	w(7))|	w(7))|	NOUN
ejpam-5455	276	70	≤	≤	PROPN
ejpam-5455	276	71	lh|w(7)−	lh|w(7)−	NUM
ejpam-5455	276	72	w(7)|	w(7)|	PROPN
ejpam-5455	276	73	.	.	PUNCT
ejpam-5455	277	1	m.	m.	PROPN
ejpam-5455	277	2	m.	m.	PROPN
ejpam-5455	277	3	arjunan	arjunan	PROPN
ejpam-5455	277	4	/	/	SYM
ejpam-5455	277	5	eur	eur	PROPN
ejpam-5455	277	6	.	.	PUNCT
ejpam-5455	278	1	j.	j.	PROPN
ejpam-5455	278	2	pure	pure	PROPN
ejpam-5455	278	3	appl	appl	PROPN
ejpam-5455	278	4	.	.	PROPN
ejpam-5455	278	5	math	math	PROPN
ejpam-5455	278	6	,	,	PUNCT
ejpam-5455	278	7	17	17	NUM
ejpam-5455	278	8	(	(	PUNCT
ejpam-5455	278	9	4	4	NUM
ejpam-5455	278	10	)	)	PUNCT
ejpam-5455	278	11	(	(	PUNCT
ejpam-5455	278	12	2024	2024	NUM
ejpam-5455	278	13	)	)	PUNCT
ejpam-5455	278	14	,	,	PUNCT
ejpam-5455	278	15	4071	4071	NUM
ejpam-5455	278	16	-	-	SYM
ejpam-5455	278	17	4092	4092	NUM
ejpam-5455	278	18	4082	4082	NUM
ejpam-5455	278	19	(	(	PUNCT
ejpam-5455	278	20	a2	a2	PROPN
ejpam-5455	278	21	)	)	PUNCT
ejpam-5455	278	22	there	there	PRON
ejpam-5455	278	23	exist	exist	VERB
ejpam-5455	278	24	functions	function	NOUN
ejpam-5455	279	1	f	f	X
ejpam-5455	279	2	,	,	PUNCT
ejpam-5455	279	3	g	g	PROPN
ejpam-5455	279	4	∈	∈	PROPN
ejpam-5455	279	5	l1(ω	l1(ω	PROPN
ejpam-5455	279	6	,	,	PUNCT
ejpam-5455	279	7	r+	r+	NOUN
ejpam-5455	279	8	)	)	PUNCT
ejpam-5455	279	9	such	such	ADJ
ejpam-5455	279	10	that	that	SCONJ
ejpam-5455	279	11	|f(7	|f(7	NOUN
ejpam-5455	279	12	,	,	PUNCT
ejpam-5455	279	13	w(7))|	w(7))|	VERB
ejpam-5455	279	14	≤	≤	PROPN
ejpam-5455	279	15	f	f	X
ejpam-5455	279	16	(	(	PUNCT
ejpam-5455	279	17	7	7	NUM
ejpam-5455	279	18	)	)	PUNCT
ejpam-5455	279	19	and	and	CCONJ
ejpam-5455	279	20	|g(7	|g(7	NOUN
ejpam-5455	279	21	,	,	PUNCT
ejpam-5455	279	22	w(7))|	w(7))|	NOUN
ejpam-5455	279	23	≤	≤	PROPN
ejpam-5455	279	24	g(7	g(7	PROPN
ejpam-5455	279	25	)	)	PUNCT
ejpam-5455	279	26	,	,	PUNCT
ejpam-5455	279	27	7	7	NUM
ejpam-5455	279	28	∈	∈	PROPN
ejpam-5455	279	29	ω	ω	NOUN
ejpam-5455	279	30	.	.	PUNCT
ejpam-5455	279	31	(	(	PUNCT
ejpam-5455	279	32	a3	a3	NOUN
ejpam-5455	279	33	)	)	PUNCT
ejpam-5455	279	34	for	for	ADP
ejpam-5455	279	35	any	any	DET
ejpam-5455	279	36	constant	constant	ADJ
ejpam-5455	279	37	lq	lq	ADP
ejpam-5455	279	38	>	>	X
ejpam-5455	279	39	0	0	NUM
ejpam-5455	279	40	,	,	PUNCT
ejpam-5455	279	41	it	it	PRON
ejpam-5455	279	42	follows	follow	VERB
ejpam-5455	279	43	that	that	SCONJ
ejpam-5455	279	44	|q(72)−q(71)|	|q(72)−q(71)|	PROPN
ejpam-5455	279	45	≤	≤	NOUN
ejpam-5455	279	46	lq|72	lq|72	ADV
ejpam-5455	279	47	−	−	PROPN
ejpam-5455	280	1	71|	71|	NUM
ejpam-5455	280	2	,	,	PUNCT
ejpam-5455	280	3	71	71	NUM
ejpam-5455	280	4	,	,	PUNCT
ejpam-5455	280	5	72	72	NUM
ejpam-5455	280	6	∈	∈	PROPN
ejpam-5455	280	7	ω	ω	NOUN
ejpam-5455	280	8	.	.	PROPN
ejpam-5455	281	1	3	3	NUM
ejpam-5455	281	2	.	.	X
ejpam-5455	281	3	existence	existence	NOUN
ejpam-5455	281	4	results	result	VERB
ejpam-5455	281	5	this	this	DET
ejpam-5455	281	6	section	section	NOUN
ejpam-5455	281	7	initiates	initiate	VERB
ejpam-5455	281	8	a	a	DET
ejpam-5455	281	9	thorough	thorough	ADJ
ejpam-5455	281	10	analysis	analysis	NOUN
ejpam-5455	281	11	aimed	aim	VERB
ejpam-5455	281	12	at	at	ADP
ejpam-5455	281	13	proving	prove	VERB
ejpam-5455	281	14	the	the	DET
ejpam-5455	281	15	existence	existence	NOUN
ejpam-5455	281	16	of	of	ADP
ejpam-5455	281	17	solutions	solution	NOUN
ejpam-5455	281	18	for	for	ADP
ejpam-5455	281	19	the	the	DET
ejpam-5455	281	20	system	system	NOUN
ejpam-5455	281	21	(	(	PUNCT
ejpam-5455	281	22	1	1	NUM
ejpam-5455	281	23	)	)	PUNCT
ejpam-5455	281	24	.	.	PUNCT
ejpam-5455	282	1	to	to	PART
ejpam-5455	282	2	accomplish	accomplish	VERB
ejpam-5455	282	3	this	this	PRON
ejpam-5455	282	4	,	,	PUNCT
ejpam-5455	282	5	we	we	PRON
ejpam-5455	282	6	effectively	effectively	ADV
ejpam-5455	282	7	utilize	utilize	VERB
ejpam-5455	282	8	two	two	NUM
ejpam-5455	282	9	fundamental	fundamental	ADJ
ejpam-5455	282	10	methodologies	methodology	NOUN
ejpam-5455	282	11	:	:	PUNCT
ejpam-5455	282	12	the	the	DET
ejpam-5455	282	13	banach	banach	NOUN
ejpam-5455	282	14	contraction	contraction	NOUN
ejpam-5455	282	15	principle	principle	NOUN
ejpam-5455	282	16	and	and	CCONJ
ejpam-5455	282	17	krasnoselskii	krasnoselskii	PROPN
ejpam-5455	282	18	fpts	fpt	NOUN
ejpam-5455	283	1	[	[	X
ejpam-5455	283	2	14	14	NUM
ejpam-5455	283	3	,	,	PUNCT
ejpam-5455	283	4	16	16	NUM
ejpam-5455	283	5	]	]	PUNCT
ejpam-5455	283	6	.	.	PUNCT
ejpam-5455	284	1	theorem	theorem	NOUN
ejpam-5455	284	2	1	1	NUM
ejpam-5455	284	3	.	.	PUNCT
ejpam-5455	285	1	given	give	VERB
ejpam-5455	285	2	the	the	DET
ejpam-5455	285	3	assumptions	assumption	NOUN
ejpam-5455	285	4	(	(	PUNCT
ejpam-5455	285	5	a1	a1	NOUN
ejpam-5455	285	6	)	)	PUNCT
ejpam-5455	285	7	−	−	PROPN
ejpam-5455	285	8	(	(	PUNCT
ejpam-5455	285	9	a3	a3	PROPN
ejpam-5455	285	10	)	)	PUNCT
ejpam-5455	285	11	,	,	PUNCT
ejpam-5455	285	12	the	the	DET
ejpam-5455	285	13	system	system	NOUN
ejpam-5455	285	14	(	(	PUNCT
ejpam-5455	285	15	1	1	X
ejpam-5455	285	16	)	)	PUNCT
ejpam-5455	285	17	possesses	possess	VERB
ejpam-5455	285	18	a	a	DET
ejpam-5455	285	19	unique	unique	ADJ
ejpam-5455	285	20	solution	solution	NOUN
ejpam-5455	285	21	when	when	SCONJ
ejpam-5455	285	22	∆	∆	PROPN
ejpam-5455	285	23	=	=	PRON
ejpam-5455	286	1	[	[	X
ejpam-5455	286	2	(	(	PUNCT
ejpam-5455	286	3	lqz	lqz	NOUN
ejpam-5455	286	4	+	+	CCONJ
ejpam-5455	286	5	|q(0)|+	|q(0)|+	NUM
ejpam-5455	286	6	zγ∥f∥l1	zγ∥f∥l1	NUM
ejpam-5455	286	7	γ(γ	γ(γ	X
ejpam-5455	286	8	+	+	CCONJ
ejpam-5455	286	9	1	1	NUM
ejpam-5455	286	10	)	)	PUNCT
ejpam-5455	286	11	)	)	PUNCT
ejpam-5455	286	12	(	(	PUNCT
ejpam-5455	286	13	(	(	PUNCT
ejpam-5455	286	14	q	q	NOUN
ejpam-5455	286	15	−	−	PROPN
ejpam-5455	286	16	1)mq−2zβ	1)mq−2zβ	NUM
ejpam-5455	286	17	b(ρ)γ(β	b(ρ)γ(β	NOUN
ejpam-5455	286	18	+	+	NOUN
ejpam-5455	286	19	1	1	X
ejpam-5455	286	20	)	)	PUNCT
ejpam-5455	286	21	{	{	PUNCT
ejpam-5455	286	22	1−	1−	NUM
ejpam-5455	286	23	ρ+	ρ+	NOUN
ejpam-5455	286	24	zρ	zρ	X
ejpam-5455	286	25	γ(ρ	γ(ρ	PROPN
ejpam-5455	286	26	)	)	PUNCT
ejpam-5455	286	27	}	}	PUNCT
ejpam-5455	286	28	lg	lg	NOUN
ejpam-5455	286	29	)	)	PUNCT
ejpam-5455	286	30	+	+	CCONJ
ejpam-5455	286	31	(	(	PUNCT
ejpam-5455	286	32	abiρ0	abiρ0	NOUN
ejpam-5455	286	33	+	+	X
ejpam-5455	286	34	|θ|+	|θ|+	ADV
ejpam-5455	286	35	1	1	NUM
ejpam-5455	286	36	b(ρ	b(ρ	NOUN
ejpam-5455	286	37	)	)	PUNCT
ejpam-5455	286	38	(	(	PUNCT
ejpam-5455	286	39	zβ∥g∥l1	zβ∥g∥l1	X
ejpam-5455	286	40	γ(β	γ(β	PROPN
ejpam-5455	286	41	+	+	CCONJ
ejpam-5455	286	42	1	1	NUM
ejpam-5455	286	43	)	)	PUNCT
ejpam-5455	286	44	)	)	PUNCT
ejpam-5455	287	1	q−1	q−1	PROPN
ejpam-5455	287	2	{	{	PUNCT
ejpam-5455	287	3	1−	1−	NUM
ejpam-5455	287	4	ρ+	ρ+	NUM
ejpam-5455	287	5	zρ	zρ	X
ejpam-5455	287	6	γ(ρ	γ(ρ	PROPN
ejpam-5455	287	7	)	)	PUNCT
ejpam-5455	287	8	}	}	PUNCT
ejpam-5455	287	9	)	)	PUNCT
ejpam-5455	287	10	(	(	PUNCT
ejpam-5455	287	11	lfz	lfz	NOUN
ejpam-5455	287	12	γ	γ	X
ejpam-5455	287	13	γ(γ	γ(γ	PROPN
ejpam-5455	287	14	+	+	CCONJ
ejpam-5455	287	15	1	1	NUM
ejpam-5455	287	16	)	)	PUNCT
ejpam-5455	287	17	)	)	PUNCT
ejpam-5455	288	1	+	+	CCONJ
ejpam-5455	288	2	lh	lh	X
ejpam-5455	288	3	]	]	PUNCT
ejpam-5455	288	4	<	<	X
ejpam-5455	288	5	1	1	X
ejpam-5455	288	6	.	.	PUNCT
ejpam-5455	288	7	(	(	PUNCT
ejpam-5455	288	8	17	17	NUM
ejpam-5455	288	9	)	)	PUNCT
ejpam-5455	288	10	proof	proof	NOUN
ejpam-5455	288	11	.	.	PUNCT
ejpam-5455	289	1	let	let	VERB
ejpam-5455	289	2	w	w	X
ejpam-5455	289	3	,	,	PUNCT
ejpam-5455	289	4	w	w	PROPN
ejpam-5455	289	5	∈	∈	PROPN
ejpam-5455	289	6	ac(ω	ac(ω	PRON
ejpam-5455	289	7	)	)	PUNCT
ejpam-5455	289	8	.	.	PUNCT
ejpam-5455	290	1	then	then	ADV
ejpam-5455	290	2	from	from	ADP
ejpam-5455	290	3	note	note	NOUN
ejpam-5455	290	4	2.1	2.1	NUM
ejpam-5455	290	5	,	,	PUNCT
ejpam-5455	290	6	we	we	PRON
ejpam-5455	290	7	have	have	AUX
ejpam-5455	290	8	∥φw	∥φw	PROPN
ejpam-5455	290	9	−	−	PROPN
ejpam-5455	290	10	φw∥	φw∥	PROPN
ejpam-5455	290	11	=	=	SYM
ejpam-5455	290	12	max	max	PROPN
ejpam-5455	290	13	7∈ω	7∈ω	PROPN
ejpam-5455	290	14	|((a+b)w)(7)−	|((a+b)w)(7)−	PROPN
ejpam-5455	290	15	(	(	PUNCT
ejpam-5455	290	16	(	(	PUNCT
ejpam-5455	290	17	a+b)w)(7)|	a+b)w)(7)|	ADJ
ejpam-5455	290	18	≤	≤	NUM
ejpam-5455	290	19	max	max	PROPN
ejpam-5455	290	20	7∈ω	7∈ω	PROPN
ejpam-5455	290	21	|(aw)(7)−	|(aw)(7)−	PROPN
ejpam-5455	290	22	(	(	PUNCT
ejpam-5455	290	23	aw)(7)|+max	aw)(7)|+max	ADP
ejpam-5455	290	24	7∈ω	7∈ω	NOUN
ejpam-5455	291	1	|(bw)(7)−	|(bw)(7)−	PROPN
ejpam-5455	291	2	(	(	PUNCT
ejpam-5455	291	3	bw)(7)|	bw)(7)|	PROPN
ejpam-5455	291	4	.	.	PUNCT
ejpam-5455	292	1	(	(	PUNCT
ejpam-5455	292	2	18	18	NUM
ejpam-5455	292	3	)	)	PUNCT
ejpam-5455	292	4	from	from	ADP
ejpam-5455	292	5	(	(	PUNCT
ejpam-5455	292	6	14)-(16	14)-(16	NOUN
ejpam-5455	292	7	)	)	PUNCT
ejpam-5455	292	8	,	,	PUNCT
ejpam-5455	292	9	we	we	PRON
ejpam-5455	292	10	have	have	VERB
ejpam-5455	292	11	∥aw	∥aw	PROPN
ejpam-5455	292	12	−aw∥	−aw∥	VERB
ejpam-5455	292	13	≤	≤	NUM
ejpam-5455	292	14	max	max	PROPN
ejpam-5455	292	15	7∈ω	7∈ω	PROPN
ejpam-5455	292	16	{	{	PUNCT
ejpam-5455	292	17	|aw||bw	|aw||bw	PROPN
ejpam-5455	292	18	−bw|+	−bw|+	PROPN
ejpam-5455	292	19	|bw||aw	|bw||aw	VERB
ejpam-5455	292	20	−aw|	−aw|	NOUN
ejpam-5455	292	21	}	}	PUNCT
ejpam-5455	292	22	.	.	PUNCT
ejpam-5455	293	1	(	(	PUNCT
ejpam-5455	293	2	19	19	NUM
ejpam-5455	293	3	)	)	PUNCT
ejpam-5455	293	4	we	we	PRON
ejpam-5455	293	5	can	can	AUX
ejpam-5455	293	6	now	now	ADV
ejpam-5455	293	7	evaluate	evaluate	VERB
ejpam-5455	293	8	the	the	DET
ejpam-5455	293	9	expression	expression	NOUN
ejpam-5455	293	10	mentioned	mention	VERB
ejpam-5455	293	11	earlier	early	ADV
ejpam-5455	293	12	in	in	ADP
ejpam-5455	293	13	the	the	DET
ejpam-5455	293	14	following	following	ADJ
ejpam-5455	293	15	manner	manner	NOUN
ejpam-5455	293	16	:	:	PUNCT
ejpam-5455	293	17	max	max	PROPN
ejpam-5455	293	18	7∈ω	7∈ω	NOUN
ejpam-5455	293	19	|aw|	|aw|	X
ejpam-5455	294	1	=	=	PUNCT
ejpam-5455	294	2	max	max	PROPN
ejpam-5455	294	3	7∈ω	7∈ω	PROPN
ejpam-5455	294	4	∣∣∣∣q(7	∣∣∣∣q(7	PROPN
ejpam-5455	294	5	)	)	PUNCT
ejpam-5455	294	6	+	+	CCONJ
ejpam-5455	294	7	1	1	NUM
ejpam-5455	294	8	γ(γ	γ(γ	NOUN
ejpam-5455	294	9	)	)	PUNCT
ejpam-5455	294	10	∫	∫	PROPN
ejpam-5455	295	1	7	7	NUM
ejpam-5455	295	2	0	0	NUM
ejpam-5455	295	3	(	(	PUNCT
ejpam-5455	295	4	7	7	NUM
ejpam-5455	295	5	−	−	NOUN
ejpam-5455	295	6	σ)γ−1f(σ	σ)γ−1f(σ	NOUN
ejpam-5455	295	7	,	,	PUNCT
ejpam-5455	295	8	w(σ))dσ	w(σ))dσ	ADP
ejpam-5455	295	9	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5455	295	10	≤	≤	NUM
ejpam-5455	295	11	max	max	PROPN
ejpam-5455	295	12	7∈ω	7∈ω	PROPN
ejpam-5455	295	13	|q(7)−q(0)|+	|q(7)−q(0)|+	SYM
ejpam-5455	295	14	|q(0)|+	|q(0)|+	NUM
ejpam-5455	295	15	1	1	NUM
ejpam-5455	295	16	γ(γ	γ(γ	NOUN
ejpam-5455	295	17	)	)	PUNCT
ejpam-5455	295	18	∫	∫	PROPN
ejpam-5455	295	19	7	7	NUM
ejpam-5455	295	20	0	0	NUM
ejpam-5455	295	21	(	(	PUNCT
ejpam-5455	295	22	7	7	NUM
ejpam-5455	295	23	−	−	NOUN
ejpam-5455	295	24	σ)γ−1max	σ)γ−1max	NOUN
ejpam-5455	295	25	7∈ω	7∈ω	NOUN
ejpam-5455	295	26	|f(σ	|f(σ	PROPN
ejpam-5455	295	27	,	,	PUNCT
ejpam-5455	295	28	w(σ))|dσ	w(σ))|dσ	ADJ
ejpam-5455	295	29	≤	≤	X
ejpam-5455	295	30	lqz	lqz	NOUN
ejpam-5455	295	31	+	+	CCONJ
ejpam-5455	295	32	|q(0)|+	|q(0)|+	NUM
ejpam-5455	295	33	1	1	NUM
ejpam-5455	295	34	γ(γ	γ(γ	NOUN
ejpam-5455	295	35	)	)	PUNCT
ejpam-5455	295	36	∫	∫	PROPN
ejpam-5455	295	37	7	7	NUM
ejpam-5455	295	38	0	0	NUM
ejpam-5455	295	39	(	(	PUNCT
ejpam-5455	295	40	7	7	NUM
ejpam-5455	295	41	−	−	NOUN
ejpam-5455	295	42	σ)γ−1max	σ)γ−1max	NOUN
ejpam-5455	295	43	7∈ω	7∈ω	NUM
ejpam-5455	295	44	f	f	X
ejpam-5455	295	45	(	(	PUNCT
ejpam-5455	295	46	σ)dσ	σ)dσ	ADJ
ejpam-5455	295	47	≤	≤	NOUN
ejpam-5455	295	48	lqz	lqz	NOUN
ejpam-5455	295	49	+	+	CCONJ
ejpam-5455	295	50	|q(0)|+	|q(0)|+	PROPN
ejpam-5455	295	51	zγ∥f∥l1	zγ∥f∥l1	NUM
ejpam-5455	295	52	γ(γ	γ(γ	PROPN
ejpam-5455	295	53	+	+	CCONJ
ejpam-5455	295	54	1	1	NUM
ejpam-5455	295	55	)	)	PUNCT
ejpam-5455	295	56	;	;	PUNCT
ejpam-5455	295	57	m.	m.	NOUN
ejpam-5455	295	58	m.	m.	PROPN
ejpam-5455	295	59	arjunan	arjunan	PROPN
ejpam-5455	295	60	/	/	SYM
ejpam-5455	295	61	eur	eur	PROPN
ejpam-5455	295	62	.	.	PUNCT
ejpam-5455	296	1	j.	j.	PROPN
ejpam-5455	296	2	pure	pure	PROPN
ejpam-5455	296	3	appl	appl	PROPN
ejpam-5455	296	4	.	.	PROPN
ejpam-5455	296	5	math	math	PROPN
ejpam-5455	296	6	,	,	PUNCT
ejpam-5455	296	7	17	17	NUM
ejpam-5455	296	8	(	(	PUNCT
ejpam-5455	296	9	4	4	NUM
ejpam-5455	296	10	)	)	PUNCT
ejpam-5455	296	11	(	(	PUNCT
ejpam-5455	296	12	2024	2024	NUM
ejpam-5455	296	13	)	)	PUNCT
ejpam-5455	296	14	,	,	PUNCT
ejpam-5455	296	15	4071	4071	NUM
ejpam-5455	296	16	-	-	SYM
ejpam-5455	296	17	4092	4092	NUM
ejpam-5455	296	18	4083	4083	NUM
ejpam-5455	296	19	max	max	PROPN
ejpam-5455	296	20	7∈ω	7∈ω	NOUN
ejpam-5455	296	21	|bw	|bw	ADP
ejpam-5455	296	22	−bw|	−bw|	PROPN
ejpam-5455	296	23	≤	≤	PROPN
ejpam-5455	296	24	(	(	PUNCT
ejpam-5455	296	25	q	q	NOUN
ejpam-5455	296	26	−	−	PROPN
ejpam-5455	297	1	1)mq−2zβ	1)mq−2zβ	NUM
ejpam-5455	297	2	b(ρ)γ(β	b(ρ)γ(β	NOUN
ejpam-5455	297	3	+	+	NOUN
ejpam-5455	297	4	1	1	X
ejpam-5455	297	5	)	)	PUNCT
ejpam-5455	297	6	{	{	PUNCT
ejpam-5455	297	7	1−	1−	NUM
ejpam-5455	297	8	ρ+	ρ+	NOUN
ejpam-5455	297	9	zρ	zρ	X
ejpam-5455	297	10	γ(ρ	γ(ρ	PROPN
ejpam-5455	297	11	)	)	PUNCT
ejpam-5455	297	12	}	}	PUNCT
ejpam-5455	298	1	lg∥w	lg∥w	VERB
ejpam-5455	298	2	−	−	NOUN
ejpam-5455	298	3	w∥	w∥	NOUN
ejpam-5455	298	4	;	;	PUNCT
ejpam-5455	298	5	since	since	SCONJ
ejpam-5455	298	6	1−	1−	NUM
ejpam-5455	298	7	ρ	ρ	PROPN
ejpam-5455	298	8	b(ρ	b(ρ	PROPN
ejpam-5455	298	9	)	)	PUNCT
ejpam-5455	298	10	{	{	PUNCT
ejpam-5455	298	11	max	max	PROPN
ejpam-5455	298	12	7∈ω	7∈ω	PROPN
ejpam-5455	298	13	∣∣∣∣∣ψq	∣∣∣∣∣ψq	NOUN
ejpam-5455	298	14	(	(	PUNCT
ejpam-5455	298	15	1	1	NUM
ejpam-5455	298	16	γ(β	γ(β	PROPN
ejpam-5455	298	17	)	)	PUNCT
ejpam-5455	298	18	∫	∫	PROPN
ejpam-5455	298	19	7	7	NUM
ejpam-5455	298	20	0	0	NUM
ejpam-5455	298	21	(	(	PUNCT
ejpam-5455	298	22	7	7	NUM
ejpam-5455	298	23	−	−	NOUN
ejpam-5455	298	24	σ)β−1g(σ	σ)β−1g(σ	NOUN
ejpam-5455	298	25	,	,	PUNCT
ejpam-5455	298	26	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	298	27	)	)	PUNCT
ejpam-5455	298	28	−ψq	−ψq	NOUN
ejpam-5455	298	29	(	(	PUNCT
ejpam-5455	298	30	1	1	NUM
ejpam-5455	298	31	γ(β	γ(β	PROPN
ejpam-5455	298	32	)	)	PUNCT
ejpam-5455	298	33	∫	∫	PROPN
ejpam-5455	298	34	7	7	NUM
ejpam-5455	298	35	0	0	NUM
ejpam-5455	298	36	(	(	PUNCT
ejpam-5455	298	37	7	7	NUM
ejpam-5455	298	38	−	−	NOUN
ejpam-5455	298	39	σ)β−1g(σ	σ)β−1g(σ	ADP
ejpam-5455	298	40	,	,	PUNCT
ejpam-5455	298	41	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	298	42	)	)	PUNCT
ejpam-5455	298	43	∣∣∣∣∣	∣∣∣∣∣	CCONJ
ejpam-5455	298	44	}	}	PUNCT
ejpam-5455	298	45	≤	≤	NUM
ejpam-5455	298	46	1−	1−	NUM
ejpam-5455	298	47	ρ	ρ	NUM
ejpam-5455	298	48	b(ρ	b(ρ	PROPN
ejpam-5455	298	49	)	)	PUNCT
ejpam-5455	298	50	(	(	PUNCT
ejpam-5455	298	51	q	q	NOUN
ejpam-5455	298	52	−	−	PROPN
ejpam-5455	298	53	1)mq−2	1)mq−2	NUM
ejpam-5455	298	54	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5455	298	55	1	1	NUM
ejpam-5455	298	56	γ(β	γ(β	PROPN
ejpam-5455	298	57	)	)	PUNCT
ejpam-5455	298	58	∫	∫	PROPN
ejpam-5455	298	59	7	7	NUM
ejpam-5455	298	60	0	0	NUM
ejpam-5455	298	61	(	(	PUNCT
ejpam-5455	298	62	7	7	NUM
ejpam-5455	298	63	−	−	NOUN
ejpam-5455	298	64	σ)β−1g(σ	σ)β−1g(σ	ADP
ejpam-5455	298	65	,	,	PUNCT
ejpam-5455	298	66	w(σ))dσ	w(σ))dσ	ADV
ejpam-5455	298	67	−	−	PROPN
ejpam-5455	298	68	1	1	NUM
ejpam-5455	298	69	γ(β	γ(β	PROPN
ejpam-5455	298	70	)	)	PUNCT
ejpam-5455	298	71	∫	∫	PROPN
ejpam-5455	298	72	7	7	NUM
ejpam-5455	298	73	0	0	NUM
ejpam-5455	298	74	(	(	PUNCT
ejpam-5455	298	75	7	7	NUM
ejpam-5455	298	76	−	−	NOUN
ejpam-5455	298	77	σ)β−1g(σ	σ)β−1g(σ	ADP
ejpam-5455	298	78	,	,	PUNCT
ejpam-5455	298	79	w(σ))dσ	w(σ))dσ	ADJ
ejpam-5455	298	80	∣∣∣∣∣	∣∣∣∣∣	ADJ
ejpam-5455	298	81	≤	≤	NOUN
ejpam-5455	298	82	1−	1−	NUM
ejpam-5455	298	83	ρ	ρ	NUM
ejpam-5455	298	84	b(ρ	b(ρ	PROPN
ejpam-5455	298	85	)	)	PUNCT
ejpam-5455	298	86	(	(	PUNCT
ejpam-5455	298	87	q	q	NOUN
ejpam-5455	298	88	−	−	PROPN
ejpam-5455	298	89	1)mq−2	1)mq−2	NUM
ejpam-5455	298	90	1	1	NUM
ejpam-5455	298	91	γ(β	γ(β	PROPN
ejpam-5455	298	92	)	)	PUNCT
ejpam-5455	298	93	∫	∫	PROPN
ejpam-5455	298	94	7	7	NUM
ejpam-5455	298	95	0	0	NUM
ejpam-5455	298	96	(	(	PUNCT
ejpam-5455	298	97	7	7	NUM
ejpam-5455	298	98	−	−	NOUN
ejpam-5455	298	99	σ)β−1|g(σ	σ)β−1|g(σ	NOUN
ejpam-5455	298	100	,	,	PUNCT
ejpam-5455	298	101	w(σ))−	w(σ))−	PRON
ejpam-5455	298	102	g(σ	g(σ	NOUN
ejpam-5455	298	103	,	,	PUNCT
ejpam-5455	298	104	w(σ))|dσ	w(σ))|dσ	VERB
ejpam-5455	298	105	≤	≤	NOUN
ejpam-5455	298	106	1−	1−	NUM
ejpam-5455	298	107	ρ	ρ	NUM
ejpam-5455	298	108	b(ρ	b(ρ	PROPN
ejpam-5455	298	109	)	)	PUNCT
ejpam-5455	298	110	(	(	PUNCT
ejpam-5455	298	111	q	q	NOUN
ejpam-5455	298	112	−	−	PROPN
ejpam-5455	298	113	1)mq−2zβ	1)mq−2zβ	NUM
ejpam-5455	298	114	γ(β	γ(β	PROPN
ejpam-5455	298	115	+	+	CCONJ
ejpam-5455	298	116	1	1	X
ejpam-5455	298	117	)	)	PUNCT
ejpam-5455	298	118	lg∥w	lg∥w	VERB
ejpam-5455	298	119	−	−	NOUN
ejpam-5455	298	120	w∥	w∥	NOUN
ejpam-5455	298	121	,	,	PUNCT
ejpam-5455	298	122	and	and	CCONJ
ejpam-5455	298	123	max	max	PROPN
ejpam-5455	298	124	7∈ω	7∈ω	PROPN
ejpam-5455	299	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5455	299	2	ρ	ρ	PROPN
ejpam-5455	299	3	b(ρ)γ(ρ	b(ρ)γ(ρ	PROPN
ejpam-5455	299	4	)	)	PUNCT
ejpam-5455	299	5	∫	∫	PROPN
ejpam-5455	299	6	7	7	NUM
ejpam-5455	299	7	0	0	NUM
ejpam-5455	299	8	(	(	PUNCT
ejpam-5455	299	9	7	7	NUM
ejpam-5455	299	10	−	−	NOUN
ejpam-5455	299	11	σ)ρ−1	σ)ρ−1	NOUN
ejpam-5455	299	12	(	(	PUNCT
ejpam-5455	299	13	ψq	ψq	X
ejpam-5455	299	14	(	(	PUNCT
ejpam-5455	299	15	1	1	NUM
ejpam-5455	299	16	γ(β	γ(β	PROPN
ejpam-5455	299	17	)	)	PUNCT
ejpam-5455	300	1	∫	∫	PROPN
ejpam-5455	301	1	σ	σ	PROPN
ejpam-5455	301	2	0	0	NUM
ejpam-5455	301	3	(	(	PUNCT
ejpam-5455	301	4	σ	σ	NOUN
ejpam-5455	301	5	−	−	PROPN
ejpam-5455	301	6	τ)β−1g(τ	τ)β−1g(τ	PUNCT
ejpam-5455	301	7	,	,	PUNCT
ejpam-5455	301	8	w(τ))dτ	w(τ))dτ	PROPN
ejpam-5455	301	9	)	)	PUNCT
ejpam-5455	301	10	)	)	PUNCT
ejpam-5455	301	11	dσ	dσ	VERB
ejpam-5455	301	12	−	−	PROPN
ejpam-5455	301	13	ρ	ρ	PROPN
ejpam-5455	301	14	b(ρ)γ(ρ	b(ρ)γ(ρ	PROPN
ejpam-5455	301	15	)	)	PUNCT
ejpam-5455	301	16	∫	∫	PROPN
ejpam-5455	301	17	7	7	NUM
ejpam-5455	301	18	0	0	NUM
ejpam-5455	301	19	(	(	PUNCT
ejpam-5455	301	20	7	7	NUM
ejpam-5455	301	21	−	−	NOUN
ejpam-5455	301	22	σ)ρ−1	σ)ρ−1	NOUN
ejpam-5455	301	23	(	(	PUNCT
ejpam-5455	301	24	ψq	ψq	X
ejpam-5455	301	25	(	(	PUNCT
ejpam-5455	301	26	1	1	NUM
ejpam-5455	301	27	γ(β	γ(β	PROPN
ejpam-5455	301	28	)	)	PUNCT
ejpam-5455	301	29	∫	∫	PROPN
ejpam-5455	302	1	σ	σ	PROPN
ejpam-5455	302	2	0	0	NUM
ejpam-5455	302	3	(	(	PUNCT
ejpam-5455	302	4	σ	σ	NOUN
ejpam-5455	302	5	−	−	PROPN
ejpam-5455	302	6	τ)β−1g(τ	τ)β−1g(τ	PUNCT
ejpam-5455	302	7	,	,	PUNCT
ejpam-5455	302	8	w(τ))dτ	w(τ))dτ	PROPN
ejpam-5455	302	9	)	)	PUNCT
ejpam-5455	302	10	)	)	PUNCT
ejpam-5455	302	11	dσ	dσ	VERB
ejpam-5455	302	12	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5455	302	13	≤	≤	NOUN
ejpam-5455	302	14	ρ	ρ	NUM
ejpam-5455	302	15	b(ρ)γ(ρ	b(ρ)γ(ρ	NOUN
ejpam-5455	302	16	)	)	PUNCT
ejpam-5455	302	17	∫	∫	PROPN
ejpam-5455	303	1	7	7	NUM
ejpam-5455	303	2	0	0	NUM
ejpam-5455	303	3	(	(	PUNCT
ejpam-5455	303	4	7	7	NUM
ejpam-5455	303	5	−	−	NOUN
ejpam-5455	303	6	σ)ρ−1max	σ)ρ−1max	NOUN
ejpam-5455	303	7	7∈ω	7∈ω	NOUN
ejpam-5455	303	8	∣∣∣∣∣ψq	∣∣∣∣∣ψq	NOUN
ejpam-5455	303	9	(	(	PUNCT
ejpam-5455	303	10	1	1	NUM
ejpam-5455	303	11	γ(β	γ(β	PROPN
ejpam-5455	303	12	)	)	PUNCT
ejpam-5455	303	13	∫	∫	PROPN
ejpam-5455	304	1	σ	σ	PROPN
ejpam-5455	304	2	0	0	NUM
ejpam-5455	304	3	(	(	PUNCT
ejpam-5455	304	4	σ	σ	NOUN
ejpam-5455	304	5	−	−	PROPN
ejpam-5455	304	6	τ)β−1g(τ	τ)β−1g(τ	PUNCT
ejpam-5455	304	7	,	,	PUNCT
ejpam-5455	304	8	w(τ))dτ	w(τ))dτ	PROPN
ejpam-5455	304	9	)	)	PUNCT
ejpam-5455	304	10	−ψq	−ψq	NOUN
ejpam-5455	304	11	(	(	PUNCT
ejpam-5455	304	12	1	1	NUM
ejpam-5455	304	13	γ(β	γ(β	PROPN
ejpam-5455	304	14	)	)	PUNCT
ejpam-5455	304	15	∫	∫	PROPN
ejpam-5455	305	1	σ	σ	PROPN
ejpam-5455	305	2	0	0	NUM
ejpam-5455	305	3	(	(	PUNCT
ejpam-5455	305	4	σ	σ	NOUN
ejpam-5455	305	5	−	−	PROPN
ejpam-5455	305	6	τ)β−1g(τ	τ)β−1g(τ	PUNCT
ejpam-5455	305	7	,	,	PUNCT
ejpam-5455	305	8	w(τ))dτ	w(τ))dτ	PROPN
ejpam-5455	305	9	)	)	PUNCT
ejpam-5455	305	10	∣∣∣∣∣dσ	∣∣∣∣∣dσ	NOUN
ejpam-5455	305	11	≤	≤	NUM
ejpam-5455	305	12	(	(	PUNCT
ejpam-5455	305	13	q	q	NOUN
ejpam-5455	305	14	−	−	PROPN
ejpam-5455	305	15	1)mq−2zβ+ρ	1)mq−2zβ+ρ	NUM
ejpam-5455	305	16	γ(β	γ(β	PROPN
ejpam-5455	305	17	+	+	PROPN
ejpam-5455	305	18	1)b(ρ)γ(ρ	1)b(ρ)γ(ρ	NUM
ejpam-5455	305	19	)	)	PUNCT
ejpam-5455	305	20	lg∥w	lg∥w	VERB
ejpam-5455	306	1	−	−	PROPN
ejpam-5455	306	2	w∥.	w∥.	INTJ
ejpam-5455	306	3	max	max	PROPN
ejpam-5455	306	4	7∈ω	7∈ω	X
ejpam-5455	306	5	|bw|	|bw|	PROPN
ejpam-5455	307	1	=	=	SYM
ejpam-5455	308	1	max	max	PROPN
ejpam-5455	309	1	7∈ω	7∈ω	PROPN
ejpam-5455	309	2	∣∣∣∣∣abiρ0+(θ	∣∣∣∣∣abiρ0+(θ	NOUN
ejpam-5455	309	3	)	)	PUNCT
ejpam-5455	310	1	+	+	CCONJ
ejpam-5455	310	2	1−	1−	NUM
ejpam-5455	310	3	ρ	ρ	NUM
ejpam-5455	310	4	b(ρ	b(ρ	PROPN
ejpam-5455	310	5	)	)	PUNCT
ejpam-5455	311	1	ψq	ψq	PROPN
ejpam-5455	311	2	(	(	PUNCT
ejpam-5455	311	3	1	1	NUM
ejpam-5455	311	4	γ(β	γ(β	PROPN
ejpam-5455	311	5	)	)	PUNCT
ejpam-5455	311	6	∫	∫	PROPN
ejpam-5455	311	7	7	7	NUM
ejpam-5455	311	8	0	0	NUM
ejpam-5455	311	9	(	(	PUNCT
ejpam-5455	311	10	7	7	NUM
ejpam-5455	311	11	−	−	NOUN
ejpam-5455	311	12	σ)β−1g(σ	σ)β−1g(σ	NOUN
ejpam-5455	311	13	,	,	PUNCT
ejpam-5455	311	14	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	311	15	)	)	PUNCT
ejpam-5455	312	1	+	+	CCONJ
ejpam-5455	312	2	ρ	ρ	PROPN
ejpam-5455	312	3	b(ρ)γ(ρ	b(ρ)γ(ρ	NOUN
ejpam-5455	312	4	)	)	PUNCT
ejpam-5455	312	5	∫	∫	PROPN
ejpam-5455	313	1	7	7	NUM
ejpam-5455	313	2	0	0	NUM
ejpam-5455	313	3	(	(	PUNCT
ejpam-5455	313	4	7	7	NUM
ejpam-5455	313	5	−	−	NOUN
ejpam-5455	313	6	σ)ρ−1	σ)ρ−1	NOUN
ejpam-5455	313	7	(	(	PUNCT
ejpam-5455	313	8	ψq	ψq	X
ejpam-5455	313	9	(	(	PUNCT
ejpam-5455	313	10	1	1	NUM
ejpam-5455	313	11	γ(β	γ(β	PROPN
ejpam-5455	313	12	)	)	PUNCT
ejpam-5455	313	13	∫	∫	PROPN
ejpam-5455	314	1	σ	σ	PROPN
ejpam-5455	314	2	0	0	NUM
ejpam-5455	314	3	(	(	PUNCT
ejpam-5455	314	4	σ	σ	NOUN
ejpam-5455	314	5	−	−	PROPN
ejpam-5455	314	6	τ)β−1g(τ	τ)β−1g(τ	PUNCT
ejpam-5455	314	7	,	,	PUNCT
ejpam-5455	314	8	w(τ))dτ	w(τ))dτ	PROPN
ejpam-5455	314	9	)	)	PUNCT
ejpam-5455	314	10	)	)	PUNCT
ejpam-5455	314	11	dσ	dσ	VERB
ejpam-5455	314	12	∣∣∣∣∣.	∣∣∣∣∣.	PROPN
ejpam-5455	314	13	since	since	SCONJ
ejpam-5455	314	14	from	from	ADP
ejpam-5455	314	15	(	(	PUNCT
ejpam-5455	314	16	7	7	NUM
ejpam-5455	314	17	)	)	PUNCT
ejpam-5455	314	18	,	,	PUNCT
ejpam-5455	314	19	we	we	PRON
ejpam-5455	314	20	have	have	VERB
ejpam-5455	314	21	∣∣∣∣ψq	∣∣∣∣ψq	ADJ
ejpam-5455	314	22	(	(	PUNCT
ejpam-5455	314	23	1	1	NUM
ejpam-5455	314	24	γ(β	γ(β	PROPN
ejpam-5455	314	25	)	)	PUNCT
ejpam-5455	314	26	∫	∫	PROPN
ejpam-5455	314	27	7	7	NUM
ejpam-5455	314	28	0	0	NUM
ejpam-5455	314	29	(	(	PUNCT
ejpam-5455	314	30	7	7	NUM
ejpam-5455	314	31	−	−	NOUN
ejpam-5455	314	32	σ)β−1g(σ	σ)β−1g(σ	ADP
ejpam-5455	314	33	,	,	PUNCT
ejpam-5455	314	34	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	314	35	)	)	PUNCT
ejpam-5455	314	36	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5455	314	37	m.	m.	NOUN
ejpam-5455	314	38	m.	m.	NOUN
ejpam-5455	314	39	arjunan	arjunan	PROPN
ejpam-5455	314	40	/	/	SYM
ejpam-5455	314	41	eur	eur	PROPN
ejpam-5455	314	42	.	.	PUNCT
ejpam-5455	315	1	j.	j.	PROPN
ejpam-5455	315	2	pure	pure	PROPN
ejpam-5455	315	3	appl	appl	PROPN
ejpam-5455	315	4	.	.	PROPN
ejpam-5455	315	5	math	math	PROPN
ejpam-5455	315	6	,	,	PUNCT
ejpam-5455	315	7	17	17	NUM
ejpam-5455	315	8	(	(	PUNCT
ejpam-5455	315	9	4	4	NUM
ejpam-5455	315	10	)	)	PUNCT
ejpam-5455	315	11	(	(	PUNCT
ejpam-5455	315	12	2024	2024	NUM
ejpam-5455	315	13	)	)	PUNCT
ejpam-5455	315	14	,	,	PUNCT
ejpam-5455	315	15	4071	4071	NUM
ejpam-5455	315	16	-	-	SYM
ejpam-5455	315	17	4092	4092	NUM
ejpam-5455	315	18	4084	4084	NUM
ejpam-5455	315	19	≤	≤	NOUN
ejpam-5455	315	20	ψq	ψq	X
ejpam-5455	315	21	(	(	PUNCT
ejpam-5455	315	22	1	1	NUM
ejpam-5455	315	23	γ(β	γ(β	PROPN
ejpam-5455	315	24	)	)	PUNCT
ejpam-5455	315	25	∫	∫	PROPN
ejpam-5455	316	1	7	7	NUM
ejpam-5455	316	2	0	0	NUM
ejpam-5455	316	3	(	(	PUNCT
ejpam-5455	316	4	7	7	NUM
ejpam-5455	316	5	−	−	NOUN
ejpam-5455	316	6	σ)β−1g(s)dσ	σ)β−1g(s)dσ	NOUN
ejpam-5455	316	7	)	)	PUNCT
ejpam-5455	316	8	≤	≤	NUM
ejpam-5455	316	9	ψq	ψq	PART
ejpam-5455	316	10	(	(	PUNCT
ejpam-5455	316	11	zβ∥g∥l1	zβ∥g∥l1	X
ejpam-5455	316	12	γ(β	γ(β	PROPN
ejpam-5455	316	13	+	+	CCONJ
ejpam-5455	316	14	1	1	NUM
ejpam-5455	316	15	)	)	PUNCT
ejpam-5455	316	16	)	)	PUNCT
ejpam-5455	317	1	∣∣	∣∣	X
ejpam-5455	317	2	∵	∵	NOUN
ejpam-5455	317	3	ψq(ū	ψq(ū	PROPN
ejpam-5455	317	4	)	)	PUNCT
ejpam-5455	318	1	=	=	SYM
ejpam-5455	318	2	ūq−1	ūq−1	X
ejpam-5455	318	3	=	=	SYM
ejpam-5455	318	4	(	(	PUNCT
ejpam-5455	318	5	zβ∥g∥l1	zβ∥g∥l1	X
ejpam-5455	318	6	γ(β	γ(β	PROPN
ejpam-5455	318	7	+	+	CCONJ
ejpam-5455	318	8	1	1	NUM
ejpam-5455	318	9	)	)	PUNCT
ejpam-5455	318	10	)	)	PUNCT
ejpam-5455	319	1	q−1	q−1	PROPN
ejpam-5455	319	2	and	and	CCONJ
ejpam-5455	319	3	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5455	319	4	ρ	ρ	PROPN
ejpam-5455	319	5	b(ρ)γ(ρ	b(ρ)γ(ρ	PROPN
ejpam-5455	319	6	)	)	PUNCT
ejpam-5455	319	7	∫	∫	PROPN
ejpam-5455	320	1	7	7	NUM
ejpam-5455	320	2	0	0	NUM
ejpam-5455	320	3	(	(	PUNCT
ejpam-5455	320	4	7	7	NUM
ejpam-5455	320	5	−	−	NOUN
ejpam-5455	320	6	σ)ρ−1	σ)ρ−1	NOUN
ejpam-5455	320	7	(	(	PUNCT
ejpam-5455	320	8	ψq	ψq	X
ejpam-5455	320	9	(	(	PUNCT
ejpam-5455	320	10	1	1	NUM
ejpam-5455	320	11	γ(β	γ(β	PROPN
ejpam-5455	320	12	)	)	PUNCT
ejpam-5455	320	13	∫	∫	PROPN
ejpam-5455	321	1	σ	σ	PROPN
ejpam-5455	321	2	0	0	NUM
ejpam-5455	321	3	(	(	PUNCT
ejpam-5455	321	4	σ	σ	NOUN
ejpam-5455	321	5	−	−	PROPN
ejpam-5455	321	6	τ)β−1g(τ	τ)β−1g(τ	PUNCT
ejpam-5455	321	7	,	,	PUNCT
ejpam-5455	321	8	w(τ))dτ	w(τ))dτ	PROPN
ejpam-5455	321	9	)	)	PUNCT
ejpam-5455	321	10	)	)	PUNCT
ejpam-5455	321	11	dσ	dσ	VERB
ejpam-5455	321	12	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5455	321	13	≤	≤	NOUN
ejpam-5455	321	14	(	(	PUNCT
ejpam-5455	321	15	zβ∥g∥l1	zβ∥g∥l1	X
ejpam-5455	321	16	γ(β	γ(β	PROPN
ejpam-5455	321	17	+	+	CCONJ
ejpam-5455	321	18	1	1	NUM
ejpam-5455	321	19	)	)	PUNCT
ejpam-5455	321	20	)	)	PUNCT
ejpam-5455	322	1	q−1	q−1	PROPN
ejpam-5455	322	2	ρ	ρ	NUM
ejpam-5455	322	3	b(ρ)γ(ρ	b(ρ)γ(ρ	PROPN
ejpam-5455	322	4	)	)	PUNCT
ejpam-5455	322	5	∫	∫	PROPN
ejpam-5455	322	6	7	7	NUM
ejpam-5455	322	7	0	0	NUM
ejpam-5455	322	8	(	(	PUNCT
ejpam-5455	322	9	7	7	NUM
ejpam-5455	322	10	−	−	PROPN
ejpam-5455	322	11	σ)ρ−1dσ	σ)ρ−1dσ	ADJ
ejpam-5455	322	12	≤	≤	NOUN
ejpam-5455	322	13	(	(	PUNCT
ejpam-5455	322	14	zβ∥g∥l1	zβ∥g∥l1	X
ejpam-5455	322	15	γ(β	γ(β	PROPN
ejpam-5455	322	16	+	+	CCONJ
ejpam-5455	322	17	1	1	NUM
ejpam-5455	322	18	)	)	PUNCT
ejpam-5455	322	19	)	)	PUNCT
ejpam-5455	323	1	q−1	q−1	PROPN
ejpam-5455	323	2	·	·	PUNCT
ejpam-5455	323	3	zρ	zρ	PROPN
ejpam-5455	323	4	b(ρ)γ(ρ	b(ρ)γ(ρ	PROPN
ejpam-5455	323	5	)	)	PUNCT
ejpam-5455	323	6	.	.	PUNCT
ejpam-5455	324	1	thus	thus	ADV
ejpam-5455	324	2	,	,	PUNCT
ejpam-5455	324	3	we	we	PRON
ejpam-5455	324	4	have	have	VERB
ejpam-5455	324	5	max	max	PROPN
ejpam-5455	324	6	7∈ω	7∈ω	PROPN
ejpam-5455	324	7	|bw|	|bw|	PROPN
ejpam-5455	324	8	≤	≤	NUM
ejpam-5455	324	9	abiρ0	abiρ0	NOUN
ejpam-5455	325	1	+	+	X
ejpam-5455	325	2	|θ|+	|θ|+	ADV
ejpam-5455	325	3	1	1	NUM
ejpam-5455	325	4	b(ρ	b(ρ	NOUN
ejpam-5455	325	5	)	)	PUNCT
ejpam-5455	325	6	(	(	PUNCT
ejpam-5455	325	7	zβ∥g∥l1	zβ∥g∥l1	X
ejpam-5455	325	8	γ(β	γ(β	PROPN
ejpam-5455	325	9	+	+	CCONJ
ejpam-5455	325	10	1	1	NUM
ejpam-5455	325	11	)	)	PUNCT
ejpam-5455	325	12	)	)	PUNCT
ejpam-5455	326	1	q−1	q−1	PROPN
ejpam-5455	326	2	{	{	PUNCT
ejpam-5455	326	3	1−	1−	NUM
ejpam-5455	326	4	ρ+	ρ+	NUM
ejpam-5455	326	5	zρ	zρ	X
ejpam-5455	326	6	γ(ρ	γ(ρ	PROPN
ejpam-5455	326	7	)	)	PUNCT
ejpam-5455	326	8	}	}	PUNCT
ejpam-5455	326	9	.	.	PUNCT
ejpam-5455	327	1	finally	finally	ADV
ejpam-5455	327	2	max	max	PROPN
ejpam-5455	327	3	7∈ω	7∈ω	PROPN
ejpam-5455	327	4	|aw	|aw	X
ejpam-5455	327	5	−aw|	−aw|	NOUN
ejpam-5455	327	6	=	=	SYM
ejpam-5455	327	7	max	max	PROPN
ejpam-5455	327	8	7∈ω	7∈ω	NUM
ejpam-5455	327	9	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5455	327	10	(	(	PUNCT
ejpam-5455	327	11	q(7	q(7	PROPN
ejpam-5455	327	12	)	)	PUNCT
ejpam-5455	327	13	+	+	CCONJ
ejpam-5455	327	14	1	1	NUM
ejpam-5455	327	15	γ(γ	γ(γ	NOUN
ejpam-5455	327	16	)	)	PUNCT
ejpam-5455	327	17	∫	∫	PROPN
ejpam-5455	327	18	7	7	NUM
ejpam-5455	327	19	0	0	NUM
ejpam-5455	327	20	(	(	PUNCT
ejpam-5455	327	21	7	7	NUM
ejpam-5455	327	22	−	−	NOUN
ejpam-5455	327	23	σ)γ−1f(σ	σ)γ−1f(σ	NOUN
ejpam-5455	327	24	,	,	PUNCT
ejpam-5455	327	25	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	327	26	)	)	PUNCT
ejpam-5455	327	27	−	−	PROPN
ejpam-5455	327	28	(	(	PUNCT
ejpam-5455	327	29	q(7	q(7	PROPN
ejpam-5455	327	30	)	)	PUNCT
ejpam-5455	327	31	+	+	CCONJ
ejpam-5455	327	32	1	1	NUM
ejpam-5455	327	33	γ(γ	γ(γ	NOUN
ejpam-5455	327	34	)	)	PUNCT
ejpam-5455	327	35	∫	∫	PROPN
ejpam-5455	327	36	7	7	NUM
ejpam-5455	327	37	0	0	NUM
ejpam-5455	327	38	(	(	PUNCT
ejpam-5455	327	39	7	7	NUM
ejpam-5455	327	40	−	−	NOUN
ejpam-5455	327	41	σ)γ−1f(σ	σ)γ−1f(σ	NOUN
ejpam-5455	327	42	,	,	PUNCT
ejpam-5455	327	43	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	327	44	)	)	PUNCT
ejpam-5455	327	45	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5455	328	1	≤	≤	NOUN
ejpam-5455	328	2	1	1	NUM
ejpam-5455	328	3	γ(γ	γ(γ	NOUN
ejpam-5455	328	4	)	)	PUNCT
ejpam-5455	328	5	∫	∫	PROPN
ejpam-5455	328	6	7	7	NUM
ejpam-5455	328	7	0	0	NUM
ejpam-5455	328	8	(	(	PUNCT
ejpam-5455	328	9	7	7	NUM
ejpam-5455	328	10	−	−	NOUN
ejpam-5455	328	11	σ)γ−1max	σ)γ−1max	NOUN
ejpam-5455	328	12	7∈ω	7∈ω	NOUN
ejpam-5455	328	13	|f(σ	|f(σ	PROPN
ejpam-5455	328	14	,	,	PUNCT
ejpam-5455	328	15	w(σ))−	w(σ))−	NOUN
ejpam-5455	328	16	f(s	f(	NOUN
ejpam-5455	328	17	,	,	PUNCT
ejpam-5455	328	18	w(s))|dσ	w(s))|dσ	PROPN
ejpam-5455	328	19	≤	≤	NOUN
ejpam-5455	328	20	lfz	lfz	VERB
ejpam-5455	328	21	γ	γ	NOUN
ejpam-5455	328	22	γ(γ	γ(γ	PROPN
ejpam-5455	329	1	+	+	CCONJ
ejpam-5455	329	2	1	1	X
ejpam-5455	329	3	)	)	PUNCT
ejpam-5455	329	4	∥w	∥w	PROPN
ejpam-5455	329	5	−	−	PROPN
ejpam-5455	329	6	w∥.	w∥.	PROPN
ejpam-5455	329	7	then	then	ADV
ejpam-5455	329	8	(	(	PUNCT
ejpam-5455	329	9	19	19	NUM
ejpam-5455	329	10	)	)	PUNCT
ejpam-5455	329	11	becomes	become	VERB
ejpam-5455	329	12	∥aw	∥aw	PROPN
ejpam-5455	329	13	−aw∥	−aw∥	AUX
ejpam-5455	329	14	≤	≤	X
ejpam-5455	330	1	[	[	X
ejpam-5455	330	2	(	(	PUNCT
ejpam-5455	330	3	lqz	lqz	NOUN
ejpam-5455	330	4	+	+	CCONJ
ejpam-5455	330	5	|q(0)|+	|q(0)|+	NUM
ejpam-5455	330	6	zγ∥f∥l1	zγ∥f∥l1	NUM
ejpam-5455	330	7	γ(γ	γ(γ	X
ejpam-5455	330	8	+	+	CCONJ
ejpam-5455	330	9	1	1	NUM
ejpam-5455	330	10	)	)	PUNCT
ejpam-5455	330	11	)	)	PUNCT
ejpam-5455	330	12	(	(	PUNCT
ejpam-5455	330	13	(	(	PUNCT
ejpam-5455	330	14	q	q	NOUN
ejpam-5455	330	15	−	−	PROPN
ejpam-5455	330	16	1)mq−2zβ	1)mq−2zβ	NUM
ejpam-5455	330	17	b(ρ)γ(β	b(ρ)γ(β	NOUN
ejpam-5455	330	18	+	+	NOUN
ejpam-5455	330	19	1	1	X
ejpam-5455	330	20	)	)	PUNCT
ejpam-5455	330	21	{	{	PUNCT
ejpam-5455	330	22	1−	1−	NUM
ejpam-5455	330	23	ρ+	ρ+	NOUN
ejpam-5455	330	24	zρ	zρ	X
ejpam-5455	330	25	γ(ρ	γ(ρ	PROPN
ejpam-5455	330	26	)	)	PUNCT
ejpam-5455	330	27	}	}	PUNCT
ejpam-5455	330	28	lg	lg	NOUN
ejpam-5455	330	29	)	)	PUNCT
ejpam-5455	330	30	+	+	CCONJ
ejpam-5455	330	31	(	(	PUNCT
ejpam-5455	330	32	abiρ0	abiρ0	NOUN
ejpam-5455	330	33	+	+	X
ejpam-5455	330	34	|θ|+	|θ|+	ADV
ejpam-5455	330	35	1	1	NUM
ejpam-5455	330	36	b(ρ	b(ρ	NOUN
ejpam-5455	330	37	)	)	PUNCT
ejpam-5455	330	38	(	(	PUNCT
ejpam-5455	330	39	zβ∥g∥l1	zβ∥g∥l1	X
ejpam-5455	330	40	γ(β	γ(β	PROPN
ejpam-5455	330	41	+	+	CCONJ
ejpam-5455	330	42	1	1	NUM
ejpam-5455	330	43	)	)	PUNCT
ejpam-5455	330	44	)	)	PUNCT
ejpam-5455	331	1	q−1	q−1	PROPN
ejpam-5455	331	2	{	{	PUNCT
ejpam-5455	331	3	1−	1−	NUM
ejpam-5455	331	4	ρ+	ρ+	NUM
ejpam-5455	331	5	zρ	zρ	X
ejpam-5455	331	6	γ(ρ	γ(ρ	PROPN
ejpam-5455	331	7	)	)	PUNCT
ejpam-5455	331	8	}	}	PUNCT
ejpam-5455	331	9	)	)	PUNCT
ejpam-5455	331	10	(	(	PUNCT
ejpam-5455	331	11	lfz	lfz	NOUN
ejpam-5455	331	12	γ	γ	X
ejpam-5455	331	13	γ(γ	γ(γ	PROPN
ejpam-5455	331	14	+	+	CCONJ
ejpam-5455	331	15	1	1	NUM
ejpam-5455	331	16	)	)	PUNCT
ejpam-5455	331	17	)	)	PUNCT
ejpam-5455	331	18	]	]	PUNCT
ejpam-5455	332	1	∥w	∥w	PROPN
ejpam-5455	332	2	−	−	PROPN
ejpam-5455	332	3	w∥.	w∥.	PROPN
ejpam-5455	332	4	consequently	consequently	ADV
ejpam-5455	332	5	(	(	PUNCT
ejpam-5455	332	6	18	18	NUM
ejpam-5455	332	7	)	)	PUNCT
ejpam-5455	332	8	becomes	become	VERB
ejpam-5455	332	9	∥φw	∥φw	PROPN
ejpam-5455	332	10	−	−	PROPN
ejpam-5455	332	11	φw∥	φw∥	ADJ
ejpam-5455	332	12	m.	m.	NOUN
ejpam-5455	332	13	m.	m.	NOUN
ejpam-5455	332	14	arjunan	arjunan	PROPN
ejpam-5455	332	15	/	/	SYM
ejpam-5455	332	16	eur	eur	PROPN
ejpam-5455	332	17	.	.	PUNCT
ejpam-5455	333	1	j.	j.	PROPN
ejpam-5455	333	2	pure	pure	PROPN
ejpam-5455	333	3	appl	appl	PROPN
ejpam-5455	333	4	.	.	PROPN
ejpam-5455	333	5	math	math	PROPN
ejpam-5455	333	6	,	,	PUNCT
ejpam-5455	333	7	17	17	NUM
ejpam-5455	333	8	(	(	PUNCT
ejpam-5455	333	9	4	4	NUM
ejpam-5455	333	10	)	)	PUNCT
ejpam-5455	333	11	(	(	PUNCT
ejpam-5455	333	12	2024	2024	NUM
ejpam-5455	333	13	)	)	PUNCT
ejpam-5455	333	14	,	,	PUNCT
ejpam-5455	333	15	4071	4071	NUM
ejpam-5455	333	16	-	-	SYM
ejpam-5455	333	17	4092	4092	NUM
ejpam-5455	333	18	4085	4085	NUM
ejpam-5455	333	19	≤	≤	NOUN
ejpam-5455	334	1	[	[	X
ejpam-5455	334	2	(	(	PUNCT
ejpam-5455	334	3	lqz	lqz	NOUN
ejpam-5455	334	4	+	+	CCONJ
ejpam-5455	334	5	|q(0)|+	|q(0)|+	NUM
ejpam-5455	334	6	zγ∥f∥l1	zγ∥f∥l1	NUM
ejpam-5455	334	7	γ(γ	γ(γ	X
ejpam-5455	334	8	+	+	CCONJ
ejpam-5455	334	9	1	1	NUM
ejpam-5455	334	10	)	)	PUNCT
ejpam-5455	334	11	)	)	PUNCT
ejpam-5455	335	1	(	(	PUNCT
ejpam-5455	335	2	(	(	PUNCT
ejpam-5455	335	3	q	q	NOUN
ejpam-5455	335	4	−	−	PROPN
ejpam-5455	335	5	1)mq−2zβ	1)mq−2zβ	NUM
ejpam-5455	335	6	b(ρ)γ(β	b(ρ)γ(β	NOUN
ejpam-5455	335	7	+	+	NOUN
ejpam-5455	335	8	1	1	X
ejpam-5455	335	9	)	)	PUNCT
ejpam-5455	335	10	{	{	PUNCT
ejpam-5455	335	11	1−	1−	NUM
ejpam-5455	335	12	ρ+	ρ+	NOUN
ejpam-5455	335	13	zρ	zρ	X
ejpam-5455	335	14	γ(ρ	γ(ρ	PROPN
ejpam-5455	335	15	)	)	PUNCT
ejpam-5455	335	16	}	}	PUNCT
ejpam-5455	335	17	lg	lg	NOUN
ejpam-5455	335	18	)	)	PUNCT
ejpam-5455	336	1	+	+	CCONJ
ejpam-5455	336	2	(	(	PUNCT
ejpam-5455	336	3	abiρ0	abiρ0	NOUN
ejpam-5455	336	4	+	+	X
ejpam-5455	336	5	|θ|+	|θ|+	ADV
ejpam-5455	336	6	1	1	NUM
ejpam-5455	336	7	b(ρ	b(ρ	NOUN
ejpam-5455	336	8	)	)	PUNCT
ejpam-5455	336	9	(	(	PUNCT
ejpam-5455	336	10	zβ∥g∥l1	zβ∥g∥l1	X
ejpam-5455	336	11	γ(β	γ(β	PROPN
ejpam-5455	336	12	+	+	CCONJ
ejpam-5455	336	13	1	1	NUM
ejpam-5455	336	14	)	)	PUNCT
ejpam-5455	336	15	)	)	PUNCT
ejpam-5455	337	1	q−1	q−1	PROPN
ejpam-5455	337	2	{	{	PUNCT
ejpam-5455	337	3	1−	1−	NUM
ejpam-5455	337	4	ρ+	ρ+	NUM
ejpam-5455	337	5	zρ	zρ	X
ejpam-5455	337	6	γ(ρ	γ(ρ	PROPN
ejpam-5455	337	7	)	)	PUNCT
ejpam-5455	337	8	}	}	PUNCT
ejpam-5455	337	9	)	)	PUNCT
ejpam-5455	337	10	(	(	PUNCT
ejpam-5455	337	11	lfz	lfz	NOUN
ejpam-5455	337	12	γ	γ	X
ejpam-5455	337	13	γ(γ	γ(γ	PROPN
ejpam-5455	337	14	+	+	CCONJ
ejpam-5455	337	15	1	1	NUM
ejpam-5455	337	16	)	)	PUNCT
ejpam-5455	337	17	)	)	PUNCT
ejpam-5455	338	1	+	+	CCONJ
ejpam-5455	339	1	lh	lh	X
ejpam-5455	339	2	]	]	PUNCT
ejpam-5455	340	1	∥w	∥w	PROPN
ejpam-5455	340	2	−	−	PROPN
ejpam-5455	340	3	w∥	w∥	NOUN
ejpam-5455	340	4	≤	≤	X
ejpam-5455	340	5	∆∥w	∆∥w	PROPN
ejpam-5455	340	6	−	−	PROPN
ejpam-5455	340	7	w∥.	w∥.	PROPN
ejpam-5455	340	8	from	from	ADP
ejpam-5455	340	9	equation	equation	NOUN
ejpam-5455	340	10	(	(	PUNCT
ejpam-5455	340	11	17	17	NUM
ejpam-5455	340	12	)	)	PUNCT
ejpam-5455	340	13	,	,	PUNCT
ejpam-5455	340	14	we	we	PRON
ejpam-5455	340	15	have	have	VERB
ejpam-5455	340	16	the	the	DET
ejpam-5455	340	17	condition	condition	NOUN
ejpam-5455	340	18	∆	∆	X
ejpam-5455	340	19	<	<	X
ejpam-5455	340	20	1	1	NUM
ejpam-5455	340	21	,	,	PUNCT
ejpam-5455	340	22	which	which	PRON
ejpam-5455	340	23	guarantees	guarantee	VERB
ejpam-5455	340	24	that	that	SCONJ
ejpam-5455	340	25	the	the	DET
ejpam-5455	340	26	operator	operator	NOUN
ejpam-5455	340	27	φ	φ	PROPN
ejpam-5455	340	28	is	be	AUX
ejpam-5455	340	29	a	a	DET
ejpam-5455	340	30	contraction	contraction	NOUN
ejpam-5455	340	31	.	.	PUNCT
ejpam-5455	341	1	by	by	ADP
ejpam-5455	341	2	applying	apply	VERB
ejpam-5455	341	3	banach	banach	NOUN
ejpam-5455	341	4	’s	’s	PART
ejpam-5455	341	5	fpt	fpt	NOUN
ejpam-5455	341	6	,	,	PUNCT
ejpam-5455	341	7	it	it	PRON
ejpam-5455	341	8	follows	follow	VERB
ejpam-5455	341	9	that	that	SCONJ
ejpam-5455	341	10	the	the	DET
ejpam-5455	341	11	hybrid	hybrid	ADJ
ejpam-5455	341	12	system	system	NOUN
ejpam-5455	341	13	ofmabchfides	ofmabchfide	NOUN
ejpam-5455	341	14	described	describe	VERB
ejpam-5455	341	15	in	in	ADP
ejpam-5455	341	16	(	(	PUNCT
ejpam-5455	341	17	1	1	X
ejpam-5455	341	18	)	)	PUNCT
ejpam-5455	341	19	possesses	possess	VERB
ejpam-5455	341	20	a	a	DET
ejpam-5455	341	21	unique	unique	ADJ
ejpam-5455	341	22	solution	solution	NOUN
ejpam-5455	341	23	,	,	PUNCT
ejpam-5455	341	24	which	which	PRON
ejpam-5455	341	25	corresponds	correspond	VERB
ejpam-5455	341	26	to	to	ADP
ejpam-5455	341	27	the	the	DET
ejpam-5455	341	28	fixed	fix	VERB
ejpam-5455	341	29	points	point	NOUN
ejpam-5455	341	30	of	of	ADP
ejpam-5455	341	31	the	the	DET
ejpam-5455	341	32	operator	operator	NOUN
ejpam-5455	341	33	φ	φ	NOUN
ejpam-5455	341	34	.	.	PUNCT
ejpam-5455	341	35	subsequently	subsequently	ADV
ejpam-5455	341	36	,	,	PUNCT
ejpam-5455	341	37	utilizing	utilize	VERB
ejpam-5455	341	38	krasnoselskii	krasnoselskii	PROPN
ejpam-5455	341	39	fpt	fpt	PROPN
ejpam-5455	341	40	[	[	X
ejpam-5455	341	41	14	14	NUM
ejpam-5455	341	42	,	,	PUNCT
ejpam-5455	341	43	16	16	NUM
ejpam-5455	341	44	]	]	PUNCT
ejpam-5455	341	45	,	,	PUNCT
ejpam-5455	341	46	we	we	PRON
ejpam-5455	341	47	establish	establish	VERB
ejpam-5455	341	48	the	the	DET
ejpam-5455	341	49	existence	existence	NOUN
ejpam-5455	341	50	of	of	ADP
ejpam-5455	341	51	solutions	solution	NOUN
ejpam-5455	341	52	for	for	ADP
ejpam-5455	341	53	the	the	DET
ejpam-5455	341	54	system	system	NOUN
ejpam-5455	341	55	(	(	PUNCT
ejpam-5455	341	56	1	1	NUM
ejpam-5455	341	57	)	)	PUNCT
ejpam-5455	341	58	.	.	PUNCT
ejpam-5455	342	1	theorem	theorem	NOUN
ejpam-5455	342	2	2	2	NUM
ejpam-5455	342	3	.	.	PUNCT
ejpam-5455	343	1	under	under	ADP
ejpam-5455	343	2	the	the	DET
ejpam-5455	343	3	conditions	condition	NOUN
ejpam-5455	343	4	set	set	VERB
ejpam-5455	343	5	by	by	ADP
ejpam-5455	343	6	hypotheses	hypothesis	NOUN
ejpam-5455	343	7	(	(	PUNCT
ejpam-5455	343	8	a1)−(a3	a1)−(a3	NOUN
ejpam-5455	343	9	)	)	PUNCT
ejpam-5455	343	10	,	,	PUNCT
ejpam-5455	343	11	the	the	DET
ejpam-5455	343	12	mabc	mabc	NOUN
ejpam-5455	343	13	-	-	PUNCT
ejpam-5455	343	14	hfides	hfide	NOUN
ejpam-5455	343	15	(	(	PUNCT
ejpam-5455	343	16	1	1	X
ejpam-5455	343	17	)	)	PUNCT
ejpam-5455	343	18	is	be	AUX
ejpam-5455	343	19	guaranteed	guarantee	VERB
ejpam-5455	343	20	to	to	PART
ejpam-5455	343	21	have	have	VERB
ejpam-5455	343	22	at	at	ADV
ejpam-5455	343	23	least	least	ADV
ejpam-5455	343	24	one	one	NUM
ejpam-5455	343	25	solution	solution	NOUN
ejpam-5455	343	26	if	if	SCONJ
ejpam-5455	343	27	lh	lh	PROPN
ejpam-5455	343	28	<	<	X
ejpam-5455	343	29	1	1	X
ejpam-5455	343	30	.	.	PUNCT
ejpam-5455	343	31	(	(	PUNCT
ejpam-5455	343	32	20	20	NUM
ejpam-5455	343	33	)	)	PUNCT
ejpam-5455	343	34	proof	proof	NOUN
ejpam-5455	343	35	.	.	PUNCT
ejpam-5455	344	1	fix	fix	VERB
ejpam-5455	344	2	b	b	NOUN
ejpam-5455	344	3	=	=	PUNCT
ejpam-5455	344	4	ac(ω	ac(ω	PROPN
ejpam-5455	344	5	,	,	PUNCT
ejpam-5455	344	6	r	r	NOUN
ejpam-5455	344	7	)	)	PUNCT
ejpam-5455	344	8	and	and	CCONJ
ejpam-5455	344	9	define	define	VERB
ejpam-5455	344	10	a	a	DET
ejpam-5455	344	11	subset	subset	NOUN
ejpam-5455	344	12	s	s	NOUN
ejpam-5455	344	13	of	of	ADP
ejpam-5455	344	14	b	b	NOUN
ejpam-5455	344	15	by	by	ADP
ejpam-5455	344	16	s	s	NOUN
ejpam-5455	344	17	=	=	PUNCT
ejpam-5455	344	18	{	{	PUNCT
ejpam-5455	344	19	w	w	PROPN
ejpam-5455	344	20	∈	∈	PROPN
ejpam-5455	344	21	b	b	PROPN
ejpam-5455	344	22	:	:	PUNCT
ejpam-5455	344	23	∥w∥	∥w∥	VERB
ejpam-5455	344	24	≤	≤	PROPN
ejpam-5455	344	25	λ	λ	SYM
ejpam-5455	344	26	}	}	PUNCT
ejpam-5455	344	27	,	,	PUNCT
ejpam-5455	344	28	where	where	SCONJ
ejpam-5455	344	29	λ	λ	X
ejpam-5455	344	30	=	=	PRON
ejpam-5455	344	31	(	(	PUNCT
ejpam-5455	344	32	lqz	lqz	PROPN
ejpam-5455	344	33	+	+	CCONJ
ejpam-5455	344	34	|q(0)|+	|q(0)|+	NUM
ejpam-5455	344	35	zγ∥f∥l1	zγ∥f∥l1	NUM
ejpam-5455	344	36	γ(γ	γ(γ	X
ejpam-5455	345	1	+	+	CCONJ
ejpam-5455	345	2	1	1	NUM
ejpam-5455	345	3	)	)	PUNCT
ejpam-5455	345	4	)	)	PUNCT
ejpam-5455	345	5	(	(	PUNCT
ejpam-5455	345	6	abiρ0	abiρ0	NOUN
ejpam-5455	345	7	+	+	X
ejpam-5455	345	8	|θ|+	|θ|+	ADV
ejpam-5455	345	9	1	1	NUM
ejpam-5455	345	10	b(ρ	b(ρ	NOUN
ejpam-5455	345	11	)	)	PUNCT
ejpam-5455	345	12	(	(	PUNCT
ejpam-5455	345	13	zβ∥g∥l1	zβ∥g∥l1	X
ejpam-5455	345	14	γ(β	γ(β	PROPN
ejpam-5455	345	15	+	+	CCONJ
ejpam-5455	345	16	1	1	NUM
ejpam-5455	345	17	)	)	PUNCT
ejpam-5455	345	18	)	)	PUNCT
ejpam-5455	346	1	q−1	q−1	PROPN
ejpam-5455	346	2	{	{	PUNCT
ejpam-5455	346	3	1−	1−	NUM
ejpam-5455	346	4	ρ+	ρ+	NUM
ejpam-5455	346	5	zρ	zρ	X
ejpam-5455	346	6	γ(ρ	γ(ρ	PROPN
ejpam-5455	346	7	)	)	PUNCT
ejpam-5455	346	8	}	}	PUNCT
ejpam-5455	346	9	)	)	PUNCT
ejpam-5455	347	1	+	+	CCONJ
ejpam-5455	347	2	lh∥w∥+h0	lh∥w∥+h0	NOUN
ejpam-5455	347	3	with	with	ADP
ejpam-5455	347	4	h0	h0	NOUN
ejpam-5455	347	5	=	=	SYM
ejpam-5455	347	6	max	max	PROPN
ejpam-5455	347	7	7∈ω	7∈ω	PROPN
ejpam-5455	347	8	|h(7	|h(7	NOUN
ejpam-5455	347	9	,	,	PUNCT
ejpam-5455	347	10	0)|	0)|	NOUN
ejpam-5455	347	11	.	.	PUNCT
ejpam-5455	348	1	it	it	PRON
ejpam-5455	348	2	is	be	AUX
ejpam-5455	348	3	evident	evident	ADJ
ejpam-5455	348	4	that	that	SCONJ
ejpam-5455	348	5	s	s	VERB
ejpam-5455	348	6	is	be	AUX
ejpam-5455	348	7	a	a	DET
ejpam-5455	348	8	closed	closed	ADJ
ejpam-5455	348	9	,	,	PUNCT
ejpam-5455	348	10	convex	convex	NOUN
ejpam-5455	348	11	,	,	PUNCT
ejpam-5455	348	12	and	and	CCONJ
ejpam-5455	348	13	bounded	bound	VERB
ejpam-5455	348	14	subset	subset	NOUN
ejpam-5455	348	15	of	of	ADP
ejpam-5455	348	16	the	the	DET
ejpam-5455	348	17	banach	banach	NOUN
ejpam-5455	348	18	space	space	NOUN
ejpam-5455	348	19	b.	b.	PROPN
ejpam-5455	349	1	we	we	PRON
ejpam-5455	349	2	will	will	AUX
ejpam-5455	349	3	now	now	ADV
ejpam-5455	349	4	examine	examine	VERB
ejpam-5455	349	5	two	two	NUM
ejpam-5455	349	6	operators	operator	NOUN
ejpam-5455	349	7	a	a	DET
ejpam-5455	349	8	and	and	CCONJ
ejpam-5455	349	9	b	b	NOUN
ejpam-5455	349	10	that	that	DET
ejpam-5455	349	11	map	map	NOUN
ejpam-5455	349	12	from	from	ADP
ejpam-5455	349	13	s	s	PRON
ejpam-5455	349	14	to	to	ADP
ejpam-5455	349	15	b	b	NUM
ejpam-5455	349	16	,	,	PUNCT
ejpam-5455	349	17	which	which	PRON
ejpam-5455	349	18	are	be	AUX
ejpam-5455	349	19	defined	define	VERB
ejpam-5455	349	20	as	as	SCONJ
ejpam-5455	349	21	specified	specify	VERB
ejpam-5455	349	22	in	in	ADP
ejpam-5455	349	23	equations	equation	NOUN
ejpam-5455	349	24	(	(	PUNCT
ejpam-5455	349	25	12	12	NUM
ejpam-5455	349	26	)	)	PUNCT
ejpam-5455	349	27	and	and	CCONJ
ejpam-5455	349	28	(	(	PUNCT
ejpam-5455	349	29	13	13	NUM
ejpam-5455	349	30	)	)	PUNCT
ejpam-5455	349	31	,	,	PUNCT
ejpam-5455	349	32	respectively	respectively	ADV
ejpam-5455	349	33	.	.	PUNCT
ejpam-5455	350	1	at	at	ADP
ejpam-5455	350	2	this	this	DET
ejpam-5455	350	3	point	point	NOUN
ejpam-5455	350	4	,	,	PUNCT
ejpam-5455	350	5	the	the	DET
ejpam-5455	350	6	expression	expression	NOUN
ejpam-5455	350	7	in	in	ADP
ejpam-5455	350	8	(	(	PUNCT
ejpam-5455	350	9	9	9	NUM
ejpam-5455	350	10	)	)	PUNCT
ejpam-5455	350	11	can	can	AUX
ejpam-5455	350	12	be	be	AUX
ejpam-5455	350	13	rewritten	rewrite	VERB
ejpam-5455	350	14	as	as	ADP
ejpam-5455	350	15	the	the	DET
ejpam-5455	350	16	operator	operator	NOUN
ejpam-5455	350	17	equation	equation	NOUN
ejpam-5455	350	18	w(7	w(7	PROPN
ejpam-5455	350	19	)	)	PUNCT
ejpam-5455	351	1	=	=	PUNCT
ejpam-5455	351	2	(	(	PUNCT
ejpam-5455	351	3	aw)(7	aw)(7	NOUN
ejpam-5455	351	4	)	)	PUNCT
ejpam-5455	351	5	+	+	CCONJ
ejpam-5455	351	6	(	(	PUNCT
ejpam-5455	351	7	bw)(7	bw)(7	NOUN
ejpam-5455	351	8	)	)	PUNCT
ejpam-5455	351	9	,	,	PUNCT
ejpam-5455	351	10	7	7	NUM
ejpam-5455	351	11	∈	∈	PROPN
ejpam-5455	351	12	ω	ω	NOUN
ejpam-5455	351	13	.	.	PUNCT
ejpam-5455	352	1	step	step	NOUN
ejpam-5455	352	2	1	1	NUM
ejpam-5455	352	3	:	:	PUNCT
ejpam-5455	352	4	let	let	VERB
ejpam-5455	352	5	w	w	NOUN
ejpam-5455	352	6	,	,	PUNCT
ejpam-5455	352	7	w	w	PROPN
ejpam-5455	352	8	∈	∈	PROPN
ejpam-5455	352	9	s.	s.	PROPN
ejpam-5455	352	10	then	then	ADV
ejpam-5455	352	11	from	from	ADP
ejpam-5455	352	12	(	(	PUNCT
ejpam-5455	352	13	13	13	NUM
ejpam-5455	352	14	)	)	PUNCT
ejpam-5455	352	15	and	and	CCONJ
ejpam-5455	352	16	(	(	PUNCT
ejpam-5455	352	17	a1	a1	NOUN
ejpam-5455	352	18	)	)	PUNCT
ejpam-5455	352	19	,	,	PUNCT
ejpam-5455	352	20	we	we	PRON
ejpam-5455	352	21	have	have	AUX
ejpam-5455	352	22	∥bw	∥bw	VERB
ejpam-5455	352	23	−bw∥	−bw∥	PROPN
ejpam-5455	352	24	=	=	SYM
ejpam-5455	352	25	max	max	PROPN
ejpam-5455	352	26	7∈ω	7∈ω	PROPN
ejpam-5455	352	27	|h(7	|h(7	NOUN
ejpam-5455	352	28	,	,	PUNCT
ejpam-5455	352	29	w(7))−	w(7))−	PROPN
ejpam-5455	352	30	h(7	h(7	PROPN
ejpam-5455	352	31	,	,	PUNCT
ejpam-5455	353	1	w(7))|	w(7))|	NOUN
ejpam-5455	353	2	≤	≤	PUNCT
ejpam-5455	354	1	lh∥w	lh∥w	PROPN
ejpam-5455	354	2	−	−	PROPN
ejpam-5455	354	3	w∥.	w∥.	PROPN
ejpam-5455	354	4	therefore	therefore	ADV
ejpam-5455	354	5	,	,	PUNCT
ejpam-5455	354	6	according	accord	VERB
ejpam-5455	354	7	to	to	ADP
ejpam-5455	354	8	(	(	PUNCT
ejpam-5455	354	9	20	20	NUM
ejpam-5455	354	10	)	)	PUNCT
ejpam-5455	354	11	,	,	PUNCT
ejpam-5455	354	12	the	the	DET
ejpam-5455	354	13	operator	operator	NOUN
ejpam-5455	354	14	b	b	NOUN
ejpam-5455	354	15	acts	act	VERB
ejpam-5455	354	16	as	as	ADP
ejpam-5455	354	17	a	a	DET
ejpam-5455	354	18	contraction	contraction	NOUN
ejpam-5455	354	19	on	on	ADP
ejpam-5455	354	20	s	s	PRON
ejpam-5455	354	21	with	with	ADP
ejpam-5455	354	22	a	a	DET
ejpam-5455	354	23	constant	constant	ADJ
ejpam-5455	354	24	lh	lh	NOUN
ejpam-5455	354	25	<	<	X
ejpam-5455	354	26	1	1	X
ejpam-5455	354	27	.	.	PUNCT
ejpam-5455	354	28	m.	m.	NOUN
ejpam-5455	354	29	m.	m.	PROPN
ejpam-5455	354	30	arjunan	arjunan	PROPN
ejpam-5455	354	31	/	/	SYM
ejpam-5455	354	32	eur	eur	PROPN
ejpam-5455	354	33	.	.	PUNCT
ejpam-5455	355	1	j.	j.	PROPN
ejpam-5455	355	2	pure	pure	PROPN
ejpam-5455	355	3	appl	appl	PROPN
ejpam-5455	355	4	.	.	PROPN
ejpam-5455	355	5	math	math	PROPN
ejpam-5455	355	6	,	,	PUNCT
ejpam-5455	355	7	17	17	NUM
ejpam-5455	355	8	(	(	PUNCT
ejpam-5455	355	9	4	4	NUM
ejpam-5455	355	10	)	)	PUNCT
ejpam-5455	355	11	(	(	PUNCT
ejpam-5455	355	12	2024	2024	NUM
ejpam-5455	355	13	)	)	PUNCT
ejpam-5455	355	14	,	,	PUNCT
ejpam-5455	355	15	4071	4071	NUM
ejpam-5455	355	16	-	-	SYM
ejpam-5455	355	17	4092	4092	NUM
ejpam-5455	355	18	4086	4086	NUM
ejpam-5455	355	19	step	step	NOUN
ejpam-5455	355	20	2	2	NUM
ejpam-5455	355	21	:	:	PUNCT
ejpam-5455	355	22	we	we	PRON
ejpam-5455	355	23	will	will	AUX
ejpam-5455	355	24	demonstrate	demonstrate	VERB
ejpam-5455	355	25	that	that	SCONJ
ejpam-5455	355	26	a	a	PRON
ejpam-5455	355	27	is	be	AUX
ejpam-5455	355	28	a	a	DET
ejpam-5455	355	29	compact	compact	ADJ
ejpam-5455	355	30	operator	operator	NOUN
ejpam-5455	355	31	mapping	mapping	NOUN
ejpam-5455	355	32	from	from	ADP
ejpam-5455	355	33	s	s	PRON
ejpam-5455	355	34	to	to	PART
ejpam-5455	355	35	b.	b.	PROPN
ejpam-5455	355	36	it	it	PRON
ejpam-5455	355	37	suffices	suffice	VERB
ejpam-5455	355	38	to	to	PART
ejpam-5455	355	39	show	show	VERB
ejpam-5455	355	40	that	that	SCONJ
ejpam-5455	355	41	a(s	a(	NOUN
ejpam-5455	355	42	)	)	PUNCT
ejpam-5455	355	43	forms	form	VERB
ejpam-5455	355	44	a	a	DET
ejpam-5455	355	45	uniformly	uniformly	ADV
ejpam-5455	355	46	bounded	bound	VERB
ejpam-5455	355	47	and	and	CCONJ
ejpam-5455	355	48	equi	equi	NOUN
ejpam-5455	355	49	-	-	PUNCT
ejpam-5455	355	50	continuous	continuous	ADJ
ejpam-5455	355	51	subset	subset	NOUN
ejpam-5455	355	52	within	within	ADP
ejpam-5455	355	53	b.	b.	PROPN
ejpam-5455	355	54	first	first	ADV
ejpam-5455	355	55	,	,	PUNCT
ejpam-5455	355	56	consider	consider	VERB
ejpam-5455	355	57	an	an	DET
ejpam-5455	355	58	arbitrary	arbitrary	ADJ
ejpam-5455	355	59	element	element	NOUN
ejpam-5455	355	60	w	w	PROPN
ejpam-5455	355	61	∈	∈	PROPN
ejpam-5455	355	62	s.	s.	PROPN
ejpam-5455	355	63	then	then	ADV
ejpam-5455	355	64	,	,	PUNCT
ejpam-5455	355	65	from	from	ADP
ejpam-5455	355	66	(	(	PUNCT
ejpam-5455	355	67	12	12	NUM
ejpam-5455	355	68	)	)	PUNCT
ejpam-5455	355	69	and	and	CCONJ
ejpam-5455	355	70	(	(	PUNCT
ejpam-5455	355	71	a2	a2	PROPN
ejpam-5455	355	72	)	)	PUNCT
ejpam-5455	355	73	,	,	PUNCT
ejpam-5455	355	74	we	we	PRON
ejpam-5455	355	75	have	have	VERB
ejpam-5455	355	76	∥aw∥	∥aw∥	NOUN
ejpam-5455	355	77	≤	≤	NUM
ejpam-5455	355	78	max	max	PROPN
ejpam-5455	355	79	7∈ω	7∈ω	PROPN
ejpam-5455	355	80	(	(	PUNCT
ejpam-5455	355	81	|q(7)|+	|q(7)|+	NUM
ejpam-5455	355	82	1	1	NUM
ejpam-5455	355	83	γ(γ	γ(γ	NOUN
ejpam-5455	355	84	)	)	PUNCT
ejpam-5455	355	85	∫	∫	PROPN
ejpam-5455	355	86	7	7	NUM
ejpam-5455	355	87	0	0	NUM
ejpam-5455	355	88	(	(	PUNCT
ejpam-5455	355	89	7	7	NUM
ejpam-5455	355	90	−	−	NOUN
ejpam-5455	355	91	σ)γ−1|f(σ	σ)γ−1|f(σ	NOUN
ejpam-5455	355	92	,	,	PUNCT
ejpam-5455	355	93	w(σ))|dσ	w(σ))|dσ	NOUN
ejpam-5455	355	94	)	)	PUNCT
ejpam-5455	355	95	(	(	PUNCT
ejpam-5455	355	96	×	×	NOUN
ejpam-5455	355	97	)	)	PUNCT
ejpam-5455	355	98	[	[	PUNCT
ejpam-5455	355	99	abiρ0	abiρ0	NOUN
ejpam-5455	355	100	+	+	SYM
ejpam-5455	355	101	|θ|+	|θ|+	ADV
ejpam-5455	355	102	1−	1−	NUM
ejpam-5455	355	103	ρ	ρ	NUM
ejpam-5455	355	104	b(ρ	b(ρ	PROPN
ejpam-5455	355	105	)	)	PUNCT
ejpam-5455	355	106	ψq	ψq	PROPN
ejpam-5455	355	107	(	(	PUNCT
ejpam-5455	355	108	1	1	NUM
ejpam-5455	355	109	γ(β	γ(β	PROPN
ejpam-5455	355	110	)	)	PUNCT
ejpam-5455	355	111	∫	∫	PROPN
ejpam-5455	355	112	7	7	NUM
ejpam-5455	355	113	0	0	NUM
ejpam-5455	355	114	(	(	PUNCT
ejpam-5455	355	115	7	7	NUM
ejpam-5455	355	116	−	−	NOUN
ejpam-5455	355	117	σ)β−1|g(σ	σ)β−1|g(σ	NOUN
ejpam-5455	355	118	,	,	PUNCT
ejpam-5455	355	119	w(σ))|dσ	w(σ))|dσ	ADJ
ejpam-5455	355	120	)	)	PUNCT
ejpam-5455	356	1	+	+	CCONJ
ejpam-5455	356	2	ρ	ρ	PROPN
ejpam-5455	356	3	b(ρ)γ(ρ	b(ρ)γ(ρ	NOUN
ejpam-5455	356	4	)	)	PUNCT
ejpam-5455	356	5	∫	∫	PROPN
ejpam-5455	357	1	7	7	NUM
ejpam-5455	357	2	0	0	NUM
ejpam-5455	357	3	(	(	PUNCT
ejpam-5455	357	4	7	7	NUM
ejpam-5455	357	5	−	−	NOUN
ejpam-5455	357	6	σ)ρ−1	σ)ρ−1	NOUN
ejpam-5455	357	7	(	(	PUNCT
ejpam-5455	357	8	ψq	ψq	X
ejpam-5455	357	9	(	(	PUNCT
ejpam-5455	357	10	1	1	NUM
ejpam-5455	357	11	γ(β	γ(β	PROPN
ejpam-5455	357	12	)	)	PUNCT
ejpam-5455	357	13	∫	∫	PROPN
ejpam-5455	358	1	σ	σ	PROPN
ejpam-5455	358	2	0	0	NUM
ejpam-5455	358	3	(	(	PUNCT
ejpam-5455	358	4	σ	σ	NOUN
ejpam-5455	358	5	−	−	PROPN
ejpam-5455	358	6	τ)β−1|g(τ	τ)β−1|g(τ	NOUN
ejpam-5455	358	7	,	,	PUNCT
ejpam-5455	358	8	w(τ))|dτ	w(τ))|dτ	NOUN
ejpam-5455	358	9	)	)	PUNCT
ejpam-5455	358	10	)	)	PUNCT
ejpam-5455	359	1	dσ	dσ	VERB
ejpam-5455	359	2	]	]	PUNCT
ejpam-5455	359	3	≤	≤	X
ejpam-5455	359	4	(	(	PUNCT
ejpam-5455	359	5	lqz	lqz	NOUN
ejpam-5455	359	6	+	+	CCONJ
ejpam-5455	359	7	|q(0)|+	|q(0)|+	NUM
ejpam-5455	359	8	zγ∥f∥l1	zγ∥f∥l1	NUM
ejpam-5455	359	9	γ(γ	γ(γ	X
ejpam-5455	360	1	+	+	CCONJ
ejpam-5455	360	2	1	1	NUM
ejpam-5455	360	3	)	)	PUNCT
ejpam-5455	360	4	)	)	PUNCT
ejpam-5455	360	5	(	(	PUNCT
ejpam-5455	360	6	abiρ0	abiρ0	NOUN
ejpam-5455	360	7	+	+	X
ejpam-5455	360	8	|θ|+	|θ|+	ADV
ejpam-5455	360	9	1	1	NUM
ejpam-5455	360	10	b(ρ	b(ρ	NOUN
ejpam-5455	360	11	)	)	PUNCT
ejpam-5455	360	12	(	(	PUNCT
ejpam-5455	360	13	zβ∥g∥l1	zβ∥g∥l1	X
ejpam-5455	360	14	γ(β	γ(β	PROPN
ejpam-5455	360	15	+	+	CCONJ
ejpam-5455	360	16	1	1	NUM
ejpam-5455	360	17	)	)	PUNCT
ejpam-5455	360	18	)	)	PUNCT
ejpam-5455	361	1	q−1	q−1	PROPN
ejpam-5455	361	2	{	{	PUNCT
ejpam-5455	361	3	1−	1−	NUM
ejpam-5455	361	4	ρ+	ρ+	NUM
ejpam-5455	361	5	zρ	zρ	X
ejpam-5455	361	6	γ(ρ	γ(ρ	PROPN
ejpam-5455	361	7	)	)	PUNCT
ejpam-5455	361	8	}	}	PUNCT
ejpam-5455	361	9	)	)	PUNCT
ejpam-5455	361	10	.	.	PUNCT
ejpam-5455	362	1	this	this	PRON
ejpam-5455	362	2	indicates	indicate	VERB
ejpam-5455	362	3	that	that	SCONJ
ejpam-5455	362	4	a(s	a(	NOUN
ejpam-5455	362	5	)	)	PUNCT
ejpam-5455	362	6	is	be	AUX
ejpam-5455	362	7	uniformly	uniformly	ADV
ejpam-5455	362	8	bounded	bound	VERB
ejpam-5455	362	9	within	within	ADP
ejpam-5455	362	10	b.	b.	PROPN
ejpam-5455	362	11	conversely	conversely	ADV
ejpam-5455	362	12	,	,	PUNCT
ejpam-5455	362	13	let	let	VERB
ejpam-5455	362	14	71	71	NUM
ejpam-5455	362	15	,	,	PUNCT
ejpam-5455	362	16	72	72	NUM
ejpam-5455	362	17	∈	∈	NOUN
ejpam-5455	362	18	ω	ω	NOUN
ejpam-5455	362	19	be	be	AUX
ejpam-5455	362	20	chosen	choose	VERB
ejpam-5455	362	21	arbitrarily	arbitrarily	ADV
ejpam-5455	362	22	such	such	ADJ
ejpam-5455	362	23	that	that	SCONJ
ejpam-5455	362	24	71	71	NUM
ejpam-5455	362	25	<	<	SYM
ejpam-5455	362	26	72	72	NUM
ejpam-5455	362	27	.	.	PUNCT
ejpam-5455	363	1	then	then	ADV
ejpam-5455	363	2	,	,	PUNCT
ejpam-5455	363	3	for	for	ADP
ejpam-5455	363	4	any	any	DET
ejpam-5455	363	5	w	w	PROPN
ejpam-5455	363	6	∈	∈	PROPN
ejpam-5455	363	7	s	s	PART
ejpam-5455	363	8	,	,	PUNCT
ejpam-5455	363	9	we	we	PRON
ejpam-5455	363	10	obtain	obtain	VERB
ejpam-5455	363	11	|(aw)(72)−	|(aw)(72)−	NOUN
ejpam-5455	363	12	(	(	PUNCT
ejpam-5455	363	13	aw)(71)|	aw)(71)|	PROPN
ejpam-5455	363	14	≤	≤	NOUN
ejpam-5455	363	15	(	(	PUNCT
ejpam-5455	363	16	|q(72)|+	|q(72)|+	NOUN
ejpam-5455	363	17	zγ∥f∥l1	zγ∥f∥l1	X
ejpam-5455	363	18	γ(γ	γ(γ	X
ejpam-5455	363	19	+	+	CCONJ
ejpam-5455	363	20	1	1	NUM
ejpam-5455	363	21	)	)	PUNCT
ejpam-5455	363	22	)	)	PUNCT
ejpam-5455	364	1	(	(	PUNCT
ejpam-5455	364	2	(	(	PUNCT
ejpam-5455	364	3	q	q	NOUN
ejpam-5455	364	4	−	−	PROPN
ejpam-5455	364	5	1)mq−2zβ	1)mq−2zβ	NUM
ejpam-5455	364	6	b(ρ)γ(β	b(ρ)γ(β	NOUN
ejpam-5455	364	7	+	+	NOUN
ejpam-5455	364	8	1	1	X
ejpam-5455	364	9	)	)	PUNCT
ejpam-5455	364	10	{	{	PUNCT
ejpam-5455	364	11	1−	1−	NUM
ejpam-5455	364	12	ρ+	ρ+	NOUN
ejpam-5455	364	13	zρ	zρ	X
ejpam-5455	364	14	γ(ρ	γ(ρ	PROPN
ejpam-5455	364	15	)	)	PUNCT
ejpam-5455	364	16	}	}	PUNCT
ejpam-5455	364	17	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-5455	364	18	72	72	NUM
ejpam-5455	364	19	71	71	NUM
ejpam-5455	364	20	g(σ)dσ	g(σ)dσ	NOUN
ejpam-5455	364	21	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5455	364	22	)	)	PUNCT
ejpam-5455	365	1	+	+	CCONJ
ejpam-5455	365	2	(	(	PUNCT
ejpam-5455	365	3	abiρ0	abiρ0	NOUN
ejpam-5455	365	4	+	+	X
ejpam-5455	365	5	|θ|+	|θ|+	ADV
ejpam-5455	365	6	1	1	NUM
ejpam-5455	365	7	b(ρ	b(ρ	NOUN
ejpam-5455	365	8	)	)	PUNCT
ejpam-5455	365	9	(	(	PUNCT
ejpam-5455	365	10	zβ∥g∥l1	zβ∥g∥l1	X
ejpam-5455	365	11	γ(β	γ(β	PROPN
ejpam-5455	365	12	+	+	CCONJ
ejpam-5455	365	13	1	1	NUM
ejpam-5455	365	14	)	)	PUNCT
ejpam-5455	365	15	)	)	PUNCT
ejpam-5455	366	1	q−1	q−1	PROPN
ejpam-5455	366	2	{	{	PUNCT
ejpam-5455	366	3	1−	1−	NUM
ejpam-5455	366	4	ρ+	ρ+	NUM
ejpam-5455	366	5	zρ	zρ	X
ejpam-5455	366	6	γ(ρ	γ(ρ	PROPN
ejpam-5455	366	7	)	)	PUNCT
ejpam-5455	366	8	}	}	PUNCT
ejpam-5455	366	9	)	)	PUNCT
ejpam-5455	366	10	(	(	PUNCT
ejpam-5455	366	11	lq|72	lq|72	ADV
ejpam-5455	366	12	−	−	X
ejpam-5455	367	1	71|	71|	NUM
ejpam-5455	367	2	+	+	PROPN
ejpam-5455	367	3	zγ	zγ	X
ejpam-5455	367	4	γ(γ	γ(γ	PROPN
ejpam-5455	367	5	+	+	CCONJ
ejpam-5455	367	6	1	1	X
ejpam-5455	367	7	)	)	PUNCT
ejpam-5455	367	8	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-5455	367	9	72	72	NUM
ejpam-5455	367	10	71	71	NUM
ejpam-5455	367	11	f	f	NOUN
ejpam-5455	367	12	(	(	PUNCT
ejpam-5455	367	13	σ)dσ	σ)dσ	PROPN
ejpam-5455	367	14	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5455	367	15	)	)	PUNCT
ejpam-5455	367	16	=	=	PRON
ejpam-5455	367	17	(	(	PUNCT
ejpam-5455	367	18	|q(72)|+	|q(72)|+	NOUN
ejpam-5455	367	19	zγ∥f∥l1	zγ∥f∥l1	X
ejpam-5455	367	20	γ(γ	γ(γ	X
ejpam-5455	367	21	+	+	CCONJ
ejpam-5455	367	22	1	1	NUM
ejpam-5455	367	23	)	)	PUNCT
ejpam-5455	367	24	)	)	PUNCT
ejpam-5455	368	1	(	(	PUNCT
ejpam-5455	368	2	(	(	PUNCT
ejpam-5455	368	3	q	q	NOUN
ejpam-5455	368	4	−	−	PROPN
ejpam-5455	368	5	1)mq−2zβ	1)mq−2zβ	NUM
ejpam-5455	368	6	b(ρ)γ(β	b(ρ)γ(β	NOUN
ejpam-5455	368	7	+	+	NOUN
ejpam-5455	368	8	1	1	X
ejpam-5455	368	9	)	)	PUNCT
ejpam-5455	368	10	{	{	PUNCT
ejpam-5455	368	11	1−	1−	NUM
ejpam-5455	368	12	ρ+	ρ+	NOUN
ejpam-5455	368	13	zρ	zρ	X
ejpam-5455	368	14	γ(ρ	γ(ρ	PROPN
ejpam-5455	368	15	)	)	PUNCT
ejpam-5455	368	16	}	}	PUNCT
ejpam-5455	368	17	|ξ(72)−	|ξ(72)−	ADJ
ejpam-5455	368	18	ξ(71)|	ξ(71)|	NOUN
ejpam-5455	368	19	)	)	PUNCT
ejpam-5455	369	1	+	+	CCONJ
ejpam-5455	369	2	(	(	PUNCT
ejpam-5455	369	3	abiρ0	abiρ0	NOUN
ejpam-5455	369	4	+	+	X
ejpam-5455	369	5	|θ|+	|θ|+	ADV
ejpam-5455	369	6	1	1	NUM
ejpam-5455	369	7	b(ρ	b(ρ	NOUN
ejpam-5455	369	8	)	)	PUNCT
ejpam-5455	369	9	(	(	PUNCT
ejpam-5455	369	10	zβ∥g∥l1	zβ∥g∥l1	X
ejpam-5455	369	11	γ(β	γ(β	PROPN
ejpam-5455	369	12	+	+	CCONJ
ejpam-5455	369	13	1	1	NUM
ejpam-5455	369	14	)	)	PUNCT
ejpam-5455	369	15	)	)	PUNCT
ejpam-5455	370	1	q−1	q−1	PROPN
ejpam-5455	370	2	{	{	PUNCT
ejpam-5455	370	3	1−	1−	NUM
ejpam-5455	370	4	ρ+	ρ+	NUM
ejpam-5455	370	5	zρ	zρ	X
ejpam-5455	370	6	γ(ρ	γ(ρ	PROPN
ejpam-5455	370	7	)	)	PUNCT
ejpam-5455	370	8	}	}	PUNCT
ejpam-5455	370	9	)	)	PUNCT
ejpam-5455	370	10	(	(	PUNCT
ejpam-5455	370	11	lq|72	lq|72	ADV
ejpam-5455	370	12	−	−	X
ejpam-5455	371	1	71|	71|	NUM
ejpam-5455	371	2	+	+	PROPN
ejpam-5455	371	3	zγ	zγ	X
ejpam-5455	371	4	γ(γ	γ(γ	PROPN
ejpam-5455	371	5	+	+	CCONJ
ejpam-5455	371	6	1	1	X
ejpam-5455	371	7	)	)	PUNCT
ejpam-5455	371	8	|ζ(72)−	|ζ(72)−	PROPN
ejpam-5455	371	9	ζ(71)|	ζ(71)|	NUM
ejpam-5455	371	10	)	)	PUNCT
ejpam-5455	371	11	,	,	PUNCT
ejpam-5455	371	12	where	where	SCONJ
ejpam-5455	371	13	ξ(7	ξ(7	NOUN
ejpam-5455	371	14	)	)	PUNCT
ejpam-5455	371	15	=	=	SYM
ejpam-5455	372	1	∫	∫	PROPN
ejpam-5455	372	2	7	7	NUM
ejpam-5455	372	3	0	0	NUM
ejpam-5455	372	4	g(σ)dσ	g(σ)dσ	NOUN
ejpam-5455	372	5	and	and	CCONJ
ejpam-5455	372	6	ζ(7	ζ(7	PROPN
ejpam-5455	372	7	)	)	PUNCT
ejpam-5455	373	1	=	=	SYM
ejpam-5455	373	2	∫	∫	PROPN
ejpam-5455	373	3	7	7	NUM
ejpam-5455	373	4	0	0	NUM
ejpam-5455	373	5	f	f	NOUN
ejpam-5455	373	6	(	(	PUNCT
ejpam-5455	373	7	σ)dσ	σ)dσ	NOUN
ejpam-5455	373	8	.	.	PUNCT
ejpam-5455	374	1	given	give	VERB
ejpam-5455	374	2	that	that	SCONJ
ejpam-5455	374	3	the	the	DET
ejpam-5455	374	4	functions	function	NOUN
ejpam-5455	374	5	ξ	ξ	PROPN
ejpam-5455	374	6	and	and	CCONJ
ejpam-5455	374	7	ζ	ζ	NOUN
ejpam-5455	374	8	are	be	AUX
ejpam-5455	374	9	continuous	continuous	ADJ
ejpam-5455	374	10	on	on	ADP
ejpam-5455	374	11	the	the	DET
ejpam-5455	374	12	compact	compact	ADJ
ejpam-5455	374	13	interval	interval	NOUN
ejpam-5455	374	14	ω	ω	PROPN
ejpam-5455	374	15	,	,	PUNCT
ejpam-5455	374	16	they	they	PRON
ejpam-5455	374	17	are	be	AUX
ejpam-5455	374	18	also	also	ADV
ejpam-5455	374	19	uniformly	uniformly	ADV
ejpam-5455	374	20	continuous	continuous	ADJ
ejpam-5455	374	21	.	.	PUNCT
ejpam-5455	375	1	therefore	therefore	ADV
ejpam-5455	375	2	,	,	PUNCT
ejpam-5455	375	3	for	for	ADP
ejpam-5455	375	4	any	any	DET
ejpam-5455	375	5	ε	ε	PROPN
ejpam-5455	375	6	>	>	X
ejpam-5455	375	7	0	0	PROPN
ejpam-5455	375	8	,	,	PUNCT
ejpam-5455	375	9	∃	∃	PROPN
ejpam-5455	375	10	a	a	PROPN
ejpam-5455	375	11	δ	δ	PROPN
ejpam-5455	375	12	>	>	X
ejpam-5455	375	13	0	0	NUM
ejpam-5455	375	14	such	such	ADJ
ejpam-5455	375	15	that	that	PRON
ejpam-5455	375	16	for	for	ADP
ejpam-5455	375	17	all	all	DET
ejpam-5455	375	18	71	71	NUM
ejpam-5455	375	19	,	,	PUNCT
ejpam-5455	375	20	72	72	NUM
ejpam-5455	375	21	∈	∈	NOUN
ejpam-5455	375	22	ω	ω	NOUN
ejpam-5455	375	23	and	and	CCONJ
ejpam-5455	375	24	w	w	PROPN
ejpam-5455	375	25	∈	∈	PROPN
ejpam-5455	375	26	s	s	PROPN
ejpam-5455	375	27	,	,	PUNCT
ejpam-5455	375	28	the	the	DET
ejpam-5455	375	29	following	follow	VERB
ejpam-5455	375	30	holds	hold	NOUN
ejpam-5455	375	31	:	:	PUNCT
ejpam-5455	375	32	|72	|72	PROPN
ejpam-5455	375	33	−	−	PROPN
ejpam-5455	375	34	71|	71|	NUM
ejpam-5455	375	35	<	<	X
ejpam-5455	375	36	δ	δ	PROPN
ejpam-5455	375	37	=	=	NOUN
ejpam-5455	375	38	⇒	⇒	NOUN
ejpam-5455	375	39	|(aw)(72)−	|(aw)(72)−	NOUN
ejpam-5455	375	40	(	(	PUNCT
ejpam-5455	375	41	aw)(71)|	aw)(71)|	PROPN
ejpam-5455	375	42	<	<	X
ejpam-5455	375	43	ε	ε	PROPN
ejpam-5455	375	44	.	.	PUNCT
ejpam-5455	376	1	this	this	PRON
ejpam-5455	376	2	establishes	establish	VERB
ejpam-5455	376	3	that	that	SCONJ
ejpam-5455	376	4	a(s	a(	NOUN
ejpam-5455	376	5	)	)	PUNCT
ejpam-5455	376	6	is	be	AUX
ejpam-5455	376	7	an	an	DET
ejpam-5455	376	8	equi	equi	NOUN
ejpam-5455	376	9	-	-	PUNCT
ejpam-5455	376	10	continuous	continuous	ADJ
ejpam-5455	376	11	subset	subset	NOUN
ejpam-5455	376	12	of	of	ADP
ejpam-5455	376	13	b.	b.	PROPN
ejpam-5455	376	14	since	since	SCONJ
ejpam-5455	376	15	a(s	a(s	PROPN
ejpam-5455	376	16	)	)	PUNCT
ejpam-5455	376	17	is	be	AUX
ejpam-5455	376	18	both	both	PRON
ejpam-5455	376	19	uniformly	uniformly	ADV
ejpam-5455	376	20	bounded	bound	VERB
ejpam-5455	376	21	and	and	CCONJ
ejpam-5455	376	22	equi	equi	NOUN
ejpam-5455	376	23	-	-	PUNCT
ejpam-5455	376	24	continuous	continuous	ADJ
ejpam-5455	376	25	in	in	ADP
ejpam-5455	376	26	b	b	PROPN
ejpam-5455	376	27	,	,	PUNCT
ejpam-5455	376	28	it	it	PRON
ejpam-5455	376	29	follows	follow	VERB
ejpam-5455	376	30	from	from	ADP
ejpam-5455	376	31	the	the	DET
ejpam-5455	376	32	arzelà-ascoli	arzelà-ascoli	PUNCT
ejpam-5455	376	33	theorem	theorem	NOUN
ejpam-5455	376	34	that	that	SCONJ
ejpam-5455	376	35	a(s	a(s	PROPN
ejpam-5455	376	36	)	)	PUNCT
ejpam-5455	376	37	is	be	AUX
ejpam-5455	376	38	relatively	relatively	ADV
ejpam-5455	376	39	compact	compact	ADJ
ejpam-5455	376	40	.	.	PUNCT
ejpam-5455	377	1	consequently	consequently	ADV
ejpam-5455	377	2	,	,	PUNCT
ejpam-5455	377	3	we	we	PRON
ejpam-5455	377	4	conclude	conclude	VERB
ejpam-5455	377	5	that	that	SCONJ
ejpam-5455	377	6	a	a	PRON
ejpam-5455	377	7	is	be	AUX
ejpam-5455	377	8	a	a	DET
ejpam-5455	377	9	compact	compact	ADJ
ejpam-5455	377	10	operator	operator	NOUN
ejpam-5455	377	11	on	on	ADP
ejpam-5455	377	12	s.	s.	PROPN
ejpam-5455	377	13	m.	m.	PROPN
ejpam-5455	377	14	m.	m.	PROPN
ejpam-5455	377	15	arjunan	arjunan	PROPN
ejpam-5455	377	16	/	/	SYM
ejpam-5455	377	17	eur	eur	PROPN
ejpam-5455	377	18	.	.	PUNCT
ejpam-5455	378	1	j.	j.	PROPN
ejpam-5455	378	2	pure	pure	PROPN
ejpam-5455	378	3	appl	appl	PROPN
ejpam-5455	378	4	.	.	PROPN
ejpam-5455	378	5	math	math	PROPN
ejpam-5455	378	6	,	,	PUNCT
ejpam-5455	378	7	17	17	NUM
ejpam-5455	378	8	(	(	PUNCT
ejpam-5455	378	9	4	4	NUM
ejpam-5455	378	10	)	)	PUNCT
ejpam-5455	378	11	(	(	PUNCT
ejpam-5455	378	12	2024	2024	NUM
ejpam-5455	378	13	)	)	PUNCT
ejpam-5455	378	14	,	,	PUNCT
ejpam-5455	378	15	4071	4071	NUM
ejpam-5455	378	16	-	-	SYM
ejpam-5455	378	17	4092	4092	NUM
ejpam-5455	378	18	4087	4087	NUM
ejpam-5455	378	19	step	step	NOUN
ejpam-5455	378	20	3	3	NUM
ejpam-5455	378	21	:	:	PUNCT
ejpam-5455	378	22	to	to	PART
ejpam-5455	378	23	demonstrate	demonstrate	VERB
ejpam-5455	378	24	that	that	SCONJ
ejpam-5455	378	25	a	a	PRON
ejpam-5455	378	26	is	be	AUX
ejpam-5455	378	27	a	a	DET
ejpam-5455	378	28	continuous	continuous	ADJ
ejpam-5455	378	29	operator	operator	NOUN
ejpam-5455	378	30	from	from	ADP
ejpam-5455	378	31	s	s	PRON
ejpam-5455	378	32	to	to	PART
ejpam-5455	378	33	b	b	NUM
ejpam-5455	378	34	,	,	PUNCT
ejpam-5455	378	35	consider	consider	VERB
ejpam-5455	378	36	a	a	DET
ejpam-5455	378	37	sequence	sequence	NOUN
ejpam-5455	378	38	{	{	PUNCT
ejpam-5455	378	39	wn	wn	NOUN
ejpam-5455	378	40	}	}	PUNCT
ejpam-5455	378	41	in	in	ADP
ejpam-5455	378	42	s	s	PRON
ejpam-5455	378	43	that	that	SCONJ
ejpam-5455	378	44	converges	converge	VERB
ejpam-5455	378	45	to	to	ADP
ejpam-5455	378	46	a	a	DET
ejpam-5455	378	47	point	point	NOUN
ejpam-5455	378	48	w	w	ADP
ejpam-5455	378	49	∈	∈	NOUN
ejpam-5455	378	50	s.	s.	PROPN
ejpam-5455	378	51	by	by	ADP
ejpam-5455	378	52	applying	apply	VERB
ejpam-5455	378	53	the	the	DET
ejpam-5455	378	54	lebesgue	lebesgue	NOUN
ejpam-5455	378	55	dominated	dominate	VERB
ejpam-5455	378	56	convergence	convergence	NOUN
ejpam-5455	378	57	theorem	theorem	VERB
ejpam-5455	378	58	,	,	PUNCT
ejpam-5455	378	59	we	we	PRON
ejpam-5455	378	60	can	can	AUX
ejpam-5455	378	61	derive	derive	VERB
ejpam-5455	378	62	the	the	DET
ejpam-5455	378	63	following	follow	VERB
ejpam-5455	378	64	result	result	NOUN
ejpam-5455	378	65	:	:	PUNCT
ejpam-5455	379	1	lim	lim	PROPN
ejpam-5455	379	2	n→∞	n→∞	X
ejpam-5455	379	3	(	(	PUNCT
ejpam-5455	379	4	awn)(7	awn)(7	NOUN
ejpam-5455	379	5	)	)	PUNCT
ejpam-5455	379	6	=	=	SYM
ejpam-5455	379	7	lim	lim	PROPN
ejpam-5455	379	8	n→∞	n→∞	NUM
ejpam-5455	379	9	{	{	PUNCT
ejpam-5455	379	10	(	(	PUNCT
ejpam-5455	379	11	q(7	q(7	PROPN
ejpam-5455	379	12	)	)	PUNCT
ejpam-5455	379	13	+	+	CCONJ
ejpam-5455	379	14	1	1	NUM
ejpam-5455	379	15	γ(γ	γ(γ	NOUN
ejpam-5455	379	16	)	)	PUNCT
ejpam-5455	379	17	∫	∫	PROPN
ejpam-5455	379	18	7	7	NUM
ejpam-5455	379	19	0	0	NUM
ejpam-5455	379	20	(	(	PUNCT
ejpam-5455	379	21	7	7	NUM
ejpam-5455	379	22	−	−	NOUN
ejpam-5455	379	23	σ)γ−1f(σ	σ)γ−1f(σ	NOUN
ejpam-5455	379	24	,	,	PUNCT
ejpam-5455	379	25	wn(σ))dσ	wn(σ))dσ	PROPN
ejpam-5455	379	26	)	)	PUNCT
ejpam-5455	379	27	(	(	PUNCT
ejpam-5455	379	28	×	×	NOUN
ejpam-5455	379	29	)	)	PUNCT
ejpam-5455	379	30	[	[	PUNCT
ejpam-5455	379	31	abiρ0+(θ	abiρ0+(θ	NOUN
ejpam-5455	379	32	)	)	PUNCT
ejpam-5455	379	33	+	+	CCONJ
ejpam-5455	379	34	1−	1−	NUM
ejpam-5455	379	35	ρ	ρ	NUM
ejpam-5455	379	36	b(ρ	b(ρ	PROPN
ejpam-5455	379	37	)	)	PUNCT
ejpam-5455	379	38	ψq	ψq	PROPN
ejpam-5455	379	39	(	(	PUNCT
ejpam-5455	379	40	1	1	NUM
ejpam-5455	379	41	γ(β	γ(β	PROPN
ejpam-5455	379	42	)	)	PUNCT
ejpam-5455	379	43	∫	∫	PROPN
ejpam-5455	379	44	7	7	NUM
ejpam-5455	379	45	0	0	NUM
ejpam-5455	379	46	(	(	PUNCT
ejpam-5455	379	47	7	7	NUM
ejpam-5455	379	48	−	−	NOUN
ejpam-5455	379	49	σ)β−1g(σ	σ)β−1g(σ	ADP
ejpam-5455	379	50	,	,	PUNCT
ejpam-5455	379	51	wn(σ))dσ	wn(σ))dσ	NOUN
ejpam-5455	379	52	)	)	PUNCT
ejpam-5455	379	53	+	+	CCONJ
ejpam-5455	379	54	ρ	ρ	PROPN
ejpam-5455	379	55	b(ρ)γ(ρ	b(ρ)γ(ρ	NOUN
ejpam-5455	379	56	)	)	PUNCT
ejpam-5455	379	57	∫	∫	PROPN
ejpam-5455	379	58	7	7	NUM
ejpam-5455	379	59	0	0	NUM
ejpam-5455	379	60	(	(	PUNCT
ejpam-5455	379	61	7	7	NUM
ejpam-5455	379	62	−	−	NOUN
ejpam-5455	379	63	σ)ρ−1	σ)ρ−1	NOUN
ejpam-5455	379	64	(	(	PUNCT
ejpam-5455	379	65	ψq	ψq	X
ejpam-5455	379	66	(	(	PUNCT
ejpam-5455	379	67	1	1	NUM
ejpam-5455	379	68	γ(β	γ(β	PROPN
ejpam-5455	379	69	)	)	PUNCT
ejpam-5455	379	70	∫	∫	PROPN
ejpam-5455	379	71	σ	σ	PROPN
ejpam-5455	379	72	0	0	NUM
ejpam-5455	379	73	(	(	PUNCT
ejpam-5455	379	74	σ	σ	NOUN
ejpam-5455	379	75	−	−	PROPN
ejpam-5455	379	76	τ)β−1g(τ	τ)β−1g(τ	PUNCT
ejpam-5455	379	77	,	,	PUNCT
ejpam-5455	379	78	wn(τ))dτ	wn(τ))dτ	PROPN
ejpam-5455	379	79	)	)	PUNCT
ejpam-5455	379	80	)	)	PUNCT
ejpam-5455	379	81	dσ	dσ	VERB
ejpam-5455	379	82	]	]	X
ejpam-5455	379	83	}	}	PUNCT
ejpam-5455	379	84	=	=	SYM
ejpam-5455	379	85	(	(	PUNCT
ejpam-5455	379	86	q(7	q(7	PROPN
ejpam-5455	379	87	)	)	PUNCT
ejpam-5455	379	88	+	+	CCONJ
ejpam-5455	379	89	1	1	NUM
ejpam-5455	379	90	γ(γ	γ(γ	NOUN
ejpam-5455	379	91	)	)	PUNCT
ejpam-5455	379	92	∫	∫	PROPN
ejpam-5455	379	93	7	7	NUM
ejpam-5455	379	94	0	0	NUM
ejpam-5455	379	95	(	(	PUNCT
ejpam-5455	379	96	7	7	NUM
ejpam-5455	379	97	−	−	NOUN
ejpam-5455	379	98	σ)γ−1	σ)γ−1	NOUN
ejpam-5455	379	99	lim	lim	PROPN
ejpam-5455	379	100	n→∞	n→∞	NUM
ejpam-5455	379	101	f(σ	f(σ	NOUN
ejpam-5455	379	102	,	,	PUNCT
ejpam-5455	379	103	wn(σ))dσ	wn(σ))dσ	PROPN
ejpam-5455	379	104	)	)	PUNCT
ejpam-5455	379	105	(	(	PUNCT
ejpam-5455	379	106	×	×	NOUN
ejpam-5455	379	107	)	)	PUNCT
ejpam-5455	379	108	[	[	PUNCT
ejpam-5455	379	109	abiρ0+(θ	abiρ0+(θ	NOUN
ejpam-5455	379	110	)	)	PUNCT
ejpam-5455	380	1	+	+	CCONJ
ejpam-5455	380	2	1−	1−	NUM
ejpam-5455	380	3	ρ	ρ	NUM
ejpam-5455	380	4	b(ρ	b(ρ	PROPN
ejpam-5455	380	5	)	)	PUNCT
ejpam-5455	380	6	ψq	ψq	PROPN
ejpam-5455	380	7	(	(	PUNCT
ejpam-5455	380	8	1	1	NUM
ejpam-5455	380	9	γ(β	γ(β	PROPN
ejpam-5455	380	10	)	)	PUNCT
ejpam-5455	380	11	∫	∫	PROPN
ejpam-5455	381	1	7	7	NUM
ejpam-5455	381	2	0	0	NUM
ejpam-5455	381	3	(	(	PUNCT
ejpam-5455	381	4	7	7	NUM
ejpam-5455	381	5	−	−	NOUN
ejpam-5455	381	6	σ)β−1	σ)β−1	ADP
ejpam-5455	381	7	lim	lim	PROPN
ejpam-5455	381	8	n→∞	n→∞	PRON
ejpam-5455	381	9	g(σ	g(σ	PROPN
ejpam-5455	381	10	,	,	PUNCT
ejpam-5455	381	11	wn(σ))dσ	wn(σ))dσ	PROPN
ejpam-5455	381	12	)	)	PUNCT
ejpam-5455	382	1	+	+	CCONJ
ejpam-5455	382	2	ρ	ρ	PROPN
ejpam-5455	382	3	b(ρ)γ(ρ	b(ρ)γ(ρ	NOUN
ejpam-5455	382	4	)	)	PUNCT
ejpam-5455	382	5	∫	∫	PROPN
ejpam-5455	383	1	7	7	NUM
ejpam-5455	383	2	0	0	NUM
ejpam-5455	383	3	(	(	PUNCT
ejpam-5455	383	4	7	7	NUM
ejpam-5455	383	5	−	−	NOUN
ejpam-5455	383	6	σ)ρ−1	σ)ρ−1	NOUN
ejpam-5455	383	7	(	(	PUNCT
ejpam-5455	383	8	ψq	ψq	X
ejpam-5455	383	9	(	(	PUNCT
ejpam-5455	383	10	1	1	NUM
ejpam-5455	383	11	γ(β	γ(β	PROPN
ejpam-5455	383	12	)	)	PUNCT
ejpam-5455	383	13	∫	∫	PROPN
ejpam-5455	384	1	σ	σ	PROPN
ejpam-5455	384	2	0	0	NUM
ejpam-5455	384	3	(	(	PUNCT
ejpam-5455	384	4	σ	σ	PROPN
ejpam-5455	384	5	−	−	PROPN
ejpam-5455	384	6	τ)β−1	τ)β−1	ADP
ejpam-5455	384	7	lim	lim	PROPN
ejpam-5455	384	8	n→∞	n→∞	NUM
ejpam-5455	384	9	g(τ	g(τ	PROPN
ejpam-5455	384	10	,	,	PUNCT
ejpam-5455	384	11	wn(τ))dτ	wn(τ))dτ	PROPN
ejpam-5455	384	12	)	)	PUNCT
ejpam-5455	384	13	)	)	PUNCT
ejpam-5455	384	14	dσ	dσ	VERB
ejpam-5455	384	15	]	]	PUNCT
ejpam-5455	385	1	=	=	PUNCT
ejpam-5455	386	1	(	(	PUNCT
ejpam-5455	386	2	q(7	q(7	PROPN
ejpam-5455	386	3	)	)	PUNCT
ejpam-5455	386	4	+	+	CCONJ
ejpam-5455	386	5	1	1	NUM
ejpam-5455	386	6	γ(γ	γ(γ	NOUN
ejpam-5455	386	7	)	)	PUNCT
ejpam-5455	386	8	∫	∫	PROPN
ejpam-5455	386	9	7	7	NUM
ejpam-5455	386	10	0	0	NUM
ejpam-5455	386	11	(	(	PUNCT
ejpam-5455	386	12	7	7	NUM
ejpam-5455	386	13	−	−	NOUN
ejpam-5455	386	14	σ)γ−1f(σ	σ)γ−1f(σ	NOUN
ejpam-5455	386	15	,	,	PUNCT
ejpam-5455	386	16	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	386	17	)	)	PUNCT
ejpam-5455	386	18	(	(	PUNCT
ejpam-5455	386	19	×	×	NOUN
ejpam-5455	386	20	)	)	PUNCT
ejpam-5455	386	21	[	[	PUNCT
ejpam-5455	386	22	abiρ0+(θ	abiρ0+(θ	NOUN
ejpam-5455	386	23	)	)	PUNCT
ejpam-5455	387	1	+	+	CCONJ
ejpam-5455	387	2	1−	1−	NUM
ejpam-5455	387	3	ρ	ρ	NUM
ejpam-5455	387	4	b(ρ	b(ρ	PROPN
ejpam-5455	387	5	)	)	PUNCT
ejpam-5455	387	6	ψq	ψq	PROPN
ejpam-5455	387	7	(	(	PUNCT
ejpam-5455	387	8	1	1	NUM
ejpam-5455	387	9	γ(β	γ(β	PROPN
ejpam-5455	387	10	)	)	PUNCT
ejpam-5455	387	11	∫	∫	PROPN
ejpam-5455	388	1	7	7	NUM
ejpam-5455	388	2	0	0	NUM
ejpam-5455	388	3	(	(	PUNCT
ejpam-5455	388	4	7	7	NUM
ejpam-5455	388	5	−	−	NOUN
ejpam-5455	388	6	σ)β−1g(σ	σ)β−1g(σ	NOUN
ejpam-5455	388	7	,	,	PUNCT
ejpam-5455	388	8	w(σ))dσ	w(σ))dσ	NOUN
ejpam-5455	388	9	)	)	PUNCT
ejpam-5455	389	1	+	+	CCONJ
ejpam-5455	389	2	ρ	ρ	PROPN
ejpam-5455	389	3	b(ρ)γ(ρ	b(ρ)γ(ρ	NOUN
ejpam-5455	389	4	)	)	PUNCT
ejpam-5455	389	5	∫	∫	PROPN
ejpam-5455	390	1	7	7	NUM
ejpam-5455	390	2	0	0	NUM
ejpam-5455	390	3	(	(	PUNCT
ejpam-5455	390	4	7	7	NUM
ejpam-5455	390	5	−	−	NOUN
ejpam-5455	390	6	σ)ρ−1	σ)ρ−1	NOUN
ejpam-5455	390	7	(	(	PUNCT
ejpam-5455	390	8	ψq	ψq	X
ejpam-5455	390	9	(	(	PUNCT
ejpam-5455	390	10	1	1	NUM
ejpam-5455	390	11	γ(β	γ(β	PROPN
ejpam-5455	390	12	)	)	PUNCT
ejpam-5455	390	13	∫	∫	PROPN
ejpam-5455	391	1	σ	σ	PROPN
ejpam-5455	391	2	0	0	NUM
ejpam-5455	391	3	(	(	PUNCT
ejpam-5455	391	4	σ	σ	NOUN
ejpam-5455	391	5	−	−	PROPN
ejpam-5455	391	6	τ)β−1g(τ	τ)β−1g(τ	PUNCT
ejpam-5455	391	7	,	,	PUNCT
ejpam-5455	391	8	w(τ))dτ	w(τ))dτ	PROPN
ejpam-5455	391	9	)	)	PUNCT
ejpam-5455	391	10	)	)	PUNCT
ejpam-5455	392	1	dσ	dσ	VERB
ejpam-5455	392	2	]	]	PUNCT
ejpam-5455	392	3	=	=	SYM
ejpam-5455	392	4	(	(	PUNCT
ejpam-5455	392	5	aw)(7	aw)(7	NOUN
ejpam-5455	392	6	)	)	PUNCT
ejpam-5455	392	7	for	for	ADP
ejpam-5455	392	8	all	all	DET
ejpam-5455	392	9	7	7	NUM
ejpam-5455	392	10	∈	∈	PROPN
ejpam-5455	392	11	ω	ω	NOUN
ejpam-5455	392	12	.	.	PUNCT
ejpam-5455	393	1	this	this	PRON
ejpam-5455	393	2	establishes	establish	VERB
ejpam-5455	393	3	that	that	SCONJ
ejpam-5455	393	4	the	the	DET
ejpam-5455	393	5	sequence	sequence	NOUN
ejpam-5455	393	6	{	{	PUNCT
ejpam-5455	393	7	awn	awn	NOUN
ejpam-5455	393	8	}	}	PUNCT
ejpam-5455	393	9	converges	converge	VERB
ejpam-5455	393	10	point	point	NOUN
ejpam-5455	393	11	-	-	PUNCT
ejpam-5455	393	12	wise	wise	ADJ
ejpam-5455	393	13	to	to	PART
ejpam-5455	393	14	aw	aw	INTJ
ejpam-5455	393	15	on	on	ADP
ejpam-5455	393	16	the	the	DET
ejpam-5455	393	17	interval	interval	NOUN
ejpam-5455	393	18	ω	ω	NOUN
ejpam-5455	393	19	.	.	PUNCT
ejpam-5455	394	1	furthermore	furthermore	ADV
ejpam-5455	394	2	,	,	PUNCT
ejpam-5455	394	3	by	by	ADP
ejpam-5455	394	4	employing	employ	VERB
ejpam-5455	394	5	a	a	DET
ejpam-5455	394	6	similar	similar	ADJ
ejpam-5455	394	7	argument	argument	NOUN
ejpam-5455	394	8	as	as	ADP
ejpam-5455	394	9	in	in	ADP
ejpam-5455	394	10	step	step	NOUN
ejpam-5455	394	11	2	2	NUM
ejpam-5455	394	12	,	,	PUNCT
ejpam-5455	394	13	we	we	PRON
ejpam-5455	394	14	can	can	AUX
ejpam-5455	394	15	demonstrate	demonstrate	VERB
ejpam-5455	394	16	that	that	SCONJ
ejpam-5455	394	17	the	the	DET
ejpam-5455	394	18	sequence	sequence	NOUN
ejpam-5455	394	19	{	{	PUNCT
ejpam-5455	394	20	awn	awn	NOUN
ejpam-5455	394	21	}	}	PUNCT
ejpam-5455	394	22	is	be	AUX
ejpam-5455	394	23	equi	equi	NOUN
ejpam-5455	394	24	-	-	PUNCT
ejpam-5455	394	25	continuous	continuous	ADJ
ejpam-5455	394	26	.	.	PUNCT
ejpam-5455	395	1	consequently	consequently	ADV
ejpam-5455	395	2	,	,	PUNCT
ejpam-5455	395	3	it	it	PRON
ejpam-5455	395	4	follows	follow	VERB
ejpam-5455	395	5	that	that	SCONJ
ejpam-5455	395	6	{	{	PUNCT
ejpam-5455	395	7	awn	awn	NOUN
ejpam-5455	395	8	}	}	PUNCT
ejpam-5455	395	9	converges	converge	VERB
ejpam-5455	395	10	uniformly	uniformly	ADV
ejpam-5455	395	11	to	to	PART
ejpam-5455	395	12	aw	aw	INTJ
ejpam-5455	395	13	,	,	PUNCT
ejpam-5455	395	14	thereby	thereby	ADV
ejpam-5455	395	15	confirming	confirm	VERB
ejpam-5455	395	16	that	that	SCONJ
ejpam-5455	395	17	a	a	PRON
ejpam-5455	395	18	is	be	AUX
ejpam-5455	395	19	a	a	DET
ejpam-5455	395	20	continuous	continuous	ADJ
ejpam-5455	395	21	operator	operator	NOUN
ejpam-5455	395	22	on	on	ADP
ejpam-5455	395	23	s.	s.	PROPN
ejpam-5455	395	24	step	step	NOUN
ejpam-5455	395	25	4	4	NUM
ejpam-5455	395	26	:	:	PUNCT
ejpam-5455	395	27	we	we	PRON
ejpam-5455	395	28	demonstrate	demonstrate	VERB
ejpam-5455	395	29	that	that	SCONJ
ejpam-5455	395	30	aw+bw	aw+bw	NUM
ejpam-5455	395	31	∈	∈	NOUN
ejpam-5455	395	32	s	s	X
ejpam-5455	395	33	for	for	ADP
ejpam-5455	395	34	all	all	DET
ejpam-5455	395	35	w	w	NOUN
ejpam-5455	395	36	,	,	PUNCT
ejpam-5455	395	37	w	w	PROPN
ejpam-5455	395	38	∈	∈	PROPN
ejpam-5455	395	39	s.	s.	PROPN
ejpam-5455	395	40	for	for	ADP
ejpam-5455	395	41	any	any	DET
ejpam-5455	395	42	w	w	NOUN
ejpam-5455	395	43	,	,	PUNCT
ejpam-5455	395	44	w	w	PROPN
ejpam-5455	395	45	∈	∈	PROPN
ejpam-5455	395	46	s	s	X
ejpam-5455	395	47	and	and	CCONJ
ejpam-5455	395	48	7	7	NUM
ejpam-5455	395	49	∈	∈	PROPN
ejpam-5455	395	50	ω	ω	NOUN
ejpam-5455	395	51	,	,	PUNCT
ejpam-5455	395	52	it	it	PRON
ejpam-5455	395	53	follows	follow	VERB
ejpam-5455	395	54	that	that	SCONJ
ejpam-5455	395	55	|(aw)(7	|(aw)(7	NOUN
ejpam-5455	395	56	)	)	PUNCT
ejpam-5455	395	57	+	+	CCONJ
ejpam-5455	395	58	(	(	PUNCT
ejpam-5455	395	59	bw)(7)|	bw)(7)|	PROPN
ejpam-5455	395	60	≤	≤	NOUN
ejpam-5455	395	61	(	(	PUNCT
ejpam-5455	395	62	lqz	lqz	NOUN
ejpam-5455	395	63	+	+	CCONJ
ejpam-5455	395	64	|q(0)|+	|q(0)|+	NUM
ejpam-5455	395	65	zγ∥f∥l1	zγ∥f∥l1	NUM
ejpam-5455	395	66	γ(γ	γ(γ	X
ejpam-5455	396	1	+	+	CCONJ
ejpam-5455	396	2	1	1	NUM
ejpam-5455	396	3	)	)	PUNCT
ejpam-5455	396	4	)	)	PUNCT
ejpam-5455	396	5	(	(	PUNCT
ejpam-5455	396	6	abiρ0	abiρ0	NOUN
ejpam-5455	396	7	+	+	X
ejpam-5455	396	8	|θ|+	|θ|+	ADV
ejpam-5455	396	9	1	1	NUM
ejpam-5455	396	10	b(ρ	b(ρ	NOUN
ejpam-5455	396	11	)	)	PUNCT
ejpam-5455	396	12	(	(	PUNCT
ejpam-5455	396	13	zβ∥g∥l1	zβ∥g∥l1	X
ejpam-5455	396	14	γ(β	γ(β	PROPN
ejpam-5455	396	15	+	+	CCONJ
ejpam-5455	396	16	1	1	NUM
ejpam-5455	396	17	)	)	PUNCT
ejpam-5455	396	18	)	)	PUNCT
ejpam-5455	397	1	q−1	q−1	PROPN
ejpam-5455	397	2	{	{	PUNCT
ejpam-5455	397	3	1−	1−	NUM
ejpam-5455	397	4	ρ+	ρ+	NUM
ejpam-5455	397	5	zρ	zρ	X
ejpam-5455	397	6	γ(ρ	γ(ρ	PROPN
ejpam-5455	397	7	)	)	PUNCT
ejpam-5455	397	8	}	}	PUNCT
ejpam-5455	397	9	)	)	PUNCT
ejpam-5455	398	1	+	+	CCONJ
ejpam-5455	398	2	lf∥w∥+	lf∥w∥+	PROPN
ejpam-5455	398	3	f0	f0	PROPN
ejpam-5455	398	4	m.	m.	NOUN
ejpam-5455	398	5	m.	m.	PROPN
ejpam-5455	398	6	arjunan	arjunan	PROPN
ejpam-5455	398	7	/	/	SYM
ejpam-5455	398	8	eur	eur	PROPN
ejpam-5455	398	9	.	.	PUNCT
ejpam-5455	399	1	j.	j.	PROPN
ejpam-5455	399	2	pure	pure	PROPN
ejpam-5455	399	3	appl	appl	PROPN
ejpam-5455	399	4	.	.	PROPN
ejpam-5455	399	5	math	math	PROPN
ejpam-5455	399	6	,	,	PUNCT
ejpam-5455	399	7	17	17	NUM
ejpam-5455	399	8	(	(	PUNCT
ejpam-5455	399	9	4	4	NUM
ejpam-5455	399	10	)	)	PUNCT
ejpam-5455	399	11	(	(	PUNCT
ejpam-5455	399	12	2024	2024	NUM
ejpam-5455	399	13	)	)	PUNCT
ejpam-5455	399	14	,	,	PUNCT
ejpam-5455	399	15	4071	4071	NUM
ejpam-5455	399	16	-	-	SYM
ejpam-5455	399	17	4092	4092	NUM
ejpam-5455	399	18	4088	4088	NUM
ejpam-5455	399	19	≤	≤	NUM
ejpam-5455	399	20	λ	λ	PROPN
ejpam-5455	400	1	,	,	PUNCT
ejpam-5455	400	2	it	it	PRON
ejpam-5455	400	3	follows	follow	VERB
ejpam-5455	400	4	that	that	SCONJ
ejpam-5455	401	1	aw	aw	INTJ
ejpam-5455	401	2	+	+	CCONJ
ejpam-5455	401	3	bw	bw	PROPN
ejpam-5455	401	4	∈	∈	PROPN
ejpam-5455	401	5	s	s	PROPN
ejpam-5455	401	6	for	for	ADP
ejpam-5455	401	7	all	all	DET
ejpam-5455	401	8	w	w	NOUN
ejpam-5455	401	9	,	,	PUNCT
ejpam-5455	401	10	w	w	PROPN
ejpam-5455	401	11	∈	∈	PROPN
ejpam-5455	401	12	s.	s.	PROPN
ejpam-5455	402	1	this	this	PRON
ejpam-5455	402	2	confirms	confirm	VERB
ejpam-5455	402	3	that	that	SCONJ
ejpam-5455	402	4	all	all	DET
ejpam-5455	402	5	the	the	DET
ejpam-5455	402	6	conditions	condition	NOUN
ejpam-5455	402	7	specified	specify	VERB
ejpam-5455	402	8	in	in	ADP
ejpam-5455	402	9	[	[	X
ejpam-5455	402	10	17	17	NUM
ejpam-5455	402	11	,	,	PUNCT
ejpam-5455	402	12	theorem	theorem	VERB
ejpam-5455	402	13	2.6	2.6	NUM
ejpam-5455	402	14	]	]	PUNCT
ejpam-5455	402	15	are	be	AUX
ejpam-5455	402	16	satisfied	satisfied	ADJ
ejpam-5455	402	17	,	,	PUNCT
ejpam-5455	402	18	leading	lead	VERB
ejpam-5455	402	19	to	to	ADP
ejpam-5455	402	20	the	the	DET
ejpam-5455	402	21	conclusion	conclusion	NOUN
ejpam-5455	402	22	that	that	SCONJ
ejpam-5455	402	23	the	the	DET
ejpam-5455	402	24	operator	operator	NOUN
ejpam-5455	402	25	equation	equation	NOUN
ejpam-5455	402	26	aw+bw	aw+bw	NOUN
ejpam-5455	402	27	=	=	SYM
ejpam-5455	402	28	w	w	NOUN
ejpam-5455	402	29	has	have	AUX
ejpam-5455	402	30	a	a	DET
ejpam-5455	402	31	solution	solution	NOUN
ejpam-5455	402	32	in	in	ADP
ejpam-5455	402	33	the	the	DET
ejpam-5455	402	34	set	set	NOUN
ejpam-5455	402	35	s.	s.	PROPN
ejpam-5455	402	36	consequently	consequently	ADV
ejpam-5455	402	37	,	,	PUNCT
ejpam-5455	402	38	the	the	DET
ejpam-5455	402	39	mabc	mabc	NOUN
ejpam-5455	402	40	-	-	PUNCT
ejpam-5455	402	41	hfides	hfide	NOUN
ejpam-5455	402	42	(	(	PUNCT
ejpam-5455	402	43	1	1	X
ejpam-5455	402	44	)	)	PUNCT
ejpam-5455	402	45	has	have	VERB
ejpam-5455	402	46	a	a	DET
ejpam-5455	402	47	solution	solution	NOUN
ejpam-5455	402	48	that	that	PRON
ejpam-5455	402	49	is	be	AUX
ejpam-5455	402	50	defined	define	VERB
ejpam-5455	402	51	on	on	ADP
ejpam-5455	402	52	the	the	DET
ejpam-5455	402	53	interval	interval	NOUN
ejpam-5455	402	54	ω	ω	PROPN
ejpam-5455	402	55	.	.	PROPN
ejpam-5455	402	56	4	4	NUM
ejpam-5455	402	57	.	.	X
ejpam-5455	402	58	stability	stability	NOUN
ejpam-5455	402	59	analysis	analysis	NOUN
ejpam-5455	402	60	this	this	DET
ejpam-5455	402	61	section	section	NOUN
ejpam-5455	402	62	is	be	AUX
ejpam-5455	402	63	dedicated	dedicate	VERB
ejpam-5455	402	64	to	to	ADP
ejpam-5455	402	65	the	the	DET
ejpam-5455	402	66	study	study	NOUN
ejpam-5455	402	67	of	of	ADP
ejpam-5455	402	68	u	u	PROPN
ejpam-5455	402	69	-	-	PROPN
ejpam-5455	402	70	h	h	NOUN
ejpam-5455	402	71	-	-	PUNCT
ejpam-5455	402	72	stability	stability	NOUN
ejpam-5455	402	73	of	of	ADP
ejpam-5455	402	74	the	the	DET
ejpam-5455	402	75	mabc	mabc	NOUN
ejpam-5455	402	76	-	-	PUNCT
ejpam-5455	402	77	hfides	hfide	NOUN
ejpam-5455	402	78	(	(	PUNCT
ejpam-5455	402	79	1	1	NUM
ejpam-5455	402	80	)	)	PUNCT
ejpam-5455	402	81	.	.	PUNCT
ejpam-5455	403	1	to	to	PART
ejpam-5455	403	2	proceed	proceed	VERB
ejpam-5455	403	3	,	,	PUNCT
ejpam-5455	403	4	we	we	PRON
ejpam-5455	403	5	will	will	AUX
ejpam-5455	403	6	first	first	ADV
ejpam-5455	403	7	recall	recall	VERB
ejpam-5455	403	8	the	the	DET
ejpam-5455	403	9	following	follow	VERB
ejpam-5455	403	10	definition	definition	NOUN
ejpam-5455	403	11	:	:	PUNCT
ejpam-5455	403	12	definition	definition	NOUN
ejpam-5455	403	13	7	7	NUM
ejpam-5455	403	14	.	.	PUNCT
ejpam-5455	404	1	the	the	DET
ejpam-5455	404	2	integral	integral	ADJ
ejpam-5455	404	3	equation	equation	NOUN
ejpam-5455	404	4	(	(	PUNCT
ejpam-5455	404	5	11	11	NUM
ejpam-5455	404	6	)	)	PUNCT
ejpam-5455	404	7	is	be	AUX
ejpam-5455	404	8	ulam	ulam	NOUN
ejpam-5455	404	9	-	-	PUNCT
ejpam-5455	404	10	hyers	hyer	NOUN
ejpam-5455	404	11	stable	stable	ADJ
ejpam-5455	404	12	,	,	PUNCT
ejpam-5455	404	13	if	if	SCONJ
ejpam-5455	404	14	for	for	ADP
ejpam-5455	404	15	some	some	DET
ejpam-5455	404	16	λ1	λ1	PROPN
ejpam-5455	404	17	>	>	X
ejpam-5455	404	18	0	0	PROPN
ejpam-5455	404	19	,	,	PUNCT
ejpam-5455	404	20	we	we	PRON
ejpam-5455	404	21	have	have	VERB
ejpam-5455	404	22	ϑ	ϑ	X
ejpam-5455	404	23	>	>	X
ejpam-5455	404	24	0	0	PUNCT
ejpam-5455	404	25	with	with	ADP
ejpam-5455	404	26	w	w	PROPN
ejpam-5455	404	27	satisfying	satisfy	VERB
ejpam-5455	404	28	∥w	∥w	PROPN
ejpam-5455	404	29	−	−	PROPN
ejpam-5455	404	30	φw∥	φw∥	PROPN
ejpam-5455	404	31	<	<	X
ejpam-5455	404	32	ϑ	ϑ	X
ejpam-5455	404	33	(	(	PUNCT
ejpam-5455	404	34	21	21	NUM
ejpam-5455	404	35	)	)	PUNCT
ejpam-5455	404	36	with	with	ADP
ejpam-5455	404	37	w(7	w(7	PROPN
ejpam-5455	404	38	)	)	PUNCT
ejpam-5455	404	39	of	of	ADP
ejpam-5455	404	40	(	(	PUNCT
ejpam-5455	404	41	11	11	NUM
ejpam-5455	404	42	)	)	PUNCT
ejpam-5455	404	43	with	with	ADP
ejpam-5455	404	44	w(7	w(7	PROPN
ejpam-5455	404	45	)	)	PUNCT
ejpam-5455	404	46	=	=	SYM
ejpam-5455	404	47	φw(7	φw(7	NOUN
ejpam-5455	404	48	)	)	PUNCT
ejpam-5455	404	49	(	(	PUNCT
ejpam-5455	404	50	22	22	NUM
ejpam-5455	404	51	)	)	PUNCT
ejpam-5455	404	52	and	and	CCONJ
ejpam-5455	404	53	∥w	∥w	PROPN
ejpam-5455	404	54	−	−	PROPN
ejpam-5455	404	55	w∥	w∥	X
ejpam-5455	404	56	<	<	X
ejpam-5455	404	57	ϑλ1	ϑλ1	NOUN
ejpam-5455	404	58	.	.	PUNCT
ejpam-5455	405	1	theorem	theorem	NOUN
ejpam-5455	405	2	3	3	NUM
ejpam-5455	405	3	.	.	PUNCT
ejpam-5455	406	1	under	under	ADP
ejpam-5455	406	2	the	the	DET
ejpam-5455	406	3	conditions	condition	NOUN
ejpam-5455	406	4	of	of	ADP
ejpam-5455	406	5	theorem	theorem	NOUN
ejpam-5455	406	6	1	1	NUM
ejpam-5455	406	7	,	,	PUNCT
ejpam-5455	406	8	the	the	DET
ejpam-5455	406	9	system	system	NOUN
ejpam-5455	406	10	(	(	PUNCT
ejpam-5455	406	11	11	11	NUM
ejpam-5455	406	12	)	)	PUNCT
ejpam-5455	406	13	demonstrates	demonstrate	VERB
ejpam-5455	406	14	u	u	NOUN
ejpam-5455	406	15	-	-	ADJ
ejpam-5455	406	16	h	h	ADJ
ejpam-5455	406	17	stability	stability	NOUN
ejpam-5455	406	18	,	,	PUNCT
ejpam-5455	406	19	which	which	PRON
ejpam-5455	406	20	implies	imply	VERB
ejpam-5455	406	21	the	the	DET
ejpam-5455	406	22	u	u	NOUN
ejpam-5455	406	23	-	-	PROPN
ejpam-5455	406	24	h	h	ADJ
ejpam-5455	406	25	stability	stability	NOUN
ejpam-5455	406	26	of	of	ADP
ejpam-5455	406	27	the	the	DET
ejpam-5455	406	28	hybrid	hybrid	ADJ
ejpam-5455	406	29	system	system	NOUN
ejpam-5455	406	30	of	of	ADP
ejpam-5455	406	31	mabc	mabc	NOUN
ejpam-5455	406	32	-	-	PUNCT
ejpam-5455	406	33	fdes	fde	NOUN
ejpam-5455	406	34	(	(	PUNCT
ejpam-5455	406	35	1	1	NUM
ejpam-5455	406	36	)	)	PUNCT
ejpam-5455	406	37	.	.	PUNCT
ejpam-5455	407	1	proof	proof	NOUN
ejpam-5455	407	2	.	.	PUNCT
ejpam-5455	408	1	for	for	ADP
ejpam-5455	408	2	any	any	DET
ejpam-5455	408	3	w	w	NOUN
ejpam-5455	408	4	,	,	PUNCT
ejpam-5455	408	5	w∗	w∗	PROPN
ejpam-5455	408	6	∈	∈	PROPN
ejpam-5455	408	7	ac(ω	ac(ω	PRON
ejpam-5455	408	8	,	,	PUNCT
ejpam-5455	408	9	r	r	NOUN
ejpam-5455	408	10	)	)	PUNCT
ejpam-5455	408	11	,	,	PUNCT
ejpam-5455	408	12	we	we	PRON
ejpam-5455	408	13	have	have	AUX
ejpam-5455	408	14	∥φw	∥φw	PROPN
ejpam-5455	408	15	−	−	PROPN
ejpam-5455	408	16	φw∗∥	φw∗∥	NOUN
ejpam-5455	408	17	=	=	SYM
ejpam-5455	408	18	max	max	PROPN
ejpam-5455	408	19	7∈ω	7∈ω	PROPN
ejpam-5455	408	20	|((a+b)w)(7)−	|((a+b)w)(7)−	PROPN
ejpam-5455	408	21	(	(	PUNCT
ejpam-5455	408	22	(	(	PUNCT
ejpam-5455	408	23	a+b)w)(7)|	a+b)w)(7)|	ADJ
ejpam-5455	408	24	≤	≤	NUM
ejpam-5455	408	25	max	max	PROPN
ejpam-5455	408	26	7∈ω	7∈ω	PROPN
ejpam-5455	408	27	|(aw)(7)−	|(aw)(7)−	PROPN
ejpam-5455	408	28	(	(	PUNCT
ejpam-5455	408	29	aw)(7)|+max	aw)(7)|+max	ADP
ejpam-5455	408	30	7∈ω	7∈ω	NOUN
ejpam-5455	409	1	|(bw)(7)−	|(bw)(7)−	PROPN
ejpam-5455	409	2	(	(	PUNCT
ejpam-5455	409	3	bw)(7)|	bw)(7)|	PROPN
ejpam-5455	409	4	.	.	PUNCT
ejpam-5455	410	1	in	in	ADP
ejpam-5455	410	2	view	view	NOUN
ejpam-5455	410	3	of	of	ADP
ejpam-5455	410	4	theorem	theorem	NOUN
ejpam-5455	410	5	1	1	NUM
ejpam-5455	410	6	,	,	PUNCT
ejpam-5455	410	7	we	we	PRON
ejpam-5455	410	8	have	have	AUX
ejpam-5455	410	9	∥φw	∥φw	PROPN
ejpam-5455	410	10	−	−	PROPN
ejpam-5455	410	11	φw∗∥	φw∗∥	NOUN
ejpam-5455	410	12	≤	≤	NOUN
ejpam-5455	411	1	[	[	X
ejpam-5455	411	2	(	(	PUNCT
ejpam-5455	411	3	lqz	lqz	NOUN
ejpam-5455	411	4	+	+	CCONJ
ejpam-5455	411	5	|q(0)|+	|q(0)|+	NUM
ejpam-5455	411	6	zγ∥f∥l1	zγ∥f∥l1	NUM
ejpam-5455	411	7	γ(γ	γ(γ	X
ejpam-5455	411	8	+	+	CCONJ
ejpam-5455	411	9	1	1	NUM
ejpam-5455	411	10	)	)	PUNCT
ejpam-5455	411	11	)	)	PUNCT
ejpam-5455	412	1	(	(	PUNCT
ejpam-5455	412	2	(	(	PUNCT
ejpam-5455	412	3	q	q	NOUN
ejpam-5455	412	4	−	−	PROPN
ejpam-5455	412	5	1)mq−2zβ	1)mq−2zβ	NUM
ejpam-5455	412	6	b(ρ)γ(β	b(ρ)γ(β	NOUN
ejpam-5455	412	7	+	+	NOUN
ejpam-5455	412	8	1	1	X
ejpam-5455	412	9	)	)	PUNCT
ejpam-5455	412	10	{	{	PUNCT
ejpam-5455	412	11	1−	1−	NUM
ejpam-5455	412	12	ρ+	ρ+	NOUN
ejpam-5455	412	13	zρ	zρ	X
ejpam-5455	412	14	γ(ρ	γ(ρ	PROPN
ejpam-5455	412	15	)	)	PUNCT
ejpam-5455	412	16	}	}	PUNCT
ejpam-5455	412	17	lg	lg	NOUN
ejpam-5455	412	18	)	)	PUNCT
ejpam-5455	413	1	+	+	CCONJ
ejpam-5455	413	2	(	(	PUNCT
ejpam-5455	413	3	abiρ0	abiρ0	NOUN
ejpam-5455	413	4	+	+	X
ejpam-5455	413	5	|θ|+	|θ|+	ADV
ejpam-5455	413	6	1	1	NUM
ejpam-5455	413	7	b(ρ	b(ρ	NOUN
ejpam-5455	413	8	)	)	PUNCT
ejpam-5455	413	9	(	(	PUNCT
ejpam-5455	413	10	zβ∥g∥l1	zβ∥g∥l1	X
ejpam-5455	413	11	γ(β	γ(β	PROPN
ejpam-5455	413	12	+	+	CCONJ
ejpam-5455	413	13	1	1	NUM
ejpam-5455	413	14	)	)	PUNCT
ejpam-5455	413	15	)	)	PUNCT
ejpam-5455	414	1	q−1	q−1	PROPN
ejpam-5455	414	2	{	{	PUNCT
ejpam-5455	414	3	1−	1−	NUM
ejpam-5455	414	4	ρ+	ρ+	NUM
ejpam-5455	414	5	zρ	zρ	X
ejpam-5455	414	6	γ(ρ	γ(ρ	PROPN
ejpam-5455	414	7	)	)	PUNCT
ejpam-5455	414	8	}	}	PUNCT
ejpam-5455	414	9	)	)	PUNCT
ejpam-5455	414	10	(	(	PUNCT
ejpam-5455	414	11	lfz	lfz	NOUN
ejpam-5455	414	12	γ	γ	X
ejpam-5455	414	13	γ(γ	γ(γ	PROPN
ejpam-5455	414	14	+	+	CCONJ
ejpam-5455	414	15	1	1	NUM
ejpam-5455	414	16	)	)	PUNCT
ejpam-5455	414	17	)	)	PUNCT
ejpam-5455	415	1	+	+	CCONJ
ejpam-5455	416	1	lh	lh	X
ejpam-5455	416	2	]	]	PUNCT
ejpam-5455	417	1	∥w	∥w	PROPN
ejpam-5455	417	2	−	−	PROPN
ejpam-5455	417	3	w∗∥	w∗∥	PROPN
ejpam-5455	417	4	=	=	SYM
ejpam-5455	417	5	∆∥w	∆∥w	PROPN
ejpam-5455	417	6	−	−	PROPN
ejpam-5455	417	7	w∗∥.	w∗∥.	NOUN
ejpam-5455	417	8	(	(	PUNCT
ejpam-5455	417	9	23	23	NUM
ejpam-5455	417	10	)	)	PUNCT
ejpam-5455	417	11	for	for	ADP
ejpam-5455	417	12	∆	∆	PROPN
ejpam-5455	417	13	<	<	X
ejpam-5455	417	14	1	1	NUM
ejpam-5455	417	15	,	,	PUNCT
ejpam-5455	417	16	by	by	ADP
ejpam-5455	417	17	(	(	PUNCT
ejpam-5455	417	18	21)-(23	21)-(23	NOUN
ejpam-5455	417	19	)	)	PUNCT
ejpam-5455	417	20	,	,	PUNCT
ejpam-5455	417	21	consider	consider	VERB
ejpam-5455	417	22	the	the	DET
ejpam-5455	417	23	following	follow	VERB
ejpam-5455	417	24	norm	norm	NOUN
ejpam-5455	417	25	∥w	∥w	PROPN
ejpam-5455	417	26	−	−	PROPN
ejpam-5455	417	27	w∗∥	w∗∥	PROPN
ejpam-5455	417	28	=	=	SYM
ejpam-5455	417	29	∥w	∥w	PROPN
ejpam-5455	417	30	−	−	PROPN
ejpam-5455	417	31	φw	φw	NOUN
ejpam-5455	417	32	+	+	PROPN
ejpam-5455	417	33	φw	φw	PROPN
ejpam-5455	417	34	−	−	PROPN
ejpam-5455	417	35	w∗∥	w∗∥	PROPN
ejpam-5455	417	36	m.	m.	NOUN
ejpam-5455	417	37	m.	m.	NOUN
ejpam-5455	417	38	arjunan	arjunan	PROPN
ejpam-5455	417	39	/	/	SYM
ejpam-5455	417	40	eur	eur	PROPN
ejpam-5455	417	41	.	.	PUNCT
ejpam-5455	418	1	j.	j.	PROPN
ejpam-5455	418	2	pure	pure	PROPN
ejpam-5455	418	3	appl	appl	PROPN
ejpam-5455	418	4	.	.	PROPN
ejpam-5455	418	5	math	math	PROPN
ejpam-5455	418	6	,	,	PUNCT
ejpam-5455	418	7	17	17	NUM
ejpam-5455	418	8	(	(	PUNCT
ejpam-5455	418	9	4	4	NUM
ejpam-5455	418	10	)	)	PUNCT
ejpam-5455	418	11	(	(	PUNCT
ejpam-5455	418	12	2024	2024	NUM
ejpam-5455	418	13	)	)	PUNCT
ejpam-5455	418	14	,	,	PUNCT
ejpam-5455	418	15	4071	4071	NUM
ejpam-5455	418	16	-	-	SYM
ejpam-5455	418	17	4092	4092	NUM
ejpam-5455	418	18	4089	4089	NUM
ejpam-5455	418	19	≤	≤	NOUN
ejpam-5455	419	1	∥w	∥w	PROPN
ejpam-5455	419	2	−	−	NOUN
ejpam-5455	419	3	φw∥+	φw∥+	PRON
ejpam-5455	419	4	∥φw	∥φw	PROPN
ejpam-5455	419	5	−	−	PROPN
ejpam-5455	419	6	φw∗∥	φw∗∥	PROPN
ejpam-5455	419	7	≤	≤	NUM
ejpam-5455	419	8	ϑ+∆∥w	ϑ+∆∥w	NOUN
ejpam-5455	419	9	−	−	NOUN
ejpam-5455	419	10	w∗∥.	w∗∥.	NOUN
ejpam-5455	419	11	hence	hence	ADV
ejpam-5455	419	12	∥w	∥w	PROPN
ejpam-5455	419	13	−	−	PROPN
ejpam-5455	419	14	w∗∥	w∗∥	PROPN
ejpam-5455	419	15	≤	≤	NOUN
ejpam-5455	419	16	ϑ	ϑ	PRON
ejpam-5455	419	17	1−∆	1−∆	NUM
ejpam-5455	419	18	with	with	ADP
ejpam-5455	419	19	λ	λ	PROPN
ejpam-5455	419	20	=	=	PROPN
ejpam-5455	419	21	1	1	NUM
ejpam-5455	419	22	1−∆	1−∆	NUM
ejpam-5455	419	23	.	.	PUNCT
ejpam-5455	420	1	hence	hence	ADV
ejpam-5455	420	2	(	(	PUNCT
ejpam-5455	420	3	11	11	NUM
ejpam-5455	420	4	)	)	PUNCT
ejpam-5455	420	5	is	be	AUX
ejpam-5455	420	6	stable	stable	ADJ
ejpam-5455	420	7	.	.	PUNCT
ejpam-5455	421	1	this	this	PRON
ejpam-5455	421	2	implies	imply	VERB
ejpam-5455	421	3	the	the	DET
ejpam-5455	421	4	stability	stability	NOUN
ejpam-5455	421	5	of	of	ADP
ejpam-5455	421	6	the	the	DET
ejpam-5455	421	7	addressing	address	VERB
ejpam-5455	421	8	system	system	NOUN
ejpam-5455	421	9	represented	represent	VERB
ejpam-5455	421	10	by	by	ADP
ejpam-5455	421	11	(	(	PUNCT
ejpam-5455	421	12	1	1	NUM
ejpam-5455	421	13	)	)	PUNCT
ejpam-5455	421	14	.	.	PUNCT
ejpam-5455	422	1	5	5	X
ejpam-5455	422	2	.	.	NOUN
ejpam-5455	422	3	example	example	NOUN
ejpam-5455	422	4	in	in	ADP
ejpam-5455	422	5	this	this	DET
ejpam-5455	422	6	section	section	NOUN
ejpam-5455	422	7	,	,	PUNCT
ejpam-5455	422	8	we	we	PRON
ejpam-5455	422	9	will	will	AUX
ejpam-5455	422	10	provide	provide	VERB
ejpam-5455	422	11	a	a	DET
ejpam-5455	422	12	justification	justification	NOUN
ejpam-5455	422	13	for	for	ADP
ejpam-5455	422	14	our	our	PRON
ejpam-5455	422	15	findings	finding	NOUN
ejpam-5455	422	16	by	by	ADP
ejpam-5455	422	17	presenting	present	VERB
ejpam-5455	422	18	an	an	DET
ejpam-5455	422	19	illustrative	illustrative	ADJ
ejpam-5455	422	20	example	example	NOUN
ejpam-5455	422	21	.	.	PUNCT
ejpam-5455	423	1	consider	consider	VERB
ejpam-5455	423	2	the	the	DET
ejpam-5455	423	3	given	give	VERB
ejpam-5455	423	4	mabc	mabc	PROPN
ejpam-5455	423	5	-	-	PUNCT
ejpam-5455	423	6	hfides	hfides	PROPN
ejpam-5455	423	7	cdβ	cdβ	PROPN
ejpam-5455	423	8	ψp	ψp	NOUN
ejpam-5455	423	9	mabcdρ	mabcdρ	NOUN
ejpam-5455	423	10	0	0	PUNCT
ejpam-5455	423	11	+	+	NUM
ejpam-5455	423	12			NUM
ejpam-5455	423	13	w(7)−	w(7)−	NOUN
ejpam-5455	423	14	1	1	NUM
ejpam-5455	423	15	16	16	NUM
ejpam-5455	423	16	sinw(7	sinw(7	NOUN
ejpam-5455	423	17	)	)	PUNCT
ejpam-5455	423	18	π+sin	π+sin	PUNCT
ejpam-5455	423	19	7	7	NUM
ejpam-5455	423	20	+	+	SYM
ejpam-5455	423	21	1	1	NUM
ejpam-5455	423	22	γ	γ	X
ejpam-5455	423	23	(	(	PUNCT
ejpam-5455	423	24	1	1	NUM
ejpam-5455	423	25	3	3	NUM
ejpam-5455	423	26	)	)	PUNCT
ejpam-5455	423	27	∫	∫	PROPN
ejpam-5455	423	28	7	7	NUM
ejpam-5455	423	29	0	0	NUM
ejpam-5455	423	30	(	(	PUNCT
ejpam-5455	423	31	7	7	NUM
ejpam-5455	423	32	−	−	PROPN
ejpam-5455	423	33	σ)−	σ)−	PROPN
ejpam-5455	423	34	2	2	NUM
ejpam-5455	423	35	3	3	NUM
ejpam-5455	423	36	1	1	NUM
ejpam-5455	423	37	σ	σ	NOUN
ejpam-5455	423	38	+	+	CCONJ
ejpam-5455	423	39	25	25	NUM
ejpam-5455	423	40	sinw(σ)dσ	sinw(σ)dσ	NOUN
ejpam-5455	423	41			NOUN
ejpam-5455	423	42			NOUN
ejpam-5455	423	43			NOUN
ejpam-5455	423	44	=	=	NOUN
ejpam-5455	423	45	1	1	NUM
ejpam-5455	423	46	7	7	NUM
ejpam-5455	423	47	+	+	NUM
ejpam-5455	423	48	36	36	NUM
ejpam-5455	423	49	cosw(7	cosw(7	NOUN
ejpam-5455	423	50	)	)	PUNCT
ejpam-5455	423	51	,	,	PUNCT
ejpam-5455	424	1	7	7	NUM
ejpam-5455	424	2	∈	∈	NOUN
ejpam-5455	424	3	[	[	X
ejpam-5455	424	4	0	0	NUM
ejpam-5455	424	5	,	,	PUNCT
ejpam-5455	424	6	1	1	NUM
ejpam-5455	424	7	]	]	PUNCT
ejpam-5455	424	8	,	,	PUNCT
ejpam-5455	424	9	w(0	w(0	PROPN
ejpam-5455	424	10	)	)	PUNCT
ejpam-5455	424	11	=	=	SYM
ejpam-5455	424	12	1	1	NUM
ejpam-5455	424	13	16	16	NUM
ejpam-5455	424	14	sinw(0	sinw(0	PROPN
ejpam-5455	424	15	)	)	PUNCT
ejpam-5455	425	1	+	+	CCONJ
ejpam-5455	426	1	π	π	X
ejpam-5455	426	2	.	.	PUNCT
ejpam-5455	427	1	(	(	PUNCT
ejpam-5455	427	2	24	24	NUM
ejpam-5455	427	3	)	)	PUNCT
ejpam-5455	427	4	set	set	VERB
ejpam-5455	427	5	β	β	X
ejpam-5455	427	6	=	=	NOUN
ejpam-5455	427	7	1	1	NUM
ejpam-5455	427	8	4	4	NUM
ejpam-5455	427	9	,	,	PUNCT
ejpam-5455	427	10	ρ	ρ	PROPN
ejpam-5455	427	11	=	=	SYM
ejpam-5455	427	12	1	1	NUM
ejpam-5455	427	13	2	2	NUM
ejpam-5455	427	14	,	,	PUNCT
ejpam-5455	427	15	γ	γ	NOUN
ejpam-5455	427	16	=	=	SYM
ejpam-5455	427	17	1	1	NUM
ejpam-5455	427	18	3	3	NUM
ejpam-5455	427	19	,	,	PUNCT
ejpam-5455	427	20	z	z	NOUN
ejpam-5455	427	21	=	=	SYM
ejpam-5455	427	22	1	1	NUM
ejpam-5455	427	23	,	,	PUNCT
ejpam-5455	427	24	lq	lq	VERB
ejpam-5455	427	25	=	=	PUNCT
ejpam-5455	427	26	1,θ	1,θ	NUM
ejpam-5455	427	27	=	=	SYM
ejpam-5455	427	28	0.735,abiρ0+θ	0.735,abiρ0+θ	NUM
ejpam-5455	427	29	=	=	SYM
ejpam-5455	427	30	1	1	NUM
ejpam-5455	427	31	,	,	PUNCT
ejpam-5455	427	32	p	p	NOUN
ejpam-5455	427	33	=	=	X
ejpam-5455	427	34	q	q	NOUN
ejpam-5455	427	35	=	=	SYM
ejpam-5455	427	36	2,m	2,m	NOUN
ejpam-5455	427	37	=	=	SYM
ejpam-5455	427	38	1,b(ρ	1,b(ρ	NUM
ejpam-5455	427	39	)	)	PUNCT
ejpam-5455	427	40	=	=	SYM
ejpam-5455	428	1	1−	1−	NUM
ejpam-5455	428	2	ρ+	ρ+	NUM
ejpam-5455	428	3	ρ	ρ	PROPN
ejpam-5455	428	4	γ(ρ	γ(ρ	PROPN
ejpam-5455	428	5	)	)	PUNCT
ejpam-5455	428	6	,	,	PUNCT
ejpam-5455	429	1	h(7	h(7	PROPN
ejpam-5455	429	2	,	,	PUNCT
ejpam-5455	429	3	w(7	w(7	PROPN
ejpam-5455	429	4	)	)	PUNCT
ejpam-5455	429	5	)	)	PUNCT
ejpam-5455	429	6	=	=	PUNCT
ejpam-5455	429	7	1	1	NUM
ejpam-5455	429	8	16	16	NUM
ejpam-5455	429	9	sinw(7	sinw(7	NOUN
ejpam-5455	429	10	)	)	PUNCT
ejpam-5455	429	11	,	,	PUNCT
ejpam-5455	429	12	q(7	q(7	PROPN
ejpam-5455	429	13	)	)	PUNCT
ejpam-5455	429	14	=	=	PUNCT
ejpam-5455	430	1	π	π	X
ejpam-5455	430	2	+	+	CCONJ
ejpam-5455	430	3	sin	sin	NOUN
ejpam-5455	430	4	7	7	NUM
ejpam-5455	430	5	,	,	PUNCT
ejpam-5455	430	6	q(0	q(0	PROPN
ejpam-5455	430	7	)	)	PUNCT
ejpam-5455	430	8	=	=	SYM
ejpam-5455	430	9	π	π	PROPN
ejpam-5455	430	10	,	,	PUNCT
ejpam-5455	430	11	f(7	f(7	NOUN
ejpam-5455	430	12	,	,	PUNCT
ejpam-5455	430	13	w(7	w(7	PROPN
ejpam-5455	430	14	)	)	PUNCT
ejpam-5455	430	15	)	)	PUNCT
ejpam-5455	431	1	=	=	PUNCT
ejpam-5455	431	2	1	1	NUM
ejpam-5455	431	3	7	7	NUM
ejpam-5455	431	4	+	+	CCONJ
ejpam-5455	431	5	25	25	NUM
ejpam-5455	431	6	sinw(7	sinw(7	NOUN
ejpam-5455	431	7	)	)	PUNCT
ejpam-5455	431	8	,	,	PUNCT
ejpam-5455	431	9	g(7	g(7	PROPN
ejpam-5455	431	10	,	,	PUNCT
ejpam-5455	431	11	w(7	w(7	PROPN
ejpam-5455	431	12	)	)	PUNCT
ejpam-5455	431	13	)	)	PUNCT
ejpam-5455	431	14	=	=	PUNCT
ejpam-5455	432	1	1	1	NUM
ejpam-5455	432	2	7	7	NUM
ejpam-5455	432	3	+	+	NUM
ejpam-5455	432	4	36	36	NUM
ejpam-5455	432	5	cosw(7	cosw(7	NOUN
ejpam-5455	432	6	)	)	PUNCT
ejpam-5455	432	7	.	.	PUNCT
ejpam-5455	433	1	let	let	VERB
ejpam-5455	433	2	w	w	X
ejpam-5455	433	3	,	,	PUNCT
ejpam-5455	433	4	w	w	PROPN
ejpam-5455	433	5	∈	∈	NOUN
ejpam-5455	433	6	ac([0	ac([0	NOUN
ejpam-5455	433	7	,	,	PUNCT
ejpam-5455	433	8	1	1	NUM
ejpam-5455	433	9	]	]	PUNCT
ejpam-5455	433	10	)	)	PUNCT
ejpam-5455	433	11	.	.	PUNCT
ejpam-5455	434	1	then	then	ADV
ejpam-5455	434	2	,	,	PUNCT
ejpam-5455	434	3	we	we	PRON
ejpam-5455	434	4	have	have	VERB
ejpam-5455	434	5	|f(7	|f(7	ADV
ejpam-5455	434	6	,	,	PUNCT
ejpam-5455	434	7	w(7))−	w(7))−	NOUN
ejpam-5455	434	8	f(7	f(7	NOUN
ejpam-5455	434	9	,	,	PUNCT
ejpam-5455	434	10	w(7))|	w(7))|	NOUN
ejpam-5455	434	11	≤	≤	NUM
ejpam-5455	434	12	1	1	NUM
ejpam-5455	434	13	26	26	NUM
ejpam-5455	434	14	|w(7)−	|w(7)−	PROPN
ejpam-5455	434	15	w(7)|	w(7)|	PROPN
ejpam-5455	434	16	,	,	PUNCT
ejpam-5455	434	17	|g(7	|g(7	NOUN
ejpam-5455	434	18	,	,	PUNCT
ejpam-5455	434	19	w(7))−	w(7))−	PROPN
ejpam-5455	434	20	g(7	g(7	PROPN
ejpam-5455	434	21	,	,	PUNCT
ejpam-5455	434	22	w(7))|	w(7))|	VERB
ejpam-5455	434	23	≤	≤	NUM
ejpam-5455	434	24	1	1	NUM
ejpam-5455	434	25	37	37	NUM
ejpam-5455	434	26	|w(7)−	|w(7)−	PROPN
ejpam-5455	434	27	w(7)|	w(7)|	PROPN
ejpam-5455	434	28	,	,	PUNCT
ejpam-5455	434	29	and	and	CCONJ
ejpam-5455	434	30	|h(7	|h(7	NUM
ejpam-5455	434	31	,	,	PUNCT
ejpam-5455	434	32	w(7))−	w(7))−	PROPN
ejpam-5455	434	33	h(7	h(7	PROPN
ejpam-5455	434	34	,	,	PUNCT
ejpam-5455	434	35	w(7))|	w(7))|	NOUN
ejpam-5455	434	36	≤	≤	NUM
ejpam-5455	434	37	1	1	NUM
ejpam-5455	434	38	16	16	NUM
ejpam-5455	434	39	|w(7)−	|w(7)−	PROPN
ejpam-5455	434	40	w(7)|	w(7)|	PROPN
ejpam-5455	434	41	.	.	PUNCT
ejpam-5455	435	1	then	then	ADV
ejpam-5455	435	2	the	the	DET
ejpam-5455	435	3	assumptions	assumption	NOUN
ejpam-5455	435	4	(	(	PUNCT
ejpam-5455	435	5	a1)-(a3	a1)-(a3	NOUN
ejpam-5455	435	6	)	)	PUNCT
ejpam-5455	435	7	holds	hold	VERB
ejpam-5455	435	8	with	with	ADP
ejpam-5455	435	9	lf	lf	NOUN
ejpam-5455	435	10	=	=	SYM
ejpam-5455	435	11	1	1	NUM
ejpam-5455	435	12	26	26	NUM
ejpam-5455	435	13	,	,	PUNCT
ejpam-5455	435	14	lg	lg	NOUN
ejpam-5455	435	15	=	=	PROPN
ejpam-5455	435	16	1	1	NUM
ejpam-5455	435	17	37	37	NUM
ejpam-5455	435	18	,	,	PUNCT
ejpam-5455	435	19	lh	lh	PROPN
ejpam-5455	435	20	=	=	NOUN
ejpam-5455	435	21	1	1	NUM
ejpam-5455	435	22	16	16	NUM
ejpam-5455	435	23	,	,	PUNCT
ejpam-5455	435	24	lq	lq	NOUN
ejpam-5455	435	25	=	=	NOUN
ejpam-5455	435	26	1	1	NUM
ejpam-5455	435	27	,	,	PUNCT
ejpam-5455	435	28	∥f∥l1	∥f∥l1	PROPN
ejpam-5455	436	1	=	=	SYM
ejpam-5455	436	2	ln	ln	PROPN
ejpam-5455	436	3	(	(	PUNCT
ejpam-5455	436	4	26	26	NUM
ejpam-5455	436	5	25	25	NUM
ejpam-5455	436	6	)	)	PUNCT
ejpam-5455	436	7	=	=	SYM
ejpam-5455	436	8	0.03922	0.03922	NUM
ejpam-5455	436	9	,	,	PUNCT
ejpam-5455	436	10	∥g∥l1	∥g∥l1	NOUN
ejpam-5455	436	11	=	=	SYM
ejpam-5455	436	12	ln	ln	NOUN
ejpam-5455	436	13	(	(	PUNCT
ejpam-5455	436	14	37	37	NUM
ejpam-5455	436	15	36	36	NUM
ejpam-5455	436	16	)	)	PUNCT
ejpam-5455	437	1	=	=	SYM
ejpam-5455	437	2	0.02731	0.02731	NUM
ejpam-5455	437	3	.	.	PUNCT
ejpam-5455	438	1	references	reference	NOUN
ejpam-5455	438	2	4090	4090	NUM
ejpam-5455	438	3	at	at	ADP
ejpam-5455	438	4	this	this	DET
ejpam-5455	438	5	point	point	NOUN
ejpam-5455	438	6	,	,	PUNCT
ejpam-5455	438	7	we	we	PRON
ejpam-5455	438	8	will	will	AUX
ejpam-5455	438	9	examine	examine	VERB
ejpam-5455	438	10	the	the	DET
ejpam-5455	438	11	conditions	condition	NOUN
ejpam-5455	438	12	outlined	outline	VERB
ejpam-5455	438	13	in	in	ADP
ejpam-5455	438	14	the	the	DET
ejpam-5455	438	15	theorems	theorem	NOUN
ejpam-5455	438	16	to	to	PART
ejpam-5455	438	17	ensure	ensure	VERB
ejpam-5455	438	18	they	they	PRON
ejpam-5455	438	19	are	be	AUX
ejpam-5455	438	20	satisfied	satisfied	ADJ
ejpam-5455	438	21	.	.	PUNCT
ejpam-5455	439	1	by	by	ADP
ejpam-5455	439	2	carefully	carefully	ADV
ejpam-5455	439	3	analyzing	analyze	VERB
ejpam-5455	439	4	these	these	DET
ejpam-5455	439	5	conditions	condition	NOUN
ejpam-5455	439	6	,	,	PUNCT
ejpam-5455	439	7	we	we	PRON
ejpam-5455	439	8	can	can	AUX
ejpam-5455	439	9	derive	derive	VERB
ejpam-5455	439	10	the	the	DET
ejpam-5455	439	11	necessary	necessary	ADJ
ejpam-5455	439	12	conclusions	conclusion	NOUN
ejpam-5455	439	13	and	and	CCONJ
ejpam-5455	439	14	results	result	NOUN
ejpam-5455	439	15	that	that	PRON
ejpam-5455	439	16	follow	follow	VERB
ejpam-5455	439	17	from	from	ADP
ejpam-5455	439	18	them	they	PRON
ejpam-5455	439	19	.	.	PUNCT
ejpam-5455	440	1	this	this	DET
ejpam-5455	440	2	thorough	thorough	ADJ
ejpam-5455	440	3	verification	verification	NOUN
ejpam-5455	440	4	process	process	NOUN
ejpam-5455	440	5	will	will	AUX
ejpam-5455	440	6	allow	allow	VERB
ejpam-5455	440	7	us	we	PRON
ejpam-5455	440	8	to	to	PART
ejpam-5455	440	9	confirm	confirm	VERB
ejpam-5455	440	10	the	the	DET
ejpam-5455	440	11	validity	validity	NOUN
ejpam-5455	440	12	of	of	ADP
ejpam-5455	440	13	our	our	PRON
ejpam-5455	440	14	findings	finding	NOUN
ejpam-5455	440	15	.	.	PUNCT
ejpam-5455	441	1	now	now	ADV
ejpam-5455	441	2	λ	λ	X
ejpam-5455	441	3	=	=	PUNCT
ejpam-5455	442	1	[	[	X
ejpam-5455	442	2	(	(	PUNCT
ejpam-5455	442	3	lqz	lqz	NOUN
ejpam-5455	442	4	+	+	CCONJ
ejpam-5455	442	5	|q(0)|+	|q(0)|+	NUM
ejpam-5455	442	6	zγ∥f∥l1	zγ∥f∥l1	NUM
ejpam-5455	442	7	γ(γ	γ(γ	X
ejpam-5455	442	8	+	+	CCONJ
ejpam-5455	442	9	1	1	NUM
ejpam-5455	442	10	)	)	PUNCT
ejpam-5455	442	11	)	)	PUNCT
ejpam-5455	442	12	(	(	PUNCT
ejpam-5455	442	13	(	(	PUNCT
ejpam-5455	442	14	q	q	NOUN
ejpam-5455	442	15	−	−	PROPN
ejpam-5455	442	16	1)mq−2zβ	1)mq−2zβ	NUM
ejpam-5455	442	17	b(ρ)γ(β	b(ρ)γ(β	NOUN
ejpam-5455	442	18	+	+	NOUN
ejpam-5455	442	19	1	1	X
ejpam-5455	442	20	)	)	PUNCT
ejpam-5455	442	21	{	{	PUNCT
ejpam-5455	442	22	1−	1−	NUM
ejpam-5455	442	23	ρ+	ρ+	NOUN
ejpam-5455	442	24	zρ	zρ	X
ejpam-5455	442	25	γ(ρ	γ(ρ	PROPN
ejpam-5455	442	26	)	)	PUNCT
ejpam-5455	442	27	}	}	PUNCT
ejpam-5455	442	28	lg	lg	NOUN
ejpam-5455	442	29	)	)	PUNCT
ejpam-5455	443	1	+	+	CCONJ
ejpam-5455	443	2	(	(	PUNCT
ejpam-5455	443	3	abiρ0	abiρ0	NOUN
ejpam-5455	443	4	+	+	X
ejpam-5455	443	5	|θ|+	|θ|+	ADV
ejpam-5455	443	6	1	1	NUM
ejpam-5455	443	7	b(ρ	b(ρ	NOUN
ejpam-5455	443	8	)	)	PUNCT
ejpam-5455	443	9	(	(	PUNCT
ejpam-5455	443	10	zβ∥g∥l1	zβ∥g∥l1	X
ejpam-5455	443	11	γ(β	γ(β	PROPN
ejpam-5455	443	12	+	+	CCONJ
ejpam-5455	443	13	1	1	NUM
ejpam-5455	443	14	)	)	PUNCT
ejpam-5455	443	15	)	)	PUNCT
ejpam-5455	444	1	q−1	q−1	PROPN
ejpam-5455	444	2	{	{	PUNCT
ejpam-5455	444	3	1−	1−	NUM
ejpam-5455	444	4	ρ+	ρ+	NUM
ejpam-5455	444	5	zρ	zρ	X
ejpam-5455	444	6	γ(ρ	γ(ρ	PROPN
ejpam-5455	444	7	)	)	PUNCT
ejpam-5455	444	8	}	}	PUNCT
ejpam-5455	444	9	)	)	PUNCT
ejpam-5455	444	10	(	(	PUNCT
ejpam-5455	444	11	lfz	lfz	NOUN
ejpam-5455	444	12	γ	γ	X
ejpam-5455	444	13	γ(γ	γ(γ	PROPN
ejpam-5455	444	14	+	+	CCONJ
ejpam-5455	444	15	1	1	NUM
ejpam-5455	444	16	)	)	PUNCT
ejpam-5455	444	17	)	)	PUNCT
ejpam-5455	445	1	+	+	CCONJ
ejpam-5455	445	2	lh	lh	X
ejpam-5455	445	3	]	]	PUNCT
ejpam-5455	445	4	=	=	PUNCT
ejpam-5455	446	1	0.2782	0.2782	NUM
ejpam-5455	446	2	<	<	X
ejpam-5455	446	3	1	1	NUM
ejpam-5455	446	4	.	.	PUNCT
ejpam-5455	447	1	consequently	consequently	ADV
ejpam-5455	447	2	,	,	PUNCT
ejpam-5455	447	3	we	we	PRON
ejpam-5455	447	4	have	have	AUX
ejpam-5455	447	5	established	establish	VERB
ejpam-5455	447	6	that	that	SCONJ
ejpam-5455	447	7	the	the	DET
ejpam-5455	447	8	conditions	condition	NOUN
ejpam-5455	447	9	specified	specify	VERB
ejpam-5455	447	10	in	in	ADP
ejpam-5455	447	11	theorem	theorem	ADJ
ejpam-5455	447	12	1	1	NUM
ejpam-5455	447	13	are	be	AUX
ejpam-5455	447	14	indeed	indeed	ADV
ejpam-5455	447	15	met	meet	VERB
ejpam-5455	447	16	.	.	PUNCT
ejpam-5455	448	1	as	as	ADP
ejpam-5455	448	2	a	a	DET
ejpam-5455	448	3	result	result	NOUN
ejpam-5455	448	4	of	of	ADP
ejpam-5455	448	5	this	this	DET
ejpam-5455	448	6	verification	verification	NOUN
ejpam-5455	448	7	,	,	PUNCT
ejpam-5455	448	8	we	we	PRON
ejpam-5455	448	9	can	can	AUX
ejpam-5455	448	10	confidently	confidently	ADV
ejpam-5455	448	11	conclude	conclude	VERB
ejpam-5455	448	12	that	that	DET
ejpam-5455	448	13	problem	problem	NOUN
ejpam-5455	448	14	(	(	PUNCT
ejpam-5455	448	15	24	24	NUM
ejpam-5455	448	16	)	)	PUNCT
ejpam-5455	448	17	possesses	possess	VERB
ejpam-5455	448	18	a	a	DET
ejpam-5455	448	19	unique	unique	ADJ
ejpam-5455	448	20	solution	solution	NOUN
ejpam-5455	448	21	.	.	PUNCT
ejpam-5455	449	1	next	next	ADV
ejpam-5455	449	2	,	,	PUNCT
ejpam-5455	449	3	lh	lh	PROPN
ejpam-5455	449	4	=	=	PROPN
ejpam-5455	450	1	0.0625	0.0625	NUM
ejpam-5455	450	2	<	<	X
ejpam-5455	450	3	1	1	NUM
ejpam-5455	450	4	.	.	PUNCT
ejpam-5455	451	1	therefore	therefore	ADV
ejpam-5455	451	2	,	,	PUNCT
ejpam-5455	451	3	we	we	PRON
ejpam-5455	451	4	can	can	AUX
ejpam-5455	451	5	confirm	confirm	VERB
ejpam-5455	451	6	that	that	SCONJ
ejpam-5455	451	7	the	the	DET
ejpam-5455	451	8	criteria	criterion	NOUN
ejpam-5455	451	9	outlined	outline	VERB
ejpam-5455	451	10	in	in	ADP
ejpam-5455	451	11	theorem	theorem	ADJ
ejpam-5455	451	12	2	2	NUM
ejpam-5455	451	13	are	be	AUX
ejpam-5455	451	14	also	also	ADV
ejpam-5455	451	15	fulfilled	fulfil	VERB
ejpam-5455	451	16	.	.	PUNCT
ejpam-5455	452	1	this	this	DET
ejpam-5455	452	2	affirmation	affirmation	NOUN
ejpam-5455	452	3	leads	lead	VERB
ejpam-5455	452	4	us	we	PRON
ejpam-5455	452	5	to	to	PART
ejpam-5455	452	6	conclude	conclude	VERB
ejpam-5455	452	7	that	that	SCONJ
ejpam-5455	452	8	the	the	DET
ejpam-5455	452	9	problem	problem	NOUN
ejpam-5455	452	10	presented	present	VERB
ejpam-5455	452	11	in	in	ADP
ejpam-5455	452	12	equation	equation	NOUN
ejpam-5455	452	13	(	(	PUNCT
ejpam-5455	452	14	24	24	NUM
ejpam-5455	452	15	)	)	PUNCT
ejpam-5455	452	16	has	have	VERB
ejpam-5455	452	17	at	at	ADV
ejpam-5455	452	18	least	least	ADV
ejpam-5455	452	19	one	one	NUM
ejpam-5455	452	20	solution	solution	NOUN
ejpam-5455	452	21	.	.	PUNCT
ejpam-5455	453	1	also	also	ADV
ejpam-5455	453	2	1−	1−	NUM
ejpam-5455	453	3	0.2782	0.2782	NUM
ejpam-5455	453	4	=	=	SYM
ejpam-5455	453	5	0.7218	0.7218	NUM
ejpam-5455	453	6	̸=	̸=	PROPN
ejpam-5455	453	7	0	0	NUM
ejpam-5455	453	8	.	.	PUNCT
ejpam-5455	454	1	thus	thus	ADV
ejpam-5455	454	2	(	(	PUNCT
ejpam-5455	454	3	24	24	NUM
ejpam-5455	454	4	)	)	PUNCT
ejpam-5455	454	5	is	be	AUX
ejpam-5455	454	6	u	u	NOUN
ejpam-5455	454	7	-	-	ADJ
ejpam-5455	454	8	h	h	ADV
ejpam-5455	454	9	stable	stable	ADJ
ejpam-5455	454	10	.	.	PUNCT
ejpam-5455	455	1	references	reference	NOUN
ejpam-5455	455	2	[	[	X
ejpam-5455	455	3	1	1	NUM
ejpam-5455	455	4	]	]	PUNCT
ejpam-5455	455	5	b.	b.	PROPN
ejpam-5455	455	6	ahmad	ahmad	PROPN
ejpam-5455	455	7	and	and	CCONJ
ejpam-5455	455	8	s.	s.	PROPN
ejpam-5455	455	9	k.	k.	PROPN
ejpam-5455	455	10	ntouyas	ntouyas	PROPN
ejpam-5455	455	11	.	.	PUNCT
ejpam-5455	456	1	initial	initial	ADJ
ejpam-5455	456	2	-	-	PUNCT
ejpam-5455	456	3	value	value	NOUN
ejpam-5455	456	4	problems	problem	NOUN
ejpam-5455	456	5	for	for	ADP
ejpam-5455	456	6	hybrid	hybrid	ADJ
ejpam-5455	456	7	hadamard	hadamard	ADJ
ejpam-5455	456	8	fractional	fractional	ADJ
ejpam-5455	456	9	differential	differential	NOUN
ejpam-5455	456	10	equations	equation	NOUN
ejpam-5455	456	11	.	.	PUNCT
ejpam-5455	457	1	electronic	electronic	ADJ
ejpam-5455	457	2	journal	journal	NOUN
ejpam-5455	457	3	of	of	ADP
ejpam-5455	457	4	differential	differential	ADJ
ejpam-5455	457	5	equations	equation	NOUN
ejpam-5455	457	6	,	,	PUNCT
ejpam-5455	457	7	2014(161):1–8	2014(161):1–8	NUM
ejpam-5455	457	8	,	,	PUNCT
ejpam-5455	457	9	2014	2014	NUM
ejpam-5455	457	10	.	.	PUNCT
ejpam-5455	458	1	[	[	X
ejpam-5455	458	2	2	2	X
ejpam-5455	458	3	]	]	PUNCT
ejpam-5455	458	4	m.	m.	NOUN
ejpam-5455	458	5	al	al	PROPN
ejpam-5455	458	6	-	-	PUNCT
ejpam-5455	458	7	refai	refai	PROPN
ejpam-5455	458	8	and	and	CCONJ
ejpam-5455	458	9	d.	d.	PROPN
ejpam-5455	458	10	baleanu	baleanu	PROPN
ejpam-5455	458	11	.	.	PUNCT
ejpam-5455	459	1	on	on	ADP
ejpam-5455	459	2	an	an	DET
ejpam-5455	459	3	extension	extension	NOUN
ejpam-5455	459	4	of	of	ADP
ejpam-5455	459	5	the	the	DET
ejpam-5455	459	6	operator	operator	NOUN
ejpam-5455	459	7	with	with	ADP
ejpam-5455	459	8	mittag	mittag	ADJ
ejpam-5455	459	9	-	-	PUNCT
ejpam-5455	459	10	leffler	leffler	NOUN
ejpam-5455	459	11	kernel	kernel	NOUN
ejpam-5455	459	12	.	.	PUNCT
ejpam-5455	460	1	fractals	fractal	NOUN
ejpam-5455	460	2	,	,	PUNCT
ejpam-5455	460	3	30(5):2240129	30(5):2240129	NUM
ejpam-5455	460	4	,	,	PUNCT
ejpam-5455	460	5	2022	2022	NUM
ejpam-5455	460	6	.	.	PUNCT
ejpam-5455	461	1	[	[	X
ejpam-5455	461	2	3	3	X
ejpam-5455	461	3	]	]	X
ejpam-5455	461	4	s.	s.	PROPN
ejpam-5455	461	5	alshammari	alshammari	PROPN
ejpam-5455	461	6	,	,	PUNCT
ejpam-5455	461	7	m.	m.	NOUN
ejpam-5455	461	8	alshammari	alshammari	NOUN
ejpam-5455	461	9	,	,	PUNCT
ejpam-5455	461	10	and	and	CCONJ
ejpam-5455	461	11	m.	m.	NOUN
ejpam-5455	461	12	s.	s.	PROPN
ejpam-5455	461	13	abdo	abdo	PROPN
ejpam-5455	461	14	.	.	PUNCT
ejpam-5455	462	1	nonlocal	nonlocal	ADJ
ejpam-5455	462	2	hybrid	hybrid	ADJ
ejpam-5455	462	3	integro	integro	ADJ
ejpam-5455	462	4	-	-	PUNCT
ejpam-5455	462	5	differential	differential	NOUN
ejpam-5455	462	6	equations	equation	NOUN
ejpam-5455	462	7	involving	involve	VERB
ejpam-5455	462	8	atangana	atangana	PROPN
ejpam-5455	462	9	-	-	PUNCT
ejpam-5455	462	10	baleanu	baleanu	ADJ
ejpam-5455	462	11	fractional	fractional	ADJ
ejpam-5455	462	12	operators	operator	NOUN
ejpam-5455	462	13	.	.	PUNCT
ejpam-5455	463	1	journal	journal	NOUN
ejpam-5455	463	2	of	of	ADP
ejpam-5455	463	3	mathematics	mathematic	NOUN
ejpam-5455	463	4	,	,	PUNCT
ejpam-5455	463	5	2023	2023	NUM
ejpam-5455	463	6	:	:	PUNCT
ejpam-5455	463	7	article	article	NOUN
ejpam-5455	463	8	i	i	PROPN
ejpam-5455	463	9	d	d	PROPN
ejpam-5455	463	10	5891342	5891342	NUM
ejpam-5455	463	11	,	,	PUNCT
ejpam-5455	463	12	11	11	NUM
ejpam-5455	463	13	pages	page	NOUN
ejpam-5455	463	14	,	,	PUNCT
ejpam-5455	463	15	2023	2023	NUM
ejpam-5455	463	16	.	.	PUNCT
ejpam-5455	464	1	[	[	X
ejpam-5455	464	2	4	4	NUM
ejpam-5455	464	3	]	]	PUNCT
ejpam-5455	464	4	a.	a.	NOUN
ejpam-5455	464	5	atangana	atangana	PROPN
ejpam-5455	464	6	and	and	CCONJ
ejpam-5455	464	7	d.	d.	PROPN
ejpam-5455	464	8	baleanu	baleanu	PROPN
ejpam-5455	464	9	.	.	PUNCT
ejpam-5455	465	1	new	new	ADJ
ejpam-5455	465	2	fractional	fractional	ADJ
ejpam-5455	465	3	derivatives	derivative	NOUN
ejpam-5455	465	4	with	with	ADP
ejpam-5455	465	5	non	non	ADJ
ejpam-5455	465	6	-	-	ADJ
ejpam-5455	465	7	local	local	ADJ
ejpam-5455	465	8	and	and	CCONJ
ejpam-5455	465	9	nonsingular	nonsingular	ADJ
ejpam-5455	465	10	kernel	kernel	PROPN
ejpam-5455	465	11	:	:	PUNCT
ejpam-5455	465	12	theory	theory	NOUN
ejpam-5455	465	13	and	and	CCONJ
ejpam-5455	465	14	application	application	NOUN
ejpam-5455	465	15	to	to	PART
ejpam-5455	465	16	heat	heat	NOUN
ejpam-5455	465	17	transfer	transfer	NOUN
ejpam-5455	465	18	model	model	NOUN
ejpam-5455	465	19	.	.	PUNCT
ejpam-5455	466	1	thermal	thermal	ADJ
ejpam-5455	466	2	science	science	NOUN
ejpam-5455	466	3	,	,	PUNCT
ejpam-5455	466	4	20(2):763–769	20(2):763–769	NOUN
ejpam-5455	466	5	,	,	PUNCT
ejpam-5455	466	6	2016	2016	NUM
ejpam-5455	466	7	.	.	PUNCT
ejpam-5455	467	1	[	[	X
ejpam-5455	467	2	5	5	X
ejpam-5455	467	3	]	]	X
ejpam-5455	467	4	d.	d.	PROPN
ejpam-5455	467	5	baleanu	baleanu	PROPN
ejpam-5455	467	6	,	,	PUNCT
ejpam-5455	467	7	s.	s.	PROPN
ejpam-5455	467	8	etemad	etemad	PROPN
ejpam-5455	467	9	,	,	PUNCT
ejpam-5455	467	10	and	and	CCONJ
ejpam-5455	467	11	s.	s.	PROPN
ejpam-5455	467	12	rezapour	rezapour	PROPN
ejpam-5455	467	13	.	.	PUNCT
ejpam-5455	468	1	a	a	DET
ejpam-5455	468	2	hybrid	hybrid	ADJ
ejpam-5455	468	3	caputo	caputo	PROPN
ejpam-5455	468	4	fractional	fractional	NOUN
ejpam-5455	468	5	modeling	modeling	NOUN
ejpam-5455	468	6	for	for	ADP
ejpam-5455	468	7	thermostat	thermostat	NOUN
ejpam-5455	468	8	with	with	ADP
ejpam-5455	468	9	hybrid	hybrid	ADJ
ejpam-5455	468	10	boundary	boundary	ADJ
ejpam-5455	468	11	value	value	NOUN
ejpam-5455	468	12	conditions	condition	NOUN
ejpam-5455	468	13	.	.	PUNCT
ejpam-5455	469	1	boundary	boundary	ADJ
ejpam-5455	469	2	value	value	NOUN
ejpam-5455	469	3	problems	problem	NOUN
ejpam-5455	469	4	,	,	PUNCT
ejpam-5455	469	5	2020:1–16	2020:1–16	NOUN
ejpam-5455	469	6	,	,	PUNCT
ejpam-5455	469	7	2020	2020	NUM
ejpam-5455	469	8	.	.	PUNCT
ejpam-5455	470	1	[	[	X
ejpam-5455	470	2	6	6	NUM
ejpam-5455	470	3	]	]	X
ejpam-5455	470	4	d.	d.	PROPN
ejpam-5455	470	5	baleanu	baleanu	PROPN
ejpam-5455	470	6	,	,	PUNCT
ejpam-5455	470	7	j.	j.	PROPN
ejpam-5455	470	8	a.	a.	PROPN
ejpam-5455	470	9	t.	t.	PROPN
ejpam-5455	470	10	machado	machado	PROPN
ejpam-5455	470	11	,	,	PUNCT
ejpam-5455	470	12	and	and	CCONJ
ejpam-5455	470	13	a.	a.	PROPN
ejpam-5455	470	14	c.	c.	PROPN
ejpam-5455	470	15	j.	j.	PROPN
ejpam-5455	470	16	luo	luo	PROPN
ejpam-5455	470	17	.	.	PROPN
ejpam-5455	470	18	fractional	fractional	ADJ
ejpam-5455	470	19	dynamics	dynamic	NOUN
ejpam-5455	470	20	and	and	CCONJ
ejpam-5455	470	21	control	control	NOUN
ejpam-5455	470	22	.	.	PUNCT
ejpam-5455	471	1	springer	springer	NOUN
ejpam-5455	471	2	,	,	PUNCT
ejpam-5455	471	3	new	new	PROPN
ejpam-5455	471	4	york	york	PROPN
ejpam-5455	471	5	,	,	PUNCT
ejpam-5455	471	6	usa	usa	PROPN
ejpam-5455	471	7	,	,	PUNCT
ejpam-5455	471	8	2012	2012	NUM
ejpam-5455	471	9	.	.	PUNCT
ejpam-5455	472	1	references	reference	NOUN
ejpam-5455	472	2	4091	4091	NUM
ejpam-5455	472	3	[	[	X
ejpam-5455	472	4	7	7	NUM
ejpam-5455	472	5	]	]	X
ejpam-5455	472	6	m.	m.	PROPN
ejpam-5455	472	7	caputo	caputo	PROPN
ejpam-5455	472	8	.	.	PUNCT
ejpam-5455	472	9	linear	linear	PROPN
ejpam-5455	472	10	models	model	NOUN
ejpam-5455	472	11	of	of	ADP
ejpam-5455	472	12	dissipation	dissipation	NOUN
ejpam-5455	472	13	whose	whose	DET
ejpam-5455	472	14	q	q	NOUN
ejpam-5455	472	15	is	be	AUX
ejpam-5455	472	16	almost	almost	ADV
ejpam-5455	472	17	frequency	frequency	VERB
ejpam-5455	472	18	independent	independent	ADJ
ejpam-5455	472	19	-	-	PUNCT
ejpam-5455	472	20	ii	ii	NOUN
ejpam-5455	472	21	.	.	PUNCT
ejpam-5455	472	22	geophysical	geophysical	ADJ
ejpam-5455	472	23	journal	journal	PROPN
ejpam-5455	472	24	international	international	PROPN
ejpam-5455	472	25	,	,	PUNCT
ejpam-5455	472	26	13(5):529–539	13(5):529–539	NUM
ejpam-5455	472	27	,	,	PUNCT
ejpam-5455	472	28	1967	1967	NUM
ejpam-5455	472	29	.	.	PUNCT
ejpam-5455	473	1	[	[	X
ejpam-5455	473	2	8	8	NUM
ejpam-5455	473	3	]	]	PUNCT
ejpam-5455	473	4	m.	m.	NOUN
ejpam-5455	473	5	caputo	caputo	PROPN
ejpam-5455	473	6	and	and	CCONJ
ejpam-5455	473	7	m.	m.	PROPN
ejpam-5455	473	8	fabrizio	fabrizio	PROPN
ejpam-5455	473	9	.	.	PUNCT
ejpam-5455	474	1	a	a	DET
ejpam-5455	474	2	new	new	ADJ
ejpam-5455	474	3	definition	definition	NOUN
ejpam-5455	474	4	of	of	ADP
ejpam-5455	474	5	fractional	fractional	ADJ
ejpam-5455	474	6	derivative	derivative	NOUN
ejpam-5455	474	7	without	without	ADP
ejpam-5455	474	8	singular	singular	ADJ
ejpam-5455	474	9	kernel	kernel	PROPN
ejpam-5455	474	10	.	.	PUNCT
ejpam-5455	475	1	progress	progress	NOUN
ejpam-5455	475	2	in	in	ADP
ejpam-5455	475	3	fractional	fractional	ADJ
ejpam-5455	475	4	differentiation	differentiation	NOUN
ejpam-5455	475	5	and	and	CCONJ
ejpam-5455	475	6	applications	application	NOUN
ejpam-5455	475	7	,	,	PUNCT
ejpam-5455	475	8	1(2):73–85	1(2):73–85	NUM
ejpam-5455	475	9	,	,	PUNCT
ejpam-5455	475	10	2015	2015	NUM
ejpam-5455	475	11	.	.	PUNCT
ejpam-5455	476	1	[	[	X
ejpam-5455	476	2	9	9	NUM
ejpam-5455	476	3	]	]	PUNCT
ejpam-5455	476	4	m.	m.	NOUN
ejpam-5455	476	5	derhab	derhab	PROPN
ejpam-5455	476	6	.	.	PUNCT
ejpam-5455	477	1	on	on	ADP
ejpam-5455	477	2	a	a	DET
ejpam-5455	477	3	conformable	conformable	ADJ
ejpam-5455	477	4	fractional	fractional	ADJ
ejpam-5455	477	5	differential	differential	ADJ
ejpam-5455	477	6	equations	equation	NOUN
ejpam-5455	477	7	with	with	ADP
ejpam-5455	477	8	maxima	maxima	PROPN
ejpam-5455	477	9	.	.	PUNCT
ejpam-5455	478	1	malaya	malaya	PROPN
ejpam-5455	478	2	journal	journal	PROPN
ejpam-5455	478	3	of	of	ADP
ejpam-5455	478	4	matematik	matematik	PROPN
ejpam-5455	478	5	,	,	PUNCT
ejpam-5455	478	6	129(01):85–103	129(01):85–103	NUM
ejpam-5455	478	7	,	,	PUNCT
ejpam-5455	478	8	2024	2024	NUM
ejpam-5455	478	9	.	.	PUNCT
ejpam-5455	479	1	[	[	X
ejpam-5455	479	2	10	10	NUM
ejpam-5455	479	3	]	]	PUNCT
ejpam-5455	479	4	b.	b.	NOUN
ejpam-5455	479	5	dhage	dhage	NOUN
ejpam-5455	479	6	.	.	PUNCT
ejpam-5455	480	1	quadratic	quadratic	ADJ
ejpam-5455	480	2	perturbations	perturbation	NOUN
ejpam-5455	480	3	of	of	ADP
ejpam-5455	480	4	periodic	periodic	ADJ
ejpam-5455	480	5	boundary	boundary	ADJ
ejpam-5455	480	6	value	value	NOUN
ejpam-5455	480	7	problems	problem	NOUN
ejpam-5455	480	8	of	of	ADP
ejpam-5455	480	9	second	second	ADJ
ejpam-5455	480	10	order	order	NOUN
ejpam-5455	480	11	ordinary	ordinary	ADJ
ejpam-5455	480	12	differential	differential	ADJ
ejpam-5455	480	13	equations	equation	NOUN
ejpam-5455	480	14	.	.	PUNCT
ejpam-5455	481	1	differential	differential	ADJ
ejpam-5455	481	2	equations	equation	NOUN
ejpam-5455	481	3	&	&	CCONJ
ejpam-5455	481	4	applications	application	NOUN
ejpam-5455	481	5	,	,	PUNCT
ejpam-5455	481	6	2:465	2:465	NUM
ejpam-5455	481	7	–	–	PUNCT
ejpam-5455	481	8	486	486	NUM
ejpam-5455	481	9	,	,	PUNCT
ejpam-5455	481	10	2010	2010	NUM
ejpam-5455	481	11	.	.	PUNCT
ejpam-5455	482	1	[	[	X
ejpam-5455	482	2	11	11	NUM
ejpam-5455	482	3	]	]	PUNCT
ejpam-5455	482	4	b.	b.	NOUN
ejpam-5455	482	5	dhage	dhage	NOUN
ejpam-5455	482	6	.	.	PUNCT
ejpam-5455	483	1	existence	existence	NOUN
ejpam-5455	483	2	and	and	CCONJ
ejpam-5455	483	3	attractivity	attractivity	NOUN
ejpam-5455	483	4	theorems	theorem	NOUN
ejpam-5455	483	5	for	for	ADP
ejpam-5455	483	6	nonlinear	nonlinear	ADJ
ejpam-5455	483	7	hybrid	hybrid	ADJ
ejpam-5455	483	8	fractional	fractional	ADJ
ejpam-5455	483	9	differential	differential	ADJ
ejpam-5455	483	10	equations	equation	NOUN
ejpam-5455	483	11	with	with	ADP
ejpam-5455	483	12	anticipation	anticipation	NOUN
ejpam-5455	483	13	and	and	CCONJ
ejpam-5455	483	14	retardation	retardation	NOUN
ejpam-5455	483	15	.	.	PUNCT
ejpam-5455	484	1	journal	journal	NOUN
ejpam-5455	484	2	of	of	ADP
ejpam-5455	484	3	nonlinear	nonlinear	ADJ
ejpam-5455	484	4	functional	functional	ADJ
ejpam-5455	484	5	analysis	analysis	NOUN
ejpam-5455	484	6	,	,	PUNCT
ejpam-5455	484	7	2020:47	2020:47	NUM
ejpam-5455	484	8	,	,	PUNCT
ejpam-5455	484	9	2020	2020	NUM
ejpam-5455	484	10	.	.	PUNCT
ejpam-5455	485	1	[	[	X
ejpam-5455	485	2	12	12	NUM
ejpam-5455	485	3	]	]	PUNCT
ejpam-5455	485	4	b.	b.	NOUN
ejpam-5455	485	5	dhage	dhage	PROPN
ejpam-5455	485	6	,	,	PUNCT
ejpam-5455	485	7	g.	g.	PROPN
ejpam-5455	485	8	khurape	khurape	PROPN
ejpam-5455	485	9	,	,	PUNCT
ejpam-5455	485	10	a.	a.	NOUN
ejpam-5455	485	11	shete	shete	PROPN
ejpam-5455	485	12	,	,	PUNCT
ejpam-5455	485	13	and	and	CCONJ
ejpam-5455	485	14	j.	j.	PROPN
ejpam-5455	485	15	salunkhe	salunkhe	PROPN
ejpam-5455	485	16	.	.	PUNCT
ejpam-5455	486	1	existence	existence	NOUN
ejpam-5455	486	2	and	and	CCONJ
ejpam-5455	486	3	approximate	approximate	ADJ
ejpam-5455	486	4	solutions	solution	NOUN
ejpam-5455	486	5	for	for	ADP
ejpam-5455	486	6	nonlinear	nonlinear	ADJ
ejpam-5455	486	7	hybrid	hybrid	ADJ
ejpam-5455	486	8	fractional	fractional	ADJ
ejpam-5455	486	9	integro	integro	ADJ
ejpam-5455	486	10	-	-	PUNCT
ejpam-5455	486	11	differential	differential	NOUN
ejpam-5455	486	12	equations	equation	NOUN
ejpam-5455	486	13	.	.	PUNCT
ejpam-5455	487	1	international	international	ADJ
ejpam-5455	487	2	journal	journal	NOUN
ejpam-5455	487	3	of	of	ADP
ejpam-5455	487	4	analysis	analysis	NOUN
ejpam-5455	487	5	and	and	CCONJ
ejpam-5455	487	6	applications	application	NOUN
ejpam-5455	487	7	,	,	PUNCT
ejpam-5455	487	8	11:157–167	11:157–167	NUM
ejpam-5455	487	9	,	,	PUNCT
ejpam-5455	487	10	2016	2016	NUM
ejpam-5455	487	11	.	.	PUNCT
ejpam-5455	488	1	[	[	X
ejpam-5455	488	2	13	13	NUM
ejpam-5455	488	3	]	]	X
ejpam-5455	488	4	b.	b.	PROPN
ejpam-5455	488	5	c.	c.	PROPN
ejpam-5455	488	6	dhage	dhage	PROPN
ejpam-5455	488	7	and	and	CCONJ
ejpam-5455	488	8	v.	v.	ADP
ejpam-5455	488	9	lakshimikantham	lakshimikantham	PROPN
ejpam-5455	488	10	.	.	PUNCT
ejpam-5455	489	1	basic	basic	ADJ
ejpam-5455	489	2	results	result	NOUN
ejpam-5455	489	3	on	on	ADP
ejpam-5455	489	4	hybrid	hybrid	ADJ
ejpam-5455	489	5	differential	differential	ADJ
ejpam-5455	489	6	equations	equation	NOUN
ejpam-5455	489	7	.	.	PUNCT
ejpam-5455	490	1	nonlinear	nonlinear	ADJ
ejpam-5455	490	2	analysis	analysis	NOUN
ejpam-5455	490	3	:	:	PUNCT
ejpam-5455	490	4	hybrid	hybrid	ADJ
ejpam-5455	490	5	systems	system	NOUN
ejpam-5455	490	6	,	,	PUNCT
ejpam-5455	490	7	4:414–424	4:414–424	NUM
ejpam-5455	490	8	,	,	PUNCT
ejpam-5455	490	9	2010	2010	NUM
ejpam-5455	490	10	.	.	PUNCT
ejpam-5455	491	1	[	[	X
ejpam-5455	491	2	14	14	NUM
ejpam-5455	491	3	]	]	X
ejpam-5455	491	4	eiman	eiman	NOUN
ejpam-5455	491	5	,	,	PUNCT
ejpam-5455	491	6	k.	k.	PROPN
ejpam-5455	491	7	shah	shah	PROPN
ejpam-5455	491	8	,	,	PUNCT
ejpam-5455	491	9	m.	m.	NOUN
ejpam-5455	491	10	sarwar	sarwar	PROPN
ejpam-5455	491	11	,	,	PUNCT
ejpam-5455	491	12	and	and	CCONJ
ejpam-5455	491	13	d.	d.	PROPN
ejpam-5455	491	14	baleanu	baleanu	PROPN
ejpam-5455	491	15	.	.	PUNCT
ejpam-5455	492	1	study	study	NOUN
ejpam-5455	492	2	on	on	ADP
ejpam-5455	492	3	krasnoselskii	krasnoselskii	PROPN
ejpam-5455	492	4	’s	’s	PART
ejpam-5455	492	5	fixed	fix	VERB
ejpam-5455	492	6	point	point	NOUN
ejpam-5455	492	7	theorem	theorem	NOUN
ejpam-5455	492	8	for	for	ADP
ejpam-5455	492	9	caputo	caputo	PROPN
ejpam-5455	492	10	-	-	PUNCT
ejpam-5455	492	11	fabrizio	fabrizio	PROPN
ejpam-5455	492	12	fractional	fractional	ADJ
ejpam-5455	492	13	differential	differential	NOUN
ejpam-5455	492	14	equations	equation	NOUN
ejpam-5455	492	15	.	.	PUNCT
ejpam-5455	493	1	advances	advance	NOUN
ejpam-5455	493	2	in	in	ADP
ejpam-5455	493	3	difference	difference	NOUN
ejpam-5455	493	4	equations	equation	NOUN
ejpam-5455	493	5	,	,	PUNCT
ejpam-5455	493	6	2020:178	2020:178	NUM
ejpam-5455	493	7	,	,	PUNCT
ejpam-5455	493	8	2020	2020	NUM
ejpam-5455	493	9	.	.	PUNCT
ejpam-5455	494	1	[	[	X
ejpam-5455	494	2	15	15	NUM
ejpam-5455	494	3	]	]	PUNCT
ejpam-5455	494	4	m.	m.	NOUN
ejpam-5455	494	5	etefa	etefa	PROPN
ejpam-5455	494	6	,	,	PUNCT
ejpam-5455	494	7	g.	g.	PROPN
ejpam-5455	494	8	m.	m.	PROPN
ejpam-5455	494	9	n.	n.	PROPN
ejpam-5455	494	10	guerekata	guerekata	PROPN
ejpam-5455	494	11	,	,	PUNCT
ejpam-5455	494	12	p.	p.	PROPN
ejpam-5455	494	13	ngnepieba	ngnepieba	PROPN
ejpam-5455	494	14	,	,	PUNCT
ejpam-5455	494	15	and	and	CCONJ
ejpam-5455	494	16	o.	o.	PROPN
ejpam-5455	494	17	s.	s.	PROPN
ejpam-5455	494	18	iyiola	iyiola	PROPN
ejpam-5455	494	19	.	.	PUNCT
ejpam-5455	495	1	on	on	ADP
ejpam-5455	495	2	a	a	DET
ejpam-5455	495	3	generalized	generalize	VERB
ejpam-5455	495	4	fractional	fractional	ADJ
ejpam-5455	495	5	differential	differential	NOUN
ejpam-5455	495	6	cauchy	cauchy	PROPN
ejpam-5455	495	7	problem	problem	NOUN
ejpam-5455	495	8	.	.	PUNCT
ejpam-5455	496	1	malaya	malaya	PROPN
ejpam-5455	496	2	journal	journal	PROPN
ejpam-5455	496	3	of	of	ADP
ejpam-5455	496	4	matematik	matematik	PROPN
ejpam-5455	496	5	,	,	PUNCT
ejpam-5455	496	6	11(01):80–93	11(01):80–93	NUM
ejpam-5455	496	7	,	,	PUNCT
ejpam-5455	496	8	2023	2023	NUM
ejpam-5455	496	9	.	.	PUNCT
ejpam-5455	497	1	[	[	X
ejpam-5455	497	2	16	16	NUM
ejpam-5455	497	3	]	]	PUNCT
ejpam-5455	497	4	a.	a.	NOUN
ejpam-5455	497	5	granas	grana	NOUN
ejpam-5455	497	6	and	and	CCONJ
ejpam-5455	497	7	j.	j.	PROPN
ejpam-5455	497	8	dugundji	dugundji	PROPN
ejpam-5455	497	9	.	.	PUNCT
ejpam-5455	498	1	fixed	fix	VERB
ejpam-5455	498	2	point	point	NOUN
ejpam-5455	498	3	theory	theory	NOUN
ejpam-5455	498	4	.	.	PUNCT
ejpam-5455	499	1	springer	springer	NOUN
ejpam-5455	499	2	-	-	PUNCT
ejpam-5455	499	3	verlag	verlag	PROPN
ejpam-5455	499	4	,	,	PUNCT
ejpam-5455	499	5	new	new	PROPN
ejpam-5455	499	6	york	york	PROPN
ejpam-5455	499	7	,	,	PUNCT
ejpam-5455	499	8	2003	2003	NUM
ejpam-5455	499	9	.	.	PUNCT
ejpam-5455	500	1	[	[	X
ejpam-5455	500	2	17	17	NUM
ejpam-5455	500	3	]	]	PUNCT
ejpam-5455	500	4	a.	a.	NOUN
ejpam-5455	500	5	guerfi	guerfi	PROPN
ejpam-5455	500	6	and	and	CCONJ
ejpam-5455	500	7	a.	a.	NOUN
ejpam-5455	500	8	ardjouni	ardjouni	PROPN
ejpam-5455	500	9	.	.	PUNCT
ejpam-5455	501	1	existence	existence	NOUN
ejpam-5455	501	2	and	and	CCONJ
ejpam-5455	501	3	uniqueness	uniqueness	NOUN
ejpam-5455	501	4	of	of	ADP
ejpam-5455	501	5	mild	mild	ADJ
ejpam-5455	501	6	solutions	solution	NOUN
ejpam-5455	501	7	for	for	ADP
ejpam-5455	501	8	nonlinear	nonlinear	ADJ
ejpam-5455	501	9	hybrid	hybrid	ADJ
ejpam-5455	501	10	caputo	caputo	PROPN
ejpam-5455	501	11	fractional	fractional	PROPN
ejpam-5455	501	12	integro	integro	PROPN
ejpam-5455	501	13	-	-	PUNCT
ejpam-5455	501	14	differential	differential	NOUN
ejpam-5455	501	15	equations	equation	NOUN
ejpam-5455	501	16	via	via	ADP
ejpam-5455	501	17	fixed	fix	VERB
ejpam-5455	501	18	point	point	NOUN
ejpam-5455	501	19	theorems	theorem	NOUN
ejpam-5455	501	20	.	.	PUNCT
ejpam-5455	502	1	results	result	NOUN
ejpam-5455	502	2	in	in	ADP
ejpam-5455	502	3	nonlinear	nonlinear	ADJ
ejpam-5455	502	4	analysis	analysis	NOUN
ejpam-5455	502	5	,	,	PUNCT
ejpam-5455	502	6	4(4):207–216	4(4):207–216	NUM
ejpam-5455	502	7	,	,	PUNCT
ejpam-5455	502	8	2021	2021	NUM
ejpam-5455	502	9	.	.	PUNCT
ejpam-5455	503	1	[	[	X
ejpam-5455	503	2	18	18	NUM
ejpam-5455	503	3	]	]	X
ejpam-5455	503	4	r.	r.	PROPN
ejpam-5455	503	5	gul	gul	PROPN
ejpam-5455	503	6	,	,	PUNCT
ejpam-5455	503	7	k.	k.	PROPN
ejpam-5455	503	8	shah	shah	PROPN
ejpam-5455	503	9	,	,	PUNCT
ejpam-5455	503	10	z.	z.	PROPN
ejpam-5455	503	11	a.	a.	PROPN
ejpam-5455	503	12	khan	khan	PROPN
ejpam-5455	503	13	,	,	PUNCT
ejpam-5455	503	14	and	and	CCONJ
ejpam-5455	503	15	f.	f.	PROPN
ejpam-5455	503	16	jarad	jarad	PROPN
ejpam-5455	503	17	.	.	PUNCT
ejpam-5455	504	1	on	on	ADP
ejpam-5455	504	2	a	a	DET
ejpam-5455	504	3	class	class	NOUN
ejpam-5455	504	4	of	of	ADP
ejpam-5455	504	5	boundary	boundary	ADJ
ejpam-5455	504	6	value	value	NOUN
ejpam-5455	504	7	problems	problem	NOUN
ejpam-5455	504	8	under	under	ADP
ejpam-5455	504	9	abc	abc	PROPN
ejpam-5455	504	10	fractional	fractional	PROPN
ejpam-5455	504	11	derivative	derivative	PROPN
ejpam-5455	504	12	.	.	PUNCT
ejpam-5455	505	1	advances	advance	NOUN
ejpam-5455	505	2	in	in	ADP
ejpam-5455	505	3	difference	difference	NOUN
ejpam-5455	505	4	equations	equation	NOUN
ejpam-5455	505	5	,	,	PUNCT
ejpam-5455	505	6	2021:437	2021:437	NUM
ejpam-5455	505	7	,	,	PUNCT
ejpam-5455	505	8	2021	2021	NUM
ejpam-5455	505	9	.	.	PUNCT
ejpam-5455	506	1	[	[	X
ejpam-5455	506	2	19	19	NUM
ejpam-5455	506	3	]	]	PUNCT
ejpam-5455	506	4	a.	a.	NOUN
ejpam-5455	506	5	khan	khan	PROPN
ejpam-5455	506	6	,	,	PUNCT
ejpam-5455	506	7	z.	z.	PROPN
ejpam-5455	506	8	a.	a.	PROPN
ejpam-5455	506	9	khan	khan	PROPN
ejpam-5455	506	10	,	,	PUNCT
ejpam-5455	506	11	t.	t.	NOUN
ejpam-5455	506	12	abdeljawad	abdeljawad	NOUN
ejpam-5455	506	13	,	,	PUNCT
ejpam-5455	506	14	and	and	CCONJ
ejpam-5455	506	15	h.	h.	PROPN
ejpam-5455	506	16	khan	khan	PROPN
ejpam-5455	506	17	.	.	PUNCT
ejpam-5455	507	1	analytical	analytical	ADJ
ejpam-5455	507	2	analysis	analysis	NOUN
ejpam-5455	507	3	of	of	ADP
ejpam-5455	507	4	fractionalorder	fractionalorder	ADJ
ejpam-5455	507	5	sequential	sequential	ADJ
ejpam-5455	507	6	hybrid	hybrid	ADJ
ejpam-5455	507	7	system	system	NOUN
ejpam-5455	507	8	with	with	ADP
ejpam-5455	507	9	numerical	numerical	ADJ
ejpam-5455	507	10	application	application	NOUN
ejpam-5455	507	11	.	.	PUNCT
ejpam-5455	508	1	advances	advance	NOUN
ejpam-5455	508	2	in	in	ADP
ejpam-5455	508	3	continuous	continuous	ADJ
ejpam-5455	508	4	and	and	CCONJ
ejpam-5455	508	5	discrete	discrete	ADJ
ejpam-5455	508	6	models	model	NOUN
ejpam-5455	508	7	,	,	PUNCT
ejpam-5455	508	8	2022	2022	NUM
ejpam-5455	508	9	:	:	PUNCT
ejpam-5455	508	10	article	article	NOUN
ejpam-5455	508	11	12	12	NUM
ejpam-5455	508	12	,	,	PUNCT
ejpam-5455	508	13	2022	2022	NUM
ejpam-5455	508	14	.	.	PUNCT
ejpam-5455	509	1	[	[	X
ejpam-5455	509	2	20	20	NUM
ejpam-5455	509	3	]	]	X
ejpam-5455	509	4	h.	h.	PROPN
ejpam-5455	509	5	khan	khan	PROPN
ejpam-5455	509	6	,	,	PUNCT
ejpam-5455	509	7	j.	j.	PROPN
ejpam-5455	509	8	alzabut	alzabut	PROPN
ejpam-5455	509	9	,	,	PUNCT
ejpam-5455	509	10	d.	d.	PROPN
ejpam-5455	509	11	baleanu	baleanu	PROPN
ejpam-5455	509	12	,	,	PUNCT
ejpam-5455	509	13	g.	g.	PROPN
ejpam-5455	509	14	alobaidi	alobaidi	PROPN
ejpam-5455	509	15	,	,	PUNCT
ejpam-5455	509	16	and	and	CCONJ
ejpam-5455	509	17	m.-ur	m.-ur	PROPN
ejpam-5455	509	18	rehman	rehman	PROPN
ejpam-5455	509	19	.	.	PUNCT
ejpam-5455	510	1	existence	existence	NOUN
ejpam-5455	510	2	of	of	ADP
ejpam-5455	510	3	solutions	solution	NOUN
ejpam-5455	510	4	and	and	CCONJ
ejpam-5455	510	5	a	a	DET
ejpam-5455	510	6	numerical	numerical	ADJ
ejpam-5455	510	7	scheme	scheme	NOUN
ejpam-5455	510	8	for	for	ADP
ejpam-5455	510	9	a	a	DET
ejpam-5455	510	10	generalized	generalize	VERB
ejpam-5455	510	11	hybrid	hybrid	ADJ
ejpam-5455	510	12	class	class	NOUN
ejpam-5455	510	13	of	of	ADP
ejpam-5455	510	14	n	n	ADV
ejpam-5455	510	15	-	-	PUNCT
ejpam-5455	510	16	coupled	couple	VERB
ejpam-5455	510	17	modified	modify	VERB
ejpam-5455	510	18	abc	abc	PROPN
ejpam-5455	510	19	-	-	PUNCT
ejpam-5455	510	20	fractional	fractional	ADJ
ejpam-5455	510	21	differential	differential	ADJ
ejpam-5455	510	22	equations	equation	NOUN
ejpam-5455	510	23	with	with	ADP
ejpam-5455	510	24	an	an	DET
ejpam-5455	510	25	application	application	NOUN
ejpam-5455	510	26	.	.	PUNCT
ejpam-5455	511	1	aims	aim	VERB
ejpam-5455	511	2	mathematics	mathematic	NOUN
ejpam-5455	511	3	,	,	PUNCT
ejpam-5455	511	4	8(3):6609–6625	8(3):6609–6625	NUM
ejpam-5455	511	5	,	,	PUNCT
ejpam-5455	511	6	2023	2023	NUM
ejpam-5455	511	7	.	.	PUNCT
ejpam-5455	512	1	references	reference	NOUN
ejpam-5455	512	2	4092	4092	NUM
ejpam-5455	512	3	[	[	X
ejpam-5455	512	4	21	21	NUM
ejpam-5455	512	5	]	]	X
ejpam-5455	512	6	h.	h.	PROPN
ejpam-5455	512	7	khan	khan	PROPN
ejpam-5455	512	8	,	,	PUNCT
ejpam-5455	512	9	j.	j.	PROPN
ejpam-5455	512	10	alzabut	alzabut	PROPN
ejpam-5455	512	11	,	,	PUNCT
ejpam-5455	512	12	and	and	CCONJ
ejpam-5455	512	13	h.	h.	PROPN
ejpam-5455	512	14	gulzar	gulzar	PROPN
ejpam-5455	512	15	.	.	PUNCT
ejpam-5455	513	1	existence	existence	NOUN
ejpam-5455	513	2	of	of	ADP
ejpam-5455	513	3	solutions	solution	NOUN
ejpam-5455	513	4	for	for	ADP
ejpam-5455	513	5	hybrid	hybrid	ADJ
ejpam-5455	513	6	modified	modify	VERB
ejpam-5455	513	7	abc	abc	PROPN
ejpam-5455	513	8	-	-	PUNCT
ejpam-5455	513	9	fractional	fractional	ADJ
ejpam-5455	513	10	differential	differential	ADJ
ejpam-5455	513	11	equations	equation	NOUN
ejpam-5455	513	12	with	with	ADP
ejpam-5455	513	13	p	p	ADJ
ejpam-5455	513	14	-	-	PUNCT
ejpam-5455	513	15	laplacian	laplacian	ADJ
ejpam-5455	513	16	operator	operator	NOUN
ejpam-5455	513	17	and	and	CCONJ
ejpam-5455	513	18	an	an	DET
ejpam-5455	513	19	application	application	NOUN
ejpam-5455	513	20	to	to	ADP
ejpam-5455	513	21	a	a	DET
ejpam-5455	513	22	waterborne	waterborne	ADJ
ejpam-5455	513	23	disease	disease	NOUN
ejpam-5455	513	24	model	model	NOUN
ejpam-5455	513	25	.	.	PUNCT
ejpam-5455	514	1	alexandria	alexandria	PROPN
ejpam-5455	514	2	engineering	engineering	PROPN
ejpam-5455	514	3	journal	journal	PROPN
ejpam-5455	514	4	,	,	PUNCT
ejpam-5455	514	5	70:665–672	70:665–672	NUM
ejpam-5455	514	6	,	,	PUNCT
ejpam-5455	514	7	2023	2023	NUM
ejpam-5455	514	8	.	.	PUNCT
ejpam-5455	515	1	[	[	X
ejpam-5455	515	2	22	22	NUM
ejpam-5455	515	3	]	]	PUNCT
ejpam-5455	515	4	a.	a.	NOUN
ejpam-5455	515	5	a.	a.	NOUN
ejpam-5455	515	6	kilbas	kilbas	PROPN
ejpam-5455	515	7	,	,	PUNCT
ejpam-5455	515	8	h.	h.	PROPN
ejpam-5455	515	9	m.	m.	PROPN
ejpam-5455	515	10	srivastava	srivastava	PROPN
ejpam-5455	515	11	,	,	PUNCT
ejpam-5455	515	12	and	and	CCONJ
ejpam-5455	515	13	j.	j.	PROPN
ejpam-5455	515	14	j.	j.	PROPN
ejpam-5455	515	15	trujillo	trujillo	PROPN
ejpam-5455	515	16	.	.	PUNCT
ejpam-5455	515	17	theory	theory	NOUN
ejpam-5455	515	18	and	and	CCONJ
ejpam-5455	515	19	applications	application	NOUN
ejpam-5455	515	20	of	of	ADP
ejpam-5455	515	21	fractional	fractional	ADJ
ejpam-5455	515	22	differential	differential	ADJ
ejpam-5455	515	23	equations	equation	NOUN
ejpam-5455	515	24	.	.	PUNCT
ejpam-5455	516	1	elsevier	elsevier	PROPN
ejpam-5455	516	2	,	,	PUNCT
ejpam-5455	516	3	amsterdam	amsterdam	PROPN
ejpam-5455	516	4	,	,	PUNCT
ejpam-5455	516	5	2006	2006	NUM
ejpam-5455	516	6	.	.	PUNCT
ejpam-5455	517	1	[	[	X
ejpam-5455	517	2	23	23	NUM
ejpam-5455	517	3	]	]	PUNCT
ejpam-5455	517	4	m.	m.	NOUN
ejpam-5455	517	5	m.	m.	NOUN
ejpam-5455	517	6	matar	matar	PROPN
ejpam-5455	517	7	,	,	PUNCT
ejpam-5455	517	8	a.	a.	PROPN
ejpam-5455	517	9	a.	a.	PROPN
ejpam-5455	517	10	lubbad	lubbad	PROPN
ejpam-5455	517	11	,	,	PUNCT
ejpam-5455	517	12	and	and	CCONJ
ejpam-5455	517	13	j.	j.	PROPN
ejpam-5455	517	14	alzabut	alzabut	PROPN
ejpam-5455	517	15	.	.	PUNCT
ejpam-5455	518	1	on	on	ADP
ejpam-5455	518	2	p	p	X
ejpam-5455	518	3	–	–	PUNCT
ejpam-5455	518	4	laplacian	laplacian	ADJ
ejpam-5455	518	5	boundary	boundary	ADJ
ejpam-5455	518	6	value	value	NOUN
ejpam-5455	518	7	problems	problem	NOUN
ejpam-5455	518	8	involving	involve	VERB
ejpam-5455	518	9	caputo	caputo	PROPN
ejpam-5455	518	10	–	–	PUNCT
ejpam-5455	518	11	katugampula	katugampula	ADJ
ejpam-5455	518	12	fractional	fractional	ADJ
ejpam-5455	518	13	derivatives	derivative	NOUN
ejpam-5455	518	14	.	.	PUNCT
ejpam-5455	519	1	mathematical	mathematical	ADJ
ejpam-5455	519	2	methods	method	NOUN
ejpam-5455	519	3	in	in	ADP
ejpam-5455	519	4	the	the	DET
ejpam-5455	519	5	applied	apply	VERB
ejpam-5455	519	6	sciences	science	NOUN
ejpam-5455	519	7	,	,	PUNCT
ejpam-5455	519	8	pages	page	NOUN
ejpam-5455	519	9	1–18	1–18	NUM
ejpam-5455	519	10	,	,	PUNCT
ejpam-5455	519	11	2020	2020	NUM
ejpam-5455	519	12	.	.	PUNCT
ejpam-5455	520	1	[	[	X
ejpam-5455	520	2	24	24	NUM
ejpam-5455	520	3	]	]	X
ejpam-5455	520	4	r.	r.	PROPN
ejpam-5455	520	5	metzler	metzler	PROPN
ejpam-5455	520	6	,	,	PUNCT
ejpam-5455	520	7	w.	w.	PROPN
ejpam-5455	520	8	g.	g.	PROPN
ejpam-5455	520	9	glockle	glockle	PROPN
ejpam-5455	520	10	,	,	PUNCT
ejpam-5455	520	11	and	and	CCONJ
ejpam-5455	520	12	t.	t.	PROPN
ejpam-5455	520	13	f.	f.	PROPN
ejpam-5455	520	14	nonnenmacher	nonnenmacher	PROPN
ejpam-5455	520	15	.	.	PUNCT
ejpam-5455	521	1	fractional	fractional	ADJ
ejpam-5455	521	2	model	model	NOUN
ejpam-5455	521	3	equation	equation	NOUN
ejpam-5455	521	4	for	for	ADP
ejpam-5455	521	5	anomalous	anomalous	ADJ
ejpam-5455	521	6	diffusion	diffusion	NOUN
ejpam-5455	521	7	.	.	PUNCT
ejpam-5455	522	1	physica	physica	PROPN
ejpam-5455	522	2	a	a	DET
ejpam-5455	522	3	:	:	PUNCT
ejpam-5455	522	4	statistical	statistical	ADJ
ejpam-5455	522	5	mechanics	mechanic	NOUN
ejpam-5455	522	6	and	and	CCONJ
ejpam-5455	522	7	its	its	PRON
ejpam-5455	522	8	applications	application	NOUN
ejpam-5455	522	9	,	,	PUNCT
ejpam-5455	522	10	211(1):13	211(1):13	NUM
ejpam-5455	522	11	–	–	PUNCT
ejpam-5455	522	12	24	24	NUM
ejpam-5455	522	13	,	,	PUNCT
ejpam-5455	522	14	1994	1994	NUM
ejpam-5455	522	15	.	.	PUNCT
ejpam-5455	523	1	[	[	X
ejpam-5455	523	2	25	25	NUM
ejpam-5455	523	3	]	]	PUNCT
ejpam-5455	523	4	z.	z.	PROPN
ejpam-5455	523	5	odibat	odibat	PROPN
ejpam-5455	523	6	and	and	CCONJ
ejpam-5455	523	7	d.	d.	PROPN
ejpam-5455	523	8	baleanu	baleanu	PROPN
ejpam-5455	523	9	.	.	PUNCT
ejpam-5455	524	1	new	new	ADJ
ejpam-5455	524	2	solutions	solution	NOUN
ejpam-5455	524	3	of	of	ADP
ejpam-5455	524	4	the	the	DET
ejpam-5455	524	5	fractional	fractional	ADJ
ejpam-5455	524	6	differential	differential	ADJ
ejpam-5455	524	7	equations	equation	NOUN
ejpam-5455	524	8	with	with	ADP
ejpam-5455	524	9	modified	modify	VERB
ejpam-5455	524	10	mittag	mittag	ADJ
ejpam-5455	524	11	-	-	PUNCT
ejpam-5455	524	12	leffler	leffler	NOUN
ejpam-5455	524	13	kernel	kernel	NOUN
ejpam-5455	524	14	.	.	PUNCT
ejpam-5455	525	1	journal	journal	PROPN
ejpam-5455	525	2	of	of	ADP
ejpam-5455	525	3	computational	computational	ADJ
ejpam-5455	525	4	and	and	CCONJ
ejpam-5455	525	5	nonlinear	nonlinear	ADJ
ejpam-5455	525	6	dynamics	dynamic	NOUN
ejpam-5455	525	7	,	,	PUNCT
ejpam-5455	525	8	18:091007–1–091007–9	18:091007–1–091007–9	NUM
ejpam-5455	525	9	,	,	PUNCT
ejpam-5455	525	10	2023	2023	NUM
ejpam-5455	525	11	.	.	PUNCT
ejpam-5455	526	1	[	[	X
ejpam-5455	526	2	26	26	NUM
ejpam-5455	526	3	]	]	PUNCT
ejpam-5455	526	4	i.	i.	NOUN
ejpam-5455	526	5	podlubny	podlubny	PROPN
ejpam-5455	526	6	.	.	PUNCT
ejpam-5455	527	1	fractional	fractional	ADJ
ejpam-5455	527	2	differential	differential	ADJ
ejpam-5455	527	3	equations	equation	NOUN
ejpam-5455	527	4	.	.	PUNCT
ejpam-5455	528	1	academic	academic	ADJ
ejpam-5455	528	2	press	press	NOUN
ejpam-5455	528	3	,	,	PUNCT
ejpam-5455	528	4	new	new	PROPN
ejpam-5455	528	5	york	york	PROPN
ejpam-5455	528	6	,	,	PUNCT
ejpam-5455	528	7	1999	1999	NUM
ejpam-5455	528	8	.	.	PUNCT
ejpam-5455	529	1	[	[	X
ejpam-5455	529	2	27	27	NUM
ejpam-5455	529	3	]	]	X
ejpam-5455	529	4	li	li	PROPN
ejpam-5455	529	5	-	-	PROPN
ejpam-5455	529	6	jun	jun	PROPN
ejpam-5455	529	7	shen	shen	PROPN
ejpam-5455	529	8	.	.	PUNCT
ejpam-5455	530	1	fractional	fractional	ADJ
ejpam-5455	530	2	derivative	derivative	ADJ
ejpam-5455	530	3	models	model	NOUN
ejpam-5455	530	4	for	for	ADP
ejpam-5455	530	5	viscoelastic	viscoelastic	ADJ
ejpam-5455	530	6	materials	material	NOUN
ejpam-5455	530	7	at	at	ADP
ejpam-5455	530	8	finite	finite	ADJ
ejpam-5455	530	9	deformations	deformation	NOUN
ejpam-5455	530	10	.	.	PUNCT
ejpam-5455	531	1	international	international	ADJ
ejpam-5455	531	2	journal	journal	NOUN
ejpam-5455	531	3	of	of	ADP
ejpam-5455	531	4	solids	solid	NOUN
ejpam-5455	531	5	and	and	CCONJ
ejpam-5455	531	6	structures	structure	NOUN
ejpam-5455	531	7	,	,	PUNCT
ejpam-5455	531	8	190:226–237	190:226–237	NUM
ejpam-5455	531	9	,	,	PUNCT
ejpam-5455	531	10	2020	2020	NUM
ejpam-5455	531	11	.	.	PUNCT
ejpam-5455	532	1	[	[	X
ejpam-5455	532	2	28	28	NUM
ejpam-5455	532	3	]	]	X
ejpam-5455	532	4	i.	i.	PROPN
ejpam-5455	532	5	slimane	slimane	PROPN
ejpam-5455	532	6	,	,	PUNCT
ejpam-5455	532	7	z.	z.	PROPN
ejpam-5455	532	8	dahmani	dahmani	PROPN
ejpam-5455	532	9	,	,	PUNCT
ejpam-5455	532	10	j.	j.	PROPN
ejpam-5455	532	11	j.	j.	PROPN
ejpam-5455	532	12	nieto	nieto	PROPN
ejpam-5455	532	13	,	,	PUNCT
ejpam-5455	532	14	and	and	CCONJ
ejpam-5455	532	15	t.	t.	PROPN
ejpam-5455	532	16	abdeljawad	abdeljawad	NOUN
ejpam-5455	532	17	.	.	PUNCT
ejpam-5455	533	1	existence	existence	NOUN
ejpam-5455	533	2	and	and	CCONJ
ejpam-5455	533	3	stability	stability	NOUN
ejpam-5455	533	4	for	for	ADP
ejpam-5455	533	5	a	a	DET
ejpam-5455	533	6	nonlinear	nonlinear	ADJ
ejpam-5455	533	7	hybrid	hybrid	ADJ
ejpam-5455	533	8	differential	differential	ADJ
ejpam-5455	533	9	equation	equation	NOUN
ejpam-5455	533	10	of	of	ADP
ejpam-5455	533	11	fractional	fractional	ADJ
ejpam-5455	533	12	order	order	NOUN
ejpam-5455	533	13	via	via	ADP
ejpam-5455	533	14	regular	regular	ADJ
ejpam-5455	533	15	mittag	mittag	ADJ
ejpam-5455	533	16	-	-	PUNCT
ejpam-5455	533	17	leffler	leffler	NOUN
ejpam-5455	533	18	kernel	kernel	NOUN
ejpam-5455	533	19	.	.	PUNCT
ejpam-5455	534	1	mathematical	mathematical	ADJ
ejpam-5455	534	2	methods	method	NOUN
ejpam-5455	534	3	in	in	ADP
ejpam-5455	534	4	the	the	DET
ejpam-5455	534	5	applied	apply	VERB
ejpam-5455	534	6	sciences	science	NOUN
ejpam-5455	534	7	,	,	PUNCT
ejpam-5455	534	8	46(7):8043–8053	46(7):8043–8053	NUM
ejpam-5455	534	9	,	,	PUNCT
ejpam-5455	534	10	2023	2023	NUM
ejpam-5455	534	11	.	.	PUNCT
ejpam-5455	535	1	[	[	X
ejpam-5455	535	2	29	29	NUM
ejpam-5455	535	3	]	]	PUNCT
ejpam-5455	535	4	s.	s.	PROPN
ejpam-5455	535	5	t.	t.	PROPN
ejpam-5455	535	6	sutar	sutar	PROPN
ejpam-5455	535	7	and	and	CCONJ
ejpam-5455	535	8	k.	k.	PROPN
ejpam-5455	535	9	d.	d.	PROPN
ejpam-5455	535	10	kucche	kucche	PROPN
ejpam-5455	535	11	.	.	PUNCT
ejpam-5455	536	1	on	on	ADP
ejpam-5455	536	2	nonlinear	nonlinear	ADJ
ejpam-5455	536	3	hybrid	hybrid	ADJ
ejpam-5455	536	4	fractional	fractional	ADJ
ejpam-5455	536	5	differential	differential	ADJ
ejpam-5455	536	6	equations	equation	NOUN
ejpam-5455	536	7	with	with	ADP
ejpam-5455	536	8	atangana	atangana	PROPN
ejpam-5455	536	9	-	-	PUNCT
ejpam-5455	536	10	baleanu	baleanu	PROPN
ejpam-5455	536	11	-	-	PUNCT
ejpam-5455	536	12	caputo	caputo	PROPN
ejpam-5455	536	13	derivative	derivative	NOUN
ejpam-5455	536	14	.	.	PUNCT
ejpam-5455	537	1	chaos	chaos	NOUN
ejpam-5455	537	2	,	,	PUNCT
ejpam-5455	537	3	solitons	soliton	NOUN
ejpam-5455	537	4	&	&	CCONJ
ejpam-5455	537	5	fractals	fractal	NOUN
ejpam-5455	537	6	,	,	PUNCT
ejpam-5455	537	7	143	143	NUM
ejpam-5455	537	8	:	:	PUNCT
ejpam-5455	537	9	article	article	NOUN
ejpam-5455	537	10	i	i	PROPN
ejpam-5455	537	11	d	d	PROPN
ejpam-5455	537	12	110557	110557	NUM
ejpam-5455	537	13	,	,	PUNCT
ejpam-5455	537	14	2021	2021	NUM
ejpam-5455	537	15	.	.	PUNCT
ejpam-5455	538	1	[	[	X
ejpam-5455	538	2	30	30	NUM
ejpam-5455	538	3	]	]	X
ejpam-5455	538	4	d.	d.	PROPN
ejpam-5455	538	5	vivek	vivek	PROPN
ejpam-5455	538	6	,	,	PUNCT
ejpam-5455	538	7	o.	o.	PROPN
ejpam-5455	538	8	baghani	baghani	PROPN
ejpam-5455	538	9	,	,	PUNCT
ejpam-5455	538	10	and	and	CCONJ
ejpam-5455	538	11	k.	k.	PROPN
ejpam-5455	538	12	kanagarajan	kanagarajan	PROPN
ejpam-5455	538	13	.	.	PUNCT
ejpam-5455	539	1	existence	existence	NOUN
ejpam-5455	539	2	results	result	VERB
ejpam-5455	539	3	for	for	ADP
ejpam-5455	539	4	hybrid	hybrid	ADJ
ejpam-5455	539	5	fractional	fractional	ADJ
ejpam-5455	539	6	differential	differential	ADJ
ejpam-5455	539	7	equations	equation	NOUN
ejpam-5455	539	8	with	with	ADP
ejpam-5455	539	9	hilfer	hilfer	NOUN
ejpam-5455	539	10	fractional	fractional	ADJ
ejpam-5455	539	11	derivative	derivative	NOUN
ejpam-5455	539	12	.	.	PUNCT
ejpam-5455	540	1	caspian	caspian	PROPN
ejpam-5455	540	2	journal	journal	PROPN
ejpam-5455	540	3	of	of	ADP
ejpam-5455	540	4	mathematical	mathematical	ADJ
ejpam-5455	540	5	sciences	sciences	PROPN
ejpam-5455	540	6	,	,	PUNCT
ejpam-5455	540	7	9(2):294–304	9(2):294–304	NUM
ejpam-5455	540	8	,	,	PUNCT
ejpam-5455	540	9	2020	2020	NUM
ejpam-5455	540	10	.	.	PUNCT
ejpam-5455	541	1	[	[	X
ejpam-5455	541	2	31	31	NUM
ejpam-5455	541	3	]	]	PUNCT
ejpam-5455	541	4	l.	l.	PROPN
ejpam-5455	541	5	zhao	zhao	PROPN
ejpam-5455	541	6	and	and	CCONJ
ejpam-5455	541	7	y.	y.	PROPN
ejpam-5455	541	8	jiang	jiang	PROPN
ejpam-5455	541	9	.	.	PUNCT
ejpam-5455	542	1	existence	existence	NOUN
ejpam-5455	542	2	and	and	CCONJ
ejpam-5455	542	3	stability	stability	NOUN
ejpam-5455	542	4	for	for	ADP
ejpam-5455	542	5	a	a	DET
ejpam-5455	542	6	coupled	couple	VERB
ejpam-5455	542	7	hybrid	hybrid	NOUN
ejpam-5455	542	8	system	system	NOUN
ejpam-5455	542	9	of	of	ADP
ejpam-5455	542	10	fractional	fractional	ADJ
ejpam-5455	542	11	differential	differential	ADJ
ejpam-5455	542	12	equations	equation	NOUN
ejpam-5455	542	13	with	with	ADP
ejpam-5455	542	14	atangana	atangana	PROPN
ejpam-5455	542	15	-	-	PUNCT
ejpam-5455	542	16	baleanu	baleanu	PROPN
ejpam-5455	542	17	-	-	PUNCT
ejpam-5455	542	18	caputo	caputo	PROPN
ejpam-5455	542	19	derivative	derivative	NOUN
ejpam-5455	542	20	.	.	PUNCT
ejpam-5455	543	1	journal	journal	PROPN
ejpam-5455	543	2	of	of	ADP
ejpam-5455	543	3	mathematics	mathematic	NOUN
ejpam-5455	543	4	,	,	PUNCT
ejpam-5455	543	5	2022	2022	NUM
ejpam-5455	543	6	:	:	PUNCT
ejpam-5455	543	7	article	article	NOUN
ejpam-5455	543	8	i	i	PROPN
ejpam-5455	543	9	d	d	PROPN
ejpam-5455	543	10	4741224	4741224	NUM
ejpam-5455	543	11	,	,	PUNCT
ejpam-5455	543	12	12	12	NUM
ejpam-5455	543	13	pages	page	NOUN
ejpam-5455	543	14	,	,	PUNCT
ejpam-5455	543	15	2022	2022	NUM
ejpam-5455	543	16	.	.	PUNCT
ejpam-5455	544	1	[	[	X
ejpam-5455	544	2	32	32	NUM
ejpam-5455	544	3	]	]	X
ejpam-5455	544	4	y.	y.	PROPN
ejpam-5455	544	5	zhao	zhao	PROPN
ejpam-5455	544	6	,	,	PUNCT
ejpam-5455	544	7	s.	s.	PROPN
ejpam-5455	544	8	sun	sun	PROPN
ejpam-5455	544	9	,	,	PUNCT
ejpam-5455	544	10	z.	z.	PROPN
ejpam-5455	544	11	han	han	PROPN
ejpam-5455	544	12	,	,	PUNCT
ejpam-5455	544	13	and	and	CCONJ
ejpam-5455	544	14	q.	q.	PROPN
ejpam-5455	544	15	li	li	PROPN
ejpam-5455	544	16	.	.	PROPN
ejpam-5455	544	17	theory	theory	NOUN
ejpam-5455	544	18	of	of	ADP
ejpam-5455	544	19	fractional	fractional	ADJ
ejpam-5455	544	20	hybrid	hybrid	ADJ
ejpam-5455	544	21	differential	differential	NOUN
ejpam-5455	544	22	equations	equation	NOUN
ejpam-5455	544	23	.	.	PUNCT
ejpam-5455	545	1	computers	computer	NOUN
ejpam-5455	545	2	&	&	CCONJ
ejpam-5455	545	3	mathematics	mathematics	PROPN
ejpam-5455	545	4	with	with	ADP
ejpam-5455	545	5	applications	application	NOUN
ejpam-5455	545	6	,	,	PUNCT
ejpam-5455	545	7	62(3):1312–1324	62(3):1312–1324	NUM
ejpam-5455	545	8	,	,	PUNCT
ejpam-5455	545	9	2011	2011	NUM
ejpam-5455	545	10	.	.	PUNCT