id	sid	tid	token	lemma	pos
ejpam-556	1	1	6_556_hussain.dvi	6_556_hussain.dvi	NUM
ejpam-556	1	2	european	european	ADJ
ejpam-556	1	3	journal	journal	NOUN
ejpam-556	1	4	of	of	ADP
ejpam-556	1	5	pure	pure	ADJ
ejpam-556	1	6	and	and	CCONJ
ejpam-556	1	7	applied	apply	VERB
ejpam-556	1	8	mathematics	mathematic	NOUN
ejpam-556	1	9	vol	vol	NOUN
ejpam-556	1	10	.	.	PUNCT
ejpam-556	2	1	3	3	NUM
ejpam-556	2	2	,	,	PUNCT
ejpam-556	2	3	no	no	INTJ
ejpam-556	2	4	.	.	NOUN
ejpam-556	2	5	2	2	NUM
ejpam-556	2	6	,	,	PUNCT
ejpam-556	2	7	2010	2010	NUM
ejpam-556	2	8	,	,	PUNCT
ejpam-556	2	9	194	194	NUM
ejpam-556	2	10	-	-	SYM
ejpam-556	2	11	212	212	NUM
ejpam-556	2	12	issn	issn	PROPN
ejpam-556	2	13	1307	1307	NUM
ejpam-556	2	14	-	-	SYM
ejpam-556	2	15	5543	5543	NUM
ejpam-556	2	16	–	–	PUNCT
ejpam-556	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-556	2	18	scientific	scientific	ADJ
ejpam-556	2	19	data	data	NOUN
ejpam-556	2	20	visualization	visualization	NOUN
ejpam-556	2	21	with	with	ADP
ejpam-556	2	22	shape	shape	NOUN
ejpam-556	2	23	preserving	preserve	VERB
ejpam-556	2	24	c1	c1	NOUN
ejpam-556	2	25	rational	rational	ADJ
ejpam-556	2	26	cubic	cubic	ADJ
ejpam-556	2	27	interpolation	interpolation	NOUN
ejpam-556	2	28	malik	malik	PROPN
ejpam-556	2	29	zawwar	zawwar	PROPN
ejpam-556	2	30	hussain1∗	hussain1∗	PROPN
ejpam-556	2	31	,	,	PUNCT
ejpam-556	2	32	muhammad	muhammad	PROPN
ejpam-556	2	33	sarfraz2	sarfraz2	PROPN
ejpam-556	2	34	,	,	PUNCT
ejpam-556	2	35	maria	maria	PROPN
ejpam-556	2	36	hussain3	hussain3	PROPN
ejpam-556	2	37	1	1	NUM
ejpam-556	2	38	department	department	NOUN
ejpam-556	2	39	of	of	ADP
ejpam-556	2	40	mathematics	mathematic	NOUN
ejpam-556	2	41	,	,	PUNCT
ejpam-556	2	42	university	university	NOUN
ejpam-556	2	43	of	of	ADP
ejpam-556	2	44	the	the	DET
ejpam-556	2	45	punjab	punjab	ADJ
ejpam-556	2	46	,	,	PUNCT
ejpam-556	2	47	lahore	lahore	PROPN
ejpam-556	2	48	,	,	PUNCT
ejpam-556	2	49	pakistan	pakistan	PROPN
ejpam-556	2	50	2	2	NUM
ejpam-556	2	51	department	department	NOUN
ejpam-556	2	52	of	of	ADP
ejpam-556	2	53	information	information	NOUN
ejpam-556	2	54	sciences	sciences	PROPN
ejpam-556	2	55	,	,	PUNCT
ejpam-556	2	56	adailiya	adailiya	PROPN
ejpam-556	2	57	campus	campus	PROPN
ejpam-556	2	58	,	,	PUNCT
ejpam-556	2	59	kuwait	kuwait	PROPN
ejpam-556	2	60	university	university	PROPN
ejpam-556	2	61	,	,	PUNCT
ejpam-556	2	62	kuwait	kuwait	PROPN
ejpam-556	2	63	3	3	NUM
ejpam-556	2	64	lahore	lahore	PROPN
ejpam-556	2	65	college	college	NOUN
ejpam-556	2	66	for	for	ADP
ejpam-556	2	67	women	woman	NOUN
ejpam-556	2	68	university	university	NOUN
ejpam-556	2	69	,	,	PUNCT
ejpam-556	2	70	lahore	lahore	PROPN
ejpam-556	2	71	,	,	PUNCT
ejpam-556	2	72	pakistan	pakistan	PROPN
ejpam-556	2	73	abstract	abstract	NOUN
ejpam-556	2	74	.	.	PUNCT
ejpam-556	3	1	this	this	DET
ejpam-556	3	2	paper	paper	NOUN
ejpam-556	3	3	deals	deal	NOUN
ejpam-556	3	4	with	with	ADP
ejpam-556	3	5	the	the	DET
ejpam-556	3	6	shape	shape	NOUN
ejpam-556	3	7	preserving	preserve	VERB
ejpam-556	3	8	c1	c1	NOUN
ejpam-556	3	9	rational	rational	ADJ
ejpam-556	3	10	cubic	cubic	ADJ
ejpam-556	3	11	interpolation	interpolation	NOUN
ejpam-556	3	12	.	.	PUNCT
ejpam-556	4	1	the	the	DET
ejpam-556	4	2	developed	develop	VERB
ejpam-556	4	3	rational	rational	ADJ
ejpam-556	4	4	cubic	cubic	ADJ
ejpam-556	4	5	interpolating	interpolate	VERB
ejpam-556	4	6	function	function	NOUN
ejpam-556	4	7	has	have	VERB
ejpam-556	4	8	only	only	ADV
ejpam-556	4	9	one	one	NUM
ejpam-556	4	10	free	free	ADJ
ejpam-556	4	11	parameter	parameter	NOUN
ejpam-556	4	12	.	.	PUNCT
ejpam-556	5	1	the	the	DET
ejpam-556	5	2	approximation	approximation	NOUN
ejpam-556	5	3	order	order	NOUN
ejpam-556	5	4	of	of	ADP
ejpam-556	5	5	rational	rational	ADJ
ejpam-556	5	6	cubic	cubic	ADJ
ejpam-556	5	7	function	function	NOUN
ejpam-556	5	8	is	be	AUX
ejpam-556	5	9	investigated	investigate	VERB
ejpam-556	5	10	and	and	CCONJ
ejpam-556	5	11	range	range	NOUN
ejpam-556	5	12	of	of	ADP
ejpam-556	5	13	optimal	optimal	ADJ
ejpam-556	5	14	error	error	NOUN
ejpam-556	5	15	constant	constant	ADJ
ejpam-556	5	16	is	be	AUX
ejpam-556	5	17	determined	determine	VERB
ejpam-556	5	18	.	.	PUNCT
ejpam-556	6	1	moreover	moreover	ADV
ejpam-556	6	2	,	,	PUNCT
ejpam-556	6	3	positive	positive	ADJ
ejpam-556	6	4	,	,	PUNCT
ejpam-556	6	5	constrained	constrained	ADJ
ejpam-556	6	6	and	and	CCONJ
ejpam-556	6	7	monotone	monotone	ADJ
ejpam-556	6	8	data	datum	NOUN
ejpam-556	6	9	preserving	preserve	VERB
ejpam-556	6	10	schemes	scheme	NOUN
ejpam-556	6	11	are	be	AUX
ejpam-556	6	12	developed	develop	VERB
ejpam-556	6	13	.	.	PUNCT
ejpam-556	7	1	2000	2000	NUM
ejpam-556	7	2	mathematics	mathematic	NOUN
ejpam-556	7	3	subject	subject	NOUN
ejpam-556	7	4	classifications	classification	NOUN
ejpam-556	7	5	:	:	PUNCT
ejpam-556	7	6	68u05	68u05	NUM
ejpam-556	7	7	,	,	PUNCT
ejpam-556	7	8	65d05	65d05	NUM
ejpam-556	7	9	,	,	PUNCT
ejpam-556	7	10	65d07	65d07	NUM
ejpam-556	7	11	,	,	PUNCT
ejpam-556	7	12	65d18	65d18	NUM
ejpam-556	7	13	.	.	PUNCT
ejpam-556	8	1	key	key	ADJ
ejpam-556	8	2	words	word	NOUN
ejpam-556	8	3	and	and	CCONJ
ejpam-556	8	4	phrases	phrase	NOUN
ejpam-556	8	5	:	:	PUNCT
ejpam-556	8	6	rational	rational	ADJ
ejpam-556	8	7	cubic	cubic	ADJ
ejpam-556	8	8	,	,	PUNCT
ejpam-556	8	9	spline	spline	NOUN
ejpam-556	8	10	,	,	PUNCT
ejpam-556	8	11	peano	peano	PROPN
ejpam-556	8	12	kernel	kernel	PROPN
ejpam-556	8	13	theorem	theorem	PROPN
ejpam-556	8	14	,	,	PUNCT
ejpam-556	8	15	interpolation	interpolation	NOUN
ejpam-556	8	16	,	,	PUNCT
ejpam-556	8	17	visualization	visualization	NOUN
ejpam-556	8	18	.	.	PUNCT
ejpam-556	9	1	1	1	X
ejpam-556	9	2	.	.	X
ejpam-556	9	3	introduction	introduction	NOUN
ejpam-556	9	4	the	the	DET
ejpam-556	9	5	development	development	NOUN
ejpam-556	9	6	of	of	ADP
ejpam-556	9	7	interpolating	interpolate	VERB
ejpam-556	9	8	and	and	CCONJ
ejpam-556	9	9	approximating	approximate	VERB
ejpam-556	9	10	techniques	technique	NOUN
ejpam-556	9	11	for	for	ADP
ejpam-556	9	12	shape	shape	NOUN
ejpam-556	9	13	control	control	NOUN
ejpam-556	9	14	and	and	CCONJ
ejpam-556	9	15	shape	shape	NOUN
ejpam-556	9	16	preservation	preservation	NOUN
ejpam-556	9	17	is	be	AUX
ejpam-556	9	18	a	a	DET
ejpam-556	9	19	germane	germane	ADJ
ejpam-556	9	20	area	area	NOUN
ejpam-556	9	21	of	of	ADP
ejpam-556	9	22	research	research	NOUN
ejpam-556	9	23	in	in	ADP
ejpam-556	9	24	computer	computer	NOUN
ejpam-556	9	25	graphics	graphic	NOUN
ejpam-556	9	26	and	and	CCONJ
ejpam-556	9	27	data	datum	NOUN
ejpam-556	9	28	visualization	visualization	NOUN
ejpam-556	9	29	environment	environment	NOUN
ejpam-556	9	30	.	.	PUNCT
ejpam-556	10	1	the	the	DET
ejpam-556	10	2	data	datum	NOUN
ejpam-556	10	3	are	be	AUX
ejpam-556	10	4	classified	classify	VERB
ejpam-556	10	5	as	as	ADP
ejpam-556	10	6	positive	positive	ADJ
ejpam-556	10	7	,	,	PUNCT
ejpam-556	10	8	constrained	constrained	ADJ
ejpam-556	10	9	,	,	PUNCT
ejpam-556	10	10	monotone	monotone	ADJ
ejpam-556	10	11	and	and	CCONJ
ejpam-556	10	12	convex	convex	NOUN
ejpam-556	10	13	according	accord	VERB
ejpam-556	10	14	to	to	ADP
ejpam-556	10	15	their	their	PRON
ejpam-556	10	16	shapes	shape	NOUN
ejpam-556	10	17	.	.	PUNCT
ejpam-556	11	1	stability	stability	NOUN
ejpam-556	11	2	of	of	ADP
ejpam-556	11	3	radioactive	radioactive	ADJ
ejpam-556	11	4	substance	substance	NOUN
ejpam-556	11	5	and	and	CCONJ
ejpam-556	11	6	chemical	chemical	NOUN
ejpam-556	11	7	reactions	reaction	NOUN
ejpam-556	11	8	,	,	PUNCT
ejpam-556	11	9	solvability	solvability	NOUN
ejpam-556	11	10	of	of	ADP
ejpam-556	11	11	solute	solute	NOUN
ejpam-556	11	12	in	in	ADP
ejpam-556	11	13	solvent	solvent	NOUN
ejpam-556	11	14	,	,	PUNCT
ejpam-556	11	15	population	population	NOUN
ejpam-556	11	16	statistics	statistic	NOUN
ejpam-556	12	1	[	[	X
ejpam-556	12	2	3	3	NUM
ejpam-556	12	3	]	]	PUNCT
ejpam-556	12	4	,	,	PUNCT
ejpam-556	12	5	resistance	resistance	NOUN
ejpam-556	12	6	offered	offer	VERB
ejpam-556	12	7	by	by	ADP
ejpam-556	12	8	an	an	DET
ejpam-556	12	9	electric	electric	ADJ
ejpam-556	12	10	circuit	circuit	NOUN
ejpam-556	12	11	,	,	PUNCT
ejpam-556	12	12	probability	probability	NOUN
ejpam-556	12	13	distribution	distribution	NOUN
ejpam-556	12	14	[	[	X
ejpam-556	12	15	3	3	NUM
ejpam-556	12	16	]	]	PUNCT
ejpam-556	12	17	are	be	AUX
ejpam-556	12	18	a	a	DET
ejpam-556	12	19	few	few	ADJ
ejpam-556	12	20	examples	example	NOUN
ejpam-556	12	21	of	of	ADP
ejpam-556	12	22	entities	entity	NOUN
ejpam-556	12	23	which	which	PRON
ejpam-556	12	24	are	be	AUX
ejpam-556	12	25	always	always	ADV
ejpam-556	12	26	positive	positive	ADJ
ejpam-556	12	27	.	.	PUNCT
ejpam-556	13	1	monotonicity	monotonicity	NOUN
ejpam-556	13	2	is	be	AUX
ejpam-556	13	3	applied	apply	VERB
ejpam-556	13	4	in	in	ADP
ejpam-556	13	5	the	the	DET
ejpam-556	13	6	specification	specification	NOUN
ejpam-556	13	7	of	of	ADP
ejpam-556	13	8	digital	digital	PROPN
ejpam-556	13	9	to	to	PART
ejpam-556	13	10	analog	analog	NOUN
ejpam-556	13	11	converters	converter	NOUN
ejpam-556	13	12	(	(	PUNCT
ejpam-556	13	13	dacs	dac	NOUN
ejpam-556	13	14	)	)	PUNCT
ejpam-556	13	15	,	,	PUNCT
ejpam-556	13	16	analog	analog	NOUN
ejpam-556	13	17	to	to	ADP
ejpam-556	13	18	digital	digital	ADJ
ejpam-556	13	19	converters	converter	NOUN
ejpam-556	13	20	(	(	PUNCT
ejpam-556	13	21	adcs	adcs	ADJ
ejpam-556	13	22	)	)	PUNCT
ejpam-556	13	23	and	and	CCONJ
ejpam-556	13	24	sensors	sensor	NOUN
ejpam-556	13	25	.	.	PUNCT
ejpam-556	14	1	these	these	DET
ejpam-556	14	2	devices	device	NOUN
ejpam-556	14	3	are	be	AUX
ejpam-556	14	4	used	use	VERB
ejpam-556	14	5	in	in	ADP
ejpam-556	14	6	control	control	NOUN
ejpam-556	14	7	system	system	NOUN
ejpam-556	14	8	applications	application	NOUN
ejpam-556	14	9	where	where	SCONJ
ejpam-556	14	10	non	non	ADJ
ejpam-556	14	11	-	-	ADJ
ejpam-556	14	12	monotonicity	monotonicity	ADJ
ejpam-556	14	13	is	be	AUX
ejpam-556	14	14	unacceptable	unacceptable	ADJ
ejpam-556	14	15	[	[	PUNCT
ejpam-556	14	16	9	9	NUM
ejpam-556	14	17	]	]	PUNCT
ejpam-556	14	18	.	.	PUNCT
ejpam-556	15	1	erythrocyte	erythrocyte	PROPN
ejpam-556	15	2	sedimentation	sedimentation	NOUN
ejpam-556	15	3	rate	rate	NOUN
ejpam-556	15	4	(	(	PUNCT
ejpam-556	15	5	e.s.r	e.s.r	PROPN
ejpam-556	15	6	.	.	PUNCT
ejpam-556	15	7	)	)	PUNCT
ejpam-556	16	1	in	in	ADP
ejpam-556	16	2	cancer	cancer	NOUN
ejpam-556	16	3	patients	patient	NOUN
ejpam-556	16	4	[	[	X
ejpam-556	16	5	9	9	NUM
ejpam-556	16	6	]	]	PUNCT
ejpam-556	16	7	,	,	PUNCT
ejpam-556	16	8	uric	uric	ADJ
ejpam-556	16	9	acid	acid	NOUN
ejpam-556	16	10	level	level	NOUN
ejpam-556	16	11	in	in	ADP
ejpam-556	16	12	patients	patient	NOUN
ejpam-556	16	13	suffering	suffer	VERB
ejpam-556	16	14	from	from	ADP
ejpam-556	16	15	gout	gout	NOUN
ejpam-556	16	16	[	[	X
ejpam-556	16	17	9	9	NUM
ejpam-556	16	18	]	]	PUNCT
ejpam-556	16	19	,	,	PUNCT
ejpam-556	16	20	approximation	approximation	NOUN
ejpam-556	16	21	of	of	ADP
ejpam-556	16	22	couples	couple	NOUN
ejpam-556	16	23	and	and	CCONJ
ejpam-556	16	24	quasi	quasi	ADJ
ejpam-556	16	25	couples	couple	NOUN
ejpam-556	16	26	in	in	ADP
ejpam-556	16	27	statistics	statistic	NOUN
ejpam-556	17	1	[	[	X
ejpam-556	17	2	2	2	NUM
ejpam-556	17	3	]	]	PUNCT
ejpam-556	17	4	,	,	PUNCT
ejpam-556	18	1	data	datum	NOUN
ejpam-556	18	2	generated	generate	VERB
ejpam-556	18	3	from	from	ADP
ejpam-556	18	4	stress	stress	NOUN
ejpam-556	18	5	of	of	ADP
ejpam-556	18	6	a	a	DET
ejpam-556	18	7	material	material	NOUN
ejpam-556	18	8	[	[	X
ejpam-556	18	9	9	9	NUM
ejpam-556	18	10	]	]	PUNCT
ejpam-556	18	11	,	,	PUNCT
ejpam-556	18	12	rate	rate	NOUN
ejpam-556	18	13	of	of	ADP
ejpam-556	18	14	dissemination	dissemination	NOUN
ejpam-556	18	15	of	of	ADP
ejpam-556	18	16	drug	drug	NOUN
ejpam-556	18	17	in	in	ADP
ejpam-556	18	18	blood	blood	NOUN
ejpam-556	18	19	[	[	X
ejpam-556	18	20	2	2	NUM
ejpam-556	18	21	]	]	PUNCT
ejpam-556	18	22	are	be	AUX
ejpam-556	18	23	a	a	DET
ejpam-556	18	24	few	few	ADJ
ejpam-556	18	25	examples	example	NOUN
ejpam-556	18	26	of	of	ADP
ejpam-556	18	27	entities	entity	NOUN
ejpam-556	18	28	which	which	PRON
ejpam-556	18	29	are	be	AUX
ejpam-556	18	30	always	always	ADV
ejpam-556	18	31	monotone	monotone	ADJ
ejpam-556	18	32	.	.	PUNCT
ejpam-556	19	1	∗corresponding	∗corresponde	VERB
ejpam-556	19	2	author	author	NOUN
ejpam-556	19	3	.	.	PUNCT
ejpam-556	20	1	email	email	NOUN
ejpam-556	20	2	addresses	address	NOUN
ejpam-556	20	3	:	:	PUNCT
ejpam-556	21	1	malikzawwar�math.pu.edu.pk	malikzawwar�math.pu.edu.pk	X
ejpam-556	21	2	(	(	PUNCT
ejpam-556	21	3	m.	m.	PROPN
ejpam-556	21	4	z.	z.	PROPN
ejpam-556	21	5	hussain	hussain	PROPN
ejpam-556	21	6	)	)	PUNCT
ejpam-556	21	7	,	,	PUNCT
ejpam-556	21	8	prof.m.sarfraz	prof.m.sarfraz	PROPN
ejpam-556	21	9	�	�	NOUN
ejpam-556	21	10	gmail	gmail	NOUN
ejpam-556	21	11	.	.	PUNCT
ejpam-556	22	1	om	om	PROPN
ejpam-556	22	2	(	(	PUNCT
ejpam-556	22	3	m.	m.	NOUN
ejpam-556	22	4	sarfraz	sarfraz	PROPN
ejpam-556	22	5	)	)	PUNCT
ejpam-556	22	6	,	,	PUNCT
ejpam-556	22	7	mariahussain_1	mariahussain_1	PROPN
ejpam-556	22	8	�	�	PROPN
ejpam-556	22	9	yahoo	yahoo	PROPN
ejpam-556	22	10	.	.	PUNCT
ejpam-556	23	1	om	om	PROPN
ejpam-556	23	2	(	(	PUNCT
ejpam-556	23	3	m.	m.	NOUN
ejpam-556	23	4	hussain	hussain	PROPN
ejpam-556	23	5	)	)	PUNCT
ejpam-556	23	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-556	24	1	194	194	NUM
ejpam-556	25	1	c	c	X
ejpam-556	25	2	©	©	PROPN
ejpam-556	25	3	2010	2010	NUM
ejpam-556	25	4	ejpam	ejpam	NOUN
ejpam-556	25	5	all	all	DET
ejpam-556	25	6	rights	right	NOUN
ejpam-556	25	7	reserved	reserve	VERB
ejpam-556	25	8	.	.	PUNCT
ejpam-556	26	1	m.	m.	NOUN
ejpam-556	26	2	z.	z.	PROPN
ejpam-556	26	3	hussain	hussain	PROPN
ejpam-556	26	4	,	,	PUNCT
ejpam-556	26	5	m.	m.	NOUN
ejpam-556	26	6	sarfraz	sarfraz	PROPN
ejpam-556	26	7	,	,	PUNCT
ejpam-556	26	8	m.	m.	NOUN
ejpam-556	26	9	hussain	hussain	PROPN
ejpam-556	26	10	/	/	SYM
ejpam-556	26	11	eur	eur	PROPN
ejpam-556	26	12	.	.	PUNCT
ejpam-556	27	1	j.	j.	PROPN
ejpam-556	27	2	pure	pure	PROPN
ejpam-556	27	3	appl	appl	PROPN
ejpam-556	27	4	.	.	PROPN
ejpam-556	27	5	math	math	PROPN
ejpam-556	27	6	,	,	PUNCT
ejpam-556	27	7	3	3	NUM
ejpam-556	27	8	(	(	PUNCT
ejpam-556	27	9	2010	2010	NUM
ejpam-556	27	10	)	)	PUNCT
ejpam-556	27	11	,	,	PUNCT
ejpam-556	27	12	194	194	NUM
ejpam-556	27	13	-	-	SYM
ejpam-556	27	14	212	212	NUM
ejpam-556	27	15	195	195	NUM
ejpam-556	27	16	in	in	ADP
ejpam-556	27	17	the	the	DET
ejpam-556	27	18	past	past	NOUN
ejpam-556	27	19	quite	quite	DET
ejpam-556	27	20	a	a	DET
ejpam-556	27	21	few	few	ADJ
ejpam-556	27	22	authors	author	NOUN
ejpam-556	27	23	have	have	AUX
ejpam-556	27	24	worked	work	VERB
ejpam-556	27	25	in	in	ADP
ejpam-556	27	26	the	the	DET
ejpam-556	27	27	area	area	NOUN
ejpam-556	27	28	of	of	ADP
ejpam-556	27	29	shape	shape	NOUN
ejpam-556	27	30	preserving	preserve	VERB
ejpam-556	27	31	interpolation	interpolation	NOUN
ejpam-556	27	32	.	.	PUNCT
ejpam-556	28	1	the	the	DET
ejpam-556	28	2	positivity	positivity	NOUN
ejpam-556	28	3	preserving	preserve	VERB
ejpam-556	28	4	scheme	scheme	NOUN
ejpam-556	28	5	,	,	PUNCT
ejpam-556	28	6	by	by	ADP
ejpam-556	28	7	butt	butt	NOUN
ejpam-556	28	8	and	and	CCONJ
ejpam-556	28	9	brodlie	brodlie	NOUN
ejpam-556	28	10	[	[	X
ejpam-556	28	11	3	3	NUM
ejpam-556	28	12	]	]	PUNCT
ejpam-556	28	13	,	,	PUNCT
ejpam-556	28	14	preserved	preserve	VERB
ejpam-556	28	15	the	the	DET
ejpam-556	28	16	shape	shape	NOUN
ejpam-556	28	17	of	of	ADP
ejpam-556	28	18	data	datum	NOUN
ejpam-556	28	19	by	by	ADP
ejpam-556	28	20	interval	interval	NOUN
ejpam-556	28	21	subdivision	subdivision	NOUN
ejpam-556	28	22	technique	technique	NOUN
ejpam-556	28	23	.	.	PUNCT
ejpam-556	29	1	in	in	ADP
ejpam-556	29	2	the	the	DET
ejpam-556	29	3	interval	interval	NOUN
ejpam-556	29	4	,	,	PUNCT
ejpam-556	29	5	where	where	SCONJ
ejpam-556	29	6	the	the	DET
ejpam-556	29	7	piecewise	piecewise	NOUN
ejpam-556	29	8	cubic	cubic	ADJ
ejpam-556	29	9	interpolant	interpolant	NOUN
ejpam-556	29	10	lost	lose	VERB
ejpam-556	29	11	the	the	DET
ejpam-556	29	12	positive	positive	ADJ
ejpam-556	29	13	shape	shape	NOUN
ejpam-556	29	14	of	of	ADP
ejpam-556	29	15	data	datum	NOUN
ejpam-556	29	16	,	,	PUNCT
ejpam-556	29	17	the	the	DET
ejpam-556	29	18	authors	author	NOUN
ejpam-556	29	19	inserted	insert	VERB
ejpam-556	29	20	an	an	DET
ejpam-556	29	21	additional	additional	ADJ
ejpam-556	29	22	knot	knot	NOUN
ejpam-556	29	23	(	(	PUNCT
ejpam-556	29	24	increase	increase	VERB
ejpam-556	29	25	in	in	ADP
ejpam-556	29	26	number	number	NOUN
ejpam-556	29	27	of	of	ADP
ejpam-556	29	28	data	datum	NOUN
ejpam-556	29	29	points	point	NOUN
ejpam-556	29	30	)	)	PUNCT
ejpam-556	29	31	in	in	ADP
ejpam-556	29	32	such	such	DET
ejpam-556	29	33	a	a	DET
ejpam-556	29	34	way	way	NOUN
ejpam-556	29	35	that	that	PRON
ejpam-556	29	36	original	original	ADJ
ejpam-556	29	37	shape	shape	NOUN
ejpam-556	29	38	of	of	ADP
ejpam-556	29	39	the	the	DET
ejpam-556	29	40	data	datum	NOUN
ejpam-556	29	41	was	be	AUX
ejpam-556	29	42	preserved	preserve	VERB
ejpam-556	29	43	.	.	PUNCT
ejpam-556	30	1	fahr	fahr	PROPN
ejpam-556	30	2	and	and	CCONJ
ejpam-556	30	3	kallay	kallay	PROPN
ejpam-556	30	4	[	[	X
ejpam-556	30	5	5	5	NUM
ejpam-556	30	6	]	]	PUNCT
ejpam-556	30	7	used	use	VERB
ejpam-556	30	8	a	a	DET
ejpam-556	30	9	monotone	monotone	ADJ
ejpam-556	30	10	rational	rational	ADJ
ejpam-556	30	11	b	b	NOUN
ejpam-556	30	12	-	-	PUNCT
ejpam-556	30	13	spline	spline	NOUN
ejpam-556	30	14	of	of	ADP
ejpam-556	30	15	degree	degree	NOUN
ejpam-556	30	16	one	one	NOUN
ejpam-556	30	17	to	to	PART
ejpam-556	30	18	preserve	preserve	VERB
ejpam-556	30	19	the	the	DET
ejpam-556	30	20	shape	shape	NOUN
ejpam-556	30	21	of	of	ADP
ejpam-556	30	22	monotone	monotone	ADJ
ejpam-556	30	23	data	datum	NOUN
ejpam-556	30	24	.	.	PUNCT
ejpam-556	31	1	goodman	goodman	PROPN
ejpam-556	31	2	et	et	PROPN
ejpam-556	31	3	al	al	PROPN
ejpam-556	32	1	[	[	X
ejpam-556	32	2	7	7	NUM
ejpam-556	32	3	]	]	PUNCT
ejpam-556	32	4	developed	develop	VERB
ejpam-556	32	5	rational	rational	ADJ
ejpam-556	32	6	cubic	cubic	ADJ
ejpam-556	32	7	interpolating	interpolate	VERB
ejpam-556	32	8	schemes	scheme	NOUN
ejpam-556	32	9	to	to	PART
ejpam-556	32	10	preserve	preserve	VERB
ejpam-556	32	11	the	the	DET
ejpam-556	32	12	shape	shape	NOUN
ejpam-556	32	13	of	of	ADP
ejpam-556	32	14	data	datum	NOUN
ejpam-556	32	15	lying	lie	VERB
ejpam-556	32	16	on	on	ADP
ejpam-556	32	17	the	the	DET
ejpam-556	32	18	either	either	DET
ejpam-556	32	19	side	side	NOUN
ejpam-556	32	20	of	of	ADP
ejpam-556	32	21	straight	straight	ADJ
ejpam-556	32	22	line	line	NOUN
ejpam-556	32	23	.	.	PUNCT
ejpam-556	33	1	the	the	DET
ejpam-556	33	2	first	first	ADJ
ejpam-556	33	3	scheme	scheme	NOUN
ejpam-556	33	4	scaled	scale	VERB
ejpam-556	33	5	weights	weight	NOUN
ejpam-556	33	6	by	by	ADP
ejpam-556	33	7	some	some	DET
ejpam-556	33	8	scale	scale	NOUN
ejpam-556	33	9	factors	factor	NOUN
ejpam-556	33	10	and	and	CCONJ
ejpam-556	33	11	the	the	DET
ejpam-556	33	12	second	second	ADJ
ejpam-556	33	13	scheme	scheme	NOUN
ejpam-556	33	14	adopted	adopt	VERB
ejpam-556	33	15	the	the	DET
ejpam-556	33	16	method	method	NOUN
ejpam-556	33	17	of	of	ADP
ejpam-556	33	18	insertion	insertion	NOUN
ejpam-556	33	19	of	of	ADP
ejpam-556	33	20	a	a	DET
ejpam-556	33	21	new	new	ADJ
ejpam-556	33	22	interpolation	interpolation	NOUN
ejpam-556	33	23	point	point	NOUN
ejpam-556	33	24	.	.	PUNCT
ejpam-556	34	1	goodman	goodman	PROPN
ejpam-556	34	2	[	[	X
ejpam-556	34	3	8	8	NUM
ejpam-556	34	4	]	]	PUNCT
ejpam-556	34	5	surveyed	survey	VERB
ejpam-556	34	6	the	the	DET
ejpam-556	34	7	shape	shape	NOUN
ejpam-556	34	8	preserving	preserve	VERB
ejpam-556	34	9	interpolating	interpolate	VERB
ejpam-556	34	10	schemes	scheme	NOUN
ejpam-556	34	11	for	for	ADP
ejpam-556	34	12	planar	planar	ADJ
ejpam-556	34	13	data	datum	NOUN
ejpam-556	34	14	.	.	PUNCT
ejpam-556	35	1	hussain	hussain	PROPN
ejpam-556	35	2	and	and	CCONJ
ejpam-556	35	3	sarfraz	sarfraz	PROPN
ejpam-556	35	4	used	use	VERB
ejpam-556	35	5	four	four	NUM
ejpam-556	35	6	parameter	parameter	NOUN
ejpam-556	35	7	family	family	NOUN
ejpam-556	35	8	of	of	ADP
ejpam-556	35	9	rational	rational	ADJ
ejpam-556	35	10	cubic	cubic	ADJ
ejpam-556	35	11	function	function	NOUN
ejpam-556	35	12	to	to	PART
ejpam-556	35	13	preserve	preserve	VERB
ejpam-556	35	14	the	the	DET
ejpam-556	35	15	shape	shape	NOUN
ejpam-556	35	16	of	of	ADP
ejpam-556	35	17	positive	positive	ADJ
ejpam-556	35	18	and	and	CCONJ
ejpam-556	35	19	monotone	monotone	ADJ
ejpam-556	35	20	data	datum	NOUN
ejpam-556	35	21	in	in	ADP
ejpam-556	35	22	[	[	X
ejpam-556	35	23	10	10	NUM
ejpam-556	35	24	]	]	PUNCT
ejpam-556	35	25	and	and	CCONJ
ejpam-556	35	26	[	[	X
ejpam-556	35	27	11	11	NUM
ejpam-556	35	28	]	]	PUNCT
ejpam-556	35	29	respectively	respectively	ADV
ejpam-556	35	30	.	.	PUNCT
ejpam-556	36	1	lamberti	lamberti	PROPN
ejpam-556	36	2	and	and	CCONJ
ejpam-556	36	3	manni	manni	NOUN
ejpam-556	37	1	[	[	X
ejpam-556	37	2	12	12	NUM
ejpam-556	37	3	]	]	PUNCT
ejpam-556	37	4	used	use	VERB
ejpam-556	37	5	cubic	cubic	ADJ
ejpam-556	37	6	hermite	hermite	ADJ
ejpam-556	37	7	in	in	ADP
ejpam-556	37	8	parametric	parametric	ADJ
ejpam-556	37	9	form	form	NOUN
ejpam-556	37	10	to	to	PART
ejpam-556	37	11	preserve	preserve	VERB
ejpam-556	37	12	the	the	DET
ejpam-556	37	13	shape	shape	NOUN
ejpam-556	37	14	of	of	ADP
ejpam-556	37	15	data	datum	NOUN
ejpam-556	37	16	.	.	PUNCT
ejpam-556	38	1	the	the	DET
ejpam-556	38	2	step	step	NOUN
ejpam-556	38	3	length	length	NOUN
ejpam-556	38	4	was	be	AUX
ejpam-556	38	5	used	use	VERB
ejpam-556	38	6	as	as	ADP
ejpam-556	38	7	shape	shape	NOUN
ejpam-556	38	8	preserving	preserve	VERB
ejpam-556	38	9	parameters	parameter	NOUN
ejpam-556	38	10	.	.	PUNCT
ejpam-556	39	1	the	the	DET
ejpam-556	39	2	first	first	ADJ
ejpam-556	39	3	order	order	NOUN
ejpam-556	39	4	derivatives	derivative	NOUN
ejpam-556	39	5	at	at	ADP
ejpam-556	39	6	the	the	DET
ejpam-556	39	7	knots	knot	NOUN
ejpam-556	39	8	were	be	AUX
ejpam-556	39	9	estimated	estimate	VERB
ejpam-556	39	10	imposing	impose	VERB
ejpam-556	39	11	second	second	ADJ
ejpam-556	39	12	derivative	derivative	ADJ
ejpam-556	39	13	continuity	continuity	NOUN
ejpam-556	39	14	at	at	ADP
ejpam-556	39	15	the	the	DET
ejpam-556	39	16	knots	knot	NOUN
ejpam-556	39	17	,	,	PUNCT
ejpam-556	39	18	which	which	PRON
ejpam-556	39	19	resulted	result	VERB
ejpam-556	39	20	in	in	ADP
ejpam-556	39	21	tridiagonal	tridiagonal	ADJ
ejpam-556	39	22	system	system	NOUN
ejpam-556	39	23	of	of	ADP
ejpam-556	39	24	equations	equation	NOUN
ejpam-556	39	25	.	.	PUNCT
ejpam-556	40	1	sarfraz	sarfraz	PROPN
ejpam-556	40	2	et	et	PROPN
ejpam-556	40	3	al	al	PROPN
ejpam-556	41	1	[	[	X
ejpam-556	41	2	13	13	NUM
ejpam-556	41	3	]	]	PUNCT
ejpam-556	41	4	addressed	address	VERB
ejpam-556	41	5	the	the	DET
ejpam-556	41	6	problems	problem	NOUN
ejpam-556	41	7	of	of	ADP
ejpam-556	41	8	positive	positive	ADJ
ejpam-556	41	9	and	and	CCONJ
ejpam-556	41	10	monotone	monotone	ADJ
ejpam-556	41	11	curve	curve	NOUN
ejpam-556	41	12	data	datum	NOUN
ejpam-556	41	13	interpolation	interpolation	NOUN
ejpam-556	41	14	using	use	VERB
ejpam-556	41	15	rational	rational	ADJ
ejpam-556	41	16	cubic	cubic	ADJ
ejpam-556	41	17	function	function	NOUN
ejpam-556	41	18	with	with	ADP
ejpam-556	41	19	two	two	NUM
ejpam-556	41	20	parameters	parameter	NOUN
ejpam-556	41	21	.	.	PUNCT
ejpam-556	42	1	sarfraz	sarfraz	PROPN
ejpam-556	42	2	et	et	PROPN
ejpam-556	42	3	al	al	PROPN
ejpam-556	43	1	[	[	X
ejpam-556	43	2	14	14	NUM
ejpam-556	43	3	]	]	PUNCT
ejpam-556	43	4	developed	develop	VERB
ejpam-556	43	5	a	a	DET
ejpam-556	43	6	gc1	gc1	NOUN
ejpam-556	43	7	cubic	cubic	ADJ
ejpam-556	43	8	function	function	NOUN
ejpam-556	43	9	with	with	ADP
ejpam-556	43	10	one	one	NUM
ejpam-556	43	11	free	free	ADJ
ejpam-556	43	12	parameter	parameter	NOUN
ejpam-556	43	13	to	to	PART
ejpam-556	43	14	preserve	preserve	VERB
ejpam-556	43	15	the	the	DET
ejpam-556	43	16	positive	positive	ADJ
ejpam-556	43	17	,	,	PUNCT
ejpam-556	43	18	monotone	monotone	ADJ
ejpam-556	43	19	and	and	CCONJ
ejpam-556	43	20	convex	convex	PROPN
ejpam-556	43	21	data	datum	NOUN
ejpam-556	43	22	.	.	PUNCT
ejpam-556	44	1	schmidt	schmidt	PROPN
ejpam-556	44	2	and	and	CCONJ
ejpam-556	44	3	hess	hess	NOUN
ejpam-556	45	1	[	[	X
ejpam-556	45	2	15	15	NUM
ejpam-556	45	3	]	]	PUNCT
ejpam-556	45	4	developed	develop	VERB
ejpam-556	45	5	sufficient	sufficient	ADJ
ejpam-556	45	6	conditions	condition	NOUN
ejpam-556	45	7	on	on	ADP
ejpam-556	45	8	derivatives	derivative	NOUN
ejpam-556	45	9	at	at	ADP
ejpam-556	45	10	the	the	DET
ejpam-556	45	11	knots	knot	NOUN
ejpam-556	45	12	to	to	PART
ejpam-556	45	13	assure	assure	VERB
ejpam-556	45	14	positivity	positivity	NOUN
ejpam-556	45	15	of	of	ADP
ejpam-556	45	16	interpolating	interpolate	VERB
ejpam-556	45	17	cubic	cubic	ADJ
ejpam-556	45	18	polynomial	polynomial	NOUN
ejpam-556	45	19	.	.	PUNCT
ejpam-556	46	1	this	this	DET
ejpam-556	46	2	paper	paper	NOUN
ejpam-556	46	3	presents	present	VERB
ejpam-556	46	4	shape	shape	NOUN
ejpam-556	46	5	preserving	preserve	VERB
ejpam-556	46	6	interpolating	interpolate	VERB
ejpam-556	46	7	schemes	scheme	NOUN
ejpam-556	46	8	for	for	ADP
ejpam-556	46	9	positive	positive	ADJ
ejpam-556	46	10	,	,	PUNCT
ejpam-556	46	11	constrained	constrained	ADJ
ejpam-556	46	12	and	and	CCONJ
ejpam-556	46	13	monotone	monotone	ADJ
ejpam-556	46	14	data	datum	NOUN
ejpam-556	46	15	.	.	PUNCT
ejpam-556	47	1	a	a	DET
ejpam-556	47	2	one	one	NUM
ejpam-556	47	3	parameter	parameter	NOUN
ejpam-556	47	4	family	family	NOUN
ejpam-556	47	5	of	of	ADP
ejpam-556	47	6	rational	rational	ADJ
ejpam-556	47	7	cubic	cubic	ADJ
ejpam-556	47	8	function	function	NOUN
ejpam-556	47	9	has	have	AUX
ejpam-556	47	10	been	be	AUX
ejpam-556	47	11	developed	develop	VERB
ejpam-556	47	12	to	to	PART
ejpam-556	47	13	preserve	preserve	VERB
ejpam-556	47	14	the	the	DET
ejpam-556	47	15	shape	shape	NOUN
ejpam-556	47	16	of	of	ADP
ejpam-556	47	17	the	the	DET
ejpam-556	47	18	data	datum	NOUN
ejpam-556	47	19	.	.	PUNCT
ejpam-556	48	1	in	in	ADP
ejpam-556	48	2	different	different	ADJ
ejpam-556	48	3	intervals	interval	NOUN
ejpam-556	48	4	,	,	PUNCT
ejpam-556	48	5	the	the	DET
ejpam-556	48	6	free	free	ADJ
ejpam-556	48	7	parameter	parameter	NOUN
ejpam-556	48	8	adopts	adopt	VERB
ejpam-556	48	9	different	different	ADJ
ejpam-556	48	10	value	value	NOUN
ejpam-556	48	11	.	.	PUNCT
ejpam-556	49	1	that	that	PRON
ejpam-556	49	2	is	is	ADV
ejpam-556	49	3	,	,	PUNCT
ejpam-556	49	4	the	the	DET
ejpam-556	49	5	interpolant	interpolant	NOUN
ejpam-556	49	6	has	have	VERB
ejpam-556	49	7	same	same	ADJ
ejpam-556	49	8	structure	structure	NOUN
ejpam-556	49	9	but	but	CCONJ
ejpam-556	49	10	different	different	ADJ
ejpam-556	49	11	functions	function	NOUN
ejpam-556	49	12	in	in	ADP
ejpam-556	49	13	different	different	ADJ
ejpam-556	49	14	intervals	interval	NOUN
ejpam-556	49	15	.	.	PUNCT
ejpam-556	50	1	the	the	DET
ejpam-556	50	2	presented	present	VERB
ejpam-556	50	3	schemes	scheme	NOUN
ejpam-556	50	4	are	be	AUX
ejpam-556	50	5	neither	neither	ADV
ejpam-556	50	6	dependent	dependent	ADJ
ejpam-556	50	7	on	on	ADP
ejpam-556	50	8	data	datum	NOUN
ejpam-556	50	9	nor	nor	CCONJ
ejpam-556	50	10	on	on	ADP
ejpam-556	50	11	derivatives	derivative	NOUN
ejpam-556	50	12	.	.	PUNCT
ejpam-556	51	1	unlike	unlike	ADP
ejpam-556	51	2	the	the	DET
ejpam-556	51	3	methodologies	methodology	NOUN
ejpam-556	51	4	in	in	ADP
ejpam-556	51	5	[	[	X
ejpam-556	51	6	3	3	NUM
ejpam-556	51	7	,	,	PUNCT
ejpam-556	51	8	7,12	7,12	NUM
ejpam-556	51	9	]	]	PUNCT
ejpam-556	51	10	,	,	PUNCT
ejpam-556	51	11	the	the	DET
ejpam-556	51	12	scheme	scheme	NOUN
ejpam-556	51	13	developed	develop	VERB
ejpam-556	51	14	in	in	ADP
ejpam-556	51	15	this	this	DET
ejpam-556	51	16	paper	paper	NOUN
ejpam-556	51	17	does	do	AUX
ejpam-556	51	18	not	not	PART
ejpam-556	51	19	constrain	constrain	VERB
ejpam-556	51	20	interval	interval	NOUN
ejpam-556	51	21	length	length	NOUN
ejpam-556	51	22	.	.	PUNCT
ejpam-556	52	1	the	the	DET
ejpam-556	52	2	developed	develop	VERB
ejpam-556	52	3	scheme	scheme	NOUN
ejpam-556	52	4	is	be	AUX
ejpam-556	52	5	equally	equally	ADV
ejpam-556	52	6	applicable	applicable	ADJ
ejpam-556	52	7	whether	whether	SCONJ
ejpam-556	52	8	the	the	DET
ejpam-556	52	9	data	data	NOUN
ejpam-556	52	10	is	be	AUX
ejpam-556	52	11	with	with	ADP
ejpam-556	52	12	derivatives	derivative	NOUN
ejpam-556	52	13	or	or	CCONJ
ejpam-556	52	14	the	the	DET
ejpam-556	52	15	derivative	derivative	NOUN
ejpam-556	52	16	is	be	AUX
ejpam-556	52	17	estimated	estimate	VERB
ejpam-556	52	18	by	by	ADP
ejpam-556	52	19	derivative	derivative	ADJ
ejpam-556	52	20	estimation	estimation	NOUN
ejpam-556	52	21	techniques	technique	NOUN
ejpam-556	52	22	[	[	X
ejpam-556	52	23	10	10	NUM
ejpam-556	52	24	-	-	SYM
ejpam-556	52	25	11	11	NUM
ejpam-556	52	26	]	]	PUNCT
ejpam-556	52	27	.	.	PUNCT
ejpam-556	53	1	the	the	DET
ejpam-556	53	2	schemes	scheme	NOUN
ejpam-556	53	3	presented	present	VERB
ejpam-556	53	4	in	in	ADP
ejpam-556	53	5	this	this	DET
ejpam-556	53	6	paper	paper	NOUN
ejpam-556	53	7	use	use	VERB
ejpam-556	53	8	one	one	NUM
ejpam-556	53	9	parameter	parameter	NOUN
ejpam-556	53	10	family	family	NOUN
ejpam-556	53	11	of	of	ADP
ejpam-556	53	12	rational	rational	ADJ
ejpam-556	53	13	function	function	NOUN
ejpam-556	53	14	to	to	PART
ejpam-556	53	15	preserve	preserve	VERB
ejpam-556	53	16	the	the	DET
ejpam-556	53	17	shape	shape	NOUN
ejpam-556	53	18	of	of	ADP
ejpam-556	53	19	data	datum	NOUN
ejpam-556	53	20	thus	thus	ADV
ejpam-556	53	21	computationally	computationally	ADV
ejpam-556	53	22	less	less	ADV
ejpam-556	53	23	expansive	expansive	ADJ
ejpam-556	53	24	than	than	ADP
ejpam-556	53	25	[	[	X
ejpam-556	53	26	10	10	NUM
ejpam-556	53	27	-	-	SYM
ejpam-556	53	28	11	11	NUM
ejpam-556	53	29	,	,	PUNCT
ejpam-556	53	30	13	13	NUM
ejpam-556	53	31	]	]	PUNCT
ejpam-556	53	32	.	.	PUNCT
ejpam-556	54	1	the	the	DET
ejpam-556	54	2	order	order	NOUN
ejpam-556	54	3	of	of	ADP
ejpam-556	54	4	continuity	continuity	NOUN
ejpam-556	54	5	achieved	achieve	VERB
ejpam-556	54	6	is	be	AUX
ejpam-556	54	7	c1	c1	PROPN
ejpam-556	54	8	,	,	PUNCT
ejpam-556	54	9	whereas	whereas	SCONJ
ejpam-556	54	10	,	,	PUNCT
ejpam-556	54	11	in	in	ADP
ejpam-556	54	12	[	[	NOUN
ejpam-556	54	13	14	14	NUM
ejpam-556	54	14	]	]	X
ejpam-556	54	15	it	it	PRON
ejpam-556	54	16	was	be	AUX
ejpam-556	54	17	gc1	gc1	NOUN
ejpam-556	54	18	.	.	PUNCT
ejpam-556	55	1	the	the	DET
ejpam-556	55	2	remainder	remainder	NOUN
ejpam-556	55	3	of	of	ADP
ejpam-556	55	4	the	the	DET
ejpam-556	55	5	paper	paper	NOUN
ejpam-556	55	6	is	be	AUX
ejpam-556	55	7	organized	organize	VERB
ejpam-556	55	8	as	as	SCONJ
ejpam-556	55	9	follows	follow	VERB
ejpam-556	55	10	.	.	PUNCT
ejpam-556	56	1	in	in	ADP
ejpam-556	56	2	section	section	NOUN
ejpam-556	56	3	2	2	NUM
ejpam-556	56	4	,	,	PUNCT
ejpam-556	56	5	the	the	DET
ejpam-556	56	6	c1	c1	PROPN
ejpam-556	56	7	rational	rational	ADJ
ejpam-556	56	8	cubic	cubic	ADJ
ejpam-556	56	9	interpolant	interpolant	NOUN
ejpam-556	56	10	with	with	ADP
ejpam-556	56	11	one	one	NUM
ejpam-556	56	12	free	free	ADJ
ejpam-556	56	13	parameter	parameter	NOUN
ejpam-556	56	14	is	be	AUX
ejpam-556	56	15	developed	develop	VERB
ejpam-556	56	16	and	and	CCONJ
ejpam-556	56	17	section	section	NOUN
ejpam-556	56	18	2.1	2.1	NUM
ejpam-556	56	19	discusses	discuss	VERB
ejpam-556	56	20	its	its	PRON
ejpam-556	56	21	approximation	approximation	NOUN
ejpam-556	56	22	properties	property	NOUN
ejpam-556	56	23	.	.	PUNCT
ejpam-556	57	1	the	the	DET
ejpam-556	57	2	visualization	visualization	NOUN
ejpam-556	57	3	problems	problem	NOUN
ejpam-556	57	4	of	of	ADP
ejpam-556	57	5	positive	positive	ADJ
ejpam-556	57	6	,	,	PUNCT
ejpam-556	57	7	constrained	constrain	VERB
ejpam-556	57	8	,	,	PUNCT
ejpam-556	57	9	and	and	CCONJ
ejpam-556	57	10	monotone	monotone	ADJ
ejpam-556	57	11	data	datum	NOUN
ejpam-556	57	12	interpolation	interpolation	NOUN
ejpam-556	57	13	are	be	AUX
ejpam-556	57	14	discussed	discuss	VERB
ejpam-556	57	15	in	in	ADP
ejpam-556	57	16	sections	section	NOUN
ejpam-556	57	17	3	3	NUM
ejpam-556	57	18	,	,	PUNCT
ejpam-556	57	19	4	4	NUM
ejpam-556	57	20	and	and	CCONJ
ejpam-556	57	21	5	5	NUM
ejpam-556	57	22	respectively	respectively	ADV
ejpam-556	57	23	.	.	PUNCT
ejpam-556	58	1	section	section	NOUN
ejpam-556	58	2	6	6	NUM
ejpam-556	58	3	concludes	conclude	VERB
ejpam-556	58	4	the	the	DET
ejpam-556	58	5	paper	paper	NOUN
ejpam-556	58	6	.	.	PUNCT
ejpam-556	59	1	2	2	X
ejpam-556	59	2	.	.	X
ejpam-556	59	3	rational	rational	ADJ
ejpam-556	59	4	cubic	cubic	ADJ
ejpam-556	59	5	function	function	NOUN
ejpam-556	59	6	in	in	ADP
ejpam-556	59	7	this	this	DET
ejpam-556	59	8	section	section	NOUN
ejpam-556	59	9	,	,	PUNCT
ejpam-556	59	10	a	a	DET
ejpam-556	59	11	c1	c1	NOUN
ejpam-556	59	12	rational	rational	ADJ
ejpam-556	59	13	cubic	cubic	ADJ
ejpam-556	59	14	function	function	NOUN
ejpam-556	59	15	with	with	ADP
ejpam-556	59	16	one	one	NUM
ejpam-556	59	17	parameter	parameter	NOUN
ejpam-556	59	18	and	and	CCONJ
ejpam-556	59	19	linear	linear	ADJ
ejpam-556	59	20	denominator	denominator	NOUN
ejpam-556	59	21	has	have	AUX
ejpam-556	59	22	been	be	AUX
ejpam-556	59	23	developed	develop	VERB
ejpam-556	59	24	.	.	PUNCT
ejpam-556	60	1	let	let	VERB
ejpam-556	60	2	{	{	PUNCT
ejpam-556	60	3	(	(	PUNCT
ejpam-556	60	4	x	x	PROPN
ejpam-556	60	5	i	i	PROPN
ejpam-556	60	6	,	,	PUNCT
ejpam-556	60	7	fi	fi	NOUN
ejpam-556	60	8	)	)	PUNCT
ejpam-556	60	9	,	,	PUNCT
ejpam-556	60	10	i	i	PRON
ejpam-556	60	11	=	=	NOUN
ejpam-556	60	12	0,1,2	0,1,2	NUM
ejpam-556	60	13	,	,	PUNCT
ejpam-556	60	14	.	.	PUNCT
ejpam-556	60	15	.	.	PUNCT
ejpam-556	61	1	.	.	PUNCT
ejpam-556	62	1	,	,	PUNCT
ejpam-556	62	2	n	n	CCONJ
ejpam-556	62	3	}	}	PUNCT
ejpam-556	62	4	be	be	AUX
ejpam-556	62	5	a	a	DET
ejpam-556	62	6	given	give	VERB
ejpam-556	62	7	set	set	NOUN
ejpam-556	62	8	of	of	ADP
ejpam-556	62	9	data	datum	NOUN
ejpam-556	62	10	points	point	NOUN
ejpam-556	62	11	defined	define	VERB
ejpam-556	62	12	over	over	ADP
ejpam-556	62	13	the	the	DET
ejpam-556	62	14	interval	interval	NOUN
ejpam-556	62	15	[	[	X
ejpam-556	62	16	a	a	X
ejpam-556	62	17	,	,	PUNCT
ejpam-556	62	18	b	b	NOUN
ejpam-556	62	19	]	]	X
ejpam-556	62	20	,	,	PUNCT
ejpam-556	63	1	where	where	SCONJ
ejpam-556	63	2	a	a	PRON
ejpam-556	63	3	=	=	X
ejpam-556	63	4	x0	x0	PROPN
ejpam-556	63	5	<	<	X
ejpam-556	64	1	x1	x1	X
ejpam-556	64	2	<	<	X
ejpam-556	64	3	x2	x2	X
ejpam-556	64	4	<	<	X
ejpam-556	64	5	·	·	PUNCT
ejpam-556	64	6	·	·	PUNCT
ejpam-556	64	7	·	·	PUNCT
ejpam-556	64	8	<	<	X
ejpam-556	64	9	xn	xn	PUNCT
ejpam-556	64	10	=	=	SYM
ejpam-556	64	11	b.	b.	PROPN
ejpam-556	65	1	the	the	DET
ejpam-556	65	2	c1	c1	PROPN
ejpam-556	65	3	piecewise	piecewise	VERB
ejpam-556	65	4	rational	rational	ADJ
ejpam-556	65	5	cubic	cubic	ADJ
ejpam-556	65	6	function	function	NOUN
ejpam-556	65	7	with	with	ADP
ejpam-556	65	8	one	one	NUM
ejpam-556	65	9	parameter	parameter	NOUN
ejpam-556	65	10	αi	αi	VERB
ejpam-556	65	11	is	be	AUX
ejpam-556	65	12	defined	define	VERB
ejpam-556	65	13	over	over	ADP
ejpam-556	65	14	each	each	DET
ejpam-556	65	15	subinterval	subinterval	NOUN
ejpam-556	65	16	ii	ii	NOUN
ejpam-556	65	17	=	=	PUNCT
ejpam-556	66	1	[	[	X
ejpam-556	66	2	x	x	X
ejpam-556	66	3	i	i	NOUN
ejpam-556	66	4	,	,	PUNCT
ejpam-556	66	5	x	x	PROPN
ejpam-556	66	6	i+1	i+1	VERB
ejpam-556	66	7	]	]	X
ejpam-556	66	8	,	,	PUNCT
ejpam-556	66	9	i	i	PRON
ejpam-556	66	10	=	=	VERB
ejpam-556	66	11	m.	m.	NOUN
ejpam-556	66	12	z.	z.	PROPN
ejpam-556	66	13	hussain	hussain	PROPN
ejpam-556	66	14	,	,	PUNCT
ejpam-556	66	15	m.	m.	NOUN
ejpam-556	66	16	sarfraz	sarfraz	PROPN
ejpam-556	66	17	,	,	PUNCT
ejpam-556	66	18	m.	m.	NOUN
ejpam-556	66	19	hussain	hussain	PROPN
ejpam-556	66	20	/	/	SYM
ejpam-556	66	21	eur	eur	PROPN
ejpam-556	66	22	.	.	PUNCT
ejpam-556	67	1	j.	j.	PROPN
ejpam-556	67	2	pure	pure	PROPN
ejpam-556	67	3	appl	appl	PROPN
ejpam-556	67	4	.	.	PROPN
ejpam-556	67	5	math	math	PROPN
ejpam-556	67	6	,	,	PUNCT
ejpam-556	67	7	3	3	NUM
ejpam-556	67	8	(	(	PUNCT
ejpam-556	67	9	2010	2010	NUM
ejpam-556	67	10	)	)	PUNCT
ejpam-556	67	11	,	,	PUNCT
ejpam-556	67	12	194	194	NUM
ejpam-556	67	13	-	-	SYM
ejpam-556	67	14	212	212	NUM
ejpam-556	67	15	196	196	NUM
ejpam-556	67	16	0,1,2	0,1,2	NUM
ejpam-556	67	17	,	,	PUNCT
ejpam-556	67	18	.	.	PUNCT
ejpam-556	67	19	.	.	PUNCT
ejpam-556	68	1	.	.	PUNCT
ejpam-556	69	1	,	,	PUNCT
ejpam-556	69	2	n−	n−	NOUN
ejpam-556	69	3	1	1	NUM
ejpam-556	69	4	as	as	ADP
ejpam-556	69	5	:	:	PUNCT
ejpam-556	69	6	s(x)≡	s(x)≡	X
ejpam-556	69	7	si(x	si(x	X
ejpam-556	69	8	)	)	PUNCT
ejpam-556	69	9	=	=	SYM
ejpam-556	69	10	pi(θ	pi(θ	NOUN
ejpam-556	69	11	)	)	PUNCT
ejpam-556	69	12	qi(θ	qi(θ	NOUN
ejpam-556	69	13	)	)	PUNCT
ejpam-556	69	14	,	,	PUNCT
ejpam-556	69	15	(	(	PUNCT
ejpam-556	69	16	1	1	X
ejpam-556	69	17	)	)	PUNCT
ejpam-556	69	18	where	where	SCONJ
ejpam-556	69	19	pi(θ	pi(θ	NOUN
ejpam-556	69	20	)	)	PUNCT
ejpam-556	69	21	=	=	SYM
ejpam-556	69	22	3	3	NUM
ejpam-556	69	23	∑	∑	PROPN
ejpam-556	69	24	i=0	i=0	PROPN
ejpam-556	69	25	(	(	PUNCT
ejpam-556	69	26	1−	1−	NUM
ejpam-556	69	27	θ)3−iθai	θ)3−iθai	NOUN
ejpam-556	69	28	,	,	PUNCT
ejpam-556	69	29	a0	a0	PROPN
ejpam-556	69	30	=	=	PUNCT
ejpam-556	69	31	(	(	PUNCT
ejpam-556	69	32	αi	αi	VERB
ejpam-556	69	33	+	+	CCONJ
ejpam-556	69	34	1	1	X
ejpam-556	69	35	)	)	PUNCT
ejpam-556	69	36	fi	fi	NOUN
ejpam-556	69	37	,	,	PUNCT
ejpam-556	69	38	a1	a1	NOUN
ejpam-556	69	39	=	=	SYM
ejpam-556	69	40	(	(	PUNCT
ejpam-556	69	41	2αi	2αi	NOUN
ejpam-556	69	42	+	+	CCONJ
ejpam-556	69	43	3	3	X
ejpam-556	69	44	)	)	PUNCT
ejpam-556	69	45	fi	fi	NOUN
ejpam-556	69	46	+	+	CCONJ
ejpam-556	69	47	hidi	hidi	ADJ
ejpam-556	69	48	,	,	PUNCT
ejpam-556	69	49	a2	a2	PROPN
ejpam-556	69	50	=	=	PUNCT
ejpam-556	69	51	(	(	PUNCT
ejpam-556	69	52	αi	αi	X
ejpam-556	69	53	+	+	CCONJ
ejpam-556	69	54	3	3	X
ejpam-556	69	55	)	)	PUNCT
ejpam-556	69	56	fi+1	fi+1	NOUN
ejpam-556	69	57	−	−	PROPN
ejpam-556	69	58	hidi+1	hidi+1	PROPN
ejpam-556	69	59	,	,	PUNCT
ejpam-556	69	60	a3	a3	NOUN
ejpam-556	69	61	=	=	SYM
ejpam-556	69	62	fi+1	fi+1	NOUN
ejpam-556	69	63	,	,	PUNCT
ejpam-556	69	64	qi(θ	qi(θ	X
ejpam-556	69	65	)	)	PUNCT
ejpam-556	69	66	=	=	SYM
ejpam-556	69	67	1+αi(1−	1+αi(1−	NUM
ejpam-556	69	68	θ	θ	X
ejpam-556	69	69	)	)	PUNCT
ejpam-556	69	70	,	,	PUNCT
ejpam-556	69	71	hi	hi	INTJ
ejpam-556	70	1	=	=	PUNCT
ejpam-556	70	2	x	x	PUNCT
ejpam-556	71	1	i+1	i+1	ADV
ejpam-556	71	2	−	−	PROPN
ejpam-556	72	1	x	x	INTJ
ejpam-556	72	2	i	i	PROPN
ejpam-556	72	3	,	,	PUNCT
ejpam-556	72	4	θ	θ	PROPN
ejpam-556	72	5	=	=	PUNCT
ejpam-556	72	6	(	(	PUNCT
ejpam-556	72	7	x	x	X
ejpam-556	72	8	−	−	PROPN
ejpam-556	72	9	x	x	SYM
ejpam-556	72	10	i	i	NOUN
ejpam-556	72	11	)	)	PUNCT
ejpam-556	72	12	hi	hi	INTJ
ejpam-556	72	13	,	,	PUNCT
ejpam-556	72	14	s(x	s(x	PROPN
ejpam-556	72	15	i	i	PRON
ejpam-556	72	16	)	)	PUNCT
ejpam-556	72	17	=	=	NOUN
ejpam-556	72	18	fi	fi	NOUN
ejpam-556	72	19	,	,	PUNCT
ejpam-556	72	20	s(x	s(x	PROPN
ejpam-556	72	21	i+1	i+1	NUM
ejpam-556	72	22	)	)	PUNCT
ejpam-556	72	23	=	=	SYM
ejpam-556	72	24	fi+1	fi+1	NOUN
ejpam-556	72	25	,	,	PUNCT
ejpam-556	72	26	s(1)(x	s(1)(x	NOUN
ejpam-556	72	27	i	i	NOUN
ejpam-556	72	28	)	)	PUNCT
ejpam-556	72	29	=	=	SYM
ejpam-556	72	30	di	di	NOUN
ejpam-556	72	31	,	,	PUNCT
ejpam-556	72	32	s(1)(x	s(1)(x	NOUN
ejpam-556	72	33	i+1	i+1	NUM
ejpam-556	72	34	)	)	PUNCT
ejpam-556	72	35	=	=	SYM
ejpam-556	72	36	di+1	di+1	NOUN
ejpam-556	72	37	.	.	PUNCT
ejpam-556	73	1	(	(	PUNCT
ejpam-556	73	2	2	2	X
ejpam-556	73	3	)	)	PUNCT
ejpam-556	73	4	s(1)(x	s(1)(x	NOUN
ejpam-556	73	5	)	)	PUNCT
ejpam-556	73	6	denotes	denote	VERB
ejpam-556	73	7	the	the	DET
ejpam-556	73	8	derivative	derivative	NOUN
ejpam-556	73	9	with	with	ADP
ejpam-556	73	10	respect	respect	NOUN
ejpam-556	73	11	to	to	ADP
ejpam-556	73	12	x	x	PUNCT
ejpam-556	73	13	and	and	CCONJ
ejpam-556	73	14	di	di	NOUN
ejpam-556	73	15	denotes	denote	NOUN
ejpam-556	73	16	derivative	derivative	ADJ
ejpam-556	73	17	values	value	NOUN
ejpam-556	73	18	estimated	estimate	VERB
ejpam-556	73	19	or	or	CCONJ
ejpam-556	73	20	given	give	VERB
ejpam-556	73	21	.	.	PUNCT
ejpam-556	74	1	it	it	PRON
ejpam-556	74	2	is	be	AUX
ejpam-556	74	3	noted	note	VERB
ejpam-556	74	4	that	that	SCONJ
ejpam-556	74	5	when	when	SCONJ
ejpam-556	74	6	αi	αi	ADV
ejpam-556	74	7	=	=	SYM
ejpam-556	74	8	0	0	PROPN
ejpam-556	74	9	,	,	PUNCT
ejpam-556	74	10	the	the	DET
ejpam-556	74	11	piecewise	piecewise	NOUN
ejpam-556	74	12	rational	rational	ADJ
ejpam-556	74	13	cubic	cubic	ADJ
ejpam-556	74	14	function	function	NOUN
ejpam-556	74	15	(	(	PUNCT
ejpam-556	74	16	1	1	X
ejpam-556	74	17	)	)	PUNCT
ejpam-556	74	18	reduces	reduce	VERB
ejpam-556	74	19	to	to	ADP
ejpam-556	74	20	cubic	cubic	ADJ
ejpam-556	74	21	hermite	hermite	ADJ
ejpam-556	74	22	spline	spline	NOUN
ejpam-556	74	23	.	.	PUNCT
ejpam-556	75	1	in	in	ADP
ejpam-556	75	2	this	this	DET
ejpam-556	75	3	paper	paper	NOUN
ejpam-556	75	4	,	,	PUNCT
ejpam-556	75	5	the	the	DET
ejpam-556	75	6	parameter	parameter	NOUN
ejpam-556	75	7	αi	αi	PART
ejpam-556	75	8	can	can	AUX
ejpam-556	75	9	assume	assume	VERB
ejpam-556	75	10	any	any	DET
ejpam-556	75	11	positive	positive	ADJ
ejpam-556	75	12	real	real	ADJ
ejpam-556	75	13	value	value	NOUN
ejpam-556	75	14	.	.	PUNCT
ejpam-556	76	1	2.1	2.1	NUM
ejpam-556	76	2	.	.	PUNCT
ejpam-556	76	3	error	error	NOUN
ejpam-556	76	4	estimation	estimation	NOUN
ejpam-556	76	5	of	of	ADP
ejpam-556	76	6	interpolation	interpolation	NOUN
ejpam-556	76	7	in	in	ADP
ejpam-556	76	8	this	this	DET
ejpam-556	76	9	section	section	NOUN
ejpam-556	76	10	,	,	PUNCT
ejpam-556	76	11	the	the	DET
ejpam-556	76	12	error	error	NOUN
ejpam-556	76	13	of	of	ADP
ejpam-556	76	14	interpolation	interpolation	NOUN
ejpam-556	76	15	is	be	AUX
ejpam-556	76	16	estimated	estimate	VERB
ejpam-556	76	17	when	when	SCONJ
ejpam-556	76	18	the	the	DET
ejpam-556	76	19	function	function	NOUN
ejpam-556	76	20	being	be	AUX
ejpam-556	76	21	interpolated	interpolate	VERB
ejpam-556	76	22	is	be	AUX
ejpam-556	76	23	f	f	PROPN
ejpam-556	76	24	(	(	PUNCT
ejpam-556	76	25	x	x	X
ejpam-556	76	26	)	)	PUNCT
ejpam-556	76	27	∈	∈	PROPN
ejpam-556	76	28	c2[x0	c2[x0	PROPN
ejpam-556	76	29	,	,	PUNCT
ejpam-556	76	30	xn	xn	PROPN
ejpam-556	76	31	]	]	X
ejpam-556	76	32	.	.	PUNCT
ejpam-556	77	1	the	the	DET
ejpam-556	77	2	interpolation	interpolation	NOUN
ejpam-556	77	3	scheme	scheme	NOUN
ejpam-556	77	4	developed	develop	VERB
ejpam-556	77	5	in	in	ADP
ejpam-556	77	6	section	section	NOUN
ejpam-556	77	7	2	2	NUM
ejpam-556	77	8	is	be	AUX
ejpam-556	77	9	local	local	ADJ
ejpam-556	77	10	,	,	PUNCT
ejpam-556	77	11	which	which	PRON
ejpam-556	77	12	allows	allow	VERB
ejpam-556	77	13	investigating	investigate	VERB
ejpam-556	77	14	the	the	DET
ejpam-556	77	15	error	error	NOUN
ejpam-556	77	16	in	in	ADP
ejpam-556	77	17	an	an	DET
ejpam-556	77	18	arbitrary	arbitrary	ADJ
ejpam-556	77	19	subinterval	subinterval	NOUN
ejpam-556	77	20	ii	ii	NOUN
ejpam-556	77	21	=	=	PUNCT
ejpam-556	78	1	[	[	X
ejpam-556	78	2	x	x	X
ejpam-556	78	3	i	i	NOUN
ejpam-556	78	4	,	,	PUNCT
ejpam-556	78	5	x	x	PROPN
ejpam-556	78	6	i+1	i+1	X
ejpam-556	78	7	]	]	PUNCT
ejpam-556	78	8	without	without	ADP
ejpam-556	78	9	loss	loss	NOUN
ejpam-556	78	10	of	of	ADP
ejpam-556	78	11	generality	generality	NOUN
ejpam-556	78	12	.	.	PUNCT
ejpam-556	79	1	using	use	VERB
ejpam-556	79	2	peano	peano	PROPN
ejpam-556	79	3	kernel	kernel	PROPN
ejpam-556	79	4	theorem	theorem	VERB
ejpam-556	79	5	[	[	X
ejpam-556	79	6	16	16	NUM
ejpam-556	79	7	]	]	PUNCT
ejpam-556	79	8	the	the	DET
ejpam-556	79	9	error	error	NOUN
ejpam-556	79	10	of	of	ADP
ejpam-556	79	11	interpolation	interpolation	NOUN
ejpam-556	79	12	in	in	ADP
ejpam-556	79	13	each	each	DET
ejpam-556	79	14	subinterval	subinterval	NOUN
ejpam-556	79	15	ii	ii	NOUN
ejpam-556	80	1	=	=	PUNCT
ejpam-556	81	1	[	[	X
ejpam-556	81	2	x	x	X
ejpam-556	81	3	i	i	NOUN
ejpam-556	81	4	,	,	PUNCT
ejpam-556	81	5	x	x	PUNCT
ejpam-556	81	6	i+1	i+1	VERB
ejpam-556	81	7	]	]	X
ejpam-556	81	8	is	be	AUX
ejpam-556	81	9	:	:	PUNCT
ejpam-556	81	10	r	r	X
ejpam-556	81	11	[	[	X
ejpam-556	81	12	f	f	X
ejpam-556	81	13	]	]	PUNCT
ejpam-556	81	14	=	=	PUNCT
ejpam-556	81	15	f	f	X
ejpam-556	81	16	(	(	PUNCT
ejpam-556	81	17	x)−	x)−	PROPN
ejpam-556	81	18	si(x	si(x	NOUN
ejpam-556	81	19	)	)	PUNCT
ejpam-556	81	20	=	=	SYM
ejpam-556	81	21	1	1	NUM
ejpam-556	81	22	2	2	NUM
ejpam-556	81	23	∫	∫	NOUN
ejpam-556	81	24	xi+1	xi+1	PROPN
ejpam-556	82	1	xi	xi	PROPN
ejpam-556	82	2	f	f	PROPN
ejpam-556	82	3	(	(	PUNCT
ejpam-556	82	4	2)(τ)rx[(x	2)(τ)rx[(x	NOUN
ejpam-556	82	5	−τ)+]dτ	−τ)+]dτ	ADV
ejpam-556	82	6	.	.	PUNCT
ejpam-556	83	1	(	(	PUNCT
ejpam-556	83	2	3	3	X
ejpam-556	83	3	)	)	PUNCT
ejpam-556	83	4	it	it	PRON
ejpam-556	83	5	is	be	AUX
ejpam-556	83	6	assumed	assume	VERB
ejpam-556	83	7	that	that	SCONJ
ejpam-556	83	8	the	the	DET
ejpam-556	83	9	function	function	NOUN
ejpam-556	83	10	being	be	AUX
ejpam-556	83	11	interpolated	interpolate	VERB
ejpam-556	83	12	is	be	AUX
ejpam-556	83	13	f	f	PROPN
ejpam-556	83	14	(	(	PUNCT
ejpam-556	83	15	x	x	X
ejpam-556	83	16	)	)	PUNCT
ejpam-556	83	17	∈	∈	PROPN
ejpam-556	83	18	c2[x0	c2[x0	PROPN
ejpam-556	83	19	,	,	PUNCT
ejpam-556	83	20	xn	xn	PROPN
ejpam-556	83	21	]	]	X
ejpam-556	83	22	.	.	PUNCT
ejpam-556	84	1	the	the	DET
ejpam-556	84	2	absolute	absolute	ADJ
ejpam-556	84	3	error	error	NOUN
ejpam-556	84	4	in	in	ADP
ejpam-556	84	5	ii	ii	NOUN
ejpam-556	84	6	=	=	PUNCT
ejpam-556	85	1	[	[	X
ejpam-556	85	2	x	x	X
ejpam-556	85	3	i	i	NOUN
ejpam-556	85	4	,	,	PUNCT
ejpam-556	85	5	x	x	PUNCT
ejpam-556	85	6	i+1	i+1	VERB
ejpam-556	85	7	]	]	X
ejpam-556	85	8	is	be	AUX
ejpam-556	85	9	:	:	PUNCT
ejpam-556	85	10	|	|	ADV
ejpam-556	85	11	f	f	X
ejpam-556	85	12	(	(	PUNCT
ejpam-556	85	13	x)−	x)−	PROPN
ejpam-556	85	14	si(x)|	si(x)|	VERB
ejpam-556	85	15	≤	≤	ADV
ejpam-556	85	16	1	1	NUM
ejpam-556	85	17	2	2	NUM
ejpam-556	85	18	‖	‖	PROPN
ejpam-556	85	19	f	f	PROPN
ejpam-556	85	20	(	(	PUNCT
ejpam-556	85	21	2)(τ)‖	2)(τ)‖	NUM
ejpam-556	85	22	∫	∫	PROPN
ejpam-556	85	23	xi+1	xi+1	PROPN
ejpam-556	85	24	xi	xi	PROPN
ejpam-556	86	1	|rx[(x	|rx[(x	PROPN
ejpam-556	86	2	−τ)+]|dτ	−τ)+]|dτ	X
ejpam-556	86	3	,	,	PUNCT
ejpam-556	86	4	(	(	PUNCT
ejpam-556	86	5	4	4	X
ejpam-556	86	6	)	)	PUNCT
ejpam-556	86	7	where	where	SCONJ
ejpam-556	86	8	rx[(x	rx[(x	NOUN
ejpam-556	86	9	−τ)+	−τ)+	NOUN
ejpam-556	86	10	]	]	X
ejpam-556	86	11	=	=	SYM
ejpam-556	86	12	¨	¨	X
ejpam-556	86	13	u(τ	u(τ	X
ejpam-556	86	14	,	,	PUNCT
ejpam-556	86	15	x	x	NOUN
ejpam-556	86	16	)	)	PUNCT
ejpam-556	86	17	,	,	PUNCT
ejpam-556	86	18	x	x	PUNCT
ejpam-556	87	1	i	i	PRON
ejpam-556	87	2	<	<	X
ejpam-556	87	3	τ	τ	X
ejpam-556	87	4	<	<	X
ejpam-556	87	5	x	x	X
ejpam-556	87	6	,	,	PUNCT
ejpam-556	87	7	v(τ	v(τ	PROPN
ejpam-556	87	8	,	,	PUNCT
ejpam-556	87	9	x	x	NOUN
ejpam-556	87	10	)	)	PUNCT
ejpam-556	87	11	,	,	PUNCT
ejpam-556	87	12	x	x	X
ejpam-556	87	13	<	<	X
ejpam-556	87	14	τ	τ	X
ejpam-556	87	15	<	<	X
ejpam-556	87	16	x	x	X
ejpam-556	87	17	i+1	i+1	NUM
ejpam-556	87	18	.	.	PUNCT
ejpam-556	87	19	«	«	PUNCT
ejpam-556	87	20	,	,	PUNCT
ejpam-556	87	21	(	(	PUNCT
ejpam-556	87	22	5	5	X
ejpam-556	87	23	)	)	PUNCT
ejpam-556	87	24	the	the	DET
ejpam-556	87	25	integral	integral	ADJ
ejpam-556	87	26	involved	involve	VERB
ejpam-556	87	27	in	in	ADP
ejpam-556	87	28	(	(	PUNCT
ejpam-556	87	29	4	4	NUM
ejpam-556	87	30	)	)	PUNCT
ejpam-556	87	31	is	be	AUX
ejpam-556	87	32	expressed	express	VERB
ejpam-556	87	33	as	as	ADP
ejpam-556	87	34	:	:	PUNCT
ejpam-556	87	35	∫	∫	PROPN
ejpam-556	87	36	xi+1	xi+1	PROPN
ejpam-556	87	37	xi	xi	PUNCT
ejpam-556	88	1	|rx[(x	|rx[(x	PROPN
ejpam-556	89	1	−τ)+]|dτ=	−τ)+]|dτ=	VERB
ejpam-556	89	2	∫	∫	PROPN
ejpam-556	89	3	x	x	X
ejpam-556	89	4	xi	xi	PROPN
ejpam-556	89	5	|u(τ	|u(τ	PROPN
ejpam-556	89	6	,	,	PUNCT
ejpam-556	89	7	x)|dτ+	x)|dτ+	PRON
ejpam-556	89	8	∫	∫	PROPN
ejpam-556	89	9	xi+1	xi+1	X
ejpam-556	90	1	x	x	SYM
ejpam-556	90	2	|v(τ	|v(τ	PROPN
ejpam-556	90	3	,	,	PUNCT
ejpam-556	90	4	x)|dτ	x)|dτ	PROPN
ejpam-556	90	5	.	.	PUNCT
ejpam-556	91	1	(	(	PUNCT
ejpam-556	91	2	6	6	NUM
ejpam-556	91	3	)	)	PUNCT
ejpam-556	91	4	m.	m.	NOUN
ejpam-556	91	5	z.	z.	PROPN
ejpam-556	91	6	hussain	hussain	PROPN
ejpam-556	91	7	,	,	PUNCT
ejpam-556	91	8	m.	m.	NOUN
ejpam-556	91	9	sarfraz	sarfraz	PROPN
ejpam-556	91	10	,	,	PUNCT
ejpam-556	91	11	m.	m.	NOUN
ejpam-556	91	12	hussain	hussain	PROPN
ejpam-556	91	13	/	/	SYM
ejpam-556	91	14	eur	eur	PROPN
ejpam-556	91	15	.	.	PUNCT
ejpam-556	92	1	j.	j.	PROPN
ejpam-556	92	2	pure	pure	PROPN
ejpam-556	92	3	appl	appl	PROPN
ejpam-556	92	4	.	.	PROPN
ejpam-556	92	5	math	math	PROPN
ejpam-556	92	6	,	,	PUNCT
ejpam-556	92	7	3	3	NUM
ejpam-556	92	8	(	(	PUNCT
ejpam-556	92	9	2010	2010	NUM
ejpam-556	92	10	)	)	PUNCT
ejpam-556	92	11	,	,	PUNCT
ejpam-556	92	12	194	194	NUM
ejpam-556	92	13	-	-	SYM
ejpam-556	92	14	212	212	NUM
ejpam-556	92	15	197	197	NUM
ejpam-556	92	16	for	for	ADP
ejpam-556	92	17	the	the	DET
ejpam-556	92	18	c1	c1	PROPN
ejpam-556	92	19	rational	rational	ADJ
ejpam-556	92	20	cubic	cubic	ADJ
ejpam-556	92	21	function	function	NOUN
ejpam-556	92	22	(	(	PUNCT
ejpam-556	92	23	1	1	NUM
ejpam-556	92	24	)	)	PUNCT
ejpam-556	92	25	,	,	PUNCT
ejpam-556	92	26	u(τ	u(τ	PROPN
ejpam-556	92	27	,	,	PUNCT
ejpam-556	92	28	x	x	NOUN
ejpam-556	92	29	)	)	PUNCT
ejpam-556	92	30	and	and	CCONJ
ejpam-556	92	31	v(τ	v(τ	PROPN
ejpam-556	92	32	,	,	PUNCT
ejpam-556	92	33	x	x	X
ejpam-556	92	34	)	)	PUNCT
ejpam-556	92	35	have	have	VERB
ejpam-556	92	36	the	the	DET
ejpam-556	92	37	values	value	NOUN
ejpam-556	92	38	u(τ	u(τ	VERB
ejpam-556	92	39	,	,	PUNCT
ejpam-556	92	40	x	x	X
ejpam-556	92	41	)	)	PUNCT
ejpam-556	92	42	=	=	SYM
ejpam-556	93	1	(	(	PUNCT
ejpam-556	93	2	x	x	SYM
ejpam-556	93	3	−τ)−	−τ)−	PROPN
ejpam-556	93	4	θ2	θ2	PROPN
ejpam-556	93	5	qi(θ	qi(θ	PUNCT
ejpam-556	93	6	)	)	PUNCT
ejpam-556	94	1	[	[	X
ejpam-556	94	2	(	(	PUNCT
ejpam-556	94	3	1−	1−	NUM
ejpam-556	94	4	θ){(αi	θ){(αi	NOUN
ejpam-556	94	5	+	+	PROPN
ejpam-556	94	6	3)(x	3)(x	PROPN
ejpam-556	94	7	i+1−τ)−	i+1−τ)−	NOUN
ejpam-556	94	8	hi}+	hi}+	PROPN
ejpam-556	94	9	θ(x	θ(x	PROPN
ejpam-556	94	10	i+1	i+1	NUM
ejpam-556	94	11	−τ	−τ	NOUN
ejpam-556	94	12	)	)	PUNCT
ejpam-556	94	13	]	]	PUNCT
ejpam-556	94	14	,	,	PUNCT
ejpam-556	94	15	(	(	PUNCT
ejpam-556	94	16	7	7	X
ejpam-556	94	17	)	)	PUNCT
ejpam-556	94	18	v(τ	v(τ	PROPN
ejpam-556	94	19	,	,	PUNCT
ejpam-556	94	20	x	x	NOUN
ejpam-556	94	21	)	)	PUNCT
ejpam-556	94	22	=	=	SYM
ejpam-556	95	1	−	−	PROPN
ejpam-556	95	2	θ2	θ2	PROPN
ejpam-556	95	3	qi(θ	qi(θ	PUNCT
ejpam-556	95	4	)	)	PUNCT
ejpam-556	96	1	[	[	X
ejpam-556	96	2	(	(	PUNCT
ejpam-556	96	3	1−	1−	NUM
ejpam-556	96	4	θ){(αi	θ){(αi	NOUN
ejpam-556	96	5	+	+	PROPN
ejpam-556	96	6	3)(x	3)(x	PROPN
ejpam-556	96	7	i+1−τ)−	i+1−τ)−	NOUN
ejpam-556	96	8	hi}+	hi}+	PROPN
ejpam-556	96	9	θ(x	θ(x	PROPN
ejpam-556	96	10	i+1	i+1	NUM
ejpam-556	96	11	−τ	−τ	ADJ
ejpam-556	96	12	)	)	PUNCT
ejpam-556	96	13	]	]	PUNCT
ejpam-556	96	14	.	.	PUNCT
ejpam-556	97	1	(	(	PUNCT
ejpam-556	97	2	8)	8)	NUM
ejpam-556	97	3	the	the	DET
ejpam-556	97	4	roots	root	NOUN
ejpam-556	97	5	of	of	ADP
ejpam-556	97	6	u(x	u(x	NOUN
ejpam-556	97	7	,	,	PUNCT
ejpam-556	97	8	x	x	X
ejpam-556	97	9	)	)	PUNCT
ejpam-556	97	10	and	and	CCONJ
ejpam-556	97	11	v(x	v(x	PROPN
ejpam-556	97	12	,	,	PUNCT
ejpam-556	97	13	x	x	X
ejpam-556	97	14	)	)	PUNCT
ejpam-556	97	15	in	in	ADP
ejpam-556	97	16	[	[	X
ejpam-556	97	17	0,1	0,1	NUM
ejpam-556	97	18	]	]	PUNCT
ejpam-556	97	19	are	be	AUX
ejpam-556	97	20	θ	θ	X
ejpam-556	97	21	=	=	SYM
ejpam-556	97	22	0	0	NUM
ejpam-556	97	23	and	and	CCONJ
ejpam-556	97	24	θ	θ	PROPN
ejpam-556	98	1	=	=	SYM
ejpam-556	98	2	1	1	X
ejpam-556	98	3	.	.	PUNCT
ejpam-556	99	1	the	the	DET
ejpam-556	99	2	root	root	NOUN
ejpam-556	99	3	of	of	ADP
ejpam-556	99	4	u(τ	u(τ	ADJ
ejpam-556	99	5	,	,	PUNCT
ejpam-556	99	6	x	x	NOUN
ejpam-556	99	7	)	)	PUNCT
ejpam-556	99	8	=	=	SYM
ejpam-556	99	9	0	0	NUM
ejpam-556	99	10	is	be	AUX
ejpam-556	99	11	τ1	τ1	NOUN
ejpam-556	99	12	=	=	SYM
ejpam-556	99	13	x	x	SYM
ejpam-556	99	14	−	−	PROPN
ejpam-556	99	15	hiθ	hiθ	NOUN
ejpam-556	99	16	2(αi+2	2(αi+2	NUM
ejpam-556	99	17	)	)	PUNCT
ejpam-556	100	1	(	(	PUNCT
ejpam-556	100	2	αi+1)+θ	αi+1)+θ	NUM
ejpam-556	100	3	(	(	PUNCT
ejpam-556	100	4	αi+2	αi+2	NUM
ejpam-556	100	5	)	)	PUNCT
ejpam-556	100	6	.	.	PUNCT
ejpam-556	101	1	the	the	DET
ejpam-556	101	2	root	root	NOUN
ejpam-556	101	3	of	of	ADP
ejpam-556	101	4	v(τ	v(τ	PROPN
ejpam-556	101	5	,	,	PUNCT
ejpam-556	101	6	x	x	NOUN
ejpam-556	101	7	)	)	PUNCT
ejpam-556	101	8	=	=	SYM
ejpam-556	101	9	0	0	NUM
ejpam-556	101	10	is	be	AUX
ejpam-556	101	11	τ2	τ2	NOUN
ejpam-556	101	12	=	=	PUNCT
ejpam-556	101	13	x	x	PUNCT
ejpam-556	101	14	i+1	i+1	ADP
ejpam-556	101	15	−	−	PROPN
ejpam-556	101	16	hi(1−θ	hi(1−θ	NOUN
ejpam-556	101	17	)	)	PUNCT
ejpam-556	101	18	1+(αi+2)(1−θ	1+(αi+2)(1−θ	NUM
ejpam-556	101	19	)	)	PUNCT
ejpam-556	101	20	.	.	PUNCT
ejpam-556	102	1	the	the	DET
ejpam-556	102	2	above	above	ADJ
ejpam-556	102	3	discussion	discussion	NOUN
ejpam-556	102	4	leads	lead	VERB
ejpam-556	102	5	to	to	ADP
ejpam-556	102	6	the	the	DET
ejpam-556	102	7	following	follow	VERB
ejpam-556	102	8	manipulation	manipulation	NOUN
ejpam-556	102	9	:	:	PUNCT
ejpam-556	103	1	|	|	ADV
ejpam-556	103	2	f	f	X
ejpam-556	103	3	(	(	PUNCT
ejpam-556	103	4	x)−	x)−	PROPN
ejpam-556	103	5	si(x)|	si(x)|	VERB
ejpam-556	103	6	≤	≤	ADV
ejpam-556	103	7	1	1	NUM
ejpam-556	103	8	2	2	NUM
ejpam-556	103	9	‖	‖	PROPN
ejpam-556	103	10	f	f	PROPN
ejpam-556	103	11	(	(	PUNCT
ejpam-556	103	12	2)(τ)‖h2	2)(τ)‖h2	PROPN
ejpam-556	103	13	iω(αi	iω(αi	PROPN
ejpam-556	103	14	,	,	PUNCT
ejpam-556	103	15	θ	θ	NOUN
ejpam-556	103	16	)	)	PUNCT
ejpam-556	103	17	,	,	PUNCT
ejpam-556	103	18	ω(αi	ω(αi	PROPN
ejpam-556	103	19	,	,	PUNCT
ejpam-556	103	20	θ	θ	NOUN
ejpam-556	103	21	)	)	PUNCT
ejpam-556	103	22	=	=	SYM
ejpam-556	103	23	∫	∫	PROPN
ejpam-556	103	24	x	x	X
ejpam-556	103	25	xi	xi	PROPN
ejpam-556	103	26	|u(τ	|u(τ	PROPN
ejpam-556	103	27	,	,	PUNCT
ejpam-556	103	28	x)|dτ+	x)|dτ+	PRON
ejpam-556	103	29	∫	∫	PROPN
ejpam-556	103	30	xi+1	xi+1	X
ejpam-556	104	1	x	x	SYM
ejpam-556	104	2	|v(τ	|v(τ	PROPN
ejpam-556	104	3	,	,	PUNCT
ejpam-556	104	4	x)|dτ	x)|dτ	PROPN
ejpam-556	104	5	=	=	SYM
ejpam-556	104	6	∫	∫	PROPN
ejpam-556	104	7	τ1	τ1	NOUN
ejpam-556	104	8	xi	xi	X
ejpam-556	104	9	u(τ	u(τ	PROPN
ejpam-556	104	10	,	,	PUNCT
ejpam-556	104	11	x)dτ−	x)dτ−	PROPN
ejpam-556	104	12	∫	∫	PROPN
ejpam-556	105	1	x	x	PUNCT
ejpam-556	105	2	τ1	τ1	ADP
ejpam-556	105	3	u(τ	u(τ	PROPN
ejpam-556	105	4	,	,	PUNCT
ejpam-556	105	5	x)dτ−	x)dτ−	PROPN
ejpam-556	105	6	∫	∫	PROPN
ejpam-556	106	1	τ2	τ2	PROPN
ejpam-556	106	2	x	x	PUNCT
ejpam-556	106	3	v(τ	v(τ	PROPN
ejpam-556	106	4	,	,	PUNCT
ejpam-556	106	5	x)dτ+	x)dτ+	PUNCT
ejpam-556	106	6	∫	∫	PROPN
ejpam-556	106	7	xi+1	xi+1	PROPN
ejpam-556	106	8	τ2	τ2	PROPN
ejpam-556	106	9	v(τ	v(τ	PROPN
ejpam-556	106	10	,	,	PUNCT
ejpam-556	106	11	x)dτ	x)dτ	PROPN
ejpam-556	106	12	=	=	PRON
ejpam-556	106	13	θ2{−θ2(αi	θ2{−θ2(αi	NOUN
ejpam-556	106	14	+	+	ADJ
ejpam-556	106	15	2)2qi(θ	2)2qi(θ	NUM
ejpam-556	106	16	)	)	PUNCT
ejpam-556	107	1	+	+	CCONJ
ejpam-556	107	2	(	(	PUNCT
ejpam-556	107	3	αi	αi	X
ejpam-556	107	4	+	+	CCONJ
ejpam-556	107	5	1)2(1	1)2(1	NUM
ejpam-556	107	6	+	+	NUM
ejpam-556	107	7	θ)2((αi	θ)2((αi	NOUN
ejpam-556	108	1	+	+	CCONJ
ejpam-556	108	2	3)−	3)−	NUM
ejpam-556	108	3	θ(αi	θ(αi	NOUN
ejpam-556	108	4	+	+	NOUN
ejpam-556	108	5	2	2	NUM
ejpam-556	108	6	)	)	PUNCT
ejpam-556	108	7	)	)	PUNCT
ejpam-556	108	8	}	}	PUNCT
ejpam-556	109	1	qi(θ){1+αi	qi(θ){1+αi	PROPN
ejpam-556	109	2	+	+	NOUN
ejpam-556	109	3	θ(αi	θ(αi	VERB
ejpam-556	109	4	+	+	CCONJ
ejpam-556	109	5	2)}2	2)}2	NUM
ejpam-556	109	6	+	+	CCONJ
ejpam-556	109	7	2θ2(1−	2θ2(1−	NUM
ejpam-556	109	8	θ)2	θ)2	NOUN
ejpam-556	109	9	qi(θ	qi(θ	NOUN
ejpam-556	109	10	)	)	PUNCT
ejpam-556	109	11	−	−	PROPN
ejpam-556	110	1	2θ4(1−	2θ4(1−	NUM
ejpam-556	110	2	θ)(αi	θ)(αi	NOUN
ejpam-556	110	3	+	+	CCONJ
ejpam-556	110	4	2	2	X
ejpam-556	110	5	)	)	PUNCT
ejpam-556	110	6	qi(θ){1+αi	qi(θ){1+αi	NOUN
ejpam-556	110	7	+	+	NOUN
ejpam-556	110	8	θ(αi	θ(αi	NUM
ejpam-556	110	9	+	+	NOUN
ejpam-556	110	10	2	2	NUM
ejpam-556	110	11	)	)	PUNCT
ejpam-556	110	12	}	}	PUNCT
ejpam-556	111	1	+	+	CCONJ
ejpam-556	111	2	θ2(1−	θ2(1−	ADJ
ejpam-556	111	3	θ)2	θ)2	NOUN
ejpam-556	111	4	qi(θ){1	qi(θ){1	PROPN
ejpam-556	111	5	+	+	CCONJ
ejpam-556	111	6	(	(	PUNCT
ejpam-556	111	7	αi	αi	VERB
ejpam-556	111	8	+	+	CCONJ
ejpam-556	111	9	2)(1−	2)(1−	NUM
ejpam-556	111	10	θ	θ	NOUN
ejpam-556	111	11	)	)	PUNCT
ejpam-556	111	12	}	}	PUNCT
ejpam-556	111	13	.	.	PUNCT
ejpam-556	112	1	the	the	DET
ejpam-556	112	2	above	above	ADJ
ejpam-556	112	3	discussion	discussion	NOUN
ejpam-556	112	4	is	be	AUX
ejpam-556	112	5	summarized	summarize	VERB
ejpam-556	112	6	as	as	SCONJ
ejpam-556	112	7	follows	follow	VERB
ejpam-556	112	8	:	:	PUNCT
ejpam-556	112	9	theorem	theorem	NOUN
ejpam-556	112	10	1	1	NUM
ejpam-556	112	11	.	.	PUNCT
ejpam-556	113	1	the	the	DET
ejpam-556	113	2	error	error	NOUN
ejpam-556	113	3	of	of	ADP
ejpam-556	113	4	c1	c1	PROPN
ejpam-556	113	5	rational	rational	ADJ
ejpam-556	113	6	cubic	cubic	ADJ
ejpam-556	113	7	function	function	NOUN
ejpam-556	113	8	(	(	PUNCT
ejpam-556	113	9	1	1	NUM
ejpam-556	113	10	)	)	PUNCT
ejpam-556	113	11	,	,	PUNCT
ejpam-556	113	12	for	for	ADP
ejpam-556	113	13	f	f	PROPN
ejpam-556	113	14	(	(	PUNCT
ejpam-556	113	15	x	x	X
ejpam-556	113	16	)	)	PUNCT
ejpam-556	113	17	∈	∈	PROPN
ejpam-556	113	18	c2[x0	c2[x0	PROPN
ejpam-556	113	19	,	,	PUNCT
ejpam-556	113	20	xn	xn	PROPN
ejpam-556	113	21	]	]	X
ejpam-556	113	22	,	,	PUNCT
ejpam-556	113	23	in	in	ADP
ejpam-556	113	24	each	each	DET
ejpam-556	113	25	subinterval	subinterval	NOUN
ejpam-556	113	26	ii	ii	NOUN
ejpam-556	114	1	=	=	PUNCT
ejpam-556	115	1	[	[	X
ejpam-556	115	2	x	x	X
ejpam-556	115	3	i	i	NOUN
ejpam-556	115	4	,	,	PUNCT
ejpam-556	115	5	x	x	PUNCT
ejpam-556	115	6	i+1	i+1	VERB
ejpam-556	115	7	]	]	X
ejpam-556	115	8	is	be	AUX
ejpam-556	115	9	|	|	ADV
ejpam-556	115	10	f	f	X
ejpam-556	115	11	(	(	PUNCT
ejpam-556	115	12	x)−	x)−	PROPN
ejpam-556	115	13	si(x)|	si(x)|	VERB
ejpam-556	115	14	≤	≤	ADV
ejpam-556	115	15	1	1	NUM
ejpam-556	115	16	2	2	NUM
ejpam-556	115	17	‖	‖	PROPN
ejpam-556	115	18	f	f	PROPN
ejpam-556	115	19	(	(	PUNCT
ejpam-556	115	20	2)(τ)‖h2	2)(τ)‖h2	NUM
ejpam-556	115	21	i	i	PRON
ejpam-556	115	22	ci	ci	NOUN
ejpam-556	115	23	,	,	PUNCT
ejpam-556	115	24	(	(	PUNCT
ejpam-556	115	25	9	9	X
ejpam-556	115	26	)	)	PUNCT
ejpam-556	115	27	where	where	SCONJ
ejpam-556	115	28	ci	ci	PROPN
ejpam-556	115	29	is	be	AUX
ejpam-556	115	30	the	the	DET
ejpam-556	115	31	maximum	maximum	ADJ
ejpam-556	115	32	value	value	NOUN
ejpam-556	115	33	of	of	ADP
ejpam-556	115	34	ω(αi	ω(αi	PROPN
ejpam-556	115	35	,	,	PUNCT
ejpam-556	115	36	θ	θ	NOUN
ejpam-556	115	37	)	)	PUNCT
ejpam-556	115	38	for	for	ADP
ejpam-556	115	39	0≤	0≤	NUM
ejpam-556	115	40	θ	θ	NOUN
ejpam-556	115	41	≤	≤	NUM
ejpam-556	115	42	1	1	NUM
ejpam-556	115	43	and	and	CCONJ
ejpam-556	115	44	αi	αi	PRON
ejpam-556	115	45	≥	≥	NUM
ejpam-556	115	46	0	0	NUM
ejpam-556	115	47	.	.	PUNCT
ejpam-556	115	48	theorem	theorem	NOUN
ejpam-556	115	49	2	2	NUM
ejpam-556	115	50	.	.	X
ejpam-556	115	51	for	for	ADP
ejpam-556	115	52	any	any	DET
ejpam-556	115	53	given	give	VERB
ejpam-556	115	54	positive	positive	ADJ
ejpam-556	115	55	parameter	parameter	NOUN
ejpam-556	115	56	αi	αi	NOUN
ejpam-556	115	57	,	,	PUNCT
ejpam-556	115	58	the	the	DET
ejpam-556	115	59	error	error	NOUN
ejpam-556	115	60	optimal	optimal	ADJ
ejpam-556	115	61	constant	constant	ADJ
ejpam-556	115	62	ci	ci	NOUN
ejpam-556	115	63	in	in	ADP
ejpam-556	115	64	theorem	theorem	NOUN
ejpam-556	115	65	1	1	NUM
ejpam-556	115	66	are	be	AUX
ejpam-556	115	67	bounded	bound	VERB
ejpam-556	115	68	with	with	ADP
ejpam-556	115	69	0≤	0≤	NUM
ejpam-556	115	70	ci	ci	NOUN
ejpam-556	115	71	≤	≤	NOUN
ejpam-556	115	72	0.2685	0.2685	NUM
ejpam-556	115	73	.	.	PUNCT
ejpam-556	116	1	3	3	X
ejpam-556	116	2	.	.	X
ejpam-556	116	3	positivity	positivity	NOUN
ejpam-556	116	4	preserving	preserve	VERB
ejpam-556	116	5	interpolation	interpolation	NOUN
ejpam-556	116	6	this	this	DET
ejpam-556	116	7	section	section	NOUN
ejpam-556	116	8	provides	provide	VERB
ejpam-556	116	9	sufficient	sufficient	ADJ
ejpam-556	116	10	conditions	condition	NOUN
ejpam-556	116	11	on	on	ADP
ejpam-556	116	12	parameters	parameter	NOUN
ejpam-556	116	13	for	for	ADP
ejpam-556	116	14	positive	positive	ADJ
ejpam-556	116	15	interpolation	interpolation	NOUN
ejpam-556	116	16	of	of	ADP
ejpam-556	116	17	curve	curve	NOUN
ejpam-556	116	18	data	datum	NOUN
ejpam-556	116	19	.	.	PUNCT
ejpam-556	117	1	let	let	VERB
ejpam-556	117	2	{	{	PUNCT
ejpam-556	117	3	(	(	PUNCT
ejpam-556	117	4	x	x	PROPN
ejpam-556	117	5	i	i	PROPN
ejpam-556	117	6	,	,	PUNCT
ejpam-556	117	7	fi	fi	NOUN
ejpam-556	117	8	)	)	PUNCT
ejpam-556	117	9	,	,	PUNCT
ejpam-556	117	10	i	i	PRON
ejpam-556	117	11	=	=	NOUN
ejpam-556	117	12	0,1,2	0,1,2	NUM
ejpam-556	117	13	,	,	PUNCT
ejpam-556	117	14	.	.	PUNCT
ejpam-556	117	15	.	.	PUNCT
ejpam-556	118	1	.	.	PUNCT
ejpam-556	119	1	,	,	PUNCT
ejpam-556	119	2	n	n	CCONJ
ejpam-556	119	3	}	}	PUNCT
ejpam-556	119	4	be	be	AUX
ejpam-556	119	5	the	the	DET
ejpam-556	119	6	positive	positive	ADJ
ejpam-556	119	7	data	datum	NOUN
ejpam-556	119	8	defined	define	VERB
ejpam-556	119	9	over	over	ADP
ejpam-556	119	10	the	the	DET
ejpam-556	119	11	interval	interval	NOUN
ejpam-556	119	12	[	[	X
ejpam-556	119	13	a	a	X
ejpam-556	119	14	,	,	PUNCT
ejpam-556	119	15	b	b	NOUN
ejpam-556	119	16	]	]	X
ejpam-556	119	17	.	.	PUNCT
ejpam-556	120	1	the	the	DET
ejpam-556	120	2	necessary	necessary	ADJ
ejpam-556	120	3	condition	condition	NOUN
ejpam-556	120	4	for	for	ADP
ejpam-556	120	5	the	the	DET
ejpam-556	120	6	positivity	positivity	NOUN
ejpam-556	120	7	of	of	ADP
ejpam-556	120	8	data	datum	NOUN
ejpam-556	120	9	is	be	AUX
ejpam-556	120	10	fi	fi	NOUN
ejpam-556	120	11	>	>	X
ejpam-556	120	12	0	0	NUM
ejpam-556	120	13	,	,	PUNCT
ejpam-556	120	14	i	i	PRON
ejpam-556	120	15	=	=	NOUN
ejpam-556	120	16	0,1,2	0,1,2	NUM
ejpam-556	120	17	,	,	PUNCT
ejpam-556	120	18	.	.	PUNCT
ejpam-556	120	19	.	.	PUNCT
ejpam-556	121	1	.	.	PUNCT
ejpam-556	122	1	,	,	PUNCT
ejpam-556	122	2	n−	n−	NOUN
ejpam-556	122	3	1	1	NUM
ejpam-556	122	4	.	.	PUNCT
ejpam-556	123	1	(	(	PUNCT
ejpam-556	123	2	10	10	NUM
ejpam-556	123	3	)	)	PUNCT
ejpam-556	123	4	m.	m.	NOUN
ejpam-556	123	5	z.	z.	PROPN
ejpam-556	123	6	hussain	hussain	PROPN
ejpam-556	123	7	,	,	PUNCT
ejpam-556	123	8	m.	m.	NOUN
ejpam-556	123	9	sarfraz	sarfraz	PROPN
ejpam-556	123	10	,	,	PUNCT
ejpam-556	123	11	m.	m.	NOUN
ejpam-556	123	12	hussain	hussain	PROPN
ejpam-556	123	13	/	/	SYM
ejpam-556	123	14	eur	eur	PROPN
ejpam-556	123	15	.	.	PUNCT
ejpam-556	124	1	j.	j.	PROPN
ejpam-556	124	2	pure	pure	PROPN
ejpam-556	124	3	appl	appl	PROPN
ejpam-556	124	4	.	.	PROPN
ejpam-556	124	5	math	math	PROPN
ejpam-556	124	6	,	,	PUNCT
ejpam-556	124	7	3	3	NUM
ejpam-556	124	8	(	(	PUNCT
ejpam-556	124	9	2010	2010	NUM
ejpam-556	124	10	)	)	PUNCT
ejpam-556	124	11	,	,	PUNCT
ejpam-556	124	12	194	194	NUM
ejpam-556	124	13	-	-	SYM
ejpam-556	124	14	212	212	NUM
ejpam-556	124	15	198	198	NUM
ejpam-556	124	16	the	the	DET
ejpam-556	124	17	piecewise	piecewise	NOUN
ejpam-556	124	18	rational	rational	ADJ
ejpam-556	124	19	cubic	cubic	ADJ
ejpam-556	124	20	function	function	NOUN
ejpam-556	124	21	(	(	PUNCT
ejpam-556	124	22	1	1	X
ejpam-556	124	23	)	)	PUNCT
ejpam-556	124	24	preserves	preserve	VERB
ejpam-556	124	25	positivity	positivity	NOUN
ejpam-556	124	26	if	if	SCONJ
ejpam-556	124	27	si(x	si(x	NUM
ejpam-556	124	28	)	)	PUNCT
ejpam-556	124	29	>	>	X
ejpam-556	124	30	0	0	NUM
ejpam-556	124	31	,	,	PUNCT
ejpam-556	124	32	i	i	PRON
ejpam-556	124	33	=	=	NOUN
ejpam-556	124	34	0,1,2	0,1,2	NUM
ejpam-556	124	35	,	,	PUNCT
ejpam-556	124	36	.	.	PUNCT
ejpam-556	124	37	.	.	PUNCT
ejpam-556	125	1	.	.	PUNCT
ejpam-556	126	1	,	,	PUNCT
ejpam-556	126	2	n−	n−	NOUN
ejpam-556	126	3	1	1	NUM
ejpam-556	126	4	.	.	PUNCT
ejpam-556	127	1	now	now	ADV
ejpam-556	127	2	,	,	PUNCT
ejpam-556	127	3	si(x	si(x	NUM
ejpam-556	127	4	)	)	PUNCT
ejpam-556	127	5	>	>	X
ejpam-556	127	6	0	0	PUNCT
ejpam-556	128	1	if	if	SCONJ
ejpam-556	128	2	pi(θ	pi(θ	NOUN
ejpam-556	128	3	)	)	PUNCT
ejpam-556	128	4	>	>	X
ejpam-556	128	5	0	0	PUNCT
ejpam-556	128	6	and	and	CCONJ
ejpam-556	128	7	qi(θ	qi(θ	NOUN
ejpam-556	128	8	)	)	PUNCT
ejpam-556	128	9	.	.	PUNCT
ejpam-556	129	1	but	but	CCONJ
ejpam-556	129	2	,	,	PUNCT
ejpam-556	129	3	qi(θ	qi(θ	PUNCT
ejpam-556	129	4	)	)	PUNCT
ejpam-556	129	5	if	if	SCONJ
ejpam-556	129	6	αi	αi	ADV
ejpam-556	129	7	>	>	X
ejpam-556	129	8	0	0	X
ejpam-556	129	9	.	.	PUNCT
ejpam-556	130	1	using	use	VERB
ejpam-556	130	2	the	the	DET
ejpam-556	130	3	result	result	NOUN
ejpam-556	130	4	developed	develop	VERB
ejpam-556	130	5	by	by	ADP
ejpam-556	130	6	schmidt	schmidt	NOUN
ejpam-556	130	7	and	and	CCONJ
ejpam-556	130	8	hess	hess	NOUN
ejpam-556	130	9	in	in	ADP
ejpam-556	130	10	[	[	X
ejpam-556	130	11	15	15	NUM
ejpam-556	130	12	]	]	PUNCT
ejpam-556	130	13	,	,	PUNCT
ejpam-556	130	14	the	the	DET
ejpam-556	130	15	cubic	cubic	ADJ
ejpam-556	130	16	polynomial	polynomial	ADJ
ejpam-556	130	17	pi(θ	pi(θ	NOUN
ejpam-556	130	18	)	)	PUNCT
ejpam-556	130	19	>	>	X
ejpam-556	130	20	0	0	PUNCT
ejpam-556	131	1	if	if	SCONJ
ejpam-556	131	2	(	(	PUNCT
ejpam-556	131	3	p′i(0	p′i(0	NUM
ejpam-556	131	4	)	)	PUNCT
ejpam-556	131	5	,	,	PUNCT
ejpam-556	131	6	p′i(1	p′i(1	NUM
ejpam-556	131	7	)	)	PUNCT
ejpam-556	131	8	)	)	PUNCT
ejpam-556	131	9	∈	∈	PROPN
ejpam-556	131	10	r1ur2	r1ur2	NOUN
ejpam-556	131	11	,	,	PUNCT
ejpam-556	131	12	where	where	SCONJ
ejpam-556	131	13	r1	r1	PROPN
ejpam-556	131	14	=	=	SYM
ejpam-556	131	15	�	�	PROPN
ejpam-556	131	16	(	(	PUNCT
ejpam-556	131	17	a	a	DET
ejpam-556	131	18	,	,	PUNCT
ejpam-556	131	19	b	b	NOUN
ejpam-556	131	20	)	)	PUNCT
ejpam-556	131	21	:	:	PUNCT
ejpam-556	131	22	a	a	PRON
ejpam-556	131	23	>	>	X
ejpam-556	131	24	−3	−3	PROPN
ejpam-556	131	25	fi	fi	NOUN
ejpam-556	131	26	hi	hi	INTJ
ejpam-556	131	27	,	,	PUNCT
ejpam-556	131	28	b	b	X
ejpam-556	131	29	<	<	X
ejpam-556	131	30	3	3	NUM
ejpam-556	131	31	fi+1	fi+1	NOUN
ejpam-556	131	32	hi	hi	INTJ
ejpam-556	131	33	�	�	PROPN
ejpam-556	131	34	,	,	PUNCT
ejpam-556	131	35	r2	r2	PROPN
ejpam-556	131	36	=	=	SYM
ejpam-556	131	37	{	{	PUNCT
ejpam-556	131	38	(	(	PUNCT
ejpam-556	131	39	a	a	DET
ejpam-556	131	40	,	,	PUNCT
ejpam-556	131	41	b	b	NOUN
ejpam-556	131	42	)	)	PUNCT
ejpam-556	131	43	:	:	PUNCT
ejpam-556	131	44	36	36	NUM
ejpam-556	131	45	fi	fi	NOUN
ejpam-556	131	46	fi+1(a	fi+1(a	NOUN
ejpam-556	131	47	2	2	NUM
ejpam-556	131	48	+	+	NOUN
ejpam-556	131	49	b2	b2	NOUN
ejpam-556	131	50	+	+	CCONJ
ejpam-556	131	51	ab−	ab−	NUM
ejpam-556	131	52	3∆i(a+	3∆i(a+	NUM
ejpam-556	131	53	b	b	X
ejpam-556	131	54	)	)	PUNCT
ejpam-556	131	55	+	+	NUM
ejpam-556	132	1	3∆2	3∆2	NUM
ejpam-556	132	2	i	i	NOUN
ejpam-556	132	3	)	)	PUNCT
ejpam-556	133	1	+	+	CCONJ
ejpam-556	133	2	4hi(a	4hi(a	NUM
ejpam-556	133	3	3	3	NUM
ejpam-556	133	4	fi+1	fi+1	NOUN
ejpam-556	133	5	−	−	PROPN
ejpam-556	133	6	b3	b3	PROPN
ejpam-556	133	7	fi	fi	NOUN
ejpam-556	133	8	)	)	PUNCT
ejpam-556	133	9	+3(a	+3(a	PROPN
ejpam-556	133	10	fi+1	fi+1	NOUN
ejpam-556	133	11	−	−	PROPN
ejpam-556	133	12	b	b	SYM
ejpam-556	133	13	fi)(2hiab−	fi)(2hiab−	PROPN
ejpam-556	133	14	3a	3a	NUM
ejpam-556	133	15	fi+1	fi+1	NOUN
ejpam-556	134	1	+	+	CCONJ
ejpam-556	134	2	3b	3b	PROPN
ejpam-556	134	3	fi)−	fi)−	NOUN
ejpam-556	134	4	h2	h2	NOUN
ejpam-556	134	5	i	i	PROPN
ejpam-556	134	6	a2	a2	PROPN
ejpam-556	134	7	b2	b2	PROPN
ejpam-556	134	8	≥	≥	NOUN
ejpam-556	134	9	0	0	NUM
ejpam-556	134	10	}	}	PUNCT
ejpam-556	134	11	.	.	PUNCT
ejpam-556	135	1	for	for	ADP
ejpam-556	135	2	the	the	DET
ejpam-556	135	3	rational	rational	ADJ
ejpam-556	135	4	cubic	cubic	ADJ
ejpam-556	135	5	function	function	NOUN
ejpam-556	135	6	(	(	PUNCT
ejpam-556	135	7	1	1	NUM
ejpam-556	135	8	)	)	PUNCT
ejpam-556	135	9	,	,	PUNCT
ejpam-556	135	10	we	we	PRON
ejpam-556	135	11	have	have	VERB
ejpam-556	135	12	p′i(0	p′i(0	NUM
ejpam-556	135	13	)	)	PUNCT
ejpam-556	136	1	=	=	SYM
ejpam-556	136	2	−αi	−αi	NOUN
ejpam-556	136	3	fi	fi	NOUN
ejpam-556	136	4	+	+	CCONJ
ejpam-556	136	5	hidi	hidi	NOUN
ejpam-556	136	6	hi	hi	INTJ
ejpam-556	136	7	and	and	CCONJ
ejpam-556	136	8	p′i(1	p′i(1	NUM
ejpam-556	136	9	)	)	PUNCT
ejpam-556	137	1	=	=	PUNCT
ejpam-556	137	2	−αi	−αi	NOUN
ejpam-556	137	3	fi+1	fi+1	NOUN
ejpam-556	138	1	+	+	CCONJ
ejpam-556	138	2	hidi+1	hidi+1	NOUN
ejpam-556	138	3	hi	hi	INTJ
ejpam-556	138	4	.	.	PUNCT
ejpam-556	139	1	(	(	PUNCT
ejpam-556	139	2	p′	p′	X
ejpam-556	139	3	i	i	PRON
ejpam-556	139	4	(	(	PUNCT
ejpam-556	139	5	0	0	NUM
ejpam-556	139	6	)	)	PUNCT
ejpam-556	139	7	,	,	PUNCT
ejpam-556	139	8	p′	p′	NUM
ejpam-556	140	1	i	i	PRON
ejpam-556	140	2	(	(	PUNCT
ejpam-556	140	3	1	1	NUM
ejpam-556	140	4	)	)	PUNCT
ejpam-556	140	5	)	)	PUNCT
ejpam-556	141	1	∈	∈	PROPN
ejpam-556	141	2	r1	r1	NOUN
ejpam-556	141	3	if	if	SCONJ
ejpam-556	141	4	−αi	−αi	VERB
ejpam-556	141	5	fi	fi	NOUN
ejpam-556	141	6	+	+	CCONJ
ejpam-556	141	7	hidi	hidi	PROPN
ejpam-556	141	8	hi	hi	INTJ
ejpam-556	141	9	>	>	X
ejpam-556	141	10	−3	−3	PROPN
ejpam-556	141	11	fi	fi	NOUN
ejpam-556	141	12	hi	hi	INTJ
ejpam-556	141	13	,	,	PUNCT
ejpam-556	141	14	(	(	PUNCT
ejpam-556	141	15	11	11	NUM
ejpam-556	141	16	)	)	PUNCT
ejpam-556	141	17	and	and	CCONJ
ejpam-556	141	18	−αi	−αi	VERB
ejpam-556	141	19	fi+1	fi+1	NOUN
ejpam-556	141	20	+	+	CCONJ
ejpam-556	141	21	hidi+1	hidi+1	NOUN
ejpam-556	142	1	hi	hi	INTJ
ejpam-556	142	2	<	<	X
ejpam-556	142	3	3	3	NUM
ejpam-556	142	4	fi+1	fi+1	NOUN
ejpam-556	142	5	hi	hi	INTJ
ejpam-556	142	6	.	.	PUNCT
ejpam-556	143	1	(	(	PUNCT
ejpam-556	143	2	12	12	NUM
ejpam-556	143	3	)	)	PUNCT
ejpam-556	143	4	the	the	DET
ejpam-556	143	5	inequality	inequality	NOUN
ejpam-556	143	6	(	(	PUNCT
ejpam-556	143	7	11	11	NUM
ejpam-556	143	8	)	)	PUNCT
ejpam-556	143	9	leads	lead	VERB
ejpam-556	143	10	to	to	ADP
ejpam-556	143	11	the	the	DET
ejpam-556	143	12	following	follow	VERB
ejpam-556	143	13	relation	relation	NOUN
ejpam-556	143	14	:	:	PUNCT
ejpam-556	143	15	αi	αi	VERB
ejpam-556	143	16	<	<	X
ejpam-556	143	17	hidi	hidi	PROPN
ejpam-556	143	18	fi	fi	NOUN
ejpam-556	143	19	+	+	CCONJ
ejpam-556	143	20	3	3	X
ejpam-556	143	21	.	.	PUNCT
ejpam-556	144	1	(	(	PUNCT
ejpam-556	144	2	13	13	NUM
ejpam-556	144	3	)	)	PUNCT
ejpam-556	144	4	the	the	DET
ejpam-556	144	5	inequality	inequality	NOUN
ejpam-556	144	6	(	(	PUNCT
ejpam-556	144	7	12	12	NUM
ejpam-556	144	8	)	)	PUNCT
ejpam-556	144	9	imposes	impose	VERB
ejpam-556	144	10	the	the	DET
ejpam-556	144	11	following	follow	VERB
ejpam-556	144	12	restriction	restriction	NOUN
ejpam-556	144	13	on	on	ADP
ejpam-556	144	14	the	the	DET
ejpam-556	144	15	free	free	ADJ
ejpam-556	144	16	parameter	parameter	NOUN
ejpam-556	144	17	αi	αi	NOUN
ejpam-556	144	18	:	:	PUNCT
ejpam-556	144	19	αi	αi	X
ejpam-556	144	20	>	>	X
ejpam-556	144	21	hidi+1	hidi+1	PROPN
ejpam-556	145	1	fi+1	fi+1	NOUN
ejpam-556	145	2	−	−	PROPN
ejpam-556	145	3	3	3	X
ejpam-556	145	4	.	.	PUNCT
ejpam-556	146	1	(	(	PUNCT
ejpam-556	146	2	14	14	NUM
ejpam-556	146	3	)	)	PUNCT
ejpam-556	146	4	further	far	ADV
ejpam-556	146	5	(	(	PUNCT
ejpam-556	146	6	p′i(0	p′i(0	NUM
ejpam-556	146	7	)	)	PUNCT
ejpam-556	146	8	,	,	PUNCT
ejpam-556	146	9	p′i(1	p′i(1	NUM
ejpam-556	146	10	)	)	PUNCT
ejpam-556	146	11	)	)	PUNCT
ejpam-556	147	1	∈	∈	PROPN
ejpam-556	147	2	r2	r2	NOUN
ejpam-556	147	3	if	if	SCONJ
ejpam-556	147	4	φ(αi	φ(αi	ADV
ejpam-556	147	5	)	)	PUNCT
ejpam-556	147	6	=	=	SYM
ejpam-556	147	7	36	36	NUM
ejpam-556	147	8	fi	fi	NOUN
ejpam-556	147	9	fi+1[φ	fi+1[φ	PUNCT
ejpam-556	147	10	2	2	NUM
ejpam-556	147	11	1(αi	1(αi	NUM
ejpam-556	147	12	)	)	PUNCT
ejpam-556	148	1	+	+	NOUN
ejpam-556	148	2	φ	φ	PROPN
ejpam-556	148	3	2	2	NUM
ejpam-556	148	4	2(αi	2(αi	NOUN
ejpam-556	148	5	)	)	PUNCT
ejpam-556	149	1	+	+	ADP
ejpam-556	149	2	φ1(αi)φ2(αi)−	φ1(αi)φ2(αi)−	NUM
ejpam-556	149	3	3∆i(φ1(αi	3∆i(φ1(αi	NUM
ejpam-556	149	4	)	)	PUNCT
ejpam-556	150	1	+	+	NOUN
ejpam-556	150	2	φ2(αi))+	φ2(αi))+	PROPN
ejpam-556	150	3	3∆2	3∆2	NUM
ejpam-556	150	4	i	i	NOUN
ejpam-556	150	5	]	]	PUNCT
ejpam-556	151	1	+3	+3	PROPN
ejpam-556	151	2	[	[	PUNCT
ejpam-556	151	3	fi+1φ1(αi)−	fi+1φ1(αi)−	PROPN
ejpam-556	151	4	fiφ2(αi)][2hiφ1(αi)φ2(αi)−	fiφ2(αi)][2hiφ1(αi)φ2(αi)−	VERB
ejpam-556	151	5	3	3	NUM
ejpam-556	151	6	fi+1φ1(αi	fi+1φ1(αi	NOUN
ejpam-556	151	7	)	)	PUNCT
ejpam-556	151	8	+	+	CCONJ
ejpam-556	151	9	3	3	NUM
ejpam-556	151	10	fiφ2(αi	fiφ2(αi	ADP
ejpam-556	151	11	)	)	PUNCT
ejpam-556	151	12	]	]	PUNCT
ejpam-556	152	1	+4hi	+4hi	PUNCT
ejpam-556	152	2	[	[	PUNCT
ejpam-556	152	3	fi+1φ	fi+1φ	NOUN
ejpam-556	152	4	3	3	NUM
ejpam-556	152	5	1(αi)−	1(αi)−	NUM
ejpam-556	152	6	fiφ	fiφ	NOUN
ejpam-556	152	7	3	3	NUM
ejpam-556	152	8	2(αi)]−	2(αi)]−	NUM
ejpam-556	152	9	h2	h2	NOUN
ejpam-556	152	10	iφ	iφ	ADP
ejpam-556	152	11	2	2	NUM
ejpam-556	152	12	1(αi)φ	1(αi)φ	NUM
ejpam-556	152	13	2	2	NUM
ejpam-556	152	14	2(αi	2(αi	NOUN
ejpam-556	152	15	)	)	PUNCT
ejpam-556	152	16	>	>	X
ejpam-556	152	17	0	0	NUM
ejpam-556	152	18	,	,	PUNCT
ejpam-556	152	19	(	(	PUNCT
ejpam-556	152	20	15	15	NUM
ejpam-556	152	21	)	)	PUNCT
ejpam-556	152	22	with	with	ADP
ejpam-556	152	23	φ1(αi	φ1(αi	NUM
ejpam-556	152	24	)	)	PUNCT
ejpam-556	152	25	=	=	PUNCT
ejpam-556	152	26	p′i(0	p′i(0	X
ejpam-556	152	27	)	)	PUNCT
ejpam-556	152	28	and	and	CCONJ
ejpam-556	152	29	φ2(αi	φ2(αi	NOUN
ejpam-556	152	30	)	)	PUNCT
ejpam-556	152	31	=	=	NOUN
ejpam-556	152	32	p′i	p′i	NOUN
ejpam-556	152	33	(	(	PUNCT
ejpam-556	152	34	1	1	NUM
ejpam-556	152	35	)	)	PUNCT
ejpam-556	152	36	.	.	PUNCT
ejpam-556	153	1	the	the	DET
ejpam-556	153	2	c1	c1	PROPN
ejpam-556	153	3	rational	rational	ADJ
ejpam-556	153	4	cubic	cubic	ADJ
ejpam-556	153	5	function	function	NOUN
ejpam-556	153	6	is	be	AUX
ejpam-556	153	7	positive	positive	ADJ
ejpam-556	153	8	if	if	SCONJ
ejpam-556	153	9	either	either	CCONJ
ejpam-556	153	10	(	(	PUNCT
ejpam-556	153	11	13)-(14	13)-(14	NUM
ejpam-556	153	12	)	)	PUNCT
ejpam-556	153	13	or	or	CCONJ
ejpam-556	153	14	(	(	PUNCT
ejpam-556	153	15	15	15	NUM
ejpam-556	153	16	)	)	PUNCT
ejpam-556	153	17	are	be	AUX
ejpam-556	153	18	satisfied	satisfied	ADJ
ejpam-556	153	19	,	,	PUNCT
ejpam-556	153	20	but	but	CCONJ
ejpam-556	153	21	(	(	PUNCT
ejpam-556	153	22	13)-(14	13)-(14	NOUN
ejpam-556	153	23	)	)	PUNCT
ejpam-556	153	24	involves	involve	VERB
ejpam-556	153	25	less	less	ADJ
ejpam-556	153	26	computation	computation	NOUN
ejpam-556	153	27	hence	hence	ADV
ejpam-556	153	28	more	more	ADV
ejpam-556	153	29	suitable	suitable	ADJ
ejpam-556	153	30	for	for	ADP
ejpam-556	153	31	practical	practical	ADJ
ejpam-556	153	32	applications	application	NOUN
ejpam-556	153	33	.	.	PUNCT
ejpam-556	154	1	this	this	DET
ejpam-556	154	2	discussion	discussion	NOUN
ejpam-556	154	3	can	can	AUX
ejpam-556	154	4	be	be	AUX
ejpam-556	154	5	summarized	summarize	VERB
ejpam-556	154	6	as	as	ADP
ejpam-556	154	7	:	:	PUNCT
ejpam-556	154	8	m.	m.	NOUN
ejpam-556	154	9	z.	z.	PROPN
ejpam-556	154	10	hussain	hussain	PROPN
ejpam-556	154	11	,	,	PUNCT
ejpam-556	154	12	m.	m.	NOUN
ejpam-556	154	13	sarfraz	sarfraz	PROPN
ejpam-556	154	14	,	,	PUNCT
ejpam-556	154	15	m.	m.	NOUN
ejpam-556	154	16	hussain	hussain	PROPN
ejpam-556	154	17	/	/	SYM
ejpam-556	154	18	eur	eur	PROPN
ejpam-556	154	19	.	.	PUNCT
ejpam-556	155	1	j.	j.	PROPN
ejpam-556	155	2	pure	pure	PROPN
ejpam-556	155	3	appl	appl	PROPN
ejpam-556	155	4	.	.	PROPN
ejpam-556	155	5	math	math	PROPN
ejpam-556	155	6	,	,	PUNCT
ejpam-556	155	7	3	3	NUM
ejpam-556	155	8	(	(	PUNCT
ejpam-556	155	9	2010	2010	NUM
ejpam-556	155	10	)	)	PUNCT
ejpam-556	155	11	,	,	PUNCT
ejpam-556	155	12	194	194	NUM
ejpam-556	155	13	-	-	SYM
ejpam-556	155	14	212	212	NUM
ejpam-556	155	15	199	199	NUM
ejpam-556	155	16	theorem	theorem	NOUN
ejpam-556	155	17	3	3	NUM
ejpam-556	155	18	.	.	PUNCT
ejpam-556	156	1	the	the	DET
ejpam-556	156	2	piecewise	piecewise	PROPN
ejpam-556	156	3	c1	c1	PROPN
ejpam-556	156	4	rational	rational	ADJ
ejpam-556	156	5	cubic	cubic	ADJ
ejpam-556	156	6	interpolant	interpolant	NOUN
ejpam-556	156	7	s(x	s(x	PROPN
ejpam-556	156	8	)	)	PUNCT
ejpam-556	156	9	,	,	PUNCT
ejpam-556	156	10	defined	define	VERB
ejpam-556	156	11	over	over	ADP
ejpam-556	156	12	the	the	DET
ejpam-556	156	13	interval	interval	NOUN
ejpam-556	156	14	[	[	X
ejpam-556	156	15	a	a	X
ejpam-556	156	16	,	,	PUNCT
ejpam-556	156	17	b	b	NOUN
ejpam-556	156	18	]	]	X
ejpam-556	156	19	,	,	PUNCT
ejpam-556	156	20	in	in	ADP
ejpam-556	156	21	(	(	PUNCT
ejpam-556	156	22	1	1	NUM
ejpam-556	156	23	)	)	PUNCT
ejpam-556	156	24	,	,	PUNCT
ejpam-556	156	25	is	be	AUX
ejpam-556	156	26	positive	positive	ADJ
ejpam-556	156	27	if	if	SCONJ
ejpam-556	156	28	in	in	ADP
ejpam-556	156	29	each	each	DET
ejpam-556	156	30	subinterval	subinterval	NOUN
ejpam-556	156	31	ii	ii	NOUN
ejpam-556	157	1	=	=	PUNCT
ejpam-556	158	1	[	[	X
ejpam-556	158	2	x	x	X
ejpam-556	158	3	i	i	NOUN
ejpam-556	158	4	,	,	PUNCT
ejpam-556	158	5	x	x	PROPN
ejpam-556	158	6	i+1	i+1	VERB
ejpam-556	158	7	]	]	X
ejpam-556	158	8	the	the	DET
ejpam-556	158	9	following	follow	VERB
ejpam-556	158	10	sufficient	sufficient	ADJ
ejpam-556	158	11	conditions	condition	NOUN
ejpam-556	158	12	are	be	AUX
ejpam-556	158	13	satisfied	satisfied	ADJ
ejpam-556	158	14	:	:	PUNCT
ejpam-556	158	15	con1	con1	NOUN
ejpam-556	158	16	<	<	X
ejpam-556	158	17	αi	αi	X
ejpam-556	158	18	<	<	X
ejpam-556	158	19	con2	con2	PROPN
ejpam-556	158	20	,	,	PUNCT
ejpam-556	158	21	where	where	SCONJ
ejpam-556	158	22	con1	con1	NOUN
ejpam-556	158	23	=	=	SYM
ejpam-556	158	24	max	max	PROPN
ejpam-556	158	25	�	�	PROPN
ejpam-556	158	26	0	0	NUM
ejpam-556	158	27	,	,	PUNCT
ejpam-556	158	28	hidi+1	hidi+1	NOUN
ejpam-556	158	29	fi+1	fi+1	NOUN
ejpam-556	158	30	−	−	PROPN
ejpam-556	158	31	3	3	NUM
ejpam-556	158	32	�	�	PROPN
ejpam-556	158	33	and	and	CCONJ
ejpam-556	158	34	con2	con2	NOUN
ejpam-556	158	35	=	=	SYM
ejpam-556	158	36	hidi	hidi	PROPN
ejpam-556	158	37	fi	fi	NOUN
ejpam-556	159	1	+	+	CCONJ
ejpam-556	159	2	3	3	X
ejpam-556	159	3	.	.	PUNCT
ejpam-556	159	4	the	the	DET
ejpam-556	159	5	above	above	ADJ
ejpam-556	159	6	constraints	constraint	NOUN
ejpam-556	159	7	can	can	AUX
ejpam-556	159	8	be	be	AUX
ejpam-556	159	9	rearranged	rearrange	VERB
ejpam-556	159	10	as	as	ADP
ejpam-556	159	11	:	:	PUNCT
ejpam-556	159	12	con1	con1	NOUN
ejpam-556	160	1	+	+	CCONJ
ejpam-556	160	2	ki	ki	PROPN
ejpam-556	160	3	=	=	PUNCT
ejpam-556	160	4	αi	αi	NOUN
ejpam-556	160	5	=	=	SYM
ejpam-556	160	6	con2	con2	PROPN
ejpam-556	160	7	−	−	PROPN
ejpam-556	160	8	li	li	PROPN
ejpam-556	160	9	,	,	PUNCT
ejpam-556	160	10	where	where	SCONJ
ejpam-556	160	11	ki	ki	PROPN
ejpam-556	160	12	>	>	X
ejpam-556	160	13	0	0	PROPN
ejpam-556	160	14	and	and	CCONJ
ejpam-556	160	15	li	li	PROPN
ejpam-556	160	16	>	>	X
ejpam-556	160	17	0	0	PROPN
ejpam-556	160	18	.	.	PUNCT
ejpam-556	161	1	thus	thus	ADV
ejpam-556	161	2	we	we	PRON
ejpam-556	161	3	have	have	VERB
ejpam-556	161	4	the	the	DET
ejpam-556	161	5	following	follow	VERB
ejpam-556	161	6	algorithm	algorithm	NOUN
ejpam-556	161	7	for	for	ADP
ejpam-556	161	8	the	the	DET
ejpam-556	161	9	manipulation	manipulation	NOUN
ejpam-556	161	10	of	of	ADP
ejpam-556	161	11	positive	positive	ADJ
ejpam-556	161	12	curve	curve	NOUN
ejpam-556	161	13	design	design	NOUN
ejpam-556	161	14	.	.	PUNCT
ejpam-556	162	1	algorithm	algorithm	NOUN
ejpam-556	162	2	1	1	NUM
ejpam-556	162	3	step	step	NOUN
ejpam-556	162	4	1	1	NUM
ejpam-556	162	5	.	.	PUNCT
ejpam-556	162	6	enter	enter	VERB
ejpam-556	162	7	the	the	DET
ejpam-556	162	8	(	(	PUNCT
ejpam-556	162	9	n+	n+	NOUN
ejpam-556	162	10	1	1	NUM
ejpam-556	162	11	)	)	PUNCT
ejpam-556	162	12	positive	positive	ADJ
ejpam-556	162	13	data	data	NOUN
ejpam-556	162	14	points	point	NOUN
ejpam-556	162	15	{	{	PUNCT
ejpam-556	162	16	(	(	PUNCT
ejpam-556	162	17	x	x	SYM
ejpam-556	162	18	i	i	PROPN
ejpam-556	162	19	,	,	PUNCT
ejpam-556	162	20	fi	fi	NOUN
ejpam-556	162	21	)	)	PUNCT
ejpam-556	162	22	:	:	PUNCT
ejpam-556	163	1	i	i	PRON
ejpam-556	163	2	=	=	NOUN
ejpam-556	163	3	0,1,2	0,1,2	NUM
ejpam-556	163	4	,	,	PUNCT
ejpam-556	163	5	.	.	PUNCT
ejpam-556	163	6	.	.	PUNCT
ejpam-556	163	7	.	.	PUNCT
ejpam-556	163	8	,	,	PUNCT
ejpam-556	163	9	n	n	CCONJ
ejpam-556	163	10	}	}	PUNCT
ejpam-556	163	11	.	.	PUNCT
ejpam-556	164	1	step	step	NOUN
ejpam-556	164	2	2	2	NUM
ejpam-556	164	3	.	.	NUM
ejpam-556	164	4	estimate	estimate	VERB
ejpam-556	164	5	the	the	DET
ejpam-556	164	6	first	first	ADJ
ejpam-556	164	7	order	order	NOUN
ejpam-556	164	8	derivatives	derivative	NOUN
ejpam-556	164	9	di	di	VERB
ejpam-556	164	10	,	,	PUNCT
ejpam-556	164	11	i	i	PRON
ejpam-556	164	12	=	=	NOUN
ejpam-556	164	13	0,1,2	0,1,2	NUM
ejpam-556	164	14	,	,	PUNCT
ejpam-556	164	15	.	.	PUNCT
ejpam-556	164	16	.	.	PUNCT
ejpam-556	165	1	.	.	PUNCT
ejpam-556	166	1	,	,	PUNCT
ejpam-556	166	2	n	n	CCONJ
ejpam-556	166	3	at	at	ADP
ejpam-556	166	4	knots	knot	NOUN
ejpam-556	166	5	.	.	PUNCT
ejpam-556	167	1	(	(	PUNCT
ejpam-556	167	2	note	note	VERB
ejpam-556	167	3	:	:	PUNCT
ejpam-556	167	4	the	the	DET
ejpam-556	167	5	step	step	NOUN
ejpam-556	167	6	2	2	NUM
ejpam-556	167	7	is	be	AUX
ejpam-556	167	8	only	only	ADV
ejpam-556	167	9	applicable	applicable	ADJ
ejpam-556	167	10	if	if	SCONJ
ejpam-556	167	11	data	datum	NOUN
ejpam-556	167	12	is	be	AUX
ejpam-556	167	13	not	not	PART
ejpam-556	167	14	provided	provide	VERB
ejpam-556	167	15	with	with	ADP
ejpam-556	167	16	derivatives	derivative	NOUN
ejpam-556	167	17	)	)	PUNCT
ejpam-556	167	18	.	.	PUNCT
ejpam-556	168	1	step	step	NOUN
ejpam-556	168	2	3	3	NUM
ejpam-556	168	3	.	.	PUNCT
ejpam-556	168	4	calculate	calculate	VERB
ejpam-556	168	5	the	the	DET
ejpam-556	168	6	value	value	NOUN
ejpam-556	168	7	of	of	ADP
ejpam-556	168	8	free	free	ADJ
ejpam-556	168	9	parameter	parameter	NOUN
ejpam-556	168	10	αi	αi	NOUN
ejpam-556	168	11	using	use	VERB
ejpam-556	168	12	theorem	theorem	NOUN
ejpam-556	168	13	3	3	NUM
ejpam-556	168	14	.	.	NOUN
ejpam-556	168	15	step	step	NOUN
ejpam-556	168	16	4	4	NUM
ejpam-556	168	17	.	.	PUNCT
ejpam-556	168	18	substitute	substitute	VERB
ejpam-556	168	19	the	the	DET
ejpam-556	168	20	values	value	NOUN
ejpam-556	168	21	of	of	ADP
ejpam-556	168	22	fi	fi	NOUN
ejpam-556	168	23	,	,	PUNCT
ejpam-556	168	24	di	di	NOUN
ejpam-556	168	25	,	,	PUNCT
ejpam-556	168	26	i	i	NOUN
ejpam-556	168	27	=	=	NOUN
ejpam-556	168	28	0,1,2	0,1,2	NUM
ejpam-556	168	29	,	,	PUNCT
ejpam-556	168	30	.	.	PUNCT
ejpam-556	168	31	.	.	PUNCT
ejpam-556	169	1	.	.	PUNCT
ejpam-556	170	1	,	,	PUNCT
ejpam-556	170	2	n	n	PROPN
ejpam-556	170	3	and	and	CCONJ
ejpam-556	170	4	αi	αi	VERB
ejpam-556	170	5	,	,	PUNCT
ejpam-556	170	6	i	i	PRON
ejpam-556	171	1	=	=	NOUN
ejpam-556	171	2	0,1,2	0,1,2	NUM
ejpam-556	171	3	,	,	PUNCT
ejpam-556	171	4	.	.	PUNCT
ejpam-556	171	5	.	.	PUNCT
ejpam-556	172	1	.	.	PUNCT
ejpam-556	173	1	,	,	PUNCT
ejpam-556	173	2	n−	n−	NOUN
ejpam-556	173	3	1	1	NUM
ejpam-556	173	4	in	in	ADP
ejpam-556	173	5	rational	rational	ADJ
ejpam-556	173	6	cubic	cubic	ADJ
ejpam-556	173	7	function	function	NOUN
ejpam-556	173	8	(	(	PUNCT
ejpam-556	173	9	1	1	NUM
ejpam-556	173	10	)	)	PUNCT
ejpam-556	173	11	to	to	PART
ejpam-556	173	12	obtain	obtain	VERB
ejpam-556	173	13	positive	positive	ADJ
ejpam-556	173	14	curve	curve	NOUN
ejpam-556	173	15	through	through	ADP
ejpam-556	173	16	positive	positive	ADJ
ejpam-556	173	17	data	datum	NOUN
ejpam-556	173	18	.	.	PUNCT
ejpam-556	174	1	3.1	3.1	NUM
ejpam-556	174	2	.	.	PUNCT
ejpam-556	174	3	demonstration	demonstration	NOUN
ejpam-556	174	4	example	example	NOUN
ejpam-556	174	5	1	1	X
ejpam-556	174	6	.	.	PUNCT
ejpam-556	175	1	a	a	DET
ejpam-556	175	2	positive	positive	ADJ
ejpam-556	175	3	data	datum	NOUN
ejpam-556	175	4	set	set	VERB
ejpam-556	175	5	in	in	ADP
ejpam-556	175	6	table	table	NOUN
ejpam-556	175	7	1	1	NUM
ejpam-556	175	8	is	be	AUX
ejpam-556	175	9	taken	take	VERB
ejpam-556	175	10	from	from	ADP
ejpam-556	175	11	[	[	X
ejpam-556	175	12	6	6	NUM
ejpam-556	175	13	]	]	PUNCT
ejpam-556	175	14	.	.	PUNCT
ejpam-556	176	1	the	the	DET
ejpam-556	176	2	figure	figure	NOUN
ejpam-556	176	3	1	1	NUM
ejpam-556	176	4	is	be	AUX
ejpam-556	176	5	produced	produce	VERB
ejpam-556	176	6	fromtable	fromtable	ADJ
ejpam-556	176	7	1	1	NUM
ejpam-556	176	8	:	:	PUNCT
ejpam-556	176	9	a	a	DET
ejpam-556	176	10	positive	positive	ADJ
ejpam-556	176	11	data	datum	NOUN
ejpam-556	176	12	taken	take	VERB
ejpam-556	176	13	from	from	ADP
ejpam-556	176	14	[	[	X
ejpam-556	176	15	6	6	NUM
ejpam-556	176	16	℄	℄	NOUN
ejpam-556	176	17	.	.	PUNCT
ejpam-556	177	1	x	x	SYM
ejpam-556	177	2	0.5	0.5	NUM
ejpam-556	177	3	0.6	0.6	NUM
ejpam-556	177	4	0.7	0.7	NUM
ejpam-556	177	5	0.8	0.8	NUM
ejpam-556	177	6	0.9	0.9	NUM
ejpam-556	177	7	1.0	1.0	NUM
ejpam-556	177	8	1.1	1.1	NUM
ejpam-556	177	9	f	f	NOUN
ejpam-556	177	10	0.4804	0.4804	NUM
ejpam-556	177	11	0.5669	0.5669	NUM
ejpam-556	177	12	0.7262	0.7262	NUM
ejpam-556	177	13	0.1	0.1	NUM
ejpam-556	177	14	7985	7985	NUM
ejpam-556	177	15	0.8658	0.8658	NUM
ejpam-556	177	16	0.9281	0.9281	NUM
ejpam-556	177	17	the	the	DET
ejpam-556	177	18	data	datum	NOUN
ejpam-556	177	19	set	set	VERB
ejpam-556	177	20	in	in	ADP
ejpam-556	177	21	table	table	NOUN
ejpam-556	177	22	1	1	NUM
ejpam-556	177	23	using	use	VERB
ejpam-556	177	24	the	the	DET
ejpam-556	177	25	cubic	cubic	ADJ
ejpam-556	177	26	hermite	hermite	ADJ
ejpam-556	177	27	spline	spline	NOUN
ejpam-556	177	28	interpolation	interpolation	NOUN
ejpam-556	177	29	technique	technique	NOUN
ejpam-556	177	30	which	which	PRON
ejpam-556	177	31	loses	lose	VERB
ejpam-556	177	32	the	the	DET
ejpam-556	177	33	positive	positive	ADJ
ejpam-556	177	34	shape	shape	NOUN
ejpam-556	177	35	of	of	ADP
ejpam-556	177	36	data	datum	NOUN
ejpam-556	177	37	.	.	PUNCT
ejpam-556	178	1	the	the	DET
ejpam-556	178	2	positive	positive	ADJ
ejpam-556	178	3	curve	curve	NOUN
ejpam-556	178	4	in	in	ADP
ejpam-556	178	5	figure	figure	NOUN
ejpam-556	178	6	2	2	NUM
ejpam-556	178	7	is	be	AUX
ejpam-556	178	8	produced	produce	VERB
ejpam-556	178	9	by	by	ADP
ejpam-556	178	10	using	use	VERB
ejpam-556	178	11	positive	positive	ADJ
ejpam-556	178	12	curve	curve	NOUN
ejpam-556	178	13	data	datum	NOUN
ejpam-556	178	14	interpolation	interpolation	NOUN
ejpam-556	178	15	scheme	scheme	NOUN
ejpam-556	178	16	developed	develop	VERB
ejpam-556	178	17	in	in	ADP
ejpam-556	178	18	section	section	NOUN
ejpam-556	178	19	3	3	NUM
ejpam-556	178	20	.	.	PUNCT
ejpam-556	178	21	example	example	NOUN
ejpam-556	179	1	2	2	NUM
ejpam-556	179	2	.	.	PUNCT
ejpam-556	180	1	the	the	DET
ejpam-556	180	2	positive	positive	ADJ
ejpam-556	180	3	data	datum	NOUN
ejpam-556	180	4	set	set	VERB
ejpam-556	180	5	in	in	ADP
ejpam-556	180	6	table	table	NOUN
ejpam-556	180	7	2	2	NUM
ejpam-556	180	8	is	be	AUX
ejpam-556	180	9	taken	take	VERB
ejpam-556	180	10	from	from	ADP
ejpam-556	180	11	[	[	X
ejpam-556	180	12	6	6	NUM
ejpam-556	180	13	]	]	PUNCT
ejpam-556	180	14	.	.	PUNCT
ejpam-556	181	1	the	the	DET
ejpam-556	181	2	figure	figure	NOUN
ejpam-556	181	3	3	3	NUM
ejpam-556	181	4	is	be	AUX
ejpam-556	181	5	produced	produce	VERB
ejpam-556	181	6	from	from	ADP
ejpam-556	181	7	thetable	thetable	ADJ
ejpam-556	181	8	2	2	NUM
ejpam-556	181	9	:	:	PUNCT
ejpam-556	181	10	another	another	DET
ejpam-556	181	11	positive	positive	ADJ
ejpam-556	181	12	data	datum	NOUN
ejpam-556	181	13	taken	take	VERB
ejpam-556	181	14	from	from	ADP
ejpam-556	181	15	[	[	X
ejpam-556	181	16	6	6	NUM
ejpam-556	181	17	℄	℄	NOUN
ejpam-556	181	18	.	.	PUNCT
ejpam-556	182	1	x	x	X
ejpam-556	182	2	0.0	0.0	NUM
ejpam-556	182	3	0.05	0.05	NUM
ejpam-556	182	4	0.10	0.10	NUM
ejpam-556	182	5	0.15	0.15	NUM
ejpam-556	182	6	0.20	0.20	NUM
ejpam-556	182	7	f	f	NOUN
ejpam-556	182	8	0.302	0.302	NUM
ejpam-556	182	9	0.278	0.278	NUM
ejpam-556	182	10	0.10	0.10	NUM
ejpam-556	182	11	0.268	0.268	NUM
ejpam-556	182	12	0.298	0.298	NUM
ejpam-556	182	13	m.	m.	NOUN
ejpam-556	182	14	z.	z.	PROPN
ejpam-556	182	15	hussain	hussain	PROPN
ejpam-556	182	16	,	,	PUNCT
ejpam-556	182	17	m.	m.	NOUN
ejpam-556	182	18	sarfraz	sarfraz	PROPN
ejpam-556	182	19	,	,	PUNCT
ejpam-556	182	20	m.	m.	NOUN
ejpam-556	182	21	hussain	hussain	PROPN
ejpam-556	182	22	/	/	SYM
ejpam-556	182	23	eur	eur	PROPN
ejpam-556	182	24	.	.	PUNCT
ejpam-556	183	1	j.	j.	PROPN
ejpam-556	183	2	pure	pure	PROPN
ejpam-556	183	3	appl	appl	PROPN
ejpam-556	183	4	.	.	PROPN
ejpam-556	183	5	math	math	PROPN
ejpam-556	183	6	,	,	PUNCT
ejpam-556	183	7	3	3	NUM
ejpam-556	183	8	(	(	PUNCT
ejpam-556	183	9	2010	2010	NUM
ejpam-556	183	10	)	)	PUNCT
ejpam-556	183	11	,	,	PUNCT
ejpam-556	183	12	194	194	NUM
ejpam-556	183	13	-	-	SYM
ejpam-556	183	14	212	212	NUM
ejpam-556	183	15	200	200	NUM
ejpam-556	183	16	data	datum	NOUN
ejpam-556	183	17	set	set	VERB
ejpam-556	183	18	in	in	ADP
ejpam-556	183	19	table	table	NOUN
ejpam-556	183	20	2	2	NUM
ejpam-556	183	21	using	use	VERB
ejpam-556	183	22	the	the	DET
ejpam-556	183	23	cubic	cubic	ADJ
ejpam-556	183	24	hermite	hermite	ADJ
ejpam-556	183	25	spline	spline	NOUN
ejpam-556	183	26	interpolation	interpolation	NOUN
ejpam-556	183	27	technique	technique	NOUN
ejpam-556	183	28	which	which	PRON
ejpam-556	183	29	looses	loose	VERB
ejpam-556	183	30	the	the	DET
ejpam-556	183	31	positive	positive	ADJ
ejpam-556	183	32	shape	shape	NOUN
ejpam-556	183	33	of	of	ADP
ejpam-556	183	34	data	datum	NOUN
ejpam-556	183	35	.	.	PUNCT
ejpam-556	184	1	positive	positive	ADJ
ejpam-556	184	2	curve	curve	NOUN
ejpam-556	184	3	is	be	AUX
ejpam-556	184	4	produced	produce	VERB
ejpam-556	184	5	in	in	ADP
ejpam-556	184	6	figure	figure	NOUN
ejpam-556	184	7	4	4	NUM
ejpam-556	184	8	using	use	VERB
ejpam-556	184	9	positive	positive	ADJ
ejpam-556	184	10	curve	curve	NOUN
ejpam-556	184	11	data	datum	NOUN
ejpam-556	184	12	interpolation	interpolation	NOUN
ejpam-556	184	13	scheme	scheme	NOUN
ejpam-556	184	14	developed	develop	VERB
ejpam-556	184	15	in	in	ADP
ejpam-556	184	16	section	section	NOUN
ejpam-556	184	17	3	3	NUM
ejpam-556	184	18	.	.	PUNCT
ejpam-556	184	19	m.	m.	NOUN
ejpam-556	184	20	z.	z.	PROPN
ejpam-556	184	21	hussain	hussain	PROPN
ejpam-556	184	22	,	,	PUNCT
ejpam-556	184	23	m.	m.	NOUN
ejpam-556	184	24	sarfraz	sarfraz	PROPN
ejpam-556	184	25	,	,	PUNCT
ejpam-556	184	26	m.	m.	NOUN
ejpam-556	184	27	hussain	hussain	PROPN
ejpam-556	184	28	/	/	SYM
ejpam-556	184	29	eur	eur	PROPN
ejpam-556	184	30	.	.	PUNCT
ejpam-556	185	1	j.	j.	PROPN
ejpam-556	185	2	pure	pure	PROPN
ejpam-556	185	3	appl	appl	PROPN
ejpam-556	185	4	.	.	PROPN
ejpam-556	185	5	math	math	PROPN
ejpam-556	185	6	,	,	PUNCT
ejpam-556	185	7	3	3	NUM
ejpam-556	185	8	(	(	PUNCT
ejpam-556	185	9	2010	2010	NUM
ejpam-556	185	10	)	)	PUNCT
ejpam-556	185	11	,	,	PUNCT
ejpam-556	185	12	194	194	NUM
ejpam-556	185	13	-	-	SYM
ejpam-556	185	14	212	212	NUM
ejpam-556	185	15	201	201	NUM
ejpam-556	185	16	0.5	0.5	NUM
ejpam-556	185	17	0.6	0.6	NUM
ejpam-556	185	18	0.7	0.7	NUM
ejpam-556	185	19	0.8	0.8	NUM
ejpam-556	185	20	0.9	0.9	NUM
ejpam-556	185	21	1	1	NUM
ejpam-556	185	22	1.1	1.1	NUM
ejpam-556	185	23	1.2	1.2	NUM
ejpam-556	185	24	1.3	1.3	NUM
ejpam-556	185	25	−1000	−1000	NOUN
ejpam-556	185	26	0	0	NUM
ejpam-556	185	27	1000	1000	NUM
ejpam-556	185	28	2000	2000	NUM
ejpam-556	185	29	3000	3000	NUM
ejpam-556	185	30	4000	4000	NUM
ejpam-556	185	31	5000	5000	NUM
ejpam-556	185	32	6000	6000	NUM
ejpam-556	185	33	7000	7000	NUM
ejpam-556	185	34	8000	8000	NUM
ejpam-556	185	35	x−axis	x−axis	PUNCT
ejpam-556	186	1	y−	y−	NOUN
ejpam-556	186	2	ax	ax	NOUN
ejpam-556	186	3	is	be	AUX
ejpam-556	186	4	figure	figure	NOUN
ejpam-556	186	5	1	1	NUM
ejpam-556	186	6	:	:	PUNCT
ejpam-556	186	7	cubi	cubi	PROPN
ejpam-556	186	8	hermite	hermite	ADJ
ejpam-556	186	9	spline	spline	NOUN
ejpam-556	186	10	.	.	PUNCT
ejpam-556	187	1	0.5	0.5	NUM
ejpam-556	187	2	0.6	0.6	NUM
ejpam-556	187	3	0.7	0.7	NUM
ejpam-556	187	4	0.8	0.8	NUM
ejpam-556	187	5	0.9	0.9	NUM
ejpam-556	187	6	1	1	NUM
ejpam-556	187	7	1.1	1.1	NUM
ejpam-556	187	8	1.2	1.2	NUM
ejpam-556	187	9	1.3	1.3	NUM
ejpam-556	187	10	0	0	NUM
ejpam-556	187	11	1000	1000	NUM
ejpam-556	187	12	2000	2000	NUM
ejpam-556	187	13	3000	3000	NUM
ejpam-556	187	14	4000	4000	NUM
ejpam-556	187	15	5000	5000	NUM
ejpam-556	187	16	6000	6000	NUM
ejpam-556	187	17	7000	7000	NUM
ejpam-556	187	18	8000	8000	NUM
ejpam-556	187	19	x−axis	x−axis	PUNCT
ejpam-556	188	1	y−	y−	NOUN
ejpam-556	188	2	ax	ax	NOUN
ejpam-556	188	3	is	be	AUX
ejpam-556	188	4	figure	figure	NOUN
ejpam-556	188	5	2	2	NUM
ejpam-556	188	6	:	:	PUNCT
ejpam-556	188	7	positive	positive	ADJ
ejpam-556	188	8	c1	c1	NOUN
ejpam-556	188	9	rational	rational	ADJ
ejpam-556	188	10	ubi	ubi	PROPN
ejpam-556	188	11	fun	fun	ADJ
ejpam-556	188	12	tion	tion	NOUN
ejpam-556	188	13	.	.	PUNCT
ejpam-556	189	1	m.	m.	NOUN
ejpam-556	189	2	z.	z.	PROPN
ejpam-556	189	3	hussain	hussain	PROPN
ejpam-556	189	4	,	,	PUNCT
ejpam-556	189	5	m.	m.	NOUN
ejpam-556	189	6	sarfraz	sarfraz	PROPN
ejpam-556	189	7	,	,	PUNCT
ejpam-556	189	8	m.	m.	NOUN
ejpam-556	189	9	hussain	hussain	PROPN
ejpam-556	189	10	/	/	SYM
ejpam-556	189	11	eur	eur	PROPN
ejpam-556	189	12	.	.	PUNCT
ejpam-556	190	1	j.	j.	PROPN
ejpam-556	190	2	pure	pure	PROPN
ejpam-556	190	3	appl	appl	PROPN
ejpam-556	190	4	.	.	PROPN
ejpam-556	190	5	math	math	PROPN
ejpam-556	190	6	,	,	PUNCT
ejpam-556	190	7	3	3	NUM
ejpam-556	190	8	(	(	PUNCT
ejpam-556	190	9	2010	2010	NUM
ejpam-556	190	10	)	)	PUNCT
ejpam-556	190	11	,	,	PUNCT
ejpam-556	190	12	194	194	NUM
ejpam-556	190	13	-	-	SYM
ejpam-556	190	14	212	212	NUM
ejpam-556	191	1	202	202	NUM
ejpam-556	191	2	0	0	NUM
ejpam-556	191	3	0.05	0.05	NUM
ejpam-556	191	4	0.1	0.1	NUM
ejpam-556	191	5	0.15	0.15	NUM
ejpam-556	191	6	0.2	0.2	NUM
ejpam-556	191	7	0.25	0.25	NUM
ejpam-556	191	8	−0.5	−0.5	NOUN
ejpam-556	191	9	0	0	NUM
ejpam-556	191	10	0.5	0.5	NUM
ejpam-556	191	11	1	1	NUM
ejpam-556	191	12	1.5	1.5	NUM
ejpam-556	191	13	2	2	NUM
ejpam-556	191	14	2.5	2.5	NUM
ejpam-556	191	15	3	3	NUM
ejpam-556	191	16	x−axis	x−axis	PUNCT
ejpam-556	191	17	y−	y−	NOUN
ejpam-556	191	18	ax	ax	NOUN
ejpam-556	191	19	is	be	AUX
ejpam-556	191	20	figure	figure	NOUN
ejpam-556	191	21	3	3	NUM
ejpam-556	191	22	:	:	PUNCT
ejpam-556	191	23	cubi	cubi	PROPN
ejpam-556	191	24	hermite	hermite	ADJ
ejpam-556	191	25	spline	spline	NOUN
ejpam-556	191	26	.	.	PUNCT
ejpam-556	192	1	0	0	NUM
ejpam-556	192	2	0.05	0.05	NUM
ejpam-556	192	3	0.1	0.1	NUM
ejpam-556	192	4	0.15	0.15	NUM
ejpam-556	192	5	0.2	0.2	NUM
ejpam-556	192	6	0.25	0.25	NUM
ejpam-556	192	7	0	0	NUM
ejpam-556	192	8	0.5	0.5	NUM
ejpam-556	192	9	1	1	NUM
ejpam-556	192	10	1.5	1.5	NUM
ejpam-556	192	11	2	2	NUM
ejpam-556	192	12	2.5	2.5	NUM
ejpam-556	192	13	3	3	NUM
ejpam-556	192	14	x−axis	x−axis	PUNCT
ejpam-556	192	15	y−	y−	NOUN
ejpam-556	192	16	ax	ax	NOUN
ejpam-556	192	17	is	be	AUX
ejpam-556	192	18	figure	figure	VERB
ejpam-556	192	19	4	4	NUM
ejpam-556	192	20	:	:	PUNCT
ejpam-556	192	21	positive	positive	ADJ
ejpam-556	192	22	c1	c1	NOUN
ejpam-556	192	23	rational	rational	ADJ
ejpam-556	192	24	ubi	ubi	PROPN
ejpam-556	192	25	fun	fun	ADJ
ejpam-556	192	26	tion	tion	NOUN
ejpam-556	192	27	.	.	PUNCT
ejpam-556	193	1	m.	m.	NOUN
ejpam-556	193	2	z.	z.	PROPN
ejpam-556	193	3	hussain	hussain	PROPN
ejpam-556	193	4	,	,	PUNCT
ejpam-556	193	5	m.	m.	NOUN
ejpam-556	193	6	sarfraz	sarfraz	PROPN
ejpam-556	193	7	,	,	PUNCT
ejpam-556	193	8	m.	m.	NOUN
ejpam-556	193	9	hussain	hussain	PROPN
ejpam-556	193	10	/	/	SYM
ejpam-556	193	11	eur	eur	PROPN
ejpam-556	193	12	.	.	PUNCT
ejpam-556	194	1	j.	j.	PROPN
ejpam-556	194	2	pure	pure	PROPN
ejpam-556	194	3	appl	appl	PROPN
ejpam-556	194	4	.	.	PROPN
ejpam-556	194	5	math	math	PROPN
ejpam-556	194	6	,	,	PUNCT
ejpam-556	194	7	3	3	NUM
ejpam-556	194	8	(	(	PUNCT
ejpam-556	194	9	2010	2010	NUM
ejpam-556	194	10	)	)	PUNCT
ejpam-556	194	11	,	,	PUNCT
ejpam-556	194	12	194	194	NUM
ejpam-556	194	13	-	-	SYM
ejpam-556	194	14	212	212	NUM
ejpam-556	194	15	203	203	NUM
ejpam-556	194	16	4	4	NUM
ejpam-556	194	17	.	.	PUNCT
ejpam-556	194	18	constrained	constrain	VERB
ejpam-556	194	19	data	datum	NOUN
ejpam-556	194	20	interpolation	interpolation	NOUN
ejpam-556	194	21	let	let	VERB
ejpam-556	194	22	{	{	PUNCT
ejpam-556	194	23	(	(	PUNCT
ejpam-556	194	24	x	x	PROPN
ejpam-556	194	25	i	i	PROPN
ejpam-556	194	26	,	,	PUNCT
ejpam-556	194	27	fi	fi	NOUN
ejpam-556	194	28	)	)	PUNCT
ejpam-556	194	29	,	,	PUNCT
ejpam-556	194	30	i	i	PRON
ejpam-556	194	31	=	=	NOUN
ejpam-556	194	32	0,1,2	0,1,2	NUM
ejpam-556	194	33	,	,	PUNCT
ejpam-556	194	34	.	.	PUNCT
ejpam-556	194	35	.	.	PUNCT
ejpam-556	194	36	.	.	PUNCT
ejpam-556	195	1	,	,	PUNCT
ejpam-556	195	2	n	n	CCONJ
ejpam-556	195	3	}	}	PUNCT
ejpam-556	195	4	be	be	AUX
ejpam-556	195	5	the	the	DET
ejpam-556	195	6	given	give	VERB
ejpam-556	195	7	set	set	NOUN
ejpam-556	195	8	of	of	ADP
ejpam-556	195	9	data	datum	NOUN
ejpam-556	195	10	points	point	NOUN
ejpam-556	195	11	lying	lie	VERB
ejpam-556	195	12	above	above	ADP
ejpam-556	195	13	the	the	DET
ejpam-556	195	14	straight	straight	ADJ
ejpam-556	195	15	line	line	NOUN
ejpam-556	195	16	y	y	PROPN
ejpam-556	195	17	=	=	SYM
ejpam-556	195	18	mx	mx	PROPN
ejpam-556	196	1	+	+	CCONJ
ejpam-556	196	2	c	c	X
ejpam-556	196	3	i.e.	i.e.	X
ejpam-556	196	4	fi	fi	X
ejpam-556	196	5	>	>	X
ejpam-556	196	6	mx	mx	PROPN
ejpam-556	197	1	i	i	PRON
ejpam-556	197	2	+	+	PROPN
ejpam-556	197	3	c	c	X
ejpam-556	197	4	,	,	PUNCT
ejpam-556	197	5	∀	∀	VERB
ejpam-556	197	6	i	i	NOUN
ejpam-556	198	1	=	=	NOUN
ejpam-556	198	2	0,1,2	0,1,2	NUM
ejpam-556	198	3	,	,	PUNCT
ejpam-556	198	4	.	.	PUNCT
ejpam-556	198	5	.	.	PUNCT
ejpam-556	199	1	.	.	PUNCT
ejpam-556	200	1	,	,	PUNCT
ejpam-556	200	2	n.	n.	NOUN
ejpam-556	200	3	(	(	PUNCT
ejpam-556	200	4	16	16	NUM
ejpam-556	200	5	)	)	PUNCT
ejpam-556	200	6	the	the	DET
ejpam-556	200	7	curve	curve	NOUN
ejpam-556	200	8	will	will	AUX
ejpam-556	200	9	lie	lie	VERB
ejpam-556	200	10	above	above	ADP
ejpam-556	200	11	the	the	DET
ejpam-556	200	12	straight	straight	ADJ
ejpam-556	200	13	line	line	NOUN
ejpam-556	200	14	if	if	SCONJ
ejpam-556	200	15	the	the	DET
ejpam-556	200	16	c1	c1	PROPN
ejpam-556	200	17	rational	rational	ADJ
ejpam-556	200	18	cubic	cubic	ADJ
ejpam-556	200	19	function	function	NOUN
ejpam-556	200	20	(	(	PUNCT
ejpam-556	200	21	1	1	X
ejpam-556	200	22	)	)	PUNCT
ejpam-556	200	23	satisfies	satisfy	VERB
ejpam-556	200	24	the	the	DET
ejpam-556	200	25	following	follow	VERB
ejpam-556	200	26	condition	condition	NOUN
ejpam-556	200	27	:	:	PUNCT
ejpam-556	200	28	s(x	s(x	NUM
ejpam-556	200	29	)	)	PUNCT
ejpam-556	200	30	>	>	X
ejpam-556	200	31	mx	mx	PROPN
ejpam-556	201	1	+	+	CCONJ
ejpam-556	201	2	c	c	X
ejpam-556	201	3	,	,	PUNCT
ejpam-556	201	4	∀	∀	X
ejpam-556	202	1	x	x	SYM
ejpam-556	202	2	∈	∈	PROPN
ejpam-556	203	1	[	[	X
ejpam-556	203	2	x0	x0	PROPN
ejpam-556	203	3	,	,	PUNCT
ejpam-556	203	4	xn	xn	PROPN
ejpam-556	203	5	]	]	X
ejpam-556	203	6	.	.	PUNCT
ejpam-556	204	1	for	for	ADP
ejpam-556	204	2	each	each	DET
ejpam-556	204	3	subinterval	subinterval	NOUN
ejpam-556	204	4	ii	ii	NOUN
ejpam-556	205	1	=	=	PUNCT
ejpam-556	206	1	[	[	X
ejpam-556	206	2	x	x	X
ejpam-556	206	3	i	i	NOUN
ejpam-556	206	4	,	,	PUNCT
ejpam-556	206	5	x	x	PROPN
ejpam-556	206	6	i+1	i+1	VERB
ejpam-556	206	7	]	]	X
ejpam-556	206	8	,	,	PUNCT
ejpam-556	206	9	the	the	DET
ejpam-556	206	10	above	above	ADJ
ejpam-556	206	11	relation	relation	NOUN
ejpam-556	206	12	in	in	ADP
ejpam-556	206	13	parametric	parametric	ADJ
ejpam-556	206	14	form	form	NOUN
ejpam-556	206	15	is	be	AUX
ejpam-556	206	16	expressed	express	VERB
ejpam-556	206	17	as	as	ADP
ejpam-556	206	18	si(x	si(x	NOUN
ejpam-556	206	19	)	)	PUNCT
ejpam-556	206	20	>	>	X
ejpam-556	207	1	ai(1−	ai(1−	PROPN
ejpam-556	207	2	θ	θ	PROPN
ejpam-556	207	3	)	)	PUNCT
ejpam-556	207	4	+	+	NUM
ejpam-556	207	5	biθ	biθ	NOUN
ejpam-556	207	6	,	,	PUNCT
ejpam-556	207	7	(	(	PUNCT
ejpam-556	207	8	17	17	NUM
ejpam-556	207	9	)	)	PUNCT
ejpam-556	207	10	where	where	SCONJ
ejpam-556	207	11	θ	θ	PROPN
ejpam-556	207	12	=	=	PUNCT
ejpam-556	208	1	x−xi	x−xi	PROPN
ejpam-556	208	2	hi	hi	INTJ
ejpam-556	209	1	and	and	CCONJ
ejpam-556	209	2	ai(1−θ)+biθ	ai(1−θ)+biθ	PROPN
ejpam-556	209	3	is	be	AUX
ejpam-556	209	4	the	the	DET
ejpam-556	209	5	parametric	parametric	ADJ
ejpam-556	209	6	equation	equation	NOUN
ejpam-556	209	7	of	of	ADP
ejpam-556	209	8	straight	straight	ADJ
ejpam-556	209	9	line	line	NOUN
ejpam-556	209	10	with	with	ADP
ejpam-556	209	11	ai	ai	PROPN
ejpam-556	209	12	=	=	SYM
ejpam-556	209	13	mx	mx	PROPN
ejpam-556	209	14	i+c	i+c	PROPN
ejpam-556	209	15	and	and	CCONJ
ejpam-556	209	16	bi	bi	NOUN
ejpam-556	209	17	=	=	PROPN
ejpam-556	209	18	mx	mx	PROPN
ejpam-556	210	1	i+1	i+1	PRON
ejpam-556	210	2	+	+	CCONJ
ejpam-556	210	3	c.	c.	NOUN
ejpam-556	210	4	the	the	DET
ejpam-556	210	5	rearrangement	rearrangement	NOUN
ejpam-556	210	6	of	of	ADP
ejpam-556	210	7	(	(	PUNCT
ejpam-556	210	8	17	17	NUM
ejpam-556	210	9	)	)	PUNCT
ejpam-556	210	10	leads	lead	VERB
ejpam-556	210	11	to	to	ADP
ejpam-556	210	12	the	the	DET
ejpam-556	210	13	following	follow	VERB
ejpam-556	210	14	relation	relation	NOUN
ejpam-556	210	15	:	:	PUNCT
ejpam-556	210	16	ui(θ	ui(θ	X
ejpam-556	210	17	)	)	PUNCT
ejpam-556	210	18	=	=	SYM
ejpam-556	210	19	3	3	NUM
ejpam-556	210	20	∑	∑	PROPN
ejpam-556	210	21	i=0	i=0	PROPN
ejpam-556	210	22	(	(	PUNCT
ejpam-556	210	23	1−	1−	NUM
ejpam-556	210	24	θ)3−iθ	θ)3−iθ	PROPN
ejpam-556	210	25	ibi	ibi	NOUN
ejpam-556	210	26	,	,	PUNCT
ejpam-556	210	27	(	(	PUNCT
ejpam-556	210	28	18	18	NUM
ejpam-556	210	29	)	)	PUNCT
ejpam-556	210	30	where	where	SCONJ
ejpam-556	210	31	b0	b0	NOUN
ejpam-556	210	32	=	=	SYM
ejpam-556	210	33	(	(	PUNCT
ejpam-556	210	34	αi	αi	X
ejpam-556	210	35	+	+	CCONJ
ejpam-556	210	36	1	1	X
ejpam-556	210	37	)	)	PUNCT
ejpam-556	210	38	(	(	PUNCT
ejpam-556	210	39	fi	fi	NOUN
ejpam-556	210	40	−	−	NOUN
ejpam-556	210	41	ai	ai	NOUN
ejpam-556	210	42	)	)	PUNCT
ejpam-556	210	43	,	,	PUNCT
ejpam-556	210	44	b1	b1	NOUN
ejpam-556	210	45	=	=	SYM
ejpam-556	210	46	αi(2	αi(2	NUM
ejpam-556	210	47	fi	fi	NOUN
ejpam-556	210	48	−	−	NOUN
ejpam-556	210	49	ai	ai	INTJ
ejpam-556	210	50	−	−	PROPN
ejpam-556	210	51	bi	bi	NOUN
ejpam-556	210	52	)	)	PUNCT
ejpam-556	211	1	+	+	CCONJ
ejpam-556	211	2	3	3	NUM
ejpam-556	211	3	fi	fi	NOUN
ejpam-556	211	4	−	−	PROPN
ejpam-556	211	5	2ai	2ai	ADJ
ejpam-556	211	6	−	−	PROPN
ejpam-556	212	1	bi	bi	NOUN
ejpam-556	212	2	+	+	CCONJ
ejpam-556	212	3	hidi	hidi	ADJ
ejpam-556	212	4	,	,	PUNCT
ejpam-556	212	5	b2	b2	NOUN
ejpam-556	212	6	=	=	SYM
ejpam-556	212	7	(	(	PUNCT
ejpam-556	212	8	αi	αi	X
ejpam-556	212	9	+	+	CCONJ
ejpam-556	212	10	2	2	X
ejpam-556	212	11	)	)	PUNCT
ejpam-556	212	12	(	(	PUNCT
ejpam-556	212	13	fi+1	fi+1	NOUN
ejpam-556	212	14	−	−	PROPN
ejpam-556	212	15	bi	bi	NOUN
ejpam-556	212	16	)	)	PUNCT
ejpam-556	213	1	+	+	NUM
ejpam-556	213	2	fi+1	fi+1	NOUN
ejpam-556	213	3	−	−	PROPN
ejpam-556	213	4	hidi+1	hidi+1	NOUN
ejpam-556	214	1	−	−	PROPN
ejpam-556	214	2	ai	ai	VERB
ejpam-556	214	3	,	,	PUNCT
ejpam-556	214	4	b3	b3	PROPN
ejpam-556	214	5	=	=	SYM
ejpam-556	214	6	fi+1	fi+1	NOUN
ejpam-556	215	1	−	−	PROPN
ejpam-556	215	2	bi	bi	PROPN
ejpam-556	215	3	.	.	PUNCT
ejpam-556	216	1	now	now	ADV
ejpam-556	216	2	,	,	PUNCT
ejpam-556	216	3	ui(θ	ui(θ	X
ejpam-556	216	4	)	)	PUNCT
ejpam-556	216	5	>	>	X
ejpam-556	216	6	0	0	PUNCT
ejpam-556	217	1	if	if	SCONJ
ejpam-556	217	2	bi	bi	PROPN
ejpam-556	217	3	>	>	X
ejpam-556	217	4	0	0	PROPN
ejpam-556	217	5	,	,	PUNCT
ejpam-556	217	6	i	i	PRON
ejpam-556	217	7	=	=	NOUN
ejpam-556	217	8	0,1,2,3	0,1,2,3	NUM
ejpam-556	217	9	.	.	PUNCT
ejpam-556	218	1	it	it	PRON
ejpam-556	218	2	is	be	AUX
ejpam-556	218	3	straightforward	straightforward	ADJ
ejpam-556	218	4	to	to	PART
ejpam-556	218	5	know	know	VERB
ejpam-556	218	6	that	that	DET
ejpam-556	218	7	b0	b0	NOUN
ejpam-556	218	8	>	>	X
ejpam-556	218	9	0	0	PUNCT
ejpam-556	218	10	and	and	CCONJ
ejpam-556	218	11	b3	b3	PROPN
ejpam-556	218	12	>	>	SYM
ejpam-556	218	13	0	0	NUM
ejpam-556	218	14	are	be	AUX
ejpam-556	218	15	true	true	ADJ
ejpam-556	218	16	from	from	ADP
ejpam-556	218	17	the	the	DET
ejpam-556	218	18	necessary	necessary	ADJ
ejpam-556	218	19	condition	condition	NOUN
ejpam-556	218	20	defined	define	VERB
ejpam-556	218	21	in	in	ADP
ejpam-556	218	22	(	(	PUNCT
ejpam-556	218	23	16	16	NUM
ejpam-556	218	24	)	)	PUNCT
ejpam-556	218	25	and	and	CCONJ
ejpam-556	218	26	αi	αi	VERB
ejpam-556	218	27	>	>	X
ejpam-556	218	28	0	0	X
ejpam-556	218	29	.	.	PUNCT
ejpam-556	219	1	b1	b1	PROPN
ejpam-556	219	2	>	>	X
ejpam-556	219	3	0	0	PUNCT
ejpam-556	219	4	provides	provide	VERB
ejpam-556	219	5	the	the	DET
ejpam-556	219	6	following	follow	VERB
ejpam-556	219	7	constraints	constraint	NOUN
ejpam-556	219	8	on	on	ADP
ejpam-556	219	9	αi	αi	NOUN
ejpam-556	219	10	:	:	PUNCT
ejpam-556	219	11	if	if	SCONJ
ejpam-556	219	12	2	2	NUM
ejpam-556	219	13	fi−ai−	fi−ai−	PROPN
ejpam-556	219	14	bi	bi	NOUN
ejpam-556	219	15	>	>	X
ejpam-556	219	16	0	0	PUNCT
ejpam-556	220	1	then	then	ADV
ejpam-556	220	2	αi	αi	VERB
ejpam-556	220	3	>	>	X
ejpam-556	220	4	−	−	PROPN
ejpam-556	220	5	fi+bi−hi	fi+bi−hi	NOUN
ejpam-556	220	6	di	di	NOUN
ejpam-556	220	7	2	2	NUM
ejpam-556	220	8	fi−ai−bi	fi−ai−bi	PROPN
ejpam-556	220	9	.	.	PUNCT
ejpam-556	221	1	similarly	similarly	ADV
ejpam-556	221	2	,	,	PUNCT
ejpam-556	221	3	if	if	SCONJ
ejpam-556	221	4	2	2	NUM
ejpam-556	221	5	fi−ai−	fi−ai−	NOUN
ejpam-556	221	6	bi	bi	NOUN
ejpam-556	221	7	<	<	X
ejpam-556	221	8	0	0	PROPN
ejpam-556	222	1	then	then	ADV
ejpam-556	222	2	αi	αi	VERB
ejpam-556	222	3	<	<	X
ejpam-556	222	4	−	−	PROPN
ejpam-556	222	5	fi+bi−hi	fi+bi−hi	PROPN
ejpam-556	222	6	di	di	NOUN
ejpam-556	222	7	2	2	NUM
ejpam-556	222	8	fi−ai−bi	fi−ai−bi	PROPN
ejpam-556	222	9	.	.	PUNCT
ejpam-556	223	1	one	one	PRON
ejpam-556	223	2	can	can	AUX
ejpam-556	223	3	also	also	ADV
ejpam-556	223	4	note	note	VERB
ejpam-556	223	5	that	that	DET
ejpam-556	223	6	b2	b2	NOUN
ejpam-556	223	7	>	>	X
ejpam-556	223	8	0	0	PUNCT
ejpam-556	224	1	if	if	SCONJ
ejpam-556	224	2	αi	αi	VERB
ejpam-556	224	3	>	>	X
ejpam-556	224	4	−	−	PROPN
ejpam-556	224	5	fi+1+hi	fi+1+hi	VERB
ejpam-556	224	6	di+1+ai	di+1+ai	PROPN
ejpam-556	224	7	fi+1−bi	fi+1−bi	PROPN
ejpam-556	224	8	.	.	PUNCT
ejpam-556	225	1	the	the	DET
ejpam-556	225	2	above	above	ADJ
ejpam-556	225	3	discussion	discussion	NOUN
ejpam-556	225	4	can	can	AUX
ejpam-556	225	5	be	be	AUX
ejpam-556	225	6	summarized	summarize	VERB
ejpam-556	225	7	as	as	ADP
ejpam-556	225	8	:	:	PUNCT
ejpam-556	225	9	theorem	theorem	NOUN
ejpam-556	225	10	4	4	NUM
ejpam-556	225	11	.	.	PUNCT
ejpam-556	226	1	the	the	DET
ejpam-556	226	2	piecewise	piecewise	PROPN
ejpam-556	226	3	c1	c1	PROPN
ejpam-556	226	4	rational	rational	ADJ
ejpam-556	226	5	cubic	cubic	ADJ
ejpam-556	226	6	interpolant	interpolant	NOUN
ejpam-556	226	7	s(x	s(x	PROPN
ejpam-556	226	8	)	)	PUNCT
ejpam-556	226	9	,	,	PUNCT
ejpam-556	226	10	defined	define	VERB
ejpam-556	226	11	over	over	ADP
ejpam-556	226	12	the	the	DET
ejpam-556	226	13	interval	interval	NOUN
ejpam-556	226	14	[	[	X
ejpam-556	226	15	a	a	X
ejpam-556	226	16	,	,	PUNCT
ejpam-556	226	17	b	b	NOUN
ejpam-556	226	18	]	]	X
ejpam-556	226	19	,	,	PUNCT
ejpam-556	226	20	in	in	ADP
ejpam-556	226	21	(	(	PUNCT
ejpam-556	226	22	1	1	NUM
ejpam-556	226	23	)	)	PUNCT
ejpam-556	226	24	,	,	PUNCT
ejpam-556	226	25	preserves	preserve	VERB
ejpam-556	226	26	the	the	DET
ejpam-556	226	27	shape	shape	NOUN
ejpam-556	226	28	of	of	ADP
ejpam-556	226	29	data	datum	NOUN
ejpam-556	226	30	that	that	PRON
ejpam-556	226	31	lies	lie	VERB
ejpam-556	226	32	above	above	ADP
ejpam-556	226	33	the	the	DET
ejpam-556	226	34	straight	straight	ADJ
ejpam-556	226	35	line	line	NOUN
ejpam-556	226	36	if	if	SCONJ
ejpam-556	226	37	in	in	ADP
ejpam-556	226	38	each	each	DET
ejpam-556	226	39	subinterval	subinterval	NOUN
ejpam-556	226	40	ii	ii	NOUN
ejpam-556	227	1	=	=	PUNCT
ejpam-556	228	1	[	[	X
ejpam-556	228	2	x	x	X
ejpam-556	228	3	i	i	NOUN
ejpam-556	228	4	,	,	PUNCT
ejpam-556	228	5	x	x	PROPN
ejpam-556	228	6	i+1	i+1	VERB
ejpam-556	228	7	]	]	X
ejpam-556	228	8	the	the	DET
ejpam-556	228	9	following	follow	VERB
ejpam-556	228	10	sufficient	sufficient	ADJ
ejpam-556	228	11	conditions	condition	NOUN
ejpam-556	228	12	are	be	AUX
ejpam-556	228	13	satisfied	satisfied	ADJ
ejpam-556	228	14	:	:	PUNCT
ejpam-556	228	15	con3	con3	PROPN
ejpam-556	228	16	<	<	X
ejpam-556	228	17	αi	αi	X
ejpam-556	228	18	<	<	X
ejpam-556	228	19	con4	con4	PROPN
ejpam-556	228	20	,	,	PUNCT
ejpam-556	228	21	con3	con3	PROPN
ejpam-556	228	22	=	=	PUNCT
ejpam-556	228	23	max	max	PROPN
ejpam-556	228	24	�	�	PROPN
ejpam-556	228	25	0	0	NUM
ejpam-556	228	26	,	,	PUNCT
ejpam-556	228	27	−	−	PROPN
ejpam-556	228	28	fi	fi	NOUN
ejpam-556	229	1	+	+	CCONJ
ejpam-556	229	2	bi	bi	ADJ
ejpam-556	229	3	−	−	PROPN
ejpam-556	229	4	hidi	hidi	NOUN
ejpam-556	229	5	2	2	NUM
ejpam-556	229	6	fi	fi	NOUN
ejpam-556	229	7	−	−	PROPN
ejpam-556	229	8	ai	ai	INTJ
ejpam-556	229	9	−	−	PROPN
ejpam-556	229	10	bi	bi	NOUN
ejpam-556	229	11	,	,	PUNCT
ejpam-556	229	12	−	−	PROPN
ejpam-556	229	13	fi+1	fi+1	NOUN
ejpam-556	229	14	+	+	CCONJ
ejpam-556	229	15	hidi+1	hidi+1	NOUN
ejpam-556	230	1	+	+	CCONJ
ejpam-556	230	2	ai	ai	VERB
ejpam-556	230	3	fi+1	fi+1	NOUN
ejpam-556	230	4	−	−	PROPN
ejpam-556	230	5	bi	bi	PROPN
ejpam-556	230	6	�	�	PROPN
ejpam-556	230	7	,	,	PUNCT
ejpam-556	230	8	con4	con4	PROPN
ejpam-556	230	9	=	=	PUNCT
ejpam-556	231	1	−	−	PROPN
ejpam-556	231	2	fi	fi	NOUN
ejpam-556	231	3	+	+	CCONJ
ejpam-556	231	4	bi	bi	ADJ
ejpam-556	231	5	−	−	PROPN
ejpam-556	231	6	hidi	hidi	NOUN
ejpam-556	231	7	2	2	NUM
ejpam-556	231	8	fi	fi	NOUN
ejpam-556	231	9	−	−	PROPN
ejpam-556	231	10	ai	ai	INTJ
ejpam-556	231	11	−	−	PROPN
ejpam-556	231	12	bi	bi	NOUN
ejpam-556	231	13	.	.	PUNCT
ejpam-556	232	1	m.	m.	PROPN
ejpam-556	232	2	z.	z.	PROPN
ejpam-556	232	3	hussain	hussain	PROPN
ejpam-556	232	4	,	,	PUNCT
ejpam-556	232	5	m.	m.	NOUN
ejpam-556	232	6	sarfraz	sarfraz	PROPN
ejpam-556	232	7	,	,	PUNCT
ejpam-556	232	8	m.	m.	NOUN
ejpam-556	232	9	hussain	hussain	PROPN
ejpam-556	232	10	/	/	SYM
ejpam-556	232	11	eur	eur	PROPN
ejpam-556	232	12	.	.	PUNCT
ejpam-556	233	1	j.	j.	PROPN
ejpam-556	233	2	pure	pure	PROPN
ejpam-556	233	3	appl	appl	PROPN
ejpam-556	233	4	.	.	PROPN
ejpam-556	233	5	math	math	PROPN
ejpam-556	233	6	,	,	PUNCT
ejpam-556	233	7	3	3	NUM
ejpam-556	233	8	(	(	PUNCT
ejpam-556	233	9	2010	2010	NUM
ejpam-556	233	10	)	)	PUNCT
ejpam-556	233	11	,	,	PUNCT
ejpam-556	233	12	194	194	NUM
ejpam-556	233	13	-	-	SYM
ejpam-556	233	14	212	212	NUM
ejpam-556	233	15	204	204	NUM
ejpam-556	233	16	the	the	DET
ejpam-556	233	17	above	above	ADJ
ejpam-556	233	18	constraints	constraint	NOUN
ejpam-556	233	19	can	can	AUX
ejpam-556	233	20	be	be	AUX
ejpam-556	233	21	rearranged	rearrange	VERB
ejpam-556	233	22	as	as	ADP
ejpam-556	233	23	:	:	PUNCT
ejpam-556	233	24	con3	con3	PROPN
ejpam-556	233	25	+	+	PROPN
ejpam-556	233	26	mi	mi	NOUN
ejpam-556	233	27	=	=	NOUN
ejpam-556	233	28	αi	αi	VERB
ejpam-556	233	29	=	=	SYM
ejpam-556	233	30	con4	con4	PROPN
ejpam-556	233	31	−	−	PROPN
ejpam-556	233	32	ni	ni	PROPN
ejpam-556	233	33	,	,	PUNCT
ejpam-556	233	34	where	where	SCONJ
ejpam-556	233	35	mi	mi	PROPN
ejpam-556	233	36	>	>	X
ejpam-556	233	37	0	0	PROPN
ejpam-556	233	38	and	and	CCONJ
ejpam-556	233	39	ni	ni	PROPN
ejpam-556	233	40	>	>	X
ejpam-556	233	41	0	0	PROPN
ejpam-556	233	42	.	.	PUNCT
ejpam-556	234	1	thus	thus	ADV
ejpam-556	234	2	we	we	PRON
ejpam-556	234	3	have	have	VERB
ejpam-556	234	4	the	the	DET
ejpam-556	234	5	following	follow	VERB
ejpam-556	234	6	algorithm	algorithm	NOUN
ejpam-556	234	7	for	for	ADP
ejpam-556	234	8	the	the	DET
ejpam-556	234	9	manipulation	manipulation	NOUN
ejpam-556	234	10	of	of	ADP
ejpam-556	234	11	curve	curve	NOUN
ejpam-556	234	12	design	design	NOUN
ejpam-556	234	13	.	.	PUNCT
ejpam-556	235	1	algorithm	algorithm	NOUN
ejpam-556	235	2	2	2	NUM
ejpam-556	235	3	step	step	NOUN
ejpam-556	235	4	1	1	NUM
ejpam-556	235	5	.	.	PUNCT
ejpam-556	235	6	enter	enter	VERB
ejpam-556	235	7	the	the	DET
ejpam-556	235	8	(	(	PUNCT
ejpam-556	235	9	n+	n+	NOUN
ejpam-556	235	10	1	1	NUM
ejpam-556	235	11	)	)	PUNCT
ejpam-556	235	12	positive	positive	ADJ
ejpam-556	235	13	data	data	NOUN
ejpam-556	235	14	points	point	NOUN
ejpam-556	235	15	{	{	PUNCT
ejpam-556	235	16	(	(	PUNCT
ejpam-556	235	17	x	x	SYM
ejpam-556	235	18	i	i	PROPN
ejpam-556	235	19	,	,	PUNCT
ejpam-556	235	20	fi	fi	NOUN
ejpam-556	235	21	)	)	PUNCT
ejpam-556	235	22	:	:	PUNCT
ejpam-556	236	1	i	i	PRON
ejpam-556	236	2	=	=	NOUN
ejpam-556	236	3	0,1,2	0,1,2	NUM
ejpam-556	236	4	,	,	PUNCT
ejpam-556	236	5	.	.	PUNCT
ejpam-556	236	6	.	.	PUNCT
ejpam-556	236	7	.	.	PUNCT
ejpam-556	236	8	,	,	PUNCT
ejpam-556	236	9	n	n	CCONJ
ejpam-556	236	10	}	}	PUNCT
ejpam-556	236	11	.	.	PUNCT
ejpam-556	237	1	step	step	NOUN
ejpam-556	237	2	2	2	NUM
ejpam-556	237	3	.	.	NUM
ejpam-556	237	4	estimate	estimate	VERB
ejpam-556	237	5	the	the	DET
ejpam-556	237	6	first	first	ADJ
ejpam-556	237	7	order	order	NOUN
ejpam-556	237	8	derivatives	derivative	NOUN
ejpam-556	237	9	di	di	VERB
ejpam-556	237	10	,	,	PUNCT
ejpam-556	237	11	i	i	PRON
ejpam-556	237	12	=	=	NOUN
ejpam-556	237	13	0,1,2	0,1,2	NUM
ejpam-556	237	14	,	,	PUNCT
ejpam-556	237	15	.	.	PUNCT
ejpam-556	237	16	.	.	PUNCT
ejpam-556	238	1	.	.	PUNCT
ejpam-556	239	1	,	,	PUNCT
ejpam-556	239	2	n	n	CCONJ
ejpam-556	239	3	at	at	ADP
ejpam-556	239	4	knots	knot	NOUN
ejpam-556	239	5	.	.	PUNCT
ejpam-556	240	1	(	(	PUNCT
ejpam-556	240	2	note	note	VERB
ejpam-556	240	3	:	:	PUNCT
ejpam-556	240	4	the	the	DET
ejpam-556	240	5	step	step	NOUN
ejpam-556	240	6	2	2	NUM
ejpam-556	240	7	is	be	AUX
ejpam-556	240	8	only	only	ADV
ejpam-556	240	9	applicable	applicable	ADJ
ejpam-556	240	10	if	if	SCONJ
ejpam-556	240	11	data	datum	NOUN
ejpam-556	240	12	is	be	AUX
ejpam-556	240	13	not	not	PART
ejpam-556	240	14	provided	provide	VERB
ejpam-556	240	15	with	with	ADP
ejpam-556	240	16	derivatives	derivative	NOUN
ejpam-556	240	17	)	)	PUNCT
ejpam-556	240	18	.	.	PUNCT
ejpam-556	241	1	step	step	NOUN
ejpam-556	241	2	3	3	NUM
ejpam-556	241	3	.	.	PUNCT
ejpam-556	241	4	calculate	calculate	VERB
ejpam-556	241	5	the	the	DET
ejpam-556	241	6	value	value	NOUN
ejpam-556	241	7	of	of	ADP
ejpam-556	241	8	free	free	ADJ
ejpam-556	241	9	parameter	parameter	NOUN
ejpam-556	241	10	αiusing	αiusing	NOUN
ejpam-556	241	11	theorem	theorem	NOUN
ejpam-556	241	12	4	4	NUM
ejpam-556	241	13	.	.	NOUN
ejpam-556	241	14	step	step	NOUN
ejpam-556	241	15	4	4	NUM
ejpam-556	241	16	.	.	PUNCT
ejpam-556	241	17	substitute	substitute	VERB
ejpam-556	241	18	the	the	DET
ejpam-556	241	19	values	value	NOUN
ejpam-556	241	20	of	of	ADP
ejpam-556	241	21	fi	fi	NOUN
ejpam-556	241	22	,	,	PUNCT
ejpam-556	241	23	di	di	NOUN
ejpam-556	241	24	,	,	PUNCT
ejpam-556	241	25	i	i	NOUN
ejpam-556	241	26	=	=	NOUN
ejpam-556	241	27	0,1,2	0,1,2	NUM
ejpam-556	241	28	,	,	PUNCT
ejpam-556	241	29	.	.	PUNCT
ejpam-556	241	30	.	.	PUNCT
ejpam-556	242	1	.	.	PUNCT
ejpam-556	243	1	,	,	PUNCT
ejpam-556	243	2	n	n	PROPN
ejpam-556	243	3	and	and	CCONJ
ejpam-556	243	4	αi	αi	NOUN
ejpam-556	243	5	,	,	PUNCT
ejpam-556	243	6	i	i	PRON
ejpam-556	243	7	=	=	NOUN
ejpam-556	243	8	0,1,2	0,1,2	NUM
ejpam-556	243	9	,	,	PUNCT
ejpam-556	243	10	.	.	PUNCT
ejpam-556	243	11	.	.	PUNCT
ejpam-556	244	1	.	.	PUNCT
ejpam-556	245	1	,	,	PUNCT
ejpam-556	245	2	n−	n−	NOUN
ejpam-556	245	3	1	1	NUM
ejpam-556	245	4	in	in	ADP
ejpam-556	245	5	rational	rational	ADJ
ejpam-556	245	6	cubic	cubic	ADJ
ejpam-556	245	7	function	function	NOUN
ejpam-556	245	8	(	(	PUNCT
ejpam-556	245	9	1	1	NUM
ejpam-556	245	10	)	)	PUNCT
ejpam-556	245	11	to	to	PART
ejpam-556	245	12	obtain	obtain	VERB
ejpam-556	245	13	the	the	DET
ejpam-556	245	14	curve	curve	NOUN
ejpam-556	245	15	lying	lie	VERB
ejpam-556	245	16	above	above	ADP
ejpam-556	245	17	the	the	DET
ejpam-556	245	18	straight	straight	ADJ
ejpam-556	245	19	line	line	NOUN
ejpam-556	245	20	.	.	PUNCT
ejpam-556	246	1	4.1	4.1	NUM
ejpam-556	246	2	.	.	PUNCT
ejpam-556	246	3	demonstration	demonstration	NOUN
ejpam-556	246	4	example	example	NOUN
ejpam-556	246	5	3	3	X
ejpam-556	246	6	.	.	PUNCT
ejpam-556	247	1	the	the	DET
ejpam-556	247	2	data	datum	NOUN
ejpam-556	247	3	set	set	VERB
ejpam-556	247	4	in	in	ADP
ejpam-556	247	5	table	table	NOUN
ejpam-556	247	6	3	3	NUM
ejpam-556	247	7	is	be	AUX
ejpam-556	247	8	lying	lie	VERB
ejpam-556	247	9	above	above	ADP
ejpam-556	247	10	the	the	DET
ejpam-556	247	11	straight	straight	ADJ
ejpam-556	247	12	line	line	NOUN
ejpam-556	247	13	y	y	NOUN
ejpam-556	247	14	=	=	PUNCT
ejpam-556	247	15	x	x	SYM
ejpam-556	247	16	2	2	NUM
ejpam-556	247	17	+	+	SYM
ejpam-556	247	18	1	1	NUM
ejpam-556	247	19	and	and	CCONJ
ejpam-556	247	20	is	be	AUX
ejpam-556	247	21	taken	take	VERB
ejpam-556	247	22	from	from	ADP
ejpam-556	247	23	[	[	X
ejpam-556	247	24	1	1	NUM
ejpam-556	247	25	]	]	PUNCT
ejpam-556	247	26	with	with	ADP
ejpam-556	247	27	slight	slight	ADJ
ejpam-556	247	28	modification	modification	NOUN
ejpam-556	247	29	.	.	PUNCT
ejpam-556	248	1	the	the	DET
ejpam-556	248	2	figure	figure	NOUN
ejpam-556	248	3	5	5	NUM
ejpam-556	248	4	is	be	AUX
ejpam-556	248	5	produced	produce	VERB
ejpam-556	248	6	from	from	ADP
ejpam-556	248	7	the	the	DET
ejpam-556	248	8	data	datum	NOUN
ejpam-556	248	9	set	set	VERB
ejpam-556	248	10	in	in	ADP
ejpam-556	248	11	table	table	NOUN
ejpam-556	248	12	3	3	NUM
ejpam-556	248	13	using	use	VERB
ejpam-556	248	14	cubictable	cubictable	NOUN
ejpam-556	248	15	3	3	NUM
ejpam-556	248	16	:	:	PUNCT
ejpam-556	248	17	x	x	SYM
ejpam-556	248	18	0	0	NUM
ejpam-556	248	19	2	2	NUM
ejpam-556	248	20	3	3	NUM
ejpam-556	248	21	5	5	NUM
ejpam-556	248	22	6	6	NUM
ejpam-556	248	23	8	8	NUM
ejpam-556	248	24	11	11	NUM
ejpam-556	248	25	12	12	NUM
ejpam-556	248	26	14	14	NUM
ejpam-556	248	27	15	15	NUM
ejpam-556	248	28	f	f	PROPN
ejpam-556	248	29	6.5	6.5	NUM
ejpam-556	248	30	6.5	6.5	NUM
ejpam-556	248	31	6.5	6.5	NUM
ejpam-556	248	32	6.5	6.5	NUM
ejpam-556	248	33	6.5	6.5	NUM
ejpam-556	248	34	6.5	6.5	NUM
ejpam-556	248	35	16	16	NUM
ejpam-556	248	36	50	50	NUM
ejpam-556	248	37	60	60	NUM
ejpam-556	248	38	85	85	NUM
ejpam-556	248	39	hermite	hermite	ADJ
ejpam-556	248	40	spline	spline	NOUN
ejpam-556	248	41	.	.	PUNCT
ejpam-556	249	1	it	it	PRON
ejpam-556	249	2	is	be	AUX
ejpam-556	249	3	clear	clear	ADJ
ejpam-556	249	4	from	from	ADP
ejpam-556	249	5	the	the	DET
ejpam-556	249	6	figure	figure	NOUN
ejpam-556	249	7	5	5	NUM
ejpam-556	249	8	that	that	SCONJ
ejpam-556	249	9	some	some	DET
ejpam-556	249	10	part	part	NOUN
ejpam-556	249	11	of	of	ADP
ejpam-556	249	12	the	the	DET
ejpam-556	249	13	curve	curve	NOUN
ejpam-556	249	14	is	be	AUX
ejpam-556	249	15	lying	lie	VERB
ejpam-556	249	16	below	below	ADP
ejpam-556	249	17	the	the	DET
ejpam-556	249	18	line	line	NOUN
ejpam-556	249	19	y	y	NOUN
ejpam-556	249	20	=	=	PUNCT
ejpam-556	249	21	x	x	SYM
ejpam-556	249	22	2	2	NUM
ejpam-556	249	23	+	+	NUM
ejpam-556	249	24	1	1	NUM
ejpam-556	249	25	.	.	PUNCT
ejpam-556	250	1	this	this	DET
ejpam-556	250	2	flaw	flaw	NOUN
ejpam-556	250	3	is	be	AUX
ejpam-556	250	4	recovered	recover	VERB
ejpam-556	250	5	nicely	nicely	ADV
ejpam-556	250	6	in	in	ADP
ejpam-556	250	7	figure	figure	NOUN
ejpam-556	250	8	6	6	NUM
ejpam-556	250	9	using	use	VERB
ejpam-556	250	10	constrained	constrained	ADJ
ejpam-556	250	11	data	datum	NOUN
ejpam-556	250	12	interpolation	interpolation	NOUN
ejpam-556	250	13	scheme	scheme	NOUN
ejpam-556	250	14	developed	develop	VERB
ejpam-556	250	15	in	in	ADP
ejpam-556	250	16	section	section	NOUN
ejpam-556	250	17	4	4	NUM
ejpam-556	250	18	.	.	PUNCT
ejpam-556	251	1	it	it	PRON
ejpam-556	251	2	is	be	AUX
ejpam-556	251	3	clear	clear	ADJ
ejpam-556	251	4	from	from	ADP
ejpam-556	251	5	figure	figure	NOUN
ejpam-556	251	6	6	6	NUM
ejpam-556	251	7	shape	shape	NOUN
ejpam-556	251	8	of	of	ADP
ejpam-556	251	9	the	the	DET
ejpam-556	251	10	data	data	NOUN
ejpam-556	251	11	is	be	AUX
ejpam-556	251	12	recovered	recover	VERB
ejpam-556	251	13	.	.	PUNCT
ejpam-556	252	1	example	example	NOUN
ejpam-556	253	1	4	4	NUM
ejpam-556	253	2	.	.	PUNCT
ejpam-556	254	1	the	the	DET
ejpam-556	254	2	data	datum	NOUN
ejpam-556	254	3	set	set	VERB
ejpam-556	254	4	[	[	X
ejpam-556	254	5	10	10	NUM
ejpam-556	254	6	]	]	PUNCT
ejpam-556	254	7	in	in	ADP
ejpam-556	254	8	table	table	NOUN
ejpam-556	254	9	4	4	NUM
ejpam-556	254	10	is	be	AUX
ejpam-556	254	11	lying	lie	VERB
ejpam-556	254	12	above	above	ADP
ejpam-556	254	13	the	the	DET
ejpam-556	254	14	straight	straight	ADJ
ejpam-556	254	15	line	line	NOUN
ejpam-556	255	1	y	y	NOUN
ejpam-556	255	2	=	=	PUNCT
ejpam-556	255	3	x	x	SYM
ejpam-556	255	4	2	2	NUM
ejpam-556	255	5	+	+	NUM
ejpam-556	255	6	1	1	NUM
ejpam-556	255	7	.	.	X
ejpam-556	255	8	figure	figure	VERB
ejpam-556	255	9	7table	7table	ADJ
ejpam-556	255	10	4	4	NUM
ejpam-556	255	11	:	:	PUNCT
ejpam-556	255	12	the	the	DET
ejpam-556	255	13	data	datum	NOUN
ejpam-556	255	14	set	set	VERB
ejpam-556	255	15	lying	lie	VERB
ejpam-556	255	16	above	above	ADP
ejpam-556	255	17	the	the	DET
ejpam-556	255	18	straight	straight	ADJ
ejpam-556	255	19	line	line	NOUN
ejpam-556	255	20	y	y	NOUN
ejpam-556	255	21	=	=	PUNCT
ejpam-556	255	22	x	x	SYM
ejpam-556	255	23	2	2	NUM
ejpam-556	255	24	+	+	NUM
ejpam-556	255	25	1	1	NUM
ejpam-556	255	26	.	.	X
ejpam-556	255	27	x	x	SYM
ejpam-556	255	28	2	2	NUM
ejpam-556	255	29	3	3	NUM
ejpam-556	255	30	7	7	NUM
ejpam-556	255	31	8	8	NUM
ejpam-556	255	32	10	10	NUM
ejpam-556	255	33	13	13	NUM
ejpam-556	255	34	14	14	NUM
ejpam-556	255	35	f	f	NOUN
ejpam-556	255	36	12	12	NUM
ejpam-556	255	37	4.5	4.5	NUM
ejpam-556	255	38	6.5	6.5	NUM
ejpam-556	255	39	10	10	NUM
ejpam-556	255	40	6.3	6.3	NUM
ejpam-556	255	41	12	12	NUM
ejpam-556	255	42	18	18	NUM
ejpam-556	255	43	is	be	AUX
ejpam-556	255	44	produced	produce	VERB
ejpam-556	255	45	from	from	ADP
ejpam-556	255	46	the	the	DET
ejpam-556	255	47	data	datum	NOUN
ejpam-556	255	48	set	set	VERB
ejpam-556	255	49	in	in	ADP
ejpam-556	255	50	table	table	NOUN
ejpam-556	255	51	4	4	NUM
ejpam-556	255	52	using	use	VERB
ejpam-556	255	53	cubic	cubic	ADJ
ejpam-556	255	54	hermite	hermite	ADJ
ejpam-556	255	55	spline	spline	NOUN
ejpam-556	255	56	.	.	PUNCT
ejpam-556	256	1	it	it	PRON
ejpam-556	256	2	is	be	AUX
ejpam-556	256	3	clear	clear	ADJ
ejpam-556	256	4	from	from	ADP
ejpam-556	256	5	figure	figure	NOUN
ejpam-556	256	6	7	7	NUM
ejpam-556	256	7	that	that	SCONJ
ejpam-556	256	8	cubic	cubic	ADJ
ejpam-556	256	9	hermite	hermite	ADJ
ejpam-556	256	10	spline	spline	NOUN
ejpam-556	256	11	loses	lose	VERB
ejpam-556	256	12	the	the	DET
ejpam-556	256	13	shape	shape	NOUN
ejpam-556	256	14	of	of	ADP
ejpam-556	256	15	data	datum	NOUN
ejpam-556	256	16	.	.	PUNCT
ejpam-556	257	1	figure	figure	NOUN
ejpam-556	257	2	8	8	NUM
ejpam-556	257	3	is	be	AUX
ejpam-556	257	4	produced	produce	VERB
ejpam-556	257	5	from	from	ADP
ejpam-556	257	6	the	the	DET
ejpam-556	257	7	same	same	ADJ
ejpam-556	257	8	data	datum	NOUN
ejpam-556	257	9	set	set	VERB
ejpam-556	257	10	using	use	VERB
ejpam-556	257	11	constrained	constrain	VERB
ejpam-556	257	12	curve	curve	NOUN
ejpam-556	257	13	data	datum	NOUN
ejpam-556	257	14	interpolation	interpolation	NOUN
ejpam-556	257	15	scheme	scheme	NOUN
ejpam-556	257	16	developed	develop	VERB
ejpam-556	257	17	in	in	ADP
ejpam-556	257	18	section	section	NOUN
ejpam-556	257	19	4	4	NUM
ejpam-556	257	20	.	.	PUNCT
ejpam-556	258	1	it	it	PRON
ejpam-556	258	2	is	be	AUX
ejpam-556	258	3	clear	clear	ADJ
ejpam-556	258	4	from	from	ADP
ejpam-556	258	5	the	the	DET
ejpam-556	258	6	figure	figure	NOUN
ejpam-556	258	7	8	8	NUM
ejpam-556	258	8	that	that	DET
ejpam-556	258	9	curve	curve	NOUN
ejpam-556	258	10	is	be	AUX
ejpam-556	258	11	lying	lie	VERB
ejpam-556	258	12	above	above	ADP
ejpam-556	258	13	the	the	DET
ejpam-556	258	14	straight	straight	ADJ
ejpam-556	258	15	line	line	NOUN
ejpam-556	259	1	y	y	NOUN
ejpam-556	259	2	=	=	PUNCT
ejpam-556	259	3	x	x	SYM
ejpam-556	259	4	2	2	NUM
ejpam-556	259	5	+	+	NUM
ejpam-556	259	6	1	1	NUM
ejpam-556	259	7	.	.	PUNCT
ejpam-556	259	8	m.	m.	NOUN
ejpam-556	259	9	z.	z.	PROPN
ejpam-556	259	10	hussain	hussain	PROPN
ejpam-556	259	11	,	,	PUNCT
ejpam-556	259	12	m.	m.	NOUN
ejpam-556	259	13	sarfraz	sarfraz	PROPN
ejpam-556	259	14	,	,	PUNCT
ejpam-556	259	15	m.	m.	NOUN
ejpam-556	259	16	hussain	hussain	PROPN
ejpam-556	259	17	/	/	SYM
ejpam-556	259	18	eur	eur	PROPN
ejpam-556	259	19	.	.	PUNCT
ejpam-556	260	1	j.	j.	PROPN
ejpam-556	260	2	pure	pure	PROPN
ejpam-556	260	3	appl	appl	PROPN
ejpam-556	260	4	.	.	PROPN
ejpam-556	260	5	math	math	PROPN
ejpam-556	260	6	,	,	PUNCT
ejpam-556	260	7	3	3	NUM
ejpam-556	260	8	(	(	PUNCT
ejpam-556	260	9	2010	2010	NUM
ejpam-556	260	10	)	)	PUNCT
ejpam-556	260	11	,	,	PUNCT
ejpam-556	260	12	194	194	NUM
ejpam-556	260	13	-	-	SYM
ejpam-556	260	14	212	212	NUM
ejpam-556	260	15	205	205	NUM
ejpam-556	260	16	0	0	NUM
ejpam-556	260	17	2	2	NUM
ejpam-556	260	18	4	4	NUM
ejpam-556	260	19	6	6	NUM
ejpam-556	260	20	8	8	NUM
ejpam-556	260	21	10	10	NUM
ejpam-556	260	22	12	12	NUM
ejpam-556	260	23	14	14	NUM
ejpam-556	260	24	16	16	NUM
ejpam-556	260	25	0	0	NUM
ejpam-556	260	26	10	10	NUM
ejpam-556	260	27	20	20	NUM
ejpam-556	260	28	30	30	NUM
ejpam-556	260	29	40	40	NUM
ejpam-556	260	30	50	50	NUM
ejpam-556	260	31	60	60	NUM
ejpam-556	260	32	70	70	NUM
ejpam-556	260	33	80	80	NUM
ejpam-556	260	34	90	90	NUM
ejpam-556	260	35	x−axis	x−axis	PUNCT
ejpam-556	260	36	y−	y−	NOUN
ejpam-556	260	37	ax	ax	NOUN
ejpam-556	260	38	is	be	AUX
ejpam-556	260	39	figure	figure	NOUN
ejpam-556	260	40	5	5	NUM
ejpam-556	260	41	:	:	PUNCT
ejpam-556	260	42	cubi	cubi	PROPN
ejpam-556	260	43	hermite	hermite	ADJ
ejpam-556	260	44	spline	spline	NOUN
ejpam-556	260	45	.	.	PUNCT
ejpam-556	261	1	0	0	NUM
ejpam-556	261	2	2	2	NUM
ejpam-556	261	3	4	4	NUM
ejpam-556	261	4	6	6	NUM
ejpam-556	261	5	8	8	NUM
ejpam-556	261	6	10	10	NUM
ejpam-556	261	7	12	12	NUM
ejpam-556	261	8	14	14	NUM
ejpam-556	261	9	16	16	NUM
ejpam-556	261	10	0	0	NUM
ejpam-556	261	11	10	10	NUM
ejpam-556	261	12	20	20	NUM
ejpam-556	261	13	30	30	NUM
ejpam-556	261	14	40	40	NUM
ejpam-556	261	15	50	50	NUM
ejpam-556	261	16	60	60	NUM
ejpam-556	261	17	70	70	NUM
ejpam-556	261	18	80	80	NUM
ejpam-556	261	19	90	90	NUM
ejpam-556	261	20	x−axis	x−axis	PUNCT
ejpam-556	261	21	y−	y−	NOUN
ejpam-556	261	22	ax	ax	NOUN
ejpam-556	261	23	is	be	AUX
ejpam-556	261	24	figure	figure	VERB
ejpam-556	261	25	6	6	NUM
ejpam-556	261	26	:	:	PUNCT
ejpam-556	261	27	constrained	constrain	VERB
ejpam-556	261	28	c1rational	c1rational	ADJ
ejpam-556	261	29	ubi	ubi	PROPN
ejpam-556	261	30	fun	fun	PROPN
ejpam-556	261	31	tion	tion	NOUN
ejpam-556	261	32	.	.	PUNCT
ejpam-556	262	1	m.	m.	NOUN
ejpam-556	262	2	z.	z.	PROPN
ejpam-556	262	3	hussain	hussain	PROPN
ejpam-556	262	4	,	,	PUNCT
ejpam-556	262	5	m.	m.	NOUN
ejpam-556	262	6	sarfraz	sarfraz	PROPN
ejpam-556	262	7	,	,	PUNCT
ejpam-556	262	8	m.	m.	NOUN
ejpam-556	262	9	hussain	hussain	PROPN
ejpam-556	262	10	/	/	SYM
ejpam-556	262	11	eur	eur	PROPN
ejpam-556	262	12	.	.	PUNCT
ejpam-556	263	1	j.	j.	PROPN
ejpam-556	263	2	pure	pure	PROPN
ejpam-556	263	3	appl	appl	PROPN
ejpam-556	263	4	.	.	PROPN
ejpam-556	263	5	math	math	PROPN
ejpam-556	263	6	,	,	PUNCT
ejpam-556	263	7	3	3	NUM
ejpam-556	263	8	(	(	PUNCT
ejpam-556	263	9	2010	2010	NUM
ejpam-556	263	10	)	)	PUNCT
ejpam-556	263	11	,	,	PUNCT
ejpam-556	263	12	194	194	NUM
ejpam-556	263	13	-	-	SYM
ejpam-556	263	14	212	212	NUM
ejpam-556	263	15	206	206	NUM
ejpam-556	263	16	2	2	NUM
ejpam-556	263	17	4	4	NUM
ejpam-556	263	18	6	6	NUM
ejpam-556	263	19	8	8	NUM
ejpam-556	263	20	10	10	NUM
ejpam-556	263	21	12	12	NUM
ejpam-556	263	22	14	14	NUM
ejpam-556	263	23	16	16	NUM
ejpam-556	263	24	2	2	NUM
ejpam-556	263	25	4	4	NUM
ejpam-556	263	26	6	6	NUM
ejpam-556	263	27	8	8	NUM
ejpam-556	263	28	10	10	NUM
ejpam-556	263	29	12	12	NUM
ejpam-556	263	30	14	14	NUM
ejpam-556	263	31	16	16	NUM
ejpam-556	263	32	18	18	NUM
ejpam-556	263	33	20	20	NUM
ejpam-556	263	34	x−axis	x−axis	PUNCT
ejpam-556	263	35	y−	y−	NOUN
ejpam-556	263	36	ax	ax	NOUN
ejpam-556	263	37	is	be	AUX
ejpam-556	263	38	figure	figure	NOUN
ejpam-556	263	39	7	7	NUM
ejpam-556	263	40	:	:	PUNCT
ejpam-556	263	41	cubi	cubi	PROPN
ejpam-556	263	42	hermite	hermite	ADJ
ejpam-556	263	43	spline	spline	NOUN
ejpam-556	263	44	.	.	PUNCT
ejpam-556	264	1	2	2	NUM
ejpam-556	264	2	4	4	NUM
ejpam-556	264	3	6	6	NUM
ejpam-556	264	4	8	8	NUM
ejpam-556	264	5	10	10	NUM
ejpam-556	264	6	12	12	NUM
ejpam-556	264	7	14	14	NUM
ejpam-556	264	8	16	16	NUM
ejpam-556	264	9	2	2	NUM
ejpam-556	264	10	4	4	NUM
ejpam-556	264	11	6	6	NUM
ejpam-556	264	12	8	8	NUM
ejpam-556	264	13	10	10	NUM
ejpam-556	264	14	12	12	NUM
ejpam-556	264	15	14	14	NUM
ejpam-556	264	16	16	16	NUM
ejpam-556	264	17	18	18	NUM
ejpam-556	264	18	20	20	NUM
ejpam-556	264	19	x−axis	x−axis	PUNCT
ejpam-556	264	20	y−	y−	NOUN
ejpam-556	264	21	ax	ax	NOUN
ejpam-556	264	22	is	be	AUX
ejpam-556	264	23	figure	figure	NOUN
ejpam-556	264	24	8	8	NUM
ejpam-556	264	25	:	:	PUNCT
ejpam-556	264	26	constrained	constrained	ADJ
ejpam-556	264	27	c1	c1	PROPN
ejpam-556	264	28	rational	rational	ADJ
ejpam-556	264	29	ubi	ubi	PROPN
ejpam-556	264	30	fun	fun	ADJ
ejpam-556	264	31	tion	tion	NOUN
ejpam-556	264	32	.	.	PUNCT
ejpam-556	265	1	m.	m.	NOUN
ejpam-556	265	2	z.	z.	PROPN
ejpam-556	265	3	hussain	hussain	PROPN
ejpam-556	265	4	,	,	PUNCT
ejpam-556	265	5	m.	m.	NOUN
ejpam-556	265	6	sarfraz	sarfraz	PROPN
ejpam-556	265	7	,	,	PUNCT
ejpam-556	265	8	m.	m.	NOUN
ejpam-556	265	9	hussain	hussain	PROPN
ejpam-556	265	10	/	/	SYM
ejpam-556	265	11	eur	eur	PROPN
ejpam-556	265	12	.	.	PUNCT
ejpam-556	266	1	j.	j.	PROPN
ejpam-556	266	2	pure	pure	PROPN
ejpam-556	266	3	appl	appl	PROPN
ejpam-556	266	4	.	.	PROPN
ejpam-556	266	5	math	math	PROPN
ejpam-556	266	6	,	,	PUNCT
ejpam-556	266	7	3	3	NUM
ejpam-556	266	8	(	(	PUNCT
ejpam-556	266	9	2010	2010	NUM
ejpam-556	266	10	)	)	PUNCT
ejpam-556	266	11	,	,	PUNCT
ejpam-556	266	12	194	194	NUM
ejpam-556	266	13	-	-	SYM
ejpam-556	266	14	212	212	NUM
ejpam-556	266	15	207	207	NUM
ejpam-556	266	16	5	5	NUM
ejpam-556	266	17	.	.	PUNCT
ejpam-556	267	1	monotonicity	monotonicity	NOUN
ejpam-556	267	2	preserving	preserve	VERB
ejpam-556	267	3	interpolation	interpolation	NOUN
ejpam-556	267	4	let	let	VERB
ejpam-556	267	5	{	{	PUNCT
ejpam-556	267	6	(	(	PUNCT
ejpam-556	267	7	x	x	PROPN
ejpam-556	267	8	i	i	PROPN
ejpam-556	267	9	,	,	PUNCT
ejpam-556	267	10	fi	fi	NOUN
ejpam-556	267	11	)	)	PUNCT
ejpam-556	267	12	,	,	PUNCT
ejpam-556	267	13	i	i	PRON
ejpam-556	267	14	=	=	NOUN
ejpam-556	267	15	0,1,2	0,1,2	NUM
ejpam-556	267	16	,	,	PUNCT
ejpam-556	267	17	.	.	PUNCT
ejpam-556	267	18	.	.	PUNCT
ejpam-556	268	1	.	.	PUNCT
ejpam-556	269	1	,	,	PUNCT
ejpam-556	269	2	n	n	CCONJ
ejpam-556	269	3	}	}	PUNCT
ejpam-556	269	4	be	be	AUX
ejpam-556	269	5	the	the	DET
ejpam-556	269	6	monotone	monotone	ADJ
ejpam-556	269	7	data	datum	NOUN
ejpam-556	269	8	defined	define	VERB
ejpam-556	269	9	over	over	ADP
ejpam-556	269	10	the	the	DET
ejpam-556	269	11	interval	interval	NOUN
ejpam-556	269	12	[	[	X
ejpam-556	269	13	a	a	X
ejpam-556	269	14	,	,	PUNCT
ejpam-556	269	15	b	b	NOUN
ejpam-556	269	16	]	]	X
ejpam-556	270	1	such	such	ADJ
ejpam-556	270	2	that	that	DET
ejpam-556	270	3	∆i	∆i	PROPN
ejpam-556	270	4	=	=	PUNCT
ejpam-556	270	5	fi+1	fi+1	NOUN
ejpam-556	271	1	−	−	PROPN
ejpam-556	272	1	fi	fi	NOUN
ejpam-556	272	2	hi	hi	INTJ
ejpam-556	272	3	>	>	X
ejpam-556	272	4	,	,	PUNCT
ejpam-556	272	5	di	di	X
ejpam-556	272	6	>	>	X
ejpam-556	272	7	0	0	PROPN
ejpam-556	272	8	,	,	PUNCT
ejpam-556	272	9	i	i	PRON
ejpam-556	272	10	=	=	NOUN
ejpam-556	272	11	0,1,2	0,1,2	NUM
ejpam-556	272	12	,	,	PUNCT
ejpam-556	272	13	.	.	PUNCT
ejpam-556	272	14	.	.	PUNCT
ejpam-556	273	1	.	.	PUNCT
ejpam-556	274	1	,	,	PUNCT
ejpam-556	274	2	n−	n−	NOUN
ejpam-556	274	3	1	1	NUM
ejpam-556	274	4	.	.	PUNCT
ejpam-556	275	1	(	(	PUNCT
ejpam-556	275	2	19	19	NUM
ejpam-556	275	3	)	)	PUNCT
ejpam-556	275	4	the	the	DET
ejpam-556	275	5	piecewise	piecewise	NOUN
ejpam-556	275	6	rational	rational	ADJ
ejpam-556	275	7	cubic	cubic	ADJ
ejpam-556	275	8	function	function	NOUN
ejpam-556	275	9	(	(	PUNCT
ejpam-556	275	10	1	1	X
ejpam-556	275	11	)	)	PUNCT
ejpam-556	275	12	preserves	preserve	VERB
ejpam-556	275	13	monotonicity	monotonicity	NOUN
ejpam-556	275	14	if	if	SCONJ
ejpam-556	275	15	s(1)(x	s(1)(x	NOUN
ejpam-556	275	16	)	)	PUNCT
ejpam-556	275	17	>	>	X
ejpam-556	275	18	0	0	NUM
ejpam-556	275	19	,	,	PUNCT
ejpam-556	275	20	i	i	PRON
ejpam-556	275	21	=	=	NOUN
ejpam-556	275	22	0,1,2	0,1,2	NUM
ejpam-556	275	23	,	,	PUNCT
ejpam-556	275	24	.	.	PUNCT
ejpam-556	275	25	.	.	PUNCT
ejpam-556	276	1	.	.	PUNCT
ejpam-556	277	1	,	,	PUNCT
ejpam-556	277	2	n−	n−	NOUN
ejpam-556	277	3	1	1	NUM
ejpam-556	277	4	,	,	PUNCT
ejpam-556	277	5	where	where	SCONJ
ejpam-556	277	6	s	s	X
ejpam-556	277	7	(	(	PUNCT
ejpam-556	277	8	1	1	NUM
ejpam-556	277	9	)	)	PUNCT
ejpam-556	277	10	i	i	PRON
ejpam-556	277	11	(	(	PUNCT
ejpam-556	277	12	x	x	X
ejpam-556	277	13	)	)	PUNCT
ejpam-556	277	14	=	=	SYM
ejpam-556	277	15	∑3	∑3	PROPN
ejpam-556	277	16	i=0(1−	i=0(1−	PROPN
ejpam-556	277	17	θ	θ	PROPN
ejpam-556	277	18	)	)	PUNCT
ejpam-556	277	19	3−iθ	3−iθ	PROPN
ejpam-556	277	20	ici	ici	NOUN
ejpam-556	277	21	(	(	PUNCT
ejpam-556	277	22	qi(θ	qi(θ	NOUN
ejpam-556	277	23	)	)	PUNCT
ejpam-556	277	24	)	)	PUNCT
ejpam-556	277	25	2	2	NUM
ejpam-556	277	26	,	,	PUNCT
ejpam-556	277	27	(	(	PUNCT
ejpam-556	277	28	20	20	NUM
ejpam-556	277	29	)	)	PUNCT
ejpam-556	277	30	c0	c0	NOUN
ejpam-556	277	31	=	=	PUNCT
ejpam-556	277	32	(	(	PUNCT
ejpam-556	277	33	αi	αi	X
ejpam-556	277	34	+	+	CCONJ
ejpam-556	277	35	1)di	1)di	PROPN
ejpam-556	277	36	,	,	PUNCT
ejpam-556	277	37	c1	c1	NOUN
ejpam-556	277	38	=	=	PUNCT
ejpam-556	277	39	(	(	PUNCT
ejpam-556	277	40	αi	αi	VERB
ejpam-556	277	41	+	+	CCONJ
ejpam-556	278	1	1){(2αi	1){(2αi	NUM
ejpam-556	279	1	+	+	CCONJ
ejpam-556	279	2	6)∆i	6)∆i	NUM
ejpam-556	279	3	−	−	NUM
ejpam-556	279	4	2di+1	2di+1	NUM
ejpam-556	279	5	−	−	PROPN
ejpam-556	279	6	di	di	NOUN
ejpam-556	279	7	}	}	PUNCT
ejpam-556	279	8	,	,	PUNCT
ejpam-556	279	9	c2	c2	PROPN
ejpam-556	279	10	=	=	PUNCT
ejpam-556	279	11	(	(	PUNCT
ejpam-556	279	12	4αi	4αi	ADJ
ejpam-556	280	1	+	+	PUNCT
ejpam-556	281	1	6)∆i	6)∆i	NUM
ejpam-556	281	2	−	−	NOUN
ejpam-556	281	3	di+1	di+1	NOUN
ejpam-556	282	1	−	−	PROPN
ejpam-556	282	2	2di	2di	ADJ
ejpam-556	282	3	,	,	PUNCT
ejpam-556	282	4	c3	c3	PROPN
ejpam-556	282	5	=	=	PUNCT
ejpam-556	282	6	di+1	di+1	PROPN
ejpam-556	282	7	.	.	PUNCT
ejpam-556	282	8	from	from	ADP
ejpam-556	282	9	(	(	PUNCT
ejpam-556	282	10	20	20	NUM
ejpam-556	282	11	)	)	PUNCT
ejpam-556	282	12	,	,	PUNCT
ejpam-556	282	13	s	s	X
ejpam-556	282	14	(	(	PUNCT
ejpam-556	282	15	1	1	NUM
ejpam-556	282	16	)	)	PUNCT
ejpam-556	282	17	i	i	PRON
ejpam-556	282	18	(	(	PUNCT
ejpam-556	282	19	x	x	X
ejpam-556	282	20	)	)	PUNCT
ejpam-556	282	21	if	if	SCONJ
ejpam-556	282	22	ci	ci	PROPN
ejpam-556	282	23	>	>	X
ejpam-556	282	24	0	0	PROPN
ejpam-556	282	25	,	,	PUNCT
ejpam-556	282	26	i	i	PRON
ejpam-556	282	27	=	=	NOUN
ejpam-556	282	28	0,1,2,3	0,1,2,3	NUM
ejpam-556	282	29	.	.	PUNCT
ejpam-556	283	1	we	we	PRON
ejpam-556	283	2	know	know	VERB
ejpam-556	283	3	that	that	SCONJ
ejpam-556	283	4	c0	c0	PROPN
ejpam-556	283	5	>	>	X
ejpam-556	283	6	0	0	PUNCT
ejpam-556	284	1	and	and	CCONJ
ejpam-556	284	2	c3	c3	X
ejpam-556	284	3	>	>	X
ejpam-556	284	4	0	0	PUNCT
ejpam-556	284	5	are	be	AUX
ejpam-556	284	6	always	always	ADV
ejpam-556	284	7	true	true	ADJ
ejpam-556	284	8	from	from	ADP
ejpam-556	284	9	the	the	DET
ejpam-556	284	10	necessary	necessary	ADJ
ejpam-556	284	11	condition	condition	NOUN
ejpam-556	284	12	of	of	ADP
ejpam-556	284	13	monotonicity	monotonicity	NOUN
ejpam-556	284	14	defined	define	VERB
ejpam-556	284	15	in	in	ADP
ejpam-556	284	16	(	(	PUNCT
ejpam-556	284	17	19	19	NUM
ejpam-556	284	18	)	)	PUNCT
ejpam-556	284	19	and	and	CCONJ
ejpam-556	284	20	αi	αi	VERB
ejpam-556	284	21	>	>	X
ejpam-556	284	22	0	0	X
ejpam-556	284	23	.	.	PUNCT
ejpam-556	285	1	one	one	PRON
ejpam-556	285	2	can	can	AUX
ejpam-556	285	3	see	see	VERB
ejpam-556	285	4	that	that	DET
ejpam-556	285	5	c1	c1	PROPN
ejpam-556	285	6	>	>	X
ejpam-556	285	7	0	0	PUNCT
ejpam-556	286	1	if	if	SCONJ
ejpam-556	286	2	αi	αi	ADV
ejpam-556	286	3	>	>	X
ejpam-556	286	4	max	max	PROPN
ejpam-556	286	5	�	�	PROPN
ejpam-556	286	6	0	0	NUM
ejpam-556	286	7	,	,	PUNCT
ejpam-556	286	8	2di+1	2di+1	NUM
ejpam-556	286	9	+	+	NOUN
ejpam-556	286	10	di	di	X
ejpam-556	286	11	2∆i	2∆i	NUM
ejpam-556	286	12	�	�	PROPN
ejpam-556	286	13	.	.	PUNCT
ejpam-556	287	1	similarly	similarly	ADV
ejpam-556	287	2	,	,	PUNCT
ejpam-556	287	3	c2	c2	PROPN
ejpam-556	287	4	>	>	X
ejpam-556	287	5	0	0	PUNCT
ejpam-556	288	1	if	if	SCONJ
ejpam-556	288	2	αi	αi	ADV
ejpam-556	288	3	>	>	X
ejpam-556	288	4	max	max	PROPN
ejpam-556	288	5	�	�	PROPN
ejpam-556	288	6	0	0	NUM
ejpam-556	288	7	,	,	PUNCT
ejpam-556	288	8	di+1	di+1	ADJ
ejpam-556	289	1	+	+	CCONJ
ejpam-556	289	2	2di	2di	ADJ
ejpam-556	289	3	4∆i	4∆i	NUM
ejpam-556	289	4	�	�	PROPN
ejpam-556	289	5	.	.	PUNCT
ejpam-556	290	1	the	the	DET
ejpam-556	290	2	above	above	ADJ
ejpam-556	290	3	can	can	AUX
ejpam-556	290	4	be	be	AUX
ejpam-556	290	5	summarized	summarize	VERB
ejpam-556	290	6	as	as	ADP
ejpam-556	290	7	:	:	PUNCT
ejpam-556	290	8	theorem	theorem	NOUN
ejpam-556	290	9	5	5	NUM
ejpam-556	290	10	.	.	PUNCT
ejpam-556	291	1	the	the	DET
ejpam-556	291	2	piecewise	piecewise	PROPN
ejpam-556	291	3	c1	c1	PROPN
ejpam-556	291	4	rational	rational	ADJ
ejpam-556	291	5	cubic	cubic	ADJ
ejpam-556	291	6	interpolant	interpolant	NOUN
ejpam-556	291	7	s(x	s(x	PROPN
ejpam-556	291	8	)	)	PUNCT
ejpam-556	291	9	,	,	PUNCT
ejpam-556	291	10	defined	define	VERB
ejpam-556	291	11	over	over	ADP
ejpam-556	291	12	the	the	DET
ejpam-556	291	13	interval	interval	NOUN
ejpam-556	291	14	[	[	X
ejpam-556	291	15	a	a	X
ejpam-556	291	16	,	,	PUNCT
ejpam-556	291	17	b	b	NOUN
ejpam-556	291	18	]	]	X
ejpam-556	291	19	,	,	PUNCT
ejpam-556	291	20	in	in	ADP
ejpam-556	291	21	(	(	PUNCT
ejpam-556	291	22	1	1	NUM
ejpam-556	291	23	)	)	PUNCT
ejpam-556	291	24	,	,	PUNCT
ejpam-556	291	25	is	be	AUX
ejpam-556	291	26	monotone	monotone	ADJ
ejpam-556	291	27	if	if	SCONJ
ejpam-556	291	28	in	in	ADP
ejpam-556	291	29	each	each	DET
ejpam-556	291	30	subinterval	subinterval	NOUN
ejpam-556	291	31	ii	ii	NOUN
ejpam-556	292	1	=	=	PUNCT
ejpam-556	293	1	[	[	X
ejpam-556	293	2	x	x	X
ejpam-556	293	3	i	i	NOUN
ejpam-556	293	4	,	,	PUNCT
ejpam-556	293	5	x	x	PROPN
ejpam-556	293	6	i+1	i+1	VERB
ejpam-556	293	7	]	]	X
ejpam-556	293	8	the	the	DET
ejpam-556	293	9	following	follow	VERB
ejpam-556	293	10	sufficient	sufficient	ADJ
ejpam-556	293	11	conditions	condition	NOUN
ejpam-556	293	12	are	be	AUX
ejpam-556	293	13	satisfied	satisfied	ADJ
ejpam-556	293	14	:	:	PUNCT
ejpam-556	293	15	αi	αi	VERB
ejpam-556	293	16	>	>	X
ejpam-556	293	17	max	max	PROPN
ejpam-556	293	18	�	�	PROPN
ejpam-556	293	19	0	0	NUM
ejpam-556	293	20	,	,	PUNCT
ejpam-556	293	21	2di+1	2di+1	NUM
ejpam-556	293	22	+	+	X
ejpam-556	293	23	di	di	X
ejpam-556	293	24	2∆i	2∆i	NUM
ejpam-556	293	25	,	,	PUNCT
ejpam-556	293	26	di+1	di+1	PROPN
ejpam-556	294	1	+	+	CCONJ
ejpam-556	294	2	2di	2di	ADJ
ejpam-556	294	3	4∆i	4∆i	NUM
ejpam-556	294	4	�	�	PROPN
ejpam-556	294	5	.	.	PUNCT
ejpam-556	295	1	the	the	DET
ejpam-556	295	2	above	above	ADJ
ejpam-556	295	3	constraints	constraint	NOUN
ejpam-556	295	4	can	can	AUX
ejpam-556	295	5	be	be	AUX
ejpam-556	295	6	rearranged	rearrange	VERB
ejpam-556	295	7	as	as	ADP
ejpam-556	295	8	:	:	PUNCT
ejpam-556	295	9	αi	αi	PROPN
ejpam-556	296	1	=	=	SYM
ejpam-556	296	2	mi	mi	PROPN
ejpam-556	297	1	+	+	PROPN
ejpam-556	297	2	max	max	PROPN
ejpam-556	297	3	�	�	PROPN
ejpam-556	297	4	0	0	NUM
ejpam-556	297	5	,	,	PUNCT
ejpam-556	297	6	2di+1	2di+1	NUM
ejpam-556	297	7	+	+	X
ejpam-556	297	8	di	di	X
ejpam-556	297	9	2∆i	2∆i	NUM
ejpam-556	297	10	,	,	PUNCT
ejpam-556	297	11	di+1	di+1	PROPN
ejpam-556	297	12	+	+	CCONJ
ejpam-556	297	13	2di	2di	ADJ
ejpam-556	297	14	4∆i	4∆i	NUM
ejpam-556	297	15	�	�	PROPN
ejpam-556	297	16	,	,	PUNCT
ejpam-556	297	17	mi	mi	PROPN
ejpam-556	297	18	>	>	X
ejpam-556	297	19	0	0	PROPN
ejpam-556	297	20	.	.	PUNCT
ejpam-556	298	1	thus	thus	ADV
ejpam-556	298	2	we	we	PRON
ejpam-556	298	3	have	have	VERB
ejpam-556	298	4	the	the	DET
ejpam-556	298	5	following	follow	VERB
ejpam-556	298	6	algorithm	algorithm	NOUN
ejpam-556	298	7	for	for	ADP
ejpam-556	298	8	the	the	DET
ejpam-556	298	9	manipulation	manipulation	NOUN
ejpam-556	298	10	of	of	ADP
ejpam-556	298	11	curve	curve	NOUN
ejpam-556	298	12	design	design	NOUN
ejpam-556	298	13	.	.	PUNCT
ejpam-556	299	1	m.	m.	NOUN
ejpam-556	299	2	z.	z.	PROPN
ejpam-556	299	3	hussain	hussain	PROPN
ejpam-556	299	4	,	,	PUNCT
ejpam-556	299	5	m.	m.	NOUN
ejpam-556	299	6	sarfraz	sarfraz	PROPN
ejpam-556	299	7	,	,	PUNCT
ejpam-556	299	8	m.	m.	NOUN
ejpam-556	299	9	hussain	hussain	PROPN
ejpam-556	299	10	/	/	SYM
ejpam-556	299	11	eur	eur	PROPN
ejpam-556	299	12	.	.	PUNCT
ejpam-556	300	1	j.	j.	PROPN
ejpam-556	300	2	pure	pure	PROPN
ejpam-556	300	3	appl	appl	PROPN
ejpam-556	300	4	.	.	PROPN
ejpam-556	300	5	math	math	PROPN
ejpam-556	300	6	,	,	PUNCT
ejpam-556	300	7	3	3	NUM
ejpam-556	300	8	(	(	PUNCT
ejpam-556	300	9	2010	2010	NUM
ejpam-556	300	10	)	)	PUNCT
ejpam-556	300	11	,	,	PUNCT
ejpam-556	300	12	194	194	NUM
ejpam-556	300	13	-	-	SYM
ejpam-556	300	14	212	212	NUM
ejpam-556	300	15	208	208	NUM
ejpam-556	300	16	algorithm	algorithm	NOUN
ejpam-556	300	17	3	3	NUM
ejpam-556	300	18	step	step	NOUN
ejpam-556	300	19	1	1	NUM
ejpam-556	300	20	.	.	PUNCT
ejpam-556	300	21	enter	enter	VERB
ejpam-556	300	22	the	the	DET
ejpam-556	300	23	(	(	PUNCT
ejpam-556	300	24	n+	n+	NOUN
ejpam-556	300	25	1	1	NUM
ejpam-556	300	26	)	)	PUNCT
ejpam-556	300	27	points	point	NOUN
ejpam-556	300	28	{	{	PUNCT
ejpam-556	300	29	(	(	PUNCT
ejpam-556	300	30	x	x	SYM
ejpam-556	300	31	i	i	PROPN
ejpam-556	300	32	,	,	PUNCT
ejpam-556	300	33	fi	fi	NOUN
ejpam-556	300	34	)	)	PUNCT
ejpam-556	300	35	:	:	PUNCT
ejpam-556	301	1	i	i	PRON
ejpam-556	301	2	=	=	NOUN
ejpam-556	301	3	0,1,2	0,1,2	NUM
ejpam-556	301	4	,	,	PUNCT
ejpam-556	301	5	.	.	PUNCT
ejpam-556	301	6	.	.	PUNCT
ejpam-556	301	7	.	.	PUNCT
ejpam-556	301	8	,	,	PUNCT
ejpam-556	301	9	n	n	CCONJ
ejpam-556	301	10	}	}	PUNCT
ejpam-556	301	11	.	.	PUNCT
ejpam-556	302	1	step	step	NOUN
ejpam-556	302	2	2	2	NUM
ejpam-556	302	3	.	.	NUM
ejpam-556	302	4	estimate	estimate	VERB
ejpam-556	302	5	the	the	DET
ejpam-556	302	6	first	first	ADJ
ejpam-556	302	7	order	order	NOUN
ejpam-556	302	8	derivatives	derivative	NOUN
ejpam-556	302	9	di	di	X
ejpam-556	302	10	,	,	PUNCT
ejpam-556	302	11	i	i	PRON
ejpam-556	302	12	=	=	NOUN
ejpam-556	302	13	0,1,2	0,1,2	NUM
ejpam-556	302	14	,	,	PUNCT
ejpam-556	302	15	.	.	PUNCT
ejpam-556	302	16	.	.	PUNCT
ejpam-556	303	1	.	.	PUNCT
ejpam-556	304	1	,	,	PUNCT
ejpam-556	304	2	n	n	CCONJ
ejpam-556	304	3	at	at	ADP
ejpam-556	304	4	knots	knot	NOUN
ejpam-556	304	5	.	.	PUNCT
ejpam-556	305	1	(	(	PUNCT
ejpam-556	305	2	note	note	VERB
ejpam-556	305	3	:	:	PUNCT
ejpam-556	305	4	the	the	DET
ejpam-556	305	5	step	step	NOUN
ejpam-556	305	6	2	2	NUM
ejpam-556	305	7	is	be	AUX
ejpam-556	305	8	only	only	ADV
ejpam-556	305	9	applicable	applicable	ADJ
ejpam-556	305	10	if	if	SCONJ
ejpam-556	305	11	data	datum	NOUN
ejpam-556	305	12	is	be	AUX
ejpam-556	305	13	not	not	PART
ejpam-556	305	14	provided	provide	VERB
ejpam-556	305	15	with	with	ADP
ejpam-556	305	16	derivatives	derivative	NOUN
ejpam-556	305	17	)	)	PUNCT
ejpam-556	305	18	.	.	PUNCT
ejpam-556	306	1	step	step	NOUN
ejpam-556	306	2	3	3	NUM
ejpam-556	306	3	.	.	PUNCT
ejpam-556	306	4	calculate	calculate	VERB
ejpam-556	306	5	the	the	DET
ejpam-556	306	6	value	value	NOUN
ejpam-556	306	7	of	of	ADP
ejpam-556	306	8	free	free	ADJ
ejpam-556	306	9	parameter	parameter	NOUN
ejpam-556	306	10	αi	αi	NOUN
ejpam-556	306	11	using	use	VERB
ejpam-556	306	12	theorem	theorem	NOUN
ejpam-556	306	13	5	5	NUM
ejpam-556	306	14	.	.	NOUN
ejpam-556	306	15	step	step	NOUN
ejpam-556	306	16	4	4	NUM
ejpam-556	306	17	.	.	PUNCT
ejpam-556	307	1	if	if	SCONJ
ejpam-556	307	2	∆i	∆i	PROPN
ejpam-556	307	3	>	>	X
ejpam-556	307	4	0	0	PUNCT
ejpam-556	307	5	then	then	ADV
ejpam-556	307	6	di	di	X
ejpam-556	307	7	=	=	SYM
ejpam-556	307	8	0	0	NUM
ejpam-556	307	9	s(x)≡	s(x)≡	NOUN
ejpam-556	307	10	si(x	si(x	NOUN
ejpam-556	307	11	)	)	PUNCT
ejpam-556	308	1	=	=	SYM
ejpam-556	308	2	fi	fi	NOUN
ejpam-556	308	3	else	else	ADV
ejpam-556	308	4	s(x)≡	s(x)≡	NOUN
ejpam-556	308	5	si(x	si(x	X
ejpam-556	308	6	)	)	PUNCT
ejpam-556	308	7	=	=	SYM
ejpam-556	308	8	pi(θ	pi(θ	NOUN
ejpam-556	308	9	)	)	PUNCT
ejpam-556	308	10	qi(θ	qi(θ	PUNCT
ejpam-556	308	11	)	)	PUNCT
ejpam-556	308	12	end	end	VERB
ejpam-556	308	13	5.1	5.1	NUM
ejpam-556	308	14	.	.	PUNCT
ejpam-556	309	1	demonstration	demonstration	NOUN
ejpam-556	309	2	table	table	NOUN
ejpam-556	309	3	5	5	NUM
ejpam-556	309	4	:	:	PUNCT
ejpam-556	309	5	a	a	DET
ejpam-556	309	6	monotone	monotone	ADJ
ejpam-556	309	7	data	datum	NOUN
ejpam-556	309	8	set	set	VERB
ejpam-556	309	9	.	.	PUNCT
ejpam-556	310	1	x	x	PUNCT
ejpam-556	310	2	4.0	4.0	NUM
ejpam-556	310	3	6.0	6.0	NUM
ejpam-556	310	4	7.0	7.0	NUM
ejpam-556	310	5	f	f	PROPN
ejpam-556	310	6	3.9	3.9	NUM
ejpam-556	310	7	4.2	4.2	NUM
ejpam-556	310	8	5.7	5.7	NUM
ejpam-556	310	9	example	example	NOUN
ejpam-556	310	10	5	5	NUM
ejpam-556	310	11	.	.	PUNCT
ejpam-556	311	1	a	a	DET
ejpam-556	311	2	monotone	monotone	ADJ
ejpam-556	311	3	data	datum	NOUN
ejpam-556	311	4	set	set	VERB
ejpam-556	311	5	is	be	AUX
ejpam-556	311	6	taken	take	VERB
ejpam-556	311	7	in	in	ADP
ejpam-556	311	8	table	table	NOUN
ejpam-556	311	9	5	5	NUM
ejpam-556	311	10	.	.	PUNCT
ejpam-556	312	1	non	non	ADJ
ejpam-556	312	2	-	-	ADJ
ejpam-556	312	3	monotone	monotone	ADJ
ejpam-556	312	4	curve	curve	NOUN
ejpam-556	312	5	in	in	ADP
ejpam-556	312	6	figure	figure	NOUN
ejpam-556	312	7	9	9	NUM
ejpam-556	312	8	is	be	AUX
ejpam-556	312	9	produced	produce	VERB
ejpam-556	312	10	from	from	ADP
ejpam-556	312	11	the	the	DET
ejpam-556	312	12	monotone	monotone	ADJ
ejpam-556	312	13	data	datum	NOUN
ejpam-556	312	14	set	set	VERB
ejpam-556	312	15	taken	take	VERB
ejpam-556	312	16	in	in	ADP
ejpam-556	312	17	table	table	NOUN
ejpam-556	312	18	5	5	NUM
ejpam-556	312	19	using	use	VERB
ejpam-556	312	20	cubic	cubic	ADJ
ejpam-556	312	21	hermite	hermite	ADJ
ejpam-556	312	22	spline	spline	NOUN
ejpam-556	312	23	.	.	PUNCT
ejpam-556	313	1	the	the	DET
ejpam-556	313	2	monotone	monotone	ADJ
ejpam-556	313	3	curve	curve	NOUN
ejpam-556	313	4	(	(	PUNCT
ejpam-556	313	5	from	from	ADP
ejpam-556	313	6	the	the	DET
ejpam-556	313	7	same	same	ADJ
ejpam-556	313	8	data	datum	NOUN
ejpam-556	313	9	set	set	NOUN
ejpam-556	313	10	)	)	PUNCT
ejpam-556	313	11	is	be	AUX
ejpam-556	313	12	produced	produce	VERB
ejpam-556	313	13	in	in	ADP
ejpam-556	313	14	figure	figure	NOUN
ejpam-556	313	15	10	10	NUM
ejpam-556	313	16	using	use	VERB
ejpam-556	313	17	monotonicity	monotonicity	NOUN
ejpam-556	313	18	preserving	preserve	VERB
ejpam-556	313	19	scheme	scheme	NOUN
ejpam-556	313	20	developed	develop	VERB
ejpam-556	313	21	in	in	ADP
ejpam-556	313	22	section	section	NOUN
ejpam-556	313	23	5	5	NUM
ejpam-556	313	24	.	.	PUNCT
ejpam-556	313	25	table	table	NOUN
ejpam-556	313	26	6	6	NUM
ejpam-556	313	27	:	:	PUNCT
ejpam-556	313	28	a	a	DET
ejpam-556	313	29	monotone	monotone	ADJ
ejpam-556	313	30	data	datum	NOUN
ejpam-556	313	31	set	set	VERB
ejpam-556	313	32	.	.	PUNCT
ejpam-556	314	1	x	x	PUNCT
ejpam-556	314	2	1710	1710	NUM
ejpam-556	314	3	2650	2650	NUM
ejpam-556	314	4	2760	2760	NUM
ejpam-556	315	1	f	f	NOUN
ejpam-556	315	2	500	500	NUM
ejpam-556	315	3	1360	1360	NUM
ejpam-556	315	4	2940	2940	NUM
ejpam-556	315	5	example	example	NOUN
ejpam-556	315	6	6	6	NUM
ejpam-556	315	7	.	.	PUNCT
ejpam-556	316	1	a	a	DET
ejpam-556	316	2	monotone	monotone	ADJ
ejpam-556	316	3	data	datum	NOUN
ejpam-556	316	4	set	set	VERB
ejpam-556	316	5	is	be	AUX
ejpam-556	316	6	taken	take	VERB
ejpam-556	316	7	in	in	ADP
ejpam-556	316	8	table	table	NOUN
ejpam-556	316	9	6	6	NUM
ejpam-556	316	10	.	.	PUNCT
ejpam-556	317	1	the	the	DET
ejpam-556	317	2	figure	figure	NOUN
ejpam-556	317	3	11	11	NUM
ejpam-556	317	4	is	be	AUX
ejpam-556	317	5	produced	produce	VERB
ejpam-556	317	6	from	from	ADP
ejpam-556	317	7	the	the	DET
ejpam-556	317	8	monotone	monotone	ADJ
ejpam-556	317	9	data	datum	NOUN
ejpam-556	317	10	set	set	VERB
ejpam-556	317	11	taken	take	VERB
ejpam-556	317	12	in	in	ADP
ejpam-556	317	13	table	table	NOUN
ejpam-556	317	14	6	6	NUM
ejpam-556	317	15	using	use	VERB
ejpam-556	317	16	cubic	cubic	ADJ
ejpam-556	317	17	hermite	hermite	ADJ
ejpam-556	317	18	spline	spline	NOUN
ejpam-556	317	19	which	which	PRON
ejpam-556	317	20	loses	lose	VERB
ejpam-556	317	21	the	the	DET
ejpam-556	317	22	monotone	monotone	ADJ
ejpam-556	317	23	shape	shape	NOUN
ejpam-556	317	24	of	of	ADP
ejpam-556	317	25	data	datum	NOUN
ejpam-556	317	26	.	.	PUNCT
ejpam-556	318	1	monotone	monotone	ADJ
ejpam-556	318	2	curve	curve	NOUN
ejpam-556	318	3	in	in	ADP
ejpam-556	318	4	figure	figure	NOUN
ejpam-556	318	5	12	12	NUM
ejpam-556	318	6	is	be	AUX
ejpam-556	318	7	produced	produce	VERB
ejpam-556	318	8	using	use	VERB
ejpam-556	318	9	the	the	DET
ejpam-556	318	10	monotonicity	monotonicity	NOUN
ejpam-556	318	11	preserving	preserve	VERB
ejpam-556	318	12	scheme	scheme	NOUN
ejpam-556	318	13	developed	develop	VERB
ejpam-556	318	14	in	in	ADP
ejpam-556	318	15	section	section	NOUN
ejpam-556	318	16	5	5	NUM
ejpam-556	318	17	.	.	PUNCT
ejpam-556	318	18	m.	m.	NOUN
ejpam-556	318	19	z.	z.	PROPN
ejpam-556	318	20	hussain	hussain	PROPN
ejpam-556	318	21	,	,	PUNCT
ejpam-556	318	22	m.	m.	NOUN
ejpam-556	318	23	sarfraz	sarfraz	PROPN
ejpam-556	318	24	,	,	PUNCT
ejpam-556	318	25	m.	m.	NOUN
ejpam-556	318	26	hussain	hussain	PROPN
ejpam-556	318	27	/	/	SYM
ejpam-556	318	28	eur	eur	PROPN
ejpam-556	318	29	.	.	PUNCT
ejpam-556	319	1	j.	j.	PROPN
ejpam-556	319	2	pure	pure	PROPN
ejpam-556	319	3	appl	appl	PROPN
ejpam-556	319	4	.	.	PROPN
ejpam-556	319	5	math	math	PROPN
ejpam-556	319	6	,	,	PUNCT
ejpam-556	319	7	3	3	NUM
ejpam-556	319	8	(	(	PUNCT
ejpam-556	319	9	2010	2010	NUM
ejpam-556	319	10	)	)	PUNCT
ejpam-556	319	11	,	,	PUNCT
ejpam-556	319	12	194	194	NUM
ejpam-556	319	13	-	-	SYM
ejpam-556	319	14	212	212	NUM
ejpam-556	319	15	209	209	NUM
ejpam-556	319	16	4	4	NUM
ejpam-556	319	17	4.5	4.5	NUM
ejpam-556	319	18	5	5	NUM
ejpam-556	319	19	5.5	5.5	NUM
ejpam-556	319	20	6	6	NUM
ejpam-556	319	21	6.5	6.5	NUM
ejpam-556	319	22	7	7	NUM
ejpam-556	319	23	7.5	7.5	NUM
ejpam-556	319	24	3.5	3.5	NUM
ejpam-556	319	25	4	4	NUM
ejpam-556	319	26	4.5	4.5	NUM
ejpam-556	319	27	5	5	NUM
ejpam-556	319	28	5.5	5.5	NUM
ejpam-556	319	29	6	6	NUM
ejpam-556	319	30	x−axis	x−axis	PUNCT
ejpam-556	319	31	y−	y−	NOUN
ejpam-556	319	32	ax	ax	NOUN
ejpam-556	319	33	is	be	AUX
ejpam-556	319	34	figure	figure	NOUN
ejpam-556	319	35	9	9	NUM
ejpam-556	319	36	:	:	PUNCT
ejpam-556	319	37	cubi	cubi	PROPN
ejpam-556	319	38	hermite	hermite	ADJ
ejpam-556	319	39	spline	spline	NOUN
ejpam-556	319	40	.	.	PUNCT
ejpam-556	320	1	4	4	NUM
ejpam-556	320	2	4.5	4.5	NUM
ejpam-556	320	3	5	5	NUM
ejpam-556	320	4	5.5	5.5	NUM
ejpam-556	320	5	6	6	NUM
ejpam-556	320	6	6.5	6.5	NUM
ejpam-556	320	7	7	7	NUM
ejpam-556	320	8	7.5	7.5	NUM
ejpam-556	320	9	3.5	3.5	NUM
ejpam-556	320	10	4	4	NUM
ejpam-556	320	11	4.5	4.5	NUM
ejpam-556	320	12	5	5	NUM
ejpam-556	320	13	5.5	5.5	NUM
ejpam-556	320	14	6	6	NUM
ejpam-556	320	15	x−axis	x−axis	PUNCT
ejpam-556	320	16	y−	y−	NOUN
ejpam-556	320	17	ax	ax	NOUN
ejpam-556	320	18	is	be	AUX
ejpam-556	320	19	figure	figure	NOUN
ejpam-556	320	20	10	10	NUM
ejpam-556	320	21	:	:	PUNCT
ejpam-556	320	22	monotone	monotone	ADJ
ejpam-556	320	23	c1	c1	PROPN
ejpam-556	320	24	rational	rational	ADJ
ejpam-556	320	25	ubi	ubi	PROPN
ejpam-556	320	26	fun	fun	ADJ
ejpam-556	320	27	tion	tion	NOUN
ejpam-556	320	28	.	.	PUNCT
ejpam-556	321	1	m.	m.	NOUN
ejpam-556	321	2	z.	z.	PROPN
ejpam-556	321	3	hussain	hussain	PROPN
ejpam-556	321	4	,	,	PUNCT
ejpam-556	321	5	m.	m.	NOUN
ejpam-556	321	6	sarfraz	sarfraz	PROPN
ejpam-556	321	7	,	,	PUNCT
ejpam-556	321	8	m.	m.	NOUN
ejpam-556	321	9	hussain	hussain	PROPN
ejpam-556	321	10	/	/	SYM
ejpam-556	321	11	eur	eur	PROPN
ejpam-556	321	12	.	.	PUNCT
ejpam-556	322	1	j.	j.	PROPN
ejpam-556	322	2	pure	pure	PROPN
ejpam-556	322	3	appl	appl	PROPN
ejpam-556	322	4	.	.	PROPN
ejpam-556	322	5	math	math	PROPN
ejpam-556	322	6	,	,	PUNCT
ejpam-556	322	7	3	3	NUM
ejpam-556	322	8	(	(	PUNCT
ejpam-556	322	9	2010	2010	NUM
ejpam-556	322	10	)	)	PUNCT
ejpam-556	322	11	,	,	PUNCT
ejpam-556	322	12	194	194	NUM
ejpam-556	322	13	-	-	SYM
ejpam-556	322	14	212	212	NUM
ejpam-556	322	15	210	210	NUM
ejpam-556	322	16	1600	1600	NUM
ejpam-556	322	17	1800	1800	NUM
ejpam-556	322	18	2000	2000	NUM
ejpam-556	322	19	2200	2200	NUM
ejpam-556	322	20	2400	2400	NUM
ejpam-556	322	21	2600	2600	NUM
ejpam-556	322	22	2800	2800	NUM
ejpam-556	322	23	−4000	−4000	PROPN
ejpam-556	322	24	−3000	−3000	PROPN
ejpam-556	323	1	−2000	−2000	PROPN
ejpam-556	323	2	−1000	−1000	NOUN
ejpam-556	323	3	0	0	NUM
ejpam-556	323	4	1000	1000	NUM
ejpam-556	323	5	2000	2000	NUM
ejpam-556	323	6	3000	3000	NUM
ejpam-556	323	7	x−axis	x−axis	PUNCT
ejpam-556	324	1	y−	y−	NOUN
ejpam-556	324	2	ax	ax	NOUN
ejpam-556	324	3	is	be	AUX
ejpam-556	324	4	figure	figure	NOUN
ejpam-556	324	5	11	11	NUM
ejpam-556	324	6	:	:	PUNCT
ejpam-556	324	7	cubi	cubi	PROPN
ejpam-556	324	8	hermite	hermite	ADJ
ejpam-556	324	9	spline	spline	NOUN
ejpam-556	324	10	.	.	PUNCT
ejpam-556	325	1	1600	1600	NUM
ejpam-556	325	2	1800	1800	NUM
ejpam-556	325	3	2000	2000	NUM
ejpam-556	325	4	2200	2200	NUM
ejpam-556	325	5	2400	2400	NUM
ejpam-556	325	6	2600	2600	NUM
ejpam-556	325	7	2800	2800	NUM
ejpam-556	325	8	500	500	NUM
ejpam-556	325	9	1000	1000	NUM
ejpam-556	325	10	1500	1500	NUM
ejpam-556	325	11	2000	2000	NUM
ejpam-556	325	12	2500	2500	NUM
ejpam-556	325	13	3000	3000	NUM
ejpam-556	325	14	x−axis	x−axis	PUNCT
ejpam-556	326	1	y−	y−	NOUN
ejpam-556	326	2	ax	ax	NOUN
ejpam-556	326	3	is	be	AUX
ejpam-556	326	4	figure	figure	NOUN
ejpam-556	326	5	12	12	NUM
ejpam-556	326	6	:	:	PUNCT
ejpam-556	326	7	monotone	monotone	ADJ
ejpam-556	326	8	c1rational	c1rational	ADJ
ejpam-556	326	9	ubi	ubi	PROPN
ejpam-556	326	10	fun	fun	PROPN
ejpam-556	326	11	tion	tion	NOUN
ejpam-556	326	12	.	.	PUNCT
ejpam-556	327	1	references	reference	NOUN
ejpam-556	327	2	211	211	NUM
ejpam-556	327	3	6	6	NUM
ejpam-556	327	4	.	.	PUNCT
ejpam-556	327	5	conclusion	conclusion	VERB
ejpam-556	327	6	the	the	DET
ejpam-556	327	7	work	work	NOUN
ejpam-556	327	8	in	in	ADP
ejpam-556	327	9	this	this	DET
ejpam-556	327	10	paper	paper	NOUN
ejpam-556	327	11	is	be	AUX
ejpam-556	327	12	concerned	concern	VERB
ejpam-556	327	13	to	to	ADP
ejpam-556	327	14	the	the	DET
ejpam-556	327	15	development	development	NOUN
ejpam-556	327	16	of	of	ADP
ejpam-556	327	17	shape	shape	NOUN
ejpam-556	327	18	preserving	preserve	VERB
ejpam-556	327	19	interpolating	interpolate	VERB
ejpam-556	327	20	schemes	scheme	NOUN
ejpam-556	327	21	.	.	PUNCT
ejpam-556	328	1	the	the	DET
ejpam-556	328	2	developed	develop	VERB
ejpam-556	328	3	schemes	scheme	NOUN
ejpam-556	328	4	have	have	VERB
ejpam-556	328	5	the	the	DET
ejpam-556	328	6	following	follow	VERB
ejpam-556	328	7	advantageous	advantageous	ADJ
ejpam-556	328	8	features	feature	NOUN
ejpam-556	328	9	over	over	ADP
ejpam-556	328	10	the	the	DET
ejpam-556	328	11	existing	exist	VERB
ejpam-556	328	12	schemes	scheme	NOUN
ejpam-556	328	13	.	.	PUNCT
ejpam-556	329	1	these	these	PRON
ejpam-556	329	2	are	be	AUX
ejpam-556	329	3	equally	equally	ADV
ejpam-556	329	4	worthy	worthy	ADJ
ejpam-556	329	5	for	for	ADP
ejpam-556	329	6	data	datum	NOUN
ejpam-556	329	7	with	with	ADP
ejpam-556	329	8	and	and	CCONJ
ejpam-556	329	9	without	without	ADP
ejpam-556	329	10	derivatives	derivative	NOUN
ejpam-556	329	11	,	,	PUNCT
ejpam-556	329	12	whereas	whereas	SCONJ
ejpam-556	329	13	,	,	PUNCT
ejpam-556	329	14	authors	author	NOUN
ejpam-556	329	15	in	in	ADP
ejpam-556	329	16	[	[	X
ejpam-556	329	17	15	15	NUM
ejpam-556	329	18	]	]	PUNCT
ejpam-556	329	19	had	have	VERB
ejpam-556	329	20	to	to	PART
ejpam-556	329	21	constrain	constrain	VERB
ejpam-556	329	22	derivatives	derivative	NOUN
ejpam-556	329	23	at	at	ADP
ejpam-556	329	24	knots	knot	NOUN
ejpam-556	329	25	to	to	PART
ejpam-556	329	26	preserve	preserve	VERB
ejpam-556	329	27	the	the	DET
ejpam-556	329	28	shape	shape	NOUN
ejpam-556	329	29	of	of	ADP
ejpam-556	329	30	positive	positive	ADJ
ejpam-556	329	31	data	datum	NOUN
ejpam-556	329	32	.	.	PUNCT
ejpam-556	330	1	the	the	DET
ejpam-556	330	2	developed	develop	VERB
ejpam-556	330	3	schemers	schemer	NOUN
ejpam-556	330	4	are	be	AUX
ejpam-556	330	5	based	base	VERB
ejpam-556	330	6	on	on	ADP
ejpam-556	330	7	automated	automate	VERB
ejpam-556	330	8	selection	selection	NOUN
ejpam-556	330	9	of	of	ADP
ejpam-556	330	10	free	free	ADJ
ejpam-556	330	11	parameters	parameter	NOUN
ejpam-556	330	12	thus	thus	ADV
ejpam-556	330	13	do	do	AUX
ejpam-556	330	14	not	not	PART
ejpam-556	330	15	require	require	VERB
ejpam-556	330	16	the	the	DET
ejpam-556	330	17	modification	modification	NOUN
ejpam-556	330	18	of	of	ADP
ejpam-556	330	19	data	datum	NOUN
ejpam-556	330	20	.	.	PUNCT
ejpam-556	331	1	but	but	CCONJ
ejpam-556	331	2	,	,	PUNCT
ejpam-556	331	3	the	the	DET
ejpam-556	331	4	authors	author	NOUN
ejpam-556	331	5	in	in	ADP
ejpam-556	331	6	[	[	X
ejpam-556	331	7	3	3	NUM
ejpam-556	331	8	,	,	PUNCT
ejpam-556	331	9	7	7	NUM
ejpam-556	331	10	,	,	PUNCT
ejpam-556	331	11	12	12	NUM
ejpam-556	331	12	]	]	PUNCT
ejpam-556	331	13	constrained	constrain	VERB
ejpam-556	331	14	the	the	DET
ejpam-556	331	15	interval	interval	NOUN
ejpam-556	331	16	length	length	NOUN
ejpam-556	331	17	to	to	PART
ejpam-556	331	18	preserve	preserve	VERB
ejpam-556	331	19	the	the	DET
ejpam-556	331	20	shape	shape	NOUN
ejpam-556	331	21	of	of	ADP
ejpam-556	331	22	data	datum	NOUN
ejpam-556	331	23	.	.	PUNCT
ejpam-556	332	1	in	in	ADP
ejpam-556	332	2	[	[	X
ejpam-556	332	3	13	13	NUM
ejpam-556	332	4	]	]	PUNCT
ejpam-556	332	5	and	and	CCONJ
ejpam-556	332	6	[	[	X
ejpam-556	332	7	10	10	NUM
ejpam-556	332	8	-	-	SYM
ejpam-556	332	9	11	11	NUM
ejpam-556	332	10	]	]	PUNCT
ejpam-556	332	11	,	,	PUNCT
ejpam-556	332	12	rational	rational	ADJ
ejpam-556	332	13	functions	function	NOUN
ejpam-556	332	14	with	with	ADP
ejpam-556	332	15	two	two	NUM
ejpam-556	332	16	and	and	CCONJ
ejpam-556	332	17	four	four	NUM
ejpam-556	332	18	family	family	NOUN
ejpam-556	332	19	of	of	ADP
ejpam-556	332	20	free	free	ADJ
ejpam-556	332	21	parameters	parameter	NOUN
ejpam-556	332	22	were	be	AUX
ejpam-556	332	23	used	use	VERB
ejpam-556	332	24	to	to	PART
ejpam-556	332	25	preserve	preserve	VERB
ejpam-556	332	26	the	the	DET
ejpam-556	332	27	shape	shape	NOUN
ejpam-556	332	28	of	of	ADP
ejpam-556	332	29	data	datum	NOUN
ejpam-556	332	30	hence	hence	ADV
ejpam-556	332	31	computationally	computationally	ADV
ejpam-556	332	32	expansive	expansive	ADJ
ejpam-556	332	33	than	than	ADP
ejpam-556	332	34	shape	shape	NOUN
ejpam-556	332	35	preserving	preserve	VERB
ejpam-556	332	36	schemes	scheme	NOUN
ejpam-556	332	37	developed	develop	VERB
ejpam-556	332	38	in	in	ADP
ejpam-556	332	39	this	this	DET
ejpam-556	332	40	paper	paper	NOUN
ejpam-556	332	41	.	.	PUNCT
ejpam-556	333	1	the	the	DET
ejpam-556	333	2	order	order	NOUN
ejpam-556	333	3	of	of	ADP
ejpam-556	333	4	continuity	continuity	NOUN
ejpam-556	333	5	attained	attain	VERB
ejpam-556	333	6	in	in	ADP
ejpam-556	333	7	[	[	X
ejpam-556	333	8	14	14	NUM
ejpam-556	333	9	]	]	PUNCT
ejpam-556	333	10	was	be	AUX
ejpam-556	333	11	gc1	gc1	NOUN
ejpam-556	333	12	,	,	PUNCT
ejpam-556	333	13	whereas	whereas	SCONJ
ejpam-556	333	14	,	,	PUNCT
ejpam-556	333	15	in	in	ADP
ejpam-556	333	16	this	this	DET
ejpam-556	333	17	paper	paper	NOUN
ejpam-556	333	18	it	it	PRON
ejpam-556	333	19	is	be	AUX
ejpam-556	333	20	c1	c1	NOUN
ejpam-556	333	21	.	.	PUNCT
ejpam-556	334	1	references	reference	NOUN
ejpam-556	334	2	[	[	X
ejpam-556	334	3	1	1	NUM
ejpam-556	334	4	]	]	PUNCT
ejpam-556	334	5	akima	akima	PROPN
ejpam-556	334	6	,	,	PUNCT
ejpam-556	334	7	h.	h.	PROPN
ejpam-556	334	8	,	,	PUNCT
ejpam-556	334	9	a	a	DET
ejpam-556	334	10	new	new	ADJ
ejpam-556	334	11	method	method	NOUN
ejpam-556	334	12	of	of	ADP
ejpam-556	334	13	interpolation	interpolation	NOUN
ejpam-556	334	14	and	and	CCONJ
ejpam-556	334	15	smooth	smooth	ADJ
ejpam-556	334	16	curve	curve	NOUN
ejpam-556	334	17	fitting	fitting	NOUN
ejpam-556	334	18	based	base	VERB
ejpam-556	334	19	on	on	ADP
ejpam-556	334	20	local	local	ADJ
ejpam-556	334	21	procedures	procedure	NOUN
ejpam-556	334	22	,	,	PUNCT
ejpam-556	334	23	journal	journal	NOUN
ejpam-556	334	24	of	of	ADP
ejpam-556	334	25	the	the	DET
ejpam-556	334	26	association	association	NOUN
ejpam-556	334	27	for	for	ADP
ejpam-556	334	28	computing	compute	VERB
ejpam-556	334	29	machinery	machinery	NOUN
ejpam-556	334	30	,	,	PUNCT
ejpam-556	334	31	17	17	NUM
ejpam-556	334	32	,	,	PUNCT
ejpam-556	334	33	(	(	PUNCT
ejpam-556	334	34	1970	1970	NUM
ejpam-556	334	35	)	)	PUNCT
ejpam-556	334	36	,	,	PUNCT
ejpam-556	334	37	589	589	NUM
ejpam-556	334	38	-	-	SYM
ejpam-556	334	39	602	602	NUM
ejpam-556	334	40	.	.	PUNCT
ejpam-556	335	1	[	[	X
ejpam-556	335	2	2	2	NUM
ejpam-556	335	3	]	]	SYM
ejpam-556	335	4	beliakov	beliakov	PROPN
ejpam-556	335	5	,	,	PUNCT
ejpam-556	335	6	g.	g.	PROPN
ejpam-556	335	7	,	,	PUNCT
ejpam-556	335	8	monotonicity	monotonicity	NOUN
ejpam-556	335	9	preserving	preserve	VERB
ejpam-556	335	10	approximation	approximation	NOUN
ejpam-556	335	11	of	of	ADP
ejpam-556	335	12	multivariate	multivariate	NOUN
ejpam-556	335	13	scattered	scatter	VERB
ejpam-556	335	14	data	datum	NOUN
ejpam-556	335	15	,	,	PUNCT
ejpam-556	335	16	bit	bit	NOUN
ejpam-556	335	17	,	,	PUNCT
ejpam-556	335	18	45(4	45(4	NUM
ejpam-556	335	19	)	)	PUNCT
ejpam-556	335	20	,	,	PUNCT
ejpam-556	335	21	(	(	PUNCT
ejpam-556	335	22	2005	2005	NUM
ejpam-556	335	23	)	)	PUNCT
ejpam-556	335	24	,	,	PUNCT
ejpam-556	335	25	653	653	NUM
ejpam-556	335	26	-	-	SYM
ejpam-556	335	27	677	677	NUM
ejpam-556	335	28	.	.	PUNCT
ejpam-556	336	1	[	[	X
ejpam-556	336	2	3	3	NUM
ejpam-556	336	3	]	]	X
ejpam-556	336	4	butt	butt	NOUN
ejpam-556	336	5	,	,	PUNCT
ejpam-556	336	6	s.	s.	PROPN
ejpam-556	336	7	and	and	CCONJ
ejpam-556	336	8	brodlie	brodlie	PROPN
ejpam-556	336	9	,	,	PUNCT
ejpam-556	336	10	k.	k.	PROPN
ejpam-556	336	11	w.	w.	PROPN
ejpam-556	336	12	,	,	PUNCT
ejpam-556	336	13	preserving	preserve	VERB
ejpam-556	336	14	positivity	positivity	NOUN
ejpam-556	336	15	using	use	VERB
ejpam-556	336	16	piecewise	piecewise	NOUN
ejpam-556	336	17	cubic	cubic	ADJ
ejpam-556	336	18	interpolation	interpolation	NOUN
ejpam-556	336	19	,	,	PUNCT
ejpam-556	336	20	computers	computer	NOUN
ejpam-556	336	21	and	and	CCONJ
ejpam-556	336	22	graphics	graphic	NOUN
ejpam-556	336	23	,	,	PUNCT
ejpam-556	336	24	17(1	17(1	NUM
ejpam-556	336	25	)	)	PUNCT
ejpam-556	336	26	,	,	PUNCT
ejpam-556	336	27	(	(	PUNCT
ejpam-556	336	28	1993	1993	NUM
ejpam-556	336	29	)	)	PUNCT
ejpam-556	336	30	,	,	PUNCT
ejpam-556	336	31	55	55	NUM
ejpam-556	336	32	-	-	SYM
ejpam-556	336	33	64	64	NUM
ejpam-556	336	34	.	.	PUNCT
ejpam-556	337	1	[	[	X
ejpam-556	337	2	4	4	NUM
ejpam-556	337	3	]	]	X
ejpam-556	337	4	duan	duan	PROPN
ejpam-556	337	5	,	,	PUNCT
ejpam-556	337	6	q.	q.	PROPN
ejpam-556	337	7	,	,	PUNCT
ejpam-556	337	8	zhang	zhang	PROPN
ejpam-556	337	9	,	,	PUNCT
ejpam-556	337	10	h.	h.	PROPN
ejpam-556	337	11	,	,	PUNCT
ejpam-556	337	12	zhang	zhang	PROPN
ejpam-556	337	13	,	,	PUNCT
ejpam-556	337	14	y.	y.	PROPN
ejpam-556	337	15	and	and	CCONJ
ejpam-556	337	16	twizell	twizell	PROPN
ejpam-556	337	17	,	,	PUNCT
ejpam-556	337	18	e.	e.	PROPN
ejpam-556	337	19	h.	h.	PROPN
ejpam-556	337	20	,	,	PUNCT
ejpam-556	337	21	error	error	NOUN
ejpam-556	337	22	estimation	estimation	NOUN
ejpam-556	337	23	of	of	ADP
ejpam-556	337	24	a	a	DET
ejpam-556	337	25	kind	kind	NOUN
ejpam-556	337	26	of	of	ADP
ejpam-556	337	27	rational	rational	ADJ
ejpam-556	337	28	spline	spline	NOUN
ejpam-556	337	29	,	,	PUNCT
ejpam-556	337	30	journal	journal	NOUN
ejpam-556	337	31	of	of	ADP
ejpam-556	337	32	computational	computational	ADJ
ejpam-556	337	33	and	and	CCONJ
ejpam-556	337	34	applied	applied	ADJ
ejpam-556	337	35	mathematics	mathematic	NOUN
ejpam-556	337	36	,	,	PUNCT
ejpam-556	337	37	200(1	200(1	NUM
ejpam-556	337	38	)	)	PUNCT
ejpam-556	337	39	,	,	PUNCT
ejpam-556	337	40	(	(	PUNCT
ejpam-556	337	41	2007	2007	NUM
ejpam-556	337	42	)	)	PUNCT
ejpam-556	337	43	,	,	PUNCT
ejpam-556	337	44	1	1	NUM
ejpam-556	337	45	-	-	SYM
ejpam-556	337	46	11	11	NUM
ejpam-556	337	47	.	.	PUNCT
ejpam-556	338	1	[	[	X
ejpam-556	338	2	5	5	NUM
ejpam-556	338	3	]	]	X
ejpam-556	338	4	fahr	fahr	PROPN
ejpam-556	338	5	,	,	PUNCT
ejpam-556	338	6	r.	r.	PROPN
ejpam-556	338	7	d.	d.	PROPN
ejpam-556	338	8	and	and	CCONJ
ejpam-556	338	9	kallay	kallay	PROPN
ejpam-556	338	10	,	,	PUNCT
ejpam-556	338	11	m.	m.	NOUN
ejpam-556	338	12	,	,	PUNCT
ejpam-556	338	13	monotone	monotone	ADJ
ejpam-556	338	14	linear	linear	ADJ
ejpam-556	338	15	rational	rational	ADJ
ejpam-556	338	16	spline	spline	NOUN
ejpam-556	338	17	interpolation	interpolation	NOUN
ejpam-556	338	18	,	,	PUNCT
ejpam-556	338	19	computer	computer	NOUN
ejpam-556	338	20	aided	aid	VERB
ejpam-556	338	21	geometric	geometric	ADJ
ejpam-556	338	22	design	design	NOUN
ejpam-556	338	23	,	,	PUNCT
ejpam-556	338	24	9	9	NUM
ejpam-556	338	25	,	,	PUNCT
ejpam-556	338	26	(	(	PUNCT
ejpam-556	338	27	1992	1992	NUM
ejpam-556	338	28	)	)	PUNCT
ejpam-556	338	29	,	,	PUNCT
ejpam-556	338	30	313	313	NUM
ejpam-556	338	31	-	-	SYM
ejpam-556	338	32	319	319	NUM
ejpam-556	338	33	.	.	PUNCT
ejpam-556	339	1	[	[	X
ejpam-556	339	2	6	6	NUM
ejpam-556	339	3	]	]	X
ejpam-556	339	4	gerald	gerald	PROPN
ejpam-556	339	5	,	,	PUNCT
ejpam-556	339	6	c.	c.	PROPN
ejpam-556	339	7	f.	f.	PROPN
ejpam-556	339	8	and	and	CCONJ
ejpam-556	339	9	wheatley	wheatley	PROPN
ejpam-556	339	10	,	,	PUNCT
ejpam-556	339	11	p.	p.	PROPN
ejpam-556	339	12	o.	o.	PROPN
ejpam-556	339	13	,	,	PUNCT
ejpam-556	339	14	applied	apply	VERB
ejpam-556	339	15	numerical	numerical	ADJ
ejpam-556	339	16	analysis	analysis	NOUN
ejpam-556	339	17	,	,	PUNCT
ejpam-556	339	18	7th	7th	ADJ
ejpam-556	339	19	edition	edition	NOUN
ejpam-556	339	20	,	,	PUNCT
ejpam-556	339	21	addison	addison	PROPN
ejpam-556	339	22	wesley	wesley	PROPN
ejpam-556	339	23	publishing	publishing	PROPN
ejpam-556	339	24	company	company	NOUN
ejpam-556	339	25	,	,	PUNCT
ejpam-556	339	26	(	(	PUNCT
ejpam-556	339	27	2003	2003	NUM
ejpam-556	339	28	)	)	PUNCT
ejpam-556	339	29	.	.	PUNCT
ejpam-556	340	1	[	[	X
ejpam-556	340	2	7	7	NUM
ejpam-556	340	3	]	]	X
ejpam-556	340	4	goodman	goodman	PROPN
ejpam-556	340	5	,	,	PUNCT
ejpam-556	340	6	t.	t.	PROPN
ejpam-556	340	7	n.	n.	PROPN
ejpam-556	340	8	t.	t.	PROPN
ejpam-556	340	9	,	,	PUNCT
ejpam-556	340	10	ong	ong	PROPN
ejpam-556	340	11	,	,	PUNCT
ejpam-556	340	12	b.	b.	PROPN
ejpam-556	340	13	h.	h.	PROPN
ejpam-556	340	14	and	and	CCONJ
ejpam-556	340	15	unsworth	unsworth	PROPN
ejpam-556	340	16	,	,	PUNCT
ejpam-556	340	17	k.	k.	PROPN
ejpam-556	340	18	,	,	PUNCT
ejpam-556	340	19	constrained	constrain	VERB
ejpam-556	340	20	interpolation	interpolation	NOUN
ejpam-556	340	21	using	use	VERB
ejpam-556	340	22	rational	rational	ADJ
ejpam-556	340	23	cubic	cubic	ADJ
ejpam-556	340	24	splines	spline	NOUN
ejpam-556	340	25	,	,	PUNCT
ejpam-556	340	26	proceedings	proceeding	NOUN
ejpam-556	340	27	of	of	ADP
ejpam-556	340	28	nurbs	nurb	NOUN
ejpam-556	340	29	for	for	ADP
ejpam-556	340	30	curve	curve	NOUN
ejpam-556	340	31	and	and	CCONJ
ejpam-556	340	32	surface	surface	NOUN
ejpam-556	340	33	design	design	NOUN
ejpam-556	340	34	,	,	PUNCT
ejpam-556	340	35	g.	g.	PROPN
ejpam-556	340	36	farin	farin	PROPN
ejpam-556	340	37	(	(	PUNCT
ejpam-556	340	38	eds	eds	PROPN
ejpam-556	340	39	)	)	PUNCT
ejpam-556	340	40	,	,	PUNCT
ejpam-556	340	41	(	(	PUNCT
ejpam-556	340	42	1991	1991	NUM
ejpam-556	340	43	)	)	PUNCT
ejpam-556	340	44	,	,	PUNCT
ejpam-556	340	45	59	59	NUM
ejpam-556	340	46	-	-	SYM
ejpam-556	340	47	74	74	NUM
ejpam-556	340	48	.	.	PUNCT
ejpam-556	341	1	[	[	X
ejpam-556	341	2	8	8	NUM
ejpam-556	341	3	]	]	X
ejpam-556	341	4	goodman	goodman	PROPN
ejpam-556	341	5	,	,	PUNCT
ejpam-556	341	6	t.	t.	PROPN
ejpam-556	341	7	n.	n.	PROPN
ejpam-556	341	8	t.	t.	PROPN
ejpam-556	341	9	,	,	PUNCT
ejpam-556	341	10	shape	shape	NOUN
ejpam-556	341	11	preserving	preserve	VERB
ejpam-556	341	12	interpolation	interpolation	NOUN
ejpam-556	341	13	by	by	ADP
ejpam-556	341	14	curves	curve	NOUN
ejpam-556	341	15	,	,	PUNCT
ejpam-556	341	16	proceeding	proceeding	NOUN
ejpam-556	341	17	of	of	ADP
ejpam-556	341	18	algorithms	algorithm	NOUN
ejpam-556	341	19	for	for	ADP
ejpam-556	341	20	approximation	approximation	NOUN
ejpam-556	341	21	iv	iv	NUM
ejpam-556	341	22	,	,	PUNCT
ejpam-556	341	23	j.	j.	PROPN
ejpam-556	341	24	levesley	levesley	PROPN
ejpam-556	341	25	,	,	PUNCT
ejpam-556	341	26	i.	i.	PROPN
ejpam-556	341	27	j.	j.	PROPN
ejpam-556	341	28	anderson	anderson	PROPN
ejpam-556	341	29	and	and	CCONJ
ejpam-556	341	30	j.	j.	PROPN
ejpam-556	341	31	c.	c.	PROPN
ejpam-556	341	32	mason(eds	mason(eds	PROPN
ejpam-556	341	33	.	.	PUNCT
ejpam-556	341	34	)	)	PUNCT
ejpam-556	342	1	,	,	PUNCT
ejpam-556	342	2	university	university	NOUN
ejpam-556	342	3	of	of	ADP
ejpam-556	342	4	huddersfeld	huddersfeld	ADJ
ejpam-556	342	5	,	,	PUNCT
ejpam-556	342	6	(	(	PUNCT
ejpam-556	342	7	2002	2002	NUM
ejpam-556	342	8	)	)	PUNCT
ejpam-556	342	9	,	,	PUNCT
ejpam-556	342	10	24	24	NUM
ejpam-556	342	11	-	-	SYM
ejpam-556	342	12	35	35	NUM
ejpam-556	342	13	.	.	PUNCT
ejpam-556	343	1	[	[	X
ejpam-556	343	2	9	9	NUM
ejpam-556	343	3	]	]	SYM
ejpam-556	343	4	hussain	hussain	PROPN
ejpam-556	343	5	,	,	PUNCT
ejpam-556	343	6	m.	m.	NOUN
ejpam-556	343	7	z.	z.	PROPN
ejpam-556	343	8	and	and	CCONJ
ejpam-556	343	9	hussain	hussain	PROPN
ejpam-556	343	10	,	,	PUNCT
ejpam-556	343	11	m.	m.	NOUN
ejpam-556	343	12	,	,	PUNCT
ejpam-556	343	13	visualization	visualization	NOUN
ejpam-556	343	14	of	of	ADP
ejpam-556	343	15	data	datum	NOUN
ejpam-556	343	16	preserving	preserve	VERB
ejpam-556	343	17	monotonicity	monotonicity	NOUN
ejpam-556	343	18	,	,	PUNCT
ejpam-556	343	19	applied	apply	VERB
ejpam-556	343	20	mathematics	mathematic	NOUN
ejpam-556	343	21	and	and	CCONJ
ejpam-556	343	22	computation	computation	NOUN
ejpam-556	343	23	,	,	PUNCT
ejpam-556	343	24	190	190	NUM
ejpam-556	343	25	,	,	PUNCT
ejpam-556	343	26	(	(	PUNCT
ejpam-556	343	27	2007	2007	NUM
ejpam-556	343	28	)	)	PUNCT
ejpam-556	343	29	,	,	PUNCT
ejpam-556	343	30	1353	1353	NUM
ejpam-556	343	31	-	-	SYM
ejpam-556	343	32	1364	1364	NUM
ejpam-556	343	33	.	.	PUNCT
ejpam-556	344	1	[	[	X
ejpam-556	344	2	10	10	NUM
ejpam-556	344	3	]	]	X
ejpam-556	344	4	hussain	hussain	PROPN
ejpam-556	344	5	,	,	PUNCT
ejpam-556	344	6	m.	m.	NOUN
ejpam-556	344	7	z.	z.	PROPN
ejpam-556	344	8	and	and	CCONJ
ejpam-556	344	9	sarfraz	sarfraz	PROPN
ejpam-556	344	10	,	,	PUNCT
ejpam-556	344	11	m.	m.	NOUN
ejpam-556	344	12	,	,	PUNCT
ejpam-556	344	13	positivity	positivity	NOUN
ejpam-556	344	14	-	-	PUNCT
ejpam-556	344	15	preserving	preserve	VERB
ejpam-556	344	16	interpolation	interpolation	NOUN
ejpam-556	344	17	of	of	ADP
ejpam-556	344	18	positive	positive	ADJ
ejpam-556	344	19	data	datum	NOUN
ejpam-556	344	20	by	by	ADP
ejpam-556	344	21	rational	rational	ADJ
ejpam-556	344	22	cubics	cubic	NOUN
ejpam-556	344	23	,	,	PUNCT
ejpam-556	344	24	journal	journal	NOUN
ejpam-556	344	25	of	of	ADP
ejpam-556	344	26	computational	computational	ADJ
ejpam-556	344	27	and	and	CCONJ
ejpam-556	344	28	applied	applied	ADJ
ejpam-556	344	29	mathematics	mathematic	NOUN
ejpam-556	344	30	,	,	PUNCT
ejpam-556	344	31	218(2	218(2	NUM
ejpam-556	344	32	)	)	PUNCT
ejpam-556	344	33	,	,	PUNCT
ejpam-556	344	34	(	(	PUNCT
ejpam-556	344	35	2008	2008	NUM
ejpam-556	344	36	)	)	PUNCT
ejpam-556	344	37	,	,	PUNCT
ejpam-556	344	38	446	446	NUM
ejpam-556	344	39	-	-	SYM
ejpam-556	344	40	458	458	NUM
ejpam-556	344	41	.	.	PUNCT
ejpam-556	345	1	references	reference	NOUN
ejpam-556	345	2	212	212	NUM
ejpam-556	345	3	[	[	X
ejpam-556	345	4	11	11	NUM
ejpam-556	345	5	]	]	SYM
ejpam-556	345	6	hussain	hussain	PROPN
ejpam-556	345	7	,	,	PUNCT
ejpam-556	345	8	m.	m.	NOUN
ejpam-556	345	9	z.	z.	PROPN
ejpam-556	345	10	and	and	CCONJ
ejpam-556	345	11	sarfraz	sarfraz	PROPN
ejpam-556	345	12	,	,	PUNCT
ejpam-556	345	13	m.	m.	NOUN
ejpam-556	345	14	,	,	PUNCT
ejpam-556	345	15	monotone	monotone	ADJ
ejpam-556	345	16	piecewise	piecewise	NOUN
ejpam-556	345	17	rational	rational	ADJ
ejpam-556	345	18	cubic	cubic	ADJ
ejpam-556	345	19	interpolation	interpolation	NOUN
ejpam-556	345	20	,	,	PUNCT
ejpam-556	345	21	to	to	PART
ejpam-556	345	22	be	be	AUX
ejpam-556	345	23	appeared	appear	VERB
ejpam-556	345	24	in	in	ADP
ejpam-556	345	25	international	international	ADJ
ejpam-556	345	26	journal	journal	NOUN
ejpam-556	345	27	of	of	ADP
ejpam-556	345	28	computer	computer	NOUN
ejpam-556	345	29	mathematics	mathematic	NOUN
ejpam-556	345	30	,	,	PUNCT
ejpam-556	345	31	86	86	NUM
ejpam-556	345	32	,	,	PUNCT
ejpam-556	345	33	(	(	PUNCT
ejpam-556	345	34	2009	2009	NUM
ejpam-556	345	35	)	)	PUNCT
ejpam-556	345	36	.	.	PUNCT
ejpam-556	346	1	[	[	X
ejpam-556	346	2	12	12	NUM
ejpam-556	346	3	]	]	PUNCT
ejpam-556	346	4	lamberti	lamberti	PROPN
ejpam-556	346	5	,	,	PUNCT
ejpam-556	346	6	p.	p.	NOUN
ejpam-556	346	7	and	and	CCONJ
ejpam-556	346	8	manni	manni	PROPN
ejpam-556	346	9	,	,	PUNCT
ejpam-556	346	10	c.	c.	PROPN
ejpam-556	346	11	,	,	PUNCT
ejpam-556	346	12	shape	shape	NOUN
ejpam-556	346	13	-	-	PUNCT
ejpam-556	346	14	preserving	preserve	VERB
ejpam-556	346	15	functional	functional	ADJ
ejpam-556	346	16	interpolation	interpolation	NOUN
ejpam-556	346	17	via	via	ADP
ejpam-556	346	18	parametric	parametric	ADJ
ejpam-556	346	19	cubics	cubic	NOUN
ejpam-556	346	20	,	,	PUNCT
ejpam-556	346	21	numerical	numerical	ADJ
ejpam-556	346	22	algorithms	algorithm	NOUN
ejpam-556	346	23	,	,	PUNCT
ejpam-556	346	24	28	28	NUM
ejpam-556	346	25	,	,	PUNCT
ejpam-556	346	26	(	(	PUNCT
ejpam-556	346	27	2001	2001	NUM
ejpam-556	346	28	)	)	PUNCT
ejpam-556	346	29	,	,	PUNCT
ejpam-556	346	30	229	229	NUM
ejpam-556	346	31	-	-	SYM
ejpam-556	346	32	254	254	NUM
ejpam-556	346	33	.	.	PUNCT
ejpam-556	347	1	[	[	X
ejpam-556	347	2	13	13	NUM
ejpam-556	347	3	]	]	X
ejpam-556	347	4	sarfraz	sarfraz	NOUN
ejpam-556	347	5	,	,	PUNCT
ejpam-556	347	6	m.	m.	NOUN
ejpam-556	347	7	,	,	PUNCT
ejpam-556	347	8	butt	butt	PROPN
ejpam-556	347	9	,	,	PUNCT
ejpam-556	347	10	s.	s.	PROPN
ejpam-556	347	11	and	and	CCONJ
ejpam-556	347	12	hussain	hussain	PROPN
ejpam-556	347	13	,	,	PUNCT
ejpam-556	347	14	m.	m.	NOUN
ejpam-556	347	15	z.	z.	PROPN
ejpam-556	347	16	,	,	PUNCT
ejpam-556	347	17	visualization	visualization	NOUN
ejpam-556	347	18	of	of	ADP
ejpam-556	347	19	shaped	shape	VERB
ejpam-556	347	20	data	datum	NOUN
ejpam-556	347	21	by	by	ADP
ejpam-556	347	22	a	a	DET
ejpam-556	347	23	rational	rational	ADJ
ejpam-556	347	24	cubic	cubic	ADJ
ejpam-556	347	25	spline	spline	NOUN
ejpam-556	347	26	interpolation	interpolation	NOUN
ejpam-556	347	27	,	,	PUNCT
ejpam-556	347	28	computers	computer	NOUN
ejpam-556	347	29	and	and	CCONJ
ejpam-556	347	30	graphics	graphic	NOUN
ejpam-556	347	31	,	,	PUNCT
ejpam-556	347	32	25(5	25(5	NUM
ejpam-556	347	33	)	)	PUNCT
ejpam-556	347	34	,	,	PUNCT
ejpam-556	347	35	(	(	PUNCT
ejpam-556	347	36	2001	2001	NUM
ejpam-556	347	37	)	)	PUNCT
ejpam-556	347	38	,	,	PUNCT
ejpam-556	347	39	833	833	NUM
ejpam-556	347	40	-	-	SYM
ejpam-556	347	41	845	845	NUM
ejpam-556	347	42	.	.	PUNCT
ejpam-556	348	1	[	[	X
ejpam-556	348	2	14	14	NUM
ejpam-556	348	3	]	]	X
ejpam-556	348	4	sarfraz	sarfraz	NOUN
ejpam-556	348	5	,	,	PUNCT
ejpam-556	348	6	m.	m.	NOUN
ejpam-556	348	7	,	,	PUNCT
ejpam-556	348	8	hussain	hussain	PROPN
ejpam-556	348	9	,	,	PUNCT
ejpam-556	348	10	m.	m.	NOUN
ejpam-556	348	11	z.	z.	PROPN
ejpam-556	348	12	and	and	CCONJ
ejpam-556	348	13	chaudhry	chaudhry	PROPN
ejpam-556	348	14	,	,	PUNCT
ejpam-556	348	15	f.	f.	PROPN
ejpam-556	348	16	s.	s.	PROPN
ejpam-556	348	17	,	,	PUNCT
ejpam-556	348	18	shape	shape	VERB
ejpam-556	348	19	preserving	preserve	VERB
ejpam-556	348	20	cubic	cubic	ADJ
ejpam-556	348	21	spline	spline	NOUN
ejpam-556	348	22	for	for	ADP
ejpam-556	348	23	data	data	NOUN
ejpam-556	348	24	visualization	visualization	NOUN
ejpam-556	348	25	,	,	PUNCT
ejpam-556	348	26	computer	computer	NOUN
ejpam-556	348	27	graphics	graphic	NOUN
ejpam-556	348	28	and	and	CCONJ
ejpam-556	348	29	cad	cad	PROPN
ejpam-556	348	30	/	/	SYM
ejpam-556	348	31	cam	cam	PROPN
ejpam-556	348	32	,	,	PUNCT
ejpam-556	348	33	01	01	NUM
ejpam-556	348	34	,	,	PUNCT
ejpam-556	348	35	(	(	PUNCT
ejpam-556	348	36	2005	2005	NUM
ejpam-556	348	37	)	)	PUNCT
ejpam-556	348	38	,	,	PUNCT
ejpam-556	348	39	189	189	NUM
ejpam-556	348	40	-	-	SYM
ejpam-556	348	41	193	193	NUM
ejpam-556	348	42	.	.	PUNCT
ejpam-556	349	1	[	[	X
ejpam-556	349	2	15	15	NUM
ejpam-556	349	3	]	]	X
ejpam-556	349	4	schmidt	schmidt	PROPN
ejpam-556	349	5	,	,	PUNCT
ejpam-556	349	6	j.	j.	PROPN
ejpam-556	349	7	w.	w.	PROPN
ejpam-556	349	8	and	and	CCONJ
ejpam-556	349	9	hess	hess	PROPN
ejpam-556	349	10	,	,	PUNCT
ejpam-556	349	11	w.	w.	PROPN
ejpam-556	349	12	,	,	PUNCT
ejpam-556	349	13	positivity	positivity	NOUN
ejpam-556	349	14	of	of	ADP
ejpam-556	349	15	cubic	cubic	ADJ
ejpam-556	349	16	polynomial	polynomial	NOUN
ejpam-556	349	17	on	on	ADP
ejpam-556	349	18	intervals	interval	NOUN
ejpam-556	349	19	and	and	CCONJ
ejpam-556	349	20	positive	positive	ADJ
ejpam-556	349	21	spline	spline	NOUN
ejpam-556	349	22	interpolation	interpolation	NOUN
ejpam-556	349	23	,	,	PUNCT
ejpam-556	349	24	bit	bit	NOUN
ejpam-556	349	25	,	,	PUNCT
ejpam-556	349	26	28	28	NUM
ejpam-556	349	27	,	,	PUNCT
ejpam-556	349	28	(	(	PUNCT
ejpam-556	349	29	1988	1988	NUM
ejpam-556	349	30	)	)	PUNCT
ejpam-556	349	31	,	,	PUNCT
ejpam-556	349	32	340	340	NUM
ejpam-556	349	33	-	-	SYM
ejpam-556	349	34	352	352	NUM
ejpam-556	349	35	.	.	PUNCT
ejpam-556	350	1	[	[	X
ejpam-556	350	2	16	16	NUM
ejpam-556	350	3	]	]	X
ejpam-556	350	4	schultz	schultz	PROPN
ejpam-556	350	5	,	,	PUNCT
ejpam-556	350	6	m.	m.	PROPN
ejpam-556	350	7	h.	h.	PROPN
ejpam-556	350	8	,	,	PUNCT
ejpam-556	350	9	spline	spline	NOUN
ejpam-556	350	10	analysis	analysis	NOUN
ejpam-556	350	11	,	,	PUNCT
ejpam-556	350	12	prentice	prentice	NOUN
ejpam-556	350	13	-	-	PUNCT
ejpam-556	350	14	hall	hall	NOUN
ejpam-556	350	15	,	,	PUNCT
ejpam-556	350	16	englewood	englewood	PROPN
ejpam-556	350	17	cliffs	cliffs	PROPN
ejpam-556	350	18	,	,	PUNCT
ejpam-556	350	19	new	new	PROPN
ejpam-556	350	20	jersey	jersey	PROPN
ejpam-556	350	21	,	,	PUNCT
ejpam-556	350	22	(	(	PUNCT
ejpam-556	350	23	1973	1973	NUM
ejpam-556	350	24	)	)	PUNCT
ejpam-556	350	25	.	.	PUNCT