id	sid	tid	token	lemma	pos
ejpam-5246	1	1	european	european	PROPN
ejpam-5246	1	2	journal	journal	PROPN
ejpam-5246	1	3	of	of	ADP
ejpam-5246	1	4	pure	pure	ADJ
ejpam-5246	1	5	and	and	CCONJ
ejpam-5246	1	6	applied	apply	VERB
ejpam-5246	1	7	mathematics	mathematic	NOUN
ejpam-5246	1	8	vol	vol	NOUN
ejpam-5246	1	9	.	.	PROPN
ejpam-5246	2	1	17	17	NUM
ejpam-5246	2	2	,	,	PUNCT
ejpam-5246	2	3	no	no	INTJ
ejpam-5246	2	4	.	.	NOUN
ejpam-5246	2	5	3	3	NUM
ejpam-5246	2	6	,	,	PUNCT
ejpam-5246	2	7	2024	2024	NUM
ejpam-5246	2	8	,	,	PUNCT
ejpam-5246	2	9	1516	1516	NUM
ejpam-5246	2	10	-	-	SYM
ejpam-5246	2	11	1538	1538	NUM
ejpam-5246	2	12	issn	issn	PROPN
ejpam-5246	2	13	1307	1307	NUM
ejpam-5246	2	14	-	-	SYM
ejpam-5246	2	15	5543	5543	NUM
ejpam-5246	2	16	–	–	PUNCT
ejpam-5246	2	17	ejpam.com	ejpam.com	X
ejpam-5246	2	18	published	publish	VERB
ejpam-5246	2	19	by	by	ADP
ejpam-5246	2	20	new	new	PROPN
ejpam-5246	2	21	york	york	PROPN
ejpam-5246	2	22	business	business	PROPN
ejpam-5246	2	23	global	global	PROPN
ejpam-5246	2	24	numerical	numerical	PROPN
ejpam-5246	2	25	finite	finite	ADJ
ejpam-5246	2	26	-	-	PUNCT
ejpam-5246	2	27	difference	difference	ADJ
ejpam-5246	2	28	approximations	approximation	NOUN
ejpam-5246	2	29	of	of	ADP
ejpam-5246	2	30	a	a	DET
ejpam-5246	2	31	coupled	couple	VERB
ejpam-5246	2	32	reaction	reaction	NOUN
ejpam-5246	2	33	-	-	PUNCT
ejpam-5246	2	34	diffusion	diffusion	NOUN
ejpam-5246	2	35	system	system	NOUN
ejpam-5246	2	36	with	with	ADP
ejpam-5246	2	37	gradient	gradient	ADJ
ejpam-5246	2	38	terms	term	NOUN
ejpam-5246	2	39	manar	manar	PROPN
ejpam-5246	2	40	i.	i.	PROPN
ejpam-5246	2	41	khalil1,2,∗	khalil1,2,∗	PROPN
ejpam-5246	2	42	,	,	PUNCT
ejpam-5246	2	43	ishak	ishak	PROPN
ejpam-5246	2	44	hashim1,3	hashim1,3	PROPN
ejpam-5246	2	45	,	,	PUNCT
ejpam-5246	2	46	maan	maan	PROPN
ejpam-5246	2	47	a.	a.	PROPN
ejpam-5246	2	48	rasheed4	rasheed4	PROPN
ejpam-5246	2	49	,	,	PUNCT
ejpam-5246	2	50	faieza	faieza	PROPN
ejpam-5246	2	51	samat5	samat5	ADJ
ejpam-5246	2	52	,	,	PUNCT
ejpam-5246	2	53	shaher	shaher	INTJ
ejpam-5246	2	54	momani6,7	momani6,7	PROPN
ejpam-5246	2	55	1	1	NUM
ejpam-5246	2	56	department	department	NOUN
ejpam-5246	2	57	of	of	ADP
ejpam-5246	2	58	mathematical	mathematical	ADJ
ejpam-5246	2	59	sciences	science	NOUN
ejpam-5246	2	60	,	,	PUNCT
ejpam-5246	2	61	faculty	faculty	NOUN
ejpam-5246	2	62	of	of	ADP
ejpam-5246	2	63	science	science	NOUN
ejpam-5246	2	64	and	and	CCONJ
ejpam-5246	2	65	technology	technology	NOUN
ejpam-5246	2	66	,	,	PUNCT
ejpam-5246	2	67	universiti	universiti	PROPN
ejpam-5246	2	68	kebangsaan	kebangsaan	PROPN
ejpam-5246	2	69	malaysiay	malaysiay	PROPN
ejpam-5246	2	70	,	,	PUNCT
ejpam-5246	2	71	43600	43600	NUM
ejpam-5246	2	72	ukm	ukm	PROPN
ejpam-5246	2	73	bangi	bangi	PROPN
ejpam-5246	2	74	selangor	selangor	PROPN
ejpam-5246	2	75	,	,	PUNCT
ejpam-5246	2	76	malaysia	malaysia	PROPN
ejpam-5246	2	77	2	2	NUM
ejpam-5246	2	78	department	department	NOUN
ejpam-5246	2	79	of	of	ADP
ejpam-5246	2	80	applied	apply	VERB
ejpam-5246	2	81	geology	geology	NOUN
ejpam-5246	2	82	,	,	PUNCT
ejpam-5246	2	83	college	college	NOUN
ejpam-5246	2	84	of	of	ADP
ejpam-5246	2	85	science	science	NOUN
ejpam-5246	2	86	,	,	PUNCT
ejpam-5246	2	87	tikrit	tikrit	NOUN
ejpam-5246	2	88	university	university	NOUN
ejpam-5246	2	89	,	,	PUNCT
ejpam-5246	2	90	iraq	iraq	PROPN
ejpam-5246	2	91	3	3	NUM
ejpam-5246	2	92	nonlinear	nonlinear	ADJ
ejpam-5246	2	93	dynamics	dynamic	NOUN
ejpam-5246	2	94	research	research	NOUN
ejpam-5246	2	95	center	center	NOUN
ejpam-5246	2	96	(	(	PUNCT
ejpam-5246	2	97	ndrc	ndrc	PROPN
ejpam-5246	2	98	)	)	PUNCT
ejpam-5246	2	99	,	,	PUNCT
ejpam-5246	2	100	ajman	ajman	PROPN
ejpam-5246	2	101	university	university	PROPN
ejpam-5246	2	102	,	,	PUNCT
ejpam-5246	2	103	ajman	ajman	PROPN
ejpam-5246	2	104	po	po	PROPN
ejpam-5246	2	105	box	box	PROPN
ejpam-5246	2	106	346	346	NUM
ejpam-5246	2	107	,	,	PUNCT
ejpam-5246	2	108	united	united	PROPN
ejpam-5246	2	109	arab	arab	PROPN
ejpam-5246	2	110	emirates	emirates	PROPN
ejpam-5246	2	111	4	4	NUM
ejpam-5246	2	112	department	department	NOUN
ejpam-5246	2	113	of	of	ADP
ejpam-5246	2	114	mathematics	mathematic	NOUN
ejpam-5246	2	115	,	,	PUNCT
ejpam-5246	2	116	college	college	NOUN
ejpam-5246	2	117	of	of	ADP
ejpam-5246	2	118	basic	basic	ADJ
ejpam-5246	2	119	education	education	NOUN
ejpam-5246	2	120	,	,	PUNCT
ejpam-5246	2	121	mustansiriyah	mustansiriyah	NOUN
ejpam-5246	2	122	university	university	NOUN
ejpam-5246	2	123	,	,	PUNCT
ejpam-5246	2	124	baghdad	baghdad	PROPN
ejpam-5246	2	125	,	,	PUNCT
ejpam-5246	2	126	iraq	iraq	PROPN
ejpam-5246	2	127	5	5	NUM
ejpam-5246	2	128	pusat	pusat	PROPN
ejpam-5246	2	129	genius@pintar	genius@pintar	X
ejpam-5246	2	130	negara	negara	PROPN
ejpam-5246	2	131	,	,	PUNCT
ejpam-5246	2	132	universiti	universiti	PROPN
ejpam-5246	2	133	kebangsaan	kebangsaan	PROPN
ejpam-5246	2	134	malaysiay	malaysiay	PROPN
ejpam-5246	2	135	,	,	PUNCT
ejpam-5246	2	136	43600	43600	NUM
ejpam-5246	2	137	ukm	ukm	PROPN
ejpam-5246	2	138	bangi	bangi	PROPN
ejpam-5246	2	139	selangor	selangor	PROPN
ejpam-5246	2	140	,	,	PUNCT
ejpam-5246	2	141	malaysia	malaysia	PROPN
ejpam-5246	2	142	6	6	NUM
ejpam-5246	2	143	nonlinear	nonlinear	ADJ
ejpam-5246	2	144	dynamics	dynamic	NOUN
ejpam-5246	2	145	research	research	NOUN
ejpam-5246	2	146	center	center	NOUN
ejpam-5246	2	147	(	(	PUNCT
ejpam-5246	2	148	ndrc	ndrc	PROPN
ejpam-5246	2	149	)	)	PUNCT
ejpam-5246	2	150	,	,	PUNCT
ejpam-5246	2	151	ajman	ajman	PROPN
ejpam-5246	2	152	university	university	PROPN
ejpam-5246	2	153	,	,	PUNCT
ejpam-5246	2	154	ajman	ajman	PROPN
ejpam-5246	2	155	po	po	PROPN
ejpam-5246	2	156	box	box	PROPN
ejpam-5246	2	157	346	346	NUM
ejpam-5246	2	158	,	,	PUNCT
ejpam-5246	2	159	united	united	PROPN
ejpam-5246	2	160	arab	arab	PROPN
ejpam-5246	2	161	emirates	emirates	PROPN
ejpam-5246	2	162	7	7	NUM
ejpam-5246	2	163	department	department	NOUN
ejpam-5246	2	164	of	of	ADP
ejpam-5246	2	165	mathematics	mathematic	NOUN
ejpam-5246	2	166	,	,	PUNCT
ejpam-5246	2	167	faculty	faculty	NOUN
ejpam-5246	2	168	of	of	ADP
ejpam-5246	2	169	science	science	NOUN
ejpam-5246	2	170	,	,	PUNCT
ejpam-5246	2	171	jordan	jordan	PROPN
ejpam-5246	2	172	university	university	PROPN
ejpam-5246	2	173	,	,	PUNCT
ejpam-5246	2	174	amman	amman	NOUN
ejpam-5246	2	175	11942	11942	NUM
ejpam-5246	2	176	,	,	PUNCT
ejpam-5246	2	177	jordan	jordan	PROPN
ejpam-5246	2	178	abstract	abstract	PROPN
ejpam-5246	2	179	.	.	PUNCT
ejpam-5246	3	1	this	this	DET
ejpam-5246	3	2	study	study	NOUN
ejpam-5246	3	3	focuses	focus	VERB
ejpam-5246	3	4	on	on	ADP
ejpam-5246	3	5	the	the	DET
ejpam-5246	3	6	derivation	derivation	NOUN
ejpam-5246	3	7	of	of	ADP
ejpam-5246	3	8	explicit	explicit	ADJ
ejpam-5246	3	9	and	and	CCONJ
ejpam-5246	3	10	implicit	implicit	ADJ
ejpam-5246	3	11	finite	finite	ADJ
ejpam-5246	3	12	difference	difference	NOUN
ejpam-5246	3	13	formulas.the	formulas.the	DET
ejpam-5246	3	14	objective	objective	NOUN
ejpam-5246	3	15	of	of	ADP
ejpam-5246	3	16	this	this	DET
ejpam-5246	3	17	study	study	NOUN
ejpam-5246	3	18	is	be	AUX
ejpam-5246	3	19	to	to	PART
ejpam-5246	3	20	derive	derive	VERB
ejpam-5246	3	21	an	an	DET
ejpam-5246	3	22	estimation	estimation	NOUN
ejpam-5246	3	23	of	of	ADP
ejpam-5246	3	24	the	the	DET
ejpam-5246	3	25	blow	blow	NOUN
ejpam-5246	3	26	-	-	PUNCT
ejpam-5246	3	27	up	up	ADP
ejpam-5246	3	28	time	time	NOUN
ejpam-5246	3	29	for	for	ADP
ejpam-5246	3	30	a	a	DET
ejpam-5246	3	31	coupled	couple	VERB
ejpam-5246	3	32	reactiondiffusion	reactiondiffusion	NOUN
ejpam-5246	3	33	system	system	NOUN
ejpam-5246	3	34	incorporating	incorporate	VERB
ejpam-5246	3	35	gradient	gradient	ADJ
ejpam-5246	3	36	terms	term	NOUN
ejpam-5246	3	37	,	,	PUNCT
ejpam-5246	3	38	employing	employ	VERB
ejpam-5246	3	39	numerical	numerical	ADJ
ejpam-5246	3	40	finite	finite	ADJ
ejpam-5246	3	41	difference	difference	NOUN
ejpam-5246	3	42	approximations	approximation	NOUN
ejpam-5246	3	43	.	.	PUNCT
ejpam-5246	4	1	furthermore	furthermore	ADV
ejpam-5246	4	2	,	,	PUNCT
ejpam-5246	4	3	an	an	DET
ejpam-5246	4	4	examination	examination	NOUN
ejpam-5246	4	5	is	be	AUX
ejpam-5246	4	6	conducted	conduct	VERB
ejpam-5246	4	7	on	on	ADP
ejpam-5246	4	8	the	the	DET
ejpam-5246	4	9	consistency	consistency	NOUN
ejpam-5246	4	10	,	,	PUNCT
ejpam-5246	4	11	stability	stability	NOUN
ejpam-5246	4	12	,	,	PUNCT
ejpam-5246	4	13	and	and	CCONJ
ejpam-5246	4	14	convergence	convergence	NOUN
ejpam-5246	4	15	of	of	ADP
ejpam-5246	4	16	the	the	DET
ejpam-5246	4	17	proposed	propose	VERB
ejpam-5246	4	18	schemes	scheme	NOUN
ejpam-5246	4	19	.	.	PUNCT
ejpam-5246	5	1	additionally	additionally	ADV
ejpam-5246	5	2	,	,	PUNCT
ejpam-5246	5	3	the	the	DET
ejpam-5246	5	4	study	study	NOUN
ejpam-5246	5	5	presents	present	VERB
ejpam-5246	5	6	two	two	NUM
ejpam-5246	5	7	numerical	numerical	ADJ
ejpam-5246	5	8	experiments	experiment	NOUN
ejpam-5246	5	9	.	.	PUNCT
ejpam-5246	6	1	in	in	ADP
ejpam-5246	6	2	each	each	DET
ejpam-5246	6	3	instance	instance	NOUN
ejpam-5246	6	4	,	,	PUNCT
ejpam-5246	6	5	the	the	DET
ejpam-5246	6	6	numerical	numerical	ADJ
ejpam-5246	6	7	blow	blow	VERB
ejpam-5246	6	8	-	-	PUNCT
ejpam-5246	6	9	up	up	ADP
ejpam-5246	6	10	time	time	NOUN
ejpam-5246	6	11	is	be	AUX
ejpam-5246	6	12	calculated	calculate	VERB
ejpam-5246	6	13	benefit	benefit	NOUN
ejpam-5246	6	14	the	the	DET
ejpam-5246	6	15	suggested	suggest	VERB
ejpam-5246	6	16	methodologies	methodology	NOUN
ejpam-5246	6	17	,	,	PUNCT
ejpam-5246	6	18	employing	employ	VERB
ejpam-5246	6	19	varying	vary	VERB
ejpam-5246	6	20	space	space	NOUN
ejpam-5246	6	21	steps	step	NOUN
ejpam-5246	6	22	and	and	CCONJ
ejpam-5246	6	23	non	non	ADJ
ejpam-5246	6	24	-	-	ADJ
ejpam-5246	6	25	fixed	fixed	ADJ
ejpam-5246	6	26	time	time	NOUN
ejpam-5246	6	27	-	-	PUNCT
ejpam-5246	6	28	stepping	stepping	ADJ
ejpam-5246	6	29	.	.	PUNCT
ejpam-5246	7	1	the	the	DET
ejpam-5246	7	2	numerical	numerical	PROPN
ejpam-5246	7	3	findings	finding	NOUN
ejpam-5246	7	4	obtained	obtain	VERB
ejpam-5246	7	5	demonstrate	demonstrate	VERB
ejpam-5246	7	6	that	that	SCONJ
ejpam-5246	7	7	the	the	DET
ejpam-5246	7	8	blow	blow	NOUN
ejpam-5246	7	9	-	-	PUNCT
ejpam-5246	7	10	up	up	ADP
ejpam-5246	7	11	time	time	NOUN
ejpam-5246	7	12	sequence	sequence	NOUN
ejpam-5246	7	13	exhibits	exhibit	VERB
ejpam-5246	7	14	convergence	convergence	NOUN
ejpam-5246	7	15	as	as	SCONJ
ejpam-5246	7	16	the	the	DET
ejpam-5246	7	17	space	space	NOUN
ejpam-5246	7	18	step	step	NOUN
ejpam-5246	7	19	decreases	decrease	VERB
ejpam-5246	7	20	.	.	PUNCT
ejpam-5246	8	1	moreover	moreover	ADV
ejpam-5246	8	2	,	,	PUNCT
ejpam-5246	8	3	the	the	DET
ejpam-5246	8	4	numerical	numerical	ADJ
ejpam-5246	8	5	orders	order	NOUN
ejpam-5246	8	6	of	of	ADP
ejpam-5246	8	7	convergence	convergence	NOUN
ejpam-5246	8	8	for	for	ADP
ejpam-5246	8	9	the	the	DET
ejpam-5246	8	10	blow	blow	NOUN
ejpam-5246	8	11	-	-	PUNCT
ejpam-5246	8	12	up	up	ADP
ejpam-5246	8	13	time	time	NOUN
ejpam-5246	8	14	goes	go	VERB
ejpam-5246	8	15	well	well	ADV
ejpam-5246	8	16	with	with	ADP
ejpam-5246	8	17	the	the	DET
ejpam-5246	8	18	theoretical	theoretical	ADJ
ejpam-5246	8	19	orders	order	NOUN
ejpam-5246	8	20	observed	observe	VERB
ejpam-5246	8	21	in	in	ADP
ejpam-5246	8	22	the	the	DET
ejpam-5246	8	23	numerical	numerical	ADJ
ejpam-5246	8	24	solutions	solution	NOUN
ejpam-5246	8	25	.	.	PUNCT
ejpam-5246	9	1	2020	2020	NUM
ejpam-5246	9	2	mathematics	mathematic	NOUN
ejpam-5246	9	3	subject	subject	NOUN
ejpam-5246	9	4	classifications	classification	NOUN
ejpam-5246	9	5	:	:	PUNCT
ejpam-5246	9	6	47h05	47h05	NUM
ejpam-5246	9	7	,	,	PUNCT
ejpam-5246	9	8	90c33	90c33	NUM
ejpam-5246	9	9	key	key	ADJ
ejpam-5246	9	10	words	word	NOUN
ejpam-5246	9	11	and	and	CCONJ
ejpam-5246	9	12	phrases	phrase	NOUN
ejpam-5246	9	13	:	:	PUNCT
ejpam-5246	9	14	explicit	explicit	ADJ
ejpam-5246	9	15	and	and	CCONJ
ejpam-5246	9	16	implicit	implicit	ADJ
ejpam-5246	9	17	finite	finite	ADJ
ejpam-5246	9	18	difference	difference	NOUN
ejpam-5246	9	19	formulas	formula	NOUN
ejpam-5246	9	20	,	,	PUNCT
ejpam-5246	9	21	blow	blow	NOUN
ejpam-5246	9	22	-	-	PUNCT
ejpam-5246	9	23	up	up	ADP
ejpam-5246	9	24	time	time	NOUN
ejpam-5246	9	25	,	,	PUNCT
ejpam-5246	9	26	convergence	convergence	NOUN
ejpam-5246	9	27	analysis	analysis	NOUN
ejpam-5246	9	28	,	,	PUNCT
ejpam-5246	9	29	consistency	consistency	NOUN
ejpam-5246	9	30	,	,	PUNCT
ejpam-5246	9	31	stability	stability	NOUN
ejpam-5246	9	32	,	,	PUNCT
ejpam-5246	9	33	gradient	gradient	ADJ
ejpam-5246	9	34	terms	term	NOUN
ejpam-5246	9	35	∗corresponding	∗corresponde	VERB
ejpam-5246	9	36	author	author	NOUN
ejpam-5246	9	37	.	.	PUNCT
ejpam-5246	10	1	doi	doi	NOUN
ejpam-5246	10	2	:	:	PUNCT
ejpam-5246	10	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5246	https://doi.org/10.29020/nybg.ejpam.v17i3.5246	PROPN
ejpam-5246	10	4	email	email	NOUN
ejpam-5246	10	5	addresses	address	NOUN
ejpam-5246	10	6	:	:	PUNCT
ejpam-5246	10	7	p119266@siswa.ukm.edu.my	p119266@siswa.ukm.edu.my	X
ejpam-5246	10	8	(	(	PUNCT
ejpam-5246	10	9	manar	manar	PROPN
ejpam-5246	10	10	i.	i.	PROPN
ejpam-5246	10	11	khalil	khalil	PROPN
ejpam-5246	10	12	)	)	PUNCT
ejpam-5246	10	13	,	,	PUNCT
ejpam-5246	10	14	xxxxx@email.com	xxxxx@email.com	X
ejpam-5246	11	1	(	(	PUNCT
ejpam-5246	11	2	missing	miss	VERB
ejpam-5246	11	3	author	author	NOUN
ejpam-5246	11	4	emails	email	NOUN
ejpam-5246	11	5	)	)	PUNCT
ejpam-5246	11	6	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5246	11	7	1516	1516	NUM
ejpam-5246	12	1	©	©	ADP
ejpam-5246	12	2	2024	2024	NUM
ejpam-5246	12	3	ejpam	ejpam	NOUN
ejpam-5246	12	4	all	all	DET
ejpam-5246	12	5	rights	right	NOUN
ejpam-5246	12	6	reserved	reserve	VERB
ejpam-5246	12	7	.	.	PUNCT
ejpam-5246	13	1	m.i.khalil	m.i.khalil	NOUN
ejpam-5246	13	2	et	et	PROPN
ejpam-5246	13	3	al	al	PROPN
ejpam-5246	13	4	.	.	PUNCT
ejpam-5246	13	5	/	/	SYM
ejpam-5246	13	6	eur	eur	PROPN
ejpam-5246	13	7	.	.	PUNCT
ejpam-5246	14	1	j.	j.	PROPN
ejpam-5246	14	2	pure	pure	PROPN
ejpam-5246	14	3	appl	appl	PROPN
ejpam-5246	14	4	.	.	PROPN
ejpam-5246	14	5	math	math	PROPN
ejpam-5246	14	6	,	,	PUNCT
ejpam-5246	14	7	17	17	NUM
ejpam-5246	14	8	(	(	PUNCT
ejpam-5246	14	9	3	3	NUM
ejpam-5246	14	10	)	)	PUNCT
ejpam-5246	14	11	(	(	PUNCT
ejpam-5246	14	12	2024	2024	NUM
ejpam-5246	14	13	)	)	PUNCT
ejpam-5246	14	14	,	,	PUNCT
ejpam-5246	14	15	1516	1516	NUM
ejpam-5246	14	16	-	-	SYM
ejpam-5246	14	17	1538	1538	NUM
ejpam-5246	14	18	1517	1517	NUM
ejpam-5246	14	19	1	1	NUM
ejpam-5246	14	20	.	.	PUNCT
ejpam-5246	15	1	introduction	introduction	NOUN
ejpam-5246	15	2	there	there	PRON
ejpam-5246	15	3	are	be	VERB
ejpam-5246	15	4	many	many	ADJ
ejpam-5246	15	5	non	non	ADJ
ejpam-5246	15	6	-	-	ADJ
ejpam-5246	15	7	linear	linear	ADJ
ejpam-5246	15	8	partial	partial	ADJ
ejpam-5246	15	9	differential	differential	ADJ
ejpam-5246	15	10	equations	equation	NOUN
ejpam-5246	15	11	of	of	ADP
ejpam-5246	15	12	the	the	DET
ejpam-5246	15	13	parabolic	parabolic	ADJ
ejpam-5246	15	14	type	type	NOUN
ejpam-5246	15	15	that	that	PRON
ejpam-5246	15	16	can	can	AUX
ejpam-5246	15	17	not	not	PART
ejpam-5246	15	18	be	be	AUX
ejpam-5246	15	19	extended	extend	VERB
ejpam-5246	15	20	globally	globally	ADV
ejpam-5246	15	21	in	in	ADP
ejpam-5246	15	22	time	time	NOUN
ejpam-5246	15	23	for	for	ADP
ejpam-5246	15	24	a	a	DET
ejpam-5246	15	25	given	give	VERB
ejpam-5246	15	26	initial	initial	ADJ
ejpam-5246	15	27	data	datum	NOUN
ejpam-5246	15	28	and	and	CCONJ
ejpam-5246	15	29	become	become	VERB
ejpam-5246	15	30	unbounded	unbounded	ADJ
ejpam-5246	15	31	in	in	ADP
ejpam-5246	15	32	a	a	DET
ejpam-5246	15	33	limited	limited	ADJ
ejpam-5246	15	34	time	time	NOUN
ejpam-5246	15	35	.	.	PUNCT
ejpam-5246	16	1	the	the	DET
ejpam-5246	16	2	occurrence	occurrence	NOUN
ejpam-5246	16	3	of	of	ADP
ejpam-5246	16	4	this	this	DET
ejpam-5246	16	5	phenomenon	phenomenon	NOUN
ejpam-5246	16	6	is	be	AUX
ejpam-5246	16	7	referred	refer	VERB
ejpam-5246	16	8	to	to	ADP
ejpam-5246	16	9	as	as	ADP
ejpam-5246	16	10	blow	blow	NOUN
ejpam-5246	16	11	-	-	PUNCT
ejpam-5246	16	12	up	up	NOUN
ejpam-5246	16	13	,	,	PUNCT
ejpam-5246	16	14	and	and	CCONJ
ejpam-5246	16	15	it	it	PRON
ejpam-5246	16	16	can	can	AUX
ejpam-5246	16	17	manifest	manifest	VERB
ejpam-5246	16	18	in	in	ADP
ejpam-5246	16	19	time	time	NOUN
ejpam-5246	16	20	-	-	PUNCT
ejpam-5246	16	21	dependent	dependent	ADJ
ejpam-5246	16	22	nonlinear	nonlinear	ADJ
ejpam-5246	16	23	equations	equation	NOUN
ejpam-5246	16	24	,	,	PUNCT
ejpam-5246	16	25	provided	provide	VERB
ejpam-5246	16	26	that	that	SCONJ
ejpam-5246	16	27	the	the	DET
ejpam-5246	16	28	non	non	ADJ
ejpam-5246	16	29	-	-	ADJ
ejpam-5246	16	30	linear	linear	ADJ
ejpam-5246	16	31	factors	factor	NOUN
ejpam-5246	16	32	possess	possess	VERB
ejpam-5246	16	33	sufficient	sufficient	ADJ
ejpam-5246	16	34	strength	strength	NOUN
ejpam-5246	16	35	,	,	PUNCT
ejpam-5246	16	36	as	as	SCONJ
ejpam-5246	16	37	evidenced	evidence	VERB
ejpam-5246	16	38	by	by	ADP
ejpam-5246	16	39	references	reference	NOUN
ejpam-5246	16	40	[	[	X
ejpam-5246	16	41	9	9	NUM
ejpam-5246	16	42	,	,	PUNCT
ejpam-5246	16	43	10	10	NUM
ejpam-5246	16	44	,	,	PUNCT
ejpam-5246	16	45	14	14	NUM
ejpam-5246	16	46	,	,	PUNCT
ejpam-5246	16	47	17	17	NUM
ejpam-5246	16	48	,	,	PUNCT
ejpam-5246	16	49	21	21	NUM
ejpam-5246	16	50	]	]	PUNCT
ejpam-5246	16	51	.	.	PUNCT
ejpam-5246	17	1	this	this	DET
ejpam-5246	17	2	phenomenon	phenomenon	NOUN
ejpam-5246	17	3	can	can	AUX
ejpam-5246	17	4	be	be	AUX
ejpam-5246	17	5	expanded	expand	VERB
ejpam-5246	17	6	to	to	ADP
ejpam-5246	17	7	coupled	couple	VERB
ejpam-5246	17	8	systems	system	NOUN
ejpam-5246	17	9	when	when	SCONJ
ejpam-5246	17	10	each	each	DET
ejpam-5246	17	11	dependent	dependent	ADJ
ejpam-5246	17	12	variable	variable	NOUN
ejpam-5246	17	13	has	have	VERB
ejpam-5246	17	14	a	a	DET
ejpam-5246	17	15	finite	finite	ADJ
ejpam-5246	17	16	increase	increase	NOUN
ejpam-5246	17	17	within	within	ADP
ejpam-5246	17	18	a	a	DET
ejpam-5246	17	19	specific	specific	ADJ
ejpam-5246	17	20	time	time	NOUN
ejpam-5246	17	21	-	-	PUNCT
ejpam-5246	17	22	frame	frame	NOUN
ejpam-5246	17	23	.	.	PUNCT
ejpam-5246	18	1	in	in	ADP
ejpam-5246	18	2	this	this	DET
ejpam-5246	18	3	particular	particular	ADJ
ejpam-5246	18	4	scenario	scenario	NOUN
ejpam-5246	18	5	,	,	PUNCT
ejpam-5246	18	6	it	it	PRON
ejpam-5246	18	7	is	be	AUX
ejpam-5246	18	8	asserted	assert	VERB
ejpam-5246	18	9	that	that	SCONJ
ejpam-5246	18	10	the	the	DET
ejpam-5246	18	11	dependent	dependent	ADJ
ejpam-5246	18	12	variables	variable	NOUN
ejpam-5246	18	13	exhibit	exhibit	VERB
ejpam-5246	18	14	synchronous	synchronous	ADJ
ejpam-5246	18	15	increases	increase	NOUN
ejpam-5246	18	16	[	[	X
ejpam-5246	18	17	7	7	NUM
ejpam-5246	18	18	,	,	PUNCT
ejpam-5246	18	19	18	18	NUM
ejpam-5246	18	20	,	,	PUNCT
ejpam-5246	18	21	19	19	NUM
ejpam-5246	18	22	,	,	PUNCT
ejpam-5246	18	23	22	22	NUM
ejpam-5246	18	24	,	,	PUNCT
ejpam-5246	18	25	23	23	NUM
ejpam-5246	18	26	]	]	PUNCT
ejpam-5246	18	27	.	.	PUNCT
ejpam-5246	19	1	in	in	ADP
ejpam-5246	19	2	this	this	DET
ejpam-5246	19	3	paper	paper	NOUN
ejpam-5246	19	4	,	,	PUNCT
ejpam-5246	19	5	we	we	PRON
ejpam-5246	19	6	consider	consider	VERB
ejpam-5246	19	7	a	a	DET
ejpam-5246	19	8	coupled	couple	VERB
ejpam-5246	19	9	parabolic	parabolic	NOUN
ejpam-5246	19	10	system	system	NOUN
ejpam-5246	19	11	:	:	PUNCT
ejpam-5246	19	12	ut	ut	PROPN
ejpam-5246	19	13	=	=	PROPN
ejpam-5246	19	14	uxx	uxx	PROPN
ejpam-5246	20	1	−	−	X
ejpam-5246	20	2	|ux|q1	|ux|q1	PRON
ejpam-5246	20	3	+	+	CCONJ
ejpam-5246	20	4	|v|p1	|v|p1	ADV
ejpam-5246	20	5	,	,	PUNCT
ejpam-5246	20	6	vt	vt	PROPN
ejpam-5246	20	7	=	=	PROPN
ejpam-5246	20	8	vxx	vxx	PROPN
ejpam-5246	20	9	−	−	PROPN
ejpam-5246	20	10	|vx|q2	|vx|q2	PROPN
ejpam-5246	20	11	+	+	NUM
ejpam-5246	20	12	|u|p2	|u|p2	NOUN
ejpam-5246	20	13	,	,	PUNCT
ejpam-5246	20	14	(	(	PUNCT
ejpam-5246	20	15	x	x	X
ejpam-5246	20	16	,	,	PUNCT
ejpam-5246	20	17	t	t	PROPN
ejpam-5246	20	18	)	)	PUNCT
ejpam-5246	20	19	∈	∈	PROPN
ejpam-5246	20	20	(	(	PUNCT
ejpam-5246	20	21	0	0	NUM
ejpam-5246	20	22	,	,	PUNCT
ejpam-5246	20	23	1)×	1)×	NUM
ejpam-5246	20	24	(	(	PUNCT
ejpam-5246	20	25	0	0	NUM
ejpam-5246	20	26	,	,	PUNCT
ejpam-5246	20	27	t	t	NOUN
ejpam-5246	20	28	)	)	PUNCT
ejpam-5246	20	29	,	,	PUNCT
ejpam-5246	20	30	u(0	u(0	PROPN
ejpam-5246	20	31	,	,	PUNCT
ejpam-5246	20	32	t	t	PROPN
ejpam-5246	20	33	)	)	PUNCT
ejpam-5246	21	1	=	=	SYM
ejpam-5246	21	2	u(1	u(1	PROPN
ejpam-5246	21	3	,	,	PUNCT
ejpam-5246	21	4	t	t	PROPN
ejpam-5246	21	5	)	)	PUNCT
ejpam-5246	21	6	=	=	SYM
ejpam-5246	21	7	0	0	NUM
ejpam-5246	21	8	,	,	PUNCT
ejpam-5246	21	9	v(0	v(0	PROPN
ejpam-5246	21	10	,	,	PUNCT
ejpam-5246	21	11	t	t	PROPN
ejpam-5246	21	12	)	)	PUNCT
ejpam-5246	21	13	=	=	SYM
ejpam-5246	22	1	v(1	v(1	PROPN
ejpam-5246	22	2	,	,	PUNCT
ejpam-5246	22	3	t	t	PROPN
ejpam-5246	22	4	)	)	PUNCT
ejpam-5246	22	5	=	=	SYM
ejpam-5246	22	6	0	0	NUM
ejpam-5246	22	7	,	,	PUNCT
ejpam-5246	22	8	t	t	PROPN
ejpam-5246	22	9	∈	∈	PROPN
ejpam-5246	22	10	(	(	PUNCT
ejpam-5246	22	11	0	0	NUM
ejpam-5246	22	12	,	,	PUNCT
ejpam-5246	22	13	t	t	NOUN
ejpam-5246	22	14	)	)	PUNCT
ejpam-5246	22	15	,	,	PUNCT
ejpam-5246	22	16	u(x	u(x	NOUN
ejpam-5246	22	17	,	,	PUNCT
ejpam-5246	22	18	0	0	NUM
ejpam-5246	22	19	)	)	PUNCT
ejpam-5246	22	20	=	=	SYM
ejpam-5246	22	21	u0(x	u0(x	NOUN
ejpam-5246	22	22	)	)	PUNCT
ejpam-5246	22	23	,	,	PUNCT
ejpam-5246	22	24	v(x	v(x	PROPN
ejpam-5246	22	25	,	,	PUNCT
ejpam-5246	22	26	0	0	NUM
ejpam-5246	22	27	)	)	PUNCT
ejpam-5246	22	28	=	=	SYM
ejpam-5246	22	29	v0(x	v0(x	PROPN
ejpam-5246	22	30	)	)	PUNCT
ejpam-5246	22	31	,	,	PUNCT
ejpam-5246	22	32	x	x	PUNCT
ejpam-5246	22	33	∈	∈	PROPN
ejpam-5246	22	34	(	(	PUNCT
ejpam-5246	22	35	0	0	NUM
ejpam-5246	22	36	,	,	PUNCT
ejpam-5246	22	37	1	1	NUM
ejpam-5246	22	38	)	)	PUNCT
ejpam-5246	22	39	,	,	PUNCT
ejpam-5246	22	40			PROPN
ejpam-5246	22	41	(	(	PUNCT
ejpam-5246	22	42	1.1	1.1	NUM
ejpam-5246	22	43	)	)	PUNCT
ejpam-5246	22	44	where	where	SCONJ
ejpam-5246	22	45	p1	p1	NOUN
ejpam-5246	22	46	,	,	PUNCT
ejpam-5246	22	47	p2	p2	PROPN
ejpam-5246	22	48	>	>	X
ejpam-5246	22	49	1	1	NUM
ejpam-5246	22	50	,	,	PUNCT
ejpam-5246	22	51	q1	q1	PROPN
ejpam-5246	22	52	,	,	PUNCT
ejpam-5246	22	53	q2	q2	PROPN
ejpam-5246	22	54	∈	∈	PROPN
ejpam-5246	22	55	(	(	PUNCT
ejpam-5246	22	56	1	1	NUM
ejpam-5246	22	57	,	,	PUNCT
ejpam-5246	22	58	2	2	NUM
ejpam-5246	22	59	)	)	PUNCT
ejpam-5246	22	60	,	,	PUNCT
ejpam-5246	22	61	u0	u0	PROPN
ejpam-5246	22	62	,	,	PUNCT
ejpam-5246	22	63	v0	v0	PROPN
ejpam-5246	22	64	≥	≥	NOUN
ejpam-5246	22	65	0	0	NUM
ejpam-5246	22	66	.	.	PUNCT
ejpam-5246	23	1	for	for	ADP
ejpam-5246	23	2	some	some	DET
ejpam-5246	23	3	details	detail	NOUN
ejpam-5246	23	4	regarding	regard	VERB
ejpam-5246	23	5	the	the	DET
ejpam-5246	23	6	local	local	ADJ
ejpam-5246	23	7	existence	existence	NOUN
ejpam-5246	23	8	and	and	CCONJ
ejpam-5246	23	9	uniqueness	uniqueness	NOUN
ejpam-5246	23	10	and	and	CCONJ
ejpam-5246	23	11	blow	blow	NOUN
ejpam-5246	23	12	-	-	PUNCT
ejpam-5246	23	13	up	up	NOUN
ejpam-5246	23	14	of	of	ADP
ejpam-5246	23	15	this	this	DET
ejpam-5246	23	16	system	system	NOUN
ejpam-5246	23	17	,	,	PUNCT
ejpam-5246	23	18	see	see	VERB
ejpam-5246	23	19	[	[	X
ejpam-5246	23	20	21	21	NUM
ejpam-5246	23	21	]	]	PUNCT
ejpam-5246	23	22	.	.	PUNCT
ejpam-5246	24	1	the	the	DET
ejpam-5246	24	2	system	system	NOUN
ejpam-5246	24	3	(	(	PUNCT
ejpam-5246	24	4	1.1	1.1	NUM
ejpam-5246	24	5	)	)	PUNCT
ejpam-5246	24	6	has	have	AUX
ejpam-5246	24	7	been	be	AUX
ejpam-5246	24	8	studied	study	VERB
ejpam-5246	24	9	in	in	ADP
ejpam-5246	24	10	[	[	X
ejpam-5246	24	11	15	15	NUM
ejpam-5246	24	12	]	]	PUNCT
ejpam-5246	24	13	,	,	PUNCT
ejpam-5246	24	14	where	where	SCONJ
ejpam-5246	24	15	ω	ω	PROPN
ejpam-5246	24	16	∈	∈	PROPN
ejpam-5246	24	17	r3	r3	PROPN
ejpam-5246	24	18	and	and	CCONJ
ejpam-5246	24	19	is	be	AUX
ejpam-5246	24	20	a	a	DET
ejpam-5246	24	21	bounded	bounded	ADJ
ejpam-5246	24	22	convex	convex	NOUN
ejpam-5246	24	23	domain	domain	NOUN
ejpam-5246	24	24	,	,	PUNCT
ejpam-5246	24	25	and	and	CCONJ
ejpam-5246	24	26	p	p	NOUN
ejpam-5246	24	27	=	=	PROPN
ejpam-5246	24	28	p1	p1	NOUN
ejpam-5246	24	29	=	=	PUNCT
ejpam-5246	24	30	p2	p2	NOUN
ejpam-5246	24	31	,	,	PUNCT
ejpam-5246	24	32	(	(	PUNCT
ejpam-5246	24	33	α	α	NOUN
ejpam-5246	24	34	=	=	X
ejpam-5246	24	35	β	β	X
ejpam-5246	24	36	=	=	SYM
ejpam-5246	24	37	1	1	NUM
ejpam-5246	24	38	1−	1−	NUM
ejpam-5246	24	39	p	p	NOUN
ejpam-5246	24	40	)	)	PUNCT
ejpam-5246	24	41	,	,	PUNCT
ejpam-5246	24	42	q	q	NOUN
ejpam-5246	24	43	=	=	PUNCT
ejpam-5246	24	44	q1	q1	PROPN
ejpam-5246	24	45	=	=	SYM
ejpam-5246	24	46	q2	q2	NOUN
ejpam-5246	24	47	;	;	PUNCT
ejpam-5246	24	48	p	p	X
ejpam-5246	24	49	>	>	X
ejpam-5246	24	50	q	q	X
ejpam-5246	24	51	>	>	X
ejpam-5246	25	1	1	1	X
ejpam-5246	25	2	.	.	PUNCT
ejpam-5246	26	1	this	this	PRON
ejpam-5246	26	2	is	be	AUX
ejpam-5246	26	3	shown	show	VERB
ejpam-5246	26	4	as	as	ADP
ejpam-5246	26	5	the	the	DET
ejpam-5246	26	6	traditional	traditional	ADJ
ejpam-5246	26	7	solution	solution	NOUN
ejpam-5246	26	8	of	of	ADP
ejpam-5246	26	9	the	the	DET
ejpam-5246	26	10	system	system	NOUN
ejpam-5246	26	11	blows	blow	VERB
ejpam-5246	26	12	up	up	ADP
ejpam-5246	26	13	(	(	PUNCT
ejpam-5246	26	14	becomes	become	VERB
ejpam-5246	26	15	unbounded	unbounded	ADJ
ejpam-5246	26	16	)	)	PUNCT
ejpam-5246	26	17	in	in	ADP
ejpam-5246	26	18	the	the	DET
ejpam-5246	26	19	w	w	NOUN
ejpam-5246	26	20	-	-	NOUN
ejpam-5246	26	21	norm	norm	NOUN
ejpam-5246	26	22	,	,	PUNCT
ejpam-5246	26	23	where	where	SCONJ
ejpam-5246	26	24	w	w	PROPN
ejpam-5246	26	25	(	(	PUNCT
ejpam-5246	26	26	t	t	PROPN
ejpam-5246	26	27	)	)	PUNCT
ejpam-5246	26	28	=	=	SYM
ejpam-5246	27	1	∫	∫	PROPN
ejpam-5246	27	2	ω	ω	INTJ
ejpam-5246	27	3	(	(	PUNCT
ejpam-5246	27	4	u2p	u2p	PROPN
ejpam-5246	27	5	+	+	CCONJ
ejpam-5246	27	6	v2p	v2p	X
ejpam-5246	27	7	)	)	PUNCT
ejpam-5246	27	8	dx	dx	PROPN
ejpam-5246	27	9	,	,	PUNCT
ejpam-5246	27	10	then	then	ADV
ejpam-5246	27	11	blow	blow	VERB
ejpam-5246	27	12	-	-	PUNCT
ejpam-5246	27	13	up	up	ADP
ejpam-5246	27	14	time	time	NOUN
ejpam-5246	27	15	for	for	ADP
ejpam-5246	27	16	this	this	DET
ejpam-5246	27	17	problem	problem	NOUN
ejpam-5246	27	18	can	can	AUX
ejpam-5246	27	19	be	be	AUX
ejpam-5246	27	20	estimated	estimate	VERB
ejpam-5246	27	21	from	from	ADP
ejpam-5246	27	22	below	below	ADV
ejpam-5246	27	23	as	as	SCONJ
ejpam-5246	27	24	follows	follow	VERB
ejpam-5246	27	25	:	:	PUNCT
ejpam-5246	27	26	t	t	PROPN
ejpam-5246	27	27	≥	≥	NUM
ejpam-5246	27	28	1	1	NUM
ejpam-5246	27	29	2aw	2aw	NOUN
ejpam-5246	27	30	2	2	NUM
ejpam-5246	27	31	0	0	NUM
ejpam-5246	27	32	,	,	PUNCT
ejpam-5246	27	33	where	where	SCONJ
ejpam-5246	28	1	w	w	NOUN
ejpam-5246	28	2	(	(	PUNCT
ejpam-5246	28	3	0	0	NUM
ejpam-5246	28	4	)	)	PUNCT
ejpam-5246	28	5	=	=	NOUN
ejpam-5246	28	6	w0	w0	PROPN
ejpam-5246	28	7	=	=	SYM
ejpam-5246	28	8	∫	∫	PROPN
ejpam-5246	28	9	ω	ω	PROPN
ejpam-5246	28	10	(	(	PUNCT
ejpam-5246	28	11	u2p0	u2p0	PROPN
ejpam-5246	28	12	+	+	CCONJ
ejpam-5246	28	13	v2p0	v2p0	PUNCT
ejpam-5246	28	14	)	)	PUNCT
ejpam-5246	28	15	dx	dx	PROPN
ejpam-5246	28	16	and	and	CCONJ
ejpam-5246	28	17	a	a	PRON
ejpam-5246	28	18	is	be	AUX
ejpam-5246	28	19	a	a	DET
ejpam-5246	28	20	constant	constant	ADJ
ejpam-5246	28	21	which	which	PRON
ejpam-5246	28	22	depends	depend	VERB
ejpam-5246	28	23	on	on	ADP
ejpam-5246	28	24	the	the	DET
ejpam-5246	28	25	data	datum	NOUN
ejpam-5246	28	26	.	.	PUNCT
ejpam-5246	29	1	in	in	ADP
ejpam-5246	29	2	[	[	X
ejpam-5246	29	3	21	21	NUM
ejpam-5246	29	4	]	]	PUNCT
ejpam-5246	29	5	,	,	PUNCT
ejpam-5246	29	6	with	with	ADP
ejpam-5246	29	7	some	some	DET
ejpam-5246	29	8	restricted	restricted	ADJ
ejpam-5246	29	9	conditions	condition	NOUN
ejpam-5246	29	10	on	on	ADP
ejpam-5246	29	11	system	system	NOUN
ejpam-5246	29	12	(	(	PUNCT
ejpam-5246	29	13	1.1	1.1	NUM
ejpam-5246	29	14	)	)	PUNCT
ejpam-5246	29	15	,	,	PUNCT
ejpam-5246	29	16	it	it	PRON
ejpam-5246	29	17	was	be	AUX
ejpam-5246	29	18	shown	show	VERB
ejpam-5246	29	19	that	that	SCONJ
ejpam-5246	29	20	the	the	DET
ejpam-5246	29	21	upper	upper	ADJ
ejpam-5246	29	22	blow	blow	NOUN
ejpam-5246	29	23	-	-	PUNCT
ejpam-5246	29	24	up	up	ADP
ejpam-5246	29	25	rate	rate	NOUN
ejpam-5246	29	26	estimates	estimate	NOUN
ejpam-5246	29	27	for	for	ADP
ejpam-5246	29	28	this	this	DET
ejpam-5246	29	29	solution	solution	NOUN
ejpam-5246	29	30	and	and	CCONJ
ejpam-5246	29	31	its	its	PRON
ejpam-5246	29	32	gradients	gradient	NOUN
ejpam-5246	29	33	terms	term	NOUN
ejpam-5246	29	34	take	take	VERB
ejpam-5246	29	35	the	the	DET
ejpam-5246	29	36	following	follow	VERB
ejpam-5246	29	37	forms	form	NOUN
ejpam-5246	29	38	:	:	PUNCT
ejpam-5246	29	39	u(x	u(x	PROPN
ejpam-5246	29	40	,	,	PUNCT
ejpam-5246	29	41	t	t	PROPN
ejpam-5246	29	42	)	)	PUNCT
ejpam-5246	29	43	≤	≤	PUNCT
ejpam-5246	30	1	c1(t	c1(t	DET
ejpam-5246	30	2	−	−	PUNCT
ejpam-5246	30	3	t)−α	t)−α	PROPN
ejpam-5246	30	4	,	,	PUNCT
ejpam-5246	30	5	|∇u(x	|∇u(x	ADV
ejpam-5246	30	6	,	,	PUNCT
ejpam-5246	30	7	t)|	t)|	ADJ
ejpam-5246	30	8	≤	≤	PUNCT
ejpam-5246	31	1	c1(t	c1(t	DET
ejpam-5246	31	2	−	−	PUNCT
ejpam-5246	31	3	t)−	t)−	PROPN
ejpam-5246	31	4	(	(	PUNCT
ejpam-5246	31	5	1	1	NUM
ejpam-5246	31	6	+	+	NOUN
ejpam-5246	31	7	2α	2α	NOUN
ejpam-5246	31	8	)	)	PUNCT
ejpam-5246	31	9	2	2	NUM
ejpam-5246	31	10	,	,	PUNCT
ejpam-5246	31	11	v(x	v(x	PROPN
ejpam-5246	31	12	,	,	PUNCT
ejpam-5246	31	13	t	t	PROPN
ejpam-5246	31	14	)	)	PUNCT
ejpam-5246	31	15	≤	≤	PUNCT
ejpam-5246	31	16	c2(t	c2(t	PUNCT
ejpam-5246	32	1	−	−	NOUN
ejpam-5246	32	2	t)−β	t)−β	ADP
ejpam-5246	32	3	,	,	PUNCT
ejpam-5246	32	4	|∇v(x	|∇v(x	NUM
ejpam-5246	32	5	,	,	PUNCT
ejpam-5246	32	6	t)|	t)|	ADV
ejpam-5246	32	7	≤	≤	ADJ
ejpam-5246	33	1	c2(t	c2(t	PRON
ejpam-5246	34	1	−	−	NOUN
ejpam-5246	34	2	t)−	t)−	PROPN
ejpam-5246	34	3	(	(	PUNCT
ejpam-5246	34	4	1	1	NUM
ejpam-5246	34	5	+	+	NOUN
ejpam-5246	34	6	2β	2β	NOUN
ejpam-5246	34	7	)	)	PUNCT
ejpam-5246	34	8	2	2	NUM
ejpam-5246	34	9	,	,	PUNCT
ejpam-5246	34	10	where	where	SCONJ
ejpam-5246	34	11	(	(	PUNCT
ejpam-5246	34	12	x	x	NOUN
ejpam-5246	34	13	,	,	PUNCT
ejpam-5246	34	14	t	t	PROPN
ejpam-5246	34	15	)	)	PUNCT
ejpam-5246	34	16	∈	∈	PROPN
ejpam-5246	34	17	ω×	ω×	PUNCT
ejpam-5246	34	18	(	(	PUNCT
ejpam-5246	34	19	0	0	NUM
ejpam-5246	34	20	,	,	PUNCT
ejpam-5246	34	21	t	t	NOUN
ejpam-5246	34	22	)	)	PUNCT
ejpam-5246	34	23	,	,	PUNCT
ejpam-5246	34	24	c1	c1	PROPN
ejpam-5246	34	25	,	,	PUNCT
ejpam-5246	34	26	c2	c2	PROPN
ejpam-5246	34	27	>	>	X
ejpam-5246	34	28	0	0	PROPN
ejpam-5246	34	29	,	,	PUNCT
ejpam-5246	34	30	α	α	NOUN
ejpam-5246	34	31	=	=	SYM
ejpam-5246	34	32	p1	p1	PROPN
ejpam-5246	34	33	+	+	PROPN
ejpam-5246	34	34	1	1	NUM
ejpam-5246	34	35	p1p2−1	p1p2−1	NOUN
ejpam-5246	34	36	and	and	CCONJ
ejpam-5246	34	37	β	β	X
ejpam-5246	34	38	=	=	PUNCT
ejpam-5246	34	39	p2	p2	X
ejpam-5246	34	40	+	+	PROPN
ejpam-5246	34	41	1	1	NUM
ejpam-5246	34	42	p1p2−1	p1p2−1	NOUN
ejpam-5246	34	43	.	.	PUNCT
ejpam-5246	35	1	the	the	DET
ejpam-5246	35	2	numerical	numerical	ADJ
ejpam-5246	35	3	approximation	approximation	NOUN
ejpam-5246	35	4	of	of	ADP
ejpam-5246	35	5	time	time	NOUN
ejpam-5246	35	6	-	-	PUNCT
ejpam-5246	35	7	dependent	dependent	ADJ
ejpam-5246	35	8	parabolic	parabolic	NOUN
ejpam-5246	35	9	problems	problem	NOUN
ejpam-5246	35	10	has	have	AUX
ejpam-5246	35	11	been	be	AUX
ejpam-5246	35	12	studied	study	VERB
ejpam-5246	35	13	by	by	ADP
ejpam-5246	35	14	many	many	ADJ
ejpam-5246	35	15	authors	author	NOUN
ejpam-5246	35	16	,	,	PUNCT
ejpam-5246	35	17	see	see	VERB
ejpam-5246	35	18	for	for	ADP
ejpam-5246	35	19	instance	instance	NOUN
ejpam-5246	36	1	[	[	X
ejpam-5246	36	2	1–4	1–4	PROPN
ejpam-5246	36	3	,	,	PUNCT
ejpam-5246	36	4	11–13	11–13	NUM
ejpam-5246	36	5	,	,	PUNCT
ejpam-5246	36	6	16	16	NUM
ejpam-5246	36	7	,	,	PUNCT
ejpam-5246	36	8	23	23	NUM
ejpam-5246	36	9	,	,	PUNCT
ejpam-5246	36	10	24	24	NUM
ejpam-5246	36	11	]	]	PUNCT
ejpam-5246	36	12	.	.	PUNCT
ejpam-5246	37	1	the	the	DET
ejpam-5246	37	2	main	main	ADJ
ejpam-5246	37	3	aim	aim	NOUN
ejpam-5246	37	4	of	of	ADP
ejpam-5246	37	5	these	these	DET
ejpam-5246	37	6	works	work	NOUN
ejpam-5246	37	7	m.i.khalil	m.i.khalil	PROPN
ejpam-5246	37	8	et	et	PROPN
ejpam-5246	37	9	al	al	PROPN
ejpam-5246	37	10	.	.	PUNCT
ejpam-5246	37	11	/	/	SYM
ejpam-5246	37	12	eur	eur	PROPN
ejpam-5246	37	13	.	.	PUNCT
ejpam-5246	38	1	j.	j.	PROPN
ejpam-5246	38	2	pure	pure	PROPN
ejpam-5246	38	3	appl	appl	PROPN
ejpam-5246	38	4	.	.	PROPN
ejpam-5246	38	5	math	math	PROPN
ejpam-5246	38	6	,	,	PUNCT
ejpam-5246	38	7	17	17	NUM
ejpam-5246	38	8	(	(	PUNCT
ejpam-5246	38	9	3	3	NUM
ejpam-5246	38	10	)	)	PUNCT
ejpam-5246	38	11	(	(	PUNCT
ejpam-5246	38	12	2024	2024	NUM
ejpam-5246	38	13	)	)	PUNCT
ejpam-5246	38	14	,	,	PUNCT
ejpam-5246	38	15	1516	1516	NUM
ejpam-5246	38	16	-	-	SYM
ejpam-5246	38	17	1538	1538	NUM
ejpam-5246	38	18	1518	1518	NUM
ejpam-5246	38	19	was	be	AUX
ejpam-5246	38	20	to	to	PART
ejpam-5246	38	21	estimate	estimate	VERB
ejpam-5246	38	22	the	the	DET
ejpam-5246	38	23	numerical	numerical	ADJ
ejpam-5246	38	24	blow	blow	VERB
ejpam-5246	38	25	-	-	PUNCT
ejpam-5246	38	26	up	up	ADP
ejpam-5246	38	27	time	time	NOUN
ejpam-5246	38	28	of	of	ADP
ejpam-5246	38	29	the	the	DET
ejpam-5246	38	30	considered	consider	VERB
ejpam-5246	38	31	problems	problem	NOUN
ejpam-5246	38	32	.	.	PUNCT
ejpam-5246	39	1	blow	blow	VERB
ejpam-5246	39	2	-	-	PUNCT
ejpam-5246	39	3	up	up	NOUN
ejpam-5246	39	4	means	mean	VERB
ejpam-5246	39	5	the	the	DET
ejpam-5246	39	6	solution	solution	NOUN
ejpam-5246	39	7	of	of	ADP
ejpam-5246	39	8	the	the	DET
ejpam-5246	39	9	problem	problem	NOUN
ejpam-5246	39	10	becomes	become	VERB
ejpam-5246	39	11	unbounded	unbounded	ADJ
ejpam-5246	39	12	in	in	ADP
ejpam-5246	39	13	finite	finite	ADJ
ejpam-5246	39	14	time	time	NOUN
ejpam-5246	39	15	.	.	PUNCT
ejpam-5246	40	1	the	the	DET
ejpam-5246	40	2	semi	semi	ADJ
ejpam-5246	40	3	-	-	ADJ
ejpam-5246	40	4	linear	linear	ADJ
ejpam-5246	40	5	coupled	couple	VERB
ejpam-5246	40	6	reaction	reaction	NOUN
ejpam-5246	40	7	-	-	PUNCT
ejpam-5246	40	8	diffusion	diffusion	NOUN
ejpam-5246	40	9	system	system	NOUN
ejpam-5246	40	10	was	be	AUX
ejpam-5246	40	11	one	one	NUM
ejpam-5246	40	12	of	of	ADP
ejpam-5246	40	13	the	the	DET
ejpam-5246	40	14	investigated	investigate	VERB
ejpam-5246	40	15	problems	problem	NOUN
ejpam-5246	40	16	:	:	PUNCT
ejpam-5246	40	17	ut	ut	PROPN
ejpam-5246	40	18	=	=	PROPN
ejpam-5246	40	19	uxx	uxx	PROPN
ejpam-5246	40	20	+	+	CCONJ
ejpam-5246	40	21	vp	vp	PROPN
ejpam-5246	40	22	,	,	PUNCT
ejpam-5246	40	23	vt	vt	PROPN
ejpam-5246	40	24	=	=	PROPN
ejpam-5246	40	25	vxx	vxx	PROPN
ejpam-5246	40	26	+	+	CCONJ
ejpam-5246	40	27	uq	uq	NOUN
ejpam-5246	40	28	,	,	PUNCT
ejpam-5246	40	29	x	x	SYM
ejpam-5246	40	30	∈	∈	PROPN
ejpam-5246	40	31	(	(	PUNCT
ejpam-5246	40	32	0	0	NUM
ejpam-5246	40	33	,	,	PUNCT
ejpam-5246	40	34	1	1	NUM
ejpam-5246	40	35	)	)	PUNCT
ejpam-5246	40	36	,	,	PUNCT
ejpam-5246	40	37	t	t	PROPN
ejpam-5246	40	38	∈	∈	PROPN
ejpam-5246	40	39	(	(	PUNCT
ejpam-5246	40	40	0	0	NUM
ejpam-5246	40	41	,	,	PUNCT
ejpam-5246	40	42	t	t	NOUN
ejpam-5246	40	43	)	)	PUNCT
ejpam-5246	40	44	,	,	PUNCT
ejpam-5246	40	45	u(0	u(0	PROPN
ejpam-5246	40	46	,	,	PUNCT
ejpam-5246	40	47	t	t	PROPN
ejpam-5246	40	48	)	)	PUNCT
ejpam-5246	41	1	=	=	SYM
ejpam-5246	41	2	u(1	u(1	PROPN
ejpam-5246	41	3	,	,	PUNCT
ejpam-5246	41	4	t	t	PROPN
ejpam-5246	41	5	)	)	PUNCT
ejpam-5246	41	6	=	=	SYM
ejpam-5246	41	7	0	0	NUM
ejpam-5246	41	8	,	,	PUNCT
ejpam-5246	41	9	v(0	v(0	PROPN
ejpam-5246	41	10	,	,	PUNCT
ejpam-5246	41	11	t	t	PROPN
ejpam-5246	41	12	)	)	PUNCT
ejpam-5246	41	13	=	=	SYM
ejpam-5246	42	1	v(1	v(1	PROPN
ejpam-5246	42	2	,	,	PUNCT
ejpam-5246	42	3	t	t	PROPN
ejpam-5246	42	4	)	)	PUNCT
ejpam-5246	42	5	=	=	SYM
ejpam-5246	42	6	0	0	NUM
ejpam-5246	42	7	,	,	PUNCT
ejpam-5246	42	8	t	t	PROPN
ejpam-5246	42	9	∈	∈	PROPN
ejpam-5246	42	10	(	(	PUNCT
ejpam-5246	42	11	0	0	NUM
ejpam-5246	42	12	,	,	PUNCT
ejpam-5246	42	13	t	t	NOUN
ejpam-5246	42	14	)	)	PUNCT
ejpam-5246	42	15	,	,	PUNCT
ejpam-5246	42	16	u(x	u(x	NOUN
ejpam-5246	42	17	,	,	PUNCT
ejpam-5246	42	18	0	0	NUM
ejpam-5246	42	19	)	)	PUNCT
ejpam-5246	42	20	=	=	SYM
ejpam-5246	42	21	u0(x	u0(x	NOUN
ejpam-5246	42	22	)	)	PUNCT
ejpam-5246	42	23	,	,	PUNCT
ejpam-5246	42	24	v(x	v(x	PROPN
ejpam-5246	42	25	,	,	PUNCT
ejpam-5246	42	26	0	0	NUM
ejpam-5246	42	27	)	)	PUNCT
ejpam-5246	42	28	=	=	SYM
ejpam-5246	42	29	v0(x	v0(x	PROPN
ejpam-5246	42	30	)	)	PUNCT
ejpam-5246	42	31	,	,	PUNCT
ejpam-5246	42	32	x	x	PUNCT
ejpam-5246	42	33	∈	∈	PROPN
ejpam-5246	42	34	(	(	PUNCT
ejpam-5246	42	35	0	0	NUM
ejpam-5246	42	36	,	,	PUNCT
ejpam-5246	42	37	1	1	NUM
ejpam-5246	42	38	)	)	PUNCT
ejpam-5246	42	39	,	,	PUNCT
ejpam-5246	42	40			PROPN
ejpam-5246	42	41	(	(	PUNCT
ejpam-5246	42	42	1.2	1.2	NUM
ejpam-5246	42	43	)	)	PUNCT
ejpam-5246	42	44	where	where	SCONJ
ejpam-5246	42	45	p	p	X
ejpam-5246	42	46	,	,	PUNCT
ejpam-5246	42	47	q	q	ADJ
ejpam-5246	42	48	>	>	X
ejpam-5246	42	49	1	1	NUM
ejpam-5246	42	50	and	and	CCONJ
ejpam-5246	42	51	u0(x	u0(x	NUM
ejpam-5246	42	52	)	)	PUNCT
ejpam-5246	42	53	,	,	PUNCT
ejpam-5246	42	54	v0(x	v0(x	X
ejpam-5246	42	55	)	)	PUNCT
ejpam-5246	42	56	are	be	AUX
ejpam-5246	42	57	both	both	DET
ejpam-5246	42	58	smooth	smooth	ADJ
ejpam-5246	42	59	functions	function	NOUN
ejpam-5246	42	60	.	.	PUNCT
ejpam-5246	43	1	the	the	DET
ejpam-5246	43	2	semi	semi	ADJ
ejpam-5246	43	3	-	-	ADJ
ejpam-5246	43	4	discrete	discrete	ADJ
ejpam-5246	43	5	approximation	approximation	NOUN
ejpam-5246	43	6	problem	problem	NOUN
ejpam-5246	43	7	for	for	ADP
ejpam-5246	43	8	system	system	NOUN
ejpam-5246	43	9	(	(	PUNCT
ejpam-5246	43	10	1.2	1.2	NUM
ejpam-5246	43	11	)	)	PUNCT
ejpam-5246	43	12	is	be	AUX
ejpam-5246	43	13	derived	derive	VERB
ejpam-5246	43	14	in	in	ADP
ejpam-5246	43	15	[	[	X
ejpam-5246	43	16	13	13	NUM
ejpam-5246	43	17	]	]	PUNCT
ejpam-5246	43	18	,	,	PUNCT
ejpam-5246	43	19	and	and	CCONJ
ejpam-5246	43	20	theoretical	theoretical	ADJ
ejpam-5246	43	21	notions	notion	NOUN
ejpam-5246	43	22	regarding	regard	VERB
ejpam-5246	43	23	the	the	DET
ejpam-5246	43	24	rapprochement	rapprochement	NOUN
ejpam-5246	43	25	of	of	ADP
ejpam-5246	43	26	blow	blow	NOUN
ejpam-5246	43	27	-	-	PUNCT
ejpam-5246	43	28	up	up	NOUN
ejpam-5246	43	29	times	time	NOUN
ejpam-5246	43	30	and	and	CCONJ
ejpam-5246	43	31	blow	blow	NOUN
ejpam-5246	43	32	-	-	PUNCT
ejpam-5246	43	33	up	up	ADP
ejpam-5246	43	34	solutions	solution	NOUN
ejpam-5246	43	35	of	of	ADP
ejpam-5246	43	36	the	the	DET
ejpam-5246	43	37	semi	semi	ADJ
ejpam-5246	43	38	-	-	ADJ
ejpam-5246	43	39	discrete	discrete	ADJ
ejpam-5246	43	40	issue	issue	NOUN
ejpam-5246	43	41	are	be	AUX
ejpam-5246	43	42	proven	prove	VERB
ejpam-5246	43	43	.	.	PUNCT
ejpam-5246	44	1	furthermore	furthermore	ADV
ejpam-5246	44	2	,	,	PUNCT
ejpam-5246	44	3	this	this	DET
ejpam-5246	44	4	study	study	NOUN
ejpam-5246	44	5	introduces	introduce	VERB
ejpam-5246	44	6	two	two	NUM
ejpam-5246	44	7	alternative	alternative	ADJ
ejpam-5246	44	8	approximations	approximation	NOUN
ejpam-5246	44	9	to	to	ADP
ejpam-5246	44	10	problem	problem	NOUN
ejpam-5246	44	11	(	(	PUNCT
ejpam-5246	44	12	1.2	1.2	NUM
ejpam-5246	44	13	)	)	PUNCT
ejpam-5246	44	14	,	,	PUNCT
ejpam-5246	44	15	namely	namely	ADV
ejpam-5246	44	16	euler	euler	NOUN
ejpam-5246	44	17	schemes	scheme	NOUN
ejpam-5246	44	18	,	,	PUNCT
ejpam-5246	44	19	which	which	PRON
ejpam-5246	44	20	incorporate	incorporate	VERB
ejpam-5246	44	21	a	a	DET
ejpam-5246	44	22	non	non	ADJ
ejpam-5246	44	23	-	-	ADJ
ejpam-5246	44	24	fixed	fix	VERB
ejpam-5246	44	25	time	time	NOUN
ejpam-5246	44	26	stepping	step	VERB
ejpam-5246	44	27	formula	formula	NOUN
ejpam-5246	44	28	.	.	PUNCT
ejpam-5246	45	1	furthermore	furthermore	ADV
ejpam-5246	45	2	,	,	PUNCT
ejpam-5246	45	3	two	two	NUM
ejpam-5246	45	4	numerical	numerical	ADJ
ejpam-5246	45	5	experiments	experiment	NOUN
ejpam-5246	45	6	were	be	AUX
ejpam-5246	45	7	conducted	conduct	VERB
ejpam-5246	45	8	to	to	PART
ejpam-5246	45	9	provide	provide	VERB
ejpam-5246	45	10	empirical	empirical	ADJ
ejpam-5246	45	11	support	support	NOUN
ejpam-5246	45	12	for	for	ADP
ejpam-5246	45	13	the	the	DET
ejpam-5246	45	14	numerical	numerical	ADJ
ejpam-5246	45	15	results	result	NOUN
ejpam-5246	45	16	.	.	PUNCT
ejpam-5246	46	1	specifically	specifically	ADV
ejpam-5246	46	2	,	,	PUNCT
ejpam-5246	46	3	the	the	DET
ejpam-5246	46	4	authors	author	NOUN
ejpam-5246	46	5	conducted	conduct	VERB
ejpam-5246	46	6	estimations	estimation	NOUN
ejpam-5246	46	7	for	for	ADP
ejpam-5246	46	8	a	a	DET
ejpam-5246	46	9	numerical	numerical	ADJ
ejpam-5246	46	10	blow	blow	NOUN
ejpam-5246	46	11	-	-	PUNCT
ejpam-5246	46	12	up	up	ADP
ejpam-5246	46	13	time	time	NOUN
ejpam-5246	46	14	,	,	PUNCT
ejpam-5246	46	15	error	error	NOUN
ejpam-5246	46	16	bounds	bound	NOUN
ejpam-5246	46	17	,	,	PUNCT
ejpam-5246	46	18	cput	cput	ADJ
ejpam-5246	46	19	,	,	PUNCT
ejpam-5246	46	20	and	and	CCONJ
ejpam-5246	46	21	numerical	numerical	ADJ
ejpam-5246	46	22	order	order	NOUN
ejpam-5246	46	23	of	of	ADP
ejpam-5246	46	24	convergence	convergence	NOUN
ejpam-5246	46	25	.	.	PUNCT
ejpam-5246	47	1	the	the	DET
ejpam-5246	47	2	chipot	chipot	ADJ
ejpam-5246	47	3	-	-	PUNCT
ejpam-5246	47	4	weissler	weissler	ADJ
ejpam-5246	47	5	equation	equation	NOUN
ejpam-5246	47	6	[	[	X
ejpam-5246	47	7	5	5	NUM
ejpam-5246	47	8	]	]	PUNCT
ejpam-5246	47	9	:	:	PUNCT
ejpam-5246	47	10	refers	refer	VERB
ejpam-5246	47	11	to	to	ADP
ejpam-5246	47	12	the	the	DET
ejpam-5246	47	13	single	single	ADJ
ejpam-5246	47	14	equation	equation	NOUN
ejpam-5246	47	15	of	of	ADP
ejpam-5246	47	16	system	system	NOUN
ejpam-5246	47	17	(	(	PUNCT
ejpam-5246	47	18	1.1	1.1	NUM
ejpam-5246	47	19	)	)	PUNCT
ejpam-5246	47	20	.	.	PUNCT
ejpam-5246	48	1	ut	ut	PROPN
ejpam-5246	48	2	=	=	PROPN
ejpam-5246	48	3	uxx	uxx	PROPN
ejpam-5246	48	4	+	+	X
ejpam-5246	48	5	up	up	ADP
ejpam-5246	48	6	−	−	PROPN
ejpam-5246	48	7	|ux|q	|ux|q	PROPN
ejpam-5246	48	8	,	,	PUNCT
ejpam-5246	48	9	(	(	PUNCT
ejpam-5246	48	10	x	x	NOUN
ejpam-5246	48	11	,	,	PUNCT
ejpam-5246	48	12	t	t	PROPN
ejpam-5246	48	13	)	)	PUNCT
ejpam-5246	48	14	∈	∈	PROPN
ejpam-5246	48	15	(	(	PUNCT
ejpam-5246	48	16	0	0	NUM
ejpam-5246	48	17	,	,	PUNCT
ejpam-5246	48	18	1)×	1)×	NUM
ejpam-5246	48	19	(	(	PUNCT
ejpam-5246	48	20	0	0	NUM
ejpam-5246	48	21	,	,	PUNCT
ejpam-5246	48	22	t	t	NOUN
ejpam-5246	48	23	)	)	PUNCT
ejpam-5246	48	24	,	,	PUNCT
ejpam-5246	48	25	u(0	u(0	PROPN
ejpam-5246	48	26	,	,	PUNCT
ejpam-5246	48	27	t	t	PROPN
ejpam-5246	48	28	)	)	PUNCT
ejpam-5246	49	1	=	=	SYM
ejpam-5246	49	2	u(1	u(1	PROPN
ejpam-5246	49	3	,	,	PUNCT
ejpam-5246	49	4	t	t	PROPN
ejpam-5246	49	5	)	)	PUNCT
ejpam-5246	49	6	=	=	SYM
ejpam-5246	49	7	0	0	NUM
ejpam-5246	49	8	,	,	PUNCT
ejpam-5246	49	9	t	t	PROPN
ejpam-5246	49	10	∈	∈	PROPN
ejpam-5246	49	11	(	(	PUNCT
ejpam-5246	49	12	0	0	NUM
ejpam-5246	49	13	,	,	PUNCT
ejpam-5246	49	14	t	t	NOUN
ejpam-5246	49	15	)	)	PUNCT
ejpam-5246	49	16	,	,	PUNCT
ejpam-5246	49	17	u(x	u(x	NOUN
ejpam-5246	49	18	,	,	PUNCT
ejpam-5246	49	19	0	0	NUM
ejpam-5246	49	20	)	)	PUNCT
ejpam-5246	49	21	=	=	SYM
ejpam-5246	49	22	u0(x	u0(x	NOUN
ejpam-5246	49	23	)	)	PUNCT
ejpam-5246	49	24	,	,	PUNCT
ejpam-5246	49	25	x	x	PUNCT
ejpam-5246	49	26	∈	∈	PROPN
ejpam-5246	49	27	(	(	PUNCT
ejpam-5246	49	28	0	0	NUM
ejpam-5246	49	29	,	,	PUNCT
ejpam-5246	49	30	1	1	NUM
ejpam-5246	49	31	)	)	PUNCT
ejpam-5246	49	32	.	.	PUNCT
ejpam-5246	50	1			NOUN
ejpam-5246	50	2	(	(	PUNCT
ejpam-5246	50	3	1.3	1.3	NUM
ejpam-5246	50	4	)	)	PUNCT
ejpam-5246	50	5	system	system	NOUN
ejpam-5246	50	6	(	(	PUNCT
ejpam-5246	50	7	1.3	1.3	NUM
ejpam-5246	50	8	)	)	PUNCT
ejpam-5246	50	9	is	be	AUX
ejpam-5246	50	10	associated	associate	VERB
ejpam-5246	50	11	with	with	ADP
ejpam-5246	50	12	a	a	DET
ejpam-5246	50	13	widely	widely	ADV
ejpam-5246	50	14	recognized	recognize	VERB
ejpam-5246	50	15	model	model	NOUN
ejpam-5246	50	16	that	that	PRON
ejpam-5246	50	17	has	have	AUX
ejpam-5246	50	18	emerged	emerge	VERB
ejpam-5246	50	19	in	in	ADP
ejpam-5246	50	20	the	the	DET
ejpam-5246	50	21	field	field	NOUN
ejpam-5246	50	22	of	of	ADP
ejpam-5246	50	23	population	population	NOUN
ejpam-5246	50	24	dynamics	dynamic	NOUN
ejpam-5246	50	25	research	research	NOUN
ejpam-5246	50	26	[	[	X
ejpam-5246	50	27	20	20	NUM
ejpam-5246	50	28	]	]	PUNCT
ejpam-5246	50	29	.	.	PUNCT
ejpam-5246	51	1	it	it	PRON
ejpam-5246	51	2	is	be	AUX
ejpam-5246	51	3	worth	worth	ADJ
ejpam-5246	51	4	noting	note	VERB
ejpam-5246	51	5	that	that	SCONJ
ejpam-5246	51	6	the	the	DET
ejpam-5246	51	7	inclusion	inclusion	NOUN
ejpam-5246	51	8	of	of	ADP
ejpam-5246	51	9	the	the	DET
ejpam-5246	51	10	term	term	NOUN
ejpam-5246	51	11	may	may	AUX
ejpam-5246	51	12	be	be	AUX
ejpam-5246	51	13	gradation	gradation	NOUN
ejpam-5246	51	14	offer	offer	VERB
ejpam-5246	51	15	a	a	DET
ejpam-5246	51	16	damping	damp	VERB
ejpam-5246	51	17	effect	effect	NOUN
ejpam-5246	51	18	that	that	PRON
ejpam-5246	51	19	mitigates	mitigate	VERB
ejpam-5246	51	20	blow	blow	NOUN
ejpam-5246	51	21	-	-	PUNCT
ejpam-5246	51	22	up	up	NOUN
ejpam-5246	51	23	.	.	PUNCT
ejpam-5246	52	1	consequently	consequently	ADV
ejpam-5246	52	2	,	,	PUNCT
ejpam-5246	52	3	numerous	numerous	ADJ
ejpam-5246	52	4	scholars	scholar	NOUN
ejpam-5246	52	5	have	have	AUX
ejpam-5246	52	6	expressed	express	VERB
ejpam-5246	52	7	interest	interest	NOUN
ejpam-5246	52	8	in	in	ADP
ejpam-5246	52	9	investigating	investigate	VERB
ejpam-5246	52	10	the	the	DET
ejpam-5246	52	11	impact	impact	NOUN
ejpam-5246	52	12	of	of	ADP
ejpam-5246	52	13	the	the	DET
ejpam-5246	52	14	gradient	gradient	ADJ
ejpam-5246	52	15	term	term	NOUN
ejpam-5246	52	16	on	on	ADP
ejpam-5246	52	17	blow	blow	NOUN
ejpam-5246	52	18	-	-	PUNCT
ejpam-5246	52	19	up	up	ADP
ejpam-5246	52	20	characteristics	characteristic	NOUN
ejpam-5246	52	21	,	,	PUNCT
ejpam-5246	52	22	including	include	VERB
ejpam-5246	52	23	blow	blow	NOUN
ejpam-5246	52	24	-	-	PUNCT
ejpam-5246	52	25	up	up	ADP
ejpam-5246	52	26	set	set	NOUN
ejpam-5246	52	27	and	and	CCONJ
ejpam-5246	52	28	blow	blow	NOUN
ejpam-5246	52	29	-	-	PUNCT
ejpam-5246	52	30	up	up	ADP
ejpam-5246	52	31	rate	rate	NOUN
ejpam-5246	52	32	estimations	estimation	NOUN
ejpam-5246	52	33	[	[	X
ejpam-5246	52	34	6	6	NUM
ejpam-5246	52	35	,	,	PUNCT
ejpam-5246	52	36	8	8	NUM
ejpam-5246	52	37	,	,	PUNCT
ejpam-5246	52	38	25	25	NUM
ejpam-5246	52	39	]	]	PUNCT
ejpam-5246	52	40	.	.	PUNCT
ejpam-5246	53	1	the	the	DET
ejpam-5246	53	2	problem	problem	NOUN
ejpam-5246	53	3	’s	’s	PART
ejpam-5246	53	4	numerical	numerical	ADJ
ejpam-5246	53	5	approximation	approximation	NOUN
ejpam-5246	53	6	is	be	AUX
ejpam-5246	53	7	examined	examine	VERB
ejpam-5246	53	8	in	in	ADP
ejpam-5246	53	9	reference	reference	NOUN
ejpam-5246	53	10	[	[	X
ejpam-5246	53	11	24	24	NUM
ejpam-5246	53	12	]	]	PUNCT
ejpam-5246	53	13	.	.	PUNCT
ejpam-5246	54	1	the	the	DET
ejpam-5246	54	2	semi	semi	ADJ
ejpam-5246	54	3	-	-	ADJ
ejpam-5246	54	4	discrete	discrete	ADJ
ejpam-5246	54	5	approximation	approximation	NOUN
ejpam-5246	54	6	of	of	ADP
ejpam-5246	54	7	equation	equation	NOUN
ejpam-5246	54	8	(	(	PUNCT
ejpam-5246	54	9	1.1	1.1	NUM
ejpam-5246	54	10	)	)	PUNCT
ejpam-5246	54	11	was	be	AUX
ejpam-5246	54	12	derived	derive	VERB
ejpam-5246	54	13	by	by	ADP
ejpam-5246	54	14	the	the	DET
ejpam-5246	54	15	authors	author	NOUN
ejpam-5246	54	16	,	,	PUNCT
ejpam-5246	54	17	who	who	PRON
ejpam-5246	54	18	also	also	ADV
ejpam-5246	54	19	conducted	conduct	VERB
ejpam-5246	54	20	theorems	theorem	NOUN
ejpam-5246	54	21	to	to	PART
ejpam-5246	54	22	establish	establish	VERB
ejpam-5246	54	23	the	the	DET
ejpam-5246	54	24	convergence	convergence	NOUN
ejpam-5246	54	25	and	and	CCONJ
ejpam-5246	54	26	blow	blow	NOUN
ejpam-5246	54	27	-	-	PUNCT
ejpam-5246	54	28	up	up	NOUN
ejpam-5246	54	29	of	of	ADP
ejpam-5246	54	30	the	the	DET
ejpam-5246	54	31	semi	semi	ADJ
ejpam-5246	54	32	-	-	ADJ
ejpam-5246	54	33	discrete	discrete	ADJ
ejpam-5246	54	34	problem	problem	NOUN
ejpam-5246	54	35	.	.	PUNCT
ejpam-5246	55	1	moreover	moreover	ADV
ejpam-5246	55	2	,	,	PUNCT
ejpam-5246	55	3	the	the	DET
ejpam-5246	55	4	authors	author	NOUN
ejpam-5246	55	5	put	put	VERB
ejpam-5246	55	6	forth	forth	ADP
ejpam-5246	55	7	two	two	NUM
ejpam-5246	55	8	approximation	approximation	NOUN
ejpam-5246	55	9	equations	equation	NOUN
ejpam-5246	55	10	for	for	ADP
ejpam-5246	55	11	(	(	PUNCT
ejpam-5246	55	12	1.1	1.1	NUM
ejpam-5246	55	13	)	)	PUNCT
ejpam-5246	55	14	that	that	PRON
ejpam-5246	55	15	are	be	AUX
ejpam-5246	55	16	fully	fully	ADV
ejpam-5246	55	17	discrete	discrete	ADJ
ejpam-5246	55	18	:	:	PUNCT
ejpam-5246	55	19	explicit	explicit	ADJ
ejpam-5246	55	20	euler	euler	NOUN
ejpam-5246	55	21	equations	equation	NOUN
ejpam-5246	55	22	and	and	CCONJ
ejpam-5246	55	23	implicit	implicit	ADJ
ejpam-5246	55	24	finite	finite	ADJ
ejpam-5246	55	25	difference	difference	NOUN
ejpam-5246	55	26	equations	equation	NOUN
ejpam-5246	55	27	.	.	PUNCT
ejpam-5246	56	1	these	these	DET
ejpam-5246	56	2	equations	equation	NOUN
ejpam-5246	56	3	are	be	AUX
ejpam-5246	56	4	formulated	formulate	VERB
ejpam-5246	56	5	using	use	VERB
ejpam-5246	56	6	a	a	DET
ejpam-5246	56	7	non	non	ADJ
ejpam-5246	56	8	-	-	ADJ
ejpam-5246	56	9	fixed	fixed	ADJ
ejpam-5246	56	10	timestepping	timestepping	NOUN
ejpam-5246	56	11	algorithm	algorithm	NOUN
ejpam-5246	56	12	.	.	PUNCT
ejpam-5246	57	1	furthermore	furthermore	ADV
ejpam-5246	57	2	,	,	PUNCT
ejpam-5246	57	3	two	two	NUM
ejpam-5246	57	4	numerical	numerical	ADJ
ejpam-5246	57	5	experiments	experiment	NOUN
ejpam-5246	57	6	are	be	AUX
ejpam-5246	57	7	conducted	conduct	VERB
ejpam-5246	57	8	to	to	PART
ejpam-5246	57	9	determine	determine	VERB
ejpam-5246	57	10	the	the	DET
ejpam-5246	57	11	numerical	numerical	ADJ
ejpam-5246	57	12	blow	blow	VERB
ejpam-5246	57	13	-	-	PUNCT
ejpam-5246	57	14	up	up	ADP
ejpam-5246	57	15	time	time	NOUN
ejpam-5246	57	16	,	,	PUNCT
ejpam-5246	57	17	error	error	NOUN
ejpam-5246	57	18	limits	limit	NOUN
ejpam-5246	57	19	,	,	PUNCT
ejpam-5246	57	20	and	and	CCONJ
ejpam-5246	57	21	numerical	numerical	ADJ
ejpam-5246	57	22	convergence	convergence	NOUN
ejpam-5246	57	23	order	order	NOUN
ejpam-5246	57	24	.	.	PUNCT
ejpam-5246	58	1	the	the	DET
ejpam-5246	58	2	primary	primary	ADJ
ejpam-5246	58	3	objective	objective	NOUN
ejpam-5246	58	4	of	of	ADP
ejpam-5246	58	5	this	this	DET
ejpam-5246	58	6	study	study	NOUN
ejpam-5246	58	7	is	be	AUX
ejpam-5246	58	8	to	to	PART
ejpam-5246	58	9	employ	employ	VERB
ejpam-5246	58	10	numerical	numerical	ADJ
ejpam-5246	58	11	finite	finite	ADJ
ejpam-5246	58	12	difference	difference	NOUN
ejpam-5246	58	13	approximations	approximation	NOUN
ejpam-5246	58	14	in	in	ADP
ejpam-5246	58	15	order	order	NOUN
ejpam-5246	58	16	to	to	PART
ejpam-5246	58	17	estimate	estimate	VERB
ejpam-5246	58	18	the	the	DET
ejpam-5246	58	19	blow	blow	NOUN
ejpam-5246	58	20	-	-	PUNCT
ejpam-5246	58	21	up	up	ADP
ejpam-5246	58	22	time	time	NOUN
ejpam-5246	58	23	of	of	ADP
ejpam-5246	58	24	a	a	DET
ejpam-5246	58	25	coupled	couple	VERB
ejpam-5246	58	26	reaction	reaction	NOUN
ejpam-5246	58	27	-	-	PUNCT
ejpam-5246	58	28	diffusion	diffusion	NOUN
ejpam-5246	58	29	system	system	NOUN
ejpam-5246	58	30	that	that	PRON
ejpam-5246	58	31	incorporates	incorporate	VERB
ejpam-5246	58	32	gradient	gradient	ADJ
ejpam-5246	58	33	terms	term	NOUN
ejpam-5246	58	34	.	.	PUNCT
ejpam-5246	59	1	the	the	DET
ejpam-5246	59	2	explicit	explicit	ADJ
ejpam-5246	59	3	and	and	CCONJ
ejpam-5246	59	4	implicit	implicit	ADJ
ejpam-5246	59	5	finite	finite	ADJ
ejpam-5246	59	6	difference	difference	NOUN
ejpam-5246	59	7	formulas	formula	NOUN
ejpam-5246	59	8	are	be	AUX
ejpam-5246	59	9	developed	develop	VERB
ejpam-5246	59	10	in	in	ADP
ejpam-5246	59	11	parts	part	NOUN
ejpam-5246	59	12	two	two	NUM
ejpam-5246	59	13	and	and	CCONJ
ejpam-5246	59	14	three	three	NUM
ejpam-5246	59	15	,	,	PUNCT
ejpam-5246	59	16	respectively	respectively	ADV
ejpam-5246	59	17	.	.	PUNCT
ejpam-5246	60	1	furthermore	furthermore	ADV
ejpam-5246	60	2	,	,	PUNCT
ejpam-5246	60	3	an	an	DET
ejpam-5246	60	4	examination	examination	NOUN
ejpam-5246	60	5	is	be	AUX
ejpam-5246	60	6	conducted	conduct	VERB
ejpam-5246	60	7	on	on	ADP
ejpam-5246	60	8	the	the	DET
ejpam-5246	60	9	stability	stability	NOUN
ejpam-5246	60	10	,	,	PUNCT
ejpam-5246	60	11	convergence	convergence	NOUN
ejpam-5246	60	12	,	,	PUNCT
ejpam-5246	60	13	and	and	CCONJ
ejpam-5246	60	14	consistency	consistency	NOUN
ejpam-5246	60	15	of	of	ADP
ejpam-5246	60	16	the	the	DET
ejpam-5246	60	17	proposed	propose	VERB
ejpam-5246	60	18	schemes	scheme	NOUN
ejpam-5246	60	19	.	.	PUNCT
ejpam-5246	61	1	two	two	NUM
ejpam-5246	61	2	numerical	numerical	ADJ
ejpam-5246	61	3	experiments	experiment	NOUN
ejpam-5246	61	4	are	be	AUX
ejpam-5246	61	5	presented	present	VERB
ejpam-5246	61	6	in	in	ADP
ejpam-5246	61	7	a	a	DET
ejpam-5246	61	8	fourth	fourth	ADJ
ejpam-5246	61	9	part	part	NOUN
ejpam-5246	61	10	.	.	PUNCT
ejpam-5246	62	1	in	in	ADP
ejpam-5246	62	2	each	each	DET
ejpam-5246	62	3	instance	instance	NOUN
ejpam-5246	62	4	,	,	PUNCT
ejpam-5246	62	5	the	the	DET
ejpam-5246	62	6	numerical	numerical	ADJ
ejpam-5246	62	7	blow	blow	VERB
ejpam-5246	62	8	-	-	PUNCT
ejpam-5246	62	9	up	up	ADP
ejpam-5246	62	10	time	time	NOUN
ejpam-5246	62	11	is	be	AUX
ejpam-5246	62	12	calculated	calculate	VERB
ejpam-5246	62	13	utilizing	utilize	VERB
ejpam-5246	62	14	the	the	DET
ejpam-5246	62	15	suggested	suggest	VERB
ejpam-5246	62	16	methodologies	methodology	NOUN
ejpam-5246	62	17	,	,	PUNCT
ejpam-5246	62	18	employing	employ	VERB
ejpam-5246	62	19	varying	vary	VERB
ejpam-5246	62	20	space	space	NOUN
ejpam-5246	62	21	stages	stage	NOUN
ejpam-5246	62	22	and	and	CCONJ
ejpam-5246	62	23	non	non	ADJ
ejpam-5246	62	24	-	-	ADJ
ejpam-5246	62	25	fixed	fix	VERB
ejpam-5246	62	26	time	time	NOUN
ejpam-5246	62	27	steps	step	NOUN
ejpam-5246	62	28	.	.	PUNCT
ejpam-5246	63	1	in	in	ADP
ejpam-5246	63	2	the	the	DET
ejpam-5246	63	3	final	final	ADJ
ejpam-5246	63	4	section	section	NOUN
ejpam-5246	63	5	,	,	PUNCT
ejpam-5246	63	6	we	we	PRON
ejpam-5246	63	7	present	present	VERB
ejpam-5246	63	8	a	a	DET
ejpam-5246	63	9	set	set	NOUN
ejpam-5246	63	10	of	of	ADP
ejpam-5246	63	11	conclusions	conclusion	NOUN
ejpam-5246	63	12	and	and	CCONJ
ejpam-5246	63	13	potential	potential	ADJ
ejpam-5246	63	14	avenues	avenue	NOUN
ejpam-5246	63	15	for	for	ADP
ejpam-5246	63	16	future	future	ADJ
ejpam-5246	63	17	works	work	NOUN
ejpam-5246	63	18	.	.	PUNCT
ejpam-5246	64	1	m.i.khalil	m.i.khalil	NOUN
ejpam-5246	64	2	et	et	PROPN
ejpam-5246	64	3	al	al	PROPN
ejpam-5246	64	4	.	.	PUNCT
ejpam-5246	64	5	/	/	SYM
ejpam-5246	64	6	eur	eur	PROPN
ejpam-5246	64	7	.	.	PUNCT
ejpam-5246	65	1	j.	j.	PROPN
ejpam-5246	65	2	pure	pure	PROPN
ejpam-5246	65	3	appl	appl	PROPN
ejpam-5246	65	4	.	.	PROPN
ejpam-5246	65	5	math	math	PROPN
ejpam-5246	65	6	,	,	PUNCT
ejpam-5246	65	7	17	17	NUM
ejpam-5246	65	8	(	(	PUNCT
ejpam-5246	65	9	3	3	NUM
ejpam-5246	65	10	)	)	PUNCT
ejpam-5246	65	11	(	(	PUNCT
ejpam-5246	65	12	2024	2024	NUM
ejpam-5246	65	13	)	)	PUNCT
ejpam-5246	65	14	,	,	PUNCT
ejpam-5246	65	15	1516	1516	NUM
ejpam-5246	65	16	-	-	SYM
ejpam-5246	65	17	1538	1538	NUM
ejpam-5246	65	18	1519	1519	NUM
ejpam-5246	65	19	2	2	NUM
ejpam-5246	65	20	.	.	PUNCT
ejpam-5246	65	21	explicit	explicit	ADJ
ejpam-5246	65	22	euler	euler	NOUN
ejpam-5246	65	23	scheme	scheme	NOUN
ejpam-5246	65	24	here	here	ADV
ejpam-5246	66	1	,	,	PUNCT
ejpam-5246	66	2	we	we	PRON
ejpam-5246	66	3	derive	derive	VERB
ejpam-5246	66	4	the	the	DET
ejpam-5246	66	5	explicit	explicit	ADJ
ejpam-5246	66	6	fully	fully	ADV
ejpam-5246	66	7	-	-	PUNCT
ejpam-5246	66	8	discrete	discrete	ADJ
ejpam-5246	66	9	finite	finite	ADJ
ejpam-5246	66	10	difference	difference	NOUN
ejpam-5246	66	11	formulas	formula	NOUN
ejpam-5246	66	12	for	for	ADP
ejpam-5246	66	13	the	the	DET
ejpam-5246	66	14	problem	problem	NOUN
ejpam-5246	66	15	(	(	PUNCT
ejpam-5246	66	16	1.1),by	1.1),by	NUM
ejpam-5246	66	17	approximating	approximate	VERB
ejpam-5246	66	18	the	the	DET
ejpam-5246	66	19	time	time	NOUN
ejpam-5246	66	20	derivative	derivative	ADJ
ejpam-5246	66	21	in	in	ADP
ejpam-5246	66	22	problem(1.2	problem(1.2	NOUN
ejpam-5246	66	23	)	)	PUNCT
ejpam-5246	66	24	,	,	PUNCT
ejpam-5246	66	25	using	use	VERB
ejpam-5246	66	26	the	the	DET
ejpam-5246	66	27	forward	forward	ADJ
ejpam-5246	66	28	finite	finite	ADJ
ejpam-5246	66	29	difference	difference	NOUN
ejpam-5246	66	30	formula	formula	NOUN
ejpam-5246	66	31	:	:	PUNCT
ejpam-5246	66	32	we	we	PRON
ejpam-5246	66	33	consider	consider	VERB
ejpam-5246	66	34	that	that	DET
ejpam-5246	66	35	un	un	PROPN
ejpam-5246	66	36	i	i	PROPN
ejpam-5246	66	37	and	and	CCONJ
ejpam-5246	66	38	v	v	X
ejpam-5246	66	39	n	n	NOUN
ejpam-5246	66	40	i	i	PRON
ejpam-5246	66	41	,	,	PUNCT
ejpam-5246	66	42	are	be	AUX
ejpam-5246	66	43	the	the	DET
ejpam-5246	66	44	approximate	approximate	ADJ
ejpam-5246	66	45	values	value	NOUN
ejpam-5246	66	46	of	of	ADP
ejpam-5246	66	47	u	u	PROPN
ejpam-5246	66	48	(	(	PUNCT
ejpam-5246	66	49	xi	xi	PROPN
ejpam-5246	66	50	,	,	PUNCT
ejpam-5246	66	51	tn	tn	PROPN
ejpam-5246	66	52	)	)	PUNCT
ejpam-5246	66	53	and	and	CCONJ
ejpam-5246	66	54	v	v	NOUN
ejpam-5246	66	55	(	(	PUNCT
ejpam-5246	66	56	xi	xi	PROPN
ejpam-5246	66	57	,	,	PUNCT
ejpam-5246	66	58	tn	tn	PROPN
ejpam-5246	66	59	)	)	PUNCT
ejpam-5246	66	60	,	,	PUNCT
ejpam-5246	66	61	respectively	respectively	ADV
ejpam-5246	66	62	,	,	PUNCT
ejpam-5246	66	63	where	where	SCONJ
ejpam-5246	66	64	tn+1	tn+1	NOUN
ejpam-5246	66	65	=	=	SYM
ejpam-5246	66	66	tn	tn	PROPN
ejpam-5246	67	1	+	+	CCONJ
ejpam-5246	67	2	kn	kn	PROPN
ejpam-5246	67	3	,	,	PUNCT
ejpam-5246	67	4	i	i	PRON
ejpam-5246	67	5	be	be	VERB
ejpam-5246	67	6	a	a	DET
ejpam-5246	67	7	positive	positive	ADJ
ejpam-5246	67	8	integer	integer	NOUN
ejpam-5246	67	9	,	,	PUNCT
ejpam-5246	67	10	and	and	CCONJ
ejpam-5246	67	11	consider	consider	VERB
ejpam-5246	67	12	the	the	DET
ejpam-5246	67	13	grid	grid	NOUN
ejpam-5246	67	14	:	:	PUNCT
ejpam-5246	67	15	xi	xi	X
ejpam-5246	67	16	=	=	PUNCT
ejpam-5246	67	17	ih	ih	X
ejpam-5246	67	18	,	,	PUNCT
ejpam-5246	67	19	0	0	NUM
ejpam-5246	67	20	≤	≤	NUM
ejpam-5246	68	1	i	i	PRON
ejpam-5246	68	2	≤	≤	PUNCT
ejpam-5246	69	1	i	i	PRON
ejpam-5246	69	2	,	,	PUNCT
ejpam-5246	69	3	h	h	NOUN
ejpam-5246	69	4	=	=	NOUN
ejpam-5246	69	5	1	1	NUM
ejpam-5246	69	6	i	i	NOUN
ejpam-5246	69	7	,	,	PUNCT
ejpam-5246	69	8	tn+1	tn+1	PROPN
ejpam-5246	69	9	=	=	SYM
ejpam-5246	69	10	tn	tn	PROPN
ejpam-5246	69	11	+	+	CCONJ
ejpam-5246	69	12	kn	kn	PROPN
ejpam-5246	69	13	,	,	PUNCT
ejpam-5246	69	14	xi+1	xi+1	PROPN
ejpam-5246	69	15	=	=	PUNCT
ejpam-5246	69	16	xi	xi	PROPN
ejpam-5246	70	1	+	+	CCONJ
ejpam-5246	70	2	h	h	NOUN
ejpam-5246	70	3	,	,	PUNCT
ejpam-5246	70	4	h	h	PROPN
ejpam-5246	70	5	is	be	AUX
ejpam-5246	70	6	the	the	DET
ejpam-5246	70	7	space	space	NOUN
ejpam-5246	70	8	-	-	PUNCT
ejpam-5246	70	9	step	step	NOUN
ejpam-5246	70	10	,	,	PUNCT
ejpam-5246	70	11	and	and	CCONJ
ejpam-5246	70	12	kn	kn	PROPN
ejpam-5246	70	13	is	be	AUX
ejpam-5246	70	14	the	the	DET
ejpam-5246	70	15	time	time	NOUN
ejpam-5246	70	16	-	-	PUNCT
ejpam-5246	70	17	step	step	NOUN
ejpam-5246	70	18	.	.	PUNCT
ejpam-5246	71	1	we	we	PRON
ejpam-5246	71	2	approximate	approximate	VERB
ejpam-5246	71	3	ut	ut	PROPN
ejpam-5246	71	4	,	,	PUNCT
ejpam-5246	71	5	vt	vt	PROPN
ejpam-5246	71	6	by	by	ADP
ejpam-5246	71	7	forward	forward	ADJ
ejpam-5246	71	8	finite	finite	ADJ
ejpam-5246	71	9	difference	difference	NOUN
ejpam-5246	71	10	formulas	formula	NOUN
ejpam-5246	71	11	at	at	ADP
ejpam-5246	71	12	the	the	DET
ejpam-5246	71	13	mesh	mesh	NOUN
ejpam-5246	71	14	-	-	PUNCT
ejpam-5246	71	15	point	point	NOUN
ejpam-5246	71	16	(	(	PUNCT
ejpam-5246	71	17	xi	xi	PROPN
ejpam-5246	71	18	,	,	PUNCT
ejpam-5246	71	19	tn	tn	PROPN
ejpam-5246	71	20	)	)	PUNCT
ejpam-5246	71	21	,	,	PUNCT
ejpam-5246	71	22	as	as	ADP
ejpam-5246	71	23	below	below	ADV
ejpam-5246	71	24	:	:	PUNCT
ejpam-5246	72	1	ut|ni	ut|ni	PROPN
ejpam-5246	72	2	=	=	PUNCT
ejpam-5246	72	3	un+1	un+1	PROPN
ejpam-5246	73	1	i	i	PRON
ejpam-5246	73	2	−	−	PROPN
ejpam-5246	73	3	un	un	PROPN
ejpam-5246	74	1	i	i	PRON
ejpam-5246	74	2	kn	kn	PROPN
ejpam-5246	75	1	+	+	NOUN
ejpam-5246	75	2	o	o	X
ejpam-5246	75	3	(	(	PUNCT
ejpam-5246	75	4	kn	kn	PROPN
ejpam-5246	75	5	)	)	PUNCT
ejpam-5246	75	6	,	,	PUNCT
ejpam-5246	75	7	vt|ni	vt|ni	X
ejpam-5246	75	8	=	=	PUNCT
ejpam-5246	76	1	v	v	X
ejpam-5246	76	2	n+1	n+1	PROPN
ejpam-5246	77	1	i	i	PRON
ejpam-5246	77	2	−	−	PROPN
ejpam-5246	77	3	v	v	ADP
ejpam-5246	77	4	n	n	NOUN
ejpam-5246	78	1	i	i	PRON
ejpam-5246	78	2	kn	kn	PROPN
ejpam-5246	79	1	+	+	NOUN
ejpam-5246	79	2	o	o	X
ejpam-5246	79	3	(	(	PUNCT
ejpam-5246	79	4	kn	kn	PROPN
ejpam-5246	79	5	)	)	PUNCT
ejpam-5246	79	6	,	,	PUNCT
ejpam-5246	79	7	while	while	SCONJ
ejpam-5246	79	8	uxx	uxx	PROPN
ejpam-5246	79	9	,	,	PUNCT
ejpam-5246	79	10	vxx	vxx	PROPN
ejpam-5246	79	11	the	the	DET
ejpam-5246	79	12	second	second	ADJ
ejpam-5246	79	13	-	-	PUNCT
ejpam-5246	79	14	order	order	NOUN
ejpam-5246	79	15	central	central	ADJ
ejpam-5246	79	16	finite	finite	ADJ
ejpam-5246	79	17	difference	difference	NOUN
ejpam-5246	79	18	formula	formula	NOUN
ejpam-5246	79	19	is	be	AUX
ejpam-5246	79	20	used	use	VERB
ejpam-5246	79	21	to	to	PART
ejpam-5246	79	22	approximate	approximate	VERB
ejpam-5246	79	23	the	the	DET
ejpam-5246	79	24	following	follow	VERB
ejpam-5246	79	25	:	:	PUNCT
ejpam-5246	79	26	uxx|ni	uxx|ni	PROPN
ejpam-5246	79	27	=	=	PUNCT
ejpam-5246	79	28	un+1	un+1	PROPN
ejpam-5246	80	1	i	i	PRON
ejpam-5246	80	2	−	−	PROPN
ejpam-5246	80	3	2un	2un	ADJ
ejpam-5246	81	1	i	i	PRON
ejpam-5246	81	2	+	+	NUM
ejpam-5246	81	3	un	un	PROPN
ejpam-5246	81	4	i−1	i−1	PROPN
ejpam-5246	81	5	h2	h2	PROPN
ejpam-5246	82	1	+	+	PROPN
ejpam-5246	82	2	o	o	X
ejpam-5246	82	3	(	(	PUNCT
ejpam-5246	82	4	h2	h2	PROPN
ejpam-5246	82	5	)	)	PUNCT
ejpam-5246	82	6	,	,	PUNCT
ejpam-5246	82	7	vxx|ni	vxx|ni	PROPN
ejpam-5246	82	8	=	=	PUNCT
ejpam-5246	82	9	v	v	PROPN
ejpam-5246	82	10	n+1	n+1	PROPN
ejpam-5246	83	1	i	i	PRON
ejpam-5246	83	2	−	−	PROPN
ejpam-5246	83	3	2v	2v	PROPN
ejpam-5246	83	4	n	n	CCONJ
ejpam-5246	83	5	i	i	PRON
ejpam-5246	84	1	+	+	CCONJ
ejpam-5246	84	2	v	v	NOUN
ejpam-5246	84	3	n	n	NOUN
ejpam-5246	84	4	i−1	i−1	PROPN
ejpam-5246	84	5	h2	h2	PROPN
ejpam-5246	85	1	+	+	PROPN
ejpam-5246	85	2	o	o	X
ejpam-5246	85	3	(	(	PUNCT
ejpam-5246	85	4	h2	h2	PROPN
ejpam-5246	85	5	)	)	PUNCT
ejpam-5246	85	6	.	.	PUNCT
ejpam-5246	86	1	also	also	ADV
ejpam-5246	86	2	,	,	PUNCT
ejpam-5246	86	3	ux	ux	PROPN
ejpam-5246	86	4	,	,	PUNCT
ejpam-5246	86	5	vx	vx	PROPN
ejpam-5246	86	6	are	be	AUX
ejpam-5246	86	7	approximated	approximate	VERB
ejpam-5246	86	8	using	use	VERB
ejpam-5246	86	9	first	first	ADJ
ejpam-5246	86	10	-	-	PUNCT
ejpam-5246	86	11	order	order	NOUN
ejpam-5246	86	12	central	central	ADJ
ejpam-5246	86	13	finite	finite	ADJ
ejpam-5246	86	14	difference	difference	NOUN
ejpam-5246	86	15	formula	formula	NOUN
ejpam-5246	86	16	as	as	SCONJ
ejpam-5246	86	17	follows	follow	VERB
ejpam-5246	86	18	:	:	PUNCT
ejpam-5246	86	19	ux|ni	ux|ni	PROPN
ejpam-5246	86	20	=	=	PUNCT
ejpam-5246	86	21	un	un	PROPN
ejpam-5246	86	22	i+1	i+1	ADV
ejpam-5246	87	1	−	−	PROPN
ejpam-5246	87	2	un	un	PROPN
ejpam-5246	87	3	i−1	i−1	PROPN
ejpam-5246	87	4	2h	2h	NUM
ejpam-5246	87	5	+	+	NOUN
ejpam-5246	87	6	o	o	X
ejpam-5246	87	7	(	(	PUNCT
ejpam-5246	87	8	h2	h2	PROPN
ejpam-5246	87	9	)	)	PUNCT
ejpam-5246	87	10	,	,	PUNCT
ejpam-5246	87	11	vx|ni	vx|ni	NOUN
ejpam-5246	87	12	=	=	SYM
ejpam-5246	87	13	v	v	PROPN
ejpam-5246	87	14	n	n	NOUN
ejpam-5246	87	15	i+1	i+1	ADV
ejpam-5246	87	16	−	−	PROPN
ejpam-5246	87	17	v	v	NOUN
ejpam-5246	87	18	n	n	NOUN
ejpam-5246	87	19	i−1	i−1	PROPN
ejpam-5246	87	20	2h	2h	NUM
ejpam-5246	88	1	+	+	NOUN
ejpam-5246	88	2	o	o	X
ejpam-5246	88	3	(	(	PUNCT
ejpam-5246	88	4	h2	h2	PROPN
ejpam-5246	88	5	)	)	PUNCT
ejpam-5246	88	6	.	.	PUNCT
ejpam-5246	89	1	substituting	substitute	VERB
ejpam-5246	89	2	in	in	ADP
ejpam-5246	89	3	system	system	NOUN
ejpam-5246	89	4	(	(	PUNCT
ejpam-5246	89	5	1.1	1.1	NUM
ejpam-5246	89	6	)	)	PUNCT
ejpam-5246	89	7	yields	yield	VERB
ejpam-5246	89	8	un+1	un+1	VERB
ejpam-5246	90	1	i	i	PRON
ejpam-5246	90	2	−	−	PROPN
ejpam-5246	90	3	un	un	PROPN
ejpam-5246	91	1	i	i	PRON
ejpam-5246	91	2	kn	kn	PROPN
ejpam-5246	92	1	=	=	PUNCT
ejpam-5246	92	2	un	un	PROPN
ejpam-5246	93	1	i	i	PRON
ejpam-5246	93	2	−	−	PROPN
ejpam-5246	93	3	2un	2un	ADJ
ejpam-5246	94	1	i	i	PRON
ejpam-5246	94	2	+	+	NUM
ejpam-5246	94	3	un	un	PROPN
ejpam-5246	94	4	i−1	i−1	PROPN
ejpam-5246	94	5	h2	h2	PROPN
ejpam-5246	94	6	+	+	CCONJ
ejpam-5246	94	7	f	f	X
ejpam-5246	94	8	(	(	PUNCT
ejpam-5246	94	9	δxu	δxu	VERB
ejpam-5246	94	10	n	n	INTJ
ejpam-5246	95	1	i	i	PRON
ejpam-5246	95	2	,	,	PUNCT
ejpam-5246	95	3	v	v	ADP
ejpam-5246	95	4	n	n	INTJ
ejpam-5246	95	5	i	i	PRON
ejpam-5246	95	6	)	)	PUNCT
ejpam-5246	95	7	,	,	PUNCT
ejpam-5246	95	8	v	v	X
ejpam-5246	95	9	n+1	n+1	PROPN
ejpam-5246	96	1	i	i	PRON
ejpam-5246	96	2	−	−	PROPN
ejpam-5246	96	3	v	v	ADP
ejpam-5246	96	4	n	n	NOUN
ejpam-5246	97	1	i	i	PRON
ejpam-5246	97	2	kn	kn	NOUN
ejpam-5246	98	1	=	=	PUNCT
ejpam-5246	98	2	v	v	PROPN
ejpam-5246	98	3	n	n	NOUN
ejpam-5246	99	1	i	i	PRON
ejpam-5246	99	2	−	−	PROPN
ejpam-5246	99	3	2v	2v	PROPN
ejpam-5246	99	4	n	n	CCONJ
ejpam-5246	99	5	i	i	PRON
ejpam-5246	100	1	+	+	CCONJ
ejpam-5246	100	2	v	v	NOUN
ejpam-5246	100	3	n	n	NOUN
ejpam-5246	100	4	i−1	i−1	PROPN
ejpam-5246	100	5	h2	h2	PROPN
ejpam-5246	101	1	+	+	PROPN
ejpam-5246	101	2	g	g	PROPN
ejpam-5246	101	3	(	(	PUNCT
ejpam-5246	101	4	δxv	δxv	PROPN
ejpam-5246	101	5	n	n	INTJ
ejpam-5246	101	6	i	i	PRON
ejpam-5246	101	7	,	,	PUNCT
ejpam-5246	101	8	un	un	PROPN
ejpam-5246	101	9	i	i	PROPN
ejpam-5246	101	10	)	)	PUNCT
ejpam-5246	101	11	,	,	PUNCT
ejpam-5246	101	12	where	where	SCONJ
ejpam-5246	101	13	f	f	PROPN
ejpam-5246	101	14	(	(	PUNCT
ejpam-5246	101	15	δxu	δxu	VERB
ejpam-5246	101	16	n	n	INTJ
ejpam-5246	101	17	i	i	PRON
ejpam-5246	101	18	,	,	PUNCT
ejpam-5246	101	19	v	v	ADP
ejpam-5246	101	20	n	n	NOUN
ejpam-5246	101	21	i	i	PRON
ejpam-5246	101	22	)	)	PUNCT
ejpam-5246	101	23	=	=	PUNCT
ejpam-5246	101	24	(	(	PUNCT
ejpam-5246	101	25	v	v	NOUN
ejpam-5246	101	26	n	n	NOUN
ejpam-5246	101	27	i	i	NOUN
ejpam-5246	101	28	)	)	PUNCT
ejpam-5246	101	29	p1	p1	NOUN
ejpam-5246	101	30	−	−	PROPN
ejpam-5246	101	31	∣∣∣∣un	∣∣∣∣un	PROPN
ejpam-5246	101	32	i+1	i+1	NUM
ejpam-5246	101	33	−	−	PROPN
ejpam-5246	101	34	un	un	PROPN
ejpam-5246	101	35	i−1	i−1	PROPN
ejpam-5246	101	36	2h	2h	NUM
ejpam-5246	101	37	∣∣∣∣q1	∣∣∣∣q1	NUM
ejpam-5246	101	38	,	,	PUNCT
ejpam-5246	101	39	g	g	PROPN
ejpam-5246	101	40	(	(	PUNCT
ejpam-5246	101	41	δxv	δxv	PROPN
ejpam-5246	101	42	n	n	INTJ
ejpam-5246	101	43	i	i	PRON
ejpam-5246	101	44	,	,	PUNCT
ejpam-5246	101	45	un	un	PROPN
ejpam-5246	101	46	i	i	PROPN
ejpam-5246	101	47	)	)	PUNCT
ejpam-5246	101	48	=	=	PUNCT
ejpam-5246	102	1	(	(	PUNCT
ejpam-5246	102	2	un	un	PROPN
ejpam-5246	102	3	i	i	PROPN
ejpam-5246	102	4	)	)	PUNCT
ejpam-5246	102	5	p2	p2	PROPN
ejpam-5246	102	6	−	−	PROPN
ejpam-5246	102	7	∣∣∣∣v	∣∣∣∣v	PROPN
ejpam-5246	102	8	n	n	CCONJ
ejpam-5246	102	9	i+1	i+1	ADV
ejpam-5246	102	10	−	−	PROPN
ejpam-5246	102	11	v	v	NOUN
ejpam-5246	102	12	n	n	NOUN
ejpam-5246	102	13	i−1	i−1	PROPN
ejpam-5246	102	14	2h	2h	NUM
ejpam-5246	102	15	∣∣∣∣q2	∣∣∣∣q2	NUM
ejpam-5246	102	16	.	.	PUNCT
ejpam-5246	103	1	these	these	DET
ejpam-5246	103	2	equations	equation	NOUN
ejpam-5246	103	3	can	can	AUX
ejpam-5246	103	4	be	be	AUX
ejpam-5246	103	5	rewritten	rewrite	VERB
ejpam-5246	103	6	as	as	ADP
ejpam-5246	103	7	un+1	un+1	NOUN
ejpam-5246	103	8	i	i	NOUN
ejpam-5246	103	9	=	=	PUNCT
ejpam-5246	103	10	(	(	PUNCT
ejpam-5246	103	11	1−	1−	NUM
ejpam-5246	103	12	2rn)u	2rn)u	NUM
ejpam-5246	104	1	n	n	NOUN
ejpam-5246	104	2	i	i	PROPN
ejpam-5246	104	3	+	+	PROPN
ejpam-5246	104	4	rn	rn	PROPN
ejpam-5246	104	5	(	(	PUNCT
ejpam-5246	104	6	un	un	PROPN
ejpam-5246	104	7	i+1	i+1	PRON
ejpam-5246	104	8	+	+	PROPN
ejpam-5246	104	9	un	un	PROPN
ejpam-5246	104	10	i−1	i−1	PROPN
ejpam-5246	104	11	)	)	PUNCT
ejpam-5246	105	1	+	+	CCONJ
ejpam-5246	105	2	knf	knf	X
ejpam-5246	105	3	(	(	PUNCT
ejpam-5246	105	4	δxu	δxu	VERB
ejpam-5246	105	5	n	n	INTJ
ejpam-5246	105	6	i	i	PRON
ejpam-5246	105	7	,	,	PUNCT
ejpam-5246	105	8	v	v	ADP
ejpam-5246	105	9	n	n	INTJ
ejpam-5246	105	10	i	i	PRON
ejpam-5246	105	11	)	)	PUNCT
ejpam-5246	105	12	,	,	PUNCT
ejpam-5246	105	13	(	(	PUNCT
ejpam-5246	105	14	2.1	2.1	NUM
ejpam-5246	105	15	)	)	PUNCT
ejpam-5246	105	16	v	v	ADP
ejpam-5246	105	17	n+1	n+1	PROPN
ejpam-5246	105	18	i	i	NOUN
ejpam-5246	105	19	=	=	PUNCT
ejpam-5246	105	20	(	(	PUNCT
ejpam-5246	105	21	1−	1−	NUM
ejpam-5246	105	22	2rn)v	2rn)v	NUM
ejpam-5246	105	23	n	n	NOUN
ejpam-5246	105	24	i	i	PROPN
ejpam-5246	105	25	+	+	PROPN
ejpam-5246	105	26	rn	rn	PROPN
ejpam-5246	105	27	(	(	PUNCT
ejpam-5246	105	28	v	v	NOUN
ejpam-5246	105	29	n	n	PRON
ejpam-5246	105	30	i+1	i+1	NOUN
ejpam-5246	105	31	+	+	CCONJ
ejpam-5246	105	32	v	v	NOUN
ejpam-5246	105	33	n	n	NOUN
ejpam-5246	105	34	i−1	i−1	PROPN
ejpam-5246	105	35	)	)	PUNCT
ejpam-5246	106	1	+	+	CCONJ
ejpam-5246	106	2	kng	kng	PROPN
ejpam-5246	106	3	(	(	PUNCT
ejpam-5246	106	4	δxv	δxv	PROPN
ejpam-5246	106	5	n	n	INTJ
ejpam-5246	106	6	i	i	PRON
ejpam-5246	106	7	,	,	PUNCT
ejpam-5246	106	8	un	un	PROPN
ejpam-5246	106	9	i	i	PROPN
ejpam-5246	106	10	)	)	PUNCT
ejpam-5246	106	11	,	,	PUNCT
ejpam-5246	106	12	(	(	PUNCT
ejpam-5246	106	13	2.2	2.2	NUM
ejpam-5246	106	14	)	)	PUNCT
ejpam-5246	106	15	where	where	SCONJ
ejpam-5246	106	16	i	i	PRON
ejpam-5246	106	17	=	=	NOUN
ejpam-5246	106	18	1	1	NUM
ejpam-5246	106	19	,	,	PUNCT
ejpam-5246	106	20	2	2	NUM
ejpam-5246	106	21	,	,	PUNCT
ejpam-5246	106	22	.	.	PUNCT
ejpam-5246	106	23	.	.	PUNCT
ejpam-5246	106	24	.	.	PUNCT
ejpam-5246	107	1	,	,	PUNCT
ejpam-5246	107	2	i	i	PRON
ejpam-5246	107	3	−	−	VERB
ejpam-5246	107	4	1	1	NUM
ejpam-5246	107	5	,	,	PUNCT
ejpam-5246	107	6	n	n	NOUN
ejpam-5246	107	7	=	=	SYM
ejpam-5246	107	8	0	0	NUM
ejpam-5246	107	9	,	,	PUNCT
ejpam-5246	107	10	1	1	NUM
ejpam-5246	107	11	,	,	PUNCT
ejpam-5246	107	12	2	2	NUM
ejpam-5246	107	13	,	,	PUNCT
ejpam-5246	107	14	.	.	PUNCT
ejpam-5246	107	15	.	.	PUNCT
ejpam-5246	107	16	.	.	PUNCT
ejpam-5246	108	1	,	,	PUNCT
ejpam-5246	108	2	un	un	PROPN
ejpam-5246	108	3	h	h	PROPN
ejpam-5246	108	4	=	=	PRON
ejpam-5246	108	5	(	(	PUNCT
ejpam-5246	108	6	un	un	PROPN
ejpam-5246	108	7	1	1	NUM
ejpam-5246	108	8	,	,	PUNCT
ejpam-5246	108	9	u	u	NOUN
ejpam-5246	108	10	n	n	PRON
ejpam-5246	108	11	2	2	NUM
ejpam-5246	108	12	,	,	PUNCT
ejpam-5246	108	13	.	.	PUNCT
ejpam-5246	108	14	.	.	PUNCT
ejpam-5246	108	15	.	.	PUNCT
ejpam-5246	109	1	,	,	PUNCT
ejpam-5246	109	2	u	u	NOUN
ejpam-5246	109	3	n	n	ADJ
ejpam-5246	109	4	1−i	1−i	NUM
ejpam-5246	109	5	)	)	PUNCT
ejpam-5246	109	6	,	,	PUNCT
ejpam-5246	109	7	v	v	NOUN
ejpam-5246	109	8	n	n	PRON
ejpam-5246	109	9	h	h	NOUN
ejpam-5246	110	1	=	=	PUNCT
ejpam-5246	111	1	(	(	PUNCT
ejpam-5246	111	2	v	v	NOUN
ejpam-5246	111	3	n	n	PRON
ejpam-5246	111	4	1	1	NUM
ejpam-5246	111	5	,	,	PUNCT
ejpam-5246	111	6	v	v	NOUN
ejpam-5246	111	7	n	n	PRON
ejpam-5246	111	8	2	2	NUM
ejpam-5246	111	9	,	,	PUNCT
ejpam-5246	111	10	.	.	PUNCT
ejpam-5246	111	11	.	.	PUNCT
ejpam-5246	112	1	.	.	PUNCT
ejpam-5246	113	1	,	,	PUNCT
ejpam-5246	113	2	v	v	NOUN
ejpam-5246	113	3	n	n	CCONJ
ejpam-5246	113	4	1−i	1−i	NUM
ejpam-5246	113	5	)	)	PUNCT
ejpam-5246	113	6	,	,	PUNCT
ejpam-5246	113	7	rn	rn	PROPN
ejpam-5246	113	8	=	=	PROPN
ejpam-5246	113	9	kn	kn	PROPN
ejpam-5246	113	10	h2	h2	PROPN
ejpam-5246	113	11	.	.	PUNCT
ejpam-5246	114	1	m.i.khalil	m.i.khalil	PROPN
ejpam-5246	114	2	et	et	PROPN
ejpam-5246	114	3	al	al	PROPN
ejpam-5246	114	4	.	.	PUNCT
ejpam-5246	114	5	/	/	SYM
ejpam-5246	114	6	eur	eur	PROPN
ejpam-5246	114	7	.	.	PUNCT
ejpam-5246	115	1	j.	j.	PROPN
ejpam-5246	115	2	pure	pure	PROPN
ejpam-5246	115	3	appl	appl	PROPN
ejpam-5246	115	4	.	.	PROPN
ejpam-5246	115	5	math	math	PROPN
ejpam-5246	115	6	,	,	PUNCT
ejpam-5246	115	7	17	17	NUM
ejpam-5246	115	8	(	(	PUNCT
ejpam-5246	115	9	3	3	NUM
ejpam-5246	115	10	)	)	PUNCT
ejpam-5246	115	11	(	(	PUNCT
ejpam-5246	115	12	2024	2024	NUM
ejpam-5246	115	13	)	)	PUNCT
ejpam-5246	115	14	,	,	PUNCT
ejpam-5246	115	15	1516	1516	NUM
ejpam-5246	115	16	-	-	SYM
ejpam-5246	115	17	1538	1538	NUM
ejpam-5246	115	18	1520	1520	NUM
ejpam-5246	115	19	furthermore	furthermore	ADV
ejpam-5246	115	20	,	,	PUNCT
ejpam-5246	115	21	to	to	PART
ejpam-5246	115	22	ensure	ensure	VERB
ejpam-5246	115	23	that	that	SCONJ
ejpam-5246	115	24	the	the	DET
ejpam-5246	115	25	stability	stability	NOUN
ejpam-5246	115	26	(	(	PUNCT
ejpam-5246	115	27	convergence	convergence	NOUN
ejpam-5246	115	28	)	)	PUNCT
ejpam-5246	115	29	criterion	criterion	NOUN
ejpam-5246	115	30	of	of	ADP
ejpam-5246	115	31	the	the	DET
ejpam-5246	115	32	explicit	explicit	ADJ
ejpam-5246	115	33	scheme	scheme	NOUN
ejpam-5246	115	34	is	be	AUX
ejpam-5246	115	35	satisfied	satisfied	ADJ
ejpam-5246	115	36	,	,	PUNCT
ejpam-5246	115	37	the	the	DET
ejpam-5246	115	38	non	non	ADJ
ejpam-5246	115	39	-	-	ADJ
ejpam-5246	115	40	stationary	stationary	ADJ
ejpam-5246	115	41	time	time	NOUN
ejpam-5246	115	42	step	step	NOUN
ejpam-5246	115	43	formula	formula	NOUN
ejpam-5246	115	44	is	be	AUX
ejpam-5246	115	45	taken	take	VERB
ejpam-5246	115	46	as	as	ADP
ejpam-5246	115	47	below	below	ADV
ejpam-5246	115	48	:	:	PUNCT
ejpam-5246	116	1	kn	kn	PROPN
ejpam-5246	116	2	=	=	PUNCT
ejpam-5246	116	3	min	min	PROPN
ejpam-5246	116	4	(	(	PUNCT
ejpam-5246	116	5	h2	h2	PROPN
ejpam-5246	116	6	3	3	NUM
ejpam-5246	116	7	,	,	PUNCT
ejpam-5246	116	8	hα∥∥un	hα∥∥un	PROPN
ejpam-5246	116	9	h	h	NOUN
ejpam-5246	116	10	∥∥	∥∥	X
ejpam-5246	116	11	,	,	PUNCT
ejpam-5246	116	12	hα∥∥vn	hα∥∥vn	PROPN
ejpam-5246	116	13	h	h	NOUN
ejpam-5246	116	14	∥∥	∥∥	PROPN
ejpam-5246	116	15	)	)	PUNCT
ejpam-5246	116	16	,	,	PUNCT
ejpam-5246	116	17	α	α	PRON
ejpam-5246	116	18	≥	≥	NOUN
ejpam-5246	116	19	1	1	NUM
ejpam-5246	116	20	.	.	PUNCT
ejpam-5246	117	1	(	(	PUNCT
ejpam-5246	117	2	2.3	2.3	NUM
ejpam-5246	117	3	)	)	PUNCT
ejpam-5246	117	4	lemma	lemma	PROPN
ejpam-5246	117	5	1	1	NUM
ejpam-5246	117	6	.	.	PUNCT
ejpam-5246	118	1	the	the	DET
ejpam-5246	118	2	functions	function	NOUN
ejpam-5246	118	3	f	f	X
ejpam-5246	118	4	,	,	PUNCT
ejpam-5246	118	5	g	g	PROPN
ejpam-5246	118	6	satisfy	satisfy	PROPN
ejpam-5246	118	7	lipshtiz	lipshtiz	PROPN
ejpam-5246	118	8	condition	condition	NOUN
ejpam-5246	118	9	,	,	PUNCT
ejpam-5246	118	10	that	that	PRON
ejpam-5246	118	11	is	be	AUX
ejpam-5246	118	12	there	there	PRON
ejpam-5246	118	13	exists	exist	VERB
ejpam-5246	118	14	positive	positive	ADJ
ejpam-5246	118	15	constants	constant	NOUN
ejpam-5246	118	16	l1	l1	PROPN
ejpam-5246	118	17	,	,	PUNCT
ejpam-5246	118	18	l2	l2	NOUN
ejpam-5246	118	19	,	,	PUNCT
ejpam-5246	118	20	l3	l3	PROPN
ejpam-5246	118	21	,	,	PUNCT
ejpam-5246	118	22	l4	l4	PROPN
ejpam-5246	118	23	>	>	X
ejpam-5246	118	24	0	0	PROPN
ejpam-5246	118	25	,	,	PUNCT
ejpam-5246	118	26	such	such	ADJ
ejpam-5246	118	27	as∣∣∣f	as∣∣∣f	NUM
ejpam-5246	118	28	(	(	PUNCT
ejpam-5246	118	29	δxu	δxu	VERB
ejpam-5246	118	30	n	n	INTJ
ejpam-5246	118	31	i	i	PRON
ejpam-5246	118	32	,	,	PUNCT
ejpam-5246	118	33	v	v	ADP
ejpam-5246	118	34	n	n	INTJ
ejpam-5246	118	35	i	i	NOUN
ejpam-5246	118	36	)	)	PUNCT
ejpam-5246	119	1	−	−	PROPN
ejpam-5246	119	2	f	f	PROPN
ejpam-5246	119	3	(	(	PUNCT
ejpam-5246	119	4	δxũ	δxũ	X
ejpam-5246	119	5	n	n	CCONJ
ejpam-5246	119	6	i	i	PRON
ejpam-5246	119	7	,	,	PUNCT
ejpam-5246	119	8	ṽ	ṽ	PROPN
ejpam-5246	119	9	n	n	CCONJ
ejpam-5246	119	10	i	i	NOUN
ejpam-5246	119	11	)	)	PUNCT
ejpam-5246	119	12	∣∣∣	∣∣∣	PROPN
ejpam-5246	119	13	≤	≤	NUM
ejpam-5246	119	14	l1	l1	PROPN
ejpam-5246	119	15	∣∣∣δx	∣∣∣δx	PROPN
ejpam-5246	119	16	(	(	PUNCT
ejpam-5246	119	17	un	un	PROPN
ejpam-5246	119	18	i	i	PRON
ejpam-5246	119	19	−	−	VERB
ejpam-5246	119	20	ũn	ũn	VERB
ejpam-5246	119	21	i	i	PRON
ejpam-5246	119	22	)	)	PUNCT
ejpam-5246	119	23	∣∣∣+	∣∣∣+	PROPN
ejpam-5246	119	24	l2	l2	VERB
ejpam-5246	119	25	∣∣∣v	∣∣∣v	NOUN
ejpam-5246	119	26	n	n	NOUN
ejpam-5246	119	27	i	i	PRON
ejpam-5246	119	28	−	−	PROPN
ejpam-5246	119	29	ṽ	ṽ	PROPN
ejpam-5246	120	1	n	n	CCONJ
ejpam-5246	120	2	i	i	PRON
ejpam-5246	120	3	∣∣∣	∣∣∣	ADJ
ejpam-5246	120	4	,	,	PUNCT
ejpam-5246	120	5	(	(	PUNCT
ejpam-5246	120	6	2.4)∣∣∣g	2.4)∣∣∣g	NUM
ejpam-5246	120	7	(	(	PUNCT
ejpam-5246	120	8	un	un	PROPN
ejpam-5246	120	9	i	i	PROPN
ejpam-5246	120	10	,	,	PUNCT
ejpam-5246	120	11	δxv	δxv	PROPN
ejpam-5246	120	12	n	n	CCONJ
ejpam-5246	120	13	i	i	NOUN
ejpam-5246	120	14	)	)	PUNCT
ejpam-5246	120	15	−g	−g	NOUN
ejpam-5246	120	16	(	(	PUNCT
ejpam-5246	120	17	ũn	ũn	NOUN
ejpam-5246	120	18	i	i	PRON
ejpam-5246	120	19	,	,	PUNCT
ejpam-5246	120	20	δxṽ	δxṽ	VERB
ejpam-5246	121	1	n	n	PROPN
ejpam-5246	121	2	i	i	NOUN
ejpam-5246	121	3	)	)	PUNCT
ejpam-5246	121	4	∣∣∣	∣∣∣	PROPN
ejpam-5246	121	5	≤	≤	NUM
ejpam-5246	121	6	l3	l3	PROPN
ejpam-5246	122	1	∣∣∣δx	∣∣∣δx	PROPN
ejpam-5246	122	2	(	(	PUNCT
ejpam-5246	122	3	v	v	NOUN
ejpam-5246	122	4	n	n	NOUN
ejpam-5246	123	1	i	i	PRON
ejpam-5246	123	2	−	−	PROPN
ejpam-5246	123	3	ṽ	ṽ	PROPN
ejpam-5246	123	4	n	n	PROPN
ejpam-5246	123	5	i	i	NOUN
ejpam-5246	123	6	)	)	PUNCT
ejpam-5246	123	7	∣∣∣+	∣∣∣+	PROPN
ejpam-5246	123	8	l4	l4	PROPN
ejpam-5246	123	9	∣∣∣un	∣∣∣un	PROPN
ejpam-5246	124	1	i	i	PRON
ejpam-5246	124	2	−	−	VERB
ejpam-5246	124	3	ũn	ũn	VERB
ejpam-5246	124	4	i	i	PRON
ejpam-5246	124	5	∣∣∣	∣∣∣	ADJ
ejpam-5246	124	6	,	,	PUNCT
ejpam-5246	124	7	(	(	PUNCT
ejpam-5246	124	8	2.5	2.5	NUM
ejpam-5246	124	9	)	)	PUNCT
ejpam-5246	124	10	where	where	SCONJ
ejpam-5246	124	11	un	un	PROPN
ejpam-5246	124	12	i	i	PROPN
ejpam-5246	124	13	,	,	PUNCT
ejpam-5246	124	14	v	v	ADP
ejpam-5246	124	15	n	n	ADV
ejpam-5246	125	1	i	i	PRON
ejpam-5246	125	2	,	,	PUNCT
ejpam-5246	125	3	ũn	ũn	VERB
ejpam-5246	125	4	i	i	PRON
ejpam-5246	125	5	,	,	PUNCT
ejpam-5246	125	6	ṽ	ṽ	PROPN
ejpam-5246	125	7	n	n	CCONJ
ejpam-5246	125	8	i	i	PRON
ejpam-5246	125	9	(	(	PUNCT
ejpam-5246	125	10	i	i	NOUN
ejpam-5246	125	11	=	=	NOUN
ejpam-5246	125	12	0	0	NUM
ejpam-5246	125	13	,	,	PUNCT
ejpam-5246	125	14	1	1	NUM
ejpam-5246	125	15	,	,	PUNCT
ejpam-5246	125	16	2	2	NUM
ejpam-5246	125	17	,	,	PUNCT
ejpam-5246	125	18	.	.	PUNCT
ejpam-5246	125	19	.	.	PUNCT
ejpam-5246	125	20	.	.	PUNCT
ejpam-5246	126	1	i	i	PRON
ejpam-5246	126	2	)	)	PUNCT
ejpam-5246	126	3	are	be	AUX
ejpam-5246	126	4	bounded	bound	VERB
ejpam-5246	126	5	values	value	NOUN
ejpam-5246	126	6	.	.	PUNCT
ejpam-5246	127	1	proof	proof	NOUN
ejpam-5246	127	2	.	.	PUNCT
ejpam-5246	128	1	we	we	PRON
ejpam-5246	128	2	denote	denote	VERB
ejpam-5246	128	3	f(s	f(s	ADV
ejpam-5246	128	4	)	)	PUNCT
ejpam-5246	129	1	=	=	SYM
ejpam-5246	129	2	sp	sp	ADP
ejpam-5246	130	1	and	and	CCONJ
ejpam-5246	130	2	we	we	PRON
ejpam-5246	130	3	use	use	VERB
ejpam-5246	130	4	the	the	DET
ejpam-5246	130	5	mean	mean	ADJ
ejpam-5246	130	6	value	value	NOUN
ejpam-5246	130	7	theorem	theorem	VERB
ejpam-5246	130	8	we	we	PRON
ejpam-5246	130	9	get∣∣∣(v	get∣∣∣(v	VERB
ejpam-5246	130	10	n	n	PROPN
ejpam-5246	130	11	i	i	NOUN
ejpam-5246	130	12	)	)	PUNCT
ejpam-5246	130	13	p1	p1	NOUN
ejpam-5246	130	14	−	−	PROPN
ejpam-5246	131	1	(	(	PUNCT
ejpam-5246	131	2	ṽ	ṽ	PROPN
ejpam-5246	131	3	n	n	PROPN
ejpam-5246	131	4	i	i	NOUN
ejpam-5246	131	5	)	)	PUNCT
ejpam-5246	131	6	p1∣∣∣	p1∣∣∣	PROPN
ejpam-5246	131	7	≤	≤	NUM
ejpam-5246	131	8	∣∣f	∣∣f	NOUN
ejpam-5246	131	9	′	′	NUM
ejpam-5246	131	10	(	(	PUNCT
ejpam-5246	131	11	zi	zi	NOUN
ejpam-5246	131	12	)	)	PUNCT
ejpam-5246	131	13	∣∣	∣∣	AUX
ejpam-5246	132	1	∣∣∣v	∣∣∣v	PROPN
ejpam-5246	132	2	n	n	NOUN
ejpam-5246	132	3	i	i	PRON
ejpam-5246	132	4	−	−	PROPN
ejpam-5246	132	5	ṽ	ṽ	PROPN
ejpam-5246	133	1	n	n	CCONJ
ejpam-5246	133	2	i	i	PRON
ejpam-5246	133	3	∣∣∣	∣∣∣	ADJ
ejpam-5246	133	4	,	,	PUNCT
ejpam-5246	133	5	(	(	PUNCT
ejpam-5246	133	6	2.6	2.6	NUM
ejpam-5246	133	7	)	)	PUNCT
ejpam-5246	133	8	where	where	SCONJ
ejpam-5246	133	9	zi	zi	NOUN
ejpam-5246	133	10	is	be	AUX
ejpam-5246	133	11	an	an	DET
ejpam-5246	133	12	intermediate	intermediate	ADJ
ejpam-5246	133	13	value	value	NOUN
ejpam-5246	133	14	between	between	ADP
ejpam-5246	133	15	v	v	NOUN
ejpam-5246	133	16	n	n	PRON
ejpam-5246	133	17	i	i	PRON
ejpam-5246	133	18	and	and	CCONJ
ejpam-5246	133	19	v̄	v̄	PROPN
ejpam-5246	134	1	n	n	ADV
ejpam-5246	134	2	i	i	PRON
ejpam-5246	134	3	.	.	PUNCT
ejpam-5246	135	1	since	since	SCONJ
ejpam-5246	135	2	v	v	NUM
ejpam-5246	135	3	n	n	PRON
ejpam-5246	135	4	h	h	NOUN
ejpam-5246	135	5	,	,	PUNCT
ejpam-5246	135	6	v	v	NOUN
ejpam-5246	135	7	n	n	PRON
ejpam-5246	135	8	h	h	NOUN
ejpam-5246	135	9	are	be	AUX
ejpam-5246	135	10	bounded	bound	VERB
ejpam-5246	135	11	,	,	PUNCT
ejpam-5246	135	12	then	then	ADV
ejpam-5246	135	13	there	there	PRON
ejpam-5246	135	14	exists	exist	VERB
ejpam-5246	135	15	c1	c1	PROPN
ejpam-5246	135	16	>	>	X
ejpam-5246	135	17	0	0	PUNCT
ejpam-5246	136	1	such	such	ADJ
ejpam-5246	136	2	that	that	PRON
ejpam-5246	136	3	|f	|f	PROPN
ejpam-5246	136	4	′	′	NUM
ejpam-5246	137	1	(	(	PUNCT
ejpam-5246	137	2	zi)|	zi)|	X
ejpam-5246	137	3	<	<	X
ejpam-5246	137	4	c1	c1	PROPN
ejpam-5246	137	5	.	.	PUNCT
ejpam-5246	138	1	now	now	ADV
ejpam-5246	138	2	,	,	PUNCT
ejpam-5246	138	3	we	we	PRON
ejpam-5246	138	4	denote	denote	VERB
ejpam-5246	138	5	g(s	g(s	PROPN
ejpam-5246	138	6	)	)	PUNCT
ejpam-5246	139	1	=	=	PUNCT
ejpam-5246	139	2	|s|q1	|s|q1	NOUN
ejpam-5246	139	3	,	,	PUNCT
ejpam-5246	139	4	with	with	ADP
ejpam-5246	139	5	using	use	VERB
ejpam-5246	139	6	the	the	DET
ejpam-5246	139	7	mean	mean	ADJ
ejpam-5246	139	8	value	value	NOUN
ejpam-5246	139	9	theorem	theorem	VERB
ejpam-5246	139	10	,	,	PUNCT
ejpam-5246	139	11	we	we	PRON
ejpam-5246	139	12	find∣∣∣∣∣	find∣∣∣∣∣	VERB
ejpam-5246	139	13	∣∣∣∣un	∣∣∣∣un	PROPN
ejpam-5246	139	14	i+1	i+1	ADV
ejpam-5246	139	15	−	−	PROPN
ejpam-5246	140	1	un	un	PROPN
ejpam-5246	141	1	i−1	i−1	PROPN
ejpam-5246	141	2	2h	2h	NUM
ejpam-5246	141	3	∣∣∣∣q1	∣∣∣∣q1	PUNCT
ejpam-5246	141	4	−	−	PROPN
ejpam-5246	142	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5246	142	2	ũn	ũn	NOUN
ejpam-5246	142	3	i+1	i+1	ADV
ejpam-5246	142	4	−	−	NOUN
ejpam-5246	142	5	ũn	ũn	VERB
ejpam-5246	143	1	i−1	i−1	PROPN
ejpam-5246	143	2	2h	2h	NUM
ejpam-5246	143	3	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5246	143	4	q1	q1	PROPN
ejpam-5246	143	5	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-5246	143	6	≤	≤	ADJ
ejpam-5246	143	7	∣∣g′	∣∣g′	NOUN
ejpam-5246	143	8	(	(	PUNCT
ejpam-5246	143	9	εi)∣∣	εi)∣∣	VERB
ejpam-5246	143	10	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5246	143	11	(	(	PUNCT
ejpam-5246	143	12	un	un	PROPN
ejpam-5246	143	13	i+1	i+1	X
ejpam-5246	143	14	−	−	PROPN
ejpam-5246	143	15	un	un	PROPN
ejpam-5246	143	16	i−1	i−1	PROPN
ejpam-5246	143	17	2h	2h	NUM
ejpam-5246	143	18	)	)	PUNCT
ejpam-5246	143	19	−	−	PROPN
ejpam-5246	143	20	(	(	PUNCT
ejpam-5246	143	21	ũn	ũn	NOUN
ejpam-5246	143	22	i+1	i+1	ADV
ejpam-5246	143	23	−	−	NOUN
ejpam-5246	143	24	ũn	ũn	VERB
ejpam-5246	143	25	i−1	i−1	PROPN
ejpam-5246	143	26	2h	2h	NUM
ejpam-5246	143	27	)	)	PUNCT
ejpam-5246	143	28	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-5246	143	29	,	,	PUNCT
ejpam-5246	143	30	(	(	PUNCT
ejpam-5246	143	31	2.7	2.7	NUM
ejpam-5246	143	32	)	)	PUNCT
ejpam-5246	143	33	where	where	SCONJ
ejpam-5246	143	34	εi	εi	NOUN
ejpam-5246	143	35	is	be	AUX
ejpam-5246	143	36	an	an	DET
ejpam-5246	143	37	intermediate	intermediate	ADJ
ejpam-5246	143	38	value	value	NOUN
ejpam-5246	143	39	between	between	ADP
ejpam-5246	143	40	a1i	a1i	PROPN
ejpam-5246	143	41	=	=	SYM
ejpam-5246	143	42	(	(	PUNCT
ejpam-5246	143	43	un	un	PROPN
ejpam-5246	143	44	i+1	i+1	X
ejpam-5246	143	45	−	−	PROPN
ejpam-5246	143	46	un	un	PROPN
ejpam-5246	143	47	i−1	i−1	PROPN
ejpam-5246	143	48	2h	2h	NUM
ejpam-5246	143	49	)	)	PUNCT
ejpam-5246	143	50	and	and	CCONJ
ejpam-5246	143	51	a2i	a2i	NOUN
ejpam-5246	144	1	=	=	PUNCT
ejpam-5246	144	2	(	(	PUNCT
ejpam-5246	144	3	ũn	ũn	NOUN
ejpam-5246	144	4	i+1	i+1	ADV
ejpam-5246	144	5	−	−	NOUN
ejpam-5246	144	6	ũn	ũn	VERB
ejpam-5246	144	7	i−1	i−1	PROPN
ejpam-5246	144	8	2h	2h	NUM
ejpam-5246	144	9	)	)	PUNCT
ejpam-5246	144	10	,	,	PUNCT
ejpam-5246	144	11	since	since	SCONJ
ejpam-5246	144	12	un	un	PROPN
ejpam-5246	144	13	h	h	PROPN
ejpam-5246	144	14	ũ	ũ	PROPN
ejpam-5246	144	15	n	n	DET
ejpam-5246	144	16	h	h	NOUN
ejpam-5246	144	17	are	be	AUX
ejpam-5246	144	18	bounded	bound	VERB
ejpam-5246	144	19	in	in	ADP
ejpam-5246	144	20	[	[	X
ejpam-5246	144	21	0	0	NUM
ejpam-5246	144	22	,	,	PUNCT
ejpam-5246	144	23	t	t	X
ejpam-5246	144	24	]	]	PUNCT
ejpam-5246	144	25	.	.	PUNCT
ejpam-5246	145	1	therefore	therefore	ADV
ejpam-5246	145	2	,	,	PUNCT
ejpam-5246	145	3	there	there	PRON
ejpam-5246	145	4	exists	exist	VERB
ejpam-5246	145	5	c2	c2	PROPN
ejpam-5246	145	6	>	>	X
ejpam-5246	145	7	0	0	NUM
ejpam-5246	146	1	such	such	ADJ
ejpam-5246	146	2	that	that	DET
ejpam-5246	146	3	|g′	|g′	NOUN
ejpam-5246	146	4	(	(	PUNCT
ejpam-5246	146	5	εi)|	εi)|	PROPN
ejpam-5246	146	6	≤	≤	PROPN
ejpam-5246	146	7	c2	c2	PROPN
ejpam-5246	146	8	.	.	PUNCT
ejpam-5246	147	1	from	from	ADP
ejpam-5246	147	2	(	(	PUNCT
ejpam-5246	147	3	2.6	2.6	NUM
ejpam-5246	147	4	)	)	PUNCT
ejpam-5246	147	5	and	and	CCONJ
ejpam-5246	147	6	(	(	PUNCT
ejpam-5246	147	7	2.7	2.7	NUM
ejpam-5246	147	8	)	)	PUNCT
ejpam-5246	147	9	,	,	PUNCT
ejpam-5246	147	10	we	we	PRON
ejpam-5246	147	11	get	get	VERB
ejpam-5246	147	12	(	(	PUNCT
ejpam-5246	147	13	2.4	2.4	NUM
ejpam-5246	147	14	)	)	PUNCT
ejpam-5246	147	15	.	.	PUNCT
ejpam-5246	148	1	similarly	similarly	ADV
ejpam-5246	148	2	,	,	PUNCT
ejpam-5246	148	3	we	we	PRON
ejpam-5246	148	4	can	can	AUX
ejpam-5246	148	5	show	show	VERB
ejpam-5246	148	6	that	that	SCONJ
ejpam-5246	148	7	(	(	PUNCT
ejpam-5246	148	8	2.5	2.5	NUM
ejpam-5246	148	9	)	)	PUNCT
ejpam-5246	148	10	is	be	AUX
ejpam-5246	148	11	held	hold	VERB
ejpam-5246	148	12	.	.	PUNCT
ejpam-5246	149	1	2.1	2.1	NUM
ejpam-5246	149	2	.	.	PUNCT
ejpam-5246	150	1	the	the	DET
ejpam-5246	150	2	algorithm	algorithm	NOUN
ejpam-5246	150	3	steps	step	VERB
ejpam-5246	150	4	for	for	ADP
ejpam-5246	150	5	euler	euler	NOUN
ejpam-5246	150	6	explicit	explicit	ADJ
ejpam-5246	150	7	method	method	NOUN
ejpam-5246	150	8	1	1	NUM
ejpam-5246	150	9	.	.	PUNCT
ejpam-5246	150	10	input	input	PROPN
ejpam-5246	150	11	h	h	NOUN
ejpam-5246	150	12	,	,	PUNCT
ejpam-5246	150	13	u0	u0	ADJ
ejpam-5246	150	14	h	h	PROPN
ejpam-5246	150	15	,	,	PUNCT
ejpam-5246	150	16	v	v	NOUN
ejpam-5246	150	17	0	0	NUM
ejpam-5246	150	18	h	h	NOUN
ejpam-5246	150	19	,	,	PUNCT
ejpam-5246	150	20	p1,p2	p1,p2	PROPN
ejpam-5246	150	21	,	,	PUNCT
ejpam-5246	150	22	q1	q1	PROPN
ejpam-5246	150	23	,	,	PUNCT
ejpam-5246	150	24	q2	q2	PROPN
ejpam-5246	150	25	,	,	PUNCT
ejpam-5246	150	26	α	α	PROPN
ejpam-5246	150	27	2	2	X
ejpam-5246	150	28	.	.	PUNCT
ejpam-5246	150	29	put	put	VERB
ejpam-5246	150	30	n	n	NOUN
ejpam-5246	150	31	=	=	SYM
ejpam-5246	150	32	0	0	NUM
ejpam-5246	150	33	;	;	PUNCT
ejpam-5246	150	34	3	3	X
ejpam-5246	150	35	.	.	X
ejpam-5246	150	36	choose	choose	VERB
ejpam-5246	150	37	kn	kn	PROPN
ejpam-5246	150	38	according	accord	VERB
ejpam-5246	150	39	to	to	ADP
ejpam-5246	150	40	(	(	PUNCT
ejpam-5246	150	41	2.3	2.3	NUM
ejpam-5246	150	42	)	)	PUNCT
ejpam-5246	150	43	.	.	PUNCT
ejpam-5246	151	1	4	4	X
ejpam-5246	151	2	.	.	X
ejpam-5246	151	3	compute	compute	VERB
ejpam-5246	151	4	the	the	DET
ejpam-5246	151	5	numerical	numerical	ADJ
ejpam-5246	151	6	vectors	vector	NOUN
ejpam-5246	151	7	:	:	PUNCT
ejpam-5246	151	8	un+1	un+1	PROPN
ejpam-5246	151	9	h	h	NOUN
ejpam-5246	151	10	,	,	PUNCT
ejpam-5246	151	11	v	v	NOUN
ejpam-5246	151	12	n+1	n+1	PROPN
ejpam-5246	151	13	h	h	NOUN
ejpam-5246	151	14	,	,	PUNCT
ejpam-5246	151	15	using	use	VERB
ejpam-5246	151	16	the	the	DET
ejpam-5246	151	17	explicit	explicit	ADJ
ejpam-5246	151	18	formula	formula	NOUN
ejpam-5246	151	19	(	(	PUNCT
ejpam-5246	151	20	2.1	2.1	NUM
ejpam-5246	151	21	)	)	PUNCT
ejpam-5246	151	22	and	and	CCONJ
ejpam-5246	151	23	(	(	PUNCT
ejpam-5246	151	24	2.2	2.2	NUM
ejpam-5246	151	25	)	)	PUNCT
ejpam-5246	151	26	.	.	PUNCT
ejpam-5246	152	1	5	5	X
ejpam-5246	152	2	.	.	X
ejpam-5246	152	3	for	for	ADP
ejpam-5246	152	4	n	n	NOUN
ejpam-5246	152	5	=	=	SYM
ejpam-5246	152	6	1	1	NUM
ejpam-5246	152	7	,	,	PUNCT
ejpam-5246	152	8	2	2	NUM
ejpam-5246	152	9	,	,	PUNCT
ejpam-5246	152	10	.	.	PUNCT
ejpam-5246	152	11	.	.	PUNCT
ejpam-5246	152	12	.	.	PUNCT
ejpam-5246	153	1	..	..	PUNCT
ejpam-5246	153	2	,	,	PUNCT
ejpam-5246	153	3	repeat	repeat	VERB
ejpam-5246	153	4	steps	step	NOUN
ejpam-5246	153	5	3,4	3,4	NUM
ejpam-5246	153	6	until	until	ADP
ejpam-5246	153	7	for	for	ADP
ejpam-5246	153	8	n	n	NOUN
ejpam-5246	153	9	=	=	SYM
ejpam-5246	153	10	m	m	PROPN
ejpam-5246	153	11	,	,	PUNCT
ejpam-5246	153	12	we	we	PRON
ejpam-5246	153	13	get	get	VERB
ejpam-5246	153	14	∥un	∥un	PROPN
ejpam-5246	153	15	h	h	PROPN
ejpam-5246	153	16	∥∞	∥∞	PROPN
ejpam-5246	153	17	≥	≥	NUM
ejpam-5246	153	18	1015	1015	NUM
ejpam-5246	153	19	,	,	PUNCT
ejpam-5246	153	20	or	or	CCONJ
ejpam-5246	153	21	∥v	∥v	PROPN
ejpam-5246	153	22	n	n	PRON
ejpam-5246	153	23	h	h	NOUN
ejpam-5246	153	24	∥∞	∥∞	ADJ
ejpam-5246	153	25	≥	≥	NUM
ejpam-5246	153	26	1015	1015	NUM
ejpam-5246	153	27	6	6	NUM
ejpam-5246	153	28	.	.	PUNCT
ejpam-5246	154	1	the	the	DET
ejpam-5246	154	2	numerical	numerical	ADJ
ejpam-5246	154	3	blow	blow	VERB
ejpam-5246	154	4	-	-	PUNCT
ejpam-5246	154	5	up	up	ADP
ejpam-5246	154	6	time	time	NOUN
ejpam-5246	154	7	is	be	AUX
ejpam-5246	154	8	tm	tm	PROPN
ejpam-5246	154	9	=	=	PROPN
ejpam-5246	154	10	∑m	∑m	PROPN
ejpam-5246	154	11	n=0	n=0	PROPN
ejpam-5246	154	12	kn	kn	PROPN
ejpam-5246	154	13	.	.	PROPN
ejpam-5246	154	14	m.i.khalil	m.i.khalil	PROPN
ejpam-5246	154	15	et	et	PROPN
ejpam-5246	154	16	al	al	PROPN
ejpam-5246	154	17	.	.	PUNCT
ejpam-5246	154	18	/	/	SYM
ejpam-5246	154	19	eur	eur	PROPN
ejpam-5246	154	20	.	.	PUNCT
ejpam-5246	155	1	j.	j.	PROPN
ejpam-5246	155	2	pure	pure	PROPN
ejpam-5246	155	3	appl	appl	PROPN
ejpam-5246	155	4	.	.	PROPN
ejpam-5246	155	5	math	math	PROPN
ejpam-5246	155	6	,	,	PUNCT
ejpam-5246	155	7	17	17	NUM
ejpam-5246	155	8	(	(	PUNCT
ejpam-5246	155	9	3	3	NUM
ejpam-5246	155	10	)	)	PUNCT
ejpam-5246	155	11	(	(	PUNCT
ejpam-5246	155	12	2024	2024	NUM
ejpam-5246	155	13	)	)	PUNCT
ejpam-5246	155	14	,	,	PUNCT
ejpam-5246	155	15	1516	1516	NUM
ejpam-5246	155	16	-	-	SYM
ejpam-5246	155	17	1538	1538	NUM
ejpam-5246	155	18	1521	1521	NUM
ejpam-5246	155	19	2.2	2.2	NUM
ejpam-5246	155	20	.	.	PUNCT
ejpam-5246	156	1	local	local	ADJ
ejpam-5246	156	2	truncation	truncation	NOUN
ejpam-5246	156	3	error	error	NOUN
ejpam-5246	156	4	of	of	ADP
ejpam-5246	156	5	explicit	explicit	ADJ
ejpam-5246	156	6	euler	euler	NOUN
ejpam-5246	156	7	scheme	scheme	NOUN
ejpam-5246	156	8	theorem	theorem	NOUN
ejpam-5246	156	9	1	1	X
ejpam-5246	156	10	.	.	PUNCT
ejpam-5246	157	1	let	let	VERB
ejpam-5246	157	2	(	(	PUNCT
ejpam-5246	157	3	tn	tn	PROPN
ejpam-5246	157	4	ui	ui	PROPN
ejpam-5246	157	5	,	,	PUNCT
ejpam-5246	157	6	t	t	PROPN
ejpam-5246	157	7	n	n	PRON
ejpam-5246	157	8	vi	vi	PROPN
ejpam-5246	157	9	)	)	PUNCT
ejpam-5246	157	10	be	be	VERB
ejpam-5246	157	11	the	the	DET
ejpam-5246	157	12	local	local	ADJ
ejpam-5246	157	13	error	error	NOUN
ejpam-5246	157	14	truncation	truncation	NOUN
ejpam-5246	157	15	of	of	ADP
ejpam-5246	157	16	the	the	DET
ejpam-5246	157	17	explicit	explicit	ADJ
ejpam-5246	157	18	euler	euler	NOUN
ejpam-5246	157	19	chart	chart	NOUN
ejpam-5246	157	20	(	(	PUNCT
ejpam-5246	157	21	2.1	2.1	NUM
ejpam-5246	157	22	)	)	PUNCT
ejpam-5246	157	23	and	and	CCONJ
ejpam-5246	157	24	(	(	PUNCT
ejpam-5246	157	25	2.2	2.2	NUM
ejpam-5246	157	26	)	)	PUNCT
ejpam-5246	157	27	at	at	ADP
ejpam-5246	157	28	the	the	DET
ejpam-5246	157	29	grid	grid	NOUN
ejpam-5246	157	30	-	-	PUNCT
ejpam-5246	157	31	point	point	NOUN
ejpam-5246	157	32	(	(	PUNCT
ejpam-5246	157	33	xi	xi	PROPN
ejpam-5246	157	34	,	,	PUNCT
ejpam-5246	157	35	tn	tn	PROPN
ejpam-5246	157	36	)	)	PUNCT
ejpam-5246	157	37	.	.	PUNCT
ejpam-5246	158	1	after	after	ADP
ejpam-5246	158	2	that	that	PRON
ejpam-5246	158	3	,	,	PUNCT
ejpam-5246	158	4	here	here	ADV
ejpam-5246	158	5	it	it	PRON
ejpam-5246	158	6	isc1	isc1	PROPN
ejpam-5246	158	7	,	,	PUNCT
ejpam-5246	158	8	c2	c2	PROPN
ejpam-5246	158	9	,	,	PUNCT
ejpam-5246	158	10	c3	c3	PROPN
ejpam-5246	158	11	,	,	PUNCT
ejpam-5246	158	12	c4	c4	NOUN
ejpam-5246	158	13	>	>	X
ejpam-5246	158	14	0	0	PUNCT
ejpam-5246	159	1	like	like	ADP
ejpam-5246	159	2	this	this	PRON
ejpam-5246	159	3	|tn	|tn	PUNCT
ejpam-5246	159	4	ui|	ui|	PROPN
ejpam-5246	159	5	≤	≤	PROPN
ejpam-5246	159	6	c1k	c1k	NOUN
ejpam-5246	159	7	+	+	CCONJ
ejpam-5246	159	8	c2h	c2h	PROPN
ejpam-5246	159	9	2	2	NUM
ejpam-5246	159	10	,	,	PUNCT
ejpam-5246	159	11	|tn	|tn	X
ejpam-5246	159	12	vi|	vi|	PROPN
ejpam-5246	159	13	≤	≤	NUM
ejpam-5246	159	14	c3k	c3k	PROPN
ejpam-5246	159	15	+	+	CCONJ
ejpam-5246	159	16	c4h	c4h	NOUN
ejpam-5246	159	17	2	2	NUM
ejpam-5246	159	18	,	,	PUNCT
ejpam-5246	159	19	where	where	SCONJ
ejpam-5246	159	20	k	k	NOUN
ejpam-5246	159	21	=	=	SYM
ejpam-5246	159	22	maxn∈n	maxn∈n	PROPN
ejpam-5246	159	23	kn	kn	PROPN
ejpam-5246	159	24	,	,	PUNCT
ejpam-5246	159	25	i.e.	i.e.	X
ejpam-5246	159	26	tn	tn	NOUN
ejpam-5246	159	27	ui	ui	PROPN
ejpam-5246	160	1	=	=	PUNCT
ejpam-5246	160	2	o	o	X
ejpam-5246	160	3	(	(	PUNCT
ejpam-5246	160	4	k	k	PROPN
ejpam-5246	160	5	+	+	CCONJ
ejpam-5246	160	6	h2	h2	NOUN
ejpam-5246	160	7	)	)	PUNCT
ejpam-5246	160	8	and	and	CCONJ
ejpam-5246	160	9	tn	tn	PROPN
ejpam-5246	160	10	vi	vi	PROPN
ejpam-5246	161	1	=	=	NOUN
ejpam-5246	161	2	o	o	X
ejpam-5246	161	3	(	(	PUNCT
ejpam-5246	161	4	k	k	PROPN
ejpam-5246	161	5	+	+	CCONJ
ejpam-5246	161	6	h2	h2	NOUN
ejpam-5246	161	7	)	)	PUNCT
ejpam-5246	161	8	.	.	PUNCT
ejpam-5246	162	1	proof	proof	NOUN
ejpam-5246	162	2	.	.	PUNCT
ejpam-5246	163	1	replace	replace	VERB
ejpam-5246	163	2	the	the	DET
ejpam-5246	163	3	precise	precise	ADJ
ejpam-5246	163	4	solution	solution	NOUN
ejpam-5246	163	5	uni	uni	PROPN
ejpam-5246	164	1	=	=	PUNCT
ejpam-5246	164	2	u	u	PROPN
ejpam-5246	164	3	(	(	PUNCT
ejpam-5246	164	4	xi	xi	PROPN
ejpam-5246	164	5	,	,	PUNCT
ejpam-5246	164	6	tn	tn	PROPN
ejpam-5246	164	7	)	)	PUNCT
ejpam-5246	164	8	and	and	CCONJ
ejpam-5246	164	9	vni	vni	X
ejpam-5246	164	10	=	=	SYM
ejpam-5246	164	11	v	v	PROPN
ejpam-5246	164	12	(	(	PUNCT
ejpam-5246	164	13	xi	xi	PROPN
ejpam-5246	164	14	,	,	PUNCT
ejpam-5246	164	15	tn	tn	PROPN
ejpam-5246	164	16	)	)	PUNCT
ejpam-5246	164	17	into	into	ADP
ejpam-5246	164	18	the	the	DET
ejpam-5246	164	19	explicit	explicit	ADJ
ejpam-5246	164	20	(	(	PUNCT
ejpam-5246	164	21	2.1	2.1	NUM
ejpam-5246	164	22	)	)	PUNCT
ejpam-5246	164	23	yields	yield	NOUN
ejpam-5246	164	24	tn	tn	NOUN
ejpam-5246	164	25	ui	ui	PROPN
ejpam-5246	165	1	=	=	PUNCT
ejpam-5246	166	1	(	(	PUNCT
ejpam-5246	166	2	un+1	un+1	ADV
ejpam-5246	166	3	i	i	PRON
ejpam-5246	166	4	−	−	PROPN
ejpam-5246	166	5	uni	uni	INTJ
ejpam-5246	166	6	)	)	PUNCT
ejpam-5246	166	7	−	−	PROPN
ejpam-5246	167	1	kn	kn	PROPN
ejpam-5246	167	2	h2	h2	PROPN
ejpam-5246	167	3	(	(	PUNCT
ejpam-5246	167	4	uni+1	uni+1	NOUN
ejpam-5246	167	5	−	−	PROPN
ejpam-5246	167	6	2uni	2uni	NUM
ejpam-5246	167	7	+	+	CCONJ
ejpam-5246	167	8	uni−1	uni−1	PROPN
ejpam-5246	167	9	)	)	PUNCT
ejpam-5246	168	1	−	−	PROPN
ejpam-5246	168	2	kn	kn	PROPN
ejpam-5246	168	3	(	(	PUNCT
ejpam-5246	168	4	v	v	NOUN
ejpam-5246	168	5	n	n	NOUN
ejpam-5246	168	6	i	i	NOUN
ejpam-5246	168	7	)	)	PUNCT
ejpam-5246	168	8	p1	p1	PROPN
ejpam-5246	168	9	+	+	CCONJ
ejpam-5246	168	10	kn	kn	PROPN
ejpam-5246	168	11	∣∣∣∣un	∣∣∣∣un	PROPN
ejpam-5246	168	12	i+1	i+1	ADV
ejpam-5246	168	13	−	−	PROPN
ejpam-5246	168	14	un	un	PROPN
ejpam-5246	168	15	i−1	i−1	PROPN
ejpam-5246	168	16	2h	2h	NUM
ejpam-5246	168	17	∣∣∣∣q1	∣∣∣∣q1	PUNCT
ejpam-5246	168	18	=	=	SYM
ejpam-5246	168	19	kn	kn	PROPN
ejpam-5246	168	20	[	[	PUNCT
ejpam-5246	168	21	∂uni	∂uni	PUNCT
ejpam-5246	168	22	∂t	∂t	PROPN
ejpam-5246	168	23	+	+	NOUN
ejpam-5246	168	24	o(kn	o(kn	PROPN
ejpam-5246	168	25	)	)	PUNCT
ejpam-5246	168	26	]	]	PUNCT
ejpam-5246	169	1	−	−	PROPN
ejpam-5246	169	2	kn	kn	PROPN
ejpam-5246	169	3	[	[	PUNCT
ejpam-5246	169	4	∂2uni	∂2uni	X
ejpam-5246	169	5	∂x2	∂x2	VERB
ejpam-5246	169	6	+	+	NOUN
ejpam-5246	169	7	o	o	X
ejpam-5246	169	8	(	(	PUNCT
ejpam-5246	169	9	h2	h2	PROPN
ejpam-5246	169	10	)	)	PUNCT
ejpam-5246	169	11	]	]	PUNCT
ejpam-5246	170	1	−	−	PROPN
ejpam-5246	170	2	kn	kn	PROPN
ejpam-5246	170	3	(	(	PUNCT
ejpam-5246	170	4	v	v	NOUN
ejpam-5246	170	5	n	n	NOUN
ejpam-5246	170	6	i	i	NOUN
ejpam-5246	170	7	)	)	PUNCT
ejpam-5246	170	8	p1	p1	PROPN
ejpam-5246	170	9	+	+	CCONJ
ejpam-5246	170	10	kn	kn	PROPN
ejpam-5246	171	1	[	[	X
ejpam-5246	171	2	∣∣∣∣∂uni∂x	∣∣∣∣∂uni∂x	PROPN
ejpam-5246	171	3	∣∣∣∣q1	∣∣∣∣q1	PUNCT
ejpam-5246	172	1	+	+	ADJ
ejpam-5246	172	2	o	o	PROPN
ejpam-5246	172	3	(	(	PUNCT
ejpam-5246	172	4	h2	h2	PROPN
ejpam-5246	172	5	)	)	PUNCT
ejpam-5246	172	6	]	]	PUNCT
ejpam-5246	173	1	=	=	PUNCT
ejpam-5246	173	2	kn	kn	PROPN
ejpam-5246	173	3	[	[	PUNCT
ejpam-5246	173	4	∂uni	∂uni	PUNCT
ejpam-5246	173	5	∂t	∂t	PROPN
ejpam-5246	173	6	−	−	PROPN
ejpam-5246	173	7	∂2uni	∂2uni	PROPN
ejpam-5246	173	8	∂x2	∂x2	NOUN
ejpam-5246	173	9	−	−	NOUN
ejpam-5246	173	10	(	(	PUNCT
ejpam-5246	173	11	vni	vni	NOUN
ejpam-5246	173	12	)	)	PUNCT
ejpam-5246	173	13	p1	p1	PROPN
ejpam-5246	173	14	+	+	CCONJ
ejpam-5246	173	15	∣∣∣∣∂uni∂x	∣∣∣∣∂uni∂x	VERB
ejpam-5246	173	16	∣∣∣∣q1]+	∣∣∣∣q1]+	PROPN
ejpam-5246	173	17	kn	kn	PROPN
ejpam-5246	173	18	[	[	PUNCT
ejpam-5246	173	19	o(kn	o(kn	NUM
ejpam-5246	173	20	)	)	PUNCT
ejpam-5246	174	1	+	+	NOUN
ejpam-5246	174	2	o	o	X
ejpam-5246	174	3	(	(	PUNCT
ejpam-5246	174	4	h2	h2	PROPN
ejpam-5246	174	5	)	)	PUNCT
ejpam-5246	174	6	]	]	PUNCT
ejpam-5246	174	7	.	.	PUNCT
ejpam-5246	175	1	from	from	ADP
ejpam-5246	175	2	system	system	NOUN
ejpam-5246	175	3	(	(	PUNCT
ejpam-5246	175	4	1.1	1.1	NUM
ejpam-5246	175	5	)	)	PUNCT
ejpam-5246	175	6	,	,	PUNCT
ejpam-5246	175	7	assuming	assume	VERB
ejpam-5246	175	8	all	all	DET
ejpam-5246	175	9	the	the	DET
ejpam-5246	175	10	partial	partial	ADJ
ejpam-5246	175	11	derivatives	derivative	NOUN
ejpam-5246	175	12	are	be	AUX
ejpam-5246	175	13	bounded	bound	VERB
ejpam-5246	175	14	at	at	ADP
ejpam-5246	175	15	the	the	DET
ejpam-5246	175	16	grid	grid	NOUN
ejpam-5246	175	17	-	-	PUNCT
ejpam-5246	175	18	point	point	NOUN
ejpam-5246	175	19	(	(	PUNCT
ejpam-5246	175	20	xi	xi	PROPN
ejpam-5246	175	21	,	,	PUNCT
ejpam-5246	175	22	tn	tn	PROPN
ejpam-5246	175	23	)	)	PUNCT
ejpam-5246	175	24	,	,	PUNCT
ejpam-5246	175	25	we	we	PRON
ejpam-5246	175	26	obtain	obtain	VERB
ejpam-5246	175	27	|tn	|tn	PUNCT
ejpam-5246	175	28	ui|	ui|	PROPN
ejpam-5246	175	29	≤	≤	NUM
ejpam-5246	175	30	c1kn	c1kn	PUNCT
ejpam-5246	176	1	+	+	CCONJ
ejpam-5246	176	2	c2h	c2h	PROPN
ejpam-5246	176	3	2	2	NUM
ejpam-5246	176	4	≤	≤	NOUN
ejpam-5246	176	5	c1k	c1k	NOUN
ejpam-5246	176	6	+	+	CCONJ
ejpam-5246	176	7	c2h	c2h	PROPN
ejpam-5246	176	8	2	2	NUM
ejpam-5246	176	9	,	,	PUNCT
ejpam-5246	176	10	where	where	SCONJ
ejpam-5246	176	11	c1	c1	PROPN
ejpam-5246	176	12	,	,	PUNCT
ejpam-5246	176	13	c2	c2	PROPN
ejpam-5246	176	14	>	>	X
ejpam-5246	176	15	0	0	PROPN
ejpam-5246	176	16	,	,	PUNCT
ejpam-5246	176	17	i.e.	i.e.	X
ejpam-5246	176	18	tn	tn	NOUN
ejpam-5246	176	19	ui	ui	PROPN
ejpam-5246	177	1	=	=	PUNCT
ejpam-5246	177	2	o	o	X
ejpam-5246	177	3	(	(	PUNCT
ejpam-5246	177	4	k	k	PROPN
ejpam-5246	177	5	+	+	CCONJ
ejpam-5246	177	6	h2	h2	NOUN
ejpam-5246	177	7	)	)	PUNCT
ejpam-5246	177	8	,	,	PUNCT
ejpam-5246	177	9	c	c	X
ejpam-5246	177	10	>	>	X
ejpam-5246	177	11	0	0	X
ejpam-5246	177	12	.	.	PUNCT
ejpam-5246	178	1	likewise	likewise	ADV
ejpam-5246	178	2	,	,	PUNCT
ejpam-5246	178	3	we	we	PRON
ejpam-5246	178	4	show	show	VERB
ejpam-5246	178	5	that	that	SCONJ
ejpam-5246	178	6	tn	tn	PROPN
ejpam-5246	178	7	vi	vi	PROPN
ejpam-5246	179	1	=	=	NOUN
ejpam-5246	179	2	o	o	X
ejpam-5246	179	3	(	(	PUNCT
ejpam-5246	179	4	k	k	PROPN
ejpam-5246	179	5	+	+	CCONJ
ejpam-5246	179	6	h2	h2	NOUN
ejpam-5246	179	7	)	)	PUNCT
ejpam-5246	179	8	,	,	PUNCT
ejpam-5246	179	9	c	c	X
ejpam-5246	179	10	>	>	X
ejpam-5246	179	11	0	0	NUM
ejpam-5246	179	12	.	.	PROPN
ejpam-5246	179	13	2.3	2.3	NUM
ejpam-5246	179	14	.	.	PUNCT
ejpam-5246	180	1	the	the	DET
ejpam-5246	180	2	stability	stability	NOUN
ejpam-5246	180	3	analysis	analysis	NOUN
ejpam-5246	180	4	of	of	ADP
ejpam-5246	180	5	explicit	explicit	ADJ
ejpam-5246	180	6	euler	euler	NOUN
ejpam-5246	180	7	method	method	NOUN
ejpam-5246	180	8	the	the	DET
ejpam-5246	180	9	stability	stability	NOUN
ejpam-5246	180	10	condition	condition	NOUN
ejpam-5246	180	11	for	for	ADP
ejpam-5246	180	12	explicit	explicit	ADJ
ejpam-5246	180	13	euler	euler	NOUN
ejpam-5246	180	14	scheme	scheme	NOUN
ejpam-5246	180	15	can	can	AUX
ejpam-5246	180	16	be	be	AUX
ejpam-5246	180	17	obtained	obtain	VERB
ejpam-5246	180	18	based	base	VERB
ejpam-5246	180	19	on	on	ADP
ejpam-5246	180	20	the	the	DET
ejpam-5246	180	21	the	the	DET
ejpam-5246	180	22	following	follow	VERB
ejpam-5246	180	23	definition	definition	NOUN
ejpam-5246	180	24	definition	definition	NOUN
ejpam-5246	180	25	1	1	NUM
ejpam-5246	180	26	.	.	PUNCT
ejpam-5246	181	1	[	[	X
ejpam-5246	181	2	13	13	NUM
ejpam-5246	181	3	]	]	PUNCT
ejpam-5246	181	4	.	.	PUNCT
ejpam-5246	182	1	for	for	ADP
ejpam-5246	182	2	i	i	PRON
ejpam-5246	182	3	=	=	SYM
ejpam-5246	182	4	1	1	NUM
ejpam-5246	182	5	,	,	PUNCT
ejpam-5246	182	6	2	2	NUM
ejpam-5246	182	7	,	,	PUNCT
ejpam-5246	182	8	.	.	PUNCT
ejpam-5246	182	9	.	.	PUNCT
ejpam-5246	182	10	.	.	PUNCT
ejpam-5246	183	1	,	,	PUNCT
ejpam-5246	183	2	i	i	PRON
ejpam-5246	183	3	−	−	PROPN
ejpam-5246	183	4	1	1	NUM
ejpam-5246	183	5	,	,	PUNCT
ejpam-5246	183	6	set	set	VERB
ejpam-5246	183	7	en	en	PROPN
ejpam-5246	183	8	u	u	NOUN
ejpam-5246	183	9	=	=	SYM
ejpam-5246	183	10	(	(	PUNCT
ejpam-5246	183	11	enui	enui	NOUN
ejpam-5246	183	12	)	)	PUNCT
ejpam-5246	183	13	,	,	PUNCT
ejpam-5246	183	14	e	e	PROPN
ejpam-5246	183	15	n	n	CCONJ
ejpam-5246	183	16	v	v	NOUN
ejpam-5246	183	17	=	=	SYM
ejpam-5246	183	18	(	(	PUNCT
ejpam-5246	183	19	envi	envi	NOUN
ejpam-5246	183	20	)	)	PUNCT
ejpam-5246	183	21	,	,	PUNCT
ejpam-5246	183	22	e	e	X
ejpam-5246	183	23	n	n	PRON
ejpam-5246	183	24	ui	ui	NOUN
ejpam-5246	184	1	=	=	PUNCT
ejpam-5246	184	2	uni	uni	PROPN
ejpam-5246	185	1	−	−	PROPN
ejpam-5246	185	2	un	un	PROPN
ejpam-5246	185	3	i	i	PROPN
ejpam-5246	185	4	and	and	CCONJ
ejpam-5246	185	5	envi	envi	PROPN
ejpam-5246	185	6	=	=	PUNCT
ejpam-5246	185	7	vni	vni	PROPN
ejpam-5246	185	8	−	−	PROPN
ejpam-5246	185	9	v	v	NOUN
ejpam-5246	185	10	n	n	NOUN
ejpam-5246	186	1	i	i	PRON
ejpam-5246	186	2	,	,	PUNCT
ejpam-5246	186	3	where	where	SCONJ
ejpam-5246	186	4	uni	uni	PROPN
ejpam-5246	186	5	=	=	SYM
ejpam-5246	186	6	u(xi	u(xi	PROPN
ejpam-5246	186	7	,	,	PUNCT
ejpam-5246	186	8	tn	tn	PROPN
ejpam-5246	186	9	)	)	PUNCT
ejpam-5246	186	10	,	,	PUNCT
ejpam-5246	186	11	v	v	PART
ejpam-5246	186	12	n	n	NOUN
ejpam-5246	186	13	i	i	NOUN
ejpam-5246	186	14	=	=	SYM
ejpam-5246	186	15	v(xi	v(xi	PROPN
ejpam-5246	186	16	,	,	PUNCT
ejpam-5246	186	17	tn	tn	PROPN
ejpam-5246	186	18	)	)	PUNCT
ejpam-5246	186	19	and	and	CCONJ
ejpam-5246	186	20	(	(	PUNCT
ejpam-5246	186	21	un	un	PROPN
ejpam-5246	186	22	i	i	PROPN
ejpam-5246	186	23	,	,	PUNCT
ejpam-5246	186	24	v	v	ADP
ejpam-5246	186	25	n	n	NOUN
ejpam-5246	186	26	i	i	PRON
ejpam-5246	186	27	)	)	PUNCT
ejpam-5246	186	28	are	be	AUX
ejpam-5246	186	29	a	a	DET
ejpam-5246	186	30	accurate	accurate	ADJ
ejpam-5246	186	31	and	and	CCONJ
ejpam-5246	186	32	numerical	numerical	ADJ
ejpam-5246	186	33	solutions	solution	NOUN
ejpam-5246	186	34	of	of	ADP
ejpam-5246	186	35	a	a	DET
ejpam-5246	186	36	one	one	NUM
ejpam-5246	186	37	-	-	PUNCT
ejpam-5246	186	38	dimensional	dimensional	ADJ
ejpam-5246	186	39	time	time	NOUN
ejpam-5246	186	40	-	-	PUNCT
ejpam-5246	186	41	dependent	dependent	ADJ
ejpam-5246	186	42	coupled	couple	VERB
ejpam-5246	186	43	system	system	NOUN
ejpam-5246	186	44	of	of	ADP
ejpam-5246	186	45	two	two	NUM
ejpam-5246	186	46	pdes	pde	NOUN
ejpam-5246	186	47	,	,	PUNCT
ejpam-5246	186	48	consecutively	consecutively	ADV
ejpam-5246	186	49	.	.	PUNCT
ejpam-5246	187	1	for	for	ADP
ejpam-5246	187	2	any	any	DET
ejpam-5246	187	3	hypothetical	hypothetical	ADJ
ejpam-5246	187	4	initial	initial	ADJ
ejpam-5246	187	5	rounding	rounding	NOUN
ejpam-5246	187	6	error	error	NOUN
ejpam-5246	187	7	(	(	PUNCT
ejpam-5246	187	8	e0	e0	PROPN
ejpam-5246	187	9	u	u	PROPN
ejpam-5246	187	10	,	,	PUNCT
ejpam-5246	187	11	e	e	PROPN
ejpam-5246	187	12	0	0	NUM
ejpam-5246	187	13	v	v	NOUN
ejpam-5246	187	14	)	)	PUNCT
ejpam-5246	187	15	,	,	PUNCT
ejpam-5246	187	16	we	we	PRON
ejpam-5246	187	17	say	say	VERB
ejpam-5246	187	18	that	that	SCONJ
ejpam-5246	187	19	the	the	DET
ejpam-5246	187	20	numerical	numerical	ADJ
ejpam-5246	187	21	solution	solution	NOUN
ejpam-5246	187	22	is	be	AUX
ejpam-5246	187	23	stable	stable	ADJ
ejpam-5246	187	24	,	,	PUNCT
ejpam-5246	187	25	if	if	SCONJ
ejpam-5246	187	26	a	a	DET
ejpam-5246	187	27	positive	positive	ADJ
ejpam-5246	187	28	number	number	NOUN
ejpam-5246	187	29	is	be	AUX
ejpam-5246	187	30	foundµ	foundµ	NOUN
ejpam-5246	187	31	freelance	freelance	NOUN
ejpam-5246	187	32	on	on	ADP
ejpam-5246	187	33	the	the	DET
ejpam-5246	187	34	space	space	NOUN
ejpam-5246	187	35	-	-	PUNCT
ejpam-5246	187	36	step	step	NOUN
ejpam-5246	187	37	(	(	PUNCT
ejpam-5246	187	38	h	h	NOUN
ejpam-5246	187	39	)	)	PUNCT
ejpam-5246	187	40	and	and	CCONJ
ejpam-5246	187	41	time	time	NOUN
ejpam-5246	187	42	-	-	PUNCT
ejpam-5246	187	43	step	step	NOUN
ejpam-5246	187	44	(	(	PUNCT
ejpam-5246	187	45	k	k	NOUN
ejpam-5246	187	46	)	)	PUNCT
ejpam-5246	187	47	,	,	PUNCT
ejpam-5246	187	48	as	as	SCONJ
ejpam-5246	187	49	follows	follow	VERB
ejpam-5246	187	50	∥en	∥en	PROPN
ejpam-5246	187	51	u∥	u∥	ADJ
ejpam-5246	187	52	≤	≤	ADV
ejpam-5246	187	53	µmax	µmax	ADJ
ejpam-5246	187	54	{	{	PUNCT
ejpam-5246	187	55	∥∥e0	∥∥e0	PROPN
ejpam-5246	187	56	u	u	PROPN
ejpam-5246	187	57	∥∥	∥∥	X
ejpam-5246	187	58	,	,	PUNCT
ejpam-5246	187	59	∥∥e0	∥∥e0	PROPN
ejpam-5246	187	60	v	v	X
ejpam-5246	187	61	∥∥	∥∥	PROPN
ejpam-5246	187	62	}	}	PUNCT
ejpam-5246	187	63	and	and	CCONJ
ejpam-5246	187	64	∥en	∥en	PROPN
ejpam-5246	187	65	v	v	NUM
ejpam-5246	187	66	∥	∥	PUNCT
ejpam-5246	187	67	≤	≤	NUM
ejpam-5246	187	68	µmax	µmax	ADJ
ejpam-5246	187	69	{	{	PUNCT
ejpam-5246	187	70	∥∥e0	∥∥e0	PROPN
ejpam-5246	187	71	u	u	PROPN
ejpam-5246	187	72	∥∥	∥∥	X
ejpam-5246	187	73	,	,	PUNCT
ejpam-5246	187	74	∥∥e0	∥∥e0	PROPN
ejpam-5246	187	75	v	v	X
ejpam-5246	187	76	∥∥	∥∥	PROPN
ejpam-5246	187	77	}	}	PUNCT
ejpam-5246	187	78	,	,	PUNCT
ejpam-5246	187	79	where	where	SCONJ
ejpam-5246	187	80	∥en	∥en	X
ejpam-5246	187	81	u∥	u∥	X
ejpam-5246	187	82	=	=	PUNCT
ejpam-5246	187	83	max1≤i≤i	max1≤i≤i	X
ejpam-5246	187	84	|enui|	|enui|	ADJ
ejpam-5246	187	85	and	and	CCONJ
ejpam-5246	187	86	∥en	∥en	PROPN
ejpam-5246	187	87	v	v	NOUN
ejpam-5246	187	88	∥	∥	NOUN
ejpam-5246	187	89	=	=	PUNCT
ejpam-5246	187	90	max1≤i≤i	max1≤i≤i	X
ejpam-5246	187	91	|envi|	|envi|	NOUN
ejpam-5246	187	92	,	,	PUNCT
ejpam-5246	187	93	n	n	NOUN
ejpam-5246	187	94	=	=	SYM
ejpam-5246	187	95	0	0	NUM
ejpam-5246	187	96	,	,	PUNCT
ejpam-5246	187	97	1	1	NUM
ejpam-5246	187	98	,	,	PUNCT
ejpam-5246	187	99	2	2	NUM
ejpam-5246	187	100	,	,	PUNCT
ejpam-5246	187	101	.	.	PUNCT
ejpam-5246	187	102	.	.	PUNCT
ejpam-5246	187	103	.	.	PUNCT
ejpam-5246	187	104	.	.	PUNCT
ejpam-5246	188	1	theorem	theorem	VERB
ejpam-5246	188	2	2	2	NUM
ejpam-5246	188	3	.	.	PUNCT
ejpam-5246	189	1	the	the	DET
ejpam-5246	189	2	explicit	explicit	ADJ
ejpam-5246	189	3	formulae(2.1	formulae(2.1	NOUN
ejpam-5246	189	4	)	)	PUNCT
ejpam-5246	189	5	,	,	PUNCT
ejpam-5246	189	6	(	(	PUNCT
ejpam-5246	189	7	2.2	2.2	NUM
ejpam-5246	189	8	)	)	PUNCT
ejpam-5246	189	9	is	be	AUX
ejpam-5246	189	10	stable	stable	ADJ
ejpam-5246	189	11	,	,	PUNCT
ejpam-5246	189	12	if	if	SCONJ
ejpam-5246	189	13	(	(	PUNCT
ejpam-5246	189	14	1	1	NUM
ejpam-5246	189	15	−	−	NOUN
ejpam-5246	189	16	2r	2r	NUM
ejpam-5246	189	17	)	)	PUNCT
ejpam-5246	189	18	≥	≥	NOUN
ejpam-5246	189	19	0	0	NUM
ejpam-5246	189	20	,	,	PUNCT
ejpam-5246	189	21	where	where	SCONJ
ejpam-5246	189	22	k	k	NOUN
ejpam-5246	189	23	=	=	SYM
ejpam-5246	189	24	maxn∈n	maxn∈n	PROPN
ejpam-5246	189	25	kn	kn	PROPN
ejpam-5246	189	26	,	,	PUNCT
ejpam-5246	189	27	r	r	NOUN
ejpam-5246	189	28	=	=	SYM
ejpam-5246	189	29	k	k	PROPN
ejpam-5246	189	30	/	/	SYM
ejpam-5246	189	31	h2	h2	PROPN
ejpam-5246	189	32	.	.	PUNCT
ejpam-5246	190	1	m.i.khalil	m.i.khalil	PROPN
ejpam-5246	190	2	et	et	PROPN
ejpam-5246	190	3	al	al	PROPN
ejpam-5246	190	4	.	.	PUNCT
ejpam-5246	190	5	/	/	SYM
ejpam-5246	190	6	eur	eur	PROPN
ejpam-5246	190	7	.	.	PUNCT
ejpam-5246	191	1	j.	j.	PROPN
ejpam-5246	191	2	pure	pure	PROPN
ejpam-5246	191	3	appl	appl	PROPN
ejpam-5246	191	4	.	.	PROPN
ejpam-5246	191	5	math	math	PROPN
ejpam-5246	191	6	,	,	PUNCT
ejpam-5246	191	7	17	17	NUM
ejpam-5246	191	8	(	(	PUNCT
ejpam-5246	191	9	3	3	NUM
ejpam-5246	191	10	)	)	PUNCT
ejpam-5246	191	11	(	(	PUNCT
ejpam-5246	191	12	2024	2024	NUM
ejpam-5246	191	13	)	)	PUNCT
ejpam-5246	191	14	,	,	PUNCT
ejpam-5246	191	15	1516	1516	NUM
ejpam-5246	191	16	-	-	SYM
ejpam-5246	191	17	1538	1538	NUM
ejpam-5246	191	18	1522	1522	NUM
ejpam-5246	191	19	proof	proof	NOUN
ejpam-5246	191	20	.	.	PUNCT
ejpam-5246	192	1	for	for	ADP
ejpam-5246	192	2	proof	proof	NOUN
ejpam-5246	192	3	this	this	PRON
ejpam-5246	192	4	theorem	theorem	VERB
ejpam-5246	192	5	,	,	PUNCT
ejpam-5246	192	6	we	we	PRON
ejpam-5246	192	7	use	use	VERB
ejpam-5246	192	8	the	the	DET
ejpam-5246	192	9	maximum	maximum	ADJ
ejpam-5246	192	10	error	error	NOUN
ejpam-5246	192	11	stability	stability	NOUN
ejpam-5246	192	12	-	-	PUNCT
ejpam-5246	192	13	technicality	technicality	NOUN
ejpam-5246	192	14	[	[	X
ejpam-5246	192	15	27	27	NUM
ejpam-5246	192	16	]	]	PUNCT
ejpam-5246	192	17	.	.	PUNCT
ejpam-5246	193	1	let	let	VERB
ejpam-5246	193	2	enui	enui	NOUN
ejpam-5246	193	3	=	=	SYM
ejpam-5246	193	4	uni	uni	PROPN
ejpam-5246	194	1	−	−	PROPN
ejpam-5246	195	1	un	un	PROPN
ejpam-5246	196	1	i	i	PROPN
ejpam-5246	196	2	,	,	PUNCT
ejpam-5246	196	3	envi	envi	PROPN
ejpam-5246	196	4	=	=	PUNCT
ejpam-5246	196	5	vni	vni	PROPN
ejpam-5246	196	6	−	−	PROPN
ejpam-5246	196	7	v	v	NOUN
ejpam-5246	196	8	n	n	NOUN
ejpam-5246	196	9	i	i	PRON
ejpam-5246	196	10	,	,	PUNCT
ejpam-5246	196	11	(	(	PUNCT
ejpam-5246	196	12	uni	uni	PROPN
ejpam-5246	196	13	=	=	SYM
ejpam-5246	196	14	u(xi	u(xi	PROPN
ejpam-5246	196	15	,	,	PUNCT
ejpam-5246	196	16	tn	tn	PROPN
ejpam-5246	196	17	)	)	PUNCT
ejpam-5246	196	18	,	,	PUNCT
ejpam-5246	196	19	v	v	PART
ejpam-5246	196	20	n	n	NOUN
ejpam-5246	196	21	i	i	NOUN
ejpam-5246	196	22	=	=	SYM
ejpam-5246	196	23	v(xi	v(xi	PROPN
ejpam-5246	196	24	,	,	PUNCT
ejpam-5246	196	25	tn	tn	PROPN
ejpam-5246	196	26	)	)	PUNCT
ejpam-5246	196	27	)	)	PUNCT
ejpam-5246	196	28	be	be	AUX
ejpam-5246	196	29	accurate	accurate	ADJ
ejpam-5246	196	30	solution	solution	NOUN
ejpam-5246	196	31	to	to	ADP
ejpam-5246	196	32	the	the	DET
ejpam-5246	196	33	issue	issue	NOUN
ejpam-5246	196	34	(	(	PUNCT
ejpam-5246	196	35	1.1	1.1	NUM
ejpam-5246	196	36	)	)	PUNCT
ejpam-5246	196	37	.	.	PUNCT
ejpam-5246	197	1	to	to	PART
ejpam-5246	197	2	finish	finish	VERB
ejpam-5246	197	3	this	this	PRON
ejpam-5246	197	4	,	,	PUNCT
ejpam-5246	197	5	we	we	PRON
ejpam-5246	197	6	implement	implement	VERB
ejpam-5246	197	7	mathematical	mathematical	ADJ
ejpam-5246	197	8	induction	induction	NOUN
ejpam-5246	197	9	.	.	PUNCT
ejpam-5246	198	1	for	for	ADP
ejpam-5246	198	2	n	n	NOUN
ejpam-5246	198	3	=	=	SYM
ejpam-5246	198	4	1	1	NUM
ejpam-5246	198	5	,	,	PUNCT
ejpam-5246	198	6	set	set	VERB
ejpam-5246	198	7	∥∥e1	∥∥e1	PROPN
ejpam-5246	198	8	u	u	NOUN
ejpam-5246	198	9	∥∥	∥∥	X
ejpam-5246	198	10	=	=	SYM
ejpam-5246	198	11	max1≤i≤i	max1≤i≤i	NUM
ejpam-5246	198	12	∣∣e1ui∣∣	∣∣e1ui∣∣	NOUN
ejpam-5246	198	13	=	=	NOUN
ejpam-5246	198	14	∣∣∣e1uj∣∣∣	∣∣∣e1uj∣∣∣	NOUN
ejpam-5246	198	15	,	,	PUNCT
ejpam-5246	198	16	∥∥e1	∥∥e1	PROPN
ejpam-5246	198	17	v	v	X
ejpam-5246	198	18	∥∥	∥∥	X
ejpam-5246	198	19	=	=	SYM
ejpam-5246	198	20	max1≤i≤i	max1≤i≤i	X
ejpam-5246	198	21	∣∣e1vi∣∣	∣∣e1vi∣∣	NOUN
ejpam-5246	198	22	=	=	SYM
ejpam-5246	198	23	∣∣e1um∣∣.	∣∣e1um∣∣.	PROPN
ejpam-5246	198	24	by	by	ADP
ejpam-5246	198	25	substituting	substitute	VERB
ejpam-5246	198	26	enuj	enuj	NOUN
ejpam-5246	198	27	in	in	ADP
ejpam-5246	198	28	the	the	DET
ejpam-5246	198	29	explicit	explicit	ADJ
ejpam-5246	198	30	formula	formula	NOUN
ejpam-5246	198	31	(	(	PUNCT
ejpam-5246	198	32	2.1	2.1	NUM
ejpam-5246	198	33	)	)	PUNCT
ejpam-5246	198	34	,	,	PUNCT
ejpam-5246	198	35	we	we	PRON
ejpam-5246	198	36	obtain	obtain	VERB
ejpam-5246	198	37	e1uj	e1uj	PUNCT
ejpam-5246	199	1	=	=	SYM
ejpam-5246	199	2	(	(	PUNCT
ejpam-5246	199	3	1−	1−	NUM
ejpam-5246	199	4	2r1)e	2r1)e	NUM
ejpam-5246	199	5	0	0	NUM
ejpam-5246	199	6	uj	uj	PROPN
ejpam-5246	199	7	+	+	CCONJ
ejpam-5246	199	8	r1	r1	PROPN
ejpam-5246	199	9	(	(	PUNCT
ejpam-5246	199	10	e0uj+1	e0uj+1	VERB
ejpam-5246	199	11	+	+	CCONJ
ejpam-5246	199	12	e0uj−1	e0uj−1	NOUN
ejpam-5246	199	13	)	)	PUNCT
ejpam-5246	200	1	+	+	CCONJ
ejpam-5246	200	2	k1	k1	X
ejpam-5246	200	3	(	(	PUNCT
ejpam-5246	200	4	f	f	X
ejpam-5246	200	5	(	(	PUNCT
ejpam-5246	200	6	δxu	δxu	PROPN
ejpam-5246	200	7	0	0	NUM
ejpam-5246	200	8	j	j	PROPN
ejpam-5246	200	9	,	,	PUNCT
ejpam-5246	200	10	v	v	NOUN
ejpam-5246	200	11	0	0	NUM
ejpam-5246	200	12	j	j	NOUN
ejpam-5246	200	13	)	)	PUNCT
ejpam-5246	201	1	−	−	PROPN
ejpam-5246	201	2	f	f	X
ejpam-5246	201	3	(	(	PUNCT
ejpam-5246	201	4	δxu	δxu	PROPN
ejpam-5246	201	5	0	0	NUM
ejpam-5246	201	6	j	j	PROPN
ejpam-5246	201	7	,	,	PUNCT
ejpam-5246	201	8	v	v	NOUN
ejpam-5246	201	9	0	0	NUM
ejpam-5246	201	10	j	j	PROPN
ejpam-5246	201	11	)	)	PUNCT
ejpam-5246	201	12	)	)	PUNCT
ejpam-5246	201	13	.	.	PUNCT
ejpam-5246	202	1	since	since	SCONJ
ejpam-5246	202	2	(	(	PUNCT
ejpam-5246	202	3	1−	1−	NUM
ejpam-5246	202	4	2r1	2r1	NUM
ejpam-5246	202	5	)	)	PUNCT
ejpam-5246	202	6	≥	≥	NOUN
ejpam-5246	202	7	0	0	NUM
ejpam-5246	202	8	,	,	PUNCT
ejpam-5246	202	9	we	we	PRON
ejpam-5246	202	10	have∣∣e1uj∣∣	have∣∣e1uj∣∣	VERB
ejpam-5246	202	11	≤	≤	NUM
ejpam-5246	202	12	(	(	PUNCT
ejpam-5246	202	13	1−	1−	NUM
ejpam-5246	202	14	2r1	2r1	NUM
ejpam-5246	202	15	)	)	PUNCT
ejpam-5246	202	16	∣∣e0uj∣∣+	∣∣e0uj∣∣+	PROPN
ejpam-5246	202	17	r1	r1	PROPN
ejpam-5246	202	18	(	(	PUNCT
ejpam-5246	202	19	∣∣e0uj+1	∣∣e0uj+1	PRON
ejpam-5246	202	20	∣∣+	∣∣+	PROPN
ejpam-5246	202	21	∣∣e0uj−1	∣∣e0uj−1	PROPN
ejpam-5246	202	22	∣∣)+	∣∣)+	PROPN
ejpam-5246	202	23	k1	k1	NOUN
ejpam-5246	202	24	∣∣f	∣∣f	NOUN
ejpam-5246	202	25	(	(	PUNCT
ejpam-5246	202	26	δxu0j	δxu0j	X
ejpam-5246	202	27	,	,	PUNCT
ejpam-5246	202	28	v0j	v0j	NOUN
ejpam-5246	202	29	)	)	PUNCT
ejpam-5246	202	30	−	−	PROPN
ejpam-5246	203	1	f	f	PROPN
ejpam-5246	203	2	(	(	PUNCT
ejpam-5246	203	3	δxu	δxu	PROPN
ejpam-5246	203	4	0	0	NUM
ejpam-5246	203	5	j	j	PROPN
ejpam-5246	203	6	,	,	PUNCT
ejpam-5246	203	7	v	v	NOUN
ejpam-5246	203	8	0	0	NUM
ejpam-5246	203	9	j	j	NOUN
ejpam-5246	203	10	)	)	PUNCT
ejpam-5246	203	11	∣∣	∣∣	X
ejpam-5246	203	12	.	.	PUNCT
ejpam-5246	204	1	from	from	ADP
ejpam-5246	204	2	(	(	PUNCT
ejpam-5246	204	3	1.2	1.2	NUM
ejpam-5246	204	4	)	)	PUNCT
ejpam-5246	204	5	,	,	PUNCT
ejpam-5246	204	6	it	it	PRON
ejpam-5246	204	7	follows	follow	VERB
ejpam-5246	204	8	that∣∣e1uj∣∣	that∣∣e1uj∣∣	ADP
ejpam-5246	204	9	≤	≤	NUM
ejpam-5246	204	10	(	(	PUNCT
ejpam-5246	204	11	1−	1−	NUM
ejpam-5246	204	12	2r1	2r1	NUM
ejpam-5246	204	13	)	)	PUNCT
ejpam-5246	204	14	∣∣e0uj∣∣+	∣∣e0uj∣∣+	PROPN
ejpam-5246	204	15	r1	r1	PROPN
ejpam-5246	204	16	(	(	PUNCT
ejpam-5246	204	17	∣∣e0uj+1	∣∣e0uj+1	PRON
ejpam-5246	204	18	∣∣+	∣∣+	X
ejpam-5246	204	19	∣∣e0uj−1	∣∣e0uj−1	PROPN
ejpam-5246	204	20	∣∣)+	∣∣)+	PROPN
ejpam-5246	204	21	k1l1	k1l1	VERB
ejpam-5246	204	22	∣∣δx	∣∣δx	ADJ
ejpam-5246	204	23	(	(	PUNCT
ejpam-5246	204	24	u0j	u0j	ADP
ejpam-5246	204	25	−	−	PROPN
ejpam-5246	204	26	u0	u0	ADJ
ejpam-5246	204	27	j	j	PROPN
ejpam-5246	204	28	)	)	PUNCT
ejpam-5246	204	29	∣∣+	∣∣+	PROPN
ejpam-5246	205	1	k1l2	k1l2	X
ejpam-5246	205	2	∣∣v0j	∣∣v0j	NOUN
ejpam-5246	206	1	−	−	NOUN
ejpam-5246	206	2	v	v	SYM
ejpam-5246	206	3	0	0	NUM
ejpam-5246	206	4	j	j	PROPN
ejpam-5246	206	5	∣∣∣∣e1uj∣∣	∣∣∣∣e1uj∣∣	PROPN
ejpam-5246	206	6	≤	≤	X
ejpam-5246	206	7	(	(	PUNCT
ejpam-5246	206	8	1−	1−	NUM
ejpam-5246	206	9	2r1	2r1	NUM
ejpam-5246	206	10	)	)	PUNCT
ejpam-5246	206	11	∥∥e0	∥∥e0	PROPN
ejpam-5246	206	12	u	u	SYM
ejpam-5246	206	13	∥∥+	∥∥+	X
ejpam-5246	206	14	2r1	2r1	NUM
ejpam-5246	206	15	∥∥e0	∥∥e0	PROPN
ejpam-5246	206	16	u	u	X
ejpam-5246	206	17	∥∥+	∥∥+	X
ejpam-5246	206	18	k1l1	k1l1	VERB
ejpam-5246	206	19	∣∣δxe0uj∣∣+	∣∣δxe0uj∣∣+	NUM
ejpam-5246	206	20	k1l2	k1l2	PROPN
ejpam-5246	206	21	∣∣e0vj∣∣∥∥e1	∣∣e0vj∣∣∥∥e1	PUNCT
ejpam-5246	206	22	u	u	X
ejpam-5246	206	23	∥∥	∥∥	X
ejpam-5246	206	24	≤	≤	PROPN
ejpam-5246	206	25	∥∥e0	∥∥e0	PROPN
ejpam-5246	206	26	u	u	PROPN
ejpam-5246	206	27	∥∥+	∥∥+	SYM
ejpam-5246	206	28	2k1l1	2k1l1	PROPN
ejpam-5246	206	29	∥∥e0	∥∥e0	PROPN
ejpam-5246	206	30	u	u	PROPN
ejpam-5246	206	31	∥∥+	∥∥+	X
ejpam-5246	206	32	k1l2	k1l2	PROPN
ejpam-5246	206	33	∥∥e0	∥∥e0	PROPN
ejpam-5246	206	34	v	v	ADP
ejpam-5246	206	35	∥∥	∥∥	X
ejpam-5246	206	36	≤	≤	X
ejpam-5246	206	37	(	(	PUNCT
ejpam-5246	206	38	1	1	NUM
ejpam-5246	206	39	+	+	NUM
ejpam-5246	206	40	2k1l1	2k1l1	NUM
ejpam-5246	206	41	+	+	CCONJ
ejpam-5246	206	42	k1l2)max	k1l2)max	X
ejpam-5246	206	43	{	{	PUNCT
ejpam-5246	206	44	∥∥e0	∥∥e0	PROPN
ejpam-5246	206	45	u	u	PROPN
ejpam-5246	206	46	∥∥	∥∥	X
ejpam-5246	206	47	,	,	PUNCT
ejpam-5246	206	48	∥∥e0	∥∥e0	PROPN
ejpam-5246	206	49	v	v	X
ejpam-5246	206	50	∥∥	∥∥	PROPN
ejpam-5246	206	51	}	}	PUNCT
ejpam-5246	206	52	≤	≤	NOUN
ejpam-5246	206	53	(	(	PUNCT
ejpam-5246	206	54	1	1	NUM
ejpam-5246	206	55	+	+	SYM
ejpam-5246	206	56	3kl)max	3kl)max	NUM
ejpam-5246	206	57	{	{	PUNCT
ejpam-5246	206	58	∥∥e0	∥∥e0	PROPN
ejpam-5246	206	59	u	u	PROPN
ejpam-5246	206	60	∥∥	∥∥	X
ejpam-5246	206	61	,	,	PUNCT
ejpam-5246	206	62	∥∥e0	∥∥e0	PROPN
ejpam-5246	206	63	v	v	X
ejpam-5246	206	64	∥∥	∥∥	NOUN
ejpam-5246	206	65	}	}	PUNCT
ejpam-5246	206	66	.	.	PUNCT
ejpam-5246	207	1	similarly	similarly	ADV
ejpam-5246	207	2	,	,	PUNCT
ejpam-5246	207	3	we	we	PRON
ejpam-5246	207	4	can	can	AUX
ejpam-5246	207	5	show	show	VERB
ejpam-5246	207	6	that∥∥e1	that∥∥e1	VERB
ejpam-5246	207	7	v	v	ADP
ejpam-5246	207	8	∥∥	∥∥	X
ejpam-5246	207	9	≤	≤	NUM
ejpam-5246	207	10	(	(	PUNCT
ejpam-5246	207	11	1	1	NUM
ejpam-5246	207	12	+	+	NUM
ejpam-5246	207	13	2kl3	2kl3	NUM
ejpam-5246	207	14	+	+	CCONJ
ejpam-5246	207	15	kl4)max	kl4)max	PROPN
ejpam-5246	207	16	{	{	PUNCT
ejpam-5246	207	17	∥∥e0	∥∥e0	PROPN
ejpam-5246	207	18	u	u	X
ejpam-5246	207	19	∥∥	∥∥	X
ejpam-5246	207	20	,	,	PUNCT
ejpam-5246	207	21	∥∥e0	∥∥e0	PROPN
ejpam-5246	207	22	v	v	X
ejpam-5246	207	23	∥∥	∥∥	PROPN
ejpam-5246	207	24	}	}	PUNCT
ejpam-5246	207	25	≤	≤	NOUN
ejpam-5246	207	26	(	(	PUNCT
ejpam-5246	207	27	1	1	NUM
ejpam-5246	207	28	+	+	SYM
ejpam-5246	207	29	3kl)max	3kl)max	NUM
ejpam-5246	207	30	{	{	PUNCT
ejpam-5246	207	31	∥∥e0	∥∥e0	PROPN
ejpam-5246	207	32	u	u	PROPN
ejpam-5246	207	33	∥∥	∥∥	X
ejpam-5246	207	34	,	,	PUNCT
ejpam-5246	207	35	∥∥e0	∥∥e0	PROPN
ejpam-5246	207	36	v	v	X
ejpam-5246	207	37	∥∥	∥∥	PROPN
ejpam-5246	207	38	}	}	PUNCT
ejpam-5246	207	39	,	,	PUNCT
ejpam-5246	207	40	where	where	SCONJ
ejpam-5246	207	41	l	l	NOUN
ejpam-5246	207	42	=	=	SYM
ejpam-5246	207	43	max	max	PROPN
ejpam-5246	207	44	{	{	PUNCT
ejpam-5246	207	45	l1	l1	PROPN
ejpam-5246	207	46	,	,	PUNCT
ejpam-5246	207	47	l2	l2	NOUN
ejpam-5246	207	48	,	,	PUNCT
ejpam-5246	207	49	l3	l3	PROPN
ejpam-5246	207	50	,	,	PUNCT
ejpam-5246	207	51	l4	l4	PROPN
ejpam-5246	207	52	}	}	PUNCT
ejpam-5246	207	53	.	.	PUNCT
ejpam-5246	208	1	now	now	ADV
ejpam-5246	208	2	,	,	PUNCT
ejpam-5246	208	3	we	we	PRON
ejpam-5246	208	4	suppose	suppose	VERB
ejpam-5246	208	5	that	that	SCONJ
ejpam-5246	208	6	∥es	∥es	VERB
ejpam-5246	208	7	u∥	u∥	ADJ
ejpam-5246	208	8	≤	≤	NUM
ejpam-5246	208	9	(	(	PUNCT
ejpam-5246	208	10	1	1	NUM
ejpam-5246	208	11	+	+	NUM
ejpam-5246	208	12	3kl)smax	3kl)smax	NUM
ejpam-5246	208	13	{	{	PUNCT
ejpam-5246	208	14	∥∥e0	∥∥e0	PROPN
ejpam-5246	208	15	u	u	PROPN
ejpam-5246	208	16	∥∥	∥∥	X
ejpam-5246	208	17	,	,	PUNCT
ejpam-5246	208	18	∥∥e0	∥∥e0	PROPN
ejpam-5246	208	19	v	v	X
ejpam-5246	208	20	∥∥	∥∥	PROPN
ejpam-5246	208	21	}	}	PUNCT
ejpam-5246	208	22	,	,	PUNCT
ejpam-5246	208	23	s	s	NOUN
ejpam-5246	208	24	=	=	SYM
ejpam-5246	208	25	1	1	NUM
ejpam-5246	208	26	,	,	PUNCT
ejpam-5246	208	27	2	2	NUM
ejpam-5246	208	28	,	,	PUNCT
ejpam-5246	208	29	3	3	NUM
ejpam-5246	208	30	,	,	PUNCT
ejpam-5246	208	31	.	.	PUNCT
ejpam-5246	208	32	.	.	PUNCT
ejpam-5246	208	33	.	.	PUNCT
ejpam-5246	209	1	n	n	CCONJ
ejpam-5246	209	2	,	,	PUNCT
ejpam-5246	209	3	∥es	∥es	VERB
ejpam-5246	209	4	v∥	v∥	PROPN
ejpam-5246	209	5	≤	≤	NUM
ejpam-5246	209	6	(	(	PUNCT
ejpam-5246	209	7	1	1	NUM
ejpam-5246	209	8	+	+	NUM
ejpam-5246	209	9	3kl)smax	3kl)smax	NUM
ejpam-5246	209	10	{	{	PUNCT
ejpam-5246	209	11	∥∥e0	∥∥e0	PROPN
ejpam-5246	209	12	u	u	PROPN
ejpam-5246	209	13	∥∥	∥∥	X
ejpam-5246	209	14	,	,	PUNCT
ejpam-5246	209	15	∥∥e0	∥∥e0	PROPN
ejpam-5246	209	16	v	v	X
ejpam-5246	209	17	∥∥	∥∥	PROPN
ejpam-5246	209	18	}	}	PUNCT
ejpam-5246	209	19	,	,	PUNCT
ejpam-5246	209	20	s	s	NOUN
ejpam-5246	209	21	=	=	SYM
ejpam-5246	209	22	1	1	NUM
ejpam-5246	209	23	,	,	PUNCT
ejpam-5246	209	24	2	2	NUM
ejpam-5246	209	25	,	,	PUNCT
ejpam-5246	209	26	3	3	NUM
ejpam-5246	209	27	,	,	PUNCT
ejpam-5246	209	28	.	.	PUNCT
ejpam-5246	209	29	.	.	PUNCT
ejpam-5246	209	30	.	.	PUNCT
ejpam-5246	210	1	n.	n.	NOUN
ejpam-5246	210	2	for	for	ADP
ejpam-5246	210	3	n	n	PROPN
ejpam-5246	210	4	+	+	NUM
ejpam-5246	210	5	1	1	NUM
ejpam-5246	210	6	,	,	PUNCT
ejpam-5246	210	7	set	set	VERB
ejpam-5246	210	8	∥∥en+1	∥∥en+1	PROPN
ejpam-5246	210	9	u	u	NOUN
ejpam-5246	210	10	∥∥	∥∥	X
ejpam-5246	210	11	=	=	SYM
ejpam-5246	210	12	max1≤i≤i	max1≤i≤i	NUM
ejpam-5246	210	13	∣∣en+1	∣∣en+1	NOUN
ejpam-5246	210	14	ui	ui	NOUN
ejpam-5246	210	15	∣∣	∣∣	PUNCT
ejpam-5246	210	16	=	=	SYM
ejpam-5246	210	17	∣∣∣en+1	∣∣∣en+1	X
ejpam-5246	210	18	uj	uj	PROPN
ejpam-5246	210	19	∣∣∣	∣∣∣	NOUN
ejpam-5246	210	20	,	,	PUNCT
ejpam-5246	210	21	∥∥en+1	∥∥en+1	PROPN
ejpam-5246	210	22	v	v	NOUN
ejpam-5246	210	23	∥∥	∥∥	X
ejpam-5246	210	24	=	=	SYM
ejpam-5246	210	25	max1≤i≤l	max1≤i≤l	PROPN
ejpam-5246	210	26	∣∣en+1	∣∣en+1	PROPN
ejpam-5246	210	27	vi	vi	X
ejpam-5246	210	28	∣∣	∣∣	X
ejpam-5246	210	29	=	=	SYM
ejpam-5246	210	30	∣∣en+1	∣∣en+1	PROPN
ejpam-5246	210	31	um	um	INTJ
ejpam-5246	210	32	∣∣.	∣∣.	NOUN
ejpam-5246	210	33	by	by	ADP
ejpam-5246	210	34	substituting	substitute	VERB
ejpam-5246	210	35	enuj	enuj	NOUN
ejpam-5246	210	36	in	in	ADP
ejpam-5246	210	37	the	the	DET
ejpam-5246	210	38	explicit	explicit	ADJ
ejpam-5246	210	39	formula	formula	NOUN
ejpam-5246	210	40	(	(	PUNCT
ejpam-5246	210	41	2.1	2.1	NUM
ejpam-5246	210	42	)	)	PUNCT
ejpam-5246	210	43	,	,	PUNCT
ejpam-5246	210	44	we	we	PRON
ejpam-5246	210	45	obtain	obtain	VERB
ejpam-5246	210	46	en+1	en+1	PROPN
ejpam-5246	210	47	uj	uj	NOUN
ejpam-5246	210	48	=	=	SYM
ejpam-5246	210	49	(	(	PUNCT
ejpam-5246	210	50	1−	1−	NUM
ejpam-5246	210	51	2rn)e	2rn)e	PROPN
ejpam-5246	210	52	n	n	PROPN
ejpam-5246	210	53	uj	uj	PROPN
ejpam-5246	211	1	+	+	PROPN
ejpam-5246	211	2	rn	rn	PROPN
ejpam-5246	211	3	(	(	PUNCT
ejpam-5246	211	4	enuj+1	enuj+1	NOUN
ejpam-5246	211	5	+	+	CCONJ
ejpam-5246	211	6	enuj−1	enuj−1	NOUN
ejpam-5246	211	7	)	)	PUNCT
ejpam-5246	212	1	+	+	CCONJ
ejpam-5246	212	2	kn	kn	PROPN
ejpam-5246	212	3	(	(	PUNCT
ejpam-5246	212	4	f	f	X
ejpam-5246	212	5	(	(	PUNCT
ejpam-5246	212	6	δxu	δxu	PROPN
ejpam-5246	212	7	n	n	PRON
ejpam-5246	212	8	j	j	PROPN
ejpam-5246	212	9	,	,	PUNCT
ejpam-5246	212	10	v	v	PROPN
ejpam-5246	212	11	n	n	PROPN
ejpam-5246	212	12	j	j	PROPN
ejpam-5246	212	13	)	)	PUNCT
ejpam-5246	213	1	−	−	PROPN
ejpam-5246	213	2	f	f	X
ejpam-5246	213	3	(	(	PUNCT
ejpam-5246	213	4	δxu	δxu	PROPN
ejpam-5246	213	5	n	n	PRON
ejpam-5246	213	6	j	j	PROPN
ejpam-5246	213	7	,	,	PUNCT
ejpam-5246	213	8	v	v	PROPN
ejpam-5246	213	9	n	n	PROPN
ejpam-5246	213	10	j	j	PROPN
ejpam-5246	213	11	)	)	PUNCT
ejpam-5246	213	12	)	)	PUNCT
ejpam-5246	213	13	.	.	PUNCT
ejpam-5246	214	1	since	since	SCONJ
ejpam-5246	214	2	(	(	PUNCT
ejpam-5246	214	3	1−	1−	NUM
ejpam-5246	214	4	2r	2r	NUM
ejpam-5246	214	5	)	)	PUNCT
ejpam-5246	214	6	≥	≥	NOUN
ejpam-5246	214	7	0	0	NUM
ejpam-5246	214	8	,	,	PUNCT
ejpam-5246	214	9	we	we	PRON
ejpam-5246	214	10	have∣∣∣en+1	have∣∣∣en+1	VERB
ejpam-5246	214	11	uj	uj	VERB
ejpam-5246	214	12	∣∣∣	∣∣∣	ADJ
ejpam-5246	214	13	≤	≤	PROPN
ejpam-5246	214	14	(	(	PUNCT
ejpam-5246	214	15	1−	1−	NUM
ejpam-5246	214	16	2rn	2rn	NOUN
ejpam-5246	214	17	)	)	PUNCT
ejpam-5246	214	18	∣∣enuj∣∣+	∣∣enuj∣∣+	PROPN
ejpam-5246	214	19	rn	rn	PROPN
ejpam-5246	214	20	(	(	PUNCT
ejpam-5246	214	21	∣∣enuj+1	∣∣enuj+1	X
ejpam-5246	214	22	∣∣+	∣∣+	PROPN
ejpam-5246	214	23	∣∣enuj−1	∣∣enuj−1	PROPN
ejpam-5246	214	24	∣∣)+	∣∣)+	PROPN
ejpam-5246	214	25	kn	kn	PROPN
ejpam-5246	214	26	∣∣f	∣∣f	PROPN
ejpam-5246	214	27	(	(	PUNCT
ejpam-5246	214	28	δxunj	δxunj	NOUN
ejpam-5246	214	29	,	,	PUNCT
ejpam-5246	214	30	vnj	vnj	INTJ
ejpam-5246	214	31	)	)	PUNCT
ejpam-5246	215	1	−	−	PROPN
ejpam-5246	215	2	f	f	PROPN
ejpam-5246	215	3	(	(	PUNCT
ejpam-5246	215	4	δxu	δxu	PROPN
ejpam-5246	215	5	n	n	PRON
ejpam-5246	215	6	j	j	PROPN
ejpam-5246	215	7	,	,	PUNCT
ejpam-5246	215	8	v	v	PROPN
ejpam-5246	215	9	n	n	PROPN
ejpam-5246	215	10	j	j	PROPN
ejpam-5246	215	11	)	)	PUNCT
ejpam-5246	215	12	∣∣	∣∣	PROPN
ejpam-5246	215	13	.	.	PUNCT
ejpam-5246	216	1	thus	thus	ADV
ejpam-5246	216	2	,	,	PUNCT
ejpam-5246	216	3	from	from	ADP
ejpam-5246	216	4	(	(	PUNCT
ejpam-5246	216	5	1.2	1.2	NUM
ejpam-5246	216	6	)	)	PUNCT
ejpam-5246	216	7	,	,	PUNCT
ejpam-5246	216	8	it	it	PRON
ejpam-5246	216	9	follows	follow	VERB
ejpam-5246	216	10	that∣∣∣en+1	that∣∣∣en+1	PROPN
ejpam-5246	216	11	uj	uj	PROPN
ejpam-5246	216	12	∣∣∣	∣∣∣	ADJ
ejpam-5246	216	13	≤	≤	PROPN
ejpam-5246	216	14	(	(	PUNCT
ejpam-5246	216	15	1−	1−	NUM
ejpam-5246	216	16	2rn	2rn	NOUN
ejpam-5246	216	17	)	)	PUNCT
ejpam-5246	216	18	∥en	∥en	PROPN
ejpam-5246	216	19	u∥+	u∥+	PROPN
ejpam-5246	216	20	2rn	2rn	PROPN
ejpam-5246	216	21	∥en	∥en	ADP
ejpam-5246	216	22	u∥+	u∥+	ADJ
ejpam-5246	216	23	knl1	knl1	NOUN
ejpam-5246	216	24	∣∣δx	∣∣δx	PROPN
ejpam-5246	216	25	(	(	PUNCT
ejpam-5246	216	26	unj	unj	NOUN
ejpam-5246	216	27	−	−	PROPN
ejpam-5246	216	28	un	un	PROPN
ejpam-5246	216	29	j	j	PROPN
ejpam-5246	216	30	)	)	PUNCT
ejpam-5246	216	31	∣∣+	∣∣+	PROPN
ejpam-5246	217	1	knl2	knl2	PROPN
ejpam-5246	217	2	∣∣vnj	∣∣vnj	PROPN
ejpam-5246	217	3	−	−	PROPN
ejpam-5246	217	4	v	v	PROPN
ejpam-5246	217	5	n	n	CCONJ
ejpam-5246	217	6	j	j	PROPN
ejpam-5246	217	7	∣∣	∣∣	PROPN
ejpam-5246	217	8	m.i.khalil	m.i.khalil	PROPN
ejpam-5246	217	9	et	et	PROPN
ejpam-5246	217	10	al	al	PROPN
ejpam-5246	217	11	.	.	PUNCT
ejpam-5246	217	12	/	/	SYM
ejpam-5246	217	13	eur	eur	PROPN
ejpam-5246	217	14	.	.	PUNCT
ejpam-5246	218	1	j.	j.	PROPN
ejpam-5246	218	2	pure	pure	PROPN
ejpam-5246	218	3	appl	appl	PROPN
ejpam-5246	218	4	.	.	PROPN
ejpam-5246	218	5	math	math	PROPN
ejpam-5246	218	6	,	,	PUNCT
ejpam-5246	218	7	17	17	NUM
ejpam-5246	218	8	(	(	PUNCT
ejpam-5246	218	9	3	3	NUM
ejpam-5246	218	10	)	)	PUNCT
ejpam-5246	218	11	(	(	PUNCT
ejpam-5246	218	12	2024	2024	NUM
ejpam-5246	218	13	)	)	PUNCT
ejpam-5246	218	14	,	,	PUNCT
ejpam-5246	218	15	1516	1516	NUM
ejpam-5246	218	16	-	-	SYM
ejpam-5246	218	17	1538	1538	NUM
ejpam-5246	218	18	1523	1523	NUM
ejpam-5246	218	19	≤	≤	NOUN
ejpam-5246	218	20	∥en	∥en	PUNCT
ejpam-5246	218	21	u∥+	u∥+	ADJ
ejpam-5246	218	22	knl1	knl1	PROPN
ejpam-5246	218	23	∣∣δxenuj∣∣+	∣∣δxenuj∣∣+	PROPN
ejpam-5246	218	24	knl2	knl2	PROPN
ejpam-5246	218	25	∣∣envj∣∣∥∥en+1	∣∣envj∣∣∥∥en+1	PROPN
ejpam-5246	218	26	u	u	NOUN
ejpam-5246	218	27	∥∥	∥∥	PROPN
ejpam-5246	218	28	≤	≤	X
ejpam-5246	218	29	∥en	∥en	NUM
ejpam-5246	218	30	u∥+	u∥+	PROPN
ejpam-5246	218	31	2knl1	2knl1	NUM
ejpam-5246	218	32	∥en	∥en	NUM
ejpam-5246	218	33	u∥+	u∥+	PROPN
ejpam-5246	218	34	knl2	knl2	PROPN
ejpam-5246	218	35	∥en	∥en	PROPN
ejpam-5246	218	36	v	v	NOUN
ejpam-5246	218	37	∥	∥	PUNCT
ejpam-5246	218	38	≤	≤	NOUN
ejpam-5246	218	39	(	(	PUNCT
ejpam-5246	218	40	1	1	NUM
ejpam-5246	218	41	+	+	SYM
ejpam-5246	218	42	3kl)max	3kl)max	NUM
ejpam-5246	218	43	{	{	PUNCT
ejpam-5246	218	44	∥en	∥en	PROPN
ejpam-5246	218	45	u∥	u∥	PROPN
ejpam-5246	218	46	,	,	PUNCT
ejpam-5246	218	47	∥en	∥en	PROPN
ejpam-5246	218	48	v	v	ADP
ejpam-5246	218	49	∥	∥	NOUN
ejpam-5246	218	50	}	}	PUNCT
ejpam-5246	218	51	≤	≤	NOUN
ejpam-5246	218	52	(	(	PUNCT
ejpam-5246	218	53	1	1	NUM
ejpam-5246	218	54	+	+	NUM
ejpam-5246	218	55	3kl)(1	3kl)(1	NUM
ejpam-5246	218	56	+	+	CCONJ
ejpam-5246	218	57	3kl)nmax	3kl)nmax	NUM
ejpam-5246	218	58	{	{	PUNCT
ejpam-5246	218	59	∥∥e0	∥∥e0	PROPN
ejpam-5246	218	60	u	u	PROPN
ejpam-5246	218	61	∥∥	∥∥	X
ejpam-5246	218	62	,	,	PUNCT
ejpam-5246	218	63	∥∥e0	∥∥e0	PROPN
ejpam-5246	218	64	v	v	X
ejpam-5246	218	65	∥∥	∥∥	PROPN
ejpam-5246	218	66	}	}	PUNCT
ejpam-5246	218	67	≤	≤	NOUN
ejpam-5246	218	68	(	(	PUNCT
ejpam-5246	218	69	1	1	NUM
ejpam-5246	218	70	+	+	SYM
ejpam-5246	218	71	3kl)n+1max	3kl)n+1max	NUM
ejpam-5246	218	72	{	{	PUNCT
ejpam-5246	218	73	∥∥e0	∥∥e0	PROPN
ejpam-5246	218	74	u	u	PROPN
ejpam-5246	218	75	∥∥	∥∥	X
ejpam-5246	218	76	,	,	PUNCT
ejpam-5246	218	77	∥∥e0	∥∥e0	PROPN
ejpam-5246	218	78	v	v	X
ejpam-5246	218	79	∥∥	∥∥	PROPN
ejpam-5246	218	80	}	}	PUNCT
ejpam-5246	218	81	≤	≤	NOUN
ejpam-5246	218	82	exp(3(n+	exp(3(n+	X
ejpam-5246	219	1	1)kl)max	1)kl)max	NUM
ejpam-5246	219	2	{	{	PUNCT
ejpam-5246	219	3	∥∥e0	∥∥e0	PROPN
ejpam-5246	219	4	u	u	PROPN
ejpam-5246	219	5	∥∥	∥∥	X
ejpam-5246	219	6	,	,	PUNCT
ejpam-5246	219	7	∥∥e0	∥∥e0	PROPN
ejpam-5246	219	8	v	v	X
ejpam-5246	219	9	∥∥	∥∥	PROPN
ejpam-5246	219	10	}	}	PUNCT
ejpam-5246	219	11	=	=	SYM
ejpam-5246	219	12	exp	exp	NOUN
ejpam-5246	219	13	(	(	PUNCT
ejpam-5246	219	14	3tn+1l)max	3tn+1l)max	NUM
ejpam-5246	219	15	{	{	PUNCT
ejpam-5246	219	16	∥∥e0	∥∥e0	PROPN
ejpam-5246	219	17	u	u	PROPN
ejpam-5246	219	18	∥∥	∥∥	X
ejpam-5246	219	19	,	,	PUNCT
ejpam-5246	219	20	∥∥e0	∥∥e0	PROPN
ejpam-5246	219	21	v	v	X
ejpam-5246	219	22	∥∥	∥∥	NOUN
ejpam-5246	219	23	}	}	PUNCT
ejpam-5246	219	24	.	.	PUNCT
ejpam-5246	220	1	likewise	likewise	ADV
ejpam-5246	220	2	,	,	PUNCT
ejpam-5246	220	3	∥∥en+1	∥∥en+1	PROPN
ejpam-5246	220	4	v	v	ADP
ejpam-5246	220	5	∥∥	∥∥	PROPN
ejpam-5246	220	6	≤	≤	NUM
ejpam-5246	220	7	exp	exp	NOUN
ejpam-5246	220	8	(	(	PUNCT
ejpam-5246	220	9	3tn+1l)max	3tn+1l)max	NUM
ejpam-5246	220	10	{	{	PUNCT
ejpam-5246	220	11	∥∥e0	∥∥e0	PROPN
ejpam-5246	220	12	u	u	PROPN
ejpam-5246	220	13	∥∥	∥∥	X
ejpam-5246	220	14	,	,	PUNCT
ejpam-5246	220	15	∥∥e0	∥∥e0	PROPN
ejpam-5246	220	16	v	v	X
ejpam-5246	220	17	∥∥	∥∥	NOUN
ejpam-5246	220	18	}	}	PUNCT
ejpam-5246	220	19	.	.	PUNCT
ejpam-5246	221	1	so	so	ADV
ejpam-5246	221	2	,	,	PUNCT
ejpam-5246	221	3	this	this	PRON
ejpam-5246	221	4	implies	imply	VERB
ejpam-5246	221	5	the	the	DET
ejpam-5246	221	6	stability	stability	NOUN
ejpam-5246	221	7	for	for	ADP
ejpam-5246	221	8	explicit	explicit	ADJ
ejpam-5246	221	9	scheme	scheme	NOUN
ejpam-5246	221	10	,	,	PUNCT
ejpam-5246	221	11	if	if	SCONJ
ejpam-5246	221	12	r	r	NOUN
ejpam-5246	221	13	≤	≤	NUM
ejpam-5246	221	14	1/2	1/2	NUM
ejpam-5246	221	15	.	.	PUNCT
ejpam-5246	222	1	2.4	2.4	NUM
ejpam-5246	222	2	.	.	PUNCT
ejpam-5246	223	1	convergence	convergence	NOUN
ejpam-5246	223	2	analysis	analysis	NOUN
ejpam-5246	223	3	of	of	ADP
ejpam-5246	223	4	explicit	explicit	ADJ
ejpam-5246	223	5	euler	euler	NOUN
ejpam-5246	223	6	scheme	scheme	NOUN
ejpam-5246	223	7	theorem	theorem	NOUN
ejpam-5246	223	8	3	3	NUM
ejpam-5246	223	9	.	.	PUNCT
ejpam-5246	224	1	the	the	DET
ejpam-5246	224	2	explicit	explicit	ADJ
ejpam-5246	224	3	euler	euler	NOUN
ejpam-5246	224	4	formulas	formula	NOUN
ejpam-5246	224	5	(	(	PUNCT
ejpam-5246	224	6	2.1	2.1	NUM
ejpam-5246	224	7	)	)	PUNCT
ejpam-5246	224	8	,	,	PUNCT
ejpam-5246	224	9	(	(	PUNCT
ejpam-5246	224	10	2.2	2.2	NUM
ejpam-5246	224	11	)	)	PUNCT
ejpam-5246	224	12	are	be	AUX
ejpam-5246	224	13	convergent	convergent	ADJ
ejpam-5246	224	14	with	with	ADP
ejpam-5246	224	15	:	:	PUNCT
ejpam-5246	225	1	o	o	X
ejpam-5246	225	2	(	(	PUNCT
ejpam-5246	225	3	k	k	PROPN
ejpam-5246	225	4	+	+	CCONJ
ejpam-5246	225	5	h2	h2	NOUN
ejpam-5246	225	6	)	)	PUNCT
ejpam-5246	225	7	,	,	PUNCT
ejpam-5246	225	8	if	if	SCONJ
ejpam-5246	225	9	(	(	PUNCT
ejpam-5246	225	10	1−	1−	NUM
ejpam-5246	225	11	2r	2r	NUM
ejpam-5246	225	12	)	)	PUNCT
ejpam-5246	225	13	≥	≥	NOUN
ejpam-5246	225	14	0	0	NUM
ejpam-5246	225	15	,	,	PUNCT
ejpam-5246	225	16	where	where	SCONJ
ejpam-5246	225	17	k	k	NOUN
ejpam-5246	225	18	=	=	SYM
ejpam-5246	225	19	maxn∈n	maxn∈n	PROPN
ejpam-5246	225	20	kn	kn	PROPN
ejpam-5246	225	21	,	,	PUNCT
ejpam-5246	225	22	r	r	NOUN
ejpam-5246	225	23	=	=	SYM
ejpam-5246	225	24	k	k	PROPN
ejpam-5246	225	25	/	/	SYM
ejpam-5246	225	26	h2	h2	NOUN
ejpam-5246	225	27	.	.	PUNCT
ejpam-5246	226	1	proof	proof	NOUN
ejpam-5246	226	2	.	.	PUNCT
ejpam-5246	227	1	set	set	VERB
ejpam-5246	227	2	enui	enui	NOUN
ejpam-5246	227	3	=	=	SYM
ejpam-5246	227	4	uni	uni	INTJ
ejpam-5246	227	5	−un	−un	PROPN
ejpam-5246	227	6	i	i	INTJ
ejpam-5246	227	7	,	,	PUNCT
ejpam-5246	228	1	e	e	PROPN
ejpam-5246	228	2	n	n	CCONJ
ejpam-5246	228	3	vi	vi	PROPN
ejpam-5246	228	4	=	=	NOUN
ejpam-5246	228	5	vni	vni	NOUN
ejpam-5246	228	6	−v	−v	NOUN
ejpam-5246	228	7	n	n	INTJ
ejpam-5246	229	1	i	i	PRON
ejpam-5246	229	2	,	,	PUNCT
ejpam-5246	229	3	(	(	PUNCT
ejpam-5246	229	4	uni	uni	PROPN
ejpam-5246	229	5	=	=	SYM
ejpam-5246	229	6	u(xi	u(xi	PROPN
ejpam-5246	229	7	,	,	PUNCT
ejpam-5246	229	8	tn	tn	PROPN
ejpam-5246	229	9	)	)	PUNCT
ejpam-5246	229	10	,	,	PUNCT
ejpam-5246	229	11	v	v	PART
ejpam-5246	229	12	n	n	NOUN
ejpam-5246	229	13	i	i	NOUN
ejpam-5246	229	14	=	=	SYM
ejpam-5246	229	15	v(xi	v(xi	PROPN
ejpam-5246	229	16	,	,	PUNCT
ejpam-5246	229	17	tn	tn	PROPN
ejpam-5246	229	18	)	)	PUNCT
ejpam-5246	229	19	)	)	PUNCT
ejpam-5246	229	20	is	be	AUX
ejpam-5246	229	21	the	the	DET
ejpam-5246	229	22	accurate	accurate	ADJ
ejpam-5246	229	23	solution	solution	NOUN
ejpam-5246	229	24	to	to	ADP
ejpam-5246	229	25	the	the	DET
ejpam-5246	229	26	problem	problem	NOUN
ejpam-5246	229	27	(	(	PUNCT
ejpam-5246	229	28	1.1	1.1	NUM
ejpam-5246	229	29	)	)	PUNCT
ejpam-5246	229	30	.	.	PUNCT
ejpam-5246	230	1	suppose	suppose	VERB
ejpam-5246	230	2	that	that	SCONJ
ejpam-5246	230	3	e0ui	e0ui	PUNCT
ejpam-5246	230	4	=	=	SYM
ejpam-5246	230	5	0	0	NUM
ejpam-5246	230	6	,	,	PUNCT
ejpam-5246	230	7	e0vi	e0vi	X
ejpam-5246	230	8	=	=	SYM
ejpam-5246	230	9	0	0	NUM
ejpam-5246	230	10	,	,	PUNCT
ejpam-5246	230	11	∀i	∀i	NOUN
ejpam-5246	230	12	=	=	SYM
ejpam-5246	230	13	0	0	NUM
ejpam-5246	230	14	,	,	PUNCT
ejpam-5246	230	15	1	1	NUM
ejpam-5246	230	16	,	,	PUNCT
ejpam-5246	230	17	.	.	PUNCT
ejpam-5246	230	18	.	.	PUNCT
ejpam-5246	231	1	.	.	PUNCT
ejpam-5246	232	1	,	,	PUNCT
ejpam-5246	232	2	i.	i.	NOUN
ejpam-5246	232	3	we	we	PRON
ejpam-5246	232	4	seek	seek	VERB
ejpam-5246	232	5	for	for	ADP
ejpam-5246	232	6	c	c	PROPN
ejpam-5246	232	7	>	>	X
ejpam-5246	232	8	0	0	PROPN
ejpam-5246	232	9	,	,	PUNCT
ejpam-5246	232	10	such	such	ADJ
ejpam-5246	232	11	that	that	PRON
ejpam-5246	232	12	en+1	en+1	ADJ
ejpam-5246	232	13	ui	ui	PROPN
ejpam-5246	232	14	≤	≤	NUM
ejpam-5246	232	15	c	c	X
ejpam-5246	232	16	(	(	PUNCT
ejpam-5246	232	17	k	k	PROPN
ejpam-5246	232	18	+	+	CCONJ
ejpam-5246	232	19	h2	h2	PROPN
ejpam-5246	232	20	)	)	PUNCT
ejpam-5246	232	21	,	,	PUNCT
ejpam-5246	232	22	en+1	en+1	PROPN
ejpam-5246	232	23	vi	vi	ADJ
ejpam-5246	232	24	≤	≤	NUM
ejpam-5246	232	25	c	c	NOUN
ejpam-5246	233	1	(	(	PUNCT
ejpam-5246	233	2	k	k	PROPN
ejpam-5246	233	3	+	+	CCONJ
ejpam-5246	233	4	h2	h2	PROPN
ejpam-5246	233	5	)	)	PUNCT
ejpam-5246	233	6	,	,	PUNCT
ejpam-5246	233	7	n	n	NOUN
ejpam-5246	233	8	=	=	SYM
ejpam-5246	233	9	0	0	NUM
ejpam-5246	233	10	,	,	PUNCT
ejpam-5246	233	11	1	1	NUM
ejpam-5246	233	12	,	,	PUNCT
ejpam-5246	233	13	.	.	PUNCT
ejpam-5246	233	14	.	.	PUNCT
ejpam-5246	234	1	.	.	PUNCT
ejpam-5246	235	1	.	.	PUNCT
ejpam-5246	236	1	to	to	PART
ejpam-5246	236	2	finish	finish	VERB
ejpam-5246	236	3	this	this	PRON
ejpam-5246	236	4	,	,	PUNCT
ejpam-5246	236	5	we	we	PRON
ejpam-5246	236	6	use	use	VERB
ejpam-5246	236	7	the	the	DET
ejpam-5246	236	8	tech	tech	NOUN
ejpam-5246	236	9	of	of	ADP
ejpam-5246	236	10	mathematical	mathematical	ADJ
ejpam-5246	236	11	induction	induction	NOUN
ejpam-5246	236	12	for	for	ADP
ejpam-5246	236	13	n	n	NOUN
ejpam-5246	236	14	=	=	SYM
ejpam-5246	236	15	1	1	NUM
ejpam-5246	236	16	,	,	PUNCT
ejpam-5246	236	17	we	we	PRON
ejpam-5246	236	18	set	set	VERB
ejpam-5246	236	19	∣∣∣e1uj∣∣∣	∣∣∣e1uj∣∣∣	NOUN
ejpam-5246	236	20	=	=	SYM
ejpam-5246	236	21	max1≤i≤i−1	max1≤i≤i−1	PROPN
ejpam-5246	236	22	∣∣e1ui∣∣.	∣∣e1ui∣∣.	PROPN
ejpam-5246	236	23	substituting	substitute	VERB
ejpam-5246	236	24	e1uj	e1uj	PUNCT
ejpam-5246	236	25	in	in	ADP
ejpam-5246	236	26	the	the	DET
ejpam-5246	236	27	explicit	explicit	ADJ
ejpam-5246	236	28	formula	formula	NOUN
ejpam-5246	236	29	(	(	PUNCT
ejpam-5246	236	30	2.1	2.1	NUM
ejpam-5246	236	31	)	)	PUNCT
ejpam-5246	236	32	yields	yield	NOUN
ejpam-5246	236	33	that	that	PRON
ejpam-5246	236	34	e1uj	e1uj	PUNCT
ejpam-5246	237	1	=	=	SYM
ejpam-5246	237	2	(	(	PUNCT
ejpam-5246	237	3	1−	1−	NUM
ejpam-5246	237	4	2rn)e	2rn)e	NUM
ejpam-5246	237	5	0	0	NUM
ejpam-5246	237	6	uj	uj	PROPN
ejpam-5246	237	7	+	+	NUM
ejpam-5246	237	8	rn	rn	PROPN
ejpam-5246	237	9	(	(	PUNCT
ejpam-5246	237	10	e0uj+1	e0uj+1	VERB
ejpam-5246	237	11	+	+	CCONJ
ejpam-5246	237	12	e0uj−1	e0uj−1	NOUN
ejpam-5246	237	13	)	)	PUNCT
ejpam-5246	238	1	+	+	CCONJ
ejpam-5246	238	2	kn	kn	PROPN
ejpam-5246	238	3	(	(	PUNCT
ejpam-5246	238	4	f	f	X
ejpam-5246	238	5	(	(	PUNCT
ejpam-5246	238	6	δxu	δxu	PROPN
ejpam-5246	238	7	0	0	NUM
ejpam-5246	238	8	j	j	PROPN
ejpam-5246	238	9	,	,	PUNCT
ejpam-5246	238	10	v	v	NOUN
ejpam-5246	238	11	0	0	NUM
ejpam-5246	238	12	j	j	NOUN
ejpam-5246	238	13	)	)	PUNCT
ejpam-5246	239	1	−	−	PROPN
ejpam-5246	239	2	f	f	X
ejpam-5246	239	3	(	(	PUNCT
ejpam-5246	239	4	δxu	δxu	PROPN
ejpam-5246	239	5	0	0	NUM
ejpam-5246	239	6	j	j	PROPN
ejpam-5246	239	7	,	,	PUNCT
ejpam-5246	239	8	v	v	NOUN
ejpam-5246	239	9	0	0	NUM
ejpam-5246	239	10	j	j	NOUN
ejpam-5246	239	11	)	)	PUNCT
ejpam-5246	239	12	)	)	PUNCT
ejpam-5246	240	1	+	+	CCONJ
ejpam-5246	240	2	tui	tui	NOUN
ejpam-5246	240	3	0	0	X
ejpam-5246	241	1	=	=	SYM
ejpam-5246	241	2	kn	kn	PROPN
ejpam-5246	241	3	(	(	PUNCT
ejpam-5246	241	4	f	f	X
ejpam-5246	241	5	(	(	PUNCT
ejpam-5246	241	6	δxu	δxu	PROPN
ejpam-5246	241	7	0	0	NUM
ejpam-5246	241	8	j	j	PROPN
ejpam-5246	241	9	,	,	PUNCT
ejpam-5246	241	10	v	v	NOUN
ejpam-5246	241	11	0	0	NUM
ejpam-5246	241	12	j	j	NOUN
ejpam-5246	241	13	)	)	PUNCT
ejpam-5246	242	1	−	−	PROPN
ejpam-5246	242	2	f	f	X
ejpam-5246	242	3	(	(	PUNCT
ejpam-5246	242	4	δxu	δxu	PROPN
ejpam-5246	242	5	0	0	NUM
ejpam-5246	242	6	j	j	PROPN
ejpam-5246	242	7	,	,	PUNCT
ejpam-5246	242	8	v	v	NOUN
ejpam-5246	242	9	0	0	NUM
ejpam-5246	242	10	j	j	NOUN
ejpam-5246	242	11	)	)	PUNCT
ejpam-5246	242	12	)	)	PUNCT
ejpam-5246	243	1	+	+	CCONJ
ejpam-5246	243	2	tui	tui	NOUN
ejpam-5246	243	3	0	0	NUM
ejpam-5246	243	4	.	.	PUNCT
ejpam-5246	243	5	from	from	ADP
ejpam-5246	243	6	lemma	lemma	PROPN
ejpam-5246	243	7	(	(	PUNCT
ejpam-5246	243	8	1	1	X
ejpam-5246	243	9	)	)	PUNCT
ejpam-5246	243	10	we	we	PRON
ejpam-5246	243	11	obtain∣∣e1uj∣∣	obtain∣∣e1uj∣∣	X
ejpam-5246	243	12	≤	≤	PROPN
ejpam-5246	243	13	knl1	knl1	PROPN
ejpam-5246	243	14	∣∣δx	∣∣δx	PROPN
ejpam-5246	243	15	(	(	PUNCT
ejpam-5246	243	16	u0j	u0j	ADP
ejpam-5246	243	17	−	−	PROPN
ejpam-5246	243	18	u0	u0	ADJ
ejpam-5246	243	19	j	j	PROPN
ejpam-5246	243	20	)	)	PUNCT
ejpam-5246	243	21	∣∣+	∣∣+	PROPN
ejpam-5246	243	22	knl2	knl2	PROPN
ejpam-5246	244	1	∣∣v0j	∣∣v0j	PROPN
ejpam-5246	245	1	−	−	PROPN
ejpam-5246	246	1	v	v	NOUN
ejpam-5246	246	2	0	0	NUM
ejpam-5246	246	3	j	j	PROPN
ejpam-5246	246	4	∣∣+	∣∣+	PROPN
ejpam-5246	246	5	∣∣t	∣∣t	PROPN
ejpam-5246	246	6	0	0	NUM
ejpam-5246	246	7	ui	ui	PROPN
ejpam-5246	246	8	∣∣	∣∣	NUM
ejpam-5246	246	9	=	=	SYM
ejpam-5246	246	10	∣∣t	∣∣t	NOUN
ejpam-5246	246	11	0	0	NUM
ejpam-5246	246	12	ui	ui	PROPN
ejpam-5246	246	13	∣∣	∣∣	X
ejpam-5246	246	14	≤	≤	PROPN
ejpam-5246	246	15	c	c	X
ejpam-5246	246	16	(	(	PUNCT
ejpam-5246	246	17	k	k	PROPN
ejpam-5246	246	18	+	+	CCONJ
ejpam-5246	246	19	h2	h2	NOUN
ejpam-5246	246	20	)	)	PUNCT
ejpam-5246	246	21	.	.	PUNCT
ejpam-5246	247	1	hence	hence	ADV
ejpam-5246	247	2	∣∣e1ui∣∣	∣∣e1ui∣∣	ADV
ejpam-5246	247	3	≤	≤	NOUN
ejpam-5246	247	4	c	c	NOUN
ejpam-5246	247	5	(	(	PUNCT
ejpam-5246	247	6	k	k	PROPN
ejpam-5246	247	7	+	+	CCONJ
ejpam-5246	247	8	h2	h2	NOUN
ejpam-5246	247	9	)	)	PUNCT
ejpam-5246	247	10	,	,	PUNCT
ejpam-5246	247	11	i	i	PRON
ejpam-5246	247	12	=	=	NOUN
ejpam-5246	247	13	1	1	NUM
ejpam-5246	247	14	,	,	PUNCT
ejpam-5246	247	15	2	2	NUM
ejpam-5246	247	16	,	,	PUNCT
ejpam-5246	247	17	.	.	PUNCT
ejpam-5246	247	18	.	.	PUNCT
ejpam-5246	247	19	.	.	PUNCT
ejpam-5246	248	1	i	i	PRON
ejpam-5246	248	2	−	−	VERB
ejpam-5246	249	1	1	1	X
ejpam-5246	249	2	.	.	PUNCT
ejpam-5246	250	1	likewise	likewise	ADV
ejpam-5246	250	2	,	,	PUNCT
ejpam-5246	250	3	we	we	PRON
ejpam-5246	250	4	show	show	VERB
ejpam-5246	250	5	that∣∣e1vi∣∣	that∣∣e1vi∣∣	NOUN
ejpam-5246	250	6	≤	≤	NUM
ejpam-5246	250	7	c	c	NOUN
ejpam-5246	250	8	(	(	PUNCT
ejpam-5246	250	9	k	k	PROPN
ejpam-5246	250	10	+	+	CCONJ
ejpam-5246	250	11	h2	h2	NOUN
ejpam-5246	250	12	)	)	PUNCT
ejpam-5246	250	13	,	,	PUNCT
ejpam-5246	250	14	i	i	PRON
ejpam-5246	250	15	=	=	NOUN
ejpam-5246	250	16	1	1	NUM
ejpam-5246	250	17	,	,	PUNCT
ejpam-5246	250	18	2	2	NUM
ejpam-5246	250	19	,	,	PUNCT
ejpam-5246	250	20	.	.	PUNCT
ejpam-5246	250	21	.	.	PUNCT
ejpam-5246	251	1	.	.	PUNCT
ejpam-5246	252	1	,	,	PUNCT
ejpam-5246	252	2	i	i	PRON
ejpam-5246	252	3	−	−	PROPN
ejpam-5246	253	1	1	1	X
ejpam-5246	253	2	.	.	PUNCT
ejpam-5246	253	3	assume	assume	VERB
ejpam-5246	253	4	∣∣esui∣∣	∣∣esui∣∣	ADJ
ejpam-5246	253	5	≤	≤	PUNCT
ejpam-5246	253	6	cs	cs	X
ejpam-5246	253	7	(	(	PUNCT
ejpam-5246	253	8	k	k	PROPN
ejpam-5246	253	9	+	+	CCONJ
ejpam-5246	253	10	h2	h2	NOUN
ejpam-5246	253	11	)	)	PUNCT
ejpam-5246	253	12	,	,	PUNCT
ejpam-5246	253	13	∣∣esvi∣∣	∣∣esvi∣∣	VERB
ejpam-5246	253	14	≤	≤	ADJ
ejpam-5246	253	15	cs	cs	X
ejpam-5246	253	16	(	(	PUNCT
ejpam-5246	253	17	k	k	PROPN
ejpam-5246	253	18	+	+	CCONJ
ejpam-5246	253	19	h2	h2	PROPN
ejpam-5246	253	20	)	)	PUNCT
ejpam-5246	253	21	,	,	PUNCT
ejpam-5246	253	22	s	s	NOUN
ejpam-5246	253	23	=	=	SYM
ejpam-5246	253	24	0	0	NUM
ejpam-5246	253	25	,	,	PUNCT
ejpam-5246	253	26	1	1	NUM
ejpam-5246	253	27	,	,	PUNCT
ejpam-5246	253	28	2	2	NUM
ejpam-5246	253	29	,	,	PUNCT
ejpam-5246	253	30	.	.	PUNCT
ejpam-5246	253	31	.	.	PUNCT
ejpam-5246	254	1	.	.	PUNCT
ejpam-5246	255	1	,	,	PUNCT
ejpam-5246	255	2	n	n	CCONJ
ejpam-5246	255	3	,	,	PUNCT
ejpam-5246	255	4	cs	cs	X
ejpam-5246	255	5	>	>	X
ejpam-5246	255	6	0	0	X
ejpam-5246	255	7	.	.	PUNCT
ejpam-5246	256	1	let	let	VERB
ejpam-5246	256	2	c∗	c∗	NOUN
ejpam-5246	256	3	=	=	SYM
ejpam-5246	256	4	max0≤s≤ncs	max0≤s≤nc	NOUN
ejpam-5246	256	5	.	.	PUNCT
ejpam-5246	257	1	for	for	ADP
ejpam-5246	257	2	n+	n+	NUM
ejpam-5246	257	3	1	1	NUM
ejpam-5246	257	4	,	,	PUNCT
ejpam-5246	257	5	we	we	PRON
ejpam-5246	257	6	set∣∣∣en+1	set∣∣∣en+1	VERB
ejpam-5246	257	7	uj	uj	VERB
ejpam-5246	257	8	∣∣∣	∣∣∣	NOUN
ejpam-5246	257	9	=	=	SYM
ejpam-5246	257	10	max1≤i≤i−1	max1≤i≤i−1	PROPN
ejpam-5246	257	11	∣∣en+1	∣∣en+1	PROPN
ejpam-5246	257	12	ui	ui	PROPN
ejpam-5246	257	13	∣∣.	∣∣.	PROPN
ejpam-5246	257	14	replace	replace	VERB
ejpam-5246	257	15	en+1	en+1	PROPN
ejpam-5246	257	16	uj	uj	PROPN
ejpam-5246	257	17	in	in	ADP
ejpam-5246	257	18	the	the	DET
ejpam-5246	257	19	explicit	explicit	ADJ
ejpam-5246	257	20	scheme	scheme	NOUN
ejpam-5246	257	21	(	(	PUNCT
ejpam-5246	257	22	2.1	2.1	NUM
ejpam-5246	257	23	)	)	PUNCT
ejpam-5246	257	24	yields	yield	NOUN
ejpam-5246	257	25	en+1	en+1	PART
ejpam-5246	258	1	uj	uj	PROPN
ejpam-5246	258	2	=	=	SYM
ejpam-5246	258	3	(	(	PUNCT
ejpam-5246	258	4	1−	1−	NUM
ejpam-5246	258	5	2rn)e	2rn)e	PROPN
ejpam-5246	258	6	n	n	PROPN
ejpam-5246	258	7	uj	uj	PROPN
ejpam-5246	259	1	+	+	PROPN
ejpam-5246	260	1	rn	rn	PROPN
ejpam-5246	261	1	(	(	PUNCT
ejpam-5246	261	2	enuj+1	enuj+1	NOUN
ejpam-5246	261	3	+	+	CCONJ
ejpam-5246	261	4	enuj−1	enuj−1	NOUN
ejpam-5246	261	5	)	)	PUNCT
ejpam-5246	262	1	+	+	CCONJ
ejpam-5246	262	2	kn	kn	PROPN
ejpam-5246	262	3	(	(	PUNCT
ejpam-5246	262	4	f	f	X
ejpam-5246	262	5	(	(	PUNCT
ejpam-5246	262	6	δxu	δxu	PROPN
ejpam-5246	262	7	n	n	PRON
ejpam-5246	262	8	j	j	PROPN
ejpam-5246	262	9	,	,	PUNCT
ejpam-5246	262	10	v	v	PROPN
ejpam-5246	262	11	n	n	PROPN
ejpam-5246	262	12	j	j	PROPN
ejpam-5246	262	13	)	)	PUNCT
ejpam-5246	263	1	−	−	PROPN
ejpam-5246	263	2	f	f	X
ejpam-5246	263	3	(	(	PUNCT
ejpam-5246	263	4	δxu	δxu	PROPN
ejpam-5246	263	5	n	n	PRON
ejpam-5246	263	6	j	j	PROPN
ejpam-5246	263	7	,	,	PUNCT
ejpam-5246	263	8	v	v	PROPN
ejpam-5246	263	9	n	n	PROPN
ejpam-5246	263	10	j	j	PROPN
ejpam-5246	263	11	)	)	PUNCT
ejpam-5246	263	12	)	)	PUNCT
ejpam-5246	264	1	+	+	CCONJ
ejpam-5246	264	2	tn	tn	PROPN
ejpam-5246	264	3	ui	ui	PROPN
ejpam-5246	264	4	.	.	PUNCT
ejpam-5246	264	5	m.i.khalil	m.i.khalil	PROPN
ejpam-5246	264	6	et	et	PROPN
ejpam-5246	264	7	al	al	PROPN
ejpam-5246	264	8	.	.	PUNCT
ejpam-5246	264	9	/	/	SYM
ejpam-5246	264	10	eur	eur	PROPN
ejpam-5246	264	11	.	.	PUNCT
ejpam-5246	265	1	j.	j.	PROPN
ejpam-5246	265	2	pure	pure	PROPN
ejpam-5246	265	3	appl	appl	PROPN
ejpam-5246	265	4	.	.	PROPN
ejpam-5246	265	5	math	math	PROPN
ejpam-5246	265	6	,	,	PUNCT
ejpam-5246	265	7	17	17	NUM
ejpam-5246	265	8	(	(	PUNCT
ejpam-5246	265	9	3	3	NUM
ejpam-5246	265	10	)	)	PUNCT
ejpam-5246	265	11	(	(	PUNCT
ejpam-5246	265	12	2024	2024	NUM
ejpam-5246	265	13	)	)	PUNCT
ejpam-5246	265	14	,	,	PUNCT
ejpam-5246	265	15	1516	1516	NUM
ejpam-5246	265	16	-	-	SYM
ejpam-5246	265	17	1538	1538	NUM
ejpam-5246	265	18	1524	1524	NUM
ejpam-5246	265	19	thus∣∣∣en+1	thus∣∣∣en+1	PROPN
ejpam-5246	265	20	uj	uj	VERB
ejpam-5246	265	21	∣∣∣	∣∣∣	ADJ
ejpam-5246	265	22	≤	≤	PROPN
ejpam-5246	265	23	(	(	PUNCT
ejpam-5246	265	24	1−	1−	NUM
ejpam-5246	265	25	2rn	2rn	NOUN
ejpam-5246	265	26	)	)	PUNCT
ejpam-5246	265	27	∥en	∥en	PROPN
ejpam-5246	265	28	u∥+	u∥+	PROPN
ejpam-5246	265	29	2rn	2rn	PROPN
ejpam-5246	265	30	∥en	∥en	PROPN
ejpam-5246	265	31	u∥+	u∥+	ADJ
ejpam-5246	265	32	kn	kn	PROPN
ejpam-5246	265	33	∣∣f	∣∣f	PROPN
ejpam-5246	265	34	(	(	PUNCT
ejpam-5246	265	35	δxunj	δxunj	NOUN
ejpam-5246	265	36	,	,	PUNCT
ejpam-5246	265	37	vnj	vnj	INTJ
ejpam-5246	265	38	)	)	PUNCT
ejpam-5246	266	1	−	−	PROPN
ejpam-5246	267	1	f	f	PROPN
ejpam-5246	267	2	(	(	PUNCT
ejpam-5246	267	3	δxu	δxu	PROPN
ejpam-5246	267	4	n	n	PRON
ejpam-5246	267	5	j	j	PROPN
ejpam-5246	267	6	,	,	PUNCT
ejpam-5246	267	7	v	v	PROPN
ejpam-5246	267	8	n	n	PROPN
ejpam-5246	267	9	j	j	PROPN
ejpam-5246	267	10	)	)	PUNCT
ejpam-5246	267	11	∣∣+	∣∣+	PROPN
ejpam-5246	267	12	∣∣tn	∣∣tn	PROPN
ejpam-5246	267	13	uj	uj	PROPN
ejpam-5246	267	14	∣∣	∣∣	NUM
ejpam-5246	267	15	≤	≤	PROPN
ejpam-5246	267	16	(	(	PUNCT
ejpam-5246	267	17	1−	1−	NUM
ejpam-5246	267	18	2rn	2rn	NOUN
ejpam-5246	267	19	)	)	PUNCT
ejpam-5246	267	20	∥en	∥en	PROPN
ejpam-5246	268	1	u∥+	u∥+	PROPN
ejpam-5246	268	2	2rn	2rn	PROPN
ejpam-5246	268	3	∥en	∥en	ADP
ejpam-5246	268	4	u∥+	u∥+	ADJ
ejpam-5246	268	5	knl1	knl1	NOUN
ejpam-5246	268	6	∣∣δx	∣∣δx	PROPN
ejpam-5246	268	7	(	(	PUNCT
ejpam-5246	268	8	unj	unj	NOUN
ejpam-5246	268	9	−	−	PROPN
ejpam-5246	268	10	un	un	PROPN
ejpam-5246	268	11	j	j	PROPN
ejpam-5246	268	12	)	)	PUNCT
ejpam-5246	268	13	∣∣+	∣∣+	PROPN
ejpam-5246	269	1	knl2	knl2	PROPN
ejpam-5246	269	2	∣∣vnj	∣∣vnj	PROPN
ejpam-5246	269	3	−	−	PROPN
ejpam-5246	269	4	v	v	ADP
ejpam-5246	269	5	n	n	PROPN
ejpam-5246	269	6	j	j	PROPN
ejpam-5246	269	7	∣∣+	∣∣+	PROPN
ejpam-5246	269	8	∣∣tn	∣∣tn	PROPN
ejpam-5246	269	9	uj	uj	PROPN
ejpam-5246	269	10	∣∣	∣∣	X
ejpam-5246	269	11	.	.	PUNCT
ejpam-5246	270	1	from	from	ADP
ejpam-5246	270	2	lemma	lemma	PROPN
ejpam-5246	270	3	(	(	PUNCT
ejpam-5246	270	4	1	1	NUM
ejpam-5246	270	5	)	)	PUNCT
ejpam-5246	270	6	,	,	PUNCT
ejpam-5246	270	7	we	we	PRON
ejpam-5246	270	8	have∥∥en+1	have∥∥en+1	VERB
ejpam-5246	270	9	u	u	NOUN
ejpam-5246	270	10	∥∥	∥∥	X
ejpam-5246	270	11	≤	≤	X
ejpam-5246	270	12	∥en	∥en	NUM
ejpam-5246	270	13	u∥+	u∥+	ADJ
ejpam-5246	270	14	knl1	knl1	NOUN
ejpam-5246	270	15	∣∣δxenuj∣∣+	∣∣δxenuj∣∣+	PROPN
ejpam-5246	270	16	knl2	knl2	PROPN
ejpam-5246	271	1	∣∣envj∣∣+	∣∣envj∣∣+	PROPN
ejpam-5246	271	2	∣∣tn	∣∣tn	PROPN
ejpam-5246	271	3	j	j	PROPN
ejpam-5246	271	4	∣∣	∣∣	NUM
ejpam-5246	271	5	≤	≤	X
ejpam-5246	271	6	∥en	∥en	NUM
ejpam-5246	272	1	u∥+	u∥+	PROPN
ejpam-5246	272	2	2knl1	2knl1	NUM
ejpam-5246	272	3	∥en	∥en	NUM
ejpam-5246	272	4	u∥+	u∥+	PROPN
ejpam-5246	272	5	knl2	knl2	PROPN
ejpam-5246	272	6	∥en	∥en	PROPN
ejpam-5246	272	7	v	v	NOUN
ejpam-5246	272	8	∥+	∥+	NUM
ejpam-5246	272	9	∣∣tn	∣∣tn	PROPN
ejpam-5246	272	10	j	j	PROPN
ejpam-5246	272	11	∣∣	∣∣	X
ejpam-5246	272	12	≤	≤	NUM
ejpam-5246	272	13	(	(	PUNCT
ejpam-5246	272	14	1	1	NUM
ejpam-5246	272	15	+	+	SYM
ejpam-5246	272	16	2knl1	2knl1	NUM
ejpam-5246	272	17	+	+	NUM
ejpam-5246	272	18	knl2)c	knl2)c	NOUN
ejpam-5246	272	19	∗	∗	NOUN
ejpam-5246	272	20	(	(	PUNCT
ejpam-5246	272	21	k	k	PROPN
ejpam-5246	272	22	+	+	CCONJ
ejpam-5246	272	23	h2	h2	NOUN
ejpam-5246	272	24	)	)	PUNCT
ejpam-5246	273	1	+	+	CCONJ
ejpam-5246	273	2	c	c	X
ejpam-5246	273	3	(	(	PUNCT
ejpam-5246	273	4	k	k	NOUN
ejpam-5246	273	5	+	+	CCONJ
ejpam-5246	273	6	h2	h2	NOUN
ejpam-5246	273	7	)	)	PUNCT
ejpam-5246	274	1	=	=	PUNCT
ejpam-5246	275	1	[	[	X
ejpam-5246	275	2	(	(	PUNCT
ejpam-5246	275	3	1	1	NUM
ejpam-5246	275	4	+	+	NUM
ejpam-5246	275	5	2kl1	2kl1	NUM
ejpam-5246	275	6	+	+	CCONJ
ejpam-5246	275	7	kl2)c	kl2)c	NOUN
ejpam-5246	275	8	∗	∗	NOUN
ejpam-5246	275	9	+	+	CCONJ
ejpam-5246	275	10	c	c	X
ejpam-5246	275	11	]	]	X
ejpam-5246	275	12	(	(	PUNCT
ejpam-5246	275	13	k	k	X
ejpam-5246	275	14	+	+	CCONJ
ejpam-5246	275	15	h2	h2	NOUN
ejpam-5246	275	16	)	)	PUNCT
ejpam-5246	275	17	.	.	PUNCT
ejpam-5246	276	1	next	next	ADJ
ejpam-5246	276	2	∥∥en+1	∥∥en+1	PROPN
ejpam-5246	276	3	u	u	NOUN
ejpam-5246	276	4	∥∥	∥∥	PROPN
ejpam-5246	276	5	≤	≤	PROPN
ejpam-5246	276	6	c	c	X
ejpam-5246	276	7	(	(	PUNCT
ejpam-5246	276	8	k	k	PROPN
ejpam-5246	276	9	+	+	CCONJ
ejpam-5246	276	10	h2	h2	PROPN
ejpam-5246	276	11	)	)	PUNCT
ejpam-5246	276	12	,	,	PUNCT
ejpam-5246	276	13	n	n	NOUN
ejpam-5246	276	14	=	=	SYM
ejpam-5246	276	15	0	0	NUM
ejpam-5246	276	16	,	,	PUNCT
ejpam-5246	276	17	1	1	NUM
ejpam-5246	276	18	,	,	PUNCT
ejpam-5246	276	19	.	.	PUNCT
ejpam-5246	276	20	.	.	PUNCT
ejpam-5246	276	21	..	..	PUNCT
ejpam-5246	277	1	likewise	likewise	ADV
ejpam-5246	277	2	,	,	PUNCT
ejpam-5246	277	3	we	we	PRON
ejpam-5246	277	4	show	show	VERB
ejpam-5246	277	5	that∥∥en+1	that∥∥en+1	PROPN
ejpam-5246	277	6	v	v	ADP
ejpam-5246	277	7	∥∥	∥∥	X
ejpam-5246	277	8	≤	≤	PROPN
ejpam-5246	277	9	c	c	NOUN
ejpam-5246	277	10	(	(	PUNCT
ejpam-5246	277	11	k	k	PROPN
ejpam-5246	277	12	+	+	CCONJ
ejpam-5246	277	13	h2	h2	PROPN
ejpam-5246	277	14	)	)	PUNCT
ejpam-5246	277	15	,	,	PUNCT
ejpam-5246	277	16	n	n	NOUN
ejpam-5246	277	17	=	=	SYM
ejpam-5246	277	18	0	0	NUM
ejpam-5246	277	19	,	,	PUNCT
ejpam-5246	277	20	1	1	NUM
ejpam-5246	277	21	,	,	PUNCT
ejpam-5246	277	22	.	.	PUNCT
ejpam-5246	277	23	.	.	PUNCT
ejpam-5246	277	24	.	.	PUNCT
ejpam-5246	277	25	.	.	PUNCT
ejpam-5246	278	1	3	3	X
ejpam-5246	278	2	.	.	X
ejpam-5246	278	3	implicit	implicit	ADJ
ejpam-5246	278	4	euler	euler	NOUN
ejpam-5246	278	5	scheme	scheme	NOUN
ejpam-5246	278	6	now	now	ADV
ejpam-5246	278	7	,	,	PUNCT
ejpam-5246	278	8	in	in	ADP
ejpam-5246	278	9	order	order	NOUN
ejpam-5246	278	10	to	to	PART
ejpam-5246	278	11	obtain	obtain	VERB
ejpam-5246	278	12	the	the	DET
ejpam-5246	278	13	implicit	implicit	ADJ
ejpam-5246	278	14	fully	fully	ADV
ejpam-5246	278	15	-	-	PUNCT
ejpam-5246	278	16	discrete	discrete	ADJ
ejpam-5246	278	17	finite	finite	ADJ
ejpam-5246	278	18	difference	difference	NOUN
ejpam-5246	278	19	formulae	formulae	NOUN
ejpam-5246	278	20	for	for	ADP
ejpam-5246	278	21	problem	problem	NOUN
ejpam-5246	278	22	(	(	PUNCT
ejpam-5246	278	23	1.1	1.1	NUM
ejpam-5246	278	24	)	)	PUNCT
ejpam-5246	278	25	,	,	PUNCT
ejpam-5246	278	26	we	we	PRON
ejpam-5246	278	27	will	will	AUX
ejpam-5246	278	28	employ	employ	VERB
ejpam-5246	278	29	the	the	DET
ejpam-5246	278	30	backward	backward	ADJ
ejpam-5246	278	31	finite	finite	ADJ
ejpam-5246	278	32	difference	difference	NOUN
ejpam-5246	278	33	formula	formula	NOUN
ejpam-5246	278	34	to	to	PART
ejpam-5246	278	35	approximate	approximate	VERB
ejpam-5246	278	36	the	the	DET
ejpam-5246	278	37	time	time	NOUN
ejpam-5246	278	38	derivative	derivative	ADJ
ejpam-5246	278	39	in	in	ADP
ejpam-5246	278	40	problem	problem	NOUN
ejpam-5246	278	41	(	(	PUNCT
ejpam-5246	278	42	1.1	1.1	NUM
ejpam-5246	278	43	)	)	PUNCT
ejpam-5246	278	44	.	.	PUNCT
ejpam-5246	279	1	in	in	ADP
ejpam-5246	279	2	this	this	DET
ejpam-5246	279	3	analysis	analysis	NOUN
ejpam-5246	279	4	,	,	PUNCT
ejpam-5246	279	5	we	we	PRON
ejpam-5246	279	6	define	define	VERB
ejpam-5246	279	7	un	un	PROPN
ejpam-5246	279	8	i	i	PROPN
ejpam-5246	279	9	and	and	CCONJ
ejpam-5246	279	10	v	v	X
ejpam-5246	279	11	n	n	INTJ
ejpam-5246	280	1	i	i	PRON
ejpam-5246	280	2	,	,	PUNCT
ejpam-5246	280	3	as	as	ADP
ejpam-5246	280	4	the	the	DET
ejpam-5246	280	5	estimated	estimate	VERB
ejpam-5246	280	6	values	value	NOUN
ejpam-5246	280	7	of	of	ADP
ejpam-5246	280	8	u	u	PROPN
ejpam-5246	280	9	(	(	PUNCT
ejpam-5246	280	10	xi	xi	PROPN
ejpam-5246	280	11	,	,	PUNCT
ejpam-5246	280	12	tn	tn	PROPN
ejpam-5246	280	13	)	)	PUNCT
ejpam-5246	280	14	and	and	CCONJ
ejpam-5246	280	15	v	v	NOUN
ejpam-5246	280	16	(	(	PUNCT
ejpam-5246	280	17	xi	xi	PROPN
ejpam-5246	280	18	,	,	PUNCT
ejpam-5246	280	19	tn	tn	PROPN
ejpam-5246	280	20	)	)	PUNCT
ejpam-5246	280	21	,	,	PUNCT
ejpam-5246	280	22	consecutively	consecutively	ADV
ejpam-5246	280	23	,	,	PUNCT
ejpam-5246	280	24	let	let	VERB
ejpam-5246	280	25	tn+1	tn+1	VERB
ejpam-5246	280	26	=	=	SYM
ejpam-5246	280	27	tn	tn	PROPN
ejpam-5246	281	1	+	+	CCONJ
ejpam-5246	281	2	kn	kn	PROPN
ejpam-5246	281	3	,	,	PUNCT
ejpam-5246	281	4	where	where	SCONJ
ejpam-5246	281	5	i	i	PRON
ejpam-5246	281	6	represent	represent	VERB
ejpam-5246	281	7	a	a	DET
ejpam-5246	281	8	positive	positive	ADJ
ejpam-5246	281	9	integer	integer	NOUN
ejpam-5246	281	10	,	,	PUNCT
ejpam-5246	281	11	and	and	CCONJ
ejpam-5246	281	12	proceed	proceed	VERB
ejpam-5246	281	13	to	to	PART
ejpam-5246	281	14	examine	examine	VERB
ejpam-5246	281	15	the	the	DET
ejpam-5246	281	16	grid	grid	NOUN
ejpam-5246	281	17	:	:	PUNCT
ejpam-5246	281	18	:	:	PUNCT
ejpam-5246	282	1	xi	xi	X
ejpam-5246	282	2	=	=	PUNCT
ejpam-5246	282	3	ih	ih	X
ejpam-5246	282	4	,	,	PUNCT
ejpam-5246	282	5	0	0	NUM
ejpam-5246	282	6	≤	≤	NUM
ejpam-5246	283	1	i	i	PRON
ejpam-5246	283	2	≤	≤	PUNCT
ejpam-5246	284	1	i	i	PRON
ejpam-5246	284	2	,	,	PUNCT
ejpam-5246	284	3	h	h	NOUN
ejpam-5246	284	4	=	=	NOUN
ejpam-5246	284	5	1	1	NUM
ejpam-5246	284	6	i	i	NOUN
ejpam-5246	284	7	,	,	PUNCT
ejpam-5246	284	8	tn+1	tn+1	PROPN
ejpam-5246	284	9	=	=	SYM
ejpam-5246	284	10	tn	tn	PROPN
ejpam-5246	284	11	+	+	CCONJ
ejpam-5246	284	12	kn	kn	PROPN
ejpam-5246	284	13	,	,	PUNCT
ejpam-5246	284	14	xi+1	xi+1	PROPN
ejpam-5246	284	15	=	=	PUNCT
ejpam-5246	284	16	xi	xi	PROPN
ejpam-5246	285	1	+	+	CCONJ
ejpam-5246	285	2	h	h	NOUN
ejpam-5246	285	3	,	,	PUNCT
ejpam-5246	285	4	h	h	PROPN
ejpam-5246	285	5	is	be	AUX
ejpam-5246	285	6	the	the	DET
ejpam-5246	285	7	space	space	NOUN
ejpam-5246	285	8	-	-	PUNCT
ejpam-5246	285	9	step	step	NOUN
ejpam-5246	285	10	,	,	PUNCT
ejpam-5246	285	11	kn	kn	PROPN
ejpam-5246	285	12	is	be	AUX
ejpam-5246	285	13	the	the	DET
ejpam-5246	285	14	time	time	NOUN
ejpam-5246	285	15	-	-	PUNCT
ejpam-5246	285	16	step	step	NOUN
ejpam-5246	285	17	.	.	PUNCT
ejpam-5246	286	1	at	at	ADP
ejpam-5246	286	2	the	the	DET
ejpam-5246	286	3	grid	grid	NOUN
ejpam-5246	286	4	point	point	NOUN
ejpam-5246	286	5	(	(	PUNCT
ejpam-5246	286	6	xi	xi	PROPN
ejpam-5246	286	7	,	,	PUNCT
ejpam-5246	286	8	tn+1),we	tn+1),we	NOUN
ejpam-5246	286	9	employ	employ	VERB
ejpam-5246	286	10	backward	backward	ADJ
ejpam-5246	286	11	finite	finite	ADJ
ejpam-5246	286	12	difference	difference	NOUN
ejpam-5246	286	13	formulas	formula	NOUN
ejpam-5246	286	14	to	to	PART
ejpam-5246	286	15	approximate	approximate	VERB
ejpam-5246	286	16	the	the	DET
ejpam-5246	286	17	values	value	NOUN
ejpam-5246	286	18	of	of	ADP
ejpam-5246	286	19	ut	ut	PROPN
ejpam-5246	286	20	,	,	PUNCT
ejpam-5246	286	21	vt	vt	PROPN
ejpam-5246	286	22	as	as	ADP
ejpam-5246	286	23	below	below	ADV
ejpam-5246	286	24	:	:	PUNCT
ejpam-5246	287	1	∂u	∂u	PROPN
ejpam-5246	287	2	∂t	∂t	PROPN
ejpam-5246	287	3	∣∣∣∣n+1	∣∣∣∣n+1	NOUN
ejpam-5246	287	4	i	i	NOUN
ejpam-5246	287	5	=	=	SYM
ejpam-5246	287	6	1	1	NUM
ejpam-5246	287	7	kn	kn	NOUN
ejpam-5246	287	8	(	(	PUNCT
ejpam-5246	287	9	un+1	un+1	PROPN
ejpam-5246	287	10	i	i	PRON
ejpam-5246	287	11	−	−	PROPN
ejpam-5246	287	12	un	un	PROPN
ejpam-5246	287	13	i	i	PROPN
ejpam-5246	287	14	)	)	PUNCT
ejpam-5246	288	1	+	+	NOUN
ejpam-5246	288	2	o	o	X
ejpam-5246	288	3	(	(	PUNCT
ejpam-5246	288	4	kn	kn	PROPN
ejpam-5246	288	5	)	)	PUNCT
ejpam-5246	288	6	,	,	PUNCT
ejpam-5246	288	7	∂v	∂v	PROPN
ejpam-5246	288	8	∂t	∂t	PROPN
ejpam-5246	288	9	∣∣∣∣n+1	∣∣∣∣n+1	NOUN
ejpam-5246	289	1	i	i	NOUN
ejpam-5246	289	2	=	=	SYM
ejpam-5246	289	3	1	1	NUM
ejpam-5246	289	4	kn	kn	NOUN
ejpam-5246	289	5	(	(	PUNCT
ejpam-5246	289	6	v	v	NOUN
ejpam-5246	289	7	n+1	n+1	PROPN
ejpam-5246	290	1	i	i	PRON
ejpam-5246	290	2	−	−	PROPN
ejpam-5246	290	3	v	v	ADP
ejpam-5246	290	4	n	n	NOUN
ejpam-5246	290	5	i	i	PRON
ejpam-5246	290	6	)	)	PUNCT
ejpam-5246	291	1	+	+	NOUN
ejpam-5246	291	2	o	o	X
ejpam-5246	291	3	(	(	PUNCT
ejpam-5246	291	4	kn	kn	PROPN
ejpam-5246	291	5	)	)	PUNCT
ejpam-5246	291	6	.	.	PUNCT
ejpam-5246	292	1	while	while	SCONJ
ejpam-5246	292	2	uxx	uxx	PROPN
ejpam-5246	292	3	,	,	PUNCT
ejpam-5246	292	4	vxx	vxx	PROPN
ejpam-5246	292	5	are	be	AUX
ejpam-5246	292	6	approximated	approximate	VERB
ejpam-5246	292	7	as	as	ADP
ejpam-5246	292	8	using	use	VERB
ejpam-5246	292	9	the	the	DET
ejpam-5246	292	10	second	second	ADJ
ejpam-5246	292	11	-	-	PUNCT
ejpam-5246	292	12	order	order	NOUN
ejpam-5246	292	13	central	central	ADJ
ejpam-5246	292	14	finite	finite	ADJ
ejpam-5246	292	15	difference	difference	NOUN
ejpam-5246	292	16	formulas	formula	NOUN
ejpam-5246	292	17	below	below	ADV
ejpam-5246	292	18	:	:	PUNCT
ejpam-5246	292	19	uxx|n+1	uxx|n+1	INTJ
ejpam-5246	292	20	i	i	NOUN
ejpam-5246	293	1	=	=	SYM
ejpam-5246	294	1	un+1	un+1	PROPN
ejpam-5246	295	1	i	i	PRON
ejpam-5246	295	2	−	−	PROPN
ejpam-5246	296	1	2un+1	2un+1	NUM
ejpam-5246	297	1	i	i	PRON
ejpam-5246	297	2	+	+	CCONJ
ejpam-5246	297	3	un+1	un+1	PROPN
ejpam-5246	297	4	i−1	i−1	PROPN
ejpam-5246	297	5	h2	h2	PROPN
ejpam-5246	298	1	+	+	PROPN
ejpam-5246	298	2	o	o	PROPN
ejpam-5246	298	3	(	(	PUNCT
ejpam-5246	298	4	h2	h2	PROPN
ejpam-5246	298	5	)	)	PUNCT
ejpam-5246	298	6	,	,	PUNCT
ejpam-5246	298	7	vxx|n+1	vxx|n+1	INTJ
ejpam-5246	298	8	i	i	NOUN
ejpam-5246	298	9	=	=	PUNCT
ejpam-5246	298	10	v	v	ADP
ejpam-5246	298	11	n+1	n+1	NUM
ejpam-5246	299	1	i	i	PRON
ejpam-5246	299	2	−	−	PROPN
ejpam-5246	299	3	2v	2v	PROPN
ejpam-5246	299	4	n+1	n+1	PROPN
ejpam-5246	300	1	i	i	PROPN
ejpam-5246	300	2	+	+	CCONJ
ejpam-5246	300	3	v	v	VERB
ejpam-5246	300	4	n+1	n+1	PROPN
ejpam-5246	300	5	i−1	i−1	PROPN
ejpam-5246	300	6	h2	h2	PROPN
ejpam-5246	301	1	+	+	PROPN
ejpam-5246	301	2	o	o	X
ejpam-5246	301	3	(	(	PUNCT
ejpam-5246	301	4	h2	h2	PROPN
ejpam-5246	301	5	)	)	PUNCT
ejpam-5246	301	6	.	.	PUNCT
ejpam-5246	302	1	moreover	moreover	ADV
ejpam-5246	302	2	,	,	PUNCT
ejpam-5246	302	3	the	the	DET
ejpam-5246	302	4	non	non	ADJ
ejpam-5246	302	5	-	-	ADJ
ejpam-5246	302	6	linear	linear	ADJ
ejpam-5246	302	7	terms	term	NOUN
ejpam-5246	302	8	are	be	AUX
ejpam-5246	302	9	approximated	approximate	VERB
ejpam-5246	302	10	as	as	SCONJ
ejpam-5246	302	11	follows	follow	VERB
ejpam-5246	302	12	:	:	PUNCT
ejpam-5246	302	13	f	f	PROPN
ejpam-5246	302	14	(	(	PUNCT
ejpam-5246	302	15	δxu	δxu	VERB
ejpam-5246	302	16	n+1	n+1	PROPN
ejpam-5246	302	17	j	j	PROPN
ejpam-5246	302	18	,	,	PUNCT
ejpam-5246	302	19	v	v	PROPN
ejpam-5246	302	20	n+1	n+1	PROPN
ejpam-5246	302	21	j	j	PROPN
ejpam-5246	302	22	)	)	PUNCT
ejpam-5246	303	1	=	=	SYM
ejpam-5246	303	2	f	f	PROPN
ejpam-5246	303	3	(	(	PUNCT
ejpam-5246	303	4	δxu	δxu	PROPN
ejpam-5246	303	5	n	n	PRON
ejpam-5246	303	6	j	j	PROPN
ejpam-5246	303	7	,	,	PUNCT
ejpam-5246	303	8	v	v	PROPN
ejpam-5246	303	9	n	n	PROPN
ejpam-5246	303	10	j	j	PROPN
ejpam-5246	303	11	)	)	PUNCT
ejpam-5246	304	1	+	+	VERB
ejpam-5246	304	2	o(k	o(k	NOUN
ejpam-5246	304	3	)	)	PUNCT
ejpam-5246	304	4	,	,	PUNCT
ejpam-5246	304	5	g	g	PROPN
ejpam-5246	304	6	(	(	PUNCT
ejpam-5246	304	7	δxv	δxv	PROPN
ejpam-5246	304	8	n+1	n+1	PROPN
ejpam-5246	304	9	i	i	PROPN
ejpam-5246	304	10	,	,	PUNCT
ejpam-5246	304	11	un+1	un+1	PROPN
ejpam-5246	304	12	i	i	NOUN
ejpam-5246	304	13	)	)	PUNCT
ejpam-5246	305	1	=	=	SYM
ejpam-5246	305	2	g	g	PROPN
ejpam-5246	305	3	(	(	PUNCT
ejpam-5246	305	4	δxv	δxv	PROPN
ejpam-5246	305	5	n	n	INTJ
ejpam-5246	305	6	i	i	PRON
ejpam-5246	305	7	,	,	PUNCT
ejpam-5246	305	8	un	un	PROPN
ejpam-5246	305	9	i	i	PROPN
ejpam-5246	305	10	)	)	PUNCT
ejpam-5246	306	1	+	+	ADJ
ejpam-5246	306	2	o(k	o(k	NOUN
ejpam-5246	306	3	)	)	PUNCT
ejpam-5246	306	4	.	.	PUNCT
ejpam-5246	307	1	m.i.khalil	m.i.khalil	PROPN
ejpam-5246	307	2	et	et	PROPN
ejpam-5246	307	3	al	al	PROPN
ejpam-5246	307	4	.	.	PUNCT
ejpam-5246	307	5	/	/	SYM
ejpam-5246	307	6	eur	eur	PROPN
ejpam-5246	307	7	.	.	PUNCT
ejpam-5246	308	1	j.	j.	PROPN
ejpam-5246	308	2	pure	pure	PROPN
ejpam-5246	308	3	appl	appl	PROPN
ejpam-5246	308	4	.	.	PROPN
ejpam-5246	308	5	math	math	PROPN
ejpam-5246	308	6	,	,	PUNCT
ejpam-5246	308	7	17	17	NUM
ejpam-5246	308	8	(	(	PUNCT
ejpam-5246	308	9	3	3	NUM
ejpam-5246	308	10	)	)	PUNCT
ejpam-5246	308	11	(	(	PUNCT
ejpam-5246	308	12	2024	2024	NUM
ejpam-5246	308	13	)	)	PUNCT
ejpam-5246	308	14	,	,	PUNCT
ejpam-5246	308	15	1516	1516	NUM
ejpam-5246	308	16	-	-	SYM
ejpam-5246	308	17	1538	1538	NUM
ejpam-5246	308	18	1525	1525	NUM
ejpam-5246	308	19	substituting	substitute	VERB
ejpam-5246	308	20	all	all	PRON
ejpam-5246	308	21	of	of	ADP
ejpam-5246	308	22	these	these	DET
ejpam-5246	308	23	formulas	formula	NOUN
ejpam-5246	308	24	into	into	ADP
ejpam-5246	308	25	system	system	NOUN
ejpam-5246	308	26	(	(	PUNCT
ejpam-5246	308	27	1.1	1.1	NUM
ejpam-5246	308	28	)	)	PUNCT
ejpam-5246	308	29	gives	give	VERB
ejpam-5246	308	30	un+1	un+1	PROPN
ejpam-5246	309	1	i	i	PRON
ejpam-5246	309	2	−	−	PROPN
ejpam-5246	309	3	un	un	PROPN
ejpam-5246	310	1	i	i	PRON
ejpam-5246	310	2	kn	kn	PROPN
ejpam-5246	310	3	=	=	PUNCT
ejpam-5246	311	1	un+1	un+1	PROPN
ejpam-5246	311	2	i+1	i+1	NUM
ejpam-5246	312	1	−	−	PROPN
ejpam-5246	312	2	2un+1	2un+1	NUM
ejpam-5246	312	3	i	i	PRON
ejpam-5246	313	1	+	+	CCONJ
ejpam-5246	313	2	un+1	un+1	ADJ
ejpam-5246	313	3	i−1	i−1	PROPN
ejpam-5246	313	4	h2	h2	PROPN
ejpam-5246	313	5	+	+	CCONJ
ejpam-5246	313	6	f	f	PROPN
ejpam-5246	313	7	(	(	PUNCT
ejpam-5246	313	8	δxu	δxu	PROPN
ejpam-5246	313	9	n	n	PRON
ejpam-5246	313	10	j	j	PROPN
ejpam-5246	313	11	,	,	PUNCT
ejpam-5246	313	12	v	v	PROPN
ejpam-5246	313	13	n	n	PROPN
ejpam-5246	313	14	j	j	PROPN
ejpam-5246	313	15	)	)	PUNCT
ejpam-5246	313	16	,	,	PUNCT
ejpam-5246	313	17	1	1	NUM
ejpam-5246	313	18	≤	≤	NUM
ejpam-5246	313	19	i	i	PRON
ejpam-5246	313	20	≤	≤	PUNCT
ejpam-5246	314	1	i	i	PRON
ejpam-5246	314	2	−	−	PROPN
ejpam-5246	314	3	1	1	NUM
ejpam-5246	314	4	,	,	PUNCT
ejpam-5246	314	5	v	v	ADP
ejpam-5246	314	6	n+1	n+1	PROPN
ejpam-5246	315	1	i	i	PRON
ejpam-5246	315	2	−	−	PROPN
ejpam-5246	315	3	v	v	ADP
ejpam-5246	315	4	n	n	NOUN
ejpam-5246	316	1	i	i	PRON
ejpam-5246	316	2	kn	kn	NOUN
ejpam-5246	317	1	=	=	PUNCT
ejpam-5246	317	2	v	v	ADP
ejpam-5246	317	3	n+1	n+1	PROPN
ejpam-5246	317	4	i+1	i+1	NOUN
ejpam-5246	317	5	−	−	PROPN
ejpam-5246	317	6	2v	2v	PROPN
ejpam-5246	317	7	n+1	n+1	PROPN
ejpam-5246	318	1	i	i	PROPN
ejpam-5246	318	2	+	+	CCONJ
ejpam-5246	318	3	v	v	VERB
ejpam-5246	318	4	n+1	n+1	PROPN
ejpam-5246	318	5	i−1	i−1	PROPN
ejpam-5246	318	6	h2	h2	PROPN
ejpam-5246	318	7	+	+	PROPN
ejpam-5246	318	8	g	g	PROPN
ejpam-5246	318	9	(	(	PUNCT
ejpam-5246	318	10	δxv	δxv	PROPN
ejpam-5246	318	11	n	n	INTJ
ejpam-5246	318	12	i	i	PRON
ejpam-5246	318	13	,	,	PUNCT
ejpam-5246	318	14	un	un	PROPN
ejpam-5246	318	15	i	i	PROPN
ejpam-5246	318	16	)	)	PUNCT
ejpam-5246	318	17	,	,	PUNCT
ejpam-5246	318	18	1	1	NUM
ejpam-5246	318	19	≤	≤	NUM
ejpam-5246	318	20	i	i	PRON
ejpam-5246	318	21	≤	≤	PUNCT
ejpam-5246	319	1	i	i	PRON
ejpam-5246	319	2	−	−	PROPN
ejpam-5246	320	1	1	1	X
ejpam-5246	320	2	.	.	PUNCT
ejpam-5246	321	1	thus	thus	ADV
ejpam-5246	321	2	(	(	PUNCT
ejpam-5246	321	3	1	1	NUM
ejpam-5246	321	4	+	+	CCONJ
ejpam-5246	321	5	2rn)u	2rn)u	NUM
ejpam-5246	321	6	n+1	n+1	PROPN
ejpam-5246	321	7	i	i	PRON
ejpam-5246	321	8	−	−	PROPN
ejpam-5246	321	9	rn	rn	PROPN
ejpam-5246	321	10	(	(	PUNCT
ejpam-5246	321	11	un+1	un+1	PROPN
ejpam-5246	321	12	i+1	i+1	NUM
ejpam-5246	321	13	+	+	NOUN
ejpam-5246	321	14	un+1	un+1	PROPN
ejpam-5246	321	15	i−1	i−1	PROPN
ejpam-5246	321	16	)	)	PUNCT
ejpam-5246	322	1	=	=	PUNCT
ejpam-5246	322	2	un	un	PROPN
ejpam-5246	323	1	i	i	PRON
ejpam-5246	323	2	+	+	CCONJ
ejpam-5246	323	3	knf	knf	PROPN
ejpam-5246	323	4	(	(	PUNCT
ejpam-5246	323	5	δxu	δxu	PROPN
ejpam-5246	323	6	n	n	PRON
ejpam-5246	323	7	j	j	PROPN
ejpam-5246	323	8	,	,	PUNCT
ejpam-5246	323	9	v	v	PROPN
ejpam-5246	323	10	n	n	PROPN
ejpam-5246	323	11	j	j	PROPN
ejpam-5246	323	12	)	)	PUNCT
ejpam-5246	323	13	,	,	PUNCT
ejpam-5246	323	14	(	(	PUNCT
ejpam-5246	323	15	3.1	3.1	NUM
ejpam-5246	323	16	)	)	PUNCT
ejpam-5246	323	17	(	(	PUNCT
ejpam-5246	323	18	1	1	NUM
ejpam-5246	323	19	+	+	NUM
ejpam-5246	323	20	2rn)v	2rn)v	NOUN
ejpam-5246	323	21	n+1	n+1	PROPN
ejpam-5246	323	22	i	i	PRON
ejpam-5246	323	23	−	−	PROPN
ejpam-5246	323	24	rn	rn	PROPN
ejpam-5246	323	25	(	(	PUNCT
ejpam-5246	323	26	v	v	ADP
ejpam-5246	323	27	n+1	n+1	PROPN
ejpam-5246	323	28	i+1	i+1	NUM
ejpam-5246	323	29	+	+	NOUN
ejpam-5246	323	30	v	v	ADP
ejpam-5246	323	31	n+1	n+1	PROPN
ejpam-5246	323	32	i−1	i−1	PROPN
ejpam-5246	323	33	)	)	PUNCT
ejpam-5246	324	1	=	=	PUNCT
ejpam-5246	324	2	v	v	NOUN
ejpam-5246	324	3	n	n	NOUN
ejpam-5246	325	1	i	i	PRON
ejpam-5246	325	2	+	+	CCONJ
ejpam-5246	325	3	kng	kng	PROPN
ejpam-5246	325	4	(	(	PUNCT
ejpam-5246	325	5	δxv	δxv	PROPN
ejpam-5246	325	6	n	n	INTJ
ejpam-5246	325	7	i	i	PRON
ejpam-5246	325	8	,	,	PUNCT
ejpam-5246	325	9	un	un	PROPN
ejpam-5246	325	10	i	i	PROPN
ejpam-5246	325	11	)	)	PUNCT
ejpam-5246	325	12	,	,	PUNCT
ejpam-5246	325	13	(	(	PUNCT
ejpam-5246	325	14	3.2	3.2	NUM
ejpam-5246	325	15	)	)	PUNCT
ejpam-5246	325	16	where	where	SCONJ
ejpam-5246	325	17	rn	rn	NOUN
ejpam-5246	325	18	=	=	PROPN
ejpam-5246	325	19	kn	kn	PROPN
ejpam-5246	325	20	h2	h2	PROPN
ejpam-5246	325	21	,	,	PUNCT
ejpam-5246	325	22	1	1	NUM
ejpam-5246	325	23	≤	≤	NUM
ejpam-5246	325	24	i	i	PRON
ejpam-5246	325	25	≤	≤	PUNCT
ejpam-5246	326	1	i	i	PRON
ejpam-5246	326	2	−	−	PROPN
ejpam-5246	326	3	1	1	NUM
ejpam-5246	326	4	,	,	PUNCT
ejpam-5246	326	5	n	n	NOUN
ejpam-5246	326	6	=	=	SYM
ejpam-5246	326	7	0	0	NUM
ejpam-5246	326	8	,	,	PUNCT
ejpam-5246	326	9	1	1	NUM
ejpam-5246	326	10	,	,	PUNCT
ejpam-5246	326	11	2	2	NUM
ejpam-5246	326	12	,	,	PUNCT
ejpam-5246	326	13	.	.	PUNCT
ejpam-5246	326	14	.	.	PUNCT
ejpam-5246	327	1	..	..	PUNCT
ejpam-5246	328	1	moreover	moreover	ADV
ejpam-5246	328	2	,	,	PUNCT
ejpam-5246	328	3	the	the	DET
ejpam-5246	328	4	non	non	ADJ
ejpam-5246	328	5	-	-	ADJ
ejpam-5246	328	6	fixed	fixed	ADJ
ejpam-5246	328	7	time	time	NOUN
ejpam-5246	328	8	-	-	PUNCT
ejpam-5246	328	9	stepping	step	VERB
ejpam-5246	328	10	formula	formula	NOUN
ejpam-5246	328	11	is	be	AUX
ejpam-5246	328	12	employed	employ	VERB
ejpam-5246	328	13	due	due	ADP
ejpam-5246	328	14	to	to	ADP
ejpam-5246	328	15	the	the	DET
ejpam-5246	328	16	lack	lack	NOUN
ejpam-5246	328	17	of	of	ADP
ejpam-5246	328	18	condition	condition	NOUN
ejpam-5246	328	19	stability	stability	NOUN
ejpam-5246	328	20	in	in	ADP
ejpam-5246	328	21	the	the	DET
ejpam-5246	328	22	implicit	implicit	ADJ
ejpam-5246	328	23	euler	euler	NOUN
ejpam-5246	328	24	chart	chart	NOUN
ejpam-5246	328	25	.	.	PUNCT
ejpam-5246	329	1	kn	kn	NOUN
ejpam-5246	329	2	=	=	PUNCT
ejpam-5246	329	3	min	min	PROPN
ejpam-5246	330	1	(	(	PUNCT
ejpam-5246	330	2	hα∥∥un	hα∥∥un	PROPN
ejpam-5246	330	3	h	h	NOUN
ejpam-5246	330	4	∥∥	∥∥	X
ejpam-5246	330	5	,	,	PUNCT
ejpam-5246	330	6	hα∥∥vn	hα∥∥vn	PROPN
ejpam-5246	330	7	h	h	NOUN
ejpam-5246	330	8	∥∥	∥∥	PROPN
ejpam-5246	330	9	)	)	PUNCT
ejpam-5246	330	10	,	,	PUNCT
ejpam-5246	330	11	α	α	PRON
ejpam-5246	330	12	≥	≥	NOUN
ejpam-5246	330	13	1	1	NUM
ejpam-5246	330	14	.	.	PUNCT
ejpam-5246	331	1	(	(	PUNCT
ejpam-5246	331	2	3.3	3.3	NUM
ejpam-5246	331	3	)	)	PUNCT
ejpam-5246	331	4	we	we	PRON
ejpam-5246	331	5	write	write	VERB
ejpam-5246	331	6	(	(	PUNCT
ejpam-5246	331	7	3.1)–(3.2	3.1)–(3.2	NUM
ejpam-5246	331	8	)	)	PUNCT
ejpam-5246	331	9	in	in	ADP
ejpam-5246	331	10	matrix	matrix	NOUN
ejpam-5246	331	11	form	form	NOUN
ejpam-5246	331	12	as	as	ADP
ejpam-5246	331	13	below	below	ADV
ejpam-5246	331	14	:	:	PUNCT
ejpam-5246	331	15	(	(	PUNCT
ejpam-5246	331	16	i	i	PRON
ejpam-5246	331	17	−	−	VERB
ejpam-5246	331	18	rnhh)un+1	rnhh)un+1	PROPN
ejpam-5246	331	19	h	h	PROPN
ejpam-5246	331	20	=	=	PROPN
ejpam-5246	331	21	un	un	PROPN
ejpam-5246	331	22	h	h	PROPN
ejpam-5246	331	23	+	+	CCONJ
ejpam-5246	331	24	knf	knf	PROPN
ejpam-5246	331	25	(	(	PUNCT
ejpam-5246	331	26	v	v	NOUN
ejpam-5246	331	27	n	n	NOUN
ejpam-5246	331	28	h	h	NOUN
ejpam-5246	331	29	)	)	PUNCT
ejpam-5246	331	30	,	,	PUNCT
ejpam-5246	331	31	(	(	PUNCT
ejpam-5246	331	32	3.4	3.4	NUM
ejpam-5246	331	33	)	)	PUNCT
ejpam-5246	331	34	(	(	PUNCT
ejpam-5246	331	35	i	i	PRON
ejpam-5246	331	36	−	−	PROPN
ejpam-5246	331	37	rnhh)v	rnhh)v	PROPN
ejpam-5246	332	1	n+1	n+1	NUM
ejpam-5246	332	2	h	h	NOUN
ejpam-5246	332	3	=	=	NOUN
ejpam-5246	332	4	v	v	PROPN
ejpam-5246	332	5	n	n	NOUN
ejpam-5246	332	6	h	h	NOUN
ejpam-5246	332	7	+	+	CCONJ
ejpam-5246	332	8	kng	kng	PROPN
ejpam-5246	332	9	(	(	PUNCT
ejpam-5246	332	10	un	un	PROPN
ejpam-5246	332	11	h	h	PROPN
ejpam-5246	332	12	)	)	PUNCT
ejpam-5246	332	13	,	,	PUNCT
ejpam-5246	332	14	(	(	PUNCT
ejpam-5246	332	15	3.5	3.5	NUM
ejpam-5246	332	16	)	)	PUNCT
ejpam-5246	333	1	where	where	SCONJ
ejpam-5246	333	2	h	h	NOUN
ejpam-5246	334	1	=	=	SYM
ejpam-5246	335	1			NOUN
ejpam-5246	336	1	−2	−2	NOUN
ejpam-5246	336	2	1	1	NUM
ejpam-5246	336	3	0	0	NUM
ejpam-5246	336	4	·	·	PUNCT
ejpam-5246	336	5	·	·	PUNCT
ejpam-5246	336	6	·	·	PUNCT
ejpam-5246	337	1	0	0	NUM
ejpam-5246	337	2	1	1	NUM
ejpam-5246	337	3	−2	−2	NOUN
ejpam-5246	337	4	1	1	NUM
ejpam-5246	337	5	·	·	PUNCT
ejpam-5246	337	6	·	·	PUNCT
ejpam-5246	337	7	·	·	PUNCT
ejpam-5246	337	8	0	0	NUM
ejpam-5246	337	9	.	.	PUNCT
ejpam-5246	337	10	.	.	PUNCT
ejpam-5246	337	11	.	.	PUNCT
ejpam-5246	337	12	...	...	PUNCT
ejpam-5246	337	13	.	.	PUNCT
ejpam-5246	337	14	.	.	PUNCT
ejpam-5246	337	15	.	.	PUNCT
ejpam-5246	338	1	0	0	PUNCT
ejpam-5246	338	2	·	·	PUNCT
ejpam-5246	338	3	·	·	PUNCT
ejpam-5246	338	4	·	·	PUNCT
ejpam-5246	338	5	0	0	NUM
ejpam-5246	338	6	1	1	NUM
ejpam-5246	338	7	−2	−2	NOUN
ejpam-5246	338	8			NUM
ejpam-5246	338	9	(	(	PUNCT
ejpam-5246	338	10	i−1)×(i−1	i−1)×(i−1	NUM
ejpam-5246	338	11	)	)	PUNCT
ejpam-5246	338	12	,	,	PUNCT
ejpam-5246	338	13	f	f	PROPN
ejpam-5246	338	14	(	(	PUNCT
ejpam-5246	338	15	v	v	NOUN
ejpam-5246	338	16	n	n	PRON
ejpam-5246	338	17	h	h	NOUN
ejpam-5246	338	18	)	)	PUNCT
ejpam-5246	339	1	=	=	PUNCT
ejpam-5246	339	2	(	(	PUNCT
ejpam-5246	339	3	f	f	X
ejpam-5246	339	4	(	(	PUNCT
ejpam-5246	339	5	v	v	NOUN
ejpam-5246	339	6	n	n	PRON
ejpam-5246	339	7	1	1	NUM
ejpam-5246	339	8	)	)	PUNCT
ejpam-5246	339	9	,	,	PUNCT
ejpam-5246	339	10	f	f	PROPN
ejpam-5246	339	11	(	(	PUNCT
ejpam-5246	339	12	v	v	NOUN
ejpam-5246	339	13	n	n	PRON
ejpam-5246	339	14	2	2	NUM
ejpam-5246	339	15	)	)	PUNCT
ejpam-5246	339	16	,	,	PUNCT
ejpam-5246	339	17	.	.	PUNCT
ejpam-5246	339	18	.	.	PUNCT
ejpam-5246	340	1	.	.	PUNCT
ejpam-5246	341	1	,	,	PUNCT
ejpam-5246	341	2	f	f	PROPN
ejpam-5246	341	3	(	(	PUNCT
ejpam-5246	341	4	v	v	NOUN
ejpam-5246	341	5	n	n	CCONJ
ejpam-5246	341	6	i−1	i−1	PROPN
ejpam-5246	341	7	)	)	PUNCT
ejpam-5246	341	8	)	)	PUNCT
ejpam-5246	342	1	t	t	NOUN
ejpam-5246	342	2	,	,	PUNCT
ejpam-5246	342	3	g	g	PROPN
ejpam-5246	342	4	(	(	PUNCT
ejpam-5246	342	5	un	un	PROPN
ejpam-5246	342	6	h	h	PROPN
ejpam-5246	342	7	)	)	PUNCT
ejpam-5246	343	1	=	=	PRON
ejpam-5246	343	2	(	(	PUNCT
ejpam-5246	343	3	g	g	PROPN
ejpam-5246	343	4	(	(	PUNCT
ejpam-5246	343	5	un	un	PROPN
ejpam-5246	343	6	1	1	NUM
ejpam-5246	343	7	)	)	PUNCT
ejpam-5246	343	8	,	,	PUNCT
ejpam-5246	343	9	g	g	PROPN
ejpam-5246	343	10	(	(	PUNCT
ejpam-5246	343	11	u	u	NOUN
ejpam-5246	343	12	n	n	PRON
ejpam-5246	343	13	2	2	NUM
ejpam-5246	343	14	)	)	PUNCT
ejpam-5246	343	15	,	,	PUNCT
ejpam-5246	343	16	.	.	PUNCT
ejpam-5246	343	17	.	.	PUNCT
ejpam-5246	344	1	.	.	PUNCT
ejpam-5246	345	1	,	,	PUNCT
ejpam-5246	345	2	g	g	PROPN
ejpam-5246	345	3	(	(	PUNCT
ejpam-5246	345	4	un	un	PROPN
ejpam-5246	345	5	i−1	i−1	PROPN
ejpam-5246	345	6	)	)	PUNCT
ejpam-5246	345	7	)	)	PUNCT
ejpam-5246	345	8	t	t	NOUN
ejpam-5246	345	9	.	.	PUNCT
ejpam-5246	346	1	3.1	3.1	NUM
ejpam-5246	346	2	.	.	PUNCT
ejpam-5246	347	1	the	the	DET
ejpam-5246	347	2	algorithm	algorithm	NOUN
ejpam-5246	347	3	steps	step	VERB
ejpam-5246	347	4	for	for	ADP
ejpam-5246	347	5	euler	euler	NOUN
ejpam-5246	347	6	implicit	implicit	ADJ
ejpam-5246	347	7	method	method	NOUN
ejpam-5246	347	8	1	1	NUM
ejpam-5246	347	9	.	.	PUNCT
ejpam-5246	347	10	input	input	PROPN
ejpam-5246	347	11	h	h	NOUN
ejpam-5246	347	12	,	,	PUNCT
ejpam-5246	347	13	u0	u0	ADJ
ejpam-5246	347	14	h	h	PROPN
ejpam-5246	347	15	,	,	PUNCT
ejpam-5246	347	16	v	v	NOUN
ejpam-5246	347	17	0	0	NUM
ejpam-5246	347	18	h	h	NOUN
ejpam-5246	347	19	,	,	PUNCT
ejpam-5246	347	20	p1,p2	p1,p2	PROPN
ejpam-5246	347	21	,	,	PUNCT
ejpam-5246	347	22	q1	q1	PROPN
ejpam-5246	347	23	,	,	PUNCT
ejpam-5246	347	24	q2	q2	PROPN
ejpam-5246	347	25	,	,	PUNCT
ejpam-5246	347	26	α	α	PROPN
ejpam-5246	347	27	2	2	X
ejpam-5246	347	28	.	.	PUNCT
ejpam-5246	347	29	put	put	VERB
ejpam-5246	347	30	n	n	NOUN
ejpam-5246	347	31	=	=	SYM
ejpam-5246	347	32	0	0	NUM
ejpam-5246	347	33	;	;	PUNCT
ejpam-5246	347	34	3	3	X
ejpam-5246	347	35	.	.	X
ejpam-5246	347	36	choose	choose	VERB
ejpam-5246	347	37	kn	kn	PROPN
ejpam-5246	347	38	according	accord	VERB
ejpam-5246	347	39	to	to	ADP
ejpam-5246	347	40	(	(	PUNCT
ejpam-5246	347	41	3.3	3.3	NUM
ejpam-5246	347	42	)	)	PUNCT
ejpam-5246	347	43	.	.	PUNCT
ejpam-5246	348	1	4	4	X
ejpam-5246	348	2	.	.	X
ejpam-5246	348	3	compute	compute	VERB
ejpam-5246	348	4	the	the	DET
ejpam-5246	348	5	numerical	numerical	ADJ
ejpam-5246	348	6	vectors	vector	NOUN
ejpam-5246	348	7	:	:	PUNCT
ejpam-5246	348	8	un+1	un+1	PROPN
ejpam-5246	348	9	h	h	NOUN
ejpam-5246	348	10	,	,	PUNCT
ejpam-5246	348	11	v	v	NOUN
ejpam-5246	348	12	n+1	n+1	PROPN
ejpam-5246	348	13	h	h	NOUN
ejpam-5246	348	14	,	,	PUNCT
ejpam-5246	348	15	by	by	ADP
ejpam-5246	348	16	solving	solve	VERB
ejpam-5246	348	17	the	the	DET
ejpam-5246	348	18	linear	linear	PROPN
ejpam-5246	348	19	systems	system	NOUN
ejpam-5246	348	20	(	(	PUNCT
ejpam-5246	348	21	3.4	3.4	NUM
ejpam-5246	348	22	)	)	PUNCT
ejpam-5246	348	23	and	and	CCONJ
ejpam-5246	348	24	(	(	PUNCT
ejpam-5246	348	25	3.5	3.5	NUM
ejpam-5246	348	26	)	)	PUNCT
ejpam-5246	348	27	.	.	PUNCT
ejpam-5246	349	1	5	5	X
ejpam-5246	349	2	.	.	X
ejpam-5246	349	3	for	for	ADP
ejpam-5246	349	4	n	n	NOUN
ejpam-5246	349	5	=	=	SYM
ejpam-5246	349	6	1	1	NUM
ejpam-5246	349	7	,	,	PUNCT
ejpam-5246	349	8	2	2	NUM
ejpam-5246	349	9	,	,	PUNCT
ejpam-5246	349	10	.	.	PUNCT
ejpam-5246	349	11	.	.	PUNCT
ejpam-5246	349	12	.	.	PUNCT
ejpam-5246	350	1	..	..	PUNCT
ejpam-5246	350	2	,	,	PUNCT
ejpam-5246	350	3	repeat	repeat	VERB
ejpam-5246	350	4	steps	step	NOUN
ejpam-5246	350	5	3,4	3,4	NUM
ejpam-5246	350	6	until	until	ADP
ejpam-5246	350	7	for	for	ADP
ejpam-5246	350	8	n	n	NOUN
ejpam-5246	350	9	=	=	SYM
ejpam-5246	350	10	m	m	PROPN
ejpam-5246	350	11	,	,	PUNCT
ejpam-5246	350	12	we	we	PRON
ejpam-5246	350	13	get	get	VERB
ejpam-5246	350	14	∥un	∥un	PROPN
ejpam-5246	350	15	h	h	PROPN
ejpam-5246	350	16	∥∞	∥∞	PROPN
ejpam-5246	350	17	≥	≥	NUM
ejpam-5246	350	18	1015	1015	NUM
ejpam-5246	350	19	,	,	PUNCT
ejpam-5246	350	20	or	or	CCONJ
ejpam-5246	350	21	∥v	∥v	PROPN
ejpam-5246	350	22	n	n	PRON
ejpam-5246	350	23	h	h	NOUN
ejpam-5246	350	24	∥∞	∥∞	ADJ
ejpam-5246	350	25	≥	≥	NUM
ejpam-5246	350	26	1015	1015	NUM
ejpam-5246	350	27	m.i.khalil	m.i.khalil	PROPN
ejpam-5246	350	28	et	et	PROPN
ejpam-5246	350	29	al	al	PROPN
ejpam-5246	350	30	.	.	PUNCT
ejpam-5246	350	31	/	/	SYM
ejpam-5246	350	32	eur	eur	PROPN
ejpam-5246	350	33	.	.	PUNCT
ejpam-5246	351	1	j.	j.	PROPN
ejpam-5246	351	2	pure	pure	PROPN
ejpam-5246	351	3	appl	appl	PROPN
ejpam-5246	351	4	.	.	PROPN
ejpam-5246	351	5	math	math	PROPN
ejpam-5246	351	6	,	,	PUNCT
ejpam-5246	351	7	17	17	NUM
ejpam-5246	351	8	(	(	PUNCT
ejpam-5246	351	9	3	3	NUM
ejpam-5246	351	10	)	)	PUNCT
ejpam-5246	351	11	(	(	PUNCT
ejpam-5246	351	12	2024	2024	NUM
ejpam-5246	351	13	)	)	PUNCT
ejpam-5246	351	14	,	,	PUNCT
ejpam-5246	351	15	1516	1516	NUM
ejpam-5246	351	16	-	-	SYM
ejpam-5246	351	17	1538	1538	NUM
ejpam-5246	351	18	1526	1526	NUM
ejpam-5246	351	19	6	6	NUM
ejpam-5246	351	20	.	.	PUNCT
ejpam-5246	352	1	the	the	DET
ejpam-5246	352	2	numerical	numerical	ADJ
ejpam-5246	352	3	blow	blow	VERB
ejpam-5246	352	4	-	-	PUNCT
ejpam-5246	352	5	up	up	ADP
ejpam-5246	352	6	time	time	NOUN
ejpam-5246	352	7	is	be	AUX
ejpam-5246	352	8	tm	tm	PROPN
ejpam-5246	352	9	=	=	PROPN
ejpam-5246	352	10	∑m	∑m	PROPN
ejpam-5246	352	11	n=0	n=0	PROPN
ejpam-5246	352	12	kn	kn	NOUN
ejpam-5246	352	13	.	.	PROPN
ejpam-5246	352	14	7	7	NUM
ejpam-5246	352	15	.	.	NOUN
ejpam-5246	352	16	3.2	3.2	NUM
ejpam-5246	352	17	.	.	PUNCT
ejpam-5246	353	1	local	local	ADJ
ejpam-5246	353	2	truncation	truncation	NOUN
ejpam-5246	353	3	error	error	NOUN
ejpam-5246	353	4	of	of	ADP
ejpam-5246	353	5	implicit	implicit	ADJ
ejpam-5246	353	6	euler	euler	NOUN
ejpam-5246	353	7	scheme	scheme	NOUN
ejpam-5246	353	8	theorem	theorem	NOUN
ejpam-5246	353	9	4	4	X
ejpam-5246	353	10	.	.	PUNCT
ejpam-5246	354	1	let	let	VERB
ejpam-5246	354	2	(	(	PUNCT
ejpam-5246	354	3	tn	tn	PROPN
ejpam-5246	354	4	ui	ui	PROPN
ejpam-5246	354	5	,	,	PUNCT
ejpam-5246	354	6	t	t	PROPN
ejpam-5246	354	7	n	n	PRON
ejpam-5246	354	8	vi	vi	PROPN
ejpam-5246	354	9	)	)	PUNCT
ejpam-5246	354	10	be	be	VERB
ejpam-5246	354	11	the	the	DET
ejpam-5246	354	12	local	local	ADJ
ejpam-5246	354	13	truncation	truncation	NOUN
ejpam-5246	354	14	error	error	NOUN
ejpam-5246	354	15	of	of	ADP
ejpam-5246	354	16	the	the	DET
ejpam-5246	354	17	implicit	implicit	ADJ
ejpam-5246	354	18	euler	euler	NOUN
ejpam-5246	354	19	scheme	scheme	NOUN
ejpam-5246	354	20	(	(	PUNCT
ejpam-5246	354	21	3.1	3.1	NUM
ejpam-5246	354	22	)	)	PUNCT
ejpam-5246	354	23	–	–	PUNCT
ejpam-5246	354	24	(	(	PUNCT
ejpam-5246	354	25	3.2	3.2	NUM
ejpam-5246	354	26	)	)	PUNCT
ejpam-5246	354	27	at	at	ADP
ejpam-5246	354	28	the	the	DET
ejpam-5246	354	29	mesh	mesh	NOUN
ejpam-5246	354	30	point	point	NOUN
ejpam-5246	354	31	(	(	PUNCT
ejpam-5246	354	32	xi	xi	PROPN
ejpam-5246	354	33	,	,	PUNCT
ejpam-5246	354	34	tn+1	tn+1	NOUN
ejpam-5246	354	35	)	)	PUNCT
ejpam-5246	354	36	.	.	PUNCT
ejpam-5246	355	1	then	then	ADV
ejpam-5246	355	2	,	,	PUNCT
ejpam-5246	355	3	there	there	PRON
ejpam-5246	355	4	exist	exist	VERB
ejpam-5246	355	5	c1	c1	PROPN
ejpam-5246	355	6	,	,	PUNCT
ejpam-5246	355	7	c2	c2	PROPN
ejpam-5246	355	8	,	,	PUNCT
ejpam-5246	355	9	c3	c3	PROPN
ejpam-5246	355	10	,	,	PUNCT
ejpam-5246	355	11	c4	c4	NOUN
ejpam-5246	355	12	>	>	X
ejpam-5246	355	13	0	0	PROPN
ejpam-5246	355	14	,	,	PUNCT
ejpam-5246	355	15	such	such	ADJ
ejpam-5246	355	16	that	that	DET
ejpam-5246	355	17	∣∣tn+1	∣∣tn+1	NOUN
ejpam-5246	355	18	ui	ui	PROPN
ejpam-5246	355	19	∣∣	∣∣	X
ejpam-5246	355	20	≤	≤	ADV
ejpam-5246	355	21	c1k+c2h	c1k+c2h	PROPN
ejpam-5246	355	22	2	2	NUM
ejpam-5246	355	23	and	and	CCONJ
ejpam-5246	355	24	∣∣tn+1	∣∣tn+1	PROPN
ejpam-5246	355	25	vi	vi	PROPN
ejpam-5246	355	26	∣∣	∣∣	X
ejpam-5246	356	1	≤	≤	X
ejpam-5246	356	2	c3k+c4h	c3k+c4h	PROPN
ejpam-5246	356	3	2	2	NUM
ejpam-5246	356	4	,	,	PUNCT
ejpam-5246	356	5	where	where	SCONJ
ejpam-5246	356	6	k	k	PROPN
ejpam-5246	356	7	=	=	SYM
ejpam-5246	356	8	maxn∈n	maxn∈n	PROPN
ejpam-5246	356	9	kn	kn	PROPN
ejpam-5246	356	10	,	,	PUNCT
ejpam-5246	356	11	i.e.	i.e.	X
ejpam-5246	356	12	tn+1	tn+1	X
ejpam-5246	356	13	ui	ui	NOUN
ejpam-5246	356	14	=	=	PUNCT
ejpam-5246	356	15	o	o	X
ejpam-5246	356	16	(	(	PUNCT
ejpam-5246	356	17	k	k	PROPN
ejpam-5246	356	18	+	+	CCONJ
ejpam-5246	356	19	h2	h2	NOUN
ejpam-5246	356	20	)	)	PUNCT
ejpam-5246	356	21	and	and	CCONJ
ejpam-5246	356	22	tn+1	tn+1	X
ejpam-5246	356	23	vi	vi	NOUN
ejpam-5246	357	1	=	=	NOUN
ejpam-5246	357	2	o	o	X
ejpam-5246	357	3	(	(	PUNCT
ejpam-5246	357	4	k	k	PROPN
ejpam-5246	357	5	+	+	CCONJ
ejpam-5246	357	6	h2	h2	NOUN
ejpam-5246	357	7	)	)	PUNCT
ejpam-5246	357	8	.	.	PUNCT
ejpam-5246	358	1	proof	proof	NOUN
ejpam-5246	358	2	.	.	PUNCT
ejpam-5246	359	1	replace	replace	VERB
ejpam-5246	359	2	the	the	DET
ejpam-5246	359	3	precise	precise	ADJ
ejpam-5246	359	4	solution	solution	NOUN
ejpam-5246	359	5	uni	uni	PROPN
ejpam-5246	360	1	=	=	PUNCT
ejpam-5246	360	2	u	u	PROPN
ejpam-5246	360	3	(	(	PUNCT
ejpam-5246	360	4	xi	xi	PROPN
ejpam-5246	360	5	,	,	PUNCT
ejpam-5246	360	6	tn	tn	PROPN
ejpam-5246	360	7	)	)	PUNCT
ejpam-5246	360	8	,	,	PUNCT
ejpam-5246	360	9	v	v	PART
ejpam-5246	360	10	n	n	NOUN
ejpam-5246	360	11	i	i	NOUN
ejpam-5246	360	12	=	=	NOUN
ejpam-5246	360	13	v	v	X
ejpam-5246	360	14	(	(	PUNCT
ejpam-5246	360	15	xi	xi	PROPN
ejpam-5246	360	16	,	,	PUNCT
ejpam-5246	360	17	tn	tn	PROPN
ejpam-5246	360	18	)	)	PUNCT
ejpam-5246	360	19	into	into	ADP
ejpam-5246	360	20	the	the	DET
ejpam-5246	360	21	implicit	implicit	ADJ
ejpam-5246	360	22	euler	euler	NOUN
ejpam-5246	360	23	scheme	scheme	NOUN
ejpam-5246	360	24	(	(	PUNCT
ejpam-5246	360	25	3.1	3.1	NUM
ejpam-5246	360	26	)	)	PUNCT
ejpam-5246	360	27	yields	yield	NOUN
ejpam-5246	360	28	tn+1	tn+1	VERB
ejpam-5246	360	29	ui	ui	NOUN
ejpam-5246	361	1	=	=	PUNCT
ejpam-5246	362	1	(	(	PUNCT
ejpam-5246	362	2	un+1	un+1	NOUN
ejpam-5246	362	3	i	i	PRON
ejpam-5246	362	4	−	−	PROPN
ejpam-5246	362	5	uni	uni	INTJ
ejpam-5246	362	6	)	)	PUNCT
ejpam-5246	363	1	−	−	PROPN
ejpam-5246	364	1	kn	kn	PROPN
ejpam-5246	364	2	h2	h2	PROPN
ejpam-5246	364	3	[	[	PUNCT
ejpam-5246	364	4	un+1	un+1	PROPN
ejpam-5246	364	5	i+1	i+1	ADV
ejpam-5246	364	6	−	−	PROPN
ejpam-5246	364	7	2un+1	2un+1	NUM
ejpam-5246	365	1	i	i	PRON
ejpam-5246	365	2	+	+	CCONJ
ejpam-5246	365	3	un+1	un+1	PROPN
ejpam-5246	365	4	i−1	i−1	PROPN
ejpam-5246	365	5	]	]	PUNCT
ejpam-5246	365	6	−	−	PROPN
ejpam-5246	365	7	knf	knf	NOUN
ejpam-5246	365	8	(	(	PUNCT
ejpam-5246	365	9	δxu	δxu	PROPN
ejpam-5246	365	10	n	n	PRON
ejpam-5246	365	11	j	j	PROPN
ejpam-5246	365	12	,	,	PUNCT
ejpam-5246	365	13	v	v	PROPN
ejpam-5246	365	14	n	n	PROPN
ejpam-5246	365	15	j	j	PROPN
ejpam-5246	365	16	)	)	PUNCT
ejpam-5246	366	1	=	=	SYM
ejpam-5246	366	2	kn	kn	PROPN
ejpam-5246	366	3	[	[	PUNCT
ejpam-5246	366	4	∂un+1	∂un+1	VERB
ejpam-5246	366	5	i	i	PRON
ejpam-5246	366	6	∂t	∂t	PROPN
ejpam-5246	367	1	+	+	NOUN
ejpam-5246	367	2	o(kn	o(kn	PROPN
ejpam-5246	367	3	)	)	PUNCT
ejpam-5246	367	4	]	]	PUNCT
ejpam-5246	368	1	−	−	PROPN
ejpam-5246	368	2	kn	kn	PROPN
ejpam-5246	368	3	[	[	PUNCT
ejpam-5246	368	4	∂2un+1	∂2un+1	PROPN
ejpam-5246	368	5	i	i	PRON
ejpam-5246	368	6	∂x2	∂x2	VERB
ejpam-5246	368	7	+	+	NOUN
ejpam-5246	368	8	o	o	X
ejpam-5246	368	9	(	(	PUNCT
ejpam-5246	368	10	h2	h2	PROPN
ejpam-5246	368	11	)	)	PUNCT
ejpam-5246	368	12	]	]	PUNCT
ejpam-5246	369	1	=	=	PUNCT
ejpam-5246	369	2	−k	−k	PROPN
ejpam-5246	369	3	[	[	X
ejpam-5246	369	4	(	(	PUNCT
ejpam-5246	369	5	vn+1	vn+1	X
ejpam-5246	369	6	i	i	NOUN
ejpam-5246	369	7	)	)	PUNCT
ejpam-5246	369	8	p1	p1	PROPN
ejpam-5246	369	9	−	−	PROPN
ejpam-5246	370	1	∣∣∣∣∂un+1	∣∣∣∣∂un+1	PROPN
ejpam-5246	371	1	i	i	PRON
ejpam-5246	371	2	∂x	∂x	PROPN
ejpam-5246	371	3	∣∣∣∣q1	∣∣∣∣q1	PUNCT
ejpam-5246	372	1	+	+	NOUN
ejpam-5246	372	2	o(kn	o(kn	NUM
ejpam-5246	372	3	)	)	PUNCT
ejpam-5246	373	1	+	+	NOUN
ejpam-5246	373	2	o	o	X
ejpam-5246	373	3	(	(	PUNCT
ejpam-5246	373	4	h2	h2	PROPN
ejpam-5246	373	5	)	)	PUNCT
ejpam-5246	373	6	]	]	PUNCT
ejpam-5246	373	7	.	.	PUNCT
ejpam-5246	374	1	it	it	PRON
ejpam-5246	374	2	follows	follow	VERB
ejpam-5246	374	3	that	that	PRON
ejpam-5246	374	4	tn+1	tn+1	VERB
ejpam-5246	374	5	ui	ui	NOUN
ejpam-5246	375	1	=	=	PUNCT
ejpam-5246	375	2	kn	kn	PROPN
ejpam-5246	376	1	[	[	PUNCT
ejpam-5246	376	2	∂un+1	∂un+1	VERB
ejpam-5246	376	3	i	i	PRON
ejpam-5246	376	4	∂t	∂t	PROPN
ejpam-5246	376	5	−	−	PROPN
ejpam-5246	376	6	∂2un+1	∂2un+1	PROPN
ejpam-5246	377	1	i	i	PRON
ejpam-5246	377	2	∂x2	∂x2	VERB
ejpam-5246	377	3	−	−	NOUN
ejpam-5246	377	4	(	(	PUNCT
ejpam-5246	377	5	vn+1	vn+1	PROPN
ejpam-5246	377	6	i	i	NOUN
ejpam-5246	377	7	)	)	PUNCT
ejpam-5246	377	8	p1	p1	PROPN
ejpam-5246	377	9	+	+	CCONJ
ejpam-5246	377	10	∣∣∣∣∂un+1	∣∣∣∣∂un+1	PROPN
ejpam-5246	377	11	i	i	PRON
ejpam-5246	377	12	∂x	∂x	PROPN
ejpam-5246	377	13	∣∣∣∣q1	∣∣∣∣q1	PRON
ejpam-5246	377	14	]	]	PUNCT
ejpam-5246	378	1	+	+	CCONJ
ejpam-5246	378	2	kn	kn	PROPN
ejpam-5246	378	3	[	[	PUNCT
ejpam-5246	378	4	o(kn	o(kn	NUM
ejpam-5246	378	5	)	)	PUNCT
ejpam-5246	379	1	+	+	NOUN
ejpam-5246	379	2	o	o	X
ejpam-5246	379	3	(	(	PUNCT
ejpam-5246	379	4	h2	h2	PROPN
ejpam-5246	379	5	)	)	PUNCT
ejpam-5246	379	6	]	]	PUNCT
ejpam-5246	379	7	.	.	PUNCT
ejpam-5246	380	1	from	from	ADP
ejpam-5246	380	2	equation	equation	NOUN
ejpam-5246	380	3	(	(	PUNCT
ejpam-5246	380	4	1.1	1.1	NUM
ejpam-5246	380	5	)	)	PUNCT
ejpam-5246	380	6	and	and	CCONJ
ejpam-5246	380	7	presuming	presume	VERB
ejpam-5246	380	8	all	all	DET
ejpam-5246	380	9	the	the	DET
ejpam-5246	380	10	partial	partial	ADJ
ejpam-5246	380	11	derivatives	derivative	NOUN
ejpam-5246	380	12	are	be	AUX
ejpam-5246	380	13	bounded	bound	VERB
ejpam-5246	380	14	at	at	ADP
ejpam-5246	380	15	the	the	DET
ejpam-5246	380	16	meshpoint	meshpoint	NOUN
ejpam-5246	380	17	(	(	PUNCT
ejpam-5246	380	18	xi	xi	PROPN
ejpam-5246	380	19	,	,	PUNCT
ejpam-5246	380	20	tn+1	tn+1	PROPN
ejpam-5246	380	21	)	)	PUNCT
ejpam-5246	380	22	,	,	PUNCT
ejpam-5246	380	23	we	we	PRON
ejpam-5246	380	24	obtain	obtain	VERB
ejpam-5246	380	25	∣∣tn+1	∣∣tn+1	PROPN
ejpam-5246	380	26	ui	ui	NOUN
ejpam-5246	380	27	∣∣	∣∣	X
ejpam-5246	380	28	≤	≤	X
ejpam-5246	380	29	c1kn	c1kn	PUNCT
ejpam-5246	381	1	+	+	CCONJ
ejpam-5246	381	2	c2h	c2h	PROPN
ejpam-5246	381	3	2	2	NUM
ejpam-5246	381	4	≤	≤	NOUN
ejpam-5246	381	5	c1k	c1k	NOUN
ejpam-5246	381	6	+	+	CCONJ
ejpam-5246	381	7	c2h	c2h	PROPN
ejpam-5246	381	8	2	2	NUM
ejpam-5246	381	9	,	,	PUNCT
ejpam-5246	381	10	where	where	SCONJ
ejpam-5246	381	11	c1	c1	PROPN
ejpam-5246	381	12	,	,	PUNCT
ejpam-5246	381	13	c2	c2	PROPN
ejpam-5246	381	14	>	>	X
ejpam-5246	381	15	0	0	PROPN
ejpam-5246	381	16	.	.	NUM
ejpam-5246	381	17	,	,	PUNCT
ejpam-5246	381	18	i.e.∣∣tn+1	i.e.∣∣tn+1	PUNCT
ejpam-5246	381	19	i	i	PRON
ejpam-5246	381	20	∣∣	∣∣	NUM
ejpam-5246	381	21	=	=	PUNCT
ejpam-5246	381	22	o	o	X
ejpam-5246	381	23	(	(	PUNCT
ejpam-5246	381	24	k	k	PROPN
ejpam-5246	381	25	+	+	CCONJ
ejpam-5246	381	26	h2	h2	NOUN
ejpam-5246	381	27	)	)	PUNCT
ejpam-5246	381	28	,	,	PUNCT
ejpam-5246	381	29	c	c	X
ejpam-5246	381	30	>	>	X
ejpam-5246	381	31	0	0	X
ejpam-5246	381	32	.	.	PUNCT
ejpam-5246	382	1	similarly	similarly	ADV
ejpam-5246	382	2	,	,	PUNCT
ejpam-5246	382	3	we	we	PRON
ejpam-5246	382	4	show	show	VERB
ejpam-5246	382	5	that	that	SCONJ
ejpam-5246	382	6	there	there	PRON
ejpam-5246	382	7	exist	exist	VERB
ejpam-5246	382	8	c3	c3	NOUN
ejpam-5246	382	9	,	,	PUNCT
ejpam-5246	382	10	c4	c4	NOUN
ejpam-5246	382	11	>	>	X
ejpam-5246	382	12	0	0	PUNCT
ejpam-5246	383	1	such	such	ADJ
ejpam-5246	383	2	that∣∣tn+1	that∣∣tn+1	PROPN
ejpam-5246	383	3	vi	vi	X
ejpam-5246	383	4	∣∣	∣∣	X
ejpam-5246	383	5	≤	≤	PUNCT
ejpam-5246	383	6	c3k	c3k	PROPN
ejpam-5246	383	7	+	+	PUNCT
ejpam-5246	383	8	c4h	c4h	NOUN
ejpam-5246	383	9	2	2	NUM
ejpam-5246	383	10	.	.	NOUN
ejpam-5246	383	11	3.3	3.3	NUM
ejpam-5246	383	12	.	.	PUNCT
ejpam-5246	384	1	the	the	DET
ejpam-5246	384	2	stability	stability	NOUN
ejpam-5246	384	3	analysis	analysis	NOUN
ejpam-5246	384	4	of	of	ADP
ejpam-5246	384	5	implicit	implicit	ADJ
ejpam-5246	384	6	euler	euler	NOUN
ejpam-5246	384	7	method	method	NOUN
ejpam-5246	384	8	theorem	theorem	VERB
ejpam-5246	384	9	5	5	NUM
ejpam-5246	384	10	.	.	PUNCT
ejpam-5246	385	1	the	the	DET
ejpam-5246	385	2	implicit	implicit	ADJ
ejpam-5246	385	3	euler	euler	NOUN
ejpam-5246	385	4	scheme	scheme	NOUN
ejpam-5246	385	5	(	(	PUNCT
ejpam-5246	385	6	3.1)–(3.2	3.1)–(3.2	NUM
ejpam-5246	385	7	)	)	PUNCT
ejpam-5246	385	8	is	be	AUX
ejpam-5246	385	9	unconditionally	unconditionally	ADV
ejpam-5246	385	10	stable	stable	ADJ
ejpam-5246	385	11	.	.	PUNCT
ejpam-5246	386	1	proof	proof	NOUN
ejpam-5246	386	2	.	.	PUNCT
ejpam-5246	387	1	to	to	PART
ejpam-5246	387	2	demonstrate	demonstrate	VERB
ejpam-5246	387	3	the	the	DET
ejpam-5246	387	4	validity	validity	NOUN
ejpam-5246	387	5	of	of	ADP
ejpam-5246	387	6	this	this	DET
ejpam-5246	387	7	theorem	theorem	NOUN
ejpam-5246	387	8	,	,	PUNCT
ejpam-5246	387	9	the	the	DET
ejpam-5246	387	10	maximum	maximum	ADJ
ejpam-5246	387	11	error	error	NOUN
ejpam-5246	387	12	stability	stability	NOUN
ejpam-5246	387	13	technique	technique	NOUN
ejpam-5246	387	14	can	can	AUX
ejpam-5246	387	15	be	be	AUX
ejpam-5246	387	16	employed	employ	VERB
ejpam-5246	387	17	.	.	PUNCT
ejpam-5246	388	1	[	[	X
ejpam-5246	388	2	6	6	NUM
ejpam-5246	388	3	]	]	PUNCT
ejpam-5246	388	4	.	.	PUNCT
ejpam-5246	389	1	let	let	VERB
ejpam-5246	389	2	enui	enui	NOUN
ejpam-5246	389	3	=	=	SYM
ejpam-5246	389	4	uni	uni	PROPN
ejpam-5246	390	1	−	−	PROPN
ejpam-5246	390	2	un	un	PROPN
ejpam-5246	390	3	i	i	PROPN
ejpam-5246	390	4	,	,	PUNCT
ejpam-5246	390	5	envi	envi	PROPN
ejpam-5246	390	6	=	=	PUNCT
ejpam-5246	390	7	vni	vni	PROPN
ejpam-5246	390	8	−	−	PROPN
ejpam-5246	390	9	v	v	NOUN
ejpam-5246	390	10	n	n	NOUN
ejpam-5246	391	1	i	i	PRON
ejpam-5246	391	2	,	,	PUNCT
ejpam-5246	391	3	(	(	PUNCT
ejpam-5246	391	4	uni	uni	PROPN
ejpam-5246	391	5	=	=	SYM
ejpam-5246	391	6	u	u	PROPN
ejpam-5246	391	7	(	(	PUNCT
ejpam-5246	391	8	xi	xi	PROPN
ejpam-5246	391	9	,	,	PUNCT
ejpam-5246	391	10	tn	tn	PROPN
ejpam-5246	391	11	)	)	PUNCT
ejpam-5246	391	12	,	,	PUNCT
ejpam-5246	391	13	v	v	PART
ejpam-5246	391	14	n	n	NOUN
ejpam-5246	392	1	i	i	NOUN
ejpam-5246	392	2	=	=	NOUN
ejpam-5246	392	3	v	v	X
ejpam-5246	392	4	(	(	PUNCT
ejpam-5246	392	5	xi	xi	PROPN
ejpam-5246	392	6	,	,	PUNCT
ejpam-5246	392	7	tn	tn	PROPN
ejpam-5246	392	8	)	)	PUNCT
ejpam-5246	392	9	)	)	PUNCT
ejpam-5246	392	10	is	be	AUX
ejpam-5246	392	11	the	the	DET
ejpam-5246	392	12	accurate	accurate	ADJ
ejpam-5246	392	13	solution	solution	NOUN
ejpam-5246	392	14	to	to	ADP
ejpam-5246	392	15	the	the	DET
ejpam-5246	392	16	problem	problem	NOUN
ejpam-5246	392	17	(	(	PUNCT
ejpam-5246	392	18	1.1	1.1	NUM
ejpam-5246	392	19	)	)	PUNCT
ejpam-5246	392	20	.	.	PUNCT
ejpam-5246	393	1	to	to	PART
ejpam-5246	393	2	finish	finish	VERB
ejpam-5246	393	3	this	this	PRON
ejpam-5246	393	4	,	,	PUNCT
ejpam-5246	393	5	we	we	PRON
ejpam-5246	393	6	implement	implement	VERB
ejpam-5246	393	7	the	the	DET
ejpam-5246	393	8	mathematical	mathematical	ADJ
ejpam-5246	393	9	induction	induction	NOUN
ejpam-5246	393	10	.	.	PUNCT
ejpam-5246	394	1	for	for	ADP
ejpam-5246	394	2	n	n	NOUN
ejpam-5246	394	3	=	=	SYM
ejpam-5246	394	4	1	1	NUM
ejpam-5246	394	5	and	and	CCONJ
ejpam-5246	394	6	setting∥∥e1	setting∥∥e1	PROPN
ejpam-5246	394	7	u	u	PROPN
ejpam-5246	394	8	∥∥	∥∥	X
ejpam-5246	394	9	=	=	SYM
ejpam-5246	394	10	max1≤i≤i	max1≤i≤i	NUM
ejpam-5246	394	11	∣∣e1ui∣∣	∣∣e1ui∣∣	NOUN
ejpam-5246	394	12	=	=	SYM
ejpam-5246	394	13	∣∣∣e1uj∣∣∣	∣∣∣e1uj∣∣∣	NOUN
ejpam-5246	394	14	,	,	PUNCT
ejpam-5246	394	15	k	k	NOUN
ejpam-5246	394	16	=	=	SYM
ejpam-5246	394	17	maxn∈n	maxn∈n	NOUN
ejpam-5246	394	18	kn	kn	PROPN
ejpam-5246	394	19	,	,	PUNCT
ejpam-5246	394	20	r	r	NOUN
ejpam-5246	394	21	=	=	SYM
ejpam-5246	394	22	k	k	PROPN
ejpam-5246	394	23	/	/	SYM
ejpam-5246	394	24	h2	h2	NOUN
ejpam-5246	394	25	,	,	PUNCT
ejpam-5246	394	26	we	we	PRON
ejpam-5246	394	27	have∣∣e1uj∣∣	have∣∣e1uj∣∣	X
ejpam-5246	394	28	=	=	PUNCT
ejpam-5246	394	29	(	(	PUNCT
ejpam-5246	394	30	1	1	NUM
ejpam-5246	394	31	+	+	CCONJ
ejpam-5246	394	32	2r1	2r1	NUM
ejpam-5246	394	33	)	)	PUNCT
ejpam-5246	394	34	∣∣e1uj∣∣−	∣∣e1uj∣∣−	NOUN
ejpam-5246	394	35	r1	r1	PROPN
ejpam-5246	394	36	(	(	PUNCT
ejpam-5246	394	37	∣∣e1uj∣∣+	∣∣e1uj∣∣+	PROPN
ejpam-5246	394	38	∣∣e1uj∣∣	∣∣e1uj∣∣	PROPN
ejpam-5246	394	39	)	)	PUNCT
ejpam-5246	394	40	m.i.khalil	m.i.khalil	NOUN
ejpam-5246	394	41	et	et	PROPN
ejpam-5246	394	42	al	al	PROPN
ejpam-5246	394	43	.	.	PUNCT
ejpam-5246	394	44	/	/	SYM
ejpam-5246	394	45	eur	eur	PROPN
ejpam-5246	394	46	.	.	PUNCT
ejpam-5246	395	1	j.	j.	PROPN
ejpam-5246	395	2	pure	pure	PROPN
ejpam-5246	395	3	appl	appl	PROPN
ejpam-5246	395	4	.	.	PROPN
ejpam-5246	395	5	math	math	PROPN
ejpam-5246	395	6	,	,	PUNCT
ejpam-5246	395	7	17	17	NUM
ejpam-5246	395	8	(	(	PUNCT
ejpam-5246	395	9	3	3	NUM
ejpam-5246	395	10	)	)	PUNCT
ejpam-5246	395	11	(	(	PUNCT
ejpam-5246	395	12	2024	2024	NUM
ejpam-5246	395	13	)	)	PUNCT
ejpam-5246	395	14	,	,	PUNCT
ejpam-5246	395	15	1516	1516	NUM
ejpam-5246	395	16	-	-	SYM
ejpam-5246	395	17	1538	1538	NUM
ejpam-5246	395	18	1527	1527	NUM
ejpam-5246	395	19	≤	≤	NOUN
ejpam-5246	395	20	(	(	PUNCT
ejpam-5246	395	21	1	1	NUM
ejpam-5246	395	22	+	+	NUM
ejpam-5246	395	23	2r1	2r1	NUM
ejpam-5246	395	24	)	)	PUNCT
ejpam-5246	395	25	∣∣e1uj∣∣−	∣∣e1uj∣∣−	NOUN
ejpam-5246	395	26	r1	r1	NOUN
ejpam-5246	395	27	(	(	PUNCT
ejpam-5246	395	28	∣∣e1uj+1	∣∣e1uj+1	PRON
ejpam-5246	395	29	∣∣+	∣∣+	PROPN
ejpam-5246	395	30	∣∣e1uj−1	∣∣e1uj−1	PROPN
ejpam-5246	395	31	∣∣	∣∣	PROPN
ejpam-5246	395	32	)	)	PUNCT
ejpam-5246	395	33	≤	≤	PUNCT
ejpam-5246	396	1	∣∣(1	∣∣(1	NOUN
ejpam-5246	396	2	+	+	CCONJ
ejpam-5246	396	3	2r1)e	2r1)e	NUM
ejpam-5246	396	4	1	1	NUM
ejpam-5246	396	5	uj	uj	NOUN
ejpam-5246	396	6	−	−	PROPN
ejpam-5246	396	7	r1	r1	PROPN
ejpam-5246	396	8	(	(	PUNCT
ejpam-5246	396	9	e1uj+1	e1uj+1	NOUN
ejpam-5246	396	10	+	+	CCONJ
ejpam-5246	396	11	e1uj−1	e1uj−1	NOUN
ejpam-5246	396	12	)	)	PUNCT
ejpam-5246	396	13	∣∣	∣∣	NUM
ejpam-5246	396	14	=	=	PUNCT
ejpam-5246	396	15	∣∣e0uj	∣∣e0uj	NOUN
ejpam-5246	396	16	+	+	CCONJ
ejpam-5246	396	17	k1	k1	NOUN
ejpam-5246	396	18	(	(	PUNCT
ejpam-5246	396	19	f	f	X
ejpam-5246	396	20	(	(	PUNCT
ejpam-5246	396	21	δxu	δxu	PROPN
ejpam-5246	396	22	0	0	NUM
ejpam-5246	396	23	j	j	PROPN
ejpam-5246	396	24	,	,	PUNCT
ejpam-5246	396	25	v	v	NOUN
ejpam-5246	396	26	0	0	NUM
ejpam-5246	396	27	j	j	NOUN
ejpam-5246	396	28	)	)	PUNCT
ejpam-5246	397	1	−	−	PROPN
ejpam-5246	397	2	f	f	X
ejpam-5246	397	3	(	(	PUNCT
ejpam-5246	397	4	δxu	δxu	PROPN
ejpam-5246	397	5	0	0	NUM
ejpam-5246	397	6	j	j	PROPN
ejpam-5246	397	7	,	,	PUNCT
ejpam-5246	397	8	v	v	NOUN
ejpam-5246	397	9	0	0	NUM
ejpam-5246	397	10	j	j	NOUN
ejpam-5246	397	11	)	)	PUNCT
ejpam-5246	397	12	)	)	PUNCT
ejpam-5246	397	13	∣∣	∣∣	X
ejpam-5246	397	14	.	.	PUNCT
ejpam-5246	398	1	lemma	lemma	PROPN
ejpam-5246	398	2	(	(	PUNCT
ejpam-5246	398	3	1	1	NUM
ejpam-5246	398	4	)	)	PUNCT
ejpam-5246	398	5	then	then	ADV
ejpam-5246	398	6	gives∣∣e1uj∣∣	gives∣∣e1uj∣∣	X
ejpam-5246	398	7	≤	≤	NUM
ejpam-5246	398	8	∣∣e0j	∣∣e0j	NUM
ejpam-5246	398	9	∣∣+	∣∣+	PROPN
ejpam-5246	398	10	k1	k1	PROPN
ejpam-5246	398	11	∣∣f	∣∣f	PROPN
ejpam-5246	398	12	(	(	PUNCT
ejpam-5246	398	13	δxu0j	δxu0j	X
ejpam-5246	398	14	,	,	PUNCT
ejpam-5246	398	15	v0j	v0j	NOUN
ejpam-5246	398	16	)	)	PUNCT
ejpam-5246	398	17	−	−	PROPN
ejpam-5246	399	1	f	f	PROPN
ejpam-5246	399	2	(	(	PUNCT
ejpam-5246	399	3	δxu	δxu	PROPN
ejpam-5246	399	4	0	0	NUM
ejpam-5246	399	5	j	j	PROPN
ejpam-5246	399	6	,	,	PUNCT
ejpam-5246	399	7	v	v	NOUN
ejpam-5246	399	8	0	0	NUM
ejpam-5246	399	9	j	j	NOUN
ejpam-5246	399	10	)	)	PUNCT
ejpam-5246	399	11	∣∣	∣∣	PROPN
ejpam-5246	399	12	≤	≤	NUM
ejpam-5246	399	13	∣∣e0j	∣∣e0j	NUM
ejpam-5246	399	14	∣∣+	∣∣+	X
ejpam-5246	399	15	k1l1	k1l1	X
ejpam-5246	399	16	∣∣δx	∣∣δx	ADJ
ejpam-5246	399	17	(	(	PUNCT
ejpam-5246	399	18	u0j	u0j	ADP
ejpam-5246	399	19	−	−	PROPN
ejpam-5246	399	20	u0	u0	ADJ
ejpam-5246	399	21	j	j	PROPN
ejpam-5246	399	22	)	)	PUNCT
ejpam-5246	399	23	∣∣+	∣∣+	PROPN
ejpam-5246	400	1	k1l2	k1l2	X
ejpam-5246	400	2	∣∣v0j	∣∣v0j	NOUN
ejpam-5246	401	1	−	−	NOUN
ejpam-5246	401	2	v	v	NOUN
ejpam-5246	401	3	0	0	NUM
ejpam-5246	401	4	j	j	PROPN
ejpam-5246	401	5	∣∣	∣∣	X
ejpam-5246	401	6	=	=	SYM
ejpam-5246	401	7	∣∣e0j	∣∣e0j	NUM
ejpam-5246	401	8	∣∣+	∣∣+	X
ejpam-5246	401	9	k1l1	k1l1	X
ejpam-5246	401	10	∣∣δxe0uj∣∣+	∣∣δxe0uj∣∣+	PROPN
ejpam-5246	401	11	k1l2	k1l2	PROPN
ejpam-5246	401	12	∣∣e0vj∣∣	∣∣e0vj∣∣	PROPN
ejpam-5246	401	13	.	.	PUNCT
ejpam-5246	402	1	it	it	PRON
ejpam-5246	402	2	follows	follow	VERB
ejpam-5246	402	3	that∥∥e1	that∥∥e1	VERB
ejpam-5246	402	4	u	u	PROPN
ejpam-5246	402	5	∥∥	∥∥	X
ejpam-5246	402	6	≤	≤	PROPN
ejpam-5246	403	1	∥∥e0	∥∥e0	PROPN
ejpam-5246	403	2	u	u	PROPN
ejpam-5246	403	3	∥∥+	∥∥+	PROPN
ejpam-5246	403	4	2kl1	2kl1	NUM
ejpam-5246	403	5	∥∥e0	∥∥e0	PROPN
ejpam-5246	403	6	u	u	PROPN
ejpam-5246	403	7	∥∥+	∥∥+	PROPN
ejpam-5246	403	8	kl2	kl2	PROPN
ejpam-5246	403	9	∥∥e0	∥∥e0	PROPN
ejpam-5246	403	10	v	v	ADP
ejpam-5246	403	11	∥∥	∥∥	X
ejpam-5246	403	12	≤	≤	X
ejpam-5246	403	13	(	(	PUNCT
ejpam-5246	403	14	1	1	NUM
ejpam-5246	403	15	+	+	SYM
ejpam-5246	403	16	3kl)max	3kl)max	NUM
ejpam-5246	403	17	{	{	PUNCT
ejpam-5246	403	18	∥∥e0	∥∥e0	PROPN
ejpam-5246	403	19	u	u	PROPN
ejpam-5246	403	20	∥∥	∥∥	X
ejpam-5246	403	21	,	,	PUNCT
ejpam-5246	403	22	∥∥e0	∥∥e0	PROPN
ejpam-5246	403	23	v	v	X
ejpam-5246	403	24	∥∥	∥∥	NOUN
ejpam-5246	403	25	}	}	PUNCT
ejpam-5246	403	26	.	.	PUNCT
ejpam-5246	404	1	similarly	similarly	ADV
ejpam-5246	404	2	,	,	PUNCT
ejpam-5246	404	3	we	we	PRON
ejpam-5246	404	4	can	can	AUX
ejpam-5246	404	5	show	show	VERB
ejpam-5246	404	6	that∥∥e1	that∥∥e1	VERB
ejpam-5246	404	7	v	v	ADP
ejpam-5246	404	8	∥∥	∥∥	X
ejpam-5246	404	9	≤	≤	PROPN
ejpam-5246	404	10	∥∥e0	∥∥e0	PROPN
ejpam-5246	404	11	v	v	ADP
ejpam-5246	404	12	∥∥+	∥∥+	SYM
ejpam-5246	404	13	2kl3	2kl3	NUM
ejpam-5246	404	14	∥∥e0	∥∥e0	NOUN
ejpam-5246	404	15	v	v	NUM
ejpam-5246	404	16	∥∥+	∥∥+	PROPN
ejpam-5246	404	17	kl4	kl4	PROPN
ejpam-5246	404	18	∥∥e0	∥∥e0	PROPN
ejpam-5246	404	19	u	u	PROPN
ejpam-5246	404	20	∥∥	∥∥	PROPN
ejpam-5246	404	21	≤	≤	X
ejpam-5246	404	22	(	(	PUNCT
ejpam-5246	404	23	1	1	NUM
ejpam-5246	404	24	+	+	SYM
ejpam-5246	404	25	3kl)max	3kl)max	NUM
ejpam-5246	404	26	{	{	PUNCT
ejpam-5246	404	27	∥∥e0	∥∥e0	PROPN
ejpam-5246	404	28	u	u	PROPN
ejpam-5246	404	29	∥∥	∥∥	X
ejpam-5246	404	30	,	,	PUNCT
ejpam-5246	404	31	∥∥e0	∥∥e0	PROPN
ejpam-5246	404	32	v	v	X
ejpam-5246	404	33	∥∥	∥∥	PROPN
ejpam-5246	404	34	}	}	PUNCT
ejpam-5246	404	35	,	,	PUNCT
ejpam-5246	404	36	where	where	SCONJ
ejpam-5246	404	37	l	l	NOUN
ejpam-5246	404	38	=	=	SYM
ejpam-5246	404	39	max	max	PROPN
ejpam-5246	404	40	{	{	PUNCT
ejpam-5246	404	41	l1	l1	PROPN
ejpam-5246	404	42	,	,	PUNCT
ejpam-5246	404	43	l2	l2	NOUN
ejpam-5246	404	44	,	,	PUNCT
ejpam-5246	404	45	l3	l3	PROPN
ejpam-5246	404	46	,	,	PUNCT
ejpam-5246	404	47	l4	l4	PROPN
ejpam-5246	404	48	}	}	PUNCT
ejpam-5246	404	49	.	.	PUNCT
ejpam-5246	405	1	now	now	ADV
ejpam-5246	405	2	,	,	PUNCT
ejpam-5246	405	3	we	we	PRON
ejpam-5246	405	4	suppose	suppose	VERB
ejpam-5246	405	5	that	that	SCONJ
ejpam-5246	405	6	∥es	∥es	VERB
ejpam-5246	405	7	u∥	u∥	ADJ
ejpam-5246	405	8	≤	≤	NUM
ejpam-5246	405	9	(	(	PUNCT
ejpam-5246	405	10	1	1	NUM
ejpam-5246	405	11	+	+	NUM
ejpam-5246	405	12	3kl)smax	3kl)smax	NUM
ejpam-5246	405	13	{	{	PUNCT
ejpam-5246	405	14	∥∥e0	∥∥e0	PROPN
ejpam-5246	405	15	u	u	PROPN
ejpam-5246	405	16	∥∥	∥∥	X
ejpam-5246	405	17	,	,	PUNCT
ejpam-5246	405	18	∥∥e0	∥∥e0	PROPN
ejpam-5246	405	19	v	v	X
ejpam-5246	405	20	∥∥	∥∥	PROPN
ejpam-5246	405	21	}	}	PUNCT
ejpam-5246	405	22	,	,	PUNCT
ejpam-5246	405	23	s	s	NOUN
ejpam-5246	405	24	=	=	SYM
ejpam-5246	405	25	1	1	NUM
ejpam-5246	405	26	,	,	PUNCT
ejpam-5246	405	27	2	2	NUM
ejpam-5246	405	28	,	,	PUNCT
ejpam-5246	405	29	3	3	NUM
ejpam-5246	405	30	,	,	PUNCT
ejpam-5246	405	31	.	.	PUNCT
ejpam-5246	405	32	.	.	PUNCT
ejpam-5246	405	33	.	.	PUNCT
ejpam-5246	406	1	n	n	CCONJ
ejpam-5246	406	2	,	,	PUNCT
ejpam-5246	406	3	∥es	∥es	VERB
ejpam-5246	406	4	v∥	v∥	PROPN
ejpam-5246	406	5	≤	≤	NUM
ejpam-5246	406	6	(	(	PUNCT
ejpam-5246	406	7	1	1	NUM
ejpam-5246	406	8	+	+	NUM
ejpam-5246	406	9	3kl)smax	3kl)smax	NUM
ejpam-5246	406	10	{	{	PUNCT
ejpam-5246	406	11	∥∥e0	∥∥e0	PROPN
ejpam-5246	406	12	u	u	PROPN
ejpam-5246	406	13	∥∥	∥∥	X
ejpam-5246	406	14	,	,	PUNCT
ejpam-5246	406	15	∥∥e0	∥∥e0	PROPN
ejpam-5246	406	16	v	v	X
ejpam-5246	406	17	∥∥	∥∥	PROPN
ejpam-5246	406	18	}	}	PUNCT
ejpam-5246	406	19	,	,	PUNCT
ejpam-5246	406	20	s	s	NOUN
ejpam-5246	406	21	=	=	SYM
ejpam-5246	406	22	1	1	NUM
ejpam-5246	406	23	,	,	PUNCT
ejpam-5246	406	24	2	2	NUM
ejpam-5246	406	25	,	,	PUNCT
ejpam-5246	406	26	3	3	NUM
ejpam-5246	406	27	,	,	PUNCT
ejpam-5246	406	28	.	.	PUNCT
ejpam-5246	406	29	.	.	PUNCT
ejpam-5246	406	30	.	.	PUNCT
ejpam-5246	407	1	n.	n.	VERB
ejpam-5246	407	2	for	for	ADP
ejpam-5246	407	3	n+1	n+1	ADV
ejpam-5246	407	4	and	and	CCONJ
ejpam-5246	407	5	setting	set	VERB
ejpam-5246	407	6	∥∥en+1	∥∥en+1	PROPN
ejpam-5246	407	7	u	u	NOUN
ejpam-5246	407	8	∥∥	∥∥	X
ejpam-5246	407	9	=	=	SYM
ejpam-5246	407	10	max1≤i≤i	max1≤i≤i	NUM
ejpam-5246	407	11	∣∣en+1	∣∣en+1	NOUN
ejpam-5246	407	12	ui	ui	NOUN
ejpam-5246	407	13	∣∣	∣∣	PUNCT
ejpam-5246	407	14	=	=	SYM
ejpam-5246	407	15	∣∣∣en+1	∣∣∣en+1	X
ejpam-5246	407	16	uj	uj	PROPN
ejpam-5246	407	17	∣∣∣	∣∣∣	NOUN
ejpam-5246	407	18	and	and	CCONJ
ejpam-5246	407	19	∥∥en+1	∥∥en+1	VERB
ejpam-5246	407	20	v	v	NOUN
ejpam-5246	407	21	∥∥	∥∥	X
ejpam-5246	407	22	=	=	SYM
ejpam-5246	407	23	max1≤i≤i	max1≤i≤i	X
ejpam-5246	407	24	∣∣en+1	∣∣en+1	NOUN
ejpam-5246	407	25	vi	vi	X
ejpam-5246	407	26	∣∣	∣∣	PROPN
ejpam-5246	407	27	,	,	PUNCT
ejpam-5246	407	28	k	k	NOUN
ejpam-5246	407	29	=	=	SYM
ejpam-5246	407	30	maxn∈n	maxn∈n	NOUN
ejpam-5246	407	31	kn	kn	PROPN
ejpam-5246	407	32	,	,	PUNCT
ejpam-5246	407	33	r	r	NOUN
ejpam-5246	407	34	=	=	SYM
ejpam-5246	407	35	k	k	NOUN
ejpam-5246	407	36	/	/	SYM
ejpam-5246	407	37	h2	h2	PROPN
ejpam-5246	407	38	yields∣∣∣en+1	yields∣∣∣en+1	PROPN
ejpam-5246	407	39	uj	uj	PROPN
ejpam-5246	407	40	∣∣∣	∣∣∣	NOUN
ejpam-5246	407	41	=	=	SYM
ejpam-5246	407	42	(	(	PUNCT
ejpam-5246	407	43	1	1	NUM
ejpam-5246	407	44	+	+	NUM
ejpam-5246	407	45	2rn	2rn	ADJ
ejpam-5246	407	46	)	)	PUNCT
ejpam-5246	407	47	∣∣∣en+1	∣∣∣en+1	NOUN
ejpam-5246	408	1	uj	uj	PROPN
ejpam-5246	408	2	∣∣∣−	∣∣∣−	PROPN
ejpam-5246	408	3	rn	rn	PROPN
ejpam-5246	408	4	(	(	PUNCT
ejpam-5246	408	5	∣∣∣en+1	∣∣∣en+1	PROPN
ejpam-5246	408	6	uj	uj	PROPN
ejpam-5246	408	7	∣∣∣+	∣∣∣+	PROPN
ejpam-5246	408	8	∣∣∣en+1	∣∣∣en+1	NOUN
ejpam-5246	408	9	uj	uj	PROPN
ejpam-5246	408	10	∣∣∣	∣∣∣	NOUN
ejpam-5246	408	11	)	)	PUNCT
ejpam-5246	408	12	≤	≤	NOUN
ejpam-5246	408	13	(	(	PUNCT
ejpam-5246	408	14	1	1	NUM
ejpam-5246	408	15	+	+	NUM
ejpam-5246	408	16	2rn	2rn	ADJ
ejpam-5246	408	17	)	)	PUNCT
ejpam-5246	408	18	∣∣∣en+1	∣∣∣en+1	NOUN
ejpam-5246	408	19	uj	uj	PROPN
ejpam-5246	408	20	∣∣∣−	∣∣∣−	PROPN
ejpam-5246	408	21	rn	rn	PROPN
ejpam-5246	408	22	(	(	PUNCT
ejpam-5246	408	23	∣∣∣en+1	∣∣∣en+1	X
ejpam-5246	408	24	uj+1	uj+1	PROPN
ejpam-5246	408	25	∣∣∣+	∣∣∣+	PROPN
ejpam-5246	408	26	∣∣∣en+1	∣∣∣en+1	NOUN
ejpam-5246	408	27	uj−1	uj−1	NOUN
ejpam-5246	408	28	∣∣∣	∣∣∣	ADJ
ejpam-5246	408	29	)	)	PUNCT
ejpam-5246	408	30	≤	≤	NUM
ejpam-5246	408	31	∣∣∣(1	∣∣∣(1	NOUN
ejpam-5246	408	32	+	+	CCONJ
ejpam-5246	408	33	2rn)e	2rn)e	PROPN
ejpam-5246	408	34	n+1	n+1	PROPN
ejpam-5246	408	35	uj	uj	PROPN
ejpam-5246	408	36	−	−	PROPN
ejpam-5246	408	37	rn	rn	PROPN
ejpam-5246	408	38	(	(	PUNCT
ejpam-5246	408	39	en+1	en+1	PROPN
ejpam-5246	408	40	uj+1	uj+1	NUM
ejpam-5246	408	41	+	+	CCONJ
ejpam-5246	408	42	en+1	en+1	ADJ
ejpam-5246	408	43	uj−1	uj−1	NOUN
ejpam-5246	408	44	)	)	PUNCT
ejpam-5246	408	45	∣∣∣	∣∣∣	NOUN
ejpam-5246	408	46	=	=	SYM
ejpam-5246	408	47	∣∣enuj	∣∣enuj	NOUN
ejpam-5246	408	48	+	+	CCONJ
ejpam-5246	408	49	kn	kn	PROPN
ejpam-5246	408	50	(	(	PUNCT
ejpam-5246	408	51	f	f	X
ejpam-5246	408	52	(	(	PUNCT
ejpam-5246	408	53	δxu	δxu	PROPN
ejpam-5246	408	54	n	n	PRON
ejpam-5246	408	55	j	j	PROPN
ejpam-5246	408	56	,	,	PUNCT
ejpam-5246	408	57	v	v	PROPN
ejpam-5246	408	58	n	n	PROPN
ejpam-5246	408	59	j	j	PROPN
ejpam-5246	408	60	)	)	PUNCT
ejpam-5246	409	1	−	−	PROPN
ejpam-5246	409	2	f	f	X
ejpam-5246	409	3	(	(	PUNCT
ejpam-5246	409	4	δxu	δxu	PROPN
ejpam-5246	409	5	n	n	PRON
ejpam-5246	409	6	j	j	PROPN
ejpam-5246	409	7	,	,	PUNCT
ejpam-5246	409	8	v	v	PROPN
ejpam-5246	409	9	n	n	PROPN
ejpam-5246	409	10	j	j	PROPN
ejpam-5246	409	11	)	)	PUNCT
ejpam-5246	409	12	)	)	PUNCT
ejpam-5246	409	13	∣∣	∣∣	PROPN
ejpam-5246	409	14	.	.	PUNCT
ejpam-5246	410	1	by	by	ADP
ejpam-5246	410	2	lemma	lemma	PROPN
ejpam-5246	410	3	(	(	PUNCT
ejpam-5246	410	4	1	1	NUM
ejpam-5246	410	5	)	)	PUNCT
ejpam-5246	410	6	,	,	PUNCT
ejpam-5246	410	7	we	we	PRON
ejpam-5246	410	8	obtain∣∣∣en+1	obtain∣∣∣en+1	PROPN
ejpam-5246	410	9	uj	uj	PROPN
ejpam-5246	410	10	∣∣∣	∣∣∣	PROPN
ejpam-5246	410	11	≤	≤	PROPN
ejpam-5246	410	12	∣∣enuj∣∣+	∣∣enuj∣∣+	PROPN
ejpam-5246	410	13	kn	kn	PROPN
ejpam-5246	410	14	∣∣ff	∣∣ff	PROPN
ejpam-5246	410	15	(	(	PUNCT
ejpam-5246	410	16	δxunj	δxunj	NOUN
ejpam-5246	410	17	,	,	PUNCT
ejpam-5246	410	18	vnj	vnj	INTJ
ejpam-5246	410	19	)	)	PUNCT
ejpam-5246	411	1	−	−	PROPN
ejpam-5246	411	2	f	f	PROPN
ejpam-5246	411	3	(	(	PUNCT
ejpam-5246	411	4	δxu	δxu	PROPN
ejpam-5246	411	5	n	n	PRON
ejpam-5246	411	6	j	j	PROPN
ejpam-5246	411	7	,	,	PUNCT
ejpam-5246	411	8	v	v	PROPN
ejpam-5246	411	9	n	n	PROPN
ejpam-5246	411	10	j	j	PROPN
ejpam-5246	411	11	)	)	PUNCT
ejpam-5246	411	12	∣∣	∣∣	PROPN
ejpam-5246	411	13	≤	≤	PROPN
ejpam-5246	411	14	∣∣enuj∣∣+	∣∣enuj∣∣+	PROPN
ejpam-5246	411	15	knl1	knl1	PROPN
ejpam-5246	411	16	∣∣δx	∣∣δx	PROPN
ejpam-5246	411	17	(	(	PUNCT
ejpam-5246	411	18	unj	unj	NOUN
ejpam-5246	411	19	−	−	PROPN
ejpam-5246	411	20	un	un	PROPN
ejpam-5246	411	21	j	j	PROPN
ejpam-5246	411	22	)	)	PUNCT
ejpam-5246	411	23	∣∣+	∣∣+	PROPN
ejpam-5246	412	1	knl2	knl2	PROPN
ejpam-5246	412	2	∣∣vnj	∣∣vnj	PROPN
ejpam-5246	412	3	−	−	PROPN
ejpam-5246	412	4	v	v	PROPN
ejpam-5246	412	5	n	n	CCONJ
ejpam-5246	412	6	j	j	X
ejpam-5246	412	7	∣∣	∣∣	X
ejpam-5246	412	8	=	=	SYM
ejpam-5246	412	9	∣∣enj	∣∣enj	PROPN
ejpam-5246	412	10	∣∣+	∣∣+	PROPN
ejpam-5246	412	11	knl1	knl1	PROPN
ejpam-5246	412	12	∣∣δxenuj∣∣+	∣∣δxenuj∣∣+	PROPN
ejpam-5246	412	13	knl2	knl2	PROPN
ejpam-5246	412	14	∣∣envj∣∣	∣∣envj∣∣	PROPN
ejpam-5246	412	15	.	.	PUNCT
ejpam-5246	413	1	it	it	PRON
ejpam-5246	413	2	follows	follow	VERB
ejpam-5246	413	3	that∥∥en+1	that∥∥en+1	PROPN
ejpam-5246	413	4	u	u	PROPN
ejpam-5246	413	5	∥∥	∥∥	X
ejpam-5246	413	6	≤	≤	X
ejpam-5246	413	7	∥en	∥en	NUM
ejpam-5246	413	8	u∥+	u∥+	PROPN
ejpam-5246	413	9	2knl	2knl	PROPN
ejpam-5246	413	10	∥en	∥en	NUM
ejpam-5246	413	11	u∥+	u∥+	ADJ
ejpam-5246	413	12	knl	knl	NOUN
ejpam-5246	413	13	∥en	∥en	PROPN
ejpam-5246	413	14	v	v	NUM
ejpam-5246	413	15	∥	∥	PUNCT
ejpam-5246	413	16	m.i.khalil	m.i.khalil	NOUN
ejpam-5246	413	17	et	et	PROPN
ejpam-5246	413	18	al	al	PROPN
ejpam-5246	413	19	.	.	PUNCT
ejpam-5246	413	20	/	/	SYM
ejpam-5246	413	21	eur	eur	PROPN
ejpam-5246	413	22	.	.	PUNCT
ejpam-5246	414	1	j.	j.	PROPN
ejpam-5246	414	2	pure	pure	PROPN
ejpam-5246	414	3	appl	appl	PROPN
ejpam-5246	414	4	.	.	PROPN
ejpam-5246	414	5	math	math	PROPN
ejpam-5246	414	6	,	,	PUNCT
ejpam-5246	414	7	17	17	NUM
ejpam-5246	414	8	(	(	PUNCT
ejpam-5246	414	9	3	3	NUM
ejpam-5246	414	10	)	)	PUNCT
ejpam-5246	414	11	(	(	PUNCT
ejpam-5246	414	12	2024	2024	NUM
ejpam-5246	414	13	)	)	PUNCT
ejpam-5246	414	14	,	,	PUNCT
ejpam-5246	414	15	1516	1516	NUM
ejpam-5246	414	16	-	-	SYM
ejpam-5246	414	17	1538	1538	NUM
ejpam-5246	414	18	1528	1528	NUM
ejpam-5246	414	19	≤	≤	NOUN
ejpam-5246	414	20	(	(	PUNCT
ejpam-5246	414	21	1	1	NUM
ejpam-5246	414	22	+	+	NUM
ejpam-5246	414	23	3kl)nmax	3kl)nmax	NUM
ejpam-5246	414	24	{	{	PUNCT
ejpam-5246	414	25	∥∥e0	∥∥e0	PROPN
ejpam-5246	414	26	u	u	PROPN
ejpam-5246	414	27	∥∥	∥∥	X
ejpam-5246	414	28	,	,	PUNCT
ejpam-5246	414	29	∥∥e0	∥∥e0	PROPN
ejpam-5246	414	30	v	v	NUM
ejpam-5246	414	31	∥∥}+	∥∥}+	NOUN
ejpam-5246	414	32	3kl(1	3kl(1	NOUN
ejpam-5246	414	33	+	+	CCONJ
ejpam-5246	414	34	3kl)nmax	3kl)nmax	NUM
ejpam-5246	414	35	{	{	PUNCT
ejpam-5246	414	36	∥∥e0	∥∥e0	PROPN
ejpam-5246	414	37	u	u	PROPN
ejpam-5246	414	38	∥∥	∥∥	X
ejpam-5246	414	39	,	,	PUNCT
ejpam-5246	414	40	∥∥e0	∥∥e0	PROPN
ejpam-5246	414	41	v	v	X
ejpam-5246	414	42	∥∥	∥∥	PROPN
ejpam-5246	414	43	}	}	PUNCT
ejpam-5246	414	44	≤	≤	NOUN
ejpam-5246	414	45	(	(	PUNCT
ejpam-5246	414	46	1	1	NUM
ejpam-5246	414	47	+	+	SYM
ejpam-5246	414	48	3kl)n+1max	3kl)n+1max	NUM
ejpam-5246	414	49	{	{	PUNCT
ejpam-5246	414	50	∥∥e0	∥∥e0	PROPN
ejpam-5246	414	51	u	u	PROPN
ejpam-5246	414	52	∥∥	∥∥	X
ejpam-5246	414	53	,	,	PUNCT
ejpam-5246	414	54	∥∥e0	∥∥e0	PROPN
ejpam-5246	414	55	v	v	X
ejpam-5246	414	56	∥∥	∥∥	PROPN
ejpam-5246	414	57	}	}	PUNCT
ejpam-5246	414	58	≤	≤	NOUN
ejpam-5246	414	59	exp(3(n+	exp(3(n+	X
ejpam-5246	415	1	1)kl)max	1)kl)max	NUM
ejpam-5246	415	2	{	{	PUNCT
ejpam-5246	415	3	∥∥e0	∥∥e0	PROPN
ejpam-5246	415	4	u	u	PROPN
ejpam-5246	415	5	∥∥	∥∥	X
ejpam-5246	415	6	,	,	PUNCT
ejpam-5246	415	7	∥∥e0	∥∥e0	PROPN
ejpam-5246	415	8	v	v	X
ejpam-5246	415	9	∥∥	∥∥	PROPN
ejpam-5246	415	10	}	}	PUNCT
ejpam-5246	415	11	=	=	SYM
ejpam-5246	415	12	exp	exp	NOUN
ejpam-5246	415	13	(	(	PUNCT
ejpam-5246	415	14	3tn+1l)max	3tn+1l)max	NUM
ejpam-5246	415	15	{	{	PUNCT
ejpam-5246	415	16	∥∥e0	∥∥e0	PROPN
ejpam-5246	415	17	u	u	PROPN
ejpam-5246	415	18	∥∥	∥∥	X
ejpam-5246	415	19	,	,	PUNCT
ejpam-5246	415	20	∥∥e0	∥∥e0	PROPN
ejpam-5246	415	21	v	v	X
ejpam-5246	415	22	∥∥	∥∥	NOUN
ejpam-5246	415	23	}	}	PUNCT
ejpam-5246	415	24	.	.	PUNCT
ejpam-5246	416	1	similarly	similarly	ADV
ejpam-5246	416	2	,	,	PUNCT
ejpam-5246	416	3	we	we	PRON
ejpam-5246	416	4	can	can	AUX
ejpam-5246	416	5	show	show	VERB
ejpam-5246	416	6	that∥∥en+1	that∥∥en+1	PROPN
ejpam-5246	416	7	v	v	ADP
ejpam-5246	416	8	∥∥	∥∥	PROPN
ejpam-5246	416	9	≤	≤	NUM
ejpam-5246	416	10	exp	exp	NOUN
ejpam-5246	416	11	(	(	PUNCT
ejpam-5246	416	12	3tn+1l)max	3tn+1l)max	NUM
ejpam-5246	416	13	{	{	PUNCT
ejpam-5246	416	14	∥∥e0	∥∥e0	PROPN
ejpam-5246	416	15	u	u	PROPN
ejpam-5246	416	16	∥∥	∥∥	X
ejpam-5246	416	17	,	,	PUNCT
ejpam-5246	416	18	∥∥e0	∥∥e0	PROPN
ejpam-5246	416	19	v	v	X
ejpam-5246	416	20	∥∥	∥∥	PROPN
ejpam-5246	416	21	}	}	PUNCT
ejpam-5246	416	22	.	.	PUNCT
ejpam-5246	417	1	where	where	SCONJ
ejpam-5246	417	2	l	l	NOUN
ejpam-5246	417	3	=	=	SYM
ejpam-5246	417	4	max	max	PROPN
ejpam-5246	417	5	{	{	PUNCT
ejpam-5246	417	6	l1	l1	PROPN
ejpam-5246	417	7	,	,	PUNCT
ejpam-5246	417	8	l2	l2	NOUN
ejpam-5246	417	9	,	,	PUNCT
ejpam-5246	417	10	l3	l3	PROPN
ejpam-5246	417	11	,	,	PUNCT
ejpam-5246	417	12	l4	l4	PROPN
ejpam-5246	417	13	}	}	PUNCT
ejpam-5246	417	14	so	so	ADV
ejpam-5246	417	15	,	,	PUNCT
ejpam-5246	417	16	the	the	DET
ejpam-5246	417	17	implicit	implicit	ADJ
ejpam-5246	417	18	euler	euler	NOUN
ejpam-5246	417	19	scheme	scheme	NOUN
ejpam-5246	417	20	(	(	PUNCT
ejpam-5246	417	21	2.4)–(2.5	2.4)–(2.5	NUM
ejpam-5246	417	22	)	)	PUNCT
ejpam-5246	417	23	is	be	AUX
ejpam-5246	417	24	unconditionally	unconditionally	ADV
ejpam-5246	417	25	stable	stable	ADJ
ejpam-5246	417	26	.	.	PUNCT
ejpam-5246	418	1	3.4	3.4	NUM
ejpam-5246	418	2	.	.	PUNCT
ejpam-5246	418	3	convergence	convergence	NOUN
ejpam-5246	418	4	analysis	analysis	NOUN
ejpam-5246	418	5	of	of	ADP
ejpam-5246	418	6	implicit	implicit	ADJ
ejpam-5246	418	7	euler	euler	NOUN
ejpam-5246	418	8	scheme	scheme	NOUN
ejpam-5246	418	9	theorem	theorem	NOUN
ejpam-5246	418	10	6	6	NUM
ejpam-5246	418	11	.	.	PUNCT
ejpam-5246	419	1	the	the	DET
ejpam-5246	419	2	implicit	implicit	ADJ
ejpam-5246	419	3	euler	euler	NOUN
ejpam-5246	419	4	formula	formula	NOUN
ejpam-5246	419	5	(	(	PUNCT
ejpam-5246	419	6	3.1)–(3.2	3.1)–(3.2	NUM
ejpam-5246	419	7	)	)	PUNCT
ejpam-5246	419	8	is	be	AUX
ejpam-5246	419	9	convergent	convergent	ADJ
ejpam-5246	419	10	with	with	ADP
ejpam-5246	419	11	r	r	NOUN
ejpam-5246	419	12	=	=	SYM
ejpam-5246	419	13	k	k	NOUN
ejpam-5246	419	14	/	/	SYM
ejpam-5246	419	15	h2	h2	PROPN
ejpam-5246	419	16	>	>	X
ejpam-5246	419	17	0	0	NUM
ejpam-5246	419	18	,	,	PUNCT
ejpam-5246	419	19	if	if	SCONJ
ejpam-5246	419	20	r	r	NOUN
ejpam-5246	419	21	>	>	X
ejpam-5246	419	22	0	0	NUM
ejpam-5246	419	23	,	,	PUNCT
ejpam-5246	419	24	where	where	SCONJ
ejpam-5246	419	25	k	k	PROPN
ejpam-5246	419	26	=	=	SYM
ejpam-5246	419	27	maxn∈n	maxn∈n	PROPN
ejpam-5246	419	28	kn	kn	PROPN
ejpam-5246	419	29	.	.	PUNCT
ejpam-5246	420	1	proof	proof	NOUN
ejpam-5246	420	2	.	.	PUNCT
ejpam-5246	421	1	set	set	VERB
ejpam-5246	421	2	enui	enui	NOUN
ejpam-5246	421	3	=	=	SYM
ejpam-5246	421	4	uni	uni	PROPN
ejpam-5246	422	1	−	−	PROPN
ejpam-5246	422	2	un	un	PROPN
ejpam-5246	422	3	i	i	PRON
ejpam-5246	422	4	,	,	PUNCT
ejpam-5246	422	5	e	e	PROPN
ejpam-5246	422	6	n	n	CCONJ
ejpam-5246	422	7	vi	vi	PROPN
ejpam-5246	422	8	=	=	NOUN
ejpam-5246	422	9	vni	vni	NOUN
ejpam-5246	422	10	−	−	PROPN
ejpam-5246	422	11	v	v	NOUN
ejpam-5246	422	12	n	n	NOUN
ejpam-5246	422	13	i	i	PRON
ejpam-5246	422	14	,	,	PUNCT
ejpam-5246	422	15	and	and	CCONJ
ejpam-5246	422	16	let	let	VERB
ejpam-5246	422	17	(	(	PUNCT
ejpam-5246	422	18	uni	uni	NOUN
ejpam-5246	422	19	=	=	SYM
ejpam-5246	422	20	u(xi	u(xi	X
ejpam-5246	422	21	,	,	PUNCT
ejpam-5246	422	22	tn	tn	PROPN
ejpam-5246	422	23	)	)	PUNCT
ejpam-5246	422	24	and	and	CCONJ
ejpam-5246	422	25	vni	vni	X
ejpam-5246	422	26	=	=	SYM
ejpam-5246	422	27	v(xi	v(xi	PROPN
ejpam-5246	422	28	,	,	PUNCT
ejpam-5246	422	29	tn	tn	PROPN
ejpam-5246	422	30	)	)	PUNCT
ejpam-5246	422	31	)	)	PUNCT
ejpam-5246	422	32	be	be	AUX
ejpam-5246	422	33	accurate	accurate	ADJ
ejpam-5246	422	34	solution	solution	NOUN
ejpam-5246	422	35	to	to	ADP
ejpam-5246	422	36	the	the	DET
ejpam-5246	422	37	issue	issue	NOUN
ejpam-5246	422	38	(	(	PUNCT
ejpam-5246	422	39	1.1	1.1	NUM
ejpam-5246	422	40	)	)	PUNCT
ejpam-5246	422	41	.	.	PUNCT
ejpam-5246	423	1	suppose	suppose	VERB
ejpam-5246	423	2	that	that	SCONJ
ejpam-5246	423	3	e0ui	e0ui	PUNCT
ejpam-5246	423	4	=	=	SYM
ejpam-5246	423	5	0	0	NUM
ejpam-5246	423	6	,	,	PUNCT
ejpam-5246	423	7	e0vi	e0vi	X
ejpam-5246	423	8	=	=	SYM
ejpam-5246	423	9	0	0	NUM
ejpam-5246	423	10	,	,	PUNCT
ejpam-5246	423	11	∀i	∀i	NOUN
ejpam-5246	423	12	=	=	SYM
ejpam-5246	423	13	0	0	NUM
ejpam-5246	423	14	,	,	PUNCT
ejpam-5246	423	15	1	1	NUM
ejpam-5246	423	16	,	,	PUNCT
ejpam-5246	423	17	.	.	PUNCT
ejpam-5246	423	18	.	.	PUNCT
ejpam-5246	424	1	.	.	PUNCT
ejpam-5246	425	1	,	,	PUNCT
ejpam-5246	425	2	i.	i.	NOUN
ejpam-5246	425	3	we	we	PRON
ejpam-5246	425	4	aim	aim	VERB
ejpam-5246	425	5	to	to	PART
ejpam-5246	425	6	show	show	VERB
ejpam-5246	425	7	that	that	SCONJ
ejpam-5246	425	8	there	there	PRON
ejpam-5246	425	9	exists	exist	VERB
ejpam-5246	425	10	c	c	NOUN
ejpam-5246	425	11	>	>	X
ejpam-5246	425	12	0	0	NUM
ejpam-5246	425	13	such	such	ADJ
ejpam-5246	425	14	that	that	PRON
ejpam-5246	425	15	en+1	en+1	ADJ
ejpam-5246	425	16	ui	ui	PROPN
ejpam-5246	425	17	≤	≤	NUM
ejpam-5246	425	18	c	c	X
ejpam-5246	426	1	(	(	PUNCT
ejpam-5246	426	2	k	k	PROPN
ejpam-5246	426	3	+	+	CCONJ
ejpam-5246	426	4	h2	h2	PROPN
ejpam-5246	426	5	)	)	PUNCT
ejpam-5246	426	6	,	,	PUNCT
ejpam-5246	426	7	en+1	en+1	PROPN
ejpam-5246	426	8	vi	vi	ADJ
ejpam-5246	426	9	≤	≤	NUM
ejpam-5246	426	10	c	c	NOUN
ejpam-5246	427	1	(	(	PUNCT
ejpam-5246	427	2	k	k	PROPN
ejpam-5246	427	3	+	+	CCONJ
ejpam-5246	427	4	h2	h2	PROPN
ejpam-5246	427	5	)	)	PUNCT
ejpam-5246	427	6	,	,	PUNCT
ejpam-5246	427	7	n	n	NOUN
ejpam-5246	427	8	=	=	SYM
ejpam-5246	427	9	0	0	NUM
ejpam-5246	427	10	,	,	PUNCT
ejpam-5246	427	11	1	1	NUM
ejpam-5246	427	12	,	,	PUNCT
ejpam-5246	427	13	.	.	PUNCT
ejpam-5246	427	14	.	.	PUNCT
ejpam-5246	428	1	.	.	PUNCT
ejpam-5246	429	1	.	.	PUNCT
ejpam-5246	430	1	to	to	PART
ejpam-5246	430	2	finish	finish	VERB
ejpam-5246	430	3	this	this	PRON
ejpam-5246	430	4	,	,	PUNCT
ejpam-5246	430	5	we	we	PRON
ejpam-5246	430	6	use	use	VERB
ejpam-5246	430	7	the	the	DET
ejpam-5246	430	8	mathematical	mathematical	ADJ
ejpam-5246	430	9	induction	induction	NOUN
ejpam-5246	430	10	tech	tech	NOUN
ejpam-5246	430	11	.	.	PUNCT
ejpam-5246	431	1	for	for	ADP
ejpam-5246	431	2	n	n	NOUN
ejpam-5246	431	3	=	=	SYM
ejpam-5246	431	4	1	1	NUM
ejpam-5246	431	5	,	,	PUNCT
ejpam-5246	431	6	we	we	PRON
ejpam-5246	431	7	set	set	VERB
ejpam-5246	431	8	|e1uj	|e1uj	PROPN
ejpam-5246	431	9	|	|	ADV
ejpam-5246	431	10	=	=	PUNCT
ejpam-5246	431	11	max1≤i≤i−1	max1≤i≤i−1	PROPN
ejpam-5246	431	12	|e1ui|	|e1ui|	NOUN
ejpam-5246	431	13	.	.	PUNCT
ejpam-5246	432	1	thus	thus	ADV
ejpam-5246	432	2	|e1uj	|e1uj	ADV
ejpam-5246	432	3	|	|	ADV
ejpam-5246	432	4	=	=	PUNCT
ejpam-5246	432	5	(	(	PUNCT
ejpam-5246	432	6	1	1	NUM
ejpam-5246	432	7	+	+	SYM
ejpam-5246	432	8	2r1)|e1uj	2r1)|e1uj	NUM
ejpam-5246	432	9	|	|	ADV
ejpam-5246	432	10	−	−	PROPN
ejpam-5246	432	11	r1(|e1uj	r1(|e1uj	PROPN
ejpam-5246	432	12	|+	|+	NOUN
ejpam-5246	432	13	|e1uj	|e1uj	ADJ
ejpam-5246	432	14	|	|	ADJ
ejpam-5246	432	15	)	)	PUNCT
ejpam-5246	432	16	≤	≤	NOUN
ejpam-5246	432	17	(	(	PUNCT
ejpam-5246	432	18	1	1	NUM
ejpam-5246	432	19	+	+	NUM
ejpam-5246	432	20	2r1	2r1	NUM
ejpam-5246	432	21	)	)	PUNCT
ejpam-5246	432	22	∣∣e1uj∣∣−	∣∣e1uj∣∣−	NOUN
ejpam-5246	432	23	r1	r1	NOUN
ejpam-5246	432	24	(	(	PUNCT
ejpam-5246	432	25	∣∣e1uj+1	∣∣e1uj+1	PRON
ejpam-5246	432	26	∣∣+	∣∣+	PROPN
ejpam-5246	432	27	∣∣e1uj−1	∣∣e1uj−1	PROPN
ejpam-5246	432	28	∣∣	∣∣	PROPN
ejpam-5246	432	29	)	)	PUNCT
ejpam-5246	432	30	≤	≤	PUNCT
ejpam-5246	432	31	∣∣(1	∣∣(1	NOUN
ejpam-5246	432	32	+	+	CCONJ
ejpam-5246	432	33	2r1)e	2r1)e	NUM
ejpam-5246	432	34	1	1	NUM
ejpam-5246	432	35	uj	uj	NOUN
ejpam-5246	432	36	−	−	PROPN
ejpam-5246	432	37	r1	r1	PROPN
ejpam-5246	432	38	(	(	PUNCT
ejpam-5246	432	39	e1uj+1	e1uj+1	NOUN
ejpam-5246	432	40	+	+	CCONJ
ejpam-5246	432	41	e1uj−1	e1uj−1	NOUN
ejpam-5246	432	42	)	)	PUNCT
ejpam-5246	432	43	∣∣	∣∣	NUM
ejpam-5246	432	44	=	=	PUNCT
ejpam-5246	432	45	∣∣e0uj	∣∣e0uj	NOUN
ejpam-5246	432	46	+	+	CCONJ
ejpam-5246	432	47	k1	k1	NOUN
ejpam-5246	432	48	(	(	PUNCT
ejpam-5246	432	49	f	f	X
ejpam-5246	432	50	(	(	PUNCT
ejpam-5246	432	51	δxu	δxu	PROPN
ejpam-5246	432	52	0	0	NUM
ejpam-5246	432	53	j	j	PROPN
ejpam-5246	432	54	,	,	PUNCT
ejpam-5246	432	55	v	v	NOUN
ejpam-5246	432	56	0	0	NUM
ejpam-5246	432	57	j	j	NOUN
ejpam-5246	432	58	)	)	PUNCT
ejpam-5246	433	1	−	−	PROPN
ejpam-5246	433	2	f	f	X
ejpam-5246	433	3	(	(	PUNCT
ejpam-5246	433	4	δxu	δxu	PROPN
ejpam-5246	433	5	0	0	NUM
ejpam-5246	433	6	j	j	PROPN
ejpam-5246	433	7	,	,	PUNCT
ejpam-5246	433	8	v	v	NOUN
ejpam-5246	433	9	0	0	NUM
ejpam-5246	433	10	j	j	NOUN
ejpam-5246	433	11	)	)	PUNCT
ejpam-5246	433	12	)	)	PUNCT
ejpam-5246	434	1	+	+	CCONJ
ejpam-5246	434	2	t	t	NOUN
ejpam-5246	434	3	0	0	PUNCT
ejpam-5246	435	1	i	i	PRON
ejpam-5246	435	2	∣∣	∣∣	NUM
ejpam-5246	435	3	=	=	PUNCT
ejpam-5246	435	4	∣∣k1	∣∣k1	NOUN
ejpam-5246	435	5	(	(	PUNCT
ejpam-5246	435	6	f	f	X
ejpam-5246	435	7	(	(	PUNCT
ejpam-5246	435	8	δxu0j	δxu0j	X
ejpam-5246	435	9	,	,	PUNCT
ejpam-5246	435	10	v0j	v0j	NOUN
ejpam-5246	435	11	)	)	PUNCT
ejpam-5246	435	12	−	−	PROPN
ejpam-5246	436	1	f	f	PROPN
ejpam-5246	436	2	(	(	PUNCT
ejpam-5246	436	3	δxu	δxu	PROPN
ejpam-5246	436	4	0	0	NUM
ejpam-5246	436	5	j	j	PROPN
ejpam-5246	436	6	,	,	PUNCT
ejpam-5246	436	7	v	v	NOUN
ejpam-5246	436	8	0	0	NUM
ejpam-5246	436	9	j	j	NOUN
ejpam-5246	436	10	)	)	PUNCT
ejpam-5246	436	11	)	)	PUNCT
ejpam-5246	437	1	+	+	CCONJ
ejpam-5246	437	2	t	t	NOUN
ejpam-5246	437	3	0	0	NUM
ejpam-5246	437	4	j	j	PROPN
ejpam-5246	437	5	∣∣	∣∣	NUM
ejpam-5246	437	6	.	.	PUNCT
ejpam-5246	438	1	from	from	ADP
ejpam-5246	438	2	lemma	lemma	PROPN
ejpam-5246	438	3	(	(	PUNCT
ejpam-5246	438	4	1	1	NUM
ejpam-5246	438	5	)	)	PUNCT
ejpam-5246	438	6	,	,	PUNCT
ejpam-5246	438	7	we	we	PRON
ejpam-5246	438	8	have∣∣e1uj∣∣	have∣∣e1uj∣∣	VERB
ejpam-5246	438	9	≤	≤	NUM
ejpam-5246	438	10	k1l1	k1l1	VERB
ejpam-5246	438	11	∣∣δx	∣∣δx	ADJ
ejpam-5246	438	12	(	(	PUNCT
ejpam-5246	438	13	u0j	u0j	ADP
ejpam-5246	438	14	−	−	PROPN
ejpam-5246	438	15	u0	u0	ADJ
ejpam-5246	438	16	j	j	PROPN
ejpam-5246	438	17	)	)	PUNCT
ejpam-5246	438	18	∣∣+	∣∣+	PROPN
ejpam-5246	439	1	k1l2	k1l2	X
ejpam-5246	439	2	∣∣v0j	∣∣v0j	NOUN
ejpam-5246	440	1	−	−	NOUN
ejpam-5246	440	2	v	v	NOUN
ejpam-5246	440	3	0	0	NUM
ejpam-5246	440	4	j	j	PROPN
ejpam-5246	440	5	∣∣+	∣∣+	PROPN
ejpam-5246	440	6	∣∣t	∣∣t	PROPN
ejpam-5246	440	7	0	0	NUM
ejpam-5246	440	8	j	j	PROPN
ejpam-5246	440	9	∣∣	∣∣	NUM
ejpam-5246	440	10	,	,	PUNCT
ejpam-5246	440	11	=	=	PUNCT
ejpam-5246	440	12	k1l1	k1l1	X
ejpam-5246	440	13	∣∣δxe0uj∣∣+	∣∣δxe0uj∣∣+	NUM
ejpam-5246	440	14	k1l2	k1l2	PROPN
ejpam-5246	440	15	∣∣e0vj∣∣+	∣∣e0vj∣∣+	PROPN
ejpam-5246	440	16	∣∣t	∣∣t	VERB
ejpam-5246	440	17	0	0	NUM
ejpam-5246	440	18	j	j	PROPN
ejpam-5246	440	19	∣∣	∣∣	NUM
ejpam-5246	440	20	where	where	SCONJ
ejpam-5246	440	21	l	l	NOUN
ejpam-5246	440	22	=	=	SYM
ejpam-5246	440	23	max	max	PROPN
ejpam-5246	440	24	{	{	PUNCT
ejpam-5246	440	25	l1	l1	PROPN
ejpam-5246	440	26	,	,	PUNCT
ejpam-5246	440	27	l2	l2	NOUN
ejpam-5246	440	28	}	}	PUNCT
ejpam-5246	440	29	.	.	PUNCT
ejpam-5246	441	1	so,∣∣e1uj∣∣	so,∣∣e1uj∣∣	PROPN
ejpam-5246	442	1	≤	≤	NOUN
ejpam-5246	442	2	2kl1	2kl1	NUM
ejpam-5246	442	3	∥∥e0	∥∥e0	PROPN
ejpam-5246	442	4	u	u	PROPN
ejpam-5246	442	5	∥∥+	∥∥+	PROPN
ejpam-5246	442	6	kl2	kl2	PROPN
ejpam-5246	442	7	∥∥e0	∥∥e0	PROPN
ejpam-5246	442	8	v	v	X
ejpam-5246	442	9	∥∥+	∥∥+	SYM
ejpam-5246	442	10	∣∣t	∣∣t	NOUN
ejpam-5246	442	11	0	0	NUM
ejpam-5246	443	1	i	i	PRON
ejpam-5246	443	2	∣∣	∣∣	NUM
ejpam-5246	443	3	=	=	PUNCT
ejpam-5246	443	4	∣∣t	∣∣t	NOUN
ejpam-5246	443	5	0	0	NUM
ejpam-5246	444	1	i	i	PRON
ejpam-5246	444	2	∣∣	∣∣	VERB
ejpam-5246	444	3	≤	≤	PUNCT
ejpam-5246	444	4	c	c	X
ejpam-5246	444	5	(	(	PUNCT
ejpam-5246	444	6	k	k	PROPN
ejpam-5246	444	7	+	+	CCONJ
ejpam-5246	444	8	h2	h2	NOUN
ejpam-5246	444	9	)	)	PUNCT
ejpam-5246	444	10	.	.	PUNCT
ejpam-5246	445	1	thus	thus	ADV
ejpam-5246	445	2	|e1ui|	|e1ui|	VERB
ejpam-5246	445	3	≤	≤	NUM
ejpam-5246	445	4	c(k	c(k	NOUN
ejpam-5246	445	5	+	+	CCONJ
ejpam-5246	445	6	h2	h2	NOUN
ejpam-5246	445	7	)	)	PUNCT
ejpam-5246	445	8	,	,	PUNCT
ejpam-5246	445	9	i	i	PRON
ejpam-5246	445	10	=	=	NOUN
ejpam-5246	445	11	1	1	NUM
ejpam-5246	445	12	,	,	PUNCT
ejpam-5246	445	13	2	2	NUM
ejpam-5246	445	14	,	,	PUNCT
ejpam-5246	445	15	.	.	PUNCT
ejpam-5246	445	16	.	.	PUNCT
ejpam-5246	445	17	.	.	PUNCT
ejpam-5246	446	1	i	i	PRON
ejpam-5246	446	2	−	−	VERB
ejpam-5246	447	1	1	1	X
ejpam-5246	447	2	.	.	PUNCT
ejpam-5246	448	1	likewise	likewise	ADV
ejpam-5246	448	2	,	,	PUNCT
ejpam-5246	448	3	∣∣e1vi∣∣	∣∣e1vi∣∣	PRON
ejpam-5246	448	4	≤	≤	NUM
ejpam-5246	448	5	c	c	X
ejpam-5246	448	6	(	(	PUNCT
ejpam-5246	448	7	k	k	PROPN
ejpam-5246	448	8	+	+	CCONJ
ejpam-5246	448	9	h2	h2	NOUN
ejpam-5246	448	10	)	)	PUNCT
ejpam-5246	448	11	,	,	PUNCT
ejpam-5246	448	12	i	i	PRON
ejpam-5246	448	13	=	=	NOUN
ejpam-5246	448	14	1	1	NUM
ejpam-5246	448	15	,	,	PUNCT
ejpam-5246	448	16	2	2	NUM
ejpam-5246	448	17	,	,	PUNCT
ejpam-5246	448	18	.	.	PUNCT
ejpam-5246	448	19	.	.	PUNCT
ejpam-5246	448	20	.	.	PUNCT
ejpam-5246	449	1	,	,	PUNCT
ejpam-5246	449	2	i	i	PRON
ejpam-5246	449	3	−	−	VERB
ejpam-5246	450	1	1	1	X
ejpam-5246	450	2	.	.	PUNCT
ejpam-5246	450	3	m.i.khalil	m.i.khalil	PROPN
ejpam-5246	450	4	et	et	PROPN
ejpam-5246	450	5	al	al	PROPN
ejpam-5246	450	6	.	.	PUNCT
ejpam-5246	450	7	/	/	SYM
ejpam-5246	450	8	eur	eur	PROPN
ejpam-5246	450	9	.	.	PUNCT
ejpam-5246	451	1	j.	j.	PROPN
ejpam-5246	451	2	pure	pure	PROPN
ejpam-5246	451	3	appl	appl	PROPN
ejpam-5246	451	4	.	.	PROPN
ejpam-5246	451	5	math	math	PROPN
ejpam-5246	451	6	,	,	PUNCT
ejpam-5246	451	7	17	17	NUM
ejpam-5246	451	8	(	(	PUNCT
ejpam-5246	451	9	3	3	NUM
ejpam-5246	451	10	)	)	PUNCT
ejpam-5246	451	11	(	(	PUNCT
ejpam-5246	451	12	2024	2024	NUM
ejpam-5246	451	13	)	)	PUNCT
ejpam-5246	451	14	,	,	PUNCT
ejpam-5246	451	15	1516	1516	NUM
ejpam-5246	451	16	-	-	SYM
ejpam-5246	451	17	1538	1538	NUM
ejpam-5246	451	18	1529	1529	NUM
ejpam-5246	451	19	now	now	ADV
ejpam-5246	451	20	assume	assume	VERB
ejpam-5246	451	21	that	that	SCONJ
ejpam-5246	451	22	|esui|	|esui|	ADJ
ejpam-5246	451	23	≤	≤	PROPN
ejpam-5246	451	24	cs	cs	PROPN
ejpam-5246	451	25	(	(	PUNCT
ejpam-5246	451	26	k	k	PROPN
ejpam-5246	451	27	+	+	CCONJ
ejpam-5246	451	28	h2	h2	NOUN
ejpam-5246	451	29	)	)	PUNCT
ejpam-5246	451	30	and	and	CCONJ
ejpam-5246	451	31	|esvi|	|esvi|	NUM
ejpam-5246	451	32	≤	≤	NOUN
ejpam-5246	451	33	cs	cs	X
ejpam-5246	451	34	(	(	PUNCT
ejpam-5246	451	35	k	k	PROPN
ejpam-5246	451	36	+	+	CCONJ
ejpam-5246	451	37	h2	h2	NOUN
ejpam-5246	451	38	)	)	PUNCT
ejpam-5246	451	39	,	,	PUNCT
ejpam-5246	451	40	where	where	SCONJ
ejpam-5246	451	41	s	s	VERB
ejpam-5246	451	42	=	=	SYM
ejpam-5246	451	43	0	0	NUM
ejpam-5246	451	44	,	,	PUNCT
ejpam-5246	451	45	1	1	NUM
ejpam-5246	451	46	,	,	PUNCT
ejpam-5246	451	47	2	2	NUM
ejpam-5246	451	48	,	,	PUNCT
ejpam-5246	451	49	.	.	PUNCT
ejpam-5246	451	50	.	.	PUNCT
ejpam-5246	451	51	.	.	PUNCT
ejpam-5246	452	1	,	,	PUNCT
ejpam-5246	452	2	n	n	CCONJ
ejpam-5246	452	3	,	,	PUNCT
ejpam-5246	452	4	cs	cs	X
ejpam-5246	452	5	>	>	X
ejpam-5246	452	6	0	0	PROPN
ejpam-5246	452	7	,	,	PUNCT
ejpam-5246	452	8	c∗	c∗	NOUN
ejpam-5246	452	9	=	=	SYM
ejpam-5246	452	10	max0≤s≤ncs	max0≤s≤nc	NOUN
ejpam-5246	452	11	.	.	PUNCT
ejpam-5246	453	1	for	for	ADP
ejpam-5246	453	2	n+	n+	NUM
ejpam-5246	453	3	1	1	NUM
ejpam-5246	453	4	,	,	PUNCT
ejpam-5246	453	5	we	we	PRON
ejpam-5246	453	6	set	set	VERB
ejpam-5246	453	7	|en+1	|en+1	ADJ
ejpam-5246	453	8	uj	uj	NOUN
ejpam-5246	453	9	|	|	NOUN
ejpam-5246	453	10	=	=	SYM
ejpam-5246	453	11	max1≤i≤i−1	max1≤i≤i−1	PROPN
ejpam-5246	453	12	|en+1	|en+1	ADJ
ejpam-5246	453	13	ui	ui	NOUN
ejpam-5246	453	14	|	|	NOUN
ejpam-5246	453	15	,	,	PUNCT
ejpam-5246	453	16	and	and	CCONJ
ejpam-5246	453	17	so∣∣∣en+1	so∣∣∣en+1	PROPN
ejpam-5246	453	18	uj	uj	NOUN
ejpam-5246	453	19	∣∣∣	∣∣∣	NOUN
ejpam-5246	453	20	=	=	SYM
ejpam-5246	453	21	(	(	PUNCT
ejpam-5246	453	22	1	1	NUM
ejpam-5246	453	23	+	+	NUM
ejpam-5246	453	24	2rn	2rn	ADJ
ejpam-5246	453	25	)	)	PUNCT
ejpam-5246	453	26	∣∣∣en+1	∣∣∣en+1	NOUN
ejpam-5246	454	1	uj	uj	PROPN
ejpam-5246	454	2	∣∣∣−	∣∣∣−	PROPN
ejpam-5246	454	3	rn	rn	PROPN
ejpam-5246	454	4	(	(	PUNCT
ejpam-5246	454	5	∣∣∣en+1	∣∣∣en+1	PROPN
ejpam-5246	454	6	uj	uj	PROPN
ejpam-5246	454	7	∣∣∣+	∣∣∣+	PROPN
ejpam-5246	454	8	∣∣∣en+1	∣∣∣en+1	NOUN
ejpam-5246	454	9	uj	uj	PROPN
ejpam-5246	454	10	∣∣∣	∣∣∣	NOUN
ejpam-5246	454	11	)	)	PUNCT
ejpam-5246	454	12	≤	≤	NOUN
ejpam-5246	454	13	(	(	PUNCT
ejpam-5246	454	14	1	1	NUM
ejpam-5246	454	15	+	+	NUM
ejpam-5246	454	16	2rn	2rn	ADJ
ejpam-5246	454	17	)	)	PUNCT
ejpam-5246	454	18	∣∣∣en+1	∣∣∣en+1	NOUN
ejpam-5246	454	19	uj	uj	PROPN
ejpam-5246	454	20	∣∣∣−	∣∣∣−	PROPN
ejpam-5246	454	21	rn	rn	PROPN
ejpam-5246	454	22	(	(	PUNCT
ejpam-5246	454	23	∣∣∣en+1	∣∣∣en+1	X
ejpam-5246	454	24	uj+1	uj+1	PROPN
ejpam-5246	454	25	∣∣∣+	∣∣∣+	PROPN
ejpam-5246	454	26	∣∣∣en+1	∣∣∣en+1	NOUN
ejpam-5246	454	27	uj−1	uj−1	NOUN
ejpam-5246	454	28	∣∣∣	∣∣∣	ADJ
ejpam-5246	454	29	)	)	PUNCT
ejpam-5246	454	30	≤	≤	NUM
ejpam-5246	454	31	∣∣∣(1	∣∣∣(1	NOUN
ejpam-5246	454	32	+	+	CCONJ
ejpam-5246	454	33	2rn)e	2rn)e	PROPN
ejpam-5246	454	34	n+1	n+1	PROPN
ejpam-5246	454	35	uj	uj	PROPN
ejpam-5246	454	36	−	−	PROPN
ejpam-5246	454	37	rn	rn	PROPN
ejpam-5246	454	38	(	(	PUNCT
ejpam-5246	454	39	en+1	en+1	PROPN
ejpam-5246	454	40	uj+1	uj+1	NUM
ejpam-5246	454	41	+	+	CCONJ
ejpam-5246	454	42	en+1	en+1	ADJ
ejpam-5246	454	43	uj−1	uj−1	NOUN
ejpam-5246	454	44	)	)	PUNCT
ejpam-5246	454	45	∣∣∣	∣∣∣	NOUN
ejpam-5246	454	46	=	=	SYM
ejpam-5246	454	47	∣∣∣enuj	∣∣∣enuj	PROPN
ejpam-5246	454	48	+	+	PROPN
ejpam-5246	454	49	kn	kn	PROPN
ejpam-5246	454	50	(	(	PUNCT
ejpam-5246	454	51	f	f	X
ejpam-5246	454	52	(	(	PUNCT
ejpam-5246	454	53	δxu	δxu	PROPN
ejpam-5246	454	54	n	n	PRON
ejpam-5246	454	55	j	j	PROPN
ejpam-5246	454	56	,	,	PUNCT
ejpam-5246	454	57	v	v	PROPN
ejpam-5246	454	58	n	n	PROPN
ejpam-5246	454	59	j	j	PROPN
ejpam-5246	454	60	)	)	PUNCT
ejpam-5246	455	1	−	−	PROPN
ejpam-5246	455	2	f	f	X
ejpam-5246	455	3	(	(	PUNCT
ejpam-5246	455	4	δxu	δxu	PROPN
ejpam-5246	455	5	n	n	PRON
ejpam-5246	455	6	j	j	PROPN
ejpam-5246	455	7	,	,	PUNCT
ejpam-5246	455	8	v	v	PROPN
ejpam-5246	455	9	n	n	PROPN
ejpam-5246	455	10	j	j	PROPN
ejpam-5246	455	11	)	)	PUNCT
ejpam-5246	455	12	)	)	PUNCT
ejpam-5246	456	1	+	+	CCONJ
ejpam-5246	456	2	tn+1	tn+1	VERB
ejpam-5246	456	3	j	j	NOUN
ejpam-5246	456	4	∣∣∣	∣∣∣	NOUN
ejpam-5246	456	5	.	.	PUNCT
ejpam-5246	457	1	thus	thus	ADV
ejpam-5246	457	2	∣∣∣en+1	∣∣∣en+1	ADJ
ejpam-5246	457	3	uj	uj	PROPN
ejpam-5246	457	4	∣∣∣	∣∣∣	PROPN
ejpam-5246	457	5	≤	≤	PROPN
ejpam-5246	457	6	∣∣enuj∣∣+	∣∣enuj∣∣+	PROPN
ejpam-5246	458	1	kn	kn	PROPN
ejpam-5246	458	2	∣∣f	∣∣f	PROPN
ejpam-5246	458	3	(	(	PUNCT
ejpam-5246	458	4	δxunj	δxunj	NOUN
ejpam-5246	458	5	,	,	PUNCT
ejpam-5246	458	6	vnj	vnj	INTJ
ejpam-5246	458	7	)	)	PUNCT
ejpam-5246	458	8	−	−	PROPN
ejpam-5246	459	1	f	f	PROPN
ejpam-5246	459	2	(	(	PUNCT
ejpam-5246	459	3	δxu	δxu	PROPN
ejpam-5246	459	4	n	n	PRON
ejpam-5246	459	5	j	j	PROPN
ejpam-5246	459	6	,	,	PUNCT
ejpam-5246	459	7	v	v	PROPN
ejpam-5246	459	8	n	n	PROPN
ejpam-5246	459	9	j	j	PROPN
ejpam-5246	459	10	)	)	PUNCT
ejpam-5246	459	11	∣∣+	∣∣+	PROPN
ejpam-5246	459	12	∣∣∣tn+1	∣∣∣tn+1	PROPN
ejpam-5246	459	13	j	j	PROPN
ejpam-5246	459	14	∣∣∣	∣∣∣	NOUN
ejpam-5246	459	15	.	.	PUNCT
ejpam-5246	460	1	by	by	ADP
ejpam-5246	460	2	lemma	lemma	PROPN
ejpam-5246	460	3	(	(	PUNCT
ejpam-5246	460	4	1	1	NUM
ejpam-5246	460	5	)	)	PUNCT
ejpam-5246	460	6	,	,	PUNCT
ejpam-5246	460	7	we	we	PRON
ejpam-5246	460	8	obtain∣∣∣en+1	obtain∣∣∣en+1	PROPN
ejpam-5246	460	9	uj	uj	PROPN
ejpam-5246	460	10	∣∣∣	∣∣∣	PROPN
ejpam-5246	460	11	≤	≤	PROPN
ejpam-5246	460	12	∣∣enuj∣∣+	∣∣enuj∣∣+	PROPN
ejpam-5246	460	13	knl1	knl1	PROPN
ejpam-5246	460	14	∣∣δx	∣∣δx	PROPN
ejpam-5246	460	15	(	(	PUNCT
ejpam-5246	460	16	unj	unj	NOUN
ejpam-5246	460	17	−	−	PROPN
ejpam-5246	460	18	un	un	PROPN
ejpam-5246	460	19	j	j	PROPN
ejpam-5246	460	20	)	)	PUNCT
ejpam-5246	461	1	∣∣+	∣∣+	PROPN
ejpam-5246	461	2	knl2	knl2	PROPN
ejpam-5246	462	1	∣∣vnj	∣∣vnj	PROPN
ejpam-5246	462	2	−	−	PROPN
ejpam-5246	463	1	v	v	ADP
ejpam-5246	463	2	n	n	PROPN
ejpam-5246	463	3	j	j	PROPN
ejpam-5246	463	4	∣∣+	∣∣+	PROPN
ejpam-5246	463	5	∣∣∣tn+1	∣∣∣tn+1	PROPN
ejpam-5246	463	6	j	j	PROPN
ejpam-5246	463	7	∣∣∣	∣∣∣	PROPN
ejpam-5246	463	8	≤	≤	PROPN
ejpam-5246	463	9	∣∣enuj∣∣+	∣∣enuj∣∣+	PROPN
ejpam-5246	463	10	kl1	kl1	PROPN
ejpam-5246	463	11	∣∣δxenuj∣∣+	∣∣δxenuj∣∣+	PROPN
ejpam-5246	463	12	kl2	kl2	PROPN
ejpam-5246	463	13	∣∣envj∣∣+	∣∣envj∣∣+	PROPN
ejpam-5246	463	14	∣∣∣tn+1	∣∣∣tn+1	PROPN
ejpam-5246	463	15	j	j	PROPN
ejpam-5246	463	16	∣∣∣	∣∣∣	NOUN
ejpam-5246	463	17	.	.	PUNCT
ejpam-5246	464	1	by	by	ADP
ejpam-5246	464	2	setting	set	VERB
ejpam-5246	464	3	l	l	NOUN
ejpam-5246	464	4	=	=	PUNCT
ejpam-5246	464	5	max	max	PROPN
ejpam-5246	464	6	{	{	PUNCT
ejpam-5246	464	7	l1	l1	PROPN
ejpam-5246	464	8	,	,	PUNCT
ejpam-5246	464	9	l2	l2	NOUN
ejpam-5246	464	10	}	}	PUNCT
ejpam-5246	464	11	,	,	PUNCT
ejpam-5246	464	12	we	we	PRON
ejpam-5246	464	13	get∥∥en+1	get∥∥en+1	VERB
ejpam-5246	464	14	u	u	NOUN
ejpam-5246	464	15	∥∥	∥∥	X
ejpam-5246	464	16	≤	≤	X
ejpam-5246	464	17	∥en	∥en	PUNCT
ejpam-5246	464	18	u∥+	u∥+	PROPN
ejpam-5246	464	19	2kl1	2kl1	NUM
ejpam-5246	464	20	∥en	∥en	NUM
ejpam-5246	464	21	u∥+	u∥+	PROPN
ejpam-5246	464	22	kl2	kl2	PROPN
ejpam-5246	464	23	∥en	∥en	PROPN
ejpam-5246	464	24	v	v	PROPN
ejpam-5246	464	25	∥+	∥+	PROPN
ejpam-5246	464	26	∣∣∣tn+1	∣∣∣tn+1	PROPN
ejpam-5246	464	27	j	j	PROPN
ejpam-5246	464	28	∣∣∣	∣∣∣	ADJ
ejpam-5246	464	29	≤	≤	X
ejpam-5246	464	30	c∗	c∗	NOUN
ejpam-5246	464	31	(	(	PUNCT
ejpam-5246	464	32	k	k	PROPN
ejpam-5246	464	33	+	+	CCONJ
ejpam-5246	464	34	h2	h2	NOUN
ejpam-5246	464	35	)	)	PUNCT
ejpam-5246	465	1	+	+	CCONJ
ejpam-5246	465	2	3klc∗	3klc∗	NUM
ejpam-5246	465	3	(	(	PUNCT
ejpam-5246	465	4	k	k	PROPN
ejpam-5246	465	5	+	+	X
ejpam-5246	465	6	h2	h2	NOUN
ejpam-5246	465	7	)	)	PUNCT
ejpam-5246	466	1	+	+	CCONJ
ejpam-5246	466	2	c	c	X
ejpam-5246	466	3	(	(	PUNCT
ejpam-5246	466	4	k	k	NOUN
ejpam-5246	466	5	+	+	CCONJ
ejpam-5246	466	6	h2	h2	NOUN
ejpam-5246	466	7	)	)	PUNCT
ejpam-5246	466	8	≤	≤	NOUN
ejpam-5246	466	9	(	(	PUNCT
ejpam-5246	466	10	1	1	NUM
ejpam-5246	466	11	+	+	SYM
ejpam-5246	466	12	3kl)c∗	3kl)c∗	NUM
ejpam-5246	466	13	(	(	PUNCT
ejpam-5246	466	14	k	k	PROPN
ejpam-5246	466	15	+	+	CCONJ
ejpam-5246	466	16	h2	h2	NOUN
ejpam-5246	466	17	)	)	PUNCT
ejpam-5246	467	1	+	+	CCONJ
ejpam-5246	467	2	c	c	X
ejpam-5246	467	3	(	(	PUNCT
ejpam-5246	467	4	k	k	NOUN
ejpam-5246	467	5	+	+	CCONJ
ejpam-5246	467	6	h2	h2	NOUN
ejpam-5246	467	7	)	)	PUNCT
ejpam-5246	468	1	=	=	PUNCT
ejpam-5246	469	1	[	[	X
ejpam-5246	469	2	(	(	PUNCT
ejpam-5246	469	3	1	1	NUM
ejpam-5246	469	4	+	+	SYM
ejpam-5246	469	5	3kl)c∗	3kl)c∗	NUM
ejpam-5246	469	6	+	+	CCONJ
ejpam-5246	469	7	c	c	X
ejpam-5246	469	8	]	]	X
ejpam-5246	469	9	(	(	PUNCT
ejpam-5246	469	10	k	k	X
ejpam-5246	469	11	+	+	CCONJ
ejpam-5246	469	12	h2	h2	NOUN
ejpam-5246	469	13	)	)	PUNCT
ejpam-5246	469	14	.	.	PUNCT
ejpam-5246	470	1	it	it	PRON
ejpam-5246	470	2	follows	follow	VERB
ejpam-5246	470	3	that	that	SCONJ
ejpam-5246	470	4	∥∥en+1	∥∥en+1	PROPN
ejpam-5246	470	5	u	u	NOUN
ejpam-5246	470	6	∥∥	∥∥	X
ejpam-5246	470	7	≤	≤	PROPN
ejpam-5246	470	8	c	c	X
ejpam-5246	470	9	(	(	PUNCT
ejpam-5246	470	10	k	k	PROPN
ejpam-5246	470	11	+	+	CCONJ
ejpam-5246	470	12	h2	h2	PROPN
ejpam-5246	470	13	)	)	PUNCT
ejpam-5246	470	14	,	,	PUNCT
ejpam-5246	470	15	n	n	NOUN
ejpam-5246	470	16	=	=	SYM
ejpam-5246	470	17	0	0	NUM
ejpam-5246	470	18	,	,	PUNCT
ejpam-5246	470	19	1	1	NUM
ejpam-5246	470	20	,	,	PUNCT
ejpam-5246	470	21	.	.	PUNCT
ejpam-5246	470	22	.	.	PUNCT
ejpam-5246	471	1	.	.	PUNCT
ejpam-5246	472	1	,	,	PUNCT
ejpam-5246	472	2	i	i	PRON
ejpam-5246	472	3	=	=	NOUN
ejpam-5246	472	4	1	1	NUM
ejpam-5246	472	5	,	,	PUNCT
ejpam-5246	472	6	2	2	NUM
ejpam-5246	472	7	,	,	PUNCT
ejpam-5246	472	8	.	.	PUNCT
ejpam-5246	472	9	.	.	PUNCT
ejpam-5246	473	1	.	.	PUNCT
ejpam-5246	474	1	,	,	PUNCT
ejpam-5246	474	2	i	i	PRON
ejpam-5246	474	3	−	−	VERB
ejpam-5246	475	1	1	1	X
ejpam-5246	475	2	.	.	PUNCT
ejpam-5246	475	3	similarly	similarly	ADV
ejpam-5246	475	4	,	,	PUNCT
ejpam-5246	475	5	we	we	PRON
ejpam-5246	475	6	can	can	AUX
ejpam-5246	475	7	show	show	VERB
ejpam-5246	475	8	that∥∥en+1	that∥∥en+1	PROPN
ejpam-5246	475	9	v	v	ADP
ejpam-5246	475	10	∥∥	∥∥	X
ejpam-5246	475	11	≤	≤	PROPN
ejpam-5246	475	12	c	c	NOUN
ejpam-5246	475	13	(	(	PUNCT
ejpam-5246	475	14	k	k	PROPN
ejpam-5246	475	15	+	+	CCONJ
ejpam-5246	475	16	h2	h2	PROPN
ejpam-5246	475	17	)	)	PUNCT
ejpam-5246	475	18	,	,	PUNCT
ejpam-5246	475	19	n	n	NOUN
ejpam-5246	475	20	=	=	SYM
ejpam-5246	475	21	0	0	NUM
ejpam-5246	475	22	,	,	PUNCT
ejpam-5246	475	23	1	1	NUM
ejpam-5246	475	24	,	,	PUNCT
ejpam-5246	475	25	.	.	PUNCT
ejpam-5246	475	26	.	.	PUNCT
ejpam-5246	475	27	.	.	PUNCT
ejpam-5246	475	28	.	.	PUNCT
ejpam-5246	476	1	definition	definition	NOUN
ejpam-5246	476	2	2	2	NUM
ejpam-5246	476	3	.	.	PUNCT
ejpam-5246	477	1	if	if	SCONJ
ejpam-5246	477	2	the	the	DET
ejpam-5246	477	3	specified	specified	ADJ
ejpam-5246	477	4	conditions	condition	NOUN
ejpam-5246	477	5	are	be	AUX
ejpam-5246	477	6	satisfied	satisfied	ADJ
ejpam-5246	477	7	,	,	PUNCT
ejpam-5246	477	8	a	a	DET
ejpam-5246	477	9	solution	solution	NOUN
ejpam-5246	477	10	of	of	ADP
ejpam-5246	477	11	both	both	CCONJ
ejpam-5246	477	12	the	the	DET
ejpam-5246	477	13	explicit	explicit	ADJ
ejpam-5246	477	14	and	and	CCONJ
ejpam-5246	477	15	implicit	implicit	ADJ
ejpam-5246	477	16	euler	euler	NOUN
ejpam-5246	477	17	schemes	scheme	NOUN
ejpam-5246	477	18	will	will	AUX
ejpam-5246	477	19	together	together	ADV
ejpam-5246	477	20	blow	blow	VERB
ejpam-5246	477	21	up	up	ADP
ejpam-5246	477	22	within	within	ADP
ejpam-5246	477	23	a	a	DET
ejpam-5246	477	24	finite	finite	ADJ
ejpam-5246	477	25	time	time	NOUN
ejpam-5246	477	26	denoted	denote	VERB
ejpam-5246	477	27	as	as	ADP
ejpam-5246	477	28	th	th	NOUN
ejpam-5246	477	29	:	:	PUNCT
ejpam-5246	477	30	•	•	NUM
ejpam-5246	477	31	∥un	∥un	PROPN
ejpam-5246	477	32	h	h	NOUN
ejpam-5246	477	33	∥∞	∥∞	PROPN
ejpam-5246	477	34	→	→	SYM
ejpam-5246	477	35	∞	∞	PROPN
ejpam-5246	477	36	,	,	PUNCT
ejpam-5246	477	37	∥v	∥v	PROPN
ejpam-5246	477	38	n	n	CCONJ
ejpam-5246	477	39	h	h	NOUN
ejpam-5246	477	40	∥∞	∥∞	ADJ
ejpam-5246	477	41	→	→	SYM
ejpam-5246	477	42	∞	∞	PROPN
ejpam-5246	477	43	,	,	PUNCT
ejpam-5246	477	44	as	as	ADP
ejpam-5246	477	45	n	n	X
ejpam-5246	477	46	→	→	SYM
ejpam-5246	477	47	∞	∞	PROPN
ejpam-5246	477	48	,	,	PUNCT
ejpam-5246	477	49	•	•	NUM
ejpam-5246	477	50	th	th	X
ejpam-5246	477	51	=	=	PUNCT
ejpam-5246	477	52	∑∞	∑∞	NOUN
ejpam-5246	477	53	n	n	PROPN
ejpam-5246	477	54	kn	kn	PROPN
ejpam-5246	477	55	.	.	PROPN
ejpam-5246	477	56	remark	remark	PROPN
ejpam-5246	477	57	1	1	NUM
ejpam-5246	477	58	.	.	NOUN
ejpam-5246	477	59	•	•	NUM
ejpam-5246	478	1	the	the	DET
ejpam-5246	478	2	matrix	matrix	NOUN
ejpam-5246	478	3	a	a	PRON
ejpam-5246	478	4	=	=	X
ejpam-5246	478	5	(	(	PUNCT
ejpam-5246	478	6	i	i	NOUN
ejpam-5246	478	7	−	−	PROPN
ejpam-5246	478	8	rnhh	rnhh	PROPN
ejpam-5246	478	9	)	)	PUNCT
ejpam-5246	478	10	exhibits	exhibit	VERB
ejpam-5246	478	11	diagonal	diagonal	ADJ
ejpam-5246	478	12	dominance	dominance	NOUN
ejpam-5246	478	13	,	,	PUNCT
ejpam-5246	478	14	characterized	characterize	VERB
ejpam-5246	478	15	by	by	ADP
ejpam-5246	478	16	the	the	DET
ejpam-5246	478	17	presence	presence	NOUN
ejpam-5246	478	18	of	of	ADP
ejpam-5246	478	19	positive	positive	ADJ
ejpam-5246	478	20	real	real	ADJ
ejpam-5246	478	21	diagonal	diagonal	ADJ
ejpam-5246	478	22	components	component	NOUN
ejpam-5246	478	23	.	.	PUNCT
ejpam-5246	479	1	this	this	DET
ejpam-5246	479	2	observation	observation	NOUN
ejpam-5246	479	3	suggests	suggest	VERB
ejpam-5246	479	4	that	that	PRON
ejpam-5246	479	5	matrix	matrix	VERB
ejpam-5246	479	6	a	a	PRON
ejpam-5246	479	7	is	be	AUX
ejpam-5246	479	8	positive	positive	ADJ
ejpam-5246	479	9	-	-	PUNCT
ejpam-5246	479	10	definite	definite	ADJ
ejpam-5246	479	11	and	and	CCONJ
ejpam-5246	479	12	non	non	ADJ
ejpam-5246	479	13	singular	singular	NOUN
ejpam-5246	480	1	[	[	X
ejpam-5246	480	2	26	26	NUM
ejpam-5246	480	3	]	]	PUNCT
ejpam-5246	480	4	,	,	PUNCT
ejpam-5246	480	5	therefore	therefore	ADV
ejpam-5246	480	6	,	,	PUNCT
ejpam-5246	480	7	it	it	PRON
ejpam-5246	480	8	is	be	AUX
ejpam-5246	480	9	possible	possible	ADJ
ejpam-5246	480	10	to	to	PART
ejpam-5246	480	11	solve	solve	VERB
ejpam-5246	480	12	the	the	DET
ejpam-5246	480	13	linear	linear	PROPN
ejpam-5246	480	14	systems(3.4)-(3.5	systems(3.4)-(3.5	PROPN
ejpam-5246	480	15	)	)	PUNCT
ejpam-5246	480	16	and	and	CCONJ
ejpam-5246	480	17	get	get	VERB
ejpam-5246	480	18	a	a	DET
ejpam-5246	480	19	unique	unique	ADJ
ejpam-5246	480	20	solution	solution	NOUN
ejpam-5246	480	21	.	.	PUNCT
ejpam-5246	481	1	m.i.khalil	m.i.khalil	NOUN
ejpam-5246	481	2	et	et	PROPN
ejpam-5246	481	3	al	al	PROPN
ejpam-5246	481	4	.	.	PUNCT
ejpam-5246	481	5	/	/	SYM
ejpam-5246	481	6	eur	eur	PROPN
ejpam-5246	481	7	.	.	PUNCT
ejpam-5246	482	1	j.	j.	PROPN
ejpam-5246	482	2	pure	pure	PROPN
ejpam-5246	482	3	appl	appl	PROPN
ejpam-5246	482	4	.	.	PROPN
ejpam-5246	482	5	math	math	PROPN
ejpam-5246	482	6	,	,	PUNCT
ejpam-5246	482	7	17	17	NUM
ejpam-5246	482	8	(	(	PUNCT
ejpam-5246	482	9	3	3	NUM
ejpam-5246	482	10	)	)	PUNCT
ejpam-5246	482	11	(	(	PUNCT
ejpam-5246	482	12	2024	2024	NUM
ejpam-5246	482	13	)	)	PUNCT
ejpam-5246	482	14	,	,	PUNCT
ejpam-5246	482	15	1516	1516	NUM
ejpam-5246	482	16	-	-	SYM
ejpam-5246	482	17	1538	1538	NUM
ejpam-5246	482	18	1530	1530	NUM
ejpam-5246	482	19	•	•	ADP
ejpam-5246	482	20	the	the	DET
ejpam-5246	482	21	finite	finite	ADJ
ejpam-5246	482	22	difference	difference	NOUN
ejpam-5246	482	23	schemes	scheme	NOUN
ejpam-5246	482	24	,	,	PUNCT
ejpam-5246	482	25	explicit	explicit	ADJ
ejpam-5246	482	26	euler	euler	NOUN
ejpam-5246	482	27	schemes	scheme	NOUN
ejpam-5246	482	28	,	,	PUNCT
ejpam-5246	482	29	and	and	CCONJ
ejpam-5246	482	30	implicit	implicit	ADJ
ejpam-5246	482	31	euler	euler	NOUN
ejpam-5246	482	32	schemes	scheme	NOUN
ejpam-5246	482	33	that	that	PRON
ejpam-5246	482	34	have	have	AUX
ejpam-5246	482	35	been	be	AUX
ejpam-5246	482	36	developed	develop	VERB
ejpam-5246	482	37	demonstrate	demonstrate	NOUN
ejpam-5246	482	38	consistency	consistency	NOUN
ejpam-5246	482	39	,	,	PUNCT
ejpam-5246	482	40	stability	stability	NOUN
ejpam-5246	482	41	,	,	PUNCT
ejpam-5246	482	42	and	and	CCONJ
ejpam-5246	482	43	convergence	convergence	NOUN
ejpam-5246	482	44	.	.	PUNCT
ejpam-5246	483	1	•	•	ADV
ejpam-5246	483	2	explicit	explicit	ADJ
ejpam-5246	483	3	(	(	PUNCT
ejpam-5246	483	4	implicit	implicit	ADJ
ejpam-5246	483	5	)	)	PUNCT
ejpam-5246	483	6	euler	euler	PROPN
ejpam-5246	483	7	numerical	numerical	PROPN
ejpam-5246	483	8	systems	systems	PROPN
ejpam-5246	483	9	provide	provide	VERB
ejpam-5246	483	10	approximate	approximate	ADJ
ejpam-5246	483	11	solutions	solution	NOUN
ejpam-5246	483	12	for	for	ADP
ejpam-5246	483	13	each	each	DET
ejpam-5246	483	14	set	set	VERB
ejpam-5246	483	15	time	time	NOUN
ejpam-5246	483	16	interval	interval	NOUN
ejpam-5246	483	17	l	l	NOUN
ejpam-5246	484	1	[	[	X
ejpam-5246	484	2	0	0	NUM
ejpam-5246	484	3	,	,	PUNCT
ejpam-5246	484	4	t	t	X
ejpam-5246	484	5	]	]	PUNCT
ejpam-5246	484	6	,	,	PUNCT
ejpam-5246	484	7	with	with	ADP
ejpam-5246	484	8	a	a	DET
ejpam-5246	484	9	convergence	convergence	NOUN
ejpam-5246	484	10	rate	rate	NOUN
ejpam-5246	484	11	of	of	ADP
ejpam-5246	484	12	o	o	PROPN
ejpam-5246	484	13	(	(	PUNCT
ejpam-5246	484	14	k	k	PROPN
ejpam-5246	484	15	+	+	CCONJ
ejpam-5246	484	16	h2	h2	NOUN
ejpam-5246	484	17	)	)	PUNCT
ejpam-5246	485	1	where	where	SCONJ
ejpam-5246	485	2	k	k	NOUN
ejpam-5246	485	3	=	=	SYM
ejpam-5246	485	4	maxn	maxn	ADJ
ejpam-5246	485	5	kn	kn	NOUN
ejpam-5246	485	6	,	,	PUNCT
ejpam-5246	485	7	however	however	ADV
ejpam-5246	485	8	,	,	PUNCT
ejpam-5246	485	9	when	when	SCONJ
ejpam-5246	485	10	using	use	VERB
ejpam-5246	485	11	the	the	DET
ejpam-5246	485	12	time	time	NOUN
ejpam-5246	485	13	-	-	PUNCT
ejpam-5246	485	14	steps	step	NOUN
ejpam-5246	485	15	formulas	formula	NOUN
ejpam-5246	485	16	(	(	PUNCT
ejpam-5246	485	17	2.3	2.3	NUM
ejpam-5246	485	18	)	)	PUNCT
ejpam-5246	485	19	and	and	CCONJ
ejpam-5246	485	20	(	(	PUNCT
ejpam-5246	485	21	3.3	3.3	NUM
ejpam-5246	485	22	)	)	PUNCT
ejpam-5246	485	23	,	,	PUNCT
ejpam-5246	485	24	the	the	DET
ejpam-5246	485	25	convergence	convergence	NOUN
ejpam-5246	485	26	rate	rate	NOUN
ejpam-5246	485	27	becomes	become	VERB
ejpam-5246	485	28	o	o	NOUN
ejpam-5246	485	29	(	(	PUNCT
ejpam-5246	485	30	hα	hα	NOUN
ejpam-5246	485	31	)	)	PUNCT
ejpam-5246	485	32	,	,	PUNCT
ejpam-5246	485	33	as	as	ADP
ejpam-5246	485	34	h	h	NOUN
ejpam-5246	485	35	→	→	SYM
ejpam-5246	485	36	0	0	NUM
ejpam-5246	485	37	,	,	PUNCT
ejpam-5246	485	38	for	for	ADP
ejpam-5246	485	39	α	α	DET
ejpam-5246	485	40	≤	≤	ADJ
ejpam-5246	485	41	2	2	NUM
ejpam-5246	485	42	.	.	PUNCT
ejpam-5246	486	1	the	the	DET
ejpam-5246	486	2	numerical	numerical	ADJ
ejpam-5246	486	3	blow	blow	VERB
ejpam-5246	486	4	-	-	PUNCT
ejpam-5246	486	5	up	up	ADP
ejpam-5246	486	6	time	time	NOUN
ejpam-5246	486	7	is	be	AUX
ejpam-5246	486	8	likely	likely	ADJ
ejpam-5246	486	9	to	to	PART
ejpam-5246	486	10	exhibit	exhibit	VERB
ejpam-5246	486	11	a	a	DET
ejpam-5246	486	12	similar	similar	ADJ
ejpam-5246	486	13	pattern	pattern	NOUN
ejpam-5246	486	14	of	of	ADP
ejpam-5246	486	15	convergence	convergence	NOUN
ejpam-5246	486	16	.	.	PUNCT
ejpam-5246	487	1	•	•	NUM
ejpam-5246	487	2	the	the	DET
ejpam-5246	487	3	numerical	numerical	ADJ
ejpam-5246	487	4	blow	blow	VERB
ejpam-5246	487	5	-	-	PUNCT
ejpam-5246	487	6	up	up	ADP
ejpam-5246	487	7	time	time	NOUN
ejpam-5246	487	8	of	of	ADP
ejpam-5246	487	9	a	a	DET
ejpam-5246	487	10	fully	fully	ADV
ejpam-5246	487	11	discrete	discrete	ADJ
ejpam-5246	487	12	formula	formula	NOUN
ejpam-5246	487	13	,	,	PUNCT
ejpam-5246	487	14	such	such	ADJ
ejpam-5246	487	15	as	as	ADP
ejpam-5246	487	16	explicit	explicit	ADJ
ejpam-5246	487	17	euler	euler	NOUN
ejpam-5246	487	18	or	or	CCONJ
ejpam-5246	487	19	implicit	implicit	ADJ
ejpam-5246	487	20	euler	euler	NOUN
ejpam-5246	487	21	,	,	PUNCT
ejpam-5246	487	22	is	be	AUX
ejpam-5246	487	23	considered	consider	VERB
ejpam-5246	487	24	the	the	DET
ejpam-5246	487	25	blow	blow	VERB
ejpam-5246	487	26	-	-	PUNCT
ejpam-5246	487	27	up	up	ADP
ejpam-5246	487	28	time	time	NOUN
ejpam-5246	487	29	for	for	ADP
ejpam-5246	487	30	system	system	NOUN
ejpam-5246	487	31	(	(	PUNCT
ejpam-5246	487	32	1.1	1.1	NUM
ejpam-5246	487	33	)	)	PUNCT
ejpam-5246	487	34	.	.	PUNCT
ejpam-5246	488	1	•	•	NUM
ejpam-5246	488	2	the	the	DET
ejpam-5246	488	3	duration	duration	NOUN
ejpam-5246	488	4	of	of	ADP
ejpam-5246	488	5	numerical	numerical	ADJ
ejpam-5246	488	6	blow	blow	NOUN
ejpam-5246	488	7	-	-	PUNCT
ejpam-5246	488	8	up	up	NOUN
ejpam-5246	488	9	achieved	achieve	VERB
ejpam-5246	488	10	through	through	ADP
ejpam-5246	488	11	the	the	DET
ejpam-5246	488	12	utilization	utilization	NOUN
ejpam-5246	488	13	of	of	ADP
ejpam-5246	488	14	a	a	DET
ejpam-5246	488	15	discrete	discrete	ADJ
ejpam-5246	488	16	scheme	scheme	NOUN
ejpam-5246	488	17	is	be	AUX
ejpam-5246	488	18	contingent	contingent	ADJ
ejpam-5246	488	19	upon	upon	SCONJ
ejpam-5246	488	20	both	both	CCONJ
ejpam-5246	488	21	the	the	DET
ejpam-5246	488	22	space	space	NOUN
ejpam-5246	488	23	-	-	PUNCT
ejpam-5246	488	24	step	step	NOUN
ejpam-5246	488	25	h	h	NOUN
ejpam-5246	488	26	and	and	CCONJ
ejpam-5246	488	27	the	the	DET
ejpam-5246	488	28	selection	selection	NOUN
ejpam-5246	488	29	of	of	ADP
ejpam-5246	488	30	time	time	NOUN
ejpam-5246	488	31	-	-	PUNCT
ejpam-5246	488	32	steps	step	NOUN
ejpam-5246	488	33	kn.nevertheless	kn.nevertheless	NOUN
ejpam-5246	488	34	,	,	PUNCT
ejpam-5246	488	35	it	it	PRON
ejpam-5246	488	36	should	should	AUX
ejpam-5246	488	37	be	be	AUX
ejpam-5246	488	38	noted	note	VERB
ejpam-5246	488	39	that	that	SCONJ
ejpam-5246	488	40	the	the	DET
ejpam-5246	488	41	time	time	NOUN
ejpam-5246	488	42	-	-	PUNCT
ejpam-5246	488	43	stepping	step	VERB
ejpam-5246	488	44	formulas	formula	NOUN
ejpam-5246	488	45	(	(	PUNCT
ejpam-5246	488	46	2.3	2.3	NUM
ejpam-5246	488	47	)	)	PUNCT
ejpam-5246	488	48	and	and	CCONJ
ejpam-5246	488	49	(	(	PUNCT
ejpam-5246	488	50	3.3	3.3	NUM
ejpam-5246	488	51	)	)	PUNCT
ejpam-5246	488	52	are	be	AUX
ejpam-5246	488	53	also	also	ADV
ejpam-5246	488	54	contingent	contingent	ADJ
ejpam-5246	488	55	upon	upon	SCONJ
ejpam-5246	488	56	the	the	DET
ejpam-5246	488	57	space	space	NOUN
ejpam-5246	488	58	-	-	PUNCT
ejpam-5246	488	59	step	step	NOUN
ejpam-5246	488	60	.	.	PUNCT
ejpam-5246	489	1	hence	hence	ADV
ejpam-5246	489	2	,	,	PUNCT
ejpam-5246	489	3	in	in	ADP
ejpam-5246	489	4	the	the	DET
ejpam-5246	489	5	examination	examination	NOUN
ejpam-5246	489	6	of	of	ADP
ejpam-5246	489	7	the	the	DET
ejpam-5246	489	8	numerical	numerical	ADJ
ejpam-5246	489	9	convergence	convergence	NOUN
ejpam-5246	489	10	of	of	ADP
ejpam-5246	489	11	the	the	DET
ejpam-5246	489	12	aforementioned	aforementioned	ADJ
ejpam-5246	489	13	schemes	scheme	NOUN
ejpam-5246	489	14	,	,	PUNCT
ejpam-5246	489	15	namely	namely	ADV
ejpam-5246	489	16	explicit	explicit	ADJ
ejpam-5246	489	17	euler	euler	NOUN
ejpam-5246	489	18	and	and	CCONJ
ejpam-5246	489	19	implicit	implicit	ADJ
ejpam-5246	489	20	euler	euler	NOUN
ejpam-5246	489	21	,	,	PUNCT
ejpam-5246	489	22	it	it	PRON
ejpam-5246	489	23	is	be	AUX
ejpam-5246	489	24	sufficient	sufficient	ADJ
ejpam-5246	489	25	to	to	PART
ejpam-5246	489	26	enhance	enhance	VERB
ejpam-5246	489	27	the	the	DET
ejpam-5246	489	28	space	space	NOUN
ejpam-5246	489	29	-	-	PUNCT
ejpam-5246	489	30	stepping	step	VERB
ejpam-5246	489	31	technique	technique	NOUN
ejpam-5246	489	32	in	in	ADP
ejpam-5246	489	33	order	order	NOUN
ejpam-5246	489	34	to	to	PART
ejpam-5246	489	35	calculate	calculate	VERB
ejpam-5246	489	36	the	the	DET
ejpam-5246	489	37	error	error	NOUN
ejpam-5246	489	38	boundaries	boundary	NOUN
ejpam-5246	489	39	and	and	CCONJ
ejpam-5246	489	40	numerical	numerical	ADJ
ejpam-5246	489	41	order	order	NOUN
ejpam-5246	489	42	of	of	ADP
ejpam-5246	489	43	convergence	convergence	NOUN
ejpam-5246	489	44	.	.	PUNCT
ejpam-5246	490	1	4	4	X
ejpam-5246	490	2	.	.	NOUN
ejpam-5246	490	3	numerical	numerical	ADJ
ejpam-5246	490	4	experiments	experiment	NOUN
ejpam-5246	490	5	in	in	ADP
ejpam-5246	490	6	this	this	DET
ejpam-5246	490	7	section	section	NOUN
ejpam-5246	490	8	,	,	PUNCT
ejpam-5246	490	9	we	we	PRON
ejpam-5246	490	10	present	present	VERB
ejpam-5246	490	11	an	an	DET
ejpam-5246	490	12	estimation	estimation	NOUN
ejpam-5246	490	13	of	of	ADP
ejpam-5246	490	14	the	the	DET
ejpam-5246	490	15	numerical	numerical	ADJ
ejpam-5246	490	16	blow	blow	VERB
ejpam-5246	490	17	-	-	PUNCT
ejpam-5246	490	18	up	up	ADP
ejpam-5246	490	19	times	time	NOUN
ejpam-5246	490	20	for	for	ADP
ejpam-5246	490	21	two	two	NUM
ejpam-5246	490	22	numerical	numerical	ADJ
ejpam-5246	490	23	experiments	experiment	NOUN
ejpam-5246	490	24	,	,	PUNCT
ejpam-5246	490	25	employing	employ	VERB
ejpam-5246	490	26	distinct	distinct	ADJ
ejpam-5246	490	27	space	space	NOUN
ejpam-5246	490	28	steps	step	NOUN
ejpam-5246	490	29	,	,	PUNCT
ejpam-5246	490	30	utilizing	utilize	VERB
ejpam-5246	490	31	the	the	DET
ejpam-5246	490	32	finite	finite	ADJ
ejpam-5246	490	33	difference	difference	NOUN
ejpam-5246	490	34	techniques	technique	NOUN
ejpam-5246	490	35	described	describe	VERB
ejpam-5246	490	36	in	in	ADP
ejpam-5246	490	37	this	this	DET
ejpam-5246	490	38	study	study	NOUN
ejpam-5246	490	39	,	,	PUNCT
ejpam-5246	490	40	namely	namely	ADV
ejpam-5246	490	41	explicit	explicit	ADJ
ejpam-5246	490	42	euler	euler	NOUN
ejpam-5246	490	43	and	and	CCONJ
ejpam-5246	490	44	implicit	implicit	ADJ
ejpam-5246	490	45	euler	euler	NOUN
ejpam-5246	490	46	.	.	PUNCT
ejpam-5246	491	1	the	the	DET
ejpam-5246	491	2	matlab	matlab	PROPN
ejpam-5246	491	3	(	(	PUNCT
ejpam-5246	491	4	r2020a	r2020a	NOUN
ejpam-5246	491	5	)	)	PUNCT
ejpam-5246	491	6	software	software	NOUN
ejpam-5246	491	7	is	be	AUX
ejpam-5246	491	8	used	use	VERB
ejpam-5246	491	9	to	to	PART
ejpam-5246	491	10	write	write	VERB
ejpam-5246	491	11	all	all	DET
ejpam-5246	491	12	the	the	DET
ejpam-5246	491	13	numerical	numerical	ADJ
ejpam-5246	491	14	computing	computing	NOUN
ejpam-5246	492	1	codes.we	codes.we	PUNCT
ejpam-5246	492	2	use	use	VERB
ejpam-5246	492	3	h	h	NOUN
ejpam-5246	492	4	to	to	PART
ejpam-5246	492	5	denote	denote	VERB
ejpam-5246	492	6	the	the	DET
ejpam-5246	492	7	spacestep	spacestep	NOUN
ejpam-5246	492	8	,	,	PUNCT
ejpam-5246	492	9	and	and	CCONJ
ejpam-5246	492	10	kn	kn	PROPN
ejpam-5246	492	11	.	.	PROPN
ejpam-5246	492	12	is	be	AUX
ejpam-5246	492	13	the	the	DET
ejpam-5246	492	14	time	time	NOUN
ejpam-5246	492	15	-	-	PUNCT
ejpam-5246	492	16	step	step	NOUN
ejpam-5246	492	17	,	,	PUNCT
ejpam-5246	492	18	h	h	NOUN
ejpam-5246	493	1	=	=	NOUN
ejpam-5246	493	2	1	1	NUM
ejpam-5246	493	3	i	i	PRON
ejpam-5246	493	4	.	.	PUNCT
ejpam-5246	494	1	furthermore	furthermore	ADV
ejpam-5246	494	2	,	,	PUNCT
ejpam-5246	494	3	we	we	PRON
ejpam-5246	494	4	assess	assess	VERB
ejpam-5246	494	5	the	the	DET
ejpam-5246	494	6	rate	rate	NOUN
ejpam-5246	494	7	at	at	ADP
ejpam-5246	494	8	which	which	PRON
ejpam-5246	494	9	the	the	DET
ejpam-5246	494	10	numerical	numerical	ADJ
ejpam-5246	494	11	blow	blow	VERB
ejpam-5246	494	12	-	-	PUNCT
ejpam-5246	494	13	up	up	ADP
ejpam-5246	494	14	time	time	NOUN
ejpam-5246	494	15	increases	increase	NOUN
ejpam-5246	494	16	for	for	ADP
ejpam-5246	494	17	each	each	PRON
ejpam-5246	494	18	of	of	ADP
ejpam-5246	494	19	these	these	DET
ejpam-5246	494	20	strategies	strategy	NOUN
ejpam-5246	494	21	.	.	PUNCT
ejpam-5246	495	1	the	the	DET
ejpam-5246	495	2	numerical	numerical	ADJ
ejpam-5246	495	3	blow	blow	VERB
ejpam-5246	495	4	-	-	PUNCT
ejpam-5246	495	5	up	up	ADP
ejpam-5246	495	6	time	time	NOUN
ejpam-5246	495	7	is	be	AUX
ejpam-5246	495	8	determined	determine	VERB
ejpam-5246	495	9	by	by	ADP
ejpam-5246	495	10	identifying	identify	VERB
ejpam-5246	495	11	a	a	DET
ejpam-5246	495	12	value	value	NOUN
ejpam-5246	495	13	of	of	ADP
ejpam-5246	495	14	m	m	PROPN
ejpam-5246	495	15	∈	∈	PROPN
ejpam-5246	495	16	n	n	PRON
ejpam-5246	495	17	such	such	ADJ
ejpam-5246	495	18	that	that	SCONJ
ejpam-5246	495	19	the	the	DET
ejpam-5246	495	20	condition:∥um	condition:∥um	ADJ
ejpam-5246	495	21	h	h	NOUN
ejpam-5246	495	22	∥∞	∥∞	PROPN
ejpam-5246	495	23	≥	≥	NUM
ejpam-5246	495	24	1015	1015	NUM
ejpam-5246	495	25	or	or	CCONJ
ejpam-5246	495	26	∥v	∥v	PROPN
ejpam-5246	495	27	n	n	PRON
ejpam-5246	495	28	h	h	NOUN
ejpam-5246	495	29	∥∞	∥∞	ADJ
ejpam-5246	495	30	≥	≥	NUM
ejpam-5246	495	31	1015	1015	NUM
ejpam-5246	495	32	holds	hold	NOUN
ejpam-5246	495	33	.	.	PUNCT
ejpam-5246	496	1	furthermore	furthermore	ADV
ejpam-5246	496	2	,	,	PUNCT
ejpam-5246	496	3	the	the	DET
ejpam-5246	496	4	numerical	numerical	ADJ
ejpam-5246	496	5	blow	blow	VERB
ejpam-5246	496	6	-	-	PUNCT
ejpam-5246	496	7	up	up	ADP
ejpam-5246	496	8	time	time	NOUN
ejpam-5246	496	9	to	to	ADP
ejpam-5246	496	10	the	the	DET
ejpam-5246	496	11	examined	examine	VERB
ejpam-5246	496	12	problem	problem	NOUN
ejpam-5246	496	13	is	be	AUX
ejpam-5246	496	14	denoted	denote	VERB
ejpam-5246	496	15	as	as	ADP
ejpam-5246	496	16	th	th	X
ejpam-5246	496	17	=	=	PUNCT
ejpam-5246	496	18	tm	tm	NOUN
ejpam-5246	496	19	=	=	PROPN
ejpam-5246	496	20	∑m	∑m	PROPN
ejpam-5246	496	21	n=0	n=0	PUNCT
ejpam-5246	497	1	kn	kn	NOUN
ejpam-5246	497	2	the	the	DET
ejpam-5246	497	3	error	error	NOUN
ejpam-5246	497	4	bounds	bound	NOUN
ejpam-5246	497	5	between	between	ADP
ejpam-5246	497	6	t2h	t2h	PROPN
ejpam-5246	497	7	and	and	CCONJ
ejpam-5246	497	8	th	th	NOUN
ejpam-5246	497	9	are	be	AUX
ejpam-5246	497	10	denoted	denote	VERB
ejpam-5246	497	11	as	as	ADP
ejpam-5246	497	12	.	.	PUNCT
ejpam-5246	498	1	eh	eh	INTJ
ejpam-5246	498	2	=	=	SYM
ejpam-5246	498	3	|t2h	|t2h	NOUN
ejpam-5246	498	4	−	−	PROPN
ejpam-5246	498	5	th|	th|	PROPN
ejpam-5246	498	6	,	,	PUNCT
ejpam-5246	498	7	.the	.the	PROPN
ejpam-5246	498	8	numerical	numerical	PROPN
ejpam-5246	498	9	results	result	NOUN
ejpam-5246	498	10	obtained	obtain	VERB
ejpam-5246	498	11	using	use	VERB
ejpam-5246	498	12	the	the	DET
ejpam-5246	498	13	suggested	suggest	VERB
ejpam-5246	498	14	schemes	scheme	NOUN
ejpam-5246	498	15	(	(	PUNCT
ejpam-5246	498	16	explicit	explicit	ADJ
ejpam-5246	498	17	euler	euler	NOUN
ejpam-5246	498	18	and	and	CCONJ
ejpam-5246	498	19	implicit	implicit	ADJ
ejpam-5246	498	20	euler	euler	NOUN
ejpam-5246	498	21	)	)	PUNCT
ejpam-5246	498	22	are	be	AUX
ejpam-5246	498	23	presented	present	VERB
ejpam-5246	498	24	in	in	ADP
ejpam-5246	498	25	tables	table	NOUN
ejpam-5246	498	26	for	for	ADP
ejpam-5246	498	27	each	each	DET
ejpam-5246	498	28	case	case	NOUN
ejpam-5246	498	29	.	.	PUNCT
ejpam-5246	499	1	the	the	DET
ejpam-5246	499	2	mesh	mesh	NOUN
ejpam-5246	499	3	sizes	size	NOUN
ejpam-5246	499	4	used	use	VERB
ejpam-5246	499	5	are	be	AUX
ejpam-5246	499	6	i	i	PRON
ejpam-5246	499	7	=	=	PUNCT
ejpam-5246	499	8	{	{	PUNCT
ejpam-5246	499	9	20	20	NUM
ejpam-5246	499	10	,	,	PUNCT
ejpam-5246	499	11	40	40	NUM
ejpam-5246	499	12	,	,	PUNCT
ejpam-5246	499	13	80	80	NUM
ejpam-5246	499	14	,	,	PUNCT
ejpam-5246	499	15	160	160	NUM
ejpam-5246	499	16	,	,	PUNCT
ejpam-5246	499	17	320	320	NUM
ejpam-5246	499	18	}	}	PUNCT
ejpam-5246	499	19	,	,	PUNCT
ejpam-5246	499	20	the	the	DET
ejpam-5246	499	21	tables	table	NOUN
ejpam-5246	499	22	display	display	VERB
ejpam-5246	499	23	the	the	DET
ejpam-5246	499	24	iteration	iteration	NOUN
ejpam-5246	499	25	count	count	NOUN
ejpam-5246	499	26	,	,	PUNCT
ejpam-5246	499	27	occurrence	occurrence	NOUN
ejpam-5246	499	28	of	of	ADP
ejpam-5246	499	29	numerical	numerical	ADJ
ejpam-5246	499	30	blow	blow	NOUN
ejpam-5246	499	31	-	-	PUNCT
ejpam-5246	499	32	up	up	NOUN
ejpam-5246	499	33	,	,	PUNCT
ejpam-5246	499	34	numerical	numerical	ADJ
ejpam-5246	499	35	blow	blow	NOUN
ejpam-5246	499	36	-	-	PUNCT
ejpam-5246	499	37	up	up	ADP
ejpam-5246	499	38	durations	duration	NOUN
ejpam-5246	499	39	,	,	PUNCT
ejpam-5246	499	40	central	central	ADJ
ejpam-5246	499	41	processing	processing	NOUN
ejpam-5246	499	42	unit	unit	NOUN
ejpam-5246	499	43	(	(	PUNCT
ejpam-5246	499	44	cput	cput	NOUN
ejpam-5246	499	45	)	)	PUNCT
ejpam-5246	499	46	durations	duration	NOUN
ejpam-5246	499	47	in	in	ADP
ejpam-5246	499	48	seconds	second	NOUN
ejpam-5246	499	49	,	,	PUNCT
ejpam-5246	499	50	and	and	CCONJ
ejpam-5246	499	51	the	the	DET
ejpam-5246	499	52	error	error	NOUN
ejpam-5246	499	53	limits	limit	NOUN
ejpam-5246	499	54	of	of	ADP
ejpam-5246	499	55	numerical	numerical	ADJ
ejpam-5246	499	56	blow	blow	NOUN
ejpam-5246	499	57	-	-	PUNCT
ejpam-5246	499	58	up	up	ADP
ejpam-5246	499	59	durations	duration	NOUN
ejpam-5246	499	60	.	.	PUNCT
ejpam-5246	500	1	in	in	ADP
ejpam-5246	500	2	order	order	NOUN
ejpam-5246	500	3	to	to	PART
ejpam-5246	500	4	empirically	empirically	ADV
ejpam-5246	500	5	investigate	investigate	VERB
ejpam-5246	500	6	the	the	DET
ejpam-5246	500	7	rate	rate	NOUN
ejpam-5246	500	8	of	of	ADP
ejpam-5246	500	9	numerical	numerical	ADJ
ejpam-5246	500	10	convergence	convergence	NOUN
ejpam-5246	500	11	for	for	ADP
ejpam-5246	500	12	numerical	numerical	ADJ
ejpam-5246	500	13	blow	blow	NOUN
ejpam-5246	500	14	-	-	PUNCT
ejpam-5246	500	15	up	up	ADP
ejpam-5246	500	16	durations	duration	NOUN
ejpam-5246	500	17	,	,	PUNCT
ejpam-5246	500	18	it	it	PRON
ejpam-5246	500	19	is	be	AUX
ejpam-5246	500	20	necessary	necessary	ADJ
ejpam-5246	500	21	to	to	PART
ejpam-5246	500	22	consider	consider	VERB
ejpam-5246	500	23	various	various	ADJ
ejpam-5246	500	24	mesh	mesh	NOUN
ejpam-5246	500	25	sizes	size	NOUN
ejpam-5246	500	26	with	with	ADP
ejpam-5246	500	27	specific	specific	ADJ
ejpam-5246	500	28	values	value	NOUN
ejpam-5246	500	29	ofα	ofα	ADJ
ejpam-5246	500	30	,	,	PUNCT
ejpam-5246	500	31	the	the	DET
ejpam-5246	500	32	formula	formula	NOUN
ejpam-5246	500	33	employed	employ	VERB
ejpam-5246	500	34	for	for	ADP
ejpam-5246	500	35	this	this	DET
ejpam-5246	500	36	purpose	purpose	NOUN
ejpam-5246	500	37	is	be	AUX
ejpam-5246	500	38	sh	sh	PROPN
ejpam-5246	500	39	=	=	PUNCT
ejpam-5246	500	40	log(e2h	log(e2h	PROPN
ejpam-5246	500	41	/	/	SYM
ejpam-5246	500	42	eh	eh	INTJ
ejpam-5246	500	43	)	)	PUNCT
ejpam-5246	500	44	log	log	NOUN
ejpam-5246	500	45	2	2	NUM
ejpam-5246	500	46	.	.	PUNCT
ejpam-5246	501	1	in	in	ADP
ejpam-5246	501	2	addition	addition	NOUN
ejpam-5246	501	3	,	,	PUNCT
ejpam-5246	501	4	numerical	numerical	ADJ
ejpam-5246	501	5	simulations	simulation	NOUN
ejpam-5246	501	6	are	be	AUX
ejpam-5246	501	7	conducted	conduct	VERB
ejpam-5246	501	8	to	to	PART
ejpam-5246	501	9	corroborate	corroborate	VERB
ejpam-5246	501	10	the	the	DET
ejpam-5246	501	11	numerical	numerical	ADJ
ejpam-5246	501	12	findings	finding	NOUN
ejpam-5246	501	13	.	.	PUNCT
ejpam-5246	502	1	m.i.khalil	m.i.khalil	PROPN
ejpam-5246	502	2	et	et	PROPN
ejpam-5246	502	3	al	al	PROPN
ejpam-5246	502	4	.	.	PUNCT
ejpam-5246	502	5	/	/	SYM
ejpam-5246	502	6	eur	eur	PROPN
ejpam-5246	502	7	.	.	PUNCT
ejpam-5246	503	1	j.	j.	PROPN
ejpam-5246	503	2	pure	pure	PROPN
ejpam-5246	503	3	appl	appl	PROPN
ejpam-5246	503	4	.	.	PROPN
ejpam-5246	503	5	math	math	PROPN
ejpam-5246	503	6	,	,	PUNCT
ejpam-5246	503	7	17	17	NUM
ejpam-5246	503	8	(	(	PUNCT
ejpam-5246	503	9	3	3	NUM
ejpam-5246	503	10	)	)	PUNCT
ejpam-5246	503	11	(	(	PUNCT
ejpam-5246	503	12	2024	2024	NUM
ejpam-5246	503	13	)	)	PUNCT
ejpam-5246	503	14	,	,	PUNCT
ejpam-5246	503	15	1516	1516	NUM
ejpam-5246	503	16	-	-	SYM
ejpam-5246	503	17	1538	1538	NUM
ejpam-5246	503	18	1531	1531	NUM
ejpam-5246	503	19	4.1	4.1	NUM
ejpam-5246	503	20	.	.	PUNCT
ejpam-5246	504	1	numerical	numerical	ADJ
ejpam-5246	504	2	experiments	experiment	NOUN
ejpam-5246	504	3	example	example	VERB
ejpam-5246	504	4	1	1	NUM
ejpam-5246	504	5	.	.	PUNCT
ejpam-5246	504	6	ut	ut	PROPN
ejpam-5246	504	7	=	=	PROPN
ejpam-5246	504	8	uxx	uxx	PROPN
ejpam-5246	505	1	+	+	CCONJ
ejpam-5246	505	2	v5	v5	PROPN
ejpam-5246	505	3	−	−	PROPN
ejpam-5246	505	4	|ux|1.6	|ux|1.6	PROPN
ejpam-5246	505	5	,	,	PUNCT
ejpam-5246	505	6	vt	vt	PROPN
ejpam-5246	505	7	=	=	SYM
ejpam-5246	505	8	vxx	vxx	PROPN
ejpam-5246	505	9	+	+	NUM
ejpam-5246	505	10	u6	u6	PROPN
ejpam-5246	505	11	−	−	PROPN
ejpam-5246	505	12	|vx|1.6	|vx|1.6	PROPN
ejpam-5246	505	13	,	,	PUNCT
ejpam-5246	505	14	x	x	SYM
ejpam-5246	505	15	∈	∈	PROPN
ejpam-5246	505	16	(	(	PUNCT
ejpam-5246	505	17	0	0	NUM
ejpam-5246	505	18	,	,	PUNCT
ejpam-5246	505	19	1	1	NUM
ejpam-5246	505	20	)	)	PUNCT
ejpam-5246	505	21	,	,	PUNCT
ejpam-5246	505	22	t	t	PROPN
ejpam-5246	505	23	∈	∈	PROPN
ejpam-5246	505	24	(	(	PUNCT
ejpam-5246	505	25	0	0	NUM
ejpam-5246	505	26	,	,	PUNCT
ejpam-5246	505	27	t	t	NOUN
ejpam-5246	505	28	)	)	PUNCT
ejpam-5246	505	29	,	,	PUNCT
ejpam-5246	505	30	u(0	u(0	PROPN
ejpam-5246	505	31	,	,	PUNCT
ejpam-5246	505	32	t	t	PROPN
ejpam-5246	505	33	)	)	PUNCT
ejpam-5246	505	34	=	=	SYM
ejpam-5246	506	1	u(1	u(1	PROPN
ejpam-5246	506	2	,	,	PUNCT
ejpam-5246	506	3	t	t	PROPN
ejpam-5246	506	4	)	)	PUNCT
ejpam-5246	506	5	=	=	SYM
ejpam-5246	506	6	0	0	NUM
ejpam-5246	506	7	,	,	PUNCT
ejpam-5246	506	8	v(0	v(0	PROPN
ejpam-5246	506	9	,	,	PUNCT
ejpam-5246	506	10	t	t	PROPN
ejpam-5246	506	11	)	)	PUNCT
ejpam-5246	506	12	=	=	SYM
ejpam-5246	507	1	v(1	v(1	PROPN
ejpam-5246	507	2	,	,	PUNCT
ejpam-5246	507	3	t	t	PROPN
ejpam-5246	507	4	)	)	PUNCT
ejpam-5246	507	5	=	=	SYM
ejpam-5246	507	6	0	0	NUM
ejpam-5246	507	7	,	,	PUNCT
ejpam-5246	507	8	t	t	PROPN
ejpam-5246	507	9	∈	∈	PROPN
ejpam-5246	507	10	(	(	PUNCT
ejpam-5246	507	11	0	0	NUM
ejpam-5246	507	12	,	,	PUNCT
ejpam-5246	507	13	t	t	NOUN
ejpam-5246	507	14	)	)	PUNCT
ejpam-5246	507	15	,	,	PUNCT
ejpam-5246	507	16	u(x	u(x	NOUN
ejpam-5246	507	17	,	,	PUNCT
ejpam-5246	507	18	0	0	NUM
ejpam-5246	507	19	)	)	PUNCT
ejpam-5246	507	20	=	=	SYM
ejpam-5246	507	21	80	80	NUM
ejpam-5246	507	22	(	(	PUNCT
ejpam-5246	507	23	x−	x−	PROPN
ejpam-5246	507	24	x2	x2	PROPN
ejpam-5246	507	25	)	)	PUNCT
ejpam-5246	507	26	,	,	PUNCT
ejpam-5246	507	27	v(x	v(x	PROPN
ejpam-5246	507	28	,	,	PUNCT
ejpam-5246	507	29	0	0	NUM
ejpam-5246	507	30	)	)	PUNCT
ejpam-5246	507	31	=	=	SYM
ejpam-5246	508	1	90	90	NUM
ejpam-5246	508	2	(	(	PUNCT
ejpam-5246	508	3	x−	x−	PROPN
ejpam-5246	508	4	x2	x2	PROPN
ejpam-5246	508	5	)	)	PUNCT
ejpam-5246	508	6	,	,	PUNCT
ejpam-5246	508	7	x	x	PUNCT
ejpam-5246	508	8	∈	∈	PROPN
ejpam-5246	508	9	(	(	PUNCT
ejpam-5246	508	10	0	0	NUM
ejpam-5246	508	11	,	,	PUNCT
ejpam-5246	508	12	1	1	NUM
ejpam-5246	508	13	)	)	PUNCT
ejpam-5246	508	14	.	.	PUNCT
ejpam-5246	509	1			NOUN
ejpam-5246	509	2	(	(	PUNCT
ejpam-5246	509	3	4.1	4.1	NUM
ejpam-5246	509	4	)	)	PUNCT
ejpam-5246	509	5	example	example	NOUN
ejpam-5246	509	6	2	2	NUM
ejpam-5246	509	7	.	.	PUNCT
ejpam-5246	509	8	ut	ut	PROPN
ejpam-5246	509	9	=	=	PROPN
ejpam-5246	509	10	uxx	uxx	PROPN
ejpam-5246	509	11	+	+	CCONJ
ejpam-5246	509	12	v3	v3	PROPN
ejpam-5246	509	13	−	−	PROPN
ejpam-5246	509	14	|ux|1.1	|ux|1.1	NOUN
ejpam-5246	509	15	,	,	PUNCT
ejpam-5246	509	16	vt	vt	PROPN
ejpam-5246	509	17	=	=	SYM
ejpam-5246	509	18	vxx	vxx	PROPN
ejpam-5246	510	1	+	+	CCONJ
ejpam-5246	510	2	u4	u4	PROPN
ejpam-5246	510	3	−	−	PROPN
ejpam-5246	510	4	|vx|1.2	|vx|1.2	NOUN
ejpam-5246	510	5	,	,	PUNCT
ejpam-5246	510	6	x	x	SYM
ejpam-5246	510	7	∈	∈	PROPN
ejpam-5246	510	8	(	(	PUNCT
ejpam-5246	510	9	0	0	NUM
ejpam-5246	510	10	,	,	PUNCT
ejpam-5246	510	11	1	1	NUM
ejpam-5246	510	12	)	)	PUNCT
ejpam-5246	510	13	,	,	PUNCT
ejpam-5246	510	14	t	t	PROPN
ejpam-5246	510	15	∈	∈	PROPN
ejpam-5246	510	16	(	(	PUNCT
ejpam-5246	510	17	0	0	NUM
ejpam-5246	510	18	,	,	PUNCT
ejpam-5246	510	19	t	t	NOUN
ejpam-5246	510	20	)	)	PUNCT
ejpam-5246	510	21	,	,	PUNCT
ejpam-5246	510	22	u(0	u(0	PROPN
ejpam-5246	510	23	,	,	PUNCT
ejpam-5246	510	24	t	t	PROPN
ejpam-5246	510	25	)	)	PUNCT
ejpam-5246	510	26	=	=	SYM
ejpam-5246	511	1	u(1	u(1	PROPN
ejpam-5246	511	2	,	,	PUNCT
ejpam-5246	511	3	t	t	PROPN
ejpam-5246	511	4	)	)	PUNCT
ejpam-5246	511	5	=	=	SYM
ejpam-5246	511	6	0	0	NUM
ejpam-5246	511	7	,	,	PUNCT
ejpam-5246	511	8	v(0	v(0	PROPN
ejpam-5246	511	9	,	,	PUNCT
ejpam-5246	511	10	t	t	PROPN
ejpam-5246	511	11	)	)	PUNCT
ejpam-5246	511	12	=	=	SYM
ejpam-5246	512	1	v(1	v(1	PROPN
ejpam-5246	512	2	,	,	PUNCT
ejpam-5246	512	3	t	t	PROPN
ejpam-5246	512	4	)	)	PUNCT
ejpam-5246	512	5	=	=	SYM
ejpam-5246	512	6	0	0	NUM
ejpam-5246	512	7	,	,	PUNCT
ejpam-5246	512	8	t	t	PROPN
ejpam-5246	512	9	∈	∈	PROPN
ejpam-5246	512	10	(	(	PUNCT
ejpam-5246	512	11	0	0	NUM
ejpam-5246	512	12	,	,	PUNCT
ejpam-5246	512	13	t	t	NOUN
ejpam-5246	512	14	)	)	PUNCT
ejpam-5246	512	15	,	,	PUNCT
ejpam-5246	512	16	u(x	u(x	NOUN
ejpam-5246	512	17	,	,	PUNCT
ejpam-5246	512	18	0	0	NUM
ejpam-5246	512	19	)	)	PUNCT
ejpam-5246	512	20	=	=	SYM
ejpam-5246	512	21	100(sinπx	100(sinπx	NUM
ejpam-5246	512	22	)	)	PUNCT
ejpam-5246	512	23	,	,	PUNCT
ejpam-5246	512	24	v(x	v(x	PROPN
ejpam-5246	512	25	,	,	PUNCT
ejpam-5246	512	26	0	0	NUM
ejpam-5246	512	27	)	)	PUNCT
ejpam-5246	512	28	=	=	NOUN
ejpam-5246	512	29	90(sinπx	90(sinπx	NUM
ejpam-5246	512	30	)	)	PUNCT
ejpam-5246	512	31	,	,	PUNCT
ejpam-5246	512	32	x	x	PUNCT
ejpam-5246	512	33	∈	∈	PROPN
ejpam-5246	512	34	(	(	PUNCT
ejpam-5246	512	35	0	0	NUM
ejpam-5246	512	36	,	,	PUNCT
ejpam-5246	512	37	1	1	NUM
ejpam-5246	512	38	)	)	PUNCT
ejpam-5246	512	39	.	.	PUNCT
ejpam-5246	513	1			PROPN
ejpam-5246	513	2	(	(	PUNCT
ejpam-5246	513	3	4.2	4.2	NUM
ejpam-5246	513	4	)	)	PUNCT
ejpam-5246	513	5	m.i.khalil	m.i.khalil	NOUN
ejpam-5246	513	6	et	et	PROPN
ejpam-5246	513	7	al	al	PROPN
ejpam-5246	513	8	.	.	PUNCT
ejpam-5246	513	9	/	/	SYM
ejpam-5246	513	10	eur	eur	PROPN
ejpam-5246	513	11	.	.	PUNCT
ejpam-5246	514	1	j.	j.	PROPN
ejpam-5246	514	2	pure	pure	PROPN
ejpam-5246	514	3	appl	appl	PROPN
ejpam-5246	514	4	.	.	PROPN
ejpam-5246	514	5	math	math	PROPN
ejpam-5246	514	6	,	,	PUNCT
ejpam-5246	514	7	17	17	NUM
ejpam-5246	514	8	(	(	PUNCT
ejpam-5246	514	9	3	3	NUM
ejpam-5246	514	10	)	)	PUNCT
ejpam-5246	514	11	(	(	PUNCT
ejpam-5246	514	12	2024	2024	NUM
ejpam-5246	514	13	)	)	PUNCT
ejpam-5246	514	14	,	,	PUNCT
ejpam-5246	514	15	1516	1516	NUM
ejpam-5246	514	16	-	-	SYM
ejpam-5246	514	17	1538	1538	NUM
ejpam-5246	514	18	1532	1532	NUM
ejpam-5246	514	19	table	table	NOUN
ejpam-5246	514	20	1	1	NUM
ejpam-5246	514	21	:	:	PUNCT
ejpam-5246	514	22	example	example	NOUN
ejpam-5246	514	23	1	1	NUM
ejpam-5246	514	24	,	,	PUNCT
ejpam-5246	514	25	explicit	explicit	ADJ
ejpam-5246	514	26	formula	formula	NOUN
ejpam-5246	514	27	,	,	PUNCT
ejpam-5246	514	28	α	α	NOUN
ejpam-5246	514	29	=	=	SYM
ejpam-5246	514	30	1	1	NUM
ejpam-5246	514	31	h	h	NOUN
ejpam-5246	514	32	m	m	VERB
ejpam-5246	514	33	th	th	INTJ
ejpam-5246	514	34	cput	cput	ADJ
ejpam-5246	514	35	eh	eh	INTJ
ejpam-5246	514	36	sh	sh	PROPN
ejpam-5246	514	37	1/20	1/20	NUM
ejpam-5246	514	38	3	3	NUM
ejpam-5246	514	39	6.81e-04	6.81e-04	NUM
ejpam-5246	514	40	0.088252	0.088252	NUM
ejpam-5246	514	41	·	·	PUNCT
ejpam-5246	514	42	·	·	PUNCT
ejpam-5246	514	43	·	·	PUNCT
ejpam-5246	514	44	·	·	PUNCT
ejpam-5246	514	45	·	·	PUNCT
ejpam-5246	514	46	·	·	PUNCT
ejpam-5246	515	1	1/40	1/40	NUM
ejpam-5246	515	2	4	4	NUM
ejpam-5246	515	3	2.09e-04	2.09e-04	NUM
ejpam-5246	515	4	0.082713	0.082713	NUM
ejpam-5246	515	5	4.72e-04	4.72e-04	NUM
ejpam-5246	515	6	·	·	PUNCT
ejpam-5246	515	7	·	·	PUNCT
ejpam-5246	515	8	·	·	PUNCT
ejpam-5246	516	1	1/80	1/80	NUM
ejpam-5246	516	2	4	4	NUM
ejpam-5246	516	3	5.29e-05	5.29e-05	NUM
ejpam-5246	516	4	0.127637	0.127637	NUM
ejpam-5246	516	5	1.56e-04	1.56e-04	NUM
ejpam-5246	516	6	1.5971	1.5971	NUM
ejpam-5246	516	7	1/160	1/160	NUM
ejpam-5246	516	8	4	4	NUM
ejpam-5246	516	9	1.42e-05	1.42e-05	NUM
ejpam-5246	516	10	0.154282	0.154282	NUM
ejpam-5246	516	11	3.87e-05	3.87e-05	NUM
ejpam-5246	516	12	2.0095	2.0095	NUM
ejpam-5246	516	13	1/320	1/320	NUM
ejpam-5246	516	14	4	4	NUM
ejpam-5246	516	15	4.73e-06	4.73e-06	NUM
ejpam-5246	516	16	0.261390	0.261390	NUM
ejpam-5246	516	17	9.44e-06	9.44e-06	NUM
ejpam-5246	516	18	2.0372	2.0372	NUM
ejpam-5246	516	19	table	table	NOUN
ejpam-5246	516	20	2	2	NUM
ejpam-5246	516	21	:	:	PUNCT
ejpam-5246	516	22	example	example	NOUN
ejpam-5246	516	23	1	1	NUM
ejpam-5246	516	24	,	,	PUNCT
ejpam-5246	516	25	explicit	explicit	ADJ
ejpam-5246	516	26	formula	formula	NOUN
ejpam-5246	516	27	,	,	PUNCT
ejpam-5246	516	28	α	α	NOUN
ejpam-5246	516	29	=	=	SYM
ejpam-5246	516	30	2	2	NUM
ejpam-5246	516	31	h	h	NOUN
ejpam-5246	516	32	m	m	VERB
ejpam-5246	516	33	th	th	INTJ
ejpam-5246	516	34	cput	cput	ADJ
ejpam-5246	516	35	eh	eh	INTJ
ejpam-5246	516	36	sh	sh	PROPN
ejpam-5246	516	37	1/20	1/20	NUM
ejpam-5246	516	38	4	4	NUM
ejpam-5246	516	39	3.45e-05	3.45e-05	NUM
ejpam-5246	516	40	0.096988	0.096988	NUM
ejpam-5246	516	41	·	·	PUNCT
ejpam-5246	516	42	·	·	PUNCT
ejpam-5246	516	43	·	·	PUNCT
ejpam-5246	516	44	·	·	PUNCT
ejpam-5246	516	45	·	·	PUNCT
ejpam-5246	516	46	·	·	PUNCT
ejpam-5246	517	1	1/40	1/40	NUM
ejpam-5246	517	2	4	4	NUM
ejpam-5246	517	3	6.49e-06	6.49e-06	NUM
ejpam-5246	517	4	0.081515	0.081515	NUM
ejpam-5246	517	5	2.80e-05	2.80e-05	NUM
ejpam-5246	517	6	·	·	PUNCT
ejpam-5246	517	7	·	·	PUNCT
ejpam-5246	517	8	·	·	PUNCT
ejpam-5246	518	1	1/80	1/80	NUM
ejpam-5246	518	2	5	5	NUM
ejpam-5246	518	3	1.44e-06	1.44e-06	NUM
ejpam-5246	518	4	0.104819	0.104819	NUM
ejpam-5246	518	5	5.05e-06	5.05e-06	NUM
ejpam-5246	518	6	2.4727	2.4727	NUM
ejpam-5246	518	7	1/160	1/160	NUM
ejpam-5246	518	8	7	7	NUM
ejpam-5246	518	9	5.16e-07	5.16e-07	NUM
ejpam-5246	518	10	0.151543	0.151543	NUM
ejpam-5246	518	11	9.26e-07	9.26e-07	NUM
ejpam-5246	518	12	2.4473	2.4473	NUM
ejpam-5246	518	13	1/320	1/320	NUM
ejpam-5246	518	14	15	15	NUM
ejpam-5246	518	15	2.88e-07	2.88e-07	NUM
ejpam-5246	518	16	0.486987	0.486987	NUM
ejpam-5246	518	17	2.28e-07	2.28e-07	NUM
ejpam-5246	518	18	2.0231	2.0231	NUM
ejpam-5246	518	19	table	table	NOUN
ejpam-5246	518	20	3	3	NUM
ejpam-5246	518	21	:	:	PUNCT
ejpam-5246	518	22	example	example	NOUN
ejpam-5246	518	23	1	1	NUM
ejpam-5246	518	24	,	,	PUNCT
ejpam-5246	518	25	implicit	implicit	ADJ
ejpam-5246	518	26	formula	formula	NOUN
ejpam-5246	518	27	,	,	PUNCT
ejpam-5246	518	28	α	α	NOUN
ejpam-5246	518	29	=	=	SYM
ejpam-5246	518	30	1	1	NUM
ejpam-5246	518	31	h	h	NOUN
ejpam-5246	518	32	m	m	VERB
ejpam-5246	518	33	th	th	INTJ
ejpam-5246	518	34	cput	cput	ADJ
ejpam-5246	518	35	eh	eh	INTJ
ejpam-5246	518	36	sh	sh	PROPN
ejpam-5246	518	37	1/20	1/20	NUM
ejpam-5246	518	38	3	3	NUM
ejpam-5246	518	39	6.81e-04	6.81e-04	NUM
ejpam-5246	518	40	0.333453	0.333453	NUM
ejpam-5246	518	41	·	·	PUNCT
ejpam-5246	518	42	·	·	PUNCT
ejpam-5246	518	43	·	·	PUNCT
ejpam-5246	518	44	·	·	PUNCT
ejpam-5246	518	45	·	·	PUNCT
ejpam-5246	518	46	·	·	PUNCT
ejpam-5246	519	1	1/40	1/40	NUM
ejpam-5246	519	2	4	4	NUM
ejpam-5246	519	3	2.09e-04	2.09e-04	NUM
ejpam-5246	519	4	0.242359	0.242359	NUM
ejpam-5246	519	5	4.72e-04	4.72e-04	NUM
ejpam-5246	519	6	·	·	PUNCT
ejpam-5246	519	7	·	·	PUNCT
ejpam-5246	519	8	·	·	PUNCT
ejpam-5246	520	1	1/80	1/80	NUM
ejpam-5246	520	2	4	4	NUM
ejpam-5246	520	3	5.29e-05	5.29e-05	NUM
ejpam-5246	520	4	0.447964	0.447964	NUM
ejpam-5246	520	5	1.56e-04	1.56e-04	NUM
ejpam-5246	520	6	1.5972	1.5972	NUM
ejpam-5246	520	7	1/160	1/160	NUM
ejpam-5246	520	8	4	4	NUM
ejpam-5246	520	9	1.42e-05	1.42e-05	NUM
ejpam-5246	520	10	1.003357	1.003357	NUM
ejpam-5246	520	11	3.87e-05	3.87e-05	NUM
ejpam-5246	520	12	2.0094	2.0094	NUM
ejpam-5246	520	13	1/320	1/320	NUM
ejpam-5246	520	14	5	5	NUM
ejpam-5246	520	15	4.73e-06	4.73e-06	NUM
ejpam-5246	520	16	2.699985	2.699985	NUM
ejpam-5246	520	17	9.44e-06	9.44e-06	NUM
ejpam-5246	520	18	2.0373	2.0373	NUM
ejpam-5246	520	19	m.i.khalil	m.i.khalil	NOUN
ejpam-5246	520	20	et	et	PROPN
ejpam-5246	520	21	al	al	PROPN
ejpam-5246	520	22	.	.	PUNCT
ejpam-5246	520	23	/	/	SYM
ejpam-5246	520	24	eur	eur	PROPN
ejpam-5246	520	25	.	.	PUNCT
ejpam-5246	521	1	j.	j.	PROPN
ejpam-5246	521	2	pure	pure	PROPN
ejpam-5246	521	3	appl	appl	PROPN
ejpam-5246	521	4	.	.	PROPN
ejpam-5246	521	5	math	math	PROPN
ejpam-5246	521	6	,	,	PUNCT
ejpam-5246	521	7	17	17	NUM
ejpam-5246	521	8	(	(	PUNCT
ejpam-5246	521	9	3	3	NUM
ejpam-5246	521	10	)	)	PUNCT
ejpam-5246	521	11	(	(	PUNCT
ejpam-5246	521	12	2024	2024	NUM
ejpam-5246	521	13	)	)	PUNCT
ejpam-5246	521	14	,	,	PUNCT
ejpam-5246	521	15	1516	1516	NUM
ejpam-5246	521	16	-	-	SYM
ejpam-5246	521	17	1538	1538	NUM
ejpam-5246	521	18	1533	1533	NUM
ejpam-5246	521	19	table	table	NOUN
ejpam-5246	521	20	4	4	NUM
ejpam-5246	521	21	:	:	PUNCT
ejpam-5246	521	22	example	example	NOUN
ejpam-5246	521	23	1	1	NUM
ejpam-5246	521	24	,	,	PUNCT
ejpam-5246	521	25	implicit	implicit	ADJ
ejpam-5246	521	26	formula	formula	NOUN
ejpam-5246	521	27	,	,	PUNCT
ejpam-5246	521	28	α	α	NOUN
ejpam-5246	521	29	=	=	SYM
ejpam-5246	521	30	2	2	NUM
ejpam-5246	521	31	h	h	NOUN
ejpam-5246	521	32	m	m	VERB
ejpam-5246	521	33	th	th	INTJ
ejpam-5246	521	34	cput	cput	ADJ
ejpam-5246	522	1	eh	eh	INTJ
ejpam-5246	522	2	sh	sh	PROPN
ejpam-5246	522	3	1/20	1/20	NUM
ejpam-5246	522	4	4	4	NUM
ejpam-5246	522	5	3.45e-05	3.45e-05	NUM
ejpam-5246	522	6	0.202292	0.202292	NUM
ejpam-5246	522	7	·	·	PUNCT
ejpam-5246	522	8	·	·	PUNCT
ejpam-5246	522	9	·	·	PUNCT
ejpam-5246	522	10	·	·	PUNCT
ejpam-5246	522	11	·	·	PUNCT
ejpam-5246	522	12	·	·	PUNCT
ejpam-5246	522	13	1/40	1/40	NUM
ejpam-5246	522	14	4	4	NUM
ejpam-5246	522	15	6.49e-06	6.49e-06	NUM
ejpam-5246	522	16	0.219009	0.219009	NUM
ejpam-5246	522	17	2.80e-05	2.80e-05	NUM
ejpam-5246	522	18	·	·	PUNCT
ejpam-5246	522	19	·	·	PUNCT
ejpam-5246	522	20	·	·	PUNCT
ejpam-5246	523	1	1/80	1/80	NUM
ejpam-5246	523	2	5	5	NUM
ejpam-5246	523	3	1.44e-06	1.44e-06	NUM
ejpam-5246	523	4	0.259753	0.259753	NUM
ejpam-5246	523	5	5.05e-06	5.05e-06	NUM
ejpam-5246	523	6	2.4727	2.4727	NUM
ejpam-5246	523	7	1/160	1/160	NUM
ejpam-5246	523	8	7	7	NUM
ejpam-5246	523	9	5.16e-07	5.16e-07	NUM
ejpam-5246	523	10	0.847733	0.847733	NUM
ejpam-5246	523	11	9.26e-07	9.26e-07	NUM
ejpam-5246	523	12	2.4473	2.4473	NUM
ejpam-5246	523	13	1/320	1/320	NUM
ejpam-5246	523	14	15	15	NUM
ejpam-5246	523	15	2.88e-07	2.88e-07	NUM
ejpam-5246	523	16	2.355910	2.355910	NUM
ejpam-5246	523	17	2.28e-07	2.28e-07	NUM
ejpam-5246	523	18	2.0231	2.0231	NUM
ejpam-5246	523	19	table	table	NOUN
ejpam-5246	523	20	5	5	NUM
ejpam-5246	523	21	:	:	PUNCT
ejpam-5246	523	22	example	example	NOUN
ejpam-5246	523	23	2	2	NUM
ejpam-5246	523	24	,	,	PUNCT
ejpam-5246	523	25	explicit	explicit	ADJ
ejpam-5246	523	26	formula	formula	NOUN
ejpam-5246	523	27	,	,	PUNCT
ejpam-5246	523	28	α	α	NOUN
ejpam-5246	523	29	=	=	SYM
ejpam-5246	523	30	1	1	NUM
ejpam-5246	523	31	h	h	NOUN
ejpam-5246	523	32	m	m	VERB
ejpam-5246	523	33	th	th	INTJ
ejpam-5246	523	34	cput	cput	ADJ
ejpam-5246	523	35	eh	eh	INTJ
ejpam-5246	523	36	sh	sh	PROPN
ejpam-5246	523	37	1/20	1/20	NUM
ejpam-5246	523	38	4	4	NUM
ejpam-5246	523	39	1.59e-04	1.59e-04	NUM
ejpam-5246	523	40	0.337957	0.337957	NUM
ejpam-5246	523	41	·	·	PUNCT
ejpam-5246	523	42	·	·	PUNCT
ejpam-5246	523	43	·	·	PUNCT
ejpam-5246	523	44	·	·	PUNCT
ejpam-5246	523	45	·	·	PUNCT
ejpam-5246	523	46	·	·	PUNCT
ejpam-5246	524	1	1/40	1/40	NUM
ejpam-5246	524	2	5	5	NUM
ejpam-5246	524	3	5.73e-05	5.73e-05	NUM
ejpam-5246	524	4	0.086509	0.086509	NUM
ejpam-5246	524	5	1.02e-04	1.02e-04	NUM
ejpam-5246	524	6	·	·	PUNCT
ejpam-5246	524	7	·	·	PUNCT
ejpam-5246	524	8	·	·	PUNCT
ejpam-5246	525	1	1/80	1/80	NUM
ejpam-5246	525	2	6	6	NUM
ejpam-5246	525	3	2.135e-05	2.135e-05	NUM
ejpam-5246	525	4	0.135266	0.135266	NUM
ejpam-5246	525	5	3.59e-05	3.59e-05	NUM
ejpam-5246	525	6	1.5083	1.5083	NUM
ejpam-5246	525	7	1/160	1/160	NUM
ejpam-5246	525	8	7	7	NUM
ejpam-5246	525	9	9.15e-06	9.15e-06	NUM
ejpam-5246	525	10	0.165087	0.165087	NUM
ejpam-5246	525	11	1.22e-05	1.22e-05	NUM
ejpam-5246	525	12	1.5590	1.5590	NUM
ejpam-5246	525	13	1/320	1/320	NUM
ejpam-5246	525	14	9	9	NUM
ejpam-5246	525	15	5.01e-06	5.01e-06	NUM
ejpam-5246	525	16	0.316164	0.316164	NUM
ejpam-5246	525	17	4.14e-06	4.14e-06	NUM
ejpam-5246	525	18	1.5566	1.5566	NUM
ejpam-5246	525	19	table	table	NOUN
ejpam-5246	525	20	6	6	NUM
ejpam-5246	525	21	:	:	PUNCT
ejpam-5246	525	22	example	example	NOUN
ejpam-5246	525	23	2	2	NUM
ejpam-5246	525	24	,	,	PUNCT
ejpam-5246	525	25	explicit	explicit	ADJ
ejpam-5246	525	26	formula	formula	NOUN
ejpam-5246	525	27	,	,	PUNCT
ejpam-5246	525	28	α	α	NOUN
ejpam-5246	525	29	=	=	SYM
ejpam-5246	525	30	2	2	NUM
ejpam-5246	525	31	h	h	NOUN
ejpam-5246	525	32	m	m	VERB
ejpam-5246	525	33	th	th	INTJ
ejpam-5246	525	34	cput	cput	ADJ
ejpam-5246	525	35	eh	eh	INTJ
ejpam-5246	525	36	sh	sh	PROPN
ejpam-5246	525	37	1/20	1/20	NUM
ejpam-5246	525	38	7	7	NUM
ejpam-5246	525	39	1.01e-05	1.01e-05	NUM
ejpam-5246	525	40	0.785978	0.785978	NUM
ejpam-5246	525	41	·	·	PUNCT
ejpam-5246	525	42	·	·	PUNCT
ejpam-5246	525	43	·	·	PUNCT
ejpam-5246	525	44	·	·	PUNCT
ejpam-5246	525	45	·	·	PUNCT
ejpam-5246	525	46	·	·	PUNCT
ejpam-5246	526	1	1/40	1/40	NUM
ejpam-5246	526	2	12	12	NUM
ejpam-5246	526	3	4.15e-06	4.15e-06	NUM
ejpam-5246	526	4	0.102545	0.102545	NUM
ejpam-5246	526	5	5.96e-06	5.96e-06	NUM
ejpam-5246	526	6	·	·	PUNCT
ejpam-5246	526	7	·	·	PUNCT
ejpam-5246	526	8	·	·	PUNCT
ejpam-5246	527	1	1/80	1/80	NUM
ejpam-5246	527	2	36	36	NUM
ejpam-5246	527	3	3.145e-06	3.145e-06	NUM
ejpam-5246	527	4	0.113383	0.113383	NUM
ejpam-5246	527	5	1.01e-06	1.01e-06	NUM
ejpam-5246	527	6	2.5626	2.5626	NUM
ejpam-5246	527	7	1/160	1/160	NUM
ejpam-5246	527	8	163	163	NUM
ejpam-5246	527	9	2.93e-06	2.93e-06	NUM
ejpam-5246	527	10	0.155124	0.155124	NUM
ejpam-5246	527	11	2.17e-07	2.17e-07	NUM
ejpam-5246	527	12	2.2135	2.2135	NUM
ejpam-5246	527	13	1/320	1/320	NUM
ejpam-5246	527	14	879	879	NUM
ejpam-5246	527	15	2.89e-06	2.89e-06	NUM
ejpam-5246	527	16	0.424556	0.424556	NUM
ejpam-5246	527	17	4.31e-08	4.31e-08	NUM
ejpam-5246	527	18	2.3346	2.3346	NUM
ejpam-5246	527	19	4.2	4.2	NUM
ejpam-5246	527	20	.	.	PUNCT
ejpam-5246	528	1	discussion	discussion	NOUN
ejpam-5246	528	2	by	by	ADP
ejpam-5246	528	3	the	the	DET
ejpam-5246	528	4	numerical	numerical	ADJ
ejpam-5246	528	5	results	result	NOUN
ejpam-5246	528	6	in	in	ADP
ejpam-5246	528	7	examples	example	NOUN
ejpam-5246	528	8	1	1	NUM
ejpam-5246	528	9	and	and	CCONJ
ejpam-5246	528	10	2	2	NUM
ejpam-5246	528	11	,	,	PUNCT
ejpam-5246	528	12	we	we	PRON
ejpam-5246	528	13	refer	refer	VERB
ejpam-5246	528	14	to	to	ADP
ejpam-5246	528	15	the	the	DET
ejpam-5246	528	16	following	follow	VERB
ejpam-5246	528	17	comments	comment	NOUN
ejpam-5246	528	18	:	:	PUNCT
ejpam-5246	528	19	•	•	ADP
ejpam-5246	528	20	the	the	DET
ejpam-5246	528	21	numerical	numerical	ADJ
ejpam-5246	528	22	blow	blow	NOUN
ejpam-5246	528	23	-	-	PUNCT
ejpam-5246	528	24	up	up	NOUN
ejpam-5246	528	25	can	can	AUX
ejpam-5246	528	26	happen	happen	VERB
ejpam-5246	528	27	simultaneously	simultaneously	ADV
ejpam-5246	528	28	at	at	ADP
ejpam-5246	528	29	one	one	NUM
ejpam-5246	528	30	time	time	NOUN
ejpam-5246	528	31	and	and	CCONJ
ejpam-5246	528	32	one	one	NUM
ejpam-5246	528	33	point	point	NOUN
ejpam-5246	528	34	(	(	PUNCT
ejpam-5246	528	35	x	x	SYM
ejpam-5246	528	36	=	=	NUM
ejpam-5246	528	37	0.5	0.5	NUM
ejpam-5246	528	38	)	)	PUNCT
ejpam-5246	528	39	,	,	PUNCT
ejpam-5246	528	40	and	and	CCONJ
ejpam-5246	528	41	that	that	PRON
ejpam-5246	528	42	agreed	agree	VERB
ejpam-5246	528	43	with	with	ADP
ejpam-5246	528	44	the	the	DET
ejpam-5246	528	45	known	know	VERB
ejpam-5246	528	46	theoretical	theoretical	ADJ
ejpam-5246	528	47	blow	blow	NOUN
ejpam-5246	528	48	-	-	PUNCT
ejpam-5246	528	49	up	up	ADP
ejpam-5246	528	50	results	result	NOUN
ejpam-5246	528	51	of	of	ADP
ejpam-5246	528	52	the	the	DET
ejpam-5246	528	53	single	single	ADJ
ejpam-5246	528	54	equation	equation	NOUN
ejpam-5246	528	55	of	of	ADP
ejpam-5246	528	56	system	system	NOUN
ejpam-5246	528	57	(	(	PUNCT
ejpam-5246	528	58	1.1	1.1	NUM
ejpam-5246	528	59	)	)	PUNCT
ejpam-5246	528	60	,	,	PUNCT
ejpam-5246	529	1	[	[	X
ejpam-5246	529	2	25	25	NUM
ejpam-5246	529	3	]	]	PUNCT
ejpam-5246	529	4	.	.	PUNCT
ejpam-5246	530	1	•	•	NUM
ejpam-5246	530	2	when	when	SCONJ
ejpam-5246	530	3	the	the	DET
ejpam-5246	530	4	space	space	NOUN
ejpam-5246	530	5	-	-	PUNCT
ejpam-5246	530	6	steps	step	NOUN
ejpam-5246	530	7	are	be	AUX
ejpam-5246	530	8	refined	refine	VERB
ejpam-5246	530	9	,	,	PUNCT
ejpam-5246	530	10	the	the	DET
ejpam-5246	530	11	blow	blow	NOUN
ejpam-5246	530	12	-	-	PUNCT
ejpam-5246	530	13	up	up	ADP
ejpam-5246	530	14	time	time	NOUN
ejpam-5246	530	15	errors	error	NOUN
ejpam-5246	530	16	-	-	PUNCT
ejpam-5246	530	17	bounds	bound	NOUN
ejpam-5246	530	18	decrease	decrease	NOUN
ejpam-5246	530	19	.	.	PUNCT
ejpam-5246	531	1	this	this	PRON
ejpam-5246	531	2	refers	refer	VERB
ejpam-5246	531	3	that	that	SCONJ
ejpam-5246	531	4	the	the	DET
ejpam-5246	531	5	numerical	numerical	ADJ
ejpam-5246	531	6	blow	blow	VERB
ejpam-5246	531	7	-	-	PUNCT
ejpam-5246	531	8	up	up	ADP
ejpam-5246	531	9	times	time	NOUN
ejpam-5246	531	10	sequence	sequence	NOUN
ejpam-5246	531	11	th	th	NOUN
ejpam-5246	531	12	,	,	PUNCT
ejpam-5246	531	13	is	be	AUX
ejpam-5246	531	14	convergent	convergent	ADJ
ejpam-5246	531	15	,	,	PUNCT
ejpam-5246	531	16	as	as	ADP
ejpam-5246	531	17	the	the	DET
ejpam-5246	531	18	space	space	NOUN
ejpam-5246	531	19	-	-	PUNCT
ejpam-5246	531	20	step	step	NOUN
ejpam-5246	531	21	approaches	approach	NOUN
ejpam-5246	531	22	to	to	ADP
ejpam-5246	531	23	0	0	NUM
ejpam-5246	531	24	m.i.khalil	m.i.khalil	NOUN
ejpam-5246	531	25	et	et	PROPN
ejpam-5246	531	26	al	al	PROPN
ejpam-5246	532	1	.	.	PUNCT
ejpam-5246	532	2	/	/	SYM
ejpam-5246	532	3	eur	eur	PROPN
ejpam-5246	532	4	.	.	PUNCT
ejpam-5246	533	1	j.	j.	PROPN
ejpam-5246	533	2	pure	pure	PROPN
ejpam-5246	533	3	appl	appl	PROPN
ejpam-5246	533	4	.	.	PROPN
ejpam-5246	533	5	math	math	PROPN
ejpam-5246	533	6	,	,	PUNCT
ejpam-5246	533	7	17	17	NUM
ejpam-5246	533	8	(	(	PUNCT
ejpam-5246	533	9	3	3	NUM
ejpam-5246	533	10	)	)	PUNCT
ejpam-5246	533	11	(	(	PUNCT
ejpam-5246	533	12	2024	2024	NUM
ejpam-5246	533	13	)	)	PUNCT
ejpam-5246	533	14	,	,	PUNCT
ejpam-5246	533	15	1516	1516	NUM
ejpam-5246	533	16	-	-	SYM
ejpam-5246	533	17	1538	1538	NUM
ejpam-5246	533	18	1534	1534	NUM
ejpam-5246	533	19	table	table	NOUN
ejpam-5246	533	20	7	7	NUM
ejpam-5246	533	21	:	:	PUNCT
ejpam-5246	533	22	example	example	NOUN
ejpam-5246	533	23	2	2	NUM
ejpam-5246	533	24	,	,	PUNCT
ejpam-5246	533	25	implicit	implicit	ADJ
ejpam-5246	533	26	formula	formula	NOUN
ejpam-5246	533	27	,	,	PUNCT
ejpam-5246	533	28	α	α	NOUN
ejpam-5246	533	29	=	=	SYM
ejpam-5246	533	30	1	1	NUM
ejpam-5246	533	31	h	h	NOUN
ejpam-5246	533	32	m	m	VERB
ejpam-5246	533	33	th	th	INTJ
ejpam-5246	533	34	cput	cput	ADJ
ejpam-5246	533	35	eh	eh	INTJ
ejpam-5246	533	36	sh	sh	PROPN
ejpam-5246	533	37	1/20	1/20	NUM
ejpam-5246	533	38	4	4	NUM
ejpam-5246	533	39	1.59e-04	1.59e-04	NUM
ejpam-5246	533	40	0.360841	0.360841	NUM
ejpam-5246	533	41	·	·	PUNCT
ejpam-5246	533	42	·	·	PUNCT
ejpam-5246	533	43	·	·	PUNCT
ejpam-5246	533	44	·	·	PUNCT
ejpam-5246	533	45	·	·	PUNCT
ejpam-5246	533	46	·	·	PUNCT
ejpam-5246	534	1	1/40	1/40	NUM
ejpam-5246	534	2	5	5	NUM
ejpam-5246	534	3	5.73e-05	5.73e-05	NUM
ejpam-5246	534	4	0.237088	0.237088	NUM
ejpam-5246	534	5	1.02e-04	1.02e-04	NUM
ejpam-5246	534	6	·	·	PUNCT
ejpam-5246	534	7	·	·	PUNCT
ejpam-5246	534	8	·	·	PUNCT
ejpam-5246	535	1	1/80	1/80	NUM
ejpam-5246	535	2	6	6	NUM
ejpam-5246	535	3	2.13e-05	2.13e-05	NUM
ejpam-5246	535	4	0.329224	0.329224	NUM
ejpam-5246	535	5	3.59e-05	3.59e-05	NUM
ejpam-5246	535	6	1.5084	1.5084	NUM
ejpam-5246	535	7	1/160	1/160	NUM
ejpam-5246	535	8	7	7	NUM
ejpam-5246	535	9	9.15e-06	9.15e-06	NUM
ejpam-5246	535	10	0.855710	0.855710	NUM
ejpam-5246	535	11	1.22e-05	1.22e-05	NUM
ejpam-5246	535	12	1.5589	1.5589	NUM
ejpam-5246	535	13	1/320	1/320	NUM
ejpam-5246	535	14	9	9	NUM
ejpam-5246	535	15	5.01e-06	5.01e-06	NUM
ejpam-5246	535	16	2.501314	2.501314	NUM
ejpam-5246	535	17	4.14e-06	4.14e-06	NUM
ejpam-5246	535	18	1.5567	1.5567	NUM
ejpam-5246	535	19	table	table	NOUN
ejpam-5246	535	20	8	8	NUM
ejpam-5246	535	21	:	:	PUNCT
ejpam-5246	535	22	example	example	NOUN
ejpam-5246	535	23	2	2	NUM
ejpam-5246	535	24	,	,	PUNCT
ejpam-5246	535	25	implicit	implicit	ADJ
ejpam-5246	535	26	formula	formula	NOUN
ejpam-5246	535	27	,	,	PUNCT
ejpam-5246	535	28	α	α	NOUN
ejpam-5246	535	29	=	=	SYM
ejpam-5246	535	30	2	2	NUM
ejpam-5246	535	31	h	h	NOUN
ejpam-5246	535	32	m	m	VERB
ejpam-5246	535	33	th	th	INTJ
ejpam-5246	535	34	cput	cput	ADJ
ejpam-5246	535	35	eh	eh	INTJ
ejpam-5246	535	36	sh	sh	PROPN
ejpam-5246	535	37	1/20	1/20	NUM
ejpam-5246	535	38	6	6	NUM
ejpam-5246	535	39	1.01e-05	1.01e-05	NUM
ejpam-5246	535	40	0.459823	0.459823	NUM
ejpam-5246	535	41	·	·	PUNCT
ejpam-5246	535	42	·	·	PUNCT
ejpam-5246	535	43	·	·	PUNCT
ejpam-5246	535	44	·	·	PUNCT
ejpam-5246	535	45	·	·	PUNCT
ejpam-5246	535	46	·	·	PUNCT
ejpam-5246	536	1	1/40	1/40	NUM
ejpam-5246	536	2	12	12	NUM
ejpam-5246	536	3	4.15e-06	4.15e-06	NUM
ejpam-5246	536	4	0.246959	0.246959	NUM
ejpam-5246	536	5	5.96e-06	5.96e-06	NUM
ejpam-5246	536	6	·	·	PUNCT
ejpam-5246	536	7	·	·	PUNCT
ejpam-5246	536	8	·	·	PUNCT
ejpam-5246	537	1	1/80	1/80	NUM
ejpam-5246	537	2	36	36	NUM
ejpam-5246	537	3	3.15e-06	3.15e-06	NUM
ejpam-5246	537	4	0.305770	0.305770	NUM
ejpam-5246	537	5	1.01e-06	1.01e-06	NUM
ejpam-5246	537	6	2.5627	2.5627	NUM
ejpam-5246	537	7	1/160	1/160	NUM
ejpam-5246	537	8	163	163	NUM
ejpam-5246	537	9	2.93e-06	2.93e-06	NUM
ejpam-5246	537	10	0.858916	0.858916	NUM
ejpam-5246	537	11	2.17e-07	2.17e-07	NUM
ejpam-5246	537	12	2.2136	2.2136	NUM
ejpam-5246	537	13	1/320	1/320	NUM
ejpam-5246	537	14	879	879	NUM
ejpam-5246	537	15	2.89e-06	2.89e-06	NUM
ejpam-5246	537	16	2.554193	2.554193	NUM
ejpam-5246	537	17	4.31e-08	4.31e-08	NUM
ejpam-5246	537	18	2.3346	2.3346	NUM
ejpam-5246	537	19	figure	figure	NOUN
ejpam-5246	537	20	1	1	NUM
ejpam-5246	537	21	:	:	PUNCT
ejpam-5246	537	22	development	development	NOUN
ejpam-5246	537	23	of	of	ADP
ejpam-5246	537	24	numerical	numerical	ADJ
ejpam-5246	537	25	blow	blow	NOUN
ejpam-5246	537	26	-	-	PUNCT
ejpam-5246	537	27	up	up	ADP
ejpam-5246	537	28	solution	solution	NOUN
ejpam-5246	537	29	with	with	ADP
ejpam-5246	537	30	passage	passage	NOUN
ejpam-5246	537	31	of	of	ADP
ejpam-5246	537	32	time	time	NOUN
ejpam-5246	537	33	emerging	emerge	VERB
ejpam-5246	537	34	from	from	ADP
ejpam-5246	537	35	using	use	VERB
ejpam-5246	537	36	explicit	explicit	ADJ
ejpam-5246	537	37	for	for	ADP
ejpam-5246	537	38	example	example	NOUN
ejpam-5246	537	39	1	1	NUM
ejpam-5246	537	40	,	,	PUNCT
ejpam-5246	537	41	withh	withh	NOUN
ejpam-5246	537	42	=	=	SYM
ejpam-5246	537	43	320	320	NUM
ejpam-5246	537	44	,	,	PUNCT
ejpam-5246	537	45	α	α	NOUN
ejpam-5246	537	46	=	=	SYM
ejpam-5246	537	47	2	2	NUM
ejpam-5246	537	48	•	•	NOUN
ejpam-5246	537	49	convergence	convergence	NOUN
ejpam-5246	537	50	order	order	NOUN
ejpam-5246	537	51	of	of	ADP
ejpam-5246	537	52	the	the	DET
ejpam-5246	537	53	numerical	numerical	ADJ
ejpam-5246	537	54	blow	blow	VERB
ejpam-5246	537	55	-	-	PUNCT
ejpam-5246	537	56	up	up	ADP
ejpam-5246	537	57	times	time	NOUN
ejpam-5246	537	58	,	,	PUNCT
ejpam-5246	537	59	sh	sh	PROPN
ejpam-5246	537	60	is	be	AUX
ejpam-5246	537	61	close	close	ADJ
ejpam-5246	537	62	to	to	ADP
ejpam-5246	537	63	or	or	CCONJ
ejpam-5246	537	64	larger	large	ADJ
ejpam-5246	537	65	than	than	ADP
ejpam-5246	537	66	the	the	DET
ejpam-5246	537	67	value	value	NOUN
ejpam-5246	537	68	of	of	ADP
ejpam-5246	537	69	α	α	NOUN
ejpam-5246	537	70	,	,	PUNCT
ejpam-5246	537	71	this	this	PRON
ejpam-5246	537	72	refers	refer	VERB
ejpam-5246	537	73	,	,	PUNCT
ejpam-5246	537	74	the	the	DET
ejpam-5246	537	75	numerical	numerical	ADJ
ejpam-5246	537	76	order	order	NOUN
ejpam-5246	537	77	of	of	ADP
ejpam-5246	537	78	convergence	convergence	NOUN
ejpam-5246	537	79	is	be	AUX
ejpam-5246	537	80	:	:	PUNCT
ejpam-5246	537	81	0	0	NUM
ejpam-5246	537	82	(	(	PUNCT
ejpam-5246	537	83	hα+ϵ	hα+ϵ	NOUN
ejpam-5246	537	84	)	)	PUNCT
ejpam-5246	537	85	,	,	PUNCT
ejpam-5246	537	86	where	where	SCONJ
ejpam-5246	537	87	ϵ	ϵ	X
ejpam-5246	537	88	>	>	X
ejpam-5246	537	89	0	0	NUM
ejpam-5246	537	90	•	•	NOUN
ejpam-5246	537	91	with	with	ADP
ejpam-5246	537	92	the	the	DET
ejpam-5246	537	93	time	time	NOUN
ejpam-5246	537	94	-	-	PUNCT
ejpam-5246	537	95	stepping	step	VERB
ejpam-5246	537	96	formulas	formula	NOUN
ejpam-5246	537	97	(	(	PUNCT
ejpam-5246	537	98	2.3	2.3	NUM
ejpam-5246	537	99	)	)	PUNCT
ejpam-5246	537	100	and	and	CCONJ
ejpam-5246	537	101	(	(	PUNCT
ejpam-5246	537	102	3.3	3.3	NUM
ejpam-5246	537	103	)	)	PUNCT
ejpam-5246	537	104	,	,	PUNCT
ejpam-5246	537	105	the	the	DET
ejpam-5246	537	106	number	number	NOUN
ejpam-5246	537	107	of	of	ADP
ejpam-5246	537	108	iteration	iteration	NOUN
ejpam-5246	537	109	that	that	PRON
ejpam-5246	537	110	is	be	AUX
ejpam-5246	537	111	required	require	VERB
ejpam-5246	537	112	to	to	PART
ejpam-5246	537	113	achieve	achieve	VERB
ejpam-5246	537	114	blow	blow	NOUN
ejpam-5246	537	115	-	-	PUNCT
ejpam-5246	537	116	up	up	NOUN
ejpam-5246	537	117	is	be	AUX
ejpam-5246	537	118	increasing	increase	VERB
ejpam-5246	537	119	as	as	ADP
ejpam-5246	537	120	the	the	DET
ejpam-5246	537	121	value	value	NOUN
ejpam-5246	537	122	of	of	ADP
ejpam-5246	537	123	α	α	PRON
ejpam-5246	537	124	increases	increase	NOUN
ejpam-5246	537	125	.	.	PUNCT
ejpam-5246	538	1	•	•	NUM
ejpam-5246	538	2	when	when	SCONJ
ejpam-5246	538	3	we	we	PRON
ejpam-5246	538	4	refine	refine	VERB
ejpam-5246	538	5	the	the	DET
ejpam-5246	538	6	spatial	spatial	ADJ
ejpam-5246	538	7	step	step	NOUN
ejpam-5246	538	8	,	,	PUNCT
ejpam-5246	538	9	or	or	CCONJ
ejpam-5246	538	10	compare	compare	VERB
ejpam-5246	538	11	cput	cput	NOUN
ejpam-5246	538	12	of	of	ADP
ejpam-5246	538	13	implicit	implicit	ADJ
ejpam-5246	538	14	method	method	NOUN
ejpam-5246	538	15	with	with	ADP
ejpam-5246	538	16	that	that	PRON
ejpam-5246	538	17	of	of	ADP
ejpam-5246	538	18	explicit	explicit	ADJ
ejpam-5246	538	19	method	method	NOUN
ejpam-5246	538	20	,	,	PUNCT
ejpam-5246	538	21	we	we	PRON
ejpam-5246	538	22	find	find	VERB
ejpam-5246	538	23	the	the	DET
ejpam-5246	538	24	cput	cput	ADJ
ejpam-5246	538	25	times	time	NOUN
ejpam-5246	538	26	are	be	AUX
ejpam-5246	538	27	increasing	increase	VERB
ejpam-5246	538	28	.	.	PUNCT
ejpam-5246	539	1	m.i.khalil	m.i.khalil	NOUN
ejpam-5246	539	2	et	et	PROPN
ejpam-5246	539	3	al	al	PROPN
ejpam-5246	539	4	.	.	PUNCT
ejpam-5246	539	5	/	/	SYM
ejpam-5246	539	6	eur	eur	PROPN
ejpam-5246	539	7	.	.	PUNCT
ejpam-5246	540	1	j.	j.	PROPN
ejpam-5246	540	2	pure	pure	PROPN
ejpam-5246	540	3	appl	appl	PROPN
ejpam-5246	540	4	.	.	PROPN
ejpam-5246	540	5	math	math	PROPN
ejpam-5246	540	6	,	,	PUNCT
ejpam-5246	540	7	17	17	NUM
ejpam-5246	540	8	(	(	PUNCT
ejpam-5246	540	9	3	3	NUM
ejpam-5246	540	10	)	)	PUNCT
ejpam-5246	540	11	(	(	PUNCT
ejpam-5246	540	12	2024	2024	NUM
ejpam-5246	540	13	)	)	PUNCT
ejpam-5246	540	14	,	,	PUNCT
ejpam-5246	540	15	1516	1516	NUM
ejpam-5246	540	16	-	-	SYM
ejpam-5246	540	17	1538	1538	NUM
ejpam-5246	540	18	1535	1535	NUM
ejpam-5246	540	19	figure	figure	NOUN
ejpam-5246	540	20	2	2	NUM
ejpam-5246	540	21	:	:	PUNCT
ejpam-5246	540	22	development	development	NOUN
ejpam-5246	540	23	of	of	ADP
ejpam-5246	540	24	numerical	numerical	ADJ
ejpam-5246	540	25	blow	blow	NOUN
ejpam-5246	540	26	-	-	PUNCT
ejpam-5246	540	27	up	up	ADP
ejpam-5246	540	28	solution	solution	NOUN
ejpam-5246	540	29	with	with	ADP
ejpam-5246	540	30	passage	passage	NOUN
ejpam-5246	540	31	of	of	ADP
ejpam-5246	540	32	time	time	NOUN
ejpam-5246	540	33	emerging	emerge	VERB
ejpam-5246	540	34	from	from	ADP
ejpam-5246	540	35	using	use	VERB
ejpam-5246	540	36	implicit	implicit	NOUN
ejpam-5246	540	37	for	for	ADP
ejpam-5246	540	38	example	example	NOUN
ejpam-5246	540	39	1	1	NUM
ejpam-5246	540	40	,	,	PUNCT
ejpam-5246	540	41	with	with	ADP
ejpam-5246	540	42	h	h	NOUN
ejpam-5246	540	43	=	=	SYM
ejpam-5246	540	44	320	320	NUM
ejpam-5246	540	45	,	,	PUNCT
ejpam-5246	540	46	α	α	NOUN
ejpam-5246	540	47	=	=	SYM
ejpam-5246	540	48	2	2	NUM
ejpam-5246	540	49	figure	figure	NOUN
ejpam-5246	540	50	3	3	NUM
ejpam-5246	540	51	:	:	PUNCT
ejpam-5246	540	52	development	development	NOUN
ejpam-5246	540	53	of	of	ADP
ejpam-5246	540	54	numerical	numerical	ADJ
ejpam-5246	540	55	blow	blow	NOUN
ejpam-5246	540	56	-	-	PUNCT
ejpam-5246	540	57	up	up	ADP
ejpam-5246	540	58	solution	solution	NOUN
ejpam-5246	540	59	with	with	ADP
ejpam-5246	540	60	passage	passage	NOUN
ejpam-5246	540	61	of	of	ADP
ejpam-5246	540	62	time	time	NOUN
ejpam-5246	540	63	emerging	emerge	VERB
ejpam-5246	540	64	from	from	ADP
ejpam-5246	540	65	using	use	VERB
ejpam-5246	540	66	explicit	explicit	ADJ
ejpam-5246	540	67	for	for	ADP
ejpam-5246	540	68	example	example	NOUN
ejpam-5246	540	69	2	2	NUM
ejpam-5246	540	70	,	,	PUNCT
ejpam-5246	540	71	with	with	ADP
ejpam-5246	540	72	h	h	NOUN
ejpam-5246	540	73	=	=	SYM
ejpam-5246	540	74	320	320	NUM
ejpam-5246	540	75	,	,	PUNCT
ejpam-5246	540	76	α	α	NOUN
ejpam-5246	540	77	=	=	SYM
ejpam-5246	540	78	2	2	NUM
ejpam-5246	540	79	figure	figure	NOUN
ejpam-5246	540	80	4	4	NUM
ejpam-5246	540	81	:	:	PUNCT
ejpam-5246	540	82	development	development	NOUN
ejpam-5246	540	83	of	of	ADP
ejpam-5246	540	84	numerical	numerical	ADJ
ejpam-5246	540	85	blow	blow	NOUN
ejpam-5246	540	86	-	-	PUNCT
ejpam-5246	540	87	up	up	ADP
ejpam-5246	540	88	solution	solution	NOUN
ejpam-5246	540	89	with	with	ADP
ejpam-5246	540	90	passage	passage	NOUN
ejpam-5246	540	91	of	of	ADP
ejpam-5246	540	92	time	time	NOUN
ejpam-5246	540	93	emerging	emerge	VERB
ejpam-5246	540	94	from	from	ADP
ejpam-5246	540	95	using	use	VERB
ejpam-5246	540	96	implicit	implicit	NOUN
ejpam-5246	540	97	for	for	ADP
ejpam-5246	540	98	example	example	NOUN
ejpam-5246	540	99	2	2	NUM
ejpam-5246	540	100	—	—	PUNCT
ejpam-5246	540	101	with	with	ADP
ejpam-5246	540	102	h	h	NOUN
ejpam-5246	540	103	=	=	SYM
ejpam-5246	540	104	320	320	NUM
ejpam-5246	540	105	,	,	PUNCT
ejpam-5246	540	106	α	α	NOUN
ejpam-5246	540	107	=	=	SYM
ejpam-5246	540	108	2	2	NUM
ejpam-5246	540	109	•	•	NUM
ejpam-5246	540	110	from	from	ADP
ejpam-5246	540	111	tow	tow	NOUN
ejpam-5246	540	112	figures	figure	NOUN
ejpam-5246	540	113	(	(	PUNCT
ejpam-5246	540	114	1	1	NUM
ejpam-5246	540	115	)	)	PUNCT
ejpam-5246	540	116	and	and	CCONJ
ejpam-5246	540	117	(	(	PUNCT
ejpam-5246	540	118	2	2	NUM
ejpam-5246	540	119	)	)	PUNCT
ejpam-5246	540	120	,	,	PUNCT
ejpam-5246	540	121	we	we	PRON
ejpam-5246	540	122	find	find	VERB
ejpam-5246	540	123	in	in	ADP
ejpam-5246	540	124	each	each	PRON
ejpam-5246	540	125	of	of	ADP
ejpam-5246	540	126	studied	study	VERB
ejpam-5246	540	127	problem	problem	NOUN
ejpam-5246	540	128	,	,	PUNCT
ejpam-5246	540	129	the	the	DET
ejpam-5246	540	130	numerical	numerical	ADJ
ejpam-5246	540	131	blow	blow	VERB
ejpam-5246	540	132	-	-	PUNCT
ejpam-5246	540	133	up	up	ADP
ejpam-5246	540	134	growth	growth	NOUN
ejpam-5246	540	135	-	-	PUNCT
ejpam-5246	540	136	rates	rate	NOUN
ejpam-5246	540	137	,	,	PUNCT
ejpam-5246	540	138	obtained	obtain	VERB
ejpam-5246	540	139	by	by	ADP
ejpam-5246	540	140	use	use	NOUN
ejpam-5246	540	141	explicit	explicit	ADJ
ejpam-5246	540	142	euler	euler	NOUN
ejpam-5246	540	143	scheme	scheme	NOUN
ejpam-5246	540	144	,	,	PUNCT
ejpam-5246	540	145	is	be	AUX
ejpam-5246	540	146	almost	almost	ADV
ejpam-5246	540	147	the	the	DET
ejpam-5246	540	148	same	same	ADJ
ejpam-5246	540	149	as	as	ADP
ejpam-5246	540	150	that	that	PRON
ejpam-5246	540	151	obtained	obtain	VERB
ejpam-5246	540	152	by	by	ADP
ejpam-5246	540	153	use	use	NOUN
ejpam-5246	540	154	implicit	implicit	ADJ
ejpam-5246	540	155	euler	euler	NOUN
ejpam-5246	540	156	scheme	scheme	NOUN
ejpam-5246	540	157	.	.	PUNCT
ejpam-5246	541	1	references	reference	NOUN
ejpam-5246	541	2	1536	1536	NUM
ejpam-5246	541	3	5	5	NUM
ejpam-5246	541	4	.	.	PUNCT
ejpam-5246	542	1	conclusions	conclusion	NOUN
ejpam-5246	542	2	this	this	DET
ejpam-5246	542	3	paper	paper	NOUN
ejpam-5246	542	4	deals	deal	NOUN
ejpam-5246	542	5	with	with	ADP
ejpam-5246	542	6	numerical	numerical	ADJ
ejpam-5246	542	7	approximations	approximation	NOUN
ejpam-5246	542	8	of	of	ADP
ejpam-5246	542	9	a	a	DET
ejpam-5246	542	10	one	one	NUM
ejpam-5246	542	11	-	-	PUNCT
ejpam-5246	542	12	dimensional	dimensional	ADJ
ejpam-5246	542	13	coupled	couple	VERB
ejpam-5246	542	14	reactiondiffusion	reactiondiffusion	NOUN
ejpam-5246	542	15	system	system	NOUN
ejpam-5246	542	16	with	with	ADP
ejpam-5246	542	17	gradient	gradient	ADJ
ejpam-5246	542	18	terms	term	NOUN
ejpam-5246	542	19	.	.	PUNCT
ejpam-5246	543	1	namely	namely	ADV
ejpam-5246	543	2	,	,	PUNCT
ejpam-5246	543	3	we	we	PRON
ejpam-5246	543	4	propose	propose	VERB
ejpam-5246	543	5	both	both	DET
ejpam-5246	543	6	euler	euler	NOUN
ejpam-5246	543	7	explicit	explicit	ADJ
ejpam-5246	543	8	and	and	CCONJ
ejpam-5246	543	9	implicit	implicit	ADJ
ejpam-5246	543	10	finite	finite	ADJ
ejpam-5246	543	11	difference	difference	NOUN
ejpam-5246	543	12	methods	method	NOUN
ejpam-5246	543	13	with	with	ADP
ejpam-5246	543	14	a	a	DET
ejpam-5246	543	15	non	non	ADJ
ejpam-5246	543	16	-	-	ADJ
ejpam-5246	543	17	fixed	fixed	ADJ
ejpam-5246	543	18	time	time	NOUN
ejpam-5246	543	19	-	-	PUNCT
ejpam-5246	543	20	stepping	step	VERB
ejpam-5246	543	21	procedure	procedure	NOUN
ejpam-5246	543	22	to	to	PART
ejpam-5246	543	23	estimate	estimate	VERB
ejpam-5246	543	24	the	the	DET
ejpam-5246	543	25	numerical	numerical	ADJ
ejpam-5246	543	26	blow	blow	VERB
ejpam-5246	543	27	-	-	PUNCT
ejpam-5246	543	28	up	up	ADP
ejpam-5246	543	29	time	time	NOUN
ejpam-5246	543	30	of	of	ADP
ejpam-5246	543	31	the	the	DET
ejpam-5246	543	32	considered	consider	VERB
ejpam-5246	543	33	problem	problem	NOUN
ejpam-5246	543	34	.	.	PUNCT
ejpam-5246	544	1	moreover	moreover	ADV
ejpam-5246	544	2	,	,	PUNCT
ejpam-5246	544	3	some	some	DET
ejpam-5246	544	4	numerical	numerical	ADJ
ejpam-5246	544	5	experiments	experiment	NOUN
ejpam-5246	544	6	are	be	AUX
ejpam-5246	544	7	given	give	VERB
ejpam-5246	544	8	to	to	PART
ejpam-5246	544	9	illustrate	illustrate	VERB
ejpam-5246	544	10	the	the	DET
ejpam-5246	544	11	efficiency	efficiency	NOUN
ejpam-5246	544	12	,	,	PUNCT
ejpam-5246	544	13	accuracy	accuracy	NOUN
ejpam-5246	544	14	,	,	PUNCT
ejpam-5246	544	15	and	and	CCONJ
ejpam-5246	544	16	numerical	numerical	ADJ
ejpam-5246	544	17	order	order	NOUN
ejpam-5246	544	18	of	of	ADP
ejpam-5246	544	19	convergence	convergence	NOUN
ejpam-5246	544	20	of	of	ADP
ejpam-5246	544	21	the	the	DET
ejpam-5246	544	22	proposed	propose	VERB
ejpam-5246	544	23	technique	technique	NOUN
ejpam-5246	544	24	.	.	PUNCT
ejpam-5246	545	1	the	the	DET
ejpam-5246	545	2	obtained	obtain	VERB
ejpam-5246	545	3	numerical	numerical	ADJ
ejpam-5246	545	4	results	result	NOUN
ejpam-5246	545	5	show	show	VERB
ejpam-5246	545	6	that	that	SCONJ
ejpam-5246	545	7	the	the	DET
ejpam-5246	545	8	used	use	VERB
ejpam-5246	545	9	finite	finite	ADJ
ejpam-5246	545	10	difference	difference	NOUN
ejpam-5246	545	11	schemes	scheme	NOUN
ejpam-5246	545	12	with	with	ADP
ejpam-5246	545	13	the	the	DET
ejpam-5246	545	14	proposed	propose	VERB
ejpam-5246	545	15	non	non	ADJ
ejpam-5246	545	16	-	-	ADJ
ejpam-5246	545	17	fixed	fixed	ADJ
ejpam-5246	545	18	time	time	NOUN
ejpam-5246	545	19	-	-	PUNCT
ejpam-5246	545	20	stepping	step	VERB
ejpam-5246	545	21	procedure	procedure	NOUN
ejpam-5246	545	22	can	can	AUX
ejpam-5246	545	23	give	give	VERB
ejpam-5246	545	24	accurate	accurate	ADJ
ejpam-5246	545	25	results	result	NOUN
ejpam-5246	545	26	with	with	ADP
ejpam-5246	545	27	high	high	ADJ
ejpam-5246	545	28	order	order	NOUN
ejpam-5246	545	29	of	of	ADP
ejpam-5246	545	30	numerical	numerical	ADJ
ejpam-5246	545	31	convergence	convergence	NOUN
ejpam-5246	545	32	.	.	PUNCT
ejpam-5246	546	1	furthermore	furthermore	ADV
ejpam-5246	546	2	,	,	PUNCT
ejpam-5246	546	3	the	the	DET
ejpam-5246	546	4	numerical	numerical	ADJ
ejpam-5246	546	5	results	result	NOUN
ejpam-5246	546	6	show	show	VERB
ejpam-5246	546	7	that	that	SCONJ
ejpam-5246	546	8	the	the	DET
ejpam-5246	546	9	blow	blow	NOUN
ejpam-5246	546	10	-	-	PUNCT
ejpam-5246	546	11	up	up	NOUN
ejpam-5246	546	12	can	can	AUX
ejpam-5246	546	13	only	only	ADV
ejpam-5246	546	14	occur	occur	VERB
ejpam-5246	546	15	at	at	ADP
ejpam-5246	546	16	the	the	DET
ejpam-5246	546	17	center	center	ADJ
ejpam-5246	546	18	point	point	NOUN
ejpam-5246	546	19	.	.	PUNCT
ejpam-5246	547	1	the	the	DET
ejpam-5246	547	2	two	two	NUM
ejpam-5246	547	3	proposed	propose	VERB
ejpam-5246	547	4	schemes	scheme	NOUN
ejpam-5246	547	5	are	be	AUX
ejpam-5246	547	6	effective	effective	ADJ
ejpam-5246	547	7	and	and	CCONJ
ejpam-5246	547	8	can	can	AUX
ejpam-5246	547	9	be	be	AUX
ejpam-5246	547	10	easily	easily	ADV
ejpam-5246	547	11	used	use	VERB
ejpam-5246	547	12	comprised	comprise	VERB
ejpam-5246	547	13	with	with	ADP
ejpam-5246	547	14	other	other	ADJ
ejpam-5246	547	15	numerical	numerical	ADJ
ejpam-5246	547	16	techniques	technique	NOUN
ejpam-5246	547	17	.	.	PUNCT
ejpam-5246	548	1	as	as	ADP
ejpam-5246	548	2	future	future	ADJ
ejpam-5246	548	3	work	work	NOUN
ejpam-5246	548	4	,	,	PUNCT
ejpam-5246	548	5	we	we	PRON
ejpam-5246	548	6	may	may	AUX
ejpam-5246	548	7	use	use	VERB
ejpam-5246	548	8	crank	crank	NOUN
ejpam-5246	548	9	-	-	PUNCT
ejpam-5246	548	10	nicolson	nicolson	PROPN
ejpam-5246	548	11	technique	technique	NOUN
ejpam-5246	548	12	to	to	PART
ejpam-5246	548	13	computer	computer	VERB
ejpam-5246	548	14	the	the	DET
ejpam-5246	548	15	numerical	numerical	ADJ
ejpam-5246	548	16	solution	solution	NOUN
ejpam-5246	548	17	of	of	ADP
ejpam-5246	548	18	the	the	DET
ejpam-5246	548	19	considered	consider	VERB
ejpam-5246	548	20	system	system	NOUN
ejpam-5246	548	21	.	.	PUNCT
ejpam-5246	549	1	acknowledgements	acknowledgement	NOUN
ejpam-5246	549	2	the	the	DET
ejpam-5246	549	3	authors	author	NOUN
ejpam-5246	549	4	would	would	AUX
ejpam-5246	549	5	like	like	VERB
ejpam-5246	549	6	to	to	PART
ejpam-5246	549	7	thank	thank	VERB
ejpam-5246	549	8	universiti	universiti	PROPN
ejpam-5246	549	9	kebangsaan	kebangsaan	PROPN
ejpam-5246	549	10	malaysia	malaysia	PROPN
ejpam-5246	549	11	(	(	PUNCT
ejpam-5246	549	12	ukm	ukm	PROPN
ejpam-5246	549	13	)	)	PUNCT
ejpam-5246	549	14	for	for	ADP
ejpam-5246	549	15	supporting	support	VERB
ejpam-5246	549	16	their	their	PRON
ejpam-5246	549	17	work	work	NOUN
ejpam-5246	549	18	.	.	PUNCT
ejpam-5246	550	1	references	reference	NOUN
ejpam-5246	550	2	[	[	X
ejpam-5246	550	3	1	1	NUM
ejpam-5246	550	4	]	]	X
ejpam-5246	550	5	luis	luis	PROPN
ejpam-5246	550	6	m	m	PROPN
ejpam-5246	550	7	abia	abia	PROPN
ejpam-5246	550	8	,	,	PUNCT
ejpam-5246	550	9	jc	jc	PROPN
ejpam-5246	550	10	lopez	lopez	PROPN
ejpam-5246	550	11	-	-	PUNCT
ejpam-5246	550	12	marcos	marcos	PROPN
ejpam-5246	550	13	,	,	PUNCT
ejpam-5246	550	14	and	and	CCONJ
ejpam-5246	550	15	julia	julia	PROPN
ejpam-5246	550	16	mart́ınez	mart́ınez	PROPN
ejpam-5246	550	17	.	.	PUNCT
ejpam-5246	551	1	blow	blow	NOUN
ejpam-5246	551	2	-	-	PUNCT
ejpam-5246	551	3	up	up	NOUN
ejpam-5246	551	4	for	for	ADP
ejpam-5246	551	5	semidiscretizations	semidiscretization	NOUN
ejpam-5246	551	6	of	of	ADP
ejpam-5246	551	7	reaction	reaction	NOUN
ejpam-5246	551	8	-	-	PUNCT
ejpam-5246	551	9	diffusion	diffusion	NOUN
ejpam-5246	551	10	equations	equation	NOUN
ejpam-5246	551	11	.	.	PUNCT
ejpam-5246	552	1	applied	apply	VERB
ejpam-5246	552	2	numerical	numerical	ADJ
ejpam-5246	552	3	mathematics	mathematic	NOUN
ejpam-5246	552	4	,	,	PUNCT
ejpam-5246	552	5	20(1	20(1	PROPN
ejpam-5246	552	6	-	-	PUNCT
ejpam-5246	552	7	2):145	2):145	NUM
ejpam-5246	552	8	–	–	PUNCT
ejpam-5246	552	9	156	156	NUM
ejpam-5246	552	10	,	,	PUNCT
ejpam-5246	552	11	1996	1996	NUM
ejpam-5246	552	12	.	.	PUNCT
ejpam-5246	553	1	[	[	X
ejpam-5246	553	2	2	2	NUM
ejpam-5246	553	3	]	]	X
ejpam-5246	553	4	omar	omar	PROPN
ejpam-5246	553	5	abu	abu	PROPN
ejpam-5246	553	6	arqub	arqub	PROPN
ejpam-5246	553	7	.	.	PUNCT
ejpam-5246	554	1	numerical	numerical	PROPN
ejpam-5246	554	2	simulation	simulation	PROPN
ejpam-5246	554	3	of	of	ADP
ejpam-5246	554	4	time	time	NOUN
ejpam-5246	554	5	-	-	PUNCT
ejpam-5246	554	6	fractional	fractional	ADJ
ejpam-5246	554	7	partial	partial	ADJ
ejpam-5246	554	8	differential	differential	NOUN
ejpam-5246	554	9	equations	equation	NOUN
ejpam-5246	554	10	arising	arise	VERB
ejpam-5246	554	11	in	in	ADP
ejpam-5246	554	12	fluid	fluid	ADJ
ejpam-5246	554	13	flows	flow	NOUN
ejpam-5246	554	14	via	via	ADP
ejpam-5246	554	15	reproducing	reproduce	VERB
ejpam-5246	554	16	kernel	kernel	NOUN
ejpam-5246	554	17	method	method	NOUN
ejpam-5246	554	18	.	.	PUNCT
ejpam-5246	555	1	international	international	ADJ
ejpam-5246	555	2	journal	journal	PROPN
ejpam-5246	555	3	of	of	ADP
ejpam-5246	555	4	numerical	numerical	ADJ
ejpam-5246	555	5	methods	method	NOUN
ejpam-5246	555	6	for	for	ADP
ejpam-5246	555	7	heat	heat	NOUN
ejpam-5246	555	8	&	&	CCONJ
ejpam-5246	555	9	fluid	fluid	ADJ
ejpam-5246	555	10	flow	flow	NOUN
ejpam-5246	555	11	,	,	PUNCT
ejpam-5246	555	12	30(11):4711–4733	30(11):4711–4733	NUM
ejpam-5246	555	13	,	,	PUNCT
ejpam-5246	555	14	2020	2020	NUM
ejpam-5246	555	15	.	.	PUNCT
ejpam-5246	556	1	[	[	X
ejpam-5246	556	2	3	3	NUM
ejpam-5246	556	3	]	]	SYM
ejpam-5246	556	4	ea	ea	PROPN
ejpam-5246	556	5	az	az	PROPN
ejpam-5246	556	6	-	-	PROPN
ejpam-5246	556	7	zo’bi	zo’bi	PROPN
ejpam-5246	556	8	.	.	PUNCT
ejpam-5246	557	1	a	a	DET
ejpam-5246	557	2	reliable	reliable	ADJ
ejpam-5246	557	3	analytic	analytic	ADJ
ejpam-5246	557	4	study	study	NOUN
ejpam-5246	557	5	for	for	ADP
ejpam-5246	557	6	higher	high	ADJ
ejpam-5246	557	7	-	-	PUNCT
ejpam-5246	557	8	dimensional	dimensional	ADJ
ejpam-5246	557	9	telegraph	telegraph	NOUN
ejpam-5246	557	10	equation	equation	NOUN
ejpam-5246	557	11	.	.	PUNCT
ejpam-5246	558	1	j.	j.	PROPN
ejpam-5246	558	2	math	math	PROPN
ejpam-5246	558	3	.	.	PUNCT
ejpam-5246	559	1	comput	comput	NOUN
ejpam-5246	559	2	.	.	PUNCT
ejpam-5246	560	1	sci	sci	PROPN
ejpam-5246	560	2	,	,	PUNCT
ejpam-5246	560	3	18(4):423–429	18(4):423–429	PROPN
ejpam-5246	560	4	,	,	PUNCT
ejpam-5246	560	5	2018	2018	NUM
ejpam-5246	560	6	.	.	PUNCT
ejpam-5246	561	1	[	[	X
ejpam-5246	561	2	4	4	NUM
ejpam-5246	561	3	]	]	X
ejpam-5246	561	4	emad	emad	PROPN
ejpam-5246	561	5	az	az	PROPN
ejpam-5246	561	6	-	-	PROPN
ejpam-5246	561	7	zo’bi	zo’bi	PROPN
ejpam-5246	561	8	,	,	PUNCT
ejpam-5246	561	9	ahmet	ahmet	PROPN
ejpam-5246	561	10	yildirim	yildirim	PROPN
ejpam-5246	561	11	,	,	PUNCT
ejpam-5246	561	12	and	and	CCONJ
ejpam-5246	561	13	lanre	lanre	NOUN
ejpam-5246	561	14	akinyemi	akinyemi	NOUN
ejpam-5246	561	15	.	.	PUNCT
ejpam-5246	562	1	semi	semi	ADJ
ejpam-5246	562	2	-	-	ADJ
ejpam-5246	562	3	analytic	analytic	ADJ
ejpam-5246	562	4	treatment	treatment	NOUN
ejpam-5246	562	5	of	of	ADP
ejpam-5246	562	6	mixed	mixed	ADJ
ejpam-5246	562	7	hyperbolic	hyperbolic	ADJ
ejpam-5246	562	8	–	–	PUNCT
ejpam-5246	562	9	elliptic	elliptic	ADJ
ejpam-5246	562	10	cauchy	cauchy	NOUN
ejpam-5246	562	11	problem	problem	NOUN
ejpam-5246	562	12	modeling	model	VERB
ejpam-5246	562	13	three	three	NUM
ejpam-5246	562	14	-	-	PUNCT
ejpam-5246	562	15	phase	phase	NOUN
ejpam-5246	562	16	flow	flow	NOUN
ejpam-5246	562	17	in	in	ADP
ejpam-5246	562	18	porous	porous	ADJ
ejpam-5246	562	19	media	medium	NOUN
ejpam-5246	562	20	.	.	PUNCT
ejpam-5246	563	1	international	international	ADJ
ejpam-5246	563	2	journal	journal	NOUN
ejpam-5246	563	3	of	of	ADP
ejpam-5246	563	4	modern	modern	ADJ
ejpam-5246	563	5	physics	physics	PROPN
ejpam-5246	563	6	b	b	PROPN
ejpam-5246	563	7	,	,	PUNCT
ejpam-5246	563	8	35(29):2150293	35(29):2150293	NUM
ejpam-5246	563	9	,	,	PUNCT
ejpam-5246	563	10	2021	2021	NUM
ejpam-5246	563	11	.	.	PUNCT
ejpam-5246	564	1	[	[	X
ejpam-5246	564	2	5	5	NUM
ejpam-5246	564	3	]	]	PUNCT
ejpam-5246	564	4	m	m	VERB
ejpam-5246	564	5	chipot	chipot	ADJ
ejpam-5246	564	6	and	and	CCONJ
ejpam-5246	564	7	fb	fb	ADJ
ejpam-5246	564	8	weissler	weissler	NOUN
ejpam-5246	564	9	.	.	PUNCT
ejpam-5246	565	1	some	some	DET
ejpam-5246	565	2	blowup	blowup	ADJ
ejpam-5246	565	3	results	result	NOUN
ejpam-5246	565	4	for	for	ADP
ejpam-5246	565	5	a	a	DET
ejpam-5246	565	6	nonlinear	nonlinear	ADJ
ejpam-5246	565	7	parabolic	parabolic	ADJ
ejpam-5246	565	8	equation	equation	NOUN
ejpam-5246	565	9	with	with	ADP
ejpam-5246	565	10	a	a	DET
ejpam-5246	565	11	gradient	gradient	ADJ
ejpam-5246	565	12	term	term	NOUN
ejpam-5246	565	13	.	.	PUNCT
ejpam-5246	566	1	siam	siam	PROPN
ejpam-5246	566	2	journal	journal	PROPN
ejpam-5246	566	3	on	on	ADP
ejpam-5246	566	4	mathematical	mathematical	ADJ
ejpam-5246	566	5	analysis	analysis	NOUN
ejpam-5246	566	6	,	,	PUNCT
ejpam-5246	566	7	20(4):886–907	20(4):886–907	NUM
ejpam-5246	566	8	,	,	PUNCT
ejpam-5246	566	9	1989	1989	NUM
ejpam-5246	566	10	.	.	PUNCT
ejpam-5246	567	1	[	[	X
ejpam-5246	567	2	6	6	NUM
ejpam-5246	567	3	]	]	PUNCT
ejpam-5246	567	4	miroslav	miroslav	PROPN
ejpam-5246	567	5	chlebik	chlebik	PROPN
ejpam-5246	567	6	,	,	PUNCT
ejpam-5246	567	7	marek	marek	PROPN
ejpam-5246	567	8	fila	fila	PROPN
ejpam-5246	567	9	,	,	PUNCT
ejpam-5246	567	10	and	and	CCONJ
ejpam-5246	567	11	pavol	pavol	PROPN
ejpam-5246	567	12	quittner	quittner	PROPN
ejpam-5246	567	13	.	.	PUNCT
ejpam-5246	568	1	blow	blow	NOUN
ejpam-5246	568	2	-	-	PUNCT
ejpam-5246	568	3	up	up	NOUN
ejpam-5246	568	4	of	of	ADP
ejpam-5246	568	5	positive	positive	ADJ
ejpam-5246	568	6	solutions	solution	NOUN
ejpam-5246	568	7	of	of	ADP
ejpam-5246	568	8	a	a	DET
ejpam-5246	568	9	semilinear	semilinear	ADJ
ejpam-5246	568	10	parabolic	parabolic	NOUN
ejpam-5246	568	11	equation	equation	NOUN
ejpam-5246	568	12	with	with	ADP
ejpam-5246	568	13	a	a	DET
ejpam-5246	568	14	gradient	gradient	ADJ
ejpam-5246	568	15	term	term	NOUN
ejpam-5246	568	16	.	.	PUNCT
ejpam-5246	569	1	dynamics	dynamic	NOUN
ejpam-5246	569	2	of	of	ADP
ejpam-5246	569	3	continuous	continuous	ADJ
ejpam-5246	569	4	,	,	PUNCT
ejpam-5246	569	5	discrete	discrete	ADJ
ejpam-5246	569	6	and	and	CCONJ
ejpam-5246	569	7	impulsive	impulsive	ADJ
ejpam-5246	569	8	systems	system	NOUN
ejpam-5246	569	9	series	series	NOUN
ejpam-5246	569	10	a	a	PRON
ejpam-5246	569	11	:	:	PUNCT
ejpam-5246	569	12	mathematical	mathematical	ADJ
ejpam-5246	569	13	analysis	analysis	NOUN
ejpam-5246	569	14	,	,	PUNCT
ejpam-5246	569	15	10:525–537	10:525–537	NUM
ejpam-5246	569	16	,	,	PUNCT
ejpam-5246	569	17	02	02	NUM
ejpam-5246	569	18	2003	2003	NUM
ejpam-5246	569	19	.	.	PUNCT
ejpam-5246	570	1	[	[	X
ejpam-5246	570	2	7	7	X
ejpam-5246	570	3	]	]	X
ejpam-5246	570	4	keng	keng	PROPN
ejpam-5246	570	5	deng	deng	PROPN
ejpam-5246	570	6	.	.	PUNCT
ejpam-5246	570	7	blow	blow	PROPN
ejpam-5246	570	8	-	-	PUNCT
ejpam-5246	570	9	up	up	ADP
ejpam-5246	570	10	rates	rate	NOUN
ejpam-5246	570	11	for	for	ADP
ejpam-5246	570	12	parabolic	parabolic	NOUN
ejpam-5246	570	13	systems	system	NOUN
ejpam-5246	570	14	.	.	PUNCT
ejpam-5246	571	1	zeitschrift	zeitschrift	NOUN
ejpam-5246	571	2	für	für	PROPN
ejpam-5246	571	3	angewandte	angewandte	PROPN
ejpam-5246	571	4	mathematik	mathematik	PROPN
ejpam-5246	571	5	und	und	PROPN
ejpam-5246	571	6	physik	physik	PROPN
ejpam-5246	571	7	zamp	zamp	PROPN
ejpam-5246	571	8	,	,	PUNCT
ejpam-5246	571	9	47:132–143	47:132–143	PROPN
ejpam-5246	571	10	,	,	PUNCT
ejpam-5246	571	11	1996	1996	NUM
ejpam-5246	571	12	.	.	PUNCT
ejpam-5246	572	1	references	reference	NOUN
ejpam-5246	572	2	1537	1537	NUM
ejpam-5246	572	3	[	[	SYM
ejpam-5246	572	4	8	8	NUM
ejpam-5246	572	5	]	]	X
ejpam-5246	572	6	marek	marek	PROPN
ejpam-5246	572	7	fila	fila	PROPN
ejpam-5246	572	8	.	.	PUNCT
ejpam-5246	573	1	remarks	remark	NOUN
ejpam-5246	573	2	on	on	ADP
ejpam-5246	573	3	blow	blow	NOUN
ejpam-5246	573	4	up	up	ADP
ejpam-5246	573	5	for	for	ADP
ejpam-5246	573	6	a	a	DET
ejpam-5246	573	7	nonlinear	nonlinear	ADJ
ejpam-5246	573	8	parabolic	parabolic	ADJ
ejpam-5246	573	9	equation	equation	NOUN
ejpam-5246	573	10	with	with	ADP
ejpam-5246	573	11	a	a	DET
ejpam-5246	573	12	gradient	gradient	ADJ
ejpam-5246	573	13	term	term	NOUN
ejpam-5246	573	14	.	.	PUNCT
ejpam-5246	574	1	proceedings	proceeding	NOUN
ejpam-5246	574	2	of	of	ADP
ejpam-5246	574	3	the	the	DET
ejpam-5246	574	4	american	american	PROPN
ejpam-5246	574	5	mathematical	mathematical	PROPN
ejpam-5246	574	6	society	society	NOUN
ejpam-5246	574	7	,	,	PUNCT
ejpam-5246	574	8	111(3):795–801	111(3):795–801	NUM
ejpam-5246	574	9	,	,	PUNCT
ejpam-5246	574	10	1991	1991	NUM
ejpam-5246	574	11	.	.	PUNCT
ejpam-5246	575	1	[	[	X
ejpam-5246	575	2	9	9	NUM
ejpam-5246	575	3	]	]	PUNCT
ejpam-5246	575	4	avner	avner	PROPN
ejpam-5246	575	5	friedman	friedman	PROPN
ejpam-5246	575	6	and	and	CCONJ
ejpam-5246	575	7	yoshikazu	yoshikazu	NOUN
ejpam-5246	575	8	giga	giga	PROPN
ejpam-5246	575	9	.	.	PUNCT
ejpam-5246	576	1	a	a	DET
ejpam-5246	576	2	single	single	ADJ
ejpam-5246	576	3	point	point	NOUN
ejpam-5246	576	4	blow	blow	NOUN
ejpam-5246	576	5	-	-	PUNCT
ejpam-5246	576	6	up	up	NOUN
ejpam-5246	576	7	for	for	ADP
ejpam-5246	576	8	solutions	solution	NOUN
ejpam-5246	576	9	of	of	ADP
ejpam-5246	576	10	semilinear	semilinear	ADJ
ejpam-5246	576	11	parabolic	parabolic	PROPN
ejpam-5246	576	12	systems	system	NOUN
ejpam-5246	576	13	.	.	PUNCT
ejpam-5246	577	1	j.	j.	PROPN
ejpam-5246	577	2	fac	fac	PROPN
ejpam-5246	577	3	.	.	PUNCT
ejpam-5246	578	1	sci	sci	PROPN
ejpam-5246	578	2	.	.	PROPN
ejpam-5246	578	3	univ	univ	PROPN
ejpam-5246	578	4	.	.	PUNCT
ejpam-5246	579	1	tokyo	tokyo	PROPN
ejpam-5246	579	2	sect	sect	NOUN
ejpam-5246	579	3	.	.	PUNCT
ejpam-5246	580	1	ia	ia	PROPN
ejpam-5246	580	2	math	math	PROPN
ejpam-5246	580	3	,	,	PUNCT
ejpam-5246	580	4	34(1):65–79	34(1):65–79	ADV
ejpam-5246	580	5	,	,	PUNCT
ejpam-5246	580	6	1987	1987	NUM
ejpam-5246	580	7	.	.	PUNCT
ejpam-5246	581	1	[	[	X
ejpam-5246	581	2	10	10	NUM
ejpam-5246	581	3	]	]	X
ejpam-5246	581	4	hiroshi	hiroshi	PROPN
ejpam-5246	581	5	fujita	fujita	PROPN
ejpam-5246	581	6	.	.	PUNCT
ejpam-5246	582	1	on	on	ADP
ejpam-5246	582	2	the	the	DET
ejpam-5246	582	3	blowing	blow	VERB
ejpam-5246	582	4	up	up	ADP
ejpam-5246	582	5	of	of	ADP
ejpam-5246	582	6	solutions	solution	NOUN
ejpam-5246	582	7	of	of	ADP
ejpam-5246	582	8	the	the	DET
ejpam-5246	582	9	cauchy	cauchy	ADJ
ejpam-5246	582	10	problem	problem	NOUN
ejpam-5246	582	11	for	for	ADP
ejpam-5246	582	12	ut	ut	PROPN
ejpam-5246	582	13	=	=	PRON
ejpam-5246	582	14	δu+	δu+	NOUN
ejpam-5246	582	15	u1+α	u1+α	PROPN
ejpam-5246	582	16	.	.	PUNCT
ejpam-5246	582	17	j.	j.	PROPN
ejpam-5246	582	18	fac	fac	PROPN
ejpam-5246	582	19	.	.	PUNCT
ejpam-5246	582	20	sci	sci	PROPN
ejpam-5246	582	21	.	.	PROPN
ejpam-5246	582	22	univ	univ	PROPN
ejpam-5246	582	23	.	.	PUNCT
ejpam-5246	583	1	tokyo	tokyo	PROPN
ejpam-5246	583	2	sect	sect	NOUN
ejpam-5246	583	3	.	.	PUNCT
ejpam-5246	584	1	i	i	PRON
ejpam-5246	584	2	,	,	PUNCT
ejpam-5246	584	3	13:109	13:109	NUM
ejpam-5246	584	4	,	,	PUNCT
ejpam-5246	584	5	1966	1966	NUM
ejpam-5246	584	6	.	.	PUNCT
ejpam-5246	585	1	[	[	X
ejpam-5246	585	2	11	11	NUM
ejpam-5246	585	3	]	]	PUNCT
ejpam-5246	585	4	houda	houda	PROPN
ejpam-5246	585	5	hani	hani	PROPN
ejpam-5246	585	6	and	and	CCONJ
ejpam-5246	585	7	moez	moez	PROPN
ejpam-5246	585	8	khenissi	khenissi	PROPN
ejpam-5246	585	9	.	.	PUNCT
ejpam-5246	586	1	on	on	ADP
ejpam-5246	586	2	a	a	DET
ejpam-5246	586	3	finite	finite	ADJ
ejpam-5246	586	4	difference	difference	NOUN
ejpam-5246	586	5	scheme	scheme	NOUN
ejpam-5246	586	6	for	for	ADP
ejpam-5246	586	7	blow	blow	NOUN
ejpam-5246	586	8	up	up	ADP
ejpam-5246	586	9	solutions	solution	NOUN
ejpam-5246	586	10	for	for	ADP
ejpam-5246	586	11	the	the	DET
ejpam-5246	586	12	chipot	chipot	ADJ
ejpam-5246	586	13	–	–	PUNCT
ejpam-5246	586	14	weissler	weissler	ADJ
ejpam-5246	586	15	equation	equation	NOUN
ejpam-5246	586	16	.	.	PUNCT
ejpam-5246	587	1	applied	apply	VERB
ejpam-5246	587	2	mathematics	mathematic	NOUN
ejpam-5246	587	3	and	and	CCONJ
ejpam-5246	587	4	computation	computation	NOUN
ejpam-5246	587	5	,	,	PUNCT
ejpam-5246	587	6	268:1199	268:1199	NUM
ejpam-5246	587	7	–	–	PUNCT
ejpam-5246	587	8	1216	1216	NUM
ejpam-5246	587	9	,	,	PUNCT
ejpam-5246	587	10	2015	2015	NUM
ejpam-5246	587	11	.	.	PUNCT
ejpam-5246	588	1	[	[	X
ejpam-5246	588	2	12	12	NUM
ejpam-5246	588	3	]	]	PUNCT
ejpam-5246	588	4	houda	houda	PROPN
ejpam-5246	588	5	hani	hani	PROPN
ejpam-5246	588	6	and	and	CCONJ
ejpam-5246	588	7	moez	moez	PROPN
ejpam-5246	588	8	khenissi	khenissi	PROPN
ejpam-5246	588	9	.	.	PUNCT
ejpam-5246	589	1	blow	blow	NOUN
ejpam-5246	589	2	-	-	PUNCT
ejpam-5246	589	3	up	up	NOUN
ejpam-5246	589	4	of	of	ADP
ejpam-5246	589	5	semi	semi	ADJ
ejpam-5246	589	6	-	-	ADJ
ejpam-5246	589	7	discrete	discrete	ADJ
ejpam-5246	589	8	solution	solution	NOUN
ejpam-5246	589	9	of	of	ADP
ejpam-5246	589	10	a	a	DET
ejpam-5246	589	11	nonlinear	nonlinear	ADJ
ejpam-5246	589	12	parabolic	parabolic	ADJ
ejpam-5246	589	13	equation	equation	NOUN
ejpam-5246	589	14	with	with	ADP
ejpam-5246	589	15	gradient	gradient	ADJ
ejpam-5246	589	16	term	term	NOUN
ejpam-5246	589	17	.	.	PUNCT
ejpam-5246	590	1	arxiv	arxiv	PROPN
ejpam-5246	590	2	preprint	preprint	VERB
ejpam-5246	590	3	arxiv:2010.08867	arxiv:2010.08867	NUM
ejpam-5246	590	4	,	,	PUNCT
ejpam-5246	590	5	2020	2020	NUM
ejpam-5246	590	6	.	.	PUNCT
ejpam-5246	591	1	[	[	X
ejpam-5246	591	2	13	13	NUM
ejpam-5246	591	3	]	]	PUNCT
ejpam-5246	591	4	manar	manar	PROPN
ejpam-5246	591	5	ismael	ismael	PROPN
ejpam-5246	591	6	,	,	PUNCT
ejpam-5246	591	7	ishak	ishak	PROPN
ejpam-5246	591	8	hashim	hashim	PROPN
ejpam-5246	591	9	,	,	PUNCT
ejpam-5246	591	10	maan	maan	PROPN
ejpam-5246	591	11	rasheed	rasheed	PROPN
ejpam-5246	591	12	,	,	PUNCT
ejpam-5246	591	13	and	and	CCONJ
ejpam-5246	591	14	eddie	eddie	PROPN
ejpam-5246	591	15	ismail	ismail	PROPN
ejpam-5246	591	16	.	.	PUNCT
ejpam-5246	592	1	numerical	numerical	PROPN
ejpam-5246	592	2	finite	finite	PROPN
ejpam-5246	592	3	difference	difference	NOUN
ejpam-5246	592	4	approximations	approximation	NOUN
ejpam-5246	592	5	of	of	ADP
ejpam-5246	592	6	a	a	DET
ejpam-5246	592	7	coupled	couple	VERB
ejpam-5246	592	8	parabolic	parabolic	NOUN
ejpam-5246	592	9	system	system	NOUN
ejpam-5246	592	10	with	with	ADP
ejpam-5246	592	11	blow	blow	NOUN
ejpam-5246	592	12	-	-	PUNCT
ejpam-5246	592	13	up	up	NOUN
ejpam-5246	592	14	.	.	PUNCT
ejpam-5246	593	1	journal	journal	NOUN
ejpam-5246	593	2	of	of	ADP
ejpam-5246	593	3	mathematics	mathematics	PROPN
ejpam-5246	593	4	and	and	CCONJ
ejpam-5246	593	5	computer	computer	NOUN
ejpam-5246	593	6	science	science	NOUN
ejpam-5246	593	7	,	,	PUNCT
ejpam-5246	593	8	32:387–407	32:387–407	PROPN
ejpam-5246	593	9	,	,	PUNCT
ejpam-5246	593	10	11	11	NUM
ejpam-5246	593	11	2023	2023	NUM
ejpam-5246	593	12	.	.	PUNCT
ejpam-5246	594	1	[	[	X
ejpam-5246	594	2	14	14	NUM
ejpam-5246	594	3	]	]	SYM
ejpam-5246	594	4	stanley	stanley	PROPN
ejpam-5246	594	5	kaplan	kaplan	PROPN
ejpam-5246	594	6	.	.	PUNCT
ejpam-5246	595	1	on	on	ADP
ejpam-5246	595	2	the	the	DET
ejpam-5246	595	3	growth	growth	NOUN
ejpam-5246	595	4	of	of	ADP
ejpam-5246	595	5	solutions	solution	NOUN
ejpam-5246	595	6	of	of	ADP
ejpam-5246	595	7	quasi	quasi	ADJ
ejpam-5246	595	8	-	-	ADJ
ejpam-5246	595	9	linear	linear	ADJ
ejpam-5246	595	10	parabolic	parabolic	ADJ
ejpam-5246	595	11	equations	equation	NOUN
ejpam-5246	595	12	.	.	PUNCT
ejpam-5246	596	1	communications	communication	NOUN
ejpam-5246	596	2	on	on	ADP
ejpam-5246	596	3	pure	pure	ADJ
ejpam-5246	596	4	and	and	CCONJ
ejpam-5246	596	5	applied	applied	ADJ
ejpam-5246	596	6	mathematics	mathematic	NOUN
ejpam-5246	596	7	,	,	PUNCT
ejpam-5246	596	8	16(3):305–330	16(3):305–330	PROPN
ejpam-5246	596	9	,	,	PUNCT
ejpam-5246	596	10	1963	1963	NUM
ejpam-5246	596	11	.	.	PUNCT
ejpam-5246	597	1	[	[	X
ejpam-5246	597	2	15	15	NUM
ejpam-5246	597	3	]	]	X
ejpam-5246	597	4	monica	monica	PROPN
ejpam-5246	597	5	marras	marras	PROPN
ejpam-5246	597	6	,	,	PUNCT
ejpam-5246	597	7	s	s	PART
ejpam-5246	597	8	vernier	vernier	NOUN
ejpam-5246	597	9	-	-	PUNCT
ejpam-5246	597	10	piro	piro	PROPN
ejpam-5246	597	11	,	,	PUNCT
ejpam-5246	597	12	and	and	CCONJ
ejpam-5246	597	13	giuseppe	giuseppe	PROPN
ejpam-5246	597	14	viglialoro	viglialoro	PROPN
ejpam-5246	597	15	.	.	PUNCT
ejpam-5246	598	1	estimates	estimate	NOUN
ejpam-5246	598	2	from	from	ADP
ejpam-5246	598	3	below	below	ADP
ejpam-5246	598	4	of	of	ADP
ejpam-5246	598	5	blow	blow	NOUN
ejpam-5246	598	6	-	-	PUNCT
ejpam-5246	598	7	up	up	ADP
ejpam-5246	598	8	time	time	NOUN
ejpam-5246	598	9	in	in	ADP
ejpam-5246	598	10	a	a	DET
ejpam-5246	598	11	parabolic	parabolic	ADJ
ejpam-5246	598	12	system	system	NOUN
ejpam-5246	598	13	with	with	ADP
ejpam-5246	598	14	gradient	gradient	ADJ
ejpam-5246	598	15	term	term	NOUN
ejpam-5246	598	16	.	.	PUNCT
ejpam-5246	599	1	int	int	NOUN
ejpam-5246	599	2	.	.	PUNCT
ejpam-5246	600	1	j.	j.	PROPN
ejpam-5246	600	2	pure	pure	PROPN
ejpam-5246	600	3	appl	appl	PROPN
ejpam-5246	600	4	.	.	PROPN
ejpam-5246	600	5	math	math	PROPN
ejpam-5246	600	6	,	,	PUNCT
ejpam-5246	600	7	93(2):297–306	93(2):297–306	NOUN
ejpam-5246	600	8	,	,	PUNCT
ejpam-5246	600	9	2014	2014	NUM
ejpam-5246	600	10	.	.	PUNCT
ejpam-5246	601	1	[	[	X
ejpam-5246	601	2	16	16	NUM
ejpam-5246	601	3	]	]	PUNCT
ejpam-5246	601	4	niraj	niraj	VERB
ejpam-5246	601	5	mehta	mehta	PROPN
ejpam-5246	601	6	,	,	PUNCT
ejpam-5246	601	7	vipul	vipul	PROPN
ejpam-5246	601	8	b	b	PROPN
ejpam-5246	601	9	gondaliya	gondaliya	PROPN
ejpam-5246	601	10	,	,	PUNCT
ejpam-5246	601	11	and	and	CCONJ
ejpam-5246	601	12	jayesh	jayesh	PROPN
ejpam-5246	601	13	gundaniya	gundaniya	PROPN
ejpam-5246	601	14	.	.	PUNCT
ejpam-5246	602	1	applications	application	NOUN
ejpam-5246	602	2	of	of	ADP
ejpam-5246	602	3	different	different	ADJ
ejpam-5246	602	4	numerical	numerical	ADJ
ejpam-5246	602	5	methods	method	NOUN
ejpam-5246	602	6	in	in	ADP
ejpam-5246	602	7	heat	heat	NOUN
ejpam-5246	602	8	transfer	transfer	NOUN
ejpam-5246	602	9	-	-	PUNCT
ejpam-5246	602	10	a	a	DET
ejpam-5246	602	11	review	review	NOUN
ejpam-5246	602	12	.	.	PUNCT
ejpam-5246	603	1	international	international	ADJ
ejpam-5246	603	2	journal	journal	NOUN
ejpam-5246	603	3	of	of	ADP
ejpam-5246	603	4	emerging	emerge	VERB
ejpam-5246	603	5	technology	technology	NOUN
ejpam-5246	603	6	and	and	CCONJ
ejpam-5246	603	7	advanced	advanced	ADJ
ejpam-5246	603	8	engineering	engineering	NOUN
ejpam-5246	603	9	,	,	PUNCT
ejpam-5246	603	10	3(2):363–368	3(2):363–368	NUM
ejpam-5246	603	11	,	,	PUNCT
ejpam-5246	603	12	2013	2013	NUM
ejpam-5246	603	13	.	.	PUNCT
ejpam-5246	604	1	[	[	X
ejpam-5246	604	2	17	17	NUM
ejpam-5246	604	3	]	]	X
ejpam-5246	604	4	pavol	pavol	NOUN
ejpam-5246	604	5	quittner	quittner	NOUN
ejpam-5246	604	6	and	and	CCONJ
ejpam-5246	604	7	philippe	philippe	PROPN
ejpam-5246	604	8	souplet	souplet	NOUN
ejpam-5246	604	9	.	.	PUNCT
ejpam-5246	605	1	superlinear	superlinear	PROPN
ejpam-5246	605	2	parabolic	parabolic	PROPN
ejpam-5246	605	3	problems	problem	NOUN
ejpam-5246	605	4	.	.	PUNCT
ejpam-5246	606	1	springer	springer	NOUN
ejpam-5246	606	2	,	,	PUNCT
ejpam-5246	606	3	2019	2019	NUM
ejpam-5246	606	4	.	.	PUNCT
ejpam-5246	607	1	[	[	X
ejpam-5246	607	2	18	18	NUM
ejpam-5246	607	3	]	]	X
ejpam-5246	607	4	maan	maan	PROPN
ejpam-5246	607	5	a	a	DET
ejpam-5246	607	6	rasheed	rasheed	NOUN
ejpam-5246	607	7	.	.	PUNCT
ejpam-5246	607	8	blow	blow	VERB
ejpam-5246	607	9	-	-	PUNCT
ejpam-5246	607	10	up	up	ADP
ejpam-5246	607	11	properties	property	NOUN
ejpam-5246	607	12	of	of	ADP
ejpam-5246	607	13	a	a	DET
ejpam-5246	607	14	coupled	couple	VERB
ejpam-5246	607	15	system	system	NOUN
ejpam-5246	607	16	of	of	ADP
ejpam-5246	607	17	reaction	reaction	NOUN
ejpam-5246	607	18	-	-	PUNCT
ejpam-5246	607	19	diffusion	diffusion	NOUN
ejpam-5246	607	20	equations	equation	NOUN
ejpam-5246	607	21	.	.	PUNCT
ejpam-5246	608	1	iraqi	iraqi	ADJ
ejpam-5246	608	2	journal	journal	PROPN
ejpam-5246	608	3	of	of	ADP
ejpam-5246	608	4	science	science	NOUN
ejpam-5246	608	5	,	,	PUNCT
ejpam-5246	608	6	pages	page	NOUN
ejpam-5246	608	7	3052–3060	3052–3060	NUM
ejpam-5246	608	8	,	,	PUNCT
ejpam-5246	608	9	2021	2021	NUM
ejpam-5246	608	10	.	.	PUNCT
ejpam-5246	609	1	[	[	X
ejpam-5246	609	2	19	19	NUM
ejpam-5246	609	3	]	]	PUNCT
ejpam-5246	609	4	maan	maan	PROPN
ejpam-5246	609	5	a	a	DET
ejpam-5246	609	6	rasheed	rasheed	NOUN
ejpam-5246	609	7	.	.	PUNCT
ejpam-5246	610	1	on	on	ADP
ejpam-5246	610	2	blow	blow	NOUN
ejpam-5246	610	3	-	-	PUNCT
ejpam-5246	610	4	up	up	ADP
ejpam-5246	610	5	solutions	solution	NOUN
ejpam-5246	610	6	of	of	ADP
ejpam-5246	610	7	a	a	DET
ejpam-5246	610	8	parabolic	parabolic	ADJ
ejpam-5246	610	9	system	system	NOUN
ejpam-5246	610	10	coupled	couple	VERB
ejpam-5246	610	11	in	in	ADP
ejpam-5246	610	12	both	both	DET
ejpam-5246	610	13	equations	equation	NOUN
ejpam-5246	610	14	and	and	CCONJ
ejpam-5246	610	15	boundary	boundary	ADJ
ejpam-5246	610	16	conditions	condition	NOUN
ejpam-5246	610	17	.	.	PUNCT
ejpam-5246	611	1	baghdad	baghdad	PROPN
ejpam-5246	611	2	science	science	PROPN
ejpam-5246	611	3	journal	journal	PROPN
ejpam-5246	611	4	,	,	PUNCT
ejpam-5246	611	5	18(2):0315–0315	18(2):0315–0315	NUM
ejpam-5246	611	6	,	,	PUNCT
ejpam-5246	611	7	2021	2021	NUM
ejpam-5246	611	8	.	.	PUNCT
ejpam-5246	612	1	[	[	X
ejpam-5246	612	2	20	20	NUM
ejpam-5246	612	3	]	]	PUNCT
ejpam-5246	612	4	maan	maan	PROPN
ejpam-5246	612	5	a	a	DET
ejpam-5246	612	6	rasheed	rasheed	NOUN
ejpam-5246	612	7	,	,	PUNCT
ejpam-5246	612	8	hassan	hassan	PROPN
ejpam-5246	612	9	abd	abd	PROPN
ejpam-5246	612	10	salman	salman	PROPN
ejpam-5246	612	11	al	al	PROPN
ejpam-5246	612	12	-	-	PUNCT
ejpam-5246	612	13	dujaly	dujaly	PROPN
ejpam-5246	612	14	,	,	PUNCT
ejpam-5246	612	15	talat	talat	PROPN
ejpam-5246	612	16	jassim	jassim	PROPN
ejpam-5246	612	17	aldhlki	aldhlki	PROPN
ejpam-5246	612	18	,	,	PUNCT
ejpam-5246	612	19	et	et	PROPN
ejpam-5246	612	20	al	al	PROPN
ejpam-5246	612	21	.	.	PUNCT
ejpam-5246	613	1	blowup	blowup	ADJ
ejpam-5246	613	2	rate	rate	NOUN
ejpam-5246	613	3	estimates	estimate	NOUN
ejpam-5246	613	4	for	for	ADP
ejpam-5246	613	5	a	a	DET
ejpam-5246	613	6	system	system	NOUN
ejpam-5246	613	7	of	of	ADP
ejpam-5246	613	8	reaction	reaction	NOUN
ejpam-5246	613	9	-	-	PUNCT
ejpam-5246	613	10	diffusion	diffusion	NOUN
ejpam-5246	613	11	equations	equation	NOUN
ejpam-5246	613	12	with	with	ADP
ejpam-5246	613	13	gradient	gradient	ADJ
ejpam-5246	613	14	terms	term	NOUN
ejpam-5246	613	15	.	.	PUNCT
ejpam-5246	614	1	international	international	ADJ
ejpam-5246	614	2	journal	journal	NOUN
ejpam-5246	614	3	of	of	ADP
ejpam-5246	614	4	mathematics	mathematics	PROPN
ejpam-5246	614	5	and	and	CCONJ
ejpam-5246	614	6	mathematical	mathematical	ADJ
ejpam-5246	614	7	sciences	science	NOUN
ejpam-5246	614	8	,	,	PUNCT
ejpam-5246	614	9	2019	2019	NUM
ejpam-5246	614	10	,	,	PUNCT
ejpam-5246	614	11	2019	2019	NUM
ejpam-5246	614	12	.	.	PUNCT
ejpam-5246	615	1	[	[	X
ejpam-5246	615	2	21	21	NUM
ejpam-5246	615	3	]	]	X
ejpam-5246	615	4	maan	maan	PROPN
ejpam-5246	615	5	a	a	DET
ejpam-5246	615	6	rasheed	rasheed	NOUN
ejpam-5246	615	7	and	and	CCONJ
ejpam-5246	615	8	luma	luma	PROPN
ejpam-5246	615	9	j	j	PROPN
ejpam-5246	615	10	barghooth	barghooth	PROPN
ejpam-5246	615	11	.	.	PUNCT
ejpam-5246	616	1	blow	blow	VERB
ejpam-5246	616	2	-	-	PUNCT
ejpam-5246	616	3	up	up	ADP
ejpam-5246	616	4	set	set	NOUN
ejpam-5246	616	5	and	and	CCONJ
ejpam-5246	616	6	upper	upper	ADJ
ejpam-5246	616	7	rate	rate	NOUN
ejpam-5246	616	8	estimate	estimate	NOUN
ejpam-5246	616	9	for	for	ADP
ejpam-5246	616	10	a	a	DET
ejpam-5246	616	11	semilinear	semilinear	ADJ
ejpam-5246	616	12	heat	heat	NOUN
ejpam-5246	616	13	equation	equation	NOUN
ejpam-5246	616	14	.	.	PUNCT
ejpam-5246	617	1	in	in	ADP
ejpam-5246	617	2	journal	journal	PROPN
ejpam-5246	617	3	of	of	ADP
ejpam-5246	617	4	physics	physics	PROPN
ejpam-5246	617	5	:	:	PUNCT
ejpam-5246	617	6	conference	conference	NOUN
ejpam-5246	617	7	series	series	NOUN
ejpam-5246	617	8	,	,	PUNCT
ejpam-5246	617	9	volume	volume	NOUN
ejpam-5246	617	10	1294	1294	NUM
ejpam-5246	617	11	,	,	PUNCT
ejpam-5246	617	12	page	page	NOUN
ejpam-5246	617	13	032013	032013	NUM
ejpam-5246	617	14	.	.	PUNCT
ejpam-5246	618	1	iop	iop	PROPN
ejpam-5246	618	2	publishing	publishing	NOUN
ejpam-5246	618	3	,	,	PUNCT
ejpam-5246	618	4	2019	2019	NUM
ejpam-5246	618	5	.	.	PUNCT
ejpam-5246	619	1	references	reference	NOUN
ejpam-5246	619	2	1538	1538	NUM
ejpam-5246	619	3	[	[	X
ejpam-5246	619	4	22	22	NUM
ejpam-5246	619	5	]	]	PUNCT
ejpam-5246	619	6	maan	maan	PROPN
ejpam-5246	619	7	a	a	DET
ejpam-5246	619	8	rasheed	rasheed	NOUN
ejpam-5246	619	9	and	and	CCONJ
ejpam-5246	619	10	miroslav	miroslav	PROPN
ejpam-5246	619	11	chlebik	chlebik	PROPN
ejpam-5246	619	12	.	.	PUNCT
ejpam-5246	620	1	blow	blow	VERB
ejpam-5246	620	2	-	-	PUNCT
ejpam-5246	620	3	up	up	ADP
ejpam-5246	620	4	rate	rate	NOUN
ejpam-5246	620	5	estimates	estimate	NOUN
ejpam-5246	620	6	and	and	CCONJ
ejpam-5246	620	7	blow	blow	NOUN
ejpam-5246	620	8	-	-	PUNCT
ejpam-5246	620	9	up	up	ADP
ejpam-5246	620	10	set	set	NOUN
ejpam-5246	620	11	for	for	ADP
ejpam-5246	620	12	a	a	DET
ejpam-5246	620	13	system	system	NOUN
ejpam-5246	620	14	of	of	ADP
ejpam-5246	620	15	two	two	NUM
ejpam-5246	620	16	heat	heat	NOUN
ejpam-5246	620	17	equations	equation	NOUN
ejpam-5246	620	18	with	with	ADP
ejpam-5246	620	19	coupled	couple	VERB
ejpam-5246	620	20	nonlinear	nonlinear	PROPN
ejpam-5246	620	21	neumann	neumann	PROPN
ejpam-5246	620	22	boundary	boundary	PROPN
ejpam-5246	620	23	conditions	condition	NOUN
ejpam-5246	620	24	.	.	PUNCT
ejpam-5246	621	1	iraqi	iraqi	ADJ
ejpam-5246	621	2	journal	journal	PROPN
ejpam-5246	621	3	of	of	ADP
ejpam-5246	621	4	science	science	NOUN
ejpam-5246	621	5	,	,	PUNCT
ejpam-5246	621	6	pages	page	NOUN
ejpam-5246	621	7	147–152	147–152	NUM
ejpam-5246	621	8	,	,	PUNCT
ejpam-5246	621	9	2020	2020	NUM
ejpam-5246	621	10	.	.	PUNCT
ejpam-5246	622	1	[	[	X
ejpam-5246	622	2	23	23	NUM
ejpam-5246	622	3	]	]	X
ejpam-5246	622	4	maan	maan	PROPN
ejpam-5246	622	5	a	a	DET
ejpam-5246	622	6	rasheed	rasheed	NOUN
ejpam-5246	622	7	,	,	PUNCT
ejpam-5246	622	8	raad	raad	VERB
ejpam-5246	622	9	a	a	DET
ejpam-5246	622	10	hameed	hameed	NOUN
ejpam-5246	622	11	,	,	PUNCT
ejpam-5246	622	12	sameer	sameer	PROPN
ejpam-5246	622	13	k	k	PROPN
ejpam-5246	622	14	obeid	obeid	PROPN
ejpam-5246	622	15	,	,	PUNCT
ejpam-5246	622	16	and	and	CCONJ
ejpam-5246	622	17	ali	ali	PROPN
ejpam-5246	622	18	f	f	PROPN
ejpam-5246	622	19	jameel	jameel	PROPN
ejpam-5246	622	20	.	.	PUNCT
ejpam-5246	623	1	on	on	ADP
ejpam-5246	623	2	numerical	numerical	ADJ
ejpam-5246	623	3	blow	blow	VERB
ejpam-5246	623	4	-	-	PUNCT
ejpam-5246	623	5	up	up	ADP
ejpam-5246	623	6	solutions	solution	NOUN
ejpam-5246	623	7	of	of	ADP
ejpam-5246	623	8	semilinear	semilinear	ADJ
ejpam-5246	623	9	heat	heat	NOUN
ejpam-5246	623	10	equations	equation	NOUN
ejpam-5246	623	11	.	.	PUNCT
ejpam-5246	624	1	iraqi	iraqi	ADJ
ejpam-5246	624	2	journal	journal	PROPN
ejpam-5246	624	3	of	of	ADP
ejpam-5246	624	4	science	science	NOUN
ejpam-5246	624	5	,	,	PUNCT
ejpam-5246	624	6	61(8):2077	61(8):2077	NUM
ejpam-5246	624	7	–	–	PUNCT
ejpam-5246	624	8	2086	2086	NUM
ejpam-5246	624	9	,	,	PUNCT
ejpam-5246	624	10	2020	2020	NUM
ejpam-5246	624	11	.	.	PUNCT
ejpam-5246	625	1	[	[	X
ejpam-5246	625	2	24	24	NUM
ejpam-5246	625	3	]	]	X
ejpam-5246	625	4	maan	maan	PROPN
ejpam-5246	625	5	a	a	DET
ejpam-5246	625	6	rasheed	rasheed	NOUN
ejpam-5246	625	7	,	,	PUNCT
ejpam-5246	625	8	raad	raad	PROPN
ejpam-5246	625	9	awad	awad	PROPN
ejpam-5246	625	10	hameed	hameed	PROPN
ejpam-5246	625	11	,	,	PUNCT
ejpam-5246	625	12	and	and	CCONJ
ejpam-5246	625	13	amal	amal	PROPN
ejpam-5246	625	14	nouman	nouman	PROPN
ejpam-5246	625	15	khalaf	khalaf	PROPN
ejpam-5246	625	16	.	.	PUNCT
ejpam-5246	626	1	numerical	numerical	PROPN
ejpam-5246	626	2	blowup	blowup	ADJ
ejpam-5246	626	3	time	time	NOUN
ejpam-5246	626	4	of	of	ADP
ejpam-5246	626	5	a	a	DET
ejpam-5246	626	6	one	one	NUM
ejpam-5246	626	7	-	-	PUNCT
ejpam-5246	626	8	dimensional	dimensional	ADJ
ejpam-5246	626	9	semilinear	semilinear	ADJ
ejpam-5246	626	10	parabolic	parabolic	NOUN
ejpam-5246	626	11	equation	equation	NOUN
ejpam-5246	626	12	with	with	ADP
ejpam-5246	626	13	a	a	DET
ejpam-5246	626	14	gradient	gradient	ADJ
ejpam-5246	626	15	term	term	NOUN
ejpam-5246	626	16	.	.	PUNCT
ejpam-5246	627	1	iraqi	iraqi	ADJ
ejpam-5246	627	2	journal	journal	PROPN
ejpam-5246	627	3	of	of	ADP
ejpam-5246	627	4	science	science	NOUN
ejpam-5246	627	5	,	,	PUNCT
ejpam-5246	627	6	pages	page	NOUN
ejpam-5246	627	7	354–364	354–364	NUM
ejpam-5246	627	8	,	,	PUNCT
ejpam-5246	627	9	2023	2023	NUM
ejpam-5246	627	10	.	.	PUNCT
ejpam-5246	628	1	[	[	X
ejpam-5246	628	2	25	25	NUM
ejpam-5246	628	3	]	]	PUNCT
ejpam-5246	628	4	philippe	philippe	PROPN
ejpam-5246	628	5	souplet	souplet	NOUN
ejpam-5246	628	6	.	.	PUNCT
ejpam-5246	629	1	recent	recent	ADJ
ejpam-5246	629	2	results	result	NOUN
ejpam-5246	629	3	and	and	CCONJ
ejpam-5246	629	4	open	open	ADJ
ejpam-5246	629	5	problems	problem	NOUN
ejpam-5246	629	6	on	on	ADP
ejpam-5246	629	7	parabolic	parabolic	ADJ
ejpam-5246	629	8	equations	equation	NOUN
ejpam-5246	629	9	with	with	ADP
ejpam-5246	629	10	gradient	gradient	ADJ
ejpam-5246	629	11	nonlinearities	nonlinearitie	NOUN
ejpam-5246	629	12	.	.	PUNCT
ejpam-5246	630	1	electronic	electronic	ADJ
ejpam-5246	630	2	journal	journal	NOUN
ejpam-5246	630	3	of	of	ADP
ejpam-5246	630	4	differential	differential	ADJ
ejpam-5246	630	5	equations	equation	NOUN
ejpam-5246	630	6	(	(	PUNCT
ejpam-5246	630	7	ejde)[electronic	ejde)[electronic	ADJ
ejpam-5246	630	8	only	only	ADV
ejpam-5246	630	9	]	]	PUNCT
ejpam-5246	630	10	,	,	PUNCT
ejpam-5246	630	11	2001	2001	NUM
ejpam-5246	630	12	:	:	PUNCT
ejpam-5246	630	13	paper	paper	NOUN
ejpam-5246	630	14	–	–	PUNCT
ejpam-5246	630	15	no	no	NOUN
ejpam-5246	630	16	,	,	PUNCT
ejpam-5246	630	17	2001	2001	NUM
ejpam-5246	630	18	.	.	PUNCT
ejpam-5246	631	1	[	[	X
ejpam-5246	631	2	26	26	NUM
ejpam-5246	631	3	]	]	X
ejpam-5246	631	4	richard	richard	PROPN
ejpam-5246	631	5	s.	s.	PROPN
ejpam-5246	631	6	varga	varga	PROPN
ejpam-5246	631	7	.	.	PUNCT
ejpam-5246	631	8	matrix	matrix	NOUN
ejpam-5246	631	9	iterative	iterative	NOUN
ejpam-5246	631	10	analysis	analysis	NOUN
ejpam-5246	631	11	.	.	PUNCT
ejpam-5246	632	1	prentice	prentice	NOUN
ejpam-5246	632	2	-	-	PUNCT
ejpam-5246	632	3	hall	hall	NOUN
ejpam-5246	632	4	series	series	NOUN
ejpam-5246	632	5	in	in	ADP
ejpam-5246	632	6	automatic	automatic	ADJ
ejpam-5246	632	7	computation	computation	NOUN
ejpam-5246	632	8	.	.	PUNCT
ejpam-5246	633	1	prentice	prentice	NOUN
ejpam-5246	633	2	-	-	PUNCT
ejpam-5246	633	3	hall	hall	PROPN
ejpam-5246	633	4	,	,	PUNCT
ejpam-5246	633	5	englewood	englewood	PROPN
ejpam-5246	633	6	cliffs	cliff	NOUN
ejpam-5246	633	7	,	,	PUNCT
ejpam-5246	633	8	1962	1962	NUM
ejpam-5246	633	9	.	.	PUNCT
ejpam-5246	634	1	[	[	X
ejpam-5246	634	2	27	27	NUM
ejpam-5246	634	3	]	]	PUNCT
ejpam-5246	634	4	pinghui	pinghui	PROPN
ejpam-5246	634	5	zhuang	zhuang	PROPN
ejpam-5246	634	6	and	and	CCONJ
ejpam-5246	634	7	fawang	fawang	PROPN
ejpam-5246	634	8	liu	liu	PROPN
ejpam-5246	634	9	.	.	PUNCT
ejpam-5246	635	1	finite	finite	PROPN
ejpam-5246	635	2	difference	difference	NOUN
ejpam-5246	635	3	approximation	approximation	NOUN
ejpam-5246	635	4	for	for	ADP
ejpam-5246	635	5	two	two	NUM
ejpam-5246	635	6	-	-	PUNCT
ejpam-5246	635	7	dimensional	dimensional	ADJ
ejpam-5246	635	8	time	time	NOUN
ejpam-5246	635	9	fractional	fractional	ADJ
ejpam-5246	635	10	diffusion	diffusion	NOUN
ejpam-5246	635	11	equation	equation	NOUN
ejpam-5246	635	12	.	.	PUNCT
ejpam-5246	636	1	journal	journal	PROPN
ejpam-5246	636	2	of	of	ADP
ejpam-5246	636	3	algorithms	algorithms	PROPN
ejpam-5246	636	4	&	&	CCONJ
ejpam-5246	636	5	computational	computational	ADJ
ejpam-5246	636	6	technology	technology	NOUN
ejpam-5246	636	7	,	,	PUNCT
ejpam-5246	636	8	1(1):1–16	1(1):1–16	NUM
ejpam-5246	636	9	,	,	PUNCT
ejpam-5246	636	10	2007	2007	NUM
ejpam-5246	636	11	.	.	PUNCT