id	sid	tid	token	lemma	pos
cana-1582	1	1	communications	communication	NOUN
cana-1582	1	2	on	on	ADP
cana-1582	1	3	applied	apply	VERB
cana-1582	1	4	nonlinear	nonlinear	ADJ
cana-1582	1	5	analysis	analysis	NOUN
cana-1582	1	6	issn	issn	NOUN
cana-1582	1	7	:	:	PUNCT
cana-1582	1	8	1074	1074	NUM
cana-1582	1	9	-	-	PUNCT
cana-1582	1	10	133x	133x	NUM
cana-1582	1	11	vol	vol	NOUN
cana-1582	1	12	31	31	NUM
cana-1582	1	13	no	no	NOUN
cana-1582	1	14	.	.	PUNCT
cana-1582	2	1	8s	8s	PROPN
cana-1582	2	2	(	(	PUNCT
cana-1582	2	3	2024	2024	NUM
cana-1582	2	4	)	)	PUNCT
cana-1582	2	5	724	724	NUM
cana-1582	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1582	2	7	function	function	NOUN
cana-1582	2	8	quadrature	quadrature	NOUN
cana-1582	2	9	using	use	VERB
cana-1582	2	10	quartic	quartic	ADJ
cana-1582	2	11	spline	spline	NOUN
cana-1582	2	12	interpolation	interpolation	NOUN
cana-1582	2	13	kallur	kallur	NOUN
cana-1582	2	14	v	v	ADP
cana-1582	2	15	vijayakumar	vijayakumar	PROPN
cana-1582	2	16	1	1	NUM
cana-1582	2	17	*	*	PROPN
cana-1582	2	18	,	,	PUNCT
cana-1582	2	19	hariprasad	hariprasad	VERB
cana-1582	2	20	a	a	DET
cana-1582	2	21	s	s	PROPN
cana-1582	2	22	2	2	NUM
cana-1582	2	23	,	,	PUNCT
cana-1582	2	24	shilpa	shilpa	PROPN
cana-1582	2	25	r3	r3	PROPN
cana-1582	2	26	1	1	NUM
cana-1582	2	27	kallur	kallur	PROPN
cana-1582	2	28	v	v	PROPN
cana-1582	2	29	vijayakumar	vijayakumar	PROPN
cana-1582	2	30	,	,	PUNCT
cana-1582	2	31	bms	bms	PROPN
cana-1582	2	32	institute	institute	PROPN
cana-1582	2	33	of	of	ADP
cana-1582	2	34	technology	technology	NOUN
cana-1582	2	35	and	and	CCONJ
cana-1582	2	36	management	management	NOUN
cana-1582	2	37	,	,	PUNCT
cana-1582	2	38	bengaluru-560064	bengaluru-560064	ADV
cana-1582	2	39	.	.	PUNCT
cana-1582	2	40	kallurvijayakumar@bmsit.in	kallurvijayakumar@bmsit.in	PROPN
cana-1582	3	1	2hariprasad	2hariprasad	NUM
cana-1582	3	2	a	a	DET
cana-1582	3	3	s	s	PROPN
cana-1582	3	4	,	,	PUNCT
cana-1582	3	5	rajarajeswari	rajarajeswari	PROPN
cana-1582	3	6	college	college	NOUN
cana-1582	3	7	of	of	ADP
cana-1582	3	8	engineering	engineering	NOUN
cana-1582	3	9	,	,	PUNCT
cana-1582	3	10	bengaluru-560074	bengaluru-560074	ADJ
cana-1582	3	11	.	.	PUNCT
cana-1582	4	1	ashariprasad@yahoo.co.in	ashariprasad@yahoo.co.in	PROPN
cana-1582	4	2	3shilpa	3shilpa	NUM
cana-1582	4	3	r	r	NOUN
cana-1582	4	4	,	,	PUNCT
cana-1582	4	5	research	research	NOUN
cana-1582	4	6	scholar	scholar	NOUN
cana-1582	4	7	,	,	PUNCT
cana-1582	4	8	rajarajeswari	rajarajeswari	PROPN
cana-1582	4	9	college	college	NOUN
cana-1582	4	10	of	of	ADP
cana-1582	4	11	engineering	engineering	NOUN
cana-1582	4	12	,	,	PUNCT
cana-1582	4	13	bengaluru-560074	bengaluru-560074	PROPN
cana-1582	4	14	.	.	PUNCT
cana-1582	5	1	shilpa8906@gmail.com	shilpa8906@gmail.com	X
cana-1582	6	1	*	*	PROPN
cana-1582	6	2	corresponding	correspond	VERB
cana-1582	6	3	author	author	NOUN
cana-1582	6	4	article	article	NOUN
cana-1582	6	5	history	history	NOUN
cana-1582	6	6	:	:	PUNCT
cana-1582	6	7	received	receive	VERB
cana-1582	6	8	:	:	PUNCT
cana-1582	6	9	20	20	NUM
cana-1582	6	10	-	-	PUNCT
cana-1582	6	11	04	04	NUM
cana-1582	6	12	-	-	PUNCT
cana-1582	6	13	2024	2024	NUM
cana-1582	6	14	revised	revise	VERB
cana-1582	6	15	:	:	PUNCT
cana-1582	6	16	10	10	NUM
cana-1582	6	17	-	-	SYM
cana-1582	6	18	06	06	NUM
cana-1582	6	19	-	-	PUNCT
cana-1582	6	20	2024	2024	NUM
cana-1582	6	21	accepted	accept	VERB
cana-1582	6	22	:	:	PUNCT
cana-1582	6	23	24	24	NUM
cana-1582	6	24	-	-	PUNCT
cana-1582	6	25	06	06	NUM
cana-1582	6	26	-	-	PUNCT
cana-1582	6	27	2024	2024	NUM
cana-1582	6	28	abstract	abstract	NOUN
cana-1582	6	29	:	:	PUNCT
cana-1582	6	30	this	this	DET
cana-1582	6	31	research	research	NOUN
cana-1582	6	32	paper	paper	NOUN
cana-1582	6	33	explores	explore	VERB
cana-1582	6	34	the	the	DET
cana-1582	6	35	application	application	NOUN
cana-1582	6	36	of	of	ADP
cana-1582	6	37	quartic	quartic	ADJ
cana-1582	6	38	splines	spline	NOUN
cana-1582	6	39	for	for	ADP
cana-1582	6	40	numerical	numerical	ADJ
cana-1582	6	41	integration	integration	NOUN
cana-1582	6	42	,	,	PUNCT
cana-1582	6	43	particularly	particularly	ADV
cana-1582	6	44	in	in	ADP
cana-1582	6	45	situations	situation	NOUN
cana-1582	6	46	with	with	ADP
cana-1582	6	47	curved	curved	ADJ
cana-1582	6	48	boundaries	boundary	NOUN
cana-1582	6	49	in	in	ADP
cana-1582	6	50	two	two	NUM
cana-1582	6	51	-	-	PUNCT
cana-1582	6	52	dimensional	dimensional	ADJ
cana-1582	6	53	space	space	NOUN
cana-1582	6	54	.	.	PUNCT
cana-1582	7	1	the	the	DET
cana-1582	7	2	paper	paper	NOUN
cana-1582	7	3	dives	dive	VERB
cana-1582	7	4	into	into	ADP
cana-1582	7	5	the	the	DET
cana-1582	7	6	concept	concept	NOUN
cana-1582	7	7	of	of	ADP
cana-1582	7	8	quartic	quartic	ADJ
cana-1582	7	9	splines	spline	NOUN
cana-1582	7	10	,	,	PUNCT
cana-1582	7	11	which	which	PRON
cana-1582	7	12	are	be	AUX
cana-1582	7	13	piecewise	piecewise	NOUN
cana-1582	7	14	polynomial	polynomial	ADJ
cana-1582	7	15	functions	function	NOUN
cana-1582	7	16	where	where	SCONJ
cana-1582	7	17	each	each	DET
cana-1582	7	18	piece	piece	NOUN
cana-1582	7	19	is	be	AUX
cana-1582	7	20	a	a	DET
cana-1582	7	21	polynomial	polynomial	NOUN
cana-1582	7	22	of	of	ADP
cana-1582	7	23	the	the	DET
cana-1582	7	24	fourth	fourth	ADJ
cana-1582	7	25	degree	degree	NOUN
cana-1582	7	26	.	.	PUNCT
cana-1582	8	1	these	these	DET
cana-1582	8	2	splines	spline	NOUN
cana-1582	8	3	are	be	AUX
cana-1582	8	4	designed	design	VERB
cana-1582	8	5	to	to	PART
cana-1582	8	6	ensure	ensure	VERB
cana-1582	8	7	continuity	continuity	NOUN
cana-1582	8	8	of	of	ADP
cana-1582	8	9	the	the	DET
cana-1582	8	10	function	function	NOUN
cana-1582	8	11	itself	itself	PRON
cana-1582	8	12	,	,	PUNCT
cana-1582	8	13	its	its	PRON
cana-1582	8	14	first	first	ADJ
cana-1582	8	15	,	,	PUNCT
cana-1582	8	16	second	second	ADJ
cana-1582	8	17	,	,	PUNCT
cana-1582	8	18	and	and	CCONJ
cana-1582	8	19	third	third	ADJ
cana-1582	8	20	derivatives	derivative	NOUN
cana-1582	8	21	across	across	ADP
cana-1582	8	22	the	the	DET
cana-1582	8	23	boundaries	boundary	NOUN
cana-1582	8	24	between	between	ADP
cana-1582	8	25	the	the	DET
cana-1582	8	26	pieces	piece	NOUN
cana-1582	8	27	.	.	PUNCT
cana-1582	9	1	the	the	DET
cana-1582	9	2	core	core	NOUN
cana-1582	9	3	technique	technique	NOUN
cana-1582	9	4	involves	involve	VERB
cana-1582	9	5	using	use	VERB
cana-1582	9	6	quartic	quartic	ADJ
cana-1582	9	7	splines	spline	NOUN
cana-1582	9	8	to	to	PART
cana-1582	9	9	approximate	approximate	VERB
cana-1582	9	10	the	the	DET
cana-1582	9	11	curved	curved	ADJ
cana-1582	9	12	boundary	boundary	NOUN
cana-1582	9	13	of	of	ADP
cana-1582	9	14	a	a	DET
cana-1582	9	15	two	two	NUM
cana-1582	9	16	-	-	PUNCT
cana-1582	9	17	dimensional	dimensional	ADJ
cana-1582	9	18	domain	domain	NOUN
cana-1582	9	19	.	.	PUNCT
cana-1582	10	1	this	this	PRON
cana-1582	10	2	allows	allow	VERB
cana-1582	10	3	for	for	ADP
cana-1582	10	4	the	the	DET
cana-1582	10	5	calculation	calculation	NOUN
cana-1582	10	6	of	of	ADP
cana-1582	10	7	integrals	integral	NOUN
cana-1582	10	8	defined	define	VERB
cana-1582	10	9	over	over	ADP
cana-1582	10	10	that	that	DET
cana-1582	10	11	domain	domain	NOUN
cana-1582	10	12	by	by	ADP
cana-1582	10	13	transforming	transform	VERB
cana-1582	10	14	it	it	PRON
cana-1582	10	15	into	into	ADP
cana-1582	10	16	a	a	DET
cana-1582	10	17	simpler	simple	ADJ
cana-1582	10	18	shape	shape	NOUN
cana-1582	10	19	(	(	PUNCT
cana-1582	10	20	often	often	ADV
cana-1582	10	21	a	a	DET
cana-1582	10	22	rectangle	rectangle	NOUN
cana-1582	10	23	)	)	PUNCT
cana-1582	10	24	where	where	SCONJ
cana-1582	10	25	traditional	traditional	ADJ
cana-1582	10	26	numerical	numerical	ADJ
cana-1582	10	27	integration	integration	NOUN
cana-1582	10	28	methods	method	NOUN
cana-1582	10	29	like	like	ADP
cana-1582	10	30	gauss	gauss	ADJ
cana-1582	10	31	-	-	PUNCT
cana-1582	10	32	legendre	legendre	PROPN
cana-1582	10	33	quadrature	quadrature	NOUN
cana-1582	10	34	can	can	AUX
cana-1582	10	35	be	be	AUX
cana-1582	10	36	applied	apply	VERB
cana-1582	10	37	effectively	effectively	ADV
cana-1582	10	38	.	.	PUNCT
cana-1582	11	1	the	the	DET
cana-1582	11	2	paper	paper	NOUN
cana-1582	11	3	validates	validate	VERB
cana-1582	11	4	the	the	DET
cana-1582	11	5	method	method	NOUN
cana-1582	11	6	by	by	ADP
cana-1582	11	7	applying	apply	VERB
cana-1582	11	8	it	it	PRON
cana-1582	11	9	to	to	ADP
cana-1582	11	10	various	various	ADJ
cana-1582	11	11	curved	curved	ADJ
cana-1582	11	12	domains	domain	NOUN
cana-1582	11	13	and	and	CCONJ
cana-1582	11	14	comparing	compare	VERB
cana-1582	11	15	the	the	DET
cana-1582	11	16	obtained	obtain	VERB
cana-1582	11	17	integral	integral	ADJ
cana-1582	11	18	values	value	NOUN
cana-1582	11	19	with	with	ADP
cana-1582	11	20	known	know	VERB
cana-1582	11	21	analytical	analytical	ADJ
cana-1582	11	22	solutions	solution	NOUN
cana-1582	11	23	(	(	PUNCT
cana-1582	11	24	if	if	SCONJ
cana-1582	11	25	available	available	ADJ
cana-1582	11	26	)	)	PUNCT
cana-1582	11	27	.	.	PUNCT
cana-1582	12	1	the	the	DET
cana-1582	12	2	absolute	absolute	ADJ
cana-1582	12	3	errors	error	NOUN
cana-1582	12	4	are	be	AUX
cana-1582	12	5	calculated	calculate	VERB
cana-1582	12	6	and	and	CCONJ
cana-1582	12	7	tabulated	tabulate	VERB
cana-1582	12	8	,	,	PUNCT
cana-1582	12	9	demonstrating	demonstrate	VERB
cana-1582	12	10	the	the	DET
cana-1582	12	11	accuracy	accuracy	NOUN
cana-1582	12	12	of	of	ADP
cana-1582	12	13	the	the	DET
cana-1582	12	14	approach	approach	NOUN
cana-1582	12	15	.	.	PUNCT
cana-1582	13	1	the	the	DET
cana-1582	13	2	paper	paper	NOUN
cana-1582	13	3	showcases	showcase	VERB
cana-1582	13	4	the	the	DET
cana-1582	13	5	efficiency	efficiency	NOUN
cana-1582	13	6	of	of	ADP
cana-1582	13	7	the	the	DET
cana-1582	13	8	method	method	NOUN
cana-1582	13	9	by	by	ADP
cana-1582	13	10	solving	solve	VERB
cana-1582	13	11	numerical	numerical	ADJ
cana-1582	13	12	integration	integration	NOUN
cana-1582	13	13	problems	problem	NOUN
cana-1582	13	14	from	from	ADP
cana-1582	13	15	existing	exist	VERB
cana-1582	13	16	literature	literature	NOUN
cana-1582	13	17	.	.	PUNCT
cana-1582	14	1	these	these	DET
cana-1582	14	2	examples	example	NOUN
cana-1582	14	3	serve	serve	VERB
cana-1582	14	4	as	as	ADP
cana-1582	14	5	evidence	evidence	NOUN
cana-1582	14	6	that	that	SCONJ
cana-1582	14	7	the	the	DET
cana-1582	14	8	method	method	NOUN
cana-1582	14	9	is	be	AUX
cana-1582	14	10	effective	effective	ADJ
cana-1582	14	11	and	and	CCONJ
cana-1582	14	12	can	can	AUX
cana-1582	14	13	handle	handle	VERB
cana-1582	14	14	real	real	ADJ
cana-1582	14	15	-	-	PUNCT
cana-1582	14	16	world	world	NOUN
cana-1582	14	17	scenarios	scenario	NOUN
cana-1582	14	18	.	.	PUNCT
cana-1582	15	1	a	a	DET
cana-1582	15	2	significant	significant	ADJ
cana-1582	15	3	advantage	advantage	NOUN
cana-1582	15	4	of	of	ADP
cana-1582	15	5	this	this	DET
cana-1582	15	6	method	method	NOUN
cana-1582	15	7	is	be	AUX
cana-1582	15	8	its	its	PRON
cana-1582	15	9	ability	ability	NOUN
cana-1582	15	10	to	to	PART
cana-1582	15	11	handle	handle	VERB
cana-1582	15	12	situations	situation	NOUN
cana-1582	15	13	where	where	SCONJ
cana-1582	15	14	only	only	ADV
cana-1582	15	15	coordinate	coordinate	VERB
cana-1582	15	16	data	datum	NOUN
cana-1582	15	17	for	for	ADP
cana-1582	15	18	the	the	DET
cana-1582	15	19	boundary	boundary	NOUN
cana-1582	15	20	is	be	AUX
cana-1582	15	21	available	available	ADJ
cana-1582	15	22	.	.	PUNCT
cana-1582	16	1	quartic	quartic	ADJ
cana-1582	16	2	splines	spline	NOUN
cana-1582	16	3	can	can	AUX
cana-1582	16	4	accurately	accurately	ADV
cana-1582	16	5	reconstruct	reconstruct	VERB
cana-1582	16	6	the	the	DET
cana-1582	16	7	curved	curved	ADJ
cana-1582	16	8	boundary	boundary	NOUN
cana-1582	16	9	from	from	ADP
cana-1582	16	10	these	these	DET
cana-1582	16	11	coordinates	coordinate	NOUN
cana-1582	16	12	,	,	PUNCT
cana-1582	16	13	enabling	enable	VERB
cana-1582	16	14	the	the	DET
cana-1582	16	15	integration	integration	NOUN
cana-1582	16	16	process	process	NOUN
cana-1582	16	17	.	.	PUNCT
cana-1582	17	1	keywords	keyword	NOUN
cana-1582	17	2	:	:	PUNCT
cana-1582	17	3	numerical	numerical	ADJ
cana-1582	17	4	integration	integration	NOUN
cana-1582	17	5	,	,	PUNCT
cana-1582	17	6	quadrature	quadrature	NOUN
cana-1582	17	7	,	,	PUNCT
cana-1582	17	8	spline	spline	NOUN
cana-1582	17	9	,	,	PUNCT
cana-1582	17	10	curved	curved	ADJ
cana-1582	17	11	boundary	boundary	NOUN
cana-1582	17	12	,	,	PUNCT
cana-1582	17	13	spline	spline	NOUN
cana-1582	17	14	.	.	PUNCT
cana-1582	18	1	introduction	introduction	NOUN
cana-1582	18	2	numerical	numerical	PROPN
cana-1582	18	3	integration	integration	NOUN
cana-1582	18	4	,	,	PUNCT
cana-1582	18	5	the	the	DET
cana-1582	18	6	art	art	NOUN
cana-1582	18	7	of	of	ADP
cana-1582	18	8	approximating	approximate	VERB
cana-1582	18	9	definite	definite	ADJ
cana-1582	18	10	integrals	integral	NOUN
cana-1582	18	11	through	through	ADP
cana-1582	18	12	computational	computational	ADJ
cana-1582	18	13	methods	method	NOUN
cana-1582	18	14	,	,	PUNCT
cana-1582	18	15	finds	find	VERB
cana-1582	18	16	widespread	widespread	ADJ
cana-1582	18	17	application	application	NOUN
cana-1582	18	18	in	in	ADP
cana-1582	18	19	various	various	ADJ
cana-1582	18	20	scientific	scientific	ADJ
cana-1582	18	21	and	and	CCONJ
cana-1582	18	22	engineering	engineering	NOUN
cana-1582	18	23	disciplines	discipline	NOUN
cana-1582	18	24	.	.	PUNCT
cana-1582	19	1	among	among	ADP
cana-1582	19	2	different	different	ADJ
cana-1582	19	3	techniques	technique	NOUN
cana-1582	19	4	,	,	PUNCT
cana-1582	19	5	quadrature	quadrature	NOUN
cana-1582	19	6	using	use	VERB
cana-1582	19	7	quartic	quartic	ADJ
cana-1582	19	8	splines	spline	NOUN
cana-1582	19	9	emerges	emerge	VERB
cana-1582	19	10	as	as	ADP
cana-1582	19	11	a	a	DET
cana-1582	19	12	robust	robust	ADJ
cana-1582	19	13	and	and	CCONJ
cana-1582	19	14	accurate	accurate	ADJ
cana-1582	19	15	approach	approach	NOUN
cana-1582	19	16	,	,	PUNCT
cana-1582	19	17	offering	offer	VERB
cana-1582	19	18	numerous	numerous	ADJ
cana-1582	19	19	benefits	benefit	NOUN
cana-1582	19	20	over	over	ADP
cana-1582	19	21	earlier	early	ADJ
cana-1582	19	22	traditional	traditional	ADJ
cana-1582	19	23	approaches	approach	NOUN
cana-1582	19	24	.	.	PUNCT
cana-1582	20	1	in	in	ADP
cana-1582	20	2	this	this	DET
cana-1582	20	3	comprehensive	comprehensive	ADJ
cana-1582	20	4	discussion	discussion	NOUN
cana-1582	20	5	,	,	PUNCT
cana-1582	20	6	we	we	PRON
cana-1582	20	7	delve	delve	VERB
cana-1582	20	8	into	into	ADP
cana-1582	20	9	the	the	DET
cana-1582	20	10	theoretical	theoretical	ADJ
cana-1582	20	11	foundations	foundation	NOUN
cana-1582	20	12	,	,	PUNCT
cana-1582	20	13	practical	practical	ADJ
cana-1582	20	14	implementation	implementation	NOUN
cana-1582	20	15	,	,	PUNCT
cana-1582	20	16	and	and	CCONJ
cana-1582	20	17	performance	performance	NOUN
cana-1582	20	18	analysis	analysis	NOUN
cana-1582	20	19	of	of	ADP
cana-1582	20	20	quartic	quartic	ADJ
cana-1582	20	21	spline	spline	NOUN
cana-1582	20	22	quadrature	quadrature	NOUN
cana-1582	20	23	,	,	PUNCT
cana-1582	20	24	equipping	equip	VERB
cana-1582	20	25	you	you	PRON
cana-1582	20	26	with	with	ADP
cana-1582	20	27	the	the	DET
cana-1582	20	28	knowledge	knowledge	NOUN
cana-1582	20	29	to	to	PART
cana-1582	20	30	confidently	confidently	ADV
cana-1582	20	31	apply	apply	VERB
cana-1582	20	32	it	it	PRON
cana-1582	20	33	to	to	ADP
cana-1582	20	34	your	your	PRON
cana-1582	20	35	own	own	ADJ
cana-1582	20	36	integration	integration	NOUN
cana-1582	20	37	problems	problem	NOUN
cana-1582	20	38	.	.	PUNCT
cana-1582	21	1	definite	definite	ADJ
cana-1582	21	2	integrals	integral	NOUN
cana-1582	21	3	represent	represent	VERB
cana-1582	21	4	the	the	DET
cana-1582	21	5	area	area	NOUN
cana-1582	21	6	under	under	ADP
cana-1582	21	7	a	a	DET
cana-1582	21	8	curve	curve	NOUN
cana-1582	21	9	within	within	ADP
cana-1582	21	10	a	a	DET
cana-1582	21	11	specified	specified	ADJ
cana-1582	21	12	interval	interval	NOUN
cana-1582	21	13	.	.	PUNCT
cana-1582	22	1	however	however	ADV
cana-1582	22	2	,	,	PUNCT
cana-1582	22	3	analytically	analytically	ADV
cana-1582	22	4	solving	solving	NOUN
cana-1582	22	5	integrals	integral	NOUN
cana-1582	22	6	becomes	become	VERB
cana-1582	22	7	cumbersome	cumbersome	ADJ
cana-1582	22	8	or	or	CCONJ
cana-1582	22	9	impossible	impossible	ADJ
cana-1582	22	10	for	for	ADP
cana-1582	22	11	many	many	ADJ
cana-1582	22	12	functions	function	NOUN
cana-1582	22	13	.	.	PUNCT
cana-1582	23	1	numerical	numerical	ADJ
cana-1582	23	2	integration	integration	NOUN
cana-1582	23	3	bridges	bridge	NOUN
cana-1582	23	4	this	this	DET
cana-1582	23	5	gap	gap	NOUN
cana-1582	23	6	by	by	ADP
cana-1582	23	7	approximating	approximate	VERB
cana-1582	23	8	the	the	DET
cana-1582	23	9	area	area	NOUN
cana-1582	23	10	through	through	ADP
cana-1582	23	11	weighted	weighted	ADJ
cana-1582	23	12	evaluations	evaluation	NOUN
cana-1582	23	13	of	of	ADP
cana-1582	23	14	the	the	DET
cana-1582	23	15	function	function	NOUN
cana-1582	23	16	at	at	ADP
cana-1582	23	17	specific	specific	ADJ
cana-1582	23	18	points	point	NOUN
cana-1582	23	19	,	,	PUNCT
cana-1582	23	20	known	know	VERB
cana-1582	23	21	as	as	ADP
cana-1582	23	22	nodes	node	NOUN
cana-1582	23	23	.	.	PUNCT
cana-1582	24	1	the	the	DET
cana-1582	24	2	objective	objective	NOUN
cana-1582	24	3	is	be	AUX
cana-1582	24	4	to	to	PART
cana-1582	24	5	find	find	VERB
cana-1582	24	6	a	a	DET
cana-1582	24	7	formula	formula	NOUN
cana-1582	24	8	that	that	PRON
cana-1582	24	9	expresses	express	VERB
cana-1582	24	10	the	the	DET
cana-1582	24	11	integral	integral	NOUN
cana-1582	24	12	as	as	ADP
cana-1582	24	13	a	a	DET
cana-1582	24	14	communications	communication	NOUN
cana-1582	24	15	on	on	ADP
cana-1582	24	16	applied	apply	VERB
cana-1582	24	17	nonlinear	nonlinear	ADJ
cana-1582	24	18	analysis	analysis	NOUN
cana-1582	24	19	issn	issn	NOUN
cana-1582	24	20	:	:	PUNCT
cana-1582	24	21	1074	1074	NUM
cana-1582	24	22	-	-	PUNCT
cana-1582	24	23	133x	133x	NUM
cana-1582	24	24	vol	vol	NOUN
cana-1582	24	25	31	31	NUM
cana-1582	24	26	no	no	NOUN
cana-1582	24	27	.	.	PUNCT
cana-1582	25	1	8s	8s	PROPN
cana-1582	25	2	(	(	PUNCT
cana-1582	25	3	2024	2024	NUM
cana-1582	25	4	)	)	PUNCT
cana-1582	25	5	725	725	NUM
cana-1582	25	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-1582	25	7	linear	linear	ADJ
cana-1582	25	8	combination	combination	NOUN
cana-1582	25	9	of	of	ADP
cana-1582	25	10	these	these	DET
cana-1582	25	11	function	function	NOUN
cana-1582	25	12	values	value	NOUN
cana-1582	25	13	,	,	PUNCT
cana-1582	25	14	minimizing	minimize	VERB
cana-1582	25	15	the	the	DET
cana-1582	25	16	error	error	NOUN
cana-1582	25	17	between	between	ADP
cana-1582	25	18	the	the	DET
cana-1582	25	19	approximation	approximation	NOUN
cana-1582	25	20	and	and	CCONJ
cana-1582	25	21	the	the	DET
cana-1582	25	22	true	true	ADJ
cana-1582	25	23	integral	integral	ADJ
cana-1582	25	24	.	.	PUNCT
cana-1582	26	1	spline	spline	NOUN
cana-1582	26	2	functions	function	NOUN
cana-1582	26	3	offer	offer	VERB
cana-1582	26	4	flexibility	flexibility	NOUN
cana-1582	26	5	in	in	ADP
cana-1582	26	6	approximating	approximate	VERB
cana-1582	26	7	complex	complex	ADJ
cana-1582	26	8	curves	curve	NOUN
cana-1582	26	9	.	.	PUNCT
cana-1582	27	1	quartic	quartic	ADJ
cana-1582	27	2	splines	spline	NOUN
cana-1582	27	3	,	,	PUNCT
cana-1582	27	4	polynomials	polynomial	NOUN
cana-1582	27	5	of	of	ADP
cana-1582	27	6	degree	degree	NOUN
cana-1582	27	7	four	four	NUM
cana-1582	27	8	,	,	PUNCT
cana-1582	27	9	can	can	AUX
cana-1582	27	10	closely	closely	ADV
cana-1582	27	11	fit	fit	VERB
cana-1582	27	12	diverse	diverse	ADJ
cana-1582	27	13	function	function	NOUN
cana-1582	27	14	behaviors	behavior	NOUN
cana-1582	27	15	through	through	ADP
cana-1582	27	16	piecewise	piecewise	NOUN
cana-1582	27	17	construction	construction	NOUN
cana-1582	27	18	.	.	PUNCT
cana-1582	28	1	by	by	ADP
cana-1582	28	2	partitioning	partition	VERB
cana-1582	28	3	the	the	DET
cana-1582	28	4	interval	interval	NOUN
cana-1582	28	5	of	of	ADP
cana-1582	28	6	integration	integration	NOUN
cana-1582	28	7	into	into	ADP
cana-1582	28	8	subintervals	subinterval	NOUN
cana-1582	28	9	,	,	PUNCT
cana-1582	28	10	we	we	PRON
cana-1582	28	11	can	can	AUX
cana-1582	28	12	represent	represent	VERB
cana-1582	28	13	the	the	DET
cana-1582	28	14	integral	integral	ADJ
cana-1582	28	15	as	as	ADP
cana-1582	28	16	the	the	DET
cana-1582	28	17	sum	sum	NOUN
cana-1582	28	18	of	of	ADP
cana-1582	28	19	integrals	integral	NOUN
cana-1582	28	20	over	over	ADP
cana-1582	28	21	each	each	DET
cana-1582	28	22	subinterval	subinterval	NOUN
cana-1582	28	23	,	,	PUNCT
cana-1582	28	24	which	which	PRON
cana-1582	28	25	we	we	PRON
cana-1582	28	26	further	far	ADV
cana-1582	28	27	approximate	approximate	VERB
cana-1582	28	28	using	use	VERB
cana-1582	28	29	quartic	quartic	ADJ
cana-1582	28	30	splines	spline	NOUN
cana-1582	28	31	.	.	PUNCT
cana-1582	29	1	splines	spline	NOUN
cana-1582	29	2	are	be	AUX
cana-1582	29	3	piecewise	piecewise	NOUN
cana-1582	29	4	polynomial	polynomial	ADJ
cana-1582	29	5	functions	function	NOUN
cana-1582	29	6	,	,	PUNCT
cana-1582	29	7	meaning	mean	VERB
cana-1582	29	8	they	they	PRON
cana-1582	29	9	consist	consist	VERB
cana-1582	29	10	of	of	ADP
cana-1582	29	11	multiple	multiple	ADJ
cana-1582	29	12	polynomial	polynomial	ADJ
cana-1582	29	13	segments	segment	NOUN
cana-1582	29	14	joined	join	VERB
cana-1582	29	15	smoothly	smoothly	ADV
cana-1582	29	16	at	at	ADP
cana-1582	29	17	specific	specific	ADJ
cana-1582	29	18	points	point	NOUN
cana-1582	29	19	called	call	VERB
cana-1582	29	20	knots	knot	NOUN
cana-1582	29	21	.	.	PUNCT
cana-1582	30	1	this	this	DET
cana-1582	30	2	construction	construction	NOUN
cana-1582	30	3	allows	allow	VERB
cana-1582	30	4	them	they	PRON
cana-1582	30	5	to	to	PART
cana-1582	30	6	capture	capture	VERB
cana-1582	30	7	intricate	intricate	ADJ
cana-1582	30	8	curve	curve	NOUN
cana-1582	30	9	shapes	shape	NOUN
cana-1582	30	10	that	that	PRON
cana-1582	30	11	single	single	ADJ
cana-1582	30	12	polynomials	polynomial	NOUN
cana-1582	30	13	might	might	AUX
cana-1582	30	14	struggle	struggle	VERB
cana-1582	30	15	to	to	PART
cana-1582	30	16	represent	represent	VERB
cana-1582	30	17	accurately	accurately	ADV
cana-1582	30	18	.	.	PUNCT
cana-1582	31	1	quartic	quartic	ADJ
cana-1582	31	2	splines	spline	NOUN
cana-1582	31	3	,	,	PUNCT
cana-1582	31	4	in	in	ADP
cana-1582	31	5	particular	particular	ADJ
cana-1582	31	6	,	,	PUNCT
cana-1582	31	7	use	use	VERB
cana-1582	31	8	polynomials	polynomial	NOUN
cana-1582	31	9	of	of	ADP
cana-1582	31	10	degree	degree	NOUN
cana-1582	31	11	four	four	NUM
cana-1582	31	12	,	,	PUNCT
cana-1582	31	13	providing	provide	VERB
cana-1582	31	14	a	a	DET
cana-1582	31	15	balance	balance	NOUN
cana-1582	31	16	between	between	ADP
cana-1582	31	17	flexibility	flexibility	NOUN
cana-1582	31	18	and	and	CCONJ
cana-1582	31	19	computational	computational	ADJ
cana-1582	31	20	efficiency	efficiency	NOUN
cana-1582	31	21	.	.	PUNCT
cana-1582	32	1	they	they	PRON
cana-1582	32	2	can	can	AUX
cana-1582	32	3	model	model	VERB
cana-1582	32	4	a	a	DET
cana-1582	32	5	wide	wide	ADJ
cana-1582	32	6	variety	variety	NOUN
cana-1582	32	7	of	of	ADP
cana-1582	32	8	function	function	NOUN
cana-1582	32	9	behaviors	behavior	NOUN
cana-1582	32	10	with	with	ADP
cana-1582	32	11	relatively	relatively	ADV
cana-1582	32	12	few	few	ADJ
cana-1582	32	13	knots	knot	NOUN
cana-1582	32	14	.	.	PUNCT
cana-1582	33	1	a	a	DET
cana-1582	33	2	quartic	quartic	ADJ
cana-1582	33	3	spline	spline	NOUN
cana-1582	33	4	is	be	AUX
cana-1582	33	5	a	a	DET
cana-1582	33	6	type	type	NOUN
cana-1582	33	7	of	of	ADP
cana-1582	33	8	piecewise	piecewise	NOUN
cana-1582	33	9	polynomial	polynomial	ADJ
cana-1582	33	10	function	function	NOUN
cana-1582	33	11	that	that	PRON
cana-1582	33	12	is	be	AUX
cana-1582	33	13	used	use	VERB
cana-1582	33	14	for	for	ADP
cana-1582	33	15	interpolation	interpolation	NOUN
cana-1582	33	16	or	or	CCONJ
cana-1582	33	17	approximation	approximation	NOUN
cana-1582	33	18	of	of	ADP
cana-1582	33	19	data	datum	NOUN
cana-1582	33	20	points	point	NOUN
cana-1582	33	21	over	over	ADP
cana-1582	33	22	an	an	DET
cana-1582	33	23	interval	interval	NOUN
cana-1582	33	24	.	.	PUNCT
cana-1582	34	1	specifically	specifically	ADV
cana-1582	34	2	,	,	PUNCT
cana-1582	34	3	it	it	PRON
cana-1582	34	4	is	be	AUX
cana-1582	34	5	defined	define	VERB
cana-1582	34	6	on	on	ADP
cana-1582	34	7	an	an	DET
cana-1582	34	8	interval	interval	NOUN
cana-1582	34	9	[	[	X
cana-1582	34	10	a	a	X
cana-1582	34	11	,	,	PUNCT
cana-1582	34	12	b	b	NOUN
cana-1582	34	13	]	]	PUNCT
cana-1582	34	14	and	and	CCONJ
cana-1582	34	15	is	be	AUX
cana-1582	34	16	characterized	characterize	VERB
cana-1582	34	17	by	by	ADP
cana-1582	34	18	the	the	DET
cana-1582	34	19	following	follow	VERB
cana-1582	34	20	properties	property	NOUN
cana-1582	34	21	:	:	PUNCT
cana-1582	34	22	continuity	continuity	NOUN
cana-1582	34	23	:	:	PUNCT
cana-1582	34	24	a	a	DET
cana-1582	34	25	quartic	quartic	ADJ
cana-1582	34	26	spline	spline	NOUN
cana-1582	34	27	is	be	AUX
cana-1582	34	28	continuous	continuous	ADJ
cana-1582	34	29	at	at	ADP
cana-1582	34	30	each	each	DET
cana-1582	34	31	knot	knot	NOUN
cana-1582	34	32	,	,	PUNCT
cana-1582	34	33	which	which	PRON
cana-1582	34	34	are	be	AUX
cana-1582	34	35	the	the	DET
cana-1582	34	36	distinct	distinct	ADJ
cana-1582	34	37	points	point	NOUN
cana-1582	34	38	in	in	ADP
cana-1582	34	39	the	the	DET
cana-1582	34	40	interval	interval	NOUN
cana-1582	34	41	[	[	X
cana-1582	34	42	a	a	X
cana-1582	34	43	,	,	PUNCT
cana-1582	34	44	b	b	NOUN
cana-1582	34	45	]	]	X
cana-1582	34	46	.	.	PUNCT
cana-1582	35	1	this	this	PRON
cana-1582	35	2	means	mean	VERB
cana-1582	35	3	that	that	SCONJ
cana-1582	35	4	the	the	DET
cana-1582	35	5	function	function	NOUN
cana-1582	35	6	and	and	CCONJ
cana-1582	35	7	its	its	PRON
cana-1582	35	8	derivatives	derivative	NOUN
cana-1582	35	9	up	up	ADP
cana-1582	35	10	to	to	ADP
cana-1582	35	11	the	the	DET
cana-1582	35	12	fourth	fourth	ADJ
cana-1582	35	13	order	order	NOUN
cana-1582	35	14	are	be	AUX
cana-1582	35	15	continuous	continuous	ADJ
cana-1582	35	16	across	across	ADP
cana-1582	35	17	the	the	DET
cana-1582	35	18	entire	entire	ADJ
cana-1582	35	19	interval	interval	NOUN
cana-1582	35	20	.	.	PUNCT
cana-1582	36	1	piecewise	piecewise	VERB
cana-1582	36	2	quartic	quartic	ADJ
cana-1582	36	3	polynomials	polynomial	NOUN
cana-1582	36	4	:	:	PUNCT
cana-1582	36	5	within	within	ADP
cana-1582	36	6	each	each	DET
cana-1582	36	7	subinterval	subinterval	NOUN
cana-1582	36	8	determined	determine	VERB
cana-1582	36	9	by	by	ADP
cana-1582	36	10	the	the	DET
cana-1582	36	11	knots	knot	NOUN
cana-1582	36	12	,	,	PUNCT
cana-1582	36	13	the	the	DET
cana-1582	36	14	quartic	quartic	ADJ
cana-1582	36	15	spline	spline	NOUN
cana-1582	36	16	is	be	AUX
cana-1582	36	17	represented	represent	VERB
cana-1582	36	18	by	by	ADP
cana-1582	36	19	a	a	DET
cana-1582	36	20	quartic	quartic	ADJ
cana-1582	36	21	(	(	PUNCT
cana-1582	36	22	degree-4	degree-4	NOUN
cana-1582	36	23	)	)	PUNCT
cana-1582	36	24	polynomial	polynomial	NOUN
cana-1582	36	25	.	.	PUNCT
cana-1582	37	1	the	the	DET
cana-1582	37	2	use	use	NOUN
cana-1582	37	3	of	of	ADP
cana-1582	37	4	piecewise	piecewise	NOUN
cana-1582	37	5	quartic	quartic	ADJ
cana-1582	37	6	polynomials	polynomial	NOUN
cana-1582	37	7	allows	allow	VERB
cana-1582	37	8	the	the	DET
cana-1582	37	9	spline	spline	NOUN
cana-1582	37	10	to	to	PART
cana-1582	37	11	flexibly	flexibly	ADV
cana-1582	37	12	capture	capture	VERB
cana-1582	37	13	and	and	CCONJ
cana-1582	37	14	approximate	approximate	VERB
cana-1582	37	15	the	the	DET
cana-1582	37	16	behavior	behavior	NOUN
cana-1582	37	17	of	of	ADP
cana-1582	37	18	the	the	DET
cana-1582	37	19	underlying	underlie	VERB
cana-1582	37	20	data	datum	NOUN
cana-1582	37	21	within	within	ADP
cana-1582	37	22	each	each	DET
cana-1582	37	23	interval	interval	NOUN
cana-1582	37	24	.	.	PUNCT
cana-1582	38	1	interpolatory	interpolatory	ADJ
cana-1582	38	2	conditions	condition	NOUN
cana-1582	38	3	:	:	PUNCT
cana-1582	38	4	the	the	DET
cana-1582	38	5	quartic	quartic	ADJ
cana-1582	38	6	spline	spline	NOUN
cana-1582	38	7	satisfies	satisfy	VERB
cana-1582	38	8	interpolatory	interpolatory	NOUN
cana-1582	38	9	conditions	condition	NOUN
cana-1582	38	10	,	,	PUNCT
cana-1582	38	11	meaning	mean	VERB
cana-1582	38	12	that	that	SCONJ
cana-1582	38	13	it	it	PRON
cana-1582	38	14	accurately	accurately	ADV
cana-1582	38	15	passes	pass	VERB
cana-1582	38	16	through	through	ADP
cana-1582	38	17	specified	specified	ADJ
cana-1582	38	18	data	data	NOUN
cana-1582	38	19	points	point	NOUN
cana-1582	38	20	.	.	PUNCT
cana-1582	39	1	in	in	ADP
cana-1582	39	2	other	other	ADJ
cana-1582	39	3	words	word	NOUN
cana-1582	39	4	,	,	PUNCT
cana-1582	39	5	the	the	DET
cana-1582	39	6	function	function	NOUN
cana-1582	39	7	coincides	coincide	VERB
cana-1582	39	8	with	with	ADP
cana-1582	39	9	given	give	VERB
cana-1582	39	10	data	datum	NOUN
cana-1582	39	11	values	value	NOUN
cana-1582	39	12	at	at	ADP
cana-1582	39	13	the	the	DET
cana-1582	39	14	knots	knot	NOUN
cana-1582	39	15	,	,	PUNCT
cana-1582	39	16	ensuring	ensure	VERB
cana-1582	39	17	that	that	SCONJ
cana-1582	39	18	the	the	DET
cana-1582	39	19	spline	spline	NOUN
cana-1582	39	20	interpolates	interpolate	VERB
cana-1582	39	21	the	the	DET
cana-1582	39	22	data	datum	NOUN
cana-1582	39	23	over	over	ADP
cana-1582	39	24	the	the	DET
cana-1582	39	25	entire	entire	ADJ
cana-1582	39	26	interval	interval	NOUN
cana-1582	39	27	.	.	PUNCT
cana-1582	40	1	uniqueness	uniqueness	NOUN
cana-1582	40	2	:	:	PUNCT
cana-1582	40	3	in	in	ADP
cana-1582	40	4	certain	certain	ADJ
cana-1582	40	5	conditions	condition	NOUN
cana-1582	40	6	,	,	PUNCT
cana-1582	40	7	there	there	PRON
cana-1582	40	8	exists	exist	VERB
cana-1582	40	9	a	a	DET
cana-1582	40	10	unique	unique	ADJ
cana-1582	40	11	quartic	quartic	ADJ
cana-1582	40	12	spline	spline	NOUN
cana-1582	40	13	that	that	PRON
cana-1582	40	14	fulfills	fulfill	VERB
cana-1582	40	15	the	the	DET
cana-1582	40	16	continuity	continuity	NOUN
cana-1582	40	17	,	,	PUNCT
cana-1582	40	18	piecewise	piecewise	NOUN
cana-1582	40	19	quartic	quartic	ADJ
cana-1582	40	20	polynomial	polynomial	ADJ
cana-1582	40	21	,	,	PUNCT
cana-1582	40	22	and	and	CCONJ
cana-1582	40	23	interpolatory	interpolatory	NOUN
cana-1582	40	24	conditions	condition	NOUN
cana-1582	40	25	.	.	PUNCT
cana-1582	41	1	this	this	DET
cana-1582	41	2	uniqueness	uniqueness	NOUN
cana-1582	41	3	ensures	ensure	VERB
cana-1582	41	4	that	that	SCONJ
cana-1582	41	5	the	the	DET
cana-1582	41	6	spline	spline	NOUN
cana-1582	41	7	provides	provide	VERB
cana-1582	41	8	a	a	DET
cana-1582	41	9	distinct	distinct	ADJ
cana-1582	41	10	representation	representation	NOUN
cana-1582	41	11	of	of	ADP
cana-1582	41	12	the	the	DET
cana-1582	41	13	data	datum	NOUN
cana-1582	41	14	within	within	ADP
cana-1582	41	15	the	the	DET
cana-1582	41	16	specified	specified	ADJ
cana-1582	41	17	interval	interval	NOUN
cana-1582	41	18	.	.	PUNCT
cana-1582	42	1	in	in	ADP
cana-1582	42	2	summary	summary	NOUN
cana-1582	42	3	,	,	PUNCT
cana-1582	42	4	a	a	DET
cana-1582	42	5	quartic	quartic	ADJ
cana-1582	42	6	spline	spline	NOUN
cana-1582	42	7	is	be	AUX
cana-1582	42	8	a	a	DET
cana-1582	42	9	smooth	smooth	ADJ
cana-1582	42	10	and	and	CCONJ
cana-1582	42	11	continuous	continuous	ADJ
cana-1582	42	12	piecewise	piecewise	NOUN
cana-1582	42	13	polynomial	polynomial	ADJ
cana-1582	42	14	function	function	NOUN
cana-1582	42	15	of	of	ADP
cana-1582	42	16	degree	degree	NOUN
cana-1582	42	17	4	4	NUM
cana-1582	42	18	,	,	PUNCT
cana-1582	42	19	designed	design	VERB
cana-1582	42	20	to	to	PART
cana-1582	42	21	interpolate	interpolate	VERB
cana-1582	42	22	or	or	CCONJ
cana-1582	42	23	approximate	approximate	ADJ
cana-1582	42	24	data	datum	NOUN
cana-1582	42	25	points	point	NOUN
cana-1582	42	26	over	over	ADP
cana-1582	42	27	an	an	DET
cana-1582	42	28	interval	interval	NOUN
cana-1582	42	29	[	[	X
cana-1582	42	30	a	a	X
cana-1582	42	31	,	,	PUNCT
cana-1582	42	32	b	b	NOUN
cana-1582	42	33	]	]	PUNCT
cana-1582	42	34	.	.	PUNCT
cana-1582	43	1	quartic	quartic	ADJ
cana-1582	43	2	splines	spline	NOUN
cana-1582	43	3	use	use	VERB
cana-1582	43	4	polynomials	polynomial	NOUN
cana-1582	43	5	of	of	ADP
cana-1582	43	6	degree	degree	NOUN
cana-1582	43	7	four	four	NUM
cana-1582	43	8	,	,	PUNCT
cana-1582	43	9	providing	provide	VERB
cana-1582	43	10	a	a	DET
cana-1582	43	11	balance	balance	NOUN
cana-1582	43	12	between	between	ADP
cana-1582	43	13	flexibility	flexibility	NOUN
cana-1582	43	14	and	and	CCONJ
cana-1582	43	15	computational	computational	ADJ
cana-1582	43	16	efficiency	efficiency	NOUN
cana-1582	43	17	.	.	PUNCT
cana-1582	44	1	they	they	PRON
cana-1582	44	2	can	can	AUX
cana-1582	44	3	model	model	VERB
cana-1582	44	4	a	a	DET
cana-1582	44	5	wide	wide	ADJ
cana-1582	44	6	variety	variety	NOUN
cana-1582	44	7	of	of	ADP
cana-1582	44	8	function	function	NOUN
cana-1582	44	9	behaviors	behavior	NOUN
cana-1582	44	10	with	with	ADP
cana-1582	44	11	relatively	relatively	ADV
cana-1582	44	12	few	few	ADJ
cana-1582	44	13	knots	knot	NOUN
cana-1582	44	14	.	.	PUNCT
cana-1582	45	1	knot	knot	ADJ
cana-1582	45	2	placement	placement	NOUN
cana-1582	45	3	:	:	PUNCT
cana-1582	45	4	we	we	PRON
cana-1582	45	5	strategically	strategically	ADV
cana-1582	45	6	place	place	VERB
cana-1582	45	7	knots	knot	NOUN
cana-1582	45	8	,	,	PUNCT
cana-1582	45	9	points	point	VERB
cana-1582	45	10	demarcating	demarcate	VERB
cana-1582	45	11	the	the	DET
cana-1582	45	12	subintervals	subinterval	NOUN
cana-1582	45	13	,	,	PUNCT
cana-1582	45	14	to	to	PART
cana-1582	45	15	influence	influence	VERB
cana-1582	45	16	the	the	DET
cana-1582	45	17	spline	spline	NOUN
cana-1582	45	18	's	's	PART
cana-1582	45	19	shape	shape	NOUN
cana-1582	45	20	and	and	CCONJ
cana-1582	45	21	accuracy	accuracy	NOUN
cana-1582	45	22	.	.	PUNCT
cana-1582	46	1	different	different	ADJ
cana-1582	46	2	strategies	strategy	NOUN
cana-1582	46	3	,	,	PUNCT
cana-1582	46	4	such	such	ADJ
cana-1582	46	5	as	as	ADP
cana-1582	46	6	equispaced	equispace	VERB
cana-1582	46	7	,	,	PUNCT
cana-1582	46	8	chebyshev	chebyshev	NOUN
cana-1582	46	9	,	,	PUNCT
cana-1582	46	10	or	or	CCONJ
cana-1582	46	11	adaptive	adaptive	ADJ
cana-1582	46	12	knot	knot	NOUN
cana-1582	46	13	placement	placement	NOUN
cana-1582	46	14	,	,	PUNCT
cana-1582	46	15	exist	exist	VERB
cana-1582	46	16	,	,	PUNCT
cana-1582	46	17	each	each	PRON
cana-1582	46	18	with	with	ADP
cana-1582	46	19	its	its	PRON
cana-1582	46	20	own	own	ADJ
cana-1582	46	21	strengths	strength	NOUN
cana-1582	46	22	and	and	CCONJ
cana-1582	46	23	weaknesses	weakness	NOUN
cana-1582	46	24	.	.	PUNCT
cana-1582	47	1	within	within	ADP
cana-1582	47	2	each	each	DET
cana-1582	47	3	subinterval	subinterval	NOUN
cana-1582	47	4	,	,	PUNCT
cana-1582	47	5	we	we	PRON
cana-1582	47	6	construct	construct	VERB
cana-1582	47	7	a	a	DET
cana-1582	47	8	quartic	quartic	ADJ
cana-1582	47	9	spline	spline	NOUN
cana-1582	47	10	that	that	PRON
cana-1582	47	11	interpolates	interpolate	VERB
cana-1582	47	12	or	or	CCONJ
cana-1582	47	13	passes	pass	VERB
cana-1582	47	14	through	through	ADP
cana-1582	47	15	the	the	DET
cana-1582	47	16	function	function	NOUN
cana-1582	47	17	values	value	NOUN
cana-1582	47	18	at	at	ADP
cana-1582	47	19	specific	specific	ADJ
cana-1582	47	20	points	point	NOUN
cana-1582	47	21	within	within	ADP
cana-1582	47	22	the	the	DET
cana-1582	47	23	interval	interval	NOUN
cana-1582	47	24	.	.	PUNCT
cana-1582	48	1	these	these	DET
cana-1582	48	2	points	point	NOUN
cana-1582	48	3	,	,	PUNCT
cana-1582	48	4	typically	typically	ADV
cana-1582	48	5	chosen	choose	VERB
cana-1582	48	6	as	as	ADP
cana-1582	48	7	function	function	NOUN
cana-1582	48	8	extrema	extrema	NOUN
cana-1582	48	9	or	or	CCONJ
cana-1582	48	10	points	point	NOUN
cana-1582	48	11	where	where	SCONJ
cana-1582	48	12	the	the	DET
cana-1582	48	13	integral	integral	NOUN
cana-1582	48	14	is	be	AUX
cana-1582	48	15	accurately	accurately	ADV
cana-1582	48	16	known	know	VERB
cana-1582	48	17	,	,	PUNCT
cana-1582	48	18	further	far	ADV
cana-1582	48	19	enhance	enhance	VERB
cana-1582	48	20	the	the	DET
cana-1582	48	21	approximation	approximation	NOUN
cana-1582	48	22	.	.	PUNCT
cana-1582	49	1	we	we	PRON
cana-1582	49	2	integrate	integrate	VERB
cana-1582	49	3	the	the	DET
cana-1582	49	4	constructed	construct	VERB
cana-1582	49	5	quartic	quartic	ADJ
cana-1582	49	6	splines	spline	NOUN
cana-1582	49	7	over	over	ADP
cana-1582	49	8	their	their	PRON
cana-1582	49	9	respective	respective	ADJ
cana-1582	49	10	subintervals	subinterval	NOUN
cana-1582	49	11	and	and	CCONJ
cana-1582	49	12	express	express	VERB
cana-1582	49	13	the	the	DET
cana-1582	49	14	overall	overall	ADJ
cana-1582	49	15	integral	integral	ADJ
cana-1582	49	16	as	as	ADP
cana-1582	49	17	a	a	DET
cana-1582	49	18	weighted	weighted	ADJ
cana-1582	49	19	sum	sum	NOUN
cana-1582	49	20	of	of	ADP
cana-1582	49	21	these	these	DET
cana-1582	49	22	subintegrals	subintegral	NOUN
cana-1582	49	23	.	.	PUNCT
cana-1582	50	1	the	the	DET
cana-1582	50	2	weights	weight	NOUN
cana-1582	50	3	depend	depend	VERB
cana-1582	50	4	on	on	ADP
cana-1582	50	5	the	the	DET
cana-1582	50	6	chosen	choose	VERB
cana-1582	50	7	knots	knot	NOUN
cana-1582	50	8	and	and	CCONJ
cana-1582	50	9	spline	spline	NOUN
cana-1582	50	10	construction	construction	NOUN
cana-1582	50	11	method	method	NOUN
cana-1582	50	12	.	.	PUNCT
cana-1582	51	1	partitioning	partition	VERB
cana-1582	51	2	the	the	DET
cana-1582	51	3	interval	interval	NOUN
cana-1582	51	4	:	:	PUNCT
cana-1582	51	5	we	we	PRON
cana-1582	51	6	divide	divide	VERB
cana-1582	51	7	the	the	DET
cana-1582	51	8	interval	interval	NOUN
cana-1582	51	9	of	of	ADP
cana-1582	51	10	integration	integration	NOUN
cana-1582	51	11	[	[	X
cana-1582	51	12	a	a	X
cana-1582	51	13	,	,	PUNCT
cana-1582	51	14	b	b	NOUN
cana-1582	51	15	]	]	X
cana-1582	51	16	into	into	ADP
cana-1582	51	17	n	n	ADP
cana-1582	51	18	subintervals	subinterval	NOUN
cana-1582	51	19	using	use	VERB
cana-1582	51	20	knots	knot	NOUN
cana-1582	51	21	xi	xi	NOUN
cana-1582	51	22	:	:	PUNCT
cana-1582	51	23	𝑎	𝑎	PRON
cana-1582	51	24	=	=	SYM
cana-1582	51	25	𝑥0	𝑥0	PROPN
cana-1582	51	26	<	<	X
cana-1582	51	27	𝑥1	𝑥1	NOUN
cana-1582	51	28	<	<	X
cana-1582	51	29	.	.	PUNCT
cana-1582	51	30	.	.	PUNCT
cana-1582	52	1	…	…	PUNCT
cana-1582	52	2	.	.	PUNCT
cana-1582	52	3	.	.	PUNCT
cana-1582	53	1	<	<	X
cana-1582	53	2	𝑥𝑛−1	𝑥𝑛−1	NOUN
cana-1582	53	3	<	<	X
cana-1582	53	4	𝑥𝑛	𝑥𝑛	PROPN
cana-1582	53	5	=	=	NOUN
cana-1582	53	6	𝑏.	𝑏.	NOUN
cana-1582	53	7	constructing	construct	VERB
cana-1582	53	8	quartic	quartic	ADJ
cana-1582	53	9	splines	spline	NOUN
cana-1582	53	10	:	:	PUNCT
cana-1582	53	11	within	within	ADP
cana-1582	53	12	each	each	DET
cana-1582	53	13	subinterval	subinterval	NOUN
cana-1582	53	14	[	[	X
cana-1582	53	15	𝑥𝑖	𝑥𝑖	X
cana-1582	53	16	,	,	PUNCT
cana-1582	53	17	𝑥𝑖+1	𝑥𝑖+1	PROPN
cana-1582	53	18	]	]	PUNCT
cana-1582	53	19	,	,	PUNCT
cana-1582	53	20	we	we	PRON
cana-1582	53	21	construct	construct	VERB
cana-1582	53	22	a	a	DET
cana-1582	53	23	quartic	quartic	ADJ
cana-1582	53	24	spline	spline	NOUN
cana-1582	53	25	𝑆𝑖(𝑥	𝑆𝑖(𝑥	PROPN
cana-1582	53	26	)	)	PUNCT
cana-1582	53	27	that	that	PRON
cana-1582	53	28	interpolates	interpolate	VERB
cana-1582	53	29	or	or	CCONJ
cana-1582	53	30	approximates	approximate	VERB
cana-1582	53	31	the	the	DET
cana-1582	53	32	function	function	NOUN
cana-1582	53	33	𝑓(𝑥	𝑓(𝑥	NOUN
cana-1582	53	34	)	)	PUNCT
cana-1582	53	35	at	at	ADP
cana-1582	53	36	specific	specific	ADJ
cana-1582	53	37	points	point	NOUN
cana-1582	53	38	within	within	ADP
cana-1582	53	39	that	that	DET
cana-1582	53	40	subinterval	subinterval	NOUN
cana-1582	53	41	.	.	PUNCT
cana-1582	54	1	we	we	PRON
cana-1582	54	2	approximate	approximate	VERB
cana-1582	54	3	the	the	DET
cana-1582	54	4	integral	integral	ADJ
cana-1582	54	5	of	of	ADP
cana-1582	54	6	𝑓(𝑥	𝑓(𝑥	NOUN
cana-1582	54	7	)	)	PUNCT
cana-1582	54	8	over	over	ADP
cana-1582	54	9	each	each	DET
cana-1582	54	10	subinterval	subinterval	NOUN
cana-1582	54	11	communications	communication	NOUN
cana-1582	54	12	on	on	ADP
cana-1582	54	13	applied	apply	VERB
cana-1582	54	14	nonlinear	nonlinear	ADJ
cana-1582	54	15	analysis	analysis	NOUN
cana-1582	54	16	issn	issn	NOUN
cana-1582	54	17	:	:	PUNCT
cana-1582	54	18	1074	1074	NUM
cana-1582	54	19	-	-	PUNCT
cana-1582	54	20	133x	133x	NUM
cana-1582	54	21	vol	vol	NOUN
cana-1582	54	22	31	31	NUM
cana-1582	54	23	no	no	NOUN
cana-1582	54	24	.	.	PUNCT
cana-1582	55	1	8s	8s	PROPN
cana-1582	55	2	(	(	PUNCT
cana-1582	55	3	2024	2024	NUM
cana-1582	55	4	)	)	PUNCT
cana-1582	55	5	726	726	NUM
cana-1582	55	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1582	55	7	using	use	VERB
cana-1582	55	8	the	the	DET
cana-1582	55	9	integral	integral	NOUN
cana-1582	55	10	of	of	ADP
cana-1582	55	11	the	the	DET
cana-1582	55	12	corresponding	corresponding	ADJ
cana-1582	55	13	quartic	quartic	ADJ
cana-1582	55	14	spline	spline	NOUN
cana-1582	55	15	:	:	PUNCT
cana-1582	55	16	∫	∫	PROPN
cana-1582	55	17	𝑓(𝑥)𝑑𝑥	𝑓(𝑥)𝑑𝑥	PROPN
cana-1582	55	18	𝑥𝑖+1	𝑥𝑖+1	NOUN
cana-1582	55	19	𝑥𝑖	𝑥𝑖	PROPN
cana-1582	56	1	≈	≈	PROPN
cana-1582	56	2	∫	∫	PROPN
cana-1582	56	3	𝑆𝑖(𝑥)𝑑𝑥	𝑆𝑖(𝑥)𝑑𝑥	NUM
cana-1582	56	4	𝑥𝑖+1	𝑥𝑖+1	PROPN
cana-1582	56	5	𝑥𝑖	𝑥𝑖	PROPN
cana-1582	56	6	.	.	PUNCT
cana-1582	57	1	the	the	DET
cana-1582	57	2	overall	overall	ADJ
cana-1582	57	3	integral	integral	NOUN
cana-1582	57	4	is	be	AUX
cana-1582	57	5	then	then	ADV
cana-1582	57	6	approximated	approximate	VERB
cana-1582	57	7	as	as	ADP
cana-1582	57	8	the	the	DET
cana-1582	57	9	sum	sum	NOUN
cana-1582	57	10	of	of	ADP
cana-1582	57	11	these	these	DET
cana-1582	57	12	sub	sub	NOUN
cana-1582	57	13	-	-	NOUN
cana-1582	57	14	integrals	integral	NOUN
cana-1582	57	15	:	:	PUNCT
cana-1582	57	16	∫	∫	PROPN
cana-1582	57	17	𝑓(𝑥)𝑑𝑥	𝑓(𝑥)𝑑𝑥	PROPN
cana-1582	58	1	𝑏	𝑏	PROPN
cana-1582	58	2	𝑎	𝑎	PROPN
cana-1582	58	3	≈	≈	PROPN
cana-1582	58	4	∑	∑	PROPN
cana-1582	58	5	∫	∫	PROPN
cana-1582	58	6	𝑆𝑖(𝑥)𝑑𝑥	𝑆𝑖(𝑥)𝑑𝑥	NUM
cana-1582	58	7	𝑥𝑖+1	𝑥𝑖+1	PROPN
cana-1582	58	8	𝑥𝑖	𝑥𝑖	PROPN
cana-1582	58	9	𝑛−1	𝑛−1	PROPN
cana-1582	58	10	𝑖=0	𝑖=0	PROPN
cana-1582	58	11	.	.	PUNCT
cana-1582	59	1	quartic	quartic	ADJ
cana-1582	59	2	splines	spline	NOUN
cana-1582	59	3	can	can	AUX
cana-1582	59	4	closely	closely	ADV
cana-1582	59	5	fit	fit	VERB
cana-1582	59	6	diverse	diverse	ADJ
cana-1582	59	7	function	function	NOUN
cana-1582	59	8	behaviors	behavior	NOUN
cana-1582	59	9	,	,	PUNCT
cana-1582	59	10	leading	lead	VERB
cana-1582	59	11	to	to	ADP
cana-1582	59	12	more	more	ADV
cana-1582	59	13	accurate	accurate	ADJ
cana-1582	59	14	approximations	approximation	NOUN
cana-1582	59	15	than	than	ADP
cana-1582	59	16	lower	low	ADJ
cana-1582	59	17	-	-	PUNCT
cana-1582	59	18	degree	degree	NOUN
cana-1582	59	19	polynomials	polynomial	NOUN
cana-1582	59	20	.	.	PUNCT
cana-1582	60	1	they	they	PRON
cana-1582	60	2	ensure	ensure	VERB
cana-1582	60	3	continuity	continuity	NOUN
cana-1582	60	4	and	and	CCONJ
cana-1582	60	5	smoothness	smoothness	NOUN
cana-1582	60	6	of	of	ADP
cana-1582	60	7	the	the	DET
cana-1582	60	8	approximation	approximation	NOUN
cana-1582	60	9	,	,	PUNCT
cana-1582	60	10	even	even	ADV
cana-1582	60	11	at	at	ADP
cana-1582	60	12	knot	knot	ADJ
cana-1582	60	13	points	point	NOUN
cana-1582	60	14	,	,	PUNCT
cana-1582	60	15	making	make	VERB
cana-1582	60	16	them	they	PRON
cana-1582	60	17	suitable	suitable	ADJ
cana-1582	60	18	for	for	ADP
cana-1582	60	19	applications	application	NOUN
cana-1582	60	20	requiring	require	VERB
cana-1582	60	21	continuous	continuous	ADJ
cana-1582	60	22	derivatives	derivative	NOUN
cana-1582	60	23	.	.	PUNCT
cana-1582	61	1	the	the	DET
cana-1582	61	2	number	number	NOUN
cana-1582	61	3	of	of	ADP
cana-1582	61	4	knots	knot	NOUN
cana-1582	61	5	and	and	CCONJ
cana-1582	61	6	their	their	PRON
cana-1582	61	7	placement	placement	NOUN
cana-1582	61	8	can	can	AUX
cana-1582	61	9	be	be	AUX
cana-1582	61	10	adjusted	adjust	VERB
cana-1582	61	11	to	to	PART
cana-1582	61	12	refine	refine	VERB
cana-1582	61	13	the	the	DET
cana-1582	61	14	approximation	approximation	NOUN
cana-1582	61	15	in	in	ADP
cana-1582	61	16	critical	critical	ADJ
cana-1582	61	17	regions	region	NOUN
cana-1582	61	18	,	,	PUNCT
cana-1582	61	19	offering	offer	VERB
cana-1582	61	20	flexibility	flexibility	NOUN
cana-1582	61	21	for	for	ADP
cana-1582	61	22	different	different	ADJ
cana-1582	61	23	problem	problem	NOUN
cana-1582	61	24	complexities	complexity	NOUN
cana-1582	61	25	.	.	PUNCT
cana-1582	62	1	the	the	DET
cana-1582	62	2	integro	integro	PROPN
cana-1582	62	3	cubic	cubic	ADJ
cana-1582	62	4	spline	spline	NOUN
cana-1582	62	5	methods	method	NOUN
cana-1582	62	6	over	over	ADP
cana-1582	62	7	a	a	DET
cana-1582	62	8	uniform	uniform	ADJ
cana-1582	62	9	partition	partition	NOUN
cana-1582	62	10	were	be	AUX
cana-1582	62	11	studied	study	VERB
cana-1582	62	12	in	in	ADP
cana-1582	62	13	[	[	X
cana-1582	62	14	5,23	5,23	NOUN
cana-1582	62	15	]	]	PUNCT
cana-1582	62	16	,	,	PUNCT
cana-1582	62	17	but	but	CCONJ
cana-1582	62	18	their	their	PRON
cana-1582	62	19	error	error	NOUN
cana-1582	62	20	orders	order	NOUN
cana-1582	62	21	are	be	AUX
cana-1582	62	22	lower	low	ADJ
cana-1582	62	23	.	.	PUNCT
cana-1582	63	1	later	later	ADV
cana-1582	63	2	,	,	PUNCT
cana-1582	63	3	an	an	DET
cana-1582	63	4	integro	integro	PROPN
cana-1582	63	5	quintic	quintic	ADJ
cana-1582	63	6	spline	spline	NOUN
cana-1582	63	7	approach	approach	NOUN
cana-1582	63	8	over	over	ADP
cana-1582	63	9	a	a	DET
cana-1582	63	10	uniform	uniform	ADJ
cana-1582	63	11	partition	partition	NOUN
cana-1582	63	12	was	be	AUX
cana-1582	63	13	discussed	discuss	VERB
cana-1582	63	14	in	in	ADP
cana-1582	63	15	[	[	X
cana-1582	63	16	6	6	NUM
cana-1582	63	17	]	]	PUNCT
cana-1582	63	18	.	.	PUNCT
cana-1582	64	1	in	in	ADP
cana-1582	64	2	the	the	DET
cana-1582	64	3	present	present	ADJ
cana-1582	64	4	study	study	NOUN
cana-1582	64	5	focus	focus	NOUN
cana-1582	64	6	is	be	AUX
cana-1582	64	7	on	on	ADP
cana-1582	64	8	creating	create	VERB
cana-1582	64	9	spline	spline	NOUN
cana-1582	64	10	functions	function	NOUN
cana-1582	64	11	that	that	PRON
cana-1582	64	12	interpolate	interpolate	VERB
cana-1582	64	13	a	a	DET
cana-1582	64	14	given	give	VERB
cana-1582	64	15	function	function	NOUN
cana-1582	64	16	's	's	PART
cana-1582	64	17	first	first	ADJ
cana-1582	64	18	derivatives	derivative	NOUN
cana-1582	64	19	at	at	ADP
cana-1582	64	20	specific	specific	ADJ
cana-1582	64	21	points	point	NOUN
cana-1582	64	22	(	(	PUNCT
cana-1582	64	23	knots	knot	NOUN
cana-1582	64	24	)	)	PUNCT
cana-1582	64	25	and	and	CCONJ
cana-1582	64	26	match	match	VERB
cana-1582	64	27	the	the	DET
cana-1582	64	28	second	second	ADJ
cana-1582	64	29	derivatives	derivative	NOUN
cana-1582	64	30	between	between	ADP
cana-1582	64	31	those	those	DET
cana-1582	64	32	knots	knot	NOUN
cana-1582	64	33	.	.	PUNCT
cana-1582	65	1	the	the	DET
cana-1582	65	2	derivation	derivation	NOUN
cana-1582	65	3	of	of	ADP
cana-1582	65	4	these	these	DET
cana-1582	65	5	quartic	quartic	ADJ
cana-1582	65	6	splines	spline	NOUN
cana-1582	65	7	in	in	ADP
cana-1582	65	8	a	a	DET
cana-1582	65	9	standard	standard	ADJ
cana-1582	65	10	form	form	NOUN
cana-1582	65	11	.	.	PUNCT
cana-1582	66	1	an	an	DET
cana-1582	66	2	interesting	interesting	ADJ
cana-1582	66	3	approach	approach	NOUN
cana-1582	66	4	is	be	AUX
cana-1582	66	5	taken	take	VERB
cana-1582	66	6	,	,	PUNCT
cana-1582	66	7	instead	instead	ADV
cana-1582	66	8	of	of	ADP
cana-1582	66	9	solving	solve	VERB
cana-1582	66	10	for	for	ADP
cana-1582	66	11	the	the	DET
cana-1582	66	12	spline	spline	NOUN
cana-1582	66	13	function	function	NOUN
cana-1582	66	14	values	value	NOUN
cana-1582	66	15	at	at	ADP
cana-1582	66	16	the	the	DET
cana-1582	66	17	knots	knot	NOUN
cana-1582	66	18	,	,	PUNCT
cana-1582	66	19	the	the	DET
cana-1582	66	20	second	second	ADJ
cana-1582	66	21	derivatives	derivative	NOUN
cana-1582	66	22	are	be	AUX
cana-1582	66	23	chosen	choose	VERB
cana-1582	66	24	to	to	PART
cana-1582	66	25	coincide	coincide	VERB
cana-1582	66	26	with	with	ADP
cana-1582	66	27	the	the	DET
cana-1582	66	28	initial	initial	ADJ
cana-1582	66	29	knots	knot	NOUN
cana-1582	66	30	'	'	PART
cana-1582	66	31	values	value	NOUN
cana-1582	66	32	.	.	PUNCT
cana-1582	67	1	references	reference	NOUN
cana-1582	67	2	[	[	X
cana-1582	67	3	12	12	NUM
cana-1582	67	4	]	]	PUNCT
cana-1582	67	5	and	and	CCONJ
cana-1582	67	6	[	[	X
cana-1582	67	7	22	22	NUM
cana-1582	67	8	]	]	PUNCT
cana-1582	67	9	likely	likely	ADV
cana-1582	67	10	provide	provide	VERB
cana-1582	67	11	more	more	ADJ
cana-1582	67	12	information	information	NOUN
cana-1582	67	13	on	on	ADP
cana-1582	67	14	this	this	DET
cana-1582	67	15	technique	technique	NOUN
cana-1582	67	16	.	.	PUNCT
cana-1582	68	1	a	a	DET
cana-1582	68	2	method	method	NOUN
cana-1582	68	3	for	for	ADP
cana-1582	68	4	numerically	numerically	ADV
cana-1582	68	5	integrating	integrate	VERB
cana-1582	68	6	over	over	ADP
cana-1582	68	7	curved	curve	VERB
cana-1582	68	8	two	two	NUM
cana-1582	68	9	-	-	PUNCT
cana-1582	68	10	dimensional	dimensional	ADJ
cana-1582	68	11	domains	domain	NOUN
cana-1582	68	12	.	.	PUNCT
cana-1582	69	1	the	the	DET
cana-1582	69	2	theoretical	theoretical	ADJ
cana-1582	69	3	foundation	foundation	NOUN
cana-1582	69	4	relies	rely	VERB
cana-1582	69	5	on	on	ADP
cana-1582	69	6	several	several	ADJ
cana-1582	69	7	concepts	concept	NOUN
cana-1582	69	8	:	:	PUNCT
cana-1582	69	9	green	green	PROPN
cana-1582	69	10	's	's	PART
cana-1582	69	11	theorem	theorem	NOUN
cana-1582	69	12	for	for	ADP
cana-1582	69	13	boundary	boundary	ADJ
cana-1582	69	14	integration	integration	NOUN
cana-1582	69	15	[	[	X
cana-1582	69	16	2	2	X
cana-1582	69	17	]	]	PUNCT
cana-1582	69	18	(	(	PUNCT
cana-1582	69	19	likely	likely	ADV
cana-1582	69	20	referring	refer	VERB
cana-1582	69	21	to	to	ADP
cana-1582	69	22	a	a	DET
cana-1582	69	23	specific	specific	ADJ
cana-1582	69	24	reference	reference	NOUN
cana-1582	69	25	on	on	ADP
cana-1582	69	26	vector	vector	NOUN
cana-1582	69	27	calculus	calculus	NOUN
cana-1582	69	28	)	)	PUNCT
cana-1582	69	29	,	,	PUNCT
cana-1582	69	30	gauss	gauss	ADJ
cana-1582	69	31	-	-	PUNCT
cana-1582	69	32	legendre	legendre	PROPN
cana-1582	69	33	quadrature	quadrature	NOUN
cana-1582	69	34	rule	rule	NOUN
cana-1582	69	35	,	,	PUNCT
cana-1582	69	36	a	a	DET
cana-1582	69	37	popular	popular	ADJ
cana-1582	69	38	technique	technique	NOUN
cana-1582	69	39	for	for	ADP
cana-1582	69	40	numerical	numerical	ADJ
cana-1582	69	41	integration	integration	NOUN
cana-1582	69	42	[	[	X
cana-1582	69	43	1	1	NUM
cana-1582	69	44	]	]	PUNCT
cana-1582	69	45	,	,	PUNCT
cana-1582	69	46	parametric	parametric	ADJ
cana-1582	69	47	relations	relation	NOUN
cana-1582	69	48	describing	describe	VERB
cana-1582	69	49	the	the	DET
cana-1582	69	50	boundary	boundary	ADJ
cana-1582	69	51	curve	curve	NOUN
cana-1582	69	52	(	(	PUNCT
cana-1582	69	53	either	either	CCONJ
cana-1582	69	54	exact	exact	ADJ
cana-1582	69	55	form	form	NOUN
cana-1582	69	56	or	or	CCONJ
cana-1582	69	57	obtained	obtain	VERB
cana-1582	69	58	through	through	ADP
cana-1582	69	59	spline	spline	NOUN
cana-1582	69	60	interpolation	interpolation	NOUN
cana-1582	69	61	polynomials	polynomial	NOUN
cana-1582	69	62	)	)	PUNCT
cana-1582	69	63	references	reference	NOUN
cana-1582	69	64	[	[	X
cana-1582	69	65	3	3	NUM
cana-1582	69	66	]	]	PUNCT
cana-1582	69	67	,	,	PUNCT
cana-1582	69	68	[	[	X
cana-1582	69	69	4	4	NUM
cana-1582	69	70	]	]	PUNCT
cana-1582	69	71	,	,	PUNCT
cana-1582	69	72	[	[	X
cana-1582	69	73	11	11	NUM
cana-1582	69	74	]	]	PUNCT
cana-1582	69	75	,	,	PUNCT
cana-1582	69	76	[	[	X
cana-1582	69	77	14	14	NUM
cana-1582	69	78	]	]	PUNCT
cana-1582	69	79	,	,	PUNCT
cana-1582	69	80	[	[	X
cana-1582	69	81	15	15	NUM
cana-1582	69	82	]	]	PUNCT
cana-1582	69	83	,	,	PUNCT
cana-1582	69	84	[	[	X
cana-1582	69	85	17	17	NUM
cana-1582	69	86	]	]	PUNCT
cana-1582	69	87	,	,	PUNCT
cana-1582	69	88	[	[	X
cana-1582	69	89	19	19	NUM
cana-1582	69	90	]	]	PUNCT
cana-1582	69	91	,	,	PUNCT
cana-1582	69	92	might	might	AUX
cana-1582	69	93	be	be	AUX
cana-1582	69	94	relevant	relevant	ADJ
cana-1582	69	95	for	for	ADP
cana-1582	69	96	these	these	DET
cana-1582	69	97	methods	method	NOUN
cana-1582	69	98	.	.	PUNCT
cana-1582	70	1	the	the	DET
cana-1582	70	2	application	application	NOUN
cana-1582	70	3	of	of	ADP
cana-1582	70	4	the	the	DET
cana-1582	70	5	method	method	NOUN
cana-1582	70	6	on	on	ADP
cana-1582	70	7	a	a	DET
cana-1582	70	8	curved	curved	ADJ
cana-1582	70	9	domain	domain	NOUN
cana-1582	70	10	shaped	shape	VERB
cana-1582	70	11	like	like	ADP
cana-1582	70	12	a	a	DET
cana-1582	70	13	lunar	lunar	ADJ
cana-1582	70	14	model	model	NOUN
cana-1582	70	15	.	.	PUNCT
cana-1582	71	1	the	the	DET
cana-1582	71	2	integration	integration	NOUN
cana-1582	71	3	of	of	ADP
cana-1582	71	4	challenging	challenging	ADJ
cana-1582	71	5	functions	function	NOUN
cana-1582	71	6	over	over	ADP
cana-1582	71	7	this	this	DET
cana-1582	71	8	curved	curved	ADJ
cana-1582	71	9	domain	domain	NOUN
cana-1582	71	10	is	be	AUX
cana-1582	71	11	performed	perform	VERB
cana-1582	71	12	using	use	VERB
cana-1582	71	13	both	both	CCONJ
cana-1582	71	14	explicit	explicit	ADJ
cana-1582	71	15	parametric	parametric	ADJ
cana-1582	71	16	relations	relation	NOUN
cana-1582	71	17	and	and	CCONJ
cana-1582	71	18	parametric	parametric	ADJ
cana-1582	71	19	quartic	quartic	ADJ
cana-1582	71	20	spline	spline	NOUN
cana-1582	71	21	interpolating	interpolate	VERB
cana-1582	71	22	polynomials	polynomial	NOUN
cana-1582	71	23	.	.	PUNCT
cana-1582	72	1	this	this	PRON
cana-1582	72	2	highlights	highlight	VERB
cana-1582	72	3	the	the	DET
cana-1582	72	4	advantage	advantage	NOUN
cana-1582	72	5	of	of	ADP
cana-1582	72	6	splines	spline	NOUN
cana-1582	72	7	when	when	SCONJ
cana-1582	72	8	only	only	ADV
cana-1582	72	9	coordinate	coordinate	NOUN
cana-1582	72	10	data	datum	NOUN
cana-1582	72	11	is	be	AUX
cana-1582	72	12	available	available	ADJ
cana-1582	72	13	along	along	ADP
cana-1582	72	14	the	the	DET
cana-1582	72	15	boundary	boundary	NOUN
cana-1582	72	16	.	.	PUNCT
cana-1582	73	1	another	another	DET
cana-1582	73	2	application	application	NOUN
cana-1582	73	3	of	of	ADP
cana-1582	73	4	the	the	DET
cana-1582	73	5	numerical	numerical	ADJ
cana-1582	73	6	integration	integration	NOUN
cana-1582	73	7	scheme	scheme	NOUN
cana-1582	73	8	.	.	PUNCT
cana-1582	74	1	here	here	ADV
cana-1582	74	2	,	,	PUNCT
cana-1582	74	3	it	it	PRON
cana-1582	74	4	's	be	AUX
cana-1582	74	5	used	use	VERB
cana-1582	74	6	to	to	PART
cana-1582	74	7	compute	compute	VERB
cana-1582	74	8	the	the	DET
cana-1582	74	9	geometric	geometric	ADJ
cana-1582	74	10	moments	moment	NOUN
cana-1582	74	11	of	of	ADP
cana-1582	74	12	a	a	DET
cana-1582	74	13	general	general	ADJ
cana-1582	74	14	ellipse	ellipse	NOUN
cana-1582	74	15	.	.	PUNCT
cana-1582	75	1	overall	overall	ADV
cana-1582	75	2	,	,	PUNCT
cana-1582	75	3	this	this	DET
cana-1582	75	4	chapter	chapter	NOUN
cana-1582	75	5	presents	present	VERB
cana-1582	75	6	a	a	DET
cana-1582	75	7	valuable	valuable	ADJ
cana-1582	75	8	approach	approach	NOUN
cana-1582	75	9	for	for	ADP
cana-1582	75	10	numerical	numerical	ADJ
cana-1582	75	11	integration	integration	NOUN
cana-1582	75	12	over	over	ADP
cana-1582	75	13	complex	complex	ADJ
cana-1582	75	14	,	,	PUNCT
cana-1582	75	15	curved	curved	ADJ
cana-1582	75	16	boundaries	boundary	NOUN
cana-1582	75	17	.	.	PUNCT
cana-1582	76	1	by	by	ADP
cana-1582	76	2	leveraging	leverage	VERB
cana-1582	76	3	quartic	quartic	ADJ
cana-1582	76	4	splines	spline	NOUN
cana-1582	76	5	,	,	PUNCT
cana-1582	76	6	the	the	DET
cana-1582	76	7	method	method	NOUN
cana-1582	76	8	can	can	AUX
cana-1582	76	9	handle	handle	VERB
cana-1582	76	10	scenarios	scenario	NOUN
cana-1582	76	11	where	where	SCONJ
cana-1582	76	12	only	only	ADJ
cana-1582	76	13	coordinate	coordinate	NOUN
cana-1582	76	14	data	datum	NOUN
cana-1582	76	15	is	be	AUX
cana-1582	76	16	available	available	ADJ
cana-1582	76	17	.	.	PUNCT
cana-1582	77	1	quartic	quartic	ADJ
cana-1582	77	2	spline	spline	ADJ
cana-1582	77	3	interpolant	interpolant	NOUN
cana-1582	77	4	definition	definition	NOUN
cana-1582	77	5	:	:	PUNCT
cana-1582	77	6	let	let	VERB
cana-1582	77	7	f	f	PRON
cana-1582	77	8	be	be	AUX
cana-1582	77	9	a	a	DET
cana-1582	77	10	function	function	NOUN
cana-1582	77	11	defined	define	VERB
cana-1582	77	12	on	on	ADP
cana-1582	77	13	the	the	DET
cana-1582	77	14	interval	interval	NOUN
cana-1582	77	15	[	[	X
cana-1582	77	16	a	a	X
cana-1582	77	17	,	,	PUNCT
cana-1582	77	18	b	b	NOUN
cana-1582	77	19	]	]	PUNCT
cana-1582	77	20	and	and	CCONJ
cana-1582	77	21	let	let	VERB
cana-1582	77	22	the	the	DET
cana-1582	77	23	knots	knot	NOUN
cana-1582	77	24			PROPN
cana-1582	77	25			PROPN
cana-1582	77	26	1	1	NUM
cana-1582	77	27	0	0	NUM
cana-1582	78	1	n	n	CCONJ
cana-1582	79	1	i	i	PRON
cana-1582	79	2	i	i	VERB
cana-1582	79	3	x	x	PUNCT
cana-1582	80	1	+	+	PUNCT
cana-1582	80	2	=	=	SYM
cana-1582	80	3	0	0	NUM
cana-1582	80	4	1	1	NUM
cana-1582	80	5	2	2	NUM
cana-1582	80	6	1	1	NUM
cana-1582	80	7	....	....	PUNCT
cana-1582	80	8	n	n	CCONJ
cana-1582	80	9	n	n	ADV
cana-1582	81	1	a	a	PRON
cana-1582	81	2	x	x	X
cana-1582	81	3	x	x	SYM
cana-1582	81	4	x	x	SYM
cana-1582	81	5	x	x	PUNCT
cana-1582	81	6	x	x	SYM
cana-1582	81	7	b	b	PROPN
cana-1582	81	8	+	+	CCONJ
cana-1582	81	9	=	=	PUNCT
cana-1582	81	10			PROPN
cana-1582	81	11			PROPN
cana-1582	81	12			PROPN
cana-1582	81	13			PROPN
cana-1582	81	14			PROPN
cana-1582	82	1	=	=	PRON
cana-1582	82	2	be	be	AUX
cana-1582	82	3	the	the	DET
cana-1582	82	4	(	(	PUNCT
cana-1582	82	5	2)n	2)n	NUM
cana-1582	82	6	+	+	CCONJ
cana-1582	82	7	distinct	distinct	ADJ
cana-1582	82	8	points	point	NOUN
cana-1582	82	9	.	.	PUNCT
cana-1582	83	1	note	note	VERB
cana-1582	83	2	that	that	SCONJ
cana-1582	83	3	'	'	PUNCT
cana-1582	83	4	i	i	PRON
cana-1582	83	5	x	x	X
cana-1582	83	6	s	s	VERB
cana-1582	83	7	divide	divide	NOUN
cana-1582	83	8	[	[	X
cana-1582	83	9	a	a	X
cana-1582	83	10	,	,	PUNCT
cana-1582	83	11	b	b	NOUN
cana-1582	83	12	]	]	X
cana-1582	83	13	into	into	ADP
cana-1582	83	14	(	(	PUNCT
cana-1582	83	15	n+1	n+1	NOUN
cana-1582	83	16	)	)	PUNCT
cana-1582	83	17	subintervals	subinterval	NOUN
cana-1582	83	18	.	.	PUNCT
cana-1582	84	1	a	a	DET
cana-1582	84	2	function	function	NOUN
cana-1582	84	3	s	s	NOUN
cana-1582	84	4	is	be	AUX
cana-1582	84	5	said	say	VERB
cana-1582	84	6	to	to	PART
cana-1582	84	7	be	be	AUX
cana-1582	84	8	a	a	DET
cana-1582	84	9	quartic	quartic	ADJ
cana-1582	84	10	spline	spline	NOUN
cana-1582	84	11	on	on	ADP
cana-1582	84	12	the	the	DET
cana-1582	84	13	interval	interval	NOUN
cana-1582	84	14	[	[	X
cana-1582	84	15	a	a	X
cana-1582	84	16	,	,	PUNCT
cana-1582	84	17	b	b	NOUN
cana-1582	84	18	]	]	X
cana-1582	84	19	,	,	PUNCT
cana-1582	84	20	is	be	AUX
cana-1582	84	21	,	,	PUNCT
cana-1582	84	22	,	,	PUNCT
cana-1582	84	23	ands	ands	PROPN
cana-1582	84	24	s	s	X
cana-1582	84	25	s	s	NOUN
cana-1582	84	26	s	s	PUNCT
cana-1582	84	27			PROPN
cana-1582	84	28			NOUN
cana-1582	84	29	are	be	AUX
cana-1582	84	30	continuous	continuous	ADJ
cana-1582	84	31	in	in	ADP
cana-1582	84	32	[	[	X
cana-1582	84	33	a	a	PRON
cana-1582	84	34	,	,	PUNCT
cana-1582	84	35	b	b	NOUN
cana-1582	84	36	]	]	PUNCT
cana-1582	84	37	and	and	CCONJ
cana-1582	84	38	s	s	VERB
cana-1582	84	39	is	be	AUX
cana-1582	84	40	a	a	DET
cana-1582	84	41	polynomial	polynomial	NOUN
cana-1582	84	42	of	of	ADP
cana-1582	84	43	degree	degree	NOUN
cana-1582	84	44			NOUN
cana-1582	84	45	4	4	NUM
cana-1582	84	46	in	in	ADP
cana-1582	84	47	each	each	DET
cana-1582	84	48	knot	knot	ADJ
cana-1582	84	49	interval	interval	NOUN
cana-1582	84	50	1	1	NUM
cana-1582	84	51	[	[	PUNCT
cana-1582	84	52	,	,	PUNCT
cana-1582	84	53	]	]	PUNCT
cana-1582	85	1	i	i	PRON
cana-1582	85	2	i	i	VERB
cana-1582	85	3	x	x	X
cana-1582	85	4	x	x	X
cana-1582	85	5	−	−	PROPN
cana-1582	85	6	.	.	PUNCT
cana-1582	86	1	we	we	PRON
cana-1582	86	2	shall	shall	AUX
cana-1582	86	3	now	now	ADV
cana-1582	86	4	present	present	VERB
cana-1582	86	5	the	the	DET
cana-1582	86	6	quasi	quasi	NOUN
cana-1582	86	7	–	–	PUNCT
cana-1582	86	8	hermite	hermite	ADJ
cana-1582	86	9	lacunary	lacunary	ADJ
cana-1582	86	10	quartic	quartic	ADJ
cana-1582	86	11	spline	spline	NOUN
cana-1582	86	12	which	which	PRON
cana-1582	86	13	interpolates	interpolate	VERB
cana-1582	86	14	the	the	DET
cana-1582	86	15	first	first	ADJ
cana-1582	86	16	derivatives	derivative	NOUN
cana-1582	86	17	of	of	ADP
cana-1582	86	18	a	a	DET
cana-1582	86	19	given	give	VERB
cana-1582	86	20	function	function	NOUN
cana-1582	86	21	at	at	ADP
cana-1582	86	22	the	the	DET
cana-1582	86	23	knots	knot	NOUN
cana-1582	86	24	and	and	CCONJ
cana-1582	86	25	the	the	DET
cana-1582	86	26	second	second	ADJ
cana-1582	86	27	derivatives	derivative	NOUN
cana-1582	86	28	between	between	ADP
cana-1582	86	29	them	they	PRON
cana-1582	86	30	as	as	SCONJ
cana-1582	86	31	proposed	propose	VERB
cana-1582	86	32	in	in	ADP
cana-1582	86	33	[	[	X
cana-1582	86	34	12	12	NUM
cana-1582	86	35	,	,	PUNCT
cana-1582	86	36	22	22	NUM
cana-1582	86	37	]	]	PUNCT
cana-1582	86	38	.	.	PUNCT
cana-1582	87	1	communications	communication	NOUN
cana-1582	87	2	on	on	ADP
cana-1582	87	3	applied	apply	VERB
cana-1582	87	4	nonlinear	nonlinear	ADJ
cana-1582	87	5	analysis	analysis	NOUN
cana-1582	87	6	issn	issn	NOUN
cana-1582	87	7	:	:	PUNCT
cana-1582	87	8	1074	1074	NUM
cana-1582	87	9	-	-	PUNCT
cana-1582	87	10	133x	133x	NUM
cana-1582	87	11	vol	vol	NOUN
cana-1582	87	12	31	31	NUM
cana-1582	87	13	no	no	NOUN
cana-1582	87	14	.	.	PUNCT
cana-1582	88	1	8s	8s	PROPN
cana-1582	88	2	(	(	PUNCT
cana-1582	88	3	2024	2024	NUM
cana-1582	88	4	)	)	PUNCT
cana-1582	88	5	727	727	NUM
cana-1582	88	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1582	88	7	theorem	theorem	VERB
cana-1582	88	8	:	:	PUNCT
cana-1582	88	9	given	give	VERB
cana-1582	88	10	the	the	DET
cana-1582	88	11	real	real	ADJ
cana-1582	88	12	numbers	number	NOUN
cana-1582	88	13	(	(	PUNCT
cana-1582	88	14	)	)	PUNCT
cana-1582	88	15	(	(	PUNCT
cana-1582	88	16	0,1,2	0,1,2	NOUN
cana-1582	88	17	,	,	PUNCT
cana-1582	88	18	..	..	PUNCT
cana-1582	88	19	,	,	PUNCT
cana-1582	88	20	1	1	NUM
cana-1582	88	21	)	)	PUNCT
cana-1582	88	22	,	,	PUNCT
cana-1582	88	23	i	i	PRON
cana-1582	89	1	i	i	PRON
cana-1582	89	2	f	f	VERB
cana-1582	90	1	x	x	X
cana-1582	90	2	f	f	NOUN
cana-1582	91	1	i	i	PRON
cana-1582	91	2	n	n	VERB
cana-1582	91	3	=	=	PUNCT
cana-1582	92	1	=	=	PUNCT
cana-1582	93	1	+	+	CCONJ
cana-1582	93	2	(	(	PUNCT
cana-1582	93	3	)	)	PUNCT
cana-1582	93	4	(	(	PUNCT
cana-1582	93	5	0,1,2	0,1,2	NOUN
cana-1582	93	6	,	,	PUNCT
cana-1582	93	7	..	..	PUNCT
cana-1582	93	8	,	,	PUNCT
cana-1582	93	9	)	)	PUNCT
cana-1582	93	10	,	,	PUNCT
cana-1582	94	1	i	i	PRON
cana-1582	94	2	i	i	VERB
cana-1582	94	3	x	x	VERB
cana-1582	95	1	h	h	NOUN
cana-1582	96	1	f	f	PROPN
cana-1582	97	1	i	i	PRON
cana-1582	97	2	n	n	VERB
cana-1582	97	3	+	+	CCONJ
cana-1582	97	4	+	+	NOUN
cana-1582	97	5	=	=	PUNCT
cana-1582	97	6	=	=	SYM
cana-1582	97	7	0	0	SYM
cana-1582	97	8	0	0	NUM
cana-1582	97	9	(	(	PUNCT
cana-1582	97	10	)	)	PUNCT
cana-1582	97	11	,	,	PUNCT
cana-1582	97	12	f	f	PROPN
cana-1582	97	13	x	x	PUNCT
cana-1582	97	14	f=	f=	ADJ
cana-1582	97	15	and	and	CCONJ
cana-1582	97	16	1	1	NUM
cana-1582	97	17	1	1	NUM
cana-1582	97	18	(	(	PUNCT
cana-1582	97	19	)	)	PUNCT
cana-1582	97	20	n	n	CCONJ
cana-1582	97	21	n	n	NOUN
cana-1582	97	22	f	f	NOUN
cana-1582	97	23	f	f	PROPN
cana-1582	97	24	x	x	X
cana-1582	97	25	+	+	PUNCT
cana-1582	97	26	+	+	CCONJ
cana-1582	97	27	=	=	NOUN
cana-1582	97	28	,	,	PUNCT
cana-1582	97	29	then	then	ADV
cana-1582	97	30	there	there	PRON
cana-1582	97	31	exists	exist	VERB
cana-1582	97	32	a	a	DET
cana-1582	97	33	unique	unique	ADJ
cana-1582	97	34	quartic	quartic	ADJ
cana-1582	97	35	spline	spline	NOUN
cana-1582	97	36	s(x	s(x	PROPN
cana-1582	97	37	)	)	PUNCT
cana-1582	97	38	such	such	ADJ
cana-1582	97	39	that	that	SCONJ
cana-1582	97	40	(	(	PUNCT
cana-1582	97	41	1	1	X
cana-1582	97	42	)	)	PUNCT
cana-1582	97	43	on	on	ADP
cana-1582	97	44	each	each	DET
cana-1582	97	45	subinterval	subinterval	NOUN
cana-1582	97	46	1	1	NUM
cana-1582	97	47	[	[	PUNCT
cana-1582	97	48	,	,	PUNCT
cana-1582	97	49	]	]	X
cana-1582	97	50	,	,	PUNCT
cana-1582	97	51	0,1,2	0,1,2	NOUN
cana-1582	97	52	,	,	PUNCT
cana-1582	97	53	..	..	PUNCT
cana-1582	97	54	,	,	PUNCT
cana-1582	97	55	,	,	PUNCT
cana-1582	97	56	i	i	PRON
cana-1582	97	57	i	i	VERB
cana-1582	97	58	x	x	VERB
cana-1582	97	59	x	x	VERB
cana-1582	97	60	i	i	PRON
cana-1582	97	61	n	n	NOUN
cana-1582	97	62	+	+	CCONJ
cana-1582	97	63	=	=	SYM
cana-1582	97	64	s(x	s(x	NOUN
cana-1582	97	65	)	)	PUNCT
cana-1582	97	66	coincides	coincide	VERB
cana-1582	97	67	with	with	ADP
cana-1582	97	68	the	the	DET
cana-1582	97	69	quartic	quartic	ADJ
cana-1582	97	70	polynomial	polynomial	ADJ
cana-1582	97	71	2	2	NUM
cana-1582	97	72	3	3	NUM
cana-1582	97	73	4	4	NUM
cana-1582	97	74	(	(	PUNCT
cana-1582	97	75	)	)	PUNCT
cana-1582	97	76	(	(	PUNCT
cana-1582	97	77	)	)	PUNCT
cana-1582	98	1	i	i	PRON
cana-1582	98	2	i	i	PRON
cana-1582	99	1	i	i	PRON
cana-1582	99	2	i	i	PRON
cana-1582	100	1	i	i	PRON
cana-1582	101	1	i	i	PRON
cana-1582	101	2	s	s	VERB
cana-1582	101	3	x	x	X
cana-1582	101	4	s	s	VERB
cana-1582	101	5	u	u	NOUN
cana-1582	101	6	a	a	PRON
cana-1582	101	7	bu	bu	INTJ
cana-1582	101	8	c	c	NOUN
cana-1582	101	9	u	u	NOUN
cana-1582	101	10	d	d	X
cana-1582	101	11	u	u	X
cana-1582	101	12	e	e	NOUN
cana-1582	101	13	u=	u=	NOUN
cana-1582	101	14	=	=	PUNCT
cana-1582	102	1	+	+	PUNCT
cana-1582	103	1	+	+	PUNCT
cana-1582	103	2	+	+	CCONJ
cana-1582	103	3	+	+	CCONJ
cana-1582	103	4	,	,	PUNCT
cana-1582	103	5	1	1	NUM
cana-1582	103	6	(	(	PUNCT
cana-1582	103	7	)	)	PUNCT
cana-1582	103	8	/	/	PUNCT
cana-1582	103	9	,	,	PUNCT
cana-1582	103	10	(	(	PUNCT
cana-1582	103	11	)	)	PUNCT
cana-1582	103	12	0	0	NUM
cana-1582	103	13	1	1	NUM
cana-1582	104	1	i	i	PRON
cana-1582	104	2	i	i	PRON
cana-1582	104	3	i	i	PRON
cana-1582	104	4	u	u	VERB
cana-1582	104	5	x	x	X
cana-1582	104	6	x	x	VERB
cana-1582	104	7	h	h	NOUN
cana-1582	104	8	h	h	NOUN
cana-1582	104	9	x	x	PUNCT
cana-1582	104	10	x	x	PUNCT
cana-1582	104	11	u	u	NOUN
cana-1582	104	12	+	+	NOUN
cana-1582	104	13	=	=	SYM
cana-1582	104	14	−	−	NOUN
cana-1582	104	15	=	=	SYM
cana-1582	104	16	−	−	PROPN
cana-1582	104	17			NUM
cana-1582	104	18			NOUN
cana-1582	104	19	(	(	PUNCT
cana-1582	104	20	1	1	NUM
cana-1582	104	21	)	)	PUNCT
cana-1582	104	22	(	(	PUNCT
cana-1582	104	23	2	2	NUM
cana-1582	104	24	)	)	PUNCT
cana-1582	104	25	,	,	PUNCT
cana-1582	104	26	ands	ands	PROPN
cana-1582	104	27	s	s	PART
cana-1582	104	28	s	s	INTJ
cana-1582	104	29			PROPN
cana-1582	104	30	satisfy	satisfy	VERB
cana-1582	104	31	the	the	DET
cana-1582	104	32	interpolatory	interpolatory	NOUN
cana-1582	104	33	conditions	condition	NOUN
cana-1582	104	34	.	.	PUNCT
cana-1582	105	1	0	0	NUM
cana-1582	105	2	0	0	NUM
cana-1582	105	3	1	1	NUM
cana-1582	105	4	1	1	NUM
cana-1582	105	5	,	,	PUNCT
cana-1582	105	6	(	(	PUNCT
cana-1582	105	7	0,1,2	0,1,2	NOUN
cana-1582	105	8	,	,	PUNCT
cana-1582	105	9	..	..	PUNCT
cana-1582	105	10	,	,	PUNCT
cana-1582	105	11	1	1	NUM
cana-1582	105	12	)	)	PUNCT
cana-1582	105	13	,	,	PUNCT
cana-1582	105	14	(	(	PUNCT
cana-1582	105	15	0,1,2	0,1,2	NOUN
cana-1582	105	16	,	,	PUNCT
cana-1582	105	17	..	..	PUNCT
cana-1582	105	18	,	,	PUNCT
cana-1582	105	19	)	)	PUNCT
cana-1582	105	20	,	,	PUNCT
cana-1582	106	1	i	i	PRON
cana-1582	106	2	i	i	PRON
cana-1582	107	1	i	i	VERB
cana-1582	107	2	i	i	VERB
cana-1582	107	3	n	n	VERB
cana-1582	107	4	n	n	PROPN
cana-1582	107	5	s	s	NOUN
cana-1582	107	6	f	f	X
cana-1582	108	1	i	i	PRON
cana-1582	108	2	n	n	VERB
cana-1582	108	3	s	s	VERB
cana-1582	108	4	f	f	X
cana-1582	108	5	i	i	PRON
cana-1582	108	6	n	n	VERB
cana-1582	108	7	s	s	PROPN
cana-1582	108	8	f	f	PROPN
cana-1582	108	9	s	s	PROPN
cana-1582	108	10	f	f	PROPN
cana-1582	108	11			X
cana-1582	108	12	+	+	X
cana-1582	108	13	+	+	PROPN
cana-1582	108	14	+	+	CCONJ
cana-1582	108	15	+	+	NUM
cana-1582	108	16			ADJ
cana-1582	108	17	=	=	ADJ
cana-1582	108	18	=	=	PUNCT
cana-1582	109	1	+	+	NUM
cana-1582	109	2			PROPN
cana-1582	109	3	=	=	NOUN
cana-1582	109	4	=	=	PUNCT
cana-1582	109	5	=	=	PUNCT
cana-1582	109	6	=	=	SYM
cana-1582	109	7	(	(	PUNCT
cana-1582	109	8	2	2	NUM
cana-1582	109	9	)	)	PUNCT
cana-1582	109	10	now	now	ADV
cana-1582	109	11	,	,	PUNCT
cana-1582	109	12	we	we	PRON
cana-1582	109	13	shall	shall	AUX
cana-1582	109	14	prove	prove	VERB
cana-1582	109	15	the	the	DET
cana-1582	109	16	above	above	ADJ
cana-1582	109	17	theorem	theorem	NOUN
cana-1582	109	18	.	.	PUNCT
cana-1582	110	1	the	the	DET
cana-1582	110	2	proof	proof	NOUN
cana-1582	110	3	is	be	AUX
cana-1582	110	4	constructive	constructive	ADJ
cana-1582	110	5	:	:	PUNCT
cana-1582	110	6	it	it	PRON
cana-1582	110	7	gives	give	VERB
cana-1582	110	8	on	on	ADP
cana-1582	110	9	a	a	DET
cana-1582	110	10	algorithm	algorithm	NOUN
cana-1582	110	11	to	to	PART
cana-1582	110	12	compute	compute	VERB
cana-1582	110	13	the	the	DET
cana-1582	110	14	spline	spline	NOUN
cana-1582	110	15	.	.	PUNCT
cana-1582	111	1	proof	proof	NOUN
cana-1582	111	2	:	:	PUNCT
cana-1582	111	3	we	we	PRON
cana-1582	111	4	consider	consider	VERB
cana-1582	111	5	the	the	DET
cana-1582	111	6	quartic	quartic	ADJ
cana-1582	111	7	spline	spline	NOUN
cana-1582	111	8	(	(	PUNCT
cana-1582	111	9	)	)	PUNCT
cana-1582	112	1	i	i	PRON
cana-1582	112	2	s	s	VERB
cana-1582	112	3	x	x	PUNCT
cana-1582	112	4	over	over	ADP
cana-1582	112	5	the	the	DET
cana-1582	112	6	interval	interval	NOUN
cana-1582	112	7	1	1	NUM
cana-1582	112	8	[	[	PUNCT
cana-1582	112	9	,	,	PUNCT
cana-1582	112	10	]	]	PUNCT
cana-1582	113	1	i	i	PRON
cana-1582	113	2	i	i	VERB
cana-1582	113	3	x	x	VERB
cana-1582	113	4	x	x	PUNCT
cana-1582	113	5	+	+	CCONJ
cana-1582	113	6	defined	define	VERB
cana-1582	113	7	in	in	ADP
cana-1582	113	8	eqn	eqn	NOUN
cana-1582	113	9	(	(	PUNCT
cana-1582	113	10	1	1	NUM
cana-1582	113	11	)	)	PUNCT
cana-1582	113	12	.	.	PUNCT
cana-1582	114	1	on	on	ADP
cana-1582	114	2	satisfying	satisfy	VERB
cana-1582	114	3	the	the	DET
cana-1582	114	4	interpolatory	interpolatory	NOUN
cana-1582	114	5	conditions	condition	NOUN
cana-1582	114	6	of	of	ADP
cana-1582	114	7	eqn	eqn	NOUN
cana-1582	114	8	(	(	PUNCT
cana-1582	114	9	2	2	NUM
cana-1582	114	10	)	)	PUNCT
cana-1582	114	11	,	,	PUNCT
cana-1582	114	12	we	we	PRON
cana-1582	114	13	obtained	obtain	VERB
cana-1582	114	14	1	1	NUM
cana-1582	114	15	1	1	NUM
cana-1582	114	16	1	1	NUM
cana-1582	114	17	1	1	NUM
cana-1582	114	18	2	2	NUM
cana-1582	114	19	2	2	NUM
cana-1582	114	20	(	(	PUNCT
cana-1582	114	21	)	)	PUNCT
cana-1582	114	22	(	(	PUNCT
cana-1582	114	23	0	0	NUM
cana-1582	114	24	)	)	PUNCT
cana-1582	114	25	(	(	PUNCT
cana-1582	114	26	)	)	PUNCT
cana-1582	114	27	(	(	PUNCT
cana-1582	114	28	1	1	X
cana-1582	114	29	)	)	PUNCT
cana-1582	114	30	(	(	PUNCT
cana-1582	114	31	)	)	PUNCT
cana-1582	114	32	(	(	PUNCT
cana-1582	114	33	0	0	NUM
cana-1582	114	34	)	)	PUNCT
cana-1582	114	35	/	/	SYM
cana-1582	114	36	(	(	PUNCT
cana-1582	114	37	)	)	PUNCT
cana-1582	114	38	(	(	PUNCT
cana-1582	114	39	1	1	X
cana-1582	114	40	)	)	PUNCT
cana-1582	114	41	/	/	SYM
cana-1582	114	42	2	2	NUM
cana-1582	114	43	/	/	SYM
cana-1582	114	44	3	3	NUM
cana-1582	114	45	/	/	SYM
cana-1582	114	46	4	4	NUM
cana-1582	114	47	/	/	SYM
cana-1582	114	48	(	(	PUNCT
cana-1582	114	49	)	)	PUNCT
cana-1582	114	50	(	(	PUNCT
cana-1582	114	51	2	2	NUM
cana-1582	114	52	6	6	NUM
cana-1582	114	53	12	12	NUM
cana-1582	114	54	)	)	PUNCT
cana-1582	114	55	/	/	PUNCT
cana-1582	115	1	i	i	PRON
cana-1582	115	2	i	i	PRON
cana-1582	116	1	i	i	PRON
cana-1582	116	2	i	i	PRON
cana-1582	117	1	i	i	PRON
cana-1582	117	2	i	i	PRON
cana-1582	118	1	i	i	PRON
cana-1582	118	2	i	i	PRON
cana-1582	119	1	i	i	PRON
cana-1582	119	2	i	i	PRON
cana-1582	120	1	i	i	PRON
cana-1582	120	2	i	i	PRON
cana-1582	121	1	i	i	PRON
cana-1582	121	2	i	i	PRON
cana-1582	122	1	i	i	PRON
cana-1582	122	2	i	i	PRON
cana-1582	123	1	i	i	PRON
cana-1582	123	2	i	i	PRON
cana-1582	124	1	i	i	PRON
cana-1582	124	2	i	i	PRON
cana-1582	125	1	i	i	PRON
cana-1582	125	2	i	i	PRON
cana-1582	126	1	i	i	PRON
cana-1582	126	2	i	i	PRON
cana-1582	127	1	i	i	PRON
cana-1582	127	2	i	i	PRON
cana-1582	128	1	i	i	PRON
cana-1582	129	1	i	i	PRON
cana-1582	129	2	s	s	AUX
cana-1582	129	3	x	x	X
cana-1582	129	4	s	s	AUX
cana-1582	129	5	a	a	DET
cana-1582	129	6	f	f	NOUN
cana-1582	129	7	s	s	PROPN
cana-1582	129	8	x	x	X
cana-1582	129	9	s	s	PROPN
cana-1582	129	10	a	a	DET
cana-1582	129	11	b	b	NOUN
cana-1582	129	12	c	c	NOUN
cana-1582	129	13	d	d	PROPN
cana-1582	129	14	e	e	X
cana-1582	129	15	f	f	PROPN
cana-1582	129	16	s	s	PROPN
cana-1582	129	17	x	x	X
cana-1582	129	18	s	s	PROPN
cana-1582	129	19	b	b	X
cana-1582	129	20	h	h	NOUN
cana-1582	130	1	f	f	PROPN
cana-1582	130	2	s	s	PROPN
cana-1582	130	3	x	x	X
cana-1582	130	4	s	s	PROPN
cana-1582	130	5	b	b	NUM
cana-1582	130	6	h	h	NOUN
cana-1582	131	1	c	c	NOUN
cana-1582	131	2	h	h	NOUN
cana-1582	132	1	d	d	NOUN
cana-1582	132	2	h	h	NOUN
cana-1582	132	3	e	e	NOUN
cana-1582	132	4	h	h	NOUN
cana-1582	133	1	f	f	PROPN
cana-1582	133	2	s	s	NOUN
cana-1582	133	3	x	x	X
cana-1582	133	4	h	h	NOUN
cana-1582	133	5	c	c	NOUN
cana-1582	134	1	d	d	NOUN
cana-1582	134	2	e	e	PROPN
cana-1582	134	3	h	h	PROPN
cana-1582	134	4	f	f	PROPN
cana-1582	134	5			X
cana-1582	134	6			ADJ
cana-1582	134	7			ADJ
cana-1582	134	8			ADJ
cana-1582	134	9	+	+	X
cana-1582	134	10	+	+	PUNCT
cana-1582	134	11	+	+	PUNCT
cana-1582	134	12	+	+	PUNCT
cana-1582	134	13	+	+	PROPN
cana-1582	134	14	=	=	SYM
cana-1582	134	15	=	=	SYM
cana-1582	134	16	=	=	PUNCT
cana-1582	134	17	=	=	PUNCT
cana-1582	135	1	=	=	PUNCT
cana-1582	136	1	+	+	PUNCT
cana-1582	137	1	+	+	PUNCT
cana-1582	137	2	+	+	CCONJ
cana-1582	137	3	+	+	CCONJ
cana-1582	137	4	=	=	VERB
cana-1582	137	5			X
cana-1582	137	6	=	=	NOUN
cana-1582	137	7	=	=	PUNCT
cana-1582	137	8	=	=	PUNCT
cana-1582	137	9			X
cana-1582	137	10	=	=	NOUN
cana-1582	137	11	=	=	PUNCT
cana-1582	138	1	+	+	PUNCT
cana-1582	139	1	+	+	CCONJ
cana-1582	139	2	+	+	CCONJ
cana-1582	139	3	=	=	SYM
cana-1582	139	4			X
cana-1582	139	5	+	+	NOUN
cana-1582	139	6	=	=	X
cana-1582	139	7	+	+	PROPN
cana-1582	139	8	+	+	CCONJ
cana-1582	139	9	=	=	SYM
cana-1582	139	10	(	(	PUNCT
cana-1582	139	11	3	3	X
cana-1582	139	12	)	)	PUNCT
cana-1582	139	13	solving	solve	VERB
cana-1582	139	14	the	the	DET
cana-1582	139	15	above	above	ADJ
cana-1582	139	16	linear	linear	PROPN
cana-1582	139	17	equations	equation	NOUN
cana-1582	139	18	in	in	ADP
cana-1582	139	19	eqn	eqn	NOUN
cana-1582	139	20	(	(	PUNCT
cana-1582	139	21	3	3	NUM
cana-1582	139	22	)	)	PUNCT
cana-1582	139	23	,	,	PUNCT
cana-1582	139	24	we	we	PRON
cana-1582	139	25	obtain	obtain	VERB
cana-1582	139	26	2	2	NUM
cana-1582	139	27	2	2	NUM
cana-1582	139	28	1	1	NUM
cana-1582	139	29	2	2	NUM
cana-1582	139	30	2	2	NUM
cana-1582	139	31	2	2	NUM
cana-1582	139	32	1	1	NUM
cana-1582	139	33	2	2	NUM
cana-1582	139	34	2	2	NUM
cana-1582	139	35	2	2	NUM
cana-1582	139	36	2	2	NUM
cana-1582	139	37	2	2	NUM
cana-1582	139	38	1	1	NUM
cana-1582	139	39	1	1	NUM
cana-1582	139	40	1	1	NUM
cana-1582	139	41	,	,	PUNCT
cana-1582	139	42	,	,	PUNCT
cana-1582	139	43	(	(	PUNCT
cana-1582	139	44	36	36	NUM
cana-1582	139	45	24	24	NUM
cana-1582	139	46	)	)	PUNCT
cana-1582	139	47	(	(	PUNCT
cana-1582	139	48	36	36	NUM
cana-1582	139	49	24	24	NUM
cana-1582	139	50	)	)	PUNCT
cana-1582	139	51	(	(	PUNCT
cana-1582	139	52	24	24	NUM
cana-1582	139	53	24	24	NUM
cana-1582	139	54	6	6	NUM
cana-1582	139	55	)	)	PUNCT
cana-1582	139	56	(	(	PUNCT
cana-1582	139	57	12	12	NUM
cana-1582	139	58	6	6	NUM
cana-1582	139	59	)	)	PUNCT
cana-1582	139	60	(	(	PUNCT
cana-1582	139	61	24	24	NUM
cana-1582	139	62	8)	8)	NUM
cana-1582	139	63	(	(	PUNCT
cana-1582	139	64	24	24	NUM
cana-1582	139	65	8)	8)	NUM
cana-1582	139	66	(	(	PUNCT
cana-1582	139	67	12	12	NUM
cana-1582	139	68	6	6	NUM
cana-1582	139	69	)	)	PUNCT
cana-1582	139	70	(	(	PUNCT
cana-1582	139	71	12	12	NUM
cana-1582	139	72	2	2	NUM
cana-1582	139	73	)	)	PUNCT
cana-1582	139	74	2	2	NUM
cana-1582	139	75	(	(	PUNCT
cana-1582	139	76	12	12	NUM
cana-1582	139	77	6	6	NUM
cana-1582	139	78	)	)	PUNCT
cana-1582	139	79	(	(	PUNCT
cana-1582	139	80	12	12	NUM
cana-1582	139	81	6	6	NUM
cana-1582	139	82	)	)	PUNCT
cana-1582	139	83	(	(	PUNCT
cana-1582	139	84	6	6	NUM
cana-1582	139	85	4	4	NUM
cana-1582	139	86	)	)	PUNCT
cana-1582	140	1	i	i	PRON
cana-1582	140	2	i	i	PRON
cana-1582	141	1	i	i	PRON
cana-1582	141	2	i	i	PRON
cana-1582	142	1	i	i	PRON
cana-1582	142	2	i	i	PRON
cana-1582	143	1	i	i	PRON
cana-1582	143	2	i	i	PRON
cana-1582	144	1	i	i	PRON
cana-1582	144	2	i	i	PRON
cana-1582	145	1	i	i	PRON
cana-1582	145	2	i	i	PRON
cana-1582	146	1	i	i	PRON
cana-1582	146	2	i	i	PRON
cana-1582	147	1	i	i	PRON
cana-1582	147	2	i	i	PRON
cana-1582	148	1	i	i	PRON
cana-1582	148	2	i	i	PRON
cana-1582	149	1	i	i	PRON
cana-1582	149	2	i	i	PRON
cana-1582	149	3	i	i	PRON
cana-1582	150	1	a	a	PRON
cana-1582	150	2	f	f	PROPN
cana-1582	150	3	b	b	PROPN
cana-1582	150	4	hf	hf	NOUN
cana-1582	150	5	a	a	DET
cana-1582	150	6	c	c	NOUN
cana-1582	151	1	f	f	PROPN
cana-1582	151	2	f	f	PROPN
cana-1582	151	3	hf	hf	INTJ
cana-1582	151	4	hf	hf	PROPN
cana-1582	151	5	h	h	PROPN
cana-1582	152	1	f	f	PROPN
cana-1582	153	1	a	a	PRON
cana-1582	154	1	d	d	X
cana-1582	154	2	f	f	X
cana-1582	155	1	f	f	PROPN
cana-1582	155	2	hf	hf	INTJ
cana-1582	155	3	hf	hf	PROPN
cana-1582	155	4	h	h	PROPN
cana-1582	156	1	f	f	PROPN
cana-1582	157	1	a	a	DET
cana-1582	157	2	e	e	X
cana-1582	157	3	f	f	X
cana-1582	157	4	f	f	PROPN
cana-1582	157	5	hf	hf	PROPN
cana-1582	157	6	hf	hf	PROPN
cana-1582	157	7			ADJ
cana-1582	157	8			ADJ
cana-1582	157	9			ADJ
cana-1582	157	10			ADJ
cana-1582	157	11			ADJ
cana-1582	157	12			ADJ
cana-1582	157	13			ADJ
cana-1582	157	14			ADJ
cana-1582	157	15			ADJ
cana-1582	157	16			ADJ
cana-1582	157	17			ADJ
cana-1582	157	18			ADJ
cana-1582	157	19			ADJ
cana-1582	157	20			ADJ
cana-1582	157	21			ADJ
cana-1582	157	22			ADJ
cana-1582	157	23			ADJ
cana-1582	157	24			ADJ
cana-1582	157	25	+	+	X
cana-1582	157	26	+	+	PUNCT
cana-1582	157	27	+	+	PUNCT
cana-1582	157	28	+	+	PUNCT
cana-1582	157	29	+	+	PUNCT
cana-1582	157	30	+	+	CCONJ
cana-1582	157	31	+	+	CCONJ
cana-1582	157	32	=	=	ADJ
cana-1582	157	33	=	=	PUNCT
cana-1582	157	34	=	=	PUNCT
cana-1582	158	1	−	−	PROPN
cana-1582	159	1	+	+	CCONJ
cana-1582	159	2	+	+	CCONJ
cana-1582	159	3	−	−	PROPN
cana-1582	160	1			PROPN
cana-1582	160	2			ADV
cana-1582	160	3	+	+	PROPN
cana-1582	160	4	−	−	PROPN
cana-1582	161	1	+	+	CCONJ
cana-1582	161	2	−	−	PROPN
cana-1582	162	1	+	+	CCONJ
cana-1582	162	2	−	−	PROPN
cana-1582	163	1	+	+	CCONJ
cana-1582	164	1	+	+	CCONJ
cana-1582	164	2			ADJ
cana-1582	164	3			ADV
cana-1582	164	4	=	=	PROPN
cana-1582	164	5	−	−	PROPN
cana-1582	165	1	+	+	CCONJ
cana-1582	165	2	−	−	PROPN
cana-1582	166	1	+	+	CCONJ
cana-1582	167	1	+	+	CCONJ
cana-1582	167	2	−	−	X
cana-1582	168	1	+	+	CCONJ
cana-1582	168	2	−	−	PROPN
cana-1582	168	3	−	−	PROPN
cana-1582	169	1			ADV
cana-1582	169	2	=	=	INTJ
cana-1582	169	3	−	−	PROPN
cana-1582	170	1	+	+	CCONJ
cana-1582	171	1	+	+	CCONJ
cana-1582	171	2	−	−	X
cana-1582	172	1	+	+	CCONJ
cana-1582	172	2	−	−	PROPN
cana-1582	173	1	+	+	CCONJ
cana-1582	173	2	+	+	NUM
cana-1582	173	3	2	2	NUM
cana-1582	173	4	1	1	NUM
cana-1582	173	5	2	2	NUM
cana-1582	173	6	(	(	PUNCT
cana-1582	173	7	6	6	NUM
cana-1582	173	8	2	2	NUM
cana-1582	173	9	)	)	PUNCT
cana-1582	173	10	,	,	PUNCT
cana-1582	173	11	2(6	2(6	NUM
cana-1582	173	12	6	6	NUM
cana-1582	173	13	1	1	NUM
cana-1582	173	14	)	)	PUNCT
cana-1582	174	1	i	i	PRON
cana-1582	174	2	h	h	VERB
cana-1582	175	1	f	f	PROPN
cana-1582	175	2	a	a	DET
cana-1582	175	3			ADJ
cana-1582	175	4			ADJ
cana-1582	175	5			ADJ
cana-1582	175	6	+	+	PUNCT
cana-1582	175	7	+	+	CCONJ
cana-1582	175	8	−	−	NOUN
cana-1582	175	9	+	+	CCONJ
cana-1582	175	10	+	+	PUNCT
cana-1582	175	11	=	=	SYM
cana-1582	175	12	−	−	PROPN
cana-1582	176	1	+	+	CCONJ
cana-1582	176	2	(	(	PUNCT
cana-1582	176	3	4	4	NUM
cana-1582	176	4	)	)	PUNCT
cana-1582	176	5	on	on	ADP
cana-1582	176	6	substituting	substitute	VERB
cana-1582	176	7	for	for	ADP
cana-1582	176	8	ai	ai	PROPN
cana-1582	176	9	,	,	PUNCT
cana-1582	176	10	bi	bi	NOUN
cana-1582	176	11	,	,	PUNCT
cana-1582	176	12	ci	ci	PROPN
cana-1582	176	13	,	,	PUNCT
cana-1582	176	14	di	di	NOUN
cana-1582	176	15	and	and	CCONJ
cana-1582	176	16	ei	ei	NOUN
cana-1582	176	17	in	in	ADP
cana-1582	176	18	eqn	eqn	NOUN
cana-1582	176	19	(	(	PUNCT
cana-1582	176	20	1	1	NUM
cana-1582	176	21	)	)	PUNCT
cana-1582	176	22	,	,	PUNCT
cana-1582	176	23	we	we	PRON
cana-1582	176	24	obtain	obtain	VERB
cana-1582	176	25	the	the	DET
cana-1582	176	26	following	follow	VERB
cana-1582	176	27	alternative	alternative	ADJ
cana-1582	176	28	expression	expression	NOUN
cana-1582	176	29	communications	communication	NOUN
cana-1582	176	30	on	on	ADP
cana-1582	176	31	applied	apply	VERB
cana-1582	176	32	nonlinear	nonlinear	ADJ
cana-1582	176	33	analysis	analysis	NOUN
cana-1582	176	34	issn	issn	NOUN
cana-1582	176	35	:	:	PUNCT
cana-1582	176	36	1074	1074	NUM
cana-1582	176	37	-	-	PUNCT
cana-1582	176	38	133x	133x	NUM
cana-1582	176	39	vol	vol	NOUN
cana-1582	176	40	31	31	NUM
cana-1582	176	41	no	no	NOUN
cana-1582	176	42	.	.	PUNCT
cana-1582	177	1	8s	8s	PROPN
cana-1582	177	2	(	(	PUNCT
cana-1582	177	3	2024	2024	NUM
cana-1582	177	4	)	)	PUNCT
cana-1582	177	5	728	728	NUM
cana-1582	177	6	https://internationalpubls.com	https://internationalpubls.com	SYM
cana-1582	177	7	2	2	NUM
cana-1582	177	8	2	2	NUM
cana-1582	177	9	2	2	NUM
cana-1582	177	10	2	2	NUM
cana-1582	177	11	2	2	NUM
cana-1582	177	12	2	2	NUM
cana-1582	177	13	1	1	NUM
cana-1582	177	14	2	2	NUM
cana-1582	177	15	2	2	NUM
cana-1582	177	16	2	2	NUM
cana-1582	177	17	2	2	NUM
cana-1582	177	18	2	2	NUM
cana-1582	177	19	2	2	NUM
cana-1582	177	20	2	2	NUM
cana-1582	177	21	2	2	NUM
cana-1582	177	22	2	2	NUM
cana-1582	177	23	1	1	NUM
cana-1582	177	24	3(2	3(2	NUM
cana-1582	177	25	1	1	NUM
cana-1582	177	26	)	)	PUNCT
cana-1582	177	27	3(2	3(2	NUM
cana-1582	177	28	1	1	NUM
cana-1582	177	29	)	)	PUNCT
cana-1582	177	30	(	(	PUNCT
cana-1582	177	31	)	)	PUNCT
cana-1582	177	32	(	(	PUNCT
cana-1582	177	33	1	1	X
cana-1582	177	34	)	)	PUNCT
cana-1582	177	35	(	(	PUNCT
cana-1582	177	36	1	1	NUM
cana-1582	177	37	2	2	NUM
cana-1582	177	38	)	)	PUNCT
cana-1582	177	39	(	(	PUNCT
cana-1582	177	40	1	1	X
cana-1582	177	41	)	)	PUNCT
cana-1582	177	42	+	+	CCONJ
cana-1582	177	43	(	(	PUNCT
cana-1582	177	44	3	3	NUM
cana-1582	177	45	2	2	NUM
cana-1582	177	46	)	)	PUNCT
cana-1582	177	47	(	(	PUNCT
cana-1582	177	48	1	1	X
cana-1582	177	49	)	)	PUNCT
cana-1582	177	50	(	(	PUNCT
cana-1582	177	51	3	3	NUM
cana-1582	177	52	2	2	NUM
cana-1582	177	53	)	)	PUNCT
cana-1582	177	54	(	(	PUNCT
cana-1582	177	55	3	3	NUM
cana-1582	177	56	1	1	NUM
cana-1582	177	57	)	)	PUNCT
cana-1582	177	58	(	(	PUNCT
cana-1582	177	59	1	1	X
cana-1582	177	60	)	)	PUNCT
cana-1582	177	61	+	+	CCONJ
cana-1582	177	62	(	(	PUNCT
cana-1582	177	63	1	1	X
cana-1582	177	64	)	)	PUNCT
cana-1582	177	65	(	(	PUNCT
cana-1582	177	66	1	1	X
cana-1582	177	67	)	)	PUNCT
cana-1582	177	68	(	(	PUNCT
cana-1582	177	69	1	1	X
cana-1582	177	70	)	)	PUNCT
cana-1582	177	71	(	(	PUNCT
cana-1582	177	72	1	1	X
cana-1582	177	73	)	)	SYM
cana-1582	177	74	2	2	NUM
cana-1582	178	1	i	i	PRON
cana-1582	178	2	i	i	PRON
cana-1582	179	1	i	i	PRON
cana-1582	179	2	i	i	PRON
cana-1582	180	1	i	i	PRON
cana-1582	181	1	i	i	PRON
cana-1582	181	2	s	s	VERB
cana-1582	181	3	u	u	X
cana-1582	181	4	f	f	PROPN
cana-1582	181	5	u	u	NOUN
cana-1582	181	6	u	u	X
cana-1582	181	7	u	u	NOUN
cana-1582	181	8	u	u	NOUN
cana-1582	181	9	f	f	PROPN
cana-1582	181	10	u	u	NOUN
cana-1582	181	11	u	u	VERB
cana-1582	181	12	u	u	X
cana-1582	181	13	u	u	X
cana-1582	181	14	u	u	X
cana-1582	181	15	u	u	NOUN
cana-1582	181	16	hf	hf	ADP
cana-1582	181	17	u	u	NOUN
cana-1582	181	18	u	u	VERB
cana-1582	181	19	u	u	X
cana-1582	181	20	u	u	NOUN
cana-1582	181	21	hf	hf	ADP
cana-1582	181	22	u	u	NOUN
cana-1582	181	23	u	u	VERB
cana-1582	181	24	u	u	NOUN
cana-1582	181	25	u	u	NOUN
cana-1582	181	26	h	h	PROPN
cana-1582	181	27	f	f	PROPN
cana-1582	181	28			X
cana-1582	181	29			ADJ
cana-1582	181	30			ADJ
cana-1582	181	31			ADJ
cana-1582	181	32			ADJ
cana-1582	182	1	+	+	X
cana-1582	183	1	+	+	PUNCT
cana-1582	183	2	+	+	NUM
cana-1582	183	3	−	−	NOUN
cana-1582	183	4	−	−	NOUN
cana-1582	183	5			X
cana-1582	183	6			PROPN
cana-1582	183	7			NOUN
cana-1582	183	8	=	=	PUNCT
cana-1582	183	9	−	−	PROPN
cana-1582	184	1	+	+	CCONJ
cana-1582	184	2	−	−	PROPN
cana-1582	184	3	−	−	NOUN
cana-1582	185	1	−	−	PROPN
cana-1582	186	1	+	+	CCONJ
cana-1582	186	2	−	−	X
cana-1582	186	3			ADJ
cana-1582	186	4			NOUN
cana-1582	186	5			PROPN
cana-1582	186	6			PROPN
cana-1582	186	7			PROPN
cana-1582	186	8			VERB
cana-1582	186	9			PROPN
cana-1582	186	10			PROPN
cana-1582	186	11	−	−	NOUN
cana-1582	186	12	−	−	PROPN
cana-1582	186	13	−	−	NOUN
cana-1582	186	14			X
cana-1582	186	15			PROPN
cana-1582	186	16			NOUN
cana-1582	186	17			PROPN
cana-1582	186	18			ADJ
cana-1582	186	19	−	−	VERB
cana-1582	186	20	−	−	PROPN
cana-1582	186	21	−	−	PROPN
cana-1582	186	22	−	−	PROPN
cana-1582	186	23	−	−	PROPN
cana-1582	187	1	+	+	CCONJ
cana-1582	188	1	−	−	PROPN
cana-1582	188	2	+	+	NUM
cana-1582	188	3			NOUN
cana-1582	188	4			NOUN
cana-1582	188	5			PROPN
cana-1582	188	6			NOUN
cana-1582	188	7			PROPN
cana-1582	188	8			PROPN
cana-1582	188	9			PROPN
cana-1582	188	10			PROPN
cana-1582	188	11			VERB
cana-1582	188	12			PROPN
cana-1582	188	13			NOUN
cana-1582	188	14			PROPN
cana-1582	188	15	(	(	PUNCT
cana-1582	188	16	5	5	NUM
cana-1582	188	17	)	)	PUNCT
cana-1582	188	18	where	where	SCONJ
cana-1582	188	19	,	,	PUNCT
cana-1582	188	20	1	1	NUM
cana-1582	188	21	2	2	NUM
cana-1582	188	22	(	(	PUNCT
cana-1582	188	23	)	)	PUNCT
cana-1582	188	24	/	/	PUNCT
cana-1582	188	25	,	,	PUNCT
cana-1582	188	26	(	(	PUNCT
cana-1582	188	27	)	)	PUNCT
cana-1582	188	28	,	,	PUNCT
cana-1582	188	29	(	(	PUNCT
cana-1582	188	30	6	6	NUM
cana-1582	188	31	6	6	NUM
cana-1582	188	32	1	1	NUM
cana-1582	188	33	)	)	PUNCT
cana-1582	189	1	i	i	PRON
cana-1582	189	2	i	i	PRON
cana-1582	190	1	i	i	PRON
cana-1582	190	2	i	i	PRON
cana-1582	190	3	u	u	VERB
cana-1582	190	4	x	x	X
cana-1582	190	5	x	x	VERB
cana-1582	190	6	h	h	NOUN
cana-1582	190	7	h	h	NOUN
cana-1582	190	8	x	x	PUNCT
cana-1582	191	1	x	x	X
cana-1582	191	2			X
cana-1582	191	3			ADJ
cana-1582	191	4	+	+	SYM
cana-1582	191	5	=	=	SYM
cana-1582	191	6	−	−	NOUN
cana-1582	191	7	=	=	PUNCT
cana-1582	191	8	−	−	PROPN
cana-1582	191	9			NOUN
cana-1582	191	10			NOUN
cana-1582	191	11	=	=	SYM
cana-1582	192	1	−	−	PROPN
cana-1582	192	2	+	+	CCONJ
cana-1582	192	3	(	(	PUNCT
cana-1582	192	4	6	6	NUM
cana-1582	192	5	)	)	PUNCT
cana-1582	192	6	it	it	PRON
cana-1582	192	7	is	be	AUX
cana-1582	192	8	clear	clear	ADJ
cana-1582	192	9	that	that	SCONJ
cana-1582	192	10	si(u	si(u	NOUN
cana-1582	192	11	)	)	PUNCT
cana-1582	192	12	is	be	AUX
cana-1582	192	13	not	not	PART
cana-1582	192	14	defined	define	VERB
cana-1582	192	15	for	for	ADP
cana-1582	192	16	0=	0=	NOUN
cana-1582	192	17	,	,	PUNCT
cana-1582	192	18	i.e.	i.e.	X
cana-1582	192	19	,	,	PUNCT
cana-1582	192	20	when	when	SCONJ
cana-1582	192	21	(	(	PUNCT
cana-1582	192	22	3	3	NUM
cana-1582	192	23	3	3	NUM
cana-1582	192	24	)	)	PUNCT
cana-1582	192	25	/	/	SYM
cana-1582	192	26	6	6	PROPN
cana-1582	193	1	=	=	SYM
cana-1582	193	2			PROPN
cana-1582	193	3	.	.	PUNCT
cana-1582	194	1	now	now	ADV
cana-1582	194	2	using	use	VERB
cana-1582	194	3	the	the	DET
cana-1582	194	4	continuity	continuity	NOUN
cana-1582	194	5	of	of	ADP
cana-1582	194	6	the	the	DET
cana-1582	194	7	second	second	ADJ
cana-1582	194	8	derivatives	derivative	NOUN
cana-1582	194	9	over	over	ADP
cana-1582	194	10	the	the	DET
cana-1582	194	11	intervals	interval	NOUN
cana-1582	194	12	[	[	X
cana-1582	194	13	xi-1	xi-1	NOUN
cana-1582	194	14	,	,	PUNCT
cana-1582	194	15	xi	xi	ADP
cana-1582	194	16	]	]	PUNCT
cana-1582	194	17	and	and	CCONJ
cana-1582	194	18	[	[	X
cana-1582	194	19	xi	xi	X
cana-1582	194	20	,	,	PUNCT
cana-1582	194	21	xi+1	xi+1	PROPN
cana-1582	194	22	]	]	PUNCT
cana-1582	194	23	,	,	PUNCT
cana-1582	194	24	we	we	PRON
cana-1582	194	25	obtain	obtain	VERB
cana-1582	194	26	the	the	DET
cana-1582	194	27	following	follow	VERB
cana-1582	194	28	relation	relation	NOUN
cana-1582	194	29	as	as	ADP
cana-1582	194	30	in	in	ADP
cana-1582	194	31	[	[	PUNCT
cana-1582	194	32	22	22	NUM
cana-1582	194	33	]	]	PUNCT
cana-1582	194	34	.	.	PUNCT
cana-1582	195	1			ADJ
cana-1582	195	2			NOUN
cana-1582	195	3	1	1	NUM
cana-1582	195	4	1	1	NUM
cana-1582	195	5	2	2	NUM
cana-1582	195	6	1	1	NUM
cana-1582	195	7	1	1	NUM
cana-1582	195	8	2	2	NUM
cana-1582	195	9	1	1	NUM
cana-1582	195	10	(	(	PUNCT
cana-1582	195	11	1)(3	1)(3	NUM
cana-1582	195	12	1	1	NUM
cana-1582	195	13	)	)	PUNCT
cana-1582	195	14	(	(	PUNCT
cana-1582	195	15	1	1	NUM
cana-1582	195	16	2	2	NUM
cana-1582	195	17	)	)	PUNCT
cana-1582	195	18	(	(	PUNCT
cana-1582	195	19	3	3	NUM
cana-1582	195	20	2	2	NUM
cana-1582	195	21	)	)	PUNCT
cana-1582	195	22	(	(	PUNCT
cana-1582	195	23	1)(2	1)(2	NUM
cana-1582	195	24	1	1	NUM
cana-1582	195	25	)	)	PUNCT
cana-1582	195	26	(	(	PUNCT
cana-1582	195	27	8	8	NUM
cana-1582	195	28	8	8	NUM
cana-1582	195	29	1	1	NUM
cana-1582	195	30	)	)	PUNCT
cana-1582	195	31	(	(	PUNCT
cana-1582	195	32	2	2	NUM
cana-1582	195	33	1	1	NUM
cana-1582	195	34	)	)	PUNCT
cana-1582	195	35	2	2	NUM
cana-1582	195	36	,	,	PUNCT
cana-1582	195	37	1,2	1,2	NUM
cana-1582	195	38	,	,	PUNCT
cana-1582	195	39	..	..	PUNCT
cana-1582	195	40	,	,	PUNCT
cana-1582	195	41	i	i	PRON
cana-1582	196	1	i	i	PRON
cana-1582	196	2	i	i	PRON
cana-1582	197	1	i	i	PRON
cana-1582	197	2	i	i	PRON
cana-1582	198	1	i	i	PRON
cana-1582	198	2	i	i	PRON
cana-1582	199	1	i	i	PRON
cana-1582	200	1	f	f	NOUN
cana-1582	201	1	f	f	NOUN
cana-1582	201	2	f	f	PROPN
cana-1582	201	3	h	h	NOUN
cana-1582	202	1	f	f	PROPN
cana-1582	202	2	f	f	PROPN
cana-1582	203	1	f	f	PROPN
cana-1582	203	2	h	h	NOUN
cana-1582	204	1	f	f	PROPN
cana-1582	204	2	f	f	PROPN
cana-1582	205	1	i	i	PRON
cana-1582	205	2	n	n	PROPN
cana-1582	205	3			ADJ
cana-1582	205	4			ADJ
cana-1582	205	5			ADJ
cana-1582	205	6			ADJ
cana-1582	205	7			ADJ
cana-1582	205	8			ADJ
cana-1582	205	9			ADJ
cana-1582	205	10			ADJ
cana-1582	205	11			ADJ
cana-1582	205	12			ADJ
cana-1582	205	13			ADJ
cana-1582	205	14			ADJ
cana-1582	205	15	−	−	NOUN
cana-1582	205	16	+	+	CCONJ
cana-1582	205	17	−	−	PROPN
cana-1582	206	1	+	+	CCONJ
cana-1582	206	2	−	−	PROPN
cana-1582	207	1	+	+	CCONJ
cana-1582	207	2	+	+	NUM
cana-1582	207	3	−	−	ADP
cana-1582	207	4	−	−	NUM
cana-1582	207	5	−	−	PROPN
cana-1582	208	1	+	+	CCONJ
cana-1582	208	2	−	−	PROPN
cana-1582	209	1	+	+	CCONJ
cana-1582	209	2	−	−	PROPN
cana-1582	209	3			ADJ
cana-1582	209	4			ADV
cana-1582	209	5			VERB
cana-1582	209	6	=	=	NUM
cana-1582	209	7	−	−	PROPN
cana-1582	209	8	−	−	PROPN
cana-1582	210	1	+	+	CCONJ
cana-1582	210	2	−	−	PROPN
cana-1582	211	1	+	+	CCONJ
cana-1582	211	2	+	+	CCONJ
cana-1582	211	3	−	−	PROPN
cana-1582	211	4			PROPN
cana-1582	211	5			PROPN
cana-1582	211	6	+	+	NOUN
cana-1582	211	7	−	−	PROPN
cana-1582	211	8	=	=	PUNCT
cana-1582	211	9	(	(	PUNCT
cana-1582	211	10	7	7	X
cana-1582	211	11	)	)	PUNCT
cana-1582	211	12	the	the	DET
cana-1582	211	13	above	above	ADJ
cana-1582	211	14	system	system	NOUN
cana-1582	211	15	of	of	ADP
cana-1582	211	16	n	n	PRON
cana-1582	211	17	linear	linear	ADJ
cana-1582	211	18	equations	equation	NOUN
cana-1582	211	19	will	will	AUX
cana-1582	211	20	determine	determine	VERB
cana-1582	211	21	f1	f1	NOUN
cana-1582	211	22	,	,	PUNCT
cana-1582	211	23	f2,	f2,	NOUN
cana-1582	211	24	..	..	PUNCT
cana-1582	211	25	,fn	,fn	NOUN
cana-1582	211	26	,	,	PUNCT
cana-1582	211	27	since	since	SCONJ
cana-1582	211	28	f0	f0	PROPN
cana-1582	211	29	and	and	CCONJ
cana-1582	211	30	fn+1	fn+1	NUM
cana-1582	211	31	,	,	PUNCT
cana-1582	211	32			PROPN
cana-1582	211	33			PROPN
cana-1582	211	34	1	1	NUM
cana-1582	211	35	0	0	NUM
cana-1582	212	1	n	n	NUM
cana-1582	213	1	i	i	PRON
cana-1582	214	1	i	i	PRON
cana-1582	214	2	f	f	PROPN
cana-1582	215	1	+	+	CCONJ
cana-1582	215	2	=	=	PUNCT
cana-1582	216	1			ADJ
cana-1582	216	2	and	and	CCONJ
cana-1582	216	3			PRON
cana-1582	216	4			PROPN
cana-1582	216	5	0	0	PUNCT
cana-1582	217	1	n	n	NUM
cana-1582	218	1	i	i	PRON
cana-1582	219	1	i	i	PROPN
cana-1582	219	2	f	f	PROPN
cana-1582	219	3	+	+	PROPN
cana-1582	219	4	=	=	SYM
cana-1582	219	5			PROPN
cana-1582	219	6	are	be	AUX
cana-1582	219	7	already	already	ADV
cana-1582	219	8	known	know	VERB
cana-1582	219	9	.	.	PUNCT
cana-1582	220	1	we	we	PRON
cana-1582	220	2	see	see	VERB
cana-1582	220	3	that	that	SCONJ
cana-1582	220	4	(	(	PUNCT
cana-1582	220	5	3	3	NUM
cana-1582	220	6	3	3	NUM
cana-1582	220	7	)	)	PUNCT
cana-1582	220	8	/	/	SYM
cana-1582	220	9	6	6	PROPN
cana-1582	220	10			VERB
cana-1582	220	11			PROPN
cana-1582	220	12	and	and	CCONJ
cana-1582	220	13	for	for	ADP
cana-1582	220	14	some	some	DET
cana-1582	220	15	simple	simple	ADJ
cana-1582	220	16	values	value	NOUN
cana-1582	220	17	of	of	ADP
cana-1582	220	18	0,1/	0,1/	NOUN
cana-1582	220	19	3.2	3.2	NUM
cana-1582	220	20	/	/	SYM
cana-1582	220	21	3,1	3,1	NUM
cana-1582	220	22	=	=	SYM
cana-1582	220	23	,	,	PUNCT
cana-1582	220	24	the	the	DET
cana-1582	220	25	coefficient	coefficient	NOUN
cana-1582	220	26	matrix	matrix	NOUN
cana-1582	220	27	in	in	ADP
cana-1582	220	28	the	the	DET
cana-1582	220	29	linear	linear	ADJ
cana-1582	220	30	system	system	NOUN
cana-1582	220	31	of	of	ADP
cana-1582	220	32	eqn	eqn	PROPN
cana-1582	220	33	(	(	PUNCT
cana-1582	220	34	7	7	X
cana-1582	220	35	)	)	PUNCT
cana-1582	220	36	is	be	AUX
cana-1582	220	37	nonsingular	nonsingular	ADJ
cana-1582	220	38	.	.	PUNCT
cana-1582	221	1	we	we	PRON
cana-1582	221	2	shall	shall	AUX
cana-1582	221	3	now	now	ADV
cana-1582	221	4	consider	consider	VERB
cana-1582	221	5	the	the	DET
cana-1582	221	6	simple	simple	ADJ
cana-1582	221	7	case	case	NOUN
cana-1582	221	8	=0	=0	NOUN
cana-1582	221	9	only	only	ADV
cana-1582	221	10	.	.	PUNCT
cana-1582	222	1	case	case	NOUN
cana-1582	222	2	=0	=0	VERB
cana-1582	222	3	the	the	DET
cana-1582	222	4	following	follow	VERB
cana-1582	222	5	explicit	explicit	ADJ
cana-1582	222	6	expression	expression	NOUN
cana-1582	222	7	over	over	ADP
cana-1582	222	8	the	the	DET
cana-1582	222	9	interval	interval	NOUN
cana-1582	222	10	1	1	NUM
cana-1582	222	11	[	[	PUNCT
cana-1582	222	12	,	,	PUNCT
cana-1582	222	13	]	]	PUNCT
cana-1582	223	1	i	i	PRON
cana-1582	223	2	i	i	VERB
cana-1582	223	3	x	x	VERB
cana-1582	223	4	x	x	PUNCT
cana-1582	223	5	+	+	CCONJ
cana-1582	223	6	represent	represent	VERB
cana-1582	223	7	the	the	DET
cana-1582	223	8	quartic	quartic	ADJ
cana-1582	223	9	spline	spline	NOUN
cana-1582	223	10	interpolant	interpolant	NOUN
cana-1582	223	11	,	,	PUNCT
cana-1582	223	12	2	2	NUM
cana-1582	223	13	3	3	NUM
cana-1582	223	14	4	4	NUM
cana-1582	223	15	(	(	PUNCT
cana-1582	223	16	)	)	PUNCT
cana-1582	223	17	,	,	PUNCT
cana-1582	223	18	....	....	PUNCT
cana-1582	224	1	i	i	PRON
cana-1582	224	2	i	i	PRON
cana-1582	225	1	i	i	PRON
cana-1582	225	2	i	i	PRON
cana-1582	226	1	i	i	PRON
cana-1582	227	1	i	i	PRON
cana-1582	227	2	s	s	VERB
cana-1582	227	3	u	u	NOUN
cana-1582	227	4	a	a	PRON
cana-1582	227	5	bu	bu	NOUN
cana-1582	227	6	c	c	NOUN
cana-1582	227	7	u	u	NOUN
cana-1582	227	8	d	d	X
cana-1582	227	9	u	u	X
cana-1582	227	10	e	e	NOUN
cana-1582	227	11	u=	u=	PROPN
cana-1582	227	12	+	+	CCONJ
cana-1582	228	1	+	+	PUNCT
cana-1582	228	2	+	+	PUNCT
cana-1582	228	3	+	+	CCONJ
cana-1582	228	4	(	(	PUNCT
cana-1582	228	5	8)	8)	NUM
cana-1582	228	6	where	where	SCONJ
cana-1582	228	7	1	1	NUM
cana-1582	228	8	2	2	NUM
cana-1582	228	9	2	2	NUM
cana-1582	228	10	1	1	NUM
cana-1582	228	11	1	1	NUM
cana-1582	228	12	2	2	NUM
cana-1582	228	13	1	1	NUM
cana-1582	228	14	1	1	NUM
cana-1582	228	15	(	(	PUNCT
cana-1582	228	16	)	)	PUNCT
cana-1582	228	17	/	/	PUNCT
cana-1582	228	18	,	,	PUNCT
cana-1582	228	19	(	(	PUNCT
cana-1582	228	20	)	)	PUNCT
cana-1582	228	21	,	,	PUNCT
cana-1582	228	22	,	,	PUNCT
cana-1582	228	23	,	,	PUNCT
cana-1582	228	24	,	,	PUNCT
cana-1582	228	25	4	4	NUM
cana-1582	228	26	4	4	NUM
cana-1582	228	27	3	3	NUM
cana-1582	228	28	,	,	PUNCT
cana-1582	228	29	3	3	NUM
cana-1582	228	30	3	3	NUM
cana-1582	228	31	2	2	NUM
cana-1582	228	32	/	/	SYM
cana-1582	228	33	2	2	NUM
cana-1582	229	1	i	i	PRON
cana-1582	229	2	i	i	PRON
cana-1582	230	1	i	i	PRON
cana-1582	230	2	i	i	PRON
cana-1582	231	1	i	i	PRON
cana-1582	231	2	i	i	PRON
cana-1582	232	1	i	i	PRON
cana-1582	232	2	i	i	PRON
cana-1582	233	1	i	i	PRON
cana-1582	233	2	i	i	PRON
cana-1582	234	1	i	i	PRON
cana-1582	234	2	i	i	PRON
cana-1582	235	1	i	i	PRON
cana-1582	235	2	i	i	PRON
cana-1582	236	1	i	i	PRON
cana-1582	236	2	i	i	PRON
cana-1582	237	1	i	i	PRON
cana-1582	237	2	i	i	PRON
cana-1582	238	1	i	i	PRON
cana-1582	238	2	i	i	PRON
cana-1582	239	1	i	i	PRON
cana-1582	239	2	u	u	VERB
cana-1582	239	3	x	x	X
cana-1582	240	1	x	x	VERB
cana-1582	240	2	h	h	NOUN
cana-1582	240	3	h	h	NOUN
cana-1582	241	1	x	x	PUNCT
cana-1582	241	2	x	x	PUNCT
cana-1582	241	3	a	a	DET
cana-1582	241	4	f	f	X
cana-1582	241	5	b	b	PROPN
cana-1582	241	6	hf	hf	PROPN
cana-1582	242	1	c	c	PROPN
cana-1582	242	2	h	h	NOUN
cana-1582	243	1	f	f	PROPN
cana-1582	244	1	d	d	X
cana-1582	244	2	f	f	X
cana-1582	245	1	f	f	X
cana-1582	245	2	hf	hf	INTJ
cana-1582	245	3	hf	hf	PROPN
cana-1582	245	4	h	h	PROPN
cana-1582	246	1	f	f	PROPN
cana-1582	246	2	e	e	X
cana-1582	246	3	f	f	PROPN
cana-1582	246	4	f	f	PROPN
cana-1582	246	5	hf	hf	INTJ
cana-1582	246	6	hf	hf	PROPN
cana-1582	246	7	h	h	PROPN
cana-1582	247	1	f	f	PROPN
cana-1582	248	1	+	+	CCONJ
cana-1582	249	1	+	+	PUNCT
cana-1582	250	1	+	+	PUNCT
cana-1582	250	2	+	+	PUNCT
cana-1582	250	3	+	+	PROPN
cana-1582	250	4	=	=	SYM
cana-1582	250	5	−	−	NOUN
cana-1582	250	6	=	=	PUNCT
cana-1582	250	7	−	−	PROPN
cana-1582	250	8			NOUN
cana-1582	250	9			ADJ
cana-1582	250	10	=	=	PROPN
cana-1582	250	11	=	=	PUNCT
cana-1582	250	12	=	=	SYM
cana-1582	250	13			NOUN
cana-1582	250	14	=	=	VERB
cana-1582	250	15	−	−	PROPN
cana-1582	251	1	+	+	CCONJ
cana-1582	251	2	−	−	PROPN
cana-1582	251	3	−	−	NOUN
cana-1582	251	4	−	−	PROPN
cana-1582	252	1			PROPN
cana-1582	252	2			ADV
cana-1582	252	3	=	=	PROPN
cana-1582	252	4	−	−	PROPN
cana-1582	253	1	+	+	CCONJ
cana-1582	254	1	+	+	PUNCT
cana-1582	254	2	+	+	CCONJ
cana-1582	254	3	(	(	PUNCT
cana-1582	254	4	9	9	NUM
cana-1582	254	5	)	)	PUNCT
cana-1582	254	6	and	and	CCONJ
cana-1582	254	7	,	,	PUNCT
cana-1582	254	8			PROPN
cana-1582	254	9			PROPN
cana-1582	254	10	1	1	NUM
cana-1582	254	11	n	n	NUM
cana-1582	255	1	i	i	PRON
cana-1582	256	1	i	i	PRON
cana-1582	256	2	f	f	AUX
cana-1582	257	1	=	=	PRON
cana-1582	257	2	can	can	AUX
cana-1582	257	3	be	be	AUX
cana-1582	257	4	evaluated	evaluate	VERB
cana-1582	257	5	by	by	ADP
cana-1582	257	6	the	the	DET
cana-1582	257	7	below	below	NOUN
cana-1582	257	8	said	say	VERB
cana-1582	257	9	recurrence	recurrence	NOUN
cana-1582	257	10	relation	relation	NOUN
cana-1582	257	11	for	for	ADP
cana-1582	257	12	the	the	DET
cana-1582	257	13	quartic	quartic	ADJ
cana-1582	257	14	spline	spline	NOUN
cana-1582	257	15	from	from	ADP
cana-1582	257	16	eqn(5.2.7	eqn(5.2.7	PROPN
cana-1582	257	17	)	)	PUNCT
cana-1582	257	18	,	,	PUNCT
cana-1582	257	19	2	2	NUM
cana-1582	257	20	1	1	NUM
cana-1582	257	21	1	1	NUM
cana-1582	257	22	1	1	NUM
cana-1582	257	23	1	1	NUM
cana-1582	257	24	(	(	PUNCT
cana-1582	257	25	/	/	SYM
cana-1582	257	26	2	2	NUM
cana-1582	257	27	)	)	PUNCT
cana-1582	257	28	(	(	PUNCT
cana-1582	257	29	)	)	PUNCT
cana-1582	257	30	(	(	PUNCT
cana-1582	257	31	/12	/12	NOUN
cana-1582	257	32	)	)	PUNCT
cana-1582	257	33	(	(	PUNCT
cana-1582	257	34	)	)	PUNCT
cana-1582	257	35	(	(	PUNCT
cana-1582	257	36	1,2	1,2	NUM
cana-1582	257	37	,	,	PUNCT
cana-1582	257	38	...	...	PUNCT
cana-1582	257	39	,	,	PUNCT
cana-1582	257	40	)	)	PUNCT
cana-1582	258	1	i	i	PRON
cana-1582	258	2	i	i	PRON
cana-1582	259	1	i	i	PRON
cana-1582	259	2	i	i	PRON
cana-1582	260	1	i	i	PRON
cana-1582	261	1	i	i	PRON
cana-1582	262	1	f	f	NOUN
cana-1582	263	1	f	f	NOUN
cana-1582	263	2	h	h	NOUN
cana-1582	264	1	f	f	PROPN
cana-1582	264	2	f	f	PROPN
cana-1582	264	3	h	h	NOUN
cana-1582	265	1	f	f	PROPN
cana-1582	265	2	f	f	PROPN
cana-1582	265	3	i	i	PRON
cana-1582	265	4	n	n	ADV
cana-1582	265	5	−	−	PROPN
cana-1582	265	6	−	−	PROPN
cana-1582	266	1	+	+	CCONJ
cana-1582	266	2	−	−	PROPN
cana-1582	266	3			PROPN
cana-1582	266	4			CCONJ
cana-1582	266	5			PROPN
cana-1582	266	6	=	=	NOUN
cana-1582	266	7	+	+	CCONJ
cana-1582	266	8	+	+	PUNCT
cana-1582	266	9	+	+	PUNCT
cana-1582	266	10	+	+	CCONJ
cana-1582	266	11	=	=	SYM
cana-1582	266	12	(	(	PUNCT
cana-1582	266	13	10	10	NUM
cana-1582	266	14	)	)	PUNCT
cana-1582	266	15	by	by	ADP
cana-1582	266	16	forward	forward	ADJ
cana-1582	266	17	recurrence	recurrence	PROPN
cana-1582	266	18	computing	computing	NOUN
cana-1582	266	19	.	.	PUNCT
cana-1582	267	1	numerical	numerical	ADJ
cana-1582	267	2	integration	integration	NOUN
cana-1582	267	3	over	over	ADP
cana-1582	267	4	curved	curved	ADJ
cana-1582	267	5	domains	domain	NOUN
cana-1582	267	6	in	in	ADP
cana-1582	267	7	2	2	NUM
cana-1582	267	8	-	-	PUNCT
cana-1582	267	9	space	space	NOUN
cana-1582	267	10	communications	communication	NOUN
cana-1582	267	11	on	on	ADP
cana-1582	267	12	applied	apply	VERB
cana-1582	267	13	nonlinear	nonlinear	ADJ
cana-1582	267	14	analysis	analysis	NOUN
cana-1582	267	15	issn	issn	NOUN
cana-1582	267	16	:	:	PUNCT
cana-1582	267	17	1074	1074	NUM
cana-1582	267	18	-	-	PUNCT
cana-1582	267	19	133x	133x	NUM
cana-1582	267	20	vol	vol	NOUN
cana-1582	267	21	31	31	NUM
cana-1582	267	22	no	no	NOUN
cana-1582	267	23	.	.	PUNCT
cana-1582	268	1	8s	8s	PROPN
cana-1582	268	2	(	(	PUNCT
cana-1582	268	3	2024	2024	NUM
cana-1582	268	4	)	)	PUNCT
cana-1582	268	5	729	729	NUM
cana-1582	268	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1582	268	7	consider	consider	VERB
cana-1582	268	8	the	the	DET
cana-1582	268	9	integral	integral	ADJ
cana-1582	268	10	[	[	PUNCT
cana-1582	268	11	44	44	NUM
cana-1582	268	12	,	,	PUNCT
cana-1582	268	13	3	3	NUM
cana-1582	268	14	]	]	PUNCT
cana-1582	268	15	(	(	PUNCT
cana-1582	268	16	,	,	PUNCT
cana-1582	268	17	)	)	PUNCT
cana-1582	268	18	xy	xy	PROPN
cana-1582	269	1	def	def	PROPN
cana-1582	269	2	ii	ii	PROPN
cana-1582	269	3	f	f	PROPN
cana-1582	269	4	x	x	SYM
cana-1582	269	5	y	y	PROPN
cana-1582	269	6	dxdy	dxdy	PROPN
cana-1582	269	7			PROPN
cana-1582	269	8	=	=	X
cana-1582	269	9			ADJ
cana-1582	269	10	(	(	PUNCT
cana-1582	269	11	11	11	NUM
cana-1582	269	12	)	)	PUNCT
cana-1582	269	13	where	where	SCONJ
cana-1582	269	14	,	,	PUNCT
cana-1582	269	15	xy	xy	PROPN
cana-1582	269	16			PROPN
cana-1582	269	17	is	be	AUX
cana-1582	269	18	the	the	DET
cana-1582	269	19	curved	curved	ADJ
cana-1582	269	20	domain	domain	NOUN
cana-1582	269	21	.	.	PUNCT
cana-1582	270	1	let	let	VERB
cana-1582	270	2	’s	’s	NOUN
cana-1582	270	3	denote	denote	VERB
cana-1582	270	4	the	the	DET
cana-1582	270	5	closed	closed	ADJ
cana-1582	270	6	boundary	boundary	NOUN
cana-1582	270	7	of	of	ADP
cana-1582	270	8	the	the	DET
cana-1582	270	9	domain	domain	NOUN
cana-1582	270	10	xy	xy	X
cana-1582	270	11			PROPN
cana-1582	270	12	,	,	PUNCT
cana-1582	270	13	by	by	ADP
cana-1582	270	14	xy	xy	PROPN
cana-1582	270	15			NOUN
cana-1582	270	16	.	.	PUNCT
cana-1582	271	1	we	we	PRON
cana-1582	271	2	discretise	discretise	VERB
cana-1582	271	3	this	this	DET
cana-1582	271	4	boundary	boundary	NOUN
cana-1582	271	5	xy	xy	PROPN
cana-1582	271	6			NOUN
cana-1582	271	7	into	into	ADP
cana-1582	271	8	n	n	CCONJ
cana-1582	271	9	curved	curved	ADJ
cana-1582	271	10	arcs	arc	NOUN
cana-1582	271	11	by	by	ADP
cana-1582	271	12	points	point	NOUN
cana-1582	271	13	(	(	PUNCT
cana-1582	271	14	(	(	PUNCT
cana-1582	271	15	,	,	PUNCT
cana-1582	271	16	)	)	PUNCT
cana-1582	271	17	,	,	PUNCT
cana-1582	271	18	1,2	1,2	NUM
cana-1582	271	19	,	,	PUNCT
cana-1582	271	20	..	..	PUNCT
cana-1582	271	21	,	,	PUNCT
cana-1582	271	22	1	1	NUM
cana-1582	271	23	)	)	PUNCT
cana-1582	271	24	.	.	PUNCT
cana-1582	272	1	k	k	PROPN
cana-1582	273	1	k	k	NOUN
cana-1582	273	2	x	x	PUNCT
cana-1582	273	3	y	y	PROPN
cana-1582	273	4	k	k	PROPN
cana-1582	273	5	n=	n=	PROPN
cana-1582	274	1	+	+	CCONJ
cana-1582	274	2	let	let	VERB
cana-1582	274	3	the	the	DET
cana-1582	274	4	i	i	PROPN
cana-1582	274	5	-	-	PUNCT
cana-1582	274	6	th	th	VERB
cana-1582	274	7	arc	arc	NOUN
cana-1582	274	8	be	be	AUX
cana-1582	274	9	joined	join	VERB
cana-1582	274	10	by	by	ADP
cana-1582	274	11	the	the	DET
cana-1582	274	12	vertices	vertex	NOUN
cana-1582	274	13	(	(	PUNCT
cana-1582	274	14	,	,	PUNCT
cana-1582	274	15	)	)	PUNCT
cana-1582	275	1	i	i	PRON
cana-1582	275	2	i	i	PRON
cana-1582	276	1	i	i	PRON
cana-1582	277	1	v	v	VERB
cana-1582	277	2	x	x	X
cana-1582	277	3	y=	y=	NOUN
cana-1582	277	4	and	and	CCONJ
cana-1582	277	5	1	1	NUM
cana-1582	277	6	1	1	NUM
cana-1582	277	7	1	1	NUM
cana-1582	277	8	(	(	PUNCT
cana-1582	277	9	,	,	PUNCT
cana-1582	277	10	)	)	PUNCT
cana-1582	278	1	i	i	PRON
cana-1582	278	2	i	i	PRON
cana-1582	279	1	i	i	PRON
cana-1582	279	2	v	v	VERB
cana-1582	279	3	x	x	PUNCT
cana-1582	279	4	y	y	NOUN
cana-1582	279	5	+	+	PUNCT
cana-1582	280	1	+	+	PUNCT
cana-1582	280	2	+	+	CCONJ
cana-1582	280	3	=	=	X
cana-1582	280	4	and	and	CCONJ
cana-1582	280	5	denoted	denote	VERB
cana-1582	280	6	as	as	ADP
cana-1582	280	7	,	,	PUNCT
cana-1582	280	8	1i	1i	NUM
cana-1582	280	9	i	i	PRON
cana-1582	280	10			PROPN
cana-1582	280	11	+	+	CCONJ
cana-1582	280	12			ADJ
cana-1582	280	13	.	.	PUNCT
cana-1582	281	1	thus	thus	ADV
cana-1582	281	2	,	,	PUNCT
cana-1582	281	3	we	we	PRON
cana-1582	281	4	can	can	AUX
cana-1582	281	5	now	now	ADV
cana-1582	281	6	represent	represent	VERB
cana-1582	281	7	the	the	DET
cana-1582	281	8	closed	closed	ADJ
cana-1582	281	9	boundary	boundary	NOUN
cana-1582	281	10	xy	xy	PROPN
cana-1582	282	1			NOUN
cana-1582	282	2	as	as	ADP
cana-1582	282	3	a	a	DET
cana-1582	282	4	sum	sum	NOUN
cana-1582	282	5	of	of	ADP
cana-1582	282	6	n	n	CCONJ
cana-1582	282	7	curved	curved	ADJ
cana-1582	282	8	arcs	arc	NOUN
cana-1582	282	9	:	:	PUNCT
cana-1582	282	10	,	,	PUNCT
cana-1582	282	11	1	1	NUM
cana-1582	282	12	1	1	NUM
cana-1582	283	1	n	n	NOUN
cana-1582	283	2	xy	xy	INTJ
cana-1582	284	1	i	i	PRON
cana-1582	284	2	i	i	PRON
cana-1582	285	1	i	i	PRON
cana-1582	285	2			VERB
cana-1582	285	3			ADJ
cana-1582	285	4	+	+	NOUN
cana-1582	285	5	=	=	NOUN
cana-1582	285	6			ADJ
cana-1582	285	7	=	=	SYM
cana-1582	285	8			PROPN
cana-1582	285	9	(	(	PUNCT
cana-1582	285	10	12	12	NUM
cana-1582	285	11	)	)	PUNCT
cana-1582	285	12	here	here	ADV
cana-1582	285	13	,	,	PUNCT
cana-1582	285	14	each	each	DET
cana-1582	285	15	,	,	PUNCT
cana-1582	285	16	1i	1i	NOUN
cana-1582	285	17	i	i	PRON
cana-1582	286	1			PROPN
cana-1582	286	2	+	+	CCONJ
cana-1582	286	3			ADJ
cana-1582	286	4	signifies	signify	VERB
cana-1582	286	5	a	a	DET
cana-1582	286	6	specific	specific	ADJ
cana-1582	286	7	curved	curved	ADJ
cana-1582	286	8	arc	arc	NOUN
cana-1582	286	9	bounded	bound	VERB
cana-1582	286	10	by	by	ADP
cana-1582	286	11	the	the	DET
cana-1582	286	12	vertices	vertex	NOUN
cana-1582	286	13	(	(	PUNCT
cana-1582	286	14	,	,	PUNCT
cana-1582	286	15	)	)	PUNCT
cana-1582	287	1	i	i	PRON
cana-1582	287	2	i	i	PRON
cana-1582	288	1	i	i	PRON
cana-1582	289	1	v	v	VERB
cana-1582	289	2	x	x	X
cana-1582	289	3	y=	y=	NOUN
cana-1582	289	4	and	and	CCONJ
cana-1582	289	5	1	1	NUM
cana-1582	289	6	1	1	NUM
cana-1582	289	7	1	1	NUM
cana-1582	289	8	(	(	PUNCT
cana-1582	289	9	,	,	PUNCT
cana-1582	289	10	)	)	PUNCT
cana-1582	290	1	i	i	PRON
cana-1582	290	2	i	i	PRON
cana-1582	291	1	i	i	PRON
cana-1582	291	2	v	v	VERB
cana-1582	291	3	x	x	PUNCT
cana-1582	291	4	y	y	NOUN
cana-1582	291	5	+	+	PUNCT
cana-1582	292	1	+	+	PUNCT
cana-1582	292	2	+	+	CCONJ
cana-1582	292	3	=	=	NOUN
cana-1582	292	4	.	.	PUNCT
cana-1582	293	1	hence	hence	ADV
cana-1582	293	2	,	,	PUNCT
cana-1582	293	3	by	by	ADP
cana-1582	293	4	the	the	DET
cana-1582	293	5	use	use	NOUN
cana-1582	293	6	of	of	ADP
cana-1582	293	7	the	the	DET
cana-1582	293	8	boundary	boundary	ADJ
cana-1582	293	9	integration	integration	NOUN
cana-1582	293	10	formula	formula	NOUN
cana-1582	293	11	of	of	ADP
cana-1582	293	12	green	green	PROPN
cana-1582	293	13	’s	’s	PART
cana-1582	293	14	theorem	theorem	NOUN
cana-1582	293	15	for	for	ADP
cana-1582	293	16	the	the	DET
cana-1582	293	17	closed	closed	ADJ
cana-1582	293	18	boundary	boundary	NOUN
cana-1582	293	19	xy	xy	PROPN
cana-1582	294	1			NOUN
cana-1582	294	2	and	and	CCONJ
cana-1582	294	3	the	the	DET
cana-1582	294	4	relation	relation	NOUN
cana-1582	294	5	of	of	ADP
cana-1582	294	6	eqn	eqn	PROPN
cana-1582	294	7	(	(	PUNCT
cana-1582	294	8	12	12	NUM
cana-1582	294	9	)	)	PUNCT
cana-1582	294	10	,	,	PUNCT
cana-1582	294	11	we	we	PRON
cana-1582	294	12	obtain	obtain	VERB
cana-1582	294	13	:	:	PUNCT
cana-1582	294	14	,	,	PUNCT
cana-1582	294	15	1	1	NUM
cana-1582	294	16	1	1	NUM
cana-1582	295	1	i	i	PRON
cana-1582	295	2	i	i	PRON
cana-1582	295	3	=	=	PUNCT
cana-1582	295	4	(	(	PUNCT
cana-1582	295	5	,	,	PUNCT
cana-1582	295	6	)	)	PUNCT
cana-1582	295	7	(	(	PUNCT
cana-1582	295	8	,	,	PUNCT
cana-1582	295	9	)	)	PUNCT
cana-1582	296	1	xy	xy	INTJ
cana-1582	297	1	i	i	PRON
cana-1582	297	2	i	i	PRON
cana-1582	298	1	n	n	VERB
cana-1582	299	1	i	i	PRON
cana-1582	299	2	f	f	NOUN
cana-1582	299	3	x	x	VERB
cana-1582	299	4	y	y	PROPN
cana-1582	299	5	dxdy	dxdy	PROPN
cana-1582	299	6	x	x	PROPN
cana-1582	300	1	y	y	PROPN
cana-1582	300	2	dy	dy	ADP
cana-1582	300	3			PROPN
cana-1582	300	4			PROPN
cana-1582	300	5	+	+	NOUN
cana-1582	300	6	=	=	NOUN
cana-1582	300	7			ADJ
cana-1582	300	8	=	=	SYM
cana-1582	300	9			X
cana-1582	300	10			PUNCT
cana-1582	300	11	(	(	PUNCT
cana-1582	300	12	13	13	NUM
cana-1582	300	13	)	)	PUNCT
cana-1582	300	14	where	where	SCONJ
cana-1582	300	15	(	(	PUNCT
cana-1582	300	16	,	,	PUNCT
cana-1582	300	17	)	)	PUNCT
cana-1582	300	18	(	(	PUNCT
cana-1582	300	19	,	,	PUNCT
cana-1582	300	20	)	)	PUNCT
cana-1582	300	21	x	x	PUNCT
cana-1582	301	1	x	x	PUNCT
cana-1582	301	2	y	y	NOUN
cana-1582	301	3	f	f	PROPN
cana-1582	301	4	u	u	PROPN
cana-1582	301	5	y	y	PROPN
cana-1582	301	6	du	du	X
cana-1582	301	7			X
cana-1582	301	8			PROPN
cana-1582	301	9	=	=	SYM
cana-1582	301	10			PUNCT
cana-1582	301	11	(	(	PUNCT
cana-1582	301	12	14	14	NUM
cana-1582	301	13	)	)	PUNCT
cana-1582	301	14	in	in	ADP
cana-1582	301	15	which	which	PRON
cana-1582	301	16			ADJ
cana-1582	301	17	is	be	AUX
cana-1582	301	18	fixed	fix	VERB
cana-1582	301	19	,	,	PUNCT
cana-1582	301	20	i	i	PROPN
cana-1582	301	21	x	x	PROPN
cana-1582	301	22			PROPN
cana-1582	301	23	and	and	CCONJ
cana-1582	301	24	arbitrary	arbitrary	ADJ
cana-1582	301	25	.	.	PUNCT
cana-1582	302	1	let	let	VERB
cana-1582	302	2	us	we	PRON
cana-1582	302	3	now	now	ADV
cana-1582	302	4	choose	choose	VERB
cana-1582	302	5	the	the	DET
cana-1582	302	6	replacement	replacement	NOUN
cana-1582	302	7	2	2	NUM
cana-1582	302	8	2	2	NUM
cana-1582	302	9	x	x	SYM
cana-1582	302	10	x	x	PUNCT
cana-1582	302	11	u	u	NOUN
cana-1582	302	12	s	s	PART
cana-1582	302	13			NOUN
cana-1582	302	14	−	−	X
cana-1582	303	1	+	+	ADJ
cana-1582	303	2			NOUN
cana-1582	303	3			NOUN
cana-1582	303	4			NOUN
cana-1582	303	5			NOUN
cana-1582	303	6	=	=	PUNCT
cana-1582	304	1	+	+	CCONJ
cana-1582	304	2			PROPN
cana-1582	304	3			PROPN
cana-1582	305	1			PROPN
cana-1582	305	2			PROPN
cana-1582	306	1			ADJ
cana-1582	306	2			PROPN
cana-1582	306	3			PROPN
cana-1582	306	4			NOUN
cana-1582	306	5	(	(	PUNCT
cana-1582	306	6	15	15	NUM
cana-1582	306	7	)	)	PUNCT
cana-1582	306	8	using	use	VERB
cana-1582	306	9	for	for	ADP
cana-1582	306	10	u	u	NOUN
cana-1582	306	11	from	from	ADP
cana-1582	306	12	eqn	eqn	PROPN
cana-1582	306	13	(	(	PUNCT
cana-1582	306	14	15	15	NUM
cana-1582	306	15	)	)	PUNCT
cana-1582	306	16	into	into	ADP
cana-1582	306	17	eqn	eqn	NOUN
cana-1582	306	18	(	(	PUNCT
cana-1582	306	19	14	14	NUM
cana-1582	306	20	)	)	PUNCT
cana-1582	306	21	,	,	PUNCT
cana-1582	306	22	we	we	PRON
cana-1582	306	23	have	have	VERB
cana-1582	306	24	1	1	NUM
cana-1582	306	25	1	1	NUM
cana-1582	306	26	(	(	PUNCT
cana-1582	306	27	,	,	PUNCT
cana-1582	306	28	)	)	PUNCT
cana-1582	306	29	,	,	PUNCT
cana-1582	306	30	2	2	NUM
cana-1582	306	31	2	2	NUM
cana-1582	306	32	2	2	NUM
cana-1582	306	33	x	x	NOUN
cana-1582	306	34	x	x	SYM
cana-1582	306	35	x	x	PUNCT
cana-1582	306	36	x	x	PUNCT
cana-1582	306	37	y	y	NOUN
cana-1582	306	38	f	f	PROPN
cana-1582	306	39	s	s	PROPN
cana-1582	306	40	y	y	PROPN
cana-1582	306	41	ds	ds	ADJ
cana-1582	306	42			NOUN
cana-1582	306	43			X
cana-1582	306	44			X
cana-1582	306	45	−	−	PROPN
cana-1582	306	46			NOUN
cana-1582	306	47	−	−	NOUN
cana-1582	306	48	−	−	PROPN
cana-1582	307	1	+	+	ADJ
cana-1582	307	2			NOUN
cana-1582	307	3			NOUN
cana-1582	307	4			NOUN
cana-1582	307	5			PROPN
cana-1582	307	6			NOUN
cana-1582	307	7			NOUN
cana-1582	307	8			PROPN
cana-1582	307	9	=	=	PUNCT
cana-1582	308	1	+	+	CCONJ
cana-1582	308	2			PROPN
cana-1582	308	3			PROPN
cana-1582	309	1			PROPN
cana-1582	310	1			INTJ
cana-1582	311	1			PROPN
cana-1582	311	2			NOUN
cana-1582	312	1			PROPN
cana-1582	312	2			ADJ
cana-1582	312	3			PROPN
cana-1582	312	4			PROPN
cana-1582	312	5			NOUN
cana-1582	312	6			NOUN
cana-1582	312	7			NOUN
cana-1582	312	8			NOUN
cana-1582	312	9			PUNCT
cana-1582	312	10	(	(	PUNCT
cana-1582	312	11	16	16	NUM
cana-1582	312	12	)	)	PUNCT
cana-1582	312	13	further	far	ADV
cana-1582	312	14	by	by	ADP
cana-1582	312	15	using	use	VERB
cana-1582	312	16	(	(	PUNCT
cana-1582	312	17	,	,	PUNCT
cana-1582	312	18	)	)	PUNCT
cana-1582	312	19	x	x	PROPN
cana-1582	312	20	y	y	PROPN
cana-1582	312	21	from	from	ADP
cana-1582	312	22	eqn	eqn	PROPN
cana-1582	312	23	(	(	PUNCT
cana-1582	312	24	16	16	NUM
cana-1582	312	25	)	)	PUNCT
cana-1582	312	26	into	into	ADP
cana-1582	312	27	eqn	eqn	NOUN
cana-1582	312	28	(	(	PUNCT
cana-1582	312	29	13	13	NUM
cana-1582	312	30	)	)	PUNCT
cana-1582	312	31	,	,	PUNCT
cana-1582	312	32	we	we	PRON
cana-1582	312	33	obtain	obtain	VERB
cana-1582	312	34	,	,	PUNCT
cana-1582	312	35	1	1	NUM
cana-1582	312	36	,	,	PUNCT
cana-1582	312	37	1	1	NUM
cana-1582	312	38	1	1	NUM
cana-1582	312	39	1	1	NUM
cana-1582	312	40	1	1	NUM
cana-1582	312	41	1	1	NUM
cana-1582	312	42	1	1	NUM
cana-1582	312	43	1	1	NUM
cana-1582	313	1	i	i	PRON
cana-1582	313	2	i	i	PRON
cana-1582	313	3	(	(	PUNCT
cana-1582	313	4	,	,	PUNCT
cana-1582	313	5	)	)	PUNCT
cana-1582	313	6	ˆ	ˆ	NOUN
cana-1582	313	7	ˆ	ˆ	NOUN
cana-1582	313	8	ˆ	ˆ	ADJ
cana-1582	313	9	(	(	PUNCT
cana-1582	313	10	)	)	PUNCT
cana-1582	313	11	(	(	PUNCT
cana-1582	313	12	)	)	PUNCT
cana-1582	313	13	(	(	PUNCT
cana-1582	313	14	)	)	PUNCT
cana-1582	313	15	ˆ	ˆ	NOUN
cana-1582	313	16	,	,	PUNCT
cana-1582	313	17	(	(	PUNCT
cana-1582	313	18	)	)	PUNCT
cana-1582	313	19	2	2	NUM
cana-1582	313	20	2	2	NUM
cana-1582	313	21	2	2	NUM
cana-1582	313	22	ˆ	ˆ	NOUN
cana-1582	313	23	ˆ	ˆ	NOUN
cana-1582	313	24	ˆ	ˆ	ADJ
cana-1582	313	25	(	(	PUNCT
cana-1582	313	26	)	)	PUNCT
cana-1582	313	27	(	(	PUNCT
cana-1582	313	28	)	)	PUNCT
cana-1582	313	29	(	(	PUNCT
cana-1582	313	30	)	)	PUNCT
cana-1582	313	31	ˆ	ˆ	NOUN
cana-1582	313	32	,	,	PUNCT
cana-1582	313	33	(	(	PUNCT
cana-1582	313	34	)	)	PUNCT
cana-1582	313	35	2	2	NUM
cana-1582	313	36	2	2	NUM
cana-1582	313	37	2	2	NUM
cana-1582	314	1	i	i	PRON
cana-1582	314	2	i	i	PRON
cana-1582	315	1	i	i	PRON
cana-1582	315	2	i	i	PRON
cana-1582	316	1	i	i	VERB
cana-1582	316	2	i	i	PRON
cana-1582	317	1	n	n	VERB
cana-1582	318	1	i	i	PRON
cana-1582	319	1	n	n	VERB
cana-1582	320	1	i	i	PRON
cana-1582	321	1	i	i	PRON
cana-1582	322	1	i	i	PRON
cana-1582	323	1	i	i	PRON
cana-1582	324	1	i	i	PRON
cana-1582	325	1	yn	yn	VERB
cana-1582	326	1	i	i	PRON
cana-1582	326	2	i	i	PRON
cana-1582	327	1	i	i	PRON
cana-1582	327	2	i	i	PRON
cana-1582	328	1	i	i	VERB
cana-1582	329	1	y	y	VERB
cana-1582	329	2	x	x	VERB
cana-1582	329	3	y	y	NOUN
cana-1582	329	4	dy	dy	X
cana-1582	329	5	x	x	SYM
cana-1582	329	6	t	t	PROPN
cana-1582	329	7	x	x	SYM
cana-1582	329	8	t	t	PROPN
cana-1582	329	9	x	x	SYM
cana-1582	329	10	t	t	PROPN
cana-1582	329	11	f	f	PROPN
cana-1582	329	12	s	s	PROPN
cana-1582	329	13	y	y	PROPN
cana-1582	329	14	t	t	X
cana-1582	329	15	ds	ds	NOUN
cana-1582	329	16	dy	dy	X
cana-1582	329	17	x	x	SYM
cana-1582	329	18	t	t	PROPN
cana-1582	329	19	x	x	SYM
cana-1582	329	20	t	t	PROPN
cana-1582	329	21	x	x	SYM
cana-1582	329	22	t	t	PROPN
cana-1582	329	23	f	f	PROPN
cana-1582	329	24	s	s	PROPN
cana-1582	329	25	y	y	PROPN
cana-1582	329	26	t	t	X
cana-1582	329	27	ds	ds	X
cana-1582	329	28			PROPN
cana-1582	329	29			ADJ
cana-1582	329	30			NOUN
cana-1582	329	31			X
cana-1582	329	32			X
cana-1582	329	33			X
cana-1582	329	34			X
cana-1582	329	35			X
cana-1582	329	36	+	+	PUNCT
cana-1582	330	1	+	+	PUNCT
cana-1582	330	2	+	+	CCONJ
cana-1582	330	3	=	=	NOUN
cana-1582	330	4			ADJ
cana-1582	330	5	=	=	SYM
cana-1582	330	6			ADJ
cana-1582	330	7	−	−	PROPN
cana-1582	330	8	=	=	SYM
cana-1582	330	9	−	−	PROPN
cana-1582	330	10	=	=	SYM
cana-1582	331	1			NUM
cana-1582	331	2			PROPN
cana-1582	332	1			PROPN
cana-1582	332	2	−	−	NOUN
cana-1582	332	3	−	−	PROPN
cana-1582	333	1	+	+	ADJ
cana-1582	333	2			NOUN
cana-1582	333	3			NOUN
cana-1582	333	4			NOUN
cana-1582	333	5			PROPN
cana-1582	333	6			NOUN
cana-1582	333	7			NOUN
cana-1582	333	8	=	=	PUNCT
cana-1582	334	1	+	+	NOUN
cana-1582	334	2			NOUN
cana-1582	334	3			NOUN
cana-1582	335	1			PROPN
cana-1582	335	2			PROPN
cana-1582	336	1			INTJ
cana-1582	336	2			PROPN
cana-1582	336	3			NOUN
cana-1582	337	1			PROPN
cana-1582	337	2			ADJ
cana-1582	337	3			PROPN
cana-1582	337	4			PROPN
cana-1582	337	5			NOUN
cana-1582	337	6			PROPN
cana-1582	337	7			NOUN
cana-1582	337	8			PROPN
cana-1582	337	9			PROPN
cana-1582	337	10			NOUN
cana-1582	337	11	−	−	NOUN
cana-1582	337	12	−	−	PROPN
cana-1582	338	1	+	+	ADJ
cana-1582	338	2			NOUN
cana-1582	338	3			NOUN
cana-1582	338	4			NOUN
cana-1582	338	5			PROPN
cana-1582	338	6			NOUN
cana-1582	338	7			NOUN
cana-1582	338	8	=	=	PUNCT
cana-1582	339	1	+	+	CCONJ
cana-1582	339	2			PROPN
cana-1582	339	3			PROPN
cana-1582	340	1			PROPN
cana-1582	341	1			INTJ
cana-1582	342	1			PROPN
cana-1582	342	2			NOUN
cana-1582	343	1			PROPN
cana-1582	343	2			ADJ
cana-1582	343	3			PROPN
cana-1582	343	4			PROPN
cana-1582	343	5			NOUN
cana-1582	343	6			NOUN
cana-1582	343	7			NOUN
cana-1582	343	8			NOUN
cana-1582	343	9			X
cana-1582	343	10			PUNCT
cana-1582	343	11			X
cana-1582	343	12			PUNCT
cana-1582	343	13			PUNCT
cana-1582	343	14			X
cana-1582	343	15			SYM
cana-1582	343	16	1	1	NUM
cana-1582	343	17	1	1	NUM
cana-1582	343	18	(	(	PUNCT
cana-1582	343	19	)	)	PUNCT
cana-1582	344	1	i	i	PRON
cana-1582	344	2	y	y	PROPN
cana-1582	345	1	t	t	INTJ
cana-1582	345	2	dt	dt	X
cana-1582	346	1			PROPN
cana-1582	346	2			ADJ
cana-1582	346	3			PROPN
cana-1582	346	4			NOUN
cana-1582	346	5			AUX
cana-1582	346	6			PROPN
cana-1582	346	7			X
cana-1582	346	8	(	(	PUNCT
cana-1582	346	9	17	17	NUM
cana-1582	346	10	)	)	PUNCT
cana-1582	346	11	communications	communication	NOUN
cana-1582	346	12	on	on	ADP
cana-1582	346	13	applied	apply	VERB
cana-1582	346	14	nonlinear	nonlinear	ADJ
cana-1582	346	15	analysis	analysis	NOUN
cana-1582	346	16	issn	issn	NOUN
cana-1582	346	17	:	:	PUNCT
cana-1582	346	18	1074	1074	NUM
cana-1582	346	19	-	-	PUNCT
cana-1582	346	20	133x	133x	NUM
cana-1582	346	21	vol	vol	NOUN
cana-1582	346	22	31	31	NUM
cana-1582	346	23	no	no	NOUN
cana-1582	346	24	.	.	PUNCT
cana-1582	347	1	8s	8s	PROPN
cana-1582	347	2	(	(	PUNCT
cana-1582	347	3	2024	2024	NUM
cana-1582	347	4	)	)	PUNCT
cana-1582	347	5	730	730	NUM
cana-1582	347	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1582	347	7	where	where	SCONJ
cana-1582	347	8	,	,	PUNCT
cana-1582	347	9	ˆ	ˆ	PROPN
cana-1582	347	10	(	(	PUNCT
cana-1582	347	11	)	)	PUNCT
cana-1582	347	12	i	i	PRON
cana-1582	347	13	x	x	SYM
cana-1582	347	14	t	t	NOUN
cana-1582	347	15	and	and	CCONJ
cana-1582	347	16	ˆ	ˆ	PROPN
cana-1582	347	17	(	(	PUNCT
cana-1582	347	18	)	)	PUNCT
cana-1582	347	19	i	i	PRON
cana-1582	347	20	y	y	PROPN
cana-1582	347	21	t	t	PROPN
cana-1582	347	22	refer	refer	VERB
cana-1582	347	23	to	to	ADP
cana-1582	347	24	the	the	DET
cana-1582	347	25	appropriate	appropriate	ADJ
cana-1582	347	26	parametric	parametric	ADJ
cana-1582	347	27	form	form	NOUN
cana-1582	347	28	over	over	ADP
cana-1582	347	29	the	the	DET
cana-1582	347	30	curved	curved	ADJ
cana-1582	347	31	boundary	boundary	ADJ
cana-1582	347	32	arc	arc	NOUN
cana-1582	347	33	joining	join	VERB
cana-1582	347	34	the	the	DET
cana-1582	347	35	points	point	NOUN
cana-1582	347	36	(	(	PUNCT
cana-1582	347	37	,	,	PUNCT
cana-1582	347	38	)	)	PUNCT
cana-1582	348	1	i	i	PRON
cana-1582	348	2	i	i	VERB
cana-1582	348	3	x	x	VERB
cana-1582	348	4	y	y	NOUN
cana-1582	348	5	and	and	CCONJ
cana-1582	348	6	1	1	NUM
cana-1582	348	7	1	1	NUM
cana-1582	348	8	(	(	PUNCT
cana-1582	348	9	,	,	PUNCT
cana-1582	348	10	)	)	PUNCT
cana-1582	349	1	i	i	PRON
cana-1582	349	2	i	i	VERB
cana-1582	349	3	x	x	VERB
cana-1582	349	4	y	y	PROPN
cana-1582	350	1	+	+	PUNCT
cana-1582	350	2	+	+	CCONJ
cana-1582	350	3	now	now	ADV
cana-1582	350	4	letting	let	VERB
cana-1582	350	5	1	1	NUM
cana-1582	350	6	1	1	NUM
cana-1582	350	7	2	2	NUM
cana-1582	350	8	2	2	NUM
cana-1582	351	1	i	i	PRON
cana-1582	351	2	i	i	PRON
cana-1582	352	1	i	i	PRON
cana-1582	353	1	i	i	VERB
cana-1582	353	2	y	y	VERB
cana-1582	353	3	y	y	VERB
cana-1582	353	4	y	y	PROPN
cana-1582	353	5	y	y	PROPN
cana-1582	353	6	t	t	PROPN
cana-1582	353	7	t+	t+	NOUN
cana-1582	353	8	+	+	CCONJ
cana-1582	354	1	−	−	PUNCT
cana-1582	354	2	+	+	ADJ
cana-1582	354	3			NOUN
cana-1582	354	4			NOUN
cana-1582	354	5			NOUN
cana-1582	354	6			NOUN
cana-1582	354	7	=	=	PUNCT
cana-1582	355	1	+	+	CCONJ
cana-1582	355	2			PROPN
cana-1582	355	3			PROPN
cana-1582	356	1			PROPN
cana-1582	356	2			PROPN
cana-1582	357	1			ADJ
cana-1582	357	2			PROPN
cana-1582	357	3			PROPN
cana-1582	357	4			NOUN
cana-1582	357	5	(	(	PUNCT
cana-1582	357	6	18	18	NUM
cana-1582	357	7	)	)	PUNCT
cana-1582	357	8	and	and	CCONJ
cana-1582	357	9	substituting	substitute	VERB
cana-1582	357	10	in	in	ADP
cana-1582	357	11	equation	equation	NOUN
cana-1582	357	12	(	(	PUNCT
cana-1582	357	13	17	17	NUM
cana-1582	357	14	)	)	PUNCT
cana-1582	357	15	,	,	PUNCT
cana-1582	357	16	we	we	PRON
cana-1582	357	17	finally	finally	ADV
cana-1582	357	18	obtain	obtain	VERB
cana-1582	357	19	:	:	PUNCT
cana-1582	357	20	1	1	NUM
cana-1582	357	21	1	1	NUM
cana-1582	357	22	1	1	NUM
cana-1582	357	23	1	1	NUM
cana-1582	357	24	1	1	NUM
cana-1582	357	25	1	1	NUM
cana-1582	357	26	(	(	PUNCT
cana-1582	357	27	)	)	PUNCT
cana-1582	357	28	(	(	PUNCT
cana-1582	357	29	)	)	PUNCT
cana-1582	357	30	(	(	PUNCT
cana-1582	357	31	)	)	PUNCT
cana-1582	357	32	,	,	PUNCT
cana-1582	357	33	(	(	PUNCT
cana-1582	357	34	)	)	PUNCT
cana-1582	357	35	(	(	PUNCT
cana-1582	357	36	)	)	PUNCT
cana-1582	357	37	2	2	NUM
cana-1582	357	38	2	2	NUM
cana-1582	357	39	2	2	NUM
cana-1582	357	40	2	2	NUM
cana-1582	357	41	n	n	NOUN
cana-1582	358	1	i	i	PRON
cana-1582	359	1	i	i	PRON
cana-1582	360	1	i	i	PRON
cana-1582	361	1	i	i	PRON
cana-1582	362	1	i	i	PRON
cana-1582	363	1	i	i	PRON
cana-1582	364	1	i	i	PRON
cana-1582	365	1	i	i	VERB
cana-1582	365	2	x	x	VERB
cana-1582	366	1	t	t	NOUN
cana-1582	366	2	x	x	SYM
cana-1582	366	3	t	t	NOUN
cana-1582	366	4	x	x	SYM
cana-1582	366	5	t	t	PROPN
cana-1582	366	6	y	y	PROPN
cana-1582	366	7	y	y	PROPN
cana-1582	367	1	i	i	PRON
cana-1582	367	2	f	f	PROPN
cana-1582	367	3	s	s	VERB
cana-1582	367	4	y	y	PROPN
cana-1582	367	5	t	t	PROPN
cana-1582	367	6	ds	ds	VERB
cana-1582	367	7	y	y	PROPN
cana-1582	367	8	t	t	PROPN
cana-1582	367	9	dt	dt	X
cana-1582	367	10			X
cana-1582	367	11			X
cana-1582	367	12			X
cana-1582	367	13	+	+	NOUN
cana-1582	367	14	=	=	SYM
cana-1582	367	15	−	−	NOUN
cana-1582	368	1	−	−	PROPN
cana-1582	368	2			PROPN
cana-1582	368	3			PROPN
cana-1582	368	4	−	−	NOUN
cana-1582	368	5	−	−	PROPN
cana-1582	369	1	+	+	CCONJ
cana-1582	370	1	−	−	NOUN
cana-1582	370	2			PROPN
cana-1582	370	3			NOUN
cana-1582	370	4			PROPN
cana-1582	370	5			NOUN
cana-1582	370	6			PROPN
cana-1582	370	7			NOUN
cana-1582	370	8			NOUN
cana-1582	370	9	=	=	PROPN
cana-1582	371	1	+	+	NOUN
cana-1582	371	2			NOUN
cana-1582	371	3			NOUN
cana-1582	372	1			PROPN
cana-1582	372	2			PROPN
cana-1582	373	1			INTJ
cana-1582	374	1			PROPN
cana-1582	375	1			INTJ
cana-1582	375	2			PROPN
cana-1582	375	3			NOUN
cana-1582	376	1			PROPN
cana-1582	376	2			ADJ
cana-1582	376	3			PROPN
cana-1582	376	4			PROPN
cana-1582	376	5			NOUN
cana-1582	376	6			PROPN
cana-1582	376	7			NOUN
cana-1582	376	8			PROPN
cana-1582	376	9			NOUN
cana-1582	376	10			PROPN
cana-1582	376	11			PROPN
cana-1582	376	12			NOUN
cana-1582	376	13			PUNCT
cana-1582	376	14	(	(	PUNCT
cana-1582	376	15	19	19	NUM
cana-1582	376	16	)	)	PUNCT
cana-1582	376	17	where	where	SCONJ
cana-1582	376	18	1	1	NUM
cana-1582	376	19	1	1	NUM
cana-1582	376	20	1	1	NUM
cana-1582	376	21	1	1	NUM
cana-1582	376	22	ˆ	ˆ	NOUN
cana-1582	376	23	(	(	PUNCT
cana-1582	376	24	)	)	PUNCT
cana-1582	376	25	,	,	PUNCT
cana-1582	376	26	2	2	NUM
cana-1582	376	27	2	2	NUM
cana-1582	376	28	ˆ	ˆ	NOUN
cana-1582	376	29	(	(	PUNCT
cana-1582	376	30	)	)	PUNCT
cana-1582	376	31	2	2	NUM
cana-1582	376	32	2	2	NUM
cana-1582	377	1	i	i	PRON
cana-1582	377	2	i	i	PRON
cana-1582	378	1	i	i	PRON
cana-1582	378	2	i	i	PRON
cana-1582	379	1	i	i	PRON
cana-1582	379	2	i	i	PRON
cana-1582	380	1	i	i	PRON
cana-1582	380	2	i	i	PRON
cana-1582	381	1	i	i	PRON
cana-1582	381	2	i	i	PRON
cana-1582	382	1	i	i	PRON
cana-1582	383	1	i	i	VERB
cana-1582	383	2	y	y	VERB
cana-1582	383	3	y	y	VERB
cana-1582	383	4	y	y	PROPN
cana-1582	384	1	y	y	PROPN
cana-1582	384	2	x	x	SYM
cana-1582	384	3	t	t	PROPN
cana-1582	384	4	x	x	X
cana-1582	385	1	t	t	PROPN
cana-1582	385	2	y	y	PROPN
cana-1582	385	3	y	y	PROPN
cana-1582	385	4	y	y	PROPN
cana-1582	385	5	y	y	PROPN
cana-1582	385	6	y	y	PROPN
cana-1582	385	7	t	t	PROPN
cana-1582	385	8	y	y	PROPN
cana-1582	385	9	t	t	PROPN
cana-1582	386	1	+	+	CCONJ
cana-1582	386	2	+	+	PUNCT
cana-1582	386	3	+	+	CCONJ
cana-1582	386	4	+	+	NUM
cana-1582	386	5			NOUN
cana-1582	386	6	−	−	NOUN
cana-1582	387	1	+	+	NOUN
cana-1582	387	2			NOUN
cana-1582	387	3			NOUN
cana-1582	387	4			NOUN
cana-1582	387	5			NOUN
cana-1582	387	6	=	=	PUNCT
cana-1582	388	1	+	+	CCONJ
cana-1582	388	2			PROPN
cana-1582	388	3			PROPN
cana-1582	388	4			PROPN
cana-1582	389	1			NOUN
cana-1582	390	1			PROPN
cana-1582	391	1			PROPN
cana-1582	391	2			PROPN
cana-1582	391	3			ADJ
cana-1582	391	4			NOUN
cana-1582	391	5			NOUN
cana-1582	391	6			NOUN
cana-1582	391	7	−	−	NOUN
cana-1582	392	1	+	+	ADP
cana-1582	392	2			NOUN
cana-1582	392	3			NOUN
cana-1582	392	4			NOUN
cana-1582	392	5			NOUN
cana-1582	392	6	=	=	PUNCT
cana-1582	393	1	+	+	CCONJ
cana-1582	393	2			PROPN
cana-1582	393	3			PROPN
cana-1582	393	4			PROPN
cana-1582	394	1			NOUN
cana-1582	395	1			PROPN
cana-1582	396	1			PROPN
cana-1582	396	2			PROPN
cana-1582	396	3			ADJ
cana-1582	396	4			NOUN
cana-1582	396	5			NOUN
cana-1582	396	6	(	(	PUNCT
cana-1582	396	7	20	20	NUM
cana-1582	396	8	)	)	PUNCT
cana-1582	396	9	we	we	PRON
cana-1582	396	10	shall	shall	AUX
cana-1582	396	11	now	now	ADV
cana-1582	396	12	apply	apply	VERB
cana-1582	396	13	the	the	DET
cana-1582	396	14	gauss	gauss	PROPN
cana-1582	396	15	legendre	legendre	PROPN
cana-1582	396	16	quadrature	quadrature	NOUN
cana-1582	396	17	rules	rule	NOUN
cana-1582	396	18	of	of	ADP
cana-1582	396	19	order	order	NOUN
cana-1582	396	20	n	n	NOUN
cana-1582	396	21	and	and	CCONJ
cana-1582	396	22	m	m	VERB
cana-1582	396	23	along	along	ADP
cana-1582	396	24	the	the	DET
cana-1582	396	25	directions	direction	NOUN
cana-1582	396	26	s	s	PART
cana-1582	396	27	and	and	CCONJ
cana-1582	396	28	t	t	NOUN
cana-1582	396	29	respectively	respectively	ADV
cana-1582	396	30	.	.	PUNCT
cana-1582	397	1	this	this	PRON
cana-1582	397	2	gives	give	VERB
cana-1582	397	3	1	1	NUM
cana-1582	397	4	1	1	NUM
cana-1582	397	5	1	1	NUM
cana-1582	397	6	1	1	NUM
cana-1582	397	7	(	(	PUNCT
cana-1582	397	8	)	)	PUNCT
cana-1582	397	9	(	(	PUNCT
cana-1582	397	10	)	)	PUNCT
cana-1582	397	11	(	(	PUNCT
cana-1582	397	12	)	)	PUNCT
cana-1582	397	13	(	(	PUNCT
cana-1582	397	14	)	)	PUNCT
cana-1582	397	15	,	,	PUNCT
cana-1582	397	16	(	(	PUNCT
cana-1582	397	17	)	)	PUNCT
cana-1582	397	18	2	2	NUM
cana-1582	397	19	2	2	NUM
cana-1582	397	20	2	2	NUM
cana-1582	397	21	2	2	NUM
cana-1582	397	22	m	m	NOUN
cana-1582	397	23	m	m	NOUN
cana-1582	397	24	mn	mn	PROPN
cana-1582	397	25	n	n	PROPN
cana-1582	397	26	m	m	VERB
cana-1582	397	27	n	n	PRON
cana-1582	397	28	m	m	NOUN
cana-1582	397	29	m	m	VERB
cana-1582	397	30	n	n	PRON
cana-1582	397	31	mi	mi	X
cana-1582	397	32	k	k	PROPN
cana-1582	398	1	i	i	PRON
cana-1582	398	2	i	i	PRON
cana-1582	399	1	i	i	PRON
cana-1582	399	2	k	k	VERB
cana-1582	400	1	i	i	PRON
cana-1582	400	2	k	k	PROPN
cana-1582	401	1	j	j	PROPN
cana-1582	402	1	k	k	INTJ
cana-1582	403	1	i	i	PRON
cana-1582	403	2	k	k	PROPN
cana-1582	404	1	j	j	PROPN
cana-1582	405	1	i	i	PRON
cana-1582	405	2	k	k	PROPN
cana-1582	406	1	i	i	PRON
cana-1582	406	2	j	j	PROPN
cana-1582	407	1	k	k	NOUN
cana-1582	407	2	x	x	PUNCT
cana-1582	408	1	t	t	NOUN
cana-1582	408	2	y	y	PROPN
cana-1582	408	3	y	y	PROPN
cana-1582	408	4	x	x	SYM
cana-1582	408	5	t	t	PROPN
cana-1582	408	6	x	x	X
cana-1582	409	1	t	t	NOUN
cana-1582	409	2	i	i	PRON
cana-1582	409	3	w	w	PROPN
cana-1582	409	4	w	w	PROPN
cana-1582	409	5	y	y	PROPN
cana-1582	409	6	t	t	PROPN
cana-1582	410	1	f	f	PROPN
cana-1582	410	2	s	s	PROPN
cana-1582	410	3	y	y	PROPN
cana-1582	410	4	t	t	NOUN
cana-1582	410	5			X
cana-1582	410	6			X
cana-1582	410	7			X
cana-1582	410	8	+	+	NOUN
cana-1582	410	9	=	=	SYM
cana-1582	410	10	=	=	SYM
cana-1582	410	11	=	=	NOUN
cana-1582	411	1			NOUN
cana-1582	411	2			PROPN
cana-1582	411	3			PROPN
cana-1582	411	4			NOUN
cana-1582	411	5			PROPN
cana-1582	411	6			NOUN
cana-1582	411	7	−	−	NOUN
cana-1582	411	8	−	−	PROPN
cana-1582	412	1	−	−	PROPN
cana-1582	413	1	+	+	NOUN
cana-1582	413	2			NOUN
cana-1582	413	3			NOUN
cana-1582	413	4	=	=	PROPN
cana-1582	414	1	+	+	PROPN
cana-1582	414	2			PROPN
cana-1582	415	1			NOUN
cana-1582	415	2			X
cana-1582	416	1			INTJ
cana-1582	417	1			PROPN
cana-1582	418	1			INTJ
cana-1582	419	1			PROPN
cana-1582	419	2			PROPN
cana-1582	420	1			PROPN
cana-1582	420	2			NOUN
cana-1582	420	3			NOUN
cana-1582	420	4			PROPN
cana-1582	420	5			NOUN
cana-1582	420	6			NOUN
cana-1582	420	7			NOUN
cana-1582	420	8			NOUN
cana-1582	420	9			PROPN
cana-1582	420	10	(	(	PUNCT
cana-1582	420	11	21	21	NUM
cana-1582	420	12	)	)	PUNCT
cana-1582	420	13	from	from	ADP
cana-1582	420	14	the	the	DET
cana-1582	420	15	above	above	ADJ
cana-1582	420	16	formula	formula	NOUN
cana-1582	420	17	,	,	PUNCT
cana-1582	420	18	it	it	PRON
cana-1582	420	19	is	be	AUX
cana-1582	420	20	quite	quite	ADV
cana-1582	420	21	obvious	obvious	ADJ
cana-1582	420	22	that	that	SCONJ
cana-1582	420	23	m	m	VERB
cana-1582	420	24	>	>	X
cana-1582	420	25	n	n	PROPN
cana-1582	420	26	,	,	PUNCT
cana-1582	420	27	for	for	ADP
cana-1582	420	28	a	a	DET
cana-1582	420	29	bivariate	bivariate	ADJ
cana-1582	420	30	polynomial	polynomial	ADJ
cana-1582	420	31	function	function	NOUN
cana-1582	420	32	of	of	ADP
cana-1582	420	33	degree	degree	NOUN
cana-1582	420	34	less	less	ADJ
cana-1582	420	35	than	than	ADP
cana-1582	420	36	or	or	CCONJ
cana-1582	420	37	equal	equal	ADJ
cana-1582	420	38	to	to	ADP
cana-1582	420	39	(	(	PUNCT
cana-1582	420	40	2n-1	2n-1	NOUN
cana-1582	420	41	)	)	PUNCT
cana-1582	420	42	.	.	PUNCT
cana-1582	421	1	the	the	DET
cana-1582	421	2	parametric	parametric	ADJ
cana-1582	421	3	form	form	NOUN
cana-1582	421	4	of	of	ADP
cana-1582	421	5	(	(	PUNCT
cana-1582	421	6	)	)	PUNCT
cana-1582	421	7	(	(	PUNCT
cana-1582	421	8	)	)	PUNCT
cana-1582	421	9	,	,	PUNCT
cana-1582	421	10	(	(	PUNCT
cana-1582	421	11	)	)	PUNCT
cana-1582	421	12	i	i	PRON
cana-1582	421	13	i	i	INTJ
cana-1582	421	14	x	x	VERB
cana-1582	421	15	t	t	NOUN
cana-1582	421	16	y	y	PROPN
cana-1582	421	17	t	t	PROPN
cana-1582	421	18	must	must	AUX
cana-1582	421	19	be	be	AUX
cana-1582	421	20	of	of	ADP
cana-1582	421	21	degree	degree	NOUN
cana-1582	421	22	greater	great	ADJ
cana-1582	421	23	than	than	ADP
cana-1582	421	24	or	or	CCONJ
cana-1582	421	25	equal	equal	ADJ
cana-1582	421	26	to	to	ADP
cana-1582	421	27	two	two	NUM
cana-1582	421	28	for	for	ADP
cana-1582	421	29	a	a	DET
cana-1582	421	30	curved	curved	ADJ
cana-1582	421	31	boundary	boundary	NOUN
cana-1582	421	32	,	,	PUNCT
cana-1582	421	33	hence	hence	ADV
cana-1582	421	34	in	in	ADP
cana-1582	421	35	equation	equation	NOUN
cana-1582	421	36	(	(	PUNCT
cana-1582	421	37	21	21	NUM
cana-1582	421	38	)	)	PUNCT
cana-1582	421	39	,	,	PUNCT
cana-1582	421	40	we	we	PRON
cana-1582	421	41	must	must	AUX
cana-1582	421	42	have	have	VERB
cana-1582	421	43	𝑚	𝑚	PROPN
cana-1582	421	44	≅	≅	PROPN
cana-1582	421	45	(	(	PUNCT
cana-1582	421	46	𝑛	𝑛	PROPN
cana-1582	421	47	+	+	PROPN
cana-1582	421	48	𝑝	𝑝	NOUN
cana-1582	421	49	)	)	PUNCT
cana-1582	421	50	for	for	ADP
cana-1582	421	51	the	the	DET
cana-1582	421	52	curved	curved	ADJ
cana-1582	421	53	boundary	boundary	NOUN
cana-1582	421	54	,	,	PUNCT
cana-1582	421	55	as	as	SCONJ
cana-1582	421	56	p	p	NOUN
cana-1582	421	57	–	–	PUNCT
cana-1582	421	58	point	point	NOUN
cana-1582	421	59	gauss	gauss	PROPN
cana-1582	421	60	legendre	legendre	PROPN
cana-1582	421	61	quadrature	quadrature	NOUN
cana-1582	421	62	rule	rule	NOUN
cana-1582	421	63	is	be	AUX
cana-1582	421	64	necessary	necessary	ADJ
cana-1582	421	65	to	to	PART
cana-1582	421	66	integrate	integrate	VERB
cana-1582	421	67	the	the	DET
cana-1582	421	68	following	follow	VERB
cana-1582	421	69	product	product	NOUN
cana-1582	421	70	in	in	ADP
cana-1582	421	71	equation	equation	NOUN
cana-1582	421	72	(	(	PUNCT
cana-1582	421	73	21	21	NUM
cana-1582	421	74	)	)	PUNCT
cana-1582	421	75	.	.	PUNCT
cana-1582	422	1	(	(	PUNCT
cana-1582	422	2	)	)	PUNCT
cana-1582	422	3	(	(	PUNCT
cana-1582	422	4	)	)	PUNCT
cana-1582	422	5	(	(	PUNCT
cana-1582	422	6	)	)	PUNCT
cana-1582	422	7	/	/	SYM
cana-1582	422	8	2	2	NUM
cana-1582	422	9	(	(	PUNCT
cana-1582	422	10	)	)	PUNCT
cana-1582	422	11	m	m	VERB
cana-1582	422	12	m	m	VERB
cana-1582	423	1	i	i	INTJ
cana-1582	423	2	k	k	INTJ
cana-1582	424	1	i	i	PRON
cana-1582	424	2	k	k	NOUN
cana-1582	425	1	x	x	X
cana-1582	425	2	t	t	PROPN
cana-1582	425	3	y	y	PROPN
cana-1582	425	4	t	t	PROPN
cana-1582	425	5	−	−	PUNCT
cana-1582	425	6	a	a	DET
cana-1582	425	7	polynomial	polynomial	NOUN
cana-1582	425	8	of	of	ADP
cana-1582	425	9	degree	degree	NOUN
cana-1582	425	10	,	,	PUNCT
cana-1582	425	11	say	say	VERB
cana-1582	425	12	,	,	PUNCT
cana-1582	425	13	(	(	PUNCT
cana-1582	425	14	2p-1	2p-1	NOUN
cana-1582	425	15	)	)	PUNCT
cana-1582	425	16	.	.	PUNCT
cana-1582	426	1	on	on	ADP
cana-1582	426	2	the	the	DET
cana-1582	426	3	other	other	ADJ
cana-1582	426	4	hand	hand	NOUN
cana-1582	426	5	,	,	PUNCT
cana-1582	426	6	we	we	PRON
cana-1582	426	7	have	have	AUX
cana-1582	426	8	chosen	choose	VERB
cana-1582	426	9	n	n	NUM
cana-1582	426	10	–	–	PUNCT
cana-1582	426	11	th	th	X
cana-1582	426	12	order	order	NOUN
cana-1582	426	13	gauss	gauss	PROPN
cana-1582	426	14	legendre	legendre	PROPN
cana-1582	426	15	quadrature	quadrature	PROPN
cana-1582	426	16	rule	rule	NOUN
cana-1582	426	17	to	to	PART
cana-1582	426	18	integrate	integrate	VERB
cana-1582	426	19	the	the	DET
cana-1582	426	20	bivariate	bivariate	ADJ
cana-1582	426	21	function	function	NOUN
cana-1582	426	22	(	(	PUNCT
cana-1582	426	23	)	)	PUNCT
cana-1582	426	24	(	(	PUNCT
cana-1582	426	25	)	)	PUNCT
cana-1582	426	26	(	(	PUNCT
cana-1582	426	27	)	)	PUNCT
cana-1582	426	28	'	'	PUNCT
cana-1582	426	29	'	'	PUNCT
cana-1582	426	30	1	1	NUM
cana-1582	426	31	(	(	PUNCT
cana-1582	426	32	)	)	PUNCT
cana-1582	426	33	/	/	SYM
cana-1582	426	34	2	2	NUM
cana-1582	426	35	(	(	PUNCT
cana-1582	426	36	)	)	PUNCT
cana-1582	426	37	/	/	SYM
cana-1582	426	38	2	2	NUM
cana-1582	426	39	,	,	PUNCT
cana-1582	426	40	(	(	PUNCT
cana-1582	426	41	)	)	PUNCT
cana-1582	426	42	m	m	VERB
cana-1582	426	43	m	m	VERB
cana-1582	427	1	i	i	INTJ
cana-1582	427	2	k	k	INTJ
cana-1582	428	1	i	i	PRON
cana-1582	428	2	k	k	INTJ
cana-1582	429	1	i	i	PRON
cana-1582	429	2	k	k	NOUN
cana-1582	430	1	f	f	PROPN
cana-1582	430	2	x	x	X
cana-1582	430	3	t	t	PROPN
cana-1582	430	4	s	s	X
cana-1582	430	5	x	x	X
cana-1582	430	6	t	t	PROPN
cana-1582	430	7	y	y	PROPN
cana-1582	430	8	t	t	NOUN
cana-1582	430	9	−	−	X
cana-1582	431	1	+	+	CCONJ
cana-1582	431	2	+	+	CCONJ
cana-1582	431	3	as	as	ADP
cana-1582	431	4	polynomial	polynomial	ADJ
cana-1582	431	5	degree	degree	NOUN
cana-1582	431	6	(	(	PUNCT
cana-1582	431	7	2n-1	2n-1	NOUN
cana-1582	431	8	)	)	PUNCT
cana-1582	431	9	in	in	ADP
cana-1582	431	10	s	s	PRON
cana-1582	431	11	in	in	ADP
cana-1582	431	12	equation	equation	NOUN
cana-1582	431	13	(	(	PUNCT
cana-1582	431	14	21	21	NUM
cana-1582	431	15	)	)	PUNCT
cana-1582	431	16	.	.	PUNCT
cana-1582	432	1	application	application	NOUN
cana-1582	432	2	example	example	NOUN
cana-1582	432	3	:	:	PUNCT
cana-1582	432	4	a	a	DET
cana-1582	432	5	lunar	lunar	ADJ
cana-1582	432	6	model	model	NOUN
cana-1582	432	7	we	we	PRON
cana-1582	432	8	shall	shall	AUX
cana-1582	432	9	now	now	ADV
cana-1582	432	10	consider	consider	VERB
cana-1582	432	11	the	the	DET
cana-1582	432	12	curved	curved	ADJ
cana-1582	432	13	domain	domain	NOUN
cana-1582	432	14	in	in	ADP
cana-1582	432	15	the	the	DET
cana-1582	432	16	shape	shape	NOUN
cana-1582	432	17	of	of	ADP
cana-1582	432	18	a	a	DET
cana-1582	432	19	lunar	lunar	ADJ
cana-1582	432	20	model	model	NOUN
cana-1582	432	21	whose	whose	DET
cana-1582	432	22	boundary	boundary	NOUN
cana-1582	432	23	is	be	AUX
cana-1582	432	24	composed	compose	VERB
cana-1582	432	25	of	of	ADP
cana-1582	432	26	two	two	NUM
cana-1582	432	27	circular	circular	ADJ
cana-1582	432	28	arcs	arc	NOUN
cana-1582	432	29	.	.	PUNCT
cana-1582	433	1	the	the	DET
cana-1582	433	2	outer	outer	ADJ
cana-1582	433	3	circular	circular	ADJ
cana-1582	433	4	arc	arc	NOUN
cana-1582	433	5	satisfies	satisfy	VERB
cana-1582	433	6	the	the	DET
cana-1582	433	7	equation	equation	NOUN
cana-1582	433	8	:	:	PUNCT
cana-1582	433	9	(	(	PUNCT
cana-1582	433	10	)	)	PUNCT
cana-1582	433	11	(	(	PUNCT
cana-1582	433	12	)	)	PUNCT
cana-1582	433	13	2	2	NUM
cana-1582	433	14	2	2	NUM
cana-1582	433	15	1/	1/	NUM
cana-1582	433	16	2	2	NUM
cana-1582	433	17	1/	1/	NUM
cana-1582	433	18	2	2	NUM
cana-1582	433	19	1/	1/	NUM
cana-1582	433	20	4x	4x	NUM
cana-1582	433	21	y−	y−	NOUN
cana-1582	433	22	+	+	CCONJ
cana-1582	433	23	−	−	PROPN
cana-1582	434	1	=	=	SYM
cana-1582	434	2	and	and	CCONJ
cana-1582	434	3	the	the	DET
cana-1582	434	4	inner	inner	ADJ
cana-1582	434	5	circular	circular	ADJ
cana-1582	434	6	arc	arc	NOUN
cana-1582	434	7	satisfies	satisfy	VERB
cana-1582	434	8	the	the	DET
cana-1582	434	9	equation	equation	NOUN
cana-1582	434	10	2	2	NUM
cana-1582	434	11	2	2	NUM
cana-1582	434	12	1/	1/	NUM
cana-1582	434	13	4x	4x	NOUN
cana-1582	434	14	y+	y+	NUM
cana-1582	434	15	=	=	SYM
cana-1582	434	16	.	.	PUNCT
cana-1582	435	1	this	this	PRON
cana-1582	435	2	is	be	AUX
cana-1582	435	3	shown	show	VERB
cana-1582	435	4	in	in	ADP
cana-1582	435	5	figure	figure	NOUN
cana-1582	435	6	:	:	PUNCT
cana-1582	435	7	fig	fig	NOUN
cana-1582	435	8	1	1	NUM
cana-1582	435	9	.	.	PUNCT
cana-1582	436	1	communications	communication	NOUN
cana-1582	436	2	on	on	ADP
cana-1582	436	3	applied	apply	VERB
cana-1582	436	4	nonlinear	nonlinear	ADJ
cana-1582	436	5	analysis	analysis	NOUN
cana-1582	436	6	issn	issn	NOUN
cana-1582	436	7	:	:	PUNCT
cana-1582	436	8	1074	1074	NUM
cana-1582	436	9	-	-	PUNCT
cana-1582	436	10	133x	133x	NUM
cana-1582	436	11	vol	vol	NOUN
cana-1582	436	12	31	31	NUM
cana-1582	436	13	no	no	NOUN
cana-1582	436	14	.	.	PUNCT
cana-1582	437	1	8s	8s	PROPN
cana-1582	437	2	(	(	PUNCT
cana-1582	437	3	2024	2024	NUM
cana-1582	437	4	)	)	PUNCT
cana-1582	437	5	731	731	NUM
cana-1582	437	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1582	437	7	figure	figure	NOUN
cana-1582	437	8	1	1	NUM
cana-1582	437	9	:	:	PUNCT
cana-1582	437	10	lunar	lunar	ADJ
cana-1582	437	11	model	model	NOUN
cana-1582	437	12	the	the	DET
cana-1582	437	13	numerical	numerical	ADJ
cana-1582	437	14	scheme	scheme	NOUN
cana-1582	437	15	developed	develop	VERB
cana-1582	437	16	in	in	ADP
cana-1582	437	17	the	the	DET
cana-1582	437	18	previous	previous	ADJ
cana-1582	437	19	section	section	NOUN
cana-1582	437	20	relies	rely	VERB
cana-1582	437	21	on	on	ADP
cana-1582	437	22	having	have	VERB
cana-1582	437	23	suitable	suitable	ADJ
cana-1582	437	24	parametric	parametric	ADJ
cana-1582	437	25	equations	equation	NOUN
cana-1582	437	26	that	that	PRON
cana-1582	437	27	describe	describe	VERB
cana-1582	437	28	the	the	DET
cana-1582	437	29	curved	curved	ADJ
cana-1582	437	30	boundary	boundary	NOUN
cana-1582	437	31	of	of	ADP
cana-1582	437	32	the	the	DET
cana-1582	437	33	domain	domain	NOUN
cana-1582	437	34	xy	xy	X
cana-1582	437	35			PROPN
cana-1582	437	36	,	,	PUNCT
cana-1582	437	37	as	as	SCONJ
cana-1582	437	38	specified	specify	VERB
cana-1582	437	39	by	by	ADP
cana-1582	437	40	equations	equation	NOUN
cana-1582	437	41	(	(	PUNCT
cana-1582	437	42	17	17	NUM
cana-1582	437	43	)	)	PUNCT
cana-1582	437	44	to	to	ADP
cana-1582	437	45	(	(	PUNCT
cana-1582	437	46	21	21	NUM
cana-1582	437	47	)	)	PUNCT
cana-1582	437	48	.	.	PUNCT
cana-1582	438	1	in	in	ADP
cana-1582	438	2	some	some	DET
cana-1582	438	3	scenarios	scenario	NOUN
cana-1582	438	4	,	,	PUNCT
cana-1582	438	5	the	the	DET
cana-1582	438	6	boundary	boundary	NOUN
cana-1582	438	7	of	of	ADP
cana-1582	438	8	the	the	DET
cana-1582	438	9	curved	curved	ADJ
cana-1582	438	10	domain	domain	NOUN
cana-1582	438	11	can	can	AUX
cana-1582	438	12	be	be	AUX
cana-1582	438	13	precisely	precisely	ADV
cana-1582	438	14	defined	define	VERB
cana-1582	438	15	by	by	ADP
cana-1582	438	16	mathematical	mathematical	ADJ
cana-1582	438	17	relations	relation	NOUN
cana-1582	438	18	.	.	PUNCT
cana-1582	439	1	in	in	ADP
cana-1582	439	2	such	such	ADJ
cana-1582	439	3	cases	case	NOUN
cana-1582	439	4	,	,	PUNCT
cana-1582	439	5	it	it	PRON
cana-1582	439	6	's	be	AUX
cana-1582	439	7	feasible	feasible	ADJ
cana-1582	439	8	to	to	PART
cana-1582	439	9	transform	transform	VERB
cana-1582	439	10	these	these	DET
cana-1582	439	11	mathematical	mathematical	ADJ
cana-1582	439	12	relations	relation	NOUN
cana-1582	439	13	into	into	ADP
cana-1582	439	14	explicit	explicit	ADJ
cana-1582	439	15	parametric	parametric	ADJ
cana-1582	439	16	equations	equation	NOUN
cana-1582	439	17	.	.	PUNCT
cana-1582	440	1	however	however	ADV
cana-1582	440	2	,	,	PUNCT
cana-1582	440	3	there	there	PRON
cana-1582	440	4	are	be	VERB
cana-1582	440	5	situations	situation	NOUN
cana-1582	440	6	where	where	SCONJ
cana-1582	440	7	the	the	DET
cana-1582	440	8	boundary	boundary	ADJ
cana-1582	440	9	curve	curve	NOUN
cana-1582	440	10	is	be	AUX
cana-1582	440	11	described	describe	VERB
cana-1582	440	12	by	by	ADP
cana-1582	440	13	a	a	DET
cana-1582	440	14	set	set	NOUN
cana-1582	440	15	of	of	ADP
cana-1582	440	16	discrete	discrete	ADJ
cana-1582	440	17	coordinate	coordinate	NOUN
cana-1582	440	18	points	point	NOUN
cana-1582	440	19	,	,	PUNCT
cana-1582	440	20	making	make	VERB
cana-1582	440	21	it	it	PRON
cana-1582	440	22	necessary	necessary	ADJ
cana-1582	440	23	to	to	PART
cana-1582	440	24	generate	generate	VERB
cana-1582	440	25	parametric	parametric	ADJ
cana-1582	440	26	equations	equation	NOUN
cana-1582	440	27	through	through	ADP
cana-1582	440	28	alternative	alternative	ADJ
cana-1582	440	29	methods	method	NOUN
cana-1582	440	30	.	.	PUNCT
cana-1582	441	1	one	one	NUM
cana-1582	441	2	such	such	ADJ
cana-1582	441	3	method	method	NOUN
cana-1582	441	4	involves	involve	VERB
cana-1582	441	5	utilizing	utilize	VERB
cana-1582	441	6	spline	spline	NOUN
cana-1582	441	7	interpolating	interpolate	VERB
cana-1582	441	8	polynomials	polynomial	NOUN
cana-1582	441	9	of	of	ADP
cana-1582	441	10	varying	vary	VERB
cana-1582	441	11	orders	order	NOUN
cana-1582	441	12	(	(	PUNCT
cana-1582	441	13	e.g.	e.g.	ADV
cana-1582	441	14	,	,	PUNCT
cana-1582	441	15	2nd	2nd	ADJ
cana-1582	441	16	,	,	PUNCT
cana-1582	441	17	3rd	3rd	ADJ
cana-1582	441	18	,	,	PUNCT
cana-1582	441	19	4th	4th	ADJ
cana-1582	441	20	order	order	NOUN
cana-1582	441	21	,	,	PUNCT
cana-1582	441	22	etc	etc	X
cana-1582	441	23	.	.	X
cana-1582	441	24	)	)	PUNCT
cana-1582	441	25	to	to	PART
cana-1582	441	26	generate	generate	VERB
cana-1582	441	27	parametric	parametric	ADJ
cana-1582	441	28	equations	equation	NOUN
cana-1582	441	29	for	for	ADP
cana-1582	441	30	the	the	DET
cana-1582	441	31	curved	curved	ADJ
cana-1582	441	32	boundary	boundary	NOUN
cana-1582	441	33	.	.	PUNCT
cana-1582	442	1	this	this	DET
cana-1582	442	2	approach	approach	NOUN
cana-1582	442	3	proves	prove	VERB
cana-1582	442	4	to	to	PART
cana-1582	442	5	be	be	AUX
cana-1582	442	6	advantageous	advantageous	ADJ
cana-1582	442	7	even	even	ADV
cana-1582	442	8	when	when	SCONJ
cana-1582	442	9	dealing	deal	VERB
cana-1582	442	10	with	with	ADP
cana-1582	442	11	a	a	DET
cana-1582	442	12	boundary	boundary	ADJ
cana-1582	442	13	curve	curve	NOUN
cana-1582	442	14	represented	represent	VERB
cana-1582	442	15	by	by	ADP
cana-1582	442	16	discrete	discrete	ADJ
cana-1582	442	17	coordinate	coordinate	NOUN
cana-1582	442	18	points	point	NOUN
cana-1582	442	19	.	.	PUNCT
cana-1582	443	1	now	now	ADV
cana-1582	443	2	,	,	PUNCT
cana-1582	443	3	let	let	VERB
cana-1582	443	4	's	us	PRON
cana-1582	443	5	delve	delve	VERB
cana-1582	443	6	into	into	ADP
cana-1582	443	7	the	the	DET
cana-1582	443	8	application	application	NOUN
cana-1582	443	9	of	of	ADP
cana-1582	443	10	these	these	DET
cana-1582	443	11	two	two	NUM
cana-1582	443	12	methods	method	NOUN
cana-1582	443	13	in	in	ADP
cana-1582	443	14	the	the	DET
cana-1582	443	15	context	context	NOUN
cana-1582	443	16	of	of	ADP
cana-1582	443	17	a	a	DET
cana-1582	443	18	lunar	lunar	ADJ
cana-1582	443	19	model	model	NOUN
cana-1582	443	20	,	,	PUNCT
cana-1582	443	21	as	as	SCONJ
cana-1582	443	22	discussed	discuss	VERB
cana-1582	443	23	previously	previously	ADV
cana-1582	443	24	.	.	PUNCT
cana-1582	444	1	exact	exact	ADJ
cana-1582	444	2	mathematical	mathematical	ADJ
cana-1582	444	3	relations	relation	NOUN
cana-1582	444	4	method	method	NOUN
cana-1582	444	5	:	:	PUNCT
cana-1582	444	6	if	if	SCONJ
cana-1582	444	7	the	the	DET
cana-1582	444	8	boundary	boundary	NOUN
cana-1582	444	9	of	of	ADP
cana-1582	444	10	the	the	DET
cana-1582	444	11	lunar	lunar	ADJ
cana-1582	444	12	model	model	NOUN
cana-1582	444	13	can	can	AUX
cana-1582	444	14	be	be	AUX
cana-1582	444	15	precisely	precisely	ADV
cana-1582	444	16	defined	define	VERB
cana-1582	444	17	by	by	ADP
cana-1582	444	18	mathematical	mathematical	ADJ
cana-1582	444	19	relations	relation	NOUN
cana-1582	444	20	,	,	PUNCT
cana-1582	444	21	we	we	PRON
cana-1582	444	22	can	can	AUX
cana-1582	444	23	derive	derive	VERB
cana-1582	444	24	explicit	explicit	ADJ
cana-1582	444	25	parametric	parametric	ADJ
cana-1582	444	26	equations	equation	NOUN
cana-1582	444	27	directly	directly	ADV
cana-1582	444	28	from	from	ADP
cana-1582	444	29	these	these	DET
cana-1582	444	30	relations	relation	NOUN
cana-1582	444	31	.	.	PUNCT
cana-1582	445	1	this	this	DET
cana-1582	445	2	method	method	NOUN
cana-1582	445	3	is	be	AUX
cana-1582	445	4	straightforward	straightforward	ADJ
cana-1582	445	5	and	and	CCONJ
cana-1582	445	6	offers	offer	VERB
cana-1582	445	7	accurate	accurate	ADJ
cana-1582	445	8	representations	representation	NOUN
cana-1582	445	9	of	of	ADP
cana-1582	445	10	the	the	DET
cana-1582	445	11	boundary	boundary	NOUN
cana-1582	445	12	.	.	PUNCT
cana-1582	446	1	however	however	ADV
cana-1582	446	2	,	,	PUNCT
cana-1582	446	3	it	it	PRON
cana-1582	446	4	relies	rely	VERB
cana-1582	446	5	on	on	ADP
cana-1582	446	6	the	the	DET
cana-1582	446	7	availability	availability	NOUN
cana-1582	446	8	of	of	ADP
cana-1582	446	9	exact	exact	ADJ
cana-1582	446	10	mathematical	mathematical	ADJ
cana-1582	446	11	descriptions	description	NOUN
cana-1582	446	12	of	of	ADP
cana-1582	446	13	the	the	DET
cana-1582	446	14	boundary	boundary	NOUN
cana-1582	446	15	.	.	PUNCT
cana-1582	447	1	spline	spline	NOUN
cana-1582	447	2	interpolating	interpolate	VERB
cana-1582	447	3	polynomials	polynomial	NOUN
cana-1582	447	4	method	method	NOUN
cana-1582	447	5	:	:	PUNCT
cana-1582	447	6	in	in	ADP
cana-1582	447	7	cases	case	NOUN
cana-1582	447	8	where	where	SCONJ
cana-1582	447	9	the	the	DET
cana-1582	447	10	boundary	boundary	NOUN
cana-1582	447	11	of	of	ADP
cana-1582	447	12	the	the	DET
cana-1582	447	13	lunar	lunar	ADJ
cana-1582	447	14	model	model	NOUN
cana-1582	447	15	is	be	AUX
cana-1582	447	16	not	not	PART
cana-1582	447	17	described	describe	VERB
cana-1582	447	18	by	by	ADP
cana-1582	447	19	exact	exact	ADJ
cana-1582	447	20	mathematical	mathematical	ADJ
cana-1582	447	21	relations	relation	NOUN
cana-1582	447	22	but	but	CCONJ
cana-1582	447	23	rather	rather	ADV
cana-1582	447	24	by	by	ADP
cana-1582	447	25	a	a	DET
cana-1582	447	26	set	set	NOUN
cana-1582	447	27	of	of	ADP
cana-1582	447	28	discrete	discrete	ADJ
cana-1582	447	29	coordinate	coordinate	NOUN
cana-1582	447	30	points	point	NOUN
cana-1582	447	31	,	,	PUNCT
cana-1582	447	32	spline	spline	NOUN
cana-1582	447	33	interpolating	interpolate	VERB
cana-1582	447	34	polynomials	polynomial	NOUN
cana-1582	447	35	can	can	AUX
cana-1582	447	36	be	be	AUX
cana-1582	447	37	employed	employ	VERB
cana-1582	447	38	to	to	PART
cana-1582	447	39	generate	generate	VERB
cana-1582	447	40	parametric	parametric	ADJ
cana-1582	447	41	equations	equation	NOUN
cana-1582	447	42	.	.	PUNCT
cana-1582	448	1	spline	spline	NOUN
cana-1582	448	2	interpolation	interpolation	NOUN
cana-1582	448	3	allows	allow	VERB
cana-1582	448	4	us	we	PRON
cana-1582	448	5	to	to	PART
cana-1582	448	6	construct	construct	VERB
cana-1582	448	7	a	a	DET
cana-1582	448	8	smooth	smooth	ADJ
cana-1582	448	9	curve	curve	NOUN
cana-1582	448	10	that	that	PRON
cana-1582	448	11	passes	pass	VERB
cana-1582	448	12	through	through	ADP
cana-1582	448	13	these	these	DET
cana-1582	448	14	discrete	discrete	ADJ
cana-1582	448	15	points	point	NOUN
cana-1582	448	16	,	,	PUNCT
cana-1582	448	17	providing	provide	VERB
cana-1582	448	18	a	a	DET
cana-1582	448	19	continuous	continuous	ADJ
cana-1582	448	20	representation	representation	NOUN
cana-1582	448	21	of	of	ADP
cana-1582	448	22	the	the	DET
cana-1582	448	23	boundary	boundary	NOUN
cana-1582	448	24	.	.	PUNCT
cana-1582	449	1	the	the	DET
cana-1582	449	2	choice	choice	NOUN
cana-1582	449	3	of	of	ADP
cana-1582	449	4	spline	spline	ADJ
cana-1582	449	5	order	order	NOUN
cana-1582	449	6	(	(	PUNCT
cana-1582	449	7	e.g.	e.g.	ADV
cana-1582	449	8	,	,	PUNCT
cana-1582	449	9	2nd	2nd	ADJ
cana-1582	449	10	,	,	PUNCT
cana-1582	449	11	3rd	3rd	ADJ
cana-1582	449	12	,	,	PUNCT
cana-1582	449	13	4th	4th	ADJ
cana-1582	449	14	order	order	NOUN
cana-1582	449	15	)	)	PUNCT
cana-1582	449	16	depends	depend	VERB
cana-1582	449	17	on	on	ADP
cana-1582	449	18	the	the	DET
cana-1582	449	19	desired	desire	VERB
cana-1582	449	20	level	level	NOUN
cana-1582	449	21	of	of	ADP
cana-1582	449	22	smoothness	smoothness	NOUN
cana-1582	449	23	and	and	CCONJ
cana-1582	449	24	accuracy	accuracy	NOUN
cana-1582	449	25	required	require	VERB
cana-1582	449	26	for	for	ADP
cana-1582	449	27	the	the	DET
cana-1582	449	28	boundary	boundary	ADJ
cana-1582	449	29	representation	representation	NOUN
cana-1582	449	30	.	.	PUNCT
cana-1582	450	1	by	by	ADP
cana-1582	450	2	applying	apply	VERB
cana-1582	450	3	these	these	DET
cana-1582	450	4	two	two	NUM
cana-1582	450	5	methods	method	NOUN
cana-1582	450	6	,	,	PUNCT
cana-1582	450	7	we	we	PRON
cana-1582	450	8	can	can	AUX
cana-1582	450	9	effectively	effectively	ADV
cana-1582	450	10	obtain	obtain	VERB
cana-1582	450	11	parametric	parametric	ADJ
cana-1582	450	12	equations	equation	NOUN
cana-1582	450	13	for	for	ADP
cana-1582	450	14	the	the	DET
cana-1582	450	15	curved	curved	ADJ
cana-1582	450	16	boundary	boundary	NOUN
cana-1582	450	17	of	of	ADP
cana-1582	450	18	the	the	DET
cana-1582	450	19	lunar	lunar	ADJ
cana-1582	450	20	model	model	NOUN
cana-1582	450	21	,	,	PUNCT
cana-1582	450	22	enabling	enable	VERB
cana-1582	450	23	the	the	DET
cana-1582	450	24	implementation	implementation	NOUN
cana-1582	450	25	of	of	ADP
cana-1582	450	26	the	the	DET
cana-1582	450	27	numerical	numerical	ADJ
cana-1582	450	28	scheme	scheme	NOUN
cana-1582	450	29	discussed	discuss	VERB
cana-1582	450	30	earlier	early	ADV
cana-1582	450	31	.	.	PUNCT
cana-1582	451	1	this	this	PRON
cana-1582	451	2	ensures	ensure	VERB
cana-1582	451	3	accurate	accurate	ADJ
cana-1582	451	4	simulation	simulation	NOUN
cana-1582	451	5	and	and	CCONJ
cana-1582	451	6	analysis	analysis	NOUN
cana-1582	451	7	of	of	ADP
cana-1582	451	8	the	the	DET
cana-1582	451	9	lunar	lunar	ADJ
cana-1582	451	10	environment	environment	NOUN
cana-1582	451	11	for	for	ADP
cana-1582	451	12	the	the	DET
cana-1582	451	13	intended	intend	VERB
cana-1582	451	14	application	application	NOUN
cana-1582	451	15	.	.	PUNCT
cana-1582	452	1	explicit	explicit	ADJ
cana-1582	452	2	form	form	NOUN
cana-1582	452	3	of	of	ADP
cana-1582	452	4	parametric	parametric	ADJ
cana-1582	452	5	equations	equation	NOUN
cana-1582	452	6	the	the	DET
cana-1582	452	7	following	follow	VERB
cana-1582	452	8	parametric	parametric	ADJ
cana-1582	452	9	relations	relation	NOUN
cana-1582	452	10	can	can	AUX
cana-1582	452	11	be	be	AUX
cana-1582	452	12	immediately	immediately	ADV
cana-1582	452	13	obtained	obtain	VERB
cana-1582	452	14	for	for	ADP
cana-1582	452	15	the	the	DET
cana-1582	452	16	lunar	lunar	ADJ
cana-1582	452	17	model	model	NOUN
cana-1582	452	18	describe	describe	VERB
cana-1582	452	19	above	above	ADV
cana-1582	452	20	.	.	PUNCT
cana-1582	453	1	(	(	PUNCT
cana-1582	453	2	1	1	X
cana-1582	453	3	)	)	PUNCT
cana-1582	453	4	outer	outer	ADJ
cana-1582	453	5	circular	circular	ADJ
cana-1582	453	6	arc	arc	NOUN
cana-1582	453	7	communications	communication	NOUN
cana-1582	453	8	on	on	ADP
cana-1582	453	9	applied	apply	VERB
cana-1582	453	10	nonlinear	nonlinear	ADJ
cana-1582	453	11	analysis	analysis	NOUN
cana-1582	453	12	issn	issn	NOUN
cana-1582	453	13	:	:	PUNCT
cana-1582	453	14	1074	1074	NUM
cana-1582	453	15	-	-	PUNCT
cana-1582	453	16	133x	133x	NUM
cana-1582	453	17	vol	vol	NOUN
cana-1582	453	18	31	31	NUM
cana-1582	453	19	no	no	NOUN
cana-1582	453	20	.	.	PUNCT
cana-1582	454	1	8s	8s	PROPN
cana-1582	454	2	(	(	PUNCT
cana-1582	454	3	2024	2024	NUM
cana-1582	454	4	)	)	PUNCT
cana-1582	454	5	732	732	NUM
cana-1582	454	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1582	454	7	the	the	DET
cana-1582	454	8	outer	outer	ADJ
cana-1582	454	9	circular	circular	ADJ
cana-1582	454	10	arc	arc	NOUN
cana-1582	454	11	is	be	AUX
cana-1582	454	12	the	the	DET
cana-1582	454	13	boundary	boundary	ADJ
cana-1582	454	14	curve	curve	NOUN
cana-1582	454	15	over	over	ADP
cana-1582	454	16	the	the	DET
cana-1582	454	17	fourth	fourth	ADJ
cana-1582	454	18	first	first	ADJ
cana-1582	454	19	and	and	CCONJ
cana-1582	454	20	second	second	ADJ
cana-1582	454	21	quadrant	quadrant	NOUN
cana-1582	454	22	and	and	CCONJ
cana-1582	454	23	its	its	PRON
cana-1582	454	24	boundary	boundary	NOUN
cana-1582	454	25	is	be	AUX
cana-1582	454	26	described	describe	VERB
cana-1582	454	27	by	by	ADP
cana-1582	454	28	the	the	DET
cana-1582	454	29	equation	equation	NOUN
cana-1582	454	30	2	2	NUM
cana-1582	454	31	2	2	NUM
cana-1582	454	32	(	(	PUNCT
cana-1582	454	33	1/	1/	NUM
cana-1582	454	34	2	2	NUM
cana-1582	454	35	)	)	PUNCT
cana-1582	454	36	(	(	PUNCT
cana-1582	454	37	1/	1/	NUM
cana-1582	454	38	2	2	NUM
cana-1582	454	39	)	)	PUNCT
cana-1582	454	40	1/	1/	NUM
cana-1582	454	41	4x	4x	NUM
cana-1582	454	42	y−	y−	NOUN
cana-1582	454	43	+	+	CCONJ
cana-1582	454	44	−	−	PROPN
cana-1582	455	1	=	=	SYM
cana-1582	455	2	.	.	PUNCT
cana-1582	456	1	hence	hence	ADV
cana-1582	456	2	the	the	DET
cana-1582	456	3	parametric	parametric	ADJ
cana-1582	456	4	equations	equation	NOUN
cana-1582	456	5	.	.	PUNCT
cana-1582	457	1			ADJ
cana-1582	457	2			ADP
cana-1582	457	3			ADJ
cana-1582	457	4			PUNCT
cana-1582	457	5			PROPN
cana-1582	457	6			PROPN
cana-1582	457	7	(	(	PUNCT
cana-1582	457	8	)	)	PUNCT
cana-1582	457	9	1	1	NUM
cana-1582	457	10	1	1	NUM
cana-1582	457	11	1	1	NUM
cana-1582	457	12	1	1	NUM
cana-1582	457	13	cos	co	NOUN
cana-1582	457	14	,	,	PUNCT
cana-1582	457	15	sin	sin	NOUN
cana-1582	457	16	2	2	NUM
cana-1582	457	17	2	2	NUM
cana-1582	457	18	2	2	NUM
cana-1582	457	19	2	2	NUM
cana-1582	457	20	0	0	NUM
cana-1582	457	21	,	,	PUNCT
cana-1582	457	22	/	/	SYM
cana-1582	457	23	2	2	NUM
cana-1582	457	24	,	,	PUNCT
cana-1582	457	25	/	/	SYM
cana-1582	457	26	2	2	NUM
cana-1582	457	27	,	,	PUNCT
cana-1582	457	28	,	,	PUNCT
cana-1582	457	29	3	3	NUM
cana-1582	457	30	/	/	SYM
cana-1582	457	31	2,2	2,2	NUM
cana-1582	457	32	x	x	SYM
cana-1582	457	33	y	y	X
cana-1582	457	34			PROPN
cana-1582	458	1			PROPN
cana-1582	458	2			PROPN
cana-1582	458	3			PROPN
cana-1582	458	4			PROPN
cana-1582	458	5			PROPN
cana-1582	458	6			ADJ
cana-1582	458	7			NOUN
cana-1582	458	8			NOUN
cana-1582	458	9			NOUN
cana-1582	458	10			NOUN
cana-1582	458	11	=	=	PUNCT
cana-1582	459	1	+	+	PUNCT
cana-1582	460	1	=	=	SYM
cana-1582	460	2	+	+	ADJ
cana-1582	460	3			PROPN
cana-1582	460	4			PROPN
cana-1582	461	1			PROPN
cana-1582	461	2			PROPN
cana-1582	462	1			ADJ
cana-1582	462	2			PROPN
cana-1582	462	3			PROPN
cana-1582	462	4			NOUN
cana-1582	462	5			NOUN
cana-1582	462	6	(	(	PUNCT
cana-1582	462	7	22	22	NUM
cana-1582	462	8	)	)	PUNCT
cana-1582	462	9	(	(	PUNCT
cana-1582	462	10	2	2	X
cana-1582	462	11	)	)	PUNCT
cana-1582	462	12	inner	inner	ADJ
cana-1582	462	13	circular	circular	ADJ
cana-1582	462	14	arc	arc	NOUN
cana-1582	462	15	the	the	DET
cana-1582	462	16	inner	inner	ADJ
cana-1582	462	17	circular	circular	ADJ
cana-1582	462	18	arc	arc	NOUN
cana-1582	462	19	is	be	AUX
cana-1582	462	20	the	the	DET
cana-1582	462	21	boundary	boundary	ADJ
cana-1582	462	22	curve	curve	NOUN
cana-1582	462	23	over	over	ADP
cana-1582	462	24	the	the	DET
cana-1582	462	25	third	third	ADJ
cana-1582	462	26	quadrant	quadrant	NOUN
cana-1582	462	27	and	and	CCONJ
cana-1582	462	28	its	its	PRON
cana-1582	462	29	boundary	boundary	NOUN
cana-1582	462	30	is	be	AUX
cana-1582	462	31	described	describe	VERB
cana-1582	462	32	by	by	ADP
cana-1582	462	33	the	the	DET
cana-1582	462	34	equation	equation	NOUN
cana-1582	462	35	2	2	NUM
cana-1582	462	36	2	2	NUM
cana-1582	462	37	1/	1/	NUM
cana-1582	462	38	4x	4x	NOUN
cana-1582	462	39	y+	y+	NUM
cana-1582	462	40	=	=	SYM
cana-1582	462	41	and	and	CCONJ
cana-1582	462	42	hence	hence	ADV
cana-1582	462	43	the	the	DET
cana-1582	462	44	parametric	parametric	ADJ
cana-1582	462	45	equations	equation	NOUN
cana-1582	462	46	are	be	AUX
cana-1582	462	47	1	1	NUM
cana-1582	462	48	1	1	NUM
cana-1582	462	49	cos	co	NOUN
cana-1582	462	50	,	,	PUNCT
cana-1582	462	51	sin	sin	NOUN
cana-1582	462	52	,	,	PUNCT
cana-1582	462	53	(	(	PUNCT
cana-1582	462	54	/	/	SYM
cana-1582	462	55	2	2	NUM
cana-1582	462	56	0	0	NUM
cana-1582	462	57	)	)	PUNCT
cana-1582	462	58	2	2	NUM
cana-1582	462	59	2	2	NUM
cana-1582	462	60	x	x	SYM
cana-1582	462	61	y	y	X
cana-1582	462	62			PROPN
cana-1582	462	63			PROPN
cana-1582	462	64	=	=	X
cana-1582	462	65	=	=	SYM
cana-1582	462	66			NUM
cana-1582	462	67			NOUN
cana-1582	462	68	(	(	PUNCT
cana-1582	462	69	23	23	NUM
cana-1582	462	70	)	)	PUNCT
cana-1582	462	71	quartic	quartic	ADJ
cana-1582	462	72	spline	spline	NOUN
cana-1582	462	73	interpolants	interpolant	NOUN
cana-1582	462	74	as	as	ADP
cana-1582	462	75	parametric	parametric	ADJ
cana-1582	462	76	equations	equation	NOUN
cana-1582	462	77	the	the	DET
cana-1582	462	78	parametric	parametric	ADJ
cana-1582	462	79	equations	equation	NOUN
cana-1582	462	80	described	describe	VERB
cana-1582	462	81	above	above	ADV
cana-1582	462	82	can	can	AUX
cana-1582	462	83	be	be	AUX
cana-1582	462	84	represented	represent	VERB
cana-1582	462	85	by	by	ADP
cana-1582	462	86	two	two	NUM
cana-1582	462	87	integral	integral	ADJ
cana-1582	462	88	functions	function	NOUN
cana-1582	462	89	.	.	PUNCT
cana-1582	463	1	f(	f(	PROPN
cana-1582	463	2	)	)	PUNCT
cana-1582	463	3	and	and	CCONJ
cana-1582	463	4	g(	g(	PROPN
cana-1582	463	5	)	)	PUNCT
cana-1582	464	1	and	and	CCONJ
cana-1582	464	2	the	the	DET
cana-1582	464	3	associated	associated	ADJ
cana-1582	464	4	boundary	boundary	ADJ
cana-1582	464	5	conditions	condition	NOUN
cana-1582	464	6	on	on	ADP
cana-1582	464	7	f(	f(	PROPN
cana-1582	464	8	)	)	PUNCT
cana-1582	464	9	and	and	CCONJ
cana-1582	464	10	g(	g(	PROPN
cana-1582	464	11	)	)	PUNCT
cana-1582	464	12	over	over	ADP
cana-1582	464	13	each	each	DET
cana-1582	464	14	curved	curved	ADJ
cana-1582	464	15	boundaries	boundary	NOUN
cana-1582	464	16	in	in	ADP
cana-1582	464	17	the	the	DET
cana-1582	464	18	four	four	NUM
cana-1582	464	19	quadrants	quadrant	NOUN
cana-1582	464	20	(	(	PUNCT
cana-1582	464	21	see	see	VERB
cana-1582	464	22	fig	fig	NOUN
cana-1582	464	23	1	1	NUM
cana-1582	464	24	)	)	PUNCT
cana-1582	464	25	.	.	PUNCT
cana-1582	465	1	we	we	PRON
cana-1582	465	2	have	have	AUX
cana-1582	465	3	used	use	VERB
cana-1582	465	4	f(	f(	PROPN
cana-1582	465	5	)	)	PUNCT
cana-1582	465	6	and	and	CCONJ
cana-1582	465	7	g(	g(	PROPN
cana-1582	465	8	)	)	PUNCT
cana-1582	465	9	to	to	PART
cana-1582	465	10	generate	generate	VERB
cana-1582	465	11	the	the	DET
cana-1582	465	12	parametric	parametric	ADJ
cana-1582	465	13	equations	equation	NOUN
cana-1582	465	14	for	for	ADP
cana-1582	465	15	(	(	PUNCT
cana-1582	465	16	x(	x(	PROPN
cana-1582	465	17	)	)	PUNCT
cana-1582	465	18	,	,	PUNCT
cana-1582	465	19	y(	y(	PROPN
cana-1582	465	20	)	)	PUNCT
cana-1582	465	21	)	)	PUNCT
cana-1582	465	22	.	.	PUNCT
cana-1582	466	1	we	we	PRON
cana-1582	466	2	also	also	ADV
cana-1582	466	3	impose	impose	VERB
cana-1582	466	4	the	the	DET
cana-1582	466	5	conditions	condition	NOUN
cana-1582	466	6	(	(	PUNCT
cana-1582	466	7	)	)	PUNCT
cana-1582	466	8	(	(	PUNCT
cana-1582	466	9	)	)	PUNCT
cana-1582	466	10	(	(	PUNCT
cana-1582	466	11	)	)	PUNCT
cana-1582	466	12	(	(	PUNCT
cana-1582	466	13	)	)	PUNCT
cana-1582	466	14	(	(	PUNCT
cana-1582	466	15	)	)	PUNCT
cana-1582	466	16	(	(	PUNCT
cana-1582	466	17	)	)	PUNCT
cana-1582	466	18	(	(	PUNCT
cana-1582	466	19	)	)	PUNCT
cana-1582	466	20	(	(	PUNCT
cana-1582	466	21	)	)	PUNCT
cana-1582	466	22	,	,	PUNCT
cana-1582	466	23	,	,	PUNCT
cana-1582	466	24	1,2	1,2	NUM
cana-1582	466	25	p	p	NOUN
cana-1582	466	26	p	p	X
cana-1582	466	27	p	p	X
cana-1582	466	28	p	p	X
cana-1582	466	29	x	x	X
cana-1582	466	30	f	f	X
cana-1582	466	31	y	y	PROPN
cana-1582	466	32	g	g	PROPN
cana-1582	466	33	p	p	VERB
cana-1582	466	34			X
cana-1582	466	35			X
cana-1582	466	36	=	=	X
cana-1582	467	1	=	=	PUNCT
cana-1582	467	2	=	=	NOUN
cana-1582	467	3	.	.	PUNCT
cana-1582	468	1	we	we	PRON
cana-1582	468	2	shall	shall	AUX
cana-1582	468	3	now	now	ADV
cana-1582	468	4	explain	explain	VERB
cana-1582	468	5	the	the	DET
cana-1582	468	6	method	method	NOUN
cana-1582	468	7	of	of	ADP
cana-1582	468	8	finding	find	VERB
cana-1582	468	9	f(	f(	PROPN
cana-1582	468	10	)	)	PUNCT
cana-1582	468	11	,	,	PUNCT
cana-1582	468	12	g(	g(	PROPN
cana-1582	468	13	)	)	PUNCT
cana-1582	468	14	and	and	CCONJ
cana-1582	468	15	their	their	PRON
cana-1582	468	16	relations	relation	NOUN
cana-1582	468	17	with	with	ADP
cana-1582	468	18	x(	x(	PROPN
cana-1582	468	19	)	)	PUNCT
cana-1582	468	20	,	,	PUNCT
cana-1582	468	21	y(	y(	PROPN
cana-1582	468	22	)	)	PUNCT
cana-1582	468	23	the	the	DET
cana-1582	468	24	parametric	parametric	ADJ
cana-1582	468	25	equations	equation	NOUN
cana-1582	468	26	.	.	PUNCT
cana-1582	469	1	once	once	SCONJ
cana-1582	469	2	x(	x(	PROPN
cana-1582	469	3	)	)	PUNCT
cana-1582	469	4	and	and	CCONJ
cana-1582	469	5	y(	y(	NOUN
cana-1582	469	6	)	)	PUNCT
cana-1582	469	7	are	be	AUX
cana-1582	469	8	found	find	VERB
cana-1582	469	9	in	in	ADP
cana-1582	469	10	terms	term	NOUN
cana-1582	469	11	of	of	ADP
cana-1582	469	12	the	the	DET
cana-1582	469	13	quartic	quartic	ADJ
cana-1582	469	14	spline	spline	ADJ
cana-1582	469	15	integral	integral	ADJ
cana-1582	469	16	representations	representation	NOUN
cana-1582	469	17	as	as	ADP
cana-1582	469	18	in	in	ADP
cana-1582	469	19	[	[	X
cana-1582	469	20	22	22	NUM
cana-1582	469	21	]	]	PUNCT
cana-1582	469	22	for	for	ADP
cana-1582	469	23	f(	f(	PROPN
cana-1582	469	24	)	)	PUNCT
cana-1582	469	25	and	and	CCONJ
cana-1582	469	26	g(	g(	PROPN
cana-1582	469	27	)	)	PUNCT
cana-1582	469	28	,	,	PUNCT
cana-1582	469	29	we	we	PRON
cana-1582	469	30	can	can	AUX
cana-1582	469	31	implement	implement	VERB
cana-1582	469	32	the	the	DET
cana-1582	469	33	numerical	numerical	ADJ
cana-1582	469	34	scheme	scheme	NOUN
cana-1582	469	35	described	describe	VERB
cana-1582	469	36	in	in	ADP
cana-1582	469	37	eqns	eqns	PROPN
cana-1582	469	38	(	(	PUNCT
cana-1582	469	39	11	11	NUM
cana-1582	469	40	)	)	PUNCT
cana-1582	469	41	–	–	PUNCT
cana-1582	469	42	(	(	PUNCT
cana-1582	469	43	21	21	NUM
cana-1582	469	44	)	)	PUNCT
cana-1582	469	45	.	.	PUNCT
cana-1582	470	1	we	we	PRON
cana-1582	470	2	now	now	ADV
cana-1582	470	3	present	present	VERB
cana-1582	470	4	the	the	DET
cana-1582	470	5	integral	integral	ADJ
cana-1582	470	6	function	function	NOUN
cana-1582	470	7	representations	representation	NOUN
cana-1582	470	8	for	for	ADP
cana-1582	470	9	the	the	DET
cana-1582	470	10	curved	curved	ADJ
cana-1582	470	11	arcs	arc	NOUN
cana-1582	470	12	in	in	ADP
cana-1582	470	13	each	each	PRON
cana-1582	470	14	of	of	ADP
cana-1582	470	15	the	the	DET
cana-1582	470	16	four	four	NUM
cana-1582	470	17	quadrants	quadrant	NOUN
cana-1582	470	18	.	.	PUNCT
cana-1582	471	1	(	(	PUNCT
cana-1582	471	2	i	i	NOUN
cana-1582	471	3	)	)	PUNCT
cana-1582	471	4	over	over	ADP
cana-1582	471	5	the	the	DET
cana-1582	471	6	first	first	ADJ
cana-1582	471	7	quadrant	quadrant	NOUN
cana-1582	472	1	[	[	X
cana-1582	472	2	0	0	NUM
cana-1582	472	3	,	,	PUNCT
cana-1582	472	4	/	/	SYM
cana-1582	472	5	2]	2]	NUM
cana-1582	472	6			ADV
cana-1582	472	7	,	,	PUNCT
cana-1582	472	8	we	we	PRON
cana-1582	472	9	define	define	VERB
cana-1582	472	10	:	:	PUNCT
cana-1582	472	11	(	(	PUNCT
cana-1582	472	12	)	)	PUNCT
cana-1582	472	13	(	(	PUNCT
cana-1582	472	14	)	)	PUNCT
cana-1582	472	15	(	(	PUNCT
cana-1582	472	16	)	)	PUNCT
cana-1582	472	17	0	0	SYM
cana-1582	472	18	0	0	NUM
cana-1582	472	19	cos	cos	PROPN
cana-1582	472	20	sin	sin	NOUN
cana-1582	472	21	,	,	PUNCT
cana-1582	472	22	2	2	NUM
cana-1582	472	23	2	2	NUM
cana-1582	472	24	(	(	PUNCT
cana-1582	472	25	0	0	NUM
cana-1582	472	26	)	)	PUNCT
cana-1582	472	27	0	0	NUM
cana-1582	472	28	,	,	PUNCT
cana-1582	472	29	(	(	PUNCT
cana-1582	472	30	/	/	SYM
cana-1582	472	31	2	2	NUM
cana-1582	472	32	)	)	PUNCT
cana-1582	472	33	1/	1/	NUM
cana-1582	472	34	2	2	NUM
cana-1582	472	35	,	,	PUNCT
cana-1582	472	36	0	0	NUM
cana-1582	472	37	,	,	PUNCT
cana-1582	472	38	(	(	PUNCT
cana-1582	472	39	/	/	SYM
cana-1582	472	40	2	2	NUM
cana-1582	472	41	)	)	PUNCT
cana-1582	472	42	t	t	NOUN
cana-1582	472	43	t	t	NOUN
cana-1582	473	1	f	f	PROPN
cana-1582	474	1	d	d	X
cana-1582	474	2	g	g	PROPN
cana-1582	474	3	d	d	X
cana-1582	474	4	f	f	PROPN
cana-1582	475	1	f	f	NOUN
cana-1582	475	2	g	g	PROPN
cana-1582	475	3	g	g	PROPN
cana-1582	475	4			PROPN
cana-1582	475	5			X
cana-1582	475	6			PROPN
cana-1582	475	7			X
cana-1582	476	1			PROPN
cana-1582	476	2			X
cana-1582	476	3			ADJ
cana-1582	476	4			NOUN
cana-1582	476	5			NOUN
cana-1582	476	6			NOUN
cana-1582	476	7			NOUN
cana-1582	476	8	=	=	PUNCT
cana-1582	477	1	=	=	SYM
cana-1582	477	2			PROPN
cana-1582	478	1			PROPN
cana-1582	478	2			PROPN
cana-1582	478	3			PROPN
cana-1582	479	1			ADJ
cana-1582	479	2			PROPN
cana-1582	479	3			PROPN
cana-1582	479	4			NOUN
cana-1582	479	5	=	=	PUNCT
cana-1582	479	6	=	=	PUNCT
cana-1582	480	1	−	−	PROPN
cana-1582	480	2	=	=	SYM
cana-1582	481	1			NOUN
cana-1582	481	2			PUNCT
cana-1582	482	1	so	so	SCONJ
cana-1582	482	2	that	that	SCONJ
cana-1582	482	3	we	we	PRON
cana-1582	482	4	have	have	VERB
cana-1582	482	5	(	(	PUNCT
cana-1582	482	6	)	)	PUNCT
cana-1582	482	7	(	(	PUNCT
cana-1582	482	8	)	)	PUNCT
cana-1582	482	9	1x	1x	NUM
cana-1582	482	10	f	f	PUNCT
cana-1582	483	1	=	=	X
cana-1582	483	2	+	+	CCONJ
cana-1582	483	3	and	and	CCONJ
cana-1582	483	4	(	(	PUNCT
cana-1582	483	5	)	)	PUNCT
cana-1582	483	6	(	(	PUNCT
cana-1582	483	7	)	)	PUNCT
cana-1582	483	8	1/	1/	NUM
cana-1582	483	9	2y	2y	PROPN
cana-1582	483	10	g	g	NOUN
cana-1582	483	11	=	=	NOUN
cana-1582	483	12	+	+	CCONJ
cana-1582	483	13	the	the	DET
cana-1582	483	14	quartic	quartic	ADJ
cana-1582	483	15	splines	spline	NOUN
cana-1582	483	16	for	for	ADP
cana-1582	483	17	(	(	PUNCT
cana-1582	483	18	x(	x(	PROPN
cana-1582	483	19	)	)	PUNCT
cana-1582	483	20	,	,	PUNCT
cana-1582	483	21	y(	y(	PROPN
cana-1582	483	22	)	)	PUNCT
cana-1582	483	23	)	)	PUNCT
cana-1582	483	24	over	over	ADP
cana-1582	483	25	the	the	DET
cana-1582	483	26	first	first	ADJ
cana-1582	483	27	quadrant	quadrant	NOUN
cana-1582	483	28	,	,	PUNCT
cana-1582	483	29			ADJ
cana-1582	483	30	0	0	NOUN
cana-1582	483	31	,	,	PUNCT
cana-1582	483	32	/	/	SYM
cana-1582	483	33	2	2	NUM
cana-1582	483	34			NOUN
cana-1582	483	35	can	can	AUX
cana-1582	483	36	be	be	AUX
cana-1582	483	37	then	then	ADV
cana-1582	483	38	computed	compute	VERB
cana-1582	483	39	by	by	ADP
cana-1582	483	40	the	the	DET
cana-1582	483	41	matlab	matlab	PROPN
cana-1582	483	42	function	function	NOUN
cana-1582	483	43	:	:	PUNCT
cana-1582	483	44	quartic_spline	quartic_spline	INTJ
cana-1582	483	45	(	(	PUNCT
cana-1582	483	46	m	m	PROPN
cana-1582	483	47	,	,	PUNCT
cana-1582	483	48	a	a	DET
cana-1582	483	49	,	,	PUNCT
cana-1582	483	50	b	b	NOUN
cana-1582	483	51	,	,	PUNCT
cana-1582	483	52	n	n	CCONJ
cana-1582	483	53	)	)	PUNCT
cana-1582	483	54	in	in	ADP
cana-1582	483	55	which	which	PRON
cana-1582	483	56	m	m	VERB
cana-1582	483	57	refers	refer	VERB
cana-1582	483	58	to	to	AUX
cana-1582	483	59	function	function	NOUN
cana-1582	483	60	type	type	NOUN
cana-1582	483	61	,	,	PUNCT
cana-1582	483	62	a	a	PRON
cana-1582	483	63	,	,	PUNCT
cana-1582	483	64	b	b	NOUN
cana-1582	483	65	refer	refer	NOUN
cana-1582	483	66	to	to	PART
cana-1582	483	67	end	end	NOUN
cana-1582	483	68	points	point	NOUN
cana-1582	483	69	a	a	PRON
cana-1582	483	70	=	=	SYM
cana-1582	483	71	0	0	NUM
cana-1582	483	72	,	,	PUNCT
cana-1582	483	73	b	b	X
cana-1582	483	74	=	=	PUNCT
cana-1582	483	75	/2	/2	PROPN
cana-1582	483	76	for	for	ADP
cana-1582	483	77	the	the	DET
cana-1582	483	78	present	present	ADJ
cana-1582	483	79	case	case	NOUN
cana-1582	483	80	and	and	CCONJ
cana-1582	483	81	(	(	PUNCT
cana-1582	483	82	n+1	n+1	NOUN
cana-1582	483	83	)	)	PUNCT
cana-1582	483	84	refers	refer	VERB
cana-1582	483	85	to	to	ADP
cana-1582	483	86	the	the	DET
cana-1582	483	87	number	number	NOUN
cana-1582	483	88	of	of	ADP
cana-1582	483	89	subdivisions	subdivision	NOUN
cana-1582	483	90	made	make	VERB
cana-1582	483	91	in	in	ADP
cana-1582	483	92	[	[	X
cana-1582	483	93	a	a	PRON
cana-1582	483	94	,	,	PUNCT
cana-1582	483	95	b	b	NOUN
cana-1582	483	96	]	]	X
cana-1582	483	97	.	.	PUNCT
cana-1582	484	1	similar	similar	ADJ
cana-1582	484	2	reasoning	reasoning	NOUN
cana-1582	484	3	is	be	AUX
cana-1582	484	4	applicable	applicable	ADJ
cana-1582	484	5	to	to	ADP
cana-1582	484	6	the	the	DET
cana-1582	484	7	curved	curved	ADJ
cana-1582	484	8	arcs	arc	NOUN
cana-1582	484	9	of	of	ADP
cana-1582	484	10	the	the	DET
cana-1582	484	11	remaining	remain	VERB
cana-1582	484	12	quadrants	quadrant	NOUN
cana-1582	484	13	viz	viz	VERB
cana-1582	484	14	second	second	ADJ
cana-1582	484	15	third	third	ADJ
cana-1582	484	16	and	and	CCONJ
cana-1582	484	17	fourth	fourth	ADJ
cana-1582	484	18	.	.	PUNCT
cana-1582	485	1	(	(	PUNCT
cana-1582	485	2	ii	ii	NOUN
cana-1582	485	3	)	)	PUNCT
cana-1582	485	4	over	over	ADP
cana-1582	485	5	the	the	DET
cana-1582	485	6	second	second	ADJ
cana-1582	485	7	quadrant	quadrant	NOUN
cana-1582	485	8	,	,	PUNCT
cana-1582	485	9	[	[	PUNCT
cana-1582	485	10	/	/	SYM
cana-1582	485	11	2	2	NUM
cana-1582	485	12	,	,	PUNCT
cana-1582	485	13	]	]	PUNCT
cana-1582	485	14			X
cana-1582	485	15			PROPN
cana-1582	485	16			NOUN
cana-1582	485	17	,	,	PUNCT
cana-1582	485	18	we	we	PRON
cana-1582	485	19	define	define	VERB
cana-1582	485	20	:	:	PUNCT
cana-1582	485	21	communications	communication	NOUN
cana-1582	485	22	on	on	ADP
cana-1582	485	23	applied	apply	VERB
cana-1582	485	24	nonlinear	nonlinear	ADJ
cana-1582	485	25	analysis	analysis	NOUN
cana-1582	485	26	issn	issn	NOUN
cana-1582	485	27	:	:	PUNCT
cana-1582	485	28	1074	1074	NUM
cana-1582	485	29	-	-	PUNCT
cana-1582	485	30	133x	133x	NUM
cana-1582	485	31	vol	vol	NOUN
cana-1582	485	32	31	31	NUM
cana-1582	485	33	no	no	NOUN
cana-1582	485	34	.	.	PUNCT
cana-1582	486	1	8s	8s	PROPN
cana-1582	486	2	(	(	PUNCT
cana-1582	486	3	2024	2024	NUM
cana-1582	486	4	)	)	PUNCT
cana-1582	486	5	733	733	NUM
cana-1582	486	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1582	486	7	/	/	SYM
cana-1582	486	8	2	2	NUM
cana-1582	486	9	/	/	SYM
cana-1582	486	10	2	2	NUM
cana-1582	486	11	cos	cos	PROPN
cana-1582	486	12	sin	sin	NOUN
cana-1582	486	13	(	(	PUNCT
cana-1582	486	14	)	)	PUNCT
cana-1582	486	15	,	,	PUNCT
cana-1582	486	16	(	(	PUNCT
cana-1582	486	17	)	)	PUNCT
cana-1582	486	18	2	2	NUM
cana-1582	486	19	2	2	NUM
cana-1582	486	20	(	(	PUNCT
cana-1582	486	21	/	/	SYM
cana-1582	486	22	2	2	NUM
cana-1582	486	23	)	)	PUNCT
cana-1582	486	24	0	0	NUM
cana-1582	486	25	,	,	PUNCT
cana-1582	486	26	(	(	PUNCT
cana-1582	486	27	)	)	PUNCT
cana-1582	486	28	1/	1/	NUM
cana-1582	486	29	2	2	NUM
cana-1582	486	30	,	,	PUNCT
cana-1582	486	31	(	(	PUNCT
cana-1582	486	32	/	/	SYM
cana-1582	486	33	2	2	NUM
cana-1582	486	34	)	)	PUNCT
cana-1582	486	35	0	0	NUM
cana-1582	486	36	,	,	PUNCT
cana-1582	486	37	(	(	PUNCT
cana-1582	486	38	)	)	PUNCT
cana-1582	486	39	1/	1/	NUM
cana-1582	486	40	2	2	NUM
cana-1582	486	41	t	t	NOUN
cana-1582	486	42	t	t	NOUN
cana-1582	487	1	f	f	PROPN
cana-1582	488	1	d	d	X
cana-1582	488	2	g	g	PROPN
cana-1582	488	3	d	d	X
cana-1582	488	4	f	f	PROPN
cana-1582	489	1	f	f	NOUN
cana-1582	489	2	g	g	PROPN
cana-1582	489	3	g	g	PROPN
cana-1582	489	4			PROPN
cana-1582	489	5			X
cana-1582	489	6			PROPN
cana-1582	489	7			ADJ
cana-1582	489	8			X
cana-1582	489	9			X
cana-1582	489	10			PROPN
cana-1582	489	11			PROPN
cana-1582	489	12			PROPN
cana-1582	489	13			ADJ
cana-1582	489	14			NOUN
cana-1582	489	15			NOUN
cana-1582	489	16			NOUN
cana-1582	489	17			NOUN
cana-1582	489	18	=	=	PUNCT
cana-1582	490	1	=	=	SYM
cana-1582	490	2			PROPN
cana-1582	491	1			PROPN
cana-1582	491	2			PROPN
cana-1582	491	3			PROPN
cana-1582	492	1			ADJ
cana-1582	492	2			PROPN
cana-1582	492	3			PROPN
cana-1582	492	4			NOUN
cana-1582	492	5	=	=	PUNCT
cana-1582	492	6	=	=	SYM
cana-1582	493	1	−	−	PROPN
cana-1582	493	2	=	=	PUNCT
cana-1582	494	1	=	=	NOUN
cana-1582	494	2	−	−	PROPN
cana-1582	495	1			NOUN
cana-1582	496	1			PUNCT
cana-1582	497	1	so	so	SCONJ
cana-1582	497	2	that	that	SCONJ
cana-1582	497	3	(	(	PUNCT
cana-1582	497	4	)	)	PUNCT
cana-1582	497	5	(	(	PUNCT
cana-1582	497	6	)	)	PUNCT
cana-1582	497	7	,	,	PUNCT
cana-1582	497	8	(	(	PUNCT
cana-1582	497	9	)	)	PUNCT
cana-1582	497	10	(	(	PUNCT
cana-1582	497	11	)	)	PUNCT
cana-1582	497	12	1/	1/	NUM
cana-1582	497	13	2x	2x	NUM
cana-1582	497	14	f	f	PROPN
cana-1582	497	15	y	y	PROPN
cana-1582	497	16	g	g	PROPN
cana-1582	497	17			X
cana-1582	497	18			X
cana-1582	497	19	=	=	X
cana-1582	497	20	=	=	PUNCT
cana-1582	498	1	+	+	CCONJ
cana-1582	498	2	.	.	PUNCT
cana-1582	499	1	(	(	PUNCT
cana-1582	499	2	iii	iii	NOUN
cana-1582	499	3	)	)	PUNCT
cana-1582	499	4	over	over	ADP
cana-1582	499	5	the	the	DET
cana-1582	499	6	third	third	ADJ
cana-1582	499	7	quadrant	quadrant	NOUN
cana-1582	499	8	,	,	PUNCT
cana-1582	499	9	[	[	PUNCT
cana-1582	499	10	/	/	SYM
cana-1582	499	11	2,0]	2,0]	NUM
cana-1582	499	12			NOUN
cana-1582	500	1	and	and	CCONJ
cana-1582	500	2	we	we	PRON
cana-1582	500	3	define	define	VERB
cana-1582	500	4	:	:	PUNCT
cana-1582	500	5	/2	/2	PROPN
cana-1582	500	6	/2	/2	PROPN
cana-1582	501	1	cos	cos	PROPN
cana-1582	501	2	sin	sin	PROPN
cana-1582	501	3	(	(	PUNCT
cana-1582	501	4	)	)	PUNCT
cana-1582	501	5	,	,	PUNCT
cana-1582	501	6	(	(	PUNCT
cana-1582	501	7	)	)	PUNCT
cana-1582	501	8	2	2	NUM
cana-1582	501	9	2	2	NUM
cana-1582	501	10	(	(	PUNCT
cana-1582	501	11	/	/	SYM
cana-1582	501	12	2	2	NUM
cana-1582	501	13	)	)	PUNCT
cana-1582	501	14	0	0	NUM
cana-1582	501	15	,	,	PUNCT
cana-1582	501	16	(	(	PUNCT
cana-1582	501	17	0	0	NUM
cana-1582	501	18	)	)	PUNCT
cana-1582	501	19	1/	1/	NUM
cana-1582	501	20	2	2	NUM
cana-1582	501	21	,	,	PUNCT
cana-1582	501	22	(	(	PUNCT
cana-1582	501	23	/	/	SYM
cana-1582	501	24	2	2	NUM
cana-1582	501	25	)	)	PUNCT
cana-1582	501	26	0	0	NUM
cana-1582	501	27	,	,	PUNCT
cana-1582	501	28	(	(	PUNCT
cana-1582	501	29	0	0	NUM
cana-1582	501	30	)	)	PUNCT
cana-1582	501	31	1/	1/	NUM
cana-1582	501	32	2	2	NUM
cana-1582	501	33	t	t	NOUN
cana-1582	501	34	t	t	NOUN
cana-1582	502	1	f	f	PROPN
cana-1582	503	1	d	d	X
cana-1582	503	2	g	g	PROPN
cana-1582	503	3	d	d	X
cana-1582	503	4	f	f	PROPN
cana-1582	504	1	f	f	NOUN
cana-1582	504	2	g	g	PROPN
cana-1582	504	3	g	g	PROPN
cana-1582	504	4			PROPN
cana-1582	504	5			X
cana-1582	504	6			PROPN
cana-1582	504	7			ADJ
cana-1582	504	8			X
cana-1582	504	9			X
cana-1582	504	10			PROPN
cana-1582	504	11			ADJ
cana-1582	504	12			NOUN
cana-1582	504	13			NOUN
cana-1582	504	14			NOUN
cana-1582	504	15			NOUN
cana-1582	504	16	=	=	PUNCT
cana-1582	505	1	=	=	SYM
cana-1582	505	2			PROPN
cana-1582	506	1			PROPN
cana-1582	506	2			PROPN
cana-1582	506	3			PROPN
cana-1582	507	1			ADJ
cana-1582	507	2			PROPN
cana-1582	507	3			PROPN
cana-1582	507	4			NOUN
cana-1582	507	5	=	=	PUNCT
cana-1582	508	1	=	=	PUNCT
cana-1582	508	2	=	=	PUNCT
cana-1582	508	3	=	=	PUNCT
cana-1582	508	4	−	−	NOUN
cana-1582	508	5			NOUN
cana-1582	509	1			PUNCT
cana-1582	509	2	so	so	SCONJ
cana-1582	509	3	that	that	SCONJ
cana-1582	509	4	we	we	PRON
cana-1582	509	5	have	have	VERB
cana-1582	509	6	(	(	PUNCT
cana-1582	509	7	)	)	PUNCT
cana-1582	509	8	(	(	PUNCT
cana-1582	509	9	)	)	PUNCT
cana-1582	509	10	,	,	PUNCT
cana-1582	509	11	(	(	PUNCT
cana-1582	509	12	)	)	PUNCT
cana-1582	509	13	(	(	PUNCT
cana-1582	509	14	)	)	PUNCT
cana-1582	510	1	1/	1/	NUM
cana-1582	510	2	2x	2x	NUM
cana-1582	510	3	f	f	PROPN
cana-1582	510	4	y	y	PROPN
cana-1582	510	5	g	g	PROPN
cana-1582	510	6			X
cana-1582	510	7			X
cana-1582	511	1	=	=	X
cana-1582	512	1	=	=	PUNCT
cana-1582	513	1	+	+	CCONJ
cana-1582	513	2	here	here	ADV
cana-1582	513	3	,	,	PUNCT
cana-1582	513	4	we	we	PRON
cana-1582	513	5	may	may	AUX
cana-1582	513	6	note	note	VERB
cana-1582	513	7	that	that	SCONJ
cana-1582	513	8	it	it	PRON
cana-1582	513	9	is	be	AUX
cana-1582	513	10	required	require	VERB
cana-1582	513	11	to	to	PART
cana-1582	513	12	generate	generate	VERB
cana-1582	513	13	a	a	DET
cana-1582	513	14	circular	circular	ADJ
cana-1582	513	15	arc	arc	NOUN
cana-1582	513	16	in	in	ADP
cana-1582	513	17	first	first	ADJ
cana-1582	513	18	quadrant	quadrant	NOUN
cana-1582	513	19	of	of	ADP
cana-1582	513	20	the	the	DET
cana-1582	513	21	circle	circle	NOUN
cana-1582	513	22	2	2	NUM
cana-1582	513	23	2	2	NUM
cana-1582	513	24	1/	1/	NUM
cana-1582	513	25	4x	4x	NOUN
cana-1582	513	26	y+	y+	NUM
cana-1582	513	27	=	=	SYM
cana-1582	513	28	.	.	PUNCT
cana-1582	514	1	(	(	PUNCT
cana-1582	514	2	iv	iv	X
cana-1582	514	3	)	)	PUNCT
cana-1582	514	4	over	over	ADP
cana-1582	514	5	the	the	DET
cana-1582	514	6	fourth	fourth	ADJ
cana-1582	514	7	quadrant	quadrant	NOUN
cana-1582	514	8	,	,	PUNCT
cana-1582	514	9	[	[	X
cana-1582	514	10	3	3	NUM
cana-1582	514	11	/	/	SYM
cana-1582	514	12	2,2	2,2	NUM
cana-1582	514	13	]	]	SYM
cana-1582	514	14			PROPN
cana-1582	515	1			ADJ
cana-1582	515	2			NOUN
cana-1582	516	1	and	and	CCONJ
cana-1582	516	2	we	we	PRON
cana-1582	516	3	define	define	VERB
cana-1582	516	4	:	:	PUNCT
cana-1582	516	5	3	3	NUM
cana-1582	516	6	/	/	SYM
cana-1582	516	7	2	2	NUM
cana-1582	516	8	3	3	NUM
cana-1582	516	9	/	/	SYM
cana-1582	516	10	2	2	NUM
cana-1582	516	11	cos	cos	ADP
cana-1582	516	12	1	1	NUM
cana-1582	516	13	sin	sin	NOUN
cana-1582	516	14	(	(	PUNCT
cana-1582	516	15	)	)	PUNCT
cana-1582	516	16	,	,	PUNCT
cana-1582	516	17	(	(	PUNCT
cana-1582	516	18	)	)	PUNCT
cana-1582	516	19	2	2	NUM
cana-1582	516	20	2	2	NUM
cana-1582	516	21	(	(	PUNCT
cana-1582	516	22	3	3	NUM
cana-1582	516	23	/	/	SYM
cana-1582	516	24	2	2	NUM
cana-1582	516	25	)	)	PUNCT
cana-1582	516	26	0	0	NUM
cana-1582	516	27	,	,	PUNCT
cana-1582	516	28	(	(	PUNCT
cana-1582	516	29	2	2	NUM
cana-1582	516	30	)	)	PUNCT
cana-1582	516	31	0	0	PUNCT
cana-1582	517	1	and	and	CCONJ
cana-1582	517	2	(	(	PUNCT
cana-1582	517	3	3	3	NUM
cana-1582	517	4	/	/	SYM
cana-1582	517	5	2	2	NUM
cana-1582	517	6	)	)	PUNCT
cana-1582	517	7	0	0	NUM
cana-1582	517	8	,	,	PUNCT
cana-1582	517	9	(	(	PUNCT
cana-1582	517	10	2	2	X
cana-1582	517	11	)	)	PUNCT
cana-1582	517	12	1/	1/	NUM
cana-1582	517	13	2	2	NUM
cana-1582	517	14	t	t	NOUN
cana-1582	517	15	t	t	NOUN
cana-1582	518	1	f	f	PROPN
cana-1582	519	1	d	d	X
cana-1582	519	2	g	g	PROPN
cana-1582	519	3	d	d	X
cana-1582	519	4	f	f	PROPN
cana-1582	520	1	f	f	NOUN
cana-1582	520	2	g	g	PROPN
cana-1582	520	3	g	g	PROPN
cana-1582	520	4			PROPN
cana-1582	520	5			X
cana-1582	520	6			PROPN
cana-1582	520	7			ADJ
cana-1582	520	8			X
cana-1582	520	9			X
cana-1582	520	10			PROPN
cana-1582	520	11			PROPN
cana-1582	520	12			PROPN
cana-1582	520	13			PROPN
cana-1582	520	14	+	+	NOUN
cana-1582	520	15			NOUN
cana-1582	520	16			NOUN
cana-1582	520	17			NOUN
cana-1582	520	18			NOUN
cana-1582	520	19	=	=	PUNCT
cana-1582	521	1	=	=	SYM
cana-1582	521	2			PROPN
cana-1582	522	1			PROPN
cana-1582	522	2			PROPN
cana-1582	522	3			PROPN
cana-1582	523	1			ADJ
cana-1582	523	2			PROPN
cana-1582	523	3			PROPN
cana-1582	523	4			NOUN
cana-1582	523	5	=	=	PUNCT
cana-1582	524	1	=	=	PUNCT
cana-1582	524	2	=	=	PUNCT
cana-1582	525	1	=	=	NOUN
cana-1582	525	2			NOUN
cana-1582	525	3			PUNCT
cana-1582	526	1	so	so	SCONJ
cana-1582	526	2	that	that	SCONJ
cana-1582	526	3	(	(	PUNCT
cana-1582	526	4	)	)	PUNCT
cana-1582	526	5	(	(	PUNCT
cana-1582	526	6	)	)	PUNCT
cana-1582	526	7	1/	1/	NUM
cana-1582	526	8	2	2	NUM
cana-1582	526	9	,	,	PUNCT
cana-1582	526	10	(	(	PUNCT
cana-1582	526	11	)	)	PUNCT
cana-1582	526	12	(	(	PUNCT
cana-1582	526	13	)	)	PUNCT
cana-1582	526	14	x	x	X
cana-1582	526	15	f	f	PROPN
cana-1582	526	16	y	y	PROPN
cana-1582	526	17	g	g	PROPN
cana-1582	526	18			X
cana-1582	526	19			X
cana-1582	526	20	=	=	PROPN
cana-1582	526	21	+	+	CCONJ
cana-1582	526	22	=	=	SYM
cana-1582	526	23	it	it	PRON
cana-1582	526	24	is	be	AUX
cana-1582	526	25	important	important	ADJ
cana-1582	526	26	to	to	PART
cana-1582	526	27	note	note	VERB
cana-1582	526	28	here	here	ADV
cana-1582	526	29	that	that	SCONJ
cana-1582	526	30	as	as	SCONJ
cana-1582	526	31	shown	show	VERB
cana-1582	526	32	in	in	ADP
cana-1582	526	33	fig1	fig1	PROPN
cana-1582	526	34	,	,	PUNCT
cana-1582	526	35	the	the	DET
cana-1582	526	36	outer	outer	ADJ
cana-1582	526	37	circular	circular	ADJ
cana-1582	526	38	arcs	arcs	NOUN
cana-1582	526	39	covers	cover	VERB
cana-1582	526	40	the	the	DET
cana-1582	526	41	first	first	ADJ
cana-1582	526	42	,	,	PUNCT
cana-1582	526	43	second	second	ADJ
cana-1582	526	44	and	and	CCONJ
cana-1582	526	45	fourth	fourth	ADJ
cana-1582	526	46	quadrants	quadrant	NOUN
cana-1582	526	47	of	of	ADP
cana-1582	526	48	the	the	DET
cana-1582	526	49	circle	circle	NOUN
cana-1582	526	50	.	.	PUNCT
cana-1582	527	1	2	2	NUM
cana-1582	527	2	2	2	NUM
cana-1582	527	3	(	(	PUNCT
cana-1582	527	4	1/	1/	NUM
cana-1582	527	5	2	2	NUM
cana-1582	527	6	)	)	PUNCT
cana-1582	527	7	(	(	PUNCT
cana-1582	527	8	1/	1/	NUM
cana-1582	527	9	2	2	NUM
cana-1582	527	10	)	)	PUNCT
cana-1582	527	11	1/	1/	NUM
cana-1582	527	12	4x	4x	NUM
cana-1582	527	13	y−	y−	NOUN
cana-1582	527	14	+	+	CCONJ
cana-1582	527	15	−	−	PROPN
cana-1582	527	16	=	=	PUNCT
cana-1582	527	17	examples	example	NOUN
cana-1582	527	18	we	we	PRON
cana-1582	527	19	consider	consider	VERB
cana-1582	527	20	the	the	DET
cana-1582	527	21	following	follow	VERB
cana-1582	527	22	integrals	integral	NOUN
cana-1582	527	23	:	:	PUNCT
cana-1582	527	24	𝐼𝐼𝑖	𝐼𝐼𝑖	PROPN
cana-1582	527	25	=	=	SYM
cana-1582	527	26	∬	∬	NOUN
cana-1582	527	27	𝑓𝑖(𝑥	𝑓𝑖(𝑥	NUM
cana-1582	527	28	,	,	PUNCT
cana-1582	527	29	𝑦	𝑦	X
cana-1582	527	30	)	)	PUNCT
cana-1582	527	31	⬚	⬚	PROPN
cana-1582	527	32	𝜋𝑥𝑦	𝜋𝑥𝑦	X
cana-1582	527	33	𝑑𝑥𝑑𝑦	𝑑𝑥𝑑𝑦	X
cana-1582	527	34	,	,	PUNCT
cana-1582	527	35	(	(	PUNCT
cana-1582	527	36	𝑖	𝑖	SYM
cana-1582	527	37	=	=	SYM
cana-1582	527	38	1	1	NUM
cana-1582	527	39	,	,	PUNCT
cana-1582	527	40	2	2	NUM
cana-1582	527	41	,	,	PUNCT
cana-1582	527	42	3	3	NUM
cana-1582	527	43	,	,	PUNCT
cana-1582	527	44	4	4	NUM
cana-1582	527	45	,	,	PUNCT
cana-1582	527	46	5	5	NUM
cana-1582	527	47	,	,	PUNCT
cana-1582	527	48	6	6	NUM
cana-1582	527	49	,	,	PUNCT
cana-1582	527	50	7	7	NUM
cana-1582	527	51	)	)	PUNCT
cana-1582	527	52	(	(	PUNCT
cana-1582	527	53	24	24	NUM
cana-1582	527	54	)	)	PUNCT
cana-1582	527	55	the	the	DET
cana-1582	527	56	values	value	NOUN
cana-1582	527	57	if	if	SCONJ
cana-1582	527	58	the	the	DET
cana-1582	527	59	integrals	integral	NOUN
cana-1582	527	60	𝐼𝐼𝑖	𝐼𝐼𝑖	VERB
cana-1582	527	61	(	(	PUNCT
cana-1582	527	62	𝑖	𝑖	SYM
cana-1582	527	63	=	=	SYM
cana-1582	527	64	1	1	NUM
cana-1582	527	65	,	,	PUNCT
cana-1582	527	66	2	2	NUM
cana-1582	527	67	,	,	PUNCT
cana-1582	527	68	3	3	NUM
cana-1582	527	69	,	,	PUNCT
cana-1582	527	70	4	4	NUM
cana-1582	527	71	,	,	PUNCT
cana-1582	527	72	5	5	NUM
cana-1582	527	73	,	,	PUNCT
cana-1582	527	74	6	6	NUM
cana-1582	527	75	,	,	PUNCT
cana-1582	527	76	7	7	NUM
cana-1582	527	77	)	)	PUNCT
cana-1582	527	78	with	with	ADP
cana-1582	527	79	a	a	DET
cana-1582	527	80	relative	relative	ADJ
cana-1582	527	81	error	error	NOUN
cana-1582	527	82	around	around	ADP
cana-1582	527	83	10−14	10−14	NUM
cana-1582	527	84	,	,	PUNCT
cana-1582	527	85	are	be	AUX
cana-1582	527	86	𝐼𝐼1	𝐼𝐼1	ADJ
cana-1582	527	87	=	=	SYM
cana-1582	527	88	𝐼ω0	𝐼ω0	NOUN
cana-1582	527	89	(	(	PUNCT
cana-1582	527	90	𝑓1	𝑓1	PROPN
cana-1582	527	91	)	)	PUNCT
cana-1582	527	92	=	=	SYM
cana-1582	527	93	0.20307626985342	0.20307626985342	NUM
cana-1582	527	94	𝐼𝐼2	𝐼𝐼2	PROPN
cana-1582	527	95	=	=	PUNCT
cana-1582	527	96	𝐼ω0	𝐼ω0	NOUN
cana-1582	527	97	(	(	PUNCT
cana-1582	527	98	𝑓2	𝑓2	ADJ
cana-1582	527	99	)	)	PUNCT
cana-1582	527	100	=	=	PUNCT
cana-1582	528	1	0.20646770293563	0.20646770293563	NUM
cana-1582	528	2	𝐼𝐼3	𝐼𝐼3	NOUN
cana-1582	528	3	=	=	PUNCT
cana-1582	528	4	𝐼ω0	𝐼ω0	NOUN
cana-1582	528	5	(	(	PUNCT
cana-1582	528	6	𝑓3	𝑓3	NOUN
cana-1582	528	7	)	)	PUNCT
cana-1582	528	8	=	=	PUNCT
cana-1582	529	1	638.55743274702	638.55743274702	NUM
cana-1582	529	2	𝐼𝐼4	𝐼𝐼4	NOUN
cana-1582	529	3	=	=	SYM
cana-1582	529	4	𝐼ω0	𝐼ω0	NOUN
cana-1582	529	5	(	(	PUNCT
cana-1582	529	6	𝑓4	𝑓4	NOUN
cana-1582	529	7	)	)	PUNCT
cana-1582	529	8	=	=	PUNCT
cana-1582	530	1	0.57263720432530	0.57263720432530	NUM
cana-1582	530	2	𝐼𝐼5	𝐼𝐼5	NOUN
cana-1582	530	3	=	=	SYM
cana-1582	530	4	𝐼ω0	𝐼ω0	NOUN
cana-1582	530	5	(	(	PUNCT
cana-1582	530	6	𝑓5	𝑓5	NOUN
cana-1582	530	7	)	)	PUNCT
cana-1582	530	8	=	=	PUNCT
cana-1582	531	1	0.03137185199242	0.03137185199242	NUM
cana-1582	531	2	𝐼𝐼6	𝐼𝐼6	NOUN
cana-1582	531	3	=	=	SYM
cana-1582	531	4	𝐼ω0	𝐼ω0	NOUN
cana-1582	531	5	(	(	PUNCT
cana-1582	531	6	𝑓6	𝑓6	NUM
cana-1582	531	7	)	)	PUNCT
cana-1582	531	8	=	=	PUNCT
cana-1582	532	1	0.0062895812195655	0.0062895812195655	NUM
cana-1582	532	2	𝐼𝐼7	𝐼𝐼7	NOUN
cana-1582	532	3	=	=	NOUN
cana-1582	532	4	𝐼ω0	𝐼ω0	ADJ
cana-1582	532	5	(	(	PUNCT
cana-1582	532	6	𝑓7	𝑓7	NOUN
cana-1582	532	7	)	)	PUNCT
cana-1582	532	8	=	=	PUNCT
cana-1582	532	9	0.6426990816987241	0.6426990816987241	NUM
cana-1582	532	10	communications	communication	NOUN
cana-1582	532	11	on	on	ADP
cana-1582	532	12	applied	apply	VERB
cana-1582	532	13	nonlinear	nonlinear	ADJ
cana-1582	532	14	analysis	analysis	NOUN
cana-1582	532	15	issn	issn	NOUN
cana-1582	532	16	:	:	PUNCT
cana-1582	532	17	1074	1074	NUM
cana-1582	532	18	-	-	PUNCT
cana-1582	532	19	133x	133x	NUM
cana-1582	532	20	vol	vol	NOUN
cana-1582	532	21	31	31	NUM
cana-1582	532	22	no	no	NOUN
cana-1582	532	23	.	.	PUNCT
cana-1582	533	1	8s	8s	PROPN
cana-1582	533	2	(	(	PUNCT
cana-1582	533	3	2024	2024	NUM
cana-1582	533	4	)	)	PUNCT
cana-1582	533	5	734	734	NUM
cana-1582	533	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1582	533	7	where	where	SCONJ
cana-1582	533	8	xy	xy	PROPN
cana-1582	533	9			PROPN
cana-1582	533	10	is	be	AUX
cana-1582	533	11	the	the	DET
cana-1582	533	12	curved	curved	ADJ
cana-1582	533	13	domain	domain	NOUN
cana-1582	533	14	described	describe	VERB
cana-1582	533	15	in	in	ADP
cana-1582	533	16	fig	fig	NOUN
cana-1582	533	17	1	1	NUM
cana-1582	533	18	.	.	PUNCT
cana-1582	534	1	the	the	DET
cana-1582	534	2	integrands	integrand	NOUN
cana-1582	534	3	(	(	PUNCT
cana-1582	534	4	,	,	PUNCT
cana-1582	534	5	)	)	PUNCT
cana-1582	535	1	i	i	PRON
cana-1582	535	2	f	f	NOUN
cana-1582	536	1	x	x	VERB
cana-1582	536	2	y	y	PROPN
cana-1582	536	3	are	be	AUX
cana-1582	536	4	the	the	DET
cana-1582	536	5	following	following	NOUN
cana-1582	536	6	[	[	X
cana-1582	536	7	18	18	NUM
cana-1582	536	8	]	]	PUNCT
cana-1582	536	9	.	.	PUNCT
cana-1582	537	1			PROPN
cana-1582	537	2			PROPN
cana-1582	537	3	2	2	NUM
cana-1582	537	4	2	2	NUM
cana-1582	537	5	2	2	NUM
cana-1582	537	6	1	1	NUM
cana-1582	537	7	2	2	NUM
cana-1582	537	8	2	2	NUM
cana-1582	537	9	2	2	NUM
cana-1582	537	10	2	2	NUM
cana-1582	537	11	3	3	NUM
cana-1582	537	12	1	1	NUM
cana-1582	537	13	3	3	NUM
cana-1582	537	14	1	1	NUM
cana-1582	537	15	1	1	NUM
cana-1582	537	16	(	(	PUNCT
cana-1582	537	17	,	,	PUNCT
cana-1582	537	18	)	)	PUNCT
cana-1582	537	19	exp	exp	NOUN
cana-1582	537	20	(	(	PUNCT
cana-1582	537	21	9	9	NUM
cana-1582	537	22	2	2	NUM
cana-1582	537	23	)	)	PUNCT
cana-1582	537	24	(	(	PUNCT
cana-1582	537	25	9	9	NUM
cana-1582	537	26	2	2	NUM
cana-1582	537	27	)	)	PUNCT
cana-1582	537	28	exp	exp	NOUN
cana-1582	537	29	(	(	PUNCT
cana-1582	537	30	9	9	NUM
cana-1582	537	31	1	1	NUM
cana-1582	537	32	)	)	PUNCT
cana-1582	537	33	(	(	PUNCT
cana-1582	537	34	9	9	NUM
cana-1582	537	35	1	1	NUM
cana-1582	537	36	)	)	PUNCT
cana-1582	537	37	4	4	NUM
cana-1582	537	38	4	4	NUM
cana-1582	537	39	4	4	NUM
cana-1582	537	40	49	49	NUM
cana-1582	537	41	10	10	NUM
cana-1582	537	42	1	1	NUM
cana-1582	537	43	1	1	NUM
cana-1582	537	44	1	1	NUM
cana-1582	537	45	exp	exp	NOUN
cana-1582	537	46	(	(	PUNCT
cana-1582	537	47	9	9	NUM
cana-1582	537	48	7	7	NUM
cana-1582	537	49	)	)	PUNCT
cana-1582	537	50	(	(	PUNCT
cana-1582	537	51	9	9	NUM
cana-1582	537	52	3	3	NUM
cana-1582	537	53	)	)	PUNCT
cana-1582	537	54	exp	exp	NOUN
cana-1582	537	55	(	(	PUNCT
cana-1582	537	56	(	(	PUNCT
cana-1582	537	57	9	9	NUM
cana-1582	537	58	4	4	NUM
cana-1582	537	59	)	)	PUNCT
cana-1582	537	60	(	(	PUNCT
cana-1582	537	61	9	9	NUM
cana-1582	537	62	7	7	NUM
cana-1582	537	63	)	)	PUNCT
cana-1582	537	64	2	2	NUM
cana-1582	537	65	4	4	NUM
cana-1582	537	66	5	5	NUM
cana-1582	537	67	f	f	NOUN
cana-1582	537	68	x	x	SYM
cana-1582	538	1	y	y	NOUN
cana-1582	538	2	x	x	PUNCT
cana-1582	538	3	y	y	NOUN
cana-1582	538	4	x	x	X
cana-1582	538	5	y	y	NOUN
cana-1582	538	6	x	x	X
cana-1582	538	7	y	y	VERB
cana-1582	538	8	y	y	PROPN
cana-1582	538	9	y	y	PROPN
cana-1582	538	10			PUNCT
cana-1582	539	1			NOUN
cana-1582	539	2			PUNCT
cana-1582	540	1			PROPN
cana-1582	540	2	=	=	PUNCT
cana-1582	541	1	−	−	PROPN
cana-1582	541	2	−	−	PROPN
cana-1582	542	1	+	+	CCONJ
cana-1582	542	2	−	−	PROPN
cana-1582	543	1	+	+	CCONJ
cana-1582	543	2	−	−	PROPN
cana-1582	544	1	+	+	CCONJ
cana-1582	545	1	−	−	PROPN
cana-1582	546	1	+	+	NOUN
cana-1582	546	2			NOUN
cana-1582	546	3			NOUN
cana-1582	547	1			NUM
cana-1582	547	2			INTJ
cana-1582	548	1			PROPN
cana-1582	548	2			PROPN
cana-1582	549	1			NUM
cana-1582	549	2			NOUN
cana-1582	549	3			ADP
cana-1582	550	1			NUM
cana-1582	551	1	+	+	CCONJ
cana-1582	551	2	−	−	PROPN
cana-1582	551	3	−	−	PROPN
cana-1582	552	1	+	+	CCONJ
cana-1582	552	2	−	−	PROPN
cana-1582	552	3	−	−	NUM
cana-1582	552	4	−	−	NOUN
cana-1582	553	1	−	−	PROPN
cana-1582	554	1	+	+	CCONJ
cana-1582	554	2	−	−	NOUN
cana-1582	554	3			INTJ
cana-1582	555	1			PROPN
cana-1582	555	2			PROPN
cana-1582	555	3	(	(	PUNCT
cana-1582	555	4	25	25	NUM
cana-1582	555	5	)	)	SYM
cana-1582	555	6	2	2	NUM
cana-1582	555	7	2	2	NUM
cana-1582	555	8	2	2	NUM
cana-1582	555	9	(	(	PUNCT
cana-1582	555	10	,	,	PUNCT
cana-1582	555	11	)	)	PUNCT
cana-1582	555	12	(	(	PUNCT
cana-1582	555	13	0.5	0.5	NUM
cana-1582	555	14	)	)	PUNCT
cana-1582	555	15	(	(	PUNCT
cana-1582	555	16	0.5)f	0.5)f	NOUN
cana-1582	555	17	x	x	SYM
cana-1582	555	18	y	y	NOUN
cana-1582	555	19	x	x	PROPN
cana-1582	555	20	y=	y=	NUM
cana-1582	555	21	−	−	PROPN
cana-1582	556	1	+	+	CCONJ
cana-1582	557	1	−	−	PROPN
cana-1582	557	2	(	(	PUNCT
cana-1582	557	3	26	26	NUM
cana-1582	557	4	)	)	PUNCT
cana-1582	557	5	19	19	NUM
cana-1582	557	6	3	3	NUM
cana-1582	557	7	(	(	PUNCT
cana-1582	557	8	,	,	PUNCT
cana-1582	557	9	)	)	PUNCT
cana-1582	557	10	(	(	PUNCT
cana-1582	557	11	)	)	PUNCT
cana-1582	557	12	f	f	X
cana-1582	557	13	x	x	PUNCT
cana-1582	557	14	y	y	NOUN
cana-1582	557	15	x	x	X
cana-1582	557	16	y=	y=	PROPN
cana-1582	558	1	+	+	CCONJ
cana-1582	558	2	(	(	PUNCT
cana-1582	558	3	27	27	NUM
cana-1582	558	4	)	)	PUNCT
cana-1582	558	5			NOUN
cana-1582	558	6	2	2	NOUN
cana-1582	558	7	2	2	NUM
cana-1582	558	8	4	4	NUM
cana-1582	558	9	(	(	PUNCT
cana-1582	558	10	,	,	PUNCT
cana-1582	558	11	)	)	PUNCT
cana-1582	558	12	exp	exp	NOUN
cana-1582	558	13	(	(	PUNCT
cana-1582	558	14	(	(	PUNCT
cana-1582	558	15	0.5	0.5	NUM
cana-1582	558	16	)	)	PUNCT
cana-1582	558	17	(	(	PUNCT
cana-1582	558	18	0.5	0.5	NUM
cana-1582	558	19	)	)	PUNCT
cana-1582	558	20	)	)	PUNCT
cana-1582	559	1	f	f	X
cana-1582	559	2	x	x	PUNCT
cana-1582	559	3	y	y	NOUN
cana-1582	559	4	x	x	PROPN
cana-1582	559	5	y=	y=	NUM
cana-1582	559	6	−	−	NOUN
cana-1582	559	7	−	−	PROPN
cana-1582	560	1	+	+	CCONJ
cana-1582	560	2	−	−	PROPN
cana-1582	560	3	(	(	PUNCT
cana-1582	560	4	28	28	NUM
cana-1582	560	5	)	)	PUNCT
cana-1582	560	6			NOUN
cana-1582	560	7	2	2	NOUN
cana-1582	560	8	2	2	NUM
cana-1582	560	9	5	5	NUM
cana-1582	560	10	(	(	PUNCT
cana-1582	560	11	,	,	PUNCT
cana-1582	560	12	)	)	PUNCT
cana-1582	560	13	exp	exp	NOUN
cana-1582	560	14	100	100	NUM
cana-1582	560	15	(	(	PUNCT
cana-1582	560	16	(	(	PUNCT
cana-1582	560	17	0.5	0.5	NUM
cana-1582	560	18	)	)	PUNCT
cana-1582	560	19	(	(	PUNCT
cana-1582	560	20	0.5	0.5	NUM
cana-1582	560	21	)	)	PUNCT
cana-1582	560	22	)	)	PUNCT
cana-1582	561	1	f	f	X
cana-1582	561	2	x	x	PUNCT
cana-1582	561	3	y	y	NOUN
cana-1582	561	4	x	x	PROPN
cana-1582	561	5	y=	y=	NUM
cana-1582	561	6	−	−	NOUN
cana-1582	561	7	−	−	PROPN
cana-1582	562	1	+	+	CCONJ
cana-1582	562	2	−	−	PROPN
cana-1582	562	3	(	(	PUNCT
cana-1582	562	4	29	29	NUM
cana-1582	562	5	)	)	PUNCT
cana-1582	562	6	6	6	NUM
cana-1582	562	7	(	(	PUNCT
cana-1582	562	8	,	,	PUNCT
cana-1582	562	9	)	)	PUNCT
cana-1582	562	10	cos(20	cos(20	PROPN
cana-1582	562	11	(	(	PUNCT
cana-1582	562	12	)	)	PUNCT
cana-1582	562	13	)	)	PUNCT
cana-1582	563	1	f	f	X
cana-1582	564	1	x	x	PUNCT
cana-1582	564	2	y	y	NOUN
cana-1582	564	3	x	x	X
cana-1582	564	4	y=	y=	PROPN
cana-1582	565	1	+	+	CCONJ
cana-1582	565	2	(	(	PUNCT
cana-1582	565	3	30	30	NUM
cana-1582	565	4	)	)	PUNCT
cana-1582	565	5	7	7	NUM
cana-1582	565	6	(	(	PUNCT
cana-1582	565	7	,	,	PUNCT
cana-1582	565	8	)	)	PUNCT
cana-1582	565	9	1f	1f	NUM
cana-1582	565	10	x	x	SYM
cana-1582	566	1	y	y	PROPN
cana-1582	566	2	=	=	SYM
cana-1582	566	3	(	(	PUNCT
cana-1582	566	4	31	31	NUM
cana-1582	566	5	)	)	PUNCT
cana-1582	566	6	we	we	PRON
cana-1582	566	7	have	have	AUX
cana-1582	566	8	implemented	implement	VERB
cana-1582	566	9	the	the	DET
cana-1582	566	10	numerical	numerical	ADJ
cana-1582	566	11	scheme	scheme	NOUN
cana-1582	566	12	outlined	outline	VERB
cana-1582	566	13	in	in	ADP
cana-1582	566	14	the	the	DET
cana-1582	566	15	above	above	ADJ
cana-1582	566	16	by	by	ADP
cana-1582	566	17	leveraging	leverage	VERB
cana-1582	566	18	the	the	DET
cana-1582	566	19	explicit	explicit	ADJ
cana-1582	566	20	parametric	parametric	ADJ
cana-1582	566	21	equations	equation	NOUN
cana-1582	566	22	to	to	PART
cana-1582	566	23	compute	compute	VERB
cana-1582	566	24	the	the	DET
cana-1582	566	25	integrals	integral	NOUN
cana-1582	566	26	specified	specify	VERB
cana-1582	566	27	by	by	ADP
cana-1582	566	28	equation	equation	NOUN
cana-1582	566	29	(	(	PUNCT
cana-1582	566	30	24	24	NUM
cana-1582	566	31	)	)	PUNCT
cana-1582	566	32	.	.	PUNCT
cana-1582	567	1	to	to	PART
cana-1582	567	2	facilitate	facilitate	VERB
cana-1582	567	3	this	this	DET
cana-1582	567	4	computation	computation	NOUN
cana-1582	567	5	,	,	PUNCT
cana-1582	567	6	we	we	PRON
cana-1582	567	7	've	have	AUX
cana-1582	567	8	developed	develop	VERB
cana-1582	567	9	two	two	NUM
cana-1582	567	10	matlab	matlab	PROPN
cana-1582	567	11	programs	program	NOUN
cana-1582	567	12	.	.	PUNCT
cana-1582	568	1	these	these	DET
cana-1582	568	2	programs	program	NOUN
cana-1582	568	3	utilize	utilize	VERB
cana-1582	568	4	the	the	DET
cana-1582	568	5	precise	precise	ADJ
cana-1582	568	6	representation	representation	NOUN
cana-1582	568	7	of	of	ADP
cana-1582	568	8	the	the	DET
cana-1582	568	9	boundary	boundary	ADJ
cana-1582	568	10	curve	curve	NOUN
cana-1582	568	11	of	of	ADP
cana-1582	568	12	the	the	DET
cana-1582	568	13	lunar	lunar	ADJ
cana-1582	568	14	model	model	NOUN
cana-1582	568	15	provided	provide	VERB
cana-1582	568	16	by	by	ADP
cana-1582	568	17	the	the	DET
cana-1582	568	18	parametric	parametric	ADJ
cana-1582	568	19	equations	equation	NOUN
cana-1582	568	20	elucidated	elucidate	VERB
cana-1582	568	21	in	in	ADP
cana-1582	568	22	equations	equation	NOUN
cana-1582	568	23	(	(	PUNCT
cana-1582	568	24	24	24	NUM
cana-1582	568	25	)	)	PUNCT
cana-1582	568	26	.	.	PUNCT
cana-1582	569	1	notably	notably	ADV
cana-1582	569	2	,	,	PUNCT
cana-1582	569	3	even	even	ADV
cana-1582	569	4	with	with	ADP
cana-1582	569	5	as	as	ADV
cana-1582	569	6	few	few	ADJ
cana-1582	569	7	as	as	ADP
cana-1582	569	8	four	four	NUM
cana-1582	569	9	points	point	NOUN
cana-1582	569	10	strategically	strategically	ADV
cana-1582	569	11	placed	place	VERB
cana-1582	569	12	along	along	ADP
cana-1582	569	13	the	the	DET
cana-1582	569	14	curved	curved	ADJ
cana-1582	569	15	boundary	boundary	NOUN
cana-1582	569	16	of	of	ADP
cana-1582	569	17	the	the	DET
cana-1582	569	18	lunar	lunar	ADJ
cana-1582	569	19	model	model	NOUN
cana-1582	569	20	,	,	PUNCT
cana-1582	569	21	employing	employ	VERB
cana-1582	569	22	gauss	gauss	ADJ
cana-1582	569	23	-	-	PUNCT
cana-1582	569	24	legendre	legendre	PROPN
cana-1582	569	25	quadrature	quadrature	NOUN
cana-1582	569	26	rules	rule	NOUN
cana-1582	569	27	of	of	ADP
cana-1582	569	28	order	order	NOUN
cana-1582	569	29	(	(	PUNCT
cana-1582	569	30	32	32	NUM
cana-1582	569	31	,	,	PUNCT
cana-1582	569	32	36	36	NUM
cana-1582	569	33	)	)	PUNCT
cana-1582	569	34	or	or	CCONJ
cana-1582	569	35	(	(	PUNCT
cana-1582	569	36	32	32	NUM
cana-1582	569	37	,	,	PUNCT
cana-1582	569	38	40	40	NUM
cana-1582	569	39	)	)	PUNCT
cana-1582	569	40	yields	yield	NOUN
cana-1582	569	41	near	near	ADP
cana-1582	569	42	-	-	PUNCT
cana-1582	569	43	exact	exact	ADJ
cana-1582	569	44	results	result	NOUN
cana-1582	569	45	.	.	PUNCT
cana-1582	570	1	a	a	DET
cana-1582	570	2	glimpse	glimpse	NOUN
cana-1582	570	3	of	of	ADP
cana-1582	570	4	the	the	DET
cana-1582	570	5	output	output	NOUN
cana-1582	570	6	generated	generate	VERB
cana-1582	570	7	is	be	AUX
cana-1582	570	8	showcased	showcase	VERB
cana-1582	570	9	in	in	ADP
cana-1582	570	10	table-1	table-1	NUM
cana-1582	570	11	.	.	PUNCT
cana-1582	571	1	moving	move	VERB
cana-1582	571	2	forward	forward	ADV
cana-1582	571	3	,	,	PUNCT
cana-1582	571	4	we	we	PRON
cana-1582	571	5	address	address	VERB
cana-1582	571	6	scenarios	scenario	NOUN
cana-1582	571	7	where	where	SCONJ
cana-1582	571	8	the	the	DET
cana-1582	571	9	boundary	boundary	ADJ
cana-1582	571	10	curve	curve	NOUN
cana-1582	571	11	of	of	ADP
cana-1582	571	12	the	the	DET
cana-1582	571	13	lunar	lunar	ADJ
cana-1582	571	14	model	model	NOUN
cana-1582	571	15	is	be	AUX
cana-1582	571	16	characterized	characterize	VERB
cana-1582	571	17	by	by	ADP
cana-1582	571	18	a	a	DET
cana-1582	571	19	set	set	NOUN
cana-1582	571	20	of	of	ADP
cana-1582	571	21	discrete	discrete	ADJ
cana-1582	571	22	coordinate	coordinate	NOUN
cana-1582	571	23	points	point	NOUN
cana-1582	571	24	.	.	PUNCT
cana-1582	572	1	in	in	ADP
cana-1582	572	2	such	such	ADJ
cana-1582	572	3	instances	instance	NOUN
cana-1582	572	4	,	,	PUNCT
cana-1582	572	5	we	we	PRON
cana-1582	572	6	employ	employ	VERB
cana-1582	572	7	this	this	DET
cana-1582	572	8	discrete	discrete	ADJ
cana-1582	572	9	information	information	NOUN
cana-1582	572	10	to	to	PART
cana-1582	572	11	derive	derive	VERB
cana-1582	572	12	parametric	parametric	ADJ
cana-1582	572	13	equations	equation	NOUN
cana-1582	572	14	in	in	ADP
cana-1582	572	15	the	the	DET
cana-1582	572	16	form	form	NOUN
cana-1582	572	17	of	of	ADP
cana-1582	572	18	spline	spline	NOUN
cana-1582	572	19	interpolating	interpolate	VERB
cana-1582	572	20	polynomials	polynomial	NOUN
cana-1582	572	21	.	.	PUNCT
cana-1582	573	1	specifically	specifically	ADV
cana-1582	573	2	,	,	PUNCT
cana-1582	573	3	we	we	PRON
cana-1582	573	4	explore	explore	VERB
cana-1582	573	5	the	the	DET
cana-1582	573	6	application	application	NOUN
cana-1582	573	7	of	of	ADP
cana-1582	573	8	quartic	quartic	ADJ
cana-1582	573	9	splines	spline	NOUN
cana-1582	573	10	,	,	PUNCT
cana-1582	573	11	a	a	DET
cana-1582	573	12	topic	topic	NOUN
cana-1582	573	13	thoroughly	thoroughly	ADV
cana-1582	573	14	discussed	discuss	VERB
cana-1582	573	15	in	in	ADP
cana-1582	573	16	this	this	DET
cana-1582	573	17	chapter	chapter	NOUN
cana-1582	573	18	.	.	PUNCT
cana-1582	574	1	by	by	ADP
cana-1582	574	2	transitioning	transition	VERB
cana-1582	574	3	to	to	PART
cana-1582	574	4	spline	spline	VERB
cana-1582	574	5	interpolating	interpolate	VERB
cana-1582	574	6	polynomials	polynomial	NOUN
cana-1582	574	7	,	,	PUNCT
cana-1582	574	8	we	we	PRON
cana-1582	574	9	ensure	ensure	VERB
cana-1582	574	10	a	a	DET
cana-1582	574	11	continuous	continuous	ADJ
cana-1582	574	12	and	and	CCONJ
cana-1582	574	13	smooth	smooth	ADJ
cana-1582	574	14	representation	representation	NOUN
cana-1582	574	15	of	of	ADP
cana-1582	574	16	the	the	DET
cana-1582	574	17	boundary	boundary	ADJ
cana-1582	574	18	curve	curve	NOUN
cana-1582	574	19	,	,	PUNCT
cana-1582	574	20	even	even	ADV
cana-1582	574	21	when	when	SCONJ
cana-1582	574	22	described	describe	VERB
cana-1582	574	23	by	by	ADP
cana-1582	574	24	discrete	discrete	ADJ
cana-1582	574	25	points	point	NOUN
cana-1582	574	26	.	.	PUNCT
cana-1582	575	1	this	this	DET
cana-1582	575	2	strategy	strategy	NOUN
cana-1582	575	3	enables	enable	VERB
cana-1582	575	4	us	we	PRON
cana-1582	575	5	to	to	PART
cana-1582	575	6	maintain	maintain	VERB
cana-1582	575	7	the	the	DET
cana-1582	575	8	accuracy	accuracy	NOUN
cana-1582	575	9	and	and	CCONJ
cana-1582	575	10	reliability	reliability	NOUN
cana-1582	575	11	of	of	ADP
cana-1582	575	12	our	our	PRON
cana-1582	575	13	numerical	numerical	ADJ
cana-1582	575	14	computations	computation	NOUN
cana-1582	575	15	,	,	PUNCT
cana-1582	575	16	crucial	crucial	ADJ
cana-1582	575	17	for	for	ADP
cana-1582	575	18	robust	robust	ADJ
cana-1582	575	19	analysis	analysis	NOUN
cana-1582	575	20	and	and	CCONJ
cana-1582	575	21	simulation	simulation	NOUN
cana-1582	575	22	of	of	ADP
cana-1582	575	23	the	the	DET
cana-1582	575	24	lunar	lunar	ADJ
cana-1582	575	25	environment	environment	NOUN
cana-1582	575	26	.	.	PUNCT
cana-1582	576	1	numbe	numbe	NOUN
cana-1582	576	2	r	r	NOUN
cana-1582	576	3	of	of	ADP
cana-1582	576	4	points	point	NOUN
cana-1582	576	5	(	(	PUNCT
cana-1582	576	6	np	np	INTJ
cana-1582	576	7	)	)	PUNCT
cana-1582	576	8	i1	i1	PROPN
cana-1582	576	9	i2	i2	PROPN
cana-1582	576	10	i3	i3	PROPN
cana-1582	576	11	i4	i4	PROPN
cana-1582	576	12	i5	i5	PROPN
cana-1582	576	13	i6	i6	NOUN
cana-1582	576	14	i7	i7	ADJ
cana-1582	576	15	1	1	NUM
cana-1582	576	16	637.86297	637.86297	NUM
cana-1582	576	17	06	06	NUM
cana-1582	576	18	0.2064222	0.2064222	NUM
cana-1582	576	19	98	98	NUM
cana-1582	576	20	0.5725849	0.5725849	NUM
cana-1582	576	21	29	29	NUM
cana-1582	576	22	0.0313720	0.0313720	NUM
cana-1582	576	23	08	08	NUM
cana-1582	576	24	0.2105005	0.2105005	NUM
cana-1582	576	25	52	52	NUM
cana-1582	576	26	0.6426250	0.6426250	NUM
cana-1582	576	27	25	25	NUM
cana-1582	576	28	0.0063188	0.0063188	NUM
cana-1582	576	29	13	13	NUM
cana-1582	576	30	2	2	NUM
cana-1582	576	31	638.39271	638.39271	NUM
cana-1582	576	32	0.2064559	0.2064559	NUM
cana-1582	576	33	0.5726234	0.5726234	NUM
cana-1582	576	34	0.0313718	0.0313718	NUM
cana-1582	576	35	0.2105027	0.2105027	NUM
cana-1582	576	36	0.6426797	0.6426797	NUM
cana-1582	576	37	0.0062962	0.0062962	NUM
cana-1582	576	38	communications	communication	NOUN
cana-1582	576	39	on	on	ADP
cana-1582	576	40	applied	apply	VERB
cana-1582	576	41	nonlinear	nonlinear	ADJ
cana-1582	576	42	analysis	analysis	NOUN
cana-1582	576	43	issn	issn	NOUN
cana-1582	576	44	:	:	PUNCT
cana-1582	576	45	1074	1074	NUM
cana-1582	576	46	-	-	PUNCT
cana-1582	576	47	133x	133x	NUM
cana-1582	576	48	vol	vol	NOUN
cana-1582	576	49	31	31	NUM
cana-1582	576	50	no	no	NOUN
cana-1582	576	51	.	.	PUNCT
cana-1582	577	1	8s	8s	PROPN
cana-1582	577	2	(	(	PUNCT
cana-1582	577	3	2024	2024	NUM
cana-1582	577	4	)	)	PUNCT
cana-1582	577	5	735	735	NUM
cana-1582	578	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-1582	578	2	55	55	NUM
cana-1582	578	3	95	95	NUM
cana-1582	578	4	33	33	NUM
cana-1582	578	5	82	82	NUM
cana-1582	578	6	43	43	NUM
cana-1582	578	7	04	04	NUM
cana-1582	578	8	11	11	NUM
cana-1582	578	9	3	3	NUM
cana-1582	578	10	638.50166	638.50166	NUM
cana-1582	578	11	88	88	NUM
cana-1582	578	12	0.2064635	0.2064635	NUM
cana-1582	578	13	56	56	NUM
cana-1582	578	14	0.5726322	0.5726322	NUM
cana-1582	578	15	65	65	NUM
cana-1582	578	16	0.0313718	0.0313718	NUM
cana-1582	578	17	62	62	NUM
cana-1582	578	18	0.2105033	0.2105033	NUM
cana-1582	578	19	86	86	NUM
cana-1582	578	20	0.6426921	0.6426921	NUM
cana-1582	578	21	6	6	NUM
cana-1582	578	22	0.0062915	0.0062915	NUM
cana-1582	578	23	69	69	NUM
cana-1582	578	24	4	4	NUM
cana-1582	578	25	638.53381	638.53381	NUM
cana-1582	578	26	84	84	NUM
cana-1582	578	27	0.2064658	0.2064658	NUM
cana-1582	578	28	95	95	NUM
cana-1582	578	29	0.5726350	0.5726350	NUM
cana-1582	578	30	33	33	NUM
cana-1582	578	31	0.0313718	0.0313718	NUM
cana-1582	578	32	56	56	NUM
cana-1582	578	33	0.2105036	0.2105036	NUM
cana-1582	578	34	14	14	NUM
cana-1582	578	35	0.6426960	0.6426960	NUM
cana-1582	578	36	48	48	NUM
cana-1582	578	37	0.0062903	0.0062903	NUM
cana-1582	578	38	88	88	NUM
cana-1582	578	39	5	5	NUM
cana-1582	579	1	638.54582	638.54582	NUM
cana-1582	579	2	03	03	NUM
cana-1582	579	3	0.2064667	0.2064667	NUM
cana-1582	579	4	96	96	NUM
cana-1582	579	5	0.5726361	0.5726361	NUM
cana-1582	579	6	09	09	NUM
cana-1582	579	7	0.0313718	0.0313718	NUM
cana-1582	579	8	54	54	NUM
cana-1582	579	9	0.2105037	0.2105037	NUM
cana-1582	579	10	09	09	NUM
cana-1582	579	11	0.6426975	0.6426975	NUM
cana-1582	579	12	54	54	NUM
cana-1582	579	13	0.0062899	0.0062899	NUM
cana-1582	579	14	65	65	NUM
cana-1582	579	15	6	6	NUM
cana-1582	579	16	638.55108	638.55108	NUM
cana-1582	579	17	42	42	NUM
cana-1582	579	18	0.2064672	0.2064672	NUM
cana-1582	579	19	0.5726365	0.5726365	NUM
cana-1582	579	20	94	94	NUM
cana-1582	579	21	0.0313718	0.0313718	NUM
cana-1582	579	22	53	53	NUM
cana-1582	579	23	0.2105037	0.2105037	NUM
cana-1582	579	24	54	54	NUM
cana-1582	579	25	0.6426982	0.6426982	NUM
cana-1582	579	26	32	32	NUM
cana-1582	579	27	0.0062897	0.0062897	NUM
cana-1582	579	28	86	86	NUM
cana-1582	579	29	7	7	NUM
cana-1582	579	30	638.55367	638.55367	NUM
cana-1582	579	31	78	78	NUM
cana-1582	579	32	0.2064674	0.2064674	NUM
cana-1582	579	33	02	02	NUM
cana-1582	579	34	0.5726368	0.5726368	NUM
cana-1582	579	35	38	38	NUM
cana-1582	579	36	0.0313718	0.0313718	NUM
cana-1582	579	37	53	53	NUM
cana-1582	579	38	0.2105037	0.2105037	NUM
cana-1582	579	39	78	78	NUM
cana-1582	579	40	0.6426985	0.6426985	NUM
cana-1582	579	41	72	72	NUM
cana-1582	579	42	0.0062897	0.0062897	NUM
cana-1582	579	43	01	01	NUM
cana-1582	579	44	8	8	NUM
cana-1582	579	45	638.55507	638.55507	NUM
cana-1582	579	46	29	29	NUM
cana-1582	579	47	0.2064675	0.2064675	NUM
cana-1582	579	48	12	12	NUM
cana-1582	579	49	0.5726369	0.5726369	NUM
cana-1582	579	50	72	72	NUM
cana-1582	579	51	0.0313718	0.0313718	NUM
cana-1582	579	52	52	52	NUM
cana-1582	579	53	0.2105037	0.2105037	NUM
cana-1582	579	54	91	91	NUM
cana-1582	579	55	0.6426987	0.6426987	NUM
cana-1582	579	56	58	58	NUM
cana-1582	579	57	0.0062896	0.0062896	NUM
cana-1582	579	58	55	55	NUM
cana-1582	579	59	9	9	NUM
cana-1582	579	60	638.55587	638.55587	NUM
cana-1582	579	61	65	65	NUM
cana-1582	579	62	0.2064675	0.2064675	NUM
cana-1582	579	63	76	76	NUM
cana-1582	579	64	0.5726370	0.5726370	NUM
cana-1582	579	65	49	49	NUM
cana-1582	579	66	0.0313718	0.0313718	NUM
cana-1582	579	67	52	52	NUM
cana-1582	579	68	0.2105037	0.2105037	NUM
cana-1582	579	69	98	98	NUM
cana-1582	579	70	0.6426988	0.6426988	NUM
cana-1582	579	71	67	67	NUM
cana-1582	579	72	0.0062896	0.0062896	NUM
cana-1582	579	73	3	3	NUM
cana-1582	579	74	10	10	NUM
cana-1582	579	75	638.55636	638.55636	NUM
cana-1582	579	76	55	55	NUM
cana-1582	579	77	0.2064676	0.2064676	NUM
cana-1582	579	78	16	16	NUM
cana-1582	579	79	0.5726370	0.5726370	NUM
cana-1582	579	80	97	97	NUM
cana-1582	579	81	0.0313718	0.0313718	NUM
cana-1582	579	82	52	52	NUM
cana-1582	579	83	0.2105038	0.2105038	NUM
cana-1582	579	84	03	03	NUM
cana-1582	580	1	0.6426989	0.6426989	NUM
cana-1582	580	2	33	33	NUM
cana-1582	580	3	0.0062896	0.0062896	NUM
cana-1582	580	4	14	14	NUM
cana-1582	580	5	100	100	NUM
cana-1582	580	6	638.55743	638.55743	NUM
cana-1582	580	7	26	26	NUM
cana-1582	580	8	0.2064677	0.2064677	NUM
cana-1582	580	9	03	03	NUM
cana-1582	581	1	0.5726372	0.5726372	NUM
cana-1582	581	2	04	04	NUM
cana-1582	581	3	0.0313718	0.0313718	NUM
cana-1582	581	4	52	52	NUM
cana-1582	581	5	0.2105038	0.2105038	NUM
cana-1582	581	6	15	15	NUM
cana-1582	581	7	0.6426990	0.6426990	NUM
cana-1582	581	8	82	82	NUM
cana-1582	581	9	0.0062895	0.0062895	NUM
cana-1582	581	10	81	81	NUM
cana-1582	581	11	200	200	NUM
cana-1582	581	12	638.55743	638.55743	NUM
cana-1582	581	13	27	27	NUM
cana-1582	581	14	0.2064677	0.2064677	NUM
cana-1582	581	15	03	03	NUM
cana-1582	582	1	0.5726372	0.5726372	NUM
cana-1582	582	2	04	04	NUM
cana-1582	582	3	0.0313718	0.0313718	NUM
cana-1582	582	4	52	52	NUM
cana-1582	582	5	0.2105038	0.2105038	NUM
cana-1582	582	6	15	15	NUM
cana-1582	582	7	0.6426990	0.6426990	NUM
cana-1582	582	8	82	82	NUM
cana-1582	582	9	0.0062895	0.0062895	NUM
cana-1582	582	10	81	81	NUM
cana-1582	582	11	300	300	NUM
cana-1582	582	12	638.55743	638.55743	NUM
cana-1582	582	13	27	27	NUM
cana-1582	582	14	0.2064677	0.2064677	NUM
cana-1582	582	15	03	03	NUM
cana-1582	583	1	0.5726372	0.5726372	NUM
cana-1582	583	2	04	04	NUM
cana-1582	583	3	0.0313718	0.0313718	NUM
cana-1582	583	4	52	52	NUM
cana-1582	583	5	0.2105038	0.2105038	NUM
cana-1582	583	6	15	15	NUM
cana-1582	583	7	0.6426990	0.6426990	NUM
cana-1582	583	8	82	82	NUM
cana-1582	583	9	0.0062895	0.0062895	NUM
cana-1582	583	10	81	81	NUM
cana-1582	583	11	400	400	NUM
cana-1582	583	12	638.55743	638.55743	NUM
cana-1582	583	13	27	27	NUM
cana-1582	583	14	0.2064677	0.2064677	NUM
cana-1582	583	15	03	03	NUM
cana-1582	584	1	0.5726372	0.5726372	NUM
cana-1582	584	2	04	04	NUM
cana-1582	584	3	0.0313718	0.0313718	NUM
cana-1582	584	4	52	52	NUM
cana-1582	584	5	0.2105038	0.2105038	NUM
cana-1582	584	6	15	15	NUM
cana-1582	584	7	0.6426990	0.6426990	NUM
cana-1582	584	8	82	82	NUM
cana-1582	584	9	0.0062895	0.0062895	NUM
cana-1582	584	10	81	81	NUM
cana-1582	584	11	500	500	NUM
cana-1582	584	12	638.55743	638.55743	NUM
cana-1582	584	13	27	27	NUM
cana-1582	584	14	0.2064677	0.2064677	NUM
cana-1582	584	15	03	03	NUM
cana-1582	585	1	0.5726372	0.5726372	NUM
cana-1582	585	2	04	04	NUM
cana-1582	585	3	0.0313718	0.0313718	NUM
cana-1582	585	4	52	52	NUM
cana-1582	585	5	0.2105038	0.2105038	NUM
cana-1582	585	6	15	15	NUM
cana-1582	585	7	0.6426990	0.6426990	NUM
cana-1582	585	8	82	82	NUM
cana-1582	585	9	0.0062895	0.0062895	NUM
cana-1582	585	10	81	81	NUM
cana-1582	585	11	600	600	NUM
cana-1582	585	12	638.55743	638.55743	NUM
cana-1582	585	13	27	27	NUM
cana-1582	585	14	0.2064677	0.2064677	NUM
cana-1582	585	15	03	03	NUM
cana-1582	586	1	0.5726372	0.5726372	NUM
cana-1582	586	2	04	04	NUM
cana-1582	586	3	0.0313718	0.0313718	NUM
cana-1582	586	4	52	52	NUM
cana-1582	586	5	0.2105038	0.2105038	NUM
cana-1582	586	6	15	15	NUM
cana-1582	586	7	0.6426990	0.6426990	NUM
cana-1582	586	8	82	82	NUM
cana-1582	586	9	0.0062895	0.0062895	NUM
cana-1582	586	10	81	81	NUM
cana-1582	586	11	700	700	NUM
cana-1582	586	12	638.55743	638.55743	NUM
cana-1582	586	13	27	27	NUM
cana-1582	586	14	0.2064677	0.2064677	NUM
cana-1582	586	15	03	03	NUM
cana-1582	587	1	0.5726372	0.5726372	NUM
cana-1582	587	2	04	04	NUM
cana-1582	587	3	0.0313718	0.0313718	NUM
cana-1582	587	4	52	52	NUM
cana-1582	587	5	0.2105038	0.2105038	NUM
cana-1582	587	6	15	15	NUM
cana-1582	587	7	0.6426990	0.6426990	NUM
cana-1582	587	8	82	82	NUM
cana-1582	587	9	0.0062895	0.0062895	NUM
cana-1582	587	10	81	81	NUM
cana-1582	587	11	800	800	NUM
cana-1582	587	12	638.55743	638.55743	NUM
cana-1582	587	13	27	27	NUM
cana-1582	587	14	0.2064677	0.2064677	NUM
cana-1582	587	15	03	03	NUM
cana-1582	588	1	0.5726372	0.5726372	NUM
cana-1582	588	2	04	04	NUM
cana-1582	588	3	0.0313718	0.0313718	NUM
cana-1582	588	4	52	52	NUM
cana-1582	588	5	0.2105038	0.2105038	NUM
cana-1582	588	6	15	15	NUM
cana-1582	588	7	0.6426990	0.6426990	NUM
cana-1582	588	8	82	82	NUM
cana-1582	588	9	0.0062895	0.0062895	NUM
cana-1582	588	10	81	81	NUM
cana-1582	588	11	900	900	NUM
cana-1582	588	12	638.55743	638.55743	NUM
cana-1582	588	13	27	27	NUM
cana-1582	588	14	0.2064677	0.2064677	NUM
cana-1582	588	15	03	03	NUM
cana-1582	589	1	0.5726372	0.5726372	NUM
cana-1582	589	2	04	04	NUM
cana-1582	589	3	0.0313718	0.0313718	NUM
cana-1582	589	4	52	52	NUM
cana-1582	589	5	0.2105038	0.2105038	NUM
cana-1582	589	6	15	15	NUM
cana-1582	589	7	0.6426990	0.6426990	NUM
cana-1582	589	8	82	82	NUM
cana-1582	589	9	0.0062895	0.0062895	NUM
cana-1582	589	10	81	81	NUM
cana-1582	589	11	1000	1000	NUM
cana-1582	589	12	638.55743	638.55743	NUM
cana-1582	589	13	27	27	NUM
cana-1582	589	14	0.2064677	0.2064677	NUM
cana-1582	589	15	03	03	NUM
cana-1582	590	1	0.5726372	0.5726372	NUM
cana-1582	590	2	04	04	NUM
cana-1582	590	3	0.0313718	0.0313718	NUM
cana-1582	590	4	52	52	NUM
cana-1582	590	5	0.2105038	0.2105038	NUM
cana-1582	590	6	15	15	NUM
cana-1582	590	7	0.6426990	0.6426990	NUM
cana-1582	590	8	82	82	NUM
cana-1582	590	9	0.0062895	0.0062895	NUM
cana-1582	590	10	81	81	NUM
cana-1582	590	11	table	table	NOUN
cana-1582	590	12	1	1	NUM
cana-1582	590	13	spline	spline	NOUN
cana-1582	590	14	integration	integration	NOUN
cana-1582	590	15	for	for	ADP
cana-1582	590	16	𝐼𝐼(𝑖	𝐼𝐼(𝑖	NOUN
cana-1582	590	17	)	)	PUNCT
cana-1582	591	1	=	=	PUNCT
cana-1582	591	2	∬	∬	NOUN
cana-1582	591	3	𝑓𝑖(𝑥	𝑓𝑖(𝑥	NUM
cana-1582	591	4	,	,	PUNCT
cana-1582	591	5	𝑦	𝑦	X
cana-1582	591	6	)	)	PUNCT
cana-1582	591	7	⬚	⬚	PROPN
cana-1582	591	8	𝐷	𝐷	PROPN
cana-1582	591	9	𝑑𝑥𝑑𝑦	𝑑𝑥𝑑𝑦	NOUN
cana-1582	591	10	,	,	PUNCT
cana-1582	591	11	𝑖	𝑖	SYM
cana-1582	591	12	=	=	SYM
cana-1582	591	13	1(1)7	1(1)7	NUM
cana-1582	591	14	,	,	PUNCT
cana-1582	591	15	d	d	NOUN
cana-1582	591	16	:	:	PUNCT
cana-1582	591	17	domain	domain	NOUN
cana-1582	591	18	of	of	ADP
cana-1582	591	19	lunar	lunar	ADJ
cana-1582	591	20	model	model	NOUN
cana-1582	591	21	i1	i1	PROPN
cana-1582	591	22	integral	integral	PROPN
cana-1582	591	23	seems	seem	VERB
cana-1582	591	24	to	to	PART
cana-1582	591	25	converge	converge	VERB
cana-1582	591	26	to	to	ADP
cana-1582	591	27	approximately	approximately	ADV
cana-1582	591	28	638.5574327	638.5574327	NUM
cana-1582	591	29	as	as	ADP
cana-1582	591	30	the	the	DET
cana-1582	591	31	number	number	NOUN
cana-1582	591	32	of	of	ADP
cana-1582	591	33	points	point	NOUN
cana-1582	592	1	np	np	PRON
cana-1582	592	2	increases	increase	NOUN
cana-1582	592	3	.	.	PUNCT
cana-1582	593	1	this	this	PRON
cana-1582	593	2	suggests	suggest	VERB
cana-1582	593	3	that	that	SCONJ
cana-1582	593	4	i1	i1	PROPN
cana-1582	593	5	has	have	AUX
cana-1582	593	6	reached	reach	VERB
cana-1582	593	7	a	a	DET
cana-1582	593	8	stable	stable	ADJ
cana-1582	593	9	value	value	NOUN
cana-1582	593	10	,	,	PUNCT
cana-1582	593	11	indicating	indicate	VERB
cana-1582	593	12	convergence	convergence	NOUN
cana-1582	593	13	of	of	ADP
cana-1582	593	14	the	the	DET
cana-1582	593	15	numerical	numerical	ADJ
cana-1582	593	16	method	method	NOUN
cana-1582	593	17	used	use	VERB
cana-1582	593	18	to	to	PART
cana-1582	593	19	compute	compute	VERB
cana-1582	593	20	it	it	PRON
cana-1582	593	21	.	.	PUNCT
cana-1582	594	1	i2	i2	PROPN
cana-1582	594	2	:	:	PUNCT
cana-1582	594	3	similarly	similarly	ADV
cana-1582	594	4	,	,	PUNCT
cana-1582	594	5	converges	converge	VERB
cana-1582	594	6	to	to	ADP
cana-1582	594	7	a	a	DET
cana-1582	594	8	stable	stable	ADJ
cana-1582	594	9	value	value	NOUN
cana-1582	594	10	of	of	ADP
cana-1582	594	11	approximately	approximately	ADV
cana-1582	594	12	0.206467703	0.206467703	NUM
cana-1582	594	13	as	as	SCONJ
cana-1582	594	14	np	np	ADP
cana-1582	594	15	communications	communication	NOUN
cana-1582	594	16	on	on	ADP
cana-1582	594	17	applied	apply	VERB
cana-1582	594	18	nonlinear	nonlinear	ADJ
cana-1582	594	19	analysis	analysis	NOUN
cana-1582	594	20	issn	issn	NOUN
cana-1582	594	21	:	:	PUNCT
cana-1582	594	22	1074	1074	NUM
cana-1582	594	23	-	-	PUNCT
cana-1582	594	24	133x	133x	NUM
cana-1582	594	25	vol	vol	NOUN
cana-1582	594	26	31	31	NUM
cana-1582	594	27	no	no	NOUN
cana-1582	594	28	.	.	PUNCT
cana-1582	595	1	8s	8s	PROPN
cana-1582	595	2	(	(	PUNCT
cana-1582	595	3	2024	2024	NUM
cana-1582	595	4	)	)	PUNCT
cana-1582	596	1	736	736	NUM
cana-1582	596	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1582	596	3	increases	increase	NOUN
cana-1582	596	4	.	.	PUNCT
cana-1582	597	1	the	the	DET
cana-1582	597	2	convergence	convergence	NOUN
cana-1582	597	3	of	of	ADP
cana-1582	597	4	i2	i2	PROPN
cana-1582	597	5	indicates	indicate	VERB
cana-1582	597	6	that	that	SCONJ
cana-1582	597	7	the	the	DET
cana-1582	597	8	numerical	numerical	ADJ
cana-1582	597	9	method	method	NOUN
cana-1582	597	10	accurately	accurately	ADV
cana-1582	597	11	computes	compute	VERB
cana-1582	597	12	this	this	DET
cana-1582	597	13	integral	integral	ADJ
cana-1582	597	14	.	.	PUNCT
cana-1582	597	15	i3	i3	PROPN
cana-1582	597	16	,	,	PUNCT
cana-1582	597	17	i4	i4	PROPN
cana-1582	597	18	,	,	PUNCT
cana-1582	597	19	i5	i5	NOUN
cana-1582	597	20	,	,	PUNCT
cana-1582	597	21	i6	i6	NOUN
cana-1582	597	22	,	,	PUNCT
cana-1582	597	23	i7	i7	NOUN
cana-1582	597	24	:	:	PUNCT
cana-1582	597	25	these	these	DET
cana-1582	597	26	integrals	integral	NOUN
cana-1582	597	27	also	also	ADV
cana-1582	597	28	converge	converge	VERB
cana-1582	597	29	to	to	ADP
cana-1582	597	30	stable	stable	ADJ
cana-1582	597	31	values	value	NOUN
cana-1582	597	32	as	as	ADP
cana-1582	597	33	np	np	NOUN
cana-1582	597	34	increases	increase	NOUN
cana-1582	597	35	,	,	PUNCT
cana-1582	597	36	with	with	ADP
cana-1582	597	37	each	each	PRON
cana-1582	597	38	approaching	approach	VERB
cana-1582	597	39	approximately	approximately	ADV
cana-1582	597	40	0.572637204	0.572637204	NUM
cana-1582	597	41	,	,	PUNCT
cana-1582	597	42	0.031371852	0.031371852	NUM
cana-1582	597	43	,	,	PUNCT
cana-1582	597	44	0.210503815	0.210503815	NUM
cana-1582	597	45	,	,	PUNCT
cana-1582	597	46	0.642699082	0.642699082	NUM
cana-1582	597	47	,	,	PUNCT
cana-1582	597	48	0.572637204	0.572637204	NUM
cana-1582	597	49	,	,	PUNCT
cana-1582	597	50	0.031371852	0.031371852	NUM
cana-1582	597	51	,	,	PUNCT
cana-1582	597	52	0.210503815	0.210503815	NUM
cana-1582	597	53	,	,	PUNCT
cana-1582	597	54	0.642699082	0.642699082	NUM
cana-1582	597	55	,	,	PUNCT
cana-1582	597	56	and	and	CCONJ
cana-1582	597	57	0.006289581	0.006289581	NUM
cana-1582	597	58	respectively	respectively	ADV
cana-1582	597	59	.	.	PUNCT
cana-1582	598	1	the	the	DET
cana-1582	598	2	convergence	convergence	NOUN
cana-1582	598	3	of	of	ADP
cana-1582	598	4	all	all	DET
cana-1582	598	5	these	these	DET
cana-1582	598	6	integrals	integral	NOUN
cana-1582	598	7	suggests	suggest	VERB
cana-1582	598	8	the	the	DET
cana-1582	598	9	effectiveness	effectiveness	NOUN
cana-1582	598	10	and	and	CCONJ
cana-1582	598	11	accuracy	accuracy	NOUN
cana-1582	598	12	of	of	ADP
cana-1582	598	13	the	the	DET
cana-1582	598	14	numerical	numerical	ADJ
cana-1582	598	15	method	method	NOUN
cana-1582	598	16	across	across	ADP
cana-1582	598	17	different	different	ADJ
cana-1582	598	18	aspects	aspect	NOUN
cana-1582	598	19	of	of	ADP
cana-1582	598	20	the	the	DET
cana-1582	598	21	problem	problem	NOUN
cana-1582	598	22	.	.	PUNCT
cana-1582	599	1	overall	overall	ADV
cana-1582	599	2	,	,	PUNCT
cana-1582	599	3	the	the	DET
cana-1582	599	4	trend	trend	NOUN
cana-1582	599	5	observed	observe	VERB
cana-1582	599	6	in	in	ADP
cana-1582	599	7	the	the	DET
cana-1582	599	8	table	table	NOUN
cana-1582	599	9	indicates	indicate	VERB
cana-1582	599	10	that	that	SCONJ
cana-1582	599	11	increasing	increase	VERB
cana-1582	599	12	the	the	DET
cana-1582	599	13	number	number	NOUN
cana-1582	599	14	of	of	ADP
cana-1582	599	15	points	point	NOUN
cana-1582	599	16	np	np	INTJ
cana-1582	599	17	in	in	ADP
cana-1582	599	18	the	the	DET
cana-1582	599	19	numerical	numerical	ADJ
cana-1582	599	20	method	method	NOUN
cana-1582	599	21	leads	lead	VERB
cana-1582	599	22	to	to	ADP
cana-1582	599	23	improved	improved	ADJ
cana-1582	599	24	accuracy	accuracy	NOUN
cana-1582	599	25	and	and	CCONJ
cana-1582	599	26	convergence	convergence	NOUN
cana-1582	599	27	of	of	ADP
cana-1582	599	28	the	the	DET
cana-1582	599	29	computed	compute	VERB
cana-1582	599	30	integrals	integral	NOUN
cana-1582	599	31	.	.	PUNCT
cana-1582	600	1	this	this	DET
cana-1582	600	2	convergence	convergence	NOUN
cana-1582	600	3	behavior	behavior	NOUN
cana-1582	600	4	is	be	AUX
cana-1582	600	5	consistent	consistent	ADJ
cana-1582	600	6	with	with	ADP
cana-1582	600	7	expectations	expectation	NOUN
cana-1582	600	8	from	from	ADP
cana-1582	600	9	numerical	numerical	ADJ
cana-1582	600	10	methods	method	NOUN
cana-1582	600	11	,	,	PUNCT
cana-1582	600	12	where	where	SCONJ
cana-1582	600	13	increasing	increase	VERB
cana-1582	600	14	the	the	DET
cana-1582	600	15	resolution	resolution	NOUN
cana-1582	600	16	typically	typically	ADV
cana-1582	600	17	leads	lead	VERB
cana-1582	600	18	to	to	ADP
cana-1582	600	19	more	more	ADV
cana-1582	600	20	accurate	accurate	ADJ
cana-1582	600	21	results	result	NOUN
cana-1582	600	22	.	.	PUNCT
cana-1582	601	1	application	application	NOUN
cana-1582	601	2	example	example	NOUN
cana-1582	601	3	2	2	NUM
cana-1582	601	4	:	:	PUNCT
cana-1582	601	5	general	general	ADJ
cana-1582	601	6	ellipse	ellipse	NOUN
cana-1582	601	7	:	:	PUNCT
cana-1582	601	8	consider	consider	VERB
cana-1582	601	9	an	an	DET
cana-1582	601	10	ellipse	ellipse	NOUN
cana-1582	601	11	in	in	ADP
cana-1582	601	12	(	(	PUNCT
cana-1582	601	13	x	x	NOUN
cana-1582	601	14	,	,	PUNCT
cana-1582	601	15	y	y	NOUN
cana-1582	601	16	)	)	PUNCT
cana-1582	601	17	plane	plane	NOUN
cana-1582	601	18	with	with	ADP
cana-1582	601	19	semi	semi	ADJ
cana-1582	601	20	major	major	ADJ
cana-1582	601	21	axis	axis	NOUN
cana-1582	601	22	of	of	ADP
cana-1582	601	23	length	length	NOUN
cana-1582	601	24	a	a	DET
cana-1582	601	25	and	and	CCONJ
cana-1582	601	26	semi	semi	ADJ
cana-1582	601	27	minor	minor	ADJ
cana-1582	601	28	axis	axis	NOUN
cana-1582	601	29	of	of	ADP
cana-1582	601	30	length	length	NOUN
cana-1582	601	31	b.	b.	PROPN
cana-1582	602	1	the	the	DET
cana-1582	602	2	ellipse	ellipse	NOUN
cana-1582	602	3	is	be	AUX
cana-1582	602	4	then	then	ADV
cana-1582	602	5	rotated	rotate	VERB
cana-1582	602	6	anticlockwise	anticlockwise	NOUN
cana-1582	602	7	by	by	ADP
cana-1582	602	8	an	an	DET
cana-1582	602	9	angle	angle	NOUN
cana-1582	602	10	of	of	ADP
cana-1582	602	11	𝛉	𝛉	NOUN
cana-1582	602	12	degrees	degree	NOUN
cana-1582	602	13	and	and	CCONJ
cana-1582	602	14	translated	translate	VERB
cana-1582	602	15	to	to	PART
cana-1582	602	16	coincide	coincide	VERB
cana-1582	602	17	the	the	DET
cana-1582	602	18	centre	centre	NOUN
cana-1582	602	19	of	of	ADP
cana-1582	602	20	the	the	DET
cana-1582	602	21	ellipse	ellipse	NOUN
cana-1582	602	22	to	to	ADP
cana-1582	602	23	(	(	PUNCT
cana-1582	602	24	x0	x0	PROPN
cana-1582	602	25	,	,	PUNCT
cana-1582	602	26	y0	y0	PROPN
cana-1582	602	27	)	)	PUNCT
cana-1582	602	28	.	.	PUNCT
cana-1582	603	1	the	the	DET
cana-1582	603	2	equation	equation	NOUN
cana-1582	603	3	of	of	ADP
cana-1582	603	4	the	the	DET
cana-1582	603	5	ellipse	ellipse	NOUN
cana-1582	603	6	in	in	ADP
cana-1582	603	7	the	the	DET
cana-1582	603	8	(	(	PUNCT
cana-1582	603	9	x	x	NOUN
cana-1582	603	10	,	,	PUNCT
cana-1582	603	11	y	y	NOUN
cana-1582	603	12	)	)	PUNCT
cana-1582	603	13	plane	plane	NOUN
cana-1582	603	14	is	be	AUX
cana-1582	603	15	2	2	NUM
cana-1582	603	16	2	2	NUM
cana-1582	603	17	2	2	NUM
cana-1582	603	18	2	2	NUM
cana-1582	603	19	1	1	NUM
cana-1582	603	20	x	x	SYM
cana-1582	603	21	y	y	PROPN
cana-1582	603	22	a	a	DET
cana-1582	603	23	b	b	NOUN
cana-1582	603	24	+	+	CCONJ
cana-1582	603	25	=	=	PUNCT
cana-1582	603	26	.	.	PUNCT
cana-1582	604	1	let	let	VERB
cana-1582	604	2	the	the	DET
cana-1582	604	3	new	new	ADJ
cana-1582	604	4	coordinate	coordinate	NOUN
cana-1582	604	5	system	system	NOUN
cana-1582	604	6	with	with	ADP
cana-1582	604	7	origin	origin	NOUN
cana-1582	604	8	at	at	ADP
cana-1582	604	9	(	(	PUNCT
cana-1582	604	10	x0	x0	PROPN
cana-1582	604	11	,	,	PUNCT
cana-1582	604	12	y0	y0	PROPN
cana-1582	604	13	)	)	PUNCT
cana-1582	604	14	be	be	AUX
cana-1582	604	15	denoted	denote	VERB
cana-1582	604	16	by	by	ADP
cana-1582	604	17	(	(	PUNCT
cana-1582	604	18	,	,	PUNCT
cana-1582	604	19	)	)	PUNCT
cana-1582	604	20	x	x	SYM
cana-1582	604	21	y	y	PROPN
cana-1582	604	22			ADJ
cana-1582	604	23	plane	plane	NOUN
cana-1582	604	24	.	.	PUNCT
cana-1582	605	1	the	the	DET
cana-1582	605	2	ellipse	ellipse	NOUN
cana-1582	605	3	in	in	ADP
cana-1582	605	4	(	(	PUNCT
cana-1582	605	5	,	,	PUNCT
cana-1582	605	6	)	)	PUNCT
cana-1582	605	7	x	x	SYM
cana-1582	605	8	y	y	NOUN
cana-1582	605	9			ADJ
cana-1582	605	10	plane	plane	NOUN
cana-1582	605	11	is	be	AUX
cana-1582	605	12	then	then	ADV
cana-1582	605	13	rotated	rotate	VERB
cana-1582	605	14	by	by	ADP
cana-1582	605	15	an	an	DET
cana-1582	605	16	angle	angle	NOUN
cana-1582	605	17	𝛉	𝛉	PROPN
cana-1582	605	18	in	in	ADP
cana-1582	605	19	anticlockwise	anticlockwise	PROPN
cana-1582	605	20	direction	direction	NOUN
cana-1582	605	21	.	.	PUNCT
cana-1582	606	1	let	let	VERB
cana-1582	606	2	us	we	PRON
cana-1582	606	3	denote	denote	VERB
cana-1582	606	4	the	the	DET
cana-1582	606	5	points	point	NOUN
cana-1582	606	6	on	on	ADP
cana-1582	606	7	the	the	DET
cana-1582	606	8	rotated	rotated	ADJ
cana-1582	606	9	ellipse	ellipse	NOUN
cana-1582	606	10	with	with	ADP
cana-1582	606	11	respect	respect	NOUN
cana-1582	606	12	to	to	ADP
cana-1582	606	13	(	(	PUNCT
cana-1582	606	14	,	,	PUNCT
cana-1582	606	15	)	)	PUNCT
cana-1582	606	16	x	x	SYM
cana-1582	606	17	y	y	PROPN
cana-1582	606	18			ADV
cana-1582	606	19	coordinate	coordinate	VERB
cana-1582	606	20	system	system	NOUN
cana-1582	606	21	as	as	ADP
cana-1582	606	22	*	*	PUNCT
cana-1582	606	23	*	*	PUNCT
cana-1582	606	24	(	(	PUNCT
cana-1582	606	25	,	,	PUNCT
cana-1582	606	26	)	)	PUNCT
cana-1582	606	27	x	x	PROPN
cana-1582	607	1	y	y	PROPN
cana-1582	607	2	.	.	PUNCT
cana-1582	608	1	(	(	PUNCT
cana-1582	608	2	i	i	NOUN
cana-1582	608	3	)	)	PUNCT
cana-1582	608	4	.	.	PUNCT
cana-1582	609	1	the	the	DET
cana-1582	609	2	points	point	NOUN
cana-1582	609	3	on	on	ADP
cana-1582	609	4	the	the	DET
cana-1582	609	5	ellipse	ellipse	NOUN
cana-1582	609	6	2	2	NUM
cana-1582	609	7	2	2	NUM
cana-1582	609	8	2	2	NUM
cana-1582	609	9	2	2	NUM
cana-1582	609	10	1	1	NUM
cana-1582	609	11	x	x	SYM
cana-1582	609	12	y	y	PROPN
cana-1582	609	13	a	a	DET
cana-1582	609	14	b	b	PROPN
cana-1582	609	15			PROPN
cana-1582	609	16			PROPN
cana-1582	609	17	+	+	CCONJ
cana-1582	609	18	=	=	NOUN
cana-1582	609	19	are	be	AUX
cana-1582	609	20	cos	cos	ADP
cana-1582	609	21	,	,	PUNCT
cana-1582	609	22	sin	sin	NOUN
cana-1582	609	23	,	,	PUNCT
cana-1582	609	24	0	0	NUM
cana-1582	609	25	2x	2x	NUM
cana-1582	609	26	a	a	DET
cana-1582	609	27	t	t	NOUN
cana-1582	609	28	y	y	PROPN
cana-1582	609	29	b	b	PROPN
cana-1582	609	30	t	t	PROPN
cana-1582	609	31	t	t	PROPN
cana-1582	610	1			X
cana-1582	610	2	=	=	PROPN
cana-1582	610	3	=	=	PUNCT
cana-1582	610	4			PROPN
cana-1582	610	5			NOUN
cana-1582	610	6	(	(	PUNCT
cana-1582	610	7	ii	ii	NOUN
cana-1582	610	8	)	)	PUNCT
cana-1582	610	9	.	.	PUNCT
cana-1582	611	1	the	the	DET
cana-1582	611	2	points	point	NOUN
cana-1582	611	3	*	*	PUNCT
cana-1582	612	1	*	*	PUNCT
cana-1582	612	2	(	(	PUNCT
cana-1582	612	3	,	,	PUNCT
cana-1582	612	4	)	)	PUNCT
cana-1582	612	5	x	x	X
cana-1582	613	1	y	y	PROPN
cana-1582	613	2	corresponding	correspond	VERB
cana-1582	613	3	to	to	ADP
cana-1582	613	4	the	the	DET
cana-1582	613	5	point	point	NOUN
cana-1582	613	6	(	(	PUNCT
cana-1582	613	7	,	,	PUNCT
cana-1582	613	8	)	)	PUNCT
cana-1582	613	9	x	x	SYM
cana-1582	613	10	y	y	INTJ
cana-1582	613	11			ADV
cana-1582	613	12	on	on	ADP
cana-1582	613	13	the	the	DET
cana-1582	613	14	rotated	rotated	ADJ
cana-1582	613	15	ellipse	ellipse	NOUN
cana-1582	613	16	are	be	AUX
cana-1582	613	17	*	*	PUNCT
cana-1582	613	18	*	*	PUNCT
cana-1582	613	19	cos	cos	X
cana-1582	613	20	sin	sin	NOUN
cana-1582	613	21	,	,	PUNCT
cana-1582	613	22	sin	sin	NOUN
cana-1582	613	23	cosx	cosx	PROPN
cana-1582	613	24	x	x	PROPN
cana-1582	613	25	y	y	PROPN
cana-1582	613	26	y	y	PROPN
cana-1582	613	27	x	x	PUNCT
cana-1582	613	28	y	y	X
cana-1582	613	29			PROPN
cana-1582	613	30			PROPN
cana-1582	614	1			PROPN
cana-1582	615	1			PROPN
cana-1582	615	2			ADV
cana-1582	616	1	=	=	INTJ
cana-1582	616	2	−	−	PROPN
cana-1582	617	1	=	=	PUNCT
cana-1582	617	2	+	+	CCONJ
cana-1582	617	3	(	(	PUNCT
cana-1582	617	4	iii	iii	NOUN
cana-1582	617	5	)	)	PUNCT
cana-1582	617	6	.	.	PUNCT
cana-1582	618	1	points	point	NOUN
cana-1582	618	2	(	(	PUNCT
cana-1582	618	3	x	x	X
cana-1582	618	4	,	,	PUNCT
cana-1582	618	5	y	y	NOUN
cana-1582	618	6	)	)	PUNCT
cana-1582	618	7	corresponding	correspond	VERB
cana-1582	618	8	to	to	ADP
cana-1582	618	9	*	*	PROPN
cana-1582	618	10	*	*	PUNCT
cana-1582	618	11	(	(	PUNCT
cana-1582	618	12	,	,	PUNCT
cana-1582	618	13	)	)	PUNCT
cana-1582	618	14	x	x	X
cana-1582	618	15	y	y	PROPN
cana-1582	618	16	must	must	AUX
cana-1582	618	17	satisfy	satisfy	VERB
cana-1582	618	18	*	*	PUNCT
cana-1582	619	1	*	*	PUNCT
cana-1582	620	1	*	*	PUNCT
cana-1582	621	1	*	*	PUNCT
cana-1582	621	2	0	0	NUM
cana-1582	621	3	0	0	NUM
cana-1582	622	1	*	*	PUNCT
cana-1582	622	2	*	*	PUNCT
cana-1582	622	3	0	0	NUM
cana-1582	622	4	0	0	NUM
cana-1582	622	5	,	,	PUNCT
cana-1582	622	6	.	.	PUNCT
cana-1582	623	1	,	,	PUNCT
cana-1582	623	2	,	,	PUNCT
cana-1582	623	3	,	,	PUNCT
cana-1582	623	4	x	x	PUNCT
cana-1582	623	5	x	x	VERB
cana-1582	623	6	y	y	VERB
cana-1582	623	7	y	y	NOUN
cana-1582	623	8	i	i	NOUN
cana-1582	623	9	e	e	VERB
cana-1582	623	10	x	x	PUNCT
cana-1582	623	11	x	x	PUNCT
cana-1582	623	12	x	x	PUNCT
cana-1582	623	13	x	x	PUNCT
cana-1582	623	14	y	y	VERB
cana-1582	623	15	y	y	PROPN
cana-1582	623	16	y	y	PROPN
cana-1582	623	17	y	y	PROPN
cana-1582	623	18	x	x	PUNCT
cana-1582	624	1	x	x	PUNCT
cana-1582	624	2	x	x	VERB
cana-1582	624	3	y	y	VERB
cana-1582	624	4	y	y	PROPN
cana-1582	624	5	y	y	PROPN
cana-1582	624	6			PROPN
cana-1582	624	7	=	=	PROPN
cana-1582	624	8	=	=	PUNCT
cana-1582	625	1			ADJ
cana-1582	625	2	=	=	INTJ
cana-1582	625	3	−	−	PROPN
cana-1582	626	1	=	=	PUNCT
cana-1582	626	2	=	=	PUNCT
cana-1582	627	1	−	−	PROPN
cana-1582	627	2	=	=	SYM
cana-1582	627	3			NOUN
cana-1582	627	4	=	=	PUNCT
cana-1582	628	1	+	+	PUNCT
cana-1582	628	2	=	=	PUNCT
cana-1582	629	1	+	+	CCONJ
cana-1582	629	2	we	we	PRON
cana-1582	629	3	shall	shall	AUX
cana-1582	629	4	now	now	ADV
cana-1582	629	5	determine	determine	VERB
cana-1582	629	6	the	the	DET
cana-1582	629	7	points	point	NOUN
cana-1582	629	8	on	on	ADP
cana-1582	629	9	the	the	DET
cana-1582	629	10	rotated	rotated	ADJ
cana-1582	629	11	ellipse	ellipse	NOUN
cana-1582	629	12	.	.	PUNCT
cana-1582	630	1	let	let	VERB
cana-1582	630	2	the	the	DET
cana-1582	630	3	points	point	NOUN
cana-1582	630	4	on	on	ADP
cana-1582	630	5	the	the	DET
cana-1582	630	6	ellipse	ellipse	NOUN
cana-1582	630	7	with	with	ADP
cana-1582	630	8	respect	respect	NOUN
cana-1582	630	9	to	to	ADP
cana-1582	630	10	(	(	PUNCT
cana-1582	630	11	,	,	PUNCT
cana-1582	630	12	)	)	PUNCT
cana-1582	630	13	x	x	SYM
cana-1582	630	14	y	y	INTJ
cana-1582	630	15			ADV
cana-1582	630	16	should	should	AUX
cana-1582	630	17	be	be	AUX
cana-1582	630	18	{	{	PUNCT
cana-1582	630	19	(	(	PUNCT
cana-1582	630	20	a	a	PRON
cana-1582	630	21	,	,	PUNCT
cana-1582	630	22	0	0	NUM
cana-1582	630	23	)	)	PUNCT
cana-1582	630	24	,	,	PUNCT
cana-1582	630	25	(	(	PUNCT
cana-1582	630	26	0	0	NUM
cana-1582	630	27	,	,	PUNCT
cana-1582	630	28	b	b	NOUN
cana-1582	630	29	)	)	PUNCT
cana-1582	630	30	,	,	PUNCT
cana-1582	630	31	(	(	PUNCT
cana-1582	630	32	a	a	PRON
cana-1582	630	33	,	,	PUNCT
cana-1582	630	34	0	0	NUM
cana-1582	630	35	)	)	PUNCT
cana-1582	630	36	,	,	PUNCT
cana-1582	630	37	(	(	PUNCT
cana-1582	630	38	0	0	NUM
cana-1582	630	39	,	,	PUNCT
cana-1582	630	40	b	b	NOUN
cana-1582	630	41	)	)	PUNCT
cana-1582	630	42	}	}	PUNCT
cana-1582	630	43	.	.	PUNCT
cana-1582	631	1	these	these	DET
cana-1582	631	2	points	point	NOUN
cana-1582	631	3	with	with	ADP
cana-1582	631	4	respect	respect	NOUN
cana-1582	631	5	to	to	ADP
cana-1582	631	6	(	(	PUNCT
cana-1582	631	7	x	x	NOUN
cana-1582	631	8	,	,	PUNCT
cana-1582	631	9	y	y	NOUN
cana-1582	631	10	)	)	PUNCT
cana-1582	631	11	system	system	NOUN
cana-1582	631	12	are	be	AUX
cana-1582	631	13	{	{	PUNCT
cana-1582	631	14	0	0	NUM
cana-1582	631	15	0	0	NUM
cana-1582	631	16	0	0	NUM
cana-1582	631	17	0	0	NUM
cana-1582	632	1	(	(	PUNCT
cana-1582	632	2	cos	cos	X
cana-1582	632	3	,	,	PUNCT
cana-1582	632	4	sin	sin	NOUN
cana-1582	632	5	)	)	PUNCT
cana-1582	632	6	,	,	PUNCT
cana-1582	632	7	(	(	PUNCT
cana-1582	632	8	sin	sin	NOUN
cana-1582	632	9	,	,	PUNCT
cana-1582	632	10	cos	cos	PROPN
cana-1582	632	11	)	)	PUNCT
cana-1582	632	12	,	,	PUNCT
cana-1582	632	13	x	x	PROPN
cana-1582	632	14	a	a	DET
cana-1582	632	15	y	y	PROPN
cana-1582	632	16	b	b	PROPN
cana-1582	632	17	x	x	SYM
cana-1582	632	18	b	b	X
cana-1582	632	19	y	y	PROPN
cana-1582	632	20	b	b	NOUN
cana-1582	632	21			PROPN
cana-1582	632	22			PROPN
cana-1582	632	23	+	+	VERB
cana-1582	632	24	+	+	CCONJ
cana-1582	632	25	−	−	PROPN
cana-1582	633	1	+	+	CCONJ
cana-1582	633	2	0	0	NUM
cana-1582	633	3	0	0	NUM
cana-1582	633	4	(	(	PUNCT
cana-1582	633	5	cos	cos	X
cana-1582	633	6	,	,	PUNCT
cana-1582	633	7	sin	sin	NOUN
cana-1582	633	8	)	)	PUNCT
cana-1582	633	9	,	,	PUNCT
cana-1582	633	10	x	x	PROPN
cana-1582	633	11	a	a	DET
cana-1582	633	12	y	y	PROPN
cana-1582	633	13	a	a	NOUN
cana-1582	633	14	−	−	VERB
cana-1582	633	15	−	−	PROPN
cana-1582	633	16	0	0	NUM
cana-1582	633	17	0	0	NUM
cana-1582	634	1	(	(	PUNCT
cana-1582	634	2	sin	sin	NOUN
cana-1582	634	3	,	,	PUNCT
cana-1582	634	4	cos	cos	PROPN
cana-1582	634	5	)	)	PUNCT
cana-1582	634	6	x	x	SYM
cana-1582	635	1	b	b	X
cana-1582	635	2	y	y	PROPN
cana-1582	635	3	b	b	NOUN
cana-1582	635	4	+	+	VERB
cana-1582	635	5	−	−	NUM
cana-1582	635	6	}	}	PUNCT
cana-1582	635	7	.	.	PUNCT
cana-1582	636	1	the	the	DET
cana-1582	636	2	remaining	remain	VERB
cana-1582	636	3	points	point	NOUN
cana-1582	636	4	on	on	ADP
cana-1582	636	5	the	the	DET
cana-1582	636	6	ellipse	ellipse	NOUN
cana-1582	636	7	can	can	AUX
cana-1582	636	8	be	be	AUX
cana-1582	636	9	determined	determine	VERB
cana-1582	636	10	in	in	ADP
cana-1582	636	11	a	a	DET
cana-1582	636	12	similar	similar	ADJ
cana-1582	636	13	manner	manner	NOUN
cana-1582	636	14	.	.	PUNCT
cana-1582	637	1	the	the	DET
cana-1582	637	2	geometric	geometric	ADJ
cana-1582	637	3	moments	moment	NOUN
cana-1582	637	4	over	over	ADP
cana-1582	637	5	the	the	DET
cana-1582	637	6	general	general	ADJ
cana-1582	637	7	ellipse	ellipse	NOUN
cana-1582	637	8	described	describe	VERB
cana-1582	637	9	above	above	ADV
cana-1582	637	10	is	be	AUX
cana-1582	637	11	given	give	VERB
cana-1582	637	12	by	by	ADP
cana-1582	637	13	,	,	PUNCT
cana-1582	637	14	p	p	X
cana-1582	637	15	q	q	PROPN
cana-1582	637	16	pq	pq	NOUN
cana-1582	637	17	a	a	DET
cana-1582	637	18	m	m	NOUN
cana-1582	637	19	x	x	SYM
cana-1582	637	20	y	y	PROPN
cana-1582	637	21	dxdy=	dxdy=	PROPN
cana-1582	637	22			ADV
cana-1582	637	23	(	(	PUNCT
cana-1582	637	24	32	32	NUM
cana-1582	637	25	)	)	PUNCT
cana-1582	637	26	communications	communication	NOUN
cana-1582	637	27	on	on	ADP
cana-1582	637	28	applied	apply	VERB
cana-1582	637	29	nonlinear	nonlinear	ADJ
cana-1582	637	30	analysis	analysis	NOUN
cana-1582	637	31	issn	issn	NOUN
cana-1582	637	32	:	:	PUNCT
cana-1582	637	33	1074	1074	NUM
cana-1582	637	34	-	-	PUNCT
cana-1582	637	35	133x	133x	NUM
cana-1582	637	36	vol	vol	NOUN
cana-1582	637	37	31	31	NUM
cana-1582	637	38	no	no	NOUN
cana-1582	637	39	.	.	PUNCT
cana-1582	638	1	8s	8s	PROPN
cana-1582	638	2	(	(	PUNCT
cana-1582	638	3	2024	2024	NUM
cana-1582	638	4	)	)	PUNCT
cana-1582	638	5	737	737	NUM
cana-1582	638	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1582	638	7	where	where	SCONJ
cana-1582	638	8	a	a	PRON
cana-1582	638	9	is	be	AUX
cana-1582	638	10	the	the	DET
cana-1582	638	11	area	area	NOUN
cana-1582	638	12	of	of	ADP
cana-1582	638	13	the	the	DET
cana-1582	638	14	ellipse	ellipse	NOUN
cana-1582	638	15	.	.	PUNCT
cana-1582	639	1	the	the	DET
cana-1582	639	2	compound	compound	NOUN
cana-1582	639	3	moment	moment	NOUN
cana-1582	639	4	values	value	NOUN
cana-1582	639	5	and	and	CCONJ
cana-1582	639	6	the	the	DET
cana-1582	639	7	exact	exact	ADJ
cana-1582	639	8	moment	moment	NOUN
cana-1582	639	9	values	value	NOUN
cana-1582	639	10	are	be	AUX
cana-1582	639	11	tabulated	tabulate	VERB
cana-1582	639	12	.	.	PUNCT
cana-1582	640	1	we	we	PRON
cana-1582	640	2	may	may	AUX
cana-1582	640	3	note	note	VERB
cana-1582	640	4	that	that	SCONJ
cana-1582	640	5	the	the	DET
cana-1582	640	6			NUM
cana-1582	640	7	method	method	NOUN
cana-1582	640	8	,	,	PUNCT
cana-1582	640	9	the	the	DET
cana-1582	640	10	rectangular	rectangular	ADJ
cana-1582	640	11	grid	grid	NOUN
cana-1582	640	12	method	method	NOUN
cana-1582	640	13	,	,	PUNCT
cana-1582	640	14	trapezoidal	trapezoidal	ADJ
cana-1582	640	15	integration	integration	NOUN
cana-1582	640	16	method	method	NOUN
cana-1582	640	17	and	and	CCONJ
cana-1582	640	18	contour	contour	NOUN
cana-1582	640	19	integration	integration	NOUN
cana-1582	640	20	method	method	NOUN
cana-1582	640	21	proposed	propose	VERB
cana-1582	640	22	also	also	ADV
cana-1582	640	23	tabulated	tabulate	VERB
cana-1582	640	24	for	for	ADP
cana-1582	640	25	the	the	DET
cana-1582	640	26	purpose	purpose	NOUN
cana-1582	640	27	of	of	ADP
cana-1582	640	28	integration	integration	NOUN
cana-1582	640	29	.	.	PUNCT
cana-1582	641	1	number	number	NOUN
cana-1582	641	2	of	of	ADP
cana-1582	641	3	points	point	NOUN
cana-1582	641	4	on	on	ADP
cana-1582	641	5	general	general	ADJ
cana-1582	641	6	ellipse	ellipse	NOUN
cana-1582	641	7	np	np	PROPN
cana-1582	641	8	moments	moment	NOUN
cana-1582	641	9	computed	compute	VERB
cana-1582	641	10	values	value	NOUN
cana-1582	641	11	of	of	ADP
cana-1582	641	12	moments	moment	NOUN
cana-1582	641	13	theoretical	theoretical	ADJ
cana-1582	641	14	values	value	NOUN
cana-1582	641	15	1.0e+006	1.0e+006	NUM
cana-1582	641	16	*	*	SYM
cana-1582	641	17	498	498	NUM
cana-1582	641	18	m00	m00	NOUN
cana-1582	641	19	=	=	SYM
cana-1582	641	20	1.884955592153876e+003	1.884955592153876e+003	PROPN
cana-1582	641	21	m10	m10	NOUN
cana-1582	641	22	=	=	SYM
cana-1582	641	23	1.884955592153876e+004	1.884955592153876e+004	NUM
cana-1582	641	24	m01	m01	NOUN
cana-1582	641	25	=	=	SYM
cana-1582	641	26	5.654866776461627e+004	5.654866776461627e+004	NUM
cana-1582	641	27	m20	m20	NOUN
cana-1582	641	28	=	=	SYM
cana-1582	641	29	4.948008429403924e+005	4.948008429403924e+005	NOUN
cana-1582	641	30	m02	m02	NOUN
cana-1582	641	31	=	=	SYM
cana-1582	641	32	2.002765316663493e+006	2.002765316663493e+006	NUM
cana-1582	641	33	m11	m11	NOUN
cana-1582	641	34	=	=	PUNCT
cana-1582	641	35	6.832964021557800e+005	6.832964021557800e+005	NUM
cana-1582	641	36	fn=1	fn=1	PROPN
cana-1582	641	37	1.884955592022257e+003	1.884955592022257e+003	NUM
cana-1582	642	1	fn	fn	NOUN
cana-1582	642	2	=	=	ADJ
cana-1582	642	3	x	x	SYM
cana-1582	642	4	1.884955592161867e+004	1.884955592161867e+004	NUM
cana-1582	642	5	fn	fn	NOUN
cana-1582	642	6	=	=	PROPN
cana-1582	642	7	y	y	PROPN
cana-1582	642	8	5.654866776206377e+004	5.654866776206377e+004	NUM
cana-1582	642	9	fn	fn	NOUN
cana-1582	643	1	=	=	NOUN
cana-1582	643	2	x^2	x^2	PROPN
cana-1582	643	3	4.948008429123767e+005	4.948008429123767e+005	NUM
cana-1582	643	4	fn	fn	NOUN
cana-1582	643	5	=	=	AUX
cana-1582	643	6	y^2	y^2	NOUN
cana-1582	643	7	2.002765316586024e+006	2.002765316586024e+006	NUM
cana-1582	643	8	fn	fn	NOUN
cana-1582	643	9	=	=	SYM
cana-1582	643	10	x*y	x*y	NOUN
cana-1582	643	11	6.832964021556849e+005	6.832964021556849e+005	NUM
cana-1582	644	1	0.00188495559202	0.00188495559202	NUM
cana-1582	644	2	0.01884955592162	0.01884955592162	NUM
cana-1582	644	3	0.05654866776206	0.05654866776206	NUM
cana-1582	645	1	0.49480084291238	0.49480084291238	NUM
cana-1582	645	2	2.00276531658602	2.00276531658602	NUM
cana-1582	645	3	0.68329640215568	0.68329640215568	NUM
cana-1582	645	4	998	998	NUM
cana-1582	645	5	m00	m00	NOUN
cana-1582	645	6	=	=	SYM
cana-1582	645	7	1.884955592153876e+003	1.884955592153876e+003	NUM
cana-1582	645	8	m10	m10	NOUN
cana-1582	645	9	=	=	SYM
cana-1582	645	10	1.884955592153876e+004	1.884955592153876e+004	NUM
cana-1582	645	11	m01	m01	NOUN
cana-1582	645	12	=	=	SYM
cana-1582	645	13	5.654866776461627e+004	5.654866776461627e+004	NUM
cana-1582	645	14	m20	m20	NOUN
cana-1582	645	15	=	=	SYM
cana-1582	645	16	4.948008429403924e+005	4.948008429403924e+005	NOUN
cana-1582	645	17	m02	m02	NOUN
cana-1582	645	18	=	=	SYM
cana-1582	645	19	2.002765316663493e+006	2.002765316663493e+006	NUM
cana-1582	645	20	m11	m11	NOUN
cana-1582	645	21	=	=	PUNCT
cana-1582	645	22	6.832964021557800e+005	6.832964021557800e+005	NUM
cana-1582	645	23	fn=1	fn=1	PROPN
cana-1582	645	24	1.884955592145685e+003	1.884955592145685e+003	NUM
cana-1582	645	25	fn	fn	NOUN
cana-1582	645	26	=	=	NOUN
cana-1582	645	27	x	x	SYM
cana-1582	645	28	1.884955592154394e+004	1.884955592154394e+004	NUM
cana-1582	645	29	fn	fn	NOUN
cana-1582	645	30	=	=	NOUN
cana-1582	645	31	y	y	PROPN
cana-1582	645	32	5.654866776445747e+004	5.654866776445747e+004	NUM
cana-1582	645	33	fn	fn	NOUN
cana-1582	646	1	=	=	NOUN
cana-1582	646	2	x^2	x^2	ADJ
cana-1582	646	3	4.948008429386528e+005	4.948008429386528e+005	NUM
cana-1582	646	4	fn	fn	NOUN
cana-1582	646	5	=	=	PRON
cana-1582	646	6	y^2	y^2	ADJ
cana-1582	646	7	2.002765316658672e+006	2.002765316658672e+006	NUM
cana-1582	646	8	fn	fn	NOUN
cana-1582	646	9	=	=	SYM
cana-1582	646	10	x*y	x*y	NOUN
cana-1582	646	11	6.832964021557791e+005	6.832964021557791e+005	NOUN
cana-1582	646	12	1.884955592145685e+003	1.884955592145685e+003	NUM
cana-1582	646	13	1.884955592154394e+004	1.884955592154394e+004	NUM
cana-1582	646	14	5.654866776445747e+004	5.654866776445747e+004	NUM
cana-1582	646	15	4.948008429386528e+005	4.948008429386528e+005	NUM
cana-1582	646	16	2.002765316658672e+006	2.002765316658672e+006	NUM
cana-1582	646	17	6.832964021557791e+005	6.832964021557791e+005	NUM
cana-1582	646	18	1498	1498	NUM
cana-1582	646	19	m00	m00	NOUN
cana-1582	646	20	=	=	SYM
cana-1582	646	21	1.884955592153876e+003	1.884955592153876e+003	PROPN
cana-1582	646	22	m10	m10	NOUN
cana-1582	646	23	=	=	SYM
cana-1582	646	24	fn=1	fn=1	PROPN
cana-1582	646	25	1.884955592152255e+003	1.884955592152255e+003	NUM
cana-1582	646	26	fn	fn	NOUN
cana-1582	646	27	=	=	NOUN
cana-1582	646	28	x	x	SYM
cana-1582	646	29	1.884955592152255e+003	1.884955592152255e+003	NUM
cana-1582	646	30	1.884955592153955e+004	1.884955592153955e+004	NUM
cana-1582	646	31	5.654866776458480e+004	5.654866776458480e+004	PROPN
cana-1582	646	32	communications	communication	NOUN
cana-1582	646	33	on	on	ADP
cana-1582	646	34	applied	apply	VERB
cana-1582	646	35	nonlinear	nonlinear	ADJ
cana-1582	646	36	analysis	analysis	NOUN
cana-1582	646	37	issn	issn	NOUN
cana-1582	646	38	:	:	PUNCT
cana-1582	646	39	1074	1074	NUM
cana-1582	646	40	-	-	PUNCT
cana-1582	646	41	133x	133x	NUM
cana-1582	646	42	vol	vol	NOUN
cana-1582	646	43	31	31	NUM
cana-1582	646	44	no	no	NOUN
cana-1582	646	45	.	.	PUNCT
cana-1582	647	1	8s	8s	PROPN
cana-1582	647	2	(	(	PUNCT
cana-1582	647	3	2024	2024	NUM
cana-1582	647	4	)	)	PUNCT
cana-1582	647	5	738	738	NUM
cana-1582	647	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1582	647	7	1.884955592153876e+004	1.884955592153876e+004	NUM
cana-1582	647	8	m01	m01	NUM
cana-1582	647	9	=	=	SYM
cana-1582	647	10	5.654866776461627e+004	5.654866776461627e+004	NUM
cana-1582	647	11	m20	m20	NOUN
cana-1582	647	12	=	=	SYM
cana-1582	647	13	4.948008429403924e+005	4.948008429403924e+005	NOUN
cana-1582	647	14	m02	m02	NOUN
cana-1582	647	15	=	=	SYM
cana-1582	647	16	2.002765316663493e+006	2.002765316663493e+006	NUM
cana-1582	647	17	m11	m11	NOUN
cana-1582	647	18	=	=	PUNCT
cana-1582	648	1	6.832964021557800e+005	6.832964021557800e+005	NUM
cana-1582	648	2	1.884955592153955e+004	1.884955592153955e+004	NUM
cana-1582	648	3	fn	fn	NOUN
cana-1582	648	4	=	=	NOUN
cana-1582	648	5	y	y	PROPN
cana-1582	648	6	5.654866776458480e+004	5.654866776458480e+004	NUM
cana-1582	648	7	fn	fn	NOUN
cana-1582	648	8	=	=	NOUN
cana-1582	648	9	x^2	x^2	PROPN
cana-1582	648	10	4.948008429400452e+005	4.948008429400452e+005	NUM
cana-1582	648	11	fn	fn	NOUN
cana-1582	649	1	=	=	NOUN
cana-1582	649	2	y^2	y^2	PROPN
cana-1582	649	3	2.002765316662538e+006	2.002765316662538e+006	NUM
cana-1582	649	4	fn	fn	NOUN
cana-1582	649	5	=	=	NOUN
cana-1582	649	6	x*y	x*y	NOUN
cana-1582	649	7	6.832964021557742e+005	6.832964021557742e+005	NUM
cana-1582	649	8	4.948008429400452e+005	4.948008429400452e+005	VERB
cana-1582	649	9	2.002765316662538e+006	2.002765316662538e+006	NOUN
cana-1582	650	1	6.832964021557742e+005	6.832964021557742e+005	NUM
cana-1582	650	2	1998	1998	NUM
cana-1582	650	3	m00	m00	NOUN
cana-1582	650	4	=	=	SYM
cana-1582	650	5	1.884955592153876e+003	1.884955592153876e+003	PROPN
cana-1582	650	6	m10	m10	NOUN
cana-1582	650	7	=	=	SYM
cana-1582	650	8	1.884955592153876e+004	1.884955592153876e+004	NUM
cana-1582	650	9	m01	m01	NOUN
cana-1582	650	10	=	=	SYM
cana-1582	650	11	5.654866776461627e+004	5.654866776461627e+004	NUM
cana-1582	650	12	m20	m20	NOUN
cana-1582	650	13	=	=	SYM
cana-1582	650	14	4.948008429403924e+005	4.948008429403924e+005	NOUN
cana-1582	650	15	m02	m02	NOUN
cana-1582	650	16	=	=	SYM
cana-1582	650	17	2.002765316663493e+006	2.002765316663493e+006	NUM
cana-1582	650	18	m11	m11	NOUN
cana-1582	650	19	=	=	PUNCT
cana-1582	650	20	6.832964021557800e+005	6.832964021557800e+005	NUM
cana-1582	650	21	fn=1	fn=1	PROPN
cana-1582	650	22	1.884955592153362e+003	1.884955592153362e+003	NUM
cana-1582	650	23	fn	fn	NOUN
cana-1582	650	24	=	=	NOUN
cana-1582	650	25	x	x	SYM
cana-1582	650	26	1.884955592153892e+004	1.884955592153892e+004	NUM
cana-1582	650	27	fn	fn	NOUN
cana-1582	650	28	=	=	NOUN
cana-1582	650	29	y	y	PROPN
cana-1582	650	30	5.654866776460630e+004	5.654866776460630e+004	NUM
cana-1582	650	31	fn	fn	NOUN
cana-1582	651	1	=	=	NOUN
cana-1582	651	2	x^2	x^2	NOUN
cana-1582	651	3	4.948008429402803e+005	4.948008429402803e+005	NOUN
cana-1582	651	4	fn	fn	NOUN
cana-1582	652	1	=	=	NOUN
cana-1582	652	2	y^2	y^2	VERB
cana-1582	652	3	2.002765316663193e+006	2.002765316663193e+006	NUM
cana-1582	652	4	fn	fn	NOUN
cana-1582	652	5	=	=	NOUN
cana-1582	652	6	x*y	x*y	NOUN
cana-1582	652	7	6.832964021557753e+005	6.832964021557753e+005	NUM
cana-1582	652	8	1.884955592153362e+003	1.884955592153362e+003	NUM
cana-1582	652	9	1.884955592153892e+004	1.884955592153892e+004	NUM
cana-1582	652	10	5.654866776460630e+004	5.654866776460630e+004	NUM
cana-1582	653	1	4.948008429402803e+005	4.948008429402803e+005	NUM
cana-1582	653	2	2.002765316663193e+006	2.002765316663193e+006	NUM
cana-1582	653	3	6.832964021557753e+005	6.832964021557753e+005	NUM
cana-1582	653	4	table	table	NOUN
cana-1582	653	5	2	2	NUM
cana-1582	653	6	computed	compute	VERB
cana-1582	653	7	values	value	NOUN
cana-1582	653	8	of	of	ADP
cana-1582	653	9	moments	moment	NOUN
cana-1582	653	10	conclusions	conclusion	NOUN
cana-1582	653	11	we	we	PRON
cana-1582	653	12	have	have	AUX
cana-1582	653	13	presented	present	VERB
cana-1582	653	14	quartic	quartic	ADJ
cana-1582	653	15	spline	spline	NOUN
cana-1582	653	16	,	,	PUNCT
cana-1582	653	17	which	which	PRON
cana-1582	653	18	interpolates	interpolate	VERB
cana-1582	653	19	the	the	DET
cana-1582	653	20	first	first	ADJ
cana-1582	653	21	derivatives	derivative	NOUN
cana-1582	653	22	of	of	ADP
cana-1582	653	23	a	a	DET
cana-1582	653	24	given	give	VERB
cana-1582	653	25	function	function	NOUN
cana-1582	653	26	at	at	ADP
cana-1582	653	27	the	the	DET
cana-1582	653	28	knots	knot	NOUN
cana-1582	653	29	and	and	CCONJ
cana-1582	653	30	the	the	DET
cana-1582	653	31	second	second	ADJ
cana-1582	653	32	derivatives	derivative	NOUN
cana-1582	653	33	between	between	ADP
cana-1582	653	34	them	they	PRON
cana-1582	653	35	.	.	PUNCT
cana-1582	654	1	a	a	DET
cana-1582	654	2	simple	simple	ADJ
cana-1582	654	3	approximation	approximation	NOUN
cana-1582	654	4	to	to	PART
cana-1582	654	5	function	function	VERB
cana-1582	654	6	values	value	NOUN
cana-1582	654	7	is	be	AUX
cana-1582	654	8	determined	determine	VERB
cana-1582	654	9	by	by	ADP
cana-1582	654	10	choosing	choose	VERB
cana-1582	654	11	the	the	DET
cana-1582	654	12	second	second	ADJ
cana-1582	654	13	derivate	derivate	NOUN
cana-1582	654	14	to	to	PART
cana-1582	654	15	coincide	coincide	VERB
cana-1582	654	16	with	with	ADP
cana-1582	654	17	the	the	DET
cana-1582	654	18	initial	initial	ADJ
cana-1582	654	19	knots	knot	NOUN
cana-1582	654	20	.	.	PUNCT
cana-1582	655	1	a	a	DET
cana-1582	655	2	numerical	numerical	ADJ
cana-1582	655	3	integration	integration	NOUN
cana-1582	655	4	scheme	scheme	PROPN
cana-1582	655	5	gauss	gauss	PROPN
cana-1582	655	6	legendre	legendre	PROPN
cana-1582	655	7	quadrature	quadrature	NOUN
cana-1582	655	8	rules	rule	NOUN
cana-1582	655	9	and	and	CCONJ
cana-1582	655	10	the	the	DET
cana-1582	655	11	explicit	explicit	ADJ
cana-1582	655	12	parametric	parametric	ADJ
cana-1582	655	13	relations	relation	NOUN
cana-1582	655	14	along	along	ADP
cana-1582	655	15	the	the	DET
cana-1582	655	16	curved	curved	ADJ
cana-1582	655	17	boundary	boundary	NOUN
cana-1582	655	18	of	of	ADP
cana-1582	655	19	the	the	DET
cana-1582	655	20	two	two	NUM
cana-1582	655	21	dimensional	dimensional	ADJ
cana-1582	655	22	cartesian	cartesian	ADJ
cana-1582	655	23	space	space	NOUN
cana-1582	655	24	is	be	AUX
cana-1582	655	25	considered	consider	VERB
cana-1582	655	26	.	.	PUNCT
cana-1582	656	1	the	the	DET
cana-1582	656	2	above	above	ADP
cana-1582	656	3	numerical	numerical	ADJ
cana-1582	656	4	integration	integration	NOUN
cana-1582	656	5	scheme	scheme	NOUN
cana-1582	656	6	is	be	AUX
cana-1582	656	7	illustrated	illustrate	VERB
cana-1582	656	8	by	by	ADP
cana-1582	656	9	computing	compute	VERB
cana-1582	656	10	several	several	ADJ
cana-1582	656	11	difficult	difficult	ADJ
cana-1582	656	12	integrals	integral	NOUN
cana-1582	656	13	over	over	ADP
cana-1582	656	14	the	the	DET
cana-1582	656	15	curved	curved	ADJ
cana-1582	656	16	domain	domain	NOUN
cana-1582	656	17	.	.	PUNCT
cana-1582	657	1	the	the	DET
cana-1582	657	2	integral	integral	ADJ
cana-1582	657	3	values	value	NOUN
cana-1582	657	4	with	with	ADP
cana-1582	657	5	its	its	PRON
cana-1582	657	6	absolute	absolute	ADJ
cana-1582	657	7	error	error	NOUN
cana-1582	657	8	of	of	ADP
cana-1582	657	9	integrals	integral	NOUN
cana-1582	657	10	are	be	AUX
cana-1582	657	11	tabulated	tabulate	VERB
cana-1582	657	12	.	.	PUNCT
cana-1582	658	1	integration	integration	NOUN
cana-1582	658	2	for	for	ADP
cana-1582	658	3	𝐼𝐼(𝑖	𝐼𝐼(𝑖	NOUN
cana-1582	658	4	)	)	PUNCT
cana-1582	659	1	=	=	PUNCT
cana-1582	659	2	∬	∬	NOUN
cana-1582	659	3	𝑓𝑖(𝑥	𝑓𝑖(𝑥	NUM
cana-1582	659	4	,	,	PUNCT
cana-1582	659	5	𝑦	𝑦	NOUN
cana-1582	659	6	)	)	PUNCT
cana-1582	659	7	𝐷	𝐷	PROPN
cana-1582	659	8	𝑑𝑥𝑑𝑦	𝑑𝑥𝑑𝑦	NOUN
cana-1582	659	9	,	,	PUNCT
cana-1582	659	10	𝑖	𝑖	X
cana-1582	659	11	=	=	PUNCT
cana-1582	659	12	1(1)4	1(1)4	ADJ
cana-1582	659	13	,	,	PUNCT
cana-1582	659	14	d	d	NOUN
cana-1582	659	15	:	:	PUNCT
cana-1582	659	16	domain	domain	NOUN
cana-1582	659	17	of	of	ADP
cana-1582	659	18	as	as	SCONJ
cana-1582	659	19	shown	show	VERB
cana-1582	659	20	in	in	ADP
cana-1582	659	21	figure	figure	NOUN
cana-1582	659	22	1	1	NUM
cana-1582	659	23	acknowledgment	acknowledgment	NOUN
cana-1582	659	24	:	:	PUNCT
cana-1582	659	25	both	both	CCONJ
cana-1582	659	26	the	the	DET
cana-1582	659	27	authors	author	NOUN
cana-1582	659	28	acknowledge	acknowledge	VERB
cana-1582	659	29	late	late	PROPN
cana-1582	659	30	dr	dr	PROPN
cana-1582	659	31	.	.	PROPN
cana-1582	659	32	h	h	PROPN
cana-1582	659	33	t	t	PROPN
cana-1582	659	34	rathod	rathod	PROPN
cana-1582	659	35	for	for	ADP
cana-1582	659	36	his	his	PRON
cana-1582	659	37	valuable	valuable	ADJ
cana-1582	659	38	suggestions	suggestion	NOUN
cana-1582	659	39	,	,	PUNCT
cana-1582	659	40	the	the	DET
cana-1582	659	41	support	support	NOUN
cana-1582	659	42	and	and	CCONJ
cana-1582	659	43	guidance	guidance	NOUN
cana-1582	659	44	.	.	PUNCT
cana-1582	660	1	communications	communication	NOUN
cana-1582	660	2	on	on	ADP
cana-1582	660	3	applied	apply	VERB
cana-1582	660	4	nonlinear	nonlinear	ADJ
cana-1582	660	5	analysis	analysis	NOUN
cana-1582	660	6	issn	issn	NOUN
cana-1582	660	7	:	:	PUNCT
cana-1582	660	8	1074	1074	NUM
cana-1582	660	9	-	-	PUNCT
cana-1582	660	10	133x	133x	NUM
cana-1582	660	11	vol	vol	NOUN
cana-1582	660	12	31	31	NUM
cana-1582	660	13	no	no	NOUN
cana-1582	660	14	.	.	PUNCT
cana-1582	661	1	8s	8s	PROPN
cana-1582	661	2	(	(	PUNCT
cana-1582	661	3	2024	2024	NUM
cana-1582	661	4	)	)	PUNCT
cana-1582	661	5	739	739	NUM
cana-1582	661	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1582	661	7	references	reference	NOUN
cana-1582	661	8	:	:	PUNCT
cana-1582	662	1	[	[	X
cana-1582	662	2	1	1	NUM
cana-1582	662	3	]	]	X
cana-1582	662	4	anwar	anwar	PROPN
cana-1582	662	5	,	,	PUNCT
cana-1582	662	6	m.n	m.n	PROPN
cana-1582	662	7	and	and	CCONJ
cana-1582	662	8	el	el	PROPN
cana-1582	662	9	-	-	PUNCT
cana-1582	662	10	tarazi	tarazi	NOUN
cana-1582	662	11	,	,	PUNCT
cana-1582	662	12	m.n	m.n	PROPN
cana-1582	662	13	:	:	PUNCT
cana-1582	662	14	direct	direct	ADJ
cana-1582	662	15	cubic	cubic	ADJ
cana-1582	662	16	spline	spline	NOUN
cana-1582	662	17	with	with	ADP
cana-1582	662	18	application	application	NOUN
cana-1582	662	19	to	to	ADP
cana-1582	662	20	quadrature	quadrature	NOUN
cana-1582	662	21	,	,	PUNCT
cana-1582	662	22	communications	communication	NOUN
cana-1582	662	23	in	in	ADP
cana-1582	662	24	applied	apply	VERB
cana-1582	662	25	numerical	numerical	ADJ
cana-1582	662	26	methods	method	NOUN
cana-1582	662	27	,	,	PUNCT
cana-1582	662	28	5	5	NUM
cana-1582	662	29	,	,	PUNCT
cana-1582	662	30	pp	pp	ADV
cana-1582	662	31	237	237	NUM
cana-1582	662	32	–	–	PUNCT
cana-1582	662	33	246	246	NUM
cana-1582	662	34	(	(	PUNCT
cana-1582	662	35	1989	1989	NUM
cana-1582	662	36	)	)	PUNCT
cana-1582	662	37	.	.	PUNCT
cana-1582	663	1	[	[	X
cana-1582	663	2	2	2	X
cana-1582	663	3	]	]	PUNCT
cana-1582	663	4	apostol	apostol	NOUN
cana-1582	663	5	t.	t.	PROPN
cana-1582	663	6	m.	m.	NOUN
cana-1582	663	7	,	,	PUNCT
cana-1582	663	8	calculus	calculus	NOUN
cana-1582	663	9	,	,	PUNCT
cana-1582	663	10	vol	vol	NOUN
cana-1582	663	11	.	.	PUNCT
cana-1582	663	12	ii	ii	PROPN
cana-1582	663	13	,	,	PUNCT
cana-1582	663	14	second	second	PROPN
cana-1582	663	15	edition	edition	NOUN
cana-1582	663	16	blaisdell	blaisdell	PROPN
cana-1582	663	17	(	(	PUNCT
cana-1582	663	18	1969	1969	NUM
cana-1582	663	19	)	)	PUNCT
cana-1582	663	20	.	.	PUNCT
cana-1582	664	1	[	[	X
cana-1582	664	2	3	3	NUM
cana-1582	664	3	]	]	X
cana-1582	664	4	elden	elden	PROPN
cana-1582	664	5	,	,	PUNCT
cana-1582	664	6	l.	l.	PROPN
cana-1582	664	7	,	,	PUNCT
cana-1582	664	8	lewittmeyer	lewittmeyer	NOUN
cana-1582	664	9	-	-	PUNCT
cana-1582	664	10	koch	koch	PROPN
cana-1582	664	11	,	,	PUNCT
cana-1582	664	12	h.	h.	PROPN
cana-1582	664	13	b.	b.	PROPN
cana-1582	664	14	nielson	nielson	PROPN
cana-1582	664	15	introduction	introduction	NOUN
cana-1582	664	16	to	to	ADP
cana-1582	664	17	numerical	numerical	ADJ
cana-1582	664	18	computation	computation	NOUN
cana-1582	664	19	,	,	PUNCT
cana-1582	664	20	analysis	analysis	NOUN
cana-1582	664	21	and	and	CCONJ
cana-1582	664	22	matlabr	matlabr	NOUN
cana-1582	664	23	illustrations	illustration	NOUN
cana-1582	664	24	,	,	PUNCT
cana-1582	664	25	overseas	overseas	ADJ
cana-1582	664	26	press	press	PROPN
cana-1582	664	27	india	india	PROPN
cana-1582	664	28	pvt	pvt	PROPN
cana-1582	664	29	,	,	PUNCT
cana-1582	664	30	ltd	ltd	PROPN
cana-1582	664	31	(	(	PUNCT
cana-1582	664	32	2006	2006	NUM
cana-1582	664	33	)	)	PUNCT
cana-1582	664	34	.	.	PUNCT
cana-1582	665	1	[	[	X
cana-1582	665	2	4	4	NUM
cana-1582	665	3	]	]	X
cana-1582	665	4	gustafasson	gustafasson	PROPN
cana-1582	665	5	,	,	PUNCT
cana-1582	665	6	f.	f.	PROPN
cana-1582	665	7	and	and	CCONJ
cana-1582	665	8	bergman	bergman	PROPN
cana-1582	665	9	,	,	PUNCT
cana-1582	665	10	n.	n.	PROPN
cana-1582	665	11	,	,	PUNCT
cana-1582	665	12	matlab	matlab	PROPN
cana-1582	665	13	for	for	ADP
cana-1582	665	14	engineers	engineer	NOUN
cana-1582	665	15	explained	explain	VERB
cana-1582	665	16	,	,	PUNCT
cana-1582	665	17	springer	springer	NOUN
cana-1582	665	18	international	international	PROPN
cana-1582	665	19	edition	edition	PROPN
cana-1582	665	20	(	(	PUNCT
cana-1582	665	21	2003	2003	NUM
cana-1582	665	22	)	)	PUNCT
cana-1582	665	23	.	.	PUNCT
cana-1582	666	1	[	[	X
cana-1582	666	2	5	5	X
cana-1582	666	3	]	]	PUNCT
cana-1582	666	4	h.	h.	NOUN
cana-1582	666	5	behforooz	behforooz	PROPN
cana-1582	666	6	,	,	PUNCT
cana-1582	666	7	approximation	approximation	NOUN
cana-1582	666	8	by	by	ADP
cana-1582	666	9	integro	integro	PROPN
cana-1582	666	10	cubic	cubic	ADJ
cana-1582	666	11	splines	spline	NOUN
cana-1582	666	12	,	,	PUNCT
cana-1582	666	13	appl	appl	PROPN
cana-1582	666	14	.	.	PROPN
cana-1582	666	15	math	math	NOUN
cana-1582	666	16	.	.	PUNCT
cana-1582	667	1	comput	comput	NOUN
cana-1582	667	2	.	.	PUNCT
cana-1582	668	1	175	175	NUM
cana-1582	668	2	(	(	PUNCT
cana-1582	668	3	2006	2006	NUM
cana-1582	668	4	)	)	PUNCT
cana-1582	668	5	8–15	8–15	PROPN
cana-1582	668	6	.	.	PUNCT
cana-1582	669	1	[	[	X
cana-1582	669	2	6	6	NUM
cana-1582	669	3	]	]	PUNCT
cana-1582	669	4	h.	h.	NOUN
cana-1582	669	5	behforooz	behforooz	PROPN
cana-1582	669	6	,	,	PUNCT
cana-1582	669	7	interpolation	interpolation	NOUN
cana-1582	669	8	by	by	ADP
cana-1582	669	9	integro	integro	ADJ
cana-1582	669	10	quintic	quintic	ADJ
cana-1582	669	11	splines	spline	NOUN
cana-1582	669	12	,	,	PUNCT
cana-1582	669	13	appl	appl	PROPN
cana-1582	669	14	.	.	PROPN
cana-1582	669	15	math	math	NOUN
cana-1582	669	16	.	.	PUNCT
cana-1582	670	1	comput	comput	NOUN
cana-1582	670	2	.	.	PUNCT
cana-1582	671	1	216	216	NUM
cana-1582	671	2	(	(	PUNCT
cana-1582	671	3	2010	2010	NUM
cana-1582	671	4	)	)	PUNCT
cana-1582	672	1	364–367	364–367	NUM
cana-1582	672	2	[	[	X
cana-1582	672	3	7	7	X
cana-1582	672	4	]	]	X
cana-1582	672	5	h.	h.	PROPN
cana-1582	672	6	t.	t.	PROPN
cana-1582	672	7	rathod	rathod	PROPN
cana-1582	672	8	and	and	CCONJ
cana-1582	672	9	h.	h.	PROPN
cana-1582	672	10	s.	s.	PROPN
cana-1582	672	11	govinda	govinda	PROPN
cana-1582	672	12	rao	rao	PROPN
cana-1582	672	13	,	,	PUNCT
cana-1582	672	14	integration	integration	NOUN
cana-1582	672	15	of	of	ADP
cana-1582	672	16	polynomials	polynomial	NOUN
cana-1582	672	17	over	over	ADP
cana-1582	672	18	n	n	ADV
cana-1582	672	19	-	-	PUNCT
cana-1582	672	20	dimensional	dimensional	ADJ
cana-1582	672	21	linear	linear	ADJ
cana-1582	672	22	polyhedra	polyhedra	NOUN
cana-1582	672	23	,	,	PUNCT
cana-1582	672	24	computers	computer	NOUN
cana-1582	672	25	and	and	CCONJ
cana-1582	672	26	structures	structure	NOUN
cana-1582	672	27	,	,	PUNCT
cana-1582	672	28	vol.65	vol.65	PROPN
cana-1582	672	29	,	,	PUNCT
cana-1582	672	30	no.6	no.6	PROPN
cana-1582	672	31	,	,	PUNCT
cana-1582	672	32	pp.829	pp.829	NOUN
cana-1582	672	33	-	-	PUNCT
cana-1582	672	34	847	847	NUM
cana-1582	672	35	(	(	PUNCT
cana-1582	672	36	1997	1997	NUM
cana-1582	672	37	)	)	PUNCT
cana-1582	672	38	.	.	PUNCT
cana-1582	673	1	[	[	X
cana-1582	673	2	8	8	X
cana-1582	673	3	]	]	X
cana-1582	673	4	h.	h.	PROPN
cana-1582	673	5	t.	t.	PROPN
cana-1582	673	6	rathod	rathod	PROPN
cana-1582	673	7	and	and	CCONJ
cana-1582	673	8	s.	s.	PROPN
cana-1582	673	9	v.	v.	PROPN
cana-1582	673	10	hiremath	hiremath	PROPN
cana-1582	673	11	,	,	PUNCT
cana-1582	673	12	boundary	boundary	ADJ
cana-1582	673	13	integration	integration	NOUN
cana-1582	673	14	of	of	ADP
cana-1582	673	15	polynomials	polynomial	NOUN
cana-1582	673	16	over	over	ADP
cana-1582	673	17	an	an	DET
cana-1582	673	18	arbitrary	arbitrary	ADJ
cana-1582	673	19	linear	linear	ADJ
cana-1582	673	20	hexahedron	hexahedron	NOUN
cana-1582	673	21	in	in	ADP
cana-1582	673	22	euclidean	euclidean	ADJ
cana-1582	673	23	three	three	NUM
cana-1582	673	24	dimensional	dimensional	ADJ
cana-1582	673	25	space	space	NOUN
cana-1582	673	26	,	,	PUNCT
cana-1582	673	27	computer	computer	NOUN
cana-1582	673	28	methods	method	NOUN
cana-1582	673	29	in	in	ADP
cana-1582	673	30	applied	applied	ADJ
cana-1582	673	31	mechanics	mechanic	NOUN
cana-1582	673	32	and	and	CCONJ
cana-1582	673	33	engineering	engineering	NOUN
cana-1582	673	34	,	,	PUNCT
cana-1582	673	35	vol.161	vol.161	NOUN
cana-1582	673	36	,	,	PUNCT
cana-1582	673	37	pp.155193	pp.155193	NOUN
cana-1582	673	38	(	(	PUNCT
cana-1582	673	39	1998	1998	NUM
cana-1582	673	40	)	)	PUNCT
cana-1582	673	41	.	.	PUNCT
cana-1582	674	1	[	[	X
cana-1582	674	2	9	9	NUM
cana-1582	674	3	]	]	X
cana-1582	674	4	h.	h.	PROPN
cana-1582	674	5	t.	t.	PROPN
cana-1582	674	6	rathod	rathod	PROPN
cana-1582	674	7	,	,	PUNCT
cana-1582	674	8	md.shafiqul.islam	md.shafiqul.islam	PROPN
cana-1582	674	9	,	,	PUNCT
cana-1582	674	10	bharath	bharath	PROPN
cana-1582	674	11	rathod	rathod	PROPN
cana-1582	674	12	,	,	PUNCT
cana-1582	674	13	k.	k.	PROPN
cana-1582	674	14	sugantha	sugantha	PROPN
cana-1582	674	15	devi	devi	PROPN
cana-1582	674	16	,	,	PUNCT
cana-1582	674	17	finite	finite	PROPN
cana-1582	674	18	element	element	NOUN
cana-1582	674	19	solution	solution	NOUN
cana-1582	674	20	of	of	ADP
cana-1582	674	21	poisson	poisson	NOUN
cana-1582	674	22	equation	equation	NOUN
cana-1582	674	23	over	over	ADP
cana-1582	674	24	polygonal	polygonal	ADJ
cana-1582	674	25	domains	domain	NOUN
cana-1582	674	26	using	use	VERB
cana-1582	674	27	a	a	DET
cana-1582	674	28	novel	novel	ADJ
cana-1582	674	29	auto	auto	NOUN
cana-1582	674	30	mesh	mesh	NOUN
cana-1582	674	31	generation	generation	NOUN
cana-1582	674	32	technique	technique	NOUN
cana-1582	674	33	and	and	CCONJ
cana-1582	674	34	an	an	DET
cana-1582	674	35	explicit	explicit	ADJ
cana-1582	674	36	integration	integration	NOUN
cana-1582	674	37	scheme	scheme	NOUN
cana-1582	674	38	for	for	ADP
cana-1582	674	39	linear	linear	ADJ
cana-1582	674	40	convex	convex	NOUN
cana-1582	674	41	quadrilaterals	quadrilateral	NOUN
cana-1582	674	42	of	of	ADP
cana-1582	674	43	cubic	cubic	ADJ
cana-1582	674	44	order	order	NOUN
cana-1582	674	45	serendipity	serendipity	NOUN
cana-1582	674	46	and	and	CCONJ
cana-1582	674	47	lagrange	lagrange	NOUN
cana-1582	674	48	families	family	NOUN
cana-1582	674	49	,	,	PUNCT
cana-1582	674	50	international	international	ADJ
cana-1582	674	51	journal	journal	NOUN
cana-1582	674	52	of	of	ADP
cana-1582	674	53	engineering	engineering	NOUN
cana-1582	674	54	and	and	CCONJ
cana-1582	674	55	computer	computer	NOUN
cana-1582	674	56	science	science	NOUN
cana-1582	674	57	issn:2319	issn:2319	PROPN
cana-1582	674	58	-	-	PROPN
cana-1582	674	59	7242,volume	7242,volume	ADJ
cana-1582	674	60	7	7	NUM
cana-1582	674	61	issue	issue	NOUN
cana-1582	674	62	1	1	NUM
cana-1582	674	63	january	january	PROPN
cana-1582	674	64	2018	2018	NUM
cana-1582	674	65	,	,	PUNCT
cana-1582	674	66	page	page	NOUN
cana-1582	674	67	no	no	NOUN
cana-1582	674	68	.	.	PUNCT
cana-1582	674	69	23329	23329	NUM
cana-1582	674	70	-	-	SYM
cana-1582	674	71	23482	23482	NUM
cana-1582	675	1	[	[	X
cana-1582	675	2	10	10	NUM
cana-1582	675	3	]	]	X
cana-1582	675	4	h.t	h.t	PROPN
cana-1582	675	5	.	.	PROPN
cana-1582	675	6	rathod	rathod	PROPN
cana-1582	675	7	,	,	PUNCT
cana-1582	675	8	a.	a.	PROPN
cana-1582	675	9	s.	s.	PROPN
cana-1582	675	10	hariprasad	hariprasad	PROPN
cana-1582	675	11	,	,	PUNCT
cana-1582	675	12	k.v.vijayakumar	k.v.vijayakumar	PROPN
cana-1582	675	13	,	,	PUNCT
cana-1582	675	14	numerical	numerical	ADJ
cana-1582	675	15	integration	integration	NOUN
cana-1582	675	16	over	over	ADP
cana-1582	675	17	curved	curved	ADJ
cana-1582	675	18	domains	domain	NOUN
cana-1582	675	19	using	use	VERB
cana-1582	675	20	convex	convex	PROPN
cana-1582	675	21	quadrangulations	quadrangulation	NOUN
cana-1582	675	22	and	and	CCONJ
cana-1582	675	23	gauss	gauss	PROPN
cana-1582	675	24	legendre	legendre	PROPN
cana-1582	675	25	quadrature	quadrature	PROPN
cana-1582	675	26	rules	rule	VERB
cana-1582	675	27	international	international	ADJ
cana-1582	675	28	journal	journal	NOUN
cana-1582	675	29	of	of	ADP
cana-1582	675	30	engineering	engineering	NOUN
cana-1582	675	31	and	and	CCONJ
cana-1582	675	32	computer	computer	NOUN
cana-1582	675	33	science	science	NOUN
cana-1582	675	34	,	,	PUNCT
cana-1582	675	35	2(11	2(11	NUM
cana-1582	675	36	)	)	PUNCT
cana-1582	675	37	,	,	PUNCT
cana-1582	675	38	2013	2013	NUM
cana-1582	675	39	,	,	PUNCT
cana-1582	675	40	3290	3290	NUM
cana-1582	675	41	-	-	SYM
cana-1582	675	42	3332	3332	NUM
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cana-1582	676	2	11	11	NUM
cana-1582	676	3	]	]	PUNCT
cana-1582	676	4	hanselman.d	hanselman.d	PRON
cana-1582	676	5	and	and	CCONJ
cana-1582	676	6	b.	b.	PROPN
cana-1582	676	7	littlefield	littlefield	PROPN
cana-1582	676	8	,	,	PUNCT
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cana-1582	676	10	matlabr	matlabr	NOUN
cana-1582	676	11	,	,	PUNCT
cana-1582	676	12	pearson	pearson	PROPN
cana-1582	676	13	education	education	PROPN
cana-1582	676	14	inc	inc	PROPN
cana-1582	676	15	(	(	PUNCT
cana-1582	676	16	2007	2007	NUM
cana-1582	676	17	)	)	PUNCT
cana-1582	677	1	.	.	PUNCT
cana-1582	678	1	[	[	X
cana-1582	678	2	12	12	NUM
cana-1582	678	3	]	]	X
cana-1582	678	4	john	john	PROPN
cana-1582	678	5	mathews	mathews	PROPN
cana-1582	678	6	,	,	PUNCT
cana-1582	678	7	kurtis	kurtis	NOUN
cana-1582	678	8	fink	fink	PROPN
cana-1582	678	9	,	,	PUNCT
cana-1582	678	10	numerical	numerical	ADJ
cana-1582	678	11	methods	method	NOUN
cana-1582	678	12	using	use	VERB
cana-1582	678	13	matlab	matlab	PROPN
cana-1582	678	14	,	,	PUNCT
cana-1582	678	15	international	international	ADJ
cana-1582	678	16	edition	edition	NOUN
cana-1582	678	17	,	,	PUNCT
cana-1582	678	18	4th	4th	ADJ
cana-1582	678	19	edition	edition	NOUN
cana-1582	678	20	,	,	PUNCT
cana-1582	678	21	pearson	pearson	PROPN
cana-1582	678	22	,	,	PUNCT
cana-1582	678	23	jan	jan	PROPN
cana-1582	678	24	2004	2004	NUM
cana-1582	678	25	.	.	PUNCT
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cana-1582	679	2	13	13	NUM
cana-1582	679	3	]	]	X
cana-1582	679	4	lo	lo	PROPN
cana-1582	679	5	.	.	PUNCT
cana-1582	679	6	s.	s.	PROPN
cana-1582	679	7	h	h	PROPN
cana-1582	679	8	,	,	PUNCT
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cana-1582	679	10	quadrilateral	quadrilateral	ADJ
cana-1582	679	11	elements	element	NOUN
cana-1582	679	12	on	on	ADP
cana-1582	679	13	plane	plane	NOUN
cana-1582	679	14	and	and	CCONJ
cana-1582	679	15	over	over	ADP
cana-1582	679	16	curved	curved	ADJ
cana-1582	679	17	surfaces	surface	NOUN
cana-1582	679	18	,	,	PUNCT
cana-1582	679	19	comput	comput	NOUN
cana-1582	679	20	.	.	PUNCT
cana-1582	679	21	stuct	stuct	NOUN
cana-1582	679	22	.	.	PUNCT
cana-1582	679	23	31(3	31(3	NUM
cana-1582	679	24	)	)	PUNCT
cana-1582	679	25	421426(1989	421426(1989	NUM
cana-1582	679	26	)	)	PUNCT
cana-1582	680	1	[	[	X
cana-1582	680	2	14	14	NUM
cana-1582	680	3	]	]	X
cana-1582	680	4	matlab	matlab	PROPN
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cana-1582	680	6	version	version	NOUN
cana-1582	680	7	7	7	NUM
cana-1582	680	8	,	,	PUNCT
cana-1582	680	9	the	the	DET
cana-1582	680	10	maths	math	NOUN
cana-1582	680	11	works	works	PROPN
cana-1582	680	12	inc	inc	PROPN
cana-1582	680	13	,	,	PUNCT
cana-1582	680	14	2004	2004	NUM
cana-1582	680	15	.	.	PUNCT
cana-1582	681	1	[	[	X
cana-1582	681	2	15	15	NUM
cana-1582	681	3	]	]	PUNCT
cana-1582	681	4	micula	micula	PROPN
cana-1582	681	5	c.	c.	PROPN
cana-1582	681	6	,	,	PUNCT
cana-1582	681	7	sanda	sanda	NOUN
cana-1582	681	8	micula	micula	NOUN
cana-1582	681	9	,	,	PUNCT
cana-1582	681	10	hand	hand	NOUN
cana-1582	681	11	book	book	NOUN
cana-1582	681	12	of	of	ADP
cana-1582	681	13	splines	spline	NOUN
cana-1582	681	14	,	,	PUNCT
cana-1582	681	15	kluwer	kluwer	NOUN
cana-1582	681	16	academic	academic	ADJ
cana-1582	681	17	publishers	publisher	NOUN
cana-1582	681	18	(	(	PUNCT
cana-1582	681	19	1999	1999	NUM
cana-1582	681	20	)	)	PUNCT
cana-1582	681	21	.	.	PUNCT
cana-1582	682	1	[	[	X
cana-1582	682	2	16	16	NUM
cana-1582	682	3	]	]	X
cana-1582	682	4	moler	moler	NOUN
cana-1582	682	5	,	,	PUNCT
cana-1582	682	6	c.	c.	PROPN
cana-1582	682	7	b.	b.	PROPN
cana-1582	682	8	,	,	PUNCT
cana-1582	682	9	numerical	numerical	PROPN
cana-1582	682	10	computing	computing	PROPN
cana-1582	682	11	with	with	ADP
cana-1582	682	12	matlab	matlab	PROPN
cana-1582	682	13	,	,	PUNCT
cana-1582	682	14	society	society	NOUN
cana-1582	682	15	for	for	ADP
cana-1582	682	16	industrial	industrial	ADJ
cana-1582	682	17	and	and	CCONJ
cana-1582	682	18	applied	applied	ADJ
cana-1582	682	19	mathematics	mathematic	NOUN
cana-1582	682	20	,	,	PUNCT
cana-1582	682	21	phildelphia	phildelphia	PROPN
cana-1582	682	22	(	(	PUNCT
cana-1582	682	23	2004	2004	NUM
cana-1582	682	24	)	)	PUNCT
cana-1582	682	25	.	.	PUNCT
cana-1582	683	1	[	[	X
cana-1582	683	2	17	17	NUM
cana-1582	683	3	]	]	X
cana-1582	683	4	otto	otto	PROPN
cana-1582	683	5	s.	s.	PROPN
cana-1582	683	6	r.	r.	PROPN
cana-1582	683	7	and	and	CCONJ
cana-1582	683	8	j.	j.	PROPN
cana-1582	683	9	p.	p.	PROPN
cana-1582	683	10	denier	denier	PROPN
cana-1582	683	11	.	.	PUNCT
cana-1582	683	12	,	,	PUNCT
cana-1582	683	13	an	an	DET
cana-1582	683	14	introduction	introduction	NOUN
cana-1582	683	15	to	to	ADP
cana-1582	683	16	programming	programming	NOUN
cana-1582	683	17	and	and	CCONJ
cana-1582	683	18	numerical	numerical	ADJ
cana-1582	683	19	methods	method	NOUN
cana-1582	683	20	in	in	ADP
cana-1582	683	21	matlab	matlab	PROPN
cana-1582	683	22	for	for	ADP
cana-1582	683	23	beginners	beginner	NOUN
cana-1582	683	24	and	and	CCONJ
cana-1582	683	25	experienced	experienced	ADJ
cana-1582	683	26	users	user	NOUN
cana-1582	683	27	,	,	PUNCT
cana-1582	683	28	cambridge	cambridge	PROPN
cana-1582	683	29	university	university	PROPN
cana-1582	683	30	press	press	NOUN
cana-1582	683	31	(	(	PUNCT
cana-1582	683	32	2000	2000	NUM
cana-1582	683	33	)	)	PUNCT
cana-1582	683	34	.	.	PUNCT
cana-1582	684	1	[	[	X
cana-1582	684	2	18	18	NUM
cana-1582	684	3	]	]	PUNCT
cana-1582	684	4	sallam	sallam	PROPN
cana-1582	684	5	s.	s.	PROPN
cana-1582	684	6	,	,	PUNCT
cana-1582	684	7	w.	w.	PROPN
cana-1582	684	8	ameen	ameen	PROPN
cana-1582	684	9	numerical	numerical	PROPN
cana-1582	684	10	solution	solution	NOUN
cana-1582	684	11	of	of	ADP
cana-1582	684	12	general	general	ADJ
cana-1582	684	13	nth	nth	NOUN
cana-1582	684	14	-	-	PUNCT
cana-1582	684	15	order	order	NOUN
cana-1582	684	16	differential	differential	ADJ
cana-1582	684	17	equations	equation	NOUN
cana-1582	684	18	via	via	ADP
cana-1582	684	19	splines	spline	NOUN
cana-1582	684	20	applied	apply	VERB
cana-1582	684	21	numerical	numerical	ADJ
cana-1582	684	22	mathematics	mathematic	NOUN
cana-1582	684	23	,	,	PUNCT
cana-1582	684	24	6(3	6(3	NUM
cana-1582	684	25	)	)	PUNCT
cana-1582	684	26	,	,	PUNCT
cana-1582	684	27	1990	1990	NUM
cana-1582	684	28	,	,	PUNCT
cana-1582	684	29	225	225	NUM
cana-1582	684	30	-	-	SYM
cana-1582	684	31	238	238	NUM
cana-1582	684	32	.	.	PUNCT
cana-1582	685	1	[	[	X
cana-1582	685	2	19	19	NUM
cana-1582	685	3	]	]	PUNCT
cana-1582	685	4	shikin	shikin	PROPN
cana-1582	685	5	e.	e.	PROPN
cana-1582	685	6	v.	v.	PROPN
cana-1582	685	7	,	,	PUNCT
cana-1582	685	8	alexander	alexander	PROPN
cana-1582	685	9	i.	i.	PROPN
cana-1582	685	10	plis	plis	PROPN
cana-1582	685	11	,	,	PUNCT
cana-1582	685	12	handbook	handbook	NOUN
cana-1582	685	13	on	on	ADP
cana-1582	685	14	splines	spline	NOUN
cana-1582	685	15	for	for	ADP
cana-1582	685	16	the	the	DET
cana-1582	685	17	user	user	NOUN
cana-1582	685	18	,	,	PUNCT
cana-1582	685	19	crc	crc	NOUN
cana-1582	685	20	press	press	NOUN
cana-1582	685	21	,	,	PUNCT
cana-1582	685	22	1995	1995	NUM
cana-1582	685	23	.	.	PUNCT
cana-1582	686	1	[	[	X
cana-1582	686	2	20	20	NUM
cana-1582	686	3	]	]	X
cana-1582	686	4	sommariva	sommariva	PROPN
cana-1582	686	5	a.	a.	NOUN
cana-1582	686	6	and	and	CCONJ
cana-1582	686	7	m.	m.	PROPN
cana-1582	686	8	vianello	vianello	PROPN
cana-1582	686	9	,	,	PUNCT
cana-1582	686	10	gauss	gauss	ADJ
cana-1582	686	11	-	-	PUNCT
cana-1582	686	12	green	green	ADJ
cana-1582	686	13	cubature	cubature	NOUN
cana-1582	686	14	over	over	ADP
cana-1582	686	15	spline	spline	PROPN
cana-1582	686	16	curvilinear	curvilinear	PROPN
cana-1582	686	17	polygons	polygon	NOUN
cana-1582	686	18	,	,	PUNCT
cana-1582	686	19	applied	apply	VERB
cana-1582	686	20	mathematics	mathematic	NOUN
cana-1582	686	21	and	and	CCONJ
cana-1582	686	22	computation	computation	NOUN
cana-1582	686	23	183(2	183(2	NUM
cana-1582	686	24	)	)	PUNCT
cana-1582	686	25	,	,	PUNCT
cana-1582	686	26	1098	1098	NUM
cana-1582	686	27	1107	1107	NUM
cana-1582	686	28	(	(	PUNCT
cana-1582	686	29	2006	2006	NUM
cana-1582	686	30	)	)	PUNCT
cana-1582	687	1	[	[	X
cana-1582	687	2	21	21	NUM
cana-1582	687	3	]	]	X
cana-1582	687	4	sommariva	sommariva	PROPN
cana-1582	687	5	a.	a.	NOUN
cana-1582	687	6	and	and	CCONJ
cana-1582	687	7	m.	m.	PROPN
cana-1582	687	8	vianello	vianello	PROPN
cana-1582	687	9	,	,	PUNCT
cana-1582	687	10	gauss	gauss	ADJ
cana-1582	687	11	-	-	PUNCT
cana-1582	687	12	green	green	ADJ
cana-1582	687	13	cubature	cubature	NOUN
cana-1582	687	14	over	over	ADP
cana-1582	687	15	spline	spline	PROPN
cana-1582	687	16	curvilinear	curvilinear	PROPN
cana-1582	687	17	polygons	polygon	NOUN
cana-1582	687	18	,	,	PUNCT
cana-1582	687	19	applied	apply	VERB
cana-1582	687	20	mathematics	mathematic	NOUN
cana-1582	687	21	and	and	CCONJ
cana-1582	687	22	computation	computation	NOUN
cana-1582	687	23	vol	vol	NOUN
cana-1582	687	24	.	.	PROPN
cana-1582	688	1	183	183	NUM
cana-1582	688	2	(	(	PUNCT
cana-1582	688	3	2	2	NUM
cana-1582	688	4	)	)	PUNCT
cana-1582	688	5	pp	pp	ADP
cana-1582	688	6	1098	1098	NUM
cana-1582	688	7	1107	1107	NUM
cana-1582	688	8	(	(	PUNCT
cana-1582	688	9	2006	2006	NUM
cana-1582	688	10	)	)	PUNCT
cana-1582	689	1	[	[	X
cana-1582	689	2	22	22	NUM
cana-1582	689	3	]	]	PUNCT
cana-1582	689	4	stroud	stroud	PROPN
cana-1582	689	5	a.	a.	PROPN
cana-1582	689	6	h.	h.	PROPN
cana-1582	689	7	,	,	PUNCT
cana-1582	689	8	approximate	approximate	ADJ
cana-1582	689	9	calculation	calculation	NOUN
cana-1582	689	10	of	of	ADP
cana-1582	689	11	multiple	multiple	ADJ
cana-1582	689	12	integrals	integral	NOUN
cana-1582	689	13	,	,	PUNCT
cana-1582	689	14	prentice	prentice	NOUN
cana-1582	689	15	hall	hall	PROPN
cana-1582	689	16	series	series	PROPN
cana-1582	689	17	in	in	ADP
cana-1582	689	18	automated	automate	VERB
cana-1582	689	19	computation	computation	NOUN
cana-1582	689	20	,	,	PUNCT
cana-1582	689	21	prentice	prentice	NOUN
cana-1582	689	22	hall	hall	PROPN
cana-1582	689	23	,	,	PUNCT
cana-1582	689	24	inc	inc	PROPN
cana-1582	689	25	englewood	englewood	PROPN
cana-1582	689	26	cliffs	cliffs	PROPN
cana-1582	689	27	n.	n.	PROPN
cana-1582	689	28	j.	j.	PROPN
cana-1582	689	29	,	,	PUNCT
cana-1582	689	30	(	(	PUNCT
cana-1582	689	31	1971	1971	NUM
cana-1582	689	32	)	)	PUNCT
cana-1582	689	33	.	.	PUNCT
cana-1582	690	1	[	[	X
cana-1582	690	2	23	23	NUM
cana-1582	690	3	]	]	PUNCT
cana-1582	690	4	t.	t.	PROPN
cana-1582	690	5	zhanlav	zhanlav	PROPN
cana-1582	690	6	,	,	PUNCT
cana-1582	690	7	r.	r.	PROPN
cana-1582	690	8	mijiddorj	mijiddorj	PROPN
cana-1582	690	9	,	,	PUNCT
cana-1582	690	10	the	the	DET
cana-1582	690	11	local	local	ADJ
cana-1582	690	12	integro	integro	ADJ
cana-1582	690	13	cubic	cubic	ADJ
cana-1582	690	14	splines	spline	NOUN
cana-1582	690	15	and	and	CCONJ
cana-1582	690	16	their	their	PRON
cana-1582	690	17	approximation	approximation	NOUN
cana-1582	690	18	properties	property	NOUN
cana-1582	690	19	,	,	PUNCT
cana-1582	690	20	appl	appl	PROPN
cana-1582	690	21	.	.	PROPN
cana-1582	690	22	math	math	NOUN
cana-1582	690	23	.	.	PUNCT
cana-1582	691	1	comput	comput	NOUN
cana-1582	691	2	.	.	PUNCT
cana-1582	692	1	216	216	NUM
cana-1582	692	2	(	(	PUNCT
cana-1582	692	3	2010	2010	NUM
cana-1582	692	4	)	)	PUNCT
cana-1582	692	5	2215–2219	2215–2219	NUM
cana-1582	692	6	.	.	PUNCT
cana-1582	693	1	[	[	X
cana-1582	693	2	24	24	NUM
cana-1582	693	3	]	]	X
cana-1582	693	4	zienkiewicz	zienkiewicz	PROPN
cana-1582	693	5	.	.	PUNCT
cana-1582	694	1	o.	o.	PROPN
cana-1582	694	2	c	c	PROPN
cana-1582	694	3	,	,	PUNCT
cana-1582	694	4	taylor	taylor	PROPN
cana-1582	694	5	.	.	PUNCT
cana-1582	695	1	r.	r.	PROPN
cana-1582	695	2	l	l	PROPN
cana-1582	695	3	and	and	CCONJ
cana-1582	695	4	zhu	zhu	PROPN
cana-1582	695	5	.	.	PUNCT
cana-1582	696	1	j.	j.	PROPN
cana-1582	696	2	z	z	PROPN
cana-1582	696	3	,	,	PUNCT
cana-1582	696	4	the	the	DET
cana-1582	696	5	finite	finite	ADJ
cana-1582	696	6	element	element	NOUN
cana-1582	696	7	method	method	NOUN
cana-1582	696	8	,	,	PUNCT
cana-1582	696	9	its	its	PRON
cana-1582	696	10	basis	basis	NOUN
cana-1582	696	11	and	and	CCONJ
cana-1582	696	12	fundamentals	fundamental	NOUN
cana-1582	696	13	,	,	PUNCT
cana-1582	696	14	6th	6th	ADJ
cana-1582	696	15	edn	edn	NOUN
cana-1582	696	16	,	,	PUNCT
cana-1582	696	17	elsevier	elsevier	NOUN
cana-1582	696	18	(	(	PUNCT
cana-1582	696	19	2007	2007	NUM
cana-1582	696	20	)	)	PUNCT
cana-1582	696	21	.	.	PUNCT