id	sid	tid	token	lemma	pos
american_scientific_journal-667	1	1	american	american	PROPN
american_scientific_journal-667	1	2	scientific	scientific	ADJ
american_scientific_journal-667	1	3	research	research	NOUN
american_scientific_journal-667	1	4	journal	journal	NOUN
american_scientific_journal-667	1	5	for	for	ADP
american_scientific_journal-667	1	6	engineering	engineering	NOUN
american_scientific_journal-667	1	7	,	,	PUNCT
american_scientific_journal-667	1	8	technology	technology	NOUN
american_scientific_journal-667	1	9	,	,	PUNCT
american_scientific_journal-667	1	10	and	and	CCONJ
american_scientific_journal-667	1	11	sciences	science	NOUN
american_scientific_journal-667	1	12	(	(	PUNCT
american_scientific_journal-667	1	13	asrjets	asrjet	NOUN
american_scientific_journal-667	1	14	)	)	PUNCT
american_scientific_journal-667	1	15	issn	issn	PROPN
american_scientific_journal-667	1	16	(	(	PUNCT
american_scientific_journal-667	1	17	print	print	NOUN
american_scientific_journal-667	1	18	)	)	PUNCT
american_scientific_journal-667	1	19	2313	2313	NUM
american_scientific_journal-667	1	20	-	-	SYM
american_scientific_journal-667	1	21	4410	4410	NUM
american_scientific_journal-667	1	22	,	,	PUNCT
american_scientific_journal-667	1	23	issn	issn	PROPN
american_scientific_journal-667	1	24	(	(	PUNCT
american_scientific_journal-667	1	25	online	online	ADJ
american_scientific_journal-667	1	26	)	)	PUNCT
american_scientific_journal-667	1	27	2313	2313	NUM
american_scientific_journal-667	1	28	-	-	SYM
american_scientific_journal-667	1	29	4402	4402	NUM
american_scientific_journal-667	1	30	©	©	PROPN
american_scientific_journal-667	1	31	global	global	ADJ
american_scientific_journal-667	1	32	society	society	NOUN
american_scientific_journal-667	1	33	of	of	ADP
american_scientific_journal-667	1	34	scientific	scientific	ADJ
american_scientific_journal-667	1	35	research	research	NOUN
american_scientific_journal-667	1	36	and	and	CCONJ
american_scientific_journal-667	1	37	researchers	researcher	NOUN
american_scientific_journal-667	1	38	http://asrjetsjournal.org/	http://asrjetsjournal.org/	NOUN
american_scientific_journal-667	1	39	shape	shape	NOUN
american_scientific_journal-667	1	40	preserving	preserve	VERB
american_scientific_journal-667	1	41	c2	c2	PROPN
american_scientific_journal-667	1	42	rational	rational	ADJ
american_scientific_journal-667	1	43	cubic	cubic	ADJ
american_scientific_journal-667	1	44	spline	spline	PROPN
american_scientific_journal-667	1	45	interpolation	interpolation	NOUN
american_scientific_journal-667	1	46	abdurkadir	abdurkadir	PROPN
american_scientific_journal-667	1	47	edeoa	edeoa	VERB
american_scientific_journal-667	1	48	*	*	PROPN
american_scientific_journal-667	1	49	,	,	PUNCT
american_scientific_journal-667	1	50	genanew	genanew	ADJ
american_scientific_journal-667	1	51	gofeb	gofeb	NOUN
american_scientific_journal-667	1	52	,	,	PUNCT
american_scientific_journal-667	1	53	teshome	teshome	NOUN
american_scientific_journal-667	1	54	teferac	teferac	PROPN
american_scientific_journal-667	1	55	abule	abule	PROPN
american_scientific_journal-667	1	56	hora	hora	PROPN
american_scientific_journal-667	1	57	college	college	PROPN
american_scientific_journal-667	1	58	of	of	ADP
american_scientific_journal-667	1	59	teachers	teachers	PROPN
american_scientific_journal-667	1	60	education	education	PROPN
american_scientific_journal-667	1	61	,	,	PUNCT
american_scientific_journal-667	1	62	department	department	NOUN
american_scientific_journal-667	1	63	of	of	ADP
american_scientific_journal-667	1	64	mathematics	mathematics	PROPN
american_scientific_journal-667	1	65	,	,	PUNCT
american_scientific_journal-667	1	66	bule	bule	PROPN
american_scientific_journal-667	1	67	hora	hora	PROPN
american_scientific_journal-667	1	68	133	133	NUM
american_scientific_journal-667	1	69	,	,	PUNCT
american_scientific_journal-667	1	70	ethiopia	ethiopia	PROPN
american_scientific_journal-667	1	71	bjimma	bjimma	PROPN
american_scientific_journal-667	1	72	university	university	PROPN
american_scientific_journal-667	1	73	,	,	PUNCT
american_scientific_journal-667	1	74	department	department	NOUN
american_scientific_journal-667	1	75	of	of	ADP
american_scientific_journal-667	1	76	mathematics	mathematics	PROPN
american_scientific_journal-667	1	77	,	,	PUNCT
american_scientific_journal-667	1	78	jimma	jimma	PROPN
american_scientific_journal-667	1	79	378	378	NUM
american_scientific_journal-667	1	80	,	,	PUNCT
american_scientific_journal-667	1	81	ethiopia	ethiopia	PROPN
american_scientific_journal-667	1	82	c	c	PROPN
american_scientific_journal-667	1	83	jimma	jimma	PROPN
american_scientific_journal-667	1	84	university	university	PROPN
american_scientific_journal-667	1	85	,	,	PUNCT
american_scientific_journal-667	1	86	department	department	NOUN
american_scientific_journal-667	1	87	of	of	ADP
american_scientific_journal-667	1	88	mathematics	mathematics	PROPN
american_scientific_journal-667	1	89	,	,	PUNCT
american_scientific_journal-667	1	90	jimma	jimma	PROPN
american_scientific_journal-667	1	91	378	378	NUM
american_scientific_journal-667	1	92	,	,	PUNCT
american_scientific_journal-667	1	93	ethiopia	ethiopia	PROPN
american_scientific_journal-667	1	94	aemail:edeoabdurkadir@gmail.com	aemail:edeoabdurkadir@gmail.com	X
american_scientific_journal-667	1	95	bemail:genagof@gmail.com	bemail:genagof@gmail.com	X
american_scientific_journal-667	1	96	c	c	X
american_scientific_journal-667	1	97	email:teshometefera596@yahoo.com	email:teshometefera596@yahoo.com	PROPN
american_scientific_journal-667	1	98	abstract	abstract	NOUN
american_scientific_journal-667	1	99	in	in	ADP
american_scientific_journal-667	1	100	this	this	DET
american_scientific_journal-667	1	101	study	study	NOUN
american_scientific_journal-667	1	102	a	a	DET
american_scientific_journal-667	1	103	piecewise	piecewise	NOUN
american_scientific_journal-667	1	104	rational	rational	ADJ
american_scientific_journal-667	1	105	function	function	NOUN
american_scientific_journal-667	1	106	s	s	PART
american_scientific_journal-667	1	107	∈	∈	PROPN
american_scientific_journal-667	1	108	c2[a	c2[a	NOUN
american_scientific_journal-667	1	109	,	,	PUNCT
american_scientific_journal-667	1	110	b	b	X
american_scientific_journal-667	1	111	]	]	X
american_scientific_journal-667	1	112	with	with	ADP
american_scientific_journal-667	1	113	cubic	cubic	ADJ
american_scientific_journal-667	1	114	numerator	numerator	NOUN
american_scientific_journal-667	1	115	and	and	CCONJ
american_scientific_journal-667	1	116	linear	linear	ADJ
american_scientific_journal-667	1	117	denominator	denominator	NOUN
american_scientific_journal-667	1	118	involving	involve	VERB
american_scientific_journal-667	1	119	two	two	NUM
american_scientific_journal-667	1	120	shape	shape	NOUN
american_scientific_journal-667	1	121	parameters	parameter	NOUN
american_scientific_journal-667	1	122	has	have	AUX
american_scientific_journal-667	1	123	been	be	AUX
american_scientific_journal-667	1	124	developed	develop	VERB
american_scientific_journal-667	1	125	to	to	PART
american_scientific_journal-667	1	126	address	address	VERB
american_scientific_journal-667	1	127	the	the	DET
american_scientific_journal-667	1	128	problem	problem	NOUN
american_scientific_journal-667	1	129	of	of	ADP
american_scientific_journal-667	1	130	constructing	construct	VERB
american_scientific_journal-667	1	131	positivity	positivity	NOUN
american_scientific_journal-667	1	132	preserving	preserve	VERB
american_scientific_journal-667	1	133	curve	curve	NOUN
american_scientific_journal-667	1	134	through	through	ADP
american_scientific_journal-667	1	135	positive	positive	ADJ
american_scientific_journal-667	1	136	data	datum	NOUN
american_scientific_journal-667	1	137	,	,	PUNCT
american_scientific_journal-667	1	138	monotonicity	monotonicity	NOUN
american_scientific_journal-667	1	139	preserving	preserve	VERB
american_scientific_journal-667	1	140	curve	curve	NOUN
american_scientific_journal-667	1	141	through	through	ADP
american_scientific_journal-667	1	142	monotone	monotone	ADJ
american_scientific_journal-667	1	143	data	datum	NOUN
american_scientific_journal-667	1	144	and	and	CCONJ
american_scientific_journal-667	1	145	convexity	convexity	NOUN
american_scientific_journal-667	1	146	preserving	preserve	VERB
american_scientific_journal-667	1	147	curve	curve	NOUN
american_scientific_journal-667	1	148	through	through	ADP
american_scientific_journal-667	1	149	convex	convex	PROPN
american_scientific_journal-667	1	150	data	datum	NOUN
american_scientific_journal-667	1	151	within	within	ADP
american_scientific_journal-667	1	152	one	one	NUM
american_scientific_journal-667	1	153	mathematical	mathematical	ADJ
american_scientific_journal-667	1	154	model	model	NOUN
american_scientific_journal-667	1	155	.	.	PUNCT
american_scientific_journal-667	2	1	a	a	DET
american_scientific_journal-667	2	2	simple	simple	ADJ
american_scientific_journal-667	2	3	data	datum	NOUN
american_scientific_journal-667	2	4	dependent	dependent	ADJ
american_scientific_journal-667	2	5	condition	condition	NOUN
american_scientific_journal-667	2	6	for	for	ADP
american_scientific_journal-667	2	7	a	a	DET
american_scientific_journal-667	2	8	single	single	ADJ
american_scientific_journal-667	2	9	shape	shape	NOUN
american_scientific_journal-667	2	10	parameter	parameter	NOUN
american_scientific_journal-667	2	11	has	have	AUX
american_scientific_journal-667	2	12	been	be	AUX
american_scientific_journal-667	2	13	derived	derive	VERB
american_scientific_journal-667	2	14	to	to	PART
american_scientific_journal-667	2	15	preserve	preserve	VERB
american_scientific_journal-667	2	16	the	the	DET
american_scientific_journal-667	2	17	positivity	positivity	NOUN
american_scientific_journal-667	2	18	,	,	PUNCT
american_scientific_journal-667	2	19	monotonicity	monotonicity	NOUN
american_scientific_journal-667	2	20	and	and	CCONJ
american_scientific_journal-667	2	21	convexity	convexity	NOUN
american_scientific_journal-667	2	22	of	of	ADP
american_scientific_journal-667	2	23	respectively	respectively	ADV
american_scientific_journal-667	2	24	positive	positive	ADJ
american_scientific_journal-667	2	25	,	,	PUNCT
american_scientific_journal-667	2	26	monotone	monotone	ADJ
american_scientific_journal-667	2	27	and	and	CCONJ
american_scientific_journal-667	2	28	convex	convex	PROPN
american_scientific_journal-667	2	29	data	datum	NOUN
american_scientific_journal-667	2	30	.	.	PUNCT
american_scientific_journal-667	3	1	the	the	DET
american_scientific_journal-667	3	2	remaining	remain	VERB
american_scientific_journal-667	3	3	shape	shape	NOUN
american_scientific_journal-667	3	4	parameter	parameter	NOUN
american_scientific_journal-667	3	5	is	be	AUX
american_scientific_journal-667	3	6	left	leave	VERB
american_scientific_journal-667	3	7	free	free	ADJ
american_scientific_journal-667	3	8	for	for	SCONJ
american_scientific_journal-667	3	9	the	the	DET
american_scientific_journal-667	3	10	user	user	NOUN
american_scientific_journal-667	3	11	to	to	PART
american_scientific_journal-667	3	12	modify	modify	VERB
american_scientific_journal-667	3	13	the	the	DET
american_scientific_journal-667	3	14	shape	shape	NOUN
american_scientific_journal-667	3	15	of	of	ADP
american_scientific_journal-667	3	16	positive	positive	ADJ
american_scientific_journal-667	3	17	,	,	PUNCT
american_scientific_journal-667	3	18	monotone	monotone	ADJ
american_scientific_journal-667	3	19	and	and	CCONJ
american_scientific_journal-667	3	20	convex	convex	NOUN
american_scientific_journal-667	3	21	curves	curve	NOUN
american_scientific_journal-667	3	22	when	when	SCONJ
american_scientific_journal-667	3	23	needs	need	NOUN
american_scientific_journal-667	3	24	arise	arise	VERB
american_scientific_journal-667	3	25	.	.	PUNCT
american_scientific_journal-667	4	1	we	we	PRON
american_scientific_journal-667	4	2	extended	extend	VERB
american_scientific_journal-667	4	3	the	the	DET
american_scientific_journal-667	4	4	result	result	NOUN
american_scientific_journal-667	4	5	of	of	ADP
american_scientific_journal-667	4	6	[	[	X
american_scientific_journal-667	4	7	1	1	X
american_scientific_journal-667	4	8	]	]	PUNCT
american_scientific_journal-667	4	9	to	to	ADP
american_scientific_journal-667	4	10	a	a	DET
american_scientific_journal-667	4	11	piecewise	piecewise	NOUN
american_scientific_journal-667	4	12	rational	rational	ADJ
american_scientific_journal-667	4	13	cubic	cubic	ADJ
american_scientific_journal-667	4	14	function	function	NOUN
american_scientific_journal-667	4	15	s	s	PROPN
american_scientific_journal-667	4	16	∈	∈	PROPN
american_scientific_journal-667	4	17	c2[a	c2[a	NOUN
american_scientific_journal-667	4	18	,	,	PUNCT
american_scientific_journal-667	4	19	b	b	NOUN
american_scientific_journal-667	4	20	]	]	PUNCT
american_scientific_journal-667	4	21	.	.	PUNCT
american_scientific_journal-667	5	1	keywords	keyword	NOUN
american_scientific_journal-667	5	2	:	:	PUNCT
american_scientific_journal-667	5	3	shape	shape	NOUN
american_scientific_journal-667	5	4	preservation	preservation	NOUN
american_scientific_journal-667	5	5	;	;	PUNCT
american_scientific_journal-667	5	6	spline	spline	NOUN
american_scientific_journal-667	5	7	interpolation	interpolation	NOUN
american_scientific_journal-667	5	8	;	;	PUNCT
american_scientific_journal-667	5	9	positivity	positivity	NOUN
american_scientific_journal-667	5	10	;	;	PUNCT
american_scientific_journal-667	5	11	monotonicity	monotonicity	NOUN
american_scientific_journal-667	5	12	;	;	PUNCT
american_scientific_journal-667	5	13	convexity	convexity	NOUN
american_scientific_journal-667	5	14	1	1	NUM
american_scientific_journal-667	5	15	.	.	PUNCT
american_scientific_journal-667	5	16	introduction	introduction	NOUN
american_scientific_journal-667	5	17	shape	shape	NOUN
american_scientific_journal-667	5	18	preservation	preservation	NOUN
american_scientific_journal-667	5	19	of	of	ADP
american_scientific_journal-667	5	20	a	a	DET
american_scientific_journal-667	5	21	given	give	VERB
american_scientific_journal-667	5	22	data	datum	NOUN
american_scientific_journal-667	5	23	is	be	AUX
american_scientific_journal-667	5	24	an	an	DET
american_scientific_journal-667	5	25	important	important	ADJ
american_scientific_journal-667	5	26	topic	topic	NOUN
american_scientific_journal-667	5	27	in	in	ADP
american_scientific_journal-667	5	28	the	the	DET
american_scientific_journal-667	5	29	field	field	NOUN
american_scientific_journal-667	5	30	of	of	ADP
american_scientific_journal-667	5	31	data	datum	NOUN
american_scientific_journal-667	5	32	visualization	visualization	NOUN
american_scientific_journal-667	5	33	.	.	PUNCT
american_scientific_journal-667	6	1	in	in	ADP
american_scientific_journal-667	6	2	data	data	NOUN
american_scientific_journal-667	6	3	visualization	visualization	NOUN
american_scientific_journal-667	6	4	techniques	technique	NOUN
american_scientific_journal-667	6	5	researchers	researcher	NOUN
american_scientific_journal-667	6	6	convert	convert	VERB
american_scientific_journal-667	6	7	any	any	DET
american_scientific_journal-667	6	8	information	information	NOUN
american_scientific_journal-667	6	9	into	into	ADP
american_scientific_journal-667	6	10	graphical	graphical	ADJ
american_scientific_journal-667	6	11	views	view	NOUN
american_scientific_journal-667	6	12	.	.	PUNCT
american_scientific_journal-667	7	1	these	these	DET
american_scientific_journal-667	7	2	graphical	graphical	ADJ
american_scientific_journal-667	7	3	views	view	NOUN
american_scientific_journal-667	7	4	have	have	VERB
american_scientific_journal-667	7	5	great	great	ADJ
american_scientific_journal-667	7	6	importance	importance	NOUN
american_scientific_journal-667	7	7	in	in	ADP
american_scientific_journal-667	7	8	many	many	ADJ
american_scientific_journal-667	7	9	fields	field	NOUN
american_scientific_journal-667	7	10	including	include	VERB
american_scientific_journal-667	7	11	engineering	engineering	NOUN
american_scientific_journal-667	7	12	,	,	PUNCT
american_scientific_journal-667	7	13	military	military	NOUN
american_scientific_journal-667	7	14	,	,	PUNCT
american_scientific_journal-667	7	15	transport	transport	NOUN
american_scientific_journal-667	7	16	,	,	PUNCT
american_scientific_journal-667	7	17	advertising	advertising	NOUN
american_scientific_journal-667	7	18	,	,	PUNCT
american_scientific_journal-667	7	19	medicine	medicine	NOUN
american_scientific_journal-667	7	20	,	,	PUNCT
american_scientific_journal-667	7	21	education	education	NOUN
american_scientific_journal-667	7	22	,	,	PUNCT
american_scientific_journal-667	7	23	art	art	NOUN
american_scientific_journal-667	7	24	,	,	PUNCT
american_scientific_journal-667	7	25	etc	etc	X
american_scientific_journal-667	7	26	.	.	X
american_scientific_journal-667	7	27	data	datum	NOUN
american_scientific_journal-667	7	28	that	that	PRON
american_scientific_journal-667	7	29	is	be	AUX
american_scientific_journal-667	7	30	used	use	VERB
american_scientific_journal-667	7	31	for	for	ADP
american_scientific_journal-667	7	32	the	the	DET
american_scientific_journal-667	7	33	visualization	visualization	NOUN
american_scientific_journal-667	7	34	has	have	VERB
american_scientific_journal-667	7	35	some	some	DET
american_scientific_journal-667	7	36	hidden	hide	VERB
american_scientific_journal-667	7	37	properties	property	NOUN
american_scientific_journal-667	7	38	such	such	ADJ
american_scientific_journal-667	7	39	as	as	ADP
american_scientific_journal-667	7	40	positive	positive	ADJ
american_scientific_journal-667	7	41	or	or	CCONJ
american_scientific_journal-667	7	42	convex	convex	ADJ
american_scientific_journal-667	7	43	[	[	X
american_scientific_journal-667	7	44	2	2	NUM
american_scientific_journal-667	7	45	]	]	PUNCT
american_scientific_journal-667	7	46	.	.	PUNCT
american_scientific_journal-667	8	1	curve	curve	NOUN
american_scientific_journal-667	8	2	design	design	NOUN
american_scientific_journal-667	8	3	plays	play	VERB
american_scientific_journal-667	8	4	a	a	DET
american_scientific_journal-667	8	5	significant	significant	ADJ
american_scientific_journal-667	8	6	role	role	NOUN
american_scientific_journal-667	8	7	in	in	ADP
american_scientific_journal-667	8	8	manufacturing	manufacture	VERB
american_scientific_journal-667	8	9	different	different	ADJ
american_scientific_journal-667	8	10	products	product	NOUN
american_scientific_journal-667	8	11	such	such	ADJ
american_scientific_journal-667	8	12	as	as	ADP
american_scientific_journal-667	8	13	ship	ship	NOUN
american_scientific_journal-667	8	14	design	design	NOUN
american_scientific_journal-667	8	15	,	,	PUNCT
american_scientific_journal-667	8	16	car	car	NOUN
american_scientific_journal-667	8	17	modeling	modeling	NOUN
american_scientific_journal-667	8	18	,	,	PUNCT
american_scientific_journal-667	8	19	and	and	CCONJ
american_scientific_journal-667	8	20	aero	aero	PROPN
american_scientific_journal-667	8	21	plane	plane	NOUN
american_scientific_journal-667	8	22	fuselages	fuselage	NOUN
american_scientific_journal-667	8	23	and	and	CCONJ
american_scientific_journal-667	8	24	wings	wing	NOUN
american_scientific_journal-667	8	25	[	[	X
american_scientific_journal-667	8	26	3	3	NUM
american_scientific_journal-667	8	27	]	]	PUNCT
american_scientific_journal-667	8	28	.	.	PUNCT
american_scientific_journal-667	9	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
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american_scientific_journal-667	10	2	corresponding	correspond	VERB
american_scientific_journal-667	10	3	author	author	NOUN
american_scientific_journal-667	10	4	.	.	PUNCT
american_scientific_journal-667	11	1	e	e	X
american_scientific_journal-667	11	2	-	-	NOUN
american_scientific_journal-667	11	3	mail	mail	NOUN
american_scientific_journal-667	11	4	address	address	NOUN
american_scientific_journal-667	11	5	:	:	PUNCT
american_scientific_journal-667	11	6	edeoabdurkadir@gmail.com	edeoabdurkadir@gmail.com	X
american_scientific_journal-667	12	1	110	110	NUM
american_scientific_journal-667	12	2	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-667	12	3	american	american	ADJ
american_scientific_journal-667	12	4	scientific	scientific	ADJ
american_scientific_journal-667	12	5	research	research	NOUN
american_scientific_journal-667	12	6	journal	journal	NOUN
american_scientific_journal-667	12	7	for	for	ADP
american_scientific_journal-667	12	8	engineering	engineering	NOUN
american_scientific_journal-667	12	9	,	,	PUNCT
american_scientific_journal-667	12	10	technology	technology	NOUN
american_scientific_journal-667	12	11	,	,	PUNCT
american_scientific_journal-667	12	12	and	and	CCONJ
american_scientific_journal-667	12	13	sciences	science	NOUN
american_scientific_journal-667	12	14	(	(	PUNCT
american_scientific_journal-667	12	15	asrjets	asrjet	NOUN
american_scientific_journal-667	12	16	)	)	PUNCT
american_scientific_journal-667	12	17	(	(	PUNCT
american_scientific_journal-667	12	18	2015	2015	NUM
american_scientific_journal-667	12	19	)	)	PUNCT
american_scientific_journal-667	12	20	volume	volume	NOUN
american_scientific_journal-667	12	21	12	12	NUM
american_scientific_journal-667	12	22	,	,	PUNCT
american_scientific_journal-667	12	23	no	no	DET
american_scientific_journal-667	12	24	1	1	NUM
american_scientific_journal-667	12	25	,	,	PUNCT
american_scientific_journal-667	12	26	pp	pp	ADV
american_scientific_journal-667	12	27	110	110	NUM
american_scientific_journal-667	12	28	-	-	SYM
american_scientific_journal-667	12	29	122	122	NUM
american_scientific_journal-667	12	30	monthly	monthly	ADJ
american_scientific_journal-667	12	31	rainfall	rainfall	NOUN
american_scientific_journal-667	12	32	amounts	amount	NOUN
american_scientific_journal-667	12	33	,	,	PUNCT
american_scientific_journal-667	12	34	levels	level	NOUN
american_scientific_journal-667	12	35	of	of	ADP
american_scientific_journal-667	12	36	gas	gas	NOUN
american_scientific_journal-667	12	37	discharge	discharge	NOUN
american_scientific_journal-667	12	38	in	in	ADP
american_scientific_journal-667	12	39	certain	certain	ADJ
american_scientific_journal-667	12	40	chemical	chemical	NOUN
american_scientific_journal-667	12	41	reactions	reaction	NOUN
american_scientific_journal-667	12	42	,	,	PUNCT
american_scientific_journal-667	12	43	progress	progress	NOUN
american_scientific_journal-667	12	44	of	of	ADP
american_scientific_journal-667	12	45	an	an	DET
american_scientific_journal-667	12	46	irreversible	irreversible	ADJ
american_scientific_journal-667	12	47	process	process	NOUN
american_scientific_journal-667	12	48	,	,	PUNCT
american_scientific_journal-667	12	49	resistance	resistance	NOUN
american_scientific_journal-667	12	50	offered	offer	VERB
american_scientific_journal-667	12	51	by	by	ADP
american_scientific_journal-667	12	52	an	an	DET
american_scientific_journal-667	12	53	electric	electric	ADJ
american_scientific_journal-667	12	54	circuit	circuit	NOUN
american_scientific_journal-667	12	55	,	,	PUNCT
american_scientific_journal-667	12	56	volume	volume	NOUN
american_scientific_journal-667	12	57	and	and	CCONJ
american_scientific_journal-667	12	58	density	density	NOUN
american_scientific_journal-667	12	59	,	,	PUNCT
american_scientific_journal-667	12	60	etc	etc	X
american_scientific_journal-667	12	61	.	.	X
american_scientific_journal-667	12	62	are	be	AUX
american_scientific_journal-667	12	63	some	some	PRON
american_scientific_journal-667	12	64	of	of	ADP
american_scientific_journal-667	12	65	the	the	DET
american_scientific_journal-667	12	66	physical	physical	ADJ
american_scientific_journal-667	12	67	quantities	quantity	NOUN
american_scientific_journal-667	12	68	which	which	PRON
american_scientific_journal-667	12	69	are	be	AUX
american_scientific_journal-667	12	70	always	always	ADV
american_scientific_journal-667	12	71	positive	positive	ADJ
american_scientific_journal-667	12	72	[	[	X
american_scientific_journal-667	12	73	1	1	NUM
american_scientific_journal-667	12	74	]	]	PUNCT
american_scientific_journal-667	12	75	.	.	PUNCT
american_scientific_journal-667	13	1	dose	dose	NOUN
american_scientific_journal-667	13	2	–	–	PUNCT
american_scientific_journal-667	13	3	response	response	NOUN
american_scientific_journal-667	13	4	curves	curve	NOUN
american_scientific_journal-667	13	5	and	and	CCONJ
american_scientific_journal-667	13	6	surfaces	surface	NOUN
american_scientific_journal-667	13	7	in	in	ADP
american_scientific_journal-667	13	8	biochemistry	biochemistry	NOUN
american_scientific_journal-667	13	9	and	and	CCONJ
american_scientific_journal-667	13	10	pharmacology	pharmacology	NOUN
american_scientific_journal-667	13	11	,	,	PUNCT
american_scientific_journal-667	13	12	approximations	approximation	NOUN
american_scientific_journal-667	13	13	of	of	ADP
american_scientific_journal-667	13	14	couples	couple	NOUN
american_scientific_journal-667	13	15	and	and	CCONJ
american_scientific_journal-667	13	16	quasi	quasi	NOUN
american_scientific_journal-667	13	17	-	-	NOUN
american_scientific_journal-667	13	18	couples	couple	NOUN
american_scientific_journal-667	13	19	in	in	ADP
american_scientific_journal-667	13	20	statistics	statistic	NOUN
american_scientific_journal-667	13	21	,	,	PUNCT
american_scientific_journal-667	13	22	empirical	empirical	ADJ
american_scientific_journal-667	13	23	option	option	NOUN
american_scientific_journal-667	13	24	pricing	pricing	NOUN
american_scientific_journal-667	13	25	model	model	NOUN
american_scientific_journal-667	13	26	in	in	ADP
american_scientific_journal-667	13	27	finance	finance	NOUN
american_scientific_journal-667	13	28	and	and	CCONJ
american_scientific_journal-667	13	29	approximation	approximation	NOUN
american_scientific_journal-667	13	30	of	of	ADP
american_scientific_journal-667	13	31	potential	potential	ADJ
american_scientific_journal-667	13	32	functions	function	NOUN
american_scientific_journal-667	13	33	in	in	ADP
american_scientific_journal-667	13	34	physical	physical	ADJ
american_scientific_journal-667	13	35	and	and	CCONJ
american_scientific_journal-667	13	36	chemical	chemical	NOUN
american_scientific_journal-667	13	37	systems	system	NOUN
american_scientific_journal-667	13	38	are	be	AUX
american_scientific_journal-667	13	39	always	always	ADV
american_scientific_journal-667	13	40	monotone	monotone	ADJ
american_scientific_journal-667	13	41	[	[	X
american_scientific_journal-667	13	42	4	4	NUM
american_scientific_journal-667	13	43	]	]	PUNCT
american_scientific_journal-667	13	44	.	.	PUNCT
american_scientific_journal-667	14	1	convexity	convexity	NOUN
american_scientific_journal-667	14	2	has	have	VERB
american_scientific_journal-667	14	3	various	various	ADJ
american_scientific_journal-667	14	4	applications	application	NOUN
american_scientific_journal-667	14	5	in	in	ADP
american_scientific_journal-667	14	6	different	different	ADJ
american_scientific_journal-667	14	7	disciplines	discipline	NOUN
american_scientific_journal-667	14	8	including	include	VERB
american_scientific_journal-667	14	9	telecommunication	telecommunication	NOUN
american_scientific_journal-667	14	10	systems	system	NOUN
american_scientific_journal-667	14	11	designing	designing	NOUN
american_scientific_journal-667	14	12	,	,	PUNCT
american_scientific_journal-667	14	13	nonlinear	nonlinear	ADJ
american_scientific_journal-667	14	14	programming	programming	NOUN
american_scientific_journal-667	14	15	,	,	PUNCT
american_scientific_journal-667	14	16	engineering	engineering	NOUN
american_scientific_journal-667	14	17	,	,	PUNCT
american_scientific_journal-667	14	18	optimization	optimization	NOUN
american_scientific_journal-667	14	19	,	,	PUNCT
american_scientific_journal-667	14	20	parameter	parameter	NOUN
american_scientific_journal-667	14	21	estimation	estimation	NOUN
american_scientific_journal-667	14	22	,	,	PUNCT
american_scientific_journal-667	14	23	approximation	approximation	NOUN
american_scientific_journal-667	14	24	theory	theory	NOUN
american_scientific_journal-667	14	25	s.	s.	PROPN
american_scientific_journal-667	14	26	butt	butt	PROPN
american_scientific_journal-667	14	27	,	,	PUNCT
american_scientific_journal-667	14	28	1991	1991	NUM
american_scientific_journal-667	14	29	cited	cite	VERB
american_scientific_journal-667	14	30	in	in	ADP
american_scientific_journal-667	14	31	[	[	X
american_scientific_journal-667	14	32	1	1	NUM
american_scientific_journal-667	14	33	]	]	PUNCT
american_scientific_journal-667	14	34	.	.	PUNCT
american_scientific_journal-667	15	1	a	a	DET
american_scientific_journal-667	15	2	lot	lot	NOUN
american_scientific_journal-667	15	3	of	of	ADP
american_scientific_journal-667	15	4	research	research	NOUN
american_scientific_journal-667	15	5	has	have	AUX
american_scientific_journal-667	15	6	been	be	AUX
american_scientific_journal-667	15	7	done	do	VERB
american_scientific_journal-667	15	8	on	on	ADP
american_scientific_journal-667	15	9	this	this	DET
american_scientific_journal-667	15	10	topic	topic	NOUN
american_scientific_journal-667	15	11	.	.	PUNCT
american_scientific_journal-667	16	1	in	in	ADP
american_scientific_journal-667	16	2	[	[	X
american_scientific_journal-667	16	3	5	5	NUM
american_scientific_journal-667	16	4	]	]	PUNCT
american_scientific_journal-667	16	5	the	the	DET
american_scientific_journal-667	16	6	authors	author	NOUN
american_scientific_journal-667	16	7	used	use	VERB
american_scientific_journal-667	16	8	a	a	DET
american_scientific_journal-667	16	9	rational	rational	ADJ
american_scientific_journal-667	16	10	cubic	cubic	ADJ
american_scientific_journal-667	16	11	function	function	NOUN
american_scientific_journal-667	16	12	in	in	ADP
american_scientific_journal-667	16	13	its	its	PRON
american_scientific_journal-667	16	14	most	most	ADV
american_scientific_journal-667	16	15	generalized	generalized	ADJ
american_scientific_journal-667	16	16	form	form	NOUN
american_scientific_journal-667	16	17	to	to	PART
american_scientific_journal-667	16	18	preserve	preserve	VERB
american_scientific_journal-667	16	19	the	the	DET
american_scientific_journal-667	16	20	shape	shape	NOUN
american_scientific_journal-667	16	21	of	of	ADP
american_scientific_journal-667	16	22	positive	positive	ADJ
american_scientific_journal-667	16	23	planar	planar	ADJ
american_scientific_journal-667	16	24	data	datum	NOUN
american_scientific_journal-667	16	25	.	.	PUNCT
american_scientific_journal-667	17	1	schmidt	schmidt	PROPN
american_scientific_journal-667	17	2	and	and	CCONJ
american_scientific_journal-667	17	3	heβ	heβ	PROPN
american_scientific_journal-667	17	4	cited	cite	VERB
american_scientific_journal-667	17	5	in	in	ADP
american_scientific_journal-667	17	6	[	[	X
american_scientific_journal-667	17	7	1	1	NUM
american_scientific_journal-667	17	8	]	]	PUNCT
american_scientific_journal-667	17	9	developed	develop	VERB
american_scientific_journal-667	17	10	sufficient	sufficient	ADJ
american_scientific_journal-667	17	11	conditions	condition	NOUN
american_scientific_journal-667	17	12	on	on	ADP
american_scientific_journal-667	17	13	derivatives	derivative	NOUN
american_scientific_journal-667	17	14	at	at	ADP
american_scientific_journal-667	17	15	the	the	DET
american_scientific_journal-667	17	16	end	end	NOUN
american_scientific_journal-667	17	17	points	point	NOUN
american_scientific_journal-667	17	18	of	of	ADP
american_scientific_journal-667	17	19	an	an	DET
american_scientific_journal-667	17	20	interval	interval	NOUN
american_scientific_journal-667	17	21	to	to	PART
american_scientific_journal-667	17	22	assure	assure	VERB
american_scientific_journal-667	17	23	the	the	DET
american_scientific_journal-667	17	24	positivity	positivity	NOUN
american_scientific_journal-667	17	25	of	of	ADP
american_scientific_journal-667	17	26	the	the	DET
american_scientific_journal-667	17	27	cubic	cubic	ADJ
american_scientific_journal-667	17	28	polynomial	polynomial	NOUN
american_scientific_journal-667	17	29	over	over	ADP
american_scientific_journal-667	17	30	the	the	DET
american_scientific_journal-667	17	31	whole	whole	ADJ
american_scientific_journal-667	17	32	interval	interval	NOUN
american_scientific_journal-667	17	33	.	.	PUNCT
american_scientific_journal-667	18	1	the	the	DET
american_scientific_journal-667	18	2	authors	author	NOUN
american_scientific_journal-667	18	3	in	in	ADP
american_scientific_journal-667	18	4	[	[	X
american_scientific_journal-667	18	5	3	3	NUM
american_scientific_journal-667	18	6	]	]	PUNCT
american_scientific_journal-667	18	7	developed	develop	VERB
american_scientific_journal-667	18	8	a	a	DET
american_scientific_journal-667	18	9	c2	c2	PROPN
american_scientific_journal-667	18	10	piecewise	piecewise	NOUN
american_scientific_journal-667	18	11	rational	rational	ADJ
american_scientific_journal-667	18	12	cubic	cubic	ADJ
american_scientific_journal-667	18	13	spline	spline	NOUN
american_scientific_journal-667	18	14	scheme	scheme	NOUN
american_scientific_journal-667	18	15	to	to	PART
american_scientific_journal-667	18	16	address	address	VERB
american_scientific_journal-667	18	17	the	the	DET
american_scientific_journal-667	18	18	problem	problem	NOUN
american_scientific_journal-667	18	19	of	of	ADP
american_scientific_journal-667	18	20	constructing	construct	VERB
american_scientific_journal-667	18	21	a	a	DET
american_scientific_journal-667	18	22	positivity	positivity	NOUN
american_scientific_journal-667	18	23	-	-	PUNCT
american_scientific_journal-667	18	24	preserving	preserve	VERB
american_scientific_journal-667	18	25	curve	curve	NOUN
american_scientific_journal-667	18	26	through	through	ADP
american_scientific_journal-667	18	27	positive	positive	ADJ
american_scientific_journal-667	18	28	data	datum	NOUN
american_scientific_journal-667	18	29	.	.	PUNCT
american_scientific_journal-667	19	1	in	in	ADP
american_scientific_journal-667	19	2	[	[	X
american_scientific_journal-667	19	3	2	2	X
american_scientific_journal-667	19	4	]	]	PUNCT
american_scientific_journal-667	19	5	the	the	DET
american_scientific_journal-667	19	6	authors	author	NOUN
american_scientific_journal-667	19	7	introduced	introduce	VERB
american_scientific_journal-667	19	8	c2	c2	PROPN
american_scientific_journal-667	19	9	rational	rational	ADJ
american_scientific_journal-667	19	10	cubic	cubic	ADJ
american_scientific_journal-667	19	11	function	function	NOUN
american_scientific_journal-667	19	12	with	with	ADP
american_scientific_journal-667	19	13	two	two	NUM
american_scientific_journal-667	19	14	families	family	NOUN
american_scientific_journal-667	19	15	of	of	ADP
american_scientific_journal-667	19	16	free	free	ADJ
american_scientific_journal-667	19	17	parameters	parameter	NOUN
american_scientific_journal-667	19	18	to	to	PART
american_scientific_journal-667	19	19	attain	attain	VERB
american_scientific_journal-667	19	20	the	the	DET
american_scientific_journal-667	19	21	c2	c2	PROPN
american_scientific_journal-667	19	22	positive	positive	ADJ
american_scientific_journal-667	19	23	curves	curve	NOUN
american_scientific_journal-667	19	24	from	from	ADP
american_scientific_journal-667	19	25	positive	positive	ADJ
american_scientific_journal-667	19	26	data	datum	NOUN
american_scientific_journal-667	19	27	.	.	PUNCT
american_scientific_journal-667	20	1	in	in	ADP
american_scientific_journal-667	20	2	[	[	X
american_scientific_journal-667	20	3	6	6	NUM
american_scientific_journal-667	20	4	]	]	PUNCT
american_scientific_journal-667	20	5	the	the	DET
american_scientific_journal-667	20	6	authors	author	NOUN
american_scientific_journal-667	20	7	addressed	address	VERB
american_scientific_journal-667	20	8	the	the	DET
american_scientific_journal-667	20	9	problem	problem	NOUN
american_scientific_journal-667	20	10	of	of	ADP
american_scientific_journal-667	20	11	visualizing	visualize	VERB
american_scientific_journal-667	20	12	positive	positive	ADJ
american_scientific_journal-667	20	13	data	datum	NOUN
american_scientific_journal-667	20	14	by	by	ADP
american_scientific_journal-667	20	15	imposing	impose	VERB
american_scientific_journal-667	20	16	c1	c1	NOUN
american_scientific_journal-667	20	17	continuity	continuity	NOUN
american_scientific_journal-667	20	18	on	on	ADP
american_scientific_journal-667	20	19	rational	rational	ADJ
american_scientific_journal-667	20	20	cubic	cubic	ADJ
american_scientific_journal-667	20	21	function	function	NOUN
american_scientific_journal-667	20	22	.	.	PUNCT
american_scientific_journal-667	21	1	fuhr	fuhr	PROPN
american_scientific_journal-667	21	2	and	and	CCONJ
american_scientific_journal-667	21	3	kallay	kallay	PROPN
american_scientific_journal-667	21	4	1992	1992	NUM
american_scientific_journal-667	21	5	cited	cite	VERB
american_scientific_journal-667	21	6	in	in	ADP
american_scientific_journal-667	21	7	[	[	X
american_scientific_journal-667	21	8	1	1	NUM
american_scientific_journal-667	21	9	]	]	PUNCT
american_scientific_journal-667	21	10	used	use	VERB
american_scientific_journal-667	21	11	a	a	DET
american_scientific_journal-667	21	12	c1	c1	NOUN
american_scientific_journal-667	21	13	monotone	monotone	ADJ
american_scientific_journal-667	21	14	rational	rational	ADJ
american_scientific_journal-667	21	15	b	b	NOUN
american_scientific_journal-667	21	16	-	-	PUNCT
american_scientific_journal-667	21	17	spline	spline	NOUN
american_scientific_journal-667	21	18	of	of	ADP
american_scientific_journal-667	21	19	degree	degree	NOUN
american_scientific_journal-667	21	20	one	one	NOUN
american_scientific_journal-667	21	21	to	to	PART
american_scientific_journal-667	21	22	preserve	preserve	VERB
american_scientific_journal-667	21	23	the	the	DET
american_scientific_journal-667	21	24	shape	shape	NOUN
american_scientific_journal-667	21	25	of	of	ADP
american_scientific_journal-667	21	26	monotone	monotone	ADJ
american_scientific_journal-667	21	27	data	datum	NOUN
american_scientific_journal-667	21	28	.	.	PUNCT
american_scientific_journal-667	22	1	the	the	DET
american_scientific_journal-667	22	2	authors	author	NOUN
american_scientific_journal-667	22	3	in	in	ADP
american_scientific_journal-667	22	4	[	[	X
american_scientific_journal-667	22	5	7	7	NUM
american_scientific_journal-667	22	6	]	]	PUNCT
american_scientific_journal-667	22	7	studied	study	VERB
american_scientific_journal-667	22	8	the	the	DET
american_scientific_journal-667	22	9	problem	problem	NOUN
american_scientific_journal-667	22	10	of	of	ADP
american_scientific_journal-667	22	11	constructing	construct	VERB
american_scientific_journal-667	22	12	a	a	DET
american_scientific_journal-667	22	13	monotonicity	monotonicity	NOUN
american_scientific_journal-667	22	14	preserving	preserve	VERB
american_scientific_journal-667	22	15	curve	curve	NOUN
american_scientific_journal-667	22	16	through	through	ADP
american_scientific_journal-667	22	17	monotone	monotone	ADJ
american_scientific_journal-667	22	18	data	datum	NOUN
american_scientific_journal-667	22	19	using	use	VERB
american_scientific_journal-667	22	20	c2	c2	PROPN
american_scientific_journal-667	22	21	rational	rational	ADJ
american_scientific_journal-667	22	22	cubic	cubic	ADJ
american_scientific_journal-667	22	23	spline	spline	NOUN
american_scientific_journal-667	22	24	.	.	PUNCT
american_scientific_journal-667	23	1	in	in	ADP
american_scientific_journal-667	23	2	[	[	X
american_scientific_journal-667	23	3	8	8	NUM
american_scientific_journal-667	23	4	]	]	PUNCT
american_scientific_journal-667	23	5	the	the	DET
american_scientific_journal-667	23	6	authors	author	NOUN
american_scientific_journal-667	23	7	visualized	visualize	VERB
american_scientific_journal-667	23	8	monotone	monotone	ADJ
american_scientific_journal-667	23	9	data	datum	NOUN
american_scientific_journal-667	23	10	by	by	ADP
american_scientific_journal-667	23	11	using	use	VERB
american_scientific_journal-667	23	12	piecewise	piecewise	NOUN
american_scientific_journal-667	23	13	rational	rational	ADJ
american_scientific_journal-667	23	14	cubic	cubic	ADJ
american_scientific_journal-667	23	15	function	function	NOUN
american_scientific_journal-667	23	16	.	.	PUNCT
american_scientific_journal-667	24	1	the	the	DET
american_scientific_journal-667	24	2	smoothness	smoothness	NOUN
american_scientific_journal-667	24	3	of	of	ADP
american_scientific_journal-667	24	4	the	the	DET
american_scientific_journal-667	24	5	interpolation	interpolation	NOUN
american_scientific_journal-667	24	6	is	be	AUX
american_scientific_journal-667	24	7	c1	c1	NOUN
american_scientific_journal-667	24	8	continuity	continuity	NOUN
american_scientific_journal-667	24	9	.	.	PUNCT
american_scientific_journal-667	25	1	reference	reference	NOUN
american_scientific_journal-667	25	2	[	[	X
american_scientific_journal-667	25	3	9	9	NUM
american_scientific_journal-667	25	4	]	]	PUNCT
american_scientific_journal-667	25	5	developed	develop	VERB
american_scientific_journal-667	25	6	an	an	DET
american_scientific_journal-667	25	7	explicit	explicit	ADJ
american_scientific_journal-667	25	8	representation	representation	NOUN
american_scientific_journal-667	25	9	of	of	ADP
american_scientific_journal-667	25	10	a	a	DET
american_scientific_journal-667	25	11	c1	c1	PROPN
american_scientific_journal-667	25	12	piecewise	piecewise	NOUN
american_scientific_journal-667	25	13	rational	rational	ADJ
american_scientific_journal-667	25	14	cubic	cubic	ADJ
american_scientific_journal-667	25	15	spline	spline	NOUN
american_scientific_journal-667	25	16	which	which	PRON
american_scientific_journal-667	25	17	can	can	AUX
american_scientific_journal-667	25	18	produce	produce	VERB
american_scientific_journal-667	25	19	a	a	DET
american_scientific_journal-667	25	20	monotonic	monotonic	ADJ
american_scientific_journal-667	25	21	interpolant	interpolant	NOUN
american_scientific_journal-667	25	22	to	to	ADP
american_scientific_journal-667	25	23	a	a	DET
american_scientific_journal-667	25	24	given	give	VERB
american_scientific_journal-667	25	25	monotone	monotone	ADJ
american_scientific_journal-667	25	26	data	datum	NOUN
american_scientific_journal-667	25	27	.	.	PUNCT
american_scientific_journal-667	26	1	brodlie	brodlie	PROPN
american_scientific_journal-667	26	2	and	and	CCONJ
american_scientific_journal-667	26	3	butt	butt	PROPN
american_scientific_journal-667	26	4	1991	1991	NUM
american_scientific_journal-667	26	5	cited	cite	VERB
american_scientific_journal-667	26	6	in	in	ADP
american_scientific_journal-667	26	7	[	[	X
american_scientific_journal-667	26	8	1	1	NUM
american_scientific_journal-667	26	9	]	]	PUNCT
american_scientific_journal-667	26	10	preserved	preserve	VERB
american_scientific_journal-667	26	11	the	the	DET
american_scientific_journal-667	26	12	shape	shape	NOUN
american_scientific_journal-667	26	13	of	of	ADP
american_scientific_journal-667	26	14	convex	convex	NOUN
american_scientific_journal-667	26	15	data	datum	NOUN
american_scientific_journal-667	26	16	by	by	ADP
american_scientific_journal-667	26	17	piecewise	piecewise	NOUN
american_scientific_journal-667	26	18	cubic	cubic	ADJ
american_scientific_journal-667	26	19	interpolation	interpolation	NOUN
american_scientific_journal-667	26	20	.	.	PUNCT
american_scientific_journal-667	27	1	in	in	ADP
american_scientific_journal-667	27	2	any	any	DET
american_scientific_journal-667	27	3	interval	interval	NOUN
american_scientific_journal-667	27	4	where	where	SCONJ
american_scientific_journal-667	27	5	convexity	convexity	NOUN
american_scientific_journal-667	27	6	was	be	AUX
american_scientific_journal-667	27	7	lost	lose	VERB
american_scientific_journal-667	27	8	,	,	PUNCT
american_scientific_journal-667	27	9	they	they	PRON
american_scientific_journal-667	27	10	divided	divide	VERB
american_scientific_journal-667	27	11	the	the	DET
american_scientific_journal-667	27	12	interval	interval	NOUN
american_scientific_journal-667	27	13	into	into	ADP
american_scientific_journal-667	27	14	two	two	NUM
american_scientific_journal-667	27	15	subintervals	subinterval	NOUN
american_scientific_journal-667	27	16	by	by	ADP
american_scientific_journal-667	27	17	inserting	insert	VERB
american_scientific_journal-667	27	18	extra	extra	ADJ
american_scientific_journal-667	27	19	knots	knot	NOUN
american_scientific_journal-667	27	20	into	into	ADP
american_scientific_journal-667	27	21	that	that	DET
american_scientific_journal-667	27	22	interval	interval	NOUN
american_scientific_journal-667	27	23	.	.	PUNCT
american_scientific_journal-667	28	1	the	the	DET
american_scientific_journal-667	28	2	method	method	NOUN
american_scientific_journal-667	28	3	that	that	PRON
american_scientific_journal-667	28	4	was	be	AUX
american_scientific_journal-667	28	5	presented	present	VERB
american_scientific_journal-667	28	6	was	be	AUX
american_scientific_journal-667	28	7	c1.a	c1.a	PROPN
american_scientific_journal-667	28	8	c2	c2	PROPN
american_scientific_journal-667	28	9	rational	rational	ADJ
american_scientific_journal-667	28	10	cubic	cubic	ADJ
american_scientific_journal-667	28	11	function	function	NOUN
american_scientific_journal-667	28	12	with	with	SCONJ
american_scientific_journal-667	28	13	two	two	NUM
american_scientific_journal-667	28	14	families	family	NOUN
american_scientific_journal-667	28	15	of	of	ADP
american_scientific_journal-667	28	16	free	free	ADJ
american_scientific_journal-667	28	17	parameters	parameter	NOUN
american_scientific_journal-667	28	18	has	have	AUX
american_scientific_journal-667	28	19	been	be	AUX
american_scientific_journal-667	28	20	introduced	introduce	VERB
american_scientific_journal-667	28	21	to	to	PART
american_scientific_journal-667	28	22	attain	attain	VERB
american_scientific_journal-667	28	23	c2	c2	PROPN
american_scientific_journal-667	28	24	convex	convex	PROPN
american_scientific_journal-667	28	25	curves	curve	NOUN
american_scientific_journal-667	28	26	from	from	ADP
american_scientific_journal-667	28	27	convex	convex	ADJ
american_scientific_journal-667	28	28	data	datum	NOUN
american_scientific_journal-667	28	29	[	[	X
american_scientific_journal-667	28	30	2	2	NUM
american_scientific_journal-667	28	31	]	]	PUNCT
american_scientific_journal-667	28	32	.	.	PUNCT
american_scientific_journal-667	29	1	reference	reference	NOUN
american_scientific_journal-667	29	2	[	[	X
american_scientific_journal-667	29	3	10	10	NUM
american_scientific_journal-667	29	4	]	]	PUNCT
american_scientific_journal-667	29	5	surveyed	survey	VERB
american_scientific_journal-667	29	6	the	the	DET
american_scientific_journal-667	29	7	shape	shape	NOUN
american_scientific_journal-667	29	8	-	-	PUNCT
american_scientific_journal-667	29	9	preserving	preserve	VERB
american_scientific_journal-667	29	10	interpolating	interpolate	VERB
american_scientific_journal-667	29	11	algorithms	algorithm	NOUN
american_scientific_journal-667	29	12	for	for	ADP
american_scientific_journal-667	29	13	2d	2d	PROPN
american_scientific_journal-667	29	14	data	datum	NOUN
american_scientific_journal-667	29	15	.	.	PUNCT
american_scientific_journal-667	30	1	reference	reference	NOUN
american_scientific_journal-667	31	1	[	[	X
american_scientific_journal-667	31	2	11	11	NUM
american_scientific_journal-667	31	3	]	]	PUNCT
american_scientific_journal-667	31	4	used	use	VERB
american_scientific_journal-667	31	5	cubic	cubic	ADJ
american_scientific_journal-667	31	6	hermite	hermite	ADJ
american_scientific_journal-667	31	7	in	in	ADP
american_scientific_journal-667	31	8	a	a	DET
american_scientific_journal-667	31	9	parametric	parametric	ADJ
american_scientific_journal-667	31	10	form	form	NOUN
american_scientific_journal-667	31	11	to	to	PART
american_scientific_journal-667	31	12	preserve	preserve	VERB
american_scientific_journal-667	31	13	the	the	DET
american_scientific_journal-667	31	14	shape	shape	NOUN
american_scientific_journal-667	31	15	of	of	ADP
american_scientific_journal-667	31	16	data	datum	NOUN
american_scientific_journal-667	31	17	.	.	PUNCT
american_scientific_journal-667	32	1	the	the	DET
american_scientific_journal-667	32	2	step	step	NOUN
american_scientific_journal-667	32	3	lengths	length	NOUN
american_scientific_journal-667	32	4	were	be	AUX
american_scientific_journal-667	32	5	used	use	VERB
american_scientific_journal-667	32	6	as	as	ADP
american_scientific_journal-667	32	7	tension	tension	NOUN
american_scientific_journal-667	32	8	parameters	parameter	NOUN
american_scientific_journal-667	32	9	to	to	PART
american_scientific_journal-667	32	10	preserve	preserve	VERB
american_scientific_journal-667	32	11	the	the	DET
american_scientific_journal-667	32	12	shape	shape	NOUN
american_scientific_journal-667	32	13	of	of	ADP
american_scientific_journal-667	32	14	planar	planar	ADJ
american_scientific_journal-667	32	15	functional	functional	ADJ
american_scientific_journal-667	32	16	data	datum	NOUN
american_scientific_journal-667	32	17	.	.	PUNCT
american_scientific_journal-667	33	1	the	the	DET
american_scientific_journal-667	33	2	first	first	ADJ
american_scientific_journal-667	33	3	-	-	PUNCT
american_scientific_journal-667	33	4	order	order	NOUN
american_scientific_journal-667	33	5	derivatives	derivative	NOUN
american_scientific_journal-667	33	6	at	at	ADP
american_scientific_journal-667	33	7	the	the	DET
american_scientific_journal-667	33	8	knots	knot	NOUN
american_scientific_journal-667	33	9	were	be	AUX
american_scientific_journal-667	33	10	estimated	estimate	VERB
american_scientific_journal-667	33	11	by	by	ADP
american_scientific_journal-667	33	12	a	a	DET
american_scientific_journal-667	33	13	tridiagonal	tridiagonal	ADJ
american_scientific_journal-667	33	14	system	system	NOUN
american_scientific_journal-667	33	15	of	of	ADP
american_scientific_journal-667	33	16	equations	equation	NOUN
american_scientific_journal-667	33	17	which	which	PRON
american_scientific_journal-667	33	18	assured	assure	VERB
american_scientific_journal-667	33	19	c2	c2	PROPN
american_scientific_journal-667	33	20	continuity	continuity	NOUN
american_scientific_journal-667	33	21	at	at	ADP
american_scientific_journal-667	33	22	the	the	DET
american_scientific_journal-667	33	23	knots	knot	NOUN
american_scientific_journal-667	33	24	.	.	PUNCT
american_scientific_journal-667	34	1	reference	reference	NOUN
american_scientific_journal-667	35	1	[	[	X
american_scientific_journal-667	35	2	12	12	NUM
american_scientific_journal-667	35	3	]	]	PUNCT
american_scientific_journal-667	35	4	proposed	propose	VERB
american_scientific_journal-667	35	5	a	a	DET
american_scientific_journal-667	35	6	direct	direct	ADJ
american_scientific_journal-667	35	7	,	,	PUNCT
american_scientific_journal-667	35	8	inexpensive	inexpensive	ADJ
american_scientific_journal-667	35	9	,	,	PUNCT
american_scientific_journal-667	35	10	constructive	constructive	ADJ
american_scientific_journal-667	35	11	method	method	NOUN
american_scientific_journal-667	35	12	for	for	ADP
american_scientific_journal-667	35	13	interpolating	interpolate	VERB
american_scientific_journal-667	35	14	convex	convex	NOUN
american_scientific_journal-667	35	15	,	,	PUNCT
american_scientific_journal-667	35	16	monotone	monotone	ADJ
american_scientific_journal-667	35	17	data	datum	NOUN
american_scientific_journal-667	35	18	using	use	VERB
american_scientific_journal-667	35	19	shape	shape	NOUN
american_scientific_journal-667	35	20	-	-	PUNCT
american_scientific_journal-667	35	21	preserving	preserve	VERB
american_scientific_journal-667	35	22	c2	c2	PROPN
american_scientific_journal-667	35	23	cubic	cubic	ADJ
american_scientific_journal-667	35	24	polynomial	polynomial	ADJ
american_scientific_journal-667	35	25	splines	spline	NOUN
american_scientific_journal-667	35	26	[	[	X
american_scientific_journal-667	35	27	1	1	X
american_scientific_journal-667	35	28	]	]	PUNCT
american_scientific_journal-667	35	29	discussed	discuss	VERB
american_scientific_journal-667	35	30	the	the	DET
american_scientific_journal-667	35	31	three	three	NUM
american_scientific_journal-667	35	32	important	important	ADJ
american_scientific_journal-667	35	33	shapes	shape	NOUN
american_scientific_journal-667	35	34	within	within	ADP
american_scientific_journal-667	35	35	one	one	NUM
american_scientific_journal-667	35	36	mathematical	mathematical	ADJ
american_scientific_journal-667	35	37	model	model	NOUN
american_scientific_journal-667	35	38	.	.	PUNCT
american_scientific_journal-667	36	1	they	they	PRON
american_scientific_journal-667	36	2	introduced	introduce	VERB
american_scientific_journal-667	36	3	a	a	DET
american_scientific_journal-667	36	4	c1	c1	NOUN
american_scientific_journal-667	36	5	rational	rational	ADJ
american_scientific_journal-667	36	6	function	function	NOUN
american_scientific_journal-667	36	7	with	with	ADP
american_scientific_journal-667	36	8	cubic	cubic	ADJ
american_scientific_journal-667	36	9	numerator	numerator	NOUN
american_scientific_journal-667	36	10	and	and	CCONJ
american_scientific_journal-667	36	11	cubic	cubic	ADJ
american_scientific_journal-667	36	12	denominator	denominator	NOUN
american_scientific_journal-667	36	13	involving	involve	VERB
american_scientific_journal-667	36	14	four	four	NUM
american_scientific_journal-667	36	15	free	free	ADJ
american_scientific_journal-667	36	16	parameters	parameter	NOUN
american_scientific_journal-667	36	17	.	.	PUNCT
american_scientific_journal-667	37	1	positivity	positivity	NOUN
american_scientific_journal-667	37	2	,	,	PUNCT
american_scientific_journal-667	37	3	monotony	monotony	NOUN
american_scientific_journal-667	37	4	and	and	CCONJ
american_scientific_journal-667	37	5	convexity	convexity	NOUN
american_scientific_journal-667	37	6	are	be	AUX
american_scientific_journal-667	37	7	very	very	ADV
american_scientific_journal-667	37	8	important	important	ADJ
american_scientific_journal-667	37	9	independent	independent	ADJ
american_scientific_journal-667	37	10	shape	shape	NOUN
american_scientific_journal-667	37	11	features	feature	NOUN
american_scientific_journal-667	37	12	which	which	PRON
american_scientific_journal-667	37	13	are	be	AUX
american_scientific_journal-667	37	14	found	find	VERB
american_scientific_journal-667	37	15	inherited	inherit	VERB
american_scientific_journal-667	37	16	in	in	ADP
american_scientific_journal-667	37	17	a	a	DET
american_scientific_journal-667	37	18	data	data	NOUN
american_scientific_journal-667	37	19	,	,	PUNCT
american_scientific_journal-667	37	20	under	under	ADP
american_scientific_journal-667	37	21	different	different	ADJ
american_scientific_journal-667	37	22	conditions	condition	NOUN
american_scientific_journal-667	37	23	and	and	CCONJ
american_scientific_journal-667	37	24	circumstances	circumstance	NOUN
american_scientific_journal-667	37	25	,	,	PUNCT
american_scientific_journal-667	37	26	in	in	ADP
american_scientific_journal-667	37	27	one	one	NUM
american_scientific_journal-667	37	28	form	form	NOUN
american_scientific_journal-667	37	29	or	or	CCONJ
american_scientific_journal-667	37	30	the	the	DET
american_scientific_journal-667	37	31	other	other	ADJ
american_scientific_journal-667	37	32	.	.	PUNCT
american_scientific_journal-667	38	1	in	in	ADP
american_scientific_journal-667	38	2	computer	computer	NOUN
american_scientific_journal-667	38	3	graphics	graphic	NOUN
american_scientific_journal-667	38	4	environment	environment	PROPN
american_scientific_journal-667	38	5	,	,	PUNCT
american_scientific_journal-667	38	6	a	a	DET
american_scientific_journal-667	38	7	user	user	NOUN
american_scientific_journal-667	38	8	is	be	AUX
american_scientific_journal-667	38	9	always	always	ADV
american_scientific_journal-667	38	10	in	in	ADP
american_scientific_journal-667	38	11	need	need	NOUN
american_scientific_journal-667	38	12	of	of	ADP
american_scientific_journal-667	38	13	interpolatory	interpolatory	NOUN
american_scientific_journal-667	38	14	schemes	scheme	NOUN
american_scientific_journal-667	38	15	which	which	PRON
american_scientific_journal-667	38	16	preserve	preserve	VERB
american_scientific_journal-667	38	17	the	the	DET
american_scientific_journal-667	38	18	shape	shape	NOUN
american_scientific_journal-667	38	19	of	of	ADP
american_scientific_journal-667	38	20	the	the	DET
american_scientific_journal-667	38	21	data	datum	NOUN
american_scientific_journal-667	38	22	under	under	ADP
american_scientific_journal-667	38	23	consideration	consideration	NOUN
american_scientific_journal-667	38	24	under	under	ADP
american_scientific_journal-667	38	25	different	different	ADJ
american_scientific_journal-667	38	26	conditions	condition	NOUN
american_scientific_journal-667	38	27	and	and	CCONJ
american_scientific_journal-667	38	28	circumstances	circumstance	NOUN
american_scientific_journal-667	38	29	[	[	X
american_scientific_journal-667	38	30	1	1	NUM
american_scientific_journal-667	38	31	]	]	PUNCT
american_scientific_journal-667	38	32	.	.	PUNCT
american_scientific_journal-667	39	1	the	the	DET
american_scientific_journal-667	39	2	problem	problem	NOUN
american_scientific_journal-667	39	3	of	of	ADP
american_scientific_journal-667	39	4	constructing	construct	VERB
american_scientific_journal-667	39	5	a	a	DET
american_scientific_journal-667	39	6	shape	shape	NOUN
american_scientific_journal-667	39	7	preserving	preserve	VERB
american_scientific_journal-667	39	8	curve	curve	NOUN
american_scientific_journal-667	39	9	through	through	ADP
american_scientific_journal-667	39	10	given	give	VERB
american_scientific_journal-667	39	11	data	datum	NOUN
american_scientific_journal-667	39	12	points	point	NOUN
american_scientific_journal-667	39	13	is	be	AUX
american_scientific_journal-667	39	14	one	one	NUM
american_scientific_journal-667	39	15	of	of	ADP
american_scientific_journal-667	39	16	the	the	DET
american_scientific_journal-667	39	17	basic	basic	ADJ
american_scientific_journal-667	39	18	problems	problem	NOUN
american_scientific_journal-667	39	19	in	in	ADP
american_scientific_journal-667	39	20	computer	computer	NOUN
american_scientific_journal-667	39	21	graphics	graphic	NOUN
american_scientific_journal-667	39	22	,	,	PUNCT
american_scientific_journal-667	39	23	computer	computer	NOUN
american_scientific_journal-667	39	24	aided	aid	VERB
american_scientific_journal-667	39	25	geometric	geometric	ADJ
american_scientific_journal-667	39	26	111	111	NUM
american_scientific_journal-667	39	27	american	american	ADJ
american_scientific_journal-667	39	28	scientific	scientific	ADJ
american_scientific_journal-667	39	29	research	research	NOUN
american_scientific_journal-667	39	30	journal	journal	NOUN
american_scientific_journal-667	39	31	for	for	ADP
american_scientific_journal-667	39	32	engineering	engineering	NOUN
american_scientific_journal-667	39	33	,	,	PUNCT
american_scientific_journal-667	39	34	technology	technology	NOUN
american_scientific_journal-667	39	35	,	,	PUNCT
american_scientific_journal-667	39	36	and	and	CCONJ
american_scientific_journal-667	39	37	sciences	science	NOUN
american_scientific_journal-667	39	38	(	(	PUNCT
american_scientific_journal-667	39	39	asrjets	asrjet	NOUN
american_scientific_journal-667	39	40	)	)	PUNCT
american_scientific_journal-667	39	41	(	(	PUNCT
american_scientific_journal-667	39	42	2015	2015	NUM
american_scientific_journal-667	39	43	)	)	PUNCT
american_scientific_journal-667	39	44	volume	volume	NOUN
american_scientific_journal-667	39	45	12	12	NUM
american_scientific_journal-667	39	46	,	,	PUNCT
american_scientific_journal-667	39	47	no	no	DET
american_scientific_journal-667	39	48	1	1	NUM
american_scientific_journal-667	39	49	,	,	PUNCT
american_scientific_journal-667	39	50	pp	pp	ADV
american_scientific_journal-667	39	51	110	110	NUM
american_scientific_journal-667	39	52	-	-	SYM
american_scientific_journal-667	39	53	122	122	NUM
american_scientific_journal-667	39	54	design	design	NOUN
american_scientific_journal-667	39	55	,	,	PUNCT
american_scientific_journal-667	39	56	data	data	NOUN
american_scientific_journal-667	39	57	visualization	visualization	NOUN
american_scientific_journal-667	39	58	and	and	CCONJ
american_scientific_journal-667	39	59	engineering	engineering	NOUN
american_scientific_journal-667	39	60	.	.	PUNCT
american_scientific_journal-667	40	1	classical	classical	ADJ
american_scientific_journal-667	40	2	methods	method	NOUN
american_scientific_journal-667	40	3	,	,	PUNCT
american_scientific_journal-667	40	4	with	with	ADP
american_scientific_journal-667	40	5	the	the	DET
american_scientific_journal-667	40	6	polynomial	polynomial	ADJ
american_scientific_journal-667	40	7	spline	spline	NOUN
american_scientific_journal-667	40	8	functions	function	NOUN
american_scientific_journal-667	40	9	,	,	PUNCT
american_scientific_journal-667	40	10	show	show	VERB
american_scientific_journal-667	40	11	smooth	smooth	ADJ
american_scientific_journal-667	40	12	and	and	CCONJ
american_scientific_journal-667	40	13	visually	visually	ADV
american_scientific_journal-667	40	14	pleasing	pleasing	ADJ
american_scientific_journal-667	40	15	results	result	NOUN
american_scientific_journal-667	40	16	but	but	CCONJ
american_scientific_journal-667	40	17	usually	usually	ADV
american_scientific_journal-667	40	18	ignore	ignore	VERB
american_scientific_journal-667	40	19	these	these	DET
american_scientific_journal-667	40	20	shape	shape	NOUN
american_scientific_journal-667	40	21	features	feature	NOUN
american_scientific_journal-667	40	22	of	of	ADP
american_scientific_journal-667	40	23	data	datum	NOUN
american_scientific_journal-667	40	24	and	and	CCONJ
american_scientific_journal-667	40	25	thus	thus	ADV
american_scientific_journal-667	40	26	yield	yield	VERB
american_scientific_journal-667	40	27	solutions	solution	NOUN
american_scientific_journal-667	40	28	exhibiting	exhibit	VERB
american_scientific_journal-667	40	29	undesirable	undesirable	ADJ
american_scientific_journal-667	40	30	undulations	undulation	NOUN
american_scientific_journal-667	40	31	or	or	CCONJ
american_scientific_journal-667	40	32	oscillations	oscillation	NOUN
american_scientific_journal-667	40	33	[	[	X
american_scientific_journal-667	40	34	3	3	NUM
american_scientific_journal-667	40	35	]	]	PUNCT
american_scientific_journal-667	40	36	.	.	PUNCT
american_scientific_journal-667	41	1	this	this	DET
american_scientific_journal-667	41	2	study	study	NOUN
american_scientific_journal-667	41	3	is	be	AUX
american_scientific_journal-667	41	4	a	a	DET
american_scientific_journal-667	41	5	contribution	contribution	NOUN
american_scientific_journal-667	41	6	towards	towards	ADP
american_scientific_journal-667	41	7	achieving	achieve	VERB
american_scientific_journal-667	41	8	shape	shape	NOUN
american_scientific_journal-667	41	9	preserving	preserve	VERB
american_scientific_journal-667	41	10	curves	curve	NOUN
american_scientific_journal-667	41	11	for	for	ADP
american_scientific_journal-667	41	12	positive	positive	ADJ
american_scientific_journal-667	41	13	,	,	PUNCT
american_scientific_journal-667	41	14	monotone	monotone	ADJ
american_scientific_journal-667	41	15	and	and	CCONJ
american_scientific_journal-667	41	16	convex	convex	ADJ
american_scientific_journal-667	41	17	data	datum	NOUN
american_scientific_journal-667	41	18	using	use	VERB
american_scientific_journal-667	41	19	one	one	NUM
american_scientific_journal-667	41	20	mathematical	mathematical	ADJ
american_scientific_journal-667	41	21	model	model	NOUN
american_scientific_journal-667	41	22	.	.	PUNCT
american_scientific_journal-667	42	1	several	several	ADJ
american_scientific_journal-667	42	2	researches	research	NOUN
american_scientific_journal-667	42	3	were	be	AUX
american_scientific_journal-667	42	4	focused	focus	VERB
american_scientific_journal-667	42	5	on	on	ADP
american_scientific_journal-667	42	6	studying	study	VERB
american_scientific_journal-667	42	7	the	the	DET
american_scientific_journal-667	42	8	three	three	NUM
american_scientific_journal-667	42	9	shape	shape	NOUN
american_scientific_journal-667	42	10	features	feature	NOUN
american_scientific_journal-667	42	11	independently	independently	ADV
american_scientific_journal-667	42	12	using	use	VERB
american_scientific_journal-667	42	13	different	different	ADJ
american_scientific_journal-667	42	14	mathematical	mathematical	ADJ
american_scientific_journal-667	42	15	models	model	NOUN
american_scientific_journal-667	42	16	and	and	CCONJ
american_scientific_journal-667	42	17	methodologies	methodology	NOUN
american_scientific_journal-667	42	18	.	.	PUNCT
american_scientific_journal-667	43	1	even	even	ADV
american_scientific_journal-667	43	2	though	though	ADV
american_scientific_journal-667	43	3	,	,	PUNCT
american_scientific_journal-667	43	4	the	the	DET
american_scientific_journal-667	43	5	authors	author	NOUN
american_scientific_journal-667	43	6	in	in	ADP
american_scientific_journal-667	43	7	[	[	X
american_scientific_journal-667	43	8	1	1	NUM
american_scientific_journal-667	43	9	]	]	PUNCT
american_scientific_journal-667	43	10	tried	try	VERB
american_scientific_journal-667	43	11	to	to	PART
american_scientific_journal-667	43	12	preserve	preserve	VERB
american_scientific_journal-667	43	13	these	these	DET
american_scientific_journal-667	43	14	three	three	NUM
american_scientific_journal-667	43	15	shape	shape	NOUN
american_scientific_journal-667	43	16	features	feature	NOUN
american_scientific_journal-667	43	17	of	of	ADP
american_scientific_journal-667	43	18	data	datum	NOUN
american_scientific_journal-667	43	19	under	under	ADP
american_scientific_journal-667	43	20	one	one	NUM
american_scientific_journal-667	43	21	mathematical	mathematical	ADJ
american_scientific_journal-667	43	22	model	model	NOUN
american_scientific_journal-667	43	23	and	and	CCONJ
american_scientific_journal-667	43	24	methodologies	methodology	NOUN
american_scientific_journal-667	43	25	,	,	PUNCT
american_scientific_journal-667	43	26	they	they	PRON
american_scientific_journal-667	43	27	imposed	impose	VERB
american_scientific_journal-667	43	28	a	a	DET
american_scientific_journal-667	43	29	rational	rational	ADJ
american_scientific_journal-667	43	30	cubic	cubic	ADJ
american_scientific_journal-667	43	31	interpolant	interpolant	NOUN
american_scientific_journal-667	43	32	∈	∈	PROPN
american_scientific_journal-667	43	33	𝐶1[𝑎	𝐶1[𝑎	PROPN
american_scientific_journal-667	43	34	,	,	PUNCT
american_scientific_journal-667	43	35	𝑏	𝑏	NOUN
american_scientific_journal-667	43	36	]	]	PUNCT
american_scientific_journal-667	43	37	.	.	PUNCT
american_scientific_journal-667	44	1	thus	thus	ADV
american_scientific_journal-667	44	2	,	,	PUNCT
american_scientific_journal-667	44	3	the	the	DET
american_scientific_journal-667	44	4	purpose	purpose	NOUN
american_scientific_journal-667	44	5	of	of	ADP
american_scientific_journal-667	44	6	this	this	DET
american_scientific_journal-667	44	7	study	study	NOUN
american_scientific_journal-667	44	8	was	be	AUX
american_scientific_journal-667	44	9	to	to	PART
american_scientific_journal-667	44	10	construct	construct	VERB
american_scientific_journal-667	44	11	a	a	DET
american_scientific_journal-667	44	12	piecewise	piecewise	NOUN
american_scientific_journal-667	44	13	rational	rational	ADJ
american_scientific_journal-667	44	14	cubic	cubic	ADJ
american_scientific_journal-667	44	15	spline	spline	NOUN
american_scientific_journal-667	44	16	function	function	NOUN
american_scientific_journal-667	44	17	which	which	PRON
american_scientific_journal-667	44	18	can	can	AUX
american_scientific_journal-667	44	19	preserve	preserve	VERB
american_scientific_journal-667	44	20	the	the	DET
american_scientific_journal-667	44	21	three	three	NUM
american_scientific_journal-667	44	22	important	important	ADJ
american_scientific_journal-667	44	23	shapes	shape	NOUN
american_scientific_journal-667	44	24	within	within	ADP
american_scientific_journal-667	44	25	one	one	NUM
american_scientific_journal-667	44	26	mathematical	mathematical	ADJ
american_scientific_journal-667	44	27	model	model	NOUN
american_scientific_journal-667	44	28	.	.	PUNCT
american_scientific_journal-667	45	1	in	in	ADP
american_scientific_journal-667	45	2	addition	addition	NOUN
american_scientific_journal-667	45	3	,	,	PUNCT
american_scientific_journal-667	45	4	this	this	DET
american_scientific_journal-667	45	5	study	study	NOUN
american_scientific_journal-667	45	6	is	be	AUX
american_scientific_journal-667	45	7	aimed	aim	VERB
american_scientific_journal-667	45	8	to	to	PART
american_scientific_journal-667	45	9	extend	extend	VERB
american_scientific_journal-667	45	10	the	the	DET
american_scientific_journal-667	45	11	result	result	NOUN
american_scientific_journal-667	45	12	of	of	ADP
american_scientific_journal-667	45	13	[	[	X
american_scientific_journal-667	45	14	1	1	X
american_scientific_journal-667	45	15	]	]	PUNCT
american_scientific_journal-667	45	16	to	to	ADP
american_scientific_journal-667	45	17	a	a	DET
american_scientific_journal-667	45	18	rational	rational	ADJ
american_scientific_journal-667	45	19	cubic	cubic	ADJ
american_scientific_journal-667	45	20	interpolant	interpolant	NOUN
american_scientific_journal-667	45	21	𝑆	𝑆	PROPN
american_scientific_journal-667	45	22	∈	∈	PROPN
american_scientific_journal-667	45	23	𝐶2[𝑎	𝐶2[𝑎	NOUN
american_scientific_journal-667	45	24	,	,	PUNCT
american_scientific_journal-667	45	25	𝑏	𝑏	NOUN
american_scientific_journal-667	45	26	]	]	X
american_scientific_journal-667	45	27	.	.	PUNCT
american_scientific_journal-667	46	1	the	the	DET
american_scientific_journal-667	46	2	developed	develop	VERB
american_scientific_journal-667	46	3	scheme	scheme	NOUN
american_scientific_journal-667	46	4	has	have	VERB
american_scientific_journal-667	46	5	the	the	DET
american_scientific_journal-667	46	6	following	follow	VERB
american_scientific_journal-667	46	7	advantageous	advantageous	ADJ
american_scientific_journal-667	46	8	over	over	ADP
american_scientific_journal-667	46	9	the	the	DET
american_scientific_journal-667	46	10	other	other	ADJ
american_scientific_journal-667	46	11	existing	exist	VERB
american_scientific_journal-667	46	12	schemes	scheme	NOUN
american_scientific_journal-667	46	13	:	:	PUNCT
american_scientific_journal-667	46	14	•	•	NUM
american_scientific_journal-667	46	15	it	it	PRON
american_scientific_journal-667	46	16	works	work	VERB
american_scientific_journal-667	46	17	for	for	ADP
american_scientific_journal-667	46	18	both	both	CCONJ
american_scientific_journal-667	46	19	equally	equally	ADV
american_scientific_journal-667	46	20	and	and	CCONJ
american_scientific_journal-667	46	21	unequally	unequally	ADV
american_scientific_journal-667	46	22	spaced	space	VERB
american_scientific_journal-667	46	23	data	datum	NOUN
american_scientific_journal-667	46	24	.	.	PUNCT
american_scientific_journal-667	47	1	•	•	NUM
american_scientific_journal-667	47	2	the	the	DET
american_scientific_journal-667	47	3	order	order	NOUN
american_scientific_journal-667	47	4	of	of	ADP
american_scientific_journal-667	47	5	continuity	continuity	NOUN
american_scientific_journal-667	47	6	attained	attain	VERB
american_scientific_journal-667	47	7	is	be	AUX
american_scientific_journal-667	47	8	c2	c2	PROPN
american_scientific_journal-667	47	9	.	.	PUNCT
american_scientific_journal-667	48	1	•	•	NUM
american_scientific_journal-667	48	2	we	we	PRON
american_scientific_journal-667	48	3	obtained	obtain	VERB
american_scientific_journal-667	48	4	only	only	ADV
american_scientific_journal-667	48	5	one	one	NUM
american_scientific_journal-667	48	6	tridiagonal	tridiagonal	ADJ
american_scientific_journal-667	48	7	system	system	NOUN
american_scientific_journal-667	48	8	of	of	ADP
american_scientific_journal-667	48	9	linear	linear	PROPN
american_scientific_journal-667	48	10	equations	equation	NOUN
american_scientific_journal-667	48	11	,	,	PUNCT
american_scientific_journal-667	48	12	for	for	ADP
american_scientific_journal-667	48	13	finding	find	VERB
american_scientific_journal-667	48	14	the	the	DET
american_scientific_journal-667	48	15	values	value	NOUN
american_scientific_journal-667	48	16	of	of	ADP
american_scientific_journal-667	48	17	derivative	derivative	ADJ
american_scientific_journal-667	48	18	parameters	parameter	NOUN
american_scientific_journal-667	48	19	.	.	PUNCT
american_scientific_journal-667	49	1	•	•	NUM
american_scientific_journal-667	49	2	the	the	DET
american_scientific_journal-667	49	3	schemes	scheme	NOUN
american_scientific_journal-667	49	4	developed	develop	VERB
american_scientific_journal-667	49	5	in	in	ADP
american_scientific_journal-667	49	6	this	this	DET
american_scientific_journal-667	49	7	study	study	NOUN
american_scientific_journal-667	49	8	is	be	AUX
american_scientific_journal-667	49	9	smoother	smooth	ADJ
american_scientific_journal-667	49	10	and	and	CCONJ
american_scientific_journal-667	49	11	visually	visually	ADV
american_scientific_journal-667	49	12	pleasing	pleasing	ADJ
american_scientific_journal-667	49	13	as	as	SCONJ
american_scientific_journal-667	49	14	compared	compare	VERB
american_scientific_journal-667	49	15	to	to	ADP
american_scientific_journal-667	49	16	the	the	DET
american_scientific_journal-667	49	17	other	other	ADJ
american_scientific_journal-667	49	18	schemes	scheme	NOUN
american_scientific_journal-667	49	19	with	with	ADP
american_scientific_journal-667	49	20	order	order	NOUN
american_scientific_journal-667	49	21	of	of	ADP
american_scientific_journal-667	49	22	continuity	continuity	NOUN
american_scientific_journal-667	49	23	c1	c1	NOUN
american_scientific_journal-667	49	24	.	.	PUNCT
american_scientific_journal-667	50	1	•	•	NUM
american_scientific_journal-667	50	2	the	the	DET
american_scientific_journal-667	50	3	schemes	scheme	NOUN
american_scientific_journal-667	50	4	developed	develop	VERB
american_scientific_journal-667	50	5	in	in	ADP
american_scientific_journal-667	50	6	this	this	DET
american_scientific_journal-667	50	7	study	study	NOUN
american_scientific_journal-667	50	8	preserves	preserve	VERB
american_scientific_journal-667	50	9	these	these	DET
american_scientific_journal-667	50	10	three	three	NUM
american_scientific_journal-667	50	11	important	important	ADJ
american_scientific_journal-667	50	12	shape	shape	NOUN
american_scientific_journal-667	50	13	features	feature	NOUN
american_scientific_journal-667	50	14	of	of	ADP
american_scientific_journal-667	50	15	data	datum	NOUN
american_scientific_journal-667	50	16	within	within	ADP
american_scientific_journal-667	50	17	one	one	NUM
american_scientific_journal-667	50	18	mathematical	mathematical	ADJ
american_scientific_journal-667	50	19	model	model	NOUN
american_scientific_journal-667	50	20	.	.	PUNCT
american_scientific_journal-667	51	1	besides	besides	SCONJ
american_scientific_journal-667	51	2	shape	shape	NOUN
american_scientific_journal-667	51	3	preservation	preservation	NOUN
american_scientific_journal-667	51	4	,	,	PUNCT
american_scientific_journal-667	51	5	shape	shape	NOUN
american_scientific_journal-667	51	6	control	control	NOUN
american_scientific_journal-667	51	7	and	and	CCONJ
american_scientific_journal-667	51	8	shape	shape	NOUN
american_scientific_journal-667	51	9	design	design	NOUN
american_scientific_journal-667	51	10	are	be	AUX
american_scientific_journal-667	51	11	important	important	ADJ
american_scientific_journal-667	51	12	areas	area	NOUN
american_scientific_journal-667	51	13	for	for	ADP
american_scientific_journal-667	51	14	the	the	DET
american_scientific_journal-667	51	15	graphical	graphical	ADJ
american_scientific_journal-667	51	16	representation	representation	NOUN
american_scientific_journal-667	51	17	of	of	ADP
american_scientific_journal-667	51	18	data	datum	NOUN
american_scientific_journal-667	51	19	.	.	PUNCT
american_scientific_journal-667	52	1	this	this	DET
american_scientific_journal-667	52	2	paper	paper	NOUN
american_scientific_journal-667	52	3	is	be	AUX
american_scientific_journal-667	52	4	delimited	delimit	VERB
american_scientific_journal-667	52	5	to	to	ADP
american_scientific_journal-667	52	6	the	the	DET
american_scientific_journal-667	52	7	area	area	NOUN
american_scientific_journal-667	52	8	of	of	ADP
american_scientific_journal-667	52	9	shape	shape	NOUN
american_scientific_journal-667	52	10	preservation	preservation	NOUN
american_scientific_journal-667	52	11	.	.	PUNCT
american_scientific_journal-667	53	1	the	the	DET
american_scientific_journal-667	53	2	remainder	remainder	NOUN
american_scientific_journal-667	53	3	of	of	ADP
american_scientific_journal-667	53	4	this	this	DET
american_scientific_journal-667	53	5	paper	paper	NOUN
american_scientific_journal-667	53	6	has	have	AUX
american_scientific_journal-667	53	7	been	be	AUX
american_scientific_journal-667	53	8	organized	organize	VERB
american_scientific_journal-667	53	9	as	as	ADP
american_scientific_journal-667	53	10	in	in	ADP
american_scientific_journal-667	53	11	the	the	DET
american_scientific_journal-667	53	12	following	follow	VERB
american_scientific_journal-667	53	13	order	order	NOUN
american_scientific_journal-667	53	14	and	and	CCONJ
american_scientific_journal-667	53	15	procedures	procedure	NOUN
american_scientific_journal-667	53	16	:	:	PUNCT
american_scientific_journal-667	53	17	•	•	NUM
american_scientific_journal-667	53	18	c2	c2	PROPN
american_scientific_journal-667	53	19	rational	rational	ADJ
american_scientific_journal-667	53	20	cubic	cubic	ADJ
american_scientific_journal-667	53	21	function	function	NOUN
american_scientific_journal-667	53	22	with	with	ADP
american_scientific_journal-667	53	23	two	two	NUM
american_scientific_journal-667	53	24	free	free	ADJ
american_scientific_journal-667	53	25	parameters	parameter	NOUN
american_scientific_journal-667	53	26	in	in	ADP
american_scientific_journal-667	53	27	its	its	PRON
american_scientific_journal-667	53	28	description	description	NOUN
american_scientific_journal-667	53	29	has	have	AUX
american_scientific_journal-667	53	30	been	be	AUX
american_scientific_journal-667	53	31	discussed	discuss	VERB
american_scientific_journal-667	53	32	.	.	PUNCT
american_scientific_journal-667	54	1	•	•	INTJ
american_scientific_journal-667	54	2	we	we	PRON
american_scientific_journal-667	54	3	developed	develop	VERB
american_scientific_journal-667	54	4	the	the	DET
american_scientific_journal-667	54	5	conditions	condition	NOUN
american_scientific_journal-667	54	6	on	on	ADP
american_scientific_journal-667	54	7	a	a	DET
american_scientific_journal-667	54	8	single	single	ADJ
american_scientific_journal-667	54	9	shape	shape	NOUN
american_scientific_journal-667	54	10	parameter	parameter	NOUN
american_scientific_journal-667	54	11	to	to	PART
american_scientific_journal-667	54	12	preserve	preserve	VERB
american_scientific_journal-667	54	13	the	the	DET
american_scientific_journal-667	54	14	positivity	positivity	NOUN
american_scientific_journal-667	54	15	of	of	ADP
american_scientific_journal-667	54	16	a	a	DET
american_scientific_journal-667	54	17	positive	positive	ADJ
american_scientific_journal-667	54	18	data	datum	NOUN
american_scientific_journal-667	54	19	.	.	PUNCT
american_scientific_journal-667	55	1	•	•	NUM
american_scientific_journal-667	55	2	the	the	DET
american_scientific_journal-667	55	3	conditions	condition	NOUN
american_scientific_journal-667	55	4	on	on	ADP
american_scientific_journal-667	55	5	a	a	DET
american_scientific_journal-667	55	6	single	single	ADJ
american_scientific_journal-667	55	7	shape	shape	NOUN
american_scientific_journal-667	55	8	parameter	parameter	NOUN
american_scientific_journal-667	55	9	has	have	AUX
american_scientific_journal-667	55	10	been	be	AUX
american_scientific_journal-667	55	11	derived	derive	VERB
american_scientific_journal-667	55	12	to	to	PART
american_scientific_journal-667	55	13	preserve	preserve	VERB
american_scientific_journal-667	55	14	respectively	respectively	ADV
american_scientific_journal-667	55	15	,	,	PUNCT
american_scientific_journal-667	55	16	the	the	DET
american_scientific_journal-667	55	17	monotonicity	monotonicity	NOUN
american_scientific_journal-667	55	18	and	and	CCONJ
american_scientific_journal-667	55	19	convexity	convexity	NOUN
american_scientific_journal-667	55	20	of	of	ADP
american_scientific_journal-667	55	21	monotone	monotone	ADJ
american_scientific_journal-667	55	22	and	and	CCONJ
american_scientific_journal-667	55	23	convex	convex	PROPN
american_scientific_journal-667	55	24	data	datum	NOUN
american_scientific_journal-667	55	25	.	.	PUNCT
american_scientific_journal-667	56	1	•	•	INTJ
american_scientific_journal-667	56	2	we	we	PRON
american_scientific_journal-667	56	3	provided	provide	VERB
american_scientific_journal-667	56	4	numerical	numerical	ADJ
american_scientific_journal-667	56	5	examples	example	NOUN
american_scientific_journal-667	56	6	and	and	CCONJ
american_scientific_journal-667	56	7	demonstrated	demonstrate	VERB
american_scientific_journal-667	56	8	the	the	DET
american_scientific_journal-667	56	9	results	result	NOUN
american_scientific_journal-667	56	10	visually	visually	ADV
american_scientific_journal-667	56	11	using	use	VERB
american_scientific_journal-667	56	12	graphs	graph	NOUN
american_scientific_journal-667	56	13	.	.	PUNCT
american_scientific_journal-667	57	1	•	•	NUM
american_scientific_journal-667	57	2	finally	finally	ADV
american_scientific_journal-667	57	3	,	,	PUNCT
american_scientific_journal-667	57	4	we	we	PRON
american_scientific_journal-667	57	5	concluded	conclude	VERB
american_scientific_journal-667	57	6	the	the	DET
american_scientific_journal-667	57	7	paper	paper	NOUN
american_scientific_journal-667	57	8	and	and	CCONJ
american_scientific_journal-667	57	9	recommended	recommend	VERB
american_scientific_journal-667	57	10	.	.	PUNCT
american_scientific_journal-667	58	1	2	2	X
american_scientific_journal-667	58	2	.	.	X
american_scientific_journal-667	58	3	materials	material	NOUN
american_scientific_journal-667	58	4	and	and	CCONJ
american_scientific_journal-667	58	5	methods	method	NOUN
american_scientific_journal-667	58	6	let	let	VERB
american_scientific_journal-667	58	7	{	{	PUNCT
american_scientific_journal-667	58	8	(	(	PUNCT
american_scientific_journal-667	58	9	𝑥𝑖	𝑥𝑖	PROPN
american_scientific_journal-667	58	10	,	,	PUNCT
american_scientific_journal-667	58	11	𝑓𝑖	𝑓𝑖	PROPN
american_scientific_journal-667	58	12	)	)	PUNCT
american_scientific_journal-667	58	13	,	,	PUNCT
american_scientific_journal-667	58	14	𝑖	𝑖	NOUN
american_scientific_journal-667	58	15	=	=	SYM
american_scientific_journal-667	58	16	1	1	NUM
american_scientific_journal-667	58	17	,	,	PUNCT
american_scientific_journal-667	58	18	2	2	NUM
american_scientific_journal-667	58	19	,	,	PUNCT
american_scientific_journal-667	58	20	.	.	PUNCT
american_scientific_journal-667	58	21	.	.	PUNCT
american_scientific_journal-667	58	22	.	.	PUNCT
american_scientific_journal-667	59	1	,	,	PUNCT
american_scientific_journal-667	59	2	𝑛	𝑛	X
american_scientific_journal-667	59	3	}	}	PUNCT
american_scientific_journal-667	59	4	be	be	AUX
american_scientific_journal-667	59	5	a	a	DET
american_scientific_journal-667	59	6	given	give	VERB
american_scientific_journal-667	59	7	set	set	NOUN
american_scientific_journal-667	59	8	of	of	ADP
american_scientific_journal-667	59	9	data	datum	NOUN
american_scientific_journal-667	59	10	points	point	NOUN
american_scientific_journal-667	59	11	defined	define	VERB
american_scientific_journal-667	59	12	over	over	ADP
american_scientific_journal-667	59	13	the	the	DET
american_scientific_journal-667	59	14	interval	interval	NOUN
american_scientific_journal-667	59	15	[	[	X
american_scientific_journal-667	59	16	𝑎	𝑎	X
american_scientific_journal-667	59	17	,	,	PUNCT
american_scientific_journal-667	59	18	𝑏	𝑏	NOUN
american_scientific_journal-667	59	19	]	]	X
american_scientific_journal-667	59	20	,	,	PUNCT
american_scientific_journal-667	60	1	where	where	SCONJ
american_scientific_journal-667	60	2	𝑎	𝑎	PROPN
american_scientific_journal-667	60	3	=	=	SYM
american_scientific_journal-667	60	4	𝑥1	𝑥1	NOUN
american_scientific_journal-667	60	5	<	<	X
american_scientific_journal-667	60	6	𝑥2	𝑥2	NOUN
american_scientific_journal-667	60	7	<	<	X
american_scientific_journal-667	60	8	·	·	PUNCT
american_scientific_journal-667	60	9	·	·	PUNCT
american_scientific_journal-667	60	10	·	·	PUNCT
american_scientific_journal-667	60	11	<	<	X
american_scientific_journal-667	60	12	𝑥𝑛	𝑥𝑛	X
american_scientific_journal-667	60	13	=	=	PUNCT
american_scientific_journal-667	60	14	𝑏.	𝑏.	VERB
american_scientific_journal-667	60	15	the	the	DET
american_scientific_journal-667	60	16	piecewise	piecewise	NOUN
american_scientific_journal-667	60	17	rational	rational	ADJ
american_scientific_journal-667	60	18	cubic	cubic	ADJ
american_scientific_journal-667	60	19	function	function	NOUN
american_scientific_journal-667	60	20	𝑆	𝑆	PROPN
american_scientific_journal-667	60	21	∈	∈	PROPN
american_scientific_journal-667	60	22	𝐶2[𝑎	𝐶2[𝑎	NOUN
american_scientific_journal-667	60	23	,	,	PUNCT
american_scientific_journal-667	60	24	𝑏	𝑏	NOUN
american_scientific_journal-667	60	25	]	]	PUNCT
american_scientific_journal-667	60	26	involving	involve	VERB
american_scientific_journal-667	60	27	two	two	NUM
american_scientific_journal-667	60	28	free	free	ADJ
american_scientific_journal-667	60	29	parameters	parameter	NOUN
american_scientific_journal-667	60	30	(	(	PUNCT
american_scientific_journal-667	60	31	𝑢𝑖	𝑢𝑖	INTJ
american_scientific_journal-667	60	32	,	,	PUNCT
american_scientific_journal-667	60	33	𝑣𝑖	𝑣𝑖	ADV
american_scientific_journal-667	60	34	>	>	X
american_scientific_journal-667	60	35	0	0	NUM
american_scientific_journal-667	60	36	)	)	PUNCT
american_scientific_journal-667	60	37	,	,	PUNCT
american_scientific_journal-667	60	38	over	over	ADP
american_scientific_journal-667	60	39	each	each	DET
american_scientific_journal-667	60	40	subinterval	subinterval	NOUN
american_scientific_journal-667	60	41	𝐼𝑖	𝐼𝑖	PROPN
american_scientific_journal-667	60	42	=	=	PUNCT
american_scientific_journal-667	61	1	[	[	X
american_scientific_journal-667	61	2	𝑥𝑖	𝑥𝑖	X
american_scientific_journal-667	61	3	,	,	PUNCT
american_scientific_journal-667	61	4	𝑥𝑖+1	𝑥𝑖+1	PROPN
american_scientific_journal-667	61	5	]	]	PUNCT
american_scientific_journal-667	61	6	,	,	PUNCT
american_scientific_journal-667	61	7	𝑖	𝑖	SYM
american_scientific_journal-667	61	8	=	=	SYM
american_scientific_journal-667	61	9	1	1	NUM
american_scientific_journal-667	61	10	,	,	PUNCT
american_scientific_journal-667	61	11	2	2	NUM
american_scientific_journal-667	61	12	,	,	PUNCT
american_scientific_journal-667	61	13	.	.	PUNCT
american_scientific_journal-667	61	14	.	.	PUNCT
american_scientific_journal-667	61	15	.	.	PUNCT
american_scientific_journal-667	62	1	,	,	PUNCT
american_scientific_journal-667	62	2	𝑛	𝑛	DET
american_scientific_journal-667	62	3	−	−	NOUN
american_scientific_journal-667	62	4	1	1	NUM
american_scientific_journal-667	62	5	,	,	PUNCT
american_scientific_journal-667	62	6	is	be	AUX
american_scientific_journal-667	62	7	defined	define	VERB
american_scientific_journal-667	62	8	by	by	ADP
american_scientific_journal-667	62	9	[	[	X
american_scientific_journal-667	62	10	13	13	NUM
american_scientific_journal-667	62	11	]	]	PUNCT
american_scientific_journal-667	62	12	as	as	ADP
american_scientific_journal-667	62	13	:	:	PUNCT
american_scientific_journal-667	62	14	112	112	NUM
american_scientific_journal-667	62	15	american	american	ADJ
american_scientific_journal-667	62	16	scientific	scientific	ADJ
american_scientific_journal-667	62	17	research	research	NOUN
american_scientific_journal-667	62	18	journal	journal	NOUN
american_scientific_journal-667	62	19	for	for	ADP
american_scientific_journal-667	62	20	engineering	engineering	NOUN
american_scientific_journal-667	62	21	,	,	PUNCT
american_scientific_journal-667	62	22	technology	technology	NOUN
american_scientific_journal-667	62	23	,	,	PUNCT
american_scientific_journal-667	62	24	and	and	CCONJ
american_scientific_journal-667	62	25	sciences	science	NOUN
american_scientific_journal-667	62	26	(	(	PUNCT
american_scientific_journal-667	62	27	asrjets	asrjet	NOUN
american_scientific_journal-667	62	28	)	)	PUNCT
american_scientific_journal-667	62	29	(	(	PUNCT
american_scientific_journal-667	62	30	2015	2015	NUM
american_scientific_journal-667	62	31	)	)	PUNCT
american_scientific_journal-667	62	32	volume	volume	NOUN
american_scientific_journal-667	62	33	12	12	NUM
american_scientific_journal-667	62	34	,	,	PUNCT
american_scientific_journal-667	62	35	no	no	DET
american_scientific_journal-667	62	36	1	1	NUM
american_scientific_journal-667	62	37	,	,	PUNCT
american_scientific_journal-667	62	38	pp	pp	ADV
american_scientific_journal-667	62	39	110	110	NUM
american_scientific_journal-667	62	40	-	-	SYM
american_scientific_journal-667	62	41	122	122	NUM
american_scientific_journal-667	62	42	𝑆(𝑥	𝑆(𝑥	NOUN
american_scientific_journal-667	62	43	)	)	PUNCT
american_scientific_journal-667	62	44	=	=	PUNCT
american_scientific_journal-667	62	45	∑	∑	PUNCT
american_scientific_journal-667	62	46	(	(	PUNCT
american_scientific_journal-667	62	47	1−𝜃)3−𝑖𝜃𝑖𝐴𝑖3	1−𝜃)3−𝑖𝜃𝑖𝐴𝑖3	NUM
american_scientific_journal-667	62	48	𝑖=0	𝑖=0	PROPN
american_scientific_journal-667	62	49	𝑢𝑖(1−𝜃)+	𝑢𝑖(1−𝜃)+	ADJ
american_scientific_journal-667	62	50	𝑣𝑖𝜃	𝑣𝑖𝜃	NOUN
american_scientific_journal-667	62	51	(	(	PUNCT
american_scientific_journal-667	62	52	1	1	NUM
american_scientific_journal-667	62	53	)	)	PUNCT
american_scientific_journal-667	62	54	where	where	SCONJ
american_scientific_journal-667	62	55	ℎ𝑖	ℎ𝑖	NOUN
american_scientific_journal-667	62	56	=	=	PUNCT
american_scientific_journal-667	62	57	𝑥𝑖+1	𝑥𝑖+1	PROPN
american_scientific_journal-667	62	58	−	−	PROPN
american_scientific_journal-667	62	59	𝑥𝑖	𝑥𝑖	PROPN
american_scientific_journal-667	62	60	,	,	PUNCT
american_scientific_journal-667	62	61	𝑥𝑖	𝑥𝑖	ADV
american_scientific_journal-667	62	62	≤	≤	NUM
american_scientific_journal-667	62	63	𝑥	𝑥	DET
american_scientific_journal-667	62	64	≤	≤	NUM
american_scientific_journal-667	62	65	𝑥𝑖+1	𝑥𝑖+1	PROPN
american_scientific_journal-667	62	66	,	,	PUNCT
american_scientific_journal-667	62	67	𝜃	𝜃	X
american_scientific_journal-667	62	68	=	=	SYM
american_scientific_journal-667	62	69	(	(	PUNCT
american_scientific_journal-667	62	70	𝑥−𝑥𝑖	𝑥−𝑥𝑖	PROPN
american_scientific_journal-667	62	71	)	)	PUNCT
american_scientific_journal-667	62	72	ℎ𝑖	ℎ𝑖	NOUN
american_scientific_journal-667	62	73	,	,	PUNCT
american_scientific_journal-667	62	74	𝜃	𝜃	X
american_scientific_journal-667	62	75	∈	∈	NOUN
american_scientific_journal-667	63	1	[	[	X
american_scientific_journal-667	63	2	0,1	0,1	NUM
american_scientific_journal-667	63	3	]	]	PUNCT
american_scientific_journal-667	63	4	with	with	ADP
american_scientific_journal-667	63	5	c2	c2	PROPN
american_scientific_journal-667	63	6	interpolatory	interpolatory	NOUN
american_scientific_journal-667	63	7	conditions	condition	NOUN
american_scientific_journal-667	63	8	:	:	PUNCT
american_scientific_journal-667	63	9	𝑆(𝑥𝑖	𝑆(𝑥𝑖	PROPN
american_scientific_journal-667	63	10	)	)	PUNCT
american_scientific_journal-667	63	11	=	=	SYM
american_scientific_journal-667	63	12	𝑓𝑖	𝑓𝑖	PROPN
american_scientific_journal-667	63	13	,	,	PUNCT
american_scientific_journal-667	63	14	𝑆(𝑥𝑖+1	𝑆(𝑥𝑖+1	PROPN
american_scientific_journal-667	63	15	)	)	PUNCT
american_scientific_journal-667	63	16	=	=	SYM
american_scientific_journal-667	63	17	𝑓𝑖+1	𝑓𝑖+1	NOUN
american_scientific_journal-667	63	18	,	,	PUNCT
american_scientific_journal-667	63	19	𝑆(1)(𝑥𝑖	𝑆(1)(𝑥𝑖	PROPN
american_scientific_journal-667	63	20	)	)	PUNCT
american_scientific_journal-667	63	21	=	=	SYM
american_scientific_journal-667	63	22	𝑑𝑖	𝑑𝑖	PROPN
american_scientific_journal-667	63	23	,	,	PUNCT
american_scientific_journal-667	63	24	𝑆(1)(𝑥𝑖+1	𝑆(1)(𝑥𝑖+1	PROPN
american_scientific_journal-667	63	25	)	)	PUNCT
american_scientific_journal-667	63	26	=	=	SYM
american_scientific_journal-667	63	27	𝑑𝑖+1	𝑑𝑖+1	NUM
american_scientific_journal-667	63	28	,	,	PUNCT
american_scientific_journal-667	63	29	(	(	PUNCT
american_scientific_journal-667	63	30	2	2	X
american_scientific_journal-667	63	31	)	)	PUNCT
american_scientific_journal-667	63	32	𝑆(2)(𝑥𝑖+	𝑆(2)(𝑥𝑖+	NUM
american_scientific_journal-667	63	33	)	)	PUNCT
american_scientific_journal-667	63	34	=	=	SYM
american_scientific_journal-667	63	35	𝑆(2)(𝑥𝑖−	𝑆(2)(𝑥𝑖−	PROPN
american_scientific_journal-667	63	36	)	)	PUNCT
american_scientific_journal-667	63	37	;	;	PUNCT
american_scientific_journal-667	63	38	𝑖	𝑖	SYM
american_scientific_journal-667	63	39	=	=	SYM
american_scientific_journal-667	63	40	2	2	NUM
american_scientific_journal-667	63	41	,	,	PUNCT
american_scientific_journal-667	63	42	3	3	NUM
american_scientific_journal-667	63	43	,	,	PUNCT
american_scientific_journal-667	63	44	.	.	PUNCT
american_scientific_journal-667	63	45	.	.	PUNCT
american_scientific_journal-667	63	46	.	.	PUNCT
american_scientific_journal-667	64	1	,	,	PUNCT
american_scientific_journal-667	64	2	𝑛	𝑛	DET
american_scientific_journal-667	64	3	−	−	PROPN
american_scientific_journal-667	64	4	1	1	NUM
american_scientific_journal-667	64	5	;	;	PUNCT
american_scientific_journal-667	64	6	where	where	SCONJ
american_scientific_journal-667	64	7	𝑆(1)(𝑥	𝑆(1)(𝑥	NOUN
american_scientific_journal-667	64	8	)	)	PUNCT
american_scientific_journal-667	64	9	and	and	CCONJ
american_scientific_journal-667	64	10	𝑆(2)(𝑥	𝑆(2)(𝑥	PROPN
american_scientific_journal-667	64	11	)	)	PUNCT
american_scientific_journal-667	64	12	denote	denote	VERB
american_scientific_journal-667	64	13	the	the	DET
american_scientific_journal-667	64	14	first	first	ADJ
american_scientific_journal-667	64	15	and	and	CCONJ
american_scientific_journal-667	64	16	second	second	ADJ
american_scientific_journal-667	64	17	ordered	order	VERB
american_scientific_journal-667	64	18	derivatives	derivative	NOUN
american_scientific_journal-667	64	19	with	with	ADP
american_scientific_journal-667	64	20	respect	respect	NOUN
american_scientific_journal-667	64	21	to	to	ADP
american_scientific_journal-667	64	22	𝑥	𝑥	PRON
american_scientific_journal-667	64	23	,	,	PUNCT
american_scientific_journal-667	64	24	the	the	DET
american_scientific_journal-667	64	25	+	+	ADJ
american_scientific_journal-667	64	26	and	and	CCONJ
american_scientific_journal-667	64	27	−	−	PROPN
american_scientific_journal-667	64	28	subscripts	subscript	NOUN
american_scientific_journal-667	64	29	denote	denote	VERB
american_scientific_journal-667	64	30	the	the	DET
american_scientific_journal-667	64	31	right	right	NOUN
american_scientific_journal-667	64	32	and	and	CCONJ
american_scientific_journal-667	64	33	left	leave	VERB
american_scientific_journal-667	64	34	derivatives	derivative	NOUN
american_scientific_journal-667	64	35	respectively	respectively	ADV
american_scientific_journal-667	64	36	,	,	PUNCT
american_scientific_journal-667	64	37	𝑑𝑖	𝑑𝑖	PROPN
american_scientific_journal-667	64	38	denote	denote	VERB
american_scientific_journal-667	64	39	the	the	DET
american_scientific_journal-667	64	40	unknown	unknown	ADJ
american_scientific_journal-667	64	41	derivative	derivative	ADJ
american_scientific_journal-667	64	42	values	value	NOUN
american_scientific_journal-667	64	43	at	at	ADP
american_scientific_journal-667	64	44	given	give	VERB
american_scientific_journal-667	64	45	knots	knot	NOUN
american_scientific_journal-667	64	46	𝑥𝑖	𝑥𝑖	PROPN
american_scientific_journal-667	64	47	that	that	PRON
american_scientific_journal-667	64	48	are	be	AUX
american_scientific_journal-667	64	49	used	use	VERB
american_scientific_journal-667	64	50	for	for	ADP
american_scientific_journal-667	64	51	the	the	DET
american_scientific_journal-667	64	52	smoothness	smoothness	NOUN
american_scientific_journal-667	64	53	of	of	ADP
american_scientific_journal-667	64	54	curve	curve	NOUN
american_scientific_journal-667	64	55	.	.	PUNCT
american_scientific_journal-667	65	1	the	the	DET
american_scientific_journal-667	65	2	c2	c2	PROPN
american_scientific_journal-667	65	3	interpolating	interpolate	VERB
american_scientific_journal-667	65	4	conditions	condition	NOUN
american_scientific_journal-667	65	5	produce	produce	VERB
american_scientific_journal-667	65	6	the	the	DET
american_scientific_journal-667	65	7	following	follow	VERB
american_scientific_journal-667	65	8	unknown	unknown	ADJ
american_scientific_journal-667	65	9	coefficients	coefficient	NOUN
american_scientific_journal-667	66	1	𝐴𝑖	𝐴𝑖	PROPN
american_scientific_journal-667	66	2	,	,	PUNCT
american_scientific_journal-667	66	3	𝑖	𝑖	X
american_scientific_journal-667	66	4	=	=	SYM
american_scientific_journal-667	66	5	0	0	NUM
american_scientific_journal-667	66	6	,	,	PUNCT
american_scientific_journal-667	66	7	1	1	NUM
american_scientific_journal-667	66	8	,	,	PUNCT
american_scientific_journal-667	66	9	2	2	NUM
american_scientific_journal-667	66	10	,	,	PUNCT
american_scientific_journal-667	67	1	3	3	NUM
american_scientific_journal-667	67	2	𝐴0	𝐴0	NOUN
american_scientific_journal-667	67	3	=	=	SYM
american_scientific_journal-667	67	4	𝑢𝑖𝑓𝑖	𝑢𝑖𝑓𝑖	NOUN
american_scientific_journal-667	67	5	𝐴1	𝐴1	PROPN
american_scientific_journal-667	67	6	=	=	SYM
american_scientific_journal-667	68	1	𝑓𝑖(2𝑢𝑖	𝑓𝑖(2𝑢𝑖	PROPN
american_scientific_journal-667	68	2	+	+	CCONJ
american_scientific_journal-667	68	3	𝑣𝑖	𝑣𝑖	ADP
american_scientific_journal-667	68	4	)	)	PUNCT
american_scientific_journal-667	69	1	+	+	CCONJ
american_scientific_journal-667	69	2	𝑢𝑖ℎ𝑖𝑑𝑖	𝑢𝑖ℎ𝑖𝑑𝑖	VERB
american_scientific_journal-667	69	3	𝐴2	𝐴2	NOUN
american_scientific_journal-667	69	4	=	=	SYM
american_scientific_journal-667	69	5	𝑓𝑖+1(𝑢𝑖	𝑓𝑖+1(𝑢𝑖	PROPN
american_scientific_journal-667	70	1	+	+	NUM
american_scientific_journal-667	70	2	2𝑣𝑖	2𝑣𝑖	NOUN
american_scientific_journal-667	70	3	)	)	PUNCT
american_scientific_journal-667	71	1	−	−	PROPN
american_scientific_journal-667	71	2	𝑣𝑖ℎ𝑖𝑑𝑖+1	𝑣𝑖ℎ𝑖𝑑𝑖+1	PROPN
american_scientific_journal-667	71	3	𝐴3	𝐴3	PROPN
american_scientific_journal-667	71	4	=	=	PUNCT
american_scientific_journal-667	71	5	𝑣𝑖𝑓𝑖+1	𝑣𝑖𝑓𝑖+1	PROPN
american_scientific_journal-667	71	6	(	(	PUNCT
american_scientific_journal-667	71	7	3	3	NUM
american_scientific_journal-667	71	8	)	)	PUNCT
american_scientific_journal-667	71	9	thus	thus	ADV
american_scientific_journal-667	71	10	equation	equation	NOUN
american_scientific_journal-667	71	11	(	(	PUNCT
american_scientific_journal-667	71	12	1	1	X
american_scientific_journal-667	71	13	)	)	PUNCT
american_scientific_journal-667	71	14	can	can	AUX
american_scientific_journal-667	71	15	be	be	AUX
american_scientific_journal-667	71	16	reduced	reduce	VERB
american_scientific_journal-667	71	17	to	to	ADP
american_scientific_journal-667	71	18	a	a	DET
american_scientific_journal-667	71	19	rational	rational	ADJ
american_scientific_journal-667	71	20	cubic	cubic	ADJ
american_scientific_journal-667	71	21	spline	spline	NOUN
american_scientific_journal-667	71	22	:	:	PUNCT
american_scientific_journal-667	72	1	𝑆(𝑥	𝑆(𝑥	X
american_scientific_journal-667	72	2	)	)	PUNCT
american_scientific_journal-667	72	3	=	=	SYM
american_scientific_journal-667	72	4	𝑆𝑖(𝑥	𝑆𝑖(𝑥	PROPN
american_scientific_journal-667	72	5	)	)	PUNCT
american_scientific_journal-667	72	6	=	=	SYM
american_scientific_journal-667	72	7	𝑝𝑖(𝜃	𝑝𝑖(𝜃	X
american_scientific_journal-667	72	8	)	)	PUNCT
american_scientific_journal-667	72	9	𝑞𝑖(𝜃	𝑞𝑖(𝜃	NUM
american_scientific_journal-667	72	10	)	)	PUNCT
american_scientific_journal-667	72	11	(	(	PUNCT
american_scientific_journal-667	72	12	4	4	X
american_scientific_journal-667	72	13	)	)	PUNCT
american_scientific_journal-667	72	14	with	with	ADP
american_scientific_journal-667	72	15	,	,	PUNCT
american_scientific_journal-667	72	16	𝑝𝑖(𝜃	𝑝𝑖(𝜃	PROPN
american_scientific_journal-667	72	17	)	)	PUNCT
american_scientific_journal-667	72	18	=	=	NOUN
american_scientific_journal-667	73	1	𝑢𝑖𝑓𝑖(1	𝑢𝑖𝑓𝑖(1	PROPN
american_scientific_journal-667	73	2	−	−	PROPN
american_scientific_journal-667	73	3	𝜃)3	𝜃)3	NOUN
american_scientific_journal-667	74	1	+	+	CCONJ
american_scientific_journal-667	74	2	(	(	PUNCT
american_scientific_journal-667	74	3	𝑓𝑖(2𝑢𝑖	𝑓𝑖(2𝑢𝑖	NOUN
american_scientific_journal-667	74	4	+	+	CCONJ
american_scientific_journal-667	74	5	𝑣𝑖	𝑣𝑖	ADV
american_scientific_journal-667	74	6	)	)	PUNCT
american_scientific_journal-667	74	7	+	+	NUM
american_scientific_journal-667	74	8	𝑢𝑖ℎ𝑖𝑑𝑖)𝜃(1	𝑢𝑖ℎ𝑖𝑑𝑖)𝜃(1	NUM
american_scientific_journal-667	74	9	−	−	NOUN
american_scientific_journal-667	74	10	𝜃)2	𝜃)2	VERB
american_scientific_journal-667	74	11	+	+	CCONJ
american_scientific_journal-667	74	12	(	(	PUNCT
american_scientific_journal-667	74	13	𝑓𝑖+1(𝑢𝑖	𝑓𝑖+1(𝑢𝑖	NOUN
american_scientific_journal-667	74	14	+	+	NUM
american_scientific_journal-667	74	15	2𝑣𝑖	2𝑣𝑖	NOUN
american_scientific_journal-667	74	16	)	)	PUNCT
american_scientific_journal-667	75	1	−	−	PROPN
american_scientific_journal-667	75	2	𝑣𝑖ℎ𝑖𝑑𝑖+1)𝜃2(1	𝑣𝑖ℎ𝑖𝑑𝑖+1)𝜃2(1	NOUN
american_scientific_journal-667	76	1	−	−	NOUN
american_scientific_journal-667	76	2	𝜃	𝜃	X
american_scientific_journal-667	76	3	)	)	PUNCT
american_scientific_journal-667	77	1	+	+	ADJ
american_scientific_journal-667	77	2	𝑣𝑖𝑓𝑖+1	𝑣𝑖𝑓𝑖+1	NOUN
american_scientific_journal-667	77	3	𝜃3	𝜃3	ADJ
american_scientific_journal-667	77	4	𝑞𝑖(𝜃	𝑞𝑖(𝜃	PART
american_scientific_journal-667	77	5	)	)	PUNCT
american_scientific_journal-667	77	6	=	=	SYM
american_scientific_journal-667	78	1	𝑢𝑖(1	𝑢𝑖(1	PROPN
american_scientific_journal-667	78	2	−	−	PROPN
american_scientific_journal-667	78	3	𝜃	𝜃	X
american_scientific_journal-667	78	4	)	)	PUNCT
american_scientific_journal-667	78	5	+	+	CCONJ
american_scientific_journal-667	78	6	𝑣𝑖𝜃	𝑣𝑖𝜃	AUX
american_scientific_journal-667	78	7	again	again	ADV
american_scientific_journal-667	78	8	a	a	DET
american_scientific_journal-667	78	9	c2	c2	PROPN
american_scientific_journal-667	78	10	interpolating	interpolate	VERB
american_scientific_journal-667	78	11	conditions	condition	NOUN
american_scientific_journal-667	78	12	(	(	PUNCT
american_scientific_journal-667	78	13	2	2	X
american_scientific_journal-667	78	14	)	)	PUNCT
american_scientific_journal-667	78	15	produce	produce	VERB
american_scientific_journal-667	78	16	the	the	DET
american_scientific_journal-667	78	17	following	follow	VERB
american_scientific_journal-667	78	18	system	system	NOUN
american_scientific_journal-667	78	19	of	of	ADP
american_scientific_journal-667	78	20	linear	linear	PROPN
american_scientific_journal-667	78	21	equations	equation	NOUN
american_scientific_journal-667	78	22	for	for	ADP
american_scientific_journal-667	78	23	the	the	DET
american_scientific_journal-667	78	24	computation	computation	NOUN
american_scientific_journal-667	78	25	of	of	ADP
american_scientific_journal-667	78	26	derivatives	derivative	NOUN
american_scientific_journal-667	78	27	parameters	parameter	NOUN
american_scientific_journal-667	78	28	𝑑𝑖(𝑖	𝑑𝑖(𝑖	NOUN
american_scientific_journal-667	78	29	=	=	SYM
american_scientific_journal-667	78	30	2	2	NUM
american_scientific_journal-667	78	31	,	,	PUNCT
american_scientific_journal-667	78	32	.	.	PUNCT
american_scientific_journal-667	78	33	.	.	PUNCT
american_scientific_journal-667	79	1	.	.	PUNCT
american_scientific_journal-667	80	1	,	,	PUNCT
american_scientific_journal-667	80	2	𝑛	𝑛	DET
american_scientific_journal-667	80	3	−	−	NOUN
american_scientific_journal-667	80	4	1	1	NUM
american_scientific_journal-667	80	5	)	)	PUNCT
american_scientific_journal-667	80	6	.	.	PUNCT
american_scientific_journal-667	81	1	𝛼𝑖𝑑𝑖−1	𝛼𝑖𝑑𝑖−1	PROPN
american_scientific_journal-667	81	2	+	+	SYM
american_scientific_journal-667	81	3	𝛽𝑖𝑑𝑖	𝛽𝑖𝑑𝑖	NOUN
american_scientific_journal-667	81	4	+	+	CCONJ
american_scientific_journal-667	81	5	𝛾𝑖𝑑𝑖+1	𝛾𝑖𝑑𝑖+1	X
american_scientific_journal-667	81	6	=	=	PUNCT
american_scientific_journal-667	81	7	𝜎𝑖	𝜎𝑖	INTJ
american_scientific_journal-667	81	8	,	,	PUNCT
american_scientific_journal-667	81	9	for	for	ADP
american_scientific_journal-667	81	10	𝑖	𝑖	PRON
american_scientific_journal-667	81	11	=	=	SYM
american_scientific_journal-667	81	12	2,3	2,3	NUM
american_scientific_journal-667	81	13	,	,	PUNCT
american_scientific_journal-667	81	14	…	…	PUNCT
american_scientific_journal-667	81	15	,	,	PUNCT
american_scientific_journal-667	81	16	𝑛	𝑛	DET
american_scientific_journal-667	81	17	−	−	NUM
american_scientific_journal-667	81	18	1	1	NUM
american_scientific_journal-667	81	19	(	(	PUNCT
american_scientific_journal-667	81	20	5	5	NUM
american_scientific_journal-667	81	21	)	)	PUNCT
american_scientific_journal-667	81	22	with	with	ADP
american_scientific_journal-667	81	23	;	;	PUNCT
american_scientific_journal-667	81	24	𝛼𝑖	𝛼𝑖	PROPN
american_scientific_journal-667	81	25	=	=	SYM
american_scientific_journal-667	81	26	𝑢𝑖ℎ𝑖𝑢𝑖−1	𝑢𝑖ℎ𝑖𝑢𝑖−1	PROPN
american_scientific_journal-667	81	27	113	113	NUM
american_scientific_journal-667	81	28	american	american	ADJ
american_scientific_journal-667	81	29	scientific	scientific	ADJ
american_scientific_journal-667	81	30	research	research	NOUN
american_scientific_journal-667	81	31	journal	journal	NOUN
american_scientific_journal-667	81	32	for	for	ADP
american_scientific_journal-667	81	33	engineering	engineering	NOUN
american_scientific_journal-667	81	34	,	,	PUNCT
american_scientific_journal-667	81	35	technology	technology	NOUN
american_scientific_journal-667	81	36	,	,	PUNCT
american_scientific_journal-667	81	37	and	and	CCONJ
american_scientific_journal-667	81	38	sciences	science	NOUN
american_scientific_journal-667	81	39	(	(	PUNCT
american_scientific_journal-667	81	40	asrjets	asrjet	NOUN
american_scientific_journal-667	81	41	)	)	PUNCT
american_scientific_journal-667	81	42	(	(	PUNCT
american_scientific_journal-667	81	43	2015	2015	NUM
american_scientific_journal-667	81	44	)	)	PUNCT
american_scientific_journal-667	81	45	volume	volume	NOUN
american_scientific_journal-667	81	46	12	12	NUM
american_scientific_journal-667	81	47	,	,	PUNCT
american_scientific_journal-667	81	48	no	no	DET
american_scientific_journal-667	81	49	1	1	NUM
american_scientific_journal-667	81	50	,	,	PUNCT
american_scientific_journal-667	81	51	pp	pp	ADV
american_scientific_journal-667	81	52	110	110	NUM
american_scientific_journal-667	81	53	-	-	SYM
american_scientific_journal-667	81	54	122	122	NUM
american_scientific_journal-667	81	55	𝛽𝑖	𝛽𝑖	NOUN
american_scientific_journal-667	81	56	=	=	PUNCT
american_scientific_journal-667	82	1	[	[	X
american_scientific_journal-667	82	2	𝑢𝑖ℎ𝑖(𝑣𝑖−1	𝑢𝑖ℎ𝑖(𝑣𝑖−1	X
american_scientific_journal-667	82	3	+	+	X
american_scientific_journal-667	82	4	𝑢𝑖−1	𝑢𝑖−1	NOUN
american_scientific_journal-667	82	5	)	)	PUNCT
american_scientific_journal-667	82	6	+	+	NUM
american_scientific_journal-667	82	7	𝑣𝑖−1ℎ𝑖−1(𝑢𝑖	𝑣𝑖−1ℎ𝑖−1(𝑢𝑖	NOUN
american_scientific_journal-667	82	8	+	+	CCONJ
american_scientific_journal-667	82	9	𝑣𝑖	𝑣𝑖	NOUN
american_scientific_journal-667	82	10	)	)	PUNCT
american_scientific_journal-667	82	11	]	]	PUNCT
american_scientific_journal-667	83	1	𝛾𝑖	𝛾𝑖	NOUN
american_scientific_journal-667	83	2	=	=	SYM
american_scientific_journal-667	83	3	𝑣𝑖−1ℎ𝑖−1𝑣𝑖	𝑣𝑖−1ℎ𝑖−1𝑣𝑖	NOUN
american_scientific_journal-667	83	4	and	and	CCONJ
american_scientific_journal-667	83	5	𝜎𝑖	𝜎𝑖	DET
american_scientific_journal-667	83	6	=	=	NOUN
american_scientific_journal-667	83	7	𝑢𝑖ℎ𝑖(𝑣𝑖−1	𝑢𝑖ℎ𝑖(𝑣𝑖−1	NOUN
american_scientific_journal-667	83	8	+	+	PROPN
american_scientific_journal-667	83	9	2𝑢𝑖−1)∆𝑖−1	2𝑢𝑖−1)∆𝑖−1	NUM
american_scientific_journal-667	83	10	+	+	NUM
american_scientific_journal-667	83	11	𝑣𝑖−1ℎ𝑖−1(𝑢𝑖	𝑣𝑖−1ℎ𝑖−1(𝑢𝑖	NOUN
american_scientific_journal-667	84	1	+	+	CCONJ
american_scientific_journal-667	84	2	2𝑣𝑖)∆𝑖	2𝑣𝑖)∆𝑖	NUM
american_scientific_journal-667	85	1	where	where	SCONJ
american_scientific_journal-667	85	2	∆𝑖	∆𝑖	PROPN
american_scientific_journal-667	85	3	=	=	PUNCT
american_scientific_journal-667	85	4	(	(	PUNCT
american_scientific_journal-667	85	5	𝑓𝑖+1	𝑓𝑖+1	NOUN
american_scientific_journal-667	85	6	−	−	PROPN
american_scientific_journal-667	85	7	𝑓𝑖)/ℎ𝑖	𝑓𝑖)/ℎ𝑖	NOUN
american_scientific_journal-667	85	8	.	.	PUNCT
american_scientific_journal-667	86	1	remark-1	remark-1	NUM
american_scientific_journal-667	86	2	:	:	PUNCT
american_scientific_journal-667	86	3	if	if	SCONJ
american_scientific_journal-667	86	4	in	in	ADP
american_scientific_journal-667	86	5	each	each	DET
american_scientific_journal-667	86	6	subinterval	subinterval	NOUN
american_scientific_journal-667	86	7	we	we	PRON
american_scientific_journal-667	86	8	use	use	VERB
american_scientific_journal-667	86	9	𝑢𝑖	𝑢𝑖	NOUN
american_scientific_journal-667	86	10	=	=	SYM
american_scientific_journal-667	86	11	𝑣𝑖	𝑣𝑖	ADP
american_scientific_journal-667	86	12	=	=	SYM
american_scientific_journal-667	86	13	1,then	1,then	NUM
american_scientific_journal-667	86	14	the	the	DET
american_scientific_journal-667	86	15	rational	rational	ADJ
american_scientific_journal-667	86	16	cubic	cubic	ADJ
american_scientific_journal-667	86	17	function	function	NOUN
american_scientific_journal-667	86	18	(	(	PUNCT
american_scientific_journal-667	86	19	1	1	X
american_scientific_journal-667	86	20	)	)	PUNCT
american_scientific_journal-667	86	21	reduces	reduce	VERB
american_scientific_journal-667	86	22	to	to	ADP
american_scientific_journal-667	86	23	the	the	DET
american_scientific_journal-667	86	24	standard	standard	ADJ
american_scientific_journal-667	86	25	cubic	cubic	ADJ
american_scientific_journal-667	86	26	hermite	hermite	PROPN
american_scientific_journal-667	86	27	.	.	PUNCT
american_scientific_journal-667	87	1	remark-2	remark-2	PROPN
american_scientific_journal-667	87	2	:	:	PUNCT
american_scientific_journal-667	87	3	in	in	ADP
american_scientific_journal-667	87	4	(	(	PUNCT
american_scientific_journal-667	87	5	5	5	NUM
american_scientific_journal-667	87	6	)	)	PUNCT
american_scientific_journal-667	87	7	since	since	SCONJ
american_scientific_journal-667	87	8	all	all	ADV
american_scientific_journal-667	87	9	𝑢𝑖	𝑢𝑖	NOUN
american_scientific_journal-667	87	10	,	,	PUNCT
american_scientific_journal-667	87	11	𝑣𝑖	𝑣𝑖	INTJ
american_scientific_journal-667	87	12	,	,	PUNCT
american_scientific_journal-667	87	13	ℎ𝑖	ℎ𝑖	NOUN
american_scientific_journal-667	87	14	are	be	AUX
american_scientific_journal-667	87	15	non	non	ADJ
american_scientific_journal-667	87	16	-	-	ADJ
american_scientific_journal-667	87	17	negative	negative	ADJ
american_scientific_journal-667	87	18	we	we	PRON
american_scientific_journal-667	87	19	see	see	VERB
american_scientific_journal-667	87	20	that	that	SCONJ
american_scientific_journal-667	87	21	𝛼𝑖,𝛽𝑖	𝛼𝑖,𝛽𝑖	NOUN
american_scientific_journal-667	87	22	,	,	PUNCT
american_scientific_journal-667	87	23	𝛾𝑖	𝛾𝑖	ADV
american_scientific_journal-667	87	24	>	>	X
american_scientific_journal-667	87	25	0	0	X
american_scientific_journal-667	87	26	.	.	PUNCT
american_scientific_journal-667	88	1	moreover	moreover	ADV
american_scientific_journal-667	88	2	𝛽𝑖	𝛽𝑖	PROPN
american_scientific_journal-667	88	3	exceeds	exceed	VERB
american_scientific_journal-667	88	4	the	the	DET
american_scientific_journal-667	88	5	sum	sum	NOUN
american_scientific_journal-667	88	6	of	of	ADP
american_scientific_journal-667	88	7	𝛼𝑖	𝛼𝑖	PROPN
american_scientific_journal-667	88	8	and	and	CCONJ
american_scientific_journal-667	88	9	𝛾𝑖	𝛾𝑖	ADV
american_scientific_journal-667	88	10	by	by	ADP
american_scientific_journal-667	88	11	𝑢𝑖𝑣𝑖−1(ℎ𝑖	𝑢𝑖𝑣𝑖−1(ℎ𝑖	NOUN
american_scientific_journal-667	88	12	+	+	CCONJ
american_scientific_journal-667	88	13	ℎ𝑖−1	ℎ𝑖−1	NOUN
american_scientific_journal-667	88	14	)	)	PUNCT
american_scientific_journal-667	88	15	.	.	PUNCT
american_scientific_journal-667	89	1	⇒	⇒	NOUN
american_scientific_journal-667	89	2	𝛽𝑖	𝛽𝑖	VERB
american_scientific_journal-667	89	3	>	>	X
american_scientific_journal-667	89	4	𝛼𝑖	𝛼𝑖	PROPN
american_scientific_journal-667	89	5	+	+	CCONJ
american_scientific_journal-667	89	6	𝛾𝑖	𝛾𝑖	ADV
american_scientific_journal-667	89	7	⇒	⇒	VERB
american_scientific_journal-667	89	8	|𝛽𝑖|	|𝛽𝑖|	PROPN
american_scientific_journal-667	89	9	>	>	X
american_scientific_journal-667	90	1	|𝛼𝑖	|𝛼𝑖	X
american_scientific_journal-667	91	1	+	+	CCONJ
american_scientific_journal-667	92	1	𝛾𝑖|	𝛾𝑖|	NOUN
american_scientific_journal-667	92	2	.	.	PUNCT
american_scientific_journal-667	93	1	therefore	therefore	ADV
american_scientific_journal-667	93	2	eq	eq	ADJ
american_scientific_journal-667	93	3	.	.	PUNCT
american_scientific_journal-667	94	1	(	(	PUNCT
american_scientific_journal-667	94	2	5	5	NUM
american_scientific_journal-667	94	3	)	)	PUNCT
american_scientific_journal-667	94	4	represents	represent	VERB
american_scientific_journal-667	94	5	a	a	DET
american_scientific_journal-667	94	6	diagonally	diagonally	ADV
american_scientific_journal-667	94	7	dominant	dominant	ADJ
american_scientific_journal-667	94	8	system	system	NOUN
american_scientific_journal-667	94	9	of	of	ADP
american_scientific_journal-667	94	10	linear	linear	ADJ
american_scientific_journal-667	94	11	algebraic	algebraic	ADJ
american_scientific_journal-667	94	12	equation	equation	NOUN
american_scientific_journal-667	94	13	.	.	PUNCT
american_scientific_journal-667	95	1	thus	thus	ADV
american_scientific_journal-667	95	2	it	it	PRON
american_scientific_journal-667	95	3	has	have	VERB
american_scientific_journal-667	95	4	a	a	DET
american_scientific_journal-667	95	5	unique	unique	ADJ
american_scientific_journal-667	95	6	solution	solution	NOUN
american_scientific_journal-667	95	7	for	for	ADP
american_scientific_journal-667	95	8	the	the	DET
american_scientific_journal-667	95	9	n-2	n-2	NOUN
american_scientific_journal-667	95	10	unknown	unknown	ADJ
american_scientific_journal-667	95	11	derivative	derivative	ADJ
american_scientific_journal-667	95	12	parameter	parameter	NOUN
american_scientific_journal-667	95	13	and	and	CCONJ
american_scientific_journal-667	95	14	can	can	AUX
american_scientific_journal-667	95	15	be	be	AUX
american_scientific_journal-667	95	16	solved	solve	VERB
american_scientific_journal-667	95	17	either	either	CCONJ
american_scientific_journal-667	95	18	by	by	ADP
american_scientific_journal-667	95	19	using	use	VERB
american_scientific_journal-667	95	20	the	the	DET
american_scientific_journal-667	95	21	lu	lu	NOUN
american_scientific_journal-667	95	22	decomposition	decomposition	NOUN
american_scientific_journal-667	95	23	method	method	NOUN
american_scientific_journal-667	95	24	or	or	CCONJ
american_scientific_journal-667	95	25	any	any	DET
american_scientific_journal-667	95	26	other	other	ADJ
american_scientific_journal-667	95	27	suitable	suitable	ADJ
american_scientific_journal-667	95	28	method	method	NOUN
american_scientific_journal-667	95	29	.	.	PUNCT
american_scientific_journal-667	96	1	remark-3	remark-3	NOUN
american_scientific_journal-667	96	2	:	:	PUNCT
american_scientific_journal-667	96	3	since	since	SCONJ
american_scientific_journal-667	96	4	there	there	PRON
american_scientific_journal-667	96	5	are	be	VERB
american_scientific_journal-667	96	6	n	n	PRON
american_scientific_journal-667	96	7	unknown	unknown	ADJ
american_scientific_journal-667	96	8	derivative	derivative	ADJ
american_scientific_journal-667	96	9	values	value	NOUN
american_scientific_journal-667	96	10	we	we	PRON
american_scientific_journal-667	96	11	need	need	VERB
american_scientific_journal-667	96	12	two	two	NUM
american_scientific_journal-667	96	13	more	more	ADJ
american_scientific_journal-667	96	14	equations	equation	NOUN
american_scientific_journal-667	96	15	for	for	ADP
american_scientific_journal-667	96	16	the	the	DET
american_scientific_journal-667	96	17	unique	unique	ADJ
american_scientific_journal-667	96	18	solution	solution	NOUN
american_scientific_journal-667	96	19	.	.	PUNCT
american_scientific_journal-667	97	1	therefore	therefore	ADV
american_scientific_journal-667	97	2	,	,	PUNCT
american_scientific_journal-667	97	3	we	we	PRON
american_scientific_journal-667	97	4	have	have	VERB
american_scientific_journal-667	97	5	to	to	PART
american_scientific_journal-667	97	6	impose	impose	VERB
american_scientific_journal-667	97	7	the	the	DET
american_scientific_journal-667	97	8	end	end	NOUN
american_scientific_journal-667	97	9	conditions	condition	NOUN
american_scientific_journal-667	97	10	at	at	ADP
american_scientific_journal-667	97	11	end	end	NOUN
american_scientific_journal-667	97	12	knots	knot	NOUN
american_scientific_journal-667	97	13	as	as	ADP
american_scientific_journal-667	97	14	:	:	PUNCT
american_scientific_journal-667	97	15	𝑆(1)(𝑥1	𝑆(1)(𝑥1	NUM
american_scientific_journal-667	97	16	)	)	PUNCT
american_scientific_journal-667	97	17	=	=	NOUN
american_scientific_journal-667	97	18	𝑑1	𝑑1	NOUN
american_scientific_journal-667	97	19	and	and	CCONJ
american_scientific_journal-667	97	20	𝑆(1)(𝑥𝑛	𝑆(1)(𝑥𝑛	PROPN
american_scientific_journal-667	97	21	)	)	PUNCT
american_scientific_journal-667	98	1	=	=	PRON
american_scientific_journal-667	98	2	𝑑𝑛	𝑑𝑛	X
american_scientific_journal-667	98	3	(	(	PUNCT
american_scientific_journal-667	98	4	6	6	NUM
american_scientific_journal-667	98	5	)	)	SYM
american_scientific_journal-667	98	6	3	3	NUM
american_scientific_journal-667	98	7	.	.	NOUN
american_scientific_journal-667	98	8	results	result	NOUN
american_scientific_journal-667	98	9	and	and	CCONJ
american_scientific_journal-667	98	10	discussion	discussion	NOUN
american_scientific_journal-667	98	11	3.1	3.1	NUM
american_scientific_journal-667	98	12	.	.	PUNCT
american_scientific_journal-667	99	1	positivity	positivity	NOUN
american_scientific_journal-667	99	2	preserving	preserve	VERB
american_scientific_journal-667	99	3	c2	c2	PROPN
american_scientific_journal-667	99	4	rational	rational	ADJ
american_scientific_journal-667	99	5	cubic	cubic	ADJ
american_scientific_journal-667	99	6	function	function	NOUN
american_scientific_journal-667	99	7	let	let	VERB
american_scientific_journal-667	99	8	{	{	PUNCT
american_scientific_journal-667	99	9	(	(	PUNCT
american_scientific_journal-667	99	10	𝑥𝑖	𝑥𝑖	PROPN
american_scientific_journal-667	99	11	,	,	PUNCT
american_scientific_journal-667	99	12	𝑓𝑖	𝑓𝑖	PROPN
american_scientific_journal-667	99	13	)	)	PUNCT
american_scientific_journal-667	99	14	}	}	PUNCT
american_scientific_journal-667	99	15	such	such	ADJ
american_scientific_journal-667	99	16	that	that	SCONJ
american_scientific_journal-667	99	17	𝑥𝑖	𝑥𝑖	PROPN
american_scientific_journal-667	99	18	<	<	X
american_scientific_journal-667	99	19	𝑥𝑖+1	𝑥𝑖+1	PROPN
american_scientific_journal-667	99	20	for	for	ADP
american_scientific_journal-667	99	21	all	all	PRON
american_scientific_journal-667	99	22	𝑖	𝑖	SYM
american_scientific_journal-667	99	23	=	=	SYM
american_scientific_journal-667	99	24	1	1	NUM
american_scientific_journal-667	99	25	,	,	PUNCT
american_scientific_journal-667	99	26	2	2	NUM
american_scientific_journal-667	99	27	.	.	PUNCT
american_scientific_journal-667	99	28	.	.	PUNCT
american_scientific_journal-667	100	1	.𝑛	.𝑛	PUNCT
american_scientific_journal-667	101	1	−	−	NOUN
american_scientific_journal-667	101	2	1	1	NUM
american_scientific_journal-667	101	3	be	be	AUX
american_scientific_journal-667	101	4	the	the	DET
american_scientific_journal-667	101	5	set	set	NOUN
american_scientific_journal-667	101	6	of	of	ADP
american_scientific_journal-667	101	7	positive	positive	ADJ
american_scientific_journal-667	101	8	data	datum	NOUN
american_scientific_journal-667	101	9	points	point	NOUN
american_scientific_journal-667	101	10	,	,	PUNCT
american_scientific_journal-667	101	11	we	we	PRON
american_scientific_journal-667	101	12	need	need	VERB
american_scientific_journal-667	101	13	to	to	PART
american_scientific_journal-667	101	14	develop	develop	VERB
american_scientific_journal-667	101	15	the	the	DET
american_scientific_journal-667	101	16	conditions	condition	NOUN
american_scientific_journal-667	101	17	on	on	ADP
american_scientific_journal-667	101	18	which	which	PRON
american_scientific_journal-667	101	19	our	our	PRON
american_scientific_journal-667	101	20	interpolant	interpolant	NOUN
american_scientific_journal-667	101	21	produces	produce	VERB
american_scientific_journal-667	101	22	a	a	DET
american_scientific_journal-667	101	23	positive	positive	ADJ
american_scientific_journal-667	101	24	curve	curve	NOUN
american_scientific_journal-667	101	25	.	.	PUNCT
american_scientific_journal-667	102	1	thus	thus	ADV
american_scientific_journal-667	102	2	a	a	DET
american_scientific_journal-667	102	3	rational	rational	ADJ
american_scientific_journal-667	102	4	cubic	cubic	ADJ
american_scientific_journal-667	102	5	function	function	NOUN
american_scientific_journal-667	102	6	(	(	PUNCT
american_scientific_journal-667	102	7	1	1	X
american_scientific_journal-667	102	8	)	)	PUNCT
american_scientific_journal-667	102	9	is	be	AUX
american_scientific_journal-667	102	10	positive	positive	ADJ
american_scientific_journal-667	102	11	if	if	SCONJ
american_scientific_journal-667	102	12	both	both	PRON
american_scientific_journal-667	102	13	𝑝𝑖(𝜃	𝑝𝑖(𝜃	NOUN
american_scientific_journal-667	102	14	)	)	PUNCT
american_scientific_journal-667	102	15	and	and	CCONJ
american_scientific_journal-667	102	16	𝑞𝑖(𝜃	𝑞𝑖(𝜃	NUM
american_scientific_journal-667	102	17	)	)	PUNCT
american_scientific_journal-667	102	18	are	be	AUX
american_scientific_journal-667	102	19	positive	positive	ADJ
american_scientific_journal-667	102	20	.	.	PUNCT
american_scientific_journal-667	103	1	since	since	SCONJ
american_scientific_journal-667	103	2	𝑞𝑖(𝜃	𝑞𝑖(𝜃	NUM
american_scientific_journal-667	103	3	)	)	PUNCT
american_scientific_journal-667	103	4	>	>	X
american_scientific_journal-667	103	5	0	0	PUNCT
american_scientific_journal-667	104	1	for	for	ADP
american_scientific_journal-667	104	2	all	all	DET
american_scientific_journal-667	104	3	𝑢𝑖	𝑢𝑖	NOUN
american_scientific_journal-667	104	4	,	,	PUNCT
american_scientific_journal-667	104	5	𝑣𝑖	𝑣𝑖	ADV
american_scientific_journal-667	104	6	>	>	X
american_scientific_journal-667	104	7	0	0	NUM
american_scientific_journal-667	104	8	,	,	PUNCT
american_scientific_journal-667	104	9	we	we	PRON
american_scientific_journal-667	104	10	only	only	ADV
american_scientific_journal-667	104	11	construct	construct	VERB
american_scientific_journal-667	104	12	the	the	DET
american_scientific_journal-667	104	13	condition	condition	NOUN
american_scientific_journal-667	104	14	on	on	ADP
american_scientific_journal-667	104	15	a	a	DET
american_scientific_journal-667	104	16	shape	shape	NOUN
american_scientific_journal-667	104	17	parameter	parameter	NOUN
american_scientific_journal-667	104	18	𝑢𝑖	𝑢𝑖	NOUN
american_scientific_journal-667	104	19	for	for	ADP
american_scientific_journal-667	104	20	which	which	PRON
american_scientific_journal-667	104	21	𝑝𝑖(𝜃	𝑝𝑖(𝜃	NOUN
american_scientific_journal-667	104	22	)	)	PUNCT
american_scientific_journal-667	104	23	>	>	X
american_scientific_journal-667	104	24	0	0	X
american_scientific_journal-667	104	25	.	.	PUNCT
american_scientific_journal-667	105	1	according	accord	VERB
american_scientific_journal-667	105	2	to	to	ADP
american_scientific_journal-667	105	3	the	the	DET
american_scientific_journal-667	105	4	result	result	NOUN
american_scientific_journal-667	105	5	developed	develop	VERB
american_scientific_journal-667	105	6	by	by	ADP
american_scientific_journal-667	105	7	schmidt	schmidt	PROPN
american_scientific_journal-667	105	8	and	and	CCONJ
american_scientific_journal-667	105	9	heβ	heβ	PROPN
american_scientific_journal-667	105	10	1988	1988	NUM
american_scientific_journal-667	105	11	cited	cite	VERB
american_scientific_journal-667	105	12	in	in	ADP
american_scientific_journal-667	105	13	[	[	X
american_scientific_journal-667	105	14	1	1	NUM
american_scientific_journal-667	105	15	]	]	PUNCT
american_scientific_journal-667	105	16	𝑝𝑖(𝜃	𝑝𝑖(𝜃	X
american_scientific_journal-667	105	17	)	)	PUNCT
american_scientific_journal-667	105	18	>	>	X
american_scientific_journal-667	105	19	0	0	PUNCT
american_scientific_journal-667	106	1	if	if	SCONJ
american_scientific_journal-667	106	2	(	(	PUNCT
american_scientific_journal-667	106	3	𝑝𝑖	𝑝𝑖	NOUN
american_scientific_journal-667	106	4	(	(	PUNCT
american_scientific_journal-667	106	5	1)(0	1)(0	NUM
american_scientific_journal-667	106	6	)	)	PUNCT
american_scientific_journal-667	106	7	,	,	PUNCT
american_scientific_journal-667	106	8	𝑝𝑖	𝑝𝑖	X
american_scientific_journal-667	106	9	(	(	PUNCT
american_scientific_journal-667	106	10	1)(1	1)(1	NUM
american_scientific_journal-667	106	11	)	)	PUNCT
american_scientific_journal-667	106	12	∈	∈	PROPN
american_scientific_journal-667	106	13	𝑅1	𝑅1	PROPN
american_scientific_journal-667	106	14	∪	∪	PROPN
american_scientific_journal-667	106	15	𝑅2	𝑅2	NOUN
american_scientific_journal-667	106	16	where	where	SCONJ
american_scientific_journal-667	106	17	;	;	PUNCT
american_scientific_journal-667	106	18	𝑅1	𝑅1	PROPN
american_scientific_journal-667	106	19	=	=	SYM
american_scientific_journal-667	106	20	�	�	PROPN
american_scientific_journal-667	106	21	(	(	PUNCT
american_scientific_journal-667	106	22	𝑎	𝑎	PROPN
american_scientific_journal-667	106	23	,	,	PUNCT
american_scientific_journal-667	106	24	𝑏	𝑏	NOUN
american_scientific_journal-667	106	25	):	):	PUNCT
american_scientific_journal-667	106	26	𝑎	𝑎	X
american_scientific_journal-667	106	27	>	>	X
american_scientific_journal-667	106	28	−3𝑝𝑖(0	−3𝑝𝑖(0	PROPN
american_scientific_journal-667	106	29	)	)	PUNCT
american_scientific_journal-667	106	30	ℎ𝑖	ℎ𝑖	NOUN
american_scientific_journal-667	106	31	,	,	PUNCT
american_scientific_journal-667	106	32	𝑏	𝑏	PROPN
american_scientific_journal-667	106	33	<	<	X
american_scientific_journal-667	106	34	3𝑝𝑖(1	3𝑝𝑖(1	NUM
american_scientific_journal-667	106	35	)	)	PUNCT
american_scientific_journal-667	106	36	ℎ𝑖	ℎ𝑖	PROPN
american_scientific_journal-667	106	37	�	�	PROPN
american_scientific_journal-667	106	38	(	(	PUNCT
american_scientific_journal-667	106	39	7	7	NUM
american_scientific_journal-667	106	40	)	)	PUNCT
american_scientific_journal-667	106	41	𝑅2	𝑅2	NOUN
american_scientific_journal-667	106	42	=	=	SYM
american_scientific_journal-667	106	43	�	�	PROPN
american_scientific_journal-667	106	44	(	(	PUNCT
american_scientific_journal-667	106	45	𝑎	𝑎	PROPN
american_scientific_journal-667	106	46	,	,	PUNCT
american_scientific_journal-667	106	47	𝑏	𝑏	NOUN
american_scientific_journal-667	106	48	):	):	PUNCT
american_scientific_journal-667	106	49	36𝑓𝑖𝑓𝑖+1	36𝑓𝑖𝑓𝑖+1	PROPN
american_scientific_journal-667	106	50	�	�	PROPN
american_scientific_journal-667	106	51	𝑎2	𝑎2	NOUN
american_scientific_journal-667	106	52	+	+	CCONJ
american_scientific_journal-667	106	53	𝑏2	𝑏2	PROPN
american_scientific_journal-667	106	54	+	+	CCONJ
american_scientific_journal-667	106	55	𝑎𝑏	𝑎𝑏	PROPN
american_scientific_journal-667	106	56	−	−	PROPN
american_scientific_journal-667	106	57	3∆𝑖(𝑎	3∆𝑖(𝑎	NUM
american_scientific_journal-667	106	58	+	+	CCONJ
american_scientific_journal-667	106	59	𝑏	𝑏	NOUN
american_scientific_journal-667	106	60	)	)	PUNCT
american_scientific_journal-667	106	61	+	+	CCONJ
american_scientific_journal-667	106	62	3∆𝑖2	3∆𝑖2	NUM
american_scientific_journal-667	106	63	�	�	NOUN
american_scientific_journal-667	106	64	+	+	NUM
american_scientific_journal-667	106	65	4ℎ𝑖(𝑓𝑖+1𝑎3	4ℎ𝑖(𝑓𝑖+1𝑎3	NUM
american_scientific_journal-667	106	66	−	−	NOUN
american_scientific_journal-667	106	67	𝑓𝑖𝑏3	𝑓𝑖𝑏3	NOUN
american_scientific_journal-667	106	68	)	)	PUNCT
american_scientific_journal-667	107	1	−ℎ𝑖2𝑎2𝑏2	−ℎ𝑖2𝑎2𝑏2	PROPN
american_scientific_journal-667	107	2	+	+	NOUN
american_scientific_journal-667	108	1	3(𝑓𝑖+1𝑎	3(𝑓𝑖+1𝑎	NUM
american_scientific_journal-667	108	2	−	−	NOUN
american_scientific_journal-667	108	3	𝑓𝑖𝑏)(2ℎ𝑖𝑎𝑏	𝑓𝑖𝑏)(2ℎ𝑖𝑎𝑏	PROPN
american_scientific_journal-667	108	4	−	−	PROPN
american_scientific_journal-667	108	5	3𝑓𝑖+1𝑎	3𝑓𝑖+1𝑎	NUM
american_scientific_journal-667	109	1	+	+	CCONJ
american_scientific_journal-667	109	2	3𝑓𝑖𝑏	3𝑓𝑖𝑏	NUM
american_scientific_journal-667	109	3	)	)	PUNCT
american_scientific_journal-667	109	4	>	>	SYM
american_scientific_journal-667	109	5	0	0	NUM
american_scientific_journal-667	109	6	�	�	PROPN
american_scientific_journal-667	109	7	(	(	PUNCT
american_scientific_journal-667	109	8	8)	8)	NUM
american_scientific_journal-667	109	9	114	114	NUM
american_scientific_journal-667	109	10	american	american	ADJ
american_scientific_journal-667	109	11	scientific	scientific	ADJ
american_scientific_journal-667	109	12	research	research	NOUN
american_scientific_journal-667	109	13	journal	journal	NOUN
american_scientific_journal-667	109	14	for	for	ADP
american_scientific_journal-667	109	15	engineering	engineering	NOUN
american_scientific_journal-667	109	16	,	,	PUNCT
american_scientific_journal-667	109	17	technology	technology	NOUN
american_scientific_journal-667	109	18	,	,	PUNCT
american_scientific_journal-667	109	19	and	and	CCONJ
american_scientific_journal-667	109	20	sciences	science	NOUN
american_scientific_journal-667	109	21	(	(	PUNCT
american_scientific_journal-667	109	22	asrjets	asrjet	NOUN
american_scientific_journal-667	109	23	)	)	PUNCT
american_scientific_journal-667	109	24	(	(	PUNCT
american_scientific_journal-667	109	25	2015	2015	NUM
american_scientific_journal-667	109	26	)	)	PUNCT
american_scientific_journal-667	109	27	volume	volume	NOUN
american_scientific_journal-667	109	28	12	12	NUM
american_scientific_journal-667	109	29	,	,	PUNCT
american_scientific_journal-667	109	30	no	no	DET
american_scientific_journal-667	109	31	1	1	NUM
american_scientific_journal-667	109	32	,	,	PUNCT
american_scientific_journal-667	109	33	pp	pp	ADV
american_scientific_journal-667	109	34	110	110	NUM
american_scientific_journal-667	109	35	-	-	SYM
american_scientific_journal-667	109	36	122	122	NUM
american_scientific_journal-667	109	37	suppose	suppose	VERB
american_scientific_journal-667	109	38	(	(	PUNCT
american_scientific_journal-667	109	39	𝑝𝑖	𝑝𝑖	X
american_scientific_journal-667	109	40	(	(	PUNCT
american_scientific_journal-667	109	41	1)(0	1)(0	NUM
american_scientific_journal-667	109	42	)	)	PUNCT
american_scientific_journal-667	109	43	,	,	PUNCT
american_scientific_journal-667	109	44	𝑝𝑖	𝑝𝑖	X
american_scientific_journal-667	109	45	(	(	PUNCT
american_scientific_journal-667	109	46	1)(1	1)(1	NUM
american_scientific_journal-667	109	47	)	)	PUNCT
american_scientific_journal-667	109	48	)	)	PUNCT
american_scientific_journal-667	110	1	∈	∈	PROPN
american_scientific_journal-667	110	2	𝑅1	𝑅1	PROPN
american_scientific_journal-667	110	3	∪	∪	PROPN
american_scientific_journal-667	110	4	𝑅2	𝑅2	NOUN
american_scientific_journal-667	110	5	then	then	ADV
american_scientific_journal-667	110	6	,	,	PUNCT
american_scientific_journal-667	110	7	(	(	PUNCT
american_scientific_journal-667	110	8	𝑝𝑖	𝑝𝑖	X
american_scientific_journal-667	110	9	(	(	PUNCT
american_scientific_journal-667	110	10	1)(0	1)(0	NUM
american_scientific_journal-667	110	11	)	)	PUNCT
american_scientific_journal-667	110	12	,	,	PUNCT
american_scientific_journal-667	110	13	𝑝𝑖	𝑝𝑖	X
american_scientific_journal-667	110	14	(	(	PUNCT
american_scientific_journal-667	110	15	1)(1	1)(1	NUM
american_scientific_journal-667	110	16	)	)	PUNCT
american_scientific_journal-667	110	17	)	)	PUNCT
american_scientific_journal-667	111	1	∈	∈	PROPN
american_scientific_journal-667	111	2	𝑅1	𝑅1	PROPN
american_scientific_journal-667	111	3	⇒	⇒	PROPN
american_scientific_journal-667	111	4	𝑝𝑖	𝑝𝑖	PROPN
american_scientific_journal-667	111	5	(	(	PUNCT
american_scientific_journal-667	111	6	1)(0	1)(0	NUM
american_scientific_journal-667	111	7	)	)	PUNCT
american_scientific_journal-667	111	8	>	>	X
american_scientific_journal-667	111	9	−3𝑝𝑖(0	−3𝑝𝑖(0	NUM
american_scientific_journal-667	111	10	)	)	PUNCT
american_scientific_journal-667	111	11	ℎ𝑖	ℎ𝑖	NOUN
american_scientific_journal-667	111	12	,	,	PUNCT
american_scientific_journal-667	111	13	𝑝𝑖	𝑝𝑖	X
american_scientific_journal-667	111	14	(	(	PUNCT
american_scientific_journal-667	111	15	1)(1	1)(1	NUM
american_scientific_journal-667	111	16	)	)	PUNCT
american_scientific_journal-667	111	17	<	<	X
american_scientific_journal-667	111	18	3𝑝𝑖(1	3𝑝𝑖(1	NUM
american_scientific_journal-667	111	19	)	)	PUNCT
american_scientific_journal-667	111	20	ℎ𝑖	ℎ𝑖	NOUN
american_scientific_journal-667	111	21	simplifying	simplify	VERB
american_scientific_journal-667	111	22	these	these	DET
american_scientific_journal-667	111	23	inequalities	inequality	NOUN
american_scientific_journal-667	111	24	gives	give	VERB
american_scientific_journal-667	111	25	𝑢𝑖	𝑢𝑖	ADP
american_scientific_journal-667	111	26	>	>	X
american_scientific_journal-667	111	27	−𝑣𝑖𝑓𝑖	−𝑣𝑖𝑓𝑖	PROPN
american_scientific_journal-667	111	28	2𝑓𝑖+	2𝑓𝑖+	NUM
american_scientific_journal-667	111	29	ℎ𝑖𝑑𝑖	ℎ𝑖𝑑𝑖	NOUN
american_scientific_journal-667	111	30	,	,	PUNCT
american_scientific_journal-667	111	31	𝑢𝑖	𝑢𝑖	INTJ
american_scientific_journal-667	111	32	>	>	X
american_scientific_journal-667	111	33	𝑣𝑖(ℎ𝑖𝑑𝑖+1−2𝑓𝑖+1	𝑣𝑖(ℎ𝑖𝑑𝑖+1−2𝑓𝑖+1	PROPN
american_scientific_journal-667	111	34	)	)	PUNCT
american_scientific_journal-667	111	35	𝑓𝑖+1	𝑓𝑖+1	VERB
american_scientific_journal-667	111	36	the	the	DET
american_scientific_journal-667	111	37	constraints	constraint	NOUN
american_scientific_journal-667	111	38	on	on	ADP
american_scientific_journal-667	111	39	𝑢𝑖	𝑢𝑖	PRON
american_scientific_journal-667	111	40	can	can	AUX
american_scientific_journal-667	111	41	also	also	ADV
american_scientific_journal-667	111	42	be	be	AUX
american_scientific_journal-667	111	43	derived	derive	VERB
american_scientific_journal-667	111	44	from	from	ADP
american_scientific_journal-667	111	45	(	(	PUNCT
american_scientific_journal-667	111	46	8)	8)	NUM
american_scientific_journal-667	111	47	but	but	CCONJ
american_scientific_journal-667	111	48	for	for	ADP
american_scientific_journal-667	111	49	simplicity	simplicity	NOUN
american_scientific_journal-667	111	50	we	we	PRON
american_scientific_journal-667	111	51	use	use	VERB
american_scientific_journal-667	111	52	the	the	DET
american_scientific_journal-667	111	53	constraints	constraint	NOUN
american_scientific_journal-667	111	54	obtained	obtain	VERB
american_scientific_journal-667	111	55	in	in	ADP
american_scientific_journal-667	111	56	(	(	PUNCT
american_scientific_journal-667	111	57	7	7	NUM
american_scientific_journal-667	111	58	)	)	PUNCT
american_scientific_journal-667	111	59	for	for	ADP
american_scientific_journal-667	111	60	positivity	positivity	NOUN
american_scientific_journal-667	111	61	-	-	PUNCT
american_scientific_journal-667	111	62	preserving	preserve	VERB
american_scientific_journal-667	111	63	graphical	graphical	ADJ
american_scientific_journal-667	111	64	results	result	NOUN
american_scientific_journal-667	111	65	.	.	PUNCT
american_scientific_journal-667	112	1	theorem-1	theorem-1	NUM
american_scientific_journal-667	112	2	:	:	PUNCT
american_scientific_journal-667	112	3	the	the	DET
american_scientific_journal-667	112	4	c2	c2	PROPN
american_scientific_journal-667	112	5	rational	rational	ADJ
american_scientific_journal-667	112	6	cubic	cubic	ADJ
american_scientific_journal-667	112	7	spline	spline	NOUN
american_scientific_journal-667	112	8	(	(	PUNCT
american_scientific_journal-667	112	9	1	1	X
american_scientific_journal-667	112	10	)	)	PUNCT
american_scientific_journal-667	112	11	preserves	preserve	VERB
american_scientific_journal-667	112	12	positivity	positivity	NOUN
american_scientific_journal-667	112	13	in	in	ADP
american_scientific_journal-667	112	14	each	each	DET
american_scientific_journal-667	112	15	subinterval	subinterval	NOUN
american_scientific_journal-667	112	16	𝐼𝑖	𝐼𝑖	PROPN
american_scientific_journal-667	112	17	=	=	PUNCT
american_scientific_journal-667	113	1	[	[	X
american_scientific_journal-667	113	2	𝑥𝑖	𝑥𝑖	X
american_scientific_journal-667	113	3	,	,	PUNCT
american_scientific_journal-667	113	4	𝑥𝑖+1	𝑥𝑖+1	PROPN
american_scientific_journal-667	113	5	]	]	PUNCT
american_scientific_journal-667	113	6	,	,	PUNCT
american_scientific_journal-667	113	7	𝑖	𝑖	SYM
american_scientific_journal-667	113	8	=	=	SYM
american_scientific_journal-667	113	9	1	1	NUM
american_scientific_journal-667	113	10	,	,	PUNCT
american_scientific_journal-667	113	11	2	2	NUM
american_scientific_journal-667	113	12	,	,	PUNCT
american_scientific_journal-667	113	13	.	.	PUNCT
american_scientific_journal-667	113	14	.	.	PUNCT
american_scientific_journal-667	113	15	.	.	PUNCT
american_scientific_journal-667	114	1	,	,	PUNCT
american_scientific_journal-667	114	2	𝑛	𝑛	DET
american_scientific_journal-667	114	3	−	−	NOUN
american_scientific_journal-667	114	4	1	1	NUM
american_scientific_journal-667	114	5	,	,	PUNCT
american_scientific_journal-667	114	6	if	if	SCONJ
american_scientific_journal-667	114	7	the	the	DET
american_scientific_journal-667	114	8	shape	shape	NOUN
american_scientific_journal-667	114	9	parameters	parameter	NOUN
american_scientific_journal-667	114	10	satisfy	satisfy	VERB
american_scientific_journal-667	114	11	the	the	DET
american_scientific_journal-667	114	12	following	follow	VERB
american_scientific_journal-667	114	13	conditions	condition	NOUN
american_scientific_journal-667	114	14	:	:	PUNCT
american_scientific_journal-667	114	15	𝑣𝑖	𝑣𝑖	ADP
american_scientific_journal-667	114	16	>	>	X
american_scientific_journal-667	114	17	0	0	NUM
american_scientific_journal-667	114	18	,	,	PUNCT
american_scientific_journal-667	114	19	𝑢𝑖	𝑢𝑖	ADP
american_scientific_journal-667	114	20	=	=	SYM
american_scientific_journal-667	114	21	𝑤𝑖	𝑤𝑖	ADP
american_scientific_journal-667	115	1	+	+	NUM
american_scientific_journal-667	115	2	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
american_scientific_journal-667	115	3	�	�	NOUN
american_scientific_journal-667	115	4	0	0	NUM
american_scientific_journal-667	115	5	,	,	PUNCT
american_scientific_journal-667	115	6	−𝑣𝑖𝑓𝑖	−𝑣𝑖𝑓𝑖	PROPN
american_scientific_journal-667	115	7	2𝑓𝑖+	2𝑓𝑖+	NUM
american_scientific_journal-667	115	8	ℎ𝑖𝑑𝑖	ℎ𝑖𝑑𝑖	NOUN
american_scientific_journal-667	115	9	,	,	PUNCT
american_scientific_journal-667	115	10	𝑣𝑖(ℎ𝑖𝑑𝑖+1−2𝑓𝑖+1	𝑣𝑖(ℎ𝑖𝑑𝑖+1−2𝑓𝑖+1	PROPN
american_scientific_journal-667	115	11	)	)	PUNCT
american_scientific_journal-667	115	12	𝑓𝑖+1	𝑓𝑖+1	VERB
american_scientific_journal-667	115	13	�	�	PROPN
american_scientific_journal-667	115	14	𝑓𝑜𝑟	𝑓𝑜𝑟	ADP
american_scientific_journal-667	115	15	𝑠𝑜𝑚𝑒	𝑠𝑜𝑚𝑒	PROPN
american_scientific_journal-667	115	16	𝑤𝑖	𝑤𝑖	ADP
american_scientific_journal-667	115	17	>	>	X
american_scientific_journal-667	115	18	0	0	PUNCT
american_scientific_journal-667	116	1	the	the	DET
american_scientific_journal-667	116	2	proof	proof	NOUN
american_scientific_journal-667	116	3	follows	follow	VERB
american_scientific_journal-667	116	4	the	the	DET
american_scientific_journal-667	116	5	above	above	ADJ
american_scientific_journal-667	116	6	derivation	derivation	NOUN
american_scientific_journal-667	116	7	.	.	PUNCT
american_scientific_journal-667	117	1	numerical	numerical	ADJ
american_scientific_journal-667	117	2	example	example	NOUN
american_scientific_journal-667	117	3	:	:	PUNCT
american_scientific_journal-667	117	4	consider	consider	VERB
american_scientific_journal-667	117	5	the	the	DET
american_scientific_journal-667	117	6	positive	positive	ADJ
american_scientific_journal-667	117	7	data	datum	NOUN
american_scientific_journal-667	117	8	given	give	VERB
american_scientific_journal-667	117	9	in	in	ADP
american_scientific_journal-667	117	10	table−1	table−1	NUM
american_scientific_journal-667	117	11	.	.	PUNCT
american_scientific_journal-667	118	1	from	from	ADP
american_scientific_journal-667	118	2	figure	figure	NOUN
american_scientific_journal-667	118	3	1	1	NUM
american_scientific_journal-667	118	4	,	,	PUNCT
american_scientific_journal-667	118	5	it	it	PRON
american_scientific_journal-667	118	6	is	be	AUX
american_scientific_journal-667	118	7	clear	clear	ADJ
american_scientific_journal-667	118	8	that	that	SCONJ
american_scientific_journal-667	118	9	the	the	DET
american_scientific_journal-667	118	10	cubic	cubic	ADJ
american_scientific_journal-667	118	11	hermite	hermite	ADJ
american_scientific_journal-667	118	12	function	function	NOUN
american_scientific_journal-667	118	13	has	have	AUX
american_scientific_journal-667	118	14	failed	fail	VERB
american_scientific_journal-667	118	15	to	to	PART
american_scientific_journal-667	118	16	preserve	preserve	VERB
american_scientific_journal-667	118	17	a	a	DET
american_scientific_journal-667	118	18	positive	positive	ADJ
american_scientific_journal-667	118	19	shape	shape	NOUN
american_scientific_journal-667	118	20	of	of	ADP
american_scientific_journal-667	118	21	the	the	DET
american_scientific_journal-667	118	22	data	datum	NOUN
american_scientific_journal-667	118	23	,	,	PUNCT
american_scientific_journal-667	118	24	whereas	whereas	SCONJ
american_scientific_journal-667	118	25	figure	figure	NOUN
american_scientific_journal-667	118	26	2	2	NUM
american_scientific_journal-667	118	27	which	which	PRON
american_scientific_journal-667	118	28	is	be	AUX
american_scientific_journal-667	118	29	drawn	draw	VERB
american_scientific_journal-667	118	30	by	by	ADP
american_scientific_journal-667	118	31	applying	apply	VERB
american_scientific_journal-667	118	32	theorem−1	theorem−1	PRON
american_scientific_journal-667	118	33	with	with	ADP
american_scientific_journal-667	118	34	𝑣𝑖	𝑣𝑖	NOUN
american_scientific_journal-667	118	35	=	=	SYM
american_scientific_journal-667	118	36	0.25	0.25	NUM
american_scientific_journal-667	118	37	preserves	preserve	VERB
american_scientific_journal-667	118	38	the	the	DET
american_scientific_journal-667	118	39	shape	shape	NOUN
american_scientific_journal-667	118	40	of	of	ADP
american_scientific_journal-667	118	41	the	the	DET
american_scientific_journal-667	118	42	positive	positive	ADJ
american_scientific_journal-667	118	43	data	datum	NOUN
american_scientific_journal-667	118	44	.	.	PUNCT
american_scientific_journal-667	119	1	table−2	table−2	PROPN
american_scientific_journal-667	119	2	demonstrates	demonstrate	VERB
american_scientific_journal-667	119	3	the	the	DET
american_scientific_journal-667	119	4	numerical	numerical	ADJ
american_scientific_journal-667	119	5	results	result	NOUN
american_scientific_journal-667	119	6	which	which	PRON
american_scientific_journal-667	119	7	are	be	AUX
american_scientific_journal-667	119	8	computed	compute	VERB
american_scientific_journal-667	119	9	from	from	ADP
american_scientific_journal-667	119	10	the	the	DET
american_scientific_journal-667	119	11	developed	develop	VERB
american_scientific_journal-667	119	12	scheme	scheme	NOUN
american_scientific_journal-667	119	13	of	of	ADP
american_scientific_journal-667	119	14	figure	figure	NOUN
american_scientific_journal-667	119	15	2	2	NUM
american_scientific_journal-667	119	16	.	.	PUNCT
american_scientific_journal-667	119	17	table	table	NOUN
american_scientific_journal-667	119	18	1	1	NUM
american_scientific_journal-667	119	19	:	:	PUNCT
american_scientific_journal-667	119	20	a	a	DET
american_scientific_journal-667	119	21	positive	positive	ADJ
american_scientific_journal-667	119	22	data	datum	NOUN
american_scientific_journal-667	119	23	set	set	VERB
american_scientific_journal-667	119	24	𝒊	𝒊	X
american_scientific_journal-667	119	25	𝟏	𝟏	NUM
american_scientific_journal-667	119	26	𝟐	𝟐	NUM
american_scientific_journal-667	119	27	𝟑	𝟑	NUM
american_scientific_journal-667	119	28	𝟒	𝟒	NUM
american_scientific_journal-667	119	29	𝟓	𝟓	NUM
american_scientific_journal-667	119	30	𝟔	𝟔	NUM
american_scientific_journal-667	119	31	𝟕	𝟕	NUM
american_scientific_journal-667	119	32	𝒙𝒊	𝒙𝒊	PROPN
american_scientific_journal-667	119	33	1	1	NUM
american_scientific_journal-667	119	34	3	3	NUM
american_scientific_journal-667	119	35	5	5	NUM
american_scientific_journal-667	119	36	8	8	NUM
american_scientific_journal-667	119	37	10	10	NUM
american_scientific_journal-667	119	38	11	11	NUM
american_scientific_journal-667	119	39	12	12	NUM
american_scientific_journal-667	119	40	𝒇𝒊	𝒇𝒊	ADP
american_scientific_journal-667	119	41	2.50	2.50	NUM
american_scientific_journal-667	119	42	1.00	1.00	NUM
american_scientific_journal-667	119	43	0.05	0.05	NUM
american_scientific_journal-667	119	44	0.03	0.03	NUM
american_scientific_journal-667	119	45	0.14	0.14	NUM
american_scientific_journal-667	119	46	0.20	0.20	NUM
american_scientific_journal-667	119	47	0.22	0.22	NUM
american_scientific_journal-667	119	48	figure	figure	NOUN
american_scientific_journal-667	119	49	1	1	NUM
american_scientific_journal-667	119	50	:	:	PUNCT
american_scientific_journal-667	119	51	cubic	cubic	ADJ
american_scientific_journal-667	119	52	hermite	hermite	ADJ
american_scientific_journal-667	119	53	function	function	NOUN
american_scientific_journal-667	119	54	for	for	ADP
american_scientific_journal-667	119	55	positive	positive	ADJ
american_scientific_journal-667	119	56	data	datum	NOUN
american_scientific_journal-667	119	57	0	0	NUM
american_scientific_journal-667	119	58	2	2	NUM
american_scientific_journal-667	119	59	4	4	NUM
american_scientific_journal-667	119	60	6	6	NUM
american_scientific_journal-667	119	61	8	8	NUM
american_scientific_journal-667	119	62	10	10	NUM
american_scientific_journal-667	119	63	12	12	NUM
american_scientific_journal-667	119	64	-0.5	-0.5	NUM
american_scientific_journal-667	119	65	0	0	NUM
american_scientific_journal-667	119	66	0.5	0.5	NUM
american_scientific_journal-667	119	67	1	1	NUM
american_scientific_journal-667	119	68	1.5	1.5	NUM
american_scientific_journal-667	119	69	2	2	NUM
american_scientific_journal-667	119	70	2.5	2.5	NUM
american_scientific_journal-667	119	71	x	x	NOUN
american_scientific_journal-667	119	72	-	-	NOUN
american_scientific_journal-667	119	73	axis	axis	ADJ
american_scientific_journal-667	119	74	y	y	PROPN
american_scientific_journal-667	119	75	-	-	PUNCT
american_scientific_journal-667	119	76	a	a	PRON
american_scientific_journal-667	119	77	xis	xis	PROPN
american_scientific_journal-667	119	78	115	115	NUM
american_scientific_journal-667	119	79	american	american	PROPN
american_scientific_journal-667	119	80	scientific	scientific	ADJ
american_scientific_journal-667	119	81	research	research	NOUN
american_scientific_journal-667	119	82	journal	journal	NOUN
american_scientific_journal-667	119	83	for	for	ADP
american_scientific_journal-667	119	84	engineering	engineering	NOUN
american_scientific_journal-667	119	85	,	,	PUNCT
american_scientific_journal-667	119	86	technology	technology	NOUN
american_scientific_journal-667	119	87	,	,	PUNCT
american_scientific_journal-667	119	88	and	and	CCONJ
american_scientific_journal-667	119	89	sciences	science	NOUN
american_scientific_journal-667	119	90	(	(	PUNCT
american_scientific_journal-667	119	91	asrjets	asrjet	NOUN
american_scientific_journal-667	119	92	)	)	PUNCT
american_scientific_journal-667	119	93	(	(	PUNCT
american_scientific_journal-667	119	94	2015	2015	NUM
american_scientific_journal-667	119	95	)	)	PUNCT
american_scientific_journal-667	119	96	volume	volume	NOUN
american_scientific_journal-667	119	97	12	12	NUM
american_scientific_journal-667	119	98	,	,	PUNCT
american_scientific_journal-667	119	99	no	no	DET
american_scientific_journal-667	119	100	1	1	NUM
american_scientific_journal-667	119	101	,	,	PUNCT
american_scientific_journal-667	119	102	pp	pp	ADV
american_scientific_journal-667	119	103	110	110	NUM
american_scientific_journal-667	119	104	-	-	SYM
american_scientific_journal-667	119	105	122	122	NUM
american_scientific_journal-667	119	106	figure	figure	NOUN
american_scientific_journal-667	119	107	2	2	NUM
american_scientific_journal-667	119	108	:	:	PUNCT
american_scientific_journal-667	119	109	positivity	positivity	NOUN
american_scientific_journal-667	119	110	preserving	preserve	VERB
american_scientific_journal-667	119	111	c2	c2	PROPN
american_scientific_journal-667	119	112	rational	rational	ADJ
american_scientific_journal-667	119	113	cubic	cubic	ADJ
american_scientific_journal-667	119	114	function	function	NOUN
american_scientific_journal-667	119	115	with	with	ADP
american_scientific_journal-667	119	116	𝒗𝒊	𝒗𝒊	ADV
american_scientific_journal-667	119	117	=	=	SYM
american_scientific_journal-667	119	118	𝟎.𝟐𝟓	𝟎.𝟐𝟓	NUM
american_scientific_journal-667	119	119	table	table	NOUN
american_scientific_journal-667	119	120	2	2	NUM
american_scientific_journal-667	119	121	:	:	PUNCT
american_scientific_journal-667	119	122	numerical	numerical	ADJ
american_scientific_journal-667	119	123	results	result	NOUN
american_scientific_journal-667	119	124	of	of	ADP
american_scientific_journal-667	119	125	figure	figure	NOUN
american_scientific_journal-667	119	126	𝟐	𝟐	NUM
american_scientific_journal-667	119	127	𝒊	𝒊	NOUN
american_scientific_journal-667	119	128	𝒅𝒊	𝒅𝒊	NOUN
american_scientific_journal-667	119	129	∆𝒊	∆𝒊	PROPN
american_scientific_journal-667	119	130	𝒖𝒊	𝒖𝒊	NOUN
american_scientific_journal-667	119	131	𝒗𝒊	𝒗𝒊	NOUN
american_scientific_journal-667	119	132	𝟏	𝟏	NUM
american_scientific_journal-667	119	133	0	0	NUM
american_scientific_journal-667	119	134	−0.7500	−0.7500	NOUN
american_scientific_journal-667	119	135	0.0010	0.0010	NUM
american_scientific_journal-667	119	136	0.25	0.25	NUM
american_scientific_journal-667	119	137	𝟐	𝟐	NUM
american_scientific_journal-667	119	138	−0.8192	−0.8192	NOUN
american_scientific_journal-667	119	139	−0.4750	−0.4750	NUM
american_scientific_journal-667	119	140	0.0010	0.0010	NUM
american_scientific_journal-667	119	141	0.25	0.25	NUM
american_scientific_journal-667	119	142	𝟑	𝟑	NUM
american_scientific_journal-667	119	143	−0.1291	−0.1291	PROPN
american_scientific_journal-667	119	144	−0.0067	−0.0067	X
american_scientific_journal-667	119	145	0.0445	0.0445	NUM
american_scientific_journal-667	119	146	0.25	0.25	NUM
american_scientific_journal-667	119	147	𝟒	𝟒	NUM
american_scientific_journal-667	119	148	0.0302	0.0302	NUM
american_scientific_journal-667	119	149	0.0550	0.0550	NUM
american_scientific_journal-667	119	150	0.0010	0.0010	NUM
american_scientific_journal-667	119	151	0.25	0.25	NUM
american_scientific_journal-667	119	152	𝟓	𝟓	NUM
american_scientific_journal-667	119	153	0.0799	0.0799	NUM
american_scientific_journal-667	119	154	0.0600	0.0600	NUM
american_scientific_journal-667	119	155	0.0010	0.0010	NUM
american_scientific_journal-667	119	156	0.25	0.25	NUM
american_scientific_journal-667	119	157	𝟔	𝟔	NUM
american_scientific_journal-667	119	158	0.0400	0.0400	NUM
american_scientific_journal-667	119	159	0.0200	0.0200	NUM
american_scientific_journal-667	119	160	0.0010	0.0010	NUM
american_scientific_journal-667	119	161	0.25	0.25	NUM
american_scientific_journal-667	119	162	𝟕	𝟕	NUM
american_scientific_journal-667	119	163	0	0	NUM
american_scientific_journal-667	119	164	−	−	NOUN
american_scientific_journal-667	119	165	−	−	NOUN
american_scientific_journal-667	119	166	−	−	NUM
american_scientific_journal-667	119	167	3.2	3.2	NUM
american_scientific_journal-667	119	168	.	.	PUNCT
american_scientific_journal-667	120	1	monotonicity	monotonicity	NOUN
american_scientific_journal-667	120	2	preserving	preserve	VERB
american_scientific_journal-667	120	3	c2	c2	PROPN
american_scientific_journal-667	120	4	rational	rational	ADJ
american_scientific_journal-667	120	5	cubic	cubic	ADJ
american_scientific_journal-667	120	6	function	function	NOUN
american_scientific_journal-667	120	7	let	let	VERB
american_scientific_journal-667	120	8	{	{	PUNCT
american_scientific_journal-667	120	9	(	(	PUNCT
american_scientific_journal-667	120	10	𝑥𝑖	𝑥𝑖	PROPN
american_scientific_journal-667	120	11	,	,	PUNCT
american_scientific_journal-667	120	12	𝑓𝑖	𝑓𝑖	PROPN
american_scientific_journal-667	120	13	)	)	PUNCT
american_scientific_journal-667	120	14	𝑖	𝑖	NOUN
american_scientific_journal-667	121	1	=	=	SYM
american_scientific_journal-667	121	2	1	1	NUM
american_scientific_journal-667	121	3	,	,	PUNCT
american_scientific_journal-667	121	4	2	2	NUM
american_scientific_journal-667	121	5	.	.	PUNCT
american_scientific_journal-667	121	6	.	.	PUNCT
american_scientific_journal-667	122	1	.𝑛	.𝑛	PUNCT
american_scientific_journal-667	123	1	−	−	NOUN
american_scientific_journal-667	123	2	1	1	X
american_scientific_journal-667	123	3	}	}	PUNCT
american_scientific_journal-667	123	4	𝑖	𝑖	NOUN
american_scientific_journal-667	123	5	=	=	SYM
american_scientific_journal-667	123	6	1	1	NUM
american_scientific_journal-667	123	7	,	,	PUNCT
american_scientific_journal-667	123	8	2	2	NUM
american_scientific_journal-667	123	9	.	.	PUNCT
american_scientific_journal-667	123	10	.	.	PUNCT
american_scientific_journal-667	124	1	.𝑛	.𝑛	PUNCT
american_scientific_journal-667	125	1	−	−	NOUN
american_scientific_journal-667	125	2	1	1	NUM
american_scientific_journal-667	125	3	be	be	AUX
american_scientific_journal-667	125	4	the	the	DET
american_scientific_journal-667	125	5	set	set	NOUN
american_scientific_journal-667	125	6	of	of	ADP
american_scientific_journal-667	125	7	monotone	monotone	ADJ
american_scientific_journal-667	125	8	increasing	increase	VERB
american_scientific_journal-667	125	9	data	datum	NOUN
american_scientific_journal-667	125	10	points	point	NOUN
american_scientific_journal-667	125	11	,	,	PUNCT
american_scientific_journal-667	125	12	such	such	ADJ
american_scientific_journal-667	125	13	that	that	SCONJ
american_scientific_journal-667	125	14	𝑓1	𝑓1	PROPN
american_scientific_journal-667	125	15	≤	≤	PROPN
american_scientific_journal-667	125	16	𝑓2	𝑓2	NOUN
american_scientific_journal-667	125	17	≤	≤	NOUN
american_scientific_journal-667	125	18	.	.	PUNCT
american_scientific_journal-667	125	19	.	.	PUNCT
american_scientific_journal-667	125	20	.	.	PUNCT
american_scientific_journal-667	126	1	≤	≤	NUM
american_scientific_journal-667	127	1	𝑓𝑛	𝑓𝑛	ADV
american_scientific_journal-667	127	2	,	,	PUNCT
american_scientific_journal-667	127	3	or	or	CCONJ
american_scientific_journal-667	127	4	∆𝑖≥	∆𝑖≥	PRON
american_scientific_journal-667	127	5	0	0	X
american_scientific_journal-667	127	6	.	.	PUNCT
american_scientific_journal-667	127	7	suppose	suppose	VERB
american_scientific_journal-667	127	8	𝑑𝑖	𝑑𝑖	PROPN
american_scientific_journal-667	127	9	≥	≥	PRON
american_scientific_journal-667	127	10	0	0	NUM
american_scientific_journal-667	127	11	then	then	ADV
american_scientific_journal-667	127	12	the	the	DET
american_scientific_journal-667	127	13	given	give	VERB
american_scientific_journal-667	127	14	piecewise	piecewise	NOUN
american_scientific_journal-667	127	15	rational	rational	ADJ
american_scientific_journal-667	127	16	cubic	cubic	ADJ
american_scientific_journal-667	127	17	spline	spline	NOUN
american_scientific_journal-667	127	18	function	function	NOUN
american_scientific_journal-667	127	19	(	(	PUNCT
american_scientific_journal-667	127	20	1	1	X
american_scientific_journal-667	127	21	)	)	PUNCT
american_scientific_journal-667	127	22	is	be	AUX
american_scientific_journal-667	127	23	monotone	monotone	ADJ
american_scientific_journal-667	127	24	increasing	increase	VERB
american_scientific_journal-667	127	25	in	in	ADP
american_scientific_journal-667	127	26	each	each	DET
american_scientific_journal-667	127	27	subinterval	subinterval	NOUN
american_scientific_journal-667	127	28	𝐼𝑖	𝐼𝑖	PROPN
american_scientific_journal-667	127	29	=	=	PUNCT
american_scientific_journal-667	128	1	[	[	AUX
american_scientific_journal-667	128	2	𝑥𝑖	𝑥𝑖	X
american_scientific_journal-667	128	3	,	,	PUNCT
american_scientific_journal-667	128	4	𝑥𝑖+1	𝑥𝑖+1	PROPN
american_scientific_journal-667	128	5	]	]	PUNCT
american_scientific_journal-667	128	6	,	,	PUNCT
american_scientific_journal-667	128	7	if	if	SCONJ
american_scientific_journal-667	128	8	𝑆(1)(𝑥	𝑆(1)(𝑥	NOUN
american_scientific_journal-667	128	9	)	)	PUNCT
american_scientific_journal-667	128	10	≥	≥	NOUN
american_scientific_journal-667	128	11	0	0	NUM
american_scientific_journal-667	128	12	.	.	PUNCT
american_scientific_journal-667	128	13	differentiating	differentiate	VERB
american_scientific_journal-667	128	14	(	(	PUNCT
american_scientific_journal-667	128	15	1	1	NUM
american_scientific_journal-667	128	16	)	)	PUNCT
american_scientific_journal-667	128	17	ones	one	NOUN
american_scientific_journal-667	128	18	with	with	ADP
american_scientific_journal-667	128	19	respect	respect	NOUN
american_scientific_journal-667	128	20	to	to	ADP
american_scientific_journal-667	128	21	𝑥	𝑥	PROPN
american_scientific_journal-667	128	22	we	we	PRON
american_scientific_journal-667	128	23	get	get	VERB
american_scientific_journal-667	128	24	:	:	PUNCT
american_scientific_journal-667	128	25	𝑆(1)(𝑥	𝑆(1)(𝑥	NOUN
american_scientific_journal-667	128	26	)	)	PUNCT
american_scientific_journal-667	128	27	=	=	SYM
american_scientific_journal-667	128	28	𝑟𝑖(𝜃	𝑟𝑖(𝜃	X
american_scientific_journal-667	128	29	)	)	PUNCT
american_scientific_journal-667	128	30	ℎ𝑖[𝑞𝑖(𝜃)]2	ℎ𝑖[𝑞𝑖(𝜃)]2	PROPN
american_scientific_journal-667	128	31	(	(	PUNCT
american_scientific_journal-667	128	32	9	9	NUM
american_scientific_journal-667	128	33	)	)	PUNCT
american_scientific_journal-667	128	34	with	with	ADP
american_scientific_journal-667	128	35	𝑟𝑖(𝜃	𝑟𝑖(𝜃	NOUN
american_scientific_journal-667	128	36	)	)	PUNCT
american_scientific_journal-667	128	37	=	=	PUNCT
american_scientific_journal-667	128	38	(	(	PUNCT
american_scientific_journal-667	128	39	1	1	NUM
american_scientific_journal-667	128	40	−	−	PART
american_scientific_journal-667	128	41	𝜃)3𝐵0	𝜃)3𝐵0	NOUN
american_scientific_journal-667	128	42	+	+	CCONJ
american_scientific_journal-667	128	43	𝜃(1	𝜃(1	X
american_scientific_journal-667	128	44	−	−	ADP
american_scientific_journal-667	128	45	𝜃)2𝐵1	𝜃)2𝐵1	NUM
american_scientific_journal-667	128	46	+	+	NUM
american_scientific_journal-667	128	47	𝜃2(1	𝜃2(1	NOUN
american_scientific_journal-667	128	48	−	−	NOUN
american_scientific_journal-667	128	49	𝜃)𝐵2	𝜃)𝐵2	NOUN
american_scientific_journal-667	128	50	+	+	X
american_scientific_journal-667	128	51	𝜃3𝐵3	𝜃3𝐵3	PUNCT
american_scientific_journal-667	128	52	where	where	SCONJ
american_scientific_journal-667	128	53	𝐵0	𝐵0	NOUN
american_scientific_journal-667	128	54	=	=	PUNCT
american_scientific_journal-667	128	55	𝑢𝑖2ℎ𝑖𝑑𝑖	𝑢𝑖2ℎ𝑖𝑑𝑖	PROPN
american_scientific_journal-667	128	56	𝐵1	𝐵1	NOUN
american_scientific_journal-667	128	57	=	=	PUNCT
american_scientific_journal-667	128	58	ℎ𝑖[𝑢𝑖2(2∆𝑖	ℎ𝑖[𝑢𝑖2(2∆𝑖	PROPN
american_scientific_journal-667	128	59	−	−	PROPN
american_scientific_journal-667	128	60	𝑑𝑖	𝑑𝑖	PART
american_scientific_journal-667	128	61	)	)	PUNCT
american_scientific_journal-667	129	1	+	+	CCONJ
american_scientific_journal-667	129	2	2𝑢𝑖𝑣𝑖(2∆𝑖	2𝑢𝑖𝑣𝑖(2∆𝑖	NUM
american_scientific_journal-667	129	3	−	−	NOUN
american_scientific_journal-667	129	4	𝑑𝑖+1	𝑑𝑖+1	NUM
american_scientific_journal-667	129	5	)	)	PUNCT
american_scientific_journal-667	129	6	]	]	PUNCT
american_scientific_journal-667	129	7	0	0	NUM
american_scientific_journal-667	129	8	2	2	NUM
american_scientific_journal-667	129	9	4	4	NUM
american_scientific_journal-667	129	10	6	6	NUM
american_scientific_journal-667	129	11	8	8	NUM
american_scientific_journal-667	129	12	10	10	NUM
american_scientific_journal-667	129	13	12	12	NUM
american_scientific_journal-667	129	14	0	0	NUM
american_scientific_journal-667	129	15	0.5	0.5	NUM
american_scientific_journal-667	129	16	1	1	NUM
american_scientific_journal-667	129	17	1.5	1.5	NUM
american_scientific_journal-667	129	18	2	2	NUM
american_scientific_journal-667	129	19	2.5	2.5	NUM
american_scientific_journal-667	129	20	x	x	NOUN
american_scientific_journal-667	129	21	-	-	NOUN
american_scientific_journal-667	129	22	axis	axis	ADJ
american_scientific_journal-667	129	23	y	y	PROPN
american_scientific_journal-667	129	24	-	-	PUNCT
american_scientific_journal-667	129	25	a	a	PRON
american_scientific_journal-667	129	26	xis	xis	PROPN
american_scientific_journal-667	129	27	116	116	NUM
american_scientific_journal-667	129	28	american	american	PROPN
american_scientific_journal-667	129	29	scientific	scientific	ADJ
american_scientific_journal-667	129	30	research	research	NOUN
american_scientific_journal-667	129	31	journal	journal	NOUN
american_scientific_journal-667	129	32	for	for	ADP
american_scientific_journal-667	129	33	engineering	engineering	NOUN
american_scientific_journal-667	129	34	,	,	PUNCT
american_scientific_journal-667	129	35	technology	technology	NOUN
american_scientific_journal-667	129	36	,	,	PUNCT
american_scientific_journal-667	129	37	and	and	CCONJ
american_scientific_journal-667	129	38	sciences	science	NOUN
american_scientific_journal-667	129	39	(	(	PUNCT
american_scientific_journal-667	129	40	asrjets	asrjet	NOUN
american_scientific_journal-667	129	41	)	)	PUNCT
american_scientific_journal-667	129	42	(	(	PUNCT
american_scientific_journal-667	129	43	2015	2015	NUM
american_scientific_journal-667	129	44	)	)	PUNCT
american_scientific_journal-667	129	45	volume	volume	NOUN
american_scientific_journal-667	129	46	12	12	NUM
american_scientific_journal-667	129	47	,	,	PUNCT
american_scientific_journal-667	129	48	no	no	DET
american_scientific_journal-667	129	49	1	1	NUM
american_scientific_journal-667	129	50	,	,	PUNCT
american_scientific_journal-667	129	51	pp	pp	ADV
american_scientific_journal-667	129	52	110	110	NUM
american_scientific_journal-667	129	53	-	-	SYM
american_scientific_journal-667	129	54	122	122	NUM
american_scientific_journal-667	129	55	𝐵2	𝐵2	NOUN
american_scientific_journal-667	129	56	=	=	SYM
american_scientific_journal-667	129	57	ℎ𝑖[𝑣𝑖2(2∆𝑖	ℎ𝑖[𝑣𝑖2(2∆𝑖	PROPN
american_scientific_journal-667	129	58	−	−	NOUN
american_scientific_journal-667	129	59	𝑑𝑖+1	𝑑𝑖+1	NUM
american_scientific_journal-667	129	60	)	)	PUNCT
american_scientific_journal-667	130	1	+	+	CCONJ
american_scientific_journal-667	130	2	2𝑢𝑖𝑣𝑖(2∆𝑖	2𝑢𝑖𝑣𝑖(2∆𝑖	NUM
american_scientific_journal-667	130	3	−	−	NOUN
american_scientific_journal-667	130	4	𝑑𝑖	𝑑𝑖	NOUN
american_scientific_journal-667	130	5	)	)	PUNCT
american_scientific_journal-667	130	6	]	]	PUNCT
american_scientific_journal-667	130	7	𝐵3	𝐵3	X
american_scientific_journal-667	131	1	=	=	PUNCT
american_scientific_journal-667	131	2	𝑣𝑖2ℎ𝑖𝑑𝑖+1	𝑣𝑖2ℎ𝑖𝑑𝑖+1	PROPN
american_scientific_journal-667	131	3	now	now	ADV
american_scientific_journal-667	131	4	𝑆(1)(𝑥	𝑆(1)(𝑥	NOUN
american_scientific_journal-667	131	5	)	)	PUNCT
american_scientific_journal-667	131	6	≥	≥	NOUN
american_scientific_journal-667	131	7	0	0	NUM
american_scientific_journal-667	131	8	provided	provide	VERB
american_scientific_journal-667	131	9	that	that	DET
american_scientific_journal-667	131	10	𝐵0	𝐵0	NOUN
american_scientific_journal-667	131	11	,	,	PUNCT
american_scientific_journal-667	131	12	𝐵1	𝐵1	NOUN
american_scientific_journal-667	131	13	,	,	PUNCT
american_scientific_journal-667	131	14	𝐵2	𝐵2	NOUN
american_scientific_journal-667	131	15	,	,	PUNCT
american_scientific_journal-667	131	16	𝐵3	𝐵3	PROPN
american_scientific_journal-667	131	17	≥	≥	NOUN
american_scientific_journal-667	131	18	0	0	NUM
american_scientific_journal-667	131	19	.	.	PUNCT
american_scientific_journal-667	132	1	from	from	ADP
american_scientific_journal-667	132	2	our	our	PRON
american_scientific_journal-667	132	3	hypothesis	hypothesis	NOUN
american_scientific_journal-667	132	4	𝐵0	𝐵0	NOUN
american_scientific_journal-667	132	5	,	,	PUNCT
american_scientific_journal-667	132	6	𝐵3	𝐵3	PROPN
american_scientific_journal-667	132	7	≥	≥	NUM
american_scientific_journal-667	132	8	0	0	NUM
american_scientific_journal-667	132	9	is	be	AUX
american_scientific_journal-667	132	10	obvious	obvious	ADJ
american_scientific_journal-667	132	11	.	.	PUNCT
american_scientific_journal-667	133	1	both	both	DET
american_scientific_journal-667	133	2	𝐵1,𝐵2	𝐵1,𝐵2	NOUN
american_scientific_journal-667	133	3	are	be	AUX
american_scientific_journal-667	133	4	non	non	ADJ
american_scientific_journal-667	133	5	-	-	ADJ
american_scientific_journal-667	133	6	negative	negative	ADJ
american_scientific_journal-667	133	7	if	if	SCONJ
american_scientific_journal-667	133	8	𝑢𝑖	𝑢𝑖	PRON
american_scientific_journal-667	133	9	≥	≥	PROPN
american_scientific_journal-667	133	10	𝑣𝑖(𝑑𝑖+1−2∆𝑖	𝑣𝑖(𝑑𝑖+1−2∆𝑖	NUM
american_scientific_journal-667	133	11	)	)	PUNCT
american_scientific_journal-667	133	12	2∆𝑖−𝑑𝑖	2∆𝑖−𝑑𝑖	PROPN
american_scientific_journal-667	133	13	theorem-2	theorem-2	NUM
american_scientific_journal-667	133	14	:	:	PUNCT
american_scientific_journal-667	133	15	the	the	DET
american_scientific_journal-667	133	16	c2	c2	PROPN
american_scientific_journal-667	133	17	rational	rational	ADJ
american_scientific_journal-667	133	18	cubic	cubic	ADJ
american_scientific_journal-667	133	19	spline	spline	NOUN
american_scientific_journal-667	133	20	(	(	PUNCT
american_scientific_journal-667	133	21	1	1	X
american_scientific_journal-667	133	22	)	)	PUNCT
american_scientific_journal-667	133	23	preserves	preserve	VERB
american_scientific_journal-667	133	24	monotonicity	monotonicity	NOUN
american_scientific_journal-667	133	25	in	in	ADP
american_scientific_journal-667	133	26	each	each	DET
american_scientific_journal-667	133	27	subinterval	subinterval	NOUN
american_scientific_journal-667	133	28	𝐼𝑖	𝐼𝑖	PROPN
american_scientific_journal-667	133	29	=	=	PUNCT
american_scientific_journal-667	134	1	[	[	X
american_scientific_journal-667	134	2	𝑥𝑖	𝑥𝑖	X
american_scientific_journal-667	134	3	,	,	PUNCT
american_scientific_journal-667	134	4	𝑥𝑖+1	𝑥𝑖+1	PROPN
american_scientific_journal-667	134	5	]	]	PUNCT
american_scientific_journal-667	134	6	,	,	PUNCT
american_scientific_journal-667	134	7	𝑖	𝑖	SYM
american_scientific_journal-667	134	8	=	=	SYM
american_scientific_journal-667	134	9	1	1	NUM
american_scientific_journal-667	134	10	,	,	PUNCT
american_scientific_journal-667	134	11	2	2	NUM
american_scientific_journal-667	134	12	,	,	PUNCT
american_scientific_journal-667	134	13	.	.	PUNCT
american_scientific_journal-667	134	14	.	.	PUNCT
american_scientific_journal-667	134	15	.	.	PUNCT
american_scientific_journal-667	135	1	,	,	PUNCT
american_scientific_journal-667	135	2	𝑛	𝑛	DET
american_scientific_journal-667	135	3	−	−	NOUN
american_scientific_journal-667	135	4	1	1	NUM
american_scientific_journal-667	135	5	,	,	PUNCT
american_scientific_journal-667	135	6	if	if	SCONJ
american_scientific_journal-667	135	7	the	the	DET
american_scientific_journal-667	135	8	shape	shape	NOUN
american_scientific_journal-667	135	9	parameters	parameter	NOUN
american_scientific_journal-667	135	10	satisfy	satisfy	VERB
american_scientific_journal-667	135	11	the	the	DET
american_scientific_journal-667	135	12	following	follow	VERB
american_scientific_journal-667	135	13	conditions	condition	NOUN
american_scientific_journal-667	135	14	:	:	PUNCT
american_scientific_journal-667	135	15	𝑣𝑖	𝑣𝑖	ADP
american_scientific_journal-667	135	16	>	>	X
american_scientific_journal-667	135	17	0	0	NUM
american_scientific_journal-667	135	18	,	,	PUNCT
american_scientific_journal-667	135	19	𝑢𝑖	𝑢𝑖	PRON
american_scientific_journal-667	135	20	=	=	PUNCT
american_scientific_journal-667	135	21	𝑘𝑖	𝑘𝑖	ADP
american_scientific_journal-667	135	22	+	+	CCONJ
american_scientific_journal-667	135	23	𝑚𝑎𝑥	𝑚𝑎𝑥	ADJ
american_scientific_journal-667	135	24	�	�	NOUN
american_scientific_journal-667	135	25	0	0	NUM
american_scientific_journal-667	135	26	,	,	PUNCT
american_scientific_journal-667	135	27	𝑣𝑖(𝑑𝑖+1−2∆𝑖	𝑣𝑖(𝑑𝑖+1−2∆𝑖	NUM
american_scientific_journal-667	135	28	)	)	PUNCT
american_scientific_journal-667	135	29	2∆𝑖−𝑑𝑖	2∆𝑖−𝑑𝑖	NUM
american_scientific_journal-667	135	30	�	�	PROPN
american_scientific_journal-667	135	31	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
american_scientific_journal-667	135	32	𝑠𝑜𝑚𝑒	𝑠𝑜𝑚𝑒	PROPN
american_scientific_journal-667	136	1	𝑘𝑖	𝑘𝑖	ADP
american_scientific_journal-667	136	2	>	>	X
american_scientific_journal-667	136	3	0	0	PUNCT
american_scientific_journal-667	137	1	the	the	DET
american_scientific_journal-667	137	2	proof	proof	NOUN
american_scientific_journal-667	137	3	follows	follow	VERB
american_scientific_journal-667	137	4	the	the	DET
american_scientific_journal-667	137	5	above	above	ADJ
american_scientific_journal-667	137	6	derivation	derivation	NOUN
american_scientific_journal-667	137	7	.	.	PUNCT
american_scientific_journal-667	138	1	numerical	numerical	ADJ
american_scientific_journal-667	138	2	example	example	NOUN
american_scientific_journal-667	138	3	a	a	DET
american_scientific_journal-667	138	4	monotone	monotone	ADJ
american_scientific_journal-667	138	5	data	datum	NOUN
american_scientific_journal-667	138	6	set	set	VERB
american_scientific_journal-667	138	7	given	give	VERB
american_scientific_journal-667	138	8	in	in	ADP
american_scientific_journal-667	138	9	table-2	table-2	NUM
american_scientific_journal-667	138	10	below	below	ADP
american_scientific_journal-667	138	11	which	which	PRON
american_scientific_journal-667	138	12	shows	show	VERB
american_scientific_journal-667	138	13	the	the	DET
american_scientific_journal-667	138	14	world	world	NOUN
american_scientific_journal-667	138	15	population	population	NOUN
american_scientific_journal-667	138	16	from	from	ADP
american_scientific_journal-667	138	17	the	the	DET
american_scientific_journal-667	138	18	year	year	NOUN
american_scientific_journal-667	138	19	1000	1000	NUM
american_scientific_journal-667	138	20	−	−	PROPN
american_scientific_journal-667	138	21	2011	2011	NUM
american_scientific_journal-667	138	22	in	in	ADP
american_scientific_journal-667	138	23	billions	billion	NOUN
american_scientific_journal-667	138	24	is	be	AUX
american_scientific_journal-667	138	25	borrowed	borrow	VERB
american_scientific_journal-667	138	26	from	from	ADP
american_scientific_journal-667	138	27	[	[	X
american_scientific_journal-667	138	28	7	7	NUM
american_scientific_journal-667	138	29	]	]	PUNCT
american_scientific_journal-667	138	30	.	.	PUNCT
american_scientific_journal-667	139	1	figure	figure	NOUN
american_scientific_journal-667	139	2	3	3	NUM
american_scientific_journal-667	139	3	,	,	PUNCT
american_scientific_journal-667	139	4	which	which	PRON
american_scientific_journal-667	139	5	is	be	AUX
american_scientific_journal-667	139	6	drawn	draw	VERB
american_scientific_journal-667	139	7	by	by	ADP
american_scientific_journal-667	139	8	cubic	cubic	ADJ
american_scientific_journal-667	139	9	hermite	hermite	PROPN
american_scientific_journal-667	139	10	function	function	NOUN
american_scientific_journal-667	139	11	,	,	PUNCT
american_scientific_journal-667	139	12	does	do	AUX
american_scientific_journal-667	139	13	not	not	PART
american_scientific_journal-667	139	14	preserve	preserve	VERB
american_scientific_journal-667	139	15	the	the	DET
american_scientific_journal-667	139	16	monotonicity	monotonicity	NOUN
american_scientific_journal-667	139	17	of	of	ADP
american_scientific_journal-667	139	18	this	this	DET
american_scientific_journal-667	139	19	data	data	NOUN
american_scientific_journal-667	139	20	.	.	PUNCT
american_scientific_journal-667	140	1	on	on	ADP
american_scientific_journal-667	140	2	the	the	DET
american_scientific_journal-667	140	3	other	other	ADJ
american_scientific_journal-667	140	4	hand	hand	NOUN
american_scientific_journal-667	140	5	,	,	PUNCT
american_scientific_journal-667	140	6	figure	figure	NOUN
american_scientific_journal-667	140	7	4	4	NUM
american_scientific_journal-667	140	8	which	which	PRON
american_scientific_journal-667	140	9	is	be	AUX
american_scientific_journal-667	140	10	drawn	draw	VERB
american_scientific_journal-667	140	11	by	by	ADP
american_scientific_journal-667	140	12	monotonicity	monotonicity	NOUN
american_scientific_journal-667	140	13	preserving	preserve	VERB
american_scientific_journal-667	140	14	c2	c2	PROPN
american_scientific_journal-667	140	15	rational	rational	ADJ
american_scientific_journal-667	140	16	cubic	cubic	ADJ
american_scientific_journal-667	140	17	function	function	NOUN
american_scientific_journal-667	140	18	stated	state	VERB
american_scientific_journal-667	140	19	under	under	ADP
american_scientific_journal-667	140	20	theorem−2	theorem−2	NUM
american_scientific_journal-667	140	21	preserves	preserve	VERB
american_scientific_journal-667	140	22	the	the	DET
american_scientific_journal-667	140	23	shape	shape	NOUN
american_scientific_journal-667	140	24	of	of	ADP
american_scientific_journal-667	140	25	this	this	DET
american_scientific_journal-667	140	26	monotone	monotone	ADJ
american_scientific_journal-667	140	27	data	datum	NOUN
american_scientific_journal-667	140	28	everywhere	everywhere	ADV
american_scientific_journal-667	140	29	.	.	PUNCT
american_scientific_journal-667	141	1	table−4	table−4	PRON
american_scientific_journal-667	141	2	demonstrates	demonstrate	VERB
american_scientific_journal-667	141	3	the	the	DET
american_scientific_journal-667	141	4	numerical	numerical	ADJ
american_scientific_journal-667	141	5	results	result	NOUN
american_scientific_journal-667	141	6	which	which	PRON
american_scientific_journal-667	141	7	are	be	AUX
american_scientific_journal-667	141	8	computed	compute	VERB
american_scientific_journal-667	141	9	from	from	ADP
american_scientific_journal-667	141	10	the	the	DET
american_scientific_journal-667	141	11	developed	develop	VERB
american_scientific_journal-667	141	12	scheme	scheme	NOUN
american_scientific_journal-667	141	13	of	of	ADP
american_scientific_journal-667	141	14	figure	figure	NOUN
american_scientific_journal-667	141	15	4	4	NUM
american_scientific_journal-667	141	16	table	table	NOUN
american_scientific_journal-667	141	17	3	3	NUM
american_scientific_journal-667	141	18	:	:	PUNCT
american_scientific_journal-667	141	19	a	a	DET
american_scientific_journal-667	141	20	monotone	monotone	ADJ
american_scientific_journal-667	141	21	data	datum	NOUN
american_scientific_journal-667	141	22	set	set	VERB
american_scientific_journal-667	141	23	𝒊	𝒊	SYM
american_scientific_journal-667	141	24	𝟏	𝟏	NUM
american_scientific_journal-667	141	25	𝟐	𝟐	NUM
american_scientific_journal-667	141	26	𝟑	𝟑	NUM
american_scientific_journal-667	141	27	𝟒	𝟒	NUM
american_scientific_journal-667	141	28	𝟓	𝟓	NUM
american_scientific_journal-667	141	29	𝟔	𝟔	NUM
american_scientific_journal-667	141	30	𝟕	𝟕	NUM
american_scientific_journal-667	141	31	𝟖	𝟖	NUM
american_scientific_journal-667	141	32	𝟗	𝟗	NUM
american_scientific_journal-667	141	33	𝟏𝟎	𝟏𝟎	NUM
american_scientific_journal-667	141	34	years	year	NOUN
american_scientific_journal-667	141	35	(	(	PUNCT
american_scientific_journal-667	141	36	𝒙𝒊	𝒙𝒊	PROPN
american_scientific_journal-667	141	37	)	)	PUNCT
american_scientific_journal-667	141	38	1000	1000	NUM
american_scientific_journal-667	141	39	1250	1250	NUM
american_scientific_journal-667	141	40	1500	1500	NUM
american_scientific_journal-667	141	41	1920	1920	NUM
american_scientific_journal-667	141	42	1960	1960	NUM
american_scientific_journal-667	141	43	1980	1980	NUM
american_scientific_journal-667	141	44	1990	1990	NUM
american_scientific_journal-667	141	45	2000	2000	NUM
american_scientific_journal-667	141	46	2005	2005	NUM
american_scientific_journal-667	141	47	2011	2011	NUM
american_scientific_journal-667	141	48	population	population	NOUN
american_scientific_journal-667	141	49	(	(	PUNCT
american_scientific_journal-667	141	50	𝒇𝒊	𝒇𝒊	PROPN
american_scientific_journal-667	141	51	)	)	PUNCT
american_scientific_journal-667	141	52	0.31	0.31	NUM
american_scientific_journal-667	141	53	0.40	0.40	NUM
american_scientific_journal-667	141	54	0.50	0.50	NUM
american_scientific_journal-667	141	55	1.86	1.86	NUM
american_scientific_journal-667	141	56	3.02	3.02	NUM
american_scientific_journal-667	141	57	4.44	4.44	NUM
american_scientific_journal-667	141	58	5.27	5.27	NUM
american_scientific_journal-667	141	59	6.06	6.06	NUM
american_scientific_journal-667	141	60	6.45	6.45	NUM
american_scientific_journal-667	141	61	7.02	7.02	NUM
american_scientific_journal-667	141	62	figure	figure	NOUN
american_scientific_journal-667	141	63	3	3	NUM
american_scientific_journal-667	141	64	:	:	PUNCT
american_scientific_journal-667	141	65	cubic	cubic	ADJ
american_scientific_journal-667	141	66	hermite	hermite	ADJ
american_scientific_journal-667	141	67	function	function	NOUN
american_scientific_journal-667	141	68	for	for	ADP
american_scientific_journal-667	141	69	monotone	monotone	ADJ
american_scientific_journal-667	141	70	data	datum	NOUN
american_scientific_journal-667	141	71	1000	1000	NUM
american_scientific_journal-667	141	72	1200	1200	NUM
american_scientific_journal-667	141	73	1400	1400	NUM
american_scientific_journal-667	141	74	1600	1600	NUM
american_scientific_journal-667	141	75	1800	1800	NUM
american_scientific_journal-667	141	76	2000	2000	NUM
american_scientific_journal-667	141	77	2200	2200	NUM
american_scientific_journal-667	141	78	0	0	NUM
american_scientific_journal-667	141	79	1	1	NUM
american_scientific_journal-667	141	80	2	2	NUM
american_scientific_journal-667	141	81	3	3	NUM
american_scientific_journal-667	141	82	4	4	NUM
american_scientific_journal-667	141	83	5	5	NUM
american_scientific_journal-667	141	84	6	6	NUM
american_scientific_journal-667	141	85	7	7	NUM
american_scientific_journal-667	141	86	8	8	NUM
american_scientific_journal-667	141	87	x	x	ADJ
american_scientific_journal-667	141	88	-	-	NOUN
american_scientific_journal-667	141	89	axis	axis	ADJ
american_scientific_journal-667	141	90	y	y	NOUN
american_scientific_journal-667	141	91	-	-	PUNCT
american_scientific_journal-667	141	92	a	a	PRON
american_scientific_journal-667	141	93	xis	xis	PROPN
american_scientific_journal-667	141	94	117	117	NUM
american_scientific_journal-667	141	95	american	american	PROPN
american_scientific_journal-667	141	96	scientific	scientific	ADJ
american_scientific_journal-667	141	97	research	research	NOUN
american_scientific_journal-667	141	98	journal	journal	NOUN
american_scientific_journal-667	141	99	for	for	ADP
american_scientific_journal-667	141	100	engineering	engineering	NOUN
american_scientific_journal-667	141	101	,	,	PUNCT
american_scientific_journal-667	141	102	technology	technology	NOUN
american_scientific_journal-667	141	103	,	,	PUNCT
american_scientific_journal-667	141	104	and	and	CCONJ
american_scientific_journal-667	141	105	sciences	science	NOUN
american_scientific_journal-667	141	106	(	(	PUNCT
american_scientific_journal-667	141	107	asrjets	asrjet	NOUN
american_scientific_journal-667	141	108	)	)	PUNCT
american_scientific_journal-667	141	109	(	(	PUNCT
american_scientific_journal-667	141	110	2015	2015	NUM
american_scientific_journal-667	141	111	)	)	PUNCT
american_scientific_journal-667	141	112	volume	volume	NOUN
american_scientific_journal-667	141	113	12	12	NUM
american_scientific_journal-667	141	114	,	,	PUNCT
american_scientific_journal-667	141	115	no	no	DET
american_scientific_journal-667	141	116	1	1	NUM
american_scientific_journal-667	141	117	,	,	PUNCT
american_scientific_journal-667	141	118	pp	pp	ADV
american_scientific_journal-667	141	119	110	110	NUM
american_scientific_journal-667	141	120	-	-	SYM
american_scientific_journal-667	141	121	122	122	NUM
american_scientific_journal-667	141	122	figure	figure	NOUN
american_scientific_journal-667	141	123	4	4	NUM
american_scientific_journal-667	141	124	:	:	PUNCT
american_scientific_journal-667	141	125	monotonicity	monotonicity	NOUN
american_scientific_journal-667	141	126	preserving	preserve	VERB
american_scientific_journal-667	141	127	c2	c2	PROPN
american_scientific_journal-667	141	128	rational	rational	ADJ
american_scientific_journal-667	141	129	cubic	cubic	ADJ
american_scientific_journal-667	141	130	function	function	NOUN
american_scientific_journal-667	141	131	with	with	ADP
american_scientific_journal-667	141	132	𝒗𝒊	𝒗𝒊	ADV
american_scientific_journal-667	141	133	=	=	SYM
american_scientific_journal-667	141	134	𝟎.𝟐𝟓	𝟎.𝟐𝟓	NUM
american_scientific_journal-667	141	135	table	table	NOUN
american_scientific_journal-667	141	136	4	4	NUM
american_scientific_journal-667	141	137	:	:	PUNCT
american_scientific_journal-667	141	138	numerical	numerical	ADJ
american_scientific_journal-667	141	139	results	result	NOUN
american_scientific_journal-667	141	140	of	of	ADP
american_scientific_journal-667	141	141	figure	figure	NOUN
american_scientific_journal-667	141	142	𝟒	𝟒	NUM
american_scientific_journal-667	141	143	𝒊	𝒊	NOUN
american_scientific_journal-667	141	144	𝒅𝒊	𝒅𝒊	NOUN
american_scientific_journal-667	141	145	∆𝒊	∆𝒊	PROPN
american_scientific_journal-667	141	146	𝒖𝒊	𝒖𝒊	NOUN
american_scientific_journal-667	141	147	𝒗𝒊	𝒗𝒊	NOUN
american_scientific_journal-667	141	148	𝟏	𝟏	NUM
american_scientific_journal-667	141	149	0.0000	0.0000	NUM
american_scientific_journal-667	141	150	0.0004	0.0004	NUM
american_scientific_journal-667	141	151	1.5	1.5	NUM
american_scientific_journal-667	141	152	0.25	0.25	NUM
american_scientific_journal-667	141	153	𝟐	𝟐	NUM
american_scientific_journal-667	141	154	0.0006	0.0006	NUM
american_scientific_journal-667	141	155	0.0004	0.0004	NUM
american_scientific_journal-667	141	156	1.5	1.5	NUM
american_scientific_journal-667	141	157	0.25	0.25	NUM
american_scientific_journal-667	141	158	𝟑	𝟑	NUM
american_scientific_journal-667	141	159	0.0001	0.0001	NUM
american_scientific_journal-667	141	160	0.0032	0.0032	NUM
american_scientific_journal-667	141	161	1.5	1.5	NUM
american_scientific_journal-667	141	162	0.25	0.25	NUM
american_scientific_journal-667	141	163	𝟒	𝟒	NUM
american_scientific_journal-667	141	164	0.0191	0.0191	NUM
american_scientific_journal-667	141	165	0.0290	0.0290	NUM
american_scientific_journal-667	141	166	1.5	1.5	NUM
american_scientific_journal-667	141	167	0.25	0.25	NUM
american_scientific_journal-667	141	168	𝟓	𝟓	NUM
american_scientific_journal-667	141	169	0.0451	0.0451	NUM
american_scientific_journal-667	141	170	0.0710	0.0710	NUM
american_scientific_journal-667	141	171	1.5	1.5	NUM
american_scientific_journal-667	141	172	0.25	0.25	NUM
american_scientific_journal-667	141	173	𝟔	𝟔	NUM
american_scientific_journal-667	141	174	0.0909	0.0909	NUM
american_scientific_journal-667	141	175	0.0830	0.0830	NUM
american_scientific_journal-667	141	176	1.5	1.5	NUM
american_scientific_journal-667	141	177	0.25	0.25	NUM
american_scientific_journal-667	141	178	𝟕	𝟕	NUM
american_scientific_journal-667	141	179	0.0766	0.0766	NUM
american_scientific_journal-667	141	180	0.0790	0.0790	NUM
american_scientific_journal-667	141	181	1.5	1.5	NUM
american_scientific_journal-667	141	182	0.25	0.25	NUM
american_scientific_journal-667	141	183	𝟖	𝟖	NUM
american_scientific_journal-667	141	184	0.0802	0.0802	NUM
american_scientific_journal-667	141	185	0.0780	0.0780	NUM
american_scientific_journal-667	141	186	1.5	1.5	NUM
american_scientific_journal-667	141	187	0.25	0.25	NUM
american_scientific_journal-667	141	188	𝟗	𝟗	NUM
american_scientific_journal-667	141	189	0.0801	0.0801	NUM
american_scientific_journal-667	141	190	0.0950	0.0950	NUM
american_scientific_journal-667	141	191	1.5	1.5	NUM
american_scientific_journal-667	141	192	0.25	0.25	NUM
american_scientific_journal-667	141	193	𝟏𝟎	𝟏𝟎	NUM
american_scientific_journal-667	141	194	0.0000	0.0000	NUM
american_scientific_journal-667	141	195	−	−	NOUN
american_scientific_journal-667	142	1	−	−	NOUN
american_scientific_journal-667	142	2	−	−	PROPN
american_scientific_journal-667	142	3	3.3	3.3	NUM
american_scientific_journal-667	142	4	.	.	PUNCT
american_scientific_journal-667	143	1	convexity	convexity	NOUN
american_scientific_journal-667	143	2	preserving	preserve	VERB
american_scientific_journal-667	143	3	c2	c2	PROPN
american_scientific_journal-667	143	4	rational	rational	ADJ
american_scientific_journal-667	143	5	cubic	cubic	ADJ
american_scientific_journal-667	143	6	function	function	NOUN
american_scientific_journal-667	143	7	in	in	ADP
american_scientific_journal-667	143	8	this	this	DET
american_scientific_journal-667	143	9	section	section	NOUN
american_scientific_journal-667	143	10	,	,	PUNCT
american_scientific_journal-667	143	11	we	we	PRON
american_scientific_journal-667	143	12	discuss	discuss	VERB
american_scientific_journal-667	143	13	the	the	DET
american_scientific_journal-667	143	14	problem	problem	NOUN
american_scientific_journal-667	143	15	of	of	ADP
american_scientific_journal-667	143	16	convexity	convexity	NOUN
american_scientific_journal-667	143	17	preserving	preserve	VERB
american_scientific_journal-667	143	18	c2	c2	PROPN
american_scientific_journal-667	143	19	rational	rational	ADJ
american_scientific_journal-667	143	20	cubic	cubic	ADJ
american_scientific_journal-667	143	21	spline	spline	NOUN
american_scientific_journal-667	143	22	.	.	PUNCT
american_scientific_journal-667	144	1	let	let	VERB
american_scientific_journal-667	144	2	{	{	PUNCT
american_scientific_journal-667	144	3	(	(	PUNCT
american_scientific_journal-667	144	4	𝑥𝑖	𝑥𝑖	PROPN
american_scientific_journal-667	144	5	,	,	PUNCT
american_scientific_journal-667	144	6	𝑓𝑖	𝑓𝑖	PROPN
american_scientific_journal-667	144	7	)	)	PUNCT
american_scientific_journal-667	144	8	}	}	PUNCT
american_scientific_journal-667	145	1	such	such	ADJ
american_scientific_journal-667	145	2	that	that	SCONJ
american_scientific_journal-667	145	3	∆𝑖	∆𝑖	PROPN
american_scientific_journal-667	145	4	<	<	X
american_scientific_journal-667	145	5	∆𝑖+1	∆𝑖+1	PROPN
american_scientific_journal-667	145	6	for	for	ADP
american_scientific_journal-667	145	7	all	all	PRON
american_scientific_journal-667	145	8	𝑖	𝑖	SYM
american_scientific_journal-667	145	9	=	=	SYM
american_scientific_journal-667	145	10	1	1	NUM
american_scientific_journal-667	145	11	,	,	PUNCT
american_scientific_journal-667	145	12	2	2	NUM
american_scientific_journal-667	145	13	.	.	PUNCT
american_scientific_journal-667	145	14	.	.	PUNCT
american_scientific_journal-667	145	15	.𝑛	.𝑛	PUNCT
american_scientific_journal-667	146	1	−	−	NOUN
american_scientific_journal-667	146	2	1	1	NUM
american_scientific_journal-667	146	3	be	be	AUX
american_scientific_journal-667	146	4	the	the	DET
american_scientific_journal-667	146	5	set	set	NOUN
american_scientific_journal-667	146	6	of	of	ADP
american_scientific_journal-667	146	7	convex	convex	ADJ
american_scientific_journal-667	146	8	data	datum	NOUN
american_scientific_journal-667	146	9	points	point	NOUN
american_scientific_journal-667	146	10	.	.	PUNCT
american_scientific_journal-667	147	1	suppose	suppose	VERB
american_scientific_journal-667	147	2	𝑑𝑖	𝑑𝑖	VERB
american_scientific_journal-667	147	3	<	<	X
american_scientific_journal-667	147	4	∆𝑖	∆𝑖	PROPN
american_scientific_journal-667	147	5	<	<	X
american_scientific_journal-667	147	6	𝑑𝑖+1	𝑑𝑖+1	NUM
american_scientific_journal-667	147	7	𝑓𝑜𝑟	𝑓𝑜𝑟	NOUN
american_scientific_journal-667	147	8	𝑖	𝑖	NOUN
american_scientific_journal-667	147	9	=	=	SYM
american_scientific_journal-667	147	10	2	2	NUM
american_scientific_journal-667	147	11	,	,	PUNCT
american_scientific_journal-667	147	12	.	.	PUNCT
american_scientific_journal-667	147	13	.	.	PUNCT
american_scientific_journal-667	148	1	.𝑛	.𝑛	PUNCT
american_scientific_journal-667	149	1	−	−	NOUN
american_scientific_journal-667	149	2	2	2	NUM
american_scientific_journal-667	149	3	then	then	ADV
american_scientific_journal-667	149	4	,	,	PUNCT
american_scientific_journal-667	149	5	for	for	ADP
american_scientific_journal-667	149	6	the	the	DET
american_scientific_journal-667	149	7	given	give	VERB
american_scientific_journal-667	149	8	piecewise	piecewise	NOUN
american_scientific_journal-667	149	9	rational	rational	ADJ
american_scientific_journal-667	149	10	cubic	cubic	ADJ
american_scientific_journal-667	149	11	spline	spline	NOUN
american_scientific_journal-667	149	12	function	function	NOUN
american_scientific_journal-667	149	13	(	(	PUNCT
american_scientific_journal-667	149	14	1	1	NUM
american_scientific_journal-667	149	15	)	)	PUNCT
american_scientific_journal-667	149	16	to	to	PART
american_scientific_journal-667	149	17	produce	produce	VERB
american_scientific_journal-667	149	18	a	a	DET
american_scientific_journal-667	149	19	convex	convex	NOUN
american_scientific_journal-667	149	20	curve	curve	NOUN
american_scientific_journal-667	149	21	,	,	PUNCT
american_scientific_journal-667	149	22	we	we	PRON
american_scientific_journal-667	149	23	need	need	VERB
american_scientific_journal-667	149	24	𝑆(2)(𝑥	𝑆(2)(𝑥	NOUN
american_scientific_journal-667	149	25	)	)	PUNCT
american_scientific_journal-667	149	26	≥	≥	NOUN
american_scientific_journal-667	149	27	0.differentiating	0.differentiating	X
american_scientific_journal-667	149	28	(	(	PUNCT
american_scientific_journal-667	149	29	1	1	NUM
american_scientific_journal-667	149	30	)	)	PUNCT
american_scientific_journal-667	149	31	twice	twice	ADV
american_scientific_journal-667	149	32	with	with	ADP
american_scientific_journal-667	149	33	respect	respect	NOUN
american_scientific_journal-667	149	34	to	to	ADP
american_scientific_journal-667	149	35	𝑥	𝑥	PROPN
american_scientific_journal-667	149	36	we	we	PRON
american_scientific_journal-667	149	37	get	get	VERB
american_scientific_journal-667	149	38	:	:	PUNCT
american_scientific_journal-667	149	39	𝑆(2)(𝑥	𝑆(2)(𝑥	NOUN
american_scientific_journal-667	149	40	)	)	PUNCT
american_scientific_journal-667	149	41	=	=	PUNCT
american_scientific_journal-667	150	1	(	(	PUNCT
american_scientific_journal-667	150	2	1−𝜃)3𝐶0	1−𝜃)3𝐶0	NUM
american_scientific_journal-667	150	3	+	+	SYM
american_scientific_journal-667	150	4	𝜃(1−𝜃)2𝐶1+𝜃2(1−𝜃)𝐶2+𝜃3𝐶3	𝜃(1−𝜃)2𝐶1+𝜃2(1−𝜃)𝐶2+𝜃3𝐶3	PRON
american_scientific_journal-667	150	5	ℎ𝑖[𝑢𝑖(1−𝜃)+	ℎ𝑖[𝑢𝑖(1−𝜃)+	NUM
american_scientific_journal-667	150	6	𝑣𝑖𝜃]3	𝑣𝑖𝜃]3	X
american_scientific_journal-667	150	7	(	(	PUNCT
american_scientific_journal-667	150	8	10	10	NUM
american_scientific_journal-667	150	9	)	)	PUNCT
american_scientific_journal-667	150	10	where	where	SCONJ
american_scientific_journal-667	150	11	1000	1000	NUM
american_scientific_journal-667	150	12	1200	1200	NUM
american_scientific_journal-667	150	13	1400	1400	NUM
american_scientific_journal-667	150	14	1600	1600	NUM
american_scientific_journal-667	150	15	1800	1800	NUM
american_scientific_journal-667	150	16	2000	2000	NUM
american_scientific_journal-667	150	17	2200	2200	NUM
american_scientific_journal-667	150	18	0	0	NUM
american_scientific_journal-667	150	19	1	1	NUM
american_scientific_journal-667	150	20	2	2	NUM
american_scientific_journal-667	150	21	3	3	NUM
american_scientific_journal-667	150	22	4	4	NUM
american_scientific_journal-667	150	23	5	5	NUM
american_scientific_journal-667	150	24	6	6	NUM
american_scientific_journal-667	150	25	7	7	NUM
american_scientific_journal-667	150	26	8	8	NUM
american_scientific_journal-667	150	27	x	x	ADJ
american_scientific_journal-667	150	28	-	-	NOUN
american_scientific_journal-667	150	29	axis	axis	ADJ
american_scientific_journal-667	150	30	y	y	PROPN
american_scientific_journal-667	150	31	-	-	PUNCT
american_scientific_journal-667	150	32	a	a	PRON
american_scientific_journal-667	150	33	xis	xis	PROPN
american_scientific_journal-667	150	34	118	118	NUM
american_scientific_journal-667	150	35	american	american	PROPN
american_scientific_journal-667	150	36	scientific	scientific	ADJ
american_scientific_journal-667	150	37	research	research	NOUN
american_scientific_journal-667	150	38	journal	journal	NOUN
american_scientific_journal-667	150	39	for	for	ADP
american_scientific_journal-667	150	40	engineering	engineering	NOUN
american_scientific_journal-667	150	41	,	,	PUNCT
american_scientific_journal-667	150	42	technology	technology	NOUN
american_scientific_journal-667	150	43	,	,	PUNCT
american_scientific_journal-667	150	44	and	and	CCONJ
american_scientific_journal-667	150	45	sciences	science	NOUN
american_scientific_journal-667	150	46	(	(	PUNCT
american_scientific_journal-667	150	47	asrjets	asrjet	NOUN
american_scientific_journal-667	150	48	)	)	PUNCT
american_scientific_journal-667	150	49	(	(	PUNCT
american_scientific_journal-667	150	50	2015	2015	NUM
american_scientific_journal-667	150	51	)	)	PUNCT
american_scientific_journal-667	150	52	volume	volume	NOUN
american_scientific_journal-667	150	53	12	12	NUM
american_scientific_journal-667	150	54	,	,	PUNCT
american_scientific_journal-667	150	55	no	no	DET
american_scientific_journal-667	150	56	1	1	NUM
american_scientific_journal-667	150	57	,	,	PUNCT
american_scientific_journal-667	150	58	pp	pp	ADV
american_scientific_journal-667	150	59	110	110	NUM
american_scientific_journal-667	150	60	-	-	SYM
american_scientific_journal-667	150	61	122	122	NUM
american_scientific_journal-667	150	62	𝐶0	𝐶0	NOUN
american_scientific_journal-667	150	63	=	=	NOUN
american_scientific_journal-667	150	64	2𝑢𝑖3(∆𝑖	2𝑢𝑖3(∆𝑖	NUM
american_scientific_journal-667	150	65	−	−	PROPN
american_scientific_journal-667	150	66	𝑑𝑖	𝑑𝑖	NOUN
american_scientific_journal-667	150	67	)	)	PUNCT
american_scientific_journal-667	150	68	+	+	CCONJ
american_scientific_journal-667	151	1	2𝑢𝑖2𝑣𝑖(∆𝑖	2𝑢𝑖2𝑣𝑖(∆𝑖	NUM
american_scientific_journal-667	151	2	−	−	NOUN
american_scientific_journal-667	151	3	𝑑𝑖	𝑑𝑖	NOUN
american_scientific_journal-667	151	4	)	)	PUNCT
american_scientific_journal-667	151	5	−	−	PROPN
american_scientific_journal-667	151	6	2𝑢𝑖2𝑣𝑖(𝑑𝑖+1	2𝑢𝑖2𝑣𝑖(𝑑𝑖+1	NUM
american_scientific_journal-667	151	7	−	−	PROPN
american_scientific_journal-667	151	8	∆𝑖	∆𝑖	PROPN
american_scientific_journal-667	151	9	)	)	PUNCT
american_scientific_journal-667	151	10	𝐶1	𝐶1	NOUN
american_scientific_journal-667	152	1	=	=	SYM
american_scientific_journal-667	152	2	6𝑢𝑖2𝑣𝑖(∆𝑖	6𝑢𝑖2𝑣𝑖(∆𝑖	NUM
american_scientific_journal-667	152	3	−	−	NUM
american_scientific_journal-667	152	4	𝑑𝑖	𝑑𝑖	NOUN
american_scientific_journal-667	152	5	)	)	PUNCT
american_scientific_journal-667	152	6	𝐶2	𝐶2	PUNCT
american_scientific_journal-667	153	1	=	=	SYM
american_scientific_journal-667	153	2	6𝑢𝑖𝑣𝑖2(𝑑𝑖+1	6𝑢𝑖𝑣𝑖2(𝑑𝑖+1	NUM
american_scientific_journal-667	153	3	−	−	PROPN
american_scientific_journal-667	153	4	∆𝑖	∆𝑖	PROPN
american_scientific_journal-667	153	5	)	)	PUNCT
american_scientific_journal-667	153	6	𝐶3	𝐶3	NOUN
american_scientific_journal-667	153	7	=	=	SYM
american_scientific_journal-667	153	8	2𝑣𝑖3(𝑑𝑖+1	2𝑣𝑖3(𝑑𝑖+1	NUM
american_scientific_journal-667	153	9	−	−	PROPN
american_scientific_journal-667	153	10	∆𝑖	∆𝑖	PROPN
american_scientific_journal-667	153	11	)	)	PUNCT
american_scientific_journal-667	154	1	+	+	PUNCT
american_scientific_journal-667	154	2	2𝑢𝑖𝑣𝑖2(𝑑𝑖	2𝑢𝑖𝑣𝑖2(𝑑𝑖	NUM
american_scientific_journal-667	154	3	−	−	PROPN
american_scientific_journal-667	154	4	∆𝑖	∆𝑖	NUM
american_scientific_journal-667	154	5	)	)	PUNCT
american_scientific_journal-667	155	1	+	+	CCONJ
american_scientific_journal-667	155	2	2𝑢𝑖𝑣𝑖2(𝑑𝑖+1	2𝑢𝑖𝑣𝑖2(𝑑𝑖+1	NUM
american_scientific_journal-667	155	3	−	−	PROPN
american_scientific_journal-667	155	4	∆𝑖	∆𝑖	PROPN
american_scientific_journal-667	155	5	)	)	PUNCT
american_scientific_journal-667	155	6	from	from	ADP
american_scientific_journal-667	155	7	(	(	PUNCT
american_scientific_journal-667	155	8	10	10	NUM
american_scientific_journal-667	155	9	)	)	PUNCT
american_scientific_journal-667	155	10	,	,	PUNCT
american_scientific_journal-667	155	11	𝑆(2)(𝑥	𝑆(2)(𝑥	PROPN
american_scientific_journal-667	155	12	)	)	PUNCT
american_scientific_journal-667	155	13	≥	≥	NOUN
american_scientific_journal-667	155	14	0	0	PUNCT
american_scientific_journal-667	156	1	if	if	SCONJ
american_scientific_journal-667	156	2	𝐶𝑖	𝐶𝑖	PROPN
american_scientific_journal-667	156	3	≥	≥	NOUN
american_scientific_journal-667	156	4	0	0	NUM
american_scientific_journal-667	156	5	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
american_scientific_journal-667	156	6	𝑎𝑙𝑙	𝑎𝑙𝑙	X
american_scientific_journal-667	156	7	𝑖	𝑖	SYM
american_scientific_journal-667	156	8	=	=	SYM
american_scientific_journal-667	156	9	0,1,2,3	0,1,2,3	NUM
american_scientific_journal-667	156	10	.	.	PUNCT
american_scientific_journal-667	157	1	since	since	SCONJ
american_scientific_journal-667	157	2	𝑑𝑖	𝑑𝑖	PROPN
american_scientific_journal-667	157	3	<	<	X
american_scientific_journal-667	157	4	∆𝑖	∆𝑖	PROPN
american_scientific_journal-667	157	5	<	<	X
american_scientific_journal-667	157	6	𝑑𝑖+1	𝑑𝑖+1	NUM
american_scientific_journal-667	157	7	by	by	ADP
american_scientific_journal-667	157	8	assumption	assumption	NOUN
american_scientific_journal-667	157	9	,	,	PUNCT
american_scientific_journal-667	157	10	we	we	PRON
american_scientific_journal-667	157	11	have	have	VERB
american_scientific_journal-667	157	12	𝐶1	𝐶1	NUM
american_scientific_journal-667	157	13	>	>	X
american_scientific_journal-667	157	14	0	0	NUM
american_scientific_journal-667	157	15	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
american_scientific_journal-667	157	16	𝐶2	𝐶2	PROPN
american_scientific_journal-667	157	17	>	>	X
american_scientific_journal-667	157	18	0	0	X
american_scientific_journal-667	157	19	.	.	PUNCT
american_scientific_journal-667	157	20	to	to	PART
american_scientific_journal-667	157	21	get	get	VERB
american_scientific_journal-667	157	22	𝐶0	𝐶0	PROPN
american_scientific_journal-667	157	23	≥	≥	NOUN
american_scientific_journal-667	157	24	0	0	NUM
american_scientific_journal-667	158	1	we	we	PRON
american_scientific_journal-667	158	2	must	must	AUX
american_scientific_journal-667	158	3	have	have	VERB
american_scientific_journal-667	158	4	:	:	PUNCT
american_scientific_journal-667	158	5	2𝑢𝑖3(∆𝑖	2𝑢𝑖3(∆𝑖	NUM
american_scientific_journal-667	158	6	−	−	PROPN
american_scientific_journal-667	158	7	𝑑𝑖	𝑑𝑖	PART
american_scientific_journal-667	158	8	)	)	PUNCT
american_scientific_journal-667	158	9	≥	≥	NOUN
american_scientific_journal-667	158	10	2𝑢𝑖2𝑣𝑖(𝑑𝑖+1	2𝑢𝑖2𝑣𝑖(𝑑𝑖+1	NUM
american_scientific_journal-667	158	11	−	−	PROPN
american_scientific_journal-667	158	12	∆𝑖	∆𝑖	PROPN
american_scientific_journal-667	158	13	)	)	PUNCT
american_scientific_journal-667	158	14	,	,	PUNCT
american_scientific_journal-667	158	15	this	this	PRON
american_scientific_journal-667	158	16	gives	give	VERB
american_scientific_journal-667	158	17	𝑢𝑖	𝑢𝑖	ADP
american_scientific_journal-667	158	18	≥	≥	NOUN
american_scientific_journal-667	158	19	𝑣𝑖(𝑑𝑖+1−∆𝑖	𝑣𝑖(𝑑𝑖+1−∆𝑖	NUM
american_scientific_journal-667	158	20	)	)	PUNCT
american_scientific_journal-667	158	21	∆𝑖−𝑑𝑖	∆𝑖−𝑑𝑖	NOUN
american_scientific_journal-667	158	22	(	(	PUNCT
american_scientific_journal-667	158	23	11	11	NUM
american_scientific_journal-667	158	24	)	)	PUNCT
american_scientific_journal-667	158	25	to	to	PART
american_scientific_journal-667	158	26	get	get	VERB
american_scientific_journal-667	158	27	𝐶3	𝐶3	ADJ
american_scientific_journal-667	158	28	≥	≥	NOUN
american_scientific_journal-667	158	29	0	0	NUM
american_scientific_journal-667	159	1	we	we	PRON
american_scientific_journal-667	159	2	must	must	AUX
american_scientific_journal-667	159	3	have	have	VERB
american_scientific_journal-667	159	4	:	:	PUNCT
american_scientific_journal-667	159	5	2𝑣𝑖3(𝑑𝑖+1	2𝑣𝑖3(𝑑𝑖+1	NUM
american_scientific_journal-667	159	6	−	−	PROPN
american_scientific_journal-667	159	7	∆𝑖	∆𝑖	PROPN
american_scientific_journal-667	159	8	)	)	PUNCT
american_scientific_journal-667	159	9	≥	≥	NOUN
american_scientific_journal-667	159	10	−2𝑢𝑖𝑣𝑖2(𝑑𝑖	−2𝑢𝑖𝑣𝑖2(𝑑𝑖	NOUN
american_scientific_journal-667	159	11	−	−	PROPN
american_scientific_journal-667	159	12	∆𝑖	∆𝑖	PROPN
american_scientific_journal-667	159	13	)	)	PUNCT
american_scientific_journal-667	159	14	this	this	PRON
american_scientific_journal-667	159	15	gives	give	VERB
american_scientific_journal-667	159	16	𝑢𝑖	𝑢𝑖	ADP
american_scientific_journal-667	159	17	≤	≤	NUM
american_scientific_journal-667	159	18	𝑣𝑖(𝑑𝑖+1−∆𝑖	𝑣𝑖(𝑑𝑖+1−∆𝑖	NUM
american_scientific_journal-667	159	19	)	)	PUNCT
american_scientific_journal-667	159	20	∆𝑖−𝑑𝑖	∆𝑖−𝑑𝑖	NOUN
american_scientific_journal-667	159	21	(	(	PUNCT
american_scientific_journal-667	159	22	12	12	NUM
american_scientific_journal-667	159	23	)	)	PUNCT
american_scientific_journal-667	159	24	from	from	ADP
american_scientific_journal-667	159	25	(	(	PUNCT
american_scientific_journal-667	159	26	11	11	NUM
american_scientific_journal-667	159	27	)	)	PUNCT
american_scientific_journal-667	159	28	and	and	CCONJ
american_scientific_journal-667	159	29	(	(	PUNCT
american_scientific_journal-667	159	30	12	12	NUM
american_scientific_journal-667	159	31	)	)	PUNCT
american_scientific_journal-667	159	32	we	we	PRON
american_scientific_journal-667	159	33	get	get	VERB
american_scientific_journal-667	159	34	𝑢𝑖	𝑢𝑖	ADP
american_scientific_journal-667	159	35	=	=	SYM
american_scientific_journal-667	159	36	𝑣𝑖(𝑑𝑖+1−∆𝑖	𝑣𝑖(𝑑𝑖+1−∆𝑖	NUM
american_scientific_journal-667	159	37	)	)	PUNCT
american_scientific_journal-667	159	38	∆𝑖−𝑑𝑖	∆𝑖−𝑑𝑖	NOUN
american_scientific_journal-667	159	39	therefore	therefore	ADV
american_scientific_journal-667	159	40	all	all	DET
american_scientific_journal-667	159	41	the	the	DET
american_scientific_journal-667	159	42	above	above	ADJ
american_scientific_journal-667	159	43	discussion	discussion	NOUN
american_scientific_journal-667	159	44	yields	yield	NOUN
american_scientific_journal-667	159	45	to	to	ADP
american_scientific_journal-667	159	46	the	the	DET
american_scientific_journal-667	159	47	following	following	NOUN
american_scientific_journal-667	159	48	theorem	theorem	VERB
american_scientific_journal-667	159	49	.	.	PUNCT
american_scientific_journal-667	160	1	theorem-3	theorem-3	NUM
american_scientific_journal-667	160	2	:	:	PUNCT
american_scientific_journal-667	160	3	the	the	DET
american_scientific_journal-667	160	4	c2	c2	PROPN
american_scientific_journal-667	160	5	rational	rational	ADJ
american_scientific_journal-667	160	6	cubic	cubic	ADJ
american_scientific_journal-667	160	7	spline	spline	NOUN
american_scientific_journal-667	160	8	(	(	PUNCT
american_scientific_journal-667	160	9	1	1	X
american_scientific_journal-667	160	10	)	)	PUNCT
american_scientific_journal-667	160	11	preserves	preserve	VERB
american_scientific_journal-667	160	12	convexity	convexity	NOUN
american_scientific_journal-667	160	13	in	in	ADP
american_scientific_journal-667	160	14	each	each	DET
american_scientific_journal-667	160	15	subinterval	subinterval	NOUN
american_scientific_journal-667	160	16	𝐼𝑖	𝐼𝑖	PROPN
american_scientific_journal-667	160	17	=	=	PUNCT
american_scientific_journal-667	161	1	[	[	X
american_scientific_journal-667	161	2	𝑥𝑖	𝑥𝑖	X
american_scientific_journal-667	161	3	,	,	PUNCT
american_scientific_journal-667	161	4	𝑥𝑖+1	𝑥𝑖+1	PROPN
american_scientific_journal-667	161	5	]	]	PUNCT
american_scientific_journal-667	161	6	,	,	PUNCT
american_scientific_journal-667	161	7	𝑖	𝑖	SYM
american_scientific_journal-667	161	8	=	=	SYM
american_scientific_journal-667	161	9	1	1	NUM
american_scientific_journal-667	161	10	,	,	PUNCT
american_scientific_journal-667	161	11	2	2	NUM
american_scientific_journal-667	161	12	,	,	PUNCT
american_scientific_journal-667	161	13	.	.	PUNCT
american_scientific_journal-667	161	14	.	.	PUNCT
american_scientific_journal-667	161	15	.	.	PUNCT
american_scientific_journal-667	162	1	,	,	PUNCT
american_scientific_journal-667	162	2	𝑛	𝑛	DET
american_scientific_journal-667	162	3	−	−	NOUN
american_scientific_journal-667	162	4	1	1	NUM
american_scientific_journal-667	162	5	,	,	PUNCT
american_scientific_journal-667	162	6	if	if	SCONJ
american_scientific_journal-667	162	7	the	the	DET
american_scientific_journal-667	162	8	shape	shape	NOUN
american_scientific_journal-667	162	9	parameters	parameter	NOUN
american_scientific_journal-667	162	10	satisfy	satisfy	VERB
american_scientific_journal-667	162	11	the	the	DET
american_scientific_journal-667	162	12	following	follow	VERB
american_scientific_journal-667	162	13	conditions	condition	NOUN
american_scientific_journal-667	162	14	:	:	PUNCT
american_scientific_journal-667	162	15	𝑣𝑖	𝑣𝑖	ADP
american_scientific_journal-667	162	16	>	>	X
american_scientific_journal-667	162	17	0,𝑢𝑖	0,𝑢𝑖	X
american_scientific_journal-667	163	1	=	=	PUNCT
american_scientific_journal-667	164	1	𝑚𝑖	𝑚𝑖	X
american_scientific_journal-667	164	2	+	+	CCONJ
american_scientific_journal-667	164	3	𝑣𝑖(𝑑𝑖+1	𝑣𝑖(𝑑𝑖+1	PRON
american_scientific_journal-667	164	4	−	−	PROPN
american_scientific_journal-667	164	5	∆𝑖	∆𝑖	PROPN
american_scientific_journal-667	164	6	)	)	PUNCT
american_scientific_journal-667	164	7	∆𝑖	∆𝑖	PROPN
american_scientific_journal-667	164	8	−	−	PROPN
american_scientific_journal-667	164	9	𝑑𝑖	𝑑𝑖	VERB
american_scientific_journal-667	164	10	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
american_scientific_journal-667	164	11	𝑠𝑜𝑚𝑒	𝑠𝑜𝑚𝑒	VERB
american_scientific_journal-667	164	12	𝑚𝑖	𝑚𝑖	ADP
american_scientific_journal-667	164	13	>	>	X
american_scientific_journal-667	164	14	0	0	PUNCT
american_scientific_journal-667	165	1	the	the	DET
american_scientific_journal-667	165	2	proof	proof	NOUN
american_scientific_journal-667	165	3	follows	follow	VERB
american_scientific_journal-667	165	4	the	the	DET
american_scientific_journal-667	165	5	above	above	ADJ
american_scientific_journal-667	165	6	derivation	derivation	NOUN
american_scientific_journal-667	165	7	.	.	PUNCT
american_scientific_journal-667	166	1	numerical	numerical	ADJ
american_scientific_journal-667	166	2	example	example	NOUN
american_scientific_journal-667	166	3	:	:	PUNCT
american_scientific_journal-667	166	4	table	table	NOUN
american_scientific_journal-667	166	5	5	5	NUM
american_scientific_journal-667	166	6	below	below	ADP
american_scientific_journal-667	166	7	which	which	PRON
american_scientific_journal-667	166	8	show	show	VERB
american_scientific_journal-667	166	9	a	a	DET
american_scientific_journal-667	166	10	convex	convex	NOUN
american_scientific_journal-667	166	11	data	datum	NOUN
american_scientific_journal-667	166	12	set	set	VERB
american_scientific_journal-667	166	13	is	be	AUX
american_scientific_journal-667	166	14	the	the	DET
american_scientific_journal-667	166	15	modification	modification	NOUN
american_scientific_journal-667	166	16	of	of	ADP
american_scientific_journal-667	166	17	a	a	DET
american_scientific_journal-667	166	18	non	non	ADJ
american_scientific_journal-667	166	19	-	-	ADJ
american_scientific_journal-667	166	20	convex	convex	ADJ
american_scientific_journal-667	166	21	data	datum	NOUN
american_scientific_journal-667	166	22	set	set	VERB
american_scientific_journal-667	166	23	given	give	VERB
american_scientific_journal-667	166	24	under	under	ADP
american_scientific_journal-667	166	25	table	table	NOUN
american_scientific_journal-667	166	26	4	4	NUM
american_scientific_journal-667	166	27	of	of	ADP
american_scientific_journal-667	166	28	[	[	X
american_scientific_journal-667	166	29	1	1	NUM
american_scientific_journal-667	166	30	]	]	PUNCT
american_scientific_journal-667	166	31	.	.	PUNCT
american_scientific_journal-667	167	1	the	the	DET
american_scientific_journal-667	167	2	authors	author	NOUN
american_scientific_journal-667	167	3	wrongly	wrongly	ADV
american_scientific_journal-667	167	4	considered	consider	VERB
american_scientific_journal-667	167	5	the	the	DET
american_scientific_journal-667	167	6	data	datum	NOUN
american_scientific_journal-667	167	7	as	as	SCONJ
american_scientific_journal-667	167	8	if	if	SCONJ
american_scientific_journal-667	167	9	it	it	PRON
american_scientific_journal-667	167	10	was	be	AUX
american_scientific_journal-667	167	11	convex	convex	PROPN
american_scientific_journal-667	167	12	.	.	PUNCT
american_scientific_journal-667	168	1	figure	figure	NOUN
american_scientific_journal-667	168	2	5	5	NUM
american_scientific_journal-667	168	3	,	,	PUNCT
american_scientific_journal-667	168	4	which	which	PRON
american_scientific_journal-667	168	5	is	be	AUX
american_scientific_journal-667	168	6	drawn	draw	VERB
american_scientific_journal-667	168	7	by	by	ADP
american_scientific_journal-667	168	8	cubic	cubic	ADJ
american_scientific_journal-667	168	9	hermite	hermite	PROPN
american_scientific_journal-667	168	10	function	function	NOUN
american_scientific_journal-667	168	11	,	,	PUNCT
american_scientific_journal-667	168	12	does	do	AUX
american_scientific_journal-667	168	13	not	not	PART
american_scientific_journal-667	168	14	preserve	preserve	VERB
american_scientific_journal-667	168	15	the	the	DET
american_scientific_journal-667	168	16	convexity	convexity	NOUN
american_scientific_journal-667	168	17	of	of	ADP
american_scientific_journal-667	168	18	this	this	DET
american_scientific_journal-667	168	19	data	data	NOUN
american_scientific_journal-667	168	20	.	.	PUNCT
american_scientific_journal-667	169	1	on	on	ADP
american_scientific_journal-667	169	2	the	the	DET
american_scientific_journal-667	169	3	other	other	ADJ
american_scientific_journal-667	169	4	hand	hand	NOUN
american_scientific_journal-667	169	5	,	,	PUNCT
american_scientific_journal-667	169	6	figure	figure	NOUN
american_scientific_journal-667	169	7	6	6	NUM
american_scientific_journal-667	169	8	which	which	PRON
american_scientific_journal-667	169	9	is	be	AUX
american_scientific_journal-667	169	10	drawn	draw	VERB
american_scientific_journal-667	169	11	by	by	ADP
american_scientific_journal-667	169	12	convexity	convexity	NOUN
american_scientific_journal-667	169	13	119	119	NUM
american_scientific_journal-667	169	14	american	american	PROPN
american_scientific_journal-667	169	15	scientific	scientific	ADJ
american_scientific_journal-667	169	16	research	research	NOUN
american_scientific_journal-667	169	17	journal	journal	NOUN
american_scientific_journal-667	169	18	for	for	ADP
american_scientific_journal-667	169	19	engineering	engineering	NOUN
american_scientific_journal-667	169	20	,	,	PUNCT
american_scientific_journal-667	169	21	technology	technology	NOUN
american_scientific_journal-667	169	22	,	,	PUNCT
american_scientific_journal-667	169	23	and	and	CCONJ
american_scientific_journal-667	169	24	sciences	science	NOUN
american_scientific_journal-667	169	25	(	(	PUNCT
american_scientific_journal-667	169	26	asrjets	asrjet	NOUN
american_scientific_journal-667	169	27	)	)	PUNCT
american_scientific_journal-667	169	28	(	(	PUNCT
american_scientific_journal-667	169	29	2015	2015	NUM
american_scientific_journal-667	169	30	)	)	PUNCT
american_scientific_journal-667	169	31	volume	volume	NOUN
american_scientific_journal-667	169	32	12	12	NUM
american_scientific_journal-667	169	33	,	,	PUNCT
american_scientific_journal-667	169	34	no	no	DET
american_scientific_journal-667	169	35	1	1	NUM
american_scientific_journal-667	169	36	,	,	PUNCT
american_scientific_journal-667	169	37	pp	pp	ADV
american_scientific_journal-667	169	38	110	110	NUM
american_scientific_journal-667	169	39	-	-	SYM
american_scientific_journal-667	169	40	122	122	NUM
american_scientific_journal-667	169	41	preserving	preserve	VERB
american_scientific_journal-667	169	42	c2	c2	PROPN
american_scientific_journal-667	169	43	rational	rational	ADJ
american_scientific_journal-667	169	44	cubic	cubic	ADJ
american_scientific_journal-667	169	45	function	function	NOUN
american_scientific_journal-667	169	46	given	give	VERB
american_scientific_journal-667	169	47	under	under	ADP
american_scientific_journal-667	169	48	theorem−3	theorem−3	PROPN
american_scientific_journal-667	169	49	preserves	preserve	VERB
american_scientific_journal-667	169	50	the	the	DET
american_scientific_journal-667	169	51	shape	shape	NOUN
american_scientific_journal-667	169	52	of	of	ADP
american_scientific_journal-667	169	53	this	this	DET
american_scientific_journal-667	169	54	convex	convex	NOUN
american_scientific_journal-667	169	55	data	datum	NOUN
american_scientific_journal-667	169	56	everywhere	everywhere	ADV
american_scientific_journal-667	169	57	.	.	PUNCT
american_scientific_journal-667	170	1	table−6	table−6	NOUN
american_scientific_journal-667	170	2	demonstrates	demonstrate	VERB
american_scientific_journal-667	170	3	the	the	DET
american_scientific_journal-667	170	4	numerical	numerical	ADJ
american_scientific_journal-667	170	5	results	result	NOUN
american_scientific_journal-667	170	6	which	which	PRON
american_scientific_journal-667	170	7	are	be	AUX
american_scientific_journal-667	170	8	computed	compute	VERB
american_scientific_journal-667	170	9	from	from	ADP
american_scientific_journal-667	170	10	the	the	DET
american_scientific_journal-667	170	11	developed	develop	VERB
american_scientific_journal-667	170	12	scheme	scheme	NOUN
american_scientific_journal-667	170	13	of	of	ADP
american_scientific_journal-667	170	14	figure	figure	NOUN
american_scientific_journal-667	170	15	6	6	NUM
american_scientific_journal-667	170	16	.	.	PUNCT
american_scientific_journal-667	170	17	table	table	NOUN
american_scientific_journal-667	170	18	5	5	NUM
american_scientific_journal-667	170	19	:	:	PUNCT
american_scientific_journal-667	170	20	a	a	DET
american_scientific_journal-667	170	21	convex	convex	NOUN
american_scientific_journal-667	170	22	data	datum	NOUN
american_scientific_journal-667	170	23	set	set	VERB
american_scientific_journal-667	170	24	𝒊	𝒊	X
american_scientific_journal-667	170	25	𝟏	𝟏	NUM
american_scientific_journal-667	170	26	𝟐	𝟐	NUM
american_scientific_journal-667	170	27	𝟑	𝟑	NUM
american_scientific_journal-667	170	28	𝟒	𝟒	NUM
american_scientific_journal-667	170	29	𝟓	𝟓	NUM
american_scientific_journal-667	170	30	𝟔	𝟔	NUM
american_scientific_journal-667	170	31	𝟕	𝟕	NUM
american_scientific_journal-667	170	32	𝒙𝒊	𝒙𝒊	ADJ
american_scientific_journal-667	170	33	−4	−4	X
american_scientific_journal-667	171	1	−3.5	−3.5	PROPN
american_scientific_journal-667	171	2	−2	−2	PROPN
american_scientific_journal-667	171	3	0	0	NUM
american_scientific_journal-667	171	4	2	2	NUM
american_scientific_journal-667	171	5	3.5	3.5	NUM
american_scientific_journal-667	171	6	4	4	NUM
american_scientific_journal-667	171	7	𝒇𝒊	𝒇𝒊	ADP
american_scientific_journal-667	171	8	5	5	NUM
american_scientific_journal-667	171	9	3	3	NUM
american_scientific_journal-667	171	10	−1.5	−1.5	PROPN
american_scientific_journal-667	171	11	−1.75	−1.75	PROPN
american_scientific_journal-667	171	12	−1.5	−1.5	PROPN
american_scientific_journal-667	171	13	3	3	NUM
american_scientific_journal-667	171	14	5	5	NUM
american_scientific_journal-667	171	15	figure	figure	NOUN
american_scientific_journal-667	171	16	5	5	NUM
american_scientific_journal-667	171	17	:	:	PUNCT
american_scientific_journal-667	171	18	cubic	cubic	ADJ
american_scientific_journal-667	171	19	hermite	hermite	ADJ
american_scientific_journal-667	171	20	function	function	NOUN
american_scientific_journal-667	171	21	for	for	ADP
american_scientific_journal-667	171	22	convex	convex	ADJ
american_scientific_journal-667	171	23	data	datum	NOUN
american_scientific_journal-667	171	24	figure	figure	NOUN
american_scientific_journal-667	171	25	6	6	NUM
american_scientific_journal-667	171	26	:	:	PUNCT
american_scientific_journal-667	171	27	convexity	convexity	NOUN
american_scientific_journal-667	171	28	preserving	preserve	VERB
american_scientific_journal-667	171	29	c2	c2	PROPN
american_scientific_journal-667	171	30	rational	rational	ADJ
american_scientific_journal-667	171	31	cubic	cubic	ADJ
american_scientific_journal-667	171	32	function	function	NOUN
american_scientific_journal-667	171	33	with	with	ADP
american_scientific_journal-667	171	34	𝒗𝒊	𝒗𝒊	ADP
american_scientific_journal-667	171	35	=	=	SYM
american_scientific_journal-667	171	36	𝟎.𝟏	𝟎.𝟏	NUM
american_scientific_journal-667	171	37	-4	-4	INTJ
american_scientific_journal-667	171	38	-3	-3	INTJ
american_scientific_journal-667	171	39	-2	-2	INTJ
american_scientific_journal-667	172	1	-1	-1	SYM
american_scientific_journal-667	172	2	0	0	NUM
american_scientific_journal-667	172	3	1	1	NUM
american_scientific_journal-667	172	4	2	2	NUM
american_scientific_journal-667	172	5	3	3	NUM
american_scientific_journal-667	172	6	4	4	NUM
american_scientific_journal-667	172	7	-2	-2	NOUN
american_scientific_journal-667	172	8	-1	-1	NOUN
american_scientific_journal-667	172	9	0	0	NUM
american_scientific_journal-667	172	10	1	1	NUM
american_scientific_journal-667	172	11	2	2	NUM
american_scientific_journal-667	172	12	3	3	NUM
american_scientific_journal-667	172	13	4	4	NUM
american_scientific_journal-667	172	14	5	5	NUM
american_scientific_journal-667	172	15	x	x	NOUN
american_scientific_journal-667	172	16	-	-	NOUN
american_scientific_journal-667	172	17	axis	axis	ADJ
american_scientific_journal-667	172	18	y	y	PROPN
american_scientific_journal-667	172	19	-	-	PUNCT
american_scientific_journal-667	172	20	a	a	DET
american_scientific_journal-667	172	21	xis	xis	PROPN
american_scientific_journal-667	172	22	-4	-4	INTJ
american_scientific_journal-667	172	23	-3	-3	INTJ
american_scientific_journal-667	172	24	-2	-2	INTJ
american_scientific_journal-667	172	25	-1	-1	SYM
american_scientific_journal-667	172	26	0	0	NUM
american_scientific_journal-667	172	27	1	1	NUM
american_scientific_journal-667	172	28	2	2	NUM
american_scientific_journal-667	172	29	3	3	NUM
american_scientific_journal-667	172	30	4	4	NUM
american_scientific_journal-667	172	31	-2	-2	NOUN
american_scientific_journal-667	172	32	-1	-1	NOUN
american_scientific_journal-667	172	33	0	0	NUM
american_scientific_journal-667	173	1	1	1	NUM
american_scientific_journal-667	173	2	2	2	NUM
american_scientific_journal-667	173	3	3	3	NUM
american_scientific_journal-667	173	4	4	4	NUM
american_scientific_journal-667	173	5	5	5	NUM
american_scientific_journal-667	173	6	x	x	ADJ
american_scientific_journal-667	173	7	-	-	ADJ
american_scientific_journal-667	173	8	axis	axis	ADJ
american_scientific_journal-667	173	9	yax	yax	NOUN
american_scientific_journal-667	173	10	is	be	AUX
american_scientific_journal-667	173	11	120	120	NUM
american_scientific_journal-667	173	12	american	american	ADJ
american_scientific_journal-667	173	13	scientific	scientific	ADJ
american_scientific_journal-667	173	14	research	research	NOUN
american_scientific_journal-667	173	15	journal	journal	NOUN
american_scientific_journal-667	173	16	for	for	ADP
american_scientific_journal-667	173	17	engineering	engineering	NOUN
american_scientific_journal-667	173	18	,	,	PUNCT
american_scientific_journal-667	173	19	technology	technology	NOUN
american_scientific_journal-667	173	20	,	,	PUNCT
american_scientific_journal-667	173	21	and	and	CCONJ
american_scientific_journal-667	173	22	sciences	science	NOUN
american_scientific_journal-667	173	23	(	(	PUNCT
american_scientific_journal-667	173	24	asrjets	asrjet	NOUN
american_scientific_journal-667	173	25	)	)	PUNCT
american_scientific_journal-667	173	26	(	(	PUNCT
american_scientific_journal-667	173	27	2015	2015	NUM
american_scientific_journal-667	173	28	)	)	PUNCT
american_scientific_journal-667	173	29	volume	volume	NOUN
american_scientific_journal-667	173	30	12	12	NUM
american_scientific_journal-667	173	31	,	,	PUNCT
american_scientific_journal-667	173	32	no	no	DET
american_scientific_journal-667	173	33	1	1	NUM
american_scientific_journal-667	173	34	,	,	PUNCT
american_scientific_journal-667	173	35	pp	pp	ADV
american_scientific_journal-667	173	36	110	110	NUM
american_scientific_journal-667	173	37	-	-	SYM
american_scientific_journal-667	173	38	122	122	NUM
american_scientific_journal-667	173	39	table	table	NOUN
american_scientific_journal-667	173	40	6	6	NUM
american_scientific_journal-667	173	41	:	:	PUNCT
american_scientific_journal-667	173	42	numerical	numerical	ADJ
american_scientific_journal-667	173	43	results	result	NOUN
american_scientific_journal-667	173	44	of	of	ADP
american_scientific_journal-667	173	45	figure	figure	NOUN
american_scientific_journal-667	173	46	𝟔	𝟔	NUM
american_scientific_journal-667	173	47	𝒊	𝒊	NOUN
american_scientific_journal-667	173	48	𝒅𝒊	𝒅𝒊	NOUN
american_scientific_journal-667	173	49	∆𝒊	∆𝒊	PROPN
american_scientific_journal-667	173	50	𝒖𝒊	𝒖𝒊	NOUN
american_scientific_journal-667	173	51	𝒗𝒊	𝒗𝒊	NOUN
american_scientific_journal-667	173	52	𝟏	𝟏	NUM
american_scientific_journal-667	173	53	0.0000	0.0000	NUM
american_scientific_journal-667	173	54	−4.0000	−4.0000	NUM
american_scientific_journal-667	173	55	0.25	0.25	NUM
american_scientific_journal-667	173	56	0.1	0.1	NUM
american_scientific_journal-667	173	57	𝟐	𝟐	NUM
american_scientific_journal-667	173	58	−6.4895	−6.4895	NUM
american_scientific_journal-667	173	59	−3.0000	−3.0000	NUM
american_scientific_journal-667	173	60	0.25	0.25	NUM
american_scientific_journal-667	173	61	0.1	0.1	NUM
american_scientific_journal-667	173	62	𝟑	𝟑	NUM
american_scientific_journal-667	173	63	−0.4362	−0.4362	NUM
american_scientific_journal-667	173	64	−0.1250	−0.1250	NUM
american_scientific_journal-667	174	1	0.25	0.25	NUM
american_scientific_journal-667	174	2	0.1	0.1	NUM
american_scientific_journal-667	174	3	𝟒	𝟒	NUM
american_scientific_journal-667	174	4	0.0998	0.0998	NUM
american_scientific_journal-667	174	5	0.1250	0.1250	NUM
american_scientific_journal-667	174	6	1.5	1.5	NUM
american_scientific_journal-667	174	7	0.1	0.1	NUM
american_scientific_journal-667	174	8	𝟓	𝟓	NUM
american_scientific_journal-667	174	9	0.3971	0.3971	NUM
american_scientific_journal-667	174	10	3.0000	3.0000	NUM
american_scientific_journal-667	174	11	0.25	0.25	NUM
american_scientific_journal-667	174	12	0.1	0.1	NUM
american_scientific_journal-667	174	13	𝟔	𝟔	NUM
american_scientific_journal-667	174	14	4.6556	4.6556	NUM
american_scientific_journal-667	174	15	4.0000	4.0000	NUM
american_scientific_journal-667	174	16	0.8	0.8	NUM
american_scientific_journal-667	174	17	0.1	0.1	NUM
american_scientific_journal-667	174	18	𝟕	𝟕	NUM
american_scientific_journal-667	174	19	0.0000	0.0000	NUM
american_scientific_journal-667	174	20	−	−	NOUN
american_scientific_journal-667	174	21	−	−	NOUN
american_scientific_journal-667	174	22	−	−	NOUN
american_scientific_journal-667	174	23	4	4	NUM
american_scientific_journal-667	174	24	.	.	PUNCT
american_scientific_journal-667	174	25	conclusion	conclusion	NOUN
american_scientific_journal-667	174	26	in	in	ADP
american_scientific_journal-667	174	27	order	order	NOUN
american_scientific_journal-667	174	28	to	to	PART
american_scientific_journal-667	174	29	assure	assure	VERB
american_scientific_journal-667	174	30	smooth	smooth	ADJ
american_scientific_journal-667	174	31	visualization	visualization	NOUN
american_scientific_journal-667	174	32	of	of	ADP
american_scientific_journal-667	174	33	shaped	shape	VERB
american_scientific_journal-667	174	34	data	datum	NOUN
american_scientific_journal-667	174	35	,	,	PUNCT
american_scientific_journal-667	174	36	c2	c2	PROPN
american_scientific_journal-667	174	37	rational	rational	ADJ
american_scientific_journal-667	174	38	cubic	cubic	ADJ
american_scientific_journal-667	174	39	splines	spline	NOUN
american_scientific_journal-667	174	40	are	be	AUX
american_scientific_journal-667	174	41	constructed	construct	VERB
american_scientific_journal-667	174	42	.	.	PUNCT
american_scientific_journal-667	175	1	a	a	DET
american_scientific_journal-667	175	2	piecewise	piecewise	NOUN
american_scientific_journal-667	175	3	rational	rational	ADJ
american_scientific_journal-667	175	4	cubic	cubic	ADJ
american_scientific_journal-667	175	5	spline	spline	NOUN
american_scientific_journal-667	175	6	function	function	NOUN
american_scientific_journal-667	175	7	𝑆	𝑆	PROPN
american_scientific_journal-667	175	8	∈	∈	PROPN
american_scientific_journal-667	175	9	𝐶2[𝑎	𝐶2[𝑎	NOUN
american_scientific_journal-667	175	10	,	,	PUNCT
american_scientific_journal-667	175	11	𝑏	𝑏	NOUN
american_scientific_journal-667	175	12	]	]	PUNCT
american_scientific_journal-667	175	13	with	with	ADP
american_scientific_journal-667	175	14	cubic	cubic	ADJ
american_scientific_journal-667	175	15	numerator	numerator	NOUN
american_scientific_journal-667	175	16	and	and	CCONJ
american_scientific_journal-667	175	17	linear	linear	ADJ
american_scientific_journal-667	175	18	denominator	denominator	NOUN
american_scientific_journal-667	175	19	involving	involve	VERB
american_scientific_journal-667	175	20	two	two	NUM
american_scientific_journal-667	175	21	free	free	ADJ
american_scientific_journal-667	175	22	shape	shape	NOUN
american_scientific_journal-667	175	23	parameters	parameter	NOUN
american_scientific_journal-667	175	24	has	have	AUX
american_scientific_journal-667	175	25	been	be	AUX
american_scientific_journal-667	175	26	developed	develop	VERB
american_scientific_journal-667	175	27	to	to	PART
american_scientific_journal-667	175	28	address	address	VERB
american_scientific_journal-667	175	29	the	the	DET
american_scientific_journal-667	175	30	problem	problem	NOUN
american_scientific_journal-667	175	31	of	of	ADP
american_scientific_journal-667	175	32	constructing	construct	VERB
american_scientific_journal-667	175	33	positivity	positivity	NOUN
american_scientific_journal-667	175	34	preserving	preserve	VERB
american_scientific_journal-667	175	35	curve	curve	NOUN
american_scientific_journal-667	175	36	through	through	ADP
american_scientific_journal-667	175	37	positive	positive	ADJ
american_scientific_journal-667	175	38	data	datum	NOUN
american_scientific_journal-667	175	39	,	,	PUNCT
american_scientific_journal-667	175	40	monotonicity	monotonicity	NOUN
american_scientific_journal-667	175	41	preserving	preserve	VERB
american_scientific_journal-667	175	42	curve	curve	NOUN
american_scientific_journal-667	175	43	through	through	ADP
american_scientific_journal-667	175	44	monotone	monotone	ADJ
american_scientific_journal-667	175	45	data	datum	NOUN
american_scientific_journal-667	175	46	and	and	CCONJ
american_scientific_journal-667	175	47	convexity	convexity	NOUN
american_scientific_journal-667	175	48	preserving	preserve	VERB
american_scientific_journal-667	175	49	curve	curve	NOUN
american_scientific_journal-667	175	50	through	through	ADP
american_scientific_journal-667	175	51	convex	convex	PROPN
american_scientific_journal-667	175	52	data	datum	NOUN
american_scientific_journal-667	175	53	.	.	PUNCT
american_scientific_journal-667	176	1	a	a	DET
american_scientific_journal-667	176	2	simple	simple	ADJ
american_scientific_journal-667	176	3	data	datum	NOUN
american_scientific_journal-667	176	4	dependent	dependent	ADJ
american_scientific_journal-667	176	5	condition	condition	NOUN
american_scientific_journal-667	176	6	for	for	ADP
american_scientific_journal-667	176	7	a	a	DET
american_scientific_journal-667	176	8	single	single	ADJ
american_scientific_journal-667	176	9	shape	shape	NOUN
american_scientific_journal-667	176	10	parameter	parameter	NOUN
american_scientific_journal-667	176	11	is	be	AUX
american_scientific_journal-667	176	12	derived	derive	VERB
american_scientific_journal-667	176	13	to	to	PART
american_scientific_journal-667	176	14	preserve	preserve	VERB
american_scientific_journal-667	176	15	the	the	DET
american_scientific_journal-667	176	16	positivity	positivity	NOUN
american_scientific_journal-667	176	17	,	,	PUNCT
american_scientific_journal-667	176	18	monotonicity	monotonicity	NOUN
american_scientific_journal-667	176	19	and	and	CCONJ
american_scientific_journal-667	176	20	convexity	convexity	NOUN
american_scientific_journal-667	176	21	of	of	ADP
american_scientific_journal-667	176	22	respectively	respectively	ADV
american_scientific_journal-667	176	23	positive	positive	ADJ
american_scientific_journal-667	176	24	,	,	PUNCT
american_scientific_journal-667	176	25	monotone	monotone	ADJ
american_scientific_journal-667	176	26	and	and	CCONJ
american_scientific_journal-667	176	27	convex	convex	PROPN
american_scientific_journal-667	176	28	data	datum	NOUN
american_scientific_journal-667	176	29	.	.	PUNCT
american_scientific_journal-667	177	1	the	the	DET
american_scientific_journal-667	177	2	remaining	remain	VERB
american_scientific_journal-667	177	3	shape	shape	NOUN
american_scientific_journal-667	177	4	parameter	parameter	NOUN
american_scientific_journal-667	177	5	is	be	AUX
american_scientific_journal-667	177	6	left	leave	VERB
american_scientific_journal-667	177	7	free	free	ADJ
american_scientific_journal-667	177	8	for	for	SCONJ
american_scientific_journal-667	177	9	the	the	DET
american_scientific_journal-667	177	10	user	user	NOUN
american_scientific_journal-667	177	11	to	to	PART
american_scientific_journal-667	177	12	modify	modify	VERB
american_scientific_journal-667	177	13	the	the	DET
american_scientific_journal-667	177	14	shape	shape	NOUN
american_scientific_journal-667	177	15	of	of	ADP
american_scientific_journal-667	177	16	positive	positive	ADJ
american_scientific_journal-667	177	17	,	,	PUNCT
american_scientific_journal-667	177	18	monotone	monotone	ADJ
american_scientific_journal-667	177	19	and	and	CCONJ
american_scientific_journal-667	177	20	convex	convex	NOUN
american_scientific_journal-667	177	21	curves	curve	NOUN
american_scientific_journal-667	177	22	when	when	SCONJ
american_scientific_journal-667	177	23	the	the	DET
american_scientific_journal-667	177	24	needs	need	NOUN
american_scientific_journal-667	177	25	arise	arise	VERB
american_scientific_journal-667	177	26	.	.	PUNCT
american_scientific_journal-667	178	1	each	each	PRON
american_scientific_journal-667	178	2	of	of	ADP
american_scientific_journal-667	178	3	the	the	DET
american_scientific_journal-667	178	4	positivity	positivity	NOUN
american_scientific_journal-667	178	5	,	,	PUNCT
american_scientific_journal-667	178	6	monotony	monotony	NOUN
american_scientific_journal-667	178	7	and	and	CCONJ
american_scientific_journal-667	178	8	convexity	convexity	NOUN
american_scientific_journal-667	178	9	preserving	preserve	VERB
american_scientific_journal-667	178	10	schemes	scheme	NOUN
american_scientific_journal-667	178	11	has	have	AUX
american_scientific_journal-667	178	12	been	be	AUX
american_scientific_journal-667	178	13	supported	support	VERB
american_scientific_journal-667	178	14	with	with	ADP
american_scientific_journal-667	178	15	practical	practical	ADJ
american_scientific_journal-667	178	16	demonstrations	demonstration	NOUN
american_scientific_journal-667	178	17	on	on	ADP
american_scientific_journal-667	178	18	various	various	ADJ
american_scientific_journal-667	178	19	examples	example	NOUN
american_scientific_journal-667	178	20	of	of	ADP
american_scientific_journal-667	178	21	data	datum	NOUN
american_scientific_journal-667	178	22	.	.	PUNCT
american_scientific_journal-667	179	1	the	the	DET
american_scientific_journal-667	179	2	developed	develop	VERB
american_scientific_journal-667	179	3	schemes	scheme	NOUN
american_scientific_journal-667	179	4	are	be	AUX
american_scientific_journal-667	179	5	applicable	applicable	ADJ
american_scientific_journal-667	179	6	to	to	ADP
american_scientific_journal-667	179	7	such	such	ADJ
american_scientific_journal-667	179	8	problems	problem	NOUN
american_scientific_journal-667	179	9	in	in	ADP
american_scientific_journal-667	179	10	which	which	PRON
american_scientific_journal-667	179	11	only	only	ADV
american_scientific_journal-667	179	12	data	data	NOUN
american_scientific_journal-667	179	13	points	point	NOUN
american_scientific_journal-667	179	14	are	be	AUX
american_scientific_journal-667	179	15	known	know	VERB
american_scientific_journal-667	179	16	.	.	PUNCT
american_scientific_journal-667	180	1	we	we	PRON
american_scientific_journal-667	180	2	developed	develop	VERB
american_scientific_journal-667	180	3	a	a	DET
american_scientific_journal-667	180	4	tridiagonal	tridiagonal	ADJ
american_scientific_journal-667	180	5	system	system	NOUN
american_scientific_journal-667	180	6	of	of	ADP
american_scientific_journal-667	180	7	linear	linear	PROPN
american_scientific_journal-667	180	8	algebraic	algebraic	ADJ
american_scientific_journal-667	180	9	equations	equation	NOUN
american_scientific_journal-667	180	10	with	with	ADP
american_scientific_journal-667	180	11	the	the	DET
american_scientific_journal-667	180	12	help	help	NOUN
american_scientific_journal-667	180	13	of	of	ADP
american_scientific_journal-667	180	14	c2	c2	PROPN
american_scientific_journal-667	180	15	interpolating	interpolate	VERB
american_scientific_journal-667	180	16	conditions	condition	NOUN
american_scientific_journal-667	180	17	and	and	CCONJ
american_scientific_journal-667	180	18	this	this	PRON
american_scientific_journal-667	180	19	enabled	enable	VERB
american_scientific_journal-667	180	20	us	we	PRON
american_scientific_journal-667	180	21	to	to	PART
american_scientific_journal-667	180	22	find	find	VERB
american_scientific_journal-667	180	23	the	the	DET
american_scientific_journal-667	180	24	unknown	unknown	ADJ
american_scientific_journal-667	180	25	derivative	derivative	ADJ
american_scientific_journal-667	180	26	values	value	NOUN
american_scientific_journal-667	180	27	.	.	PUNCT
american_scientific_journal-667	181	1	acknowledgement	acknowledgement	NOUN
american_scientific_journal-667	181	2	the	the	DET
american_scientific_journal-667	181	3	authors	author	NOUN
american_scientific_journal-667	181	4	would	would	AUX
american_scientific_journal-667	181	5	like	like	VERB
american_scientific_journal-667	181	6	to	to	PART
american_scientific_journal-667	181	7	express	express	VERB
american_scientific_journal-667	181	8	their	their	PRON
american_scientific_journal-667	181	9	sincere	sincere	ADJ
american_scientific_journal-667	181	10	gratitude	gratitude	NOUN
american_scientific_journal-667	181	11	to	to	ADP
american_scientific_journal-667	181	12	the	the	DET
american_scientific_journal-667	181	13	anonymous	anonymous	ADJ
american_scientific_journal-667	181	14	referees	referee	NOUN
american_scientific_journal-667	181	15	for	for	ADP
american_scientific_journal-667	181	16	their	their	PRON
american_scientific_journal-667	181	17	exciting	exciting	ADJ
american_scientific_journal-667	181	18	comments	comment	NOUN
american_scientific_journal-667	181	19	which	which	PRON
american_scientific_journal-667	181	20	helped	help	VERB
american_scientific_journal-667	181	21	them	they	PRON
american_scientific_journal-667	181	22	in	in	ADP
american_scientific_journal-667	181	23	improving	improve	VERB
american_scientific_journal-667	181	24	this	this	DET
american_scientific_journal-667	181	25	manuscript	manuscript	NOUN
american_scientific_journal-667	181	26	significantly	significantly	ADV
american_scientific_journal-667	181	27	.	.	PUNCT
american_scientific_journal-667	182	1	they	they	PRON
american_scientific_journal-667	182	2	are	be	AUX
american_scientific_journal-667	182	3	also	also	ADV
american_scientific_journal-667	182	4	thankful	thankful	ADJ
american_scientific_journal-667	182	5	to	to	ADP
american_scientific_journal-667	182	6	the	the	DET
american_scientific_journal-667	182	7	previous	previous	ADJ
american_scientific_journal-667	182	8	authors	author	NOUN
american_scientific_journal-667	182	9	since	since	SCONJ
american_scientific_journal-667	182	10	their	their	PRON
american_scientific_journal-667	182	11	efforts	effort	NOUN
american_scientific_journal-667	182	12	has	have	AUX
american_scientific_journal-667	182	13	been	be	AUX
american_scientific_journal-667	182	14	used	use	VERB
american_scientific_journal-667	182	15	as	as	ADP
american_scientific_journal-667	182	16	a	a	DET
american_scientific_journal-667	182	17	references	reference	NOUN
american_scientific_journal-667	182	18	in	in	ADP
american_scientific_journal-667	182	19	the	the	DET
american_scientific_journal-667	182	20	study	study	NOUN
american_scientific_journal-667	182	21	.	.	PUNCT
american_scientific_journal-667	183	1	last	last	ADJ
american_scientific_journal-667	183	2	,	,	PUNCT
american_scientific_journal-667	183	3	but	but	CCONJ
american_scientific_journal-667	183	4	not	not	PART
american_scientific_journal-667	183	5	least	least	ADJ
american_scientific_journal-667	183	6	the	the	DET
american_scientific_journal-667	183	7	authors	author	NOUN
american_scientific_journal-667	183	8	would	would	AUX
american_scientific_journal-667	183	9	also	also	ADV
american_scientific_journal-667	183	10	like	like	VERB
american_scientific_journal-667	183	11	to	to	PART
american_scientific_journal-667	183	12	thank	thank	VERB
american_scientific_journal-667	183	13	jimma	jimma	PROPN
american_scientific_journal-667	183	14	university	university	PROPN
american_scientific_journal-667	183	15	for	for	ADP
american_scientific_journal-667	183	16	their	their	PRON
american_scientific_journal-667	183	17	financial	financial	ADJ
american_scientific_journal-667	183	18	and	and	CCONJ
american_scientific_journal-667	183	19	material	material	NOUN
american_scientific_journal-667	183	20	support	support	NOUN
american_scientific_journal-667	183	21	.	.	PUNCT
american_scientific_journal-667	184	1	references	reference	NOUN
american_scientific_journal-667	184	2	[	[	X
american_scientific_journal-667	184	3	1	1	NUM
american_scientific_journal-667	184	4	]	]	PUNCT
american_scientific_journal-667	184	5	m.	m.	NOUN
american_scientific_journal-667	184	6	sarfraz	sarfraz	PROPN
american_scientific_journal-667	184	7	,	,	PUNCT
american_scientific_journal-667	184	8	m.z	m.z	PROPN
american_scientific_journal-667	184	9	.	.	PROPN
american_scientific_journal-667	184	10	hussain	hussain	PROPN
american_scientific_journal-667	184	11	&	&	CCONJ
american_scientific_journal-667	184	12	m.	m.	PROPN
american_scientific_journal-667	184	13	hussain	hussain	PROPN
american_scientific_journal-667	184	14	.	.	PUNCT
american_scientific_journal-667	185	1	"	"	PUNCT
american_scientific_journal-667	185	2	shape	shape	VERB
american_scientific_journal-667	185	3	preserving	preserve	VERB
american_scientific_journal-667	185	4	curve	curve	NOUN
american_scientific_journal-667	185	5	interpolation	interpolation	NOUN
american_scientific_journal-667	185	6	.	.	PUNCT
american_scientific_journal-667	185	7	"	"	PUNCT
american_scientific_journal-667	186	1	international	international	ADJ
american_scientific_journal-667	186	2	journal	journal	NOUN
american_scientific_journal-667	186	3	of	of	ADP
american_scientific_journal-667	186	4	computer	computer	NOUN
american_scientific_journal-667	186	5	mathematics	mathematic	NOUN
american_scientific_journal-667	186	6	,	,	PUNCT
american_scientific_journal-667	186	7	vol.89	vol.89	NOUN
american_scientific_journal-667	186	8	,	,	PUNCT
american_scientific_journal-667	186	9	pp.35	pp.35	NOUN
american_scientific_journal-667	186	10	-	-	SYM
american_scientific_journal-667	186	11	53	53	NUM
american_scientific_journal-667	186	12	,	,	PUNCT
american_scientific_journal-667	186	13	2012	2012	NUM
american_scientific_journal-667	186	14	.	.	PUNCT
american_scientific_journal-667	187	1	[	[	X
american_scientific_journal-667	187	2	2	2	X
american_scientific_journal-667	187	3	]	]	X
american_scientific_journal-667	187	4	m.z	m.z	PROPN
american_scientific_journal-667	187	5	.	.	PROPN
american_scientific_journal-667	187	6	hussain	hussain	PROPN
american_scientific_journal-667	187	7	,	,	PUNCT
american_scientific_journal-667	187	8	m.	m.	NOUN
american_scientific_journal-667	187	9	sarfraz	sarfraz	PROPN
american_scientific_journal-667	187	10	and	and	CCONJ
american_scientific_journal-667	187	11	t.s	t.s	PROPN
american_scientific_journal-667	187	12	.	.	PROPN
american_scientific_journal-667	187	13	shaikh	shaikh	PROPN
american_scientific_journal-667	187	14	.	.	PUNCT
american_scientific_journal-667	188	1	"	"	PUNCT
american_scientific_journal-667	188	2	shape	shape	VERB
american_scientific_journal-667	188	3	preserving	preserve	VERB
american_scientific_journal-667	188	4	rational	rational	ADJ
american_scientific_journal-667	188	5	cubic	cubic	ADJ
american_scientific_journal-667	188	6	spline	spline	NOUN
american_scientific_journal-667	188	7	for	for	ADP
american_scientific_journal-667	188	8	positive	positive	ADJ
american_scientific_journal-667	188	9	and	and	CCONJ
american_scientific_journal-667	188	10	convex	convex	ADJ
american_scientific_journal-667	188	11	data	datum	NOUN
american_scientific_journal-667	188	12	.	.	PUNCT
american_scientific_journal-667	188	13	"	"	PUNCT
american_scientific_journal-667	189	1	egyptian	egyptian	ADJ
american_scientific_journal-667	189	2	informatics	informatic	NOUN
american_scientific_journal-667	189	3	journal	journal	PROPN
american_scientific_journal-667	189	4	,	,	PUNCT
american_scientific_journal-667	189	5	vol	vol	NOUN
american_scientific_journal-667	189	6	.	.	PROPN
american_scientific_journal-667	189	7	12	12	NUM
american_scientific_journal-667	189	8	,	,	PUNCT
american_scientific_journal-667	189	9	pp.231–236	pp.231–236	PROPN
american_scientific_journal-667	189	10	,	,	PUNCT
american_scientific_journal-667	189	11	2011	2011	NUM
american_scientific_journal-667	189	12	.	.	PUNCT
american_scientific_journal-667	190	1	121	121	NUM
american_scientific_journal-667	190	2	american	american	ADJ
american_scientific_journal-667	190	3	scientific	scientific	ADJ
american_scientific_journal-667	190	4	research	research	NOUN
american_scientific_journal-667	190	5	journal	journal	NOUN
american_scientific_journal-667	190	6	for	for	ADP
american_scientific_journal-667	190	7	engineering	engineering	NOUN
american_scientific_journal-667	190	8	,	,	PUNCT
american_scientific_journal-667	190	9	technology	technology	NOUN
american_scientific_journal-667	190	10	,	,	PUNCT
american_scientific_journal-667	190	11	and	and	CCONJ
american_scientific_journal-667	190	12	sciences	science	NOUN
american_scientific_journal-667	190	13	(	(	PUNCT
american_scientific_journal-667	190	14	asrjets	asrjet	NOUN
american_scientific_journal-667	190	15	)	)	PUNCT
american_scientific_journal-667	190	16	(	(	PUNCT
american_scientific_journal-667	190	17	2015	2015	NUM
american_scientific_journal-667	190	18	)	)	PUNCT
american_scientific_journal-667	190	19	volume	volume	NOUN
american_scientific_journal-667	190	20	12	12	NUM
american_scientific_journal-667	190	21	,	,	PUNCT
american_scientific_journal-667	190	22	no	no	DET
american_scientific_journal-667	190	23	1	1	NUM
american_scientific_journal-667	190	24	,	,	PUNCT
american_scientific_journal-667	190	25	pp	pp	ADV
american_scientific_journal-667	190	26	110	110	NUM
american_scientific_journal-667	190	27	-	-	SYM
american_scientific_journal-667	190	28	122	122	NUM
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american_scientific_journal-667	190	30	3	3	NUM
american_scientific_journal-667	190	31	]	]	PUNCT
american_scientific_journal-667	190	32	m.abbas	m.abba	NOUN
american_scientific_journal-667	190	33	,	,	PUNCT
american_scientific_journal-667	190	34	a.abd.majid	a.abd.majid	X
american_scientific_journal-667	190	35	,	,	PUNCT
american_scientific_journal-667	190	36	hj	hj	PROPN
american_scientific_journal-667	190	37	.	.	PUNCT
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american_scientific_journal-667	190	39	,	,	PUNCT
american_scientific_journal-667	190	40	md.n	md.n	NOUN
american_scientific_journal-667	190	41	.	.	PUNCT
american_scientific_journal-667	190	42	and	and	CCONJ
american_scientific_journal-667	190	43	j.	j.	PROPN
american_scientific_journal-667	190	44	md	md	PROPN
american_scientific_journal-667	190	45	.	.	PROPN
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american_scientific_journal-667	190	47	.	.	PUNCT
american_scientific_journal-667	191	1	"	"	PUNCT
american_scientific_journal-667	191	2	positivity	positivity	NOUN
american_scientific_journal-667	191	3	-	-	PUNCT
american_scientific_journal-667	191	4	preserving	preserve	VERB
american_scientific_journal-667	191	5	c2	c2	PROPN
american_scientific_journal-667	191	6	rational	rational	ADJ
american_scientific_journal-667	191	7	cubic	cubic	ADJ
american_scientific_journal-667	191	8	spline	spline	NOUN
american_scientific_journal-667	191	9	interpolation	interpolation	NOUN
american_scientific_journal-667	191	10	.	.	PUNCT
american_scientific_journal-667	191	11	"	"	PUNCT
american_scientific_journal-667	192	1	scienceasia	scienceasia	PROPN
american_scientific_journal-667	192	2	,	,	PUNCT
american_scientific_journal-667	192	3	vol.39,pp.208–213,2012	vol.39,pp.208–213,2012	NOUN
american_scientific_journal-667	192	4	.	.	PUNCT
american_scientific_journal-667	193	1	[	[	X
american_scientific_journal-667	193	2	4	4	X
american_scientific_journal-667	193	3	]	]	X
american_scientific_journal-667	193	4	g.	g.	PROPN
american_scientific_journal-667	193	5	beliakov	beliakov	PROPN
american_scientific_journal-667	193	6	.	.	PUNCT
american_scientific_journal-667	194	1	"	"	PUNCT
american_scientific_journal-667	194	2	monotonicity	monotonicity	NOUN
american_scientific_journal-667	194	3	preserving	preserve	VERB
american_scientific_journal-667	194	4	approximation	approximation	NOUN
american_scientific_journal-667	194	5	of	of	ADP
american_scientific_journal-667	194	6	multivariate	multivariate	NOUN
american_scientific_journal-667	194	7	scattered	scatter	VERB
american_scientific_journal-667	194	8	data	datum	NOUN
american_scientific_journal-667	194	9	.	.	PUNCT
american_scientific_journal-667	194	10	"	"	PUNCT
american_scientific_journal-667	195	1	bit	bit	NOUN
american_scientific_journal-667	195	2	numer	numer	NOUN
american_scientific_journal-667	195	3	.	.	PUNCT
american_scientific_journal-667	195	4	math	math	PROPN
american_scientific_journal-667	195	5	.	.	PUNCT
american_scientific_journal-667	195	6	,	,	PUNCT
american_scientific_journal-667	195	7	vol.45	vol.45	X
american_scientific_journal-667	195	8	,	,	PUNCT
american_scientific_journal-667	195	9	pp	pp	ADJ
american_scientific_journal-667	195	10	.	.	PUNCT
american_scientific_journal-667	196	1	653–677,aug.2005	653–677,aug.2005	NUM
american_scientific_journal-667	196	2	.	.	PUNCT
american_scientific_journal-667	197	1	[	[	X
american_scientific_journal-667	197	2	5	5	NUM
american_scientific_journal-667	197	3	]	]	X
american_scientific_journal-667	197	4	m.z	m.z	PROPN
american_scientific_journal-667	197	5	.	.	PROPN
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american_scientific_journal-667	197	7	and	and	CCONJ
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american_scientific_journal-667	197	9	.	.	PUNCT
american_scientific_journal-667	198	1	"	"	PUNCT
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american_scientific_journal-667	198	3	-	-	PUNCT
american_scientific_journal-667	198	4	preserving	preserve	VERB
american_scientific_journal-667	198	5	interpolation	interpolation	NOUN
american_scientific_journal-667	198	6	of	of	ADP
american_scientific_journal-667	198	7	positive	positive	ADJ
american_scientific_journal-667	198	8	data	datum	NOUN
american_scientific_journal-667	198	9	by	by	ADP
american_scientific_journal-667	198	10	rational	rational	ADJ
american_scientific_journal-667	198	11	cubics	cubic	NOUN
american_scientific_journal-667	198	12	.	.	PUNCT
american_scientific_journal-667	198	13	"	"	PUNCT
american_scientific_journal-667	199	1	j.	j.	PROPN
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american_scientific_journal-667	199	3	.	.	PUNCT
american_scientific_journal-667	200	1	appl	appl	PROPN
american_scientific_journal-667	200	2	.	.	PROPN
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american_scientific_journal-667	200	4	,	,	PUNCT
american_scientific_journal-667	200	5	.	.	PUNCT
american_scientific_journal-667	201	1	vol.218	vol.218	NOUN
american_scientific_journal-667	201	2	,	,	PUNCT
american_scientific_journal-667	201	3	pp	pp	ADJ
american_scientific_journal-667	201	4	.	.	PUNCT
american_scientific_journal-667	202	1	446–458,2008	446–458,2008	X
american_scientific_journal-667	202	2	.	.	PUNCT
american_scientific_journal-667	203	1	[	[	X
american_scientific_journal-667	203	2	6	6	NUM
american_scientific_journal-667	203	3	]	]	SYM
american_scientific_journal-667	203	4	m.abbas	m.abba	NOUN
american_scientific_journal-667	203	5	,	,	PUNCT
american_scientific_journal-667	203	6	a.abd	a.abd	PROPN
american_scientific_journal-667	203	7	.	.	PUNCT
american_scientific_journal-667	204	1	majid	majid	PROPN
american_scientific_journal-667	204	2	,	,	PUNCT
american_scientific_journal-667	204	3	and	and	CCONJ
american_scientific_journal-667	204	4	j.	j.	PROPN
american_scientific_journal-667	204	5	md	md	PROPN
american_scientific_journal-667	204	6	.	.	PROPN
american_scientific_journal-667	204	7	ali	ali	PROPN
american_scientific_journal-667	204	8	.	.	PUNCT
american_scientific_journal-667	205	1	"	"	PUNCT
american_scientific_journal-667	205	2	a	a	DET
american_scientific_journal-667	205	3	rational	rational	ADJ
american_scientific_journal-667	205	4	spline	spline	NOUN
american_scientific_journal-667	205	5	for	for	ADP
american_scientific_journal-667	205	6	preserving	preserve	VERB
american_scientific_journal-667	205	7	the	the	DET
american_scientific_journal-667	205	8	shape	shape	NOUN
american_scientific_journal-667	205	9	of	of	ADP
american_scientific_journal-667	205	10	positive	positive	ADJ
american_scientific_journal-667	205	11	data	datum	NOUN
american_scientific_journal-667	205	12	.	.	PUNCT
american_scientific_journal-667	205	13	"	"	PUNCT
american_scientific_journal-667	206	1	international	international	ADJ
american_scientific_journal-667	206	2	journal	journal	NOUN
american_scientific_journal-667	206	3	of	of	ADP
american_scientific_journal-667	206	4	computer	computer	NOUN
american_scientific_journal-667	206	5	and	and	CCONJ
american_scientific_journal-667	206	6	electrical	electrical	ADJ
american_scientific_journal-667	206	7	engineering	engineering	NOUN
american_scientific_journal-667	206	8	,	,	PUNCT
american_scientific_journal-667	206	9	vol.5,2013	vol.5,2013	ADJ
american_scientific_journal-667	206	10	.	.	PUNCT
american_scientific_journal-667	207	1	[	[	X
american_scientific_journal-667	207	2	7	7	X
american_scientific_journal-667	207	3	]	]	SYM
american_scientific_journal-667	207	4	m.abbas	m.abba	NOUN
american_scientific_journal-667	207	5	,	,	PUNCT
american_scientific_journal-667	207	6	a.abd	a.abd	PROPN
american_scientific_journal-667	207	7	.	.	PUNCT
american_scientific_journal-667	208	1	majid	majid	PROPN
american_scientific_journal-667	208	2	,	,	PUNCT
american_scientific_journal-667	208	3	and	and	CCONJ
american_scientific_journal-667	208	4	j.	j.	PROPN
american_scientific_journal-667	208	5	md	md	PROPN
american_scientific_journal-667	208	6	.	.	PROPN
american_scientific_journal-667	208	7	ali	ali	PROPN
american_scientific_journal-667	208	8	.	.	PUNCT
american_scientific_journal-667	209	1	"	"	PUNCT
american_scientific_journal-667	209	2	monotonicity	monotonicity	NOUN
american_scientific_journal-667	209	3	-	-	PUNCT
american_scientific_journal-667	209	4	preserving	preserve	VERB
american_scientific_journal-667	209	5	c2	c2	PROPN
american_scientific_journal-667	209	6	rational	rational	ADJ
american_scientific_journal-667	209	7	cubic	cubic	ADJ
american_scientific_journal-667	209	8	spline	spline	NOUN
american_scientific_journal-667	209	9	for	for	ADP
american_scientific_journal-667	209	10	monotone	monotone	ADJ
american_scientific_journal-667	209	11	data	datum	NOUN
american_scientific_journal-667	209	12	.	.	PUNCT
american_scientific_journal-667	209	13	"	"	PUNCT
american_scientific_journal-667	209	14	applied	apply	VERB
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american_scientific_journal-667	209	16	and	and	CCONJ
american_scientific_journal-667	209	17	computation	computation	NOUN
american_scientific_journal-667	209	18	,	,	PUNCT
american_scientific_journal-667	209	19	vol.219	vol.219	NOUN
american_scientific_journal-667	209	20	,	,	PUNCT
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american_scientific_journal-667	209	22	,	,	PUNCT
american_scientific_journal-667	209	23	2012	2012	NUM
american_scientific_journal-667	209	24	.	.	PUNCT
american_scientific_journal-667	210	1	[	[	X
american_scientific_journal-667	210	2	8	8	NUM
american_scientific_journal-667	210	3	]	]	SYM
american_scientific_journal-667	210	4	m.abbas	m.abba	NOUN
american_scientific_journal-667	210	5	,	,	PUNCT
american_scientific_journal-667	210	6	a.	a.	PROPN
american_scientific_journal-667	210	7	abd	abd	PROPN
american_scientific_journal-667	210	8	.	.	PUNCT
american_scientific_journal-667	211	1	majid	majid	PROPN
american_scientific_journal-667	211	2	,	,	PUNCT
american_scientific_journal-667	211	3	hj	hj	PROPN
american_scientific_journal-667	211	4	.	.	PROPN
american_scientific_journal-667	211	5	awang	awang	PROPN
american_scientific_journal-667	211	6	,	,	PUNCT
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american_scientific_journal-667	211	8	.	.	PUNCT
american_scientific_journal-667	211	9	and	and	CCONJ
american_scientific_journal-667	211	10	j.md	j.md	PROPN
american_scientific_journal-667	211	11	.	.	PROPN
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american_scientific_journal-667	211	13	.	.	PUNCT
american_scientific_journal-667	212	1	"	"	PUNCT
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american_scientific_journal-667	212	3	preserving	preserve	VERB
american_scientific_journal-667	212	4	interpolation	interpolation	NOUN
american_scientific_journal-667	212	5	using	use	VERB
american_scientific_journal-667	212	6	rational	rational	ADJ
american_scientific_journal-667	212	7	spline	spline	NOUN
american_scientific_journal-667	212	8	.	.	PUNCT
american_scientific_journal-667	212	9	"	"	PUNCT
american_scientific_journal-667	213	1	proceedings	proceeding	NOUN
american_scientific_journal-667	213	2	of	of	ADP
american_scientific_journal-667	213	3	the	the	DET
american_scientific_journal-667	213	4	international	international	ADJ
american_scientific_journal-667	213	5	multi	multi	PROPN
american_scientific_journal-667	213	6	conference	conference	NOUN
american_scientific_journal-667	213	7	of	of	ADP
american_scientific_journal-667	213	8	engineers	engineer	NOUN
american_scientific_journal-667	213	9	and	and	CCONJ
american_scientific_journal-667	213	10	computer	computer	NOUN
american_scientific_journal-667	213	11	scientists	scientist	NOUN
american_scientific_journal-667	213	12	i	i	PRON
american_scientific_journal-667	213	13	,	,	PUNCT
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american_scientific_journal-667	213	15	.	.	PUNCT
american_scientific_journal-667	214	1	[	[	X
american_scientific_journal-667	214	2	9	9	NUM
american_scientific_journal-667	214	3	]	]	X
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american_scientific_journal-667	214	5	.	.	PUNCT
american_scientific_journal-667	215	1	"	"	PUNCT
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american_scientific_journal-667	215	3	-	-	PUNCT
american_scientific_journal-667	215	4	preserving	preserve	VERB
american_scientific_journal-667	215	5	piecewise	piecewise	NOUN
american_scientific_journal-667	215	6	rational	rational	ADJ
american_scientific_journal-667	215	7	cubic	cubic	ADJ
american_scientific_journal-667	215	8	interpolation	interpolation	NOUN
american_scientific_journal-667	215	9	.	.	PUNCT
american_scientific_journal-667	215	10	"	"	PUNCT
american_scientific_journal-667	216	1	int	int	NOUN
american_scientific_journal-667	216	2	.	.	PUNCT
american_scientific_journal-667	217	1	journal	journal	PROPN
american_scientific_journal-667	217	2	of	of	ADP
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american_scientific_journal-667	217	4	.	.	PUNCT
american_scientific_journal-667	218	1	analysis	analysis	NOUN
american_scientific_journal-667	218	2	,	,	PUNCT
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american_scientific_journal-667	218	4	,	,	PUNCT
american_scientific_journal-667	218	5	pp	pp	ADJ
american_scientific_journal-667	218	6	.	.	PUNCT
american_scientific_journal-667	219	1	99	99	NUM
american_scientific_journal-667	219	2	–	–	PUNCT
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american_scientific_journal-667	219	4	.	.	PUNCT
american_scientific_journal-667	220	1	[	[	X
american_scientific_journal-667	220	2	10	10	NUM
american_scientific_journal-667	220	3	]	]	X
american_scientific_journal-667	220	4	t.n.t	t.n.t	PROPN
american_scientific_journal-667	220	5	.	.	PUNCT
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american_scientific_journal-667	220	7	.	.	PUNCT
american_scientific_journal-667	221	1	"	"	PUNCT
american_scientific_journal-667	221	2	shape	shape	VERB
american_scientific_journal-667	221	3	preserving	preserve	VERB
american_scientific_journal-667	221	4	interpolation	interpolation	NOUN
american_scientific_journal-667	221	5	by	by	ADP
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american_scientific_journal-667	221	7	.	.	PUNCT
american_scientific_journal-667	221	8	"	"	PUNCT
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american_scientific_journal-667	222	3	for	for	ADP
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american_scientific_journal-667	222	5	iv	iv	NUM
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american_scientific_journal-667	222	7	,	,	PUNCT
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american_scientific_journal-667	222	9	,	,	PUNCT
american_scientific_journal-667	222	10	pp	pp	ADJ
american_scientific_journal-667	222	11	.	.	PUNCT
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american_scientific_journal-667	222	13	.	.	PUNCT
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american_scientific_journal-667	223	3	]	]	SYM
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american_scientific_journal-667	223	5	and	and	CCONJ
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american_scientific_journal-667	223	7	.	.	PUNCT
american_scientific_journal-667	224	1	"	"	PUNCT
american_scientific_journal-667	224	2	shape	shape	NOUN
american_scientific_journal-667	224	3	-	-	PUNCT
american_scientific_journal-667	224	4	preserving	preserve	VERB
american_scientific_journal-667	224	5	c2	c2	PROPN
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american_scientific_journal-667	224	7	interpolation	interpolation	NOUN
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american_scientific_journal-667	224	11	.	.	PUNCT
american_scientific_journal-667	224	12	"	"	PUNCT
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american_scientific_journal-667	225	2	.	.	PUNCT
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american_scientific_journal-667	225	4	,	,	PUNCT
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american_scientific_journal-667	225	6	,	,	PUNCT
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american_scientific_journal-667	225	8	.	.	PUNCT
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american_scientific_journal-667	226	2	.	.	PUNCT
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american_scientific_journal-667	227	2	12	12	NUM
american_scientific_journal-667	227	3	]	]	PUNCT
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american_scientific_journal-667	227	5	and	and	CCONJ
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american_scientific_journal-667	227	7	.	.	PUNCT
american_scientific_journal-667	228	1	"	"	PUNCT
american_scientific_journal-667	228	2	shape	shape	NOUN
american_scientific_journal-667	228	3	-	-	PUNCT
american_scientific_journal-667	228	4	preserving	preserve	VERB
american_scientific_journal-667	228	5	c2	c2	PROPN
american_scientific_journal-667	228	6	cubic	cubic	ADJ
american_scientific_journal-667	228	7	polynomial	polynomial	ADJ
american_scientific_journal-667	228	8	interpolating	interpolate	VERB
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american_scientific_journal-667	228	10	.	.	PUNCT
american_scientific_journal-667	228	11	"	"	PUNCT
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american_scientific_journal-667	229	4	,	,	PUNCT
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american_scientific_journal-667	229	6	,	,	PUNCT
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american_scientific_journal-667	229	9	-	-	SYM
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american_scientific_journal-667	229	11	.	.	PUNCT
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american_scientific_journal-667	230	2	13	13	NUM
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american_scientific_journal-667	230	5	and	and	CCONJ
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american_scientific_journal-667	230	7	.	.	PUNCT
american_scientific_journal-667	231	1	"	"	PUNCT
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american_scientific_journal-667	231	3	-	-	PUNCT
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american_scientific_journal-667	231	7	involving	involve	VERB
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american_scientific_journal-667	231	10	.	.	PUNCT
american_scientific_journal-667	231	11	"	"	PUNCT
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american_scientific_journal-667	232	3	.	.	PUNCT
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american_scientific_journal-667	233	2	acad	acad	PROPN
american_scientific_journal-667	233	3	.	.	PUNCT
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american_scientific_journal-667	234	2	.	.	PUNCT
american_scientific_journal-667	235	1	(	(	PUNCT
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american_scientific_journal-667	235	3	.	.	PUNCT
american_scientific_journal-667	236	1	sci	sci	PROPN
american_scientific_journal-667	236	2	.	.	PROPN
american_scientific_journal-667	236	3	)	)	PUNCT
american_scientific_journal-667	236	4	,	,	PUNCT
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american_scientific_journal-667	236	6	.	.	PROPN
american_scientific_journal-667	237	1	110	110	NUM
american_scientific_journal-667	237	2	,	,	PUNCT
american_scientific_journal-667	237	3	pp	pp	ADJ
american_scientific_journal-667	237	4	.	.	PUNCT
american_scientific_journal-667	238	1	305	305	NUM
american_scientific_journal-667	238	2	-	-	SYM
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american_scientific_journal-667	238	4	,	,	PUNCT
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american_scientific_journal-667	238	6	.	.	NOUN
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american_scientific_journal-667	238	8	3	3	NUM
american_scientific_journal-667	238	9	.	.	PUNCT
american_scientific_journal-667	238	10	results	result	NOUN
american_scientific_journal-667	238	11	and	and	CCONJ
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american_scientific_journal-667	238	13	3.1	3.1	NUM
american_scientific_journal-667	238	14	.	.	PUNCT
american_scientific_journal-667	239	1	positivity	positivity	NOUN
american_scientific_journal-667	239	2	preserving	preserve	VERB
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american_scientific_journal-667	239	4	rational	rational	ADJ
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american_scientific_journal-667	239	7	3.2	3.2	NUM
american_scientific_journal-667	239	8	.	.	PUNCT
american_scientific_journal-667	240	1	monotonicity	monotonicity	NOUN
american_scientific_journal-667	240	2	preserving	preserve	VERB
american_scientific_journal-667	240	3	c2	c2	PROPN
american_scientific_journal-667	240	4	rational	rational	ADJ
american_scientific_journal-667	240	5	cubic	cubic	ADJ
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american_scientific_journal-667	240	8	.	.	PUNCT
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american_scientific_journal-667	241	2	preserving	preserve	VERB
american_scientific_journal-667	241	3	c2	c2	PROPN
american_scientific_journal-667	241	4	rational	rational	ADJ
american_scientific_journal-667	241	5	cubic	cubic	ADJ
american_scientific_journal-667	241	6	function	function	NOUN
american_scientific_journal-667	241	7	in	in	ADP
american_scientific_journal-667	241	8	order	order	NOUN
american_scientific_journal-667	241	9	to	to	PART
american_scientific_journal-667	241	10	assure	assure	VERB
american_scientific_journal-667	241	11	smooth	smooth	ADJ
american_scientific_journal-667	241	12	visualization	visualization	NOUN
american_scientific_journal-667	241	13	of	of	ADP
american_scientific_journal-667	241	14	shaped	shape	VERB
american_scientific_journal-667	241	15	data	datum	NOUN
american_scientific_journal-667	241	16	,	,	PUNCT
american_scientific_journal-667	241	17	c2	c2	PROPN
american_scientific_journal-667	241	18	rational	rational	ADJ
american_scientific_journal-667	241	19	cubic	cubic	ADJ
american_scientific_journal-667	241	20	splines	spline	NOUN
american_scientific_journal-667	241	21	are	be	AUX
american_scientific_journal-667	241	22	constructed	construct	VERB
american_scientific_journal-667	241	23	.	.	PUNCT
american_scientific_journal-667	242	1	a	a	DET
american_scientific_journal-667	242	2	piecewise	piecewise	NOUN
american_scientific_journal-667	242	3	rational	rational	ADJ
american_scientific_journal-667	242	4	cubic	cubic	ADJ
american_scientific_journal-667	242	5	spline	spline	NOUN
american_scientific_journal-667	242	6	function	function	PROPN
american_scientific_journal-667	242	7	𝑆∈,𝐶-2.[𝑎,𝑏	𝑆∈,𝐶-2.[𝑎,𝑏	PROPN
american_scientific_journal-667	242	8	]	]	PUNCT
american_scientific_journal-667	242	9	with	with	ADP
american_scientific_journal-667	242	10	cubic	cubic	ADJ
american_scientific_journal-667	242	11	numerator	numerator	NOUN
american_scientific_journal-667	242	12	and	and	CCONJ
american_scientific_journal-667	242	13	linear	linear	ADJ
american_scientific_journal-667	242	14	denominator	denominator	NOUN
american_scientific_journal-667	242	15	involving	involve	VERB
american_scientific_journal-667	242	16	two	two	NUM
american_scientific_journal-667	242	17	free	free	ADJ
american_scientific_journal-667	242	18	shape	shape	NOUN
american_scientific_journal-667	242	19	parameters	parameter	NOUN
american_scientific_journal-667	242	20	has	have	AUX
american_scientific_journal-667	242	21	been	be	AUX
american_scientific_journal-667	242	22	dev	dev	PROPN
american_scientific_journal-667	242	23	...	...	PUNCT