id	sid	tid	token	lemma	pos
ejpam-6917	1	1	european	european	PROPN
ejpam-6917	1	2	journal	journal	PROPN
ejpam-6917	1	3	of	of	ADP
ejpam-6917	1	4	pure	pure	ADJ
ejpam-6917	1	5	and	and	CCONJ
ejpam-6917	1	6	applied	applied	ADJ
ejpam-6917	1	7	mathematics	mathematic	NOUN
ejpam-6917	1	8	2025	2025	NUM
ejpam-6917	1	9	,	,	PUNCT
ejpam-6917	1	10	vol	vol	NOUN
ejpam-6917	1	11	.	.	PROPN
ejpam-6917	1	12	18	18	NUM
ejpam-6917	1	13	,	,	PUNCT
ejpam-6917	1	14	issue	issue	NOUN
ejpam-6917	1	15	4	4	NUM
ejpam-6917	1	16	,	,	PUNCT
ejpam-6917	1	17	article	article	NOUN
ejpam-6917	1	18	number	number	NOUN
ejpam-6917	1	19	6917	6917	NUM
ejpam-6917	1	20	issn	issn	PROPN
ejpam-6917	1	21	1307	1307	NUM
ejpam-6917	1	22	-	-	SYM
ejpam-6917	1	23	5543	5543	NUM
ejpam-6917	1	24	–	–	PUNCT
ejpam-6917	1	25	ejpam.com	ejpam.com	X
ejpam-6917	1	26	published	publish	VERB
ejpam-6917	1	27	by	by	ADP
ejpam-6917	1	28	new	new	PROPN
ejpam-6917	1	29	york	york	PROPN
ejpam-6917	1	30	business	business	PROPN
ejpam-6917	1	31	global	global	PROPN
ejpam-6917	1	32	a	a	DET
ejpam-6917	1	33	linear	linear	ADJ
ejpam-6917	1	34	subdivision	subdivision	NOUN
ejpam-6917	1	35	scheme	scheme	NOUN
ejpam-6917	1	36	with	with	ADP
ejpam-6917	1	37	sixth	sixth	ADJ
ejpam-6917	1	38	-	-	PUNCT
ejpam-6917	1	39	order	order	NOUN
ejpam-6917	1	40	precision	precision	NOUN
ejpam-6917	1	41	and	and	CCONJ
ejpam-6917	1	42	c5	c5	PROPN
ejpam-6917	1	43	smoothness	smoothness	PROPN
ejpam-6917	1	44	fahad	fahad	VERB
ejpam-6917	1	45	sameer	sameer	PROPN
ejpam-6917	1	46	alshammari1,∗	alshammari1,∗	PROPN
ejpam-6917	1	47	,	,	PUNCT
ejpam-6917	1	48	pakeeza	pakeeza	ADV
ejpam-6917	1	49	ashraf2,∗	ashraf2,∗	ADJ
ejpam-6917	1	50	,	,	PUNCT
ejpam-6917	1	51	saba	saba	PROPN
ejpam-6917	1	52	mehmood2	mehmood2	PROPN
ejpam-6917	1	53	,	,	PUNCT
ejpam-6917	1	54	ali	ali	PROPN
ejpam-6917	1	55	akgul3,4,5,6,7	akgul3,4,5,6,7	PROPN
ejpam-6917	1	56	1	1	NUM
ejpam-6917	1	57	department	department	NOUN
ejpam-6917	1	58	of	of	ADP
ejpam-6917	1	59	mathematics	mathematic	NOUN
ejpam-6917	1	60	,	,	PUNCT
ejpam-6917	1	61	college	college	NOUN
ejpam-6917	1	62	of	of	ADP
ejpam-6917	1	63	science	science	NOUN
ejpam-6917	1	64	and	and	CCONJ
ejpam-6917	1	65	humanities	humanity	NOUN
ejpam-6917	1	66	in	in	ADP
ejpam-6917	1	67	alkharj	alkharj	NOUN
ejpam-6917	1	68	,	,	PUNCT
ejpam-6917	1	69	prince	prince	PROPN
ejpam-6917	1	70	sattam	sattam	PROPN
ejpam-6917	1	71	bin	bin	PROPN
ejpam-6917	1	72	abdulaziz	abdulaziz	PROPN
ejpam-6917	1	73	university	university	PROPN
ejpam-6917	1	74	,	,	PUNCT
ejpam-6917	1	75	al	al	PROPN
ejpam-6917	1	76	-	-	PUNCT
ejpam-6917	1	77	kharj	kharj	PROPN
ejpam-6917	1	78	,	,	PUNCT
ejpam-6917	1	79	saudi	saudi	PROPN
ejpam-6917	1	80	arabia	arabia	PROPN
ejpam-6917	1	81	2	2	NUM
ejpam-6917	1	82	department	department	NOUN
ejpam-6917	1	83	of	of	ADP
ejpam-6917	1	84	mathematics	mathematic	NOUN
ejpam-6917	1	85	,	,	PUNCT
ejpam-6917	1	86	government	government	NOUN
ejpam-6917	1	87	sadiq	sadiq	PROPN
ejpam-6917	1	88	college	college	PROPN
ejpam-6917	1	89	women	women	PROPN
ejpam-6917	1	90	university	university	PROPN
ejpam-6917	1	91	,	,	PUNCT
ejpam-6917	1	92	bahawalpur	bahawalpur	PROPN
ejpam-6917	1	93	,	,	PUNCT
ejpam-6917	1	94	pakistan	pakistan	PROPN
ejpam-6917	1	95	3	3	NUM
ejpam-6917	1	96	department	department	NOUN
ejpam-6917	1	97	of	of	ADP
ejpam-6917	1	98	electronics	electronic	NOUN
ejpam-6917	1	99	and	and	CCONJ
ejpam-6917	1	100	communication	communication	NOUN
ejpam-6917	1	101	engineering	engineering	NOUN
ejpam-6917	1	102	,	,	PUNCT
ejpam-6917	1	103	saveetha	saveetha	PROPN
ejpam-6917	1	104	school	school	PROPN
ejpam-6917	1	105	of	of	ADP
ejpam-6917	1	106	engineering	engineering	NOUN
ejpam-6917	1	107	,	,	PUNCT
ejpam-6917	1	108	simats	simat	NOUN
ejpam-6917	1	109	,	,	PUNCT
ejpam-6917	1	110	chennai	chennai	PROPN
ejpam-6917	1	111	,	,	PUNCT
ejpam-6917	1	112	tamilnadu	tamilnadu	NOUN
ejpam-6917	1	113	,	,	PUNCT
ejpam-6917	1	114	india	india	PROPN
ejpam-6917	1	115	4	4	NUM
ejpam-6917	1	116	department	department	NOUN
ejpam-6917	1	117	of	of	ADP
ejpam-6917	1	118	mathematics	mathematic	NOUN
ejpam-6917	1	119	,	,	PUNCT
ejpam-6917	1	120	art	art	NOUN
ejpam-6917	1	121	and	and	CCONJ
ejpam-6917	1	122	science	science	NOUN
ejpam-6917	1	123	faculty	faculty	NOUN
ejpam-6917	1	124	,	,	PUNCT
ejpam-6917	1	125	siirt	siirt	PROPN
ejpam-6917	1	126	university	university	NOUN
ejpam-6917	1	127	,	,	PUNCT
ejpam-6917	1	128	siirt	siirt	NOUN
ejpam-6917	1	129	,	,	PUNCT
ejpam-6917	1	130	turkey	turkey	PROPN
ejpam-6917	1	131	5	5	NUM
ejpam-6917	1	132	department	department	NOUN
ejpam-6917	1	133	of	of	ADP
ejpam-6917	1	134	computer	computer	NOUN
ejpam-6917	1	135	engineering	engineering	NOUN
ejpam-6917	1	136	,	,	PUNCT
ejpam-6917	1	137	biruni	biruni	PROPN
ejpam-6917	1	138	university	university	PROPN
ejpam-6917	1	139	,	,	PUNCT
ejpam-6917	1	140	topkapi	topkapi	PROPN
ejpam-6917	1	141	,	,	PUNCT
ejpam-6917	1	142	istanbul	istanbul	PROPN
ejpam-6917	1	143	,	,	PUNCT
ejpam-6917	1	144	turkey	turkey	NOUN
ejpam-6917	1	145	6	6	NUM
ejpam-6917	1	146	near	near	ADP
ejpam-6917	1	147	east	east	PROPN
ejpam-6917	1	148	university	university	PROPN
ejpam-6917	1	149	,	,	PUNCT
ejpam-6917	1	150	mathematics	mathematics	PROPN
ejpam-6917	1	151	research	research	NOUN
ejpam-6917	1	152	center	center	NOUN
ejpam-6917	1	153	,	,	PUNCT
ejpam-6917	1	154	department	department	NOUN
ejpam-6917	1	155	of	of	ADP
ejpam-6917	1	156	mathematics	mathematic	NOUN
ejpam-6917	1	157	,	,	PUNCT
ejpam-6917	1	158	near	near	ADP
ejpam-6917	1	159	east	east	PROPN
ejpam-6917	1	160	boulevard	boulevard	PROPN
ejpam-6917	1	161	,	,	PUNCT
ejpam-6917	1	162	nicosia	nicosia	PROPN
ejpam-6917	1	163	/mersin	/mersin	PROPN
ejpam-6917	1	164	10	10	NUM
ejpam-6917	1	165	,	,	PUNCT
ejpam-6917	1	166	turkey	turkey	NOUN
ejpam-6917	1	167	7	7	NUM
ejpam-6917	1	168	applied	apply	VERB
ejpam-6917	1	169	science	science	NOUN
ejpam-6917	1	170	research	research	NOUN
ejpam-6917	1	171	center	center	NOUN
ejpam-6917	1	172	,	,	PUNCT
ejpam-6917	1	173	applied	apply	VERB
ejpam-6917	1	174	science	science	NOUN
ejpam-6917	1	175	private	private	ADJ
ejpam-6917	1	176	university	university	NOUN
ejpam-6917	1	177	,	,	PUNCT
ejpam-6917	1	178	amman	amman	PROPN
ejpam-6917	1	179	,	,	PUNCT
ejpam-6917	1	180	jordan	jordan	PROPN
ejpam-6917	1	181	abstract	abstract	PROPN
ejpam-6917	1	182	.	.	PUNCT
ejpam-6917	2	1	subdivision	subdivision	NOUN
ejpam-6917	2	2	schemes	scheme	NOUN
ejpam-6917	2	3	are	be	AUX
ejpam-6917	2	4	a	a	DET
ejpam-6917	2	5	crucial	crucial	ADJ
ejpam-6917	2	6	component	component	NOUN
ejpam-6917	2	7	of	of	ADP
ejpam-6917	2	8	geometric	geometric	ADJ
ejpam-6917	2	9	modeling	modeling	NOUN
ejpam-6917	2	10	,	,	PUNCT
ejpam-6917	2	11	widely	widely	ADV
ejpam-6917	2	12	applied	apply	VERB
ejpam-6917	2	13	in	in	ADP
ejpam-6917	2	14	curve	curve	NOUN
ejpam-6917	2	15	and	and	CCONJ
ejpam-6917	2	16	surface	surface	NOUN
ejpam-6917	2	17	design	design	NOUN
ejpam-6917	2	18	.	.	PUNCT
ejpam-6917	3	1	classical	classical	ADJ
ejpam-6917	3	2	schemes	scheme	NOUN
ejpam-6917	3	3	such	such	ADJ
ejpam-6917	3	4	as	as	ADP
ejpam-6917	3	5	the	the	DET
ejpam-6917	3	6	six	six	NUM
ejpam-6917	3	7	-	-	PUNCT
ejpam-6917	3	8	point	point	NOUN
ejpam-6917	3	9	interpolatory	interpolatory	NOUN
ejpam-6917	3	10	scheme	scheme	NOUN
ejpam-6917	3	11	and	and	CCONJ
ejpam-6917	3	12	the	the	DET
ejpam-6917	3	13	quintic	quintic	ADJ
ejpam-6917	3	14	b	b	NOUN
ejpam-6917	3	15	-	-	PUNCT
ejpam-6917	3	16	spline	spline	NOUN
ejpam-6917	3	17	are	be	AUX
ejpam-6917	3	18	well	well	ADV
ejpam-6917	3	19	known	known	ADJ
ejpam-6917	3	20	for	for	ADP
ejpam-6917	3	21	their	their	PRON
ejpam-6917	3	22	efficiency	efficiency	NOUN
ejpam-6917	3	23	and	and	CCONJ
ejpam-6917	3	24	smoothness	smoothness	NOUN
ejpam-6917	3	25	.	.	PUNCT
ejpam-6917	4	1	yet	yet	ADV
ejpam-6917	4	2	,	,	PUNCT
ejpam-6917	4	3	both	both	PRON
ejpam-6917	4	4	have	have	VERB
ejpam-6917	4	5	inherent	inherent	ADJ
ejpam-6917	4	6	drawbacks	drawback	NOUN
ejpam-6917	4	7	,	,	PUNCT
ejpam-6917	4	8	particularly	particularly	ADV
ejpam-6917	4	9	with	with	ADP
ejpam-6917	4	10	respect	respect	NOUN
ejpam-6917	4	11	to	to	ADP
ejpam-6917	4	12	approximation	approximation	NOUN
ejpam-6917	4	13	order	order	NOUN
ejpam-6917	4	14	and	and	CCONJ
ejpam-6917	4	15	smoothness	smoothness	ADJ
ejpam-6917	4	16	.	.	PUNCT
ejpam-6917	5	1	this	this	DET
ejpam-6917	5	2	study	study	NOUN
ejpam-6917	5	3	introduces	introduce	VERB
ejpam-6917	5	4	a	a	DET
ejpam-6917	5	5	novel	novel	ADJ
ejpam-6917	5	6	subdivision	subdivision	NOUN
ejpam-6917	5	7	scheme	scheme	NOUN
ejpam-6917	5	8	that	that	PRON
ejpam-6917	5	9	blends	blend	VERB
ejpam-6917	5	10	the	the	DET
ejpam-6917	5	11	strengths	strength	NOUN
ejpam-6917	5	12	of	of	ADP
ejpam-6917	5	13	the	the	DET
ejpam-6917	5	14	six	six	NUM
ejpam-6917	5	15	-	-	PUNCT
ejpam-6917	5	16	point	point	NOUN
ejpam-6917	5	17	interpolatory	interpolatory	NOUN
ejpam-6917	5	18	and	and	CCONJ
ejpam-6917	5	19	the	the	DET
ejpam-6917	5	20	quintic	quintic	ADJ
ejpam-6917	5	21	b	b	PROPN
ejpam-6917	5	22	-	-	PUNCT
ejpam-6917	5	23	spline	spline	NOUN
ejpam-6917	5	24	schemes	scheme	NOUN
ejpam-6917	5	25	.	.	PUNCT
ejpam-6917	6	1	the	the	DET
ejpam-6917	6	2	proposed	propose	VERB
ejpam-6917	6	3	scheme	scheme	NOUN
ejpam-6917	6	4	achieves	achieve	VERB
ejpam-6917	6	5	sixth	sixth	ADJ
ejpam-6917	6	6	-	-	PUNCT
ejpam-6917	6	7	order	order	NOUN
ejpam-6917	6	8	approximation	approximation	NOUN
ejpam-6917	6	9	and	and	CCONJ
ejpam-6917	6	10	c5	c5	PROPN
ejpam-6917	6	11	smoothness	smoothness	PROPN
ejpam-6917	6	12	while	while	SCONJ
ejpam-6917	6	13	preserving	preserve	VERB
ejpam-6917	6	14	the	the	DET
ejpam-6917	6	15	support	support	NOUN
ejpam-6917	6	16	size	size	NOUN
ejpam-6917	6	17	of	of	ADP
ejpam-6917	6	18	the	the	DET
ejpam-6917	6	19	six	six	NUM
ejpam-6917	6	20	-	-	PUNCT
ejpam-6917	6	21	point	point	NOUN
ejpam-6917	6	22	scheme	scheme	NOUN
ejpam-6917	6	23	.	.	PUNCT
ejpam-6917	7	1	a	a	DET
ejpam-6917	7	2	key	key	ADJ
ejpam-6917	7	3	feature	feature	NOUN
ejpam-6917	7	4	of	of	ADP
ejpam-6917	7	5	the	the	DET
ejpam-6917	7	6	scheme	scheme	NOUN
ejpam-6917	7	7	is	be	AUX
ejpam-6917	7	8	the	the	DET
ejpam-6917	7	9	introduction	introduction	NOUN
ejpam-6917	7	10	of	of	ADP
ejpam-6917	7	11	a	a	DET
ejpam-6917	7	12	tension	tension	NOUN
ejpam-6917	7	13	parameter	parameter	NOUN
ejpam-6917	7	14	,	,	PUNCT
ejpam-6917	7	15	which	which	PRON
ejpam-6917	7	16	provides	provide	VERB
ejpam-6917	7	17	flexibility	flexibility	NOUN
ejpam-6917	7	18	to	to	PART
ejpam-6917	7	19	control	control	VERB
ejpam-6917	7	20	the	the	DET
ejpam-6917	7	21	trade	trade	NOUN
ejpam-6917	7	22	-	-	PUNCT
ejpam-6917	7	23	off	off	NOUN
ejpam-6917	7	24	between	between	ADP
ejpam-6917	7	25	smoothness	smoothness	NOUN
ejpam-6917	7	26	and	and	CCONJ
ejpam-6917	7	27	approximation	approximation	NOUN
ejpam-6917	7	28	order	order	NOUN
ejpam-6917	7	29	.	.	PUNCT
ejpam-6917	8	1	moreover	moreover	ADV
ejpam-6917	8	2	,	,	PUNCT
ejpam-6917	8	3	the	the	DET
ejpam-6917	8	4	scheme	scheme	NOUN
ejpam-6917	8	5	preserves	preserve	VERB
ejpam-6917	8	6	essential	essential	ADJ
ejpam-6917	8	7	properties	property	NOUN
ejpam-6917	8	8	such	such	ADJ
ejpam-6917	8	9	as	as	ADP
ejpam-6917	8	10	monotonicity	monotonicity	NOUN
ejpam-6917	8	11	and	and	CCONJ
ejpam-6917	8	12	convexity	convexity	NOUN
ejpam-6917	8	13	under	under	ADP
ejpam-6917	8	14	mild	mild	ADJ
ejpam-6917	8	15	conditions	condition	NOUN
ejpam-6917	8	16	.	.	PUNCT
ejpam-6917	9	1	despite	despite	SCONJ
ejpam-6917	9	2	the	the	DET
ejpam-6917	9	3	other	other	ADJ
ejpam-6917	9	4	higher	high	ADJ
ejpam-6917	9	5	-	-	PUNCT
ejpam-6917	9	6	order	order	NOUN
ejpam-6917	9	7	shape	shape	NOUN
ejpam-6917	9	8	-	-	PUNCT
ejpam-6917	9	9	preserving	preserve	VERB
ejpam-6917	9	10	schemes	scheme	NOUN
ejpam-6917	9	11	,	,	PUNCT
ejpam-6917	9	12	which	which	PRON
ejpam-6917	9	13	are	be	AUX
ejpam-6917	9	14	non	non	ADJ
ejpam-6917	9	15	-	-	ADJ
ejpam-6917	9	16	linear	linear	ADJ
ejpam-6917	9	17	and	and	CCONJ
ejpam-6917	9	18	computationally	computationally	ADV
ejpam-6917	9	19	complex	complex	ADJ
ejpam-6917	9	20	,	,	PUNCT
ejpam-6917	9	21	this	this	DET
ejpam-6917	9	22	scheme	scheme	NOUN
ejpam-6917	9	23	is	be	AUX
ejpam-6917	9	24	linear	linear	ADJ
ejpam-6917	9	25	and	and	CCONJ
ejpam-6917	9	26	stationary	stationary	ADJ
ejpam-6917	9	27	.	.	PUNCT
ejpam-6917	10	1	experimental	experimental	ADJ
ejpam-6917	10	2	results	result	NOUN
ejpam-6917	10	3	confirm	confirm	VERB
ejpam-6917	10	4	that	that	SCONJ
ejpam-6917	10	5	the	the	DET
ejpam-6917	10	6	proposed	propose	VERB
ejpam-6917	10	7	scheme	scheme	NOUN
ejpam-6917	10	8	consistently	consistently	ADV
ejpam-6917	10	9	produces	produce	VERB
ejpam-6917	10	10	accurate	accurate	ADJ
ejpam-6917	10	11	and	and	CCONJ
ejpam-6917	10	12	visually	visually	ADV
ejpam-6917	10	13	elegant	elegant	ADJ
ejpam-6917	10	14	curves	curve	NOUN
ejpam-6917	10	15	,	,	PUNCT
ejpam-6917	10	16	outperforming	outperform	VERB
ejpam-6917	10	17	existing	exist	VERB
ejpam-6917	10	18	schemes	scheme	NOUN
ejpam-6917	10	19	in	in	ADP
ejpam-6917	10	20	both	both	DET
ejpam-6917	10	21	approximation	approximation	NOUN
ejpam-6917	10	22	order	order	NOUN
ejpam-6917	10	23	and	and	CCONJ
ejpam-6917	10	24	smoothness	smoothness	ADJ
ejpam-6917	10	25	.	.	PUNCT
ejpam-6917	11	1	2020	2020	NUM
ejpam-6917	11	2	mathematics	mathematic	NOUN
ejpam-6917	11	3	subject	subject	NOUN
ejpam-6917	11	4	classifications	classification	NOUN
ejpam-6917	11	5	:	:	PUNCT
ejpam-6917	11	6	65d17	65d17	NOUN
ejpam-6917	11	7	,	,	PUNCT
ejpam-6917	11	8	65d10	65d10	NUM
ejpam-6917	11	9	,	,	PUNCT
ejpam-6917	11	10	65d07	65d07	NUM
ejpam-6917	11	11	,	,	PUNCT
ejpam-6917	11	12	65d05	65d05	NUM
ejpam-6917	11	13	key	key	ADJ
ejpam-6917	11	14	words	word	NOUN
ejpam-6917	11	15	and	and	CCONJ
ejpam-6917	11	16	phrases	phrase	NOUN
ejpam-6917	11	17	:	:	PUNCT
ejpam-6917	11	18	subdivision	subdivision	NOUN
ejpam-6917	11	19	,	,	PUNCT
ejpam-6917	11	20	continuity	continuity	NOUN
ejpam-6917	11	21	,	,	PUNCT
ejpam-6917	11	22	monotonicity	monotonicity	NOUN
ejpam-6917	11	23	,	,	PUNCT
ejpam-6917	11	24	convexity	convexity	NOUN
ejpam-6917	11	25	,	,	PUNCT
ejpam-6917	11	26	precision	precision	NOUN
ejpam-6917	11	27	∗corresponding	∗corresponde	VERB
ejpam-6917	11	28	author	author	NOUN
ejpam-6917	11	29	.	.	PUNCT
ejpam-6917	12	1	∗corresponding	∗corresponde	VERB
ejpam-6917	12	2	author	author	NOUN
ejpam-6917	12	3	.	.	PUNCT
ejpam-6917	13	1	doi	doi	NOUN
ejpam-6917	13	2	:	:	PUNCT
ejpam-6917	13	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6917	https://doi.org/10.29020/nybg.ejpam.v18i4.6917	NOUN
ejpam-6917	13	4	email	email	NOUN
ejpam-6917	13	5	addresses	address	NOUN
ejpam-6917	13	6	:	:	PUNCT
ejpam-6917	13	7	f.alshammari@psau.edu.sa	f.alshammari@psau.edu.sa	PROPN
ejpam-6917	13	8	(	(	PUNCT
ejpam-6917	13	9	f.	f.	PROPN
ejpam-6917	13	10	s.	s.	PROPN
ejpam-6917	13	11	alshammari	alshammari	PROPN
ejpam-6917	13	12	)	)	PUNCT
ejpam-6917	13	13	,	,	PUNCT
ejpam-6917	13	14	pakeeza@gscwu.edu.pk	pakeeza@gscwu.edu.pk	INTJ
ejpam-6917	13	15	(	(	PUNCT
ejpam-6917	13	16	p.	p.	NOUN
ejpam-6917	13	17	ashraf	ashraf	PROPN
ejpam-6917	13	18	)	)	PUNCT
ejpam-6917	13	19	,	,	PUNCT
ejpam-6917	13	20	msscholargscwu@gmail.com	msscholargscwu@gmail.com	X
ejpam-6917	13	21	(	(	PUNCT
ejpam-6917	13	22	s.	s.	PROPN
ejpam-6917	13	23	mehmood	mehmood	PROPN
ejpam-6917	13	24	)	)	PUNCT
ejpam-6917	13	25	,	,	PUNCT
ejpam-6917	13	26	aliakgul00727@gmail.com	aliakgul00727@gmail.com	X
ejpam-6917	14	1	(	(	PUNCT
ejpam-6917	14	2	a.	a.	NOUN
ejpam-6917	14	3	akgul	akgul	PROPN
ejpam-6917	14	4	)	)	PUNCT
ejpam-6917	14	5	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6917	15	1	1	1	NUM
ejpam-6917	15	2	copyright	copyright	NOUN
ejpam-6917	15	3	:	:	PUNCT
ejpam-6917	15	4	©	©	PROPN
ejpam-6917	15	5	2025	2025	NUM
ejpam-6917	15	6	the	the	DET
ejpam-6917	15	7	author(s	author(s	NOUN
ejpam-6917	15	8	)	)	PUNCT
ejpam-6917	15	9	.	.	PUNCT
ejpam-6917	16	1	(	(	PUNCT
ejpam-6917	16	2	cc	cc	NOUN
ejpam-6917	16	3	by	by	ADP
ejpam-6917	16	4	-	-	PUNCT
ejpam-6917	16	5	nc	nc	PROPN
ejpam-6917	16	6	4.0	4.0	NUM
ejpam-6917	16	7	)	)	PUNCT
ejpam-6917	16	8	f.	f.	PROPN
ejpam-6917	16	9	s.	s.	PROPN
ejpam-6917	16	10	alshammari	alshammari	PROPN
ejpam-6917	16	11	et	et	PROPN
ejpam-6917	16	12	al	al	PROPN
ejpam-6917	16	13	.	.	PUNCT
ejpam-6917	16	14	/	/	SYM
ejpam-6917	16	15	eur	eur	PROPN
ejpam-6917	16	16	.	.	PUNCT
ejpam-6917	17	1	j.	j.	PROPN
ejpam-6917	17	2	pure	pure	PROPN
ejpam-6917	17	3	appl	appl	PROPN
ejpam-6917	17	4	.	.	PROPN
ejpam-6917	17	5	math	math	PROPN
ejpam-6917	17	6	,	,	PUNCT
ejpam-6917	17	7	18	18	NUM
ejpam-6917	17	8	(	(	PUNCT
ejpam-6917	17	9	4	4	NUM
ejpam-6917	17	10	)	)	PUNCT
ejpam-6917	17	11	(	(	PUNCT
ejpam-6917	17	12	2025	2025	NUM
ejpam-6917	17	13	)	)	PUNCT
ejpam-6917	17	14	,	,	PUNCT
ejpam-6917	17	15	6917	6917	NUM
ejpam-6917	17	16	2	2	NUM
ejpam-6917	17	17	of	of	ADP
ejpam-6917	17	18	26	26	NUM
ejpam-6917	17	19	1	1	NUM
ejpam-6917	17	20	.	.	PUNCT
ejpam-6917	18	1	introduction	introduction	NOUN
ejpam-6917	18	2	subdivision	subdivision	NOUN
ejpam-6917	18	3	schemes	scheme	NOUN
ejpam-6917	18	4	(	(	PUNCT
ejpam-6917	18	5	sss	sss	PROPN
ejpam-6917	18	6	)	)	PUNCT
ejpam-6917	18	7	are	be	AUX
ejpam-6917	18	8	iterative	iterative	NOUN
ejpam-6917	18	9	processes	process	NOUN
ejpam-6917	18	10	that	that	PRON
ejpam-6917	18	11	refine	refine	VERB
ejpam-6917	18	12	an	an	DET
ejpam-6917	18	13	initial	initial	ADJ
ejpam-6917	18	14	control	control	NOUN
ejpam-6917	18	15	polygon	polygon	NOUN
ejpam-6917	18	16	or	or	CCONJ
ejpam-6917	18	17	mesh	mesh	NOUN
ejpam-6917	18	18	to	to	PART
ejpam-6917	18	19	generate	generate	VERB
ejpam-6917	18	20	smooth	smooth	ADJ
ejpam-6917	18	21	curves	curve	NOUN
ejpam-6917	18	22	or	or	CCONJ
ejpam-6917	18	23	surfaces	surface	NOUN
ejpam-6917	18	24	,	,	PUNCT
ejpam-6917	18	25	using	use	VERB
ejpam-6917	18	26	predefined	predefine	VERB
ejpam-6917	18	27	refinement	refinement	NOUN
ejpam-6917	18	28	rules	rule	NOUN
ejpam-6917	18	29	.	.	PUNCT
ejpam-6917	19	1	these	these	DET
ejpam-6917	19	2	schemes	scheme	NOUN
ejpam-6917	19	3	have	have	AUX
ejpam-6917	19	4	become	become	VERB
ejpam-6917	19	5	fundamental	fundamental	ADJ
ejpam-6917	19	6	tools	tool	NOUN
ejpam-6917	19	7	in	in	ADP
ejpam-6917	19	8	computer	computer	NOUN
ejpam-6917	19	9	graphics	graphic	NOUN
ejpam-6917	19	10	due	due	ADP
ejpam-6917	19	11	to	to	ADP
ejpam-6917	19	12	their	their	PRON
ejpam-6917	19	13	extensive	extensive	ADJ
ejpam-6917	19	14	applications	application	NOUN
ejpam-6917	19	15	in	in	ADP
ejpam-6917	19	16	areas	area	NOUN
ejpam-6917	19	17	such	such	ADJ
ejpam-6917	19	18	as	as	ADP
ejpam-6917	19	19	medical	medical	ADJ
ejpam-6917	19	20	imaging	imaging	NOUN
ejpam-6917	19	21	,	,	PUNCT
ejpam-6917	19	22	engineering	engineering	NOUN
ejpam-6917	19	23	,	,	PUNCT
ejpam-6917	19	24	visual	visual	ADJ
ejpam-6917	19	25	computing	computing	NOUN
ejpam-6917	19	26	,	,	PUNCT
ejpam-6917	19	27	and	and	CCONJ
ejpam-6917	19	28	image	image	NOUN
ejpam-6917	19	29	analysis	analysis	NOUN
ejpam-6917	19	30	.	.	PUNCT
ejpam-6917	20	1	the	the	DET
ejpam-6917	20	2	two	two	NUM
ejpam-6917	20	3	major	major	ADJ
ejpam-6917	20	4	types	type	NOUN
ejpam-6917	20	5	of	of	ADP
ejpam-6917	20	6	sss	sss	PROPN
ejpam-6917	20	7	are	be	AUX
ejpam-6917	20	8	approximating	approximate	VERB
ejpam-6917	20	9	and	and	CCONJ
ejpam-6917	20	10	interpolating	interpolate	VERB
ejpam-6917	20	11	schemes	scheme	NOUN
ejpam-6917	20	12	.	.	PUNCT
ejpam-6917	21	1	interpolatory	interpolatory	NOUN
ejpam-6917	21	2	schemes	scheme	NOUN
ejpam-6917	21	3	ensure	ensure	VERB
ejpam-6917	21	4	that	that	SCONJ
ejpam-6917	21	5	the	the	DET
ejpam-6917	21	6	resulting	result	VERB
ejpam-6917	21	7	limit	limit	NOUN
ejpam-6917	21	8	curve	curve	NOUN
ejpam-6917	21	9	passes	pass	VERB
ejpam-6917	21	10	through	through	ADP
ejpam-6917	21	11	the	the	DET
ejpam-6917	21	12	initial	initial	ADJ
ejpam-6917	21	13	control	control	NOUN
ejpam-6917	21	14	points	point	NOUN
ejpam-6917	21	15	,	,	PUNCT
ejpam-6917	21	16	while	while	SCONJ
ejpam-6917	21	17	approximating	approximate	VERB
ejpam-6917	21	18	schemes	scheme	NOUN
ejpam-6917	21	19	produce	produce	VERB
ejpam-6917	21	20	curves	curve	NOUN
ejpam-6917	21	21	that	that	PRON
ejpam-6917	21	22	may	may	AUX
ejpam-6917	21	23	not	not	PART
ejpam-6917	21	24	necessarily	necessarily	ADV
ejpam-6917	21	25	interpolate	interpolate	VERB
ejpam-6917	21	26	the	the	DET
ejpam-6917	21	27	original	original	ADJ
ejpam-6917	21	28	data	data	NOUN
ejpam-6917	21	29	points	point	NOUN
ejpam-6917	21	30	.	.	PUNCT
ejpam-6917	22	1	mathematically	mathematically	ADV
ejpam-6917	22	2	,	,	PUNCT
ejpam-6917	22	3	a	a	DET
ejpam-6917	22	4	stationary	stationary	ADJ
ejpam-6917	22	5	univariate	univariate	ADJ
ejpam-6917	22	6	subdivision	subdivision	NOUN
ejpam-6917	22	7	scheme	scheme	NOUN
ejpam-6917	22	8	can	can	AUX
ejpam-6917	22	9	be	be	AUX
ejpam-6917	22	10	described	describe	VERB
ejpam-6917	22	11	using	use	VERB
ejpam-6917	22	12	a	a	DET
ejpam-6917	22	13	refinement	refinement	NOUN
ejpam-6917	22	14	rule	rule	NOUN
ejpam-6917	22	15	that	that	PRON
ejpam-6917	22	16	updates	update	VERB
ejpam-6917	22	17	the	the	DET
ejpam-6917	22	18	sequence	sequence	NOUN
ejpam-6917	22	19	of	of	ADP
ejpam-6917	22	20	points	point	NOUN
ejpam-6917	22	21	at	at	ADP
ejpam-6917	22	22	each	each	DET
ejpam-6917	22	23	level	level	NOUN
ejpam-6917	22	24	.	.	PUNCT
ejpam-6917	23	1	let	let	VERB
ejpam-6917	23	2	gn	gn	PROPN
ejpam-6917	23	3	=	=	PRON
ejpam-6917	23	4	{	{	PUNCT
ejpam-6917	23	5	gnm	gnm	PROPN
ejpam-6917	23	6	:	:	PUNCT
ejpam-6917	23	7	m	m	VERB
ejpam-6917	23	8	∈	∈	PROPN
ejpam-6917	23	9	z	z	AUX
ejpam-6917	23	10	}	}	PUNCT
ejpam-6917	23	11	represent	represent	VERB
ejpam-6917	23	12	the	the	DET
ejpam-6917	23	13	set	set	NOUN
ejpam-6917	23	14	of	of	ADP
ejpam-6917	23	15	points	point	NOUN
ejpam-6917	23	16	at	at	ADP
ejpam-6917	23	17	level	level	NOUN
ejpam-6917	23	18	n.	n.	NOUN
ejpam-6917	23	19	the	the	DET
ejpam-6917	23	20	new	new	ADJ
ejpam-6917	23	21	refined	refined	ADJ
ejpam-6917	23	22	value	value	NOUN
ejpam-6917	23	23	at	at	ADP
ejpam-6917	23	24	position	position	NOUN
ejpam-6917	23	25	i	i	PRON
ejpam-6917	23	26	is	be	AUX
ejpam-6917	23	27	given	give	VERB
ejpam-6917	23	28	by	by	ADP
ejpam-6917	23	29	:	:	PUNCT
ejpam-6917	23	30	(	(	PUNCT
ejpam-6917	23	31	spg	spg	INTJ
ejpam-6917	23	32	n)i	n)i	NOUN
ejpam-6917	23	33	=	=	SYM
ejpam-6917	23	34	∑	∑	PUNCT
ejpam-6917	23	35	m∈z	m∈z	VERB
ejpam-6917	23	36	ci−2mgnm	ci−2mgnm	PROPN
ejpam-6917	23	37	,	,	PUNCT
ejpam-6917	23	38	where	where	SCONJ
ejpam-6917	23	39	gn	gn	PROPN
ejpam-6917	23	40	=	=	X
ejpam-6917	23	41	{	{	PUNCT
ejpam-6917	23	42	gnm	gnm	PROPN
ejpam-6917	23	43	:	:	PUNCT
ejpam-6917	23	44	m	m	VERB
ejpam-6917	23	45	∈	∈	PROPN
ejpam-6917	23	46	z	z	NOUN
ejpam-6917	23	47	}	}	PUNCT
ejpam-6917	23	48	represents	represent	VERB
ejpam-6917	23	49	the	the	DET
ejpam-6917	23	50	sequence	sequence	NOUN
ejpam-6917	23	51	of	of	ADP
ejpam-6917	23	52	data	datum	NOUN
ejpam-6917	23	53	at	at	ADP
ejpam-6917	23	54	refinement	refinement	NOUN
ejpam-6917	23	55	level	level	NOUN
ejpam-6917	23	56	n	n	CCONJ
ejpam-6917	23	57	,	,	PUNCT
ejpam-6917	23	58	sp	sp	ADP
ejpam-6917	23	59	denotes	denote	NOUN
ejpam-6917	23	60	the	the	DET
ejpam-6917	23	61	subdivision	subdivision	NOUN
ejpam-6917	23	62	operator	operator	NOUN
ejpam-6917	23	63	,	,	PUNCT
ejpam-6917	23	64	which	which	PRON
ejpam-6917	23	65	can	can	AUX
ejpam-6917	23	66	be	be	AUX
ejpam-6917	23	67	represented	represent	VERB
ejpam-6917	23	68	as	as	ADP
ejpam-6917	23	69	a	a	DET
ejpam-6917	23	70	bi	bi	ADJ
ejpam-6917	23	71	-	-	ADJ
ejpam-6917	23	72	infinite	infinite	ADJ
ejpam-6917	23	73	matric	matric	NOUN
ejpam-6917	23	74	mc	mc	PROPN
ejpam-6917	24	1	=	=	PUNCT
ejpam-6917	24	2	(	(	PUNCT
ejpam-6917	24	3	ci−2	ci−2	PROPN
ejpam-6917	24	4	m	m	VERB
ejpam-6917	24	5	:	:	PUNCT
ejpam-6917	24	6	i	i	PRON
ejpam-6917	24	7	,	,	PUNCT
ejpam-6917	24	8	m	m	VERB
ejpam-6917	24	9	∈	∈	PROPN
ejpam-6917	24	10	z	z	NOUN
ejpam-6917	24	11	)	)	PUNCT
ejpam-6917	24	12	defined	define	VERB
ejpam-6917	24	13	by	by	ADP
ejpam-6917	24	14	the	the	DET
ejpam-6917	24	15	mask	mask	NOUN
ejpam-6917	24	16	c	c	NOUN
ejpam-6917	24	17	=	=	PUNCT
ejpam-6917	24	18	{	{	PUNCT
ejpam-6917	24	19	cm	cm	NOUN
ejpam-6917	24	20	:	:	PUNCT
ejpam-6917	24	21	m	m	VERB
ejpam-6917	24	22	∈	∈	PROPN
ejpam-6917	24	23	z	z	NOUN
ejpam-6917	24	24	}	}	PUNCT
ejpam-6917	24	25	.	.	PUNCT
ejpam-6917	25	1	the	the	DET
ejpam-6917	25	2	mask	mask	NOUN
ejpam-6917	25	3	′c′	′c′	PROPN
ejpam-6917	25	4	is	be	AUX
ejpam-6917	25	5	usually	usually	ADV
ejpam-6917	25	6	compactly	compactly	ADV
ejpam-6917	25	7	supported	support	VERB
ejpam-6917	25	8	,	,	PUNCT
ejpam-6917	25	9	which	which	PRON
ejpam-6917	25	10	guarantees	guarantee	VERB
ejpam-6917	25	11	that	that	SCONJ
ejpam-6917	25	12	the	the	DET
ejpam-6917	25	13	refinement	refinement	NOUN
ejpam-6917	25	14	process	process	NOUN
ejpam-6917	25	15	remains	remain	VERB
ejpam-6917	25	16	localized	localize	VERB
ejpam-6917	25	17	.	.	PUNCT
ejpam-6917	26	1	a	a	DET
ejpam-6917	26	2	ss	ss	NOUN
ejpam-6917	26	3	is	be	AUX
ejpam-6917	26	4	deemed	deem	VERB
ejpam-6917	26	5	uniformly	uniformly	ADV
ejpam-6917	26	6	convergent	convergent	NOUN
ejpam-6917	26	7	when	when	SCONJ
ejpam-6917	26	8	the	the	DET
ejpam-6917	26	9	sequence	sequence	NOUN
ejpam-6917	26	10	of	of	ADP
ejpam-6917	26	11	refined	refined	ADJ
ejpam-6917	26	12	data	datum	NOUN
ejpam-6917	26	13	gn	gn	PROPN
ejpam-6917	26	14	converges	converge	VERB
ejpam-6917	26	15	uniformly	uniformly	ADV
ejpam-6917	26	16	to	to	ADP
ejpam-6917	26	17	a	a	DET
ejpam-6917	26	18	continuous	continuous	ADJ
ejpam-6917	26	19	limiting	limiting	NOUN
ejpam-6917	26	20	function	function	NOUN
ejpam-6917	26	21	[	[	X
ejpam-6917	26	22	1	1	NUM
ejpam-6917	26	23	]	]	PUNCT
ejpam-6917	26	24	.	.	PUNCT
ejpam-6917	27	1	the	the	DET
ejpam-6917	27	2	convergence	convergence	NOUN
ejpam-6917	27	3	of	of	ADP
ejpam-6917	27	4	the	the	DET
ejpam-6917	27	5	limit	limit	NOUN
ejpam-6917	27	6	function	function	NOUN
ejpam-6917	27	7	is	be	AUX
ejpam-6917	27	8	influenced	influence	VERB
ejpam-6917	27	9	by	by	ADP
ejpam-6917	27	10	the	the	DET
ejpam-6917	27	11	mask	mask	NOUN
ejpam-6917	27	12	′c′	′c′	PROPN
ejpam-6917	27	13	and	and	CCONJ
ejpam-6917	27	14	is	be	AUX
ejpam-6917	27	15	typically	typically	ADV
ejpam-6917	27	16	evaluated	evaluate	VERB
ejpam-6917	27	17	using	use	VERB
ejpam-6917	27	18	the	the	DET
ejpam-6917	27	19	laurent	laurent	NOUN
ejpam-6917	27	20	polynomial	polynomial	NOUN
ejpam-6917	28	1	[	[	X
ejpam-6917	28	2	2	2	NUM
ejpam-6917	28	3	]	]	PUNCT
ejpam-6917	28	4	,	,	PUNCT
ejpam-6917	28	5	denoted	denote	VERB
ejpam-6917	28	6	as	as	ADP
ejpam-6917	28	7	c(v	c(v	PROPN
ejpam-6917	28	8	)	)	PUNCT
ejpam-6917	28	9	=	=	PUNCT
ejpam-6917	29	1	∑	∑	PUNCT
ejpam-6917	29	2	i∈z	i∈z	NOUN
ejpam-6917	29	3	civ	civ	VERB
ejpam-6917	29	4	i	i	PRON
ejpam-6917	29	5	,	,	PUNCT
ejpam-6917	29	6	i	i	PROPN
ejpam-6917	29	7	∈	∈	PROPN
ejpam-6917	29	8	c	c	NOUN
ejpam-6917	29	9	and	and	CCONJ
ejpam-6917	29	10	joint	joint	ADJ
ejpam-6917	29	11	spectral	spectral	ADJ
ejpam-6917	29	12	radius	radius	NOUN
ejpam-6917	29	13	[	[	X
ejpam-6917	29	14	3	3	X
ejpam-6917	29	15	]	]	PUNCT
ejpam-6917	29	16	which	which	PRON
ejpam-6917	29	17	together	together	ADV
ejpam-6917	29	18	help	help	VERB
ejpam-6917	29	19	determine	determine	VERB
ejpam-6917	29	20	the	the	DET
ejpam-6917	29	21	smoothness	smoothness	NOUN
ejpam-6917	29	22	and	and	CCONJ
ejpam-6917	29	23	stability	stability	NOUN
ejpam-6917	29	24	of	of	ADP
ejpam-6917	29	25	the	the	DET
ejpam-6917	29	26	scheme	scheme	NOUN
ejpam-6917	29	27	.	.	PUNCT
ejpam-6917	30	1	the	the	DET
ejpam-6917	30	2	design	design	NOUN
ejpam-6917	30	3	of	of	ADP
ejpam-6917	30	4	novel	novel	NOUN
ejpam-6917	30	5	sss	sss	NOUN
ejpam-6917	30	6	remains	remain	VERB
ejpam-6917	30	7	an	an	DET
ejpam-6917	30	8	important	important	ADJ
ejpam-6917	30	9	area	area	NOUN
ejpam-6917	30	10	of	of	ADP
ejpam-6917	30	11	research	research	NOUN
ejpam-6917	30	12	in	in	ADP
ejpam-6917	30	13	curve	curve	NOUN
ejpam-6917	30	14	and	and	CCONJ
ejpam-6917	30	15	surface	surface	NOUN
ejpam-6917	30	16	modeling	modeling	NOUN
ejpam-6917	30	17	.	.	PUNCT
ejpam-6917	31	1	de	de	PROPN
ejpam-6917	31	2	rham	rham	PROPN
ejpam-6917	31	3	[	[	X
ejpam-6917	31	4	4	4	NUM
ejpam-6917	31	5	]	]	PUNCT
ejpam-6917	31	6	and	and	CCONJ
ejpam-6917	31	7	chaikin	chaikin	X
ejpam-6917	31	8	[	[	X
ejpam-6917	31	9	5	5	NUM
ejpam-6917	31	10	]	]	PUNCT
ejpam-6917	31	11	were	be	AUX
ejpam-6917	31	12	renowned	renowne	VERB
ejpam-6917	31	13	as	as	ADP
ejpam-6917	31	14	the	the	DET
ejpam-6917	31	15	founding	found	VERB
ejpam-6917	31	16	fathers	father	NOUN
ejpam-6917	31	17	of	of	ADP
ejpam-6917	31	18	sss	sss	NOUN
ejpam-6917	31	19	.	.	PUNCT
ejpam-6917	32	1	they	they	PRON
ejpam-6917	32	2	pioneered	pioneer	VERB
ejpam-6917	32	3	corner	corner	NOUN
ejpam-6917	32	4	-	-	PUNCT
ejpam-6917	32	5	cutting	cut	VERB
ejpam-6917	32	6	schemes	scheme	NOUN
ejpam-6917	32	7	,	,	PUNCT
ejpam-6917	32	8	which	which	PRON
ejpam-6917	32	9	yielded	yield	VERB
ejpam-6917	32	10	c1	c1	NOUN
ejpam-6917	32	11	-	-	PUNCT
ejpam-6917	32	12	limit	limit	NOUN
ejpam-6917	32	13	curves	curve	NOUN
ejpam-6917	32	14	.	.	PUNCT
ejpam-6917	33	1	a	a	DET
ejpam-6917	33	2	significant	significant	ADJ
ejpam-6917	33	3	advancement	advancement	NOUN
ejpam-6917	33	4	came	come	VERB
ejpam-6917	33	5	with	with	ADP
ejpam-6917	33	6	the	the	DET
ejpam-6917	33	7	four	four	NUM
ejpam-6917	33	8	-	-	PUNCT
ejpam-6917	33	9	point	point	NOUN
ejpam-6917	33	10	binary	binary	ADJ
ejpam-6917	33	11	interpolatory	interpolatory	NOUN
ejpam-6917	33	12	scheme	scheme	NOUN
ejpam-6917	33	13	developed	develop	VERB
ejpam-6917	33	14	by	by	ADP
ejpam-6917	33	15	dyn	dyn	PROPN
ejpam-6917	33	16	et	et	NOUN
ejpam-6917	33	17	al	al	PROPN
ejpam-6917	33	18	.	.	PUNCT
ejpam-6917	34	1	[	[	X
ejpam-6917	34	2	6	6	NUM
ejpam-6917	34	3	]	]	PUNCT
ejpam-6917	34	4	,	,	PUNCT
ejpam-6917	34	5	which	which	PRON
ejpam-6917	34	6	also	also	ADV
ejpam-6917	34	7	achieved	achieve	VERB
ejpam-6917	34	8	c1	c1	PROPN
ejpam-6917	34	9	continuity	continuity	NOUN
ejpam-6917	34	10	.	.	PUNCT
ejpam-6917	35	1	later	later	ADV
ejpam-6917	35	2	,	,	PUNCT
ejpam-6917	35	3	deslauriers	deslaurier	NOUN
ejpam-6917	35	4	and	and	CCONJ
ejpam-6917	35	5	dubuc	dubuc	ADV
ejpam-6917	35	6	introduced	introduce	VERB
ejpam-6917	35	7	a	a	DET
ejpam-6917	35	8	widely	widely	ADV
ejpam-6917	35	9	used	use	VERB
ejpam-6917	35	10	interpolatory	interpolatory	NOUN
ejpam-6917	35	11	scheme	scheme	NOUN
ejpam-6917	35	12	known	know	VERB
ejpam-6917	35	13	as	as	ADP
ejpam-6917	35	14	the	the	DET
ejpam-6917	35	15	dd	dd	NOUN
ejpam-6917	35	16	scheme	scheme	NOUN
ejpam-6917	35	17	[	[	X
ejpam-6917	35	18	7	7	NUM
ejpam-6917	35	19	]	]	PUNCT
ejpam-6917	35	20	.	.	PUNCT
ejpam-6917	36	1	more	more	ADV
ejpam-6917	36	2	recently	recently	ADV
ejpam-6917	36	3	,	,	PUNCT
ejpam-6917	36	4	researchers	researcher	NOUN
ejpam-6917	36	5	explored	explore	VERB
ejpam-6917	36	6	the	the	DET
ejpam-6917	36	7	idea	idea	NOUN
ejpam-6917	36	8	of	of	ADP
ejpam-6917	36	9	shape	shape	NOUN
ejpam-6917	36	10	-	-	PUNCT
ejpam-6917	36	11	controlling	control	VERB
ejpam-6917	36	12	parameters	parameter	NOUN
ejpam-6917	36	13	.	.	PUNCT
ejpam-6917	37	1	for	for	ADP
ejpam-6917	37	2	instance	instance	NOUN
ejpam-6917	37	3	,	,	PUNCT
ejpam-6917	37	4	mustafa	mustafa	PROPN
ejpam-6917	37	5	et	et	PROPN
ejpam-6917	37	6	al	al	PROPN
ejpam-6917	37	7	.	.	PUNCT
ejpam-6917	38	1	[	[	X
ejpam-6917	38	2	8	8	NUM
ejpam-6917	38	3	]	]	PUNCT
ejpam-6917	38	4	introduced	introduce	VERB
ejpam-6917	38	5	a	a	DET
ejpam-6917	38	6	framework	framework	NOUN
ejpam-6917	38	7	for	for	ADP
ejpam-6917	38	8	constructing	construct	VERB
ejpam-6917	38	9	binary	binary	ADJ
ejpam-6917	38	10	approximating	approximate	VERB
ejpam-6917	38	11	schemes	scheme	NOUN
ejpam-6917	38	12	,	,	PUNCT
ejpam-6917	38	13	allowing	allow	VERB
ejpam-6917	38	14	better	well	ADJ
ejpam-6917	38	15	control	control	NOUN
ejpam-6917	38	16	over	over	ADP
ejpam-6917	38	17	curve	curve	NOUN
ejpam-6917	38	18	behavior	behavior	NOUN
ejpam-6917	38	19	.	.	PUNCT
ejpam-6917	39	1	zheng	zheng	PROPN
ejpam-6917	39	2	et	et	PROPN
ejpam-6917	39	3	al	al	PROPN
ejpam-6917	39	4	.	.	PUNCT
ejpam-6917	40	1	[	[	X
ejpam-6917	40	2	9	9	NUM
ejpam-6917	40	3	]	]	PUNCT
ejpam-6917	40	4	extended	extend	VERB
ejpam-6917	40	5	this	this	DET
ejpam-6917	40	6	idea	idea	NOUN
ejpam-6917	40	7	by	by	ADP
ejpam-6917	40	8	designing	design	VERB
ejpam-6917	40	9	multi	multi	ADJ
ejpam-6917	40	10	-	-	ADJ
ejpam-6917	40	11	parameter	parameter	ADJ
ejpam-6917	40	12	schemes	scheme	NOUN
ejpam-6917	40	13	with	with	ADP
ejpam-6917	40	14	high	high	ADJ
ejpam-6917	40	15	levels	level	NOUN
ejpam-6917	40	16	of	of	ADP
ejpam-6917	40	17	continuity	continuity	NOUN
ejpam-6917	40	18	.	.	PUNCT
ejpam-6917	41	1	similarly	similarly	ADV
ejpam-6917	41	2	,	,	PUNCT
ejpam-6917	41	3	tan	tan	PROPN
ejpam-6917	41	4	et	et	PROPN
ejpam-6917	41	5	al	al	PROPN
ejpam-6917	41	6	.	.	PUNCT
ejpam-6917	42	1	[	[	X
ejpam-6917	42	2	10	10	NUM
ejpam-6917	42	3	]	]	PUNCT
ejpam-6917	42	4	proposed	propose	VERB
ejpam-6917	42	5	a	a	DET
ejpam-6917	42	6	four	four	NUM
ejpam-6917	42	7	-	-	PUNCT
ejpam-6917	42	8	point	point	NOUN
ejpam-6917	42	9	scheme	scheme	NOUN
ejpam-6917	42	10	that	that	PRON
ejpam-6917	42	11	incorporates	incorporate	VERB
ejpam-6917	42	12	two	two	NUM
ejpam-6917	42	13	shape	shape	NOUN
ejpam-6917	42	14	parameters	parameter	NOUN
ejpam-6917	42	15	,	,	PUNCT
ejpam-6917	42	16	achieving	achieve	VERB
ejpam-6917	42	17	c3	c3	PROPN
ejpam-6917	42	18	smoothness	smoothness	NOUN
ejpam-6917	42	19	while	while	SCONJ
ejpam-6917	42	20	preserving	preserve	VERB
ejpam-6917	42	21	the	the	DET
ejpam-6917	42	22	shape	shape	NOUN
ejpam-6917	42	23	of	of	ADP
ejpam-6917	42	24	the	the	DET
ejpam-6917	42	25	original	original	ADJ
ejpam-6917	42	26	data	datum	NOUN
ejpam-6917	42	27	.	.	PUNCT
ejpam-6917	43	1	sss	sss	PROPN
ejpam-6917	43	2	are	be	AUX
ejpam-6917	43	3	valued	value	VERB
ejpam-6917	43	4	for	for	ADP
ejpam-6917	43	5	key	key	ADJ
ejpam-6917	43	6	features	feature	NOUN
ejpam-6917	43	7	such	such	ADJ
ejpam-6917	43	8	as	as	ADP
ejpam-6917	43	9	smoothness	smoothness	ADJ
ejpam-6917	43	10	and	and	CCONJ
ejpam-6917	43	11	shape	shape	NOUN
ejpam-6917	43	12	preservation	preservation	NOUN
ejpam-6917	43	13	.	.	PUNCT
ejpam-6917	44	1	for	for	ADP
ejpam-6917	44	2	deeper	deep	ADJ
ejpam-6917	44	3	discussion	discussion	NOUN
ejpam-6917	44	4	of	of	ADP
ejpam-6917	44	5	these	these	DET
ejpam-6917	44	6	properties	property	NOUN
ejpam-6917	44	7	,	,	PUNCT
ejpam-6917	44	8	readers	reader	NOUN
ejpam-6917	44	9	are	be	AUX
ejpam-6917	44	10	referred	refer	VERB
ejpam-6917	44	11	to	to	ADP
ejpam-6917	44	12	works	work	NOUN
ejpam-6917	44	13	such	such	ADJ
ejpam-6917	44	14	as	as	ADP
ejpam-6917	44	15	[	[	X
ejpam-6917	44	16	11–19	11–19	NUM
ejpam-6917	44	17	]	]	PUNCT
ejpam-6917	44	18	.	.	PUNCT
ejpam-6917	45	1	the	the	DET
ejpam-6917	45	2	quintic	quintic	ADJ
ejpam-6917	45	3	b	b	NOUN
ejpam-6917	45	4	-	-	PUNCT
ejpam-6917	45	5	spline	spline	NOUN
ejpam-6917	45	6	(	(	PUNCT
ejpam-6917	45	7	qb	qb	NOUN
ejpam-6917	45	8	-	-	PUNCT
ejpam-6917	45	9	scheme	scheme	NOUN
ejpam-6917	45	10	)	)	PUNCT
ejpam-6917	46	1	[	[	X
ejpam-6917	46	2	20	20	NUM
ejpam-6917	46	3	]	]	PUNCT
ejpam-6917	46	4	and	and	CCONJ
ejpam-6917	46	5	dd	dd	VERB
ejpam-6917	46	6	six	six	NUM
ejpam-6917	46	7	-	-	PUNCT
ejpam-6917	46	8	point	point	NOUN
ejpam-6917	46	9	interpolatory	interpolatory	NOUN
ejpam-6917	46	10	schemes	scheme	NOUN
ejpam-6917	46	11	(	(	PUNCT
ejpam-6917	46	12	sdscheme	sdscheme	NOUN
ejpam-6917	46	13	)	)	PUNCT
ejpam-6917	47	1	[	[	X
ejpam-6917	47	2	21	21	NUM
ejpam-6917	47	3	]	]	PUNCT
ejpam-6917	47	4	are	be	AUX
ejpam-6917	47	5	stationary	stationary	ADJ
ejpam-6917	47	6	sss	sss	PROPN
ejpam-6917	47	7	.	.	PROPN
ejpam-6917	47	8	based	base	VERB
ejpam-6917	47	9	on	on	ADP
ejpam-6917	47	10	quintic	quintic	ADJ
ejpam-6917	47	11	polynomials	polynomial	NOUN
ejpam-6917	47	12	,	,	PUNCT
ejpam-6917	47	13	these	these	DET
ejpam-6917	47	14	schemes	scheme	NOUN
ejpam-6917	47	15	have	have	VERB
ejpam-6917	47	16	distinct	distinct	ADJ
ejpam-6917	47	17	advantages	advantage	NOUN
ejpam-6917	47	18	and	and	CCONJ
ejpam-6917	47	19	limitations	limitation	NOUN
ejpam-6917	47	20	.	.	PUNCT
ejpam-6917	48	1	the	the	DET
ejpam-6917	48	2	quintic	quintic	ADJ
ejpam-6917	48	3	b	b	NOUN
ejpam-6917	48	4	-	-	PUNCT
ejpam-6917	48	5	spline	spline	NOUN
ejpam-6917	48	6	maintains	maintain	VERB
ejpam-6917	48	7	high	high	ADJ
ejpam-6917	48	8	-	-	PUNCT
ejpam-6917	48	9	order	order	NOUN
ejpam-6917	48	10	continuity	continuity	NOUN
ejpam-6917	48	11	while	while	SCONJ
ejpam-6917	48	12	preserving	preserve	VERB
ejpam-6917	48	13	the	the	DET
ejpam-6917	48	14	monotonicity	monotonicity	NOUN
ejpam-6917	48	15	and	and	CCONJ
ejpam-6917	48	16	convexity	convexity	NOUN
ejpam-6917	48	17	of	of	ADP
ejpam-6917	48	18	the	the	DET
ejpam-6917	48	19	initial	initial	ADJ
ejpam-6917	48	20	sequence	sequence	NOUN
ejpam-6917	48	21	,	,	PUNCT
ejpam-6917	48	22	having	have	VERB
ejpam-6917	48	23	minimal	minimal	ADJ
ejpam-6917	48	24	support	support	NOUN
ejpam-6917	48	25	f.	f.	PROPN
ejpam-6917	48	26	s.	s.	PROPN
ejpam-6917	48	27	alshammari	alshammari	PROPN
ejpam-6917	48	28	et	et	PROPN
ejpam-6917	48	29	al	al	PROPN
ejpam-6917	48	30	.	.	PUNCT
ejpam-6917	48	31	/	/	SYM
ejpam-6917	48	32	eur	eur	PROPN
ejpam-6917	48	33	.	.	PUNCT
ejpam-6917	49	1	j.	j.	PROPN
ejpam-6917	49	2	pure	pure	PROPN
ejpam-6917	49	3	appl	appl	PROPN
ejpam-6917	49	4	.	.	PROPN
ejpam-6917	49	5	math	math	PROPN
ejpam-6917	49	6	,	,	PUNCT
ejpam-6917	49	7	18	18	NUM
ejpam-6917	49	8	(	(	PUNCT
ejpam-6917	49	9	4	4	NUM
ejpam-6917	49	10	)	)	PUNCT
ejpam-6917	49	11	(	(	PUNCT
ejpam-6917	49	12	2025	2025	NUM
ejpam-6917	49	13	)	)	PUNCT
ejpam-6917	49	14	,	,	PUNCT
ejpam-6917	49	15	6917	6917	NUM
ejpam-6917	49	16	3	3	NUM
ejpam-6917	49	17	of	of	ADP
ejpam-6917	49	18	26	26	NUM
ejpam-6917	49	19	of	of	ADP
ejpam-6917	49	20	the	the	DET
ejpam-6917	49	21	fundamental	fundamental	ADJ
ejpam-6917	49	22	limit	limit	NOUN
ejpam-6917	49	23	curve	curve	NOUN
ejpam-6917	49	24	[	[	X
ejpam-6917	49	25	3	3	NUM
ejpam-6917	49	26	]	]	PUNCT
ejpam-6917	49	27	.	.	PUNCT
ejpam-6917	50	1	the	the	DET
ejpam-6917	50	2	scheme	scheme	NOUN
ejpam-6917	50	3	achieves	achieve	VERB
ejpam-6917	50	4	an	an	DET
ejpam-6917	50	5	order	order	NOUN
ejpam-6917	50	6	of	of	ADP
ejpam-6917	50	7	approximation	approximation	NOUN
ejpam-6917	50	8	limited	limit	VERB
ejpam-6917	50	9	to	to	ADP
ejpam-6917	50	10	’	'	PUNCT
ejpam-6917	50	11	two	two	NUM
ejpam-6917	50	12	’	'	PUNCT
ejpam-6917	50	13	because	because	SCONJ
ejpam-6917	50	14	it	it	PRON
ejpam-6917	50	15	can	can	AUX
ejpam-6917	50	16	only	only	ADV
ejpam-6917	50	17	reproduce	reproduce	VERB
ejpam-6917	50	18	polynomials	polynomial	NOUN
ejpam-6917	50	19	up	up	ADP
ejpam-6917	50	20	to	to	ADP
ejpam-6917	50	21	linear	linear	ADJ
ejpam-6917	50	22	accuracy	accuracy	NOUN
ejpam-6917	50	23	.	.	PUNCT
ejpam-6917	51	1	however	however	ADV
ejpam-6917	51	2	,	,	PUNCT
ejpam-6917	51	3	the	the	DET
ejpam-6917	51	4	sixpoint	sixpoint	ADJ
ejpam-6917	51	5	interpolatory	interpolatory	NOUN
ejpam-6917	51	6	scheme	scheme	NOUN
ejpam-6917	51	7	only	only	ADV
ejpam-6917	51	8	provides	provide	VERB
ejpam-6917	51	9	c2	c2	PROPN
ejpam-6917	51	10	-	-	PUNCT
ejpam-6917	51	11	smoothness	smoothness	PROPN
ejpam-6917	51	12	and	and	CCONJ
ejpam-6917	51	13	,	,	PUNCT
ejpam-6917	51	14	in	in	ADP
ejpam-6917	51	15	general	general	ADJ
ejpam-6917	51	16	,	,	PUNCT
ejpam-6917	51	17	lacks	lack	VERB
ejpam-6917	51	18	the	the	DET
ejpam-6917	51	19	shapepreserving	shapepreserve	VERB
ejpam-6917	51	20	property	property	NOUN
ejpam-6917	51	21	,	,	PUNCT
ejpam-6917	51	22	even	even	ADV
ejpam-6917	51	23	though	though	SCONJ
ejpam-6917	51	24	it	it	PRON
ejpam-6917	51	25	provides	provide	VERB
ejpam-6917	51	26	sixth	sixth	ADJ
ejpam-6917	51	27	-	-	PUNCT
ejpam-6917	51	28	order	order	NOUN
ejpam-6917	51	29	accuracy	accuracy	NOUN
ejpam-6917	51	30	.	.	PUNCT
ejpam-6917	52	1	moreover	moreover	ADV
ejpam-6917	52	2	,	,	PUNCT
ejpam-6917	52	3	a	a	DET
ejpam-6917	52	4	significant	significant	ADJ
ejpam-6917	52	5	drawback	drawback	NOUN
ejpam-6917	52	6	of	of	ADP
ejpam-6917	52	7	the	the	DET
ejpam-6917	52	8	sd	sd	NOUN
ejpam-6917	52	9	-	-	PUNCT
ejpam-6917	52	10	scheme	scheme	NOUN
ejpam-6917	52	11	is	be	AUX
ejpam-6917	52	12	its	its	PRON
ejpam-6917	52	13	interpolatory	interpolatory	ADJ
ejpam-6917	52	14	nature	nature	NOUN
ejpam-6917	52	15	.	.	PUNCT
ejpam-6917	53	1	artifacts	artifact	NOUN
ejpam-6917	53	2	like	like	ADP
ejpam-6917	53	3	self	self	NOUN
ejpam-6917	53	4	-	-	PUNCT
ejpam-6917	53	5	intersections	intersection	NOUN
ejpam-6917	53	6	and	and	CCONJ
ejpam-6917	53	7	inflection	inflection	NOUN
ejpam-6917	53	8	points	point	NOUN
ejpam-6917	53	9	may	may	AUX
ejpam-6917	53	10	arise	arise	VERB
ejpam-6917	53	11	if	if	SCONJ
ejpam-6917	53	12	the	the	DET
ejpam-6917	53	13	edges	edge	NOUN
ejpam-6917	53	14	of	of	ADP
ejpam-6917	53	15	the	the	DET
ejpam-6917	53	16	control	control	NOUN
ejpam-6917	53	17	polygon	polygon	NOUN
ejpam-6917	53	18	differ	differ	VERB
ejpam-6917	53	19	substantially	substantially	ADV
ejpam-6917	53	20	in	in	ADP
ejpam-6917	53	21	length	length	NOUN
ejpam-6917	53	22	.	.	PUNCT
ejpam-6917	54	1	furthermore	furthermore	ADV
ejpam-6917	54	2	,	,	PUNCT
ejpam-6917	54	3	the	the	DET
ejpam-6917	54	4	refinement	refinement	NOUN
ejpam-6917	54	5	mask	mask	NOUN
ejpam-6917	54	6	length	length	NOUN
ejpam-6917	54	7	,	,	PUNCT
ejpam-6917	54	8	smoothness	smoothness	ADJ
ejpam-6917	54	9	,	,	PUNCT
ejpam-6917	54	10	and	and	CCONJ
ejpam-6917	54	11	accuracy	accuracy	NOUN
ejpam-6917	54	12	are	be	AUX
ejpam-6917	54	13	essential	essential	ADJ
ejpam-6917	54	14	criteria	criterion	NOUN
ejpam-6917	54	15	for	for	ADP
ejpam-6917	54	16	selecting	select	VERB
ejpam-6917	54	17	a	a	DET
ejpam-6917	54	18	subdivision	subdivision	NOUN
ejpam-6917	54	19	algorithm	algorithm	NOUN
ejpam-6917	54	20	in	in	ADP
ejpam-6917	54	21	practical	practical	ADJ
ejpam-6917	54	22	applications	application	NOUN
ejpam-6917	54	23	.	.	PUNCT
ejpam-6917	55	1	multiple	multiple	ADJ
ejpam-6917	55	2	attempts	attempt	NOUN
ejpam-6917	55	3	are	be	AUX
ejpam-6917	55	4	made	make	VERB
ejpam-6917	55	5	to	to	PART
ejpam-6917	55	6	increase	increase	VERB
ejpam-6917	55	7	the	the	DET
ejpam-6917	55	8	smoothness	smoothness	NOUN
ejpam-6917	55	9	and	and	CCONJ
ejpam-6917	55	10	accuracy	accuracy	NOUN
ejpam-6917	55	11	by	by	ADP
ejpam-6917	55	12	using	use	VERB
ejpam-6917	55	13	non	non	ADJ
ejpam-6917	55	14	-	-	ADJ
ejpam-6917	55	15	uniform	uniform	ADJ
ejpam-6917	55	16	,	,	PUNCT
ejpam-6917	55	17	non	non	ADJ
ejpam-6917	55	18	-	-	ADJ
ejpam-6917	55	19	linear	linear	ADJ
ejpam-6917	55	20	,	,	PUNCT
ejpam-6917	55	21	and	and	CCONJ
ejpam-6917	55	22	non	non	ADJ
ejpam-6917	55	23	-	-	ADJ
ejpam-6917	55	24	stationary	stationary	ADJ
ejpam-6917	55	25	sss	sss	NOUN
ejpam-6917	55	26	[	[	X
ejpam-6917	55	27	22–24	22–24	NUM
ejpam-6917	55	28	]	]	PUNCT
ejpam-6917	55	29	.	.	PUNCT
ejpam-6917	56	1	however	however	ADV
ejpam-6917	56	2	,	,	PUNCT
ejpam-6917	56	3	it	it	PRON
ejpam-6917	56	4	increases	increase	VERB
ejpam-6917	56	5	the	the	DET
ejpam-6917	56	6	complexity	complexity	NOUN
ejpam-6917	56	7	and	and	CCONJ
ejpam-6917	56	8	demands	demand	NOUN
ejpam-6917	56	9	for	for	ADP
ejpam-6917	56	10	a	a	DET
ejpam-6917	56	11	preliminary	preliminary	ADJ
ejpam-6917	56	12	smoothing	smoothing	NOUN
ejpam-6917	56	13	process	process	NOUN
ejpam-6917	56	14	.	.	PUNCT
ejpam-6917	57	1	to	to	PART
ejpam-6917	57	2	improve	improve	VERB
ejpam-6917	57	3	the	the	DET
ejpam-6917	57	4	smoothness	smoothness	NOUN
ejpam-6917	57	5	of	of	ADP
ejpam-6917	57	6	the	the	DET
ejpam-6917	57	7	interpolatory	interpolatory	ADJ
ejpam-6917	57	8	scheme	scheme	NOUN
ejpam-6917	57	9	,	,	PUNCT
ejpam-6917	57	10	choi	choi	PROPN
ejpam-6917	57	11	et	et	PROPN
ejpam-6917	57	12	.	.	PUNCT
ejpam-6917	58	1	al.[25	al.[25	PROPN
ejpam-6917	58	2	]	]	PUNCT
ejpam-6917	58	3	introduced	introduce	VERB
ejpam-6917	58	4	a	a	DET
ejpam-6917	58	5	family	family	NOUN
ejpam-6917	58	6	of	of	ADP
ejpam-6917	58	7	quasi	quasi	ADJ
ejpam-6917	58	8	-	-	ADJ
ejpam-6917	58	9	interpolatory	interpolatory	ADJ
ejpam-6917	58	10	schemes	scheme	NOUN
ejpam-6917	58	11	by	by	ADP
ejpam-6917	58	12	enhancing	enhance	VERB
ejpam-6917	58	13	the	the	DET
ejpam-6917	58	14	support	support	NOUN
ejpam-6917	58	15	length	length	NOUN
ejpam-6917	58	16	of	of	ADP
ejpam-6917	58	17	the	the	DET
ejpam-6917	58	18	mask	mask	NOUN
ejpam-6917	58	19	.	.	PUNCT
ejpam-6917	59	1	recently	recently	ADV
ejpam-6917	59	2	,	,	PUNCT
ejpam-6917	59	3	yang	yang	PROPN
ejpam-6917	59	4	et	et	PROPN
ejpam-6917	59	5	al	al	PROPN
ejpam-6917	59	6	.	.	PUNCT
ejpam-6917	60	1	[	[	X
ejpam-6917	60	2	26	26	NUM
ejpam-6917	60	3	]	]	PUNCT
ejpam-6917	60	4	have	have	AUX
ejpam-6917	60	5	presented	present	VERB
ejpam-6917	60	6	a	a	DET
ejpam-6917	60	7	family	family	NOUN
ejpam-6917	60	8	of	of	ADP
ejpam-6917	60	9	linear	linear	PROPN
ejpam-6917	60	10	,	,	PUNCT
ejpam-6917	60	11	stationary	stationary	ADJ
ejpam-6917	60	12	ss	ss	NOUN
ejpam-6917	60	13	with	with	ADP
ejpam-6917	60	14	c2	c2	PROPN
ejpam-6917	60	15	-	-	PUNCT
ejpam-6917	60	16	smoothness	smoothness	PROPN
ejpam-6917	60	17	and	and	CCONJ
ejpam-6917	60	18	fourth	fourth	ADJ
ejpam-6917	60	19	-	-	PUNCT
ejpam-6917	60	20	order	order	NOUN
ejpam-6917	60	21	accuracy	accuracy	NOUN
ejpam-6917	60	22	.	.	PUNCT
ejpam-6917	61	1	however	however	ADV
ejpam-6917	61	2	,	,	PUNCT
ejpam-6917	61	3	this	this	DET
ejpam-6917	61	4	scheme	scheme	NOUN
ejpam-6917	61	5	in	in	ADP
ejpam-6917	61	6	[	[	X
ejpam-6917	61	7	26	26	NUM
ejpam-6917	61	8	]	]	PUNCT
ejpam-6917	61	9	achieves	achieve	VERB
ejpam-6917	61	10	c2	c2	PROPN
ejpam-6917	61	11	-	-	PUNCT
ejpam-6917	61	12	smoothness	smoothness	PROPN
ejpam-6917	61	13	;	;	PUNCT
ejpam-6917	61	14	it	it	PRON
ejpam-6917	61	15	still	still	ADV
ejpam-6917	61	16	relies	rely	VERB
ejpam-6917	61	17	on	on	ADP
ejpam-6917	61	18	a	a	DET
ejpam-6917	61	19	similar	similar	ADJ
ejpam-6917	61	20	construction	construction	NOUN
ejpam-6917	61	21	to	to	ADP
ejpam-6917	61	22	the	the	DET
ejpam-6917	61	23	cubic	cubic	ADJ
ejpam-6917	61	24	b	b	NOUN
ejpam-6917	61	25	-	-	PUNCT
ejpam-6917	61	26	spline	spline	NOUN
ejpam-6917	61	27	,	,	PUNCT
ejpam-6917	61	28	which	which	PRON
ejpam-6917	61	29	may	may	AUX
ejpam-6917	61	30	limit	limit	VERB
ejpam-6917	61	31	its	its	PRON
ejpam-6917	61	32	potential	potential	NOUN
ejpam-6917	61	33	for	for	ADP
ejpam-6917	61	34	further	far	ADV
ejpam-6917	61	35	improving	improve	VERB
ejpam-6917	61	36	approximation	approximation	NOUN
ejpam-6917	61	37	accuracy	accuracy	NOUN
ejpam-6917	61	38	.	.	PUNCT
ejpam-6917	62	1	addressing	address	VERB
ejpam-6917	62	2	the	the	DET
ejpam-6917	62	3	limitations	limitation	NOUN
ejpam-6917	62	4	mentioned	mention	VERB
ejpam-6917	62	5	above	above	ADV
ejpam-6917	62	6	,	,	PUNCT
ejpam-6917	62	7	this	this	DET
ejpam-6917	62	8	work	work	NOUN
ejpam-6917	62	9	introduces	introduce	VERB
ejpam-6917	62	10	a	a	DET
ejpam-6917	62	11	novel	novel	ADJ
ejpam-6917	62	12	class	class	NOUN
ejpam-6917	62	13	of	of	ADP
ejpam-6917	62	14	stationary	stationary	ADJ
ejpam-6917	62	15	sss	sss	NOUN
ejpam-6917	62	16	,	,	PUNCT
ejpam-6917	62	17	combining	combine	VERB
ejpam-6917	62	18	the	the	DET
ejpam-6917	62	19	benefits	benefit	NOUN
ejpam-6917	62	20	of	of	ADP
ejpam-6917	62	21	qb	qb	PROPN
ejpam-6917	62	22	and	and	CCONJ
ejpam-6917	62	23	sd	sd	NOUN
ejpam-6917	62	24	-	-	PUNCT
ejpam-6917	62	25	schemes	scheme	NOUN
ejpam-6917	62	26	.	.	PUNCT
ejpam-6917	63	1	the	the	DET
ejpam-6917	63	2	presented	present	VERB
ejpam-6917	63	3	scheme	scheme	NOUN
ejpam-6917	63	4	features	feature	VERB
ejpam-6917	63	5	a	a	DET
ejpam-6917	63	6	parameter	parameter	NOUN
ejpam-6917	63	7	µ0	µ0	NOUN
ejpam-6917	63	8	,	,	PUNCT
ejpam-6917	63	9	bridging	bridge	VERB
ejpam-6917	63	10	the	the	DET
ejpam-6917	63	11	gap	gap	NOUN
ejpam-6917	63	12	between	between	ADP
ejpam-6917	63	13	these	these	DET
ejpam-6917	63	14	two	two	NUM
ejpam-6917	63	15	schemes	scheme	NOUN
ejpam-6917	63	16	and	and	CCONJ
ejpam-6917	63	17	offering	offer	VERB
ejpam-6917	63	18	a	a	DET
ejpam-6917	63	19	versatile	versatile	ADJ
ejpam-6917	63	20	range	range	NOUN
ejpam-6917	63	21	of	of	ADP
ejpam-6917	63	22	subdivision	subdivision	NOUN
ejpam-6917	63	23	rules	rule	NOUN
ejpam-6917	63	24	to	to	PART
ejpam-6917	63	25	balance	balance	VERB
ejpam-6917	63	26	smoothness	smoothness	NOUN
ejpam-6917	63	27	,	,	PUNCT
ejpam-6917	63	28	precision	precision	NOUN
ejpam-6917	63	29	,	,	PUNCT
ejpam-6917	63	30	and	and	CCONJ
ejpam-6917	63	31	shape	shape	NOUN
ejpam-6917	63	32	-	-	PUNCT
ejpam-6917	63	33	preservation	preservation	NOUN
ejpam-6917	63	34	.	.	PUNCT
ejpam-6917	64	1	the	the	DET
ejpam-6917	64	2	main	main	ADJ
ejpam-6917	64	3	advancements	advancement	NOUN
ejpam-6917	64	4	of	of	ADP
ejpam-6917	64	5	our	our	PRON
ejpam-6917	64	6	work	work	NOUN
ejpam-6917	64	7	are	be	AUX
ejpam-6917	64	8	:	:	PUNCT
ejpam-6917	64	9	first	first	ADV
ejpam-6917	64	10	,	,	PUNCT
ejpam-6917	64	11	by	by	ADP
ejpam-6917	64	12	compromising	compromise	VERB
ejpam-6917	64	13	on	on	ADP
ejpam-6917	64	14	the	the	DET
ejpam-6917	64	15	interpolation	interpolation	NOUN
ejpam-6917	64	16	property	property	NOUN
ejpam-6917	64	17	,	,	PUNCT
ejpam-6917	64	18	our	our	PRON
ejpam-6917	64	19	scheme	scheme	NOUN
ejpam-6917	64	20	achieves	achieves	AUX
ejpam-6917	64	21	enhanced	enhance	VERB
ejpam-6917	64	22	smoothness	smoothness	NOUN
ejpam-6917	64	23	of	of	ADP
ejpam-6917	64	24	c5	c5	PROPN
ejpam-6917	64	25	,	,	PUNCT
ejpam-6917	64	26	having	have	VERB
ejpam-6917	64	27	the	the	DET
ejpam-6917	64	28	equal	equal	ADJ
ejpam-6917	64	29	support	support	NOUN
ejpam-6917	64	30	width	width	VERB
ejpam-6917	64	31	[	[	X
ejpam-6917	64	32	−5	−5	NOUN
ejpam-6917	64	33	,	,	PUNCT
ejpam-6917	64	34	5	5	NUM
ejpam-6917	64	35	]	]	PUNCT
ejpam-6917	64	36	as	as	ADP
ejpam-6917	64	37	the	the	DET
ejpam-6917	64	38	sd	sd	NOUN
ejpam-6917	64	39	-	-	PUNCT
ejpam-6917	64	40	scheme	scheme	NOUN
ejpam-6917	64	41	.	.	PUNCT
ejpam-6917	65	1	second	second	ADJ
ejpam-6917	65	2	,	,	PUNCT
ejpam-6917	65	3	despite	despite	SCONJ
ejpam-6917	65	4	only	only	ADV
ejpam-6917	65	5	reproducing	reproduce	VERB
ejpam-6917	65	6	linear	linear	ADJ
ejpam-6917	65	7	polynomials	polynomial	NOUN
ejpam-6917	65	8	,	,	PUNCT
ejpam-6917	65	9	our	our	PRON
ejpam-6917	65	10	scheme	scheme	NOUN
ejpam-6917	65	11	can	can	AUX
ejpam-6917	65	12	attain	attain	VERB
ejpam-6917	65	13	sixth	sixth	ADJ
ejpam-6917	65	14	-	-	PUNCT
ejpam-6917	65	15	order	order	NOUN
ejpam-6917	65	16	precision	precision	NOUN
ejpam-6917	65	17	using	use	VERB
ejpam-6917	65	18	the	the	DET
ejpam-6917	65	19	function	function	NOUN
ejpam-6917	65	20	that	that	PRON
ejpam-6917	65	21	belongs	belong	VERB
ejpam-6917	65	22	to	to	ADP
ejpam-6917	65	23	the	the	DET
ejpam-6917	65	24	sobolev	sobolev	NOUN
ejpam-6917	65	25	space	space	NOUN
ejpam-6917	65	26	,	,	PUNCT
ejpam-6917	65	27	such	such	ADJ
ejpam-6917	65	28	as	as	ADP
ejpam-6917	65	29	e	e	PROPN
ejpam-6917	65	30	∈	∈	PROPN
ejpam-6917	65	31	w	w	ADP
ejpam-6917	65	32	6(r	6(r	NUM
ejpam-6917	65	33	)	)	PUNCT
ejpam-6917	65	34	.	.	PUNCT
ejpam-6917	66	1	next	next	ADV
ejpam-6917	66	2	,	,	PUNCT
ejpam-6917	66	3	we	we	PRON
ejpam-6917	66	4	prove	prove	VERB
ejpam-6917	66	5	that	that	SCONJ
ejpam-6917	66	6	our	our	PRON
ejpam-6917	66	7	proposed	propose	VERB
ejpam-6917	66	8	scheme	scheme	NOUN
ejpam-6917	66	9	maintains	maintain	VERB
ejpam-6917	66	10	monotonicity	monotonicity	NOUN
ejpam-6917	66	11	and	and	CCONJ
ejpam-6917	66	12	convexity	convexity	NOUN
ejpam-6917	66	13	under	under	ADP
ejpam-6917	66	14	certain	certain	ADJ
ejpam-6917	66	15	mild	mild	ADJ
ejpam-6917	66	16	conditions	condition	NOUN
ejpam-6917	66	17	.	.	PUNCT
ejpam-6917	67	1	a	a	DET
ejpam-6917	67	2	key	key	ADJ
ejpam-6917	67	3	advantage	advantage	NOUN
ejpam-6917	67	4	of	of	ADP
ejpam-6917	67	5	our	our	PRON
ejpam-6917	67	6	scheme	scheme	NOUN
ejpam-6917	67	7	is	be	AUX
ejpam-6917	67	8	its	its	PRON
ejpam-6917	67	9	linearity	linearity	NOUN
ejpam-6917	67	10	and	and	CCONJ
ejpam-6917	67	11	stationarity	stationarity	NOUN
ejpam-6917	67	12	,	,	PUNCT
ejpam-6917	67	13	which	which	PRON
ejpam-6917	67	14	distinguishes	distinguish	VERB
ejpam-6917	67	15	it	it	PRON
ejpam-6917	67	16	from	from	ADP
ejpam-6917	67	17	other	other	ADJ
ejpam-6917	67	18	shape	shape	NOUN
ejpam-6917	67	19	-	-	PUNCT
ejpam-6917	67	20	preserving	preserve	VERB
ejpam-6917	67	21	schemes	scheme	NOUN
ejpam-6917	67	22	that	that	PRON
ejpam-6917	67	23	are	be	AUX
ejpam-6917	67	24	often	often	ADV
ejpam-6917	67	25	non	non	ADJ
ejpam-6917	67	26	-	-	ADJ
ejpam-6917	67	27	linear	linear	ADJ
ejpam-6917	67	28	,	,	PUNCT
ejpam-6917	67	29	non	non	ADJ
ejpam-6917	67	30	-	-	ADJ
ejpam-6917	67	31	uniform	uniform	ADJ
ejpam-6917	67	32	,	,	PUNCT
ejpam-6917	67	33	and	and	CCONJ
ejpam-6917	67	34	computationally	computationally	ADV
ejpam-6917	67	35	complex	complex	ADJ
ejpam-6917	67	36	.	.	PUNCT
ejpam-6917	68	1	to	to	PART
ejpam-6917	68	2	demonstrate	demonstrate	VERB
ejpam-6917	68	3	the	the	DET
ejpam-6917	68	4	effectiveness	effectiveness	NOUN
ejpam-6917	68	5	of	of	ADP
ejpam-6917	68	6	the	the	DET
ejpam-6917	68	7	proposed	proposed	ADJ
ejpam-6917	68	8	ss	ss	PROPN
ejpam-6917	68	9	,	,	PUNCT
ejpam-6917	68	10	several	several	ADJ
ejpam-6917	68	11	numerical	numerical	ADJ
ejpam-6917	68	12	examples	example	NOUN
ejpam-6917	68	13	are	be	AUX
ejpam-6917	68	14	presented	present	VERB
ejpam-6917	68	15	.	.	PUNCT
ejpam-6917	69	1	the	the	DET
ejpam-6917	69	2	design	design	NOUN
ejpam-6917	69	3	of	of	ADP
ejpam-6917	69	4	this	this	DET
ejpam-6917	69	5	paper	paper	NOUN
ejpam-6917	69	6	is	be	AUX
ejpam-6917	69	7	as	as	SCONJ
ejpam-6917	69	8	follows	follow	VERB
ejpam-6917	69	9	.	.	PUNCT
ejpam-6917	70	1	section	section	NOUN
ejpam-6917	70	2	2	2	NUM
ejpam-6917	70	3	discusses	discuss	VERB
ejpam-6917	70	4	fundamental	fundamental	ADJ
ejpam-6917	70	5	concepts	concept	NOUN
ejpam-6917	70	6	and	and	CCONJ
ejpam-6917	70	7	definitions	definition	NOUN
ejpam-6917	70	8	.	.	PUNCT
ejpam-6917	71	1	a	a	DET
ejpam-6917	71	2	novel	novel	ADJ
ejpam-6917	71	3	class	class	NOUN
ejpam-6917	71	4	of	of	ADP
ejpam-6917	71	5	binary	binary	ADJ
ejpam-6917	71	6	6	6	NUM
ejpam-6917	71	7	-	-	PUNCT
ejpam-6917	71	8	point	point	NOUN
ejpam-6917	71	9	ss	ss	NOUN
ejpam-6917	71	10	(	(	PUNCT
ejpam-6917	71	11	sp	sp	ADP
ejpam-6917	71	12	-scheme	-scheme	NOUN
ejpam-6917	71	13	)	)	PUNCT
ejpam-6917	71	14	is	be	AUX
ejpam-6917	71	15	constructed	construct	VERB
ejpam-6917	71	16	in	in	ADP
ejpam-6917	71	17	section	section	NOUN
ejpam-6917	71	18	3	3	NUM
ejpam-6917	71	19	.	.	PUNCT
ejpam-6917	72	1	the	the	DET
ejpam-6917	72	2	convergence	convergence	NOUN
ejpam-6917	72	3	and	and	CCONJ
ejpam-6917	72	4	accuracy	accuracy	NOUN
ejpam-6917	72	5	of	of	ADP
ejpam-6917	72	6	the	the	DET
ejpam-6917	72	7	sp	sp	NOUN
ejpam-6917	72	8	-scheme	-scheme	NOUN
ejpam-6917	72	9	are	be	AUX
ejpam-6917	72	10	analyzed	analyze	VERB
ejpam-6917	72	11	in	in	ADP
ejpam-6917	72	12	section	section	NOUN
ejpam-6917	72	13	4	4	NUM
ejpam-6917	72	14	.	.	PUNCT
ejpam-6917	73	1	the	the	DET
ejpam-6917	73	2	monotonicity	monotonicity	NOUN
ejpam-6917	73	3	and	and	CCONJ
ejpam-6917	73	4	convexity	convexity	NOUN
ejpam-6917	73	5	preservation	preservation	NOUN
ejpam-6917	73	6	of	of	ADP
ejpam-6917	73	7	the	the	DET
ejpam-6917	73	8	sp	sp	NOUN
ejpam-6917	73	9	-scheme	-scheme	PROPN
ejpam-6917	73	10	is	be	AUX
ejpam-6917	73	11	discussed	discuss	VERB
ejpam-6917	73	12	in	in	ADP
ejpam-6917	73	13	section	section	NOUN
ejpam-6917	73	14	5	5	NUM
ejpam-6917	73	15	.	.	PUNCT
ejpam-6917	74	1	lastly	lastly	ADV
ejpam-6917	74	2	,	,	PUNCT
ejpam-6917	74	3	in	in	ADP
ejpam-6917	74	4	section	section	NOUN
ejpam-6917	74	5	6	6	NUM
ejpam-6917	74	6	,	,	PUNCT
ejpam-6917	74	7	we	we	PRON
ejpam-6917	74	8	present	present	VERB
ejpam-6917	74	9	various	various	ADJ
ejpam-6917	74	10	experimental	experimental	ADJ
ejpam-6917	74	11	results	result	NOUN
ejpam-6917	74	12	.	.	PUNCT
ejpam-6917	75	1	2	2	X
ejpam-6917	75	2	.	.	NUM
ejpam-6917	75	3	fundamental	fundamental	ADJ
ejpam-6917	75	4	concepts	concept	NOUN
ejpam-6917	75	5	and	and	CCONJ
ejpam-6917	75	6	definitions	definition	NOUN
ejpam-6917	75	7	this	this	DET
ejpam-6917	75	8	section	section	NOUN
ejpam-6917	75	9	provides	provide	VERB
ejpam-6917	75	10	fundamental	fundamental	ADJ
ejpam-6917	75	11	concepts	concept	NOUN
ejpam-6917	75	12	and	and	CCONJ
ejpam-6917	75	13	essential	essential	ADJ
ejpam-6917	75	14	background	background	NOUN
ejpam-6917	75	15	on	on	ADP
ejpam-6917	75	16	stationary	stationary	ADJ
ejpam-6917	75	17	sss	sss	PROPN
ejpam-6917	75	18	.	.	PROPN
ejpam-6917	75	19	definition	definition	NOUN
ejpam-6917	75	20	1	1	NUM
ejpam-6917	75	21	.	.	PUNCT
ejpam-6917	76	1	a	a	DET
ejpam-6917	76	2	stationary	stationary	ADJ
ejpam-6917	76	3	binary	binary	NOUN
ejpam-6917	76	4	ss	ss	PROPN
ejpam-6917	76	5	is	be	AUX
ejpam-6917	76	6	a	a	DET
ejpam-6917	76	7	process	process	NOUN
ejpam-6917	76	8	that	that	PRON
ejpam-6917	76	9	iteratively	iteratively	ADV
ejpam-6917	76	10	generates	generate	VERB
ejpam-6917	76	11	a	a	DET
ejpam-6917	76	12	sequence	sequence	NOUN
ejpam-6917	76	13	of	of	ADP
ejpam-6917	76	14	control	control	NOUN
ejpam-6917	76	15	point	point	NOUN
ejpam-6917	76	16	grids	grid	NOUN
ejpam-6917	76	17	.	.	PUNCT
ejpam-6917	77	1	the	the	DET
ejpam-6917	77	2	control	control	NOUN
ejpam-6917	77	3	points	point	VERB
ejpam-6917	77	4	at	at	ADP
ejpam-6917	77	5	level	level	NOUN
ejpam-6917	77	6	n	n	NOUN
ejpam-6917	77	7	+	+	CCONJ
ejpam-6917	77	8	1	1	NUM
ejpam-6917	77	9	are	be	AUX
ejpam-6917	77	10	computed	compute	VERB
ejpam-6917	77	11	from	from	ADP
ejpam-6917	77	12	an	an	DET
ejpam-6917	77	13	initial	initial	ADJ
ejpam-6917	77	14	set	set	NOUN
ejpam-6917	77	15	as	as	ADP
ejpam-6917	77	16	f.	f.	PROPN
ejpam-6917	77	17	s.	s.	PROPN
ejpam-6917	77	18	alshammari	alshammari	PROPN
ejpam-6917	77	19	et	et	PROPN
ejpam-6917	77	20	al	al	PROPN
ejpam-6917	77	21	.	.	PUNCT
ejpam-6917	77	22	/	/	SYM
ejpam-6917	77	23	eur	eur	PROPN
ejpam-6917	77	24	.	.	PUNCT
ejpam-6917	78	1	j.	j.	PROPN
ejpam-6917	78	2	pure	pure	PROPN
ejpam-6917	78	3	appl	appl	PROPN
ejpam-6917	78	4	.	.	PROPN
ejpam-6917	78	5	math	math	PROPN
ejpam-6917	78	6	,	,	PUNCT
ejpam-6917	78	7	18	18	NUM
ejpam-6917	78	8	(	(	PUNCT
ejpam-6917	78	9	4	4	NUM
ejpam-6917	78	10	)	)	PUNCT
ejpam-6917	78	11	(	(	PUNCT
ejpam-6917	78	12	2025	2025	NUM
ejpam-6917	78	13	)	)	PUNCT
ejpam-6917	78	14	,	,	PUNCT
ejpam-6917	78	15	6917	6917	NUM
ejpam-6917	78	16	4	4	NUM
ejpam-6917	78	17	of	of	ADP
ejpam-6917	78	18	26	26	NUM
ejpam-6917	78	19	follows	follow	VERB
ejpam-6917	78	20	:	:	PUNCT
ejpam-6917	78	21	gn+1	gn+1	PROPN
ejpam-6917	78	22	j	j	X
ejpam-6917	79	1	=	=	PUNCT
ejpam-6917	79	2	∑	∑	PUNCT
ejpam-6917	79	3	i∈z	i∈z	NOUN
ejpam-6917	79	4	cj−2ig	cj−2ig	NOUN
ejpam-6917	79	5	n	n	PRON
ejpam-6917	79	6	i	i	PRON
ejpam-6917	79	7	,	,	PUNCT
ejpam-6917	79	8	j	j	PROPN
ejpam-6917	79	9	∈	∈	PROPN
ejpam-6917	79	10	z	z	PROPN
ejpam-6917	79	11	,	,	PUNCT
ejpam-6917	79	12	where	where	SCONJ
ejpam-6917	79	13	different	different	ADJ
ejpam-6917	79	14	masks	mask	NOUN
ejpam-6917	79	15	are	be	AUX
ejpam-6917	79	16	used	use	VERB
ejpam-6917	79	17	for	for	ADP
ejpam-6917	79	18	even	even	ADV
ejpam-6917	79	19	and	and	CCONJ
ejpam-6917	79	20	odd	odd	ADV
ejpam-6917	79	21	-	-	PUNCT
ejpam-6917	79	22	indexed	index	VERB
ejpam-6917	79	23	points	point	NOUN
ejpam-6917	79	24	.	.	PUNCT
ejpam-6917	80	1	in	in	ADP
ejpam-6917	80	2	contrast	contrast	NOUN
ejpam-6917	80	3	,	,	PUNCT
ejpam-6917	80	4	non	non	ADJ
ejpam-6917	80	5	-	-	ADJ
ejpam-6917	80	6	stationary	stationary	ADJ
ejpam-6917	80	7	ss	ss	NOUN
ejpam-6917	80	8	apply	apply	VERB
ejpam-6917	80	9	recursive	recursive	ADJ
ejpam-6917	80	10	refinements	refinement	NOUN
ejpam-6917	80	11	using	use	VERB
ejpam-6917	80	12	masks	mask	NOUN
ejpam-6917	80	13	that	that	PRON
ejpam-6917	80	14	may	may	AUX
ejpam-6917	80	15	vary	vary	VERB
ejpam-6917	80	16	at	at	ADP
ejpam-6917	80	17	different	different	ADJ
ejpam-6917	80	18	levels	level	NOUN
ejpam-6917	80	19	.	.	PUNCT
ejpam-6917	81	1	the	the	DET
ejpam-6917	81	2	subdivision	subdivision	NOUN
ejpam-6917	81	3	operator	operator	NOUN
ejpam-6917	81	4	is	be	AUX
ejpam-6917	81	5	assumed	assume	VERB
ejpam-6917	81	6	to	to	PART
ejpam-6917	81	7	be	be	AUX
ejpam-6917	81	8	bounded	bound	VERB
ejpam-6917	81	9	and	and	CCONJ
ejpam-6917	81	10	is	be	AUX
ejpam-6917	81	11	characterized	characterize	VERB
ejpam-6917	81	12	by	by	ADP
ejpam-6917	81	13	the	the	DET
ejpam-6917	81	14	sequence	sequence	NOUN
ejpam-6917	81	15	c	c	NOUN
ejpam-6917	81	16	=	=	PRON
ejpam-6917	81	17	{	{	PUNCT
ejpam-6917	81	18	ci	ci	NOUN
ejpam-6917	81	19	:	:	PUNCT
ejpam-6917	82	1	i	i	PROPN
ejpam-6917	82	2	∈	∈	PROPN
ejpam-6917	83	1	z	z	X
ejpam-6917	83	2	}	}	PUNCT
ejpam-6917	83	3	,	,	PUNCT
ejpam-6917	83	4	referred	refer	VERB
ejpam-6917	83	5	to	to	ADP
ejpam-6917	83	6	as	as	ADP
ejpam-6917	83	7	the	the	DET
ejpam-6917	83	8	subdivision	subdivision	NOUN
ejpam-6917	83	9	mask	mask	NOUN
ejpam-6917	83	10	,	,	PUNCT
ejpam-6917	83	11	which	which	PRON
ejpam-6917	83	12	is	be	AUX
ejpam-6917	83	13	generally	generally	ADV
ejpam-6917	83	14	assumed	assume	VERB
ejpam-6917	83	15	to	to	PART
ejpam-6917	83	16	have	have	VERB
ejpam-6917	83	17	finite	finite	ADJ
ejpam-6917	83	18	support	support	NOUN
ejpam-6917	83	19	.	.	PUNCT
ejpam-6917	84	1	we	we	PRON
ejpam-6917	84	2	define	define	VERB
ejpam-6917	84	3	n0	n0	NOUN
ejpam-6917	84	4	as	as	ADP
ejpam-6917	84	5	the	the	DET
ejpam-6917	84	6	set	set	NOUN
ejpam-6917	84	7	of	of	ADP
ejpam-6917	84	8	non	non	ADJ
ejpam-6917	84	9	-	-	ADJ
ejpam-6917	84	10	negative	negative	ADJ
ejpam-6917	84	11	integers	integer	NOUN
ejpam-6917	84	12	.	.	PUNCT
ejpam-6917	85	1	the	the	DET
ejpam-6917	85	2	notation	notation	NOUN
ejpam-6917	85	3	∏	∏	PROPN
ejpam-6917	85	4	i	i	PRON
ejpam-6917	85	5	represents	represent	VERB
ejpam-6917	85	6	the	the	DET
ejpam-6917	85	7	space	space	NOUN
ejpam-6917	85	8	of	of	ADP
ejpam-6917	85	9	polynomials	polynomial	NOUN
ejpam-6917	85	10	with	with	ADP
ejpam-6917	85	11	a	a	DET
ejpam-6917	85	12	degree	degree	NOUN
ejpam-6917	85	13	up	up	ADP
ejpam-6917	85	14	to	to	ADP
ejpam-6917	85	15	i.	i.	NOUN
ejpam-6917	85	16	for	for	ADP
ejpam-6917	85	17	a	a	DET
ejpam-6917	85	18	sequence	sequence	NOUN
ejpam-6917	85	19	g	g	PROPN
ejpam-6917	85	20	∈	∈	PROPN
ejpam-6917	85	21	l∞(z	l∞(z	NOUN
ejpam-6917	85	22	)	)	PUNCT
ejpam-6917	85	23	,	,	PUNCT
ejpam-6917	85	24	the	the	DET
ejpam-6917	85	25	following	follow	VERB
ejpam-6917	85	26	difference	difference	NOUN
ejpam-6917	85	27	operators	operator	NOUN
ejpam-6917	85	28	are	be	AUX
ejpam-6917	85	29	defined	define	VERB
ejpam-6917	85	30	:	:	PUNCT
ejpam-6917	85	31	(	(	PUNCT
ejpam-6917	85	32	dng	dng	X
ejpam-6917	85	33	n)i	n)i	PUNCT
ejpam-6917	86	1	=	=	SYM
ejpam-6917	86	2	2n(gni	2n(gni	NUM
ejpam-6917	86	3	−	−	PROPN
ejpam-6917	86	4	gni−1	gni−1	PROPN
ejpam-6917	86	5	)	)	PUNCT
ejpam-6917	86	6	,	,	PUNCT
ejpam-6917	86	7	(	(	PUNCT
ejpam-6917	86	8	d2	d2	PROPN
ejpam-6917	86	9	ng	ng	PROPN
ejpam-6917	86	10	n)i	n)i	PROPN
ejpam-6917	87	1	=	=	SYM
ejpam-6917	87	2	22n(gni−1	22n(gni−1	NUM
ejpam-6917	88	1	−	−	PROPN
ejpam-6917	88	2	2gni	2gni	NOUN
ejpam-6917	88	3	+	+	CCONJ
ejpam-6917	88	4	gni+1	gni+1	X
ejpam-6917	88	5	)	)	PUNCT
ejpam-6917	88	6	,	,	PUNCT
ejpam-6917	88	7	i	i	PRON
ejpam-6917	88	8	∈	∈	PROPN
ejpam-6917	88	9	z.	z.	PROPN
ejpam-6917	89	1	in	in	ADP
ejpam-6917	89	2	this	this	DET
ejpam-6917	89	3	study	study	NOUN
ejpam-6917	89	4	,	,	PUNCT
ejpam-6917	89	5	we	we	PRON
ejpam-6917	89	6	consider	consider	VERB
ejpam-6917	89	7	a	a	DET
ejpam-6917	89	8	sequence	sequence	NOUN
ejpam-6917	89	9	gn	gn	PROPN
ejpam-6917	89	10	=	=	PUNCT
ejpam-6917	89	11	{	{	PUNCT
ejpam-6917	89	12	gni	gni	NOUN
ejpam-6917	89	13	:	:	PUNCT
ejpam-6917	89	14	i	i	PROPN
ejpam-6917	89	15	∈	∈	PROPN
ejpam-6917	90	1	z	z	AUX
ejpam-6917	90	2	}	}	PUNCT
ejpam-6917	90	3	at	at	ADP
ejpam-6917	90	4	level	level	NOUN
ejpam-6917	90	5	n	n	CCONJ
ejpam-6917	90	6	∈	∈	PROPN
ejpam-6917	90	7	n0	n0	NOUN
ejpam-6917	90	8	associated	associate	VERB
ejpam-6917	90	9	with	with	ADP
ejpam-6917	90	10	grid	grid	NOUN
ejpam-6917	90	11	points	point	NOUN
ejpam-6917	90	12	2−nz	2−nz	NUM
ejpam-6917	90	13	.	.	PUNCT
ejpam-6917	91	1	definition	definition	NOUN
ejpam-6917	91	2	2	2	NUM
ejpam-6917	91	3	.	.	PUNCT
ejpam-6917	92	1	a	a	DET
ejpam-6917	92	2	binary	binary	NOUN
ejpam-6917	92	3	ss	ss	NOUN
ejpam-6917	92	4	sp	sp	ADP
ejpam-6917	92	5	applied	apply	VERB
ejpam-6917	92	6	to	to	ADP
ejpam-6917	92	7	a	a	DET
ejpam-6917	92	8	given	give	VERB
ejpam-6917	92	9	initial	initial	ADJ
ejpam-6917	92	10	sequence	sequence	NOUN
ejpam-6917	92	11	g0	g0	NOUN
ejpam-6917	92	12	∈	∈	PROPN
ejpam-6917	92	13	c∞(z	c∞(z	VERB
ejpam-6917	92	14	)	)	PUNCT
ejpam-6917	92	15	is	be	AUX
ejpam-6917	92	16	called	call	VERB
ejpam-6917	92	17	uniformly	uniformly	ADV
ejpam-6917	92	18	convergent	convergent	NOUN
ejpam-6917	92	19	when	when	SCONJ
ejpam-6917	92	20	it	it	PRON
ejpam-6917	92	21	generates	generate	VERB
ejpam-6917	92	22	a	a	DET
ejpam-6917	92	23	continuous	continuous	ADJ
ejpam-6917	92	24	limit	limit	NOUN
ejpam-6917	92	25	curve	curve	NOUN
ejpam-6917	92	26	s∞	s∞	PROPN
ejpam-6917	92	27	p	p	PROPN
ejpam-6917	92	28	g0	g0	PROPN
ejpam-6917	92	29	∈	∈	PROPN
ejpam-6917	92	30	c(r	c(r	NOUN
ejpam-6917	92	31	)	)	PUNCT
ejpam-6917	92	32	such	such	ADJ
ejpam-6917	92	33	that	that	PRON
ejpam-6917	92	34	for	for	ADP
ejpam-6917	92	35	at	at	ADV
ejpam-6917	92	36	least	least	ADV
ejpam-6917	92	37	one	one	NUM
ejpam-6917	92	38	nonzero	nonzero	NOUN
ejpam-6917	92	39	initial	initial	ADJ
ejpam-6917	92	40	data	datum	NOUN
ejpam-6917	92	41	,	,	PUNCT
ejpam-6917	92	42	the	the	DET
ejpam-6917	92	43	sequence	sequence	NOUN
ejpam-6917	92	44	of	of	ADP
ejpam-6917	92	45	linear	linear	PROPN
ejpam-6917	92	46	interpolants	interpolant	NOUN
ejpam-6917	92	47	gn	gn	PROPN
ejpam-6917	92	48	,	,	PUNCT
ejpam-6917	92	49	at	at	ADP
ejpam-6917	92	50	grid	grid	NOUN
ejpam-6917	92	51	points	point	NOUN
ejpam-6917	92	52	2−nz	2−nz	NUM
ejpam-6917	92	53	,	,	PUNCT
ejpam-6917	92	54	satisfies	satisfie	NOUN
ejpam-6917	92	55	:	:	PUNCT
ejpam-6917	92	56	limn→∞||gn	limn→∞||gn	NOUN
ejpam-6917	92	57	−	−	PROPN
ejpam-6917	92	58	s∞	s∞	PROPN
ejpam-6917	92	59	p	p	NOUN
ejpam-6917	92	60	g0||l∞(n	g0||l∞(n	NOUN
ejpam-6917	92	61	)	)	PUNCT
ejpam-6917	93	1	=	=	PUNCT
ejpam-6917	93	2	0	0	NUM
ejpam-6917	93	3	,	,	PUNCT
ejpam-6917	93	4	where	where	SCONJ
ejpam-6917	93	5	n	n	PROPN
ejpam-6917	93	6	⊂	⊂	PROPN
ejpam-6917	93	7	r.	r.	PROPN
ejpam-6917	93	8	if	if	SCONJ
ejpam-6917	93	9	s∞	s∞	PROPN
ejpam-6917	93	10	p	p	PROPN
ejpam-6917	93	11	g0	g0	PROPN
ejpam-6917	93	12	has	have	VERB
ejpam-6917	93	13	continuous	continuous	ADJ
ejpam-6917	93	14	derivatives	derivative	NOUN
ejpam-6917	93	15	up	up	ADP
ejpam-6917	93	16	to	to	PART
ejpam-6917	93	17	order	order	VERB
ejpam-6917	93	18	e	e	NOUN
ejpam-6917	93	19	,	,	PUNCT
ejpam-6917	93	20	the	the	DET
ejpam-6917	93	21	{	{	PUNCT
ejpam-6917	93	22	sp	sp	NOUN
ejpam-6917	93	23	}	}	PUNCT
ejpam-6917	93	24	scheme	scheme	NOUN
ejpam-6917	93	25	is	be	AUX
ejpam-6917	93	26	termed	term	VERB
ejpam-6917	93	27	ce	ce	PROPN
ejpam-6917	93	28	-	-	NOUN
ejpam-6917	93	29	convergent	convergent	NOUN
ejpam-6917	93	30	.	.	PUNCT
ejpam-6917	94	1	specifically	specifically	ADV
ejpam-6917	94	2	,	,	PUNCT
ejpam-6917	94	3	as	as	SCONJ
ejpam-6917	94	4	the	the	DET
ejpam-6917	94	5	provided	provide	VERB
ejpam-6917	94	6	data	datum	NOUN
ejpam-6917	94	7	set	set	VERB
ejpam-6917	94	8	δ	δ	X
ejpam-6917	94	9	=	=	PRON
ejpam-6917	94	10	{	{	PUNCT
ejpam-6917	94	11	δ0,i	δ0,i	PROPN
ejpam-6917	94	12	:	:	PUNCT
ejpam-6917	94	13	i	i	PRON
ejpam-6917	94	14	∈	∈	PROPN
ejpam-6917	95	1	z	z	X
ejpam-6917	95	2	}	}	PUNCT
ejpam-6917	95	3	,	,	PUNCT
ejpam-6917	95	4	at	at	ADP
ejpam-6917	95	5	zeroth	zeroth	ADJ
ejpam-6917	95	6	level	level	NOUN
ejpam-6917	95	7	with	with	ADP
ejpam-6917	95	8	kronecker	kronecker	NOUN
ejpam-6917	95	9	delta	delta	NOUN
ejpam-6917	95	10	the	the	DET
ejpam-6917	95	11	fundamental	fundamental	ADJ
ejpam-6917	95	12	limit	limit	NOUN
ejpam-6917	95	13	function	function	NOUN
ejpam-6917	95	14	of	of	ADP
ejpam-6917	95	15	sp	sp	ADP
ejpam-6917	95	16	-scheme	-scheme	NOUN
ejpam-6917	95	17	is	be	AUX
ejpam-6917	95	18	given	give	VERB
ejpam-6917	95	19	as	as	ADP
ejpam-6917	95	20	,	,	PUNCT
ejpam-6917	95	21	ω	ω	NUM
ejpam-6917	95	22	=	=	SYM
ejpam-6917	95	23	s∞	s∞	PROPN
ejpam-6917	95	24	p	p	PROPN
ejpam-6917	95	25	δ	δ	PROPN
ejpam-6917	95	26	.	.	PUNCT
ejpam-6917	96	1	since	since	SCONJ
ejpam-6917	96	2	the	the	DET
ejpam-6917	96	3	subdivision	subdivision	NOUN
ejpam-6917	96	4	mask	mask	NOUN
ejpam-6917	96	5	c	c	PROPN
ejpam-6917	96	6	has	have	VERB
ejpam-6917	96	7	finite	finite	ADJ
ejpam-6917	96	8	support	support	NOUN
ejpam-6917	96	9	,	,	PUNCT
ejpam-6917	96	10	the	the	DET
ejpam-6917	96	11	basic	basic	ADJ
ejpam-6917	96	12	limit	limit	NOUN
ejpam-6917	96	13	function	function	NOUN
ejpam-6917	96	14	ω	ω	PROPN
ejpam-6917	96	15	also	also	ADV
ejpam-6917	96	16	has	have	VERB
ejpam-6917	96	17	finite	finite	ADJ
ejpam-6917	96	18	support	support	NOUN
ejpam-6917	96	19	.	.	PUNCT
ejpam-6917	97	1	by	by	ADP
ejpam-6917	97	2	the	the	DET
ejpam-6917	97	3	linearity	linearity	NOUN
ejpam-6917	97	4	of	of	ADP
ejpam-6917	97	5	the	the	DET
ejpam-6917	97	6	refinement	refinement	NOUN
ejpam-6917	97	7	rule	rule	NOUN
ejpam-6917	97	8	,	,	PUNCT
ejpam-6917	97	9	it	it	PRON
ejpam-6917	97	10	follows	follow	VERB
ejpam-6917	97	11	that	that	SCONJ
ejpam-6917	97	12	s∞	s∞	PROPN
ejpam-6917	97	13	p	p	PROPN
ejpam-6917	97	14	g0	g0	NOUN
ejpam-6917	97	15	=	=	SYM
ejpam-6917	97	16	∑	∑	PROPN
ejpam-6917	97	17	i∈z	i∈z	PROPN
ejpam-6917	97	18	gn0ω	gn0ω	NOUN
ejpam-6917	97	19	(	(	PUNCT
ejpam-6917	97	20	·	·	PUNCT
ejpam-6917	97	21	−	−	PROPN
ejpam-6917	98	1	i	i	NOUN
ejpam-6917	98	2	)	)	PUNCT
ejpam-6917	98	3	.	.	PUNCT
ejpam-6917	99	1	a	a	DET
ejpam-6917	99	2	well	well	ADV
ejpam-6917	99	3	-	-	PUNCT
ejpam-6917	99	4	established	establish	VERB
ejpam-6917	99	5	condition	condition	NOUN
ejpam-6917	99	6	for	for	ADP
ejpam-6917	99	7	the	the	DET
ejpam-6917	99	8	convergence	convergence	NOUN
ejpam-6917	99	9	of	of	ADP
ejpam-6917	99	10	an	an	DET
ejpam-6917	99	11	ss	ss	NOUN
ejpam-6917	99	12	sp	sp	NOUN
ejpam-6917	99	13	with	with	ADP
ejpam-6917	99	14	mask	mask	NOUN
ejpam-6917	99	15	c	c	PROPN
ejpam-6917	99	16	=	=	SYM
ejpam-6917	99	17	{	{	PUNCT
ejpam-6917	99	18	ci	ci	NOUN
ejpam-6917	99	19	:	:	PUNCT
ejpam-6917	100	1	i	i	PROPN
ejpam-6917	100	2	∈	∈	PROPN
ejpam-6917	101	1	z	z	X
ejpam-6917	101	2	}	}	PUNCT
ejpam-6917	101	3	is	be	AUX
ejpam-6917	101	4	that	that	SCONJ
ejpam-6917	101	5	its	its	PRON
ejpam-6917	101	6	even	even	ADJ
ejpam-6917	101	7	and	and	CCONJ
ejpam-6917	101	8	odd	odd	ADJ
ejpam-6917	101	9	values	value	NOUN
ejpam-6917	101	10	satisfy	satisfy	VERB
ejpam-6917	101	11	the	the	DET
ejpam-6917	101	12	partition	partition	NOUN
ejpam-6917	101	13	of	of	ADP
ejpam-6917	101	14	unity	unity	NOUN
ejpam-6917	101	15	property:∑	property:∑	PROPN
ejpam-6917	101	16	i∈z	i∈z	NOUN
ejpam-6917	101	17	cj−2i	cj−2i	VERB
ejpam-6917	102	1	=	=	SYM
ejpam-6917	102	2	1	1	NUM
ejpam-6917	102	3	,	,	PUNCT
ejpam-6917	102	4	j	j	PROPN
ejpam-6917	102	5	=	=	SYM
ejpam-6917	102	6	0	0	NUM
ejpam-6917	102	7	,	,	PUNCT
ejpam-6917	102	8	1	1	NUM
ejpam-6917	102	9	.	.	PUNCT
ejpam-6917	103	1	indeed	indeed	ADV
ejpam-6917	103	2	,	,	PUNCT
ejpam-6917	103	3	for	for	ADP
ejpam-6917	103	4	an	an	DET
ejpam-6917	103	5	ss	ss	NOUN
ejpam-6917	103	6	defined	define	VERB
ejpam-6917	103	7	by	by	ADP
ejpam-6917	103	8	mask	mask	NOUN
ejpam-6917	103	9	c	c	PROPN
ejpam-6917	103	10	,	,	PUNCT
ejpam-6917	103	11	its	its	PRON
ejpam-6917	103	12	essential	essential	ADJ
ejpam-6917	103	13	properties	property	NOUN
ejpam-6917	103	14	,	,	PUNCT
ejpam-6917	103	15	including	include	VERB
ejpam-6917	103	16	convergence	convergence	NOUN
ejpam-6917	103	17	,	,	PUNCT
ejpam-6917	103	18	regularity	regularity	NOUN
ejpam-6917	103	19	,	,	PUNCT
ejpam-6917	103	20	and	and	CCONJ
ejpam-6917	103	21	polynomial	polynomial	ADJ
ejpam-6917	103	22	reproduction	reproduction	NOUN
ejpam-6917	103	23	(	(	PUNCT
ejpam-6917	103	24	or	or	CCONJ
ejpam-6917	103	25	generation	generation	NOUN
ejpam-6917	103	26	)	)	PUNCT
ejpam-6917	103	27	,	,	PUNCT
ejpam-6917	103	28	are	be	AUX
ejpam-6917	103	29	encapsulated	encapsulate	VERB
ejpam-6917	103	30	in	in	ADP
ejpam-6917	103	31	its	its	PRON
ejpam-6917	103	32	symbol	symbol	NOUN
ejpam-6917	103	33	,	,	PUNCT
ejpam-6917	103	34	defined	define	VERB
ejpam-6917	103	35	by	by	ADP
ejpam-6917	103	36	the	the	DET
ejpam-6917	103	37	v	v	NOUN
ejpam-6917	103	38	-	-	PUNCT
ejpam-6917	103	39	transform	transform	NOUN
ejpam-6917	103	40	:	:	PUNCT
ejpam-6917	103	41	c(v	c(v	PROPN
ejpam-6917	103	42	)	)	PUNCT
ejpam-6917	104	1	=	=	PUNCT
ejpam-6917	104	2	∑	∑	PUNCT
ejpam-6917	104	3	i∈z	i∈z	NOUN
ejpam-6917	104	4	civ	civ	VERB
ejpam-6917	104	5	i	i	PRON
ejpam-6917	104	6	,	,	PUNCT
ejpam-6917	104	7	v	v	PROPN
ejpam-6917	104	8	∈	∈	PROPN
ejpam-6917	104	9	c\{0	c\{0	NOUN
ejpam-6917	104	10	}	}	PUNCT
ejpam-6917	104	11	.	.	PUNCT
ejpam-6917	105	1	f.	f.	PROPN
ejpam-6917	105	2	s.	s.	PROPN
ejpam-6917	105	3	alshammari	alshammari	PROPN
ejpam-6917	105	4	et	et	PROPN
ejpam-6917	105	5	al	al	PROPN
ejpam-6917	105	6	.	.	PUNCT
ejpam-6917	105	7	/	/	SYM
ejpam-6917	105	8	eur	eur	PROPN
ejpam-6917	105	9	.	.	PUNCT
ejpam-6917	106	1	j.	j.	PROPN
ejpam-6917	106	2	pure	pure	PROPN
ejpam-6917	106	3	appl	appl	PROPN
ejpam-6917	106	4	.	.	PROPN
ejpam-6917	106	5	math	math	PROPN
ejpam-6917	106	6	,	,	PUNCT
ejpam-6917	106	7	18	18	NUM
ejpam-6917	106	8	(	(	PUNCT
ejpam-6917	106	9	4	4	NUM
ejpam-6917	106	10	)	)	PUNCT
ejpam-6917	106	11	(	(	PUNCT
ejpam-6917	106	12	2025	2025	NUM
ejpam-6917	106	13	)	)	PUNCT
ejpam-6917	106	14	,	,	PUNCT
ejpam-6917	106	15	6917	6917	NUM
ejpam-6917	106	16	5	5	NUM
ejpam-6917	106	17	of	of	ADP
ejpam-6917	106	18	26	26	NUM
ejpam-6917	106	19	since	since	SCONJ
ejpam-6917	106	20	c	c	PROPN
ejpam-6917	106	21	is	be	AUX
ejpam-6917	106	22	finitely	finitely	ADV
ejpam-6917	106	23	supported	support	VERB
ejpam-6917	106	24	,	,	PUNCT
ejpam-6917	106	25	the	the	DET
ejpam-6917	106	26	symbol	symbol	NOUN
ejpam-6917	106	27	c(v	c(v	PROPN
ejpam-6917	106	28	)	)	PUNCT
ejpam-6917	106	29	forms	form	VERB
ejpam-6917	106	30	a	a	DET
ejpam-6917	106	31	laurent	laurent	NOUN
ejpam-6917	106	32	polynomial	polynomial	NOUN
ejpam-6917	106	33	.	.	PUNCT
ejpam-6917	107	1	the	the	DET
ejpam-6917	107	2	norm	norm	NOUN
ejpam-6917	107	3	of	of	ADP
ejpam-6917	107	4	the	the	DET
ejpam-6917	107	5	associated	associated	ADJ
ejpam-6917	107	6	ss	ss	NOUN
ejpam-6917	107	7	sp	sp	NOUN
ejpam-6917	107	8	is	be	AUX
ejpam-6917	107	9	given	give	VERB
ejpam-6917	107	10	by	by	ADP
ejpam-6917	107	11	:	:	PUNCT
ejpam-6917	107	12	||sp	||sp	NOUN
ejpam-6917	107	13	||∞	||∞	PROPN
ejpam-6917	107	14	=	=	SYM
ejpam-6917	107	15	max	max	PROPN
ejpam-6917	107	16	{	{	PUNCT
ejpam-6917	107	17	∑	∑	PUNCT
ejpam-6917	107	18	i∈z	i∈z	PROPN
ejpam-6917	107	19	|c2i|	|c2i|	VERB
ejpam-6917	107	20	,	,	PUNCT
ejpam-6917	107	21	∑	∑	PUNCT
ejpam-6917	107	22	i∈z	i∈z	PROPN
ejpam-6917	107	23	|c1	|c1	VERB
ejpam-6917	107	24	+	+	PROPN
ejpam-6917	107	25	2i|	2i|	NUM
ejpam-6917	107	26	}	}	PUNCT
ejpam-6917	107	27	.	.	PUNCT
ejpam-6917	108	1	additionally	additionally	ADV
ejpam-6917	108	2	,	,	PUNCT
ejpam-6917	108	3	the	the	DET
ejpam-6917	108	4	laurent	laurent	NOUN
ejpam-6917	108	5	polynomial	polynomial	PROPN
ejpam-6917	108	6	corresponding	corresponding	NOUN
ejpam-6917	108	7	to	to	ADP
ejpam-6917	108	8	the	the	DET
ejpam-6917	108	9	m	m	ADV
ejpam-6917	108	10	-	-	PUNCT
ejpam-6917	108	11	iterated	iterated	ADJ
ejpam-6917	108	12	rule	rule	NOUN
ejpam-6917	108	13	sm	sm	PROPN
ejpam-6917	109	1	p	p	NOUN
ejpam-6917	109	2	is	be	AUX
ejpam-6917	109	3	:	:	PUNCT
ejpam-6917	109	4	c	c	X
ejpam-6917	110	1	[	[	X
ejpam-6917	110	2	m](v	m](v	ADJ
ejpam-6917	110	3	)	)	PUNCT
ejpam-6917	110	4	=	=	PUNCT
ejpam-6917	111	1	m−1∏	m−1∏	ADJ
ejpam-6917	111	2	l=0	l=0	PROPN
ejpam-6917	111	3	c(v2	c(v2	NOUN
ejpam-6917	111	4	l	l	NOUN
ejpam-6917	111	5	)	)	PUNCT
ejpam-6917	112	1	=	=	PUNCT
ejpam-6917	112	2	∑	∑	PUNCT
ejpam-6917	112	3	i∈z	i∈z	PROPN
ejpam-6917	112	4	c	c	AUX
ejpam-6917	113	1	[	[	X
ejpam-6917	113	2	m	m	X
ejpam-6917	113	3	]	]	X
ejpam-6917	113	4	i	i	PRON
ejpam-6917	113	5	vi	vi	PROPN
ejpam-6917	113	6	,	,	PUNCT
ejpam-6917	113	7	where	where	SCONJ
ejpam-6917	113	8	s0	s0	PROPN
ejpam-6917	113	9	p	p	NOUN
ejpam-6917	113	10	=	=	PROPN
ejpam-6917	113	11	sp	sp	ADP
ejpam-6917	113	12	and	and	CCONJ
ejpam-6917	113	13	the	the	DET
ejpam-6917	113	14	norm	norm	NOUN
ejpam-6917	113	15	of	of	ADP
ejpam-6917	113	16	sm	sm	PROPN
ejpam-6917	113	17	p	p	PROPN
ejpam-6917	113	18	is	be	AUX
ejpam-6917	113	19	given	give	VERB
ejpam-6917	113	20	by	by	ADP
ejpam-6917	113	21	:	:	PUNCT
ejpam-6917	113	22	||sm	||sm	NOUN
ejpam-6917	113	23	p	p	PROPN
ejpam-6917	113	24	||∞	||∞	PROPN
ejpam-6917	113	25	=	=	SYM
ejpam-6917	113	26	max	max	PROPN
ejpam-6917	113	27	{	{	PUNCT
ejpam-6917	113	28	∑	∑	PROPN
ejpam-6917	113	29	i∈z	i∈z	PROPN
ejpam-6917	113	30	|c[m	|c[m	X
ejpam-6917	113	31	]	]	PUNCT
ejpam-6917	114	1	j+2mi|	j+2mi|	PROPN
ejpam-6917	114	2	:	:	PUNCT
ejpam-6917	114	3	j	j	PROPN
ejpam-6917	114	4	=	=	SYM
ejpam-6917	114	5	0	0	PROPN
ejpam-6917	114	6	,	,	PUNCT
ejpam-6917	114	7	1	1	NUM
ejpam-6917	114	8	,	,	PUNCT
ejpam-6917	114	9	...	...	PUNCT
ejpam-6917	114	10	,	,	PUNCT
ejpam-6917	114	11	2	2	NUM
ejpam-6917	114	12	m	m	NOUN
ejpam-6917	114	13	−	−	NOUN
ejpam-6917	114	14	1	1	NUM
ejpam-6917	114	15	}	}	PUNCT
ejpam-6917	114	16	.	.	PUNCT
ejpam-6917	115	1	a	a	DET
ejpam-6917	115	2	crucial	crucial	ADJ
ejpam-6917	115	3	property	property	NOUN
ejpam-6917	115	4	of	of	ADP
ejpam-6917	115	5	an	an	DET
ejpam-6917	115	6	ss	ss	NOUN
ejpam-6917	115	7	is	be	AUX
ejpam-6917	115	8	its	its	PRON
ejpam-6917	115	9	order	order	NOUN
ejpam-6917	115	10	of	of	ADP
ejpam-6917	115	11	approximation	approximation	NOUN
ejpam-6917	115	12	,	,	PUNCT
ejpam-6917	115	13	which	which	PRON
ejpam-6917	115	14	is	be	AUX
ejpam-6917	115	15	related	relate	VERB
ejpam-6917	115	16	to	to	ADP
ejpam-6917	115	17	its	its	PRON
ejpam-6917	115	18	ability	ability	NOUN
ejpam-6917	115	19	to	to	PART
ejpam-6917	115	20	reproduce	reproduce	VERB
ejpam-6917	115	21	polynomials	polynomial	NOUN
ejpam-6917	115	22	.	.	PUNCT
ejpam-6917	116	1	definition	definition	NOUN
ejpam-6917	116	2	3	3	X
ejpam-6917	116	3	.	.	PUNCT
ejpam-6917	117	1	let	let	VERB
ejpam-6917	117	2	q0	q0	PROPN
ejpam-6917	117	3	=	=	PUNCT
ejpam-6917	117	4	{	{	PUNCT
ejpam-6917	117	5	q(m	q(m	PROPN
ejpam-6917	117	6	)	)	PUNCT
ejpam-6917	117	7	:	:	PUNCT
ejpam-6917	118	1	m	m	VERB
ejpam-6917	118	2	∈	∈	PROPN
ejpam-6917	118	3	z	z	NOUN
ejpam-6917	118	4	}	}	PUNCT
ejpam-6917	119	1	where	where	SCONJ
ejpam-6917	119	2	q	q	PROPN
ejpam-6917	119	3	∈	∈	PROPN
ejpam-6917	119	4	∏	∏	PROPN
ejpam-6917	119	5	e	e	NOUN
ejpam-6917	119	6	with	with	ADP
ejpam-6917	119	7	e	e	PROPN
ejpam-6917	119	8	∈	∈	PROPN
ejpam-6917	119	9	n0	n0	PROPN
ejpam-6917	119	10	.	.	PUNCT
ejpam-6917	120	1	we	we	PRON
ejpam-6917	120	2	say	say	VERB
ejpam-6917	120	3	that	that	SCONJ
ejpam-6917	120	4	a	a	DET
ejpam-6917	120	5	stationary	stationary	ADJ
ejpam-6917	120	6	ss	ss	NOUN
ejpam-6917	120	7	sp	sp	ADP
ejpam-6917	120	8	reproduces	reproduce	NOUN
ejpam-6917	120	9	polynomials	polynomial	NOUN
ejpam-6917	120	10	in	in	ADP
ejpam-6917	120	11	∏	∏	PROPN
ejpam-6917	120	12	e	e	NOUN
ejpam-6917	120	13	if	if	SCONJ
ejpam-6917	120	14	sp	sp	PROPN
ejpam-6917	120	15	is	be	AUX
ejpam-6917	120	16	convergent	convergent	ADJ
ejpam-6917	120	17	and	and	CCONJ
ejpam-6917	120	18	p	p	NOUN
ejpam-6917	120	19	=	=	PUNCT
ejpam-6917	120	20	s∞	s∞	PROPN
ejpam-6917	120	21	p	p	NOUN
ejpam-6917	120	22	q0	q0	PROPN
ejpam-6917	120	23	.	.	PUNCT
ejpam-6917	121	1	also	also	ADV
ejpam-6917	121	2	,	,	PUNCT
ejpam-6917	121	3	the	the	DET
ejpam-6917	121	4	ss	ss	PROPN
ejpam-6917	121	5	sp	sp	NOUN
ejpam-6917	121	6	is	be	AUX
ejpam-6917	121	7	said	say	VERB
ejpam-6917	121	8	to	to	PART
ejpam-6917	121	9	be	be	AUX
ejpam-6917	121	10	∏	∏	NUM
ejpam-6917	121	11	e	e	NOUN
ejpam-6917	121	12	-	-	ADJ
ejpam-6917	121	13	generating	generating	ADJ
ejpam-6917	121	14	s∞	s∞	NOUN
ejpam-6917	121	15	p	p	NOUN
ejpam-6917	121	16	q0	q0	PROPN
ejpam-6917	121	17	∈	∈	PROPN
ejpam-6917	121	18	∏	∏	PROPN
ejpam-6917	121	19	e	e	NOUN
ejpam-6917	122	1	[	[	X
ejpam-6917	122	2	26	26	NUM
ejpam-6917	122	3	]	]	PUNCT
ejpam-6917	122	4	.	.	PUNCT
ejpam-6917	123	1	polynomial	polynomial	ADJ
ejpam-6917	123	2	reproduction	reproduction	NOUN
ejpam-6917	123	3	is	be	AUX
ejpam-6917	123	4	a	a	DET
ejpam-6917	123	5	valuable	valuable	ADJ
ejpam-6917	123	6	property	property	NOUN
ejpam-6917	123	7	,	,	PUNCT
ejpam-6917	123	8	as	as	SCONJ
ejpam-6917	123	9	it	it	PRON
ejpam-6917	123	10	guarantees	guarantee	VERB
ejpam-6917	123	11	that	that	SCONJ
ejpam-6917	123	12	a	a	DET
ejpam-6917	123	13	convergent	convergent	NOUN
ejpam-6917	123	14	ss	ss	NOUN
ejpam-6917	123	15	sp	sp	NOUN
ejpam-6917	123	16	with	with	ADP
ejpam-6917	123	17	a	a	DET
ejpam-6917	123	18	compactly	compactly	ADV
ejpam-6917	123	19	supported	support	VERB
ejpam-6917	123	20	mask	mask	NOUN
ejpam-6917	123	21	reproduces	reproduce	NOUN
ejpam-6917	123	22	polynomials	polynomial	NOUN
ejpam-6917	123	23	of	of	ADP
ejpam-6917	123	24	degree	degree	NOUN
ejpam-6917	123	25	e	e	NOUN
ejpam-6917	123	26	,	,	PUNCT
ejpam-6917	123	27	ensuring	ensure	VERB
ejpam-6917	123	28	order	order	NOUN
ejpam-6917	123	29	of	of	ADP
ejpam-6917	123	30	approximation	approximation	NOUN
ejpam-6917	123	31	e+1	e+1	PUNCT
ejpam-6917	124	1	[	[	X
ejpam-6917	124	2	27	27	NUM
ejpam-6917	124	3	]	]	PUNCT
ejpam-6917	124	4	.	.	PUNCT
ejpam-6917	125	1	however	however	ADV
ejpam-6917	125	2	,	,	PUNCT
ejpam-6917	125	3	generating	generating	NOUN
ejpam-6917	125	4	polynomials	polynomial	NOUN
ejpam-6917	125	5	of	of	ADP
ejpam-6917	125	6	degree	degree	NOUN
ejpam-6917	125	7	e	e	NOUN
ejpam-6917	125	8	does	do	AUX
ejpam-6917	125	9	n’t	not	PART
ejpam-6917	125	10	necessarily	necessarily	ADV
ejpam-6917	125	11	imply	imply	VERB
ejpam-6917	125	12	the	the	DET
ejpam-6917	125	13	same	same	ADJ
ejpam-6917	125	14	level	level	NOUN
ejpam-6917	125	15	of	of	ADP
ejpam-6917	125	16	approximation	approximation	NOUN
ejpam-6917	125	17	accuracy	accuracy	NOUN
ejpam-6917	125	18	e	e	NOUN
ejpam-6917	125	19	+	+	NOUN
ejpam-6917	125	20	1	1	X
ejpam-6917	125	21	.	.	X
ejpam-6917	125	22	for	for	ADP
ejpam-6917	125	23	example	example	NOUN
ejpam-6917	125	24	,	,	PUNCT
ejpam-6917	125	25	the	the	DET
ejpam-6917	125	26	qb	qb	NOUN
ejpam-6917	125	27	-	-	PUNCT
ejpam-6917	125	28	scheme	scheme	NOUN
ejpam-6917	125	29	of	of	ADP
ejpam-6917	125	30	degree	degree	NOUN
ejpam-6917	125	31	e	e	NOUN
ejpam-6917	125	32	generates	generate	VERB
ejpam-6917	125	33	polynomials	polynomial	NOUN
ejpam-6917	125	34	in	in	ADP
ejpam-6917	125	35	∏	∏	PROPN
ejpam-6917	125	36	e	e	NOUN
ejpam-6917	125	37	,	,	PUNCT
ejpam-6917	125	38	but	but	CCONJ
ejpam-6917	125	39	only	only	ADV
ejpam-6917	125	40	reproduces	reproduce	VERB
ejpam-6917	125	41	linear	linear	ADJ
ejpam-6917	125	42	polynomials	polynomial	NOUN
ejpam-6917	125	43	(	(	PUNCT
ejpam-6917	125	44	∏	∏	PROPN
ejpam-6917	125	45	1	1	NUM
ejpam-6917	125	46	)	)	PUNCT
ejpam-6917	125	47	,	,	PUNCT
ejpam-6917	125	48	yielding	yield	VERB
ejpam-6917	125	49	an	an	DET
ejpam-6917	125	50	order	order	NOUN
ejpam-6917	125	51	of	of	ADP
ejpam-6917	125	52	approximation	approximation	NOUN
ejpam-6917	125	53	2	2	NUM
ejpam-6917	125	54	.	.	PUNCT
ejpam-6917	125	55	according	accord	VERB
ejpam-6917	125	56	to	to	ADP
ejpam-6917	125	57	levin	levin	PROPN
ejpam-6917	125	58	’s	’s	PART
ejpam-6917	125	59	work	work	NOUN
ejpam-6917	125	60	[	[	X
ejpam-6917	125	61	28	28	NUM
ejpam-6917	125	62	]	]	X
ejpam-6917	125	63	,	,	PUNCT
ejpam-6917	125	64	an	an	DET
ejpam-6917	125	65	ss	ss	NOUN
ejpam-6917	125	66	that	that	PRON
ejpam-6917	125	67	generates	generate	VERB
ejpam-6917	125	68	polynomials	polynomial	NOUN
ejpam-6917	125	69	of	of	ADP
ejpam-6917	125	70	degree	degree	NOUN
ejpam-6917	125	71	e	e	NOUN
ejpam-6917	125	72	can	can	AUX
ejpam-6917	125	73	be	be	AUX
ejpam-6917	125	74	modified	modify	VERB
ejpam-6917	125	75	to	to	PART
ejpam-6917	125	76	reproduce	reproduce	VERB
ejpam-6917	125	77	polynomials	polynomial	NOUN
ejpam-6917	125	78	in	in	ADP
ejpam-6917	125	79	∏	∏	PROPN
ejpam-6917	125	80	e	e	NOUN
ejpam-6917	125	81	by	by	ADP
ejpam-6917	125	82	applying	apply	VERB
ejpam-6917	125	83	a	a	DET
ejpam-6917	125	84	specific	specific	ADJ
ejpam-6917	125	85	operator	operator	NOUN
ejpam-6917	125	86	to	to	ADP
ejpam-6917	125	87	the	the	DET
ejpam-6917	125	88	initial	initial	ADJ
ejpam-6917	125	89	sequence	sequence	NOUN
ejpam-6917	125	90	.	.	PUNCT
ejpam-6917	126	1	nevertheless	nevertheless	ADV
ejpam-6917	126	2	,	,	PUNCT
ejpam-6917	126	3	it	it	PRON
ejpam-6917	126	4	is	be	AUX
ejpam-6917	126	5	noted	note	VERB
ejpam-6917	126	6	that	that	SCONJ
ejpam-6917	126	7	the	the	DET
ejpam-6917	126	8	resulting	result	VERB
ejpam-6917	126	9	order	order	NOUN
ejpam-6917	126	10	of	of	ADP
ejpam-6917	126	11	approximation	approximation	NOUN
ejpam-6917	126	12	is	be	AUX
ejpam-6917	126	13	often	often	ADV
ejpam-6917	126	14	not	not	PART
ejpam-6917	126	15	optimal	optimal	ADJ
ejpam-6917	126	16	.	.	PUNCT
ejpam-6917	127	1	however	however	ADV
ejpam-6917	127	2	,	,	PUNCT
ejpam-6917	127	3	we	we	PRON
ejpam-6917	127	4	introduce	introduce	VERB
ejpam-6917	127	5	a	a	DET
ejpam-6917	127	6	new	new	ADJ
ejpam-6917	127	7	ss	ss	NOUN
ejpam-6917	127	8	using	use	VERB
ejpam-6917	127	9	a	a	DET
ejpam-6917	127	10	tension	tension	NOUN
ejpam-6917	127	11	parameter	parameter	NOUN
ejpam-6917	127	12	,	,	PUNCT
ejpam-6917	127	13	offering	offer	VERB
ejpam-6917	127	14	improved	improve	VERB
ejpam-6917	127	15	smoothness	smoothness	ADJ
ejpam-6917	127	16	c5	c5	PROPN
ejpam-6917	127	17	and	and	CCONJ
ejpam-6917	127	18	sixth	sixth	ADJ
ejpam-6917	127	19	-	-	PUNCT
ejpam-6917	127	20	order	order	NOUN
ejpam-6917	127	21	of	of	ADP
ejpam-6917	127	22	approximation	approximation	NOUN
ejpam-6917	127	23	,	,	PUNCT
ejpam-6917	127	24	while	while	SCONJ
ejpam-6917	127	25	reproducing	reproduce	VERB
ejpam-6917	127	26	linear	linear	ADJ
ejpam-6917	127	27	polynomials	polynomial	NOUN
ejpam-6917	127	28	and	and	CCONJ
ejpam-6917	127	29	generating	generating	NOUN
ejpam-6917	127	30	polynomials	polynomial	NOUN
ejpam-6917	127	31	in	in	ADP
ejpam-6917	127	32	∏	∏	PROPN
ejpam-6917	127	33	5	5	NUM
ejpam-6917	127	34	.	.	NOUN
ejpam-6917	127	35	3	3	NUM
ejpam-6917	127	36	.	.	PUNCT
ejpam-6917	128	1	the	the	DET
ejpam-6917	128	2	proposed	propose	VERB
ejpam-6917	128	3	subdivision	subdivision	NOUN
ejpam-6917	128	4	scheme	scheme	VERB
ejpam-6917	128	5	the	the	DET
ejpam-6917	128	6	following	follow	VERB
ejpam-6917	128	7	section	section	NOUN
ejpam-6917	128	8	introduces	introduce	VERB
ejpam-6917	128	9	a	a	DET
ejpam-6917	128	10	new	new	ADJ
ejpam-6917	128	11	six	six	NUM
ejpam-6917	128	12	-	-	PUNCT
ejpam-6917	128	13	point	point	NOUN
ejpam-6917	128	14	binary	binary	ADJ
ejpam-6917	128	15	subdivision	subdivision	NOUN
ejpam-6917	128	16	schemes	scheme	NOUN
ejpam-6917	128	17	.	.	PUNCT
ejpam-6917	129	1	we	we	PRON
ejpam-6917	129	2	also	also	ADV
ejpam-6917	129	3	discuss	discuss	VERB
ejpam-6917	129	4	the	the	DET
ejpam-6917	129	5	properties	property	NOUN
ejpam-6917	129	6	of	of	ADP
ejpam-6917	129	7	polynomial	polynomial	ADJ
ejpam-6917	129	8	generation	generation	NOUN
ejpam-6917	129	9	.	.	PUNCT
ejpam-6917	130	1	3.1	3.1	NUM
ejpam-6917	130	2	.	.	PUNCT
ejpam-6917	130	3	construction	construction	NOUN
ejpam-6917	130	4	we	we	PRON
ejpam-6917	130	5	construct	construct	VERB
ejpam-6917	130	6	a	a	DET
ejpam-6917	130	7	novel	novel	ADJ
ejpam-6917	130	8	class	class	NOUN
ejpam-6917	130	9	of	of	ADP
ejpam-6917	130	10	stationary	stationary	ADJ
ejpam-6917	130	11	sss	sss	NOUN
ejpam-6917	130	12	that	that	SCONJ
ejpam-6917	130	13	combining	combine	VERB
ejpam-6917	130	14	the	the	DET
ejpam-6917	130	15	advantages	advantage	NOUN
ejpam-6917	130	16	of	of	ADP
ejpam-6917	130	17	the	the	DET
ejpam-6917	130	18	qb	qb	NOUN
ejpam-6917	130	19	-	-	PUNCT
ejpam-6917	130	20	scheme	scheme	NOUN
ejpam-6917	130	21	and	and	CCONJ
ejpam-6917	130	22	the	the	DET
ejpam-6917	130	23	sd	sd	NOUN
ejpam-6917	130	24	-	-	PUNCT
ejpam-6917	130	25	scheme	scheme	NOUN
ejpam-6917	130	26	via	via	ADP
ejpam-6917	130	27	a	a	DET
ejpam-6917	130	28	tension	tension	NOUN
ejpam-6917	130	29	parameter	parameter	NOUN
ejpam-6917	130	30	.	.	PUNCT
ejpam-6917	131	1	sequence	sequence	NOUN
ejpam-6917	131	2	of	of	ADP
ejpam-6917	131	3	data	datum	NOUN
ejpam-6917	131	4	is	be	AUX
ejpam-6917	131	5	given	give	VERB
ejpam-6917	131	6	by	by	ADP
ejpam-6917	131	7	f.	f.	PROPN
ejpam-6917	131	8	s.	s.	PROPN
ejpam-6917	131	9	alshammari	alshammari	PROPN
ejpam-6917	131	10	et	et	PROPN
ejpam-6917	131	11	al	al	PROPN
ejpam-6917	131	12	.	.	PUNCT
ejpam-6917	131	13	/	/	SYM
ejpam-6917	131	14	eur	eur	PROPN
ejpam-6917	131	15	.	.	PUNCT
ejpam-6917	132	1	j.	j.	PROPN
ejpam-6917	132	2	pure	pure	PROPN
ejpam-6917	132	3	appl	appl	PROPN
ejpam-6917	132	4	.	.	PROPN
ejpam-6917	132	5	math	math	PROPN
ejpam-6917	132	6	,	,	PUNCT
ejpam-6917	132	7	18	18	NUM
ejpam-6917	132	8	(	(	PUNCT
ejpam-6917	132	9	4	4	NUM
ejpam-6917	132	10	)	)	PUNCT
ejpam-6917	132	11	(	(	PUNCT
ejpam-6917	132	12	2025	2025	NUM
ejpam-6917	132	13	)	)	PUNCT
ejpam-6917	132	14	,	,	PUNCT
ejpam-6917	132	15	6917	6917	NUM
ejpam-6917	132	16	6	6	NUM
ejpam-6917	132	17	of	of	ADP
ejpam-6917	132	18	26	26	NUM
ejpam-6917	132	19	gk	gk	NOUN
ejpam-6917	132	20	=	=	PUNCT
ejpam-6917	132	21	{	{	PUNCT
ejpam-6917	132	22	gni	gni	NOUN
ejpam-6917	132	23	:	:	PUNCT
ejpam-6917	132	24	i	i	PROPN
ejpam-6917	132	25	∈	∈	PROPN
ejpam-6917	133	1	z	z	AUX
ejpam-6917	133	2	}	}	PUNCT
ejpam-6917	133	3	at	at	ADP
ejpam-6917	133	4	level	level	NOUN
ejpam-6917	133	5	n	n	CCONJ
ejpam-6917	133	6	,	,	PUNCT
ejpam-6917	133	7	sequence	sequence	NOUN
ejpam-6917	133	8	of	of	ADP
ejpam-6917	133	9	refined	refined	ADJ
ejpam-6917	133	10	data	datum	NOUN
ejpam-6917	133	11	gn+1	gn+1	NOUN
ejpam-6917	133	12	=	=	PUNCT
ejpam-6917	133	13	{	{	PUNCT
ejpam-6917	133	14	gn+1	gn+1	PROPN
ejpam-6917	133	15	i	i	PRON
ejpam-6917	133	16	:	:	PUNCT
ejpam-6917	134	1	i	i	PROPN
ejpam-6917	134	2	∈	∈	PROPN
ejpam-6917	134	3	z	z	AUX
ejpam-6917	134	4	}	}	PUNCT
ejpam-6917	134	5	is	be	AUX
ejpam-6917	134	6	computed	compute	VERB
ejpam-6917	134	7	as	as	ADP
ejpam-6917	134	8	a	a	DET
ejpam-6917	134	9	linear	linear	ADJ
ejpam-6917	134	10	combination	combination	NOUN
ejpam-6917	134	11	of	of	ADP
ejpam-6917	134	12	previous	previous	ADJ
ejpam-6917	134	13	value	value	NOUN
ejpam-6917	134	14	of	of	ADP
ejpam-6917	134	15	gn	gn	PROPN
ejpam-6917	134	16	in	in	ADP
ejpam-6917	134	17	the	the	DET
ejpam-6917	134	18	following	follow	VERB
ejpam-6917	134	19	two	two	NUM
ejpam-6917	134	20	rules:	rules:	NOUN
ejpam-6917	134	21	gn+1	gn+1	NOUN
ejpam-6917	134	22	2i	2i	NOUN
ejpam-6917	134	23	=	=	SYM
ejpam-6917	134	24	1	1	NUM
ejpam-6917	134	25	64	64	NUM
ejpam-6917	134	26	(	(	PUNCT
ejpam-6917	134	27	(	(	PUNCT
ejpam-6917	134	28	µ0)g	µ0)g	NOUN
ejpam-6917	134	29	n	n	PRON
ejpam-6917	134	30	i−2	i−2	NOUN
ejpam-6917	134	31	+	+	CCONJ
ejpam-6917	134	32	(	(	PUNCT
ejpam-6917	134	33	16µ0)g	16µ0)g	NUM
ejpam-6917	134	34	n	n	CCONJ
ejpam-6917	134	35	i−1	i−1	PROPN
ejpam-6917	134	36	+	+	CCONJ
ejpam-6917	134	37	(	(	PUNCT
ejpam-6917	134	38	64−	64−	NOUN
ejpam-6917	134	39	34µ0)g	34µ0)g	NUM
ejpam-6917	134	40	n	n	NOUN
ejpam-6917	134	41	i	i	PRON
ejpam-6917	134	42	+	+	CCONJ
ejpam-6917	134	43	(	(	PUNCT
ejpam-6917	134	44	16µ0)g	16µ0)g	NUM
ejpam-6917	134	45	n	n	PRON
ejpam-6917	134	46	i+1	i+1	NOUN
ejpam-6917	134	47	+	+	CCONJ
ejpam-6917	134	48	(	(	PUNCT
ejpam-6917	134	49	µ0)g	µ0)g	NOUN
ejpam-6917	134	50	n	n	PROPN
ejpam-6917	134	51	i+2	i+2	NUM
ejpam-6917	134	52	)	)	PUNCT
ejpam-6917	134	53	,	,	PUNCT
ejpam-6917	134	54	gn+1	gn+1	ADJ
ejpam-6917	134	55	2i+1	2i+1	PROPN
ejpam-6917	134	56	=	=	NOUN
ejpam-6917	134	57	1	1	NUM
ejpam-6917	134	58	256	256	NUM
ejpam-6917	134	59	(	(	PUNCT
ejpam-6917	134	60	(	(	PUNCT
ejpam-6917	134	61	3−	3−	NUM
ejpam-6917	134	62	3µ0)g	3µ0)g	NUM
ejpam-6917	134	63	n	n	NOUN
ejpam-6917	134	64	i−2	i−2	VERB
ejpam-6917	135	1	+	+	PUNCT
ejpam-6917	135	2	(	(	PUNCT
ejpam-6917	135	3	−25	−25	NOUN
ejpam-6917	135	4	+	+	NUM
ejpam-6917	135	5	49µ0)g	49µ0)g	NOUN
ejpam-6917	135	6	n	n	NOUN
ejpam-6917	135	7	i−1	i−1	PROPN
ejpam-6917	135	8	+	+	CCONJ
ejpam-6917	135	9	(	(	PUNCT
ejpam-6917	135	10	150−	150−	NUM
ejpam-6917	135	11	46µ0)g	46µ0)g	NOUN
ejpam-6917	135	12	n	n	NOUN
ejpam-6917	135	13	i	i	PRON
ejpam-6917	135	14	+	+	CCONJ
ejpam-6917	135	15	(	(	PUNCT
ejpam-6917	135	16	150−	150−	NUM
ejpam-6917	135	17	46µ0)g	46µ0)g	NOUN
ejpam-6917	135	18	n	n	CCONJ
ejpam-6917	135	19	i+1	i+1	NOUN
ejpam-6917	135	20	+	+	CCONJ
ejpam-6917	135	21	(	(	PUNCT
ejpam-6917	135	22	−25	−25	NOUN
ejpam-6917	135	23	+	+	NUM
ejpam-6917	135	24	49µ0)g	49µ0)g	NOUN
ejpam-6917	135	25	n	n	NOUN
ejpam-6917	135	26	i+2	i+2	X
ejpam-6917	136	1	+	+	PUNCT
ejpam-6917	136	2	(	(	PUNCT
ejpam-6917	136	3	3−	3−	NUM
ejpam-6917	136	4	3µ0)g	3µ0)g	NUM
ejpam-6917	136	5	n	n	PRON
ejpam-6917	136	6	i+3	i+3	NOUN
ejpam-6917	136	7	)	)	PUNCT
ejpam-6917	136	8	.	.	PUNCT
ejpam-6917	137	1	(	(	PUNCT
ejpam-6917	137	2	1	1	X
ejpam-6917	137	3	)	)	PUNCT
ejpam-6917	137	4	the	the	DET
ejpam-6917	137	5	construction	construction	NOUN
ejpam-6917	137	6	of	of	ADP
ejpam-6917	137	7	our	our	PRON
ejpam-6917	137	8	subdivision	subdivision	NOUN
ejpam-6917	137	9	mask	mask	NOUN
ejpam-6917	137	10	relies	rely	VERB
ejpam-6917	137	11	crucially	crucially	ADV
ejpam-6917	137	12	on	on	ADP
ejpam-6917	137	13	the	the	DET
ejpam-6917	137	14	parameter	parameter	NOUN
ejpam-6917	137	15	µ0	µ0	PROPN
ejpam-6917	137	16	.	.	PUNCT
ejpam-6917	138	1	the	the	DET
ejpam-6917	138	2	choice	choice	NOUN
ejpam-6917	138	3	of	of	ADP
ejpam-6917	138	4	µ0	µ0	NOUN
ejpam-6917	138	5	significantly	significantly	ADV
ejpam-6917	138	6	affects	affect	VERB
ejpam-6917	138	7	the	the	DET
ejpam-6917	138	8	regularity	regularity	NOUN
ejpam-6917	138	9	,	,	PUNCT
ejpam-6917	138	10	order	order	NOUN
ejpam-6917	138	11	of	of	ADP
ejpam-6917	138	12	approximation	approximation	NOUN
ejpam-6917	138	13	,	,	PUNCT
ejpam-6917	138	14	and	and	CCONJ
ejpam-6917	138	15	shape	shape	NOUN
ejpam-6917	138	16	-	-	PUNCT
ejpam-6917	138	17	preservation	preservation	NOUN
ejpam-6917	138	18	of	of	ADP
ejpam-6917	138	19	the	the	DET
ejpam-6917	138	20	resulting	result	VERB
ejpam-6917	138	21	scheme	scheme	NOUN
ejpam-6917	138	22	.	.	PUNCT
ejpam-6917	139	1	suppose	suppose	VERB
ejpam-6917	139	2	that	that	SCONJ
ejpam-6917	139	3	the	the	DET
ejpam-6917	139	4	sequence	sequence	NOUN
ejpam-6917	139	5	of	of	ADP
ejpam-6917	139	6	initial	initial	ADJ
ejpam-6917	139	7	data	datum	NOUN
ejpam-6917	139	8	is	be	AUX
ejpam-6917	139	9	sampled	sample	VERB
ejpam-6917	139	10	from	from	ADP
ejpam-6917	139	11	a	a	DET
ejpam-6917	139	12	function	function	NOUN
ejpam-6917	139	13	on	on	ADP
ejpam-6917	139	14	the	the	DET
ejpam-6917	139	15	grid	grid	NOUN
ejpam-6917	139	16	2−n0z	2−n0z	NUM
ejpam-6917	139	17	,	,	PUNCT
ejpam-6917	139	18	we	we	PRON
ejpam-6917	139	19	investigate	investigate	VERB
ejpam-6917	139	20	the	the	DET
ejpam-6917	139	21	optimal	optimal	ADJ
ejpam-6917	139	22	selection	selection	NOUN
ejpam-6917	139	23	of	of	ADP
ejpam-6917	139	24	µ0	µ0	NOUN
ejpam-6917	139	25	as	as	ADP
ejpam-6917	139	26	µ0	µ0	NOUN
ejpam-6917	139	27	=	=	SYM
ejpam-6917	139	28	τ2−2n0	τ2−2n0	PROPN
ejpam-6917	139	29	,	,	PUNCT
ejpam-6917	139	30	τ	τ	X
ejpam-6917	139	31	≥	≥	NOUN
ejpam-6917	139	32	0	0	NUM
ejpam-6917	139	33	.	.	PUNCT
ejpam-6917	140	1	(	(	PUNCT
ejpam-6917	140	2	2	2	X
ejpam-6917	140	3	)	)	PUNCT
ejpam-6917	140	4	the	the	DET
ejpam-6917	140	5	key	key	ADJ
ejpam-6917	140	6	characteristics	characteristic	NOUN
ejpam-6917	140	7	of	of	ADP
ejpam-6917	140	8	our	our	PRON
ejpam-6917	140	9	construction	construction	NOUN
ejpam-6917	140	10	in	in	ADP
ejpam-6917	140	11	(	(	PUNCT
ejpam-6917	140	12	1	1	X
ejpam-6917	140	13	)	)	PUNCT
ejpam-6917	140	14	are	be	AUX
ejpam-6917	140	15	as	as	SCONJ
ejpam-6917	140	16	follows	follow	VERB
ejpam-6917	140	17	.	.	PUNCT
ejpam-6917	141	1	first	first	ADV
ejpam-6917	141	2	of	of	ADP
ejpam-6917	141	3	all	all	PRON
ejpam-6917	141	4	,	,	PUNCT
ejpam-6917	141	5	the	the	DET
ejpam-6917	141	6	mask	mask	NOUN
ejpam-6917	141	7	of	of	ADP
ejpam-6917	141	8	sd	sd	NOUN
ejpam-6917	141	9	-	-	PUNCT
ejpam-6917	141	10	scheme	scheme	NOUN
ejpam-6917	141	11	is	be	AUX
ejpam-6917	141	12	{	{	PUNCT
ejpam-6917	141	13	3	3	NUM
ejpam-6917	141	14	256	256	NUM
ejpam-6917	141	15	,	,	PUNCT
ejpam-6917	141	16	0	0	NUM
ejpam-6917	141	17	,	,	PUNCT
ejpam-6917	141	18	−25	−25	NOUN
ejpam-6917	141	19	256	256	NUM
ejpam-6917	141	20	,	,	PUNCT
ejpam-6917	141	21	0	0	NUM
ejpam-6917	141	22	,	,	PUNCT
ejpam-6917	141	23	75	75	NUM
ejpam-6917	141	24	128	128	NUM
ejpam-6917	141	25	,	,	PUNCT
ejpam-6917	141	26	1	1	NUM
ejpam-6917	141	27	,	,	PUNCT
ejpam-6917	141	28	75	75	NUM
ejpam-6917	141	29	128	128	NUM
ejpam-6917	141	30	,	,	PUNCT
ejpam-6917	141	31	0	0	NUM
ejpam-6917	141	32	,	,	PUNCT
ejpam-6917	141	33	−25	−25	NOUN
ejpam-6917	141	34	256	256	NUM
ejpam-6917	141	35	,	,	PUNCT
ejpam-6917	141	36	0	0	NUM
ejpam-6917	141	37	,	,	PUNCT
ejpam-6917	141	38	3	3	NUM
ejpam-6917	141	39	256	256	NUM
ejpam-6917	141	40	}	}	PUNCT
ejpam-6917	141	41	,	,	PUNCT
ejpam-6917	141	42	our	our	PRON
ejpam-6917	141	43	sp	sp	ADP
ejpam-6917	141	44	-scheme	-scheme	ADJ
ejpam-6917	141	45	refinement	refinement	NOUN
ejpam-6917	141	46	rule	rule	NOUN
ejpam-6917	141	47	can	can	AUX
ejpam-6917	141	48	be	be	AUX
ejpam-6917	141	49	interpreted	interpret	VERB
ejpam-6917	141	50	as	as	ADP
ejpam-6917	141	51	a	a	DET
ejpam-6917	141	52	linear	linear	ADJ
ejpam-6917	141	53	modification	modification	NOUN
ejpam-6917	141	54	of	of	ADP
ejpam-6917	141	55	the	the	DET
ejpam-6917	141	56	sd	sd	NOUN
ejpam-6917	141	57	-	-	PUNCT
ejpam-6917	141	58	scheme	scheme	NOUN
ejpam-6917	141	59	presented	present	VERB
ejpam-6917	141	60	below	below	ADV
ejpam-6917	141	61	:	:	PUNCT
ejpam-6917	141	62	sp	sp	ADP
ejpam-6917	141	63	g	g	PROPN
ejpam-6917	141	64	n	n	NOUN
ejpam-6917	141	65	=	=	SYM
ejpam-6917	141	66	sdg	sdg	PROPN
ejpam-6917	141	67	n	n	PROPN
ejpam-6917	141	68	+	+	CCONJ
ejpam-6917	141	69	2−2nµ0	2−2nµ0	NUM
ejpam-6917	141	70	64	64	NUM
ejpam-6917	141	71	d2(g	d2(g	PROPN
ejpam-6917	141	72	n	n	NUM
ejpam-6917	141	73	)	)	PUNCT
ejpam-6917	141	74	.	.	PUNCT
ejpam-6917	142	1	(	(	PUNCT
ejpam-6917	142	2	3	3	X
ejpam-6917	142	3	)	)	PUNCT
ejpam-6917	142	4	where	where	SCONJ
ejpam-6917	142	5	linear	linear	ADJ
ejpam-6917	142	6	operator	operator	NOUN
ejpam-6917	142	7	is	be	AUX
ejpam-6917	142	8	defined	define	VERB
ejpam-6917	142	9	as	as	ADP
ejpam-6917	142	10	d2	d2	VERB
ejpam-6917	142	11	d2(g	d2(g	PROPN
ejpam-6917	142	12	n)2i	n)2i	NOUN
ejpam-6917	142	13	=	=	PUNCT
ejpam-6917	142	14	(	(	PUNCT
ejpam-6917	142	15	d2gn)i−1	d2gn)i−1	PROPN
ejpam-6917	142	16	+	+	CCONJ
ejpam-6917	142	17	18(d2gn)i	18(d2gn)i	NUM
ejpam-6917	142	18	+	+	CCONJ
ejpam-6917	142	19	(	(	PUNCT
ejpam-6917	142	20	d2gn)i+1	d2gn)i+1	PROPN
ejpam-6917	142	21	,	,	PUNCT
ejpam-6917	142	22	d2(g	d2(g	PROPN
ejpam-6917	142	23	n)2i+1	n)2i+1	NOUN
ejpam-6917	142	24	=	=	SYM
ejpam-6917	142	25	−3(d2gn)i−1	−3(d2gn)i−1	PROPN
ejpam-6917	142	26	+	+	CCONJ
ejpam-6917	142	27	43(d2gn)i	43(d2gn)i	NUM
ejpam-6917	143	1	+	+	NUM
ejpam-6917	143	2	43(d2gn)i+1	43(d2gn)i+1	NOUN
ejpam-6917	143	3	−	−	PROPN
ejpam-6917	143	4	3(d2gn)i+2	3(d2gn)i+2	NUM
ejpam-6917	143	5	4	4	NUM
ejpam-6917	143	6	.	.	PUNCT
ejpam-6917	144	1	(	(	PUNCT
ejpam-6917	144	2	4	4	X
ejpam-6917	144	3	)	)	PUNCT
ejpam-6917	144	4	the	the	DET
ejpam-6917	144	5	new	new	ADJ
ejpam-6917	144	6	sp	sp	ADP
ejpam-6917	144	7	-scheme	-scheme	NOUN
ejpam-6917	144	8	enhances	enhance	VERB
ejpam-6917	144	9	the	the	DET
ejpam-6917	144	10	sd	sd	NOUN
ejpam-6917	144	11	-	-	PUNCT
ejpam-6917	144	12	scheme	scheme	NOUN
ejpam-6917	144	13	by	by	ADP
ejpam-6917	144	14	integrating	integrate	VERB
ejpam-6917	144	15	the	the	DET
ejpam-6917	144	16	discrete	discrete	ADJ
ejpam-6917	144	17	2nd	2nd	ADJ
ejpam-6917	144	18	-	-	PUNCT
ejpam-6917	144	19	derivative	derivative	ADJ
ejpam-6917	144	20	information	information	NOUN
ejpam-6917	144	21	of	of	ADP
ejpam-6917	144	22	gn	gn	PROPN
ejpam-6917	144	23	.	.	PUNCT
ejpam-6917	144	24	additionally	additionally	ADV
ejpam-6917	144	25	,	,	PUNCT
ejpam-6917	144	26	the	the	DET
ejpam-6917	144	27	parameter	parameter	NOUN
ejpam-6917	144	28	µ0	µ0	NOUN
ejpam-6917	144	29	is	be	AUX
ejpam-6917	144	30	chosen	choose	VERB
ejpam-6917	144	31	based	base	VERB
ejpam-6917	144	32	on	on	ADP
ejpam-6917	144	33	the	the	DET
ejpam-6917	144	34	initial	initial	ADJ
ejpam-6917	144	35	data	datum	NOUN
ejpam-6917	144	36	density	density	NOUN
ejpam-6917	144	37	,	,	PUNCT
ejpam-6917	144	38	as	as	SCONJ
ejpam-6917	144	39	specified	specify	VERB
ejpam-6917	144	40	in	in	ADP
ejpam-6917	144	41	(	(	PUNCT
ejpam-6917	144	42	2	2	NUM
ejpam-6917	144	43	)	)	PUNCT
ejpam-6917	144	44	.	.	PUNCT
ejpam-6917	145	1	this	this	PRON
ejpam-6917	145	2	enables	enable	VERB
ejpam-6917	145	3	the	the	DET
ejpam-6917	145	4	new	new	ADJ
ejpam-6917	145	5	sp	sp	ADP
ejpam-6917	145	6	-scheme	-scheme	NOUN
ejpam-6917	145	7	to	to	PART
ejpam-6917	145	8	attain	attain	VERB
ejpam-6917	145	9	sixth	sixth	ADJ
ejpam-6917	145	10	-	-	PUNCT
ejpam-6917	145	11	order	order	NOUN
ejpam-6917	145	12	of	of	ADP
ejpam-6917	145	13	approximation	approximation	NOUN
ejpam-6917	145	14	,	,	PUNCT
ejpam-6917	145	15	enhancing	enhance	VERB
ejpam-6917	145	16	smoothness	smoothness	NOUN
ejpam-6917	145	17	without	without	ADP
ejpam-6917	145	18	expanding	expand	VERB
ejpam-6917	145	19	support	support	NOUN
ejpam-6917	145	20	length	length	NOUN
ejpam-6917	145	21	.	.	PUNCT
ejpam-6917	146	1	additionally	additionally	ADV
ejpam-6917	146	2	,	,	PUNCT
ejpam-6917	146	3	because	because	SCONJ
ejpam-6917	146	4	it	it	PRON
ejpam-6917	146	5	exactly	exactly	ADV
ejpam-6917	146	6	reproduces	reproduce	VERB
ejpam-6917	146	7	all	all	DET
ejpam-6917	146	8	polynomials	polynomial	NOUN
ejpam-6917	146	9	up	up	ADP
ejpam-6917	146	10	to	to	PART
ejpam-6917	146	11	degree	degree	VERB
ejpam-6917	146	12	five	five	NUM
ejpam-6917	146	13	,	,	PUNCT
ejpam-6917	146	14	i.e.	i.e.	X
ejpam-6917	146	15	,	,	PUNCT
ejpam-6917	146	16	∏	∏	PROPN
ejpam-6917	146	17	5	5	NUM
ejpam-6917	146	18	,	,	PUNCT
ejpam-6917	146	19	the	the	DET
ejpam-6917	146	20	scheme	scheme	NOUN
ejpam-6917	146	21	ensures	ensure	VERB
ejpam-6917	146	22	the	the	DET
ejpam-6917	146	23	presence	presence	NOUN
ejpam-6917	146	24	of	of	ADP
ejpam-6917	146	25	the	the	DET
ejpam-6917	146	26	smoothing	smooth	VERB
ejpam-6917	146	27	factor	factor	NOUN
ejpam-6917	146	28	(	(	PUNCT
ejpam-6917	146	29	1	1	NUM
ejpam-6917	146	30	+	+	NUM
ejpam-6917	146	31	v)6	v)6	NOUN
ejpam-6917	146	32	in	in	ADP
ejpam-6917	146	33	its	its	PRON
ejpam-6917	146	34	symbol	symbol	NOUN
ejpam-6917	146	35	.	.	PUNCT
ejpam-6917	147	1	for	for	ADP
ejpam-6917	147	2	further	further	ADJ
ejpam-6917	147	3	use	use	NOUN
ejpam-6917	147	4	,	,	PUNCT
ejpam-6917	147	5	the	the	DET
ejpam-6917	147	6	explicit	explicit	ADJ
ejpam-6917	147	7	form	form	NOUN
ejpam-6917	147	8	of	of	ADP
ejpam-6917	147	9	the	the	DET
ejpam-6917	147	10	scheme	scheme	NOUN
ejpam-6917	147	11	’s	’s	PART
ejpam-6917	147	12	symbol	symbol	NOUN
ejpam-6917	147	13	is	be	AUX
ejpam-6917	147	14	provided	provide	VERB
ejpam-6917	147	15	in	in	ADP
ejpam-6917	147	16	equation	equation	NOUN
ejpam-6917	147	17	(	(	PUNCT
ejpam-6917	147	18	5	5	NUM
ejpam-6917	147	19	):	):	PUNCT
ejpam-6917	147	20	c(v	c(v	PROPN
ejpam-6917	147	21	)	)	PUNCT
ejpam-6917	147	22	=	=	PUNCT
ejpam-6917	148	1	(	(	PUNCT
ejpam-6917	148	2	1	1	NUM
ejpam-6917	148	3	+	+	NUM
ejpam-6917	148	4	v)6	v)6	NOUN
ejpam-6917	148	5	27	27	NUM
ejpam-6917	148	6	{	{	PUNCT
ejpam-6917	148	7	1	1	NUM
ejpam-6917	148	8	2v	2v	NUM
ejpam-6917	148	9	(	(	PUNCT
ejpam-6917	148	10	3−	3−	NUM
ejpam-6917	148	11	3µ0	3µ0	NUM
ejpam-6917	148	12	)	)	PUNCT
ejpam-6917	149	1	+	+	CCONJ
ejpam-6917	149	2	1	1	NUM
ejpam-6917	149	3	v2	v2	NOUN
ejpam-6917	149	4	(	(	PUNCT
ejpam-6917	149	5	−9	−9	NOUN
ejpam-6917	149	6	+	+	CCONJ
ejpam-6917	149	7	11µ0	11µ0	NUM
ejpam-6917	149	8	)	)	PUNCT
ejpam-6917	149	9	+	+	CCONJ
ejpam-6917	149	10	1	1	NUM
ejpam-6917	149	11	2v3	2v3	NUM
ejpam-6917	149	12	(	(	PUNCT
ejpam-6917	149	13	38−	38−	NUM
ejpam-6917	149	14	38µ0	38µ0	NUM
ejpam-6917	149	15	)	)	PUNCT
ejpam-6917	149	16	+	+	CCONJ
ejpam-6917	149	17	1	1	NUM
ejpam-6917	149	18	v4	v4	NOUN
ejpam-6917	149	19	(	(	PUNCT
ejpam-6917	149	20	−9	−9	NOUN
ejpam-6917	149	21	+	+	CCONJ
ejpam-6917	149	22	11µ0	11µ0	NUM
ejpam-6917	149	23	)	)	PUNCT
ejpam-6917	149	24	+	+	CCONJ
ejpam-6917	149	25	1	1	NUM
ejpam-6917	149	26	2v5	2v5	NUM
ejpam-6917	149	27	(	(	PUNCT
ejpam-6917	149	28	3−	3−	NUM
ejpam-6917	149	29	3µ0	3µ0	NUM
ejpam-6917	149	30	)	)	PUNCT
ejpam-6917	149	31	}	}	PUNCT
ejpam-6917	149	32	.	.	PUNCT
ejpam-6917	150	1	(	(	PUNCT
ejpam-6917	150	2	5	5	X
ejpam-6917	150	3	)	)	PUNCT
ejpam-6917	150	4	remark	remark	NOUN
ejpam-6917	150	5	1	1	NUM
ejpam-6917	150	6	.	.	PUNCT
ejpam-6917	151	1	the	the	DET
ejpam-6917	151	2	suggested	suggest	VERB
ejpam-6917	151	3	scheme	scheme	NOUN
ejpam-6917	151	4	is	be	AUX
ejpam-6917	151	5	a	a	DET
ejpam-6917	151	6	generalization	generalization	NOUN
ejpam-6917	151	7	of	of	ADP
ejpam-6917	151	8	the	the	DET
ejpam-6917	151	9	sd	sd	NOUN
ejpam-6917	151	10	-	-	PUNCT
ejpam-6917	151	11	scheme	scheme	NOUN
ejpam-6917	151	12	and	and	CCONJ
ejpam-6917	151	13	the	the	DET
ejpam-6917	151	14	qbscheme	qbscheme	NOUN
ejpam-6917	151	15	.	.	PUNCT
ejpam-6917	152	1	if	if	SCONJ
ejpam-6917	152	2	µ0	µ0	NOUN
ejpam-6917	152	3	=	=	SYM
ejpam-6917	152	4	0	0	NUM
ejpam-6917	152	5	,	,	PUNCT
ejpam-6917	152	6	the	the	DET
ejpam-6917	152	7	scheme	scheme	NOUN
ejpam-6917	152	8	is	be	AUX
ejpam-6917	152	9	the	the	DET
ejpam-6917	152	10	sd	sd	NOUN
ejpam-6917	152	11	-	-	PUNCT
ejpam-6917	152	12	scheme	scheme	NOUN
ejpam-6917	152	13	.	.	PUNCT
ejpam-6917	153	1	furthermore	furthermore	ADV
ejpam-6917	153	2	,	,	PUNCT
ejpam-6917	153	3	when	when	SCONJ
ejpam-6917	153	4	µ0	µ0	NOUN
ejpam-6917	153	5	=	=	SYM
ejpam-6917	153	6	1	1	NUM
ejpam-6917	153	7	it	it	PRON
ejpam-6917	153	8	changes	change	VERB
ejpam-6917	153	9	to	to	ADP
ejpam-6917	153	10	the	the	DET
ejpam-6917	153	11	quintic	quintic	ADJ
ejpam-6917	153	12	b	b	NOUN
ejpam-6917	153	13	-	-	NOUN
ejpam-6917	153	14	spline	spline	NOUN
ejpam-6917	153	15	(	(	PUNCT
ejpam-6917	153	16	represented	represent	VERB
ejpam-6917	153	17	by	by	ADP
ejpam-6917	153	18	qb	qb	NOUN
ejpam-6917	153	19	-	-	PUNCT
ejpam-6917	153	20	scheme	scheme	NOUN
ejpam-6917	153	21	)	)	PUNCT
ejpam-6917	153	22	with	with	ADP
ejpam-6917	153	23	the	the	DET
ejpam-6917	153	24	mask	mask	NOUN
ejpam-6917	153	25	{	{	PUNCT
ejpam-6917	153	26	1	1	NUM
ejpam-6917	153	27	64	64	NUM
ejpam-6917	153	28	,	,	PUNCT
ejpam-6917	153	29	3	3	NUM
ejpam-6917	153	30	32	32	NUM
ejpam-6917	153	31	,	,	PUNCT
ejpam-6917	153	32	1	1	NUM
ejpam-6917	153	33	4	4	NUM
ejpam-6917	153	34	,	,	PUNCT
ejpam-6917	153	35	13	13	NUM
ejpam-6917	153	36	32	32	NUM
ejpam-6917	153	37	,	,	PUNCT
ejpam-6917	153	38	15	15	NUM
ejpam-6917	153	39	32	32	NUM
ejpam-6917	153	40	,	,	PUNCT
ejpam-6917	153	41	13	13	NUM
ejpam-6917	153	42	32	32	NUM
ejpam-6917	153	43	,	,	PUNCT
ejpam-6917	153	44	1	1	NUM
ejpam-6917	153	45	4	4	NUM
ejpam-6917	153	46	,	,	PUNCT
ejpam-6917	153	47	3	3	NUM
ejpam-6917	153	48	32	32	NUM
ejpam-6917	153	49	,	,	PUNCT
ejpam-6917	153	50	1	1	NUM
ejpam-6917	153	51	64	64	NUM
ejpam-6917	153	52	}	}	PUNCT
ejpam-6917	153	53	.	.	PUNCT
ejpam-6917	154	1	then	then	ADV
ejpam-6917	154	2	,	,	PUNCT
ejpam-6917	154	3	the	the	DET
ejpam-6917	154	4	quintic	quintic	ADJ
ejpam-6917	154	5	b	b	NOUN
ejpam-6917	154	6	-	-	PUNCT
ejpam-6917	154	7	spline	spline	NOUN
ejpam-6917	154	8	qb	qb	PROPN
ejpam-6917	154	9	may	may	AUX
ejpam-6917	154	10	also	also	ADV
ejpam-6917	154	11	be	be	AUX
ejpam-6917	154	12	used	use	VERB
ejpam-6917	154	13	to	to	PART
ejpam-6917	154	14	illustrate	illustrate	VERB
ejpam-6917	154	15	the	the	DET
ejpam-6917	154	16	refinement	refinement	NOUN
ejpam-6917	154	17	rule	rule	NOUN
ejpam-6917	154	18	in	in	ADP
ejpam-6917	154	19	(	(	PUNCT
ejpam-6917	154	20	1	1	NUM
ejpam-6917	154	21	)	)	PUNCT
ejpam-6917	154	22	as	as	SCONJ
ejpam-6917	154	23	follows	follow	VERB
ejpam-6917	154	24	:	:	PUNCT
ejpam-6917	154	25	sp	sp	ADP
ejpam-6917	154	26	g	g	PROPN
ejpam-6917	154	27	n	n	NOUN
ejpam-6917	154	28	=	=	NOUN
ejpam-6917	154	29	qbg	qbg	NOUN
ejpam-6917	155	1	n	n	CCONJ
ejpam-6917	155	2	−	−	PROPN
ejpam-6917	155	3	2−2n	2−2n	NUM
ejpam-6917	155	4	(	(	PUNCT
ejpam-6917	155	5	1−	1−	NUM
ejpam-6917	155	6	µ0	µ0	NOUN
ejpam-6917	155	7	)	)	PUNCT
ejpam-6917	155	8	64	64	NUM
ejpam-6917	155	9	d2(g	d2(g	PROPN
ejpam-6917	155	10	n	n	CCONJ
ejpam-6917	155	11	)	)	PUNCT
ejpam-6917	155	12	.	.	PUNCT
ejpam-6917	156	1	(	(	PUNCT
ejpam-6917	156	2	6	6	X
ejpam-6917	156	3	)	)	PUNCT
ejpam-6917	156	4	f.	f.	PROPN
ejpam-6917	156	5	s.	s.	PROPN
ejpam-6917	156	6	alshammari	alshammari	PROPN
ejpam-6917	156	7	et	et	PROPN
ejpam-6917	156	8	al	al	PROPN
ejpam-6917	156	9	.	.	PUNCT
ejpam-6917	156	10	/	/	SYM
ejpam-6917	156	11	eur	eur	PROPN
ejpam-6917	156	12	.	.	PUNCT
ejpam-6917	157	1	j.	j.	PROPN
ejpam-6917	157	2	pure	pure	PROPN
ejpam-6917	157	3	appl	appl	PROPN
ejpam-6917	157	4	.	.	PROPN
ejpam-6917	157	5	math	math	PROPN
ejpam-6917	157	6	,	,	PUNCT
ejpam-6917	157	7	18	18	NUM
ejpam-6917	157	8	(	(	PUNCT
ejpam-6917	157	9	4	4	NUM
ejpam-6917	157	10	)	)	PUNCT
ejpam-6917	157	11	(	(	PUNCT
ejpam-6917	157	12	2025	2025	NUM
ejpam-6917	157	13	)	)	PUNCT
ejpam-6917	157	14	,	,	PUNCT
ejpam-6917	157	15	6917	6917	NUM
ejpam-6917	157	16	7	7	NUM
ejpam-6917	157	17	of	of	ADP
ejpam-6917	157	18	26	26	NUM
ejpam-6917	157	19	with	with	ADP
ejpam-6917	157	20	the	the	DET
ejpam-6917	157	21	operator	operator	NOUN
ejpam-6917	157	22	d2	d2	NOUN
ejpam-6917	157	23	in	in	ADP
ejpam-6917	157	24	(	(	PUNCT
ejpam-6917	157	25	4	4	NUM
ejpam-6917	157	26	)	)	PUNCT
ejpam-6917	157	27	.	.	PUNCT
ejpam-6917	158	1	this	this	DET
ejpam-6917	158	2	representation	representation	NOUN
ejpam-6917	158	3	will	will	AUX
ejpam-6917	158	4	help	help	VERB
ejpam-6917	158	5	analyze	analyze	VERB
ejpam-6917	158	6	our	our	PRON
ejpam-6917	158	7	ss	ss	NOUN
ejpam-6917	158	8	shape	shape	NOUN
ejpam-6917	158	9	-	-	PUNCT
ejpam-6917	158	10	preserving	preserve	VERB
ejpam-6917	158	11	characteristics	characteristic	NOUN
ejpam-6917	158	12	,	,	PUNCT
ejpam-6917	158	13	as	as	SCONJ
ejpam-6917	158	14	we	we	PRON
ejpam-6917	158	15	shall	shall	AUX
ejpam-6917	158	16	see	see	VERB
ejpam-6917	158	17	later	later	ADV
ejpam-6917	158	18	.	.	PUNCT
ejpam-6917	159	1	3.2	3.2	NUM
ejpam-6917	159	2	.	.	PUNCT
ejpam-6917	159	3	property	property	NOUN
ejpam-6917	159	4	of	of	ADP
ejpam-6917	159	5	polynomial	polynomial	ADJ
ejpam-6917	159	6	generation	generation	NOUN
ejpam-6917	159	7	when	when	SCONJ
ejpam-6917	159	8	the	the	DET
ejpam-6917	159	9	corresponding	corresponding	ADJ
ejpam-6917	159	10	fundamental	fundamental	ADJ
ejpam-6917	159	11	limiting	limiting	NOUN
ejpam-6917	159	12	function	function	NOUN
ejpam-6917	159	13	ω	ω	NOUN
ejpam-6917	159	14	of	of	ADP
ejpam-6917	159	15	sp	sp	NOUN
ejpam-6917	159	16	meets	meet	VERB
ejpam-6917	159	17	the	the	DET
ejpam-6917	159	18	strangfix	strangfix	ADJ
ejpam-6917	159	19	condition	condition	NOUN
ejpam-6917	159	20	of	of	ADP
ejpam-6917	159	21	order	order	NOUN
ejpam-6917	159	22	of	of	ADP
ejpam-6917	159	23	approximation	approximation	NOUN
ejpam-6917	159	24	e	e	NOUN
ejpam-6917	159	25	,	,	PUNCT
ejpam-6917	159	26	it	it	PRON
ejpam-6917	159	27	is	be	AUX
ejpam-6917	159	28	equivalent	equivalent	ADJ
ejpam-6917	159	29	to	to	ADP
ejpam-6917	159	30	the	the	DET
ejpam-6917	159	31	ss	ss	NOUN
ejpam-6917	159	32	symbol	symbol	NOUN
ejpam-6917	159	33	having	have	VERB
ejpam-6917	159	34	the	the	DET
ejpam-6917	159	35	smoothing	smooth	VERB
ejpam-6917	159	36	parameter	parameter	NOUN
ejpam-6917	159	37	(	(	PUNCT
ejpam-6917	159	38	1+v)e	1+v)e	NUM
ejpam-6917	159	39	,	,	PUNCT
ejpam-6917	159	40	e	e	PROPN
ejpam-6917	159	41	∈	∈	PROPN
ejpam-6917	159	42	n.	n.	NOUN
ejpam-6917	159	43	up	up	ADP
ejpam-6917	159	44	to	to	PART
ejpam-6917	159	45	degree	degree	NOUN
ejpam-6917	159	46	e	e	NOUN
ejpam-6917	159	47	,	,	PUNCT
ejpam-6917	159	48	it	it	PRON
ejpam-6917	159	49	ensures	ensure	VERB
ejpam-6917	159	50	that	that	SCONJ
ejpam-6917	159	51	the	the	DET
ejpam-6917	159	52	suggested	suggest	VERB
ejpam-6917	159	53	scheme	scheme	NOUN
ejpam-6917	159	54	produces	produce	VERB
ejpam-6917	159	55	polynomials	polynomial	NOUN
ejpam-6917	159	56	.	.	PUNCT
ejpam-6917	160	1	at	at	ADP
ejpam-6917	160	2	a	a	DET
ejpam-6917	160	3	later	later	ADJ
ejpam-6917	160	4	stage	stage	NOUN
ejpam-6917	160	5	,	,	PUNCT
ejpam-6917	160	6	we	we	PRON
ejpam-6917	160	7	shall	shall	AUX
ejpam-6917	160	8	discover	discover	VERB
ejpam-6917	160	9	that	that	SCONJ
ejpam-6917	160	10	the	the	PRON
ejpam-6917	160	11	sp	sp	ADP
ejpam-6917	160	12	-scheme	-scheme	NOUN
ejpam-6917	160	13	in	in	ADP
ejpam-6917	160	14	(	(	PUNCT
ejpam-6917	160	15	3	3	NUM
ejpam-6917	160	16	)	)	PUNCT
ejpam-6917	160	17	can	can	AUX
ejpam-6917	160	18	achieve	achieve	VERB
ejpam-6917	160	19	sixth	sixth	ADJ
ejpam-6917	160	20	-	-	PUNCT
ejpam-6917	160	21	order	order	NOUN
ejpam-6917	160	22	approximation	approximation	NOUN
ejpam-6917	160	23	even	even	ADV
ejpam-6917	160	24	though	though	SCONJ
ejpam-6917	160	25	it	it	PRON
ejpam-6917	160	26	reproduces	reproduce	VERB
ejpam-6917	160	27	polynomials	polynomial	NOUN
ejpam-6917	160	28	in	in	ADP
ejpam-6917	160	29	∏	∏	PROPN
ejpam-6917	160	30	1	1	NUM
ejpam-6917	160	31	.	.	PUNCT
ejpam-6917	161	1	for	for	ADP
ejpam-6917	161	2	convenience	convenience	NOUN
ejpam-6917	161	3	,	,	PUNCT
ejpam-6917	161	4	the	the	DET
ejpam-6917	161	5	notation	notation	NOUN
ejpam-6917	161	6	used	use	VERB
ejpam-6917	161	7	is	be	AUX
ejpam-6917	161	8	as	as	SCONJ
ejpam-6917	161	9	follows	follow	VERB
ejpam-6917	161	10	:	:	PUNCT
ejpam-6917	161	11	for	for	ADP
ejpam-6917	161	12	q	q	PROPN
ejpam-6917	161	13	∈	∈	PROPN
ejpam-6917	161	14	∏	∏	NUM
ejpam-6917	161	15	5	5	NUM
ejpam-6917	161	16	and	and	CCONJ
ejpam-6917	161	17	n	n	PRON
ejpam-6917	161	18	∈	∈	PROPN
ejpam-6917	161	19	n0	n0	PROPN
ejpam-6917	161	20	,	,	PUNCT
ejpam-6917	161	21	qni	qni	NOUN
ejpam-6917	161	22	=	=	PUNCT
ejpam-6917	161	23	q(i2−n	q(i2−n	PROPN
ejpam-6917	161	24	)	)	PUNCT
ejpam-6917	161	25	and	and	CCONJ
ejpam-6917	161	26	q(4),n+1	q(4),n+1	NOUN
ejpam-6917	161	27	=	=	SYM
ejpam-6917	161	28	d2(q	d2(q	PROPN
ejpam-6917	161	29	n	n	CCONJ
ejpam-6917	161	30	)	)	PUNCT
ejpam-6917	161	31	.	.	PUNCT
ejpam-6917	162	1	where	where	SCONJ
ejpam-6917	162	2	given	give	VERB
ejpam-6917	162	3	operator	operator	NOUN
ejpam-6917	162	4	d2	d2	NOUN
ejpam-6917	162	5	is	be	AUX
ejpam-6917	162	6	defined	define	VERB
ejpam-6917	162	7	in	in	ADP
ejpam-6917	162	8	(	(	PUNCT
ejpam-6917	162	9	4	4	NUM
ejpam-6917	162	10	)	)	PUNCT
ejpam-6917	162	11	.	.	PUNCT
ejpam-6917	163	1	theorem	theorem	NOUN
ejpam-6917	163	2	1	1	NUM
ejpam-6917	163	3	.	.	PUNCT
ejpam-6917	163	4	assume	assume	VERB
ejpam-6917	163	5	that	that	SCONJ
ejpam-6917	163	6	sp	sp	NOUN
ejpam-6917	163	7	is	be	AUX
ejpam-6917	163	8	the	the	DET
ejpam-6917	163	9	subdivision	subdivision	NOUN
ejpam-6917	163	10	scheme	scheme	NOUN
ejpam-6917	163	11	in	in	ADP
ejpam-6917	163	12	(	(	PUNCT
ejpam-6917	163	13	1	1	NUM
ejpam-6917	163	14	)	)	PUNCT
ejpam-6917	163	15	with	with	ADP
ejpam-6917	163	16	parameter	parameter	PROPN
ejpam-6917	163	17	µ0	µ0	PROPN
ejpam-6917	163	18	.	.	PUNCT
ejpam-6917	164	1	each	each	PRON
ejpam-6917	164	2	of	of	ADP
ejpam-6917	164	3	the	the	DET
ejpam-6917	164	4	polynomials	polynomial	NOUN
ejpam-6917	164	5	q	q	PUNCT
ejpam-6917	164	6	represents	represent	VERB
ejpam-6917	164	7	a	a	DET
ejpam-6917	164	8	part	part	NOUN
ejpam-6917	164	9	of	of	ADP
ejpam-6917	164	10	∏	∏	NUM
ejpam-6917	164	11	5	5	NUM
ejpam-6917	164	12	.	.	PUNCT
ejpam-6917	165	1	polynomial	polynomial	ADJ
ejpam-6917	165	2	generation	generation	NOUN
ejpam-6917	165	3	satisfies	satisfy	VERB
ejpam-6917	165	4	the	the	DET
ejpam-6917	165	5	following	follow	VERB
ejpam-6917	165	6	property	property	NOUN
ejpam-6917	165	7	.	.	PUNCT
ejpam-6917	166	1	s∞	s∞	VERB
ejpam-6917	166	2	p	p	NOUN
ejpam-6917	166	3	q0	q0	NOUN
ejpam-6917	166	4	=	=	PUNCT
ejpam-6917	166	5	q	q	PROPN
ejpam-6917	167	1	+	+	NUM
ejpam-6917	167	2	µ0	µ0	NOUN
ejpam-6917	167	3	62	62	NUM
ejpam-6917	167	4	q(4	q(4	NOUN
ejpam-6917	167	5	)	)	PUNCT
ejpam-6917	167	6	proof	proof	NOUN
ejpam-6917	167	7	.	.	PUNCT
ejpam-6917	168	1	by	by	ADP
ejpam-6917	168	2	mathematical	mathematical	ADJ
ejpam-6917	168	3	induction	induction	NOUN
ejpam-6917	168	4	,	,	PUNCT
ejpam-6917	168	5	to	to	PART
ejpam-6917	168	6	begin	begin	VERB
ejpam-6917	168	7	,	,	PUNCT
ejpam-6917	168	8	let	let	VERB
ejpam-6917	168	9	for	for	ADP
ejpam-6917	168	10	any	any	DET
ejpam-6917	168	11	n	n	PRON
ejpam-6917	168	12	∈	∈	PROPN
ejpam-6917	168	13	n0	n0	PROPN
ejpam-6917	168	14	,	,	PUNCT
ejpam-6917	168	15	si+1	si+1	PROPN
ejpam-6917	169	1	p	p	NOUN
ejpam-6917	169	2	q0	q0	PROPN
ejpam-6917	169	3	=	=	SYM
ejpam-6917	169	4	qn+1	qn+1	PROPN
ejpam-6917	169	5	+	+	SYM
ejpam-6917	169	6	µ0	µ0	NOUN
ejpam-6917	169	7	64	64	NUM
ejpam-6917	169	8	q(4	q(4	PROPN
ejpam-6917	169	9	)	)	PUNCT
ejpam-6917	169	10	,	,	PUNCT
ejpam-6917	169	11	n+1	n+1	PROPN
ejpam-6917	169	12	n∑	n∑	NOUN
ejpam-6917	169	13	i=0	i=0	PROPN
ejpam-6917	169	14	2−2i	2−2i	NUM
ejpam-6917	169	15	(	(	PUNCT
ejpam-6917	169	16	7	7	NUM
ejpam-6917	169	17	)	)	PUNCT
ejpam-6917	169	18	through	through	ADP
ejpam-6917	169	19	(	(	PUNCT
ejpam-6917	169	20	3	3	NUM
ejpam-6917	169	21	)	)	PUNCT
ejpam-6917	170	1	,	,	PUNCT
ejpam-6917	170	2	this	this	DET
ejpam-6917	170	3	identity	identity	NOUN
ejpam-6917	170	4	is	be	AUX
ejpam-6917	170	5	true	true	ADJ
ejpam-6917	170	6	for	for	ADP
ejpam-6917	170	7	n	n	NOUN
ejpam-6917	170	8	=	=	SYM
ejpam-6917	170	9	0	0	PUNCT
ejpam-6917	170	10	as	as	ADP
ejpam-6917	170	11	sp	sp	ADP
ejpam-6917	170	12	-scheme	-scheme	ADJ
ejpam-6917	170	13	reproducing	reproducing	NOUN
ejpam-6917	170	14	polynomials	polynomial	NOUN
ejpam-6917	170	15	in∏	in∏	NOUN
ejpam-6917	170	16	5	5	NUM
ejpam-6917	170	17	.	.	PUNCT
ejpam-6917	171	1	next	next	ADV
ejpam-6917	171	2	,	,	PUNCT
ejpam-6917	171	3	let	let	VERB
ejpam-6917	171	4	that	that	PRON
ejpam-6917	171	5	eq.(7	eq.(7	VERB
ejpam-6917	171	6	)	)	PUNCT
ejpam-6917	171	7	is	be	AUX
ejpam-6917	171	8	valid	valid	ADJ
ejpam-6917	171	9	for	for	ADP
ejpam-6917	171	10	n	n	DET
ejpam-6917	171	11	∈	∈	PROPN
ejpam-6917	171	12	n0	n0	PROPN
ejpam-6917	171	13	.	.	PUNCT
ejpam-6917	172	1	since	since	SCONJ
ejpam-6917	172	2	q	q	PROPN
ejpam-6917	172	3	∈	∈	PROPN
ejpam-6917	172	4	∏	∏	PROPN
ejpam-6917	172	5	5	5	NUM
ejpam-6917	172	6	,	,	PUNCT
ejpam-6917	172	7	clearly	clearly	ADV
ejpam-6917	172	8	,	,	PUNCT
ejpam-6917	172	9	(	(	PUNCT
ejpam-6917	172	10	d2q	d2q	NOUN
ejpam-6917	172	11	(	(	PUNCT
ejpam-6917	172	12	4	4	NUM
ejpam-6917	172	13	)	)	PUNCT
ejpam-6917	172	14	,	,	PUNCT
ejpam-6917	172	15	n	n	CCONJ
ejpam-6917	172	16	i	i	PRON
ejpam-6917	172	17	)	)	PUNCT
ejpam-6917	172	18	=	=	PUNCT
ejpam-6917	172	19	0	0	X
ejpam-6917	172	20	.	.	PUNCT
ejpam-6917	173	1	consequently	consequently	ADV
ejpam-6917	173	2	,	,	PUNCT
ejpam-6917	173	3	based	base	VERB
ejpam-6917	173	4	on	on	ADP
ejpam-6917	173	5	the	the	DET
ejpam-6917	173	6	expression	expression	NOUN
ejpam-6917	173	7	in	in	ADP
ejpam-6917	173	8	(	(	PUNCT
ejpam-6917	173	9	3	3	NUM
ejpam-6917	173	10	)	)	PUNCT
ejpam-6917	173	11	,	,	PUNCT
ejpam-6917	173	12	by	by	ADP
ejpam-6917	173	13	induction	induction	NOUN
ejpam-6917	173	14	hypothesis	hypothesis	NOUN
ejpam-6917	173	15	,	,	PUNCT
ejpam-6917	173	16	we	we	PRON
ejpam-6917	173	17	derive	derive	VERB
ejpam-6917	173	18	the	the	DET
ejpam-6917	173	19	equation	equation	NOUN
ejpam-6917	173	20	sn+1	sn+1	VERB
ejpam-6917	173	21	p	p	NOUN
ejpam-6917	173	22	q0	q0	NOUN
ejpam-6917	173	23	=	=	SYM
ejpam-6917	173	24	sp	sp	ADP
ejpam-6917	173	25	(	(	PUNCT
ejpam-6917	173	26	q	q	PROPN
ejpam-6917	173	27	n	n	NOUN
ejpam-6917	173	28	+	+	CCONJ
ejpam-6917	173	29	µ0	µ0	NOUN
ejpam-6917	173	30	64	64	NUM
ejpam-6917	173	31	q(4),n	q(4),n	ADV
ejpam-6917	173	32	i−1∑	i−1∑	NUM
ejpam-6917	173	33	i=0	i=0	PROPN
ejpam-6917	173	34	2−2i	2−2i	NUM
ejpam-6917	173	35	)	)	PUNCT
ejpam-6917	174	1	=	=	SYM
ejpam-6917	174	2	(	(	PUNCT
ejpam-6917	174	3	sd	sd	ADP
ejpam-6917	174	4	+	+	CCONJ
ejpam-6917	174	5	2−2nµ0	2−2nµ0	NUM
ejpam-6917	174	6	64	64	NUM
ejpam-6917	174	7	d2)(q	d2)(q	NOUN
ejpam-6917	174	8	n	n	NOUN
ejpam-6917	174	9	+	+	CCONJ
ejpam-6917	174	10	µ0	µ0	NOUN
ejpam-6917	174	11	64	64	NUM
ejpam-6917	174	12	q(4),n	q(4),n	ADV
ejpam-6917	174	13	i−1∑	i−1∑	NUM
ejpam-6917	174	14	i=0	i=0	PROPN
ejpam-6917	174	15	2−2i	2−2i	NUM
ejpam-6917	174	16	)	)	PUNCT
ejpam-6917	174	17	=	=	SYM
ejpam-6917	174	18	qn+1	qn+1	PROPN
ejpam-6917	174	19	+	+	SYM
ejpam-6917	174	20	µ0	µ0	NOUN
ejpam-6917	174	21	64	64	NUM
ejpam-6917	174	22	q(4	q(4	PROPN
ejpam-6917	174	23	)	)	PUNCT
ejpam-6917	174	24	,	,	PUNCT
ejpam-6917	174	25	n+1	n+1	PROPN
ejpam-6917	174	26	n∑	n∑	NOUN
ejpam-6917	174	27	i=0	i=0	PROPN
ejpam-6917	174	28	2−2i	2−2i	NUM
ejpam-6917	174	29	so	so	ADV
ejpam-6917	174	30	,	,	PUNCT
ejpam-6917	174	31	mathematical	mathematical	ADJ
ejpam-6917	174	32	induction	induction	NOUN
ejpam-6917	174	33	has	have	AUX
ejpam-6917	174	34	been	be	AUX
ejpam-6917	174	35	proved	prove	VERB
ejpam-6917	174	36	.	.	PUNCT
ejpam-6917	175	1	then	then	ADV
ejpam-6917	175	2	,	,	PUNCT
ejpam-6917	175	3	we	we	PRON
ejpam-6917	175	4	can	can	AUX
ejpam-6917	175	5	easily	easily	ADV
ejpam-6917	175	6	find	find	VERB
ejpam-6917	175	7	that	that	SCONJ
ejpam-6917	175	8	,	,	PUNCT
ejpam-6917	175	9	q	q	X
ejpam-6917	175	10	(	(	PUNCT
ejpam-6917	175	11	4	4	NUM
ejpam-6917	175	12	)	)	PUNCT
ejpam-6917	175	13	,	,	PUNCT
ejpam-6917	175	14	n+1	n+1	PROPN
ejpam-6917	175	15	2i+m	2i+m	NUM
ejpam-6917	175	16	=	=	SYM
ejpam-6917	175	17	q(4)(i2−n	q(4)(i2−n	NOUN
ejpam-6917	175	18	)	)	PUNCT
ejpam-6917	176	1	+	+	ADV
ejpam-6917	176	2	o(2−n	o(2−n	ADJ
ejpam-6917	176	3	)	)	PUNCT
ejpam-6917	176	4	for	for	ADP
ejpam-6917	176	5	m=0,1	m=0,1	NOUN
ejpam-6917	176	6	.	.	PUNCT
ejpam-6917	177	1	it	it	PRON
ejpam-6917	177	2	precisely	precisely	ADV
ejpam-6917	177	3	ends	end	VERB
ejpam-6917	177	4	the	the	DET
ejpam-6917	177	5	proof	proof	NOUN
ejpam-6917	177	6	.	.	PUNCT
ejpam-6917	178	1	f.	f.	PROPN
ejpam-6917	178	2	s.	s.	PROPN
ejpam-6917	178	3	alshammari	alshammari	PROPN
ejpam-6917	178	4	et	et	PROPN
ejpam-6917	178	5	al	al	PROPN
ejpam-6917	178	6	.	.	PUNCT
ejpam-6917	178	7	/	/	SYM
ejpam-6917	178	8	eur	eur	PROPN
ejpam-6917	178	9	.	.	PUNCT
ejpam-6917	179	1	j.	j.	PROPN
ejpam-6917	179	2	pure	pure	PROPN
ejpam-6917	179	3	appl	appl	PROPN
ejpam-6917	179	4	.	.	PROPN
ejpam-6917	179	5	math	math	PROPN
ejpam-6917	179	6	,	,	PUNCT
ejpam-6917	179	7	18	18	NUM
ejpam-6917	179	8	(	(	PUNCT
ejpam-6917	179	9	4	4	NUM
ejpam-6917	179	10	)	)	PUNCT
ejpam-6917	179	11	(	(	PUNCT
ejpam-6917	179	12	2025	2025	NUM
ejpam-6917	179	13	)	)	PUNCT
ejpam-6917	179	14	,	,	PUNCT
ejpam-6917	179	15	6917	6917	NUM
ejpam-6917	179	16	8	8	NUM
ejpam-6917	179	17	of	of	ADP
ejpam-6917	179	18	26	26	NUM
ejpam-6917	179	19	4	4	NUM
ejpam-6917	179	20	.	.	PUNCT
ejpam-6917	180	1	evaluation	evaluation	NOUN
ejpam-6917	180	2	of	of	ADP
ejpam-6917	180	3	the	the	DET
ejpam-6917	180	4	proposed	propose	VERB
ejpam-6917	180	5	scheme	scheme	NOUN
ejpam-6917	180	6	in	in	ADP
ejpam-6917	180	7	this	this	DET
ejpam-6917	180	8	section	section	NOUN
ejpam-6917	180	9	,	,	PUNCT
ejpam-6917	180	10	we	we	PRON
ejpam-6917	180	11	discuss	discuss	VERB
ejpam-6917	180	12	the	the	DET
ejpam-6917	180	13	convergence	convergence	NOUN
ejpam-6917	180	14	rate	rate	NOUN
ejpam-6917	180	15	,	,	PUNCT
ejpam-6917	180	16	smoothness	smoothness	ADJ
ejpam-6917	180	17	,	,	PUNCT
ejpam-6917	180	18	and	and	CCONJ
ejpam-6917	180	19	order	order	NOUN
ejpam-6917	180	20	of	of	ADP
ejpam-6917	180	21	approximation	approximation	NOUN
ejpam-6917	180	22	of	of	ADP
ejpam-6917	180	23	the	the	DET
ejpam-6917	180	24	proposed	propose	VERB
ejpam-6917	180	25	scheme	scheme	NOUN
ejpam-6917	180	26	.	.	PUNCT
ejpam-6917	181	1	4.1	4.1	NUM
ejpam-6917	181	2	.	.	PUNCT
ejpam-6917	181	3	evaluation	evaluation	NOUN
ejpam-6917	181	4	of	of	ADP
ejpam-6917	181	5	convergence	convergence	NOUN
ejpam-6917	181	6	and	and	CCONJ
ejpam-6917	181	7	smoothness	smoothness	VERB
ejpam-6917	181	8	the	the	DET
ejpam-6917	181	9	convergence	convergence	NOUN
ejpam-6917	181	10	and	and	CCONJ
ejpam-6917	181	11	smoothness	smoothness	NOUN
ejpam-6917	181	12	of	of	ADP
ejpam-6917	181	13	a	a	DET
ejpam-6917	181	14	subdivision	subdivision	NOUN
ejpam-6917	181	15	scheme	scheme	NOUN
ejpam-6917	181	16	,	,	PUNCT
ejpam-6917	181	17	along	along	ADP
ejpam-6917	181	18	with	with	ADP
ejpam-6917	181	19	the	the	DET
ejpam-6917	181	20	length	length	NOUN
ejpam-6917	181	21	of	of	ADP
ejpam-6917	181	22	its	its	PRON
ejpam-6917	181	23	refinement	refinement	NOUN
ejpam-6917	181	24	mask	mask	NOUN
ejpam-6917	181	25	,	,	PUNCT
ejpam-6917	181	26	are	be	AUX
ejpam-6917	181	27	fundamental	fundamental	ADJ
ejpam-6917	181	28	criteria	criterion	NOUN
ejpam-6917	181	29	for	for	ADP
ejpam-6917	181	30	choosing	choose	VERB
ejpam-6917	181	31	a	a	DET
ejpam-6917	181	32	suitable	suitable	ADJ
ejpam-6917	181	33	subdivision	subdivision	NOUN
ejpam-6917	181	34	scheme	scheme	NOUN
ejpam-6917	181	35	.	.	PUNCT
ejpam-6917	182	1	to	to	PART
ejpam-6917	182	2	examine	examine	VERB
ejpam-6917	182	3	such	such	ADJ
ejpam-6917	182	4	properties	property	NOUN
ejpam-6917	182	5	for	for	ADP
ejpam-6917	182	6	the	the	DET
ejpam-6917	182	7	proposed	propose	VERB
ejpam-6917	182	8	scheme	scheme	NOUN
ejpam-6917	182	9	defined	define	VERB
ejpam-6917	182	10	in	in	ADP
ejpam-6917	182	11	equation	equation	NOUN
ejpam-6917	182	12	(	(	PUNCT
ejpam-6917	182	13	1	1	NUM
ejpam-6917	182	14	)	)	PUNCT
ejpam-6917	182	15	,	,	PUNCT
ejpam-6917	182	16	we	we	PRON
ejpam-6917	182	17	begin	begin	VERB
ejpam-6917	182	18	by	by	ADP
ejpam-6917	182	19	introducing	introduce	VERB
ejpam-6917	182	20	some	some	DET
ejpam-6917	182	21	essential	essential	ADJ
ejpam-6917	182	22	concepts	concept	NOUN
ejpam-6917	182	23	.	.	PUNCT
ejpam-6917	183	1	given	give	VERB
ejpam-6917	183	2	an	an	DET
ejpam-6917	183	3	sp	sp	ADP
ejpam-6917	183	4	-scheme	-scheme	NOUN
ejpam-6917	183	5	,	,	PUNCT
ejpam-6917	183	6	let	let	VERB
ejpam-6917	183	7	sp,1	sp,1	NOUN
ejpam-6917	183	8	-	-	PUNCT
ejpam-6917	183	9	scheme	scheme	NOUN
ejpam-6917	183	10	denotes	denote	NOUN
ejpam-6917	183	11	the	the	DET
ejpam-6917	183	12	scheme	scheme	NOUN
ejpam-6917	183	13	for	for	ADP
ejpam-6917	183	14	the	the	DET
ejpam-6917	183	15	divided	divide	VERB
ejpam-6917	183	16	differences	difference	NOUN
ejpam-6917	183	17	of	of	ADP
ejpam-6917	183	18	the	the	DET
ejpam-6917	183	19	initial	initial	ADJ
ejpam-6917	183	20	control	control	NOUN
ejpam-6917	183	21	points	point	NOUN
ejpam-6917	183	22	,	,	PUNCT
ejpam-6917	183	23	which	which	PRON
ejpam-6917	183	24	possesses	possess	VERB
ejpam-6917	183	25	the	the	DET
ejpam-6917	183	26	following	follow	VERB
ejpam-6917	183	27	property	property	NOUN
ejpam-6917	183	28	.	.	PUNCT
ejpam-6917	184	1	dgn+1	dgn+1	PROPN
ejpam-6917	184	2	=	=	SYM
ejpam-6917	184	3	sp,1dgn	sp,1dgn	NOUN
ejpam-6917	184	4	,	,	PUNCT
ejpam-6917	184	5	where	where	SCONJ
ejpam-6917	184	6	gn	gn	PROPN
ejpam-6917	184	7	=	=	SYM
ejpam-6917	184	8	sn	sn	PROPN
ejpam-6917	184	9	p	p	NOUN
ejpam-6917	184	10	g	g	PROPN
ejpam-6917	184	11	0	0	NUM
ejpam-6917	184	12	.	.	PUNCT
ejpam-6917	185	1	the	the	DET
ejpam-6917	185	2	characteristic	characteristic	ADJ
ejpam-6917	185	3	laurent	laurent	PROPN
ejpam-6917	185	4	polynomial	polynomial	PROPN
ejpam-6917	185	5	c1(v	c1(v	PROPN
ejpam-6917	185	6	)	)	PUNCT
ejpam-6917	185	7	for	for	ADP
ejpam-6917	185	8	sp,1	sp,1	NOUN
ejpam-6917	185	9	-	-	PUNCT
ejpam-6917	185	10	scheme	scheme	NOUN
ejpam-6917	185	11	is	be	AUX
ejpam-6917	185	12	given	give	VERB
ejpam-6917	185	13	as	as	ADP
ejpam-6917	185	14	:	:	PUNCT
ejpam-6917	185	15	c1(v	c1(v	NOUN
ejpam-6917	185	16	)	)	PUNCT
ejpam-6917	185	17	=	=	SYM
ejpam-6917	185	18	2	2	NUM
ejpam-6917	185	19	1	1	NUM
ejpam-6917	185	20	+	+	SYM
ejpam-6917	185	21	v	v	ADP
ejpam-6917	185	22	c(v	c(v	PROPN
ejpam-6917	185	23	)	)	PUNCT
ejpam-6917	185	24	,	,	PUNCT
ejpam-6917	185	25	here	here	ADV
ejpam-6917	185	26	,	,	PUNCT
ejpam-6917	185	27	c(v	c(v	PROPN
ejpam-6917	185	28	)	)	PUNCT
ejpam-6917	185	29	represents	represent	VERB
ejpam-6917	185	30	the	the	DET
ejpam-6917	185	31	symbol	symbol	NOUN
ejpam-6917	185	32	of	of	ADP
ejpam-6917	185	33	the	the	DET
ejpam-6917	185	34	scheme	scheme	NOUN
ejpam-6917	185	35	sp	sp	NOUN
ejpam-6917	185	36	.	.	PUNCT
ejpam-6917	186	1	more	more	ADJ
ejpam-6917	186	2	,	,	PUNCT
ejpam-6917	186	3	for	for	ADP
ejpam-6917	186	4	the	the	DET
ejpam-6917	186	5	γ	γ	X
ejpam-6917	186	6	-	-	PUNCT
ejpam-6917	186	7	th	th	VERB
ejpam-6917	186	8	order	order	NOUN
ejpam-6917	186	9	difference	difference	NOUN
ejpam-6917	186	10	scheme	scheme	NOUN
ejpam-6917	186	11	sp	sp	NOUN
ejpam-6917	186	12	,	,	PUNCT
ejpam-6917	186	13	γ	γ	PROPN
ejpam-6917	186	14	derived	derive	VERB
ejpam-6917	186	15	from	from	ADP
ejpam-6917	186	16	sp	sp	ADP
ejpam-6917	186	17	,	,	PUNCT
ejpam-6917	186	18	the	the	DET
ejpam-6917	186	19	associated	associated	ADJ
ejpam-6917	186	20	symbol	symbol	NOUN
ejpam-6917	186	21	is	be	AUX
ejpam-6917	186	22	given	give	VERB
ejpam-6917	186	23	as	as	ADP
ejpam-6917	186	24	cγ(v	cγ(v	NOUN
ejpam-6917	186	25	)	)	PUNCT
ejpam-6917	186	26	=	=	PUNCT
ejpam-6917	187	1	∑	∑	PUNCT
ejpam-6917	187	2	i∈z	i∈z	PROPN
ejpam-6917	187	3	c	c	AUX
ejpam-6917	188	1	[	[	X
ejpam-6917	188	2	γ	γ	X
ejpam-6917	188	3	]	]	X
ejpam-6917	188	4	i	i	NOUN
ejpam-6917	188	5	vi	vi	NOUN
ejpam-6917	188	6	=	=	PUNCT
ejpam-6917	188	7	(	(	PUNCT
ejpam-6917	188	8	2	2	NUM
ejpam-6917	188	9	1	1	NUM
ejpam-6917	188	10	+	+	NUM
ejpam-6917	188	11	v	v	NOUN
ejpam-6917	188	12	)	)	PUNCT
ejpam-6917	188	13	γ	γ	PROPN
ejpam-6917	188	14	c(v	c(v	PROPN
ejpam-6917	188	15	)	)	PUNCT
ejpam-6917	188	16	.	.	PUNCT
ejpam-6917	189	1	(	(	PUNCT
ejpam-6917	189	2	8)	8)	NUM
ejpam-6917	189	3	here	here	ADV
ejpam-6917	189	4	,	,	PUNCT
ejpam-6917	189	5	c0(v	c0(v	PROPN
ejpam-6917	189	6	)	)	PUNCT
ejpam-6917	189	7	=	=	SYM
ejpam-6917	189	8	c(v	c(v	PROPN
ejpam-6917	189	9	)	)	PUNCT
ejpam-6917	189	10	and	and	CCONJ
ejpam-6917	189	11	c	c	X
ejpam-6917	190	1	[	[	X
ejpam-6917	190	2	0	0	X
ejpam-6917	190	3	]	]	X
ejpam-6917	190	4	i	i	PROPN
ejpam-6917	190	5	=	=	SYM
ejpam-6917	190	6	ci	ci	PROPN
ejpam-6917	190	7	.	.	PUNCT
ejpam-6917	191	1	this	this	DET
ejpam-6917	191	2	result	result	NOUN
ejpam-6917	191	3	offers	offer	VERB
ejpam-6917	191	4	a	a	DET
ejpam-6917	191	5	standard	standard	ADJ
ejpam-6917	191	6	approach	approach	NOUN
ejpam-6917	191	7	for	for	ADP
ejpam-6917	191	8	determining	determine	VERB
ejpam-6917	191	9	whether	whether	SCONJ
ejpam-6917	191	10	a	a	DET
ejpam-6917	191	11	stationary	stationary	ADJ
ejpam-6917	191	12	ss	ss	NOUN
ejpam-6917	191	13	converges	converge	NOUN
ejpam-6917	191	14	.	.	PUNCT
ejpam-6917	192	1	theorem	theorem	NOUN
ejpam-6917	192	2	2	2	NUM
ejpam-6917	192	3	.	.	PUNCT
ejpam-6917	193	1	[	[	X
ejpam-6917	193	2	26	26	NUM
ejpam-6917	193	3	]	]	PUNCT
ejpam-6917	193	4	consider	consider	VERB
ejpam-6917	193	5	two	two	NUM
ejpam-6917	193	6	stationary	stationary	ADJ
ejpam-6917	193	7	subdivision	subdivision	NOUN
ejpam-6917	193	8	schemes	scheme	NOUN
ejpam-6917	193	9	,	,	PUNCT
ejpam-6917	193	10	sp	sp	ADP
ejpam-6917	193	11	and	and	CCONJ
ejpam-6917	193	12	sp,1	sp,1	NOUN
ejpam-6917	193	13	,	,	PUNCT
ejpam-6917	193	14	with	with	ADP
ejpam-6917	193	15	respective	respective	ADJ
ejpam-6917	193	16	symbols	symbol	NOUN
ejpam-6917	193	17	c(v	c(v	PROPN
ejpam-6917	193	18	)	)	PUNCT
ejpam-6917	193	19	and	and	CCONJ
ejpam-6917	193	20	c1(v	c1(v	NUM
ejpam-6917	193	21	)	)	PUNCT
ejpam-6917	193	22	.	.	PUNCT
ejpam-6917	194	1	then	then	ADV
ejpam-6917	194	2	,	,	PUNCT
ejpam-6917	194	3	the	the	DET
ejpam-6917	194	4	sp	sp	NOUN
ejpam-6917	194	5	-scheme	-scheme	NOUN
ejpam-6917	194	6	is	be	AUX
ejpam-6917	194	7	uniformly	uniformly	ADV
ejpam-6917	194	8	convergence	convergence	NOUN
ejpam-6917	194	9	(	(	PUNCT
ejpam-6917	194	10	i.e.	i.e.	X
ejpam-6917	194	11	,	,	PUNCT
ejpam-6917	194	12	c0	c0	NOUN
ejpam-6917	194	13	)	)	PUNCT
ejpam-6917	194	14	of	of	ADP
ejpam-6917	194	15	sp	sp	ADP
ejpam-6917	194	16	-scheme	-scheme	NOUN
ejpam-6917	194	17	is	be	AUX
ejpam-6917	194	18	the	the	DET
ejpam-6917	194	19	existence	existence	NOUN
ejpam-6917	194	20	of	of	ADP
ejpam-6917	194	21	a	a	DET
ejpam-6917	194	22	positive	positive	ADJ
ejpam-6917	194	23	integer	integer	NOUN
ejpam-6917	194	24	r	r	NOUN
ejpam-6917	194	25	satisfying	satisfy	VERB
ejpam-6917	194	26	∥∥(1	∥∥(1	PUNCT
ejpam-6917	194	27	2sp,1	2sp,1	NOUN
ejpam-6917	194	28	)	)	PUNCT
ejpam-6917	195	1	r∥∥	r∥∥	NOUN
ejpam-6917	195	2	∞	∞	PROPN
ejpam-6917	195	3	<	<	X
ejpam-6917	195	4	1	1	NUM
ejpam-6917	195	5	,	,	PUNCT
ejpam-6917	195	6	where	where	SCONJ
ejpam-6917	195	7	1	1	NUM
ejpam-6917	195	8	2sp,1	2sp,1	NUM
ejpam-6917	195	9	is	be	AUX
ejpam-6917	195	10	the	the	DET
ejpam-6917	195	11	scheme	scheme	NOUN
ejpam-6917	195	12	denoted	denote	VERB
ejpam-6917	195	13	by	by	ADP
ejpam-6917	195	14	the	the	DET
ejpam-6917	195	15	symbol	symbol	NOUN
ejpam-6917	195	16	1	1	NUM
ejpam-6917	195	17	2c1(v	2c1(v	NUM
ejpam-6917	195	18	)	)	PUNCT
ejpam-6917	195	19	.	.	PUNCT
ejpam-6917	196	1	moreover	moreover	ADV
ejpam-6917	196	2	,	,	PUNCT
ejpam-6917	196	3	a	a	DET
ejpam-6917	196	4	sufficient	sufficient	ADJ
ejpam-6917	196	5	condition	condition	NOUN
ejpam-6917	196	6	for	for	ADP
ejpam-6917	196	7	a	a	DET
ejpam-6917	196	8	sp	sp	ADP
ejpam-6917	196	9	-scheme	-scheme	NOUN
ejpam-6917	196	10	to	to	PART
ejpam-6917	196	11	be	be	AUX
ejpam-6917	196	12	cm	cm	NOUN
ejpam-6917	196	13	,	,	PUNCT
ejpam-6917	196	14	m	m	VERB
ejpam-6917	196	15	≥	≥	NOUN
ejpam-6917	196	16	1	1	NUM
ejpam-6917	196	17	,	,	PUNCT
ejpam-6917	196	18	is	be	AUX
ejpam-6917	196	19	given	give	VERB
ejpam-6917	196	20	below	below	ADV
ejpam-6917	196	21	.	.	PUNCT
ejpam-6917	197	1	theorem	theorem	VERB
ejpam-6917	197	2	3	3	NUM
ejpam-6917	197	3	.	.	PUNCT
ejpam-6917	198	1	[	[	X
ejpam-6917	198	2	26	26	NUM
ejpam-6917	198	3	]	]	PUNCT
ejpam-6917	198	4	suppose	suppose	VERB
ejpam-6917	198	5	that	that	SCONJ
ejpam-6917	198	6	sp	sp	AUX
ejpam-6917	198	7	be	be	AUX
ejpam-6917	198	8	a	a	DET
ejpam-6917	198	9	stationary	stationary	ADJ
ejpam-6917	198	10	ss	ss	NOUN
ejpam-6917	198	11	with	with	ADP
ejpam-6917	198	12	the	the	DET
ejpam-6917	198	13	symbol	symbol	NOUN
ejpam-6917	198	14	c(v	c(v	PROPN
ejpam-6917	198	15	)	)	PUNCT
ejpam-6917	198	16	=	=	SYM
ejpam-6917	198	17	1	1	NUM
ejpam-6917	198	18	2	2	NUM
ejpam-6917	198	19	(	(	PUNCT
ejpam-6917	198	20	1	1	NUM
ejpam-6917	198	21	+	+	NUM
ejpam-6917	198	22	v)c(v	v)c(v	NOUN
ejpam-6917	198	23	)	)	PUNCT
ejpam-6917	198	24	with	with	ADP
ejpam-6917	198	25	a	a	DET
ejpam-6917	198	26	laurent	laurent	ADJ
ejpam-6917	198	27	polynomial	polynomial	ADJ
ejpam-6917	198	28	c(v	c(v	PROPN
ejpam-6917	198	29	)	)	PUNCT
ejpam-6917	198	30	.	.	PUNCT
ejpam-6917	199	1	if	if	SCONJ
ejpam-6917	199	2	the	the	DET
ejpam-6917	199	3	sc	sc	NOUN
ejpam-6917	199	4	-	-	PUNCT
ejpam-6917	199	5	scheme	scheme	NOUN
ejpam-6917	199	6	corresponding	corresponding	NOUN
ejpam-6917	199	7	with	with	ADP
ejpam-6917	199	8	c(v	c(v	PROPN
ejpam-6917	199	9	)	)	PUNCT
ejpam-6917	199	10	is	be	AUX
ejpam-6917	199	11	cm	cm	PROPN
ejpam-6917	199	12	,	,	PUNCT
ejpam-6917	199	13	then	then	ADV
ejpam-6917	199	14	the	the	DET
ejpam-6917	199	15	sp	sp	NOUN
ejpam-6917	199	16	-scheme	-scheme	PROPN
ejpam-6917	199	17	is	be	AUX
ejpam-6917	199	18	cm+1(r	cm+1(r	NOUN
ejpam-6917	199	19	)	)	PUNCT
ejpam-6917	199	20	.	.	PUNCT
ejpam-6917	200	1	we	we	PRON
ejpam-6917	200	2	will	will	AUX
ejpam-6917	200	3	now	now	ADV
ejpam-6917	200	4	demonstrate	demonstrate	VERB
ejpam-6917	200	5	that	that	SCONJ
ejpam-6917	200	6	the	the	DET
ejpam-6917	200	7	scheme	scheme	NOUN
ejpam-6917	200	8	in	in	ADP
ejpam-6917	200	9	(	(	PUNCT
ejpam-6917	200	10	1	1	X
ejpam-6917	200	11	)	)	PUNCT
ejpam-6917	200	12	achieves	achieve	VERB
ejpam-6917	200	13	c5	c5	PROPN
ejpam-6917	200	14	smoothness	smoothness	PROPN
ejpam-6917	200	15	for	for	ADP
ejpam-6917	200	16	a	a	DET
ejpam-6917	200	17	specific	specific	ADJ
ejpam-6917	200	18	range	range	NOUN
ejpam-6917	200	19	of	of	ADP
ejpam-6917	200	20	µ0	µ0	NOUN
ejpam-6917	200	21	values	value	NOUN
ejpam-6917	200	22	.	.	PUNCT
ejpam-6917	201	1	note	note	VERB
ejpam-6917	201	2	that	that	SCONJ
ejpam-6917	201	3	when	when	SCONJ
ejpam-6917	201	4	µ0	µ0	NOUN
ejpam-6917	201	5	=	=	NOUN
ejpam-6917	201	6	0	0	PROPN
ejpam-6917	201	7	,	,	PUNCT
ejpam-6917	201	8	the	the	DET
ejpam-6917	201	9	mask	mask	NOUN
ejpam-6917	201	10	in	in	ADP
ejpam-6917	201	11	(	(	PUNCT
ejpam-6917	201	12	1	1	NUM
ejpam-6917	201	13	)	)	PUNCT
ejpam-6917	201	14	reduces	reduce	VERB
ejpam-6917	201	15	to	to	ADP
ejpam-6917	201	16	the	the	DET
ejpam-6917	201	17	sd	sd	NOUN
ejpam-6917	201	18	-	-	PUNCT
ejpam-6917	201	19	scheme	scheme	NOUN
ejpam-6917	201	20	,	,	PUNCT
ejpam-6917	201	21	which	which	PRON
ejpam-6917	201	22	is	be	AUX
ejpam-6917	201	23	known	know	VERB
ejpam-6917	201	24	to	to	PART
ejpam-6917	201	25	be	be	AUX
ejpam-6917	201	26	c2	c2	PROPN
ejpam-6917	201	27	.	.	PUNCT
ejpam-6917	202	1	therefore	therefore	ADV
ejpam-6917	202	2	,	,	PUNCT
ejpam-6917	202	3	we	we	PRON
ejpam-6917	202	4	focus	focus	VERB
ejpam-6917	202	5	on	on	ADP
ejpam-6917	202	6	the	the	DET
ejpam-6917	202	7	case	case	NOUN
ejpam-6917	202	8	where	where	SCONJ
ejpam-6917	202	9	µ0	µ0	NOUN
ejpam-6917	202	10	>	>	X
ejpam-6917	202	11	0	0	PROPN
ejpam-6917	202	12	.	.	PUNCT
ejpam-6917	203	1	f.	f.	PROPN
ejpam-6917	203	2	s.	s.	PROPN
ejpam-6917	203	3	alshammari	alshammari	PROPN
ejpam-6917	203	4	et	et	PROPN
ejpam-6917	203	5	al	al	PROPN
ejpam-6917	203	6	.	.	PUNCT
ejpam-6917	203	7	/	/	SYM
ejpam-6917	203	8	eur	eur	PROPN
ejpam-6917	203	9	.	.	PUNCT
ejpam-6917	204	1	j.	j.	PROPN
ejpam-6917	204	2	pure	pure	PROPN
ejpam-6917	204	3	appl	appl	PROPN
ejpam-6917	204	4	.	.	PROPN
ejpam-6917	204	5	math	math	PROPN
ejpam-6917	204	6	,	,	PUNCT
ejpam-6917	204	7	18	18	NUM
ejpam-6917	204	8	(	(	PUNCT
ejpam-6917	204	9	4	4	NUM
ejpam-6917	204	10	)	)	PUNCT
ejpam-6917	204	11	(	(	PUNCT
ejpam-6917	204	12	2025	2025	NUM
ejpam-6917	204	13	)	)	PUNCT
ejpam-6917	204	14	,	,	PUNCT
ejpam-6917	204	15	6917	6917	NUM
ejpam-6917	204	16	9	9	NUM
ejpam-6917	204	17	of	of	ADP
ejpam-6917	204	18	26	26	NUM
ejpam-6917	204	19	theorem	theorem	NOUN
ejpam-6917	204	20	4	4	NUM
ejpam-6917	204	21	.	.	PUNCT
ejpam-6917	204	22	consider	consider	VERB
ejpam-6917	204	23	the	the	DET
ejpam-6917	204	24	ss	ss	NOUN
ejpam-6917	204	25	sp	sp	ADP
ejpam-6917	204	26	using	use	VERB
ejpam-6917	204	27	the	the	DET
ejpam-6917	204	28	refinement	refinement	NOUN
ejpam-6917	204	29	rule	rule	NOUN
ejpam-6917	204	30	is	be	AUX
ejpam-6917	204	31	given	give	VERB
ejpam-6917	204	32	as	as	ADP
ejpam-6917	204	33	(	(	PUNCT
ejpam-6917	204	34	1	1	NUM
ejpam-6917	204	35	)	)	PUNCT
ejpam-6917	204	36	,	,	PUNCT
ejpam-6917	204	37	having	have	VERB
ejpam-6917	204	38	the	the	DET
ejpam-6917	204	39	tension	tension	NOUN
ejpam-6917	204	40	parameter	parameter	NOUN
ejpam-6917	204	41	µ0	µ0	NOUN
ejpam-6917	204	42	specified	specify	VERB
ejpam-6917	204	43	in	in	ADP
ejpam-6917	204	44	(	(	PUNCT
ejpam-6917	204	45	2	2	NUM
ejpam-6917	204	46	)	)	PUNCT
ejpam-6917	204	47	.	.	PUNCT
ejpam-6917	205	1	then	then	ADV
ejpam-6917	205	2	,	,	PUNCT
ejpam-6917	205	3	sp	sp	ADP
ejpam-6917	205	4	-scheme	-scheme	NOUN
ejpam-6917	205	5	generates	generate	VERB
ejpam-6917	205	6	limit	limit	NOUN
ejpam-6917	205	7	functions	function	NOUN
ejpam-6917	205	8	of	of	ADP
ejpam-6917	205	9	class	class	NOUN
ejpam-6917	205	10	c5	c5	PROPN
ejpam-6917	205	11	for	for	ADP
ejpam-6917	205	12	9	9	NUM
ejpam-6917	205	13	11	11	NUM
ejpam-6917	205	14	<	<	X
ejpam-6917	205	15	µ0	µ0	NOUN
ejpam-6917	205	16	<	<	X
ejpam-6917	205	17	1	1	NUM
ejpam-6917	205	18	.	.	PUNCT
ejpam-6917	205	19	proof	proof	NOUN
ejpam-6917	205	20	.	.	PUNCT
ejpam-6917	206	1	we	we	PRON
ejpam-6917	206	2	begin	begin	VERB
ejpam-6917	206	3	by	by	ADP
ejpam-6917	206	4	investigating	investigate	VERB
ejpam-6917	206	5	the	the	DET
ejpam-6917	206	6	uniform	uniform	ADJ
ejpam-6917	206	7	convergence	convergence	NOUN
ejpam-6917	206	8	of	of	ADP
ejpam-6917	206	9	the	the	DET
ejpam-6917	206	10	sp	sp	ADP
ejpam-6917	206	11	-scheme	-scheme	NOUN
ejpam-6917	206	12	.	.	PUNCT
ejpam-6917	207	1	to	to	PART
ejpam-6917	207	2	continue	continue	VERB
ejpam-6917	207	3	,	,	PUNCT
ejpam-6917	207	4	we	we	PRON
ejpam-6917	207	5	note	note	VERB
ejpam-6917	207	6	that	that	SCONJ
ejpam-6917	207	7	the	the	DET
ejpam-6917	207	8	laurent	laurent	PROPN
ejpam-6917	207	9	polynomial	polynomial	PROPN
ejpam-6917	207	10	c(v	c(v	PROPN
ejpam-6917	207	11	)	)	PUNCT
ejpam-6917	207	12	from	from	ADP
ejpam-6917	207	13	equation	equation	NOUN
ejpam-6917	207	14	(	(	PUNCT
ejpam-6917	207	15	5	5	NUM
ejpam-6917	207	16	)	)	PUNCT
ejpam-6917	207	17	corresponds	correspond	VERB
ejpam-6917	207	18	to	to	ADP
ejpam-6917	207	19	the	the	DET
ejpam-6917	207	20	refinement	refinement	NOUN
ejpam-6917	207	21	mask	mask	NOUN
ejpam-6917	207	22	c	c	PROPN
ejpam-6917	207	23	introduced	introduce	VERB
ejpam-6917	207	24	in	in	ADP
ejpam-6917	207	25	equation	equation	NOUN
ejpam-6917	207	26	(	(	PUNCT
ejpam-6917	207	27	1	1	NUM
ejpam-6917	207	28	)	)	PUNCT
ejpam-6917	207	29	.	.	PUNCT
ejpam-6917	208	1	using	use	VERB
ejpam-6917	208	2	the	the	DET
ejpam-6917	208	3	relation	relation	NOUN
ejpam-6917	208	4	in	in	ADP
ejpam-6917	208	5	equation	equation	NOUN
ejpam-6917	208	6	(	(	PUNCT
ejpam-6917	208	7	8)	8)	NUM
ejpam-6917	208	8	,	,	PUNCT
ejpam-6917	208	9	the	the	DET
ejpam-6917	208	10	laurent	laurent	NOUN
ejpam-6917	208	11	polynomial	polynomial	NOUN
ejpam-6917	208	12	for	for	ADP
ejpam-6917	208	13	the	the	DET
ejpam-6917	208	14	1st	1st	ADJ
ejpam-6917	208	15	-	-	PUNCT
ejpam-6917	208	16	order	order	NOUN
ejpam-6917	208	17	difference	difference	NOUN
ejpam-6917	208	18	sp,1	sp,1	NOUN
ejpam-6917	208	19	-	-	PUNCT
ejpam-6917	208	20	scheme	scheme	NOUN
ejpam-6917	208	21	is	be	AUX
ejpam-6917	208	22	expressed	express	VERB
ejpam-6917	208	23	as	as	SCONJ
ejpam-6917	208	24	follows	follow	VERB
ejpam-6917	208	25	:	:	PUNCT
ejpam-6917	208	26	c1(v	c1(v	NOUN
ejpam-6917	208	27	)	)	PUNCT
ejpam-6917	208	28	=	=	PUNCT
ejpam-6917	209	1	(	(	PUNCT
ejpam-6917	209	2	1	1	NUM
ejpam-6917	209	3	+	+	NUM
ejpam-6917	209	4	v)5	v)5	PROPN
ejpam-6917	209	5	64	64	NUM
ejpam-6917	209	6	{	{	PUNCT
ejpam-6917	209	7	1	1	NUM
ejpam-6917	209	8	2	2	NUM
ejpam-6917	209	9	(	(	PUNCT
ejpam-6917	209	10	3−	3−	NUM
ejpam-6917	209	11	3µ0	3µ0	NUM
ejpam-6917	209	12	)	)	PUNCT
ejpam-6917	210	1	+	+	CCONJ
ejpam-6917	210	2	1	1	NUM
ejpam-6917	210	3	v	v	NOUN
ejpam-6917	210	4	(	(	PUNCT
ejpam-6917	210	5	−9	−9	NOUN
ejpam-6917	210	6	+	+	CCONJ
ejpam-6917	210	7	11µ0	11µ0	NUM
ejpam-6917	210	8	)	)	PUNCT
ejpam-6917	210	9	+	+	CCONJ
ejpam-6917	210	10	1	1	NUM
ejpam-6917	210	11	2v2	2v2	NUM
ejpam-6917	210	12	(	(	PUNCT
ejpam-6917	210	13	38−	38−	NUM
ejpam-6917	210	14	38µ0	38µ0	NUM
ejpam-6917	210	15	)	)	PUNCT
ejpam-6917	210	16	+	+	CCONJ
ejpam-6917	210	17	1	1	NUM
ejpam-6917	210	18	v3	v3	PROPN
ejpam-6917	210	19	(	(	PUNCT
ejpam-6917	210	20	−9	−9	PROPN
ejpam-6917	210	21	+	+	CCONJ
ejpam-6917	210	22	11µ0	11µ0	NUM
ejpam-6917	210	23	)	)	PUNCT
ejpam-6917	210	24	+	+	CCONJ
ejpam-6917	210	25	1	1	NUM
ejpam-6917	210	26	2v4	2v4	NUM
ejpam-6917	210	27	(	(	PUNCT
ejpam-6917	210	28	3−	3−	NUM
ejpam-6917	210	29	3µ0	3µ0	NUM
ejpam-6917	210	30	)	)	PUNCT
ejpam-6917	210	31	}	}	PUNCT
ejpam-6917	210	32	the	the	DET
ejpam-6917	210	33	mask	mask	NOUN
ejpam-6917	210	34	c[1	c[1	PROPN
ejpam-6917	210	35	]	]	X
ejpam-6917	210	36	=	=	PUNCT
ejpam-6917	210	37	(	(	PUNCT
ejpam-6917	210	38	c	c	X
ejpam-6917	211	1	[	[	X
ejpam-6917	211	2	1	1	X
ejpam-6917	211	3	]	]	X
ejpam-6917	211	4	i	i	PRON
ejpam-6917	211	5	:	:	PUNCT
ejpam-6917	212	1	i	i	PROPN
ejpam-6917	212	2	∈	∈	PROPN
ejpam-6917	212	3	z	z	X
ejpam-6917	212	4	)	)	PUNCT
ejpam-6917	212	5	which	which	PRON
ejpam-6917	212	6	is	be	AUX
ejpam-6917	212	7	used	use	VERB
ejpam-6917	212	8	in	in	ADP
ejpam-6917	212	9	the	the	DET
ejpam-6917	212	10	sp,1	sp,1	NOUN
ejpam-6917	212	11	-	-	PUNCT
ejpam-6917	212	12	scheme	scheme	NOUN
ejpam-6917	212	13	is	be	AUX
ejpam-6917	212	14	defined	define	VERB
ejpam-6917	212	15	as	as	SCONJ
ejpam-6917	212	16	follows	follow	VERB
ejpam-6917	212	17	:	:	PUNCT
ejpam-6917	212	18	c[1	c[1	NOUN
ejpam-6917	212	19	]	]	X
ejpam-6917	212	20	=	=	SYM
ejpam-6917	212	21	1	1	NUM
ejpam-6917	212	22	128	128	NUM
ejpam-6917	212	23	{	{	PUNCT
ejpam-6917	212	24	3−	3−	NUM
ejpam-6917	212	25	3µ0,−3	3µ0,−3	NUM
ejpam-6917	212	26	+	+	CCONJ
ejpam-6917	212	27	7µ0,−22	7µ0,−22	NUM
ejpam-6917	212	28	+	+	CCONJ
ejpam-6917	212	29	42µ0	42µ0	NUM
ejpam-6917	212	30	,	,	PUNCT
ejpam-6917	212	31	22	22	NUM
ejpam-6917	212	32	+	+	SYM
ejpam-6917	212	33	22µ0	22µ0	NUM
ejpam-6917	212	34	,	,	PUNCT
ejpam-6917	212	35	128−	128−	NOUN
ejpam-6917	212	36	68µ0	68µ0	NUM
ejpam-6917	212	37	,	,	PUNCT
ejpam-6917	212	38	128−	128−	NOUN
ejpam-6917	212	39	68µ0	68µ0	NUM
ejpam-6917	212	40	,	,	PUNCT
ejpam-6917	212	41	22	22	NUM
ejpam-6917	212	42	+	+	SYM
ejpam-6917	212	43	22µ0,−22	22µ0,−22	NUM
ejpam-6917	212	44	+	+	CCONJ
ejpam-6917	212	45	42µ0,−3	42µ0,−3	NUM
ejpam-6917	212	46	+	+	NUM
ejpam-6917	212	47	7µ0	7µ0	NOUN
ejpam-6917	212	48	,	,	PUNCT
ejpam-6917	212	49	3−	3−	NUM
ejpam-6917	212	50	3µ0	3µ0	NUM
ejpam-6917	212	51	}	}	PUNCT
ejpam-6917	212	52	.	.	PUNCT
ejpam-6917	213	1	now	now	ADV
ejpam-6917	213	2	,	,	PUNCT
ejpam-6917	213	3	‖1	‖1	NOUN
ejpam-6917	213	4	2sp,1‖	2sp,1‖	NUM
ejpam-6917	213	5	<	<	X
ejpam-6917	213	6	1	1	NUM
ejpam-6917	213	7	for	for	ADP
ejpam-6917	213	8	−39	−39	PROPN
ejpam-6917	213	9	49	49	NUM
ejpam-6917	213	10	<	<	X
ejpam-6917	213	11	µ0	µ0	NOUN
ejpam-6917	213	12	<	<	X
ejpam-6917	213	13	195	195	NUM
ejpam-6917	213	14	71	71	NUM
ejpam-6917	213	15	.	.	PUNCT
ejpam-6917	214	1	this	this	PRON
ejpam-6917	214	2	implies	imply	VERB
ejpam-6917	214	3	that	that	SCONJ
ejpam-6917	214	4	,	,	PUNCT
ejpam-6917	214	5	it	it	PRON
ejpam-6917	214	6	has	have	VERB
ejpam-6917	214	7	c0	c0	NOUN
ejpam-6917	214	8	-	-	PUNCT
ejpam-6917	214	9	continuity	continuity	NOUN
ejpam-6917	214	10	.	.	PUNCT
ejpam-6917	215	1	next	next	ADV
ejpam-6917	215	2	,	,	PUNCT
ejpam-6917	215	3	we	we	PRON
ejpam-6917	215	4	will	will	AUX
ejpam-6917	215	5	check	check	VERB
ejpam-6917	215	6	for	for	ADP
ejpam-6917	215	7	c1	c1	PROPN
ejpam-6917	215	8	smoothness	smoothness	NOUN
ejpam-6917	215	9	for	for	ADP
ejpam-6917	215	10	sp	sp	NOUN
ejpam-6917	215	11	,	,	PUNCT
ejpam-6917	215	12	consider	consider	VERB
ejpam-6917	215	13	the	the	DET
ejpam-6917	215	14	2nd	2nd	ADJ
ejpam-6917	215	15	-	-	PUNCT
ejpam-6917	215	16	order	order	NOUN
ejpam-6917	215	17	difference	difference	NOUN
ejpam-6917	215	18	sp,2scheme	sp,2scheme	NOUN
ejpam-6917	215	19	is	be	AUX
ejpam-6917	215	20	,	,	PUNCT
ejpam-6917	215	21	c2(v	c2(v	X
ejpam-6917	215	22	)	)	PUNCT
ejpam-6917	215	23	=	=	PUNCT
ejpam-6917	216	1	(	(	PUNCT
ejpam-6917	216	2	1	1	NUM
ejpam-6917	216	3	+	+	NUM
ejpam-6917	216	4	v)4	v)4	PROPN
ejpam-6917	216	5	32	32	NUM
ejpam-6917	216	6	{	{	PUNCT
ejpam-6917	216	7	v	v	NOUN
ejpam-6917	216	8	2	2	NUM
ejpam-6917	216	9	(	(	PUNCT
ejpam-6917	216	10	3−	3−	NUM
ejpam-6917	216	11	3µ0	3µ0	NUM
ejpam-6917	216	12	)	)	PUNCT
ejpam-6917	217	1	+	+	CCONJ
ejpam-6917	217	2	(	(	PUNCT
ejpam-6917	217	3	−9	−9	NOUN
ejpam-6917	217	4	+	+	NOUN
ejpam-6917	217	5	11µ0	11µ0	NUM
ejpam-6917	217	6	)	)	PUNCT
ejpam-6917	218	1	+	+	CCONJ
ejpam-6917	218	2	1	1	NUM
ejpam-6917	218	3	2v	2v	NUM
ejpam-6917	218	4	(	(	PUNCT
ejpam-6917	218	5	38−	38−	NUM
ejpam-6917	218	6	38µ0	38µ0	NUM
ejpam-6917	218	7	)	)	PUNCT
ejpam-6917	218	8	+	+	CCONJ
ejpam-6917	218	9	1	1	NUM
ejpam-6917	218	10	v2	v2	NOUN
ejpam-6917	218	11	(	(	PUNCT
ejpam-6917	218	12	−9	−9	NOUN
ejpam-6917	218	13	+	+	CCONJ
ejpam-6917	218	14	11µ0	11µ0	NUM
ejpam-6917	218	15	)	)	PUNCT
ejpam-6917	218	16	+	+	CCONJ
ejpam-6917	218	17	1	1	NUM
ejpam-6917	218	18	2v3	2v3	NUM
ejpam-6917	218	19	(	(	PUNCT
ejpam-6917	218	20	3−	3−	NUM
ejpam-6917	218	21	3µ0	3µ0	NUM
ejpam-6917	218	22	)	)	PUNCT
ejpam-6917	218	23	}	}	PUNCT
ejpam-6917	218	24	the	the	DET
ejpam-6917	218	25	mask	mask	NOUN
ejpam-6917	218	26	c[2	c[2	X
ejpam-6917	218	27	]	]	X
ejpam-6917	218	28	=	=	PUNCT
ejpam-6917	218	29	(	(	PUNCT
ejpam-6917	218	30	c	c	X
ejpam-6917	219	1	[	[	X
ejpam-6917	219	2	2	2	X
ejpam-6917	219	3	]	]	X
ejpam-6917	219	4	i	i	PRON
ejpam-6917	219	5	:	:	PUNCT
ejpam-6917	220	1	i	i	PROPN
ejpam-6917	220	2	∈	∈	PROPN
ejpam-6917	220	3	z	z	X
ejpam-6917	220	4	)	)	PUNCT
ejpam-6917	220	5	which	which	PRON
ejpam-6917	220	6	is	be	AUX
ejpam-6917	220	7	used	use	VERB
ejpam-6917	220	8	in	in	ADP
ejpam-6917	220	9	the	the	DET
ejpam-6917	220	10	sp,2	sp,2	NOUN
ejpam-6917	220	11	-	-	PUNCT
ejpam-6917	220	12	scheme	scheme	NOUN
ejpam-6917	220	13	is	be	AUX
ejpam-6917	220	14	defined	define	VERB
ejpam-6917	220	15	as	as	SCONJ
ejpam-6917	220	16	follows	follow	VERB
ejpam-6917	220	17	:	:	PUNCT
ejpam-6917	220	18	c[2	c[2	X
ejpam-6917	220	19	]	]	X
ejpam-6917	221	1	=	=	SYM
ejpam-6917	221	2	1	1	NUM
ejpam-6917	221	3	64	64	NUM
ejpam-6917	221	4	{	{	PUNCT
ejpam-6917	221	5	3−	3−	NUM
ejpam-6917	221	6	3µ0,−6	3µ0,−6	NUM
ejpam-6917	221	7	+	+	CCONJ
ejpam-6917	221	8	10µ0,−16	10µ0,−16	NUM
ejpam-6917	221	9	+	+	SYM
ejpam-6917	221	10	32µ0	32µ0	NUM
ejpam-6917	221	11	,	,	PUNCT
ejpam-6917	221	12	38−	38−	NUM
ejpam-6917	221	13	10µ0	10µ0	NUM
ejpam-6917	221	14	,	,	PUNCT
ejpam-6917	221	15	90−	90−	NOUN
ejpam-6917	221	16	58µ0	58µ0	NUM
ejpam-6917	221	17	,	,	PUNCT
ejpam-6917	221	18	38−	38−	NUM
ejpam-6917	221	19	10µ0	10µ0	NUM
ejpam-6917	221	20	,	,	PUNCT
ejpam-6917	221	21	16	16	NUM
ejpam-6917	221	22	+	+	CCONJ
ejpam-6917	221	23	32µ0,−6	32µ0,−6	NUM
ejpam-6917	221	24	+	+	CCONJ
ejpam-6917	221	25	10µ0	10µ0	NUM
ejpam-6917	221	26	,	,	PUNCT
ejpam-6917	221	27	3−	3−	NUM
ejpam-6917	221	28	3µ0	3µ0	NUM
ejpam-6917	221	29	}	}	PUNCT
ejpam-6917	221	30	.	.	PUNCT
ejpam-6917	222	1	now	now	ADV
ejpam-6917	222	2	,	,	PUNCT
ejpam-6917	222	3	‖1	‖1	VERB
ejpam-6917	222	4	2sp,2‖	2sp,2‖	NUM
ejpam-6917	222	5	<	<	X
ejpam-6917	222	6	1	1	NUM
ejpam-6917	222	7	for	for	ADP
ejpam-6917	222	8	0	0	NUM
ejpam-6917	222	9	<	<	X
ejpam-6917	222	10	µ0	µ0	NOUN
ejpam-6917	222	11	<	<	X
ejpam-6917	222	12	2	2	NUM
ejpam-6917	222	13	.	.	PUNCT
ejpam-6917	223	1	this	this	PRON
ejpam-6917	223	2	implies	imply	VERB
ejpam-6917	223	3	that	that	SCONJ
ejpam-6917	223	4	,	,	PUNCT
ejpam-6917	223	5	it	it	PRON
ejpam-6917	223	6	has	have	VERB
ejpam-6917	223	7	c1	c1	NOUN
ejpam-6917	223	8	-	-	PUNCT
ejpam-6917	223	9	continuity	continuity	NOUN
ejpam-6917	223	10	.	.	PUNCT
ejpam-6917	224	1	next	next	ADV
ejpam-6917	224	2	,	,	PUNCT
ejpam-6917	224	3	we	we	PRON
ejpam-6917	224	4	will	will	AUX
ejpam-6917	224	5	check	check	VERB
ejpam-6917	224	6	for	for	ADP
ejpam-6917	224	7	c2	c2	PROPN
ejpam-6917	224	8	smoothness	smoothness	PROPN
ejpam-6917	224	9	for	for	ADP
ejpam-6917	224	10	sp	sp	NOUN
ejpam-6917	224	11	,	,	PUNCT
ejpam-6917	224	12	consider	consider	VERB
ejpam-6917	224	13	the	the	DET
ejpam-6917	224	14	3rd	3rd	ADJ
ejpam-6917	224	15	-	-	PUNCT
ejpam-6917	224	16	order	order	NOUN
ejpam-6917	224	17	difference	difference	NOUN
ejpam-6917	224	18	sp,3	sp,3	NOUN
ejpam-6917	224	19	-	-	PUNCT
ejpam-6917	224	20	scheme	scheme	NOUN
ejpam-6917	224	21	is	be	AUX
ejpam-6917	224	22	,	,	PUNCT
ejpam-6917	224	23	c3(v	c3(v	X
ejpam-6917	224	24	)	)	PUNCT
ejpam-6917	224	25	=	=	SYM
ejpam-6917	225	1	(	(	PUNCT
ejpam-6917	225	2	1	1	NUM
ejpam-6917	225	3	+	+	NUM
ejpam-6917	225	4	z)3	z)3	NOUN
ejpam-6917	225	5	16	16	NUM
ejpam-6917	225	6	{	{	PUNCT
ejpam-6917	225	7	v	v	NOUN
ejpam-6917	225	8	2	2	NUM
ejpam-6917	225	9	2	2	NUM
ejpam-6917	225	10	(	(	PUNCT
ejpam-6917	225	11	3−	3−	NUM
ejpam-6917	225	12	3µ0	3µ0	NUM
ejpam-6917	225	13	)	)	PUNCT
ejpam-6917	225	14	+	+	CCONJ
ejpam-6917	225	15	(	(	PUNCT
ejpam-6917	225	16	v)(−9	v)(−9	PROPN
ejpam-6917	225	17	+	+	CCONJ
ejpam-6917	225	18	11µ0	11µ0	NUM
ejpam-6917	225	19	)	)	PUNCT
ejpam-6917	225	20	+	+	CCONJ
ejpam-6917	225	21	1	1	NUM
ejpam-6917	225	22	2	2	NUM
ejpam-6917	225	23	(	(	PUNCT
ejpam-6917	225	24	38−	38−	NUM
ejpam-6917	225	25	38µ0	38µ0	NUM
ejpam-6917	225	26	)	)	PUNCT
ejpam-6917	225	27	+	+	CCONJ
ejpam-6917	225	28	1	1	NUM
ejpam-6917	225	29	v	v	NOUN
ejpam-6917	225	30	(	(	PUNCT
ejpam-6917	225	31	−9	−9	NOUN
ejpam-6917	225	32	+	+	CCONJ
ejpam-6917	225	33	11µ0	11µ0	NUM
ejpam-6917	225	34	)	)	PUNCT
ejpam-6917	225	35	+	+	CCONJ
ejpam-6917	225	36	1	1	NUM
ejpam-6917	225	37	2v2	2v2	NUM
ejpam-6917	225	38	(	(	PUNCT
ejpam-6917	225	39	3−	3−	NUM
ejpam-6917	225	40	3µ0	3µ0	NUM
ejpam-6917	225	41	)	)	PUNCT
ejpam-6917	225	42	}	}	PUNCT
ejpam-6917	225	43	the	the	DET
ejpam-6917	225	44	mask	mask	NOUN
ejpam-6917	225	45	c[3	c[3	X
ejpam-6917	225	46	]	]	X
ejpam-6917	225	47	=	=	PUNCT
ejpam-6917	225	48	(	(	PUNCT
ejpam-6917	225	49	c	c	X
ejpam-6917	225	50	[	[	X
ejpam-6917	225	51	3	3	X
ejpam-6917	225	52	]	]	X
ejpam-6917	225	53	i	i	PRON
ejpam-6917	225	54	:	:	PUNCT
ejpam-6917	226	1	i	i	PROPN
ejpam-6917	226	2	∈	∈	PROPN
ejpam-6917	226	3	z	z	X
ejpam-6917	226	4	)	)	PUNCT
ejpam-6917	226	5	which	which	PRON
ejpam-6917	226	6	is	be	AUX
ejpam-6917	226	7	used	use	VERB
ejpam-6917	226	8	in	in	ADP
ejpam-6917	226	9	the	the	DET
ejpam-6917	226	10	sp,3	sp,3	NOUN
ejpam-6917	226	11	-	-	PUNCT
ejpam-6917	226	12	scheme	scheme	NOUN
ejpam-6917	226	13	is	be	AUX
ejpam-6917	226	14	defined	define	VERB
ejpam-6917	226	15	as	as	SCONJ
ejpam-6917	226	16	follows	follow	VERB
ejpam-6917	226	17	:	:	PUNCT
ejpam-6917	226	18	c[3	c[3	X
ejpam-6917	226	19	]	]	X
ejpam-6917	226	20	=	=	SYM
ejpam-6917	226	21	1	1	NUM
ejpam-6917	226	22	32	32	NUM
ejpam-6917	226	23	{	{	PUNCT
ejpam-6917	226	24	3−	3−	NUM
ejpam-6917	226	25	3µ0,−9	3µ0,−9	NUM
ejpam-6917	226	26	+	+	CCONJ
ejpam-6917	226	27	13µ0,−7	13µ0,−7	NUM
ejpam-6917	226	28	+	+	CCONJ
ejpam-6917	226	29	19µ0	19µ0	NUM
ejpam-6917	226	30	,	,	PUNCT
ejpam-6917	226	31	45−	45−	PRON
ejpam-6917	226	32	29µ0	29µ0	NUM
ejpam-6917	226	33	,	,	PUNCT
ejpam-6917	226	34	45−	45−	PRON
ejpam-6917	226	35	29µ0,−7	29µ0,−7	NUM
ejpam-6917	227	1	+	+	CCONJ
ejpam-6917	227	2	19µ0	19µ0	NUM
ejpam-6917	227	3	,	,	PUNCT
ejpam-6917	227	4	−	−	PROPN
ejpam-6917	227	5	9	9	NUM
ejpam-6917	227	6	+	+	SYM
ejpam-6917	227	7	13µ0	13µ0	NUM
ejpam-6917	227	8	,	,	PUNCT
ejpam-6917	227	9	3−	3−	NUM
ejpam-6917	227	10	3µ0	3µ0	NUM
ejpam-6917	227	11	}	}	PUNCT
ejpam-6917	227	12	.	.	PUNCT
ejpam-6917	228	1	f.	f.	PROPN
ejpam-6917	228	2	s.	s.	PROPN
ejpam-6917	228	3	alshammari	alshammari	PROPN
ejpam-6917	228	4	et	et	PROPN
ejpam-6917	228	5	al	al	PROPN
ejpam-6917	228	6	.	.	PUNCT
ejpam-6917	228	7	/	/	SYM
ejpam-6917	228	8	eur	eur	PROPN
ejpam-6917	228	9	.	.	PUNCT
ejpam-6917	229	1	j.	j.	PROPN
ejpam-6917	229	2	pure	pure	PROPN
ejpam-6917	229	3	appl	appl	PROPN
ejpam-6917	229	4	.	.	PROPN
ejpam-6917	229	5	math	math	PROPN
ejpam-6917	229	6	,	,	PUNCT
ejpam-6917	229	7	18	18	NUM
ejpam-6917	229	8	(	(	PUNCT
ejpam-6917	229	9	4	4	NUM
ejpam-6917	229	10	)	)	PUNCT
ejpam-6917	229	11	(	(	PUNCT
ejpam-6917	229	12	2025	2025	NUM
ejpam-6917	229	13	)	)	PUNCT
ejpam-6917	229	14	,	,	PUNCT
ejpam-6917	229	15	6917	6917	NUM
ejpam-6917	229	16	10	10	NUM
ejpam-6917	229	17	of	of	ADP
ejpam-6917	229	18	26	26	NUM
ejpam-6917	229	19	now	now	ADV
ejpam-6917	229	20	,	,	PUNCT
ejpam-6917	229	21	‖1	‖1	VERB
ejpam-6917	229	22	2sp,3‖	2sp,3‖	NUM
ejpam-6917	229	23	<	<	X
ejpam-6917	229	24	1	1	NUM
ejpam-6917	229	25	for	for	ADP
ejpam-6917	229	26	0	0	NUM
ejpam-6917	229	27	<	<	X
ejpam-6917	229	28	µ0	µ0	NOUN
ejpam-6917	229	29	<	<	X
ejpam-6917	229	30	2	2	NUM
ejpam-6917	229	31	.	.	PUNCT
ejpam-6917	230	1	this	this	PRON
ejpam-6917	230	2	implies	imply	VERB
ejpam-6917	230	3	that	that	SCONJ
ejpam-6917	230	4	,	,	PUNCT
ejpam-6917	230	5	it	it	PRON
ejpam-6917	230	6	has	have	VERB
ejpam-6917	230	7	c2	c2	PROPN
ejpam-6917	230	8	-	-	PUNCT
ejpam-6917	230	9	continuity	continuity	NOUN
ejpam-6917	230	10	.	.	PUNCT
ejpam-6917	231	1	next	next	ADV
ejpam-6917	231	2	,	,	PUNCT
ejpam-6917	231	3	we	we	PRON
ejpam-6917	231	4	will	will	AUX
ejpam-6917	231	5	check	check	VERB
ejpam-6917	231	6	for	for	ADP
ejpam-6917	231	7	c3	c3	PROPN
ejpam-6917	231	8	smoothness	smoothness	NOUN
ejpam-6917	231	9	for	for	ADP
ejpam-6917	231	10	sp	sp	NOUN
ejpam-6917	231	11	,	,	PUNCT
ejpam-6917	231	12	consider	consider	VERB
ejpam-6917	231	13	the	the	DET
ejpam-6917	231	14	4th	4th	ADJ
ejpam-6917	231	15	-	-	PUNCT
ejpam-6917	231	16	order	order	NOUN
ejpam-6917	231	17	difference	difference	NOUN
ejpam-6917	231	18	sp,4	sp,4	NOUN
ejpam-6917	231	19	-	-	PUNCT
ejpam-6917	231	20	scheme	scheme	NOUN
ejpam-6917	231	21	is	be	AUX
ejpam-6917	231	22	,	,	PUNCT
ejpam-6917	231	23	c4(v	c4(v	NOUN
ejpam-6917	231	24	)	)	PUNCT
ejpam-6917	231	25	=	=	SYM
ejpam-6917	232	1	(	(	PUNCT
ejpam-6917	232	2	1	1	NUM
ejpam-6917	232	3	+	+	NUM
ejpam-6917	232	4	z)2	z)2	NOUN
ejpam-6917	232	5	8	8	NUM
ejpam-6917	232	6	{	{	PUNCT
ejpam-6917	232	7	v	v	NOUN
ejpam-6917	232	8	3	3	NUM
ejpam-6917	232	9	2	2	NUM
ejpam-6917	232	10	(	(	PUNCT
ejpam-6917	232	11	3−	3−	NUM
ejpam-6917	232	12	3µ0	3µ0	NUM
ejpam-6917	232	13	)	)	PUNCT
ejpam-6917	233	1	+	+	CCONJ
ejpam-6917	233	2	(	(	PUNCT
ejpam-6917	233	3	v2)(−9	v2)(−9	ADJ
ejpam-6917	233	4	+	+	CCONJ
ejpam-6917	233	5	11µ0	11µ0	NUM
ejpam-6917	233	6	)	)	PUNCT
ejpam-6917	233	7	+	+	CCONJ
ejpam-6917	233	8	v	v	NUM
ejpam-6917	233	9	2	2	NUM
ejpam-6917	233	10	(	(	PUNCT
ejpam-6917	233	11	38−	38−	NUM
ejpam-6917	233	12	38µ0	38µ0	NUM
ejpam-6917	233	13	)	)	PUNCT
ejpam-6917	234	1	+	+	PROPN
ejpam-6917	234	2	(	(	PUNCT
ejpam-6917	234	3	−9	−9	NOUN
ejpam-6917	234	4	+	+	NOUN
ejpam-6917	234	5	11µ0	11µ0	NUM
ejpam-6917	234	6	)	)	PUNCT
ejpam-6917	234	7	+	+	CCONJ
ejpam-6917	234	8	1	1	NUM
ejpam-6917	234	9	2v	2v	NUM
ejpam-6917	234	10	(	(	PUNCT
ejpam-6917	234	11	3−	3−	NUM
ejpam-6917	234	12	3µ0	3µ0	NUM
ejpam-6917	234	13	)	)	PUNCT
ejpam-6917	234	14	}	}	PUNCT
ejpam-6917	234	15	the	the	DET
ejpam-6917	234	16	mask	mask	NOUN
ejpam-6917	234	17	c[4	c[4	X
ejpam-6917	234	18	]	]	X
ejpam-6917	234	19	=	=	PUNCT
ejpam-6917	234	20	(	(	PUNCT
ejpam-6917	234	21	c	c	X
ejpam-6917	235	1	[	[	X
ejpam-6917	235	2	4	4	X
ejpam-6917	235	3	]	]	X
ejpam-6917	235	4	i	i	PRON
ejpam-6917	235	5	:	:	PUNCT
ejpam-6917	236	1	i	i	PROPN
ejpam-6917	236	2	∈	∈	PROPN
ejpam-6917	236	3	z	z	X
ejpam-6917	236	4	)	)	PUNCT
ejpam-6917	236	5	which	which	PRON
ejpam-6917	236	6	is	be	AUX
ejpam-6917	236	7	used	use	VERB
ejpam-6917	236	8	in	in	ADP
ejpam-6917	236	9	the	the	DET
ejpam-6917	236	10	sp,4	sp,4	NOUN
ejpam-6917	236	11	-	-	PUNCT
ejpam-6917	236	12	scheme	scheme	NOUN
ejpam-6917	236	13	is	be	AUX
ejpam-6917	236	14	defined	define	VERB
ejpam-6917	236	15	as	as	SCONJ
ejpam-6917	236	16	follows	follow	VERB
ejpam-6917	236	17	:	:	PUNCT
ejpam-6917	236	18	c[4	c[4	X
ejpam-6917	236	19	]	]	X
ejpam-6917	236	20	=	=	SYM
ejpam-6917	236	21	1	1	NUM
ejpam-6917	236	22	16	16	NUM
ejpam-6917	236	23	{	{	PUNCT
ejpam-6917	236	24	3−	3−	NUM
ejpam-6917	236	25	3µ0	3µ0	NUM
ejpam-6917	236	26	,	,	PUNCT
ejpam-6917	236	27	5	5	NUM
ejpam-6917	236	28	+	+	SYM
ejpam-6917	236	29	3µ0,−12	3µ0,−12	NUM
ejpam-6917	236	30	+	+	SYM
ejpam-6917	236	31	16µ0	16µ0	NUM
ejpam-6917	236	32	,	,	PUNCT
ejpam-6917	236	33	40−	40−	NOUN
ejpam-6917	236	34	32µ0,−12	32µ0,−12	NUM
ejpam-6917	236	35	+	+	CCONJ
ejpam-6917	236	36	16µ0	16µ0	NUM
ejpam-6917	236	37	,	,	PUNCT
ejpam-6917	236	38	5	5	NUM
ejpam-6917	236	39	+	+	SYM
ejpam-6917	236	40	3µ0	3µ0	NUM
ejpam-6917	236	41	,	,	PUNCT
ejpam-6917	236	42	3−	3−	NUM
ejpam-6917	236	43	3µ0	3µ0	NUM
ejpam-6917	236	44	,	,	PUNCT
ejpam-6917	236	45	}	}	PUNCT
ejpam-6917	236	46	.	.	PUNCT
ejpam-6917	237	1	now	now	ADV
ejpam-6917	237	2	,	,	PUNCT
ejpam-6917	237	3	‖1	‖1	NOUN
ejpam-6917	237	4	2sp,4‖	2sp,4‖	NUM
ejpam-6917	237	5	<	<	X
ejpam-6917	237	6	1	1	NUM
ejpam-6917	237	7	for	for	ADP
ejpam-6917	237	8	1	1	NUM
ejpam-6917	237	9	2	2	NUM
ejpam-6917	237	10	<	<	X
ejpam-6917	237	11	µ0	µ0	NOUN
ejpam-6917	237	12	<	<	X
ejpam-6917	237	13	3	3	NUM
ejpam-6917	237	14	2	2	NUM
ejpam-6917	237	15	.	.	PUNCT
ejpam-6917	238	1	this	this	PRON
ejpam-6917	238	2	implies	imply	VERB
ejpam-6917	238	3	that	that	SCONJ
ejpam-6917	238	4	,	,	PUNCT
ejpam-6917	238	5	it	it	PRON
ejpam-6917	238	6	has	have	VERB
ejpam-6917	238	7	c3	c3	NOUN
ejpam-6917	238	8	-	-	NOUN
ejpam-6917	238	9	continuity	continuity	NOUN
ejpam-6917	238	10	.	.	PUNCT
ejpam-6917	239	1	next	next	ADV
ejpam-6917	239	2	,	,	PUNCT
ejpam-6917	239	3	we	we	PRON
ejpam-6917	239	4	will	will	AUX
ejpam-6917	239	5	check	check	VERB
ejpam-6917	239	6	for	for	ADP
ejpam-6917	239	7	c4	c4	NOUN
ejpam-6917	239	8	smoothness	smoothness	NOUN
ejpam-6917	239	9	for	for	ADP
ejpam-6917	239	10	sp	sp	NOUN
ejpam-6917	239	11	,	,	PUNCT
ejpam-6917	239	12	consider	consider	VERB
ejpam-6917	239	13	the	the	DET
ejpam-6917	239	14	5th	5th	ADJ
ejpam-6917	239	15	-	-	PUNCT
ejpam-6917	239	16	order	order	NOUN
ejpam-6917	239	17	difference	difference	NOUN
ejpam-6917	239	18	sp,5	sp,5	NOUN
ejpam-6917	239	19	-	-	PUNCT
ejpam-6917	239	20	scheme	scheme	NOUN
ejpam-6917	239	21	is	be	AUX
ejpam-6917	239	22	,	,	PUNCT
ejpam-6917	239	23	c5(v	c5(v	PROPN
ejpam-6917	239	24	)	)	PUNCT
ejpam-6917	239	25	=	=	SYM
ejpam-6917	239	26	(	(	PUNCT
ejpam-6917	239	27	1	1	NUM
ejpam-6917	239	28	+	+	CCONJ
ejpam-6917	239	29	z	z	NOUN
ejpam-6917	239	30	)	)	PUNCT
ejpam-6917	239	31	4	4	NUM
ejpam-6917	239	32	{	{	PUNCT
ejpam-6917	239	33	v	v	NOUN
ejpam-6917	239	34	4	4	NUM
ejpam-6917	239	35	2	2	NUM
ejpam-6917	239	36	(	(	PUNCT
ejpam-6917	239	37	3−	3−	NUM
ejpam-6917	239	38	3µ0	3µ0	NUM
ejpam-6917	239	39	)	)	PUNCT
ejpam-6917	240	1	+	+	CCONJ
ejpam-6917	240	2	(	(	PUNCT
ejpam-6917	240	3	v3)(−9	v3)(−9	X
ejpam-6917	240	4	+	+	CCONJ
ejpam-6917	240	5	11µ0	11µ0	NUM
ejpam-6917	240	6	)	)	PUNCT
ejpam-6917	241	1	+	+	CCONJ
ejpam-6917	241	2	v2	v2	NOUN
ejpam-6917	241	3	2	2	NUM
ejpam-6917	241	4	(	(	PUNCT
ejpam-6917	241	5	38−	38−	NUM
ejpam-6917	241	6	38µ0	38µ0	NUM
ejpam-6917	241	7	)	)	PUNCT
ejpam-6917	241	8	+	+	PROPN
ejpam-6917	241	9	(	(	PUNCT
ejpam-6917	241	10	v)(−9	v)(−9	PROPN
ejpam-6917	241	11	+	+	CCONJ
ejpam-6917	241	12	11µ0	11µ0	NUM
ejpam-6917	241	13	)	)	PUNCT
ejpam-6917	241	14	+	+	CCONJ
ejpam-6917	241	15	1	1	NUM
ejpam-6917	241	16	2	2	NUM
ejpam-6917	241	17	(	(	PUNCT
ejpam-6917	241	18	3−	3−	NUM
ejpam-6917	241	19	3µ0	3µ0	NUM
ejpam-6917	241	20	)	)	PUNCT
ejpam-6917	241	21	}	}	PUNCT
ejpam-6917	241	22	the	the	DET
ejpam-6917	241	23	mask	mask	NOUN
ejpam-6917	241	24	c[5	c[5	PROPN
ejpam-6917	241	25	]	]	X
ejpam-6917	241	26	=	=	X
ejpam-6917	241	27	(	(	PUNCT
ejpam-6917	241	28	c	c	X
ejpam-6917	241	29	[	[	X
ejpam-6917	241	30	5	5	NUM
ejpam-6917	241	31	]	]	PUNCT
ejpam-6917	241	32	i	i	PRON
ejpam-6917	241	33	:	:	PUNCT
ejpam-6917	242	1	i	i	PROPN
ejpam-6917	242	2	∈	∈	PROPN
ejpam-6917	242	3	z	z	X
ejpam-6917	242	4	)	)	PUNCT
ejpam-6917	242	5	which	which	PRON
ejpam-6917	242	6	is	be	AUX
ejpam-6917	242	7	used	use	VERB
ejpam-6917	242	8	in	in	ADP
ejpam-6917	242	9	the	the	DET
ejpam-6917	242	10	sp,5	sp,5	NOUN
ejpam-6917	242	11	-	-	PUNCT
ejpam-6917	242	12	scheme	scheme	NOUN
ejpam-6917	242	13	is	be	AUX
ejpam-6917	242	14	defined	define	VERB
ejpam-6917	242	15	as	as	SCONJ
ejpam-6917	242	16	follows	follow	VERB
ejpam-6917	242	17	:	:	PUNCT
ejpam-6917	242	18	c[5	c[5	ADJ
ejpam-6917	242	19	]	]	X
ejpam-6917	242	20	=	=	SYM
ejpam-6917	242	21	1	1	NUM
ejpam-6917	242	22	8	8	NUM
ejpam-6917	242	23	{	{	PUNCT
ejpam-6917	242	24	3−	3−	NUM
ejpam-6917	242	25	3µ0,−15	3µ0,−15	NUM
ejpam-6917	242	26	+	+	CCONJ
ejpam-6917	242	27	19µ0	19µ0	NUM
ejpam-6917	242	28	,	,	PUNCT
ejpam-6917	242	29	20−	20−	NUM
ejpam-6917	242	30	16µ0	16µ0	NUM
ejpam-6917	242	31	,	,	PUNCT
ejpam-6917	242	32	20−	20−	NUM
ejpam-6917	242	33	16µ0,−15	16µ0,−15	NUM
ejpam-6917	242	34	+	+	CCONJ
ejpam-6917	242	35	19µ0	19µ0	NUM
ejpam-6917	242	36	,	,	PUNCT
ejpam-6917	242	37	3−	3−	NUM
ejpam-6917	242	38	3µ0	3µ0	NUM
ejpam-6917	242	39	}	}	PUNCT
ejpam-6917	242	40	.	.	PUNCT
ejpam-6917	243	1	now	now	ADV
ejpam-6917	243	2	,	,	PUNCT
ejpam-6917	243	3	‖1	‖1	NOUN
ejpam-6917	243	4	2sp,5‖	2sp,5‖	NUM
ejpam-6917	243	5	<	<	X
ejpam-6917	243	6	1	1	NUM
ejpam-6917	243	7	for	for	ADP
ejpam-6917	243	8	11	11	NUM
ejpam-6917	243	9	19	19	NUM
ejpam-6917	243	10	<	<	X
ejpam-6917	243	11	µ0	µ0	NOUN
ejpam-6917	243	12	<	<	X
ejpam-6917	243	13	27	27	NUM
ejpam-6917	243	14	19	19	NUM
ejpam-6917	243	15	.	.	PUNCT
ejpam-6917	244	1	this	this	PRON
ejpam-6917	244	2	implies	imply	VERB
ejpam-6917	244	3	that	that	SCONJ
ejpam-6917	244	4	,	,	PUNCT
ejpam-6917	244	5	it	it	PRON
ejpam-6917	244	6	has	have	VERB
ejpam-6917	244	7	c4	c4	NOUN
ejpam-6917	244	8	-	-	PUNCT
ejpam-6917	244	9	continuity	continuity	NOUN
ejpam-6917	244	10	.	.	PUNCT
ejpam-6917	245	1	figure	figure	NOUN
ejpam-6917	245	2	1	1	NUM
ejpam-6917	245	3	:	:	PUNCT
ejpam-6917	245	4	basic	basic	ADJ
ejpam-6917	245	5	limit	limit	NOUN
ejpam-6917	245	6	function	function	NOUN
ejpam-6917	245	7	for	for	ADP
ejpam-6917	245	8	µ0	µ0	NOUN
ejpam-6917	245	9	=	=	SYM
ejpam-6917	245	10	0.6	0.6	NUM
ejpam-6917	245	11	,	,	PUNCT
ejpam-6917	245	12	0.7	0.7	NUM
ejpam-6917	245	13	,	,	PUNCT
ejpam-6917	245	14	0.8	0.8	NUM
ejpam-6917	245	15	,	,	PUNCT
ejpam-6917	245	16	0.9	0.9	NUM
ejpam-6917	245	17	.	.	PUNCT
ejpam-6917	246	1	f.	f.	PROPN
ejpam-6917	246	2	s.	s.	PROPN
ejpam-6917	246	3	alshammari	alshammari	PROPN
ejpam-6917	246	4	et	et	PROPN
ejpam-6917	246	5	al	al	PROPN
ejpam-6917	246	6	.	.	PUNCT
ejpam-6917	246	7	/	/	SYM
ejpam-6917	246	8	eur	eur	PROPN
ejpam-6917	246	9	.	.	PUNCT
ejpam-6917	247	1	j.	j.	PROPN
ejpam-6917	247	2	pure	pure	PROPN
ejpam-6917	247	3	appl	appl	PROPN
ejpam-6917	247	4	.	.	PROPN
ejpam-6917	247	5	math	math	PROPN
ejpam-6917	247	6	,	,	PUNCT
ejpam-6917	247	7	18	18	NUM
ejpam-6917	247	8	(	(	PUNCT
ejpam-6917	247	9	4	4	NUM
ejpam-6917	247	10	)	)	PUNCT
ejpam-6917	247	11	(	(	PUNCT
ejpam-6917	247	12	2025	2025	NUM
ejpam-6917	247	13	)	)	PUNCT
ejpam-6917	247	14	,	,	PUNCT
ejpam-6917	247	15	6917	6917	NUM
ejpam-6917	247	16	11	11	NUM
ejpam-6917	247	17	of	of	ADP
ejpam-6917	247	18	26	26	NUM
ejpam-6917	247	19	next	next	ADV
ejpam-6917	247	20	,	,	PUNCT
ejpam-6917	247	21	we	we	PRON
ejpam-6917	247	22	will	will	AUX
ejpam-6917	247	23	check	check	VERB
ejpam-6917	247	24	for	for	ADP
ejpam-6917	247	25	c5	c5	PROPN
ejpam-6917	247	26	smoothness	smoothness	PROPN
ejpam-6917	247	27	for	for	ADP
ejpam-6917	247	28	sp	sp	NOUN
ejpam-6917	247	29	,	,	PUNCT
ejpam-6917	247	30	consider	consider	VERB
ejpam-6917	247	31	the	the	DET
ejpam-6917	247	32	6th	6th	ADJ
ejpam-6917	247	33	-	-	PUNCT
ejpam-6917	247	34	order	order	NOUN
ejpam-6917	247	35	difference	difference	NOUN
ejpam-6917	247	36	sp,6scheme	sp,6scheme	NOUN
ejpam-6917	247	37	is	be	AUX
ejpam-6917	247	38	,	,	PUNCT
ejpam-6917	247	39	c6(v	c6(v	X
ejpam-6917	247	40	)	)	PUNCT
ejpam-6917	247	41	=	=	SYM
ejpam-6917	247	42	1	1	NUM
ejpam-6917	247	43	2	2	NUM
ejpam-6917	247	44	{	{	PUNCT
ejpam-6917	247	45	v	v	NOUN
ejpam-6917	247	46	5	5	NUM
ejpam-6917	247	47	2	2	NUM
ejpam-6917	247	48	(	(	PUNCT
ejpam-6917	247	49	3−	3−	NUM
ejpam-6917	247	50	3µ0	3µ0	NUM
ejpam-6917	247	51	)	)	PUNCT
ejpam-6917	248	1	+	+	CCONJ
ejpam-6917	248	2	(	(	PUNCT
ejpam-6917	248	3	v4)(−9	v4)(−9	X
ejpam-6917	248	4	+	+	CCONJ
ejpam-6917	248	5	11µ0	11µ0	NUM
ejpam-6917	248	6	)	)	PUNCT
ejpam-6917	248	7	+	+	CCONJ
ejpam-6917	248	8	v3	v3	PROPN
ejpam-6917	248	9	2	2	NUM
ejpam-6917	248	10	(	(	PUNCT
ejpam-6917	248	11	38−	38−	NUM
ejpam-6917	248	12	38µ0	38µ0	NUM
ejpam-6917	248	13	)	)	PUNCT
ejpam-6917	249	1	+	+	PROPN
ejpam-6917	249	2	(	(	PUNCT
ejpam-6917	249	3	v2)(−9	v2)(−9	ADJ
ejpam-6917	249	4	+	+	CCONJ
ejpam-6917	249	5	11µ0	11µ0	NUM
ejpam-6917	249	6	)	)	PUNCT
ejpam-6917	250	1	+	+	CCONJ
ejpam-6917	250	2	v	v	NUM
ejpam-6917	250	3	2	2	NUM
ejpam-6917	250	4	(	(	PUNCT
ejpam-6917	250	5	3−	3−	NUM
ejpam-6917	250	6	3µ0	3µ0	NUM
ejpam-6917	250	7	)	)	PUNCT
ejpam-6917	250	8	}	}	PUNCT
ejpam-6917	250	9	the	the	DET
ejpam-6917	250	10	mask	mask	NOUN
ejpam-6917	250	11	c[6	c[6	NOUN
ejpam-6917	250	12	]	]	X
ejpam-6917	250	13	=	=	PUNCT
ejpam-6917	250	14	(	(	PUNCT
ejpam-6917	250	15	c	c	X
ejpam-6917	251	1	[	[	X
ejpam-6917	251	2	6	6	NUM
ejpam-6917	251	3	]	]	X
ejpam-6917	251	4	i	i	PRON
ejpam-6917	251	5	:	:	PUNCT
ejpam-6917	252	1	i	i	PROPN
ejpam-6917	252	2	∈	∈	PROPN
ejpam-6917	252	3	z	z	X
ejpam-6917	252	4	)	)	PUNCT
ejpam-6917	252	5	which	which	PRON
ejpam-6917	252	6	is	be	AUX
ejpam-6917	252	7	used	use	VERB
ejpam-6917	252	8	in	in	ADP
ejpam-6917	252	9	the	the	DET
ejpam-6917	252	10	sp,6	sp,6	ADJ
ejpam-6917	252	11	-	-	PUNCT
ejpam-6917	252	12	scheme	scheme	NOUN
ejpam-6917	252	13	is	be	AUX
ejpam-6917	252	14	defined	define	VERB
ejpam-6917	252	15	as	as	SCONJ
ejpam-6917	252	16	follows	follow	VERB
ejpam-6917	252	17	:	:	PUNCT
ejpam-6917	252	18	c[6	c[6	ADP
ejpam-6917	252	19	]	]	X
ejpam-6917	252	20	=	=	SYM
ejpam-6917	252	21	1	1	NUM
ejpam-6917	252	22	4	4	NUM
ejpam-6917	252	23	{	{	PUNCT
ejpam-6917	252	24	3−	3−	NUM
ejpam-6917	252	25	3µ0,−18	3µ0,−18	NUM
ejpam-6917	252	26	+	+	SYM
ejpam-6917	252	27	22µ0	22µ0	NUM
ejpam-6917	252	28	,	,	PUNCT
ejpam-6917	252	29	38−	38−	NUM
ejpam-6917	252	30	38µ0,−18	38µ0,−18	NUM
ejpam-6917	252	31	+	+	SYM
ejpam-6917	252	32	22µ0	22µ0	NUM
ejpam-6917	252	33	,	,	PUNCT
ejpam-6917	252	34	3−	3−	NUM
ejpam-6917	252	35	3µ0	3µ0	NUM
ejpam-6917	252	36	}	}	PUNCT
ejpam-6917	252	37	.	.	PUNCT
ejpam-6917	253	1	now	now	ADV
ejpam-6917	253	2	,	,	PUNCT
ejpam-6917	253	3	‖1	‖1	VERB
ejpam-6917	253	4	2sp,6‖	2sp,6‖	NUM
ejpam-6917	253	5	<	<	X
ejpam-6917	253	6	1	1	NUM
ejpam-6917	253	7	for	for	ADP
ejpam-6917	253	8	9	9	NUM
ejpam-6917	253	9	11	11	NUM
ejpam-6917	253	10	<	<	X
ejpam-6917	253	11	µ0	µ0	NOUN
ejpam-6917	253	12	<	<	X
ejpam-6917	253	13	1	1	NUM
ejpam-6917	253	14	.	.	PUNCT
ejpam-6917	254	1	this	this	PRON
ejpam-6917	254	2	implies	imply	VERB
ejpam-6917	254	3	that	that	SCONJ
ejpam-6917	254	4	,	,	PUNCT
ejpam-6917	254	5	it	it	PRON
ejpam-6917	254	6	has	have	VERB
ejpam-6917	254	7	c5	c5	PROPN
ejpam-6917	254	8	-	-	PUNCT
ejpam-6917	254	9	continuity	continuity	NOUN
ejpam-6917	254	10	.	.	PUNCT
ejpam-6917	255	1	next	next	ADV
ejpam-6917	255	2	,	,	PUNCT
ejpam-6917	255	3	for	for	ADP
ejpam-6917	255	4	c6	c6	PROPN
ejpam-6917	255	5	smoothness	smoothness	PROPN
ejpam-6917	255	6	,	,	PUNCT
ejpam-6917	255	7	the	the	DET
ejpam-6917	255	8	divided	divided	ADJ
ejpam-6917	255	9	difference	difference	NOUN
ejpam-6917	255	10	of	of	ADP
ejpam-6917	255	11	7th	7th	ADJ
ejpam-6917	255	12	-	-	PUNCT
ejpam-6917	255	13	order	order	NOUN
ejpam-6917	255	14	does	do	AUX
ejpam-6917	255	15	not	not	PART
ejpam-6917	255	16	exist	exist	VERB
ejpam-6917	255	17	making	make	VERB
ejpam-6917	255	18	sp	sp	ADP
ejpam-6917	255	19	scheme	scheme	NOUN
ejpam-6917	255	20	of	of	ADP
ejpam-6917	255	21	c5	c5	PROPN
ejpam-6917	255	22	-	-	PUNCT
ejpam-6917	255	23	continuity	continuity	NOUN
ejpam-6917	255	24	.	.	PUNCT
ejpam-6917	256	1	remark	remark	NOUN
ejpam-6917	256	2	2	2	NUM
ejpam-6917	256	3	.	.	PUNCT
ejpam-6917	257	1	the	the	DET
ejpam-6917	257	2	fundamental	fundamental	ADJ
ejpam-6917	257	3	limit	limit	NOUN
ejpam-6917	257	4	function	function	NOUN
ejpam-6917	257	5	of	of	ADP
ejpam-6917	257	6	the	the	DET
ejpam-6917	257	7	sp	sp	NOUN
ejpam-6917	257	8	-scheme	-scheme	NOUN
ejpam-6917	257	9	is	be	AUX
ejpam-6917	257	10	expressed	express	VERB
ejpam-6917	257	11	as	as	ADP
ejpam-6917	257	12	φ	φ	NUM
ejpam-6917	257	13	=	=	SYM
ejpam-6917	257	14	s∞	s∞	PROPN
ejpam-6917	257	15	p	p	PROPN
ejpam-6917	257	16	δ	δ	PROPN
ejpam-6917	257	17	,	,	PUNCT
ejpam-6917	257	18	where	where	SCONJ
ejpam-6917	257	19	δ	δ	PROPN
ejpam-6917	257	20	=	=	PRON
ejpam-6917	257	21	{	{	PUNCT
ejpam-6917	257	22	δ0,i	δ0,i	PROPN
ejpam-6917	257	23	:	:	PUNCT
ejpam-6917	258	1	i	i	PRON
ejpam-6917	258	2	∈	∈	PROPN
ejpam-6917	258	3	z	z	AUX
ejpam-6917	258	4	}	}	PUNCT
ejpam-6917	258	5	is	be	AUX
ejpam-6917	258	6	a	a	DET
ejpam-6917	258	7	sequence	sequence	NOUN
ejpam-6917	258	8	at	at	ADP
ejpam-6917	258	9	level	level	NOUN
ejpam-6917	258	10	0	0	NUM
ejpam-6917	258	11	,	,	PUNCT
ejpam-6917	258	12	and	and	CCONJ
ejpam-6917	258	13	δi,0	δi,0	PROPN
ejpam-6917	258	14	denotes	denote	VERB
ejpam-6917	258	15	the	the	DET
ejpam-6917	258	16	kronecker	kronecker	NOUN
ejpam-6917	258	17	delta	delta	NOUN
ejpam-6917	258	18	.	.	PUNCT
ejpam-6917	259	1	it	it	PRON
ejpam-6917	259	2	is	be	AUX
ejpam-6917	259	3	important	important	ADJ
ejpam-6917	259	4	to	to	PART
ejpam-6917	259	5	note	note	VERB
ejpam-6917	259	6	that	that	SCONJ
ejpam-6917	259	7	the	the	DET
ejpam-6917	259	8	support	support	NOUN
ejpam-6917	259	9	of	of	ADP
ejpam-6917	259	10	this	this	DET
ejpam-6917	259	11	function	function	NOUN
ejpam-6917	259	12	is	be	AUX
ejpam-6917	259	13	[	[	X
ejpam-6917	259	14	-5,5	-5,5	X
ejpam-6917	259	15	]	]	X
ejpam-6917	259	16	,	,	PUNCT
ejpam-6917	259	17	which	which	PRON
ejpam-6917	259	18	is	be	AUX
ejpam-6917	259	19	equivalent	equivalent	ADJ
ejpam-6917	259	20	to	to	ADP
ejpam-6917	259	21	the	the	DET
ejpam-6917	259	22	sd	sd	NOUN
ejpam-6917	259	23	-	-	PUNCT
ejpam-6917	259	24	scheme	scheme	NOUN
ejpam-6917	259	25	.	.	PUNCT
ejpam-6917	260	1	a	a	DET
ejpam-6917	260	2	visualization	visualization	NOUN
ejpam-6917	260	3	of	of	ADP
ejpam-6917	260	4	the	the	DET
ejpam-6917	260	5	basic	basic	ADJ
ejpam-6917	260	6	limit	limit	NOUN
ejpam-6917	260	7	function	function	NOUN
ejpam-6917	260	8	of	of	ADP
ejpam-6917	260	9	the	the	DET
ejpam-6917	260	10	sp	sp	NOUN
ejpam-6917	260	11	-scheme	-scheme	NOUN
ejpam-6917	260	12	for	for	ADP
ejpam-6917	260	13	varying	vary	VERB
ejpam-6917	260	14	values	value	NOUN
ejpam-6917	260	15	of	of	ADP
ejpam-6917	260	16	the	the	DET
ejpam-6917	260	17	tension	tension	NOUN
ejpam-6917	260	18	parameter	parameter	NOUN
ejpam-6917	260	19	µ0	µ0	PROPN
ejpam-6917	260	20	is	be	AUX
ejpam-6917	260	21	provided	provide	VERB
ejpam-6917	260	22	in	in	ADP
ejpam-6917	260	23	figure	figure	NOUN
ejpam-6917	260	24	1	1	NUM
ejpam-6917	260	25	.	.	NOUN
ejpam-6917	260	26	4.2	4.2	NUM
ejpam-6917	260	27	.	.	PUNCT
ejpam-6917	261	1	order	order	NOUN
ejpam-6917	261	2	of	of	ADP
ejpam-6917	261	3	approximation	approximation	NOUN
ejpam-6917	261	4	we	we	PRON
ejpam-6917	261	5	investigate	investigate	VERB
ejpam-6917	261	6	the	the	DET
ejpam-6917	261	7	order	order	NOUN
ejpam-6917	261	8	of	of	ADP
ejpam-6917	261	9	approximation	approximation	NOUN
ejpam-6917	261	10	of	of	ADP
ejpam-6917	261	11	the	the	DET
ejpam-6917	261	12	sp	sp	NOUN
ejpam-6917	261	13	-scheme	-scheme	NOUN
ejpam-6917	261	14	with	with	ADP
ejpam-6917	261	15	the	the	DET
ejpam-6917	261	16	mask	mask	NOUN
ejpam-6917	261	17	in	in	ADP
ejpam-6917	261	18	(	(	PUNCT
ejpam-6917	261	19	1	1	NUM
ejpam-6917	261	20	)	)	PUNCT
ejpam-6917	261	21	,	,	PUNCT
ejpam-6917	261	22	focusing	focus	VERB
ejpam-6917	261	23	on	on	ADP
ejpam-6917	261	24	its	its	PRON
ejpam-6917	261	25	connection	connection	NOUN
ejpam-6917	261	26	to	to	ADP
ejpam-6917	261	27	the	the	DET
ejpam-6917	261	28	parameter	parameter	PROPN
ejpam-6917	261	29	µ0	µ0	PROPN
ejpam-6917	261	30	.	.	PUNCT
ejpam-6917	262	1	specifically	specifically	ADV
ejpam-6917	262	2	,	,	PUNCT
ejpam-6917	262	3	our	our	PRON
ejpam-6917	262	4	objective	objective	NOUN
ejpam-6917	262	5	is	be	AUX
ejpam-6917	262	6	to	to	PART
ejpam-6917	262	7	demonstrate	demonstrate	VERB
ejpam-6917	262	8	that	that	SCONJ
ejpam-6917	262	9	the	the	DET
ejpam-6917	262	10	sp	sp	ADP
ejpam-6917	262	11	-scheme	-scheme	PROPN
ejpam-6917	262	12	achieves	achieve	VERB
ejpam-6917	262	13	sixth	sixth	ADJ
ejpam-6917	262	14	-	-	PUNCT
ejpam-6917	262	15	order	order	NOUN
ejpam-6917	262	16	of	of	ADP
ejpam-6917	262	17	approximation	approximation	NOUN
ejpam-6917	262	18	with	with	ADP
ejpam-6917	262	19	an	an	DET
ejpam-6917	262	20	appropriate	appropriate	ADJ
ejpam-6917	262	21	choice	choice	NOUN
ejpam-6917	262	22	of	of	ADP
ejpam-6917	262	23	µ0	µ0	NOUN
ejpam-6917	262	24	.	.	PUNCT
ejpam-6917	263	1	subsequently	subsequently	ADV
ejpam-6917	263	2	,	,	PUNCT
ejpam-6917	263	3	we	we	PRON
ejpam-6917	263	4	will	will	AUX
ejpam-6917	263	5	prove	prove	VERB
ejpam-6917	263	6	that	that	SCONJ
ejpam-6917	263	7	if	if	SCONJ
ejpam-6917	263	8	the	the	DET
ejpam-6917	263	9	initial	initial	ADJ
ejpam-6917	263	10	data	datum	NOUN
ejpam-6917	263	11	sequence	sequence	NOUN
ejpam-6917	263	12	is	be	AUX
ejpam-6917	263	13	given	give	VERB
ejpam-6917	263	14	by	by	ADP
ejpam-6917	263	15	g0	g0	ADJ
ejpam-6917	263	16	=	=	PROPN
ejpam-6917	263	17	{	{	PUNCT
ejpam-6917	263	18	g(i2−n0	g(i2−n0	PROPN
ejpam-6917	263	19	)	)	PUNCT
ejpam-6917	263	20	:	:	PUNCT
ejpam-6917	264	1	i	i	PRON
ejpam-6917	264	2	∈	∈	PROPN
ejpam-6917	265	1	z	z	X
ejpam-6917	265	2	}	}	PUNCT
ejpam-6917	265	3	,	,	PUNCT
ejpam-6917	265	4	where	where	SCONJ
ejpam-6917	265	5	g	g	PROPN
ejpam-6917	265	6	is	be	AUX
ejpam-6917	265	7	a	a	DET
ejpam-6917	265	8	smooth	smooth	ADJ
ejpam-6917	265	9	function	function	NOUN
ejpam-6917	265	10	in	in	ADP
ejpam-6917	265	11	w6	w6	PROPN
ejpam-6917	265	12	∞(r	∞(r	PROPN
ejpam-6917	265	13	)	)	PUNCT
ejpam-6917	265	14	,	,	PUNCT
ejpam-6917	265	15	then	then	ADV
ejpam-6917	265	16	the	the	DET
ejpam-6917	265	17	scheme	scheme	NOUN
ejpam-6917	265	18	sp	sp	ADP
ejpam-6917	265	19	generates	generate	VERB
ejpam-6917	265	20	a	a	DET
ejpam-6917	265	21	limit	limit	NOUN
ejpam-6917	265	22	function	function	NOUN
ejpam-6917	265	23	s∞	s∞	NOUN
ejpam-6917	265	24	p	p	NOUN
ejpam-6917	265	25	gn0	gn0	NOUN
ejpam-6917	265	26	such	such	ADJ
ejpam-6917	265	27	that	that	DET
ejpam-6917	265	28	‖g	‖g	NOUN
ejpam-6917	265	29	−	−	PROPN
ejpam-6917	265	30	s∞	s∞	PROPN
ejpam-6917	265	31	p	p	ADJ
ejpam-6917	265	32	g0‖	g0‖	PROPN
ejpam-6917	265	33	≤	≤	PROPN
ejpam-6917	265	34	kg2	kg2	PROPN
ejpam-6917	265	35	−6n0	−6n0	PUNCT
ejpam-6917	265	36	(	(	PUNCT
ejpam-6917	265	37	9	9	NUM
ejpam-6917	265	38	)	)	PUNCT
ejpam-6917	265	39	to	to	PART
ejpam-6917	265	40	simplify	simplify	VERB
ejpam-6917	265	41	our	our	PRON
ejpam-6917	265	42	presentation	presentation	NOUN
ejpam-6917	265	43	,	,	PUNCT
ejpam-6917	265	44	we	we	PRON
ejpam-6917	265	45	use	use	VERB
ejpam-6917	265	46	the	the	DET
ejpam-6917	265	47	notation	notation	NOUN
ejpam-6917	265	48	ĝn	ĝn	PROPN
ejpam-6917	265	49	,	,	PUNCT
ejpam-6917	265	50	for	for	ADP
ejpam-6917	265	51	n	n	DET
ejpam-6917	265	52	∈	∈	NOUN
ejpam-6917	265	53	z+	z+	NUM
ejpam-6917	265	54	,	,	PUNCT
ejpam-6917	265	55	to	to	PART
ejpam-6917	265	56	represent	represent	VERB
ejpam-6917	265	57	the	the	DET
ejpam-6917	265	58	sequence	sequence	NOUN
ejpam-6917	265	59	obtained	obtain	VERB
ejpam-6917	265	60	by	by	ADP
ejpam-6917	265	61	sampling	sample	VERB
ejpam-6917	265	62	a	a	DET
ejpam-6917	265	63	smooth	smooth	ADJ
ejpam-6917	265	64	function	function	NOUN
ejpam-6917	265	65	g	g	NOUN
ejpam-6917	265	66	at	at	ADP
ejpam-6917	265	67	the	the	DET
ejpam-6917	265	68	grid	grid	NOUN
ejpam-6917	265	69	points	point	NOUN
ejpam-6917	265	70	2−nz	2−nz	NUM
ejpam-6917	265	71	.	.	PUNCT
ejpam-6917	266	1	that	that	PRON
ejpam-6917	266	2	is	be	AUX
ejpam-6917	266	3	,	,	PUNCT
ejpam-6917	266	4	ĝn	ĝn	X
ejpam-6917	266	5	=	=	SYM
ejpam-6917	266	6	{	{	PUNCT
ejpam-6917	266	7	g(i2−n	g(i2−n	NOUN
ejpam-6917	266	8	:	:	PUNCT
ejpam-6917	267	1	i	i	PRON
ejpam-6917	267	2	∈	∈	PROPN
ejpam-6917	268	1	z	z	X
ejpam-6917	268	2	}	}	PUNCT
ejpam-6917	268	3	,	,	PUNCT
ejpam-6917	268	4	n	n	PROPN
ejpam-6917	268	5	∈	∈	PROPN
ejpam-6917	268	6	z+	z+	NUM
ejpam-6917	268	7	.	.	PUNCT
ejpam-6917	269	1	(	(	PUNCT
ejpam-6917	269	2	10	10	NUM
ejpam-6917	269	3	)	)	PUNCT
ejpam-6917	269	4	lemma	lemma	PROPN
ejpam-6917	269	5	1	1	X
ejpam-6917	269	6	.	.	PUNCT
ejpam-6917	270	1	let	let	VERB
ejpam-6917	270	2	sp	sp	AUX
ejpam-6917	270	3	be	be	AUX
ejpam-6917	270	4	the	the	DET
ejpam-6917	270	5	spss	spss	NOUN
ejpam-6917	270	6	with	with	ADP
ejpam-6917	270	7	the	the	DET
ejpam-6917	270	8	parameter	parameter	NOUN
ejpam-6917	270	9	µ0	µ0	NOUN
ejpam-6917	270	10	=	=	SYM
ejpam-6917	270	11	τ2−2n0	τ2−2n0	NOUN
ejpam-6917	270	12	.	.	PUNCT
ejpam-6917	271	1	let	let	VERB
ejpam-6917	271	2	ĝn	ĝn	PROPN
ejpam-6917	271	3	,	,	PUNCT
ejpam-6917	271	4	n	n	PRON
ejpam-6917	271	5	≥	≥	PROPN
ejpam-6917	271	6	n0	n0	NUM
ejpam-6917	271	7	be	be	AUX
ejpam-6917	271	8	a	a	DET
ejpam-6917	271	9	sequence	sequence	NOUN
ejpam-6917	271	10	of	of	ADP
ejpam-6917	271	11	data	datum	NOUN
ejpam-6917	271	12	points	point	NOUN
ejpam-6917	271	13	obtained	obtain	VERB
ejpam-6917	271	14	by	by	ADP
ejpam-6917	271	15	sampling	sample	VERB
ejpam-6917	271	16	a	a	DET
ejpam-6917	271	17	function	function	NOUN
ejpam-6917	271	18	g	g	PROPN
ejpam-6917	271	19	∈	∈	PROPN
ejpam-6917	271	20	w6	w6	PROPN
ejpam-6917	271	21	∞(r	∞(r	NOUN
ejpam-6917	271	22	)	)	PUNCT
ejpam-6917	271	23	with	with	ADP
ejpam-6917	271	24	density	density	NOUN
ejpam-6917	271	25	2−n	2−n	NUM
ejpam-6917	271	26	.	.	PUNCT
ejpam-6917	272	1	then	then	ADV
ejpam-6917	272	2	‖spĝ	‖spĝ	PROPN
ejpam-6917	272	3	n	n	CCONJ
ejpam-6917	272	4	−	−	PROPN
ejpam-6917	272	5	ĝn+1‖∞	ĝn+1‖∞	PROPN
ejpam-6917	272	6	≤	≤	PROPN
ejpam-6917	272	7	kg2	kg2	PROPN
ejpam-6917	272	8	−2(2n+n0	−2(2n+n0	PROPN
ejpam-6917	272	9	)	)	PUNCT
ejpam-6917	272	10	for	for	ADP
ejpam-6917	272	11	some	some	DET
ejpam-6917	272	12	constant	constant	ADJ
ejpam-6917	272	13	kg	kg	NOUN
ejpam-6917	272	14	>	>	X
ejpam-6917	272	15	0	0	PUNCT
ejpam-6917	273	1	depending	depend	VERB
ejpam-6917	273	2	on	on	ADP
ejpam-6917	273	3	g	g	PROPN
ejpam-6917	273	4	.	.	PUNCT
ejpam-6917	274	1	f.	f.	PROPN
ejpam-6917	274	2	s.	s.	PROPN
ejpam-6917	274	3	alshammari	alshammari	PROPN
ejpam-6917	274	4	et	et	PROPN
ejpam-6917	274	5	al	al	PROPN
ejpam-6917	274	6	.	.	PUNCT
ejpam-6917	274	7	/	/	SYM
ejpam-6917	274	8	eur	eur	PROPN
ejpam-6917	274	9	.	.	PUNCT
ejpam-6917	275	1	j.	j.	PROPN
ejpam-6917	275	2	pure	pure	PROPN
ejpam-6917	275	3	appl	appl	PROPN
ejpam-6917	275	4	.	.	PROPN
ejpam-6917	275	5	math	math	PROPN
ejpam-6917	275	6	,	,	PUNCT
ejpam-6917	275	7	18	18	NUM
ejpam-6917	275	8	(	(	PUNCT
ejpam-6917	275	9	4	4	NUM
ejpam-6917	275	10	)	)	PUNCT
ejpam-6917	275	11	(	(	PUNCT
ejpam-6917	275	12	2025	2025	NUM
ejpam-6917	275	13	)	)	PUNCT
ejpam-6917	275	14	,	,	PUNCT
ejpam-6917	275	15	6917	6917	NUM
ejpam-6917	275	16	12	12	NUM
ejpam-6917	275	17	of	of	ADP
ejpam-6917	275	18	26	26	NUM
ejpam-6917	275	19	proof	proof	NOUN
ejpam-6917	275	20	.	.	PUNCT
ejpam-6917	276	1	let	let	VERB
ejpam-6917	276	2	us	we	PRON
ejpam-6917	276	3	first	first	ADV
ejpam-6917	276	4	estimate	estimate	VERB
ejpam-6917	276	5	the	the	DET
ejpam-6917	276	6	case	case	NOUN
ejpam-6917	276	7	of	of	ADP
ejpam-6917	276	8	odd	odd	ADJ
ejpam-6917	276	9	rule	rule	NOUN
ejpam-6917	276	10	,	,	PUNCT
ejpam-6917	276	11	i.e.	i.e.	X
ejpam-6917	276	12	,|sp	,|sp	PUNCT
ejpam-6917	276	13	ĝ	ĝ	X
ejpam-6917	276	14	n	n	PRON
ejpam-6917	276	15	2i+1	2i+1	PROPN
ejpam-6917	276	16	−	−	PROPN
ejpam-6917	277	1	ĝn+1	ĝn+1	PROPN
ejpam-6917	277	2	2i+1|	2i+1|	PROPN
ejpam-6917	277	3	.	.	PUNCT
ejpam-6917	278	1	to	to	PART
ejpam-6917	278	2	do	do	VERB
ejpam-6917	278	3	this	this	PRON
ejpam-6917	278	4	,	,	PUNCT
ejpam-6917	278	5	the	the	DET
ejpam-6917	278	6	proposed	propose	VERB
ejpam-6917	278	7	scheme	scheme	NOUN
ejpam-6917	278	8	is	be	AUX
ejpam-6917	278	9	represented	represent	VERB
ejpam-6917	278	10	using	use	VERB
ejpam-6917	278	11	sd	sd	NOUN
ejpam-6917	278	12	-	-	PUNCT
ejpam-6917	278	13	scheme	scheme	NOUN
ejpam-6917	278	14	:	:	PUNCT
ejpam-6917	278	15	(	(	PUNCT
ejpam-6917	278	16	sp	sp	ADP
ejpam-6917	278	17	ĝ	ĝ	X
ejpam-6917	279	1	n)2i+1	n)2i+1	NOUN
ejpam-6917	280	1	=	=	PUNCT
ejpam-6917	280	2	sdĝ	sdĝ	PROPN
ejpam-6917	280	3	n	n	NOUN
ejpam-6917	280	4	2i+1	2i+1	NOUN
ejpam-6917	280	5	−	−	PROPN
ejpam-6917	281	1	τ	τ	PROPN
ejpam-6917	281	2	64	64	NUM
ejpam-6917	281	3	2−2n0	2−2n0	NUM
ejpam-6917	281	4	.2−2n(d2	.2−2n(d2	NOUN
ejpam-6917	281	5	g	g	PROPN
ejpam-6917	281	6	n	n	PROPN
ejpam-6917	281	7	2i+1	2i+1	NUM
ejpam-6917	281	8	)	)	PUNCT
ejpam-6917	281	9	(	(	PUNCT
ejpam-6917	281	10	11	11	NUM
ejpam-6917	281	11	)	)	PUNCT
ejpam-6917	281	12	clearly	clearly	ADV
ejpam-6917	281	13	d2	d2	VERB
ejpam-6917	281	14	g	g	PROPN
ejpam-6917	281	15	n	n	NUM
ejpam-6917	281	16	2i+1	2i+1	NOUN
ejpam-6917	281	17	=	=	SYM
ejpam-6917	281	18	o(2−4n	o(2−4n	PROPN
ejpam-6917	281	19	)	)	PUNCT
ejpam-6917	281	20	for	for	ADP
ejpam-6917	281	21	i	i	PROPN
ejpam-6917	281	22	∈	∈	PROPN
ejpam-6917	281	23	z	z	NOUN
ejpam-6917	281	24	because	because	SCONJ
ejpam-6917	281	25	g	g	PROPN
ejpam-6917	281	26	is	be	AUX
ejpam-6917	281	27	c5	c5	PROPN
ejpam-6917	281	28	and	and	CCONJ
ejpam-6917	281	29	giv	giv	PROPN
ejpam-6917	281	30	is	be	AUX
ejpam-6917	281	31	bounded	bound	VERB
ejpam-6917	281	32	.	.	PUNCT
ejpam-6917	282	1	it	it	PRON
ejpam-6917	282	2	follows	follow	VERB
ejpam-6917	282	3	that	that	SCONJ
ejpam-6917	282	4	|(sp	|(sp	VERB
ejpam-6917	282	5	ĝ	ĝ	X
ejpam-6917	282	6	n)2i+1	n)2i+1	NOUN
ejpam-6917	282	7	−	−	PROPN
ejpam-6917	282	8	ĝn+1	ĝn+1	NOUN
ejpam-6917	283	1	2i+1|	2i+1|	NOUN
ejpam-6917	283	2	≤	≤	NOUN
ejpam-6917	283	3	|(sdĝ	|(sdĝ	ADP
ejpam-6917	283	4	n)2i+1	n)2i+1	PROPN
ejpam-6917	283	5	−	−	PROPN
ejpam-6917	283	6	ĝn+1	ĝn+1	PROPN
ejpam-6917	283	7	2i+1|+o(2−2(2n+n0	2i+1|+o(2−2(2n+n0	NOUN
ejpam-6917	283	8	)	)	PUNCT
ejpam-6917	283	9	)	)	PUNCT
ejpam-6917	284	1	=	=	SYM
ejpam-6917	284	2	o(2−2(2n+n0	o(2−2(2n+n0	NOUN
ejpam-6917	284	3	)	)	PUNCT
ejpam-6917	284	4	)	)	PUNCT
ejpam-6917	284	5	(	(	PUNCT
ejpam-6917	284	6	12	12	NUM
ejpam-6917	284	7	)	)	PUNCT
ejpam-6917	284	8	since	since	SCONJ
ejpam-6917	284	9	,	,	PUNCT
ejpam-6917	284	10	the	the	DET
ejpam-6917	284	11	sd	sd	NOUN
ejpam-6917	284	12	-	-	PUNCT
ejpam-6917	284	13	scheme	scheme	NOUN
ejpam-6917	284	14	provides	provide	VERB
ejpam-6917	284	15	the	the	DET
ejpam-6917	284	16	sixth	sixth	ADJ
ejpam-6917	284	17	-	-	PUNCT
ejpam-6917	284	18	order	order	NOUN
ejpam-6917	284	19	approximation	approximation	NOUN
ejpam-6917	284	20	and	and	CCONJ
ejpam-6917	284	21	g	g	PROPN
ejpam-6917	284	22	∈	∈	PROPN
ejpam-6917	284	23	w6	w6	PROPN
ejpam-6917	284	24	∞(r	∞(r	NOUN
ejpam-6917	284	25	)	)	PUNCT
ejpam-6917	284	26	,	,	PUNCT
ejpam-6917	284	27	it	it	PRON
ejpam-6917	284	28	readily	readily	ADV
ejpam-6917	284	29	holds	hold	VERB
ejpam-6917	284	30	that	that	SCONJ
ejpam-6917	284	31	|(sdĝ	|(sdĝ	ADP
ejpam-6917	284	32	n)2i+1	n)2i+1	PROPN
ejpam-6917	284	33	−	−	PROPN
ejpam-6917	284	34	ĝn+1	ĝn+1	NOUN
ejpam-6917	285	1	2i+1|	2i+1|	NUM
ejpam-6917	285	2	=	=	SYM
ejpam-6917	285	3	o(2−6n	o(2−6n	PROPN
ejpam-6917	285	4	)	)	PUNCT
ejpam-6917	285	5	.	.	PUNCT
ejpam-6917	286	1	combining	combine	VERB
ejpam-6917	286	2	this	this	PRON
ejpam-6917	286	3	with	with	ADP
ejpam-6917	286	4	(	(	PUNCT
ejpam-6917	286	5	4	4	X
ejpam-6917	286	6	)	)	PUNCT
ejpam-6917	286	7	verifies	verifie	NOUN
ejpam-6917	286	8	the	the	DET
ejpam-6917	286	9	lemmas	lemmas	ADJ
ejpam-6917	286	10	claim	claim	NOUN
ejpam-6917	286	11	,	,	PUNCT
ejpam-6917	286	12	‖spĝ	‖spĝ	PROPN
ejpam-6917	286	13	n	n	CCONJ
ejpam-6917	286	14	−	−	PROPN
ejpam-6917	286	15	ĝn+1‖∞	ĝn+1‖∞	PROPN
ejpam-6917	286	16	≤	≤	PROPN
ejpam-6917	286	17	kg2	kg2	PROPN
ejpam-6917	286	18	−2(2n+n0	−2(2n+n0	PROPN
ejpam-6917	286	19	)	)	PUNCT
ejpam-6917	286	20	in	in	ADP
ejpam-6917	286	21	a	a	DET
ejpam-6917	286	22	similar	similar	ADJ
ejpam-6917	286	23	way	way	NOUN
ejpam-6917	286	24	,	,	PUNCT
ejpam-6917	286	25	we	we	PRON
ejpam-6917	286	26	can	can	AUX
ejpam-6917	286	27	verify	verify	VERB
ejpam-6917	286	28	the	the	DET
ejpam-6917	286	29	even	even	ADJ
ejpam-6917	286	30	rule	rule	NOUN
ejpam-6917	286	31	.	.	PUNCT
ejpam-6917	287	1	theorem	theorem	ADJ
ejpam-6917	287	2	5	5	NUM
ejpam-6917	287	3	.	.	PUNCT
ejpam-6917	288	1	assume	assume	VERB
ejpam-6917	288	2	that	that	SCONJ
ejpam-6917	288	3	the	the	DET
ejpam-6917	288	4	initial	initial	ADJ
ejpam-6917	288	5	data	datum	NOUN
ejpam-6917	288	6	sequence	sequence	NOUN
ejpam-6917	288	7	g0	g0	NOUN
ejpam-6917	288	8	:	:	PUNCT
ejpam-6917	288	9	=	=	SYM
ejpam-6917	288	10	{	{	PUNCT
ejpam-6917	288	11	g(2−n0i	g(2−n0i	PROPN
ejpam-6917	288	12	)	)	PUNCT
ejpam-6917	288	13	:	:	PUNCT
ejpam-6917	289	1	i	i	PRON
ejpam-6917	289	2	∈	∈	PROPN
ejpam-6917	289	3	z	z	AUX
ejpam-6917	289	4	}	}	PUNCT
ejpam-6917	289	5	is	be	AUX
ejpam-6917	289	6	obtained	obtain	VERB
ejpam-6917	289	7	by	by	ADP
ejpam-6917	289	8	sampling	sample	VERB
ejpam-6917	289	9	a	a	DET
ejpam-6917	289	10	function	function	NOUN
ejpam-6917	289	11	g	g	PROPN
ejpam-6917	289	12	∈	∈	PROPN
ejpam-6917	289	13	w	w	ADP
ejpam-6917	289	14	6	6	NUM
ejpam-6917	289	15	∞(r	∞(r	NUM
ejpam-6917	289	16	)	)	PUNCT
ejpam-6917	289	17	,	,	PUNCT
ejpam-6917	289	18	i.e.	i.e.	X
ejpam-6917	289	19	,	,	PUNCT
ejpam-6917	289	20	g0	g0	NOUN
ejpam-6917	289	21	:	:	PUNCT
ejpam-6917	289	22	=	=	SYM
ejpam-6917	289	23	ĝn0	ĝn0	NOUN
ejpam-6917	289	24	.	.	PUNCT
ejpam-6917	290	1	let	let	AUX
ejpam-6917	290	2	{	{	PUNCT
ejpam-6917	290	3	sp	sp	VERB
ejpam-6917	290	4	}	}	PUNCT
ejpam-6917	290	5	denote	denote	VERB
ejpam-6917	290	6	the	the	DET
ejpam-6917	290	7	spss	spss	NOUN
ejpam-6917	290	8	defined	define	VERB
ejpam-6917	290	9	by	by	ADP
ejpam-6917	290	10	the	the	DET
ejpam-6917	290	11	refinement	refinement	NOUN
ejpam-6917	290	12	rule	rule	NOUN
ejpam-6917	290	13	given	give	VERB
ejpam-6917	290	14	in	in	ADP
ejpam-6917	290	15	equation	equation	NOUN
ejpam-6917	290	16	(	(	PUNCT
ejpam-6917	290	17	2.1	2.1	NUM
ejpam-6917	290	18	)	)	PUNCT
ejpam-6917	290	19	,	,	PUNCT
ejpam-6917	290	20	and	and	CCONJ
ejpam-6917	290	21	suppose	suppose	VERB
ejpam-6917	290	22	the	the	DET
ejpam-6917	290	23	shape	shape	NOUN
ejpam-6917	290	24	parameter	parameter	NOUN
ejpam-6917	290	25	µ0	µ0	NOUN
ejpam-6917	290	26	satisfies	satisfie	NOUN
ejpam-6917	290	27	0	0	NUM
ejpam-6917	290	28	≤	≤	NUM
ejpam-6917	290	29	µ0	µ0	NOUN
ejpam-6917	290	30	≤	≤	NOUN
ejpam-6917	290	31	τ2−n0	τ2−n0	NOUN
ejpam-6917	290	32	,	,	PUNCT
ejpam-6917	290	33	for	for	ADP
ejpam-6917	290	34	some	some	DET
ejpam-6917	290	35	constant	constant	ADJ
ejpam-6917	290	36	τ	τ	X
ejpam-6917	290	37	>	>	X
ejpam-6917	290	38	0	0	PROPN
ejpam-6917	290	39	.	.	PUNCT
ejpam-6917	291	1	under	under	ADP
ejpam-6917	291	2	these	these	DET
ejpam-6917	291	3	conditions	condition	NOUN
ejpam-6917	291	4	,	,	PUNCT
ejpam-6917	291	5	the	the	DET
ejpam-6917	291	6	following	follow	VERB
ejpam-6917	291	7	error	error	NOUN
ejpam-6917	291	8	estimate	estimate	NOUN
ejpam-6917	291	9	holds	hold	VERB
ejpam-6917	291	10	:	:	PUNCT
ejpam-6917	291	11	‖s∞	‖s∞	PROPN
ejpam-6917	291	12	p	p	PROPN
ejpam-6917	291	13	g0	g0	PROPN
ejpam-6917	291	14	−	−	PROPN
ejpam-6917	291	15	g‖∞	g‖∞	NOUN
ejpam-6917	291	16	≤	≤	NUM
ejpam-6917	291	17	kg	kg	PROPN
ejpam-6917	291	18	,	,	PUNCT
ejpam-6917	291	19	τ2	τ2	NOUN
ejpam-6917	291	20	−6n0	−6n0	NOUN
ejpam-6917	291	21	,	,	PUNCT
ejpam-6917	291	22	where	where	SCONJ
ejpam-6917	291	23	kg	kg	PROPN
ejpam-6917	291	24	,	,	PUNCT
ejpam-6917	291	25	τ	τ	PROPN
ejpam-6917	291	26	>	>	X
ejpam-6917	291	27	0	0	PUNCT
ejpam-6917	291	28	is	be	AUX
ejpam-6917	291	29	a	a	DET
ejpam-6917	291	30	constant	constant	ADJ
ejpam-6917	291	31	that	that	PRON
ejpam-6917	291	32	depends	depend	VERB
ejpam-6917	291	33	only	only	ADV
ejpam-6917	291	34	on	on	ADP
ejpam-6917	291	35	the	the	DET
ejpam-6917	291	36	function	function	NOUN
ejpam-6917	291	37	g	g	NOUN
ejpam-6917	291	38	and	and	CCONJ
ejpam-6917	291	39	the	the	DET
ejpam-6917	291	40	parameter	parameter	NOUN
ejpam-6917	291	41	τ	τ	PROPN
ejpam-6917	291	42	,	,	PUNCT
ejpam-6917	291	43	but	but	CCONJ
ejpam-6917	291	44	is	be	AUX
ejpam-6917	291	45	independent	independent	ADJ
ejpam-6917	291	46	of	of	ADP
ejpam-6917	291	47	the	the	DET
ejpam-6917	291	48	refinement	refinement	NOUN
ejpam-6917	291	49	level	level	NOUN
ejpam-6917	291	50	n0	n0	PROPN
ejpam-6917	291	51	.	.	PUNCT
ejpam-6917	292	1	proof	proof	NOUN
ejpam-6917	292	2	.	.	PUNCT
ejpam-6917	293	1	let	let	VERB
ejpam-6917	293	2	d	d	NOUN
ejpam-6917	293	3	=	=	PRON
ejpam-6917	293	4	{	{	PUNCT
ejpam-6917	293	5	i2−n	i2−n	PROPN
ejpam-6917	293	6	:	:	PUNCT
ejpam-6917	294	1	i	i	PROPN
ejpam-6917	294	2	∈	∈	PROPN
ejpam-6917	295	1	z	z	NOUN
ejpam-6917	295	2	,	,	PUNCT
ejpam-6917	295	3	n	n	PRON
ejpam-6917	295	4	∈	∈	NOUN
ejpam-6917	295	5	z+	z+	PRON
ejpam-6917	295	6	}	}	PUNCT
ejpam-6917	295	7	be	be	AUX
ejpam-6917	295	8	the	the	DET
ejpam-6917	295	9	set	set	NOUN
ejpam-6917	295	10	of	of	ADP
ejpam-6917	295	11	dyadic	dyadic	ADJ
ejpam-6917	295	12	points	point	NOUN
ejpam-6917	295	13	.	.	PUNCT
ejpam-6917	296	1	suppose	suppose	VERB
ejpam-6917	296	2	the	the	DET
ejpam-6917	296	3	initial	initial	ADJ
ejpam-6917	296	4	data	datum	NOUN
ejpam-6917	296	5	g0	g0	NOUN
ejpam-6917	296	6	is	be	AUX
ejpam-6917	296	7	defined	define	VERB
ejpam-6917	296	8	on	on	ADP
ejpam-6917	296	9	the	the	DET
ejpam-6917	296	10	grid	grid	NOUN
ejpam-6917	296	11	2−n0z	2−n0z	NUM
ejpam-6917	296	12	,	,	PUNCT
ejpam-6917	296	13	and	and	CCONJ
ejpam-6917	296	14	let	let	VERB
ejpam-6917	296	15	the	the	DET
ejpam-6917	296	16	iterated	iterated	ADJ
ejpam-6917	296	17	subdivision	subdivision	NOUN
ejpam-6917	296	18	sequence	sequence	NOUN
ejpam-6917	296	19	be	be	AUX
ejpam-6917	296	20	given	give	VERB
ejpam-6917	296	21	by	by	ADP
ejpam-6917	296	22	gn	gn	PROPN
ejpam-6917	296	23	=	=	NOUN
ejpam-6917	296	24	sn−n0	sn−n0	PROPN
ejpam-6917	296	25	p	p	PROPN
ejpam-6917	296	26	ĝn0	ĝn0	PROPN
ejpam-6917	296	27	.	.	PUNCT
ejpam-6917	297	1	then	then	ADV
ejpam-6917	297	2	the	the	DET
ejpam-6917	297	3	sequence	sequence	NOUN
ejpam-6917	297	4	gn	gn	PROPN
ejpam-6917	297	5	satisfies	satisfy	VERB
ejpam-6917	297	6	the	the	DET
ejpam-6917	297	7	telescoping	telescope	VERB
ejpam-6917	297	8	identity	identity	NOUN
ejpam-6917	297	9	gn	gn	PROPN
ejpam-6917	297	10	=	=	PUNCT
ejpam-6917	297	11	sp	sp	ADP
ejpam-6917	297	12	ĝ	ĝ	X
ejpam-6917	297	13	n−1	n−1	PROPN
ejpam-6917	297	14	+	+	CCONJ
ejpam-6917	297	15	n−2∑	n−2∑	NUM
ejpam-6917	297	16	l	l	NOUN
ejpam-6917	297	17	=	=	SYM
ejpam-6917	297	18	n0	n0	X
ejpam-6917	297	19	sn−l−1(sp	sn−l−1(sp	NOUN
ejpam-6917	297	20	ĝ	ĝ	X
ejpam-6917	297	21	l	l	NOUN
ejpam-6917	297	22	−	−	PROPN
ejpam-6917	297	23	ĝl+1	ĝl+1	PROPN
ejpam-6917	297	24	)	)	PUNCT
ejpam-6917	297	25	.	.	PUNCT
ejpam-6917	298	1	assume	assume	VERB
ejpam-6917	298	2	the	the	DET
ejpam-6917	298	3	proposed	propose	VERB
ejpam-6917	298	4	sp	sp	ADP
ejpam-6917	298	5	-scheme	-scheme	PROPN
ejpam-6917	298	6	is	be	AUX
ejpam-6917	298	7	stable	stable	ADJ
ejpam-6917	298	8	i.e.	i.e.	ADV
ejpam-6917	298	9	,	,	PUNCT
ejpam-6917	298	10	there	there	PRON
ejpam-6917	298	11	exists	exist	VERB
ejpam-6917	298	12	a	a	DET
ejpam-6917	298	13	constant	constant	ADJ
ejpam-6917	298	14	k	k	X
ejpam-6917	298	15	>	>	X
ejpam-6917	298	16	0	0	NUM
ejpam-6917	298	17	such	such	ADJ
ejpam-6917	298	18	that	that	DET
ejpam-6917	298	19	||sm	||sm	NOUN
ejpam-6917	298	20	p	p	PROPN
ejpam-6917	298	21	||∞	||∞	PROPN
ejpam-6917	298	22	≤	≤	NOUN
ejpam-6917	298	23	k	k	NOUN
ejpam-6917	298	24	for	for	ADP
ejpam-6917	298	25	any	any	DET
ejpam-6917	298	26	m	m	PROPN
ejpam-6917	298	27	∈	∈	PROPN
ejpam-6917	298	28	n.	n.	NOUN
ejpam-6917	298	29	then	then	ADV
ejpam-6917	298	30	,	,	PUNCT
ejpam-6917	298	31	for	for	ADP
ejpam-6917	298	32	any	any	DET
ejpam-6917	298	33	n	n	PRON
ejpam-6917	298	34	≥	≥	NOUN
ejpam-6917	298	35	n0	n0	NUM
ejpam-6917	298	36	and	and	CCONJ
ejpam-6917	299	1	i	i	PROPN
ejpam-6917	299	2	∈	∈	PROPN
ejpam-6917	299	3	z	z	NOUN
ejpam-6917	299	4	,	,	PUNCT
ejpam-6917	299	5	the	the	DET
ejpam-6917	299	6	following	follow	VERB
ejpam-6917	299	7	estimate	estimate	NOUN
ejpam-6917	299	8	holds	hold	VERB
ejpam-6917	299	9	:	:	PUNCT
ejpam-6917	299	10	|gni	|gni	PUNCT
ejpam-6917	299	11	−	−	PROPN
ejpam-6917	299	12	g(i2−n)|	g(i2−n)|	PROPN
ejpam-6917	299	13	≤	≤	NUM
ejpam-6917	299	14	||sp	||sp	NOUN
ejpam-6917	299	15	ĝ	ĝ	X
ejpam-6917	299	16	n−1	n−1	PROPN
ejpam-6917	299	17	−	−	PROPN
ejpam-6917	299	18	ĝn||∞	ĝn||∞	PROPN
ejpam-6917	299	19	+	+	CCONJ
ejpam-6917	299	20	n−2∑	n−2∑	NUM
ejpam-6917	299	21	l	l	NOUN
ejpam-6917	299	22	=	=	PROPN
ejpam-6917	299	23	n0	n0	X
ejpam-6917	299	24	||sn−l−1	||sn−l−1	PROPN
ejpam-6917	299	25	p	p	PROPN
ejpam-6917	299	26	||∞||sp	||∞||sp	NOUN
ejpam-6917	299	27	ĝ	ĝ	X
ejpam-6917	299	28	l	l	NOUN
ejpam-6917	299	29	−	−	PROPN
ejpam-6917	299	30	ĝl−1||∞	ĝl−1||∞	NOUN
ejpam-6917	299	31	≤	≤	NUM
ejpam-6917	299	32	k	k	ADP
ejpam-6917	299	33	n−1∑	n−1∑	NUM
ejpam-6917	299	34	l	l	NOUN
ejpam-6917	299	35	=	=	NOUN
ejpam-6917	299	36	n0	n0	ADJ
ejpam-6917	299	37	||sp	||sp	NOUN
ejpam-6917	299	38	ĝ	ĝ	X
ejpam-6917	299	39	n	n	CCONJ
ejpam-6917	299	40	−	−	PROPN
ejpam-6917	299	41	ĝl+1||∞.	ĝl+1||∞.	PROPN
ejpam-6917	300	1	f.	f.	PROPN
ejpam-6917	300	2	s.	s.	PROPN
ejpam-6917	300	3	alshammari	alshammari	PROPN
ejpam-6917	300	4	et	et	PROPN
ejpam-6917	300	5	al	al	PROPN
ejpam-6917	300	6	.	.	PUNCT
ejpam-6917	300	7	/	/	SYM
ejpam-6917	300	8	eur	eur	PROPN
ejpam-6917	300	9	.	.	PUNCT
ejpam-6917	301	1	j.	j.	PROPN
ejpam-6917	301	2	pure	pure	PROPN
ejpam-6917	301	3	appl	appl	PROPN
ejpam-6917	301	4	.	.	PROPN
ejpam-6917	301	5	math	math	PROPN
ejpam-6917	301	6	,	,	PUNCT
ejpam-6917	301	7	18	18	NUM
ejpam-6917	301	8	(	(	PUNCT
ejpam-6917	301	9	4	4	NUM
ejpam-6917	301	10	)	)	PUNCT
ejpam-6917	301	11	(	(	PUNCT
ejpam-6917	301	12	2025	2025	NUM
ejpam-6917	301	13	)	)	PUNCT
ejpam-6917	301	14	,	,	PUNCT
ejpam-6917	301	15	6917	6917	NUM
ejpam-6917	301	16	13	13	NUM
ejpam-6917	301	17	of	of	ADP
ejpam-6917	301	18	26	26	NUM
ejpam-6917	301	19	our	our	PRON
ejpam-6917	301	20	next	next	ADJ
ejpam-6917	301	21	step	step	NOUN
ejpam-6917	301	22	is	be	AUX
ejpam-6917	301	23	to	to	PART
ejpam-6917	301	24	approximate	approximate	VERB
ejpam-6917	301	25	the	the	DET
ejpam-6917	301	26	term	term	NOUN
ejpam-6917	301	27	||sĝl	||sĝl	ADP
ejpam-6917	301	28	−	−	PROPN
ejpam-6917	301	29	ĝl+1||∞.	ĝl+1||∞.	NOUN
ejpam-6917	301	30	by	by	ADP
ejpam-6917	301	31	assumption	assumption	NOUN
ejpam-6917	301	32	,	,	PUNCT
ejpam-6917	301	33	0	0	NUM
ejpam-6917	301	34	≤	≤	NUM
ejpam-6917	301	35	µ0	µ0	NOUN
ejpam-6917	301	36	≤	≤	PUNCT
ejpam-6917	301	37	τ2−2n0	τ2−2n0	NOUN
ejpam-6917	301	38	for	for	ADP
ejpam-6917	301	39	some	some	PRON
ejpam-6917	301	40	τ	τ	PROPN
ejpam-6917	301	41	>	>	X
ejpam-6917	301	42	0	0	PROPN
ejpam-6917	301	43	.	.	PUNCT
ejpam-6917	302	1	thus	thus	ADV
ejpam-6917	302	2	||sĝl	||sĝl	ADP
ejpam-6917	302	3	−	−	PROPN
ejpam-6917	302	4	ĝl+1||∞	ĝl+1||∞	PROPN
ejpam-6917	302	5	≤	≤	ADJ
ejpam-6917	302	6	kg	kg	NOUN
ejpam-6917	302	7	,	,	PUNCT
ejpam-6917	302	8	τ2	τ2	PROPN
ejpam-6917	302	9	−2(n0+l	−2(n0+l	PROPN
ejpam-6917	302	10	)	)	PUNCT
ejpam-6917	302	11	for	for	ADP
ejpam-6917	302	12	some	some	DET
ejpam-6917	302	13	l	l	NOUN
ejpam-6917	302	14	≥	≥	NOUN
ejpam-6917	302	15	g0	g0	NOUN
ejpam-6917	302	16	with	with	ADP
ejpam-6917	302	17	a	a	DET
ejpam-6917	302	18	fixed	fix	VERB
ejpam-6917	302	19	value	value	NOUN
ejpam-6917	302	20	kg	kg	PROPN
ejpam-6917	302	21	,	,	PUNCT
ejpam-6917	302	22	τ	τ	PROPN
ejpam-6917	302	23	>	>	X
ejpam-6917	302	24	0	0	PUNCT
ejpam-6917	303	1	depending	depend	VERB
ejpam-6917	303	2	on	on	ADP
ejpam-6917	303	3	g	g	PROPN
ejpam-6917	303	4	and	and	CCONJ
ejpam-6917	303	5	τ	τ	PROPN
ejpam-6917	303	6	.	.	PUNCT
ejpam-6917	304	1	it	it	PRON
ejpam-6917	304	2	leads	lead	VERB
ejpam-6917	304	3	to	to	ADP
ejpam-6917	304	4	the	the	DET
ejpam-6917	304	5	bound	bound	ADJ
ejpam-6917	304	6	n−1∑	n−1∑	NUM
ejpam-6917	304	7	l	l	NOUN
ejpam-6917	304	8	=	=	NOUN
ejpam-6917	304	9	n0	n0	ADJ
ejpam-6917	304	10	||sp	||sp	NOUN
ejpam-6917	304	11	ĝ	ĝ	NOUN
ejpam-6917	304	12	n	n	CCONJ
ejpam-6917	304	13	−	−	PROPN
ejpam-6917	304	14	ĝl+1||∞	ĝl+1||∞	PROPN
ejpam-6917	304	15	≤	≤	PUNCT
ejpam-6917	304	16	kg	kg	VERB
ejpam-6917	304	17	n−1∑	n−1∑	NUM
ejpam-6917	304	18	l	l	NOUN
ejpam-6917	304	19	=	=	NOUN
ejpam-6917	304	20	n0	n0	NUM
ejpam-6917	304	21	2−2(n0+l	2−2(n0+l	NUM
ejpam-6917	304	22	)	)	PUNCT
ejpam-6917	304	23	≤	≤	PROPN
ejpam-6917	304	24	kg2	kg2	PROPN
ejpam-6917	304	25	−6n0	−6n0	PROPN
ejpam-6917	304	26	.	.	PUNCT
ejpam-6917	305	1	5	5	X
ejpam-6917	305	2	.	.	X
ejpam-6917	305	3	shape	shape	NOUN
ejpam-6917	305	4	-	-	PUNCT
ejpam-6917	305	5	preserving	preserve	VERB
ejpam-6917	305	6	properties	property	NOUN
ejpam-6917	305	7	smoothness	smoothness	ADJ
ejpam-6917	305	8	,	,	PUNCT
ejpam-6917	305	9	precision	precision	NOUN
ejpam-6917	305	10	,	,	PUNCT
ejpam-6917	305	11	and	and	CCONJ
ejpam-6917	305	12	shape	shape	NOUN
ejpam-6917	305	13	preservation	preservation	NOUN
ejpam-6917	305	14	,	,	PUNCT
ejpam-6917	305	15	such	such	ADJ
ejpam-6917	305	16	as	as	ADP
ejpam-6917	305	17	monotonicity	monotonicity	NOUN
ejpam-6917	305	18	and	and	CCONJ
ejpam-6917	305	19	convexity	convexity	NOUN
ejpam-6917	305	20	,	,	PUNCT
ejpam-6917	305	21	are	be	AUX
ejpam-6917	305	22	all	all	PRON
ejpam-6917	305	23	important	important	ADJ
ejpam-6917	305	24	aspects	aspect	NOUN
ejpam-6917	305	25	of	of	ADP
ejpam-6917	305	26	an	an	DET
ejpam-6917	305	27	ss	ss	NOUN
ejpam-6917	305	28	in	in	ADP
ejpam-6917	305	29	practical	practical	ADJ
ejpam-6917	305	30	and	and	CCONJ
ejpam-6917	305	31	commercial	commercial	ADJ
ejpam-6917	305	32	contexts	contexts	NOUN
ejpam-6917	305	33	.	.	PUNCT
ejpam-6917	306	1	thus	thus	ADV
ejpam-6917	306	2	,	,	PUNCT
ejpam-6917	306	3	this	this	DET
ejpam-6917	306	4	section	section	NOUN
ejpam-6917	306	5	’s	’s	PART
ejpam-6917	306	6	goal	goal	NOUN
ejpam-6917	306	7	is	be	AUX
ejpam-6917	306	8	to	to	PART
ejpam-6917	306	9	examine	examine	VERB
ejpam-6917	306	10	our	our	PRON
ejpam-6917	306	11	ss	ss	NOUN
ejpam-6917	306	12	shape	shape	NOUN
ejpam-6917	306	13	-	-	PUNCT
ejpam-6917	306	14	preserving	preserve	VERB
ejpam-6917	306	15	characteristics	characteristic	NOUN
ejpam-6917	306	16	.	.	PUNCT
ejpam-6917	307	1	to	to	PART
ejpam-6917	307	2	proceed	proceed	VERB
ejpam-6917	307	3	,	,	PUNCT
ejpam-6917	307	4	we	we	PRON
ejpam-6917	307	5	express	express	VERB
ejpam-6917	307	6	the	the	DET
ejpam-6917	307	7	refinement	refinement	NOUN
ejpam-6917	307	8	rules	rule	NOUN
ejpam-6917	307	9	given	give	VERB
ejpam-6917	307	10	in	in	ADP
ejpam-6917	307	11	equation	equation	NOUN
ejpam-6917	307	12	(	(	PUNCT
ejpam-6917	307	13	1	1	NUM
ejpam-6917	307	14	)	)	PUNCT
ejpam-6917	307	15	in	in	ADP
ejpam-6917	307	16	the	the	DET
ejpam-6917	307	17	following	follow	VERB
ejpam-6917	307	18	rewritten	rewrite	VERB
ejpam-6917	307	19	form	form	NOUN
ejpam-6917	307	20	:	:	PUNCT
ejpam-6917	307	21	sp	sp	ADP
ejpam-6917	307	22	g	g	PROPN
ejpam-6917	307	23	n	n	NOUN
ejpam-6917	307	24	=	=	NOUN
ejpam-6917	307	25	qbg	qbg	NOUN
ejpam-6917	307	26	n	n	CCONJ
ejpam-6917	307	27	−	−	PROPN
ejpam-6917	307	28	2−2n−6(1−	2−2n−6(1−	NUM
ejpam-6917	307	29	µ0)d2(g	µ0)d2(g	NUM
ejpam-6917	307	30	n	n	CCONJ
ejpam-6917	307	31	)	)	PUNCT
ejpam-6917	307	32	.	.	PUNCT
ejpam-6917	308	1	(	(	PUNCT
ejpam-6917	308	2	13	13	NUM
ejpam-6917	308	3	)	)	PUNCT
ejpam-6917	308	4	where	where	SCONJ
ejpam-6917	308	5	d2	d2	PROPN
ejpam-6917	308	6	is	be	AUX
ejpam-6917	308	7	given	give	VERB
ejpam-6917	308	8	in	in	ADP
ejpam-6917	308	9	(	(	PUNCT
ejpam-6917	308	10	4	4	NUM
ejpam-6917	308	11	)	)	PUNCT
ejpam-6917	308	12	and	and	CCONJ
ejpam-6917	308	13	qb	qb	PROPN
ejpam-6917	308	14	is	be	AUX
ejpam-6917	308	15	the	the	DET
ejpam-6917	308	16	quintic	quintic	ADJ
ejpam-6917	308	17	b	b	NOUN
ejpam-6917	308	18	-	-	NOUN
ejpam-6917	308	19	spline	spline	NOUN
ejpam-6917	308	20	with	with	ADP
ejpam-6917	308	21	the	the	DET
ejpam-6917	308	22	mask	mask	NOUN
ejpam-6917	308	23	{	{	PUNCT
ejpam-6917	308	24	1	1	NUM
ejpam-6917	308	25	64	64	NUM
ejpam-6917	308	26	,	,	PUNCT
ejpam-6917	308	27	3	3	NUM
ejpam-6917	308	28	32	32	NUM
ejpam-6917	308	29	,	,	PUNCT
ejpam-6917	308	30	1	1	NUM
ejpam-6917	308	31	4	4	NUM
ejpam-6917	308	32	,	,	PUNCT
ejpam-6917	308	33	13	13	NUM
ejpam-6917	308	34	32	32	NUM
ejpam-6917	308	35	,	,	PUNCT
ejpam-6917	308	36	15	15	NUM
ejpam-6917	308	37	32	32	NUM
ejpam-6917	308	38	,	,	PUNCT
ejpam-6917	308	39	13	13	NUM
ejpam-6917	308	40	32	32	NUM
ejpam-6917	308	41	,	,	PUNCT
ejpam-6917	308	42	1	1	NUM
ejpam-6917	308	43	4	4	NUM
ejpam-6917	308	44	,	,	PUNCT
ejpam-6917	308	45	3	3	NUM
ejpam-6917	308	46	32	32	NUM
ejpam-6917	308	47	,	,	PUNCT
ejpam-6917	308	48	1	1	NUM
ejpam-6917	308	49	64	64	NUM
ejpam-6917	308	50	}	}	PUNCT
ejpam-6917	308	51	.	.	PUNCT
ejpam-6917	309	1	if	if	SCONJ
ejpam-6917	309	2	µ0	µ0	NOUN
ejpam-6917	309	3	=	=	SYM
ejpam-6917	309	4	0	0	NUM
ejpam-6917	309	5	,	,	PUNCT
ejpam-6917	309	6	our	our	PRON
ejpam-6917	309	7	scheme	scheme	NOUN
ejpam-6917	309	8	reduces	reduce	VERB
ejpam-6917	309	9	to	to	ADP
ejpam-6917	309	10	the	the	DET
ejpam-6917	309	11	sd	sd	NOUN
ejpam-6917	309	12	-	-	PUNCT
ejpam-6917	309	13	scheme	scheme	NOUN
ejpam-6917	309	14	.	.	PUNCT
ejpam-6917	310	1	it	it	PRON
ejpam-6917	310	2	is	be	AUX
ejpam-6917	310	3	a	a	DET
ejpam-6917	310	4	known	known	ADJ
ejpam-6917	310	5	fact	fact	NOUN
ejpam-6917	310	6	that	that	SCONJ
ejpam-6917	310	7	the	the	DET
ejpam-6917	310	8	sd	sd	NOUN
ejpam-6917	310	9	-	-	PUNCT
ejpam-6917	310	10	scheme	scheme	NOUN
ejpam-6917	310	11	has	have	AUX
ejpam-6917	310	12	the	the	DET
ejpam-6917	310	13	inherent	inherent	ADJ
ejpam-6917	310	14	drawback	drawback	NOUN
ejpam-6917	310	15	of	of	ADP
ejpam-6917	310	16	being	be	AUX
ejpam-6917	310	17	interpolatory	interpolatory	NOUN
ejpam-6917	310	18	.	.	PUNCT
ejpam-6917	311	1	if	if	SCONJ
ejpam-6917	311	2	the	the	DET
ejpam-6917	311	3	initial	initial	ADJ
ejpam-6917	311	4	control	control	NOUN
ejpam-6917	311	5	points	point	NOUN
ejpam-6917	311	6	are	be	AUX
ejpam-6917	311	7	irregularly	irregularly	ADV
ejpam-6917	311	8	distributed	distribute	VERB
ejpam-6917	311	9	,	,	PUNCT
ejpam-6917	311	10	this	this	DET
ejpam-6917	311	11	property	property	NOUN
ejpam-6917	311	12	can	can	AUX
ejpam-6917	311	13	lead	lead	VERB
ejpam-6917	311	14	to	to	ADP
ejpam-6917	311	15	undesirable	undesirable	ADJ
ejpam-6917	311	16	artifacts	artifact	NOUN
ejpam-6917	311	17	in	in	ADP
ejpam-6917	311	18	the	the	DET
ejpam-6917	311	19	resulting	result	VERB
ejpam-6917	311	20	curve	curve	NOUN
ejpam-6917	311	21	,	,	PUNCT
ejpam-6917	311	22	such	such	ADJ
ejpam-6917	311	23	as	as	ADP
ejpam-6917	311	24	self	self	NOUN
ejpam-6917	311	25	-	-	PUNCT
ejpam-6917	311	26	intersections	intersection	NOUN
ejpam-6917	311	27	.	.	PUNCT
ejpam-6917	312	1	thus	thus	ADV
ejpam-6917	312	2	,	,	PUNCT
ejpam-6917	312	3	it	it	PRON
ejpam-6917	312	4	is	be	AUX
ejpam-6917	312	5	appropriate	appropriate	ADJ
ejpam-6917	312	6	to	to	PART
ejpam-6917	312	7	examine	examine	VERB
ejpam-6917	312	8	the	the	DET
ejpam-6917	312	9	parameter	parameter	NOUN
ejpam-6917	312	10	µ0	µ0	NOUN
ejpam-6917	312	11	away	away	ADV
ejpam-6917	312	12	from	from	ADP
ejpam-6917	312	13	zero	zero	NUM
ejpam-6917	312	14	.	.	PUNCT
ejpam-6917	313	1	however	however	ADV
ejpam-6917	313	2	,	,	PUNCT
ejpam-6917	313	3	if	if	SCONJ
ejpam-6917	313	4	µ0	µ0	NOUN
ejpam-6917	313	5	=	=	SYM
ejpam-6917	313	6	1	1	NUM
ejpam-6917	313	7	,	,	PUNCT
ejpam-6917	313	8	the	the	DET
ejpam-6917	313	9	scheme	scheme	NOUN
ejpam-6917	313	10	transforms	transform	VERB
ejpam-6917	313	11	into	into	ADP
ejpam-6917	313	12	the	the	DET
ejpam-6917	313	13	qb	qb	NOUN
ejpam-6917	313	14	-	-	PUNCT
ejpam-6917	313	15	scheme	scheme	NOUN
ejpam-6917	313	16	.	.	PUNCT
ejpam-6917	314	1	in	in	ADP
ejpam-6917	314	2	essence	essence	NOUN
ejpam-6917	314	3	,	,	PUNCT
ejpam-6917	314	4	the	the	DET
ejpam-6917	314	5	parameter	parameter	NOUN
ejpam-6917	314	6	µ0	µ0	NOUN
ejpam-6917	314	7	acts	act	VERB
ejpam-6917	314	8	as	as	ADP
ejpam-6917	314	9	a	a	DET
ejpam-6917	314	10	balancing	balancing	NOUN
ejpam-6917	314	11	factor	factor	NOUN
ejpam-6917	314	12	between	between	ADP
ejpam-6917	314	13	the	the	DET
ejpam-6917	314	14	sd	sd	NOUN
ejpam-6917	314	15	-	-	PUNCT
ejpam-6917	314	16	scheme	scheme	NOUN
ejpam-6917	314	17	and	and	CCONJ
ejpam-6917	314	18	qb	qb	NOUN
ejpam-6917	314	19	-	-	PUNCT
ejpam-6917	314	20	scheme	scheme	NOUN
ejpam-6917	314	21	.	.	PUNCT
ejpam-6917	315	1	by	by	ADP
ejpam-6917	315	2	conducting	conduct	VERB
ejpam-6917	315	3	numerical	numerical	ADJ
ejpam-6917	315	4	experiments	experiment	NOUN
ejpam-6917	315	5	on	on	ADP
ejpam-6917	315	6	various	various	ADJ
ejpam-6917	315	7	µ0	µ0	NOUN
ejpam-6917	315	8	,	,	PUNCT
ejpam-6917	315	9	we	we	PRON
ejpam-6917	315	10	note	note	VERB
ejpam-6917	315	11	that	that	SCONJ
ejpam-6917	315	12	a	a	DET
ejpam-6917	315	13	suitable	suitable	ADJ
ejpam-6917	315	14	choice	choice	NOUN
ejpam-6917	315	15	of	of	ADP
ejpam-6917	315	16	µ0	µ0	NOUN
ejpam-6917	315	17	is	be	AUX
ejpam-6917	315	18	in	in	ADP
ejpam-6917	315	19	the	the	DET
ejpam-6917	315	20	range	range	NOUN
ejpam-6917	315	21	9	9	NUM
ejpam-6917	315	22	11	11	NUM
ejpam-6917	315	23	<	<	X
ejpam-6917	315	24	µ0	µ0	NOUN
ejpam-6917	315	25	<	<	X
ejpam-6917	315	26	1	1	NUM
ejpam-6917	315	27	.	.	PUNCT
ejpam-6917	316	1	(	(	PUNCT
ejpam-6917	316	2	14	14	NUM
ejpam-6917	316	3	)	)	PUNCT
ejpam-6917	316	4	5.1	5.1	NUM
ejpam-6917	316	5	.	.	PUNCT
ejpam-6917	317	1	preservation	preservation	NOUN
ejpam-6917	317	2	of	of	ADP
ejpam-6917	317	3	monotonicity	monotonicity	NOUN
ejpam-6917	317	4	we	we	PRON
ejpam-6917	317	5	first	first	ADV
ejpam-6917	317	6	demonstrate	demonstrate	VERB
ejpam-6917	317	7	that	that	SCONJ
ejpam-6917	317	8	sp	sp	ADP
ejpam-6917	317	9	-scheme	-scheme	NOUN
ejpam-6917	317	10	in	in	ADP
ejpam-6917	317	11	(	(	PUNCT
ejpam-6917	317	12	13	13	NUM
ejpam-6917	317	13	)	)	PUNCT
ejpam-6917	317	14	preserves	preserve	VERB
ejpam-6917	317	15	monotonicity	monotonicity	NOUN
ejpam-6917	317	16	under	under	ADP
ejpam-6917	317	17	a	a	DET
ejpam-6917	317	18	mild	mild	ADJ
ejpam-6917	317	19	condition	condition	NOUN
ejpam-6917	317	20	.	.	PUNCT
ejpam-6917	318	1	specifically	specifically	ADV
ejpam-6917	318	2	,	,	PUNCT
ejpam-6917	318	3	we	we	PRON
ejpam-6917	318	4	show	show	VERB
ejpam-6917	318	5	that	that	SCONJ
ejpam-6917	318	6	(	(	PUNCT
ejpam-6917	318	7	dgn+1)i	dgn+1)i	X
ejpam-6917	318	8	≥	≥	NOUN
ejpam-6917	318	9	0	0	NUM
ejpam-6917	318	10	whenever	whenever	SCONJ
ejpam-6917	318	11	(	(	PUNCT
ejpam-6917	318	12	dgn)i	dgn)i	X
ejpam-6917	318	13	≥	≥	NOUN
ejpam-6917	318	14	0	0	NUM
ejpam-6917	318	15	for	for	ADP
ejpam-6917	318	16	all	all	PRON
ejpam-6917	318	17	i	i	PRON
ejpam-6917	318	18	∈	∈	PROPN
ejpam-6917	318	19	z	z	NOUN
ejpam-6917	318	20	and	and	CCONJ
ejpam-6917	318	21	n	n	PRON
ejpam-6917	318	22	∈	∈	PROPN
ejpam-6917	318	23	n0	n0	PROPN
ejpam-6917	318	24	.	.	PUNCT
ejpam-6917	319	1	it	it	PRON
ejpam-6917	319	2	is	be	AUX
ejpam-6917	319	3	important	important	ADJ
ejpam-6917	319	4	to	to	PART
ejpam-6917	319	5	note	note	VERB
ejpam-6917	319	6	that	that	SCONJ
ejpam-6917	319	7	the	the	DET
ejpam-6917	319	8	qb	qb	PROPN
ejpam-6917	319	9	-	-	PUNCT
ejpam-6917	319	10	scheme	scheme	NOUN
ejpam-6917	319	11	fulfills	fulfill	VERB
ejpam-6917	319	12	the	the	DET
ejpam-6917	319	13	following	follow	VERB
ejpam-6917	319	14	equations	equation	NOUN
ejpam-6917	319	15	before	before	ADP
ejpam-6917	319	16	proceeding:	proceeding:	PROPN
ejpam-6917	319	17	(	(	PUNCT
ejpam-6917	319	18	dqbg	dqbg	PROPN
ejpam-6917	319	19	n)2i	n)2i	NOUN
ejpam-6917	319	20	=	=	NOUN
ejpam-6917	319	21	5	5	NUM
ejpam-6917	319	22	32	32	NUM
ejpam-6917	319	23	(	(	PUNCT
ejpam-6917	319	24	dgn)i−1	dgn)i−1	NOUN
ejpam-6917	319	25	+	+	CCONJ
ejpam-6917	319	26	15	15	NUM
ejpam-6917	319	27	32	32	NUM
ejpam-6917	319	28	(	(	PUNCT
ejpam-6917	319	29	dgn)i	dgn)i	PROPN
ejpam-6917	319	30	+	+	NOUN
ejpam-6917	319	31	11	11	NUM
ejpam-6917	319	32	32	32	NUM
ejpam-6917	319	33	(	(	PUNCT
ejpam-6917	319	34	dgn)i+1	dgn)i+1	VERB
ejpam-6917	319	35	1	1	NUM
ejpam-6917	319	36	32	32	NUM
ejpam-6917	319	37	(	(	PUNCT
ejpam-6917	319	38	dgn)i+2	dgn)i+2	NOUN
ejpam-6917	319	39	,	,	PUNCT
ejpam-6917	319	40	(	(	PUNCT
ejpam-6917	319	41	dqbg	dqbg	X
ejpam-6917	319	42	n)2i+1	n)2i+1	NOUN
ejpam-6917	320	1	=	=	NOUN
ejpam-6917	320	2	1	1	NUM
ejpam-6917	320	3	32	32	NUM
ejpam-6917	320	4	(	(	PUNCT
ejpam-6917	320	5	dgn)i−1	dgn)i−1	NOUN
ejpam-6917	320	6	+	+	CCONJ
ejpam-6917	320	7	11	11	NUM
ejpam-6917	320	8	32	32	NUM
ejpam-6917	320	9	(	(	PUNCT
ejpam-6917	320	10	dgn)i	dgn)i	X
ejpam-6917	320	11	+	+	NUM
ejpam-6917	320	12	15	15	NUM
ejpam-6917	320	13	32	32	NUM
ejpam-6917	320	14	(	(	PUNCT
ejpam-6917	320	15	dgn)i+1	dgn)i+1	VERB
ejpam-6917	320	16	5	5	NUM
ejpam-6917	320	17	32	32	NUM
ejpam-6917	320	18	(	(	PUNCT
ejpam-6917	320	19	dgn)i+2	dgn)i+2	NOUN
ejpam-6917	320	20	.	.	PUNCT
ejpam-6917	321	1	(	(	PUNCT
ejpam-6917	321	2	15	15	NUM
ejpam-6917	321	3	)	)	PUNCT
ejpam-6917	321	4	f.	f.	PROPN
ejpam-6917	321	5	s.	s.	PROPN
ejpam-6917	321	6	alshammari	alshammari	PROPN
ejpam-6917	321	7	et	et	PROPN
ejpam-6917	321	8	al	al	PROPN
ejpam-6917	321	9	.	.	PUNCT
ejpam-6917	321	10	/	/	SYM
ejpam-6917	321	11	eur	eur	PROPN
ejpam-6917	321	12	.	.	PUNCT
ejpam-6917	322	1	j.	j.	PROPN
ejpam-6917	322	2	pure	pure	PROPN
ejpam-6917	322	3	appl	appl	PROPN
ejpam-6917	322	4	.	.	PROPN
ejpam-6917	322	5	math	math	PROPN
ejpam-6917	322	6	,	,	PUNCT
ejpam-6917	322	7	18	18	NUM
ejpam-6917	322	8	(	(	PUNCT
ejpam-6917	322	9	4	4	NUM
ejpam-6917	322	10	)	)	PUNCT
ejpam-6917	322	11	(	(	PUNCT
ejpam-6917	322	12	2025	2025	NUM
ejpam-6917	322	13	)	)	PUNCT
ejpam-6917	322	14	,	,	PUNCT
ejpam-6917	322	15	6917	6917	NUM
ejpam-6917	322	16	14	14	NUM
ejpam-6917	322	17	of	of	ADP
ejpam-6917	322	18	26	26	NUM
ejpam-6917	322	19	which	which	PRON
ejpam-6917	322	20	means	mean	VERB
ejpam-6917	322	21	that	that	SCONJ
ejpam-6917	322	22	qb	qb	PROPN
ejpam-6917	322	23	-	-	PUNCT
ejpam-6917	322	24	scheme	scheme	NOUN
ejpam-6917	322	25	is	be	AUX
ejpam-6917	322	26	preserves	preserve	VERB
ejpam-6917	322	27	the	the	DET
ejpam-6917	322	28	monotonicity	monotonicity	NOUN
ejpam-6917	322	29	.	.	PUNCT
ejpam-6917	323	1	then	then	ADV
ejpam-6917	323	2	,	,	PUNCT
ejpam-6917	323	3	given	give	VERB
ejpam-6917	323	4	(	(	PUNCT
ejpam-6917	323	5	13	13	NUM
ejpam-6917	323	6	)	)	PUNCT
ejpam-6917	323	7	and	and	CCONJ
ejpam-6917	323	8	(	(	PUNCT
ejpam-6917	323	9	15	15	NUM
ejpam-6917	323	10	)	)	PUNCT
ejpam-6917	323	11	,	,	PUNCT
ejpam-6917	323	12	we	we	PRON
ejpam-6917	323	13	can	can	AUX
ejpam-6917	323	14	derive	derive	VERB
ejpam-6917	323	15	the	the	DET
ejpam-6917	323	16	following	follow	VERB
ejpam-6917	323	17	identities.	identities.	PROPN
ejpam-6917	323	18	(	(	PUNCT
ejpam-6917	323	19	dgn)2i	dgn)2i	NOUN
ejpam-6917	323	20	=	=	SYM
ejpam-6917	323	21	(	(	PUNCT
ejpam-6917	323	22	5(dgn)i−1	5(dgn)i−1	NUM
ejpam-6917	323	23	+	+	SYM
ejpam-6917	323	24	15(dgn)i	15(dgn)i	NUM
ejpam-6917	323	25	+	+	CCONJ
ejpam-6917	323	26	11(dgn)i+1	11(dgn)i+1	NOUN
ejpam-6917	324	1	+	+	CCONJ
ejpam-6917	324	2	(	(	PUNCT
ejpam-6917	324	3	dgn)i+2	dgn)i+2	NOUN
ejpam-6917	324	4	32	32	NUM
ejpam-6917	324	5	)	)	PUNCT
ejpam-6917	324	6	−	−	PROPN
ejpam-6917	324	7	2−2n	2−2n	NUM
ejpam-6917	324	8	(	(	PUNCT
ejpam-6917	324	9	1−	1−	NUM
ejpam-6917	324	10	µ0	µ0	NOUN
ejpam-6917	324	11	)	)	PUNCT
ejpam-6917	324	12	128	128	NUM
ejpam-6917	324	13	(	(	PUNCT
ejpam-6917	324	14	−3(d3gn)i−1	−3(d3gn)i−1	X
ejpam-6917	324	15	+	+	CCONJ
ejpam-6917	324	16	36(d3gn)i	36(d3gn)i	NUM
ejpam-6917	324	17	+	+	CCONJ
ejpam-6917	324	18	7(d3gn)i+1	7(d3gn)i+1	NUM
ejpam-6917	324	19	)	)	PUNCT
ejpam-6917	324	20	,	,	PUNCT
ejpam-6917	324	21	(	(	PUNCT
ejpam-6917	324	22	dgn)2i+1	dgn)2i+1	X
ejpam-6917	324	23	=	=	PUNCT
ejpam-6917	324	24	(	(	PUNCT
ejpam-6917	324	25	(	(	PUNCT
ejpam-6917	324	26	dgn)i−1	dgn)i−1	NOUN
ejpam-6917	324	27	+	+	CCONJ
ejpam-6917	324	28	11(dgn)i	11(dgn)i	NUM
ejpam-6917	324	29	+	+	NUM
ejpam-6917	324	30	15(dgn)i+1	15(dgn)i+1	NOUN
ejpam-6917	325	1	+	+	CCONJ
ejpam-6917	325	2	5(dgn)i+2	5(dgn)i+2	NUM
ejpam-6917	325	3	32	32	NUM
ejpam-6917	325	4	)	)	PUNCT
ejpam-6917	325	5	−	−	PROPN
ejpam-6917	325	6	2−2n	2−2n	NUM
ejpam-6917	325	7	(	(	PUNCT
ejpam-6917	325	8	1−	1−	NUM
ejpam-6917	325	9	µ0	µ0	NOUN
ejpam-6917	325	10	)	)	PUNCT
ejpam-6917	325	11	128	128	NUM
ejpam-6917	325	12	(	(	PUNCT
ejpam-6917	325	13	7(d3gn)i	7(d3gn)i	NUM
ejpam-6917	325	14	+	+	CCONJ
ejpam-6917	325	15	36(d3gn)i+1	36(d3gn)i+1	NUM
ejpam-6917	325	16	−	−	PROPN
ejpam-6917	325	17	3(d3gn)i+2	3(d3gn)i+2	NUM
ejpam-6917	325	18	)	)	PUNCT
ejpam-6917	325	19	.	.	PUNCT
ejpam-6917	326	1	(	(	PUNCT
ejpam-6917	326	2	16	16	NUM
ejpam-6917	326	3	)	)	PUNCT
ejpam-6917	326	4	definition	definition	NOUN
ejpam-6917	326	5	4	4	NUM
ejpam-6917	326	6	.	.	PUNCT
ejpam-6917	327	1	(	(	PUNCT
ejpam-6917	327	2	condition	condition	NOUN
ejpam-6917	327	3	-	-	PUNCT
ejpam-6917	327	4	m	m	PROPN
ejpam-6917	327	5	)	)	PUNCT
ejpam-6917	327	6	.	.	PUNCT
ejpam-6917	328	1	suppose	suppose	VERB
ejpam-6917	328	2	given	give	VERB
ejpam-6917	328	3	a	a	DET
ejpam-6917	328	4	number	number	NOUN
ejpam-6917	328	5	µ0	µ0	NOUN
ejpam-6917	328	6	and	and	CCONJ
ejpam-6917	328	7	gn0	gn0	NOUN
ejpam-6917	328	8	be	be	AUX
ejpam-6917	328	9	an	an	DET
ejpam-6917	328	10	initial	initial	ADJ
ejpam-6917	328	11	sequence	sequence	NOUN
ejpam-6917	328	12	defined	define	VERB
ejpam-6917	328	13	on	on	ADP
ejpam-6917	328	14	the	the	DET
ejpam-6917	328	15	grid	grid	NOUN
ejpam-6917	328	16	2−n0z	2−n0z	NUM
ejpam-6917	328	17	.	.	PUNCT
ejpam-6917	329	1	let	let	VERB
ejpam-6917	329	2	the	the	DET
ejpam-6917	329	3	sequence	sequence	NOUN
ejpam-6917	329	4	gn0	gn0	NOUN
ejpam-6917	329	5	satisfies	satisfie	NOUN
ejpam-6917	329	6	’	'	PUNCT
ejpam-6917	329	7	condition	condition	NOUN
ejpam-6917	329	8	-	-	PUNCT
ejpam-6917	329	9	m	m	NOUN
ejpam-6917	329	10	’	'	PUNCT
ejpam-6917	329	11	when	when	SCONJ
ejpam-6917	329	12	(	(	PUNCT
ejpam-6917	329	13	dgn0)i	dgn0)i	ADJ
ejpam-6917	329	14	≥	≥	NOUN
ejpam-6917	329	15	2−2n0	2−2n0	NUM
ejpam-6917	329	16	(	(	PUNCT
ejpam-6917	329	17	1−	1−	NUM
ejpam-6917	329	18	µ0	µ0	NOUN
ejpam-6917	329	19	)	)	PUNCT
ejpam-6917	329	20	k	k	PROPN
ejpam-6917	329	21	|(d3gn0)i|	|(d3gn0)i|	PROPN
ejpam-6917	329	22	,	,	PUNCT
ejpam-6917	329	23	(	(	PUNCT
ejpam-6917	329	24	17	17	NUM
ejpam-6917	329	25	)	)	PUNCT
ejpam-6917	329	26	where	where	SCONJ
ejpam-6917	329	27	k	k	PROPN
ejpam-6917	329	28	>	>	X
ejpam-6917	329	29	0	0	X
ejpam-6917	329	30	.	.	PUNCT
ejpam-6917	330	1	lemma	lemma	PROPN
ejpam-6917	330	2	2	2	X
ejpam-6917	330	3	.	.	PUNCT
ejpam-6917	331	1	let	let	VERB
ejpam-6917	331	2	gn0	gn0	NOUN
ejpam-6917	331	3	denote	denote	VERB
ejpam-6917	331	4	the	the	DET
ejpam-6917	331	5	initial	initial	ADJ
ejpam-6917	331	6	data	datum	NOUN
ejpam-6917	331	7	associated	associate	VERB
ejpam-6917	331	8	with	with	ADP
ejpam-6917	331	9	the	the	DET
ejpam-6917	331	10	grid	grid	NOUN
ejpam-6917	331	11	points	point	NOUN
ejpam-6917	331	12	2−n0z	2−n0z	NUM
ejpam-6917	331	13	,	,	PUNCT
ejpam-6917	331	14	and	and	CCONJ
ejpam-6917	331	15	suppose	suppose	VERB
ejpam-6917	331	16	that	that	SCONJ
ejpam-6917	331	17	gn+1	gn+1	VERB
ejpam-6917	331	18	=	=	SYM
ejpam-6917	331	19	sp	sp	ADP
ejpam-6917	331	20	g	g	NOUN
ejpam-6917	331	21	n	n	CCONJ
ejpam-6917	331	22	,	,	PUNCT
ejpam-6917	331	23	n	n	PRON
ejpam-6917	331	24	≥	≥	NOUN
ejpam-6917	331	25	n0	n0	NUM
ejpam-6917	331	26	,	,	PUNCT
ejpam-6917	331	27	with	with	ADP
ejpam-6917	331	28	sp	sp	ADP
ejpam-6917	331	29	in	in	ADP
ejpam-6917	331	30	(	(	PUNCT
ejpam-6917	331	31	1	1	NUM
ejpam-6917	331	32	)	)	PUNCT
ejpam-6917	331	33	.	.	PUNCT
ejpam-6917	332	1	if	if	SCONJ
ejpam-6917	332	2	gn0	gn0	NOUN
ejpam-6917	332	3	fulfills	fulfill	VERB
ejpam-6917	332	4	the	the	DET
ejpam-6917	332	5	condition	condition	NOUN
ejpam-6917	332	6	-	-	PUNCT
ejpam-6917	332	7	m.	m.	NOUN
ejpam-6917	332	8	thus	thus	ADV
ejpam-6917	332	9	for	for	ADP
ejpam-6917	332	10	all	all	DET
ejpam-6917	332	11	n	n	PRON
ejpam-6917	332	12	≥	≥	NOUN
ejpam-6917	332	13	n0	n0	NUM
ejpam-6917	332	14	,	,	PUNCT
ejpam-6917	332	15	(	(	PUNCT
ejpam-6917	332	16	dgn)i	dgn)i	PROPN
ejpam-6917	332	17	≥	≥	NOUN
ejpam-6917	332	18	2−2n	2−2n	NUM
ejpam-6917	332	19	(	(	PUNCT
ejpam-6917	332	20	1−	1−	NUM
ejpam-6917	332	21	µ0	µ0	NOUN
ejpam-6917	332	22	)	)	PUNCT
ejpam-6917	332	23	k	k	PROPN
ejpam-6917	332	24	|(d3gn)i|	|(d3gn)i|	PROPN
ejpam-6917	332	25	,	,	PUNCT
ejpam-6917	332	26	(	(	PUNCT
ejpam-6917	332	27	18	18	NUM
ejpam-6917	332	28	)	)	PUNCT
ejpam-6917	332	29	where	where	SCONJ
ejpam-6917	332	30	k	k	PROPN
ejpam-6917	332	31	>	>	X
ejpam-6917	332	32	0	0	X
ejpam-6917	332	33	.	.	PUNCT
ejpam-6917	333	1	proof	proof	NOUN
ejpam-6917	333	2	.	.	PUNCT
ejpam-6917	334	1	using	use	VERB
ejpam-6917	334	2	mathematical	mathematical	ADJ
ejpam-6917	334	3	induction	induction	NOUN
ejpam-6917	334	4	,	,	PUNCT
ejpam-6917	334	5	we	we	PRON
ejpam-6917	334	6	establish	establish	VERB
ejpam-6917	334	7	this	this	DET
ejpam-6917	334	8	lemma	lemma	PROPN
ejpam-6917	334	9	.	.	PUNCT
ejpam-6917	335	1	given	give	VERB
ejpam-6917	335	2	that	that	SCONJ
ejpam-6917	335	3	the	the	DET
ejpam-6917	335	4	initial	initial	ADJ
ejpam-6917	335	5	sequence	sequence	NOUN
ejpam-6917	335	6	fulfills	fulfill	VERB
ejpam-6917	335	7	’	'	PUNCT
ejpam-6917	335	8	condition	condition	NOUN
ejpam-6917	335	9	-	-	PUNCT
ejpam-6917	335	10	m	m	NOUN
ejpam-6917	335	11	’	'	PUNCT
ejpam-6917	335	12	,	,	PUNCT
ejpam-6917	335	13	inequality	inequality	NOUN
ejpam-6917	335	14	(	(	PUNCT
ejpam-6917	335	15	18	18	NUM
ejpam-6917	335	16	)	)	PUNCT
ejpam-6917	335	17	holds	hold	VERB
ejpam-6917	335	18	.	.	PUNCT
ejpam-6917	336	1	we	we	PRON
ejpam-6917	336	2	now	now	ADV
ejpam-6917	336	3	assume	assume	VERB
ejpam-6917	336	4	that	that	SCONJ
ejpam-6917	336	5	(	(	PUNCT
ejpam-6917	336	6	18	18	NUM
ejpam-6917	336	7	)	)	PUNCT
ejpam-6917	336	8	is	be	AUX
ejpam-6917	336	9	true	true	ADJ
ejpam-6917	336	10	for	for	ADP
ejpam-6917	336	11	n	n	PROPN
ejpam-6917	336	12	>	>	X
ejpam-6917	336	13	n0	n0	NOUN
ejpam-6917	336	14	and	and	CCONJ
ejpam-6917	336	15	strive	strive	VERB
ejpam-6917	336	16	to	to	PART
ejpam-6917	336	17	prove	prove	VERB
ejpam-6917	336	18	that	that	SCONJ
ejpam-6917	336	19	(	(	PUNCT
ejpam-6917	336	20	dgn+1)i	dgn+1)i	X
ejpam-6917	336	21	≥	≥	NOUN
ejpam-6917	336	22	2−2n+1	2−2n+1	NUM
ejpam-6917	336	23	(	(	PUNCT
ejpam-6917	336	24	1−	1−	NUM
ejpam-6917	336	25	µ0	µ0	NOUN
ejpam-6917	336	26	)	)	PUNCT
ejpam-6917	336	27	k	k	PROPN
ejpam-6917	336	28	|(d3gn+1)i|	|(d3gn+1)i|	PROPN
ejpam-6917	336	29	.	.	PROPN
ejpam-6917	336	30	to	to	PART
ejpam-6917	336	31	prove	prove	VERB
ejpam-6917	336	32	the	the	DET
ejpam-6917	336	33	result	result	NOUN
ejpam-6917	336	34	,	,	PUNCT
ejpam-6917	336	35	we	we	PRON
ejpam-6917	336	36	consider	consider	VERB
ejpam-6917	336	37	the	the	DET
ejpam-6917	336	38	following	follow	VERB
ejpam-6917	336	39	two	two	NUM
ejpam-6917	336	40	cases	case	NOUN
ejpam-6917	336	41	:	:	PUNCT
ejpam-6917	336	42	(	(	PUNCT
ejpam-6917	336	43	i	i	NOUN
ejpam-6917	336	44	)	)	PUNCT
ejpam-6917	336	45	i	i	PRON
ejpam-6917	337	1	=	=	PUNCT
ejpam-6917	337	2	2j	2j	NUM
ejpam-6917	337	3	and	and	CCONJ
ejpam-6917	337	4	(	(	PUNCT
ejpam-6917	337	5	ii	ii	NOUN
ejpam-6917	337	6	)	)	PUNCT
ejpam-6917	338	1	i	i	NOUN
ejpam-6917	338	2	=	=	PUNCT
ejpam-6917	338	3	2j	2j	X
ejpam-6917	339	1	+	+	CCONJ
ejpam-6917	339	2	1	1	X
ejpam-6917	339	3	.	.	X
ejpam-6917	339	4	we	we	PRON
ejpam-6917	339	5	begin	begin	VERB
ejpam-6917	339	6	with	with	ADP
ejpam-6917	339	7	case	case	NOUN
ejpam-6917	339	8	(	(	PUNCT
ejpam-6917	339	9	i	i	NOUN
ejpam-6917	339	10	)	)	PUNCT
ejpam-6917	339	11	,	,	PUNCT
ejpam-6917	339	12	i	i	PRON
ejpam-6917	339	13	=	=	PUNCT
ejpam-6917	339	14	2j	2j	NUM
ejpam-6917	339	15	,	,	PUNCT
ejpam-6917	339	16	and	and	CCONJ
ejpam-6917	339	17	we	we	PRON
ejpam-6917	339	18	can	can	AUX
ejpam-6917	339	19	readily	readily	ADV
ejpam-6917	339	20	obtain	obtain	VERB
ejpam-6917	339	21	the	the	DET
ejpam-6917	339	22	expression	expression	NOUN
ejpam-6917	339	23	using	use	VERB
ejpam-6917	339	24	equation	equation	NOUN
ejpam-6917	339	25	(	(	PUNCT
ejpam-6917	339	26	16	16	NUM
ejpam-6917	339	27	)	)	PUNCT
ejpam-6917	339	28	(	(	PUNCT
ejpam-6917	339	29	d3gn+1)2j	d3gn+1)2j	NOUN
ejpam-6917	339	30	=	=	SYM
ejpam-6917	339	31	22(n+1	22(n+1	NUM
ejpam-6917	339	32	)	)	PUNCT
ejpam-6917	339	33	1	1	NUM
ejpam-6917	339	34	2	2	NUM
ejpam-6917	339	35	(	(	PUNCT
ejpam-6917	339	36	−3(d3gn+1)2j−1	−3(d3gn+1)2j−1	NOUN
ejpam-6917	339	37	+	+	CCONJ
ejpam-6917	339	38	36(d3gn+1)2j	36(d3gn+1)2j	NUM
ejpam-6917	339	39	+	+	CCONJ
ejpam-6917	339	40	7(d3gn+1)2j+1	7(d3gn+1)2j+1	NUM
ejpam-6917	339	41	)	)	PUNCT
ejpam-6917	339	42	=	=	NOUN
ejpam-6917	339	43	(	(	PUNCT
ejpam-6917	339	44	27(d3gn)j−1	27(d3gn)j−1	NUM
ejpam-6917	340	1	+	+	CCONJ
ejpam-6917	341	1	153(d3gn)j	153(d3gn)j	NUM
ejpam-6917	341	2	+	+	CCONJ
ejpam-6917	341	3	133(d3gn)j+1	133(d3gn)j+1	NUM
ejpam-6917	342	1	+	+	CCONJ
ejpam-6917	342	2	7(d3gn)j+2	7(d3gn)j+2	NUM
ejpam-6917	342	3	32	32	NUM
ejpam-6917	342	4	)	)	PUNCT
ejpam-6917	343	1	−	−	PROPN
ejpam-6917	343	2	(	(	PUNCT
ejpam-6917	343	3	1−	1−	NUM
ejpam-6917	343	4	µ0	µ0	NOUN
ejpam-6917	343	5	)	)	PUNCT
ejpam-6917	343	6	128	128	NUM
ejpam-6917	343	7	(	(	PUNCT
ejpam-6917	343	8	417(d3gn)j−1	417(d3gn)j−1	NOUN
ejpam-6917	343	9	−	−	PROPN
ejpam-6917	343	10	851(d3gn)j	851(d3gn)j	NOUN
ejpam-6917	343	11	+	+	CCONJ
ejpam-6917	344	1	451(d3gn)j+1	451(d3gn)j+1	NUM
ejpam-6917	344	2	−	−	NUM
ejpam-6917	344	3	17(d3gn)j+2	17(d3gn)j+2	NUM
ejpam-6917	344	4	)	)	PUNCT
ejpam-6917	344	5	thus	thus	ADV
ejpam-6917	344	6	,	,	PUNCT
ejpam-6917	344	7	it	it	PRON
ejpam-6917	344	8	follows	follow	VERB
ejpam-6917	344	9	that	that	DET
ejpam-6917	344	10	|(d3gn+1)2j	|(d3gn+1)2j	NOUN
ejpam-6917	344	11	|	|	ADV
ejpam-6917	344	12	≤	≤	NUM
ejpam-6917	344	13	618	618	NUM
ejpam-6917	344	14	128	128	NUM
ejpam-6917	344	15	|(d3gn)j−1|+	|(d3gn)j−1|+	NOUN
ejpam-6917	344	16	2926	2926	NUM
ejpam-6917	344	17	128	128	NUM
ejpam-6917	344	18	|(d3gn)j	|(d3gn)j	NOUN
ejpam-6917	344	19	|+	|+	NOUN
ejpam-6917	344	20	162	162	NUM
ejpam-6917	344	21	128	128	NUM
ejpam-6917	344	22	|(d3gn)j+1|+	|(d3gn)j+1|+	NOUN
ejpam-6917	344	23	90	90	NUM
ejpam-6917	344	24	128	128	NUM
ejpam-6917	344	25	|(d3gn)j+2|	|(d3gn)j+2|	PROPN
ejpam-6917	344	26	.	.	PUNCT
ejpam-6917	345	1	this	this	PRON
ejpam-6917	345	2	,	,	PUNCT
ejpam-6917	345	3	together	together	ADV
ejpam-6917	345	4	with	with	ADP
ejpam-6917	345	5	(	(	PUNCT
ejpam-6917	345	6	9	9	NUM
ejpam-6917	345	7	)	)	PUNCT
ejpam-6917	345	8	,	,	PUNCT
ejpam-6917	345	9	induces	induce	VERB
ejpam-6917	345	10	the	the	DET
ejpam-6917	345	11	relation	relation	NOUN
ejpam-6917	345	12	f.	f.	PROPN
ejpam-6917	345	13	s.	s.	PROPN
ejpam-6917	345	14	alshammari	alshammari	PROPN
ejpam-6917	345	15	et	et	PROPN
ejpam-6917	345	16	al	al	PROPN
ejpam-6917	345	17	.	.	PUNCT
ejpam-6917	345	18	/	/	SYM
ejpam-6917	345	19	eur	eur	PROPN
ejpam-6917	345	20	.	.	PUNCT
ejpam-6917	346	1	j.	j.	PROPN
ejpam-6917	346	2	pure	pure	PROPN
ejpam-6917	346	3	appl	appl	PROPN
ejpam-6917	346	4	.	.	PROPN
ejpam-6917	346	5	math	math	PROPN
ejpam-6917	346	6	,	,	PUNCT
ejpam-6917	346	7	18	18	NUM
ejpam-6917	346	8	(	(	PUNCT
ejpam-6917	346	9	4	4	NUM
ejpam-6917	346	10	)	)	PUNCT
ejpam-6917	346	11	(	(	PUNCT
ejpam-6917	346	12	2025	2025	NUM
ejpam-6917	346	13	)	)	PUNCT
ejpam-6917	346	14	,	,	PUNCT
ejpam-6917	346	15	6917	6917	NUM
ejpam-6917	346	16	15	15	NUM
ejpam-6917	346	17	of	of	ADP
ejpam-6917	346	18	26	26	NUM
ejpam-6917	346	19	(	(	PUNCT
ejpam-6917	346	20	dgn+1)2j	dgn+1)2j	ADJ
ejpam-6917	346	21	−	−	PROPN
ejpam-6917	346	22	2−2(n+1	2−2(n+1	NUM
ejpam-6917	346	23	)	)	PUNCT
ejpam-6917	346	24	(	(	PUNCT
ejpam-6917	346	25	1−µ0	1−µ0	NUM
ejpam-6917	346	26	)	)	PUNCT
ejpam-6917	347	1	k	k	NOUN
ejpam-6917	347	2	|(d3gn+1)2j	|(d3gn+1)2j	NOUN
ejpam-6917	348	1	|	|	ADV
ejpam-6917	348	2	≥	≥	NUM
ejpam-6917	348	3	5	5	NUM
ejpam-6917	348	4	32((dgn)j−1	32((dgn)j−1	NUM
ejpam-6917	348	5	−	−	ADP
ejpam-6917	348	6	2−2(n	2−2(n	NUM
ejpam-6917	348	7	)	)	PUNCT
ejpam-6917	348	8	(	(	PUNCT
ejpam-6917	348	9	1−µ0	1−µ0	NUM
ejpam-6917	348	10	)	)	PUNCT
ejpam-6917	348	11	k	k	NOUN
ejpam-6917	349	1	|(d3gn)j−1|	|(d3gn)j−1|	X
ejpam-6917	349	2	)	)	PUNCT
ejpam-6917	349	3	+15	+15	ADJ
ejpam-6917	349	4	32((dgn)j	32((dgn)j	NUM
ejpam-6917	349	5	−	−	PROPN
ejpam-6917	349	6	2−2(n	2−2(n	NUM
ejpam-6917	349	7	)	)	PUNCT
ejpam-6917	349	8	(	(	PUNCT
ejpam-6917	349	9	1−µ0	1−µ0	NUM
ejpam-6917	349	10	)	)	PUNCT
ejpam-6917	349	11	k	k	PROPN
ejpam-6917	349	12	|(d3gn)j	|(d3gn)j	NOUN
ejpam-6917	349	13	|	|	ADV
ejpam-6917	349	14	)	)	PUNCT
ejpam-6917	349	15	+11	+11	ADJ
ejpam-6917	349	16	32((dgn)j+1	32((dgn)j+1	NUM
ejpam-6917	349	17	−	−	NUM
ejpam-6917	349	18	2−2(n	2−2(n	NUM
ejpam-6917	349	19	)	)	PUNCT
ejpam-6917	349	20	(	(	PUNCT
ejpam-6917	349	21	1−µ0	1−µ0	NUM
ejpam-6917	349	22	)	)	PUNCT
ejpam-6917	350	1	k	k	PROPN
ejpam-6917	350	2	|(d3gn)j+1|	|(d3gn)j+1|	PROPN
ejpam-6917	350	3	)	)	PUNCT
ejpam-6917	351	1	+	+	CCONJ
ejpam-6917	351	2	1	1	NUM
ejpam-6917	351	3	32((dgn)j+2	32((dgn)j+2	NUM
ejpam-6917	351	4	−	−	NUM
ejpam-6917	351	5	2−2(n	2−2(n	NUM
ejpam-6917	351	6	)	)	PUNCT
ejpam-6917	351	7	(	(	PUNCT
ejpam-6917	351	8	1−µ0	1−µ0	NUM
ejpam-6917	351	9	)	)	PUNCT
ejpam-6917	352	1	k	k	PROPN
ejpam-6917	352	2	|(d3gn)j+2|	|(d3gn)j+2|	PROPN
ejpam-6917	352	3	)	)	PUNCT
ejpam-6917	352	4	.	.	PUNCT
ejpam-6917	353	1	based	base	VERB
ejpam-6917	353	2	on	on	ADP
ejpam-6917	353	3	the	the	DET
ejpam-6917	353	4	inductive	inductive	ADJ
ejpam-6917	353	5	assumption	assumption	NOUN
ejpam-6917	353	6	for	for	ADP
ejpam-6917	353	7	n	n	PRON
ejpam-6917	353	8	,	,	PUNCT
ejpam-6917	353	9	the	the	DET
ejpam-6917	353	10	nonnegativity	nonnegativity	NOUN
ejpam-6917	353	11	of	of	ADP
ejpam-6917	353	12	the	the	DET
ejpam-6917	353	13	final	final	ADJ
ejpam-6917	353	14	term	term	NOUN
ejpam-6917	353	15	follows	follow	VERB
ejpam-6917	353	16	.	.	PUNCT
ejpam-6917	354	1	we	we	PRON
ejpam-6917	354	2	now	now	ADV
ejpam-6917	354	3	turn	turn	VERB
ejpam-6917	354	4	our	our	PRON
ejpam-6917	354	5	attention	attention	NOUN
ejpam-6917	354	6	to	to	ADP
ejpam-6917	354	7	the	the	DET
ejpam-6917	354	8	case	case	NOUN
ejpam-6917	354	9	i	i	PRON
ejpam-6917	354	10	=	=	PUNCT
ejpam-6917	355	1	2j	2j	X
ejpam-6917	356	1	+	+	CCONJ
ejpam-6917	356	2	1	1	NUM
ejpam-6917	356	3	,	,	PUNCT
ejpam-6917	356	4	where	where	SCONJ
ejpam-6917	356	5	the	the	DET
ejpam-6917	356	6	identities	identity	NOUN
ejpam-6917	356	7	in	in	ADP
ejpam-6917	356	8	(	(	PUNCT
ejpam-6917	356	9	16	16	NUM
ejpam-6917	356	10	)	)	PUNCT
ejpam-6917	356	11	enable	enable	VERB
ejpam-6917	356	12	us	we	PRON
ejpam-6917	356	13	to	to	AUX
ejpam-6917	356	14	|(d3gn+1)2j+1|	|(d3gn+1)2j+1|	NOUN
ejpam-6917	357	1	=	=	SYM
ejpam-6917	357	2	|	|	NOUN
ejpam-6917	357	3	(	(	PUNCT
ejpam-6917	357	4	7	7	NUM
ejpam-6917	357	5	16	16	NUM
ejpam-6917	357	6	(	(	PUNCT
ejpam-6917	357	7	d3gn)j−1	d3gn)j−1	NOUN
ejpam-6917	357	8	+	+	CCONJ
ejpam-6917	357	9	133	133	NUM
ejpam-6917	357	10	16	16	NUM
ejpam-6917	358	1	(	(	PUNCT
ejpam-6917	358	2	d3gn)j	d3gn)j	NOUN
ejpam-6917	358	3	+	+	NOUN
ejpam-6917	358	4	153	153	NUM
ejpam-6917	358	5	16	16	NUM
ejpam-6917	358	6	(	(	PUNCT
ejpam-6917	358	7	d3gn)j+1	d3gn)j+1	PROPN
ejpam-6917	358	8	+	+	CCONJ
ejpam-6917	358	9	27	27	NUM
ejpam-6917	358	10	16	16	NUM
ejpam-6917	358	11	(	(	PUNCT
ejpam-6917	358	12	d3gn)j+2	d3gn)j+2	PROPN
ejpam-6917	358	13	)	)	PUNCT
ejpam-6917	358	14	+	+	CCONJ
ejpam-6917	358	15	(	(	PUNCT
ejpam-6917	358	16	1−	1−	NUM
ejpam-6917	358	17	µ0	µ0	NOUN
ejpam-6917	358	18	)	)	PUNCT
ejpam-6917	358	19	128	128	NUM
ejpam-6917	358	20	(	(	PUNCT
ejpam-6917	358	21	−17(d3gn)j−1	−17(d3gn)j−1	NOUN
ejpam-6917	358	22	+	+	CCONJ
ejpam-6917	358	23	451(d3gn)j	451(d3gn)j	NUM
ejpam-6917	358	24	−	−	PROPN
ejpam-6917	358	25	851(d3gn)j+1	851(d3gn)j+1	NUM
ejpam-6917	359	1	+417(d3gn)j+2)|	+417(d3gn)j+2)|	PROPN
ejpam-6917	359	2	≤	≤	NUM
ejpam-6917	359	3	90	90	NUM
ejpam-6917	359	4	128	128	NUM
ejpam-6917	359	5	|(d3gn)j−1|+	|(d3gn)j−1|+	NOUN
ejpam-6917	359	6	162	162	NUM
ejpam-6917	359	7	128	128	NUM
ejpam-6917	359	8	|(d3gn)j	|(d3gn)j	NOUN
ejpam-6917	359	9	|+	|+	ADP
ejpam-6917	359	10	2926	2926	NUM
ejpam-6917	359	11	128	128	NUM
ejpam-6917	359	12	|(d3gn)j+1|+	|(d3gn)j+1|+	NOUN
ejpam-6917	359	13	618	618	NUM
ejpam-6917	359	14	128	128	NUM
ejpam-6917	359	15	|(d3gn)j+2|	|(d3gn)j+2|	PROPN
ejpam-6917	359	16	.	.	PUNCT
ejpam-6917	360	1	by	by	ADP
ejpam-6917	360	2	the	the	DET
ejpam-6917	360	3	same	same	ADJ
ejpam-6917	360	4	argument	argument	NOUN
ejpam-6917	360	5	as	as	SCONJ
ejpam-6917	360	6	given	give	VERB
ejpam-6917	360	7	above	above	ADV
ejpam-6917	360	8	,	,	PUNCT
ejpam-6917	360	9	a	a	DET
ejpam-6917	360	10	direct	direct	ADJ
ejpam-6917	360	11	calculation	calculation	NOUN
ejpam-6917	360	12	using	use	VERB
ejpam-6917	360	13	(	(	PUNCT
ejpam-6917	360	14	16	16	NUM
ejpam-6917	360	15	)	)	PUNCT
ejpam-6917	360	16	shows	show	VERB
ejpam-6917	360	17	that	that	SCONJ
ejpam-6917	360	18	(	(	PUNCT
ejpam-6917	360	19	dgn+1)2j+1	dgn+1)2j+1	ADJ
ejpam-6917	360	20	−	−	NOUN
ejpam-6917	360	21	2−2(n+1	2−2(n+1	NUM
ejpam-6917	360	22	)	)	PUNCT
ejpam-6917	360	23	(	(	PUNCT
ejpam-6917	360	24	1−	1−	NUM
ejpam-6917	360	25	µ0	µ0	NOUN
ejpam-6917	360	26	)	)	PUNCT
ejpam-6917	360	27	k	k	PROPN
ejpam-6917	360	28	|(d3gn+1)2j+1|	|(d3gn+1)2j+1|	PROPN
ejpam-6917	360	29	≥	≥	NOUN
ejpam-6917	360	30	0	0	NUM
ejpam-6917	360	31	.	.	PUNCT
ejpam-6917	360	32	where	where	SCONJ
ejpam-6917	360	33	k	k	PROPN
ejpam-6917	360	34	>	>	X
ejpam-6917	360	35	0	0	X
ejpam-6917	360	36	.	.	PUNCT
ejpam-6917	360	37	theorem	theorem	NOUN
ejpam-6917	360	38	6	6	NUM
ejpam-6917	360	39	.	.	PUNCT
ejpam-6917	361	1	let	let	VERB
ejpam-6917	361	2	the	the	DET
ejpam-6917	361	3	initial	initial	ADJ
ejpam-6917	361	4	sequence	sequence	NOUN
ejpam-6917	361	5	gn0	gn0	NOUN
ejpam-6917	361	6	be	be	AUX
ejpam-6917	361	7	defined	define	VERB
ejpam-6917	361	8	on	on	ADP
ejpam-6917	361	9	the	the	DET
ejpam-6917	361	10	grid	grid	NOUN
ejpam-6917	361	11	2−n0z	2−n0z	NUM
ejpam-6917	361	12	,	,	PUNCT
ejpam-6917	361	13	and	and	CCONJ
ejpam-6917	361	14	consider	consider	VERB
ejpam-6917	361	15	the	the	DET
ejpam-6917	361	16	subdivision	subdivision	NOUN
ejpam-6917	361	17	process	process	NOUN
ejpam-6917	361	18	given	give	VERB
ejpam-6917	361	19	by	by	ADP
ejpam-6917	361	20	gn+1	gn+1	PROPN
ejpam-6917	361	21	=	=	SYM
ejpam-6917	361	22	sp	sp	ADP
ejpam-6917	361	23	g	g	NOUN
ejpam-6917	361	24	n	n	CCONJ
ejpam-6917	361	25	,	,	PUNCT
ejpam-6917	361	26	for	for	ADP
ejpam-6917	361	27	all	all	DET
ejpam-6917	361	28	n	n	PRON
ejpam-6917	361	29	≥	≥	NOUN
ejpam-6917	361	30	n0	n0	NUM
ejpam-6917	361	31	,	,	PUNCT
ejpam-6917	361	32	where	where	SCONJ
ejpam-6917	361	33	sp	sp	NOUN
ejpam-6917	361	34	is	be	AUX
ejpam-6917	361	35	the	the	DET
ejpam-6917	361	36	subdivision	subdivision	NOUN
ejpam-6917	361	37	scheme	scheme	NOUN
ejpam-6917	361	38	defined	define	VERB
ejpam-6917	361	39	in	in	ADP
ejpam-6917	361	40	equation	equation	NOUN
ejpam-6917	361	41	(	(	PUNCT
ejpam-6917	361	42	1	1	NUM
ejpam-6917	361	43	)	)	PUNCT
ejpam-6917	361	44	.	.	PUNCT
ejpam-6917	362	1	if	if	SCONJ
ejpam-6917	362	2	the	the	DET
ejpam-6917	362	3	initial	initial	ADJ
ejpam-6917	362	4	data	datum	NOUN
ejpam-6917	362	5	gn0	gn0	NOUN
ejpam-6917	362	6	satisfies	satisfie	NOUN
ejpam-6917	362	7	condition	condition	NOUN
ejpam-6917	362	8	-	-	PUNCT
ejpam-6917	362	9	m	m	PROPN
ejpam-6917	362	10	,	,	PUNCT
ejpam-6917	362	11	then	then	ADV
ejpam-6917	362	12	the	the	DET
ejpam-6917	362	13	discrete	discrete	ADJ
ejpam-6917	362	14	first	first	ADJ
ejpam-6917	362	15	differences	difference	NOUN
ejpam-6917	362	16	satisfy	satisfy	VERB
ejpam-6917	362	17	(	(	PUNCT
ejpam-6917	362	18	dgn)i	dgn)i	X
ejpam-6917	362	19	≥	≥	NOUN
ejpam-6917	362	20	0	0	NUM
ejpam-6917	362	21	,	,	PUNCT
ejpam-6917	362	22	for	for	ADP
ejpam-6917	362	23	all	all	DET
ejpam-6917	362	24	n	n	PRON
ejpam-6917	362	25	≥	≥	NOUN
ejpam-6917	362	26	n0	n0	NUM
ejpam-6917	362	27	and	and	CCONJ
ejpam-6917	362	28	i	i	PROPN
ejpam-6917	362	29	∈	∈	PROPN
ejpam-6917	362	30	z.	z.	PROPN
ejpam-6917	363	1	therefore	therefore	ADV
ejpam-6917	363	2	,	,	PUNCT
ejpam-6917	363	3	the	the	DET
ejpam-6917	363	4	scheme	scheme	NOUN
ejpam-6917	363	5	sp	sp	ADP
ejpam-6917	363	6	preserves	preserve	NOUN
ejpam-6917	363	7	monotonicity	monotonicity	NOUN
ejpam-6917	363	8	.	.	PUNCT
ejpam-6917	364	1	proof	proof	NOUN
ejpam-6917	364	2	.	.	PUNCT
ejpam-6917	365	1	by	by	ADP
ejpam-6917	365	2	lemma	lemma	PROPN
ejpam-6917	365	3	2	2	NUM
ejpam-6917	365	4	,	,	PUNCT
ejpam-6917	365	5	we	we	PRON
ejpam-6917	365	6	have	have	AUX
ejpam-6917	365	7	already	already	ADV
ejpam-6917	365	8	shown	show	VERB
ejpam-6917	365	9	that	that	SCONJ
ejpam-6917	365	10	(	(	PUNCT
ejpam-6917	365	11	dgn)i	dgn)i	PROPN
ejpam-6917	365	12	≥	≥	NOUN
ejpam-6917	365	13	2−2n	2−2n	NUM
ejpam-6917	365	14	(	(	PUNCT
ejpam-6917	365	15	1−µ0	1−µ0	NUM
ejpam-6917	365	16	)	)	PUNCT
ejpam-6917	366	1	k	k	PROPN
ejpam-6917	366	2	|(d3gn)i|	|(d3gn)i|	X
ejpam-6917	366	3	≥	≥	PROPN
ejpam-6917	366	4	0	0	NUM
ejpam-6917	366	5	for	for	ADP
ejpam-6917	366	6	any	any	DET
ejpam-6917	366	7	n	n	PRON
ejpam-6917	366	8	≥	≥	NOUN
ejpam-6917	366	9	n0	n0	NUM
ejpam-6917	366	10	.	.	PUNCT
ejpam-6917	367	1	hence	hence	ADV
ejpam-6917	367	2	,	,	PUNCT
ejpam-6917	367	3	the	the	DET
ejpam-6917	367	4	result	result	NOUN
ejpam-6917	367	5	follows	follow	VERB
ejpam-6917	367	6	directly	directly	ADV
ejpam-6917	367	7	.	.	PUNCT
ejpam-6917	368	1	5.2	5.2	NUM
ejpam-6917	368	2	.	.	PUNCT
ejpam-6917	368	3	preservation	preservation	NOUN
ejpam-6917	368	4	of	of	ADP
ejpam-6917	368	5	convexity	convexity	NOUN
ejpam-6917	368	6	next	next	ADV
ejpam-6917	368	7	,	,	PUNCT
ejpam-6917	368	8	we	we	PRON
ejpam-6917	368	9	show	show	VERB
ejpam-6917	368	10	that	that	SCONJ
ejpam-6917	368	11	sp	sp	ADP
ejpam-6917	368	12	-scheme	-scheme	PROPN
ejpam-6917	368	13	maintains	maintain	VERB
ejpam-6917	368	14	convexity	convexity	NOUN
ejpam-6917	368	15	under	under	ADP
ejpam-6917	368	16	a	a	DET
ejpam-6917	368	17	mild	mild	ADJ
ejpam-6917	368	18	condition	condition	NOUN
ejpam-6917	368	19	.	.	PUNCT
ejpam-6917	369	1	for	for	ADP
ejpam-6917	369	2	simplicity	simplicity	NOUN
ejpam-6917	369	3	,	,	PUNCT
ejpam-6917	369	4	we	we	PRON
ejpam-6917	369	5	introduce	introduce	VERB
ejpam-6917	369	6	the	the	DET
ejpam-6917	369	7	following	follow	VERB
ejpam-6917	369	8	notation	notation	NOUN
ejpam-6917	369	9	∇gni	∇gni	NOUN
ejpam-6917	369	10	=	=	SYM
ejpam-6917	369	11	gni	gni	PROPN
ejpam-6917	369	12	−	−	PROPN
ejpam-6917	369	13	gni−1	gni−1	PROPN
ejpam-6917	369	14	and	and	CCONJ
ejpam-6917	369	15	∆gni	∆gni	NOUN
ejpam-6917	369	16	=	=	PUNCT
ejpam-6917	369	17	gni−1	gni−1	PROPN
ejpam-6917	369	18	−	−	PROPN
ejpam-6917	369	19	2gni	2gni	PROPN
ejpam-6917	370	1	+	+	CCONJ
ejpam-6917	370	2	gni+1	gni+1	ADJ
ejpam-6917	370	3	.	.	PUNCT
ejpam-6917	371	1	f.	f.	PROPN
ejpam-6917	371	2	s.	s.	PROPN
ejpam-6917	371	3	alshammari	alshammari	PROPN
ejpam-6917	371	4	et	et	PROPN
ejpam-6917	371	5	al	al	PROPN
ejpam-6917	371	6	.	.	PUNCT
ejpam-6917	371	7	/	/	SYM
ejpam-6917	371	8	eur	eur	PROPN
ejpam-6917	371	9	.	.	PUNCT
ejpam-6917	372	1	j.	j.	PROPN
ejpam-6917	372	2	pure	pure	PROPN
ejpam-6917	372	3	appl	appl	PROPN
ejpam-6917	372	4	.	.	PROPN
ejpam-6917	372	5	math	math	PROPN
ejpam-6917	372	6	,	,	PUNCT
ejpam-6917	372	7	18	18	NUM
ejpam-6917	372	8	(	(	PUNCT
ejpam-6917	372	9	4	4	NUM
ejpam-6917	372	10	)	)	PUNCT
ejpam-6917	372	11	(	(	PUNCT
ejpam-6917	372	12	2025	2025	NUM
ejpam-6917	372	13	)	)	PUNCT
ejpam-6917	372	14	,	,	PUNCT
ejpam-6917	372	15	6917	6917	NUM
ejpam-6917	372	16	16	16	NUM
ejpam-6917	372	17	of	of	ADP
ejpam-6917	372	18	26	26	NUM
ejpam-6917	372	19	lemma	lemma	PROPN
ejpam-6917	372	20	3	3	X
ejpam-6917	372	21	.	.	PUNCT
ejpam-6917	373	1	let	let	VERB
ejpam-6917	373	2	qb	qb	PROPN
ejpam-6917	373	3	denote	denote	VERB
ejpam-6917	373	4	the	the	DET
ejpam-6917	373	5	quintic	quintic	ADJ
ejpam-6917	373	6	b	b	NOUN
ejpam-6917	373	7	-	-	NOUN
ejpam-6917	373	8	spline	spline	NOUN
ejpam-6917	373	9	.	.	PUNCT
ejpam-6917	374	1	thus	thus	ADV
ejpam-6917	374	2	,	,	PUNCT
ejpam-6917	374	3	for	for	SCONJ
ejpam-6917	374	4	any	any	DET
ejpam-6917	374	5	i	i	PROPN
ejpam-6917	374	6	∈	∈	PROPN
ejpam-6917	374	7	z	z	NOUN
ejpam-6917	374	8	,	,	PUNCT
ejpam-6917	374	9			PRON
ejpam-6917	374	10	(	(	PUNCT
ejpam-6917	374	11	d2qbg	d2qbg	PROPN
ejpam-6917	374	12	n)2i	n)2i	NOUN
ejpam-6917	374	13	=	=	NOUN
ejpam-6917	374	14	1	1	NUM
ejpam-6917	374	15	16	16	NUM
ejpam-6917	374	16	(	(	PUNCT
ejpam-6917	374	17	d2gn)i−1	d2gn)i−1	PROPN
ejpam-6917	374	18	+	+	CCONJ
ejpam-6917	374	19	7	7	NUM
ejpam-6917	374	20	16	16	NUM
ejpam-6917	374	21	(	(	PUNCT
ejpam-6917	374	22	d2gn)i	d2gn)i	PROPN
ejpam-6917	374	23	+	+	CCONJ
ejpam-6917	374	24	7	7	NUM
ejpam-6917	374	25	16	16	NUM
ejpam-6917	374	26	(	(	PUNCT
ejpam-6917	374	27	d2gn)i+1	d2gn)i+1	PROPN
ejpam-6917	374	28	+	+	NOUN
ejpam-6917	374	29	1	1	NUM
ejpam-6917	374	30	16	16	NUM
ejpam-6917	374	31	(	(	PUNCT
ejpam-6917	374	32	d2gn)i+2	d2gn)i+2	PROPN
ejpam-6917	374	33	,	,	PUNCT
ejpam-6917	374	34	(	(	PUNCT
ejpam-6917	374	35	d2qbg	d2qbg	PROPN
ejpam-6917	374	36	n)2i+1	n)2i+1	NOUN
ejpam-6917	375	1	=	=	NOUN
ejpam-6917	375	2	4	4	NUM
ejpam-6917	375	3	16	16	NUM
ejpam-6917	375	4	(	(	PUNCT
ejpam-6917	375	5	d2gn)i	d2gn)i	PROPN
ejpam-6917	375	6	+	+	CCONJ
ejpam-6917	375	7	8	8	NUM
ejpam-6917	375	8	16	16	NUM
ejpam-6917	375	9	(	(	PUNCT
ejpam-6917	375	10	d2gn)i+1	d2gn)i+1	PROPN
ejpam-6917	375	11	4	4	NUM
ejpam-6917	375	12	16	16	NUM
ejpam-6917	375	13	(	(	PUNCT
ejpam-6917	375	14	d2gn)i+2	d2gn)i+2	PROPN
ejpam-6917	375	15	.	.	PUNCT
ejpam-6917	376	1	(	(	PUNCT
ejpam-6917	376	2	19	19	NUM
ejpam-6917	376	3	)	)	PUNCT
ejpam-6917	376	4	this	this	PRON
ejpam-6917	376	5	shows	show	VERB
ejpam-6917	376	6	that	that	SCONJ
ejpam-6917	376	7	the	the	DET
ejpam-6917	376	8	qb	qb	PROPN
ejpam-6917	376	9	-	-	PUNCT
ejpam-6917	376	10	scheme	scheme	NOUN
ejpam-6917	376	11	preserves	preserve	NOUN
ejpam-6917	376	12	convexity	convexity	NOUN
ejpam-6917	376	13	.	.	PUNCT
ejpam-6917	377	1	lemma	lemma	PROPN
ejpam-6917	377	2	4	4	X
ejpam-6917	377	3	.	.	PUNCT
ejpam-6917	377	4	assume	assume	VERB
ejpam-6917	377	5	sp	sp	ADP
ejpam-6917	377	6	is	be	AUX
ejpam-6917	377	7	the	the	DET
ejpam-6917	377	8	ss	ss	NOUN
ejpam-6917	377	9	using	use	VERB
ejpam-6917	377	10	the	the	DET
ejpam-6917	377	11	refinement	refinement	NOUN
ejpam-6917	377	12	rule	rule	NOUN
ejpam-6917	377	13	given	give	VERB
ejpam-6917	377	14	in	in	ADP
ejpam-6917	377	15	(	(	PUNCT
ejpam-6917	377	16	1	1	NUM
ejpam-6917	377	17	)	)	PUNCT
ejpam-6917	377	18	,	,	PUNCT
ejpam-6917	377	19	suppose	suppose	VERB
ejpam-6917	377	20	that	that	SCONJ
ejpam-6917	377	21	µ0	µ0	NOUN
ejpam-6917	377	22	is	be	AUX
ejpam-6917	377	23	given	give	VERB
ejpam-6917	377	24	in	in	ADP
ejpam-6917	377	25	(	(	PUNCT
ejpam-6917	377	26	2	2	NUM
ejpam-6917	377	27	)	)	PUNCT
ejpam-6917	377	28	.	.	PUNCT
ejpam-6917	378	1	when	when	SCONJ
ejpam-6917	378	2	gn+1	gn+1	VERB
ejpam-6917	378	3	=	=	SYM
ejpam-6917	378	4	sp	sp	ADP
ejpam-6917	378	5	g	g	PROPN
ejpam-6917	378	6	n	n	PROPN
ejpam-6917	378	7	for	for	ADP
ejpam-6917	378	8	n	n	PRON
ejpam-6917	378	9	≥	≥	NOUN
ejpam-6917	378	10	n0	n0	NUM
ejpam-6917	378	11	.	.	PUNCT
ejpam-6917	379	1	next	next	ADV
ejpam-6917	379	2	,	,	PUNCT
ejpam-6917	379	3	we	we	PRON
ejpam-6917	379	4	obtain	obtain	VERB
ejpam-6917	379	5	(	(	PUNCT
ejpam-6917	379	6	d2gn+1)2i	d2gn+1)2i	NOUN
ejpam-6917	379	7	=	=	SYM
ejpam-6917	379	8	(	(	PUNCT
ejpam-6917	379	9	1	1	NUM
ejpam-6917	379	10	16	16	NUM
ejpam-6917	379	11	(	(	PUNCT
ejpam-6917	379	12	d2gn)i−1	d2gn)i−1	PROPN
ejpam-6917	379	13	+	+	CCONJ
ejpam-6917	379	14	7	7	NUM
ejpam-6917	379	15	16	16	NUM
ejpam-6917	379	16	(	(	PUNCT
ejpam-6917	379	17	d2gn)i	d2gn)i	PROPN
ejpam-6917	380	1	+	+	CCONJ
ejpam-6917	380	2	7	7	NUM
ejpam-6917	380	3	16	16	NUM
ejpam-6917	380	4	(	(	PUNCT
ejpam-6917	380	5	d2gn)i+1	d2gn)i+1	PROPN
ejpam-6917	380	6	+	+	NOUN
ejpam-6917	380	7	1	1	NUM
ejpam-6917	380	8	16	16	NUM
ejpam-6917	380	9	(	(	PUNCT
ejpam-6917	380	10	d2gn)i+2	d2gn)i+2	PROPN
ejpam-6917	380	11	)	)	PUNCT
ejpam-6917	380	12	−(1−	−(1−	VERB
ejpam-6917	380	13	µ0	µ0	NOUN
ejpam-6917	380	14	)	)	PUNCT
ejpam-6917	380	15	32	32	NUM
ejpam-6917	380	16	2−n(10∇(d3gn)i+1	2−n(10∇(d3gn)i+1	NUM
ejpam-6917	380	17	+	+	CCONJ
ejpam-6917	380	18	10∇(d3gn)i+2	10∇(d3gn)i+2	NUM
ejpam-6917	380	19	)	)	PUNCT
ejpam-6917	380	20	,	,	PUNCT
ejpam-6917	380	21	(	(	PUNCT
ejpam-6917	380	22	d2gn+1)2i+1	d2gn+1)2i+1	NOUN
ejpam-6917	380	23	=	=	SYM
ejpam-6917	380	24	(	(	PUNCT
ejpam-6917	380	25	4	4	NUM
ejpam-6917	380	26	16	16	NUM
ejpam-6917	380	27	(	(	PUNCT
ejpam-6917	380	28	d2gn)i	d2gn)i	PROPN
ejpam-6917	380	29	+	+	CCONJ
ejpam-6917	380	30	8	8	NUM
ejpam-6917	380	31	16	16	NUM
ejpam-6917	380	32	(	(	PUNCT
ejpam-6917	380	33	d2gn)i+1	d2gn)i+1	PROPN
ejpam-6917	380	34	4	4	NUM
ejpam-6917	380	35	16	16	NUM
ejpam-6917	380	36	(	(	PUNCT
ejpam-6917	380	37	d2gn)n+2)−	d2gn)n+2)−	NUM
ejpam-6917	380	38	(	(	PUNCT
ejpam-6917	380	39	1−	1−	NUM
ejpam-6917	380	40	µ0	µ0	NOUN
ejpam-6917	380	41	)	)	PUNCT
ejpam-6917	380	42	32	32	NUM
ejpam-6917	380	43	2−n	2−n	NUM
ejpam-6917	380	44	(	(	PUNCT
ejpam-6917	380	45	−3∇(d3gn)i+1	−3∇(d3gn)i+1	NOUN
ejpam-6917	381	1	+	+	X
ejpam-6917	381	2	26∇(d3gn)i+2	26∇(d3gn)i+2	NUM
ejpam-6917	381	3	−	−	NOUN
ejpam-6917	381	4	3∇(d3gn)i+3	3∇(d3gn)i+3	NUM
ejpam-6917	381	5	)	)	PUNCT
ejpam-6917	381	6	.	.	PUNCT
ejpam-6917	382	1	(	(	PUNCT
ejpam-6917	382	2	20	20	X
ejpam-6917	382	3	)	)	PUNCT
ejpam-6917	382	4	proof	proof	NOUN
ejpam-6917	382	5	.	.	PUNCT
ejpam-6917	383	1	we	we	PRON
ejpam-6917	383	2	now	now	ADV
ejpam-6917	383	3	concentrate	concentrate	VERB
ejpam-6917	383	4	on	on	ADP
ejpam-6917	383	5	proving	prove	VERB
ejpam-6917	383	6	the	the	DET
ejpam-6917	383	7	first	first	ADJ
ejpam-6917	383	8	equation	equation	NOUN
ejpam-6917	383	9	in	in	ADP
ejpam-6917	383	10	(	(	PUNCT
ejpam-6917	383	11	20	20	NUM
ejpam-6917	383	12	)	)	PUNCT
ejpam-6917	383	13	.	.	PUNCT
ejpam-6917	384	1	we	we	PRON
ejpam-6917	384	2	note	note	VERB
ejpam-6917	384	3	that	that	SCONJ
ejpam-6917	384	4	qb	qb	PROPN
ejpam-6917	384	5	implies	imply	VERB
ejpam-6917	384	6	that	that	SCONJ
ejpam-6917	384	7	the	the	DET
ejpam-6917	384	8	quintic	quintic	ADJ
ejpam-6917	384	9	b	b	NOUN
ejpam-6917	384	10	-	-	PUNCT
ejpam-6917	384	11	spline	spline	NOUN
ejpam-6917	384	12	,	,	PUNCT
ejpam-6917	384	13	using	use	VERB
ejpam-6917	384	14	(	(	PUNCT
ejpam-6917	384	15	13	13	NUM
ejpam-6917	384	16	)	)	PUNCT
ejpam-6917	384	17	and	and	CCONJ
ejpam-6917	384	18	lemma	lemma	PROPN
ejpam-6917	384	19	3	3	NUM
ejpam-6917	384	20	to	to	PART
ejpam-6917	384	21	obtain	obtain	VERB
ejpam-6917	384	22	(	(	PUNCT
ejpam-6917	384	23	d2gn+1)2n	d2gn+1)2n	NOUN
ejpam-6917	384	24	=	=	PUNCT
ejpam-6917	384	25	(	(	PUNCT
ejpam-6917	384	26	1	1	NUM
ejpam-6917	384	27	16	16	NUM
ejpam-6917	384	28	(	(	PUNCT
ejpam-6917	384	29	d2gn)i−1	d2gn)i−1	PROPN
ejpam-6917	384	30	+	+	CCONJ
ejpam-6917	384	31	7	7	NUM
ejpam-6917	384	32	16	16	NUM
ejpam-6917	384	33	(	(	PUNCT
ejpam-6917	384	34	d2gn)i	d2gn)i	PROPN
ejpam-6917	384	35	+	+	CCONJ
ejpam-6917	384	36	7	7	NUM
ejpam-6917	384	37	16	16	NUM
ejpam-6917	384	38	(	(	PUNCT
ejpam-6917	384	39	d2gn)i+1	d2gn)i+1	PROPN
ejpam-6917	384	40	+	+	NOUN
ejpam-6917	384	41	1	1	NUM
ejpam-6917	384	42	16	16	NUM
ejpam-6917	384	43	(	(	PUNCT
ejpam-6917	384	44	d2gn)i+2	d2gn)i+2	PROPN
ejpam-6917	384	45	)	)	PUNCT
ejpam-6917	384	46	−(1−	−(1−	VERB
ejpam-6917	384	47	µ0	µ0	NOUN
ejpam-6917	384	48	)	)	PUNCT
ejpam-6917	384	49	32	32	NUM
ejpam-6917	384	50	(	(	PUNCT
ejpam-6917	384	51	10(d2gn)i−1	10(d2gn)i−1	NUM
ejpam-6917	384	52	−	−	NUM
ejpam-6917	384	53	10(d2gn)i	10(d2gn)i	NUM
ejpam-6917	384	54	−	−	NOUN
ejpam-6917	384	55	10(d2gn)i+1	10(d2gn)i+1	NUM
ejpam-6917	385	1	+	+	SYM
ejpam-6917	385	2	10(d2gn)i+2	10(d2gn)i+2	NUM
ejpam-6917	385	3	)	)	PUNCT
ejpam-6917	385	4	=	=	PUNCT
ejpam-6917	385	5	(	(	PUNCT
ejpam-6917	385	6	1	1	NUM
ejpam-6917	385	7	16	16	NUM
ejpam-6917	385	8	(	(	PUNCT
ejpam-6917	385	9	d2gn)i−1	d2gn)i−1	PROPN
ejpam-6917	385	10	+	+	CCONJ
ejpam-6917	385	11	7	7	NUM
ejpam-6917	385	12	16	16	NUM
ejpam-6917	385	13	(	(	PUNCT
ejpam-6917	385	14	d2gn)i	d2gn)i	PROPN
ejpam-6917	385	15	+	+	CCONJ
ejpam-6917	385	16	7	7	NUM
ejpam-6917	385	17	16	16	NUM
ejpam-6917	385	18	(	(	PUNCT
ejpam-6917	385	19	d2gn)i+1	d2gn)i+1	PROPN
ejpam-6917	385	20	+	+	NOUN
ejpam-6917	385	21	1	1	NUM
ejpam-6917	385	22	16	16	NUM
ejpam-6917	385	23	(	(	PUNCT
ejpam-6917	385	24	d2gn)i+2	d2gn)i+2	PROPN
ejpam-6917	385	25	)	)	PUNCT
ejpam-6917	385	26	−(1−	−(1−	VERB
ejpam-6917	385	27	µ0	µ0	NOUN
ejpam-6917	385	28	)	)	PUNCT
ejpam-6917	385	29	32	32	NUM
ejpam-6917	385	30	2−n(10∇(d3gn)i+1	2−n(10∇(d3gn)i+1	NUM
ejpam-6917	385	31	+	+	CCONJ
ejpam-6917	385	32	10∇(d3gn)i+2	10∇(d3gn)i+2	NUM
ejpam-6917	385	33	)	)	PUNCT
ejpam-6917	385	34	.	.	PUNCT
ejpam-6917	386	1	by	by	ADP
ejpam-6917	386	2	applying	apply	VERB
ejpam-6917	386	3	equation	equation	NOUN
ejpam-6917	386	4	(	(	PUNCT
ejpam-6917	386	5	13	13	NUM
ejpam-6917	386	6	)	)	PUNCT
ejpam-6917	386	7	and	and	CCONJ
ejpam-6917	386	8	lemma	lemma	PROPN
ejpam-6917	386	9	3	3	NUM
ejpam-6917	386	10	,	,	PUNCT
ejpam-6917	386	11	we	we	PRON
ejpam-6917	386	12	obtain	obtain	VERB
ejpam-6917	386	13	the	the	DET
ejpam-6917	386	14	following	follow	VERB
ejpam-6917	386	15	expression	expression	NOUN
ejpam-6917	386	16	through	through	ADP
ejpam-6917	386	17	basic	basic	ADJ
ejpam-6917	386	18	calculation	calculation	NOUN
ejpam-6917	386	19	(	(	PUNCT
ejpam-6917	386	20	d2gn+1)2n+1	d2gn+1)2n+1	NOUN
ejpam-6917	386	21	=	=	SYM
ejpam-6917	386	22	(	(	PUNCT
ejpam-6917	386	23	4	4	NUM
ejpam-6917	386	24	16	16	NUM
ejpam-6917	386	25	(	(	PUNCT
ejpam-6917	386	26	d2gn)i	d2gn)i	PROPN
ejpam-6917	386	27	+	+	CCONJ
ejpam-6917	386	28	8	8	NUM
ejpam-6917	386	29	16	16	NUM
ejpam-6917	386	30	(	(	PUNCT
ejpam-6917	386	31	d2gn)i+1	d2gn)i+1	PROPN
ejpam-6917	386	32	+	+	NOUN
ejpam-6917	386	33	4	4	NUM
ejpam-6917	386	34	16	16	NUM
ejpam-6917	386	35	(	(	PUNCT
ejpam-6917	386	36	d2gn)i+2)−	d2gn)i+2)−	PROPN
ejpam-6917	386	37	(	(	PUNCT
ejpam-6917	386	38	1−	1−	NUM
ejpam-6917	386	39	µ0	µ0	NOUN
ejpam-6917	386	40	)	)	PUNCT
ejpam-6917	386	41	32	32	NUM
ejpam-6917	386	42	(	(	PUNCT
ejpam-6917	386	43	−3d2gni−1	−3d2gni−1	NOUN
ejpam-6917	386	44	+	+	CCONJ
ejpam-6917	386	45	32d2gni	32d2gni	NOUN
ejpam-6917	386	46	−	−	PROPN
ejpam-6917	386	47	58d2gni+1	58d2gni+1	NUM
ejpam-6917	387	1	+	+	CCONJ
ejpam-6917	387	2	32d2gni+2	32d2gni+2	NUM
ejpam-6917	387	3	−	−	PROPN
ejpam-6917	387	4	3d2gni+3	3d2gni+3	NUM
ejpam-6917	387	5	)	)	PUNCT
ejpam-6917	387	6	=	=	PUNCT
ejpam-6917	387	7	(	(	PUNCT
ejpam-6917	387	8	4	4	NUM
ejpam-6917	387	9	16	16	NUM
ejpam-6917	387	10	(	(	PUNCT
ejpam-6917	387	11	d2gn)i	d2gn)i	PROPN
ejpam-6917	388	1	+	+	CCONJ
ejpam-6917	388	2	8	8	NUM
ejpam-6917	388	3	16	16	NUM
ejpam-6917	388	4	(	(	PUNCT
ejpam-6917	388	5	d2gn)i+1	d2gn)i+1	PROPN
ejpam-6917	388	6	4	4	NUM
ejpam-6917	388	7	16	16	NUM
ejpam-6917	388	8	(	(	PUNCT
ejpam-6917	388	9	d2gn)n+2)−	d2gn)n+2)−	NUM
ejpam-6917	388	10	(	(	PUNCT
ejpam-6917	388	11	1−	1−	NUM
ejpam-6917	388	12	µ0	µ0	NOUN
ejpam-6917	388	13	)	)	PUNCT
ejpam-6917	388	14	32	32	NUM
ejpam-6917	388	15	2−n	2−n	NUM
ejpam-6917	388	16	(	(	PUNCT
ejpam-6917	388	17	−3∇(d3gn)i+1	−3∇(d3gn)i+1	NOUN
ejpam-6917	388	18	+	+	X
ejpam-6917	389	1	26∇(d3gn)i+2	26∇(d3gn)i+2	NUM
ejpam-6917	389	2	−	−	NOUN
ejpam-6917	389	3	3∇(d3gn)i+3	3∇(d3gn)i+3	NUM
ejpam-6917	389	4	)	)	PUNCT
ejpam-6917	389	5	.	.	PUNCT
ejpam-6917	390	1	lemma	lemma	PROPN
ejpam-6917	390	2	5	5	X
ejpam-6917	390	3	.	.	PUNCT
ejpam-6917	390	4	suppose	suppose	VERB
ejpam-6917	390	5	sp	sp	PART
ejpam-6917	390	6	be	be	AUX
ejpam-6917	390	7	the	the	DET
ejpam-6917	390	8	ss	ss	NOUN
ejpam-6917	390	9	given	give	VERB
ejpam-6917	390	10	by	by	ADP
ejpam-6917	390	11	(	(	PUNCT
ejpam-6917	390	12	1	1	NUM
ejpam-6917	390	13	)	)	PUNCT
ejpam-6917	390	14	,	,	PUNCT
ejpam-6917	390	15	acting	act	VERB
ejpam-6917	390	16	on	on	ADP
ejpam-6917	390	17	the	the	DET
ejpam-6917	390	18	initial	initial	ADJ
ejpam-6917	390	19	data	datum	NOUN
ejpam-6917	390	20	gn0	gn0	VERB
ejpam-6917	390	21	at	at	ADP
ejpam-6917	390	22	grid	grid	NOUN
ejpam-6917	390	23	points	point	NOUN
ejpam-6917	390	24	2−n0z	2−n0z	NUM
ejpam-6917	390	25	.	.	PUNCT
ejpam-6917	391	1	we	we	PRON
ejpam-6917	391	2	then	then	ADV
ejpam-6917	391	3	define	define	VERB
ejpam-6917	391	4	the	the	DET
ejpam-6917	391	5	sequence	sequence	NOUN
ejpam-6917	391	6	gn+1	gn+1	NOUN
ejpam-6917	391	7	=	=	PUNCT
ejpam-6917	391	8	spg	spg	X
ejpam-6917	391	9	n	n	X
ejpam-6917	391	10	for	for	ADP
ejpam-6917	391	11	n	n	PRON
ejpam-6917	391	12	≥	≥	NOUN
ejpam-6917	391	13	n0	n0	NUM
ejpam-6917	391	14	,	,	PUNCT
ejpam-6917	391	15	we	we	PRON
ejpam-6917	391	16	obtain	obtain	VERB
ejpam-6917	391	17	∇(d3gn+1)2i	∇(d3gn+1)2i	PROPN
ejpam-6917	391	18	=	=	X
ejpam-6917	391	19	(	(	PUNCT
ejpam-6917	391	20	−5	−5	ADV
ejpam-6917	391	21	32	32	NUM
ejpam-6917	391	22	∇(d3gn)i−1	∇(d3gn)i−1	NOUN
ejpam-6917	391	23	+	+	CCONJ
ejpam-6917	391	24	11	11	NUM
ejpam-6917	391	25	32	32	NUM
ejpam-6917	391	26	∇(d3gn)i	∇(d3gn)i	NOUN
ejpam-6917	391	27	+	+	CCONJ
ejpam-6917	391	28	5	5	NUM
ejpam-6917	391	29	16	16	NUM
ejpam-6917	391	30	∇(d3gn)i+1	∇(d3gn)i+1	PROPN
ejpam-6917	391	31	)	)	PUNCT
ejpam-6917	391	32	,	,	PUNCT
ejpam-6917	391	33	f.	f.	PROPN
ejpam-6917	391	34	s.	s.	PROPN
ejpam-6917	391	35	alshammari	alshammari	PROPN
ejpam-6917	391	36	et	et	PROPN
ejpam-6917	391	37	al	al	PROPN
ejpam-6917	391	38	.	.	PUNCT
ejpam-6917	391	39	/	/	SYM
ejpam-6917	391	40	eur	eur	PROPN
ejpam-6917	391	41	.	.	PUNCT
ejpam-6917	392	1	j.	j.	PROPN
ejpam-6917	392	2	pure	pure	PROPN
ejpam-6917	392	3	appl	appl	PROPN
ejpam-6917	392	4	.	.	PROPN
ejpam-6917	392	5	math	math	PROPN
ejpam-6917	392	6	,	,	PUNCT
ejpam-6917	392	7	18	18	NUM
ejpam-6917	392	8	(	(	PUNCT
ejpam-6917	392	9	4	4	NUM
ejpam-6917	392	10	)	)	PUNCT
ejpam-6917	392	11	(	(	PUNCT
ejpam-6917	392	12	2025	2025	NUM
ejpam-6917	392	13	)	)	PUNCT
ejpam-6917	392	14	,	,	PUNCT
ejpam-6917	392	15	6917	6917	NUM
ejpam-6917	392	16	17	17	NUM
ejpam-6917	392	17	of	of	ADP
ejpam-6917	392	18	26	26	NUM
ejpam-6917	392	19	∇(d3gn+1)2i+1	∇(d3gn+1)2i+1	NOUN
ejpam-6917	392	20	=	=	PUNCT
ejpam-6917	392	21	(	(	PUNCT
ejpam-6917	392	22	3	3	NUM
ejpam-6917	392	23	64	64	NUM
ejpam-6917	392	24	∇(d3gn)i−1	∇(d3gn)i−1	NOUN
ejpam-6917	392	25	−	−	PROPN
ejpam-6917	392	26	24	24	NUM
ejpam-6917	392	27	64	64	NUM
ejpam-6917	392	28	∇(d3gn)i	∇(d3gn)i	NOUN
ejpam-6917	392	29	+	+	CCONJ
ejpam-6917	392	30	85	85	NUM
ejpam-6917	392	31	64	64	NUM
ejpam-6917	392	32	∇(d3gn)i+1	∇(d3gn)i+1	NOUN
ejpam-6917	392	33	−32	−32	VERB
ejpam-6917	392	34	64	64	NUM
ejpam-6917	392	35	∇(d3gni+2	∇(d3gni+2	NOUN
ejpam-6917	392	36	)	)	PUNCT
ejpam-6917	392	37	)	)	PUNCT
ejpam-6917	392	38	.	.	PUNCT
ejpam-6917	393	1	(	(	PUNCT
ejpam-6917	393	2	21	21	NUM
ejpam-6917	393	3	)	)	PUNCT
ejpam-6917	393	4	proof	proof	NOUN
ejpam-6917	393	5	.	.	PUNCT
ejpam-6917	394	1	from	from	ADP
ejpam-6917	394	2	lemma	lemma	PROPN
ejpam-6917	394	3	4	4	NUM
ejpam-6917	394	4	,	,	PUNCT
ejpam-6917	394	5	it	it	PRON
ejpam-6917	394	6	follows	follow	VERB
ejpam-6917	394	7	by	by	ADP
ejpam-6917	394	8	direct	direct	ADJ
ejpam-6917	394	9	calculation	calculation	NOUN
ejpam-6917	394	10	that	that	SCONJ
ejpam-6917	394	11	2−(n+1)∇(d3gn+1)2i+1	2−(n+1)∇(d3gn+1)2i+1	NUM
ejpam-6917	395	1	=	=	SYM
ejpam-6917	395	2	(	(	PUNCT
ejpam-6917	395	3	−3(d2gn+1)2i−1	−3(d2gn+1)2i−1	PROPN
ejpam-6917	395	4	+	+	CCONJ
ejpam-6917	395	5	32(d2gn+1)2i	32(d2gn+1)2i	NUM
ejpam-6917	395	6	−	−	ADP
ejpam-6917	395	7	58(d2gn+1)2i+1	58(d2gn+1)2i+1	NUM
ejpam-6917	395	8	+32(d2gn+1)2i+2	+32(d2gn+1)2i+2	NUM
ejpam-6917	395	9	−	−	NOUN
ejpam-6917	395	10	3(d2gn+1)2i+3	3(d2gn+1)2i+3	NUM
ejpam-6917	395	11	)	)	PUNCT
ejpam-6917	395	12	=	=	PUNCT
ejpam-6917	395	13	(	(	PUNCT
ejpam-6917	395	14	10	10	NUM
ejpam-6917	395	15	16	16	NUM
ejpam-6917	395	16	(	(	PUNCT
ejpam-6917	395	17	d2gn)i−1	d2gn)i−1	PROPN
ejpam-6917	395	18	+	+	CCONJ
ejpam-6917	395	19	20	20	NUM
ejpam-6917	395	20	16	16	NUM
ejpam-6917	395	21	(	(	PUNCT
ejpam-6917	395	22	d2gn)i	d2gn)i	PROPN
ejpam-6917	395	23	−	−	NUM
ejpam-6917	395	24	40	40	NUM
ejpam-6917	395	25	16	16	NUM
ejpam-6917	395	26	(	(	PUNCT
ejpam-6917	395	27	d2gn)i+1	d2gn)i+1	PROPN
ejpam-6917	395	28	−	−	PROPN
ejpam-6917	395	29	20	20	NUM
ejpam-6917	395	30	16	16	NUM
ejpam-6917	395	31	(	(	PUNCT
ejpam-6917	395	32	d2gn)i+2	d2gn)i+2	PROPN
ejpam-6917	395	33	+	+	CCONJ
ejpam-6917	395	34	30	30	NUM
ejpam-6917	395	35	16	16	NUM
ejpam-6917	395	36	(	(	PUNCT
ejpam-6917	395	37	d2gn)i+3)−	d2gn)i+3)−	PROPN
ejpam-6917	395	38	(	(	PUNCT
ejpam-6917	395	39	1−	1−	NUM
ejpam-6917	395	40	µ0	µ0	NOUN
ejpam-6917	395	41	)	)	PUNCT
ejpam-6917	395	42	32	32	NUM
ejpam-6917	395	43	2−n(130∇d3fn	2−n(130∇d3fn	NOUN
ejpam-6917	396	1	i	i	PRON
ejpam-6917	396	2	−290∇d3fn	−290∇d3fn	VERB
ejpam-6917	397	1	i+1	i+1	X
ejpam-6917	397	2	+	+	NOUN
ejpam-6917	397	3	190∇d3gni+2	190∇d3gni+2	NUM
ejpam-6917	397	4	−	−	NUM
ejpam-6917	397	5	30∇d3gni+3	30∇d3gni+3	NUM
ejpam-6917	397	6	)	)	PUNCT
ejpam-6917	397	7	∇(d3gn+1)2i+1	∇(d3gn+1)2i+1	NOUN
ejpam-6917	397	8	=	=	SYM
ejpam-6917	397	9	(	(	PUNCT
ejpam-6917	397	10	−30	−30	NOUN
ejpam-6917	397	11	32	32	NUM
ejpam-6917	397	12	∇(d3gn)i−1	∇(d3gn)i−1	NOUN
ejpam-6917	397	13	−	−	NUM
ejpam-6917	397	14	40	40	NUM
ejpam-6917	397	15	32	32	NUM
ejpam-6917	397	16	∇(d3gn)i	∇(d3gn)i	NOUN
ejpam-6917	397	17	+	+	CCONJ
ejpam-6917	397	18	62	62	NUM
ejpam-6917	397	19	32	32	NUM
ejpam-6917	397	20	∇(d3gn)i+1	∇(d3gn)i+1	NOUN
ejpam-6917	397	21	−	−	NUM
ejpam-6917	397	22	2	2	NUM
ejpam-6917	397	23	32	32	NUM
ejpam-6917	397	24	∇(d3gni+2	∇(d3gni+2	NOUN
ejpam-6917	397	25	)	)	PUNCT
ejpam-6917	397	26	)	)	PUNCT
ejpam-6917	397	27	.	.	PUNCT
ejpam-6917	398	1	2−(n+1)∇(d3gn+1)2i	2−(n+1)∇(d3gn+1)2i	NUM
ejpam-6917	398	2	=	=	SYM
ejpam-6917	398	3	(	(	PUNCT
ejpam-6917	398	4	10(d2gn+1)2i−1	10(d2gn+1)2i−1	NUM
ejpam-6917	398	5	−	−	PROPN
ejpam-6917	398	6	10(d2gn+1)2i	10(d2gn+1)2i	NUM
ejpam-6917	398	7	−	−	PROPN
ejpam-6917	398	8	10(d2gn+1)2i+1	10(d2gn+1)2i+1	NUM
ejpam-6917	398	9	+10(d2gn+1)2i+2	+10(d2gn+1)2i+2	NUM
ejpam-6917	398	10	)	)	PUNCT
ejpam-6917	399	1	=	=	PRON
ejpam-6917	399	2	(	(	PUNCT
ejpam-6917	399	3	30	30	NUM
ejpam-6917	399	4	16	16	NUM
ejpam-6917	399	5	(	(	PUNCT
ejpam-6917	399	6	d2gn)i−1	d2gn)i−1	PROPN
ejpam-6917	399	7	−	−	PROPN
ejpam-6917	399	8	20	20	NUM
ejpam-6917	399	9	16	16	NUM
ejpam-6917	399	10	(	(	PUNCT
ejpam-6917	399	11	d2gn)i	d2gn)i	PROPN
ejpam-6917	399	12	−	−	NUM
ejpam-6917	399	13	40	40	NUM
ejpam-6917	399	14	16	16	NUM
ejpam-6917	399	15	(	(	PUNCT
ejpam-6917	399	16	d2gn)i+1	d2gn)i+1	PROPN
ejpam-6917	399	17	+	+	NOUN
ejpam-6917	399	18	20	20	NUM
ejpam-6917	399	19	16	16	NUM
ejpam-6917	399	20	(	(	PUNCT
ejpam-6917	399	21	d2gn)i+2	d2gn)i+2	PROPN
ejpam-6917	399	22	+	+	CCONJ
ejpam-6917	399	23	10	10	NUM
ejpam-6917	399	24	16	16	NUM
ejpam-6917	399	25	(	(	PUNCT
ejpam-6917	399	26	d2gn)i+3)−	d2gn)i+3)−	PROPN
ejpam-6917	399	27	(	(	PUNCT
ejpam-6917	399	28	1−	1−	NUM
ejpam-6917	399	29	µ0	µ0	NOUN
ejpam-6917	399	30	)	)	PUNCT
ejpam-6917	399	31	32	32	NUM
ejpam-6917	399	32	2−n(−30∇d3fn	2−n(−30∇d3fn	NOUN
ejpam-6917	400	1	i	i	PRON
ejpam-6917	400	2	+190∇d3fn	+190∇d3fn	VERB
ejpam-6917	400	3	i+1	i+1	ADV
ejpam-6917	401	1	−	−	PROPN
ejpam-6917	401	2	290∇d3gni+2	290∇d3gni+2	NUM
ejpam-6917	401	3	+	+	NUM
ejpam-6917	401	4	130∇d3gni+3	130∇d3gni+3	NUM
ejpam-6917	401	5	)	)	PUNCT
ejpam-6917	402	1	∇(d3gn+1)2i	∇(d3gn+1)2i	PROPN
ejpam-6917	402	2	=	=	X
ejpam-6917	402	3	(	(	PUNCT
ejpam-6917	402	4	−	−	PROPN
ejpam-6917	402	5	2	2	NUM
ejpam-6917	402	6	32	32	NUM
ejpam-6917	402	7	∇(d3gn)i−1	∇(d3gn)i−1	NOUN
ejpam-6917	402	8	+	+	CCONJ
ejpam-6917	402	9	62	62	NUM
ejpam-6917	402	10	32	32	NUM
ejpam-6917	402	11	∇(d3gn)i	∇(d3gn)i	NOUN
ejpam-6917	402	12	−	−	PROPN
ejpam-6917	403	1	40	40	NUM
ejpam-6917	403	2	32	32	NUM
ejpam-6917	403	3	∇(d3gn)i+1	∇(d3gn)i+1	NOUN
ejpam-6917	403	4	−30	−30	NOUN
ejpam-6917	403	5	32	32	NUM
ejpam-6917	403	6	∇(d3gn)i+1	∇(d3gn)i+1	PROPN
ejpam-6917	403	7	)	)	PUNCT
ejpam-6917	403	8	.	.	PUNCT
ejpam-6917	404	1	definition	definition	NOUN
ejpam-6917	404	2	5	5	NUM
ejpam-6917	404	3	.	.	PUNCT
ejpam-6917	405	1	(	(	PUNCT
ejpam-6917	405	2	condition	condition	NOUN
ejpam-6917	405	3	-	-	PUNCT
ejpam-6917	405	4	c	c	NOUN
ejpam-6917	405	5	)	)	PUNCT
ejpam-6917	405	6	.	.	PUNCT
ejpam-6917	406	1	given	give	VERB
ejpam-6917	406	2	a	a	DET
ejpam-6917	406	3	number	number	NOUN
ejpam-6917	406	4	µ0	µ0	NOUN
ejpam-6917	406	5	as	as	ADP
ejpam-6917	406	6	in	in	ADP
ejpam-6917	406	7	(	(	PUNCT
ejpam-6917	406	8	2	2	NUM
ejpam-6917	406	9	)	)	PUNCT
ejpam-6917	406	10	,	,	PUNCT
ejpam-6917	406	11	and	and	CCONJ
ejpam-6917	406	12	an	an	DET
ejpam-6917	406	13	initial	initial	ADJ
ejpam-6917	406	14	sequence	sequence	NOUN
ejpam-6917	406	15	gn0	gn0	NOUN
ejpam-6917	406	16	defined	define	VERB
ejpam-6917	406	17	on	on	ADP
ejpam-6917	406	18	2−n0z	2−n0z	NUM
ejpam-6917	406	19	,	,	PUNCT
ejpam-6917	406	20	we	we	PRON
ejpam-6917	406	21	say	say	VERB
ejpam-6917	406	22	gn0	gn0	NOUN
ejpam-6917	406	23	fulfills	fulfill	VERB
ejpam-6917	406	24	’	'	PUNCT
ejpam-6917	406	25	condition	condition	NOUN
ejpam-6917	406	26	-	-	PUNCT
ejpam-6917	406	27	c	c	NOUN
ejpam-6917	406	28	’	'	PUNCT
ejpam-6917	406	29	if	if	SCONJ
ejpam-6917	406	30	(	(	PUNCT
ejpam-6917	406	31	d2gn0)j	d2gn0)j	PROPN
ejpam-6917	406	32	≥	≥	X
ejpam-6917	406	33	(	(	PUNCT
ejpam-6917	406	34	1−	1−	NUM
ejpam-6917	406	35	µ0	µ0	NOUN
ejpam-6917	406	36	)	)	PUNCT
ejpam-6917	406	37	k	k	NOUN
ejpam-6917	406	38	2−n0	2−n0	NUM
ejpam-6917	406	39	|∇(d3gn)j+1|	|∇(d3gn)j+1|	NOUN
ejpam-6917	406	40	,	,	PUNCT
ejpam-6917	406	41	∀j	∀j	PROPN
ejpam-6917	406	42	∈	∈	PROPN
ejpam-6917	406	43	z.	z.	PROPN
ejpam-6917	406	44	(	(	PUNCT
ejpam-6917	406	45	22	22	NUM
ejpam-6917	406	46	)	)	PUNCT
ejpam-6917	406	47	where	where	SCONJ
ejpam-6917	406	48	,	,	PUNCT
ejpam-6917	406	49	k	k	PROPN
ejpam-6917	406	50	>	>	X
ejpam-6917	406	51	0	0	X
ejpam-6917	406	52	.	.	PUNCT
ejpam-6917	406	53	theorem	theorem	ADJ
ejpam-6917	406	54	7	7	NUM
ejpam-6917	406	55	.	.	PUNCT
ejpam-6917	406	56	suppose	suppose	VERB
ejpam-6917	406	57	sp	sp	PART
ejpam-6917	406	58	be	be	AUX
ejpam-6917	406	59	the	the	DET
ejpam-6917	406	60	ss	ss	NOUN
ejpam-6917	406	61	in	in	ADP
ejpam-6917	406	62	(	(	PUNCT
ejpam-6917	406	63	1	1	NUM
ejpam-6917	406	64	)	)	PUNCT
ejpam-6917	406	65	with	with	ADP
ejpam-6917	406	66	µ0	µ0	NOUN
ejpam-6917	406	67	in	in	ADP
ejpam-6917	406	68	(	(	PUNCT
ejpam-6917	406	69	14	14	NUM
ejpam-6917	406	70	)	)	PUNCT
ejpam-6917	406	71	.	.	PUNCT
ejpam-6917	407	1	assume	assume	VERB
ejpam-6917	407	2	that	that	SCONJ
ejpam-6917	407	3	the	the	DET
ejpam-6917	407	4	initial	initial	ADJ
ejpam-6917	407	5	sequence	sequence	NOUN
ejpam-6917	407	6	gn0	gn0	NOUN
ejpam-6917	407	7	be	be	AUX
ejpam-6917	407	8	connected	connect	VERB
ejpam-6917	407	9	to	to	ADP
ejpam-6917	407	10	2−n0z	2−n0z	NUM
ejpam-6917	407	11	,	,	PUNCT
ejpam-6917	407	12	and	and	CCONJ
ejpam-6917	407	13	suppose	suppose	VERB
ejpam-6917	407	14	that	that	SCONJ
ejpam-6917	407	15	it	it	PRON
ejpam-6917	407	16	fulfills	fulfill	VERB
ejpam-6917	407	17	the	the	DET
ejpam-6917	407	18	condition	condition	NOUN
ejpam-6917	407	19	-	-	PUNCT
ejpam-6917	407	20	c.	c.	NOUN
ejpam-6917	407	21	then	then	ADV
ejpam-6917	407	22	,	,	PUNCT
ejpam-6917	407	23	for	for	ADP
ejpam-6917	407	24	any	any	DET
ejpam-6917	407	25	n	n	PROPN
ejpam-6917	407	26	>	>	X
ejpam-6917	407	27	n0	n0	PROPN
ejpam-6917	407	28	,	,	PUNCT
ejpam-6917	407	29	(	(	PUNCT
ejpam-6917	407	30	∆gn)i	∆gn)i	NOUN
ejpam-6917	407	31	≥	≥	NOUN
ejpam-6917	407	32	0	0	NUM
ejpam-6917	407	33	for	for	ADP
ejpam-6917	407	34	i	i	PROPN
ejpam-6917	407	35	∈	∈	PROPN
ejpam-6917	407	36	z	z	PROPN
ejpam-6917	407	37	,	,	PUNCT
ejpam-6917	407	38	which	which	PRON
ejpam-6917	407	39	implies	imply	VERB
ejpam-6917	407	40	that	that	SCONJ
ejpam-6917	407	41	the	the	DET
ejpam-6917	407	42	sp	sp	ADP
ejpam-6917	407	43	-scheme	-scheme	PROPN
ejpam-6917	407	44	preserves	preserve	VERB
ejpam-6917	407	45	the	the	DET
ejpam-6917	407	46	convexity	convexity	NOUN
ejpam-6917	407	47	.	.	PUNCT
ejpam-6917	408	1	f.	f.	PROPN
ejpam-6917	408	2	s.	s.	PROPN
ejpam-6917	408	3	alshammari	alshammari	PROPN
ejpam-6917	408	4	et	et	PROPN
ejpam-6917	408	5	al	al	PROPN
ejpam-6917	408	6	.	.	PUNCT
ejpam-6917	408	7	/	/	SYM
ejpam-6917	408	8	eur	eur	PROPN
ejpam-6917	408	9	.	.	PUNCT
ejpam-6917	409	1	j.	j.	PROPN
ejpam-6917	409	2	pure	pure	PROPN
ejpam-6917	409	3	appl	appl	PROPN
ejpam-6917	409	4	.	.	PROPN
ejpam-6917	409	5	math	math	PROPN
ejpam-6917	409	6	,	,	PUNCT
ejpam-6917	409	7	18	18	NUM
ejpam-6917	409	8	(	(	PUNCT
ejpam-6917	409	9	4	4	NUM
ejpam-6917	409	10	)	)	PUNCT
ejpam-6917	409	11	(	(	PUNCT
ejpam-6917	409	12	2025	2025	NUM
ejpam-6917	409	13	)	)	PUNCT
ejpam-6917	409	14	,	,	PUNCT
ejpam-6917	409	15	6917	6917	NUM
ejpam-6917	409	16	18	18	NUM
ejpam-6917	409	17	of	of	ADP
ejpam-6917	409	18	26	26	NUM
ejpam-6917	409	19	table	table	NOUN
ejpam-6917	409	20	1	1	NUM
ejpam-6917	409	21	:	:	PUNCT
ejpam-6917	409	22	maximum	maximum	ADJ
ejpam-6917	409	23	errors	error	NOUN
ejpam-6917	409	24	in	in	ADP
ejpam-6917	409	25	l∞-norm	l∞-norm	NOUN
ejpam-6917	409	26	and	and	CCONJ
ejpam-6917	409	27	corresponding	corresponding	ADJ
ejpam-6917	409	28	order	order	NOUN
ejpam-6917	409	29	of	of	ADP
ejpam-6917	409	30	approximations	approximation	NOUN
ejpam-6917	409	31	for	for	ADP
ejpam-6917	409	32	g1	g1	NOUN
ejpam-6917	409	33	and	and	CCONJ
ejpam-6917	409	34	g2	g2	PROPN
ejpam-6917	409	35	given	give	VERB
ejpam-6917	409	36	in	in	ADP
ejpam-6917	409	37	example	example	NOUN
ejpam-6917	409	38	1	1	NUM
ejpam-6917	409	39	.	.	PUNCT
ejpam-6917	409	40	initial	initial	ADJ
ejpam-6917	409	41	sampling	sampling	NOUN
ejpam-6917	409	42	interval	interval	NOUN
ejpam-6917	409	43	g1	g1	PROPN
ejpam-6917	409	44	∈	∈	PROPN
ejpam-6917	409	45	w	w	ADP
ejpam-6917	409	46	6	6	NUM
ejpam-6917	409	47	∞(r	∞(r	NOUN
ejpam-6917	409	48	)	)	PUNCT
ejpam-6917	409	49	g2	g2	PROPN
ejpam-6917	409	50	∈	∈	PROPN
ejpam-6917	410	1	w	w	ADP
ejpam-6917	410	2	6	6	NUM
ejpam-6917	410	3	∞(r	∞(r	NOUN
ejpam-6917	410	4	)	)	PUNCT
ejpam-6917	410	5	||.||∞	||.||∞	PROPN
ejpam-6917	410	6	error	error	NOUN
ejpam-6917	410	7	order	order	NOUN
ejpam-6917	410	8	||.||∞	||.||∞	PROPN
ejpam-6917	410	9	error	error	NOUN
ejpam-6917	410	10	order	order	NOUN
ejpam-6917	410	11	2−1	2−1	NUM
ejpam-6917	410	12	5.9981e−05	5.9981e−05	NUM
ejpam-6917	410	13	–	–	PUNCT
ejpam-6917	410	14	5.8756e−05	5.8756e−05	NUM
ejpam-6917	410	15	–	–	PUNCT
ejpam-6917	411	1	2−2	2−2	NUM
ejpam-6917	411	2	9.37e−07	9.37e−07	NUM
ejpam-6917	411	3	6.0	6.0	NUM
ejpam-6917	411	4	9.32e−07	9.32e−07	NUM
ejpam-6917	411	5	5.9	5.9	NUM
ejpam-6917	411	6	2−3	2−3	NUM
ejpam-6917	411	7	1.5e−08	1.5e−08	NUM
ejpam-6917	411	8	6.0	6.0	NUM
ejpam-6917	411	9	1.5e−08	1.5e−08	NUM
ejpam-6917	411	10	6.0	6.0	NUM
ejpam-6917	411	11	2−4	2−4	NUM
ejpam-6917	411	12	2.288e−10	2.288e−10	NUM
ejpam-6917	411	13	6.0	6.0	NUM
ejpam-6917	411	14	2.3e−10	2.3e−10	NUM
ejpam-6917	411	15	6.0	6.0	NUM
ejpam-6917	411	16	2−5	2−5	NUM
ejpam-6917	411	17	3.6e−12	3.6e−12	NUM
ejpam-6917	411	18	6.0	6.0	NUM
ejpam-6917	411	19	3.7e−12	3.7e−12	NUM
ejpam-6917	411	20	6.0	6.0	NUM
ejpam-6917	411	21	2−6	2−6	NUM
ejpam-6917	411	22	5.59e−14	5.59e−14	NUM
ejpam-6917	411	23	6.0	6.0	NUM
ejpam-6917	411	24	5.6e−14	5.6e−14	NUM
ejpam-6917	411	25	6.0	6.0	NUM
ejpam-6917	411	26	note	note	NOUN
ejpam-6917	411	27	:	:	PUNCT
ejpam-6917	411	28	the	the	DET
ejpam-6917	411	29	results	result	NOUN
ejpam-6917	411	30	confirm	confirm	VERB
ejpam-6917	411	31	that	that	SCONJ
ejpam-6917	411	32	both	both	DET
ejpam-6917	411	33	test	test	NOUN
ejpam-6917	411	34	functions	function	NOUN
ejpam-6917	411	35	g1	g1	PROPN
ejpam-6917	411	36	and	and	CCONJ
ejpam-6917	411	37	g2	g2	PROPN
ejpam-6917	411	38	achieve	achieve	VERB
ejpam-6917	411	39	sixth	sixth	ADJ
ejpam-6917	411	40	-	-	PUNCT
ejpam-6917	411	41	order	order	NOUN
ejpam-6917	411	42	convergence	convergence	NOUN
ejpam-6917	411	43	in	in	ADP
ejpam-6917	411	44	the	the	DET
ejpam-6917	411	45	l∞-norm	l∞-norm	NOUN
ejpam-6917	411	46	as	as	SCONJ
ejpam-6917	411	47	the	the	DET
ejpam-6917	411	48	sampling	sample	VERB
ejpam-6917	411	49	interval	interval	NOUN
ejpam-6917	411	50	decreases	decrease	VERB
ejpam-6917	411	51	.	.	PUNCT
ejpam-6917	412	1	proof	proof	NOUN
ejpam-6917	412	2	.	.	PUNCT
ejpam-6917	413	1	applying	apply	VERB
ejpam-6917	413	2	the	the	DET
ejpam-6917	413	3	principle	principle	NOUN
ejpam-6917	413	4	of	of	ADP
ejpam-6917	413	5	mathematical	mathematical	ADJ
ejpam-6917	413	6	induction	induction	NOUN
ejpam-6917	413	7	,	,	PUNCT
ejpam-6917	413	8	prove	prove	VERB
ejpam-6917	413	9	that	that	SCONJ
ejpam-6917	413	10	for	for	ADP
ejpam-6917	413	11	any	any	DET
ejpam-6917	413	12	n	n	PRON
ejpam-6917	413	13	≥	≥	NOUN
ejpam-6917	413	14	n0	n0	NUM
ejpam-6917	413	15	,	,	PUNCT
ejpam-6917	413	16	(	(	PUNCT
ejpam-6917	413	17	d2gn)j	d2gn)j	PROPN
ejpam-6917	413	18	≥	≥	NOUN
ejpam-6917	413	19	(	(	PUNCT
ejpam-6917	413	20	1−	1−	NUM
ejpam-6917	413	21	µ0	µ0	NOUN
ejpam-6917	413	22	)	)	PUNCT
ejpam-6917	413	23	k	k	NOUN
ejpam-6917	413	24	2−n|∇(d3gn)j+1|	2−n|∇(d3gn)j+1|	NUM
ejpam-6917	413	25	,	,	PUNCT
ejpam-6917	413	26	∀	∀	X
ejpam-6917	413	27	j	j	PROPN
ejpam-6917	413	28	∈	∈	PROPN
ejpam-6917	413	29	z.	z.	PROPN
ejpam-6917	413	30	(	(	PUNCT
ejpam-6917	413	31	23	23	NUM
ejpam-6917	413	32	)	)	PUNCT
ejpam-6917	413	33	the	the	DET
ejpam-6917	413	34	initial	initial	ADJ
ejpam-6917	413	35	sequence	sequence	NOUN
ejpam-6917	413	36	gn0	gn0	NOUN
ejpam-6917	413	37	satisfies	satisfie	NOUN
ejpam-6917	413	38	by	by	ADP
ejpam-6917	413	39	hypothesis	hypothesis	NOUN
ejpam-6917	413	40	.	.	PUNCT
ejpam-6917	414	1	assuming	assume	VERB
ejpam-6917	414	2	the	the	DET
ejpam-6917	414	3	inequality	inequality	NOUN
ejpam-6917	414	4	is	be	AUX
ejpam-6917	414	5	true	true	ADJ
ejpam-6917	414	6	for	for	ADP
ejpam-6917	414	7	some	some	DET
ejpam-6917	414	8	i.	i.	NOUN
ejpam-6917	414	9	now	now	ADV
ejpam-6917	414	10	,	,	PUNCT
ejpam-6917	414	11	we	we	PRON
ejpam-6917	414	12	check	check	VERB
ejpam-6917	414	13	if	if	SCONJ
ejpam-6917	414	14	it	it	PRON
ejpam-6917	414	15	is	be	AUX
ejpam-6917	414	16	true	true	ADJ
ejpam-6917	414	17	for	for	ADP
ejpam-6917	414	18	i	i	PRON
ejpam-6917	414	19	+	+	NOUN
ejpam-6917	414	20	1	1	NUM
ejpam-6917	414	21	,	,	PUNCT
ejpam-6917	414	22	starting	start	VERB
ejpam-6917	414	23	with	with	ADP
ejpam-6917	414	24	the	the	DET
ejpam-6917	414	25	case	case	NOUN
ejpam-6917	414	26	where	where	SCONJ
ejpam-6917	414	27	j	j	PROPN
ejpam-6917	414	28	=	=	NOUN
ejpam-6917	414	29	2i	2i	NUM
ejpam-6917	414	30	.	.	PUNCT
ejpam-6917	415	1	by	by	ADP
ejpam-6917	415	2	applying	apply	VERB
ejpam-6917	415	3	lemma	lemma	PROPN
ejpam-6917	415	4	4	4	NUM
ejpam-6917	415	5	and	and	CCONJ
ejpam-6917	415	6	5	5	NUM
ejpam-6917	415	7	,	,	PUNCT
ejpam-6917	415	8	we	we	PRON
ejpam-6917	415	9	deduce	deduce	VERB
ejpam-6917	415	10	(	(	PUNCT
ejpam-6917	415	11	d2gn+1)2i	d2gn+1)2i	ADJ
ejpam-6917	415	12	−	−	PROPN
ejpam-6917	415	13	2−n−1	2−n−1	NUM
ejpam-6917	415	14	(	(	PUNCT
ejpam-6917	415	15	1−µ0	1−µ0	NUM
ejpam-6917	415	16	)	)	PUNCT
ejpam-6917	416	1	k	k	NOUN
ejpam-6917	417	1	|	|	ADV
ejpam-6917	417	2	∇(d3gn+1)2i+1	∇(d3gn+1)2i+1	ADV
ejpam-6917	417	3	|≥	|≥	ADJ
ejpam-6917	417	4	4	4	NUM
ejpam-6917	417	5	16((d	16((d	NUM
ejpam-6917	417	6	2gn)i−1	2gn)i−1	NUM
ejpam-6917	417	7	−	−	NOUN
ejpam-6917	417	8	2−n	2−n	NUM
ejpam-6917	417	9	(	(	PUNCT
ejpam-6917	417	10	1−µ0	1−µ0	NUM
ejpam-6917	417	11	)	)	PUNCT
ejpam-6917	417	12	k	k	NOUN
ejpam-6917	418	1	|∇(d3gn)i−1|	|∇(d3gn)i−1|	NOUN
ejpam-6917	418	2	)	)	PUNCT
ejpam-6917	418	3	+	+	CCONJ
ejpam-6917	418	4	8	8	NUM
ejpam-6917	418	5	16((d	16((d	NUM
ejpam-6917	418	6	2gn)i	2gn)i	NUM
ejpam-6917	418	7	−	−	PROPN
ejpam-6917	418	8	2−n	2−n	NUM
ejpam-6917	418	9	(	(	PUNCT
ejpam-6917	418	10	1−µ0	1−µ0	NUM
ejpam-6917	418	11	)	)	PUNCT
ejpam-6917	418	12	k	k	NOUN
ejpam-6917	418	13	|∇(d3gn)i|	|∇(d3gn)i|	NOUN
ejpam-6917	418	14	)	)	PUNCT
ejpam-6917	418	15	+	+	CCONJ
ejpam-6917	418	16	4	4	NUM
ejpam-6917	418	17	16((d	16((d	NUM
ejpam-6917	418	18	2gn)i+1	2gn)i+1	NUM
ejpam-6917	418	19	−	−	PROPN
ejpam-6917	418	20	2−n	2−n	NUM
ejpam-6917	418	21	(	(	PUNCT
ejpam-6917	418	22	1−µ0	1−µ0	NUM
ejpam-6917	418	23	)	)	PUNCT
ejpam-6917	418	24	k	k	NOUN
ejpam-6917	418	25	|∇(d3gn)i+1|	|∇(d3gn)i+1|	NOUN
ejpam-6917	418	26	)	)	PUNCT
ejpam-6917	418	27	.	.	PUNCT
ejpam-6917	419	1	according	accord	VERB
ejpam-6917	419	2	to	to	ADP
ejpam-6917	419	3	our	our	PRON
ejpam-6917	419	4	inductive	inductive	ADJ
ejpam-6917	419	5	hypothesis	hypothesis	NOUN
ejpam-6917	419	6	,	,	PUNCT
ejpam-6917	419	7	the	the	DET
ejpam-6917	419	8	final	final	ADJ
ejpam-6917	419	9	result	result	NOUN
ejpam-6917	419	10	is	be	AUX
ejpam-6917	419	11	positive	positive	ADJ
ejpam-6917	419	12	.	.	PUNCT
ejpam-6917	420	1	we	we	PRON
ejpam-6917	420	2	now	now	ADV
ejpam-6917	420	3	turn	turn	VERB
ejpam-6917	420	4	j	j	PROPN
ejpam-6917	420	5	=	=	SYM
ejpam-6917	420	6	2i−1	2i−1	NUM
ejpam-6917	420	7	,	,	PUNCT
ejpam-6917	420	8	and	and	CCONJ
ejpam-6917	420	9	use	use	VERB
ejpam-6917	420	10	lemma	lemma	PROPN
ejpam-6917	420	11	5	5	NUM
ejpam-6917	420	12	to	to	PART
ejpam-6917	420	13	drive	drive	VERB
ejpam-6917	420	14	(	(	PUNCT
ejpam-6917	420	15	d2gn+1)j	d2gn+1)j	PROPN
ejpam-6917	420	16	−	−	PROPN
ejpam-6917	420	17	2−n−1	2−n−1	NUM
ejpam-6917	420	18	(	(	PUNCT
ejpam-6917	420	19	1−µ0	1−µ0	NUM
ejpam-6917	420	20	)	)	PUNCT
ejpam-6917	421	1	k	k	NOUN
ejpam-6917	422	1	|	|	ADV
ejpam-6917	422	2	∇(d3gn+1)j	∇(d3gn+1)j	ADV
ejpam-6917	422	3	|≥	|≥	ADJ
ejpam-6917	422	4	1	1	NUM
ejpam-6917	422	5	16((d	16((d	NUM
ejpam-6917	422	6	2gn)i−1	2gn)i−1	NUM
ejpam-6917	422	7	−	−	NOUN
ejpam-6917	422	8	2−n	2−n	NUM
ejpam-6917	422	9	(	(	PUNCT
ejpam-6917	422	10	1−µ0	1−µ0	NUM
ejpam-6917	422	11	)	)	PUNCT
ejpam-6917	422	12	k	k	NOUN
ejpam-6917	423	1	|∇(d3gn)i−1|	|∇(d3gn)i−1|	NOUN
ejpam-6917	423	2	)	)	PUNCT
ejpam-6917	423	3	+	+	CCONJ
ejpam-6917	423	4	7	7	NUM
ejpam-6917	423	5	16((d	16((d	NUM
ejpam-6917	423	6	2gn)i	2gn)i	NUM
ejpam-6917	423	7	−	−	PROPN
ejpam-6917	423	8	2−n	2−n	NUM
ejpam-6917	423	9	(	(	PUNCT
ejpam-6917	423	10	1−µ0	1−µ0	NUM
ejpam-6917	423	11	)	)	PUNCT
ejpam-6917	423	12	k	k	NOUN
ejpam-6917	423	13	|∇(d3gn)i|	|∇(d3gn)i|	NOUN
ejpam-6917	423	14	)	)	PUNCT
ejpam-6917	423	15	+	+	CCONJ
ejpam-6917	423	16	7	7	NUM
ejpam-6917	423	17	16((d	16((d	NUM
ejpam-6917	423	18	2gn)i+1	2gn)i+1	NUM
ejpam-6917	423	19	−	−	PROPN
ejpam-6917	423	20	2−n	2−n	NUM
ejpam-6917	423	21	(	(	PUNCT
ejpam-6917	423	22	1−µ0	1−µ0	NUM
ejpam-6917	423	23	)	)	PUNCT
ejpam-6917	423	24	k	k	NOUN
ejpam-6917	423	25	|∇(d3gn)i+1|	|∇(d3gn)i+1|	NOUN
ejpam-6917	423	26	)	)	PUNCT
ejpam-6917	424	1	+	+	CCONJ
ejpam-6917	424	2	1	1	NUM
ejpam-6917	424	3	16((d	16((d	NUM
ejpam-6917	424	4	2gn)i+2	2gn)i+2	NUM
ejpam-6917	424	5	−	−	PROPN
ejpam-6917	424	6	2−n	2−n	NUM
ejpam-6917	424	7	(	(	PUNCT
ejpam-6917	424	8	1−µ0	1−µ0	NUM
ejpam-6917	424	9	)	)	PUNCT
ejpam-6917	424	10	k	k	NOUN
ejpam-6917	424	11	|∇(d3gn)i+2|	|∇(d3gn)i+2|	NOUN
ejpam-6917	424	12	)	)	PUNCT
ejpam-6917	424	13	.	.	PUNCT
ejpam-6917	425	1	based	base	VERB
ejpam-6917	425	2	on	on	ADP
ejpam-6917	425	3	the	the	DET
ejpam-6917	425	4	assumption	assumption	NOUN
ejpam-6917	425	5	for	for	ADP
ejpam-6917	425	6	the	the	DET
ejpam-6917	425	7	case	case	NOUN
ejpam-6917	425	8	n	n	CCONJ
ejpam-6917	425	9	,	,	PUNCT
ejpam-6917	425	10	we	we	PRON
ejpam-6917	425	11	can	can	AUX
ejpam-6917	425	12	conclude	conclude	VERB
ejpam-6917	425	13	that	that	SCONJ
ejpam-6917	425	14	the	the	DET
ejpam-6917	425	15	final	final	ADJ
ejpam-6917	425	16	term	term	NOUN
ejpam-6917	425	17	is	be	AUX
ejpam-6917	425	18	positive	positive	ADJ
ejpam-6917	425	19	,	,	PUNCT
ejpam-6917	425	20	thereby	thereby	ADV
ejpam-6917	425	21	completing	complete	VERB
ejpam-6917	425	22	the	the	DET
ejpam-6917	425	23	proof	proof	NOUN
ejpam-6917	425	24	.	.	PUNCT
ejpam-6917	426	1	6	6	X
ejpam-6917	426	2	.	.	X
ejpam-6917	426	3	numerical	numerical	ADJ
ejpam-6917	426	4	applications	application	NOUN
ejpam-6917	426	5	this	this	DET
ejpam-6917	426	6	section	section	NOUN
ejpam-6917	426	7	presents	present	VERB
ejpam-6917	426	8	numerical	numerical	ADJ
ejpam-6917	426	9	experiments	experiment	NOUN
ejpam-6917	426	10	to	to	PART
ejpam-6917	426	11	demonstrate	demonstrate	VERB
ejpam-6917	426	12	the	the	DET
ejpam-6917	426	13	effectiveness	effectiveness	NOUN
ejpam-6917	426	14	of	of	ADP
ejpam-6917	426	15	the	the	DET
ejpam-6917	426	16	proposed	propose	VERB
ejpam-6917	426	17	subdivision	subdivision	NOUN
ejpam-6917	426	18	schemes	scheme	NOUN
ejpam-6917	426	19	.	.	PUNCT
ejpam-6917	427	1	f.	f.	PROPN
ejpam-6917	427	2	s.	s.	PROPN
ejpam-6917	427	3	alshammari	alshammari	PROPN
ejpam-6917	427	4	et	et	PROPN
ejpam-6917	427	5	al	al	PROPN
ejpam-6917	427	6	.	.	PUNCT
ejpam-6917	427	7	/	/	SYM
ejpam-6917	427	8	eur	eur	PROPN
ejpam-6917	427	9	.	.	PUNCT
ejpam-6917	428	1	j.	j.	PROPN
ejpam-6917	428	2	pure	pure	PROPN
ejpam-6917	428	3	appl	appl	PROPN
ejpam-6917	428	4	.	.	PROPN
ejpam-6917	428	5	math	math	PROPN
ejpam-6917	428	6	,	,	PUNCT
ejpam-6917	428	7	18	18	NUM
ejpam-6917	428	8	(	(	PUNCT
ejpam-6917	428	9	4	4	NUM
ejpam-6917	428	10	)	)	PUNCT
ejpam-6917	428	11	(	(	PUNCT
ejpam-6917	428	12	2025	2025	NUM
ejpam-6917	428	13	)	)	PUNCT
ejpam-6917	428	14	,	,	PUNCT
ejpam-6917	428	15	6917	6917	NUM
ejpam-6917	428	16	19	19	NUM
ejpam-6917	428	17	of	of	ADP
ejpam-6917	428	18	26	26	NUM
ejpam-6917	428	19	example	example	NOUN
ejpam-6917	428	20	1	1	NUM
ejpam-6917	428	21	.	.	PUNCT
ejpam-6917	429	1	(	(	PUNCT
ejpam-6917	429	2	order	order	NOUN
ejpam-6917	429	3	of	of	ADP
ejpam-6917	429	4	approximation	approximation	NOUN
ejpam-6917	429	5	)	)	PUNCT
ejpam-6917	429	6	to	to	PART
ejpam-6917	429	7	verify	verify	VERB
ejpam-6917	429	8	the	the	DET
ejpam-6917	429	9	order	order	NOUN
ejpam-6917	429	10	of	of	ADP
ejpam-6917	429	11	approximation	approximation	NOUN
ejpam-6917	429	12	of	of	ADP
ejpam-6917	429	13	sp	sp	ADP
ejpam-6917	429	14	-scheme	-scheme	NOUN
ejpam-6917	429	15	given	give	VERB
ejpam-6917	429	16	in	in	ADP
ejpam-6917	429	17	equation	equation	NOUN
ejpam-6917	429	18	(	(	PUNCT
ejpam-6917	429	19	1	1	NUM
ejpam-6917	429	20	)	)	PUNCT
ejpam-6917	429	21	,	,	PUNCT
ejpam-6917	429	22	we	we	PRON
ejpam-6917	429	23	consider	consider	VERB
ejpam-6917	429	24	the	the	DET
ejpam-6917	429	25	following	follow	VERB
ejpam-6917	429	26	two	two	NUM
ejpam-6917	429	27	smooth	smooth	ADJ
ejpam-6917	429	28	functions	function	NOUN
ejpam-6917	429	29	:	:	PUNCT
ejpam-6917	429	30	g1(x	g1(x	NOUN
ejpam-6917	429	31	)	)	PUNCT
ejpam-6917	429	32	=	=	SYM
ejpam-6917	429	33	x6	x6	PROPN
ejpam-6917	429	34	,	,	PUNCT
ejpam-6917	429	35	g2(x	g2(x	NOUN
ejpam-6917	429	36	)	)	PUNCT
ejpam-6917	429	37	=	=	SYM
ejpam-6917	430	1	x6	x6	PROPN
ejpam-6917	430	2	cos(x	cos(x	PROPN
ejpam-6917	430	3	)	)	PUNCT
ejpam-6917	430	4	.	.	PUNCT
ejpam-6917	431	1	the	the	DET
ejpam-6917	431	2	initial	initial	ADJ
ejpam-6917	431	3	data	datum	NOUN
ejpam-6917	431	4	sequences	sequence	NOUN
ejpam-6917	431	5	are	be	AUX
ejpam-6917	431	6	sampled	sample	VERB
ejpam-6917	431	7	from	from	ADP
ejpam-6917	431	8	each	each	DET
ejpam-6917	431	9	function	function	NOUN
ejpam-6917	431	10	over	over	ADP
ejpam-6917	431	11	the	the	DET
ejpam-6917	431	12	interval	interval	NOUN
ejpam-6917	431	13	[	[	X
ejpam-6917	431	14	0	0	NUM
ejpam-6917	431	15	,	,	PUNCT
ejpam-6917	431	16	0.2	0.2	NUM
ejpam-6917	431	17	]	]	PUNCT
ejpam-6917	431	18	at	at	ADP
ejpam-6917	431	19	sampling	sample	VERB
ejpam-6917	431	20	densities	density	NOUN
ejpam-6917	431	21	2−n0	2−n0	NUM
ejpam-6917	431	22	,	,	PUNCT
ejpam-6917	431	23	where	where	SCONJ
ejpam-6917	431	24	n0	n0	X
ejpam-6917	431	25	=	=	SYM
ejpam-6917	431	26	0	0	PROPN
ejpam-6917	431	27	,	,	PUNCT
ejpam-6917	431	28	.	.	PUNCT
ejpam-6917	431	29	.	.	PUNCT
ejpam-6917	432	1	.	.	PUNCT
ejpam-6917	433	1	,	,	PUNCT
ejpam-6917	433	2	6	6	X
ejpam-6917	433	3	.	.	X
ejpam-6917	434	1	for	for	ADP
ejpam-6917	434	2	every	every	DET
ejpam-6917	434	3	refinement	refinement	NOUN
ejpam-6917	434	4	level	level	NOUN
ejpam-6917	434	5	,	,	PUNCT
ejpam-6917	434	6	the	the	DET
ejpam-6917	434	7	parameter	parameter	NOUN
ejpam-6917	434	8	µ0	µ0	PROPN
ejpam-6917	434	9	is	be	AUX
ejpam-6917	434	10	selected	select	VERB
ejpam-6917	434	11	as	as	ADP
ejpam-6917	434	12	µ0	µ0	NOUN
ejpam-6917	434	13	=	=	NOUN
ejpam-6917	434	14	2−n0	2−n0	NUM
ejpam-6917	434	15	,	,	PUNCT
ejpam-6917	434	16	corresponding	correspond	VERB
ejpam-6917	434	17	to	to	ADP
ejpam-6917	434	18	the	the	DET
ejpam-6917	434	19	choice	choice	NOUN
ejpam-6917	434	20	τ	τ	X
ejpam-6917	434	21	=	=	SYM
ejpam-6917	434	22	1	1	NUM
ejpam-6917	434	23	in	in	ADP
ejpam-6917	434	24	equation	equation	NOUN
ejpam-6917	434	25	(	(	PUNCT
ejpam-6917	434	26	2	2	NUM
ejpam-6917	434	27	)	)	PUNCT
ejpam-6917	434	28	.	.	PUNCT
ejpam-6917	435	1	table	table	NOUN
ejpam-6917	435	2	1	1	NUM
ejpam-6917	435	3	presents	present	VERB
ejpam-6917	435	4	the	the	DET
ejpam-6917	435	5	computed	computed	ADJ
ejpam-6917	435	6	maximum	maximum	ADJ
ejpam-6917	435	7	errors	error	NOUN
ejpam-6917	435	8	,	,	PUNCT
ejpam-6917	435	9	based	base	VERB
ejpam-6917	435	10	on	on	ADP
ejpam-6917	435	11	the	the	DET
ejpam-6917	435	12	l∞-norms	l∞-norm	NOUN
ejpam-6917	435	13	,	,	PUNCT
ejpam-6917	435	14	along	along	ADP
ejpam-6917	435	15	with	with	ADP
ejpam-6917	435	16	the	the	DET
ejpam-6917	435	17	estimated	estimate	VERB
ejpam-6917	435	18	rate	rate	NOUN
ejpam-6917	435	19	of	of	ADP
ejpam-6917	435	20	convergence	convergence	NOUN
ejpam-6917	435	21	.	.	PUNCT
ejpam-6917	436	1	the	the	DET
ejpam-6917	436	2	functions	function	NOUN
ejpam-6917	436	3	g1	g1	PROPN
ejpam-6917	436	4	and	and	CCONJ
ejpam-6917	436	5	g2	g2	PROPN
ejpam-6917	436	6	belong	belong	VERB
ejpam-6917	436	7	to	to	ADP
ejpam-6917	436	8	the	the	DET
ejpam-6917	436	9	sobolev	sobolev	NOUN
ejpam-6917	436	10	space	space	NOUN
ejpam-6917	436	11	and	and	CCONJ
ejpam-6917	436	12	achieve	achieve	VERB
ejpam-6917	436	13	the	the	DET
ejpam-6917	436	14	optimal	optimal	ADJ
ejpam-6917	436	15	order	order	NOUN
ejpam-6917	436	16	of	of	ADP
ejpam-6917	436	17	approximation	approximation	NOUN
ejpam-6917	436	18	six	six	NUM
ejpam-6917	436	19	.	.	PUNCT
ejpam-6917	437	1	these	these	DET
ejpam-6917	437	2	numerical	numerical	ADJ
ejpam-6917	437	3	results	result	NOUN
ejpam-6917	437	4	validate	validate	VERB
ejpam-6917	437	5	the	the	DET
ejpam-6917	437	6	theoretical	theoretical	ADJ
ejpam-6917	437	7	order	order	NOUN
ejpam-6917	437	8	of	of	ADP
ejpam-6917	437	9	approximations	approximation	NOUN
ejpam-6917	437	10	described	describe	VERB
ejpam-6917	437	11	in	in	ADP
ejpam-6917	437	12	theorem	theorem	ADJ
ejpam-6917	437	13	5	5	NUM
ejpam-6917	437	14	.	.	NOUN
ejpam-6917	437	15	example	example	NOUN
ejpam-6917	437	16	2	2	NUM
ejpam-6917	437	17	.	.	PUNCT
ejpam-6917	437	18	(	(	PUNCT
ejpam-6917	437	19	tension	tension	NOUN
ejpam-6917	437	20	parameter	parameter	NOUN
ejpam-6917	437	21	)	)	PUNCT
ejpam-6917	437	22	to	to	PART
ejpam-6917	437	23	show	show	VERB
ejpam-6917	437	24	the	the	DET
ejpam-6917	437	25	effect	effect	NOUN
ejpam-6917	437	26	of	of	ADP
ejpam-6917	437	27	the	the	DET
ejpam-6917	437	28	parameter	parameter	NOUN
ejpam-6917	437	29	µ0	µ0	PROPN
ejpam-6917	437	30	on	on	ADP
ejpam-6917	437	31	the	the	DET
ejpam-6917	437	32	limit	limit	NOUN
ejpam-6917	437	33	curves	curve	NOUN
ejpam-6917	437	34	,	,	PUNCT
ejpam-6917	437	35	we	we	PRON
ejpam-6917	437	36	provide	provide	VERB
ejpam-6917	437	37	a	a	DET
ejpam-6917	437	38	numerical	numerical	ADJ
ejpam-6917	437	39	example	example	NOUN
ejpam-6917	437	40	.	.	PUNCT
ejpam-6917	438	1	the	the	DET
ejpam-6917	438	2	dotted	dotted	ADJ
ejpam-6917	438	3	lines	line	NOUN
ejpam-6917	438	4	represent	represent	VERB
ejpam-6917	438	5	the	the	DET
ejpam-6917	438	6	control	control	NOUN
ejpam-6917	438	7	polygon	polygon	NOUN
ejpam-6917	438	8	,	,	PUNCT
ejpam-6917	438	9	and	and	CCONJ
ejpam-6917	438	10	the	the	DET
ejpam-6917	438	11	control	control	NOUN
ejpam-6917	438	12	points	point	NOUN
ejpam-6917	438	13	are	be	AUX
ejpam-6917	438	14	marked	mark	VERB
ejpam-6917	438	15	with	with	ADP
ejpam-6917	438	16	circles	circle	NOUN
ejpam-6917	438	17	.	.	PUNCT
ejpam-6917	439	1	figure	figure	NOUN
ejpam-6917	439	2	2	2	NUM
ejpam-6917	439	3	presents	present	VERB
ejpam-6917	439	4	the	the	DET
ejpam-6917	439	5	curves	curve	NOUN
ejpam-6917	439	6	produced	produce	VERB
ejpam-6917	439	7	by	by	ADP
ejpam-6917	439	8	the	the	DET
ejpam-6917	439	9	proposed	propose	VERB
ejpam-6917	439	10	scheme	scheme	NOUN
ejpam-6917	439	11	for	for	ADP
ejpam-6917	439	12	µ0	µ0	NOUN
ejpam-6917	439	13	=	=	SYM
ejpam-6917	439	14	3/10	3/10	NUM
ejpam-6917	439	15	,	,	PUNCT
ejpam-6917	439	16	5/10	5/10	NUM
ejpam-6917	439	17	,	,	PUNCT
ejpam-6917	439	18	8/11	8/11	NUM
ejpam-6917	439	19	,	,	PUNCT
ejpam-6917	439	20	10/11	10/11	NUM
ejpam-6917	439	21	.	.	PUNCT
ejpam-6917	440	1	as	as	SCONJ
ejpam-6917	440	2	µ0	µ0	NOUN
ejpam-6917	440	3	increases	increase	NOUN
ejpam-6917	440	4	,	,	PUNCT
ejpam-6917	440	5	the	the	DET
ejpam-6917	440	6	curves	curve	NOUN
ejpam-6917	440	7	become	become	VERB
ejpam-6917	440	8	smoother	smooth	ADJ
ejpam-6917	440	9	and	and	CCONJ
ejpam-6917	440	10	deviate	deviate	VERB
ejpam-6917	440	11	more	more	ADJ
ejpam-6917	440	12	from	from	ADP
ejpam-6917	440	13	the	the	DET
ejpam-6917	440	14	original	original	ADJ
ejpam-6917	440	15	control	control	NOUN
ejpam-6917	440	16	polygon	polygon	NOUN
ejpam-6917	440	17	.	.	PUNCT
ejpam-6917	441	1	it	it	PRON
ejpam-6917	441	2	shows	show	VERB
ejpam-6917	441	3	how	how	SCONJ
ejpam-6917	441	4	the	the	DET
ejpam-6917	441	5	tension	tension	NOUN
ejpam-6917	441	6	parameter	parameter	NOUN
ejpam-6917	441	7	affects	affect	VERB
ejpam-6917	441	8	the	the	DET
ejpam-6917	441	9	limit	limit	NOUN
ejpam-6917	441	10	curve	curve	NOUN
ejpam-6917	441	11	,	,	PUNCT
ejpam-6917	441	12	resulting	result	VERB
ejpam-6917	441	13	in	in	ADP
ejpam-6917	441	14	different	different	ADJ
ejpam-6917	441	15	rates	rate	NOUN
ejpam-6917	441	16	of	of	ADP
ejpam-6917	441	17	convergence	convergence	NOUN
ejpam-6917	441	18	.	.	PUNCT
ejpam-6917	442	1	figure	figure	NOUN
ejpam-6917	442	2	2	2	NUM
ejpam-6917	442	3	:	:	PUNCT
ejpam-6917	442	4	subdivision	subdivision	NOUN
ejpam-6917	442	5	limit	limit	NOUN
ejpam-6917	442	6	curves	curve	NOUN
ejpam-6917	442	7	produced	produce	VERB
ejpam-6917	442	8	with	with	ADP
ejpam-6917	442	9	the	the	DET
ejpam-6917	442	10	parameter	parameter	NOUN
ejpam-6917	442	11	µ0	µ0	NOUN
ejpam-6917	442	12	=	=	SYM
ejpam-6917	442	13	3/10	3/10	NUM
ejpam-6917	442	14	,	,	PUNCT
ejpam-6917	442	15	5/10	5/10	NUM
ejpam-6917	442	16	,	,	PUNCT
ejpam-6917	442	17	8/11	8/11	NUM
ejpam-6917	442	18	and	and	CCONJ
ejpam-6917	442	19	10/11	10/11	NUM
ejpam-6917	442	20	,	,	PUNCT
ejpam-6917	442	21	respectively	respectively	ADV
ejpam-6917	442	22	.	.	PUNCT
ejpam-6917	442	23	example	example	NOUN
ejpam-6917	443	1	3	3	NUM
ejpam-6917	443	2	.	.	PUNCT
ejpam-6917	443	3	(	(	PUNCT
ejpam-6917	443	4	curve	curve	NOUN
ejpam-6917	443	5	design	design	NOUN
ejpam-6917	443	6	)	)	PUNCT
ejpam-6917	443	7	this	this	DET
ejpam-6917	443	8	example	example	NOUN
ejpam-6917	443	9	illustrates	illustrate	VERB
ejpam-6917	443	10	the	the	DET
ejpam-6917	443	11	numerical	numerical	ADJ
ejpam-6917	443	12	results	result	NOUN
ejpam-6917	443	13	of	of	ADP
ejpam-6917	443	14	our	our	PRON
ejpam-6917	443	15	subdivision	subdivision	NOUN
ejpam-6917	443	16	sp	sp	ADP
ejpam-6917	443	17	-scheme	-scheme	NOUN
ejpam-6917	443	18	with	with	ADP
ejpam-6917	443	19	its	its	PRON
ejpam-6917	443	20	parent	parent	NOUN
ejpam-6917	443	21	schemes	scheme	NOUN
ejpam-6917	443	22	.	.	PUNCT
ejpam-6917	444	1	figure	figure	NOUN
ejpam-6917	444	2	3	3	NUM
ejpam-6917	444	3	and	and	CCONJ
ejpam-6917	444	4	4	4	NUM
ejpam-6917	444	5	show	show	VERB
ejpam-6917	444	6	the	the	DET
ejpam-6917	444	7	limit	limit	NOUN
ejpam-6917	444	8	curve	curve	NOUN
ejpam-6917	444	9	when	when	SCONJ
ejpam-6917	444	10	µ0	µ0	NOUN
ejpam-6917	444	11	is	be	AUX
ejpam-6917	444	12	set	set	VERB
ejpam-6917	444	13	to	to	ADP
ejpam-6917	444	14	zero	zero	NUM
ejpam-6917	444	15	,	,	PUNCT
ejpam-6917	444	16	the	the	DET
ejpam-6917	444	17	curve	curve	NOUN
ejpam-6917	444	18	corresponds	correspond	VERB
ejpam-6917	444	19	to	to	ADP
ejpam-6917	444	20	the	the	DET
ejpam-6917	444	21	limit	limit	NOUN
ejpam-6917	444	22	curve	curve	NOUN
ejpam-6917	444	23	of	of	ADP
ejpam-6917	444	24	the	the	DET
ejpam-6917	444	25	sd	sd	NOUN
ejpam-6917	444	26	-	-	PUNCT
ejpam-6917	444	27	scheme	scheme	NOUN
ejpam-6917	444	28	algorithm	algorithm	NOUN
ejpam-6917	444	29	through	through	ADP
ejpam-6917	444	30	this	this	DET
ejpam-6917	444	31	results	result	NOUN
ejpam-6917	444	32	in	in	ADP
ejpam-6917	444	33	an	an	DET
ejpam-6917	444	34	undesirable	undesirable	ADJ
ejpam-6917	444	35	artifact	artifact	NOUN
ejpam-6917	444	36	and	and	CCONJ
ejpam-6917	444	37	when	when	SCONJ
ejpam-6917	444	38	µ0	µ0	NOUN
ejpam-6917	444	39	increases	increase	VERB
ejpam-6917	444	40	toward	toward	ADP
ejpam-6917	444	41	1	1	NUM
ejpam-6917	444	42	it	it	PRON
ejpam-6917	444	43	becomes	become	VERB
ejpam-6917	444	44	qb	qb	NOUN
ejpam-6917	444	45	-	-	PUNCT
ejpam-6917	444	46	scheme	scheme	NOUN
ejpam-6917	444	47	the	the	DET
ejpam-6917	444	48	curves	curve	NOUN
ejpam-6917	444	49	deviate	deviate	VERB
ejpam-6917	444	50	more	more	ADV
ejpam-6917	444	51	significantly	significantly	ADV
ejpam-6917	444	52	from	from	ADP
ejpam-6917	444	53	the	the	DET
ejpam-6917	444	54	control	control	NOUN
ejpam-6917	444	55	polygon	polygon	PROPN
ejpam-6917	444	56	.	.	PUNCT
ejpam-6917	445	1	f.	f.	PROPN
ejpam-6917	445	2	s.	s.	PROPN
ejpam-6917	445	3	alshammari	alshammari	PROPN
ejpam-6917	445	4	et	et	PROPN
ejpam-6917	445	5	al	al	PROPN
ejpam-6917	445	6	.	.	PUNCT
ejpam-6917	445	7	/	/	SYM
ejpam-6917	445	8	eur	eur	PROPN
ejpam-6917	445	9	.	.	PUNCT
ejpam-6917	446	1	j.	j.	PROPN
ejpam-6917	446	2	pure	pure	PROPN
ejpam-6917	446	3	appl	appl	PROPN
ejpam-6917	446	4	.	.	PROPN
ejpam-6917	446	5	math	math	PROPN
ejpam-6917	446	6	,	,	PUNCT
ejpam-6917	446	7	18	18	NUM
ejpam-6917	446	8	(	(	PUNCT
ejpam-6917	446	9	4	4	NUM
ejpam-6917	446	10	)	)	PUNCT
ejpam-6917	446	11	(	(	PUNCT
ejpam-6917	446	12	2025	2025	NUM
ejpam-6917	446	13	)	)	PUNCT
ejpam-6917	446	14	,	,	PUNCT
ejpam-6917	446	15	6917	6917	NUM
ejpam-6917	446	16	20	20	NUM
ejpam-6917	446	17	of	of	ADP
ejpam-6917	446	18	26	26	NUM
ejpam-6917	446	19	(	(	PUNCT
ejpam-6917	446	20	a	a	NOUN
ejpam-6917	446	21	)	)	PUNCT
ejpam-6917	446	22	sp	sp	ADP
ejpam-6917	446	23	-scheme	-scheme	PROPN
ejpam-6917	446	24	(	(	PUNCT
ejpam-6917	446	25	b	b	NOUN
ejpam-6917	446	26	)	)	PUNCT
ejpam-6917	446	27	sd	sd	NOUN
ejpam-6917	446	28	-	-	PUNCT
ejpam-6917	446	29	scheme	scheme	NOUN
ejpam-6917	446	30	(	(	PUNCT
ejpam-6917	446	31	c	c	NOUN
ejpam-6917	446	32	)	)	PUNCT
ejpam-6917	446	33	zoomed	zoomed	PROPN
ejpam-6917	446	34	area	area	PROPN
ejpam-6917	446	35	figure	figure	NOUN
ejpam-6917	446	36	3	3	NUM
ejpam-6917	446	37	:	:	PUNCT
ejpam-6917	446	38	2d	2d	NOUN
ejpam-6917	446	39	-	-	PUNCT
ejpam-6917	446	40	model	model	NOUN
ejpam-6917	446	41	generated	generate	VERB
ejpam-6917	446	42	by	by	ADP
ejpam-6917	446	43	sd	sd	NOUN
ejpam-6917	446	44	-	-	PUNCT
ejpam-6917	446	45	scheme	scheme	NOUN
ejpam-6917	446	46	and	and	CCONJ
ejpam-6917	446	47	sp	sp	ADP
ejpam-6917	446	48	-scheme	-scheme	NOUN
ejpam-6917	446	49	at	at	ADP
ejpam-6917	446	50	µ0	µ0	NOUN
ejpam-6917	446	51	=	=	SYM
ejpam-6917	446	52	10/11	10/11	NUM
ejpam-6917	446	53	.	.	PUNCT
ejpam-6917	447	1	f.	f.	PROPN
ejpam-6917	447	2	s.	s.	PROPN
ejpam-6917	447	3	alshammari	alshammari	PROPN
ejpam-6917	447	4	et	et	PROPN
ejpam-6917	447	5	al	al	PROPN
ejpam-6917	447	6	.	.	PUNCT
ejpam-6917	447	7	/	/	SYM
ejpam-6917	447	8	eur	eur	PROPN
ejpam-6917	447	9	.	.	PUNCT
ejpam-6917	448	1	j.	j.	PROPN
ejpam-6917	448	2	pure	pure	PROPN
ejpam-6917	448	3	appl	appl	PROPN
ejpam-6917	448	4	.	.	PROPN
ejpam-6917	448	5	math	math	PROPN
ejpam-6917	448	6	,	,	PUNCT
ejpam-6917	448	7	18	18	NUM
ejpam-6917	448	8	(	(	PUNCT
ejpam-6917	448	9	4	4	NUM
ejpam-6917	448	10	)	)	PUNCT
ejpam-6917	448	11	(	(	PUNCT
ejpam-6917	448	12	2025	2025	NUM
ejpam-6917	448	13	)	)	PUNCT
ejpam-6917	448	14	,	,	PUNCT
ejpam-6917	448	15	6917	6917	NUM
ejpam-6917	448	16	21	21	NUM
ejpam-6917	448	17	of	of	ADP
ejpam-6917	448	18	26	26	NUM
ejpam-6917	448	19	(	(	PUNCT
ejpam-6917	448	20	a	a	NOUN
ejpam-6917	448	21	)	)	PUNCT
ejpam-6917	448	22	sp	sp	ADP
ejpam-6917	448	23	-scheme	-scheme	PROPN
ejpam-6917	448	24	(	(	PUNCT
ejpam-6917	448	25	b	b	NOUN
ejpam-6917	448	26	)	)	PUNCT
ejpam-6917	448	27	qb	qb	NOUN
ejpam-6917	448	28	-	-	PUNCT
ejpam-6917	448	29	scheme	scheme	NOUN
ejpam-6917	448	30	(	(	PUNCT
ejpam-6917	448	31	c	c	NOUN
ejpam-6917	448	32	)	)	PUNCT
ejpam-6917	448	33	zoomed	zoomed	PROPN
ejpam-6917	448	34	area	area	NOUN
ejpam-6917	448	35	figure	figure	NOUN
ejpam-6917	448	36	4	4	NUM
ejpam-6917	448	37	:	:	PUNCT
ejpam-6917	448	38	2d	2d	NOUN
ejpam-6917	448	39	-	-	PUNCT
ejpam-6917	448	40	model	model	NOUN
ejpam-6917	448	41	generated	generate	VERB
ejpam-6917	448	42	by	by	ADP
ejpam-6917	448	43	sp	sp	ADP
ejpam-6917	448	44	-scheme	-scheme	PROPN
ejpam-6917	448	45	and	and	CCONJ
ejpam-6917	448	46	qb	qb	NOUN
ejpam-6917	448	47	-	-	PUNCT
ejpam-6917	448	48	scheme	scheme	NOUN
ejpam-6917	448	49	at	at	ADP
ejpam-6917	448	50	µ0	µ0	NOUN
ejpam-6917	448	51	=	=	SYM
ejpam-6917	448	52	10/11	10/11	NUM
ejpam-6917	448	53	.	.	PUNCT
ejpam-6917	448	54	example	example	NOUN
ejpam-6917	449	1	4	4	NUM
ejpam-6917	449	2	.	.	PUNCT
ejpam-6917	449	3	(	(	PUNCT
ejpam-6917	449	4	monotonicity	monotonicity	NOUN
ejpam-6917	449	5	preservation	preservation	NOUN
ejpam-6917	449	6	)	)	PUNCT
ejpam-6917	449	7	this	this	DET
ejpam-6917	449	8	example	example	NOUN
ejpam-6917	449	9	illustrates	illustrate	VERB
ejpam-6917	449	10	the	the	DET
ejpam-6917	449	11	effectiveness	effectiveness	NOUN
ejpam-6917	449	12	of	of	ADP
ejpam-6917	449	13	the	the	DET
ejpam-6917	449	14	ss	ss	NOUN
ejpam-6917	449	15	sp	sp	NOUN
ejpam-6917	449	16	in	in	ADP
ejpam-6917	449	17	monotonicity	monotonicity	NOUN
ejpam-6917	449	18	preservation	preservation	NOUN
ejpam-6917	449	19	.	.	PUNCT
ejpam-6917	450	1	suppose	suppose	VERB
ejpam-6917	450	2	that	that	SCONJ
ejpam-6917	450	3	initial	initial	ADJ
ejpam-6917	450	4	data	datum	NOUN
ejpam-6917	450	5	set	set	VERB
ejpam-6917	450	6	gn0	gn0	NOUN
ejpam-6917	450	7	be	be	AUX
ejpam-6917	450	8	given	give	VERB
ejpam-6917	450	9	on	on	ADP
ejpam-6917	450	10	[	[	X
ejpam-6917	450	11	-5,5	-5,5	X
ejpam-6917	450	12	]	]	X
ejpam-6917	450	13	as	as	SCONJ
ejpam-6917	450	14	follows	follow	VERB
ejpam-6917	450	15	:	:	PUNCT
ejpam-6917	450	16	gn0	gn0	NOUN
ejpam-6917	450	17	=	=	PUNCT
ejpam-6917	450	18	{	{	PUNCT
ejpam-6917	450	19	0.007	0.007	NUM
ejpam-6917	450	20	,	,	PUNCT
ejpam-6917	450	21	0.018	0.018	NUM
ejpam-6917	450	22	,	,	PUNCT
ejpam-6917	450	23	0.047	0.047	NUM
ejpam-6917	450	24	,	,	PUNCT
ejpam-6917	450	25	0.119	0.119	NUM
ejpam-6917	450	26	,	,	PUNCT
ejpam-6917	450	27	0.269	0.269	NUM
ejpam-6917	450	28	,	,	PUNCT
ejpam-6917	450	29	0.500	0.500	NUM
ejpam-6917	450	30	,	,	PUNCT
ejpam-6917	450	31	0.731	0.731	NUM
ejpam-6917	450	32	,	,	PUNCT
ejpam-6917	450	33	0.881	0.881	NUM
ejpam-6917	450	34	,	,	PUNCT
ejpam-6917	450	35	0.952	0.952	NUM
ejpam-6917	450	36	,	,	PUNCT
ejpam-6917	450	37	0.982	0.982	NUM
ejpam-6917	450	38	,	,	PUNCT
ejpam-6917	450	39	0.993	0.993	NUM
ejpam-6917	450	40	}	}	PUNCT
ejpam-6917	450	41	.	.	PUNCT
ejpam-6917	451	1	a	a	DET
ejpam-6917	451	2	strictly	strictly	ADV
ejpam-6917	451	3	monotone	monotone	ADJ
ejpam-6917	451	4	initial	initial	ADJ
ejpam-6917	451	5	dataset	dataset	NOUN
ejpam-6917	451	6	gn0	gn0	NOUN
ejpam-6917	451	7	is	be	AUX
ejpam-6917	451	8	provided	provide	VERB
ejpam-6917	451	9	,	,	PUNCT
ejpam-6917	451	10	and	and	CCONJ
ejpam-6917	451	11	the	the	DET
ejpam-6917	451	12	scheme	scheme	NOUN
ejpam-6917	451	13	is	be	AUX
ejpam-6917	451	14	applied	apply	VERB
ejpam-6917	451	15	with	with	ADP
ejpam-6917	451	16	varying	vary	VERB
ejpam-6917	451	17	tension	tension	NOUN
ejpam-6917	451	18	parameter	parameter	NOUN
ejpam-6917	451	19	values	value	NOUN
ejpam-6917	452	1	µ0	µ0	NOUN
ejpam-6917	452	2	=	=	NOUN
ejpam-6917	452	3	0.5	0.5	NUM
ejpam-6917	452	4	,	,	PUNCT
ejpam-6917	452	5	0.6	0.6	NUM
ejpam-6917	452	6	,	,	PUNCT
ejpam-6917	452	7	0.7	0.7	NUM
ejpam-6917	452	8	,	,	PUNCT
ejpam-6917	452	9	0.8	0.8	NUM
ejpam-6917	452	10	,	,	PUNCT
ejpam-6917	452	11	0.9	0.9	NUM
ejpam-6917	452	12	.	.	PUNCT
ejpam-6917	453	1	the	the	DET
ejpam-6917	453	2	results	result	NOUN
ejpam-6917	453	3	demonstrate	demonstrate	VERB
ejpam-6917	453	4	that	that	SCONJ
ejpam-6917	453	5	the	the	DET
ejpam-6917	453	6	limit	limit	NOUN
ejpam-6917	453	7	curves	curve	NOUN
ejpam-6917	453	8	generated	generate	VERB
ejpam-6917	453	9	by	by	ADP
ejpam-6917	453	10	the	the	DET
ejpam-6917	453	11	scheme	scheme	NOUN
ejpam-6917	453	12	preserve	preserve	VERB
ejpam-6917	453	13	the	the	DET
ejpam-6917	453	14	monotonicity	monotonicity	NOUN
ejpam-6917	453	15	of	of	ADP
ejpam-6917	453	16	the	the	DET
ejpam-6917	453	17	initial	initial	ADJ
ejpam-6917	453	18	data	datum	NOUN
ejpam-6917	453	19	in	in	ADP
ejpam-6917	453	20	figure	figure	NOUN
ejpam-6917	453	21	5(a	5(a	NUM
ejpam-6917	453	22	)	)	PUNCT
ejpam-6917	453	23	,	,	PUNCT
ejpam-6917	453	24	and	and	CCONJ
ejpam-6917	453	25	their	their	PRON
ejpam-6917	453	26	first	first	ADJ
ejpam-6917	453	27	derivatives	derivative	NOUN
ejpam-6917	453	28	in	in	ADP
ejpam-6917	453	29	figure	figure	NOUN
ejpam-6917	453	30	5(b	5(b	NUM
ejpam-6917	453	31	)	)	PUNCT
ejpam-6917	453	32	are	be	AUX
ejpam-6917	453	33	also	also	ADV
ejpam-6917	453	34	examined	examine	VERB
ejpam-6917	453	35	.	.	PUNCT
ejpam-6917	454	1	the	the	DET
ejpam-6917	454	2	scheme	scheme	NOUN
ejpam-6917	454	3	’s	’s	PART
ejpam-6917	454	4	performance	performance	NOUN
ejpam-6917	454	5	is	be	AUX
ejpam-6917	454	6	showcased	showcase	VERB
ejpam-6917	454	7	within	within	ADP
ejpam-6917	454	8	the	the	DET
ejpam-6917	454	9	applicable	applicable	ADJ
ejpam-6917	454	10	domain	domain	NOUN
ejpam-6917	454	11	,	,	PUNCT
ejpam-6917	454	12	confirming	confirm	VERB
ejpam-6917	454	13	its	its	PRON
ejpam-6917	454	14	ability	ability	NOUN
ejpam-6917	454	15	to	to	PART
ejpam-6917	454	16	maintain	maintain	VERB
ejpam-6917	454	17	monotonicity	monotonicity	NOUN
ejpam-6917	454	18	.	.	PUNCT
ejpam-6917	455	1	f.	f.	PROPN
ejpam-6917	455	2	s.	s.	PROPN
ejpam-6917	455	3	alshammari	alshammari	PROPN
ejpam-6917	455	4	et	et	PROPN
ejpam-6917	455	5	al	al	PROPN
ejpam-6917	455	6	.	.	PUNCT
ejpam-6917	455	7	/	/	SYM
ejpam-6917	455	8	eur	eur	PROPN
ejpam-6917	455	9	.	.	PUNCT
ejpam-6917	456	1	j.	j.	PROPN
ejpam-6917	456	2	pure	pure	PROPN
ejpam-6917	456	3	appl	appl	PROPN
ejpam-6917	456	4	.	.	PROPN
ejpam-6917	456	5	math	math	PROPN
ejpam-6917	456	6	,	,	PUNCT
ejpam-6917	456	7	18	18	NUM
ejpam-6917	456	8	(	(	PUNCT
ejpam-6917	456	9	4	4	NUM
ejpam-6917	456	10	)	)	PUNCT
ejpam-6917	456	11	(	(	PUNCT
ejpam-6917	456	12	2025	2025	NUM
ejpam-6917	456	13	)	)	PUNCT
ejpam-6917	456	14	,	,	PUNCT
ejpam-6917	456	15	6917	6917	NUM
ejpam-6917	456	16	22	22	NUM
ejpam-6917	456	17	of	of	ADP
ejpam-6917	456	18	26	26	NUM
ejpam-6917	456	19	(	(	PUNCT
ejpam-6917	456	20	a	a	NOUN
ejpam-6917	456	21	)	)	PUNCT
ejpam-6917	456	22	(	(	PUNCT
ejpam-6917	456	23	b	b	X
ejpam-6917	456	24	)	)	PUNCT
ejpam-6917	456	25	figure	figure	NOUN
ejpam-6917	456	26	5	5	NUM
ejpam-6917	456	27	:	:	PUNCT
ejpam-6917	456	28	monotonicity	monotonicity	NOUN
ejpam-6917	456	29	preservation	preservation	NOUN
ejpam-6917	456	30	.	.	PUNCT
ejpam-6917	457	1	limit	limit	NOUN
ejpam-6917	457	2	function	function	NOUN
ejpam-6917	457	3	for	for	ADP
ejpam-6917	457	4	(	(	PUNCT
ejpam-6917	457	5	a	a	PRON
ejpam-6917	457	6	)	)	PUNCT
ejpam-6917	457	7	µ0	µ0	NOUN
ejpam-6917	457	8	=	=	SYM
ejpam-6917	457	9	0.5	0.5	NUM
ejpam-6917	457	10	,	,	PUNCT
ejpam-6917	457	11	0.6	0.6	NUM
ejpam-6917	457	12	,	,	PUNCT
ejpam-6917	457	13	0.7	0.7	NUM
ejpam-6917	457	14	,	,	PUNCT
ejpam-6917	457	15	0.8	0.8	NUM
ejpam-6917	457	16	,	,	PUNCT
ejpam-6917	457	17	0.9	0.9	NUM
ejpam-6917	457	18	and	and	CCONJ
ejpam-6917	457	19	(	(	PUNCT
ejpam-6917	457	20	b	b	X
ejpam-6917	457	21	)	)	PUNCT
ejpam-6917	457	22	their	their	PRON
ejpam-6917	457	23	first	first	ADJ
ejpam-6917	457	24	derivatives	derivative	NOUN
ejpam-6917	457	25	.	.	PUNCT
ejpam-6917	458	1	example	example	NOUN
ejpam-6917	458	2	5	5	NUM
ejpam-6917	458	3	.	.	PUNCT
ejpam-6917	459	1	(	(	PUNCT
ejpam-6917	459	2	convexity	convexity	NOUN
ejpam-6917	459	3	preservation	preservation	NOUN
ejpam-6917	459	4	)	)	PUNCT
ejpam-6917	459	5	this	this	DET
ejpam-6917	459	6	example	example	NOUN
ejpam-6917	459	7	demonstrates	demonstrate	VERB
ejpam-6917	459	8	the	the	DET
ejpam-6917	459	9	effectiveness	effectiveness	NOUN
ejpam-6917	459	10	of	of	ADP
ejpam-6917	459	11	the	the	DET
ejpam-6917	459	12	ss	ss	NOUN
ejpam-6917	459	13	sp	sp	NOUN
ejpam-6917	459	14	in	in	ADP
ejpam-6917	459	15	convexity	convexity	NOUN
ejpam-6917	459	16	preservation	preservation	NOUN
ejpam-6917	459	17	.	.	PUNCT
ejpam-6917	460	1	suppose	suppose	VERB
ejpam-6917	460	2	that	that	SCONJ
ejpam-6917	460	3	initial	initial	ADJ
ejpam-6917	460	4	data	datum	NOUN
ejpam-6917	460	5	set	set	VERB
ejpam-6917	460	6	gn0	gn0	NOUN
ejpam-6917	460	7	be	be	AUX
ejpam-6917	460	8	given	give	VERB
ejpam-6917	460	9	on	on	ADP
ejpam-6917	460	10	[	[	X
ejpam-6917	460	11	-5,5	-5,5	X
ejpam-6917	460	12	]	]	X
ejpam-6917	460	13	as	as	SCONJ
ejpam-6917	460	14	follows	follow	VERB
ejpam-6917	460	15	:	:	PUNCT
ejpam-6917	460	16	gn0	gn0	NOUN
ejpam-6917	460	17	=	=	PUNCT
ejpam-6917	460	18	{	{	PUNCT
ejpam-6917	460	19	0.00	0.00	NUM
ejpam-6917	460	20	,	,	PUNCT
ejpam-6917	460	21	0.0816	0.0816	NUM
ejpam-6917	460	22	,	,	PUNCT
ejpam-6917	460	23	0.3265	0.3265	NUM
ejpam-6917	460	24	,	,	PUNCT
ejpam-6917	460	25	0.7347	0.7347	NUM
ejpam-6917	460	26	,	,	PUNCT
ejpam-6917	460	27	1.3061	1.3061	NUM
ejpam-6917	460	28	,	,	PUNCT
ejpam-6917	460	29	2.0408	2.0408	NUM
ejpam-6917	460	30	,	,	PUNCT
ejpam-6917	460	31	2.9388	2.9388	NUM
ejpam-6917	460	32	,	,	PUNCT
ejpam-6917	460	33	4.00	4.00	NUM
ejpam-6917	460	34	}	}	PUNCT
ejpam-6917	460	35	.	.	PUNCT
ejpam-6917	461	1	a	a	DET
ejpam-6917	461	2	strictly	strictly	ADV
ejpam-6917	461	3	convex	convex	ADJ
ejpam-6917	461	4	initial	initial	ADJ
ejpam-6917	461	5	dataset	dataset	NOUN
ejpam-6917	461	6	gn0	gn0	NOUN
ejpam-6917	461	7	is	be	AUX
ejpam-6917	461	8	provided	provide	VERB
ejpam-6917	461	9	,	,	PUNCT
ejpam-6917	461	10	and	and	CCONJ
ejpam-6917	461	11	the	the	DET
ejpam-6917	461	12	scheme	scheme	NOUN
ejpam-6917	461	13	is	be	AUX
ejpam-6917	461	14	applied	apply	VERB
ejpam-6917	461	15	with	with	ADP
ejpam-6917	461	16	varying	vary	VERB
ejpam-6917	461	17	tension	tension	NOUN
ejpam-6917	461	18	parameter	parameter	NOUN
ejpam-6917	461	19	values	value	NOUN
ejpam-6917	461	20	mu0	mu0	VERB
ejpam-6917	462	1	=	=	SYM
ejpam-6917	462	2	(	(	PUNCT
ejpam-6917	462	3	0.5	0.5	NUM
ejpam-6917	462	4	,	,	PUNCT
ejpam-6917	462	5	0.6	0.6	NUM
ejpam-6917	462	6	,	,	PUNCT
ejpam-6917	462	7	0.7	0.7	NUM
ejpam-6917	462	8	,	,	PUNCT
ejpam-6917	462	9	0.8	0.8	NUM
ejpam-6917	462	10	,	,	PUNCT
ejpam-6917	462	11	0.9	0.9	NUM
ejpam-6917	462	12	)	)	PUNCT
ejpam-6917	462	13	.	.	PUNCT
ejpam-6917	463	1	the	the	DET
ejpam-6917	463	2	results	result	NOUN
ejpam-6917	463	3	illustrate	illustrate	VERB
ejpam-6917	463	4	that	that	SCONJ
ejpam-6917	463	5	the	the	DET
ejpam-6917	463	6	limit	limit	NOUN
ejpam-6917	463	7	curves	curve	NOUN
ejpam-6917	463	8	generated	generate	VERB
ejpam-6917	463	9	by	by	ADP
ejpam-6917	463	10	the	the	DET
ejpam-6917	463	11	scheme	scheme	NOUN
ejpam-6917	463	12	preserve	preserve	VERB
ejpam-6917	463	13	the	the	DET
ejpam-6917	463	14	convexity	convexity	NOUN
ejpam-6917	463	15	of	of	ADP
ejpam-6917	463	16	the	the	DET
ejpam-6917	463	17	initial	initial	ADJ
ejpam-6917	463	18	data	datum	NOUN
ejpam-6917	463	19	in	in	ADP
ejpam-6917	463	20	figure	figure	NOUN
ejpam-6917	463	21	6	6	NUM
ejpam-6917	463	22	(	(	PUNCT
ejpam-6917	463	23	a	a	NOUN
ejpam-6917	463	24	)	)	PUNCT
ejpam-6917	463	25	,	,	PUNCT
ejpam-6917	463	26	and	and	CCONJ
ejpam-6917	463	27	their	their	PRON
ejpam-6917	463	28	second	second	ADJ
ejpam-6917	463	29	derivatives	derivative	NOUN
ejpam-6917	463	30	in	in	ADP
ejpam-6917	463	31	figure	figure	NOUN
ejpam-6917	463	32	6	6	NUM
ejpam-6917	463	33	(	(	PUNCT
ejpam-6917	463	34	b	b	NOUN
ejpam-6917	463	35	)	)	PUNCT
ejpam-6917	463	36	are	be	AUX
ejpam-6917	463	37	also	also	ADV
ejpam-6917	463	38	examined	examine	VERB
ejpam-6917	463	39	.	.	PUNCT
ejpam-6917	464	1	the	the	DET
ejpam-6917	464	2	scheme	scheme	NOUN
ejpam-6917	464	3	’s	’s	PART
ejpam-6917	464	4	performance	performance	NOUN
ejpam-6917	464	5	is	be	AUX
ejpam-6917	464	6	showcased	showcase	VERB
ejpam-6917	464	7	within	within	ADP
ejpam-6917	464	8	the	the	DET
ejpam-6917	464	9	applicable	applicable	ADJ
ejpam-6917	464	10	domain	domain	NOUN
ejpam-6917	464	11	,	,	PUNCT
ejpam-6917	464	12	confirming	confirm	VERB
ejpam-6917	464	13	its	its	PRON
ejpam-6917	464	14	ability	ability	NOUN
ejpam-6917	464	15	to	to	PART
ejpam-6917	464	16	maintain	maintain	VERB
ejpam-6917	464	17	convexity	convexity	NOUN
ejpam-6917	464	18	.	.	PUNCT
ejpam-6917	465	1	(	(	PUNCT
ejpam-6917	465	2	a	a	X
ejpam-6917	465	3	)	)	PUNCT
ejpam-6917	465	4	(	(	PUNCT
ejpam-6917	465	5	b	b	X
ejpam-6917	465	6	)	)	PUNCT
ejpam-6917	465	7	figure	figure	NOUN
ejpam-6917	465	8	6	6	NUM
ejpam-6917	465	9	:	:	PUNCT
ejpam-6917	465	10	convexity	convexity	NOUN
ejpam-6917	465	11	preservation	preservation	NOUN
ejpam-6917	465	12	.	.	PUNCT
ejpam-6917	466	1	limit	limit	NOUN
ejpam-6917	466	2	functions	function	NOUN
ejpam-6917	466	3	for	for	ADP
ejpam-6917	466	4	(	(	PUNCT
ejpam-6917	466	5	a	a	PRON
ejpam-6917	466	6	)	)	PUNCT
ejpam-6917	466	7	µ0	µ0	NOUN
ejpam-6917	466	8	=	=	SYM
ejpam-6917	466	9	0.5	0.5	NUM
ejpam-6917	466	10	,	,	PUNCT
ejpam-6917	466	11	0.6	0.6	NUM
ejpam-6917	466	12	,	,	PUNCT
ejpam-6917	466	13	0.7	0.7	NUM
ejpam-6917	466	14	,	,	PUNCT
ejpam-6917	466	15	0.8	0.8	NUM
ejpam-6917	466	16	,	,	PUNCT
ejpam-6917	466	17	0.9	0.9	NUM
ejpam-6917	466	18	and	and	CCONJ
ejpam-6917	466	19	(	(	PUNCT
ejpam-6917	466	20	b	b	X
ejpam-6917	466	21	)	)	PUNCT
ejpam-6917	466	22	their	their	PRON
ejpam-6917	466	23	second	second	ADJ
ejpam-6917	466	24	derivatives	derivative	NOUN
ejpam-6917	466	25	.	.	PUNCT
ejpam-6917	467	1	example	example	NOUN
ejpam-6917	467	2	6	6	NUM
ejpam-6917	467	3	.	.	PUNCT
ejpam-6917	468	1	(	(	PUNCT
ejpam-6917	468	2	discontinuous	discontinuous	ADJ
ejpam-6917	468	3	function	function	NOUN
ejpam-6917	468	4	)	)	PUNCT
ejpam-6917	468	5	in	in	ADP
ejpam-6917	468	6	this	this	DET
ejpam-6917	468	7	example	example	NOUN
ejpam-6917	468	8	,	,	PUNCT
ejpam-6917	468	9	we	we	PRON
ejpam-6917	468	10	analyze	analyze	VERB
ejpam-6917	468	11	the	the	DET
ejpam-6917	468	12	performance	performance	NOUN
ejpam-6917	468	13	of	of	ADP
ejpam-6917	468	14	the	the	DET
ejpam-6917	468	15	proposed	propose	VERB
ejpam-6917	468	16	scheme	scheme	NOUN
ejpam-6917	468	17	on	on	ADP
ejpam-6917	468	18	a	a	DET
ejpam-6917	468	19	discontinuous	discontinuous	ADJ
ejpam-6917	468	20	f.	f.	PROPN
ejpam-6917	468	21	s.	s.	PROPN
ejpam-6917	468	22	alshammari	alshammari	PROPN
ejpam-6917	468	23	et	et	PROPN
ejpam-6917	468	24	al	al	PROPN
ejpam-6917	468	25	.	.	PUNCT
ejpam-6917	468	26	/	/	SYM
ejpam-6917	468	27	eur	eur	PROPN
ejpam-6917	468	28	.	.	PUNCT
ejpam-6917	469	1	j.	j.	PROPN
ejpam-6917	469	2	pure	pure	PROPN
ejpam-6917	469	3	appl	appl	PROPN
ejpam-6917	469	4	.	.	PROPN
ejpam-6917	469	5	math	math	PROPN
ejpam-6917	469	6	,	,	PUNCT
ejpam-6917	469	7	18	18	NUM
ejpam-6917	469	8	(	(	PUNCT
ejpam-6917	469	9	4	4	NUM
ejpam-6917	469	10	)	)	PUNCT
ejpam-6917	469	11	(	(	PUNCT
ejpam-6917	469	12	2025	2025	NUM
ejpam-6917	469	13	)	)	PUNCT
ejpam-6917	469	14	,	,	PUNCT
ejpam-6917	469	15	6917	6917	NUM
ejpam-6917	469	16	23	23	NUM
ejpam-6917	469	17	of	of	ADP
ejpam-6917	469	18	26	26	NUM
ejpam-6917	469	19	table	table	NOUN
ejpam-6917	469	20	2	2	NUM
ejpam-6917	469	21	:	:	PUNCT
ejpam-6917	469	22	comparison	comparison	NOUN
ejpam-6917	469	23	with	with	ADP
ejpam-6917	469	24	existing	exist	VERB
ejpam-6917	469	25	schemes	scheme	NOUN
ejpam-6917	469	26	.	.	PUNCT
ejpam-6917	470	1	scheme	scheme	NOUN
ejpam-6917	470	2	type	type	NOUN
ejpam-6917	470	3	support	support	NOUN
ejpam-6917	470	4	order	order	NOUN
ejpam-6917	471	1	cn	cn	AUX
ejpam-6917	471	2	binary	binary	NOUN
ejpam-6917	471	3	3	3	NUM
ejpam-6917	471	4	-	-	PUNCT
ejpam-6917	471	5	point	point	NOUN
ejpam-6917	471	6	[	[	X
ejpam-6917	471	7	29	29	NUM
ejpam-6917	471	8	]	]	PUNCT
ejpam-6917	471	9	approximating	approximate	VERB
ejpam-6917	471	10	5	5	NUM
ejpam-6917	471	11	3	3	NUM
ejpam-6917	471	12	c3	c3	PROPN
ejpam-6917	471	13	binary	binary	NOUN
ejpam-6917	471	14	4	4	NUM
ejpam-6917	471	15	-	-	PUNCT
ejpam-6917	471	16	point	point	NOUN
ejpam-6917	471	17	[	[	X
ejpam-6917	471	18	30	30	NUM
ejpam-6917	471	19	]	]	PUNCT
ejpam-6917	471	20	interpolating	interpolate	VERB
ejpam-6917	471	21	6	6	NUM
ejpam-6917	471	22	4	4	NUM
ejpam-6917	471	23	c1	c1	NOUN
ejpam-6917	471	24	binary	binary	NOUN
ejpam-6917	471	25	4	4	NUM
ejpam-6917	471	26	-	-	PUNCT
ejpam-6917	471	27	point	point	NOUN
ejpam-6917	471	28	[	[	X
ejpam-6917	471	29	31	31	NUM
ejpam-6917	471	30	]	]	PUNCT
ejpam-6917	471	31	approximating	approximate	VERB
ejpam-6917	471	32	7	7	NUM
ejpam-6917	471	33	4	4	NUM
ejpam-6917	471	34	c2	c2	PROPN
ejpam-6917	471	35	binary	binary	NOUN
ejpam-6917	471	36	5	5	NUM
ejpam-6917	471	37	-	-	PUNCT
ejpam-6917	471	38	point	point	NOUN
ejpam-6917	471	39	[	[	X
ejpam-6917	471	40	32	32	NUM
ejpam-6917	471	41	]	]	PUNCT
ejpam-6917	471	42	approximating	approximate	VERB
ejpam-6917	471	43	9	9	NUM
ejpam-6917	471	44	2	2	NUM
ejpam-6917	471	45	c4	c4	NOUN
ejpam-6917	471	46	binary	binary	NOUN
ejpam-6917	471	47	4	4	NUM
ejpam-6917	471	48	-	-	PUNCT
ejpam-6917	471	49	point	point	NOUN
ejpam-6917	471	50	[	[	X
ejpam-6917	471	51	26	26	NUM
ejpam-6917	471	52	]	]	PUNCT
ejpam-6917	471	53	approximating	approximate	VERB
ejpam-6917	471	54	6	6	NUM
ejpam-6917	471	55	4	4	NUM
ejpam-6917	471	56	c2	c2	PROPN
ejpam-6917	471	57	binary	binary	NOUN
ejpam-6917	471	58	6	6	NUM
ejpam-6917	471	59	-	-	PUNCT
ejpam-6917	471	60	point	point	NOUN
ejpam-6917	471	61	[	[	X
ejpam-6917	471	62	21	21	NUM
ejpam-6917	471	63	]	]	PUNCT
ejpam-6917	471	64	interpolating	interpolate	VERB
ejpam-6917	471	65	10	10	NUM
ejpam-6917	471	66	6	6	NUM
ejpam-6917	471	67	c2	c2	NOUN
ejpam-6917	471	68	sp	sp	ADP
ejpam-6917	471	69	-scheme	-scheme	PROPN
ejpam-6917	471	70	approximating	approximate	VERB
ejpam-6917	471	71	10	10	NUM
ejpam-6917	471	72	6	6	NUM
ejpam-6917	471	73	c5	c5	PROPN
ejpam-6917	471	74	function	function	NOUN
ejpam-6917	471	75	defined	define	VERB
ejpam-6917	471	76	as	as	ADP
ejpam-6917	471	77	:	:	PUNCT
ejpam-6917	471	78	f(x	f(x	PROPN
ejpam-6917	471	79	)	)	PUNCT
ejpam-6917	472	1	=	=	PRON
ejpam-6917	472	2	{	{	PUNCT
ejpam-6917	472	3	1	1	NUM
ejpam-6917	472	4	,	,	PUNCT
ejpam-6917	472	5	if	if	SCONJ
ejpam-6917	472	6	0	0	NUM
ejpam-6917	472	7	≤	≤	NUM
ejpam-6917	472	8	x	x	X
ejpam-6917	472	9	<	<	X
ejpam-6917	472	10	0.4	0.4	NUM
ejpam-6917	472	11	0	0	NUM
ejpam-6917	472	12	,	,	PUNCT
ejpam-6917	472	13	if	if	SCONJ
ejpam-6917	472	14	0.4	0.4	NUM
ejpam-6917	472	15	≤	≤	NUM
ejpam-6917	472	16	x	x	SYM
ejpam-6917	472	17	≤	≤	NUM
ejpam-6917	472	18	0.8	0.8	NUM
ejpam-6917	472	19	this	this	DET
ejpam-6917	472	20	step	step	NOUN
ejpam-6917	472	21	function	function	NOUN
ejpam-6917	472	22	is	be	AUX
ejpam-6917	472	23	sampled	sample	VERB
ejpam-6917	472	24	uniformly	uniformly	ADV
ejpam-6917	472	25	at	at	ADP
ejpam-6917	472	26	nine	nine	NUM
ejpam-6917	472	27	points	point	NOUN
ejpam-6917	472	28	from	from	ADP
ejpam-6917	472	29	x=0	x=0	NUM
ejpam-6917	472	30	to	to	ADP
ejpam-6917	472	31	x=0.8	x=0.8	PROPN
ejpam-6917	472	32	.	.	PUNCT
ejpam-6917	473	1	the	the	DET
ejpam-6917	473	2	scheme	scheme	NOUN
ejpam-6917	473	3	is	be	AUX
ejpam-6917	473	4	applied	apply	VERB
ejpam-6917	473	5	using	use	VERB
ejpam-6917	473	6	a	a	DET
ejpam-6917	473	7	fixed	fix	VERB
ejpam-6917	473	8	tension	tension	NOUN
ejpam-6917	473	9	parameter	parameter	NOUN
ejpam-6917	473	10	µ0	µ0	PROPN
ejpam-6917	473	11	=	=	SYM
ejpam-6917	473	12	9/11	9/11	NUM
ejpam-6917	473	13	.	.	PUNCT
ejpam-6917	474	1	in	in	ADP
ejpam-6917	474	2	figure	figure	NOUN
ejpam-6917	474	3	7	7	NUM
ejpam-6917	474	4	,	,	PUNCT
ejpam-6917	474	5	the	the	DET
ejpam-6917	474	6	results	result	NOUN
ejpam-6917	474	7	show	show	VERB
ejpam-6917	474	8	that	that	SCONJ
ejpam-6917	474	9	the	the	DET
ejpam-6917	474	10	scheme	scheme	NOUN
ejpam-6917	474	11	handles	handle	VERB
ejpam-6917	474	12	the	the	DET
ejpam-6917	474	13	jump	jump	NOUN
ejpam-6917	474	14	without	without	ADP
ejpam-6917	474	15	introducing	introduce	VERB
ejpam-6917	474	16	oscillations	oscillation	NOUN
ejpam-6917	474	17	and	and	CCONJ
ejpam-6917	474	18	preserves	preserve	VERB
ejpam-6917	474	19	locality	locality	NOUN
ejpam-6917	474	20	near	near	ADP
ejpam-6917	474	21	the	the	DET
ejpam-6917	474	22	discontinuity	discontinuity	NOUN
ejpam-6917	474	23	,	,	PUNCT
ejpam-6917	474	24	demonstrating	demonstrate	VERB
ejpam-6917	474	25	its	its	PRON
ejpam-6917	474	26	robustness	robustness	NOUN
ejpam-6917	474	27	on	on	ADP
ejpam-6917	474	28	non	non	ADJ
ejpam-6917	474	29	-	-	ADJ
ejpam-6917	474	30	smooth	smooth	ADJ
ejpam-6917	474	31	data	datum	NOUN
ejpam-6917	474	32	.	.	PUNCT
ejpam-6917	475	1	]	]	PUNCT
ejpam-6917	475	2	figure	figure	NOUN
ejpam-6917	475	3	7	7	NUM
ejpam-6917	475	4	:	:	PUNCT
ejpam-6917	475	5	graph	graph	NOUN
ejpam-6917	475	6	of	of	ADP
ejpam-6917	475	7	the	the	DET
ejpam-6917	475	8	discontinuous	discontinuous	ADJ
ejpam-6917	475	9	function	function	NOUN
ejpam-6917	475	10	g(x	g(x	NOUN
ejpam-6917	475	11	)	)	PUNCT
ejpam-6917	475	12	.	.	PUNCT
ejpam-6917	476	1	7	7	X
ejpam-6917	476	2	.	.	X
ejpam-6917	476	3	comparison	comparison	NOUN
ejpam-6917	476	4	and	and	CCONJ
ejpam-6917	476	5	conclusion	conclusion	NOUN
ejpam-6917	476	6	in	in	ADP
ejpam-6917	476	7	conclusion	conclusion	NOUN
ejpam-6917	476	8	,	,	PUNCT
ejpam-6917	476	9	we	we	PRON
ejpam-6917	476	10	have	have	AUX
ejpam-6917	476	11	proposed	propose	VERB
ejpam-6917	476	12	a	a	DET
ejpam-6917	476	13	new	new	ADJ
ejpam-6917	476	14	linear	linear	NOUN
ejpam-6917	476	15	,	,	PUNCT
ejpam-6917	476	16	stationary	stationary	ADJ
ejpam-6917	476	17	subdivision	subdivision	NOUN
ejpam-6917	476	18	scheme	scheme	NOUN
ejpam-6917	476	19	that	that	PRON
ejpam-6917	476	20	unifies	unify	VERB
ejpam-6917	476	21	the	the	DET
ejpam-6917	476	22	strengths	strength	NOUN
ejpam-6917	476	23	of	of	ADP
ejpam-6917	476	24	the	the	DET
ejpam-6917	476	25	quintic	quintic	ADJ
ejpam-6917	476	26	b	b	NOUN
ejpam-6917	476	27	-	-	PUNCT
ejpam-6917	476	28	spline	spline	NOUN
ejpam-6917	476	29	and	and	CCONJ
ejpam-6917	476	30	six	six	NUM
ejpam-6917	476	31	-	-	PUNCT
ejpam-6917	476	32	point	point	NOUN
ejpam-6917	476	33	interpolatory	interpolatory	NOUN
ejpam-6917	476	34	scheme	scheme	NOUN
ejpam-6917	476	35	.	.	PUNCT
ejpam-6917	477	1	the	the	DET
ejpam-6917	477	2	proposed	propose	VERB
ejpam-6917	477	3	scheme	scheme	NOUN
ejpam-6917	477	4	achieves	achieve	VERB
ejpam-6917	477	5	c5	c5	PROPN
ejpam-6917	477	6	-	-	PUNCT
ejpam-6917	477	7	smoothness	smoothness	PROPN
ejpam-6917	477	8	and	and	CCONJ
ejpam-6917	477	9	sixth	sixth	ADJ
ejpam-6917	477	10	-	-	PUNCT
ejpam-6917	477	11	order	order	NOUN
ejpam-6917	477	12	approximation	approximation	NOUN
ejpam-6917	477	13	with	with	ADP
ejpam-6917	477	14	same	same	ADJ
ejpam-6917	477	15	support	support	NOUN
ejpam-6917	477	16	f.	f.	PROPN
ejpam-6917	477	17	s.	s.	PROPN
ejpam-6917	477	18	alshammari	alshammari	PROPN
ejpam-6917	477	19	et	et	PROPN
ejpam-6917	477	20	al	al	PROPN
ejpam-6917	477	21	.	.	PUNCT
ejpam-6917	477	22	/	/	SYM
ejpam-6917	477	23	eur	eur	PROPN
ejpam-6917	477	24	.	.	PUNCT
ejpam-6917	478	1	j.	j.	PROPN
ejpam-6917	478	2	pure	pure	PROPN
ejpam-6917	478	3	appl	appl	PROPN
ejpam-6917	478	4	.	.	PROPN
ejpam-6917	478	5	math	math	PROPN
ejpam-6917	478	6	,	,	PUNCT
ejpam-6917	478	7	18	18	NUM
ejpam-6917	478	8	(	(	PUNCT
ejpam-6917	478	9	4	4	NUM
ejpam-6917	478	10	)	)	PUNCT
ejpam-6917	478	11	(	(	PUNCT
ejpam-6917	478	12	2025	2025	NUM
ejpam-6917	478	13	)	)	PUNCT
ejpam-6917	478	14	,	,	PUNCT
ejpam-6917	478	15	6917	6917	NUM
ejpam-6917	478	16	24	24	NUM
ejpam-6917	478	17	of	of	ADP
ejpam-6917	478	18	26	26	NUM
ejpam-6917	478	19	as	as	ADP
ejpam-6917	478	20	of	of	ADP
ejpam-6917	478	21	interpolatory	interpolatory	NOUN
ejpam-6917	478	22	scheme	scheme	NOUN
ejpam-6917	478	23	.	.	PUNCT
ejpam-6917	479	1	the	the	DET
ejpam-6917	479	2	inclusion	inclusion	NOUN
ejpam-6917	479	3	of	of	ADP
ejpam-6917	479	4	a	a	DET
ejpam-6917	479	5	tension	tension	NOUN
ejpam-6917	479	6	parameter	parameter	NOUN
ejpam-6917	479	7	allows	allow	VERB
ejpam-6917	479	8	for	for	ADP
ejpam-6917	479	9	shape	shape	NOUN
ejpam-6917	479	10	control	control	NOUN
ejpam-6917	479	11	,	,	PUNCT
ejpam-6917	479	12	making	make	VERB
ejpam-6917	479	13	the	the	DET
ejpam-6917	479	14	scheme	scheme	NOUN
ejpam-6917	479	15	flexible	flexible	ADJ
ejpam-6917	479	16	for	for	ADP
ejpam-6917	479	17	preserving	preserve	VERB
ejpam-6917	479	18	essential	essential	ADJ
ejpam-6917	479	19	properties	property	NOUN
ejpam-6917	479	20	such	such	ADJ
ejpam-6917	479	21	as	as	ADP
ejpam-6917	479	22	convexity	convexity	NOUN
ejpam-6917	479	23	and	and	CCONJ
ejpam-6917	479	24	monotonicity	monotonicity	NOUN
ejpam-6917	479	25	.	.	PUNCT
ejpam-6917	480	1	a	a	DET
ejpam-6917	480	2	comparative	comparative	ADJ
ejpam-6917	480	3	analysis	analysis	NOUN
ejpam-6917	480	4	in	in	ADP
ejpam-6917	480	5	table	table	NOUN
ejpam-6917	480	6	2	2	NUM
ejpam-6917	480	7	with	with	ADP
ejpam-6917	480	8	existing	exist	VERB
ejpam-6917	480	9	schemes	scheme	NOUN
ejpam-6917	480	10	highlights	highlight	NOUN
ejpam-6917	480	11	that	that	SCONJ
ejpam-6917	480	12	the	the	DET
ejpam-6917	480	13	proposed	propose	VERB
ejpam-6917	480	14	scheme	scheme	NOUN
ejpam-6917	480	15	offers	offer	VERB
ejpam-6917	480	16	superior	superior	ADJ
ejpam-6917	480	17	smoothness	smoothness	NOUN
ejpam-6917	480	18	(	(	PUNCT
ejpam-6917	480	19	c5	c5	PROPN
ejpam-6917	480	20	continuity	continuity	NOUN
ejpam-6917	480	21	)	)	PUNCT
ejpam-6917	480	22	and	and	CCONJ
ejpam-6917	480	23	higher	high	ADJ
ejpam-6917	480	24	approximation	approximation	NOUN
ejpam-6917	480	25	order	order	NOUN
ejpam-6917	480	26	(	(	PUNCT
ejpam-6917	480	27	sixth	sixth	ADJ
ejpam-6917	480	28	order	order	NOUN
ejpam-6917	480	29	)	)	PUNCT
ejpam-6917	480	30	,	,	PUNCT
ejpam-6917	480	31	while	while	SCONJ
ejpam-6917	480	32	maintaining	maintain	VERB
ejpam-6917	480	33	same	same	ADJ
ejpam-6917	480	34	support	support	NOUN
ejpam-6917	480	35	of	of	ADP
ejpam-6917	480	36	interpolatory	interpolatory	ADJ
ejpam-6917	480	37	scheme	scheme	NOUN
ejpam-6917	480	38	.	.	PUNCT
ejpam-6917	481	1	numerical	numerical	ADJ
ejpam-6917	481	2	experiments	experiment	NOUN
ejpam-6917	481	3	further	far	ADV
ejpam-6917	481	4	confirm	confirm	VERB
ejpam-6917	481	5	its	its	PRON
ejpam-6917	481	6	effectiveness	effectiveness	NOUN
ejpam-6917	481	7	in	in	ADP
ejpam-6917	481	8	producing	produce	VERB
ejpam-6917	481	9	smooth	smooth	ADJ
ejpam-6917	481	10	,	,	PUNCT
ejpam-6917	481	11	accurate	accurate	ADJ
ejpam-6917	481	12	,	,	PUNCT
ejpam-6917	481	13	and	and	CCONJ
ejpam-6917	481	14	visually	visually	ADV
ejpam-6917	481	15	elegant	elegant	ADJ
ejpam-6917	481	16	curves	curve	NOUN
ejpam-6917	481	17	,	,	PUNCT
ejpam-6917	481	18	demonstrating	demonstrate	VERB
ejpam-6917	481	19	its	its	PRON
ejpam-6917	481	20	potential	potential	NOUN
ejpam-6917	481	21	for	for	ADP
ejpam-6917	481	22	practical	practical	ADJ
ejpam-6917	481	23	applications	application	NOUN
ejpam-6917	481	24	in	in	ADP
ejpam-6917	481	25	geometric	geometric	ADJ
ejpam-6917	481	26	modeling	modeling	NOUN
ejpam-6917	481	27	and	and	CCONJ
ejpam-6917	481	28	computer	computer	NOUN
ejpam-6917	481	29	-	-	PUNCT
ejpam-6917	481	30	aided	aid	VERB
ejpam-6917	481	31	design	design	NOUN
ejpam-6917	481	32	.	.	PUNCT
ejpam-6917	482	1	despite	despite	SCONJ
ejpam-6917	482	2	these	these	DET
ejpam-6917	482	3	strengths	strength	NOUN
ejpam-6917	482	4	,	,	PUNCT
ejpam-6917	482	5	the	the	DET
ejpam-6917	482	6	scheme	scheme	NOUN
ejpam-6917	482	7	has	have	VERB
ejpam-6917	482	8	some	some	DET
ejpam-6917	482	9	limitations	limitation	NOUN
ejpam-6917	482	10	.	.	PUNCT
ejpam-6917	483	1	at	at	ADP
ejpam-6917	483	2	present	present	ADJ
ejpam-6917	483	3	,	,	PUNCT
ejpam-6917	483	4	it	it	PRON
ejpam-6917	483	5	is	be	AUX
ejpam-6917	483	6	restricted	restrict	VERB
ejpam-6917	483	7	to	to	PART
ejpam-6917	483	8	univariate	univariate	ADJ
ejpam-6917	483	9	curve	curve	NOUN
ejpam-6917	483	10	subdivision	subdivision	NOUN
ejpam-6917	483	11	,	,	PUNCT
ejpam-6917	483	12	and	and	CCONJ
ejpam-6917	483	13	the	the	DET
ejpam-6917	483	14	choice	choice	NOUN
ejpam-6917	483	15	of	of	ADP
ejpam-6917	483	16	the	the	DET
ejpam-6917	483	17	tension	tension	NOUN
ejpam-6917	483	18	parameter	parameter	NOUN
ejpam-6917	483	19	may	may	AUX
ejpam-6917	483	20	vary	vary	VERB
ejpam-6917	483	21	depending	depend	VERB
ejpam-6917	483	22	on	on	ADP
ejpam-6917	483	23	the	the	DET
ejpam-6917	483	24	data	datum	NOUN
ejpam-6917	483	25	set	set	VERB
ejpam-6917	483	26	or	or	CCONJ
ejpam-6917	483	27	application	application	NOUN
ejpam-6917	483	28	.	.	PUNCT
ejpam-6917	484	1	as	as	ADP
ejpam-6917	484	2	future	future	ADJ
ejpam-6917	484	3	work	work	NOUN
ejpam-6917	484	4	,	,	PUNCT
ejpam-6917	484	5	the	the	DET
ejpam-6917	484	6	scheme	scheme	NOUN
ejpam-6917	484	7	can	can	AUX
ejpam-6917	484	8	be	be	AUX
ejpam-6917	484	9	extended	extend	VERB
ejpam-6917	484	10	to	to	PART
ejpam-6917	484	11	bivariate	bivariate	ADJ
ejpam-6917	484	12	surfaces	surface	NOUN
ejpam-6917	484	13	using	use	VERB
ejpam-6917	484	14	the	the	DET
ejpam-6917	484	15	tensor	tensor	NOUN
ejpam-6917	484	16	product	product	NOUN
ejpam-6917	484	17	approach	approach	NOUN
ejpam-6917	484	18	,	,	PUNCT
ejpam-6917	484	19	which	which	PRON
ejpam-6917	484	20	is	be	AUX
ejpam-6917	484	21	expected	expect	VERB
ejpam-6917	484	22	to	to	PART
ejpam-6917	484	23	further	far	ADV
ejpam-6917	484	24	enhance	enhance	VERB
ejpam-6917	484	25	smoothness	smoothness	NOUN
ejpam-6917	484	26	and	and	CCONJ
ejpam-6917	484	27	approximation	approximation	NOUN
ejpam-6917	484	28	order	order	NOUN
ejpam-6917	484	29	.	.	PUNCT
ejpam-6917	485	1	another	another	DET
ejpam-6917	485	2	promising	promising	ADJ
ejpam-6917	485	3	direction	direction	NOUN
ejpam-6917	485	4	is	be	AUX
ejpam-6917	485	5	the	the	DET
ejpam-6917	485	6	development	development	NOUN
ejpam-6917	485	7	of	of	ADP
ejpam-6917	485	8	adaptive	adaptive	ADJ
ejpam-6917	485	9	strategies	strategy	NOUN
ejpam-6917	485	10	for	for	ADP
ejpam-6917	485	11	selecting	select	VERB
ejpam-6917	485	12	the	the	DET
ejpam-6917	485	13	tension	tension	NOUN
ejpam-6917	485	14	parameter	parameter	NOUN
ejpam-6917	485	15	automatically	automatically	ADV
ejpam-6917	485	16	,	,	PUNCT
ejpam-6917	485	17	along	along	ADP
ejpam-6917	485	18	with	with	ADP
ejpam-6917	485	19	exploring	explore	VERB
ejpam-6917	485	20	applications	application	NOUN
ejpam-6917	485	21	in	in	ADP
ejpam-6917	485	22	cad	cad	PROPN
ejpam-6917	485	23	,	,	PUNCT
ejpam-6917	485	24	image	image	NOUN
ejpam-6917	485	25	processing	processing	NOUN
ejpam-6917	485	26	,	,	PUNCT
ejpam-6917	485	27	and	and	CCONJ
ejpam-6917	485	28	scientific	scientific	ADJ
ejpam-6917	485	29	visualization	visualization	NOUN
ejpam-6917	485	30	.	.	PUNCT
ejpam-6917	486	1	acknowledgements	acknowledgement	NOUN
ejpam-6917	486	2	the	the	DET
ejpam-6917	486	3	authors	author	NOUN
ejpam-6917	486	4	extend	extend	VERB
ejpam-6917	486	5	their	their	PRON
ejpam-6917	486	6	gratitude	gratitude	NOUN
ejpam-6917	486	7	to	to	ADP
ejpam-6917	486	8	the	the	DET
ejpam-6917	486	9	deanship	deanship	NOUN
ejpam-6917	486	10	of	of	ADP
ejpam-6917	486	11	scientific	scientific	ADJ
ejpam-6917	486	12	research	research	NOUN
ejpam-6917	486	13	at	at	ADP
ejpam-6917	486	14	prince	prince	PROPN
ejpam-6917	486	15	sattam	sattam	PROPN
ejpam-6917	486	16	bin	bin	PROPN
ejpam-6917	486	17	abdulaziz	abdulaziz	PROPN
ejpam-6917	486	18	university	university	PROPN
ejpam-6917	486	19	,	,	PUNCT
ejpam-6917	486	20	kingdom	kingdom	NOUN
ejpam-6917	486	21	of	of	ADP
ejpam-6917	486	22	saudi	saudi	PROPN
ejpam-6917	486	23	arabia	arabia	PROPN
ejpam-6917	486	24	.	.	PUNCT
ejpam-6917	487	1	references	reference	NOUN
ejpam-6917	487	2	[	[	X
ejpam-6917	487	3	1	1	NUM
ejpam-6917	487	4	]	]	PUNCT
ejpam-6917	487	5	c.	c.	PROPN
ejpam-6917	487	6	conti	conti	PROPN
ejpam-6917	487	7	,	,	PUNCT
ejpam-6917	487	8	l.	l.	PROPN
ejpam-6917	487	9	romani	romani	PROPN
ejpam-6917	487	10	,	,	PUNCT
ejpam-6917	487	11	and	and	CCONJ
ejpam-6917	487	12	j.	j.	PROPN
ejpam-6917	487	13	yoon	yoon	PROPN
ejpam-6917	487	14	.	.	PUNCT
ejpam-6917	488	1	approximation	approximation	NOUN
ejpam-6917	488	2	order	order	NOUN
ejpam-6917	488	3	and	and	CCONJ
ejpam-6917	488	4	approximate	approximate	ADJ
ejpam-6917	488	5	sum	sum	NOUN
ejpam-6917	488	6	rules	rule	NOUN
ejpam-6917	488	7	in	in	ADP
ejpam-6917	488	8	subdivision	subdivision	NOUN
ejpam-6917	488	9	.	.	PUNCT
ejpam-6917	489	1	journal	journal	NOUN
ejpam-6917	489	2	of	of	ADP
ejpam-6917	489	3	approximation	approximation	NOUN
ejpam-6917	489	4	theory	theory	NOUN
ejpam-6917	489	5	,	,	PUNCT
ejpam-6917	489	6	207:380–401	207:380–401	NUM
ejpam-6917	489	7	,	,	PUNCT
ejpam-6917	489	8	2016	2016	NUM
ejpam-6917	489	9	.	.	PUNCT
ejpam-6917	490	1	[	[	X
ejpam-6917	490	2	2	2	NUM
ejpam-6917	490	3	]	]	X
ejpam-6917	490	4	n.	n.	PROPN
ejpam-6917	490	5	dyn	dyn	PROPN
ejpam-6917	490	6	.	.	PUNCT
ejpam-6917	491	1	subdivision	subdivision	NOUN
ejpam-6917	491	2	schemes	scheme	NOUN
ejpam-6917	491	3	in	in	ADP
ejpam-6917	491	4	cagd	cagd	NOUN
ejpam-6917	491	5	.	.	PUNCT
ejpam-6917	492	1	advances	advance	NOUN
ejpam-6917	492	2	in	in	ADP
ejpam-6917	492	3	numerical	numerical	ADJ
ejpam-6917	492	4	analysis	analysis	NOUN
ejpam-6917	492	5	,	,	PUNCT
ejpam-6917	492	6	2:36–104	2:36–104	NUM
ejpam-6917	492	7	,	,	PUNCT
ejpam-6917	492	8	1992	1992	NUM
ejpam-6917	492	9	.	.	PUNCT
ejpam-6917	493	1	[	[	X
ejpam-6917	493	2	3	3	X
ejpam-6917	493	3	]	]	X
ejpam-6917	493	4	n.	n.	PROPN
ejpam-6917	493	5	dyn	dyn	PROPN
ejpam-6917	493	6	and	and	CCONJ
ejpam-6917	493	7	d.	d.	PROPN
ejpam-6917	493	8	levin	levin	PROPN
ejpam-6917	493	9	.	.	PUNCT
ejpam-6917	494	1	subdivision	subdivision	NOUN
ejpam-6917	494	2	schemes	scheme	NOUN
ejpam-6917	494	3	in	in	ADP
ejpam-6917	494	4	geometric	geometric	ADJ
ejpam-6917	494	5	modelling	modelling	NOUN
ejpam-6917	494	6	.	.	PUNCT
ejpam-6917	495	1	acta	acta	PROPN
ejpam-6917	495	2	numerica	numerica	PROPN
ejpam-6917	495	3	,	,	PUNCT
ejpam-6917	495	4	11:73–144	11:73–144	NUM
ejpam-6917	495	5	,	,	PUNCT
ejpam-6917	495	6	2002	2002	NUM
ejpam-6917	495	7	.	.	PUNCT
ejpam-6917	496	1	[	[	X
ejpam-6917	496	2	4	4	X
ejpam-6917	496	3	]	]	X
ejpam-6917	496	4	g.	g.	PROPN
ejpam-6917	496	5	de	de	X
ejpam-6917	496	6	rham	rham	PROPN
ejpam-6917	496	7	.	.	PUNCT
ejpam-6917	496	8	sur	sur	PROPN
ejpam-6917	496	9	une	une	PROPN
ejpam-6917	496	10	courbe	courbe	PROPN
ejpam-6917	496	11	plane	plane	PROPN
ejpam-6917	496	12	.	.	PUNCT
ejpam-6917	496	13	journal	journal	PROPN
ejpam-6917	496	14	de	de	PROPN
ejpam-6917	496	15	mathématiques	mathématiques	PROPN
ejpam-6917	496	16	pures	pure	NOUN
ejpam-6917	496	17	et	et	PROPN
ejpam-6917	496	18	appliquées	appliquées	PROPN
ejpam-6917	496	19	,	,	PUNCT
ejpam-6917	496	20	35:25–42	35:25–42	NUM
ejpam-6917	496	21	,	,	PUNCT
ejpam-6917	496	22	1956	1956	NUM
ejpam-6917	496	23	.	.	PUNCT
ejpam-6917	497	1	[	[	X
ejpam-6917	497	2	5	5	X
ejpam-6917	497	3	]	]	PUNCT
ejpam-6917	497	4	g.	g.	PROPN
ejpam-6917	497	5	m.	m.	PROPN
ejpam-6917	497	6	chaikin	chaikin	PROPN
ejpam-6917	497	7	.	.	PUNCT
ejpam-6917	498	1	an	an	DET
ejpam-6917	498	2	algorithm	algorithm	NOUN
ejpam-6917	498	3	for	for	ADP
ejpam-6917	498	4	high	high	ADJ
ejpam-6917	498	5	-	-	PUNCT
ejpam-6917	498	6	speed	speed	NOUN
ejpam-6917	498	7	curve	curve	NOUN
ejpam-6917	498	8	generation	generation	NOUN
ejpam-6917	498	9	.	.	PUNCT
ejpam-6917	499	1	computer	computer	NOUN
ejpam-6917	499	2	graphics	graphic	NOUN
ejpam-6917	499	3	and	and	CCONJ
ejpam-6917	499	4	image	image	NOUN
ejpam-6917	499	5	processing	processing	NOUN
ejpam-6917	499	6	,	,	PUNCT
ejpam-6917	499	7	3(4):346–349	3(4):346–349	NUM
ejpam-6917	499	8	,	,	PUNCT
ejpam-6917	499	9	1974	1974	NUM
ejpam-6917	499	10	.	.	PUNCT
ejpam-6917	500	1	[	[	X
ejpam-6917	500	2	6	6	NUM
ejpam-6917	500	3	]	]	X
ejpam-6917	500	4	n.	n.	PROPN
ejpam-6917	500	5	dyn	dyn	PROPN
ejpam-6917	500	6	,	,	PUNCT
ejpam-6917	500	7	d.	d.	PROPN
ejpam-6917	500	8	levin	levin	PROPN
ejpam-6917	500	9	,	,	PUNCT
ejpam-6917	500	10	and	and	CCONJ
ejpam-6917	500	11	j.	j.	PROPN
ejpam-6917	500	12	a.	a.	PROPN
ejpam-6917	500	13	gregory	gregory	PROPN
ejpam-6917	500	14	.	.	PUNCT
ejpam-6917	501	1	a	a	DET
ejpam-6917	501	2	4	4	NUM
ejpam-6917	501	3	-	-	PUNCT
ejpam-6917	501	4	point	point	NOUN
ejpam-6917	501	5	interpolatory	interpolatory	NOUN
ejpam-6917	501	6	subdivision	subdivision	NOUN
ejpam-6917	501	7	scheme	scheme	NOUN
ejpam-6917	501	8	for	for	ADP
ejpam-6917	501	9	curve	curve	NOUN
ejpam-6917	501	10	design	design	NOUN
ejpam-6917	501	11	.	.	PUNCT
ejpam-6917	502	1	computer	computer	NOUN
ejpam-6917	502	2	aided	aid	VERB
ejpam-6917	502	3	geometric	geometric	ADJ
ejpam-6917	502	4	design	design	NOUN
ejpam-6917	502	5	,	,	PUNCT
ejpam-6917	502	6	4(4):257–268	4(4):257–268	NUM
ejpam-6917	502	7	,	,	PUNCT
ejpam-6917	502	8	1987	1987	NUM
ejpam-6917	502	9	.	.	PUNCT
ejpam-6917	503	1	[	[	X
ejpam-6917	503	2	7	7	X
ejpam-6917	503	3	]	]	X
ejpam-6917	503	4	g.	g.	NOUN
ejpam-6917	503	5	deslauriers	deslauriers	PROPN
ejpam-6917	503	6	and	and	CCONJ
ejpam-6917	503	7	s.	s.	PROPN
ejpam-6917	503	8	dubuc	dubuc	PROPN
ejpam-6917	503	9	.	.	PUNCT
ejpam-6917	504	1	symmetric	symmetric	ADJ
ejpam-6917	504	2	iterative	iterative	NOUN
ejpam-6917	504	3	interpolation	interpolation	NOUN
ejpam-6917	504	4	processes	process	NOUN
ejpam-6917	504	5	.	.	PUNCT
ejpam-6917	505	1	constructive	constructive	ADJ
ejpam-6917	505	2	approximation	approximation	NOUN
ejpam-6917	505	3	,	,	PUNCT
ejpam-6917	505	4	5:49–68	5:49–68	NUM
ejpam-6917	505	5	,	,	PUNCT
ejpam-6917	505	6	1989	1989	NUM
ejpam-6917	505	7	.	.	PUNCT
ejpam-6917	506	1	[	[	X
ejpam-6917	506	2	8	8	NUM
ejpam-6917	506	3	]	]	X
ejpam-6917	506	4	g.	g.	PROPN
ejpam-6917	506	5	mustafa	mustafa	PROPN
ejpam-6917	506	6	,	,	PUNCT
ejpam-6917	506	7	p.	p.	PROPN
ejpam-6917	506	8	ashraf	ashraf	PROPN
ejpam-6917	506	9	,	,	PUNCT
ejpam-6917	506	10	and	and	CCONJ
ejpam-6917	506	11	n.	n.	PROPN
ejpam-6917	506	12	saba	saba	PROPN
ejpam-6917	506	13	.	.	PUNCT
ejpam-6917	507	1	a	a	DET
ejpam-6917	507	2	new	new	ADJ
ejpam-6917	507	3	class	class	NOUN
ejpam-6917	507	4	of	of	ADP
ejpam-6917	507	5	binary	binary	ADJ
ejpam-6917	507	6	approximating	approximate	VERB
ejpam-6917	507	7	subdivision	subdivision	NOUN
ejpam-6917	507	8	schemes	scheme	NOUN
ejpam-6917	507	9	.	.	PUNCT
ejpam-6917	508	1	jurnal	jurnal	ADJ
ejpam-6917	508	2	teknologi	teknologi	PROPN
ejpam-6917	508	3	,	,	PUNCT
ejpam-6917	508	4	78(4	78(4	PROPN
ejpam-6917	508	5	-	-	SYM
ejpam-6917	508	6	4	4	NUM
ejpam-6917	508	7	)	)	PUNCT
ejpam-6917	508	8	,	,	PUNCT
ejpam-6917	508	9	2016	2016	NUM
ejpam-6917	508	10	.	.	PUNCT
ejpam-6917	509	1	[	[	X
ejpam-6917	509	2	9	9	NUM
ejpam-6917	509	3	]	]	PUNCT
ejpam-6917	509	4	j.	j.	PROPN
ejpam-6917	509	5	tan	tan	PROPN
ejpam-6917	509	6	,	,	PUNCT
ejpam-6917	509	7	x.	x.	PROPN
ejpam-6917	509	8	zhuang	zhuang	PROPN
ejpam-6917	509	9	,	,	PUNCT
ejpam-6917	509	10	and	and	CCONJ
ejpam-6917	509	11	l.	l.	PROPN
ejpam-6917	509	12	zhang	zhang	PROPN
ejpam-6917	509	13	.	.	PUNCT
ejpam-6917	510	1	a	a	DET
ejpam-6917	510	2	new	new	ADJ
ejpam-6917	510	3	four	four	NUM
ejpam-6917	510	4	-	-	PUNCT
ejpam-6917	510	5	point	point	NOUN
ejpam-6917	510	6	shape	shape	NOUN
ejpam-6917	510	7	-	-	PUNCT
ejpam-6917	510	8	preserving	preserve	VERB
ejpam-6917	510	9	c3	c3	NOUN
ejpam-6917	510	10	subdivision	subdivision	NOUN
ejpam-6917	510	11	scheme	scheme	NOUN
ejpam-6917	510	12	.	.	PUNCT
ejpam-6917	511	1	computer	computer	NOUN
ejpam-6917	511	2	aided	aid	VERB
ejpam-6917	511	3	geometric	geometric	ADJ
ejpam-6917	511	4	design	design	NOUN
ejpam-6917	511	5	,	,	PUNCT
ejpam-6917	511	6	31(1):57–62	31(1):57–62	NUM
ejpam-6917	511	7	,	,	PUNCT
ejpam-6917	511	8	2014	2014	NUM
ejpam-6917	511	9	.	.	PUNCT
ejpam-6917	512	1	[	[	X
ejpam-6917	512	2	10	10	NUM
ejpam-6917	512	3	]	]	X
ejpam-6917	512	4	h.	h.	PROPN
ejpam-6917	512	5	c.	c.	PROPN
ejpam-6917	512	6	zheng	zheng	PROPN
ejpam-6917	512	7	,	,	PUNCT
ejpam-6917	512	8	s.	s.	PROPN
ejpam-6917	512	9	p.	p.	PROPN
ejpam-6917	512	10	huang	huang	PROPN
ejpam-6917	512	11	,	,	PUNCT
ejpam-6917	512	12	f.	f.	PROPN
ejpam-6917	512	13	guo	guo	PROPN
ejpam-6917	512	14	,	,	PUNCT
ejpam-6917	512	15	and	and	CCONJ
ejpam-6917	512	16	g.	g.	PROPN
ejpam-6917	512	17	h.	h.	PROPN
ejpam-6917	512	18	peng	peng	PROPN
ejpam-6917	512	19	.	.	PUNCT
ejpam-6917	513	1	designing	design	VERB
ejpam-6917	513	2	multi	multi	ADJ
ejpam-6917	513	3	-	-	ADJ
ejpam-6917	513	4	parameter	parameter	ADJ
ejpam-6917	513	5	curve	curve	NOUN
ejpam-6917	513	6	subdivision	subdivision	NOUN
ejpam-6917	513	7	schemes	scheme	NOUN
ejpam-6917	513	8	with	with	ADP
ejpam-6917	513	9	high	high	ADJ
ejpam-6917	513	10	continuity	continuity	NOUN
ejpam-6917	513	11	.	.	PUNCT
ejpam-6917	514	1	applied	apply	VERB
ejpam-6917	514	2	mathematics	mathematic	NOUN
ejpam-6917	514	3	and	and	CCONJ
ejpam-6917	514	4	computation	computation	NOUN
ejpam-6917	514	5	,	,	PUNCT
ejpam-6917	514	6	243:197–208	243:197–208	NUM
ejpam-6917	514	7	,	,	PUNCT
ejpam-6917	514	8	2014	2014	NUM
ejpam-6917	514	9	.	.	PUNCT
ejpam-6917	515	1	f.	f.	PROPN
ejpam-6917	515	2	s.	s.	PROPN
ejpam-6917	515	3	alshammari	alshammari	PROPN
ejpam-6917	515	4	et	et	PROPN
ejpam-6917	515	5	al	al	PROPN
ejpam-6917	515	6	.	.	PUNCT
ejpam-6917	515	7	/	/	SYM
ejpam-6917	515	8	eur	eur	PROPN
ejpam-6917	515	9	.	.	PUNCT
ejpam-6917	516	1	j.	j.	PROPN
ejpam-6917	516	2	pure	pure	PROPN
ejpam-6917	516	3	appl	appl	PROPN
ejpam-6917	516	4	.	.	PROPN
ejpam-6917	516	5	math	math	PROPN
ejpam-6917	516	6	,	,	PUNCT
ejpam-6917	516	7	18	18	NUM
ejpam-6917	516	8	(	(	PUNCT
ejpam-6917	516	9	4	4	NUM
ejpam-6917	516	10	)	)	PUNCT
ejpam-6917	516	11	(	(	PUNCT
ejpam-6917	516	12	2025	2025	NUM
ejpam-6917	516	13	)	)	PUNCT
ejpam-6917	516	14	,	,	PUNCT
ejpam-6917	516	15	6917	6917	NUM
ejpam-6917	516	16	25	25	NUM
ejpam-6917	516	17	of	of	ADP
ejpam-6917	516	18	26	26	NUM
ejpam-6917	517	1	[	[	X
ejpam-6917	517	2	11	11	NUM
ejpam-6917	517	3	]	]	PUNCT
ejpam-6917	517	4	i.	i.	NOUN
ejpam-6917	517	5	yadshalom	yadshalom	PROPN
ejpam-6917	517	6	.	.	PUNCT
ejpam-6917	518	1	monotonicity	monotonicity	NOUN
ejpam-6917	518	2	preserving	preserve	VERB
ejpam-6917	518	3	subdivision	subdivision	NOUN
ejpam-6917	518	4	schemes	scheme	NOUN
ejpam-6917	518	5	.	.	PUNCT
ejpam-6917	519	1	journal	journal	NOUN
ejpam-6917	519	2	of	of	ADP
ejpam-6917	519	3	approximation	approximation	NOUN
ejpam-6917	519	4	theory	theory	NOUN
ejpam-6917	519	5	,	,	PUNCT
ejpam-6917	519	6	74(1):41–58	74(1):41–58	NUM
ejpam-6917	519	7	,	,	PUNCT
ejpam-6917	519	8	1993	1993	NUM
ejpam-6917	519	9	.	.	PUNCT
ejpam-6917	520	1	[	[	X
ejpam-6917	520	2	12	12	NUM
ejpam-6917	520	3	]	]	X
ejpam-6917	520	4	g.	g.	PROPN
ejpam-6917	520	5	mustafa	mustafa	PROPN
ejpam-6917	520	6	and	and	CCONJ
ejpam-6917	520	7	r.	r.	PROPN
ejpam-6917	520	8	bashir	bashir	PROPN
ejpam-6917	520	9	.	.	PUNCT
ejpam-6917	521	1	four	four	NUM
ejpam-6917	521	2	-	-	PUNCT
ejpam-6917	521	3	point	point	NOUN
ejpam-6917	521	4	n	n	CCONJ
ejpam-6917	521	5	-	-	PUNCT
ejpam-6917	521	6	ary	ary	NOUN
ejpam-6917	521	7	interpolating	interpolate	VERB
ejpam-6917	521	8	subdivision	subdivision	NOUN
ejpam-6917	521	9	schemes	scheme	NOUN
ejpam-6917	521	10	.	.	PUNCT
ejpam-6917	522	1	international	international	ADJ
ejpam-6917	522	2	journal	journal	NOUN
ejpam-6917	522	3	of	of	ADP
ejpam-6917	522	4	mathematics	mathematics	PROPN
ejpam-6917	522	5	and	and	CCONJ
ejpam-6917	522	6	mathematical	mathematical	ADJ
ejpam-6917	522	7	sciences	science	NOUN
ejpam-6917	522	8	,	,	PUNCT
ejpam-6917	522	9	page	page	NOUN
ejpam-6917	522	10	893414	893414	NUM
ejpam-6917	522	11	,	,	PUNCT
ejpam-6917	522	12	2013	2013	NUM
ejpam-6917	522	13	.	.	PUNCT
ejpam-6917	523	1	[	[	X
ejpam-6917	523	2	13	13	NUM
ejpam-6917	523	3	]	]	X
ejpam-6917	523	4	g.	g.	PROPN
ejpam-6917	523	5	mustafa	mustafa	PROPN
ejpam-6917	523	6	,	,	PUNCT
ejpam-6917	523	7	p.	p.	PROPN
ejpam-6917	523	8	ashraf	ashraf	PROPN
ejpam-6917	523	9	,	,	PUNCT
ejpam-6917	523	10	and	and	CCONJ
ejpam-6917	523	11	j.	j.	PROPN
ejpam-6917	523	12	deng	deng	PROPN
ejpam-6917	523	13	.	.	PROPN
ejpam-6917	524	1	generalized	generalized	ADJ
ejpam-6917	524	2	and	and	CCONJ
ejpam-6917	524	3	unified	unified	ADJ
ejpam-6917	524	4	families	family	NOUN
ejpam-6917	524	5	of	of	ADP
ejpam-6917	524	6	interpolating	interpolate	VERB
ejpam-6917	524	7	subdivision	subdivision	NOUN
ejpam-6917	524	8	schemes	scheme	NOUN
ejpam-6917	524	9	.	.	PUNCT
ejpam-6917	525	1	numerical	numerical	ADJ
ejpam-6917	525	2	mathematics	mathematics	PROPN
ejpam-6917	525	3	:	:	PUNCT
ejpam-6917	525	4	theory	theory	NOUN
ejpam-6917	525	5	,	,	PUNCT
ejpam-6917	525	6	methods	method	NOUN
ejpam-6917	525	7	and	and	CCONJ
ejpam-6917	525	8	applications	application	NOUN
ejpam-6917	525	9	,	,	PUNCT
ejpam-6917	525	10	7(2):193–213	7(2):193–213	NOUN
ejpam-6917	525	11	,	,	PUNCT
ejpam-6917	525	12	2014	2014	NUM
ejpam-6917	525	13	.	.	PUNCT
ejpam-6917	526	1	[	[	X
ejpam-6917	526	2	14	14	NUM
ejpam-6917	526	3	]	]	X
ejpam-6917	526	4	g.	g.	PROPN
ejpam-6917	526	5	akram	akram	PROPN
ejpam-6917	526	6	,	,	PUNCT
ejpam-6917	526	7	k.	k.	PROPN
ejpam-6917	526	8	bibi	bibi	PROPN
ejpam-6917	526	9	,	,	PUNCT
ejpam-6917	526	10	k.	k.	PROPN
ejpam-6917	526	11	rehan	rehan	PROPN
ejpam-6917	526	12	,	,	PUNCT
ejpam-6917	526	13	and	and	CCONJ
ejpam-6917	526	14	s.	s.	PROPN
ejpam-6917	526	15	s.	s.	PROPN
ejpam-6917	526	16	siddiqi	siddiqi	PROPN
ejpam-6917	526	17	.	.	PUNCT
ejpam-6917	526	18	shape	shape	NOUN
ejpam-6917	526	19	preservation	preservation	NOUN
ejpam-6917	526	20	of	of	ADP
ejpam-6917	526	21	4	4	NUM
ejpam-6917	526	22	-	-	PUNCT
ejpam-6917	526	23	point	point	NOUN
ejpam-6917	526	24	interpolating	interpolate	VERB
ejpam-6917	526	25	non	non	ADJ
ejpam-6917	526	26	-	-	ADJ
ejpam-6917	526	27	stationary	stationary	ADJ
ejpam-6917	526	28	subdivision	subdivision	NOUN
ejpam-6917	526	29	scheme	scheme	NOUN
ejpam-6917	526	30	.	.	PUNCT
ejpam-6917	527	1	journal	journal	NOUN
ejpam-6917	527	2	of	of	ADP
ejpam-6917	527	3	computational	computational	ADJ
ejpam-6917	527	4	and	and	CCONJ
ejpam-6917	527	5	applied	applied	ADJ
ejpam-6917	527	6	mathematics	mathematic	NOUN
ejpam-6917	527	7	,	,	PUNCT
ejpam-6917	527	8	319:480–492	319:480–492	NUM
ejpam-6917	527	9	,	,	PUNCT
ejpam-6917	527	10	2017	2017	NUM
ejpam-6917	527	11	.	.	PUNCT
ejpam-6917	528	1	[	[	X
ejpam-6917	528	2	15	15	NUM
ejpam-6917	528	3	]	]	X
ejpam-6917	528	4	h.	h.	PROPN
ejpam-6917	528	5	yang	yang	PROPN
ejpam-6917	528	6	and	and	CCONJ
ejpam-6917	528	7	j.	j.	PROPN
ejpam-6917	528	8	yoon	yoon	PROPN
ejpam-6917	528	9	.	.	PUNCT
ejpam-6917	529	1	a	a	DET
ejpam-6917	529	2	shape	shape	NOUN
ejpam-6917	529	3	preserving	preserve	VERB
ejpam-6917	529	4	c2	c2	PROPN
ejpam-6917	529	5	non	non	ADJ
ejpam-6917	529	6	-	-	ADJ
ejpam-6917	529	7	linear	linear	ADJ
ejpam-6917	529	8	,	,	PUNCT
ejpam-6917	529	9	non	non	ADJ
ejpam-6917	529	10	-	-	ADJ
ejpam-6917	529	11	uniform	uniform	ADJ
ejpam-6917	529	12	subdivision	subdivision	NOUN
ejpam-6917	529	13	scheme	scheme	NOUN
ejpam-6917	529	14	with	with	ADP
ejpam-6917	529	15	fourth	fourth	ADJ
ejpam-6917	529	16	-	-	PUNCT
ejpam-6917	529	17	order	order	NOUN
ejpam-6917	529	18	accuracy	accuracy	NOUN
ejpam-6917	529	19	.	.	PUNCT
ejpam-6917	530	1	applied	apply	VERB
ejpam-6917	530	2	and	and	CCONJ
ejpam-6917	530	3	computational	computational	ADJ
ejpam-6917	530	4	harmonic	harmonic	ADJ
ejpam-6917	530	5	analysis	analysis	NOUN
ejpam-6917	530	6	,	,	PUNCT
ejpam-6917	530	7	60:267–292	60:267–292	NUM
ejpam-6917	530	8	,	,	PUNCT
ejpam-6917	530	9	2022	2022	NUM
ejpam-6917	530	10	.	.	PUNCT
ejpam-6917	531	1	[	[	X
ejpam-6917	531	2	16	16	NUM
ejpam-6917	531	3	]	]	PUNCT
ejpam-6917	531	4	h.	h.	PROPN
ejpam-6917	531	5	yang	yang	PROPN
ejpam-6917	531	6	,	,	PUNCT
ejpam-6917	531	7	j.	j.	PROPN
ejpam-6917	531	8	kim	kim	PROPN
ejpam-6917	531	9	,	,	PUNCT
ejpam-6917	531	10	and	and	CCONJ
ejpam-6917	531	11	j.	j.	PROPN
ejpam-6917	531	12	yoon	yoon	PROPN
ejpam-6917	531	13	.	.	PUNCT
ejpam-6917	532	1	a	a	DET
ejpam-6917	532	2	shape	shape	NOUN
ejpam-6917	532	3	preserving	preserve	VERB
ejpam-6917	532	4	corner	corner	NOUN
ejpam-6917	532	5	cutting	cut	VERB
ejpam-6917	532	6	algorithm	algorithm	NOUN
ejpam-6917	532	7	with	with	ADP
ejpam-6917	532	8	an	an	DET
ejpam-6917	532	9	enhanced	enhanced	ADJ
ejpam-6917	532	10	accuracy	accuracy	NOUN
ejpam-6917	532	11	.	.	PUNCT
ejpam-6917	533	1	applied	apply	VERB
ejpam-6917	533	2	mathematics	mathematics	NOUN
ejpam-6917	533	3	letters	letter	NOUN
ejpam-6917	533	4	,	,	PUNCT
ejpam-6917	533	5	137:108487	137:108487	NUM
ejpam-6917	533	6	,	,	PUNCT
ejpam-6917	533	7	2023	2023	NUM
ejpam-6917	533	8	.	.	PUNCT
ejpam-6917	534	1	[	[	X
ejpam-6917	534	2	17	17	NUM
ejpam-6917	534	3	]	]	X
ejpam-6917	534	4	c.	c.	PROPN
ejpam-6917	534	5	conti	conti	PROPN
ejpam-6917	534	6	and	and	CCONJ
ejpam-6917	534	7	k.	k.	PROPN
ejpam-6917	534	8	hormann	hormann	PROPN
ejpam-6917	534	9	.	.	PUNCT
ejpam-6917	535	1	polynomial	polynomial	ADJ
ejpam-6917	535	2	reproduction	reproduction	NOUN
ejpam-6917	535	3	for	for	ADP
ejpam-6917	535	4	univariate	univariate	ADJ
ejpam-6917	535	5	subdivision	subdivision	NOUN
ejpam-6917	535	6	schemes	scheme	NOUN
ejpam-6917	535	7	of	of	ADP
ejpam-6917	535	8	any	any	DET
ejpam-6917	535	9	arity	arity	NOUN
ejpam-6917	535	10	.	.	PUNCT
ejpam-6917	536	1	journal	journal	PROPN
ejpam-6917	536	2	of	of	ADP
ejpam-6917	536	3	approximation	approximation	NOUN
ejpam-6917	536	4	theory	theory	NOUN
ejpam-6917	536	5	,	,	PUNCT
ejpam-6917	536	6	163(4):413–437	163(4):413–437	NUM
ejpam-6917	536	7	,	,	PUNCT
ejpam-6917	536	8	2011	2011	NUM
ejpam-6917	536	9	.	.	PUNCT
ejpam-6917	537	1	[	[	X
ejpam-6917	537	2	18	18	NUM
ejpam-6917	537	3	]	]	X
ejpam-6917	537	4	n.	n.	PROPN
ejpam-6917	537	5	dyn	dyn	PROPN
ejpam-6917	537	6	,	,	PUNCT
ejpam-6917	537	7	d.	d.	PROPN
ejpam-6917	537	8	levin	levin	PROPN
ejpam-6917	537	9	,	,	PUNCT
ejpam-6917	537	10	and	and	CCONJ
ejpam-6917	537	11	j.	j.	PROPN
ejpam-6917	537	12	yoon	yoon	PROPN
ejpam-6917	537	13	.	.	PUNCT
ejpam-6917	538	1	a	a	DET
ejpam-6917	538	2	new	new	ADJ
ejpam-6917	538	3	method	method	NOUN
ejpam-6917	538	4	for	for	ADP
ejpam-6917	538	5	the	the	DET
ejpam-6917	538	6	analysis	analysis	NOUN
ejpam-6917	538	7	of	of	ADP
ejpam-6917	538	8	univariate	univariate	ADJ
ejpam-6917	538	9	nonuniform	nonuniform	ADJ
ejpam-6917	538	10	subdivision	subdivision	NOUN
ejpam-6917	538	11	schemes	scheme	NOUN
ejpam-6917	538	12	.	.	PUNCT
ejpam-6917	539	1	constructive	constructive	ADJ
ejpam-6917	539	2	approximation	approximation	NOUN
ejpam-6917	539	3	,	,	PUNCT
ejpam-6917	539	4	40:173–188	40:173–188	PROPN
ejpam-6917	539	5	,	,	PUNCT
ejpam-6917	539	6	2014	2014	NUM
ejpam-6917	539	7	.	.	PUNCT
ejpam-6917	540	1	[	[	X
ejpam-6917	540	2	19	19	NUM
ejpam-6917	540	3	]	]	X
ejpam-6917	540	4	y.	y.	PROPN
ejpam-6917	540	5	kim	kim	PROPN
ejpam-6917	540	6	,	,	PUNCT
ejpam-6917	540	7	h.	h.	PROPN
ejpam-6917	540	8	yang	yang	PROPN
ejpam-6917	540	9	,	,	PUNCT
ejpam-6917	540	10	and	and	CCONJ
ejpam-6917	540	11	j.	j.	PROPN
ejpam-6917	540	12	yoon	yoon	PROPN
ejpam-6917	540	13	.	.	PUNCT
ejpam-6917	540	14	shape	shape	NOUN
ejpam-6917	540	15	-	-	PUNCT
ejpam-6917	540	16	preserving	preserve	VERB
ejpam-6917	540	17	subdivision	subdivision	NOUN
ejpam-6917	540	18	scheme	scheme	NOUN
ejpam-6917	540	19	with	with	ADP
ejpam-6917	540	20	the	the	DET
ejpam-6917	540	21	thirdorder	thirdorder	NOUN
ejpam-6917	540	22	accuracy	accuracy	NOUN
ejpam-6917	540	23	and	and	CCONJ
ejpam-6917	540	24	c2	c2	PROPN
ejpam-6917	540	25	smoothness	smoothness	PROPN
ejpam-6917	540	26	.	.	PUNCT
ejpam-6917	541	1	mathematics	mathematic	NOUN
ejpam-6917	541	2	and	and	CCONJ
ejpam-6917	541	3	computers	computer	NOUN
ejpam-6917	541	4	in	in	ADP
ejpam-6917	541	5	simulation	simulation	NOUN
ejpam-6917	541	6	,	,	PUNCT
ejpam-6917	541	7	235:160–174	235:160–174	NUM
ejpam-6917	541	8	,	,	PUNCT
ejpam-6917	541	9	2025	2025	NUM
ejpam-6917	541	10	.	.	PUNCT
ejpam-6917	542	1	[	[	X
ejpam-6917	542	2	20	20	NUM
ejpam-6917	542	3	]	]	PUNCT
ejpam-6917	542	4	j.	j.	PROPN
ejpam-6917	542	5	tan	tan	PROPN
ejpam-6917	542	6	,	,	PUNCT
ejpam-6917	542	7	y.	y.	PROPN
ejpam-6917	542	8	yao	yao	PROPN
ejpam-6917	542	9	,	,	PUNCT
ejpam-6917	542	10	h.	h.	PROPN
ejpam-6917	542	11	cao	cao	PROPN
ejpam-6917	542	12	,	,	PUNCT
ejpam-6917	542	13	and	and	CCONJ
ejpam-6917	542	14	l.	l.	PROPN
ejpam-6917	542	15	zhang	zhang	PROPN
ejpam-6917	542	16	.	.	PUNCT
ejpam-6917	543	1	convexity	convexity	PROPN
ejpam-6917	543	2	preservation	preservation	NOUN
ejpam-6917	543	3	of	of	ADP
ejpam-6917	543	4	five	five	NUM
ejpam-6917	543	5	-	-	PUNCT
ejpam-6917	543	6	point	point	NOUN
ejpam-6917	543	7	binary	binary	ADJ
ejpam-6917	543	8	subdivision	subdivision	NOUN
ejpam-6917	543	9	scheme	scheme	NOUN
ejpam-6917	543	10	with	with	ADP
ejpam-6917	543	11	a	a	DET
ejpam-6917	543	12	parameter	parameter	NOUN
ejpam-6917	543	13	.	.	PUNCT
ejpam-6917	544	1	applied	apply	VERB
ejpam-6917	544	2	mathematics	mathematic	NOUN
ejpam-6917	544	3	and	and	CCONJ
ejpam-6917	544	4	computation	computation	NOUN
ejpam-6917	544	5	,	,	PUNCT
ejpam-6917	544	6	245:279–288	245:279–288	NUM
ejpam-6917	544	7	,	,	PUNCT
ejpam-6917	544	8	2014	2014	NUM
ejpam-6917	544	9	.	.	PUNCT
ejpam-6917	545	1	[	[	X
ejpam-6917	545	2	21	21	NUM
ejpam-6917	545	3	]	]	PUNCT
ejpam-6917	545	4	s.	s.	PROPN
ejpam-6917	545	5	s.	s.	PROPN
ejpam-6917	545	6	siddiqi	siddiqi	PROPN
ejpam-6917	545	7	,	,	PUNCT
ejpam-6917	545	8	w.	w.	PROPN
ejpam-6917	545	9	us	us	PROPN
ejpam-6917	545	10	salam	salam	PROPN
ejpam-6917	545	11	,	,	PUNCT
ejpam-6917	545	12	and	and	CCONJ
ejpam-6917	545	13	k.	k.	PROPN
ejpam-6917	545	14	rehan	rehan	PROPN
ejpam-6917	545	15	.	.	PUNCT
ejpam-6917	546	1	a	a	DET
ejpam-6917	546	2	new	new	ADJ
ejpam-6917	546	3	non	non	ADJ
ejpam-6917	546	4	-	-	ADJ
ejpam-6917	546	5	stationary	stationary	ADJ
ejpam-6917	546	6	binary	binary	ADJ
ejpam-6917	546	7	6	6	NUM
ejpam-6917	546	8	-	-	PUNCT
ejpam-6917	546	9	point	point	NOUN
ejpam-6917	546	10	subdivision	subdivision	NOUN
ejpam-6917	546	11	scheme	scheme	NOUN
ejpam-6917	546	12	.	.	PUNCT
ejpam-6917	547	1	applied	apply	VERB
ejpam-6917	547	2	mathematics	mathematic	NOUN
ejpam-6917	547	3	and	and	CCONJ
ejpam-6917	547	4	computation	computation	NOUN
ejpam-6917	547	5	,	,	PUNCT
ejpam-6917	547	6	268:1227–1239	268:1227–1239	NUM
ejpam-6917	547	7	,	,	PUNCT
ejpam-6917	547	8	2015	2015	NUM
ejpam-6917	547	9	.	.	PUNCT
ejpam-6917	548	1	[	[	X
ejpam-6917	548	2	22	22	NUM
ejpam-6917	548	3	]	]	PUNCT
ejpam-6917	548	4	s.	s.	PROPN
ejpam-6917	548	5	zouaoui	zouaoui	PROPN
ejpam-6917	548	6	,	,	PUNCT
ejpam-6917	548	7	s.	s.	PROPN
ejpam-6917	548	8	amat	amat	PROPN
ejpam-6917	548	9	,	,	PUNCT
ejpam-6917	548	10	s.	s.	PROPN
ejpam-6917	548	11	busquier	busquier	PROPN
ejpam-6917	548	12	,	,	PUNCT
ejpam-6917	548	13	and	and	CCONJ
ejpam-6917	548	14	j.	j.	PROPN
ejpam-6917	548	15	ruiz	ruiz	PROPN
ejpam-6917	548	16	.	.	PUNCT
ejpam-6917	549	1	on	on	ADP
ejpam-6917	549	2	a	a	DET
ejpam-6917	549	3	nonlinear	nonlinear	ADJ
ejpam-6917	549	4	three	three	NUM
ejpam-6917	549	5	-	-	PUNCT
ejpam-6917	549	6	point	point	NOUN
ejpam-6917	549	7	subdivision	subdivision	NOUN
ejpam-6917	549	8	scheme	scheme	NOUN
ejpam-6917	549	9	reproducing	reproduce	VERB
ejpam-6917	549	10	piecewise	piecewise	NOUN
ejpam-6917	549	11	constant	constant	ADJ
ejpam-6917	549	12	functions	function	NOUN
ejpam-6917	549	13	.	.	PUNCT
ejpam-6917	550	1	mathematics	mathematic	NOUN
ejpam-6917	550	2	,	,	PUNCT
ejpam-6917	550	3	10(15):2790	10(15):2790	NUM
ejpam-6917	550	4	,	,	PUNCT
ejpam-6917	550	5	2022	2022	NUM
ejpam-6917	550	6	.	.	PUNCT
ejpam-6917	551	1	[	[	X
ejpam-6917	551	2	23	23	NUM
ejpam-6917	551	3	]	]	X
ejpam-6917	551	4	n.	n.	PROPN
ejpam-6917	551	5	dyn	dyn	PROPN
ejpam-6917	551	6	,	,	PUNCT
ejpam-6917	551	7	k.	k.	PROPN
ejpam-6917	551	8	hormann	hormann	PROPN
ejpam-6917	551	9	,	,	PUNCT
ejpam-6917	551	10	and	and	CCONJ
ejpam-6917	551	11	c.	c.	PROPN
ejpam-6917	551	12	mancinelli	mancinelli	PROPN
ejpam-6917	551	13	.	.	PUNCT
ejpam-6917	552	1	non	non	ADJ
ejpam-6917	552	2	-	-	ADJ
ejpam-6917	552	3	uniform	uniform	ADJ
ejpam-6917	552	4	interpolatory	interpolatory	NOUN
ejpam-6917	552	5	subdivision	subdivision	NOUN
ejpam-6917	552	6	schemes	scheme	NOUN
ejpam-6917	552	7	with	with	ADP
ejpam-6917	552	8	improved	improved	ADJ
ejpam-6917	552	9	smoothness	smoothness	NOUN
ejpam-6917	552	10	.	.	PUNCT
ejpam-6917	553	1	computer	computer	NOUN
ejpam-6917	553	2	aided	aid	VERB
ejpam-6917	553	3	geometric	geometric	ADJ
ejpam-6917	553	4	design	design	NOUN
ejpam-6917	553	5	,	,	PUNCT
ejpam-6917	553	6	94:102083	94:102083	X
ejpam-6917	553	7	,	,	PUNCT
ejpam-6917	553	8	2022	2022	NUM
ejpam-6917	553	9	.	.	PUNCT
ejpam-6917	554	1	[	[	X
ejpam-6917	554	2	24	24	NUM
ejpam-6917	554	3	]	]	X
ejpam-6917	554	4	r.	r.	PROPN
ejpam-6917	554	5	hameed	hameed	PROPN
ejpam-6917	554	6	,	,	PUNCT
ejpam-6917	554	7	a.	a.	PROPN
ejpam-6917	554	8	jamil	jamil	PROPN
ejpam-6917	554	9	,	,	PUNCT
ejpam-6917	554	10	and	and	CCONJ
ejpam-6917	554	11	j.	j.	PROPN
ejpam-6917	554	12	younis	younis	PROPN
ejpam-6917	554	13	.	.	PUNCT
ejpam-6917	555	1	enhanced	enhance	VERB
ejpam-6917	555	2	curve	curve	NOUN
ejpam-6917	555	3	representations	representation	NOUN
ejpam-6917	555	4	using	use	VERB
ejpam-6917	555	5	piecewise	piecewise	NOUN
ejpam-6917	555	6	non	non	ADJ
ejpam-6917	555	7	-	-	ADJ
ejpam-6917	555	8	linear	linear	ADJ
ejpam-6917	555	9	binary	binary	ADJ
ejpam-6917	555	10	subdivision	subdivision	NOUN
ejpam-6917	555	11	scheme	scheme	NOUN
ejpam-6917	555	12	.	.	PUNCT
ejpam-6917	556	1	arab	arab	PROPN
ejpam-6917	556	2	journal	journal	PROPN
ejpam-6917	556	3	of	of	ADP
ejpam-6917	556	4	basic	basic	ADJ
ejpam-6917	556	5	and	and	CCONJ
ejpam-6917	556	6	applied	applied	ADJ
ejpam-6917	556	7	sciences	science	NOUN
ejpam-6917	556	8	,	,	PUNCT
ejpam-6917	556	9	31(1):554–570	31(1):554–570	NUM
ejpam-6917	556	10	,	,	PUNCT
ejpam-6917	556	11	2024	2024	NUM
ejpam-6917	556	12	.	.	PUNCT
ejpam-6917	557	1	[	[	X
ejpam-6917	557	2	25	25	NUM
ejpam-6917	557	3	]	]	PUNCT
ejpam-6917	557	4	s.	s.	PROPN
ejpam-6917	557	5	w.	w.	PROPN
ejpam-6917	557	6	choi	choi	PROPN
ejpam-6917	557	7	,	,	PUNCT
ejpam-6917	557	8	b.	b.	PROPN
ejpam-6917	557	9	g.	g.	PROPN
ejpam-6917	557	10	lee	lee	PROPN
ejpam-6917	557	11	,	,	PUNCT
ejpam-6917	557	12	y.	y.	PROPN
ejpam-6917	557	13	j.	j.	PROPN
ejpam-6917	557	14	lee	lee	PROPN
ejpam-6917	557	15	,	,	PUNCT
ejpam-6917	557	16	and	and	CCONJ
ejpam-6917	557	17	j.	j.	PROPN
ejpam-6917	557	18	yoon	yoon	PROPN
ejpam-6917	557	19	.	.	PUNCT
ejpam-6917	558	1	stationary	stationary	ADJ
ejpam-6917	558	2	subdivision	subdivision	NOUN
ejpam-6917	558	3	schemes	scheme	NOUN
ejpam-6917	558	4	reproducing	reproduce	VERB
ejpam-6917	558	5	polynomials	polynomial	NOUN
ejpam-6917	558	6	.	.	PUNCT
ejpam-6917	559	1	computer	computer	NOUN
ejpam-6917	559	2	aided	aid	VERB
ejpam-6917	559	3	geometric	geometric	ADJ
ejpam-6917	559	4	design	design	NOUN
ejpam-6917	559	5	,	,	PUNCT
ejpam-6917	559	6	23(4):351–360	23(4):351–360	PROPN
ejpam-6917	559	7	,	,	PUNCT
ejpam-6917	559	8	2006	2006	NUM
ejpam-6917	559	9	.	.	PUNCT
ejpam-6917	560	1	[	[	X
ejpam-6917	560	2	26	26	NUM
ejpam-6917	560	3	]	]	X
ejpam-6917	560	4	h.	h.	PROPN
ejpam-6917	560	5	yang	yang	PROPN
ejpam-6917	560	6	,	,	PUNCT
ejpam-6917	560	7	k.	k.	PROPN
ejpam-6917	560	8	kim	kim	PROPN
ejpam-6917	560	9	,	,	PUNCT
ejpam-6917	560	10	and	and	CCONJ
ejpam-6917	560	11	j.	j.	PROPN
ejpam-6917	560	12	yoon	yoon	PROPN
ejpam-6917	560	13	.	.	PUNCT
ejpam-6917	561	1	a	a	DET
ejpam-6917	561	2	family	family	NOUN
ejpam-6917	561	3	of	of	ADP
ejpam-6917	561	4	c2	c2	PROPN
ejpam-6917	561	5	four	four	NUM
ejpam-6917	561	6	-	-	PUNCT
ejpam-6917	561	7	point	point	NOUN
ejpam-6917	561	8	stationary	stationary	ADJ
ejpam-6917	561	9	subdivision	subdivision	NOUN
ejpam-6917	561	10	schemes	scheme	NOUN
ejpam-6917	561	11	with	with	ADP
ejpam-6917	561	12	fourth	fourth	ADJ
ejpam-6917	561	13	-	-	PUNCT
ejpam-6917	561	14	order	order	NOUN
ejpam-6917	561	15	accuracy	accuracy	NOUN
ejpam-6917	561	16	and	and	CCONJ
ejpam-6917	561	17	shape	shape	NOUN
ejpam-6917	561	18	-	-	PUNCT
ejpam-6917	561	19	preserving	preserve	VERB
ejpam-6917	561	20	properties	property	NOUN
ejpam-6917	561	21	.	.	PUNCT
ejpam-6917	562	1	journal	journal	NOUN
ejpam-6917	562	2	of	of	ADP
ejpam-6917	562	3	computational	computational	ADJ
ejpam-6917	562	4	and	and	CCONJ
ejpam-6917	562	5	applied	applied	ADJ
ejpam-6917	562	6	mathematics	mathematic	NOUN
ejpam-6917	562	7	,	,	PUNCT
ejpam-6917	562	8	446:115843	446:115843	NUM
ejpam-6917	562	9	,	,	PUNCT
ejpam-6917	562	10	2024	2024	NUM
ejpam-6917	562	11	.	.	PUNCT
ejpam-6917	563	1	[	[	X
ejpam-6917	563	2	27	27	NUM
ejpam-6917	563	3	]	]	X
ejpam-6917	563	4	n.	n.	PROPN
ejpam-6917	563	5	dyn	dyn	PROPN
ejpam-6917	563	6	.	.	PUNCT
ejpam-6917	564	1	interpolatory	interpolatory	ADJ
ejpam-6917	564	2	subdivision	subdivision	NOUN
ejpam-6917	564	3	schemes	scheme	NOUN
ejpam-6917	564	4	.	.	PUNCT
ejpam-6917	565	1	in	in	ADP
ejpam-6917	565	2	tutorials	tutorial	NOUN
ejpam-6917	565	3	on	on	ADP
ejpam-6917	565	4	multiresolution	multiresolution	NOUN
ejpam-6917	565	5	in	in	ADP
ejpam-6917	565	6	geometric	geometric	ADJ
ejpam-6917	565	7	modeling	modeling	NOUN
ejpam-6917	565	8	,	,	PUNCT
ejpam-6917	565	9	pages	page	NOUN
ejpam-6917	565	10	25–50	25–50	NUM
ejpam-6917	565	11	.	.	PUNCT
ejpam-6917	565	12	2002	2002	NUM
ejpam-6917	565	13	.	.	PUNCT
ejpam-6917	566	1	[	[	X
ejpam-6917	566	2	28	28	NUM
ejpam-6917	566	3	]	]	X
ejpam-6917	566	4	a.	a.	PROPN
ejpam-6917	566	5	levin	levin	PROPN
ejpam-6917	566	6	.	.	PUNCT
ejpam-6917	567	1	polynomial	polynomial	ADJ
ejpam-6917	567	2	generation	generation	NOUN
ejpam-6917	567	3	and	and	CCONJ
ejpam-6917	567	4	quasi	quasi	NOUN
ejpam-6917	567	5	-	-	NOUN
ejpam-6917	567	6	interpolation	interpolation	NOUN
ejpam-6917	567	7	in	in	ADP
ejpam-6917	567	8	stationary	stationary	ADJ
ejpam-6917	567	9	non	non	ADJ
ejpam-6917	567	10	-	-	ADJ
ejpam-6917	567	11	uniform	uniform	ADJ
ejpam-6917	567	12	f.	f.	PROPN
ejpam-6917	567	13	s.	s.	PROPN
ejpam-6917	567	14	alshammari	alshammari	PROPN
ejpam-6917	567	15	et	et	PROPN
ejpam-6917	567	16	al	al	PROPN
ejpam-6917	567	17	.	.	PUNCT
ejpam-6917	567	18	/	/	SYM
ejpam-6917	567	19	eur	eur	PROPN
ejpam-6917	567	20	.	.	PUNCT
ejpam-6917	568	1	j.	j.	PROPN
ejpam-6917	568	2	pure	pure	PROPN
ejpam-6917	568	3	appl	appl	PROPN
ejpam-6917	568	4	.	.	PROPN
ejpam-6917	568	5	math	math	PROPN
ejpam-6917	568	6	,	,	PUNCT
ejpam-6917	568	7	18	18	NUM
ejpam-6917	568	8	(	(	PUNCT
ejpam-6917	568	9	4	4	NUM
ejpam-6917	568	10	)	)	PUNCT
ejpam-6917	568	11	(	(	PUNCT
ejpam-6917	568	12	2025	2025	NUM
ejpam-6917	568	13	)	)	PUNCT
ejpam-6917	568	14	,	,	PUNCT
ejpam-6917	568	15	6917	6917	NUM
ejpam-6917	568	16	26	26	NUM
ejpam-6917	568	17	of	of	ADP
ejpam-6917	568	18	26	26	NUM
ejpam-6917	568	19	subdivision	subdivision	NOUN
ejpam-6917	568	20	.	.	PUNCT
ejpam-6917	569	1	computer	computer	NOUN
ejpam-6917	569	2	aided	aid	VERB
ejpam-6917	569	3	geometric	geometric	ADJ
ejpam-6917	569	4	design	design	NOUN
ejpam-6917	569	5	,	,	PUNCT
ejpam-6917	569	6	20(1):41–60	20(1):41–60	NUM
ejpam-6917	569	7	,	,	PUNCT
ejpam-6917	569	8	2003	2003	NUM
ejpam-6917	569	9	.	.	PUNCT
ejpam-6917	570	1	[	[	X
ejpam-6917	570	2	29	29	NUM
ejpam-6917	570	3	]	]	X
ejpam-6917	570	4	g.	g.	PROPN
ejpam-6917	570	5	mustafa	mustafa	PROPN
ejpam-6917	570	6	and	and	CCONJ
ejpam-6917	570	7	a.	a.	PROPN
ejpam-6917	570	8	h.	h.	PROPN
ejpam-6917	570	9	randhawa	randhawa	PROPN
ejpam-6917	570	10	.	.	PUNCT
ejpam-6917	571	1	complete	complete	ADJ
ejpam-6917	571	2	analysis	analysis	NOUN
ejpam-6917	571	3	of	of	ADP
ejpam-6917	571	4	3	3	NUM
ejpam-6917	571	5	-	-	PUNCT
ejpam-6917	571	6	point	point	NOUN
ejpam-6917	571	7	binary	binary	ADJ
ejpam-6917	571	8	subdivision	subdivision	NOUN
ejpam-6917	571	9	scheme	scheme	NOUN
ejpam-6917	571	10	.	.	PUNCT
ejpam-6917	572	1	journal	journal	NOUN
ejpam-6917	572	2	of	of	ADP
ejpam-6917	572	3	pure	pure	ADJ
ejpam-6917	572	4	and	and	CCONJ
ejpam-6917	572	5	applied	apply	VERB
ejpam-6917	572	6	science	science	NOUN
ejpam-6917	572	7	,	,	PUNCT
ejpam-6917	572	8	24:33	24:33	NUM
ejpam-6917	572	9	,	,	PUNCT
ejpam-6917	572	10	2014	2014	NUM
ejpam-6917	572	11	.	.	PUNCT
ejpam-6917	573	1	[	[	X
ejpam-6917	573	2	30	30	NUM
ejpam-6917	573	3	]	]	X
ejpam-6917	573	4	c.	c.	PROPN
ejpam-6917	573	5	beccari	beccari	PROPN
ejpam-6917	573	6	,	,	PUNCT
ejpam-6917	573	7	g.	g.	PROPN
ejpam-6917	573	8	casciola	casciola	PROPN
ejpam-6917	573	9	,	,	PUNCT
ejpam-6917	573	10	and	and	CCONJ
ejpam-6917	573	11	l.	l.	PROPN
ejpam-6917	573	12	romani	romani	PROPN
ejpam-6917	573	13	.	.	PUNCT
ejpam-6917	574	1	a	a	DET
ejpam-6917	574	2	non	non	ADJ
ejpam-6917	574	3	-	-	ADJ
ejpam-6917	574	4	stationary	stationary	ADJ
ejpam-6917	574	5	uniform	uniform	ADJ
ejpam-6917	574	6	tension	tension	NOUN
ejpam-6917	574	7	controlled	control	VERB
ejpam-6917	574	8	interpolating	interpolate	VERB
ejpam-6917	574	9	4	4	NUM
ejpam-6917	574	10	-	-	PUNCT
ejpam-6917	574	11	point	point	NOUN
ejpam-6917	574	12	scheme	scheme	NOUN
ejpam-6917	574	13	reproducing	reproduce	VERB
ejpam-6917	574	14	conics	conic	NOUN
ejpam-6917	574	15	.	.	PUNCT
ejpam-6917	575	1	computer	computer	NOUN
ejpam-6917	575	2	aided	aid	VERB
ejpam-6917	575	3	geometric	geometric	ADJ
ejpam-6917	575	4	design	design	NOUN
ejpam-6917	575	5	,	,	PUNCT
ejpam-6917	575	6	24(1):1–9	24(1):1–9	NUM
ejpam-6917	575	7	,	,	PUNCT
ejpam-6917	575	8	2007	2007	NUM
ejpam-6917	575	9	.	.	PUNCT
ejpam-6917	576	1	[	[	X
ejpam-6917	576	2	31	31	NUM
ejpam-6917	576	3	]	]	X
ejpam-6917	576	4	n.	n.	PROPN
ejpam-6917	576	5	dyn	dyn	PROPN
ejpam-6917	576	6	,	,	PUNCT
ejpam-6917	576	7	m.	m.	NOUN
ejpam-6917	576	8	s.	s.	PROPN
ejpam-6917	576	9	floater	floater	PROPN
ejpam-6917	576	10	,	,	PUNCT
ejpam-6917	576	11	and	and	CCONJ
ejpam-6917	576	12	k.	k.	PROPN
ejpam-6917	576	13	hormann	hormann	PROPN
ejpam-6917	576	14	.	.	PUNCT
ejpam-6917	577	1	c2	c2	PROPN
ejpam-6917	577	2	four	four	NUM
ejpam-6917	577	3	-	-	PUNCT
ejpam-6917	577	4	point	point	NOUN
ejpam-6917	577	5	subdivision	subdivision	NOUN
ejpam-6917	577	6	scheme	scheme	NOUN
ejpam-6917	577	7	with	with	ADP
ejpam-6917	577	8	fourth	fourth	ADJ
ejpam-6917	577	9	-	-	PUNCT
ejpam-6917	577	10	order	order	NOUN
ejpam-6917	577	11	accuracy	accuracy	NOUN
ejpam-6917	577	12	and	and	CCONJ
ejpam-6917	577	13	its	its	PRON
ejpam-6917	577	14	extensions	extension	NOUN
ejpam-6917	577	15	.	.	PUNCT
ejpam-6917	578	1	in	in	ADP
ejpam-6917	578	2	mathematical	mathematical	ADJ
ejpam-6917	578	3	methods	method	NOUN
ejpam-6917	578	4	for	for	ADP
ejpam-6917	578	5	curves	curve	NOUN
ejpam-6917	578	6	and	and	CCONJ
ejpam-6917	578	7	surfaces	surface	NOUN
ejpam-6917	578	8	,	,	PUNCT
ejpam-6917	578	9	pages	page	NOUN
ejpam-6917	578	10	145–156	145–156	NUM
ejpam-6917	578	11	,	,	PUNCT
ejpam-6917	578	12	2005	2005	NUM
ejpam-6917	578	13	.	.	PUNCT
ejpam-6917	579	1	[	[	X
ejpam-6917	579	2	32	32	NUM
ejpam-6917	579	3	]	]	PUNCT
ejpam-6917	579	4	s.	s.	PROPN
ejpam-6917	579	5	s.	s.	PROPN
ejpam-6917	579	6	siddiqi	siddiqi	PROPN
ejpam-6917	579	7	and	and	CCONJ
ejpam-6917	579	8	n.	n.	PROPN
ejpam-6917	579	9	ahmad	ahmad	PROPN
ejpam-6917	579	10	.	.	PUNCT
ejpam-6917	580	1	a	a	DET
ejpam-6917	580	2	new	new	ADJ
ejpam-6917	580	3	five	five	NUM
ejpam-6917	580	4	-	-	PUNCT
ejpam-6917	580	5	point	point	NOUN
ejpam-6917	580	6	approximating	approximate	VERB
ejpam-6917	580	7	subdivision	subdivision	NOUN
ejpam-6917	580	8	scheme	scheme	NOUN
ejpam-6917	580	9	.	.	PUNCT
ejpam-6917	581	1	international	international	ADJ
ejpam-6917	581	2	journal	journal	NOUN
ejpam-6917	581	3	of	of	ADP
ejpam-6917	581	4	computational	computational	ADJ
ejpam-6917	581	5	mathematics	mathematic	NOUN
ejpam-6917	581	6	,	,	PUNCT
ejpam-6917	581	7	85(1):65–72	85(1):65–72	NUM
ejpam-6917	581	8	,	,	PUNCT
ejpam-6917	581	9	2008	2008	NUM
ejpam-6917	581	10	.	.	PUNCT