id	sid	tid	token	lemma	pos
ejpam-6466	1	1	european	european	PROPN
ejpam-6466	1	2	journal	journal	PROPN
ejpam-6466	1	3	of	of	ADP
ejpam-6466	1	4	pure	pure	ADJ
ejpam-6466	1	5	and	and	CCONJ
ejpam-6466	1	6	applied	applied	ADJ
ejpam-6466	1	7	mathematics	mathematic	NOUN
ejpam-6466	1	8	2025	2025	NUM
ejpam-6466	1	9	,	,	PUNCT
ejpam-6466	1	10	vol	vol	NOUN
ejpam-6466	1	11	.	.	PROPN
ejpam-6466	1	12	18	18	NUM
ejpam-6466	1	13	,	,	PUNCT
ejpam-6466	1	14	issue	issue	NOUN
ejpam-6466	1	15	4	4	NUM
ejpam-6466	1	16	,	,	PUNCT
ejpam-6466	1	17	article	article	NOUN
ejpam-6466	1	18	number	number	NOUN
ejpam-6466	1	19	6466	6466	NUM
ejpam-6466	1	20	issn	issn	VERB
ejpam-6466	1	21	1307	1307	NUM
ejpam-6466	1	22	-	-	SYM
ejpam-6466	1	23	5543	5543	NUM
ejpam-6466	1	24	–	–	PUNCT
ejpam-6466	1	25	ejpam.com	ejpam.com	X
ejpam-6466	1	26	published	publish	VERB
ejpam-6466	1	27	by	by	ADP
ejpam-6466	1	28	new	new	PROPN
ejpam-6466	1	29	york	york	PROPN
ejpam-6466	1	30	business	business	PROPN
ejpam-6466	1	31	global	global	ADJ
ejpam-6466	1	32	stability	stability	NOUN
ejpam-6466	1	33	results	result	VERB
ejpam-6466	1	34	for	for	ADP
ejpam-6466	1	35	stochastic	stochastic	ADJ
ejpam-6466	1	36	delay	delay	NOUN
ejpam-6466	1	37	differential	differential	NOUN
ejpam-6466	1	38	equations	equation	NOUN
ejpam-6466	1	39	in	in	ADP
ejpam-6466	1	40	the	the	DET
ejpam-6466	1	41	framework	framework	NOUN
ejpam-6466	1	42	of	of	ADP
ejpam-6466	1	43	conformable	conformable	ADJ
ejpam-6466	1	44	fractional	fractional	ADJ
ejpam-6466	1	45	derivatives	derivative	NOUN
ejpam-6466	1	46	muhammad	muhammad	PROPN
ejpam-6466	1	47	imran	imran	PROPN
ejpam-6466	1	48	liaqat1	liaqat1	PROPN
ejpam-6466	1	49	,	,	PUNCT
ejpam-6466	1	50	dumitru	dumitru	PROPN
ejpam-6466	1	51	baleanu2	baleanu2	NOUN
ejpam-6466	1	52	,	,	PUNCT
ejpam-6466	1	53	majeed	majeed	PROPN
ejpam-6466	1	54	ahmad	ahmad	PROPN
ejpam-6466	1	55	yousif3	yousif3	PROPN
ejpam-6466	1	56	,	,	PUNCT
ejpam-6466	1	57	pshtiwan	pshtiwan	PROPN
ejpam-6466	1	58	othman	othman	PROPN
ejpam-6466	1	59	mohammed4,5,6,∗	mohammed4,5,6,∗	PROPN
ejpam-6466	1	60	1	1	NUM
ejpam-6466	1	61	abdus	abdus	NOUN
ejpam-6466	1	62	salam	salam	PROPN
ejpam-6466	1	63	school	school	PROPN
ejpam-6466	1	64	of	of	ADP
ejpam-6466	1	65	mathematical	mathematical	ADJ
ejpam-6466	1	66	sciences	science	NOUN
ejpam-6466	1	67	,	,	PUNCT
ejpam-6466	1	68	government	government	NOUN
ejpam-6466	1	69	college	college	NOUN
ejpam-6466	1	70	university	university	NOUN
ejpam-6466	1	71	,	,	PUNCT
ejpam-6466	1	72	68	68	NUM
ejpam-6466	1	73	-	-	SYM
ejpam-6466	1	74	b	b	NOUN
ejpam-6466	1	75	,	,	PUNCT
ejpam-6466	1	76	new	new	ADJ
ejpam-6466	1	77	muslim	muslim	ADJ
ejpam-6466	1	78	town	town	NOUN
ejpam-6466	1	79	,	,	PUNCT
ejpam-6466	1	80	lahore	lahore	PROPN
ejpam-6466	1	81	54600	54600	NUM
ejpam-6466	1	82	,	,	PUNCT
ejpam-6466	1	83	pakistan	pakistan	PROPN
ejpam-6466	1	84	2	2	NUM
ejpam-6466	1	85	department	department	NOUN
ejpam-6466	1	86	of	of	ADP
ejpam-6466	1	87	computer	computer	NOUN
ejpam-6466	1	88	science	science	NOUN
ejpam-6466	1	89	and	and	CCONJ
ejpam-6466	1	90	mathematics	mathematic	NOUN
ejpam-6466	1	91	,	,	PUNCT
ejpam-6466	1	92	lebanese	lebanese	ADJ
ejpam-6466	1	93	american	american	PROPN
ejpam-6466	1	94	university	university	PROPN
ejpam-6466	1	95	,	,	PUNCT
ejpam-6466	1	96	beirut	beirut	PROPN
ejpam-6466	1	97	11022801	11022801	NUM
ejpam-6466	1	98	,	,	PUNCT
ejpam-6466	1	99	lebanon	lebanon	PROPN
ejpam-6466	1	100	3	3	NUM
ejpam-6466	1	101	department	department	PROPN
ejpam-6466	1	102	of	of	ADP
ejpam-6466	1	103	mathematics	mathematics	PROPN
ejpam-6466	1	104	,	,	PUNCT
ejpam-6466	1	105	college	college	NOUN
ejpam-6466	1	106	of	of	ADP
ejpam-6466	1	107	education	education	NOUN
ejpam-6466	1	108	,	,	PUNCT
ejpam-6466	1	109	university	university	NOUN
ejpam-6466	1	110	of	of	ADP
ejpam-6466	1	111	zakho	zakho	PROPN
ejpam-6466	1	112	,	,	PUNCT
ejpam-6466	1	113	zakho	zakho	PROPN
ejpam-6466	1	114	42002	42002	NUM
ejpam-6466	1	115	,	,	PUNCT
ejpam-6466	1	116	iraq	iraq	PROPN
ejpam-6466	1	117	4	4	NUM
ejpam-6466	1	118	research	research	NOUN
ejpam-6466	1	119	and	and	CCONJ
ejpam-6466	1	120	development	development	NOUN
ejpam-6466	1	121	center	center	NOUN
ejpam-6466	1	122	,	,	PUNCT
ejpam-6466	1	123	university	university	NOUN
ejpam-6466	1	124	of	of	ADP
ejpam-6466	1	125	sulaimani	sulaimani	PROPN
ejpam-6466	1	126	,	,	PUNCT
ejpam-6466	1	127	sulaymaniyah	sulaymaniyah	NOUN
ejpam-6466	1	128	46001	46001	NUM
ejpam-6466	1	129	,	,	PUNCT
ejpam-6466	1	130	iraq	iraq	PROPN
ejpam-6466	1	131	5	5	NUM
ejpam-6466	1	132	research	research	NOUN
ejpam-6466	1	133	center	center	NOUN
ejpam-6466	1	134	,	,	PUNCT
ejpam-6466	1	135	university	university	NOUN
ejpam-6466	1	136	of	of	ADP
ejpam-6466	1	137	halabja	halabja	PROPN
ejpam-6466	1	138	,	,	PUNCT
ejpam-6466	1	139	halabja	halabja	PROPN
ejpam-6466	1	140	46018	46018	NUM
ejpam-6466	1	141	,	,	PUNCT
ejpam-6466	1	142	iraq	iraq	PROPN
ejpam-6466	1	143	6	6	NUM
ejpam-6466	1	144	associate	associate	NOUN
ejpam-6466	1	145	member	member	NOUN
ejpam-6466	1	146	,	,	PUNCT
ejpam-6466	1	147	section	section	NOUN
ejpam-6466	1	148	of	of	ADP
ejpam-6466	1	149	mathematics	mathematic	NOUN
ejpam-6466	1	150	,	,	PUNCT
ejpam-6466	1	151	international	international	ADJ
ejpam-6466	1	152	telematic	telematic	ADJ
ejpam-6466	1	153	university	university	NOUN
ejpam-6466	1	154	uninettuno	uninettuno	NOUN
ejpam-6466	1	155	,	,	PUNCT
ejpam-6466	1	156	corso	corso	PROPN
ejpam-6466	1	157	vittorio	vittorio	PROPN
ejpam-6466	1	158	,	,	PUNCT
ejpam-6466	1	159	italy	italy	PROPN
ejpam-6466	1	160	abstract	abstract	NOUN
ejpam-6466	1	161	.	.	PUNCT
ejpam-6466	2	1	well	well	ADV
ejpam-6466	2	2	-	-	PUNCT
ejpam-6466	2	3	posedness	posedness	NOUN
ejpam-6466	2	4	is	be	AUX
ejpam-6466	2	5	essential	essential	ADJ
ejpam-6466	2	6	in	in	ADP
ejpam-6466	2	7	various	various	ADJ
ejpam-6466	2	8	scientific	scientific	ADJ
ejpam-6466	2	9	and	and	CCONJ
ejpam-6466	2	10	engineering	engineering	NOUN
ejpam-6466	2	11	fields	field	NOUN
ejpam-6466	2	12	,	,	PUNCT
ejpam-6466	2	13	including	include	VERB
ejpam-6466	2	14	physics	physics	NOUN
ejpam-6466	2	15	,	,	PUNCT
ejpam-6466	2	16	engineering	engineering	NOUN
ejpam-6466	2	17	,	,	PUNCT
ejpam-6466	2	18	biological	biological	ADJ
ejpam-6466	2	19	sciences	science	NOUN
ejpam-6466	2	20	,	,	PUNCT
ejpam-6466	2	21	economics	economic	NOUN
ejpam-6466	2	22	,	,	PUNCT
ejpam-6466	2	23	and	and	CCONJ
ejpam-6466	2	24	environmental	environmental	ADJ
ejpam-6466	2	25	science	science	NOUN
ejpam-6466	2	26	.	.	PUNCT
ejpam-6466	3	1	well	well	ADJ
ejpam-6466	3	2	-	-	PUNCT
ejpam-6466	3	3	posedness	posedness	NOUN
ejpam-6466	3	4	ensures	ensure	VERB
ejpam-6466	3	5	that	that	SCONJ
ejpam-6466	3	6	the	the	DET
ejpam-6466	3	7	mathematical	mathematical	ADJ
ejpam-6466	3	8	model	model	NOUN
ejpam-6466	3	9	corresponds	correspond	VERB
ejpam-6466	3	10	to	to	ADP
ejpam-6466	3	11	a	a	DET
ejpam-6466	3	12	physically	physically	ADV
ejpam-6466	3	13	meaningful	meaningful	ADJ
ejpam-6466	3	14	situation	situation	NOUN
ejpam-6466	3	15	.	.	PUNCT
ejpam-6466	4	1	without	without	ADP
ejpam-6466	4	2	well	well	ADV
ejpam-6466	4	3	-	-	PUNCT
ejpam-6466	4	4	posedness	posedness	NOUN
ejpam-6466	4	5	,	,	PUNCT
ejpam-6466	4	6	the	the	DET
ejpam-6466	4	7	solution	solution	NOUN
ejpam-6466	4	8	might	might	AUX
ejpam-6466	4	9	not	not	PART
ejpam-6466	4	10	make	make	VERB
ejpam-6466	4	11	sense	sense	NOUN
ejpam-6466	4	12	in	in	ADP
ejpam-6466	4	13	the	the	DET
ejpam-6466	4	14	context	context	NOUN
ejpam-6466	4	15	of	of	ADP
ejpam-6466	4	16	the	the	DET
ejpam-6466	4	17	problem	problem	NOUN
ejpam-6466	4	18	being	be	AUX
ejpam-6466	4	19	modeled	model	VERB
ejpam-6466	4	20	.	.	PUNCT
ejpam-6466	5	1	the	the	DET
ejpam-6466	5	2	concept	concept	NOUN
ejpam-6466	5	3	of	of	ADP
ejpam-6466	5	4	well	well	NOUN
ejpam-6466	5	5	-	-	PUNCT
ejpam-6466	5	6	posedness	posedness	NOUN
ejpam-6466	5	7	refers	refer	VERB
ejpam-6466	5	8	to	to	ADP
ejpam-6466	5	9	certain	certain	ADJ
ejpam-6466	5	10	desirable	desirable	ADJ
ejpam-6466	5	11	properties	property	NOUN
ejpam-6466	5	12	that	that	PRON
ejpam-6466	5	13	a	a	DET
ejpam-6466	5	14	differential	differential	ADJ
ejpam-6466	5	15	equation	equation	NOUN
ejpam-6466	5	16	must	must	AUX
ejpam-6466	5	17	satisfy	satisfy	VERB
ejpam-6466	5	18	,	,	PUNCT
ejpam-6466	5	19	which	which	PRON
ejpam-6466	5	20	are	be	AUX
ejpam-6466	5	21	existence	existence	NOUN
ejpam-6466	5	22	,	,	PUNCT
ejpam-6466	5	23	uniqueness	uniqueness	NOUN
ejpam-6466	5	24	,	,	PUNCT
ejpam-6466	5	25	and	and	CCONJ
ejpam-6466	5	26	continuous	continuous	ADJ
ejpam-6466	5	27	dependency	dependency	NOUN
ejpam-6466	5	28	.	.	PUNCT
ejpam-6466	6	1	regularization	regularization	NOUN
ejpam-6466	6	2	is	be	AUX
ejpam-6466	6	3	an	an	DET
ejpam-6466	6	4	additional	additional	ADJ
ejpam-6466	6	5	feature	feature	NOUN
ejpam-6466	6	6	of	of	ADP
ejpam-6466	6	7	the	the	DET
ejpam-6466	6	8	solution	solution	NOUN
ejpam-6466	6	9	of	of	ADP
ejpam-6466	6	10	the	the	DET
ejpam-6466	6	11	differential	differential	ADJ
ejpam-6466	6	12	equation	equation	NOUN
ejpam-6466	6	13	,	,	PUNCT
ejpam-6466	6	14	such	such	ADJ
ejpam-6466	6	15	as	as	ADP
ejpam-6466	6	16	the	the	DET
ejpam-6466	6	17	smoothness	smoothness	NOUN
ejpam-6466	6	18	of	of	ADP
ejpam-6466	6	19	the	the	DET
ejpam-6466	6	20	solution	solution	NOUN
ejpam-6466	6	21	.	.	PUNCT
ejpam-6466	7	1	stability	stability	NOUN
ejpam-6466	7	2	theory	theory	NOUN
ejpam-6466	7	3	is	be	AUX
ejpam-6466	7	4	one	one	NUM
ejpam-6466	7	5	of	of	ADP
ejpam-6466	7	6	the	the	DET
ejpam-6466	7	7	indispensable	indispensable	ADJ
ejpam-6466	7	8	qualitative	qualitative	ADJ
ejpam-6466	7	9	concepts	concept	NOUN
ejpam-6466	7	10	of	of	ADP
ejpam-6466	7	11	dynamical	dynamical	ADJ
ejpam-6466	7	12	systems	system	NOUN
ejpam-6466	7	13	.	.	PUNCT
ejpam-6466	8	1	we	we	PRON
ejpam-6466	8	2	established	establish	VERB
ejpam-6466	8	3	results	result	NOUN
ejpam-6466	8	4	about	about	ADP
ejpam-6466	8	5	the	the	DET
ejpam-6466	8	6	well	well	NOUN
ejpam-6466	8	7	-	-	PUNCT
ejpam-6466	8	8	posedness	posedness	NOUN
ejpam-6466	8	9	,	,	PUNCT
ejpam-6466	8	10	regularity	regularity	NOUN
ejpam-6466	8	11	,	,	PUNCT
ejpam-6466	8	12	and	and	CCONJ
ejpam-6466	8	13	ulam	ulam	NOUN
ejpam-6466	8	14	-	-	PUNCT
ejpam-6466	8	15	hyers	hyer	NOUN
ejpam-6466	8	16	stability	stability	NOUN
ejpam-6466	8	17	of	of	ADP
ejpam-6466	8	18	solutions	solution	NOUN
ejpam-6466	8	19	to	to	PART
ejpam-6466	8	20	conformable	conformable	VERB
ejpam-6466	8	21	fractional	fractional	ADJ
ejpam-6466	8	22	stochastic	stochastic	ADJ
ejpam-6466	8	23	delay	delay	NOUN
ejpam-6466	8	24	differential	differential	NOUN
ejpam-6466	8	25	equations	equation	NOUN
ejpam-6466	8	26	.	.	PUNCT
ejpam-6466	9	1	first	first	ADV
ejpam-6466	9	2	,	,	PUNCT
ejpam-6466	9	3	we	we	PRON
ejpam-6466	9	4	discussed	discuss	VERB
ejpam-6466	9	5	the	the	DET
ejpam-6466	9	6	results	result	NOUN
ejpam-6466	9	7	about	about	ADP
ejpam-6466	9	8	the	the	DET
ejpam-6466	9	9	existence	existence	NOUN
ejpam-6466	9	10	and	and	CCONJ
ejpam-6466	9	11	uniqueness	uniqueness	NOUN
ejpam-6466	9	12	of	of	ADP
ejpam-6466	9	13	solutions	solution	NOUN
ejpam-6466	9	14	when	when	SCONJ
ejpam-6466	9	15	the	the	DET
ejpam-6466	9	16	global	global	ADJ
ejpam-6466	9	17	and	and	CCONJ
ejpam-6466	9	18	local	local	ADJ
ejpam-6466	9	19	lipschitz	lipschitz	NOUN
ejpam-6466	9	20	conditions	condition	NOUN
ejpam-6466	9	21	of	of	ADP
ejpam-6466	9	22	the	the	DET
ejpam-6466	9	23	coefficients	coefficient	NOUN
ejpam-6466	9	24	are	be	AUX
ejpam-6466	9	25	satisfied	satisfied	ADJ
ejpam-6466	9	26	.	.	PUNCT
ejpam-6466	10	1	second	second	ADV
ejpam-6466	10	2	,	,	PUNCT
ejpam-6466	10	3	we	we	PRON
ejpam-6466	10	4	demonstrated	demonstrate	VERB
ejpam-6466	10	5	the	the	DET
ejpam-6466	10	6	results	result	NOUN
ejpam-6466	10	7	about	about	ADP
ejpam-6466	10	8	continuously	continuously	ADV
ejpam-6466	10	9	depending	depend	VERB
ejpam-6466	10	10	on	on	ADP
ejpam-6466	10	11	the	the	DET
ejpam-6466	10	12	fractional	fractional	ADJ
ejpam-6466	10	13	order	order	NOUN
ejpam-6466	10	14	ξ	ξ	NOUN
ejpam-6466	10	15	and	and	CCONJ
ejpam-6466	10	16	initial	initial	ADJ
ejpam-6466	10	17	values	value	NOUN
ejpam-6466	10	18	under	under	ADP
ejpam-6466	10	19	the	the	DET
ejpam-6466	10	20	global	global	ADJ
ejpam-6466	10	21	lipschitz	lipschitz	NOUN
ejpam-6466	10	22	condition	condition	NOUN
ejpam-6466	10	23	of	of	ADP
ejpam-6466	10	24	coefficients	coefficient	NOUN
ejpam-6466	10	25	.	.	PUNCT
ejpam-6466	11	1	thirdly	thirdly	ADV
ejpam-6466	11	2	,	,	PUNCT
ejpam-6466	11	3	we	we	PRON
ejpam-6466	11	4	constructed	construct	VERB
ejpam-6466	11	5	results	result	NOUN
ejpam-6466	11	6	regarding	regard	VERB
ejpam-6466	11	7	regularity	regularity	NOUN
ejpam-6466	11	8	and	and	CCONJ
ejpam-6466	11	9	ulam	ulam	NOUN
ejpam-6466	11	10	-	-	PUNCT
ejpam-6466	11	11	hyers	hyer	NOUN
ejpam-6466	11	12	stability	stability	NOUN
ejpam-6466	11	13	,	,	PUNCT
ejpam-6466	11	14	and	and	CCONJ
ejpam-6466	11	15	two	two	NUM
ejpam-6466	11	16	examples	example	NOUN
ejpam-6466	11	17	that	that	PRON
ejpam-6466	11	18	demonstrate	demonstrate	VERB
ejpam-6466	11	19	our	our	PRON
ejpam-6466	11	20	results	result	NOUN
ejpam-6466	11	21	are	be	AUX
ejpam-6466	11	22	presented	present	VERB
ejpam-6466	11	23	.	.	PUNCT
ejpam-6466	12	1	the	the	DET
ejpam-6466	12	2	main	main	ADJ
ejpam-6466	12	3	part	part	NOUN
ejpam-6466	12	4	of	of	ADP
ejpam-6466	12	5	the	the	DET
ejpam-6466	12	6	proof	proof	NOUN
ejpam-6466	12	7	made	make	VERB
ejpam-6466	12	8	use	use	NOUN
ejpam-6466	12	9	of	of	ADP
ejpam-6466	12	10	the	the	DET
ejpam-6466	12	11	truncation	truncation	NOUN
ejpam-6466	12	12	process	process	NOUN
ejpam-6466	12	13	,	,	PUNCT
ejpam-6466	12	14	the	the	DET
ejpam-6466	12	15	banach	banach	ADV
ejpam-6466	12	16	fixed	fix	VERB
ejpam-6466	12	17	point	point	NOUN
ejpam-6466	12	18	theorem	theorem	VERB
ejpam-6466	12	19	,	,	PUNCT
ejpam-6466	12	20	itô	itô	PROPN
ejpam-6466	12	21	isometry	isometry	NOUN
ejpam-6466	12	22	,	,	PUNCT
ejpam-6466	12	23	temporally	temporally	ADV
ejpam-6466	12	24	weighted	weight	VERB
ejpam-6466	12	25	norm	norm	NOUN
ejpam-6466	12	26	,	,	PUNCT
ejpam-6466	12	27	grönwall	grönwall	PROPN
ejpam-6466	12	28	’s	’s	PART
ejpam-6466	12	29	inequality	inequality	NOUN
ejpam-6466	12	30	,	,	PUNCT
ejpam-6466	12	31	and	and	CCONJ
ejpam-6466	12	32	hölder	hölder	NOUN
ejpam-6466	12	33	’s	’s	PART
ejpam-6466	12	34	inequality	inequality	NOUN
ejpam-6466	12	35	.	.	PUNCT
ejpam-6466	13	1	2020	2020	NUM
ejpam-6466	13	2	mathematics	mathematic	NOUN
ejpam-6466	13	3	subject	subject	NOUN
ejpam-6466	13	4	classifications	classification	NOUN
ejpam-6466	13	5	:	:	PUNCT
ejpam-6466	13	6	34a07	34a07	NUM
ejpam-6466	13	7	,	,	PUNCT
ejpam-6466	13	8	34a08	34a08	NUM
ejpam-6466	13	9	,	,	PUNCT
ejpam-6466	13	10	60g22	60g22	NUM
ejpam-6466	13	11	key	key	ADJ
ejpam-6466	13	12	words	word	NOUN
ejpam-6466	13	13	and	and	CCONJ
ejpam-6466	13	14	phrases	phrase	NOUN
ejpam-6466	13	15	:	:	PUNCT
ejpam-6466	13	16	conformable	conformable	ADJ
ejpam-6466	13	17	fractional	fractional	ADJ
ejpam-6466	13	18	derivatives	derivative	NOUN
ejpam-6466	13	19	,	,	PUNCT
ejpam-6466	13	20	delay	delay	NOUN
ejpam-6466	13	21	differential	differential	ADJ
ejpam-6466	13	22	equations	equation	NOUN
ejpam-6466	13	23	,	,	PUNCT
ejpam-6466	13	24	stochastic	stochastic	ADJ
ejpam-6466	13	25	process	process	NOUN
ejpam-6466	13	26	,	,	PUNCT
ejpam-6466	13	27	well	well	NOUN
ejpam-6466	13	28	-	-	PUNCT
ejpam-6466	13	29	posedness	posedness	NOUN
ejpam-6466	13	30	,	,	PUNCT
ejpam-6466	13	31	regularity	regularity	NOUN
ejpam-6466	13	32	,	,	PUNCT
ejpam-6466	13	33	ulam	ulam	NOUN
ejpam-6466	13	34	-	-	PUNCT
ejpam-6466	13	35	hyers	hyer	NOUN
ejpam-6466	13	36	stability	stability	NOUN
ejpam-6466	13	37	∗corresponding	∗corresponde	VERB
ejpam-6466	13	38	author	author	NOUN
ejpam-6466	13	39	.	.	PUNCT
ejpam-6466	14	1	doi	doi	NOUN
ejpam-6466	14	2	:	:	PUNCT
ejpam-6466	14	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6466	https://doi.org/10.29020/nybg.ejpam.v18i4.6466	ADJ
ejpam-6466	14	4	email	email	NOUN
ejpam-6466	14	5	addresses	address	NOUN
ejpam-6466	14	6	:	:	PUNCT
ejpam-6466	14	7	imran	imran	PROPN
ejpam-6466	14	8	liaqat	liaqat	PROPN
ejpam-6466	14	9	22@sms.edu.pk	22@sms.edu.pk	PROPN
ejpam-6466	14	10	(	(	PUNCT
ejpam-6466	14	11	m.	m.	NOUN
ejpam-6466	14	12	i.	i.	PROPN
ejpam-6466	14	13	liaqat	liaqat	PROPN
ejpam-6466	14	14	)	)	PUNCT
ejpam-6466	14	15	,	,	PUNCT
ejpam-6466	14	16	dumitru.baleanu@lau.edu.lb	dumitru.baleanu@lau.edu.lb	PROPN
ejpam-6466	14	17	(	(	PUNCT
ejpam-6466	14	18	d.	d.	PROPN
ejpam-6466	14	19	baleanu	baleanu	PROPN
ejpam-6466	14	20	)	)	PUNCT
ejpam-6466	14	21	,	,	PUNCT
ejpam-6466	14	22	majeed.yousif@uoz.edu.krd	majeed.yousif@uoz.edu.krd	PROPN
ejpam-6466	14	23	(	(	PUNCT
ejpam-6466	14	24	m.	m.	NOUN
ejpam-6466	14	25	a.	a.	PROPN
ejpam-6466	14	26	yousif	yousif	PROPN
ejpam-6466	14	27	)	)	PUNCT
ejpam-6466	14	28	,	,	PUNCT
ejpam-6466	14	29	pshtiwansangawi@gmail.com	pshtiwansangawi@gmail.com	X
ejpam-6466	14	30	(	(	PUNCT
ejpam-6466	14	31	p.	p.	NOUN
ejpam-6466	14	32	o.	o.	PROPN
ejpam-6466	14	33	mohammed	mohammed	PROPN
ejpam-6466	14	34	)	)	PUNCT
ejpam-6466	14	35	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6466	15	1	1	1	NUM
ejpam-6466	15	2	copyright	copyright	NOUN
ejpam-6466	15	3	:	:	PUNCT
ejpam-6466	15	4	©	©	PROPN
ejpam-6466	15	5	2025	2025	NUM
ejpam-6466	15	6	the	the	DET
ejpam-6466	15	7	author(s	author(s	NOUN
ejpam-6466	15	8	)	)	PUNCT
ejpam-6466	15	9	.	.	PUNCT
ejpam-6466	16	1	(	(	PUNCT
ejpam-6466	16	2	cc	cc	NOUN
ejpam-6466	16	3	by	by	ADP
ejpam-6466	16	4	-	-	PUNCT
ejpam-6466	16	5	nc	nc	PROPN
ejpam-6466	16	6	4.0	4.0	NUM
ejpam-6466	16	7	)	)	PUNCT
ejpam-6466	16	8	m.	m.	NOUN
ejpam-6466	16	9	i.	i.	PROPN
ejpam-6466	16	10	liaqat	liaqat	PROPN
ejpam-6466	16	11	et	et	PROPN
ejpam-6466	16	12	al	al	PROPN
ejpam-6466	16	13	.	.	PUNCT
ejpam-6466	16	14	/	/	SYM
ejpam-6466	16	15	eur	eur	PROPN
ejpam-6466	16	16	.	.	PUNCT
ejpam-6466	17	1	j.	j.	PROPN
ejpam-6466	17	2	pure	pure	PROPN
ejpam-6466	17	3	appl	appl	PROPN
ejpam-6466	17	4	.	.	PROPN
ejpam-6466	17	5	math	math	PROPN
ejpam-6466	17	6	,	,	PUNCT
ejpam-6466	17	7	18	18	NUM
ejpam-6466	17	8	(	(	PUNCT
ejpam-6466	17	9	4	4	NUM
ejpam-6466	17	10	)	)	PUNCT
ejpam-6466	17	11	(	(	PUNCT
ejpam-6466	17	12	2025	2025	NUM
ejpam-6466	17	13	)	)	PUNCT
ejpam-6466	17	14	,	,	PUNCT
ejpam-6466	17	15	6466	6466	NUM
ejpam-6466	17	16	2	2	NUM
ejpam-6466	17	17	of	of	ADP
ejpam-6466	17	18	28	28	NUM
ejpam-6466	17	19	1	1	NUM
ejpam-6466	17	20	.	.	PUNCT
ejpam-6466	18	1	introduction	introduction	NOUN
ejpam-6466	18	2	fractional	fractional	ADJ
ejpam-6466	18	3	calculus	calculus	NOUN
ejpam-6466	18	4	(	(	PUNCT
ejpam-6466	18	5	fc	fc	INTJ
ejpam-6466	18	6	)	)	PUNCT
ejpam-6466	18	7	is	be	AUX
ejpam-6466	18	8	a	a	DET
ejpam-6466	18	9	branch	branch	NOUN
ejpam-6466	18	10	of	of	ADP
ejpam-6466	18	11	mathematical	mathematical	ADJ
ejpam-6466	18	12	analysis	analysis	NOUN
ejpam-6466	18	13	that	that	PRON
ejpam-6466	18	14	extends	extend	VERB
ejpam-6466	18	15	the	the	DET
ejpam-6466	18	16	concepts	concept	NOUN
ejpam-6466	18	17	of	of	ADP
ejpam-6466	18	18	differentiation	differentiation	NOUN
ejpam-6466	18	19	and	and	CCONJ
ejpam-6466	18	20	integration	integration	NOUN
ejpam-6466	18	21	to	to	ADP
ejpam-6466	18	22	non	non	ADJ
ejpam-6466	18	23	-	-	ADJ
ejpam-6466	18	24	integer	integer	ADJ
ejpam-6466	18	25	orders	order	NOUN
ejpam-6466	18	26	.	.	PUNCT
ejpam-6466	19	1	instead	instead	ADV
ejpam-6466	19	2	of	of	ADP
ejpam-6466	19	3	dealing	deal	VERB
ejpam-6466	19	4	exclusively	exclusively	ADV
ejpam-6466	19	5	with	with	ADP
ejpam-6466	19	6	integer	integer	NOUN
ejpam-6466	19	7	-	-	PUNCT
ejpam-6466	19	8	order	order	NOUN
ejpam-6466	19	9	derivatives	derivative	NOUN
ejpam-6466	19	10	and	and	CCONJ
ejpam-6466	19	11	integrals	integral	NOUN
ejpam-6466	19	12	,	,	PUNCT
ejpam-6466	19	13	fc	fc	PROPN
ejpam-6466	19	14	involves	involve	VERB
ejpam-6466	19	15	operations	operation	NOUN
ejpam-6466	19	16	of	of	ADP
ejpam-6466	19	17	differentiation	differentiation	NOUN
ejpam-6466	19	18	and	and	CCONJ
ejpam-6466	19	19	integration	integration	NOUN
ejpam-6466	19	20	of	of	ADP
ejpam-6466	19	21	fractional	fractional	ADJ
ejpam-6466	19	22	orders	order	NOUN
ejpam-6466	19	23	.	.	PUNCT
ejpam-6466	20	1	the	the	DET
ejpam-6466	20	2	history	history	NOUN
ejpam-6466	20	3	of	of	ADP
ejpam-6466	20	4	fc	fc	PROPN
ejpam-6466	20	5	dates	date	VERB
ejpam-6466	20	6	back	back	ADV
ejpam-6466	20	7	to	to	ADP
ejpam-6466	20	8	the	the	DET
ejpam-6466	20	9	17th	17th	ADJ
ejpam-6466	20	10	century	century	NOUN
ejpam-6466	20	11	,	,	PUNCT
ejpam-6466	20	12	with	with	ADP
ejpam-6466	20	13	the	the	DET
ejpam-6466	20	14	concept	concept	NOUN
ejpam-6466	20	15	of	of	ADP
ejpam-6466	20	16	fractional	fractional	ADJ
ejpam-6466	20	17	derivatives	derivative	NOUN
ejpam-6466	20	18	and	and	CCONJ
ejpam-6466	20	19	integrals	integral	NOUN
ejpam-6466	20	20	emerging	emerge	VERB
ejpam-6466	20	21	alongside	alongside	ADP
ejpam-6466	20	22	the	the	DET
ejpam-6466	20	23	development	development	NOUN
ejpam-6466	20	24	of	of	ADP
ejpam-6466	20	25	traditional	traditional	ADJ
ejpam-6466	20	26	calculus	calculus	NOUN
ejpam-6466	20	27	.	.	PUNCT
ejpam-6466	21	1	here	here	ADV
ejpam-6466	21	2	is	be	AUX
ejpam-6466	21	3	a	a	DET
ejpam-6466	21	4	brief	brief	ADJ
ejpam-6466	21	5	overview	overview	NOUN
ejpam-6466	21	6	of	of	ADP
ejpam-6466	21	7	the	the	DET
ejpam-6466	21	8	history	history	NOUN
ejpam-6466	21	9	of	of	ADP
ejpam-6466	21	10	fc	fc	PROPN
ejpam-6466	22	1	[	[	X
ejpam-6466	22	2	1–3	1–3	NOUN
ejpam-6466	22	3	]	]	X
ejpam-6466	22	4	:	:	PUNCT
ejpam-6466	22	5	i.	i.	NOUN
ejpam-6466	22	6	beginnings	beginning	NOUN
ejpam-6466	22	7	(	(	PUNCT
ejpam-6466	22	8	17th	17th	ADJ
ejpam-6466	22	9	century	century	NOUN
ejpam-6466	22	10	)	)	PUNCT
ejpam-6466	22	11	•	•	NOUN
ejpam-6466	22	12	leibniz	leibniz	NOUN
ejpam-6466	22	13	and	and	CCONJ
ejpam-6466	22	14	l’hôpital	l’hôpital	PROPN
ejpam-6466	22	15	:	:	PUNCT
ejpam-6466	22	16	leibniz	leibniz	NOUN
ejpam-6466	22	17	introduced	introduce	VERB
ejpam-6466	22	18	the	the	DET
ejpam-6466	22	19	idea	idea	NOUN
ejpam-6466	22	20	of	of	ADP
ejpam-6466	22	21	non	non	ADJ
ejpam-6466	22	22	-	-	ADJ
ejpam-6466	22	23	integer	integer	ADJ
ejpam-6466	22	24	order	order	NOUN
ejpam-6466	22	25	derivatives	derivative	NOUN
ejpam-6466	22	26	in	in	ADP
ejpam-6466	22	27	correspondence	correspondence	NOUN
ejpam-6466	22	28	with	with	ADP
ejpam-6466	22	29	l’hôpital	l’hôpital	ADJ
ejpam-6466	22	30	,	,	PUNCT
ejpam-6466	22	31	pondering	ponder	VERB
ejpam-6466	22	32	the	the	DET
ejpam-6466	22	33	concept	concept	NOUN
ejpam-6466	22	34	of	of	ADP
ejpam-6466	22	35	a	a	DET
ejpam-6466	22	36	half	half	ADJ
ejpam-6466	22	37	-	-	PUNCT
ejpam-6466	22	38	order	order	NOUN
ejpam-6466	22	39	derivative	derivative	NOUN
ejpam-6466	22	40	.	.	PUNCT
ejpam-6466	23	1	ii	ii	PROPN
ejpam-6466	23	2	.	.	PUNCT
ejpam-6466	24	1	exploration	exploration	NOUN
ejpam-6466	24	2	and	and	CCONJ
ejpam-6466	24	3	early	early	ADJ
ejpam-6466	24	4	development	development	NOUN
ejpam-6466	24	5	(	(	PUNCT
ejpam-6466	24	6	18th	18th	ADJ
ejpam-6466	24	7	and	and	CCONJ
ejpam-6466	24	8	19th	19th	ADJ
ejpam-6466	24	9	centuries	century	NOUN
ejpam-6466	24	10	)	)	PUNCT
ejpam-6466	24	11	•	•	NUM
ejpam-6466	24	12	euler	euler	PROPN
ejpam-6466	24	13	:	:	PUNCT
ejpam-6466	24	14	leonhard	leonhard	PROPN
ejpam-6466	24	15	euler	euler	PROPN
ejpam-6466	24	16	made	make	VERB
ejpam-6466	24	17	early	early	ADJ
ejpam-6466	24	18	contributions	contribution	NOUN
ejpam-6466	24	19	to	to	ADP
ejpam-6466	24	20	the	the	DET
ejpam-6466	24	21	theory	theory	NOUN
ejpam-6466	24	22	of	of	ADP
ejpam-6466	24	23	fc	fc	PROPN
ejpam-6466	24	24	,	,	PUNCT
ejpam-6466	24	25	investigating	investigate	VERB
ejpam-6466	24	26	the	the	DET
ejpam-6466	24	27	properties	property	NOUN
ejpam-6466	24	28	of	of	ADP
ejpam-6466	24	29	the	the	DET
ejpam-6466	24	30	gamma	gamma	NOUN
ejpam-6466	24	31	function	function	NOUN
ejpam-6466	24	32	and	and	CCONJ
ejpam-6466	24	33	its	its	PRON
ejpam-6466	24	34	connection	connection	NOUN
ejpam-6466	24	35	to	to	ADP
ejpam-6466	24	36	fc	fc	PROPN
ejpam-6466	24	37	.	.	PROPN
ejpam-6466	24	38	•	•	NUM
ejpam-6466	24	39	liouville	liouville	PROPN
ejpam-6466	24	40	:	:	PUNCT
ejpam-6466	25	1	joseph	joseph	PROPN
ejpam-6466	25	2	liouville	liouville	PROPN
ejpam-6466	25	3	expanded	expand	VERB
ejpam-6466	25	4	upon	upon	SCONJ
ejpam-6466	25	5	euler	euler	NOUN
ejpam-6466	25	6	’s	’s	PART
ejpam-6466	25	7	work	work	NOUN
ejpam-6466	25	8	,	,	PUNCT
ejpam-6466	25	9	developing	develop	VERB
ejpam-6466	25	10	integral	integral	ADJ
ejpam-6466	25	11	representations	representation	NOUN
ejpam-6466	25	12	for	for	ADP
ejpam-6466	25	13	fractional	fractional	ADJ
ejpam-6466	25	14	derivatives	derivative	NOUN
ejpam-6466	25	15	and	and	CCONJ
ejpam-6466	25	16	integrals	integral	NOUN
ejpam-6466	25	17	.	.	PUNCT
ejpam-6466	26	1	•	•	NUM
ejpam-6466	26	2	grnwald	grnwald	NOUN
ejpam-6466	26	3	and	and	CCONJ
ejpam-6466	26	4	letnikov	letnikov	PROPN
ejpam-6466	26	5	:	:	PUNCT
ejpam-6466	26	6	independently	independently	ADV
ejpam-6466	26	7	,	,	PUNCT
ejpam-6466	26	8	grünwald	grünwald	NOUN
ejpam-6466	26	9	and	and	CCONJ
ejpam-6466	26	10	letnikov	letnikov	ADJ
ejpam-6466	26	11	formulated	formulate	VERB
ejpam-6466	26	12	discrete	discrete	ADJ
ejpam-6466	26	13	versions	version	NOUN
ejpam-6466	26	14	of	of	ADP
ejpam-6466	26	15	fractional	fractional	ADJ
ejpam-6466	26	16	derivatives	derivative	NOUN
ejpam-6466	26	17	,	,	PUNCT
ejpam-6466	26	18	laying	lay	VERB
ejpam-6466	26	19	down	down	ADP
ejpam-6466	26	20	the	the	DET
ejpam-6466	26	21	groundwork	groundwork	NOUN
ejpam-6466	26	22	for	for	ADP
ejpam-6466	26	23	numerical	numerical	ADJ
ejpam-6466	26	24	methods	method	NOUN
ejpam-6466	26	25	in	in	ADP
ejpam-6466	26	26	fc	fc	PROPN
ejpam-6466	26	27	.	.	PROPN
ejpam-6466	26	28	•	•	NUM
ejpam-6466	26	29	riemann	riemann	PROPN
ejpam-6466	26	30	-	-	PUNCT
ejpam-6466	26	31	liouville	liouville	VERB
ejpam-6466	26	32	fc	fc	PROPN
ejpam-6466	26	33	:	:	PUNCT
ejpam-6466	26	34	bernhard	bernhard	PROPN
ejpam-6466	26	35	riemann	riemann	PROPN
ejpam-6466	26	36	and	and	CCONJ
ejpam-6466	26	37	joseph	joseph	PROPN
ejpam-6466	26	38	liouville	liouville	PROPN
ejpam-6466	26	39	developed	develop	VERB
ejpam-6466	26	40	the	the	DET
ejpam-6466	26	41	riemann	riemann	PROPN
ejpam-6466	26	42	-	-	PUNCT
ejpam-6466	26	43	liouville	liouville	VERB
ejpam-6466	26	44	approach	approach	NOUN
ejpam-6466	26	45	to	to	ADP
ejpam-6466	26	46	fc	fc	PROPN
ejpam-6466	26	47	,	,	PUNCT
ejpam-6466	26	48	providing	provide	VERB
ejpam-6466	26	49	a	a	DET
ejpam-6466	26	50	rigorous	rigorous	ADJ
ejpam-6466	26	51	mathematical	mathematical	ADJ
ejpam-6466	26	52	framework	framework	NOUN
ejpam-6466	26	53	for	for	ADP
ejpam-6466	26	54	fractional	fractional	ADJ
ejpam-6466	26	55	derivatives	derivative	NOUN
ejpam-6466	26	56	and	and	CCONJ
ejpam-6466	26	57	integrals	integral	NOUN
ejpam-6466	26	58	.	.	PUNCT
ejpam-6466	27	1	iii	iii	X
ejpam-6466	27	2	.	.	PUNCT
ejpam-6466	27	3	consolidation	consolidation	NOUN
ejpam-6466	27	4	and	and	CCONJ
ejpam-6466	27	5	formalization	formalization	NOUN
ejpam-6466	27	6	(	(	PUNCT
ejpam-6466	27	7	20th	20th	ADJ
ejpam-6466	27	8	century	century	NOUN
ejpam-6466	27	9	)	)	PUNCT
ejpam-6466	27	10	•	•	ADP
ejpam-6466	27	11	caputo	caputo	PROPN
ejpam-6466	27	12	fc	fc	PROPN
ejpam-6466	27	13	:	:	PUNCT
ejpam-6466	27	14	michele	michele	PROPN
ejpam-6466	27	15	caputo	caputo	PROPN
ejpam-6466	27	16	modified	modify	VERB
ejpam-6466	27	17	the	the	DET
ejpam-6466	27	18	riemann	riemann	PROPN
ejpam-6466	27	19	-	-	PUNCT
ejpam-6466	27	20	liouville	liouville	VERB
ejpam-6466	27	21	approach	approach	NOUN
ejpam-6466	27	22	known	know	VERB
ejpam-6466	27	23	as	as	ADP
ejpam-6466	27	24	the	the	DET
ejpam-6466	27	25	caputo	caputo	PROPN
ejpam-6466	27	26	fractional	fractional	PROPN
ejpam-6466	27	27	derivative	derivative	NOUN
ejpam-6466	27	28	,	,	PUNCT
ejpam-6466	27	29	which	which	PRON
ejpam-6466	27	30	is	be	AUX
ejpam-6466	27	31	widely	widely	ADV
ejpam-6466	27	32	used	use	VERB
ejpam-6466	27	33	due	due	ADP
ejpam-6466	27	34	to	to	ADP
ejpam-6466	27	35	its	its	PRON
ejpam-6466	27	36	compatibility	compatibility	NOUN
ejpam-6466	27	37	with	with	ADP
ejpam-6466	27	38	initial	initial	ADJ
ejpam-6466	27	39	value	value	NOUN
ejpam-6466	27	40	problems	problem	NOUN
ejpam-6466	27	41	.	.	PUNCT
ejpam-6466	28	1	•	•	NUM
ejpam-6466	28	2	modern	modern	ADJ
ejpam-6466	28	3	developments	development	NOUN
ejpam-6466	28	4	:	:	PUNCT
ejpam-6466	28	5	throughout	throughout	ADP
ejpam-6466	28	6	the	the	DET
ejpam-6466	28	7	20th	20th	ADJ
ejpam-6466	28	8	century	century	NOUN
ejpam-6466	28	9	,	,	PUNCT
ejpam-6466	28	10	mathematicians	mathematician	NOUN
ejpam-6466	28	11	continued	continue	VERB
ejpam-6466	28	12	to	to	PART
ejpam-6466	28	13	explore	explore	VERB
ejpam-6466	28	14	and	and	CCONJ
ejpam-6466	28	15	develop	develop	VERB
ejpam-6466	28	16	the	the	DET
ejpam-6466	28	17	theory	theory	NOUN
ejpam-6466	28	18	of	of	ADP
ejpam-6466	28	19	fc	fc	PROPN
ejpam-6466	28	20	,	,	PUNCT
ejpam-6466	28	21	advancing	advance	VERB
ejpam-6466	28	22	its	its	PRON
ejpam-6466	28	23	applications	application	NOUN
ejpam-6466	28	24	in	in	ADP
ejpam-6466	28	25	various	various	ADJ
ejpam-6466	28	26	scientific	scientific	ADJ
ejpam-6466	28	27	disciplines	discipline	NOUN
ejpam-6466	28	28	.	.	PUNCT
ejpam-6466	29	1	iv	iv	X
ejpam-6466	29	2	.	.	PUNCT
ejpam-6466	29	3	resurgence	resurgence	NOUN
ejpam-6466	29	4	and	and	CCONJ
ejpam-6466	29	5	application	application	NOUN
ejpam-6466	29	6	(	(	PUNCT
ejpam-6466	29	7	late	late	ADJ
ejpam-6466	29	8	20th	20th	ADJ
ejpam-6466	29	9	century	century	NOUN
ejpam-6466	29	10	to	to	PART
ejpam-6466	29	11	present	present	ADJ
ejpam-6466	29	12	):	):	PUNCT
ejpam-6466	29	13	•	•	DET
ejpam-6466	29	14	resurgence	resurgence	NOUN
ejpam-6466	29	15	of	of	ADP
ejpam-6466	29	16	interest	interest	NOUN
ejpam-6466	29	17	:	:	PUNCT
ejpam-6466	29	18	fc	fc	PROPN
ejpam-6466	29	19	experienced	experience	VERB
ejpam-6466	29	20	a	a	DET
ejpam-6466	29	21	resurgence	resurgence	NOUN
ejpam-6466	29	22	of	of	ADP
ejpam-6466	29	23	interest	interest	NOUN
ejpam-6466	29	24	in	in	ADP
ejpam-6466	29	25	the	the	DET
ejpam-6466	29	26	late	late	ADJ
ejpam-6466	29	27	20th	20th	ADJ
ejpam-6466	29	28	century	century	NOUN
ejpam-6466	29	29	and	and	CCONJ
ejpam-6466	29	30	continues	continue	VERB
ejpam-6466	29	31	to	to	PART
ejpam-6466	29	32	be	be	AUX
ejpam-6466	29	33	an	an	DET
ejpam-6466	29	34	active	active	ADJ
ejpam-6466	29	35	area	area	NOUN
ejpam-6466	29	36	of	of	ADP
ejpam-6466	29	37	research	research	NOUN
ejpam-6466	29	38	,	,	PUNCT
ejpam-6466	29	39	driven	drive	VERB
ejpam-6466	29	40	by	by	ADP
ejpam-6466	29	41	its	its	PRON
ejpam-6466	29	42	applications	application	NOUN
ejpam-6466	29	43	in	in	ADP
ejpam-6466	29	44	physics	physics	NOUN
ejpam-6466	29	45	,	,	PUNCT
ejpam-6466	29	46	engineering	engineering	NOUN
ejpam-6466	29	47	,	,	PUNCT
ejpam-6466	29	48	biology	biology	NOUN
ejpam-6466	29	49	,	,	PUNCT
ejpam-6466	29	50	finance	finance	NOUN
ejpam-6466	29	51	,	,	PUNCT
ejpam-6466	29	52	and	and	CCONJ
ejpam-6466	29	53	signal	signal	NOUN
ejpam-6466	29	54	processing	processing	NOUN
ejpam-6466	29	55	.	.	PUNCT
ejpam-6466	30	1	•	•	NUM
ejpam-6466	30	2	applications	application	NOUN
ejpam-6466	30	3	:	:	PUNCT
ejpam-6466	30	4	fc	fc	PROPN
ejpam-6466	30	5	finds	find	VERB
ejpam-6466	30	6	applications	application	NOUN
ejpam-6466	30	7	in	in	ADP
ejpam-6466	30	8	modeling	model	VERB
ejpam-6466	30	9	anomalous	anomalous	ADJ
ejpam-6466	30	10	transport	transport	NOUN
ejpam-6466	30	11	phenomena	phenomenon	NOUN
ejpam-6466	30	12	,	,	PUNCT
ejpam-6466	30	13	viscoelastic	viscoelastic	ADJ
ejpam-6466	30	14	materials	material	NOUN
ejpam-6466	30	15	,	,	PUNCT
ejpam-6466	30	16	biological	biological	ADJ
ejpam-6466	30	17	processes	process	NOUN
ejpam-6466	30	18	,	,	PUNCT
ejpam-6466	30	19	financial	financial	ADJ
ejpam-6466	30	20	markets	market	NOUN
ejpam-6466	30	21	,	,	PUNCT
ejpam-6466	30	22	signal	signal	ADJ
ejpam-6466	30	23	processing	processing	NOUN
ejpam-6466	30	24	,	,	PUNCT
ejpam-6466	30	25	and	and	CCONJ
ejpam-6466	30	26	many	many	ADJ
ejpam-6466	30	27	other	other	ADJ
ejpam-6466	30	28	fields	field	NOUN
ejpam-6466	30	29	.	.	PUNCT
ejpam-6466	31	1	m.	m.	NOUN
ejpam-6466	31	2	i.	i.	PROPN
ejpam-6466	31	3	liaqat	liaqat	PROPN
ejpam-6466	31	4	et	et	PROPN
ejpam-6466	31	5	al	al	PROPN
ejpam-6466	31	6	.	.	PUNCT
ejpam-6466	31	7	/	/	SYM
ejpam-6466	31	8	eur	eur	PROPN
ejpam-6466	31	9	.	.	PUNCT
ejpam-6466	32	1	j.	j.	PROPN
ejpam-6466	32	2	pure	pure	PROPN
ejpam-6466	32	3	appl	appl	PROPN
ejpam-6466	32	4	.	.	PROPN
ejpam-6466	32	5	math	math	PROPN
ejpam-6466	32	6	,	,	PUNCT
ejpam-6466	32	7	18	18	NUM
ejpam-6466	32	8	(	(	PUNCT
ejpam-6466	32	9	4	4	NUM
ejpam-6466	32	10	)	)	PUNCT
ejpam-6466	32	11	(	(	PUNCT
ejpam-6466	32	12	2025	2025	NUM
ejpam-6466	32	13	)	)	PUNCT
ejpam-6466	32	14	,	,	PUNCT
ejpam-6466	32	15	6466	6466	NUM
ejpam-6466	32	16	3	3	NUM
ejpam-6466	32	17	of	of	ADP
ejpam-6466	32	18	28	28	NUM
ejpam-6466	32	19	fc	fc	PROPN
ejpam-6466	32	20	offers	offer	VERB
ejpam-6466	32	21	several	several	ADJ
ejpam-6466	32	22	advantages	advantage	NOUN
ejpam-6466	32	23	over	over	ADP
ejpam-6466	32	24	traditional	traditional	ADJ
ejpam-6466	32	25	integer	integer	NOUN
ejpam-6466	32	26	-	-	PUNCT
ejpam-6466	32	27	order	order	NOUN
ejpam-6466	32	28	calculus	calculus	NOUN
ejpam-6466	32	29	,	,	PUNCT
ejpam-6466	32	30	particularly	particularly	ADV
ejpam-6466	32	31	when	when	SCONJ
ejpam-6466	32	32	dealing	deal	VERB
ejpam-6466	32	33	with	with	ADP
ejpam-6466	32	34	complex	complex	ADJ
ejpam-6466	32	35	,	,	PUNCT
ejpam-6466	32	36	real	real	ADJ
ejpam-6466	32	37	-	-	PUNCT
ejpam-6466	32	38	world	world	NOUN
ejpam-6466	32	39	systems	system	NOUN
ejpam-6466	32	40	.	.	PUNCT
ejpam-6466	33	1	here	here	ADV
ejpam-6466	33	2	are	be	AUX
ejpam-6466	33	3	some	some	PRON
ejpam-6466	33	4	of	of	ADP
ejpam-6466	33	5	the	the	DET
ejpam-6466	33	6	key	key	ADJ
ejpam-6466	33	7	benefits	benefit	NOUN
ejpam-6466	33	8	[	[	X
ejpam-6466	33	9	4–7	4–7	NOUN
ejpam-6466	33	10	]	]	X
ejpam-6466	33	11	:	:	PUNCT
ejpam-6466	33	12	i.	i.	NOUN
ejpam-6466	33	13	modeling	model	VERB
ejpam-6466	33	14	complex	complex	ADJ
ejpam-6466	33	15	phenomena	phenomenon	NOUN
ejpam-6466	33	16	:	:	PUNCT
ejpam-6466	33	17	fc	fc	PROPN
ejpam-6466	33	18	provides	provide	VERB
ejpam-6466	33	19	a	a	DET
ejpam-6466	33	20	powerful	powerful	ADJ
ejpam-6466	33	21	framework	framework	NOUN
ejpam-6466	33	22	for	for	ADP
ejpam-6466	33	23	modeling	modeling	NOUN
ejpam-6466	33	24	and	and	CCONJ
ejpam-6466	33	25	analyzing	analyze	VERB
ejpam-6466	33	26	complex	complex	ADJ
ejpam-6466	33	27	phenomena	phenomenon	NOUN
ejpam-6466	33	28	that	that	PRON
ejpam-6466	33	29	exhibit	exhibit	VERB
ejpam-6466	33	30	non	non	ADJ
ejpam-6466	33	31	-	-	ADJ
ejpam-6466	33	32	local	local	ADJ
ejpam-6466	33	33	interactions	interaction	NOUN
ejpam-6466	33	34	,	,	PUNCT
ejpam-6466	33	35	memory	memory	NOUN
ejpam-6466	33	36	effects	effect	NOUN
ejpam-6466	33	37	,	,	PUNCT
ejpam-6466	33	38	and	and	CCONJ
ejpam-6466	33	39	fractal	fractal	ADJ
ejpam-6466	33	40	properties	property	NOUN
ejpam-6466	33	41	.	.	PUNCT
ejpam-6466	34	1	systems	system	NOUN
ejpam-6466	34	2	with	with	ADP
ejpam-6466	34	3	long	long	ADJ
ejpam-6466	34	4	-	-	PUNCT
ejpam-6466	34	5	range	range	NOUN
ejpam-6466	34	6	dependencies	dependency	NOUN
ejpam-6466	34	7	,	,	PUNCT
ejpam-6466	34	8	anomalous	anomalous	ADJ
ejpam-6466	34	9	diffusion	diffusion	NOUN
ejpam-6466	34	10	,	,	PUNCT
ejpam-6466	34	11	and	and	CCONJ
ejpam-6466	34	12	hereditary	hereditary	ADJ
ejpam-6466	34	13	behaviors	behavior	NOUN
ejpam-6466	34	14	can	can	AUX
ejpam-6466	34	15	be	be	AUX
ejpam-6466	34	16	accurately	accurately	ADV
ejpam-6466	34	17	described	describe	VERB
ejpam-6466	34	18	using	use	VERB
ejpam-6466	34	19	fractional	fractional	ADJ
ejpam-6466	34	20	differential	differential	ADJ
ejpam-6466	34	21	equations	equation	NOUN
ejpam-6466	34	22	.	.	PUNCT
ejpam-6466	35	1	ii	ii	PROPN
ejpam-6466	35	2	.	.	PUNCT
ejpam-6466	35	3	memory	memory	NOUN
ejpam-6466	35	4	and	and	CCONJ
ejpam-6466	35	5	non	non	ADJ
ejpam-6466	35	6	-	-	ADJ
ejpam-6466	35	7	local	local	ADJ
ejpam-6466	35	8	effects	effect	NOUN
ejpam-6466	35	9	:	:	PUNCT
ejpam-6466	35	10	fc	fc	PROPN
ejpam-6466	35	11	captures	capture	VERB
ejpam-6466	35	12	memory	memory	NOUN
ejpam-6466	35	13	effects	effect	NOUN
ejpam-6466	35	14	and	and	CCONJ
ejpam-6466	35	15	non	non	ADJ
ejpam-6466	35	16	-	-	ADJ
ejpam-6466	35	17	local	local	ADJ
ejpam-6466	35	18	interactions	interaction	NOUN
ejpam-6466	35	19	that	that	PRON
ejpam-6466	35	20	are	be	AUX
ejpam-6466	35	21	not	not	PART
ejpam-6466	35	22	adequately	adequately	ADV
ejpam-6466	35	23	addressed	address	VERB
ejpam-6466	35	24	by	by	ADP
ejpam-6466	35	25	classical	classical	ADJ
ejpam-6466	35	26	calculus	calculus	NOUN
ejpam-6466	35	27	.	.	PUNCT
ejpam-6466	36	1	fractional	fractional	ADJ
ejpam-6466	36	2	derivatives	derivative	NOUN
ejpam-6466	36	3	and	and	CCONJ
ejpam-6466	36	4	integrals	integral	NOUN
ejpam-6466	36	5	allow	allow	VERB
ejpam-6466	36	6	for	for	ADP
ejpam-6466	36	7	the	the	DET
ejpam-6466	36	8	incorporation	incorporation	NOUN
ejpam-6466	36	9	of	of	ADP
ejpam-6466	36	10	memory	memory	NOUN
ejpam-6466	36	11	kernels	kernel	NOUN
ejpam-6466	36	12	and	and	CCONJ
ejpam-6466	36	13	long	long	ADJ
ejpam-6466	36	14	-	-	PUNCT
ejpam-6466	36	15	range	range	NOUN
ejpam-6466	36	16	dependencies	dependency	NOUN
ejpam-6466	36	17	,	,	PUNCT
ejpam-6466	36	18	leading	lead	VERB
ejpam-6466	36	19	to	to	ADP
ejpam-6466	36	20	more	more	ADV
ejpam-6466	36	21	realistic	realistic	ADJ
ejpam-6466	36	22	models	model	NOUN
ejpam-6466	36	23	of	of	ADP
ejpam-6466	36	24	dynamic	dynamic	ADJ
ejpam-6466	36	25	systems	system	NOUN
ejpam-6466	36	26	.	.	PUNCT
ejpam-6466	37	1	iii	iii	X
ejpam-6466	37	2	.	.	PROPN
ejpam-6466	37	3	flexibility	flexibility	NOUN
ejpam-6466	37	4	in	in	ADP
ejpam-6466	37	5	representation	representation	NOUN
ejpam-6466	37	6	:	:	PUNCT
ejpam-6466	37	7	fc	fc	PROPN
ejpam-6466	37	8	offers	offer	VERB
ejpam-6466	37	9	a	a	DET
ejpam-6466	37	10	flexible	flexible	ADJ
ejpam-6466	37	11	and	and	CCONJ
ejpam-6466	37	12	versatile	versatile	ADJ
ejpam-6466	37	13	approach	approach	NOUN
ejpam-6466	37	14	to	to	ADP
ejpam-6466	37	15	representing	represent	VERB
ejpam-6466	37	16	and	and	CCONJ
ejpam-6466	37	17	analyzing	analyze	VERB
ejpam-6466	37	18	dynamic	dynamic	ADJ
ejpam-6466	37	19	systems	system	NOUN
ejpam-6466	37	20	.	.	PUNCT
ejpam-6466	38	1	the	the	DET
ejpam-6466	38	2	fractional	fractional	ADJ
ejpam-6466	38	3	order	order	NOUN
ejpam-6466	38	4	provides	provide	VERB
ejpam-6466	38	5	a	a	DET
ejpam-6466	38	6	continuous	continuous	ADJ
ejpam-6466	38	7	spectrum	spectrum	NOUN
ejpam-6466	38	8	of	of	ADP
ejpam-6466	38	9	differentiation	differentiation	NOUN
ejpam-6466	38	10	and	and	CCONJ
ejpam-6466	38	11	integration	integration	NOUN
ejpam-6466	38	12	,	,	PUNCT
ejpam-6466	38	13	allowing	allow	VERB
ejpam-6466	38	14	for	for	ADP
ejpam-6466	38	15	a	a	DET
ejpam-6466	38	16	finer	finer	ADV
ejpam-6466	38	17	-	-	PUNCT
ejpam-6466	38	18	grained	grain	VERB
ejpam-6466	38	19	characterization	characterization	NOUN
ejpam-6466	38	20	of	of	ADP
ejpam-6466	38	21	system	system	NOUN
ejpam-6466	38	22	dynamics	dynamic	NOUN
ejpam-6466	38	23	compared	compare	VERB
ejpam-6466	38	24	to	to	ADP
ejpam-6466	38	25	integer	integer	NOUN
ejpam-6466	38	26	-	-	PUNCT
ejpam-6466	38	27	order	order	NOUN
ejpam-6466	38	28	models	model	NOUN
ejpam-6466	38	29	.	.	PUNCT
ejpam-6466	39	1	iv	iv	X
ejpam-6466	39	2	.	.	PUNCT
ejpam-6466	39	3	fractional	fractional	ADJ
ejpam-6466	39	4	dynamics	dynamic	NOUN
ejpam-6466	39	5	:	:	PUNCT
ejpam-6466	39	6	fc	fc	PROPN
ejpam-6466	39	7	enables	enable	VERB
ejpam-6466	39	8	the	the	DET
ejpam-6466	39	9	study	study	NOUN
ejpam-6466	39	10	of	of	ADP
ejpam-6466	39	11	fractional	fractional	ADJ
ejpam-6466	39	12	-	-	PUNCT
ejpam-6466	39	13	order	order	NOUN
ejpam-6466	39	14	dynamical	dynamical	ADJ
ejpam-6466	39	15	systems	system	NOUN
ejpam-6466	39	16	,	,	PUNCT
ejpam-6466	39	17	which	which	PRON
ejpam-6466	39	18	exhibit	exhibit	VERB
ejpam-6466	39	19	rich	rich	ADJ
ejpam-6466	39	20	and	and	CCONJ
ejpam-6466	39	21	diverse	diverse	ADJ
ejpam-6466	39	22	behaviors	behavior	NOUN
ejpam-6466	39	23	.	.	PUNCT
ejpam-6466	40	1	fractional	fractional	ADJ
ejpam-6466	40	2	dynamics	dynamic	NOUN
ejpam-6466	40	3	encompasses	encompass	VERB
ejpam-6466	40	4	phenomena	phenomenon	NOUN
ejpam-6466	40	5	such	such	ADJ
ejpam-6466	40	6	as	as	ADP
ejpam-6466	40	7	fractional	fractional	ADJ
ejpam-6466	40	8	-	-	PUNCT
ejpam-6466	40	9	order	order	NOUN
ejpam-6466	40	10	chaos	chaos	NOUN
ejpam-6466	40	11	,	,	PUNCT
ejpam-6466	40	12	fractal	fractal	ADJ
ejpam-6466	40	13	patterns	pattern	NOUN
ejpam-6466	40	14	,	,	PUNCT
ejpam-6466	40	15	and	and	CCONJ
ejpam-6466	40	16	anomalous	anomalous	ADJ
ejpam-6466	40	17	transport	transport	NOUN
ejpam-6466	40	18	processes	process	NOUN
ejpam-6466	40	19	,	,	PUNCT
ejpam-6466	40	20	providing	provide	VERB
ejpam-6466	40	21	insights	insight	NOUN
ejpam-6466	40	22	into	into	ADP
ejpam-6466	40	23	the	the	DET
ejpam-6466	40	24	underlying	underlie	VERB
ejpam-6466	40	25	mechanisms	mechanism	NOUN
ejpam-6466	40	26	governing	govern	VERB
ejpam-6466	40	27	complex	complex	ADJ
ejpam-6466	40	28	systems	system	NOUN
ejpam-6466	40	29	.	.	PUNCT
ejpam-6466	41	1	v.	v.	ADP
ejpam-6466	41	2	improved	improved	ADJ
ejpam-6466	41	3	accuracy	accuracy	NOUN
ejpam-6466	41	4	:	:	PUNCT
ejpam-6466	41	5	in	in	ADP
ejpam-6466	41	6	many	many	ADJ
ejpam-6466	41	7	cases	case	NOUN
ejpam-6466	41	8	,	,	PUNCT
ejpam-6466	41	9	fc	fc	PROPN
ejpam-6466	41	10	provides	provide	VERB
ejpam-6466	41	11	more	more	ADV
ejpam-6466	41	12	accurate	accurate	ADJ
ejpam-6466	41	13	descriptions	description	NOUN
ejpam-6466	41	14	of	of	ADP
ejpam-6466	41	15	realworld	realworld	PROPN
ejpam-6466	41	16	phenomena	phenomena	PROPN
ejpam-6466	41	17	compared	compare	VERB
ejpam-6466	41	18	to	to	ADP
ejpam-6466	41	19	classical	classical	ADJ
ejpam-6466	41	20	integer	integer	NOUN
ejpam-6466	41	21	-	-	PUNCT
ejpam-6466	41	22	order	order	NOUN
ejpam-6466	41	23	models	model	NOUN
ejpam-6466	41	24	.	.	PUNCT
ejpam-6466	42	1	by	by	ADP
ejpam-6466	42	2	capturing	capture	VERB
ejpam-6466	42	3	memory	memory	NOUN
ejpam-6466	42	4	effects	effect	NOUN
ejpam-6466	42	5	and	and	CCONJ
ejpam-6466	42	6	long	long	ADJ
ejpam-6466	42	7	-	-	PUNCT
ejpam-6466	42	8	range	range	NOUN
ejpam-6466	42	9	dependencies	dependency	NOUN
ejpam-6466	42	10	,	,	PUNCT
ejpam-6466	42	11	fc	fc	PROPN
ejpam-6466	42	12	can	can	AUX
ejpam-6466	42	13	better	well	ADV
ejpam-6466	42	14	match	match	VERB
ejpam-6466	42	15	experimental	experimental	ADJ
ejpam-6466	42	16	observations	observation	NOUN
ejpam-6466	42	17	and	and	CCONJ
ejpam-6466	42	18	empirical	empirical	ADJ
ejpam-6466	42	19	data	datum	NOUN
ejpam-6466	42	20	,	,	PUNCT
ejpam-6466	42	21	leading	lead	VERB
ejpam-6466	42	22	to	to	ADP
ejpam-6466	42	23	more	more	ADV
ejpam-6466	42	24	reliable	reliable	ADJ
ejpam-6466	42	25	predictions	prediction	NOUN
ejpam-6466	42	26	and	and	CCONJ
ejpam-6466	42	27	interpretations	interpretation	NOUN
ejpam-6466	42	28	.	.	PUNCT
ejpam-6466	43	1	vi	vi	X
ejpam-6466	43	2	.	.	NOUN
ejpam-6466	43	3	generalization	generalization	NOUN
ejpam-6466	43	4	of	of	ADP
ejpam-6466	43	5	classical	classical	ADJ
ejpam-6466	43	6	calculus	calculus	NOUN
ejpam-6466	43	7	:	:	PUNCT
ejpam-6466	43	8	fc	fc	PROPN
ejpam-6466	43	9	generalizes	generalize	VERB
ejpam-6466	43	10	classical	classical	ADJ
ejpam-6466	43	11	calculus	calculus	NOUN
ejpam-6466	43	12	by	by	ADP
ejpam-6466	43	13	extending	extend	VERB
ejpam-6466	43	14	differentiation	differentiation	NOUN
ejpam-6466	43	15	and	and	CCONJ
ejpam-6466	43	16	integration	integration	NOUN
ejpam-6466	43	17	to	to	ADP
ejpam-6466	43	18	non	non	ADJ
ejpam-6466	43	19	-	-	ADJ
ejpam-6466	43	20	integer	integer	ADJ
ejpam-6466	43	21	orders	order	NOUN
ejpam-6466	43	22	.	.	PUNCT
ejpam-6466	44	1	this	this	PRON
ejpam-6466	44	2	allows	allow	VERB
ejpam-6466	44	3	for	for	ADP
ejpam-6466	44	4	a	a	DET
ejpam-6466	44	5	seamless	seamless	ADJ
ejpam-6466	44	6	transition	transition	NOUN
ejpam-6466	44	7	between	between	ADP
ejpam-6466	44	8	classical	classical	ADJ
ejpam-6466	44	9	and	and	CCONJ
ejpam-6466	44	10	fc	fc	INTJ
ejpam-6466	44	11	,	,	PUNCT
ejpam-6466	44	12	providing	provide	VERB
ejpam-6466	44	13	a	a	DET
ejpam-6466	44	14	unified	unified	ADJ
ejpam-6466	44	15	framework	framework	NOUN
ejpam-6466	44	16	for	for	ADP
ejpam-6466	44	17	addressing	address	VERB
ejpam-6466	44	18	a	a	DET
ejpam-6466	44	19	wide	wide	ADJ
ejpam-6466	44	20	range	range	NOUN
ejpam-6466	44	21	of	of	ADP
ejpam-6466	44	22	problems	problem	NOUN
ejpam-6466	44	23	in	in	ADP
ejpam-6466	44	24	mathematics	mathematic	NOUN
ejpam-6466	44	25	,	,	PUNCT
ejpam-6466	44	26	science	science	NOUN
ejpam-6466	44	27	,	,	PUNCT
ejpam-6466	44	28	and	and	CCONJ
ejpam-6466	44	29	engineering	engineering	NOUN
ejpam-6466	44	30	.	.	PUNCT
ejpam-6466	45	1	vii	vii	PROPN
ejpam-6466	45	2	.	.	PROPN
ejpam-6466	45	3	applications	application	NOUN
ejpam-6466	45	4	in	in	ADP
ejpam-6466	45	5	various	various	ADJ
ejpam-6466	45	6	fields	field	NOUN
ejpam-6466	45	7	:	:	PUNCT
ejpam-6466	45	8	fc	fc	PROPN
ejpam-6466	45	9	has	have	VERB
ejpam-6466	45	10	diverse	diverse	ADJ
ejpam-6466	45	11	applications	application	NOUN
ejpam-6466	45	12	across	across	ADP
ejpam-6466	45	13	numerous	numerous	ADJ
ejpam-6466	45	14	fields	field	NOUN
ejpam-6466	45	15	,	,	PUNCT
ejpam-6466	45	16	including	include	VERB
ejpam-6466	45	17	physics	physics	NOUN
ejpam-6466	45	18	,	,	PUNCT
ejpam-6466	45	19	engineering	engineering	NOUN
ejpam-6466	45	20	,	,	PUNCT
ejpam-6466	45	21	biology	biology	NOUN
ejpam-6466	45	22	,	,	PUNCT
ejpam-6466	45	23	finance	finance	NOUN
ejpam-6466	45	24	,	,	PUNCT
ejpam-6466	45	25	and	and	CCONJ
ejpam-6466	45	26	signal	signal	ADJ
ejpam-6466	45	27	processing	processing	NOUN
ejpam-6466	45	28	.	.	PUNCT
ejpam-6466	46	1	it	it	PRON
ejpam-6466	46	2	is	be	AUX
ejpam-6466	46	3	used	use	VERB
ejpam-6466	46	4	to	to	PART
ejpam-6466	46	5	model	model	VERB
ejpam-6466	46	6	and	and	CCONJ
ejpam-6466	46	7	analyze	analyze	VERB
ejpam-6466	46	8	phenomena	phenomenon	NOUN
ejpam-6466	46	9	such	such	ADJ
ejpam-6466	46	10	as	as	ADP
ejpam-6466	46	11	diffusion	diffusion	NOUN
ejpam-6466	46	12	processes	process	NOUN
ejpam-6466	46	13	,	,	PUNCT
ejpam-6466	46	14	viscoelasticity	viscoelasticity	NOUN
ejpam-6466	46	15	,	,	PUNCT
ejpam-6466	46	16	population	population	NOUN
ejpam-6466	46	17	dynamics	dynamic	NOUN
ejpam-6466	46	18	,	,	PUNCT
ejpam-6466	46	19	financial	financial	ADJ
ejpam-6466	46	20	time	time	NOUN
ejpam-6466	46	21	series	series	NOUN
ejpam-6466	46	22	,	,	PUNCT
ejpam-6466	46	23	and	and	CCONJ
ejpam-6466	46	24	medical	medical	ADJ
ejpam-6466	46	25	imaging	imaging	NOUN
ejpam-6466	46	26	,	,	PUNCT
ejpam-6466	46	27	among	among	ADP
ejpam-6466	46	28	others	other	NOUN
ejpam-6466	46	29	.	.	PUNCT
ejpam-6466	47	1	viii	viii	PROPN
ejpam-6466	47	2	.	.	PUNCT
ejpam-6466	48	1	novel	novel	ADJ
ejpam-6466	48	2	mathematical	mathematical	ADJ
ejpam-6466	48	3	properties	property	NOUN
ejpam-6466	48	4	:	:	PUNCT
ejpam-6466	48	5	fc	fc	PROPN
ejpam-6466	48	6	possesses	possess	VERB
ejpam-6466	48	7	unique	unique	ADJ
ejpam-6466	48	8	mathematical	mathematical	ADJ
ejpam-6466	48	9	properties	property	NOUN
ejpam-6466	48	10	that	that	PRON
ejpam-6466	48	11	distinguish	distinguish	VERB
ejpam-6466	48	12	it	it	PRON
ejpam-6466	48	13	from	from	ADP
ejpam-6466	48	14	classical	classical	ADJ
ejpam-6466	48	15	calculus	calculus	NOUN
ejpam-6466	48	16	.	.	PUNCT
ejpam-6466	49	1	it	it	PRON
ejpam-6466	49	2	introduces	introduce	VERB
ejpam-6466	49	3	fractional	fractional	ADJ
ejpam-6466	49	4	-	-	PUNCT
ejpam-6466	49	5	order	order	NOUN
ejpam-6466	49	6	operators	operator	NOUN
ejpam-6466	49	7	,	,	PUNCT
ejpam-6466	49	8	fractional	fractional	PROPN
ejpam-6466	49	9	taylor	taylor	PROPN
ejpam-6466	49	10	series	series	PROPN
ejpam-6466	49	11	,	,	PUNCT
ejpam-6466	49	12	and	and	CCONJ
ejpam-6466	49	13	fractional	fractional	ADJ
ejpam-6466	49	14	boundary	boundary	ADJ
ejpam-6466	49	15	value	value	NOUN
ejpam-6466	49	16	problems	problem	NOUN
ejpam-6466	49	17	,	,	PUNCT
ejpam-6466	49	18	enriching	enrich	VERB
ejpam-6466	49	19	the	the	DET
ejpam-6466	49	20	theoretical	theoretical	ADJ
ejpam-6466	49	21	toolkit	toolkit	NOUN
ejpam-6466	49	22	of	of	ADP
ejpam-6466	49	23	mathematicians	mathematician	NOUN
ejpam-6466	49	24	and	and	CCONJ
ejpam-6466	49	25	researchers	researcher	NOUN
ejpam-6466	49	26	.	.	PUNCT
ejpam-6466	50	1	fractional	fractional	ADJ
ejpam-6466	50	2	derivatives	derivative	NOUN
ejpam-6466	50	3	serve	serve	VERB
ejpam-6466	50	4	as	as	ADP
ejpam-6466	50	5	a	a	DET
ejpam-6466	50	6	foundational	foundational	ADJ
ejpam-6466	50	7	element	element	NOUN
ejpam-6466	50	8	of	of	ADP
ejpam-6466	50	9	fc	fc	PROPN
ejpam-6466	50	10	,	,	PUNCT
ejpam-6466	50	11	providing	provide	VERB
ejpam-6466	50	12	a	a	DET
ejpam-6466	50	13	robust	robust	ADJ
ejpam-6466	50	14	mechanism	mechanism	NOUN
ejpam-6466	50	15	for	for	ADP
ejpam-6466	50	16	modeling	modeling	NOUN
ejpam-6466	50	17	and	and	CCONJ
ejpam-6466	50	18	analyzing	analyze	VERB
ejpam-6466	50	19	systems	system	NOUN
ejpam-6466	50	20	that	that	PRON
ejpam-6466	50	21	exhibit	exhibit	VERB
ejpam-6466	50	22	non	non	ADJ
ejpam-6466	50	23	-	-	ADJ
ejpam-6466	50	24	locality	locality	ADJ
ejpam-6466	50	25	or	or	CCONJ
ejpam-6466	50	26	memorydependent	memorydependent	ADJ
ejpam-6466	50	27	behavior	behavior	NOUN
ejpam-6466	50	28	.	.	PUNCT
ejpam-6466	51	1	in	in	ADP
ejpam-6466	51	2	contrast	contrast	NOUN
ejpam-6466	51	3	to	to	ADP
ejpam-6466	51	4	classical	classical	ADJ
ejpam-6466	51	5	integer	integer	NOUN
ejpam-6466	51	6	-	-	PUNCT
ejpam-6466	51	7	order	order	NOUN
ejpam-6466	51	8	derivatives	derivative	NOUN
ejpam-6466	51	9	,	,	PUNCT
ejpam-6466	51	10	which	which	PRON
ejpam-6466	51	11	capture	capture	VERB
ejpam-6466	51	12	only	only	ADV
ejpam-6466	51	13	m.	m.	NOUN
ejpam-6466	51	14	i.	i.	PROPN
ejpam-6466	51	15	liaqat	liaqat	PROPN
ejpam-6466	51	16	et	et	PROPN
ejpam-6466	51	17	al	al	PROPN
ejpam-6466	51	18	.	.	PUNCT
ejpam-6466	51	19	/	/	SYM
ejpam-6466	51	20	eur	eur	PROPN
ejpam-6466	51	21	.	.	PUNCT
ejpam-6466	52	1	j.	j.	PROPN
ejpam-6466	52	2	pure	pure	PROPN
ejpam-6466	52	3	appl	appl	PROPN
ejpam-6466	52	4	.	.	PROPN
ejpam-6466	52	5	math	math	PROPN
ejpam-6466	52	6	,	,	PUNCT
ejpam-6466	52	7	18	18	NUM
ejpam-6466	52	8	(	(	PUNCT
ejpam-6466	52	9	4	4	NUM
ejpam-6466	52	10	)	)	PUNCT
ejpam-6466	52	11	(	(	PUNCT
ejpam-6466	52	12	2025	2025	NUM
ejpam-6466	52	13	)	)	PUNCT
ejpam-6466	52	14	,	,	PUNCT
ejpam-6466	52	15	6466	6466	NUM
ejpam-6466	52	16	4	4	NUM
ejpam-6466	52	17	of	of	ADP
ejpam-6466	52	18	28	28	NUM
ejpam-6466	52	19	the	the	DET
ejpam-6466	52	20	instantaneous	instantaneous	ADJ
ejpam-6466	52	21	rate	rate	NOUN
ejpam-6466	52	22	of	of	ADP
ejpam-6466	52	23	change	change	NOUN
ejpam-6466	52	24	,	,	PUNCT
ejpam-6466	52	25	fractional	fractional	ADJ
ejpam-6466	52	26	derivatives	derivative	NOUN
ejpam-6466	52	27	account	account	VERB
ejpam-6466	52	28	for	for	ADP
ejpam-6466	52	29	a	a	DET
ejpam-6466	52	30	function	function	NOUN
ejpam-6466	52	31	’s	’s	PART
ejpam-6466	52	32	history	history	NOUN
ejpam-6466	52	33	over	over	ADP
ejpam-6466	52	34	an	an	DET
ejpam-6466	52	35	interval	interval	NOUN
ejpam-6466	52	36	,	,	PUNCT
ejpam-6466	52	37	effectively	effectively	ADV
ejpam-6466	52	38	incorporating	incorporate	VERB
ejpam-6466	52	39	memory	memory	NOUN
ejpam-6466	52	40	into	into	ADP
ejpam-6466	52	41	the	the	DET
ejpam-6466	52	42	system	system	NOUN
ejpam-6466	52	43	’s	’s	PART
ejpam-6466	52	44	dynamics	dynamic	NOUN
ejpam-6466	52	45	.	.	PUNCT
ejpam-6466	53	1	there	there	PRON
ejpam-6466	53	2	are	be	VERB
ejpam-6466	53	3	several	several	ADJ
ejpam-6466	53	4	formulations	formulation	NOUN
ejpam-6466	53	5	of	of	ADP
ejpam-6466	53	6	fractional	fractional	ADJ
ejpam-6466	53	7	-	-	PUNCT
ejpam-6466	53	8	order	order	NOUN
ejpam-6466	53	9	derivatives	derivative	NOUN
ejpam-6466	53	10	,	,	PUNCT
ejpam-6466	53	11	each	each	PRON
ejpam-6466	53	12	with	with	ADP
ejpam-6466	53	13	distinct	distinct	ADJ
ejpam-6466	53	14	definitions	definition	NOUN
ejpam-6466	53	15	and	and	CCONJ
ejpam-6466	53	16	characteristics	characteristic	NOUN
ejpam-6466	53	17	.	.	PUNCT
ejpam-6466	54	1	commonly	commonly	ADV
ejpam-6466	54	2	utilized	utilize	VERB
ejpam-6466	54	3	forms	form	NOUN
ejpam-6466	54	4	include	include	VERB
ejpam-6466	54	5	the	the	DET
ejpam-6466	54	6	riemann	riemann	PROPN
ejpam-6466	54	7	-	-	PUNCT
ejpam-6466	54	8	liouville	liouville	PROPN
ejpam-6466	54	9	,	,	PUNCT
ejpam-6466	54	10	caputo	caputo	PROPN
ejpam-6466	54	11	,	,	PUNCT
ejpam-6466	54	12	grünwald	grünwald	NOUN
ejpam-6466	54	13	-	-	PUNCT
ejpam-6466	54	14	letnikov	letnikov	ADJ
ejpam-6466	54	15	,	,	PUNCT
ejpam-6466	54	16	caputo	caputo	PROPN
ejpam-6466	54	17	-	-	PUNCT
ejpam-6466	54	18	fabrizio	fabrizio	PROPN
ejpam-6466	54	19	,	,	PUNCT
ejpam-6466	54	20	and	and	CCONJ
ejpam-6466	54	21	conformable	conformable	ADJ
ejpam-6466	54	22	operators	operator	NOUN
ejpam-6466	54	23	[	[	X
ejpam-6466	54	24	8–15	8–15	PROPN
ejpam-6466	54	25	]	]	PUNCT
ejpam-6466	54	26	.	.	PUNCT
ejpam-6466	55	1	the	the	DET
ejpam-6466	55	2	choice	choice	NOUN
ejpam-6466	55	3	of	of	ADP
ejpam-6466	55	4	a	a	DET
ejpam-6466	55	5	particular	particular	ADJ
ejpam-6466	55	6	definition	definition	NOUN
ejpam-6466	55	7	depends	depend	VERB
ejpam-6466	55	8	on	on	ADP
ejpam-6466	55	9	the	the	DET
ejpam-6466	55	10	nature	nature	NOUN
ejpam-6466	55	11	of	of	ADP
ejpam-6466	55	12	the	the	DET
ejpam-6466	55	13	application	application	NOUN
ejpam-6466	55	14	and	and	CCONJ
ejpam-6466	55	15	the	the	DET
ejpam-6466	55	16	mathematical	mathematical	ADJ
ejpam-6466	55	17	properties	property	NOUN
ejpam-6466	55	18	required	require	VERB
ejpam-6466	55	19	for	for	ADP
ejpam-6466	55	20	accurate	accurate	ADJ
ejpam-6466	55	21	modeling	modeling	NOUN
ejpam-6466	55	22	.	.	PUNCT
ejpam-6466	56	1	conformable	conformable	ADJ
ejpam-6466	56	2	fractional	fractional	ADJ
ejpam-6466	56	3	derivatives	derivative	NOUN
ejpam-6466	56	4	(	(	PUNCT
ejpam-6466	56	5	con	con	ADJ
ejpam-6466	56	6	-	-	PUNCT
ejpam-6466	56	7	frd	frd	ADJ
ejpam-6466	56	8	)	)	PUNCT
ejpam-6466	56	9	offer	offer	VERB
ejpam-6466	56	10	a	a	DET
ejpam-6466	56	11	practical	practical	ADJ
ejpam-6466	56	12	and	and	CCONJ
ejpam-6466	56	13	intuitive	intuitive	ADJ
ejpam-6466	56	14	framework	framework	NOUN
ejpam-6466	56	15	for	for	ADP
ejpam-6466	56	16	embedding	embed	VERB
ejpam-6466	56	17	memory	memory	NOUN
ejpam-6466	56	18	effects	effect	NOUN
ejpam-6466	56	19	into	into	ADP
ejpam-6466	56	20	differential	differential	ADJ
ejpam-6466	56	21	equations	equation	NOUN
ejpam-6466	56	22	.	.	PUNCT
ejpam-6466	57	1	they	they	PRON
ejpam-6466	57	2	preserve	preserve	VERB
ejpam-6466	57	3	several	several	ADJ
ejpam-6466	57	4	key	key	ADJ
ejpam-6466	57	5	characteristics	characteristic	NOUN
ejpam-6466	57	6	of	of	ADP
ejpam-6466	57	7	classical	classical	ADJ
ejpam-6466	57	8	derivatives	derivative	NOUN
ejpam-6466	57	9	,	,	PUNCT
ejpam-6466	57	10	which	which	PRON
ejpam-6466	57	11	simplifies	simplify	VERB
ejpam-6466	57	12	their	their	PRON
ejpam-6466	57	13	application	application	NOUN
ejpam-6466	57	14	,	,	PUNCT
ejpam-6466	57	15	while	while	SCONJ
ejpam-6466	57	16	still	still	ADV
ejpam-6466	57	17	providing	provide	VERB
ejpam-6466	57	18	the	the	DET
ejpam-6466	57	19	adaptability	adaptability	NOUN
ejpam-6466	57	20	inherent	inherent	ADJ
ejpam-6466	57	21	in	in	ADP
ejpam-6466	57	22	fc	fc	PROPN
ejpam-6466	57	23	.	.	PUNCT
ejpam-6466	58	1	this	this	DET
ejpam-6466	58	2	balance	balance	NOUN
ejpam-6466	58	3	makes	make	VERB
ejpam-6466	58	4	con	con	NOUN
ejpam-6466	58	5	-	-	PUNCT
ejpam-6466	58	6	frd	frd	ADJ
ejpam-6466	58	7	especially	especially	ADV
ejpam-6466	58	8	useful	useful	ADJ
ejpam-6466	58	9	for	for	ADP
ejpam-6466	58	10	modeling	model	VERB
ejpam-6466	58	11	real	real	ADJ
ejpam-6466	58	12	-	-	PUNCT
ejpam-6466	58	13	world	world	NOUN
ejpam-6466	58	14	processes	process	NOUN
ejpam-6466	58	15	across	across	ADP
ejpam-6466	58	16	diverse	diverse	ADJ
ejpam-6466	58	17	disciplines	discipline	NOUN
ejpam-6466	58	18	such	such	ADJ
ejpam-6466	58	19	as	as	ADP
ejpam-6466	58	20	physics	physics	NOUN
ejpam-6466	58	21	,	,	PUNCT
ejpam-6466	58	22	engineering	engineering	NOUN
ejpam-6466	58	23	,	,	PUNCT
ejpam-6466	58	24	biology	biology	NOUN
ejpam-6466	58	25	,	,	PUNCT
ejpam-6466	58	26	and	and	CCONJ
ejpam-6466	58	27	control	control	NOUN
ejpam-6466	58	28	theory	theory	NOUN
ejpam-6466	58	29	.	.	PUNCT
ejpam-6466	59	1	the	the	DET
ejpam-6466	59	2	con	con	NOUN
ejpam-6466	59	3	-	-	PUNCT
ejpam-6466	59	4	frd	frd	NOUN
ejpam-6466	59	5	of	of	ADP
ejpam-6466	59	6	order	order	NOUN
ejpam-6466	59	7	ξ	ξ	PROPN
ejpam-6466	59	8	for	for	ADP
ejpam-6466	59	9	a	a	DET
ejpam-6466	59	10	function	function	NOUN
ejpam-6466	59	11	ψ(τ	ψ(τ	PART
ejpam-6466	59	12	)	)	PUNCT
ejpam-6466	59	13	is	be	AUX
ejpam-6466	59	14	expressed	express	VERB
ejpam-6466	59	15	as	as	ADP
ejpam-6466	59	16	[	[	X
ejpam-6466	59	17	16	16	NUM
ejpam-6466	59	18	]	]	X
ejpam-6466	59	19	:	:	PUNCT
ejpam-6466	59	20	dξ	dξ	PROPN
ejpam-6466	59	21	τψ(τ	τψ(τ	PUNCT
ejpam-6466	59	22	)	)	PUNCT
ejpam-6466	60	1	=	=	SYM
ejpam-6466	60	2	lim	lim	PROPN
ejpam-6466	60	3	ϵ→0	ϵ→0	X
ejpam-6466	60	4	ψ⌈ξ⌉−1(τ	ψ⌈ξ⌉−1(τ	PROPN
ejpam-6466	60	5	+	+	CCONJ
ejpam-6466	60	6	ϵτ	ϵτ	X
ejpam-6466	60	7	⌈ξ⌉−ξ)−ψ⌈ξ⌉−1(τ	⌈ξ⌉−ξ)−ψ⌈ξ⌉−1(τ	NOUN
ejpam-6466	60	8	)	)	PUNCT
ejpam-6466	60	9	ϵ	ϵ	X
ejpam-6466	60	10	,	,	PUNCT
ejpam-6466	60	11	(	(	PUNCT
ejpam-6466	60	12	1	1	X
ejpam-6466	60	13	)	)	PUNCT
ejpam-6466	60	14	here	here	ADV
ejpam-6466	60	15	,	,	PUNCT
ejpam-6466	60	16	the	the	DET
ejpam-6466	60	17	con	con	NOUN
ejpam-6466	60	18	-	-	PUNCT
ejpam-6466	60	19	frd	frd	ADJ
ejpam-6466	60	20	with	with	ADP
ejpam-6466	60	21	respect	respect	NOUN
ejpam-6466	60	22	to	to	ADP
ejpam-6466	60	23	time	time	NOUN
ejpam-6466	60	24	is	be	AUX
ejpam-6466	60	25	represented	represent	VERB
ejpam-6466	60	26	by	by	ADP
ejpam-6466	60	27	dξ	dξ	PROPN
ejpam-6466	60	28	τ	τ	PROPN
ejpam-6466	60	29	;	;	PUNCT
ejpam-6466	60	30	⌈ξ⌉	⌈ξ⌉	ADJ
ejpam-6466	60	31	denotes	denote	VERB
ejpam-6466	60	32	the	the	DET
ejpam-6466	60	33	smallest	small	ADJ
ejpam-6466	60	34	integer	integer	NOUN
ejpam-6466	60	35	not	not	PART
ejpam-6466	60	36	less	less	ADJ
ejpam-6466	60	37	than	than	ADP
ejpam-6466	60	38	ξ	ξ	PROPN
ejpam-6466	60	39	,	,	PUNCT
ejpam-6466	60	40	where	where	SCONJ
ejpam-6466	60	41	κ	κ	PROPN
ejpam-6466	60	42	∈	∈	PROPN
ejpam-6466	60	43	n	n	ADV
ejpam-6466	60	44	and	and	CCONJ
ejpam-6466	60	45	satisfies	satisfy	VERB
ejpam-6466	60	46	κ	κ	ADP
ejpam-6466	60	47	−	−	PROPN
ejpam-6466	60	48	1	1	NUM
ejpam-6466	60	49	<	<	X
ejpam-6466	60	50	ξ	ξ	PRON
ejpam-6466	60	51	≤	≤	NOUN
ejpam-6466	60	52	κ	κ	NOUN
ejpam-6466	60	53	for	for	ADP
ejpam-6466	60	54	τ	τ	PROPN
ejpam-6466	60	55	>	>	X
ejpam-6466	60	56	0	0	PROPN
ejpam-6466	60	57	.	.	PUNCT
ejpam-6466	61	1	in	in	ADP
ejpam-6466	61	2	a	a	DET
ejpam-6466	61	3	specific	specific	ADJ
ejpam-6466	61	4	case	case	NOUN
ejpam-6466	61	5	,	,	PUNCT
ejpam-6466	61	6	if	if	SCONJ
ejpam-6466	61	7	0	0	NUM
ejpam-6466	61	8	<	<	X
ejpam-6466	61	9	ξ	ξ	X
ejpam-6466	61	10	≤	≤	NUM
ejpam-6466	61	11	1	1	NUM
ejpam-6466	61	12	,	,	PUNCT
ejpam-6466	61	13	we	we	PRON
ejpam-6466	61	14	then	then	ADV
ejpam-6466	61	15	obtain	obtain	VERB
ejpam-6466	61	16	dξ	dξ	PRON
ejpam-6466	61	17	τψ(τ	τψ(τ	PUNCT
ejpam-6466	61	18	)	)	PUNCT
ejpam-6466	62	1	=	=	SYM
ejpam-6466	62	2	lim	lim	PROPN
ejpam-6466	62	3	ϵ→0	ϵ→0	X
ejpam-6466	62	4	ψ(τ	ψ(τ	PROPN
ejpam-6466	62	5	+	+	X
ejpam-6466	62	6	ϵτ1−ξ)−ψ(τ	ϵτ1−ξ)−ψ(τ	NUM
ejpam-6466	62	7	)	)	PUNCT
ejpam-6466	62	8	ϵ	ϵ	X
ejpam-6466	62	9	,	,	PUNCT
ejpam-6466	62	10	τ	τ	PROPN
ejpam-6466	62	11	>	>	X
ejpam-6466	62	12	0	0	NUM
ejpam-6466	62	13	.	.	PUNCT
ejpam-6466	63	1	(	(	PUNCT
ejpam-6466	63	2	2	2	X
ejpam-6466	63	3	)	)	PUNCT
ejpam-6466	63	4	if	if	SCONJ
ejpam-6466	63	5	ψ(τ	ψ(τ	NOUN
ejpam-6466	63	6	)	)	PUNCT
ejpam-6466	63	7	is	be	AUX
ejpam-6466	63	8	ξ	ξ	NOUN
ejpam-6466	63	9	-	-	NOUN
ejpam-6466	63	10	differentiable	differentiable	ADJ
ejpam-6466	63	11	in	in	ADP
ejpam-6466	63	12	some	some	PRON
ejpam-6466	63	13	(	(	PUNCT
ejpam-6466	63	14	0,λ	0,λ	NOUN
ejpam-6466	63	15	)	)	PUNCT
ejpam-6466	63	16	,	,	PUNCT
ejpam-6466	63	17	λ	λ	X
ejpam-6466	63	18	>	>	X
ejpam-6466	63	19	0	0	PUNCT
ejpam-6466	63	20	and	and	CCONJ
ejpam-6466	63	21	lim	lim	PROPN
ejpam-6466	63	22	τ→0	τ→0	PUNCT
ejpam-6466	63	23	+	+	X
ejpam-6466	63	24	ψξ(τ	ψξ(τ	NOUN
ejpam-6466	63	25	)	)	PUNCT
ejpam-6466	63	26	exists	exist	VERB
ejpam-6466	63	27	,	,	PUNCT
ejpam-6466	63	28	then	then	ADV
ejpam-6466	63	29	define	define	VERB
ejpam-6466	63	30	ψ(ξ)(0	ψ(ξ)(0	PROPN
ejpam-6466	63	31	)	)	PUNCT
ejpam-6466	64	1	=	=	PROPN
ejpam-6466	64	2	lim	lim	PROPN
ejpam-6466	64	3	τ→0	τ→0	PROPN
ejpam-6466	64	4	+	+	PROPN
ejpam-6466	64	5	ψ(ξ)(τ	ψ(ξ)(τ	NUM
ejpam-6466	64	6	)	)	PUNCT
ejpam-6466	64	7	.	.	PUNCT
ejpam-6466	65	1	an	an	DET
ejpam-6466	65	2	integral	integral	NOUN
ejpam-6466	65	3	of	of	ADP
ejpam-6466	65	4	a	a	DET
ejpam-6466	65	5	function	function	NOUN
ejpam-6466	65	6	ψ(τ	ψ(τ	NOUN
ejpam-6466	65	7	)	)	PUNCT
ejpam-6466	65	8	that	that	PRON
ejpam-6466	65	9	is	be	AUX
ejpam-6466	65	10	conformable	conformable	ADJ
ejpam-6466	65	11	fractional	fractional	ADJ
ejpam-6466	65	12	ψ(τ	ψ(τ	NOUN
ejpam-6466	65	13	)	)	PUNCT
ejpam-6466	65	14	starting	start	VERB
ejpam-6466	65	15	from	from	ADP
ejpam-6466	65	16	α̃	α̃	PROPN
ejpam-6466	65	17	≥	≥	X
ejpam-6466	65	18	0	0	NUM
ejpam-6466	65	19	is	be	AUX
ejpam-6466	65	20	defined	define	VERB
ejpam-6466	65	21	as	as	ADP
ejpam-6466	65	22	:	:	PUNCT
ejpam-6466	65	23	iα̃ξ	iα̃ξ	PROPN
ejpam-6466	65	24	(	(	PUNCT
ejpam-6466	65	25	ψ)(τ	ψ)(τ	PROPN
ejpam-6466	65	26	)	)	PUNCT
ejpam-6466	66	1	=	=	SYM
ejpam-6466	67	1	∫	∫	PROPN
ejpam-6466	67	2	τ	τ	PROPN
ejpam-6466	67	3	α̃	α̃	PROPN
ejpam-6466	67	4	ψ(s	ψ(s	PROPN
ejpam-6466	67	5	)	)	PUNCT
ejpam-6466	67	6	(	(	PUNCT
ejpam-6466	67	7	s−	s−	PROPN
ejpam-6466	67	8	α̃	α̃	PROPN
ejpam-6466	67	9	)	)	PUNCT
ejpam-6466	67	10	1−ξ	1−ξ	NUM
ejpam-6466	68	1	ds	ds	PROPN
ejpam-6466	68	2	,	,	PUNCT
ejpam-6466	68	3	ξ	ξ	PROPN
ejpam-6466	68	4	∈	∈	PROPN
ejpam-6466	68	5	(	(	PUNCT
ejpam-6466	68	6	0	0	NUM
ejpam-6466	68	7	,	,	PUNCT
ejpam-6466	68	8	1	1	NUM
ejpam-6466	68	9	]	]	PUNCT
ejpam-6466	68	10	.	.	PUNCT
ejpam-6466	69	1	(	(	PUNCT
ejpam-6466	69	2	3	3	X
ejpam-6466	69	3	)	)	PUNCT
ejpam-6466	69	4	the	the	DET
ejpam-6466	69	5	con	con	NOUN
ejpam-6466	69	6	-	-	PUNCT
ejpam-6466	69	7	frd	frd	NOUN
ejpam-6466	69	8	offers	offer	VERB
ejpam-6466	69	9	a	a	DET
ejpam-6466	69	10	simplified	simplified	ADJ
ejpam-6466	69	11	approach	approach	NOUN
ejpam-6466	69	12	to	to	ADP
ejpam-6466	69	13	fractional	fractional	ADJ
ejpam-6466	69	14	differentiation	differentiation	NOUN
ejpam-6466	69	15	,	,	PUNCT
ejpam-6466	69	16	easing	ease	VERB
ejpam-6466	69	17	computational	computational	ADJ
ejpam-6466	69	18	complexity	complexity	NOUN
ejpam-6466	69	19	while	while	SCONJ
ejpam-6466	69	20	retaining	retain	VERB
ejpam-6466	69	21	essential	essential	ADJ
ejpam-6466	69	22	characteristics	characteristic	NOUN
ejpam-6466	69	23	of	of	ADP
ejpam-6466	69	24	traditional	traditional	ADJ
ejpam-6466	69	25	derivatives	derivative	NOUN
ejpam-6466	69	26	.	.	PUNCT
ejpam-6466	70	1	the	the	DET
ejpam-6466	70	2	con	con	ADJ
ejpam-6466	70	3	-	-	PUNCT
ejpam-6466	70	4	frd	frd	NOUN
ejpam-6466	70	5	offers	offer	VERB
ejpam-6466	70	6	several	several	ADJ
ejpam-6466	70	7	advantages	advantage	NOUN
ejpam-6466	70	8	compared	compare	VERB
ejpam-6466	70	9	to	to	ADP
ejpam-6466	70	10	other	other	ADJ
ejpam-6466	70	11	types	type	NOUN
ejpam-6466	70	12	of	of	ADP
ejpam-6466	70	13	fractional	fractional	ADJ
ejpam-6466	70	14	derivatives	derivative	NOUN
ejpam-6466	70	15	.	.	PUNCT
ejpam-6466	71	1	here	here	ADV
ejpam-6466	71	2	are	be	AUX
ejpam-6466	71	3	some	some	PRON
ejpam-6466	71	4	of	of	ADP
ejpam-6466	71	5	the	the	DET
ejpam-6466	71	6	key	key	ADJ
ejpam-6466	71	7	benefits	benefit	NOUN
ejpam-6466	71	8	[	[	X
ejpam-6466	71	9	17–20	17–20	NUM
ejpam-6466	71	10	]	]	X
ejpam-6466	71	11	:	:	PUNCT
ejpam-6466	71	12	i.	i.	NOUN
ejpam-6466	71	13	compatibility	compatibility	NOUN
ejpam-6466	71	14	with	with	ADP
ejpam-6466	71	15	stochastic	stochastic	ADJ
ejpam-6466	71	16	processes	process	NOUN
ejpam-6466	71	17	:	:	PUNCT
ejpam-6466	71	18	con	con	ADJ
ejpam-6466	71	19	-	-	PUNCT
ejpam-6466	71	20	frd	frd	NOUN
ejpam-6466	71	21	maintains	maintain	VERB
ejpam-6466	71	22	compatibility	compatibility	NOUN
ejpam-6466	71	23	with	with	ADP
ejpam-6466	71	24	stochastic	stochastic	ADJ
ejpam-6466	71	25	processes	process	NOUN
ejpam-6466	71	26	commonly	commonly	ADV
ejpam-6466	71	27	encountered	encounter	VERB
ejpam-6466	71	28	in	in	ADP
ejpam-6466	71	29	real	real	ADJ
ejpam-6466	71	30	-	-	PUNCT
ejpam-6466	71	31	life	life	NOUN
ejpam-6466	71	32	applications	application	NOUN
ejpam-6466	71	33	,	,	PUNCT
ejpam-6466	71	34	such	such	ADJ
ejpam-6466	71	35	as	as	ADP
ejpam-6466	71	36	brownian	brownian	ADJ
ejpam-6466	71	37	motion	motion	NOUN
ejpam-6466	71	38	and	and	CCONJ
ejpam-6466	71	39	lévy	lévy	NUM
ejpam-6466	71	40	processes	process	NOUN
ejpam-6466	71	41	.	.	PUNCT
ejpam-6466	72	1	this	this	DET
ejpam-6466	72	2	compatibility	compatibility	NOUN
ejpam-6466	72	3	ensures	ensure	VERB
ejpam-6466	72	4	that	that	SCONJ
ejpam-6466	72	5	models	model	NOUN
ejpam-6466	72	6	incorporating	incorporate	VERB
ejpam-6466	72	7	con	con	NOUN
ejpam-6466	72	8	-	-	PUNCT
ejpam-6466	72	9	frd	frd	NOUN
ejpam-6466	72	10	accurately	accurately	ADV
ejpam-6466	72	11	capture	capture	VERB
ejpam-6466	72	12	the	the	DET
ejpam-6466	72	13	stochastic	stochastic	ADJ
ejpam-6466	72	14	nature	nature	NOUN
ejpam-6466	72	15	of	of	ADP
ejpam-6466	72	16	the	the	DET
ejpam-6466	72	17	underlying	underlie	VERB
ejpam-6466	72	18	phenomena	phenomenon	NOUN
ejpam-6466	72	19	.	.	PUNCT
ejpam-6466	73	1	ii	ii	PROPN
ejpam-6466	73	2	.	.	PUNCT
ejpam-6466	73	3	conformity	conformity	NOUN
ejpam-6466	73	4	with	with	ADP
ejpam-6466	73	5	classical	classical	ADJ
ejpam-6466	73	6	calculus	calculus	NOUN
ejpam-6466	73	7	:	:	PUNCT
ejpam-6466	73	8	the	the	DET
ejpam-6466	73	9	properties	property	NOUN
ejpam-6466	73	10	of	of	ADP
ejpam-6466	73	11	con	con	NOUN
ejpam-6466	73	12	-	-	PUNCT
ejpam-6466	73	13	frd	frd	ADJ
ejpam-6466	73	14	closely	closely	ADV
ejpam-6466	73	15	resemble	resemble	VERB
ejpam-6466	73	16	those	those	PRON
ejpam-6466	73	17	of	of	ADP
ejpam-6466	73	18	classical	classical	ADJ
ejpam-6466	73	19	derivatives	derivative	NOUN
ejpam-6466	73	20	,	,	PUNCT
ejpam-6466	73	21	making	make	VERB
ejpam-6466	73	22	them	they	PRON
ejpam-6466	73	23	more	more	ADV
ejpam-6466	73	24	intuitive	intuitive	ADJ
ejpam-6466	73	25	and	and	CCONJ
ejpam-6466	73	26	easier	easy	ADJ
ejpam-6466	73	27	to	to	PART
ejpam-6466	73	28	apply	apply	VERB
ejpam-6466	73	29	in	in	ADP
ejpam-6466	73	30	the	the	DET
ejpam-6466	73	31	context	context	NOUN
ejpam-6466	73	32	of	of	ADP
ejpam-6466	73	33	stochastic	stochastic	ADJ
ejpam-6466	73	34	calculus	calculus	NOUN
ejpam-6466	73	35	.	.	PUNCT
ejpam-6466	74	1	this	this	DET
ejpam-6466	74	2	conformity	conformity	NOUN
ejpam-6466	74	3	facilitates	facilitate	VERB
ejpam-6466	74	4	the	the	DET
ejpam-6466	74	5	development	development	NOUN
ejpam-6466	74	6	and	and	CCONJ
ejpam-6466	74	7	analysis	analysis	NOUN
ejpam-6466	74	8	of	of	ADP
ejpam-6466	74	9	fractional	fractional	ADJ
ejpam-6466	74	10	stochastic	stochastic	ADJ
ejpam-6466	74	11	differential	differential	ADJ
ejpam-6466	74	12	equations	equation	NOUN
ejpam-6466	74	13	(	(	PUNCT
ejpam-6466	74	14	fsdes	fsde	NOUN
ejpam-6466	74	15	)	)	PUNCT
ejpam-6466	74	16	,	,	PUNCT
ejpam-6466	74	17	as	as	SCONJ
ejpam-6466	74	18	it	it	PRON
ejpam-6466	74	19	allows	allow	VERB
ejpam-6466	74	20	researchers	researcher	NOUN
ejpam-6466	74	21	to	to	PART
ejpam-6466	74	22	leverage	leverage	VERB
ejpam-6466	74	23	their	their	PRON
ejpam-6466	74	24	existing	exist	VERB
ejpam-6466	74	25	knowledge	knowledge	NOUN
ejpam-6466	74	26	and	and	CCONJ
ejpam-6466	74	27	techniques	technique	NOUN
ejpam-6466	74	28	from	from	ADP
ejpam-6466	74	29	classical	classical	ADJ
ejpam-6466	74	30	calculus	calculus	NOUN
ejpam-6466	74	31	.	.	PUNCT
ejpam-6466	75	1	m.	m.	PROPN
ejpam-6466	75	2	i.	i.	PROPN
ejpam-6466	75	3	liaqat	liaqat	PROPN
ejpam-6466	75	4	et	et	PROPN
ejpam-6466	75	5	al	al	PROPN
ejpam-6466	75	6	.	.	PUNCT
ejpam-6466	75	7	/	/	SYM
ejpam-6466	75	8	eur	eur	PROPN
ejpam-6466	75	9	.	.	PUNCT
ejpam-6466	76	1	j.	j.	PROPN
ejpam-6466	76	2	pure	pure	PROPN
ejpam-6466	76	3	appl	appl	PROPN
ejpam-6466	76	4	.	.	PROPN
ejpam-6466	76	5	math	math	PROPN
ejpam-6466	76	6	,	,	PUNCT
ejpam-6466	76	7	18	18	NUM
ejpam-6466	76	8	(	(	PUNCT
ejpam-6466	76	9	4	4	NUM
ejpam-6466	76	10	)	)	PUNCT
ejpam-6466	76	11	(	(	PUNCT
ejpam-6466	76	12	2025	2025	NUM
ejpam-6466	76	13	)	)	PUNCT
ejpam-6466	76	14	,	,	PUNCT
ejpam-6466	76	15	6466	6466	NUM
ejpam-6466	76	16	5	5	NUM
ejpam-6466	76	17	of	of	ADP
ejpam-6466	76	18	28	28	NUM
ejpam-6466	76	19	iii	iii	NOUN
ejpam-6466	76	20	.	.	PUNCT
ejpam-6466	76	21	simplicity	simplicity	NOUN
ejpam-6466	76	22	and	and	CCONJ
ejpam-6466	76	23	computational	computational	ADJ
ejpam-6466	76	24	efficiency	efficiency	NOUN
ejpam-6466	76	25	:	:	PUNCT
ejpam-6466	76	26	con	con	ADJ
ejpam-6466	76	27	-	-	PUNCT
ejpam-6466	76	28	frd	frd	ADJ
ejpam-6466	76	29	is	be	AUX
ejpam-6466	76	30	simpler	simple	ADJ
ejpam-6466	76	31	to	to	PART
ejpam-6466	76	32	work	work	VERB
ejpam-6466	76	33	with	with	ADP
ejpam-6466	76	34	and	and	CCONJ
ejpam-6466	76	35	manipulate	manipulate	VERB
ejpam-6466	76	36	compared	compare	VERB
ejpam-6466	76	37	to	to	ADP
ejpam-6466	76	38	other	other	ADJ
ejpam-6466	76	39	fractional	fractional	ADJ
ejpam-6466	76	40	derivatives	derivative	NOUN
ejpam-6466	76	41	,	,	PUNCT
ejpam-6466	76	42	which	which	PRON
ejpam-6466	76	43	can	can	AUX
ejpam-6466	76	44	lead	lead	VERB
ejpam-6466	76	45	to	to	ADP
ejpam-6466	76	46	more	more	ADV
ejpam-6466	76	47	efficient	efficient	ADJ
ejpam-6466	76	48	computational	computational	ADJ
ejpam-6466	76	49	algorithms	algorithm	NOUN
ejpam-6466	76	50	for	for	ADP
ejpam-6466	76	51	solving	solve	VERB
ejpam-6466	76	52	fsdes	fsde	NOUN
ejpam-6466	76	53	.	.	PUNCT
ejpam-6466	77	1	this	this	DET
ejpam-6466	77	2	simplicity	simplicity	NOUN
ejpam-6466	77	3	can	can	AUX
ejpam-6466	77	4	reduce	reduce	VERB
ejpam-6466	77	5	the	the	DET
ejpam-6466	77	6	computational	computational	ADJ
ejpam-6466	77	7	cost	cost	NOUN
ejpam-6466	77	8	associated	associate	VERB
ejpam-6466	77	9	with	with	ADP
ejpam-6466	77	10	simulating	simulate	VERB
ejpam-6466	77	11	stochastic	stochastic	ADJ
ejpam-6466	77	12	processes	process	NOUN
ejpam-6466	77	13	involving	involve	VERB
ejpam-6466	77	14	fc	fc	PROPN
ejpam-6466	77	15	.	.	PUNCT
ejpam-6466	77	16	iv	iv	PROPN
ejpam-6466	77	17	.	.	PUNCT
ejpam-6466	77	18	mathematical	mathematical	ADJ
ejpam-6466	77	19	properties	property	NOUN
ejpam-6466	77	20	:	:	PUNCT
ejpam-6466	77	21	con	con	ADJ
ejpam-6466	77	22	-	-	PUNCT
ejpam-6466	77	23	frd	frd	ADJ
ejpam-6466	77	24	possesses	possess	VERB
ejpam-6466	77	25	certain	certain	ADJ
ejpam-6466	77	26	mathematical	mathematical	ADJ
ejpam-6466	77	27	properties	property	NOUN
ejpam-6466	77	28	,	,	PUNCT
ejpam-6466	77	29	such	such	ADJ
ejpam-6466	77	30	as	as	ADP
ejpam-6466	77	31	the	the	DET
ejpam-6466	77	32	fractional	fractional	ADJ
ejpam-6466	77	33	itô	itô	PROPN
ejpam-6466	77	34	formula	formula	NOUN
ejpam-6466	77	35	,	,	PUNCT
ejpam-6466	77	36	which	which	PRON
ejpam-6466	77	37	can	can	AUX
ejpam-6466	77	38	simplify	simplify	VERB
ejpam-6466	77	39	the	the	DET
ejpam-6466	77	40	analysis	analysis	NOUN
ejpam-6466	77	41	of	of	ADP
ejpam-6466	77	42	fsdes	fsde	NOUN
ejpam-6466	77	43	and	and	CCONJ
ejpam-6466	77	44	facilitate	facilitate	VERB
ejpam-6466	77	45	the	the	DET
ejpam-6466	77	46	derivation	derivation	NOUN
ejpam-6466	77	47	of	of	ADP
ejpam-6466	77	48	important	important	ADJ
ejpam-6466	77	49	results	result	NOUN
ejpam-6466	77	50	.	.	PUNCT
ejpam-6466	78	1	these	these	DET
ejpam-6466	78	2	properties	property	NOUN
ejpam-6466	78	3	provide	provide	VERB
ejpam-6466	78	4	a	a	DET
ejpam-6466	78	5	solid	solid	ADJ
ejpam-6466	78	6	theoretical	theoretical	ADJ
ejpam-6466	78	7	foundation	foundation	NOUN
ejpam-6466	78	8	for	for	ADP
ejpam-6466	78	9	studying	study	VERB
ejpam-6466	78	10	the	the	DET
ejpam-6466	78	11	behavior	behavior	NOUN
ejpam-6466	78	12	of	of	ADP
ejpam-6466	78	13	stochastic	stochastic	ADJ
ejpam-6466	78	14	processes	process	NOUN
ejpam-6466	78	15	involving	involve	VERB
ejpam-6466	78	16	fc	fc	X
ejpam-6466	78	17	.	.	PUNCT
ejpam-6466	79	1	v.	v.	ADP
ejpam-6466	79	2	generalization	generalization	NOUN
ejpam-6466	79	3	:	:	PUNCT
ejpam-6466	79	4	con	con	ADJ
ejpam-6466	79	5	-	-	PUNCT
ejpam-6466	79	6	frd	frd	NOUN
ejpam-6466	79	7	offers	offer	VERB
ejpam-6466	79	8	a	a	DET
ejpam-6466	79	9	generalized	generalize	VERB
ejpam-6466	79	10	framework	framework	NOUN
ejpam-6466	79	11	for	for	ADP
ejpam-6466	79	12	modeling	model	VERB
ejpam-6466	79	13	stochastic	stochastic	ADJ
ejpam-6466	79	14	processes	process	NOUN
ejpam-6466	79	15	with	with	ADP
ejpam-6466	79	16	non	non	ADJ
ejpam-6466	79	17	-	-	ADJ
ejpam-6466	79	18	integer	integer	ADJ
ejpam-6466	79	19	orders	order	NOUN
ejpam-6466	79	20	of	of	ADP
ejpam-6466	79	21	differentiation	differentiation	NOUN
ejpam-6466	79	22	.	.	PUNCT
ejpam-6466	80	1	this	this	DET
ejpam-6466	80	2	generalization	generalization	NOUN
ejpam-6466	80	3	allows	allow	VERB
ejpam-6466	80	4	researchers	researcher	NOUN
ejpam-6466	80	5	to	to	PART
ejpam-6466	80	6	explore	explore	VERB
ejpam-6466	80	7	a	a	DET
ejpam-6466	80	8	broader	broad	ADJ
ejpam-6466	80	9	range	range	NOUN
ejpam-6466	80	10	of	of	ADP
ejpam-6466	80	11	stochastic	stochastic	ADJ
ejpam-6466	80	12	systems	system	NOUN
ejpam-6466	80	13	,	,	PUNCT
ejpam-6466	80	14	including	include	VERB
ejpam-6466	80	15	those	those	PRON
ejpam-6466	80	16	with	with	ADP
ejpam-6466	80	17	anomalous	anomalous	ADJ
ejpam-6466	80	18	diffusion	diffusion	NOUN
ejpam-6466	80	19	or	or	CCONJ
ejpam-6466	80	20	long	long	ADJ
ejpam-6466	80	21	-	-	PUNCT
ejpam-6466	80	22	range	range	NOUN
ejpam-6466	80	23	dependencies	dependency	NOUN
ejpam-6466	80	24	.	.	PUNCT
ejpam-6466	81	1	conformable	conformable	ADJ
ejpam-6466	81	2	derivatives	derivative	NOUN
ejpam-6466	81	3	provide	provide	VERB
ejpam-6466	81	4	a	a	DET
ejpam-6466	81	5	versatile	versatile	ADJ
ejpam-6466	81	6	tool	tool	NOUN
ejpam-6466	81	7	for	for	ADP
ejpam-6466	81	8	capturing	capture	VERB
ejpam-6466	81	9	complex	complex	ADJ
ejpam-6466	81	10	dynamics	dynamic	NOUN
ejpam-6466	81	11	in	in	ADP
ejpam-6466	81	12	various	various	ADJ
ejpam-6466	81	13	fields	field	NOUN
ejpam-6466	81	14	.	.	PUNCT
ejpam-6466	82	1	fsdes	fsde	NOUN
ejpam-6466	82	2	constitute	constitute	VERB
ejpam-6466	82	3	a	a	DET
ejpam-6466	82	4	class	class	NOUN
ejpam-6466	82	5	of	of	ADP
ejpam-6466	82	6	differential	differential	ADJ
ejpam-6466	82	7	equations	equation	NOUN
ejpam-6466	82	8	that	that	PRON
ejpam-6466	82	9	combine	combine	VERB
ejpam-6466	82	10	stochastic	stochastic	ADJ
ejpam-6466	82	11	elements	element	NOUN
ejpam-6466	82	12	with	with	ADP
ejpam-6466	82	13	fc	fc	PROPN
ejpam-6466	82	14	.	.	PUNCT
ejpam-6466	83	1	they	they	PRON
ejpam-6466	83	2	serve	serve	VERB
ejpam-6466	83	3	to	to	PART
ejpam-6466	83	4	describe	describe	VERB
ejpam-6466	83	5	systems	system	NOUN
ejpam-6466	83	6	demonstrating	demonstrate	VERB
ejpam-6466	83	7	randomness	randomness	NOUN
ejpam-6466	83	8	,	,	PUNCT
ejpam-6466	83	9	generally	generally	ADV
ejpam-6466	83	10	represented	represent	VERB
ejpam-6466	83	11	by	by	ADP
ejpam-6466	83	12	stochastic	stochastic	ADJ
ejpam-6466	83	13	processes	process	NOUN
ejpam-6466	83	14	,	,	PUNCT
ejpam-6466	83	15	alongside	alongside	ADP
ejpam-6466	83	16	non	non	ADJ
ejpam-6466	83	17	-	-	ADJ
ejpam-6466	83	18	local	local	ADJ
ejpam-6466	83	19	or	or	CCONJ
ejpam-6466	83	20	memory	memory	NOUN
ejpam-6466	83	21	-	-	PUNCT
ejpam-6466	83	22	dependent	dependent	ADJ
ejpam-6466	83	23	characteristics	characteristic	NOUN
ejpam-6466	83	24	embodied	embody	VERB
ejpam-6466	83	25	by	by	ADP
ejpam-6466	83	26	fractional	fractional	ADJ
ejpam-6466	83	27	derivatives	derivative	NOUN
ejpam-6466	83	28	.	.	PUNCT
ejpam-6466	84	1	fsdes	fsde	NOUN
ejpam-6466	84	2	play	play	VERB
ejpam-6466	84	3	a	a	DET
ejpam-6466	84	4	crucial	crucial	ADJ
ejpam-6466	84	5	role	role	NOUN
ejpam-6466	84	6	across	across	ADP
ejpam-6466	84	7	diverse	diverse	ADJ
ejpam-6466	84	8	scientific	scientific	ADJ
ejpam-6466	84	9	and	and	CCONJ
ejpam-6466	84	10	engineering	engineering	NOUN
ejpam-6466	84	11	domains	domain	NOUN
ejpam-6466	84	12	for	for	ADP
ejpam-6466	84	13	modeling	model	VERB
ejpam-6466	84	14	complex	complex	ADJ
ejpam-6466	84	15	phenomena	phenomenon	NOUN
ejpam-6466	84	16	involving	involve	VERB
ejpam-6466	84	17	both	both	CCONJ
ejpam-6466	84	18	randomness	randomness	NOUN
ejpam-6466	84	19	and	and	CCONJ
ejpam-6466	84	20	memory	memory	NOUN
ejpam-6466	84	21	effects	effect	NOUN
ejpam-6466	84	22	.	.	PUNCT
ejpam-6466	85	1	delay	delay	VERB
ejpam-6466	85	2	fractional	fractional	ADJ
ejpam-6466	85	3	stochastic	stochastic	ADJ
ejpam-6466	85	4	differential	differential	ADJ
ejpam-6466	85	5	equations	equation	NOUN
ejpam-6466	85	6	(	(	PUNCT
ejpam-6466	85	7	df	df	NOUN
ejpam-6466	85	8	-	-	PUNCT
ejpam-6466	85	9	sdes	sde	NOUN
ejpam-6466	85	10	)	)	PUNCT
ejpam-6466	85	11	are	be	AUX
ejpam-6466	85	12	a	a	DET
ejpam-6466	85	13	class	class	NOUN
ejpam-6466	85	14	of	of	ADP
ejpam-6466	85	15	differential	differential	ADJ
ejpam-6466	85	16	equations	equation	NOUN
ejpam-6466	85	17	that	that	PRON
ejpam-6466	85	18	incorporate	incorporate	VERB
ejpam-6466	85	19	both	both	DET
ejpam-6466	85	20	delay	delay	NOUN
ejpam-6466	85	21	effects	effect	NOUN
ejpam-6466	85	22	and	and	CCONJ
ejpam-6466	85	23	fc	fc	INTJ
ejpam-6466	85	24	,	,	PUNCT
ejpam-6466	85	25	along	along	ADP
ejpam-6466	85	26	with	with	ADP
ejpam-6466	85	27	stochastic	stochastic	ADJ
ejpam-6466	85	28	components	component	NOUN
ejpam-6466	85	29	,	,	PUNCT
ejpam-6466	85	30	to	to	PART
ejpam-6466	85	31	model	model	NOUN
ejpam-6466	85	32	systems	system	NOUN
ejpam-6466	85	33	influenced	influence	VERB
ejpam-6466	85	34	by	by	ADP
ejpam-6466	85	35	randomness	randomness	NOUN
ejpam-6466	85	36	.	.	PUNCT
ejpam-6466	86	1	df	df	NOUN
ejpam-6466	86	2	-	-	PUNCT
ejpam-6466	86	3	sdes	sde	NOUN
ejpam-6466	86	4	combine	combine	VERB
ejpam-6466	86	5	the	the	DET
ejpam-6466	86	6	advantages	advantage	NOUN
ejpam-6466	86	7	of	of	ADP
ejpam-6466	86	8	fc	fc	PROPN
ejpam-6466	86	9	,	,	PUNCT
ejpam-6466	86	10	delay	delay	VERB
ejpam-6466	86	11	differential	differential	ADJ
ejpam-6466	86	12	equations	equation	NOUN
ejpam-6466	86	13	,	,	PUNCT
ejpam-6466	86	14	and	and	CCONJ
ejpam-6466	86	15	stochastic	stochastic	ADJ
ejpam-6466	86	16	differential	differential	ADJ
ejpam-6466	86	17	equations	equation	NOUN
ejpam-6466	86	18	.	.	PUNCT
ejpam-6466	87	1	this	this	DET
ejpam-6466	87	2	combination	combination	NOUN
ejpam-6466	87	3	is	be	AUX
ejpam-6466	87	4	crucial	crucial	ADJ
ejpam-6466	87	5	for	for	ADP
ejpam-6466	87	6	accurately	accurately	ADV
ejpam-6466	87	7	capturing	capture	VERB
ejpam-6466	87	8	the	the	DET
ejpam-6466	87	9	dynamics	dynamic	NOUN
ejpam-6466	87	10	of	of	ADP
ejpam-6466	87	11	systems	system	NOUN
ejpam-6466	87	12	that	that	PRON
ejpam-6466	87	13	exhibit	exhibit	VERB
ejpam-6466	87	14	memory	memory	NOUN
ejpam-6466	87	15	effects	effect	NOUN
ejpam-6466	87	16	,	,	PUNCT
ejpam-6466	87	17	delays	delay	NOUN
ejpam-6466	87	18	,	,	PUNCT
ejpam-6466	87	19	and	and	CCONJ
ejpam-6466	87	20	randomness	randomness	NOUN
ejpam-6466	87	21	.	.	PUNCT
ejpam-6466	88	1	by	by	ADP
ejpam-6466	88	2	using	use	VERB
ejpam-6466	88	3	df	df	NOUN
ejpam-6466	88	4	-	-	PUNCT
ejpam-6466	88	5	sdes	sde	NOUN
ejpam-6466	88	6	,	,	PUNCT
ejpam-6466	88	7	researchers	researcher	NOUN
ejpam-6466	88	8	and	and	CCONJ
ejpam-6466	88	9	engineers	engineer	NOUN
ejpam-6466	88	10	can	can	AUX
ejpam-6466	88	11	develop	develop	VERB
ejpam-6466	88	12	more	more	ADV
ejpam-6466	88	13	realistic	realistic	ADJ
ejpam-6466	88	14	models	model	NOUN
ejpam-6466	88	15	,	,	PUNCT
ejpam-6466	88	16	leading	lead	VERB
ejpam-6466	88	17	to	to	ADP
ejpam-6466	88	18	better	well	ADJ
ejpam-6466	88	19	predictions	prediction	NOUN
ejpam-6466	88	20	,	,	PUNCT
ejpam-6466	88	21	control	control	NOUN
ejpam-6466	88	22	strategies	strategy	NOUN
ejpam-6466	88	23	,	,	PUNCT
ejpam-6466	88	24	and	and	CCONJ
ejpam-6466	88	25	understanding	understanding	NOUN
ejpam-6466	88	26	of	of	ADP
ejpam-6466	88	27	complex	complex	ADJ
ejpam-6466	88	28	phenomena	phenomenon	NOUN
ejpam-6466	88	29	across	across	ADP
ejpam-6466	88	30	various	various	ADJ
ejpam-6466	88	31	fields	field	NOUN
ejpam-6466	88	32	.	.	PUNCT
ejpam-6466	89	1	df	df	NOUN
ejpam-6466	89	2	-	-	PUNCT
ejpam-6466	89	3	sdes	sde	NOUN
ejpam-6466	89	4	offer	offer	VERB
ejpam-6466	89	5	several	several	ADJ
ejpam-6466	89	6	advantages	advantage	NOUN
ejpam-6466	89	7	in	in	ADP
ejpam-6466	89	8	understanding	understand	VERB
ejpam-6466	89	9	various	various	ADJ
ejpam-6466	89	10	phenomena	phenomenon	NOUN
ejpam-6466	89	11	across	across	ADP
ejpam-6466	89	12	different	different	ADJ
ejpam-6466	89	13	fields	field	NOUN
ejpam-6466	89	14	due	due	ADP
ejpam-6466	89	15	to	to	ADP
ejpam-6466	89	16	their	their	PRON
ejpam-6466	89	17	ability	ability	NOUN
ejpam-6466	89	18	to	to	PART
ejpam-6466	89	19	capture	capture	VERB
ejpam-6466	89	20	memory	memory	NOUN
ejpam-6466	89	21	effects	effect	NOUN
ejpam-6466	89	22	,	,	PUNCT
ejpam-6466	89	23	delays	delay	NOUN
ejpam-6466	89	24	,	,	PUNCT
ejpam-6466	89	25	and	and	CCONJ
ejpam-6466	89	26	stochastic	stochastic	ADJ
ejpam-6466	89	27	influences	influence	NOUN
ejpam-6466	89	28	.	.	PUNCT
ejpam-6466	90	1	here	here	ADV
ejpam-6466	90	2	are	be	AUX
ejpam-6466	90	3	some	some	DET
ejpam-6466	90	4	key	key	ADJ
ejpam-6466	90	5	advantages	advantage	NOUN
ejpam-6466	90	6	[	[	X
ejpam-6466	90	7	21	21	NUM
ejpam-6466	90	8	,	,	PUNCT
ejpam-6466	90	9	22	22	NUM
ejpam-6466	90	10	]	]	X
ejpam-6466	90	11	:	:	PUNCT
ejpam-6466	90	12	i.	i.	PROPN
ejpam-6466	90	13	modeling	modeling	NOUN
ejpam-6466	90	14	memory	memory	NOUN
ejpam-6466	90	15	effects	effect	NOUN
ejpam-6466	90	16	•	•	ADP
ejpam-6466	90	17	df	df	NOUN
ejpam-6466	90	18	-	-	PUNCT
ejpam-6466	90	19	sdes	sde	NOUN
ejpam-6466	90	20	can	can	AUX
ejpam-6466	90	21	effectively	effectively	ADV
ejpam-6466	90	22	model	model	VERB
ejpam-6466	90	23	systems	system	NOUN
ejpam-6466	90	24	where	where	SCONJ
ejpam-6466	90	25	future	future	ADJ
ejpam-6466	90	26	states	state	NOUN
ejpam-6466	90	27	depend	depend	VERB
ejpam-6466	90	28	not	not	PART
ejpam-6466	90	29	only	only	ADV
ejpam-6466	90	30	on	on	ADP
ejpam-6466	90	31	the	the	DET
ejpam-6466	90	32	current	current	ADJ
ejpam-6466	90	33	state	state	NOUN
ejpam-6466	90	34	but	but	CCONJ
ejpam-6466	90	35	also	also	ADV
ejpam-6466	90	36	on	on	ADP
ejpam-6466	90	37	past	past	ADJ
ejpam-6466	90	38	states	state	NOUN
ejpam-6466	90	39	.	.	PUNCT
ejpam-6466	91	1	this	this	PRON
ejpam-6466	91	2	is	be	AUX
ejpam-6466	91	3	particularly	particularly	ADV
ejpam-6466	91	4	useful	useful	ADJ
ejpam-6466	91	5	for	for	ADP
ejpam-6466	91	6	systems	system	NOUN
ejpam-6466	91	7	with	with	ADP
ejpam-6466	91	8	long	long	ADJ
ejpam-6466	91	9	memory	memory	NOUN
ejpam-6466	91	10	or	or	CCONJ
ejpam-6466	91	11	hereditary	hereditary	ADJ
ejpam-6466	91	12	properties	property	NOUN
ejpam-6466	91	13	.	.	PUNCT
ejpam-6466	92	1	for	for	ADP
ejpam-6466	92	2	example	example	NOUN
ejpam-6466	92	3	,	,	PUNCT
ejpam-6466	92	4	in	in	ADP
ejpam-6466	92	5	finance	finance	NOUN
ejpam-6466	92	6	,	,	PUNCT
ejpam-6466	92	7	asset	asset	NOUN
ejpam-6466	92	8	prices	price	NOUN
ejpam-6466	92	9	often	often	ADV
ejpam-6466	92	10	exhibit	exhibit	VERB
ejpam-6466	92	11	long	long	ADJ
ejpam-6466	92	12	-	-	PUNCT
ejpam-6466	92	13	range	range	NOUN
ejpam-6466	92	14	dependence	dependence	NOUN
ejpam-6466	92	15	and	and	CCONJ
ejpam-6466	92	16	volatility	volatility	NOUN
ejpam-6466	92	17	clustering	clustering	NOUN
ejpam-6466	92	18	.	.	PUNCT
ejpam-6466	93	1	df	df	NOUN
ejpam-6466	93	2	-	-	PUNCT
ejpam-6466	93	3	sdes	sde	NOUN
ejpam-6466	93	4	can	can	AUX
ejpam-6466	93	5	model	model	VERB
ejpam-6466	93	6	these	these	DET
ejpam-6466	93	7	phenomena	phenomenon	NOUN
ejpam-6466	93	8	more	more	ADV
ejpam-6466	93	9	accurately	accurately	ADV
ejpam-6466	93	10	than	than	ADP
ejpam-6466	93	11	traditional	traditional	ADJ
ejpam-6466	93	12	models	model	NOUN
ejpam-6466	93	13	,	,	PUNCT
ejpam-6466	93	14	capturing	capture	VERB
ejpam-6466	93	15	the	the	DET
ejpam-6466	93	16	impact	impact	NOUN
ejpam-6466	93	17	of	of	ADP
ejpam-6466	93	18	past	past	ADJ
ejpam-6466	93	19	market	market	NOUN
ejpam-6466	93	20	events	event	NOUN
ejpam-6466	93	21	on	on	ADP
ejpam-6466	93	22	current	current	ADJ
ejpam-6466	93	23	price	price	NOUN
ejpam-6466	93	24	dynamics	dynamic	NOUN
ejpam-6466	93	25	.	.	PUNCT
ejpam-6466	94	1	ii	ii	PROPN
ejpam-6466	94	2	.	.	PUNCT
ejpam-6466	95	1	incorporating	incorporate	VERB
ejpam-6466	95	2	time	time	NOUN
ejpam-6466	95	3	delays	delay	NOUN
ejpam-6466	95	4	•	•	NOUN
ejpam-6466	95	5	time	time	NOUN
ejpam-6466	95	6	delays	delay	NOUN
ejpam-6466	95	7	are	be	AUX
ejpam-6466	95	8	common	common	ADJ
ejpam-6466	95	9	in	in	ADP
ejpam-6466	95	10	many	many	ADJ
ejpam-6466	95	11	real	real	ADJ
ejpam-6466	95	12	-	-	PUNCT
ejpam-6466	95	13	world	world	NOUN
ejpam-6466	95	14	systems	system	NOUN
ejpam-6466	95	15	,	,	PUNCT
ejpam-6466	95	16	such	such	ADJ
ejpam-6466	95	17	as	as	ADP
ejpam-6466	95	18	biological	biological	ADJ
ejpam-6466	95	19	systems	system	NOUN
ejpam-6466	95	20	where	where	SCONJ
ejpam-6466	95	21	there	there	PRON
ejpam-6466	95	22	are	be	VERB
ejpam-6466	95	23	time	time	NOUN
ejpam-6466	95	24	lags	lag	NOUN
ejpam-6466	95	25	in	in	ADP
ejpam-6466	95	26	reaction	reaction	NOUN
ejpam-6466	95	27	processes	process	NOUN
ejpam-6466	95	28	or	or	CCONJ
ejpam-6466	95	29	in	in	ADP
ejpam-6466	95	30	engineering	engineering	NOUN
ejpam-6466	96	1	where	where	SCONJ
ejpam-6466	96	2	control	control	PROPN
ejpam-6466	96	3	m.	m.	PROPN
ejpam-6466	96	4	i.	i.	PROPN
ejpam-6466	96	5	liaqat	liaqat	PROPN
ejpam-6466	96	6	et	et	PROPN
ejpam-6466	96	7	al	al	PROPN
ejpam-6466	96	8	.	.	PUNCT
ejpam-6466	96	9	/	/	SYM
ejpam-6466	96	10	eur	eur	PROPN
ejpam-6466	96	11	.	.	PUNCT
ejpam-6466	97	1	j.	j.	PROPN
ejpam-6466	97	2	pure	pure	PROPN
ejpam-6466	97	3	appl	appl	PROPN
ejpam-6466	97	4	.	.	PROPN
ejpam-6466	97	5	math	math	PROPN
ejpam-6466	97	6	,	,	PUNCT
ejpam-6466	97	7	18	18	NUM
ejpam-6466	97	8	(	(	PUNCT
ejpam-6466	97	9	4	4	NUM
ejpam-6466	97	10	)	)	PUNCT
ejpam-6466	97	11	(	(	PUNCT
ejpam-6466	97	12	2025	2025	NUM
ejpam-6466	97	13	)	)	PUNCT
ejpam-6466	97	14	,	,	PUNCT
ejpam-6466	97	15	6466	6466	NUM
ejpam-6466	97	16	6	6	NUM
ejpam-6466	97	17	of	of	ADP
ejpam-6466	97	18	28	28	NUM
ejpam-6466	97	19	actions	action	NOUN
ejpam-6466	97	20	have	have	AUX
ejpam-6466	97	21	delayed	delay	VERB
ejpam-6466	97	22	effects	effect	NOUN
ejpam-6466	97	23	.	.	PUNCT
ejpam-6466	98	1	df	df	NOUN
ejpam-6466	98	2	-	-	PUNCT
ejpam-6466	98	3	sdes	sde	NOUN
ejpam-6466	98	4	explicitly	explicitly	ADV
ejpam-6466	98	5	incorporate	incorporate	VERB
ejpam-6466	98	6	these	these	DET
ejpam-6466	98	7	delays	delay	NOUN
ejpam-6466	98	8	,	,	PUNCT
ejpam-6466	98	9	leading	lead	VERB
ejpam-6466	98	10	to	to	ADP
ejpam-6466	98	11	more	more	ADV
ejpam-6466	98	12	realistic	realistic	ADJ
ejpam-6466	98	13	models	model	NOUN
ejpam-6466	98	14	.	.	PUNCT
ejpam-6466	99	1	for	for	ADP
ejpam-6466	99	2	instance	instance	NOUN
ejpam-6466	99	3	,	,	PUNCT
ejpam-6466	99	4	in	in	ADP
ejpam-6466	99	5	population	population	NOUN
ejpam-6466	99	6	dynamics	dynamic	NOUN
ejpam-6466	99	7	,	,	PUNCT
ejpam-6466	99	8	the	the	DET
ejpam-6466	99	9	birth	birth	NOUN
ejpam-6466	99	10	rate	rate	NOUN
ejpam-6466	99	11	may	may	AUX
ejpam-6466	99	12	depend	depend	VERB
ejpam-6466	99	13	on	on	ADP
ejpam-6466	99	14	the	the	DET
ejpam-6466	99	15	population	population	NOUN
ejpam-6466	99	16	size	size	NOUN
ejpam-6466	99	17	at	at	ADP
ejpam-6466	99	18	some	some	DET
ejpam-6466	99	19	previous	previous	ADJ
ejpam-6466	99	20	time	time	NOUN
ejpam-6466	99	21	due	due	ADP
ejpam-6466	99	22	to	to	ADP
ejpam-6466	99	23	gestation	gestation	NOUN
ejpam-6466	99	24	periods	period	NOUN
ejpam-6466	99	25	.	.	PUNCT
ejpam-6466	100	1	df	df	NOUN
ejpam-6466	100	2	-	-	PUNCT
ejpam-6466	100	3	sdes	sde	NOUN
ejpam-6466	100	4	can	can	AUX
ejpam-6466	100	5	model	model	VERB
ejpam-6466	100	6	this	this	PRON
ejpam-6466	100	7	by	by	ADP
ejpam-6466	100	8	including	include	VERB
ejpam-6466	100	9	a	a	DET
ejpam-6466	100	10	delay	delay	NOUN
ejpam-6466	100	11	term	term	NOUN
ejpam-6466	100	12	,	,	PUNCT
ejpam-6466	100	13	providing	provide	VERB
ejpam-6466	100	14	a	a	DET
ejpam-6466	100	15	more	more	ADV
ejpam-6466	100	16	accurate	accurate	ADJ
ejpam-6466	100	17	representation	representation	NOUN
ejpam-6466	100	18	of	of	ADP
ejpam-6466	100	19	population	population	NOUN
ejpam-6466	100	20	changes	change	VERB
ejpam-6466	100	21	over	over	ADP
ejpam-6466	100	22	time	time	NOUN
ejpam-6466	100	23	.	.	PUNCT
ejpam-6466	101	1	iii	iii	X
ejpam-6466	101	2	.	.	PUNCT
ejpam-6466	102	1	handling	handle	VERB
ejpam-6466	102	2	stochastic	stochastic	ADJ
ejpam-6466	102	3	fluctuations	fluctuation	NOUN
ejpam-6466	102	4	•	•	ADP
ejpam-6466	102	5	many	many	ADJ
ejpam-6466	102	6	systems	system	NOUN
ejpam-6466	102	7	are	be	AUX
ejpam-6466	102	8	subject	subject	ADJ
ejpam-6466	102	9	to	to	ADP
ejpam-6466	102	10	random	random	ADJ
ejpam-6466	102	11	perturbations	perturbation	NOUN
ejpam-6466	102	12	or	or	CCONJ
ejpam-6466	102	13	noise	noise	NOUN
ejpam-6466	102	14	.	.	PUNCT
ejpam-6466	103	1	df	df	NOUN
ejpam-6466	103	2	-	-	PUNCT
ejpam-6466	103	3	sdes	sde	NOUN
ejpam-6466	103	4	incorporate	incorporate	VERB
ejpam-6466	103	5	stochastic	stochastic	ADJ
ejpam-6466	103	6	processes	process	NOUN
ejpam-6466	103	7	,	,	PUNCT
ejpam-6466	103	8	allowing	allow	VERB
ejpam-6466	103	9	for	for	ADP
ejpam-6466	103	10	the	the	DET
ejpam-6466	103	11	modeling	modeling	NOUN
ejpam-6466	103	12	of	of	ADP
ejpam-6466	103	13	randomness	randomness	NOUN
ejpam-6466	103	14	alongside	alongside	ADP
ejpam-6466	103	15	deterministic	deterministic	ADJ
ejpam-6466	103	16	trends	trend	NOUN
ejpam-6466	103	17	and	and	CCONJ
ejpam-6466	103	18	memory	memory	NOUN
ejpam-6466	103	19	effects	effect	NOUN
ejpam-6466	103	20	.	.	PUNCT
ejpam-6466	104	1	for	for	ADP
ejpam-6466	104	2	instance	instance	NOUN
ejpam-6466	104	3	,	,	PUNCT
ejpam-6466	104	4	in	in	ADP
ejpam-6466	104	5	climate	climate	NOUN
ejpam-6466	104	6	modeling	modeling	NOUN
ejpam-6466	104	7	,	,	PUNCT
ejpam-6466	104	8	weather	weather	NOUN
ejpam-6466	104	9	conditions	condition	NOUN
ejpam-6466	104	10	exhibit	exhibit	VERB
ejpam-6466	104	11	both	both	CCONJ
ejpam-6466	104	12	deterministic	deterministic	ADJ
ejpam-6466	104	13	seasonal	seasonal	ADJ
ejpam-6466	104	14	trends	trend	NOUN
ejpam-6466	104	15	and	and	CCONJ
ejpam-6466	104	16	stochastic	stochastic	ADJ
ejpam-6466	104	17	variations	variation	NOUN
ejpam-6466	104	18	due	due	ADJ
ejpam-6466	104	19	to	to	ADP
ejpam-6466	104	20	unpredictable	unpredictable	ADJ
ejpam-6466	104	21	environmental	environmental	ADJ
ejpam-6466	104	22	factors	factor	NOUN
ejpam-6466	104	23	.	.	PUNCT
ejpam-6466	105	1	df	df	NOUN
ejpam-6466	105	2	-	-	PUNCT
ejpam-6466	105	3	sdes	sde	NOUN
ejpam-6466	105	4	can	can	AUX
ejpam-6466	105	5	capture	capture	VERB
ejpam-6466	105	6	both	both	DET
ejpam-6466	105	7	aspects	aspect	NOUN
ejpam-6466	105	8	,	,	PUNCT
ejpam-6466	105	9	improving	improve	VERB
ejpam-6466	105	10	climate	climate	NOUN
ejpam-6466	105	11	prediction	prediction	NOUN
ejpam-6466	105	12	models	model	NOUN
ejpam-6466	105	13	.	.	PUNCT
ejpam-6466	106	1	iv	iv	X
ejpam-6466	106	2	.	.	PUNCT
ejpam-6466	106	3	improved	improve	VERB
ejpam-6466	106	4	accuracy	accuracy	NOUN
ejpam-6466	106	5	in	in	ADP
ejpam-6466	106	6	complex	complex	ADJ
ejpam-6466	106	7	systems	system	NOUN
ejpam-6466	106	8	•	•	NUM
ejpam-6466	106	9	by	by	ADP
ejpam-6466	106	10	integrating	integrate	VERB
ejpam-6466	106	11	fractional	fractional	ADJ
ejpam-6466	106	12	derivatives	derivative	NOUN
ejpam-6466	106	13	,	,	PUNCT
ejpam-6466	106	14	delays	delay	NOUN
ejpam-6466	106	15	,	,	PUNCT
ejpam-6466	106	16	and	and	CCONJ
ejpam-6466	106	17	stochastic	stochastic	ADJ
ejpam-6466	106	18	components	component	NOUN
ejpam-6466	106	19	,	,	PUNCT
ejpam-6466	106	20	dfsdes	dfsde	NOUN
ejpam-6466	106	21	offer	offer	VERB
ejpam-6466	106	22	a	a	DET
ejpam-6466	106	23	more	more	ADV
ejpam-6466	106	24	comprehensive	comprehensive	ADJ
ejpam-6466	106	25	and	and	CCONJ
ejpam-6466	106	26	accurate	accurate	ADJ
ejpam-6466	106	27	description	description	NOUN
ejpam-6466	106	28	of	of	ADP
ejpam-6466	106	29	complex	complex	ADJ
ejpam-6466	106	30	systems	system	NOUN
ejpam-6466	106	31	than	than	ADP
ejpam-6466	106	32	traditional	traditional	ADJ
ejpam-6466	106	33	differential	differential	ADJ
ejpam-6466	106	34	equations	equation	NOUN
ejpam-6466	106	35	.	.	PUNCT
ejpam-6466	107	1	for	for	ADP
ejpam-6466	107	2	example	example	NOUN
ejpam-6466	107	3	,	,	PUNCT
ejpam-6466	107	4	in	in	ADP
ejpam-6466	107	5	epidemiology	epidemiology	NOUN
ejpam-6466	107	6	,	,	PUNCT
ejpam-6466	107	7	the	the	DET
ejpam-6466	107	8	spread	spread	NOUN
ejpam-6466	107	9	of	of	ADP
ejpam-6466	107	10	diseases	disease	NOUN
ejpam-6466	107	11	can	can	AUX
ejpam-6466	107	12	be	be	AUX
ejpam-6466	107	13	influenced	influence	VERB
ejpam-6466	107	14	by	by	ADP
ejpam-6466	107	15	past	past	ADJ
ejpam-6466	107	16	infection	infection	NOUN
ejpam-6466	107	17	rates	rate	NOUN
ejpam-6466	107	18	(	(	PUNCT
ejpam-6466	107	19	memory	memory	NOUN
ejpam-6466	107	20	)	)	PUNCT
ejpam-6466	107	21	,	,	PUNCT
ejpam-6466	107	22	delays	delay	NOUN
ejpam-6466	107	23	in	in	ADP
ejpam-6466	107	24	the	the	DET
ejpam-6466	107	25	incubation	incubation	NOUN
ejpam-6466	107	26	period	period	NOUN
ejpam-6466	107	27	,	,	PUNCT
ejpam-6466	107	28	and	and	CCONJ
ejpam-6466	107	29	random	random	ADJ
ejpam-6466	107	30	contact	contact	NOUN
ejpam-6466	107	31	rates	rate	NOUN
ejpam-6466	107	32	.	.	PUNCT
ejpam-6466	108	1	df	df	NOUN
ejpam-6466	108	2	-	-	PUNCT
ejpam-6466	108	3	sdes	sde	NOUN
ejpam-6466	108	4	can	can	AUX
ejpam-6466	108	5	simultaneously	simultaneously	ADV
ejpam-6466	108	6	account	account	VERB
ejpam-6466	108	7	for	for	ADP
ejpam-6466	108	8	these	these	DET
ejpam-6466	108	9	factors	factor	NOUN
ejpam-6466	108	10	,	,	PUNCT
ejpam-6466	108	11	leading	lead	VERB
ejpam-6466	108	12	to	to	ADP
ejpam-6466	108	13	better	well	ADJ
ejpam-6466	108	14	predictions	prediction	NOUN
ejpam-6466	108	15	of	of	ADP
ejpam-6466	108	16	disease	disease	NOUN
ejpam-6466	108	17	outbreaks	outbreak	NOUN
ejpam-6466	108	18	and	and	CCONJ
ejpam-6466	108	19	control	control	NOUN
ejpam-6466	108	20	strategies	strategy	NOUN
ejpam-6466	108	21	.	.	PUNCT
ejpam-6466	109	1	v.	v.	ADP
ejpam-6466	109	2	flexibility	flexibility	NOUN
ejpam-6466	109	3	in	in	ADP
ejpam-6466	109	4	model	model	NOUN
ejpam-6466	109	5	formulation	formulation	NOUN
ejpam-6466	109	6	•	•	ADP
ejpam-6466	109	7	df	df	NOUN
ejpam-6466	109	8	-	-	PUNCT
ejpam-6466	109	9	sdes	sde	NOUN
ejpam-6466	109	10	provide	provide	VERB
ejpam-6466	109	11	a	a	DET
ejpam-6466	109	12	flexible	flexible	ADJ
ejpam-6466	109	13	framework	framework	NOUN
ejpam-6466	109	14	for	for	ADP
ejpam-6466	109	15	model	model	NOUN
ejpam-6466	109	16	formulation	formulation	NOUN
ejpam-6466	109	17	.	.	PUNCT
ejpam-6466	110	1	the	the	DET
ejpam-6466	110	2	orders	order	NOUN
ejpam-6466	110	3	of	of	ADP
ejpam-6466	110	4	fractional	fractional	ADJ
ejpam-6466	110	5	derivatives	derivative	NOUN
ejpam-6466	110	6	and	and	CCONJ
ejpam-6466	110	7	the	the	DET
ejpam-6466	110	8	lengths	length	NOUN
ejpam-6466	110	9	of	of	ADP
ejpam-6466	110	10	delays	delay	NOUN
ejpam-6466	110	11	can	can	AUX
ejpam-6466	110	12	be	be	AUX
ejpam-6466	110	13	adjusted	adjust	VERB
ejpam-6466	110	14	to	to	PART
ejpam-6466	110	15	fit	fit	VERB
ejpam-6466	110	16	empirical	empirical	ADJ
ejpam-6466	110	17	data	datum	NOUN
ejpam-6466	110	18	more	more	ADV
ejpam-6466	110	19	closely	closely	ADV
ejpam-6466	110	20	,	,	PUNCT
ejpam-6466	110	21	allowing	allow	VERB
ejpam-6466	110	22	for	for	ADP
ejpam-6466	110	23	tailored	tailored	ADJ
ejpam-6466	110	24	models	model	NOUN
ejpam-6466	110	25	that	that	PRON
ejpam-6466	110	26	match	match	VERB
ejpam-6466	110	27	specific	specific	ADJ
ejpam-6466	110	28	system	system	NOUN
ejpam-6466	110	29	behaviors	behavior	NOUN
ejpam-6466	110	30	.	.	PUNCT
ejpam-6466	111	1	for	for	ADP
ejpam-6466	111	2	example	example	NOUN
ejpam-6466	111	3	,	,	PUNCT
ejpam-6466	111	4	in	in	ADP
ejpam-6466	111	5	mechanical	mechanical	ADJ
ejpam-6466	111	6	systems	system	NOUN
ejpam-6466	111	7	,	,	PUNCT
ejpam-6466	111	8	different	different	ADJ
ejpam-6466	111	9	materials	material	NOUN
ejpam-6466	111	10	exhibit	exhibit	VERB
ejpam-6466	111	11	varying	vary	VERB
ejpam-6466	111	12	degrees	degree	NOUN
ejpam-6466	111	13	of	of	ADP
ejpam-6466	111	14	viscoelasticity	viscoelasticity	NOUN
ejpam-6466	111	15	and	and	CCONJ
ejpam-6466	111	16	response	response	NOUN
ejpam-6466	111	17	times	time	NOUN
ejpam-6466	111	18	.	.	PUNCT
ejpam-6466	112	1	df	df	PROPN
ejpam-6466	112	2	-	-	PUNCT
ejpam-6466	112	3	sdes	sde	NOUN
ejpam-6466	112	4	can	can	AUX
ejpam-6466	112	5	be	be	AUX
ejpam-6466	112	6	customized	customize	VERB
ejpam-6466	112	7	to	to	PART
ejpam-6466	112	8	model	model	VERB
ejpam-6466	112	9	the	the	DET
ejpam-6466	112	10	specific	specific	ADJ
ejpam-6466	112	11	viscoelastic	viscoelastic	ADJ
ejpam-6466	112	12	properties	property	NOUN
ejpam-6466	112	13	and	and	CCONJ
ejpam-6466	112	14	response	response	NOUN
ejpam-6466	112	15	delays	delay	NOUN
ejpam-6466	112	16	of	of	ADP
ejpam-6466	112	17	different	different	ADJ
ejpam-6466	112	18	materials	material	NOUN
ejpam-6466	112	19	,	,	PUNCT
ejpam-6466	112	20	improving	improve	VERB
ejpam-6466	112	21	the	the	DET
ejpam-6466	112	22	design	design	NOUN
ejpam-6466	112	23	and	and	CCONJ
ejpam-6466	112	24	analysis	analysis	NOUN
ejpam-6466	112	25	of	of	ADP
ejpam-6466	112	26	mechanical	mechanical	ADJ
ejpam-6466	112	27	structures	structure	NOUN
ejpam-6466	112	28	.	.	PUNCT
ejpam-6466	113	1	vi	vi	X
ejpam-6466	113	2	.	.	NOUN
ejpam-6466	113	3	capturing	capture	VERB
ejpam-6466	113	4	anomalous	anomalous	ADJ
ejpam-6466	113	5	diffusion	diffusion	NOUN
ejpam-6466	113	6	•	•	ADP
ejpam-6466	113	7	anomalous	anomalous	ADJ
ejpam-6466	113	8	diffusion	diffusion	NOUN
ejpam-6466	113	9	,	,	PUNCT
ejpam-6466	113	10	where	where	SCONJ
ejpam-6466	113	11	the	the	DET
ejpam-6466	113	12	rate	rate	NOUN
ejpam-6466	113	13	of	of	ADP
ejpam-6466	113	14	diffusion	diffusion	NOUN
ejpam-6466	113	15	deviates	deviate	VERB
ejpam-6466	113	16	from	from	ADP
ejpam-6466	113	17	classical	classical	ADJ
ejpam-6466	113	18	behavior	behavior	NOUN
ejpam-6466	113	19	,	,	PUNCT
ejpam-6466	113	20	can	can	AUX
ejpam-6466	113	21	be	be	AUX
ejpam-6466	113	22	effectively	effectively	ADV
ejpam-6466	113	23	modeled	model	VERB
ejpam-6466	113	24	using	use	VERB
ejpam-6466	113	25	df	df	NOUN
ejpam-6466	113	26	-	-	PUNCT
ejpam-6466	113	27	sdes	sde	NOUN
ejpam-6466	113	28	.	.	PUNCT
ejpam-6466	114	1	this	this	PRON
ejpam-6466	114	2	is	be	AUX
ejpam-6466	114	3	crucial	crucial	ADJ
ejpam-6466	114	4	in	in	ADP
ejpam-6466	114	5	fields	field	NOUN
ejpam-6466	114	6	like	like	ADP
ejpam-6466	114	7	materials	material	NOUN
ejpam-6466	114	8	science	science	NOUN
ejpam-6466	114	9	and	and	CCONJ
ejpam-6466	114	10	biology	biology	NOUN
ejpam-6466	114	11	,	,	PUNCT
ejpam-6466	114	12	where	where	SCONJ
ejpam-6466	114	13	such	such	ADJ
ejpam-6466	114	14	phenomena	phenomenon	NOUN
ejpam-6466	114	15	are	be	AUX
ejpam-6466	114	16	common	common	ADJ
ejpam-6466	114	17	.	.	PUNCT
ejpam-6466	115	1	for	for	ADP
ejpam-6466	115	2	instance	instance	NOUN
ejpam-6466	115	3	,	,	PUNCT
ejpam-6466	115	4	in	in	ADP
ejpam-6466	115	5	porous	porous	ADJ
ejpam-6466	115	6	media	medium	NOUN
ejpam-6466	115	7	,	,	PUNCT
ejpam-6466	115	8	the	the	DET
ejpam-6466	115	9	diffusion	diffusion	NOUN
ejpam-6466	115	10	of	of	ADP
ejpam-6466	115	11	fluids	fluid	NOUN
ejpam-6466	115	12	can	can	AUX
ejpam-6466	115	13	be	be	AUX
ejpam-6466	115	14	anomalous	anomalous	ADJ
ejpam-6466	115	15	due	due	ADP
ejpam-6466	115	16	to	to	ADP
ejpam-6466	115	17	the	the	DET
ejpam-6466	115	18	complex	complex	ADJ
ejpam-6466	115	19	structure	structure	NOUN
ejpam-6466	115	20	of	of	ADP
ejpam-6466	115	21	the	the	DET
ejpam-6466	115	22	medium	medium	NOUN
ejpam-6466	115	23	.	.	PUNCT
ejpam-6466	116	1	df	df	NOUN
ejpam-6466	116	2	-	-	PUNCT
ejpam-6466	116	3	sdes	sde	NOUN
ejpam-6466	116	4	can	can	AUX
ejpam-6466	116	5	model	model	VERB
ejpam-6466	116	6	anomalous	anomalous	ADJ
ejpam-6466	116	7	diffusion	diffusion	NOUN
ejpam-6466	116	8	more	more	ADV
ejpam-6466	116	9	accurately	accurately	ADV
ejpam-6466	116	10	than	than	ADP
ejpam-6466	116	11	standard	standard	ADJ
ejpam-6466	116	12	models	model	NOUN
ejpam-6466	116	13	,	,	PUNCT
ejpam-6466	116	14	aiding	aid	VERB
ejpam-6466	116	15	in	in	ADP
ejpam-6466	116	16	the	the	DET
ejpam-6466	116	17	understanding	understanding	NOUN
ejpam-6466	116	18	and	and	CCONJ
ejpam-6466	116	19	prediction	prediction	NOUN
ejpam-6466	116	20	of	of	ADP
ejpam-6466	116	21	fluid	fluid	ADJ
ejpam-6466	116	22	flow	flow	NOUN
ejpam-6466	116	23	in	in	ADP
ejpam-6466	116	24	such	such	ADJ
ejpam-6466	116	25	media	medium	NOUN
ejpam-6466	116	26	.	.	PUNCT
ejpam-6466	117	1	vii	vii	PROPN
ejpam-6466	117	2	.	.	PROPN
ejpam-6466	118	1	enhanced	enhance	VERB
ejpam-6466	118	2	predictive	predictive	ADJ
ejpam-6466	118	3	power	power	NOUN
ejpam-6466	118	4	m.	m.	NOUN
ejpam-6466	118	5	i.	i.	PROPN
ejpam-6466	118	6	liaqat	liaqat	PROPN
ejpam-6466	118	7	et	et	PROPN
ejpam-6466	118	8	al	al	PROPN
ejpam-6466	118	9	.	.	PUNCT
ejpam-6466	118	10	/	/	SYM
ejpam-6466	118	11	eur	eur	PROPN
ejpam-6466	118	12	.	.	PUNCT
ejpam-6466	119	1	j.	j.	PROPN
ejpam-6466	119	2	pure	pure	PROPN
ejpam-6466	119	3	appl	appl	PROPN
ejpam-6466	119	4	.	.	PROPN
ejpam-6466	119	5	math	math	PROPN
ejpam-6466	119	6	,	,	PUNCT
ejpam-6466	119	7	18	18	NUM
ejpam-6466	119	8	(	(	PUNCT
ejpam-6466	119	9	4	4	NUM
ejpam-6466	119	10	)	)	PUNCT
ejpam-6466	119	11	(	(	PUNCT
ejpam-6466	119	12	2025	2025	NUM
ejpam-6466	119	13	)	)	PUNCT
ejpam-6466	119	14	,	,	PUNCT
ejpam-6466	119	15	6466	6466	NUM
ejpam-6466	119	16	7	7	NUM
ejpam-6466	119	17	of	of	ADP
ejpam-6466	119	18	28	28	NUM
ejpam-6466	119	19	•	•	NOUN
ejpam-6466	119	20	the	the	DET
ejpam-6466	119	21	combined	combine	VERB
ejpam-6466	119	22	effects	effect	NOUN
ejpam-6466	119	23	of	of	ADP
ejpam-6466	119	24	memory	memory	NOUN
ejpam-6466	119	25	,	,	PUNCT
ejpam-6466	119	26	delays	delay	NOUN
ejpam-6466	119	27	,	,	PUNCT
ejpam-6466	119	28	and	and	CCONJ
ejpam-6466	119	29	randomness	randomness	NOUN
ejpam-6466	119	30	in	in	ADP
ejpam-6466	119	31	df	df	NOUN
ejpam-6466	119	32	-	-	PUNCT
ejpam-6466	119	33	sdes	sde	NOUN
ejpam-6466	119	34	often	often	ADV
ejpam-6466	119	35	result	result	VERB
ejpam-6466	119	36	in	in	ADP
ejpam-6466	119	37	models	model	NOUN
ejpam-6466	119	38	with	with	ADP
ejpam-6466	119	39	superior	superior	ADJ
ejpam-6466	119	40	predictive	predictive	ADJ
ejpam-6466	119	41	power	power	NOUN
ejpam-6466	119	42	compared	compare	VERB
ejpam-6466	119	43	to	to	ADP
ejpam-6466	119	44	traditional	traditional	ADJ
ejpam-6466	119	45	models	model	NOUN
ejpam-6466	119	46	.	.	PUNCT
ejpam-6466	120	1	this	this	PRON
ejpam-6466	120	2	is	be	AUX
ejpam-6466	120	3	particularly	particularly	ADV
ejpam-6466	120	4	valuable	valuable	ADJ
ejpam-6466	120	5	in	in	ADP
ejpam-6466	120	6	fields	field	NOUN
ejpam-6466	120	7	where	where	SCONJ
ejpam-6466	120	8	accurate	accurate	ADJ
ejpam-6466	120	9	forecasting	forecasting	NOUN
ejpam-6466	120	10	is	be	AUX
ejpam-6466	120	11	critical	critical	ADJ
ejpam-6466	120	12	.	.	PUNCT
ejpam-6466	121	1	for	for	ADP
ejpam-6466	121	2	example	example	NOUN
ejpam-6466	121	3	,	,	PUNCT
ejpam-6466	121	4	in	in	ADP
ejpam-6466	121	5	financial	financial	ADJ
ejpam-6466	121	6	markets	market	NOUN
ejpam-6466	121	7	,	,	PUNCT
ejpam-6466	121	8	accurate	accurate	ADJ
ejpam-6466	121	9	prediction	prediction	NOUN
ejpam-6466	121	10	of	of	ADP
ejpam-6466	121	11	asset	asset	NOUN
ejpam-6466	121	12	prices	price	NOUN
ejpam-6466	121	13	and	and	CCONJ
ejpam-6466	121	14	risk	risk	NOUN
ejpam-6466	121	15	management	management	NOUN
ejpam-6466	121	16	are	be	AUX
ejpam-6466	121	17	crucial	crucial	ADJ
ejpam-6466	121	18	.	.	PUNCT
ejpam-6466	122	1	df	df	NOUN
ejpam-6466	122	2	-	-	PUNCT
ejpam-6466	122	3	sdes	sde	NOUN
ejpam-6466	122	4	can	can	AUX
ejpam-6466	122	5	provide	provide	VERB
ejpam-6466	122	6	better	well	ADJ
ejpam-6466	122	7	forecasts	forecast	NOUN
ejpam-6466	122	8	by	by	ADP
ejpam-6466	122	9	incorporating	incorporate	VERB
ejpam-6466	122	10	historical	historical	ADJ
ejpam-6466	122	11	data	datum	NOUN
ejpam-6466	122	12	,	,	PUNCT
ejpam-6466	122	13	delays	delay	NOUN
ejpam-6466	122	14	in	in	ADP
ejpam-6466	122	15	market	market	NOUN
ejpam-6466	122	16	reactions	reaction	NOUN
ejpam-6466	122	17	,	,	PUNCT
ejpam-6466	122	18	and	and	CCONJ
ejpam-6466	122	19	stochastic	stochastic	ADJ
ejpam-6466	122	20	volatility	volatility	NOUN
ejpam-6466	122	21	.	.	PUNCT
ejpam-6466	123	1	a	a	DET
ejpam-6466	123	2	central	central	ADJ
ejpam-6466	123	3	concept	concept	NOUN
ejpam-6466	123	4	in	in	ADP
ejpam-6466	123	5	mathematics	mathematic	NOUN
ejpam-6466	123	6	and	and	CCONJ
ejpam-6466	123	7	scientific	scientific	ADJ
ejpam-6466	123	8	computing	computing	NOUN
ejpam-6466	123	9	is	be	AUX
ejpam-6466	123	10	ensuring	ensure	VERB
ejpam-6466	123	11	the	the	DET
ejpam-6466	123	12	wellposedness	wellposedness	NOUN
ejpam-6466	123	13	of	of	ADP
ejpam-6466	123	14	differential	differential	ADJ
ejpam-6466	123	15	equations	equation	NOUN
ejpam-6466	123	16	.	.	PUNCT
ejpam-6466	124	1	existence	existence	NOUN
ejpam-6466	124	2	,	,	PUNCT
ejpam-6466	124	3	uniqueness	uniqueness	NOUN
ejpam-6466	124	4	,	,	PUNCT
ejpam-6466	124	5	and	and	CCONJ
ejpam-6466	124	6	continuous	continuous	ADJ
ejpam-6466	124	7	dependency	dependency	NOUN
ejpam-6466	124	8	are	be	AUX
ejpam-6466	124	9	three	three	NUM
ejpam-6466	124	10	desirable	desirable	ADJ
ejpam-6466	124	11	properties	property	NOUN
ejpam-6466	124	12	that	that	PRON
ejpam-6466	124	13	a	a	DET
ejpam-6466	124	14	differential	differential	ADJ
ejpam-6466	124	15	equation	equation	NOUN
ejpam-6466	124	16	must	must	AUX
ejpam-6466	124	17	meet	meet	VERB
ejpam-6466	124	18	in	in	ADP
ejpam-6466	124	19	order	order	NOUN
ejpam-6466	124	20	to	to	PART
ejpam-6466	124	21	be	be	AUX
ejpam-6466	124	22	considered	consider	VERB
ejpam-6466	124	23	well	well	ADV
ejpam-6466	124	24	-	-	PUNCT
ejpam-6466	124	25	posed	pose	VERB
ejpam-6466	124	26	.	.	PUNCT
ejpam-6466	125	1	differential	differential	ADJ
ejpam-6466	125	2	equations	equation	NOUN
ejpam-6466	125	3	are	be	AUX
ejpam-6466	125	4	excellent	excellent	ADJ
ejpam-6466	125	5	for	for	ADP
ejpam-6466	125	6	practical	practical	ADJ
ejpam-6466	125	7	usage	usage	NOUN
ejpam-6466	125	8	in	in	ADP
ejpam-6466	125	9	a	a	DET
ejpam-6466	125	10	variety	variety	NOUN
ejpam-6466	125	11	of	of	ADP
ejpam-6466	125	12	domains	domain	NOUN
ejpam-6466	125	13	,	,	PUNCT
ejpam-6466	125	14	including	include	VERB
ejpam-6466	125	15	physics	physics	NOUN
ejpam-6466	125	16	,	,	PUNCT
ejpam-6466	125	17	engineering	engineering	NOUN
ejpam-6466	125	18	,	,	PUNCT
ejpam-6466	125	19	and	and	CCONJ
ejpam-6466	125	20	biological	biological	ADJ
ejpam-6466	125	21	sciences	science	NOUN
ejpam-6466	125	22	,	,	PUNCT
ejpam-6466	125	23	since	since	SCONJ
ejpam-6466	125	24	well	well	ADV
ejpam-6466	125	25	-	-	PUNCT
ejpam-6466	125	26	posedness	posedness	NOUN
ejpam-6466	125	27	guarantees	guarantee	VERB
ejpam-6466	125	28	that	that	SCONJ
ejpam-6466	125	29	the	the	DET
ejpam-6466	125	30	equations	equation	NOUN
ejpam-6466	125	31	are	be	AUX
ejpam-6466	125	32	solvable	solvable	ADJ
ejpam-6466	125	33	,	,	PUNCT
ejpam-6466	125	34	unique	unique	ADJ
ejpam-6466	125	35	,	,	PUNCT
ejpam-6466	125	36	and	and	CCONJ
ejpam-6466	125	37	stable	stable	ADJ
ejpam-6466	125	38	.	.	PUNCT
ejpam-6466	126	1	differential	differential	ADJ
ejpam-6466	126	2	equations	equation	NOUN
ejpam-6466	126	3	must	must	AUX
ejpam-6466	126	4	be	be	AUX
ejpam-6466	126	5	well	well	ADV
ejpam-6466	126	6	-	-	PUNCT
ejpam-6466	126	7	posed	pose	VERB
ejpam-6466	126	8	in	in	ADP
ejpam-6466	126	9	order	order	NOUN
ejpam-6466	126	10	to	to	PART
ejpam-6466	126	11	have	have	AUX
ejpam-6466	126	12	meaningful	meaningful	ADJ
ejpam-6466	126	13	solutions	solution	NOUN
ejpam-6466	126	14	;	;	PUNCT
ejpam-6466	126	15	otherwise	otherwise	ADV
ejpam-6466	126	16	,	,	PUNCT
ejpam-6466	126	17	the	the	DET
ejpam-6466	126	18	solution	solution	NOUN
ejpam-6466	126	19	may	may	AUX
ejpam-6466	126	20	not	not	PART
ejpam-6466	126	21	make	make	VERB
ejpam-6466	126	22	sense	sense	NOUN
ejpam-6466	126	23	in	in	ADP
ejpam-6466	126	24	relation	relation	NOUN
ejpam-6466	126	25	to	to	ADP
ejpam-6466	126	26	the	the	DET
ejpam-6466	126	27	situation	situation	NOUN
ejpam-6466	126	28	being	be	AUX
ejpam-6466	126	29	described	describe	VERB
ejpam-6466	126	30	.	.	PUNCT
ejpam-6466	127	1	if	if	SCONJ
ejpam-6466	127	2	there	there	PRON
ejpam-6466	127	3	is	be	VERB
ejpam-6466	127	4	at	at	ADV
ejpam-6466	127	5	least	least	ADV
ejpam-6466	127	6	one	one	NUM
ejpam-6466	127	7	function	function	NOUN
ejpam-6466	127	8	that	that	PRON
ejpam-6466	127	9	can	can	AUX
ejpam-6466	127	10	satisfy	satisfy	VERB
ejpam-6466	127	11	the	the	DET
ejpam-6466	127	12	given	give	VERB
ejpam-6466	127	13	differential	differential	ADJ
ejpam-6466	127	14	equation	equation	NOUN
ejpam-6466	127	15	,	,	PUNCT
ejpam-6466	127	16	the	the	DET
ejpam-6466	127	17	differential	differential	ADJ
ejpam-6466	127	18	equation	equation	NOUN
ejpam-6466	127	19	is	be	AUX
ejpam-6466	127	20	said	say	VERB
ejpam-6466	127	21	to	to	PART
ejpam-6466	127	22	have	have	VERB
ejpam-6466	127	23	the	the	DET
ejpam-6466	127	24	existence	existence	NOUN
ejpam-6466	127	25	property	property	NOUN
ejpam-6466	127	26	.	.	PUNCT
ejpam-6466	128	1	the	the	DET
ejpam-6466	128	2	relationship	relationship	NOUN
ejpam-6466	128	3	between	between	ADP
ejpam-6466	128	4	variables	variable	NOUN
ejpam-6466	128	5	and	and	CCONJ
ejpam-6466	128	6	time	time	NOUN
ejpam-6466	128	7	or	or	CCONJ
ejpam-6466	128	8	other	other	ADJ
ejpam-6466	128	9	factors	factor	NOUN
ejpam-6466	128	10	is	be	AUX
ejpam-6466	128	11	described	describe	VERB
ejpam-6466	128	12	by	by	ADP
ejpam-6466	128	13	differential	differential	ADJ
ejpam-6466	128	14	equations	equation	NOUN
ejpam-6466	128	15	.	.	PUNCT
ejpam-6466	129	1	we	we	PRON
ejpam-6466	129	2	can	can	AUX
ejpam-6466	129	3	obtain	obtain	VERB
ejpam-6466	129	4	functions	function	NOUN
ejpam-6466	129	5	that	that	PRON
ejpam-6466	129	6	forecast	forecast	VERB
ejpam-6466	129	7	the	the	DET
ejpam-6466	129	8	behavior	behavior	NOUN
ejpam-6466	129	9	of	of	ADP
ejpam-6466	129	10	dynamic	dynamic	ADJ
ejpam-6466	129	11	systems	system	NOUN
ejpam-6466	129	12	by	by	ADP
ejpam-6466	129	13	solving	solve	VERB
ejpam-6466	129	14	these	these	DET
ejpam-6466	129	15	equations	equation	NOUN
ejpam-6466	129	16	.	.	PUNCT
ejpam-6466	130	1	differential	differential	ADJ
ejpam-6466	130	2	equations	equation	NOUN
ejpam-6466	130	3	,	,	PUNCT
ejpam-6466	130	4	for	for	ADP
ejpam-6466	130	5	example	example	NOUN
ejpam-6466	130	6	,	,	PUNCT
ejpam-6466	130	7	are	be	AUX
ejpam-6466	130	8	used	use	VERB
ejpam-6466	130	9	to	to	PART
ejpam-6466	130	10	simulate	simulate	VERB
ejpam-6466	130	11	electrical	electrical	ADJ
ejpam-6466	130	12	circuits	circuit	NOUN
ejpam-6466	130	13	,	,	PUNCT
ejpam-6466	130	14	motion	motion	NOUN
ejpam-6466	130	15	,	,	PUNCT
ejpam-6466	130	16	and	and	CCONJ
ejpam-6466	130	17	heat	heat	NOUN
ejpam-6466	130	18	transport	transport	NOUN
ejpam-6466	130	19	in	in	ADP
ejpam-6466	130	20	physics	physics	NOUN
ejpam-6466	130	21	.	.	PUNCT
ejpam-6466	131	1	we	we	PRON
ejpam-6466	131	2	are	be	AUX
ejpam-6466	131	3	unable	unable	ADJ
ejpam-6466	131	4	to	to	PART
ejpam-6466	131	5	forecast	forecast	VERB
ejpam-6466	131	6	these	these	DET
ejpam-6466	131	7	phenomena	phenomenon	NOUN
ejpam-6466	131	8	if	if	SCONJ
ejpam-6466	131	9	there	there	PRON
ejpam-6466	131	10	are	be	VERB
ejpam-6466	131	11	no	no	DET
ejpam-6466	131	12	solutions	solution	NOUN
ejpam-6466	131	13	to	to	PART
ejpam-6466	131	14	differential	differential	VERB
ejpam-6466	131	15	equations	equation	NOUN
ejpam-6466	131	16	.	.	PUNCT
ejpam-6466	132	1	in	in	ADP
ejpam-6466	132	2	scientific	scientific	ADJ
ejpam-6466	132	3	modeling	modeling	NOUN
ejpam-6466	132	4	and	and	CCONJ
ejpam-6466	132	5	engineering	engineering	NOUN
ejpam-6466	132	6	applications	application	NOUN
ejpam-6466	132	7	,	,	PUNCT
ejpam-6466	132	8	uniqueness	uniqueness	NOUN
ejpam-6466	132	9	is	be	AUX
ejpam-6466	132	10	crucial	crucial	ADJ
ejpam-6466	132	11	for	for	ADP
ejpam-6466	132	12	consistency	consistency	NOUN
ejpam-6466	132	13	and	and	CCONJ
ejpam-6466	132	14	predictability	predictability	NOUN
ejpam-6466	132	15	.	.	PUNCT
ejpam-6466	133	1	it	it	PRON
ejpam-6466	133	2	is	be	AUX
ejpam-6466	133	3	guaranteed	guarantee	VERB
ejpam-6466	133	4	that	that	SCONJ
ejpam-6466	133	5	a	a	DET
ejpam-6466	133	6	well	well	ADV
ejpam-6466	133	7	-	-	PUNCT
ejpam-6466	133	8	posed	pose	VERB
ejpam-6466	133	9	problem	problem	NOUN
ejpam-6466	133	10	has	have	VERB
ejpam-6466	133	11	a	a	DET
ejpam-6466	133	12	unique	unique	ADJ
ejpam-6466	133	13	solution	solution	NOUN
ejpam-6466	133	14	.	.	PUNCT
ejpam-6466	134	1	ambiguity	ambiguity	NOUN
ejpam-6466	134	2	can	can	AUX
ejpam-6466	134	3	result	result	VERB
ejpam-6466	134	4	from	from	ADP
ejpam-6466	134	5	a	a	DET
ejpam-6466	134	6	differential	differential	ADJ
ejpam-6466	134	7	equation	equation	NOUN
ejpam-6466	134	8	that	that	PRON
ejpam-6466	134	9	is	be	AUX
ejpam-6466	134	10	not	not	PART
ejpam-6466	134	11	wellposed	wellpose	VERB
ejpam-6466	134	12	,	,	PUNCT
ejpam-6466	134	13	as	as	SCONJ
ejpam-6466	134	14	it	it	PRON
ejpam-6466	134	15	may	may	AUX
ejpam-6466	134	16	have	have	VERB
ejpam-6466	134	17	several	several	ADJ
ejpam-6466	134	18	solutions	solution	NOUN
ejpam-6466	134	19	or	or	CCONJ
ejpam-6466	134	20	none	none	NOUN
ejpam-6466	134	21	at	at	ADV
ejpam-6466	134	22	all	all	ADV
ejpam-6466	134	23	.	.	PUNCT
ejpam-6466	135	1	the	the	DET
ejpam-6466	135	2	solution	solution	NOUN
ejpam-6466	135	3	must	must	AUX
ejpam-6466	135	4	continuously	continuously	ADV
ejpam-6466	135	5	depend	depend	VERB
ejpam-6466	135	6	on	on	ADP
ejpam-6466	135	7	initial	initial	ADJ
ejpam-6466	135	8	conditions	condition	NOUN
ejpam-6466	135	9	,	,	PUNCT
ejpam-6466	135	10	boundary	boundary	ADJ
ejpam-6466	135	11	conditions	condition	NOUN
ejpam-6466	135	12	,	,	PUNCT
ejpam-6466	135	13	and	and	CCONJ
ejpam-6466	135	14	additional	additional	ADJ
ejpam-6466	135	15	data	datum	NOUN
ejpam-6466	135	16	to	to	PART
ejpam-6466	135	17	be	be	AUX
ejpam-6466	135	18	wellposed	wellpose	VERB
ejpam-6466	135	19	.	.	PUNCT
ejpam-6466	136	1	modest	modest	ADJ
ejpam-6466	136	2	modifications	modification	NOUN
ejpam-6466	136	3	to	to	ADP
ejpam-6466	136	4	the	the	DET
ejpam-6466	136	5	input	input	NOUN
ejpam-6466	136	6	data	datum	NOUN
ejpam-6466	136	7	ought	ought	AUX
ejpam-6466	136	8	to	to	PART
ejpam-6466	136	9	yield	yield	VERB
ejpam-6466	136	10	modest	modest	ADJ
ejpam-6466	136	11	modifications	modification	NOUN
ejpam-6466	136	12	to	to	ADP
ejpam-6466	136	13	the	the	DET
ejpam-6466	136	14	solution	solution	NOUN
ejpam-6466	136	15	.	.	PUNCT
ejpam-6466	137	1	for	for	ADP
ejpam-6466	137	2	stability	stability	NOUN
ejpam-6466	137	3	and	and	CCONJ
ejpam-6466	137	4	robustness	robustness	NOUN
ejpam-6466	137	5	in	in	ADP
ejpam-6466	137	6	real	real	ADJ
ejpam-6466	137	7	-	-	PUNCT
ejpam-6466	137	8	world	world	NOUN
ejpam-6466	137	9	applications	application	NOUN
ejpam-6466	137	10	,	,	PUNCT
ejpam-6466	137	11	this	this	DET
ejpam-6466	137	12	attribute	attribute	NOUN
ejpam-6466	137	13	is	be	AUX
ejpam-6466	137	14	essential	essential	ADJ
ejpam-6466	137	15	.	.	PUNCT
ejpam-6466	138	1	regularization	regularization	NOUN
ejpam-6466	138	2	is	be	AUX
ejpam-6466	138	3	incorporating	incorporate	VERB
ejpam-6466	138	4	extra	extra	ADJ
ejpam-6466	138	5	features	feature	NOUN
ejpam-6466	138	6	,	,	PUNCT
ejpam-6466	138	7	like	like	ADP
ejpam-6466	138	8	solution	solution	NOUN
ejpam-6466	138	9	smoothness	smoothness	ADJ
ejpam-6466	138	10	,	,	PUNCT
ejpam-6466	138	11	into	into	ADP
ejpam-6466	138	12	the	the	DET
ejpam-6466	138	13	differential	differential	ADJ
ejpam-6466	138	14	equation	equation	NOUN
ejpam-6466	138	15	solution	solution	NOUN
ejpam-6466	138	16	.	.	PUNCT
ejpam-6466	139	1	stability	stability	NOUN
ejpam-6466	139	2	theory	theory	NOUN
ejpam-6466	139	3	stands	stand	VERB
ejpam-6466	139	4	out	out	ADP
ejpam-6466	139	5	as	as	ADP
ejpam-6466	139	6	a	a	DET
ejpam-6466	139	7	significant	significant	ADJ
ejpam-6466	139	8	qualitative	qualitative	ADJ
ejpam-6466	139	9	concept	concept	NOUN
ejpam-6466	139	10	in	in	ADP
ejpam-6466	139	11	dynamical	dynamical	ADJ
ejpam-6466	139	12	systems	system	NOUN
ejpam-6466	139	13	.	.	PUNCT
ejpam-6466	140	1	consequently	consequently	ADV
ejpam-6466	140	2	,	,	PUNCT
ejpam-6466	140	3	it	it	PRON
ejpam-6466	140	4	has	have	AUX
ejpam-6466	140	5	garnered	garner	VERB
ejpam-6466	140	6	heightened	heighten	VERB
ejpam-6466	140	7	attention	attention	NOUN
ejpam-6466	140	8	across	across	ADP
ejpam-6466	140	9	various	various	ADJ
ejpam-6466	140	10	fields	field	NOUN
ejpam-6466	140	11	of	of	ADP
ejpam-6466	140	12	study	study	NOUN
ejpam-6466	140	13	and	and	CCONJ
ejpam-6466	140	14	practical	practical	ADJ
ejpam-6466	140	15	applications	application	NOUN
ejpam-6466	140	16	.	.	PUNCT
ejpam-6466	141	1	understanding	understand	VERB
ejpam-6466	141	2	the	the	DET
ejpam-6466	141	3	behavior	behavior	NOUN
ejpam-6466	141	4	of	of	ADP
ejpam-6466	141	5	solutions	solution	NOUN
ejpam-6466	141	6	under	under	ADP
ejpam-6466	141	7	small	small	ADJ
ejpam-6466	141	8	perturbations	perturbation	NOUN
ejpam-6466	141	9	requires	require	VERB
ejpam-6466	141	10	an	an	DET
ejpam-6466	141	11	understanding	understanding	NOUN
ejpam-6466	141	12	of	of	ADP
ejpam-6466	141	13	the	the	DET
ejpam-6466	141	14	ulam	ulam	NOUN
ejpam-6466	141	15	-	-	PUNCT
ejpam-6466	141	16	hyers	hyer	NOUN
ejpam-6466	141	17	(	(	PUNCT
ejpam-6466	141	18	uh	uh	INTJ
ejpam-6466	141	19	)	)	PUNCT
ejpam-6466	141	20	stability	stability	NOUN
ejpam-6466	141	21	of	of	ADP
ejpam-6466	141	22	the	the	DET
ejpam-6466	141	23	differential	differential	ADJ
ejpam-6466	141	24	equations	equation	NOUN
ejpam-6466	141	25	.	.	PUNCT
ejpam-6466	142	1	numerous	numerous	ADJ
ejpam-6466	142	2	researchers	researcher	NOUN
ejpam-6466	142	3	have	have	AUX
ejpam-6466	142	4	established	establish	VERB
ejpam-6466	142	5	various	various	ADJ
ejpam-6466	142	6	results	result	NOUN
ejpam-6466	142	7	for	for	ADP
ejpam-6466	142	8	fsdes	fsde	NOUN
ejpam-6466	142	9	.	.	PUNCT
ejpam-6466	143	1	for	for	ADP
ejpam-6466	143	2	example	example	NOUN
ejpam-6466	143	3	,	,	PUNCT
ejpam-6466	143	4	kahouli	kahouli	PROPN
ejpam-6466	143	5	et	et	PROPN
ejpam-6466	143	6	al	al	PROPN
ejpam-6466	143	7	.	.	PUNCT
ejpam-6466	144	1	[	[	X
ejpam-6466	144	2	23	23	NUM
ejpam-6466	144	3	]	]	PUNCT
ejpam-6466	144	4	proved	prove	VERB
ejpam-6466	144	5	the	the	DET
ejpam-6466	144	6	stability	stability	NOUN
ejpam-6466	144	7	of	of	ADP
ejpam-6466	144	8	fsdes	fsde	NOUN
ejpam-6466	144	9	.	.	PUNCT
ejpam-6466	145	1	ali	ali	PROPN
ejpam-6466	145	2	et	et	PROPN
ejpam-6466	145	3	al	al	PROPN
ejpam-6466	145	4	.	.	PUNCT
ejpam-6466	146	1	[	[	X
ejpam-6466	146	2	24	24	NUM
ejpam-6466	146	3	]	]	PUNCT
ejpam-6466	146	4	demonstrated	demonstrate	VERB
ejpam-6466	146	5	the	the	DET
ejpam-6466	146	6	eu	eu	PROPN
ejpam-6466	146	7	of	of	ADP
ejpam-6466	146	8	solutions	solution	NOUN
ejpam-6466	146	9	using	use	VERB
ejpam-6466	146	10	picard	picard	PROPN
ejpam-6466	146	11	’s	’s	PART
ejpam-6466	146	12	iteration	iteration	NOUN
ejpam-6466	146	13	method	method	NOUN
ejpam-6466	146	14	for	for	ADP
ejpam-6466	146	15	coupled	couple	VERB
ejpam-6466	146	16	systems	system	NOUN
ejpam-6466	146	17	of	of	ADP
ejpam-6466	146	18	fsdes	fsde	NOUN
ejpam-6466	146	19	.	.	PUNCT
ejpam-6466	147	1	raheem	raheem	PROPN
ejpam-6466	147	2	et	et	PROPN
ejpam-6466	147	3	al	al	PROPN
ejpam-6466	147	4	.	.	PUNCT
ejpam-6466	148	1	[	[	X
ejpam-6466	148	2	25	25	NUM
ejpam-6466	148	3	]	]	PUNCT
ejpam-6466	148	4	investigated	investigate	VERB
ejpam-6466	148	5	the	the	DET
ejpam-6466	148	6	existence	existence	NOUN
ejpam-6466	148	7	and	and	CCONJ
ejpam-6466	148	8	uniqueness	uniqueness	NOUN
ejpam-6466	148	9	(	(	PUNCT
ejpam-6466	148	10	eu	eu	NOUN
ejpam-6466	148	11	)	)	PUNCT
ejpam-6466	148	12	of	of	ADP
ejpam-6466	148	13	mild	mild	ADJ
ejpam-6466	148	14	solutions	solution	NOUN
ejpam-6466	148	15	and	and	CCONJ
ejpam-6466	148	16	controllability	controllability	NOUN
ejpam-6466	148	17	by	by	ADP
ejpam-6466	148	18	employing	employ	VERB
ejpam-6466	148	19	sectorial	sectorial	ADJ
ejpam-6466	148	20	operators	operator	NOUN
ejpam-6466	148	21	for	for	ADP
ejpam-6466	148	22	fsdes	fsde	NOUN
ejpam-6466	148	23	involving	involve	VERB
ejpam-6466	148	24	the	the	DET
ejpam-6466	148	25	ψ	ψ	NOUN
ejpam-6466	148	26	-	-	ADJ
ejpam-6466	148	27	hilfer	hilfer	NOUN
ejpam-6466	148	28	fractional	fractional	ADJ
ejpam-6466	148	29	derivative	derivative	NOUN
ejpam-6466	148	30	.	.	PUNCT
ejpam-6466	149	1	ramkumar	ramkumar	PROPN
ejpam-6466	149	2	et	et	PROPN
ejpam-6466	149	3	al	al	PROPN
ejpam-6466	149	4	.	.	PUNCT
ejpam-6466	150	1	[	[	X
ejpam-6466	150	2	26	26	NUM
ejpam-6466	150	3	]	]	PUNCT
ejpam-6466	150	4	studied	study	VERB
ejpam-6466	150	5	mild	mild	ADJ
ejpam-6466	150	6	solutions	solution	NOUN
ejpam-6466	150	7	and	and	CCONJ
ejpam-6466	150	8	optimal	optimal	ADJ
ejpam-6466	150	9	control	control	NOUN
ejpam-6466	150	10	approaches	approach	NOUN
ejpam-6466	150	11	for	for	ADP
ejpam-6466	150	12	fsdes	fsde	NOUN
ejpam-6466	150	13	in	in	ADP
ejpam-6466	150	14	hilbert	hilbert	PROPN
ejpam-6466	150	15	spaces	space	NOUN
ejpam-6466	150	16	.	.	PUNCT
ejpam-6466	151	1	djaouti	djaouti	PROPN
ejpam-6466	151	2	and	and	CCONJ
ejpam-6466	151	3	liaqat	liaqat	NOUN
ejpam-6466	152	1	[	[	X
ejpam-6466	152	2	27	27	NUM
ejpam-6466	152	3	]	]	PUNCT
ejpam-6466	152	4	presented	present	VERB
ejpam-6466	152	5	several	several	ADJ
ejpam-6466	152	6	important	important	ADJ
ejpam-6466	152	7	results	result	NOUN
ejpam-6466	152	8	regarding	regard	VERB
ejpam-6466	152	9	the	the	DET
ejpam-6466	152	10	solutions	solution	NOUN
ejpam-6466	152	11	of	of	ADP
ejpam-6466	152	12	fsdes	fsde	NOUN
ejpam-6466	152	13	under	under	ADP
ejpam-6466	152	14	the	the	DET
ejpam-6466	152	15	caputo	caputo	PROPN
ejpam-6466	152	16	derivative	derivative	PROPN
ejpam-6466	152	17	.	.	PUNCT
ejpam-6466	153	1	ali	ali	PROPN
ejpam-6466	153	2	et	et	PROPN
ejpam-6466	153	3	al	al	PROPN
ejpam-6466	153	4	.	.	PUNCT
ejpam-6466	154	1	[	[	X
ejpam-6466	154	2	28	28	NUM
ejpam-6466	154	3	]	]	PUNCT
ejpam-6466	154	4	demonstrated	demonstrate	VERB
ejpam-6466	154	5	the	the	DET
ejpam-6466	154	6	eu	eu	PROPN
ejpam-6466	154	7	for	for	ADP
ejpam-6466	154	8	caputo	caputo	PROPN
ejpam-6466	154	9	–	–	PUNCT
ejpam-6466	154	10	fabrizio	fabrizio	PROPN
ejpam-6466	154	11	fsdes	fsde	NOUN
ejpam-6466	154	12	driven	drive	VERB
ejpam-6466	154	13	by	by	ADP
ejpam-6466	154	14	multiplicative	multiplicative	ADJ
ejpam-6466	154	15	white	white	ADJ
ejpam-6466	154	16	noise	noise	NOUN
ejpam-6466	154	17	.	.	PUNCT
ejpam-6466	155	1	they	they	PRON
ejpam-6466	155	2	also	also	ADV
ejpam-6466	155	3	verified	verify	VERB
ejpam-6466	155	4	the	the	DET
ejpam-6466	155	5	convergence	convergence	NOUN
ejpam-6466	155	6	of	of	ADP
ejpam-6466	155	7	the	the	DET
ejpam-6466	155	8	euler	euler	NOUN
ejpam-6466	155	9	–	–	PUNCT
ejpam-6466	155	10	maruyama	maruyama	NOUN
ejpam-6466	155	11	approach	approach	NOUN
ejpam-6466	155	12	.	.	PUNCT
ejpam-6466	156	1	lavanya	lavanya	NOUN
ejpam-6466	156	2	and	and	CCONJ
ejpam-6466	156	3	vadivoo	vadivoo	VERB
ejpam-6466	157	1	[	[	X
ejpam-6466	157	2	29	29	NUM
ejpam-6466	157	3	]	]	PUNCT
ejpam-6466	157	4	derived	derive	VERB
ejpam-6466	157	5	m.	m.	NOUN
ejpam-6466	157	6	i.	i.	PROPN
ejpam-6466	157	7	liaqat	liaqat	PROPN
ejpam-6466	157	8	et	et	PROPN
ejpam-6466	157	9	al	al	PROPN
ejpam-6466	157	10	.	.	PUNCT
ejpam-6466	157	11	/	/	SYM
ejpam-6466	157	12	eur	eur	PROPN
ejpam-6466	157	13	.	.	PUNCT
ejpam-6466	158	1	j.	j.	PROPN
ejpam-6466	158	2	pure	pure	PROPN
ejpam-6466	158	3	appl	appl	PROPN
ejpam-6466	158	4	.	.	PROPN
ejpam-6466	158	5	math	math	PROPN
ejpam-6466	158	6	,	,	PUNCT
ejpam-6466	158	7	18	18	NUM
ejpam-6466	158	8	(	(	PUNCT
ejpam-6466	158	9	4	4	NUM
ejpam-6466	158	10	)	)	PUNCT
ejpam-6466	158	11	(	(	PUNCT
ejpam-6466	158	12	2025	2025	NUM
ejpam-6466	158	13	)	)	PUNCT
ejpam-6466	158	14	,	,	PUNCT
ejpam-6466	158	15	6466	6466	NUM
ejpam-6466	158	16	8	8	NUM
ejpam-6466	158	17	of	of	ADP
ejpam-6466	158	18	28	28	NUM
ejpam-6466	158	19	results	result	NOUN
ejpam-6466	158	20	concerning	concern	VERB
ejpam-6466	158	21	the	the	DET
ejpam-6466	158	22	controllability	controllability	NOUN
ejpam-6466	158	23	of	of	ADP
ejpam-6466	158	24	caputo	caputo	PROPN
ejpam-6466	158	25	–	–	PUNCT
ejpam-6466	158	26	hadamard	hadamard	NOUN
ejpam-6466	158	27	fsdes	fsde	NOUN
ejpam-6466	158	28	.	.	PUNCT
ejpam-6466	159	1	the	the	DET
ejpam-6466	159	2	eu	eu	PROPN
ejpam-6466	159	3	was	be	AUX
ejpam-6466	159	4	further	far	ADV
ejpam-6466	159	5	confirmed	confirm	VERB
ejpam-6466	159	6	using	use	VERB
ejpam-6466	159	7	the	the	DET
ejpam-6466	159	8	banach	banach	NOUN
ejpam-6466	159	9	contraction	contraction	NOUN
ejpam-6466	159	10	principle	principle	NOUN
ejpam-6466	159	11	.	.	PUNCT
ejpam-6466	160	1	moualkia	moualkia	NOUN
ejpam-6466	160	2	and	and	CCONJ
ejpam-6466	160	3	xu	xu	PROPN
ejpam-6466	161	1	[	[	X
ejpam-6466	161	2	30	30	NUM
ejpam-6466	161	3	]	]	PUNCT
ejpam-6466	161	4	investigated	investigate	VERB
ejpam-6466	161	5	the	the	DET
ejpam-6466	161	6	eu	eu	PROPN
ejpam-6466	161	7	of	of	ADP
ejpam-6466	161	8	solutions	solution	NOUN
ejpam-6466	161	9	to	to	PART
ejpam-6466	161	10	fsdes	fsde	NOUN
ejpam-6466	161	11	with	with	ADP
ejpam-6466	161	12	variable	variable	ADJ
ejpam-6466	161	13	order	order	NOUN
ejpam-6466	161	14	.	.	PUNCT
ejpam-6466	162	1	they	they	PRON
ejpam-6466	162	2	additionally	additionally	ADV
ejpam-6466	162	3	obtained	obtain	VERB
ejpam-6466	162	4	solutions	solution	NOUN
ejpam-6466	162	5	via	via	ADP
ejpam-6466	162	6	picard	picard	NOUN
ejpam-6466	162	7	iterations	iteration	NOUN
ejpam-6466	162	8	and	and	CCONJ
ejpam-6466	162	9	introduced	introduce	VERB
ejpam-6466	162	10	new	new	ADJ
ejpam-6466	162	11	sufficient	sufficient	ADJ
ejpam-6466	162	12	conditions	condition	NOUN
ejpam-6466	162	13	.	.	PUNCT
ejpam-6466	163	1	liping	liping	PROPN
ejpam-6466	163	2	et	et	PROPN
ejpam-6466	163	3	al	al	PROPN
ejpam-6466	163	4	.	.	PUNCT
ejpam-6466	164	1	[	[	X
ejpam-6466	164	2	31	31	NUM
ejpam-6466	164	3	]	]	PUNCT
ejpam-6466	164	4	examined	examine	VERB
ejpam-6466	164	5	a	a	DET
ejpam-6466	164	6	novel	novel	ADJ
ejpam-6466	164	7	financial	financial	ADJ
ejpam-6466	164	8	chaotic	chaotic	ADJ
ejpam-6466	164	9	model	model	NOUN
ejpam-6466	164	10	formulated	formulate	VERB
ejpam-6466	164	11	as	as	ADP
ejpam-6466	164	12	an	an	DET
ejpam-6466	164	13	fsde	fsde	NOUN
ejpam-6466	164	14	involving	involve	VERB
ejpam-6466	164	15	the	the	DET
ejpam-6466	164	16	atangana	atangana	PROPN
ejpam-6466	164	17	–	–	PUNCT
ejpam-6466	164	18	baleanu	baleanu	NOUN
ejpam-6466	164	19	operator	operator	NOUN
ejpam-6466	164	20	.	.	PUNCT
ejpam-6466	165	1	the	the	DET
ejpam-6466	165	2	authors	author	NOUN
ejpam-6466	165	3	numerically	numerically	ADV
ejpam-6466	165	4	solved	solve	VERB
ejpam-6466	165	5	the	the	DET
ejpam-6466	165	6	model	model	NOUN
ejpam-6466	165	7	and	and	CCONJ
ejpam-6466	165	8	provided	provide	VERB
ejpam-6466	165	9	graphical	graphical	ADJ
ejpam-6466	165	10	results	result	NOUN
ejpam-6466	165	11	under	under	ADP
ejpam-6466	165	12	various	various	ADJ
ejpam-6466	165	13	scenarios	scenario	NOUN
ejpam-6466	165	14	.	.	PUNCT
ejpam-6466	166	1	abouagwa	abouagwa	ADV
ejpam-6466	166	2	et	et	PROPN
ejpam-6466	166	3	al	al	PROPN
ejpam-6466	166	4	.	.	PUNCT
ejpam-6466	167	1	[	[	X
ejpam-6466	167	2	32	32	NUM
ejpam-6466	167	3	]	]	PUNCT
ejpam-6466	167	4	explored	explore	VERB
ejpam-6466	167	5	the	the	DET
ejpam-6466	167	6	eu	eu	PROPN
ejpam-6466	167	7	for	for	ADP
ejpam-6466	167	8	fsdes	fsde	NOUN
ejpam-6466	167	9	with	with	ADP
ejpam-6466	167	10	impulses	impulse	NOUN
ejpam-6466	167	11	.	.	PUNCT
ejpam-6466	168	1	asadzade	asadzade	NOUN
ejpam-6466	168	2	and	and	CCONJ
ejpam-6466	168	3	mahmudov	mahmudov	X
ejpam-6466	169	1	[	[	X
ejpam-6466	169	2	33	33	NUM
ejpam-6466	169	3	]	]	PUNCT
ejpam-6466	169	4	addressed	address	VERB
ejpam-6466	169	5	the	the	DET
ejpam-6466	169	6	existence	existence	NOUN
ejpam-6466	169	7	of	of	ADP
ejpam-6466	169	8	a	a	DET
ejpam-6466	169	9	unique	unique	ADJ
ejpam-6466	169	10	solution	solution	NOUN
ejpam-6466	169	11	and	and	CCONJ
ejpam-6466	169	12	analyzed	analyze	VERB
ejpam-6466	169	13	the	the	DET
ejpam-6466	169	14	finite	finite	ADJ
ejpam-6466	169	15	-	-	PUNCT
ejpam-6466	169	16	time	time	NOUN
ejpam-6466	169	17	stability	stability	NOUN
ejpam-6466	169	18	of	of	ADP
ejpam-6466	169	19	a	a	DET
ejpam-6466	169	20	class	class	NOUN
ejpam-6466	169	21	of	of	ADP
ejpam-6466	169	22	fsdes	fsde	NOUN
ejpam-6466	169	23	.	.	PUNCT
ejpam-6466	170	1	in	in	ADP
ejpam-6466	170	2	this	this	DET
ejpam-6466	170	3	study	study	NOUN
ejpam-6466	170	4	,	,	PUNCT
ejpam-6466	170	5	we	we	PRON
ejpam-6466	170	6	have	have	AUX
ejpam-6466	170	7	established	establish	VERB
ejpam-6466	170	8	the	the	DET
ejpam-6466	170	9	eu	eu	PROPN
ejpam-6466	170	10	,	,	PUNCT
ejpam-6466	170	11	continuous	continuous	ADJ
ejpam-6466	170	12	dependence	dependence	NOUN
ejpam-6466	170	13	(	(	PUNCT
ejpam-6466	170	14	con	con	NOUN
ejpam-6466	170	15	-	-	PUNCT
ejpam-6466	170	16	d	d	NOUN
ejpam-6466	170	17	)	)	PUNCT
ejpam-6466	170	18	,	,	PUNCT
ejpam-6466	170	19	regularity	regularity	NOUN
ejpam-6466	170	20	,	,	PUNCT
ejpam-6466	170	21	and	and	CCONJ
ejpam-6466	170	22	uh	uh	INTJ
ejpam-6466	170	23	stability	stability	NOUN
ejpam-6466	170	24	of	of	ADP
ejpam-6466	170	25	the	the	DET
ejpam-6466	170	26	solutions	solution	NOUN
ejpam-6466	170	27	to	to	ADP
ejpam-6466	170	28	df	df	NOUN
ejpam-6466	170	29	-	-	PUNCT
ejpam-6466	170	30	sdes	sde	NOUN
ejpam-6466	170	31	in	in	ADP
ejpam-6466	170	32	the	the	DET
ejpam-6466	170	33	framework	framework	NOUN
ejpam-6466	170	34	of	of	ADP
ejpam-6466	170	35	con	con	NOUN
ejpam-6466	170	36	-	-	PUNCT
ejpam-6466	170	37	frd	frd	ADJ
ejpam-6466	170	38	.	.	PUNCT
ejpam-6466	171	1	more	more	ADV
ejpam-6466	171	2	specifically	specifically	ADV
ejpam-6466	171	3	,	,	PUNCT
ejpam-6466	171	4	there	there	PRON
ejpam-6466	171	5	have	have	AUX
ejpam-6466	171	6	been	be	AUX
ejpam-6466	171	7	two	two	NUM
ejpam-6466	171	8	steps	step	NOUN
ejpam-6466	171	9	to	to	ADP
ejpam-6466	171	10	proving	prove	VERB
ejpam-6466	171	11	eu	eu	PROPN
ejpam-6466	171	12	:	:	PUNCT
ejpam-6466	171	13	first	first	ADV
ejpam-6466	171	14	,	,	PUNCT
ejpam-6466	171	15	we	we	PRON
ejpam-6466	171	16	have	have	AUX
ejpam-6466	171	17	demonstrated	demonstrate	VERB
ejpam-6466	171	18	the	the	DET
ejpam-6466	171	19	eu	eu	PROPN
ejpam-6466	171	20	via	via	ADP
ejpam-6466	171	21	the	the	DET
ejpam-6466	171	22	global	global	ADJ
ejpam-6466	171	23	lipschitz	lipschitz	NOUN
ejpam-6466	171	24	condition	condition	NOUN
ejpam-6466	171	25	(	(	PUNCT
ejpam-6466	171	26	glc	glc	PROPN
ejpam-6466	171	27	)	)	PUNCT
ejpam-6466	171	28	of	of	ADP
ejpam-6466	171	29	the	the	DET
ejpam-6466	171	30	coefficients	coefficient	NOUN
ejpam-6466	171	31	.	.	PUNCT
ejpam-6466	172	1	in	in	ADP
ejpam-6466	172	2	the	the	DET
ejpam-6466	172	3	second	second	ADJ
ejpam-6466	172	4	stage	stage	NOUN
ejpam-6466	172	5	,	,	PUNCT
ejpam-6466	172	6	using	use	VERB
ejpam-6466	172	7	a	a	DET
ejpam-6466	172	8	truncation	truncation	NOUN
ejpam-6466	172	9	approach	approach	NOUN
ejpam-6466	172	10	,	,	PUNCT
ejpam-6466	172	11	we	we	PRON
ejpam-6466	172	12	have	have	AUX
ejpam-6466	172	13	demonstrated	demonstrate	VERB
ejpam-6466	172	14	the	the	DET
ejpam-6466	172	15	eu	eu	PROPN
ejpam-6466	172	16	according	accord	VERB
ejpam-6466	172	17	to	to	ADP
ejpam-6466	172	18	the	the	DET
ejpam-6466	172	19	local	local	ADJ
ejpam-6466	172	20	lipschitz	lipschitz	NOUN
ejpam-6466	172	21	condition	condition	NOUN
ejpam-6466	172	22	(	(	PUNCT
ejpam-6466	172	23	llc	llc	PROPN
ejpam-6466	172	24	)	)	PUNCT
ejpam-6466	172	25	of	of	ADP
ejpam-6466	172	26	the	the	DET
ejpam-6466	172	27	coefficients	coefficient	NOUN
ejpam-6466	172	28	.	.	PUNCT
ejpam-6466	173	1	we	we	PRON
ejpam-6466	173	2	have	have	AUX
ejpam-6466	173	3	also	also	ADV
ejpam-6466	173	4	shown	show	VERB
ejpam-6466	173	5	that	that	SCONJ
ejpam-6466	173	6	,	,	PUNCT
ejpam-6466	173	7	under	under	ADP
ejpam-6466	173	8	the	the	DET
ejpam-6466	173	9	glc	glc	NOUN
ejpam-6466	173	10	of	of	ADP
ejpam-6466	173	11	the	the	DET
ejpam-6466	173	12	coefficients	coefficient	NOUN
ejpam-6466	173	13	,	,	PUNCT
ejpam-6466	173	14	solutions	solution	NOUN
ejpam-6466	173	15	exhibit	exhibit	VERB
ejpam-6466	173	16	con	con	NOUN
ejpam-6466	173	17	-	-	PUNCT
ejpam-6466	173	18	d	d	NOUN
ejpam-6466	173	19	on	on	ADP
ejpam-6466	173	20	the	the	DET
ejpam-6466	173	21	initial	initial	ADJ
ejpam-6466	173	22	value	value	NOUN
ejpam-6466	173	23	and	and	CCONJ
ejpam-6466	173	24	on	on	ADP
ejpam-6466	173	25	the	the	DET
ejpam-6466	173	26	fractional	fractional	ADJ
ejpam-6466	173	27	exponent	exponent	NOUN
ejpam-6466	173	28	ξ	ξ	PROPN
ejpam-6466	173	29	of	of	ADP
ejpam-6466	173	30	con	con	NOUN
ejpam-6466	173	31	-	-	PUNCT
ejpam-6466	173	32	frd	frd	ADJ
ejpam-6466	173	33	.	.	PUNCT
ejpam-6466	174	1	next	next	ADV
ejpam-6466	174	2	,	,	PUNCT
ejpam-6466	174	3	we	we	PRON
ejpam-6466	174	4	have	have	AUX
ejpam-6466	174	5	established	establish	VERB
ejpam-6466	174	6	the	the	DET
ejpam-6466	174	7	result	result	NOUN
ejpam-6466	174	8	of	of	ADP
ejpam-6466	174	9	regularity	regularity	NOUN
ejpam-6466	174	10	in	in	ADP
ejpam-6466	174	11	time	time	NOUN
ejpam-6466	174	12	for	for	ADP
ejpam-6466	174	13	the	the	DET
ejpam-6466	174	14	solutions	solution	NOUN
ejpam-6466	174	15	to	to	ADP
ejpam-6466	174	16	the	the	DET
ejpam-6466	174	17	df	df	NOUN
ejpam-6466	174	18	-	-	PUNCT
ejpam-6466	174	19	sdes	sde	NOUN
ejpam-6466	174	20	.	.	PUNCT
ejpam-6466	175	1	using	use	VERB
ejpam-6466	175	2	the	the	DET
ejpam-6466	175	3	generalized	generalized	ADJ
ejpam-6466	175	4	grönwall	grönwall	NOUN
ejpam-6466	175	5	inequality	inequality	NOUN
ejpam-6466	175	6	,	,	PUNCT
ejpam-6466	175	7	we	we	PRON
ejpam-6466	175	8	have	have	AUX
ejpam-6466	175	9	presented	present	VERB
ejpam-6466	175	10	the	the	DET
ejpam-6466	175	11	result	result	NOUN
ejpam-6466	175	12	of	of	ADP
ejpam-6466	175	13	the	the	DET
ejpam-6466	175	14	uh	uh	INTJ
ejpam-6466	175	15	stability	stability	NOUN
ejpam-6466	175	16	for	for	ADP
ejpam-6466	175	17	the	the	DET
ejpam-6466	175	18	solutions	solution	NOUN
ejpam-6466	175	19	of	of	ADP
ejpam-6466	175	20	the	the	DET
ejpam-6466	175	21	df	df	NOUN
ejpam-6466	175	22	-	-	PUNCT
ejpam-6466	175	23	sdes	sde	NOUN
ejpam-6466	175	24	.	.	PUNCT
ejpam-6466	176	1	lastly	lastly	ADV
ejpam-6466	176	2	,	,	PUNCT
ejpam-6466	176	3	we	we	PRON
ejpam-6466	176	4	have	have	AUX
ejpam-6466	176	5	provided	provide	VERB
ejpam-6466	176	6	two	two	NUM
ejpam-6466	176	7	examples	example	NOUN
ejpam-6466	176	8	to	to	PART
ejpam-6466	176	9	help	help	VERB
ejpam-6466	176	10	illustrate	illustrate	VERB
ejpam-6466	176	11	the	the	DET
ejpam-6466	176	12	results	result	NOUN
ejpam-6466	176	13	we	we	PRON
ejpam-6466	176	14	have	have	AUX
ejpam-6466	176	15	established	establish	VERB
ejpam-6466	176	16	.	.	PUNCT
ejpam-6466	177	1	the	the	DET
ejpam-6466	177	2	main	main	ADJ
ejpam-6466	177	3	part	part	NOUN
ejpam-6466	177	4	of	of	ADP
ejpam-6466	177	5	the	the	DET
ejpam-6466	177	6	proof	proof	NOUN
ejpam-6466	177	7	of	of	ADP
ejpam-6466	177	8	our	our	PRON
ejpam-6466	177	9	established	establish	VERB
ejpam-6466	177	10	results	result	NOUN
ejpam-6466	177	11	has	have	AUX
ejpam-6466	177	12	involved	involve	VERB
ejpam-6466	177	13	the	the	DET
ejpam-6466	177	14	use	use	NOUN
ejpam-6466	177	15	of	of	ADP
ejpam-6466	177	16	the	the	DET
ejpam-6466	177	17	truncation	truncation	NOUN
ejpam-6466	177	18	process	process	NOUN
ejpam-6466	177	19	,	,	PUNCT
ejpam-6466	177	20	itô	itô	PROPN
ejpam-6466	177	21	isometry	isometry	PROPN
ejpam-6466	177	22	(	(	PUNCT
ejpam-6466	177	23	i	i	NOUN
ejpam-6466	177	24	-	-	PUNCT
ejpam-6466	177	25	is	be	AUX
ejpam-6466	177	26	)	)	PUNCT
ejpam-6466	177	27	,	,	PUNCT
ejpam-6466	177	28	grönwall	grönwall	PROPN
ejpam-6466	177	29	’s	’s	PART
ejpam-6466	177	30	inequality	inequality	NOUN
ejpam-6466	177	31	(	(	PUNCT
ejpam-6466	177	32	g	g	NOUN
ejpam-6466	177	33	-	-	PUNCT
ejpam-6466	177	34	i	i	NOUN
ejpam-6466	177	35	)	)	PUNCT
ejpam-6466	177	36	,	,	PUNCT
ejpam-6466	177	37	temporally	temporally	ADV
ejpam-6466	177	38	weighted	weight	VERB
ejpam-6466	177	39	norm	norm	NOUN
ejpam-6466	177	40	,	,	PUNCT
ejpam-6466	177	41	and	and	CCONJ
ejpam-6466	177	42	hölder	hölder	PROPN
ejpam-6466	177	43	’s	’s	PART
ejpam-6466	177	44	inequality	inequality	NOUN
ejpam-6466	177	45	(	(	PUNCT
ejpam-6466	177	46	höld	höld	NOUN
ejpam-6466	177	47	-	-	PUNCT
ejpam-6466	177	48	i	i	PROPN
ejpam-6466	177	49	)	)	PUNCT
ejpam-6466	177	50	.	.	PUNCT
ejpam-6466	178	1	the	the	DET
ejpam-6466	178	2	contributions	contribution	NOUN
ejpam-6466	178	3	of	of	ADP
ejpam-6466	178	4	this	this	DET
ejpam-6466	178	5	research	research	NOUN
ejpam-6466	178	6	are	be	AUX
ejpam-6466	178	7	outlined	outline	VERB
ejpam-6466	178	8	as	as	SCONJ
ejpam-6466	178	9	follows	follow	VERB
ejpam-6466	178	10	:	:	PUNCT
ejpam-6466	178	11	i.	i.	NOUN
ejpam-6466	178	12	in	in	ADP
ejpam-6466	178	13	contrast	contrast	NOUN
ejpam-6466	178	14	to	to	ADP
ejpam-6466	178	15	the	the	DET
ejpam-6466	178	16	findings	finding	NOUN
ejpam-6466	178	17	in	in	ADP
ejpam-6466	178	18	[	[	X
ejpam-6466	178	19	23–33	23–33	NUM
ejpam-6466	178	20	]	]	PUNCT
ejpam-6466	178	21	,	,	PUNCT
ejpam-6466	178	22	our	our	PRON
ejpam-6466	178	23	research	research	NOUN
ejpam-6466	178	24	has	have	AUX
ejpam-6466	178	25	yielded	yield	VERB
ejpam-6466	178	26	results	result	NOUN
ejpam-6466	178	27	concerning	concern	VERB
ejpam-6466	178	28	the	the	DET
ejpam-6466	178	29	eu	eu	PROPN
ejpam-6466	178	30	,	,	PUNCT
ejpam-6466	178	31	regularity	regularity	NOUN
ejpam-6466	178	32	,	,	PUNCT
ejpam-6466	178	33	con	con	NOUN
ejpam-6466	178	34	-	-	PUNCT
ejpam-6466	178	35	d	d	NOUN
ejpam-6466	178	36	on	on	ADP
ejpam-6466	178	37	both	both	CCONJ
ejpam-6466	178	38	the	the	DET
ejpam-6466	178	39	initial	initial	ADJ
ejpam-6466	178	40	condition	condition	NOUN
ejpam-6466	178	41	and	and	CCONJ
ejpam-6466	178	42	fractional	fractional	ADJ
ejpam-6466	178	43	component	component	NOUN
ejpam-6466	178	44	,	,	PUNCT
ejpam-6466	178	45	and	and	CCONJ
ejpam-6466	178	46	uh	uh	INTJ
ejpam-6466	178	47	stability	stability	NOUN
ejpam-6466	178	48	in	in	ADP
ejpam-6466	178	49	the	the	DET
ejpam-6466	178	50	context	context	NOUN
ejpam-6466	178	51	of	of	ADP
ejpam-6466	178	52	con	con	NOUN
ejpam-6466	178	53	-	-	PUNCT
ejpam-6466	178	54	frd	frd	ADJ
ejpam-6466	178	55	.	.	PUNCT
ejpam-6466	179	1	ii	ii	NOUN
ejpam-6466	179	2	.	.	PUNCT
ejpam-6466	180	1	in	in	ADP
ejpam-6466	180	2	contrast	contrast	NOUN
ejpam-6466	180	3	to	to	ADP
ejpam-6466	180	4	[	[	X
ejpam-6466	180	5	23–33	23–33	NUM
ejpam-6466	180	6	]	]	PUNCT
ejpam-6466	180	7	,	,	PUNCT
ejpam-6466	180	8	we	we	PRON
ejpam-6466	180	9	established	establish	VERB
ejpam-6466	180	10	the	the	DET
ejpam-6466	180	11	result	result	NOUN
ejpam-6466	180	12	of	of	ADP
ejpam-6466	180	13	eu	eu	PROPN
ejpam-6466	180	14	by	by	ADP
ejpam-6466	180	15	using	use	VERB
ejpam-6466	180	16	a	a	DET
ejpam-6466	180	17	truncation	truncation	NOUN
ejpam-6466	180	18	approach	approach	NOUN
ejpam-6466	180	19	based	base	VERB
ejpam-6466	180	20	on	on	ADP
ejpam-6466	180	21	the	the	DET
ejpam-6466	180	22	llc	llc	NOUN
ejpam-6466	180	23	of	of	ADP
ejpam-6466	180	24	the	the	DET
ejpam-6466	180	25	coefficients	coefficient	NOUN
ejpam-6466	180	26	.	.	PUNCT
ejpam-6466	181	1	we	we	PRON
ejpam-6466	181	2	examined	examine	VERB
ejpam-6466	181	3	the	the	DET
ejpam-6466	181	4	following	follow	VERB
ejpam-6466	181	5	df	df	NOUN
ejpam-6466	181	6	-	-	PUNCT
ejpam-6466	181	7	sdes	sde	NOUN
ejpam-6466	181	8	of	of	ADP
ejpam-6466	181	9	order	order	NOUN
ejpam-6466	181	10	1	1	NUM
ejpam-6466	181	11	2	2	NUM
ejpam-6466	181	12	<	<	X
ejpam-6466	181	13	ξ	ξ	X
ejpam-6466	181	14	<	<	X
ejpam-6466	181	15	1	1	NUM
ejpam-6466	181	16	in	in	ADP
ejpam-6466	181	17	this	this	DET
ejpam-6466	181	18	research	research	NOUN
ejpam-6466	181	19	driven	drive	VERB
ejpam-6466	181	20	by	by	ADP
ejpam-6466	181	21	brownian	brownian	ADJ
ejpam-6466	181	22	motions	motion	NOUN
ejpam-6466	181	23	,	,	PUNCT
ejpam-6466	181	24	which	which	PRON
ejpam-6466	181	25	serves	serve	VERB
ejpam-6466	181	26	as	as	ADP
ejpam-6466	181	27	the	the	DET
ejpam-6466	181	28	generalization	generalization	NOUN
ejpam-6466	181	29	of	of	ADP
ejpam-6466	181	30	the	the	DET
ejpam-6466	181	31	classical	classical	ADJ
ejpam-6466	181	32	stochastic	stochastic	ADJ
ejpam-6466	181	33	differential	differential	NOUN
ejpam-6466	181	34	equation	equation	NOUN
ejpam-6466	181	35	.	.	PUNCT
ejpam-6466	182	1	dξ	dξ	PROPN
ejpam-6466	182	2	τx(τ	τx(τ	PUNCT
ejpam-6466	182	3	)	)	PUNCT
ejpam-6466	182	4	=	=	SYM
ejpam-6466	182	5	v(τ	v(τ	PROPN
ejpam-6466	182	6	,	,	PUNCT
ejpam-6466	182	7	x(τ	x(τ	PROPN
ejpam-6466	182	8	)	)	PUNCT
ejpam-6466	182	9	,	,	PUNCT
ejpam-6466	182	10	x(τ	x(τ	PROPN
ejpam-6466	182	11	−m	−m	NOUN
ejpam-6466	182	12	)	)	PUNCT
ejpam-6466	182	13	)	)	PUNCT
ejpam-6466	183	1	+	+	PUNCT
ejpam-6466	183	2	𭟋(τ	𭟋(τ	ADJ
ejpam-6466	183	3	,	,	PUNCT
ejpam-6466	183	4	x(τ	x(τ	PROPN
ejpam-6466	183	5	)	)	PUNCT
ejpam-6466	183	6	,	,	PUNCT
ejpam-6466	183	7	x(τ	x(τ	PROPN
ejpam-6466	183	8	−m	−m	NOUN
ejpam-6466	183	9	)	)	PUNCT
ejpam-6466	183	10	)	)	PUNCT
ejpam-6466	183	11	dwτ	dwτ	ADV
ejpam-6466	183	12	dτ	dτ	INTJ
ejpam-6466	183	13	,	,	PUNCT
ejpam-6466	183	14	∀τ	∀τ	SYM
ejpam-6466	183	15	∈	∈	PROPN
ejpam-6466	184	1	[	[	X
ejpam-6466	184	2	0	0	NUM
ejpam-6466	184	3	,	,	PUNCT
ejpam-6466	184	4	ℏ	ℏ	PROPN
ejpam-6466	184	5	]	]	PUNCT
ejpam-6466	184	6	,	,	PUNCT
ejpam-6466	184	7	(	(	PUNCT
ejpam-6466	184	8	4	4	X
ejpam-6466	184	9	)	)	PUNCT
ejpam-6466	184	10	here	here	ADV
ejpam-6466	184	11	,	,	PUNCT
ejpam-6466	184	12	v	v	NOUN
ejpam-6466	184	13	and	and	CCONJ
ejpam-6466	184	14	𭟋	𭟋	PROPN
ejpam-6466	184	15	are	be	AUX
ejpam-6466	184	16	measurable	measurable	ADJ
ejpam-6466	184	17	functions	function	NOUN
ejpam-6466	184	18	from	from	ADP
ejpam-6466	184	19	[	[	X
ejpam-6466	184	20	0	0	NUM
ejpam-6466	184	21	,	,	PUNCT
ejpam-6466	184	22	ℏ	ℏ	PROPN
ejpam-6466	184	23	]	]	X
ejpam-6466	184	24	×	×	NOUN
ejpam-6466	184	25	(	(	PUNCT
ejpam-6466	184	26	rr)2	rr)2	PROPN
ejpam-6466	184	27	into	into	ADP
ejpam-6466	184	28	rr	rr	PROPN
ejpam-6466	184	29	.	.	PUNCT
ejpam-6466	185	1	the	the	DET
ejpam-6466	185	2	process	process	NOUN
ejpam-6466	185	3	wτ	wτ	NOUN
ejpam-6466	185	4	,	,	PUNCT
ejpam-6466	185	5	indexed	index	VERB
ejpam-6466	185	6	over	over	ADP
ejpam-6466	185	7	τ	τ	PROPN
ejpam-6466	185	8	∈	∈	PROPN
ejpam-6466	185	9	[	[	X
ejpam-6466	185	10	0,∞	0,∞	NOUN
ejpam-6466	185	11	)	)	PUNCT
ejpam-6466	185	12	,	,	PUNCT
ejpam-6466	185	13	denotes	denote	VERB
ejpam-6466	185	14	a	a	DET
ejpam-6466	185	15	standard	standard	ADJ
ejpam-6466	185	16	scalar	scalar	ADJ
ejpam-6466	185	17	wiener	wiener	NOUN
ejpam-6466	185	18	process	process	NOUN
ejpam-6466	185	19	on	on	ADP
ejpam-6466	185	20	the	the	DET
ejpam-6466	185	21	complete	complete	ADJ
ejpam-6466	185	22	filtered	filter	VERB
ejpam-6466	185	23	probability	probability	NOUN
ejpam-6466	185	24	space	space	NOUN
ejpam-6466	185	25	(	(	PUNCT
ejpam-6466	185	26	ω	ω	PROPN
ejpam-6466	185	27	,	,	PUNCT
ejpam-6466	185	28	f	f	NOUN
ejpam-6466	185	29	=	=	SYM
ejpam-6466	185	30	fτ∈[0,∞),p	fτ∈[0,∞),p	NOUN
ejpam-6466	185	31	)	)	PUNCT
ejpam-6466	185	32	.	.	PUNCT
ejpam-6466	186	1	the	the	DET
ejpam-6466	186	2	delay	delay	NOUN
ejpam-6466	186	3	is	be	AUX
ejpam-6466	186	4	governed	govern	VERB
ejpam-6466	186	5	by	by	ADP
ejpam-6466	186	6	a	a	DET
ejpam-6466	186	7	non	non	ADJ
ejpam-6466	186	8	-	-	ADJ
ejpam-6466	186	9	negative	negative	ADJ
ejpam-6466	186	10	real	real	ADJ
ejpam-6466	186	11	constant	constant	ADJ
ejpam-6466	186	12	m	m	NOUN
ejpam-6466	186	13	∈	∈	NOUN
ejpam-6466	186	14	r	r	NOUN
ejpam-6466	186	15	,	,	PUNCT
ejpam-6466	186	16	and	and	CCONJ
ejpam-6466	186	17	φ(τ	φ(τ	NOUN
ejpam-6466	186	18	)	)	PUNCT
ejpam-6466	186	19	denotes	denote	VERB
ejpam-6466	186	20	the	the	DET
ejpam-6466	186	21	history	history	NOUN
ejpam-6466	186	22	-	-	PUNCT
ejpam-6466	186	23	dependent	dependent	ADJ
ejpam-6466	186	24	function	function	NOUN
ejpam-6466	186	25	over	over	ADP
ejpam-6466	186	26	the	the	DET
ejpam-6466	186	27	interval	interval	NOUN
ejpam-6466	186	28	τ	τ	PROPN
ejpam-6466	186	29	∈	∈	PROPN
ejpam-6466	187	1	[	[	X
ejpam-6466	187	2	−m	−m	NOUN
ejpam-6466	187	3	,	,	PUNCT
ejpam-6466	187	4	0	0	NUM
ejpam-6466	187	5	]	]	PUNCT
ejpam-6466	187	6	.	.	PUNCT
ejpam-6466	188	1	further	far	ADV
ejpam-6466	188	2	suppose	suppose	VERB
ejpam-6466	188	3	,	,	PUNCT
ejpam-6466	188	4	xτ	xτ	PROPN
ejpam-6466	188	5	=	=	PRON
ejpam-6466	188	6	{	{	PUNCT
ejpam-6466	188	7	x(τ	x(τ	PROPN
ejpam-6466	188	8	+	+	PROPN
ejpam-6466	188	9	ϖ),−m	ϖ),−m	X
ejpam-6466	188	10	≤	≤	NUM
ejpam-6466	188	11	ϖ	ϖ	X
ejpam-6466	188	12	≤	≤	NUM
ejpam-6466	188	13	0	0	NUM
ejpam-6466	188	14	}	}	PUNCT
ejpam-6466	188	15	and	and	CCONJ
ejpam-6466	188	16	τ	τ	PROPN
ejpam-6466	188	17	∈	∈	PROPN
ejpam-6466	189	1	[	[	X
ejpam-6466	189	2	0	0	NUM
ejpam-6466	189	3	,	,	PUNCT
ejpam-6466	189	4	ℏ	ℏ	PROPN
ejpam-6466	189	5	]	]	PUNCT
ejpam-6466	189	6	.	.	PUNCT
ejpam-6466	190	1	we	we	PRON
ejpam-6466	190	2	examine	examine	VERB
ejpam-6466	190	3	eq	eq	ADP
ejpam-6466	190	4	.	.	PUNCT
ejpam-6466	191	1	(	(	PUNCT
ejpam-6466	191	2	4	4	X
ejpam-6466	191	3	)	)	PUNCT
ejpam-6466	191	4	using	use	VERB
ejpam-6466	191	5	the	the	DET
ejpam-6466	191	6	initial	initial	ADJ
ejpam-6466	191	7	value	value	NOUN
ejpam-6466	191	8	listed	list	VERB
ejpam-6466	191	9	below	below	ADV
ejpam-6466	191	10	:	:	PUNCT
ejpam-6466	192	1	x0	x0	PROPN
ejpam-6466	192	2	=	=	PUNCT
ejpam-6466	192	3	φ	φ	PROPN
ejpam-6466	192	4	=	=	PUNCT
ejpam-6466	192	5	φ(τ	φ(τ	NOUN
ejpam-6466	192	6	)	)	PUNCT
ejpam-6466	192	7	:	:	PUNCT
ejpam-6466	192	8	τ	τ	PROPN
ejpam-6466	192	9	∈	∈	PROPN
ejpam-6466	192	10	[	[	X
ejpam-6466	192	11	−m	−m	NOUN
ejpam-6466	192	12	,	,	PUNCT
ejpam-6466	192	13	0	0	NUM
ejpam-6466	192	14	]	]	PUNCT
ejpam-6466	192	15	,	,	PUNCT
ejpam-6466	192	16	(	(	PUNCT
ejpam-6466	192	17	5	5	X
ejpam-6466	192	18	)	)	PUNCT
ejpam-6466	192	19	m.	m.	NOUN
ejpam-6466	192	20	i.	i.	PROPN
ejpam-6466	192	21	liaqat	liaqat	PROPN
ejpam-6466	192	22	et	et	PROPN
ejpam-6466	192	23	al	al	PROPN
ejpam-6466	192	24	.	.	PUNCT
ejpam-6466	192	25	/	/	SYM
ejpam-6466	192	26	eur	eur	PROPN
ejpam-6466	192	27	.	.	PUNCT
ejpam-6466	193	1	j.	j.	PROPN
ejpam-6466	193	2	pure	pure	PROPN
ejpam-6466	193	3	appl	appl	PROPN
ejpam-6466	193	4	.	.	PROPN
ejpam-6466	193	5	math	math	PROPN
ejpam-6466	193	6	,	,	PUNCT
ejpam-6466	193	7	18	18	NUM
ejpam-6466	193	8	(	(	PUNCT
ejpam-6466	193	9	4	4	NUM
ejpam-6466	193	10	)	)	PUNCT
ejpam-6466	193	11	(	(	PUNCT
ejpam-6466	193	12	2025	2025	NUM
ejpam-6466	193	13	)	)	PUNCT
ejpam-6466	193	14	,	,	PUNCT
ejpam-6466	193	15	6466	6466	NUM
ejpam-6466	193	16	9	9	NUM
ejpam-6466	193	17	of	of	ADP
ejpam-6466	193	18	28	28	NUM
ejpam-6466	193	19	which	which	PRON
ejpam-6466	193	20	is	be	AUX
ejpam-6466	193	21	an	an	DET
ejpam-6466	193	22	f0−measurable	f0−measurable	ADJ
ejpam-6466	193	23	c̃([−m	c̃([−m	NOUN
ejpam-6466	193	24	,	,	PUNCT
ejpam-6466	193	25	0],rr)−	0],rr)−	NOUN
ejpam-6466	193	26	valued	value	VERB
ejpam-6466	193	27	random	random	ADJ
ejpam-6466	193	28	variable	variable	NOUN
ejpam-6466	193	29	in	in	ADP
ejpam-6466	193	30	a	a	DET
ejpam-6466	193	31	manner	manner	NOUN
ejpam-6466	193	32	that	that	PRON
ejpam-6466	193	33	e∥φ∥2	e∥φ∥2	PROPN
ejpam-6466	193	34	<	<	X
ejpam-6466	193	35	∞.	∞.	PROPN
ejpam-6466	193	36	the	the	DET
ejpam-6466	193	37	format	format	NOUN
ejpam-6466	193	38	of	of	ADP
ejpam-6466	193	39	the	the	DET
ejpam-6466	193	40	study	study	NOUN
ejpam-6466	193	41	is	be	AUX
ejpam-6466	193	42	as	as	SCONJ
ejpam-6466	193	43	follows	follow	VERB
ejpam-6466	193	44	:	:	PUNCT
ejpam-6466	193	45	in	in	ADP
ejpam-6466	193	46	the	the	DET
ejpam-6466	193	47	following	following	ADJ
ejpam-6466	193	48	part	part	NOUN
ejpam-6466	193	49	,	,	PUNCT
ejpam-6466	193	50	we	we	PRON
ejpam-6466	193	51	employ	employ	VERB
ejpam-6466	193	52	some	some	DET
ejpam-6466	193	53	important	important	ADJ
ejpam-6466	193	54	points	point	NOUN
ejpam-6466	193	55	,	,	PUNCT
ejpam-6466	193	56	assumptions	assumption	NOUN
ejpam-6466	193	57	,	,	PUNCT
ejpam-6466	193	58	and	and	CCONJ
ejpam-6466	193	59	definitions	definition	NOUN
ejpam-6466	193	60	that	that	PRON
ejpam-6466	193	61	will	will	AUX
ejpam-6466	193	62	serve	serve	VERB
ejpam-6466	193	63	as	as	ADP
ejpam-6466	193	64	foundations	foundation	NOUN
ejpam-6466	193	65	to	to	PART
ejpam-6466	193	66	establish	establish	VERB
ejpam-6466	193	67	our	our	PRON
ejpam-6466	193	68	results	result	NOUN
ejpam-6466	193	69	regarding	regard	VERB
ejpam-6466	193	70	df	df	NOUN
ejpam-6466	193	71	-	-	PUNCT
ejpam-6466	193	72	sdes	sde	NOUN
ejpam-6466	193	73	.	.	PUNCT
ejpam-6466	194	1	in	in	ADP
ejpam-6466	194	2	section	section	NOUN
ejpam-6466	194	3	3	3	NUM
ejpam-6466	194	4	,	,	PUNCT
ejpam-6466	194	5	we	we	PRON
ejpam-6466	194	6	prove	prove	VERB
ejpam-6466	194	7	the	the	DET
ejpam-6466	194	8	well	well	NOUN
ejpam-6466	194	9	-	-	PUNCT
ejpam-6466	194	10	posedness	posedness	NOUN
ejpam-6466	194	11	,	,	PUNCT
ejpam-6466	194	12	regularity	regularity	NOUN
ejpam-6466	194	13	,	,	PUNCT
ejpam-6466	194	14	and	and	CCONJ
ejpam-6466	194	15	uh	uh	INTJ
ejpam-6466	194	16	stability	stability	NOUN
ejpam-6466	194	17	of	of	ADP
ejpam-6466	194	18	solutions	solution	NOUN
ejpam-6466	194	19	to	to	ADP
ejpam-6466	194	20	df	df	NOUN
ejpam-6466	194	21	-	-	PUNCT
ejpam-6466	194	22	sdes	sde	NOUN
ejpam-6466	194	23	.	.	PUNCT
ejpam-6466	195	1	in	in	ADP
ejpam-6466	195	2	section	section	NOUN
ejpam-6466	195	3	4	4	NUM
ejpam-6466	195	4	,	,	PUNCT
ejpam-6466	195	5	we	we	PRON
ejpam-6466	195	6	present	present	VERB
ejpam-6466	195	7	two	two	NUM
ejpam-6466	195	8	examples	example	NOUN
ejpam-6466	195	9	that	that	PRON
ejpam-6466	195	10	demonstrate	demonstrate	VERB
ejpam-6466	195	11	our	our	PRON
ejpam-6466	195	12	results	result	NOUN
ejpam-6466	195	13	.	.	PUNCT
ejpam-6466	196	1	finally	finally	ADV
ejpam-6466	196	2	,	,	PUNCT
ejpam-6466	196	3	in	in	ADP
ejpam-6466	196	4	section	section	NOUN
ejpam-6466	196	5	5	5	NUM
ejpam-6466	196	6	,	,	PUNCT
ejpam-6466	196	7	we	we	PRON
ejpam-6466	196	8	present	present	VERB
ejpam-6466	196	9	conclusions	conclusion	NOUN
ejpam-6466	196	10	.	.	PUNCT
ejpam-6466	197	1	2	2	X
ejpam-6466	197	2	.	.	X
ejpam-6466	197	3	preliminaries	preliminary	NOUN
ejpam-6466	197	4	we	we	PRON
ejpam-6466	197	5	go	go	VERB
ejpam-6466	197	6	over	over	ADP
ejpam-6466	197	7	key	key	ADJ
ejpam-6466	197	8	definitions	definition	NOUN
ejpam-6466	197	9	,	,	PUNCT
ejpam-6466	197	10	assumptions	assumption	NOUN
ejpam-6466	197	11	,	,	PUNCT
ejpam-6466	197	12	and	and	CCONJ
ejpam-6466	197	13	annotations	annotation	NOUN
ejpam-6466	197	14	in	in	ADP
ejpam-6466	197	15	this	this	DET
ejpam-6466	197	16	part	part	NOUN
ejpam-6466	197	17	that	that	PRON
ejpam-6466	197	18	will	will	AUX
ejpam-6466	197	19	be	be	AUX
ejpam-6466	197	20	used	use	VERB
ejpam-6466	197	21	throughout	throughout	ADP
ejpam-6466	197	22	the	the	DET
ejpam-6466	197	23	work	work	NOUN
ejpam-6466	197	24	.	.	PUNCT
ejpam-6466	198	1	the	the	DET
ejpam-6466	198	2	paper	paper	NOUN
ejpam-6466	198	3	uses	use	VERB
ejpam-6466	198	4	the	the	DET
ejpam-6466	198	5	following	follow	VERB
ejpam-6466	198	6	annotations	annotation	NOUN
ejpam-6466	198	7	throughout	throughout	ADP
ejpam-6466	198	8	:	:	PUNCT
ejpam-6466	198	9	when	when	SCONJ
ejpam-6466	198	10	m	m	VERB
ejpam-6466	198	11	>	>	X
ejpam-6466	198	12	0	0	PROPN
ejpam-6466	198	13	,	,	PUNCT
ejpam-6466	198	14	suppose	suppose	VERB
ejpam-6466	198	15	c̃([−m	c̃([−m	ADJ
ejpam-6466	198	16	,	,	PUNCT
ejpam-6466	198	17	0],rr	0],rr	PROPN
ejpam-6466	198	18	)	)	PUNCT
ejpam-6466	198	19	indicate	indicate	VERB
ejpam-6466	198	20	the	the	DET
ejpam-6466	198	21	continuous	continuous	ADJ
ejpam-6466	198	22	function	function	NOUN
ejpam-6466	198	23	space	space	NOUN
ejpam-6466	198	24	y	y	PROPN
ejpam-6466	198	25	from	from	ADP
ejpam-6466	198	26	[	[	X
ejpam-6466	198	27	−m	−m	ADJ
ejpam-6466	198	28	,	,	PUNCT
ejpam-6466	198	29	0	0	NUM
ejpam-6466	198	30	]	]	PUNCT
ejpam-6466	198	31	to	to	PART
ejpam-6466	198	32	rr	rr	VERB
ejpam-6466	198	33	via	via	ADP
ejpam-6466	198	34	the	the	DET
ejpam-6466	198	35	norm	norm	NOUN
ejpam-6466	198	36	supm≤ϖ≤0	supm≤ϖ≤0	VERB
ejpam-6466	198	37	∥y(ϖ)∥	∥y(ϖ)∥	ADJ
ejpam-6466	199	1	when	when	SCONJ
ejpam-6466	199	2	∥	∥	X
ejpam-6466	199	3	·	·	PUNCT
ejpam-6466	199	4	∥	∥	PRON
ejpam-6466	199	5	represents	represent	VERB
ejpam-6466	199	6	in	in	ADP
ejpam-6466	199	7	rr	rr	NOUN
ejpam-6466	199	8	the	the	DET
ejpam-6466	199	9	euclidean	euclidean	ADJ
ejpam-6466	199	10	norm	norm	NOUN
ejpam-6466	200	1	.	.	PUNCT
ejpam-6466	201	1	p̃	p̃	PROPN
ejpam-6466	201	2	≥	≥	NUM
ejpam-6466	201	3	1	1	NUM
ejpam-6466	201	4	,	,	PUNCT
ejpam-6466	201	5	suppose	suppose	VERB
ejpam-6466	201	6	lp̃	lp̃	X
ejpam-6466	202	1	(	(	PUNCT
ejpam-6466	202	2	[	[	X
ejpam-6466	202	3	0	0	NUM
ejpam-6466	202	4	,	,	PUNCT
ejpam-6466	202	5	ℏ],rr	ℏ],rr	ADJ
ejpam-6466	202	6	)	)	PUNCT
ejpam-6466	202	7	indicate	indicate	VERB
ejpam-6466	202	8	the	the	DET
ejpam-6466	202	9	space	space	NOUN
ejpam-6466	202	10	where	where	SCONJ
ejpam-6466	202	11	all	all	PRON
ejpam-6466	202	12	rr−valued	rr−value	VERB
ejpam-6466	202	13	fτ−	fτ−	PUNCT
ejpam-6466	202	14	adapted	adapt	VERB
ejpam-6466	202	15	stochastic	stochastic	ADJ
ejpam-6466	202	16	process	process	NOUN
ejpam-6466	202	17	(	(	PUNCT
ejpam-6466	202	18	x(τ))0≤τ≤ℏ	x(τ))0≤τ≤ℏ	X
ejpam-6466	202	19	on	on	ADP
ejpam-6466	202	20	(	(	PUNCT
ejpam-6466	202	21	ω	ω	PROPN
ejpam-6466	202	22	,	,	PUNCT
ejpam-6466	202	23	f	f	PROPN
ejpam-6466	202	24	,	,	PUNCT
ejpam-6466	202	25	p	p	NOUN
ejpam-6466	202	26	)	)	PUNCT
ejpam-6466	202	27	,	,	PUNCT
ejpam-6466	203	1	where	where	SCONJ
ejpam-6466	203	2	∫	∫	PROPN
ejpam-6466	203	3	ℏ	ℏ	NOUN
ejpam-6466	203	4	0	0	PUNCT
ejpam-6466	203	5	∥x(τ)∥p̃dτ	∥x(τ)∥p̃dτ	PROPN
ejpam-6466	203	6	<	<	X
ejpam-6466	203	7	∞	∞	PROPN
ejpam-6466	203	8	is	be	AUX
ejpam-6466	203	9	quite	quite	ADV
ejpam-6466	203	10	certainly	certainly	ADV
ejpam-6466	203	11	achieved	achieve	VERB
ejpam-6466	203	12	using	use	VERB
ejpam-6466	203	13	a	a	DET
ejpam-6466	203	14	filtration	filtration	NOUN
ejpam-6466	204	1	f	f	NOUN
ejpam-6466	204	2	=	=	PUNCT
ejpam-6466	204	3	(	(	PUNCT
ejpam-6466	204	4	fτ	fτ	X
ejpam-6466	204	5	)	)	PUNCT
ejpam-6466	204	6	τ∈[0,ℏ	τ∈[0,ℏ	PROPN
ejpam-6466	204	7	]	]	PUNCT
ejpam-6466	204	8	.	.	PUNCT
ejpam-6466	204	9	suppose	suppose	VERB
ejpam-6466	204	10	l2(ω	l2(ω	PROPN
ejpam-6466	204	11	,	,	PUNCT
ejpam-6466	204	12	f	f	PROPN
ejpam-6466	204	13	,	,	PUNCT
ejpam-6466	204	14	p	p	NOUN
ejpam-6466	204	15	)	)	PUNCT
ejpam-6466	204	16	represent	represent	VERB
ejpam-6466	204	17	all	all	PRON
ejpam-6466	204	18	fτ−measurable	fτ−measurable	ADJ
ejpam-6466	204	19	,	,	PUNCT
ejpam-6466	204	20	mean	mean	VERB
ejpam-6466	204	21	square−integrable	square−integrable	ADJ
ejpam-6466	204	22	functions	function	NOUN
ejpam-6466	204	23	f	f	X
ejpam-6466	204	24	:	:	PUNCT
ejpam-6466	204	25	ω	ω	PROPN
ejpam-6466	204	26	→	→	SYM
ejpam-6466	204	27	rr	rr	PROPN
ejpam-6466	204	28	with	with	ADP
ejpam-6466	204	29	∥f∥2ms	∥f∥2ms	NOUN
ejpam-6466	204	30	=	=	SYM
ejpam-6466	204	31	e∥f∥2	e∥f∥2	PROPN
ejpam-6466	204	32	in	in	ADP
ejpam-6466	204	33	the	the	DET
ejpam-6466	204	34	space	space	NOUN
ejpam-6466	204	35	.	.	PUNCT
ejpam-6466	205	1	definition	definition	NOUN
ejpam-6466	205	2	1	1	NUM
ejpam-6466	205	3	.	.	PUNCT
ejpam-6466	206	1	if	if	SCONJ
ejpam-6466	206	2	the	the	DET
ejpam-6466	206	3	following	follow	VERB
ejpam-6466	206	4	conditions	condition	NOUN
ejpam-6466	206	5	are	be	AUX
ejpam-6466	206	6	met	meet	VERB
ejpam-6466	206	7	,	,	PUNCT
ejpam-6466	206	8	an	an	DET
ejpam-6466	206	9	rr−valued	rr−value	VERB
ejpam-6466	206	10	stochastic	stochastic	ADJ
ejpam-6466	206	11	process	process	NOUN
ejpam-6466	206	12	x(τ	x(τ	PROPN
ejpam-6466	206	13	)	)	PUNCT
ejpam-6466	206	14	on	on	ADP
ejpam-6466	206	15	the	the	DET
ejpam-6466	206	16	interval	interval	NOUN
ejpam-6466	206	17	[	[	X
ejpam-6466	206	18	−m	−m	NOUN
ejpam-6466	206	19	,	,	PUNCT
ejpam-6466	206	20	ℏ	ℏ	PROPN
ejpam-6466	206	21	]	]	PUNCT
ejpam-6466	206	22	is	be	AUX
ejpam-6466	206	23	referred	refer	VERB
ejpam-6466	206	24	to	to	ADP
ejpam-6466	206	25	as	as	ADP
ejpam-6466	206	26	the	the	DET
ejpam-6466	206	27	solution	solution	NOUN
ejpam-6466	206	28	of	of	ADP
ejpam-6466	206	29	eq	eq	PROPN
ejpam-6466	206	30	.	.	PUNCT
ejpam-6466	207	1	(	(	PUNCT
ejpam-6466	207	2	4	4	NUM
ejpam-6466	207	3	)	)	PUNCT
ejpam-6466	207	4	with	with	ADP
ejpam-6466	207	5	the	the	DET
ejpam-6466	207	6	initial	initial	ADJ
ejpam-6466	207	7	value	value	NOUN
ejpam-6466	207	8	eq	eq	ADJ
ejpam-6466	207	9	.	.	PUNCT
ejpam-6466	208	1	(	(	PUNCT
ejpam-6466	208	2	5	5	NUM
ejpam-6466	208	3	):	):	PUNCT
ejpam-6466	208	4	(	(	PUNCT
ejpam-6466	208	5	i	i	NOUN
ejpam-6466	208	6	)	)	PUNCT
ejpam-6466	208	7	it	it	PRON
ejpam-6466	208	8	is	be	AUX
ejpam-6466	208	9	a	a	DET
ejpam-6466	208	10	continuous	continuous	ADJ
ejpam-6466	208	11	process	process	NOUN
ejpam-6466	208	12	and	and	CCONJ
ejpam-6466	208	13	(	(	PUNCT
ejpam-6466	208	14	x(τ))0≤τ≤ℏ	x(τ))0≤τ≤ℏ	X
ejpam-6466	208	15	is	be	AUX
ejpam-6466	208	16	fτ−adapted	fτ−adapte	VERB
ejpam-6466	208	17	,	,	PUNCT
ejpam-6466	208	18	(	(	PUNCT
ejpam-6466	208	19	ii	ii	NOUN
ejpam-6466	208	20	)	)	PUNCT
ejpam-6466	208	21	v(τ	v(τ	PROPN
ejpam-6466	208	22	,	,	PUNCT
ejpam-6466	208	23	x(τ	x(τ	PROPN
ejpam-6466	208	24	)	)	PUNCT
ejpam-6466	208	25	,	,	PUNCT
ejpam-6466	208	26	x(τ	x(τ	PROPN
ejpam-6466	208	27	−m	−m	NOUN
ejpam-6466	208	28	)	)	PUNCT
ejpam-6466	208	29	)	)	PUNCT
ejpam-6466	209	1	∈	∈	PROPN
ejpam-6466	209	2	l2([0	l2([0	VERB
ejpam-6466	209	3	,	,	PUNCT
ejpam-6466	209	4	ℏ],rr	ℏ],rr	NOUN
ejpam-6466	209	5	)	)	PUNCT
ejpam-6466	209	6	and	and	CCONJ
ejpam-6466	209	7	𭟋(τ	𭟋(τ	PROPN
ejpam-6466	209	8	,	,	PUNCT
ejpam-6466	209	9	x(τ	x(τ	PROPN
ejpam-6466	209	10	)	)	PUNCT
ejpam-6466	209	11	,	,	PUNCT
ejpam-6466	209	12	x(τ	x(τ	PROPN
ejpam-6466	209	13	−m	−m	NOUN
ejpam-6466	209	14	)	)	PUNCT
ejpam-6466	209	15	)	)	PUNCT
ejpam-6466	210	1	∈	∈	PROPN
ejpam-6466	210	2	l2([0	l2([0	VERB
ejpam-6466	210	3	,	,	PUNCT
ejpam-6466	210	4	ℏ],rr	ℏ],rr	NOUN
ejpam-6466	210	5	)	)	PUNCT
ejpam-6466	210	6	(	(	PUNCT
ejpam-6466	210	7	iii	iii	X
ejpam-6466	210	8	)	)	PUNCT
ejpam-6466	210	9	probability	probability	NOUN
ejpam-6466	210	10	one	one	NOUN
ejpam-6466	210	11	gives	give	VERB
ejpam-6466	210	12	us	we	PRON
ejpam-6466	210	13	x0	x0	PROPN
ejpam-6466	210	14	=	=	SYM
ejpam-6466	210	15	φ	φ	PROPN
ejpam-6466	210	16	,	,	PUNCT
ejpam-6466	210	17	and	and	CCONJ
ejpam-6466	210	18	the	the	DET
ejpam-6466	210	19	subsequent	subsequent	ADJ
ejpam-6466	210	20	equality	equality	NOUN
ejpam-6466	210	21	holds	hold	VERB
ejpam-6466	210	22	τ	τ	X
ejpam-6466	210	23	∈	∈	PROPN
ejpam-6466	211	1	[	[	X
ejpam-6466	211	2	0	0	NUM
ejpam-6466	211	3	,	,	PUNCT
ejpam-6466	211	4	ℏ	ℏ	NOUN
ejpam-6466	211	5	]	]	PUNCT
ejpam-6466	211	6	x(τ	x(τ	PROPN
ejpam-6466	211	7	)	)	PUNCT
ejpam-6466	211	8	=	=	PUNCT
ejpam-6466	212	1	φ	φ	PROPN
ejpam-6466	212	2	+	+	CCONJ
ejpam-6466	212	3	∫	∫	PROPN
ejpam-6466	212	4	τ	τ	PROPN
ejpam-6466	212	5	0	0	NUM
ejpam-6466	212	6	sξ−1v	sξ−1v	PROPN
ejpam-6466	212	7	(	(	PUNCT
ejpam-6466	212	8	s	s	PROPN
ejpam-6466	212	9	,	,	PUNCT
ejpam-6466	212	10	x(s	x(s	PROPN
ejpam-6466	212	11	)	)	PUNCT
ejpam-6466	212	12	,	,	PUNCT
ejpam-6466	212	13	x(s−m	x(s−m	NUM
ejpam-6466	212	14	)	)	PUNCT
ejpam-6466	212	15	)	)	PUNCT
ejpam-6466	213	1	ds	ds	PROPN
ejpam-6466	214	1	+	+	CCONJ
ejpam-6466	214	2	∫	∫	PROPN
ejpam-6466	214	3	τ	τ	X
ejpam-6466	214	4	0	0	NUM
ejpam-6466	214	5	sξ−1𭟋	sξ−1𭟋	X
ejpam-6466	214	6	(	(	PUNCT
ejpam-6466	214	7	s	s	PROPN
ejpam-6466	214	8	,	,	PUNCT
ejpam-6466	214	9	x(s	x(s	PROPN
ejpam-6466	214	10	)	)	PUNCT
ejpam-6466	214	11	,	,	PUNCT
ejpam-6466	214	12	x(s−m	x(s−m	NUM
ejpam-6466	214	13	)	)	PUNCT
ejpam-6466	214	14	)	)	PUNCT
ejpam-6466	215	1	dws	dws	PROPN
ejpam-6466	215	2	.	.	PUNCT
ejpam-6466	216	1	(	(	PUNCT
ejpam-6466	216	2	6	6	NUM
ejpam-6466	216	3	)	)	PUNCT
ejpam-6466	216	4	definition	definition	NOUN
ejpam-6466	216	5	2	2	NUM
ejpam-6466	216	6	.	.	PUNCT
ejpam-6466	217	1	the	the	DET
ejpam-6466	217	2	eu	eu	PROPN
ejpam-6466	217	3	of	of	ADP
ejpam-6466	217	4	solutions	solution	NOUN
ejpam-6466	217	5	to	to	ADP
ejpam-6466	217	6	eq	eq	PROPN
ejpam-6466	217	7	.	.	PUNCT
ejpam-6466	218	1	(	(	PUNCT
ejpam-6466	218	2	4	4	NUM
ejpam-6466	218	3	)	)	PUNCT
ejpam-6466	218	4	when	when	SCONJ
ejpam-6466	218	5	the	the	DET
ejpam-6466	218	6	coefficients	coefficient	NOUN
ejpam-6466	218	7	v	v	VERB
ejpam-6466	218	8	and	and	CCONJ
ejpam-6466	218	9	𭟋	𭟋	PART
ejpam-6466	218	10	meet	meet	VERB
ejpam-6466	218	11	the	the	DET
ejpam-6466	218	12	following	follow	VERB
ejpam-6466	218	13	requirements	requirement	NOUN
ejpam-6466	218	14	is	be	AUX
ejpam-6466	218	15	our	our	PRON
ejpam-6466	218	16	first	first	ADJ
ejpam-6466	218	17	major	major	ADJ
ejpam-6466	218	18	finding	finding	NOUN
ejpam-6466	218	19	in	in	ADP
ejpam-6466	218	20	our	our	PRON
ejpam-6466	218	21	paper	paper	NOUN
ejpam-6466	218	22	.	.	PUNCT
ejpam-6466	219	1	(	(	PUNCT
ejpam-6466	219	2	i	i	NOUN
ejpam-6466	219	3	)	)	PUNCT
ejpam-6466	219	4	(	(	PUNCT
ejpam-6466	219	5	a1	a1	PROPN
ejpam-6466	219	6	)	)	PUNCT
ejpam-6466	219	7	:	:	PUNCT
ejpam-6466	219	8	with	with	ADP
ejpam-6466	219	9	each	each	DET
ejpam-6466	219	10	integer	integer	NOUN
ejpam-6466	219	11	υ	υ	PROPN
ejpam-6466	219	12	≥	≥	NOUN
ejpam-6466	219	13	1	1	NUM
ejpam-6466	219	14	,	,	PUNCT
ejpam-6466	219	15	there	there	PRON
ejpam-6466	219	16	is	be	VERB
ejpam-6466	219	17	lυ	lυ	ADP
ejpam-6466	219	18	>	>	X
ejpam-6466	219	19	0	0	PUNCT
ejpam-6466	220	1	that	that	PRON
ejpam-6466	220	2	corresponds	correspond	VERB
ejpam-6466	220	3	to	to	ADP
ejpam-6466	220	4	∀	∀	NOUN
ejpam-6466	220	5	∈	∈	NOUN
ejpam-6466	221	1	[	[	X
ejpam-6466	221	2	0	0	NUM
ejpam-6466	221	3	,	,	PUNCT
ejpam-6466	221	4	ℏ	ℏ	NOUN
ejpam-6466	221	5	]	]	PUNCT
ejpam-6466	221	6	and	and	CCONJ
ejpam-6466	221	7	all	all	DET
ejpam-6466	221	8	y1	y1	NOUN
ejpam-6466	221	9	,	,	PUNCT
ejpam-6466	221	10	y2	y2	PROPN
ejpam-6466	221	11	,	,	PUNCT
ejpam-6466	221	12	z1	z1	PROPN
ejpam-6466	221	13	,	,	PUNCT
ejpam-6466	221	14	z2	z2	PROPN
ejpam-6466	221	15	∈	∈	PROPN
ejpam-6466	221	16	rr	rr	NOUN
ejpam-6466	221	17	with	with	ADP
ejpam-6466	221	18	∥y1∥	∥y1∥	PROPN
ejpam-6466	221	19	∨	∨	NUM
ejpam-6466	221	20	∥y1∥2	∥y1∥2	PROPN
ejpam-6466	221	21	∨	∨	NOUN
ejpam-6466	221	22	∥z1∥	∥z1∥	PROPN
ejpam-6466	221	23	∨	∨	NUM
ejpam-6466	221	24	∥z2∥	∥z2∥	PROPN
ejpam-6466	221	25	≤	≤	NUM
ejpam-6466	221	26	υ	υ	PROPN
ejpam-6466	221	27	,	,	PUNCT
ejpam-6466	221	28	∥v(τ	∥v(τ	PROPN
ejpam-6466	221	29	,	,	PUNCT
ejpam-6466	221	30	y1	y1	PROPN
ejpam-6466	221	31	,	,	PUNCT
ejpam-6466	221	32	y2)−v(τ	y2)−v(τ	PROPN
ejpam-6466	221	33	,	,	PUNCT
ejpam-6466	221	34	z1	z1	PROPN
ejpam-6466	221	35	,	,	PUNCT
ejpam-6466	221	36	z2)∥2	z2)∥2	PROPN
ejpam-6466	221	37	≤	≤	NUM
ejpam-6466	221	38	lυ	lυ	NOUN
ejpam-6466	221	39	(	(	PUNCT
ejpam-6466	221	40	∥y1	∥y1	NOUN
ejpam-6466	222	1	−	−	PROPN
ejpam-6466	222	2	z1∥2	z1∥2	PROPN
ejpam-6466	222	3	+	+	CCONJ
ejpam-6466	222	4	∥y2	∥y2	X
ejpam-6466	222	5	−	−	PROPN
ejpam-6466	222	6	z2∥2	z2∥2	PROPN
ejpam-6466	222	7	)	)	PUNCT
ejpam-6466	222	8	,	,	PUNCT
ejpam-6466	222	9	∥𭟋(τ	∥𭟋(τ	VERB
ejpam-6466	222	10	,	,	PUNCT
ejpam-6466	222	11	y1	y1	NOUN
ejpam-6466	222	12	,	,	PUNCT
ejpam-6466	222	13	y2)−𭟋(τ	y2)−𭟋(τ	NOUN
ejpam-6466	222	14	,	,	PUNCT
ejpam-6466	222	15	z1	z1	PROPN
ejpam-6466	222	16	,	,	PUNCT
ejpam-6466	222	17	z2)∥2	z2)∥2	PROPN
ejpam-6466	222	18	≤	≤	NUM
ejpam-6466	222	19	lυ	lυ	NOUN
ejpam-6466	222	20	(	(	PUNCT
ejpam-6466	222	21	∥y1	∥y1	NOUN
ejpam-6466	222	22	−	−	PROPN
ejpam-6466	222	23	z1∥2	z1∥2	PROPN
ejpam-6466	222	24	+	+	CCONJ
ejpam-6466	222	25	∥y2	∥y2	X
ejpam-6466	223	1	−	−	PROPN
ejpam-6466	223	2	z2∥2	z2∥2	PROPN
ejpam-6466	223	3	)	)	PUNCT
ejpam-6466	223	4	,	,	PUNCT
ejpam-6466	223	5	where	where	SCONJ
ejpam-6466	223	6	y	y	PROPN
ejpam-6466	223	7	∨	∨	NOUN
ejpam-6466	223	8	z	z	PROPN
ejpam-6466	223	9	=	=	SYM
ejpam-6466	223	10	max(y	max(y	PROPN
ejpam-6466	223	11	,	,	PUNCT
ejpam-6466	223	12	z	z	NOUN
ejpam-6466	223	13	)	)	PUNCT
ejpam-6466	223	14	,	,	PUNCT
ejpam-6466	223	15	y	y	PROPN
ejpam-6466	223	16	,	,	PUNCT
ejpam-6466	223	17	z	z	PROPN
ejpam-6466	223	18	∈	∈	PROPN
ejpam-6466	223	19	r.	r.	PROPN
ejpam-6466	223	20	local	local	ADJ
ejpam-6466	223	21	lipschitz	lipschitz	NOUN
ejpam-6466	223	22	continuity	continuity	NOUN
ejpam-6466	223	23	is	be	AUX
ejpam-6466	223	24	a	a	DET
ejpam-6466	223	25	property	property	NOUN
ejpam-6466	223	26	of	of	ADP
ejpam-6466	223	27	a	a	DET
ejpam-6466	223	28	function	function	NOUN
ejpam-6466	223	29	that	that	PRON
ejpam-6466	223	30	ensures	ensure	VERB
ejpam-6466	223	31	it	it	PRON
ejpam-6466	223	32	behaves	behave	VERB
ejpam-6466	223	33	”	"	PUNCT
ejpam-6466	223	34	nicely	nicely	ADV
ejpam-6466	223	35	”	"	PUNCT
ejpam-6466	223	36	(	(	PUNCT
ejpam-6466	223	37	i.e.	i.e.	X
ejpam-6466	223	38	,	,	PUNCT
ejpam-6466	223	39	does	do	AUX
ejpam-6466	223	40	not	not	PART
ejpam-6466	223	41	change	change	VERB
ejpam-6466	223	42	too	too	ADV
ejpam-6466	223	43	abruptly	abruptly	ADV
ejpam-6466	223	44	)	)	PUNCT
ejpam-6466	223	45	in	in	ADP
ejpam-6466	223	46	a	a	DET
ejpam-6466	223	47	neighborhood	neighborhood	NOUN
ejpam-6466	223	48	around	around	ADP
ejpam-6466	223	49	every	every	DET
ejpam-6466	223	50	point	point	NOUN
ejpam-6466	223	51	of	of	ADP
ejpam-6466	223	52	its	its	PRON
ejpam-6466	223	53	domain	domain	NOUN
ejpam-6466	223	54	,	,	PUNCT
ejpam-6466	223	55	but	but	CCONJ
ejpam-6466	223	56	not	not	PART
ejpam-6466	223	57	necessarily	necessarily	ADV
ejpam-6466	223	58	globally	globally	ADV
ejpam-6466	223	59	.	.	PUNCT
ejpam-6466	224	1	it	it	PRON
ejpam-6466	224	2	generalizes	generalize	VERB
ejpam-6466	224	3	the	the	DET
ejpam-6466	224	4	concept	concept	NOUN
ejpam-6466	224	5	of	of	ADP
ejpam-6466	224	6	global	global	ADJ
ejpam-6466	224	7	lipschitz	lipschitz	NOUN
ejpam-6466	224	8	continuity	continuity	NOUN
ejpam-6466	224	9	by	by	ADP
ejpam-6466	224	10	relaxing	relax	VERB
ejpam-6466	224	11	the	the	DET
ejpam-6466	224	12	requirement	requirement	NOUN
ejpam-6466	224	13	of	of	ADP
ejpam-6466	224	14	a	a	DET
ejpam-6466	224	15	uniform	uniform	NOUN
ejpam-6466	224	16	bound	bind	VERB
ejpam-6466	224	17	on	on	ADP
ejpam-6466	224	18	the	the	DET
ejpam-6466	224	19	function	function	NOUN
ejpam-6466	224	20	’s	’s	PART
ejpam-6466	224	21	rate	rate	NOUN
ejpam-6466	224	22	of	of	ADP
ejpam-6466	224	23	change	change	NOUN
ejpam-6466	224	24	.	.	PUNCT
ejpam-6466	225	1	m.	m.	NOUN
ejpam-6466	225	2	i.	i.	PROPN
ejpam-6466	225	3	liaqat	liaqat	PROPN
ejpam-6466	225	4	et	et	PROPN
ejpam-6466	225	5	al	al	PROPN
ejpam-6466	225	6	.	.	PUNCT
ejpam-6466	225	7	/	/	SYM
ejpam-6466	225	8	eur	eur	PROPN
ejpam-6466	225	9	.	.	PUNCT
ejpam-6466	226	1	j.	j.	PROPN
ejpam-6466	226	2	pure	pure	PROPN
ejpam-6466	226	3	appl	appl	PROPN
ejpam-6466	226	4	.	.	PROPN
ejpam-6466	226	5	math	math	PROPN
ejpam-6466	226	6	,	,	PUNCT
ejpam-6466	226	7	18	18	NUM
ejpam-6466	226	8	(	(	PUNCT
ejpam-6466	226	9	4	4	NUM
ejpam-6466	226	10	)	)	PUNCT
ejpam-6466	226	11	(	(	PUNCT
ejpam-6466	226	12	2025	2025	NUM
ejpam-6466	226	13	)	)	PUNCT
ejpam-6466	226	14	,	,	PUNCT
ejpam-6466	226	15	6466	6466	NUM
ejpam-6466	226	16	10	10	NUM
ejpam-6466	226	17	of	of	ADP
ejpam-6466	226	18	28	28	NUM
ejpam-6466	226	19	(	(	PUNCT
ejpam-6466	226	20	ii	ii	NOUN
ejpam-6466	226	21	)	)	PUNCT
ejpam-6466	226	22	(	(	PUNCT
ejpam-6466	226	23	a2	a2	PROPN
ejpam-6466	226	24	)	)	PUNCT
ejpam-6466	226	25	:	:	PUNCT
ejpam-6466	227	1	v	v	X
ejpam-6466	227	2	(	(	PUNCT
ejpam-6466	227	3	.	.	PUNCT
ejpam-6466	227	4	,	,	PUNCT
ejpam-6466	227	5	0	0	NUM
ejpam-6466	227	6	,	,	PUNCT
ejpam-6466	227	7	0	0	NUM
ejpam-6466	227	8	)	)	PUNCT
ejpam-6466	227	9	and	and	CCONJ
ejpam-6466	227	10	𭟋	𭟋	ADJ
ejpam-6466	227	11	(	(	PUNCT
ejpam-6466	227	12	.	.	NUM
ejpam-6466	227	13	,	,	PUNCT
ejpam-6466	227	14	0	0	NUM
ejpam-6466	227	15	,	,	PUNCT
ejpam-6466	227	16	0	0	NUM
ejpam-6466	227	17	)	)	PUNCT
ejpam-6466	227	18	are	be	AUX
ejpam-6466	227	19	bounded	bound	VERB
ejpam-6466	227	20	,	,	PUNCT
ejpam-6466	227	21	i.e	i.e	PROPN
ejpam-6466	227	22	sup	sup	NOUN
ejpam-6466	227	23	τ∈[0,ℏ	τ∈[0,ℏ	NOUN
ejpam-6466	227	24	]	]	X
ejpam-6466	227	25	∥v(τ	∥v(τ	NOUN
ejpam-6466	227	26	,	,	PUNCT
ejpam-6466	227	27	0	0	NUM
ejpam-6466	227	28	,	,	PUNCT
ejpam-6466	227	29	0)∥	0)∥	NOUN
ejpam-6466	227	30	<	<	X
ejpam-6466	227	31	k	k	PROPN
ejpam-6466	227	32	,	,	PUNCT
ejpam-6466	227	33	sup	sup	NOUN
ejpam-6466	227	34	τ∈[0,ℏ	τ∈[0,ℏ	SYM
ejpam-6466	227	35	]	]	X
ejpam-6466	227	36	∥𭟋(τ	∥𭟋(τ	PROPN
ejpam-6466	227	37	,	,	PUNCT
ejpam-6466	227	38	0	0	NUM
ejpam-6466	227	39	,	,	PUNCT
ejpam-6466	227	40	0)∥	0)∥	NOUN
ejpam-6466	227	41	<	<	X
ejpam-6466	227	42	k.	k.	PROPN
ejpam-6466	228	1	the	the	DET
ejpam-6466	228	2	llc	llc	PROPN
ejpam-6466	228	3	(	(	PUNCT
ejpam-6466	228	4	a1	a1	PROPN
ejpam-6466	228	5	)	)	PUNCT
ejpam-6466	228	6	is	be	AUX
ejpam-6466	228	7	substituted	substitute	VERB
ejpam-6466	228	8	with	with	ADP
ejpam-6466	228	9	the	the	DET
ejpam-6466	228	10	following	follow	VERB
ejpam-6466	228	11	glc	glc	PROPN
ejpam-6466	228	12	in	in	ADP
ejpam-6466	228	13	order	order	NOUN
ejpam-6466	228	14	to	to	PART
ejpam-6466	228	15	examine	examine	VERB
ejpam-6466	228	16	the	the	DET
ejpam-6466	228	17	con	con	NOUN
ejpam-6466	228	18	-	-	PUNCT
ejpam-6466	228	19	d	d	NOUN
ejpam-6466	228	20	on	on	ADP
ejpam-6466	228	21	the	the	DET
ejpam-6466	228	22	initial	initial	ADJ
ejpam-6466	228	23	value	value	NOUN
ejpam-6466	228	24	,	,	PUNCT
ejpam-6466	228	25	the	the	DET
ejpam-6466	228	26	fractional	fractional	ADJ
ejpam-6466	228	27	order	order	NOUN
ejpam-6466	228	28	ξ	ξ	NOUN
ejpam-6466	228	29	,	,	PUNCT
ejpam-6466	228	30	and	and	CCONJ
ejpam-6466	228	31	the	the	DET
ejpam-6466	228	32	regularity	regularity	NOUN
ejpam-6466	228	33	of	of	ADP
ejpam-6466	228	34	the	the	DET
ejpam-6466	228	35	results	result	NOUN
ejpam-6466	228	36	of	of	ADP
ejpam-6466	228	37	df	df	NOUN
ejpam-6466	228	38	-	-	PUNCT
ejpam-6466	228	39	sdes	sde	NOUN
ejpam-6466	228	40	:	:	PUNCT
ejpam-6466	228	41	(	(	PUNCT
ejpam-6466	228	42	iii	iii	X
ejpam-6466	228	43	)	)	PUNCT
ejpam-6466	228	44	(	(	PUNCT
ejpam-6466	228	45	a3	a3	PROPN
ejpam-6466	228	46	)	)	PUNCT
ejpam-6466	228	47	:	:	PUNCT
ejpam-6466	229	1	∀y1	∀y1	PROPN
ejpam-6466	229	2	,	,	PUNCT
ejpam-6466	229	3	y2	y2	PROPN
ejpam-6466	229	4	,	,	PUNCT
ejpam-6466	229	5	z1	z1	PROPN
ejpam-6466	229	6	,	,	PUNCT
ejpam-6466	229	7	z2	z2	PROPN
ejpam-6466	229	8	∈	∈	PROPN
ejpam-6466	229	9	rr	rr	NOUN
ejpam-6466	229	10	there	there	PRON
ejpam-6466	229	11	exists	exist	VERB
ejpam-6466	229	12	l	l	NOUN
ejpam-6466	229	13	>	>	X
ejpam-6466	229	14	0	0	NUM
ejpam-6466	230	1	such	such	ADJ
ejpam-6466	230	2	that	that	DET
ejpam-6466	230	3	∥v(τ	∥v(τ	NOUN
ejpam-6466	230	4	,	,	PUNCT
ejpam-6466	230	5	y1	y1	PROPN
ejpam-6466	230	6	,	,	PUNCT
ejpam-6466	230	7	y2)−v(τ	y2)−v(τ	PROPN
ejpam-6466	230	8	,	,	PUNCT
ejpam-6466	230	9	z1	z1	PROPN
ejpam-6466	230	10	,	,	PUNCT
ejpam-6466	230	11	z2)∥2	z2)∥2	ADJ
ejpam-6466	230	12	≤	≤	NUM
ejpam-6466	230	13	l2	l2	NOUN
ejpam-6466	230	14	(	(	PUNCT
ejpam-6466	230	15	∥y1	∥y1	NOUN
ejpam-6466	230	16	−	−	PROPN
ejpam-6466	230	17	z1∥2	z1∥2	PROPN
ejpam-6466	230	18	+	+	CCONJ
ejpam-6466	230	19	∥y2	∥y2	X
ejpam-6466	231	1	−	−	PROPN
ejpam-6466	231	2	z2∥2	z2∥2	PROPN
ejpam-6466	231	3	)	)	PUNCT
ejpam-6466	231	4	,	,	PUNCT
ejpam-6466	231	5	∥𭟋(τ	∥𭟋(τ	VERB
ejpam-6466	231	6	,	,	PUNCT
ejpam-6466	231	7	y1	y1	NOUN
ejpam-6466	231	8	,	,	PUNCT
ejpam-6466	231	9	y2)−𭟋(τ	y2)−𭟋(τ	NOUN
ejpam-6466	231	10	,	,	PUNCT
ejpam-6466	231	11	z1	z1	PROPN
ejpam-6466	231	12	,	,	PUNCT
ejpam-6466	231	13	z2)∥2	z2)∥2	ADJ
ejpam-6466	231	14	≤	≤	NUM
ejpam-6466	231	15	l2	l2	NOUN
ejpam-6466	231	16	(	(	PUNCT
ejpam-6466	231	17	∥y1	∥y1	NOUN
ejpam-6466	231	18	−	−	PROPN
ejpam-6466	231	19	z1∥2	z1∥2	PROPN
ejpam-6466	231	20	+	+	CCONJ
ejpam-6466	231	21	∥y2	∥y2	X
ejpam-6466	232	1	−	−	PROPN
ejpam-6466	232	2	z2∥2	z2∥2	PROPN
ejpam-6466	232	3	)	)	PUNCT
ejpam-6466	232	4	.	.	PUNCT
ejpam-6466	233	1	in	in	ADP
ejpam-6466	233	2	the	the	DET
ejpam-6466	233	3	next	next	ADJ
ejpam-6466	233	4	section	section	NOUN
ejpam-6466	233	5	,	,	PUNCT
ejpam-6466	233	6	we	we	PRON
ejpam-6466	233	7	will	will	AUX
ejpam-6466	233	8	prove	prove	VERB
ejpam-6466	233	9	the	the	DET
ejpam-6466	233	10	well	well	NOUN
ejpam-6466	233	11	-	-	PUNCT
ejpam-6466	233	12	posedness	posedness	NOUN
ejpam-6466	233	13	,	,	PUNCT
ejpam-6466	233	14	regularity	regularity	NOUN
ejpam-6466	233	15	,	,	PUNCT
ejpam-6466	233	16	and	and	CCONJ
ejpam-6466	233	17	uh	uh	INTJ
ejpam-6466	233	18	stability	stability	NOUN
ejpam-6466	233	19	of	of	ADP
ejpam-6466	233	20	solutions	solution	NOUN
ejpam-6466	233	21	to	to	ADP
ejpam-6466	233	22	df	df	NOUN
ejpam-6466	233	23	-	-	PUNCT
ejpam-6466	233	24	sdes	sde	NOUN
ejpam-6466	233	25	.	.	PUNCT
ejpam-6466	234	1	3	3	X
ejpam-6466	234	2	.	.	X
ejpam-6466	234	3	the	the	DET
ejpam-6466	234	4	main	main	ADJ
ejpam-6466	234	5	results	result	NOUN
ejpam-6466	234	6	in	in	ADP
ejpam-6466	234	7	this	this	DET
ejpam-6466	234	8	section	section	NOUN
ejpam-6466	234	9	,	,	PUNCT
ejpam-6466	234	10	we	we	PRON
ejpam-6466	234	11	established	establish	VERB
ejpam-6466	234	12	the	the	DET
ejpam-6466	234	13	eu	eu	PROPN
ejpam-6466	234	14	,	,	PUNCT
ejpam-6466	234	15	con	con	NOUN
ejpam-6466	234	16	-	-	PUNCT
ejpam-6466	234	17	d	d	PROPN
ejpam-6466	234	18	,	,	PUNCT
ejpam-6466	234	19	and	and	CCONJ
ejpam-6466	234	20	regularity	regularity	NOUN
ejpam-6466	234	21	of	of	ADP
ejpam-6466	234	22	the	the	DET
ejpam-6466	234	23	solutions	solution	NOUN
ejpam-6466	234	24	to	to	ADP
ejpam-6466	234	25	df	df	NOUN
ejpam-6466	234	26	-	-	PUNCT
ejpam-6466	234	27	sdes	sde	NOUN
ejpam-6466	234	28	.	.	PUNCT
ejpam-6466	235	1	we	we	PRON
ejpam-6466	235	2	utilized	utilize	VERB
ejpam-6466	235	3	the	the	DET
ejpam-6466	235	4	concept	concept	NOUN
ejpam-6466	235	5	introduced	introduce	VERB
ejpam-6466	235	6	in	in	ADP
ejpam-6466	235	7	[	[	X
ejpam-6466	235	8	34	34	NUM
ejpam-6466	235	9	]	]	PUNCT
ejpam-6466	235	10	to	to	PART
ejpam-6466	235	11	demonstrate	demonstrate	VERB
ejpam-6466	235	12	the	the	DET
ejpam-6466	235	13	eu	eu	PROPN
ejpam-6466	235	14	.	.	PROPN
ejpam-6466	235	15	specifically	specifically	ADV
ejpam-6466	235	16	,	,	PUNCT
ejpam-6466	235	17	the	the	DET
ejpam-6466	235	18	process	process	NOUN
ejpam-6466	235	19	to	to	PART
ejpam-6466	235	20	prove	prove	VERB
ejpam-6466	235	21	eu	eu	PROPN
ejpam-6466	235	22	consists	consist	VERB
ejpam-6466	235	23	of	of	ADP
ejpam-6466	235	24	two	two	NUM
ejpam-6466	235	25	steps	step	NOUN
ejpam-6466	235	26	:	:	PUNCT
ejpam-6466	235	27	initially	initially	ADV
ejpam-6466	235	28	,	,	PUNCT
ejpam-6466	235	29	we	we	PRON
ejpam-6466	235	30	establish	establish	VERB
ejpam-6466	235	31	the	the	DET
ejpam-6466	235	32	eu	eu	PROPN
ejpam-6466	235	33	through	through	ADP
ejpam-6466	235	34	the	the	DET
ejpam-6466	235	35	glc	glc	NOUN
ejpam-6466	235	36	of	of	ADP
ejpam-6466	235	37	coefficients	coefficient	NOUN
ejpam-6466	235	38	.	.	PUNCT
ejpam-6466	236	1	in	in	ADP
ejpam-6466	236	2	the	the	DET
ejpam-6466	236	3	subsequent	subsequent	ADJ
ejpam-6466	236	4	phase	phase	NOUN
ejpam-6466	236	5	,	,	PUNCT
ejpam-6466	236	6	we	we	PRON
ejpam-6466	236	7	illustrate	illustrate	VERB
ejpam-6466	236	8	the	the	DET
ejpam-6466	236	9	eu	eu	PROPN
ejpam-6466	236	10	according	accord	VERB
ejpam-6466	236	11	to	to	ADP
ejpam-6466	236	12	the	the	DET
ejpam-6466	236	13	llc	llc	NOUN
ejpam-6466	236	14	of	of	ADP
ejpam-6466	236	15	coefficients	coefficient	NOUN
ejpam-6466	236	16	by	by	ADP
ejpam-6466	236	17	employing	employ	VERB
ejpam-6466	236	18	a	a	DET
ejpam-6466	236	19	truncation	truncation	NOUN
ejpam-6466	236	20	method	method	NOUN
ejpam-6466	236	21	.	.	PUNCT
ejpam-6466	237	1	to	to	PART
ejpam-6466	237	2	establish	establish	VERB
ejpam-6466	237	3	the	the	DET
ejpam-6466	237	4	con	con	NOUN
ejpam-6466	237	5	-	-	PUNCT
ejpam-6466	237	6	d	d	PROPN
ejpam-6466	237	7	of	of	ADP
ejpam-6466	237	8	solutions	solution	NOUN
ejpam-6466	237	9	,	,	PUNCT
ejpam-6466	237	10	we	we	PRON
ejpam-6466	237	11	demonstrate	demonstrate	VERB
ejpam-6466	237	12	that	that	SCONJ
ejpam-6466	237	13	solutions	solution	NOUN
ejpam-6466	237	14	are	be	AUX
ejpam-6466	237	15	contingent	contingent	ADJ
ejpam-6466	237	16	upon	upon	SCONJ
ejpam-6466	237	17	the	the	DET
ejpam-6466	237	18	initial	initial	ADJ
ejpam-6466	237	19	value	value	NOUN
ejpam-6466	237	20	of	of	ADP
ejpam-6466	237	21	the	the	DET
ejpam-6466	237	22	fractional	fractional	ADJ
ejpam-6466	237	23	order	order	NOUN
ejpam-6466	237	24	ξ	ξ	PROPN
ejpam-6466	237	25	.	.	PROPN
ejpam-6466	237	26	3.1	3.1	NUM
ejpam-6466	237	27	.	.	PUNCT
ejpam-6466	238	1	existence	existence	NOUN
ejpam-6466	238	2	,	,	PUNCT
ejpam-6466	238	3	uniqueness	uniqueness	NOUN
ejpam-6466	238	4	,	,	PUNCT
ejpam-6466	238	5	continuous	continuous	ADJ
ejpam-6466	238	6	dependence	dependence	NOUN
ejpam-6466	238	7	,	,	PUNCT
ejpam-6466	238	8	and	and	CCONJ
ejpam-6466	238	9	regularity	regularity	NOUN
ejpam-6466	238	10	result	result	NOUN
ejpam-6466	238	11	first	first	ADV
ejpam-6466	238	12	,	,	PUNCT
ejpam-6466	238	13	we	we	PRON
ejpam-6466	238	14	must	must	AUX
ejpam-6466	238	15	construct	construct	VERB
ejpam-6466	238	16	a	a	DET
ejpam-6466	238	17	sufficient	sufficient	ADJ
ejpam-6466	238	18	banach	banach	NOUN
ejpam-6466	238	19	space	space	NOUN
ejpam-6466	238	20	covering	cover	VERB
ejpam-6466	238	21	the	the	DET
ejpam-6466	238	22	solution	solution	NOUN
ejpam-6466	238	23	eq	eq	ADP
ejpam-6466	238	24	.	.	PUNCT
ejpam-6466	239	1	(	(	PUNCT
ejpam-6466	239	2	4	4	NUM
ejpam-6466	239	3	)	)	PUNCT
ejpam-6466	239	4	in	in	ADP
ejpam-6466	239	5	order	order	NOUN
ejpam-6466	239	6	to	to	PART
ejpam-6466	239	7	demonstrate	demonstrate	VERB
ejpam-6466	239	8	the	the	DET
ejpam-6466	239	9	subsequent	subsequent	ADJ
ejpam-6466	239	10	result	result	NOUN
ejpam-6466	239	11	.	.	PUNCT
ejpam-6466	240	1	assume	assume	VERB
ejpam-6466	240	2	h̃2(0	h̃2(0	PROPN
ejpam-6466	240	3	,	,	PUNCT
ejpam-6466	240	4	ℏ	ℏ	NOUN
ejpam-6466	240	5	)	)	PUNCT
ejpam-6466	240	6	is	be	AUX
ejpam-6466	240	7	the	the	DET
ejpam-6466	240	8	space	space	NOUN
ejpam-6466	240	9	where	where	SCONJ
ejpam-6466	240	10	all	all	DET
ejpam-6466	240	11	processes	process	NOUN
ejpam-6466	240	12	exist	exist	VERB
ejpam-6466	240	13	x(τ	x(τ	PROPN
ejpam-6466	240	14	)	)	PUNCT
ejpam-6466	240	15	:	:	PUNCT
ejpam-6466	241	1	[	[	X
ejpam-6466	241	2	0	0	NUM
ejpam-6466	241	3	,	,	PUNCT
ejpam-6466	241	4	ℏ	ℏ	NOUN
ejpam-6466	241	5	]	]	PUNCT
ejpam-6466	241	6	→	→	SYM
ejpam-6466	241	7	l2(ω	l2(ω	PROPN
ejpam-6466	241	8	,	,	PUNCT
ejpam-6466	241	9	f	f	PROPN
ejpam-6466	241	10	,	,	PUNCT
ejpam-6466	241	11	p	p	NOUN
ejpam-6466	241	12	)	)	PUNCT
ejpam-6466	241	13	which	which	PRON
ejpam-6466	241	14	are	be	AUX
ejpam-6466	241	15	measurable	measurable	ADJ
ejpam-6466	241	16	fℏ−adapted	fℏ−adapte	VERB
ejpam-6466	241	17	,	,	PUNCT
ejpam-6466	241	18	with	with	ADP
ejpam-6466	241	19	fℏ	fℏ	NOUN
ejpam-6466	241	20	=	=	SYM
ejpam-6466	241	21	(	(	PUNCT
ejpam-6466	241	22	fτ	fτ	X
ejpam-6466	241	23	)	)	PUNCT
ejpam-6466	241	24	τ∈[0,ℏ	τ∈[0,ℏ	SYM
ejpam-6466	241	25	]	]	PUNCT
ejpam-6466	241	26	and	and	CCONJ
ejpam-6466	241	27	satisfy	satisfy	VERB
ejpam-6466	241	28	the	the	DET
ejpam-6466	241	29	following	following	NOUN
ejpam-6466	241	30	:	:	PUNCT
ejpam-6466	241	31	∥x(τ)∥h̃2	∥x(τ)∥h̃2	PROPN
ejpam-6466	241	32	=	=	PUNCT
ejpam-6466	241	33	sup	sup	X
ejpam-6466	241	34	τ∈[0,ℏ	τ∈[0,ℏ	PROPN
ejpam-6466	241	35	]	]	X
ejpam-6466	241	36	∥x(τ)∥ms	∥x(τ)∥ms	PROPN
ejpam-6466	241	37	<	<	X
ejpam-6466	241	38	∞.	∞.	PROPN
ejpam-6466	241	39	(	(	PUNCT
ejpam-6466	241	40	7	7	NUM
ejpam-6466	241	41	)	)	PUNCT
ejpam-6466	241	42	(	(	PUNCT
ejpam-6466	241	43	h̃2([0	h̃2([0	NOUN
ejpam-6466	241	44	,	,	PUNCT
ejpam-6466	241	45	ℏ	ℏ	NOUN
ejpam-6466	241	46	]	]	X
ejpam-6466	241	47	)	)	PUNCT
ejpam-6466	241	48	,	,	PUNCT
ejpam-6466	241	49	∥	∥	X
ejpam-6466	241	50	·	·	PUNCT
ejpam-6466	241	51	∥h̃2	∥h̃2	PROPN
ejpam-6466	241	52	)	)	PUNCT
ejpam-6466	241	53	is	be	AUX
ejpam-6466	241	54	surely	surely	ADV
ejpam-6466	241	55	a	a	DET
ejpam-6466	241	56	banach	banach	NOUN
ejpam-6466	241	57	space	space	NOUN
ejpam-6466	241	58	.	.	PUNCT
ejpam-6466	242	1	we	we	PRON
ejpam-6466	242	2	construct	construct	VERB
ejpam-6466	242	3	an	an	DET
ejpam-6466	242	4	operator	operator	NOUN
ejpam-6466	242	5	gφ	gφ	NOUN
ejpam-6466	242	6	:	:	PUNCT
ejpam-6466	242	7	h̃2(0	h̃2(0	PROPN
ejpam-6466	242	8	,	,	PUNCT
ejpam-6466	242	9	ℏ	ℏ	NOUN
ejpam-6466	242	10	)	)	PUNCT
ejpam-6466	242	11	→	→	SYM
ejpam-6466	242	12	h̃2(0	h̃2(0	ADJ
ejpam-6466	242	13	,	,	PUNCT
ejpam-6466	242	14	ℏ	ℏ	PROPN
ejpam-6466	242	15	)	)	PUNCT
ejpam-6466	242	16	by	by	ADP
ejpam-6466	242	17	gφ(x(0	gφ(x(0	PROPN
ejpam-6466	242	18	)	)	PUNCT
ejpam-6466	242	19	)	)	PUNCT
ejpam-6466	243	1	=	=	PUNCT
ejpam-6466	243	2	φ	φ	PROPN
ejpam-6466	243	3	for	for	ADP
ejpam-6466	243	4	any	any	DET
ejpam-6466	243	5	φ	φ	PROPN
ejpam-6466	243	6	∈	∈	PROPN
ejpam-6466	243	7	c̃([−m	c̃([−m	NOUN
ejpam-6466	243	8	,	,	PUNCT
ejpam-6466	243	9	0],rr	0],rr	PROPN
ejpam-6466	243	10	)	)	PUNCT
ejpam-6466	243	11	and	and	CCONJ
ejpam-6466	243	12	∀τ	∀τ	NOUN
ejpam-6466	243	13	∈	∈	PROPN
ejpam-6466	244	1	[	[	X
ejpam-6466	244	2	0	0	NUM
ejpam-6466	244	3	,	,	PUNCT
ejpam-6466	244	4	ℏ	ℏ	PROPN
ejpam-6466	244	5	]	]	PUNCT
ejpam-6466	244	6	,	,	PUNCT
ejpam-6466	244	7	the	the	DET
ejpam-6466	244	8	subsequent	subsequent	ADJ
ejpam-6466	244	9	equality	equality	NOUN
ejpam-6466	244	10	is	be	AUX
ejpam-6466	244	11	valid	valid	ADJ
ejpam-6466	244	12	.	.	PUNCT
ejpam-6466	245	1	gφ(x(τ	gφ(x(τ	VERB
ejpam-6466	245	2	)	)	PUNCT
ejpam-6466	245	3	)	)	PUNCT
ejpam-6466	246	1	=	=	PUNCT
ejpam-6466	247	1	φ	φ	PROPN
ejpam-6466	247	2	+	+	CCONJ
ejpam-6466	247	3	∫	∫	PROPN
ejpam-6466	247	4	τ	τ	PROPN
ejpam-6466	247	5	0	0	NUM
ejpam-6466	247	6	sξ−1v	sξ−1v	PROPN
ejpam-6466	247	7	(	(	PUNCT
ejpam-6466	247	8	s	s	PROPN
ejpam-6466	247	9	,	,	PUNCT
ejpam-6466	247	10	x(s	x(s	PROPN
ejpam-6466	247	11	)	)	PUNCT
ejpam-6466	247	12	,	,	PUNCT
ejpam-6466	247	13	x(s−m	x(s−m	NUM
ejpam-6466	247	14	)	)	PUNCT
ejpam-6466	247	15	)	)	PUNCT
ejpam-6466	248	1	ds	ds	PROPN
ejpam-6466	249	1	+	+	CCONJ
ejpam-6466	249	2	∫	∫	PROPN
ejpam-6466	249	3	τ	τ	X
ejpam-6466	249	4	0	0	NUM
ejpam-6466	249	5	sξ−1𭟋	sξ−1𭟋	X
ejpam-6466	249	6	(	(	PUNCT
ejpam-6466	249	7	s	s	PROPN
ejpam-6466	249	8	,	,	PUNCT
ejpam-6466	249	9	x(s	x(s	PROPN
ejpam-6466	249	10	)	)	PUNCT
ejpam-6466	249	11	,	,	PUNCT
ejpam-6466	249	12	x(s−m	x(s−m	NUM
ejpam-6466	249	13	)	)	PUNCT
ejpam-6466	249	14	)	)	PUNCT
ejpam-6466	250	1	dws	dws	PROPN
ejpam-6466	250	2	.	.	PUNCT
ejpam-6466	251	1	(	(	PUNCT
ejpam-6466	251	2	8)	8)	NUM
ejpam-6466	251	3	the	the	DET
ejpam-6466	251	4	subsequent	subsequent	ADJ
ejpam-6466	251	5	lemma	lemma	PROPN
ejpam-6466	251	6	verifies	verifie	NOUN
ejpam-6466	251	7	that	that	SCONJ
ejpam-6466	251	8	the	the	DET
ejpam-6466	251	9	operator	operator	NOUN
ejpam-6466	251	10	is	be	AUX
ejpam-6466	251	11	well	well	ADV
ejpam-6466	251	12	-	-	PUNCT
ejpam-6466	251	13	defined	define	VERB
ejpam-6466	251	14	.	.	PUNCT
ejpam-6466	252	1	the	the	DET
ejpam-6466	252	2	fundamental	fundamental	ADJ
ejpam-6466	252	3	inequality	inequality	NOUN
ejpam-6466	252	4	provided	provide	VERB
ejpam-6466	252	5	below	below	ADP
ejpam-6466	252	6	supports	support	VERB
ejpam-6466	252	7	the	the	DET
ejpam-6466	252	8	proof	proof	NOUN
ejpam-6466	252	9	of	of	ADP
ejpam-6466	252	10	this	this	DET
ejpam-6466	252	11	statement	statement	NOUN
ejpam-6466	252	12	and	and	CCONJ
ejpam-6466	252	13	other	other	ADJ
ejpam-6466	252	14	later	later	ADJ
ejpam-6466	252	15	results.∥∥x1	results.∥∥x1	NOUN
ejpam-6466	253	1	+	+	CCONJ
ejpam-6466	253	2	x2	x2	PROPN
ejpam-6466	254	1	+	+	CCONJ
ejpam-6466	254	2	·	·	PUNCT
ejpam-6466	254	3	·	·	PUNCT
ejpam-6466	254	4	·	·	PUNCT
ejpam-6466	254	5	+	+	PUNCT
ejpam-6466	255	1	xυ∥2	xυ∥2	ADJ
ejpam-6466	255	2	≤	≤	NUM
ejpam-6466	255	3	υ	υ	NOUN
ejpam-6466	256	1	(	(	PUNCT
ejpam-6466	256	2	∥x1∥2	∥x1∥2	PROPN
ejpam-6466	256	3	+	+	CCONJ
ejpam-6466	256	4	∥x2∥2	∥x2∥2	NUM
ejpam-6466	256	5	+	+	X
ejpam-6466	256	6	·	·	PUNCT
ejpam-6466	256	7	·	·	PUNCT
ejpam-6466	256	8	·	·	PUNCT
ejpam-6466	256	9	+	+	NUM
ejpam-6466	256	10	∥xυ∥2	∥xυ∥2	NOUN
ejpam-6466	256	11	)	)	PUNCT
ejpam-6466	256	12	,	,	PUNCT
ejpam-6466	256	13	∀x1	∀x1	PROPN
ejpam-6466	256	14	,	,	PUNCT
ejpam-6466	256	15	x2	x2	PROPN
ejpam-6466	256	16	,	,	PUNCT
ejpam-6466	256	17	·	·	PUNCT
ejpam-6466	256	18	·	·	PUNCT
ejpam-6466	256	19	·	·	PUNCT
ejpam-6466	256	20	,	,	PUNCT
ejpam-6466	256	21	xυ	xυ	NUM
ejpam-6466	256	22	∈	∈	PROPN
ejpam-6466	256	23	rr	rr	NOUN
ejpam-6466	256	24	.	.	PUNCT
ejpam-6466	257	1	(	(	PUNCT
ejpam-6466	257	2	9	9	X
ejpam-6466	257	3	)	)	PUNCT
ejpam-6466	257	4	m.	m.	NOUN
ejpam-6466	257	5	i.	i.	PROPN
ejpam-6466	257	6	liaqat	liaqat	PROPN
ejpam-6466	257	7	et	et	PROPN
ejpam-6466	257	8	al	al	PROPN
ejpam-6466	257	9	.	.	PUNCT
ejpam-6466	257	10	/	/	SYM
ejpam-6466	257	11	eur	eur	PROPN
ejpam-6466	257	12	.	.	PUNCT
ejpam-6466	258	1	j.	j.	PROPN
ejpam-6466	258	2	pure	pure	PROPN
ejpam-6466	258	3	appl	appl	PROPN
ejpam-6466	258	4	.	.	PROPN
ejpam-6466	258	5	math	math	PROPN
ejpam-6466	258	6	,	,	PUNCT
ejpam-6466	258	7	18	18	NUM
ejpam-6466	258	8	(	(	PUNCT
ejpam-6466	258	9	4	4	NUM
ejpam-6466	258	10	)	)	PUNCT
ejpam-6466	258	11	(	(	PUNCT
ejpam-6466	258	12	2025	2025	NUM
ejpam-6466	258	13	)	)	PUNCT
ejpam-6466	258	14	,	,	PUNCT
ejpam-6466	258	15	6466	6466	NUM
ejpam-6466	258	16	11	11	NUM
ejpam-6466	258	17	of	of	ADP
ejpam-6466	258	18	28	28	NUM
ejpam-6466	258	19	lemma	lemma	PROPN
ejpam-6466	258	20	1	1	NUM
ejpam-6466	258	21	.	.	PUNCT
ejpam-6466	258	22	assume	assume	VERB
ejpam-6466	258	23	that	that	SCONJ
ejpam-6466	258	24	(	(	PUNCT
ejpam-6466	258	25	a1	a1	NOUN
ejpam-6466	258	26	)	)	PUNCT
ejpam-6466	258	27	and	and	CCONJ
ejpam-6466	258	28	(	(	PUNCT
ejpam-6466	258	29	a2	a2	PROPN
ejpam-6466	258	30	)	)	PUNCT
ejpam-6466	258	31	are	be	AUX
ejpam-6466	258	32	valid	valid	ADJ
ejpam-6466	258	33	.	.	PUNCT
ejpam-6466	259	1	the	the	DET
ejpam-6466	259	2	operator	operator	NOUN
ejpam-6466	259	3	gφ	gφ	NOUN
ejpam-6466	259	4	is	be	AUX
ejpam-6466	259	5	then	then	ADV
ejpam-6466	259	6	well	well	INTJ
ejpam-6466	259	7	defined	define	VERB
ejpam-6466	259	8	for	for	ADP
ejpam-6466	259	9	any	any	DET
ejpam-6466	259	10	φ	φ	PROPN
ejpam-6466	259	11	∈	∈	PROPN
ejpam-6466	259	12	c̃([−m	c̃([−m	NOUN
ejpam-6466	259	13	,	,	PUNCT
ejpam-6466	259	14	0],rr	0],rr	PROPN
ejpam-6466	259	15	)	)	PUNCT
ejpam-6466	259	16	)	)	PUNCT
ejpam-6466	259	17	.	.	PUNCT
ejpam-6466	260	1	proof	proof	NOUN
ejpam-6466	260	2	.	.	PUNCT
ejpam-6466	261	1	assume	assume	VERB
ejpam-6466	261	2	that	that	SCONJ
ejpam-6466	261	3	x(τ	x(τ	PROPN
ejpam-6466	261	4	)	)	PUNCT
ejpam-6466	261	5	∈	∈	PROPN
ejpam-6466	261	6	h̃2[0	h̃2[0	NOUN
ejpam-6466	261	7	,	,	PUNCT
ejpam-6466	261	8	ℏ	ℏ	X
ejpam-6466	261	9	]	]	X
ejpam-6466	261	10	,	,	PUNCT
ejpam-6466	261	11	where	where	SCONJ
ejpam-6466	261	12	x(τ	x(τ	PROPN
ejpam-6466	261	13	)	)	PUNCT
ejpam-6466	261	14	is	be	AUX
ejpam-6466	261	15	considered	consider	VERB
ejpam-6466	261	16	to	to	PART
ejpam-6466	261	17	be	be	AUX
ejpam-6466	261	18	arbitrary	arbitrary	ADJ
ejpam-6466	261	19	.	.	PUNCT
ejpam-6466	262	1	based	base	VERB
ejpam-6466	262	2	on	on	ADP
ejpam-6466	262	3	the	the	DET
ejpam-6466	262	4	formulation	formulation	NOUN
ejpam-6466	262	5	of	of	ADP
ejpam-6466	262	6	gφ(x(τ	gφ(x(τ	NOUN
ejpam-6466	262	7	)	)	PUNCT
ejpam-6466	262	8	)	)	PUNCT
ejpam-6466	262	9	given	give	VERB
ejpam-6466	262	10	in	in	ADP
ejpam-6466	262	11	eq	eq	ADP
ejpam-6466	262	12	.	.	PUNCT
ejpam-6466	263	1	(	(	PUNCT
ejpam-6466	263	2	8)	8)	NUM
ejpam-6466	263	3	and	and	CCONJ
ejpam-6466	263	4	the	the	DET
ejpam-6466	263	5	inequality	inequality	NOUN
ejpam-6466	263	6	in	in	ADP
ejpam-6466	263	7	eq	eq	ADP
ejpam-6466	263	8	.	.	PUNCT
ejpam-6466	264	1	(	(	PUNCT
ejpam-6466	264	2	9	9	NUM
ejpam-6466	264	3	)	)	PUNCT
ejpam-6466	264	4	,	,	PUNCT
ejpam-6466	264	5	we	we	PRON
ejpam-6466	264	6	derive	derive	VERB
ejpam-6466	264	7	the	the	DET
ejpam-6466	264	8	following	following	NOUN
ejpam-6466	264	9	.	.	PUNCT
ejpam-6466	265	1	e	e	X
ejpam-6466	265	2	∥∥gφ(x(τ	∥∥gφ(x(τ	VERB
ejpam-6466	265	3	)	)	PUNCT
ejpam-6466	265	4	)	)	PUNCT
ejpam-6466	265	5	∥∥2	∥∥2	PROPN
ejpam-6466	265	6	≤3e	≤3e	NOUN
ejpam-6466	265	7	∥∥φ∥∥2	∥∥φ∥∥2	PROPN
ejpam-6466	266	1	+	+	CCONJ
ejpam-6466	266	2	3e	3e	PROPN
ejpam-6466	266	3	∥∥∥∥∫	∥∥∥∥∫	PROPN
ejpam-6466	266	4	τ	τ	PROPN
ejpam-6466	266	5	0	0	NUM
ejpam-6466	266	6	sξ−1v	sξ−1v	NOUN
ejpam-6466	266	7	(	(	PUNCT
ejpam-6466	266	8	s	s	PROPN
ejpam-6466	266	9	,	,	PUNCT
ejpam-6466	266	10	x(s	x(s	PROPN
ejpam-6466	266	11	)	)	PUNCT
ejpam-6466	266	12	,	,	PUNCT
ejpam-6466	266	13	x(s−m	x(s−m	NUM
ejpam-6466	266	14	)	)	PUNCT
ejpam-6466	266	15	)	)	PUNCT
ejpam-6466	267	1	ds	ds	ADP
ejpam-6466	267	2	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-6466	267	3	+3e	+3e	NUM
ejpam-6466	267	4	∥∥∥∥∫	∥∥∥∥∫	NOUN
ejpam-6466	267	5	τ	τ	X
ejpam-6466	267	6	0	0	NUM
ejpam-6466	267	7	sξ−1𭟋	sξ−1𭟋	X
ejpam-6466	267	8	(	(	PUNCT
ejpam-6466	267	9	s	s	PROPN
ejpam-6466	267	10	,	,	PUNCT
ejpam-6466	267	11	x(s	x(s	PROPN
ejpam-6466	267	12	)	)	PUNCT
ejpam-6466	267	13	,	,	PUNCT
ejpam-6466	267	14	x(s−m	x(s−m	NUM
ejpam-6466	267	15	)	)	PUNCT
ejpam-6466	267	16	)	)	PUNCT
ejpam-6466	268	1	dws	dws	PROPN
ejpam-6466	268	2	∥∥∥∥2	∥∥∥∥2	PROPN
ejpam-6466	268	3	.	.	PUNCT
ejpam-6466	269	1	(	(	PUNCT
ejpam-6466	269	2	10	10	NUM
ejpam-6466	269	3	)	)	PUNCT
ejpam-6466	269	4	now	now	ADV
ejpam-6466	269	5	we	we	PRON
ejpam-6466	269	6	will	will	AUX
ejpam-6466	269	7	simplify	simplify	VERB
ejpam-6466	269	8	eq	eq	ADP
ejpam-6466	269	9	.	.	PUNCT
ejpam-6466	270	1	(	(	PUNCT
ejpam-6466	270	2	10	10	NUM
ejpam-6466	270	3	)	)	PUNCT
ejpam-6466	270	4	in	in	ADP
ejpam-6466	270	5	two	two	NUM
ejpam-6466	270	6	parts	part	NOUN
ejpam-6466	270	7	.	.	PUNCT
ejpam-6466	271	1	the	the	DET
ejpam-6466	271	2	höld	höld	PROPN
ejpam-6466	271	3	-	-	PUNCT
ejpam-6466	271	4	i	i	PRON
ejpam-6466	271	5	gives	give	VERB
ejpam-6466	271	6	us	we	PRON
ejpam-6466	271	7	the	the	DET
ejpam-6466	271	8	result	result	NOUN
ejpam-6466	271	9	that	that	SCONJ
ejpam-6466	271	10	e	e	X
ejpam-6466	272	1	[	[	X
ejpam-6466	272	2	∥∥∥∥	∥∥∥∥	PROPN
ejpam-6466	272	3	∫	∫	PROPN
ejpam-6466	272	4	τ	τ	PROPN
ejpam-6466	272	5	0	0	NUM
ejpam-6466	272	6	sξ−1v	sξ−1v	PROPN
ejpam-6466	272	7	(	(	PUNCT
ejpam-6466	272	8	s	s	PROPN
ejpam-6466	272	9	,	,	PUNCT
ejpam-6466	272	10	x(s	x(s	PROPN
ejpam-6466	272	11	)	)	PUNCT
ejpam-6466	272	12	,	,	PUNCT
ejpam-6466	272	13	x(s−m	x(s−m	NUM
ejpam-6466	272	14	)	)	PUNCT
ejpam-6466	272	15	)	)	PUNCT
ejpam-6466	272	16	ds	ds	ADP
ejpam-6466	272	17	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-6466	272	18	]	]	X
ejpam-6466	272	19	≤	≤	NUM
ejpam-6466	272	20	(	(	PUNCT
ejpam-6466	272	21	(	(	PUNCT
ejpam-6466	272	22	∫	∫	PROPN
ejpam-6466	272	23	τ	τ	PROPN
ejpam-6466	272	24	0	0	NUM
ejpam-6466	272	25	s(2ξ−2)ds	s(2ξ−2)ds	NOUN
ejpam-6466	272	26	)	)	PUNCT
ejpam-6466	273	1	e	e	X
ejpam-6466	273	2	[	[	PUNCT
ejpam-6466	273	3	∫	∫	PROPN
ejpam-6466	273	4	τ	τ	PROPN
ejpam-6466	273	5	0	0	PROPN
ejpam-6466	273	6	∥∥v(s	∥∥v(s	PROPN
ejpam-6466	273	7	,	,	PUNCT
ejpam-6466	273	8	x(s	x(s	PROPN
ejpam-6466	273	9	)	)	PUNCT
ejpam-6466	273	10	,	,	PUNCT
ejpam-6466	273	11	x(s−m	x(s−m	NUM
ejpam-6466	273	12	)	)	PUNCT
ejpam-6466	273	13	)	)	PUNCT
ejpam-6466	273	14	∥∥2ds	∥∥2ds	NUM
ejpam-6466	273	15	]	]	PUNCT
ejpam-6466	273	16	)	)	PUNCT
ejpam-6466	273	17	≤	≤	NUM
ejpam-6466	274	1	τ	τ	X
ejpam-6466	274	2	(	(	PUNCT
ejpam-6466	274	3	2ξ−1	2ξ−1	NUM
ejpam-6466	274	4	)	)	PUNCT
ejpam-6466	274	5	2ξ	2ξ	NOUN
ejpam-6466	274	6	−	−	NOUN
ejpam-6466	274	7	1	1	NUM
ejpam-6466	274	8	e	e	X
ejpam-6466	274	9	[	[	PUNCT
ejpam-6466	274	10	∫	∫	PROPN
ejpam-6466	274	11	τ	τ	PROPN
ejpam-6466	274	12	0	0	NUM
ejpam-6466	274	13	∥∥(s	∥∥(s	PROPN
ejpam-6466	274	14	,	,	PUNCT
ejpam-6466	274	15	x(s	x(s	PROPN
ejpam-6466	274	16	)	)	PUNCT
ejpam-6466	274	17	,	,	PUNCT
ejpam-6466	274	18	x(s−m	x(s−m	NUM
ejpam-6466	274	19	)	)	PUNCT
ejpam-6466	274	20	)	)	PUNCT
ejpam-6466	275	1	∥∥2ds	∥∥2ds	NUM
ejpam-6466	275	2	]	]	PUNCT
ejpam-6466	276	1	≤	≤	X
ejpam-6466	276	2	ℏ(2ξ−1	ℏ(2ξ−1	X
ejpam-6466	276	3	)	)	PUNCT
ejpam-6466	276	4	2ξ	2ξ	NOUN
ejpam-6466	276	5	−	−	NOUN
ejpam-6466	276	6	1	1	NUM
ejpam-6466	276	7	e	e	X
ejpam-6466	276	8	∥∥(v(s	∥∥(v(s	PROPN
ejpam-6466	276	9	,	,	PUNCT
ejpam-6466	276	10	x(s	x(s	PROPN
ejpam-6466	276	11	)	)	PUNCT
ejpam-6466	276	12	,	,	PUNCT
ejpam-6466	276	13	x(s−m	x(s−m	NUM
ejpam-6466	276	14	)	)	PUNCT
ejpam-6466	276	15	)	)	PUNCT
ejpam-6466	276	16	∥∥2ℏ.	∥∥2ℏ.	PUNCT
ejpam-6466	276	17	(	(	PUNCT
ejpam-6466	276	18	11	11	NUM
ejpam-6466	276	19	)	)	PUNCT
ejpam-6466	276	20	because	because	SCONJ
ejpam-6466	276	21	of	of	ADP
ejpam-6466	276	22	(	(	PUNCT
ejpam-6466	276	23	a2	a2	PROPN
ejpam-6466	276	24	)	)	PUNCT
ejpam-6466	276	25	and	and	CCONJ
ejpam-6466	276	26	(	(	PUNCT
ejpam-6466	276	27	a3	a3	NOUN
ejpam-6466	276	28	)	)	PUNCT
ejpam-6466	276	29	,	,	PUNCT
ejpam-6466	276	30	we	we	PRON
ejpam-6466	276	31	acquire	acquire	VERB
ejpam-6466	276	32	the	the	DET
ejpam-6466	276	33	following:∥∥(v(s	following:∥∥(v(s	PROPN
ejpam-6466	276	34	,	,	PUNCT
ejpam-6466	276	35	x(s	x(s	PROPN
ejpam-6466	276	36	)	)	PUNCT
ejpam-6466	276	37	,	,	PUNCT
ejpam-6466	276	38	x(s−m	x(s−m	NUM
ejpam-6466	276	39	)	)	PUNCT
ejpam-6466	276	40	)	)	PUNCT
ejpam-6466	277	1	∥∥2	∥∥2	PROPN
ejpam-6466	278	1	≤	≤	NOUN
ejpam-6466	278	2	2l2	2l2	NUM
ejpam-6466	278	3	(	(	PUNCT
ejpam-6466	278	4	∥x(s)∥2	∥x(s)∥2	X
ejpam-6466	278	5	+	+	PUNCT
ejpam-6466	278	6	(	(	PUNCT
ejpam-6466	278	7	∥x(s−m)∥2	∥x(s−m)∥2	PROPN
ejpam-6466	278	8	)	)	PUNCT
ejpam-6466	278	9	+	+	CCONJ
ejpam-6466	278	10	2k2	2k2	NUM
ejpam-6466	278	11	.	.	PUNCT
ejpam-6466	279	1	(	(	PUNCT
ejpam-6466	279	2	12	12	NUM
ejpam-6466	279	3	)	)	PUNCT
ejpam-6466	279	4	consequently	consequently	ADV
ejpam-6466	279	5	,	,	PUNCT
ejpam-6466	279	6	we	we	PRON
ejpam-6466	279	7	employ	employ	VERB
ejpam-6466	279	8	eq	eq	ADP
ejpam-6466	279	9	.	.	PUNCT
ejpam-6466	280	1	(	(	PUNCT
ejpam-6466	280	2	12	12	NUM
ejpam-6466	280	3	)	)	PUNCT
ejpam-6466	280	4	in	in	ADP
ejpam-6466	280	5	eq	eq	ADP
ejpam-6466	280	6	.	.	PUNCT
ejpam-6466	281	1	(	(	PUNCT
ejpam-6466	281	2	11	11	NUM
ejpam-6466	281	3	)	)	PUNCT
ejpam-6466	281	4	to	to	PART
ejpam-6466	281	5	obtain	obtain	VERB
ejpam-6466	281	6	the	the	DET
ejpam-6466	281	7	following	following	NOUN
ejpam-6466	281	8	:	:	PUNCT
ejpam-6466	282	1	e	e	X
ejpam-6466	282	2	[	[	X
ejpam-6466	282	3	∥∥∥∥	∥∥∥∥	NUM
ejpam-6466	282	4	∫	∫	PROPN
ejpam-6466	282	5	τ	τ	PROPN
ejpam-6466	282	6	0	0	NUM
ejpam-6466	282	7	sξ−1v	sξ−1v	PROPN
ejpam-6466	282	8	(	(	PUNCT
ejpam-6466	282	9	s	s	PROPN
ejpam-6466	282	10	,	,	PUNCT
ejpam-6466	282	11	x(s),x(s−m	x(s),x(s−m	PROPN
ejpam-6466	282	12	)	)	PUNCT
ejpam-6466	282	13	)	)	PUNCT
ejpam-6466	282	14	ds	ds	ADP
ejpam-6466	282	15	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-6466	282	16	]	]	PUNCT
ejpam-6466	282	17	≤ℏ(2ξ−1	≤ℏ(2ξ−1	NOUN
ejpam-6466	282	18	)	)	PUNCT
ejpam-6466	282	19	2ξ	2ξ	NOUN
ejpam-6466	282	20	−	−	NOUN
ejpam-6466	282	21	1	1	NUM
ejpam-6466	282	22	e	e	X
ejpam-6466	282	23	[	[	PUNCT
ejpam-6466	282	24	2l2	2l2	NUM
ejpam-6466	282	25	(	(	PUNCT
ejpam-6466	282	26	∥x(s)∥2	∥x(s)∥2	X
ejpam-6466	282	27	+	+	PUNCT
ejpam-6466	282	28	(	(	PUNCT
ejpam-6466	282	29	∥x(s−m)∥2	∥x(s−m)∥2	PROPN
ejpam-6466	282	30	)	)	PUNCT
ejpam-6466	282	31	+	+	NUM
ejpam-6466	283	1	2k2	2k2	NUM
ejpam-6466	283	2	]	]	X
ejpam-6466	283	3	ℏ	ℏ	X
ejpam-6466	283	4	=	=	SYM
ejpam-6466	283	5	ℏ(2ξ−1	ℏ(2ξ−1	X
ejpam-6466	283	6	)	)	PUNCT
ejpam-6466	283	7	2ξ	2ξ	NUM
ejpam-6466	283	8	−	−	NOUN
ejpam-6466	283	9	1	1	NUM
ejpam-6466	283	10	(	(	PUNCT
ejpam-6466	283	11	2l2	2l2	NUM
ejpam-6466	283	12	(	(	PUNCT
ejpam-6466	283	13	∥x(s)∥2h̃2	∥x(s)∥2h̃2	NUM
ejpam-6466	283	14	+	+	CCONJ
ejpam-6466	283	15	(	(	PUNCT
ejpam-6466	283	16	∥x(s−m)∥2h̃2	∥x(s−m)∥2h̃2	X
ejpam-6466	283	17	)	)	PUNCT
ejpam-6466	283	18	+	+	CCONJ
ejpam-6466	283	19	2k2	2k2	NUM
ejpam-6466	283	20	)	)	PUNCT
ejpam-6466	283	21	ℏ.	ℏ.	NOUN
ejpam-6466	283	22	(	(	PUNCT
ejpam-6466	283	23	13	13	NUM
ejpam-6466	283	24	)	)	PUNCT
ejpam-6466	283	25	now	now	ADV
ejpam-6466	283	26	,	,	PUNCT
ejpam-6466	283	27	we	we	PRON
ejpam-6466	283	28	will	will	AUX
ejpam-6466	283	29	simplify	simplify	VERB
ejpam-6466	283	30	the	the	DET
ejpam-6466	283	31	following	following	ADJ
ejpam-6466	283	32	result	result	NOUN
ejpam-6466	283	33	:	:	PUNCT
ejpam-6466	283	34	for	for	ADP
ejpam-6466	283	35	this	this	PRON
ejpam-6466	283	36	,	,	PUNCT
ejpam-6466	283	37	use	use	VERB
ejpam-6466	283	38	i	i	PRON
ejpam-6466	283	39	-	-	PUNCT
ejpam-6466	283	40	is	be	AUX
ejpam-6466	283	41	.	.	PUNCT
ejpam-6466	284	1	e	e	X
ejpam-6466	285	1	[	[	X
ejpam-6466	285	2	∥∥∥∥	∥∥∥∥	NUM
ejpam-6466	285	3	∫	∫	PROPN
ejpam-6466	285	4	τ	τ	X
ejpam-6466	285	5	0	0	NUM
ejpam-6466	285	6	sξ−1𭟋	sξ−1𭟋	X
ejpam-6466	285	7	(	(	PUNCT
ejpam-6466	285	8	s	s	PROPN
ejpam-6466	285	9	,	,	PUNCT
ejpam-6466	285	10	x(s	x(s	PROPN
ejpam-6466	285	11	)	)	PUNCT
ejpam-6466	285	12	,	,	PUNCT
ejpam-6466	285	13	x(s−m	x(s−m	NUM
ejpam-6466	285	14	)	)	PUNCT
ejpam-6466	285	15	)	)	PUNCT
ejpam-6466	286	1	dws	dws	PROPN
ejpam-6466	286	2	∥∥∥∥2	∥∥∥∥2	PROPN
ejpam-6466	286	3	]	]	X
ejpam-6466	286	4	=	=	SYM
ejpam-6466	286	5	e	e	X
ejpam-6466	286	6	[	[	X
ejpam-6466	286	7	(	(	PUNCT
ejpam-6466	286	8	∫	∫	PROPN
ejpam-6466	286	9	τ	τ	PROPN
ejpam-6466	286	10	0	0	PUNCT
ejpam-6466	286	11	sξ−1	sξ−1	ADJ
ejpam-6466	286	12	∥∥𭟋(s	∥∥𭟋(	NOUN
ejpam-6466	286	13	,	,	PUNCT
ejpam-6466	286	14	x(s	x(s	PROPN
ejpam-6466	286	15	)	)	PUNCT
ejpam-6466	286	16	,	,	PUNCT
ejpam-6466	286	17	x(s−m	x(s−m	NUM
ejpam-6466	286	18	)	)	PUNCT
ejpam-6466	286	19	)	)	PUNCT
ejpam-6466	286	20	∥∥ds)2	∥∥ds)2	NOUN
ejpam-6466	286	21	]	]	PUNCT
ejpam-6466	287	1	=	=	SYM
ejpam-6466	287	2	e	e	X
ejpam-6466	287	3	[	[	PUNCT
ejpam-6466	287	4	∫	∫	PROPN
ejpam-6466	287	5	τ	τ	PROPN
ejpam-6466	287	6	0	0	NUM
ejpam-6466	287	7	s2ξ−2	s2ξ−2	PROPN
ejpam-6466	287	8	∥∥𭟋(s	∥∥𭟋(	NOUN
ejpam-6466	287	9	,	,	PUNCT
ejpam-6466	287	10	x(s	x(s	PROPN
ejpam-6466	287	11	)	)	PUNCT
ejpam-6466	287	12	,	,	PUNCT
ejpam-6466	287	13	x(s−m	x(s−m	NUM
ejpam-6466	287	14	)	)	PUNCT
ejpam-6466	287	15	)	)	PUNCT
ejpam-6466	288	1	∥∥2ds	∥∥2ds	NUM
ejpam-6466	288	2	]	]	PUNCT
ejpam-6466	289	1	=	=	PUNCT
ejpam-6466	289	2	e	e	X
ejpam-6466	289	3	[	[	PUNCT
ejpam-6466	289	4	s2ξ−1	s2ξ−1	PROPN
ejpam-6466	289	5	2ξ	2ξ	NUM
ejpam-6466	289	6	−	−	NOUN
ejpam-6466	289	7	1	1	NUM
ejpam-6466	289	8	∥∥𭟋(s	∥∥𭟋(	NOUN
ejpam-6466	289	9	,	,	PUNCT
ejpam-6466	289	10	x(s	x(s	PROPN
ejpam-6466	289	11	)	)	PUNCT
ejpam-6466	289	12	,	,	PUNCT
ejpam-6466	289	13	x(s−m	x(s−m	NUM
ejpam-6466	289	14	)	)	PUNCT
ejpam-6466	289	15	)	)	PUNCT
ejpam-6466	290	1	∥∥2	∥∥2	NUM
ejpam-6466	290	2	]	]	X
ejpam-6466	290	3	m.	m.	NOUN
ejpam-6466	290	4	i.	i.	PROPN
ejpam-6466	290	5	liaqat	liaqat	PROPN
ejpam-6466	290	6	et	et	PROPN
ejpam-6466	290	7	al	al	PROPN
ejpam-6466	290	8	.	.	PUNCT
ejpam-6466	290	9	/	/	SYM
ejpam-6466	290	10	eur	eur	PROPN
ejpam-6466	290	11	.	.	PUNCT
ejpam-6466	291	1	j.	j.	PROPN
ejpam-6466	291	2	pure	pure	PROPN
ejpam-6466	291	3	appl	appl	PROPN
ejpam-6466	291	4	.	.	PROPN
ejpam-6466	291	5	math	math	PROPN
ejpam-6466	291	6	,	,	PUNCT
ejpam-6466	291	7	18	18	NUM
ejpam-6466	291	8	(	(	PUNCT
ejpam-6466	291	9	4	4	NUM
ejpam-6466	291	10	)	)	PUNCT
ejpam-6466	291	11	(	(	PUNCT
ejpam-6466	291	12	2025	2025	NUM
ejpam-6466	291	13	)	)	PUNCT
ejpam-6466	291	14	,	,	PUNCT
ejpam-6466	291	15	6466	6466	NUM
ejpam-6466	291	16	12	12	NUM
ejpam-6466	291	17	of	of	ADP
ejpam-6466	291	18	28	28	NUM
ejpam-6466	291	19	≤	≤	NUM
ejpam-6466	291	20	e	e	X
ejpam-6466	291	21	[	[	PUNCT
ejpam-6466	291	22	ℏ2ξ−1	ℏ2ξ−1	PROPN
ejpam-6466	291	23	2ξ	2ξ	NUM
ejpam-6466	291	24	−	−	NOUN
ejpam-6466	291	25	1	1	NUM
ejpam-6466	291	26	∥∥𭟋(s	∥∥𭟋(	NOUN
ejpam-6466	291	27	,	,	PUNCT
ejpam-6466	291	28	x(s	x(s	PROPN
ejpam-6466	291	29	)	)	PUNCT
ejpam-6466	291	30	,	,	PUNCT
ejpam-6466	291	31	x(s−m	x(s−m	NUM
ejpam-6466	291	32	)	)	PUNCT
ejpam-6466	291	33	)	)	PUNCT
ejpam-6466	292	1	∥∥2	∥∥2	PROPN
ejpam-6466	292	2	]	]	PUNCT
ejpam-6466	292	3	.	.	PUNCT
ejpam-6466	293	1	(	(	PUNCT
ejpam-6466	293	2	14	14	NUM
ejpam-6466	293	3	)	)	PUNCT
ejpam-6466	293	4	because	because	SCONJ
ejpam-6466	293	5	of	of	ADP
ejpam-6466	293	6	(	(	PUNCT
ejpam-6466	293	7	a2	a2	PROPN
ejpam-6466	293	8	)	)	PUNCT
ejpam-6466	293	9	and	and	CCONJ
ejpam-6466	293	10	(	(	PUNCT
ejpam-6466	293	11	a3	a3	NOUN
ejpam-6466	293	12	)	)	PUNCT
ejpam-6466	293	13	,	,	PUNCT
ejpam-6466	293	14	we	we	PRON
ejpam-6466	293	15	acquire	acquire	VERB
ejpam-6466	293	16	the	the	DET
ejpam-6466	293	17	following	following	ADJ
ejpam-6466	293	18	∥∥𭟋(s	∥∥𭟋(	NOUN
ejpam-6466	293	19	,	,	PUNCT
ejpam-6466	293	20	x(s	x(s	PROPN
ejpam-6466	293	21	)	)	PUNCT
ejpam-6466	293	22	,	,	PUNCT
ejpam-6466	293	23	x(s−m	x(s−m	NUM
ejpam-6466	293	24	)	)	PUNCT
ejpam-6466	293	25	)	)	PUNCT
ejpam-6466	294	1	∥∥2	∥∥2	PROPN
ejpam-6466	295	1	≤	≤	NOUN
ejpam-6466	295	2	2l2	2l2	NUM
ejpam-6466	295	3	(	(	PUNCT
ejpam-6466	295	4	∥x(s)∥2	∥x(s)∥2	X
ejpam-6466	295	5	+	+	PUNCT
ejpam-6466	295	6	(	(	PUNCT
ejpam-6466	295	7	∥x(s−m)∥2	∥x(s−m)∥2	PROPN
ejpam-6466	295	8	)	)	PUNCT
ejpam-6466	296	1	+	+	NUM
ejpam-6466	296	2	2k	2k	NUM
ejpam-6466	296	3	)	)	PUNCT
ejpam-6466	296	4	.	.	PUNCT
ejpam-6466	297	1	(	(	PUNCT
ejpam-6466	297	2	15	15	X
ejpam-6466	297	3	)	)	PUNCT
ejpam-6466	297	4	implementing	implement	VERB
ejpam-6466	297	5	eq	eq	X
ejpam-6466	297	6	.	.	PUNCT
ejpam-6466	298	1	(	(	PUNCT
ejpam-6466	298	2	15	15	NUM
ejpam-6466	298	3	)	)	PUNCT
ejpam-6466	298	4	to	to	ADP
ejpam-6466	298	5	eq	eq	NOUN
ejpam-6466	298	6	.	.	PUNCT
ejpam-6466	299	1	(	(	PUNCT
ejpam-6466	299	2	14	14	NUM
ejpam-6466	299	3	)	)	PUNCT
ejpam-6466	299	4	yields	yield	VERB
ejpam-6466	299	5	the	the	DET
ejpam-6466	299	6	following	follow	VERB
ejpam-6466	299	7	results	result	NOUN
ejpam-6466	299	8	:	:	PUNCT
ejpam-6466	299	9	e	e	X
ejpam-6466	300	1	[	[	X
ejpam-6466	300	2	∥∥∥∥	∥∥∥∥	NUM
ejpam-6466	300	3	∫	∫	PROPN
ejpam-6466	300	4	τ	τ	X
ejpam-6466	300	5	0	0	NUM
ejpam-6466	300	6	sξ−1𭟋	sξ−1𭟋	X
ejpam-6466	300	7	(	(	PUNCT
ejpam-6466	300	8	s	s	PROPN
ejpam-6466	300	9	,	,	PUNCT
ejpam-6466	300	10	x(s	x(s	PROPN
ejpam-6466	300	11	)	)	PUNCT
ejpam-6466	300	12	,	,	PUNCT
ejpam-6466	300	13	x(s−m	x(s−m	NUM
ejpam-6466	300	14	)	)	PUNCT
ejpam-6466	300	15	)	)	PUNCT
ejpam-6466	301	1	dws	dws	PROPN
ejpam-6466	301	2	∥∥∥∥2	∥∥∥∥2	PROPN
ejpam-6466	301	3	]	]	PUNCT
ejpam-6466	301	4	≤	≤	PROPN
ejpam-6466	302	1	ℏ2ξ−1	ℏ2ξ−1	PROPN
ejpam-6466	302	2	2ξ	2ξ	NUM
ejpam-6466	302	3	−	−	PROPN
ejpam-6466	302	4	1	1	NUM
ejpam-6466	302	5	(	(	PUNCT
ejpam-6466	302	6	2l2	2l2	NUM
ejpam-6466	302	7	(	(	PUNCT
ejpam-6466	302	8	∥x(s)∥2h̃2	∥x(s)∥2h̃2	PROPN
ejpam-6466	302	9	+	+	CCONJ
ejpam-6466	302	10	(	(	PUNCT
ejpam-6466	302	11	∥x(s−m)∥2	∥x(s−m)∥2	PROPN
ejpam-6466	302	12	)	)	PUNCT
ejpam-6466	302	13	+	+	NUM
ejpam-6466	302	14	2k2	2k2	NUM
ejpam-6466	302	15	)	)	PUNCT
ejpam-6466	302	16	.	.	PUNCT
ejpam-6466	303	1	(	(	PUNCT
ejpam-6466	303	2	16	16	X
ejpam-6466	303	3	)	)	PUNCT
ejpam-6466	303	4	combining	combine	VERB
ejpam-6466	303	5	eqs	eqs	PROPN
ejpam-6466	303	6	.	.	PUNCT
ejpam-6466	304	1	(	(	PUNCT
ejpam-6466	304	2	16	16	NUM
ejpam-6466	304	3	)	)	PUNCT
ejpam-6466	304	4	and	and	CCONJ
ejpam-6466	304	5	(	(	PUNCT
ejpam-6466	304	6	13	13	NUM
ejpam-6466	304	7	)	)	PUNCT
ejpam-6466	304	8	in	in	ADP
ejpam-6466	304	9	(	(	PUNCT
ejpam-6466	304	10	10	10	NUM
ejpam-6466	304	11	)	)	PUNCT
ejpam-6466	304	12	,	,	PUNCT
ejpam-6466	304	13	we	we	PRON
ejpam-6466	304	14	obtain	obtain	VERB
ejpam-6466	304	15	the	the	DET
ejpam-6466	304	16	subsequent	subsequent	ADJ
ejpam-6466	304	17	outcome	outcome	NOUN
ejpam-6466	304	18	:	:	PUNCT
ejpam-6466	304	19	e	e	NOUN
ejpam-6466	304	20	∥∥gφ(x(τ	∥∥gφ(x(τ	VERB
ejpam-6466	304	21	)	)	PUNCT
ejpam-6466	304	22	)	)	PUNCT
ejpam-6466	305	1	∥∥2	∥∥2	PROPN
ejpam-6466	305	2	≤	≤	ADV
ejpam-6466	305	3	6ℏ2ξ−1	6ℏ2ξ−1	NUM
ejpam-6466	305	4	2ξ	2ξ	NUM
ejpam-6466	305	5	−	−	NOUN
ejpam-6466	305	6	1	1	NUM
ejpam-6466	305	7	(	(	PUNCT
ejpam-6466	305	8	ℏ+	ℏ+	X
ejpam-6466	305	9	1	1	NUM
ejpam-6466	305	10	)	)	PUNCT
ejpam-6466	305	11	(	(	PUNCT
ejpam-6466	305	12	2l2	2l2	NUM
ejpam-6466	305	13	(	(	PUNCT
ejpam-6466	305	14	∥x(s)∥2h̃2	∥x(s)∥2h̃2	NUM
ejpam-6466	305	15	+	+	CCONJ
ejpam-6466	305	16	(	(	PUNCT
ejpam-6466	305	17	∥x(s−m)∥2h̃2	∥x(s−m)∥2h̃2	X
ejpam-6466	305	18	)	)	PUNCT
ejpam-6466	306	1	+	+	CCONJ
ejpam-6466	306	2	2k2	2k2	NUM
ejpam-6466	306	3	)	)	PUNCT
ejpam-6466	307	1	+	+	CCONJ
ejpam-6466	308	1	3∥φ∥2	3∥φ∥2	NUM
ejpam-6466	308	2	.	.	PUNCT
ejpam-6466	308	3	(	(	PUNCT
ejpam-6466	308	4	17	17	NUM
ejpam-6466	308	5	)	)	PUNCT
ejpam-6466	308	6	it	it	PRON
ejpam-6466	308	7	follows	follow	VERB
ejpam-6466	308	8	that	that	PRON
ejpam-6466	308	9	∥gφ(x(τ))∥h̃2	∥gφ(x(τ))∥h̃2	ADV
ejpam-6466	308	10	<	<	X
ejpam-6466	308	11	∞.	∞.	PROPN
ejpam-6466	308	12	therefore	therefore	ADV
ejpam-6466	308	13	,	,	PUNCT
ejpam-6466	308	14	the	the	DET
ejpam-6466	308	15	operator	operator	NOUN
ejpam-6466	308	16	gφ	gφ	NOUN
ejpam-6466	308	17	is	be	AUX
ejpam-6466	308	18	properly	properly	ADV
ejpam-6466	308	19	defined	define	VERB
ejpam-6466	308	20	.	.	PUNCT
ejpam-6466	309	1	in	in	ADP
ejpam-6466	309	2	order	order	NOUN
ejpam-6466	309	3	to	to	PART
ejpam-6466	309	4	confirm	confirm	VERB
ejpam-6466	309	5	eu	eu	PROPN
ejpam-6466	309	6	,	,	PUNCT
ejpam-6466	309	7	we	we	PRON
ejpam-6466	309	8	proceed	proceed	VERB
ejpam-6466	309	9	to	to	PART
ejpam-6466	309	10	prove	prove	VERB
ejpam-6466	309	11	the	the	DET
ejpam-6466	309	12	following	follow	VERB
ejpam-6466	309	13	lemma	lemma	PROPN
ejpam-6466	309	14	:	:	PUNCT
ejpam-6466	309	15	lemma	lemma	PROPN
ejpam-6466	309	16	2	2	X
ejpam-6466	309	17	.	.	PUNCT
ejpam-6466	310	1	in	in	ADP
ejpam-6466	310	2	the	the	DET
ejpam-6466	310	3	occurrence	occurrence	NOUN
ejpam-6466	311	1	where	where	SCONJ
ejpam-6466	311	2	τ	τ	PROPN
ejpam-6466	311	3	>	>	X
ejpam-6466	311	4	0	0	PROPN
ejpam-6466	311	5	and	and	CCONJ
ejpam-6466	311	6	ξ	ξ	X
ejpam-6466	311	7	>	>	SYM
ejpam-6466	311	8	1	1	NUM
ejpam-6466	311	9	2	2	NUM
ejpam-6466	311	10	,	,	PUNCT
ejpam-6466	311	11	the	the	DET
ejpam-6466	311	12	subsequent	subsequent	ADJ
ejpam-6466	311	13	inequality	inequality	NOUN
ejpam-6466	311	14	is	be	AUX
ejpam-6466	311	15	true	true	ADJ
ejpam-6466	311	16	:	:	PUNCT
ejpam-6466	311	17	ϑ	ϑ	X
ejpam-6466	311	18	∫	∫	PROPN
ejpam-6466	311	19	τ	τ	X
ejpam-6466	311	20	0	0	NUM
ejpam-6466	311	21	s2ξ−2e2ξ−1(ϑs	s2ξ−2e2ξ−1(ϑ	NOUN
ejpam-6466	311	22	2ξ−1)ds	2ξ−1)ds	NUM
ejpam-6466	311	23	≤	≤	NOUN
ejpam-6466	311	24	e2ξ−1(ϑτ	e2ξ−1(ϑτ	PRON
ejpam-6466	311	25	2ξ−1	2ξ−1	NUM
ejpam-6466	311	26	)	)	PUNCT
ejpam-6466	311	27	,	,	PUNCT
ejpam-6466	311	28	(	(	PUNCT
ejpam-6466	311	29	18	18	NUM
ejpam-6466	311	30	)	)	PUNCT
ejpam-6466	311	31	here	here	ADV
ejpam-6466	311	32	the	the	DET
ejpam-6466	311	33	mittag	mittag	ADJ
ejpam-6466	311	34	-	-	PUNCT
ejpam-6466	311	35	leffler	leffler	NOUN
ejpam-6466	311	36	function	function	NOUN
ejpam-6466	311	37	e2ξ−1	e2ξ−1	PROPN
ejpam-6466	311	38	(	(	PUNCT
ejpam-6466	311	39	.	.	PUNCT
ejpam-6466	311	40	)	)	PUNCT
ejpam-6466	311	41	is	be	AUX
ejpam-6466	311	42	defined	define	VERB
ejpam-6466	311	43	as	as	ADP
ejpam-6466	311	44	e(2ξ−1)(τ	e(2ξ−1)(τ	NOUN
ejpam-6466	311	45	)	)	PUNCT
ejpam-6466	311	46	=	=	PUNCT
ejpam-6466	311	47	∑∞	∑∞	NOUN
ejpam-6466	312	1	υ=0	υ=0	X
ejpam-6466	312	2	τυ	τυ	PUNCT
ejpam-6466	312	3	γ((2ξ	γ((2ξ	ADV
ejpam-6466	312	4	−	−	PROPN
ejpam-6466	312	5	1)υ	1)υ	NUM
ejpam-6466	313	1	+	+	CCONJ
ejpam-6466	313	2	1	1	NUM
ejpam-6466	313	3	)	)	PUNCT
ejpam-6466	313	4	.	.	PUNCT
ejpam-6466	314	1	(	(	PUNCT
ejpam-6466	314	2	19	19	NUM
ejpam-6466	314	3	)	)	PUNCT
ejpam-6466	314	4	proof	proof	NOUN
ejpam-6466	314	5	.	.	PUNCT
ejpam-6466	315	1	let	let	VERB
ejpam-6466	315	2	ϑ	ϑ	PRON
ejpam-6466	315	3	>	>	X
ejpam-6466	315	4	0	0	NUM
ejpam-6466	315	5	be	be	AUX
ejpam-6466	315	6	fixed	fix	VERB
ejpam-6466	315	7	arbitrarily	arbitrarily	ADV
ejpam-6466	315	8	.	.	PUNCT
ejpam-6466	316	1	we	we	PRON
ejpam-6466	316	2	begin	begin	VERB
ejpam-6466	316	3	by	by	ADP
ejpam-6466	316	4	replacing	replace	VERB
ejpam-6466	316	5	the	the	DET
ejpam-6466	316	6	integral	integral	ADJ
ejpam-6466	316	7	with	with	ADP
ejpam-6466	316	8	a	a	DET
ejpam-6466	316	9	corresponding	corresponding	ADJ
ejpam-6466	316	10	sum	sum	NOUN
ejpam-6466	316	11	,	,	PUNCT
ejpam-6466	316	12	and	and	CCONJ
ejpam-6466	316	13	subsequently	subsequently	ADV
ejpam-6466	316	14	,	,	PUNCT
ejpam-6466	316	15	we	we	PRON
ejpam-6466	316	16	employ	employ	VERB
ejpam-6466	316	17	the	the	DET
ejpam-6466	316	18	following	follow	VERB
ejpam-6466	316	19	identity.∫	identity.∫	ADP
ejpam-6466	316	20	τ	τ	X
ejpam-6466	316	21	0	0	PUNCT
ejpam-6466	317	1	s2ξ−2sυ(2ξ−1)ds	s2ξ−2sυ(2ξ−1)ds	PROPN
ejpam-6466	317	2	=	=	SYM
ejpam-6466	317	3	τ	τ	X
ejpam-6466	317	4	(	(	PUNCT
ejpam-6466	317	5	υ+1)(2ξ−1)b	υ+1)(2ξ−1)b	X
ejpam-6466	317	6	(	(	PUNCT
ejpam-6466	317	7	2ξ	2ξ	NUM
ejpam-6466	317	8	−	−	PROPN
ejpam-6466	317	9	1	1	NUM
ejpam-6466	317	10	,	,	PUNCT
ejpam-6466	317	11	υ(2ξ	υ(2ξ	NOUN
ejpam-6466	317	12	−	−	PROPN
ejpam-6466	317	13	1	1	NUM
ejpam-6466	317	14	)	)	PUNCT
ejpam-6466	317	15	+	+	CCONJ
ejpam-6466	317	16	1	1	X
ejpam-6466	317	17	)	)	PUNCT
ejpam-6466	317	18	,	,	PUNCT
ejpam-6466	317	19	υ	υ	NOUN
ejpam-6466	317	20	=	=	NOUN
ejpam-6466	317	21	0	0	NUM
ejpam-6466	317	22	,	,	PUNCT
ejpam-6466	317	23	1	1	NUM
ejpam-6466	317	24	,	,	PUNCT
ejpam-6466	317	25	2	2	NUM
ejpam-6466	317	26	,	,	PUNCT
ejpam-6466	317	27	·	·	PUNCT
ejpam-6466	317	28	·	·	PUNCT
ejpam-6466	317	29	·	·	PUNCT
ejpam-6466	317	30	.	.	PUNCT
ejpam-6466	318	1	so	so	ADV
ejpam-6466	318	2	,	,	PUNCT
ejpam-6466	318	3	we	we	PRON
ejpam-6466	318	4	get	get	VERB
ejpam-6466	318	5	ϑ	ϑ	PRON
ejpam-6466	318	6	∫	∫	PROPN
ejpam-6466	318	7	τ	τ	X
ejpam-6466	318	8	0	0	NUM
ejpam-6466	318	9	s2ξ−2e2ξ−1(ϑs	s2ξ−2e2ξ−1(ϑ	NOUN
ejpam-6466	318	10	2ξ−1)ds	2ξ−1)ds	NUM
ejpam-6466	318	11	=	=	SYM
ejpam-6466	318	12	ϑ	ϑ	X
ejpam-6466	318	13	∑∞	∑∞	NOUN
ejpam-6466	318	14	υ=0	υ=0	X
ejpam-6466	318	15	ϑυ	ϑυ	ADP
ejpam-6466	318	16	γ(υ(2ξ	γ(υ(2ξ	NUM
ejpam-6466	318	17	−	−	NUM
ejpam-6466	318	18	1	1	NUM
ejpam-6466	318	19	)	)	PUNCT
ejpam-6466	318	20	+	+	CCONJ
ejpam-6466	318	21	1	1	X
ejpam-6466	318	22	)	)	PUNCT
ejpam-6466	318	23	∫	∫	PROPN
ejpam-6466	318	24	τ	τ	PROPN
ejpam-6466	318	25	0	0	PROPN
ejpam-6466	318	26	s2ξ−2sυ(2ξ−1)ds	s2ξ−2sυ(2ξ−1)ds	PROPN
ejpam-6466	318	27	=	=	SYM
ejpam-6466	318	28	∑∞	∑∞	NOUN
ejpam-6466	318	29	υ=0	υ=0	X
ejpam-6466	318	30	ϑυ+1τ	ϑυ+1τ	NOUN
ejpam-6466	318	31	(	(	PUNCT
ejpam-6466	318	32	υ+1)(2ξ−1	υ+1)(2ξ−1	PROPN
ejpam-6466	318	33	)	)	PUNCT
ejpam-6466	318	34	γ(2ξ	γ(2ξ	PUNCT
ejpam-6466	318	35	−	−	PROPN
ejpam-6466	318	36	1)γ(υ(2ξ	1)γ(υ(2ξ	NUM
ejpam-6466	318	37	−	−	NOUN
ejpam-6466	318	38	1	1	NUM
ejpam-6466	318	39	)	)	PUNCT
ejpam-6466	318	40	+	+	CCONJ
ejpam-6466	318	41	1	1	X
ejpam-6466	318	42	)	)	PUNCT
ejpam-6466	318	43	m.	m.	NOUN
ejpam-6466	318	44	i.	i.	PROPN
ejpam-6466	318	45	liaqat	liaqat	PROPN
ejpam-6466	318	46	et	et	PROPN
ejpam-6466	318	47	al	al	PROPN
ejpam-6466	318	48	.	.	PUNCT
ejpam-6466	318	49	/	/	SYM
ejpam-6466	318	50	eur	eur	PROPN
ejpam-6466	318	51	.	.	PUNCT
ejpam-6466	319	1	j.	j.	PROPN
ejpam-6466	319	2	pure	pure	PROPN
ejpam-6466	319	3	appl	appl	PROPN
ejpam-6466	319	4	.	.	PROPN
ejpam-6466	319	5	math	math	PROPN
ejpam-6466	319	6	,	,	PUNCT
ejpam-6466	319	7	18	18	NUM
ejpam-6466	319	8	(	(	PUNCT
ejpam-6466	319	9	4	4	NUM
ejpam-6466	319	10	)	)	PUNCT
ejpam-6466	319	11	(	(	PUNCT
ejpam-6466	319	12	2025	2025	NUM
ejpam-6466	319	13	)	)	PUNCT
ejpam-6466	319	14	,	,	PUNCT
ejpam-6466	319	15	6466	6466	NUM
ejpam-6466	319	16	13	13	NUM
ejpam-6466	319	17	of	of	ADP
ejpam-6466	319	18	28	28	NUM
ejpam-6466	319	19	=	=	NOUN
ejpam-6466	319	20	∑∞	∑∞	NOUN
ejpam-6466	319	21	υ=1	υ=1	PUNCT
ejpam-6466	319	22	ϑυτυ(2ξ−1	ϑυτυ(2ξ−1	NOUN
ejpam-6466	319	23	)	)	PUNCT
ejpam-6466	319	24	γ(υ(2ξ	γ(υ(2ξ	PUNCT
ejpam-6466	319	25	−	−	NUM
ejpam-6466	319	26	1	1	NUM
ejpam-6466	319	27	)	)	PUNCT
ejpam-6466	319	28	+	+	CCONJ
ejpam-6466	319	29	1	1	X
ejpam-6466	319	30	)	)	PUNCT
ejpam-6466	320	1	=	=	NOUN
ejpam-6466	320	2	e2ξ−1(ϑτ	e2ξ−1(ϑτ	PROPN
ejpam-6466	320	3	2ξ−1)−	2ξ−1)−	NUM
ejpam-6466	320	4	1	1	NUM
ejpam-6466	320	5	≤e2ξ−1(ϑτ	≤e2ξ−1(ϑτ	VERB
ejpam-6466	320	6	2ξ−1	2ξ−1	NUM
ejpam-6466	320	7	)	)	PUNCT
ejpam-6466	320	8	,	,	PUNCT
ejpam-6466	320	9	here	here	ADV
ejpam-6466	320	10	,	,	PUNCT
ejpam-6466	320	11	b	b	PROPN
ejpam-6466	320	12	is	be	AUX
ejpam-6466	320	13	a	a	DET
ejpam-6466	320	14	beta	beta	ADJ
ejpam-6466	320	15	function	function	NOUN
ejpam-6466	320	16	.	.	PUNCT
ejpam-6466	321	1	hence	hence	ADV
ejpam-6466	321	2	,	,	PUNCT
ejpam-6466	321	3	completes	complete	VERB
ejpam-6466	321	4	the	the	DET
ejpam-6466	321	5	proof	proof	NOUN
ejpam-6466	321	6	.	.	PUNCT
ejpam-6466	322	1	to	to	PART
ejpam-6466	322	2	demonstrate	demonstrate	VERB
ejpam-6466	322	3	the	the	DET
ejpam-6466	322	4	eu	eu	PROPN
ejpam-6466	322	5	of	of	ADP
ejpam-6466	322	6	solutions	solution	NOUN
ejpam-6466	322	7	,	,	PUNCT
ejpam-6466	322	8	we	we	PRON
ejpam-6466	322	9	aim	aim	VERB
ejpam-6466	322	10	to	to	PART
ejpam-6466	322	11	prove	prove	VERB
ejpam-6466	322	12	that	that	SCONJ
ejpam-6466	322	13	the	the	DET
ejpam-6466	322	14	operator	operator	NOUN
ejpam-6466	322	15	gφ	gφ	NOUN
ejpam-6466	322	16	is	be	AUX
ejpam-6466	322	17	a	a	DET
ejpam-6466	322	18	contraction	contraction	NOUN
ejpam-6466	322	19	in	in	ADP
ejpam-6466	322	20	the	the	DET
ejpam-6466	322	21	space	space	NOUN
ejpam-6466	322	22	h̃2([0	h̃2([0	NOUN
ejpam-6466	322	23	,	,	PUNCT
ejpam-6466	322	24	ℏ	ℏ	NOUN
ejpam-6466	322	25	]	]	PUNCT
ejpam-6466	322	26	)	)	PUNCT
ejpam-6466	322	27	with	with	ADP
ejpam-6466	322	28	respect	respect	NOUN
ejpam-6466	322	29	to	to	ADP
ejpam-6466	322	30	an	an	DET
ejpam-6466	322	31	appropriately	appropriately	ADV
ejpam-6466	322	32	chosen	choose	VERB
ejpam-6466	322	33	weighted	weight	VERB
ejpam-6466	322	34	norm	norm	NOUN
ejpam-6466	322	35	(	(	PUNCT
ejpam-6466	322	36	[	[	X
ejpam-6466	322	37	]	]	X
ejpam-6466	322	38	,	,	PUNCT
ejpam-6466	322	39	[	[	X
ejpam-6466	322	40	remark	remark	NOUN
ejpam-6466	322	41	2.1	2.1	NUM
ejpam-6466	322	42	]	]	PUNCT
ejpam-6466	322	43	)	)	PUNCT
ejpam-6466	322	44	.	.	PUNCT
ejpam-6466	323	1	in	in	ADP
ejpam-6466	323	2	this	this	DET
ejpam-6466	323	3	context	context	NOUN
ejpam-6466	323	4	,	,	PUNCT
ejpam-6466	323	5	the	the	DET
ejpam-6466	323	6	mittag	mittag	ADJ
ejpam-6466	323	7	-	-	PUNCT
ejpam-6466	323	8	leffler	leffler	NOUN
ejpam-6466	323	9	function	function	NOUN
ejpam-6466	323	10	e(2ξ−1)(τ	e(2ξ−1)(τ	NOUN
ejpam-6466	323	11	)	)	PUNCT
ejpam-6466	323	12	,	,	PUNCT
ejpam-6466	323	13	defined	define	VERB
ejpam-6466	323	14	in	in	ADP
ejpam-6466	323	15	eq	eq	ADP
ejpam-6466	323	16	.	.	PUNCT
ejpam-6466	324	1	(	(	PUNCT
ejpam-6466	324	2	19	19	NUM
ejpam-6466	324	3	)	)	PUNCT
ejpam-6466	325	1	,	,	PUNCT
ejpam-6466	325	2	acts	act	VERB
ejpam-6466	325	3	as	as	ADP
ejpam-6466	325	4	the	the	DET
ejpam-6466	325	5	weighting	weighting	NOUN
ejpam-6466	325	6	function	function	NOUN
ejpam-6466	325	7	.	.	PUNCT
ejpam-6466	326	1	to	to	PART
ejpam-6466	326	2	demonstrate	demonstrate	VERB
ejpam-6466	326	3	the	the	DET
ejpam-6466	326	4	eu	eu	PROPN
ejpam-6466	326	5	of	of	ADP
ejpam-6466	326	6	solutions	solution	NOUN
ejpam-6466	326	7	,	,	PUNCT
ejpam-6466	326	8	we	we	PRON
ejpam-6466	326	9	aim	aim	VERB
ejpam-6466	326	10	to	to	PART
ejpam-6466	326	11	prove	prove	VERB
ejpam-6466	326	12	that	that	SCONJ
ejpam-6466	326	13	the	the	DET
ejpam-6466	326	14	operator	operator	NOUN
ejpam-6466	326	15	gφ	gφ	NOUN
ejpam-6466	326	16	is	be	AUX
ejpam-6466	326	17	a	a	DET
ejpam-6466	326	18	contraction	contraction	NOUN
ejpam-6466	326	19	in	in	ADP
ejpam-6466	326	20	the	the	DET
ejpam-6466	326	21	space	space	NOUN
ejpam-6466	326	22	h̃2([0	h̃2([0	NOUN
ejpam-6466	326	23	,	,	PUNCT
ejpam-6466	326	24	ℏ	ℏ	NOUN
ejpam-6466	326	25	]	]	PUNCT
ejpam-6466	326	26	)	)	PUNCT
ejpam-6466	326	27	with	with	ADP
ejpam-6466	326	28	respect	respect	NOUN
ejpam-6466	326	29	to	to	ADP
ejpam-6466	326	30	an	an	DET
ejpam-6466	326	31	appropriately	appropriately	ADV
ejpam-6466	326	32	chosen	choose	VERB
ejpam-6466	326	33	weighted	weight	VERB
ejpam-6466	326	34	norm	norm	NOUN
ejpam-6466	326	35	(	(	PUNCT
ejpam-6466	326	36	[	[	X
ejpam-6466	326	37	35	35	NUM
ejpam-6466	326	38	]	]	PUNCT
ejpam-6466	326	39	,	,	PUNCT
ejpam-6466	326	40	[	[	X
ejpam-6466	326	41	remark	remark	NOUN
ejpam-6466	326	42	2.1	2.1	NUM
ejpam-6466	326	43	]	]	PUNCT
ejpam-6466	326	44	)	)	PUNCT
ejpam-6466	326	45	.	.	PUNCT
ejpam-6466	327	1	in	in	ADP
ejpam-6466	327	2	this	this	DET
ejpam-6466	327	3	context	context	NOUN
ejpam-6466	327	4	,	,	PUNCT
ejpam-6466	327	5	the	the	DET
ejpam-6466	327	6	mittag	mittag	ADJ
ejpam-6466	327	7	-	-	PUNCT
ejpam-6466	327	8	leffler	leffler	NOUN
ejpam-6466	327	9	function	function	NOUN
ejpam-6466	327	10	e(2ξ−1)(τ	e(2ξ−1)(τ	NOUN
ejpam-6466	327	11	)	)	PUNCT
ejpam-6466	327	12	,	,	PUNCT
ejpam-6466	327	13	defined	define	VERB
ejpam-6466	327	14	in	in	ADP
ejpam-6466	327	15	eq	eq	ADP
ejpam-6466	327	16	.	.	PUNCT
ejpam-6466	328	1	(	(	PUNCT
ejpam-6466	328	2	19	19	NUM
ejpam-6466	328	3	)	)	PUNCT
ejpam-6466	329	1	,	,	PUNCT
ejpam-6466	329	2	acts	act	VERB
ejpam-6466	329	3	as	as	ADP
ejpam-6466	329	4	the	the	DET
ejpam-6466	329	5	weighting	weighting	NOUN
ejpam-6466	329	6	function	function	NOUN
ejpam-6466	329	7	.	.	PUNCT
ejpam-6466	330	1	to	to	PART
ejpam-6466	330	2	demonstrate	demonstrate	VERB
ejpam-6466	330	3	the	the	DET
ejpam-6466	330	4	eu	eu	PROPN
ejpam-6466	330	5	of	of	ADP
ejpam-6466	330	6	solutions	solution	NOUN
ejpam-6466	330	7	,	,	PUNCT
ejpam-6466	330	8	we	we	PRON
ejpam-6466	330	9	aim	aim	VERB
ejpam-6466	330	10	to	to	PART
ejpam-6466	330	11	prove	prove	VERB
ejpam-6466	330	12	that	that	SCONJ
ejpam-6466	330	13	the	the	DET
ejpam-6466	330	14	operator	operator	NOUN
ejpam-6466	330	15	gφ	gφ	NOUN
ejpam-6466	330	16	is	be	AUX
ejpam-6466	330	17	a	a	DET
ejpam-6466	330	18	contraction	contraction	NOUN
ejpam-6466	330	19	in	in	ADP
ejpam-6466	330	20	the	the	DET
ejpam-6466	330	21	space	space	NOUN
ejpam-6466	330	22	h̃2([0	h̃2([0	NOUN
ejpam-6466	330	23	,	,	PUNCT
ejpam-6466	330	24	ℏ	ℏ	NOUN
ejpam-6466	330	25	]	]	PUNCT
ejpam-6466	330	26	)	)	PUNCT
ejpam-6466	330	27	with	with	ADP
ejpam-6466	330	28	respect	respect	NOUN
ejpam-6466	330	29	to	to	ADP
ejpam-6466	330	30	an	an	DET
ejpam-6466	330	31	appropriately	appropriately	ADV
ejpam-6466	330	32	chosen	choose	VERB
ejpam-6466	330	33	weighted	weight	VERB
ejpam-6466	330	34	norm	norm	NOUN
ejpam-6466	330	35	(	(	PUNCT
ejpam-6466	330	36	[	[	X
ejpam-6466	330	37	]	]	X
ejpam-6466	330	38	,	,	PUNCT
ejpam-6466	330	39	[	[	X
ejpam-6466	330	40	remark	remark	NOUN
ejpam-6466	330	41	2.1	2.1	NUM
ejpam-6466	330	42	]	]	PUNCT
ejpam-6466	330	43	)	)	PUNCT
ejpam-6466	330	44	.	.	PUNCT
ejpam-6466	331	1	in	in	ADP
ejpam-6466	331	2	this	this	DET
ejpam-6466	331	3	context	context	NOUN
ejpam-6466	331	4	,	,	PUNCT
ejpam-6466	331	5	the	the	DET
ejpam-6466	331	6	mittag	mittag	ADJ
ejpam-6466	331	7	-	-	PUNCT
ejpam-6466	331	8	leffler	leffler	NOUN
ejpam-6466	331	9	function	function	NOUN
ejpam-6466	331	10	e(2ξ−1)(τ	e(2ξ−1)(τ	NOUN
ejpam-6466	331	11	)	)	PUNCT
ejpam-6466	331	12	,	,	PUNCT
ejpam-6466	331	13	defined	define	VERB
ejpam-6466	331	14	in	in	ADP
ejpam-6466	331	15	eq	eq	ADP
ejpam-6466	331	16	.	.	PUNCT
ejpam-6466	332	1	(	(	PUNCT
ejpam-6466	332	2	19	19	NUM
ejpam-6466	332	3	)	)	PUNCT
ejpam-6466	333	1	,	,	PUNCT
ejpam-6466	333	2	acts	act	VERB
ejpam-6466	333	3	as	as	ADP
ejpam-6466	333	4	the	the	DET
ejpam-6466	333	5	weighting	weighting	NOUN
ejpam-6466	333	6	function	function	NOUN
ejpam-6466	333	7	.	.	PUNCT
ejpam-6466	334	1	theorem	theorem	NOUN
ejpam-6466	334	2	1	1	NUM
ejpam-6466	334	3	.	.	PUNCT
ejpam-6466	335	1	if	if	SCONJ
ejpam-6466	335	2	(	(	PUNCT
ejpam-6466	335	3	a2	a2	PROPN
ejpam-6466	335	4	)	)	PUNCT
ejpam-6466	335	5	and	and	CCONJ
ejpam-6466	335	6	(	(	PUNCT
ejpam-6466	335	7	a3	a3	NOUN
ejpam-6466	335	8	)	)	PUNCT
ejpam-6466	335	9	are	be	AUX
ejpam-6466	335	10	valid	valid	ADJ
ejpam-6466	335	11	,	,	PUNCT
ejpam-6466	335	12	then	then	ADV
ejpam-6466	335	13	the	the	DET
ejpam-6466	335	14	problem	problem	NOUN
ejpam-6466	335	15	eq	eq	ADJ
ejpam-6466	335	16	.	.	PUNCT
ejpam-6466	336	1	(	(	PUNCT
ejpam-6466	336	2	4	4	NUM
ejpam-6466	336	3	)	)	PUNCT
ejpam-6466	336	4	with	with	ADP
ejpam-6466	336	5	x(0	x(0	PROPN
ejpam-6466	336	6	)	)	PUNCT
ejpam-6466	337	1	=	=	PUNCT
ejpam-6466	337	2	φ	φ	PROPN
ejpam-6466	337	3	has	have	VERB
ejpam-6466	337	4	unique	unique	ADJ
ejpam-6466	337	5	solution	solution	NOUN
ejpam-6466	337	6	on	on	ADP
ejpam-6466	337	7	[	[	X
ejpam-6466	337	8	−m	−m	NOUN
ejpam-6466	337	9	,	,	PUNCT
ejpam-6466	337	10	0	0	NUM
ejpam-6466	337	11	]	]	PUNCT
ejpam-6466	337	12	for	for	ADP
ejpam-6466	337	13	any	any	DET
ejpam-6466	337	14	φ	φ	PROPN
ejpam-6466	337	15	∈	∈	PROPN
ejpam-6466	337	16	c̃([−m	c̃([−m	NOUN
ejpam-6466	337	17	,	,	PUNCT
ejpam-6466	337	18	0],rr	0],rr	PROPN
ejpam-6466	337	19	)	)	PUNCT
ejpam-6466	337	20	.	.	PUNCT
ejpam-6466	338	1	proof	proof	NOUN
ejpam-6466	338	2	.	.	PUNCT
ejpam-6466	339	1	first	first	ADV
ejpam-6466	339	2	of	of	ADP
ejpam-6466	339	3	all	all	PRON
ejpam-6466	339	4	,	,	PUNCT
ejpam-6466	339	5	choose	choose	VERB
ejpam-6466	339	6	a	a	DET
ejpam-6466	339	7	fix	fix	NOUN
ejpam-6466	339	8	positive	positive	ADJ
ejpam-6466	339	9	constant	constant	ADJ
ejpam-6466	339	10	ϑ	ϑ	NOUN
ejpam-6466	339	11	as	as	SCONJ
ejpam-6466	339	12	follows	follow	VERB
ejpam-6466	339	13	:	:	PUNCT
ejpam-6466	339	14	ϑ	ϑ	X
ejpam-6466	339	15	>	>	X
ejpam-6466	339	16	8l2(ℏ+	8l2(ℏ+	NUM
ejpam-6466	339	17	1)γ(2ξ	1)γ(2ξ	NUM
ejpam-6466	339	18	−	−	PROPN
ejpam-6466	339	19	1	1	NUM
ejpam-6466	339	20	)	)	PUNCT
ejpam-6466	339	21	.	.	PUNCT
ejpam-6466	340	1	(	(	PUNCT
ejpam-6466	340	2	20	20	X
ejpam-6466	340	3	)	)	PUNCT
ejpam-6466	340	4	we	we	PRON
ejpam-6466	340	5	construct	construct	VERB
ejpam-6466	340	6	a	a	DET
ejpam-6466	340	7	weighted	weight	VERB
ejpam-6466	340	8	norm	norm	NOUN
ejpam-6466	340	9	∥	∥	X
ejpam-6466	340	10	·	·	PUNCT
ejpam-6466	341	1	∥ϑ	∥ϑ	NOUN
ejpam-6466	341	2	over	over	ADP
ejpam-6466	341	3	the	the	DET
ejpam-6466	341	4	space	space	NOUN
ejpam-6466	341	5	h̃2([o	h̃2([o	NOUN
ejpam-6466	341	6	,	,	PUNCT
ejpam-6466	341	7	ℏ	ℏ	PROPN
ejpam-6466	341	8	]	]	PUNCT
ejpam-6466	341	9	)	)	PUNCT
ejpam-6466	341	10	as	as	SCONJ
ejpam-6466	341	11	:	:	PUNCT
ejpam-6466	341	12	∥x(τ)∥ϑ	∥x(τ)∥ϑ	PROPN
ejpam-6466	341	13	=	=	NOUN
ejpam-6466	341	14	sup	sup	NOUN
ejpam-6466	341	15	τ∈[0,ℏ	τ∈[0,ℏ	PROPN
ejpam-6466	341	16	]	]	X
ejpam-6466	341	17	(	(	PUNCT
ejpam-6466	341	18	e(∥x(τ)∥2	e(∥x(τ)∥2	PROPN
ejpam-6466	341	19	)	)	PUNCT
ejpam-6466	341	20	e2ξ−1	e2ξ−1	PROPN
ejpam-6466	341	21	(	(	PUNCT
ejpam-6466	341	22	ϑ(τ	ϑ(τ	PROPN
ejpam-6466	341	23	+	+	PROPN
ejpam-6466	341	24	m)2ξ−1	m)2ξ−1	NUM
ejpam-6466	341	25	)	)	PUNCT
ejpam-6466	341	26	)	)	PUNCT
ejpam-6466	341	27	1	1	NUM
ejpam-6466	341	28	2	2	NUM
ejpam-6466	341	29	,	,	PUNCT
ejpam-6466	341	30	∀	∀	PUNCT
ejpam-6466	341	31	x(τ	x(τ	PROPN
ejpam-6466	341	32	)	)	PUNCT
ejpam-6466	341	33	∈	∈	PROPN
ejpam-6466	341	34	h̃2([0	h̃2([0	VERB
ejpam-6466	341	35	,	,	PUNCT
ejpam-6466	341	36	ℏ	ℏ	NOUN
ejpam-6466	341	37	]	]	PUNCT
ejpam-6466	341	38	)	)	PUNCT
ejpam-6466	341	39	.	.	PUNCT
ejpam-6466	342	1	(	(	PUNCT
ejpam-6466	342	2	21	21	NUM
ejpam-6466	342	3	)	)	PUNCT
ejpam-6466	342	4	let	let	VERB
ejpam-6466	342	5	us	we	PRON
ejpam-6466	342	6	now	now	ADV
ejpam-6466	342	7	fix	fix	VERB
ejpam-6466	342	8	an	an	DET
ejpam-6466	342	9	arbitrary	arbitrary	ADJ
ejpam-6466	342	10	φ	φ	PROPN
ejpam-6466	342	11	∈	∈	PROPN
ejpam-6466	342	12	c̃([−m	c̃([−m	NOUN
ejpam-6466	342	13	,	,	PUNCT
ejpam-6466	342	14	0],rr	0],rr	PROPN
ejpam-6466	342	15	)	)	PUNCT
ejpam-6466	342	16	.	.	PUNCT
ejpam-6466	343	1	the	the	DET
ejpam-6466	343	2	operator	operator	NOUN
ejpam-6466	343	3	gφ	gφ	NOUN
ejpam-6466	343	4	is	be	AUX
ejpam-6466	343	5	well	well	ADV
ejpam-6466	343	6	-	-	PUNCT
ejpam-6466	343	7	posed	pose	VERB
ejpam-6466	343	8	by	by	ADP
ejpam-6466	343	9	virtue	virtue	NOUN
ejpam-6466	343	10	of	of	ADP
ejpam-6466	343	11	the	the	DET
ejpam-6466	343	12	previously	previously	ADV
ejpam-6466	343	13	stated	state	VERB
ejpam-6466	343	14	lemma	lemma	PROPN
ejpam-6466	343	15	.	.	PUNCT
ejpam-6466	344	1	we	we	PRON
ejpam-6466	344	2	shall	shall	AUX
ejpam-6466	344	3	now	now	ADV
ejpam-6466	344	4	establish	establish	VERB
ejpam-6466	344	5	the	the	DET
ejpam-6466	344	6	contractive	contractive	ADJ
ejpam-6466	344	7	property	property	NOUN
ejpam-6466	344	8	of	of	ADP
ejpam-6466	344	9	the	the	DET
ejpam-6466	344	10	mapping	mapping	NOUN
ejpam-6466	344	11	gφ	gφ	NOUN
ejpam-6466	344	12	with	with	ADP
ejpam-6466	344	13	respect	respect	NOUN
ejpam-6466	344	14	to	to	ADP
ejpam-6466	344	15	the	the	DET
ejpam-6466	344	16	norm	norm	NOUN
ejpam-6466	344	17	∥	∥	X
ejpam-6466	344	18	·	·	PUNCT
ejpam-6466	344	19	∥ϑ.	∥ϑ.	ADV
ejpam-6466	344	20	to	to	ADP
ejpam-6466	344	21	this	this	DET
ejpam-6466	344	22	end	end	NOUN
ejpam-6466	344	23	,	,	PUNCT
ejpam-6466	344	24	consider	consider	VERB
ejpam-6466	344	25	arbitrary	arbitrary	ADJ
ejpam-6466	344	26	elements	element	NOUN
ejpam-6466	344	27	x(τ	x(τ	PROPN
ejpam-6466	344	28	)	)	PUNCT
ejpam-6466	344	29	,	,	PUNCT
ejpam-6466	344	30	x̃(τ	x̃(τ	PROPN
ejpam-6466	344	31	)	)	PUNCT
ejpam-6466	344	32	∈	∈	PROPN
ejpam-6466	344	33	h̃2([0	h̃2([0	VERB
ejpam-6466	344	34	,	,	PUNCT
ejpam-6466	344	35	ℏ	ℏ	NOUN
ejpam-6466	344	36	]	]	PUNCT
ejpam-6466	344	37	)	)	PUNCT
ejpam-6466	344	38	.	.	PUNCT
ejpam-6466	345	1	then	then	ADV
ejpam-6466	345	2	,	,	PUNCT
ejpam-6466	345	3	for	for	ADP
ejpam-6466	345	4	every	every	DET
ejpam-6466	345	5	τ	τ	PROPN
ejpam-6466	345	6	∈	∈	PROPN
ejpam-6466	345	7	[	[	X
ejpam-6466	345	8	0	0	NUM
ejpam-6466	345	9	,	,	PUNCT
ejpam-6466	345	10	ℏ	ℏ	PROPN
ejpam-6466	345	11	]	]	PUNCT
ejpam-6466	345	12	,	,	PUNCT
ejpam-6466	345	13	applying	apply	VERB
ejpam-6466	345	14	eqs	eqs	PROPN
ejpam-6466	345	15	.	.	PUNCT
ejpam-6466	346	1	(	(	PUNCT
ejpam-6466	346	2	7	7	NUM
ejpam-6466	346	3	)	)	PUNCT
ejpam-6466	346	4	and	and	CCONJ
ejpam-6466	346	5	(	(	PUNCT
ejpam-6466	346	6	8)	8)	NUM
ejpam-6466	346	7	,	,	PUNCT
ejpam-6466	346	8	we	we	PRON
ejpam-6466	346	9	obtain	obtain	VERB
ejpam-6466	346	10	the	the	DET
ejpam-6466	346	11	following	following	NOUN
ejpam-6466	346	12	:	:	PUNCT
ejpam-6466	346	13	e	e	X
ejpam-6466	346	14	(	(	PUNCT
ejpam-6466	346	15	∥gφ	∥gφ	X
ejpam-6466	346	16	(	(	PUNCT
ejpam-6466	346	17	x(τ))−gφ	x(τ))−gφ	PROPN
ejpam-6466	346	18	(	(	PUNCT
ejpam-6466	346	19	x̃(τ))∥2	x̃(τ))∥2	PROPN
ejpam-6466	346	20	)	)	PUNCT
ejpam-6466	347	1	≤2e	≤2e	PROPN
ejpam-6466	348	1	[	[	X
ejpam-6466	348	2	∥∥∥∥	∥∥∥∥	NUM
ejpam-6466	348	3	∫	∫	PROPN
ejpam-6466	348	4	τ	τ	PROPN
ejpam-6466	348	5	0	0	X
ejpam-6466	348	6	sξ−1	sξ−1	PROPN
ejpam-6466	348	7	(	(	PUNCT
ejpam-6466	348	8	v(s	v(s	PROPN
ejpam-6466	348	9	,	,	PUNCT
ejpam-6466	348	10	x(s	x(s	PROPN
ejpam-6466	348	11	)	)	PUNCT
ejpam-6466	348	12	,	,	PUNCT
ejpam-6466	348	13	x(s−m)−v(s	x(s−m)−v(s	PROPN
ejpam-6466	348	14	,	,	PUNCT
ejpam-6466	348	15	x̃(s	x̃(s	PROPN
ejpam-6466	348	16	)	)	PUNCT
ejpam-6466	348	17	,	,	PUNCT
ejpam-6466	348	18	x̃(s−m	x̃(s−m	NOUN
ejpam-6466	348	19	)	)	PUNCT
ejpam-6466	348	20	)	)	PUNCT
ejpam-6466	348	21	)	)	PUNCT
ejpam-6466	348	22	ds	ds	ADP
ejpam-6466	348	23	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-6466	348	24	]	]	X
ejpam-6466	348	25	+2e	+2e	PUNCT
ejpam-6466	349	1	[	[	X
ejpam-6466	349	2	∥∥∥∥	∥∥∥∥	NUM
ejpam-6466	349	3	∫	∫	PROPN
ejpam-6466	349	4	τ	τ	PROPN
ejpam-6466	349	5	0	0	X
ejpam-6466	349	6	sξ−1	sξ−1	PROPN
ejpam-6466	349	7	(	(	PUNCT
ejpam-6466	349	8	𭟋(s	𭟋(s	PROPN
ejpam-6466	349	9	,	,	PUNCT
ejpam-6466	349	10	x(s	x(s	PROPN
ejpam-6466	349	11	)	)	PUNCT
ejpam-6466	349	12	,	,	PUNCT
ejpam-6466	349	13	x(s−m)−𭟋(s	x(s−m)−𭟋(s	PROPN
ejpam-6466	349	14	,	,	PUNCT
ejpam-6466	349	15	x̃(s	x̃(s	PROPN
ejpam-6466	349	16	)	)	PUNCT
ejpam-6466	349	17	,	,	PUNCT
ejpam-6466	349	18	x̃(s−m	x̃(s−m	NOUN
ejpam-6466	349	19	)	)	PUNCT
ejpam-6466	349	20	)	)	PUNCT
ejpam-6466	349	21	)	)	PUNCT
ejpam-6466	350	1	dws	dws	PROPN
ejpam-6466	350	2	∥∥∥∥2	∥∥∥∥2	PROPN
ejpam-6466	350	3	]	]	X
ejpam-6466	350	4	.	.	PUNCT
ejpam-6466	351	1	(	(	PUNCT
ejpam-6466	351	2	22	22	NUM
ejpam-6466	351	3	)	)	PUNCT
ejpam-6466	351	4	now	now	ADV
ejpam-6466	351	5	we	we	PRON
ejpam-6466	351	6	will	will	AUX
ejpam-6466	351	7	simplify	simplify	VERB
ejpam-6466	351	8	eq	eq	ADP
ejpam-6466	351	9	.	.	PUNCT
ejpam-6466	352	1	(	(	PUNCT
ejpam-6466	352	2	22	22	NUM
ejpam-6466	352	3	)	)	PUNCT
ejpam-6466	352	4	in	in	ADP
ejpam-6466	352	5	two	two	NUM
ejpam-6466	352	6	parts	part	NOUN
ejpam-6466	352	7	.	.	PUNCT
ejpam-6466	353	1	the	the	PRON
ejpam-6466	353	2	höld	höld	PROPN
ejpam-6466	353	3	-	-	PUNCT
ejpam-6466	353	4	i	i	PRON
ejpam-6466	353	5	and	and	CCONJ
ejpam-6466	353	6	(	(	PUNCT
ejpam-6466	353	7	a3	a3	NOUN
ejpam-6466	353	8	)	)	PUNCT
ejpam-6466	353	9	gives	give	VERB
ejpam-6466	353	10	us	we	PRON
ejpam-6466	353	11	the	the	DET
ejpam-6466	353	12	result	result	NOUN
ejpam-6466	353	13	that	that	SCONJ
ejpam-6466	353	14	e	e	X
ejpam-6466	353	15	[	[	X
ejpam-6466	353	16	∥∥∥∥	∥∥∥∥	NUM
ejpam-6466	353	17	∫	∫	PROPN
ejpam-6466	353	18	τ	τ	PROPN
ejpam-6466	353	19	0	0	X
ejpam-6466	353	20	sξ−1	sξ−1	PROPN
ejpam-6466	353	21	(	(	PUNCT
ejpam-6466	353	22	v(s	v(s	PROPN
ejpam-6466	353	23	,	,	PUNCT
ejpam-6466	353	24	x(s	x(s	PROPN
ejpam-6466	353	25	)	)	PUNCT
ejpam-6466	353	26	,	,	PUNCT
ejpam-6466	353	27	x(s−m)−v(s	x(s−m)−v(s	PROPN
ejpam-6466	353	28	,	,	PUNCT
ejpam-6466	353	29	x̃(s	x̃(s	PROPN
ejpam-6466	353	30	)	)	PUNCT
ejpam-6466	353	31	,	,	PUNCT
ejpam-6466	353	32	x̃(s−m	x̃(s−m	NOUN
ejpam-6466	353	33	)	)	PUNCT
ejpam-6466	353	34	)	)	PUNCT
ejpam-6466	353	35	)	)	PUNCT
ejpam-6466	353	36	ds	ds	ADP
ejpam-6466	353	37	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-6466	353	38	]	]	PUNCT
ejpam-6466	353	39	≤	≤	NOUN
ejpam-6466	353	40	2ℏ	2ℏ	NUM
ejpam-6466	353	41	m.	m.	NOUN
ejpam-6466	353	42	i.	i.	PROPN
ejpam-6466	353	43	liaqat	liaqat	PROPN
ejpam-6466	353	44	et	et	PROPN
ejpam-6466	353	45	al	al	PROPN
ejpam-6466	353	46	.	.	PUNCT
ejpam-6466	353	47	/	/	SYM
ejpam-6466	353	48	eur	eur	PROPN
ejpam-6466	353	49	.	.	PUNCT
ejpam-6466	354	1	j.	j.	PROPN
ejpam-6466	354	2	pure	pure	PROPN
ejpam-6466	354	3	appl	appl	PROPN
ejpam-6466	354	4	.	.	PROPN
ejpam-6466	354	5	math	math	PROPN
ejpam-6466	354	6	,	,	PUNCT
ejpam-6466	354	7	18	18	NUM
ejpam-6466	354	8	(	(	PUNCT
ejpam-6466	354	9	4	4	NUM
ejpam-6466	354	10	)	)	PUNCT
ejpam-6466	354	11	(	(	PUNCT
ejpam-6466	354	12	2025	2025	NUM
ejpam-6466	354	13	)	)	PUNCT
ejpam-6466	354	14	,	,	PUNCT
ejpam-6466	354	15	6466	6466	NUM
ejpam-6466	354	16	14	14	NUM
ejpam-6466	354	17	of	of	ADP
ejpam-6466	354	18	28∫	28∫	NUM
ejpam-6466	354	19	τ	τ	X
ejpam-6466	354	20	0	0	NUM
ejpam-6466	354	21	s2ξ−2l2	s2ξ−2l2	PROPN
ejpam-6466	354	22	(	(	PUNCT
ejpam-6466	354	23	e	e	X
ejpam-6466	355	1	[	[	X
ejpam-6466	355	2	∥∥x(s)−	∥∥x(s)−	X
ejpam-6466	355	3	x̃(s	x̃(s	PROPN
ejpam-6466	355	4	)	)	PUNCT
ejpam-6466	355	5	∥∥2]+e	∥∥2]+e	PUNCT
ejpam-6466	355	6	[	[	PUNCT
ejpam-6466	355	7	∥x(s−m)−	∥x(s−m)−	NUM
ejpam-6466	355	8	x̃(s−m	x̃(s−m	NOUN
ejpam-6466	355	9	)	)	PUNCT
ejpam-6466	355	10	)	)	PUNCT
ejpam-6466	355	11	∥∥2])ds	∥∥2])ds	X
ejpam-6466	355	12	.	.	PUNCT
ejpam-6466	356	1	(	(	PUNCT
ejpam-6466	356	2	23	23	NUM
ejpam-6466	356	3	)	)	PUNCT
ejpam-6466	356	4	now	now	ADV
ejpam-6466	356	5	,	,	PUNCT
ejpam-6466	356	6	we	we	PRON
ejpam-6466	356	7	will	will	AUX
ejpam-6466	356	8	simplify	simplify	VERB
ejpam-6466	356	9	the	the	DET
ejpam-6466	356	10	following	following	ADJ
ejpam-6466	356	11	result	result	NOUN
ejpam-6466	356	12	:	:	PUNCT
ejpam-6466	356	13	for	for	ADP
ejpam-6466	356	14	this	this	PRON
ejpam-6466	356	15	,	,	PUNCT
ejpam-6466	356	16	use	use	VERB
ejpam-6466	356	17	i	i	PRON
ejpam-6466	356	18	-	-	PUNCT
ejpam-6466	356	19	is	be	AUX
ejpam-6466	356	20	and	and	CCONJ
ejpam-6466	356	21	(	(	PUNCT
ejpam-6466	356	22	a3	a3	NOUN
ejpam-6466	356	23	)	)	PUNCT
ejpam-6466	356	24	e	e	X
ejpam-6466	357	1	[	[	X
ejpam-6466	357	2	∥∥∥∥	∥∥∥∥	NUM
ejpam-6466	357	3	∫	∫	PROPN
ejpam-6466	357	4	τ	τ	PROPN
ejpam-6466	357	5	0	0	X
ejpam-6466	357	6	sξ−1	sξ−1	PROPN
ejpam-6466	357	7	(	(	PUNCT
ejpam-6466	357	8	𭟋(s	𭟋(s	PROPN
ejpam-6466	357	9	,	,	PUNCT
ejpam-6466	357	10	x(s	x(s	PROPN
ejpam-6466	357	11	)	)	PUNCT
ejpam-6466	357	12	,	,	PUNCT
ejpam-6466	357	13	x(s−m)−𭟋(s	x(s−m)−𭟋(s	PROPN
ejpam-6466	357	14	,	,	PUNCT
ejpam-6466	357	15	x̃(s	x̃(s	PROPN
ejpam-6466	357	16	)	)	PUNCT
ejpam-6466	357	17	,	,	PUNCT
ejpam-6466	357	18	x̃(s−m	x̃(s−m	NOUN
ejpam-6466	357	19	)	)	PUNCT
ejpam-6466	357	20	)	)	PUNCT
ejpam-6466	357	21	)	)	PUNCT
ejpam-6466	358	1	dws	dws	PROPN
ejpam-6466	358	2	∥∥∥∥2	∥∥∥∥2	PROPN
ejpam-6466	358	3	]	]	PUNCT
ejpam-6466	358	4	≤	≤	PROPN
ejpam-6466	358	5	2∫	2∫	NUM
ejpam-6466	358	6	τ	τ	X
ejpam-6466	358	7	0	0	NUM
ejpam-6466	358	8	s2ξ−2l2	s2ξ−2l2	PROPN
ejpam-6466	358	9	(	(	PUNCT
ejpam-6466	358	10	e	e	X
ejpam-6466	358	11	[	[	X
ejpam-6466	358	12	∥∥x(s)−	∥∥x(s)−	X
ejpam-6466	358	13	x̃(s	x̃(s	PROPN
ejpam-6466	358	14	)	)	PUNCT
ejpam-6466	358	15	∥∥2]+e	∥∥2]+e	PUNCT
ejpam-6466	359	1	[	[	PUNCT
ejpam-6466	359	2	∥x(s−m)−	∥x(s−m)−	NUM
ejpam-6466	359	3	x̃(s−m	x̃(s−m	NOUN
ejpam-6466	359	4	)	)	PUNCT
ejpam-6466	359	5	)	)	PUNCT
ejpam-6466	360	1	∥∥2])ds	∥∥2])ds	X
ejpam-6466	360	2	.	.	PUNCT
ejpam-6466	361	1	(	(	PUNCT
ejpam-6466	361	2	24	24	NUM
ejpam-6466	361	3	)	)	PUNCT
ejpam-6466	361	4	utilizing	utilize	VERB
ejpam-6466	361	5	eqs	eqs	PROPN
ejpam-6466	361	6	.	.	PUNCT
ejpam-6466	362	1	(	(	PUNCT
ejpam-6466	362	2	24	24	NUM
ejpam-6466	362	3	)	)	PUNCT
ejpam-6466	362	4	and	and	CCONJ
ejpam-6466	362	5	(	(	PUNCT
ejpam-6466	362	6	23	23	NUM
ejpam-6466	362	7	)	)	PUNCT
ejpam-6466	362	8	in	in	ADP
ejpam-6466	362	9	eq	eq	ADP
ejpam-6466	362	10	.	.	PUNCT
ejpam-6466	363	1	(	(	PUNCT
ejpam-6466	363	2	22	22	NUM
ejpam-6466	363	3	)	)	PUNCT
ejpam-6466	363	4	,	,	PUNCT
ejpam-6466	363	5	we	we	PRON
ejpam-6466	363	6	acquire	acquire	VERB
ejpam-6466	363	7	the	the	DET
ejpam-6466	363	8	subsequent	subsequent	ADJ
ejpam-6466	363	9	outcome	outcome	NOUN
ejpam-6466	363	10	.	.	PUNCT
ejpam-6466	364	1	e	e	X
ejpam-6466	364	2	(	(	PUNCT
ejpam-6466	364	3	∥gφ	∥gφ	X
ejpam-6466	364	4	(	(	PUNCT
ejpam-6466	364	5	x(τ))−gφ	x(τ))−gφ	PROPN
ejpam-6466	364	6	(	(	PUNCT
ejpam-6466	364	7	x̃(τ))∥2	x̃(τ))∥2	PROPN
ejpam-6466	364	8	)	)	PUNCT
ejpam-6466	364	9	≤2(τ	≤2(τ	PROPN
ejpam-6466	364	10	+	+	CCONJ
ejpam-6466	364	11	1	1	NUM
ejpam-6466	364	12	)	)	PUNCT
ejpam-6466	364	13	∫	∫	PROPN
ejpam-6466	365	1	τ	τ	PROPN
ejpam-6466	365	2	0	0	PROPN
ejpam-6466	365	3	s2ξ−2l2	s2ξ−2l2	PROPN
ejpam-6466	365	4	(	(	PUNCT
ejpam-6466	365	5	e∥x(s)−	e∥x(s)−	ADP
ejpam-6466	365	6	x̃(s)∥2	x̃(s)∥2	PROPN
ejpam-6466	365	7	+	+	PROPN
ejpam-6466	365	8	e∥x(s−m)−	e∥x(s−m)−	PROPN
ejpam-6466	365	9	x̃(s−m)∥2	x̃(s−m)∥2	X
ejpam-6466	365	10	)	)	PUNCT
ejpam-6466	365	11	ds	ds	PROPN
ejpam-6466	365	12	.	.	PUNCT
ejpam-6466	366	1	(	(	PUNCT
ejpam-6466	366	2	25	25	NUM
ejpam-6466	366	3	)	)	PUNCT
ejpam-6466	366	4	however	however	ADV
ejpam-6466	366	5	,	,	PUNCT
ejpam-6466	366	6	in	in	ADP
ejpam-6466	366	7	light	light	NOUN
ejpam-6466	366	8	of	of	ADP
ejpam-6466	366	9	lemma	lemma	PROPN
ejpam-6466	366	10	2	2	NUM
ejpam-6466	366	11	and	and	CCONJ
ejpam-6466	366	12	the	the	DET
ejpam-6466	366	13	monotone	monotone	NOUN
ejpam-6466	366	14	increasing	increasing	NOUN
ejpam-6466	366	15	of	of	ADP
ejpam-6466	366	16	function	function	NOUN
ejpam-6466	366	17	e2ξ−1	e2ξ−1	PROPN
ejpam-6466	366	18	on	on	ADP
ejpam-6466	366	19	r+	r+	NOUN
ejpam-6466	366	20	,	,	PUNCT
ejpam-6466	366	21	we	we	PRON
ejpam-6466	366	22	have	have	VERB
ejpam-6466	366	23	∀τ	∀τ	NOUN
ejpam-6466	366	24	∈	∈	PROPN
ejpam-6466	367	1	[	[	X
ejpam-6466	367	2	0	0	NUM
ejpam-6466	367	3	,	,	PUNCT
ejpam-6466	367	4	ℏ	ℏ	NOUN
ejpam-6466	367	5	]	]	PUNCT
ejpam-6466	367	6	.	.	PUNCT
ejpam-6466	368	1	e	e	X
ejpam-6466	368	2	(	(	PUNCT
ejpam-6466	368	3	∥gφ	∥gφ	X
ejpam-6466	368	4	(	(	PUNCT
ejpam-6466	368	5	x(τ))−gφ	x(τ))−gφ	PROPN
ejpam-6466	368	6	(	(	PUNCT
ejpam-6466	368	7	x̃(τ))∥2	x̃(τ))∥2	PROPN
ejpam-6466	368	8	)	)	PUNCT
ejpam-6466	368	9	e2ξ−1(ϑ(τ	e2ξ−1(ϑ(τ	NOUN
ejpam-6466	368	10	+	+	NOUN
ejpam-6466	368	11	m)2ξ−1	m)2ξ−1	X
ejpam-6466	368	12	)	)	PUNCT
ejpam-6466	368	13	≤γ(2ξ	≤γ(2ξ	ADV
ejpam-6466	368	14	−	−	NOUN
ejpam-6466	368	15	1	1	X
ejpam-6466	368	16	)	)	PUNCT
ejpam-6466	368	17	4l2(ℏ+	4l2(ℏ+	NUM
ejpam-6466	368	18	1	1	NUM
ejpam-6466	368	19	)	)	PUNCT
ejpam-6466	369	1	ϑ	ϑ	PROPN
ejpam-6466	369	2	sup	sup	NOUN
ejpam-6466	369	3	τ∈[0,ℏ	τ∈[0,ℏ	SYM
ejpam-6466	369	4	]	]	X
ejpam-6466	369	5	e	e	X
ejpam-6466	369	6	(	(	PUNCT
ejpam-6466	369	7	∥gφ	∥gφ	X
ejpam-6466	369	8	(	(	PUNCT
ejpam-6466	369	9	x(τ))−gφ	x(τ))−gφ	PROPN
ejpam-6466	369	10	(	(	PUNCT
ejpam-6466	369	11	x̃(τ))∥2	x̃(τ))∥2	PROPN
ejpam-6466	369	12	)	)	PUNCT
ejpam-6466	369	13	e2ξ−1(ϑ(τ	e2ξ−1(ϑ(τ	NOUN
ejpam-6466	369	14	+	+	NOUN
ejpam-6466	369	15	m)2ξ−1	m)2ξ−1	X
ejpam-6466	369	16	)	)	PUNCT
ejpam-6466	369	17	.	.	PUNCT
ejpam-6466	370	1	(	(	PUNCT
ejpam-6466	370	2	26	26	NUM
ejpam-6466	370	3	)	)	PUNCT
ejpam-6466	370	4	by	by	ADP
ejpam-6466	370	5	the	the	DET
ejpam-6466	370	6	definition	definition	NOUN
ejpam-6466	370	7	of	of	ADP
ejpam-6466	370	8	∥	∥	X
ejpam-6466	370	9	·	·	PUNCT
ejpam-6466	370	10	∥ϑ	∥ϑ	NOUN
ejpam-6466	370	11	in	in	ADP
ejpam-6466	370	12	eq	eq	ADP
ejpam-6466	370	13	.	.	PUNCT
ejpam-6466	370	14	(	(	PUNCT
ejpam-6466	370	15	21	21	NUM
ejpam-6466	370	16	)	)	PUNCT
ejpam-6466	370	17	,	,	PUNCT
ejpam-6466	370	18	consequently	consequently	ADV
ejpam-6466	370	19	∥gφ	∥gφ	PROPN
ejpam-6466	370	20	(	(	PUNCT
ejpam-6466	370	21	x(τ))−gφ	x(τ))−gφ	PROPN
ejpam-6466	370	22	(	(	PUNCT
ejpam-6466	370	23	x̃(τ))∥ϑ	x̃(τ))∥ϑ	PROPN
ejpam-6466	370	24	≤	≤	ADV
ejpam-6466	370	25	y∥x(τ)−	y∥x(τ)−	PROPN
ejpam-6466	370	26	x̃(τ)∥	x̃(τ)∥	PROPN
ejpam-6466	370	27	,	,	PUNCT
ejpam-6466	370	28	(	(	PUNCT
ejpam-6466	370	29	27	27	NUM
ejpam-6466	370	30	)	)	PUNCT
ejpam-6466	370	31	where	where	SCONJ
ejpam-6466	370	32	y	y	NOUN
ejpam-6466	370	33	=	=	PUNCT
ejpam-6466	370	34	(	(	PUNCT
ejpam-6466	370	35	γ(2ξ	γ(2ξ	X
ejpam-6466	370	36	−	−	PROPN
ejpam-6466	370	37	1)4l	1)4l	NUM
ejpam-6466	370	38	2(ℏ+1	2(ℏ+1	NUM
ejpam-6466	370	39	)	)	PUNCT
ejpam-6466	370	40	ϑ	ϑ	NOUN
ejpam-6466	370	41	)	)	PUNCT
ejpam-6466	370	42	1	1	NUM
ejpam-6466	370	43	2	2	NUM
ejpam-6466	370	44	.	.	PUNCT
ejpam-6466	371	1	in	in	ADP
ejpam-6466	371	2	light	light	NOUN
ejpam-6466	371	3	of	of	ADP
ejpam-6466	371	4	eq	eq	PROPN
ejpam-6466	371	5	.	.	PUNCT
ejpam-6466	372	1	(	(	PUNCT
ejpam-6466	372	2	20	20	NUM
ejpam-6466	372	3	)	)	PUNCT
ejpam-6466	372	4	,	,	PUNCT
ejpam-6466	372	5	we	we	PRON
ejpam-6466	372	6	derive	derive	VERB
ejpam-6466	372	7	y	y	PRON
ejpam-6466	372	8	<	<	X
ejpam-6466	372	9	1	1	NUM
ejpam-6466	372	10	and	and	CCONJ
ejpam-6466	372	11	therefore	therefore	ADV
ejpam-6466	372	12	the	the	DET
ejpam-6466	372	13	operator	operator	NOUN
ejpam-6466	372	14	gφ	gφ	NOUN
ejpam-6466	372	15	is	be	AUX
ejpam-6466	372	16	a	a	DET
ejpam-6466	372	17	contractive	contractive	ADJ
ejpam-6466	372	18	map	map	NOUN
ejpam-6466	372	19	on	on	ADP
ejpam-6466	372	20	(	(	PUNCT
ejpam-6466	372	21	h̃2[0	h̃2[0	NOUN
ejpam-6466	372	22	,	,	PUNCT
ejpam-6466	372	23	ℏ	ℏ	PROPN
ejpam-6466	372	24	]	]	X
ejpam-6466	372	25	,	,	PUNCT
ejpam-6466	372	26	∥	∥	X
ejpam-6466	372	27	·	·	PUNCT
ejpam-6466	372	28	∥ϑ	∥ϑ	NOUN
ejpam-6466	372	29	)	)	PUNCT
ejpam-6466	372	30	.	.	PUNCT
ejpam-6466	373	1	in	in	ADP
ejpam-6466	373	2	accordance	accordance	NOUN
ejpam-6466	373	3	with	with	ADP
ejpam-6466	373	4	the	the	DET
ejpam-6466	373	5	banach	banach	ADV
ejpam-6466	373	6	fixed	fix	VERB
ejpam-6466	373	7	point	point	NOUN
ejpam-6466	373	8	theorem	theorem	VERB
ejpam-6466	373	9	,	,	PUNCT
ejpam-6466	373	10	there	there	PRON
ejpam-6466	373	11	is	be	VERB
ejpam-6466	373	12	only	only	ADV
ejpam-6466	373	13	one	one	NUM
ejpam-6466	373	14	fixed	fix	VERB
ejpam-6466	373	15	point	point	NOUN
ejpam-6466	373	16	x(τ	x(τ	PROPN
ejpam-6466	373	17	)	)	PUNCT
ejpam-6466	373	18	on	on	ADP
ejpam-6466	373	19	this	this	DET
ejpam-6466	373	20	map	map	NOUN
ejpam-6466	373	21	in	in	ADP
ejpam-6466	373	22	(	(	PUNCT
ejpam-6466	373	23	h̃2[0	h̃2[0	NOUN
ejpam-6466	373	24	,	,	PUNCT
ejpam-6466	373	25	ℏ	ℏ	PROPN
ejpam-6466	373	26	]	]	X
ejpam-6466	373	27	,	,	PUNCT
ejpam-6466	373	28	∥	∥	X
ejpam-6466	373	29	·	·	PUNCT
ejpam-6466	373	30	∥ϑ	∥ϑ	NOUN
ejpam-6466	373	31	)	)	PUNCT
ejpam-6466	373	32	.	.	PUNCT
ejpam-6466	374	1	additionally	additionally	ADV
ejpam-6466	374	2	,	,	PUNCT
ejpam-6466	374	3	this	this	DET
ejpam-6466	374	4	fixed	fix	VERB
ejpam-6466	374	5	point	point	NOUN
ejpam-6466	374	6	is	be	AUX
ejpam-6466	374	7	the	the	DET
ejpam-6466	374	8	sole	sole	ADJ
ejpam-6466	374	9	solution	solution	NOUN
ejpam-6466	374	10	to	to	ADP
ejpam-6466	374	11	eq	eq	PROPN
ejpam-6466	374	12	.	.	PUNCT
ejpam-6466	375	1	(	(	PUNCT
ejpam-6466	375	2	4	4	NUM
ejpam-6466	375	3	)	)	PUNCT
ejpam-6466	375	4	with	with	ADP
ejpam-6466	375	5	the	the	DET
ejpam-6466	375	6	initial	initial	ADJ
ejpam-6466	375	7	value	value	NOUN
ejpam-6466	375	8	x(0	x(0	PROPN
ejpam-6466	375	9	)	)	PUNCT
ejpam-6466	376	1	=	=	PUNCT
ejpam-6466	376	2	φ	φ	PROPN
ejpam-6466	376	3	.	.	PUNCT
ejpam-6466	377	1	therefore	therefore	ADV
ejpam-6466	377	2	,	,	PUNCT
ejpam-6466	377	3	we	we	PRON
ejpam-6466	377	4	proved	prove	VERB
ejpam-6466	377	5	the	the	DET
ejpam-6466	377	6	required	require	VERB
ejpam-6466	377	7	result	result	NOUN
ejpam-6466	377	8	.	.	PUNCT
ejpam-6466	378	1	in	in	ADP
ejpam-6466	378	2	the	the	DET
ejpam-6466	378	3	subsequent	subsequent	ADJ
ejpam-6466	378	4	theorem	theorem	NOUN
ejpam-6466	378	5	,	,	PUNCT
ejpam-6466	378	6	we	we	PRON
ejpam-6466	378	7	establish	establish	VERB
ejpam-6466	378	8	the	the	DET
ejpam-6466	378	9	eu	eu	PROPN
ejpam-6466	378	10	according	accord	VERB
ejpam-6466	378	11	to	to	ADP
ejpam-6466	378	12	the	the	DET
ejpam-6466	378	13	llc	llc	NOUN
ejpam-6466	378	14	of	of	ADP
ejpam-6466	378	15	coefficients	coefficient	NOUN
ejpam-6466	378	16	by	by	ADP
ejpam-6466	378	17	employing	employ	VERB
ejpam-6466	378	18	a	a	DET
ejpam-6466	378	19	truncation	truncation	NOUN
ejpam-6466	378	20	method	method	NOUN
ejpam-6466	378	21	.	.	PUNCT
ejpam-6466	379	1	theorem	theorem	NOUN
ejpam-6466	379	2	2	2	NUM
ejpam-6466	379	3	.	.	PUNCT
ejpam-6466	379	4	suppose	suppose	VERB
ejpam-6466	379	5	that	that	SCONJ
ejpam-6466	379	6	(	(	PUNCT
ejpam-6466	379	7	a1	a1	NOUN
ejpam-6466	379	8	)	)	PUNCT
ejpam-6466	379	9	and	and	CCONJ
ejpam-6466	379	10	(	(	PUNCT
ejpam-6466	379	11	a2	a2	PROPN
ejpam-6466	379	12	)	)	PUNCT
ejpam-6466	379	13	are	be	AUX
ejpam-6466	379	14	valid	valid	ADJ
ejpam-6466	379	15	.	.	PUNCT
ejpam-6466	380	1	then	then	ADV
ejpam-6466	380	2	,	,	PUNCT
ejpam-6466	380	3	the	the	DET
ejpam-6466	380	4	problem	problem	NOUN
ejpam-6466	380	5	eq	eq	ADJ
ejpam-6466	380	6	.	.	PUNCT
ejpam-6466	381	1	(	(	PUNCT
ejpam-6466	381	2	4	4	X
ejpam-6466	381	3	)	)	PUNCT
ejpam-6466	381	4	involving	involve	VERB
ejpam-6466	381	5	the	the	DET
ejpam-6466	381	6	initial	initial	ADJ
ejpam-6466	381	7	value	value	NOUN
ejpam-6466	381	8	x(0	x(0	PROPN
ejpam-6466	381	9	)	)	PUNCT
ejpam-6466	382	1	=	=	PUNCT
ejpam-6466	382	2	φ	φ	PROPN
ejpam-6466	382	3	has	have	VERB
ejpam-6466	382	4	a	a	DET
ejpam-6466	382	5	unique	unique	ADJ
ejpam-6466	382	6	solution	solution	NOUN
ejpam-6466	382	7	on	on	ADP
ejpam-6466	382	8	[	[	X
ejpam-6466	382	9	−m	−m	NOUN
ejpam-6466	382	10	,	,	PUNCT
ejpam-6466	382	11	ℏ	ℏ	X
ejpam-6466	382	12	]	]	PUNCT
ejpam-6466	382	13	for	for	ADP
ejpam-6466	382	14	any	any	DET
ejpam-6466	382	15	φ	φ	PROPN
ejpam-6466	382	16	∈	∈	PROPN
ejpam-6466	382	17	c̃([−m	c̃([−m	NOUN
ejpam-6466	382	18	,	,	PUNCT
ejpam-6466	382	19	0],rr	0],rr	PROPN
ejpam-6466	382	20	)	)	PUNCT
ejpam-6466	382	21	.	.	PUNCT
ejpam-6466	383	1	proof	proof	NOUN
ejpam-6466	383	2	.	.	PUNCT
ejpam-6466	384	1	step	step	NOUN
ejpam-6466	384	2	1	1	NUM
ejpam-6466	384	3	:	:	PUNCT
ejpam-6466	384	4	existence	existence	NOUN
ejpam-6466	384	5	:	:	PUNCT
ejpam-6466	384	6	we	we	PRON
ejpam-6466	384	7	define	define	VERB
ejpam-6466	384	8	the	the	DET
ejpam-6466	384	9	truncation	truncation	NOUN
ejpam-6466	384	10	functions	function	NOUN
ejpam-6466	384	11	vυ	vυ	ADJ
ejpam-6466	384	12	and	and	CCONJ
ejpam-6466	384	13	𭟋υ	𭟋υ	PRON
ejpam-6466	384	14	for	for	ADP
ejpam-6466	384	15	each	each	DET
ejpam-6466	384	16	υ	υ	NOUN
ejpam-6466	384	17	≤	≤	ADV
ejpam-6466	384	18	1	1	NUM
ejpam-6466	384	19	.	.	PUNCT
ejpam-6466	385	1	vυ	vυ	PROPN
ejpam-6466	385	2	(	(	PUNCT
ejpam-6466	385	3	s	s	PROPN
ejpam-6466	385	4	,	,	PUNCT
ejpam-6466	385	5	x(s	x(s	PROPN
ejpam-6466	385	6	)	)	PUNCT
ejpam-6466	385	7	,	,	PUNCT
ejpam-6466	385	8	x(s−m	x(s−m	NUM
ejpam-6466	385	9	)	)	PUNCT
ejpam-6466	385	10	)	)	PUNCT
ejpam-6466	386	1	=	=	PUNCT
ejpam-6466	387	1			PRON
ejpam-6466	387	2	v	v	X
ejpam-6466	387	3	(	(	PUNCT
ejpam-6466	387	4	s	s	PROPN
ejpam-6466	387	5	,	,	PUNCT
ejpam-6466	387	6	x(s	x(s	PROPN
ejpam-6466	387	7	)	)	PUNCT
ejpam-6466	387	8	,	,	PUNCT
ejpam-6466	387	9	x(s−m	x(s−m	NUM
ejpam-6466	387	10	)	)	PUNCT
ejpam-6466	387	11	)	)	PUNCT
ejpam-6466	387	12	,	,	PUNCT
ejpam-6466	387	13	if	if	SCONJ
ejpam-6466	387	14	∥xτ∥	∥xτ∥	NOUN
ejpam-6466	387	15	≤	≤	NUM
ejpam-6466	387	16	υ	υ	PROPN
ejpam-6466	387	17	,	,	PUNCT
ejpam-6466	387	18	v	v	PROPN
ejpam-6466	387	19	(	(	PUNCT
ejpam-6466	387	20	s	s	PROPN
ejpam-6466	387	21	,	,	PUNCT
ejpam-6466	387	22	υx(s	υx(s	NUM
ejpam-6466	387	23	)	)	PUNCT
ejpam-6466	387	24	∥x(τ)∥	∥x(τ)∥	NOUN
ejpam-6466	387	25	,	,	PUNCT
ejpam-6466	387	26	υx(s−m	υx(s−m	PROPN
ejpam-6466	387	27	)	)	PUNCT
ejpam-6466	387	28	∥x(τ	∥x(τ	ADJ
ejpam-6466	387	29	−m)∥	−m)∥	NOUN
ejpam-6466	387	30	)	)	PUNCT
ejpam-6466	387	31	,	,	PUNCT
ejpam-6466	387	32	if	if	SCONJ
ejpam-6466	387	33	∥xτ∥	∥xτ∥	NOUN
ejpam-6466	387	34	>	>	X
ejpam-6466	387	35	υ	υ	PROPN
ejpam-6466	387	36	.	.	PROPN
ejpam-6466	387	37	m.	m.	PROPN
ejpam-6466	387	38	i.	i.	PROPN
ejpam-6466	387	39	liaqat	liaqat	PROPN
ejpam-6466	387	40	et	et	PROPN
ejpam-6466	387	41	al	al	PROPN
ejpam-6466	387	42	.	.	PUNCT
ejpam-6466	387	43	/	/	SYM
ejpam-6466	387	44	eur	eur	PROPN
ejpam-6466	387	45	.	.	PUNCT
ejpam-6466	388	1	j.	j.	PROPN
ejpam-6466	388	2	pure	pure	PROPN
ejpam-6466	388	3	appl	appl	PROPN
ejpam-6466	388	4	.	.	PROPN
ejpam-6466	388	5	math	math	PROPN
ejpam-6466	388	6	,	,	PUNCT
ejpam-6466	388	7	18	18	NUM
ejpam-6466	388	8	(	(	PUNCT
ejpam-6466	388	9	4	4	NUM
ejpam-6466	388	10	)	)	PUNCT
ejpam-6466	388	11	(	(	PUNCT
ejpam-6466	388	12	2025	2025	NUM
ejpam-6466	388	13	)	)	PUNCT
ejpam-6466	388	14	,	,	PUNCT
ejpam-6466	388	15	6466	6466	NUM
ejpam-6466	388	16	15	15	NUM
ejpam-6466	388	17	of	of	ADP
ejpam-6466	388	18	28	28	NUM
ejpam-6466	388	19	𭟋υ	𭟋υ	PART
ejpam-6466	388	20	(	(	PUNCT
ejpam-6466	388	21	s	s	PROPN
ejpam-6466	388	22	,	,	PUNCT
ejpam-6466	388	23	x(s	x(s	PROPN
ejpam-6466	388	24	)	)	PUNCT
ejpam-6466	388	25	,	,	PUNCT
ejpam-6466	388	26	x(s−m	x(s−m	NUM
ejpam-6466	388	27	)	)	PUNCT
ejpam-6466	388	28	)	)	PUNCT
ejpam-6466	389	1	=	=	PUNCT
ejpam-6466	390	1			PRON
ejpam-6466	390	2	𭟋	𭟋	PROPN
ejpam-6466	390	3	(	(	PUNCT
ejpam-6466	390	4	s	s	PROPN
ejpam-6466	390	5	,	,	PUNCT
ejpam-6466	390	6	x(s	x(s	PROPN
ejpam-6466	390	7	)	)	PUNCT
ejpam-6466	390	8	,	,	PUNCT
ejpam-6466	390	9	x(s−m	x(s−m	NUM
ejpam-6466	390	10	)	)	PUNCT
ejpam-6466	390	11	)	)	PUNCT
ejpam-6466	390	12	,	,	PUNCT
ejpam-6466	390	13	if	if	SCONJ
ejpam-6466	390	14	∥xτ∥	∥xτ∥	NOUN
ejpam-6466	390	15	≤	≤	NUM
ejpam-6466	390	16	υ	υ	PROPN
ejpam-6466	390	17	,	,	PUNCT
ejpam-6466	390	18	𭟋	𭟋	X
ejpam-6466	390	19	(	(	PUNCT
ejpam-6466	390	20	s	s	PROPN
ejpam-6466	390	21	,	,	PUNCT
ejpam-6466	390	22	υx(s	υx(s	NUM
ejpam-6466	390	23	)	)	PUNCT
ejpam-6466	390	24	∥x(τ)∥	∥x(τ)∥	NOUN
ejpam-6466	390	25	,	,	PUNCT
ejpam-6466	390	26	υx(s−m	υx(s−m	PROPN
ejpam-6466	390	27	)	)	PUNCT
ejpam-6466	390	28	∥x(τ	∥x(τ	ADJ
ejpam-6466	390	29	−m)∥	−m)∥	NOUN
ejpam-6466	390	30	)	)	PUNCT
ejpam-6466	390	31	,	,	PUNCT
ejpam-6466	390	32	if	if	SCONJ
ejpam-6466	390	33	∥xτ∥	∥xτ∥	NOUN
ejpam-6466	390	34	>	>	X
ejpam-6466	390	35	υ	υ	X
ejpam-6466	390	36	.	.	PUNCT
ejpam-6466	390	37	notice	notice	VERB
ejpam-6466	390	38	that	that	SCONJ
ejpam-6466	390	39	xτ	xτ	PRON
ejpam-6466	390	40	=	=	PRON
ejpam-6466	390	41	{	{	PUNCT
ejpam-6466	390	42	x(τ	x(τ	PROPN
ejpam-6466	390	43	+	+	NUM
ejpam-6466	390	44	δ),−m	δ),−m	NOUN
ejpam-6466	390	45	≤	≤	NUM
ejpam-6466	390	46	δ	δ	PROPN
ejpam-6466	390	47	≤	≤	ADV
ejpam-6466	390	48	0	0	NUM
ejpam-6466	390	49	}	}	PUNCT
ejpam-6466	390	50	and	and	CCONJ
ejpam-6466	390	51	τ	τ	PROPN
ejpam-6466	390	52	∈	∈	PROPN
ejpam-6466	391	1	[	[	X
ejpam-6466	391	2	0	0	NUM
ejpam-6466	391	3	,	,	PUNCT
ejpam-6466	391	4	ℏ	ℏ	NOUN
ejpam-6466	391	5	]	]	PUNCT
ejpam-6466	391	6	.	.	PUNCT
ejpam-6466	392	1	then	then	ADV
ejpam-6466	392	2	,	,	PUNCT
ejpam-6466	392	3	vυ	vυ	ADV
ejpam-6466	392	4	and	and	CCONJ
ejpam-6466	392	5	𭟋υ	𭟋υ	PRON
ejpam-6466	392	6	satisfy	satisfy	VERB
ejpam-6466	392	7	the	the	DET
ejpam-6466	392	8	glc	glc	PROPN
ejpam-6466	392	9	(	(	PUNCT
ejpam-6466	392	10	a3	a3	PROPN
ejpam-6466	392	11	)	)	PUNCT
ejpam-6466	392	12	and	and	CCONJ
ejpam-6466	392	13	(	(	PUNCT
ejpam-6466	392	14	a2	a2	PROPN
ejpam-6466	392	15	)	)	PUNCT
ejpam-6466	392	16	and	and	CCONJ
ejpam-6466	392	17	by	by	ADP
ejpam-6466	392	18	lemma	lemma	PROPN
ejpam-6466	392	19	2	2	NUM
ejpam-6466	392	20	,	,	PUNCT
ejpam-6466	392	21	there	there	PRON
ejpam-6466	392	22	is	be	VERB
ejpam-6466	392	23	a	a	DET
ejpam-6466	392	24	unique	unique	ADJ
ejpam-6466	392	25	solution	solution	NOUN
ejpam-6466	392	26	xυ(τ	xυ(τ	PUNCT
ejpam-6466	392	27	)	)	PUNCT
ejpam-6466	392	28	to	to	ADP
ejpam-6466	392	29	the	the	DET
ejpam-6466	392	30	following	following	NOUN
ejpam-6466	392	31	:	:	PUNCT
ejpam-6466	392	32	xυ(τ	xυ(τ	X
ejpam-6466	392	33	)	)	PUNCT
ejpam-6466	393	1	=	=	SYM
ejpam-6466	393	2	φ	φ	PROPN
ejpam-6466	393	3	+	+	CCONJ
ejpam-6466	393	4	∫	∫	PROPN
ejpam-6466	393	5	τ	τ	PROPN
ejpam-6466	393	6	0	0	NUM
ejpam-6466	393	7	sξ−1vυ	sξ−1vυ	NUM
ejpam-6466	393	8	(	(	PUNCT
ejpam-6466	393	9	s	s	PROPN
ejpam-6466	393	10	,	,	PUNCT
ejpam-6466	393	11	xυ(s	xυ(s	NUM
ejpam-6466	393	12	)	)	PUNCT
ejpam-6466	393	13	,	,	PUNCT
ejpam-6466	393	14	xυ(s−m	xυ(s−m	PROPN
ejpam-6466	393	15	)	)	PUNCT
ejpam-6466	393	16	)	)	PUNCT
ejpam-6466	394	1	ds	ds	PROPN
ejpam-6466	395	1	+	+	CCONJ
ejpam-6466	395	2	∫	∫	PROPN
ejpam-6466	395	3	τ	τ	X
ejpam-6466	395	4	0	0	NUM
ejpam-6466	395	5	sξ−1𭟋	sξ−1𭟋	X
ejpam-6466	395	6	(	(	PUNCT
ejpam-6466	395	7	s	s	PROPN
ejpam-6466	395	8	,	,	PUNCT
ejpam-6466	395	9	xυ(s	xυ(s	NUM
ejpam-6466	395	10	)	)	PUNCT
ejpam-6466	395	11	,	,	PUNCT
ejpam-6466	395	12	xυ(s−m	xυ(s−m	PROPN
ejpam-6466	395	13	)	)	PUNCT
ejpam-6466	395	14	)	)	PUNCT
ejpam-6466	396	1	dws	dws	PROPN
ejpam-6466	396	2	.	.	PUNCT
ejpam-6466	397	1	(	(	PUNCT
ejpam-6466	397	2	28	28	NUM
ejpam-6466	397	3	)	)	PUNCT
ejpam-6466	397	4	define	define	VERB
ejpam-6466	397	5	the	the	DET
ejpam-6466	397	6	stopping	stopping	NOUN
ejpam-6466	397	7	time	time	NOUN
ejpam-6466	397	8	λυ	λυ	ADP
ejpam-6466	397	9	=	=	SYM
ejpam-6466	397	10	ℏ	ℏ	PROPN
ejpam-6466	397	11	∧	∧	NOUN
ejpam-6466	397	12	inf{τ	inf{τ	PROPN
ejpam-6466	397	13	∈	∈	PROPN
ejpam-6466	398	1	[	[	X
ejpam-6466	398	2	0	0	NUM
ejpam-6466	398	3	,	,	PUNCT
ejpam-6466	398	4	ℏ	ℏ	PROPN
ejpam-6466	398	5	:	:	PUNCT
ejpam-6466	398	6	∥xυτ∥	∥xυτ∥	X
ejpam-6466	398	7	≥	≥	VERB
ejpam-6466	398	8	υ	υ	X
ejpam-6466	398	9	]	]	X
ejpam-6466	398	10	}	}	PUNCT
ejpam-6466	398	11	.	.	PUNCT
ejpam-6466	399	1	now	now	ADV
ejpam-6466	399	2	,	,	PUNCT
ejpam-6466	399	3	we	we	PRON
ejpam-6466	399	4	shall	shall	AUX
ejpam-6466	399	5	prove	prove	VERB
ejpam-6466	399	6	xυ(τ	xυ(τ	PUNCT
ejpam-6466	399	7	)	)	PUNCT
ejpam-6466	400	1	=	=	SYM
ejpam-6466	400	2	xυ+1(τ	xυ+1(τ	PROPN
ejpam-6466	400	3	)	)	PUNCT
ejpam-6466	400	4	,	,	PUNCT
ejpam-6466	400	5	∀τ	∀τ	PROPN
ejpam-6466	400	6	∈	∈	PROPN
ejpam-6466	401	1	[	[	X
ejpam-6466	401	2	0	0	NUM
ejpam-6466	401	3	,	,	PUNCT
ejpam-6466	401	4	λυ	λυ	ADP
ejpam-6466	401	5	]	]	PUNCT
ejpam-6466	401	6	.	.	PUNCT
ejpam-6466	402	1	(	(	PUNCT
ejpam-6466	402	2	29	29	NUM
ejpam-6466	402	3	)	)	PUNCT
ejpam-6466	402	4	by	by	ADP
ejpam-6466	402	5	eq	eq	PROPN
ejpam-6466	402	6	.	.	PUNCT
ejpam-6466	403	1	(	(	PUNCT
ejpam-6466	403	2	28	28	NUM
ejpam-6466	403	3	)	)	PUNCT
ejpam-6466	403	4	and	and	CCONJ
ejpam-6466	403	5	using	use	VERB
ejpam-6466	403	6	the	the	DET
ejpam-6466	403	7	höld	höld	NOUN
ejpam-6466	403	8	-	-	PUNCT
ejpam-6466	403	9	i	i	PROPN
ejpam-6466	403	10	and	and	CCONJ
ejpam-6466	403	11	i	i	PRON
ejpam-6466	403	12	-	-	PUNCT
ejpam-6466	403	13	is	be	AUX
ejpam-6466	403	14	,	,	PUNCT
ejpam-6466	403	15	we	we	PRON
ejpam-6466	403	16	obtain	obtain	VERB
ejpam-6466	403	17	e	e	NOUN
ejpam-6466	404	1	[	[	X
ejpam-6466	404	2	∥∥xυ+1(τ)−	∥∥xυ+1(τ)−	ADJ
ejpam-6466	404	3	xυ(τ	xυ(τ	NUM
ejpam-6466	404	4	)	)	PUNCT
ejpam-6466	404	5	∥∥2	∥∥2	NUM
ejpam-6466	404	6	]	]	PUNCT
ejpam-6466	405	1	≤4τe	≤4τe	PROPN
ejpam-6466	405	2	∫	∫	PROPN
ejpam-6466	405	3	τ	τ	PROPN
ejpam-6466	405	4	0	0	NUM
ejpam-6466	405	5	s2ξ−2	s2ξ−2	PROPN
ejpam-6466	405	6	∥∥vυ+1	∥∥vυ+1	PROPN
ejpam-6466	405	7	(	(	PUNCT
ejpam-6466	405	8	s	s	PROPN
ejpam-6466	405	9	,	,	PUNCT
ejpam-6466	405	10	xυ+1(s	xυ+1(s	ADJ
ejpam-6466	405	11	)	)	PUNCT
ejpam-6466	405	12	,	,	PUNCT
ejpam-6466	405	13	xυ+1(s−m)−vυ+1	xυ+1(s−m)−vυ+1	PROPN
ejpam-6466	405	14	(	(	PUNCT
ejpam-6466	405	15	s	s	PROPN
ejpam-6466	405	16	,	,	PUNCT
ejpam-6466	405	17	xυ(s	xυ(s	NUM
ejpam-6466	405	18	)	)	PUNCT
ejpam-6466	405	19	,	,	PUNCT
ejpam-6466	405	20	xυ(s−m	xυ(s−m	PROPN
ejpam-6466	405	21	)	)	PUNCT
ejpam-6466	405	22	)	)	PUNCT
ejpam-6466	405	23	∥∥2ds	∥∥2ds	NOUN
ejpam-6466	406	1	+4τe	+4τe	PROPN
ejpam-6466	406	2	∫	∫	PROPN
ejpam-6466	406	3	τ	τ	X
ejpam-6466	406	4	0	0	NUM
ejpam-6466	406	5	s2ξ−2	s2ξ−2	PROPN
ejpam-6466	406	6	∥∥vυ+1	∥∥vυ+1	PROPN
ejpam-6466	406	7	(	(	PUNCT
ejpam-6466	406	8	s	s	PROPN
ejpam-6466	406	9	,	,	PUNCT
ejpam-6466	406	10	xυ+1(s	xυ+1(s	PROPN
ejpam-6466	406	11	)	)	PUNCT
ejpam-6466	406	12	,	,	PUNCT
ejpam-6466	406	13	xυ+1(s−m)−vυ	xυ+1(s−m)−vυ	PROPN
ejpam-6466	406	14	(	(	PUNCT
ejpam-6466	406	15	s	s	PROPN
ejpam-6466	406	16	,	,	PUNCT
ejpam-6466	406	17	xυ(s	xυ(s	NUM
ejpam-6466	406	18	)	)	PUNCT
ejpam-6466	406	19	,	,	PUNCT
ejpam-6466	406	20	xυ(s−m	xυ(s−m	PROPN
ejpam-6466	406	21	)	)	PUNCT
ejpam-6466	406	22	)	)	PUNCT
ejpam-6466	406	23	∥∥2ds	∥∥2ds	NOUN
ejpam-6466	407	1	+4τe	+4τe	PROPN
ejpam-6466	407	2	∫	∫	PROPN
ejpam-6466	407	3	τ	τ	X
ejpam-6466	407	4	0	0	NUM
ejpam-6466	407	5	s2ξ−2	s2ξ−2	PROPN
ejpam-6466	407	6	∥∥𭟋υ+1	∥∥𭟋υ+1	PROPN
ejpam-6466	407	7	(	(	PUNCT
ejpam-6466	407	8	s	s	PROPN
ejpam-6466	407	9	,	,	PUNCT
ejpam-6466	407	10	xυ+1(s	xυ+1(s	ADJ
ejpam-6466	407	11	)	)	PUNCT
ejpam-6466	407	12	,	,	PUNCT
ejpam-6466	407	13	xυ+1(s−m)−𭟋υ+1	xυ+1(s−m)−𭟋υ+1	PROPN
ejpam-6466	407	14	(	(	PUNCT
ejpam-6466	407	15	s	s	PROPN
ejpam-6466	407	16	,	,	PUNCT
ejpam-6466	407	17	xυ(s	xυ(s	NUM
ejpam-6466	407	18	)	)	PUNCT
ejpam-6466	407	19	,	,	PUNCT
ejpam-6466	407	20	xυ(s−m	xυ(s−m	PROPN
ejpam-6466	407	21	)	)	PUNCT
ejpam-6466	407	22	)	)	PUNCT
ejpam-6466	407	23	∥∥2ds	∥∥2ds	NOUN
ejpam-6466	408	1	+4τe	+4τe	PROPN
ejpam-6466	408	2	∫	∫	PROPN
ejpam-6466	408	3	τ	τ	X
ejpam-6466	408	4	0	0	NUM
ejpam-6466	408	5	s2ξ−2	s2ξ−2	PROPN
ejpam-6466	408	6	∥∥𭟋υ+1	∥∥𭟋υ+1	PROPN
ejpam-6466	408	7	(	(	PUNCT
ejpam-6466	408	8	s	s	PROPN
ejpam-6466	408	9	,	,	PUNCT
ejpam-6466	408	10	xυ+1(s	xυ+1(s	PROPN
ejpam-6466	408	11	)	)	PUNCT
ejpam-6466	408	12	,	,	PUNCT
ejpam-6466	408	13	xυ+1(s−m)−𭟋υ	xυ+1(s−m)−𭟋υ	PROPN
ejpam-6466	408	14	(	(	PUNCT
ejpam-6466	408	15	s	s	PROPN
ejpam-6466	408	16	,	,	PUNCT
ejpam-6466	408	17	xυ(s	xυ(s	NUM
ejpam-6466	408	18	)	)	PUNCT
ejpam-6466	408	19	,	,	PUNCT
ejpam-6466	408	20	xυ(s−m	xυ(s−m	PROPN
ejpam-6466	408	21	)	)	PUNCT
ejpam-6466	408	22	)	)	PUNCT
ejpam-6466	408	23	∥∥2ds	∥∥2ds	NUM
ejpam-6466	408	24	.	.	PUNCT
ejpam-6466	409	1	(	(	PUNCT
ejpam-6466	409	2	30	30	NUM
ejpam-6466	409	3	)	)	PUNCT
ejpam-6466	409	4	from	from	ADP
ejpam-6466	409	5	(	(	PUNCT
ejpam-6466	409	6	a1	a1	NOUN
ejpam-6466	409	7	)	)	PUNCT
ejpam-6466	409	8	and	and	CCONJ
ejpam-6466	409	9	noting	note	VERB
ejpam-6466	409	10	that	that	SCONJ
ejpam-6466	409	11	xυ+1(s	xυ+1(s	PROPN
ejpam-6466	409	12	)	)	PUNCT
ejpam-6466	409	13	=	=	SYM
ejpam-6466	409	14	xυ(s	xυ(s	X
ejpam-6466	409	15	)	)	PUNCT
ejpam-6466	409	16	=	=	PUNCT
ejpam-6466	409	17	φ(s	φ(s	NOUN
ejpam-6466	409	18	)	)	PUNCT
ejpam-6466	409	19	,	,	PUNCT
ejpam-6466	409	20	s	s	VERB
ejpam-6466	409	21	∈	∈	PROPN
ejpam-6466	410	1	[	[	X
ejpam-6466	410	2	−m	−m	NOUN
ejpam-6466	410	3	,	,	PUNCT
ejpam-6466	410	4	0	0	NUM
ejpam-6466	410	5	]	]	PUNCT
ejpam-6466	410	6	,	,	PUNCT
ejpam-6466	410	7	we	we	PRON
ejpam-6466	410	8	derive	derive	VERB
ejpam-6466	410	9	e	e	NOUN
ejpam-6466	411	1	[	[	X
ejpam-6466	411	2	∥∥xυ+1(τ)−	∥∥xυ+1(τ)−	ADJ
ejpam-6466	411	3	xυ(τ	xυ(τ	NUM
ejpam-6466	411	4	)	)	PUNCT
ejpam-6466	411	5	∥∥2	∥∥2	NUM
ejpam-6466	411	6	]	]	PUNCT
ejpam-6466	411	7	≤	≤	NUM
ejpam-6466	411	8	4(τ	4(τ	NUM
ejpam-6466	412	1	+	+	CCONJ
ejpam-6466	413	1	1)lυ	1)lυ	PROPN
ejpam-6466	413	2	∫	∫	NOUN
ejpam-6466	413	3	τ	τ	PROPN
ejpam-6466	413	4	0	0	NUM
ejpam-6466	413	5	s2ξ−2	s2ξ−2	PROPN
ejpam-6466	413	6	(	(	PUNCT
ejpam-6466	413	7	e	e	X
ejpam-6466	413	8	[	[	PUNCT
ejpam-6466	413	9	∥xυ+1(s)−	∥xυ+1(s)−	NUM
ejpam-6466	413	10	xυ(s	xυ(s	X
ejpam-6466	413	11	)	)	PUNCT
ejpam-6466	413	12	∥∥2]+e	∥∥2]+e	PUNCT
ejpam-6466	414	1	[	[	X
ejpam-6466	414	2	∥∥xυ+1(s−m)−	∥∥xυ+1(s−m)−	PROPN
ejpam-6466	414	3	xυ(s−m	xυ(s−m	PROPN
ejpam-6466	414	4	)	)	PUNCT
ejpam-6466	414	5	∥∥2	∥∥2	PROPN
ejpam-6466	414	6	]	]	PUNCT
ejpam-6466	414	7	)	)	PUNCT
ejpam-6466	414	8	≤	≤	NOUN
ejpam-6466	414	9	8τlυ	8τlυ	NUM
ejpam-6466	414	10	∫	∫	PROPN
ejpam-6466	414	11	τ	τ	X
ejpam-6466	414	12	0	0	NUM
ejpam-6466	414	13	s2s−2	s2s−2	PROPN
ejpam-6466	414	14	sup	sup	NOUN
ejpam-6466	414	15	≤δ≤s	≤δ≤s	PROPN
ejpam-6466	414	16	e	e	PROPN
ejpam-6466	415	1	[	[	X
ejpam-6466	415	2	∥∥xυ+1(δ)−	∥∥xυ+1(δ)−	X
ejpam-6466	415	3	xυ(δ	xυ(δ	NOUN
ejpam-6466	415	4	)	)	PUNCT
ejpam-6466	415	5	∥∥2]ds	∥∥2]ds	PROPN
ejpam-6466	415	6	.	.	PUNCT
ejpam-6466	416	1	(	(	PUNCT
ejpam-6466	416	2	31	31	NUM
ejpam-6466	416	3	)	)	PUNCT
ejpam-6466	416	4	when	when	SCONJ
ejpam-6466	416	5	we	we	PRON
ejpam-6466	416	6	use	use	VERB
ejpam-6466	416	7	the	the	DET
ejpam-6466	416	8	g	g	NOUN
ejpam-6466	416	9	-	-	PUNCT
ejpam-6466	416	10	i	i	NOUN
ejpam-6466	416	11	,	,	PUNCT
ejpam-6466	416	12	we	we	PRON
ejpam-6466	416	13	get	get	VERB
ejpam-6466	416	14	sup	sup	NOUN
ejpam-6466	416	15	0≤η≤τ	0≤η≤τ	PROPN
ejpam-6466	416	16	e[∥xυ+1(η)−	e[∥xυ+1(η)−	NOUN
ejpam-6466	416	17	xυ(η)∥2	xυ(η)∥2	PROPN
ejpam-6466	416	18	]	]	PUNCT
ejpam-6466	417	1	=	=	PUNCT
ejpam-6466	417	2	0	0	NUM
ejpam-6466	417	3	,	,	PUNCT
ejpam-6466	417	4	∀0	∀0	VERB
ejpam-6466	417	5	≤	≤	NUM
ejpam-6466	417	6	τ	τ	X
ejpam-6466	417	7	≤	≤	NOUN
ejpam-6466	417	8	λυ	λυ	ADP
ejpam-6466	417	9	,	,	PUNCT
ejpam-6466	417	10	(	(	PUNCT
ejpam-6466	417	11	32	32	NUM
ejpam-6466	417	12	)	)	PUNCT
ejpam-6466	417	13	which	which	PRON
ejpam-6466	417	14	demonstrates	demonstrate	VERB
ejpam-6466	417	15	eq	eq	ADP
ejpam-6466	417	16	.	.	PUNCT
ejpam-6466	418	1	(	(	PUNCT
ejpam-6466	418	2	29	29	NUM
ejpam-6466	418	3	)	)	PUNCT
ejpam-6466	418	4	.	.	PUNCT
ejpam-6466	419	1	as	as	ADP
ejpam-6466	419	2	a	a	DET
ejpam-6466	419	3	result	result	NOUN
ejpam-6466	419	4	,	,	PUNCT
ejpam-6466	419	5	λυ	λυ	AUX
ejpam-6466	419	6	is	be	AUX
ejpam-6466	419	7	increasing	increase	VERB
ejpam-6466	419	8	.	.	PUNCT
ejpam-6466	420	1	however	however	ADV
ejpam-6466	420	2	,	,	PUNCT
ejpam-6466	420	3	vυ	vυ	ADV
ejpam-6466	420	4	and	and	CCONJ
ejpam-6466	420	5	𭟋υ	𭟋υ	PRON
ejpam-6466	420	6	meet	meet	VERB
ejpam-6466	420	7	the	the	DET
ejpam-6466	420	8	linear	linear	ADJ
ejpam-6466	420	9	growth	growth	NOUN
ejpam-6466	420	10	requirement	requirement	NOUN
ejpam-6466	420	11	since	since	SCONJ
ejpam-6466	420	12	vυ	vυ	ADV
ejpam-6466	420	13	and	and	CCONJ
ejpam-6466	420	14	𭟋υ	𭟋υ	ADP
ejpam-6466	420	15	satisfy	satisfy	NOUN
ejpam-6466	420	16	conditions	condition	NOUN
ejpam-6466	420	17	(	(	PUNCT
ejpam-6466	420	18	a2	a2	PROPN
ejpam-6466	420	19	)	)	PUNCT
ejpam-6466	420	20	and	and	CCONJ
ejpam-6466	420	21	(	(	PUNCT
ejpam-6466	420	22	a3	a3	NOUN
ejpam-6466	420	23	)	)	PUNCT
ejpam-6466	420	24	.	.	PUNCT
ejpam-6466	421	1	as	as	ADP
ejpam-6466	421	2	a	a	DET
ejpam-6466	421	3	result	result	NOUN
ejpam-6466	421	4	,	,	PUNCT
ejpam-6466	421	5	there	there	PRON
ejpam-6466	421	6	exists	exist	VERB
ejpam-6466	421	7	an	an	DET
ejpam-6466	421	8	integer	integer	NOUN
ejpam-6466	421	9	υ0	υ0	NOUN
ejpam-6466	421	10	=	=	SYM
ejpam-6466	421	11	υ0(ϖ	υ0(ϖ	PROPN
ejpam-6466	421	12	)	)	PUNCT
ejpam-6466	421	13	that	that	PRON
ejpam-6466	421	14	corresponds	correspond	VERB
ejpam-6466	421	15	to	to	ADP
ejpam-6466	421	16	λυ	λυ	ADP
ejpam-6466	421	17	=	=	SYM
ejpam-6466	421	18	ℏ	ℏ	PROPN
ejpam-6466	421	19	whenever	whenever	SCONJ
ejpam-6466	421	20	υ	υ	PRON
ejpam-6466	421	21	≥	≥	NOUN
ejpam-6466	421	22	υ0	υ0	VERB
ejpam-6466	421	23	for	for	ADP
ejpam-6466	421	24	almost	almost	ADV
ejpam-6466	421	25	every	every	PRON
ejpam-6466	421	26	value	value	NOUN
ejpam-6466	421	27	ϖ	ϖ	X
ejpam-6466	421	28	∈	∈	PROPN
ejpam-6466	421	29	ω	ω	PROPN
ejpam-6466	421	30	.	.	PUNCT
ejpam-6466	422	1	next	next	ADV
ejpam-6466	422	2	,	,	PUNCT
ejpam-6466	422	3	let	let	VERB
ejpam-6466	422	4	x(τ	x(τ	PROPN
ejpam-6466	422	5	)	)	PUNCT
ejpam-6466	422	6	be	be	AUX
ejpam-6466	422	7	defined	define	VERB
ejpam-6466	422	8	by	by	ADP
ejpam-6466	422	9	x(τ	x(τ	PROPN
ejpam-6466	422	10	)	)	PUNCT
ejpam-6466	422	11	=	=	PUNCT
ejpam-6466	423	1	x(υ0)(τ	x(υ0)(τ	PROPN
ejpam-6466	423	2	)	)	PUNCT
ejpam-6466	424	1	,	,	PUNCT
ejpam-6466	424	2	τ	τ	PROPN
ejpam-6466	424	3	∈	∈	PROPN
ejpam-6466	425	1	[	[	X
ejpam-6466	425	2	0	0	NUM
ejpam-6466	425	3	,	,	PUNCT
ejpam-6466	425	4	ℏ	ℏ	PROPN
ejpam-6466	425	5	]	]	PUNCT
ejpam-6466	425	6	.	.	PUNCT
ejpam-6466	426	1	m.	m.	PROPN
ejpam-6466	426	2	i.	i.	PROPN
ejpam-6466	426	3	liaqat	liaqat	PROPN
ejpam-6466	426	4	et	et	PROPN
ejpam-6466	426	5	al	al	PROPN
ejpam-6466	426	6	.	.	PUNCT
ejpam-6466	426	7	/	/	SYM
ejpam-6466	426	8	eur	eur	PROPN
ejpam-6466	426	9	.	.	PUNCT
ejpam-6466	427	1	j.	j.	PROPN
ejpam-6466	427	2	pure	pure	PROPN
ejpam-6466	427	3	appl	appl	PROPN
ejpam-6466	427	4	.	.	PROPN
ejpam-6466	427	5	math	math	PROPN
ejpam-6466	427	6	,	,	PUNCT
ejpam-6466	427	7	18	18	NUM
ejpam-6466	427	8	(	(	PUNCT
ejpam-6466	427	9	4	4	NUM
ejpam-6466	427	10	)	)	PUNCT
ejpam-6466	427	11	(	(	PUNCT
ejpam-6466	427	12	2025	2025	NUM
ejpam-6466	427	13	)	)	PUNCT
ejpam-6466	427	14	,	,	PUNCT
ejpam-6466	427	15	6466	6466	NUM
ejpam-6466	427	16	16	16	NUM
ejpam-6466	427	17	of	of	ADP
ejpam-6466	427	18	28	28	NUM
ejpam-6466	427	19	therefore	therefore	ADV
ejpam-6466	427	20	,	,	PUNCT
ejpam-6466	427	21	to	to	PART
ejpam-6466	427	22	complete	complete	VERB
ejpam-6466	427	23	the	the	DET
ejpam-6466	427	24	proof	proof	NOUN
ejpam-6466	427	25	,	,	PUNCT
ejpam-6466	427	26	it	it	PRON
ejpam-6466	427	27	is	be	AUX
ejpam-6466	427	28	sufficient	sufficient	ADJ
ejpam-6466	427	29	to	to	PART
ejpam-6466	427	30	show	show	VERB
ejpam-6466	427	31	that	that	SCONJ
ejpam-6466	427	32	x(τ	x(τ	PROPN
ejpam-6466	427	33	)	)	PUNCT
ejpam-6466	427	34	is	be	AUX
ejpam-6466	427	35	the	the	DET
ejpam-6466	427	36	solution	solution	NOUN
ejpam-6466	427	37	of	of	ADP
ejpam-6466	427	38	problem	problem	NOUN
ejpam-6466	427	39	eq	eq	ADJ
ejpam-6466	427	40	.	.	PUNCT
ejpam-6466	428	1	(	(	PUNCT
ejpam-6466	428	2	4	4	NUM
ejpam-6466	428	3	)	)	PUNCT
ejpam-6466	428	4	.	.	PUNCT
ejpam-6466	429	1	indeed	indeed	ADV
ejpam-6466	429	2	,	,	PUNCT
ejpam-6466	429	3	by	by	ADP
ejpam-6466	429	4	virtue	virtue	NOUN
ejpam-6466	429	5	of	of	ADP
ejpam-6466	429	6	eq	eq	PROPN
ejpam-6466	429	7	.	.	PUNCT
ejpam-6466	430	1	(	(	PUNCT
ejpam-6466	430	2	29	29	NUM
ejpam-6466	430	3	)	)	PUNCT
ejpam-6466	430	4	,	,	PUNCT
ejpam-6466	430	5	we	we	PRON
ejpam-6466	430	6	get	get	VERB
ejpam-6466	430	7	that	that	DET
ejpam-6466	430	8	x(τ	x(τ	PROPN
ejpam-6466	430	9	∧	∧	PROPN
ejpam-6466	430	10	λυ	λυ	ADP
ejpam-6466	430	11	)	)	PUNCT
ejpam-6466	430	12	=	=	PUNCT
ejpam-6466	431	1	x(υ)(τ	x(υ)(τ	PUNCT
ejpam-6466	431	2	∧	∧	NOUN
ejpam-6466	431	3	λυ	λυ	ADP
ejpam-6466	431	4	)	)	PUNCT
ejpam-6466	431	5	=	=	SYM
ejpam-6466	432	1	x(υ0)(τ	x(υ0)(τ	PUNCT
ejpam-6466	432	2	∧	∧	NOUN
ejpam-6466	432	3	λυ	λυ	ADP
ejpam-6466	432	4	)	)	PUNCT
ejpam-6466	432	5	.	.	PUNCT
ejpam-6466	433	1	(	(	PUNCT
ejpam-6466	433	2	33	33	NUM
ejpam-6466	433	3	)	)	PUNCT
ejpam-6466	433	4	using	use	VERB
ejpam-6466	433	5	eq	eq	X
ejpam-6466	433	6	.	.	PUNCT
ejpam-6466	434	1	(	(	PUNCT
ejpam-6466	434	2	28	28	NUM
ejpam-6466	434	3	)	)	PUNCT
ejpam-6466	434	4	,	,	PUNCT
ejpam-6466	434	5	we	we	PRON
ejpam-6466	434	6	yield	yield	VERB
ejpam-6466	434	7	that	that	DET
ejpam-6466	434	8	x(τ	x(τ	PROPN
ejpam-6466	434	9	∧	∧	PROPN
ejpam-6466	434	10	ℏυ	ℏυ	ADP
ejpam-6466	434	11	)	)	PUNCT
ejpam-6466	434	12	=	=	SYM
ejpam-6466	434	13	φ	φ	PROPN
ejpam-6466	434	14	+	+	CCONJ
ejpam-6466	434	15	∫	∫	PROPN
ejpam-6466	434	16	τ∧ℏυ	τ∧ℏυ	NOUN
ejpam-6466	434	17	0	0	NUM
ejpam-6466	435	1	sξ−1v	sξ−1v	NOUN
ejpam-6466	435	2	(	(	PUNCT
ejpam-6466	435	3	s	s	PROPN
ejpam-6466	435	4	,	,	PUNCT
ejpam-6466	435	5	x(s	x(s	PROPN
ejpam-6466	435	6	)	)	PUNCT
ejpam-6466	435	7	,	,	PUNCT
ejpam-6466	435	8	x(s−m	x(s−m	NUM
ejpam-6466	435	9	)	)	PUNCT
ejpam-6466	435	10	)	)	PUNCT
ejpam-6466	436	1	ds	ds	PROPN
ejpam-6466	436	2	+	+	CCONJ
ejpam-6466	436	3	∫	∫	PROPN
ejpam-6466	436	4	τ∧ℏυ	τ∧ℏυ	NOUN
ejpam-6466	436	5	0	0	NUM
ejpam-6466	436	6	sξ−1𭟋	sξ−1𭟋	X
ejpam-6466	436	7	(	(	PUNCT
ejpam-6466	436	8	s	s	PROPN
ejpam-6466	436	9	,	,	PUNCT
ejpam-6466	436	10	x(s	x(s	PROPN
ejpam-6466	436	11	)	)	PUNCT
ejpam-6466	436	12	,	,	PUNCT
ejpam-6466	436	13	x(s−m	x(s−m	NUM
ejpam-6466	436	14	)	)	PUNCT
ejpam-6466	436	15	)	)	PUNCT
ejpam-6466	437	1	dws	dws	PROPN
ejpam-6466	437	2	.	.	PUNCT
ejpam-6466	438	1	(	(	PUNCT
ejpam-6466	438	2	34	34	NUM
ejpam-6466	438	3	)	)	PUNCT
ejpam-6466	438	4	let	let	VERB
ejpam-6466	438	5	υ	υ	NOUN
ejpam-6466	438	6	→	→	SYM
ejpam-6466	438	7	∞	∞	NUM
ejpam-6466	438	8	and	and	CCONJ
ejpam-6466	438	9	by	by	ADP
ejpam-6466	438	10	λυ	λυ	ADP
ejpam-6466	438	11	→	→	SYM
ejpam-6466	438	12	ℏ	ℏ	PROPN
ejpam-6466	438	13	as	as	ADP
ejpam-6466	438	14	υ	υ	PROPN
ejpam-6466	438	15	→	→	SYM
ejpam-6466	438	16	∞	∞	PROPN
ejpam-6466	438	17	,	,	PUNCT
ejpam-6466	438	18	as	as	ADP
ejpam-6466	438	19	a	a	DET
ejpam-6466	438	20	result	result	NOUN
ejpam-6466	438	21	,	,	PUNCT
ejpam-6466	438	22	we	we	PRON
ejpam-6466	438	23	can	can	AUX
ejpam-6466	438	24	conclude	conclude	VERB
ejpam-6466	438	25	that	that	SCONJ
ejpam-6466	438	26	the	the	DET
ejpam-6466	438	27	solution	solution	NOUN
ejpam-6466	438	28	to	to	ADP
ejpam-6466	438	29	eq	eq	PROPN
ejpam-6466	438	30	.	.	PUNCT
ejpam-6466	439	1	(	(	PUNCT
ejpam-6466	439	2	4	4	X
ejpam-6466	439	3	)	)	PUNCT
ejpam-6466	439	4	is	be	AUX
ejpam-6466	439	5	x(τ	x(τ	PROPN
ejpam-6466	439	6	)	)	PUNCT
ejpam-6466	439	7	.	.	PUNCT
ejpam-6466	440	1	hence	hence	ADV
ejpam-6466	440	2	,	,	PUNCT
ejpam-6466	440	3	it	it	PRON
ejpam-6466	440	4	proved	prove	VERB
ejpam-6466	440	5	the	the	DET
ejpam-6466	440	6	desired	desire	VERB
ejpam-6466	440	7	result	result	NOUN
ejpam-6466	440	8	.	.	PUNCT
ejpam-6466	441	1	step	step	NOUN
ejpam-6466	441	2	2	2	NUM
ejpam-6466	441	3	:	:	PUNCT
ejpam-6466	441	4	uniqueness	uniqueness	NOUN
ejpam-6466	441	5	:	:	PUNCT
ejpam-6466	441	6	assume	assume	VERB
ejpam-6466	441	7	that	that	SCONJ
ejpam-6466	441	8	,	,	PUNCT
ejpam-6466	441	9	with	with	ADP
ejpam-6466	441	10	respect	respect	NOUN
ejpam-6466	441	11	to	to	ADP
ejpam-6466	441	12	the	the	DET
ejpam-6466	441	13	same	same	ADJ
ejpam-6466	441	14	brownian	brownian	ADJ
ejpam-6466	441	15	motion	motion	NOUN
ejpam-6466	441	16	wτ	wτ	NOUN
ejpam-6466	441	17	and	and	CCONJ
ejpam-6466	441	18	the	the	DET
ejpam-6466	441	19	same	same	ADJ
ejpam-6466	441	20	initial	initial	ADJ
ejpam-6466	441	21	value	value	NOUN
ejpam-6466	441	22	φ	φ	NOUN
ejpam-6466	441	23	,	,	PUNCT
ejpam-6466	441	24	x	x	SYM
ejpam-6466	441	25	and	and	CCONJ
ejpam-6466	441	26	x̃	x̃	PROPN
ejpam-6466	441	27	are	be	AUX
ejpam-6466	441	28	the	the	DET
ejpam-6466	441	29	solutions	solution	NOUN
ejpam-6466	441	30	stated	state	VERB
ejpam-6466	441	31	for	for	ADP
ejpam-6466	441	32	all	all	DET
ejpam-6466	441	33	τ	τ	PROPN
ejpam-6466	441	34	∈	∈	PROPN
ejpam-6466	441	35	[	[	X
ejpam-6466	441	36	−m	−m	NOUN
ejpam-6466	441	37	,	,	PUNCT
ejpam-6466	441	38	ℏ	ℏ	X
ejpam-6466	441	39	]	]	PUNCT
ejpam-6466	441	40	of	of	ADP
ejpam-6466	441	41	the	the	DET
ejpam-6466	441	42	eq	eq	NOUN
ejpam-6466	441	43	.	.	PUNCT
ejpam-6466	442	1	(	(	PUNCT
ejpam-6466	442	2	4	4	NUM
ejpam-6466	442	3	)	)	PUNCT
ejpam-6466	442	4	.	.	PUNCT
ejpam-6466	443	1	we	we	PRON
ejpam-6466	443	2	determine	determine	VERB
ejpam-6466	443	3	the	the	DET
ejpam-6466	443	4	stopping	stopping	NOUN
ejpam-6466	443	5	timings	timing	NOUN
ejpam-6466	443	6	associated	associate	VERB
ejpam-6466	443	7	with	with	ADP
ejpam-6466	443	8	every	every	DET
ejpam-6466	443	9	υ	υ	PROPN
ejpam-6466	443	10	≥	≥	NOUN
ejpam-6466	443	11	1	1	NUM
ejpam-6466	443	12	.	.	PUNCT
ejpam-6466	444	1	λυ	λυ	ADP
ejpam-6466	444	2	=	=	SYM
ejpam-6466	444	3	ℏ	ℏ	PROPN
ejpam-6466	444	4	∧	∧	NOUN
ejpam-6466	444	5	inf{τ	inf{τ	PROPN
ejpam-6466	444	6	∈	∈	PROPN
ejpam-6466	445	1	[	[	X
ejpam-6466	445	2	0	0	NUM
ejpam-6466	445	3	,	,	PUNCT
ejpam-6466	445	4	ℏ	ℏ	PROPN
ejpam-6466	445	5	]	]	X
ejpam-6466	445	6	:	:	PUNCT
ejpam-6466	445	7	∥xτ∥	∥xτ∥	X
ejpam-6466	445	8	≥	≥	NOUN
ejpam-6466	445	9	υ	υ	NOUN
ejpam-6466	445	10	}	}	PUNCT
ejpam-6466	445	11	,	,	PUNCT
ejpam-6466	445	12	λ̃υ	λ̃υ	VERB
ejpam-6466	445	13	=	=	PUNCT
ejpam-6466	445	14	ℏ	ℏ	PROPN
ejpam-6466	445	15	∧	∧	NOUN
ejpam-6466	445	16	inf{τ	inf{τ	PROPN
ejpam-6466	445	17	∈	∈	PROPN
ejpam-6466	446	1	[	[	X
ejpam-6466	446	2	0	0	NUM
ejpam-6466	446	3	,	,	PUNCT
ejpam-6466	446	4	ℏ	ℏ	PROPN
ejpam-6466	446	5	]	]	PUNCT
ejpam-6466	446	6	:	:	PUNCT
ejpam-6466	446	7	∥x̃τ∥	∥x̃τ∥	X
ejpam-6466	446	8	≥	≥	PROPN
ejpam-6466	447	1	υ	υ	NOUN
ejpam-6466	447	2	}	}	PUNCT
ejpam-6466	447	3	and	and	CCONJ
ejpam-6466	447	4	we	we	PRON
ejpam-6466	447	5	put	put	VERB
ejpam-6466	447	6	uυ	uυ	NOUN
ejpam-6466	447	7	=	=	PUNCT
ejpam-6466	447	8	λυ	λυ	ADP
ejpam-6466	447	9	∧	∧	PROPN
ejpam-6466	447	10	λ̃υ	λ̃υ	PROPN
ejpam-6466	447	11	.	.	PUNCT
ejpam-6466	448	1	obviously	obviously	ADV
ejpam-6466	448	2	,	,	PUNCT
ejpam-6466	448	3	limυ→∞uυ	limυ→∞uυ	PROPN
ejpam-6466	448	4	=	=	SYM
ejpam-6466	448	5	ℏ	ℏ	PROPN
ejpam-6466	448	6	p	p	NOUN
ejpam-6466	448	7	-	-	PUNCT
ejpam-6466	448	8	almost	almost	ADV
ejpam-6466	448	9	surely	surely	ADV
ejpam-6466	448	10	and	and	CCONJ
ejpam-6466	448	11	x(τ	x(τ	PROPN
ejpam-6466	449	1	∧	∧	PROPN
ejpam-6466	449	2	νυ)−x̃(τ	νυ)−x̃(τ	PROPN
ejpam-6466	449	3	∧	∧	PROPN
ejpam-6466	449	4	νυ	νυ	PROPN
ejpam-6466	449	5	)	)	PUNCT
ejpam-6466	449	6	=	=	SYM
ejpam-6466	450	1	∫	∫	PROPN
ejpam-6466	450	2	τ∧νυ	τ∧νυ	PROPN
ejpam-6466	450	3	0	0	PUNCT
ejpam-6466	450	4	sξ−1	sξ−1	PROPN
ejpam-6466	450	5	(	(	PUNCT
ejpam-6466	450	6	v	v	X
ejpam-6466	450	7	(	(	PUNCT
ejpam-6466	450	8	s	s	PROPN
ejpam-6466	450	9	,	,	PUNCT
ejpam-6466	450	10	x(s	x(s	PROPN
ejpam-6466	450	11	)	)	PUNCT
ejpam-6466	450	12	,	,	PUNCT
ejpam-6466	450	13	x(s−m−v	x(s−m−v	PROPN
ejpam-6466	450	14	(	(	PUNCT
ejpam-6466	450	15	s	s	PROPN
ejpam-6466	450	16	,	,	PUNCT
ejpam-6466	450	17	x̃(s	x̃(s	PROPN
ejpam-6466	450	18	)	)	PUNCT
ejpam-6466	450	19	,	,	PUNCT
ejpam-6466	450	20	x̃(s−m	x̃(s−m	PROPN
ejpam-6466	450	21	)	)	PUNCT
ejpam-6466	450	22	)	)	PUNCT
ejpam-6466	451	1	ds	ds	PROPN
ejpam-6466	451	2	+	+	CCONJ
ejpam-6466	451	3	∫	∫	PROPN
ejpam-6466	451	4	τ∧νυ	τ∧νυ	SYM
ejpam-6466	451	5	0	0	PUNCT
ejpam-6466	451	6	sξ−1	sξ−1	PROPN
ejpam-6466	451	7	(	(	PUNCT
ejpam-6466	451	8	𭟋	𭟋	PROPN
ejpam-6466	451	9	(	(	PUNCT
ejpam-6466	451	10	s	s	PROPN
ejpam-6466	451	11	,	,	PUNCT
ejpam-6466	451	12	x(s	x(s	PROPN
ejpam-6466	451	13	)	)	PUNCT
ejpam-6466	451	14	,	,	PUNCT
ejpam-6466	451	15	x(s−m)−𭟋	x(s−m)−𭟋	PROPN
ejpam-6466	451	16	(	(	PUNCT
ejpam-6466	451	17	s	s	PROPN
ejpam-6466	451	18	,	,	PUNCT
ejpam-6466	451	19	x̃(s	x̃(s	PROPN
ejpam-6466	451	20	)	)	PUNCT
ejpam-6466	451	21	,	,	PUNCT
ejpam-6466	451	22	x̃(s−m	x̃(s−m	PROPN
ejpam-6466	451	23	)	)	PUNCT
ejpam-6466	451	24	)	)	PUNCT
ejpam-6466	452	1	dws	dws	PROPN
ejpam-6466	452	2	.	.	PUNCT
ejpam-6466	453	1	(	(	PUNCT
ejpam-6466	453	2	35	35	NUM
ejpam-6466	453	3	)	)	PUNCT
ejpam-6466	453	4	utilizing	utilize	VERB
ejpam-6466	453	5	the	the	DET
ejpam-6466	453	6	i	i	NOUN
ejpam-6466	453	7	-	-	PUNCT
ejpam-6466	453	8	is	be	AUX
ejpam-6466	453	9	,	,	PUNCT
ejpam-6466	453	10	höld	höld	PROPN
ejpam-6466	453	11	-	-	PUNCT
ejpam-6466	453	12	i	i	PROPN
ejpam-6466	453	13	,	,	PUNCT
ejpam-6466	453	14	and	and	CCONJ
ejpam-6466	453	15	(	(	PUNCT
ejpam-6466	453	16	a1	a1	NOUN
ejpam-6466	453	17	)	)	PUNCT
ejpam-6466	453	18	,	,	PUNCT
ejpam-6466	453	19	we	we	PRON
ejpam-6466	453	20	accomplished	accomplish	VERB
ejpam-6466	453	21	e	e	X
ejpam-6466	453	22	[	[	PUNCT
ejpam-6466	453	23	∥x(τ)−	∥x(τ)−	X
ejpam-6466	453	24	x̃(τ	x̃(τ	PROPN
ejpam-6466	453	25	)	)	PUNCT
ejpam-6466	453	26	∥∥2ℵ{τ	∥∥2ℵ{τ	NOUN
ejpam-6466	453	27	≤	≤	NUM
ejpam-6466	453	28	uυ	uυ	PROPN
ejpam-6466	453	29	}	}	PUNCT
ejpam-6466	453	30	]	]	PUNCT
ejpam-6466	453	31	≤	≤	X
ejpam-6466	453	32	2(τ	2(τ	NUM
ejpam-6466	453	33	+	+	CCONJ
ejpam-6466	453	34	1)lυ	1)lυ	PROPN
ejpam-6466	453	35	e	e	NOUN
ejpam-6466	453	36	[	[	PUNCT
ejpam-6466	453	37	∫	∫	PROPN
ejpam-6466	453	38	τ	τ	PROPN
ejpam-6466	453	39	0	0	NUM
ejpam-6466	453	40	s2ξ−2	s2ξ−2	PROPN
ejpam-6466	453	41	(	(	PUNCT
ejpam-6466	453	42	∥x(τ)−	∥x(τ)−	NOUN
ejpam-6466	453	43	x̃(τ	x̃(τ	PROPN
ejpam-6466	453	44	)	)	PUNCT
ejpam-6466	453	45	∥∥2	∥∥2	PROPN
ejpam-6466	454	1	+	+	CCONJ
ejpam-6466	454	2	∥x(τ	∥x(τ	ADJ
ejpam-6466	454	3	−m)−	−m)−	NOUN
ejpam-6466	454	4	x̃(τ	x̃(τ	PROPN
ejpam-6466	454	5	−m	−m	NOUN
ejpam-6466	454	6	)	)	PUNCT
ejpam-6466	455	1	∥∥2)ℵ{τ	∥∥2)ℵ{τ	PROPN
ejpam-6466	455	2	≤	≤	NUM
ejpam-6466	455	3	uυ	uυ	PROPN
ejpam-6466	455	4	}	}	PUNCT
ejpam-6466	455	5	]	]	PUNCT
ejpam-6466	455	6	≤	≤	NUM
ejpam-6466	455	7	4(ℏ+	4(ℏ+	NUM
ejpam-6466	456	1	1)lυ	1)lυ	NUM
ejpam-6466	456	2	∫	∫	PROPN
ejpam-6466	456	3	τ	τ	PROPN
ejpam-6466	456	4	0	0	NUM
ejpam-6466	456	5	sup	sup	NOUN
ejpam-6466	456	6	0≤δ≤s	0≤δ≤s	NUM
ejpam-6466	456	7	e	e	NOUN
ejpam-6466	456	8	[	[	PUNCT
ejpam-6466	456	9	∥x(δ)−	∥x(δ)−	X
ejpam-6466	456	10	x̃(δ	x̃(δ	PROPN
ejpam-6466	456	11	)	)	PUNCT
ejpam-6466	456	12	∥∥2ℵ{τ	∥∥2ℵ{τ	NOUN
ejpam-6466	456	13	≤	≤	NUM
ejpam-6466	456	14	uυ	uυ	PROPN
ejpam-6466	456	15	}	}	PUNCT
ejpam-6466	456	16	]	]	PUNCT
ejpam-6466	456	17	s2ξ−2ds	s2ξ−2ds	NOUN
ejpam-6466	456	18	.	.	PUNCT
ejpam-6466	457	1	(	(	PUNCT
ejpam-6466	457	2	36	36	NUM
ejpam-6466	457	3	)	)	PUNCT
ejpam-6466	457	4	utilizing	utilize	VERB
ejpam-6466	457	5	the	the	DET
ejpam-6466	457	6	g	g	NOUN
ejpam-6466	457	7	-	-	PUNCT
ejpam-6466	457	8	i	i	NOUN
ejpam-6466	457	9	,	,	PUNCT
ejpam-6466	457	10	we	we	PRON
ejpam-6466	457	11	achieved	achieve	VERB
ejpam-6466	457	12	sup	sup	NOUN
ejpam-6466	457	13	0≤τ≤ℏ	0≤τ≤ℏ	NUM
ejpam-6466	457	14	e	e	NOUN
ejpam-6466	457	15	[	[	PUNCT
ejpam-6466	457	16	∥x(δ)−	∥x(δ)−	X
ejpam-6466	457	17	x̃(δ	x̃(δ	PROPN
ejpam-6466	457	18	)	)	PUNCT
ejpam-6466	457	19	∥∥2ℵ{τ	∥∥2ℵ{τ	NOUN
ejpam-6466	457	20	≤	≤	NUM
ejpam-6466	457	21	uυ	uυ	NOUN
ejpam-6466	457	22	}	}	PUNCT
ejpam-6466	457	23	]	]	PUNCT
ejpam-6466	457	24	=	=	PUNCT
ejpam-6466	458	1	0	0	X
ejpam-6466	458	2	.	.	PUNCT
ejpam-6466	459	1	(	(	PUNCT
ejpam-6466	459	2	37	37	NUM
ejpam-6466	459	3	)	)	PUNCT
ejpam-6466	459	4	however	however	ADV
ejpam-6466	459	5	,	,	PUNCT
ejpam-6466	459	6	we	we	PRON
ejpam-6466	459	7	achieve	achieve	VERB
ejpam-6466	459	8	the	the	DET
ejpam-6466	459	9	following	following	NOUN
ejpam-6466	459	10	:	:	PUNCT
ejpam-6466	459	11	sup	sup	NUM
ejpam-6466	459	12	0≤τ≤ℏ	0≤τ≤ℏ	NUM
ejpam-6466	459	13	e	e	NOUN
ejpam-6466	459	14	[	[	PUNCT
ejpam-6466	459	15	∥x(δ)−	∥x(δ)−	X
ejpam-6466	459	16	x̃(δ	x̃(δ	PROPN
ejpam-6466	459	17	)	)	PUNCT
ejpam-6466	460	1	∥∥2	∥∥2	PROPN
ejpam-6466	460	2	]	]	PUNCT
ejpam-6466	460	3	≤	≤	X
ejpam-6466	461	1	[	[	X
ejpam-6466	461	2	∥x(δ)−	∥x(δ)−	X
ejpam-6466	461	3	x̃(δ	x̃(δ	PROPN
ejpam-6466	461	4	)	)	PUNCT
ejpam-6466	461	5	∥∥2	∥∥2	PROPN
ejpam-6466	462	1	ℵ(τ	ℵ(τ	PROPN
ejpam-6466	462	2	≤	≤	PUNCT
ejpam-6466	463	1	uυ	uυ	NOUN
ejpam-6466	463	2	]	]	PUNCT
ejpam-6466	464	1	+	+	CCONJ
ejpam-6466	464	2	[	[	PUNCT
ejpam-6466	464	3	∥x(δ)−	∥x(δ)−	X
ejpam-6466	464	4	x̃(δ	x̃(δ	PROPN
ejpam-6466	464	5	)	)	PUNCT
ejpam-6466	464	6	∥∥2ℵ{τ	∥∥2ℵ{τ	NOUN
ejpam-6466	464	7	>	>	SYM
ejpam-6466	464	8	uυ	uυ	PROPN
ejpam-6466	464	9	}	}	PUNCT
ejpam-6466	464	10	]	]	PUNCT
ejpam-6466	464	11	.	.	PUNCT
ejpam-6466	465	1	(	(	PUNCT
ejpam-6466	465	2	38	38	NUM
ejpam-6466	465	3	)	)	PUNCT
ejpam-6466	465	4	m.	m.	NOUN
ejpam-6466	465	5	i.	i.	PROPN
ejpam-6466	465	6	liaqat	liaqat	PROPN
ejpam-6466	465	7	et	et	PROPN
ejpam-6466	465	8	al	al	PROPN
ejpam-6466	465	9	.	.	PUNCT
ejpam-6466	465	10	/	/	SYM
ejpam-6466	465	11	eur	eur	PROPN
ejpam-6466	465	12	.	.	PUNCT
ejpam-6466	466	1	j.	j.	PROPN
ejpam-6466	466	2	pure	pure	PROPN
ejpam-6466	466	3	appl	appl	PROPN
ejpam-6466	466	4	.	.	PROPN
ejpam-6466	466	5	math	math	PROPN
ejpam-6466	466	6	,	,	PUNCT
ejpam-6466	466	7	18	18	NUM
ejpam-6466	466	8	(	(	PUNCT
ejpam-6466	466	9	4	4	NUM
ejpam-6466	466	10	)	)	PUNCT
ejpam-6466	466	11	(	(	PUNCT
ejpam-6466	466	12	2025	2025	NUM
ejpam-6466	466	13	)	)	PUNCT
ejpam-6466	466	14	,	,	PUNCT
ejpam-6466	466	15	6466	6466	NUM
ejpam-6466	466	16	17	17	NUM
ejpam-6466	466	17	of	of	ADP
ejpam-6466	466	18	28	28	NUM
ejpam-6466	466	19	let	let	VERB
ejpam-6466	466	20	υ	υ	NOUN
ejpam-6466	466	21	→	→	SYM
ejpam-6466	466	22	∞	∞	PROPN
ejpam-6466	466	23	and	and	CCONJ
ejpam-6466	466	24	note	note	VERB
ejpam-6466	466	25	that	that	SCONJ
ejpam-6466	466	26	x(τ	x(τ	PROPN
ejpam-6466	466	27	)	)	PUNCT
ejpam-6466	466	28	=	=	PUNCT
ejpam-6466	466	29	x̃(τ	x̃(τ	PROPN
ejpam-6466	466	30	)	)	PUNCT
ejpam-6466	466	31	=	=	SYM
ejpam-6466	466	32	φ(τ	φ(τ	NOUN
ejpam-6466	466	33	)	)	PUNCT
ejpam-6466	466	34	for	for	ADP
ejpam-6466	466	35	τ	τ	PROPN
ejpam-6466	466	36	∈	∈	PROPN
ejpam-6466	466	37	[	[	X
ejpam-6466	466	38	−m	−m	NOUN
ejpam-6466	466	39	,	,	PUNCT
ejpam-6466	466	40	0	0	NUM
ejpam-6466	466	41	]	]	PUNCT
ejpam-6466	466	42	,	,	PUNCT
ejpam-6466	466	43	it	it	PRON
ejpam-6466	466	44	is	be	AUX
ejpam-6466	466	45	clear	clear	ADJ
ejpam-6466	466	46	that	that	SCONJ
ejpam-6466	466	47	{	{	PUNCT
ejpam-6466	466	48	x(τ	x(τ	PROPN
ejpam-6466	466	49	)	)	PUNCT
ejpam-6466	466	50	,	,	PUNCT
ejpam-6466	466	51	−m	−m	NOUN
ejpam-6466	466	52	≤	≤	ADV
ejpam-6466	466	53	τ	τ	PUNCT
ejpam-6466	466	54	≤	≤	NUM
ejpam-6466	466	55	ℏ	ℏ	PROPN
ejpam-6466	466	56	}	}	PUNCT
ejpam-6466	466	57	,	,	PUNCT
ejpam-6466	466	58	and	and	CCONJ
ejpam-6466	466	59	{	{	PUNCT
ejpam-6466	466	60	x̃(τ	x̃(τ	PROPN
ejpam-6466	466	61	)	)	PUNCT
ejpam-6466	466	62	,	,	PUNCT
ejpam-6466	466	63	−m	−m	NOUN
ejpam-6466	466	64	≤	≤	ADV
ejpam-6466	466	65	τ	τ	PUNCT
ejpam-6466	466	66	≤	≤	NUM
ejpam-6466	466	67	ℏ	ℏ	PROPN
ejpam-6466	466	68	}	}	PUNCT
ejpam-6466	466	69	,	,	PUNCT
ejpam-6466	466	70	are	be	AUX
ejpam-6466	466	71	the	the	DET
ejpam-6466	466	72	modification	modification	NOUN
ejpam-6466	466	73	of	of	ADP
ejpam-6466	466	74	each	each	DET
ejpam-6466	466	75	other	other	ADJ
ejpam-6466	466	76	and	and	CCONJ
ejpam-6466	466	77	thus	thus	ADV
ejpam-6466	466	78	are	be	AUX
ejpam-6466	466	79	indistinguishable	indistinguishable	ADJ
ejpam-6466	466	80	.	.	PUNCT
ejpam-6466	467	1	hence	hence	ADV
ejpam-6466	467	2	,	,	PUNCT
ejpam-6466	467	3	it	it	PRON
ejpam-6466	467	4	proved	prove	VERB
ejpam-6466	467	5	the	the	DET
ejpam-6466	467	6	required	require	VERB
ejpam-6466	467	7	result	result	NOUN
ejpam-6466	467	8	.	.	PUNCT
ejpam-6466	468	1	in	in	ADP
ejpam-6466	468	2	the	the	DET
ejpam-6466	468	3	following	following	NOUN
ejpam-6466	468	4	theorem	theorem	NOUN
ejpam-6466	468	5	,	,	PUNCT
ejpam-6466	468	6	we	we	PRON
ejpam-6466	468	7	will	will	AUX
ejpam-6466	468	8	illustrate	illustrate	VERB
ejpam-6466	468	9	the	the	DET
ejpam-6466	468	10	con	con	NOUN
ejpam-6466	468	11	-	-	PUNCT
ejpam-6466	468	12	d	d	PROPN
ejpam-6466	468	13	of	of	ADP
ejpam-6466	468	14	solutions	solution	NOUN
ejpam-6466	468	15	based	base	VERB
ejpam-6466	468	16	on	on	ADP
ejpam-6466	468	17	the	the	DET
ejpam-6466	468	18	initial	initial	ADJ
ejpam-6466	468	19	value	value	NOUN
ejpam-6466	468	20	φ	φ	NOUN
ejpam-6466	468	21	and	and	CCONJ
ejpam-6466	468	22	fractional	fractional	ADJ
ejpam-6466	468	23	exponent	exponent	NOUN
ejpam-6466	468	24	ξ	ξ	PROPN
ejpam-6466	468	25	for	for	ADP
ejpam-6466	468	26	df	df	NOUN
ejpam-6466	468	27	-	-	PUNCT
ejpam-6466	468	28	sdes	sde	NOUN
ejpam-6466	468	29	.	.	PUNCT
ejpam-6466	469	1	theorem	theorem	NOUN
ejpam-6466	469	2	3	3	NUM
ejpam-6466	469	3	.	.	PUNCT
ejpam-6466	469	4	(	(	PUNCT
ejpam-6466	469	5	a2	a2	PROPN
ejpam-6466	469	6	)	)	PUNCT
ejpam-6466	469	7	and	and	CCONJ
ejpam-6466	469	8	(	(	PUNCT
ejpam-6466	469	9	a3	a3	NOUN
ejpam-6466	469	10	)	)	PUNCT
ejpam-6466	469	11	are	be	AUX
ejpam-6466	469	12	assumed	assume	VERB
ejpam-6466	469	13	to	to	PART
ejpam-6466	469	14	be	be	AUX
ejpam-6466	469	15	valid	valid	ADJ
ejpam-6466	469	16	.	.	PUNCT
ejpam-6466	470	1	thus	thus	ADV
ejpam-6466	470	2	,	,	PUNCT
ejpam-6466	470	3	for	for	ADP
ejpam-6466	470	4	every	every	DET
ejpam-6466	470	5	φ	φ	PROPN
ejpam-6466	470	6	,	,	PUNCT
ejpam-6466	470	7	β	β	PROPN
ejpam-6466	470	8	∈	∈	PROPN
ejpam-6466	470	9	c̃([−m	c̃([−m	NOUN
ejpam-6466	470	10	,	,	PUNCT
ejpam-6466	470	11	0],rr	0],rr	PROPN
ejpam-6466	470	12	)	)	PUNCT
ejpam-6466	470	13	,	,	PUNCT
ejpam-6466	470	14	the	the	DET
ejpam-6466	470	15	solution	solution	NOUN
ejpam-6466	470	16	℧	℧	NOUN
ejpam-6466	470	17	ξ(.,φ	ξ(.,φ	NOUN
ejpam-6466	470	18	)	)	PUNCT
ejpam-6466	470	19	of	of	ADP
ejpam-6466	470	20	eq	eq	PROPN
ejpam-6466	470	21	.	.	PUNCT
ejpam-6466	470	22	(	(	PUNCT
ejpam-6466	470	23	4	4	X
ejpam-6466	470	24	)	)	PUNCT
ejpam-6466	470	25	continues	continue	VERB
ejpam-6466	470	26	to	to	PART
ejpam-6466	470	27	be	be	AUX
ejpam-6466	470	28	relying	rely	VERB
ejpam-6466	470	29	on	on	ADP
ejpam-6466	470	30	φ	φ	NUM
ejpam-6466	470	31	,	,	PUNCT
ejpam-6466	470	32	i.e.	i.e.	X
ejpam-6466	470	33	lim	lim	NOUN
ejpam-6466	470	34	φ→β	φ→β	NUM
ejpam-6466	470	35	sup	sup	PROPN
ejpam-6466	470	36	τ∈[−m,ℏ	τ∈[−m,ℏ	NOUN
ejpam-6466	470	37	]	]	X
ejpam-6466	470	38	∥	∥	X
ejpam-6466	470	39	℧	℧	NOUN
ejpam-6466	470	40	ξ(τ	ξ(τ	NOUN
ejpam-6466	470	41	,	,	PUNCT
ejpam-6466	470	42	φ)−	φ)−	PROPN
ejpam-6466	470	43	℧	℧	NOUN
ejpam-6466	470	44	ξ(τ	ξ(τ	NOUN
ejpam-6466	470	45	,	,	PUNCT
ejpam-6466	470	46	β)∥ms	β)∥ms	NOUN
ejpam-6466	470	47	=	=	SYM
ejpam-6466	470	48	0	0	X
ejpam-6466	470	49	.	.	PUNCT
ejpam-6466	471	1	(	(	PUNCT
ejpam-6466	471	2	39	39	NUM
ejpam-6466	471	3	)	)	PUNCT
ejpam-6466	471	4	proof	proof	NOUN
ejpam-6466	471	5	.	.	PUNCT
ejpam-6466	472	1	choose	choose	VERB
ejpam-6466	472	2	and	and	CCONJ
ejpam-6466	472	3	fix	fix	VERB
ejpam-6466	472	4	ℏ	ℏ	PROPN
ejpam-6466	472	5	>	>	X
ejpam-6466	472	6	0	0	PROPN
ejpam-6466	472	7	and	and	CCONJ
ejpam-6466	472	8	φ	φ	NUM
ejpam-6466	472	9	,	,	PUNCT
ejpam-6466	472	10	β	β	PROPN
ejpam-6466	472	11	∈	∈	PROPN
ejpam-6466	472	12	c̃([−m	c̃([−m	NOUN
ejpam-6466	472	13	,	,	PUNCT
ejpam-6466	472	14	0],rr	0],rr	PROPN
ejpam-6466	472	15	)	)	PUNCT
ejpam-6466	472	16	.	.	PUNCT
ejpam-6466	473	1	because	because	SCONJ
ejpam-6466	473	2	℧	℧	PROPN
ejpam-6466	473	3	ξ	ξ	X
ejpam-6466	473	4	(	(	PUNCT
ejpam-6466	473	5	.	.	PUNCT
ejpam-6466	473	6	,	,	PUNCT
ejpam-6466	473	7	β	β	X
ejpam-6466	473	8	)	)	PUNCT
ejpam-6466	473	9	and	and	CCONJ
ejpam-6466	473	10	℧	℧	NOUN
ejpam-6466	473	11	ξ(.,φ	ξ(.,φ	NOUN
ejpam-6466	473	12	)	)	PUNCT
ejpam-6466	473	13	are	be	AUX
ejpam-6466	473	14	solutions	solution	NOUN
ejpam-6466	473	15	of	of	ADP
ejpam-6466	473	16	eq	eq	PROPN
ejpam-6466	473	17	.	.	PUNCT
ejpam-6466	474	1	(	(	PUNCT
ejpam-6466	474	2	4	4	NUM
ejpam-6466	474	3	)	)	PUNCT
ejpam-6466	474	4	,	,	PUNCT
ejpam-6466	474	5	utilizing	utilize	VERB
ejpam-6466	474	6	the	the	DET
ejpam-6466	474	7	eq	eq	NOUN
ejpam-6466	474	8	.	.	PUNCT
ejpam-6466	475	1	(	(	PUNCT
ejpam-6466	475	2	9	9	NUM
ejpam-6466	475	3	)	)	PUNCT
ejpam-6466	475	4	,	,	PUNCT
ejpam-6466	475	5	the	the	DET
ejpam-6466	475	6	höld	höld	NOUN
ejpam-6466	475	7	-	-	PUNCT
ejpam-6466	475	8	i	i	PROPN
ejpam-6466	475	9	,	,	PUNCT
ejpam-6466	475	10	i	i	PRON
ejpam-6466	475	11	-	-	PUNCT
ejpam-6466	475	12	is	be	AUX
ejpam-6466	475	13	,	,	PUNCT
ejpam-6466	475	14	(	(	PUNCT
ejpam-6466	475	15	a3	a3	NOUN
ejpam-6466	475	16	)	)	PUNCT
ejpam-6466	475	17	,	,	PUNCT
ejpam-6466	475	18	and	and	CCONJ
ejpam-6466	475	19	lemma	lemma	PROPN
ejpam-6466	475	20	2	2	NUM
ejpam-6466	475	21	,	,	PUNCT
ejpam-6466	475	22	we	we	PRON
ejpam-6466	475	23	yield	yield	VERB
ejpam-6466	475	24	sup	sup	NOUN
ejpam-6466	475	25	τ∈[0,ℏ	τ∈[0,ℏ	SYM
ejpam-6466	475	26	]	]	X
ejpam-6466	475	27	e	e	X
ejpam-6466	475	28	[	[	PUNCT
ejpam-6466	475	29	∥	∥	X
ejpam-6466	475	30	℧	℧	NOUN
ejpam-6466	475	31	ξ(τ	ξ(τ	NOUN
ejpam-6466	475	32	,	,	PUNCT
ejpam-6466	475	33	φ)−	φ)−	PROPN
ejpam-6466	475	34	℧	℧	NOUN
ejpam-6466	475	35	ξ(τ	ξ(τ	NOUN
ejpam-6466	475	36	,	,	PUNCT
ejpam-6466	475	37	β)∥2	β)∥2	PROPN
ejpam-6466	475	38	]	]	PUNCT
ejpam-6466	475	39	e2φ−1(ϑ(τ	e2φ−1(ϑ(τ	NOUN
ejpam-6466	476	1	+	+	ADJ
ejpam-6466	476	2	m)2φ−1	m)2φ−1	X
ejpam-6466	476	3	)	)	PUNCT
ejpam-6466	476	4	≤3e	≤3e	NOUN
ejpam-6466	476	5	[	[	PUNCT
ejpam-6466	476	6	∥φ−	∥φ−	NUM
ejpam-6466	476	7	β∥2	β∥2	NOUN
ejpam-6466	476	8	]	]	PUNCT
ejpam-6466	477	1	+	+	CCONJ
ejpam-6466	477	2	γ(2ξ	γ(2ξ	PUNCT
ejpam-6466	477	3	−	−	PROPN
ejpam-6466	477	4	1	1	NUM
ejpam-6466	477	5	)	)	PUNCT
ejpam-6466	477	6	ϑ	ϑ	X
ejpam-6466	477	7	6l2(τ	6l2(τ	NUM
ejpam-6466	477	8	+	+	CCONJ
ejpam-6466	477	9	1	1	X
ejpam-6466	477	10	)	)	PUNCT
ejpam-6466	477	11	×	×	NOUN
ejpam-6466	477	12	sup	sup	NOUN
ejpam-6466	477	13	s∈[0,ℏ	s∈[0,ℏ	PROPN
ejpam-6466	477	14	]	]	PUNCT
ejpam-6466	477	15	e	e	X
ejpam-6466	477	16	[	[	PUNCT
ejpam-6466	477	17	∥	∥	X
ejpam-6466	477	18	℧	℧	NOUN
ejpam-6466	477	19	ξ(s	ξ(s	PROPN
ejpam-6466	477	20	,	,	PUNCT
ejpam-6466	477	21	φ)−	φ)−	PROPN
ejpam-6466	477	22	℧	℧	NOUN
ejpam-6466	477	23	ξ(s	ξ(s	PROPN
ejpam-6466	477	24	,	,	PUNCT
ejpam-6466	477	25	β)∥2	β)∥2	ADJ
ejpam-6466	477	26	]	]	PUNCT
ejpam-6466	477	27	e2φ−1(ϑ(s	e2φ−1(ϑ(s	VERB
ejpam-6466	477	28	+	+	PUNCT
ejpam-6466	477	29	m)2φ−1	m)2φ−1	NOUN
ejpam-6466	477	30	)	)	PUNCT
ejpam-6466	477	31	.	.	PUNCT
ejpam-6466	478	1	(	(	PUNCT
ejpam-6466	478	2	40	40	NUM
ejpam-6466	478	3	)	)	PUNCT
ejpam-6466	478	4	by	by	ADP
ejpam-6466	478	5	definition	definition	NOUN
ejpam-6466	478	6	of	of	ADP
ejpam-6466	478	7	∥	∥	X
ejpam-6466	478	8	·	·	PUNCT
ejpam-6466	479	1	∥ϑ	∥ϑ	NOUN
ejpam-6466	479	2	,	,	PUNCT
ejpam-6466	479	3	gives	give	VERB
ejpam-6466	479	4	us	we	PRON
ejpam-6466	479	5	(	(	PUNCT
ejpam-6466	479	6	1−	1−	NUM
ejpam-6466	479	7	γ(2ξ	γ(2ξ	PUNCT
ejpam-6466	479	8	−	−	PROPN
ejpam-6466	479	9	1	1	NUM
ejpam-6466	479	10	)	)	PUNCT
ejpam-6466	479	11	ϑ	ϑ	X
ejpam-6466	479	12	6l2(τ	6l2(τ	NUM
ejpam-6466	479	13	+	+	CCONJ
ejpam-6466	479	14	1	1	NUM
ejpam-6466	479	15	)	)	PUNCT
ejpam-6466	479	16	)	)	PUNCT
ejpam-6466	480	1	∥	∥	X
ejpam-6466	480	2	℧	℧	NOUN
ejpam-6466	480	3	ξ(τ	ξ(τ	NOUN
ejpam-6466	480	4	,	,	PUNCT
ejpam-6466	480	5	φ)−	φ)−	PROPN
ejpam-6466	480	6	℧	℧	NOUN
ejpam-6466	480	7	ξ(τ	ξ(τ	NOUN
ejpam-6466	480	8	,	,	PUNCT
ejpam-6466	480	9	β)∥2ϑ	β)∥2ϑ	PUNCT
ejpam-6466	480	10	≤	≤	NOUN
ejpam-6466	480	11	3∥φ−	3∥φ−	NUM
ejpam-6466	481	1	β∥2ms	β∥2ms	PROPN
ejpam-6466	481	2	,	,	PUNCT
ejpam-6466	481	3	(	(	PUNCT
ejpam-6466	481	4	41	41	NUM
ejpam-6466	481	5	)	)	PUNCT
ejpam-6466	481	6	which	which	PRON
ejpam-6466	481	7	together	together	ADV
ejpam-6466	481	8	with	with	ADP
ejpam-6466	481	9	eq	eq	NOUN
ejpam-6466	481	10	.	.	PUNCT
ejpam-6466	481	11	(	(	PUNCT
ejpam-6466	481	12	20	20	NUM
ejpam-6466	481	13	)	)	PUNCT
ejpam-6466	481	14	and	and	CCONJ
ejpam-6466	481	15	℧	℧	PROPN
ejpam-6466	481	16	ξ(τ	ξ(τ	PROPN
ejpam-6466	481	17	,	,	PUNCT
ejpam-6466	481	18	φ	φ	NUM
ejpam-6466	481	19	)	)	PUNCT
ejpam-6466	481	20	=	=	SYM
ejpam-6466	481	21	φ(τ	φ(τ	NOUN
ejpam-6466	481	22	)	)	PUNCT
ejpam-6466	481	23	with	with	ADP
ejpam-6466	481	24	τ	τ	PROPN
ejpam-6466	481	25	∈	∈	PROPN
ejpam-6466	481	26	[	[	X
ejpam-6466	481	27	−m	−m	NOUN
ejpam-6466	481	28	,	,	PUNCT
ejpam-6466	481	29	0	0	NUM
ejpam-6466	481	30	]	]	PUNCT
ejpam-6466	481	31	,	,	PUNCT
ejpam-6466	481	32	we	we	PRON
ejpam-6466	481	33	derive	derive	VERB
ejpam-6466	481	34	lim	lim	NOUN
ejpam-6466	481	35	φ→β	φ→β	NUM
ejpam-6466	481	36	sup	sup	PROPN
ejpam-6466	481	37	τ∈[−m,ℏ	τ∈[−m,ℏ	NOUN
ejpam-6466	481	38	]	]	X
ejpam-6466	481	39	∥	∥	X
ejpam-6466	481	40	℧	℧	NOUN
ejpam-6466	481	41	ξ(τ	ξ(τ	NOUN
ejpam-6466	481	42	,	,	PUNCT
ejpam-6466	481	43	φ)−	φ)−	PROPN
ejpam-6466	481	44	℧	℧	NOUN
ejpam-6466	481	45	ξ(τ	ξ(τ	NOUN
ejpam-6466	481	46	,	,	PUNCT
ejpam-6466	481	47	β)∥2ϑ	β)∥2ϑ	PUNCT
ejpam-6466	482	1	=	=	NOUN
ejpam-6466	482	2	0	0	X
ejpam-6466	482	3	.	.	PUNCT
ejpam-6466	483	1	(	(	PUNCT
ejpam-6466	483	2	42	42	NUM
ejpam-6466	483	3	)	)	PUNCT
ejpam-6466	483	4	the	the	DET
ejpam-6466	483	5	con	con	NOUN
ejpam-6466	483	6	-	-	PUNCT
ejpam-6466	483	7	d	d	PROPN
ejpam-6466	483	8	of	of	ADP
ejpam-6466	483	9	solutions	solution	NOUN
ejpam-6466	483	10	on	on	ADP
ejpam-6466	483	11	the	the	DET
ejpam-6466	483	12	fractional	fractional	ADJ
ejpam-6466	483	13	exponents	exponent	NOUN
ejpam-6466	483	14	ξ	ξ	PROPN
ejpam-6466	483	15	and	and	CCONJ
ejpam-6466	483	16	ξ̃	ξ̃	PROPN
ejpam-6466	483	17	for	for	ADP
ejpam-6466	483	18	df	df	NOUN
ejpam-6466	483	19	-	-	PUNCT
ejpam-6466	483	20	sdes	sde	NOUN
ejpam-6466	483	21	will	will	AUX
ejpam-6466	483	22	be	be	AUX
ejpam-6466	483	23	demonstrated	demonstrate	VERB
ejpam-6466	483	24	in	in	ADP
ejpam-6466	483	25	the	the	DET
ejpam-6466	483	26	ensuing	ensue	VERB
ejpam-6466	483	27	theorem	theorem	NOUN
ejpam-6466	483	28	.	.	PUNCT
ejpam-6466	484	1	theorem	theorem	NOUN
ejpam-6466	484	2	4	4	NUM
ejpam-6466	484	3	.	.	PUNCT
ejpam-6466	485	1	assume	assume	VERB
ejpam-6466	485	2	that	that	SCONJ
ejpam-6466	485	3	(	(	PUNCT
ejpam-6466	485	4	h2	h2	NOUN
ejpam-6466	485	5	)	)	PUNCT
ejpam-6466	485	6	and	and	CCONJ
ejpam-6466	485	7	(	(	PUNCT
ejpam-6466	485	8	h3	h3	NOUN
ejpam-6466	485	9	)	)	PUNCT
ejpam-6466	485	10	are	be	AUX
ejpam-6466	485	11	both	both	ADV
ejpam-6466	485	12	valid	valid	ADJ
ejpam-6466	485	13	.	.	PUNCT
ejpam-6466	486	1	following	follow	VERB
ejpam-6466	486	2	this	this	PRON
ejpam-6466	486	3	,	,	PUNCT
ejpam-6466	486	4	the	the	DET
ejpam-6466	486	5	solution	solution	NOUN
ejpam-6466	486	6	℧	℧	NOUN
ejpam-6466	486	7	ξ(.,φ	ξ(.,φ	NOUN
ejpam-6466	486	8	)	)	PUNCT
ejpam-6466	486	9	to	to	ADP
ejpam-6466	486	10	eq	eq	PROPN
ejpam-6466	486	11	.	.	PUNCT
ejpam-6466	487	1	(	(	PUNCT
ejpam-6466	487	2	4	4	X
ejpam-6466	487	3	)	)	PUNCT
ejpam-6466	487	4	exhibits	exhibit	VERB
ejpam-6466	487	5	con	con	NOUN
ejpam-6466	487	6	-	-	PUNCT
ejpam-6466	487	7	d	d	NOUN
ejpam-6466	487	8	on	on	ADP
ejpam-6466	487	9	ξ	ξ	PROPN
ejpam-6466	487	10	,	,	PUNCT
ejpam-6466	487	11	i.e.	i.e.	X
ejpam-6466	487	12	lim	lim	PROPN
ejpam-6466	487	13	ξ̃→ξ	ξ̃→ξ	PROPN
ejpam-6466	487	14	sup	sup	PROPN
ejpam-6466	487	15	τ∈[−m,ℏ	τ∈[−m,ℏ	NOUN
ejpam-6466	487	16	]	]	X
ejpam-6466	487	17	∥	∥	X
ejpam-6466	487	18	℧	℧	NOUN
ejpam-6466	487	19	ξ(τ	ξ(τ	NOUN
ejpam-6466	487	20	,	,	PUNCT
ejpam-6466	487	21	φ)−	φ)−	PROPN
ejpam-6466	487	22	℧	℧	PROPN
ejpam-6466	487	23	ξ̃(τ	ξ̃(τ	PROPN
ejpam-6466	487	24	,	,	PUNCT
ejpam-6466	487	25	φ)∥ms	φ)∥ms	NOUN
ejpam-6466	487	26	=	=	SYM
ejpam-6466	487	27	0	0	NUM
ejpam-6466	487	28	.	.	PUNCT
ejpam-6466	488	1	(	(	PUNCT
ejpam-6466	488	2	43	43	NUM
ejpam-6466	488	3	)	)	PUNCT
ejpam-6466	488	4	m.	m.	NOUN
ejpam-6466	488	5	i.	i.	PROPN
ejpam-6466	488	6	liaqat	liaqat	PROPN
ejpam-6466	488	7	et	et	PROPN
ejpam-6466	488	8	al	al	PROPN
ejpam-6466	488	9	.	.	PUNCT
ejpam-6466	488	10	/	/	SYM
ejpam-6466	488	11	eur	eur	PROPN
ejpam-6466	488	12	.	.	PUNCT
ejpam-6466	489	1	j.	j.	PROPN
ejpam-6466	489	2	pure	pure	PROPN
ejpam-6466	489	3	appl	appl	PROPN
ejpam-6466	489	4	.	.	PROPN
ejpam-6466	489	5	math	math	PROPN
ejpam-6466	489	6	,	,	PUNCT
ejpam-6466	489	7	18	18	NUM
ejpam-6466	489	8	(	(	PUNCT
ejpam-6466	489	9	4	4	NUM
ejpam-6466	489	10	)	)	PUNCT
ejpam-6466	489	11	(	(	PUNCT
ejpam-6466	489	12	2025	2025	NUM
ejpam-6466	489	13	)	)	PUNCT
ejpam-6466	489	14	,	,	PUNCT
ejpam-6466	489	15	6466	6466	NUM
ejpam-6466	489	16	18	18	NUM
ejpam-6466	489	17	of	of	ADP
ejpam-6466	489	18	28	28	NUM
ejpam-6466	489	19	proof	proof	NOUN
ejpam-6466	489	20	.	.	PUNCT
ejpam-6466	490	1	let	let	VERB
ejpam-6466	490	2	ξ	ξ	X
ejpam-6466	490	3	,	,	PUNCT
ejpam-6466	490	4	ξ̃	ξ̃	PROPN
ejpam-6466	490	5	∈	∈	PROPN
ejpam-6466	490	6	(	(	PUNCT
ejpam-6466	490	7	12	12	NUM
ejpam-6466	490	8	,	,	PUNCT
ejpam-6466	490	9	1	1	NUM
ejpam-6466	490	10	)	)	PUNCT
ejpam-6466	490	11	be	be	AUX
ejpam-6466	490	12	arbitrary	arbitrary	ADJ
ejpam-6466	490	13	but	but	CCONJ
ejpam-6466	490	14	fixed	fix	VERB
ejpam-6466	490	15	.	.	PUNCT
ejpam-6466	491	1	select	select	VERB
ejpam-6466	491	2	and	and	CCONJ
ejpam-6466	491	3	adjust	adjust	VERB
ejpam-6466	491	4	φ	φ	PROPN
ejpam-6466	491	5	∈	∈	PROPN
ejpam-6466	491	6	c̃([−m	c̃([−m	NOUN
ejpam-6466	491	7	,	,	PUNCT
ejpam-6466	491	8	0],rr	0],rr	PROPN
ejpam-6466	491	9	)	)	PUNCT
ejpam-6466	491	10	.	.	PUNCT
ejpam-6466	492	1	as	as	SCONJ
ejpam-6466	492	2	℧	℧	NOUN
ejpam-6466	492	3	ξ(.,φ	ξ(.,φ	NOUN
ejpam-6466	492	4	)	)	PUNCT
ejpam-6466	492	5	and	and	CCONJ
ejpam-6466	492	6	℧	℧	NOUN
ejpam-6466	492	7	ξ̃(.,φ	ξ̃(.,φ	ADJ
ejpam-6466	492	8	)	)	PUNCT
ejpam-6466	492	9	are	be	AUX
ejpam-6466	492	10	solutions	solution	NOUN
ejpam-6466	492	11	of	of	ADP
ejpam-6466	492	12	eq	eq	PROPN
ejpam-6466	492	13	.	.	PUNCT
ejpam-6466	493	1	(	(	PUNCT
ejpam-6466	493	2	4	4	NUM
ejpam-6466	493	3	)	)	PUNCT
ejpam-6466	493	4	and	and	CCONJ
ejpam-6466	493	5	by	by	ADP
ejpam-6466	493	6	utilizing	utilize	VERB
ejpam-6466	493	7	höld	höld	NOUN
ejpam-6466	493	8	-	-	PUNCT
ejpam-6466	493	9	i	i	PROPN
ejpam-6466	493	10	,	,	PUNCT
ejpam-6466	493	11	i	i	PRON
ejpam-6466	493	12	-	-	PUNCT
ejpam-6466	493	13	is	be	AUX
ejpam-6466	493	14	,	,	PUNCT
ejpam-6466	493	15	eq	eq	ADJ
ejpam-6466	493	16	.	.	PUNCT
ejpam-6466	494	1	(	(	PUNCT
ejpam-6466	494	2	9	9	NUM
ejpam-6466	494	3	)	)	PUNCT
ejpam-6466	494	4	,	,	PUNCT
ejpam-6466	494	5	and	and	CCONJ
ejpam-6466	494	6	(	(	PUNCT
ejpam-6466	494	7	a3	a3	NOUN
ejpam-6466	494	8	)	)	PUNCT
ejpam-6466	494	9	,	,	PUNCT
ejpam-6466	494	10	we	we	PRON
ejpam-6466	494	11	achieve	achieve	VERB
ejpam-6466	494	12	e	e	NOUN
ejpam-6466	494	13	[	[	PUNCT
ejpam-6466	494	14	∥	∥	X
ejpam-6466	494	15	℧	℧	NOUN
ejpam-6466	494	16	ξ(τ	ξ(τ	NOUN
ejpam-6466	494	17	,	,	PUNCT
ejpam-6466	494	18	φ)−	φ)−	PROPN
ejpam-6466	494	19	℧	℧	PROPN
ejpam-6466	494	20	ξ̃(τ	ξ̃(τ	PROPN
ejpam-6466	494	21	,	,	PUNCT
ejpam-6466	494	22	β)∥	β)∥	X
ejpam-6466	494	23	2	2	X
ejpam-6466	494	24	]	]	PUNCT
ejpam-6466	494	25	e2ξ−1(ϑ(τ	e2ξ−1(ϑ(τ	NOUN
ejpam-6466	494	26	+	+	NOUN
ejpam-6466	494	27	m)2φ−1	m)2φ−1	NOUN
ejpam-6466	494	28	)	)	PUNCT
ejpam-6466	494	29	≤	≤	NUM
ejpam-6466	494	30	sup	sup	NOUN
ejpam-6466	494	31	s∈[0,ℏ	s∈[0,ℏ	PROPN
ejpam-6466	494	32	]	]	PUNCT
ejpam-6466	494	33	e	e	X
ejpam-6466	494	34	[	[	PUNCT
ejpam-6466	494	35	∥	∥	X
ejpam-6466	494	36	℧	℧	NOUN
ejpam-6466	494	37	ξ(s	ξ(s	PROPN
ejpam-6466	494	38	,	,	PUNCT
ejpam-6466	494	39	φ)−	φ)−	PROPN
ejpam-6466	494	40	℧	℧	NOUN
ejpam-6466	494	41	ξ̃(s	ξ̃(s	NOUN
ejpam-6466	494	42	,	,	PUNCT
ejpam-6466	494	43	β)∥	β)∥	X
ejpam-6466	494	44	2	2	X
ejpam-6466	494	45	]	]	PUNCT
ejpam-6466	494	46	e2ξ−1(ϑ(s	e2ξ−1(ϑ(s	NOUN
ejpam-6466	494	47	+	+	PUNCT
ejpam-6466	494	48	m)2φ−1	m)2φ−1	NOUN
ejpam-6466	494	49	)	)	PUNCT
ejpam-6466	494	50	8(τ	8(τ	NOUN
ejpam-6466	495	1	+	+	CCONJ
ejpam-6466	495	2	1)l2	1)l2	NUM
ejpam-6466	495	3	∫	∫	NOUN
ejpam-6466	495	4	τ	τ	PROPN
ejpam-6466	495	5	0	0	NUM
ejpam-6466	495	6	s2ξ−2e2ξ−1(ϑ(s	s2ξ−2e2ξ−1(ϑ(s	PROPN
ejpam-6466	495	7	+	+	CCONJ
ejpam-6466	495	8	m)2φ−1)ds	m)2φ−1)ds	NOUN
ejpam-6466	495	9	e2ξ−1(ϑ(s	e2ξ−1(ϑ(s	VERB
ejpam-6466	495	10	+	+	SYM
ejpam-6466	495	11	m)2φ−1	m)2φ−1	NOUN
ejpam-6466	495	12	)	)	PUNCT
ejpam-6466	495	13	+4(τ	+4(τ	NOUN
ejpam-6466	496	1	+	+	CCONJ
ejpam-6466	496	2	1	1	X
ejpam-6466	496	3	)	)	PUNCT
ejpam-6466	496	4	(	(	PUNCT
ejpam-6466	496	5	4l2	4l2	NUM
ejpam-6466	496	6	sup	sup	NOUN
ejpam-6466	496	7	s∈[0,ℏ	s∈[0,ℏ	PROPN
ejpam-6466	496	8	]	]	PUNCT
ejpam-6466	496	9	∥	∥	PUNCT
ejpam-6466	497	1	℧	℧	NOUN
ejpam-6466	497	2	ξ̃(s	ξ̃(s	NOUN
ejpam-6466	497	3	,	,	PUNCT
ejpam-6466	497	4	φ)∥	φ)∥	X
ejpam-6466	497	5	2	2	NUM
ejpam-6466	498	1	+	+	NUM
ejpam-6466	498	2	2l2∥φ∥2ms	2l2∥φ∥2ms	NUM
ejpam-6466	498	3	+	+	NUM
ejpam-6466	498	4	2k2	2k2	NUM
ejpam-6466	498	5	)	)	PUNCT
ejpam-6466	498	6	×	×	NOUN
ejpam-6466	498	7	∫	∫	PROPN
ejpam-6466	498	8	τ	τ	X
ejpam-6466	498	9	0	0	NUM
ejpam-6466	498	10	(	(	PUNCT
ejpam-6466	498	11	λ(τ	λ(τ	PROPN
ejpam-6466	498	12	,	,	PUNCT
ejpam-6466	498	13	s	s	PROPN
ejpam-6466	498	14	,	,	PUNCT
ejpam-6466	498	15	φ	φ	NOUN
ejpam-6466	498	16	,	,	PUNCT
ejpam-6466	498	17	φ̃	φ̃	PROPN
ejpam-6466	498	18	)	)	PUNCT
ejpam-6466	498	19	)	)	PUNCT
ejpam-6466	498	20	2	2	NUM
ejpam-6466	498	21	,	,	PUNCT
ejpam-6466	498	22	(	(	PUNCT
ejpam-6466	498	23	44	44	NUM
ejpam-6466	498	24	)	)	PUNCT
ejpam-6466	499	1	where	where	SCONJ
ejpam-6466	499	2	λ(τ	λ(τ	NOUN
ejpam-6466	499	3	,	,	PUNCT
ejpam-6466	499	4	s	s	PROPN
ejpam-6466	499	5	,	,	PUNCT
ejpam-6466	499	6	φ	φ	NOUN
ejpam-6466	499	7	,	,	PUNCT
ejpam-6466	499	8	φ̃	φ̃	PROPN
ejpam-6466	499	9	)	)	PUNCT
ejpam-6466	499	10	=	=	NOUN
ejpam-6466	499	11	|τφ−1	|τφ−1	NOUN
ejpam-6466	500	1	−	−	NOUN
ejpam-6466	500	2	τ	τ	SYM
ejpam-6466	500	3	φ̃−1|	φ̃−1|	PROPN
ejpam-6466	500	4	.	.	PUNCT
ejpam-6466	501	1	(	(	PUNCT
ejpam-6466	501	2	45	45	NUM
ejpam-6466	501	3	)	)	PUNCT
ejpam-6466	501	4	by	by	ADP
ejpam-6466	501	5	virtue	virtue	NOUN
ejpam-6466	501	6	of	of	ADP
ejpam-6466	501	7	lemma	lemma	PROPN
ejpam-6466	501	8	2	2	NUM
ejpam-6466	501	9	and	and	CCONJ
ejpam-6466	501	10	by	by	ADP
ejpam-6466	501	11	the	the	DET
ejpam-6466	501	12	definition	definition	NOUN
ejpam-6466	501	13	of	of	ADP
ejpam-6466	501	14	∥	∥	X
ejpam-6466	501	15	·	·	PUNCT
ejpam-6466	502	1	∥ϑ	∥ϑ	NOUN
ejpam-6466	502	2	,	,	PUNCT
ejpam-6466	502	3	we	we	PRON
ejpam-6466	502	4	attain	attain	VERB
ejpam-6466	502	5	(	(	PUNCT
ejpam-6466	502	6	1−8(ℏ+	1−8(ℏ+	PROPN
ejpam-6466	502	7	1)l2γ(2ξ	1)l2γ(2ξ	NUM
ejpam-6466	502	8	−	−	PROPN
ejpam-6466	502	9	1	1	NUM
ejpam-6466	502	10	)	)	PUNCT
ejpam-6466	502	11	ϑ	ϑ	X
ejpam-6466	502	12	)	)	PUNCT
ejpam-6466	502	13	∥	∥	NUM
ejpam-6466	502	14	℧	℧	NOUN
ejpam-6466	502	15	ξ(τ	ξ(τ	NOUN
ejpam-6466	502	16	,	,	PUNCT
ejpam-6466	502	17	φ)−	φ)−	PROPN
ejpam-6466	502	18	℧	℧	PROPN
ejpam-6466	502	19	ξ̃(τ	ξ̃(τ	PROPN
ejpam-6466	502	20	,	,	PUNCT
ejpam-6466	502	21	β)∥	β)∥	X
ejpam-6466	502	22	2	2	NUM
ejpam-6466	502	23	ϑ	ϑ	NOUN
ejpam-6466	502	24	≤4(ℏ+	≤4(ℏ+	NOUN
ejpam-6466	502	25	1)4(τ	1)4(τ	NUM
ejpam-6466	502	26	+	+	CCONJ
ejpam-6466	502	27	1	1	X
ejpam-6466	502	28	)	)	PUNCT
ejpam-6466	502	29	(	(	PUNCT
ejpam-6466	502	30	4l2	4l2	NUM
ejpam-6466	502	31	sup	sup	NOUN
ejpam-6466	502	32	s∈[0,ℏ	s∈[0,ℏ	PROPN
ejpam-6466	502	33	]	]	PUNCT
ejpam-6466	502	34	∥	∥	PUNCT
ejpam-6466	502	35	℧	℧	NOUN
ejpam-6466	502	36	ξ̃(s	ξ̃(s	NOUN
ejpam-6466	502	37	,	,	PUNCT
ejpam-6466	502	38	φ)∥	φ)∥	X
ejpam-6466	502	39	2	2	NUM
ejpam-6466	502	40	+	+	NUM
ejpam-6466	502	41	2l2∥φ∥2ms	2l2∥φ∥2ms	NUM
ejpam-6466	502	42	+	+	NUM
ejpam-6466	502	43	2k2	2k2	NUM
ejpam-6466	502	44	)	)	PUNCT
ejpam-6466	503	1	×	×	NOUN
ejpam-6466	503	2	∫	∫	PROPN
ejpam-6466	503	3	τ	τ	X
ejpam-6466	503	4	0	0	NUM
ejpam-6466	504	1	(	(	PUNCT
ejpam-6466	504	2	λ(τ	λ(τ	PROPN
ejpam-6466	504	3	,	,	PUNCT
ejpam-6466	504	4	s	s	PROPN
ejpam-6466	504	5	,	,	PUNCT
ejpam-6466	504	6	φ	φ	NOUN
ejpam-6466	504	7	,	,	PUNCT
ejpam-6466	504	8	φ̃	φ̃	PROPN
ejpam-6466	504	9	)	)	PUNCT
ejpam-6466	504	10	)	)	PUNCT
ejpam-6466	504	11	2	2	NUM
ejpam-6466	504	12	ds	ds	NOUN
ejpam-6466	504	13	.	.	PUNCT
ejpam-6466	505	1	however	however	ADV
ejpam-6466	505	2	,	,	PUNCT
ejpam-6466	505	3	we	we	PRON
ejpam-6466	505	4	yield∫	yield∫	NOUN
ejpam-6466	505	5	τ	τ	PROPN
ejpam-6466	505	6	0	0	NUM
ejpam-6466	506	1	(	(	PUNCT
ejpam-6466	506	2	λ(τ	λ(τ	PROPN
ejpam-6466	506	3	,	,	PUNCT
ejpam-6466	506	4	s	s	PROPN
ejpam-6466	506	5	,	,	PUNCT
ejpam-6466	506	6	φ	φ	NOUN
ejpam-6466	506	7	,	,	PUNCT
ejpam-6466	506	8	φ̃	φ̃	PROPN
ejpam-6466	506	9	)	)	PUNCT
ejpam-6466	506	10	)	)	PUNCT
ejpam-6466	506	11	2	2	NUM
ejpam-6466	506	12	ds	ds	NOUN
ejpam-6466	506	13	=	=	SYM
ejpam-6466	506	14	∫	∫	PROPN
ejpam-6466	506	15	τ	τ	PROPN
ejpam-6466	506	16	0	0	NUM
ejpam-6466	506	17	s2ξ−2ds	s2ξ−2ds	NOUN
ejpam-6466	506	18	+	+	CCONJ
ejpam-6466	506	19	∫	∫	PROPN
ejpam-6466	506	20	τ	τ	X
ejpam-6466	506	21	0	0	NUM
ejpam-6466	507	1	s2ξ̃−2ds	s2ξ̃−2ds	NOUN
ejpam-6466	507	2	+	+	CCONJ
ejpam-6466	507	3	∫	∫	PROPN
ejpam-6466	507	4	τ	τ	X
ejpam-6466	507	5	0	0	NUM
ejpam-6466	507	6	sξ+ξ̃−2ds	sξ+ξ̃−2ds	NOUN
ejpam-6466	507	7	=	=	SYM
ejpam-6466	507	8	τ2ξ−1	τ2ξ−1	PROPN
ejpam-6466	507	9	2ξ	2ξ	NUM
ejpam-6466	507	10	−	−	ADP
ejpam-6466	507	11	1	1	NUM
ejpam-6466	507	12	+	+	CCONJ
ejpam-6466	507	13	τ2ξ̃−1	τ2ξ̃−1	X
ejpam-6466	507	14	2ξ̃	2ξ̃	NUM
ejpam-6466	507	15	−	−	NOUN
ejpam-6466	508	1	1	1	NUM
ejpam-6466	509	1	+	+	CCONJ
ejpam-6466	509	2	τ	τ	PROPN
ejpam-6466	509	3	ξ+ξ̃−1	ξ+ξ̃−1	X
ejpam-6466	509	4	ξ	ξ	X
ejpam-6466	510	1	+	+	PUNCT
ejpam-6466	510	2	ξ̃	ξ̃	NUM
ejpam-6466	510	3	−	−	NOUN
ejpam-6466	510	4	1	1	NUM
ejpam-6466	510	5	.	.	PUNCT
ejpam-6466	511	1	as	as	ADP
ejpam-6466	511	2	a	a	DET
ejpam-6466	511	3	result	result	NOUN
ejpam-6466	511	4	,	,	PUNCT
ejpam-6466	511	5	lim	lim	PROPN
ejpam-6466	511	6	ξ̃→ξ	ξ̃→ξ	PROPN
ejpam-6466	511	7	sup	sup	PROPN
ejpam-6466	511	8	τ∈[0,ℏ	τ∈[0,ℏ	PROPN
ejpam-6466	511	9	]	]	X
ejpam-6466	511	10	∫	∫	PROPN
ejpam-6466	511	11	τ	τ	X
ejpam-6466	511	12	0	0	NUM
ejpam-6466	511	13	(	(	PUNCT
ejpam-6466	511	14	λ(τ	λ(τ	PROPN
ejpam-6466	511	15	,	,	PUNCT
ejpam-6466	511	16	s	s	PROPN
ejpam-6466	511	17	,	,	PUNCT
ejpam-6466	511	18	φ	φ	NOUN
ejpam-6466	511	19	,	,	PUNCT
ejpam-6466	511	20	φ̃	φ̃	PROPN
ejpam-6466	511	21	)	)	PUNCT
ejpam-6466	511	22	)	)	PUNCT
ejpam-6466	511	23	2	2	NUM
ejpam-6466	511	24	ds	ds	NOUN
ejpam-6466	511	25	=	=	NOUN
ejpam-6466	511	26	0	0	NUM
ejpam-6466	511	27	.	.	PUNCT
ejpam-6466	511	28	when	when	SCONJ
ejpam-6466	511	29	associated	associate	VERB
ejpam-6466	511	30	with	with	ADP
ejpam-6466	511	31	eq	eq	NOUN
ejpam-6466	511	32	.	.	PUNCT
ejpam-6466	511	33	(	(	PUNCT
ejpam-6466	511	34	4	4	NUM
ejpam-6466	511	35	)	)	PUNCT
ejpam-6466	511	36	,	,	PUNCT
ejpam-6466	511	37	this	this	PRON
ejpam-6466	511	38	suggests	suggest	VERB
ejpam-6466	511	39	the	the	DET
ejpam-6466	511	40	completion	completion	NOUN
ejpam-6466	511	41	of	of	ADP
ejpam-6466	511	42	the	the	DET
ejpam-6466	511	43	proof	proof	NOUN
ejpam-6466	511	44	.	.	PUNCT
ejpam-6466	512	1	we	we	PRON
ejpam-6466	512	2	shall	shall	AUX
ejpam-6466	512	3	demonstrate	demonstrate	VERB
ejpam-6466	512	4	the	the	DET
ejpam-6466	512	5	regularity	regularity	NOUN
ejpam-6466	512	6	of	of	ADP
ejpam-6466	512	7	solutions	solution	NOUN
ejpam-6466	512	8	to	to	ADP
ejpam-6466	512	9	df	df	NOUN
ejpam-6466	512	10	-	-	PUNCT
ejpam-6466	512	11	sdes	sde	NOUN
ejpam-6466	512	12	in	in	ADP
ejpam-6466	512	13	the	the	DET
ejpam-6466	512	14	following	follow	VERB
ejpam-6466	512	15	subsection	subsection	NOUN
ejpam-6466	512	16	.	.	PUNCT
ejpam-6466	513	1	3.2	3.2	NUM
ejpam-6466	513	2	.	.	PUNCT
ejpam-6466	514	1	the	the	DET
ejpam-6466	514	2	regularity	regularity	NOUN
ejpam-6466	514	3	of	of	ADP
ejpam-6466	514	4	solutions	solution	NOUN
ejpam-6466	514	5	to	to	ADP
ejpam-6466	514	6	df	df	NOUN
ejpam-6466	514	7	-	-	PUNCT
ejpam-6466	514	8	sdes	sde	NOUN
ejpam-6466	514	9	in	in	ADP
ejpam-6466	514	10	the	the	DET
ejpam-6466	514	11	following	following	NOUN
ejpam-6466	514	12	theorem	theorem	NOUN
ejpam-6466	514	13	,	,	PUNCT
ejpam-6466	514	14	we	we	PRON
ejpam-6466	514	15	established	establish	VERB
ejpam-6466	514	16	the	the	DET
ejpam-6466	514	17	result	result	NOUN
ejpam-6466	514	18	for	for	ADP
ejpam-6466	514	19	regularity	regularity	NOUN
ejpam-6466	514	20	of	of	ADP
ejpam-6466	514	21	the	the	DET
ejpam-6466	514	22	solutions	solution	NOUN
ejpam-6466	514	23	of	of	ADP
ejpam-6466	514	24	df	df	NOUN
ejpam-6466	514	25	-	-	PUNCT
ejpam-6466	514	26	sdes	sde	NOUN
ejpam-6466	514	27	.	.	PUNCT
ejpam-6466	515	1	m.	m.	NOUN
ejpam-6466	515	2	i.	i.	PROPN
ejpam-6466	515	3	liaqat	liaqat	PROPN
ejpam-6466	515	4	et	et	PROPN
ejpam-6466	515	5	al	al	PROPN
ejpam-6466	515	6	.	.	PUNCT
ejpam-6466	515	7	/	/	SYM
ejpam-6466	515	8	eur	eur	PROPN
ejpam-6466	515	9	.	.	PUNCT
ejpam-6466	516	1	j.	j.	PROPN
ejpam-6466	516	2	pure	pure	PROPN
ejpam-6466	516	3	appl	appl	PROPN
ejpam-6466	516	4	.	.	PROPN
ejpam-6466	516	5	math	math	PROPN
ejpam-6466	516	6	,	,	PUNCT
ejpam-6466	516	7	18	18	NUM
ejpam-6466	516	8	(	(	PUNCT
ejpam-6466	516	9	4	4	NUM
ejpam-6466	516	10	)	)	PUNCT
ejpam-6466	516	11	(	(	PUNCT
ejpam-6466	516	12	2025	2025	NUM
ejpam-6466	516	13	)	)	PUNCT
ejpam-6466	516	14	,	,	PUNCT
ejpam-6466	516	15	6466	6466	NUM
ejpam-6466	516	16	19	19	NUM
ejpam-6466	516	17	of	of	ADP
ejpam-6466	516	18	28	28	NUM
ejpam-6466	516	19	theorem	theorem	NOUN
ejpam-6466	516	20	5	5	NUM
ejpam-6466	516	21	.	.	PUNCT
ejpam-6466	516	22	assume	assume	VERB
ejpam-6466	516	23	that	that	SCONJ
ejpam-6466	516	24	(	(	PUNCT
ejpam-6466	516	25	a2	a2	PROPN
ejpam-6466	516	26	)	)	PUNCT
ejpam-6466	516	27	and	and	CCONJ
ejpam-6466	516	28	(	(	PUNCT
ejpam-6466	516	29	a3	a3	NOUN
ejpam-6466	516	30	)	)	PUNCT
ejpam-6466	516	31	are	be	AUX
ejpam-6466	516	32	true	true	ADJ
ejpam-6466	516	33	.	.	PUNCT
ejpam-6466	517	1	assume	assume	VERB
ejpam-6466	517	2	further	far	ADV
ejpam-6466	517	3	that	that	SCONJ
ejpam-6466	517	4	φ	φ	PROPN
ejpam-6466	517	5	is	be	AUX
ejpam-6466	517	6	ξ	ξ	PROPN
ejpam-6466	517	7	−	−	PROPN
ejpam-6466	517	8	1	1	NUM
ejpam-6466	517	9	2	2	NUM
ejpam-6466	517	10	hölder	hölder	NOUN
ejpam-6466	517	11	continuous	continuous	ADJ
ejpam-6466	517	12	(	(	PUNCT
ejpam-6466	517	13	höld	höld	NOUN
ejpam-6466	517	14	-	-	PUNCT
ejpam-6466	517	15	con	con	NOUN
ejpam-6466	517	16	)	)	PUNCT
ejpam-6466	517	17	i.e.	i.e.	X
ejpam-6466	517	18	,	,	PUNCT
ejpam-6466	517	19	∀τ	∀τ	NOUN
ejpam-6466	517	20	,	,	PUNCT
ejpam-6466	517	21	α̃	α̃	PROPN
ejpam-6466	517	22	∈	∈	PROPN
ejpam-6466	518	1	[	[	X
ejpam-6466	518	2	−m	−m	NOUN
ejpam-6466	518	3	,	,	PUNCT
ejpam-6466	518	4	0	0	NUM
ejpam-6466	518	5	]	]	PUNCT
ejpam-6466	518	6	there	there	PRON
ejpam-6466	518	7	is	be	VERB
ejpam-6466	518	8	a	a	DET
ejpam-6466	518	9	constant	constant	ADJ
ejpam-6466	518	10	ρ1	ρ1	NOUN
ejpam-6466	518	11	>	>	SYM
ejpam-6466	518	12	0	0	PUNCT
ejpam-6466	518	13	∥φ(τ)−	∥φ(τ)−	PROPN
ejpam-6466	518	14	φ(α̃)∥	φ(α̃)∥	ADJ
ejpam-6466	518	15	≤	≤	PROPN
ejpam-6466	518	16	ρ1|τ	ρ1|τ	PROPN
ejpam-6466	518	17	−	−	PROPN
ejpam-6466	518	18	α̃|ξ−	α̃|ξ−	NOUN
ejpam-6466	518	19	1	1	NUM
ejpam-6466	518	20	2	2	NUM
ejpam-6466	518	21	.	.	PUNCT
ejpam-6466	519	1	next	next	ADV
ejpam-6466	519	2	,	,	PUNCT
ejpam-6466	519	3	based	base	VERB
ejpam-6466	519	4	on	on	ADP
ejpam-6466	519	5	ξ	ξ	PROPN
ejpam-6466	519	6	,	,	PUNCT
ejpam-6466	519	7	ℏ,k	ℏ,k	PROPN
ejpam-6466	519	8	,	,	PUNCT
ejpam-6466	519	9	l	l	NOUN
ejpam-6466	519	10	,	,	PUNCT
ejpam-6466	519	11	ρ1	ρ1	NOUN
ejpam-6466	519	12	,	,	PUNCT
ejpam-6466	519	13	there	there	PRON
ejpam-6466	519	14	is	be	VERB
ejpam-6466	519	15	a	a	DET
ejpam-6466	519	16	constant	constant	ADJ
ejpam-6466	519	17	ρ	ρ	NOUN
ejpam-6466	519	18	>	>	X
ejpam-6466	519	19	0	0	PUNCT
ejpam-6466	520	1	that	that	PRON
ejpam-6466	520	2	corresponds	correspond	VERB
ejpam-6466	520	3	to	to	ADP
ejpam-6466	520	4	∥	∥	NUM
ejpam-6466	520	5	℧	℧	NOUN
ejpam-6466	520	6	ξ(τ	ξ(τ	NOUN
ejpam-6466	520	7	,	,	PUNCT
ejpam-6466	520	8	φ)−	φ)−	PROPN
ejpam-6466	520	9	℧	℧	PROPN
ejpam-6466	520	10	ξ(α̃,φ)∥ms	ξ(α̃,φ)∥ms	PROPN
ejpam-6466	520	11	≤	≤	ADJ
ejpam-6466	520	12	ρ|τ	ρ|τ	NOUN
ejpam-6466	521	1	−	−	ADP
ejpam-6466	521	2	α̃|ξ−	α̃|ξ−	NOUN
ejpam-6466	521	3	1	1	NUM
ejpam-6466	521	4	2	2	NUM
ejpam-6466	521	5	,	,	PUNCT
ejpam-6466	521	6	∀τ	∀τ	PROPN
ejpam-6466	521	7	,	,	PUNCT
ejpam-6466	521	8	α̃	α̃	PROPN
ejpam-6466	521	9	∈	∈	PROPN
ejpam-6466	522	1	[	[	X
ejpam-6466	522	2	−m	−m	NOUN
ejpam-6466	522	3	,	,	PUNCT
ejpam-6466	522	4	ℏ	ℏ	X
ejpam-6466	522	5	]	]	PUNCT
ejpam-6466	522	6	.	.	PUNCT
ejpam-6466	523	1	proof	proof	NOUN
ejpam-6466	523	2	.	.	PUNCT
ejpam-6466	524	1	the	the	DET
ejpam-6466	524	2	proof	proof	NOUN
ejpam-6466	524	3	has	have	AUX
ejpam-6466	524	4	been	be	AUX
ejpam-6466	524	5	separated	separate	VERB
ejpam-6466	524	6	into	into	ADP
ejpam-6466	524	7	three	three	NUM
ejpam-6466	524	8	parts	part	NOUN
ejpam-6466	524	9	for	for	ADP
ejpam-6466	524	10	explanation	explanation	NOUN
ejpam-6466	524	11	.	.	PUNCT
ejpam-6466	525	1	step	step	NOUN
ejpam-6466	525	2	1	1	NUM
ejpam-6466	525	3	:	:	PUNCT
ejpam-6466	525	4	τ	τ	PROPN
ejpam-6466	525	5	,	,	PUNCT
ejpam-6466	525	6	α̃	α̃	PROPN
ejpam-6466	525	7	∈	∈	PROPN
ejpam-6466	526	1	[	[	X
ejpam-6466	526	2	0	0	NUM
ejpam-6466	526	3	,	,	PUNCT
ejpam-6466	526	4	ℏ	ℏ	PROPN
ejpam-6466	526	5	]	]	X
ejpam-6466	526	6	:	:	PUNCT
ejpam-6466	526	7	select	select	VERB
ejpam-6466	526	8	and	and	CCONJ
ejpam-6466	526	9	fix	fix	NOUN
ejpam-6466	526	10	τ	τ	PROPN
ejpam-6466	526	11	,	,	PUNCT
ejpam-6466	526	12	α̃	α̃	PROPN
ejpam-6466	526	13	∈	∈	PROPN
ejpam-6466	527	1	[	[	X
ejpam-6466	527	2	0	0	NUM
ejpam-6466	527	3	,	,	PUNCT
ejpam-6466	527	4	ℏ	ℏ	PROPN
ejpam-6466	527	5	]	]	PUNCT
ejpam-6466	527	6	,	,	PUNCT
ejpam-6466	527	7	τ	τ	PROPN
ejpam-6466	527	8	>	>	X
ejpam-6466	527	9	α̃.	α̃.	PROPN
ejpam-6466	527	10	by	by	ADP
ejpam-6466	527	11	utilizing	utilize	VERB
ejpam-6466	527	12	eq	eq	ADP
ejpam-6466	527	13	.	.	PUNCT
ejpam-6466	528	1	(	(	PUNCT
ejpam-6466	528	2	9	9	NUM
ejpam-6466	528	3	)	)	PUNCT
ejpam-6466	528	4	and	and	CCONJ
ejpam-6466	528	5	i	i	PRON
ejpam-6466	528	6	-	-	PUNCT
ejpam-6466	528	7	is	be	AUX
ejpam-6466	528	8	,	,	PUNCT
ejpam-6466	528	9	we	we	PRON
ejpam-6466	528	10	attained	attain	VERB
ejpam-6466	528	11	the	the	DET
ejpam-6466	528	12	following	following	NOUN
ejpam-6466	528	13	:	:	PUNCT
ejpam-6466	528	14	1	1	NUM
ejpam-6466	528	15	4	4	NUM
ejpam-6466	528	16	e	e	NOUN
ejpam-6466	528	17	(	(	PUNCT
ejpam-6466	528	18	∥	∥	X
ejpam-6466	528	19	℧	℧	NOUN
ejpam-6466	528	20	ξ(τ	ξ(τ	NOUN
ejpam-6466	528	21	,	,	PUNCT
ejpam-6466	528	22	φ)−	φ)−	PROPN
ejpam-6466	528	23	℧	℧	PROPN
ejpam-6466	528	24	ξ(α̃,φ)∥2	ξ(α̃,φ)∥2	PROPN
ejpam-6466	528	25	)	)	PUNCT
ejpam-6466	528	26	≤e	≤e	NOUN
ejpam-6466	528	27	(	(	PUNCT
ejpam-6466	528	28	∥	∥	X
ejpam-6466	528	29	∫	∫	PROPN
ejpam-6466	528	30	τ	τ	PROPN
ejpam-6466	528	31	c	c	PROPN
ejpam-6466	528	32	sξ−1v(s,	sξ−1v(s,	PROPN
ejpam-6466	528	33	℧	℧	ADP
ejpam-6466	528	34	ξ(s	ξ(s	PROPN
ejpam-6466	528	35	,	,	PUNCT
ejpam-6466	528	36	φ),	φ),	NOUN
ejpam-6466	528	37	℧	℧	NOUN
ejpam-6466	528	38	ξ(s−m	ξ(s−m	NUM
ejpam-6466	528	39	,	,	PUNCT
ejpam-6466	528	40	φ))ds∥2	φ))ds∥2	PROPN
ejpam-6466	528	41	)	)	PUNCT
ejpam-6466	529	1	+	+	NUM
ejpam-6466	529	2	∫	∫	PROPN
ejpam-6466	529	3	τ	τ	PROPN
ejpam-6466	529	4	c	c	PROPN
ejpam-6466	529	5	s2ξ−2e∥𭟋(s,	s2ξ−2e∥𭟋(s,	PROPN
ejpam-6466	529	6	℧	℧	PROPN
ejpam-6466	529	7	ξ(s	ξ(s	PROPN
ejpam-6466	529	8	,	,	PUNCT
ejpam-6466	529	9	φ),	φ),	NOUN
ejpam-6466	529	10	℧	℧	NOUN
ejpam-6466	529	11	ξ(s−m	ξ(s−m	NOUN
ejpam-6466	529	12	,	,	PUNCT
ejpam-6466	529	13	φ))∥2ds	φ))∥2ds	NOUN
ejpam-6466	529	14	.	.	PUNCT
ejpam-6466	530	1	additionally	additionally	ADV
ejpam-6466	530	2	,	,	PUNCT
ejpam-6466	530	3	considering	consider	VERB
ejpam-6466	530	4	℧	℧	NOUN
ejpam-6466	530	5	ξ(.,φ	ξ(.,φ	NOUN
ejpam-6466	530	6	)	)	PUNCT
ejpam-6466	530	7	∈	∈	PROPN
ejpam-6466	530	8	h̃	h̃	PROPN
ejpam-6466	530	9	(	(	PUNCT
ejpam-6466	530	10	[	[	X
ejpam-6466	530	11	−m	−m	NOUN
ejpam-6466	530	12	,	,	PUNCT
ejpam-6466	530	13	ℏ	ℏ	PROPN
ejpam-6466	530	14	]	]	PUNCT
ejpam-6466	530	15	)	)	PUNCT
ejpam-6466	530	16	,	,	PUNCT
ejpam-6466	530	17	there	there	PRON
ejpam-6466	530	18	is	be	VERB
ejpam-6466	530	19	k1	k1	PROPN
ejpam-6466	530	20	>	>	X
ejpam-6466	530	21	0	0	PROPN
ejpam-6466	530	22	,	,	PUNCT
ejpam-6466	530	23	which	which	PRON
ejpam-6466	530	24	means	mean	VERB
ejpam-6466	530	25	sup	sup	PROPN
ejpam-6466	530	26	τ∈[−m,ℏ	τ∈[−m,ℏ	PROPN
ejpam-6466	530	27	]	]	X
ejpam-6466	530	28	e∥	e∥	NOUN
ejpam-6466	530	29	℧	℧	NOUN
ejpam-6466	530	30	ξ(τ	ξ(τ	NOUN
ejpam-6466	530	31	,	,	PUNCT
ejpam-6466	530	32	φ)∥2	φ)∥2	PROPN
ejpam-6466	530	33	≤	≤	NUM
ejpam-6466	530	34	k1	k1	NOUN
ejpam-6466	530	35	.	.	PUNCT
ejpam-6466	531	1	(	(	PUNCT
ejpam-6466	531	2	42	42	NUM
ejpam-6466	531	3	)	)	PUNCT
ejpam-6466	531	4	by	by	ADP
ejpam-6466	531	5	utilizing	utilize	VERB
ejpam-6466	531	6	(	(	PUNCT
ejpam-6466	531	7	a2	a2	PROPN
ejpam-6466	531	8	)	)	PUNCT
ejpam-6466	531	9	,	,	PUNCT
ejpam-6466	531	10	(	(	PUNCT
ejpam-6466	531	11	a3	a3	NOUN
ejpam-6466	531	12	)	)	PUNCT
ejpam-6466	531	13	,	,	PUNCT
ejpam-6466	531	14	höld	höld	PROPN
ejpam-6466	531	15	-	-	PUNCT
ejpam-6466	531	16	i	i	PROPN
ejpam-6466	531	17	and	and	CCONJ
ejpam-6466	531	18	eq	eq	NOUN
ejpam-6466	531	19	.	.	PUNCT
ejpam-6466	532	1	(	(	PUNCT
ejpam-6466	532	2	3.2	3.2	NUM
ejpam-6466	532	3	)	)	PUNCT
ejpam-6466	532	4	,	,	PUNCT
ejpam-6466	532	5	we	we	PRON
ejpam-6466	532	6	have	have	VERB
ejpam-6466	532	7	the	the	DET
ejpam-6466	532	8	following	following	NOUN
ejpam-6466	532	9	:	:	PUNCT
ejpam-6466	532	10	1	1	NUM
ejpam-6466	532	11	4	4	NUM
ejpam-6466	532	12	e	e	NOUN
ejpam-6466	532	13	(	(	PUNCT
ejpam-6466	532	14	∥	∥	X
ejpam-6466	532	15	℧	℧	NOUN
ejpam-6466	532	16	ξ(τ	ξ(τ	NOUN
ejpam-6466	532	17	,	,	PUNCT
ejpam-6466	532	18	φ)−	φ)−	PROPN
ejpam-6466	532	19	℧	℧	PROPN
ejpam-6466	532	20	ξ(α̃,φ)∥2	ξ(α̃,φ)∥2	PROPN
ejpam-6466	532	21	)	)	PUNCT
ejpam-6466	532	22	≤2k2	≤2k2	PUNCT
ejpam-6466	533	1	+	+	PUNCT
ejpam-6466	533	2	4l2k1	4l2k1	NOUN
ejpam-6466	533	3	+	+	NUM
ejpam-6466	533	4	2l2e∥φ∥2	2l2e∥φ∥2	NUM
ejpam-6466	533	5	2ξ	2ξ	NUM
ejpam-6466	533	6	−	−	PROPN
ejpam-6466	533	7	1	1	NUM
ejpam-6466	533	8	(	(	PUNCT
ejpam-6466	533	9	(	(	PUNCT
ejpam-6466	533	10	τ	τ	X
ejpam-6466	533	11	−	−	PROPN
ejpam-6466	533	12	c)2ξ	c)2ξ	NOUN
ejpam-6466	533	13	+	+	CCONJ
ejpam-6466	533	14	(	(	PUNCT
ejpam-6466	533	15	τ	τ	PROPN
ejpam-6466	533	16	−	−	PROPN
ejpam-6466	533	17	c)2ξ−1	c)2ξ−1	PROPN
ejpam-6466	533	18	)	)	PUNCT
ejpam-6466	533	19	.	.	PUNCT
ejpam-6466	534	1	consequently	consequently	ADV
ejpam-6466	534	2	,	,	PUNCT
ejpam-6466	534	3	we	we	PRON
ejpam-6466	534	4	attained	attain	VERB
ejpam-6466	534	5	the	the	DET
ejpam-6466	534	6	following	following	NOUN
ejpam-6466	534	7	:	:	PUNCT
ejpam-6466	534	8	∥	∥	X
ejpam-6466	534	9	℧	℧	NOUN
ejpam-6466	534	10	ξ(τ	ξ(τ	NOUN
ejpam-6466	534	11	,	,	PUNCT
ejpam-6466	534	12	φ)−	φ)−	PROPN
ejpam-6466	534	13	℧	℧	NOUN
ejpam-6466	534	14	ξ(c	ξ(c	NOUN
ejpam-6466	534	15	,	,	PUNCT
ejpam-6466	534	16	φ)∥ms	φ)∥ms	ADV
ejpam-6466	534	17	≤	≤	X
ejpam-6466	535	1	ρ2(τ	ρ2(τ	PROPN
ejpam-6466	535	2	−	−	NOUN
ejpam-6466	535	3	c)ξ−	c)ξ−	VERB
ejpam-6466	535	4	1	1	NUM
ejpam-6466	535	5	2	2	NUM
ejpam-6466	535	6	,	,	PUNCT
ejpam-6466	535	7	where	where	SCONJ
ejpam-6466	535	8	ρ22	ρ22	NOUN
ejpam-6466	535	9	=	=	NOUN
ejpam-6466	535	10	4	4	NUM
ejpam-6466	535	11	2k2	2k2	NUM
ejpam-6466	535	12	+	+	NUM
ejpam-6466	535	13	4l2k1	4l2k1	NUM
ejpam-6466	535	14	+	+	CCONJ
ejpam-6466	535	15	2l2e∥φ∥2(3ℏ+	2l2e∥φ∥2(3ℏ+	NUM
ejpam-6466	535	16	1	1	NUM
ejpam-6466	535	17	)	)	PUNCT
ejpam-6466	535	18	2ξ	2ξ	NOUN
ejpam-6466	535	19	−	−	PROPN
ejpam-6466	535	20	1	1	NUM
ejpam-6466	535	21	as	as	ADP
ejpam-6466	535	22	a	a	DET
ejpam-6466	535	23	result	result	NOUN
ejpam-6466	535	24	,	,	PUNCT
ejpam-6466	535	25	we	we	PRON
ejpam-6466	535	26	get	get	VERB
ejpam-6466	535	27	the	the	DET
ejpam-6466	535	28	following	follow	VERB
ejpam-6466	535	29	result	result	NOUN
ejpam-6466	535	30	:	:	PUNCT
ejpam-6466	535	31	lim	lim	PROPN
ejpam-6466	535	32	c→τ	c→τ	NUM
ejpam-6466	535	33	∥	∥	PRON
ejpam-6466	535	34	℧	℧	NOUN
ejpam-6466	535	35	ξ(τ	ξ(τ	NOUN
ejpam-6466	535	36	,	,	PUNCT
ejpam-6466	535	37	φ)−	φ)−	PROPN
ejpam-6466	535	38	℧	℧	NOUN
ejpam-6466	535	39	ξ(c	ξ(c	NOUN
ejpam-6466	535	40	,	,	PUNCT
ejpam-6466	535	41	φ)∥ms	φ)∥ms	NOUN
ejpam-6466	535	42	=	=	SYM
ejpam-6466	535	43	0	0	X
ejpam-6466	535	44	.	.	PUNCT
ejpam-6466	536	1	step	step	NOUN
ejpam-6466	536	2	2	2	NUM
ejpam-6466	536	3	:	:	PUNCT
ejpam-6466	536	4	τ	τ	PROPN
ejpam-6466	536	5	,	,	PUNCT
ejpam-6466	536	6	c	c	PROPN
ejpam-6466	536	7	∈	∈	PROPN
ejpam-6466	537	1	[	[	X
ejpam-6466	537	2	−m	−m	NOUN
ejpam-6466	537	3	,	,	PUNCT
ejpam-6466	537	4	0	0	NUM
ejpam-6466	537	5	]	]	PUNCT
ejpam-6466	537	6	,	,	PUNCT
ejpam-6466	537	7	since	since	SCONJ
ejpam-6466	537	8	φ	φ	PROPN
ejpam-6466	537	9	is	be	AUX
ejpam-6466	537	10	ξ	ξ	X
ejpam-6466	537	11	−	−	NUM
ejpam-6466	537	12	1	1	NUM
ejpam-6466	537	13	2	2	NUM
ejpam-6466	537	14	-höld	-höld	NOUN
ejpam-6466	537	15	-	-	PUNCT
ejpam-6466	537	16	con	con	NOUN
ejpam-6466	537	17	and	and	CCONJ
ejpam-6466	537	18	℧	℧	PROPN
ejpam-6466	537	19	ξ(τ	ξ(τ	PROPN
ejpam-6466	537	20	,	,	PUNCT
ejpam-6466	537	21	φ	φ	NUM
ejpam-6466	537	22	)	)	PUNCT
ejpam-6466	537	23	=	=	SYM
ejpam-6466	537	24	φ(τ	φ(τ	NOUN
ejpam-6466	537	25	)	)	PUNCT
ejpam-6466	537	26	with	with	ADP
ejpam-6466	537	27	τ	τ	PROPN
ejpam-6466	537	28	∈	∈	PROPN
ejpam-6466	537	29	[	[	X
ejpam-6466	537	30	−m	−m	NOUN
ejpam-6466	537	31	,	,	PUNCT
ejpam-6466	537	32	0	0	NUM
ejpam-6466	537	33	]	]	PUNCT
ejpam-6466	537	34	,	,	PUNCT
ejpam-6466	537	35	eqs	eqs	X
ejpam-6466	537	36	.	.	PUNCT
ejpam-6466	538	1	(	(	PUNCT
ejpam-6466	538	2	5	5	NUM
ejpam-6466	538	3	)	)	PUNCT
ejpam-6466	538	4	and	and	CCONJ
ejpam-6466	538	5	(	(	PUNCT
ejpam-6466	538	6	6	6	NUM
ejpam-6466	538	7	)	)	PUNCT
ejpam-6466	538	8	,	,	PUNCT
ejpam-6466	538	9	we	we	PRON
ejpam-6466	538	10	yield	yield	VERB
ejpam-6466	538	11	the	the	DET
ejpam-6466	538	12	following	following	NOUN
ejpam-6466	538	13	:	:	PUNCT
ejpam-6466	538	14	∥	∥	PUNCT
ejpam-6466	538	15	℧	℧	NOUN
ejpam-6466	538	16	ξ(τ	ξ(τ	NOUN
ejpam-6466	538	17	,	,	PUNCT
ejpam-6466	538	18	φ)−	φ)−	PROPN
ejpam-6466	538	19	℧	℧	NOUN
ejpam-6466	538	20	ξ(c	ξ(c	NOUN
ejpam-6466	538	21	,	,	PUNCT
ejpam-6466	538	22	φ)∥ms	φ)∥ms	ADV
ejpam-6466	538	23	≤	≤	NOUN
ejpam-6466	539	1	ρ1(τ	ρ1(τ	NUM
ejpam-6466	539	2	−	−	PROPN
ejpam-6466	539	3	c)ξ−	c)ξ−	VERB
ejpam-6466	539	4	1	1	NUM
ejpam-6466	539	5	2	2	NUM
ejpam-6466	539	6	.	.	PUNCT
ejpam-6466	540	1	step	step	NOUN
ejpam-6466	540	2	3	3	NUM
ejpam-6466	540	3	:	:	PUNCT
ejpam-6466	540	4	−m	−m	NOUN
ejpam-6466	540	5	<	<	X
ejpam-6466	540	6	c	c	NOUN
ejpam-6466	540	7	≤	≤	ADV
ejpam-6466	540	8	0	0	NUM
ejpam-6466	540	9	≤	≤	NUM
ejpam-6466	540	10	τ	τ	X
ejpam-6466	540	11	≤	≤	NUM
ejpam-6466	540	12	ℏ	ℏ	PROPN
ejpam-6466	540	13	:	:	PUNCT
ejpam-6466	540	14	we	we	PRON
ejpam-6466	540	15	address	address	VERB
ejpam-6466	540	16	the	the	DET
ejpam-6466	540	17	outcomes	outcome	NOUN
ejpam-6466	540	18	in	in	ADP
ejpam-6466	540	19	step	step	NOUN
ejpam-6466	540	20	1	1	NUM
ejpam-6466	540	21	and	and	CCONJ
ejpam-6466	540	22	step	step	NOUN
ejpam-6466	540	23	2	2	NUM
ejpam-6466	540	24	and	and	CCONJ
ejpam-6466	540	25	achieve	achieve	VERB
ejpam-6466	540	26	∥	∥	NUM
ejpam-6466	540	27	℧	℧	NOUN
ejpam-6466	540	28	ξ(τ	ξ(τ	NOUN
ejpam-6466	540	29	,	,	PUNCT
ejpam-6466	540	30	φ)−	φ)−	PROPN
ejpam-6466	540	31	℧	℧	NOUN
ejpam-6466	540	32	ξ(c	ξ(c	NUM
ejpam-6466	540	33	,	,	PUNCT
ejpam-6466	540	34	φ)∥ms	φ)∥ms	ADV
ejpam-6466	540	35	≤∥	≤∥	ADJ
ejpam-6466	540	36	℧	℧	PROPN
ejpam-6466	540	37	ξ(τ	ξ(τ	PROPN
ejpam-6466	540	38	,	,	PUNCT
ejpam-6466	540	39	φ)−	φ)−	PROPN
ejpam-6466	540	40	℧	℧	NOUN
ejpam-6466	540	41	ξ(0,φ)∥ms	ξ(0,φ)∥ms	ADJ
ejpam-6466	540	42	+	+	CCONJ
ejpam-6466	540	43	∥	∥	NUM
ejpam-6466	540	44	℧	℧	NOUN
ejpam-6466	540	45	ξ(0,φ)−	ξ(0,φ)−	PRON
ejpam-6466	540	46	℧	℧	PROPN
ejpam-6466	540	47	ξ(c	ξ(c	NUM
ejpam-6466	540	48	,	,	PUNCT
ejpam-6466	540	49	φ)∥ms	φ)∥ms	PROPN
ejpam-6466	540	50	m.	m.	NOUN
ejpam-6466	540	51	i.	i.	PROPN
ejpam-6466	540	52	liaqat	liaqat	PROPN
ejpam-6466	540	53	et	et	PROPN
ejpam-6466	540	54	al	al	PROPN
ejpam-6466	540	55	.	.	PUNCT
ejpam-6466	540	56	/	/	SYM
ejpam-6466	540	57	eur	eur	PROPN
ejpam-6466	540	58	.	.	PUNCT
ejpam-6466	541	1	j.	j.	PROPN
ejpam-6466	541	2	pure	pure	PROPN
ejpam-6466	541	3	appl	appl	PROPN
ejpam-6466	541	4	.	.	PROPN
ejpam-6466	541	5	math	math	PROPN
ejpam-6466	541	6	,	,	PUNCT
ejpam-6466	541	7	18	18	NUM
ejpam-6466	541	8	(	(	PUNCT
ejpam-6466	541	9	4	4	NUM
ejpam-6466	541	10	)	)	PUNCT
ejpam-6466	541	11	(	(	PUNCT
ejpam-6466	541	12	2025	2025	NUM
ejpam-6466	541	13	)	)	PUNCT
ejpam-6466	541	14	,	,	PUNCT
ejpam-6466	541	15	6466	6466	NUM
ejpam-6466	541	16	20	20	NUM
ejpam-6466	541	17	of	of	ADP
ejpam-6466	541	18	28	28	NUM
ejpam-6466	541	19	ρ2	ρ2	PROPN
ejpam-6466	541	20	|τ	|τ	ADJ
ejpam-6466	541	21	|ξ−	|ξ−	NOUN
ejpam-6466	541	22	1	1	NUM
ejpam-6466	541	23	2	2	NUM
ejpam-6466	541	24	+	+	NUM
ejpam-6466	541	25	ρ1	ρ1	NOUN
ejpam-6466	541	26	|	|	ADV
ejpam-6466	541	27	−	−	NOUN
ejpam-6466	541	28	c|ξ−	c|ξ−	NOUN
ejpam-6466	541	29	1	1	NUM
ejpam-6466	541	30	2	2	NUM
ejpam-6466	541	31	.	.	PUNCT
ejpam-6466	542	1	in	in	ADP
ejpam-6466	542	2	addition	addition	NOUN
ejpam-6466	542	3	,	,	PUNCT
ejpam-6466	542	4	if	if	SCONJ
ejpam-6466	542	5	θ1	θ1	NOUN
ejpam-6466	542	6	,	,	PUNCT
ejpam-6466	542	7	θ2	θ2	ADV
ejpam-6466	542	8	>	>	X
ejpam-6466	542	9	0	0	PUNCT
ejpam-6466	543	1	and	and	CCONJ
ejpam-6466	543	2	0	0	NUM
ejpam-6466	543	3	<	<	X
ejpam-6466	543	4	ξ	ξ	X
ejpam-6466	543	5	<	<	X
ejpam-6466	543	6	1	1	NUM
ejpam-6466	543	7	,	,	PUNCT
ejpam-6466	543	8	then	then	ADV
ejpam-6466	543	9	there	there	PRON
ejpam-6466	543	10	is	be	VERB
ejpam-6466	543	11	a	a	DET
ejpam-6466	543	12	constant	constant	ADJ
ejpam-6466	543	13	µ	µ	X
ejpam-6466	543	14	∈	∈	NOUN
ejpam-6466	543	15	(	(	PUNCT
ejpam-6466	543	16	0	0	NUM
ejpam-6466	543	17	,	,	PUNCT
ejpam-6466	543	18	12	12	NUM
ejpam-6466	543	19	]	]	PUNCT
ejpam-6466	543	20	that	that	DET
ejpam-6466	543	21	θξ1	θξ1	NOUN
ejpam-6466	543	22	+	+	CCONJ
ejpam-6466	543	23	θξ2	θξ2	ADJ
ejpam-6466	543	24	≤	≤	X
ejpam-6466	543	25	µξ−1(θ1	µξ−1(θ1	PROPN
ejpam-6466	543	26	+	+	SYM
ejpam-6466	543	27	θ2	θ2	PROPN
ejpam-6466	543	28	)	)	PUNCT
ejpam-6466	543	29	ξ	ξ	PROPN
ejpam-6466	543	30	.	.	PUNCT
ejpam-6466	544	1	as	as	ADP
ejpam-6466	544	2	a	a	DET
ejpam-6466	544	3	result	result	NOUN
ejpam-6466	544	4	,	,	PUNCT
ejpam-6466	544	5	we	we	PRON
ejpam-6466	544	6	get	get	VERB
ejpam-6466	544	7	∥	∥	NOUN
ejpam-6466	544	8	℧	℧	NOUN
ejpam-6466	544	9	ξ(τ	ξ(τ	NOUN
ejpam-6466	544	10	,	,	PUNCT
ejpam-6466	544	11	φ)−	φ)−	PROPN
ejpam-6466	544	12	℧	℧	NOUN
ejpam-6466	544	13	ξ(c	ξ(c	NOUN
ejpam-6466	544	14	,	,	PUNCT
ejpam-6466	544	15	φ)∥ms	φ)∥ms	ADJ
ejpam-6466	544	16	≤	≤	ADJ
ejpam-6466	544	17	ρ|τ	ρ|τ	NOUN
ejpam-6466	545	1	−	−	NOUN
ejpam-6466	545	2	c|ξ−	c|ξ−	NOUN
ejpam-6466	545	3	1	1	NUM
ejpam-6466	545	4	2	2	NUM
ejpam-6466	545	5	,	,	PUNCT
ejpam-6466	545	6	where	where	SCONJ
ejpam-6466	545	7	,	,	PUNCT
ejpam-6466	545	8	ρ	ρ	PROPN
ejpam-6466	545	9	=	=	SYM
ejpam-6466	545	10	max(ρ1	max(ρ1	PROPN
ejpam-6466	545	11	,	,	PUNCT
ejpam-6466	545	12	ρ2)µ	ρ2)µ	VERB
ejpam-6466	545	13	ξ−	ξ−	PROPN
ejpam-6466	545	14	3	3	NUM
ejpam-6466	545	15	2	2	NUM
ejpam-6466	545	16	.	.	PUNCT
ejpam-6466	546	1	the	the	DET
ejpam-6466	546	2	required	required	ADJ
ejpam-6466	546	3	inequality	inequality	NOUN
ejpam-6466	546	4	is	be	AUX
ejpam-6466	546	5	established	establish	VERB
ejpam-6466	546	6	.	.	PUNCT
ejpam-6466	547	1	3.3	3.3	NUM
ejpam-6466	547	2	.	.	PUNCT
ejpam-6466	548	1	the	the	DET
ejpam-6466	548	2	uh	uh	INTJ
ejpam-6466	548	3	stability	stability	NOUN
ejpam-6466	548	4	of	of	ADP
ejpam-6466	548	5	df	df	NOUN
ejpam-6466	548	6	-	-	PUNCT
ejpam-6466	548	7	sdes	sde	NOUN
ejpam-6466	548	8	we	we	PRON
ejpam-6466	548	9	now	now	ADV
ejpam-6466	548	10	provide	provide	VERB
ejpam-6466	548	11	an	an	DET
ejpam-6466	548	12	explanation	explanation	NOUN
ejpam-6466	548	13	of	of	ADP
ejpam-6466	548	14	uh	uh	INTJ
ejpam-6466	548	15	stability	stability	NOUN
ejpam-6466	548	16	.	.	PUNCT
ejpam-6466	549	1	definition	definition	NOUN
ejpam-6466	549	2	3	3	NUM
ejpam-6466	549	3	.	.	PUNCT
ejpam-6466	550	1	the	the	DET
ejpam-6466	550	2	eq	eq	NOUN
ejpam-6466	550	3	.	.	PUNCT
ejpam-6466	551	1	(	(	PUNCT
ejpam-6466	551	2	4	4	X
ejpam-6466	551	3	)	)	PUNCT
ejpam-6466	551	4	is	be	AUX
ejpam-6466	551	5	uh	uh	INTJ
ejpam-6466	551	6	stability	stability	NOUN
ejpam-6466	551	7	with	with	ADP
ejpam-6466	551	8	respect	respect	NOUN
ejpam-6466	551	9	to	to	ADP
ejpam-6466	551	10	ϵ	ϵ	NOUN
ejpam-6466	551	11	if	if	SCONJ
ejpam-6466	551	12	there	there	PRON
ejpam-6466	551	13	is	be	VERB
ejpam-6466	551	14	a	a	DET
ejpam-6466	551	15	constant	constant	ADJ
ejpam-6466	551	16	χ	χ	X
ejpam-6466	551	17	>	>	X
ejpam-6466	551	18	0	0	NUM
ejpam-6466	551	19	such	such	ADJ
ejpam-6466	551	20	that	that	PRON
ejpam-6466	551	21	for	for	ADP
ejpam-6466	551	22	each	each	DET
ejpam-6466	551	23	ϵ	ϵ	X
ejpam-6466	551	24	>	>	X
ejpam-6466	551	25	0	0	PROPN
ejpam-6466	551	26	and	and	CCONJ
ejpam-6466	552	1	j(τ	j(τ	PROPN
ejpam-6466	552	2	)	)	PUNCT
ejpam-6466	552	3	∈	∈	PROPN
ejpam-6466	553	1	h̃2	h̃2	PROPN
ejpam-6466	553	2	(	(	PUNCT
ejpam-6466	553	3	[	[	X
ejpam-6466	553	4	0	0	NUM
ejpam-6466	553	5	,	,	PUNCT
ejpam-6466	553	6	ℏ	ℏ	PROPN
ejpam-6466	553	7	]	]	PUNCT
ejpam-6466	553	8	)	)	PUNCT
ejpam-6466	553	9	of	of	ADP
ejpam-6466	553	10	the	the	DET
ejpam-6466	553	11	following	follow	VERB
ejpam-6466	553	12	inequality	inequality	NOUN
ejpam-6466	553	13	:	:	PUNCT
ejpam-6466	553	14	∀τ	∀τ	PROPN
ejpam-6466	553	15	∈	∈	PROPN
ejpam-6466	554	1	[	[	X
ejpam-6466	554	2	0	0	NUM
ejpam-6466	554	3	,	,	PUNCT
ejpam-6466	554	4	ℏ	ℏ	X
ejpam-6466	554	5	]	]	PUNCT
ejpam-6466	554	6	e	e	X
ejpam-6466	554	7	[	[	X
ejpam-6466	554	8	∥∥∥∥∥j(τ)−	∥∥∥∥∥j(τ)−	X
ejpam-6466	554	9	j(0)−	j(0)−	NOUN
ejpam-6466	554	10	(	(	PUNCT
ejpam-6466	554	11	∫	∫	PROPN
ejpam-6466	554	12	τ	τ	PROPN
ejpam-6466	554	13	0	0	PROPN
ejpam-6466	554	14	sξ−1	sξ−1	PROPN
ejpam-6466	554	15	(	(	PUNCT
ejpam-6466	554	16	v	v	X
ejpam-6466	554	17	(	(	PUNCT
ejpam-6466	554	18	s	s	PROPN
ejpam-6466	554	19	,	,	PUNCT
ejpam-6466	554	20	j(s	j(s	NOUN
ejpam-6466	554	21	)	)	PUNCT
ejpam-6466	554	22	,	,	PUNCT
ejpam-6466	554	23	j(s−m	j(s−m	PROPN
ejpam-6466	554	24	)	)	PUNCT
ejpam-6466	554	25	)	)	PUNCT
ejpam-6466	554	26	ds	ds	VERB
ejpam-6466	554	27	+	+	ADJ
ejpam-6466	554	28	𭟋	𭟋	PROPN
ejpam-6466	554	29	(	(	PUNCT
ejpam-6466	554	30	s	s	PROPN
ejpam-6466	554	31	,	,	PUNCT
ejpam-6466	554	32	j(s	j(s	NOUN
ejpam-6466	554	33	)	)	PUNCT
ejpam-6466	554	34	,	,	PUNCT
ejpam-6466	554	35	j(s−m	j(s−m	PROPN
ejpam-6466	554	36	)	)	PUNCT
ejpam-6466	554	37	)	)	PUNCT
ejpam-6466	554	38	dw(s	dw(s	X
ejpam-6466	554	39	)	)	PUNCT
ejpam-6466	554	40	)	)	PUNCT
ejpam-6466	554	41	)	)	PUNCT
ejpam-6466	554	42	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-6466	555	1	2	2	NUM
ejpam-6466	555	2	]	]	PUNCT
ejpam-6466	555	3	≤	≤	NUM
ejpam-6466	555	4	ϵ	ϵ	X
ejpam-6466	555	5	,	,	PUNCT
ejpam-6466	555	6	there	there	PRON
ejpam-6466	555	7	exists	exist	VERB
ejpam-6466	555	8	a	a	DET
ejpam-6466	555	9	solution	solution	NOUN
ejpam-6466	555	10	x(τ	x(τ	PROPN
ejpam-6466	555	11	)	)	PUNCT
ejpam-6466	555	12	∈	∈	PROPN
ejpam-6466	556	1	h̃2	h̃2	PROPN
ejpam-6466	556	2	(	(	PUNCT
ejpam-6466	556	3	[	[	X
ejpam-6466	556	4	0	0	NUM
ejpam-6466	556	5	,	,	PUNCT
ejpam-6466	556	6	ℏ	ℏ	PROPN
ejpam-6466	556	7	]	]	PUNCT
ejpam-6466	556	8	)	)	PUNCT
ejpam-6466	556	9	of	of	ADP
ejpam-6466	556	10	eq	eq	PROPN
ejpam-6466	556	11	.	.	PUNCT
ejpam-6466	556	12	(	(	PUNCT
ejpam-6466	556	13	4	4	NUM
ejpam-6466	556	14	)	)	PUNCT
ejpam-6466	556	15	,	,	PUNCT
ejpam-6466	556	16	with	with	ADP
ejpam-6466	556	17	x0	x0	PROPN
ejpam-6466	556	18	=	=	SYM
ejpam-6466	556	19	φ	φ	PROPN
ejpam-6466	556	20	=	=	PUNCT
ejpam-6466	556	21	φ(τ	φ(τ	NOUN
ejpam-6466	556	22	)	)	PUNCT
ejpam-6466	556	23	:	:	PUNCT
ejpam-6466	556	24	τ	τ	PROPN
ejpam-6466	556	25	∈	∈	PROPN
ejpam-6466	556	26	[	[	X
ejpam-6466	556	27	−m	−m	NOUN
ejpam-6466	556	28	,	,	PUNCT
ejpam-6466	556	29	0	0	NUM
ejpam-6466	556	30	]	]	PUNCT
ejpam-6466	556	31	,	,	PUNCT
ejpam-6466	556	32	satisfies	satisfie	NOUN
ejpam-6466	556	33	e	e	X
ejpam-6466	556	34	[	[	PUNCT
ejpam-6466	556	35	∥j(τ)−	∥j(τ)−	PROPN
ejpam-6466	556	36	x(τ)∥2	x(τ)∥2	NOUN
ejpam-6466	556	37	]	]	PUNCT
ejpam-6466	556	38	≤	≤	ADV
ejpam-6466	556	39	χϵ	χϵ	ADP
ejpam-6466	556	40	,	,	PUNCT
ejpam-6466	556	41	∀τ	∀τ	SYM
ejpam-6466	556	42	∈	∈	PROPN
ejpam-6466	557	1	[	[	X
ejpam-6466	557	2	0	0	NUM
ejpam-6466	557	3	,	,	PUNCT
ejpam-6466	557	4	ℏ	ℏ	PROPN
ejpam-6466	557	5	]	]	PUNCT
ejpam-6466	557	6	.	.	PUNCT
ejpam-6466	558	1	theorem	theorem	ADJ
ejpam-6466	558	2	6	6	NUM
ejpam-6466	558	3	.	.	PUNCT
ejpam-6466	559	1	under	under	ADP
ejpam-6466	559	2	(	(	PUNCT
ejpam-6466	559	3	a2	a2	PROPN
ejpam-6466	559	4	)	)	PUNCT
ejpam-6466	559	5	and	and	CCONJ
ejpam-6466	559	6	(	(	PUNCT
ejpam-6466	559	7	a3	a3	NOUN
ejpam-6466	559	8	)	)	PUNCT
ejpam-6466	559	9	,	,	PUNCT
ejpam-6466	559	10	the	the	DET
ejpam-6466	559	11	df	df	NOUN
ejpam-6466	559	12	-	-	PUNCT
ejpam-6466	559	13	sdes	sde	NOUN
ejpam-6466	559	14	eq	eq	NOUN
ejpam-6466	559	15	.	.	PUNCT
ejpam-6466	560	1	(	(	PUNCT
ejpam-6466	560	2	4	4	X
ejpam-6466	560	3	)	)	PUNCT
ejpam-6466	560	4	is	be	AUX
ejpam-6466	560	5	uh	uh	INTJ
ejpam-6466	560	6	stability	stability	NOUN
ejpam-6466	560	7	on	on	ADP
ejpam-6466	560	8	[	[	X
ejpam-6466	560	9	0	0	NUM
ejpam-6466	560	10	,	,	PUNCT
ejpam-6466	560	11	ℏ	ℏ	NOUN
ejpam-6466	560	12	]	]	PUNCT
ejpam-6466	560	13	.	.	PUNCT
ejpam-6466	561	1	proof	proof	NOUN
ejpam-6466	561	2	.	.	PUNCT
ejpam-6466	562	1	set	set	VERB
ejpam-6466	562	2	ϵ	ϵ	PROPN
ejpam-6466	562	3	>	>	X
ejpam-6466	562	4	0	0	PUNCT
ejpam-6466	562	5	and	and	CCONJ
ejpam-6466	562	6	j(τ	j(τ	PROPN
ejpam-6466	562	7	)	)	PUNCT
ejpam-6466	562	8	∈	∈	PROPN
ejpam-6466	563	1	h̃2	h̃2	PROPN
ejpam-6466	563	2	(	(	PUNCT
ejpam-6466	563	3	[	[	X
ejpam-6466	563	4	0	0	NUM
ejpam-6466	563	5	,	,	PUNCT
ejpam-6466	563	6	ℏ	ℏ	PROPN
ejpam-6466	563	7	]	]	PUNCT
ejpam-6466	563	8	)	)	PUNCT
ejpam-6466	563	9	satisfies	satisfie	NOUN
ejpam-6466	563	10	eq	eq	ADJ
ejpam-6466	563	11	.	.	PUNCT
ejpam-6466	564	1	(	(	PUNCT
ejpam-6466	564	2	3	3	NUM
ejpam-6466	564	3	)	)	PUNCT
ejpam-6466	564	4	.	.	PUNCT
ejpam-6466	565	1	denote	denote	VERB
ejpam-6466	565	2	by	by	ADP
ejpam-6466	565	3	x(τ	x(τ	PROPN
ejpam-6466	565	4	)	)	PUNCT
ejpam-6466	565	5	∈	∈	PROPN
ejpam-6466	566	1	h̃2	h̃2	PROPN
ejpam-6466	566	2	(	(	PUNCT
ejpam-6466	566	3	[	[	X
ejpam-6466	566	4	0	0	NUM
ejpam-6466	566	5	,	,	PUNCT
ejpam-6466	566	6	ℏ	ℏ	PROPN
ejpam-6466	566	7	]	]	PUNCT
ejpam-6466	566	8	)	)	PUNCT
ejpam-6466	566	9	be	be	VERB
ejpam-6466	566	10	the	the	DET
ejpam-6466	566	11	unique	unique	ADJ
ejpam-6466	566	12	solution	solution	NOUN
ejpam-6466	566	13	of	of	ADP
ejpam-6466	566	14	eq	eq	PROPN
ejpam-6466	566	15	.	.	PUNCT
ejpam-6466	567	1	(	(	PUNCT
ejpam-6466	567	2	4	4	NUM
ejpam-6466	567	3	)	)	PUNCT
ejpam-6466	567	4	with	with	ADP
ejpam-6466	567	5	initial	initial	ADJ
ejpam-6466	567	6	value	value	NOUN
ejpam-6466	567	7	x(τ	x(τ	PROPN
ejpam-6466	567	8	)	)	PUNCT
ejpam-6466	568	1	=	=	PUNCT
ejpam-6466	568	2	j(τ	j(τ	PROPN
ejpam-6466	568	3	)	)	PUNCT
ejpam-6466	568	4	for	for	ADP
ejpam-6466	568	5	τ	τ	PROPN
ejpam-6466	568	6	∈	∈	PROPN
ejpam-6466	569	1	[	[	X
ejpam-6466	569	2	−m	−m	NOUN
ejpam-6466	569	3	,	,	PUNCT
ejpam-6466	569	4	0	0	NUM
ejpam-6466	569	5	]	]	PUNCT
ejpam-6466	569	6	,	,	PUNCT
ejpam-6466	569	7	then	then	ADV
ejpam-6466	569	8	x(τ	x(τ	PROPN
ejpam-6466	569	9	)	)	PUNCT
ejpam-6466	570	1	=	=	SYM
ejpam-6466	570	2	j(0	j(0	PROPN
ejpam-6466	570	3	)	)	PUNCT
ejpam-6466	570	4	+	+	CCONJ
ejpam-6466	570	5	(	(	PUNCT
ejpam-6466	570	6	∫	∫	PROPN
ejpam-6466	570	7	τ	τ	PROPN
ejpam-6466	570	8	0	0	NUM
ejpam-6466	570	9	sξ−1v	sξ−1v	PROPN
ejpam-6466	570	10	(	(	PUNCT
ejpam-6466	570	11	s	s	PROPN
ejpam-6466	570	12	,	,	PUNCT
ejpam-6466	570	13	x(s	x(s	PROPN
ejpam-6466	570	14	)	)	PUNCT
ejpam-6466	570	15	,	,	PUNCT
ejpam-6466	570	16	x(s−m	x(s−m	NUM
ejpam-6466	570	17	)	)	PUNCT
ejpam-6466	570	18	)	)	PUNCT
ejpam-6466	571	1	ds	ds	PROPN
ejpam-6466	572	1	+	+	CCONJ
ejpam-6466	572	2	∫	∫	PROPN
ejpam-6466	572	3	τ	τ	X
ejpam-6466	572	4	0	0	NUM
ejpam-6466	572	5	sξ−1𭟋	sξ−1𭟋	X
ejpam-6466	572	6	(	(	PUNCT
ejpam-6466	572	7	s	s	PROPN
ejpam-6466	572	8	,	,	PUNCT
ejpam-6466	572	9	x(s	x(s	PROPN
ejpam-6466	572	10	)	)	PUNCT
ejpam-6466	572	11	,	,	PUNCT
ejpam-6466	572	12	x(s−m	x(s−m	NUM
ejpam-6466	572	13	)	)	PUNCT
ejpam-6466	572	14	)	)	PUNCT
ejpam-6466	572	15	dw(s	dw(s	X
ejpam-6466	572	16	)	)	PUNCT
ejpam-6466	572	17	)	)	PUNCT
ejpam-6466	572	18	.	.	PUNCT
ejpam-6466	573	1	thus	thus	ADV
ejpam-6466	573	2	,	,	PUNCT
ejpam-6466	573	3	e	e	X
ejpam-6466	573	4	[	[	PUNCT
ejpam-6466	573	5	∥j(τ)−x(τ)∥2	∥j(τ)−x(τ)∥2	X
ejpam-6466	573	6	]	]	PUNCT
ejpam-6466	573	7	≤	≤	NUM
ejpam-6466	573	8	2e	2e	NOUN
ejpam-6466	573	9	[	[	X
ejpam-6466	573	10	∥∥∥∥j(τ)−	∥∥∥∥j(τ)−	X
ejpam-6466	573	11	j	j	X
ejpam-6466	573	12	(	(	PUNCT
ejpam-6466	573	13	0	0	NUM
ejpam-6466	573	14	)	)	PUNCT
ejpam-6466	573	15	−	−	PROPN
ejpam-6466	573	16	(	(	PUNCT
ejpam-6466	573	17	∫	∫	PROPN
ejpam-6466	573	18	τ	τ	PROPN
ejpam-6466	573	19	0	0	NUM
ejpam-6466	574	1	sξ−1v	sξ−1v	PROPN
ejpam-6466	574	2	(	(	PUNCT
ejpam-6466	574	3	s	s	PROPN
ejpam-6466	574	4	,	,	PUNCT
ejpam-6466	574	5	j(s	j(s	NOUN
ejpam-6466	574	6	)	)	PUNCT
ejpam-6466	574	7	,	,	PUNCT
ejpam-6466	574	8	j(s−m	j(s−m	PROPN
ejpam-6466	574	9	)	)	PUNCT
ejpam-6466	574	10	)	)	PUNCT
ejpam-6466	575	1	ds	ds	PROPN
ejpam-6466	576	1	+	+	CCONJ
ejpam-6466	576	2	∫	∫	PROPN
ejpam-6466	576	3	τ	τ	X
ejpam-6466	576	4	0	0	NUM
ejpam-6466	576	5	sξ−1𭟋	sξ−1𭟋	X
ejpam-6466	576	6	(	(	PUNCT
ejpam-6466	576	7	s	s	X
ejpam-6466	576	8	,	,	PUNCT
ejpam-6466	576	9	j(s	j(s	NOUN
ejpam-6466	576	10	)	)	PUNCT
ejpam-6466	576	11	,	,	PUNCT
ejpam-6466	576	12	j(s−m	j(s−m	PROPN
ejpam-6466	576	13	)	)	PUNCT
ejpam-6466	576	14	)	)	PUNCT
ejpam-6466	576	15	dw(s	dw(s	X
ejpam-6466	576	16	)	)	PUNCT
ejpam-6466	576	17	)	)	PUNCT
ejpam-6466	577	1	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-6466	577	2	]	]	PUNCT
ejpam-6466	578	1	+	+	NUM
ejpam-6466	578	2	2e	2e	NUM
ejpam-6466	578	3	[	[	X
ejpam-6466	578	4	∥∥∥∥	∥∥∥∥	PROPN
ejpam-6466	578	5	(	(	PUNCT
ejpam-6466	578	6	∫	∫	PROPN
ejpam-6466	578	7	τ	τ	PROPN
ejpam-6466	578	8	0	0	PROPN
ejpam-6466	578	9	sξ−1	sξ−1	PROPN
ejpam-6466	578	10	(	(	PUNCT
ejpam-6466	578	11	v	v	X
ejpam-6466	578	12	(	(	PUNCT
ejpam-6466	578	13	s	s	PROPN
ejpam-6466	578	14	,	,	PUNCT
ejpam-6466	578	15	j(s	j(s	NOUN
ejpam-6466	578	16	)	)	PUNCT
ejpam-6466	578	17	,	,	PUNCT
ejpam-6466	578	18	j(s−m	j(s−m	PROPN
ejpam-6466	578	19	)	)	PUNCT
ejpam-6466	578	20	)	)	PUNCT
ejpam-6466	578	21	−v	−v	NOUN
ejpam-6466	578	22	(	(	PUNCT
ejpam-6466	578	23	s	s	PROPN
ejpam-6466	578	24	,	,	PUNCT
ejpam-6466	578	25	x(s	x(s	PROPN
ejpam-6466	578	26	)	)	PUNCT
ejpam-6466	578	27	,	,	PUNCT
ejpam-6466	578	28	x(s−m	x(s−m	NUM
ejpam-6466	578	29	)	)	PUNCT
ejpam-6466	578	30	)	)	PUNCT
ejpam-6466	578	31	)	)	PUNCT
ejpam-6466	578	32	ds	ds	ADJ
ejpam-6466	578	33	m.	m.	NOUN
ejpam-6466	578	34	i.	i.	PROPN
ejpam-6466	578	35	liaqat	liaqat	PROPN
ejpam-6466	578	36	et	et	PROPN
ejpam-6466	578	37	al	al	PROPN
ejpam-6466	578	38	.	.	PUNCT
ejpam-6466	578	39	/	/	SYM
ejpam-6466	578	40	eur	eur	PROPN
ejpam-6466	578	41	.	.	PUNCT
ejpam-6466	579	1	j.	j.	PROPN
ejpam-6466	579	2	pure	pure	PROPN
ejpam-6466	579	3	appl	appl	PROPN
ejpam-6466	579	4	.	.	PROPN
ejpam-6466	579	5	math	math	PROPN
ejpam-6466	579	6	,	,	PUNCT
ejpam-6466	579	7	18	18	NUM
ejpam-6466	579	8	(	(	PUNCT
ejpam-6466	579	9	4	4	NUM
ejpam-6466	579	10	)	)	PUNCT
ejpam-6466	579	11	(	(	PUNCT
ejpam-6466	579	12	2025	2025	NUM
ejpam-6466	579	13	)	)	PUNCT
ejpam-6466	579	14	,	,	PUNCT
ejpam-6466	579	15	6466	6466	NUM
ejpam-6466	579	16	21	21	NUM
ejpam-6466	579	17	of	of	ADP
ejpam-6466	579	18	28	28	NUM
ejpam-6466	579	19	+	+	NUM
ejpam-6466	579	20	∫	∫	PROPN
ejpam-6466	579	21	τ	τ	PROPN
ejpam-6466	579	22	0	0	X
ejpam-6466	579	23	sξ−1	sξ−1	PROPN
ejpam-6466	579	24	(	(	PUNCT
ejpam-6466	579	25	𭟋	𭟋	PROPN
ejpam-6466	579	26	(	(	PUNCT
ejpam-6466	579	27	s	s	PROPN
ejpam-6466	579	28	,	,	PUNCT
ejpam-6466	579	29	j(s	j(s	NOUN
ejpam-6466	579	30	)	)	PUNCT
ejpam-6466	579	31	,	,	PUNCT
ejpam-6466	579	32	j(s−m	j(s−m	PROPN
ejpam-6466	579	33	)	)	PUNCT
ejpam-6466	579	34	)	)	PUNCT
ejpam-6466	580	1	−𭟋	−𭟋	ADV
ejpam-6466	580	2	(	(	PUNCT
ejpam-6466	580	3	s	s	PROPN
ejpam-6466	580	4	,	,	PUNCT
ejpam-6466	580	5	x(s	x(s	PROPN
ejpam-6466	580	6	)	)	PUNCT
ejpam-6466	580	7	,	,	PUNCT
ejpam-6466	580	8	x(s−m	x(s−m	NUM
ejpam-6466	580	9	)	)	PUNCT
ejpam-6466	580	10	)	)	PUNCT
ejpam-6466	580	11	)	)	PUNCT
ejpam-6466	580	12	dw(s	dw(s	X
ejpam-6466	580	13	)	)	PUNCT
ejpam-6466	580	14	)	)	PUNCT
ejpam-6466	581	1	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-6466	581	2	]	]	PUNCT
ejpam-6466	581	3	.	.	PUNCT
ejpam-6466	582	1	thus	thus	ADV
ejpam-6466	582	2	,	,	PUNCT
ejpam-6466	582	3	using	use	VERB
ejpam-6466	582	4	cauchy	cauchy	NOUN
ejpam-6466	582	5	-	-	PUNCT
ejpam-6466	582	6	schwarz	schwarz	PROPN
ejpam-6466	582	7	inequality	inequality	NOUN
ejpam-6466	582	8	,	,	PUNCT
ejpam-6466	582	9	(	(	PUNCT
ejpam-6466	582	10	a2	a2	PROPN
ejpam-6466	582	11	)	)	PUNCT
ejpam-6466	582	12	and	and	CCONJ
ejpam-6466	582	13	(	(	PUNCT
ejpam-6466	582	14	a3	a3	NOUN
ejpam-6466	582	15	)	)	PUNCT
ejpam-6466	582	16	,	,	PUNCT
ejpam-6466	582	17	we	we	PRON
ejpam-6466	582	18	can	can	AUX
ejpam-6466	582	19	derive	derive	VERB
ejpam-6466	582	20	that	that	SCONJ
ejpam-6466	582	21	e	e	NOUN
ejpam-6466	582	22	[	[	PUNCT
ejpam-6466	582	23	∥j(τ)−	∥j(τ)−	PROPN
ejpam-6466	582	24	x(τ)∥2	x(τ)∥2	PROPN
ejpam-6466	582	25	]	]	PUNCT
ejpam-6466	583	1	≤	≤	NUM
ejpam-6466	583	2	2ϵ	2ϵ	NUM
ejpam-6466	583	3	+	+	NUM
ejpam-6466	583	4	4e	4e	PRON
ejpam-6466	584	1	[	[	X
ejpam-6466	584	2	∥∥∥∥∫	∥∥∥∥∫	ADJ
ejpam-6466	584	3	τ	τ	X
ejpam-6466	584	4	0	0	NUM
ejpam-6466	584	5	sξ−1	sξ−1	PROPN
ejpam-6466	584	6	(	(	PUNCT
ejpam-6466	584	7	v	v	X
ejpam-6466	584	8	(	(	PUNCT
ejpam-6466	584	9	s	s	PROPN
ejpam-6466	584	10	,	,	PUNCT
ejpam-6466	584	11	j(s	j(s	NOUN
ejpam-6466	584	12	)	)	PUNCT
ejpam-6466	584	13	,	,	PUNCT
ejpam-6466	584	14	j(s−m	j(s−m	PROPN
ejpam-6466	584	15	)	)	PUNCT
ejpam-6466	584	16	)	)	PUNCT
ejpam-6466	584	17	−v	−v	NOUN
ejpam-6466	584	18	(	(	PUNCT
ejpam-6466	584	19	s	s	PROPN
ejpam-6466	584	20	,	,	PUNCT
ejpam-6466	584	21	x(s	x(s	PROPN
ejpam-6466	584	22	)	)	PUNCT
ejpam-6466	584	23	,	,	PUNCT
ejpam-6466	584	24	x(s−m	x(s−m	NUM
ejpam-6466	584	25	)	)	PUNCT
ejpam-6466	584	26	)	)	PUNCT
ejpam-6466	584	27	)	)	PUNCT
ejpam-6466	585	1	ds	ds	NOUN
ejpam-6466	585	2	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-6466	585	3	]	]	X
ejpam-6466	586	1	+	+	NUM
ejpam-6466	586	2	4e	4e	NOUN
ejpam-6466	586	3	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-6466	586	4	∫	∫	PROPN
ejpam-6466	586	5	τ	τ	PROPN
ejpam-6466	586	6	0	0	PUNCT
ejpam-6466	586	7	sξ−1	sξ−1	PROPN
ejpam-6466	586	8	(	(	PUNCT
ejpam-6466	586	9	𭟋	𭟋	PROPN
ejpam-6466	586	10	(	(	PUNCT
ejpam-6466	586	11	s	s	PROPN
ejpam-6466	586	12	,	,	PUNCT
ejpam-6466	586	13	j(s	j(s	NOUN
ejpam-6466	586	14	)	)	PUNCT
ejpam-6466	586	15	,	,	PUNCT
ejpam-6466	586	16	j(s−m	j(s−m	PROPN
ejpam-6466	586	17	)	)	PUNCT
ejpam-6466	586	18	)	)	PUNCT
ejpam-6466	587	1	−𭟋	−𭟋	ADV
ejpam-6466	587	2	(	(	PUNCT
ejpam-6466	587	3	s	s	PROPN
ejpam-6466	587	4	,	,	PUNCT
ejpam-6466	587	5	x(s	x(s	PROPN
ejpam-6466	587	6	)	)	PUNCT
ejpam-6466	587	7	,	,	PUNCT
ejpam-6466	587	8	x(s−m	x(s−m	NUM
ejpam-6466	587	9	)	)	PUNCT
ejpam-6466	587	10	)	)	PUNCT
ejpam-6466	587	11	)	)	PUNCT
ejpam-6466	587	12	dw(s	dw(s	X
ejpam-6466	587	13	)	)	PUNCT
ejpam-6466	587	14	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-6466	587	15	]	]	PUNCT
ejpam-6466	587	16	≤	≤	PROPN
ejpam-6466	587	17	2ϵ+	2ϵ+	NUM
ejpam-6466	587	18	8l2ℏ2ξ−1	8l2ℏ2ξ−1	NOUN
ejpam-6466	587	19	(	(	PUNCT
ejpam-6466	587	20	2ξ	2ξ	NUM
ejpam-6466	587	21	−	−	PROPN
ejpam-6466	587	22	1	1	X
ejpam-6466	587	23	)	)	PUNCT
ejpam-6466	587	24	e	e	NOUN
ejpam-6466	588	1	[	[	X
ejpam-6466	588	2	∫	∫	X
ejpam-6466	588	3	τ	τ	X
ejpam-6466	588	4	0	0	NUM
ejpam-6466	588	5	(	(	PUNCT
ejpam-6466	588	6	∥j(s)−	∥j(s)−	ADP
ejpam-6466	588	7	x(s)∥2	x(s)∥2	PROPN
ejpam-6466	588	8	+	+	X
ejpam-6466	588	9	∥j(s−m)−	∥j(s−m)−	PROPN
ejpam-6466	588	10	x(s−m)∥2	x(s−m)∥2	PUNCT
ejpam-6466	588	11	)	)	PUNCT
ejpam-6466	589	1	ds	ds	X
ejpam-6466	589	2	]	]	PUNCT
ejpam-6466	590	1	+	+	CCONJ
ejpam-6466	590	2	8l2e	8l2e	ADJ
ejpam-6466	590	3	[	[	X
ejpam-6466	590	4	∫	∫	X
ejpam-6466	590	5	τ	τ	X
ejpam-6466	590	6	0	0	NUM
ejpam-6466	590	7	s2ξ−2	s2ξ−2	PROPN
ejpam-6466	590	8	(	(	PUNCT
ejpam-6466	590	9	∥j(s)−	∥j(s)−	ADP
ejpam-6466	590	10	x(s)∥2	x(s)∥2	PROPN
ejpam-6466	590	11	+	+	X
ejpam-6466	590	12	∥j(s−m)−	∥j(s−m)−	PROPN
ejpam-6466	590	13	x(s−m)∥2	x(s−m)∥2	PUNCT
ejpam-6466	590	14	)	)	PUNCT
ejpam-6466	591	1	ds	ds	VERB
ejpam-6466	591	2	]	]	PUNCT
ejpam-6466	591	3	.	.	PUNCT
ejpam-6466	592	1	let	let	VERB
ejpam-6466	592	2	ϕ(τ	ϕ(τ	X
ejpam-6466	592	3	)	)	PUNCT
ejpam-6466	593	1	=	=	SYM
ejpam-6466	593	2	sups∈[0,ℏ]e	sups∈[0,ℏ]e	PROPN
ejpam-6466	593	3	[	[	PUNCT
ejpam-6466	593	4	∥j(s)−	∥j(s)−	ADP
ejpam-6466	593	5	x(s)∥2	x(s)∥2	NOUN
ejpam-6466	593	6	]	]	PUNCT
ejpam-6466	593	7	for	for	ADP
ejpam-6466	593	8	τ	τ	PROPN
ejpam-6466	593	9	∈	∈	PROPN
ejpam-6466	594	1	[	[	X
ejpam-6466	594	2	0	0	NUM
ejpam-6466	594	3	,	,	PUNCT
ejpam-6466	594	4	ℏ	ℏ	PROPN
ejpam-6466	594	5	]	]	PUNCT
ejpam-6466	594	6	.	.	PUNCT
ejpam-6466	595	1	we	we	PRON
ejpam-6466	595	2	have	have	VERB
ejpam-6466	595	3	e	e	X
ejpam-6466	595	4	[	[	PUNCT
ejpam-6466	595	5	∥j(s)−	∥j(s)−	ADP
ejpam-6466	595	6	x(s)∥2	x(s)∥2	NOUN
ejpam-6466	595	7	]	]	PUNCT
ejpam-6466	595	8	≤	≤	X
ejpam-6466	595	9	ϕ(s	ϕ(s	PROPN
ejpam-6466	595	10	)	)	PUNCT
ejpam-6466	595	11	,	,	PUNCT
ejpam-6466	595	12	and	and	CCONJ
ejpam-6466	595	13	e	e	X
ejpam-6466	595	14	[	[	PUNCT
ejpam-6466	595	15	∥j(s−m)−	∥j(s−m)−	PROPN
ejpam-6466	595	16	x(s−m)∥2	x(s−m)∥2	PROPN
ejpam-6466	595	17	]	]	PUNCT
ejpam-6466	596	1	≤	≤	NUM
ejpam-6466	596	2	ϕ(s	ϕ(s	PROPN
ejpam-6466	596	3	)	)	PUNCT
ejpam-6466	596	4	,	,	PUNCT
ejpam-6466	596	5	∀s	∀s	PROPN
ejpam-6466	596	6	∈	∈	PROPN
ejpam-6466	597	1	[	[	X
ejpam-6466	597	2	0	0	NUM
ejpam-6466	597	3	,	,	PUNCT
ejpam-6466	597	4	ℏ	ℏ	NOUN
ejpam-6466	597	5	]	]	PUNCT
ejpam-6466	597	6	.	.	PUNCT
ejpam-6466	598	1	then	then	ADV
ejpam-6466	598	2	,	,	PUNCT
ejpam-6466	598	3	for	for	ADP
ejpam-6466	598	4	τ	τ	PROPN
ejpam-6466	598	5	∈	∈	PROPN
ejpam-6466	599	1	[	[	X
ejpam-6466	599	2	0	0	NUM
ejpam-6466	599	3	,	,	PUNCT
ejpam-6466	599	4	ℏ	ℏ	PROPN
ejpam-6466	599	5	]	]	PUNCT
ejpam-6466	599	6	,	,	PUNCT
ejpam-6466	599	7	we	we	PRON
ejpam-6466	599	8	obtain	obtain	VERB
ejpam-6466	599	9	e	e	NOUN
ejpam-6466	599	10	[	[	PUNCT
ejpam-6466	599	11	∥j(τ)−	∥j(τ)−	PROPN
ejpam-6466	599	12	x(τ)∥2	x(τ)∥2	PROPN
ejpam-6466	599	13	]	]	PUNCT
ejpam-6466	599	14	≤2ϵ+	≤2ϵ+	PROPN
ejpam-6466	599	15	16l2ℏ2ξ−1	16l2ℏ2ξ−1	NUM
ejpam-6466	599	16	(	(	PUNCT
ejpam-6466	599	17	2ξ	2ξ	NUM
ejpam-6466	599	18	−	−	PROPN
ejpam-6466	599	19	1	1	X
ejpam-6466	599	20	)	)	PUNCT
ejpam-6466	599	21	∫	∫	PROPN
ejpam-6466	600	1	τ	τ	PROPN
ejpam-6466	600	2	0	0	PROPN
ejpam-6466	600	3	ϕ(s)ds	ϕ(s)ds	PROPN
ejpam-6466	601	1	+	+	NOUN
ejpam-6466	601	2	16l2	16l2	NUM
ejpam-6466	601	3	∫	∫	NOUN
ejpam-6466	601	4	τ	τ	PROPN
ejpam-6466	601	5	0	0	NUM
ejpam-6466	601	6	s2ξ−2ϕ(s)ds	s2ξ−2ϕ(s)ds	PROPN
ejpam-6466	601	7	.	.	PUNCT
ejpam-6466	602	1	hence	hence	ADV
ejpam-6466	602	2	,	,	PUNCT
ejpam-6466	602	3	∀τ	∀τ	SYM
ejpam-6466	602	4	∈	∈	PROPN
ejpam-6466	603	1	[	[	X
ejpam-6466	603	2	0	0	NUM
ejpam-6466	603	3	,	,	PUNCT
ejpam-6466	603	4	ℏ	ℏ	X
ejpam-6466	603	5	]	]	PUNCT
ejpam-6466	603	6	,	,	PUNCT
ejpam-6466	603	7	e	e	X
ejpam-6466	603	8	[	[	PUNCT
ejpam-6466	603	9	∥j(s)−	∥j(s)−	ADP
ejpam-6466	603	10	x(s)∥2	x(s)∥2	NOUN
ejpam-6466	603	11	]	]	PUNCT
ejpam-6466	603	12	≤2ϵ+	≤2ϵ+	NUM
ejpam-6466	603	13	16l2ℏ2ξ−1	16l2ℏ2ξ−1	NUM
ejpam-6466	603	14	(	(	PUNCT
ejpam-6466	603	15	2ξ	2ξ	NUM
ejpam-6466	603	16	−	−	PROPN
ejpam-6466	603	17	1	1	X
ejpam-6466	603	18	)	)	PUNCT
ejpam-6466	603	19	∫	∫	PROPN
ejpam-6466	603	20	τ	τ	PROPN
ejpam-6466	603	21	0	0	PROPN
ejpam-6466	603	22	ϕ(s)ds	ϕ(s)ds	PROPN
ejpam-6466	604	1	+	+	NOUN
ejpam-6466	604	2	16l2	16l2	NUM
ejpam-6466	604	3	∫	∫	NOUN
ejpam-6466	604	4	τ	τ	PROPN
ejpam-6466	604	5	0	0	NUM
ejpam-6466	604	6	s2ξ−2ϕ(s)ds	s2ξ−2ϕ(s)ds	PROPN
ejpam-6466	604	7	.	.	PUNCT
ejpam-6466	605	1	then	then	ADV
ejpam-6466	605	2	,	,	PUNCT
ejpam-6466	605	3	ϕ(τ	ϕ(τ	PROPN
ejpam-6466	605	4	)	)	PUNCT
ejpam-6466	605	5	≤	≤	PROPN
ejpam-6466	605	6	2ϵ+	2ϵ+	NUM
ejpam-6466	605	7	γ1	γ1	PROPN
ejpam-6466	605	8	∫	∫	PROPN
ejpam-6466	605	9	τ	τ	PROPN
ejpam-6466	605	10	0	0	PROPN
ejpam-6466	605	11	ϕ(s)ds	ϕ(s)ds	PROPN
ejpam-6466	605	12	+	+	CCONJ
ejpam-6466	605	13	γ2	γ2	ADJ
ejpam-6466	605	14	∫	∫	PROPN
ejpam-6466	605	15	τ	τ	PROPN
ejpam-6466	605	16	0	0	NUM
ejpam-6466	605	17	s2ξ−2ϕ(s)ds	s2ξ−2ϕ(s)ds	PROPN
ejpam-6466	605	18	,	,	PUNCT
ejpam-6466	605	19	for	for	ADP
ejpam-6466	605	20	all	all	DET
ejpam-6466	605	21	τ	τ	PRON
ejpam-6466	605	22	∈	∈	PROPN
ejpam-6466	606	1	[	[	X
ejpam-6466	606	2	0	0	NUM
ejpam-6466	606	3	,	,	PUNCT
ejpam-6466	606	4	ℏ	ℏ	PROPN
ejpam-6466	606	5	]	]	X
ejpam-6466	606	6	,	,	PUNCT
ejpam-6466	606	7	where	where	SCONJ
ejpam-6466	606	8	γ1	γ1	NOUN
ejpam-6466	606	9	=	=	NOUN
ejpam-6466	606	10	16l2ℏ2ξ−1	16l2ℏ2ξ−1	NUM
ejpam-6466	606	11	(	(	PUNCT
ejpam-6466	606	12	2ξ−1	2ξ−1	NUM
ejpam-6466	606	13	)	)	PUNCT
ejpam-6466	606	14	and	and	CCONJ
ejpam-6466	606	15	γ2	γ2	NOUN
ejpam-6466	606	16	=	=	SYM
ejpam-6466	606	17	16l2	16l2	NUM
ejpam-6466	606	18	.	.	PUNCT
ejpam-6466	607	1	using	use	VERB
ejpam-6466	607	2	g	g	PROPN
ejpam-6466	607	3	-	-	PUNCT
ejpam-6466	607	4	i	i	NOUN
ejpam-6466	607	5	,	,	PUNCT
ejpam-6466	607	6	we	we	PRON
ejpam-6466	607	7	get	get	VERB
ejpam-6466	607	8	ϕ(τ	ϕ(τ	PROPN
ejpam-6466	607	9	)	)	PUNCT
ejpam-6466	607	10	≤	≤	NOUN
ejpam-6466	608	1	(	(	PUNCT
ejpam-6466	608	2	2ϵ+	2ϵ+	NUM
ejpam-6466	608	3	γ1	γ1	PROPN
ejpam-6466	608	4	∫	∫	PROPN
ejpam-6466	608	5	τ	τ	PROPN
ejpam-6466	608	6	0	0	PROPN
ejpam-6466	608	7	ϕ(s)ds	ϕ(s)ds	CCONJ
ejpam-6466	608	8	)	)	PUNCT
ejpam-6466	608	9	e2ξ−1	e2ξ−1	PROPN
ejpam-6466	608	10	(	(	PUNCT
ejpam-6466	608	11	γ2γ(2ξ	γ2γ(2ξ	ADJ
ejpam-6466	608	12	−	−	PROPN
ejpam-6466	608	13	1	1	NUM
ejpam-6466	608	14	)	)	PUNCT
ejpam-6466	608	15	(	(	PUNCT
ejpam-6466	608	16	ξ)2ξ−1	ξ)2ξ−1	NOUN
ejpam-6466	608	17	)	)	PUNCT
ejpam-6466	608	18	m.	m.	NOUN
ejpam-6466	608	19	i.	i.	PROPN
ejpam-6466	608	20	liaqat	liaqat	PROPN
ejpam-6466	608	21	et	et	PROPN
ejpam-6466	608	22	al	al	PROPN
ejpam-6466	608	23	.	.	PUNCT
ejpam-6466	608	24	/	/	SYM
ejpam-6466	608	25	eur	eur	PROPN
ejpam-6466	608	26	.	.	PUNCT
ejpam-6466	609	1	j.	j.	PROPN
ejpam-6466	609	2	pure	pure	PROPN
ejpam-6466	609	3	appl	appl	PROPN
ejpam-6466	609	4	.	.	PROPN
ejpam-6466	609	5	math	math	PROPN
ejpam-6466	609	6	,	,	PUNCT
ejpam-6466	609	7	18	18	NUM
ejpam-6466	609	8	(	(	PUNCT
ejpam-6466	609	9	4	4	NUM
ejpam-6466	609	10	)	)	PUNCT
ejpam-6466	609	11	(	(	PUNCT
ejpam-6466	609	12	2025	2025	NUM
ejpam-6466	609	13	)	)	PUNCT
ejpam-6466	609	14	,	,	PUNCT
ejpam-6466	609	15	6466	6466	NUM
ejpam-6466	609	16	22	22	NUM
ejpam-6466	609	17	of	of	ADP
ejpam-6466	609	18	28	28	NUM
ejpam-6466	609	19	≤	≤	NUM
ejpam-6466	609	20	γ3ϵ+	γ3ϵ+	NOUN
ejpam-6466	609	21	γ4	γ4	NOUN
ejpam-6466	609	22	∫	∫	PROPN
ejpam-6466	609	23	τ	τ	X
ejpam-6466	609	24	0	0	PROPN
ejpam-6466	609	25	ϕ(s)ds	ϕ(s)ds	PROPN
ejpam-6466	609	26	,	,	PUNCT
ejpam-6466	609	27	where	where	SCONJ
ejpam-6466	609	28	γ3	γ3	NOUN
ejpam-6466	609	29	=	=	NOUN
ejpam-6466	609	30	2e2ξ−1	2e2ξ−1	NUM
ejpam-6466	609	31	(	(	PUNCT
ejpam-6466	609	32	γ2γ(2ξ	γ2γ(2ξ	ADJ
ejpam-6466	609	33	−	−	PROPN
ejpam-6466	609	34	1)ℏ2ξ−1	1)ℏ2ξ−1	NUM
ejpam-6466	609	35	)	)	PUNCT
ejpam-6466	609	36	and	and	CCONJ
ejpam-6466	609	37	γ4	γ4	NOUN
ejpam-6466	609	38	=	=	SYM
ejpam-6466	609	39	γ1e2ξ−1	γ1e2ξ−1	X
ejpam-6466	609	40	(	(	PUNCT
ejpam-6466	609	41	γ2γ(2ξ	γ2γ(2ξ	ADV
ejpam-6466	609	42	−	−	PROPN
ejpam-6466	609	43	1)x2ξ−1	1)x2ξ−1	NUM
ejpam-6466	609	44	)	)	PUNCT
ejpam-6466	609	45	.	.	PUNCT
ejpam-6466	610	1	using	use	VERB
ejpam-6466	610	2	g	g	PROPN
ejpam-6466	610	3	-	-	PUNCT
ejpam-6466	610	4	i	i	NOUN
ejpam-6466	610	5	,	,	PUNCT
ejpam-6466	610	6	we	we	PRON
ejpam-6466	610	7	get	get	VERB
ejpam-6466	610	8	ϕ(τ	ϕ(τ	PROPN
ejpam-6466	610	9	)	)	PUNCT
ejpam-6466	610	10	≤	≤	NOUN
ejpam-6466	611	1	γ3ϵe	γ3ϵe	PUNCT
ejpam-6466	611	2	γ4	γ4	NOUN
ejpam-6466	611	3	(	(	PUNCT
ejpam-6466	611	4	ξ	ξ	PROPN
ejpam-6466	611	5	)	)	PUNCT
ejpam-6466	611	6	.	.	PUNCT
ejpam-6466	612	1	hence	hence	ADV
ejpam-6466	612	2	,	,	PUNCT
ejpam-6466	612	3	e[∥j(τ)−	e[∥j(τ)−	PROPN
ejpam-6466	612	4	x(τ)∥2	x(τ)∥2	NOUN
ejpam-6466	612	5	]	]	PUNCT
ejpam-6466	612	6	≤	≤	NUM
ejpam-6466	612	7	ℵϵ	ℵϵ	NUM
ejpam-6466	612	8	,	,	PUNCT
ejpam-6466	612	9	∀τ	∀τ	SYM
ejpam-6466	612	10	∈	∈	PROPN
ejpam-6466	613	1	[	[	X
ejpam-6466	613	2	0	0	NUM
ejpam-6466	613	3	,	,	PUNCT
ejpam-6466	613	4	ℏ	ℏ	PROPN
ejpam-6466	613	5	]	]	X
ejpam-6466	613	6	,	,	PUNCT
ejpam-6466	613	7	where	where	SCONJ
ejpam-6466	613	8	χ	χ	X
ejpam-6466	613	9	=	=	PUNCT
ejpam-6466	613	10	γ3e	γ3e	PROPN
ejpam-6466	613	11	γ4ℏ.	γ4ℏ.	PROPN
ejpam-6466	613	12	thus	thus	ADV
ejpam-6466	613	13	,	,	PUNCT
ejpam-6466	613	14	eq	eq	ADJ
ejpam-6466	613	15	.	.	PUNCT
ejpam-6466	614	1	(	(	PUNCT
ejpam-6466	614	2	4	4	X
ejpam-6466	614	3	)	)	PUNCT
ejpam-6466	614	4	is	be	AUX
ejpam-6466	614	5	uh	uh	INTJ
ejpam-6466	614	6	stability	stability	NOUN
ejpam-6466	614	7	.	.	PUNCT
ejpam-6466	615	1	4	4	X
ejpam-6466	615	2	.	.	X
ejpam-6466	615	3	examples	example	NOUN
ejpam-6466	615	4	this	this	DET
ejpam-6466	615	5	section	section	NOUN
ejpam-6466	615	6	provides	provide	VERB
ejpam-6466	615	7	examples	example	NOUN
ejpam-6466	615	8	to	to	PART
ejpam-6466	615	9	demonstrate	demonstrate	VERB
ejpam-6466	615	10	our	our	PRON
ejpam-6466	615	11	results	result	NOUN
ejpam-6466	615	12	.	.	PUNCT
ejpam-6466	616	1	example	example	NOUN
ejpam-6466	617	1	1	1	NUM
ejpam-6466	617	2	.	.	PUNCT
ejpam-6466	618	1	the	the	DET
ejpam-6466	618	2	following	follow	VERB
ejpam-6466	618	3	is	be	AUX
ejpam-6466	618	4	the	the	DET
ejpam-6466	618	5	langevin	langevin	ADJ
ejpam-6466	618	6	df	df	PROPN
ejpam-6466	618	7	-	-	PUNCT
ejpam-6466	618	8	sde	sde	PROPN
ejpam-6466	618	9	:	:	PUNCT
ejpam-6466	618	10	dξ	dξ	PROPN
ejpam-6466	618	11	τx(τ	τx(τ	PUNCT
ejpam-6466	618	12	)	)	PUNCT
ejpam-6466	618	13	=	=	SYM
ejpam-6466	618	14	−υx(τ	−υx(τ	NUM
ejpam-6466	618	15	−m	−m	NOUN
ejpam-6466	618	16	)	)	PUNCT
ejpam-6466	619	1	+	+	CCONJ
ejpam-6466	619	2	ω	ω	NUM
ejpam-6466	619	3	dwτ	dwτ	ADV
ejpam-6466	619	4	dτ	dτ	NOUN
ejpam-6466	619	5	,	,	PUNCT
ejpam-6466	619	6	1	1	NUM
ejpam-6466	619	7	2	2	NUM
ejpam-6466	619	8	<	<	X
ejpam-6466	619	9	ξ	ξ	X
ejpam-6466	619	10	<	<	X
ejpam-6466	619	11	1	1	NUM
ejpam-6466	619	12	,	,	PUNCT
ejpam-6466	619	13	0	0	NUM
ejpam-6466	619	14	<	<	X
ejpam-6466	619	15	τ	τ	X
ejpam-6466	619	16	<	<	X
ejpam-6466	619	17	ℏ	ℏ	PROPN
ejpam-6466	619	18	,	,	PUNCT
ejpam-6466	619	19	(	(	PUNCT
ejpam-6466	619	20	28	28	NUM
ejpam-6466	619	21	)	)	PUNCT
ejpam-6466	619	22	x(τ	x(τ	PROPN
ejpam-6466	619	23	)	)	PUNCT
ejpam-6466	619	24	=	=	SYM
ejpam-6466	620	1	1	1	NUM
ejpam-6466	620	2	,	,	PUNCT
ejpam-6466	620	3	−m	−m	ADJ
ejpam-6466	620	4	≤	≤	ADV
ejpam-6466	620	5	τ	τ	PUNCT
ejpam-6466	620	6	≤	≤	NOUN
ejpam-6466	620	7	0	0	NUM
ejpam-6466	620	8	,	,	PUNCT
ejpam-6466	620	9	(	(	PUNCT
ejpam-6466	620	10	28	28	NUM
ejpam-6466	620	11	)	)	PUNCT
ejpam-6466	620	12	where	where	SCONJ
ejpam-6466	620	13	,	,	PUNCT
ejpam-6466	620	14	m	m	VERB
ejpam-6466	620	15	is	be	AUX
ejpam-6466	620	16	delay	delay	NOUN
ejpam-6466	620	17	factor	factor	NOUN
ejpam-6466	620	18	and	and	CCONJ
ejpam-6466	620	19	υ	υ	NOUN
ejpam-6466	620	20	,	,	PUNCT
ejpam-6466	620	21	ω	ω	PROPN
ejpam-6466	620	22	∈	∈	PROPN
ejpam-6466	620	23	r+	r+	NOUN
ejpam-6466	620	24	,	,	PUNCT
ejpam-6466	620	25	and	and	CCONJ
ejpam-6466	620	26	v	v	X
ejpam-6466	620	27	=	=	SYM
ejpam-6466	620	28	−υx(τ	−υx(τ	NUM
ejpam-6466	620	29	−	−	PROPN
ejpam-6466	620	30	m	m	PROPN
ejpam-6466	620	31	)	)	PUNCT
ejpam-6466	620	32	,	,	PUNCT
ejpam-6466	620	33	𭟋	𭟋	PROPN
ejpam-6466	620	34	=	=	SYM
ejpam-6466	620	35	ω	ω	PROPN
ejpam-6466	620	36	are	be	AUX
ejpam-6466	620	37	drift	drift	NOUN
ejpam-6466	620	38	and	and	CCONJ
ejpam-6466	620	39	diffusion	diffusion	NOUN
ejpam-6466	620	40	factors	factor	NOUN
ejpam-6466	620	41	.	.	PUNCT
ejpam-6466	621	1	in	in	ADP
ejpam-6466	621	2	the	the	DET
ejpam-6466	621	3	earlier	early	ADV
ejpam-6466	621	4	discussed	discuss	VERB
ejpam-6466	621	5	model	model	PROPN
ejpam-6466	621	6	eqs	eqs	PROPN
ejpam-6466	621	7	.	.	PUNCT
ejpam-6466	622	1	(	(	PUNCT
ejpam-6466	622	2	4	4	NUM
ejpam-6466	622	3	)	)	PUNCT
ejpam-6466	622	4	and	and	CCONJ
ejpam-6466	622	5	(	(	PUNCT
ejpam-6466	622	6	4	4	NUM
ejpam-6466	622	7	)	)	PUNCT
ejpam-6466	622	8	,	,	PUNCT
ejpam-6466	622	9	which	which	PRON
ejpam-6466	622	10	was	be	AUX
ejpam-6466	622	11	studied	study	VERB
ejpam-6466	622	12	in	in	ADP
ejpam-6466	622	13	[	[	X
ejpam-6466	622	14	36	36	NUM
ejpam-6466	622	15	]	]	PUNCT
ejpam-6466	622	16	with	with	ADP
ejpam-6466	622	17	ξ	ξ	PROPN
ejpam-6466	622	18	=	=	SYM
ejpam-6466	622	19	1	1	NUM
ejpam-6466	622	20	represented	represent	VERB
ejpam-6466	622	21	the	the	DET
ejpam-6466	622	22	statistical	statistical	ADJ
ejpam-6466	622	23	physics	physics	NOUN
ejpam-6466	622	24	of	of	ADP
ejpam-6466	622	25	auto	auto	NOUN
ejpam-6466	622	26	traffic	traffic	NOUN
ejpam-6466	622	27	.	.	PUNCT
ejpam-6466	623	1	we	we	PRON
ejpam-6466	623	2	take	take	VERB
ejpam-6466	623	3	m	m	VERB
ejpam-6466	623	4	=	=	NOUN
ejpam-6466	623	5	0.1	0.1	NUM
ejpam-6466	623	6	,	,	PUNCT
ejpam-6466	623	7	υ	υ	NOUN
ejpam-6466	623	8	=	=	NOUN
ejpam-6466	623	9	0.5	0.5	NUM
ejpam-6466	623	10	,	,	PUNCT
ejpam-6466	623	11	ω	ω	NOUN
ejpam-6466	623	12	=	=	SYM
ejpam-6466	623	13	1	1	X
ejpam-6466	623	14	.	.	PUNCT
ejpam-6466	624	1	we	we	PRON
ejpam-6466	624	2	can	can	AUX
ejpam-6466	624	3	easily	easily	ADV
ejpam-6466	624	4	see	see	VERB
ejpam-6466	624	5	that	that	SCONJ
ejpam-6466	624	6	glc	glc	PROPN
ejpam-6466	624	7	is	be	AUX
ejpam-6466	624	8	fulfilled	fulfil	VERB
ejpam-6466	624	9	by	by	ADP
ejpam-6466	624	10	the	the	DET
ejpam-6466	624	11	−υx(τ	−υx(τ	NUM
ejpam-6466	624	12	−	−	PROPN
ejpam-6466	624	13	m	m	NOUN
ejpam-6466	624	14	)	)	PUNCT
ejpam-6466	624	15	and	and	CCONJ
ejpam-6466	624	16	ω	ω	NUM
ejpam-6466	624	17	coefficients	coefficient	NOUN
ejpam-6466	624	18	in	in	ADP
ejpam-6466	624	19	eq	eq	ADP
ejpam-6466	624	20	.	.	PUNCT
ejpam-6466	625	1	(	(	PUNCT
ejpam-6466	625	2	4	4	NUM
ejpam-6466	625	3	)	)	PUNCT
ejpam-6466	625	4	.	.	PUNCT
ejpam-6466	626	1	as	as	ADP
ejpam-6466	626	2	a	a	DET
ejpam-6466	626	3	consequence	consequence	NOUN
ejpam-6466	626	4	,	,	PUNCT
ejpam-6466	626	5	theorem	theorem	ADJ
ejpam-6466	626	6	1	1	NUM
ejpam-6466	626	7	asserts	assert	VERB
ejpam-6466	626	8	the	the	DET
ejpam-6466	626	9	existence	existence	NOUN
ejpam-6466	626	10	of	of	ADP
ejpam-6466	626	11	a	a	DET
ejpam-6466	626	12	unique	unique	ADJ
ejpam-6466	626	13	solution	solution	NOUN
ejpam-6466	626	14	under	under	ADP
ejpam-6466	626	15	the	the	DET
ejpam-6466	626	16	historical	historical	ADJ
ejpam-6466	626	17	functions	function	NOUN
ejpam-6466	626	18	x(τ	x(τ	PROPN
ejpam-6466	626	19	)	)	PUNCT
ejpam-6466	627	1	=	=	SYM
ejpam-6466	627	2	1	1	NUM
ejpam-6466	627	3	,	,	PUNCT
ejpam-6466	627	4	m	m	VERB
ejpam-6466	627	5	≤	≤	NUM
ejpam-6466	627	6	τ	τ	X
ejpam-6466	627	7	≤	≤	NUM
ejpam-6466	627	8	0	0	NUM
ejpam-6466	627	9	in	in	ADP
ejpam-6466	627	10	the	the	DET
ejpam-6466	627	11	interval	interval	NOUN
ejpam-6466	627	12	−m	−m	NOUN
ejpam-6466	627	13	≤	≤	PROPN
ejpam-6466	627	14	τ	τ	X
ejpam-6466	627	15	≤	≤	NUM
ejpam-6466	627	16	ℏ.	ℏ.	NOUN
ejpam-6466	627	17	example	example	NOUN
ejpam-6466	627	18	2	2	NUM
ejpam-6466	627	19	.	.	X
ejpam-6466	627	20	consider	consider	VERB
ejpam-6466	627	21	the	the	DET
ejpam-6466	627	22	mackey	mackey	NOUN
ejpam-6466	627	23	-	-	PUNCT
ejpam-6466	627	24	glass	glass	NOUN
ejpam-6466	627	25	df	df	PROPN
ejpam-6466	627	26	-	-	PUNCT
ejpam-6466	627	27	sde	sde	PROPN
ejpam-6466	627	28	.	.	PUNCT
ejpam-6466	628	1	dξ	dξ	PROPN
ejpam-6466	628	2	τx(τ	τx(τ	PUNCT
ejpam-6466	628	3	)	)	PUNCT
ejpam-6466	628	4	=	=	SYM
ejpam-6466	628	5	κx(τ	κx(τ	VERB
ejpam-6466	628	6	−m	−m	NOUN
ejpam-6466	628	7	)	)	PUNCT
ejpam-6466	628	8	1	1	NUM
ejpam-6466	629	1	+	+	NUM
ejpam-6466	629	2	x10(τ	x10(τ	NOUN
ejpam-6466	629	3	−m	−m	NOUN
ejpam-6466	629	4	)	)	PUNCT
ejpam-6466	629	5	−	−	NOUN
ejpam-6466	629	6	λx(τ	λx(τ	PUNCT
ejpam-6466	629	7	)	)	PUNCT
ejpam-6466	630	1	+	+	CCONJ
ejpam-6466	630	2	ℓx	ℓx	VERB
ejpam-6466	630	3	dwτ	dwτ	ADV
ejpam-6466	630	4	dτ	dτ	PROPN
ejpam-6466	630	5	,	,	PUNCT
ejpam-6466	630	6	1	1	NUM
ejpam-6466	630	7	2	2	NUM
ejpam-6466	630	8	<	<	X
ejpam-6466	630	9	ξ	ξ	X
ejpam-6466	630	10	<	<	X
ejpam-6466	630	11	1	1	NUM
ejpam-6466	630	12	,	,	PUNCT
ejpam-6466	630	13	0	0	NUM
ejpam-6466	630	14	<	<	X
ejpam-6466	630	15	τ	τ	X
ejpam-6466	630	16	<	<	X
ejpam-6466	630	17	ℏ	ℏ	PROPN
ejpam-6466	630	18	,	,	PUNCT
ejpam-6466	630	19	(	(	PUNCT
ejpam-6466	630	20	28	28	NUM
ejpam-6466	630	21	)	)	PUNCT
ejpam-6466	630	22	x(τ	x(τ	PROPN
ejpam-6466	630	23	)	)	PUNCT
ejpam-6466	630	24	=	=	SYM
ejpam-6466	630	25	0.5	0.5	NUM
ejpam-6466	630	26	,	,	PUNCT
ejpam-6466	630	27	−m	−m	ADJ
ejpam-6466	630	28	≤	≤	ADV
ejpam-6466	630	29	τ	τ	PUNCT
ejpam-6466	630	30	≤	≤	NOUN
ejpam-6466	630	31	0	0	NUM
ejpam-6466	630	32	,	,	PUNCT
ejpam-6466	630	33	(	(	PUNCT
ejpam-6466	630	34	28	28	NUM
ejpam-6466	630	35	)	)	PUNCT
ejpam-6466	630	36	where	where	SCONJ
ejpam-6466	630	37	,	,	PUNCT
ejpam-6466	630	38	m	m	VERB
ejpam-6466	630	39	is	be	AUX
ejpam-6466	630	40	delay	delay	NOUN
ejpam-6466	630	41	factor	factor	NOUN
ejpam-6466	630	42	and	and	CCONJ
ejpam-6466	630	43	κ	κ	NOUN
ejpam-6466	630	44	,	,	PUNCT
ejpam-6466	630	45	λ	λ	PROPN
ejpam-6466	630	46	,	,	PUNCT
ejpam-6466	630	47	ℓ	ℓ	PROPN
ejpam-6466	630	48	∈	∈	PROPN
ejpam-6466	630	49	r+	r+	NOUN
ejpam-6466	630	50	,	,	PUNCT
ejpam-6466	630	51	with	with	ADP
ejpam-6466	630	52	v	v	NOUN
ejpam-6466	630	53	=	=	SYM
ejpam-6466	630	54	ℓx(τ−m	ℓx(τ−m	PROPN
ejpam-6466	630	55	)	)	PUNCT
ejpam-6466	630	56	1+x10(τ−m	1+x10(τ−m	NUM
ejpam-6466	630	57	)	)	PUNCT
ejpam-6466	630	58	and	and	CCONJ
ejpam-6466	630	59	𭟋	𭟋	NOUN
ejpam-6466	630	60	=	=	PUNCT
ejpam-6466	630	61	−κx(τ	−κx(τ	NUM
ejpam-6466	630	62	)	)	PUNCT
ejpam-6466	630	63	+	+	PROPN
ejpam-6466	630	64	λx	λx	NOUN
ejpam-6466	630	65	.	.	PUNCT
ejpam-6466	631	1	ξ	ξ	X
ejpam-6466	631	2	=	=	SYM
ejpam-6466	631	3	1	1	NUM
ejpam-6466	631	4	was	be	AUX
ejpam-6466	631	5	used	use	VERB
ejpam-6466	631	6	in	in	ADP
ejpam-6466	631	7	[	[	X
ejpam-6466	631	8	37	37	NUM
ejpam-6466	631	9	]	]	PUNCT
ejpam-6466	631	10	to	to	PART
ejpam-6466	631	11	analyze	analyze	VERB
ejpam-6466	631	12	the	the	DET
ejpam-6466	631	13	model	model	NOUN
ejpam-6466	631	14	eqs	eqs	PROPN
ejpam-6466	631	15	.	.	PUNCT
ejpam-6466	632	1	(	(	PUNCT
ejpam-6466	632	2	3.2	3.2	NUM
ejpam-6466	632	3	)	)	PUNCT
ejpam-6466	632	4	and	and	CCONJ
ejpam-6466	632	5	(	(	PUNCT
ejpam-6466	632	6	3.2	3.2	NUM
ejpam-6466	632	7	)	)	PUNCT
ejpam-6466	632	8	,	,	PUNCT
ejpam-6466	632	9	this	this	DET
ejpam-6466	632	10	model	model	NOUN
ejpam-6466	632	11	explains	explain	VERB
ejpam-6466	632	12	the	the	DET
ejpam-6466	632	13	stochastic	stochastic	ADJ
ejpam-6466	632	14	increase	increase	NOUN
ejpam-6466	632	15	in	in	ADP
ejpam-6466	632	16	blood	blood	NOUN
ejpam-6466	632	17	cell	cell	NOUN
ejpam-6466	632	18	density	density	NOUN
ejpam-6466	632	19	.	.	PUNCT
ejpam-6466	633	1	we	we	PRON
ejpam-6466	633	2	consider	consider	VERB
ejpam-6466	633	3	m	m	NOUN
ejpam-6466	633	4	=	=	SYM
ejpam-6466	633	5	5	5	NUM
ejpam-6466	633	6	,	,	PUNCT
ejpam-6466	633	7	κ	κ	X
ejpam-6466	633	8	=	=	SYM
ejpam-6466	634	1	1,λ	1,λ	NUM
ejpam-6466	634	2	=	=	SYM
ejpam-6466	634	3	2	2	NUM
ejpam-6466	634	4	,	,	PUNCT
ejpam-6466	635	1	ℓ	ℓ	NOUN
ejpam-6466	635	2	=	=	SYM
ejpam-6466	635	3	2	2	X
ejpam-6466	635	4	.	.	PUNCT
ejpam-6466	636	1	the	the	DET
ejpam-6466	636	2	glc	glc	PROPN
ejpam-6466	636	3	is	be	AUX
ejpam-6466	636	4	satisfied	satisfied	ADJ
ejpam-6466	636	5	by	by	ADP
ejpam-6466	636	6	the	the	DET
ejpam-6466	636	7	ℓx(τ−m	ℓx(τ−m	PROPN
ejpam-6466	636	8	)	)	PUNCT
ejpam-6466	636	9	1+x10(τ−m	1+x10(τ−m	NUM
ejpam-6466	636	10	)	)	PUNCT
ejpam-6466	636	11	and	and	CCONJ
ejpam-6466	636	12	diffusion	diffusion	NOUN
ejpam-6466	636	13	−κx(τ	−κx(τ	ADV
ejpam-6466	636	14	)	)	PUNCT
ejpam-6466	637	1	+	+	NUM
ejpam-6466	637	2	λx	λx	NOUN
ejpam-6466	637	3	coefficients	coefficient	NOUN
ejpam-6466	637	4	in	in	ADP
ejpam-6466	637	5	eq	eq	ADP
ejpam-6466	637	6	.	.	PUNCT
ejpam-6466	638	1	(	(	PUNCT
ejpam-6466	638	2	3.2	3.2	NUM
ejpam-6466	638	3	)	)	PUNCT
ejpam-6466	638	4	.	.	PUNCT
ejpam-6466	639	1	as	as	ADP
ejpam-6466	639	2	a	a	DET
ejpam-6466	639	3	result	result	NOUN
ejpam-6466	639	4	,	,	PUNCT
ejpam-6466	639	5	the	the	DET
ejpam-6466	639	6	solution	solution	NOUN
ejpam-6466	639	7	exists	exist	VERB
ejpam-6466	639	8	with	with	ADP
ejpam-6466	639	9	historical	historical	ADJ
ejpam-6466	639	10	function	function	NOUN
ejpam-6466	639	11	x	x	PUNCT
ejpam-6466	639	12	=	=	SYM
ejpam-6466	639	13	0.5	0.5	NUM
ejpam-6466	639	14	,	,	PUNCT
ejpam-6466	639	15	m	m	VERB
ejpam-6466	639	16	≤	≤	NUM
ejpam-6466	639	17	τ	τ	X
ejpam-6466	639	18	≤	≤	NUM
ejpam-6466	639	19	0	0	NUM
ejpam-6466	639	20	in	in	ADP
ejpam-6466	639	21	the	the	DET
ejpam-6466	639	22	interval	interval	NOUN
ejpam-6466	639	23	−m	−m	NOUN
ejpam-6466	639	24	≤	≤	X
ejpam-6466	639	25	τ	τ	PUNCT
ejpam-6466	639	26	≤	≤	PROPN
ejpam-6466	639	27	ℏ	ℏ	PROPN
ejpam-6466	639	28	,	,	PUNCT
ejpam-6466	639	29	and	and	CCONJ
ejpam-6466	639	30	theorem	theorem	VERB
ejpam-6466	639	31	1	1	NUM
ejpam-6466	639	32	states	state	NOUN
ejpam-6466	639	33	that	that	SCONJ
ejpam-6466	639	34	it	it	PRON
ejpam-6466	639	35	is	be	AUX
ejpam-6466	639	36	unique	unique	ADJ
ejpam-6466	639	37	.	.	PUNCT
ejpam-6466	640	1	example	example	NOUN
ejpam-6466	641	1	3	3	X
ejpam-6466	641	2	.	.	X
ejpam-6466	641	3	we	we	PRON
ejpam-6466	641	4	consider	consider	VERB
ejpam-6466	641	5	a	a	DET
ejpam-6466	641	6	population	population	NOUN
ejpam-6466	641	7	model	model	NOUN
ejpam-6466	641	8	governed	govern	VERB
ejpam-6466	641	9	by	by	ADP
ejpam-6466	641	10	a	a	DET
ejpam-6466	641	11	df	df	PROPN
ejpam-6466	641	12	-	-	PUNCT
ejpam-6466	641	13	sde	sde	NOUN
ejpam-6466	641	14	,	,	PUNCT
ejpam-6466	641	15	defined	define	VERB
ejpam-6466	641	16	as	as	ADP
ejpam-6466	641	17	:	:	PUNCT
ejpam-6466	641	18	dξ	dξ	PROPN
ejpam-6466	641	19	τp(τ	τp(τ	PUNCT
ejpam-6466	641	20	)	)	PUNCT
ejpam-6466	642	1	=	=	SYM
ejpam-6466	642	2	v(τ	v(τ	PROPN
ejpam-6466	642	3	,	,	PUNCT
ejpam-6466	642	4	p(τ),p(τ	p(τ),p(τ	NOUN
ejpam-6466	642	5	−m	−m	NOUN
ejpam-6466	642	6	)	)	PUNCT
ejpam-6466	642	7	)	)	PUNCT
ejpam-6466	643	1	+	+	VERB
ejpam-6466	643	2	𭟋(τ	𭟋(τ	ADJ
ejpam-6466	643	3	,	,	PUNCT
ejpam-6466	643	4	p(τ),p(τ	p(τ),p(τ	NOUN
ejpam-6466	643	5	−m	−m	NOUN
ejpam-6466	643	6	)	)	PUNCT
ejpam-6466	643	7	)	)	PUNCT
ejpam-6466	644	1	dwτ	dwτ	ADV
ejpam-6466	644	2	dτ	dτ	INTJ
ejpam-6466	644	3	.	.	PUNCT
ejpam-6466	645	1	the	the	DET
ejpam-6466	645	2	deterministic	deterministic	ADJ
ejpam-6466	645	3	part	part	NOUN
ejpam-6466	645	4	of	of	ADP
ejpam-6466	645	5	the	the	DET
ejpam-6466	645	6	model	model	NOUN
ejpam-6466	645	7	is	be	AUX
ejpam-6466	645	8	given	give	VERB
ejpam-6466	645	9	by	by	ADP
ejpam-6466	645	10	:	:	PUNCT
ejpam-6466	645	11	v(τ	v(τ	PROPN
ejpam-6466	645	12	,	,	PUNCT
ejpam-6466	645	13	p(τ),p(τ	p(τ),p(τ	NOUN
ejpam-6466	645	14	−m	−m	NOUN
ejpam-6466	645	15	)	)	PUNCT
ejpam-6466	645	16	)	)	PUNCT
ejpam-6466	646	1	=	=	SYM
ejpam-6466	646	2	r̃p(τ	r̃p(τ	X
ejpam-6466	646	3	)	)	PUNCT
ejpam-6466	646	4	(	(	PUNCT
ejpam-6466	646	5	1−	1−	NUM
ejpam-6466	646	6	p(τ	p(τ	NOUN
ejpam-6466	646	7	)	)	PUNCT
ejpam-6466	647	1	+	+	CCONJ
ejpam-6466	647	2	0.2p(τ	0.2p(τ	PROPN
ejpam-6466	647	3	−m	−m	NOUN
ejpam-6466	647	4	)	)	PUNCT
ejpam-6466	647	5	k	k	NOUN
ejpam-6466	647	6	)	)	PUNCT
ejpam-6466	648	1	where	where	SCONJ
ejpam-6466	648	2	:	:	PUNCT
ejpam-6466	648	3	m.	m.	NOUN
ejpam-6466	648	4	i.	i.	PROPN
ejpam-6466	648	5	liaqat	liaqat	PROPN
ejpam-6466	648	6	et	et	PROPN
ejpam-6466	648	7	al	al	PROPN
ejpam-6466	648	8	.	.	PUNCT
ejpam-6466	648	9	/	/	SYM
ejpam-6466	648	10	eur	eur	PROPN
ejpam-6466	648	11	.	.	PUNCT
ejpam-6466	649	1	j.	j.	PROPN
ejpam-6466	649	2	pure	pure	PROPN
ejpam-6466	649	3	appl	appl	PROPN
ejpam-6466	649	4	.	.	PROPN
ejpam-6466	649	5	math	math	PROPN
ejpam-6466	649	6	,	,	PUNCT
ejpam-6466	649	7	18	18	NUM
ejpam-6466	649	8	(	(	PUNCT
ejpam-6466	649	9	4	4	NUM
ejpam-6466	649	10	)	)	PUNCT
ejpam-6466	649	11	(	(	PUNCT
ejpam-6466	649	12	2025	2025	NUM
ejpam-6466	649	13	)	)	PUNCT
ejpam-6466	649	14	,	,	PUNCT
ejpam-6466	649	15	6466	6466	NUM
ejpam-6466	649	16	23	23	NUM
ejpam-6466	649	17	of	of	ADP
ejpam-6466	649	18	28	28	NUM
ejpam-6466	649	19	•	•	NOUN
ejpam-6466	649	20	r̃	r̃	PROPN
ejpam-6466	649	21	>	>	X
ejpam-6466	649	22	0	0	NUM
ejpam-6466	649	23	is	be	AUX
ejpam-6466	649	24	the	the	DET
ejpam-6466	649	25	intrinsic	intrinsic	ADJ
ejpam-6466	649	26	growth	growth	NOUN
ejpam-6466	649	27	rate	rate	NOUN
ejpam-6466	649	28	,	,	PUNCT
ejpam-6466	649	29	•	•	X
ejpam-6466	649	30	k	k	X
ejpam-6466	649	31	>	>	X
ejpam-6466	649	32	0	0	NUM
ejpam-6466	649	33	is	be	AUX
ejpam-6466	649	34	the	the	DET
ejpam-6466	649	35	carrying	carrying	NOUN
ejpam-6466	649	36	capacity	capacity	NOUN
ejpam-6466	649	37	,	,	PUNCT
ejpam-6466	649	38	•	•	CCONJ
ejpam-6466	649	39	the	the	DET
ejpam-6466	649	40	delayed	delay	VERB
ejpam-6466	649	41	feedback	feedback	NOUN
ejpam-6466	649	42	0.2p(τ	0.2p(τ	NOUN
ejpam-6466	649	43	−m	−m	NOUN
ejpam-6466	649	44	)	)	PUNCT
ejpam-6466	649	45	introduces	introduce	VERB
ejpam-6466	649	46	a	a	DET
ejpam-6466	649	47	historical	historical	ADJ
ejpam-6466	649	48	influence	influence	NOUN
ejpam-6466	649	49	on	on	ADP
ejpam-6466	649	50	growth	growth	NOUN
ejpam-6466	649	51	.	.	PUNCT
ejpam-6466	650	1	this	this	PRON
ejpam-6466	650	2	represents	represent	VERB
ejpam-6466	650	3	a	a	DET
ejpam-6466	650	4	logistic	logistic	ADJ
ejpam-6466	650	5	-	-	PUNCT
ejpam-6466	650	6	type	type	NOUN
ejpam-6466	650	7	growth	growth	NOUN
ejpam-6466	650	8	with	with	ADP
ejpam-6466	650	9	delay	delay	NOUN
ejpam-6466	650	10	,	,	PUNCT
ejpam-6466	650	11	where	where	SCONJ
ejpam-6466	650	12	the	the	DET
ejpam-6466	650	13	population	population	NOUN
ejpam-6466	650	14	’s	’s	PART
ejpam-6466	650	15	current	current	ADJ
ejpam-6466	650	16	growth	growth	NOUN
ejpam-6466	650	17	is	be	AUX
ejpam-6466	650	18	affected	affect	VERB
ejpam-6466	650	19	by	by	ADP
ejpam-6466	650	20	both	both	CCONJ
ejpam-6466	650	21	its	its	PRON
ejpam-6466	650	22	present	present	ADJ
ejpam-6466	650	23	and	and	CCONJ
ejpam-6466	650	24	past	past	ADJ
ejpam-6466	650	25	sizes	size	NOUN
ejpam-6466	650	26	.	.	PUNCT
ejpam-6466	651	1	such	such	ADJ
ejpam-6466	651	2	delayed	delay	VERB
ejpam-6466	651	3	effects	effect	NOUN
ejpam-6466	651	4	may	may	AUX
ejpam-6466	651	5	arise	arise	VERB
ejpam-6466	651	6	due	due	ADP
ejpam-6466	651	7	to	to	ADP
ejpam-6466	651	8	reproduction	reproduction	NOUN
ejpam-6466	651	9	lags	lag	NOUN
ejpam-6466	651	10	,	,	PUNCT
ejpam-6466	651	11	environmental	environmental	ADJ
ejpam-6466	651	12	responses	response	NOUN
ejpam-6466	651	13	,	,	PUNCT
ejpam-6466	651	14	or	or	CCONJ
ejpam-6466	651	15	maturation	maturation	NOUN
ejpam-6466	651	16	delays	delay	NOUN
ejpam-6466	651	17	.	.	PUNCT
ejpam-6466	652	1	the	the	DET
ejpam-6466	652	2	stochastic	stochastic	ADJ
ejpam-6466	652	3	part	part	NOUN
ejpam-6466	652	4	of	of	ADP
ejpam-6466	652	5	the	the	DET
ejpam-6466	652	6	model	model	NOUN
ejpam-6466	652	7	is	be	AUX
ejpam-6466	652	8	:	:	PUNCT
ejpam-6466	652	9	𭟋(τ	𭟋(τ	ADJ
ejpam-6466	652	10	,	,	PUNCT
ejpam-6466	652	11	p(τ),p(τ	p(τ),p(τ	NOUN
ejpam-6466	652	12	−m	−m	NOUN
ejpam-6466	652	13	)	)	PUNCT
ejpam-6466	652	14	)	)	PUNCT
ejpam-6466	653	1	=	=	SYM
ejpam-6466	653	2	1.5	1.5	NUM
ejpam-6466	653	3	√	√	ADP
ejpam-6466	653	4	p(τ	p(τ	PROPN
ejpam-6466	653	5	)	)	PUNCT
ejpam-6466	653	6	.	.	PUNCT
ejpam-6466	654	1	this	this	DET
ejpam-6466	654	2	term	term	NOUN
ejpam-6466	654	3	captures	capture	VERB
ejpam-6466	654	4	the	the	DET
ejpam-6466	654	5	influence	influence	NOUN
ejpam-6466	654	6	of	of	ADP
ejpam-6466	654	7	random	random	ADJ
ejpam-6466	654	8	environmental	environmental	ADJ
ejpam-6466	654	9	fluctuations	fluctuation	NOUN
ejpam-6466	654	10	.	.	PUNCT
ejpam-6466	655	1	the	the	DET
ejpam-6466	655	2	noise	noise	NOUN
ejpam-6466	655	3	is	be	AUX
ejpam-6466	655	4	multiplicative	multiplicative	ADJ
ejpam-6466	655	5	and	and	CCONJ
ejpam-6466	655	6	population	population	NOUN
ejpam-6466	655	7	-	-	PUNCT
ejpam-6466	655	8	dependent	dependent	ADJ
ejpam-6466	655	9	:	:	PUNCT
ejpam-6466	655	10	•	•	ADP
ejpam-6466	655	11	the	the	DET
ejpam-6466	655	12	coefficient	coefficient	NOUN
ejpam-6466	655	13	1.5	1.5	NUM
ejpam-6466	655	14	determines	determine	VERB
ejpam-6466	655	15	the	the	DET
ejpam-6466	655	16	intensity	intensity	NOUN
ejpam-6466	655	17	of	of	ADP
ejpam-6466	655	18	randomness	randomness	NOUN
ejpam-6466	655	19	.	.	PUNCT
ejpam-6466	656	1	•	•	NUM
ejpam-6466	656	2	the	the	DET
ejpam-6466	656	3	use	use	NOUN
ejpam-6466	656	4	of	of	ADP
ejpam-6466	656	5	√	√	PROPN
ejpam-6466	656	6	p(τ	p(τ	NUM
ejpam-6466	656	7	)	)	PUNCT
ejpam-6466	656	8	ensures	ensure	VERB
ejpam-6466	656	9	that	that	SCONJ
ejpam-6466	656	10	noise	noise	NOUN
ejpam-6466	656	11	increases	increase	NOUN
ejpam-6466	656	12	with	with	ADP
ejpam-6466	656	13	population	population	NOUN
ejpam-6466	656	14	size	size	NOUN
ejpam-6466	656	15	and	and	CCONJ
ejpam-6466	656	16	becomes	become	VERB
ejpam-6466	656	17	negligible	negligible	ADJ
ejpam-6466	656	18	near	near	ADP
ejpam-6466	656	19	extinction	extinction	NOUN
ejpam-6466	656	20	.	.	PUNCT
ejpam-6466	657	1	by	by	ADP
ejpam-6466	657	2	combining	combine	VERB
ejpam-6466	657	3	the	the	DET
ejpam-6466	657	4	deterministic	deterministic	ADJ
ejpam-6466	657	5	and	and	CCONJ
ejpam-6466	657	6	stochastic	stochastic	ADJ
ejpam-6466	657	7	components	component	NOUN
ejpam-6466	657	8	,	,	PUNCT
ejpam-6466	657	9	the	the	DET
ejpam-6466	657	10	population	population	NOUN
ejpam-6466	657	11	model	model	NOUN
ejpam-6466	657	12	is	be	AUX
ejpam-6466	657	13	given	give	VERB
ejpam-6466	657	14	by	by	ADP
ejpam-6466	657	15	:	:	PUNCT
ejpam-6466	657	16	dξ	dξ	PROPN
ejpam-6466	657	17	τp(τ	τp(τ	PUNCT
ejpam-6466	657	18	)	)	PUNCT
ejpam-6466	658	1	=	=	SYM
ejpam-6466	658	2	r̃p(τ	r̃p(τ	X
ejpam-6466	658	3	)	)	PUNCT
ejpam-6466	658	4	(	(	PUNCT
ejpam-6466	658	5	1−	1−	NUM
ejpam-6466	658	6	p(τ	p(τ	NOUN
ejpam-6466	658	7	)	)	PUNCT
ejpam-6466	659	1	+	+	CCONJ
ejpam-6466	659	2	0.2p(τ	0.2p(τ	PROPN
ejpam-6466	659	3	−m	−m	NOUN
ejpam-6466	659	4	)	)	PUNCT
ejpam-6466	659	5	k	k	NOUN
ejpam-6466	659	6	)	)	PUNCT
ejpam-6466	660	1	+	+	CCONJ
ejpam-6466	660	2	1.5	1.5	NUM
ejpam-6466	660	3	√	√	NUM
ejpam-6466	660	4	p(τ	p(τ	NUM
ejpam-6466	660	5	)	)	PUNCT
ejpam-6466	660	6	dwτ	dwτ	ADV
ejpam-6466	660	7	dτ	dτ	INTJ
ejpam-6466	660	8	.	.	PUNCT
ejpam-6466	661	1	this	this	DET
ejpam-6466	661	2	equation	equation	NOUN
ejpam-6466	661	3	captures	capture	VERB
ejpam-6466	661	4	•	•	ADJ
ejpam-6466	661	5	nonlinear	nonlinear	ADJ
ejpam-6466	661	6	logistic	logistic	ADJ
ejpam-6466	661	7	growth	growth	NOUN
ejpam-6466	661	8	with	with	ADP
ejpam-6466	661	9	delay	delay	NOUN
ejpam-6466	661	10	,	,	PUNCT
ejpam-6466	661	11	•	•	NUM
ejpam-6466	661	12	memory	memory	NOUN
ejpam-6466	661	13	effects	effect	NOUN
ejpam-6466	661	14	through	through	ADP
ejpam-6466	661	15	conformable	conformable	ADJ
ejpam-6466	661	16	fractional	fractional	ADJ
ejpam-6466	661	17	calculus	calculus	NOUN
ejpam-6466	661	18	,	,	PUNCT
ejpam-6466	661	19	•	•	NUM
ejpam-6466	661	20	environmental	environmental	ADJ
ejpam-6466	661	21	uncertainty	uncertainty	NOUN
ejpam-6466	661	22	via	via	ADP
ejpam-6466	661	23	stochastic	stochastic	ADJ
ejpam-6466	661	24	forcing	forcing	NOUN
ejpam-6466	661	25	.	.	PUNCT
ejpam-6466	662	1	to	to	PART
ejpam-6466	662	2	obtain	obtain	VERB
ejpam-6466	662	3	an	an	DET
ejpam-6466	662	4	approximate	approximate	ADJ
ejpam-6466	662	5	solution	solution	NOUN
ejpam-6466	662	6	of	of	ADP
ejpam-6466	662	7	the	the	DET
ejpam-6466	662	8	df	df	PROPN
ejpam-6466	662	9	-	-	PUNCT
ejpam-6466	662	10	sde	sde	PROPN
ejpam-6466	662	11	for	for	ADP
ejpam-6466	662	12	population	population	NOUN
ejpam-6466	662	13	growth	growth	NOUN
ejpam-6466	662	14	,	,	PUNCT
ejpam-6466	662	15	we	we	PRON
ejpam-6466	662	16	employ	employ	VERB
ejpam-6466	662	17	the	the	DET
ejpam-6466	662	18	euler	euler	NOUN
ejpam-6466	662	19	–	–	PUNCT
ejpam-6466	662	20	maruyama	maruyama	NOUN
ejpam-6466	662	21	method	method	NOUN
ejpam-6466	662	22	.	.	PUNCT
ejpam-6466	663	1	this	this	DET
ejpam-6466	663	2	approach	approach	NOUN
ejpam-6466	663	3	allows	allow	VERB
ejpam-6466	663	4	us	we	PRON
ejpam-6466	663	5	to	to	PART
ejpam-6466	663	6	simulate	simulate	VERB
ejpam-6466	663	7	the	the	DET
ejpam-6466	663	8	evolution	evolution	NOUN
ejpam-6466	663	9	of	of	ADP
ejpam-6466	663	10	population	population	NOUN
ejpam-6466	663	11	size	size	NOUN
ejpam-6466	663	12	under	under	ADP
ejpam-6466	663	13	the	the	DET
ejpam-6466	663	14	influence	influence	NOUN
ejpam-6466	663	15	of	of	ADP
ejpam-6466	663	16	random	random	ADJ
ejpam-6466	663	17	fluctuations	fluctuation	NOUN
ejpam-6466	663	18	,	,	PUNCT
ejpam-6466	663	19	delayed	delay	VERB
ejpam-6466	663	20	feedback	feedback	NOUN
ejpam-6466	663	21	mechanisms	mechanism	NOUN
ejpam-6466	663	22	,	,	PUNCT
ejpam-6466	663	23	and	and	CCONJ
ejpam-6466	663	24	intrinsic	intrinsic	ADJ
ejpam-6466	663	25	growth	growth	NOUN
ejpam-6466	663	26	dynamics	dynamic	NOUN
ejpam-6466	663	27	.	.	PUNCT
ejpam-6466	664	1	multiple	multiple	ADJ
ejpam-6466	664	2	simulation	simulation	NOUN
ejpam-6466	664	3	paths	path	NOUN
ejpam-6466	664	4	are	be	AUX
ejpam-6466	664	5	generated	generate	VERB
ejpam-6466	664	6	to	to	PART
ejpam-6466	664	7	capture	capture	VERB
ejpam-6466	664	8	the	the	DET
ejpam-6466	664	9	system	system	NOUN
ejpam-6466	664	10	’s	’s	PART
ejpam-6466	664	11	inherent	inherent	ADJ
ejpam-6466	664	12	stochasticity	stochasticity	NOUN
ejpam-6466	664	13	,	,	PUNCT
ejpam-6466	664	14	and	and	CCONJ
ejpam-6466	664	15	the	the	DET
ejpam-6466	664	16	average	average	NOUN
ejpam-6466	664	17	of	of	ADP
ejpam-6466	664	18	these	these	DET
ejpam-6466	664	19	trajectories	trajectory	NOUN
ejpam-6466	664	20	provides	provide	VERB
ejpam-6466	664	21	an	an	DET
ejpam-6466	664	22	estimate	estimate	NOUN
ejpam-6466	664	23	of	of	ADP
ejpam-6466	664	24	the	the	DET
ejpam-6466	664	25	expected	expect	VERB
ejpam-6466	664	26	population	population	NOUN
ejpam-6466	664	27	behavior	behavior	NOUN
ejpam-6466	664	28	over	over	ADP
ejpam-6466	664	29	time	time	NOUN
ejpam-6466	664	30	.	.	PUNCT
ejpam-6466	665	1	the	the	DET
ejpam-6466	665	2	resulting	result	VERB
ejpam-6466	665	3	population	population	NOUN
ejpam-6466	665	4	dynamics	dynamic	NOUN
ejpam-6466	665	5	are	be	AUX
ejpam-6466	665	6	illustrated	illustrate	VERB
ejpam-6466	665	7	in	in	ADP
ejpam-6466	665	8	the	the	DET
ejpam-6466	665	9	figure	figure	NOUN
ejpam-6466	665	10	below	below	ADV
ejpam-6466	665	11	.	.	PUNCT
ejpam-6466	666	1	m.	m.	PROPN
ejpam-6466	666	2	i.	i.	PROPN
ejpam-6466	666	3	liaqat	liaqat	PROPN
ejpam-6466	666	4	et	et	PROPN
ejpam-6466	666	5	al	al	PROPN
ejpam-6466	666	6	.	.	PUNCT
ejpam-6466	666	7	/	/	SYM
ejpam-6466	666	8	eur	eur	PROPN
ejpam-6466	666	9	.	.	PUNCT
ejpam-6466	667	1	j.	j.	PROPN
ejpam-6466	667	2	pure	pure	PROPN
ejpam-6466	667	3	appl	appl	PROPN
ejpam-6466	667	4	.	.	PROPN
ejpam-6466	667	5	math	math	PROPN
ejpam-6466	667	6	,	,	PUNCT
ejpam-6466	667	7	18	18	NUM
ejpam-6466	667	8	(	(	PUNCT
ejpam-6466	667	9	4	4	NUM
ejpam-6466	667	10	)	)	PUNCT
ejpam-6466	667	11	(	(	PUNCT
ejpam-6466	667	12	2025	2025	NUM
ejpam-6466	667	13	)	)	PUNCT
ejpam-6466	667	14	,	,	PUNCT
ejpam-6466	667	15	6466	6466	NUM
ejpam-6466	667	16	24	24	NUM
ejpam-6466	667	17	of	of	ADP
ejpam-6466	667	18	28	28	NUM
ejpam-6466	667	19	0	0	NUM
ejpam-6466	667	20	2	2	NUM
ejpam-6466	667	21	4	4	NUM
ejpam-6466	667	22	6	6	NUM
ejpam-6466	667	23	8	8	NUM
ejpam-6466	667	24	10	10	NUM
ejpam-6466	667	25	time	time	NOUN
ejpam-6466	667	26	(	(	PUNCT
ejpam-6466	667	27	years	year	NOUN
ejpam-6466	667	28	)	)	PUNCT
ejpam-6466	667	29	100	100	NUM
ejpam-6466	667	30	200	200	NUM
ejpam-6466	668	1	300	300	NUM
ejpam-6466	668	2	400	400	NUM
ejpam-6466	668	3	500	500	NUM
ejpam-6466	668	4	600	600	NUM
ejpam-6466	668	5	700	700	NUM
ejpam-6466	668	6	800	800	NUM
ejpam-6466	668	7	900	900	NUM
ejpam-6466	668	8	po	po	NOUN
ejpam-6466	668	9	pu	pu	PROPN
ejpam-6466	668	10	la	la	PROPN
ejpam-6466	668	11	tio	tio	PROPN
ejpam-6466	668	12	n	n	CCONJ
ejpam-6466	668	13	si	si	PROPN
ejpam-6466	668	14	ze	ze	PROPN
ejpam-6466	668	15	population	population	NOUN
ejpam-6466	668	16	dynamics	dynamic	NOUN
ejpam-6466	668	17	(	(	PUNCT
ejpam-6466	668	18	=	=	NOUN
ejpam-6466	668	19	0.7	0.7	NUM
ejpam-6466	668	20	,	,	PUNCT
ejpam-6466	668	21	delay=0.5	delay=0.5	ADJ
ejpam-6466	668	22	years	year	NOUN
ejpam-6466	668	23	)	)	PUNCT
ejpam-6466	668	24	10	10	NUM
ejpam-6466	668	25	simulations	simulation	NOUN
ejpam-6466	668	26	with	with	ADP
ejpam-6466	668	27	mean	mean	ADJ
ejpam-6466	668	28	curve	curve	NOUN
ejpam-6466	668	29	mean	mean	ADJ
ejpam-6466	668	30	population	population	NOUN
ejpam-6466	668	31	(	(	PUNCT
ejpam-6466	668	32	a	a	X
ejpam-6466	668	33	)	)	PUNCT
ejpam-6466	668	34	0	0	NUM
ejpam-6466	668	35	2	2	NUM
ejpam-6466	668	36	4	4	NUM
ejpam-6466	668	37	6	6	NUM
ejpam-6466	668	38	8	8	NUM
ejpam-6466	668	39	10	10	NUM
ejpam-6466	668	40	time	time	NOUN
ejpam-6466	668	41	(	(	PUNCT
ejpam-6466	668	42	years	year	NOUN
ejpam-6466	668	43	)	)	PUNCT
ejpam-6466	668	44	100	100	NUM
ejpam-6466	668	45	200	200	NUM
ejpam-6466	668	46	300	300	NUM
ejpam-6466	668	47	400	400	NUM
ejpam-6466	668	48	500	500	NUM
ejpam-6466	668	49	600	600	NUM
ejpam-6466	668	50	700	700	NUM
ejpam-6466	668	51	800	800	NUM
ejpam-6466	668	52	900	900	NUM
ejpam-6466	668	53	po	po	NOUN
ejpam-6466	668	54	pu	pu	PROPN
ejpam-6466	668	55	la	la	PROPN
ejpam-6466	668	56	tio	tio	PROPN
ejpam-6466	668	57	n	n	CCONJ
ejpam-6466	668	58	si	si	PROPN
ejpam-6466	668	59	ze	ze	PROPN
ejpam-6466	668	60	population	population	NOUN
ejpam-6466	668	61	dynamics	dynamic	NOUN
ejpam-6466	668	62	(	(	PUNCT
ejpam-6466	668	63	=	=	NOUN
ejpam-6466	668	64	0.8	0.8	NUM
ejpam-6466	668	65	,	,	PUNCT
ejpam-6466	668	66	delay=0.5	delay=0.5	ADJ
ejpam-6466	668	67	years	year	NOUN
ejpam-6466	668	68	)	)	PUNCT
ejpam-6466	668	69	10	10	NUM
ejpam-6466	668	70	simulations	simulation	NOUN
ejpam-6466	668	71	with	with	ADP
ejpam-6466	668	72	mean	mean	ADJ
ejpam-6466	668	73	curve	curve	NOUN
ejpam-6466	668	74	mean	mean	ADJ
ejpam-6466	668	75	population	population	NOUN
ejpam-6466	668	76	(	(	PUNCT
ejpam-6466	668	77	b	b	NOUN
ejpam-6466	668	78	)	)	PUNCT
ejpam-6466	668	79	0	0	NUM
ejpam-6466	668	80	2	2	NUM
ejpam-6466	668	81	4	4	NUM
ejpam-6466	668	82	6	6	NUM
ejpam-6466	668	83	8	8	NUM
ejpam-6466	668	84	10	10	NUM
ejpam-6466	668	85	time	time	NOUN
ejpam-6466	668	86	(	(	PUNCT
ejpam-6466	668	87	years	year	NOUN
ejpam-6466	668	88	)	)	PUNCT
ejpam-6466	668	89	100	100	NUM
ejpam-6466	668	90	200	200	NUM
ejpam-6466	668	91	300	300	NUM
ejpam-6466	668	92	400	400	NUM
ejpam-6466	668	93	500	500	NUM
ejpam-6466	668	94	600	600	NUM
ejpam-6466	668	95	700	700	NUM
ejpam-6466	668	96	800	800	NUM
ejpam-6466	668	97	900	900	NUM
ejpam-6466	668	98	po	po	NOUN
ejpam-6466	668	99	pu	pu	PROPN
ejpam-6466	668	100	la	la	PROPN
ejpam-6466	668	101	tio	tio	PROPN
ejpam-6466	668	102	n	n	CCONJ
ejpam-6466	668	103	si	si	PROPN
ejpam-6466	668	104	ze	ze	PROPN
ejpam-6466	668	105	population	population	NOUN
ejpam-6466	668	106	dynamics	dynamic	NOUN
ejpam-6466	668	107	(	(	PUNCT
ejpam-6466	668	108	=	=	NOUN
ejpam-6466	668	109	0.85	0.85	NUM
ejpam-6466	668	110	,	,	PUNCT
ejpam-6466	668	111	delay=0.5	delay=0.5	ADJ
ejpam-6466	668	112	years	year	NOUN
ejpam-6466	668	113	)	)	PUNCT
ejpam-6466	668	114	10	10	NUM
ejpam-6466	668	115	simulations	simulation	NOUN
ejpam-6466	668	116	with	with	ADP
ejpam-6466	668	117	mean	mean	ADJ
ejpam-6466	668	118	curve	curve	NOUN
ejpam-6466	668	119	mean	mean	ADJ
ejpam-6466	668	120	population	population	NOUN
ejpam-6466	668	121	(	(	PUNCT
ejpam-6466	668	122	c	c	NOUN
ejpam-6466	668	123	)	)	PUNCT
ejpam-6466	668	124	0	0	NUM
ejpam-6466	668	125	2	2	NUM
ejpam-6466	668	126	4	4	NUM
ejpam-6466	668	127	6	6	NUM
ejpam-6466	668	128	8	8	NUM
ejpam-6466	668	129	10	10	NUM
ejpam-6466	668	130	time	time	NOUN
ejpam-6466	668	131	(	(	PUNCT
ejpam-6466	668	132	years	year	NOUN
ejpam-6466	668	133	)	)	PUNCT
ejpam-6466	668	134	100	100	NUM
ejpam-6466	668	135	200	200	NUM
ejpam-6466	668	136	300	300	NUM
ejpam-6466	668	137	400	400	NUM
ejpam-6466	668	138	500	500	NUM
ejpam-6466	668	139	600	600	NUM
ejpam-6466	668	140	700	700	NUM
ejpam-6466	668	141	800	800	NUM
ejpam-6466	668	142	po	po	NOUN
ejpam-6466	668	143	pu	pu	PROPN
ejpam-6466	668	144	la	la	PROPN
ejpam-6466	668	145	tio	tio	PROPN
ejpam-6466	668	146	n	n	CCONJ
ejpam-6466	668	147	si	si	PROPN
ejpam-6466	668	148	ze	ze	PROPN
ejpam-6466	668	149	population	population	NOUN
ejpam-6466	668	150	dynamics	dynamic	NOUN
ejpam-6466	668	151	(	(	PUNCT
ejpam-6466	668	152	=	=	NOUN
ejpam-6466	668	153	0.9	0.9	NUM
ejpam-6466	668	154	,	,	PUNCT
ejpam-6466	668	155	delay=0.5	delay=0.5	ADJ
ejpam-6466	668	156	years	year	NOUN
ejpam-6466	668	157	)	)	PUNCT
ejpam-6466	668	158	10	10	NUM
ejpam-6466	668	159	simulations	simulation	NOUN
ejpam-6466	668	160	with	with	ADP
ejpam-6466	668	161	mean	mean	ADJ
ejpam-6466	668	162	curve	curve	NOUN
ejpam-6466	668	163	mean	mean	ADJ
ejpam-6466	668	164	population	population	NOUN
ejpam-6466	668	165	(	(	PUNCT
ejpam-6466	668	166	d	d	NOUN
ejpam-6466	668	167	)	)	PUNCT
ejpam-6466	668	168	figure	figure	NOUN
ejpam-6466	668	169	1	1	NUM
ejpam-6466	668	170	:	:	PUNCT
ejpam-6466	668	171	population	population	NOUN
ejpam-6466	668	172	dynamics	dynamic	NOUN
ejpam-6466	668	173	under	under	ADP
ejpam-6466	668	174	different	different	ADJ
ejpam-6466	668	175	conformable	conformable	ADJ
ejpam-6466	668	176	fractional	fractional	ADJ
ejpam-6466	668	177	orders	order	NOUN
ejpam-6466	668	178	:	:	PUNCT
ejpam-6466	668	179	(	(	PUNCT
ejpam-6466	668	180	a	a	X
ejpam-6466	668	181	)	)	PUNCT
ejpam-6466	668	182	ξ	ξ	NOUN
ejpam-6466	668	183	=	=	SYM
ejpam-6466	668	184	0.7	0.7	NUM
ejpam-6466	668	185	showing	show	VERB
ejpam-6466	668	186	strong	strong	ADJ
ejpam-6466	668	187	memory	memory	NOUN
ejpam-6466	668	188	effects	effect	NOUN
ejpam-6466	668	189	,	,	PUNCT
ejpam-6466	668	190	(	(	PUNCT
ejpam-6466	668	191	b	b	X
ejpam-6466	668	192	)	)	PUNCT
ejpam-6466	668	193	ξ	ξ	NOUN
ejpam-6466	668	194	=	=	SYM
ejpam-6466	668	195	0.8	0.8	NUM
ejpam-6466	668	196	with	with	ADP
ejpam-6466	668	197	moderate	moderate	ADJ
ejpam-6466	668	198	memory	memory	NOUN
ejpam-6466	668	199	,	,	PUNCT
ejpam-6466	668	200	(	(	PUNCT
ejpam-6466	668	201	c	c	X
ejpam-6466	668	202	)	)	PUNCT
ejpam-6466	668	203	ξ	ξ	X
ejpam-6466	668	204	=	=	SYM
ejpam-6466	668	205	0.85	0.85	NUM
ejpam-6466	668	206	demonstrating	demonstrate	VERB
ejpam-6466	668	207	weak	weak	ADJ
ejpam-6466	668	208	memory	memory	NOUN
ejpam-6466	668	209	,	,	PUNCT
ejpam-6466	668	210	and	and	CCONJ
ejpam-6466	668	211	(	(	PUNCT
ejpam-6466	668	212	d	d	X
ejpam-6466	668	213	)	)	PUNCT
ejpam-6466	668	214	ξ	ξ	X
ejpam-6466	668	215	=	=	SYM
ejpam-6466	668	216	0.9	0.9	NUM
ejpam-6466	668	217	(	(	PUNCT
ejpam-6466	668	218	near	near	ADJ
ejpam-6466	668	219	-	-	PUNCT
ejpam-6466	668	220	classical	classical	ADJ
ejpam-6466	668	221	case	case	NOUN
ejpam-6466	668	222	)	)	PUNCT
ejpam-6466	668	223	.	.	PUNCT
ejpam-6466	669	1	all	all	DET
ejpam-6466	669	2	simulations	simulation	NOUN
ejpam-6466	669	3	use	use	VERB
ejpam-6466	669	4	r̃	r̃	NOUN
ejpam-6466	669	5	=	=	SYM
ejpam-6466	669	6	0.3	0.3	NUM
ejpam-6466	669	7	,	,	PUNCT
ejpam-6466	669	8	k	k	PROPN
ejpam-6466	670	1	=	=	SYM
ejpam-6466	670	2	1000	1000	NUM
ejpam-6466	670	3	,	,	PUNCT
ejpam-6466	670	4	σ	σ	NOUN
ejpam-6466	670	5	=	=	SYM
ejpam-6466	670	6	1.5	1.5	NUM
ejpam-6466	670	7	,	,	PUNCT
ejpam-6466	670	8	m	m	VERB
ejpam-6466	670	9	=	=	NOUN
ejpam-6466	670	10	0.5	0.5	NUM
ejpam-6466	670	11	years	year	NOUN
ejpam-6466	670	12	,	,	PUNCT
ejpam-6466	670	13	and	and	CCONJ
ejpam-6466	670	14	p(0	p(0	PROPN
ejpam-6466	670	15	)	)	PUNCT
ejpam-6466	670	16	=	=	SYM
ejpam-6466	670	17	100	100	NUM
ejpam-6466	670	18	.	.	PUNCT
ejpam-6466	671	1	light	light	ADJ
ejpam-6466	671	2	curves	curve	NOUN
ejpam-6466	671	3	represent	represent	VERB
ejpam-6466	671	4	individual	individual	ADJ
ejpam-6466	671	5	realizations	realization	NOUN
ejpam-6466	671	6	;	;	PUNCT
ejpam-6466	671	7	bold	bold	ADJ
ejpam-6466	671	8	curves	curve	NOUN
ejpam-6466	671	9	show	show	VERB
ejpam-6466	671	10	the	the	DET
ejpam-6466	671	11	mean	mean	NOUN
ejpam-6466	671	12	.	.	PUNCT
ejpam-6466	672	1	example	example	NOUN
ejpam-6466	672	2	4	4	X
ejpam-6466	672	3	.	.	PUNCT
ejpam-6466	673	1	we	we	PRON
ejpam-6466	673	2	consider	consider	VERB
ejpam-6466	673	3	the	the	DET
ejpam-6466	673	4	df	df	PROPN
ejpam-6466	673	5	-	-	PUNCT
ejpam-6466	673	6	sde	sde	PROPN
ejpam-6466	673	7	for	for	ADP
ejpam-6466	673	8	modeling	model	VERB
ejpam-6466	673	9	temperature	temperature	NOUN
ejpam-6466	673	10	dynamics	dynamic	NOUN
ejpam-6466	673	11	as	as	SCONJ
ejpam-6466	673	12	follows	follow	VERB
ejpam-6466	673	13	:	:	PUNCT
ejpam-6466	673	14	dξ	dξ	PROPN
ejpam-6466	673	15	τt(τ	τt(τ	PUNCT
ejpam-6466	673	16	)	)	PUNCT
ejpam-6466	673	17	=	=	SYM
ejpam-6466	673	18	−α	−α	NOUN
ejpam-6466	673	19	(	(	PUNCT
ejpam-6466	673	20	t(τ)−	t(τ)−	PROPN
ejpam-6466	673	21	tenv(τ	tenv(τ	NOUN
ejpam-6466	673	22	)	)	PUNCT
ejpam-6466	673	23	)	)	PUNCT
ejpam-6466	674	1	+	+	CCONJ
ejpam-6466	674	2	β	β	X
ejpam-6466	674	3	(	(	PUNCT
ejpam-6466	674	4	t(τ	t(τ	NOUN
ejpam-6466	674	5	−m)−	−m)−	NOUN
ejpam-6466	674	6	tenv(τ	tenv(τ	NOUN
ejpam-6466	674	7	)	)	PUNCT
ejpam-6466	674	8	)	)	PUNCT
ejpam-6466	675	1	+	+	CCONJ
ejpam-6466	675	2	σ(t(τ	σ(t(τ	NOUN
ejpam-6466	675	3	)	)	PUNCT
ejpam-6466	675	4	)	)	PUNCT
ejpam-6466	675	5	dw(τ	dw(τ	X
ejpam-6466	675	6	)	)	PUNCT
ejpam-6466	675	7	dτ	dτ	NOUN
ejpam-6466	675	8	,	,	PUNCT
ejpam-6466	675	9	where	where	SCONJ
ejpam-6466	675	10	:	:	PUNCT
ejpam-6466	675	11	the	the	DET
ejpam-6466	675	12	drift	drift	NOUN
ejpam-6466	675	13	component	component	NOUN
ejpam-6466	675	14	is	be	AUX
ejpam-6466	675	15	given	give	VERB
ejpam-6466	675	16	below	below	ADV
ejpam-6466	675	17	:	:	PUNCT
ejpam-6466	675	18	v(τ	v(τ	PROPN
ejpam-6466	675	19	,	,	PUNCT
ejpam-6466	675	20	t(τ),t(τ	t(τ),t(τ	NOUN
ejpam-6466	675	21	−m	−m	NOUN
ejpam-6466	675	22	)	)	PUNCT
ejpam-6466	675	23	)	)	PUNCT
ejpam-6466	676	1	=	=	SYM
ejpam-6466	676	2	−α	−α	NOUN
ejpam-6466	676	3	(	(	PUNCT
ejpam-6466	676	4	t(τ)−	t(τ)−	PROPN
ejpam-6466	676	5	tenv(τ	tenv(τ	NOUN
ejpam-6466	676	6	)	)	PUNCT
ejpam-6466	676	7	)	)	PUNCT
ejpam-6466	677	1	+	+	CCONJ
ejpam-6466	677	2	β	β	X
ejpam-6466	677	3	(	(	PUNCT
ejpam-6466	677	4	t(τ	t(τ	NOUN
ejpam-6466	677	5	−m)−	−m)−	NOUN
ejpam-6466	677	6	tenv(τ	tenv(τ	NOUN
ejpam-6466	677	7	)	)	PUNCT
ejpam-6466	677	8	)	)	PUNCT
ejpam-6466	677	9	,	,	PUNCT
ejpam-6466	677	10	here	here	ADV
ejpam-6466	677	11	,	,	PUNCT
ejpam-6466	677	12	t(τ	t(τ	NOUN
ejpam-6466	677	13	)	)	PUNCT
ejpam-6466	677	14	denotes	denote	VERB
ejpam-6466	677	15	the	the	DET
ejpam-6466	677	16	indoor	indoor	ADJ
ejpam-6466	677	17	temperature	temperature	NOUN
ejpam-6466	677	18	at	at	ADP
ejpam-6466	677	19	time	time	NOUN
ejpam-6466	677	20	τ	τ	PROPN
ejpam-6466	677	21	,	,	PUNCT
ejpam-6466	677	22	t(τ	t(τ	NOUN
ejpam-6466	677	23	−m	−m	NOUN
ejpam-6466	677	24	)	)	PUNCT
ejpam-6466	677	25	represents	represent	VERB
ejpam-6466	677	26	the	the	DET
ejpam-6466	677	27	delayed	delay	VERB
ejpam-6466	677	28	temperature	temperature	NOUN
ejpam-6466	677	29	with	with	ADP
ejpam-6466	677	30	a	a	DET
ejpam-6466	677	31	delay	delay	NOUN
ejpam-6466	677	32	m	m	VERB
ejpam-6466	677	33	>	>	X
ejpam-6466	677	34	0	0	NUM
ejpam-6466	677	35	,	,	PUNCT
ejpam-6466	677	36	and	and	CCONJ
ejpam-6466	677	37	tenv(τ	tenv(τ	NOUN
ejpam-6466	677	38	)	)	PUNCT
ejpam-6466	677	39	is	be	AUX
ejpam-6466	677	40	the	the	DET
ejpam-6466	677	41	ambient	ambient	ADJ
ejpam-6466	677	42	(	(	PUNCT
ejpam-6466	677	43	environmental	environmental	ADJ
ejpam-6466	677	44	)	)	PUNCT
ejpam-6466	677	45	temperature	temperature	NOUN
ejpam-6466	677	46	.	.	PUNCT
ejpam-6466	678	1	the	the	DET
ejpam-6466	678	2	parameter	parameter	NOUN
ejpam-6466	678	3	α	α	PROPN
ejpam-6466	678	4	=	=	SYM
ejpam-6466	678	5	0.5	0.5	NUM
ejpam-6466	678	6	represents	represent	VERB
ejpam-6466	678	7	the	the	DET
ejpam-6466	678	8	rate	rate	NOUN
ejpam-6466	678	9	of	of	ADP
ejpam-6466	678	10	heat	heat	NOUN
ejpam-6466	678	11	exchange	exchange	NOUN
ejpam-6466	678	12	,	,	PUNCT
ejpam-6466	678	13	while	while	SCONJ
ejpam-6466	678	14	β	β	X
ejpam-6466	678	15	=	=	SYM
ejpam-6466	678	16	0.2	0.2	NUM
ejpam-6466	678	17	denotes	denote	VERB
ejpam-6466	678	18	the	the	DET
ejpam-6466	678	19	strength	strength	NOUN
ejpam-6466	678	20	of	of	ADP
ejpam-6466	678	21	the	the	DET
ejpam-6466	678	22	delayed	delay	VERB
ejpam-6466	678	23	feedback	feedback	NOUN
ejpam-6466	678	24	.	.	PUNCT
ejpam-6466	679	1	the	the	DET
ejpam-6466	679	2	environmental	environmental	ADJ
ejpam-6466	679	3	temperature	temperature	NOUN
ejpam-6466	679	4	is	be	AUX
ejpam-6466	679	5	modeled	model	VERB
ejpam-6466	679	6	as	as	SCONJ
ejpam-6466	679	7	follows	follow	VERB
ejpam-6466	679	8	:	:	PUNCT
ejpam-6466	679	9	tenv(τ	tenv(τ	NOUN
ejpam-6466	679	10	)	)	PUNCT
ejpam-6466	679	11	=	=	SYM
ejpam-6466	680	1	20	20	NUM
ejpam-6466	680	2	+	+	SYM
ejpam-6466	680	3	5	5	NUM
ejpam-6466	680	4	sin	sin	NOUN
ejpam-6466	680	5	(	(	PUNCT
ejpam-6466	680	6	2πτ	2πτ	NOUN
ejpam-6466	680	7	24	24	NUM
ejpam-6466	680	8	)	)	PUNCT
ejpam-6466	680	9	.	.	PUNCT
ejpam-6466	681	1	m.	m.	PROPN
ejpam-6466	681	2	i.	i.	PROPN
ejpam-6466	681	3	liaqat	liaqat	PROPN
ejpam-6466	681	4	et	et	PROPN
ejpam-6466	681	5	al	al	PROPN
ejpam-6466	681	6	.	.	PUNCT
ejpam-6466	681	7	/	/	SYM
ejpam-6466	681	8	eur	eur	PROPN
ejpam-6466	681	9	.	.	PUNCT
ejpam-6466	682	1	j.	j.	PROPN
ejpam-6466	682	2	pure	pure	PROPN
ejpam-6466	682	3	appl	appl	PROPN
ejpam-6466	682	4	.	.	PROPN
ejpam-6466	682	5	math	math	PROPN
ejpam-6466	682	6	,	,	PUNCT
ejpam-6466	682	7	18	18	NUM
ejpam-6466	682	8	(	(	PUNCT
ejpam-6466	682	9	4	4	NUM
ejpam-6466	682	10	)	)	PUNCT
ejpam-6466	682	11	(	(	PUNCT
ejpam-6466	682	12	2025	2025	NUM
ejpam-6466	682	13	)	)	PUNCT
ejpam-6466	682	14	,	,	PUNCT
ejpam-6466	682	15	6466	6466	NUM
ejpam-6466	682	16	25	25	NUM
ejpam-6466	682	17	of	of	ADP
ejpam-6466	682	18	28	28	NUM
ejpam-6466	682	19	the	the	DET
ejpam-6466	682	20	diffusion	diffusion	NOUN
ejpam-6466	682	21	component	component	NOUN
ejpam-6466	682	22	is	be	AUX
ejpam-6466	682	23	given	give	VERB
ejpam-6466	682	24	below	below	ADV
ejpam-6466	682	25	:	:	PUNCT
ejpam-6466	682	26	𭟋(τ	𭟋(τ	ADJ
ejpam-6466	682	27	,	,	PUNCT
ejpam-6466	682	28	t(τ),t(τ	t(τ),t(τ	NOUN
ejpam-6466	682	29	−m	−m	NOUN
ejpam-6466	682	30	)	)	PUNCT
ejpam-6466	682	31	)	)	PUNCT
ejpam-6466	683	1	=	=	PUNCT
ejpam-6466	684	1	0.3	0.3	NUM
ejpam-6466	684	2	√	√	NUM
ejpam-6466	684	3	|t(τ)|	|t(τ)|	PROPN
ejpam-6466	684	4	,	,	PUNCT
ejpam-6466	684	5	which	which	PRON
ejpam-6466	684	6	introduces	introduce	VERB
ejpam-6466	684	7	state	state	NOUN
ejpam-6466	684	8	-	-	PUNCT
ejpam-6466	684	9	dependent	dependent	ADJ
ejpam-6466	684	10	stochastic	stochastic	ADJ
ejpam-6466	684	11	fluctuations	fluctuation	NOUN
ejpam-6466	684	12	.	.	PUNCT
ejpam-6466	685	1	we	we	PRON
ejpam-6466	685	2	numerically	numerically	ADV
ejpam-6466	685	3	solve	solve	VERB
ejpam-6466	685	4	the	the	DET
ejpam-6466	685	5	df	df	PROPN
ejpam-6466	685	6	-	-	PUNCT
ejpam-6466	685	7	sde	sde	PROPN
ejpam-6466	685	8	governing	govern	VERB
ejpam-6466	685	9	temperature	temperature	NOUN
ejpam-6466	685	10	evolution	evolution	NOUN
ejpam-6466	685	11	using	use	VERB
ejpam-6466	685	12	an	an	DET
ejpam-6466	685	13	adapted	adapt	VERB
ejpam-6466	685	14	euler	euler	NOUN
ejpam-6466	685	15	-	-	PUNCT
ejpam-6466	685	16	maruyama	maruyama	NOUN
ejpam-6466	685	17	method	method	NOUN
ejpam-6466	685	18	.	.	PUNCT
ejpam-6466	686	1	the	the	DET
ejpam-6466	686	2	simulated	simulated	ADJ
ejpam-6466	686	3	thermal	thermal	ADJ
ejpam-6466	686	4	dynamics	dynamic	NOUN
ejpam-6466	686	5	,	,	PUNCT
ejpam-6466	686	6	including	include	VERB
ejpam-6466	686	7	stochastic	stochastic	ADJ
ejpam-6466	686	8	fluctuations	fluctuation	NOUN
ejpam-6466	686	9	and	and	CCONJ
ejpam-6466	686	10	delayed	delay	VERB
ejpam-6466	686	11	feedback	feedback	NOUN
ejpam-6466	686	12	effects	effect	NOUN
ejpam-6466	686	13	,	,	PUNCT
ejpam-6466	686	14	are	be	AUX
ejpam-6466	686	15	shown	show	VERB
ejpam-6466	686	16	in	in	ADP
ejpam-6466	686	17	figure	figure	NOUN
ejpam-6466	686	18	2	2	NUM
ejpam-6466	686	19	.	.	NOUN
ejpam-6466	686	20	0	0	NUM
ejpam-6466	686	21	5	5	NUM
ejpam-6466	686	22	10	10	NUM
ejpam-6466	686	23	15	15	NUM
ejpam-6466	686	24	20	20	NUM
ejpam-6466	686	25	25	25	NUM
ejpam-6466	686	26	time	time	NOUN
ejpam-6466	686	27	(	(	PUNCT
ejpam-6466	686	28	hours	hour	NOUN
ejpam-6466	686	29	)	)	PUNCT
ejpam-6466	686	30	14	14	NUM
ejpam-6466	686	31	16	16	NUM
ejpam-6466	686	32	18	18	NUM
ejpam-6466	686	33	20	20	NUM
ejpam-6466	686	34	22	22	NUM
ejpam-6466	686	35	24	24	NUM
ejpam-6466	686	36	26	26	NUM
ejpam-6466	686	37	28	28	NUM
ejpam-6466	686	38	te	te	INTJ
ejpam-6466	686	39	m	m	VERB
ejpam-6466	686	40	pe	pe	INTJ
ejpam-6466	686	41	ra	ra	PROPN
ejpam-6466	686	42	tu	tu	X
ejpam-6466	686	43	re	re	X
ejpam-6466	686	44	(	(	PUNCT
ejpam-6466	686	45	°	°	ADP
ejpam-6466	686	46	c	c	NOUN
ejpam-6466	686	47	)	)	PUNCT
ejpam-6466	686	48	daily	daily	ADJ
ejpam-6466	686	49	temperature	temperature	NOUN
ejpam-6466	686	50	dynamics	dynamic	NOUN
ejpam-6466	686	51	with	with	ADP
ejpam-6466	686	52	=	=	SYM
ejpam-6466	686	53	0.7	0.7	NUM
ejpam-6466	686	54	,	,	PUNCT
ejpam-6466	686	55	delay=0.5	delay=0.5	ADJ
ejpam-6466	686	56	hours	hour	NOUN
ejpam-6466	686	57	sim	sim	ADJ
ejpam-6466	686	58	1	1	NUM
ejpam-6466	686	59	sim	sim	NOUN
ejpam-6466	686	60	2	2	NUM
ejpam-6466	686	61	sim	sim	NOUN
ejpam-6466	686	62	3	3	NUM
ejpam-6466	686	63	sim	sim	NOUN
ejpam-6466	686	64	4	4	NUM
ejpam-6466	686	65	sim	sim	NOUN
ejpam-6466	686	66	5	5	NUM
ejpam-6466	686	67	sim	sim	NOUN
ejpam-6466	686	68	6	6	NUM
ejpam-6466	686	69	sim	sim	NOUN
ejpam-6466	686	70	7	7	NUM
ejpam-6466	686	71	sim	sim	NOUN
ejpam-6466	686	72	8	8	NUM
ejpam-6466	686	73	sim	sim	NOUN
ejpam-6466	686	74	9	9	NUM
ejpam-6466	686	75	sim	sim	NOUN
ejpam-6466	686	76	10	10	NUM
ejpam-6466	686	77	mean	mean	NOUN
ejpam-6466	686	78	temperature	temperature	NOUN
ejpam-6466	686	79	(	(	PUNCT
ejpam-6466	686	80	a	a	X
ejpam-6466	686	81	)	)	PUNCT
ejpam-6466	686	82	0	0	NUM
ejpam-6466	686	83	5	5	NUM
ejpam-6466	686	84	10	10	NUM
ejpam-6466	686	85	15	15	NUM
ejpam-6466	686	86	20	20	NUM
ejpam-6466	686	87	25	25	NUM
ejpam-6466	686	88	time	time	NOUN
ejpam-6466	686	89	(	(	PUNCT
ejpam-6466	686	90	hours	hour	NOUN
ejpam-6466	686	91	)	)	PUNCT
ejpam-6466	686	92	14	14	NUM
ejpam-6466	686	93	16	16	NUM
ejpam-6466	686	94	18	18	NUM
ejpam-6466	686	95	20	20	NUM
ejpam-6466	686	96	22	22	NUM
ejpam-6466	686	97	24	24	NUM
ejpam-6466	686	98	26	26	NUM
ejpam-6466	686	99	28	28	NUM
ejpam-6466	686	100	te	te	INTJ
ejpam-6466	686	101	m	m	VERB
ejpam-6466	686	102	pe	pe	INTJ
ejpam-6466	686	103	ra	ra	PROPN
ejpam-6466	686	104	tu	tu	X
ejpam-6466	686	105	re	re	X
ejpam-6466	686	106	(	(	PUNCT
ejpam-6466	686	107	°	°	ADP
ejpam-6466	686	108	c	c	NOUN
ejpam-6466	686	109	)	)	PUNCT
ejpam-6466	686	110	daily	daily	ADJ
ejpam-6466	686	111	temperature	temperature	NOUN
ejpam-6466	686	112	dynamics	dynamic	NOUN
ejpam-6466	686	113	with	with	ADP
ejpam-6466	686	114	=	=	PROPN
ejpam-6466	686	115	0.8	0.8	NUM
ejpam-6466	686	116	,	,	PUNCT
ejpam-6466	686	117	delay=0.5	delay=0.5	ADJ
ejpam-6466	686	118	hours	hour	NOUN
ejpam-6466	686	119	sim	sim	ADJ
ejpam-6466	686	120	1	1	NUM
ejpam-6466	686	121	sim	sim	NOUN
ejpam-6466	686	122	2	2	NUM
ejpam-6466	686	123	sim	sim	NOUN
ejpam-6466	686	124	3	3	NUM
ejpam-6466	686	125	sim	sim	NOUN
ejpam-6466	686	126	4	4	NUM
ejpam-6466	686	127	sim	sim	NOUN
ejpam-6466	686	128	5	5	NUM
ejpam-6466	686	129	sim	sim	NOUN
ejpam-6466	686	130	6	6	NUM
ejpam-6466	686	131	sim	sim	NOUN
ejpam-6466	686	132	7	7	NUM
ejpam-6466	686	133	sim	sim	NOUN
ejpam-6466	686	134	8	8	NUM
ejpam-6466	686	135	sim	sim	NOUN
ejpam-6466	686	136	9	9	NUM
ejpam-6466	686	137	sim	sim	NOUN
ejpam-6466	686	138	10	10	NUM
ejpam-6466	686	139	mean	mean	NOUN
ejpam-6466	686	140	temperature	temperature	NOUN
ejpam-6466	686	141	(	(	PUNCT
ejpam-6466	686	142	b	b	NOUN
ejpam-6466	686	143	)	)	PUNCT
ejpam-6466	686	144	0	0	NUM
ejpam-6466	686	145	5	5	NUM
ejpam-6466	686	146	10	10	NUM
ejpam-6466	686	147	15	15	NUM
ejpam-6466	686	148	20	20	NUM
ejpam-6466	686	149	25	25	NUM
ejpam-6466	686	150	time	time	NOUN
ejpam-6466	686	151	(	(	PUNCT
ejpam-6466	686	152	hours	hour	NOUN
ejpam-6466	686	153	)	)	PUNCT
ejpam-6466	686	154	14	14	NUM
ejpam-6466	686	155	16	16	NUM
ejpam-6466	686	156	18	18	NUM
ejpam-6466	686	157	20	20	NUM
ejpam-6466	686	158	22	22	NUM
ejpam-6466	686	159	24	24	NUM
ejpam-6466	686	160	26	26	NUM
ejpam-6466	686	161	28	28	NUM
ejpam-6466	686	162	te	te	INTJ
ejpam-6466	686	163	m	m	VERB
ejpam-6466	686	164	pe	pe	INTJ
ejpam-6466	686	165	ra	ra	PROPN
ejpam-6466	686	166	tu	tu	X
ejpam-6466	686	167	re	re	X
ejpam-6466	686	168	(	(	PUNCT
ejpam-6466	686	169	°	°	ADP
ejpam-6466	686	170	c	c	NOUN
ejpam-6466	686	171	)	)	PUNCT
ejpam-6466	686	172	daily	daily	ADJ
ejpam-6466	686	173	temperature	temperature	NOUN
ejpam-6466	686	174	dynamics	dynamic	NOUN
ejpam-6466	686	175	with	with	ADP
ejpam-6466	686	176	=	=	NOUN
ejpam-6466	686	177	0.85	0.85	NUM
ejpam-6466	686	178	,	,	PUNCT
ejpam-6466	686	179	delay=0.5	delay=0.5	ADJ
ejpam-6466	686	180	hours	hour	NOUN
ejpam-6466	686	181	sim	sim	ADJ
ejpam-6466	686	182	1	1	NUM
ejpam-6466	686	183	sim	sim	NOUN
ejpam-6466	686	184	2	2	NUM
ejpam-6466	686	185	sim	sim	NOUN
ejpam-6466	686	186	3	3	NUM
ejpam-6466	686	187	sim	sim	NOUN
ejpam-6466	686	188	4	4	NUM
ejpam-6466	686	189	sim	sim	NOUN
ejpam-6466	686	190	5	5	NUM
ejpam-6466	686	191	sim	sim	NOUN
ejpam-6466	686	192	6	6	NUM
ejpam-6466	686	193	sim	sim	NOUN
ejpam-6466	686	194	7	7	NUM
ejpam-6466	686	195	sim	sim	NOUN
ejpam-6466	686	196	8	8	NUM
ejpam-6466	686	197	sim	sim	NOUN
ejpam-6466	686	198	9	9	NUM
ejpam-6466	686	199	sim	sim	NOUN
ejpam-6466	686	200	10	10	NUM
ejpam-6466	686	201	mean	mean	NOUN
ejpam-6466	686	202	temperature	temperature	NOUN
ejpam-6466	686	203	(	(	PUNCT
ejpam-6466	686	204	c	c	NOUN
ejpam-6466	686	205	)	)	PUNCT
ejpam-6466	686	206	0	0	NUM
ejpam-6466	686	207	5	5	NUM
ejpam-6466	686	208	10	10	NUM
ejpam-6466	686	209	15	15	NUM
ejpam-6466	686	210	20	20	NUM
ejpam-6466	686	211	25	25	NUM
ejpam-6466	686	212	time	time	NOUN
ejpam-6466	686	213	(	(	PUNCT
ejpam-6466	686	214	hours	hour	NOUN
ejpam-6466	686	215	)	)	PUNCT
ejpam-6466	686	216	14	14	NUM
ejpam-6466	686	217	16	16	NUM
ejpam-6466	686	218	18	18	NUM
ejpam-6466	686	219	20	20	NUM
ejpam-6466	686	220	22	22	NUM
ejpam-6466	686	221	24	24	NUM
ejpam-6466	686	222	26	26	NUM
ejpam-6466	686	223	28	28	NUM
ejpam-6466	686	224	te	te	INTJ
ejpam-6466	686	225	m	m	VERB
ejpam-6466	686	226	pe	pe	INTJ
ejpam-6466	686	227	ra	ra	PROPN
ejpam-6466	686	228	tu	tu	X
ejpam-6466	686	229	re	re	X
ejpam-6466	686	230	(	(	PUNCT
ejpam-6466	686	231	°	°	ADP
ejpam-6466	686	232	c	c	NOUN
ejpam-6466	686	233	)	)	PUNCT
ejpam-6466	686	234	daily	daily	ADJ
ejpam-6466	686	235	temperature	temperature	NOUN
ejpam-6466	686	236	dynamics	dynamic	NOUN
ejpam-6466	686	237	with	with	ADP
ejpam-6466	686	238	=	=	NOUN
ejpam-6466	686	239	0.9	0.9	NUM
ejpam-6466	686	240	,	,	PUNCT
ejpam-6466	686	241	delay=0.5	delay=0.5	ADJ
ejpam-6466	686	242	hours	hour	NOUN
ejpam-6466	686	243	sim	sim	ADJ
ejpam-6466	686	244	1	1	NUM
ejpam-6466	686	245	sim	sim	NOUN
ejpam-6466	686	246	2	2	NUM
ejpam-6466	686	247	sim	sim	NOUN
ejpam-6466	686	248	3	3	NUM
ejpam-6466	686	249	sim	sim	NOUN
ejpam-6466	686	250	4	4	NUM
ejpam-6466	686	251	sim	sim	NOUN
ejpam-6466	686	252	5	5	NUM
ejpam-6466	686	253	sim	sim	NOUN
ejpam-6466	686	254	6	6	NUM
ejpam-6466	686	255	sim	sim	NOUN
ejpam-6466	686	256	7	7	NUM
ejpam-6466	686	257	sim	sim	NOUN
ejpam-6466	686	258	8	8	NUM
ejpam-6466	686	259	sim	sim	NOUN
ejpam-6466	686	260	9	9	NUM
ejpam-6466	686	261	sim	sim	NOUN
ejpam-6466	686	262	10	10	NUM
ejpam-6466	686	263	mean	mean	NOUN
ejpam-6466	686	264	temperature	temperature	NOUN
ejpam-6466	686	265	(	(	PUNCT
ejpam-6466	686	266	d	d	NOUN
ejpam-6466	686	267	)	)	PUNCT
ejpam-6466	686	268	figure	figure	NOUN
ejpam-6466	686	269	2	2	NUM
ejpam-6466	686	270	:	:	PUNCT
ejpam-6466	686	271	population	population	NOUN
ejpam-6466	686	272	dynamics	dynamic	NOUN
ejpam-6466	686	273	under	under	ADP
ejpam-6466	686	274	different	different	ADJ
ejpam-6466	686	275	conformable	conformable	ADJ
ejpam-6466	686	276	fractional	fractional	ADJ
ejpam-6466	686	277	orders	order	NOUN
ejpam-6466	686	278	:	:	PUNCT
ejpam-6466	686	279	(	(	PUNCT
ejpam-6466	686	280	a	a	X
ejpam-6466	686	281	)	)	PUNCT
ejpam-6466	687	1	ξ	ξ	NOUN
ejpam-6466	687	2	=	=	SYM
ejpam-6466	687	3	0.7	0.7	NUM
ejpam-6466	687	4	showing	show	VERB
ejpam-6466	687	5	strong	strong	ADJ
ejpam-6466	687	6	memory	memory	NOUN
ejpam-6466	687	7	effects	effect	NOUN
ejpam-6466	687	8	,	,	PUNCT
ejpam-6466	687	9	(	(	PUNCT
ejpam-6466	687	10	b	b	X
ejpam-6466	687	11	)	)	PUNCT
ejpam-6466	687	12	ξ	ξ	NOUN
ejpam-6466	687	13	=	=	SYM
ejpam-6466	687	14	0.8	0.8	NUM
ejpam-6466	687	15	with	with	ADP
ejpam-6466	687	16	moderate	moderate	ADJ
ejpam-6466	687	17	memory	memory	NOUN
ejpam-6466	687	18	,	,	PUNCT
ejpam-6466	687	19	(	(	PUNCT
ejpam-6466	687	20	c	c	X
ejpam-6466	687	21	)	)	PUNCT
ejpam-6466	687	22	ξ	ξ	X
ejpam-6466	687	23	=	=	SYM
ejpam-6466	687	24	0.85	0.85	NUM
ejpam-6466	687	25	demonstrating	demonstrate	VERB
ejpam-6466	687	26	weak	weak	ADJ
ejpam-6466	687	27	memory	memory	NOUN
ejpam-6466	687	28	,	,	PUNCT
ejpam-6466	687	29	and	and	CCONJ
ejpam-6466	687	30	(	(	PUNCT
ejpam-6466	687	31	d	d	X
ejpam-6466	687	32	)	)	PUNCT
ejpam-6466	687	33	ξ	ξ	X
ejpam-6466	687	34	=	=	SYM
ejpam-6466	687	35	0.9	0.9	NUM
ejpam-6466	687	36	(	(	PUNCT
ejpam-6466	687	37	near	near	ADJ
ejpam-6466	687	38	-	-	PUNCT
ejpam-6466	687	39	classical	classical	ADJ
ejpam-6466	687	40	case	case	NOUN
ejpam-6466	687	41	)	)	PUNCT
ejpam-6466	687	42	.	.	PUNCT
ejpam-6466	688	1	all	all	DET
ejpam-6466	688	2	simulations	simulation	NOUN
ejpam-6466	688	3	use	use	VERB
ejpam-6466	688	4	r̃	r̃	NOUN
ejpam-6466	688	5	=	=	SYM
ejpam-6466	688	6	0.3	0.3	NUM
ejpam-6466	688	7	,	,	PUNCT
ejpam-6466	688	8	k	k	PROPN
ejpam-6466	689	1	=	=	SYM
ejpam-6466	689	2	1000	1000	NUM
ejpam-6466	689	3	,	,	PUNCT
ejpam-6466	689	4	σ	σ	NOUN
ejpam-6466	689	5	=	=	SYM
ejpam-6466	689	6	1.5	1.5	NUM
ejpam-6466	689	7	,	,	PUNCT
ejpam-6466	689	8	m	m	VERB
ejpam-6466	689	9	=	=	NOUN
ejpam-6466	689	10	0.5	0.5	NUM
ejpam-6466	689	11	years	year	NOUN
ejpam-6466	689	12	,	,	PUNCT
ejpam-6466	689	13	and	and	CCONJ
ejpam-6466	689	14	p(0	p(0	PROPN
ejpam-6466	689	15	)	)	PUNCT
ejpam-6466	689	16	=	=	SYM
ejpam-6466	689	17	100	100	NUM
ejpam-6466	689	18	.	.	PUNCT
ejpam-6466	690	1	light	light	ADJ
ejpam-6466	690	2	curves	curve	NOUN
ejpam-6466	690	3	represent	represent	VERB
ejpam-6466	690	4	individual	individual	ADJ
ejpam-6466	690	5	realizations	realization	NOUN
ejpam-6466	690	6	;	;	PUNCT
ejpam-6466	690	7	bold	bold	ADJ
ejpam-6466	690	8	curves	curve	NOUN
ejpam-6466	690	9	show	show	VERB
ejpam-6466	690	10	the	the	DET
ejpam-6466	690	11	mean	mean	NOUN
ejpam-6466	690	12	.	.	PUNCT
ejpam-6466	691	1	m.	m.	NOUN
ejpam-6466	691	2	i.	i.	PROPN
ejpam-6466	691	3	liaqat	liaqat	PROPN
ejpam-6466	691	4	et	et	PROPN
ejpam-6466	691	5	al	al	PROPN
ejpam-6466	691	6	.	.	PUNCT
ejpam-6466	691	7	/	/	SYM
ejpam-6466	691	8	eur	eur	PROPN
ejpam-6466	691	9	.	.	PUNCT
ejpam-6466	692	1	j.	j.	PROPN
ejpam-6466	692	2	pure	pure	PROPN
ejpam-6466	692	3	appl	appl	PROPN
ejpam-6466	692	4	.	.	PROPN
ejpam-6466	692	5	math	math	PROPN
ejpam-6466	692	6	,	,	PUNCT
ejpam-6466	692	7	18	18	NUM
ejpam-6466	692	8	(	(	PUNCT
ejpam-6466	692	9	4	4	NUM
ejpam-6466	692	10	)	)	PUNCT
ejpam-6466	692	11	(	(	PUNCT
ejpam-6466	692	12	2025	2025	NUM
ejpam-6466	692	13	)	)	PUNCT
ejpam-6466	692	14	,	,	PUNCT
ejpam-6466	692	15	6466	6466	NUM
ejpam-6466	692	16	26	26	NUM
ejpam-6466	692	17	of	of	ADP
ejpam-6466	692	18	28	28	NUM
ejpam-6466	692	19	5	5	NUM
ejpam-6466	692	20	.	.	PUNCT
ejpam-6466	693	1	conclusions	conclusion	NOUN
ejpam-6466	693	2	in	in	ADP
ejpam-6466	693	3	this	this	DET
ejpam-6466	693	4	study	study	NOUN
ejpam-6466	693	5	,	,	PUNCT
ejpam-6466	693	6	we	we	PRON
ejpam-6466	693	7	have	have	AUX
ejpam-6466	693	8	established	establish	VERB
ejpam-6466	693	9	the	the	DET
ejpam-6466	693	10	eu	eu	PROPN
ejpam-6466	693	11	,	,	PUNCT
ejpam-6466	693	12	con	con	PROPN
ejpam-6466	693	13	-	-	PUNCT
ejpam-6466	693	14	d	d	PROPN
ejpam-6466	693	15	,	,	PUNCT
ejpam-6466	693	16	regularity	regularity	NOUN
ejpam-6466	693	17	,	,	PUNCT
ejpam-6466	693	18	and	and	CCONJ
ejpam-6466	693	19	uh	uh	INTJ
ejpam-6466	693	20	stability	stability	NOUN
ejpam-6466	693	21	of	of	ADP
ejpam-6466	693	22	the	the	DET
ejpam-6466	693	23	solutions	solution	NOUN
ejpam-6466	693	24	to	to	ADP
ejpam-6466	693	25	df	df	NOUN
ejpam-6466	693	26	-	-	PUNCT
ejpam-6466	693	27	sdes	sde	NOUN
ejpam-6466	693	28	in	in	ADP
ejpam-6466	693	29	the	the	DET
ejpam-6466	693	30	framework	framework	NOUN
ejpam-6466	693	31	of	of	ADP
ejpam-6466	693	32	con	con	NOUN
ejpam-6466	693	33	-	-	PUNCT
ejpam-6466	693	34	frd	frd	ADJ
ejpam-6466	693	35	.	.	PUNCT
ejpam-6466	694	1	we	we	PRON
ejpam-6466	694	2	established	establish	VERB
ejpam-6466	694	3	the	the	DET
ejpam-6466	694	4	results	result	NOUN
ejpam-6466	694	5	of	of	ADP
ejpam-6466	694	6	the	the	DET
ejpam-6466	694	7	eu	eu	PROPN
ejpam-6466	694	8	in	in	ADP
ejpam-6466	694	9	two	two	NUM
ejpam-6466	694	10	ways	way	NOUN
ejpam-6466	694	11	:	:	PUNCT
ejpam-6466	694	12	first	first	ADV
ejpam-6466	694	13	,	,	PUNCT
ejpam-6466	694	14	through	through	ADP
ejpam-6466	694	15	the	the	DET
ejpam-6466	694	16	glc	glc	NOUN
ejpam-6466	694	17	of	of	ADP
ejpam-6466	694	18	the	the	DET
ejpam-6466	694	19	coefficients	coefficient	NOUN
ejpam-6466	694	20	.	.	PUNCT
ejpam-6466	695	1	in	in	ADP
ejpam-6466	695	2	the	the	DET
ejpam-6466	695	3	second	second	ADJ
ejpam-6466	695	4	stage	stage	NOUN
ejpam-6466	695	5	,	,	PUNCT
ejpam-6466	695	6	using	use	VERB
ejpam-6466	695	7	a	a	DET
ejpam-6466	695	8	truncation	truncation	NOUN
ejpam-6466	695	9	approach	approach	NOUN
ejpam-6466	695	10	,	,	PUNCT
ejpam-6466	695	11	we	we	PRON
ejpam-6466	695	12	have	have	AUX
ejpam-6466	695	13	demonstrated	demonstrate	VERB
ejpam-6466	695	14	the	the	DET
ejpam-6466	695	15	eu	eu	PROPN
ejpam-6466	695	16	according	accord	VERB
ejpam-6466	695	17	to	to	ADP
ejpam-6466	695	18	the	the	DET
ejpam-6466	695	19	llc	llc	NOUN
ejpam-6466	695	20	of	of	ADP
ejpam-6466	695	21	the	the	DET
ejpam-6466	695	22	coefficients	coefficient	NOUN
ejpam-6466	695	23	.	.	PUNCT
ejpam-6466	696	1	we	we	PRON
ejpam-6466	696	2	have	have	AUX
ejpam-6466	696	3	also	also	ADV
ejpam-6466	696	4	demonstrated	demonstrate	VERB
ejpam-6466	696	5	that	that	SCONJ
ejpam-6466	696	6	the	the	DET
ejpam-6466	696	7	solutions	solution	NOUN
ejpam-6466	696	8	of	of	ADP
ejpam-6466	696	9	df	df	NOUN
ejpam-6466	696	10	-	-	PUNCT
ejpam-6466	696	11	sdes	sde	NOUN
ejpam-6466	696	12	exhibit	exhibit	VERB
ejpam-6466	696	13	con	con	NOUN
ejpam-6466	696	14	-	-	PUNCT
ejpam-6466	696	15	d	d	NOUN
ejpam-6466	696	16	on	on	ADP
ejpam-6466	696	17	the	the	DET
ejpam-6466	696	18	fractional	fractional	ADJ
ejpam-6466	696	19	order	order	NOUN
ejpam-6466	696	20	ξ	ξ	NOUN
ejpam-6466	696	21	and	and	CCONJ
ejpam-6466	696	22	initial	initial	ADJ
ejpam-6466	696	23	values	value	NOUN
ejpam-6466	696	24	under	under	ADP
ejpam-6466	696	25	the	the	DET
ejpam-6466	696	26	glc	glc	NOUN
ejpam-6466	696	27	of	of	ADP
ejpam-6466	696	28	the	the	DET
ejpam-6466	696	29	coefficients	coefficient	NOUN
ejpam-6466	696	30	.	.	PUNCT
ejpam-6466	697	1	additionally	additionally	ADV
ejpam-6466	697	2	,	,	PUNCT
ejpam-6466	697	3	we	we	PRON
ejpam-6466	697	4	have	have	AUX
ejpam-6466	697	5	derived	derive	VERB
ejpam-6466	697	6	results	result	NOUN
ejpam-6466	697	7	concerning	concern	VERB
ejpam-6466	697	8	regularity	regularity	NOUN
ejpam-6466	697	9	and	and	CCONJ
ejpam-6466	697	10	uh	uh	INTJ
ejpam-6466	697	11	stability	stability	NOUN
ejpam-6466	697	12	and	and	CCONJ
ejpam-6466	697	13	presented	present	VERB
ejpam-6466	697	14	two	two	NUM
ejpam-6466	697	15	examples	example	NOUN
ejpam-6466	697	16	to	to	PART
ejpam-6466	697	17	illustrate	illustrate	VERB
ejpam-6466	697	18	our	our	PRON
ejpam-6466	697	19	findings	finding	NOUN
ejpam-6466	697	20	.	.	PUNCT
ejpam-6466	698	1	the	the	DET
ejpam-6466	698	2	main	main	ADJ
ejpam-6466	698	3	part	part	NOUN
ejpam-6466	698	4	of	of	ADP
ejpam-6466	698	5	the	the	DET
ejpam-6466	698	6	proof	proof	NOUN
ejpam-6466	698	7	utilized	utilize	VERB
ejpam-6466	698	8	the	the	DET
ejpam-6466	698	9	truncation	truncation	NOUN
ejpam-6466	698	10	process	process	NOUN
ejpam-6466	698	11	,	,	PUNCT
ejpam-6466	698	12	the	the	DET
ejpam-6466	698	13	banach	banach	ADV
ejpam-6466	698	14	fixed	fix	VERB
ejpam-6466	698	15	point	point	NOUN
ejpam-6466	698	16	approach	approach	NOUN
ejpam-6466	698	17	,	,	PUNCT
ejpam-6466	698	18	i	i	PRON
ejpam-6466	698	19	-	-	PUNCT
ejpam-6466	698	20	is	be	AUX
ejpam-6466	698	21	,	,	PUNCT
ejpam-6466	698	22	temporally	temporally	ADV
ejpam-6466	698	23	weighted	weight	VERB
ejpam-6466	698	24	norm	norm	NOUN
ejpam-6466	698	25	,	,	PUNCT
ejpam-6466	698	26	g	g	PROPN
ejpam-6466	698	27	-	-	PUNCT
ejpam-6466	698	28	i	i	NOUN
ejpam-6466	698	29	,	,	PUNCT
ejpam-6466	698	30	and	and	CCONJ
ejpam-6466	698	31	höld	höld	PROPN
ejpam-6466	698	32	-	-	PUNCT
ejpam-6466	698	33	i.	i.	NOUN
ejpam-6466	698	34	in	in	ADP
ejpam-6466	698	35	the	the	DET
ejpam-6466	698	36	future	future	NOUN
ejpam-6466	698	37	,	,	PUNCT
ejpam-6466	698	38	we	we	PRON
ejpam-6466	698	39	will	will	AUX
ejpam-6466	698	40	focus	focus	VERB
ejpam-6466	698	41	on	on	ADP
ejpam-6466	698	42	developing	develop	VERB
ejpam-6466	698	43	numerical	numerical	ADJ
ejpam-6466	698	44	methods	method	NOUN
ejpam-6466	698	45	for	for	ADP
ejpam-6466	698	46	solving	solve	VERB
ejpam-6466	698	47	df	df	NOUN
ejpam-6466	698	48	-	-	PUNCT
ejpam-6466	698	49	sdes	sde	NOUN
ejpam-6466	698	50	within	within	ADP
ejpam-6466	698	51	the	the	DET
ejpam-6466	698	52	framework	framework	NOUN
ejpam-6466	698	53	of	of	ADP
ejpam-6466	698	54	con	con	NOUN
ejpam-6466	698	55	-	-	PUNCT
ejpam-6466	698	56	frd	frd	ADJ
ejpam-6466	698	57	.	.	PUNCT
ejpam-6466	699	1	references	reference	NOUN
ejpam-6466	699	2	[	[	X
ejpam-6466	699	3	1	1	NUM
ejpam-6466	699	4	]	]	PUNCT
ejpam-6466	699	5	w.	w.	PROPN
ejpam-6466	699	6	chen	chen	PROPN
ejpam-6466	699	7	,	,	PUNCT
ejpam-6466	699	8	h.	h.	PROPN
ejpam-6466	699	9	sun	sun	PROPN
ejpam-6466	699	10	,	,	PUNCT
ejpam-6466	699	11	and	and	CCONJ
ejpam-6466	699	12	x.	x.	PROPN
ejpam-6466	699	13	li	li	PROPN
ejpam-6466	699	14	.	.	PROPN
ejpam-6466	699	15	fractional	fractional	ADJ
ejpam-6466	699	16	derivative	derivative	ADJ
ejpam-6466	699	17	modeling	modeling	NOUN
ejpam-6466	699	18	in	in	ADP
ejpam-6466	699	19	mechanics	mechanic	NOUN
ejpam-6466	699	20	and	and	CCONJ
ejpam-6466	699	21	engineering	engineering	NOUN
ejpam-6466	699	22	.	.	PUNCT
ejpam-6466	700	1	springer	springer	NOUN
ejpam-6466	700	2	nature	nature	NOUN
ejpam-6466	700	3	,	,	PUNCT
ejpam-6466	700	4	2022	2022	NUM
ejpam-6466	700	5	.	.	PUNCT
ejpam-6466	701	1	[	[	X
ejpam-6466	701	2	2	2	NUM
ejpam-6466	701	3	]	]	X
ejpam-6466	701	4	b.	b.	PROPN
ejpam-6466	701	5	dumitru	dumitru	PROPN
ejpam-6466	701	6	and	and	CCONJ
ejpam-6466	701	7	r.	r.	PROPN
ejpam-6466	701	8	p.	p.	PROPN
ejpam-6466	701	9	agarwal	agarwal	PROPN
ejpam-6466	701	10	.	.	PUNCT
ejpam-6466	702	1	fractional	fractional	ADJ
ejpam-6466	702	2	calculus	calculus	NOUN
ejpam-6466	702	3	in	in	ADP
ejpam-6466	702	4	the	the	DET
ejpam-6466	702	5	sky	sky	NOUN
ejpam-6466	702	6	.	.	PUNCT
ejpam-6466	703	1	advances	advance	NOUN
ejpam-6466	703	2	in	in	ADP
ejpam-6466	703	3	difference	difference	NOUN
ejpam-6466	703	4	equations	equation	NOUN
ejpam-6466	703	5	,	,	PUNCT
ejpam-6466	703	6	2021(1	2021(1	NUM
ejpam-6466	703	7	)	)	PUNCT
ejpam-6466	703	8	,	,	PUNCT
ejpam-6466	703	9	2021	2021	NUM
ejpam-6466	703	10	.	.	PUNCT
ejpam-6466	704	1	[	[	X
ejpam-6466	704	2	3	3	NUM
ejpam-6466	704	3	]	]	PUNCT
ejpam-6466	704	4	a.	a.	NOUN
ejpam-6466	704	5	giusti	giusti	PROPN
ejpam-6466	704	6	,	,	PUNCT
ejpam-6466	704	7	i.	i.	PROPN
ejpam-6466	704	8	colombaro	colombaro	PROPN
ejpam-6466	704	9	,	,	PUNCT
ejpam-6466	704	10	r.	r.	PROPN
ejpam-6466	704	11	garra	garra	PROPN
ejpam-6466	704	12	,	,	PUNCT
ejpam-6466	704	13	r.	r.	PROPN
ejpam-6466	704	14	garrappa	garrappa	PROPN
ejpam-6466	704	15	,	,	PUNCT
ejpam-6466	704	16	f.	f.	PROPN
ejpam-6466	704	17	polito	polito	PROPN
ejpam-6466	704	18	,	,	PUNCT
ejpam-6466	704	19	m.	m.	NOUN
ejpam-6466	704	20	popolizio	popolizio	NOUN
ejpam-6466	704	21	,	,	PUNCT
ejpam-6466	704	22	and	and	CCONJ
ejpam-6466	704	23	f.	f.	PROPN
ejpam-6466	704	24	mainardi	mainardi	PROPN
ejpam-6466	704	25	.	.	PUNCT
ejpam-6466	705	1	a	a	DET
ejpam-6466	705	2	practical	practical	ADJ
ejpam-6466	705	3	guide	guide	NOUN
ejpam-6466	705	4	to	to	ADP
ejpam-6466	705	5	prabhakar	prabhakar	NOUN
ejpam-6466	705	6	fractional	fractional	ADJ
ejpam-6466	705	7	calculus	calculus	NOUN
ejpam-6466	705	8	.	.	PUNCT
ejpam-6466	706	1	fractional	fractional	ADJ
ejpam-6466	706	2	calculus	calculus	NOUN
ejpam-6466	706	3	and	and	CCONJ
ejpam-6466	706	4	applied	apply	VERB
ejpam-6466	706	5	analysis	analysis	NOUN
ejpam-6466	706	6	,	,	PUNCT
ejpam-6466	706	7	23(1):9–54	23(1):9–54	NUM
ejpam-6466	706	8	,	,	PUNCT
ejpam-6466	706	9	2020	2020	NUM
ejpam-6466	706	10	.	.	PUNCT
ejpam-6466	707	1	[	[	X
ejpam-6466	707	2	4	4	NUM
ejpam-6466	707	3	]	]	X
ejpam-6466	707	4	c.	c.	PROPN
ejpam-6466	707	5	a.	a.	PROPN
ejpam-6466	707	6	valentim	valentim	PROPN
ejpam-6466	707	7	,	,	PUNCT
ejpam-6466	707	8	j.	j.	PROPN
ejpam-6466	707	9	a.	a.	NOUN
ejpam-6466	707	10	rabi	rabi	PROPN
ejpam-6466	707	11	,	,	PUNCT
ejpam-6466	707	12	and	and	CCONJ
ejpam-6466	707	13	s.	s.	PROPN
ejpam-6466	707	14	a.	a.	PROPN
ejpam-6466	707	15	david	david	PROPN
ejpam-6466	707	16	.	.	PUNCT
ejpam-6466	708	1	fractional	fractional	ADJ
ejpam-6466	708	2	mathematical	mathematical	ADJ
ejpam-6466	708	3	oncology	oncology	NOUN
ejpam-6466	708	4	:	:	PUNCT
ejpam-6466	708	5	on	on	ADP
ejpam-6466	708	6	the	the	DET
ejpam-6466	708	7	potential	potential	NOUN
ejpam-6466	708	8	of	of	ADP
ejpam-6466	708	9	non	non	ADJ
ejpam-6466	708	10	-	-	ADJ
ejpam-6466	708	11	integer	integer	ADJ
ejpam-6466	708	12	order	order	NOUN
ejpam-6466	708	13	calculus	calculus	NOUN
ejpam-6466	708	14	applied	apply	VERB
ejpam-6466	708	15	to	to	ADP
ejpam-6466	708	16	interdisciplinary	interdisciplinary	ADJ
ejpam-6466	708	17	models	model	NOUN
ejpam-6466	708	18	.	.	PUNCT
ejpam-6466	709	1	biosystems	biosystem	NOUN
ejpam-6466	709	2	,	,	PUNCT
ejpam-6466	709	3	204:104377	204:104377	NUM
ejpam-6466	709	4	,	,	PUNCT
ejpam-6466	709	5	2021	2021	NUM
ejpam-6466	709	6	.	.	PUNCT
ejpam-6466	710	1	[	[	X
ejpam-6466	710	2	5	5	X
ejpam-6466	710	3	]	]	X
ejpam-6466	710	4	g.	g.	PROPN
ejpam-6466	710	5	huang	huang	PROPN
ejpam-6466	710	6	,	,	PUNCT
ejpam-6466	710	7	h.	h.	PROPN
ejpam-6466	710	8	y.	y.	PROPN
ejpam-6466	710	9	qin	qin	PROPN
ejpam-6466	710	10	,	,	PUNCT
ejpam-6466	710	11	q.	q.	PROPN
ejpam-6466	710	12	chen	chen	PROPN
ejpam-6466	710	13	,	,	PUNCT
ejpam-6466	710	14	z.	z.	PROPN
ejpam-6466	710	15	shi	shi	PROPN
ejpam-6466	710	16	,	,	PUNCT
ejpam-6466	710	17	s.	s.	PROPN
ejpam-6466	710	18	jiang	jiang	PROPN
ejpam-6466	710	19	,	,	PUNCT
ejpam-6466	710	20	and	and	CCONJ
ejpam-6466	710	21	c.	c.	PROPN
ejpam-6466	710	22	huang	huang	PROPN
ejpam-6466	710	23	.	.	PUNCT
ejpam-6466	711	1	research	research	NOUN
ejpam-6466	711	2	on	on	ADP
ejpam-6466	711	3	application	application	NOUN
ejpam-6466	711	4	of	of	ADP
ejpam-6466	711	5	fractional	fractional	ADJ
ejpam-6466	711	6	calculus	calculus	NOUN
ejpam-6466	711	7	operator	operator	NOUN
ejpam-6466	711	8	in	in	ADP
ejpam-6466	711	9	image	image	NOUN
ejpam-6466	711	10	underlying	underlie	VERB
ejpam-6466	711	11	processing	processing	NOUN
ejpam-6466	711	12	.	.	PUNCT
ejpam-6466	712	1	fractal	fractal	ADJ
ejpam-6466	712	2	and	and	CCONJ
ejpam-6466	712	3	fractional	fractional	ADJ
ejpam-6466	712	4	,	,	PUNCT
ejpam-6466	712	5	8(1):37	8(1):37	NUM
ejpam-6466	712	6	,	,	PUNCT
ejpam-6466	712	7	2024	2024	NUM
ejpam-6466	712	8	.	.	PUNCT
ejpam-6466	713	1	[	[	X
ejpam-6466	713	2	6	6	NUM
ejpam-6466	713	3	]	]	PUNCT
ejpam-6466	713	4	s.	s.	PROPN
ejpam-6466	713	5	arora	arora	PROPN
ejpam-6466	713	6	,	,	PUNCT
ejpam-6466	713	7	t.	t.	PROPN
ejpam-6466	713	8	mathur	mathur	PROPN
ejpam-6466	713	9	,	,	PUNCT
ejpam-6466	713	10	s.	s.	PROPN
ejpam-6466	713	11	agarwal	agarwal	PROPN
ejpam-6466	713	12	,	,	PUNCT
ejpam-6466	713	13	k.	k.	PROPN
ejpam-6466	713	14	tiwari	tiwari	PROPN
ejpam-6466	713	15	,	,	PUNCT
ejpam-6466	713	16	and	and	CCONJ
ejpam-6466	713	17	p.	p.	PROPN
ejpam-6466	713	18	gupta	gupta	PROPN
ejpam-6466	713	19	.	.	PUNCT
ejpam-6466	714	1	applications	application	NOUN
ejpam-6466	714	2	of	of	ADP
ejpam-6466	714	3	fractional	fractional	ADJ
ejpam-6466	714	4	calculus	calculus	NOUN
ejpam-6466	714	5	in	in	ADP
ejpam-6466	714	6	computer	computer	NOUN
ejpam-6466	714	7	vision	vision	NOUN
ejpam-6466	714	8	:	:	PUNCT
ejpam-6466	714	9	a	a	DET
ejpam-6466	714	10	survey	survey	NOUN
ejpam-6466	714	11	.	.	PUNCT
ejpam-6466	715	1	neurocomputing	neurocomputing	NOUN
ejpam-6466	715	2	,	,	PUNCT
ejpam-6466	715	3	489:407–428	489:407–428	NUM
ejpam-6466	715	4	,	,	PUNCT
ejpam-6466	715	5	2022	2022	NUM
ejpam-6466	715	6	.	.	PUNCT
ejpam-6466	716	1	[	[	X
ejpam-6466	716	2	7	7	X
ejpam-6466	716	3	]	]	X
ejpam-6466	716	4	t.	t.	NOUN
ejpam-6466	716	5	alinei	alinei	VERB
ejpam-6466	716	6	-	-	PUNCT
ejpam-6466	716	7	poiana	poiana	NOUN
ejpam-6466	716	8	,	,	PUNCT
ejpam-6466	716	9	e.	e.	PROPN
ejpam-6466	716	10	h.	h.	PROPN
ejpam-6466	716	11	dulf	dulf	PROPN
ejpam-6466	716	12	,	,	PUNCT
ejpam-6466	716	13	and	and	CCONJ
ejpam-6466	716	14	l.	l.	PROPN
ejpam-6466	716	15	kovacs	kovacs	PROPN
ejpam-6466	716	16	.	.	PUNCT
ejpam-6466	717	1	fractional	fractional	ADJ
ejpam-6466	717	2	calculus	calculus	NOUN
ejpam-6466	717	3	in	in	ADP
ejpam-6466	717	4	mathematical	mathematical	ADJ
ejpam-6466	717	5	oncology	oncology	NOUN
ejpam-6466	717	6	.	.	PUNCT
ejpam-6466	718	1	scientific	scientific	ADJ
ejpam-6466	718	2	reports	report	NOUN
ejpam-6466	718	3	,	,	PUNCT
ejpam-6466	718	4	13(1):10083	13(1):10083	NUM
ejpam-6466	718	5	,	,	PUNCT
ejpam-6466	718	6	2023	2023	NUM
ejpam-6466	718	7	.	.	PUNCT
ejpam-6466	719	1	[	[	X
ejpam-6466	719	2	8	8	NUM
ejpam-6466	719	3	]	]	X
ejpam-6466	719	4	miguel	miguel	PROPN
ejpam-6466	719	5	vivas	vivas	PROPN
ejpam-6466	719	6	-	-	PROPN
ejpam-6466	719	7	cortez	cortez	PROPN
ejpam-6466	719	8	,	,	PUNCT
ejpam-6466	719	9	majeed	majeed	PROPN
ejpam-6466	719	10	a.	a.	PROPN
ejpam-6466	719	11	yousif	yousif	PROPN
ejpam-6466	719	12	,	,	PUNCT
ejpam-6466	719	13	bewar	bewar	PROPN
ejpam-6466	719	14	a.	a.	PROPN
ejpam-6466	719	15	mahmood	mahmood	PROPN
ejpam-6466	719	16	,	,	PUNCT
ejpam-6466	719	17	pshtiwan	pshtiwan	PROPN
ejpam-6466	719	18	othman	othman	PROPN
ejpam-6466	719	19	mohammed	mohammed	PROPN
ejpam-6466	719	20	,	,	PUNCT
ejpam-6466	719	21	nejmeddine	nejmeddine	ADJ
ejpam-6466	719	22	chorfi	chorfi	PROPN
ejpam-6466	719	23	,	,	PUNCT
ejpam-6466	719	24	and	and	CCONJ
ejpam-6466	719	25	alina	alina	PROPN
ejpam-6466	719	26	alb	alb	PROPN
ejpam-6466	719	27	lupas	lupas	PROPN
ejpam-6466	719	28	.	.	PUNCT
ejpam-6466	720	1	high	high	ADJ
ejpam-6466	720	2	-	-	PUNCT
ejpam-6466	720	3	accuracy	accuracy	NOUN
ejpam-6466	720	4	solutions	solution	NOUN
ejpam-6466	720	5	to	to	ADP
ejpam-6466	720	6	the	the	DET
ejpam-6466	720	7	time	time	NOUN
ejpam-6466	720	8	-	-	PUNCT
ejpam-6466	720	9	fractional	fractional	ADJ
ejpam-6466	720	10	kdv	kdv	NOUN
ejpam-6466	720	11	–	–	PUNCT
ejpam-6466	720	12	burgers	burger	NOUN
ejpam-6466	720	13	equation	equation	NOUN
ejpam-6466	720	14	using	use	VERB
ejpam-6466	720	15	rational	rational	ADJ
ejpam-6466	720	16	non	non	ADJ
ejpam-6466	720	17	-	-	ADJ
ejpam-6466	720	18	polynomial	polynomial	ADJ
ejpam-6466	720	19	splines	spline	NOUN
ejpam-6466	720	20	.	.	PUNCT
ejpam-6466	721	1	symmetry	symmetry	NOUN
ejpam-6466	721	2	,	,	PUNCT
ejpam-6466	721	3	17(1	17(1	NUM
ejpam-6466	721	4	)	)	PUNCT
ejpam-6466	721	5	,	,	PUNCT
ejpam-6466	721	6	2025	2025	NUM
ejpam-6466	721	7	.	.	PUNCT
ejpam-6466	722	1	[	[	X
ejpam-6466	722	2	9	9	NUM
ejpam-6466	722	3	]	]	PUNCT
ejpam-6466	722	4	t.	t.	PROPN
ejpam-6466	722	5	zhang	zhang	PROPN
ejpam-6466	722	6	,	,	PUNCT
ejpam-6466	722	7	h.	h.	PROPN
ejpam-6466	722	8	qu	qu	PROPN
ejpam-6466	722	9	,	,	PUNCT
ejpam-6466	722	10	and	and	CCONJ
ejpam-6466	722	11	j.	j.	PROPN
ejpam-6466	722	12	zhou	zhou	PROPN
ejpam-6466	722	13	.	.	PUNCT
ejpam-6466	723	1	asymptotically	asymptotically	ADV
ejpam-6466	723	2	almost	almost	ADV
ejpam-6466	723	3	periodic	periodic	ADJ
ejpam-6466	723	4	synchronization	synchronization	NOUN
ejpam-6466	723	5	in	in	ADP
ejpam-6466	723	6	fuzzy	fuzzy	ADJ
ejpam-6466	723	7	competitive	competitive	ADJ
ejpam-6466	723	8	neural	neural	ADJ
ejpam-6466	723	9	networks	network	NOUN
ejpam-6466	723	10	with	with	ADP
ejpam-6466	723	11	caputo	caputo	PROPN
ejpam-6466	723	12	-	-	PUNCT
ejpam-6466	723	13	fabrizio	fabrizio	PROPN
ejpam-6466	723	14	operator	operator	NOUN
ejpam-6466	723	15	.	.	PUNCT
ejpam-6466	724	1	fuzzy	fuzzy	ADJ
ejpam-6466	724	2	sets	set	NOUN
ejpam-6466	724	3	and	and	CCONJ
ejpam-6466	724	4	systems	system	NOUN
ejpam-6466	724	5	,	,	PUNCT
ejpam-6466	724	6	471:108676	471:108676	NUM
ejpam-6466	724	7	,	,	PUNCT
ejpam-6466	724	8	2023	2023	NUM
ejpam-6466	724	9	.	.	PUNCT
ejpam-6466	725	1	[	[	X
ejpam-6466	725	2	10	10	NUM
ejpam-6466	725	3	]	]	X
ejpam-6466	725	4	h.	h.	PROPN
ejpam-6466	725	5	luo	luo	PROPN
ejpam-6466	725	6	and	and	CCONJ
ejpam-6466	725	7	t.	t.	PROPN
ejpam-6466	725	8	zhang	zhang	PROPN
ejpam-6466	725	9	.	.	PUNCT
ejpam-6466	726	1	equilibrium	equilibrium	NOUN
ejpam-6466	726	2	point	point	NOUN
ejpam-6466	726	3	,	,	PUNCT
ejpam-6466	726	4	exponential	exponential	ADJ
ejpam-6466	726	5	stability	stability	NOUN
ejpam-6466	726	6	and	and	CCONJ
ejpam-6466	726	7	synchronization	synchronization	NOUN
ejpam-6466	726	8	of	of	ADP
ejpam-6466	726	9	numerical	numerical	ADJ
ejpam-6466	726	10	fractional	fractional	ADJ
ejpam-6466	726	11	-	-	PUNCT
ejpam-6466	726	12	order	order	NOUN
ejpam-6466	726	13	shunting	shunt	VERB
ejpam-6466	726	14	inhibitory	inhibitory	ADJ
ejpam-6466	726	15	cellular	cellular	ADJ
ejpam-6466	726	16	neural	neural	ADJ
ejpam-6466	726	17	networks	network	NOUN
ejpam-6466	726	18	with	with	ADP
ejpam-6466	726	19	piecewise	piecewise	NOUN
ejpam-6466	726	20	feature	feature	NOUN
ejpam-6466	726	21	.	.	PUNCT
ejpam-6466	727	1	proceedings	proceeding	NOUN
ejpam-6466	727	2	of	of	ADP
ejpam-6466	727	3	the	the	DET
ejpam-6466	727	4	institution	institution	NOUN
ejpam-6466	727	5	of	of	ADP
ejpam-6466	727	6	mechanical	mechanical	ADJ
ejpam-6466	727	7	engineers	engineer	NOUN
ejpam-6466	727	8	,	,	PUNCT
ejpam-6466	727	9	part	part	NOUN
ejpam-6466	727	10	i	i	PRON
ejpam-6466	727	11	:	:	PUNCT
ejpam-6466	727	12	journal	journal	PROPN
ejpam-6466	727	13	of	of	ADP
ejpam-6466	727	14	systems	system	NOUN
ejpam-6466	727	15	and	and	CCONJ
ejpam-6466	727	16	control	control	PROPN
ejpam-6466	727	17	engineering	engineering	NOUN
ejpam-6466	727	18	,	,	PUNCT
ejpam-6466	727	19	236(10):1908–1921	236(10):1908–1921	NUM
ejpam-6466	727	20	,	,	PUNCT
ejpam-6466	727	21	2022	2022	NUM
ejpam-6466	727	22	.	.	PUNCT
ejpam-6466	728	1	m.	m.	NOUN
ejpam-6466	728	2	i.	i.	PROPN
ejpam-6466	728	3	liaqat	liaqat	PROPN
ejpam-6466	728	4	et	et	PROPN
ejpam-6466	728	5	al	al	PROPN
ejpam-6466	728	6	.	.	PUNCT
ejpam-6466	728	7	/	/	SYM
ejpam-6466	728	8	eur	eur	PROPN
ejpam-6466	728	9	.	.	PUNCT
ejpam-6466	729	1	j.	j.	PROPN
ejpam-6466	729	2	pure	pure	PROPN
ejpam-6466	729	3	appl	appl	PROPN
ejpam-6466	729	4	.	.	PROPN
ejpam-6466	729	5	math	math	PROPN
ejpam-6466	729	6	,	,	PUNCT
ejpam-6466	729	7	18	18	NUM
ejpam-6466	729	8	(	(	PUNCT
ejpam-6466	729	9	4	4	NUM
ejpam-6466	729	10	)	)	PUNCT
ejpam-6466	729	11	(	(	PUNCT
ejpam-6466	729	12	2025	2025	NUM
ejpam-6466	729	13	)	)	PUNCT
ejpam-6466	729	14	,	,	PUNCT
ejpam-6466	729	15	6466	6466	NUM
ejpam-6466	729	16	27	27	NUM
ejpam-6466	729	17	of	of	ADP
ejpam-6466	729	18	28	28	NUM
ejpam-6466	730	1	[	[	X
ejpam-6466	730	2	11	11	NUM
ejpam-6466	730	3	]	]	PUNCT
ejpam-6466	730	4	m.	m.	NOUN
ejpam-6466	730	5	i.	i.	PROPN
ejpam-6466	730	6	liaqat	liaqat	PROPN
ejpam-6466	730	7	,	,	PUNCT
ejpam-6466	730	8	a.	a.	PROPN
ejpam-6466	730	9	akgül	akgül	PROPN
ejpam-6466	730	10	,	,	PUNCT
ejpam-6466	730	11	m.	m.	PROPN
ejpam-6466	730	12	de	de	PROPN
ejpam-6466	730	13	la	la	X
ejpam-6466	730	14	sen	sen	PROPN
ejpam-6466	730	15	,	,	PUNCT
ejpam-6466	730	16	and	and	CCONJ
ejpam-6466	730	17	m.	m.	PROPN
ejpam-6466	730	18	bayram	bayram	PROPN
ejpam-6466	730	19	.	.	PROPN
ejpam-6466	731	1	approximate	approximate	ADJ
ejpam-6466	731	2	and	and	CCONJ
ejpam-6466	731	3	exact	exact	ADJ
ejpam-6466	731	4	solutions	solution	NOUN
ejpam-6466	731	5	in	in	ADP
ejpam-6466	731	6	the	the	DET
ejpam-6466	731	7	sense	sense	NOUN
ejpam-6466	731	8	of	of	ADP
ejpam-6466	731	9	conformable	conformable	ADJ
ejpam-6466	731	10	derivatives	derivative	NOUN
ejpam-6466	731	11	of	of	ADP
ejpam-6466	731	12	quantum	quantum	ADJ
ejpam-6466	731	13	mechanics	mechanic	NOUN
ejpam-6466	731	14	models	model	NOUN
ejpam-6466	731	15	using	use	VERB
ejpam-6466	731	16	a	a	DET
ejpam-6466	731	17	novel	novel	ADJ
ejpam-6466	731	18	algorithm	algorithm	NOUN
ejpam-6466	731	19	.	.	PUNCT
ejpam-6466	732	1	symmetry	symmetry	NOUN
ejpam-6466	732	2	,	,	PUNCT
ejpam-6466	732	3	15(3):744	15(3):744	NUM
ejpam-6466	732	4	,	,	PUNCT
ejpam-6466	732	5	2023	2023	NUM
ejpam-6466	732	6	.	.	PUNCT
ejpam-6466	733	1	[	[	X
ejpam-6466	733	2	12	12	NUM
ejpam-6466	733	3	]	]	PUNCT
ejpam-6466	733	4	t.	t.	PROPN
ejpam-6466	733	5	zhang	zhang	PROPN
ejpam-6466	733	6	and	and	CCONJ
ejpam-6466	733	7	y.	y.	PROPN
ejpam-6466	733	8	li	li	PROPN
ejpam-6466	733	9	.	.	PROPN
ejpam-6466	734	1	s	s	PART
ejpam-6466	734	2	-	-	PUNCT
ejpam-6466	734	3	asymptotically	asymptotically	ADV
ejpam-6466	734	4	periodic	periodic	ADJ
ejpam-6466	734	5	fractional	fractional	ADJ
ejpam-6466	734	6	functional	functional	ADJ
ejpam-6466	734	7	differential	differential	ADJ
ejpam-6466	734	8	equations	equation	NOUN
ejpam-6466	734	9	with	with	ADP
ejpam-6466	734	10	off	off	ADP
ejpam-6466	734	11	-	-	PUNCT
ejpam-6466	734	12	diagonal	diagonal	ADJ
ejpam-6466	734	13	matrix	matrix	NOUN
ejpam-6466	734	14	mittag	mittag	ADJ
ejpam-6466	734	15	-	-	PUNCT
ejpam-6466	734	16	leffler	leffler	NOUN
ejpam-6466	734	17	function	function	NOUN
ejpam-6466	734	18	kernels	kernel	NOUN
ejpam-6466	734	19	.	.	PUNCT
ejpam-6466	735	1	mathematics	mathematic	NOUN
ejpam-6466	735	2	and	and	CCONJ
ejpam-6466	735	3	computers	computer	NOUN
ejpam-6466	735	4	in	in	ADP
ejpam-6466	735	5	simulation	simulation	NOUN
ejpam-6466	735	6	,	,	PUNCT
ejpam-6466	735	7	193:331–347	193:331–347	NUM
ejpam-6466	735	8	,	,	PUNCT
ejpam-6466	735	9	2022	2022	NUM
ejpam-6466	735	10	.	.	PUNCT
ejpam-6466	736	1	[	[	X
ejpam-6466	736	2	13	13	NUM
ejpam-6466	736	3	]	]	PUNCT
ejpam-6466	736	4	m.	m.	NOUN
ejpam-6466	736	5	s.	s.	PROPN
ejpam-6466	736	6	abdelouahab	abdelouahab	PROPN
ejpam-6466	736	7	and	and	CCONJ
ejpam-6466	736	8	n.	n.	PROPN
ejpam-6466	736	9	e.	e.	PROPN
ejpam-6466	736	10	hamri	hamri	PROPN
ejpam-6466	736	11	.	.	PUNCT
ejpam-6466	737	1	the	the	DET
ejpam-6466	737	2	grünwald	grünwald	ADJ
ejpam-6466	737	3	-	-	PUNCT
ejpam-6466	737	4	letnikov	letnikov	ADJ
ejpam-6466	737	5	fractional	fractional	ADJ
ejpam-6466	737	6	-	-	PUNCT
ejpam-6466	737	7	order	order	NOUN
ejpam-6466	737	8	derivative	derivative	NOUN
ejpam-6466	737	9	with	with	ADP
ejpam-6466	737	10	fixed	fix	VERB
ejpam-6466	737	11	memory	memory	NOUN
ejpam-6466	737	12	length	length	NOUN
ejpam-6466	737	13	.	.	PUNCT
ejpam-6466	738	1	mediterranean	mediterranean	PROPN
ejpam-6466	738	2	journal	journal	PROPN
ejpam-6466	738	3	of	of	ADP
ejpam-6466	738	4	mathematics	mathematic	NOUN
ejpam-6466	738	5	,	,	PUNCT
ejpam-6466	738	6	13(2):557–572	13(2):557–572	PROPN
ejpam-6466	738	7	,	,	PUNCT
ejpam-6466	738	8	2016	2016	NUM
ejpam-6466	738	9	.	.	PUNCT
ejpam-6466	739	1	[	[	X
ejpam-6466	739	2	14	14	NUM
ejpam-6466	739	3	]	]	X
ejpam-6466	739	4	c.	c.	PROPN
ejpam-6466	739	5	e.	e.	PROPN
ejpam-6466	739	6	t.	t.	PROPN
ejpam-6466	739	7	ledesma	ledesma	PROPN
ejpam-6466	739	8	and	and	CCONJ
ejpam-6466	739	9	m.	m.	PROPN
ejpam-6466	739	10	c.	c.	PROPN
ejpam-6466	739	11	m.	m.	PROPN
ejpam-6466	739	12	bonilla	bonilla	PROPN
ejpam-6466	739	13	.	.	PUNCT
ejpam-6466	740	1	fractional	fractional	ADJ
ejpam-6466	740	2	sobolev	sobolev	PROPN
ejpam-6466	740	3	space	space	NOUN
ejpam-6466	740	4	with	with	ADP
ejpam-6466	740	5	riemannliouville	riemannliouville	NOUN
ejpam-6466	740	6	fractional	fractional	ADJ
ejpam-6466	740	7	derivative	derivative	NOUN
ejpam-6466	740	8	and	and	CCONJ
ejpam-6466	740	9	application	application	NOUN
ejpam-6466	740	10	to	to	ADP
ejpam-6466	740	11	a	a	DET
ejpam-6466	740	12	fractional	fractional	ADJ
ejpam-6466	740	13	concave	concave	ADJ
ejpam-6466	740	14	-	-	PUNCT
ejpam-6466	740	15	convex	convex	NOUN
ejpam-6466	740	16	problem	problem	NOUN
ejpam-6466	740	17	.	.	PUNCT
ejpam-6466	741	1	advances	advance	NOUN
ejpam-6466	741	2	in	in	ADP
ejpam-6466	741	3	operator	operator	NOUN
ejpam-6466	741	4	theory	theory	NOUN
ejpam-6466	741	5	,	,	PUNCT
ejpam-6466	741	6	6(4):65	6(4):65	NOUN
ejpam-6466	741	7	,	,	PUNCT
ejpam-6466	741	8	2021	2021	NUM
ejpam-6466	741	9	.	.	PUNCT
ejpam-6466	742	1	[	[	X
ejpam-6466	742	2	15	15	NUM
ejpam-6466	742	3	]	]	X
ejpam-6466	742	4	majeed	majeed	PROPN
ejpam-6466	742	5	a.	a.	PROPN
ejpam-6466	742	6	yousif	yousif	PROPN
ejpam-6466	742	7	and	and	CCONJ
ejpam-6466	742	8	faraidun	faraidun	AUX
ejpam-6466	742	9	k.	k.	PROPN
ejpam-6466	742	10	hamasalh	hamasalh	PROPN
ejpam-6466	742	11	.	.	PUNCT
ejpam-6466	743	1	conformable	conformable	ADJ
ejpam-6466	743	2	non	non	ADJ
ejpam-6466	743	3	-	-	ADJ
ejpam-6466	743	4	polynomial	polynomial	ADJ
ejpam-6466	743	5	spline	spline	NOUN
ejpam-6466	743	6	method	method	NOUN
ejpam-6466	743	7	:	:	PUNCT
ejpam-6466	743	8	a	a	DET
ejpam-6466	743	9	robust	robust	ADJ
ejpam-6466	743	10	and	and	CCONJ
ejpam-6466	743	11	accurate	accurate	ADJ
ejpam-6466	743	12	numerical	numerical	ADJ
ejpam-6466	743	13	technique	technique	NOUN
ejpam-6466	743	14	.	.	PUNCT
ejpam-6466	744	1	ain	ain	PROPN
ejpam-6466	744	2	shams	sham	VERB
ejpam-6466	744	3	engineering	engineering	NOUN
ejpam-6466	744	4	journal	journal	NOUN
ejpam-6466	744	5	,	,	PUNCT
ejpam-6466	744	6	15(2):102415	15(2):102415	NUM
ejpam-6466	744	7	,	,	PUNCT
ejpam-6466	744	8	2024	2024	NUM
ejpam-6466	744	9	.	.	PUNCT
ejpam-6466	745	1	[	[	X
ejpam-6466	745	2	16	16	NUM
ejpam-6466	745	3	]	]	X
ejpam-6466	745	4	a.	a.	PROPN
ejpam-6466	745	5	khan	khan	PROPN
ejpam-6466	745	6	,	,	PUNCT
ejpam-6466	745	7	m.	m.	NOUN
ejpam-6466	745	8	i.	i.	PROPN
ejpam-6466	745	9	liaqat	liaqat	PROPN
ejpam-6466	745	10	,	,	PUNCT
ejpam-6466	745	11	m.	m.	NOUN
ejpam-6466	745	12	a.	a.	NOUN
ejpam-6466	745	13	alqudah	alqudah	PROPN
ejpam-6466	745	14	,	,	PUNCT
ejpam-6466	745	15	and	and	CCONJ
ejpam-6466	745	16	t.	t.	PROPN
ejpam-6466	745	17	abdeljawad	abdeljawad	NOUN
ejpam-6466	745	18	.	.	PUNCT
ejpam-6466	746	1	analysis	analysis	NOUN
ejpam-6466	746	2	of	of	ADP
ejpam-6466	746	3	the	the	DET
ejpam-6466	746	4	conformable	conformable	ADJ
ejpam-6466	746	5	temporal	temporal	ADJ
ejpam-6466	746	6	-	-	PUNCT
ejpam-6466	746	7	fractional	fractional	ADJ
ejpam-6466	746	8	swift	swift	ADJ
ejpam-6466	746	9	-	-	PUNCT
ejpam-6466	746	10	hohenberg	hohenberg	NOUN
ejpam-6466	746	11	equation	equation	NOUN
ejpam-6466	746	12	using	use	VERB
ejpam-6466	746	13	a	a	DET
ejpam-6466	746	14	novel	novel	ADJ
ejpam-6466	746	15	computational	computational	ADJ
ejpam-6466	746	16	technique	technique	NOUN
ejpam-6466	746	17	.	.	PUNCT
ejpam-6466	747	1	fractals	fractal	NOUN
ejpam-6466	747	2	,	,	PUNCT
ejpam-6466	747	3	31(04):2340050	31(04):2340050	NUM
ejpam-6466	747	4	,	,	PUNCT
ejpam-6466	747	5	2023	2023	NUM
ejpam-6466	747	6	.	.	PUNCT
ejpam-6466	748	1	[	[	X
ejpam-6466	748	2	17	17	NUM
ejpam-6466	748	3	]	]	X
ejpam-6466	748	4	w.	w.	PROPN
ejpam-6466	748	5	z.	z.	PROPN
ejpam-6466	748	6	wu	wu	PROPN
ejpam-6466	748	7	,	,	PUNCT
ejpam-6466	748	8	l.	l.	PROPN
ejpam-6466	748	9	zeng	zeng	PROPN
ejpam-6466	748	10	,	,	PUNCT
ejpam-6466	748	11	c.	c.	PROPN
ejpam-6466	748	12	liu	liu	PROPN
ejpam-6466	748	13	,	,	PUNCT
ejpam-6466	748	14	w.	w.	PROPN
ejpam-6466	748	15	xie	xie	PROPN
ejpam-6466	748	16	,	,	PUNCT
ejpam-6466	748	17	and	and	CCONJ
ejpam-6466	748	18	m.	m.	PROPN
ejpam-6466	748	19	goh	goh	PROPN
ejpam-6466	748	20	.	.	PUNCT
ejpam-6466	749	1	a	a	DET
ejpam-6466	749	2	time	time	NOUN
ejpam-6466	749	3	power	power	NOUN
ejpam-6466	749	4	-	-	PUNCT
ejpam-6466	749	5	based	base	VERB
ejpam-6466	749	6	grey	grey	PROPN
ejpam-6466	749	7	model	model	NOUN
ejpam-6466	749	8	with	with	ADP
ejpam-6466	749	9	conformable	conformable	ADJ
ejpam-6466	749	10	fractional	fractional	ADJ
ejpam-6466	749	11	derivative	derivative	NOUN
ejpam-6466	749	12	and	and	CCONJ
ejpam-6466	749	13	its	its	PRON
ejpam-6466	749	14	applications	application	NOUN
ejpam-6466	749	15	.	.	PUNCT
ejpam-6466	750	1	chaos	chaos	NOUN
ejpam-6466	750	2	,	,	PUNCT
ejpam-6466	750	3	solitons	soliton	NOUN
ejpam-6466	750	4	&	&	CCONJ
ejpam-6466	750	5	fractals	fractal	NOUN
ejpam-6466	750	6	,	,	PUNCT
ejpam-6466	750	7	155:111657	155:111657	NUM
ejpam-6466	750	8	,	,	PUNCT
ejpam-6466	750	9	2022	2022	NUM
ejpam-6466	750	10	.	.	PUNCT
ejpam-6466	751	1	[	[	X
ejpam-6466	751	2	18	18	NUM
ejpam-6466	751	3	]	]	PUNCT
ejpam-6466	751	4	m.	m.	NOUN
ejpam-6466	751	5	yavari	yavari	PROPN
ejpam-6466	751	6	and	and	CCONJ
ejpam-6466	751	7	a.	a.	NOUN
ejpam-6466	751	8	nazemi	nazemi	PROPN
ejpam-6466	751	9	.	.	PUNCT
ejpam-6466	752	1	on	on	ADP
ejpam-6466	752	2	fractional	fractional	ADJ
ejpam-6466	752	3	infinite	infinite	NOUN
ejpam-6466	752	4	-	-	PUNCT
ejpam-6466	752	5	horizon	horizon	NOUN
ejpam-6466	752	6	optimal	optimal	ADJ
ejpam-6466	752	7	control	control	NOUN
ejpam-6466	752	8	problems	problem	NOUN
ejpam-6466	752	9	with	with	ADP
ejpam-6466	752	10	a	a	DET
ejpam-6466	752	11	combination	combination	NOUN
ejpam-6466	752	12	of	of	ADP
ejpam-6466	752	13	conformable	conformable	NOUN
ejpam-6466	752	14	and	and	CCONJ
ejpam-6466	752	15	caputo	caputo	PROPN
ejpam-6466	752	16	-	-	PUNCT
ejpam-6466	752	17	fabrizio	fabrizio	PROPN
ejpam-6466	752	18	fractional	fractional	ADJ
ejpam-6466	752	19	derivatives	derivative	NOUN
ejpam-6466	752	20	.	.	PUNCT
ejpam-6466	753	1	isa	isa	NOUN
ejpam-6466	753	2	transactions	transaction	NOUN
ejpam-6466	753	3	,	,	PUNCT
ejpam-6466	753	4	101:78–90	101:78–90	PROPN
ejpam-6466	753	5	,	,	PUNCT
ejpam-6466	753	6	2020	2020	NUM
ejpam-6466	753	7	.	.	PUNCT
ejpam-6466	754	1	[	[	X
ejpam-6466	754	2	19	19	NUM
ejpam-6466	754	3	]	]	PUNCT
ejpam-6466	754	4	z.	z.	PROPN
ejpam-6466	754	5	korpinar	korpinar	PROPN
ejpam-6466	754	6	,	,	PUNCT
ejpam-6466	754	7	f.	f.	PROPN
ejpam-6466	754	8	tchier	tchier	PROPN
ejpam-6466	754	9	,	,	PUNCT
ejpam-6466	754	10	m.	m.	PROPN
ejpam-6466	754	11	inc	inc	PROPN
ejpam-6466	754	12	,	,	PUNCT
ejpam-6466	754	13	f.	f.	PROPN
ejpam-6466	754	14	bousbahi	bousbahi	PROPN
ejpam-6466	754	15	,	,	PUNCT
ejpam-6466	754	16	f.	f.	PROPN
ejpam-6466	754	17	m.	m.	PROPN
ejpam-6466	754	18	tawfiq	tawfiq	PROPN
ejpam-6466	754	19	,	,	PUNCT
ejpam-6466	754	20	and	and	CCONJ
ejpam-6466	754	21	m.	m.	NOUN
ejpam-6466	754	22	a.	a.	NOUN
ejpam-6466	754	23	akinlar	akinlar	PROPN
ejpam-6466	754	24	.	.	PUNCT
ejpam-6466	755	1	applicability	applicability	NOUN
ejpam-6466	755	2	of	of	ADP
ejpam-6466	755	3	time	time	NOUN
ejpam-6466	755	4	conformable	conformable	ADJ
ejpam-6466	755	5	derivative	derivative	NOUN
ejpam-6466	755	6	to	to	ADP
ejpam-6466	755	7	wick	wick	NOUN
ejpam-6466	755	8	-	-	PUNCT
ejpam-6466	755	9	fractional	fractional	ADJ
ejpam-6466	755	10	-	-	PUNCT
ejpam-6466	755	11	stochastic	stochastic	NOUN
ejpam-6466	755	12	pdes	pde	NOUN
ejpam-6466	755	13	.	.	PUNCT
ejpam-6466	756	1	alexandria	alexandria	PROPN
ejpam-6466	756	2	engineering	engineering	PROPN
ejpam-6466	756	3	journal	journal	PROPN
ejpam-6466	756	4	,	,	PUNCT
ejpam-6466	756	5	59(3):1485–1493	59(3):1485–1493	NUM
ejpam-6466	756	6	,	,	PUNCT
ejpam-6466	756	7	2020	2020	NUM
ejpam-6466	756	8	.	.	PUNCT
ejpam-6466	757	1	[	[	X
ejpam-6466	757	2	20	20	NUM
ejpam-6466	757	3	]	]	PUNCT
ejpam-6466	757	4	s.	s.	PROPN
ejpam-6466	757	5	albosaily	albosaily	PROPN
ejpam-6466	757	6	,	,	PUNCT
ejpam-6466	757	7	e.	e.	PROPN
ejpam-6466	757	8	m.	m.	PROPN
ejpam-6466	757	9	elsayed	elsaye	VERB
ejpam-6466	757	10	,	,	PUNCT
ejpam-6466	757	11	m.	m.	PROPN
ejpam-6466	757	12	d.	d.	PROPN
ejpam-6466	757	13	albalwi	albalwi	PROPN
ejpam-6466	757	14	,	,	PUNCT
ejpam-6466	757	15	m.	m.	NOUN
ejpam-6466	757	16	alesemi	alesemi	PROPN
ejpam-6466	757	17	,	,	PUNCT
ejpam-6466	757	18	and	and	CCONJ
ejpam-6466	757	19	w.	w.	PROPN
ejpam-6466	757	20	w.	w.	PROPN
ejpam-6466	757	21	mohammed	mohammed	PROPN
ejpam-6466	757	22	.	.	PUNCT
ejpam-6466	758	1	the	the	DET
ejpam-6466	758	2	analytical	analytical	ADJ
ejpam-6466	758	3	stochastic	stochastic	ADJ
ejpam-6466	758	4	solutions	solution	NOUN
ejpam-6466	758	5	for	for	ADP
ejpam-6466	758	6	the	the	DET
ejpam-6466	758	7	stochastic	stochastic	ADJ
ejpam-6466	758	8	potential	potential	ADJ
ejpam-6466	758	9	yu	yu	PROPN
ejpam-6466	758	10	-	-	PUNCT
ejpam-6466	758	11	toda	toda	NOUN
ejpam-6466	758	12	-	-	PUNCT
ejpam-6466	758	13	sasa	sasa	NOUN
ejpam-6466	758	14	-	-	PUNCT
ejpam-6466	758	15	fukuyama	fukuyama	PROPN
ejpam-6466	758	16	equation	equation	NOUN
ejpam-6466	758	17	with	with	ADP
ejpam-6466	758	18	conformable	conformable	ADJ
ejpam-6466	758	19	derivative	derivative	NOUN
ejpam-6466	758	20	using	use	VERB
ejpam-6466	758	21	different	different	ADJ
ejpam-6466	758	22	methods	method	NOUN
ejpam-6466	758	23	.	.	PUNCT
ejpam-6466	759	1	fractal	fractal	ADJ
ejpam-6466	759	2	and	and	CCONJ
ejpam-6466	759	3	fractional	fractional	ADJ
ejpam-6466	759	4	,	,	PUNCT
ejpam-6466	759	5	7(11):787	7(11):787	NUM
ejpam-6466	759	6	,	,	PUNCT
ejpam-6466	759	7	2023	2023	NUM
ejpam-6466	759	8	.	.	PUNCT
ejpam-6466	760	1	[	[	X
ejpam-6466	760	2	21	21	NUM
ejpam-6466	760	3	]	]	X
ejpam-6466	760	4	s.	s.	PROPN
ejpam-6466	760	5	li	li	PROPN
ejpam-6466	760	6	,	,	PUNCT
ejpam-6466	760	7	s.	s.	PROPN
ejpam-6466	760	8	u.	u.	PROPN
ejpam-6466	760	9	khan	khan	PROPN
ejpam-6466	760	10	,	,	PUNCT
ejpam-6466	760	11	m.	m.	PROPN
ejpam-6466	760	12	b.	b.	PROPN
ejpam-6466	760	13	riaz	riaz	PROPN
ejpam-6466	760	14	,	,	PUNCT
ejpam-6466	760	15	s.	s.	PROPN
ejpam-6466	760	16	a.	a.	PROPN
ejpam-6466	760	17	alqahtani	alqahtani	PROPN
ejpam-6466	760	18	,	,	PUNCT
ejpam-6466	760	19	and	and	CCONJ
ejpam-6466	760	20	a.	a.	NOUN
ejpam-6466	760	21	m.	m.	NOUN
ejpam-6466	760	22	alamri	alamri	PROPN
ejpam-6466	760	23	.	.	PUNCT
ejpam-6466	761	1	numerical	numerical	PROPN
ejpam-6466	761	2	simulation	simulation	PROPN
ejpam-6466	761	3	of	of	ADP
ejpam-6466	761	4	a	a	DET
ejpam-6466	761	5	fractional	fractional	ADJ
ejpam-6466	761	6	stochastic	stochastic	ADJ
ejpam-6466	761	7	delay	delay	NOUN
ejpam-6466	761	8	differential	differential	NOUN
ejpam-6466	761	9	equations	equation	NOUN
ejpam-6466	761	10	using	use	VERB
ejpam-6466	761	11	spectral	spectral	ADJ
ejpam-6466	761	12	scheme	scheme	NOUN
ejpam-6466	761	13	:	:	PUNCT
ejpam-6466	761	14	a	a	DET
ejpam-6466	761	15	comprehensive	comprehensive	ADJ
ejpam-6466	761	16	stability	stability	NOUN
ejpam-6466	761	17	analysis	analysis	NOUN
ejpam-6466	761	18	.	.	PUNCT
ejpam-6466	762	1	scientific	scientific	ADJ
ejpam-6466	762	2	reports	report	NOUN
ejpam-6466	762	3	,	,	PUNCT
ejpam-6466	762	4	14(1):6930	14(1):6930	NUM
ejpam-6466	762	5	,	,	PUNCT
ejpam-6466	762	6	2024	2024	NUM
ejpam-6466	762	7	.	.	PUNCT
ejpam-6466	763	1	[	[	X
ejpam-6466	763	2	22	22	NUM
ejpam-6466	763	3	]	]	X
ejpam-6466	763	4	q.	q.	PROPN
ejpam-6466	763	5	wang	wang	PROPN
ejpam-6466	763	6	,	,	PUNCT
ejpam-6466	763	7	f.	f.	PROPN
ejpam-6466	763	8	chen	chen	PROPN
ejpam-6466	763	9	,	,	PUNCT
ejpam-6466	763	10	and	and	CCONJ
ejpam-6466	763	11	f.	f.	PROPN
ejpam-6466	763	12	huang	huang	PROPN
ejpam-6466	763	13	.	.	PUNCT
ejpam-6466	764	1	maximum	maximum	ADJ
ejpam-6466	764	2	principle	principle	NOUN
ejpam-6466	764	3	for	for	ADP
ejpam-6466	764	4	optimal	optimal	ADJ
ejpam-6466	764	5	control	control	NOUN
ejpam-6466	764	6	problem	problem	NOUN
ejpam-6466	764	7	of	of	ADP
ejpam-6466	764	8	stochastic	stochastic	ADJ
ejpam-6466	764	9	delay	delay	NOUN
ejpam-6466	764	10	differential	differential	NOUN
ejpam-6466	764	11	equations	equation	NOUN
ejpam-6466	764	12	driven	drive	VERB
ejpam-6466	764	13	by	by	ADP
ejpam-6466	764	14	fractional	fractional	ADJ
ejpam-6466	764	15	brownian	brownian	ADJ
ejpam-6466	764	16	motions	motion	NOUN
ejpam-6466	764	17	.	.	PUNCT
ejpam-6466	765	1	optimal	optimal	ADJ
ejpam-6466	765	2	control	control	NOUN
ejpam-6466	765	3	applications	application	NOUN
ejpam-6466	765	4	and	and	CCONJ
ejpam-6466	765	5	methods	method	NOUN
ejpam-6466	765	6	,	,	PUNCT
ejpam-6466	765	7	37(1):90–107	37(1):90–107	NUM
ejpam-6466	765	8	,	,	PUNCT
ejpam-6466	765	9	2016	2016	NUM
ejpam-6466	765	10	.	.	PUNCT
ejpam-6466	766	1	[	[	X
ejpam-6466	766	2	23	23	NUM
ejpam-6466	766	3	]	]	X
ejpam-6466	766	4	o.	o.	PROPN
ejpam-6466	766	5	kahouli	kahouli	PROPN
ejpam-6466	766	6	,	,	PUNCT
ejpam-6466	766	7	s.	s.	PROPN
ejpam-6466	766	8	albadran	albadran	PROPN
ejpam-6466	766	9	,	,	PUNCT
ejpam-6466	766	10	z.	z.	PROPN
ejpam-6466	766	11	elleuch	elleuch	PROPN
ejpam-6466	766	12	,	,	PUNCT
ejpam-6466	766	13	y.	y.	PROPN
ejpam-6466	766	14	bouteraa	bouteraa	NOUN
ejpam-6466	766	15	,	,	PUNCT
ejpam-6466	766	16	and	and	CCONJ
ejpam-6466	766	17	a.	a.	PROPN
ejpam-6466	766	18	b.	b.	PROPN
ejpam-6466	766	19	makhlouf	makhlouf	PROPN
ejpam-6466	766	20	.	.	PUNCT
ejpam-6466	767	1	stability	stability	NOUN
ejpam-6466	767	2	results	result	VERB
ejpam-6466	767	3	for	for	ADP
ejpam-6466	767	4	neutral	neutral	ADJ
ejpam-6466	767	5	fractional	fractional	ADJ
ejpam-6466	767	6	stochastic	stochastic	ADJ
ejpam-6466	767	7	differential	differential	ADJ
ejpam-6466	767	8	equations	equation	NOUN
ejpam-6466	767	9	.	.	PUNCT
ejpam-6466	768	1	aims	aim	VERB
ejpam-6466	768	2	math	math	NOUN
ejpam-6466	768	3	,	,	PUNCT
ejpam-6466	768	4	9(2):3253	9(2):3253	NUM
ejpam-6466	768	5	–	–	PUNCT
ejpam-6466	768	6	3263	3263	NUM
ejpam-6466	768	7	,	,	PUNCT
ejpam-6466	768	8	2024	2024	NUM
ejpam-6466	768	9	.	.	PUNCT
ejpam-6466	769	1	[	[	X
ejpam-6466	769	2	24	24	NUM
ejpam-6466	769	3	]	]	PUNCT
ejpam-6466	769	4	a.	a.	PROPN
ejpam-6466	769	5	ali	ali	PROPN
ejpam-6466	769	6	,	,	PUNCT
ejpam-6466	769	7	k.	k.	PROPN
ejpam-6466	769	8	hayat	hayat	PROPN
ejpam-6466	769	9	,	,	PUNCT
ejpam-6466	769	10	a.	a.	NOUN
ejpam-6466	769	11	zahir	zahir	PROPN
ejpam-6466	769	12	,	,	PUNCT
ejpam-6466	769	13	k.	k.	PROPN
ejpam-6466	769	14	shah	shah	PROPN
ejpam-6466	769	15	,	,	PUNCT
ejpam-6466	769	16	and	and	CCONJ
ejpam-6466	769	17	t.	t.	PROPN
ejpam-6466	769	18	abdeljawad	abdeljawad	NOUN
ejpam-6466	769	19	.	.	PUNCT
ejpam-6466	770	1	qualitative	qualitative	ADJ
ejpam-6466	770	2	analysis	analysis	NOUN
ejpam-6466	770	3	of	of	ADP
ejpam-6466	770	4	fractional	fractional	ADJ
ejpam-6466	770	5	stochastic	stochastic	ADJ
ejpam-6466	770	6	differential	differential	ADJ
ejpam-6466	770	7	equations	equation	NOUN
ejpam-6466	770	8	with	with	ADP
ejpam-6466	770	9	variable	variable	ADJ
ejpam-6466	770	10	order	order	NOUN
ejpam-6466	770	11	fractional	fractional	ADJ
ejpam-6466	770	12	derivative	derivative	ADJ
ejpam-6466	770	13	.	.	PUNCT
ejpam-6466	771	1	qualitative	qualitative	ADJ
ejpam-6466	771	2	theory	theory	NOUN
ejpam-6466	771	3	of	of	ADP
ejpam-6466	771	4	dynamical	dynamical	ADJ
ejpam-6466	771	5	systems	system	NOUN
ejpam-6466	771	6	,	,	PUNCT
ejpam-6466	771	7	23(3):120	23(3):120	NUM
ejpam-6466	771	8	,	,	PUNCT
ejpam-6466	771	9	2024	2024	NUM
ejpam-6466	771	10	.	.	PUNCT
ejpam-6466	772	1	m.	m.	NOUN
ejpam-6466	772	2	i.	i.	PROPN
ejpam-6466	772	3	liaqat	liaqat	PROPN
ejpam-6466	772	4	et	et	PROPN
ejpam-6466	772	5	al	al	PROPN
ejpam-6466	772	6	.	.	PUNCT
ejpam-6466	772	7	/	/	SYM
ejpam-6466	772	8	eur	eur	PROPN
ejpam-6466	772	9	.	.	PUNCT
ejpam-6466	773	1	j.	j.	PROPN
ejpam-6466	773	2	pure	pure	PROPN
ejpam-6466	773	3	appl	appl	PROPN
ejpam-6466	773	4	.	.	PROPN
ejpam-6466	773	5	math	math	PROPN
ejpam-6466	773	6	,	,	PUNCT
ejpam-6466	773	7	18	18	NUM
ejpam-6466	773	8	(	(	PUNCT
ejpam-6466	773	9	4	4	NUM
ejpam-6466	773	10	)	)	PUNCT
ejpam-6466	773	11	(	(	PUNCT
ejpam-6466	773	12	2025	2025	NUM
ejpam-6466	773	13	)	)	PUNCT
ejpam-6466	773	14	,	,	PUNCT
ejpam-6466	773	15	6466	6466	NUM
ejpam-6466	773	16	28	28	NUM
ejpam-6466	773	17	of	of	ADP
ejpam-6466	773	18	28	28	NUM
ejpam-6466	774	1	[	[	X
ejpam-6466	774	2	25	25	NUM
ejpam-6466	774	3	]	]	PUNCT
ejpam-6466	774	4	a.	a.	NOUN
ejpam-6466	774	5	raheem	raheem	PROPN
ejpam-6466	774	6	,	,	PUNCT
ejpam-6466	774	7	f.	f.	PROPN
ejpam-6466	774	8	m.	m.	PROPN
ejpam-6466	774	9	alamrani	alamrani	PROPN
ejpam-6466	774	10	,	,	PUNCT
ejpam-6466	774	11	j.	j.	PROPN
ejpam-6466	774	12	akhtar	akhtar	PROPN
ejpam-6466	774	13	,	,	PUNCT
ejpam-6466	774	14	a.	a.	PROPN
ejpam-6466	774	15	alatawi	alatawi	PROPN
ejpam-6466	774	16	,	,	PUNCT
ejpam-6466	774	17	e.	e.	PROPN
ejpam-6466	774	18	alshaban	alshaban	PROPN
ejpam-6466	774	19	,	,	PUNCT
ejpam-6466	774	20	a.	a.	NOUN
ejpam-6466	774	21	khatoon	khatoon	PROPN
ejpam-6466	774	22	,	,	PUNCT
ejpam-6466	774	23	and	and	CCONJ
ejpam-6466	774	24	f.	f.	PROPN
ejpam-6466	774	25	a.	a.	PROPN
ejpam-6466	774	26	khan	khan	PROPN
ejpam-6466	774	27	.	.	PUNCT
ejpam-6466	775	1	study	study	NOUN
ejpam-6466	775	2	on	on	ADP
ejpam-6466	775	3	controllability	controllability	NOUN
ejpam-6466	775	4	for	for	ADP
ejpam-6466	775	5	ψ	ψ	NOUN
ejpam-6466	775	6	-	-	ADJ
ejpam-6466	775	7	hilfer	hilfer	NOUN
ejpam-6466	775	8	fractional	fractional	ADJ
ejpam-6466	775	9	stochastic	stochastic	ADJ
ejpam-6466	775	10	differential	differential	ADJ
ejpam-6466	775	11	equations	equation	NOUN
ejpam-6466	775	12	.	.	PUNCT
ejpam-6466	776	1	fractal	fractal	PROPN
ejpam-6466	776	2	and	and	CCONJ
ejpam-6466	776	3	fractional	fractional	ADJ
ejpam-6466	776	4	,	,	PUNCT
ejpam-6466	776	5	8(12):727	8(12):727	NUM
ejpam-6466	776	6	,	,	PUNCT
ejpam-6466	776	7	2024	2024	NUM
ejpam-6466	776	8	.	.	PUNCT
ejpam-6466	777	1	[	[	X
ejpam-6466	777	2	26	26	NUM
ejpam-6466	777	3	]	]	PUNCT
ejpam-6466	777	4	k.	k.	PROPN
ejpam-6466	777	5	ramkumar	ramkumar	PROPN
ejpam-6466	777	6	,	,	PUNCT
ejpam-6466	777	7	k.	k.	PROPN
ejpam-6466	777	8	ravikumar	ravikumar	PROPN
ejpam-6466	777	9	,	,	PUNCT
ejpam-6466	777	10	and	and	CCONJ
ejpam-6466	777	11	s.	s.	PROPN
ejpam-6466	777	12	varshini	varshini	PROPN
ejpam-6466	777	13	.	.	PUNCT
ejpam-6466	778	1	fractional	fractional	ADJ
ejpam-6466	778	2	neutral	neutral	ADJ
ejpam-6466	778	3	stochastic	stochastic	ADJ
ejpam-6466	778	4	differential	differential	ADJ
ejpam-6466	778	5	equations	equation	NOUN
ejpam-6466	778	6	with	with	ADP
ejpam-6466	778	7	caputo	caputo	PROPN
ejpam-6466	778	8	fractional	fractional	PROPN
ejpam-6466	778	9	derivative	derivative	NOUN
ejpam-6466	778	10	:	:	PUNCT
ejpam-6466	778	11	fractional	fractional	ADJ
ejpam-6466	778	12	brownian	brownian	ADJ
ejpam-6466	778	13	motion	motion	NOUN
ejpam-6466	778	14	,	,	PUNCT
ejpam-6466	778	15	poisson	poisson	PROPN
ejpam-6466	778	16	jumps	jump	VERB
ejpam-6466	778	17	,	,	PUNCT
ejpam-6466	778	18	and	and	CCONJ
ejpam-6466	778	19	optimal	optimal	ADJ
ejpam-6466	778	20	control	control	NOUN
ejpam-6466	778	21	.	.	PUNCT
ejpam-6466	779	1	stochastic	stochastic	ADJ
ejpam-6466	779	2	analysis	analysis	NOUN
ejpam-6466	779	3	and	and	CCONJ
ejpam-6466	779	4	applications	application	NOUN
ejpam-6466	779	5	,	,	PUNCT
ejpam-6466	779	6	39(1):157	39(1):157	NUM
ejpam-6466	779	7	–	–	PUNCT
ejpam-6466	779	8	176	176	NUM
ejpam-6466	779	9	,	,	PUNCT
ejpam-6466	779	10	2021	2021	NUM
ejpam-6466	779	11	.	.	PUNCT
ejpam-6466	780	1	[	[	X
ejpam-6466	780	2	27	27	NUM
ejpam-6466	780	3	]	]	PUNCT
ejpam-6466	780	4	a.	a.	PROPN
ejpam-6466	780	5	mohammed	mohammed	PROPN
ejpam-6466	780	6	djaouti	djaouti	PROPN
ejpam-6466	780	7	and	and	CCONJ
ejpam-6466	780	8	m.	m.	NOUN
ejpam-6466	780	9	imran	imran	PROPN
ejpam-6466	780	10	liaqat	liaqat	PROPN
ejpam-6466	780	11	.	.	PUNCT
ejpam-6466	781	1	qualitative	qualitative	ADJ
ejpam-6466	781	2	analysis	analysis	NOUN
ejpam-6466	781	3	for	for	ADP
ejpam-6466	781	4	the	the	DET
ejpam-6466	781	5	solutions	solution	NOUN
ejpam-6466	781	6	of	of	ADP
ejpam-6466	781	7	fractional	fractional	ADJ
ejpam-6466	781	8	stochastic	stochastic	ADJ
ejpam-6466	781	9	differential	differential	ADJ
ejpam-6466	781	10	equations	equation	NOUN
ejpam-6466	781	11	.	.	PUNCT
ejpam-6466	782	1	axioms	axiom	NOUN
ejpam-6466	782	2	,	,	PUNCT
ejpam-6466	782	3	13(7):438	13(7):438	NOUN
ejpam-6466	782	4	,	,	PUNCT
ejpam-6466	782	5	2024	2024	NUM
ejpam-6466	782	6	.	.	PUNCT
ejpam-6466	783	1	[	[	X
ejpam-6466	783	2	28	28	NUM
ejpam-6466	783	3	]	]	X
ejpam-6466	783	4	z.	z.	PROPN
ejpam-6466	783	5	ali	ali	PROPN
ejpam-6466	783	6	,	,	PUNCT
ejpam-6466	783	7	m.	m.	NOUN
ejpam-6466	783	8	a.	a.	NOUN
ejpam-6466	783	9	abebe	abebe	PROPN
ejpam-6466	783	10	,	,	PUNCT
ejpam-6466	783	11	and	and	CCONJ
ejpam-6466	783	12	t.	t.	PROPN
ejpam-6466	783	13	nazir	nazir	PROPN
ejpam-6466	783	14	.	.	PUNCT
ejpam-6466	784	1	strong	strong	ADJ
ejpam-6466	784	2	convergence	convergence	NOUN
ejpam-6466	784	3	of	of	ADP
ejpam-6466	784	4	euler	euler	NOUN
ejpam-6466	784	5	-	-	PUNCT
ejpam-6466	784	6	type	type	NOUN
ejpam-6466	784	7	methods	method	NOUN
ejpam-6466	784	8	for	for	ADP
ejpam-6466	784	9	nonlinear	nonlinear	ADJ
ejpam-6466	784	10	fractional	fractional	ADJ
ejpam-6466	784	11	stochastic	stochastic	ADJ
ejpam-6466	784	12	differential	differential	ADJ
ejpam-6466	784	13	equations	equation	NOUN
ejpam-6466	784	14	without	without	ADP
ejpam-6466	784	15	singular	singular	ADJ
ejpam-6466	784	16	kernel	kernel	NOUN
ejpam-6466	784	17	.	.	PUNCT
ejpam-6466	785	1	mathematics	mathematic	NOUN
ejpam-6466	785	2	,	,	PUNCT
ejpam-6466	785	3	12(18	12(18	NUM
ejpam-6466	785	4	)	)	PUNCT
ejpam-6466	785	5	,	,	PUNCT
ejpam-6466	785	6	2024	2024	NUM
ejpam-6466	785	7	.	.	PUNCT
ejpam-6466	786	1	[	[	X
ejpam-6466	786	2	29	29	NUM
ejpam-6466	786	3	]	]	PUNCT
ejpam-6466	786	4	m.	m.	NOUN
ejpam-6466	786	5	lavanya	lavanya	NOUN
ejpam-6466	786	6	and	and	CCONJ
ejpam-6466	786	7	b.	b.	PROPN
ejpam-6466	786	8	s.	s.	PROPN
ejpam-6466	786	9	vadivoo	vadivoo	PROPN
ejpam-6466	786	10	.	.	PUNCT
ejpam-6466	787	1	analysis	analysis	NOUN
ejpam-6466	787	2	of	of	ADP
ejpam-6466	787	3	controllability	controllability	NOUN
ejpam-6466	787	4	in	in	ADP
ejpam-6466	787	5	caputo	caputo	PROPN
ejpam-6466	787	6	-	-	PUNCT
ejpam-6466	787	7	hadamard	hadamard	PROPN
ejpam-6466	787	8	stochastic	stochastic	ADJ
ejpam-6466	787	9	fractional	fractional	ADJ
ejpam-6466	787	10	differential	differential	ADJ
ejpam-6466	787	11	equations	equation	NOUN
ejpam-6466	787	12	with	with	ADP
ejpam-6466	787	13	fractional	fractional	ADJ
ejpam-6466	787	14	brownian	brownian	ADJ
ejpam-6466	787	15	motion	motion	NOUN
ejpam-6466	787	16	.	.	PUNCT
ejpam-6466	788	1	international	international	ADJ
ejpam-6466	788	2	journal	journal	PROPN
ejpam-6466	788	3	of	of	ADP
ejpam-6466	788	4	dynamics	dynamic	NOUN
ejpam-6466	788	5	and	and	CCONJ
ejpam-6466	788	6	control	control	NOUN
ejpam-6466	788	7	,	,	PUNCT
ejpam-6466	788	8	12(1):15–23	12(1):15–23	NUM
ejpam-6466	788	9	,	,	PUNCT
ejpam-6466	788	10	2024	2024	NUM
ejpam-6466	788	11	.	.	PUNCT
ejpam-6466	789	1	[	[	X
ejpam-6466	789	2	30	30	NUM
ejpam-6466	789	3	]	]	X
ejpam-6466	789	4	s.	s.	PROPN
ejpam-6466	789	5	moualkia	moualkia	PROPN
ejpam-6466	789	6	and	and	CCONJ
ejpam-6466	789	7	y.	y.	PROPN
ejpam-6466	789	8	xu	xu	PROPN
ejpam-6466	789	9	.	.	PUNCT
ejpam-6466	790	1	on	on	ADP
ejpam-6466	790	2	the	the	DET
ejpam-6466	790	3	existence	existence	NOUN
ejpam-6466	790	4	and	and	CCONJ
ejpam-6466	790	5	uniqueness	uniqueness	NOUN
ejpam-6466	790	6	of	of	ADP
ejpam-6466	790	7	solutions	solution	NOUN
ejpam-6466	790	8	for	for	ADP
ejpam-6466	790	9	multidimensional	multidimensional	ADJ
ejpam-6466	790	10	fractional	fractional	ADJ
ejpam-6466	790	11	stochastic	stochastic	ADJ
ejpam-6466	790	12	differential	differential	ADJ
ejpam-6466	790	13	equations	equation	NOUN
ejpam-6466	790	14	with	with	ADP
ejpam-6466	790	15	variable	variable	ADJ
ejpam-6466	790	16	order	order	NOUN
ejpam-6466	790	17	.	.	PUNCT
ejpam-6466	791	1	mathematics	mathematic	NOUN
ejpam-6466	791	2	,	,	PUNCT
ejpam-6466	791	3	9(17):2106	9(17):2106	NOUN
ejpam-6466	791	4	,	,	PUNCT
ejpam-6466	791	5	2021	2021	NUM
ejpam-6466	791	6	.	.	PUNCT
ejpam-6466	792	1	[	[	X
ejpam-6466	792	2	31	31	NUM
ejpam-6466	792	3	]	]	X
ejpam-6466	792	4	c.	c.	PROPN
ejpam-6466	792	5	liping	liping	PROPN
ejpam-6466	792	6	,	,	PUNCT
ejpam-6466	792	7	m.	m.	NOUN
ejpam-6466	792	8	a.	a.	PROPN
ejpam-6466	792	9	khan	khan	PROPN
ejpam-6466	792	10	,	,	PUNCT
ejpam-6466	792	11	a.	a.	PROPN
ejpam-6466	792	12	atangana	atangana	PROPN
ejpam-6466	792	13	,	,	PUNCT
ejpam-6466	792	14	and	and	CCONJ
ejpam-6466	792	15	s.	s.	PROPN
ejpam-6466	792	16	kumar	kumar	PROPN
ejpam-6466	792	17	.	.	PUNCT
ejpam-6466	793	1	a	a	DET
ejpam-6466	793	2	new	new	ADJ
ejpam-6466	793	3	financial	financial	ADJ
ejpam-6466	793	4	chaotic	chaotic	ADJ
ejpam-6466	793	5	model	model	NOUN
ejpam-6466	793	6	in	in	ADP
ejpam-6466	793	7	atangana	atangana	PROPN
ejpam-6466	793	8	-	-	PUNCT
ejpam-6466	793	9	baleanu	baleanu	PROPN
ejpam-6466	793	10	stochastic	stochastic	ADJ
ejpam-6466	793	11	fractional	fractional	ADJ
ejpam-6466	793	12	differential	differential	NOUN
ejpam-6466	793	13	equations	equation	NOUN
ejpam-6466	793	14	.	.	PUNCT
ejpam-6466	794	1	alexandria	alexandria	PROPN
ejpam-6466	794	2	engineering	engineering	PROPN
ejpam-6466	794	3	journal	journal	PROPN
ejpam-6466	794	4	,	,	PUNCT
ejpam-6466	794	5	60(6):5193–5204	60(6):5193–5204	NUM
ejpam-6466	794	6	,	,	PUNCT
ejpam-6466	794	7	2021	2021	NUM
ejpam-6466	794	8	.	.	PUNCT
ejpam-6466	795	1	[	[	X
ejpam-6466	795	2	32	32	NUM
ejpam-6466	795	3	]	]	PUNCT
ejpam-6466	795	4	m.	m.	NOUN
ejpam-6466	795	5	abouagwa	abouagwa	PROPN
ejpam-6466	795	6	,	,	PUNCT
ejpam-6466	795	7	f.	f.	PROPN
ejpam-6466	795	8	cheng	cheng	PROPN
ejpam-6466	795	9	,	,	PUNCT
ejpam-6466	795	10	and	and	CCONJ
ejpam-6466	795	11	j.	j.	PROPN
ejpam-6466	795	12	li	li	PROPN
ejpam-6466	795	13	.	.	PROPN
ejpam-6466	795	14	impulsive	impulsive	ADJ
ejpam-6466	795	15	stochastic	stochastic	ADJ
ejpam-6466	795	16	fractional	fractional	ADJ
ejpam-6466	795	17	differential	differential	ADJ
ejpam-6466	795	18	equations	equation	NOUN
ejpam-6466	795	19	driven	drive	VERB
ejpam-6466	795	20	by	by	ADP
ejpam-6466	795	21	fractional	fractional	ADJ
ejpam-6466	795	22	brownian	brownian	ADJ
ejpam-6466	795	23	motion	motion	NOUN
ejpam-6466	795	24	.	.	PUNCT
ejpam-6466	796	1	advances	advance	NOUN
ejpam-6466	796	2	in	in	ADP
ejpam-6466	796	3	difference	difference	NOUN
ejpam-6466	796	4	equations	equation	NOUN
ejpam-6466	796	5	,	,	PUNCT
ejpam-6466	796	6	2020(1):57	2020(1):57	NUM
ejpam-6466	796	7	,	,	PUNCT
ejpam-6466	796	8	2020	2020	NUM
ejpam-6466	796	9	.	.	PUNCT
ejpam-6466	797	1	[	[	X
ejpam-6466	797	2	33	33	NUM
ejpam-6466	797	3	]	]	PUNCT
ejpam-6466	797	4	j.	j.	PROPN
ejpam-6466	797	5	a.	a.	PROPN
ejpam-6466	797	6	asadzade	asadzade	PROPN
ejpam-6466	797	7	and	and	CCONJ
ejpam-6466	797	8	n.	n.	PROPN
ejpam-6466	797	9	i.	i.	PROPN
ejpam-6466	797	10	mahmudov	mahmudov	PROPN
ejpam-6466	797	11	.	.	PUNCT
ejpam-6466	798	1	finite	finite	PROPN
ejpam-6466	798	2	time	time	NOUN
ejpam-6466	798	3	stability	stability	NOUN
ejpam-6466	798	4	analysis	analysis	NOUN
ejpam-6466	798	5	for	for	ADP
ejpam-6466	798	6	fractional	fractional	ADJ
ejpam-6466	798	7	stochastic	stochastic	ADJ
ejpam-6466	798	8	neutral	neutral	ADJ
ejpam-6466	798	9	delay	delay	NOUN
ejpam-6466	798	10	differential	differential	NOUN
ejpam-6466	798	11	equations	equation	NOUN
ejpam-6466	798	12	.	.	PUNCT
ejpam-6466	799	1	journal	journal	PROPN
ejpam-6466	799	2	of	of	ADP
ejpam-6466	799	3	applied	apply	VERB
ejpam-6466	799	4	mathematics	mathematic	NOUN
ejpam-6466	799	5	and	and	CCONJ
ejpam-6466	799	6	computing	computing	NOUN
ejpam-6466	799	7	,	,	PUNCT
ejpam-6466	799	8	70(6):5293–5317	70(6):5293–5317	NUM
ejpam-6466	799	9	,	,	PUNCT
ejpam-6466	799	10	2024	2024	NUM
ejpam-6466	799	11	.	.	PUNCT
ejpam-6466	800	1	[	[	X
ejpam-6466	800	2	34	34	NUM
ejpam-6466	800	3	]	]	X
ejpam-6466	800	4	x.	x.	NOUN
ejpam-6466	800	5	mao	mao	PROPN
ejpam-6466	800	6	.	.	PUNCT
ejpam-6466	801	1	stochastic	stochastic	ADJ
ejpam-6466	801	2	differential	differential	ADJ
ejpam-6466	801	3	equations	equation	NOUN
ejpam-6466	801	4	and	and	CCONJ
ejpam-6466	801	5	applications	application	NOUN
ejpam-6466	801	6	.	.	PUNCT
ejpam-6466	802	1	elsevier	elsevier	NOUN
ejpam-6466	802	2	,	,	PUNCT
ejpam-6466	802	3	2007	2007	NUM
ejpam-6466	802	4	.	.	PUNCT
ejpam-6466	803	1	[	[	X
ejpam-6466	803	2	35	35	NUM
ejpam-6466	803	3	]	]	X
ejpam-6466	803	4	f.	f.	PROPN
ejpam-6466	803	5	m.	m.	PROPN
ejpam-6466	803	6	atay	atay	PROPN
ejpam-6466	803	7	,	,	PUNCT
ejpam-6466	803	8	editor	editor	NOUN
ejpam-6466	803	9	.	.	PUNCT
ejpam-6466	804	1	complex	complex	ADJ
ejpam-6466	804	2	time	time	NOUN
ejpam-6466	804	3	-	-	PUNCT
ejpam-6466	804	4	delay	delay	NOUN
ejpam-6466	804	5	systems	system	NOUN
ejpam-6466	804	6	:	:	PUNCT
ejpam-6466	804	7	theory	theory	NOUN
ejpam-6466	804	8	and	and	CCONJ
ejpam-6466	804	9	applications	application	NOUN
ejpam-6466	804	10	.	.	PUNCT
ejpam-6466	805	1	springer	springer	NOUN
ejpam-6466	805	2	,	,	PUNCT
ejpam-6466	805	3	2010	2010	NUM
ejpam-6466	805	4	.	.	PUNCT
ejpam-6466	806	1	[	[	X
ejpam-6466	806	2	36	36	NUM
ejpam-6466	806	3	]	]	X
ejpam-6466	806	4	d.	d.	PROPN
ejpam-6466	806	5	chowdhury	chowdhury	PROPN
ejpam-6466	806	6	,	,	PUNCT
ejpam-6466	806	7	l.	l.	PROPN
ejpam-6466	806	8	santen	santen	PROPN
ejpam-6466	806	9	,	,	PUNCT
ejpam-6466	806	10	and	and	CCONJ
ejpam-6466	806	11	a.	a.	NOUN
ejpam-6466	806	12	schadschneider	schadschneider	NOUN
ejpam-6466	806	13	.	.	PUNCT
ejpam-6466	807	1	statistical	statistical	ADJ
ejpam-6466	807	2	physics	physics	NOUN
ejpam-6466	807	3	of	of	ADP
ejpam-6466	807	4	vehicular	vehicular	ADJ
ejpam-6466	807	5	traffic	traffic	NOUN
ejpam-6466	807	6	and	and	CCONJ
ejpam-6466	807	7	some	some	DET
ejpam-6466	807	8	related	related	ADJ
ejpam-6466	807	9	systems	system	NOUN
ejpam-6466	807	10	.	.	PUNCT
ejpam-6466	808	1	physics	physics	NOUN
ejpam-6466	808	2	reports	report	NOUN
ejpam-6466	808	3	,	,	PUNCT
ejpam-6466	808	4	329(4	329(4	PROPN
ejpam-6466	808	5	-	-	SYM
ejpam-6466	808	6	6):199–329	6):199–329	NUM
ejpam-6466	808	7	,	,	PUNCT
ejpam-6466	808	8	2000	2000	NUM
ejpam-6466	808	9	.	.	PUNCT
ejpam-6466	809	1	[	[	X
ejpam-6466	809	2	37	37	NUM
ejpam-6466	809	3	]	]	PUNCT
ejpam-6466	809	4	x.	x.	PROPN
ejpam-6466	809	5	wang	wang	PROPN
ejpam-6466	809	6	,	,	PUNCT
ejpam-6466	809	7	s.	s.	PROPN
ejpam-6466	809	8	gan	gan	PROPN
ejpam-6466	809	9	,	,	PUNCT
ejpam-6466	809	10	and	and	CCONJ
ejpam-6466	809	11	d.	d.	PROPN
ejpam-6466	809	12	wang	wang	PROPN
ejpam-6466	809	13	.	.	PUNCT
ejpam-6466	810	1	θ	θ	X
ejpam-6466	810	2	-	-	PUNCT
ejpam-6466	810	3	maruyama	maruyama	NOUN
ejpam-6466	810	4	methods	method	NOUN
ejpam-6466	810	5	for	for	ADP
ejpam-6466	810	6	nonlinear	nonlinear	ADJ
ejpam-6466	810	7	stochastic	stochastic	ADJ
ejpam-6466	810	8	differential	differential	NOUN
ejpam-6466	810	9	delay	delay	NOUN
ejpam-6466	810	10	equations	equation	NOUN
ejpam-6466	810	11	.	.	PUNCT
ejpam-6466	811	1	applied	apply	VERB
ejpam-6466	811	2	numerical	numerical	ADJ
ejpam-6466	811	3	mathematics	mathematic	NOUN
ejpam-6466	811	4	,	,	PUNCT
ejpam-6466	811	5	98:38–58	98:38–58	NUM
ejpam-6466	811	6	,	,	PUNCT
ejpam-6466	811	7	2015	2015	NUM
ejpam-6466	811	8	.	.	PUNCT
ejpam-6466	812	1	introduction	introduction	NOUN
ejpam-6466	812	2	preliminaries	preliminary	NOUN
ejpam-6466	812	3	the	the	DET
ejpam-6466	812	4	main	main	ADJ
ejpam-6466	812	5	results	result	NOUN
ejpam-6466	812	6	existence	existence	NOUN
ejpam-6466	812	7	,	,	PUNCT
ejpam-6466	812	8	uniqueness	uniqueness	NOUN
ejpam-6466	812	9	,	,	PUNCT
ejpam-6466	812	10	continuous	continuous	ADJ
ejpam-6466	812	11	dependence	dependence	NOUN
ejpam-6466	812	12	,	,	PUNCT
ejpam-6466	812	13	and	and	CCONJ
ejpam-6466	812	14	regularity	regularity	NOUN
ejpam-6466	812	15	result	result	VERB
ejpam-6466	812	16	the	the	DET
ejpam-6466	812	17	regularity	regularity	NOUN
ejpam-6466	812	18	of	of	ADP
ejpam-6466	812	19	solutions	solution	NOUN
ejpam-6466	812	20	to	to	ADP
ejpam-6466	812	21	df	df	NOUN
ejpam-6466	812	22	-	-	PUNCT
ejpam-6466	812	23	sdes	sde	NOUN
ejpam-6466	812	24	the	the	DET
ejpam-6466	812	25	uh	uh	INTJ
ejpam-6466	812	26	stability	stability	NOUN
ejpam-6466	812	27	of	of	ADP
ejpam-6466	812	28	df	df	NOUN
ejpam-6466	812	29	-	-	PUNCT
ejpam-6466	812	30	sdes	sde	NOUN
ejpam-6466	812	31	examples	example	NOUN
ejpam-6466	812	32	conclusions	conclusion	NOUN