id	sid	tid	token	lemma	pos
ejpam-6140	1	1	european	european	PROPN
ejpam-6140	1	2	journal	journal	PROPN
ejpam-6140	1	3	of	of	ADP
ejpam-6140	1	4	pure	pure	ADJ
ejpam-6140	1	5	and	and	CCONJ
ejpam-6140	1	6	applied	applied	ADJ
ejpam-6140	1	7	mathematics	mathematic	NOUN
ejpam-6140	1	8	2025	2025	NUM
ejpam-6140	1	9	,	,	PUNCT
ejpam-6140	1	10	vol	vol	NOUN
ejpam-6140	1	11	.	.	PROPN
ejpam-6140	1	12	18	18	NUM
ejpam-6140	1	13	,	,	PUNCT
ejpam-6140	1	14	issue	issue	NOUN
ejpam-6140	1	15	3	3	NUM
ejpam-6140	1	16	,	,	PUNCT
ejpam-6140	1	17	article	article	NOUN
ejpam-6140	1	18	number	number	NOUN
ejpam-6140	1	19	6140	6140	NUM
ejpam-6140	1	20	issn	issn	PROPN
ejpam-6140	1	21	1307	1307	NUM
ejpam-6140	1	22	-	-	SYM
ejpam-6140	1	23	5543	5543	NUM
ejpam-6140	1	24	–	–	PUNCT
ejpam-6140	1	25	ejpam.com	ejpam.com	X
ejpam-6140	1	26	published	publish	VERB
ejpam-6140	1	27	by	by	ADP
ejpam-6140	1	28	new	new	PROPN
ejpam-6140	1	29	york	york	PROPN
ejpam-6140	1	30	business	business	PROPN
ejpam-6140	1	31	global	global	ADJ
ejpam-6140	1	32	finite	finite	PROPN
ejpam-6140	1	33	difference	difference	NOUN
ejpam-6140	1	34	scheme	scheme	NOUN
ejpam-6140	1	35	for	for	ADP
ejpam-6140	1	36	one	one	NUM
ejpam-6140	1	37	-	-	PUNCT
ejpam-6140	1	38	dimensional	dimensional	ADJ
ejpam-6140	1	39	coupled	couple	VERB
ejpam-6140	1	40	parabolic	parabolic	NOUN
ejpam-6140	1	41	system	system	NOUN
ejpam-6140	1	42	with	with	ADP
ejpam-6140	1	43	blow	blow	NOUN
ejpam-6140	1	44	-	-	PUNCT
ejpam-6140	1	45	up	up	ADP
ejpam-6140	1	46	manar	manar	PROPN
ejpam-6140	1	47	i.	i.	PROPN
ejpam-6140	1	48	khalil1,2,∗	khalil1,2,∗	PROPN
ejpam-6140	1	49	,	,	PUNCT
ejpam-6140	1	50	ishak	ishak	PROPN
ejpam-6140	1	51	hashim1	hashim1	PROPN
ejpam-6140	1	52	,	,	PUNCT
ejpam-6140	1	53	maan	maan	PROPN
ejpam-6140	1	54	a.	a.	PROPN
ejpam-6140	1	55	rasheed3	rasheed3	PROPN
ejpam-6140	1	56	,	,	PUNCT
ejpam-6140	1	57	shaher	shaher	ADJ
ejpam-6140	1	58	momani4	momani4	NOUN
ejpam-6140	1	59	1	1	NUM
ejpam-6140	1	60	department	department	NOUN
ejpam-6140	1	61	of	of	ADP
ejpam-6140	1	62	mathematical	mathematical	ADJ
ejpam-6140	1	63	sciences	science	NOUN
ejpam-6140	1	64	,	,	PUNCT
ejpam-6140	1	65	faculty	faculty	NOUN
ejpam-6140	1	66	of	of	ADP
ejpam-6140	1	67	science	science	NOUN
ejpam-6140	1	68	and	and	CCONJ
ejpam-6140	1	69	technology	technology	NOUN
ejpam-6140	1	70	,	,	PUNCT
ejpam-6140	1	71	universiti	universiti	PROPN
ejpam-6140	1	72	kebangsaan	kebangsaan	PROPN
ejpam-6140	1	73	malaysia	malaysia	PROPN
ejpam-6140	1	74	,	,	PUNCT
ejpam-6140	1	75	43600	43600	NUM
ejpam-6140	1	76	ukm	ukm	PROPN
ejpam-6140	1	77	bangi	bangi	PROPN
ejpam-6140	1	78	,	,	PUNCT
ejpam-6140	1	79	selangor	selangor	PROPN
ejpam-6140	1	80	,	,	PUNCT
ejpam-6140	1	81	malaysia	malaysia	PROPN
ejpam-6140	1	82	2	2	NUM
ejpam-6140	1	83	department	department	NOUN
ejpam-6140	1	84	of	of	ADP
ejpam-6140	1	85	applied	apply	VERB
ejpam-6140	1	86	earth	earth	NOUN
ejpam-6140	1	87	sciences	science	NOUN
ejpam-6140	1	88	,	,	PUNCT
ejpam-6140	1	89	college	college	NOUN
ejpam-6140	1	90	of	of	ADP
ejpam-6140	1	91	science	science	NOUN
ejpam-6140	1	92	,	,	PUNCT
ejpam-6140	1	93	tikrit	tikrit	NOUN
ejpam-6140	1	94	university	university	NOUN
ejpam-6140	1	95	,	,	PUNCT
ejpam-6140	1	96	tikrit	tikrit	NOUN
ejpam-6140	1	97	,	,	PUNCT
ejpam-6140	1	98	iraq	iraq	PROPN
ejpam-6140	1	99	3	3	NUM
ejpam-6140	1	100	department	department	NOUN
ejpam-6140	1	101	of	of	ADP
ejpam-6140	1	102	mathematics	mathematics	PROPN
ejpam-6140	1	103	,	,	PUNCT
ejpam-6140	1	104	college	college	NOUN
ejpam-6140	1	105	of	of	ADP
ejpam-6140	1	106	science	science	NOUN
ejpam-6140	1	107	for	for	ADP
ejpam-6140	1	108	women	woman	NOUN
ejpam-6140	1	109	,	,	PUNCT
ejpam-6140	1	110	university	university	NOUN
ejpam-6140	1	111	of	of	ADP
ejpam-6140	1	112	baghdad	baghdad	PROPN
ejpam-6140	1	113	,	,	PUNCT
ejpam-6140	1	114	baghdad	baghdad	PROPN
ejpam-6140	1	115	,	,	PUNCT
ejpam-6140	1	116	iraq	iraq	PROPN
ejpam-6140	1	117	4	4	NUM
ejpam-6140	1	118	nonlinear	nonlinear	ADJ
ejpam-6140	1	119	dynamics	dynamic	NOUN
ejpam-6140	1	120	research	research	NOUN
ejpam-6140	1	121	center	center	NOUN
ejpam-6140	1	122	(	(	PUNCT
ejpam-6140	1	123	ndrc	ndrc	PROPN
ejpam-6140	1	124	)	)	PUNCT
ejpam-6140	1	125	,	,	PUNCT
ejpam-6140	1	126	ajman	ajman	PROPN
ejpam-6140	1	127	university	university	PROPN
ejpam-6140	1	128	,	,	PUNCT
ejpam-6140	1	129	ajman	ajman	PROPN
ejpam-6140	1	130	,	,	PUNCT
ejpam-6140	1	131	united	united	PROPN
ejpam-6140	1	132	arab	arab	PROPN
ejpam-6140	1	133	emirates	emirates	PROPN
ejpam-6140	1	134	abstract	abstract	PROPN
ejpam-6140	1	135	.	.	PUNCT
ejpam-6140	2	1	this	this	DET
ejpam-6140	2	2	study	study	NOUN
ejpam-6140	2	3	aims	aim	VERB
ejpam-6140	2	4	to	to	PART
ejpam-6140	2	5	find	find	VERB
ejpam-6140	2	6	an	an	DET
ejpam-6140	2	7	efficient	efficient	ADJ
ejpam-6140	2	8	technique	technique	NOUN
ejpam-6140	2	9	to	to	PART
ejpam-6140	2	10	estimate	estimate	VERB
ejpam-6140	2	11	the	the	DET
ejpam-6140	2	12	blow	blow	NOUN
ejpam-6140	2	13	-	-	PUNCT
ejpam-6140	2	14	up	up	ADP
ejpam-6140	2	15	time	time	NOUN
ejpam-6140	2	16	(	(	PUNCT
ejpam-6140	2	17	but	but	CCONJ
ejpam-6140	2	18	)	)	PUNCT
ejpam-6140	2	19	of	of	ADP
ejpam-6140	2	20	one	one	NUM
ejpam-6140	2	21	-	-	PUNCT
ejpam-6140	2	22	dimensional	dimensional	ADJ
ejpam-6140	2	23	semi	semi	ADJ
ejpam-6140	2	24	-	-	ADJ
ejpam-6140	2	25	linear	linear	ADJ
ejpam-6140	2	26	coupled	couple	VERB
ejpam-6140	2	27	parabolic	parabolic	NOUN
ejpam-6140	2	28	systems	system	NOUN
ejpam-6140	2	29	.	.	PUNCT
ejpam-6140	3	1	firstly	firstly	ADV
ejpam-6140	3	2	,	,	PUNCT
ejpam-6140	3	3	a	a	DET
ejpam-6140	3	4	fully	fully	ADV
ejpam-6140	3	5	discrete	discrete	ADJ
ejpam-6140	3	6	finite	finite	ADJ
ejpam-6140	3	7	difference	difference	NOUN
ejpam-6140	3	8	formula	formula	NOUN
ejpam-6140	3	9	is	be	AUX
ejpam-6140	3	10	derived	derive	VERB
ejpam-6140	3	11	with	with	ADP
ejpam-6140	3	12	a	a	DET
ejpam-6140	3	13	non	non	ADJ
ejpam-6140	3	14	-	-	ADJ
ejpam-6140	3	15	fixed	fixed	ADJ
ejpam-6140	3	16	time	time	NOUN
ejpam-6140	3	17	-	-	PUNCT
ejpam-6140	3	18	stepping	step	VERB
ejpam-6140	3	19	formula	formula	NOUN
ejpam-6140	3	20	,	,	PUNCT
ejpam-6140	3	21	based	base	VERB
ejpam-6140	3	22	on	on	ADP
ejpam-6140	3	23	the	the	DET
ejpam-6140	3	24	crank	crank	NOUN
ejpam-6140	3	25	-	-	PUNCT
ejpam-6140	3	26	nicolson	nicolson	PROPN
ejpam-6140	3	27	method	method	NOUN
ejpam-6140	3	28	.	.	PUNCT
ejpam-6140	4	1	in	in	ADP
ejpam-6140	4	2	addition	addition	NOUN
ejpam-6140	4	3	,	,	PUNCT
ejpam-6140	4	4	the	the	DET
ejpam-6140	4	5	consistency	consistency	NOUN
ejpam-6140	4	6	,	,	PUNCT
ejpam-6140	4	7	stability	stability	NOUN
ejpam-6140	4	8	,	,	PUNCT
ejpam-6140	4	9	and	and	CCONJ
ejpam-6140	4	10	convergence	convergence	NOUN
ejpam-6140	4	11	of	of	ADP
ejpam-6140	4	12	the	the	DET
ejpam-6140	4	13	proposed	propose	VERB
ejpam-6140	4	14	scheme	scheme	NOUN
ejpam-6140	4	15	are	be	AUX
ejpam-6140	4	16	considered	consider	VERB
ejpam-6140	4	17	.	.	PUNCT
ejpam-6140	5	1	secondly	secondly	ADV
ejpam-6140	5	2	,	,	PUNCT
ejpam-6140	5	3	two	two	NUM
ejpam-6140	5	4	numerical	numerical	ADJ
ejpam-6140	5	5	experiments	experiment	NOUN
ejpam-6140	5	6	are	be	AUX
ejpam-6140	5	7	presented	present	VERB
ejpam-6140	5	8	.	.	PUNCT
ejpam-6140	6	1	for	for	ADP
ejpam-6140	6	2	each	each	DET
ejpam-6140	6	3	experiment	experiment	NOUN
ejpam-6140	6	4	,	,	PUNCT
ejpam-6140	6	5	we	we	PRON
ejpam-6140	6	6	apply	apply	VERB
ejpam-6140	6	7	the	the	DET
ejpam-6140	6	8	proposed	propose	VERB
ejpam-6140	6	9	scheme	scheme	NOUN
ejpam-6140	6	10	to	to	PART
ejpam-6140	6	11	calculate	calculate	VERB
ejpam-6140	6	12	the	the	DET
ejpam-6140	6	13	numerical	numerical	ADJ
ejpam-6140	6	14	blow	blow	VERB
ejpam-6140	6	15	-	-	PUNCT
ejpam-6140	6	16	up	up	ADP
ejpam-6140	6	17	time	time	NOUN
ejpam-6140	6	18	,	,	PUNCT
ejpam-6140	6	19	error	error	NOUN
ejpam-6140	6	20	bounds	bound	NOUN
ejpam-6140	6	21	,	,	PUNCT
ejpam-6140	6	22	and	and	CCONJ
ejpam-6140	6	23	the	the	DET
ejpam-6140	6	24	numerical	numerical	ADJ
ejpam-6140	6	25	order	order	NOUN
ejpam-6140	6	26	of	of	ADP
ejpam-6140	6	27	convergence	convergence	NOUN
ejpam-6140	6	28	for	for	ADP
ejpam-6140	6	29	blow	blow	NOUN
ejpam-6140	6	30	-	-	PUNCT
ejpam-6140	6	31	up	up	ADP
ejpam-6140	6	32	times	time	NOUN
ejpam-6140	6	33	.	.	PUNCT
ejpam-6140	7	1	the	the	DET
ejpam-6140	7	2	obtained	obtain	VERB
ejpam-6140	7	3	results	result	NOUN
ejpam-6140	7	4	show	show	VERB
ejpam-6140	7	5	that	that	SCONJ
ejpam-6140	7	6	the	the	DET
ejpam-6140	7	7	proposed	propose	VERB
ejpam-6140	7	8	c.n	c.n	NOUN
ejpam-6140	7	9	scheme	scheme	NOUN
ejpam-6140	7	10	is	be	AUX
ejpam-6140	7	11	consistent	consistent	ADJ
ejpam-6140	7	12	with	with	ADP
ejpam-6140	7	13	the	the	DET
ejpam-6140	7	14	system	system	NOUN
ejpam-6140	7	15	considered	consider	VERB
ejpam-6140	7	16	.	.	PUNCT
ejpam-6140	8	1	however	however	ADV
ejpam-6140	8	2	,	,	PUNCT
ejpam-6140	8	3	it	it	PRON
ejpam-6140	8	4	is	be	AUX
ejpam-6140	8	5	conditionally	conditionally	ADV
ejpam-6140	8	6	stable	stable	ADJ
ejpam-6140	8	7	,	,	PUNCT
ejpam-6140	8	8	and	and	CCONJ
ejpam-6140	8	9	the	the	DET
ejpam-6140	8	10	crank	crank	NOUN
ejpam-6140	8	11	-	-	PUNCT
ejpam-6140	8	12	nicolson	nicolson	PROPN
ejpam-6140	8	13	scheme	scheme	NOUN
ejpam-6140	8	14	converges	converge	NOUN
ejpam-6140	8	15	in	in	ADP
ejpam-6140	8	16	the	the	DET
ejpam-6140	8	17	stability	stability	NOUN
ejpam-6140	8	18	region	region	NOUN
ejpam-6140	8	19	and	and	CCONJ
ejpam-6140	8	20	achieves	achieve	VERB
ejpam-6140	8	21	firstand	firstand	ADJ
ejpam-6140	8	22	second	second	ADJ
ejpam-6140	8	23	-	-	PUNCT
ejpam-6140	8	24	order	order	NOUN
ejpam-6140	8	25	accuracy	accuracy	NOUN
ejpam-6140	8	26	in	in	ADP
ejpam-6140	8	27	temporal	temporal	ADJ
ejpam-6140	8	28	and	and	CCONJ
ejpam-6140	8	29	spatial	spatial	ADJ
ejpam-6140	8	30	dimensions	dimension	NOUN
ejpam-6140	8	31	,	,	PUNCT
ejpam-6140	8	32	respectively	respectively	ADV
ejpam-6140	8	33	.	.	PUNCT
ejpam-6140	9	1	also	also	ADV
ejpam-6140	9	2	,	,	PUNCT
ejpam-6140	9	3	it	it	PRON
ejpam-6140	9	4	helps	help	VERB
ejpam-6140	9	5	to	to	PART
ejpam-6140	9	6	increase	increase	VERB
ejpam-6140	9	7	the	the	DET
ejpam-6140	9	8	order	order	NOUN
ejpam-6140	9	9	of	of	ADP
ejpam-6140	9	10	numerical	numerical	ADJ
ejpam-6140	9	11	convergence	convergence	NOUN
ejpam-6140	9	12	.	.	PUNCT
ejpam-6140	10	1	furthermore	furthermore	ADV
ejpam-6140	10	2	,	,	PUNCT
ejpam-6140	10	3	the	the	DET
ejpam-6140	10	4	numerical	numerical	ADJ
ejpam-6140	10	5	experiments	experiment	NOUN
ejpam-6140	10	6	demonstrate	demonstrate	VERB
ejpam-6140	10	7	that	that	SCONJ
ejpam-6140	10	8	the	the	DET
ejpam-6140	10	9	numerical	numerical	ADJ
ejpam-6140	10	10	blow	blow	NOUN
ejpam-6140	10	11	-	-	PUNCT
ejpam-6140	10	12	up	up	NOUN
ejpam-6140	10	13	simultaneously	simultaneously	ADV
ejpam-6140	10	14	occurs	occur	VERB
ejpam-6140	10	15	at	at	ADP
ejpam-6140	10	16	only	only	ADV
ejpam-6140	10	17	the	the	DET
ejpam-6140	10	18	center	center	ADJ
ejpam-6140	10	19	point	point	NOUN
ejpam-6140	10	20	.	.	PUNCT
ejpam-6140	11	1	finally	finally	ADV
ejpam-6140	11	2	,	,	PUNCT
ejpam-6140	11	3	the	the	DET
ejpam-6140	11	4	numerical	numerical	ADJ
ejpam-6140	11	5	blow	blow	VERB
ejpam-6140	11	6	-	-	PUNCT
ejpam-6140	11	7	up	up	ADP
ejpam-6140	11	8	time	time	NOUN
ejpam-6140	11	9	sequence	sequence	NOUN
ejpam-6140	11	10	is	be	AUX
ejpam-6140	11	11	convergent	convergent	ADJ
ejpam-6140	11	12	.	.	PUNCT
ejpam-6140	12	1	moreover	moreover	ADV
ejpam-6140	12	2	,	,	PUNCT
ejpam-6140	12	3	convergence	convergence	NOUN
ejpam-6140	12	4	for	for	ADP
ejpam-6140	12	5	the	the	DET
ejpam-6140	12	6	blow	blow	NOUN
ejpam-6140	12	7	-	-	PUNCT
ejpam-6140	12	8	up	up	ADP
ejpam-6140	12	9	time	time	NOUN
ejpam-6140	12	10	agrees	agree	VERB
ejpam-6140	12	11	well	well	ADV
ejpam-6140	12	12	with	with	ADP
ejpam-6140	12	13	the	the	DET
ejpam-6140	12	14	theoretical	theoretical	ADJ
ejpam-6140	12	15	order	order	NOUN
ejpam-6140	12	16	of	of	ADP
ejpam-6140	12	17	convergence	convergence	NOUN
ejpam-6140	12	18	of	of	ADP
ejpam-6140	12	19	the	the	DET
ejpam-6140	12	20	proposed	propose	VERB
ejpam-6140	12	21	scheme	scheme	NOUN
ejpam-6140	12	22	.	.	PUNCT
ejpam-6140	13	1	2020	2020	NUM
ejpam-6140	13	2	mathematics	mathematic	NOUN
ejpam-6140	13	3	subject	subject	NOUN
ejpam-6140	13	4	classifications	classification	NOUN
ejpam-6140	13	5	:	:	PUNCT
ejpam-6140	13	6	35k57	35k57	NUM
ejpam-6140	13	7	,	,	PUNCT
ejpam-6140	13	8	65m06	65m06	NUM
ejpam-6140	13	9	,	,	PUNCT
ejpam-6140	13	10	65m12	65m12	NUM
ejpam-6140	13	11	,	,	PUNCT
ejpam-6140	13	12	35b44	35b44	NUM
ejpam-6140	13	13	key	key	ADJ
ejpam-6140	13	14	words	word	NOUN
ejpam-6140	13	15	and	and	CCONJ
ejpam-6140	13	16	phrases	phrase	NOUN
ejpam-6140	13	17	:	:	PUNCT
ejpam-6140	13	18	fully	fully	ADV
ejpam-6140	13	19	discrete	discrete	ADJ
ejpam-6140	13	20	,	,	PUNCT
ejpam-6140	13	21	crank	crank	NOUN
ejpam-6140	13	22	-	-	PUNCT
ejpam-6140	13	23	nicolson	nicolson	PROPN
ejpam-6140	13	24	formula	formula	NOUN
ejpam-6140	13	25	,	,	PUNCT
ejpam-6140	13	26	numerical	numerical	ADJ
ejpam-6140	13	27	blow	blow	NOUN
ejpam-6140	13	28	-	-	PUNCT
ejpam-6140	13	29	up	up	ADP
ejpam-6140	13	30	times	time	NOUN
ejpam-6140	13	31	,	,	PUNCT
ejpam-6140	13	32	convergence	convergence	NOUN
ejpam-6140	13	33	,	,	PUNCT
ejpam-6140	13	34	blow	blow	NOUN
ejpam-6140	13	35	-	-	PUNCT
ejpam-6140	13	36	up	up	ADP
ejpam-6140	13	37	time	time	NOUN
ejpam-6140	13	38	,	,	PUNCT
ejpam-6140	13	39	consistency	consistency	NOUN
ejpam-6140	13	40	,	,	PUNCT
ejpam-6140	13	41	stability	stability	NOUN
ejpam-6140	13	42	1	1	NUM
ejpam-6140	13	43	.	.	PUNCT
ejpam-6140	14	1	introduction	introduction	NOUN
ejpam-6140	14	2	in	in	ADP
ejpam-6140	14	3	recent	recent	ADJ
ejpam-6140	14	4	decades	decade	NOUN
ejpam-6140	14	5	,	,	PUNCT
ejpam-6140	14	6	many	many	ADJ
ejpam-6140	14	7	real	real	ADJ
ejpam-6140	14	8	-	-	PUNCT
ejpam-6140	14	9	world	world	NOUN
ejpam-6140	14	10	problems	problem	NOUN
ejpam-6140	14	11	have	have	AUX
ejpam-6140	14	12	been	be	AUX
ejpam-6140	14	13	modeled	model	VERB
ejpam-6140	14	14	by	by	ADP
ejpam-6140	14	15	pdes	pde	NOUN
ejpam-6140	14	16	,	,	PUNCT
ejpam-6140	14	17	see	see	VERB
ejpam-6140	14	18	[	[	X
ejpam-6140	14	19	1	1	NUM
ejpam-6140	14	20	–	–	PUNCT
ejpam-6140	14	21	3	3	NUM
ejpam-6140	14	22	]	]	PUNCT
ejpam-6140	14	23	.	.	PUNCT
ejpam-6140	15	1	there	there	PRON
ejpam-6140	15	2	are	be	VERB
ejpam-6140	15	3	many	many	ADJ
ejpam-6140	15	4	parabolic	parabolic	ADJ
ejpam-6140	15	5	-	-	PUNCT
ejpam-6140	15	6	type	type	NOUN
ejpam-6140	15	7	pdes	pde	NOUN
ejpam-6140	15	8	whose	whose	DET
ejpam-6140	15	9	solutions	solution	NOUN
ejpam-6140	15	10	can	can	AUX
ejpam-6140	15	11	not	not	PART
ejpam-6140	15	12	possibly	possibly	ADV
ejpam-6140	15	13	be	be	AUX
ejpam-6140	15	14	extended	extend	VERB
ejpam-6140	15	15	∗corresponding	∗corresponde	VERB
ejpam-6140	15	16	author	author	NOUN
ejpam-6140	15	17	.	.	PUNCT
ejpam-6140	16	1	doi	doi	NOUN
ejpam-6140	16	2	:	:	PUNCT
ejpam-6140	16	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6140	https://doi.org/10.29020/nybg.ejpam.v18i3.6140	ADJ
ejpam-6140	16	4	email	email	NOUN
ejpam-6140	16	5	addresses	address	VERB
ejpam-6140	16	6	:	:	PUNCT
ejpam-6140	16	7	p119266@siswa.ukm.edu.my	p119266@siswa.ukm.edu.my	X
ejpam-6140	16	8	(	(	PUNCT
ejpam-6140	16	9	m.	m.	PROPN
ejpam-6140	16	10	i.	i.	PROPN
ejpam-6140	16	11	khalil	khalil	PROPN
ejpam-6140	16	12	)	)	PUNCT
ejpam-6140	16	13	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6140	17	1	1	1	NUM
ejpam-6140	17	2	copyright	copyright	NOUN
ejpam-6140	17	3	:	:	PUNCT
ejpam-6140	17	4	©	©	PROPN
ejpam-6140	17	5	2025	2025	NUM
ejpam-6140	17	6	the	the	DET
ejpam-6140	17	7	author(s	author(s	NOUN
ejpam-6140	17	8	)	)	PUNCT
ejpam-6140	17	9	.	.	PUNCT
ejpam-6140	18	1	(	(	PUNCT
ejpam-6140	18	2	cc	cc	NOUN
ejpam-6140	18	3	by	by	ADP
ejpam-6140	18	4	-	-	PUNCT
ejpam-6140	18	5	nc	nc	PROPN
ejpam-6140	18	6	4.0	4.0	NUM
ejpam-6140	18	7	)	)	PUNCT
ejpam-6140	18	8	m.	m.	NOUN
ejpam-6140	18	9	i.	i.	PROPN
ejpam-6140	18	10	khalil	khalil	PROPN
ejpam-6140	18	11	et	et	PROPN
ejpam-6140	18	12	al	al	PROPN
ejpam-6140	18	13	.	.	PUNCT
ejpam-6140	18	14	/	/	SYM
ejpam-6140	18	15	eur	eur	PROPN
ejpam-6140	18	16	.	.	PUNCT
ejpam-6140	19	1	j.	j.	PROPN
ejpam-6140	19	2	pure	pure	PROPN
ejpam-6140	19	3	appl	appl	PROPN
ejpam-6140	19	4	.	.	PROPN
ejpam-6140	19	5	math	math	PROPN
ejpam-6140	19	6	,	,	PUNCT
ejpam-6140	19	7	18	18	NUM
ejpam-6140	19	8	(	(	PUNCT
ejpam-6140	19	9	3	3	NUM
ejpam-6140	19	10	)	)	PUNCT
ejpam-6140	19	11	(	(	PUNCT
ejpam-6140	19	12	2025	2025	NUM
ejpam-6140	19	13	)	)	PUNCT
ejpam-6140	19	14	,	,	PUNCT
ejpam-6140	19	15	6140	6140	NUM
ejpam-6140	19	16	2	2	NUM
ejpam-6140	19	17	of	of	ADP
ejpam-6140	19	18	17	17	NUM
ejpam-6140	19	19	globally	globally	ADV
ejpam-6140	19	20	over	over	ADP
ejpam-6140	19	21	time	time	NOUN
ejpam-6140	19	22	.	.	PUNCT
ejpam-6140	20	1	this	this	DET
ejpam-6140	20	2	phenomenon	phenomenon	NOUN
ejpam-6140	20	3	is	be	AUX
ejpam-6140	20	4	known	know	VERB
ejpam-6140	20	5	as	as	ADP
ejpam-6140	20	6	blow	blow	NOUN
ejpam-6140	20	7	-	-	PUNCT
ejpam-6140	20	8	up	up	NOUN
ejpam-6140	20	9	(	(	PUNCT
ejpam-6140	20	10	bu	bu	NOUN
ejpam-6140	20	11	)	)	PUNCT
ejpam-6140	20	12	,	,	PUNCT
ejpam-6140	20	13	and	and	CCONJ
ejpam-6140	20	14	it	it	PRON
ejpam-6140	20	15	occurs	occur	VERB
ejpam-6140	20	16	in	in	ADP
ejpam-6140	20	17	semilinear	semilinear	NOUN
ejpam-6140	20	18	diffusion	diffusion	NOUN
ejpam-6140	20	19	equations	equation	NOUN
ejpam-6140	20	20	,	,	PUNCT
ejpam-6140	20	21	when	when	SCONJ
ejpam-6140	20	22	the	the	DET
ejpam-6140	20	23	heat	heat	NOUN
ejpam-6140	20	24	source	source	NOUN
ejpam-6140	20	25	is	be	AUX
ejpam-6140	20	26	strong	strong	ADJ
ejpam-6140	20	27	enough	enough	ADV
ejpam-6140	20	28	[	[	X
ejpam-6140	20	29	4–8	4–8	X
ejpam-6140	20	30	]	]	X
ejpam-6140	20	31	this	this	DET
ejpam-6140	20	32	phenomenon	phenomenon	NOUN
ejpam-6140	20	33	can	can	AUX
ejpam-6140	20	34	be	be	AUX
ejpam-6140	20	35	applied	apply	VERB
ejpam-6140	20	36	to	to	ADP
ejpam-6140	20	37	interconnected	interconnected	ADJ
ejpam-6140	20	38	systems	system	NOUN
ejpam-6140	20	39	,	,	PUNCT
ejpam-6140	20	40	where	where	SCONJ
ejpam-6140	20	41	each	each	DET
ejpam-6140	20	42	variable	variable	NOUN
ejpam-6140	20	43	that	that	PRON
ejpam-6140	20	44	relies	rely	VERB
ejpam-6140	20	45	on	on	ADP
ejpam-6140	20	46	another	another	DET
ejpam-6140	20	47	experiences	experience	NOUN
ejpam-6140	20	48	finite	finite	ADJ
ejpam-6140	20	49	growth	growth	NOUN
ejpam-6140	20	50	within	within	ADP
ejpam-6140	20	51	a	a	DET
ejpam-6140	20	52	designated	designate	VERB
ejpam-6140	20	53	time	time	NOUN
ejpam-6140	20	54	frame	frame	NOUN
ejpam-6140	20	55	.	.	PUNCT
ejpam-6140	21	1	in	in	ADP
ejpam-6140	21	2	this	this	DET
ejpam-6140	21	3	specific	specific	ADJ
ejpam-6140	21	4	situation	situation	NOUN
ejpam-6140	21	5	,	,	PUNCT
ejpam-6140	21	6	it	it	PRON
ejpam-6140	21	7	is	be	AUX
ejpam-6140	21	8	known	know	VERB
ejpam-6140	21	9	that	that	SCONJ
ejpam-6140	21	10	the	the	DET
ejpam-6140	21	11	dependent	dependent	ADJ
ejpam-6140	21	12	variables	variable	NOUN
ejpam-6140	21	13	in	in	ADP
ejpam-6140	21	14	the	the	DET
ejpam-6140	21	15	equations	equation	NOUN
ejpam-6140	21	16	demonstrate	demonstrate	VERB
ejpam-6140	21	17	synchronized	synchronize	VERB
ejpam-6140	21	18	increases	increase	NOUN
ejpam-6140	22	1	[	[	X
ejpam-6140	22	2	9	9	NUM
ejpam-6140	22	3	,	,	PUNCT
ejpam-6140	22	4	10].this	10].this	PROPN
ejpam-6140	22	5	phenomenon	phenomenon	NOUN
ejpam-6140	22	6	has	have	VERB
ejpam-6140	22	7	several	several	ADJ
ejpam-6140	22	8	applications	application	NOUN
ejpam-6140	22	9	,	,	PUNCT
ejpam-6140	22	10	especially	especially	ADV
ejpam-6140	22	11	in	in	ADP
ejpam-6140	22	12	combustion	combustion	NOUN
ejpam-6140	22	13	theory	theory	NOUN
ejpam-6140	22	14	and	and	CCONJ
ejpam-6140	22	15	heat	heat	NOUN
ejpam-6140	22	16	propagation	propagation	NOUN
ejpam-6140	22	17	[	[	X
ejpam-6140	22	18	11	11	NUM
ejpam-6140	22	19	]	]	PUNCT
ejpam-6140	22	20	.	.	PUNCT
ejpam-6140	23	1	according	accord	VERB
ejpam-6140	23	2	to	to	ADP
ejpam-6140	23	3	[	[	X
ejpam-6140	23	4	10	10	NUM
ejpam-6140	23	5	]	]	PUNCT
ejpam-6140	23	6	,	,	PUNCT
ejpam-6140	23	7	a	a	DET
ejpam-6140	23	8	solution	solution	NOUN
ejpam-6140	23	9	of	of	ADP
ejpam-6140	23	10	a	a	DET
ejpam-6140	23	11	diffusion	diffusion	NOUN
ejpam-6140	23	12	equation	equation	NOUN
ejpam-6140	23	13	defined	define	VERB
ejpam-6140	23	14	on	on	ADP
ejpam-6140	23	15	ω	ω	NUM
ejpam-6140	23	16	×	×	NOUN
ejpam-6140	23	17	{	{	PUNCT
ejpam-6140	23	18	t	t	X
ejpam-6140	23	19	>	>	X
ejpam-6140	23	20	0	0	NUM
ejpam-6140	23	21	}	}	PUNCT
ejpam-6140	23	22	blows	blow	VERB
ejpam-6140	23	23	up	up	ADP
ejpam-6140	23	24	,	,	PUNCT
ejpam-6140	23	25	if	if	SCONJ
ejpam-6140	23	26	there	there	PRON
ejpam-6140	23	27	exist	exist	VERB
ejpam-6140	23	28	t	t	PROPN
ejpam-6140	23	29	<	<	X
ejpam-6140	23	30	∞	∞	PROPN
ejpam-6140	23	31	,	,	PUNCT
ejpam-6140	23	32	such	such	ADJ
ejpam-6140	23	33	that	that	SCONJ
ejpam-6140	23	34	it	it	PRON
ejpam-6140	23	35	is	be	AUX
ejpam-6140	23	36	still	still	ADV
ejpam-6140	23	37	bounded	bound	VERB
ejpam-6140	23	38	as	as	ADV
ejpam-6140	23	39	long	long	ADV
ejpam-6140	23	40	as	as	ADP
ejpam-6140	23	41	0	0	NUM
ejpam-6140	23	42	<	<	X
ejpam-6140	23	43	t	t	X
ejpam-6140	23	44	<	<	X
ejpam-6140	23	45	t	t	PROPN
ejpam-6140	23	46	,	,	PUNCT
ejpam-6140	23	47	while	while	SCONJ
ejpam-6140	23	48	it	it	PRON
ejpam-6140	23	49	is	be	AUX
ejpam-6140	23	50	unbounded	unbounded	ADJ
ejpam-6140	23	51	as	as	ADP
ejpam-6140	23	52	t	t	PROPN
ejpam-6140	23	53	is	be	AUX
ejpam-6140	23	54	close	close	ADJ
ejpam-6140	23	55	to	to	ADP
ejpam-6140	23	56	the	the	DET
ejpam-6140	23	57	blow	blow	NOUN
ejpam-6140	23	58	-	-	PUNCT
ejpam-6140	23	59	up	up	ADP
ejpam-6140	23	60	time	time	NOUN
ejpam-6140	23	61	t	t	NOUN
ejpam-6140	23	62	,	,	PUNCT
ejpam-6140	24	1	i.e.	i.e.	X
ejpam-6140	24	2	sup	sup	NOUN
ejpam-6140	24	3	x∈ω	x∈ω	NOUN
ejpam-6140	24	4	|u(x	|u(x	NOUN
ejpam-6140	24	5	,	,	PUNCT
ejpam-6140	24	6	t)|	t)|	PROPN
ejpam-6140	24	7	→	→	SYM
ejpam-6140	24	8	∞	∞	PROPN
ejpam-6140	24	9	as	as	ADP
ejpam-6140	24	10	t	t	PROPN
ejpam-6140	24	11	→	→	SYM
ejpam-6140	24	12	t−.	t−.	PROPN
ejpam-6140	24	13	for	for	ADP
ejpam-6140	24	14	a	a	DET
ejpam-6140	24	15	coupled	couple	VERB
ejpam-6140	24	16	diffusion	diffusion	NOUN
ejpam-6140	24	17	system	system	NOUN
ejpam-6140	24	18	:	:	PUNCT
ejpam-6140	24	19	ut	ut	PROPN
ejpam-6140	24	20	=	=	PROPN
ejpam-6140	24	21	uxx	uxx	PROPN
ejpam-6140	25	1	+	+	CCONJ
ejpam-6140	25	2	f	f	X
ejpam-6140	25	3	(	(	PUNCT
ejpam-6140	25	4	u	u	NOUN
ejpam-6140	25	5	,	,	PUNCT
ejpam-6140	25	6	v	v	NOUN
ejpam-6140	25	7	)	)	PUNCT
ejpam-6140	25	8	,	,	PUNCT
ejpam-6140	25	9	vt	vt	PROPN
ejpam-6140	25	10	=	=	PUNCT
ejpam-6140	25	11	vxx	vxx	PROPN
ejpam-6140	26	1	+	+	PUNCT
ejpam-6140	26	2	g(u	g(u	PROPN
ejpam-6140	26	3	,	,	PUNCT
ejpam-6140	26	4	v	v	NOUN
ejpam-6140	26	5	)	)	PUNCT
ejpam-6140	26	6	,	,	PUNCT
ejpam-6140	26	7	(	(	PUNCT
ejpam-6140	26	8	x	x	X
ejpam-6140	26	9	,	,	PUNCT
ejpam-6140	26	10	t	t	PROPN
ejpam-6140	26	11	)	)	PUNCT
ejpam-6140	26	12	∈	∈	PROPN
ejpam-6140	26	13	ω×	ω×	PUNCT
ejpam-6140	26	14	(	(	PUNCT
ejpam-6140	26	15	0	0	NUM
ejpam-6140	26	16	,	,	PUNCT
ejpam-6140	26	17	t	t	NOUN
ejpam-6140	26	18	)	)	PUNCT
ejpam-6140	26	19	,	,	PUNCT
ejpam-6140	27	1	f	f	X
ejpam-6140	27	2	,	,	PUNCT
ejpam-6140	27	3	g	g	NOUN
ejpam-6140	27	4	:	:	PUNCT
ejpam-6140	27	5	r2	r2	PROPN
ejpam-6140	27	6	→	→	SYM
ejpam-6140	27	7	r	r	NOUN
ejpam-6140	27	8	,	,	PUNCT
ejpam-6140	27	9	a	a	DET
ejpam-6140	27	10	solution	solution	NOUN
ejpam-6140	27	11	(	(	PUNCT
ejpam-6140	27	12	u	u	NOUN
ejpam-6140	27	13	,	,	PUNCT
ejpam-6140	27	14	v	v	NOUN
ejpam-6140	27	15	)	)	PUNCT
ejpam-6140	27	16	blows	blow	VERB
ejpam-6140	27	17	up	up	ADP
ejpam-6140	27	18	simultaneously	simultaneously	ADV
ejpam-6140	27	19	if	if	SCONJ
ejpam-6140	27	20	there	there	PRON
ejpam-6140	27	21	exists	exist	VERB
ejpam-6140	27	22	t	t	PROPN
ejpam-6140	27	23	<	<	X
ejpam-6140	27	24	∞	∞	NUM
ejpam-6140	27	25	such	such	ADJ
ejpam-6140	27	26	that	that	SCONJ
ejpam-6140	27	27	u	u	NOUN
ejpam-6140	27	28	and	and	CCONJ
ejpam-6140	27	29	v	v	NOUN
ejpam-6140	27	30	blow	blow	NOUN
ejpam-6140	27	31	up	up	ADP
ejpam-6140	27	32	at	at	ADP
ejpam-6140	27	33	t	t	PROPN
ejpam-6140	27	34	.	.	PUNCT
ejpam-6140	28	1	i.e.	i.e.	X
ejpam-6140	28	2	supx∈ω	supx∈ω	NOUN
ejpam-6140	28	3	|u(x	|u(x	PROPN
ejpam-6140	28	4	,	,	PUNCT
ejpam-6140	28	5	t)|	t)|	NOUN
ejpam-6140	28	6	→	→	SYM
ejpam-6140	28	7	∞	∞	PROPN
ejpam-6140	28	8	,	,	PUNCT
ejpam-6140	28	9	&	&	CCONJ
ejpam-6140	28	10	supx∈ω	supx∈ω	PROPN
ejpam-6140	28	11	|v(x	|v(x	PROPN
ejpam-6140	28	12	,	,	PUNCT
ejpam-6140	28	13	t)|	t)|	NOUN
ejpam-6140	28	14	→	→	SYM
ejpam-6140	28	15	∞	∞	PROPN
ejpam-6140	28	16	,	,	PUNCT
ejpam-6140	28	17	as	as	ADP
ejpam-6140	28	18	t	t	PROPN
ejpam-6140	28	19	→	→	SYM
ejpam-6140	28	20	t−	t−	PROPN
ejpam-6140	28	21	,	,	PUNCT
ejpam-6140	28	22	while	while	SCONJ
ejpam-6140	28	23	for	for	ADP
ejpam-6140	28	24	t	t	PROPN
ejpam-6140	28	25	<	<	X
ejpam-6140	28	26	t	t	PROPN
ejpam-6140	28	27	,	,	PUNCT
ejpam-6140	28	28	supx∈ω{|u(x	supx∈ω{|u(x	PROPN
ejpam-6140	28	29	,	,	PUNCT
ejpam-6140	28	30	t)|	t)|	NOUN
ejpam-6140	28	31	,	,	PUNCT
ejpam-6140	28	32	|v(x	|v(x	PROPN
ejpam-6140	28	33	,	,	PUNCT
ejpam-6140	28	34	t)|	t)|	NOUN
ejpam-6140	28	35	}	}	PUNCT
ejpam-6140	28	36	<	<	X
ejpam-6140	28	37	∞	∞	PROPN
ejpam-6140	28	38	,	,	PUNCT
ejpam-6140	28	39	in	in	ADP
ejpam-6140	28	40	this	this	DET
ejpam-6140	28	41	work	work	NOUN
ejpam-6140	28	42	,	,	PUNCT
ejpam-6140	28	43	we	we	PRON
ejpam-6140	28	44	consider	consider	VERB
ejpam-6140	28	45	the	the	DET
ejpam-6140	28	46	system	system	NOUN
ejpam-6140	28	47	:	:	PUNCT
ejpam-6140	28	48	ut	ut	PROPN
ejpam-6140	28	49	=	=	PROPN
ejpam-6140	28	50	uxx	uxx	PROPN
ejpam-6140	28	51	+	+	NUM
ejpam-6140	28	52	f(v	f(v	NOUN
ejpam-6140	28	53	)	)	PUNCT
ejpam-6140	28	54	,	,	PUNCT
ejpam-6140	28	55	vt	vt	PROPN
ejpam-6140	28	56	=	=	SYM
ejpam-6140	28	57	vxx	vxx	PROPN
ejpam-6140	28	58	+	+	CCONJ
ejpam-6140	28	59	g(u	g(u	PROPN
ejpam-6140	28	60	)	)	PUNCT
ejpam-6140	28	61	,	,	PUNCT
ejpam-6140	28	62	(	(	PUNCT
ejpam-6140	28	63	x	x	X
ejpam-6140	28	64	,	,	PUNCT
ejpam-6140	28	65	t	t	PROPN
ejpam-6140	28	66	)	)	PUNCT
ejpam-6140	28	67	∈	∈	PROPN
ejpam-6140	28	68	(	(	PUNCT
ejpam-6140	28	69	0	0	NUM
ejpam-6140	28	70	,	,	PUNCT
ejpam-6140	28	71	1)×	1)×	NUM
ejpam-6140	28	72	(	(	PUNCT
ejpam-6140	28	73	0	0	NUM
ejpam-6140	28	74	,	,	PUNCT
ejpam-6140	28	75	t	t	NOUN
ejpam-6140	28	76	)	)	PUNCT
ejpam-6140	29	1	u(0	u(0	PROPN
ejpam-6140	29	2	,	,	PUNCT
ejpam-6140	29	3	t	t	PROPN
ejpam-6140	29	4	)	)	PUNCT
ejpam-6140	29	5	=	=	SYM
ejpam-6140	30	1	u(1	u(1	PROPN
ejpam-6140	30	2	,	,	PUNCT
ejpam-6140	30	3	t	t	PROPN
ejpam-6140	30	4	)	)	PUNCT
ejpam-6140	30	5	=	=	SYM
ejpam-6140	30	6	0	0	NUM
ejpam-6140	30	7	,	,	PUNCT
ejpam-6140	30	8	v(0	v(0	PROPN
ejpam-6140	30	9	,	,	PUNCT
ejpam-6140	30	10	t	t	PROPN
ejpam-6140	30	11	)	)	PUNCT
ejpam-6140	30	12	=	=	SYM
ejpam-6140	31	1	v(1	v(1	PROPN
ejpam-6140	31	2	,	,	PUNCT
ejpam-6140	31	3	t	t	PROPN
ejpam-6140	31	4	)	)	PUNCT
ejpam-6140	31	5	=	=	SYM
ejpam-6140	31	6	0	0	NUM
ejpam-6140	31	7	,	,	PUNCT
ejpam-6140	31	8	t	t	PROPN
ejpam-6140	31	9	∈	∈	PROPN
ejpam-6140	31	10	(	(	PUNCT
ejpam-6140	31	11	0	0	NUM
ejpam-6140	31	12	,	,	PUNCT
ejpam-6140	31	13	t	t	NOUN
ejpam-6140	31	14	)	)	PUNCT
ejpam-6140	31	15	u(x	u(x	PROPN
ejpam-6140	31	16	,	,	PUNCT
ejpam-6140	31	17	0	0	NUM
ejpam-6140	31	18	)	)	PUNCT
ejpam-6140	31	19	=	=	SYM
ejpam-6140	31	20	u0(x	u0(x	NOUN
ejpam-6140	31	21	)	)	PUNCT
ejpam-6140	31	22	,	,	PUNCT
ejpam-6140	31	23	v(x	v(x	PROPN
ejpam-6140	31	24	,	,	PUNCT
ejpam-6140	31	25	0	0	NUM
ejpam-6140	31	26	)	)	PUNCT
ejpam-6140	31	27	=	=	SYM
ejpam-6140	31	28	v0(x	v0(x	PROPN
ejpam-6140	31	29	)	)	PUNCT
ejpam-6140	31	30	,	,	PUNCT
ejpam-6140	31	31	x	x	PUNCT
ejpam-6140	31	32	∈	∈	PROPN
ejpam-6140	31	33	(	(	PUNCT
ejpam-6140	31	34	0	0	NUM
ejpam-6140	31	35	,	,	PUNCT
ejpam-6140	31	36	1	1	X
ejpam-6140	31	37	)	)	PUNCT
ejpam-6140	31	38			NOUN
ejpam-6140	31	39	(	(	PUNCT
ejpam-6140	31	40	1	1	NUM
ejpam-6140	31	41	)	)	PUNCT
ejpam-6140	31	42	where	where	SCONJ
ejpam-6140	31	43	u0(x	u0(x	X
ejpam-6140	31	44	)	)	PUNCT
ejpam-6140	31	45	∈	∈	PROPN
ejpam-6140	31	46	c2(r	c2(r	PROPN
ejpam-6140	31	47	)	)	PUNCT
ejpam-6140	31	48	,	,	PUNCT
ejpam-6140	31	49	v0(x	v0(x	X
ejpam-6140	31	50	)	)	PUNCT
ejpam-6140	31	51	∈	∈	PROPN
ejpam-6140	31	52	c2(r	c2(r	PROPN
ejpam-6140	31	53	)	)	PUNCT
ejpam-6140	31	54	,	,	PUNCT
ejpam-6140	31	55	satisfying	satisfy	VERB
ejpam-6140	31	56	u0(0	u0(0	PROPN
ejpam-6140	31	57	)	)	PUNCT
ejpam-6140	31	58	=	=	SYM
ejpam-6140	32	1	u0(1	u0(1	ADJ
ejpam-6140	32	2	)	)	PUNCT
ejpam-6140	32	3	=	=	SYM
ejpam-6140	32	4	0	0	NUM
ejpam-6140	32	5	,	,	PUNCT
ejpam-6140	32	6	v0(0	v0(0	PROPN
ejpam-6140	32	7	)	)	PUNCT
ejpam-6140	32	8	=	=	SYM
ejpam-6140	32	9	v0(1	v0(1	ADJ
ejpam-6140	32	10	)	)	PUNCT
ejpam-6140	32	11	=	=	SYM
ejpam-6140	33	1	0	0	NUM
ejpam-6140	33	2	;	;	PUNCT
ejpam-6140	33	3	f	f	X
ejpam-6140	33	4	,	,	PUNCT
ejpam-6140	33	5	g	g	PROPN
ejpam-6140	33	6	∈	∈	PROPN
ejpam-6140	33	7	c1(r)∩c2(r\{0	c1(r)∩c2(r\{0	PROPN
ejpam-6140	33	8	}	}	PUNCT
ejpam-6140	33	9	)	)	PUNCT
ejpam-6140	33	10	,	,	PUNCT
ejpam-6140	33	11	are	be	AUX
ejpam-6140	33	12	positive	positive	ADJ
ejpam-6140	33	13	,	,	PUNCT
ejpam-6140	33	14	super	super	ADJ
ejpam-6140	33	15	-	-	ADJ
ejpam-6140	33	16	linear	linear	ADJ
ejpam-6140	33	17	differentiable	differentiable	NOUN
ejpam-6140	33	18	,	,	PUNCT
ejpam-6140	33	19	and	and	CCONJ
ejpam-6140	33	20	increasing	increase	VERB
ejpam-6140	33	21	functions	function	NOUN
ejpam-6140	33	22	on	on	ADP
ejpam-6140	33	23	(	(	PUNCT
ejpam-6140	33	24	0,∞	0,∞	NUM
ejpam-6140	33	25	)	)	PUNCT
ejpam-6140	33	26	.	.	PUNCT
ejpam-6140	34	1	to	to	PART
ejpam-6140	34	2	demonstrate	demonstrate	VERB
ejpam-6140	34	3	the	the	DET
ejpam-6140	34	4	local	local	ADJ
ejpam-6140	34	5	existence	existence	NOUN
ejpam-6140	34	6	and	and	CCONJ
ejpam-6140	34	7	distinguish	distinguish	VERB
ejpam-6140	34	8	positive	positive	ADJ
ejpam-6140	34	9	solutions	solution	NOUN
ejpam-6140	34	10	to	to	ADP
ejpam-6140	34	11	the	the	DET
ejpam-6140	34	12	problem	problem	NOUN
ejpam-6140	34	13	,	,	PUNCT
ejpam-6140	34	14	some	some	DET
ejpam-6140	34	15	authors	author	NOUN
ejpam-6140	34	16	used	use	VERB
ejpam-6140	34	17	the	the	DET
ejpam-6140	34	18	standard	standard	ADJ
ejpam-6140	34	19	parabolic	parabolic	ADJ
ejpam-6140	34	20	theory	theory	NOUN
ejpam-6140	34	21	[	[	X
ejpam-6140	34	22	12	12	NUM
ejpam-6140	34	23	]	]	PUNCT
ejpam-6140	34	24	.	.	PUNCT
ejpam-6140	35	1	moreover	moreover	ADV
ejpam-6140	35	2	,	,	PUNCT
ejpam-6140	35	3	for	for	ADP
ejpam-6140	35	4	various	various	ADJ
ejpam-6140	35	5	nonlinear	nonlinear	ADJ
ejpam-6140	35	6	functions	function	NOUN
ejpam-6140	35	7	:	:	PUNCT
ejpam-6140	35	8	f	f	X
ejpam-6140	35	9	,	,	PUNCT
ejpam-6140	35	10	g	g	PROPN
ejpam-6140	35	11	,	,	PUNCT
ejpam-6140	35	12	when	when	SCONJ
ejpam-6140	35	13	the	the	DET
ejpam-6140	35	14	initial	initial	ADJ
ejpam-6140	35	15	functions	function	NOUN
ejpam-6140	35	16	(	(	PUNCT
ejpam-6140	35	17	u0	u0	PROPN
ejpam-6140	35	18	,	,	PUNCT
ejpam-6140	35	19	v0	v0	PROPN
ejpam-6140	35	20	)	)	PUNCT
ejpam-6140	35	21	are	be	AUX
ejpam-6140	35	22	sufficiently	sufficiently	ADV
ejpam-6140	35	23	large	large	ADJ
ejpam-6140	35	24	,	,	PUNCT
ejpam-6140	35	25	a	a	DET
ejpam-6140	35	26	blow	blow	NOUN
ejpam-6140	35	27	-	-	PUNCT
ejpam-6140	35	28	up	up	NOUN
ejpam-6140	35	29	may	may	AUX
ejpam-6140	35	30	occur	occur	VERB
ejpam-6140	35	31	in	in	ADP
ejpam-6140	35	32	finite	finite	NOUN
ejpam-6140	35	33	time[9	time[9	NUM
ejpam-6140	35	34	]	]	PUNCT
ejpam-6140	35	35	.	.	PUNCT
ejpam-6140	36	1	in	in	ADP
ejpam-6140	36	2	addition	addition	NOUN
ejpam-6140	36	3	,	,	PUNCT
ejpam-6140	36	4	because	because	SCONJ
ejpam-6140	36	5	the	the	DET
ejpam-6140	36	6	system	system	NOUN
ejpam-6140	36	7	(	(	PUNCT
ejpam-6140	36	8	1	1	X
ejpam-6140	36	9	)	)	PUNCT
ejpam-6140	36	10	is	be	AUX
ejpam-6140	36	11	coupled	couple	VERB
ejpam-6140	36	12	,	,	PUNCT
ejpam-6140	36	13	only	only	ADV
ejpam-6140	36	14	a	a	DET
ejpam-6140	36	15	simultaneous	simultaneous	ADJ
ejpam-6140	36	16	blow	blow	NOUN
ejpam-6140	36	17	-	-	PUNCT
ejpam-6140	36	18	up	up	NOUN
ejpam-6140	36	19	occurs	occur	NOUN
ejpam-6140	36	20	.	.	PUNCT
ejpam-6140	37	1	regarding	regard	VERB
ejpam-6140	37	2	the	the	DET
ejpam-6140	37	3	blow	blow	NOUN
ejpam-6140	37	4	-	-	PUNCT
ejpam-6140	37	5	up	up	ADP
ejpam-6140	37	6	set	set	NOUN
ejpam-6140	37	7	and	and	CCONJ
ejpam-6140	37	8	blow	blow	NOUN
ejpam-6140	37	9	-	-	PUNCT
ejpam-6140	37	10	up	up	ADP
ejpam-6140	37	11	rate	rate	NOUN
ejpam-6140	37	12	estimate	estimate	NOUN
ejpam-6140	37	13	,	,	PUNCT
ejpam-6140	37	14	the	the	DET
ejpam-6140	37	15	system	system	NOUN
ejpam-6140	37	16	(	(	PUNCT
ejpam-6140	37	17	1	1	X
ejpam-6140	37	18	)	)	PUNCT
ejpam-6140	37	19	has	have	AUX
ejpam-6140	37	20	been	be	AUX
ejpam-6140	37	21	extensively	extensively	ADV
ejpam-6140	37	22	studied	study	VERB
ejpam-6140	37	23	in	in	ADP
ejpam-6140	37	24	[	[	X
ejpam-6140	37	25	13–19	13–19	NUM
ejpam-6140	37	26	]	]	PUNCT
ejpam-6140	37	27	.	.	PUNCT
ejpam-6140	38	1	furthermore	furthermore	ADV
ejpam-6140	38	2	,	,	PUNCT
ejpam-6140	38	3	imposing	impose	VERB
ejpam-6140	38	4	some	some	DET
ejpam-6140	38	5	related	related	ADJ
ejpam-6140	38	6	suggestions	suggestion	NOUN
ejpam-6140	38	7	in	in	ADP
ejpam-6140	38	8	f	f	PROPN
ejpam-6140	38	9	,	,	PUNCT
ejpam-6140	38	10	g	g	PROPN
ejpam-6140	38	11	,	,	PUNCT
ejpam-6140	38	12	it	it	PRON
ejpam-6140	38	13	is	be	AUX
ejpam-6140	38	14	shown	show	VERB
ejpam-6140	38	15	that	that	SCONJ
ejpam-6140	38	16	the	the	DET
ejpam-6140	38	17	(	(	PUNCT
ejpam-6140	38	18	bu	bu	NOUN
ejpam-6140	38	19	)	)	PUNCT
ejpam-6140	38	20	occurs	occur	VERB
ejpam-6140	38	21	at	at	ADP
ejpam-6140	38	22	a	a	DET
ejpam-6140	38	23	single	single	ADJ
ejpam-6140	38	24	point	point	NOUN
ejpam-6140	38	25	[	[	X
ejpam-6140	38	26	15	15	NUM
ejpam-6140	38	27	]	]	PUNCT
ejpam-6140	38	28	.	.	PUNCT
ejpam-6140	39	1	particularly	particularly	ADV
ejpam-6140	39	2	,	,	PUNCT
ejpam-6140	39	3	the	the	DET
ejpam-6140	39	4	following	follow	VERB
ejpam-6140	39	5	two	two	NUM
ejpam-6140	39	6	instances	instance	NOUN
ejpam-6140	39	7	of	of	ADP
ejpam-6140	39	8	f	f	NOUN
ejpam-6140	39	9	,	,	PUNCT
ejpam-6140	39	10	g	g	PROPN
ejpam-6140	39	11	are	be	AUX
ejpam-6140	39	12	mostly	mostly	ADV
ejpam-6140	39	13	studied	study	VERB
ejpam-6140	39	14	[	[	PUNCT
ejpam-6140	39	15	9	9	NUM
ejpam-6140	39	16	,	,	PUNCT
ejpam-6140	39	17	13	13	NUM
ejpam-6140	39	18	,	,	PUNCT
ejpam-6140	39	19	15	15	NUM
ejpam-6140	39	20	]	]	PUNCT
ejpam-6140	39	21	:	:	PUNCT
ejpam-6140	39	22	f(v	f(v	NOUN
ejpam-6140	39	23	)	)	PUNCT
ejpam-6140	39	24	=	=	SYM
ejpam-6140	39	25	vp	vp	X
ejpam-6140	39	26	,	,	PUNCT
ejpam-6140	39	27	g(u	g(u	PROPN
ejpam-6140	39	28	)	)	PUNCT
ejpam-6140	39	29	=	=	SYM
ejpam-6140	39	30	uq	uq	PROPN
ejpam-6140	39	31	,	,	PUNCT
ejpam-6140	39	32	p	p	X
ejpam-6140	39	33	,	,	PUNCT
ejpam-6140	39	34	q	q	ADJ
ejpam-6140	39	35	>	>	X
ejpam-6140	39	36	1	1	NUM
ejpam-6140	39	37	f(v	f(v	NOUN
ejpam-6140	39	38	)	)	PUNCT
ejpam-6140	39	39	=	=	PUNCT
ejpam-6140	40	1	epv	epv	PROPN
ejpam-6140	40	2	,	,	PUNCT
ejpam-6140	40	3	g(u	g(u	PROPN
ejpam-6140	40	4	)	)	PUNCT
ejpam-6140	40	5	=	=	SYM
ejpam-6140	40	6	equ	equ	PROPN
ejpam-6140	40	7	,	,	PUNCT
ejpam-6140	40	8	p	p	X
ejpam-6140	40	9	,	,	PUNCT
ejpam-6140	40	10	q	q	ADJ
ejpam-6140	40	11	>	>	X
ejpam-6140	40	12	0	0	PUNCT
ejpam-6140	41	1	since	since	SCONJ
ejpam-6140	41	2	the	the	DET
ejpam-6140	41	3	last	last	ADJ
ejpam-6140	41	4	decades	decade	NOUN
ejpam-6140	41	5	,	,	PUNCT
ejpam-6140	41	6	several	several	ADJ
ejpam-6140	41	7	numerical	numerical	ADJ
ejpam-6140	41	8	approximations	approximation	NOUN
ejpam-6140	41	9	have	have	AUX
ejpam-6140	41	10	been	be	AUX
ejpam-6140	41	11	proposed	propose	VERB
ejpam-6140	41	12	for	for	ADP
ejpam-6140	41	13	many	many	ADJ
ejpam-6140	41	14	parabolic	parabolic	ADJ
ejpam-6140	41	15	problems	problem	NOUN
ejpam-6140	41	16	with	with	ADP
ejpam-6140	41	17	bu	bu	NOUN
ejpam-6140	41	18	to	to	PART
ejpam-6140	41	19	compute	compute	VERB
ejpam-6140	41	20	the	the	DET
ejpam-6140	41	21	nbu	nbu	NOUN
ejpam-6140	41	22	solution	solution	NOUN
ejpam-6140	41	23	and	and	CCONJ
ejpam-6140	41	24	estimate	estimate	NOUN
ejpam-6140	41	25	but	but	CCONJ
ejpam-6140	41	26	[	[	X
ejpam-6140	41	27	20–26	20–26	NUM
ejpam-6140	41	28	]	]	PUNCT
ejpam-6140	41	29	.	.	PUNCT
ejpam-6140	42	1	in	in	ADP
ejpam-6140	42	2	[	[	X
ejpam-6140	42	3	25	25	NUM
ejpam-6140	42	4	]	]	PUNCT
ejpam-6140	42	5	,	,	PUNCT
ejpam-6140	42	6	the	the	DET
ejpam-6140	42	7	authors	author	NOUN
ejpam-6140	42	8	proposed	propose	VERB
ejpam-6140	42	9	an	an	DET
ejpam-6140	42	10	approximate	approximate	ADJ
ejpam-6140	42	11	explicit	explicit	ADJ
ejpam-6140	42	12	scheme	scheme	NOUN
ejpam-6140	42	13	for	for	ADP
ejpam-6140	42	14	the	the	DET
ejpam-6140	42	15	system	system	NOUN
ejpam-6140	42	16	(	(	PUNCT
ejpam-6140	42	17	1	1	NUM
ejpam-6140	42	18	)	)	PUNCT
ejpam-6140	42	19	with	with	ADP
ejpam-6140	42	20	m.	m.	PROPN
ejpam-6140	42	21	i.	i.	PROPN
ejpam-6140	42	22	khalil	khalil	PROPN
ejpam-6140	42	23	et	et	PROPN
ejpam-6140	42	24	al	al	PROPN
ejpam-6140	42	25	.	.	PUNCT
ejpam-6140	42	26	/	/	SYM
ejpam-6140	42	27	eur	eur	PROPN
ejpam-6140	42	28	.	.	PUNCT
ejpam-6140	43	1	j.	j.	PROPN
ejpam-6140	43	2	pure	pure	PROPN
ejpam-6140	43	3	appl	appl	PROPN
ejpam-6140	43	4	.	.	PROPN
ejpam-6140	43	5	math	math	PROPN
ejpam-6140	43	6	,	,	PUNCT
ejpam-6140	43	7	18	18	NUM
ejpam-6140	43	8	(	(	PUNCT
ejpam-6140	43	9	3	3	NUM
ejpam-6140	43	10	)	)	PUNCT
ejpam-6140	43	11	(	(	PUNCT
ejpam-6140	43	12	2025	2025	NUM
ejpam-6140	43	13	)	)	PUNCT
ejpam-6140	43	14	,	,	PUNCT
ejpam-6140	43	15	6140	6140	NUM
ejpam-6140	43	16	3	3	NUM
ejpam-6140	43	17	of	of	ADP
ejpam-6140	43	18	17	17	NUM
ejpam-6140	43	19	nonlinear	nonlinear	ADJ
ejpam-6140	43	20	power	power	NOUN
ejpam-6140	43	21	-	-	PUNCT
ejpam-6140	43	22	type	type	NOUN
ejpam-6140	43	23	functions	function	NOUN
ejpam-6140	43	24	,	,	PUNCT
ejpam-6140	43	25	subject	subject	ADJ
ejpam-6140	43	26	to	to	ADP
ejpam-6140	43	27	uniform	uniform	ADJ
ejpam-6140	43	28	temporal	temporal	ADJ
ejpam-6140	43	29	grids	grid	NOUN
ejpam-6140	43	30	.	.	PUNCT
ejpam-6140	44	1	in	in	ADP
ejpam-6140	44	2	addition	addition	NOUN
ejpam-6140	44	3	,	,	PUNCT
ejpam-6140	44	4	the	the	DET
ejpam-6140	44	5	computation	computation	NOUN
ejpam-6140	44	6	of	of	ADP
ejpam-6140	44	7	the	the	DET
ejpam-6140	44	8	bu	bu	ADJ
ejpam-6140	44	9	time	time	NOUN
ejpam-6140	44	10	and	and	CCONJ
ejpam-6140	44	11	bu	bu	PROPN
ejpam-6140	44	12	behaviors	behavior	NOUN
ejpam-6140	44	13	is	be	AUX
ejpam-6140	44	14	studied	study	VERB
ejpam-6140	44	15	.	.	PUNCT
ejpam-6140	45	1	moreover	moreover	ADV
ejpam-6140	45	2	,	,	PUNCT
ejpam-6140	45	3	the	the	DET
ejpam-6140	45	4	convergence	convergence	NOUN
ejpam-6140	45	5	of	of	ADP
ejpam-6140	45	6	the	the	DET
ejpam-6140	45	7	nbu	nbu	NOUN
ejpam-6140	45	8	time	time	NOUN
ejpam-6140	45	9	is	be	AUX
ejpam-6140	45	10	considered	consider	VERB
ejpam-6140	45	11	.	.	PUNCT
ejpam-6140	46	1	in	in	ADP
ejpam-6140	46	2	addition	addition	NOUN
ejpam-6140	46	3	,	,	PUNCT
ejpam-6140	46	4	the	the	DET
ejpam-6140	46	5	bu	bu	PROPN
ejpam-6140	46	6	set	set	PROPN
ejpam-6140	46	7	,	,	PUNCT
ejpam-6140	46	8	the	the	DET
ejpam-6140	46	9	bu	bu	PROPN
ejpam-6140	46	10	rate	rate	NOUN
ejpam-6140	46	11	and	and	CCONJ
ejpam-6140	46	12	the	the	DET
ejpam-6140	46	13	bu	bu	NOUN
ejpam-6140	46	14	in	in	ADP
ejpam-6140	46	15	the	the	DET
ejpam-6140	46	16	lp	lp	NOUN
ejpam-6140	46	17	-	-	PUNCT
ejpam-6140	46	18	norm	norm	NOUN
ejpam-6140	46	19	were	be	AUX
ejpam-6140	46	20	taken	take	VERB
ejpam-6140	46	21	into	into	ADP
ejpam-6140	46	22	account	account	NOUN
ejpam-6140	46	23	.	.	PUNCT
ejpam-6140	47	1	furthermore	furthermore	ADV
ejpam-6140	47	2	,	,	PUNCT
ejpam-6140	47	3	the	the	DET
ejpam-6140	47	4	relationship	relationship	NOUN
ejpam-6140	47	5	between	between	ADP
ejpam-6140	47	6	the	the	DET
ejpam-6140	47	7	bu	bu	NOUN
ejpam-6140	47	8	of	of	ADP
ejpam-6140	47	9	the	the	DET
ejpam-6140	47	10	numerical	numerical	ADJ
ejpam-6140	47	11	solution	solution	NOUN
ejpam-6140	47	12	and	and	CCONJ
ejpam-6140	47	13	that	that	PRON
ejpam-6140	47	14	of	of	ADP
ejpam-6140	47	15	the	the	DET
ejpam-6140	47	16	exact	exact	ADJ
ejpam-6140	47	17	solution	solution	NOUN
ejpam-6140	47	18	has	have	AUX
ejpam-6140	47	19	been	be	AUX
ejpam-6140	47	20	investigated	investigate	VERB
ejpam-6140	47	21	.	.	PUNCT
ejpam-6140	48	1	recently	recently	ADV
ejpam-6140	48	2	,	,	PUNCT
ejpam-6140	48	3	in	in	ADP
ejpam-6140	48	4	[	[	X
ejpam-6140	48	5	26	26	NUM
ejpam-6140	48	6	]	]	PUNCT
ejpam-6140	48	7	,	,	PUNCT
ejpam-6140	48	8	the	the	DET
ejpam-6140	48	9	authors	author	NOUN
ejpam-6140	48	10	have	have	AUX
ejpam-6140	48	11	studied	study	VERB
ejpam-6140	48	12	the	the	DET
ejpam-6140	48	13	semi	semi	ADJ
ejpam-6140	48	14	-	-	ADJ
ejpam-6140	48	15	discrete	discrete	ADJ
ejpam-6140	48	16	problem	problem	NOUN
ejpam-6140	48	17	of	of	ADP
ejpam-6140	48	18	system	system	NOUN
ejpam-6140	48	19	(	(	PUNCT
ejpam-6140	48	20	1	1	NUM
ejpam-6140	48	21	)	)	PUNCT
ejpam-6140	48	22	and	and	CCONJ
ejpam-6140	48	23	its	its	PRON
ejpam-6140	48	24	properties	property	NOUN
ejpam-6140	48	25	regarding	regard	VERB
ejpam-6140	48	26	convergence	convergence	NOUN
ejpam-6140	48	27	and	and	CCONJ
ejpam-6140	48	28	(	(	PUNCT
ejpam-6140	48	29	but	but	CCONJ
ejpam-6140	48	30	)	)	PUNCT
ejpam-6140	48	31	.	.	PUNCT
ejpam-6140	49	1	namely	namely	ADV
ejpam-6140	49	2	,	,	PUNCT
ejpam-6140	49	3	it	it	PRON
ejpam-6140	49	4	has	have	AUX
ejpam-6140	49	5	been	be	AUX
ejpam-6140	49	6	shown	show	VERB
ejpam-6140	49	7	that	that	SCONJ
ejpam-6140	49	8	the	the	DET
ejpam-6140	49	9	(	(	PUNCT
ejpam-6140	49	10	nbut	nbut	NOUN
ejpam-6140	49	11	)	)	PUNCT
ejpam-6140	49	12	and	and	CCONJ
ejpam-6140	49	13	nbus	nbus	PROPN
ejpam-6140	49	14	of	of	ADP
ejpam-6140	49	15	a	a	DET
ejpam-6140	49	16	semi	semi	ADJ
ejpam-6140	49	17	-	-	ADJ
ejpam-6140	49	18	discrete	discrete	ADJ
ejpam-6140	49	19	form	form	NOUN
ejpam-6140	49	20	of	of	ADP
ejpam-6140	49	21	(	(	PUNCT
ejpam-6140	49	22	1	1	NUM
ejpam-6140	49	23	)	)	PUNCT
ejpam-6140	49	24	converge	converge	VERB
ejpam-6140	49	25	to	to	ADP
ejpam-6140	49	26	the	the	DET
ejpam-6140	49	27	theoretical	theoretical	ADJ
ejpam-6140	49	28	ones	one	NOUN
ejpam-6140	49	29	during	during	ADP
ejpam-6140	49	30	grid	grid	NOUN
ejpam-6140	49	31	refinement	refinement	NOUN
ejpam-6140	49	32	.	.	PUNCT
ejpam-6140	50	1	moreover	moreover	ADV
ejpam-6140	50	2	,	,	PUNCT
ejpam-6140	50	3	they	they	PRON
ejpam-6140	50	4	have	have	AUX
ejpam-6140	50	5	proposed	propose	VERB
ejpam-6140	50	6	explicit	explicit	ADJ
ejpam-6140	50	7	and	and	CCONJ
ejpam-6140	50	8	implicit	implicit	ADJ
ejpam-6140	50	9	finite	finite	ADJ
ejpam-6140	50	10	difference	difference	NOUN
ejpam-6140	50	11	approximation	approximation	NOUN
ejpam-6140	50	12	schemes	scheme	NOUN
ejpam-6140	50	13	with	with	ADP
ejpam-6140	50	14	non	non	ADJ
ejpam-6140	50	15	-	-	ADJ
ejpam-6140	50	16	fixed	fixed	ADJ
ejpam-6140	50	17	time	time	NOUN
ejpam-6140	50	18	-	-	PUNCT
ejpam-6140	50	19	step	step	NOUN
ejpam-6140	50	20	to	to	PART
ejpam-6140	50	21	estimate	estimate	VERB
ejpam-6140	50	22	the	the	PRON
ejpam-6140	50	23	(	(	PUNCT
ejpam-6140	50	24	but	but	CCONJ
ejpam-6140	50	25	)	)	PUNCT
ejpam-6140	50	26	to	to	ADP
ejpam-6140	50	27	the	the	DET
ejpam-6140	50	28	system	system	NOUN
ejpam-6140	50	29	(	(	PUNCT
ejpam-6140	50	30	1).moreover	1).moreover	NUM
ejpam-6140	50	31	,	,	PUNCT
ejpam-6140	50	32	they	they	PRON
ejpam-6140	50	33	investigated	investigate	VERB
ejpam-6140	50	34	the	the	DET
ejpam-6140	50	35	stability	stability	NOUN
ejpam-6140	50	36	,	,	PUNCT
ejpam-6140	50	37	convergence	convergence	NOUN
ejpam-6140	50	38	,	,	PUNCT
ejpam-6140	50	39	and	and	CCONJ
ejpam-6140	50	40	consistency	consistency	NOUN
ejpam-6140	50	41	of	of	ADP
ejpam-6140	50	42	the	the	DET
ejpam-6140	50	43	suggested	suggest	VERB
ejpam-6140	50	44	methods	method	NOUN
ejpam-6140	50	45	.	.	PUNCT
ejpam-6140	51	1	in	in	ADP
ejpam-6140	51	2	addition	addition	NOUN
ejpam-6140	51	3	,	,	PUNCT
ejpam-6140	51	4	some	some	DET
ejpam-6140	51	5	numerical	numerical	ADJ
ejpam-6140	51	6	examples	example	NOUN
ejpam-6140	51	7	are	be	AUX
ejpam-6140	51	8	presented	present	VERB
ejpam-6140	51	9	in	in	ADP
ejpam-6140	51	10	the	the	DET
ejpam-6140	51	11	form	form	NOUN
ejpam-6140	51	12	of	of	ADP
ejpam-6140	51	13	tables	table	NOUN
ejpam-6140	51	14	and	and	CCONJ
ejpam-6140	51	15	figures	figure	NOUN
ejpam-6140	51	16	.	.	PUNCT
ejpam-6140	52	1	this	this	DET
ejpam-6140	52	2	work	work	NOUN
ejpam-6140	52	3	aims	aim	VERB
ejpam-6140	52	4	to	to	PART
ejpam-6140	52	5	find	find	VERB
ejpam-6140	52	6	an	an	DET
ejpam-6140	52	7	efficient	efficient	ADJ
ejpam-6140	52	8	technique	technique	NOUN
ejpam-6140	52	9	to	to	PART
ejpam-6140	52	10	estimate	estimate	VERB
ejpam-6140	52	11	the	the	PRON
ejpam-6140	52	12	(	(	PUNCT
ejpam-6140	52	13	but	but	CCONJ
ejpam-6140	52	14	)	)	PUNCT
ejpam-6140	52	15	of	of	ADP
ejpam-6140	52	16	the	the	DET
ejpam-6140	52	17	system	system	NOUN
ejpam-6140	52	18	(	(	PUNCT
ejpam-6140	52	19	1	1	NUM
ejpam-6140	52	20	)	)	PUNCT
ejpam-6140	52	21	.	.	PUNCT
ejpam-6140	53	1	namely	namely	ADV
ejpam-6140	53	2	,	,	PUNCT
ejpam-6140	53	3	to	to	PART
ejpam-6140	53	4	show	show	VERB
ejpam-6140	53	5	the	the	DET
ejpam-6140	53	6	accuracy	accuracy	NOUN
ejpam-6140	53	7	and	and	CCONJ
ejpam-6140	53	8	efficiency	efficiency	NOUN
ejpam-6140	53	9	of	of	ADP
ejpam-6140	53	10	the	the	DET
ejpam-6140	53	11	c.n	c.n	PROPN
ejpam-6140	53	12	.	.	PROPN
ejpam-6140	53	13	scheme	scheme	NOUN
ejpam-6140	53	14	in	in	ADP
ejpam-6140	53	15	computing	compute	VERB
ejpam-6140	53	16	bu	bu	NOUN
ejpam-6140	53	17	solution	solution	NOUN
ejpam-6140	53	18	and	and	CCONJ
ejpam-6140	53	19	but	but	CCONJ
ejpam-6140	53	20	.	.	PUNCT
ejpam-6140	54	1	this	this	DET
ejpam-6140	54	2	study	study	NOUN
ejpam-6140	54	3	has	have	VERB
ejpam-6140	54	4	six	six	NUM
ejpam-6140	54	5	sections	section	NOUN
ejpam-6140	54	6	.	.	PUNCT
ejpam-6140	55	1	in	in	ADP
ejpam-6140	55	2	the	the	DET
ejpam-6140	55	3	second	second	ADJ
ejpam-6140	55	4	section	section	NOUN
ejpam-6140	55	5	,	,	PUNCT
ejpam-6140	55	6	some	some	DET
ejpam-6140	55	7	results	result	NOUN
ejpam-6140	55	8	of	of	ADP
ejpam-6140	55	9	the	the	DET
ejpam-6140	55	10	semi	semi	ADJ
ejpam-6140	55	11	-	-	ADJ
ejpam-6140	55	12	discrete	discrete	ADJ
ejpam-6140	55	13	problem	problem	NOUN
ejpam-6140	55	14	on	on	ADP
ejpam-6140	55	15	the	the	DET
ejpam-6140	55	16	problem	problem	NOUN
ejpam-6140	55	17	(	(	PUNCT
ejpam-6140	55	18	1	1	X
ejpam-6140	55	19	)	)	PUNCT
ejpam-6140	55	20	are	be	AUX
ejpam-6140	55	21	recalled	recall	VERB
ejpam-6140	55	22	.	.	PUNCT
ejpam-6140	56	1	the	the	DET
ejpam-6140	56	2	crank	crank	NOUN
ejpam-6140	56	3	-	-	PUNCT
ejpam-6140	56	4	nicolson	nicolson	PROPN
ejpam-6140	56	5	approximation	approximation	NOUN
ejpam-6140	56	6	formulas	formula	NOUN
ejpam-6140	56	7	of	of	ADP
ejpam-6140	56	8	the	the	DET
ejpam-6140	56	9	system	system	NOUN
ejpam-6140	56	10	(	(	PUNCT
ejpam-6140	56	11	1	1	X
ejpam-6140	56	12	)	)	PUNCT
ejpam-6140	56	13	are	be	AUX
ejpam-6140	56	14	derived	derive	VERB
ejpam-6140	56	15	in	in	ADP
ejpam-6140	56	16	section	section	NOUN
ejpam-6140	56	17	three	three	NUM
ejpam-6140	56	18	.	.	PUNCT
ejpam-6140	57	1	in	in	ADP
ejpam-6140	57	2	the	the	DET
ejpam-6140	57	3	fourth	fourth	ADJ
ejpam-6140	57	4	section	section	NOUN
ejpam-6140	57	5	,	,	PUNCT
ejpam-6140	57	6	consistency	consistency	NOUN
ejpam-6140	57	7	,	,	PUNCT
ejpam-6140	57	8	stability	stability	NOUN
ejpam-6140	57	9	,	,	PUNCT
ejpam-6140	57	10	and	and	CCONJ
ejpam-6140	57	11	convergence	convergence	NOUN
ejpam-6140	57	12	are	be	AUX
ejpam-6140	57	13	considered	consider	VERB
ejpam-6140	57	14	.	.	PUNCT
ejpam-6140	58	1	in	in	ADP
ejpam-6140	58	2	section	section	NOUN
ejpam-6140	58	3	five	five	NUM
ejpam-6140	58	4	,	,	PUNCT
ejpam-6140	58	5	two	two	NUM
ejpam-6140	58	6	numerical	numerical	ADJ
ejpam-6140	58	7	experiments	experiment	NOUN
ejpam-6140	58	8	are	be	AUX
ejpam-6140	58	9	given	give	VERB
ejpam-6140	58	10	to	to	PART
ejpam-6140	58	11	estimate	estimate	VERB
ejpam-6140	58	12	the	the	DET
ejpam-6140	58	13	(	(	PUNCT
ejpam-6140	58	14	nbut	nbut	PROPN
ejpam-6140	58	15	)	)	PUNCT
ejpam-6140	58	16	,	,	PUNCT
ejpam-6140	58	17	error	error	NOUN
ejpam-6140	58	18	bounds	bound	NOUN
ejpam-6140	58	19	,	,	PUNCT
ejpam-6140	58	20	and	and	CCONJ
ejpam-6140	58	21	numerical	numerical	ADJ
ejpam-6140	58	22	order	order	NOUN
ejpam-6140	58	23	of	of	ADP
ejpam-6140	58	24	convergence	convergence	NOUN
ejpam-6140	58	25	.	.	PUNCT
ejpam-6140	59	1	lastly	lastly	ADV
ejpam-6140	59	2	,	,	PUNCT
ejpam-6140	59	3	the	the	DET
ejpam-6140	59	4	important	important	ADJ
ejpam-6140	59	5	conclusions	conclusion	NOUN
ejpam-6140	59	6	and	and	CCONJ
ejpam-6140	59	7	future	future	ADJ
ejpam-6140	59	8	work	work	NOUN
ejpam-6140	59	9	are	be	AUX
ejpam-6140	59	10	stated	state	VERB
ejpam-6140	59	11	in	in	ADP
ejpam-6140	59	12	the	the	DET
ejpam-6140	59	13	last	last	ADJ
ejpam-6140	59	14	section	section	NOUN
ejpam-6140	59	15	.	.	PUNCT
ejpam-6140	60	1	1.1	1.1	NUM
ejpam-6140	60	2	.	.	PUNCT
ejpam-6140	61	1	the	the	DET
ejpam-6140	61	2	semi	semi	ADJ
ejpam-6140	61	3	-	-	ADJ
ejpam-6140	61	4	discrete	discrete	ADJ
ejpam-6140	61	5	problem	problem	NOUN
ejpam-6140	61	6	let	let	VERB
ejpam-6140	61	7	i	i	PRON
ejpam-6140	61	8	be	be	AUX
ejpam-6140	61	9	a	a	DET
ejpam-6140	61	10	positive	positive	ADJ
ejpam-6140	61	11	integer	integer	NOUN
ejpam-6140	61	12	and	and	CCONJ
ejpam-6140	61	13	xi	xi	NOUN
ejpam-6140	61	14	=	=	PROPN
ejpam-6140	61	15	ih	ih	X
ejpam-6140	61	16	,	,	PUNCT
ejpam-6140	61	17	0	0	NUM
ejpam-6140	61	18	≤	≤	NUM
ejpam-6140	62	1	i	i	PRON
ejpam-6140	62	2	≤	≤	PUNCT
ejpam-6140	63	1	i	i	PRON
ejpam-6140	63	2	,	,	PUNCT
ejpam-6140	63	3	where	where	SCONJ
ejpam-6140	63	4	h	h	NOUN
ejpam-6140	63	5	=	=	NOUN
ejpam-6140	63	6	1	1	NUM
ejpam-6140	64	1	i	i	PRON
ejpam-6140	64	2	,	,	PUNCT
ejpam-6140	64	3	then	then	ADV
ejpam-6140	64	4	we	we	PRON
ejpam-6140	64	5	can	can	AUX
ejpam-6140	64	6	adjective	adjective	VERB
ejpam-6140	64	7	by	by	ADP
ejpam-6140	64	8	the	the	DET
ejpam-6140	64	9	solution	solution	NOUN
ejpam-6140	64	10	:	:	PUNCT
ejpam-6140	64	11	(	(	PUNCT
ejpam-6140	64	12	uh(t	uh(t	SYM
ejpam-6140	64	13	)	)	PUNCT
ejpam-6140	64	14	,	,	PUNCT
ejpam-6140	64	15	vh(t	vh(t	NUM
ejpam-6140	64	16	)	)	PUNCT
ejpam-6140	64	17	)	)	PUNCT
ejpam-6140	64	18	,	,	PUNCT
ejpam-6140	64	19	uh(t	uh(t	SYM
ejpam-6140	64	20	)	)	PUNCT
ejpam-6140	64	21	=	=	SYM
ejpam-6140	64	22	(	(	PUNCT
ejpam-6140	64	23	u0(t	u0(t	PROPN
ejpam-6140	64	24	)	)	PUNCT
ejpam-6140	64	25	,	,	PUNCT
ejpam-6140	64	26	u1(t	u1(t	PROPN
ejpam-6140	64	27	)	)	PUNCT
ejpam-6140	64	28	,	,	PUNCT
ejpam-6140	64	29	.	.	PUNCT
ejpam-6140	64	30	.	.	PUNCT
ejpam-6140	64	31	.	.	PUNCT
ejpam-6140	65	1	,	,	PUNCT
ejpam-6140	65	2	ui(t	ui(t	NOUN
ejpam-6140	65	3	)	)	PUNCT
ejpam-6140	65	4	)	)	PUNCT
ejpam-6140	66	1	t	t	PROPN
ejpam-6140	66	2	,	,	PUNCT
ejpam-6140	66	3	vh(t	vh(t	X
ejpam-6140	66	4	)	)	PUNCT
ejpam-6140	66	5	=	=	SYM
ejpam-6140	66	6	(	(	PUNCT
ejpam-6140	66	7	v0(t	v0(t	PROPN
ejpam-6140	66	8	)	)	PUNCT
ejpam-6140	66	9	,	,	PUNCT
ejpam-6140	66	10	v1(t	v1(t	CCONJ
ejpam-6140	66	11	)	)	PUNCT
ejpam-6140	66	12	,	,	PUNCT
ejpam-6140	66	13	.	.	PUNCT
ejpam-6140	66	14	.	.	PUNCT
ejpam-6140	66	15	.	.	PUNCT
ejpam-6140	67	1	,	,	PUNCT
ejpam-6140	67	2	vi(t	vi(t	NUM
ejpam-6140	67	3	)	)	PUNCT
ejpam-6140	67	4	)	)	PUNCT
ejpam-6140	68	1	t	t	NOUN
ejpam-6140	68	2	.	.	PUNCT
ejpam-6140	69	1	(	(	PUNCT
ejpam-6140	69	2	2	2	X
ejpam-6140	69	3	)	)	PUNCT
ejpam-6140	69	4	by	by	ADP
ejpam-6140	69	5	replacing	replace	VERB
ejpam-6140	69	6	the	the	DET
ejpam-6140	69	7	second	second	ADJ
ejpam-6140	69	8	-	-	PUNCT
ejpam-6140	69	9	order	order	NOUN
ejpam-6140	69	10	space	space	NOUN
ejpam-6140	69	11	derivative	derivative	NOUN
ejpam-6140	69	12	in	in	ADP
ejpam-6140	69	13	the	the	DET
ejpam-6140	69	14	problem	problem	NOUN
ejpam-6140	69	15	(	(	PUNCT
ejpam-6140	69	16	1	1	NUM
ejpam-6140	69	17	)	)	PUNCT
ejpam-6140	69	18	by	by	ADP
ejpam-6140	69	19	the	the	DET
ejpam-6140	69	20	standard	standard	ADJ
ejpam-6140	69	21	secondorder	secondorder	ADJ
ejpam-6140	69	22	central	central	ADJ
ejpam-6140	69	23	finite	finite	ADJ
ejpam-6140	69	24	difference	difference	NOUN
ejpam-6140	69	25	operator	operator	NOUN
ejpam-6140	69	26	δ2	δ2	VERB
ejpam-6140	70	1	[	[	X
ejpam-6140	70	2	27	27	NUM
ejpam-6140	70	3	]	]	PUNCT
ejpam-6140	70	4	,	,	PUNCT
ejpam-6140	70	5	we	we	PRON
ejpam-6140	70	6	obtain	obtain	VERB
ejpam-6140	70	7	the	the	DET
ejpam-6140	70	8	semi	semi	ADJ
ejpam-6140	70	9	-	-	ADJ
ejpam-6140	70	10	discrete	discrete	ADJ
ejpam-6140	70	11	problem	problem	NOUN
ejpam-6140	70	12	:	:	PUNCT
ejpam-6140	71	1	d	d	X
ejpam-6140	71	2	dt	dt	X
ejpam-6140	71	3	ui	ui	NOUN
ejpam-6140	71	4	=	=	PUNCT
ejpam-6140	71	5	ui+1	ui+1	PROPN
ejpam-6140	71	6	−	−	NOUN
ejpam-6140	71	7	2ui	2ui	NOUN
ejpam-6140	72	1	+	+	PUNCT
ejpam-6140	72	2	ui−1	ui−1	PROPN
ejpam-6140	72	3	h2	h2	PROPN
ejpam-6140	72	4	+	+	CCONJ
ejpam-6140	72	5	f	f	PROPN
ejpam-6140	72	6	(	(	PUNCT
ejpam-6140	72	7	vi	vi	NOUN
ejpam-6140	72	8	)	)	PUNCT
ejpam-6140	72	9	(	(	PUNCT
ejpam-6140	72	10	3	3	X
ejpam-6140	72	11	)	)	PUNCT
ejpam-6140	72	12	d	d	NOUN
ejpam-6140	72	13	dt	dt	X
ejpam-6140	72	14	vi	vi	X
ejpam-6140	72	15	=	=	SYM
ejpam-6140	72	16	vi+1	vi+1	ADV
ejpam-6140	72	17	−	−	PROPN
ejpam-6140	72	18	2vi	2vi	PROPN
ejpam-6140	73	1	+	+	CCONJ
ejpam-6140	73	2	vi−1	vi−1	PROPN
ejpam-6140	73	3	h2	h2	NOUN
ejpam-6140	73	4	+	+	CCONJ
ejpam-6140	73	5	g	g	PROPN
ejpam-6140	73	6	(	(	PUNCT
ejpam-6140	73	7	ui	ui	PROPN
ejpam-6140	73	8	)	)	PUNCT
ejpam-6140	73	9	(	(	PUNCT
ejpam-6140	73	10	4	4	X
ejpam-6140	73	11	)	)	PUNCT
ejpam-6140	73	12	u0(t	u0(t	ADJ
ejpam-6140	73	13	)	)	PUNCT
ejpam-6140	73	14	=	=	SYM
ejpam-6140	73	15	ui(t	ui(t	NOUN
ejpam-6140	73	16	)	)	PUNCT
ejpam-6140	73	17	=	=	SYM
ejpam-6140	73	18	0	0	NUM
ejpam-6140	73	19	,	,	PUNCT
ejpam-6140	73	20	v0(t	v0(t	PROPN
ejpam-6140	73	21	)	)	PUNCT
ejpam-6140	73	22	=	=	PUNCT
ejpam-6140	73	23	vi(t	vi(t	X
ejpam-6140	73	24	)	)	PUNCT
ejpam-6140	73	25	=	=	SYM
ejpam-6140	73	26	0	0	NUM
ejpam-6140	73	27	,	,	PUNCT
ejpam-6140	73	28	(	(	PUNCT
ejpam-6140	73	29	5	5	X
ejpam-6140	73	30	)	)	PUNCT
ejpam-6140	73	31	ui(0	ui(0	NOUN
ejpam-6140	73	32	)	)	PUNCT
ejpam-6140	73	33	=	=	PRON
ejpam-6140	73	34	u0	u0	ADJ
ejpam-6140	73	35	(	(	PUNCT
ejpam-6140	73	36	xi	xi	PROPN
ejpam-6140	73	37	)	)	PUNCT
ejpam-6140	73	38	,	,	PUNCT
ejpam-6140	73	39	vi(0	vi(0	PROPN
ejpam-6140	73	40	)	)	PUNCT
ejpam-6140	73	41	=	=	SYM
ejpam-6140	73	42	v0	v0	NOUN
ejpam-6140	73	43	(	(	PUNCT
ejpam-6140	73	44	xi	xi	PROPN
ejpam-6140	73	45	)	)	PUNCT
ejpam-6140	73	46	,	,	PUNCT
ejpam-6140	73	47	0	0	NUM
ejpam-6140	73	48	≤	≤	NUM
ejpam-6140	73	49	i	i	PRON
ejpam-6140	73	50	≤	≤	PROPN
ejpam-6140	73	51	i.	i.	NOUN
ejpam-6140	73	52	(	(	PUNCT
ejpam-6140	73	53	6	6	NUM
ejpam-6140	73	54	)	)	PUNCT
ejpam-6140	73	55	definition	definition	NOUN
ejpam-6140	73	56	1	1	NUM
ejpam-6140	73	57	.	.	PUNCT
ejpam-6140	74	1	[	[	X
ejpam-6140	74	2	26	26	NUM
ejpam-6140	74	3	]	]	X
ejpam-6140	74	4	let	let	VERB
ejpam-6140	74	5	(	(	PUNCT
ejpam-6140	74	6	uh	uh	INTJ
ejpam-6140	74	7	,	,	PUNCT
ejpam-6140	74	8	vh	vh	PROPN
ejpam-6140	74	9	)	)	PUNCT
ejpam-6140	74	10	be	be	AUX
ejpam-6140	74	11	a	a	DET
ejpam-6140	74	12	nonnegative	nonnegative	ADJ
ejpam-6140	74	13	solution	solution	NOUN
ejpam-6140	74	14	to	to	ADP
ejpam-6140	74	15	problem	problem	NOUN
ejpam-6140	74	16	(	(	PUNCT
ejpam-6140	74	17	1)–(2	1)–(2	NUM
ejpam-6140	74	18	)	)	PUNCT
ejpam-6140	74	19	.	.	PUNCT
ejpam-6140	75	1	we	we	PRON
ejpam-6140	75	2	say	say	VERB
ejpam-6140	75	3	that	that	SCONJ
ejpam-6140	75	4	(	(	PUNCT
ejpam-6140	75	5	uh	uh	INTJ
ejpam-6140	75	6	,	,	PUNCT
ejpam-6140	75	7	vh	vh	PROPN
ejpam-6140	75	8	)	)	PUNCT
ejpam-6140	75	9	achieves	achieve	VERB
ejpam-6140	75	10	blow	blow	NOUN
ejpam-6140	75	11	-	-	PUNCT
ejpam-6140	75	12	up	up	NOUN
ejpam-6140	75	13	simultaneously	simultaneously	ADV
ejpam-6140	75	14	in	in	ADP
ejpam-6140	75	15	finite	finite	ADJ
ejpam-6140	75	16	time	time	NOUN
ejpam-6140	75	17	,	,	PUNCT
ejpam-6140	75	18	if	if	SCONJ
ejpam-6140	75	19	there	there	PRON
ejpam-6140	75	20	exists	exist	VERB
ejpam-6140	75	21	th	th	X
ejpam-6140	75	22	<	<	X
ejpam-6140	75	23	∞	∞	NUM
ejpam-6140	75	24	such	such	ADJ
ejpam-6140	75	25	m.	m.	NOUN
ejpam-6140	75	26	i.	i.	PROPN
ejpam-6140	75	27	khalil	khalil	PROPN
ejpam-6140	75	28	et	et	PROPN
ejpam-6140	75	29	al	al	PROPN
ejpam-6140	75	30	.	.	PUNCT
ejpam-6140	75	31	/	/	SYM
ejpam-6140	75	32	eur	eur	PROPN
ejpam-6140	75	33	.	.	PUNCT
ejpam-6140	76	1	j.	j.	PROPN
ejpam-6140	76	2	pure	pure	PROPN
ejpam-6140	76	3	appl	appl	PROPN
ejpam-6140	76	4	.	.	PROPN
ejpam-6140	76	5	math	math	PROPN
ejpam-6140	76	6	,	,	PUNCT
ejpam-6140	76	7	18	18	NUM
ejpam-6140	76	8	(	(	PUNCT
ejpam-6140	76	9	3	3	NUM
ejpam-6140	76	10	)	)	PUNCT
ejpam-6140	76	11	(	(	PUNCT
ejpam-6140	76	12	2025	2025	NUM
ejpam-6140	76	13	)	)	PUNCT
ejpam-6140	76	14	,	,	PUNCT
ejpam-6140	76	15	6140	6140	NUM
ejpam-6140	76	16	4	4	NUM
ejpam-6140	76	17	of	of	ADP
ejpam-6140	76	18	17	17	NUM
ejpam-6140	77	1	that	that	PRON
ejpam-6140	77	2	:	:	PUNCT
ejpam-6140	77	3	∥uh(t)∥∞	∥uh(t)∥∞	PROPN
ejpam-6140	77	4	<	<	X
ejpam-6140	77	5	∞	∞	PROPN
ejpam-6140	77	6	and	and	CCONJ
ejpam-6140	77	7	∥vh(t)∥∞	∥vh(t)∥∞	ADP
ejpam-6140	77	8	<	<	X
ejpam-6140	77	9	∞	∞	PROPN
ejpam-6140	77	10	for	for	ADP
ejpam-6140	77	11	t	t	PROPN
ejpam-6140	77	12	∈	∈	PROPN
ejpam-6140	78	1	[	[	X
ejpam-6140	78	2	0	0	NUM
ejpam-6140	78	3	,	,	PUNCT
ejpam-6140	78	4	th	th	X
ejpam-6140	78	5	)	)	PUNCT
ejpam-6140	78	6	,	,	PUNCT
ejpam-6140	78	7	(	(	PUNCT
ejpam-6140	78	8	7	7	X
ejpam-6140	78	9	)	)	PUNCT
ejpam-6140	78	10	∥uh(t)∥∞	∥uh(t)∥∞	PROPN
ejpam-6140	78	11	→	→	SYM
ejpam-6140	78	12	∞	∞	PROPN
ejpam-6140	78	13	,	,	PUNCT
ejpam-6140	78	14	∥vh(t)∥∞	∥vh(t)∥∞	PROPN
ejpam-6140	78	15	→	→	SYM
ejpam-6140	78	16	∞	∞	PROPN
ejpam-6140	78	17	as	as	ADP
ejpam-6140	78	18	t	t	PROPN
ejpam-6140	78	19	→	→	SYM
ejpam-6140	78	20	th	th	PROPN
ejpam-6140	78	21	,	,	PUNCT
ejpam-6140	78	22	(	(	PUNCT
ejpam-6140	78	23	8)	8)	NUM
ejpam-6140	78	24	where	where	SCONJ
ejpam-6140	78	25	∥uh(t)∥∞	∥uh(t)∥∞	PROPN
ejpam-6140	78	26	=	=	SYM
ejpam-6140	78	27	max0≤i≤1	max0≤i≤1	NOUN
ejpam-6140	78	28	|ui(t)|	|ui(t)|	NOUN
ejpam-6140	78	29	and	and	CCONJ
ejpam-6140	78	30	∥7vh(t)∥∞	∥7vh(t)∥∞	NOUN
ejpam-6140	78	31	=	=	PUNCT
ejpam-6140	78	32	max0≤i≤1	max0≤i≤1	PROPN
ejpam-6140	78	33	|vi(t)|	|vi(t)|	PROPN
ejpam-6140	78	34	.	.	PUNCT
ejpam-6140	79	1	theorem	theorem	VERB
ejpam-6140	79	2	1	1	NUM
ejpam-6140	79	3	.	.	PUNCT
ejpam-6140	80	1	[	[	X
ejpam-6140	80	2	26	26	NUM
ejpam-6140	80	3	]	]	X
ejpam-6140	80	4	let	let	VERB
ejpam-6140	80	5	(	(	PUNCT
ejpam-6140	80	6	uh	uh	INTJ
ejpam-6140	80	7	,	,	PUNCT
ejpam-6140	80	8	vh	vh	PROPN
ejpam-6140	80	9	)	)	PUNCT
ejpam-6140	80	10	be	be	AUX
ejpam-6140	80	11	a	a	DET
ejpam-6140	80	12	non	non	ADJ
ejpam-6140	80	13	-	-	ADJ
ejpam-6140	80	14	negative	negative	ADJ
ejpam-6140	80	15	solution	solution	NOUN
ejpam-6140	80	16	of	of	ADP
ejpam-6140	80	17	the	the	DET
ejpam-6140	80	18	semi	semi	ADJ
ejpam-6140	80	19	-	-	ADJ
ejpam-6140	80	20	discrete	discrete	ADJ
ejpam-6140	80	21	problem	problem	NOUN
ejpam-6140	80	22	,	,	PUNCT
ejpam-6140	80	23	where	where	SCONJ
ejpam-6140	80	24	the	the	DET
ejpam-6140	80	25	reaction	reaction	NOUN
ejpam-6140	80	26	functions	function	NOUN
ejpam-6140	80	27	f	f	X
ejpam-6140	80	28	,	,	PUNCT
ejpam-6140	80	29	g	g	PROPN
ejpam-6140	80	30	are	be	AUX
ejpam-6140	80	31	locally	locally	ADV
ejpam-6140	80	32	lipschitz	lipschitz	ADJ
ejpam-6140	80	33	continuous	continuous	ADJ
ejpam-6140	80	34	such	such	ADJ
ejpam-6140	80	35	that	that	SCONJ
ejpam-6140	80	36	f	f	X
ejpam-6140	80	37	,	,	PUNCT
ejpam-6140	80	38	g	g	PROPN
ejpam-6140	80	39	>	>	X
ejpam-6140	80	40	0	0	PUNCT
ejpam-6140	80	41	in	in	ADP
ejpam-6140	80	42	(	(	PUNCT
ejpam-6140	80	43	0,∞	0,∞	NUM
ejpam-6140	80	44	)	)	PUNCT
ejpam-6140	80	45	.	.	PUNCT
ejpam-6140	81	1	if	if	SCONJ
ejpam-6140	81	2	(	(	PUNCT
ejpam-6140	81	3	uh	uh	INTJ
ejpam-6140	81	4	,	,	PUNCT
ejpam-6140	81	5	vh	vh	PROPN
ejpam-6140	81	6	)	)	PUNCT
ejpam-6140	81	7	achieves	achieve	VERB
ejpam-6140	81	8	blow	blow	NOUN
ejpam-6140	81	9	-	-	PUNCT
ejpam-6140	81	10	up	up	NOUN
ejpam-6140	81	11	at	at	ADP
ejpam-6140	81	12	time	time	NOUN
ejpam-6140	81	13	:	:	PUNCT
ejpam-6140	81	14	th	th	X
ejpam-6140	81	15	<	<	X
ejpam-6140	81	16	∞	∞	PROPN
ejpam-6140	81	17	,	,	PUNCT
ejpam-6140	81	18	then	then	ADV
ejpam-6140	81	19	th	th	INTJ
ejpam-6140	81	20	is	be	AUX
ejpam-6140	81	21	bounded	bound	VERB
ejpam-6140	81	22	from	from	ADP
ejpam-6140	81	23	below	below	ADV
ejpam-6140	81	24	.	.	PUNCT
ejpam-6140	82	1	corollary	corollary	ADJ
ejpam-6140	82	2	1	1	NUM
ejpam-6140	82	3	.	.	PUNCT
ejpam-6140	83	1	[	[	X
ejpam-6140	83	2	26	26	NUM
ejpam-6140	83	3	]	]	X
ejpam-6140	83	4	let	let	VERB
ejpam-6140	83	5	(	(	PUNCT
ejpam-6140	83	6	uh	uh	INTJ
ejpam-6140	83	7	,	,	PUNCT
ejpam-6140	83	8	vh	vh	PROPN
ejpam-6140	83	9	)	)	PUNCT
ejpam-6140	83	10	be	be	AUX
ejpam-6140	83	11	a	a	DET
ejpam-6140	83	12	non	non	ADJ
ejpam-6140	83	13	-	-	ADJ
ejpam-6140	83	14	negative	negative	ADJ
ejpam-6140	83	15	solution	solution	NOUN
ejpam-6140	83	16	of	of	ADP
ejpam-6140	83	17	the	the	DET
ejpam-6140	83	18	semi	semi	ADJ
ejpam-6140	83	19	-	-	ADJ
ejpam-6140	83	20	discrete	discrete	ADJ
ejpam-6140	83	21	problem	problem	NOUN
ejpam-6140	83	22	(	(	PUNCT
ejpam-6140	83	23	1)-(2	1)-(2	NUM
ejpam-6140	83	24	)	)	PUNCT
ejpam-6140	83	25	,	,	PUNCT
ejpam-6140	83	26	where	where	SCONJ
ejpam-6140	83	27	f	f	PROPN
ejpam-6140	83	28	=	=	SYM
ejpam-6140	83	29	vp	vp	PROPN
ejpam-6140	83	30	,	,	PUNCT
ejpam-6140	83	31	g	g	PROPN
ejpam-6140	83	32	=	=	SYM
ejpam-6140	83	33	uq	uq	PROPN
ejpam-6140	83	34	,	,	PUNCT
ejpam-6140	83	35	p	p	X
ejpam-6140	83	36	,	,	PUNCT
ejpam-6140	83	37	q	q	X
ejpam-6140	83	38	>	>	X
ejpam-6140	83	39	1	1	X
ejpam-6140	83	40	.	.	PUNCT
ejpam-6140	84	1	if	if	SCONJ
ejpam-6140	84	2	(	(	PUNCT
ejpam-6140	84	3	uh	uh	INTJ
ejpam-6140	84	4	,	,	PUNCT
ejpam-6140	84	5	vh	vh	PROPN
ejpam-6140	84	6	)	)	PUNCT
ejpam-6140	84	7	achieves	achieve	VERB
ejpam-6140	84	8	blow	blow	NOUN
ejpam-6140	84	9	-	-	PUNCT
ejpam-6140	84	10	up	up	NOUN
ejpam-6140	84	11	at	at	ADP
ejpam-6140	84	12	th	th	X
ejpam-6140	84	13	<	<	X
ejpam-6140	84	14	∞	∞	PROPN
ejpam-6140	84	15	,	,	PUNCT
ejpam-6140	84	16	then∫	then∫	NOUN
ejpam-6140	84	17	∞	∞	NUM
ejpam-6140	84	18	∥v0∥	∥v0∥	PROPN
ejpam-6140	84	19	ds	ds	ADJ
ejpam-6140	84	20	g2(s	g2(s	NOUN
ejpam-6140	84	21	)	)	PUNCT
ejpam-6140	85	1	=	=	SYM
ejpam-6140	86	1	∫	∫	PROPN
ejpam-6140	87	1	∞	∞	PROPN
ejpam-6140	87	2	∥u0∥	∥u0∥	PROPN
ejpam-6140	87	3	ds	ds	ADJ
ejpam-6140	87	4	g1(s	g1(s	NOUN
ejpam-6140	87	5	)	)	PUNCT
ejpam-6140	87	6	=	=	SYM
ejpam-6140	87	7	t	t	PROPN
ejpam-6140	87	8	≤	≤	PROPN
ejpam-6140	87	9	th	th	NUM
ejpam-6140	87	10	,	,	PUNCT
ejpam-6140	87	11	(	(	PUNCT
ejpam-6140	87	12	9	9	NUM
ejpam-6140	87	13	)	)	PUNCT
ejpam-6140	87	14	where	where	SCONJ
ejpam-6140	87	15	g1(s	g1(	VERB
ejpam-6140	87	16	)	)	PUNCT
ejpam-6140	87	17	=	=	NOUN
ejpam-6140	88	1	[	[	PUNCT
ejpam-6140	88	2	p+	p+	NOUN
ejpam-6140	88	3	1	1	NUM
ejpam-6140	88	4	q	q	NOUN
ejpam-6140	88	5	+	+	NUM
ejpam-6140	88	6	1	1	NUM
ejpam-6140	88	7	sq+1	sq+1	NOUN
ejpam-6140	88	8	−	−	PROPN
ejpam-6140	88	9	(	(	PUNCT
ejpam-6140	88	10	p+	p+	PROPN
ejpam-6140	88	11	1)c0	1)c0	NUM
ejpam-6140	88	12	]	]	PUNCT
ejpam-6140	88	13	p	p	X
ejpam-6140	88	14	p+1	p+1	PROPN
ejpam-6140	88	15	,	,	PUNCT
ejpam-6140	88	16	(	(	PUNCT
ejpam-6140	88	17	10	10	NUM
ejpam-6140	88	18	)	)	PUNCT
ejpam-6140	88	19	g2(s	g2(s	PROPN
ejpam-6140	88	20	)	)	PUNCT
ejpam-6140	89	1	=	=	PUNCT
ejpam-6140	90	1	[	[	PUNCT
ejpam-6140	90	2	q	q	X
ejpam-6140	90	3	+	+	NUM
ejpam-6140	90	4	1	1	NUM
ejpam-6140	90	5	p+	p+	NOUN
ejpam-6140	90	6	1	1	NUM
ejpam-6140	90	7	sp+1	sp+1	NUM
ejpam-6140	90	8	−	−	PROPN
ejpam-6140	90	9	(	(	PUNCT
ejpam-6140	90	10	q	q	X
ejpam-6140	90	11	+	+	CCONJ
ejpam-6140	90	12	1)c0	1)c0	NUM
ejpam-6140	90	13	]	]	PUNCT
ejpam-6140	90	14	q	q	PROPN
ejpam-6140	90	15	q+1	q+1	NUM
ejpam-6140	90	16	,	,	PUNCT
ejpam-6140	90	17	(	(	PUNCT
ejpam-6140	90	18	11	11	NUM
ejpam-6140	90	19	)	)	PUNCT
ejpam-6140	90	20	c0	c0	NOUN
ejpam-6140	90	21	=	=	SYM
ejpam-6140	90	22	1	1	NUM
ejpam-6140	90	23	q	q	NOUN
ejpam-6140	90	24	+	+	NUM
ejpam-6140	90	25	1	1	NUM
ejpam-6140	90	26	uq+1	uq+1	NOUN
ejpam-6140	90	27	0	0	NUM
ejpam-6140	90	28	−	−	PROPN
ejpam-6140	90	29	1	1	NUM
ejpam-6140	90	30	p+	p+	VERB
ejpam-6140	90	31	1	1	NUM
ejpam-6140	90	32	vp+1	vp+1	NOUN
ejpam-6140	90	33	0	0	NUM
ejpam-6140	90	34	.	.	PUNCT
ejpam-6140	91	1	(	(	PUNCT
ejpam-6140	91	2	12	12	NUM
ejpam-6140	91	3	)	)	PUNCT
ejpam-6140	91	4	theorem	theorem	NOUN
ejpam-6140	91	5	2	2	NUM
ejpam-6140	91	6	.	.	PUNCT
ejpam-6140	92	1	[	[	X
ejpam-6140	92	2	26	26	NUM
ejpam-6140	92	3	]	]	PUNCT
ejpam-6140	92	4	assume	assume	VERB
ejpam-6140	92	5	the	the	DET
ejpam-6140	92	6	following	following	NOUN
ejpam-6140	92	7	:	:	PUNCT
ejpam-6140	92	8	a	a	X
ejpam-6140	92	9	)	)	PUNCT
ejpam-6140	92	10	f	f	X
ejpam-6140	92	11	,	,	PUNCT
ejpam-6140	92	12	g	g	PROPN
ejpam-6140	92	13	∈	∈	PROPN
ejpam-6140	92	14	c1([0,∞	c1([0,∞	NOUN
ejpam-6140	92	15	]	]	PUNCT
ejpam-6140	92	16	)	)	PUNCT
ejpam-6140	92	17	are	be	AUX
ejpam-6140	92	18	convex	convex	ADJ
ejpam-6140	92	19	(	(	PUNCT
ejpam-6140	92	20	f	f	PROPN
ejpam-6140	92	21	′′	′′	PROPN
ejpam-6140	92	22	,	,	PUNCT
ejpam-6140	92	23	g′′	g′′	PROPN
ejpam-6140	92	24	≥	≥	NUM
ejpam-6140	92	25	0	0	NUM
ejpam-6140	92	26	,	,	PUNCT
ejpam-6140	92	27	)	)	PUNCT
ejpam-6140	92	28	,	,	PUNCT
ejpam-6140	92	29	f(z	f(z	PROPN
ejpam-6140	92	30	)	)	PUNCT
ejpam-6140	92	31	>	>	X
ejpam-6140	92	32	0	0	PUNCT
ejpam-6140	93	1	in	in	ADP
ejpam-6140	93	2	(	(	PUNCT
ejpam-6140	93	3	0,∞	0,∞	NOUN
ejpam-6140	93	4	)	)	PUNCT
ejpam-6140	93	5	,	,	PUNCT
ejpam-6140	93	6	and	and	CCONJ
ejpam-6140	93	7	∀ε	∀ε	X
ejpam-6140	93	8	>	>	X
ejpam-6140	93	9	0	0	NUM
ejpam-6140	93	10	,	,	PUNCT
ejpam-6140	93	11	we	we	PRON
ejpam-6140	93	12	have∫	have∫	VERB
ejpam-6140	93	13	∞	∞	PROPN
ejpam-6140	93	14	ε	ε	PROPN
ejpam-6140	93	15	dz	dz	PROPN
ejpam-6140	93	16	f(z	f(z	PROPN
ejpam-6140	93	17	)	)	PUNCT
ejpam-6140	93	18	<	<	X
ejpam-6140	94	1	∞	∞	PROPN
ejpam-6140	94	2	,	,	PUNCT
ejpam-6140	94	3	∫	∫	PROPN
ejpam-6140	94	4	∞	∞	PROPN
ejpam-6140	94	5	ε	ε	PROPN
ejpam-6140	94	6	dz	dz	PROPN
ejpam-6140	94	7	g(z	g(z	PROPN
ejpam-6140	94	8	)	)	PUNCT
ejpam-6140	94	9	<	<	X
ejpam-6140	94	10	∞.	∞.	PROPN
ejpam-6140	94	11	(	(	PUNCT
ejpam-6140	94	12	13	13	NUM
ejpam-6140	94	13	)	)	PUNCT
ejpam-6140	94	14	b	b	NOUN
ejpam-6140	94	15	)	)	PUNCT
ejpam-6140	94	16	∃z0	∃z0	ADJ
ejpam-6140	94	17	≥	≥	NOUN
ejpam-6140	94	18	0	0	NUM
ejpam-6140	94	19	such	such	ADJ
ejpam-6140	94	20	that	that	SCONJ
ejpam-6140	94	21	(	(	PUNCT
ejpam-6140	94	22	f(z	f(z	PROPN
ejpam-6140	94	23	)	)	PUNCT
ejpam-6140	94	24	z	z	NOUN
ejpam-6140	94	25	)	)	PUNCT
ejpam-6140	94	26	≥	≥	NOUN
ejpam-6140	94	27	λn	λn	NOUN
ejpam-6140	94	28	,	,	PUNCT
ejpam-6140	94	29	(	(	PUNCT
ejpam-6140	94	30	g(z	g(z	ADJ
ejpam-6140	94	31	)	)	PUNCT
ejpam-6140	94	32	z	z	NOUN
ejpam-6140	94	33	)	)	PUNCT
ejpam-6140	94	34	≥	≥	NOUN
ejpam-6140	94	35	λn	λn	NOUN
ejpam-6140	94	36	for	for	ADP
ejpam-6140	94	37	z	z	PROPN
ejpam-6140	94	38	∈	∈	PROPN
ejpam-6140	95	1	[	[	X
ejpam-6140	95	2	z0,∞	z0,∞	NUM
ejpam-6140	95	3	)	)	PUNCT
ejpam-6140	95	4	,	,	PUNCT
ejpam-6140	95	5	and	and	CCONJ
ejpam-6140	95	6	limz→∞	limz→∞	PROPN
ejpam-6140	95	7	z	z	PROPN
ejpam-6140	95	8	f(z	f(z	PROPN
ejpam-6140	95	9	)	)	PUNCT
ejpam-6140	96	1	=	=	SYM
ejpam-6140	96	2	0	0	PROPN
ejpam-6140	96	3	,	,	PUNCT
ejpam-6140	96	4	lim	lim	PROPN
ejpam-6140	96	5	z→∞	z→∞	PROPN
ejpam-6140	96	6	z	z	PUNCT
ejpam-6140	96	7	g(z	g(z	PROPN
ejpam-6140	96	8	)	)	PUNCT
ejpam-6140	97	1	=	=	SYM
ejpam-6140	97	2	0	0	X
ejpam-6140	97	3	.	.	PUNCT
ejpam-6140	98	1	c	c	X
ejpam-6140	98	2	)	)	PUNCT
ejpam-6140	98	3	the	the	DET
ejpam-6140	98	4	initial	initial	ADJ
ejpam-6140	98	5	conditions	condition	NOUN
ejpam-6140	98	6	are	be	AUX
ejpam-6140	98	7	non	non	ADJ
ejpam-6140	98	8	-	-	ADJ
ejpam-6140	98	9	negative	negative	ADJ
ejpam-6140	98	10	and	and	CCONJ
ejpam-6140	98	11	such	such	ADJ
ejpam-6140	98	12	that	that	DET
ejpam-6140	98	13	uh(0	uh(0	NOUN
ejpam-6140	98	14	)	)	PUNCT
ejpam-6140	98	15	̸=	̸=	PROPN
ejpam-6140	98	16	0	0	NUM
ejpam-6140	98	17	,	,	PUNCT
ejpam-6140	98	18	vh(0	vh(0	NOUN
ejpam-6140	98	19	)	)	PUNCT
ejpam-6140	98	20	̸=	̸=	PROPN
ejpam-6140	98	21	0	0	NUM
ejpam-6140	98	22	,	,	PUNCT
ejpam-6140	98	23	q1(0	q1(0	PROPN
ejpam-6140	98	24	)	)	PUNCT
ejpam-6140	98	25	≥	≥	NOUN
ejpam-6140	98	26	z0	z0	PROPN
ejpam-6140	98	27	,	,	PUNCT
ejpam-6140	98	28	q2(0	q2(0	PROPN
ejpam-6140	98	29	)	)	PUNCT
ejpam-6140	98	30	≥	≥	NOUN
ejpam-6140	98	31	z0	z0	PROPN
ejpam-6140	98	32	,	,	PUNCT
ejpam-6140	98	33	(	(	PUNCT
ejpam-6140	98	34	14	14	NUM
ejpam-6140	98	35	)	)	PUNCT
ejpam-6140	98	36	f	f	NOUN
ejpam-6140	98	37	(	(	PUNCT
ejpam-6140	98	38	q2(0))−	q2(0))−	PROPN
ejpam-6140	98	39	λnq1(0	λnq1(0	PROPN
ejpam-6140	98	40	)	)	PUNCT
ejpam-6140	98	41	>	>	X
ejpam-6140	99	1	0	0	NUM
ejpam-6140	99	2	,	,	PUNCT
ejpam-6140	99	3	g	g	PROPN
ejpam-6140	99	4	(	(	PUNCT
ejpam-6140	99	5	q1(0))−	q1(0))−	PROPN
ejpam-6140	99	6	λnq2(0	λnq2(0	PROPN
ejpam-6140	99	7	)	)	PUNCT
ejpam-6140	99	8	≥	≥	NOUN
ejpam-6140	99	9	0	0	NUM
ejpam-6140	99	10	,	,	PUNCT
ejpam-6140	99	11	(	(	PUNCT
ejpam-6140	99	12	15	15	NUM
ejpam-6140	99	13	)	)	PUNCT
ejpam-6140	99	14	where	where	SCONJ
ejpam-6140	99	15	q1(t	q1(t	X
ejpam-6140	99	16	)	)	PUNCT
ejpam-6140	99	17	=	=	SYM
ejpam-6140	99	18	i−1∑	i−1∑	NUM
ejpam-6140	99	19	i=1	i=1	PROPN
ejpam-6140	99	20	hui(t)υi	hui(t)υi	ADV
ejpam-6140	99	21	,	,	PUNCT
ejpam-6140	99	22	q2(t	q2(t	NOUN
ejpam-6140	99	23	)	)	PUNCT
ejpam-6140	99	24	=	=	SYM
ejpam-6140	99	25	i−1∑	i−1∑	NUM
ejpam-6140	99	26	i=1	i=1	PROPN
ejpam-6140	99	27	hvi(t),υi	hvi(t),υi	PROPN
ejpam-6140	99	28	,	,	PUNCT
ejpam-6140	99	29	(	(	PUNCT
ejpam-6140	99	30	16	16	NUM
ejpam-6140	99	31	)	)	PUNCT
ejpam-6140	99	32	m.	m.	NOUN
ejpam-6140	99	33	i.	i.	PROPN
ejpam-6140	99	34	khalil	khalil	PROPN
ejpam-6140	99	35	et	et	PROPN
ejpam-6140	99	36	al	al	PROPN
ejpam-6140	99	37	.	.	PUNCT
ejpam-6140	99	38	/	/	SYM
ejpam-6140	99	39	eur	eur	PROPN
ejpam-6140	99	40	.	.	PUNCT
ejpam-6140	100	1	j.	j.	PROPN
ejpam-6140	100	2	pure	pure	PROPN
ejpam-6140	100	3	appl	appl	PROPN
ejpam-6140	100	4	.	.	PROPN
ejpam-6140	100	5	math	math	PROPN
ejpam-6140	100	6	,	,	PUNCT
ejpam-6140	100	7	18	18	NUM
ejpam-6140	100	8	(	(	PUNCT
ejpam-6140	100	9	3	3	NUM
ejpam-6140	100	10	)	)	PUNCT
ejpam-6140	100	11	(	(	PUNCT
ejpam-6140	100	12	2025	2025	NUM
ejpam-6140	100	13	)	)	PUNCT
ejpam-6140	100	14	,	,	PUNCT
ejpam-6140	100	15	6140	6140	NUM
ejpam-6140	100	16	5	5	NUM
ejpam-6140	100	17	of	of	ADP
ejpam-6140	100	18	17	17	NUM
ejpam-6140	100	19	υi	υi	NOUN
ejpam-6140	100	20	=	=	SYM
ejpam-6140	100	21	sin(πih)∑i−1	sin(πih)∑i−1	PROPN
ejpam-6140	100	22	m=1	m=1	PROPN
ejpam-6140	100	23	sin(πmh	sin(πmh	PROPN
ejpam-6140	100	24	)	)	PUNCT
ejpam-6140	100	25	,	,	PUNCT
ejpam-6140	100	26	−δ2υi	−δ2υi	NUM
ejpam-6140	100	27	=	=	NUM
ejpam-6140	100	28	λnυi	λnυi	NOUN
ejpam-6140	100	29	,	,	PUNCT
ejpam-6140	100	30	i	i	PRON
ejpam-6140	100	31	=	=	NOUN
ejpam-6140	100	32	1	1	NUM
ejpam-6140	100	33	,	,	PUNCT
ejpam-6140	100	34	2	2	NUM
ejpam-6140	100	35	,	,	PUNCT
ejpam-6140	100	36	.	.	PUNCT
ejpam-6140	100	37	.	.	PUNCT
ejpam-6140	101	1	.	.	PUNCT
ejpam-6140	102	1	,	,	PUNCT
ejpam-6140	102	2	i	i	PRON
ejpam-6140	102	3	−	−	VERB
ejpam-6140	102	4	1	1	NUM
ejpam-6140	102	5	,	,	PUNCT
ejpam-6140	102	6	υ0	υ0	NOUN
ejpam-6140	102	7	=	=	NOUN
ejpam-6140	102	8	υi	υi	NOUN
ejpam-6140	102	9	=	=	NOUN
ejpam-6140	102	10	0	0	PROPN
ejpam-6140	102	11	,	,	PUNCT
ejpam-6140	102	12	λn	λn	NOUN
ejpam-6140	102	13	=	=	PUNCT
ejpam-6140	102	14	(	(	PUNCT
ejpam-6140	102	15	4	4	NUM
ejpam-6140	102	16	h2	h2	NOUN
ejpam-6140	102	17	)	)	PUNCT
ejpam-6140	102	18	sin2	sin2	NOUN
ejpam-6140	102	19	(	(	PUNCT
ejpam-6140	102	20	πh	πh	NOUN
ejpam-6140	102	21	2	2	NUM
ejpam-6140	102	22	)	)	PUNCT
ejpam-6140	102	23	.	.	PUNCT
ejpam-6140	103	1	(	(	PUNCT
ejpam-6140	103	2	17	17	NUM
ejpam-6140	103	3	)	)	PUNCT
ejpam-6140	103	4	then	then	ADV
ejpam-6140	103	5	the	the	DET
ejpam-6140	103	6	non	non	ADJ
ejpam-6140	103	7	-	-	ADJ
ejpam-6140	103	8	negative	negative	ADJ
ejpam-6140	103	9	solution	solution	NOUN
ejpam-6140	103	10	(	(	PUNCT
ejpam-6140	103	11	uh	uh	INTJ
ejpam-6140	103	12	,	,	PUNCT
ejpam-6140	103	13	vh	vh	PROPN
ejpam-6140	103	14	)	)	PUNCT
ejpam-6140	103	15	of	of	ADP
ejpam-6140	103	16	the	the	DET
ejpam-6140	103	17	discrete	discrete	ADJ
ejpam-6140	103	18	problem	problem	NOUN
ejpam-6140	103	19	achieves	achieve	VERB
ejpam-6140	103	20	blow	blow	NOUN
ejpam-6140	103	21	-	-	PUNCT
ejpam-6140	103	22	up	up	NOUN
ejpam-6140	103	23	at	at	ADP
ejpam-6140	103	24	time	time	NOUN
ejpam-6140	103	25	th	th	X
ejpam-6140	103	26	with	with	ADP
ejpam-6140	103	27	th	th	X
ejpam-6140	103	28	≤	≤	NUM
ejpam-6140	103	29	∫	∫	PROPN
ejpam-6140	103	30	∞	∞	PROPN
ejpam-6140	103	31	q1(0	q1(0	PROPN
ejpam-6140	103	32	)	)	PUNCT
ejpam-6140	103	33	dz1	dz1	VERB
ejpam-6140	104	1	f	f	PROPN
ejpam-6140	104	2	(	(	PUNCT
ejpam-6140	104	3	z2)−	z2)−	X
ejpam-6140	104	4	λnz1	λnz1	PROPN
ejpam-6140	104	5	,	,	PUNCT
ejpam-6140	104	6	∀z2	∀z2	PROPN
ejpam-6140	104	7	∈	∈	PROPN
ejpam-6140	104	8	[	[	X
ejpam-6140	104	9	z0,∞	z0,∞	NUM
ejpam-6140	104	10	)	)	PUNCT
ejpam-6140	104	11	,	,	PUNCT
ejpam-6140	104	12	(	(	PUNCT
ejpam-6140	104	13	18	18	NUM
ejpam-6140	104	14	)	)	PUNCT
ejpam-6140	104	15	or	or	CCONJ
ejpam-6140	104	16	th	th	X
ejpam-6140	104	17	≤	≤	NUM
ejpam-6140	104	18	∫	∫	PROPN
ejpam-6140	104	19	∞	∞	PROPN
ejpam-6140	104	20	q2(0	q2(0	PROPN
ejpam-6140	104	21	)	)	PUNCT
ejpam-6140	104	22	dz2	dz2	NOUN
ejpam-6140	104	23	g	g	PROPN
ejpam-6140	104	24	(	(	PUNCT
ejpam-6140	104	25	z1)−	z1)−	NOUN
ejpam-6140	104	26	λnz2	λnz2	NOUN
ejpam-6140	104	27	,	,	PUNCT
ejpam-6140	104	28	∀z1	∀z1	NOUN
ejpam-6140	104	29	∈	∈	PROPN
ejpam-6140	105	1	[	[	X
ejpam-6140	105	2	z0,∞	z0,∞	NUM
ejpam-6140	105	3	)	)	PUNCT
ejpam-6140	105	4	.	.	PUNCT
ejpam-6140	106	1	(	(	PUNCT
ejpam-6140	106	2	19	19	NUM
ejpam-6140	106	3	)	)	PUNCT
ejpam-6140	106	4	theorem	theorem	NOUN
ejpam-6140	106	5	3	3	NUM
ejpam-6140	106	6	.	.	PUNCT
ejpam-6140	107	1	[	[	X
ejpam-6140	107	2	26	26	NUM
ejpam-6140	107	3	]	]	PUNCT
ejpam-6140	107	4	assume	assume	VERB
ejpam-6140	107	5	athe	athe	ADJ
ejpam-6140	107	6	reaction	reaction	NOUN
ejpam-6140	107	7	functions	function	NOUN
ejpam-6140	107	8	:	:	PUNCT
ejpam-6140	107	9	f	f	X
ejpam-6140	107	10	,	,	PUNCT
ejpam-6140	107	11	g	g	PROPN
ejpam-6140	107	12	∈	∈	PROPN
ejpam-6140	107	13	c1([0,∞	c1([0,∞	NOUN
ejpam-6140	107	14	]	]	PUNCT
ejpam-6140	107	15	)	)	PUNCT
ejpam-6140	107	16	,	,	PUNCT
ejpam-6140	107	17	and	and	CCONJ
ejpam-6140	107	18	problem	problem	NOUN
ejpam-6140	107	19	of	of	ADP
ejpam-6140	107	20	system	system	NOUN
ejpam-6140	107	21	(	(	PUNCT
ejpam-6140	107	22	1	1	X
ejpam-6140	107	23	)	)	PUNCT
ejpam-6140	107	24	has	have	VERB
ejpam-6140	107	25	a	a	DET
ejpam-6140	107	26	solution	solution	NOUN
ejpam-6140	107	27	:	:	PUNCT
ejpam-6140	107	28	(	(	PUNCT
ejpam-6140	107	29	u	u	NOUN
ejpam-6140	107	30	,	,	PUNCT
ejpam-6140	107	31	v	v	NOUN
ejpam-6140	107	32	)	)	PUNCT
ejpam-6140	107	33	,	,	PUNCT
ejpam-6140	107	34	u	u	NOUN
ejpam-6140	107	35	,	,	PUNCT
ejpam-6140	107	36	v	v	NOUN
ejpam-6140	107	37	∈	∈	NOUN
ejpam-6140	107	38	c4,1([0	c4,1([0	NOUN
ejpam-6140	107	39	,	,	PUNCT
ejpam-6140	107	40	1]×	1]×	NUM
ejpam-6140	108	1	[	[	X
ejpam-6140	108	2	0	0	NUM
ejpam-6140	108	3	,	,	PUNCT
ejpam-6140	108	4	t	t	X
ejpam-6140	108	5	]	]	PUNCT
ejpam-6140	108	6	)	)	PUNCT
ejpam-6140	108	7	.	.	PUNCT
ejpam-6140	109	1	bthe	bthe	DET
ejpam-6140	109	2	initial	initial	ADJ
ejpam-6140	109	3	condition	condition	NOUN
ejpam-6140	109	4	(	(	PUNCT
ejpam-6140	109	5	u0	u0	PROPN
ejpam-6140	109	6	h	h	PROPN
ejpam-6140	109	7	,	,	PUNCT
ejpam-6140	109	8	v	v	NOUN
ejpam-6140	109	9	0	0	NUM
ejpam-6140	109	10	h	h	NOUN
ejpam-6140	109	11	)	)	PUNCT
ejpam-6140	109	12	satisfies	satisfy	VERB
ejpam-6140	109	13	∥∥u0	∥∥u0	PROPN
ejpam-6140	109	14	h	h	NOUN
ejpam-6140	109	15	−	−	NOUN
ejpam-6140	109	16	uh(0	uh(0	NOUN
ejpam-6140	109	17	)	)	PUNCT
ejpam-6140	109	18	∥∥	∥∥	X
ejpam-6140	109	19	∞	∞	NUM
ejpam-6140	109	20	=	=	SYM
ejpam-6140	109	21	o(1	o(1	PROPN
ejpam-6140	109	22	)	)	PUNCT
ejpam-6140	109	23	,	,	PUNCT
ejpam-6140	109	24	h	h	PROPN
ejpam-6140	109	25	→	→	SYM
ejpam-6140	109	26	0∥∥v	0∥∥v	X
ejpam-6140	109	27	0	0	NUM
ejpam-6140	109	28	h	h	NOUN
ejpam-6140	110	1	−	−	PROPN
ejpam-6140	110	2	vh(0	vh(0	NOUN
ejpam-6140	110	3	)	)	PUNCT
ejpam-6140	110	4	∥∥	∥∥	X
ejpam-6140	110	5	∞	∞	NUM
ejpam-6140	110	6	=	=	SYM
ejpam-6140	110	7	o(1	o(1	PROPN
ejpam-6140	110	8	)	)	PUNCT
ejpam-6140	110	9	,	,	PUNCT
ejpam-6140	110	10	h	h	NOUN
ejpam-6140	110	11	→	→	SYM
ejpam-6140	110	12	0	0	NUM
ejpam-6140	110	13	(	(	PUNCT
ejpam-6140	110	14	20	20	NUM
ejpam-6140	110	15	)	)	PUNCT
ejpam-6140	110	16	then	then	ADV
ejpam-6140	110	17	,	,	PUNCT
ejpam-6140	110	18	for	for	ADP
ejpam-6140	110	19	h	h	NOUN
ejpam-6140	110	20	sufficiently	sufficiently	ADV
ejpam-6140	110	21	small	small	ADJ
ejpam-6140	110	22	,	,	PUNCT
ejpam-6140	110	23	the	the	DET
ejpam-6140	110	24	semi	semi	ADJ
ejpam-6140	110	25	-	-	ADJ
ejpam-6140	110	26	discrete	discrete	ADJ
ejpam-6140	110	27	problem	problem	NOUN
ejpam-6140	110	28	(	(	PUNCT
ejpam-6140	110	29	1	1	X
ejpam-6140	110	30	)	)	PUNCT
ejpam-6140	110	31	has	have	VERB
ejpam-6140	110	32	a	a	DET
ejpam-6140	110	33	unique	unique	ADJ
ejpam-6140	110	34	solution	solution	NOUN
ejpam-6140	110	35	:	:	PUNCT
ejpam-6140	110	36	(	(	PUNCT
ejpam-6140	110	37	uh	uh	INTJ
ejpam-6140	110	38	,	,	PUNCT
ejpam-6140	110	39	vh	vh	PROPN
ejpam-6140	110	40	)	)	PUNCT
ejpam-6140	110	41	,	,	PUNCT
ejpam-6140	110	42	uh	uh	INTJ
ejpam-6140	110	43	,	,	PUNCT
ejpam-6140	110	44	vh	vh	PROPN
ejpam-6140	110	45	∈	∈	PROPN
ejpam-6140	110	46	c1([0	c1([0	PROPN
ejpam-6140	110	47	,	,	PUNCT
ejpam-6140	110	48	t	t	NOUN
ejpam-6140	110	49	]	]	PUNCT
ejpam-6140	110	50	)	)	PUNCT
ejpam-6140	110	51	,	,	PUNCT
ejpam-6140	110	52	rj+1	rj+1	PRON
ejpam-6140	110	53	such	such	ADJ
ejpam-6140	110	54	that	that	DET
ejpam-6140	110	55	maxt∈[o	maxt∈[o	NOUN
ejpam-6140	110	56	,	,	PUNCT
ejpam-6140	110	57	t	t	NOUN
ejpam-6140	110	58	]	]	PUNCT
ejpam-6140	110	59	∥uh(t)−	∥uh(t)−	PROPN
ejpam-6140	110	60	uh(t)∥∞	uh(t)∥∞	PROPN
ejpam-6140	111	1	=	=	SYM
ejpam-6140	111	2	o	o	PROPN
ejpam-6140	111	3	(	(	PUNCT
ejpam-6140	111	4	∥e(0)∥∞	∥e(0)∥∞	PROPN
ejpam-6140	111	5	+	+	NUM
ejpam-6140	111	6	h2	h2	NOUN
ejpam-6140	111	7	)	)	PUNCT
ejpam-6140	111	8	,	,	PUNCT
ejpam-6140	111	9	h	h	NOUN
ejpam-6140	111	10	→	→	SYM
ejpam-6140	111	11	0	0	NUM
ejpam-6140	111	12	maxt∈[o	maxt∈[o	NOUN
ejpam-6140	111	13	,	,	PUNCT
ejpam-6140	111	14	t	t	NOUN
ejpam-6140	111	15	]	]	PUNCT
ejpam-6140	111	16	∥vh(t)−	∥vh(t)−	PUNCT
ejpam-6140	111	17	vh(t)∥∞	vh(t)∥∞	X
ejpam-6140	111	18	=	=	SYM
ejpam-6140	111	19	o	o	X
ejpam-6140	111	20	(	(	PUNCT
ejpam-6140	111	21	∥e(0)∥∞	∥e(0)∥∞	PROPN
ejpam-6140	111	22	+	+	NUM
ejpam-6140	111	23	h2	h2	NOUN
ejpam-6140	111	24	)	)	PUNCT
ejpam-6140	111	25	,	,	PUNCT
ejpam-6140	111	26	h	h	NOUN
ejpam-6140	111	27	→	→	SYM
ejpam-6140	111	28	0	0	NUM
ejpam-6140	111	29	(	(	PUNCT
ejpam-6140	111	30	21	21	NUM
ejpam-6140	111	31	)	)	PUNCT
ejpam-6140	112	1	where	where	SCONJ
ejpam-6140	112	2	∥e(0)∥∞	∥e(0)∥∞	PROPN
ejpam-6140	112	3	=	=	SYM
ejpam-6140	112	4	max	max	PROPN
ejpam-6140	112	5	{	{	PUNCT
ejpam-6140	112	6	∥∥u0	∥∥u0	PROPN
ejpam-6140	112	7	h	h	NOUN
ejpam-6140	112	8	−	−	NOUN
ejpam-6140	112	9	uh(0	uh(0	NOUN
ejpam-6140	112	10	)	)	PUNCT
ejpam-6140	112	11	∥∥	∥∥	PROPN
ejpam-6140	112	12	∞	∞	PROPN
ejpam-6140	112	13	,	,	PUNCT
ejpam-6140	112	14	∥∥v	∥∥v	PROPN
ejpam-6140	112	15	0	0	NUM
ejpam-6140	112	16	h	h	NOUN
ejpam-6140	112	17	−	−	PROPN
ejpam-6140	112	18	vh(0	vh(0	NOUN
ejpam-6140	112	19	)	)	PUNCT
ejpam-6140	112	20	∥∥	∥∥	PROPN
ejpam-6140	112	21	∞	∞	PROPN
ejpam-6140	112	22	}	}	PUNCT
ejpam-6140	112	23	theorem	theorem	VERB
ejpam-6140	112	24	4	4	NUM
ejpam-6140	112	25	.	.	PUNCT
ejpam-6140	113	1	[	[	X
ejpam-6140	113	2	26	26	NUM
ejpam-6140	113	3	]	]	PUNCT
ejpam-6140	113	4	assume	assume	VERB
ejpam-6140	113	5	a	a	X
ejpam-6140	113	6	)	)	PUNCT
ejpam-6140	113	7	the	the	DET
ejpam-6140	113	8	functions	function	NOUN
ejpam-6140	113	9	f	f	X
ejpam-6140	113	10	,	,	PUNCT
ejpam-6140	113	11	g	g	PROPN
ejpam-6140	113	12	∈	∈	PROPN
ejpam-6140	113	13	c1([0,∞	c1([0,∞	NOUN
ejpam-6140	113	14	)	)	PUNCT
ejpam-6140	113	15	,	,	PUNCT
ejpam-6140	113	16	r	r	NOUN
ejpam-6140	113	17	)	)	PUNCT
ejpam-6140	113	18	and	and	CCONJ
ejpam-6140	113	19	f(z	f(z	NOUN
ejpam-6140	113	20	)	)	PUNCT
ejpam-6140	113	21	,	,	PUNCT
ejpam-6140	113	22	g(z	g(z	PROPN
ejpam-6140	113	23	)	)	PUNCT
ejpam-6140	113	24	>	>	X
ejpam-6140	113	25	0	0	PUNCT
ejpam-6140	114	1	in	in	ADP
ejpam-6140	114	2	(	(	PUNCT
ejpam-6140	114	3	0,∞	0,∞	NUM
ejpam-6140	114	4	)	)	PUNCT
ejpam-6140	114	5	.	.	PUNCT
ejpam-6140	115	1	b	b	X
ejpam-6140	115	2	)	)	PUNCT
ejpam-6140	115	3	there	there	PRON
ejpam-6140	115	4	exists	exist	VERB
ejpam-6140	115	5	z̄	z̄	PROPN
ejpam-6140	115	6	≥	≥	NUM
ejpam-6140	115	7	0	0	NUM
ejpam-6140	115	8	,	,	PUNCT
ejpam-6140	115	9	such	such	ADJ
ejpam-6140	115	10	that	that	DET
ejpam-6140	115	11	•	•	NOUN
ejpam-6140	115	12	(	(	PUNCT
ejpam-6140	115	13	f(z	f(z	PROPN
ejpam-6140	115	14	)	)	PUNCT
ejpam-6140	115	15	z	z	NOUN
ejpam-6140	115	16	)	)	PUNCT
ejpam-6140	115	17	≥	≥	X
ejpam-6140	115	18	π2	π2	ADV
ejpam-6140	115	19	,	,	PUNCT
ejpam-6140	115	20	(	(	PUNCT
ejpam-6140	115	21	g(z	g(z	ADJ
ejpam-6140	115	22	)	)	PUNCT
ejpam-6140	115	23	z	z	NOUN
ejpam-6140	115	24	)	)	PUNCT
ejpam-6140	115	25	≥	≥	X
ejpam-6140	116	1	π2	π2	ADV
ejpam-6140	116	2	,	,	PUNCT
ejpam-6140	116	3	for	for	ADP
ejpam-6140	116	4	z	z	PROPN
ejpam-6140	116	5	∈	∈	PROPN
ejpam-6140	117	1	[	[	X
ejpam-6140	117	2	z̄,∞	z̄,∞	NOUN
ejpam-6140	117	3	)	)	PUNCT
ejpam-6140	117	4	•	•	NUM
ejpam-6140	117	5	limz→∞	limz→∞	PROPN
ejpam-6140	117	6	z	z	PROPN
ejpam-6140	117	7	f(z	f(z	PROPN
ejpam-6140	117	8	)	)	PUNCT
ejpam-6140	117	9	=	=	SYM
ejpam-6140	117	10	0	0	NUM
ejpam-6140	117	11	,	,	PUNCT
ejpam-6140	117	12	limz→∞	limz→∞	PROPN
ejpam-6140	117	13	z	z	PROPN
ejpam-6140	117	14	g(z	g(z	PROPN
ejpam-6140	117	15	)	)	PUNCT
ejpam-6140	118	1	=	=	SYM
ejpam-6140	118	2	0	0	NUM
ejpam-6140	118	3	•	•	NUM
ejpam-6140	118	4	f(z̄)−	f(z̄)−	NOUN
ejpam-6140	118	5	π2z̄	π2z̄	X
ejpam-6140	118	6	>	>	X
ejpam-6140	118	7	0	0	NUM
ejpam-6140	118	8	,	,	PUNCT
ejpam-6140	118	9	g(z̄)−	g(z̄)−	PROPN
ejpam-6140	118	10	π2z̄	π2z̄	PUNCT
ejpam-6140	118	11	>	>	X
ejpam-6140	118	12	0	0	PUNCT
ejpam-6140	119	1	c	c	X
ejpam-6140	119	2	)	)	PUNCT
ejpam-6140	119	3	there	there	PRON
ejpam-6140	119	4	exists	exist	VERB
ejpam-6140	119	5	t	t	PROPN
ejpam-6140	119	6	<	<	X
ejpam-6140	119	7	∞	∞	NUM
ejpam-6140	119	8	such	such	ADJ
ejpam-6140	119	9	that	that	SCONJ
ejpam-6140	119	10	,	,	PUNCT
ejpam-6140	119	11	u	u	NOUN
ejpam-6140	119	12	,	,	PUNCT
ejpam-6140	119	13	v	v	NOUN
ejpam-6140	119	14	∈	∈	NOUN
ejpam-6140	119	15	c4,2([0	c4,2([0	VERB
ejpam-6140	119	16	,	,	PUNCT
ejpam-6140	119	17	1]×	1]×	NUM
ejpam-6140	120	1	[	[	X
ejpam-6140	120	2	0	0	NUM
ejpam-6140	120	3	,	,	PUNCT
ejpam-6140	120	4	t	t	NOUN
ejpam-6140	120	5	)	)	PUNCT
ejpam-6140	120	6	)	)	PUNCT
ejpam-6140	121	1	and	and	CCONJ
ejpam-6140	121	2	lim	lim	PROPN
ejpam-6140	121	3	t→t	t→t	NUM
ejpam-6140	121	4	∫	∫	NOUN
ejpam-6140	121	5	1	1	NUM
ejpam-6140	121	6	0	0	NUM
ejpam-6140	121	7	u(x	u(x	NOUN
ejpam-6140	121	8	,	,	PUNCT
ejpam-6140	121	9	t)w(x)dx	t)w(x)dx	NOUN
ejpam-6140	121	10	=	=	SYM
ejpam-6140	121	11	∞	∞	NUM
ejpam-6140	121	12	lim	lim	PROPN
ejpam-6140	122	1	t→t	t→t	NUM
ejpam-6140	122	2	∫	∫	NOUN
ejpam-6140	122	3	1	1	NUM
ejpam-6140	122	4	0	0	NUM
ejpam-6140	122	5	v(x	v(x	NOUN
ejpam-6140	122	6	,	,	PUNCT
ejpam-6140	122	7	t)w(x)dx	t)w(x)dx	NOUN
ejpam-6140	122	8	=	=	SYM
ejpam-6140	122	9	∞	∞	PROPN
ejpam-6140	122	10	(	(	PUNCT
ejpam-6140	122	11	22	22	NUM
ejpam-6140	122	12	)	)	PUNCT
ejpam-6140	122	13	m.	m.	NOUN
ejpam-6140	122	14	i.	i.	PROPN
ejpam-6140	122	15	khalil	khalil	PROPN
ejpam-6140	122	16	et	et	PROPN
ejpam-6140	122	17	al	al	PROPN
ejpam-6140	122	18	.	.	PUNCT
ejpam-6140	122	19	/	/	SYM
ejpam-6140	122	20	eur	eur	PROPN
ejpam-6140	122	21	.	.	PUNCT
ejpam-6140	123	1	j.	j.	PROPN
ejpam-6140	123	2	pure	pure	PROPN
ejpam-6140	123	3	appl	appl	PROPN
ejpam-6140	123	4	.	.	PROPN
ejpam-6140	123	5	math	math	PROPN
ejpam-6140	123	6	,	,	PUNCT
ejpam-6140	123	7	18	18	NUM
ejpam-6140	123	8	(	(	PUNCT
ejpam-6140	123	9	3	3	NUM
ejpam-6140	123	10	)	)	PUNCT
ejpam-6140	123	11	(	(	PUNCT
ejpam-6140	123	12	2025	2025	NUM
ejpam-6140	123	13	)	)	PUNCT
ejpam-6140	123	14	,	,	PUNCT
ejpam-6140	123	15	6140	6140	NUM
ejpam-6140	123	16	6	6	NUM
ejpam-6140	123	17	of	of	ADP
ejpam-6140	123	18	17	17	NUM
ejpam-6140	123	19	if	if	SCONJ
ejpam-6140	123	20	∥uh(0)−	∥uh(0)−	ADJ
ejpam-6140	123	21	uh(0)∥∞	uh(0)∥∞	PROPN
ejpam-6140	123	22	=	=	SYM
ejpam-6140	123	23	0(1	0(1	NUM
ejpam-6140	123	24	)	)	PUNCT
ejpam-6140	123	25	,	,	PUNCT
ejpam-6140	123	26	h	h	NOUN
ejpam-6140	123	27	→	→	SYM
ejpam-6140	123	28	0	0	NUM
ejpam-6140	123	29	,	,	PUNCT
ejpam-6140	123	30	then	then	ADV
ejpam-6140	123	31	the	the	DET
ejpam-6140	123	32	solution	solution	NOUN
ejpam-6140	123	33	of	of	ADP
ejpam-6140	123	34	the	the	DET
ejpam-6140	123	35	discrete	discrete	ADJ
ejpam-6140	123	36	problem	problem	NOUN
ejpam-6140	123	37	achieves	achieve	VERB
ejpam-6140	123	38	blow	blow	NOUN
ejpam-6140	123	39	-	-	PUNCT
ejpam-6140	123	40	up	up	NOUN
ejpam-6140	123	41	,	,	PUNCT
ejpam-6140	123	42	for	for	ADP
ejpam-6140	123	43	h	h	PRON
ejpam-6140	123	44	sufficiently	sufficiently	ADV
ejpam-6140	123	45	small	small	ADJ
ejpam-6140	123	46	at	at	ADP
ejpam-6140	123	47	th	th	X
ejpam-6140	123	48	and	and	CCONJ
ejpam-6140	123	49	lim	lim	PROPN
ejpam-6140	123	50	h→0	h→0	ADV
ejpam-6140	123	51	th	th	X
ejpam-6140	123	52	=	=	SYM
ejpam-6140	123	53	t	t	PROPN
ejpam-6140	123	54	2	2	NUM
ejpam-6140	123	55	.	.	PUNCT
ejpam-6140	123	56	crank	crank	NOUN
ejpam-6140	123	57	-	-	PUNCT
ejpam-6140	123	58	nicolson	nicolson	PROPN
ejpam-6140	123	59	method	method	NOUN
ejpam-6140	123	60	define	define	VERB
ejpam-6140	123	61	the	the	DET
ejpam-6140	123	62	grid	grid	NOUN
ejpam-6140	123	63	points	point	NOUN
ejpam-6140	123	64	xi	xi	X
ejpam-6140	123	65	=	=	PUNCT
ejpam-6140	123	66	ih	ih	X
ejpam-6140	123	67	,	,	PUNCT
ejpam-6140	123	68	0	0	NUM
ejpam-6140	123	69	≤	≤	NUM
ejpam-6140	124	1	i	i	PRON
ejpam-6140	124	2	≤	≤	PUNCT
ejpam-6140	125	1	i	i	PRON
ejpam-6140	125	2	,	,	PUNCT
ejpam-6140	125	3	where	where	SCONJ
ejpam-6140	125	4	i	i	PRON
ejpam-6140	125	5	∈	∈	PROPN
ejpam-6140	125	6	z+	z+	X
ejpam-6140	125	7	,	,	PUNCT
ejpam-6140	125	8	h	h	NOUN
ejpam-6140	125	9	=	=	SYM
ejpam-6140	125	10	1	1	NUM
ejpam-6140	125	11	/	/	SYM
ejpam-6140	125	12	i	i	PROPN
ejpam-6140	125	13	,	,	PUNCT
ejpam-6140	125	14	tn+1	tn+1	PROPN
ejpam-6140	125	15	=	=	SYM
ejpam-6140	125	16	tn	tn	PROPN
ejpam-6140	125	17	+	+	CCONJ
ejpam-6140	125	18	kn	kn	PROPN
ejpam-6140	125	19	,	,	PUNCT
ejpam-6140	125	20	kn	kn	PROPN
ejpam-6140	125	21	>	>	X
ejpam-6140	125	22	0,∀n	0,∀n	PROPN
ejpam-6140	125	23	.	.	PUNCT
ejpam-6140	126	1	set	set	VERB
ejpam-6140	126	2	un	un	PROPN
ejpam-6140	126	3	h	h	PROPN
ejpam-6140	127	1	=	=	PRON
ejpam-6140	127	2	(	(	PUNCT
ejpam-6140	127	3	un	un	PROPN
ejpam-6140	127	4	1	1	NUM
ejpam-6140	127	5	,	,	PUNCT
ejpam-6140	127	6	u	u	NOUN
ejpam-6140	127	7	n	n	PRON
ejpam-6140	127	8	2	2	NUM
ejpam-6140	127	9	.	.	PUNCT
ejpam-6140	127	10	.	.	PUNCT
ejpam-6140	127	11	.	.	PUNCT
ejpam-6140	128	1	un	un	PROPN
ejpam-6140	128	2	i−1	i−1	PROPN
ejpam-6140	128	3	)	)	PUNCT
ejpam-6140	128	4	t	t	PROPN
ejpam-6140	128	5	,	,	PUNCT
ejpam-6140	129	1	v	v	NOUN
ejpam-6140	129	2	n	n	NOUN
ejpam-6140	129	3	h	h	NOUN
ejpam-6140	130	1	=	=	PUNCT
ejpam-6140	130	2	(	(	PUNCT
ejpam-6140	130	3	v	v	NOUN
ejpam-6140	130	4	n	n	PRON
ejpam-6140	130	5	1	1	NUM
ejpam-6140	130	6	,	,	PUNCT
ejpam-6140	130	7	un	un	PROPN
ejpam-6140	130	8	2	2	NUM
ejpam-6140	130	9	.	.	PUNCT
ejpam-6140	130	10	.	.	PUNCT
ejpam-6140	130	11	.	.	PUNCT
ejpam-6140	131	1	v	v	X
ejpam-6140	131	2	n	n	PROPN
ejpam-6140	131	3	i−1	i−1	PROPN
ejpam-6140	131	4	)	)	PUNCT
ejpam-6140	131	5	t	t	PROPN
ejpam-6140	131	6	as	as	ADP
ejpam-6140	131	7	the	the	DET
ejpam-6140	131	8	numerical	numerical	ADJ
ejpam-6140	131	9	solution	solution	NOUN
ejpam-6140	131	10	of	of	ADP
ejpam-6140	131	11	problem	problem	NOUN
ejpam-6140	131	12	(	(	PUNCT
ejpam-6140	131	13	1	1	NUM
ejpam-6140	131	14	)	)	PUNCT
ejpam-6140	131	15	.	.	PUNCT
ejpam-6140	132	1	in	in	ADP
ejpam-6140	132	2	order	order	NOUN
ejpam-6140	132	3	to	to	PART
ejpam-6140	132	4	derive	derive	VERB
ejpam-6140	132	5	the	the	DET
ejpam-6140	132	6	crank	crank	NOUN
ejpam-6140	132	7	-	-	PUNCT
ejpam-6140	132	8	nicolson	nicolson	PROPN
ejpam-6140	132	9	method	method	NOUN
ejpam-6140	132	10	formally	formally	ADV
ejpam-6140	132	11	,	,	PUNCT
ejpam-6140	132	12	we	we	PRON
ejpam-6140	132	13	approximate	approximate	VERB
ejpam-6140	132	14	the	the	DET
ejpam-6140	132	15	partial	partial	ADJ
ejpam-6140	132	16	derivatives	derivative	NOUN
ejpam-6140	132	17	in	in	ADP
ejpam-6140	132	18	the	the	DET
ejpam-6140	132	19	semi	semi	ADJ
ejpam-6140	132	20	-	-	ADJ
ejpam-6140	132	21	discrete	discrete	ADJ
ejpam-6140	132	22	problem	problem	NOUN
ejpam-6140	132	23	(	(	PUNCT
ejpam-6140	132	24	3),(4	3),(4	PROPN
ejpam-6140	132	25	)	)	PUNCT
ejpam-6140	132	26	,	,	PUNCT
ejpam-6140	132	27	at	at	ADP
ejpam-6140	132	28	the	the	DET
ejpam-6140	132	29	mesh	mesh	NOUN
ejpam-6140	132	30	points	point	NOUN
ejpam-6140	132	31	:	:	PUNCT
ejpam-6140	132	32	(	(	PUNCT
ejpam-6140	132	33	xi	xi	INTJ
ejpam-6140	132	34	,	,	PUNCT
ejpam-6140	132	35	tn+	tn+	NOUN
ejpam-6140	132	36	1	1	NUM
ejpam-6140	132	37	2	2	NUM
ejpam-6140	132	38	)	)	PUNCT
ejpam-6140	132	39	.	.	PUNCT
ejpam-6140	133	1	firstly	firstly	ADV
ejpam-6140	133	2	,	,	PUNCT
ejpam-6140	133	3	we	we	PRON
ejpam-6140	133	4	approximate	approximate	VERB
ejpam-6140	133	5	the	the	DET
ejpam-6140	133	6	time	time	NOUN
ejpam-6140	133	7	-	-	PUNCT
ejpam-6140	133	8	derivatives	derivative	NOUN
ejpam-6140	133	9	using	use	VERB
ejpam-6140	133	10	the	the	DET
ejpam-6140	133	11	1s	1s	NUM
ejpam-6140	133	12	order	order	NOUN
ejpam-6140	133	13	central	central	ADJ
ejpam-6140	133	14	finite	finite	ADJ
ejpam-6140	133	15	difference	difference	NOUN
ejpam-6140	133	16	formula	formula	NOUN
ejpam-6140	133	17	:	:	PUNCT
ejpam-6140	133	18	∂u	∂u	PROPN
ejpam-6140	133	19	∂t	∂t	PROPN
ejpam-6140	133	20	∣∣∣∣n+	∣∣∣∣n+	NUM
ejpam-6140	133	21	1	1	NUM
ejpam-6140	133	22	2	2	NUM
ejpam-6140	133	23	i	i	NOUN
ejpam-6140	133	24	=	=	NOUN
ejpam-6140	133	25	1	1	NUM
ejpam-6140	133	26	kn	kn	NOUN
ejpam-6140	133	27	(	(	PUNCT
ejpam-6140	133	28	un+1	un+1	PROPN
ejpam-6140	133	29	i	i	PRON
ejpam-6140	133	30	−	−	PROPN
ejpam-6140	133	31	uni	uni	INTJ
ejpam-6140	133	32	)	)	PUNCT
ejpam-6140	134	1	+	+	NOUN
ejpam-6140	134	2	o	o	X
ejpam-6140	134	3	(	(	PUNCT
ejpam-6140	134	4	kn	kn	PROPN
ejpam-6140	134	5	)	)	PUNCT
ejpam-6140	134	6	,	,	PUNCT
ejpam-6140	135	1	∂v	∂v	PROPN
ejpam-6140	135	2	∂t	∂t	PROPN
ejpam-6140	135	3	∣∣∣∣n+	∣∣∣∣n+	PROPN
ejpam-6140	135	4	1	1	NUM
ejpam-6140	135	5	2	2	NUM
ejpam-6140	135	6	i	i	NOUN
ejpam-6140	135	7	=	=	NOUN
ejpam-6140	135	8	1	1	NUM
ejpam-6140	135	9	kn	kn	NOUN
ejpam-6140	135	10	(	(	PUNCT
ejpam-6140	135	11	vn+1	vn+1	PROPN
ejpam-6140	135	12	i	i	PRON
ejpam-6140	135	13	−	−	PROPN
ejpam-6140	135	14	vni	vni	NOUN
ejpam-6140	135	15	)	)	PUNCT
ejpam-6140	136	1	+	+	ADP
ejpam-6140	136	2	o	o	X
ejpam-6140	136	3	(	(	PUNCT
ejpam-6140	136	4	kn	kn	PROPN
ejpam-6140	136	5	)	)	PUNCT
ejpam-6140	136	6	,	,	PUNCT
ejpam-6140	136	7	and	and	CCONJ
ejpam-6140	136	8	δ2xu(t	δ2xu(t	NOUN
ejpam-6140	136	9	)	)	PUNCT
ejpam-6140	136	10	,	,	PUNCT
ejpam-6140	136	11	δ2xv	δ2xv	PUNCT
ejpam-6140	136	12	(	(	PUNCT
ejpam-6140	136	13	t	t	NOUN
ejpam-6140	136	14	)	)	PUNCT
ejpam-6140	136	15	are	be	AUX
ejpam-6140	136	16	approximated	approximate	VERB
ejpam-6140	136	17	as	as	SCONJ
ejpam-6140	136	18	follows	follow	VERB
ejpam-6140	136	19	:	:	PUNCT
ejpam-6140	136	20	δ2xui	δ2xui	PROPN
ejpam-6140	136	21	(	(	PUNCT
ejpam-6140	136	22	tn+1/2	tn+1/2	PROPN
ejpam-6140	136	23	)	)	PUNCT
ejpam-6140	136	24	=	=	SYM
ejpam-6140	136	25	1	1	NUM
ejpam-6140	136	26	2	2	NUM
ejpam-6140	136	27	[	[	PUNCT
ejpam-6140	136	28	δ2xui	δ2xui	PROPN
ejpam-6140	136	29	(	(	PUNCT
ejpam-6140	136	30	tn+1	tn+1	NOUN
ejpam-6140	136	31	)	)	PUNCT
ejpam-6140	136	32	+	+	CCONJ
ejpam-6140	136	33	δ2xui	δ2xui	PROPN
ejpam-6140	136	34	(	(	PUNCT
ejpam-6140	136	35	tn	tn	NOUN
ejpam-6140	136	36	)	)	PUNCT
ejpam-6140	136	37	]	]	PUNCT
ejpam-6140	137	1	+	+	PUNCT
ejpam-6140	137	2	o	o	X
ejpam-6140	137	3	(	(	PUNCT
ejpam-6140	137	4	k2n	k2n	PROPN
ejpam-6140	137	5	)	)	PUNCT
ejpam-6140	137	6	δ2xvi	δ2xvi	PROPN
ejpam-6140	137	7	(	(	PUNCT
ejpam-6140	137	8	tn+1/2	tn+1/2	NOUN
ejpam-6140	137	9	)	)	PUNCT
ejpam-6140	137	10	=	=	SYM
ejpam-6140	137	11	1	1	NUM
ejpam-6140	137	12	2	2	NUM
ejpam-6140	137	13	[	[	PUNCT
ejpam-6140	137	14	δ2xvi	δ2xvi	NUM
ejpam-6140	137	15	(	(	PUNCT
ejpam-6140	137	16	tn+1	tn+1	NOUN
ejpam-6140	137	17	)	)	PUNCT
ejpam-6140	137	18	+	+	NUM
ejpam-6140	137	19	δ2xvi	δ2xvi	NUM
ejpam-6140	137	20	(	(	PUNCT
ejpam-6140	137	21	tn	tn	NOUN
ejpam-6140	137	22	)	)	PUNCT
ejpam-6140	137	23	]	]	PUNCT
ejpam-6140	138	1	+	+	PUNCT
ejpam-6140	138	2	o	o	X
ejpam-6140	138	3	(	(	PUNCT
ejpam-6140	138	4	k2n	k2n	PROPN
ejpam-6140	138	5	)	)	PUNCT
ejpam-6140	138	6	it	it	PRON
ejpam-6140	138	7	follows	follow	VERB
ejpam-6140	138	8	that	that	SCONJ
ejpam-6140	138	9	δ2xui	δ2xui	PROPN
ejpam-6140	138	10	(	(	PUNCT
ejpam-6140	138	11	tn+1/2	tn+1/2	PROPN
ejpam-6140	138	12	)	)	PUNCT
ejpam-6140	138	13	=	=	PUNCT
ejpam-6140	139	1	1	1	NUM
ejpam-6140	139	2	2h2	2h2	NUM
ejpam-6140	140	1	[	[	X
ejpam-6140	140	2	(	(	PUNCT
ejpam-6140	140	3	un	un	PROPN
ejpam-6140	140	4	i+1	i+1	ADV
ejpam-6140	140	5	−	−	PROPN
ejpam-6140	140	6	2un	2un	ADJ
ejpam-6140	141	1	i	i	PRON
ejpam-6140	141	2	+	+	NUM
ejpam-6140	141	3	un	un	PROPN
ejpam-6140	141	4	i−1	i−1	PROPN
ejpam-6140	141	5	)	)	PUNCT
ejpam-6140	142	1	+	+	CCONJ
ejpam-6140	142	2	(	(	PUNCT
ejpam-6140	142	3	un+1	un+1	ADV
ejpam-6140	142	4	i+1	i+1	NUM
ejpam-6140	142	5	−	−	PROPN
ejpam-6140	142	6	2un+1	2un+1	NUM
ejpam-6140	142	7	i	i	PRON
ejpam-6140	143	1	+	+	CCONJ
ejpam-6140	143	2	un+1	un+1	ADJ
ejpam-6140	143	3	i−1	i−1	PROPN
ejpam-6140	143	4	)	)	PUNCT
ejpam-6140	143	5	]	]	PUNCT
ejpam-6140	144	1	δ2xvi	δ2xvi	VERB
ejpam-6140	144	2	(	(	PUNCT
ejpam-6140	144	3	tn+1/2	tn+1/2	PROPN
ejpam-6140	144	4	)	)	PUNCT
ejpam-6140	144	5	=	=	PUNCT
ejpam-6140	145	1	1	1	NUM
ejpam-6140	145	2	2h2	2h2	NUM
ejpam-6140	146	1	[	[	X
ejpam-6140	146	2	(	(	PUNCT
ejpam-6140	146	3	v	v	NOUN
ejpam-6140	146	4	n	n	NOUN
ejpam-6140	146	5	i+1	i+1	ADV
ejpam-6140	146	6	−	−	PROPN
ejpam-6140	146	7	2v	2v	PROPN
ejpam-6140	146	8	n	n	CCONJ
ejpam-6140	146	9	i	i	PRON
ejpam-6140	147	1	+	+	CCONJ
ejpam-6140	147	2	v	v	NOUN
ejpam-6140	147	3	n	n	NOUN
ejpam-6140	147	4	i−1	i−1	PROPN
ejpam-6140	147	5	)	)	PUNCT
ejpam-6140	148	1	+	+	CCONJ
ejpam-6140	148	2	(	(	PUNCT
ejpam-6140	148	3	v	v	ADP
ejpam-6140	148	4	n+1	n+1	PROPN
ejpam-6140	148	5	i+1	i+1	NOUN
ejpam-6140	148	6	−	−	PROPN
ejpam-6140	148	7	2v	2v	PROPN
ejpam-6140	148	8	n+1	n+1	PROPN
ejpam-6140	148	9	i	i	PROPN
ejpam-6140	148	10	+	+	SYM
ejpam-6140	148	11	vn+1	vn+1	PROPN
ejpam-6140	148	12	i−1	i−1	PROPN
ejpam-6140	148	13	)	)	PUNCT
ejpam-6140	148	14	]	]	PUNCT
ejpam-6140	148	15	while	while	SCONJ
ejpam-6140	148	16	the	the	DET
ejpam-6140	148	17	nonlinear	nonlinear	ADJ
ejpam-6140	148	18	terms	term	NOUN
ejpam-6140	148	19	are	be	AUX
ejpam-6140	148	20	taken	take	VERB
ejpam-6140	148	21	as	as	SCONJ
ejpam-6140	148	22	follows	follow	VERB
ejpam-6140	148	23	:	:	PUNCT
ejpam-6140	148	24	f	f	PROPN
ejpam-6140	148	25	(	(	PUNCT
ejpam-6140	148	26	v	v	X
ejpam-6140	148	27	n+1/2	n+1/2	NOUN
ejpam-6140	149	1	i	i	PROPN
ejpam-6140	149	2	)	)	PUNCT
ejpam-6140	150	1	=	=	SYM
ejpam-6140	150	2	f	f	X
ejpam-6140	150	3	(	(	PUNCT
ejpam-6140	150	4	v	v	NOUN
ejpam-6140	150	5	n	n	NOUN
ejpam-6140	150	6	i	i	PRON
ejpam-6140	150	7	)	)	PUNCT
ejpam-6140	151	1	+	+	NOUN
ejpam-6140	151	2	o	o	X
ejpam-6140	151	3	(	(	PUNCT
ejpam-6140	151	4	kn	kn	PROPN
ejpam-6140	151	5	)	)	PUNCT
ejpam-6140	151	6	,	,	PUNCT
ejpam-6140	151	7	g	g	PROPN
ejpam-6140	151	8	(	(	PUNCT
ejpam-6140	151	9	u	u	NOUN
ejpam-6140	151	10	n+1/2	n+1/2	PROPN
ejpam-6140	151	11	i	i	PROPN
ejpam-6140	151	12	)	)	PUNCT
ejpam-6140	152	1	=	=	SYM
ejpam-6140	152	2	g	g	PROPN
ejpam-6140	152	3	(	(	PUNCT
ejpam-6140	152	4	un	un	PROPN
ejpam-6140	152	5	i	i	PROPN
ejpam-6140	152	6	)	)	PUNCT
ejpam-6140	153	1	+	+	NOUN
ejpam-6140	153	2	o	o	X
ejpam-6140	153	3	(	(	PUNCT
ejpam-6140	153	4	kn	kn	PROPN
ejpam-6140	153	5	)	)	PUNCT
ejpam-6140	153	6	by	by	ADP
ejpam-6140	153	7	substituting	substitute	VERB
ejpam-6140	153	8	all	all	DET
ejpam-6140	153	9	these	these	DET
ejpam-6140	153	10	formulas	formula	NOUN
ejpam-6140	153	11	in	in	ADP
ejpam-6140	153	12	(	(	PUNCT
ejpam-6140	153	13	3),(4	3),(4	PROPN
ejpam-6140	153	14	)	)	PUNCT
ejpam-6140	153	15	,	,	PUNCT
ejpam-6140	153	16	we	we	PRON
ejpam-6140	153	17	obtain	obtain	VERB
ejpam-6140	153	18	1	1	NUM
ejpam-6140	153	19	kn	kn	NOUN
ejpam-6140	153	20	(	(	PUNCT
ejpam-6140	153	21	un+1	un+1	PROPN
ejpam-6140	153	22	i	i	PRON
ejpam-6140	153	23	−	−	PROPN
ejpam-6140	153	24	un	un	PROPN
ejpam-6140	153	25	i	i	PROPN
ejpam-6140	153	26	)	)	PUNCT
ejpam-6140	153	27	=	=	PUNCT
ejpam-6140	154	1	1	1	NUM
ejpam-6140	154	2	2h2	2h2	NUM
ejpam-6140	155	1	[	[	X
ejpam-6140	155	2	(	(	PUNCT
ejpam-6140	155	3	un	un	PROPN
ejpam-6140	155	4	i+1	i+1	ADV
ejpam-6140	155	5	−	−	PROPN
ejpam-6140	155	6	2un	2un	ADJ
ejpam-6140	156	1	i	i	PRON
ejpam-6140	156	2	+	+	NUM
ejpam-6140	156	3	un	un	PROPN
ejpam-6140	156	4	i−1	i−1	PROPN
ejpam-6140	156	5	)	)	PUNCT
ejpam-6140	157	1	+	+	CCONJ
ejpam-6140	157	2	(	(	PUNCT
ejpam-6140	157	3	un+1	un+1	ADV
ejpam-6140	157	4	i+1	i+1	NUM
ejpam-6140	157	5	−	−	PROPN
ejpam-6140	157	6	2un+1	2un+1	NUM
ejpam-6140	157	7	i	i	PRON
ejpam-6140	158	1	+	+	CCONJ
ejpam-6140	158	2	un+1	un+1	ADJ
ejpam-6140	158	3	i−1	i−1	PROPN
ejpam-6140	158	4	)	)	PUNCT
ejpam-6140	158	5	]	]	PUNCT
ejpam-6140	159	1	+	+	CCONJ
ejpam-6140	159	2	f	f	X
ejpam-6140	159	3	(	(	PUNCT
ejpam-6140	159	4	v	v	NOUN
ejpam-6140	159	5	n	n	NOUN
ejpam-6140	159	6	i	i	PRON
ejpam-6140	159	7	)	)	PUNCT
ejpam-6140	160	1	1	1	NUM
ejpam-6140	160	2	kn	kn	NOUN
ejpam-6140	160	3	(	(	PUNCT
ejpam-6140	160	4	v	v	NOUN
ejpam-6140	160	5	n+1	n+1	PROPN
ejpam-6140	160	6	i	i	PRON
ejpam-6140	160	7	−	−	PROPN
ejpam-6140	160	8	v	v	ADP
ejpam-6140	160	9	n	n	NOUN
ejpam-6140	160	10	i	i	PRON
ejpam-6140	160	11	)	)	PUNCT
ejpam-6140	160	12	=	=	PUNCT
ejpam-6140	161	1	1	1	NUM
ejpam-6140	161	2	2h2	2h2	NUM
ejpam-6140	162	1	[	[	X
ejpam-6140	162	2	(	(	PUNCT
ejpam-6140	162	3	v	v	NOUN
ejpam-6140	162	4	n	n	NOUN
ejpam-6140	162	5	i+1	i+1	ADV
ejpam-6140	162	6	−	−	PROPN
ejpam-6140	162	7	2v	2v	PROPN
ejpam-6140	162	8	n	n	CCONJ
ejpam-6140	162	9	i	i	PRON
ejpam-6140	163	1	+	+	CCONJ
ejpam-6140	163	2	v	v	NOUN
ejpam-6140	163	3	n	n	NOUN
ejpam-6140	163	4	i−1	i−1	PROPN
ejpam-6140	163	5	)	)	PUNCT
ejpam-6140	164	1	+	+	CCONJ
ejpam-6140	164	2	(	(	PUNCT
ejpam-6140	164	3	v	v	ADP
ejpam-6140	164	4	n+1	n+1	PROPN
ejpam-6140	164	5	i+1	i+1	NOUN
ejpam-6140	164	6	−	−	PROPN
ejpam-6140	164	7	2v	2v	PROPN
ejpam-6140	164	8	n+1	n+1	PROPN
ejpam-6140	165	1	i	i	PROPN
ejpam-6140	165	2	+	+	CCONJ
ejpam-6140	165	3	v	v	VERB
ejpam-6140	165	4	n+1	n+1	PROPN
ejpam-6140	165	5	i−1	i−1	PROPN
ejpam-6140	165	6	)	)	PUNCT
ejpam-6140	165	7	]	]	PUNCT
ejpam-6140	166	1	+	+	CCONJ
ejpam-6140	166	2	g	g	PROPN
ejpam-6140	166	3	(	(	PUNCT
ejpam-6140	166	4	un	un	PROPN
ejpam-6140	166	5	i	i	PROPN
ejpam-6140	166	6	)	)	PUNCT
ejpam-6140	166	7	.	.	PUNCT
ejpam-6140	167	1	m.	m.	PROPN
ejpam-6140	167	2	i.	i.	PROPN
ejpam-6140	167	3	khalil	khalil	PROPN
ejpam-6140	167	4	et	et	PROPN
ejpam-6140	167	5	al	al	PROPN
ejpam-6140	167	6	.	.	PUNCT
ejpam-6140	167	7	/	/	SYM
ejpam-6140	167	8	eur	eur	PROPN
ejpam-6140	167	9	.	.	PUNCT
ejpam-6140	168	1	j.	j.	PROPN
ejpam-6140	168	2	pure	pure	PROPN
ejpam-6140	168	3	appl	appl	PROPN
ejpam-6140	168	4	.	.	PROPN
ejpam-6140	168	5	math	math	PROPN
ejpam-6140	168	6	,	,	PUNCT
ejpam-6140	168	7	18	18	NUM
ejpam-6140	168	8	(	(	PUNCT
ejpam-6140	168	9	3	3	NUM
ejpam-6140	168	10	)	)	PUNCT
ejpam-6140	168	11	(	(	PUNCT
ejpam-6140	168	12	2025	2025	NUM
ejpam-6140	168	13	)	)	PUNCT
ejpam-6140	168	14	,	,	PUNCT
ejpam-6140	168	15	6140	6140	NUM
ejpam-6140	168	16	7	7	NUM
ejpam-6140	168	17	of	of	ADP
ejpam-6140	168	18	17	17	NUM
ejpam-6140	168	19	the	the	DET
ejpam-6140	168	20	last	last	ADJ
ejpam-6140	168	21	difference	difference	NOUN
ejpam-6140	168	22	equation	equation	NOUN
ejpam-6140	168	23	can	can	AUX
ejpam-6140	168	24	be	be	AUX
ejpam-6140	168	25	written	write	VERB
ejpam-6140	168	26	as	as	SCONJ
ejpam-6140	168	27	follows	follow	VERB
ejpam-6140	168	28	:	:	PUNCT
ejpam-6140	168	29	(	(	PUNCT
ejpam-6140	168	30	1	1	NUM
ejpam-6140	168	31	+	+	NUM
ejpam-6140	168	32	rn)u	rn)u	NOUN
ejpam-6140	168	33	n+1	n+1	PROPN
ejpam-6140	169	1	i	i	PRON
ejpam-6140	169	2	−	−	PROPN
ejpam-6140	169	3	rn	rn	PROPN
ejpam-6140	169	4	2	2	NUM
ejpam-6140	169	5	(	(	PUNCT
ejpam-6140	169	6	un+1	un+1	PROPN
ejpam-6140	169	7	i+1	i+1	NUM
ejpam-6140	169	8	+	+	NOUN
ejpam-6140	169	9	un+1	un+1	ADJ
ejpam-6140	169	10	i−1	i−1	PROPN
ejpam-6140	169	11	)	)	PUNCT
ejpam-6140	170	1	=	=	PUNCT
ejpam-6140	170	2	(	(	PUNCT
ejpam-6140	170	3	1−	1−	NUM
ejpam-6140	170	4	rn)u	rn)u	PROPN
ejpam-6140	170	5	n	n	NOUN
ejpam-6140	170	6	i	i	PROPN
ejpam-6140	171	1	+	+	PROPN
ejpam-6140	171	2	rn	rn	PROPN
ejpam-6140	171	3	2	2	NUM
ejpam-6140	171	4	(	(	PUNCT
ejpam-6140	171	5	un	un	PROPN
ejpam-6140	171	6	i+1	i+1	PRON
ejpam-6140	171	7	+	+	PROPN
ejpam-6140	171	8	un	un	PROPN
ejpam-6140	171	9	i−1	i−1	PROPN
ejpam-6140	171	10	)	)	PUNCT
ejpam-6140	172	1	+	+	CCONJ
ejpam-6140	172	2	knf	knf	X
ejpam-6140	172	3	(	(	PUNCT
ejpam-6140	172	4	v	v	NOUN
ejpam-6140	172	5	n	n	NOUN
ejpam-6140	172	6	i	i	PRON
ejpam-6140	172	7	)	)	PUNCT
ejpam-6140	172	8	(	(	PUNCT
ejpam-6140	172	9	23	23	NUM
ejpam-6140	172	10	)	)	PUNCT
ejpam-6140	172	11	(	(	PUNCT
ejpam-6140	172	12	1	1	NUM
ejpam-6140	172	13	+	+	CCONJ
ejpam-6140	172	14	rn)v	rn)v	PROPN
ejpam-6140	172	15	n+1	n+1	PROPN
ejpam-6140	172	16	i	i	PRON
ejpam-6140	172	17	−	−	PROPN
ejpam-6140	172	18	rn	rn	PROPN
ejpam-6140	172	19	2	2	NUM
ejpam-6140	172	20	(	(	PUNCT
ejpam-6140	172	21	v	v	ADP
ejpam-6140	172	22	n+1	n+1	PROPN
ejpam-6140	172	23	i+1	i+1	NUM
ejpam-6140	172	24	+	+	NOUN
ejpam-6140	172	25	v	v	ADP
ejpam-6140	172	26	n+1	n+1	PROPN
ejpam-6140	172	27	i−1	i−1	PROPN
ejpam-6140	172	28	)	)	PUNCT
ejpam-6140	173	1	=	=	PUNCT
ejpam-6140	173	2	(	(	PUNCT
ejpam-6140	173	3	1−	1−	NUM
ejpam-6140	173	4	rn)v	rn)v	PROPN
ejpam-6140	174	1	n	n	NOUN
ejpam-6140	174	2	i	i	PROPN
ejpam-6140	174	3	+	+	PROPN
ejpam-6140	174	4	rn	rn	PROPN
ejpam-6140	174	5	2	2	NUM
ejpam-6140	174	6	(	(	PUNCT
ejpam-6140	174	7	v	v	NOUN
ejpam-6140	174	8	n	n	PRON
ejpam-6140	174	9	i+1	i+1	NOUN
ejpam-6140	174	10	+	+	CCONJ
ejpam-6140	174	11	v	v	NOUN
ejpam-6140	174	12	n	n	NOUN
ejpam-6140	174	13	i−1	i−1	PROPN
ejpam-6140	174	14	)	)	PUNCT
ejpam-6140	175	1	+	+	CCONJ
ejpam-6140	175	2	kng	kng	PROPN
ejpam-6140	175	3	(	(	PUNCT
ejpam-6140	175	4	u	u	NOUN
ejpam-6140	175	5	n	n	PROPN
ejpam-6140	175	6	i	i	PROPN
ejpam-6140	175	7	)	)	PUNCT
ejpam-6140	175	8	,	,	PUNCT
ejpam-6140	175	9	(	(	PUNCT
ejpam-6140	175	10	24	24	NUM
ejpam-6140	175	11	)	)	PUNCT
ejpam-6140	175	12	when	when	SCONJ
ejpam-6140	175	13	rn	rn	PROPN
ejpam-6140	175	14	=	=	PROPN
ejpam-6140	175	15	kn	kn	PROPN
ejpam-6140	175	16	h2	h2	PROPN
ejpam-6140	175	17	.	.	PUNCT
ejpam-6140	176	1	moreover	moreover	ADV
ejpam-6140	176	2	,	,	PUNCT
ejpam-6140	176	3	one	one	PRON
ejpam-6140	176	4	can	can	AUX
ejpam-6140	176	5	choose	choose	VERB
ejpam-6140	176	6	the	the	DET
ejpam-6140	176	7	time	time	NOUN
ejpam-6140	176	8	step	step	NOUN
ejpam-6140	176	9	:	:	PUNCT
ejpam-6140	176	10	kn	kn	PROPN
ejpam-6140	176	11	=	=	PUNCT
ejpam-6140	176	12	min	min	PROPN
ejpam-6140	176	13	(	(	PUNCT
ejpam-6140	176	14	h2	h2	PROPN
ejpam-6140	176	15	,	,	PUNCT
ejpam-6140	176	16	hα∥∥un	hα∥∥un	PROPN
ejpam-6140	176	17	h	h	NOUN
ejpam-6140	176	18	∥∥	∥∥	X
ejpam-6140	176	19	∞	∞	PROPN
ejpam-6140	176	20	,	,	PUNCT
ejpam-6140	176	21	hα∥∥v	hα∥∥v	X
ejpam-6140	177	1	n	n	CCONJ
ejpam-6140	177	2	h	h	NOUN
ejpam-6140	177	3	∥∥	∥∥	X
ejpam-6140	177	4	∞	∞	NUM
ejpam-6140	177	5	)	)	PUNCT
ejpam-6140	177	6	,	,	PUNCT
ejpam-6140	177	7	1	1	NUM
ejpam-6140	177	8	≤	≤	NUM
ejpam-6140	177	9	α	α	X
ejpam-6140	177	10	.	.	PUNCT
ejpam-6140	178	1	(	(	PUNCT
ejpam-6140	178	2	25	25	NUM
ejpam-6140	178	3	)	)	PUNCT
ejpam-6140	178	4	system	system	NOUN
ejpam-6140	178	5	(	(	PUNCT
ejpam-6140	178	6	1	1	X
ejpam-6140	178	7	)	)	PUNCT
ejpam-6140	178	8	can	can	AUX
ejpam-6140	178	9	be	be	AUX
ejpam-6140	178	10	presented	present	VERB
ejpam-6140	178	11	in	in	ADP
ejpam-6140	178	12	matrix	matrix	NOUN
ejpam-6140	178	13	form	form	NOUN
ejpam-6140	178	14	as	as	SCONJ
ejpam-6140	178	15	follows	follow	VERB
ejpam-6140	178	16	:(	:(	PUNCT
ejpam-6140	179	1	i	i	PRON
ejpam-6140	179	2	+	+	PROPN
ejpam-6140	179	3	rn	rn	PROPN
ejpam-6140	179	4	2	2	NUM
ejpam-6140	179	5	h	h	NOUN
ejpam-6140	179	6	)	)	PUNCT
ejpam-6140	179	7	un+1	un+1	NOUN
ejpam-6140	179	8	h	h	NOUN
ejpam-6140	179	9	=	=	PUNCT
ejpam-6140	180	1	(	(	PUNCT
ejpam-6140	180	2	i	i	PRON
ejpam-6140	180	3	−	−	PROPN
ejpam-6140	180	4	rn	rn	PROPN
ejpam-6140	180	5	2	2	NUM
ejpam-6140	180	6	h	h	NOUN
ejpam-6140	180	7	)	)	PUNCT
ejpam-6140	180	8	un	un	PROPN
ejpam-6140	180	9	h	h	PROPN
ejpam-6140	181	1	+	+	CCONJ
ejpam-6140	181	2	knf	knf	PROPN
ejpam-6140	181	3	n	n	CCONJ
ejpam-6140	181	4	(	(	PUNCT
ejpam-6140	181	5	26	26	NUM
ejpam-6140	181	6	)	)	PUNCT
ejpam-6140	181	7	(	(	PUNCT
ejpam-6140	181	8	i	i	PRON
ejpam-6140	181	9	+	+	NUM
ejpam-6140	181	10	rn	rn	PROPN
ejpam-6140	181	11	2	2	NUM
ejpam-6140	181	12	h	h	NOUN
ejpam-6140	181	13	)	)	PUNCT
ejpam-6140	181	14	v	v	ADP
ejpam-6140	181	15	n+1	n+1	NUM
ejpam-6140	181	16	h	h	NOUN
ejpam-6140	181	17	=	=	PUNCT
ejpam-6140	181	18	(	(	PUNCT
ejpam-6140	181	19	i	i	PRON
ejpam-6140	181	20	−	−	PROPN
ejpam-6140	181	21	rn	rn	PROPN
ejpam-6140	181	22	2	2	NUM
ejpam-6140	181	23	h	h	NOUN
ejpam-6140	181	24	)	)	PUNCT
ejpam-6140	181	25	v	v	ADP
ejpam-6140	181	26	n	n	NOUN
ejpam-6140	181	27	h	h	NOUN
ejpam-6140	182	1	+	+	CCONJ
ejpam-6140	182	2	kng	kng	PROPN
ejpam-6140	182	3	n	n	PROPN
ejpam-6140	182	4	(	(	PUNCT
ejpam-6140	182	5	27	27	NUM
ejpam-6140	182	6	)	)	PUNCT
ejpam-6140	182	7	where	where	SCONJ
ejpam-6140	182	8	h	h	NOUN
ejpam-6140	182	9	=	=	SYM
ejpam-6140	182	10			NOUN
ejpam-6140	182	11	2	2	NUM
ejpam-6140	182	12	−1	−1	NOUN
ejpam-6140	182	13	0	0	NUM
ejpam-6140	182	14	·	·	PUNCT
ejpam-6140	182	15	·	·	PUNCT
ejpam-6140	182	16	·	·	PUNCT
ejpam-6140	182	17	0	0	NUM
ejpam-6140	183	1	−1	−1	NOUN
ejpam-6140	183	2	2	2	NUM
ejpam-6140	183	3	−1	−1	NOUN
ejpam-6140	183	4	·	·	PUNCT
ejpam-6140	183	5	·	·	PUNCT
ejpam-6140	183	6	·	·	PUNCT
ejpam-6140	183	7	0	0	PUNCT
ejpam-6140	183	8	.	.	PUNCT
ejpam-6140	183	9	.	.	PUNCT
ejpam-6140	183	10	.	.	PUNCT
ejpam-6140	183	11	.	.	PUNCT
ejpam-6140	183	12	.	.	PUNCT
ejpam-6140	184	1	.	.	PUNCT
ejpam-6140	185	1	0	0	PUNCT
ejpam-6140	186	1	·	·	PUNCT
ejpam-6140	186	2	·	·	PUNCT
ejpam-6140	186	3	·	·	PUNCT
ejpam-6140	186	4	0	0	NUM
ejpam-6140	186	5	−1	−1	NOUN
ejpam-6140	186	6	2	2	NUM
ejpam-6140	186	7			NUM
ejpam-6140	186	8	(	(	PUNCT
ejpam-6140	186	9	i−1)×(i−1	i−1)×(i−1	NUM
ejpam-6140	186	10	)	)	PUNCT
ejpam-6140	186	11	fn	fn	NOUN
ejpam-6140	187	1	=	=	PUNCT
ejpam-6140	187	2	(	(	PUNCT
ejpam-6140	187	3	f	f	X
ejpam-6140	187	4	(	(	PUNCT
ejpam-6140	187	5	v	v	NOUN
ejpam-6140	187	6	n	n	PRON
ejpam-6140	187	7	1	1	NUM
ejpam-6140	187	8	)	)	PUNCT
ejpam-6140	187	9	,	,	PUNCT
ejpam-6140	187	10	f	f	PROPN
ejpam-6140	187	11	(	(	PUNCT
ejpam-6140	187	12	v	v	NOUN
ejpam-6140	187	13	n	n	PRON
ejpam-6140	187	14	2	2	NUM
ejpam-6140	187	15	)	)	PUNCT
ejpam-6140	187	16	,	,	PUNCT
ejpam-6140	187	17	.	.	PUNCT
ejpam-6140	187	18	.	.	PUNCT
ejpam-6140	187	19	.	.	PUNCT
ejpam-6140	188	1	,	,	PUNCT
ejpam-6140	188	2	f	f	PROPN
ejpam-6140	188	3	(	(	PUNCT
ejpam-6140	188	4	v	v	NOUN
ejpam-6140	188	5	n	n	CCONJ
ejpam-6140	188	6	i−1	i−1	PROPN
ejpam-6140	188	7	)	)	PUNCT
ejpam-6140	188	8	)	)	PUNCT
ejpam-6140	189	1	t	t	NOUN
ejpam-6140	189	2	,	,	PUNCT
ejpam-6140	189	3	gn	gn	PROPN
ejpam-6140	190	1	=	=	PUNCT
ejpam-6140	190	2	(	(	PUNCT
ejpam-6140	190	3	g	g	PROPN
ejpam-6140	190	4	(	(	PUNCT
ejpam-6140	190	5	un	un	PROPN
ejpam-6140	190	6	1	1	NUM
ejpam-6140	190	7	,	,	PUNCT
ejpam-6140	190	8	)	)	PUNCT
ejpam-6140	190	9	,	,	PUNCT
ejpam-6140	190	10	g	g	PROPN
ejpam-6140	190	11	(	(	PUNCT
ejpam-6140	190	12	u	u	NOUN
ejpam-6140	190	13	n	n	PRON
ejpam-6140	190	14	2	2	NUM
ejpam-6140	190	15	,	,	PUNCT
ejpam-6140	190	16	)	)	PUNCT
ejpam-6140	190	17	,	,	PUNCT
ejpam-6140	190	18	.	.	PUNCT
ejpam-6140	190	19	.	.	PUNCT
ejpam-6140	190	20	.	.	PUNCT
ejpam-6140	191	1	,	,	PUNCT
ejpam-6140	191	2	g	g	PROPN
ejpam-6140	191	3	(	(	PUNCT
ejpam-6140	191	4	un	un	PROPN
ejpam-6140	191	5	i−1	i−1	PROPN
ejpam-6140	191	6	,	,	PUNCT
ejpam-6140	191	7	)	)	PUNCT
ejpam-6140	191	8	)	)	PUNCT
ejpam-6140	191	9	t	t	X
ejpam-6140	191	10	lemma	lemma	PROPN
ejpam-6140	191	11	1	1	X
ejpam-6140	191	12	.	.	PUNCT
ejpam-6140	192	1	let	let	VERB
ejpam-6140	192	2	f	f	X
ejpam-6140	192	3	,	,	PUNCT
ejpam-6140	192	4	g	g	PROPN
ejpam-6140	192	5	be	be	AUX
ejpam-6140	192	6	differentiable	differentiable	ADJ
ejpam-6140	192	7	real	real	ADJ
ejpam-6140	192	8	functions	function	NOUN
ejpam-6140	192	9	.	.	PUNCT
ejpam-6140	193	1	then	then	ADV
ejpam-6140	193	2	,	,	PUNCT
ejpam-6140	193	3	there	there	PRON
ejpam-6140	193	4	exist	exist	VERB
ejpam-6140	193	5	positive	positive	ADJ
ejpam-6140	193	6	constants	constant	NOUN
ejpam-6140	193	7	l1	l1	PROPN
ejpam-6140	193	8	,	,	PUNCT
ejpam-6140	193	9	l2	l2	NOUN
ejpam-6140	193	10	,	,	PUNCT
ejpam-6140	193	11	>	>	X
ejpam-6140	193	12	0	0	NUM
ejpam-6140	193	13	,	,	PUNCT
ejpam-6140	194	1	such	such	ADJ
ejpam-6140	194	2	that	that	DET
ejpam-6140	194	3	∣∣∣f	∣∣∣f	NOUN
ejpam-6140	194	4	(	(	PUNCT
ejpam-6140	194	5	v	v	NOUN
ejpam-6140	194	6	n	n	NOUN
ejpam-6140	194	7	i	i	NOUN
ejpam-6140	194	8	)	)	PUNCT
ejpam-6140	195	1	−	−	PROPN
ejpam-6140	196	1	f	f	PROPN
ejpam-6140	196	2	(	(	PUNCT
ejpam-6140	196	3	ṽ	ṽ	PROPN
ejpam-6140	196	4	n	n	CCONJ
ejpam-6140	196	5	i	i	NOUN
ejpam-6140	196	6	)	)	PUNCT
ejpam-6140	196	7	∣∣∣	∣∣∣	PROPN
ejpam-6140	196	8	≤	≤	NUM
ejpam-6140	196	9	l1	l1	PROPN
ejpam-6140	196	10	∣∣∣v	∣∣∣v	PROPN
ejpam-6140	197	1	n	n	CCONJ
ejpam-6140	198	1	i	i	PRON
ejpam-6140	198	2	−	−	PROPN
ejpam-6140	198	3	ṽ	ṽ	PROPN
ejpam-6140	199	1	n	n	CCONJ
ejpam-6140	199	2	i	i	PRON
ejpam-6140	199	3	∣∣∣	∣∣∣	VERB
ejpam-6140	199	4	(	(	PUNCT
ejpam-6140	199	5	28)∣∣∣g	28)∣∣∣g	NUM
ejpam-6140	199	6	(	(	PUNCT
ejpam-6140	199	7	un	un	PROPN
ejpam-6140	199	8	i	i	PROPN
ejpam-6140	199	9	)	)	PUNCT
ejpam-6140	200	1	−	−	PROPN
ejpam-6140	200	2	g	g	PROPN
ejpam-6140	200	3	(	(	PUNCT
ejpam-6140	200	4	ũn	ũn	X
ejpam-6140	200	5	i	i	NOUN
ejpam-6140	200	6	)	)	PUNCT
ejpam-6140	200	7	∣∣∣	∣∣∣	ADJ
ejpam-6140	200	8	≤	≤	NUM
ejpam-6140	200	9	l2	l2	NOUN
ejpam-6140	200	10	∣∣∣un	∣∣∣un	PRON
ejpam-6140	200	11	i	i	PRON
ejpam-6140	200	12	−	−	VERB
ejpam-6140	200	13	ũn	ũn	VERB
ejpam-6140	200	14	i	i	PRON
ejpam-6140	200	15	∣∣∣	∣∣∣	VERB
ejpam-6140	200	16	(	(	PUNCT
ejpam-6140	200	17	29	29	NUM
ejpam-6140	200	18	)	)	PUNCT
ejpam-6140	200	19	where	where	SCONJ
ejpam-6140	200	20	un	un	PROPN
ejpam-6140	200	21	i	i	PROPN
ejpam-6140	200	22	,	,	PUNCT
ejpam-6140	200	23	v	v	ADP
ejpam-6140	200	24	n	n	ADV
ejpam-6140	201	1	i	i	PRON
ejpam-6140	201	2	,	,	PUNCT
ejpam-6140	201	3	ũn	ũn	VERB
ejpam-6140	201	4	i	i	PRON
ejpam-6140	201	5	,	,	PUNCT
ejpam-6140	201	6	ṽ	ṽ	PROPN
ejpam-6140	201	7	n	n	CCONJ
ejpam-6140	201	8	i	i	PRON
ejpam-6140	201	9	,	,	PUNCT
ejpam-6140	201	10	(	(	PUNCT
ejpam-6140	201	11	i	i	NOUN
ejpam-6140	201	12	=	=	NOUN
ejpam-6140	201	13	0	0	NUM
ejpam-6140	201	14	,	,	PUNCT
ejpam-6140	201	15	1	1	NUM
ejpam-6140	201	16	,	,	PUNCT
ejpam-6140	201	17	2	2	NUM
ejpam-6140	201	18	,	,	PUNCT
ejpam-6140	201	19	.	.	PUNCT
ejpam-6140	201	20	.	.	PUNCT
ejpam-6140	201	21	.	.	PUNCT
ejpam-6140	202	1	i	i	PRON
ejpam-6140	202	2	)	)	PUNCT
ejpam-6140	202	3	are	be	AUX
ejpam-6140	202	4	bounded	bound	VERB
ejpam-6140	202	5	.	.	PUNCT
ejpam-6140	203	1	proof	proof	NOUN
ejpam-6140	203	2	.	.	PUNCT
ejpam-6140	204	1	to	to	PART
ejpam-6140	204	2	end	end	VERB
ejpam-6140	204	3	this	this	PRON
ejpam-6140	204	4	,	,	PUNCT
ejpam-6140	204	5	we	we	PRON
ejpam-6140	204	6	use	use	VERB
ejpam-6140	204	7	the	the	DET
ejpam-6140	204	8	mean	mean	ADJ
ejpam-6140	204	9	value	value	NOUN
ejpam-6140	204	10	theorem:∣∣∣f	theorem:∣∣∣f	NUM
ejpam-6140	204	11	(	(	PUNCT
ejpam-6140	204	12	v	v	NOUN
ejpam-6140	204	13	n	n	NOUN
ejpam-6140	204	14	i	i	NOUN
ejpam-6140	204	15	)	)	PUNCT
ejpam-6140	205	1	−	−	PROPN
ejpam-6140	205	2	f	f	PROPN
ejpam-6140	205	3	(	(	PUNCT
ejpam-6140	205	4	ṽ	ṽ	PROPN
ejpam-6140	205	5	n	n	CCONJ
ejpam-6140	205	6	i	i	NOUN
ejpam-6140	205	7	)	)	PUNCT
ejpam-6140	205	8	∣∣∣	∣∣∣	NOUN
ejpam-6140	205	9	≤	≤	NUM
ejpam-6140	205	10	∣∣f	∣∣f	NOUN
ejpam-6140	205	11	′	′	NUM
ejpam-6140	205	12	(	(	PUNCT
ejpam-6140	205	13	zi	zi	NOUN
ejpam-6140	205	14	)	)	PUNCT
ejpam-6140	205	15	∣∣	∣∣	AUX
ejpam-6140	205	16	∣∣∣v	∣∣∣v	PROPN
ejpam-6140	205	17	n	n	NOUN
ejpam-6140	205	18	i	i	PRON
ejpam-6140	205	19	−	−	PROPN
ejpam-6140	205	20	ṽ	ṽ	PROPN
ejpam-6140	205	21	n	n	CCONJ
ejpam-6140	205	22	i	i	PRON
ejpam-6140	205	23	∣∣∣	∣∣∣	ADJ
ejpam-6140	205	24	(	(	PUNCT
ejpam-6140	205	25	30	30	NUM
ejpam-6140	205	26	)	)	PUNCT
ejpam-6140	205	27	where	where	SCONJ
ejpam-6140	205	28	zi	zi	NOUN
ejpam-6140	205	29	is	be	AUX
ejpam-6140	205	30	an	an	DET
ejpam-6140	205	31	intermediate	intermediate	ADJ
ejpam-6140	205	32	value	value	NOUN
ejpam-6140	205	33	between	between	ADP
ejpam-6140	205	34	v	v	NOUN
ejpam-6140	205	35	n	n	PRON
ejpam-6140	205	36	i	i	PRON
ejpam-6140	205	37	and	and	CCONJ
ejpam-6140	205	38	ṽ	ṽ	PROPN
ejpam-6140	205	39	n	n	PROPN
ejpam-6140	205	40	i	i	PRON
ejpam-6140	205	41	.	.	PUNCT
ejpam-6140	206	1	sine	sine	VERB
ejpam-6140	206	2	v	v	ADP
ejpam-6140	206	3	n	n	PROPN
ejpam-6140	206	4	h	h	NOUN
ejpam-6140	206	5	,	,	PUNCT
ejpam-6140	206	6	ṽ	ṽ	PROPN
ejpam-6140	206	7	n	n	PRON
ejpam-6140	206	8	h	h	NOUN
ejpam-6140	206	9	are	be	AUX
ejpam-6140	206	10	bounded	bound	VERB
ejpam-6140	206	11	,	,	PUNCT
ejpam-6140	206	12	then	then	ADV
ejpam-6140	206	13	there	there	PRON
ejpam-6140	206	14	exists	exist	VERB
ejpam-6140	206	15	c1	c1	PROPN
ejpam-6140	206	16	>	>	X
ejpam-6140	206	17	0	0	PUNCT
ejpam-6140	207	1	such	such	ADJ
ejpam-6140	207	2	that	that	PRON
ejpam-6140	207	3	|f	|f	PROPN
ejpam-6140	207	4	′	′	NUM
ejpam-6140	208	1	(	(	PUNCT
ejpam-6140	208	2	zi)|	zi)|	X
ejpam-6140	208	3	<	<	X
ejpam-6140	208	4	c1	c1	PROPN
ejpam-6140	208	5	.	.	PUNCT
ejpam-6140	209	1	thus	thus	ADV
ejpam-6140	209	2	,	,	PUNCT
ejpam-6140	209	3	(	(	PUNCT
ejpam-6140	209	4	28	28	NUM
ejpam-6140	209	5	)	)	PUNCT
ejpam-6140	209	6	is	be	AUX
ejpam-6140	209	7	valid	valid	ADJ
ejpam-6140	209	8	.	.	PUNCT
ejpam-6140	210	1	similarly	similarly	ADV
ejpam-6140	210	2	,	,	PUNCT
ejpam-6140	210	3	one	one	PRON
ejpam-6140	210	4	can	can	AUX
ejpam-6140	210	5	show	show	VERB
ejpam-6140	210	6	that	that	SCONJ
ejpam-6140	210	7	(	(	PUNCT
ejpam-6140	210	8	29	29	NUM
ejpam-6140	210	9	)	)	PUNCT
ejpam-6140	210	10	holds	hold	VERB
ejpam-6140	210	11	true	true	ADJ
ejpam-6140	210	12	.	.	PUNCT
ejpam-6140	211	1	m.	m.	PROPN
ejpam-6140	211	2	i.	i.	PROPN
ejpam-6140	211	3	khalil	khalil	PROPN
ejpam-6140	211	4	et	et	PROPN
ejpam-6140	211	5	al	al	PROPN
ejpam-6140	211	6	.	.	PUNCT
ejpam-6140	211	7	/	/	SYM
ejpam-6140	211	8	eur	eur	PROPN
ejpam-6140	211	9	.	.	PUNCT
ejpam-6140	212	1	j.	j.	PROPN
ejpam-6140	212	2	pure	pure	PROPN
ejpam-6140	212	3	appl	appl	PROPN
ejpam-6140	212	4	.	.	PROPN
ejpam-6140	212	5	math	math	PROPN
ejpam-6140	212	6	,	,	PUNCT
ejpam-6140	212	7	18	18	NUM
ejpam-6140	212	8	(	(	PUNCT
ejpam-6140	212	9	3	3	NUM
ejpam-6140	212	10	)	)	PUNCT
ejpam-6140	212	11	(	(	PUNCT
ejpam-6140	212	12	2025	2025	NUM
ejpam-6140	212	13	)	)	PUNCT
ejpam-6140	212	14	,	,	PUNCT
ejpam-6140	212	15	6140	6140	NUM
ejpam-6140	212	16	8	8	NUM
ejpam-6140	212	17	of	of	ADP
ejpam-6140	212	18	17	17	NUM
ejpam-6140	212	19	2.1	2.1	NUM
ejpam-6140	212	20	.	.	PUNCT
ejpam-6140	213	1	the	the	DET
ejpam-6140	213	2	algorithm	algorithm	NOUN
ejpam-6140	213	3	steps	step	VERB
ejpam-6140	213	4	for	for	ADP
ejpam-6140	213	5	crank	crank	PROPN
ejpam-6140	213	6	nicolson	nicolson	PROPN
ejpam-6140	213	7	method	method	PROPN
ejpam-6140	213	8	(	(	PUNCT
ejpam-6140	213	9	i	i	NOUN
ejpam-6140	213	10	)	)	PUNCT
ejpam-6140	213	11	input	input	NOUN
ejpam-6140	213	12	h	h	NOUN
ejpam-6140	213	13	,	,	PUNCT
ejpam-6140	213	14	u0	u0	ADJ
ejpam-6140	213	15	h	h	PROPN
ejpam-6140	213	16	,	,	PUNCT
ejpam-6140	213	17	v	v	NOUN
ejpam-6140	213	18	0	0	NUM
ejpam-6140	213	19	h	h	NOUN
ejpam-6140	213	20	,	,	PUNCT
ejpam-6140	213	21	p	p	X
ejpam-6140	213	22	,	,	PUNCT
ejpam-6140	213	23	q	q	X
ejpam-6140	213	24	,	,	PUNCT
ejpam-6140	213	25	α	α	PROPN
ejpam-6140	213	26	(	(	PUNCT
ejpam-6140	213	27	ii	ii	NOUN
ejpam-6140	213	28	)	)	PUNCT
ejpam-6140	213	29	put	put	VERB
ejpam-6140	213	30	n	n	NOUN
ejpam-6140	213	31	=	=	SYM
ejpam-6140	213	32	0	0	NUM
ejpam-6140	213	33	;	;	PUNCT
ejpam-6140	213	34	(	(	PUNCT
ejpam-6140	213	35	iii	iii	X
ejpam-6140	213	36	)	)	PUNCT
ejpam-6140	213	37	choose	choose	VERB
ejpam-6140	213	38	kn	kn	PROPN
ejpam-6140	213	39	according	accord	VERB
ejpam-6140	213	40	to	to	ADP
ejpam-6140	213	41	(	(	PUNCT
ejpam-6140	213	42	25	25	NUM
ejpam-6140	213	43	)	)	PUNCT
ejpam-6140	213	44	.	.	PUNCT
ejpam-6140	214	1	(	(	PUNCT
ejpam-6140	214	2	iv	iv	X
ejpam-6140	214	3	)	)	PUNCT
ejpam-6140	214	4	calculate	calculate	VERB
ejpam-6140	214	5	the	the	DET
ejpam-6140	214	6	numerical	numerical	ADJ
ejpam-6140	214	7	vectors	vector	NOUN
ejpam-6140	214	8	:	:	PUNCT
ejpam-6140	214	9	un+1	un+1	PROPN
ejpam-6140	214	10	h	h	NOUN
ejpam-6140	214	11	,	,	PUNCT
ejpam-6140	214	12	v	v	NOUN
ejpam-6140	214	13	n+1	n+1	PROPN
ejpam-6140	214	14	h	h	NOUN
ejpam-6140	214	15	,	,	PUNCT
ejpam-6140	214	16	using	use	VERB
ejpam-6140	214	17	the	the	DET
ejpam-6140	214	18	crank	crank	NOUN
ejpam-6140	214	19	nicolson	nicolson	PROPN
ejpam-6140	214	20	formula	formula	NOUN
ejpam-6140	214	21	(	(	PUNCT
ejpam-6140	214	22	26	26	NUM
ejpam-6140	214	23	)	)	PUNCT
ejpam-6140	214	24	and	and	CCONJ
ejpam-6140	214	25	(	(	PUNCT
ejpam-6140	214	26	27	27	NUM
ejpam-6140	214	27	)	)	PUNCT
ejpam-6140	214	28	.	.	PUNCT
ejpam-6140	215	1	(	(	PUNCT
ejpam-6140	215	2	v	v	NOUN
ejpam-6140	215	3	)	)	PUNCT
ejpam-6140	215	4	for	for	ADP
ejpam-6140	215	5	n	n	NOUN
ejpam-6140	215	6	=	=	SYM
ejpam-6140	215	7	1	1	NUM
ejpam-6140	215	8	,	,	PUNCT
ejpam-6140	215	9	2	2	NUM
ejpam-6140	215	10	,	,	PUNCT
ejpam-6140	215	11	.	.	PUNCT
ejpam-6140	215	12	.	.	PUNCT
ejpam-6140	215	13	.	.	PUNCT
ejpam-6140	216	1	..	..	PUNCT
ejpam-6140	216	2	,	,	PUNCT
ejpam-6140	216	3	repeat	repeat	VERB
ejpam-6140	216	4	steps	step	NOUN
ejpam-6140	216	5	3,4	3,4	NUM
ejpam-6140	216	6	until	until	ADP
ejpam-6140	216	7	for	for	ADP
ejpam-6140	216	8	n	n	NOUN
ejpam-6140	216	9	=	=	SYM
ejpam-6140	216	10	m	m	PROPN
ejpam-6140	216	11	,	,	PUNCT
ejpam-6140	216	12	we	we	PRON
ejpam-6140	216	13	get	get	VERB
ejpam-6140	216	14	∥un	∥un	PROPN
ejpam-6140	216	15	h	h	PROPN
ejpam-6140	216	16	∥∞	∥∞	PROPN
ejpam-6140	216	17	≥	≥	NUM
ejpam-6140	216	18	1015	1015	NUM
ejpam-6140	216	19	,	,	PUNCT
ejpam-6140	216	20	or	or	CCONJ
ejpam-6140	216	21	∥v	∥v	PROPN
ejpam-6140	216	22	n	n	PRON
ejpam-6140	216	23	h	h	NOUN
ejpam-6140	216	24	∥∞	∥∞	ADJ
ejpam-6140	216	25	≥	≥	NUM
ejpam-6140	216	26	1015	1015	NUM
ejpam-6140	216	27	(	(	PUNCT
ejpam-6140	216	28	vi	vi	NOUN
ejpam-6140	216	29	)	)	PUNCT
ejpam-6140	216	30	the	the	DET
ejpam-6140	216	31	numerical	numerical	ADJ
ejpam-6140	216	32	blow	blow	VERB
ejpam-6140	216	33	-	-	PUNCT
ejpam-6140	216	34	up	up	ADP
ejpam-6140	216	35	time	time	NOUN
ejpam-6140	216	36	is	be	AUX
ejpam-6140	216	37	tm	tm	PROPN
ejpam-6140	216	38	=	=	PROPN
ejpam-6140	216	39	∑m	∑m	PROPN
ejpam-6140	216	40	n=0	n=0	PROPN
ejpam-6140	216	41	kn	kn	NOUN
ejpam-6140	216	42	.	.	PROPN
ejpam-6140	217	1	3	3	X
ejpam-6140	217	2	.	.	X
ejpam-6140	217	3	consistency	consistency	NOUN
ejpam-6140	217	4	,	,	PUNCT
ejpam-6140	217	5	stability	stability	NOUN
ejpam-6140	217	6	and	and	CCONJ
ejpam-6140	217	7	convergence	convergence	NOUN
ejpam-6140	217	8	of	of	ADP
ejpam-6140	217	9	c.	c.	PROPN
ejpam-6140	217	10	n.	n.	PROPN
ejpam-6140	217	11	scheme	scheme	NOUN
ejpam-6140	217	12	in	in	ADP
ejpam-6140	217	13	this	this	DET
ejpam-6140	217	14	section	section	NOUN
ejpam-6140	217	15	,	,	PUNCT
ejpam-6140	217	16	we	we	PRON
ejpam-6140	217	17	aim	aim	VERB
ejpam-6140	217	18	to	to	PART
ejpam-6140	217	19	analyze	analyze	VERB
ejpam-6140	217	20	the	the	DET
ejpam-6140	217	21	crank	crank	NOUN
ejpam-6140	217	22	-	-	PUNCT
ejpam-6140	217	23	nicolson	nicolson	PROPN
ejpam-6140	217	24	scheme	scheme	NOUN
ejpam-6140	217	25	in	in	ADP
ejpam-6140	217	26	terms	term	NOUN
ejpam-6140	217	27	of	of	ADP
ejpam-6140	217	28	these	these	DET
ejpam-6140	217	29	three	three	NUM
ejpam-6140	217	30	core	core	ADJ
ejpam-6140	217	31	properties	property	NOUN
ejpam-6140	217	32	.	.	PUNCT
ejpam-6140	218	1	we	we	PRON
ejpam-6140	218	2	will	will	AUX
ejpam-6140	218	3	first	first	ADV
ejpam-6140	218	4	examine	examine	VERB
ejpam-6140	218	5	its	its	PRON
ejpam-6140	218	6	consistency	consistency	NOUN
ejpam-6140	218	7	by	by	ADP
ejpam-6140	218	8	evaluating	evaluate	VERB
ejpam-6140	218	9	the	the	DET
ejpam-6140	218	10	local	local	ADJ
ejpam-6140	218	11	truncation	truncation	NOUN
ejpam-6140	218	12	error	error	NOUN
ejpam-6140	218	13	.	.	PUNCT
ejpam-6140	219	1	next	next	ADV
ejpam-6140	219	2	,	,	PUNCT
ejpam-6140	219	3	we	we	PRON
ejpam-6140	219	4	will	will	AUX
ejpam-6140	219	5	explore	explore	VERB
ejpam-6140	219	6	its	its	PRON
ejpam-6140	219	7	stability	stability	NOUN
ejpam-6140	219	8	and	and	CCONJ
ejpam-6140	219	9	conclude	conclude	VERB
ejpam-6140	219	10	the	the	DET
ejpam-6140	219	11	convergence	convergence	NOUN
ejpam-6140	219	12	of	of	ADP
ejpam-6140	219	13	the	the	DET
ejpam-6140	219	14	method	method	NOUN
ejpam-6140	219	15	,	,	PUNCT
ejpam-6140	219	16	ensuring	ensure	VERB
ejpam-6140	219	17	that	that	SCONJ
ejpam-6140	219	18	the	the	DET
ejpam-6140	219	19	numerical	numerical	ADJ
ejpam-6140	219	20	solution	solution	NOUN
ejpam-6140	219	21	approximates	approximate	VERB
ejpam-6140	219	22	the	the	DET
ejpam-6140	219	23	exact	exact	ADJ
ejpam-6140	219	24	solution	solution	NOUN
ejpam-6140	219	25	.	.	PUNCT
ejpam-6140	220	1	theorem	theorem	NOUN
ejpam-6140	220	2	5	5	NUM
ejpam-6140	220	3	.	.	PUNCT
ejpam-6140	221	1	let	let	VERB
ejpam-6140	221	2	(	(	PUNCT
ejpam-6140	221	3	tn	tn	PROPN
ejpam-6140	221	4	ui	ui	PROPN
ejpam-6140	221	5	,	,	PUNCT
ejpam-6140	221	6	t	t	PROPN
ejpam-6140	221	7	n	n	PRON
ejpam-6140	221	8	vi	vi	PROPN
ejpam-6140	221	9	)	)	PUNCT
ejpam-6140	221	10	be	be	VERB
ejpam-6140	221	11	the	the	DET
ejpam-6140	221	12	local	local	ADJ
ejpam-6140	221	13	truncation	truncation	NOUN
ejpam-6140	221	14	error	error	NOUN
ejpam-6140	221	15	of	of	ADP
ejpam-6140	221	16	the	the	DET
ejpam-6140	221	17	crank	crank	NOUN
ejpam-6140	221	18	-	-	PUNCT
ejpam-6140	221	19	nicolson	nicolson	PROPN
ejpam-6140	221	20	formulas	formula	NOUN
ejpam-6140	221	21	at	at	ADP
ejpam-6140	221	22	the	the	DET
ejpam-6140	221	23	grid	grid	NOUN
ejpam-6140	221	24	point	point	NOUN
ejpam-6140	221	25	(	(	PUNCT
ejpam-6140	221	26	xi	xi	INTJ
ejpam-6140	221	27	,	,	PUNCT
ejpam-6140	221	28	tn+	tn+	NOUN
ejpam-6140	221	29	1	1	NUM
ejpam-6140	221	30	2	2	NUM
ejpam-6140	221	31	)	)	PUNCT
ejpam-6140	221	32	.	.	PUNCT
ejpam-6140	222	1	then∣∣∣∣tn+	then∣∣∣∣tn+	NUM
ejpam-6140	222	2	1	1	NUM
ejpam-6140	222	3	2	2	NUM
ejpam-6140	222	4	ui	ui	NOUN
ejpam-6140	222	5	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6140	222	6	≤	≤	NUM
ejpam-6140	222	7	c1k	c1k	NOUN
ejpam-6140	222	8	+	+	CCONJ
ejpam-6140	222	9	c2h	c2h	PROPN
ejpam-6140	222	10	2	2	NUM
ejpam-6140	222	11	,	,	PUNCT
ejpam-6140	222	12	∣∣∣∣tn+	∣∣∣∣tn+	PROPN
ejpam-6140	222	13	1	1	NUM
ejpam-6140	222	14	2	2	NUM
ejpam-6140	222	15	vi	vi	NOUN
ejpam-6140	222	16	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6140	222	17	≤	≤	PUNCT
ejpam-6140	222	18	c3k	c3k	PROPN
ejpam-6140	222	19	+	+	PUNCT
ejpam-6140	222	20	c4h	c4h	NOUN
ejpam-6140	222	21	2	2	NUM
ejpam-6140	222	22	,	,	PUNCT
ejpam-6140	222	23	c1	c1	PROPN
ejpam-6140	222	24	,	,	PUNCT
ejpam-6140	222	25	c2	c2	PROPN
ejpam-6140	222	26	,	,	PUNCT
ejpam-6140	222	27	c3	c3	PROPN
ejpam-6140	222	28	,	,	PUNCT
ejpam-6140	222	29	c4	c4	NOUN
ejpam-6140	222	30	>	>	X
ejpam-6140	222	31	0	0	X
ejpam-6140	222	32	.	.	PUNCT
ejpam-6140	222	33	proof	proof	NOUN
ejpam-6140	222	34	.	.	PUNCT
ejpam-6140	223	1	replacing	replace	VERB
ejpam-6140	223	2	the	the	DET
ejpam-6140	223	3	precise	precise	ADJ
ejpam-6140	223	4	solution	solution	NOUN
ejpam-6140	223	5	uni	uni	PROPN
ejpam-6140	224	1	=	=	PUNCT
ejpam-6140	224	2	u	u	PROPN
ejpam-6140	224	3	(	(	PUNCT
ejpam-6140	224	4	xi	xi	PROPN
ejpam-6140	224	5	,	,	PUNCT
ejpam-6140	224	6	tn+	tn+	NOUN
ejpam-6140	224	7	1	1	NUM
ejpam-6140	224	8	2	2	NUM
ejpam-6140	224	9	)	)	PUNCT
ejpam-6140	224	10	,	,	PUNCT
ejpam-6140	224	11	vni	vni	VERB
ejpam-6140	224	12	=	=	SYM
ejpam-6140	224	13	v	v	PROPN
ejpam-6140	224	14	(	(	PUNCT
ejpam-6140	224	15	xi	xi	PROPN
ejpam-6140	224	16	,	,	PUNCT
ejpam-6140	224	17	tn+	tn+	NOUN
ejpam-6140	224	18	1	1	NUM
ejpam-6140	224	19	2	2	NUM
ejpam-6140	224	20	)	)	PUNCT
ejpam-6140	224	21	in	in	ADP
ejpam-6140	224	22	the	the	DET
ejpam-6140	224	23	cranknicolson	cranknicolson	NOUN
ejpam-6140	224	24	,	,	PUNCT
ejpam-6140	224	25	yields	yield	VERB
ejpam-6140	224	26	that	that	PRON
ejpam-6140	224	27	:	:	PUNCT
ejpam-6140	225	1	t	t	X
ejpam-6140	225	2	n+	n+	NUM
ejpam-6140	225	3	1	1	NUM
ejpam-6140	225	4	2	2	NUM
ejpam-6140	225	5	ui	ui	NOUN
ejpam-6140	225	6	=	=	PUNCT
ejpam-6140	225	7	(	(	PUNCT
ejpam-6140	225	8	un+1	un+1	NOUN
ejpam-6140	225	9	i	i	PRON
ejpam-6140	225	10	−	−	PROPN
ejpam-6140	225	11	uni	uni	INTJ
ejpam-6140	225	12	)	)	PUNCT
ejpam-6140	225	13	−	−	PROPN
ejpam-6140	226	1	kn	kn	NOUN
ejpam-6140	226	2	2h2	2h2	NUM
ejpam-6140	226	3	(	(	PUNCT
ejpam-6140	226	4	un+1	un+1	PROPN
ejpam-6140	226	5	i+1	i+1	NUM
ejpam-6140	226	6	−	−	PROPN
ejpam-6140	226	7	2un+1	2un+1	NUM
ejpam-6140	227	1	i	i	PRON
ejpam-6140	227	2	+	+	CCONJ
ejpam-6140	227	3	un+1	un+1	ADJ
ejpam-6140	227	4	i−1	i−1	PROPN
ejpam-6140	227	5	)	)	PUNCT
ejpam-6140	228	1	+	+	CCONJ
ejpam-6140	228	2	(	(	PUNCT
ejpam-6140	228	3	uni+1	uni+1	NOUN
ejpam-6140	228	4	−	−	PROPN
ejpam-6140	228	5	2uni	2uni	NUM
ejpam-6140	228	6	+	+	CCONJ
ejpam-6140	228	7	uni−1	uni−1	PROPN
ejpam-6140	228	8	)	)	PUNCT
ejpam-6140	228	9	−knf	−knf	NOUN
ejpam-6140	228	10	(	(	PUNCT
ejpam-6140	228	11	vni	vni	PROPN
ejpam-6140	228	12	)	)	PUNCT
ejpam-6140	229	1	it	it	PRON
ejpam-6140	229	2	follows	follow	VERB
ejpam-6140	229	3	that	that	SCONJ
ejpam-6140	229	4	t	t	NOUN
ejpam-6140	229	5	n+	n+	PUNCT
ejpam-6140	229	6	1	1	NUM
ejpam-6140	229	7	2	2	NUM
ejpam-6140	229	8	ui	ui	NOUN
ejpam-6140	229	9	=	=	PROPN
ejpam-6140	229	10	kn	kn	PROPN
ejpam-6140	229	11	∂un+	∂un+	ADP
ejpam-6140	229	12	1	1	NUM
ejpam-6140	229	13	2	2	NUM
ejpam-6140	230	1	i	i	NOUN
ejpam-6140	230	2	∂t	∂t	PROPN
ejpam-6140	231	1	+	+	NOUN
ejpam-6140	231	2	o	o	PROPN
ejpam-6140	231	3	(	(	PUNCT
ejpam-6140	231	4	k2n	k2n	PROPN
ejpam-6140	231	5	)	)	PUNCT
ejpam-6140	231	6	−	−	PROPN
ejpam-6140	231	7	kn	kn	PROPN
ejpam-6140	232	1	[	[	PUNCT
ejpam-6140	232	2	∂2un+1	∂2un+1	PROPN
ejpam-6140	232	3	i	i	PRON
ejpam-6140	232	4	∂x2	∂x2	VERB
ejpam-6140	232	5	+	+	NOUN
ejpam-6140	232	6	o	o	X
ejpam-6140	232	7	(	(	PUNCT
ejpam-6140	232	8	k2n	k2n	PROPN
ejpam-6140	232	9	+	+	CCONJ
ejpam-6140	232	10	h2	h2	PROPN
ejpam-6140	232	11	)	)	PUNCT
ejpam-6140	232	12	]	]	PUNCT
ejpam-6140	233	1	−kn	−kn	PROPN
ejpam-6140	233	2	[	[	PUNCT
ejpam-6140	233	3	f	f	X
ejpam-6140	233	4	(	(	PUNCT
ejpam-6140	233	5	v	v	NUM
ejpam-6140	233	6	n+	n+	NUM
ejpam-6140	233	7	1	1	NUM
ejpam-6140	233	8	2	2	NUM
ejpam-6140	233	9	i	i	NOUN
ejpam-6140	233	10	)	)	PUNCT
ejpam-6140	234	1	+	+	NOUN
ejpam-6140	234	2	o	o	X
ejpam-6140	234	3	(	(	PUNCT
ejpam-6140	234	4	kn	kn	PROPN
ejpam-6140	234	5	)	)	PUNCT
ejpam-6140	234	6	]	]	PUNCT
ejpam-6140	235	1	thus	thus	ADV
ejpam-6140	235	2	,	,	PUNCT
ejpam-6140	235	3	there	there	PRON
ejpam-6140	235	4	exists	exist	VERB
ejpam-6140	235	5	c	c	NOUN
ejpam-6140	235	6	>	>	X
ejpam-6140	235	7	0	0	NUM
ejpam-6140	235	8	,	,	PUNCT
ejpam-6140	236	1	such	such	ADJ
ejpam-6140	236	2	that∣∣∣∣tn+	that∣∣∣∣tn+	NUM
ejpam-6140	236	3	1	1	NUM
ejpam-6140	236	4	2	2	NUM
ejpam-6140	236	5	ui	ui	NOUN
ejpam-6140	236	6	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6140	236	7	≤	≤	PUNCT
ejpam-6140	236	8	c	c	X
ejpam-6140	236	9	(	(	PUNCT
ejpam-6140	236	10	k	k	PROPN
ejpam-6140	236	11	+	+	CCONJ
ejpam-6140	236	12	h2	h2	NOUN
ejpam-6140	236	13	)	)	PUNCT
ejpam-6140	236	14	,	,	PUNCT
ejpam-6140	236	15	where	where	SCONJ
ejpam-6140	236	16	k	k	PROPN
ejpam-6140	236	17	=	=	SYM
ejpam-6140	236	18	max	max	PROPN
ejpam-6140	236	19	n∈n	n∈n	PROPN
ejpam-6140	236	20	kn	kn	PROPN
ejpam-6140	236	21	,	,	PUNCT
ejpam-6140	236	22	m.	m.	PROPN
ejpam-6140	236	23	i.	i.	PROPN
ejpam-6140	236	24	khalil	khalil	PROPN
ejpam-6140	236	25	et	et	PROPN
ejpam-6140	236	26	al	al	PROPN
ejpam-6140	236	27	.	.	PUNCT
ejpam-6140	236	28	/	/	SYM
ejpam-6140	236	29	eur	eur	PROPN
ejpam-6140	236	30	.	.	PUNCT
ejpam-6140	237	1	j.	j.	PROPN
ejpam-6140	237	2	pure	pure	PROPN
ejpam-6140	237	3	appl	appl	PROPN
ejpam-6140	237	4	.	.	PROPN
ejpam-6140	237	5	math	math	PROPN
ejpam-6140	237	6	,	,	PUNCT
ejpam-6140	237	7	18	18	NUM
ejpam-6140	237	8	(	(	PUNCT
ejpam-6140	237	9	3	3	NUM
ejpam-6140	237	10	)	)	PUNCT
ejpam-6140	237	11	(	(	PUNCT
ejpam-6140	237	12	2025	2025	NUM
ejpam-6140	237	13	)	)	PUNCT
ejpam-6140	237	14	,	,	PUNCT
ejpam-6140	237	15	6140	6140	NUM
ejpam-6140	237	16	9	9	NUM
ejpam-6140	237	17	of	of	ADP
ejpam-6140	237	18	17	17	NUM
ejpam-6140	237	19	by	by	ADP
ejpam-6140	237	20	the	the	DET
ejpam-6140	237	21	same	same	ADJ
ejpam-6140	237	22	way	way	NOUN
ejpam-6140	237	23	,	,	PUNCT
ejpam-6140	237	24	one	one	PRON
ejpam-6140	237	25	can	can	AUX
ejpam-6140	237	26	get	get	VERB
ejpam-6140	237	27	∣∣∣∣tn+	∣∣∣∣tn+	PROPN
ejpam-6140	237	28	1	1	NUM
ejpam-6140	237	29	2	2	NUM
ejpam-6140	237	30	vi	vi	NOUN
ejpam-6140	237	31	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6140	237	32	≤	≤	PUNCT
ejpam-6140	237	33	c	c	X
ejpam-6140	237	34	(	(	PUNCT
ejpam-6140	237	35	k	k	PROPN
ejpam-6140	237	36	+	+	CCONJ
ejpam-6140	237	37	h2	h2	NOUN
ejpam-6140	237	38	)	)	PUNCT
ejpam-6140	237	39	clearly	clearly	ADV
ejpam-6140	237	40	,	,	PUNCT
ejpam-6140	237	41	t	t	PROPN
ejpam-6140	237	42	n+	n+	NUM
ejpam-6140	237	43	1	1	NUM
ejpam-6140	237	44	2	2	NUM
ejpam-6140	237	45	ui	ui	NOUN
ejpam-6140	237	46	and	and	CCONJ
ejpam-6140	237	47	t	t	PROPN
ejpam-6140	237	48	n+	n+	PUNCT
ejpam-6140	237	49	1	1	NUM
ejpam-6140	237	50	2	2	NUM
ejpam-6140	237	51	vi	vi	NOUN
ejpam-6140	237	52	approach	approach	NOUN
ejpam-6140	237	53	zero	zero	NUM
ejpam-6140	237	54	,	,	PUNCT
ejpam-6140	237	55	as	as	SCONJ
ejpam-6140	237	56	the	the	DET
ejpam-6140	237	57	space	space	NOUN
ejpam-6140	237	58	(	(	PUNCT
ejpam-6140	237	59	time	time	NOUN
ejpam-6140	237	60	)	)	PUNCT
ejpam-6140	237	61	steps	step	NOUN
ejpam-6140	237	62	go	go	VERB
ejpam-6140	237	63	to	to	ADP
ejpam-6140	237	64	zero	zero	NUM
ejpam-6140	237	65	.	.	PUNCT
ejpam-6140	238	1	hence	hence	ADV
ejpam-6140	238	2	,	,	PUNCT
ejpam-6140	238	3	the	the	DET
ejpam-6140	238	4	c.n	c.n	PROPN
ejpam-6140	238	5	.	.	PROPN
ejpam-6140	238	6	formulas	formula	NOUN
ejpam-6140	238	7	are	be	AUX
ejpam-6140	238	8	consistent	consistent	ADJ
ejpam-6140	238	9	.	.	PUNCT
ejpam-6140	239	1	theorem	theorem	ADJ
ejpam-6140	239	2	6	6	NUM
ejpam-6140	239	3	.	.	PUNCT
ejpam-6140	240	1	the	the	DET
ejpam-6140	240	2	crank	crank	NOUN
ejpam-6140	240	3	-	-	PUNCT
ejpam-6140	240	4	nicolson	nicolson	PROPN
ejpam-6140	240	5	scheme	scheme	NOUN
ejpam-6140	240	6	is	be	AUX
ejpam-6140	240	7	stable	stable	ADJ
ejpam-6140	240	8	if	if	SCONJ
ejpam-6140	240	9	(	(	PUNCT
ejpam-6140	240	10	1−	1−	NUM
ejpam-6140	240	11	r	r	NOUN
ejpam-6140	240	12	)	)	PUNCT
ejpam-6140	240	13	≥	≥	NOUN
ejpam-6140	240	14	0	0	NUM
ejpam-6140	240	15	,	,	PUNCT
ejpam-6140	240	16	where	where	SCONJ
ejpam-6140	240	17	k	k	NOUN
ejpam-6140	240	18	=	=	SYM
ejpam-6140	240	19	maxn∈n	maxn∈n	PROPN
ejpam-6140	240	20	kn	kn	PROPN
ejpam-6140	240	21	,	,	PUNCT
ejpam-6140	240	22	r	r	NOUN
ejpam-6140	240	23	=	=	SYM
ejpam-6140	240	24	k	k	PROPN
ejpam-6140	240	25	h2	h2	NOUN
ejpam-6140	240	26	proof	proof	NOUN
ejpam-6140	240	27	.	.	PUNCT
ejpam-6140	241	1	let	let	VERB
ejpam-6140	241	2	en	en	INTJ
ejpam-6140	241	3	u	u	NOUN
ejpam-6140	241	4	=	=	SYM
ejpam-6140	241	5	(	(	PUNCT
ejpam-6140	241	6	enui	enui	PROPN
ejpam-6140	241	7	,	,	PUNCT
ejpam-6140	241	8	i	i	NOUN
ejpam-6140	241	9	=	=	NOUN
ejpam-6140	241	10	1	1	NUM
ejpam-6140	241	11	,	,	PUNCT
ejpam-6140	241	12	2	2	NUM
ejpam-6140	241	13	,	,	PUNCT
ejpam-6140	241	14	.	.	PUNCT
ejpam-6140	241	15	.	.	PUNCT
ejpam-6140	241	16	.	.	PUNCT
ejpam-6140	242	1	i	i	PRON
ejpam-6140	242	2	−	−	VERB
ejpam-6140	243	1	1	1	NUM
ejpam-6140	243	2	)	)	PUNCT
ejpam-6140	243	3	,	,	PUNCT
ejpam-6140	243	4	en	en	ADP
ejpam-6140	243	5	v	v	NOUN
ejpam-6140	243	6	=	=	SYM
ejpam-6140	243	7	(	(	PUNCT
ejpam-6140	243	8	envi	envi	NOUN
ejpam-6140	243	9	,	,	PUNCT
ejpam-6140	243	10	i	i	NOUN
ejpam-6140	243	11	=	=	NOUN
ejpam-6140	243	12	1	1	NUM
ejpam-6140	243	13	,	,	PUNCT
ejpam-6140	243	14	2	2	NUM
ejpam-6140	243	15	,	,	PUNCT
ejpam-6140	243	16	.	.	PUNCT
ejpam-6140	243	17	.	.	PUNCT
ejpam-6140	244	1	.	.	PUNCT
ejpam-6140	245	1	i	i	PRON
ejpam-6140	245	2	−	−	VERB
ejpam-6140	246	1	1	1	X
ejpam-6140	246	2	)	)	PUNCT
ejpam-6140	246	3	where	where	SCONJ
ejpam-6140	246	4	enui	enui	NOUN
ejpam-6140	246	5	=	=	SYM
ejpam-6140	246	6	uni	uni	INTJ
ejpam-6140	246	7	−un	−un	PROPN
ejpam-6140	246	8	i	i	PROPN
ejpam-6140	246	9	,	,	PUNCT
ejpam-6140	246	10	envi	envi	PROPN
ejpam-6140	246	11	=	=	X
ejpam-6140	246	12	vni	vni	NOUN
ejpam-6140	246	13	−v	−v	NOUN
ejpam-6140	246	14	n	n	INTJ
ejpam-6140	247	1	i	i	PRON
ejpam-6140	247	2	,	,	PUNCT
ejpam-6140	247	3	uni	uni	PROPN
ejpam-6140	247	4	=	=	SYM
ejpam-6140	247	5	u	u	PROPN
ejpam-6140	247	6	(	(	PUNCT
ejpam-6140	247	7	xi	xi	PROPN
ejpam-6140	247	8	,	,	PUNCT
ejpam-6140	247	9	tn	tn	PROPN
ejpam-6140	247	10	)	)	PUNCT
ejpam-6140	247	11	,	,	PUNCT
ejpam-6140	247	12	vni	vni	VERB
ejpam-6140	247	13	=	=	SYM
ejpam-6140	247	14	v	v	PROPN
ejpam-6140	247	15	(	(	PUNCT
ejpam-6140	247	16	xi	xi	PROPN
ejpam-6140	247	17	,	,	PUNCT
ejpam-6140	247	18	tn	tn	PROPN
ejpam-6140	247	19	)	)	PUNCT
ejpam-6140	247	20	are	be	AUX
ejpam-6140	247	21	the	the	DET
ejpam-6140	247	22	precise	precise	ADJ
ejpam-6140	247	23	solution	solution	NOUN
ejpam-6140	247	24	of	of	ADP
ejpam-6140	247	25	problem	problem	NOUN
ejpam-6140	247	26	(	(	PUNCT
ejpam-6140	247	27	1	1	X
ejpam-6140	247	28	)	)	PUNCT
ejpam-6140	247	29	now	now	ADV
ejpam-6140	247	30	,	,	PUNCT
ejpam-6140	247	31	for	for	ADP
ejpam-6140	247	32	n	n	NOUN
ejpam-6140	247	33	=	=	SYM
ejpam-6140	247	34	1	1	NUM
ejpam-6140	247	35	,	,	PUNCT
ejpam-6140	248	1	∥∥e1	∥∥e1	PROPN
ejpam-6140	248	2	u	u	NOUN
ejpam-6140	248	3	∥∥	∥∥	X
ejpam-6140	248	4	=	=	SYM
ejpam-6140	248	5	max1≤i≤i	max1≤i≤i	NUM
ejpam-6140	248	6	∣∣e1ui∣∣	∣∣e1ui∣∣	ADJ
ejpam-6140	248	7	=	=	NOUN
ejpam-6140	248	8	∣∣∣e1uj∣∣∣	∣∣∣e1uj∣∣∣	NOUN
ejpam-6140	248	9	,	,	PUNCT
ejpam-6140	248	10	∥∥e1	∥∥e1	PROPN
ejpam-6140	248	11	v	v	X
ejpam-6140	248	12	∥∥	∥∥	X
ejpam-6140	248	13	=	=	SYM
ejpam-6140	248	14	max1≤i≤i	max1≤i≤i	X
ejpam-6140	248	15	∣∣e1vi∣∣.	∣∣e1vi∣∣.	PROPN
ejpam-6140	248	16	clearly	clearly	ADV
ejpam-6140	248	17	,	,	PUNCT
ejpam-6140	248	18	∣∣e1uj∣∣	∣∣e1uj∣∣	PROPN
ejpam-6140	248	19	=	=	PUNCT
ejpam-6140	248	20	(	(	PUNCT
ejpam-6140	248	21	1	1	NUM
ejpam-6140	248	22	+	+	CCONJ
ejpam-6140	248	23	r0	r0	NOUN
ejpam-6140	248	24	)	)	PUNCT
ejpam-6140	248	25	∣∣e1uj∣∣−	∣∣e1uj∣∣−	NOUN
ejpam-6140	248	26	r0	r0	NOUN
ejpam-6140	248	27	2	2	NUM
ejpam-6140	248	28	(	(	PUNCT
ejpam-6140	248	29	∣∣e1uj∣∣+	∣∣e1uj∣∣+	PROPN
ejpam-6140	248	30	∣∣e1uj∣∣	∣∣e1uj∣∣	PROPN
ejpam-6140	248	31	)	)	PUNCT
ejpam-6140	248	32	≤	≤	NOUN
ejpam-6140	248	33	(	(	PUNCT
ejpam-6140	248	34	1	1	NUM
ejpam-6140	248	35	+	+	CCONJ
ejpam-6140	248	36	r0	r0	NOUN
ejpam-6140	248	37	)	)	PUNCT
ejpam-6140	248	38	∣∣e1uj∣∣−	∣∣e1uj∣∣−	NOUN
ejpam-6140	248	39	r0	r0	NOUN
ejpam-6140	248	40	2	2	NUM
ejpam-6140	248	41	(	(	PUNCT
ejpam-6140	248	42	∣∣e1uj+1	∣∣e1uj+1	PRON
ejpam-6140	248	43	∣∣+	∣∣+	PROPN
ejpam-6140	248	44	∣∣e1uj−1	∣∣e1uj−1	PROPN
ejpam-6140	248	45	∣∣	∣∣	PROPN
ejpam-6140	248	46	)	)	PUNCT
ejpam-6140	248	47	≤	≤	NUM
ejpam-6140	248	48	∣∣∣(1	∣∣∣(1	NOUN
ejpam-6140	248	49	+	+	CCONJ
ejpam-6140	248	50	r0	r0	NOUN
ejpam-6140	248	51	)	)	PUNCT
ejpam-6140	248	52	e	e	NOUN
ejpam-6140	248	53	1	1	NUM
ejpam-6140	248	54	uj	uj	PROPN
ejpam-6140	248	55	−	−	PROPN
ejpam-6140	248	56	r0	r0	NOUN
ejpam-6140	248	57	2	2	NUM
ejpam-6140	248	58	(	(	PUNCT
ejpam-6140	248	59	e1uj+1	e1uj+1	NOUN
ejpam-6140	248	60	+	+	CCONJ
ejpam-6140	248	61	e1uj−1	e1uj−1	NOUN
ejpam-6140	248	62	)	)	PUNCT
ejpam-6140	248	63	∣∣∣	∣∣∣	NOUN
ejpam-6140	248	64	=	=	SYM
ejpam-6140	248	65	∣∣∣(1−	∣∣∣(1−	PROPN
ejpam-6140	248	66	r0	r0	NOUN
ejpam-6140	248	67	)	)	PUNCT
ejpam-6140	249	1	e	e	X
ejpam-6140	249	2	0	0	NUM
ejpam-6140	249	3	uj	uj	PROPN
ejpam-6140	249	4	+	+	CCONJ
ejpam-6140	249	5	r0	r0	NOUN
ejpam-6140	249	6	2	2	NUM
ejpam-6140	249	7	(	(	PUNCT
ejpam-6140	249	8	e0uj+1	e0uj+1	VERB
ejpam-6140	249	9	+	+	CCONJ
ejpam-6140	249	10	e0uj−1	e0uj−1	NOUN
ejpam-6140	249	11	)	)	PUNCT
ejpam-6140	250	1	+	+	CCONJ
ejpam-6140	250	2	k0	k0	PROPN
ejpam-6140	250	3	(	(	PUNCT
ejpam-6140	250	4	f	f	PROPN
ejpam-6140	250	5	(	(	PUNCT
ejpam-6140	250	6	v0j	v0j	NOUN
ejpam-6140	250	7	)	)	PUNCT
ejpam-6140	250	8	−	−	PROPN
ejpam-6140	251	1	f	f	PROPN
ejpam-6140	251	2	(	(	PUNCT
ejpam-6140	251	3	v	v	NOUN
ejpam-6140	251	4	0	0	NUM
ejpam-6140	251	5	j	j	NOUN
ejpam-6140	251	6	)	)	PUNCT
ejpam-6140	251	7	)	)	PUNCT
ejpam-6140	251	8	∣∣∣	∣∣∣	NOUN
ejpam-6140	251	9	.	.	PUNCT
ejpam-6140	252	1	since	since	SCONJ
ejpam-6140	252	2	(	(	PUNCT
ejpam-6140	252	3	1−	1−	NUM
ejpam-6140	252	4	rn	rn	NOUN
ejpam-6140	252	5	)	)	PUNCT
ejpam-6140	252	6	≥	≥	NOUN
ejpam-6140	252	7	0	0	NUM
ejpam-6140	252	8	,	,	PUNCT
ejpam-6140	252	9	it	it	PRON
ejpam-6140	252	10	follows	follow	VERB
ejpam-6140	252	11	that∥∥e1	that∥∥e1	VERB
ejpam-6140	252	12	u	u	PROPN
ejpam-6140	252	13	∥∥	∥∥	X
ejpam-6140	252	14	≤	≤	X
ejpam-6140	252	15	(	(	PUNCT
ejpam-6140	252	16	1−	1−	NUM
ejpam-6140	252	17	r0	r0	NOUN
ejpam-6140	252	18	)	)	PUNCT
ejpam-6140	252	19	∥∥e0	∥∥e0	PROPN
ejpam-6140	252	20	u	u	PROPN
ejpam-6140	252	21	∥∥+	∥∥+	X
ejpam-6140	252	22	r0	r0	PROPN
ejpam-6140	252	23	∥∥e0	∥∥e0	PROPN
ejpam-6140	252	24	u	u	PROPN
ejpam-6140	252	25	∥∥+	∥∥+	X
ejpam-6140	252	26	l1k0	l1k0	PROPN
ejpam-6140	252	27	∣∣v0j	∣∣v0j	NOUN
ejpam-6140	252	28	−	−	PROPN
ejpam-6140	252	29	v	v	NOUN
ejpam-6140	252	30	0	0	NUM
ejpam-6140	252	31	j	j	PROPN
ejpam-6140	252	32	∣∣∥∥e1	∣∣∥∥e1	PROPN
ejpam-6140	252	33	u	u	PROPN
ejpam-6140	252	34	∥∥	∥∥	PROPN
ejpam-6140	252	35	≤	≤	PROPN
ejpam-6140	252	36	∥∥e0	∥∥e0	PROPN
ejpam-6140	252	37	u	u	PROPN
ejpam-6140	252	38	∥∥+	∥∥+	PROPN
ejpam-6140	252	39	lk	lk	PROPN
ejpam-6140	252	40	∥∥e0	∥∥e0	PROPN
ejpam-6140	252	41	v	v	ADP
ejpam-6140	252	42	∥∥	∥∥	X
ejpam-6140	252	43	≤	≤	X
ejpam-6140	252	44	(	(	PUNCT
ejpam-6140	252	45	1	1	NUM
ejpam-6140	252	46	+	+	NUM
ejpam-6140	252	47	kl)max	kl)max	NUM
ejpam-6140	252	48	{	{	PUNCT
ejpam-6140	252	49	∥∥e0	∥∥e0	PROPN
ejpam-6140	252	50	u	u	X
ejpam-6140	252	51	∥∥	∥∥	X
ejpam-6140	252	52	,	,	PUNCT
ejpam-6140	252	53	∥∥e0	∥∥e0	PROPN
ejpam-6140	252	54	v	v	X
ejpam-6140	252	55	∥∥	∥∥	NOUN
ejpam-6140	252	56	}	}	PUNCT
ejpam-6140	252	57	.	.	PUNCT
ejpam-6140	253	1	by	by	ADP
ejpam-6140	253	2	the	the	DET
ejpam-6140	253	3	same	same	ADJ
ejpam-6140	253	4	way	way	NOUN
ejpam-6140	253	5	,	,	PUNCT
ejpam-6140	253	6	one	one	PRON
ejpam-6140	253	7	can	can	AUX
ejpam-6140	253	8	get:∥∥e1	get:∥∥e1	VERB
ejpam-6140	253	9	v	v	ADP
ejpam-6140	253	10	∥∥	∥∥	X
ejpam-6140	253	11	≤	≤	PROPN
ejpam-6140	253	12	∥∥e0	∥∥e0	PROPN
ejpam-6140	253	13	v	v	ADP
ejpam-6140	253	14	∥∥+	∥∥+	SYM
ejpam-6140	253	15	kl	kl	PROPN
ejpam-6140	253	16	∥∥e0	∥∥e0	PROPN
ejpam-6140	253	17	u	u	PROPN
ejpam-6140	253	18	∥∥	∥∥	PROPN
ejpam-6140	253	19	≤	≤	X
ejpam-6140	253	20	(	(	PUNCT
ejpam-6140	253	21	1	1	NUM
ejpam-6140	253	22	+	+	NUM
ejpam-6140	253	23	kl)max	kl)max	NUM
ejpam-6140	253	24	{	{	PUNCT
ejpam-6140	253	25	∥∥e0	∥∥e0	PROPN
ejpam-6140	253	26	u	u	X
ejpam-6140	253	27	∥∥	∥∥	X
ejpam-6140	253	28	,	,	PUNCT
ejpam-6140	253	29	∥∥e0	∥∥e0	PROPN
ejpam-6140	253	30	v	v	X
ejpam-6140	253	31	∥∥	∥∥	PROPN
ejpam-6140	253	32	}	}	PUNCT
ejpam-6140	253	33	where	where	SCONJ
ejpam-6140	253	34	,	,	PUNCT
ejpam-6140	253	35	l	l	PROPN
ejpam-6140	253	36	=	=	SYM
ejpam-6140	253	37	max	max	PROPN
ejpam-6140	253	38	{	{	PUNCT
ejpam-6140	253	39	l1	l1	PROPN
ejpam-6140	253	40	,	,	PUNCT
ejpam-6140	253	41	l2	l2	NOUN
ejpam-6140	253	42	}	}	PUNCT
ejpam-6140	253	43	.	.	PUNCT
ejpam-6140	253	44	assume	assume	VERB
ejpam-6140	253	45	that	that	SCONJ
ejpam-6140	253	46	:	:	PUNCT
ejpam-6140	253	47	∥es	∥es	VERB
ejpam-6140	253	48	u∥	u∥	ADJ
ejpam-6140	253	49	≤	≤	NUM
ejpam-6140	253	50	(	(	PUNCT
ejpam-6140	253	51	1	1	NUM
ejpam-6140	253	52	+	+	CCONJ
ejpam-6140	253	53	kl)smax	kl)smax	X
ejpam-6140	253	54	{	{	PUNCT
ejpam-6140	253	55	∥∥e0	∥∥e0	PROPN
ejpam-6140	253	56	u	u	X
ejpam-6140	253	57	∥∥	∥∥	X
ejpam-6140	253	58	,	,	PUNCT
ejpam-6140	253	59	∥∥e0	∥∥e0	PROPN
ejpam-6140	253	60	v	v	X
ejpam-6140	253	61	∥∥	∥∥	PROPN
ejpam-6140	253	62	}	}	PUNCT
ejpam-6140	253	63	,	,	PUNCT
ejpam-6140	253	64	s	s	NOUN
ejpam-6140	253	65	=	=	SYM
ejpam-6140	253	66	1	1	NUM
ejpam-6140	253	67	,	,	PUNCT
ejpam-6140	253	68	2	2	NUM
ejpam-6140	253	69	,	,	PUNCT
ejpam-6140	253	70	3	3	NUM
ejpam-6140	253	71	,	,	PUNCT
ejpam-6140	253	72	.	.	PUNCT
ejpam-6140	253	73	.	.	PUNCT
ejpam-6140	254	1	.	.	PUNCT
ejpam-6140	255	1	,	,	PUNCT
ejpam-6140	255	2	n	n	PROPN
ejpam-6140	255	3	∥es	∥es	VERB
ejpam-6140	255	4	v∥	v∥	PROPN
ejpam-6140	255	5	≤	≤	NUM
ejpam-6140	255	6	(	(	PUNCT
ejpam-6140	255	7	1	1	NUM
ejpam-6140	255	8	+	+	CCONJ
ejpam-6140	255	9	kl)smax	kl)smax	X
ejpam-6140	255	10	{	{	PUNCT
ejpam-6140	255	11	∥∥e0	∥∥e0	PROPN
ejpam-6140	255	12	u	u	X
ejpam-6140	255	13	∥∥	∥∥	X
ejpam-6140	255	14	,	,	PUNCT
ejpam-6140	255	15	∥∥e0	∥∥e0	PROPN
ejpam-6140	255	16	v	v	X
ejpam-6140	255	17	∥∥	∥∥	PROPN
ejpam-6140	255	18	}	}	PUNCT
ejpam-6140	255	19	,	,	PUNCT
ejpam-6140	255	20	s	s	NOUN
ejpam-6140	255	21	=	=	SYM
ejpam-6140	255	22	1	1	NUM
ejpam-6140	255	23	,	,	PUNCT
ejpam-6140	255	24	2	2	NUM
ejpam-6140	255	25	,	,	PUNCT
ejpam-6140	255	26	3	3	NUM
ejpam-6140	255	27	,	,	PUNCT
ejpam-6140	255	28	.	.	PUNCT
ejpam-6140	255	29	.	.	PUNCT
ejpam-6140	256	1	.	.	PUNCT
ejpam-6140	257	1	,	,	PUNCT
ejpam-6140	257	2	n.	n.	NOUN
ejpam-6140	257	3	regarding	regard	VERB
ejpam-6140	257	4	n+	n+	NUM
ejpam-6140	257	5	1	1	NUM
ejpam-6140	257	6	,	,	PUNCT
ejpam-6140	257	7	set	set	VERB
ejpam-6140	257	8	∥∥en+1	∥∥en+1	PROPN
ejpam-6140	257	9	u	u	NOUN
ejpam-6140	257	10	∥∥	∥∥	X
ejpam-6140	257	11	=	=	SYM
ejpam-6140	257	12	max1≤i≤i	max1≤i≤i	X
ejpam-6140	257	13	∣∣∣en+1	∣∣∣en+1	X
ejpam-6140	257	14	uj	uj	PROPN
ejpam-6140	257	15	∣∣∣	∣∣∣	NOUN
ejpam-6140	257	16	=	=	SYM
ejpam-6140	257	17	∣∣∣en+1	∣∣∣en+1	X
ejpam-6140	257	18	uj	uj	PROPN
ejpam-6140	257	19	∣∣∣	∣∣∣	NOUN
ejpam-6140	257	20	,	,	PUNCT
ejpam-6140	257	21	∥∥en+1	∥∥en+1	PROPN
ejpam-6140	257	22	v	v	NOUN
ejpam-6140	257	23	∥∥	∥∥	X
ejpam-6140	257	24	=	=	SYM
ejpam-6140	257	25	max1≤i≤i	max1≤i≤i	X
ejpam-6140	257	26	∣∣∣en+1	∣∣∣en+1	X
ejpam-6140	257	27	vj	vj	PROPN
ejpam-6140	257	28	∣∣∣	∣∣∣	PROPN
ejpam-6140	257	29	m.	m.	PROPN
ejpam-6140	257	30	i.	i.	PROPN
ejpam-6140	257	31	khalil	khalil	PROPN
ejpam-6140	257	32	et	et	PROPN
ejpam-6140	257	33	al	al	PROPN
ejpam-6140	257	34	.	.	PUNCT
ejpam-6140	257	35	/	/	SYM
ejpam-6140	257	36	eur	eur	PROPN
ejpam-6140	257	37	.	.	PUNCT
ejpam-6140	258	1	j.	j.	PROPN
ejpam-6140	258	2	pure	pure	PROPN
ejpam-6140	258	3	appl	appl	PROPN
ejpam-6140	258	4	.	.	PROPN
ejpam-6140	258	5	math	math	PROPN
ejpam-6140	258	6	,	,	PUNCT
ejpam-6140	258	7	18	18	NUM
ejpam-6140	258	8	(	(	PUNCT
ejpam-6140	258	9	3	3	NUM
ejpam-6140	258	10	)	)	PUNCT
ejpam-6140	258	11	(	(	PUNCT
ejpam-6140	258	12	2025	2025	NUM
ejpam-6140	258	13	)	)	PUNCT
ejpam-6140	258	14	,	,	PUNCT
ejpam-6140	258	15	6140	6140	NUM
ejpam-6140	258	16	10	10	NUM
ejpam-6140	258	17	of	of	ADP
ejpam-6140	258	18	17	17	NUM
ejpam-6140	258	19	it	it	PRON
ejpam-6140	258	20	is	be	AUX
ejpam-6140	258	21	clear	clear	ADJ
ejpam-6140	258	22	that	that	SCONJ
ejpam-6140	258	23	∣∣∣en+1	∣∣∣en+1	NOUN
ejpam-6140	258	24	uj	uj	VERB
ejpam-6140	258	25	∣∣∣	∣∣∣	NOUN
ejpam-6140	258	26	=	=	SYM
ejpam-6140	258	27	(	(	PUNCT
ejpam-6140	258	28	1	1	NUM
ejpam-6140	258	29	+	+	NUM
ejpam-6140	258	30	rn	rn	NOUN
ejpam-6140	258	31	)	)	PUNCT
ejpam-6140	258	32	∣∣∣en+1	∣∣∣en+1	NOUN
ejpam-6140	258	33	uj	uj	PROPN
ejpam-6140	258	34	∣∣∣−	∣∣∣−	PROPN
ejpam-6140	258	35	rn	rn	PROPN
ejpam-6140	258	36	2	2	NUM
ejpam-6140	258	37	(	(	PUNCT
ejpam-6140	258	38	∣∣∣en+1	∣∣∣en+1	NOUN
ejpam-6140	258	39	uj	uj	PROPN
ejpam-6140	258	40	∣∣∣+	∣∣∣+	PROPN
ejpam-6140	258	41	∣∣∣en+1	∣∣∣en+1	NOUN
ejpam-6140	258	42	uj	uj	PROPN
ejpam-6140	258	43	∣∣∣	∣∣∣	NOUN
ejpam-6140	258	44	)	)	PUNCT
ejpam-6140	258	45	≤	≤	NOUN
ejpam-6140	258	46	(	(	PUNCT
ejpam-6140	258	47	1	1	NUM
ejpam-6140	258	48	+	+	NUM
ejpam-6140	258	49	r0	r0	NOUN
ejpam-6140	258	50	)	)	PUNCT
ejpam-6140	258	51	∣∣∣en+1	∣∣∣en+1	NOUN
ejpam-6140	258	52	uj	uj	PROPN
ejpam-6140	258	53	∣∣∣−	∣∣∣−	PROPN
ejpam-6140	258	54	r0	r0	NOUN
ejpam-6140	258	55	2	2	NUM
ejpam-6140	258	56	(	(	PUNCT
ejpam-6140	258	57	∣∣∣en+1	∣∣∣en+1	X
ejpam-6140	258	58	uj+1	uj+1	PROPN
ejpam-6140	258	59	∣∣∣+	∣∣∣+	PROPN
ejpam-6140	258	60	∣∣∣en+1	∣∣∣en+1	NOUN
ejpam-6140	258	61	uj−1	uj−1	NOUN
ejpam-6140	258	62	∣∣∣	∣∣∣	ADJ
ejpam-6140	258	63	)	)	PUNCT
ejpam-6140	258	64	≤	≤	NUM
ejpam-6140	258	65	∣∣∣(1	∣∣∣(1	NOUN
ejpam-6140	258	66	+	+	CCONJ
ejpam-6140	258	67	rn	rn	NOUN
ejpam-6140	258	68	)	)	PUNCT
ejpam-6140	258	69	e	e	PROPN
ejpam-6140	258	70	n+1	n+1	PROPN
ejpam-6140	258	71	uj	uj	PROPN
ejpam-6140	258	72	−	−	PROPN
ejpam-6140	258	73	rn	rn	PROPN
ejpam-6140	258	74	2	2	NUM
ejpam-6140	258	75	(	(	PUNCT
ejpam-6140	258	76	en+1	en+1	VERB
ejpam-6140	258	77	uj+1	uj+1	NUM
ejpam-6140	258	78	+	+	CCONJ
ejpam-6140	258	79	en+1	en+1	ADJ
ejpam-6140	258	80	uj−1	uj−1	NOUN
ejpam-6140	258	81	)	)	PUNCT
ejpam-6140	258	82	∣∣∣	∣∣∣	NOUN
ejpam-6140	258	83	=	=	SYM
ejpam-6140	258	84	∣∣∣(1−	∣∣∣(1−	PROPN
ejpam-6140	258	85	rn	rn	PROPN
ejpam-6140	258	86	)	)	PUNCT
ejpam-6140	258	87	e	e	PROPN
ejpam-6140	258	88	n	n	ADP
ejpam-6140	258	89	uj	uj	PROPN
ejpam-6140	258	90	+	+	CCONJ
ejpam-6140	258	91	rn	rn	PROPN
ejpam-6140	258	92	2	2	NUM
ejpam-6140	258	93	(	(	PUNCT
ejpam-6140	258	94	enuj+1	enuj+1	NOUN
ejpam-6140	258	95	+	+	CCONJ
ejpam-6140	258	96	enuj−1	enuj−1	NOUN
ejpam-6140	258	97	)	)	PUNCT
ejpam-6140	259	1	+	+	CCONJ
ejpam-6140	259	2	kn	kn	PROPN
ejpam-6140	259	3	(	(	PUNCT
ejpam-6140	259	4	f	f	PROPN
ejpam-6140	259	5	(	(	PUNCT
ejpam-6140	259	6	vnj	vnj	ADV
ejpam-6140	259	7	)	)	PUNCT
ejpam-6140	260	1	−	−	PROPN
ejpam-6140	260	2	f	f	PROPN
ejpam-6140	260	3	(	(	PUNCT
ejpam-6140	260	4	v	v	PROPN
ejpam-6140	260	5	n	n	PROPN
ejpam-6140	260	6	j	j	PROPN
ejpam-6140	260	7	)	)	PUNCT
ejpam-6140	260	8	)	)	PUNCT
ejpam-6140	260	9	∣∣∣	∣∣∣	NOUN
ejpam-6140	260	10	.	.	PUNCT
ejpam-6140	261	1	since	since	SCONJ
ejpam-6140	261	2	(	(	PUNCT
ejpam-6140	261	3	1−	1−	NUM
ejpam-6140	261	4	rn	rn	NOUN
ejpam-6140	261	5	)	)	PUNCT
ejpam-6140	261	6	≥	≥	NOUN
ejpam-6140	261	7	0	0	NUM
ejpam-6140	261	8	,	,	PUNCT
ejpam-6140	261	9	it	it	PRON
ejpam-6140	261	10	follows	follow	VERB
ejpam-6140	261	11	that∥∥en+1	that∥∥en+1	PROPN
ejpam-6140	261	12	u	u	PROPN
ejpam-6140	261	13	∥∥	∥∥	X
ejpam-6140	261	14	≤	≤	X
ejpam-6140	261	15	(	(	PUNCT
ejpam-6140	261	16	1−	1−	NUM
ejpam-6140	261	17	rn	rn	NOUN
ejpam-6140	261	18	)	)	PUNCT
ejpam-6140	261	19	∥en	∥en	PROPN
ejpam-6140	262	1	u∥+	u∥+	PROPN
ejpam-6140	262	2	rn	rn	PROPN
ejpam-6140	262	3	∥en	∥en	X
ejpam-6140	262	4	u∥+	u∥+	ADJ
ejpam-6140	262	5	l1kn	l1kn	NOUN
ejpam-6140	262	6	∣∣vnj	∣∣vnj	PROPN
ejpam-6140	262	7	−	−	PROPN
ejpam-6140	262	8	v	v	VERB
ejpam-6140	262	9	n	n	PROPN
ejpam-6140	262	10	j	j	PROPN
ejpam-6140	262	11	∣∣∥∥en+1	∣∣∥∥en+1	PROPN
ejpam-6140	262	12	u	u	PROPN
ejpam-6140	262	13	∥∥	∥∥	PROPN
ejpam-6140	262	14	≤	≤	X
ejpam-6140	262	15	∥en	∥en	PUNCT
ejpam-6140	262	16	u∥+	u∥+	ADJ
ejpam-6140	262	17	lk	lk	NOUN
ejpam-6140	262	18	∥en	∥en	PROPN
ejpam-6140	262	19	v	v	NUM
ejpam-6140	262	20	∥	∥	PUNCT
ejpam-6140	262	21	≤	≤	NOUN
ejpam-6140	262	22	(	(	PUNCT
ejpam-6140	262	23	1	1	NUM
ejpam-6140	262	24	+	+	NUM
ejpam-6140	262	25	kl)n+1max	kl)n+1max	NOUN
ejpam-6140	262	26	{	{	PUNCT
ejpam-6140	262	27	∥∥e0	∥∥e0	PROPN
ejpam-6140	262	28	u	u	X
ejpam-6140	262	29	∥∥	∥∥	X
ejpam-6140	262	30	,	,	PUNCT
ejpam-6140	262	31	∥∥e0	∥∥e0	PROPN
ejpam-6140	262	32	v	v	X
ejpam-6140	262	33	∥∥	∥∥	PROPN
ejpam-6140	262	34	}	}	PUNCT
ejpam-6140	262	35	≤	≤	NOUN
ejpam-6140	262	36	exp((n+	exp((n+	X
ejpam-6140	262	37	1)kl)max	1)kl)max	NUM
ejpam-6140	262	38	{	{	PUNCT
ejpam-6140	262	39	∥∥e0	∥∥e0	PROPN
ejpam-6140	262	40	u	u	PROPN
ejpam-6140	262	41	∥∥	∥∥	X
ejpam-6140	262	42	,	,	PUNCT
ejpam-6140	262	43	∥∥e0	∥∥e0	PROPN
ejpam-6140	262	44	v	v	X
ejpam-6140	262	45	∥∥	∥∥	PROPN
ejpam-6140	262	46	}	}	PUNCT
ejpam-6140	262	47	thus	thus	ADV
ejpam-6140	262	48	∥∥en+1	∥∥en+1	VERB
ejpam-6140	262	49	u	u	NOUN
ejpam-6140	262	50	∥∥	∥∥	PROPN
ejpam-6140	262	51	≤	≤	NUM
ejpam-6140	262	52	exp	exp	NOUN
ejpam-6140	262	53	(	(	PUNCT
ejpam-6140	262	54	tn+1l)max	tn+1l)max	PROPN
ejpam-6140	262	55	{	{	PUNCT
ejpam-6140	262	56	∥∥e0	∥∥e0	PROPN
ejpam-6140	262	57	u	u	X
ejpam-6140	262	58	∥∥	∥∥	X
ejpam-6140	262	59	,	,	PUNCT
ejpam-6140	262	60	∥∥e0	∥∥e0	PROPN
ejpam-6140	262	61	v	v	X
ejpam-6140	262	62	∥∥	∥∥	NOUN
ejpam-6140	262	63	}	}	PUNCT
ejpam-6140	262	64	.	.	PUNCT
ejpam-6140	263	1	similarly	similarly	ADV
ejpam-6140	263	2	,	,	PUNCT
ejpam-6140	263	3	we	we	PRON
ejpam-6140	263	4	one	one	NUM
ejpam-6140	263	5	can	can	AUX
ejpam-6140	263	6	show	show	VERB
ejpam-6140	263	7	that∥∥en+1	that∥∥en+1	PROPN
ejpam-6140	263	8	v	v	ADP
ejpam-6140	263	9	∥∥	∥∥	PROPN
ejpam-6140	263	10	≤	≤	NUM
ejpam-6140	263	11	exp	exp	NOUN
ejpam-6140	263	12	(	(	PUNCT
ejpam-6140	263	13	tn+1l)max	tn+1l)max	PROPN
ejpam-6140	263	14	{	{	PUNCT
ejpam-6140	263	15	∥∥e0	∥∥e0	PROPN
ejpam-6140	263	16	u	u	X
ejpam-6140	263	17	∥∥	∥∥	X
ejpam-6140	263	18	,	,	PUNCT
ejpam-6140	263	19	∥∥e0	∥∥e0	PROPN
ejpam-6140	263	20	v	v	X
ejpam-6140	263	21	∥∥	∥∥	NOUN
ejpam-6140	263	22	}	}	PUNCT
ejpam-6140	263	23	.	.	PUNCT
ejpam-6140	264	1	based	base	VERB
ejpam-6140	264	2	on	on	ADP
ejpam-6140	264	3	the	the	DET
ejpam-6140	264	4	stability	stability	NOUN
ejpam-6140	264	5	definition	definition	NOUN
ejpam-6140	264	6	[	[	X
ejpam-6140	264	7	22	22	NUM
ejpam-6140	264	8	]	]	PUNCT
ejpam-6140	264	9	the	the	DET
ejpam-6140	264	10	crank	crank	NOUN
ejpam-6140	264	11	-	-	PUNCT
ejpam-6140	264	12	nicolson	nicolson	PROPN
ejpam-6140	264	13	scheme	scheme	NOUN
ejpam-6140	264	14	is	be	AUX
ejpam-6140	264	15	stable	stable	ADJ
ejpam-6140	264	16	provided	provide	VERB
ejpam-6140	264	17	that	that	SCONJ
ejpam-6140	264	18	r	r	NOUN
ejpam-6140	264	19	≤	≤	NUM
ejpam-6140	264	20	1	1	NUM
ejpam-6140	264	21	theorem	theorem	NOUN
ejpam-6140	264	22	7	7	NUM
ejpam-6140	264	23	.	.	PUNCT
ejpam-6140	265	1	under	under	ADP
ejpam-6140	265	2	the	the	DET
ejpam-6140	265	3	condition	condition	NOUN
ejpam-6140	265	4	of	of	ADP
ejpam-6140	265	5	theorem	theorem	NOUN
ejpam-6140	265	6	(	(	PUNCT
ejpam-6140	265	7	2	2	NUM
ejpam-6140	265	8	)	)	PUNCT
ejpam-6140	265	9	,	,	PUNCT
ejpam-6140	265	10	the	the	DET
ejpam-6140	265	11	crank	crank	NOUN
ejpam-6140	265	12	-	-	PUNCT
ejpam-6140	265	13	nicolson	nicolson	PROPN
ejpam-6140	265	14	scheme	scheme	NOUN
ejpam-6140	265	15	converges	converge	NOUN
ejpam-6140	265	16	with	with	ADP
ejpam-6140	265	17	the	the	DET
ejpam-6140	265	18	order	order	NOUN
ejpam-6140	265	19	o	o	NOUN
ejpam-6140	266	1	(	(	PUNCT
ejpam-6140	266	2	k	k	PROPN
ejpam-6140	266	3	+	+	CCONJ
ejpam-6140	266	4	h2	h2	NOUN
ejpam-6140	266	5	)	)	PUNCT
ejpam-6140	266	6	,	,	PUNCT
ejpam-6140	267	1	where	where	SCONJ
ejpam-6140	267	2	k	k	NOUN
ejpam-6140	267	3	=	=	SYM
ejpam-6140	267	4	maxn∈n	maxn∈n	PROPN
ejpam-6140	267	5	kn	kn	PROPN
ejpam-6140	267	6	.	.	PUNCT
ejpam-6140	267	7	proof	proof	NOUN
ejpam-6140	267	8	.	.	PUNCT
ejpam-6140	268	1	let	let	VERB
ejpam-6140	268	2	en	en	INTJ
ejpam-6140	268	3	u	u	NOUN
ejpam-6140	268	4	=	=	SYM
ejpam-6140	268	5	(	(	PUNCT
ejpam-6140	268	6	enui	enui	PROPN
ejpam-6140	268	7	,	,	PUNCT
ejpam-6140	268	8	i	i	NOUN
ejpam-6140	268	9	=	=	NOUN
ejpam-6140	268	10	1	1	NUM
ejpam-6140	268	11	,	,	PUNCT
ejpam-6140	268	12	2	2	NUM
ejpam-6140	268	13	,	,	PUNCT
ejpam-6140	268	14	.	.	PUNCT
ejpam-6140	268	15	.	.	PUNCT
ejpam-6140	268	16	.	.	PUNCT
ejpam-6140	269	1	i	i	PRON
ejpam-6140	269	2	−	−	VERB
ejpam-6140	270	1	1	1	NUM
ejpam-6140	270	2	)	)	PUNCT
ejpam-6140	270	3	,	,	PUNCT
ejpam-6140	270	4	en	en	ADP
ejpam-6140	270	5	v	v	NOUN
ejpam-6140	270	6	=	=	SYM
ejpam-6140	270	7	(	(	PUNCT
ejpam-6140	270	8	envi	envi	NOUN
ejpam-6140	270	9	,	,	PUNCT
ejpam-6140	270	10	i	i	NOUN
ejpam-6140	270	11	=	=	NOUN
ejpam-6140	270	12	1	1	NUM
ejpam-6140	270	13	,	,	PUNCT
ejpam-6140	270	14	2	2	NUM
ejpam-6140	270	15	,	,	PUNCT
ejpam-6140	270	16	.	.	PUNCT
ejpam-6140	270	17	.	.	PUNCT
ejpam-6140	271	1	.	.	PUNCT
ejpam-6140	272	1	i	i	PRON
ejpam-6140	272	2	−	−	VERB
ejpam-6140	273	1	1	1	X
ejpam-6140	273	2	)	)	PUNCT
ejpam-6140	273	3	where	where	SCONJ
ejpam-6140	273	4	enui	enui	NOUN
ejpam-6140	273	5	=	=	SYM
ejpam-6140	273	6	uni	uni	PROPN
ejpam-6140	274	1	−	−	PROPN
ejpam-6140	274	2	un	un	PROPN
ejpam-6140	274	3	i	i	PROPN
ejpam-6140	274	4	,	,	PUNCT
ejpam-6140	274	5	envi	envi	PROPN
ejpam-6140	274	6	=	=	PUNCT
ejpam-6140	274	7	vni	vni	PROPN
ejpam-6140	274	8	−	−	PROPN
ejpam-6140	274	9	v	v	NOUN
ejpam-6140	274	10	n	n	NOUN
ejpam-6140	275	1	i	i	PRON
ejpam-6140	275	2	,	,	PUNCT
ejpam-6140	275	3	uni	uni	PROPN
ejpam-6140	275	4	=	=	SYM
ejpam-6140	275	5	u	u	PROPN
ejpam-6140	275	6	(	(	PUNCT
ejpam-6140	275	7	xi	xi	PROPN
ejpam-6140	275	8	,	,	PUNCT
ejpam-6140	275	9	tn	tn	PROPN
ejpam-6140	275	10	)	)	PUNCT
ejpam-6140	275	11	,	,	PUNCT
ejpam-6140	275	12	vni	vni	VERB
ejpam-6140	275	13	=	=	SYM
ejpam-6140	275	14	v	v	PROPN
ejpam-6140	275	15	(	(	PUNCT
ejpam-6140	275	16	xi	xi	PROPN
ejpam-6140	275	17	,	,	PUNCT
ejpam-6140	275	18	tn	tn	PROPN
ejpam-6140	275	19	)	)	PUNCT
ejpam-6140	275	20	is	be	AUX
ejpam-6140	275	21	the	the	DET
ejpam-6140	275	22	exact	exact	ADJ
ejpam-6140	275	23	solution	solution	NOUN
ejpam-6140	275	24	of	of	ADP
ejpam-6140	275	25	problem	problem	NOUN
ejpam-6140	275	26	(	(	PUNCT
ejpam-6140	275	27	1	1	X
ejpam-6140	275	28	)	)	PUNCT
ejpam-6140	275	29	suppose	suppose	VERB
ejpam-6140	275	30	that	that	SCONJ
ejpam-6140	275	31	e0ui	e0ui	PUNCT
ejpam-6140	275	32	=	=	SYM
ejpam-6140	275	33	0	0	NUM
ejpam-6140	275	34	,	,	PUNCT
ejpam-6140	275	35	e0vi	e0vi	PUNCT
ejpam-6140	275	36	=	=	NOUN
ejpam-6140	275	37	0	0	NUM
ejpam-6140	275	38	∀i	∀i	NOUN
ejpam-6140	275	39	=	=	SYM
ejpam-6140	275	40	0	0	NUM
ejpam-6140	275	41	,	,	PUNCT
ejpam-6140	275	42	1	1	NUM
ejpam-6140	275	43	,	,	PUNCT
ejpam-6140	275	44	.	.	PUNCT
ejpam-6140	275	45	.	.	PUNCT
ejpam-6140	276	1	..	..	PUNCT
ejpam-6140	276	2	to	to	PART
ejpam-6140	276	3	prove	prove	VERB
ejpam-6140	276	4	this	this	DET
ejpam-6140	276	5	theorem	theorem	NOUN
ejpam-6140	276	6	,	,	PUNCT
ejpam-6140	276	7	the	the	DET
ejpam-6140	276	8	following	follow	VERB
ejpam-6140	276	9	inequalities	inequality	NOUN
ejpam-6140	276	10	should	should	AUX
ejpam-6140	276	11	be	be	AUX
ejpam-6140	276	12	held	hold	VERB
ejpam-6140	276	13	en+1	en+1	PROPN
ejpam-6140	277	1	uj	uj	PROPN
ejpam-6140	277	2	≤	≤	NUM
ejpam-6140	277	3	c	c	PROPN
ejpam-6140	277	4	(	(	PUNCT
ejpam-6140	277	5	k	k	PROPN
ejpam-6140	277	6	+	+	CCONJ
ejpam-6140	277	7	h2	h2	PROPN
ejpam-6140	277	8	)	)	PUNCT
ejpam-6140	277	9	,	,	PUNCT
ejpam-6140	277	10	en+1	en+1	VERB
ejpam-6140	277	11	vj	vj	PROPN
ejpam-6140	277	12	≤	≤	NUM
ejpam-6140	277	13	c	c	PROPN
ejpam-6140	277	14	(	(	PUNCT
ejpam-6140	277	15	k	k	PROPN
ejpam-6140	277	16	+	+	CCONJ
ejpam-6140	277	17	h2	h2	PROPN
ejpam-6140	277	18	)	)	PUNCT
ejpam-6140	277	19	,	,	PUNCT
ejpam-6140	277	20	n	n	NOUN
ejpam-6140	277	21	=	=	SYM
ejpam-6140	277	22	0	0	NUM
ejpam-6140	277	23	,	,	PUNCT
ejpam-6140	277	24	1	1	NUM
ejpam-6140	277	25	,	,	PUNCT
ejpam-6140	277	26	.	.	PUNCT
ejpam-6140	277	27	.	.	PUNCT
ejpam-6140	277	28	.	.	PUNCT
ejpam-6140	277	29	.	.	PUNCT
ejpam-6140	278	1	now	now	ADV
ejpam-6140	278	2	,	,	PUNCT
ejpam-6140	278	3	for	for	ADP
ejpam-6140	278	4	n	n	NOUN
ejpam-6140	278	5	=	=	SYM
ejpam-6140	278	6	1	1	NUM
ejpam-6140	278	7	,	,	PUNCT
ejpam-6140	278	8	set	set	VERB
ejpam-6140	278	9	∣∣∣e1uj∣∣∣	∣∣∣e1uj∣∣∣	NOUN
ejpam-6140	278	10	=	=	SYM
ejpam-6140	278	11	max1≤i≤i	max1≤i≤i	X
ejpam-6140	278	12	∣∣e1ui∣∣.	∣∣e1ui∣∣.	PROPN
ejpam-6140	278	13	it	it	PRON
ejpam-6140	278	14	clear	clear	ADJ
ejpam-6140	278	15	that	that	SCONJ
ejpam-6140	278	16	∣∣e1uj∣∣	∣∣e1uj∣∣	PROPN
ejpam-6140	278	17	=	=	PUNCT
ejpam-6140	278	18	(	(	PUNCT
ejpam-6140	278	19	1	1	NUM
ejpam-6140	278	20	+	+	CCONJ
ejpam-6140	278	21	r0	r0	NOUN
ejpam-6140	278	22	)	)	PUNCT
ejpam-6140	278	23	∣∣e1uj∣∣−	∣∣e1uj∣∣−	NOUN
ejpam-6140	278	24	r0	r0	NOUN
ejpam-6140	278	25	2	2	NUM
ejpam-6140	278	26	(	(	PUNCT
ejpam-6140	278	27	∣∣e1uj∣∣+	∣∣e1uj∣∣+	PROPN
ejpam-6140	278	28	∣∣e1uj∣∣	∣∣e1uj∣∣	PROPN
ejpam-6140	278	29	)	)	PUNCT
ejpam-6140	278	30	≤	≤	NOUN
ejpam-6140	278	31	(	(	PUNCT
ejpam-6140	278	32	1	1	NUM
ejpam-6140	278	33	+	+	CCONJ
ejpam-6140	278	34	r0	r0	NOUN
ejpam-6140	278	35	)	)	PUNCT
ejpam-6140	278	36	∣∣e1uj∣∣−	∣∣e1uj∣∣−	NOUN
ejpam-6140	278	37	r0	r0	NOUN
ejpam-6140	278	38	2	2	NUM
ejpam-6140	278	39	(	(	PUNCT
ejpam-6140	278	40	∣∣e1uj+1	∣∣e1uj+1	DET
ejpam-6140	278	41	∣∣+	∣∣+	PROPN
ejpam-6140	278	42	∣∣e1uj−1	∣∣e1uj−1	PROPN
ejpam-6140	278	43	∣∣	∣∣	PROPN
ejpam-6140	278	44	)	)	PUNCT
ejpam-6140	278	45	≤	≤	NUM
ejpam-6140	278	46	∣∣∣(1	∣∣∣(1	NOUN
ejpam-6140	278	47	+	+	CCONJ
ejpam-6140	278	48	r0	r0	NOUN
ejpam-6140	278	49	)	)	PUNCT
ejpam-6140	278	50	e	e	NOUN
ejpam-6140	278	51	1	1	NUM
ejpam-6140	278	52	uj	uj	PROPN
ejpam-6140	278	53	−	−	PROPN
ejpam-6140	278	54	r0	r0	NOUN
ejpam-6140	278	55	2	2	NUM
ejpam-6140	278	56	(	(	PUNCT
ejpam-6140	278	57	e1uj+1	e1uj+1	NOUN
ejpam-6140	278	58	+	+	CCONJ
ejpam-6140	278	59	e1uj−1	e1uj−1	NOUN
ejpam-6140	278	60	)	)	PUNCT
ejpam-6140	278	61	∣∣∣	∣∣∣	NOUN
ejpam-6140	278	62	=	=	SYM
ejpam-6140	278	63	∣∣∣(1−	∣∣∣(1−	PROPN
ejpam-6140	278	64	r0	r0	NOUN
ejpam-6140	278	65	)	)	PUNCT
ejpam-6140	279	1	e	e	X
ejpam-6140	279	2	0	0	NUM
ejpam-6140	279	3	uj	uj	PROPN
ejpam-6140	279	4	+	+	CCONJ
ejpam-6140	279	5	r0	r0	NOUN
ejpam-6140	279	6	2	2	NUM
ejpam-6140	279	7	(	(	PUNCT
ejpam-6140	279	8	e0uj+1	e0uj+1	VERB
ejpam-6140	279	9	+	+	CCONJ
ejpam-6140	279	10	e0uj−1	e0uj−1	NOUN
ejpam-6140	279	11	)	)	PUNCT
ejpam-6140	280	1	+	+	CCONJ
ejpam-6140	280	2	k0	k0	PROPN
ejpam-6140	280	3	(	(	PUNCT
ejpam-6140	280	4	f	f	PROPN
ejpam-6140	280	5	(	(	PUNCT
ejpam-6140	280	6	v0j	v0j	NOUN
ejpam-6140	280	7	)	)	PUNCT
ejpam-6140	280	8	−	−	PROPN
ejpam-6140	281	1	f	f	PROPN
ejpam-6140	281	2	(	(	PUNCT
ejpam-6140	281	3	v	v	NOUN
ejpam-6140	281	4	0	0	NUM
ejpam-6140	281	5	j	j	NOUN
ejpam-6140	281	6	)	)	PUNCT
ejpam-6140	281	7	)	)	PUNCT
ejpam-6140	282	1	+	+	CCONJ
ejpam-6140	282	2	t	t	X
ejpam-6140	282	3	0	0	NUM
ejpam-6140	282	4	ui	ui	PROPN
ejpam-6140	282	5	∣∣∣	∣∣∣	NOUN
ejpam-6140	282	6	.	.	PUNCT
ejpam-6140	283	1	m.	m.	PROPN
ejpam-6140	283	2	i.	i.	PROPN
ejpam-6140	283	3	khalil	khalil	PROPN
ejpam-6140	283	4	et	et	PROPN
ejpam-6140	283	5	al	al	PROPN
ejpam-6140	283	6	.	.	PUNCT
ejpam-6140	283	7	/	/	SYM
ejpam-6140	283	8	eur	eur	PROPN
ejpam-6140	283	9	.	.	PUNCT
ejpam-6140	284	1	j.	j.	PROPN
ejpam-6140	284	2	pure	pure	PROPN
ejpam-6140	284	3	appl	appl	PROPN
ejpam-6140	284	4	.	.	PROPN
ejpam-6140	284	5	math	math	PROPN
ejpam-6140	284	6	,	,	PUNCT
ejpam-6140	284	7	18	18	NUM
ejpam-6140	284	8	(	(	PUNCT
ejpam-6140	284	9	3	3	NUM
ejpam-6140	284	10	)	)	PUNCT
ejpam-6140	284	11	(	(	PUNCT
ejpam-6140	284	12	2025	2025	NUM
ejpam-6140	284	13	)	)	PUNCT
ejpam-6140	284	14	,	,	PUNCT
ejpam-6140	284	15	6140	6140	NUM
ejpam-6140	284	16	11	11	NUM
ejpam-6140	284	17	of	of	ADP
ejpam-6140	284	18	17	17	NUM
ejpam-6140	284	19	it	it	PRON
ejpam-6140	284	20	follows	follow	VERB
ejpam-6140	284	21	that	that	SCONJ
ejpam-6140	284	22	∣∣∣e1uj∣∣∣	∣∣∣e1uj∣∣∣	NOUN
ejpam-6140	284	23	≤	≤	X
ejpam-6140	284	24	lk	lk	PROPN
ejpam-6140	284	25	∣∣∣e0uj∣∣∣+	∣∣∣e0uj∣∣∣+	PROPN
ejpam-6140	284	26	∣∣t	∣∣t	NOUN
ejpam-6140	284	27	0	0	NUM
ejpam-6140	284	28	ui	ui	PROPN
ejpam-6140	284	29	∣∣	∣∣	NUM
ejpam-6140	284	30	=	=	SYM
ejpam-6140	284	31	∣∣t	∣∣t	NOUN
ejpam-6140	284	32	0	0	NUM
ejpam-6140	284	33	ui	ui	PROPN
ejpam-6140	284	34	∣∣	∣∣	X
ejpam-6140	285	1	≤	≤	PROPN
ejpam-6140	285	2	c	c	X
ejpam-6140	285	3	(	(	PUNCT
ejpam-6140	285	4	k	k	PROPN
ejpam-6140	285	5	+	+	CCONJ
ejpam-6140	285	6	h2	h2	NOUN
ejpam-6140	285	7	)	)	PUNCT
ejpam-6140	285	8	,	,	PUNCT
ejpam-6140	285	9	where	where	SCONJ
ejpam-6140	285	10	l	l	NOUN
ejpam-6140	285	11	=	=	SYM
ejpam-6140	285	12	max	max	PROPN
ejpam-6140	285	13	{	{	PUNCT
ejpam-6140	285	14	l1	l1	PROPN
ejpam-6140	285	15	,	,	PUNCT
ejpam-6140	285	16	l2	l2	NOUN
ejpam-6140	285	17	}	}	PUNCT
ejpam-6140	285	18	.	.	PUNCT
ejpam-6140	286	1	hence	hence	ADV
ejpam-6140	286	2	∣∣∣e1uj∣∣∣	∣∣∣e1uj∣∣∣	NOUN
ejpam-6140	286	3	≤	≤	ADJ
ejpam-6140	286	4	c1	c1	NOUN
ejpam-6140	286	5	(	(	PUNCT
ejpam-6140	286	6	k	k	PROPN
ejpam-6140	286	7	+	+	CCONJ
ejpam-6140	286	8	h2	h2	NOUN
ejpam-6140	286	9	)	)	PUNCT
ejpam-6140	286	10	,	,	PUNCT
ejpam-6140	286	11	i	i	PRON
ejpam-6140	286	12	=	=	NOUN
ejpam-6140	286	13	0	0	NUM
ejpam-6140	286	14	,	,	PUNCT
ejpam-6140	286	15	1	1	NUM
ejpam-6140	286	16	,	,	PUNCT
ejpam-6140	286	17	.	.	PUNCT
ejpam-6140	286	18	.	.	PUNCT
ejpam-6140	287	1	.	.	PUNCT
ejpam-6140	288	1	,	,	PUNCT
ejpam-6140	288	2	i	i	PRON
ejpam-6140	288	3	−	−	PROPN
ejpam-6140	288	4	1	1	NUM
ejpam-6140	288	5	,	,	PUNCT
ejpam-6140	288	6	c1	c1	PROPN
ejpam-6140	288	7	=	=	PROPN
ejpam-6140	288	8	c.	c.	PROPN
ejpam-6140	288	9	suppose	suppose	VERB
ejpam-6140	288	10	that	that	SCONJ
ejpam-6140	288	11	∥es	∥es	VERB
ejpam-6140	288	12	u∥	u∥	ADJ
ejpam-6140	288	13	≤	≤	ADJ
ejpam-6140	288	14	cs	cs	X
ejpam-6140	288	15	(	(	PUNCT
ejpam-6140	288	16	k	k	PROPN
ejpam-6140	288	17	+	+	CCONJ
ejpam-6140	288	18	h2	h2	NOUN
ejpam-6140	288	19	)	)	PUNCT
ejpam-6140	288	20	∥es	∥e	VERB
ejpam-6140	288	21	v∥	v∥	PROPN
ejpam-6140	288	22	≤	≤	NOUN
ejpam-6140	288	23	cs	cs	PROPN
ejpam-6140	288	24	(	(	PUNCT
ejpam-6140	288	25	k	k	PROPN
ejpam-6140	288	26	+	+	CCONJ
ejpam-6140	288	27	h2	h2	NOUN
ejpam-6140	288	28	)	)	PUNCT
ejpam-6140	288	29	s	s	PART
ejpam-6140	289	1	=	=	SYM
ejpam-6140	289	2	0	0	NUM
ejpam-6140	289	3	,	,	PUNCT
ejpam-6140	289	4	1	1	NUM
ejpam-6140	289	5	,	,	PUNCT
ejpam-6140	289	6	2	2	NUM
ejpam-6140	289	7	.	.	PUNCT
ejpam-6140	289	8	.	.	PUNCT
ejpam-6140	289	9	.	.	PUNCT
ejpam-6140	290	1	,	,	PUNCT
ejpam-6140	290	2	n	n	PROPN
ejpam-6140	290	3	cs	cs	X
ejpam-6140	290	4	>	>	X
ejpam-6140	290	5	0	0	X
ejpam-6140	290	6	.	.	PUNCT
ejpam-6140	291	1	for	for	ADP
ejpam-6140	291	2	n+	n+	NUM
ejpam-6140	291	3	1	1	NUM
ejpam-6140	291	4	,	,	PUNCT
ejpam-6140	291	5	set	set	VERB
ejpam-6140	291	6	∥en	∥en	PROPN
ejpam-6140	291	7	u∥	u∥	PRON
ejpam-6140	291	8	=	=	X
ejpam-6140	291	9	∣∣∣en+1	∣∣∣en+1	NOUN
ejpam-6140	291	10	uj	uj	NOUN
ejpam-6140	291	11	∣∣∣	∣∣∣	NOUN
ejpam-6140	291	12	=	=	SYM
ejpam-6140	291	13	max1≤i≤i	max1≤i≤i	NUM
ejpam-6140	291	14	∣∣en+1	∣∣en+1	NOUN
ejpam-6140	291	15	ui	ui	PROPN
ejpam-6140	291	16	∣∣	∣∣	NUM
ejpam-6140	291	17	∣∣∣en+1	∣∣∣en+1	X
ejpam-6140	291	18	uj	uj	X
ejpam-6140	291	19	∣∣∣	∣∣∣	NOUN
ejpam-6140	291	20	=	=	SYM
ejpam-6140	291	21	(	(	PUNCT
ejpam-6140	291	22	1	1	NUM
ejpam-6140	291	23	+	+	NUM
ejpam-6140	291	24	rn	rn	NOUN
ejpam-6140	291	25	)	)	PUNCT
ejpam-6140	291	26	∣∣∣en+1	∣∣∣en+1	NOUN
ejpam-6140	292	1	uj	uj	PROPN
ejpam-6140	292	2	∣∣∣−	∣∣∣−	PROPN
ejpam-6140	292	3	rn	rn	PROPN
ejpam-6140	292	4	2	2	NUM
ejpam-6140	292	5	(	(	PUNCT
ejpam-6140	292	6	∣∣∣en+1	∣∣∣en+1	NOUN
ejpam-6140	292	7	uj	uj	PROPN
ejpam-6140	292	8	∣∣∣+	∣∣∣+	PROPN
ejpam-6140	292	9	∣∣∣en+1	∣∣∣en+1	NOUN
ejpam-6140	292	10	uj	uj	PROPN
ejpam-6140	292	11	∣∣∣	∣∣∣	NOUN
ejpam-6140	292	12	)	)	PUNCT
ejpam-6140	292	13	≤	≤	NOUN
ejpam-6140	292	14	(	(	PUNCT
ejpam-6140	292	15	1	1	NUM
ejpam-6140	292	16	+	+	NUM
ejpam-6140	292	17	rn	rn	NOUN
ejpam-6140	292	18	)	)	PUNCT
ejpam-6140	292	19	∣∣∣en+1	∣∣∣en+1	NOUN
ejpam-6140	292	20	uj	uj	PROPN
ejpam-6140	292	21	∣∣∣−	∣∣∣−	PROPN
ejpam-6140	292	22	rn	rn	PROPN
ejpam-6140	292	23	2	2	NUM
ejpam-6140	292	24	(	(	PUNCT
ejpam-6140	292	25	∣∣∣en+1	∣∣∣en+1	X
ejpam-6140	292	26	uj+1	uj+1	PROPN
ejpam-6140	292	27	∣∣∣+	∣∣∣+	PROPN
ejpam-6140	292	28	∣∣∣en+1	∣∣∣en+1	NOUN
ejpam-6140	292	29	uj−1	uj−1	NOUN
ejpam-6140	292	30	∣∣∣	∣∣∣	ADJ
ejpam-6140	292	31	)	)	PUNCT
ejpam-6140	292	32	≤	≤	NUM
ejpam-6140	292	33	∣∣∣(1	∣∣∣(1	NOUN
ejpam-6140	292	34	+	+	CCONJ
ejpam-6140	292	35	rn	rn	NOUN
ejpam-6140	292	36	)	)	PUNCT
ejpam-6140	292	37	e	e	PROPN
ejpam-6140	292	38	n+1	n+1	PROPN
ejpam-6140	292	39	uj	uj	PROPN
ejpam-6140	292	40	−	−	PROPN
ejpam-6140	292	41	rn	rn	PROPN
ejpam-6140	292	42	2	2	NUM
ejpam-6140	292	43	(	(	PUNCT
ejpam-6140	292	44	en+1	en+1	VERB
ejpam-6140	292	45	uj+1	uj+1	NUM
ejpam-6140	292	46	+	+	CCONJ
ejpam-6140	292	47	en+1	en+1	ADJ
ejpam-6140	292	48	uj−1	uj−1	NOUN
ejpam-6140	292	49	)	)	PUNCT
ejpam-6140	292	50	∣∣∣	∣∣∣	NOUN
ejpam-6140	292	51	=	=	SYM
ejpam-6140	292	52	∣∣∣(1−	∣∣∣(1−	PROPN
ejpam-6140	292	53	rn	rn	PROPN
ejpam-6140	292	54	)	)	PUNCT
ejpam-6140	292	55	e	e	PROPN
ejpam-6140	292	56	n	n	ADP
ejpam-6140	292	57	uj	uj	PROPN
ejpam-6140	293	1	+	+	CCONJ
ejpam-6140	293	2	rn	rn	PROPN
ejpam-6140	293	3	2	2	NUM
ejpam-6140	293	4	(	(	PUNCT
ejpam-6140	293	5	enuj+1	enuj+1	NOUN
ejpam-6140	293	6	+	+	CCONJ
ejpam-6140	293	7	enuj−1	enuj−1	NOUN
ejpam-6140	293	8	)	)	PUNCT
ejpam-6140	294	1	+	+	CCONJ
ejpam-6140	294	2	kn	kn	PROPN
ejpam-6140	294	3	(	(	PUNCT
ejpam-6140	294	4	f	f	PROPN
ejpam-6140	294	5	(	(	PUNCT
ejpam-6140	294	6	vnj	vnj	ADV
ejpam-6140	294	7	)	)	PUNCT
ejpam-6140	295	1	−	−	PROPN
ejpam-6140	295	2	f	f	PROPN
ejpam-6140	295	3	(	(	PUNCT
ejpam-6140	295	4	v	v	PROPN
ejpam-6140	295	5	n	n	PROPN
ejpam-6140	295	6	j	j	PROPN
ejpam-6140	295	7	)	)	PUNCT
ejpam-6140	295	8	)	)	PUNCT
ejpam-6140	296	1	+	+	CCONJ
ejpam-6140	296	2	t	t	PROPN
ejpam-6140	296	3	n+1/2	n+1/2	INTJ
ejpam-6140	296	4	ui	ui	PROPN
ejpam-6140	296	5	∣∣∣	∣∣∣	NOUN
ejpam-6140	296	6	.	.	PUNCT
ejpam-6140	297	1	since	since	SCONJ
ejpam-6140	297	2	(	(	PUNCT
ejpam-6140	297	3	1−	1−	NUM
ejpam-6140	297	4	rn	rn	NOUN
ejpam-6140	297	5	)	)	PUNCT
ejpam-6140	297	6	≥	≥	NOUN
ejpam-6140	297	7	0	0	NUM
ejpam-6140	297	8	,	,	PUNCT
ejpam-6140	297	9	it	it	PRON
ejpam-6140	297	10	follows	follow	VERB
ejpam-6140	297	11	that∥∥en+1	that∥∥en+1	PROPN
ejpam-6140	297	12	u	u	PROPN
ejpam-6140	297	13	∥∥	∥∥	X
ejpam-6140	297	14	≤	≤	X
ejpam-6140	297	15	(	(	PUNCT
ejpam-6140	297	16	1−	1−	NUM
ejpam-6140	297	17	rn	rn	NOUN
ejpam-6140	297	18	)	)	PUNCT
ejpam-6140	297	19	∥en	∥en	PROPN
ejpam-6140	298	1	u∥+	u∥+	PROPN
ejpam-6140	298	2	rn	rn	PROPN
ejpam-6140	298	3	∥en	∥en	X
ejpam-6140	298	4	u∥+	u∥+	ADJ
ejpam-6140	298	5	l1kn	l1kn	NOUN
ejpam-6140	298	6	∣∣vnj	∣∣vnj	PROPN
ejpam-6140	298	7	−	−	PROPN
ejpam-6140	298	8	v	v	ADP
ejpam-6140	298	9	n	n	PROPN
ejpam-6140	298	10	j	j	PROPN
ejpam-6140	298	11	∣∣+	∣∣+	PROPN
ejpam-6140	298	12	∣∣∣tn+1/2	∣∣∣tn+1/2	PROPN
ejpam-6140	298	13	ui	ui	PROPN
ejpam-6140	298	14	∣∣∣∥∥en+1	∣∣∣∥∥en+1	PROPN
ejpam-6140	298	15	u	u	PROPN
ejpam-6140	298	16	∥∥	∥∥	PROPN
ejpam-6140	298	17	≤	≤	X
ejpam-6140	298	18	∥en	∥en	PUNCT
ejpam-6140	298	19	u∥+	u∥+	ADJ
ejpam-6140	298	20	lk	lk	NOUN
ejpam-6140	298	21	∥en	∥en	PROPN
ejpam-6140	298	22	v	v	PROPN
ejpam-6140	298	23	∥+	∥+	PROPN
ejpam-6140	298	24	∣∣∣tn+1/2	∣∣∣tn+1/2	PROPN
ejpam-6140	298	25	ui	ui	NOUN
ejpam-6140	298	26	∣∣∣	∣∣∣	NOUN
ejpam-6140	298	27	≤	≤	PROPN
ejpam-6140	299	1	cn	cn	PROPN
ejpam-6140	299	2	(	(	PUNCT
ejpam-6140	299	3	k	k	PROPN
ejpam-6140	299	4	+	+	CCONJ
ejpam-6140	299	5	h2	h2	NOUN
ejpam-6140	299	6	)	)	PUNCT
ejpam-6140	300	1	+	+	CCONJ
ejpam-6140	300	2	klcn	klcn	PROPN
ejpam-6140	300	3	(	(	PUNCT
ejpam-6140	300	4	k	k	PROPN
ejpam-6140	300	5	+	+	CCONJ
ejpam-6140	300	6	h2	h2	NOUN
ejpam-6140	300	7	)	)	PUNCT
ejpam-6140	301	1	+	+	CCONJ
ejpam-6140	301	2	c	c	X
ejpam-6140	301	3	(	(	PUNCT
ejpam-6140	301	4	k	k	NOUN
ejpam-6140	301	5	+	+	CCONJ
ejpam-6140	301	6	h2	h2	NOUN
ejpam-6140	301	7	)	)	PUNCT
ejpam-6140	301	8	≤	≤	NOUN
ejpam-6140	301	9	(	(	PUNCT
ejpam-6140	301	10	1	1	NUM
ejpam-6140	301	11	+	+	NUM
ejpam-6140	301	12	kl)cn	kl)cn	X
ejpam-6140	301	13	(	(	PUNCT
ejpam-6140	301	14	k	k	NOUN
ejpam-6140	301	15	+	+	CCONJ
ejpam-6140	301	16	h2	h2	NOUN
ejpam-6140	301	17	)	)	PUNCT
ejpam-6140	302	1	+	+	CCONJ
ejpam-6140	302	2	c	c	X
ejpam-6140	302	3	(	(	PUNCT
ejpam-6140	302	4	k	k	NOUN
ejpam-6140	302	5	+	+	CCONJ
ejpam-6140	302	6	h2	h2	NOUN
ejpam-6140	302	7	)	)	PUNCT
ejpam-6140	303	1	=	=	PUNCT
ejpam-6140	304	1	[	[	X
ejpam-6140	304	2	(	(	PUNCT
ejpam-6140	304	3	1	1	NUM
ejpam-6140	304	4	+	+	CCONJ
ejpam-6140	304	5	kl)cn	kl)cn	X
ejpam-6140	305	1	+	+	CCONJ
ejpam-6140	305	2	c	c	X
ejpam-6140	305	3	]	]	X
ejpam-6140	305	4	(	(	PUNCT
ejpam-6140	305	5	k	k	X
ejpam-6140	305	6	+	+	CCONJ
ejpam-6140	305	7	h2	h2	NOUN
ejpam-6140	305	8	)	)	PUNCT
ejpam-6140	305	9	.	.	PUNCT
ejpam-6140	306	1	it	it	PRON
ejpam-6140	306	2	follows	follow	VERB
ejpam-6140	306	3	that	that	SCONJ
ejpam-6140	306	4	∥∥en+1	∥∥en+1	PROPN
ejpam-6140	306	5	u	u	NOUN
ejpam-6140	306	6	∥∥	∥∥	PROPN
ejpam-6140	306	7	≤	≤	X
ejpam-6140	306	8	cn+1	cn+1	VERB
ejpam-6140	306	9	(	(	PUNCT
ejpam-6140	306	10	k	k	PROPN
ejpam-6140	306	11	+	+	CCONJ
ejpam-6140	306	12	h2	h2	PROPN
ejpam-6140	306	13	)	)	PUNCT
ejpam-6140	306	14	,	,	PUNCT
ejpam-6140	306	15	n	n	NOUN
ejpam-6140	306	16	=	=	SYM
ejpam-6140	306	17	0	0	NUM
ejpam-6140	306	18	,	,	PUNCT
ejpam-6140	306	19	1	1	NUM
ejpam-6140	306	20	,	,	PUNCT
ejpam-6140	306	21	.	.	PUNCT
ejpam-6140	306	22	.	.	PUNCT
ejpam-6140	307	1	..	..	PUNCT
ejpam-6140	307	2	in	in	ADP
ejpam-6140	307	3	the	the	DET
ejpam-6140	307	4	same	same	ADJ
ejpam-6140	307	5	way	way	NOUN
ejpam-6140	307	6	,	,	PUNCT
ejpam-6140	307	7	one	one	PRON
ejpam-6140	307	8	can	can	AUX
ejpam-6140	307	9	get∥∥en+1	get∥∥en+1	VERB
ejpam-6140	307	10	v	v	ADP
ejpam-6140	308	1	∥∥	∥∥	PROPN
ejpam-6140	308	2	≤	≤	X
ejpam-6140	308	3	cn+1	cn+1	NUM
ejpam-6140	308	4	(	(	PUNCT
ejpam-6140	308	5	k	k	PROPN
ejpam-6140	308	6	+	+	CCONJ
ejpam-6140	308	7	h2	h2	PROPN
ejpam-6140	308	8	)	)	PUNCT
ejpam-6140	308	9	,	,	PUNCT
ejpam-6140	308	10	n	n	NOUN
ejpam-6140	308	11	=	=	SYM
ejpam-6140	308	12	0	0	NUM
ejpam-6140	308	13	,	,	PUNCT
ejpam-6140	308	14	1	1	NUM
ejpam-6140	308	15	,	,	PUNCT
ejpam-6140	308	16	.	.	PUNCT
ejpam-6140	308	17	.	.	PUNCT
ejpam-6140	308	18	.	.	PUNCT
ejpam-6140	309	1	remark	remark	VERB
ejpam-6140	309	2	•	•	ADP
ejpam-6140	309	3	clearly	clearly	ADV
ejpam-6140	309	4	,	,	PUNCT
ejpam-6140	309	5	the	the	DET
ejpam-6140	309	6	matrix	matrix	NOUN
ejpam-6140	309	7	(	(	PUNCT
ejpam-6140	309	8	i	i	PRON
ejpam-6140	309	9	+	+	PROPN
ejpam-6140	309	10	rn	rn	PROPN
ejpam-6140	309	11	2	2	NUM
ejpam-6140	309	12	h	h	NOUN
ejpam-6140	309	13	)	)	PUNCT
ejpam-6140	309	14	is	be	AUX
ejpam-6140	309	15	diagonally	diagonally	ADV
ejpam-6140	309	16	dominated	dominate	VERB
ejpam-6140	309	17	;	;	PUNCT
ejpam-6140	309	18	hence	hence	ADV
ejpam-6140	309	19	,	,	PUNCT
ejpam-6140	309	20	it	it	PRON
ejpam-6140	309	21	is	be	AUX
ejpam-6140	309	22	non	non	ADJ
ejpam-6140	309	23	-	-	ADJ
ejpam-6140	309	24	singular	singular	ADJ
ejpam-6140	309	25	.	.	PUNCT
ejpam-6140	310	1	it	it	PRON
ejpam-6140	310	2	follows	follow	VERB
ejpam-6140	310	3	that	that	SCONJ
ejpam-6140	310	4	the	the	DET
ejpam-6140	310	5	linear	linear	PROPN
ejpam-6140	310	6	systems	system	NOUN
ejpam-6140	310	7	(	(	PUNCT
ejpam-6140	310	8	26	26	NUM
ejpam-6140	310	9	)	)	PUNCT
ejpam-6140	310	10	,	,	PUNCT
ejpam-6140	310	11	(	(	PUNCT
ejpam-6140	310	12	27	27	NUM
ejpam-6140	310	13	)	)	PUNCT
ejpam-6140	310	14	are	be	AUX
ejpam-6140	310	15	uniquely	uniquely	ADV
ejpam-6140	310	16	solvable	solvable	ADJ
ejpam-6140	310	17	[	[	X
ejpam-6140	310	18	28	28	NUM
ejpam-6140	310	19	]	]	SYM
ejpam-6140	310	20	•	•	NUM
ejpam-6140	310	21	the	the	DET
ejpam-6140	310	22	value	value	NOUN
ejpam-6140	310	23	of	of	ADP
ejpam-6140	310	24	(	(	PUNCT
ejpam-6140	310	25	nbut	nbut	PROPN
ejpam-6140	310	26	)	)	PUNCT
ejpam-6140	310	27	is	be	AUX
ejpam-6140	310	28	dependent	dependent	ADJ
ejpam-6140	310	29	on	on	ADP
ejpam-6140	310	30	the	the	DET
ejpam-6140	310	31	space	space	NOUN
ejpam-6140	310	32	and	and	CCONJ
ejpam-6140	310	33	time	time	NOUN
ejpam-6140	310	34	steps	step	NOUN
ejpam-6140	310	35	.	.	PUNCT
ejpam-6140	311	1	•	•	PUNCT
ejpam-6140	311	2	as	as	SCONJ
ejpam-6140	311	3	it	it	PRON
ejpam-6140	311	4	was	be	AUX
ejpam-6140	311	5	proved	prove	VERB
ejpam-6140	311	6	in	in	ADP
ejpam-6140	311	7	theorem	theorem	NOUN
ejpam-6140	311	8	(	(	PUNCT
ejpam-6140	311	9	3	3	NUM
ejpam-6140	311	10	)	)	PUNCT
ejpam-6140	311	11	,	,	PUNCT
ejpam-6140	311	12	the	the	DET
ejpam-6140	311	13	crank	crank	NOUN
ejpam-6140	311	14	-	-	PUNCT
ejpam-6140	311	15	nicolson	nicolson	PROPN
ejpam-6140	311	16	numerical	numerical	PROPN
ejpam-6140	311	17	scheme	scheme	PROPN
ejpam-6140	311	18	gives	give	VERB
ejpam-6140	311	19	approximate	approximate	ADJ
ejpam-6140	311	20	solutions	solution	NOUN
ejpam-6140	311	21	of	of	ADP
ejpam-6140	311	22	the	the	DET
ejpam-6140	311	23	order	order	NOUN
ejpam-6140	311	24	of	of	ADP
ejpam-6140	311	25	convergence	convergence	NOUN
ejpam-6140	311	26	o	o	NOUN
ejpam-6140	311	27	(	(	PUNCT
ejpam-6140	311	28	k	k	PROPN
ejpam-6140	311	29	+	+	CCONJ
ejpam-6140	311	30	h2	h2	NOUN
ejpam-6140	311	31	)	)	PUNCT
ejpam-6140	312	1	;	;	PUNCT
ejpam-6140	312	2	k	k	PROPN
ejpam-6140	312	3	=	=	SYM
ejpam-6140	312	4	maxn	maxn	ADJ
ejpam-6140	312	5	kn	kn	NOUN
ejpam-6140	312	6	,	,	PUNCT
ejpam-6140	312	7	while	while	SCONJ
ejpam-6140	312	8	,	,	PUNCT
ejpam-6140	312	9	with	with	ADP
ejpam-6140	312	10	the	the	DET
ejpam-6140	312	11	formula	formula	NOUN
ejpam-6140	312	12	of	of	ADP
ejpam-6140	312	13	time	time	NOUN
ejpam-6140	312	14	steps	step	NOUN
ejpam-6140	312	15	(	(	PUNCT
ejpam-6140	312	16	25	25	NUM
ejpam-6140	312	17	)	)	PUNCT
ejpam-6140	312	18	,	,	PUNCT
ejpam-6140	312	19	the	the	DET
ejpam-6140	312	20	convergence	convergence	NOUN
ejpam-6140	312	21	rate	rate	NOUN
ejpam-6140	312	22	becomes	become	VERB
ejpam-6140	312	23	o	o	NOUN
ejpam-6140	312	24	(	(	PUNCT
ejpam-6140	312	25	hα	hα	NOUN
ejpam-6140	312	26	)	)	PUNCT
ejpam-6140	312	27	,	,	PUNCT
ejpam-6140	312	28	as	as	SCONJ
ejpam-6140	312	29	the	the	DET
ejpam-6140	312	30	space	space	NOUN
ejpam-6140	312	31	step	step	NOUN
ejpam-6140	312	32	approaches	approach	VERB
ejpam-6140	312	33	zero	zero	NUM
ejpam-6140	312	34	for	for	ADP
ejpam-6140	312	35	1	1	NUM
ejpam-6140	312	36	≤	≤	NUM
ejpam-6140	312	37	α	α	NOUN
ejpam-6140	312	38	≤	≤	NOUN
ejpam-6140	312	39	2	2	NUM
ejpam-6140	312	40	.	.	PUNCT
ejpam-6140	313	1	a	a	DET
ejpam-6140	313	2	similar	similar	ADJ
ejpam-6140	313	3	convergence	convergence	NOUN
ejpam-6140	313	4	order	order	NOUN
ejpam-6140	313	5	is	be	AUX
ejpam-6140	313	6	expected	expect	VERB
ejpam-6140	313	7	for	for	ADP
ejpam-6140	313	8	(	(	PUNCT
ejpam-6140	313	9	nbut	nbut	PROPN
ejpam-6140	313	10	)	)	PUNCT
ejpam-6140	313	11	.	.	PUNCT
ejpam-6140	314	1	m.	m.	PROPN
ejpam-6140	314	2	i.	i.	PROPN
ejpam-6140	314	3	khalil	khalil	PROPN
ejpam-6140	314	4	et	et	PROPN
ejpam-6140	314	5	al	al	PROPN
ejpam-6140	314	6	.	.	PUNCT
ejpam-6140	314	7	/	/	SYM
ejpam-6140	314	8	eur	eur	PROPN
ejpam-6140	314	9	.	.	PUNCT
ejpam-6140	315	1	j.	j.	PROPN
ejpam-6140	315	2	pure	pure	PROPN
ejpam-6140	315	3	appl	appl	PROPN
ejpam-6140	315	4	.	.	PROPN
ejpam-6140	315	5	math	math	PROPN
ejpam-6140	315	6	,	,	PUNCT
ejpam-6140	315	7	18	18	NUM
ejpam-6140	315	8	(	(	PUNCT
ejpam-6140	315	9	3	3	NUM
ejpam-6140	315	10	)	)	PUNCT
ejpam-6140	315	11	(	(	PUNCT
ejpam-6140	315	12	2025	2025	NUM
ejpam-6140	315	13	)	)	PUNCT
ejpam-6140	315	14	,	,	PUNCT
ejpam-6140	315	15	6140	6140	NUM
ejpam-6140	315	16	12	12	NUM
ejpam-6140	315	17	of	of	ADP
ejpam-6140	315	18	17	17	NUM
ejpam-6140	315	19	4	4	NUM
ejpam-6140	315	20	.	.	PUNCT
ejpam-6140	315	21	numerical	numerical	ADJ
ejpam-6140	315	22	experiments	experiment	NOUN
ejpam-6140	315	23	in	in	ADP
ejpam-6140	315	24	this	this	DET
ejpam-6140	315	25	section	section	NOUN
ejpam-6140	315	26	,	,	PUNCT
ejpam-6140	315	27	the	the	DET
ejpam-6140	315	28	crank	crank	NOUN
ejpam-6140	315	29	-	-	PUNCT
ejpam-6140	315	30	nicolson	nicolson	PROPN
ejpam-6140	315	31	scheme	scheme	NOUN
ejpam-6140	315	32	is	be	AUX
ejpam-6140	315	33	used	use	VERB
ejpam-6140	315	34	for	for	ADP
ejpam-6140	315	35	two	two	NUM
ejpam-6140	315	36	numerical	numerical	ADJ
ejpam-6140	315	37	experiments	experiment	NOUN
ejpam-6140	315	38	,	,	PUNCT
ejpam-6140	315	39	with	with	ADP
ejpam-6140	315	40	various	various	ADJ
ejpam-6140	315	41	grid	grid	NOUN
ejpam-6140	315	42	sizes	size	NOUN
ejpam-6140	315	43	:	:	PUNCT
ejpam-6140	316	1	i	i	PRON
ejpam-6140	316	2	=	=	PUNCT
ejpam-6140	316	3	{	{	PUNCT
ejpam-6140	316	4	20	20	NUM
ejpam-6140	316	5	,	,	PUNCT
ejpam-6140	316	6	40	40	NUM
ejpam-6140	316	7	,	,	PUNCT
ejpam-6140	316	8	80	80	NUM
ejpam-6140	316	9	,	,	PUNCT
ejpam-6140	316	10	160	160	NUM
ejpam-6140	316	11	,	,	PUNCT
ejpam-6140	316	12	320	320	NUM
ejpam-6140	316	13	}	}	PUNCT
ejpam-6140	316	14	,	,	PUNCT
ejpam-6140	316	15	taking	take	VERB
ejpam-6140	316	16	α	α	NOUN
ejpam-6140	316	17	=	=	SYM
ejpam-6140	316	18	1	1	NUM
ejpam-6140	316	19	,	,	PUNCT
ejpam-6140	316	20	2	2	NUM
ejpam-6140	316	21	.	.	PUNCT
ejpam-6140	317	1	in	in	ADP
ejpam-6140	317	2	addition	addition	NOUN
ejpam-6140	317	3	,	,	PUNCT
ejpam-6140	317	4	matlab	matlab	PROPN
ejpam-6140	317	5	(	(	PUNCT
ejpam-6140	317	6	r2020a	r2020a	NOUN
ejpam-6140	317	7	)	)	PUNCT
ejpam-6140	317	8	software	software	NOUN
ejpam-6140	317	9	is	be	AUX
ejpam-6140	317	10	used	use	VERB
ejpam-6140	317	11	for	for	ADP
ejpam-6140	317	12	writing	write	VERB
ejpam-6140	317	13	all	all	DET
ejpam-6140	317	14	the	the	DET
ejpam-6140	317	15	numerical	numerical	PROPN
ejpam-6140	317	16	computations	computation	NOUN
ejpam-6140	317	17	codes	code	NOUN
ejpam-6140	317	18	.	.	PUNCT
ejpam-6140	318	1	for	for	ADP
ejpam-6140	318	2	each	each	DET
ejpam-6140	318	3	example	example	NOUN
ejpam-6140	318	4	,	,	PUNCT
ejpam-6140	318	5	some	some	DET
ejpam-6140	318	6	tables	table	NOUN
ejpam-6140	318	7	and	and	CCONJ
ejpam-6140	318	8	figures	figure	NOUN
ejpam-6140	318	9	are	be	AUX
ejpam-6140	318	10	presented	present	VERB
ejpam-6140	318	11	to	to	PART
ejpam-6140	318	12	show	show	VERB
ejpam-6140	318	13	the	the	DET
ejpam-6140	318	14	numerical	numerical	ADJ
ejpam-6140	318	15	results	result	NOUN
ejpam-6140	318	16	obtained	obtain	VERB
ejpam-6140	318	17	by	by	ADP
ejpam-6140	318	18	using	use	VERB
ejpam-6140	318	19	the	the	DET
ejpam-6140	318	20	proposed	propose	VERB
ejpam-6140	318	21	scheme	scheme	NOUN
ejpam-6140	318	22	.	.	PUNCT
ejpam-6140	319	1	each	each	DET
ejpam-6140	319	2	table	table	NOUN
ejpam-6140	319	3	includes	include	VERB
ejpam-6140	319	4	:	:	PUNCT
ejpam-6140	319	5	•	•	NOUN
ejpam-6140	319	6	for	for	ADP
ejpam-6140	319	7	the	the	DET
ejpam-6140	319	8	first	first	ADJ
ejpam-6140	319	9	m	m	NOUN
ejpam-6140	319	10	∈	∈	NOUN
ejpam-6140	319	11	n	n	PRON
ejpam-6140	319	12	such	such	ADJ
ejpam-6140	319	13	that	that	SCONJ
ejpam-6140	319	14	the	the	DET
ejpam-6140	319	15	condition	condition	NOUN
ejpam-6140	319	16	∥um	∥um	X
ejpam-6140	320	1	h	h	NOUN
ejpam-6140	320	2	∥∞	∥∞	PROPN
ejpam-6140	320	3	≥	≥	NUM
ejpam-6140	320	4	1015	1015	NUM
ejpam-6140	320	5	and	and	CCONJ
ejpam-6140	320	6	∥v	∥v	PROPN
ejpam-6140	320	7	m	m	PROPN
ejpam-6140	320	8	h	h	NOUN
ejpam-6140	320	9	∥∞	∥∞	ADJ
ejpam-6140	320	10	≥	≥	NUM
ejpam-6140	320	11	1015	1015	NUM
ejpam-6140	320	12	holds	hold	NOUN
ejpam-6140	320	13	,	,	PUNCT
ejpam-6140	320	14	the	the	DET
ejpam-6140	320	15	value	value	NOUN
ejpam-6140	320	16	th	th	X
ejpam-6140	320	17	=	=	SYM
ejpam-6140	320	18	tm	tm	NOUN
ejpam-6140	320	19	=	=	PROPN
ejpam-6140	320	20	∑m	∑m	PROPN
ejpam-6140	320	21	n=0	n=0	PROPN
ejpam-6140	321	1	kn	kn	NOUN
ejpam-6140	321	2	is	be	AUX
ejpam-6140	321	3	considered	consider	VERB
ejpam-6140	321	4	the	the	DET
ejpam-6140	321	5	(	(	PUNCT
ejpam-6140	321	6	nbut	nbut	NOUN
ejpam-6140	321	7	)	)	PUNCT
ejpam-6140	321	8	for	for	ADP
ejpam-6140	321	9	the	the	DET
ejpam-6140	321	10	studied	study	VERB
ejpam-6140	321	11	problems	problem	NOUN
ejpam-6140	321	12	.	.	PUNCT
ejpam-6140	322	1	•	•	INTJ
ejpam-6140	322	2	eh	eh	INTJ
ejpam-6140	322	3	=	=	SYM
ejpam-6140	322	4	|t2h	|t2h	NOUN
ejpam-6140	323	1	−	−	PROPN
ejpam-6140	323	2	th|	th|	PROPN
ejpam-6140	323	3	is	be	AUX
ejpam-6140	323	4	the	the	DET
ejpam-6140	323	5	error	error	NOUN
ejpam-6140	323	6	bond	bond	NOUN
ejpam-6140	323	7	between	between	ADP
ejpam-6140	323	8	t2h	t2h	PROPN
ejpam-6140	323	9	and	and	CCONJ
ejpam-6140	323	10	th	th	NOUN
ejpam-6140	323	11	.	.	NOUN
ejpam-6140	323	12	•	•	NUM
ejpam-6140	323	13	the	the	DET
ejpam-6140	323	14	order	order	NOUN
ejpam-6140	323	15	of	of	ADP
ejpam-6140	323	16	numerical	numerical	ADJ
ejpam-6140	323	17	convergence	convergence	NOUN
ejpam-6140	323	18	to	to	ADP
ejpam-6140	323	19	the	the	PRON
ejpam-6140	323	20	(	(	PUNCT
ejpam-6140	323	21	but	but	CCONJ
ejpam-6140	323	22	)	)	PUNCT
ejpam-6140	323	23	,	,	PUNCT
ejpam-6140	323	24	using	use	VERB
ejpam-6140	323	25	the	the	DET
ejpam-6140	323	26	formula	formula	NOUN
ejpam-6140	323	27	:	:	PUNCT
ejpam-6140	323	28	sh	sh	PROPN
ejpam-6140	323	29	=	=	PUNCT
ejpam-6140	323	30	log	log	PROPN
ejpam-6140	323	31	(	(	PUNCT
ejpam-6140	323	32	e2h	e2h	NOUN
ejpam-6140	323	33	/	/	SYM
ejpam-6140	323	34	eh	eh	INTJ
ejpam-6140	323	35	)	)	PUNCT
ejpam-6140	323	36	/	/	SYM
ejpam-6140	323	37	log	log	NOUN
ejpam-6140	323	38	2	2	NUM
ejpam-6140	323	39	.	.	NOUN
ejpam-6140	323	40	•	•	NUM
ejpam-6140	324	1	the	the	DET
ejpam-6140	324	2	unit	unit	NOUN
ejpam-6140	324	3	time	time	NOUN
ejpam-6140	324	4	of	of	ADP
ejpam-6140	324	5	the	the	DET
ejpam-6140	324	6	central	central	ADJ
ejpam-6140	324	7	processor	processor	NOUN
ejpam-6140	324	8	(	(	PUNCT
ejpam-6140	324	9	cput	cput	NOUN
ejpam-6140	324	10	)	)	PUNCT
ejpam-6140	324	11	in	in	ADP
ejpam-6140	324	12	seconds	second	NOUN
ejpam-6140	324	13	.	.	PUNCT
ejpam-6140	325	1	4.1	4.1	NUM
ejpam-6140	325	2	.	.	PUNCT
ejpam-6140	325	3	examples	example	NOUN
ejpam-6140	325	4	example	example	VERB
ejpam-6140	325	5	1	1	NUM
ejpam-6140	325	6	.	.	PUNCT
ejpam-6140	325	7	ut	ut	PROPN
ejpam-6140	325	8	=	=	PROPN
ejpam-6140	325	9	uxx	uxx	PROPN
ejpam-6140	326	1	+	+	CCONJ
ejpam-6140	326	2	v5	v5	PROPN
ejpam-6140	326	3	,	,	PUNCT
ejpam-6140	326	4	vt	vt	PROPN
ejpam-6140	326	5	=	=	PROPN
ejpam-6140	326	6	vxx	vxx	PROPN
ejpam-6140	326	7	+	+	NUM
ejpam-6140	326	8	u6	u6	PROPN
ejpam-6140	326	9	,	,	PUNCT
ejpam-6140	326	10	x	x	SYM
ejpam-6140	326	11	∈	∈	PROPN
ejpam-6140	326	12	(	(	PUNCT
ejpam-6140	326	13	0	0	NUM
ejpam-6140	326	14	,	,	PUNCT
ejpam-6140	326	15	1	1	NUM
ejpam-6140	326	16	)	)	PUNCT
ejpam-6140	326	17	,	,	PUNCT
ejpam-6140	326	18	t	t	PROPN
ejpam-6140	326	19	∈	∈	PROPN
ejpam-6140	326	20	(	(	PUNCT
ejpam-6140	326	21	0	0	NUM
ejpam-6140	326	22	,	,	PUNCT
ejpam-6140	326	23	t	t	NOUN
ejpam-6140	326	24	)	)	PUNCT
ejpam-6140	327	1	u(0	u(0	PROPN
ejpam-6140	327	2	,	,	PUNCT
ejpam-6140	327	3	t	t	PROPN
ejpam-6140	327	4	)	)	PUNCT
ejpam-6140	327	5	=	=	SYM
ejpam-6140	328	1	u(1	u(1	PROPN
ejpam-6140	328	2	,	,	PUNCT
ejpam-6140	328	3	t	t	PROPN
ejpam-6140	328	4	)	)	PUNCT
ejpam-6140	328	5	=	=	SYM
ejpam-6140	328	6	0	0	NUM
ejpam-6140	328	7	,	,	PUNCT
ejpam-6140	328	8	v(0	v(0	PROPN
ejpam-6140	328	9	,	,	PUNCT
ejpam-6140	328	10	t	t	PROPN
ejpam-6140	328	11	)	)	PUNCT
ejpam-6140	328	12	=	=	SYM
ejpam-6140	329	1	v(1	v(1	PROPN
ejpam-6140	329	2	,	,	PUNCT
ejpam-6140	329	3	t	t	PROPN
ejpam-6140	329	4	)	)	PUNCT
ejpam-6140	329	5	=	=	SYM
ejpam-6140	329	6	0	0	NUM
ejpam-6140	329	7	,	,	PUNCT
ejpam-6140	329	8	t	t	PROPN
ejpam-6140	329	9	∈	∈	PROPN
ejpam-6140	329	10	(	(	PUNCT
ejpam-6140	329	11	0	0	NUM
ejpam-6140	329	12	,	,	PUNCT
ejpam-6140	329	13	t	t	NOUN
ejpam-6140	329	14	)	)	PUNCT
ejpam-6140	329	15	u(x	u(x	PROPN
ejpam-6140	329	16	,	,	PUNCT
ejpam-6140	329	17	0	0	NUM
ejpam-6140	329	18	)	)	PUNCT
ejpam-6140	329	19	=	=	SYM
ejpam-6140	330	1	70	70	NUM
ejpam-6140	330	2	(	(	PUNCT
ejpam-6140	330	3	x−	x−	PROPN
ejpam-6140	330	4	x2	x2	PROPN
ejpam-6140	330	5	)	)	PUNCT
ejpam-6140	330	6	,	,	PUNCT
ejpam-6140	330	7	v(x	v(x	PROPN
ejpam-6140	330	8	,	,	PUNCT
ejpam-6140	330	9	0	0	NUM
ejpam-6140	330	10	)	)	PUNCT
ejpam-6140	330	11	=	=	SYM
ejpam-6140	330	12	80	80	NUM
ejpam-6140	330	13	(	(	PUNCT
ejpam-6140	330	14	x−	x−	PROPN
ejpam-6140	330	15	x2	x2	PROPN
ejpam-6140	330	16	)	)	PUNCT
ejpam-6140	330	17	,	,	PUNCT
ejpam-6140	330	18	x	x	PUNCT
ejpam-6140	330	19	∈	∈	PROPN
ejpam-6140	330	20	(	(	PUNCT
ejpam-6140	330	21	0	0	NUM
ejpam-6140	330	22	,	,	PUNCT
ejpam-6140	330	23	1	1	X
ejpam-6140	330	24	)	)	PUNCT
ejpam-6140	330	25			NOUN
ejpam-6140	330	26	(	(	PUNCT
ejpam-6140	330	27	31	31	NUM
ejpam-6140	330	28	)	)	PUNCT
ejpam-6140	330	29	example	example	NOUN
ejpam-6140	331	1	2	2	NUM
ejpam-6140	331	2	.	.	PUNCT
ejpam-6140	331	3	ut	ut	PROPN
ejpam-6140	331	4	=	=	PROPN
ejpam-6140	331	5	uxx	uxx	PROPN
ejpam-6140	331	6	+	+	CCONJ
ejpam-6140	331	7	v6	v6	PROPN
ejpam-6140	331	8	vt	vt	PROPN
ejpam-6140	331	9	=	=	PROPN
ejpam-6140	331	10	vxx	vxx	PROPN
ejpam-6140	332	1	+	+	CCONJ
ejpam-6140	332	2	u7	u7	PROPN
ejpam-6140	332	3	,	,	PUNCT
ejpam-6140	332	4	x	x	SYM
ejpam-6140	332	5	∈	∈	PROPN
ejpam-6140	332	6	(	(	PUNCT
ejpam-6140	332	7	0	0	NUM
ejpam-6140	332	8	,	,	PUNCT
ejpam-6140	332	9	1	1	NUM
ejpam-6140	332	10	)	)	PUNCT
ejpam-6140	332	11	,	,	PUNCT
ejpam-6140	332	12	t	t	PROPN
ejpam-6140	332	13	∈	∈	PROPN
ejpam-6140	332	14	(	(	PUNCT
ejpam-6140	332	15	0	0	NUM
ejpam-6140	332	16	,	,	PUNCT
ejpam-6140	332	17	t	t	NOUN
ejpam-6140	332	18	)	)	PUNCT
ejpam-6140	332	19	u(0	u(0	PROPN
ejpam-6140	332	20	,	,	PUNCT
ejpam-6140	332	21	t	t	PROPN
ejpam-6140	332	22	)	)	PUNCT
ejpam-6140	332	23	=	=	SYM
ejpam-6140	333	1	u(1	u(1	PROPN
ejpam-6140	333	2	,	,	PUNCT
ejpam-6140	333	3	t	t	PROPN
ejpam-6140	333	4	)	)	PUNCT
ejpam-6140	333	5	=	=	SYM
ejpam-6140	333	6	0	0	NUM
ejpam-6140	333	7	,	,	PUNCT
ejpam-6140	333	8	v(0	v(0	PROPN
ejpam-6140	333	9	,	,	PUNCT
ejpam-6140	333	10	t	t	PROPN
ejpam-6140	333	11	)	)	PUNCT
ejpam-6140	333	12	=	=	SYM
ejpam-6140	334	1	v(1	v(1	PROPN
ejpam-6140	334	2	,	,	PUNCT
ejpam-6140	334	3	t	t	PROPN
ejpam-6140	334	4	)	)	PUNCT
ejpam-6140	334	5	=	=	SYM
ejpam-6140	334	6	0	0	NUM
ejpam-6140	334	7	,	,	PUNCT
ejpam-6140	334	8	t	t	PROPN
ejpam-6140	334	9	∈	∈	PROPN
ejpam-6140	334	10	(	(	PUNCT
ejpam-6140	334	11	0	0	NUM
ejpam-6140	334	12	,	,	PUNCT
ejpam-6140	334	13	t	t	NOUN
ejpam-6140	334	14	)	)	PUNCT
ejpam-6140	334	15	u(x	u(x	PROPN
ejpam-6140	334	16	,	,	PUNCT
ejpam-6140	334	17	0	0	NUM
ejpam-6140	334	18	)	)	PUNCT
ejpam-6140	334	19	=	=	SYM
ejpam-6140	335	1	60	60	NUM
ejpam-6140	335	2	(	(	PUNCT
ejpam-6140	335	3	1−	1−	NUM
ejpam-6140	335	4	ex	ex	X
ejpam-6140	335	5	2−x	2−x	NUM
ejpam-6140	335	6	)	)	PUNCT
ejpam-6140	335	7	,	,	PUNCT
ejpam-6140	335	8	v(x	v(x	PROPN
ejpam-6140	335	9	,	,	PUNCT
ejpam-6140	335	10	0	0	NUM
ejpam-6140	335	11	)	)	PUNCT
ejpam-6140	335	12	=	=	SYM
ejpam-6140	335	13	70	70	NUM
ejpam-6140	335	14	(	(	PUNCT
ejpam-6140	335	15	1−	1−	NUM
ejpam-6140	335	16	ex	ex	X
ejpam-6140	335	17	2−x	2−x	NUM
ejpam-6140	335	18	)	)	PUNCT
ejpam-6140	335	19	,	,	PUNCT
ejpam-6140	335	20	x	x	PUNCT
ejpam-6140	335	21	∈	∈	PROPN
ejpam-6140	335	22	(	(	PUNCT
ejpam-6140	335	23	0	0	NUM
ejpam-6140	335	24	,	,	PUNCT
ejpam-6140	335	25	1	1	NUM
ejpam-6140	335	26	)	)	PUNCT
ejpam-6140	335	27			X
ejpam-6140	335	28	(	(	PUNCT
ejpam-6140	335	29	32	32	NUM
ejpam-6140	335	30	)	)	PUNCT
ejpam-6140	335	31	m.	m.	NOUN
ejpam-6140	335	32	i.	i.	PROPN
ejpam-6140	335	33	khalil	khalil	PROPN
ejpam-6140	335	34	et	et	PROPN
ejpam-6140	335	35	al	al	PROPN
ejpam-6140	335	36	.	.	PUNCT
ejpam-6140	335	37	/	/	SYM
ejpam-6140	335	38	eur	eur	PROPN
ejpam-6140	335	39	.	.	PUNCT
ejpam-6140	336	1	j.	j.	PROPN
ejpam-6140	336	2	pure	pure	PROPN
ejpam-6140	336	3	appl	appl	PROPN
ejpam-6140	336	4	.	.	PROPN
ejpam-6140	336	5	math	math	PROPN
ejpam-6140	336	6	,	,	PUNCT
ejpam-6140	336	7	18	18	NUM
ejpam-6140	336	8	(	(	PUNCT
ejpam-6140	336	9	3	3	NUM
ejpam-6140	336	10	)	)	PUNCT
ejpam-6140	336	11	(	(	PUNCT
ejpam-6140	336	12	2025	2025	NUM
ejpam-6140	336	13	)	)	PUNCT
ejpam-6140	336	14	,	,	PUNCT
ejpam-6140	336	15	6140	6140	NUM
ejpam-6140	336	16	13	13	NUM
ejpam-6140	336	17	of	of	ADP
ejpam-6140	336	18	17	17	NUM
ejpam-6140	336	19	table	table	NOUN
ejpam-6140	336	20	1	1	NUM
ejpam-6140	336	21	:	:	PUNCT
ejpam-6140	336	22	example	example	NOUN
ejpam-6140	336	23	1	1	NUM
ejpam-6140	336	24	,	,	PUNCT
ejpam-6140	336	25	c.n	c.n	PROPN
ejpam-6140	336	26	.	.	PROPN
ejpam-6140	336	27	scheme	scheme	NOUN
ejpam-6140	336	28	:	:	PUNCT
ejpam-6140	337	1	α	α	NOUN
ejpam-6140	337	2	=	=	SYM
ejpam-6140	337	3	1	1	NUM
ejpam-6140	337	4	h	h	NOUN
ejpam-6140	337	5	m	m	VERB
ejpam-6140	337	6	th	th	INTJ
ejpam-6140	337	7	cput	cput	ADJ
ejpam-6140	337	8	eh	eh	INTJ
ejpam-6140	337	9	sh	sh	PROPN
ejpam-6140	337	10	1/20	1/20	NUM
ejpam-6140	337	11	3	3	NUM
ejpam-6140	337	12	7.6650e-04	7.6650e-04	NUM
ejpam-6140	337	13	0.362506	0.362506	NUM
ejpam-6140	337	14	·	·	PUNCT
ejpam-6140	337	15	·	·	PUNCT
ejpam-6140	337	16	·	·	PUNCT
ejpam-6140	337	17	·	·	PUNCT
ejpam-6140	337	18	·	·	PUNCT
ejpam-6140	337	19	·	·	PUNCT
ejpam-6140	338	1	1/40	1/40	NUM
ejpam-6140	338	2	4	4	NUM
ejpam-6140	338	3	2.0966e-04	2.0966e-04	NUM
ejpam-6140	338	4	0.288462	0.288462	NUM
ejpam-6140	338	5	5.5684e-04	5.5684e-04	NUM
ejpam-6140	338	6	·	·	PUNCT
ejpam-6140	338	7	·	·	PUNCT
ejpam-6140	338	8	·	·	PUNCT
ejpam-6140	339	1	1/80	1/80	NUM
ejpam-6140	339	2	4	4	NUM
ejpam-6140	339	3	5.3939e-05	5.3939e-05	NUM
ejpam-6140	339	4	0.346336	0.346336	NUM
ejpam-6140	339	5	1.5572e-04	1.5572e-04	NUM
ejpam-6140	339	6	1.8383	1.8383	NUM
ejpam-6140	339	7	1/160	1/160	NUM
ejpam-6140	339	8	4	4	NUM
ejpam-6140	339	9	1.5557e-05	1.5557e-05	NUM
ejpam-6140	339	10	0.877538	0.877538	NUM
ejpam-6140	339	11	3.8382e-05	3.8382e-05	NUM
ejpam-6140	339	12	2.0205	2.0205	NUM
ejpam-6140	339	13	1/320	1/320	NUM
ejpam-6140	339	14	4	4	NUM
ejpam-6140	339	15	6.4259e-06	6.4259e-06	NUM
ejpam-6140	339	16	2.608468	2.608468	NUM
ejpam-6140	339	17	9.1311e-06	9.1311e-06	NUM
ejpam-6140	339	18	2.0716	2.0716	NUM
ejpam-6140	339	19	table	table	NOUN
ejpam-6140	339	20	2	2	NUM
ejpam-6140	339	21	:	:	PUNCT
ejpam-6140	339	22	example	example	NOUN
ejpam-6140	339	23	1	1	NUM
ejpam-6140	339	24	,	,	PUNCT
ejpam-6140	339	25	c.n	c.n	PROPN
ejpam-6140	339	26	.	.	PROPN
ejpam-6140	339	27	scheme	scheme	NOUN
ejpam-6140	339	28	:	:	PUNCT
ejpam-6140	339	29	α	α	NOUN
ejpam-6140	339	30	=	=	SYM
ejpam-6140	339	31	2	2	NUM
ejpam-6140	339	32	h	h	NOUN
ejpam-6140	339	33	m	m	VERB
ejpam-6140	339	34	th	th	INTJ
ejpam-6140	339	35	cput	cput	ADJ
ejpam-6140	339	36	eh	eh	INTJ
ejpam-6140	339	37	sh	sh	PROPN
ejpam-6140	339	38	1/20	1/20	NUM
ejpam-6140	339	39	4	4	NUM
ejpam-6140	339	40	3.9272e-05	3.9272e-05	NUM
ejpam-6140	339	41	0.230858	0.230858	NUM
ejpam-6140	339	42	·	·	PUNCT
ejpam-6140	339	43	·	·	PUNCT
ejpam-6140	339	44	·	·	PUNCT
ejpam-6140	339	45	·	·	PUNCT
ejpam-6140	339	46	·	·	PUNCT
ejpam-6140	339	47	·	·	PUNCT
ejpam-6140	340	1	1/40	1/40	NUM
ejpam-6140	340	2	4	4	NUM
ejpam-6140	340	3	7.6677e-06	7.6677e-06	NUM
ejpam-6140	340	4	0.335248	0.335248	NUM
ejpam-6140	340	5	3.1604e-05	3.1604e-05	NUM
ejpam-6140	340	6	·	·	PUNCT
ejpam-6140	340	7	·	·	PUNCT
ejpam-6140	340	8	·	·	PUNCT
ejpam-6140	341	1	1/80	1/80	NUM
ejpam-6140	341	2	5	5	NUM
ejpam-6140	341	3	1.9252e-06	1.9252e-06	NUM
ejpam-6140	341	4	0.326475	0.326475	NUM
ejpam-6140	341	5	5.7425e-06	5.7425e-06	NUM
ejpam-6140	341	6	2.4604	2.4604	NUM
ejpam-6140	341	7	1/160	1/160	NUM
ejpam-6140	341	8	8	8	NUM
ejpam-6140	341	9	7.8273e-07	7.8273e-07	NUM
ejpam-6140	341	10	0.789320	0.789320	NUM
ejpam-6140	341	11	1.1425e-06	1.1425e-06	NUM
ejpam-6140	341	12	2.3295	2.3295	NUM
ejpam-6140	341	13	1/320	1/320	NUM
ejpam-6140	341	14	21	21	NUM
ejpam-6140	341	15	5.2762e-07	5.2762e-07	NUM
ejpam-6140	341	16	2.642523	2.642523	NUM
ejpam-6140	341	17	2.5511e-07	2.5511e-07	NUM
ejpam-6140	341	18	2.1630	2.1630	NUM
ejpam-6140	341	19	table	table	NOUN
ejpam-6140	341	20	3	3	NUM
ejpam-6140	341	21	:	:	PUNCT
ejpam-6140	341	22	example	example	NOUN
ejpam-6140	341	23	2	2	NUM
ejpam-6140	341	24	,	,	PUNCT
ejpam-6140	341	25	c.n	c.n	PROPN
ejpam-6140	341	26	.	.	PROPN
ejpam-6140	341	27	scheme	scheme	NOUN
ejpam-6140	341	28	:	:	PUNCT
ejpam-6140	341	29	α	α	NOUN
ejpam-6140	341	30	=	=	SYM
ejpam-6140	341	31	1	1	NUM
ejpam-6140	341	32	h	h	NOUN
ejpam-6140	341	33	m	m	VERB
ejpam-6140	341	34	th	th	INTJ
ejpam-6140	341	35	cput	cput	ADJ
ejpam-6140	341	36	eh	eh	INTJ
ejpam-6140	341	37	sh	sh	PROPN
ejpam-6140	341	38	1/20	1/20	NUM
ejpam-6140	341	39	3	3	NUM
ejpam-6140	341	40	8.3371e-04	8.3371e-04	NUM
ejpam-6140	341	41	0.401556	0.401556	NUM
ejpam-6140	341	42	·	·	PUNCT
ejpam-6140	341	43	·	·	PUNCT
ejpam-6140	341	44	·	·	PUNCT
ejpam-6140	341	45	·	·	PUNCT
ejpam-6140	341	46	·	·	PUNCT
ejpam-6140	341	47	·	·	PUNCT
ejpam-6140	342	1	1/40	1/40	NUM
ejpam-6140	342	2	3	3	NUM
ejpam-6140	342	3	2.0886e-04	2.0886e-04	NUM
ejpam-6140	342	4	0.395284	0.395284	NUM
ejpam-6140	342	5	6.2485e-04	6.2485e-04	NUM
ejpam-6140	342	6	·	·	PUNCT
ejpam-6140	342	7	·	·	PUNCT
ejpam-6140	342	8	·	·	PUNCT
ejpam-6140	343	1	1/80	1/80	NUM
ejpam-6140	343	2	3	3	NUM
ejpam-6140	343	3	5.2830e-05	5.2830e-05	NUM
ejpam-6140	343	4	0.327884	0.327884	NUM
ejpam-6140	343	5	1.5603e-04	1.5603e-04	NUM
ejpam-6140	343	6	2.0017	2.0017	NUM
ejpam-6140	343	7	1/160	1/160	NUM
ejpam-6140	343	8	4	4	NUM
ejpam-6140	343	9	1.4065e-05	1.4065e-05	NUM
ejpam-6140	343	10	0.953267	0.953267	NUM
ejpam-6140	343	11	3.8765e-05	3.8765e-05	NUM
ejpam-6140	343	12	2.0090	2.0090	NUM
ejpam-6140	343	13	1/320	1/320	NUM
ejpam-6140	343	14	4	4	NUM
ejpam-6140	343	15	4.6714e-06	4.6714e-06	NUM
ejpam-6140	343	16	2.653295	2.653295	NUM
ejpam-6140	343	17	9.3936e-06	9.3936e-06	NUM
ejpam-6140	343	18	2.0450	2.0450	NUM
ejpam-6140	343	19	m.	m.	NOUN
ejpam-6140	343	20	i.	i.	PROPN
ejpam-6140	343	21	khalil	khalil	PROPN
ejpam-6140	343	22	et	et	PROPN
ejpam-6140	343	23	al	al	PROPN
ejpam-6140	343	24	.	.	PUNCT
ejpam-6140	343	25	/	/	SYM
ejpam-6140	343	26	eur	eur	PROPN
ejpam-6140	343	27	.	.	PUNCT
ejpam-6140	344	1	j.	j.	PROPN
ejpam-6140	344	2	pure	pure	PROPN
ejpam-6140	344	3	appl	appl	PROPN
ejpam-6140	344	4	.	.	PROPN
ejpam-6140	344	5	math	math	PROPN
ejpam-6140	344	6	,	,	PUNCT
ejpam-6140	344	7	18	18	NUM
ejpam-6140	344	8	(	(	PUNCT
ejpam-6140	344	9	3	3	NUM
ejpam-6140	344	10	)	)	PUNCT
ejpam-6140	344	11	(	(	PUNCT
ejpam-6140	344	12	2025	2025	NUM
ejpam-6140	344	13	)	)	PUNCT
ejpam-6140	344	14	,	,	PUNCT
ejpam-6140	344	15	6140	6140	NUM
ejpam-6140	344	16	14	14	NUM
ejpam-6140	344	17	of	of	ADP
ejpam-6140	344	18	17	17	NUM
ejpam-6140	344	19	table	table	NOUN
ejpam-6140	344	20	4	4	NUM
ejpam-6140	344	21	:	:	PUNCT
ejpam-6140	344	22	example	example	NOUN
ejpam-6140	344	23	2	2	NUM
ejpam-6140	344	24	,	,	PUNCT
ejpam-6140	344	25	c.n	c.n	PROPN
ejpam-6140	344	26	.	.	PROPN
ejpam-6140	344	27	scheme	scheme	NOUN
ejpam-6140	344	28	:	:	PUNCT
ejpam-6140	344	29	α	α	NOUN
ejpam-6140	344	30	=	=	SYM
ejpam-6140	344	31	2	2	NUM
ejpam-6140	344	32	h	h	NOUN
ejpam-6140	344	33	m	m	VERB
ejpam-6140	344	34	th	th	INTJ
ejpam-6140	344	35	cput	cput	ADJ
ejpam-6140	344	36	eh	eh	INTJ
ejpam-6140	344	37	sh	sh	PROPN
ejpam-6140	344	38	1/20	1/20	NUM
ejpam-6140	344	39	4	4	NUM
ejpam-6140	344	40	4.8891e-05	4.8891e-05	NUM
ejpam-6140	344	41	0.223913	0.223913	NUM
ejpam-6140	344	42	·	·	PUNCT
ejpam-6140	344	43	·	·	PUNCT
ejpam-6140	344	44	·	·	PUNCT
ejpam-6140	344	45	·	·	PUNCT
ejpam-6140	344	46	·	·	PUNCT
ejpam-6140	344	47	·	·	PUNCT
ejpam-6140	345	1	1/40	1/40	NUM
ejpam-6140	345	2	4	4	NUM
ejpam-6140	345	3	8.8974e-06	8.8974e-06	NUM
ejpam-6140	345	4	0.233469	0.233469	NUM
ejpam-6140	345	5	3.9994e-05	3.9994e-05	NUM
ejpam-6140	345	6	·	·	PUNCT
ejpam-6140	345	7	·	·	PUNCT
ejpam-6140	345	8	·	·	PUNCT
ejpam-6140	346	1	1/80	1/80	NUM
ejpam-6140	346	2	4	4	NUM
ejpam-6140	346	3	1.7888e-06	1.7888e-06	NUM
ejpam-6140	346	4	0.329078	0.329078	NUM
ejpam-6140	346	5	7.1086e-06	7.1086e-06	NUM
ejpam-6140	346	6	2.4921	2.4921	NUM
ejpam-6140	346	7	1/160	1/160	NUM
ejpam-6140	346	8	5	5	NUM
ejpam-6140	346	9	4.4920e-07	4.4920e-07	NUM
ejpam-6140	346	10	1.044031	1.044031	NUM
ejpam-6140	346	11	1.3396e-06	1.3396e-06	NUM
ejpam-6140	346	12	2.4078	2.4078	NUM
ejpam-6140	346	13	1/320	1/320	NUM
ejpam-6140	346	14	7	7	NUM
ejpam-6140	346	15	1.7424e-07	1.7424e-07	NUM
ejpam-6140	346	16	2.458527	2.458527	NUM
ejpam-6140	346	17	2.7496e-07	2.7496e-07	NUM
ejpam-6140	346	18	2.2845	2.2845	NUM
ejpam-6140	346	19	figure	figure	NOUN
ejpam-6140	346	20	1	1	NUM
ejpam-6140	346	21	:	:	PUNCT
ejpam-6140	346	22	for	for	ADP
ejpam-6140	346	23	example	example	NOUN
ejpam-6140	346	24	1	1	NUM
ejpam-6140	346	25	,	,	PUNCT
ejpam-6140	346	26	(	(	PUNCT
ejpam-6140	346	27	nbu	nbu	NOUN
ejpam-6140	346	28	)	)	PUNCT
ejpam-6140	346	29	solution	solution	NOUN
ejpam-6140	346	30	evolution	evolution	NOUN
ejpam-6140	346	31	over	over	ADP
ejpam-6140	346	32	time	time	NOUN
ejpam-6140	346	33	using	use	VERB
ejpam-6140	346	34	c.n	c.n	PROPN
ejpam-6140	346	35	.	.	PROPN
ejpam-6140	346	36	scheme	scheme	NOUN
ejpam-6140	346	37	,	,	PUNCT
ejpam-6140	346	38	with	with	ADP
ejpam-6140	346	39	h	h	NOUN
ejpam-6140	346	40	=	=	SYM
ejpam-6140	346	41	320	320	NUM
ejpam-6140	346	42	,	,	PUNCT
ejpam-6140	346	43	α	α	NOUN
ejpam-6140	346	44	=	=	SYM
ejpam-6140	346	45	2	2	X
ejpam-6140	346	46	.	.	X
ejpam-6140	346	47	figure	figure	NOUN
ejpam-6140	346	48	2	2	NUM
ejpam-6140	346	49	:	:	PUNCT
ejpam-6140	346	50	for	for	ADP
ejpam-6140	346	51	example	example	NOUN
ejpam-6140	346	52	2	2	NUM
ejpam-6140	346	53	,	,	PUNCT
ejpam-6140	346	54	(	(	PUNCT
ejpam-6140	346	55	nbu	nbu	NOUN
ejpam-6140	346	56	)	)	PUNCT
ejpam-6140	346	57	solution	solution	NOUN
ejpam-6140	346	58	evolution	evolution	NOUN
ejpam-6140	346	59	over	over	ADP
ejpam-6140	346	60	time	time	NOUN
ejpam-6140	346	61	using	use	VERB
ejpam-6140	346	62	c.n	c.n	PROPN
ejpam-6140	346	63	.	.	PROPN
ejpam-6140	346	64	scheme	scheme	NOUN
ejpam-6140	346	65	,	,	PUNCT
ejpam-6140	346	66	with	with	ADP
ejpam-6140	346	67	h	h	NOUN
ejpam-6140	346	68	=	=	SYM
ejpam-6140	346	69	320	320	NUM
ejpam-6140	346	70	,	,	PUNCT
ejpam-6140	346	71	α	α	NOUN
ejpam-6140	346	72	=	=	SYM
ejpam-6140	346	73	2	2	NUM
ejpam-6140	346	74	.	.	NOUN
ejpam-6140	346	75	4.2	4.2	NUM
ejpam-6140	346	76	.	.	PUNCT
ejpam-6140	346	77	results	result	NOUN
ejpam-6140	346	78	and	and	CCONJ
ejpam-6140	346	79	discussion	discussion	NOUN
ejpam-6140	346	80	in	in	ADP
ejpam-6140	346	81	tables	table	NOUN
ejpam-6140	346	82	1	1	NUM
ejpam-6140	346	83	-	-	SYM
ejpam-6140	346	84	4	4	NUM
ejpam-6140	346	85	and	and	CCONJ
ejpam-6140	346	86	figures	figure	NOUN
ejpam-6140	346	87	1	1	NUM
ejpam-6140	346	88	-	-	SYM
ejpam-6140	346	89	2	2	NUM
ejpam-6140	346	90	,	,	PUNCT
ejpam-6140	346	91	the	the	DET
ejpam-6140	346	92	following	follow	VERB
ejpam-6140	346	93	observations	observation	NOUN
ejpam-6140	346	94	can	can	AUX
ejpam-6140	346	95	be	be	AUX
ejpam-6140	346	96	made	make	VERB
ejpam-6140	346	97	:	:	PUNCT
ejpam-6140	346	98	firstly	firstly	ADV
ejpam-6140	346	99	,	,	PUNCT
ejpam-6140	346	100	the	the	DET
ejpam-6140	346	101	(	(	PUNCT
ejpam-6140	346	102	nbu	nbu	NOUN
ejpam-6140	346	103	)	)	PUNCT
ejpam-6140	346	104	simultaneously	simultaneously	ADV
ejpam-6140	346	105	occurs	occur	VERB
ejpam-6140	346	106	near	near	ADP
ejpam-6140	346	107	the	the	DET
ejpam-6140	346	108	center	center	NOUN
ejpam-6140	346	109	point	point	NOUN
ejpam-6140	346	110	(	(	PUNCT
ejpam-6140	346	111	x	x	SYM
ejpam-6140	346	112	=	=	NUM
ejpam-6140	346	113	0.5	0.5	NUM
ejpam-6140	346	114	)	)	PUNCT
ejpam-6140	346	115	,	,	PUNCT
ejpam-6140	346	116	and	and	CCONJ
ejpam-6140	346	117	this	this	PRON
ejpam-6140	346	118	is	be	AUX
ejpam-6140	346	119	consistent	consistent	ADJ
ejpam-6140	346	120	with	with	ADP
ejpam-6140	346	121	the	the	DET
ejpam-6140	346	122	known	know	VERB
ejpam-6140	346	123	(	(	PUNCT
ejpam-6140	346	124	bu	bu	NOUN
ejpam-6140	346	125	)	)	PUNCT
ejpam-6140	346	126	results	result	NOUN
ejpam-6140	346	127	of	of	ADP
ejpam-6140	346	128	the	the	DET
ejpam-6140	346	129	problem	problem	NOUN
ejpam-6140	346	130	(	(	PUNCT
ejpam-6140	346	131	1	1	NUM
ejpam-6140	346	132	)	)	PUNCT
ejpam-6140	346	133	,	,	PUNCT
ejpam-6140	346	134	see	see	VERB
ejpam-6140	346	135	[	[	X
ejpam-6140	346	136	15	15	NUM
ejpam-6140	346	137	]	]	PUNCT
ejpam-6140	346	138	.	.	PUNCT
ejpam-6140	347	1	in	in	ADP
ejpam-6140	347	2	addition	addition	NOUN
ejpam-6140	347	3	,	,	PUNCT
ejpam-6140	347	4	when	when	SCONJ
ejpam-6140	347	5	the	the	DET
ejpam-6140	347	6	space	space	NOUN
ejpam-6140	347	7	steps	step	NOUN
ejpam-6140	347	8	are	be	AUX
ejpam-6140	347	9	refined	refine	VERB
ejpam-6140	347	10	,	,	PUNCT
ejpam-6140	347	11	the	the	DET
ejpam-6140	347	12	(	(	PUNCT
ejpam-6140	347	13	but	but	CCONJ
ejpam-6140	347	14	)	)	PUNCT
ejpam-6140	347	15	error	error	NOUN
ejpam-6140	347	16	bounds	bound	NOUN
ejpam-6140	347	17	decrease	decrease	VERB
ejpam-6140	347	18	.	.	PUNCT
ejpam-6140	348	1	in	in	ADP
ejpam-6140	348	2	other	other	ADJ
ejpam-6140	348	3	words	word	NOUN
ejpam-6140	348	4	,	,	PUNCT
ejpam-6140	348	5	the	the	DET
ejpam-6140	348	6	(	(	PUNCT
ejpam-6140	348	7	nbut	nbut	NOUN
ejpam-6140	348	8	)	)	PUNCT
ejpam-6140	348	9	sequence	sequence	NOUN
ejpam-6140	348	10	th	th	NOUN
ejpam-6140	348	11	is	be	AUX
ejpam-6140	348	12	convergent	convergent	NOUN
ejpam-6140	348	13	,	,	PUNCT
ejpam-6140	348	14	since	since	SCONJ
ejpam-6140	348	15	the	the	DET
ejpam-6140	348	16	space	space	NOUN
ejpam-6140	348	17	step	step	NOUN
ejpam-6140	348	18	is	be	AUX
ejpam-6140	348	19	close	close	ADJ
ejpam-6140	348	20	to	to	ADP
ejpam-6140	348	21	zero	zero	NUM
ejpam-6140	348	22	.	.	PUNCT
ejpam-6140	349	1	furthermore	furthermore	ADV
ejpam-6140	349	2	,	,	PUNCT
ejpam-6140	349	3	the	the	DET
ejpam-6140	349	4	numerical	numerical	ADJ
ejpam-6140	349	5	convergence	convergence	NOUN
ejpam-6140	349	6	order	order	NOUN
ejpam-6140	349	7	of	of	ADP
ejpam-6140	349	8	(	(	PUNCT
ejpam-6140	349	9	nbut	nbut	PROPN
ejpam-6140	349	10	)	)	PUNCT
ejpam-6140	349	11	is	be	AUX
ejpam-6140	349	12	o	o	X
ejpam-6140	349	13	(	(	PUNCT
ejpam-6140	349	14	hα+ϵ	hα+ϵ	NOUN
ejpam-6140	349	15	)	)	PUNCT
ejpam-6140	349	16	,	,	PUNCT
ejpam-6140	349	17	where	where	SCONJ
ejpam-6140	349	18	ϵ	ϵ	X
ejpam-6140	349	19	>	>	X
ejpam-6140	349	20	0.also	0.also	NUM
ejpam-6140	349	21	,	,	PUNCT
ejpam-6140	349	22	a	a	DET
ejpam-6140	349	23	large	large	ADJ
ejpam-6140	349	24	value	value	NOUN
ejpam-6140	349	25	of	of	ADP
ejpam-6140	349	26	α	α	PROPN
ejpam-6140	349	27	requires	require	VERB
ejpam-6140	349	28	many	many	ADJ
ejpam-6140	349	29	iterations	iteration	NOUN
ejpam-6140	349	30	to	to	PART
ejpam-6140	349	31	achieve	achieve	VERB
ejpam-6140	349	32	(	(	PUNCT
ejpam-6140	349	33	bu	bu	ADJ
ejpam-6140	349	34	)	)	PUNCT
ejpam-6140	349	35	compared	compare	VERB
ejpam-6140	349	36	to	to	ADP
ejpam-6140	349	37	a	a	DET
ejpam-6140	349	38	small	small	ADJ
ejpam-6140	349	39	value	value	NOUN
ejpam-6140	349	40	.	.	PUNCT
ejpam-6140	350	1	finally	finally	ADV
ejpam-6140	350	2	,	,	PUNCT
ejpam-6140	350	3	when	when	SCONJ
ejpam-6140	350	4	spatial	spatial	ADJ
ejpam-6140	350	5	steps	step	NOUN
ejpam-6140	350	6	are	be	AUX
ejpam-6140	350	7	refined	refine	VERB
ejpam-6140	350	8	,	,	PUNCT
ejpam-6140	350	9	one	one	PRON
ejpam-6140	350	10	can	can	AUX
ejpam-6140	350	11	see	see	VERB
ejpam-6140	350	12	an	an	DET
ejpam-6140	350	13	increase	increase	NOUN
ejpam-6140	350	14	in	in	ADP
ejpam-6140	350	15	cput	cput	ADJ
ejpam-6140	350	16	times	time	NOUN
ejpam-6140	350	17	.	.	PUNCT
ejpam-6140	351	1	m.	m.	PROPN
ejpam-6140	351	2	i.	i.	PROPN
ejpam-6140	351	3	khalil	khalil	PROPN
ejpam-6140	351	4	et	et	PROPN
ejpam-6140	351	5	al	al	PROPN
ejpam-6140	351	6	.	.	PUNCT
ejpam-6140	351	7	/	/	SYM
ejpam-6140	351	8	eur	eur	PROPN
ejpam-6140	351	9	.	.	PUNCT
ejpam-6140	352	1	j.	j.	PROPN
ejpam-6140	352	2	pure	pure	PROPN
ejpam-6140	352	3	appl	appl	PROPN
ejpam-6140	352	4	.	.	PROPN
ejpam-6140	352	5	math	math	PROPN
ejpam-6140	352	6	,	,	PUNCT
ejpam-6140	352	7	18	18	NUM
ejpam-6140	352	8	(	(	PUNCT
ejpam-6140	352	9	3	3	NUM
ejpam-6140	352	10	)	)	PUNCT
ejpam-6140	352	11	(	(	PUNCT
ejpam-6140	352	12	2025	2025	NUM
ejpam-6140	352	13	)	)	PUNCT
ejpam-6140	352	14	,	,	PUNCT
ejpam-6140	352	15	6140	6140	NUM
ejpam-6140	352	16	15	15	NUM
ejpam-6140	352	17	of	of	ADP
ejpam-6140	352	18	17	17	NUM
ejpam-6140	352	19	5	5	NUM
ejpam-6140	352	20	.	.	PUNCT
ejpam-6140	353	1	conclusions	conclusion	NOUN
ejpam-6140	353	2	this	this	DET
ejpam-6140	353	3	study	study	NOUN
ejpam-6140	353	4	employs	employ	VERB
ejpam-6140	353	5	the	the	DET
ejpam-6140	353	6	crank	crank	NOUN
ejpam-6140	353	7	-	-	PUNCT
ejpam-6140	353	8	nicolson	nicolson	PROPN
ejpam-6140	353	9	scheme	scheme	NOUN
ejpam-6140	353	10	with	with	ADP
ejpam-6140	353	11	a	a	DET
ejpam-6140	353	12	non	non	ADJ
ejpam-6140	353	13	-	-	ADJ
ejpam-6140	353	14	fixed	fixed	ADJ
ejpam-6140	353	15	time	time	NOUN
ejpam-6140	353	16	-	-	PUNCT
ejpam-6140	353	17	stepping	step	VERB
ejpam-6140	353	18	formula	formula	NOUN
ejpam-6140	353	19	to	to	PART
ejpam-6140	353	20	identify	identify	VERB
ejpam-6140	353	21	(	(	PUNCT
ejpam-6140	353	22	nbu	nbu	NOUN
ejpam-6140	353	23	)	)	PUNCT
ejpam-6140	353	24	solutions	solution	NOUN
ejpam-6140	353	25	and	and	CCONJ
ejpam-6140	353	26	estimate	estimate	VERB
ejpam-6140	353	27	the	the	DET
ejpam-6140	353	28	(	(	PUNCT
ejpam-6140	353	29	nbut	nbut	PROPN
ejpam-6140	353	30	)	)	PUNCT
ejpam-6140	353	31	for	for	ADP
ejpam-6140	353	32	a	a	DET
ejpam-6140	353	33	system	system	NOUN
ejpam-6140	353	34	of	of	ADP
ejpam-6140	353	35	two	two	NUM
ejpam-6140	353	36	coupled	couple	VERB
ejpam-6140	353	37	semi	semi	ADJ
ejpam-6140	353	38	-	-	ADJ
ejpam-6140	353	39	linear	linear	ADJ
ejpam-6140	353	40	heat	heat	NOUN
ejpam-6140	353	41	equations	equation	NOUN
ejpam-6140	353	42	subject	subject	ADJ
ejpam-6140	353	43	to	to	ADP
ejpam-6140	353	44	homogeneous	homogeneous	ADJ
ejpam-6140	353	45	dirichlet	dirichlet	PROPN
ejpam-6140	353	46	boundary	boundary	PROPN
ejpam-6140	353	47	conditions	condition	NOUN
ejpam-6140	353	48	.	.	PUNCT
ejpam-6140	354	1	the	the	DET
ejpam-6140	354	2	consistency	consistency	NOUN
ejpam-6140	354	3	,	,	PUNCT
ejpam-6140	354	4	stability	stability	NOUN
ejpam-6140	354	5	,	,	PUNCT
ejpam-6140	354	6	and	and	CCONJ
ejpam-6140	354	7	convergence	convergence	NOUN
ejpam-6140	354	8	properties	property	NOUN
ejpam-6140	354	9	of	of	ADP
ejpam-6140	354	10	the	the	DET
ejpam-6140	354	11	crank	crank	NOUN
ejpam-6140	354	12	-	-	PUNCT
ejpam-6140	354	13	nicolson	nicolson	PROPN
ejpam-6140	354	14	scheme	scheme	NOUN
ejpam-6140	354	15	are	be	AUX
ejpam-6140	354	16	rigorously	rigorously	ADV
ejpam-6140	354	17	examined	examine	VERB
ejpam-6140	354	18	.	.	PUNCT
ejpam-6140	355	1	to	to	PART
ejpam-6140	355	2	validate	validate	VERB
ejpam-6140	355	3	the	the	DET
ejpam-6140	355	4	theoretical	theoretical	ADJ
ejpam-6140	355	5	findings	finding	NOUN
ejpam-6140	355	6	and	and	CCONJ
ejpam-6140	355	7	determine	determine	VERB
ejpam-6140	355	8	the	the	DET
ejpam-6140	355	9	convergence	convergence	NOUN
ejpam-6140	355	10	rate	rate	NOUN
ejpam-6140	355	11	of	of	ADP
ejpam-6140	355	12	the	the	DET
ejpam-6140	355	13	nbut	nbut	NOUN
ejpam-6140	355	14	,	,	PUNCT
ejpam-6140	355	15	two	two	NUM
ejpam-6140	355	16	numerical	numerical	ADJ
ejpam-6140	355	17	experiments	experiment	NOUN
ejpam-6140	355	18	are	be	AUX
ejpam-6140	355	19	conducted	conduct	VERB
ejpam-6140	355	20	.	.	PUNCT
ejpam-6140	356	1	the	the	DET
ejpam-6140	356	2	numerical	numerical	ADJ
ejpam-6140	356	3	results	result	NOUN
ejpam-6140	356	4	,	,	PUNCT
ejpam-6140	356	5	presented	present	VERB
ejpam-6140	356	6	through	through	ADP
ejpam-6140	356	7	tables	table	NOUN
ejpam-6140	356	8	and	and	CCONJ
ejpam-6140	356	9	figures	figure	NOUN
ejpam-6140	356	10	,	,	PUNCT
ejpam-6140	356	11	demonstrate	demonstrate	VERB
ejpam-6140	356	12	that	that	SCONJ
ejpam-6140	356	13	the	the	DET
ejpam-6140	356	14	proposed	propose	VERB
ejpam-6140	356	15	method	method	NOUN
ejpam-6140	356	16	achieves	achieve	VERB
ejpam-6140	356	17	a	a	DET
ejpam-6140	356	18	high	high	ADJ
ejpam-6140	356	19	degree	degree	NOUN
ejpam-6140	356	20	of	of	ADP
ejpam-6140	356	21	convergence	convergence	NOUN
ejpam-6140	356	22	and	and	CCONJ
ejpam-6140	356	23	exhibits	exhibit	VERB
ejpam-6140	356	24	good	good	ADJ
ejpam-6140	356	25	computational	computational	ADJ
ejpam-6140	356	26	efficiency	efficiency	NOUN
ejpam-6140	356	27	.	.	PUNCT
ejpam-6140	357	1	future	future	ADJ
ejpam-6140	357	2	research	research	NOUN
ejpam-6140	357	3	directions	direction	NOUN
ejpam-6140	357	4	may	may	AUX
ejpam-6140	357	5	include	include	VERB
ejpam-6140	357	6	exploring	explore	VERB
ejpam-6140	357	7	special	special	ADJ
ejpam-6140	357	8	approximations	approximation	NOUN
ejpam-6140	357	9	for	for	ADP
ejpam-6140	357	10	nonlinear	nonlinear	ADJ
ejpam-6140	357	11	terms	term	NOUN
ejpam-6140	357	12	in	in	ADP
ejpam-6140	357	13	the	the	DET
ejpam-6140	357	14	system	system	NOUN
ejpam-6140	357	15	to	to	PART
ejpam-6140	357	16	enhance	enhance	VERB
ejpam-6140	357	17	the	the	DET
ejpam-6140	357	18	accuracy	accuracy	NOUN
ejpam-6140	357	19	of	of	ADP
ejpam-6140	357	20	the	the	DET
ejpam-6140	357	21	scheme	scheme	NOUN
ejpam-6140	357	22	,	,	PUNCT
ejpam-6140	357	23	potentially	potentially	ADV
ejpam-6140	357	24	achieving	achieve	VERB
ejpam-6140	357	25	second	second	ADJ
ejpam-6140	357	26	-	-	PUNCT
ejpam-6140	357	27	order	order	NOUN
ejpam-6140	357	28	truncation	truncation	NOUN
ejpam-6140	357	29	errors	error	NOUN
ejpam-6140	357	30	in	in	ADP
ejpam-6140	357	31	both	both	CCONJ
ejpam-6140	357	32	temporal	temporal	ADJ
ejpam-6140	357	33	and	and	CCONJ
ejpam-6140	357	34	spatial	spatial	ADJ
ejpam-6140	357	35	dimensions	dimension	NOUN
ejpam-6140	357	36	.	.	PUNCT
ejpam-6140	358	1	references	reference	NOUN
ejpam-6140	358	2	[	[	X
ejpam-6140	358	3	1	1	X
ejpam-6140	358	4	]	]	PUNCT
ejpam-6140	358	5	maan	maan	PROPN
ejpam-6140	358	6	a	a	DET
ejpam-6140	358	7	rasheed	rasheed	NOUN
ejpam-6140	358	8	,	,	PUNCT
ejpam-6140	358	9	sean	sean	PROPN
ejpam-6140	358	10	laverty	laverty	NOUN
ejpam-6140	358	11	,	,	PUNCT
ejpam-6140	358	12	and	and	CCONJ
ejpam-6140	358	13	brittany	brittany	PROPN
ejpam-6140	358	14	bannish	bannish	PROPN
ejpam-6140	358	15	.	.	PUNCT
ejpam-6140	359	1	numerical	numerical	ADJ
ejpam-6140	359	2	solutions	solution	NOUN
ejpam-6140	359	3	of	of	ADP
ejpam-6140	359	4	a	a	DET
ejpam-6140	359	5	linear	linear	ADJ
ejpam-6140	359	6	age	age	NOUN
ejpam-6140	359	7	-	-	PUNCT
ejpam-6140	359	8	structured	structure	VERB
ejpam-6140	359	9	population	population	NOUN
ejpam-6140	359	10	model	model	NOUN
ejpam-6140	359	11	.	.	PUNCT
ejpam-6140	360	1	in	in	ADP
ejpam-6140	360	2	aip	aip	PROPN
ejpam-6140	360	3	conference	conference	NOUN
ejpam-6140	360	4	proceedings	proceeding	NOUN
ejpam-6140	360	5	,	,	PUNCT
ejpam-6140	360	6	volume	volume	NOUN
ejpam-6140	360	7	2096	2096	NUM
ejpam-6140	360	8	.	.	PUNCT
ejpam-6140	361	1	aip	aip	PROPN
ejpam-6140	361	2	publishing	publishing	PROPN
ejpam-6140	361	3	,	,	PUNCT
ejpam-6140	361	4	2019	2019	NUM
ejpam-6140	361	5	.	.	PUNCT
ejpam-6140	362	1	[	[	X
ejpam-6140	362	2	2	2	X
ejpam-6140	362	3	]	]	PUNCT
ejpam-6140	362	4	raheam	raheam	NOUN
ejpam-6140	362	5	al	al	PROPN
ejpam-6140	362	6	-	-	PUNCT
ejpam-6140	362	7	saphory	saphory	PROPN
ejpam-6140	362	8	,	,	PUNCT
ejpam-6140	362	9	zinah	zinah	PROPN
ejpam-6140	362	10	khalid	khalid	PROPN
ejpam-6140	362	11	,	,	PUNCT
ejpam-6140	362	12	and	and	CCONJ
ejpam-6140	362	13	abdelhaq	abdelhaq	PROPN
ejpam-6140	362	14	el	el	PROPN
ejpam-6140	362	15	jai	jai	PROPN
ejpam-6140	362	16	.	.	PUNCT
ejpam-6140	363	1	regional	regional	ADJ
ejpam-6140	363	2	boundary	boundary	ADJ
ejpam-6140	363	3	gradient	gradient	NOUN
ejpam-6140	363	4	closed	closed	ADJ
ejpam-6140	363	5	loop	loop	NOUN
ejpam-6140	363	6	control	control	NOUN
ejpam-6140	363	7	system	system	NOUN
ejpam-6140	363	8	and	and	CCONJ
ejpam-6140	363	9	γ	γ	NOUN
ejpam-6140	363	10	*	*	ADJ
ejpam-6140	363	11	agfo	agfo	NOUN
ejpam-6140	363	12	-	-	PUNCT
ejpam-6140	363	13	observer	observer	NOUN
ejpam-6140	363	14	.	.	PUNCT
ejpam-6140	364	1	in	in	ADP
ejpam-6140	364	2	journal	journal	PROPN
ejpam-6140	364	3	of	of	ADP
ejpam-6140	364	4	physics	physics	PROPN
ejpam-6140	364	5	:	:	PUNCT
ejpam-6140	364	6	conference	conference	NOUN
ejpam-6140	364	7	series	series	NOUN
ejpam-6140	364	8	,	,	PUNCT
ejpam-6140	364	9	volume	volume	NOUN
ejpam-6140	364	10	1664	1664	NUM
ejpam-6140	364	11	,	,	PUNCT
ejpam-6140	364	12	page	page	NOUN
ejpam-6140	364	13	012061	012061	NUM
ejpam-6140	364	14	.	.	PUNCT
ejpam-6140	365	1	iop	iop	PROPN
ejpam-6140	365	2	publishing	publishing	NOUN
ejpam-6140	365	3	,	,	PUNCT
ejpam-6140	365	4	2020	2020	NUM
ejpam-6140	365	5	.	.	PUNCT
ejpam-6140	366	1	[	[	X
ejpam-6140	366	2	3	3	NUM
ejpam-6140	366	3	]	]	X
ejpam-6140	366	4	soraya	soraya	PROPN
ejpam-6140	366	5	rekkab	rekkab	PROPN
ejpam-6140	366	6	,	,	PUNCT
ejpam-6140	366	7	samir	samir	PROPN
ejpam-6140	366	8	benhadid	benhadid	PROPN
ejpam-6140	366	9	,	,	PUNCT
ejpam-6140	366	10	and	and	CCONJ
ejpam-6140	366	11	raheam	raheam	VERB
ejpam-6140	366	12	al	al	PROPN
ejpam-6140	366	13	-	-	PUNCT
ejpam-6140	366	14	saphory	saphory	NOUN
ejpam-6140	366	15	.	.	PUNCT
ejpam-6140	367	1	an	an	DET
ejpam-6140	367	2	asymptotic	asymptotic	ADJ
ejpam-6140	367	3	analysis	analysis	NOUN
ejpam-6140	367	4	of	of	ADP
ejpam-6140	367	5	the	the	DET
ejpam-6140	367	6	gradient	gradient	ADJ
ejpam-6140	367	7	remediability	remediability	NOUN
ejpam-6140	367	8	problem	problem	NOUN
ejpam-6140	367	9	for	for	ADP
ejpam-6140	367	10	disturbed	disturbed	ADJ
ejpam-6140	367	11	distributed	distribute	VERB
ejpam-6140	367	12	linear	linear	NOUN
ejpam-6140	367	13	systems	system	NOUN
ejpam-6140	367	14	.	.	PUNCT
ejpam-6140	368	1	baghdad	baghdad	PROPN
ejpam-6140	368	2	science	science	PROPN
ejpam-6140	368	3	journal	journal	PROPN
ejpam-6140	368	4	,	,	PUNCT
ejpam-6140	368	5	19(6	19(6	NUM
ejpam-6140	368	6	(	(	PUNCT
ejpam-6140	368	7	suppl.)):1623–1623	suppl.)):1623–1623	PROPN
ejpam-6140	368	8	,	,	PUNCT
ejpam-6140	368	9	2022	2022	NUM
ejpam-6140	368	10	.	.	PUNCT
ejpam-6140	369	1	[	[	X
ejpam-6140	369	2	4	4	NUM
ejpam-6140	369	3	]	]	PUNCT
ejpam-6140	369	4	avner	avner	PROPN
ejpam-6140	369	5	friedman	friedman	PROPN
ejpam-6140	369	6	and	and	CCONJ
ejpam-6140	369	7	bryce	bryce	PROPN
ejpam-6140	369	8	mcleod	mcleod	PROPN
ejpam-6140	369	9	.	.	PUNCT
ejpam-6140	370	1	blow	blow	PROPN
ejpam-6140	370	2	-	-	PUNCT
ejpam-6140	370	3	up	up	NOUN
ejpam-6140	370	4	of	of	ADP
ejpam-6140	370	5	positive	positive	ADJ
ejpam-6140	370	6	solutions	solution	NOUN
ejpam-6140	370	7	of	of	ADP
ejpam-6140	370	8	semilinear	semilinear	ADJ
ejpam-6140	370	9	heat	heat	NOUN
ejpam-6140	370	10	equations	equation	NOUN
ejpam-6140	370	11	.	.	PUNCT
ejpam-6140	371	1	indiana	indiana	PROPN
ejpam-6140	371	2	university	university	PROPN
ejpam-6140	371	3	mathematics	mathematics	PROPN
ejpam-6140	371	4	journal	journal	PROPN
ejpam-6140	371	5	,	,	PUNCT
ejpam-6140	371	6	34(2):425–447	34(2):425–447	PROPN
ejpam-6140	371	7	,	,	PUNCT
ejpam-6140	371	8	1985	1985	NUM
ejpam-6140	371	9	.	.	PUNCT
ejpam-6140	372	1	[	[	X
ejpam-6140	372	2	5	5	NUM
ejpam-6140	372	3	]	]	SYM
ejpam-6140	372	4	stanley	stanley	PROPN
ejpam-6140	372	5	kaplan	kaplan	PROPN
ejpam-6140	372	6	.	.	PUNCT
ejpam-6140	373	1	on	on	ADP
ejpam-6140	373	2	the	the	DET
ejpam-6140	373	3	growth	growth	NOUN
ejpam-6140	373	4	of	of	ADP
ejpam-6140	373	5	solutions	solution	NOUN
ejpam-6140	373	6	of	of	ADP
ejpam-6140	373	7	quasi	quasi	ADJ
ejpam-6140	373	8	-	-	ADJ
ejpam-6140	373	9	linear	linear	ADJ
ejpam-6140	373	10	parabolic	parabolic	ADJ
ejpam-6140	373	11	equations	equation	NOUN
ejpam-6140	373	12	.	.	PUNCT
ejpam-6140	374	1	communications	communication	NOUN
ejpam-6140	374	2	on	on	ADP
ejpam-6140	374	3	pure	pure	ADJ
ejpam-6140	374	4	and	and	CCONJ
ejpam-6140	374	5	applied	applied	ADJ
ejpam-6140	374	6	mathematics	mathematic	NOUN
ejpam-6140	374	7	,	,	PUNCT
ejpam-6140	374	8	16(3):305–330	16(3):305–330	PROPN
ejpam-6140	374	9	,	,	PUNCT
ejpam-6140	374	10	1963	1963	NUM
ejpam-6140	374	11	.	.	PUNCT
ejpam-6140	375	1	[	[	X
ejpam-6140	375	2	6	6	NUM
ejpam-6140	375	3	]	]	SYM
ejpam-6140	375	4	yuzhu	yuzhu	PROPN
ejpam-6140	375	5	han	han	PROPN
ejpam-6140	375	6	.	.	PUNCT
ejpam-6140	375	7	blow	blow	NOUN
ejpam-6140	375	8	-	-	PUNCT
ejpam-6140	375	9	up	up	NOUN
ejpam-6140	375	10	at	at	ADP
ejpam-6140	375	11	infinity	infinity	NOUN
ejpam-6140	375	12	of	of	ADP
ejpam-6140	375	13	solutions	solution	NOUN
ejpam-6140	375	14	to	to	ADP
ejpam-6140	375	15	a	a	DET
ejpam-6140	375	16	semilinear	semilinear	ADJ
ejpam-6140	375	17	heat	heat	NOUN
ejpam-6140	375	18	equation	equation	NOUN
ejpam-6140	375	19	with	with	ADP
ejpam-6140	375	20	logarithmic	logarithmic	ADJ
ejpam-6140	375	21	nonlinearity	nonlinearity	NOUN
ejpam-6140	375	22	.	.	PUNCT
ejpam-6140	376	1	journal	journal	PROPN
ejpam-6140	376	2	of	of	ADP
ejpam-6140	376	3	mathematical	mathematical	ADJ
ejpam-6140	376	4	analysis	analysis	NOUN
ejpam-6140	376	5	and	and	CCONJ
ejpam-6140	376	6	applications	application	NOUN
ejpam-6140	376	7	,	,	PUNCT
ejpam-6140	376	8	474(1):513	474(1):513	NUM
ejpam-6140	376	9	–	–	PUNCT
ejpam-6140	376	10	517	517	NUM
ejpam-6140	376	11	,	,	PUNCT
ejpam-6140	376	12	2019	2019	NUM
ejpam-6140	376	13	.	.	PUNCT
ejpam-6140	377	1	[	[	X
ejpam-6140	377	2	7	7	X
ejpam-6140	377	3	]	]	X
ejpam-6140	377	4	maan	maan	PROPN
ejpam-6140	377	5	a	a	DET
ejpam-6140	377	6	rasheed	rasheed	NOUN
ejpam-6140	377	7	,	,	PUNCT
ejpam-6140	377	8	raad	raad	PROPN
ejpam-6140	377	9	awad	awad	PROPN
ejpam-6140	377	10	hameed	hameed	PROPN
ejpam-6140	377	11	,	,	PUNCT
ejpam-6140	377	12	amal	amal	PROPN
ejpam-6140	377	13	nouman	nouman	PROPN
ejpam-6140	377	14	khalaf	khalaf	PROPN
ejpam-6140	377	15	,	,	PUNCT
ejpam-6140	377	16	and	and	CCONJ
ejpam-6140	377	17	hiba	hiba	PROPN
ejpam-6140	377	18	ali	ali	PROPN
ejpam-6140	377	19	kareem	kareem	PROPN
ejpam-6140	377	20	.	.	PUNCT
ejpam-6140	378	1	estimating	estimate	VERB
ejpam-6140	378	2	the	the	DET
ejpam-6140	378	3	blow	blow	NOUN
ejpam-6140	378	4	-	-	PUNCT
ejpam-6140	378	5	up	up	ADP
ejpam-6140	378	6	time	time	NOUN
ejpam-6140	378	7	for	for	ADP
ejpam-6140	378	8	chipot	chipot	ADJ
ejpam-6140	378	9	-	-	PUNCT
ejpam-6140	378	10	weissler	weissler	ADJ
ejpam-6140	378	11	equation	equation	NOUN
ejpam-6140	378	12	using	use	VERB
ejpam-6140	378	13	crank	crank	NOUN
ejpam-6140	378	14	-	-	PUNCT
ejpam-6140	378	15	nicolson	nicolson	PROPN
ejpam-6140	378	16	method	method	PROPN
ejpam-6140	378	17	.	.	PUNCT
ejpam-6140	379	1	j.	j.	PROPN
ejpam-6140	379	2	appl	appl	PROPN
ejpam-6140	379	3	.	.	PROPN
ejpam-6140	379	4	math	math	PROPN
ejpam-6140	379	5	.	.	PUNCT
ejpam-6140	380	1	&	&	CCONJ
ejpam-6140	380	2	informatics	informatics	PROPN
ejpam-6140	380	3	vol	vol	NOUN
ejpam-6140	380	4	,	,	PUNCT
ejpam-6140	380	5	43(1):123–137	43(1):123–137	NUM
ejpam-6140	380	6	,	,	PUNCT
ejpam-6140	380	7	2025	2025	NUM
ejpam-6140	380	8	.	.	PUNCT
ejpam-6140	381	1	[	[	X
ejpam-6140	381	2	8	8	NUM
ejpam-6140	381	3	]	]	PUNCT
ejpam-6140	381	4	manar	manar	PROPN
ejpam-6140	381	5	khalil	khalil	PROPN
ejpam-6140	381	6	,	,	PUNCT
ejpam-6140	381	7	ishak	ishak	PROPN
ejpam-6140	381	8	hashim	hashim	PROPN
ejpam-6140	381	9	,	,	PUNCT
ejpam-6140	381	10	maan	maan	PROPN
ejpam-6140	381	11	rasheed	rasheed	PROPN
ejpam-6140	381	12	,	,	PUNCT
ejpam-6140	381	13	faieza	faieza	ADJ
ejpam-6140	381	14	samat	samat	NOUN
ejpam-6140	381	15	,	,	PUNCT
ejpam-6140	381	16	and	and	CCONJ
ejpam-6140	381	17	shaher	shaher	ADP
ejpam-6140	381	18	momani	momani	PROPN
ejpam-6140	381	19	.	.	PUNCT
ejpam-6140	381	20	numerical	numerical	PROPN
ejpam-6140	381	21	finite	finite	ADJ
ejpam-6140	381	22	-	-	PUNCT
ejpam-6140	381	23	difference	difference	ADJ
ejpam-6140	381	24	approximations	approximation	NOUN
ejpam-6140	381	25	of	of	ADP
ejpam-6140	381	26	a	a	DET
ejpam-6140	381	27	coupled	couple	VERB
ejpam-6140	381	28	reaction	reaction	NOUN
ejpam-6140	381	29	-	-	PUNCT
ejpam-6140	381	30	diffusion	diffusion	NOUN
ejpam-6140	381	31	system	system	NOUN
ejpam-6140	381	32	with	with	ADP
ejpam-6140	381	33	gradient	gradient	ADJ
ejpam-6140	381	34	terms	term	NOUN
ejpam-6140	381	35	.	.	PUNCT
ejpam-6140	382	1	european	european	ADJ
ejpam-6140	382	2	journal	journal	PROPN
ejpam-6140	382	3	of	of	ADP
ejpam-6140	382	4	pure	pure	ADJ
ejpam-6140	382	5	and	and	CCONJ
ejpam-6140	382	6	applied	applied	ADJ
ejpam-6140	382	7	mathematics	mathematic	NOUN
ejpam-6140	382	8	,	,	PUNCT
ejpam-6140	382	9	17(3):1516–1538	17(3):1516–1538	NUM
ejpam-6140	382	10	,	,	PUNCT
ejpam-6140	382	11	2024	2024	NUM
ejpam-6140	382	12	.	.	PUNCT
ejpam-6140	383	1	[	[	X
ejpam-6140	383	2	9	9	NUM
ejpam-6140	383	3	]	]	X
ejpam-6140	383	4	maan	maan	PROPN
ejpam-6140	383	5	a	a	DET
ejpam-6140	383	6	rasheed	rasheed	NOUN
ejpam-6140	383	7	.	.	PUNCT
ejpam-6140	383	8	blow	blow	VERB
ejpam-6140	383	9	-	-	PUNCT
ejpam-6140	383	10	up	up	ADP
ejpam-6140	383	11	properties	property	NOUN
ejpam-6140	383	12	of	of	ADP
ejpam-6140	383	13	a	a	DET
ejpam-6140	383	14	coupled	couple	VERB
ejpam-6140	383	15	system	system	NOUN
ejpam-6140	383	16	of	of	ADP
ejpam-6140	383	17	reaction	reaction	NOUN
ejpam-6140	383	18	-	-	PUNCT
ejpam-6140	383	19	diffusion	diffusion	NOUN
ejpam-6140	383	20	equations	equation	NOUN
ejpam-6140	383	21	.	.	PUNCT
ejpam-6140	384	1	iraqi	iraqi	ADJ
ejpam-6140	384	2	journal	journal	PROPN
ejpam-6140	384	3	of	of	ADP
ejpam-6140	384	4	science	science	NOUN
ejpam-6140	384	5	,	,	PUNCT
ejpam-6140	384	6	pages	page	NOUN
ejpam-6140	384	7	3052–3060	3052–3060	NUM
ejpam-6140	384	8	,	,	PUNCT
ejpam-6140	384	9	2021	2021	NUM
ejpam-6140	384	10	.	.	PUNCT
ejpam-6140	385	1	[	[	X
ejpam-6140	385	2	10	10	NUM
ejpam-6140	385	3	]	]	X
ejpam-6140	385	4	maan	maan	PROPN
ejpam-6140	385	5	a	a	DET
ejpam-6140	385	6	rasheed	rasheed	NOUN
ejpam-6140	385	7	.	.	PUNCT
ejpam-6140	386	1	on	on	ADP
ejpam-6140	386	2	blow	blow	NOUN
ejpam-6140	386	3	-	-	PUNCT
ejpam-6140	386	4	up	up	ADP
ejpam-6140	386	5	solutions	solution	NOUN
ejpam-6140	386	6	of	of	ADP
ejpam-6140	386	7	a	a	DET
ejpam-6140	386	8	parabolic	parabolic	ADJ
ejpam-6140	386	9	system	system	NOUN
ejpam-6140	386	10	coupled	couple	VERB
ejpam-6140	386	11	in	in	ADP
ejpam-6140	386	12	both	both	DET
ejpam-6140	386	13	equations	equation	NOUN
ejpam-6140	386	14	and	and	CCONJ
ejpam-6140	386	15	boundary	boundary	ADJ
ejpam-6140	386	16	conditions	condition	NOUN
ejpam-6140	386	17	.	.	PUNCT
ejpam-6140	387	1	baghdad	baghdad	PROPN
ejpam-6140	387	2	science	science	PROPN
ejpam-6140	387	3	journal	journal	PROPN
ejpam-6140	387	4	,	,	PUNCT
ejpam-6140	387	5	18(2):315–321	18(2):315–321	PROPN
ejpam-6140	387	6	,	,	PUNCT
ejpam-6140	387	7	2021	2021	NUM
ejpam-6140	387	8	.	.	PUNCT
ejpam-6140	388	1	m.	m.	NOUN
ejpam-6140	388	2	i.	i.	PROPN
ejpam-6140	388	3	khalil	khalil	PROPN
ejpam-6140	388	4	et	et	PROPN
ejpam-6140	388	5	al	al	PROPN
ejpam-6140	388	6	.	.	PUNCT
ejpam-6140	388	7	/	/	SYM
ejpam-6140	388	8	eur	eur	PROPN
ejpam-6140	388	9	.	.	PUNCT
ejpam-6140	389	1	j.	j.	PROPN
ejpam-6140	389	2	pure	pure	PROPN
ejpam-6140	389	3	appl	appl	PROPN
ejpam-6140	389	4	.	.	PROPN
ejpam-6140	389	5	math	math	PROPN
ejpam-6140	389	6	,	,	PUNCT
ejpam-6140	389	7	18	18	NUM
ejpam-6140	389	8	(	(	PUNCT
ejpam-6140	389	9	3	3	NUM
ejpam-6140	389	10	)	)	PUNCT
ejpam-6140	389	11	(	(	PUNCT
ejpam-6140	389	12	2025	2025	NUM
ejpam-6140	389	13	)	)	PUNCT
ejpam-6140	389	14	,	,	PUNCT
ejpam-6140	389	15	6140	6140	NUM
ejpam-6140	389	16	16	16	NUM
ejpam-6140	389	17	of	of	ADP
ejpam-6140	389	18	17	17	NUM
ejpam-6140	389	19	[	[	X
ejpam-6140	389	20	11	11	NUM
ejpam-6140	389	21	]	]	X
ejpam-6140	389	22	a.a	a.a	PROPN
ejpam-6140	389	23	.	.	PROPN
ejpam-6140	389	24	lacey	lacey	PROPN
ejpam-6140	389	25	.	.	PUNCT
ejpam-6140	390	1	diffusion	diffusion	NOUN
ejpam-6140	390	2	models	model	NOUN
ejpam-6140	390	3	with	with	ADP
ejpam-6140	390	4	blow	blow	NOUN
ejpam-6140	390	5	-	-	PUNCT
ejpam-6140	390	6	up	up	NOUN
ejpam-6140	390	7	.	.	PUNCT
ejpam-6140	391	1	journal	journal	NOUN
ejpam-6140	391	2	of	of	ADP
ejpam-6140	391	3	computational	computational	ADJ
ejpam-6140	391	4	and	and	CCONJ
ejpam-6140	391	5	applied	applied	ADJ
ejpam-6140	391	6	mathematics	mathematic	NOUN
ejpam-6140	391	7	,	,	PUNCT
ejpam-6140	391	8	97(1):39–49	97(1):39–49	NUM
ejpam-6140	391	9	,	,	PUNCT
ejpam-6140	391	10	1998	1998	NUM
ejpam-6140	391	11	.	.	PUNCT
ejpam-6140	392	1	[	[	X
ejpam-6140	392	2	12	12	NUM
ejpam-6140	392	3	]	]	X
ejpam-6140	392	4	olga	olga	PROPN
ejpam-6140	392	5	a	a	DET
ejpam-6140	392	6	ladyženskaja	ladyženskaja	PROPN
ejpam-6140	392	7	,	,	PUNCT
ejpam-6140	392	8	vsevolod	vsevolod	VERB
ejpam-6140	392	9	alekseevich	alekseevich	DET
ejpam-6140	392	10	solonnikov	solonnikov	PROPN
ejpam-6140	392	11	,	,	PUNCT
ejpam-6140	392	12	and	and	CCONJ
ejpam-6140	392	13	nina	nina	PROPN
ejpam-6140	392	14	n	n	PRON
ejpam-6140	392	15	ural’ceva	ural’ceva	VERB
ejpam-6140	392	16	.	.	PUNCT
ejpam-6140	393	1	linear	linear	ADJ
ejpam-6140	393	2	and	and	CCONJ
ejpam-6140	393	3	quasi	quasi	ADJ
ejpam-6140	393	4	-	-	ADJ
ejpam-6140	393	5	linear	linear	ADJ
ejpam-6140	393	6	equations	equation	NOUN
ejpam-6140	393	7	of	of	ADP
ejpam-6140	393	8	parabolic	parabolic	ADJ
ejpam-6140	393	9	type	type	NOUN
ejpam-6140	393	10	,	,	PUNCT
ejpam-6140	393	11	volume	volume	NOUN
ejpam-6140	393	12	23	23	NUM
ejpam-6140	393	13	.	.	PUNCT
ejpam-6140	394	1	american	american	PROPN
ejpam-6140	394	2	mathematical	mathematical	PROPN
ejpam-6140	394	3	soc	soc	PROPN
ejpam-6140	394	4	.	.	PUNCT
ejpam-6140	394	5	,	,	PUNCT
ejpam-6140	394	6	1988	1988	NUM
ejpam-6140	394	7	.	.	PUNCT
ejpam-6140	395	1	[	[	X
ejpam-6140	395	2	13	13	NUM
ejpam-6140	395	3	]	]	X
ejpam-6140	395	4	keng	keng	PROPN
ejpam-6140	395	5	deng	deng	PROPN
ejpam-6140	395	6	.	.	PUNCT
ejpam-6140	396	1	blow	blow	PROPN
ejpam-6140	396	2	-	-	PUNCT
ejpam-6140	396	3	up	up	ADP
ejpam-6140	396	4	rates	rate	NOUN
ejpam-6140	396	5	for	for	ADP
ejpam-6140	396	6	parabolic	parabolic	NOUN
ejpam-6140	396	7	systems	system	NOUN
ejpam-6140	396	8	.	.	PUNCT
ejpam-6140	397	1	zeitschrift	zeitschrift	NOUN
ejpam-6140	397	2	für	für	PROPN
ejpam-6140	397	3	angewandte	angewandte	PROPN
ejpam-6140	397	4	mathematik	mathematik	PROPN
ejpam-6140	397	5	und	und	PROPN
ejpam-6140	397	6	physik	physik	PROPN
ejpam-6140	397	7	zamp	zamp	PROPN
ejpam-6140	397	8	,	,	PUNCT
ejpam-6140	397	9	47:132–143	47:132–143	PROPN
ejpam-6140	397	10	,	,	PUNCT
ejpam-6140	397	11	1996	1996	NUM
ejpam-6140	397	12	.	.	PUNCT
ejpam-6140	398	1	[	[	X
ejpam-6140	398	2	14	14	NUM
ejpam-6140	398	3	]	]	X
ejpam-6140	398	4	monica	monica	PROPN
ejpam-6140	398	5	marras	marras	PROPN
ejpam-6140	398	6	,	,	PUNCT
ejpam-6140	398	7	s	s	PART
ejpam-6140	398	8	vernier	vernier	NOUN
ejpam-6140	398	9	-	-	PUNCT
ejpam-6140	398	10	piro	piro	PROPN
ejpam-6140	398	11	,	,	PUNCT
ejpam-6140	398	12	and	and	CCONJ
ejpam-6140	398	13	giuseppe	giuseppe	PROPN
ejpam-6140	398	14	viglialoro	viglialoro	PROPN
ejpam-6140	398	15	.	.	PUNCT
ejpam-6140	399	1	estimates	estimate	NOUN
ejpam-6140	399	2	from	from	ADP
ejpam-6140	399	3	below	below	ADP
ejpam-6140	399	4	of	of	ADP
ejpam-6140	399	5	blow	blow	NOUN
ejpam-6140	399	6	-	-	PUNCT
ejpam-6140	399	7	up	up	ADP
ejpam-6140	399	8	time	time	NOUN
ejpam-6140	399	9	in	in	ADP
ejpam-6140	399	10	a	a	DET
ejpam-6140	399	11	parabolic	parabolic	ADJ
ejpam-6140	399	12	system	system	NOUN
ejpam-6140	399	13	with	with	ADP
ejpam-6140	399	14	gradient	gradient	ADJ
ejpam-6140	399	15	term	term	NOUN
ejpam-6140	399	16	.	.	PUNCT
ejpam-6140	400	1	int	int	NOUN
ejpam-6140	400	2	.	.	PUNCT
ejpam-6140	401	1	j.	j.	PROPN
ejpam-6140	401	2	pure	pure	PROPN
ejpam-6140	401	3	appl	appl	PROPN
ejpam-6140	401	4	.	.	PROPN
ejpam-6140	401	5	math	math	PROPN
ejpam-6140	401	6	,	,	PUNCT
ejpam-6140	401	7	93(2):297–306	93(2):297–306	NOUN
ejpam-6140	401	8	,	,	PUNCT
ejpam-6140	401	9	2014	2014	NUM
ejpam-6140	401	10	.	.	PUNCT
ejpam-6140	402	1	[	[	X
ejpam-6140	402	2	15	15	NUM
ejpam-6140	402	3	]	]	X
ejpam-6140	402	4	avner	avner	PROPN
ejpam-6140	402	5	friedman	friedman	PROPN
ejpam-6140	402	6	and	and	CCONJ
ejpam-6140	402	7	yoshikazu	yoshikazu	NOUN
ejpam-6140	402	8	giga	giga	PROPN
ejpam-6140	402	9	.	.	PUNCT
ejpam-6140	403	1	a	a	DET
ejpam-6140	403	2	single	single	ADJ
ejpam-6140	403	3	point	point	NOUN
ejpam-6140	403	4	blow	blow	NOUN
ejpam-6140	403	5	-	-	PUNCT
ejpam-6140	403	6	up	up	NOUN
ejpam-6140	403	7	for	for	ADP
ejpam-6140	403	8	solutions	solution	NOUN
ejpam-6140	403	9	of	of	ADP
ejpam-6140	403	10	semilinear	semilinear	ADJ
ejpam-6140	403	11	parabolic	parabolic	PROPN
ejpam-6140	403	12	systems	system	NOUN
ejpam-6140	403	13	.	.	PUNCT
ejpam-6140	404	1	j.	j.	PROPN
ejpam-6140	404	2	fac	fac	PROPN
ejpam-6140	404	3	.	.	PUNCT
ejpam-6140	405	1	sci	sci	PROPN
ejpam-6140	405	2	.	.	PROPN
ejpam-6140	405	3	univ	univ	PROPN
ejpam-6140	405	4	.	.	PUNCT
ejpam-6140	406	1	tokyo	tokyo	PROPN
ejpam-6140	406	2	sect	sect	NOUN
ejpam-6140	406	3	.	.	PUNCT
ejpam-6140	407	1	ia	ia	PROPN
ejpam-6140	407	2	math	math	PROPN
ejpam-6140	407	3	,	,	PUNCT
ejpam-6140	407	4	34(1):65–79	34(1):65–79	ADV
ejpam-6140	407	5	,	,	PUNCT
ejpam-6140	407	6	1987	1987	NUM
ejpam-6140	407	7	.	.	PUNCT
ejpam-6140	408	1	[	[	X
ejpam-6140	408	2	16	16	NUM
ejpam-6140	408	3	]	]	PUNCT
ejpam-6140	408	4	v	v	ADP
ejpam-6140	408	5	galaktionov	galaktionov	PROPN
ejpam-6140	408	6	.	.	PUNCT
ejpam-6140	409	1	parabolic	parabolic	ADJ
ejpam-6140	409	2	system	system	NOUN
ejpam-6140	409	3	of	of	ADP
ejpam-6140	409	4	quasilinear	quasilinear	NOUN
ejpam-6140	409	5	equations	equation	NOUN
ejpam-6140	409	6	.	.	PUNCT
ejpam-6140	410	1	i.	i.	PROPN
ejpam-6140	410	2	differential	differential	PROPN
ejpam-6140	410	3	equat	equat	PROPN
ejpam-6140	410	4	.	.	PUNCT
ejpam-6140	410	5	,	,	PUNCT
ejpam-6140	410	6	19(12):1558–1574	19(12):1558–1574	NUM
ejpam-6140	410	7	,	,	PUNCT
ejpam-6140	410	8	1984	1984	NUM
ejpam-6140	410	9	.	.	PUNCT
ejpam-6140	411	1	[	[	X
ejpam-6140	411	2	17	17	NUM
ejpam-6140	411	3	]	]	X
ejpam-6140	411	4	zg	zg	PROPN
ejpam-6140	411	5	lin	lin	PROPN
ejpam-6140	411	6	,	,	PUNCT
ejpam-6140	411	7	ch	ch	PROPN
ejpam-6140	411	8	xie	xie	PROPN
ejpam-6140	411	9	,	,	PUNCT
ejpam-6140	411	10	and	and	CCONJ
ejpam-6140	411	11	mx	mx	PROPN
ejpam-6140	411	12	wang	wang	PROPN
ejpam-6140	411	13	.	.	PUNCT
ejpam-6140	412	1	the	the	DET
ejpam-6140	412	2	blow	blow	VERB
ejpam-6140	412	3	-	-	PUNCT
ejpam-6140	412	4	up	up	ADP
ejpam-6140	412	5	rate	rate	NOUN
ejpam-6140	412	6	of	of	ADP
ejpam-6140	412	7	positive	positive	ADJ
ejpam-6140	412	8	solutions	solution	NOUN
ejpam-6140	412	9	of	of	ADP
ejpam-6140	412	10	a	a	DET
ejpam-6140	412	11	parabolic	parabolic	ADJ
ejpam-6140	412	12	system	system	NOUN
ejpam-6140	412	13	.	.	PUNCT
ejpam-6140	413	1	northeast	northeast	ADJ
ejpam-6140	413	2	.	.	PUNCT
ejpam-6140	414	1	math	math	NOUN
ejpam-6140	414	2	.	.	PUNCT
ejpam-6140	415	1	j	j	PROPN
ejpam-6140	415	2	,	,	PUNCT
ejpam-6140	415	3	13:327–378	13:327–378	NUM
ejpam-6140	415	4	,	,	PUNCT
ejpam-6140	415	5	1997	1997	NUM
ejpam-6140	415	6	.	.	PUNCT
ejpam-6140	416	1	[	[	X
ejpam-6140	416	2	18	18	NUM
ejpam-6140	416	3	]	]	X
ejpam-6140	416	4	philippe	philippe	PROPN
ejpam-6140	416	5	souplet	souplet	NOUN
ejpam-6140	416	6	.	.	PUNCT
ejpam-6140	417	1	single	single	ADJ
ejpam-6140	417	2	-	-	PUNCT
ejpam-6140	417	3	point	point	NOUN
ejpam-6140	417	4	blow	blow	NOUN
ejpam-6140	417	5	-	-	PUNCT
ejpam-6140	417	6	up	up	NOUN
ejpam-6140	417	7	for	for	ADP
ejpam-6140	417	8	a	a	DET
ejpam-6140	417	9	semilinear	semilinear	ADJ
ejpam-6140	417	10	parabolic	parabolic	NOUN
ejpam-6140	417	11	system	system	NOUN
ejpam-6140	417	12	.	.	PUNCT
ejpam-6140	418	1	journal	journal	NOUN
ejpam-6140	418	2	of	of	ADP
ejpam-6140	418	3	the	the	DET
ejpam-6140	418	4	european	european	PROPN
ejpam-6140	418	5	mathematical	mathematical	PROPN
ejpam-6140	418	6	society	society	NOUN
ejpam-6140	418	7	,	,	PUNCT
ejpam-6140	418	8	11(1):169–188	11(1):169–188	NUM
ejpam-6140	418	9	,	,	PUNCT
ejpam-6140	418	10	2009	2009	NUM
ejpam-6140	418	11	.	.	PUNCT
ejpam-6140	419	1	[	[	X
ejpam-6140	419	2	19	19	NUM
ejpam-6140	419	3	]	]	PUNCT
ejpam-6140	419	4	sining	sin	VERB
ejpam-6140	419	5	zheng	zheng	PROPN
ejpam-6140	419	6	,	,	PUNCT
ejpam-6140	419	7	lizhong	lizhong	PROPN
ejpam-6140	419	8	zhao	zhao	PROPN
ejpam-6140	419	9	,	,	PUNCT
ejpam-6140	419	10	and	and	CCONJ
ejpam-6140	419	11	feng	feng	PROPN
ejpam-6140	419	12	chen	chen	PROPN
ejpam-6140	419	13	.	.	PUNCT
ejpam-6140	420	1	blow	blow	VERB
ejpam-6140	420	2	-	-	PUNCT
ejpam-6140	420	3	up	up	ADP
ejpam-6140	420	4	rates	rate	NOUN
ejpam-6140	420	5	in	in	ADP
ejpam-6140	420	6	a	a	DET
ejpam-6140	420	7	parabolic	parabolic	ADJ
ejpam-6140	420	8	system	system	NOUN
ejpam-6140	420	9	of	of	ADP
ejpam-6140	420	10	ignition	ignition	NOUN
ejpam-6140	420	11	model	model	NOUN
ejpam-6140	420	12	.	.	PUNCT
ejpam-6140	421	1	nonlinear	nonlinear	ADJ
ejpam-6140	421	2	analysis	analysis	NOUN
ejpam-6140	421	3	:	:	PUNCT
ejpam-6140	421	4	theory	theory	NOUN
ejpam-6140	421	5	,	,	PUNCT
ejpam-6140	421	6	methods	method	NOUN
ejpam-6140	421	7	&	&	CCONJ
ejpam-6140	421	8	applications	application	NOUN
ejpam-6140	421	9	,	,	PUNCT
ejpam-6140	421	10	51(4):663–672	51(4):663–672	NUM
ejpam-6140	421	11	,	,	PUNCT
ejpam-6140	421	12	2002	2002	NUM
ejpam-6140	421	13	.	.	PUNCT
ejpam-6140	422	1	[	[	X
ejpam-6140	422	2	20	20	NUM
ejpam-6140	422	3	]	]	X
ejpam-6140	422	4	luis	luis	PROPN
ejpam-6140	422	5	m	m	PROPN
ejpam-6140	422	6	abia	abia	PROPN
ejpam-6140	422	7	,	,	PUNCT
ejpam-6140	422	8	jc	jc	PROPN
ejpam-6140	422	9	lopez	lopez	PROPN
ejpam-6140	422	10	-	-	PUNCT
ejpam-6140	422	11	marcos	marcos	PROPN
ejpam-6140	422	12	,	,	PUNCT
ejpam-6140	422	13	and	and	CCONJ
ejpam-6140	422	14	julia	julia	PROPN
ejpam-6140	422	15	mart́ınez	mart́ınez	PROPN
ejpam-6140	422	16	.	.	PUNCT
ejpam-6140	423	1	blow	blow	NOUN
ejpam-6140	423	2	-	-	PUNCT
ejpam-6140	423	3	up	up	NOUN
ejpam-6140	423	4	for	for	ADP
ejpam-6140	423	5	semidiscretizations	semidiscretization	NOUN
ejpam-6140	423	6	of	of	ADP
ejpam-6140	423	7	reaction	reaction	NOUN
ejpam-6140	423	8	-	-	PUNCT
ejpam-6140	423	9	diffusion	diffusion	NOUN
ejpam-6140	423	10	equations	equation	NOUN
ejpam-6140	423	11	.	.	PUNCT
ejpam-6140	424	1	applied	apply	VERB
ejpam-6140	424	2	numerical	numerical	ADJ
ejpam-6140	424	3	mathematics	mathematic	NOUN
ejpam-6140	424	4	,	,	PUNCT
ejpam-6140	424	5	20(1	20(1	PROPN
ejpam-6140	424	6	-	-	PUNCT
ejpam-6140	424	7	2):145	2):145	NUM
ejpam-6140	424	8	–	–	PUNCT
ejpam-6140	424	9	156	156	NUM
ejpam-6140	424	10	,	,	PUNCT
ejpam-6140	424	11	1996	1996	NUM
ejpam-6140	424	12	.	.	PUNCT
ejpam-6140	425	1	[	[	X
ejpam-6140	425	2	21	21	NUM
ejpam-6140	425	3	]	]	X
ejpam-6140	425	4	maan	maan	PROPN
ejpam-6140	425	5	a	a	DET
ejpam-6140	425	6	rasheed	rasheed	NOUN
ejpam-6140	425	7	and	and	CCONJ
ejpam-6140	425	8	faez	faez	NOUN
ejpam-6140	425	9	n	n	PRON
ejpam-6140	425	10	ghaffoori	ghaffoori	NOUN
ejpam-6140	425	11	.	.	PUNCT
ejpam-6140	426	1	numerical	numerical	ADJ
ejpam-6140	426	2	blow	blow	PROPN
ejpam-6140	426	3	-	-	PUNCT
ejpam-6140	426	4	up	up	ADP
ejpam-6140	426	5	time	time	NOUN
ejpam-6140	426	6	and	and	CCONJ
ejpam-6140	426	7	growth	growth	NOUN
ejpam-6140	426	8	rate	rate	NOUN
ejpam-6140	426	9	of	of	ADP
ejpam-6140	426	10	a	a	DET
ejpam-6140	426	11	reaction	reaction	NOUN
ejpam-6140	426	12	-	-	PUNCT
ejpam-6140	426	13	diffusion	diffusion	NOUN
ejpam-6140	426	14	equation	equation	NOUN
ejpam-6140	426	15	.	.	PUNCT
ejpam-6140	427	1	italian	italian	ADJ
ejpam-6140	427	2	journal	journal	NOUN
ejpam-6140	427	3	of	of	ADP
ejpam-6140	427	4	pure	pure	ADJ
ejpam-6140	427	5	and	and	CCONJ
ejpam-6140	427	6	applied	applied	ADJ
ejpam-6140	427	7	mathematics	mathematic	NOUN
ejpam-6140	427	8	,	,	PUNCT
ejpam-6140	427	9	44:805–813	44:805–813	NUM
ejpam-6140	427	10	,	,	PUNCT
ejpam-6140	427	11	2020	2020	NUM
ejpam-6140	427	12	.	.	PUNCT
ejpam-6140	428	1	[	[	X
ejpam-6140	428	2	22	22	NUM
ejpam-6140	428	3	]	]	PUNCT
ejpam-6140	428	4	maan	maan	PROPN
ejpam-6140	428	5	a	a	DET
ejpam-6140	428	6	rasheed	rasheed	NOUN
ejpam-6140	428	7	,	,	PUNCT
ejpam-6140	428	8	raad	raad	PROPN
ejpam-6140	428	9	awad	awad	PROPN
ejpam-6140	428	10	hameed	hameed	PROPN
ejpam-6140	428	11	,	,	PUNCT
ejpam-6140	428	12	and	and	CCONJ
ejpam-6140	428	13	amal	amal	PROPN
ejpam-6140	428	14	nouman	nouman	PROPN
ejpam-6140	428	15	khalaf	khalaf	PROPN
ejpam-6140	428	16	.	.	PUNCT
ejpam-6140	429	1	numerical	numerical	PROPN
ejpam-6140	429	2	blowup	blowup	ADJ
ejpam-6140	429	3	time	time	NOUN
ejpam-6140	429	4	of	of	ADP
ejpam-6140	429	5	a	a	DET
ejpam-6140	429	6	one	one	NUM
ejpam-6140	429	7	-	-	PUNCT
ejpam-6140	429	8	dimensional	dimensional	ADJ
ejpam-6140	429	9	semilinear	semilinear	ADJ
ejpam-6140	429	10	parabolic	parabolic	NOUN
ejpam-6140	429	11	equation	equation	NOUN
ejpam-6140	429	12	with	with	ADP
ejpam-6140	429	13	a	a	DET
ejpam-6140	429	14	gradient	gradient	ADJ
ejpam-6140	429	15	term	term	NOUN
ejpam-6140	429	16	.	.	PUNCT
ejpam-6140	430	1	iraqi	iraqi	ADJ
ejpam-6140	430	2	journal	journal	PROPN
ejpam-6140	430	3	of	of	ADP
ejpam-6140	430	4	science	science	NOUN
ejpam-6140	430	5	,	,	PUNCT
ejpam-6140	430	6	pages	page	NOUN
ejpam-6140	430	7	354–364	354–364	NUM
ejpam-6140	430	8	,	,	PUNCT
ejpam-6140	430	9	2023	2023	NUM
ejpam-6140	430	10	.	.	PUNCT
ejpam-6140	431	1	[	[	X
ejpam-6140	431	2	23	23	NUM
ejpam-6140	431	3	]	]	X
ejpam-6140	431	4	weizhang	weizhang	PROPN
ejpam-6140	431	5	huang	huang	PROPN
ejpam-6140	431	6	,	,	PUNCT
ejpam-6140	431	7	jingtang	jingtang	PROPN
ejpam-6140	431	8	ma	ma	PROPN
ejpam-6140	431	9	,	,	PUNCT
ejpam-6140	431	10	and	and	CCONJ
ejpam-6140	431	11	robert	robert	PROPN
ejpam-6140	431	12	d	d	PROPN
ejpam-6140	431	13	russell	russell	PROPN
ejpam-6140	431	14	.	.	PUNCT
ejpam-6140	432	1	a	a	DET
ejpam-6140	432	2	study	study	NOUN
ejpam-6140	432	3	of	of	ADP
ejpam-6140	432	4	moving	move	VERB
ejpam-6140	432	5	mesh	mesh	NOUN
ejpam-6140	432	6	pde	pde	NOUN
ejpam-6140	432	7	methods	method	NOUN
ejpam-6140	432	8	for	for	ADP
ejpam-6140	432	9	numerical	numerical	ADJ
ejpam-6140	432	10	simulation	simulation	NOUN
ejpam-6140	432	11	of	of	ADP
ejpam-6140	432	12	blowup	blowup	NOUN
ejpam-6140	432	13	in	in	ADP
ejpam-6140	432	14	reaction	reaction	NOUN
ejpam-6140	432	15	diffusion	diffusion	NOUN
ejpam-6140	432	16	equations	equation	NOUN
ejpam-6140	432	17	.	.	PUNCT
ejpam-6140	433	1	journal	journal	NOUN
ejpam-6140	433	2	of	of	ADP
ejpam-6140	433	3	computational	computational	ADJ
ejpam-6140	433	4	physics	physics	NOUN
ejpam-6140	433	5	,	,	PUNCT
ejpam-6140	433	6	227(13):6532–6552	227(13):6532–6552	NUM
ejpam-6140	433	7	,	,	PUNCT
ejpam-6140	433	8	2008	2008	NUM
ejpam-6140	433	9	.	.	PUNCT
ejpam-6140	434	1	[	[	X
ejpam-6140	434	2	24	24	NUM
ejpam-6140	434	3	]	]	X
ejpam-6140	434	4	chien	chien	PROPN
ejpam-6140	434	5	-	-	PUNCT
ejpam-6140	434	6	hong	hong	PROPN
ejpam-6140	434	7	cho	cho	PROPN
ejpam-6140	434	8	and	and	CCONJ
ejpam-6140	434	9	hisashi	hisashi	PROPN
ejpam-6140	434	10	okamoto	okamoto	PROPN
ejpam-6140	434	11	.	.	PUNCT
ejpam-6140	435	1	finite	finite	ADJ
ejpam-6140	435	2	difference	difference	NOUN
ejpam-6140	435	3	schemes	scheme	NOUN
ejpam-6140	435	4	for	for	ADP
ejpam-6140	435	5	an	an	DET
ejpam-6140	435	6	axisymmetric	axisymmetric	ADJ
ejpam-6140	435	7	nonlinear	nonlinear	ADJ
ejpam-6140	435	8	heat	heat	NOUN
ejpam-6140	435	9	equation	equation	NOUN
ejpam-6140	435	10	with	with	ADP
ejpam-6140	435	11	blow	blow	NOUN
ejpam-6140	435	12	-	-	PUNCT
ejpam-6140	435	13	up	up	NOUN
ejpam-6140	435	14	.	.	PUNCT
ejpam-6140	436	1	electronic	electronic	ADJ
ejpam-6140	436	2	transactions	transaction	NOUN
ejpam-6140	436	3	on	on	ADP
ejpam-6140	436	4	numerical	numerical	ADJ
ejpam-6140	436	5	analysis	analysis	NOUN
ejpam-6140	436	6	,	,	PUNCT
ejpam-6140	436	7	52(2):391–415	52(2):391–415	NUM
ejpam-6140	436	8	,	,	PUNCT
ejpam-6140	436	9	2020	2020	NUM
ejpam-6140	436	10	.	.	PUNCT
ejpam-6140	437	1	[	[	X
ejpam-6140	437	2	25	25	NUM
ejpam-6140	437	3	]	]	X
ejpam-6140	437	4	chien	chien	PROPN
ejpam-6140	437	5	-	-	PUNCT
ejpam-6140	437	6	hong	hong	PROPN
ejpam-6140	437	7	cho	cho	PROPN
ejpam-6140	437	8	and	and	CCONJ
ejpam-6140	437	9	ying	ying	PROPN
ejpam-6140	437	10	-	-	PUNCT
ejpam-6140	437	11	jung	jung	PROPN
ejpam-6140	437	12	lu	lu	PROPN
ejpam-6140	437	13	.	.	PUNCT
ejpam-6140	438	1	on	on	ADP
ejpam-6140	438	2	the	the	DET
ejpam-6140	438	3	numerical	numerical	ADJ
ejpam-6140	438	4	solutions	solution	NOUN
ejpam-6140	438	5	for	for	ADP
ejpam-6140	438	6	a	a	DET
ejpam-6140	438	7	parabolic	parabolic	ADJ
ejpam-6140	438	8	system	system	NOUN
ejpam-6140	438	9	with	with	ADP
ejpam-6140	438	10	blow	blow	NOUN
ejpam-6140	438	11	-	-	PUNCT
ejpam-6140	438	12	up	up	NOUN
ejpam-6140	438	13	.	.	PUNCT
ejpam-6140	439	1	aims	aim	VERB
ejpam-6140	439	2	mathematics	mathematic	NOUN
ejpam-6140	439	3	,	,	PUNCT
ejpam-6140	439	4	6(11):11749–11777	6(11):11749–11777	NUM
ejpam-6140	439	5	,	,	PUNCT
ejpam-6140	439	6	2021	2021	NUM
ejpam-6140	439	7	.	.	PUNCT
ejpam-6140	440	1	[	[	X
ejpam-6140	440	2	26	26	NUM
ejpam-6140	440	3	]	]	PUNCT
ejpam-6140	440	4	manar	manar	PROPN
ejpam-6140	440	5	ismael	ismael	PROPN
ejpam-6140	440	6	,	,	PUNCT
ejpam-6140	440	7	ishak	ishak	PROPN
ejpam-6140	440	8	hashim	hashim	PROPN
ejpam-6140	440	9	,	,	PUNCT
ejpam-6140	440	10	maan	maan	PROPN
ejpam-6140	440	11	rasheed	rasheed	PROPN
ejpam-6140	440	12	,	,	PUNCT
ejpam-6140	440	13	and	and	CCONJ
ejpam-6140	440	14	eddie	eddie	PROPN
ejpam-6140	440	15	ismail	ismail	PROPN
ejpam-6140	440	16	.	.	PUNCT
ejpam-6140	441	1	numerical	numerical	PROPN
ejpam-6140	441	2	finite	finite	PROPN
ejpam-6140	441	3	difference	difference	NOUN
ejpam-6140	441	4	approximations	approximation	NOUN
ejpam-6140	441	5	of	of	ADP
ejpam-6140	441	6	a	a	DET
ejpam-6140	441	7	coupled	couple	VERB
ejpam-6140	441	8	parabolic	parabolic	NOUN
ejpam-6140	441	9	system	system	NOUN
ejpam-6140	441	10	with	with	ADP
ejpam-6140	441	11	blow	blow	NOUN
ejpam-6140	441	12	-	-	PUNCT
ejpam-6140	441	13	up	up	NOUN
ejpam-6140	441	14	.	.	PUNCT
ejpam-6140	442	1	journal	journal	NOUN
ejpam-6140	442	2	of	of	ADP
ejpam-6140	442	3	mathematics	mathematics	PROPN
ejpam-6140	442	4	and	and	CCONJ
ejpam-6140	442	5	computer	computer	NOUN
ejpam-6140	442	6	science	science	NOUN
ejpam-6140	442	7	,	,	PUNCT
ejpam-6140	442	8	32:387–407	32:387–407	PROPN
ejpam-6140	442	9	,	,	PUNCT
ejpam-6140	442	10	11	11	NUM
ejpam-6140	442	11	2023	2023	NUM
ejpam-6140	442	12	.	.	PUNCT
ejpam-6140	443	1	[	[	X
ejpam-6140	443	2	27	27	NUM
ejpam-6140	443	3	]	]	X
ejpam-6140	443	4	gordon	gordon	PROPN
ejpam-6140	443	5	d	d	PROPN
ejpam-6140	443	6	smith	smith	PROPN
ejpam-6140	443	7	.	.	PUNCT
ejpam-6140	444	1	numerical	numerical	ADJ
ejpam-6140	444	2	solution	solution	NOUN
ejpam-6140	444	3	of	of	ADP
ejpam-6140	444	4	partial	partial	ADJ
ejpam-6140	444	5	differential	differential	NOUN
ejpam-6140	444	6	equations	equation	NOUN
ejpam-6140	444	7	:	:	PUNCT
ejpam-6140	444	8	finite	finite	ADJ
ejpam-6140	444	9	difference	difference	NOUN
ejpam-6140	444	10	methods	method	NOUN
ejpam-6140	444	11	.	.	PUNCT
ejpam-6140	445	1	oxford	oxford	PROPN
ejpam-6140	445	2	university	university	PROPN
ejpam-6140	445	3	press	press	NOUN
ejpam-6140	445	4	,	,	PUNCT
ejpam-6140	445	5	1985	1985	NUM
ejpam-6140	445	6	.	.	PUNCT
ejpam-6140	446	1	m.	m.	PROPN
ejpam-6140	446	2	i.	i.	PROPN
ejpam-6140	446	3	khalil	khalil	PROPN
ejpam-6140	446	4	et	et	PROPN
ejpam-6140	446	5	al	al	PROPN
ejpam-6140	446	6	.	.	PUNCT
ejpam-6140	446	7	/	/	SYM
ejpam-6140	446	8	eur	eur	PROPN
ejpam-6140	446	9	.	.	PUNCT
ejpam-6140	447	1	j.	j.	PROPN
ejpam-6140	447	2	pure	pure	PROPN
ejpam-6140	447	3	appl	appl	PROPN
ejpam-6140	447	4	.	.	PROPN
ejpam-6140	447	5	math	math	PROPN
ejpam-6140	447	6	,	,	PUNCT
ejpam-6140	447	7	18	18	NUM
ejpam-6140	447	8	(	(	PUNCT
ejpam-6140	447	9	3	3	NUM
ejpam-6140	447	10	)	)	PUNCT
ejpam-6140	447	11	(	(	PUNCT
ejpam-6140	447	12	2025	2025	NUM
ejpam-6140	447	13	)	)	PUNCT
ejpam-6140	447	14	,	,	PUNCT
ejpam-6140	447	15	6140	6140	NUM
ejpam-6140	447	16	17	17	NUM
ejpam-6140	447	17	of	of	ADP
ejpam-6140	447	18	17	17	NUM
ejpam-6140	447	19	[	[	SYM
ejpam-6140	447	20	28	28	NUM
ejpam-6140	447	21	]	]	X
ejpam-6140	447	22	richard	richard	PROPN
ejpam-6140	447	23	varga	varga	PROPN
ejpam-6140	447	24	.	.	PUNCT
ejpam-6140	448	1	s.	s.	PROPN
ejpam-6140	448	2	1962	1962	NUM
ejpam-6140	448	3	matrix	matrix	NOUN
ejpam-6140	448	4	iterative	iterative	NOUN
ejpam-6140	448	5	analysis	analysis	NOUN
ejpam-6140	448	6	.	.	PUNCT
ejpam-6140	449	1	englewood	englewood	PROPN
ejpam-6140	449	2	cliffs	cliffs	PROPN
ejpam-6140	449	3	:	:	PUNCT
ejpam-6140	449	4	prenticeflall	prenticeflall	NOUN
ejpam-6140	449	5	,	,	PUNCT
ejpam-6140	449	6	1962	1962	NUM
ejpam-6140	449	7	.	.	PUNCT