id	sid	tid	token	lemma	pos
fumecheng-7707	1	1	facta	facta	PROPN
fumecheng-7707	1	2	universitatis	universitatis	PROPN
fumecheng-7707	1	3	series	series	NOUN
fumecheng-7707	1	4	:	:	PUNCT
fumecheng-7707	1	5	mechanical	mechanical	ADJ
fumecheng-7707	1	6	engineering	engineering	NOUN
fumecheng-7707	1	7	vol	vol	NOUN
fumecheng-7707	1	8	.	.	PROPN
fumecheng-7707	2	1	19	19	NUM
fumecheng-7707	2	2	,	,	PUNCT
fumecheng-7707	2	3	no	no	DET
fumecheng-7707	2	4	4	4	NUM
fumecheng-7707	2	5	,	,	PUNCT
fumecheng-7707	2	6	2021	2021	NUM
fumecheng-7707	2	7	,	,	PUNCT
fumecheng-7707	2	8	pp	pp	ADV
fumecheng-7707	2	9	.	.	PUNCT
fumecheng-7707	3	1	805	805	NUM
fumecheng-7707	3	2	816	816	NUM
fumecheng-7707	3	3	https://doi.org/10.22190/fume210415057w	https://doi.org/10.22190/fume210415057w	PROPN
fumecheng-7707	4	1	©	©	PROPN
fumecheng-7707	4	2	2021	2021	NUM
fumecheng-7707	4	3	by	by	ADP
fumecheng-7707	4	4	university	university	PROPN
fumecheng-7707	4	5	of	of	ADP
fumecheng-7707	4	6	niš	niš	PROPN
fumecheng-7707	4	7	,	,	PUNCT
fumecheng-7707	4	8	serbia	serbia	PROPN
fumecheng-7707	4	9	|	|	ADV
fumecheng-7707	4	10	creative	creative	ADJ
fumecheng-7707	4	11	commons	common	NOUN
fumecheng-7707	4	12	license	license	NOUN
fumecheng-7707	4	13	:	:	PUNCT
fumecheng-7707	4	14	cc	cc	VERB
fumecheng-7707	4	15	by	by	ADP
fumecheng-7707	4	16	-	-	PUNCT
fumecheng-7707	4	17	nc	nc	VERB
fumecheng-7707	4	18	-	-	PUNCT
fumecheng-7707	4	19	nd	nd	ADV
fumecheng-7707	4	20	original	original	ADJ
fumecheng-7707	4	21	scientific	scientific	ADJ
fumecheng-7707	4	22	paper	paper	ADJ
fumecheng-7707	4	23	fft	fft	NOUN
fumecheng-7707	4	24	-	-	PUNCT
fumecheng-7707	4	25	based	base	VERB
fumecheng-7707	4	26	implementation	implementation	NOUN
fumecheng-7707	4	27	of	of	ADP
fumecheng-7707	4	28	the	the	DET
fumecheng-7707	4	29	mdr	mdr	PROPN
fumecheng-7707	4	30	transformations	transformation	NOUN
fumecheng-7707	4	31	for	for	ADP
fumecheng-7707	4	32	homogeneous	homogeneous	ADJ
fumecheng-7707	4	33	and	and	CCONJ
fumecheng-7707	4	34	power	power	NOUN
fumecheng-7707	4	35	-	-	PUNCT
fumecheng-7707	4	36	law	law	NOUN
fumecheng-7707	4	37	graded	grade	VERB
fumecheng-7707	4	38	materials	material	NOUN
fumecheng-7707	4	39	emanuel	emanuel	PROPN
fumecheng-7707	4	40	willert	willert	PROPN
fumecheng-7707	4	41	technische	technische	PROPN
fumecheng-7707	4	42	universität	universität	PROPN
fumecheng-7707	4	43	berlin	berlin	PROPN
fumecheng-7707	4	44	,	,	PUNCT
fumecheng-7707	4	45	institute	institute	PROPN
fumecheng-7707	4	46	of	of	ADP
fumecheng-7707	4	47	mechanics	mechanic	NOUN
fumecheng-7707	4	48	,	,	PUNCT
fumecheng-7707	4	49	germany	germany	PROPN
fumecheng-7707	4	50	abstract	abstract	NOUN
fumecheng-7707	4	51	.	.	PUNCT
fumecheng-7707	5	1	it	it	PRON
fumecheng-7707	5	2	is	be	AUX
fumecheng-7707	5	3	shown	show	VERB
fumecheng-7707	5	4	how	how	SCONJ
fumecheng-7707	5	5	the	the	DET
fumecheng-7707	5	6	abel	abel	NOUN
fumecheng-7707	5	7	transform	transform	VERB
fumecheng-7707	5	8	solution	solution	NOUN
fumecheng-7707	5	9	to	to	ADP
fumecheng-7707	5	10	the	the	DET
fumecheng-7707	5	11	general	general	ADJ
fumecheng-7707	5	12	axisymmetric	axisymmetric	VERB
fumecheng-7707	5	13	normal	normal	ADJ
fumecheng-7707	5	14	contact	contact	NOUN
fumecheng-7707	5	15	problem	problem	NOUN
fumecheng-7707	5	16	for	for	ADP
fumecheng-7707	5	17	homogeneous	homogeneous	ADJ
fumecheng-7707	5	18	and	and	CCONJ
fumecheng-7707	5	19	power	power	NOUN
fumecheng-7707	5	20	-	-	PUNCT
fumecheng-7707	5	21	law	law	NOUN
fumecheng-7707	5	22	graded	grade	VERB
fumecheng-7707	5	23	elastic	elastic	ADJ
fumecheng-7707	5	24	materials	material	NOUN
fumecheng-7707	5	25	,	,	PUNCT
fumecheng-7707	5	26	which	which	PRON
fumecheng-7707	5	27	is	be	AUX
fumecheng-7707	5	28	paramount	paramount	ADJ
fumecheng-7707	5	29	for	for	ADP
fumecheng-7707	5	30	the	the	DET
fumecheng-7707	5	31	solution	solution	NOUN
fumecheng-7707	5	32	of	of	ADP
fumecheng-7707	5	33	different	different	ADJ
fumecheng-7707	5	34	classes	class	NOUN
fumecheng-7707	5	35	of	of	ADP
fumecheng-7707	5	36	tribological	tribological	ADJ
fumecheng-7707	5	37	problems	problem	NOUN
fumecheng-7707	5	38	with	with	ADP
fumecheng-7707	5	39	the	the	DET
fumecheng-7707	5	40	help	help	NOUN
fumecheng-7707	5	41	of	of	ADP
fumecheng-7707	5	42	the	the	DET
fumecheng-7707	5	43	method	method	NOUN
fumecheng-7707	5	44	of	of	ADP
fumecheng-7707	5	45	dimensionality	dimensionality	NOUN
fumecheng-7707	5	46	reduction	reduction	NOUN
fumecheng-7707	5	47	(	(	PUNCT
fumecheng-7707	5	48	mdr	mdr	PROPN
fumecheng-7707	5	49	)	)	PUNCT
fumecheng-7707	5	50	,	,	PUNCT
fumecheng-7707	5	51	can	can	AUX
fumecheng-7707	5	52	be	be	AUX
fumecheng-7707	5	53	written	write	VERB
fumecheng-7707	5	54	in	in	ADP
fumecheng-7707	5	55	terms	term	NOUN
fumecheng-7707	5	56	of	of	ADP
fumecheng-7707	5	57	explicit	explicit	ADJ
fumecheng-7707	5	58	convolutions	convolution	NOUN
fumecheng-7707	5	59	.	.	PUNCT
fumecheng-7707	6	1	these	these	PRON
fumecheng-7707	6	2	can	can	AUX
fumecheng-7707	6	3	be	be	AUX
fumecheng-7707	6	4	very	very	ADV
fumecheng-7707	6	5	efficiently	efficiently	ADV
fumecheng-7707	6	6	evaluated	evaluate	VERB
fumecheng-7707	6	7	with	with	ADP
fumecheng-7707	6	8	the	the	DET
fumecheng-7707	6	9	1d	1d	NUM
fumecheng-7707	6	10	fast	fast	ADJ
fumecheng-7707	6	11	fourier	fourier	NOUN
fumecheng-7707	6	12	transform	transform	NOUN
fumecheng-7707	6	13	(	(	PUNCT
fumecheng-7707	6	14	fft	fft	PROPN
fumecheng-7707	6	15	)	)	PUNCT
fumecheng-7707	6	16	,	,	PUNCT
fumecheng-7707	6	17	which	which	PRON
fumecheng-7707	6	18	reduces	reduce	VERB
fumecheng-7707	6	19	the	the	DET
fumecheng-7707	6	20	numerical	numerical	ADJ
fumecheng-7707	6	21	complexity	complexity	NOUN
fumecheng-7707	6	22	of	of	ADP
fumecheng-7707	6	23	the	the	DET
fumecheng-7707	6	24	transformations	transformation	NOUN
fumecheng-7707	6	25	from	from	ADP
fumecheng-7707	6	26	the	the	DET
fumecheng-7707	6	27	order	order	NOUN
fumecheng-7707	6	28	of	of	ADP
fumecheng-7707	6	29	n2	n2	NOUN
fumecheng-7707	6	30	for	for	ADP
fumecheng-7707	6	31	the	the	DET
fumecheng-7707	6	32	standard	standard	ADJ
fumecheng-7707	6	33	matrix	matrix	NOUN
fumecheng-7707	6	34	-	-	PUNCT
fumecheng-7707	6	35	vector	vector	NOUN
fumecheng-7707	6	36	-	-	PUNCT
fumecheng-7707	6	37	multiplication	multiplication	NOUN
fumecheng-7707	6	38	(	(	PUNCT
fumecheng-7707	6	39	mvm	mvm	NOUN
fumecheng-7707	6	40	)	)	PUNCT
fumecheng-7707	6	41	algorithm	algorithm	NOUN
fumecheng-7707	6	42	to	to	ADP
fumecheng-7707	6	43	the	the	DET
fumecheng-7707	6	44	order	order	NOUN
fumecheng-7707	6	45	of	of	ADP
fumecheng-7707	6	46	n.	n.	NOUN
fumecheng-7707	6	47	convergence	convergence	NOUN
fumecheng-7707	6	48	and	and	CCONJ
fumecheng-7707	6	49	performance	performance	NOUN
fumecheng-7707	6	50	of	of	ADP
fumecheng-7707	6	51	the	the	DET
fumecheng-7707	6	52	proposed	propose	VERB
fumecheng-7707	6	53	method	method	NOUN
fumecheng-7707	6	54	are	be	AUX
fumecheng-7707	6	55	studied	study	VERB
fumecheng-7707	6	56	in	in	ADP
fumecheng-7707	6	57	detail	detail	NOUN
fumecheng-7707	6	58	.	.	PUNCT
fumecheng-7707	7	1	as	as	ADP
fumecheng-7707	7	2	an	an	DET
fumecheng-7707	7	3	illustrative	illustrative	ADJ
fumecheng-7707	7	4	example	example	NOUN
fumecheng-7707	7	5	a	a	DET
fumecheng-7707	7	6	fretting	fret	VERB
fumecheng-7707	7	7	wear	wear	NOUN
fumecheng-7707	7	8	simulation	simulation	NOUN
fumecheng-7707	7	9	based	base	VERB
fumecheng-7707	7	10	on	on	ADP
fumecheng-7707	7	11	the	the	DET
fumecheng-7707	7	12	new	new	ADJ
fumecheng-7707	7	13	implementation	implementation	NOUN
fumecheng-7707	7	14	is	be	AUX
fumecheng-7707	7	15	shown	show	VERB
fumecheng-7707	7	16	,	,	PUNCT
fumecheng-7707	7	17	the	the	DET
fumecheng-7707	7	18	results	result	NOUN
fumecheng-7707	7	19	of	of	ADP
fumecheng-7707	7	20	which	which	PRON
fumecheng-7707	7	21	are	be	AUX
fumecheng-7707	7	22	compared	compare	VERB
fumecheng-7707	7	23	to	to	ADP
fumecheng-7707	7	24	the	the	DET
fumecheng-7707	7	25	standard	standard	ADJ
fumecheng-7707	7	26	mvm	mvm	NOUN
fumecheng-7707	7	27	implementation	implementation	NOUN
fumecheng-7707	7	28	.	.	PUNCT
fumecheng-7707	8	1	key	key	ADJ
fumecheng-7707	8	2	words	word	NOUN
fumecheng-7707	8	3	:	:	PUNCT
fumecheng-7707	8	4	method	method	NOUN
fumecheng-7707	8	5	of	of	ADP
fumecheng-7707	8	6	dimensionality	dimensionality	NOUN
fumecheng-7707	8	7	reduction	reduction	NOUN
fumecheng-7707	8	8	,	,	PUNCT
fumecheng-7707	8	9	fast	fast	ADJ
fumecheng-7707	8	10	fourier	fourier	NOUN
fumecheng-7707	8	11	transform	transform	NOUN
fumecheng-7707	8	12	,	,	PUNCT
fumecheng-7707	8	13	boussinesq	boussinesq	ADJ
fumecheng-7707	8	14	problem	problem	NOUN
fumecheng-7707	8	15	in	in	ADP
fumecheng-7707	8	16	contact	contact	NOUN
fumecheng-7707	8	17	mechanics	mechanic	NOUN
fumecheng-7707	8	18	,	,	PUNCT
fumecheng-7707	8	19	power	power	NOUN
fumecheng-7707	8	20	-	-	PUNCT
fumecheng-7707	8	21	law	law	NOUN
fumecheng-7707	8	22	graded	grade	VERB
fumecheng-7707	8	23	materials	material	NOUN
fumecheng-7707	8	24	1	1	NUM
fumecheng-7707	8	25	.	.	PUNCT
fumecheng-7707	8	26	introduction	introduction	NOUN
fumecheng-7707	8	27	the	the	DET
fumecheng-7707	8	28	boussinesq	boussinesq	ADJ
fumecheng-7707	8	29	problem	problem	NOUN
fumecheng-7707	8	30	,	,	PUNCT
fumecheng-7707	8	31	i.e.	i.e.	X
fumecheng-7707	8	32	,	,	PUNCT
fumecheng-7707	8	33	the	the	DET
fumecheng-7707	8	34	frictionless	frictionless	ADJ
fumecheng-7707	8	35	normal	normal	ADJ
fumecheng-7707	8	36	contact	contact	NOUN
fumecheng-7707	8	37	problem	problem	NOUN
fumecheng-7707	8	38	of	of	ADP
fumecheng-7707	8	39	elastic	elastic	ADJ
fumecheng-7707	8	40	bodies	body	NOUN
fumecheng-7707	8	41	,	,	PUNCT
fumecheng-7707	8	42	is	be	AUX
fumecheng-7707	8	43	one	one	NUM
fumecheng-7707	8	44	of	of	ADP
fumecheng-7707	8	45	the	the	DET
fumecheng-7707	8	46	basic	basic	ADJ
fumecheng-7707	8	47	fundaments	fundament	NOUN
fumecheng-7707	8	48	of	of	ADP
fumecheng-7707	8	49	contact	contact	NOUN
fumecheng-7707	8	50	mechanics	mechanic	NOUN
fumecheng-7707	8	51	.	.	PUNCT
fumecheng-7707	9	1	in	in	ADP
fumecheng-7707	9	2	the	the	DET
fumecheng-7707	9	3	case	case	NOUN
fumecheng-7707	9	4	of	of	ADP
fumecheng-7707	9	5	axisymmetric	axisymmetric	ADJ
fumecheng-7707	9	6	,	,	PUNCT
fumecheng-7707	9	7	convex	convex	NOUN
fumecheng-7707	9	8	contacting	contact	VERB
fumecheng-7707	9	9	bodies	body	NOUN
fumecheng-7707	9	10	within	within	ADP
fumecheng-7707	9	11	the	the	DET
fumecheng-7707	9	12	half	half	ADJ
fumecheng-7707	9	13	-	-	PUNCT
fumecheng-7707	9	14	space	space	NOUN
fumecheng-7707	9	15	approximation	approximation	NOUN
fumecheng-7707	9	16	,	,	PUNCT
fumecheng-7707	9	17	several	several	ADJ
fumecheng-7707	9	18	qualitatively	qualitatively	ADV
fumecheng-7707	9	19	different	different	ADJ
fumecheng-7707	9	20	classes	class	NOUN
fumecheng-7707	9	21	of	of	ADP
fumecheng-7707	9	22	contact	contact	NOUN
fumecheng-7707	9	23	problems	problem	NOUN
fumecheng-7707	9	24	can	can	AUX
fumecheng-7707	9	25	be	be	AUX
fumecheng-7707	9	26	reduced	reduce	VERB
fumecheng-7707	9	27	to	to	ADP
fumecheng-7707	9	28	the	the	DET
fumecheng-7707	9	29	frictionless	frictionless	NOUN
fumecheng-7707	9	30	,	,	PUNCT
fumecheng-7707	9	31	non	non	ADJ
fumecheng-7707	9	32	-	-	ADJ
fumecheng-7707	9	33	adhesive	adhesive	ADJ
fumecheng-7707	9	34	normal	normal	ADJ
fumecheng-7707	9	35	contact	contact	NOUN
fumecheng-7707	9	36	[	[	X
fumecheng-7707	9	37	1	1	NUM
fumecheng-7707	9	38	]	]	PUNCT
fumecheng-7707	9	39	,	,	PUNCT
fumecheng-7707	9	40	e.g.	e.g.	ADV
fumecheng-7707	9	41	the	the	DET
fumecheng-7707	9	42	jkr	jkr	ADJ
fumecheng-7707	9	43	-	-	PUNCT
fumecheng-7707	9	44	adhesive	adhesive	ADJ
fumecheng-7707	9	45	normal	normal	ADJ
fumecheng-7707	9	46	contact	contact	NOUN
fumecheng-7707	10	1	[	[	X
fumecheng-7707	10	2	2	2	X
fumecheng-7707	10	3	]	]	PUNCT
fumecheng-7707	10	4	the	the	DET
fumecheng-7707	10	5	tangential	tangential	ADJ
fumecheng-7707	10	6	contact	contact	NOUN
fumecheng-7707	10	7	in	in	ADP
fumecheng-7707	10	8	cattaneo	cattaneo	PROPN
fumecheng-7707	10	9	-	-	PUNCT
fumecheng-7707	10	10	mindlin	mindlin	NOUN
fumecheng-7707	10	11	approximation	approximation	NOUN
fumecheng-7707	10	12	(	(	PUNCT
fumecheng-7707	10	13	[	[	X
fumecheng-7707	10	14	3	3	NUM
fumecheng-7707	10	15	,	,	PUNCT
fumecheng-7707	10	16	4	4	NUM
fumecheng-7707	10	17	]	]	NUM
fumecheng-7707	10	18	)	)	PUNCT
fumecheng-7707	10	19	or	or	CCONJ
fumecheng-7707	10	20	–	–	PUNCT
fumecheng-7707	10	21	based	base	VERB
fumecheng-7707	10	22	on	on	ADP
fumecheng-7707	10	23	the	the	DET
fumecheng-7707	10	24	correspondence	correspondence	NOUN
fumecheng-7707	10	25	principle	principle	NOUN
fumecheng-7707	10	26	between	between	ADP
fumecheng-7707	10	27	boundary	boundary	ADJ
fumecheng-7707	10	28	value	value	NOUN
fumecheng-7707	10	29	problems	problem	NOUN
fumecheng-7707	10	30	of	of	ADP
fumecheng-7707	10	31	linear	linear	PROPN
fumecheng-7707	10	32	elasticity	elasticity	NOUN
fumecheng-7707	10	33	and	and	CCONJ
fumecheng-7707	10	34	linear	linear	ADJ
fumecheng-7707	10	35	viscoelasticity	viscoelasticity	NOUN
fumecheng-7707	10	36	–	–	PUNCT
fumecheng-7707	10	37	the	the	DET
fumecheng-7707	10	38	normal	normal	ADJ
fumecheng-7707	10	39	contact	contact	NOUN
fumecheng-7707	10	40	of	of	ADP
fumecheng-7707	10	41	viscoelastic	viscoelastic	ADJ
fumecheng-7707	10	42	bodies	body	NOUN
fumecheng-7707	10	43	(	(	PUNCT
fumecheng-7707	10	44	[	[	X
fumecheng-7707	10	45	5	5	NUM
fumecheng-7707	10	46	]	]	NUM
fumecheng-7707	10	47	)	)	PUNCT
fumecheng-7707	10	48	.	.	PUNCT
fumecheng-7707	11	1	the	the	DET
fumecheng-7707	11	2	solution	solution	NOUN
fumecheng-7707	11	3	to	to	ADP
fumecheng-7707	11	4	the	the	DET
fumecheng-7707	11	5	general	general	ADJ
fumecheng-7707	11	6	axisymmetric	axisymmetric	ADJ
fumecheng-7707	11	7	boussinesq	boussinesq	ADJ
fumecheng-7707	11	8	problem	problem	NOUN
fumecheng-7707	11	9	for	for	ADP
fumecheng-7707	11	10	homogeneous	homogeneous	ADJ
fumecheng-7707	11	11	materials	material	NOUN
fumecheng-7707	11	12	was	be	AUX
fumecheng-7707	11	13	first	first	ADV
fumecheng-7707	11	14	discovered	discover	VERB
fumecheng-7707	11	15	by	by	ADP
fumecheng-7707	11	16	schubert	schubert	PROPN
fumecheng-7707	12	1	[	[	X
fumecheng-7707	12	2	6	6	NUM
fumecheng-7707	12	3	]	]	PUNCT
fumecheng-7707	12	4	.	.	PUNCT
fumecheng-7707	13	1	a	a	DET
fumecheng-7707	13	2	very	very	ADV
fumecheng-7707	13	3	clear	clear	ADJ
fumecheng-7707	13	4	and	and	CCONJ
fumecheng-7707	13	5	convenient	convenient	ADJ
fumecheng-7707	13	6	interpretation	interpretation	NOUN
fumecheng-7707	13	7	of	of	ADP
fumecheng-7707	13	8	the	the	DET
fumecheng-7707	13	9	solution	solution	NOUN
fumecheng-7707	13	10	is	be	AUX
fumecheng-7707	13	11	given	give	VERB
fumecheng-7707	13	12	by	by	ADP
fumecheng-7707	13	13	the	the	DET
fumecheng-7707	13	14	method	method	NOUN
fumecheng-7707	13	15	of	of	ADP
fumecheng-7707	13	16	dimensionality	dimensionality	NOUN
fumecheng-7707	13	17	reduction	reduction	NOUN
fumecheng-7707	13	18	(	(	PUNCT
fumecheng-7707	13	19	mdr	mdr	NOUN
fumecheng-7707	13	20	,	,	PUNCT
fumecheng-7707	13	21	[	[	X
fumecheng-7707	13	22	7	7	NUM
fumecheng-7707	13	23	]	]	NUM
fumecheng-7707	13	24	)	)	PUNCT
fumecheng-7707	13	25	;	;	PUNCT
fumecheng-7707	13	26	the	the	DET
fumecheng-7707	13	27	solution	solution	NOUN
fumecheng-7707	13	28	received	receive	VERB
fumecheng-7707	13	29	april	april	PROPN
fumecheng-7707	13	30	15	15	NUM
fumecheng-7707	13	31	,	,	PUNCT
fumecheng-7707	13	32	2021	2021	NUM
fumecheng-7707	13	33	/	/	SYM
fumecheng-7707	13	34	accepted	accept	VERB
fumecheng-7707	13	35	august	august	PROPN
fumecheng-7707	13	36	02	02	NUM
fumecheng-7707	13	37	,	,	PUNCT
fumecheng-7707	13	38	2021	2021	NUM
fumecheng-7707	13	39	corresponding	correspond	VERB
fumecheng-7707	13	40	author	author	NOUN
fumecheng-7707	13	41	:	:	PUNCT
fumecheng-7707	13	42	willert	willert	PROPN
fumecheng-7707	13	43	emanuel	emanuel	PROPN
fumecheng-7707	13	44	technische	technische	PROPN
fumecheng-7707	13	45	universität	universität	PROPN
fumecheng-7707	13	46	berlin	berlin	PROPN
fumecheng-7707	13	47	,	,	PUNCT
fumecheng-7707	13	48	institut	institut	PROPN
fumecheng-7707	13	49	für	für	PROPN
fumecheng-7707	13	50	mechanik	mechanik	PROPN
fumecheng-7707	13	51	,	,	PUNCT
fumecheng-7707	13	52	sekr	sekr	PROPN
fumecheng-7707	13	53	.	.	PUNCT
fumecheng-7707	13	54	c8	c8	PROPN
fumecheng-7707	13	55	-	-	PUNCT
fumecheng-7707	13	56	4	4	PROPN
fumecheng-7707	13	57	,	,	PUNCT
fumecheng-7707	13	58	straße	straße	NOUN
fumecheng-7707	13	59	des	des	PROPN
fumecheng-7707	13	60	17	17	NUM
fumecheng-7707	13	61	.	.	PUNCT
fumecheng-7707	14	1	juni	juni	PROPN
fumecheng-7707	14	2	135	135	NUM
fumecheng-7707	14	3	,	,	PUNCT
fumecheng-7707	14	4	10623	10623	NUM
fumecheng-7707	14	5	berlin	berlin	PROPN
fumecheng-7707	14	6	,	,	PUNCT
fumecheng-7707	14	7	germany	germany	PROPN
fumecheng-7707	14	8	e	e	PROPN
fumecheng-7707	14	9	-	-	NOUN
fumecheng-7707	14	10	mail	mail	NOUN
fumecheng-7707	14	11	:	:	PUNCT
fumecheng-7707	14	12	e.willert@tu-berlin.de	e.willert@tu-berlin.de	NUM
fumecheng-7707	14	13	806	806	NUM
fumecheng-7707	14	14	e.	e.	PROPN
fumecheng-7707	14	15	willert	willert	PROPN
fumecheng-7707	14	16	consists	consist	VERB
fumecheng-7707	14	17	of	of	ADP
fumecheng-7707	14	18	a	a	DET
fumecheng-7707	14	19	series	series	NOUN
fumecheng-7707	14	20	of	of	ADP
fumecheng-7707	14	21	abel	abel	PROPN
fumecheng-7707	14	22	-	-	PUNCT
fumecheng-7707	14	23	like	like	ADJ
fumecheng-7707	14	24	integral	integral	ADJ
fumecheng-7707	14	25	transformations	transformation	NOUN
fumecheng-7707	14	26	,	,	PUNCT
fumecheng-7707	14	27	which	which	PRON
fumecheng-7707	14	28	will	will	AUX
fumecheng-7707	14	29	be	be	AUX
fumecheng-7707	14	30	given	give	VERB
fumecheng-7707	14	31	in	in	ADP
fumecheng-7707	14	32	detail	detail	NOUN
fumecheng-7707	14	33	below	below	ADV
fumecheng-7707	14	34	and	and	CCONJ
fumecheng-7707	14	35	whose	whose	DET
fumecheng-7707	14	36	numerical	numerical	ADJ
fumecheng-7707	14	37	implementation	implementation	NOUN
fumecheng-7707	14	38	in	in	ADP
fumecheng-7707	14	39	terms	term	NOUN
fumecheng-7707	14	40	of	of	ADP
fumecheng-7707	14	41	matrix	matrix	NOUN
fumecheng-7707	14	42	-	-	PUNCT
fumecheng-7707	14	43	vector	vector	NOUN
fumecheng-7707	14	44	-	-	PUNCT
fumecheng-7707	14	45	multiplications	multiplication	NOUN
fumecheng-7707	14	46	(	(	PUNCT
fumecheng-7707	14	47	mvm	mvm	NOUN
fumecheng-7707	14	48	)	)	PUNCT
fumecheng-7707	14	49	is	be	AUX
fumecheng-7707	14	50	straight	straight	ADJ
fumecheng-7707	14	51	-	-	PUNCT
fumecheng-7707	14	52	forward	forward	NOUN
fumecheng-7707	14	53	and	and	CCONJ
fumecheng-7707	14	54	usually	usually	ADV
fumecheng-7707	14	55	does	do	AUX
fumecheng-7707	14	56	not	not	PART
fumecheng-7707	14	57	pose	pose	VERB
fumecheng-7707	14	58	severe	severe	ADJ
fumecheng-7707	14	59	problems	problem	NOUN
fumecheng-7707	14	60	[	[	X
fumecheng-7707	14	61	8	8	NUM
fumecheng-7707	14	62	]	]	PUNCT
fumecheng-7707	14	63	.	.	PUNCT
fumecheng-7707	15	1	however	however	ADV
fumecheng-7707	15	2	,	,	PUNCT
fumecheng-7707	15	3	the	the	DET
fumecheng-7707	15	4	computational	computational	ADJ
fumecheng-7707	15	5	complexity	complexity	NOUN
fumecheng-7707	15	6	of	of	ADP
fumecheng-7707	15	7	the	the	DET
fumecheng-7707	15	8	mvm	mvm	NOUN
fumecheng-7707	15	9	is	be	AUX
fumecheng-7707	15	10	of	of	ADP
fumecheng-7707	15	11	the	the	DET
fumecheng-7707	15	12	order	order	NOUN
fumecheng-7707	15	13	of	of	ADP
fumecheng-7707	15	14	n2	n2	ADJ
fumecheng-7707	15	15	,	,	PUNCT
fumecheng-7707	15	16	where	where	SCONJ
fumecheng-7707	15	17	n	n	PRON
fumecheng-7707	15	18	denotes	denote	VERB
fumecheng-7707	15	19	the	the	DET
fumecheng-7707	15	20	number	number	NOUN
fumecheng-7707	15	21	of	of	ADP
fumecheng-7707	15	22	elements	element	NOUN
fumecheng-7707	15	23	/	/	SYM
fumecheng-7707	15	24	nodes	node	NOUN
fumecheng-7707	15	25	used	use	VERB
fumecheng-7707	15	26	for	for	ADP
fumecheng-7707	15	27	the	the	DET
fumecheng-7707	15	28	numerical	numerical	ADJ
fumecheng-7707	15	29	transformations	transformation	NOUN
fumecheng-7707	15	30	.	.	PUNCT
fumecheng-7707	16	1	if	if	SCONJ
fumecheng-7707	16	2	the	the	DET
fumecheng-7707	16	3	spatial	spatial	ADJ
fumecheng-7707	16	4	resolution	resolution	NOUN
fumecheng-7707	16	5	needs	need	VERB
fumecheng-7707	16	6	to	to	PART
fumecheng-7707	16	7	be	be	AUX
fumecheng-7707	16	8	very	very	ADV
fumecheng-7707	16	9	high	high	ADJ
fumecheng-7707	16	10	,	,	PUNCT
fumecheng-7707	16	11	or	or	CCONJ
fumecheng-7707	16	12	the	the	DET
fumecheng-7707	16	13	transformations	transformation	NOUN
fumecheng-7707	16	14	need	need	VERB
fumecheng-7707	16	15	to	to	PART
fumecheng-7707	16	16	be	be	AUX
fumecheng-7707	16	17	executed	execute	VERB
fumecheng-7707	16	18	very	very	ADV
fumecheng-7707	16	19	often	often	ADV
fumecheng-7707	16	20	,	,	PUNCT
fumecheng-7707	16	21	e.g.	e.g.	ADV
fumecheng-7707	16	22	,	,	PUNCT
fumecheng-7707	16	23	for	for	ADP
fumecheng-7707	16	24	the	the	DET
fumecheng-7707	16	25	simulation	simulation	NOUN
fumecheng-7707	16	26	of	of	ADP
fumecheng-7707	16	27	fretting	fret	VERB
fumecheng-7707	16	28	wear	wear	NOUN
fumecheng-7707	16	29	[	[	X
fumecheng-7707	16	30	9	9	NUM
fumecheng-7707	16	31	]	]	PUNCT
fumecheng-7707	16	32	or	or	CCONJ
fumecheng-7707	16	33	other	other	ADJ
fumecheng-7707	16	34	highly	highly	ADV
fumecheng-7707	16	35	transient	transient	ADJ
fumecheng-7707	16	36	phenomena	phenomenon	NOUN
fumecheng-7707	16	37	,	,	PUNCT
fumecheng-7707	16	38	this	this	DET
fumecheng-7707	16	39	complexity	complexity	NOUN
fumecheng-7707	16	40	might	might	AUX
fumecheng-7707	16	41	still	still	ADV
fumecheng-7707	16	42	lead	lead	VERB
fumecheng-7707	16	43	to	to	ADP
fumecheng-7707	16	44	undesirably	undesirably	ADV
fumecheng-7707	16	45	high	high	ADJ
fumecheng-7707	16	46	computational	computational	ADJ
fumecheng-7707	16	47	costs	cost	NOUN
fumecheng-7707	16	48	.	.	PUNCT
fumecheng-7707	17	1	on	on	ADP
fumecheng-7707	17	2	the	the	DET
fumecheng-7707	17	3	other	other	ADJ
fumecheng-7707	17	4	hand	hand	NOUN
fumecheng-7707	17	5	,	,	PUNCT
fumecheng-7707	17	6	as	as	SCONJ
fumecheng-7707	17	7	will	will	AUX
fumecheng-7707	17	8	be	be	AUX
fumecheng-7707	17	9	shown	show	VERB
fumecheng-7707	17	10	below	below	ADP
fumecheng-7707	17	11	,	,	PUNCT
fumecheng-7707	17	12	the	the	DET
fumecheng-7707	17	13	transformations	transformation	NOUN
fumecheng-7707	17	14	can	can	AUX
fumecheng-7707	17	15	be	be	AUX
fumecheng-7707	17	16	written	write	VERB
fumecheng-7707	17	17	in	in	ADP
fumecheng-7707	17	18	terms	term	NOUN
fumecheng-7707	17	19	of	of	ADP
fumecheng-7707	17	20	simple	simple	ADJ
fumecheng-7707	17	21	convolutions	convolution	NOUN
fumecheng-7707	17	22	,	,	PUNCT
fumecheng-7707	17	23	whose	whose	DET
fumecheng-7707	17	24	numerical	numerical	ADJ
fumecheng-7707	17	25	implementation	implementation	NOUN
fumecheng-7707	17	26	in	in	ADP
fumecheng-7707	17	27	one	one	NUM
fumecheng-7707	17	28	dimension	dimension	NOUN
fumecheng-7707	17	29	can	can	AUX
fumecheng-7707	17	30	be	be	AUX
fumecheng-7707	17	31	accelerated	accelerate	VERB
fumecheng-7707	17	32	with	with	ADP
fumecheng-7707	17	33	the	the	DET
fumecheng-7707	17	34	(	(	PUNCT
fumecheng-7707	17	35	discrete	discrete	NOUN
fumecheng-7707	17	36	)	)	PUNCT
fumecheng-7707	17	37	fast	fast	ADJ
fumecheng-7707	17	38	fourier	fourier	NOUN
fumecheng-7707	17	39	transform	transform	NOUN
fumecheng-7707	17	40	(	(	PUNCT
fumecheng-7707	17	41	fft	fft	PROPN
fumecheng-7707	17	42	)	)	PUNCT
fumecheng-7707	17	43	.	.	PUNCT
fumecheng-7707	18	1	the	the	DET
fumecheng-7707	18	2	1d	1d	NUM
fumecheng-7707	18	3	-	-	PUNCT
fumecheng-7707	18	4	fft	fft	NOUN
fumecheng-7707	18	5	reduces	reduce	VERB
fumecheng-7707	18	6	the	the	DET
fumecheng-7707	18	7	numerical	numerical	ADJ
fumecheng-7707	18	8	complexity	complexity	NOUN
fumecheng-7707	18	9	to	to	ADP
fumecheng-7707	18	10	the	the	DET
fumecheng-7707	18	11	order	order	NOUN
fumecheng-7707	18	12	of	of	ADP
fumecheng-7707	18	13	n	n	PROPN
fumecheng-7707	18	14	(	(	PUNCT
fumecheng-7707	18	15	omitting	omit	VERB
fumecheng-7707	18	16	logarithmic	logarithmic	ADJ
fumecheng-7707	18	17	factors	factor	NOUN
fumecheng-7707	18	18	)	)	PUNCT
fumecheng-7707	18	19	.	.	PUNCT
fumecheng-7707	19	1	therefore	therefore	ADV
fumecheng-7707	19	2	,	,	PUNCT
fumecheng-7707	19	3	in	in	ADP
fumecheng-7707	19	4	the	the	DET
fumecheng-7707	19	5	present	present	ADJ
fumecheng-7707	19	6	manuscript	manuscript	NOUN
fumecheng-7707	19	7	it	it	PRON
fumecheng-7707	19	8	will	will	AUX
fumecheng-7707	19	9	be	be	AUX
fumecheng-7707	19	10	shown	show	VERB
fumecheng-7707	19	11	,	,	PUNCT
fumecheng-7707	19	12	how	how	SCONJ
fumecheng-7707	19	13	the	the	DET
fumecheng-7707	19	14	general	general	ADJ
fumecheng-7707	19	15	solution	solution	NOUN
fumecheng-7707	19	16	to	to	ADP
fumecheng-7707	19	17	the	the	DET
fumecheng-7707	19	18	axisymmetric	axisymmetric	ADJ
fumecheng-7707	19	19	boussinesq	boussinesq	ADJ
fumecheng-7707	19	20	problem	problem	NOUN
fumecheng-7707	19	21	(	(	PUNCT
fumecheng-7707	19	22	in	in	ADP
fumecheng-7707	19	23	its	its	PRON
fumecheng-7707	19	24	mdr	mdr	PROPN
fumecheng-7707	19	25	interpretation	interpretation	NOUN
fumecheng-7707	19	26	)	)	PUNCT
fumecheng-7707	19	27	can	can	AUX
fumecheng-7707	19	28	be	be	AUX
fumecheng-7707	19	29	obtained	obtain	VERB
fumecheng-7707	19	30	extremely	extremely	ADV
fumecheng-7707	19	31	fast	fast	ADV
fumecheng-7707	19	32	based	base	VERB
fumecheng-7707	19	33	on	on	ADP
fumecheng-7707	19	34	the	the	DET
fumecheng-7707	19	35	1d	1d	NUM
fumecheng-7707	19	36	-	-	PUNCT
fumecheng-7707	19	37	fft	fft	NOUN
fumecheng-7707	19	38	.	.	PUNCT
fumecheng-7707	20	1	for	for	ADP
fumecheng-7707	20	2	homogeneous	homogeneous	ADJ
fumecheng-7707	20	3	materials	material	NOUN
fumecheng-7707	20	4	this	this	PRON
fumecheng-7707	20	5	is	be	AUX
fumecheng-7707	20	6	done	do	VERB
fumecheng-7707	20	7	in	in	ADP
fumecheng-7707	20	8	section	section	NOUN
fumecheng-7707	20	9	2	2	NUM
fumecheng-7707	20	10	.	.	PUNCT
fumecheng-7707	21	1	nevertheless	nevertheless	ADV
fumecheng-7707	21	2	,	,	PUNCT
fumecheng-7707	21	3	the	the	DET
fumecheng-7707	21	4	mdr	mdr	PROPN
fumecheng-7707	21	5	has	have	AUX
fumecheng-7707	21	6	also	also	ADV
fumecheng-7707	21	7	been	be	AUX
fumecheng-7707	21	8	extended	extend	VERB
fumecheng-7707	21	9	to	to	PART
fumecheng-7707	21	10	explicitly	explicitly	ADV
fumecheng-7707	21	11	incorporate	incorporate	VERB
fumecheng-7707	21	12	contacts	contact	NOUN
fumecheng-7707	21	13	of	of	ADP
fumecheng-7707	21	14	functionally	functionally	ADV
fumecheng-7707	21	15	graded	grade	VERB
fumecheng-7707	21	16	materials	material	NOUN
fumecheng-7707	21	17	(	(	PUNCT
fumecheng-7707	21	18	fgm	fgm	PROPN
fumecheng-7707	21	19	)	)	PUNCT
fumecheng-7707	21	20	.	.	PUNCT
fumecheng-7707	22	1	within	within	ADP
fumecheng-7707	22	2	an	an	DET
fumecheng-7707	22	3	fgm	fgm	PROPN
fumecheng-7707	22	4	,	,	PUNCT
fumecheng-7707	22	5	the	the	DET
fumecheng-7707	22	6	mechanical	mechanical	ADJ
fumecheng-7707	22	7	properties	property	NOUN
fumecheng-7707	22	8	vary	vary	VERB
fumecheng-7707	22	9	continuously	continuously	ADV
fumecheng-7707	22	10	over	over	ADP
fumecheng-7707	22	11	the	the	DET
fumecheng-7707	22	12	volume	volume	NOUN
fumecheng-7707	22	13	,	,	PUNCT
fumecheng-7707	22	14	the	the	DET
fumecheng-7707	22	15	material	material	NOUN
fumecheng-7707	22	16	is	be	AUX
fumecheng-7707	22	17	inhomogeneous	inhomogeneous	ADJ
fumecheng-7707	22	18	.	.	PUNCT
fumecheng-7707	23	1	examples	example	NOUN
fumecheng-7707	23	2	are	be	AUX
fumecheng-7707	23	3	hardened	harden	VERB
fumecheng-7707	23	4	surfaces	surface	NOUN
fumecheng-7707	23	5	as	as	ADV
fumecheng-7707	23	6	well	well	ADV
fumecheng-7707	23	7	as	as	ADP
fumecheng-7707	23	8	diverse	diverse	ADJ
fumecheng-7707	23	9	biological	biological	ADJ
fumecheng-7707	23	10	and	and	CCONJ
fumecheng-7707	23	11	biotechnological	biotechnological	ADJ
fumecheng-7707	23	12	systems	system	NOUN
fumecheng-7707	23	13	such	such	ADJ
fumecheng-7707	23	14	as	as	ADP
fumecheng-7707	23	15	bones	bone	NOUN
fumecheng-7707	23	16	,	,	PUNCT
fumecheng-7707	23	17	joints	joint	NOUN
fumecheng-7707	23	18	or	or	CCONJ
fumecheng-7707	23	19	their	their	PRON
fumecheng-7707	23	20	artificial	artificial	ADJ
fumecheng-7707	23	21	variants	variant	NOUN
fumecheng-7707	23	22	,	,	PUNCT
fumecheng-7707	23	23	adhesive	adhesive	ADJ
fumecheng-7707	23	24	devices	device	NOUN
fumecheng-7707	23	25	(	(	PUNCT
fumecheng-7707	23	26	e.g.	e.g.	ADV
fumecheng-7707	23	27	,	,	PUNCT
fumecheng-7707	23	28	on	on	ADP
fumecheng-7707	23	29	the	the	DET
fumecheng-7707	23	30	feet	foot	NOUN
fumecheng-7707	23	31	of	of	ADP
fumecheng-7707	23	32	geckos	geckos	NOUN
fumecheng-7707	23	33	)	)	PUNCT
fumecheng-7707	23	34	and	and	CCONJ
fumecheng-7707	23	35	cell	cell	NOUN
fumecheng-7707	23	36	membranes	membrane	NOUN
fumecheng-7707	23	37	[	[	X
fumecheng-7707	23	38	10	10	NUM
fumecheng-7707	23	39	]	]	PUNCT
fumecheng-7707	23	40	.	.	PUNCT
fumecheng-7707	24	1	one	one	NUM
fumecheng-7707	24	2	of	of	ADP
fumecheng-7707	24	3	the	the	DET
fumecheng-7707	24	4	most	most	ADV
fumecheng-7707	24	5	important	important	ADJ
fumecheng-7707	24	6	classes	class	NOUN
fumecheng-7707	24	7	of	of	ADP
fumecheng-7707	24	8	fgm	fgm	PROPN
fumecheng-7707	24	9	are	be	AUX
fumecheng-7707	24	10	materials	material	NOUN
fumecheng-7707	24	11	in	in	ADP
fumecheng-7707	24	12	which	which	PRON
fumecheng-7707	24	13	the	the	DET
fumecheng-7707	24	14	elastic	elastic	ADJ
fumecheng-7707	24	15	modulus	modulus	NOUN
fumecheng-7707	24	16	e	e	NOUN
fumecheng-7707	24	17	varies	vary	VERB
fumecheng-7707	24	18	with	with	ADP
fumecheng-7707	24	19	the	the	DET
fumecheng-7707	24	20	depth	depth	NOUN
fumecheng-7707	24	21	z.	z.	NOUN
fumecheng-7707	24	22	over	over	ADP
fumecheng-7707	24	23	time	time	NOUN
fumecheng-7707	24	24	,	,	PUNCT
fumecheng-7707	24	25	different	different	ADJ
fumecheng-7707	24	26	concrete	concrete	ADJ
fumecheng-7707	24	27	functions	function	NOUN
fumecheng-7707	24	28	e	e	NOUN
fumecheng-7707	24	29	=	=	SYM
fumecheng-7707	24	30	e(z	e(z	PRON
fumecheng-7707	24	31	)	)	PUNCT
fumecheng-7707	24	32	have	have	AUX
fumecheng-7707	24	33	been	be	AUX
fumecheng-7707	24	34	considered	consider	VERB
fumecheng-7707	24	35	(	(	PUNCT
fumecheng-7707	24	36	see	see	VERB
fumecheng-7707	24	37	e.g.	e.g.	ADV
fumecheng-7707	24	38	the	the	DET
fumecheng-7707	24	39	treatise	treatise	NOUN
fumecheng-7707	24	40	by	by	ADP
fumecheng-7707	24	41	selvadurai	selvadurai	PROPN
fumecheng-7707	25	1	[	[	X
fumecheng-7707	25	2	11	11	NUM
fumecheng-7707	25	3	]	]	NUM
fumecheng-7707	25	4	)	)	PUNCT
fumecheng-7707	25	5	;	;	PUNCT
fumecheng-7707	25	6	the	the	DET
fumecheng-7707	25	7	only	only	ADJ
fumecheng-7707	25	8	case	case	NOUN
fumecheng-7707	25	9	that	that	PRON
fumecheng-7707	25	10	allows	allow	VERB
fumecheng-7707	25	11	a	a	DET
fumecheng-7707	25	12	largely	largely	ADV
fumecheng-7707	25	13	analytical	analytical	ADJ
fumecheng-7707	25	14	treatment	treatment	NOUN
fumecheng-7707	25	15	seems	seem	VERB
fumecheng-7707	25	16	to	to	PART
fumecheng-7707	25	17	be	be	AUX
fumecheng-7707	25	18	the	the	DET
fumecheng-7707	25	19	power	power	NOUN
fumecheng-7707	25	20	law	law	NOUN
fumecheng-7707	25	21	e	e	X
fumecheng-7707	25	22	~	~	PUNCT
fumecheng-7707	25	23	zk	zk	PROPN
fumecheng-7707	25	24	.	.	PUNCT
fumecheng-7707	26	1	the	the	DET
fumecheng-7707	26	2	solution	solution	NOUN
fumecheng-7707	26	3	to	to	ADP
fumecheng-7707	26	4	the	the	DET
fumecheng-7707	26	5	axisymmetric	axisymmetric	ADJ
fumecheng-7707	26	6	boussinesq	boussinesq	ADJ
fumecheng-7707	26	7	problem	problem	NOUN
fumecheng-7707	26	8	for	for	ADP
fumecheng-7707	26	9	power	power	NOUN
fumecheng-7707	26	10	-	-	PUNCT
fumecheng-7707	26	11	law	law	NOUN
fumecheng-7707	26	12	graded	grade	VERB
fumecheng-7707	26	13	materials	material	NOUN
fumecheng-7707	26	14	stems	stem	VERB
fumecheng-7707	26	15	from	from	ADP
fumecheng-7707	26	16	giannakopoulos	giannakopoulos	PROPN
fumecheng-7707	26	17	&	&	CCONJ
fumecheng-7707	26	18	suresh	suresh	PROPN
fumecheng-7707	27	1	[	[	X
fumecheng-7707	27	2	12	12	NUM
fumecheng-7707	27	3	]	]	PUNCT
fumecheng-7707	27	4	and	and	CCONJ
fumecheng-7707	27	5	jin	jin	NOUN
fumecheng-7707	27	6	et	et	PROPN
fumecheng-7707	27	7	al	al	PROPN
fumecheng-7707	27	8	.	.	PUNCT
fumecheng-7707	28	1	[	[	X
fumecheng-7707	28	2	13	13	NUM
fumecheng-7707	28	3	]	]	PUNCT
fumecheng-7707	28	4	.	.	PUNCT
fumecheng-7707	29	1	in	in	ADP
fumecheng-7707	29	2	the	the	DET
fumecheng-7707	29	3	latter	latter	ADJ
fumecheng-7707	29	4	work	work	NOUN
fumecheng-7707	29	5	as	as	ADV
fumecheng-7707	29	6	well	well	ADV
fumecheng-7707	29	7	as	as	ADP
fumecheng-7707	29	8	by	by	ADP
fumecheng-7707	29	9	chen	chen	PROPN
fumecheng-7707	29	10	et	et	PROPN
fumecheng-7707	29	11	al	al	PROPN
fumecheng-7707	29	12	.	.	PUNCT
fumecheng-7707	30	1	[	[	X
fumecheng-7707	30	2	14	14	NUM
fumecheng-7707	30	3	]	]	PUNCT
fumecheng-7707	30	4	also	also	ADV
fumecheng-7707	30	5	the	the	DET
fumecheng-7707	30	6	respective	respective	ADJ
fumecheng-7707	30	7	jkr	jkr	ADJ
fumecheng-7707	30	8	-	-	PUNCT
fumecheng-7707	30	9	adhesive	adhesive	ADJ
fumecheng-7707	30	10	problem	problem	NOUN
fumecheng-7707	30	11	was	be	AUX
fumecheng-7707	30	12	solved	solve	VERB
fumecheng-7707	30	13	.	.	PUNCT
fumecheng-7707	31	1	the	the	DET
fumecheng-7707	31	2	implementation	implementation	NOUN
fumecheng-7707	31	3	of	of	ADP
fumecheng-7707	31	4	these	these	DET
fumecheng-7707	31	5	solutions	solution	NOUN
fumecheng-7707	31	6	into	into	ADP
fumecheng-7707	31	7	the	the	DET
fumecheng-7707	31	8	framework	framework	NOUN
fumecheng-7707	31	9	of	of	ADP
fumecheng-7707	31	10	the	the	DET
fumecheng-7707	31	11	mdr	mdr	PROPN
fumecheng-7707	31	12	has	have	AUX
fumecheng-7707	31	13	been	be	AUX
fumecheng-7707	31	14	demonstrated	demonstrate	VERB
fumecheng-7707	31	15	by	by	ADP
fumecheng-7707	31	16	heß	heß	PROPN
fumecheng-7707	31	17	[	[	X
fumecheng-7707	31	18	15	15	NUM
fumecheng-7707	31	19	]	]	PUNCT
fumecheng-7707	31	20	.	.	PUNCT
fumecheng-7707	32	1	moreover	moreover	ADV
fumecheng-7707	32	2	,	,	PUNCT
fumecheng-7707	32	3	tangential	tangential	ADJ
fumecheng-7707	32	4	contact	contact	NOUN
fumecheng-7707	32	5	problems	problem	NOUN
fumecheng-7707	32	6	of	of	ADP
fumecheng-7707	32	7	power	power	NOUN
fumecheng-7707	32	8	-	-	PUNCT
fumecheng-7707	32	9	law	law	NOUN
fumecheng-7707	32	10	graded	grade	VERB
fumecheng-7707	32	11	materials	material	NOUN
fumecheng-7707	32	12	can	can	AUX
fumecheng-7707	32	13	,	,	PUNCT
fumecheng-7707	32	14	within	within	ADP
fumecheng-7707	32	15	the	the	DET
fumecheng-7707	32	16	cattaneo	cattaneo	PROPN
fumecheng-7707	32	17	-	-	PUNCT
fumecheng-7707	32	18	mindlin	mindlin	NOUN
fumecheng-7707	32	19	approximation	approximation	NOUN
fumecheng-7707	32	20	,	,	PUNCT
fumecheng-7707	32	21	be	be	AUX
fumecheng-7707	32	22	analysed	analyse	VERB
fumecheng-7707	32	23	with	with	ADP
fumecheng-7707	32	24	the	the	DET
fumecheng-7707	32	25	mdr	mdr	PROPN
fumecheng-7707	33	1	[	[	X
fumecheng-7707	33	2	16	16	NUM
fumecheng-7707	33	3	]	]	PUNCT
fumecheng-7707	33	4	.	.	PUNCT
fumecheng-7707	34	1	as	as	SCONJ
fumecheng-7707	34	2	the	the	DET
fumecheng-7707	34	3	correspondence	correspondence	NOUN
fumecheng-7707	34	4	principle	principle	NOUN
fumecheng-7707	34	5	applies	apply	VERB
fumecheng-7707	34	6	to	to	ADP
fumecheng-7707	34	7	viscoelastic	viscoelastic	NOUN
fumecheng-7707	34	8	graded	grade	VERB
fumecheng-7707	34	9	materials	material	NOUN
fumecheng-7707	34	10	,	,	PUNCT
fumecheng-7707	34	11	if	if	SCONJ
fumecheng-7707	34	12	the	the	DET
fumecheng-7707	34	13	spatial	spatial	ADJ
fumecheng-7707	34	14	and	and	CCONJ
fumecheng-7707	34	15	temporal	temporal	ADJ
fumecheng-7707	34	16	variations	variation	NOUN
fumecheng-7707	34	17	of	of	ADP
fumecheng-7707	34	18	the	the	DET
fumecheng-7707	34	19	moduli	modulus	NOUN
fumecheng-7707	34	20	are	be	AUX
fumecheng-7707	34	21	separable	separable	ADJ
fumecheng-7707	35	1	[	[	X
fumecheng-7707	35	2	17	17	NUM
fumecheng-7707	35	3	]	]	PUNCT
fumecheng-7707	35	4	,	,	PUNCT
fumecheng-7707	35	5	also	also	ADV
fumecheng-7707	35	6	contacts	contact	NOUN
fumecheng-7707	35	7	of	of	ADP
fumecheng-7707	35	8	viscoelastic	viscoelastic	ADJ
fumecheng-7707	35	9	power	power	NOUN
fumecheng-7707	35	10	-	-	PUNCT
fumecheng-7707	35	11	law	law	NOUN
fumecheng-7707	35	12	graded	grade	VERB
fumecheng-7707	35	13	materials	material	NOUN
fumecheng-7707	35	14	can	can	AUX
fumecheng-7707	35	15	be	be	AUX
fumecheng-7707	35	16	studied	study	VERB
fumecheng-7707	35	17	within	within	ADP
fumecheng-7707	35	18	the	the	DET
fumecheng-7707	35	19	framework	framework	NOUN
fumecheng-7707	35	20	of	of	ADP
fumecheng-7707	35	21	mdr	mdr	PROPN
fumecheng-7707	36	1	[	[	X
fumecheng-7707	36	2	18	18	NUM
fumecheng-7707	36	3	]	]	PUNCT
fumecheng-7707	36	4	.	.	PUNCT
fumecheng-7707	37	1	this	this	PRON
fumecheng-7707	37	2	is	be	AUX
fumecheng-7707	37	3	particularly	particularly	ADV
fumecheng-7707	37	4	interesting	interesting	ADJ
fumecheng-7707	37	5	for	for	ADP
fumecheng-7707	37	6	biological	biological	ADJ
fumecheng-7707	37	7	graded	grade	VERB
fumecheng-7707	37	8	materials	material	NOUN
fumecheng-7707	37	9	,	,	PUNCT
fumecheng-7707	37	10	since	since	SCONJ
fumecheng-7707	37	11	these	these	PRON
fumecheng-7707	37	12	usually	usually	ADV
fumecheng-7707	37	13	have	have	VERB
fumecheng-7707	37	14	viscoor	viscoor	ADJ
fumecheng-7707	37	15	poroelastic	poroelastic	ADJ
fumecheng-7707	37	16	properties	property	NOUN
fumecheng-7707	37	17	[	[	X
fumecheng-7707	37	18	10	10	NUM
fumecheng-7707	37	19	]	]	PUNCT
fumecheng-7707	37	20	.	.	PUNCT
fumecheng-7707	38	1	the	the	DET
fumecheng-7707	38	2	axisymmetric	axisymmetric	ADJ
fumecheng-7707	38	3	normal	normal	ADJ
fumecheng-7707	38	4	contact	contact	NOUN
fumecheng-7707	38	5	solution	solution	NOUN
fumecheng-7707	38	6	for	for	ADP
fumecheng-7707	38	7	power	power	NOUN
fumecheng-7707	38	8	-	-	PUNCT
fumecheng-7707	38	9	law	law	NOUN
fumecheng-7707	38	10	graded	grade	VERB
fumecheng-7707	38	11	materials	material	NOUN
fumecheng-7707	38	12	is	be	AUX
fumecheng-7707	38	13	most	most	ADV
fumecheng-7707	38	14	conveniently	conveniently	ADV
fumecheng-7707	38	15	formulated	formulate	VERB
fumecheng-7707	38	16	in	in	ADP
fumecheng-7707	38	17	terms	term	NOUN
fumecheng-7707	38	18	of	of	ADP
fumecheng-7707	38	19	generalized	generalized	ADJ
fumecheng-7707	38	20	abel	abel	NOUN
fumecheng-7707	38	21	transforms	transform	VERB
fumecheng-7707	38	22	–	–	PUNCT
fumecheng-7707	38	23	the	the	DET
fumecheng-7707	38	24	homogeneous	homogeneous	ADJ
fumecheng-7707	38	25	case	case	NOUN
fumecheng-7707	38	26	is	be	AUX
fumecheng-7707	38	27	,	,	PUNCT
fumecheng-7707	38	28	of	of	ADP
fumecheng-7707	38	29	course	course	NOUN
fumecheng-7707	38	30	,	,	PUNCT
fumecheng-7707	38	31	always	always	ADV
fumecheng-7707	38	32	included	include	VERB
fumecheng-7707	38	33	as	as	ADP
fumecheng-7707	38	34	a	a	DET
fumecheng-7707	38	35	limiting	limit	VERB
fumecheng-7707	38	36	case	case	NOUN
fumecheng-7707	38	37	,	,	PUNCT
fumecheng-7707	38	38	if	if	SCONJ
fumecheng-7707	38	39	the	the	DET
fumecheng-7707	38	40	exponent	exponent	NOUN
fumecheng-7707	38	41	k	k	PROPN
fumecheng-7707	38	42	of	of	ADP
fumecheng-7707	38	43	the	the	DET
fumecheng-7707	38	44	power	power	NOUN
fumecheng-7707	38	45	-	-	PUNCT
fumecheng-7707	38	46	law	law	NOUN
fumecheng-7707	38	47	equals	equal	VERB
fumecheng-7707	38	48	zero	zero	NUM
fumecheng-7707	38	49	–	–	PUNCT
fumecheng-7707	38	50	which	which	PRON
fumecheng-7707	38	51	can	can	AUX
fumecheng-7707	38	52	also	also	ADV
fumecheng-7707	38	53	be	be	AUX
fumecheng-7707	38	54	written	write	VERB
fumecheng-7707	38	55	as	as	ADP
fumecheng-7707	38	56	explicit	explicit	ADJ
fumecheng-7707	38	57	convolutions	convolution	NOUN
fumecheng-7707	38	58	and	and	CCONJ
fumecheng-7707	38	59	thus	thus	ADV
fumecheng-7707	38	60	very	very	ADV
fumecheng-7707	38	61	efficiently	efficiently	ADV
fumecheng-7707	38	62	evaluated	evaluate	VERB
fumecheng-7707	38	63	by	by	ADP
fumecheng-7707	38	64	the	the	DET
fumecheng-7707	38	65	1d	1d	NUM
fumecheng-7707	38	66	-	-	PUNCT
fumecheng-7707	38	67	fft	fft	NOUN
fumecheng-7707	38	68	,	,	PUNCT
fumecheng-7707	38	69	as	as	SCONJ
fumecheng-7707	38	70	will	will	AUX
fumecheng-7707	38	71	be	be	AUX
fumecheng-7707	38	72	shown	show	VERB
fumecheng-7707	38	73	in	in	ADP
fumecheng-7707	38	74	section	section	NOUN
fumecheng-7707	38	75	3	3	NUM
fumecheng-7707	38	76	.	.	PUNCT
fumecheng-7707	39	1	the	the	DET
fumecheng-7707	39	2	application	application	NOUN
fumecheng-7707	39	3	of	of	ADP
fumecheng-7707	39	4	this	this	DET
fumecheng-7707	39	5	method	method	NOUN
fumecheng-7707	39	6	for	for	ADP
fumecheng-7707	39	7	the	the	DET
fumecheng-7707	39	8	simulation	simulation	NOUN
fumecheng-7707	39	9	of	of	ADP
fumecheng-7707	39	10	fretting	fret	VERB
fumecheng-7707	39	11	wear	wear	NOUN
fumecheng-7707	39	12	can	can	AUX
fumecheng-7707	39	13	be	be	AUX
fumecheng-7707	39	14	very	very	ADV
fumecheng-7707	39	15	fruitful	fruitful	ADJ
fumecheng-7707	39	16	in	in	ADP
fumecheng-7707	39	17	several	several	ADJ
fumecheng-7707	39	18	applications	application	NOUN
fumecheng-7707	39	19	,	,	PUNCT
fumecheng-7707	39	20	as	as	SCONJ
fumecheng-7707	39	21	it	it	PRON
fumecheng-7707	39	22	has	have	AUX
fumecheng-7707	39	23	been	be	AUX
fumecheng-7707	39	24	demonstrated	demonstrate	VERB
fumecheng-7707	39	25	that	that	SCONJ
fumecheng-7707	39	26	graded	grade	VERB
fumecheng-7707	39	27	materials	material	NOUN
fumecheng-7707	39	28	can	can	AUX
fumecheng-7707	39	29	offer	offer	VERB
fumecheng-7707	39	30	a	a	DET
fumecheng-7707	39	31	solution	solution	NOUN
fumecheng-7707	39	32	to	to	ADP
fumecheng-7707	39	33	the	the	DET
fumecheng-7707	39	34	wear	wear	NOUN
fumecheng-7707	39	35	-	-	PUNCT
fumecheng-7707	39	36	fatigue	fatigue	NOUN
fumecheng-7707	39	37	dilemma	dilemma	NOUN
fumecheng-7707	39	38	in	in	ADP
fumecheng-7707	39	39	fretting	fret	VERB
fumecheng-7707	39	40	[	[	X
fumecheng-7707	39	41	19	19	NUM
fumecheng-7707	39	42	]	]	PUNCT
fumecheng-7707	39	43	.	.	PUNCT
fumecheng-7707	40	1	finally	finally	ADV
fumecheng-7707	40	2	,	,	PUNCT
fumecheng-7707	40	3	section	section	NOUN
fumecheng-7707	40	4	4	4	NUM
fumecheng-7707	40	5	is	be	AUX
fumecheng-7707	40	6	devoted	devote	VERB
fumecheng-7707	40	7	to	to	ADP
fumecheng-7707	40	8	discussions	discussion	NOUN
fumecheng-7707	40	9	and	and	CCONJ
fumecheng-7707	40	10	conclusive	conclusive	ADJ
fumecheng-7707	40	11	remarks	remark	NOUN
fumecheng-7707	40	12	.	.	PUNCT
fumecheng-7707	41	1	fft	fft	NOUN
fumecheng-7707	41	2	-	-	PUNCT
fumecheng-7707	41	3	based	base	VERB
fumecheng-7707	41	4	implementation	implementation	NOUN
fumecheng-7707	41	5	of	of	ADP
fumecheng-7707	41	6	the	the	DET
fumecheng-7707	41	7	mdr	mdr	PROPN
fumecheng-7707	41	8	transformations	transformation	NOUN
fumecheng-7707	41	9	for	for	ADP
fumecheng-7707	41	10	homogeneous	homogeneous	ADJ
fumecheng-7707	41	11	and	and	CCONJ
fumecheng-7707	41	12	power	power	NOUN
fumecheng-7707	41	13	-	-	PUNCT
fumecheng-7707	41	14	law	law	NOUN
fumecheng-7707	41	15	graded	grade	VERB
fumecheng-7707	41	16	materials807	materials807	PROPN
fumecheng-7707	41	17	2	2	NUM
fumecheng-7707	41	18	.	.	PUNCT
fumecheng-7707	41	19	transformations	transformation	NOUN
fumecheng-7707	41	20	for	for	ADP
fumecheng-7707	41	21	homogeneous	homogeneous	ADJ
fumecheng-7707	41	22	materials	material	NOUN
fumecheng-7707	41	23	2.1	2.1	NUM
fumecheng-7707	41	24	.	.	PUNCT
fumecheng-7707	42	1	profile	profile	NOUN
fumecheng-7707	42	2	transformation	transformation	NOUN
fumecheng-7707	42	3	consider	consider	VERB
fumecheng-7707	42	4	a	a	DET
fumecheng-7707	42	5	rotationally	rotationally	ADV
fumecheng-7707	42	6	symmetric	symmetric	ADJ
fumecheng-7707	42	7	rigid	rigid	ADJ
fumecheng-7707	42	8	indenter	indenter	NOUN
fumecheng-7707	42	9	with	with	ADP
fumecheng-7707	42	10	the	the	DET
fumecheng-7707	42	11	convex	convex	NOUN
fumecheng-7707	42	12	profile	profile	NOUN
fumecheng-7707	42	13	f(r	f(r	NOUN
fumecheng-7707	42	14	)	)	PUNCT
fumecheng-7707	42	15	,	,	PUNCT
fumecheng-7707	42	16	that	that	PRON
fumecheng-7707	42	17	is	be	AUX
fumecheng-7707	42	18	pressed	press	VERB
fumecheng-7707	42	19	into	into	ADP
fumecheng-7707	42	20	an	an	DET
fumecheng-7707	42	21	homogeneous	homogeneous	ADJ
fumecheng-7707	42	22	,	,	PUNCT
fumecheng-7707	42	23	isotropic	isotropic	NOUN
fumecheng-7707	42	24	,	,	PUNCT
fumecheng-7707	42	25	linearly	linearly	ADV
fumecheng-7707	42	26	elastic	elastic	ADJ
fumecheng-7707	42	27	half	half	ADJ
fumecheng-7707	42	28	-	-	PUNCT
fumecheng-7707	42	29	space	space	NOUN
fumecheng-7707	42	30	with	with	ADP
fumecheng-7707	42	31	the	the	DET
fumecheng-7707	42	32	effective	effective	ADJ
fumecheng-7707	42	33	young	young	ADJ
fumecheng-7707	42	34	’s	’s	PART
fumecheng-7707	42	35	modulus	modulus	ADJ
fumecheng-7707	42	36	e	e	NOUN
fumecheng-7707	42	37	*	*	PUNCT
fumecheng-7707	42	38	=	=	SYM
fumecheng-7707	42	39	e/(1	e/(1	NOUN
fumecheng-7707	42	40	–	–	PUNCT
fumecheng-7707	42	41	υ2	υ2	NOUN
fumecheng-7707	42	42	)	)	PUNCT
fumecheng-7707	42	43	,	,	PUNCT
fumecheng-7707	42	44	with	with	ADP
fumecheng-7707	42	45	young	young	PROPN
fumecheng-7707	42	46	’s	’s	PART
fumecheng-7707	42	47	modulus	modulus	ADJ
fumecheng-7707	42	48	e	e	NOUN
fumecheng-7707	42	49	and	and	CCONJ
fumecheng-7707	42	50	the	the	DET
fumecheng-7707	42	51	poisson	poisson	PROPN
fumecheng-7707	42	52	ratio	ratio	NOUN
fumecheng-7707	42	53	υ	υ	PROPN
fumecheng-7707	42	54	(	(	PUNCT
fumecheng-7707	42	55	the	the	DET
fumecheng-7707	42	56	determination	determination	NOUN
fumecheng-7707	42	57	of	of	ADP
fumecheng-7707	42	58	f	f	PROPN
fumecheng-7707	42	59	and	and	CCONJ
fumecheng-7707	42	60	e	e	PROPN
fumecheng-7707	42	61	*	*	PROPN
fumecheng-7707	42	62	for	for	ADP
fumecheng-7707	42	63	the	the	DET
fumecheng-7707	42	64	contact	contact	NOUN
fumecheng-7707	42	65	of	of	ADP
fumecheng-7707	42	66	two	two	NUM
fumecheng-7707	42	67	elastic	elastic	ADJ
fumecheng-7707	42	68	bodies	body	NOUN
fumecheng-7707	42	69	is	be	AUX
fumecheng-7707	42	70	elementary	elementary	ADJ
fumecheng-7707	42	71	and	and	CCONJ
fumecheng-7707	42	72	can	can	AUX
fumecheng-7707	42	73	be	be	AUX
fumecheng-7707	42	74	found	find	VERB
fumecheng-7707	42	75	in	in	ADP
fumecheng-7707	42	76	any	any	DET
fumecheng-7707	42	77	textbook	textbook	NOUN
fumecheng-7707	42	78	on	on	ADP
fumecheng-7707	42	79	contact	contact	NOUN
fumecheng-7707	42	80	mechanics	mechanic	NOUN
fumecheng-7707	43	1	[	[	X
fumecheng-7707	43	2	1	1	NUM
fumecheng-7707	43	3	]	]	NUM
fumecheng-7707	43	4	)	)	PUNCT
fumecheng-7707	43	5	.	.	PUNCT
fumecheng-7707	44	1	then	then	ADV
fumecheng-7707	44	2	,	,	PUNCT
fumecheng-7707	44	3	the	the	DET
fumecheng-7707	44	4	contact	contact	NOUN
fumecheng-7707	44	5	solution	solution	NOUN
fumecheng-7707	44	6	is	be	AUX
fumecheng-7707	44	7	most	most	ADV
fumecheng-7707	44	8	conveniently	conveniently	ADV
fumecheng-7707	44	9	formulated	formulate	VERB
fumecheng-7707	44	10	in	in	ADP
fumecheng-7707	44	11	terms	term	NOUN
fumecheng-7707	44	12	of	of	ADP
fumecheng-7707	44	13	the	the	DET
fumecheng-7707	44	14	equivalent	equivalent	ADJ
fumecheng-7707	44	15	profile	profile	NOUN
fumecheng-7707	44	16	[	[	X
fumecheng-7707	44	17	1	1	NUM
fumecheng-7707	44	18	]	]	SYM
fumecheng-7707	44	19	2	2	NUM
fumecheng-7707	44	20	2	2	NUM
fumecheng-7707	44	21	0	0	NUM
fumecheng-7707	44	22	d	d	NOUN
fumecheng-7707	44	23	(	(	PUNCT
fumecheng-7707	44	24	)	)	PUNCT
fumecheng-7707	44	25	(	(	PUNCT
fumecheng-7707	44	26	)	)	PUNCT
fumecheng-7707	44	27	,	,	PUNCT
fumecheng-7707	44	28	(	(	PUNCT
fumecheng-7707	44	29	)	)	PUNCT
fumecheng-7707	44	30	:	:	PUNCT
fumecheng-7707	45	1	d	d	X
fumecheng-7707	45	2	.	.	PUNCT
fumecheng-7707	46	1	d	d	X
fumecheng-7707	46	2	x	x	X
fumecheng-7707	46	3	g	g	NOUN
fumecheng-7707	46	4	rf	rf	NOUN
fumecheng-7707	46	5	r	r	NOUN
fumecheng-7707	46	6	g	g	NOUN
fumecheng-7707	46	7	x	x	SYM
fumecheng-7707	46	8	g	g	NOUN
fumecheng-7707	46	9	x	x	SYM
fumecheng-7707	46	10	r	r	NOUN
fumecheng-7707	46	11	x	x	NOUN
fumecheng-7707	46	12	x	x	SYM
fumecheng-7707	46	13	r	r	NOUN
fumecheng-7707	46	14	=	=	PUNCT
fumecheng-7707	46	15	=	=	NOUN
fumecheng-7707	46	16	−	−	NOUN
fumecheng-7707	46	17			PUNCT
fumecheng-7707	46	18	(	(	PUNCT
fumecheng-7707	46	19	1	1	X
fumecheng-7707	46	20	)	)	PUNCT
fumecheng-7707	46	21	for	for	ADP
fumecheng-7707	46	22	example	example	NOUN
fumecheng-7707	46	23	,	,	PUNCT
fumecheng-7707	46	24	the	the	DET
fumecheng-7707	46	25	function	function	NOUN
fumecheng-7707	46	26	g	g	PROPN
fumecheng-7707	46	27	will	will	AUX
fumecheng-7707	46	28	give	give	VERB
fumecheng-7707	46	29	the	the	DET
fumecheng-7707	46	30	relations	relation	NOUN
fumecheng-7707	46	31	between	between	ADP
fumecheng-7707	46	32	the	the	DET
fumecheng-7707	46	33	macroscopic	macroscopic	ADJ
fumecheng-7707	46	34	contact	contact	NOUN
fumecheng-7707	46	35	quantities	quantity	NOUN
fumecheng-7707	46	36	–	–	PUNCT
fumecheng-7707	46	37	contact	contact	NOUN
fumecheng-7707	46	38	radius	radius	NOUN
fumecheng-7707	46	39	a	a	DET
fumecheng-7707	46	40	,	,	PUNCT
fumecheng-7707	46	41	indentation	indentation	NOUN
fumecheng-7707	46	42	depth	depth	NOUN
fumecheng-7707	46	43	δ	δ	NOUN
fumecheng-7707	46	44	and	and	CCONJ
fumecheng-7707	46	45	normal	normal	ADJ
fumecheng-7707	46	46	force	force	NOUN
fumecheng-7707	46	47	fn	fn	PROPN
fumecheng-7707	47	1	[	[	X
fumecheng-7707	47	2	1	1	NUM
fumecheng-7707	47	3	]	]	PUNCT
fumecheng-7707	47	4	*	*	PUNCT
fumecheng-7707	48	1	*	*	PUNCT
fumecheng-7707	48	2	0	0	PUNCT
fumecheng-7707	48	3	(	(	PUNCT
fumecheng-7707	48	4	)	)	PUNCT
fumecheng-7707	48	5	,	,	PUNCT
fumecheng-7707	48	6	2	2	NUM
fumecheng-7707	48	7	2	2	NUM
fumecheng-7707	48	8	(	(	PUNCT
fumecheng-7707	48	9	)	)	PUNCT
fumecheng-7707	48	10	d	d	NOUN
fumecheng-7707	48	11	.	.	PUNCT
fumecheng-7707	49	1	a	a	DET
fumecheng-7707	49	2	ng	ng	PROPN
fumecheng-7707	49	3	a	a	DET
fumecheng-7707	49	4	f	f	X
fumecheng-7707	49	5	e	e	X
fumecheng-7707	49	6	a	a	PRON
fumecheng-7707	49	7	e	e	NOUN
fumecheng-7707	49	8	g	g	NOUN
fumecheng-7707	49	9	x	x	SYM
fumecheng-7707	49	10	x=	x=	PUNCT
fumecheng-7707	50	1	=	=	PUNCT
fumecheng-7707	51	1	−	−	PROPN
fumecheng-7707	51	2			PROPN
fumecheng-7707	51	3			NUM
fumecheng-7707	51	4	(	(	PUNCT
fumecheng-7707	51	5	2	2	NUM
fumecheng-7707	51	6	)	)	PUNCT
fumecheng-7707	51	7	to	to	PART
fumecheng-7707	51	8	write	write	VERB
fumecheng-7707	51	9	the	the	DET
fumecheng-7707	51	10	transform	transform	NOUN
fumecheng-7707	51	11	(	(	PUNCT
fumecheng-7707	51	12	1	1	NUM
fumecheng-7707	51	13	)	)	PUNCT
fumecheng-7707	51	14	as	as	ADP
fumecheng-7707	51	15	an	an	DET
fumecheng-7707	51	16	explicit	explicit	ADJ
fumecheng-7707	51	17	convolution	convolution	NOUN
fumecheng-7707	51	18	,	,	PUNCT
fumecheng-7707	51	19	following	follow	VERB
fumecheng-7707	51	20	bracewell	bracewell	NOUN
fumecheng-7707	51	21	[	[	X
fumecheng-7707	51	22	20	20	NUM
fumecheng-7707	51	23	]	]	PUNCT
fumecheng-7707	51	24	we	we	PRON
fumecheng-7707	51	25	introduce	introduce	VERB
fumecheng-7707	51	26	the	the	DET
fumecheng-7707	51	27	substitutions	substitution	NOUN
fumecheng-7707	51	28	2	2	NUM
fumecheng-7707	51	29	2	2	NUM
fumecheng-7707	51	30	ˆ	ˆ	NOUN
fumecheng-7707	51	31	ˆ	ˆ	PROPN
fumecheng-7707	51	32	:	:	PUNCT
fumecheng-7707	51	33	,	,	PUNCT
fumecheng-7707	51	34	:	:	PUNCT
fumecheng-7707	51	35	,	,	PUNCT
fumecheng-7707	51	36	(	(	PUNCT
fumecheng-7707	51	37	)	)	PUNCT
fumecheng-7707	51	38	(	(	PUNCT
fumecheng-7707	51	39	)	)	PUNCT
fumecheng-7707	51	40	,	,	PUNCT
fumecheng-7707	51	41	(	(	PUNCT
fumecheng-7707	51	42	)	)	PUNCT
fumecheng-7707	51	43	(	(	PUNCT
fumecheng-7707	51	44	)	)	PUNCT
fumecheng-7707	51	45	.x	.x	PROPN
fumecheng-7707	52	1	r	r	NOUN
fumecheng-7707	52	2	f	f	NOUN
fumecheng-7707	52	3	r	r	NOUN
fumecheng-7707	52	4	f	f	PROPN
fumecheng-7707	52	5	g	g	NOUN
fumecheng-7707	52	6	x	x	X
fumecheng-7707	52	7	g=	g=	NOUN
fumecheng-7707	52	8	=	=	PUNCT
fumecheng-7707	52	9	=	=	SYM
fumecheng-7707	53	1	=	=	NOUN
fumecheng-7707	53	2			X
fumecheng-7707	53	3			ADV
fumecheng-7707	53	4			ADP
fumecheng-7707	53	5			PROPN
fumecheng-7707	53	6	(	(	PUNCT
fumecheng-7707	53	7	3	3	X
fumecheng-7707	53	8	)	)	PUNCT
fumecheng-7707	53	9	note	note	NOUN
fumecheng-7707	53	10	that	that	SCONJ
fumecheng-7707	53	11	the	the	DET
fumecheng-7707	53	12	function	function	NOUN
fumecheng-7707	53	13	g	g	PROPN
fumecheng-7707	53	14	will	will	AUX
fumecheng-7707	53	15	be	be	AUX
fumecheng-7707	53	16	given	give	VERB
fumecheng-7707	53	17	by	by	ADP
fumecheng-7707	53	18	the	the	DET
fumecheng-7707	53	19	scaled	scale	VERB
fumecheng-7707	53	20	derivative	derivative	NOUN
fumecheng-7707	53	21	ˆ	ˆ	NOUN
fumecheng-7707	53	22	ˆd	ˆd	ADP
fumecheng-7707	53	23	d	d	PROPN
fumecheng-7707	53	24	d	d	NOUN
fumecheng-7707	53	25	ˆ	ˆ	PROPN
fumecheng-7707	53	26	(	(	PUNCT
fumecheng-7707	53	27	)	)	PUNCT
fumecheng-7707	53	28	2	2	NUM
fumecheng-7707	53	29	(	(	PUNCT
fumecheng-7707	53	30	)	)	PUNCT
fumecheng-7707	53	31	.	.	PUNCT
fumecheng-7707	54	1	d	d	PUNCT
fumecheng-7707	55	1	d	d	X
fumecheng-7707	55	2	d	d	X
fumecheng-7707	55	3	g	g	NOUN
fumecheng-7707	55	4	g	g	PROPN
fumecheng-7707	55	5	g	g	PROPN
fumecheng-7707	55	6	x	x	SYM
fumecheng-7707	55	7	g	g	NOUN
fumecheng-7707	55	8	x	x	NOUN
fumecheng-7707	55	9	=	=	SYM
fumecheng-7707	55	10	=	=	SYM
fumecheng-7707	56	1	=	=	SYM
fumecheng-7707	56	2			NOUN
fumecheng-7707	56	3			NOUN
fumecheng-7707	56	4			NOUN
fumecheng-7707	56	5			NOUN
fumecheng-7707	56	6			X
fumecheng-7707	56	7	(	(	PUNCT
fumecheng-7707	56	8	4	4	NUM
fumecheng-7707	56	9	)	)	PUNCT
fumecheng-7707	56	10	after	after	ADP
fumecheng-7707	56	11	substitution	substitution	NOUN
fumecheng-7707	56	12	and	and	CCONJ
fumecheng-7707	56	13	integration	integration	NOUN
fumecheng-7707	56	14	by	by	ADP
fumecheng-7707	56	15	parts	part	NOUN
fumecheng-7707	56	16	one	one	NOUN
fumecheng-7707	56	17	obtains	obtain	VERB
fumecheng-7707	56	18	0	0	NUM
fumecheng-7707	56	19	0	0	NUM
fumecheng-7707	56	20	ˆ1	ˆ1	NOUN
fumecheng-7707	56	21	(	(	PUNCT
fumecheng-7707	56	22	)	)	PUNCT
fumecheng-7707	56	23	ˆˆ	ˆˆ	PROPN
fumecheng-7707	56	24	(	(	PUNCT
fumecheng-7707	57	1	)	)	PUNCT
fumecheng-7707	57	2	d	d	NOUN
fumecheng-7707	57	3	(	(	PUNCT
fumecheng-7707	57	4	)	)	PUNCT
fumecheng-7707	57	5	d	d	NOUN
fumecheng-7707	57	6	,	,	PUNCT
fumecheng-7707	57	7	2	2	NUM
fumecheng-7707	57	8	f	f	NOUN
fumecheng-7707	57	9	g	g	PROPN
fumecheng-7707	57	10	f	f	PROPN
fumecheng-7707	57	11	=	=	PROPN
fumecheng-7707	57	12	=	=	PUNCT
fumecheng-7707	58	1	−	−	PROPN
fumecheng-7707	58	2	−	−	NOUN
fumecheng-7707	58	3			NOUN
fumecheng-7707	58	4			ADP
fumecheng-7707	58	5			SCONJ
fumecheng-7707	58	6			NOUN
fumecheng-7707	58	7			ADP
fumecheng-7707	58	8			NOUN
fumecheng-7707	58	9			X
fumecheng-7707	58	10			ADP
fumecheng-7707	58	11			PROPN
fumecheng-7707	58	12			X
fumecheng-7707	58	13			ADP
fumecheng-7707	58	14			NOUN
fumecheng-7707	58	15			X
fumecheng-7707	58	16	(	(	PUNCT
fumecheng-7707	58	17	5	5	NUM
fumecheng-7707	58	18	)	)	PUNCT
fumecheng-7707	58	19	where	where	SCONJ
fumecheng-7707	58	20	the	the	DET
fumecheng-7707	58	21	prime	prime	ADJ
fumecheng-7707	58	22	denotes	denote	VERB
fumecheng-7707	58	23	the	the	DET
fumecheng-7707	58	24	first	first	ADJ
fumecheng-7707	58	25	derivative	derivative	NOUN
fumecheng-7707	58	26	with	with	ADP
fumecheng-7707	58	27	respect	respect	NOUN
fumecheng-7707	58	28	to	to	ADP
fumecheng-7707	58	29	the	the	DET
fumecheng-7707	58	30	given	give	VERB
fumecheng-7707	58	31	argument	argument	NOUN
fumecheng-7707	58	32	.	.	PUNCT
fumecheng-7707	59	1	the	the	DET
fumecheng-7707	59	2	last	last	ADJ
fumecheng-7707	59	3	integral	integral	ADJ
fumecheng-7707	59	4	shall	shall	AUX
fumecheng-7707	59	5	be	be	AUX
fumecheng-7707	59	6	evaluated	evaluate	VERB
fumecheng-7707	59	7	numerically	numerically	ADV
fumecheng-7707	59	8	on	on	ADP
fumecheng-7707	59	9	equidistant	equidistant	ADJ
fumecheng-7707	59	10	one	one	NUM
fumecheng-7707	59	11	-	-	PUNCT
fumecheng-7707	59	12	dimensional	dimensional	ADJ
fumecheng-7707	59	13	arrays	array	NOUN
fumecheng-7707	59	14	,	,	PUNCT
fumecheng-7707	59	15	2	2	NUM
fumecheng-7707	59	16	:	:	PUNCT
fumecheng-7707	59	17	(	(	PUNCT
fumecheng-7707	59	18	1	1	NUM
fumecheng-7707	59	19	)	)	PUNCT
fumecheng-7707	59	20	,	,	PUNCT
fumecheng-7707	59	21	:	:	PUNCT
fumecheng-7707	59	22	(	(	PUNCT
fumecheng-7707	59	23	1	1	X
fumecheng-7707	59	24	)	)	PUNCT
fumecheng-7707	59	25	,	,	PUNCT
fumecheng-7707	59	26	:	:	PUNCT
fumecheng-7707	59	27	,	,	PUNCT
fumecheng-7707	59	28	,	,	PUNCT
fumecheng-7707	59	29	1	1	NUM
fumecheng-7707	59	30	:	:	PUNCT
fumecheng-7707	59	31	,	,	PUNCT
fumecheng-7707	59	32	1	1	X
fumecheng-7707	59	33	i	i	NOUN
fumecheng-7707	59	34	j	j	PROPN
fumecheng-7707	60	1	l	l	NOUN
fumecheng-7707	61	1	i	i	PRON
fumecheng-7707	61	2	h	h	VERB
fumecheng-7707	62	1	j	j	NOUN
fumecheng-7707	62	2	h	h	NOUN
fumecheng-7707	63	1	h	h	NOUN
fumecheng-7707	64	1	i	i	PRON
fumecheng-7707	64	2	j	j	PROPN
fumecheng-7707	64	3	n	n	CCONJ
fumecheng-7707	64	4	n	n	PROPN
fumecheng-7707	64	5	=	=	SYM
fumecheng-7707	64	6	−	−	PROPN
fumecheng-7707	64	7	=	=	SYM
fumecheng-7707	65	1	−	−	PROPN
fumecheng-7707	65	2	=	=	SYM
fumecheng-7707	65	3	=	=	SYM
fumecheng-7707	66	1	−	−	PROPN
fumecheng-7707	66	2			NOUN
fumecheng-7707	66	3			X
fumecheng-7707	66	4	(	(	PUNCT
fumecheng-7707	66	5	6	6	NUM
fumecheng-7707	66	6	)	)	PUNCT
fumecheng-7707	66	7	where	where	SCONJ
fumecheng-7707	66	8	n	n	PRON
fumecheng-7707	66	9	is	be	AUX
fumecheng-7707	66	10	the	the	DET
fumecheng-7707	66	11	number	number	NOUN
fumecheng-7707	66	12	of	of	ADP
fumecheng-7707	66	13	elements	element	NOUN
fumecheng-7707	66	14	and	and	CCONJ
fumecheng-7707	66	15	l	l	NOUN
fumecheng-7707	66	16	is	be	AUX
fumecheng-7707	66	17	the	the	DET
fumecheng-7707	66	18	length	length	NOUN
fumecheng-7707	66	19	of	of	ADP
fumecheng-7707	66	20	the	the	DET
fumecheng-7707	66	21	simulation	simulation	NOUN
fumecheng-7707	66	22	area	area	NOUN
fumecheng-7707	66	23	for	for	ADP
fumecheng-7707	66	24	the	the	DET
fumecheng-7707	66	25	spatial	spatial	ADJ
fumecheng-7707	66	26	coordinates	coordinate	NOUN
fumecheng-7707	66	27	x	x	PUNCT
fumecheng-7707	66	28	and	and	CCONJ
fumecheng-7707	66	29	r.	r.	PROPN
fumecheng-7707	66	30	note	note	VERB
fumecheng-7707	66	31	that	that	SCONJ
fumecheng-7707	66	32	the	the	DET
fumecheng-7707	66	33	discretization	discretization	NOUN
fumecheng-7707	66	34	is	be	AUX
fumecheng-7707	66	35	equidistant	equidistant	ADJ
fumecheng-7707	66	36	in	in	ADP
fumecheng-7707	66	37	the	the	DET
fumecheng-7707	66	38	squares	square	NOUN
fumecheng-7707	66	39	of	of	ADP
fumecheng-7707	66	40	the	the	DET
fumecheng-7707	66	41	spatial	spatial	ADJ
fumecheng-7707	66	42	coordinates	coordinate	NOUN
fumecheng-7707	66	43	.	.	PUNCT
fumecheng-7707	67	1	applying	apply	VERB
fumecheng-7707	67	2	the	the	DET
fumecheng-7707	67	3	trapezoidal	trapezoidal	ADJ
fumecheng-7707	67	4	rule	rule	NOUN
fumecheng-7707	67	5	,	,	PUNCT
fumecheng-7707	67	6	it	it	PRON
fumecheng-7707	67	7	is	be	AUX
fumecheng-7707	67	8	(	(	PUNCT
fumecheng-7707	67	9	by	by	ADP
fumecheng-7707	67	10	convention	convention	NOUN
fumecheng-7707	67	11	the	the	DET
fumecheng-7707	67	12	sum	sum	NOUN
fumecheng-7707	67	13	over	over	ADP
fumecheng-7707	67	14	an	an	DET
fumecheng-7707	67	15	empty	empty	ADJ
fumecheng-7707	67	16	set	set	NOUN
fumecheng-7707	67	17	shall	shall	AUX
fumecheng-7707	67	18	be	be	AUX
fumecheng-7707	67	19	zero	zero	NUM
fumecheng-7707	67	20	instead	instead	ADV
fumecheng-7707	67	21	of	of	ADP
fumecheng-7707	67	22	ill	ill	ADV
fumecheng-7707	67	23	-	-	PUNCT
fumecheng-7707	67	24	defined	define	VERB
fumecheng-7707	67	25	)	)	PUNCT
fumecheng-7707	67	26	1	1	NUM
fumecheng-7707	67	27	3	3	NUM
fumecheng-7707	67	28	1	1	NUM
fumecheng-7707	67	29	2	2	NUM
fumecheng-7707	67	30	1	1	NUM
fumecheng-7707	67	31	ˆ	ˆ	NOUN
fumecheng-7707	67	32	ˆˆ	ˆˆ	PROPN
fumecheng-7707	67	33	1	1	NUM
fumecheng-7707	67	34	.	.	SYM
fumecheng-7707	68	1	2	2	NUM
fumecheng-7707	69	1	i	i	PRON
fumecheng-7707	69	2	i	i	PRON
fumecheng-7707	69	3	j	j	PROPN
fumecheng-7707	70	1	j	j	PROPN
fumecheng-7707	70	2	g	g	PROPN
fumecheng-7707	70	3	h	h	PROPN
fumecheng-7707	71	1	f	f	PROPN
fumecheng-7707	72	1	i	i	PRON
fumecheng-7707	72	2	f	f	VERB
fumecheng-7707	73	1	i	i	PRON
fumecheng-7707	73	2	j	j	PROPN
fumecheng-7707	74	1	−	−	NOUN
fumecheng-7707	74	2	=	=	SYM
fumecheng-7707	74	3			PROPN
fumecheng-7707	74	4			NOUN
fumecheng-7707	74	5			ADJ
fumecheng-7707	74	6	=	=	INTJ
fumecheng-7707	74	7	−	−	PROPN
fumecheng-7707	75	1	+	+	CCONJ
fumecheng-7707	75	2	−	−	X
fumecheng-7707	75	3			PROPN
fumecheng-7707	75	4			PROPN
fumecheng-7707	75	5			PROPN
fumecheng-7707	75	6			X
fumecheng-7707	75	7	(	(	PUNCT
fumecheng-7707	75	8	7	7	NUM
fumecheng-7707	75	9	)	)	PUNCT
fumecheng-7707	75	10	808	808	NUM
fumecheng-7707	75	11	e.	e.	PROPN
fumecheng-7707	75	12	willert	willert	PROPN
fumecheng-7707	75	13	to	to	PART
fumecheng-7707	75	14	demonstrate	demonstrate	VERB
fumecheng-7707	75	15	the	the	DET
fumecheng-7707	75	16	performance	performance	NOUN
fumecheng-7707	75	17	advantage	advantage	NOUN
fumecheng-7707	75	18	of	of	ADP
fumecheng-7707	75	19	the	the	DET
fumecheng-7707	75	20	1d	1d	NUM
fumecheng-7707	75	21	-	-	PUNCT
fumecheng-7707	75	22	fft	fft	PROPN
fumecheng-7707	75	23	,	,	PUNCT
fumecheng-7707	75	24	the	the	DET
fumecheng-7707	75	25	sum	sum	NOUN
fumecheng-7707	75	26	in	in	ADP
fumecheng-7707	75	27	the	the	DET
fumecheng-7707	75	28	last	last	ADJ
fumecheng-7707	75	29	equation	equation	NOUN
fumecheng-7707	75	30	has	have	AUX
fumecheng-7707	75	31	been	be	AUX
fumecheng-7707	75	32	evaluated	evaluate	VERB
fumecheng-7707	75	33	both	both	CCONJ
fumecheng-7707	75	34	with	with	ADP
fumecheng-7707	75	35	mvm	mvm	NOUN
fumecheng-7707	75	36	and	and	CCONJ
fumecheng-7707	75	37	as	as	ADP
fumecheng-7707	75	38	an	an	DET
fumecheng-7707	75	39	fft	fft	NOUN
fumecheng-7707	75	40	-	-	PUNCT
fumecheng-7707	75	41	accelerated	accelerate	VERB
fumecheng-7707	75	42	convolution	convolution	NOUN
fumecheng-7707	75	43	.	.	PUNCT
fumecheng-7707	76	1	the	the	DET
fumecheng-7707	76	2	calculation	calculation	NOUN
fumecheng-7707	76	3	time	time	NOUN
fumecheng-7707	76	4	for	for	ADP
fumecheng-7707	76	5	the	the	DET
fumecheng-7707	76	6	pure	pure	ADJ
fumecheng-7707	76	7	transformation	transformation	NOUN
fumecheng-7707	76	8	step	step	NOUN
fumecheng-7707	76	9	(	(	PUNCT
fumecheng-7707	76	10	without	without	ADP
fumecheng-7707	76	11	build	build	NOUN
fumecheng-7707	76	12	-	-	PUNCT
fumecheng-7707	76	13	up	up	NOUN
fumecheng-7707	76	14	of	of	ADP
fumecheng-7707	76	15	a	a	DET
fumecheng-7707	76	16	priori	priori	ADV
fumecheng-7707	76	17	known	know	VERB
fumecheng-7707	76	18	matrices	matrix	NOUN
fumecheng-7707	76	19	or	or	CCONJ
fumecheng-7707	76	20	vectors	vector	NOUN
fumecheng-7707	76	21	)	)	PUNCT
fumecheng-7707	76	22	as	as	ADP
fumecheng-7707	76	23	a	a	DET
fumecheng-7707	76	24	function	function	NOUN
fumecheng-7707	76	25	of	of	ADP
fumecheng-7707	76	26	the	the	DET
fumecheng-7707	76	27	number	number	NOUN
fumecheng-7707	76	28	of	of	ADP
fumecheng-7707	76	29	array	array	NOUN
fumecheng-7707	76	30	elements	element	NOUN
fumecheng-7707	76	31	n	n	PRON
fumecheng-7707	76	32	is	be	AUX
fumecheng-7707	76	33	shown	show	VERB
fumecheng-7707	76	34	in	in	ADP
fumecheng-7707	76	35	fig	fig	NOUN
fumecheng-7707	76	36	.	.	PUNCT
fumecheng-7707	77	1	1	1	NUM
fumecheng-7707	77	2	in	in	ADP
fumecheng-7707	77	3	doublelogarithmic	doublelogarithmic	ADJ
fumecheng-7707	77	4	scale	scale	NOUN
fumecheng-7707	77	5	.	.	PUNCT
fumecheng-7707	78	1	while	while	SCONJ
fumecheng-7707	78	2	the	the	DET
fumecheng-7707	78	3	absolute	absolute	ADJ
fumecheng-7707	78	4	value	value	NOUN
fumecheng-7707	78	5	for	for	ADP
fumecheng-7707	78	6	the	the	DET
fumecheng-7707	78	7	calculation	calculation	NOUN
fumecheng-7707	78	8	time	time	NOUN
fumecheng-7707	78	9	is	be	AUX
fumecheng-7707	78	10	not	not	PART
fumecheng-7707	78	11	too	too	ADV
fumecheng-7707	78	12	relevant	relevant	ADJ
fumecheng-7707	78	13	,	,	PUNCT
fumecheng-7707	78	14	as	as	SCONJ
fumecheng-7707	78	15	it	it	PRON
fumecheng-7707	78	16	depends	depend	VERB
fumecheng-7707	78	17	on	on	ADP
fumecheng-7707	78	18	the	the	DET
fumecheng-7707	78	19	computational	computational	ADJ
fumecheng-7707	78	20	setup	setup	NOUN
fumecheng-7707	78	21	,	,	PUNCT
fumecheng-7707	78	22	it	it	PRON
fumecheng-7707	78	23	can	can	AUX
fumecheng-7707	78	24	be	be	AUX
fumecheng-7707	78	25	easily	easily	ADV
fumecheng-7707	78	26	seen	see	VERB
fumecheng-7707	78	27	,	,	PUNCT
fumecheng-7707	78	28	that	that	SCONJ
fumecheng-7707	78	29	the	the	DET
fumecheng-7707	78	30	numerical	numerical	ADJ
fumecheng-7707	78	31	complexity	complexity	NOUN
fumecheng-7707	78	32	of	of	ADP
fumecheng-7707	78	33	the	the	DET
fumecheng-7707	78	34	mvm	mvm	NOUN
fumecheng-7707	78	35	is	be	AUX
fumecheng-7707	78	36	of	of	ADP
fumecheng-7707	78	37	the	the	DET
fumecheng-7707	78	38	order	order	NOUN
fumecheng-7707	78	39	of	of	ADP
fumecheng-7707	78	40	n2	n2	NOUN
fumecheng-7707	78	41	,	,	PUNCT
fumecheng-7707	78	42	while	while	SCONJ
fumecheng-7707	78	43	the	the	DET
fumecheng-7707	78	44	fft	fft	PROPN
fumecheng-7707	78	45	complexity	complexity	NOUN
fumecheng-7707	78	46	only	only	ADV
fumecheng-7707	78	47	increases	increase	NOUN
fumecheng-7707	78	48	with	with	ADP
fumecheng-7707	78	49	n.	n.	NOUN
fumecheng-7707	78	50	the	the	DET
fumecheng-7707	78	51	scatter	scatter	NOUN
fumecheng-7707	78	52	in	in	ADP
fumecheng-7707	78	53	the	the	DET
fumecheng-7707	78	54	calculation	calculation	NOUN
fumecheng-7707	78	55	time	time	NOUN
fumecheng-7707	78	56	for	for	ADP
fumecheng-7707	78	57	the	the	DET
fumecheng-7707	78	58	fft	fft	NOUN
fumecheng-7707	78	59	is	be	AUX
fumecheng-7707	78	60	probably	probably	ADV
fumecheng-7707	78	61	due	due	ADJ
fumecheng-7707	78	62	to	to	ADP
fumecheng-7707	78	63	performance	performance	NOUN
fumecheng-7707	78	64	variance	variance	NOUN
fumecheng-7707	78	65	of	of	ADP
fumecheng-7707	78	66	the	the	DET
fumecheng-7707	78	67	fft	fft	NOUN
fumecheng-7707	78	68	depending	depend	VERB
fumecheng-7707	78	69	on	on	ADP
fumecheng-7707	78	70	n.	n.	PROPN
fumecheng-7707	78	71	note	note	NOUN
fumecheng-7707	78	72	that	that	SCONJ
fumecheng-7707	78	73	the	the	DET
fumecheng-7707	78	74	numerical	numerical	ADJ
fumecheng-7707	78	75	error	error	NOUN
fumecheng-7707	78	76	mainly	mainly	ADV
fumecheng-7707	78	77	originates	originate	VERB
fumecheng-7707	78	78	from	from	ADP
fumecheng-7707	78	79	the	the	DET
fumecheng-7707	78	80	discretization	discretization	NOUN
fumecheng-7707	78	81	and	and	CCONJ
fumecheng-7707	78	82	the	the	DET
fumecheng-7707	78	83	trapezoidal	trapezoidal	ADJ
fumecheng-7707	78	84	rule	rule	NOUN
fumecheng-7707	78	85	.	.	PUNCT
fumecheng-7707	79	1	therefore	therefore	ADV
fumecheng-7707	79	2	,	,	PUNCT
fumecheng-7707	79	3	when	when	SCONJ
fumecheng-7707	79	4	comparing	compare	VERB
fumecheng-7707	79	5	the	the	DET
fumecheng-7707	79	6	mvm	mvm	NOUN
fumecheng-7707	79	7	and	and	CCONJ
fumecheng-7707	79	8	fft	fft	VERB
fumecheng-7707	79	9	solutions	solution	NOUN
fumecheng-7707	79	10	with	with	ADP
fumecheng-7707	79	11	analytical	analytical	ADJ
fumecheng-7707	79	12	solutions	solution	NOUN
fumecheng-7707	79	13	,	,	PUNCT
fumecheng-7707	79	14	both	both	DET
fumecheng-7707	79	15	variants	variant	NOUN
fumecheng-7707	79	16	exhibit	exhibit	VERB
fumecheng-7707	79	17	the	the	DET
fumecheng-7707	79	18	same	same	ADJ
fumecheng-7707	79	19	convergence	convergence	NOUN
fumecheng-7707	79	20	behaviour	behaviour	NOUN
fumecheng-7707	79	21	.	.	PUNCT
fumecheng-7707	80	1	fig	fig	NOUN
fumecheng-7707	80	2	.	.	PUNCT
fumecheng-7707	81	1	1	1	NUM
fumecheng-7707	81	2	comparison	comparison	NOUN
fumecheng-7707	81	3	of	of	ADP
fumecheng-7707	81	4	the	the	DET
fumecheng-7707	81	5	calculation	calculation	NOUN
fumecheng-7707	81	6	time	time	NOUN
fumecheng-7707	81	7	for	for	ADP
fumecheng-7707	81	8	the	the	DET
fumecheng-7707	81	9	transformation	transformation	NOUN
fumecheng-7707	81	10	step	step	NOUN
fumecheng-7707	81	11	(	(	PUNCT
fumecheng-7707	81	12	7	7	NUM
fumecheng-7707	81	13	)	)	PUNCT
fumecheng-7707	81	14	with	with	ADP
fumecheng-7707	81	15	matrixvector	matrixvector	NOUN
fumecheng-7707	81	16	-	-	PUNCT
fumecheng-7707	81	17	multiplication	multiplication	NOUN
fumecheng-7707	81	18	(	(	PUNCT
fumecheng-7707	81	19	mvm	mvm	NOUN
fumecheng-7707	81	20	)	)	PUNCT
fumecheng-7707	81	21	and	and	CCONJ
fumecheng-7707	81	22	as	as	ADP
fumecheng-7707	81	23	a	a	DET
fumecheng-7707	81	24	fft	fft	NOUN
fumecheng-7707	81	25	-	-	PUNCT
fumecheng-7707	81	26	accelerated	accelerate	VERB
fumecheng-7707	81	27	convolution	convolution	NOUN
fumecheng-7707	81	28	,	,	PUNCT
fumecheng-7707	81	29	depending	depend	VERB
fumecheng-7707	81	30	on	on	ADP
fumecheng-7707	81	31	the	the	DET
fumecheng-7707	81	32	number	number	NOUN
fumecheng-7707	81	33	of	of	ADP
fumecheng-7707	81	34	array	array	NOUN
fumecheng-7707	81	35	elements	element	NOUN
fumecheng-7707	81	36	used	use	VERB
fumecheng-7707	81	37	for	for	ADP
fumecheng-7707	81	38	the	the	DET
fumecheng-7707	81	39	transformations	transformation	NOUN
fumecheng-7707	81	40	.	.	PUNCT
fumecheng-7707	82	1	2.2	2.2	NUM
fumecheng-7707	82	2	.	.	PUNCT
fumecheng-7707	82	3	transformation	transformation	NOUN
fumecheng-7707	82	4	of	of	ADP
fumecheng-7707	82	5	local	local	ADJ
fumecheng-7707	82	6	displacements	displacement	NOUN
fumecheng-7707	82	7	several	several	ADJ
fumecheng-7707	82	8	classes	class	NOUN
fumecheng-7707	82	9	of	of	ADP
fumecheng-7707	82	10	tribological	tribological	ADJ
fumecheng-7707	82	11	problems	problem	NOUN
fumecheng-7707	82	12	can	can	AUX
fumecheng-7707	82	13	already	already	ADV
fumecheng-7707	82	14	be	be	AUX
fumecheng-7707	82	15	solved	solve	VERB
fumecheng-7707	82	16	with	with	ADP
fumecheng-7707	82	17	the	the	DET
fumecheng-7707	82	18	mdr	mdr	PROPN
fumecheng-7707	82	19	only	only	ADV
fumecheng-7707	82	20	based	base	VERB
fumecheng-7707	82	21	on	on	ADP
fumecheng-7707	82	22	the	the	DET
fumecheng-7707	82	23	one	one	NUM
fumecheng-7707	82	24	transformation	transformation	NOUN
fumecheng-7707	82	25	given	give	VERB
fumecheng-7707	82	26	in	in	ADP
fumecheng-7707	82	27	the	the	DET
fumecheng-7707	82	28	previous	previous	ADJ
fumecheng-7707	82	29	subsection	subsection	NOUN
fumecheng-7707	82	30	,	,	PUNCT
fumecheng-7707	82	31	as	as	SCONJ
fumecheng-7707	82	32	the	the	DET
fumecheng-7707	82	33	relations	relation	NOUN
fumecheng-7707	82	34	between	between	ADP
fumecheng-7707	82	35	the	the	DET
fumecheng-7707	82	36	macroscopic	macroscopic	ADJ
fumecheng-7707	82	37	contact	contact	NOUN
fumecheng-7707	82	38	quantities	quantity	NOUN
fumecheng-7707	82	39	(	(	PUNCT
fumecheng-7707	82	40	contact	contact	NOUN
fumecheng-7707	82	41	radii	radius	NOUN
fumecheng-7707	82	42	,	,	PUNCT
fumecheng-7707	82	43	forces	force	NOUN
fumecheng-7707	82	44	,	,	PUNCT
fumecheng-7707	82	45	and	and	CCONJ
fumecheng-7707	82	46	macroscopic	macroscopic	ADJ
fumecheng-7707	82	47	displacements	displacement	NOUN
fumecheng-7707	82	48	)	)	PUNCT
fumecheng-7707	82	49	are	be	AUX
fumecheng-7707	82	50	the	the	DET
fumecheng-7707	82	51	same	same	ADJ
fumecheng-7707	82	52	in	in	ADP
fumecheng-7707	82	53	the	the	DET
fumecheng-7707	82	54	mdr	mdr	PROPN
fumecheng-7707	82	55	model	model	NOUN
fumecheng-7707	82	56	as	as	ADP
fumecheng-7707	82	57	in	in	ADP
fumecheng-7707	82	58	the	the	DET
fumecheng-7707	82	59	axisymmetric	axisymmetric	ADJ
fumecheng-7707	82	60	original	original	ADJ
fumecheng-7707	82	61	system	system	NOUN
fumecheng-7707	82	62	[	[	X
fumecheng-7707	82	63	7	7	NUM
fumecheng-7707	82	64	]	]	PUNCT
fumecheng-7707	82	65	.	.	PUNCT
fumecheng-7707	83	1	this	this	PRON
fumecheng-7707	83	2	,	,	PUNCT
fumecheng-7707	83	3	e.g.	e.g.	ADV
fumecheng-7707	83	4	,	,	PUNCT
fumecheng-7707	83	5	already	already	ADV
fumecheng-7707	83	6	allows	allow	VERB
fumecheng-7707	83	7	the	the	DET
fumecheng-7707	83	8	extensive	extensive	ADJ
fumecheng-7707	83	9	study	study	NOUN
fumecheng-7707	83	10	of	of	ADP
fumecheng-7707	83	11	different	different	ADJ
fumecheng-7707	83	12	classes	class	NOUN
fumecheng-7707	83	13	of	of	ADP
fumecheng-7707	83	14	dynamic	dynamic	ADJ
fumecheng-7707	83	15	contact	contact	NOUN
fumecheng-7707	83	16	problems	problem	NOUN
fumecheng-7707	83	17	,	,	PUNCT
fumecheng-7707	83	18	like	like	ADP
fumecheng-7707	83	19	impacts	impact	NOUN
fumecheng-7707	83	20	,	,	PUNCT
fumecheng-7707	83	21	with	with	ADP
fumecheng-7707	83	22	the	the	DET
fumecheng-7707	83	23	mdr	mdr	PROPN
fumecheng-7707	83	24	[	[	X
fumecheng-7707	83	25	21	21	NUM
fumecheng-7707	83	26	]	]	PUNCT
fumecheng-7707	83	27	.	.	PUNCT
fumecheng-7707	84	1	however	however	ADV
fumecheng-7707	84	2	,	,	PUNCT
fumecheng-7707	84	3	local	local	ADJ
fumecheng-7707	84	4	quantities	quantity	NOUN
fumecheng-7707	84	5	,	,	PUNCT
fumecheng-7707	84	6	i.e.	i.e.	X
fumecheng-7707	84	7	,	,	PUNCT
fumecheng-7707	84	8	local	local	ADJ
fumecheng-7707	84	9	displacements	displacement	NOUN
fumecheng-7707	84	10	and	and	CCONJ
fumecheng-7707	84	11	contact	contact	NOUN
fumecheng-7707	84	12	stresses	stress	NOUN
fumecheng-7707	84	13	,	,	PUNCT
fumecheng-7707	84	14	do	do	AUX
fumecheng-7707	84	15	not	not	PART
fumecheng-7707	84	16	exist	exist	VERB
fumecheng-7707	84	17	explicitly	explicitly	ADV
fumecheng-7707	84	18	within	within	ADP
fumecheng-7707	84	19	the	the	DET
fumecheng-7707	84	20	mdr	mdr	PROPN
fumecheng-7707	84	21	model	model	NOUN
fumecheng-7707	84	22	but	but	CCONJ
fumecheng-7707	84	23	must	must	AUX
fumecheng-7707	84	24	obtained	obtain	VERB
fumecheng-7707	84	25	from	from	ADP
fumecheng-7707	84	26	the	the	DET
fumecheng-7707	84	27	respective	respective	ADJ
fumecheng-7707	84	28	mdr	mdr	PROPN
fumecheng-7707	84	29	quantities	quantity	NOUN
fumecheng-7707	84	30	by	by	ADP
fumecheng-7707	84	31	yet	yet	ADV
fumecheng-7707	84	32	different	different	ADJ
fumecheng-7707	84	33	integral	integral	ADJ
fumecheng-7707	84	34	transforms	transform	NOUN
fumecheng-7707	84	35	.	.	PUNCT
fumecheng-7707	85	1	the	the	DET
fumecheng-7707	85	2	local	local	ADJ
fumecheng-7707	85	3	displacements	displacement	NOUN
fumecheng-7707	85	4	(	(	PUNCT
fumecheng-7707	85	5	both	both	CCONJ
fumecheng-7707	85	6	normal	normal	ADJ
fumecheng-7707	85	7	and	and	CCONJ
fumecheng-7707	85	8	tangential	tangential	ADJ
fumecheng-7707	85	9	)	)	PUNCT
fumecheng-7707	85	10	in	in	ADP
fumecheng-7707	85	11	the	the	DET
fumecheng-7707	85	12	axisymmetric	axisymmetric	ADJ
fumecheng-7707	85	13	original	original	ADJ
fumecheng-7707	85	14	system	system	NOUN
fumecheng-7707	85	15	,	,	PUNCT
fumecheng-7707	85	16	u(r	u(r	NOUN
fumecheng-7707	85	17	)	)	PUNCT
fumecheng-7707	85	18	,	,	PUNCT
fumecheng-7707	85	19	and	and	CCONJ
fumecheng-7707	85	20	its	its	PRON
fumecheng-7707	85	21	mdr	mdr	PROPN
fumecheng-7707	85	22	image	image	NOUN
fumecheng-7707	85	23	,	,	PUNCT
fumecheng-7707	85	24	u(x	u(x	PROPN
fumecheng-7707	85	25	)	)	PUNCT
fumecheng-7707	85	26	,	,	PUNCT
fumecheng-7707	85	27	are	be	AUX
fumecheng-7707	85	28	connected	connect	VERB
fumecheng-7707	85	29	via	via	ADP
fumecheng-7707	85	30	the	the	DET
fumecheng-7707	85	31	transform	transform	NOUN
fumecheng-7707	85	32	[	[	X
fumecheng-7707	85	33	1	1	NUM
fumecheng-7707	85	34	]	]	SYM
fumecheng-7707	85	35	2	2	NUM
fumecheng-7707	85	36	2	2	NUM
fumecheng-7707	85	37	0	0	NUM
fumecheng-7707	85	38	2	2	NUM
fumecheng-7707	85	39	(	(	PUNCT
fumecheng-7707	85	40	)	)	PUNCT
fumecheng-7707	85	41	(	(	PUNCT
fumecheng-7707	85	42	)	)	PUNCT
fumecheng-7707	85	43	d	d	NOUN
fumecheng-7707	85	44	.	.	PUNCT
fumecheng-7707	86	1	r	r	NOUN
fumecheng-7707	86	2	u	u	NOUN
fumecheng-7707	86	3	x	x	PUNCT
fumecheng-7707	86	4	u	u	NOUN
fumecheng-7707	86	5	r	r	NOUN
fumecheng-7707	86	6	x	x	NOUN
fumecheng-7707	86	7	r	r	NOUN
fumecheng-7707	86	8	x	x	NOUN
fumecheng-7707	86	9	=	=	SYM
fumecheng-7707	86	10	−	−	NOUN
fumecheng-7707	86	11			NUM
fumecheng-7707	86	12	(	(	PUNCT
fumecheng-7707	86	13	8)	8)	NUM
fumecheng-7707	86	14	fft	fft	NOUN
fumecheng-7707	86	15	-	-	PUNCT
fumecheng-7707	86	16	based	base	VERB
fumecheng-7707	86	17	implementation	implementation	NOUN
fumecheng-7707	86	18	of	of	ADP
fumecheng-7707	86	19	the	the	DET
fumecheng-7707	86	20	mdr	mdr	PROPN
fumecheng-7707	86	21	transformations	transformation	NOUN
fumecheng-7707	86	22	for	for	ADP
fumecheng-7707	86	23	homogeneous	homogeneous	ADJ
fumecheng-7707	86	24	and	and	CCONJ
fumecheng-7707	86	25	power	power	NOUN
fumecheng-7707	86	26	-	-	PUNCT
fumecheng-7707	86	27	law	law	NOUN
fumecheng-7707	86	28	graded	grade	VERB
fumecheng-7707	86	29	materials809	materials809	PROPN
fumecheng-7707	86	30	note	note	VERB
fumecheng-7707	86	31	that	that	SCONJ
fumecheng-7707	86	32	formally	formally	ADV
fumecheng-7707	86	33	this	this	PRON
fumecheng-7707	86	34	is	be	AUX
fumecheng-7707	86	35	also	also	ADV
fumecheng-7707	86	36	the	the	DET
fumecheng-7707	86	37	inverse	inverse	NOUN
fumecheng-7707	86	38	transform	transform	NOUN
fumecheng-7707	86	39	to	to	ADP
fumecheng-7707	86	40	eq	eq	NOUN
fumecheng-7707	86	41	.	.	PUNCT
fumecheng-7707	87	1	(	(	PUNCT
fumecheng-7707	87	2	1	1	NUM
fumecheng-7707	87	3	)	)	PUNCT
fumecheng-7707	87	4	,	,	PUNCT
fumecheng-7707	87	5	to	to	PART
fumecheng-7707	87	6	obtain	obtain	VERB
fumecheng-7707	87	7	the	the	DET
fumecheng-7707	87	8	axisymmetric	axisymmetric	ADJ
fumecheng-7707	87	9	profile	profile	NOUN
fumecheng-7707	87	10	f	f	PROPN
fumecheng-7707	87	11	from	from	ADP
fumecheng-7707	87	12	the	the	DET
fumecheng-7707	87	13	equivalent	equivalent	ADJ
fumecheng-7707	87	14	profile	profile	NOUN
fumecheng-7707	87	15	g.	g.	NOUN
fumecheng-7707	87	16	introducing	introduce	VERB
fumecheng-7707	87	17	(	(	PUNCT
fumecheng-7707	87	18	)	)	PUNCT
fumecheng-7707	87	19	:	:	PUNCT
fumecheng-7707	87	20	(	(	PUNCT
fumecheng-7707	87	21	)	)	PUNCT
fumecheng-7707	87	22	(	(	PUNCT
fumecheng-7707	87	23	0),u	0),u	NUM
fumecheng-7707	87	24	x	x	SYM
fumecheng-7707	87	25	u	u	NOUN
fumecheng-7707	87	26	x	x	PROPN
fumecheng-7707	87	27	u=	u=	ADV
fumecheng-7707	87	28	−	−	PROPN
fumecheng-7707	87	29	(	(	PUNCT
fumecheng-7707	87	30	9	9	NUM
fumecheng-7707	87	31	)	)	PUNCT
fumecheng-7707	87	32	and	and	CCONJ
fumecheng-7707	87	33	the	the	DET
fumecheng-7707	87	34	substitutions	substitution	NOUN
fumecheng-7707	87	35	ˆˆ	ˆˆ	PROPN
fumecheng-7707	87	36	(	(	PUNCT
fumecheng-7707	87	37	)	)	PUNCT
fumecheng-7707	87	38	(	(	PUNCT
fumecheng-7707	87	39	)	)	PUNCT
fumecheng-7707	87	40	,	,	PUNCT
fumecheng-7707	87	41	(	(	PUNCT
fumecheng-7707	87	42	)	)	PUNCT
fumecheng-7707	87	43	(	(	PUNCT
fumecheng-7707	87	44	)	)	PUNCT
fumecheng-7707	87	45	,	,	PUNCT
fumecheng-7707	87	46	u	u	NOUN
fumecheng-7707	87	47	u	u	NOUN
fumecheng-7707	87	48	r	r	NOUN
fumecheng-7707	87	49	u	u	X
fumecheng-7707	87	50	u	u	NOUN
fumecheng-7707	87	51	x=	x=	PUNCT
fumecheng-7707	88	1	=	=	NOUN
fumecheng-7707	88	2			ADP
fumecheng-7707	88	3			X
fumecheng-7707	88	4	(	(	PUNCT
fumecheng-7707	88	5	10	10	NUM
fumecheng-7707	88	6	)	)	PUNCT
fumecheng-7707	88	7	one	one	NOUN
fumecheng-7707	88	8	obtains	obtain	VERB
fumecheng-7707	88	9	0	0	NUM
fumecheng-7707	88	10	ˆ2	ˆ2	PROPN
fumecheng-7707	88	11	(	(	PUNCT
fumecheng-7707	88	12	)	)	PUNCT
fumecheng-7707	88	13	ˆ	ˆ	PROPN
fumecheng-7707	88	14	(	(	PUNCT
fumecheng-7707	88	15	)	)	PUNCT
fumecheng-7707	88	16	(	(	PUNCT
fumecheng-7707	88	17	0	0	NUM
fumecheng-7707	88	18	)	)	PUNCT
fumecheng-7707	88	19	d	d	NOUN
fumecheng-7707	88	20	.	.	PUNCT
fumecheng-7707	88	21	2	2	NUM
fumecheng-7707	88	22	u	u	NOUN
fumecheng-7707	88	23	u	u	NOUN
fumecheng-7707	88	24	u=	u=	PROPN
fumecheng-7707	88	25	+	+	CCONJ
fumecheng-7707	88	26	−	−	NOUN
fumecheng-7707	88	27			PUNCT
fumecheng-7707	88	28			ADP
fumecheng-7707	88	29			NOUN
fumecheng-7707	88	30			SCONJ
fumecheng-7707	88	31			NOUN
fumecheng-7707	88	32			ADP
fumecheng-7707	88	33			NOUN
fumecheng-7707	88	34			ADP
fumecheng-7707	88	35			X
fumecheng-7707	88	36	(	(	PUNCT
fumecheng-7707	88	37	11	11	NUM
fumecheng-7707	88	38	)	)	PUNCT
fumecheng-7707	88	39	now	now	ADV
fumecheng-7707	88	40	,	,	PUNCT
fumecheng-7707	88	41	there	there	PRON
fumecheng-7707	88	42	are	be	VERB
fumecheng-7707	88	43	(	(	PUNCT
fumecheng-7707	88	44	among	among	ADP
fumecheng-7707	88	45	others	other	NOUN
fumecheng-7707	88	46	)	)	PUNCT
fumecheng-7707	88	47	two	two	NUM
fumecheng-7707	88	48	ways	way	NOUN
fumecheng-7707	88	49	to	to	PART
fumecheng-7707	88	50	integrate	integrate	VERB
fumecheng-7707	88	51	this	this	DET
fumecheng-7707	88	52	expression	expression	NOUN
fumecheng-7707	88	53	by	by	ADP
fumecheng-7707	88	54	parts	part	NOUN
fumecheng-7707	88	55	,	,	PUNCT
fumecheng-7707	88	56	0	0	NUM
fumecheng-7707	88	57	2	2	NUM
fumecheng-7707	88	58	ˆˆ	ˆˆ	PROPN
fumecheng-7707	88	59	(	(	PUNCT
fumecheng-7707	88	60	)	)	PUNCT
fumecheng-7707	88	61	(	(	PUNCT
fumecheng-7707	88	62	0	0	NUM
fumecheng-7707	88	63	)	)	PUNCT
fumecheng-7707	88	64	(	(	PUNCT
fumecheng-7707	88	65	)	)	PUNCT
fumecheng-7707	88	66	arccos	arccos	PROPN
fumecheng-7707	88	67	d	d	NOUN
fumecheng-7707	88	68	,	,	PUNCT
fumecheng-7707	88	69	u	u	PRON
fumecheng-7707	88	70	u	u	NOUN
fumecheng-7707	88	71	u	u	NOUN
fumecheng-7707	88	72			NOUN
fumecheng-7707	88	73			NOUN
fumecheng-7707	88	74	=	=	PROPN
fumecheng-7707	89	1	+	+	CCONJ
fumecheng-7707	90	1			PROPN
fumecheng-7707	90	2			NOUN
fumecheng-7707	90	3			PROPN
fumecheng-7707	91	1			ADJ
fumecheng-7707	91	2			NOUN
fumecheng-7707	91	3			PUNCT
fumecheng-7707	91	4			ADP
fumecheng-7707	91	5			NOUN
fumecheng-7707	91	6			ADP
fumecheng-7707	91	7			NOUN
fumecheng-7707	91	8			X
fumecheng-7707	91	9			X
fumecheng-7707	91	10			X
fumecheng-7707	91	11	(	(	PUNCT
fumecheng-7707	91	12	12	12	NUM
fumecheng-7707	91	13	)	)	PUNCT
fumecheng-7707	91	14	or	or	CCONJ
fumecheng-7707	91	15	,	,	PUNCT
fumecheng-7707	91	16	0	0	NUM
fumecheng-7707	91	17	0	0	NUM
fumecheng-7707	91	18	ˆ2	ˆ2	NOUN
fumecheng-7707	91	19	(	(	PUNCT
fumecheng-7707	91	20	)	)	PUNCT
fumecheng-7707	91	21	d	d	PROPN
fumecheng-7707	91	22	(	(	PUNCT
fumecheng-7707	91	23	)	)	PUNCT
fumecheng-7707	91	24	ˆ	ˆ	NOUN
fumecheng-7707	91	25	(	(	PUNCT
fumecheng-7707	91	26	)	)	PUNCT
fumecheng-7707	91	27	(	(	PUNCT
fumecheng-7707	91	28	0	0	X
fumecheng-7707	91	29	)	)	PUNCT
fumecheng-7707	91	30	lim	lim	NOUN
fumecheng-7707	91	31	(	(	PUNCT
fumecheng-7707	91	32	)	)	PUNCT
fumecheng-7707	91	33	d	d	NOUN
fumecheng-7707	91	34	,	,	PUNCT
fumecheng-7707	91	35	(	(	PUNCT
fumecheng-7707	91	36	)	)	PUNCT
fumecheng-7707	91	37	:	:	PUNCT
fumecheng-7707	91	38	.	.	PUNCT
fumecheng-7707	92	1	dx	dx	PROPN
fumecheng-7707	92	2	u	u	NOUN
fumecheng-7707	92	3	x	x	PUNCT
fumecheng-7707	92	4	u	u	VERB
fumecheng-7707	92	5	u	u	X
fumecheng-7707	92	6	u	u	NOUN
fumecheng-7707	92	7	x→	x→	PROPN
fumecheng-7707	92	8			PROPN
fumecheng-7707	92	9			ADJ
fumecheng-7707	93	1			PROPN
fumecheng-7707	93	2			NOUN
fumecheng-7707	93	3	=	=	PUNCT
fumecheng-7707	94	1	+	+	CCONJ
fumecheng-7707	94	2	−	−	PROPN
fumecheng-7707	95	1	+	+	CCONJ
fumecheng-7707	95	2	−	−	PROPN
fumecheng-7707	95	3	=	=	SYM
fumecheng-7707	95	4			NOUN
fumecheng-7707	95	5			NOUN
fumecheng-7707	95	6			NOUN
fumecheng-7707	95	7			PROPN
fumecheng-7707	95	8			NOUN
fumecheng-7707	95	9			NOUN
fumecheng-7707	95	10			AUX
fumecheng-7707	95	11			PROPN
fumecheng-7707	95	12			VERB
fumecheng-7707	95	13			PROPN
fumecheng-7707	95	14			PUNCT
fumecheng-7707	95	15			ADP
fumecheng-7707	95	16			NOUN
fumecheng-7707	95	17			X
fumecheng-7707	95	18			ADP
fumecheng-7707	95	19			PROPN
fumecheng-7707	95	20			NOUN
fumecheng-7707	95	21			ADP
fumecheng-7707	95	22			NOUN
fumecheng-7707	95	23			PUNCT
fumecheng-7707	95	24			NOUN
fumecheng-7707	95	25			NOUN
fumecheng-7707	95	26			ADJ
fumecheng-7707	95	27			ADJ
fumecheng-7707	95	28			X
fumecheng-7707	95	29	(	(	PUNCT
fumecheng-7707	95	30	13	13	NUM
fumecheng-7707	95	31	)	)	PUNCT
fumecheng-7707	95	32	obviously	obviously	ADV
fumecheng-7707	95	33	,	,	PUNCT
fumecheng-7707	95	34	the	the	DET
fumecheng-7707	95	35	second	second	ADJ
fumecheng-7707	95	36	variant	variant	NOUN
fumecheng-7707	95	37	has	have	VERB
fumecheng-7707	95	38	several	several	ADJ
fumecheng-7707	95	39	disadvantages	disadvantage	NOUN
fumecheng-7707	95	40	:	:	PUNCT
fumecheng-7707	95	41	the	the	DET
fumecheng-7707	95	42	occurring	occur	VERB
fumecheng-7707	95	43	limit	limit	NOUN
fumecheng-7707	95	44	value	value	NOUN
fumecheng-7707	95	45	must	must	AUX
fumecheng-7707	95	46	exist	exist	VERB
fumecheng-7707	95	47	and	and	CCONJ
fumecheng-7707	95	48	β(0	β(0	NOUN
fumecheng-7707	95	49	)	)	PUNCT
fumecheng-7707	95	50	should	should	AUX
fumecheng-7707	95	51	be	be	AUX
fumecheng-7707	95	52	finite	finite	ADJ
fumecheng-7707	95	53	for	for	SCONJ
fumecheng-7707	95	54	the	the	DET
fumecheng-7707	95	55	trapezoidal	trapezoidal	ADJ
fumecheng-7707	95	56	rule	rule	NOUN
fumecheng-7707	95	57	to	to	PART
fumecheng-7707	95	58	be	be	AUX
fumecheng-7707	95	59	applicable	applicable	ADJ
fumecheng-7707	95	60	without	without	ADP
fumecheng-7707	95	61	problems	problem	NOUN
fumecheng-7707	95	62	(	(	PUNCT
fumecheng-7707	95	63	that	that	PRON
fumecheng-7707	95	64	is	be	AUX
fumecheng-7707	95	65	e.g.	e.g.	ADV
fumecheng-7707	95	66	not	not	PART
fumecheng-7707	95	67	the	the	DET
fumecheng-7707	95	68	case	case	NOUN
fumecheng-7707	95	69	if	if	SCONJ
fumecheng-7707	95	70	u(x	u(x	NOUN
fumecheng-7707	95	71	)	)	PUNCT
fumecheng-7707	95	72	is	be	AUX
fumecheng-7707	95	73	parabolic	parabolic	ADJ
fumecheng-7707	95	74	)	)	PUNCT
fumecheng-7707	95	75	;	;	PUNCT
fumecheng-7707	95	76	however	however	ADV
fumecheng-7707	95	77	,	,	PUNCT
fumecheng-7707	95	78	the	the	DET
fumecheng-7707	95	79	remaining	remain	VERB
fumecheng-7707	95	80	integral	integral	NOUN
fumecheng-7707	95	81	in	in	ADP
fumecheng-7707	95	82	eq	eq	ADP
fumecheng-7707	95	83	.	.	PUNCT
fumecheng-7707	96	1	(	(	PUNCT
fumecheng-7707	96	2	13	13	NUM
fumecheng-7707	96	3	)	)	PUNCT
fumecheng-7707	96	4	is	be	AUX
fumecheng-7707	96	5	a	a	DET
fumecheng-7707	96	6	convolution	convolution	NOUN
fumecheng-7707	96	7	which	which	PRON
fumecheng-7707	96	8	can	can	AUX
fumecheng-7707	96	9	be	be	AUX
fumecheng-7707	96	10	evaluated	evaluate	VERB
fumecheng-7707	96	11	once	once	ADV
fumecheng-7707	96	12	again	again	ADV
fumecheng-7707	96	13	very	very	ADV
fumecheng-7707	96	14	efficiently	efficiently	ADV
fumecheng-7707	96	15	with	with	ADP
fumecheng-7707	96	16	the	the	DET
fumecheng-7707	96	17	1d	1d	NUM
fumecheng-7707	96	18	-	-	PUNCT
fumecheng-7707	96	19	fft	fft	NOUN
fumecheng-7707	96	20	.	.	PUNCT
fumecheng-7707	97	1	on	on	ADP
fumecheng-7707	97	2	the	the	DET
fumecheng-7707	97	3	other	other	ADJ
fumecheng-7707	97	4	hand	hand	NOUN
fumecheng-7707	97	5	,	,	PUNCT
fumecheng-7707	97	6	if	if	SCONJ
fumecheng-7707	97	7	the	the	DET
fumecheng-7707	97	8	given	give	VERB
fumecheng-7707	97	9	restrictions	restriction	NOUN
fumecheng-7707	97	10	are	be	AUX
fumecheng-7707	97	11	not	not	PART
fumecheng-7707	97	12	met	meet	VERB
fumecheng-7707	97	13	,	,	PUNCT
fumecheng-7707	97	14	a	a	DET
fumecheng-7707	97	15	matrix	matrix	NOUN
fumecheng-7707	97	16	-	-	PUNCT
fumecheng-7707	97	17	vector	vector	NOUN
fumecheng-7707	97	18	-	-	PUNCT
fumecheng-7707	97	19	multiplication	multiplication	NOUN
fumecheng-7707	97	20	based	base	VERB
fumecheng-7707	97	21	on	on	ADP
fumecheng-7707	97	22	the	the	DET
fumecheng-7707	97	23	less	less	ADV
fumecheng-7707	97	24	restrictive	restrictive	ADJ
fumecheng-7707	97	25	eq	eq	ADP
fumecheng-7707	97	26	.	.	PUNCT
fumecheng-7707	98	1	(	(	PUNCT
fumecheng-7707	98	2	12	12	NUM
fumecheng-7707	98	3	)	)	PUNCT
fumecheng-7707	98	4	will	will	AUX
fumecheng-7707	98	5	be	be	AUX
fumecheng-7707	98	6	preferable	preferable	ADJ
fumecheng-7707	98	7	.	.	PUNCT
fumecheng-7707	99	1	2.3	2.3	NUM
fumecheng-7707	99	2	.	.	PUNCT
fumecheng-7707	99	3	transformation	transformation	NOUN
fumecheng-7707	99	4	between	between	ADP
fumecheng-7707	99	5	line	line	NOUN
fumecheng-7707	99	6	loads	load	NOUN
fumecheng-7707	99	7	and	and	CCONJ
fumecheng-7707	99	8	stresses	stress	VERB
fumecheng-7707	99	9	the	the	DET
fumecheng-7707	99	10	line	line	NOUN
fumecheng-7707	99	11	loads	load	VERB
fumecheng-7707	99	12	in	in	ADP
fumecheng-7707	99	13	the	the	DET
fumecheng-7707	99	14	mdr	mdr	PROPN
fumecheng-7707	99	15	model	model	PROPN
fumecheng-7707	99	16	,	,	PUNCT
fumecheng-7707	99	17	q(x	q(x	PROPN
fumecheng-7707	99	18	)	)	PUNCT
fumecheng-7707	99	19	,	,	PUNCT
fumecheng-7707	99	20	and	and	CCONJ
fumecheng-7707	99	21	the	the	DET
fumecheng-7707	99	22	contact	contact	NOUN
fumecheng-7707	99	23	stresses	stress	VERB
fumecheng-7707	99	24	in	in	ADP
fumecheng-7707	99	25	the	the	DET
fumecheng-7707	99	26	axisymmetric	axisymmetric	ADJ
fumecheng-7707	99	27	original	original	NOUN
fumecheng-7707	99	28	,	,	PUNCT
fumecheng-7707	99	29	σ(r	σ(r	PROPN
fumecheng-7707	99	30	)	)	PUNCT
fumecheng-7707	99	31	,	,	PUNCT
fumecheng-7707	99	32	are	be	AUX
fumecheng-7707	99	33	connected	connect	VERB
fumecheng-7707	99	34	via	via	ADP
fumecheng-7707	99	35	the	the	DET
fumecheng-7707	99	36	abel	abel	PROPN
fumecheng-7707	99	37	inverse	inverse	NOUN
fumecheng-7707	99	38	transform	transform	NOUN
fumecheng-7707	99	39	[	[	X
fumecheng-7707	99	40	1	1	NUM
fumecheng-7707	99	41	]	]	SYM
fumecheng-7707	99	42	2	2	NUM
fumecheng-7707	99	43	2	2	NUM
fumecheng-7707	99	44	1	1	NUM
fumecheng-7707	99	45	(	(	PUNCT
fumecheng-7707	99	46	)	)	PUNCT
fumecheng-7707	100	1	(	(	PUNCT
fumecheng-7707	100	2	)	)	PUNCT
fumecheng-7707	100	3	d	d	X
fumecheng-7707	100	4	.	.	PUNCT
fumecheng-7707	101	1	a	a	DET
fumecheng-7707	101	2	r	r	NOUN
fumecheng-7707	101	3	q	q	NOUN
fumecheng-7707	101	4	x	x	NOUN
fumecheng-7707	101	5	r	r	NOUN
fumecheng-7707	101	6	x	x	NOUN
fumecheng-7707	101	7	x	x	SYM
fumecheng-7707	101	8	r	r	NOUN
fumecheng-7707	101	9			NOUN
fumecheng-7707	101	10	=	=	PUNCT
fumecheng-7707	102	1	−	−	PROPN
fumecheng-7707	102	2	−	−	PROPN
fumecheng-7707	102	3			ADP
fumecheng-7707	102	4			PROPN
fumecheng-7707	102	5	(	(	PUNCT
fumecheng-7707	102	6	14	14	NUM
fumecheng-7707	102	7	)	)	PUNCT
fumecheng-7707	102	8	note	note	NOUN
fumecheng-7707	102	9	that	that	SCONJ
fumecheng-7707	102	10	,	,	PUNCT
fumecheng-7707	102	11	once	once	ADV
fumecheng-7707	102	12	again	again	ADV
fumecheng-7707	102	13	,	,	PUNCT
fumecheng-7707	102	14	this	this	DET
fumecheng-7707	102	15	transform	transform	NOUN
fumecheng-7707	102	16	is	be	AUX
fumecheng-7707	102	17	valid	valid	ADJ
fumecheng-7707	102	18	for	for	ADP
fumecheng-7707	102	19	both	both	CCONJ
fumecheng-7707	102	20	the	the	DET
fumecheng-7707	102	21	normal	normal	ADJ
fumecheng-7707	102	22	and	and	CCONJ
fumecheng-7707	102	23	the	the	DET
fumecheng-7707	102	24	tangential	tangential	ADJ
fumecheng-7707	102	25	stresses	stress	NOUN
fumecheng-7707	102	26	or	or	CCONJ
fumecheng-7707	102	27	line	line	NOUN
fumecheng-7707	102	28	loads	load	NOUN
fumecheng-7707	102	29	.	.	PUNCT
fumecheng-7707	103	1	introducing	introduce	VERB
fumecheng-7707	103	2	the	the	DET
fumecheng-7707	103	3	usual	usual	ADJ
fumecheng-7707	103	4	substitutions	substitution	NOUN
fumecheng-7707	103	5	,	,	PUNCT
fumecheng-7707	103	6	ˆ	ˆ	PRON
fumecheng-7707	103	7	ˆ	ˆ	NOUN
fumecheng-7707	103	8	(	(	PUNCT
fumecheng-7707	103	9	)	)	PUNCT
fumecheng-7707	103	10	(	(	PUNCT
fumecheng-7707	103	11	)	)	PUNCT
fumecheng-7707	103	12	,	,	PUNCT
fumecheng-7707	103	13	(	(	PUNCT
fumecheng-7707	103	14	)	)	PUNCT
fumecheng-7707	103	15	(	(	PUNCT
fumecheng-7707	103	16	)	)	PUNCT
fumecheng-7707	103	17	,	,	PUNCT
fumecheng-7707	104	1	r	r	NOUN
fumecheng-7707	104	2	q	q	NOUN
fumecheng-7707	104	3	x	x	NOUN
fumecheng-7707	104	4	q=	q=	ADV
fumecheng-7707	104	5	=	=	NOUN
fumecheng-7707	104	6			X
fumecheng-7707	104	7			X
fumecheng-7707	104	8			X
fumecheng-7707	104	9			X
fumecheng-7707	104	10	(	(	PUNCT
fumecheng-7707	104	11	15	15	NUM
fumecheng-7707	104	12	)	)	PUNCT
fumecheng-7707	104	13	integrating	integrating	NOUN
fumecheng-7707	104	14	by	by	ADP
fumecheng-7707	104	15	parts	part	NOUN
fumecheng-7707	104	16	,	,	PUNCT
fumecheng-7707	104	17	2	2	NUM
fumecheng-7707	104	18	2	2	NUM
fumecheng-7707	104	19	2	2	NUM
fumecheng-7707	104	20	2ˆ1	2ˆ1	NUM
fumecheng-7707	104	21	(	(	PUNCT
fumecheng-7707	104	22	)	)	PUNCT
fumecheng-7707	104	23	2	2	NUM
fumecheng-7707	104	24	ˆ	ˆ	NOUN
fumecheng-7707	104	25	ˆ	ˆ	NOUN
fumecheng-7707	104	26	ˆ	ˆ	ADJ
fumecheng-7707	104	27	(	(	PUNCT
fumecheng-7707	104	28	)	)	PUNCT
fumecheng-7707	104	29	d	d	NOUN
fumecheng-7707	104	30	(	(	PUNCT
fumecheng-7707	104	31	)	)	PUNCT
fumecheng-7707	104	32	(	(	PUNCT
fumecheng-7707	104	33	)	)	PUNCT
fumecheng-7707	104	34	d	d	NOUN
fumecheng-7707	104	35	,	,	PUNCT
fumecheng-7707	104	36	a	a	DET
fumecheng-7707	104	37	a	a	DET
fumecheng-7707	104	38	q	q	NOUN
fumecheng-7707	104	39	a	a	DET
fumecheng-7707	104	40	q	q	NOUN
fumecheng-7707	104	41	a	a	DET
fumecheng-7707	104	42	q	q	X
fumecheng-7707	105	1			PROPN
fumecheng-7707	105	2			PROPN
fumecheng-7707	105	3			ADJ
fumecheng-7707	105	4	=	=	PROPN
fumecheng-7707	106	1	−	−	PROPN
fumecheng-7707	106	2	=	=	PUNCT
fumecheng-7707	107	1	−	−	PROPN
fumecheng-7707	107	2	−	−	PROPN
fumecheng-7707	108	1	+	+	CCONJ
fumecheng-7707	108	2	−	−	X
fumecheng-7707	108	3			ADJ
fumecheng-7707	108	4	−	−	NOUN
fumecheng-7707	108	5			NOUN
fumecheng-7707	108	6			PROPN
fumecheng-7707	108	7			PROPN
fumecheng-7707	108	8			X
fumecheng-7707	108	9			PUNCT
fumecheng-7707	108	10			ADP
fumecheng-7707	108	11			ADP
fumecheng-7707	108	12			X
fumecheng-7707	108	13			X
fumecheng-7707	108	14			ADP
fumecheng-7707	108	15			NOUN
fumecheng-7707	108	16			ADP
fumecheng-7707	108	17			NOUN
fumecheng-7707	108	18			VERB
fumecheng-7707	108	19			ADP
fumecheng-7707	108	20			NOUN
fumecheng-7707	108	21			X
fumecheng-7707	108	22			PUNCT
fumecheng-7707	108	23			X
fumecheng-7707	108	24	(	(	PUNCT
fumecheng-7707	108	25	16	16	NUM
fumecheng-7707	108	26	)	)	PUNCT
fumecheng-7707	108	27	and	and	CCONJ
fumecheng-7707	108	28	discretizing	discretize	VERB
fumecheng-7707	108	29	based	base	VERB
fumecheng-7707	108	30	on	on	ADP
fumecheng-7707	108	31	eq	eq	PROPN
fumecheng-7707	108	32	.	.	PUNCT
fumecheng-7707	109	1	(	(	PUNCT
fumecheng-7707	109	2	6	6	NUM
fumecheng-7707	109	3	)	)	PUNCT
fumecheng-7707	109	4	and	and	CCONJ
fumecheng-7707	109	5	the	the	DET
fumecheng-7707	109	6	trapezoidal	trapezoidal	ADJ
fumecheng-7707	109	7	rule	rule	NOUN
fumecheng-7707	109	8	,	,	PUNCT
fumecheng-7707	109	9	one	one	PRON
fumecheng-7707	109	10	obtains	obtain	VERB
fumecheng-7707	109	11	810	810	NUM
fumecheng-7707	109	12	e.	e.	PROPN
fumecheng-7707	109	13	willert	willert	PROPN
fumecheng-7707	109	14	2	2	NUM
fumecheng-7707	109	15	1	1	NUM
fumecheng-7707	109	16	3	3	NUM
fumecheng-7707	109	17	1	1	NUM
fumecheng-7707	109	18	2	2	NUM
fumecheng-7707	109	19	ˆ	ˆ	NOUN
fumecheng-7707	109	20	ˆ	ˆ	PROPN
fumecheng-7707	109	21	(	(	PUNCT
fumecheng-7707	109	22	)	)	PUNCT
fumecheng-7707	109	23	,	,	PUNCT
fumecheng-7707	109	24	1	1	NUM
fumecheng-7707	109	25	:	:	SYM
fumecheng-7707	109	26	1	1	NUM
fumecheng-7707	109	27	,	,	PUNCT
fumecheng-7707	109	28	(	(	PUNCT
fumecheng-7707	109	29	1	1	NUM
fumecheng-7707	109	30	)	)	PUNCT
fumecheng-7707	109	31	,	,	PUNCT
fumecheng-7707	109	32	1	1	NUM
fumecheng-7707	109	33	ˆ	ˆ	NOUN
fumecheng-7707	109	34	ˆ	ˆ	ADV
fumecheng-7707	109	35	.	.	PUNCT
fumecheng-7707	110	1	2	2	NUM
fumecheng-7707	110	2	j	j	PROPN
fumecheng-7707	110	3	j	j	PROPN
fumecheng-7707	111	1	j	j	PROPN
fumecheng-7707	112	1	i	i	PRON
fumecheng-7707	112	2	i	i	INTJ
fumecheng-7707	112	3	j	j	PROPN
fumecheng-7707	113	1	j	j	PROPN
fumecheng-7707	113	2	h	h	PROPN
fumecheng-7707	113	3	q	q	PROPN
fumecheng-7707	114	1	t	t	PROPN
fumecheng-7707	114	2	j	j	PROPN
fumecheng-7707	114	3	a	a	DET
fumecheng-7707	114	4	h	h	NOUN
fumecheng-7707	115	1	t	t	NOUN
fumecheng-7707	115	2	h	h	NOUN
fumecheng-7707	116	1	j	j	PROPN
fumecheng-7707	116	2	q	q	X
fumecheng-7707	116	3	q	q	X
fumecheng-7707	117	1	i	i	PRON
fumecheng-7707	117	2	j	j	NOUN
fumecheng-7707	118	1	−	−	PROPN
fumecheng-7707	118	2	=	=	SYM
fumecheng-7707	119	1	+	+	NUM
fumecheng-7707	119	2			PROPN
fumecheng-7707	119	3	=	=	NOUN
fumecheng-7707	119	4	−	−	NOUN
fumecheng-7707	119	5	−	−	PROPN
fumecheng-7707	120	1	+	+	CCONJ
fumecheng-7707	120	2	=	=	SYM
fumecheng-7707	120	3	−	−	PROPN
fumecheng-7707	120	4	=	=	PUNCT
fumecheng-7707	120	5	−	−	PROPN
fumecheng-7707	120	6			PROPN
fumecheng-7707	120	7			PROPN
fumecheng-7707	120	8			PROPN
fumecheng-7707	120	9			X
fumecheng-7707	120	10			PROPN
fumecheng-7707	120	11	=	=	PROPN
fumecheng-7707	120	12	−	−	PROPN
fumecheng-7707	121	1	+	+	CCONJ
fumecheng-7707	121	2	−	−	X
fumecheng-7707	121	3			PROPN
fumecheng-7707	121	4			NOUN
fumecheng-7707	121	5			PROPN
fumecheng-7707	121	6			X
fumecheng-7707	121	7			X
fumecheng-7707	121	8			X
fumecheng-7707	121	9			X
fumecheng-7707	121	10			PROPN
fumecheng-7707	121	11			X
fumecheng-7707	121	12			X
fumecheng-7707	121	13			X
fumecheng-7707	121	14			NOUN
fumecheng-7707	121	15			NOUN
fumecheng-7707	121	16	(	(	PUNCT
fumecheng-7707	121	17	17	17	NUM
fumecheng-7707	121	18	)	)	PUNCT
fumecheng-7707	121	19	the	the	DET
fumecheng-7707	121	20	remaining	remain	VERB
fumecheng-7707	121	21	sum	sum	NOUN
fumecheng-7707	121	22	will	will	AUX
fumecheng-7707	121	23	again	again	ADV
fumecheng-7707	121	24	be	be	AUX
fumecheng-7707	121	25	evaluated	evaluate	VERB
fumecheng-7707	121	26	with	with	ADP
fumecheng-7707	121	27	the	the	DET
fumecheng-7707	121	28	1d	1d	NUM
fumecheng-7707	121	29	-	-	PUNCT
fumecheng-7707	121	30	fft	fft	NOUN
fumecheng-7707	121	31	.	.	PUNCT
fumecheng-7707	122	1	in	in	ADP
fumecheng-7707	122	2	fig	fig	NOUN
fumecheng-7707	122	3	.	.	PUNCT
fumecheng-7707	123	1	2	2	NUM
fumecheng-7707	124	1	the	the	DET
fumecheng-7707	124	2	results	result	NOUN
fumecheng-7707	124	3	of	of	ADP
fumecheng-7707	124	4	a	a	DET
fumecheng-7707	124	5	convergence	convergence	NOUN
fumecheng-7707	124	6	study	study	NOUN
fumecheng-7707	124	7	for	for	ADP
fumecheng-7707	124	8	that	that	DET
fumecheng-7707	124	9	algorithm	algorithm	NOUN
fumecheng-7707	124	10	with	with	ADP
fumecheng-7707	124	11	an	an	DET
fumecheng-7707	124	12	analytical	analytical	ADJ
fumecheng-7707	124	13	solution	solution	NOUN
fumecheng-7707	124	14	,	,	PUNCT
fumecheng-7707	124	15	2	2	NUM
fumecheng-7707	124	16	2	2	NUM
fumecheng-7707	124	17	24	24	NUM
fumecheng-7707	124	18	ˆ	ˆ	NOUN
fumecheng-7707	124	19	ˆ	ˆ	PROPN
fumecheng-7707	124	20	(	(	PUNCT
fumecheng-7707	124	21	)	)	PUNCT
fumecheng-7707	124	22	,	,	PUNCT
fumecheng-7707	124	23	(	(	PUNCT
fumecheng-7707	124	24	)	)	PUNCT
fumecheng-7707	124	25	(	(	PUNCT
fumecheng-7707	124	26	2	2	X
fumecheng-7707	124	27	)	)	PUNCT
fumecheng-7707	124	28	3	3	NUM
fumecheng-7707	124	29	q	q	NOUN
fumecheng-7707	124	30	a	a	DET
fumecheng-7707	124	31	a=	a=	NOUN
fumecheng-7707	124	32	=	=	SYM
fumecheng-7707	124	33	−	−	NOUN
fumecheng-7707	124	34	−	−	PRON
fumecheng-7707	125	1	+	+	ADJ
fumecheng-7707	125	2			NOUN
fumecheng-7707	125	3			X
fumecheng-7707	125	4			X
fumecheng-7707	125	5			X
fumecheng-7707	125	6			X
fumecheng-7707	125	7			ADP
fumecheng-7707	125	8			PROPN
fumecheng-7707	125	9	(	(	PUNCT
fumecheng-7707	125	10	18	18	NUM
fumecheng-7707	125	11	)	)	PUNCT
fumecheng-7707	125	12	are	be	AUX
fumecheng-7707	125	13	given	give	VERB
fumecheng-7707	125	14	.	.	PUNCT
fumecheng-7707	126	1	the	the	DET
fumecheng-7707	126	2	mean	mean	ADJ
fumecheng-7707	126	3	relative	relative	ADJ
fumecheng-7707	126	4	error	error	NOUN
fumecheng-7707	126	5	(	(	PUNCT
fumecheng-7707	126	6	the	the	DET
fumecheng-7707	126	7	star	star	NOUN
fumecheng-7707	126	8	denotes	denote	VERB
fumecheng-7707	126	9	the	the	DET
fumecheng-7707	126	10	analytical	analytical	ADJ
fumecheng-7707	126	11	solution	solution	NOUN
fumecheng-7707	126	12	)	)	PUNCT
fumecheng-7707	126	13	*	*	PUNCT
fumecheng-7707	126	14	1	1	NUM
fumecheng-7707	126	15	*	*	SYM
fumecheng-7707	126	16	1	1	NUM
fumecheng-7707	126	17	ˆ	ˆ	PRON
fumecheng-7707	126	18	ˆ1	ˆ1	NOUN
fumecheng-7707	126	19	:	:	PUNCT
fumecheng-7707	126	20	ˆ1	ˆ1	NOUN
fumecheng-7707	126	21	j	j	PROPN
fumecheng-7707	126	22	j	j	PROPN
fumecheng-7707	126	23	j	j	PROPN
fumecheng-7707	126	24	j	j	PROPN
fumecheng-7707	126	25			X
fumecheng-7707	126	26			X
fumecheng-7707	126	27			X
fumecheng-7707	126	28			NOUN
fumecheng-7707	126	29			X
fumecheng-7707	126	30	−	−	PROPN
fumecheng-7707	126	31	=	=	SYM
fumecheng-7707	126	32	−	−	PROPN
fumecheng-7707	126	33			NOUN
fumecheng-7707	127	1	=	=	SYM
fumecheng-7707	127	2	−	−	NOUN
fumecheng-7707	127	3			X
fumecheng-7707	127	4	(	(	PUNCT
fumecheng-7707	127	5	19	19	NUM
fumecheng-7707	127	6	)	)	PUNCT
fumecheng-7707	127	7	is	be	AUX
fumecheng-7707	127	8	shown	show	VERB
fumecheng-7707	127	9	as	as	ADP
fumecheng-7707	127	10	a	a	DET
fumecheng-7707	127	11	function	function	NOUN
fumecheng-7707	127	12	of	of	ADP
fumecheng-7707	127	13	the	the	DET
fumecheng-7707	127	14	number	number	NOUN
fumecheng-7707	127	15	of	of	ADP
fumecheng-7707	127	16	elements	element	NOUN
fumecheng-7707	127	17	used	use	VERB
fumecheng-7707	127	18	for	for	ADP
fumecheng-7707	127	19	the	the	DET
fumecheng-7707	127	20	transformation	transformation	NOUN
fumecheng-7707	127	21	in	in	ADP
fumecheng-7707	127	22	doublelogarithmic	doublelogarithmic	ADJ
fumecheng-7707	127	23	scale	scale	NOUN
fumecheng-7707	127	24	.	.	PUNCT
fumecheng-7707	128	1	all	all	DET
fumecheng-7707	128	2	derivatives	derivative	NOUN
fumecheng-7707	128	3	were	be	AUX
fumecheng-7707	128	4	determined	determine	VERB
fumecheng-7707	128	5	by	by	ADP
fumecheng-7707	128	6	second	second	ADJ
fumecheng-7707	128	7	-	-	PUNCT
fumecheng-7707	128	8	order	order	NOUN
fumecheng-7707	128	9	finite	finite	NOUN
fumecheng-7707	128	10	differences	difference	NOUN
fumecheng-7707	128	11	.	.	PUNCT
fumecheng-7707	129	1	the	the	DET
fumecheng-7707	129	2	convergence	convergence	NOUN
fumecheng-7707	129	3	is	be	AUX
fumecheng-7707	129	4	obviously	obviously	ADV
fumecheng-7707	129	5	fast	fast	ADJ
fumecheng-7707	129	6	and	and	CCONJ
fumecheng-7707	129	7	stable	stable	ADJ
fumecheng-7707	129	8	.	.	PUNCT
fumecheng-7707	130	1	fig	fig	NOUN
fumecheng-7707	130	2	.	.	PUNCT
fumecheng-7707	131	1	2	2	NUM
fumecheng-7707	131	2	convergence	convergence	NOUN
fumecheng-7707	131	3	study	study	NOUN
fumecheng-7707	131	4	for	for	ADP
fumecheng-7707	131	5	the	the	DET
fumecheng-7707	131	6	mean	mean	ADJ
fumecheng-7707	131	7	relative	relative	ADJ
fumecheng-7707	131	8	error	error	NOUN
fumecheng-7707	131	9	depending	depend	VERB
fumecheng-7707	131	10	on	on	ADP
fumecheng-7707	131	11	the	the	DET
fumecheng-7707	131	12	number	number	NOUN
fumecheng-7707	131	13	of	of	ADP
fumecheng-7707	131	14	array	array	NOUN
fumecheng-7707	131	15	elements	element	NOUN
fumecheng-7707	131	16	for	for	ADP
fumecheng-7707	131	17	the	the	DET
fumecheng-7707	131	18	fft	fft	NOUN
fumecheng-7707	131	19	-	-	PUNCT
fumecheng-7707	131	20	based	base	VERB
fumecheng-7707	131	21	implementation	implementation	NOUN
fumecheng-7707	131	22	of	of	ADP
fumecheng-7707	131	23	the	the	DET
fumecheng-7707	131	24	discrete	discrete	ADJ
fumecheng-7707	131	25	transform	transform	NOUN
fumecheng-7707	131	26	(	(	PUNCT
fumecheng-7707	131	27	17	17	NUM
fumecheng-7707	131	28	)	)	PUNCT
fumecheng-7707	131	29	.	.	PUNCT
fumecheng-7707	132	1	3	3	X
fumecheng-7707	132	2	.	.	X
fumecheng-7707	132	3	transformations	transformation	NOUN
fumecheng-7707	132	4	for	for	ADP
fumecheng-7707	132	5	power	power	NOUN
fumecheng-7707	132	6	-	-	PUNCT
fumecheng-7707	132	7	law	law	NOUN
fumecheng-7707	132	8	graded	grade	VERB
fumecheng-7707	132	9	materials	material	NOUN
fumecheng-7707	132	10	in	in	ADP
fumecheng-7707	132	11	this	this	DET
fumecheng-7707	132	12	section	section	NOUN
fumecheng-7707	132	13	the	the	DET
fumecheng-7707	132	14	convolution	convolution	NOUN
fumecheng-7707	132	15	formulation	formulation	NOUN
fumecheng-7707	132	16	of	of	ADP
fumecheng-7707	132	17	the	the	DET
fumecheng-7707	132	18	relevant	relevant	ADJ
fumecheng-7707	132	19	transformations	transformation	NOUN
fumecheng-7707	132	20	is	be	AUX
fumecheng-7707	132	21	shown	show	VERB
fumecheng-7707	132	22	for	for	ADP
fumecheng-7707	132	23	power	power	NOUN
fumecheng-7707	132	24	-	-	PUNCT
fumecheng-7707	132	25	law	law	NOUN
fumecheng-7707	132	26	graded	grade	VERB
fumecheng-7707	132	27	materials	material	NOUN
fumecheng-7707	132	28	.	.	PUNCT
fumecheng-7707	133	1	naturally	naturally	ADV
fumecheng-7707	133	2	,	,	PUNCT
fumecheng-7707	133	3	all	all	DET
fumecheng-7707	133	4	previous	previous	ADJ
fumecheng-7707	133	5	results	result	NOUN
fumecheng-7707	133	6	for	for	ADP
fumecheng-7707	133	7	homogeneous	homogeneous	ADJ
fumecheng-7707	133	8	media	medium	NOUN
fumecheng-7707	133	9	are	be	AUX
fumecheng-7707	133	10	recovered	recover	VERB
fumecheng-7707	133	11	,	,	PUNCT
fumecheng-7707	133	12	if	if	SCONJ
fumecheng-7707	133	13	the	the	DET
fumecheng-7707	133	14	exponent	exponent	NOUN
fumecheng-7707	133	15	k	k	PROPN
fumecheng-7707	133	16	of	of	ADP
fumecheng-7707	133	17	the	the	DET
fumecheng-7707	133	18	power	power	NOUN
fumecheng-7707	133	19	-	-	PUNCT
fumecheng-7707	133	20	law	law	NOUN
fumecheng-7707	133	21	of	of	ADP
fumecheng-7707	133	22	the	the	DET
fumecheng-7707	133	23	elastic	elastic	ADJ
fumecheng-7707	133	24	grading	grading	NOUN
fumecheng-7707	133	25	equals	equal	VERB
fumecheng-7707	133	26	zero	zero	NUM
fumecheng-7707	133	27	.	.	PUNCT
fumecheng-7707	134	1	fft	fft	NOUN
fumecheng-7707	134	2	-	-	PUNCT
fumecheng-7707	134	3	based	base	VERB
fumecheng-7707	134	4	implementation	implementation	NOUN
fumecheng-7707	134	5	of	of	ADP
fumecheng-7707	134	6	the	the	DET
fumecheng-7707	134	7	mdr	mdr	PROPN
fumecheng-7707	134	8	transformations	transformation	NOUN
fumecheng-7707	134	9	for	for	ADP
fumecheng-7707	134	10	homogeneous	homogeneous	ADJ
fumecheng-7707	134	11	and	and	CCONJ
fumecheng-7707	134	12	power	power	NOUN
fumecheng-7707	134	13	-	-	PUNCT
fumecheng-7707	134	14	law	law	NOUN
fumecheng-7707	134	15	graded	grade	VERB
fumecheng-7707	134	16	materials811	materials811	PROPN
fumecheng-7707	134	17	3.1	3.1	NUM
fumecheng-7707	134	18	.	.	PUNCT
fumecheng-7707	135	1	profile	profile	NOUN
fumecheng-7707	135	2	transformation	transformation	NOUN
fumecheng-7707	135	3	for	for	ADP
fumecheng-7707	135	4	inhomogeneous	inhomogeneous	ADJ
fumecheng-7707	135	5	materials	material	NOUN
fumecheng-7707	135	6	with	with	ADP
fumecheng-7707	135	7	an	an	DET
fumecheng-7707	135	8	elastic	elastic	ADJ
fumecheng-7707	135	9	grading	grading	NOUN
fumecheng-7707	135	10	in	in	ADP
fumecheng-7707	135	11	the	the	DET
fumecheng-7707	135	12	form	form	NOUN
fumecheng-7707	135	13	of	of	ADP
fumecheng-7707	135	14	a	a	DET
fumecheng-7707	135	15	power	power	NOUN
fumecheng-7707	135	16	-	-	PUNCT
fumecheng-7707	135	17	law	law	NOUN
fumecheng-7707	135	18	the	the	DET
fumecheng-7707	135	19	profile	profile	ADJ
fumecheng-7707	135	20	transformation	transformation	NOUN
fumecheng-7707	135	21	between	between	ADP
fumecheng-7707	135	22	the	the	DET
fumecheng-7707	135	23	axisymmetric	axisymmetric	ADJ
fumecheng-7707	135	24	profile	profile	NOUN
fumecheng-7707	135	25	f	f	PROPN
fumecheng-7707	135	26	and	and	CCONJ
fumecheng-7707	135	27	the	the	DET
fumecheng-7707	135	28	profile	profile	NOUN
fumecheng-7707	135	29	g	g	NOUN
fumecheng-7707	135	30	reads	read	VERB
fumecheng-7707	135	31	[	[	X
fumecheng-7707	135	32	1	1	NUM
fumecheng-7707	135	33	]	]	SYM
fumecheng-7707	135	34	1	1	NUM
fumecheng-7707	135	35	2	2	NUM
fumecheng-7707	135	36	2	2	NUM
fumecheng-7707	135	37	1	1	NUM
fumecheng-7707	135	38	2	2	NUM
fumecheng-7707	135	39	2	2	NUM
fumecheng-7707	135	40	1	1	NUM
fumecheng-7707	135	41	0	0	NUM
fumecheng-7707	135	42	0	0	NUM
fumecheng-7707	135	43	(	(	PUNCT
fumecheng-7707	135	44	)	)	PUNCT
fumecheng-7707	135	45	d	d	SYM
fumecheng-7707	135	46	d	d	PROPN
fumecheng-7707	135	47	(	(	PUNCT
fumecheng-7707	135	48	)	)	PUNCT
fumecheng-7707	135	49	,	,	PUNCT
fumecheng-7707	135	50	(	(	PUNCT
fumecheng-7707	135	51	)	)	PUNCT
fumecheng-7707	135	52	:	:	PUNCT
fumecheng-7707	135	53	(	(	PUNCT
fumecheng-7707	135	54	)	)	PUNCT
fumecheng-7707	136	1	(	(	PUNCT
fumecheng-7707	136	2	)	)	PUNCT
fumecheng-7707	136	3	d	d	NOUN
fumecheng-7707	136	4	.	.	PUNCT
fumecheng-7707	137	1	1	1	NUM
fumecheng-7707	137	2	d	d	NOUN
fumecheng-7707	137	3	(	(	PUNCT
fumecheng-7707	137	4	)	)	PUNCT
fumecheng-7707	137	5	x	x	PROPN
fumecheng-7707	137	6	xk	xk	PROPN
fumecheng-7707	138	1	k	k	PROPN
fumecheng-7707	138	2	k	k	PROPN
fumecheng-7707	139	1	k	k	PROPN
fumecheng-7707	139	2	f	f	NOUN
fumecheng-7707	139	3	r	r	NOUN
fumecheng-7707	139	4	r	r	NOUN
fumecheng-7707	139	5	x	x	PUNCT
fumecheng-7707	139	6	g	g	NOUN
fumecheng-7707	139	7	g	g	NOUN
fumecheng-7707	139	8	x	x	X
fumecheng-7707	139	9	x	x	X
fumecheng-7707	139	10	g	g	NOUN
fumecheng-7707	139	11	x	x	X
fumecheng-7707	139	12	f	f	NOUN
fumecheng-7707	139	13	r	r	NOUN
fumecheng-7707	139	14	x	x	SYM
fumecheng-7707	139	15	r	r	NOUN
fumecheng-7707	139	16	r	r	NOUN
fumecheng-7707	139	17	k	k	NOUN
fumecheng-7707	140	1	xx	xx	NUM
fumecheng-7707	140	2	r	r	NOUN
fumecheng-7707	140	3	−	−	NOUN
fumecheng-7707	140	4	−	−	PROPN
fumecheng-7707	141	1	+	+	CCONJ
fumecheng-7707	141	2	−	−	PROPN
fumecheng-7707	141	3			ADJ
fumecheng-7707	141	4	=	=	PROPN
fumecheng-7707	141	5	=	=	PUNCT
fumecheng-7707	142	1	=	=	PUNCT
fumecheng-7707	143	1	−	−	PROPN
fumecheng-7707	144	1	+	+	NOUN
fumecheng-7707	144	2	−	−	NOUN
fumecheng-7707	144	3			NOUN
fumecheng-7707	144	4			X
fumecheng-7707	144	5	(	(	PUNCT
fumecheng-7707	144	6	20	20	X
fumecheng-7707	144	7	)	)	PUNCT
fumecheng-7707	144	8	introducing	introduce	VERB
fumecheng-7707	144	9	the	the	DET
fumecheng-7707	144	10	same	same	ADJ
fumecheng-7707	144	11	substitutions	substitution	NOUN
fumecheng-7707	144	12	as	as	ADP
fumecheng-7707	144	13	in	in	ADP
fumecheng-7707	144	14	eq	eq	NOUN
fumecheng-7707	144	15	.	.	PUNCT
fumecheng-7707	145	1	(	(	PUNCT
fumecheng-7707	145	2	3	3	X
fumecheng-7707	145	3	)	)	PUNCT
fumecheng-7707	145	4	we	we	PRON
fumecheng-7707	145	5	obtain	obtain	VERB
fumecheng-7707	145	6	1	1	NUM
fumecheng-7707	145	7	0	0	NUM
fumecheng-7707	145	8	ˆˆ	ˆˆ	PROPN
fumecheng-7707	145	9	(	(	PUNCT
fumecheng-7707	145	10	)	)	PUNCT
fumecheng-7707	145	11	(	(	PUNCT
fumecheng-7707	145	12	)	)	PUNCT
fumecheng-7707	146	1	(	(	PUNCT
fumecheng-7707	146	2	)	)	PUNCT
fumecheng-7707	146	3	d	d	INTJ
fumecheng-7707	146	4	,	,	PUNCT
fumecheng-7707	146	5	kg	kg	INTJ
fumecheng-7707	146	6	f	f	PROPN
fumecheng-7707	147	1	+	+	ADJ
fumecheng-7707	147	2	=	=	ADJ
fumecheng-7707	147	3	−	−	NOUN
fumecheng-7707	147	4			NOUN
fumecheng-7707	147	5			VERB
fumecheng-7707	147	6			ADP
fumecheng-7707	147	7			NOUN
fumecheng-7707	147	8			X
fumecheng-7707	147	9			X
fumecheng-7707	147	10	(	(	PUNCT
fumecheng-7707	147	11	21	21	NUM
fumecheng-7707	147	12	)	)	PUNCT
fumecheng-7707	147	13	and	and	CCONJ
fumecheng-7707	147	14	1	1	NUM
fumecheng-7707	147	15	ˆ2	ˆ2	PROPN
fumecheng-7707	147	16	d	d	NOUN
fumecheng-7707	147	17	ˆ	ˆ	PROPN
fumecheng-7707	147	18	(	(	PUNCT
fumecheng-7707	147	19	)	)	PUNCT
fumecheng-7707	147	20	(	(	PUNCT
fumecheng-7707	147	21	)	)	PUNCT
fumecheng-7707	147	22	.	.	PUNCT
fumecheng-7707	148	1	1	1	NUM
fumecheng-7707	148	2	d	d	NOUN
fumecheng-7707	148	3	kg	kg	NOUN
fumecheng-7707	148	4	g	g	NOUN
fumecheng-7707	148	5	x	x	SYM
fumecheng-7707	148	6	g	g	PROPN
fumecheng-7707	148	7	k	k	PROPN
fumecheng-7707	148	8	−=	−=	PROPN
fumecheng-7707	148	9	=	=	SYM
fumecheng-7707	149	1	+	+	NUM
fumecheng-7707	149	2			NOUN
fumecheng-7707	149	3			NOUN
fumecheng-7707	149	4			X
fumecheng-7707	149	5	(	(	PUNCT
fumecheng-7707	149	6	22	22	NUM
fumecheng-7707	149	7	)	)	PUNCT
fumecheng-7707	149	8	with	with	ADP
fumecheng-7707	149	9	the	the	DET
fumecheng-7707	149	10	same	same	ADJ
fumecheng-7707	149	11	discretization	discretization	NOUN
fumecheng-7707	149	12	as	as	ADP
fumecheng-7707	149	13	in	in	ADP
fumecheng-7707	149	14	eq	eq	ADP
fumecheng-7707	149	15	.	.	PUNCT
fumecheng-7707	150	1	(	(	PUNCT
fumecheng-7707	150	2	6	6	NUM
fumecheng-7707	150	3	)	)	PUNCT
fumecheng-7707	150	4	and	and	CCONJ
fumecheng-7707	150	5	the	the	DET
fumecheng-7707	150	6	trapezoidal	trapezoidal	ADJ
fumecheng-7707	150	7	rule	rule	NOUN
fumecheng-7707	150	8	we	we	PRON
fumecheng-7707	150	9	finally	finally	ADV
fumecheng-7707	150	10	arrive	arrive	VERB
fumecheng-7707	150	11	at	at	ADP
fumecheng-7707	150	12	1	1	NUM
fumecheng-7707	150	13	3	3	NUM
fumecheng-7707	150	14	1	1	NUM
fumecheng-7707	150	15	1	1	NUM
fumecheng-7707	150	16	1	1	NUM
fumecheng-7707	150	17	2	2	NUM
fumecheng-7707	150	18	1	1	NUM
fumecheng-7707	150	19	ˆ	ˆ	NOUN
fumecheng-7707	150	20	ˆˆ	ˆˆ	PROPN
fumecheng-7707	150	21	(	(	PUNCT
fumecheng-7707	150	22	1	1	NUM
fumecheng-7707	150	23	)	)	PUNCT
fumecheng-7707	150	24	(	(	PUNCT
fumecheng-7707	150	25	)	)	PUNCT
fumecheng-7707	150	26	,	,	PUNCT
fumecheng-7707	151	1	2	2	NUM
fumecheng-7707	151	2	i	i	NOUN
fumecheng-7707	151	3	k	k	PROPN
fumecheng-7707	152	1	k	k	PROPN
fumecheng-7707	153	1	k	k	PROPN
fumecheng-7707	154	1	i	i	PRON
fumecheng-7707	154	2	j	j	PROPN
fumecheng-7707	155	1	j	j	PROPN
fumecheng-7707	155	2	g	g	PROPN
fumecheng-7707	155	3	h	h	PROPN
fumecheng-7707	156	1	f	f	PROPN
fumecheng-7707	157	1	i	i	PRON
fumecheng-7707	157	2	f	f	VERB
fumecheng-7707	158	1	i	i	PRON
fumecheng-7707	158	2	j	j	PROPN
fumecheng-7707	159	1	−	−	PROPN
fumecheng-7707	160	1	+	+	CCONJ
fumecheng-7707	160	2	+	+	PUNCT
fumecheng-7707	160	3	+	+	CCONJ
fumecheng-7707	160	4	=	=	SYM
fumecheng-7707	160	5			ADJ
fumecheng-7707	160	6			NOUN
fumecheng-7707	160	7			ADJ
fumecheng-7707	160	8	=	=	INTJ
fumecheng-7707	160	9	−	−	PROPN
fumecheng-7707	161	1	+	+	CCONJ
fumecheng-7707	161	2	−	−	X
fumecheng-7707	161	3			PROPN
fumecheng-7707	161	4			PROPN
fumecheng-7707	161	5			PROPN
fumecheng-7707	161	6			X
fumecheng-7707	161	7	(	(	PUNCT
fumecheng-7707	161	8	23	23	NUM
fumecheng-7707	161	9	)	)	PUNCT
fumecheng-7707	161	10	the	the	DET
fumecheng-7707	161	11	sum	sum	NOUN
fumecheng-7707	161	12	contribution	contribution	NOUN
fumecheng-7707	161	13	of	of	ADP
fumecheng-7707	161	14	which	which	PRON
fumecheng-7707	161	15	is	be	AUX
fumecheng-7707	161	16	a	a	DET
fumecheng-7707	161	17	discrete	discrete	ADJ
fumecheng-7707	161	18	convolution	convolution	NOUN
fumecheng-7707	161	19	,	,	PUNCT
fumecheng-7707	161	20	which	which	PRON
fumecheng-7707	161	21	once	once	ADV
fumecheng-7707	161	22	again	again	ADV
fumecheng-7707	161	23	can	can	AUX
fumecheng-7707	161	24	be	be	AUX
fumecheng-7707	161	25	efficiently	efficiently	ADV
fumecheng-7707	161	26	evaluated	evaluate	VERB
fumecheng-7707	161	27	with	with	ADP
fumecheng-7707	161	28	the	the	DET
fumecheng-7707	161	29	1d	1d	NUM
fumecheng-7707	161	30	-	-	PUNCT
fumecheng-7707	161	31	fft	fft	NOUN
fumecheng-7707	161	32	.	.	PROPN
fumecheng-7707	161	33	3.2	3.2	NUM
fumecheng-7707	161	34	.	.	PUNCT
fumecheng-7707	162	1	transformation	transformation	NOUN
fumecheng-7707	162	2	of	of	ADP
fumecheng-7707	162	3	local	local	ADJ
fumecheng-7707	162	4	displacements	displacement	NOUN
fumecheng-7707	162	5	the	the	DET
fumecheng-7707	162	6	transformation	transformation	NOUN
fumecheng-7707	162	7	rule	rule	NOUN
fumecheng-7707	162	8	for	for	ADP
fumecheng-7707	162	9	the	the	DET
fumecheng-7707	162	10	local	local	ADJ
fumecheng-7707	162	11	displacements	displacement	NOUN
fumecheng-7707	162	12	in	in	ADP
fumecheng-7707	162	13	the	the	DET
fumecheng-7707	162	14	mdr	mdr	PROPN
fumecheng-7707	162	15	model	model	NOUN
fumecheng-7707	162	16	and	and	CCONJ
fumecheng-7707	162	17	the	the	DET
fumecheng-7707	162	18	original	original	ADJ
fumecheng-7707	162	19	axisymmetric	axisymmetric	ADJ
fumecheng-7707	162	20	system	system	NOUN
fumecheng-7707	162	21	in	in	ADP
fumecheng-7707	162	22	the	the	DET
fumecheng-7707	162	23	case	case	NOUN
fumecheng-7707	162	24	of	of	ADP
fumecheng-7707	162	25	power	power	NOUN
fumecheng-7707	162	26	-	-	PUNCT
fumecheng-7707	162	27	law	law	NOUN
fumecheng-7707	162	28	graded	grade	VERB
fumecheng-7707	162	29	materials	material	NOUN
fumecheng-7707	162	30	is	be	AUX
fumecheng-7707	162	31	given	give	VERB
fumecheng-7707	162	32	by	by	ADP
fumecheng-7707	162	33	[	[	X
fumecheng-7707	162	34	1	1	NUM
fumecheng-7707	162	35	]	]	SYM
fumecheng-7707	162	36	2	2	NUM
fumecheng-7707	162	37	2	2	NUM
fumecheng-7707	162	38	1	1	NUM
fumecheng-7707	162	39	0	0	NUM
fumecheng-7707	162	40	2	2	NUM
fumecheng-7707	162	41	(	(	PUNCT
fumecheng-7707	162	42	)	)	PUNCT
fumecheng-7707	162	43	(	(	PUNCT
fumecheng-7707	162	44	)	)	PUNCT
fumecheng-7707	162	45	cos	cos	PROPN
fumecheng-7707	163	1	d	d	PROPN
fumecheng-7707	163	2	.	.	PROPN
fumecheng-7707	163	3	2	2	NUM
fumecheng-7707	163	4	(	(	PUNCT
fumecheng-7707	163	5	)	)	PUNCT
fumecheng-7707	164	1	r	r	NOUN
fumecheng-7707	164	2	k	k	PROPN
fumecheng-7707	165	1	k	k	PROPN
fumecheng-7707	165	2	k	k	X
fumecheng-7707	165	3	x	x	PUNCT
fumecheng-7707	165	4	u	u	NOUN
fumecheng-7707	165	5	x	x	X
fumecheng-7707	165	6	u	u	NOUN
fumecheng-7707	165	7	r	r	NOUN
fumecheng-7707	165	8	x	x	NOUN
fumecheng-7707	165	9	r	r	NOUN
fumecheng-7707	165	10	x	x	NOUN
fumecheng-7707	165	11	+	+	NUM
fumecheng-7707	165	12			NOUN
fumecheng-7707	165	13			NOUN
fumecheng-7707	165	14	=	=	SYM
fumecheng-7707	165	15			PROPN
fumecheng-7707	165	16			PROPN
fumecheng-7707	166	1			PROPN
fumecheng-7707	166	2			NOUN
fumecheng-7707	166	3	−	−	NUM
fumecheng-7707	166	4			SYM
fumecheng-7707	166	5			PROPN
fumecheng-7707	166	6			PROPN
fumecheng-7707	166	7	(	(	PUNCT
fumecheng-7707	166	8	24	24	NUM
fumecheng-7707	166	9	)	)	PUNCT
fumecheng-7707	166	10	note	note	NOUN
fumecheng-7707	166	11	that	that	SCONJ
fumecheng-7707	166	12	,	,	PUNCT
fumecheng-7707	166	13	once	once	ADV
fumecheng-7707	166	14	again	again	ADV
fumecheng-7707	166	15	,	,	PUNCT
fumecheng-7707	166	16	this	this	PRON
fumecheng-7707	166	17	formally	formally	ADV
fumecheng-7707	166	18	is	be	AUX
fumecheng-7707	166	19	also	also	ADV
fumecheng-7707	166	20	the	the	DET
fumecheng-7707	166	21	inverse	inverse	NOUN
fumecheng-7707	166	22	transform	transform	NOUN
fumecheng-7707	166	23	of	of	ADP
fumecheng-7707	166	24	eq	eq	NOUN
fumecheng-7707	166	25	.	.	PUNCT
fumecheng-7707	167	1	(	(	PUNCT
fumecheng-7707	167	2	20	20	NUM
fumecheng-7707	167	3	)	)	PUNCT
fumecheng-7707	167	4	to	to	PART
fumecheng-7707	167	5	obtain	obtain	VERB
fumecheng-7707	167	6	the	the	DET
fumecheng-7707	167	7	axisymmetric	axisymmetric	ADJ
fumecheng-7707	167	8	profile	profile	NOUN
fumecheng-7707	168	1	f	f	PROPN
fumecheng-7707	168	2	from	from	ADP
fumecheng-7707	168	3	the	the	DET
fumecheng-7707	168	4	profile	profile	NOUN
fumecheng-7707	168	5	g.	g.	NOUN
fumecheng-7707	168	6	with	with	ADP
fumecheng-7707	168	7	the	the	DET
fumecheng-7707	168	8	same	same	ADJ
fumecheng-7707	168	9	procedure	procedure	NOUN
fumecheng-7707	168	10	as	as	ADP
fumecheng-7707	168	11	in	in	ADP
fumecheng-7707	168	12	subsection	subsection	NOUN
fumecheng-7707	168	13	2.2	2.2	NUM
fumecheng-7707	168	14	we	we	PRON
fumecheng-7707	168	15	obtain	obtain	VERB
fumecheng-7707	168	16	two	two	NUM
fumecheng-7707	168	17	different	different	ADJ
fumecheng-7707	168	18	possible	possible	ADJ
fumecheng-7707	168	19	formulations	formulation	NOUN
fumecheng-7707	168	20	after	after	ADP
fumecheng-7707	168	21	integrating	integrate	VERB
fumecheng-7707	168	22	by	by	ADP
fumecheng-7707	168	23	parts	part	NOUN
fumecheng-7707	168	24	.	.	PUNCT
fumecheng-7707	169	1	the	the	DET
fumecheng-7707	169	2	generalization	generalization	NOUN
fumecheng-7707	169	3	of	of	ADP
fumecheng-7707	169	4	eq	eq	PROPN
fumecheng-7707	169	5	.	.	PUNCT
fumecheng-7707	170	1	(	(	PUNCT
fumecheng-7707	170	2	12	12	NUM
fumecheng-7707	170	3	)	)	PUNCT
fumecheng-7707	170	4	is	be	AUX
fumecheng-7707	170	5	given	give	VERB
fumecheng-7707	170	6	by	by	ADP
fumecheng-7707	170	7	(	(	PUNCT
fumecheng-7707	170	8	)	)	PUNCT
fumecheng-7707	170	9	0	0	NUM
fumecheng-7707	170	10	1	1	NUM
fumecheng-7707	170	11	2	2	NUM
fumecheng-7707	170	12	1	1	NUM
fumecheng-7707	170	13	2ˆ	2ˆ	NUM
fumecheng-7707	170	14	ˆˆ	ˆˆ	PROPN
fumecheng-7707	170	15	(	(	PUNCT
fumecheng-7707	170	16	)	)	PUNCT
fumecheng-7707	170	17	(	(	PUNCT
fumecheng-7707	170	18	0	0	NUM
fumecheng-7707	170	19	)	)	PUNCT
fumecheng-7707	170	20	(	(	PUNCT
fumecheng-7707	170	21	)	)	PUNCT
fumecheng-7707	170	22	cos	cos	PROPN
fumecheng-7707	170	23	;	;	PUNCT
fumecheng-7707	170	24	d	d	X
fumecheng-7707	170	25	,	,	PUNCT
fumecheng-7707	170	26	2	2	NUM
fumecheng-7707	170	27	1	1	NUM
fumecheng-7707	170	28	1	1	NUM
fumecheng-7707	170	29	1	1	NUM
fumecheng-7707	170	30	3	3	NUM
fumecheng-7707	170	31	(	(	PUNCT
fumecheng-7707	170	32	;	;	PUNCT
fumecheng-7707	170	33	)	)	PUNCT
fumecheng-7707	170	34	:	:	PUNCT
fumecheng-7707	170	35	,	,	PUNCT
fumecheng-7707	170	36	;	;	PUNCT
fumecheng-7707	170	37	;	;	PUNCT
fumecheng-7707	170	38	,	,	PUNCT
fumecheng-7707	170	39	1	1	NUM
fumecheng-7707	170	40	2	2	NUM
fumecheng-7707	170	41	2	2	NUM
fumecheng-7707	170	42	2	2	NUM
fumecheng-7707	170	43	k	k	NOUN
fumecheng-7707	170	44	k	k	X
fumecheng-7707	170	45	u	u	PUNCT
fumecheng-7707	170	46	u	u	VERB
fumecheng-7707	170	47	u	u	NOUN
fumecheng-7707	170	48	u	u	NOUN
fumecheng-7707	170	49	h	h	NOUN
fumecheng-7707	171	1	k	k	PROPN
fumecheng-7707	171	2	k	k	PROPN
fumecheng-7707	172	1	k	k	PROPN
fumecheng-7707	172	2	k	k	PROPN
fumecheng-7707	173	1	h	h	NOUN
fumecheng-7707	174	1	y	y	PROPN
fumecheng-7707	174	2	k	k	PROPN
fumecheng-7707	175	1	y	y	PROPN
fumecheng-7707	175	2	f	f	PROPN
fumecheng-7707	175	3	y	y	PROPN
fumecheng-7707	175	4	k	k	PROPN
fumecheng-7707	176	1	+	+	CCONJ
fumecheng-7707	176	2			NOUN
fumecheng-7707	176	3			PROPN
fumecheng-7707	176	4			PROPN
fumecheng-7707	176	5	=	=	PROPN
fumecheng-7707	177	1	+	+	CCONJ
fumecheng-7707	177	2	−	−	PROPN
fumecheng-7707	177	3			PROPN
fumecheng-7707	177	4			NOUN
fumecheng-7707	177	5			PROPN
fumecheng-7707	178	1			ADJ
fumecheng-7707	178	2			PROPN
fumecheng-7707	178	3			PROPN
fumecheng-7707	178	4			NOUN
fumecheng-7707	178	5	+	+	PUNCT
fumecheng-7707	179	1	+	+	PUNCT
fumecheng-7707	179	2	+	+	ADJ
fumecheng-7707	179	3			NOUN
fumecheng-7707	179	4			NOUN
fumecheng-7707	179	5	=	=	SYM
fumecheng-7707	179	6			PROPN
fumecheng-7707	179	7			PROPN
fumecheng-7707	180	1	+	+	CCONJ
fumecheng-7707	180	2			PROPN
fumecheng-7707	180	3			NOUN
fumecheng-7707	180	4			PUNCT
fumecheng-7707	180	5			ADP
fumecheng-7707	180	6			ADJ
fumecheng-7707	180	7			NOUN
fumecheng-7707	180	8			ADP
fumecheng-7707	180	9			ADP
fumecheng-7707	180	10			NOUN
fumecheng-7707	180	11			X
fumecheng-7707	180	12			X
fumecheng-7707	180	13			X
fumecheng-7707	180	14	(	(	PUNCT
fumecheng-7707	180	15	25	25	NUM
fumecheng-7707	180	16	)	)	PUNCT
fumecheng-7707	180	17	with	with	ADP
fumecheng-7707	180	18	the	the	DET
fumecheng-7707	180	19	hypergeometric	hypergeometric	ADJ
fumecheng-7707	180	20	function	function	NOUN
fumecheng-7707	180	21	2f1	2f1	NUM
fumecheng-7707	180	22	.	.	PUNCT
fumecheng-7707	181	1	the	the	DET
fumecheng-7707	181	2	alternative	alternative	ADJ
fumecheng-7707	181	3	,	,	PUNCT
fumecheng-7707	181	4	more	more	ADV
fumecheng-7707	181	5	restrictive	restrictive	ADJ
fumecheng-7707	181	6	formulation	formulation	NOUN
fumecheng-7707	181	7	,	,	PUNCT
fumecheng-7707	181	8	which	which	PRON
fumecheng-7707	181	9	on	on	ADP
fumecheng-7707	181	10	the	the	DET
fumecheng-7707	181	11	other	other	ADJ
fumecheng-7707	181	12	hand	hand	NOUN
fumecheng-7707	181	13	includes	include	VERB
fumecheng-7707	181	14	an	an	DET
fumecheng-7707	181	15	explicit	explicit	ADJ
fumecheng-7707	181	16	convolution	convolution	NOUN
fumecheng-7707	181	17	,	,	PUNCT
fumecheng-7707	181	18	i.e.	i.e.	X
fumecheng-7707	181	19	,	,	PUNCT
fumecheng-7707	181	20	the	the	DET
fumecheng-7707	181	21	generalization	generalization	NOUN
fumecheng-7707	181	22	of	of	ADP
fumecheng-7707	181	23	eq	eq	PROPN
fumecheng-7707	181	24	.	.	PUNCT
fumecheng-7707	181	25	(	(	PUNCT
fumecheng-7707	181	26	13	13	NUM
fumecheng-7707	181	27	)	)	PUNCT
fumecheng-7707	181	28	,	,	PUNCT
fumecheng-7707	181	29	reads	read	VERB
fumecheng-7707	181	30	812	812	NUM
fumecheng-7707	181	31	e.	e.	PROPN
fumecheng-7707	181	32	willert	willert	PROPN
fumecheng-7707	181	33	1	1	NUM
fumecheng-7707	181	34	1	1	NUM
fumecheng-7707	181	35	10	10	NUM
fumecheng-7707	181	36	0	0	NUM
fumecheng-7707	181	37	1	1	NUM
fumecheng-7707	181	38	2	2	NUM
fumecheng-7707	181	39	(	(	PUNCT
fumecheng-7707	181	40	)	)	PUNCT
fumecheng-7707	181	41	ˆ	ˆ	PROPN
fumecheng-7707	181	42	(	(	PUNCT
fumecheng-7707	181	43	)	)	PUNCT
fumecheng-7707	181	44	(	(	PUNCT
fumecheng-7707	181	45	0	0	NUM
fumecheng-7707	181	46	)	)	PUNCT
fumecheng-7707	181	47	cos	cos	PROPN
fumecheng-7707	181	48	lim	lim	PROPN
fumecheng-7707	181	49	(	(	PUNCT
fumecheng-7707	181	50	)	)	PUNCT
fumecheng-7707	181	51	(	(	PUNCT
fumecheng-7707	181	52	)	)	PUNCT
fumecheng-7707	181	53	d	d	NOUN
fumecheng-7707	181	54	,	,	PUNCT
fumecheng-7707	181	55	2	2	NUM
fumecheng-7707	181	56	ˆd	ˆd	NOUN
fumecheng-7707	181	57	(	(	PUNCT
fumecheng-7707	181	58	)	)	PUNCT
fumecheng-7707	181	59	(	(	PUNCT
fumecheng-7707	181	60	)	)	PUNCT
fumecheng-7707	181	61	:	:	PUNCT
fumecheng-7707	181	62	.	.	PUNCT
fumecheng-7707	182	1	d	d	X
fumecheng-7707	182	2	k	k	PROPN
fumecheng-7707	183	1	k	k	PROPN
fumecheng-7707	183	2	kx	kx	PROPN
fumecheng-7707	184	1	k	k	PROPN
fumecheng-7707	184	2	k	k	PROPN
fumecheng-7707	184	3	u	u	X
fumecheng-7707	184	4	x	x	PUNCT
fumecheng-7707	184	5	u	u	NOUN
fumecheng-7707	184	6	u	u	NOUN
fumecheng-7707	184	7	x	x	X
fumecheng-7707	184	8	u	u	NOUN
fumecheng-7707	184	9	−	−	NOUN
fumecheng-7707	184	10	−	−	ADP
fumecheng-7707	184	11	−→	−→	NOUN
fumecheng-7707	184	12	−	−	PROPN
fumecheng-7707	184	13			PROPN
fumecheng-7707	184	14			PROPN
fumecheng-7707	184	15			PROPN
fumecheng-7707	184	16			PROPN
fumecheng-7707	184	17	=	=	PUNCT
fumecheng-7707	185	1	+	+	CCONJ
fumecheng-7707	185	2	−	−	X
fumecheng-7707	186	1	+	+	CCONJ
fumecheng-7707	186	2	−	−	ADV
fumecheng-7707	186	3			X
fumecheng-7707	186	4			X
fumecheng-7707	187	1			PROPN
fumecheng-7707	187	2			ADJ
fumecheng-7707	187	3			PROPN
fumecheng-7707	187	4			PROPN
fumecheng-7707	187	5			PROPN
fumecheng-7707	187	6			PROPN
fumecheng-7707	187	7			PROPN
fumecheng-7707	187	8			ADJ
fumecheng-7707	187	9			PROPN
fumecheng-7707	187	10	=	=	X
fumecheng-7707	187	11			NOUN
fumecheng-7707	187	12			PROPN
fumecheng-7707	187	13			PROPN
fumecheng-7707	187	14			PUNCT
fumecheng-7707	187	15			ADP
fumecheng-7707	187	16			PROPN
fumecheng-7707	187	17			NOUN
fumecheng-7707	187	18			ADP
fumecheng-7707	187	19			PROPN
fumecheng-7707	187	20			NOUN
fumecheng-7707	187	21			ADP
fumecheng-7707	187	22			NOUN
fumecheng-7707	187	23			PUNCT
fumecheng-7707	187	24			ADJ
fumecheng-7707	187	25			NOUN
fumecheng-7707	187	26			NOUN
fumecheng-7707	187	27			NOUN
fumecheng-7707	187	28			NOUN
fumecheng-7707	187	29			X
fumecheng-7707	187	30	(	(	PUNCT
fumecheng-7707	187	31	26	26	NUM
fumecheng-7707	187	32	)	)	PUNCT
fumecheng-7707	187	33	the	the	DET
fumecheng-7707	187	34	discretization	discretization	NOUN
fumecheng-7707	187	35	procedure	procedure	NOUN
fumecheng-7707	187	36	for	for	ADP
fumecheng-7707	187	37	eq	eq	NOUN
fumecheng-7707	187	38	.	.	PUNCT
fumecheng-7707	188	1	(	(	PUNCT
fumecheng-7707	188	2	26	26	NUM
fumecheng-7707	188	3	)	)	PUNCT
fumecheng-7707	188	4	works	work	VERB
fumecheng-7707	188	5	completely	completely	ADV
fumecheng-7707	188	6	analogous	analogous	ADJ
fumecheng-7707	188	7	to	to	ADP
fumecheng-7707	188	8	the	the	PRON
fumecheng-7707	188	9	previously	previously	ADV
fumecheng-7707	188	10	showed	show	VERB
fumecheng-7707	188	11	one	one	NUM
fumecheng-7707	188	12	and	and	CCONJ
fumecheng-7707	188	13	shall	shall	AUX
fumecheng-7707	188	14	therefore	therefore	ADV
fumecheng-7707	188	15	be	be	AUX
fumecheng-7707	188	16	omitted	omit	VERB
fumecheng-7707	188	17	here	here	ADV
fumecheng-7707	188	18	for	for	ADP
fumecheng-7707	188	19	brevity	brevity	NOUN
fumecheng-7707	188	20	.	.	PUNCT
fumecheng-7707	189	1	in	in	ADP
fumecheng-7707	189	2	fig	fig	NOUN
fumecheng-7707	189	3	.	.	PUNCT
fumecheng-7707	190	1	3	3	NUM
fumecheng-7707	190	2	the	the	DET
fumecheng-7707	190	3	results	result	NOUN
fumecheng-7707	190	4	of	of	ADP
fumecheng-7707	190	5	a	a	DET
fumecheng-7707	190	6	convergence	convergence	NOUN
fumecheng-7707	190	7	study	study	NOUN
fumecheng-7707	190	8	for	for	ADP
fumecheng-7707	190	9	that	that	DET
fumecheng-7707	190	10	algorithm	algorithm	NOUN
fumecheng-7707	190	11	with	with	ADP
fumecheng-7707	190	12	an	an	DET
fumecheng-7707	190	13	analytical	analytical	ADJ
fumecheng-7707	190	14	solution	solution	NOUN
fumecheng-7707	190	15	,	,	PUNCT
fumecheng-7707	190	16	4	4	NUM
fumecheng-7707	190	17	4(1	4(1	NUM
fumecheng-7707	190	18	)	)	PUNCT
fumecheng-7707	190	19	(	(	PUNCT
fumecheng-7707	190	20	3	3	X
fumecheng-7707	190	21	)	)	PUNCT
fumecheng-7707	190	22	(	(	PUNCT
fumecheng-7707	190	23	)	)	PUNCT
fumecheng-7707	190	24	,	,	PUNCT
fumecheng-7707	190	25	(	(	PUNCT
fumecheng-7707	190	26	)	)	PUNCT
fumecheng-7707	190	27	8	8	NUM
fumecheng-7707	191	1	k	k	NOUN
fumecheng-7707	191	2	k	k	NOUN
fumecheng-7707	192	1	g	g	NOUN
fumecheng-7707	192	2	x	x	PUNCT
fumecheng-7707	192	3	x	x	PUNCT
fumecheng-7707	192	4	f	f	NOUN
fumecheng-7707	192	5	r	r	NOUN
fumecheng-7707	192	6	r	r	NOUN
fumecheng-7707	192	7	+	+	CCONJ
fumecheng-7707	192	8	+	+	CCONJ
fumecheng-7707	192	9	=	=	SYM
fumecheng-7707	192	10	=	=	SYM
fumecheng-7707	192	11	(	(	PUNCT
fumecheng-7707	192	12	27	27	NUM
fumecheng-7707	192	13	)	)	PUNCT
fumecheng-7707	192	14	are	be	AUX
fumecheng-7707	192	15	shown	show	VERB
fumecheng-7707	192	16	.	.	PUNCT
fumecheng-7707	193	1	the	the	DET
fumecheng-7707	193	2	exponent	exponent	NOUN
fumecheng-7707	193	3	of	of	ADP
fumecheng-7707	193	4	the	the	DET
fumecheng-7707	193	5	power	power	NOUN
fumecheng-7707	193	6	-	-	PUNCT
fumecheng-7707	193	7	law	law	NOUN
fumecheng-7707	193	8	was	be	AUX
fumecheng-7707	193	9	chosen	choose	VERB
fumecheng-7707	193	10	to	to	PART
fumecheng-7707	193	11	be	be	AUX
fumecheng-7707	193	12	k	k	PROPN
fumecheng-7707	193	13	=	=	SYM
fumecheng-7707	193	14	-0.5	-0.5	PROPN
fumecheng-7707	193	15	(	(	PUNCT
fumecheng-7707	193	16	note	note	VERB
fumecheng-7707	193	17	that	that	SCONJ
fumecheng-7707	193	18	the	the	DET
fumecheng-7707	193	19	value	value	NOUN
fumecheng-7707	193	20	of	of	ADP
fumecheng-7707	193	21	k	k	PROPN
fumecheng-7707	193	22	has	have	VERB
fumecheng-7707	193	23	practically	practically	ADV
fumecheng-7707	193	24	no	no	DET
fumecheng-7707	193	25	influence	influence	NOUN
fumecheng-7707	193	26	on	on	ADP
fumecheng-7707	193	27	the	the	DET
fumecheng-7707	193	28	convergence	convergence	NOUN
fumecheng-7707	193	29	behaviour	behaviour	NOUN
fumecheng-7707	193	30	)	)	PUNCT
fumecheng-7707	193	31	.	.	PUNCT
fumecheng-7707	194	1	the	the	DET
fumecheng-7707	194	2	mean	mean	ADJ
fumecheng-7707	194	3	relative	relative	ADJ
fumecheng-7707	194	4	error	error	NOUN
fumecheng-7707	194	5	(	(	PUNCT
fumecheng-7707	194	6	defined	define	VERB
fumecheng-7707	194	7	as	as	ADP
fumecheng-7707	194	8	before	before	ADV
fumecheng-7707	194	9	)	)	PUNCT
fumecheng-7707	194	10	is	be	AUX
fumecheng-7707	194	11	shown	show	VERB
fumecheng-7707	194	12	as	as	ADP
fumecheng-7707	194	13	a	a	DET
fumecheng-7707	194	14	function	function	NOUN
fumecheng-7707	194	15	of	of	ADP
fumecheng-7707	194	16	the	the	DET
fumecheng-7707	194	17	number	number	NOUN
fumecheng-7707	194	18	of	of	ADP
fumecheng-7707	194	19	elements	element	NOUN
fumecheng-7707	194	20	used	use	VERB
fumecheng-7707	194	21	for	for	ADP
fumecheng-7707	194	22	the	the	DET
fumecheng-7707	194	23	transformation	transformation	NOUN
fumecheng-7707	194	24	in	in	ADP
fumecheng-7707	194	25	double	double	ADJ
fumecheng-7707	194	26	-	-	PUNCT
fumecheng-7707	194	27	logarithmic	logarithmic	ADJ
fumecheng-7707	194	28	scale	scale	NOUN
fumecheng-7707	194	29	.	.	PUNCT
fumecheng-7707	195	1	all	all	DET
fumecheng-7707	195	2	derivatives	derivative	NOUN
fumecheng-7707	195	3	were	be	AUX
fumecheng-7707	195	4	determined	determine	VERB
fumecheng-7707	195	5	by	by	ADP
fumecheng-7707	195	6	second	second	ADJ
fumecheng-7707	195	7	-	-	PUNCT
fumecheng-7707	195	8	order	order	NOUN
fumecheng-7707	195	9	finite	finite	NOUN
fumecheng-7707	195	10	differences	difference	NOUN
fumecheng-7707	195	11	.	.	PUNCT
fumecheng-7707	196	1	the	the	DET
fumecheng-7707	196	2	convergence	convergence	NOUN
fumecheng-7707	196	3	is	be	AUX
fumecheng-7707	196	4	stable	stable	ADJ
fumecheng-7707	196	5	but	but	CCONJ
fumecheng-7707	196	6	slower	slow	ADJ
fumecheng-7707	196	7	than	than	ADP
fumecheng-7707	196	8	the	the	DET
fumecheng-7707	196	9	one	one	NOUN
fumecheng-7707	196	10	for	for	ADP
fumecheng-7707	196	11	the	the	DET
fumecheng-7707	196	12	pressure	pressure	NOUN
fumecheng-7707	196	13	transform	transform	NOUN
fumecheng-7707	196	14	in	in	ADP
fumecheng-7707	196	15	fig	fig	NOUN
fumecheng-7707	196	16	.	.	PUNCT
fumecheng-7707	197	1	2	2	NUM
fumecheng-7707	197	2	,	,	PUNCT
fumecheng-7707	197	3	the	the	DET
fumecheng-7707	197	4	gradient	gradient	NOUN
fumecheng-7707	197	5	(	(	PUNCT
fumecheng-7707	197	6	in	in	ADP
fumecheng-7707	197	7	double	double	ADJ
fumecheng-7707	197	8	-	-	PUNCT
fumecheng-7707	197	9	logarithmic	logarithmic	ADJ
fumecheng-7707	197	10	terms	term	NOUN
fumecheng-7707	197	11	)	)	PUNCT
fumecheng-7707	197	12	of	of	ADP
fumecheng-7707	197	13	the	the	DET
fumecheng-7707	197	14	curve	curve	NOUN
fumecheng-7707	197	15	in	in	ADP
fumecheng-7707	197	16	fig	fig	NOUN
fumecheng-7707	197	17	.	.	PUNCT
fumecheng-7707	198	1	3	3	NUM
fumecheng-7707	198	2	is	be	AUX
fumecheng-7707	198	3	close	close	ADJ
fumecheng-7707	198	4	to	to	ADP
fumecheng-7707	198	5	minus	minus	CCONJ
fumecheng-7707	198	6	one	one	NUM
fumecheng-7707	198	7	.	.	PUNCT
fumecheng-7707	199	1	fig	fig	NOUN
fumecheng-7707	199	2	.	.	PUNCT
fumecheng-7707	200	1	3	3	NUM
fumecheng-7707	200	2	convergence	convergence	NOUN
fumecheng-7707	200	3	study	study	NOUN
fumecheng-7707	200	4	for	for	ADP
fumecheng-7707	200	5	the	the	DET
fumecheng-7707	200	6	mean	mean	ADJ
fumecheng-7707	200	7	relative	relative	ADJ
fumecheng-7707	200	8	error	error	NOUN
fumecheng-7707	200	9	depending	depend	VERB
fumecheng-7707	200	10	on	on	ADP
fumecheng-7707	200	11	the	the	DET
fumecheng-7707	200	12	number	number	NOUN
fumecheng-7707	200	13	of	of	ADP
fumecheng-7707	200	14	array	array	NOUN
fumecheng-7707	200	15	elements	element	NOUN
fumecheng-7707	200	16	for	for	ADP
fumecheng-7707	200	17	the	the	DET
fumecheng-7707	200	18	fft	fft	NOUN
fumecheng-7707	200	19	-	-	PUNCT
fumecheng-7707	200	20	based	base	VERB
fumecheng-7707	200	21	implementation	implementation	NOUN
fumecheng-7707	200	22	of	of	ADP
fumecheng-7707	200	23	the	the	DET
fumecheng-7707	200	24	transform	transform	NOUN
fumecheng-7707	200	25	(	(	PUNCT
fumecheng-7707	200	26	26	26	NUM
fumecheng-7707	200	27	)	)	PUNCT
fumecheng-7707	200	28	of	of	ADP
fumecheng-7707	200	29	the	the	DET
fumecheng-7707	200	30	local	local	ADJ
fumecheng-7707	200	31	displacements	displacement	NOUN
fumecheng-7707	200	32	for	for	ADP
fumecheng-7707	200	33	power	power	NOUN
fumecheng-7707	200	34	-	-	PUNCT
fumecheng-7707	200	35	law	law	NOUN
fumecheng-7707	200	36	graded	grade	VERB
fumecheng-7707	200	37	materials	material	NOUN
fumecheng-7707	200	38	.	.	PUNCT
fumecheng-7707	201	1	3.3	3.3	NUM
fumecheng-7707	201	2	.	.	PUNCT
fumecheng-7707	202	1	transformation	transformation	NOUN
fumecheng-7707	202	2	to	to	PART
fumecheng-7707	202	3	obtain	obtain	VERB
fumecheng-7707	202	4	stresses	stress	NOUN
fumecheng-7707	202	5	for	for	ADP
fumecheng-7707	202	6	power	power	NOUN
fumecheng-7707	202	7	-	-	PUNCT
fumecheng-7707	202	8	law	law	NOUN
fumecheng-7707	202	9	graded	grade	VERB
fumecheng-7707	202	10	materials	material	NOUN
fumecheng-7707	202	11	it	it	PRON
fumecheng-7707	202	12	is	be	AUX
fumecheng-7707	202	13	unfortunately	unfortunately	ADV
fumecheng-7707	202	14	not	not	PART
fumecheng-7707	202	15	that	that	ADV
fumecheng-7707	202	16	easy	easy	ADJ
fumecheng-7707	202	17	to	to	PART
fumecheng-7707	202	18	directly	directly	ADV
fumecheng-7707	202	19	transform	transform	VERB
fumecheng-7707	202	20	between	between	ADP
fumecheng-7707	202	21	the	the	DET
fumecheng-7707	202	22	line	line	NOUN
fumecheng-7707	202	23	loads	load	VERB
fumecheng-7707	202	24	in	in	ADP
fumecheng-7707	202	25	the	the	DET
fumecheng-7707	202	26	mdr	mdr	PROPN
fumecheng-7707	202	27	model	model	NOUN
fumecheng-7707	202	28	and	and	CCONJ
fumecheng-7707	202	29	the	the	DET
fumecheng-7707	202	30	contact	contact	NOUN
fumecheng-7707	202	31	stresses	stress	VERB
fumecheng-7707	202	32	in	in	ADP
fumecheng-7707	202	33	the	the	DET
fumecheng-7707	202	34	axisymmetric	axisymmetric	ADJ
fumecheng-7707	202	35	system	system	NOUN
fumecheng-7707	202	36	.	.	PUNCT
fumecheng-7707	203	1	however	however	ADV
fumecheng-7707	203	2	,	,	PUNCT
fumecheng-7707	203	3	in	in	ADP
fumecheng-7707	203	4	the	the	DET
fumecheng-7707	203	5	elastic	elastic	ADJ
fumecheng-7707	203	6	case	case	NOUN
fumecheng-7707	203	7	,	,	PUNCT
fumecheng-7707	203	8	transformations	transformation	NOUN
fumecheng-7707	203	9	exist	exist	VERB
fumecheng-7707	203	10	between	between	ADP
fumecheng-7707	203	11	the	the	DET
fumecheng-7707	203	12	local	local	ADJ
fumecheng-7707	203	13	displacements	displacement	NOUN
fumecheng-7707	203	14	in	in	ADP
fumecheng-7707	203	15	the	the	DET
fumecheng-7707	203	16	mdr	mdr	NOUN
fumecheng-7707	203	17	system	system	NOUN
fumecheng-7707	203	18	and	and	CCONJ
fumecheng-7707	203	19	the	the	DET
fumecheng-7707	203	20	contact	contact	NOUN
fumecheng-7707	203	21	stresses	stress	VERB
fumecheng-7707	203	22	.	.	PUNCT
fumecheng-7707	204	1	for	for	ADP
fumecheng-7707	204	2	example	example	NOUN
fumecheng-7707	204	3	,	,	PUNCT
fumecheng-7707	204	4	the	the	DET
fumecheng-7707	204	5	pressure	pressure	NOUN
fumecheng-7707	204	6	distribution	distribution	NOUN
fumecheng-7707	204	7	is	be	AUX
fumecheng-7707	204	8	[	[	X
fumecheng-7707	204	9	1	1	NUM
fumecheng-7707	204	10	]	]	SYM
fumecheng-7707	204	11	2	2	NUM
fumecheng-7707	204	12	2	2	NUM
fumecheng-7707	204	13	1	1	NUM
fumecheng-7707	204	14	(	(	PUNCT
fumecheng-7707	204	15	)	)	PUNCT
fumecheng-7707	204	16	d	d	NOUN
fumecheng-7707	204	17	(	(	PUNCT
fumecheng-7707	204	18	)	)	PUNCT
fumecheng-7707	204	19	,	,	PUNCT
fumecheng-7707	204	20	(	(	PUNCT
fumecheng-7707	204	21	)	)	PUNCT
fumecheng-7707	204	22	a	a	DET
fumecheng-7707	204	23	n	n	NOUN
fumecheng-7707	204	24	k	k	NOUN
fumecheng-7707	204	25	r	r	NOUN
fumecheng-7707	204	26	c	c	PROPN
fumecheng-7707	204	27	g	g	NOUN
fumecheng-7707	204	28	x	x	X
fumecheng-7707	204	29	x	x	X
fumecheng-7707	204	30	p	p	X
fumecheng-7707	204	31	r	r	NOUN
fumecheng-7707	204	32	x	x	PUNCT
fumecheng-7707	204	33	r	r	NOUN
fumecheng-7707	204	34	−	−	NOUN
fumecheng-7707	204	35			NOUN
fumecheng-7707	204	36	=	=	PUNCT
fumecheng-7707	204	37	−	−	PROPN
fumecheng-7707	204	38			NUM
fumecheng-7707	204	39	(	(	PUNCT
fumecheng-7707	204	40	28	28	NUM
fumecheng-7707	204	41	)	)	PUNCT
fumecheng-7707	204	42	fft	fft	NOUN
fumecheng-7707	204	43	-	-	PUNCT
fumecheng-7707	204	44	based	base	VERB
fumecheng-7707	204	45	implementation	implementation	NOUN
fumecheng-7707	204	46	of	of	ADP
fumecheng-7707	204	47	the	the	DET
fumecheng-7707	204	48	mdr	mdr	PROPN
fumecheng-7707	204	49	transformations	transformation	NOUN
fumecheng-7707	204	50	for	for	ADP
fumecheng-7707	204	51	homogeneous	homogeneous	ADJ
fumecheng-7707	204	52	and	and	CCONJ
fumecheng-7707	204	53	power	power	NOUN
fumecheng-7707	204	54	-	-	PUNCT
fumecheng-7707	204	55	law	law	NOUN
fumecheng-7707	204	56	graded	grade	VERB
fumecheng-7707	204	57	materials813	materials813	PROPN
fumecheng-7707	204	58	with	with	ADP
fumecheng-7707	204	59	a	a	DET
fumecheng-7707	204	60	lengthy	lengthy	ADJ
fumecheng-7707	204	61	constant	constant	ADJ
fumecheng-7707	204	62	cn	cn	PROPN
fumecheng-7707	204	63	,	,	PUNCT
fumecheng-7707	204	64	which	which	PRON
fumecheng-7707	204	65	can	can	AUX
fumecheng-7707	204	66	be	be	AUX
fumecheng-7707	204	67	found	find	VERB
fumecheng-7707	204	68	in	in	ADP
fumecheng-7707	204	69	the	the	DET
fumecheng-7707	204	70	respective	respective	ADJ
fumecheng-7707	204	71	literature	literature	NOUN
fumecheng-7707	205	1	[	[	X
fumecheng-7707	205	2	1	1	NUM
fumecheng-7707	205	3	]	]	PUNCT
fumecheng-7707	205	4	and	and	CCONJ
fumecheng-7707	205	5	which	which	PRON
fumecheng-7707	205	6	reduces	reduce	VERB
fumecheng-7707	205	7	to	to	ADP
fumecheng-7707	205	8	e	e	NOUN
fumecheng-7707	205	9	*	*	PUNCT
fumecheng-7707	205	10	in	in	ADP
fumecheng-7707	205	11	the	the	DET
fumecheng-7707	205	12	homogeneous	homogeneous	ADJ
fumecheng-7707	205	13	limit	limit	NOUN
fumecheng-7707	205	14	,	,	PUNCT
fumecheng-7707	205	15	and	and	CCONJ
fumecheng-7707	205	16	a	a	DET
fumecheng-7707	205	17	similar	similar	ADJ
fumecheng-7707	205	18	transform	transform	NOUN
fumecheng-7707	205	19	exists	exist	VERB
fumecheng-7707	205	20	for	for	ADP
fumecheng-7707	205	21	the	the	DET
fumecheng-7707	205	22	determination	determination	NOUN
fumecheng-7707	205	23	of	of	ADP
fumecheng-7707	205	24	the	the	DET
fumecheng-7707	205	25	frictional	frictional	ADJ
fumecheng-7707	205	26	shear	shear	NOUN
fumecheng-7707	205	27	stresses	stress	NOUN
fumecheng-7707	205	28	in	in	ADP
fumecheng-7707	205	29	the	the	DET
fumecheng-7707	205	30	elastic	elastic	ADJ
fumecheng-7707	205	31	tangential	tangential	ADJ
fumecheng-7707	205	32	contact	contact	NOUN
fumecheng-7707	205	33	[	[	X
fumecheng-7707	205	34	1	1	NUM
fumecheng-7707	205	35	]	]	PUNCT
fumecheng-7707	205	36	.	.	PUNCT
fumecheng-7707	206	1	after	after	ADP
fumecheng-7707	206	2	completely	completely	ADV
fumecheng-7707	206	3	the	the	DET
fumecheng-7707	206	4	same	same	ADJ
fumecheng-7707	206	5	procedure	procedure	NOUN
fumecheng-7707	206	6	as	as	ADP
fumecheng-7707	206	7	in	in	ADP
fumecheng-7707	206	8	subsection	subsection	NOUN
fumecheng-7707	206	9	2.3	2.3	NUM
fumecheng-7707	206	10	,	,	PUNCT
fumecheng-7707	206	11	the	the	DET
fumecheng-7707	206	12	discretized	discretized	ADJ
fumecheng-7707	206	13	pressure	pressure	NOUN
fumecheng-7707	206	14	distribution	distribution	NOUN
fumecheng-7707	206	15	,	,	PUNCT
fumecheng-7707	206	16	i.e.	i.e.	X
fumecheng-7707	206	17	,	,	PUNCT
fumecheng-7707	206	18	the	the	DET
fumecheng-7707	206	19	generalization	generalization	NOUN
fumecheng-7707	206	20	of	of	ADP
fumecheng-7707	206	21	eqs	eqs	PROPN
fumecheng-7707	206	22	.	.	PUNCT
fumecheng-7707	207	1	(	(	PUNCT
fumecheng-7707	207	2	17	17	NUM
fumecheng-7707	207	3	)	)	PUNCT
fumecheng-7707	207	4	,	,	PUNCT
fumecheng-7707	207	5	is	be	AUX
fumecheng-7707	207	6	given	give	VERB
fumecheng-7707	207	7	by	by	ADP
fumecheng-7707	207	8	1	1	NUM
fumecheng-7707	207	9	1	1	NUM
fumecheng-7707	207	10	2	2	NUM
fumecheng-7707	207	11	1	1	NUM
fumecheng-7707	207	12	3	3	NUM
fumecheng-7707	207	13	1	1	NUM
fumecheng-7707	207	14	1	1	NUM
fumecheng-7707	207	15	1	1	NUM
fumecheng-7707	207	16	2	2	NUM
fumecheng-7707	207	17	ˆ	ˆ	NOUN
fumecheng-7707	207	18	ˆ	ˆ	PROPN
fumecheng-7707	207	19	(	(	PUNCT
fumecheng-7707	207	20	)	)	PUNCT
fumecheng-7707	207	21	,	,	PUNCT
fumecheng-7707	207	22	1	1	NUM
fumecheng-7707	207	23	:	:	SYM
fumecheng-7707	207	24	1	1	NUM
fumecheng-7707	207	25	,	,	PUNCT
fumecheng-7707	207	26	(	(	PUNCT
fumecheng-7707	207	27	1	1	NUM
fumecheng-7707	207	28	)	)	PUNCT
fumecheng-7707	207	29	,	,	PUNCT
fumecheng-7707	207	30	(	(	PUNCT
fumecheng-7707	207	31	1	1	X
fumecheng-7707	207	32	)	)	SYM
fumecheng-7707	207	33	1	1	NUM
fumecheng-7707	207	34	ˆ	ˆ	NOUN
fumecheng-7707	207	35	ˆ	ˆ	PROPN
fumecheng-7707	207	36	(	(	PUNCT
fumecheng-7707	207	37	)	)	PUNCT
fumecheng-7707	207	38	(	(	PUNCT
fumecheng-7707	207	39	)	)	PUNCT
fumecheng-7707	207	40	.	.	PUNCT
fumecheng-7707	208	1	2	2	NUM
fumecheng-7707	208	2	k	k	X
fumecheng-7707	208	3	kn	kn	PROPN
fumecheng-7707	209	1	j	j	PROPN
fumecheng-7707	210	1	j	j	PROPN
fumecheng-7707	211	1	k	k	PROPN
fumecheng-7707	211	2	k	k	PROPN
fumecheng-7707	212	1	k	k	PROPN
fumecheng-7707	212	2	j	j	PROPN
fumecheng-7707	213	1	i	i	PRON
fumecheng-7707	213	2	i	i	PRON
fumecheng-7707	214	1	j	j	PROPN
fumecheng-7707	215	1	c	c	PROPN
fumecheng-7707	215	2	p	p	PROPN
fumecheng-7707	215	3	j	j	PROPN
fumecheng-7707	215	4	h	h	NOUN
fumecheng-7707	215	5	g	g	PROPN
fumecheng-7707	215	6	t	t	PROPN
fumecheng-7707	215	7	j	j	PROPN
fumecheng-7707	215	8	a	a	DET
fumecheng-7707	215	9	h	h	NOUN
fumecheng-7707	216	1	k	k	PROPN
fumecheng-7707	216	2	t	t	PROPN
fumecheng-7707	217	1	h	h	NOUN
fumecheng-7707	218	1	j	j	PROPN
fumecheng-7707	218	2	g	g	PROPN
fumecheng-7707	218	3	g	g	PROPN
fumecheng-7707	218	4	i	i	PRON
fumecheng-7707	218	5	j	j	PROPN
fumecheng-7707	219	1	+	+	CCONJ
fumecheng-7707	220	1	+	+	CCONJ
fumecheng-7707	220	2	−	−	X
fumecheng-7707	221	1	+	+	SYM
fumecheng-7707	221	2	+	+	PUNCT
fumecheng-7707	221	3	+	+	X
fumecheng-7707	221	4	=	=	SYM
fumecheng-7707	221	5	+	+	NUM
fumecheng-7707	221	6			PROPN
fumecheng-7707	221	7	=	=	NOUN
fumecheng-7707	221	8	−	−	NOUN
fumecheng-7707	221	9	−	−	PROPN
fumecheng-7707	221	10	=	=	SYM
fumecheng-7707	222	1	−	−	PROPN
fumecheng-7707	222	2	=	=	SYM
fumecheng-7707	222	3	−	−	PROPN
fumecheng-7707	222	4			NOUN
fumecheng-7707	222	5			PROPN
fumecheng-7707	222	6	+	+	PROPN
fumecheng-7707	222	7			PROPN
fumecheng-7707	222	8			X
fumecheng-7707	222	9			PROPN
fumecheng-7707	222	10	=	=	PROPN
fumecheng-7707	222	11	−	−	PROPN
fumecheng-7707	223	1	+	+	CCONJ
fumecheng-7707	223	2	−	−	X
fumecheng-7707	223	3			PROPN
fumecheng-7707	223	4			NOUN
fumecheng-7707	223	5			PROPN
fumecheng-7707	223	6			AUX
fumecheng-7707	223	7			X
fumecheng-7707	223	8			X
fumecheng-7707	223	9			X
fumecheng-7707	223	10			X
fumecheng-7707	223	11			X
fumecheng-7707	223	12			X
fumecheng-7707	223	13			NOUN
fumecheng-7707	223	14			NOUN
fumecheng-7707	223	15	(	(	PUNCT
fumecheng-7707	223	16	29	29	NUM
fumecheng-7707	223	17	)	)	SYM
fumecheng-7707	223	18	4	4	NUM
fumecheng-7707	223	19	.	.	PUNCT
fumecheng-7707	223	20	exemplary	exemplary	ADJ
fumecheng-7707	223	21	fretting	fretting	NOUN
fumecheng-7707	223	22	wear	wear	NOUN
fumecheng-7707	223	23	simulation	simulation	NOUN
fumecheng-7707	223	24	let	let	VERB
fumecheng-7707	223	25	us	we	PRON
fumecheng-7707	223	26	demonstrate	demonstrate	VERB
fumecheng-7707	223	27	the	the	DET
fumecheng-7707	223	28	application	application	NOUN
fumecheng-7707	223	29	of	of	ADP
fumecheng-7707	223	30	the	the	DET
fumecheng-7707	223	31	proposed	propose	VERB
fumecheng-7707	223	32	method	method	NOUN
fumecheng-7707	223	33	to	to	ADP
fumecheng-7707	223	34	a	a	DET
fumecheng-7707	223	35	simple	simple	ADJ
fumecheng-7707	223	36	fretting	fretting	NOUN
fumecheng-7707	223	37	wear	wear	NOUN
fumecheng-7707	223	38	simulation	simulation	NOUN
fumecheng-7707	223	39	.	.	PUNCT
fumecheng-7707	224	1	fretting	fret	VERB
fumecheng-7707	224	2	is	be	AUX
fumecheng-7707	224	3	a	a	DET
fumecheng-7707	224	4	phenomenon	phenomenon	NOUN
fumecheng-7707	224	5	that	that	PRON
fumecheng-7707	224	6	occurs	occur	VERB
fumecheng-7707	224	7	in	in	ADP
fumecheng-7707	224	8	dry	dry	ADJ
fumecheng-7707	224	9	,	,	PUNCT
fumecheng-7707	224	10	partial	partial	ADJ
fumecheng-7707	224	11	slip	slip	NOUN
fumecheng-7707	224	12	,	,	PUNCT
fumecheng-7707	224	13	oscillating	oscillate	VERB
fumecheng-7707	224	14	contacts	contact	NOUN
fumecheng-7707	224	15	;	;	PUNCT
fumecheng-7707	224	16	it	it	PRON
fumecheng-7707	224	17	causes	cause	VERB
fumecheng-7707	224	18	both	both	PRON
fumecheng-7707	224	19	wear	wear	VERB
fumecheng-7707	224	20	and	and	CCONJ
fumecheng-7707	224	21	fatigue	fatigue	NOUN
fumecheng-7707	224	22	and	and	CCONJ
fumecheng-7707	224	23	,	,	PUNCT
fumecheng-7707	224	24	despite	despite	SCONJ
fumecheng-7707	224	25	its	its	PRON
fumecheng-7707	224	26	high	high	ADJ
fumecheng-7707	224	27	localization	localization	NOUN
fumecheng-7707	224	28	,	,	PUNCT
fumecheng-7707	224	29	is	be	AUX
fumecheng-7707	224	30	highly	highly	ADV
fumecheng-7707	224	31	relevant	relevant	ADJ
fumecheng-7707	224	32	for	for	ADP
fumecheng-7707	224	33	the	the	DET
fumecheng-7707	224	34	lifetime	lifetime	NOUN
fumecheng-7707	224	35	of	of	ADP
fumecheng-7707	224	36	various	various	ADJ
fumecheng-7707	224	37	tribological	tribological	ADJ
fumecheng-7707	224	38	systems	system	NOUN
fumecheng-7707	224	39	in	in	ADP
fumecheng-7707	224	40	technology	technology	NOUN
fumecheng-7707	224	41	and	and	CCONJ
fumecheng-7707	224	42	biology	biology	NOUN
fumecheng-7707	224	43	[	[	X
fumecheng-7707	224	44	19	19	NUM
fumecheng-7707	224	45	]	]	PUNCT
fumecheng-7707	224	46	.	.	PUNCT
fumecheng-7707	225	1	consider	consider	VERB
fumecheng-7707	225	2	the	the	DET
fumecheng-7707	225	3	following	follow	VERB
fumecheng-7707	225	4	contact	contact	NOUN
fumecheng-7707	225	5	situation	situation	NOUN
fumecheng-7707	225	6	:	:	PUNCT
fumecheng-7707	225	7	an	an	DET
fumecheng-7707	225	8	initially	initially	ADV
fumecheng-7707	225	9	parabolic	parabolic	PROPN
fumecheng-7707	225	10	indenter	indenter	NOUN
fumecheng-7707	225	11	with	with	ADP
fumecheng-7707	225	12	the	the	DET
fumecheng-7707	225	13	radius	radius	NOUN
fumecheng-7707	225	14	of	of	ADP
fumecheng-7707	225	15	curvature	curvature	NOUN
fumecheng-7707	225	16	r	r	NOUN
fumecheng-7707	225	17	is	be	AUX
fumecheng-7707	225	18	pressed	press	VERB
fumecheng-7707	225	19	into	into	ADP
fumecheng-7707	225	20	a	a	DET
fumecheng-7707	225	21	half	half	ADJ
fumecheng-7707	225	22	-	-	PUNCT
fumecheng-7707	225	23	space	space	NOUN
fumecheng-7707	225	24	(	(	PUNCT
fumecheng-7707	225	25	which	which	PRON
fumecheng-7707	225	26	of	of	ADP
fumecheng-7707	225	27	the	the	DET
fumecheng-7707	225	28	bodies	body	NOUN
fumecheng-7707	225	29	is	be	AUX
fumecheng-7707	225	30	elastically	elastically	ADV
fumecheng-7707	225	31	deformable	deformable	ADJ
fumecheng-7707	225	32	,	,	PUNCT
fumecheng-7707	225	33	does	do	AUX
fumecheng-7707	225	34	not	not	PART
fumecheng-7707	225	35	actually	actually	ADV
fumecheng-7707	225	36	matter	matter	VERB
fumecheng-7707	225	37	)	)	PUNCT
fumecheng-7707	225	38	by	by	ADP
fumecheng-7707	225	39	a	a	DET
fumecheng-7707	225	40	constant	constant	ADJ
fumecheng-7707	225	41	indentation	indentation	NOUN
fumecheng-7707	225	42	depth	depth	NOUN
fumecheng-7707	225	43	d.	d.	NOUN
fumecheng-7707	225	44	moreover	moreover	ADV
fumecheng-7707	225	45	,	,	PUNCT
fumecheng-7707	225	46	the	the	DET
fumecheng-7707	225	47	contact	contact	NOUN
fumecheng-7707	225	48	experiences	experience	VERB
fumecheng-7707	225	49	small	small	ADJ
fumecheng-7707	225	50	tangential	tangential	ADJ
fumecheng-7707	225	51	oscillations	oscillation	NOUN
fumecheng-7707	225	52	with	with	ADP
fumecheng-7707	225	53	a	a	DET
fumecheng-7707	225	54	displacement	displacement	ADJ
fumecheng-7707	225	55	amplitude	amplitude	NOUN
fumecheng-7707	225	56	ua	ua	PROPN
fumecheng-7707	225	57	.	.	PUNCT
fumecheng-7707	226	1	these	these	DET
fumecheng-7707	226	2	oscillations	oscillation	NOUN
fumecheng-7707	226	3	shall	shall	AUX
fumecheng-7707	226	4	be	be	AUX
fumecheng-7707	226	5	too	too	ADV
fumecheng-7707	226	6	small	small	ADJ
fumecheng-7707	226	7	to	to	PART
fumecheng-7707	226	8	cause	cause	VERB
fumecheng-7707	226	9	gross	gross	ADJ
fumecheng-7707	226	10	sliding	sliding	NOUN
fumecheng-7707	226	11	of	of	ADP
fumecheng-7707	226	12	the	the	DET
fumecheng-7707	226	13	contacting	contact	VERB
fumecheng-7707	226	14	bodies	body	NOUN
fumecheng-7707	226	15	;	;	PUNCT
fumecheng-7707	226	16	however	however	ADV
fumecheng-7707	226	17	,	,	PUNCT
fumecheng-7707	226	18	due	due	ADP
fumecheng-7707	226	19	to	to	ADP
fumecheng-7707	226	20	the	the	DET
fumecheng-7707	226	21	partial	partial	ADJ
fumecheng-7707	226	22	slip	slip	NOUN
fumecheng-7707	226	23	in	in	ADP
fumecheng-7707	226	24	the	the	DET
fumecheng-7707	226	25	contact	contact	NOUN
fumecheng-7707	226	26	there	there	PRON
fumecheng-7707	226	27	will	will	AUX
fumecheng-7707	226	28	be	be	AUX
fumecheng-7707	226	29	wear	wear	NOUN
fumecheng-7707	226	30	,	,	PUNCT
fumecheng-7707	226	31	which	which	PRON
fumecheng-7707	226	32	can	can	AUX
fumecheng-7707	226	33	be	be	AUX
fumecheng-7707	226	34	modelled	model	VERB
fumecheng-7707	226	35	by	by	ADP
fumecheng-7707	226	36	the	the	DET
fumecheng-7707	226	37	archard	archard	NOUN
fumecheng-7707	226	38	law	law	NOUN
fumecheng-7707	226	39	;	;	PUNCT
fumecheng-7707	226	40	as	as	SCONJ
fumecheng-7707	226	41	the	the	DET
fumecheng-7707	226	42	wear	wear	NOUN
fumecheng-7707	226	43	will	will	AUX
fumecheng-7707	226	44	happen	happen	VERB
fumecheng-7707	226	45	on	on	ADP
fumecheng-7707	226	46	a	a	DET
fumecheng-7707	226	47	much	much	ADV
fumecheng-7707	226	48	larger	large	ADJ
fumecheng-7707	226	49	timescale	timescale	NOUN
fumecheng-7707	226	50	than	than	ADP
fumecheng-7707	226	51	the	the	DET
fumecheng-7707	226	52	period	period	NOUN
fumecheng-7707	226	53	of	of	ADP
fumecheng-7707	226	54	one	one	NUM
fumecheng-7707	226	55	fretting	fret	VERB
fumecheng-7707	226	56	oscillation	oscillation	NOUN
fumecheng-7707	226	57	,	,	PUNCT
fumecheng-7707	226	58	we	we	PRON
fumecheng-7707	226	59	can	can	AUX
fumecheng-7707	226	60	treat	treat	VERB
fumecheng-7707	226	61	one	one	NUM
fumecheng-7707	226	62	fretting	fret	VERB
fumecheng-7707	226	63	cycle	cycle	NOUN
fumecheng-7707	226	64	as	as	ADP
fumecheng-7707	226	65	the	the	DET
fumecheng-7707	226	66	time	time	NOUN
fumecheng-7707	226	67	step	step	NOUN
fumecheng-7707	226	68	for	for	ADP
fumecheng-7707	226	69	the	the	DET
fumecheng-7707	226	70	wear	wear	NOUN
fumecheng-7707	226	71	simulation	simulation	NOUN
fumecheng-7707	226	72	.	.	PUNCT
fumecheng-7707	227	1	hence	hence	ADV
fumecheng-7707	227	2	,	,	PUNCT
fumecheng-7707	227	3	the	the	DET
fumecheng-7707	227	4	local	local	ADJ
fumecheng-7707	227	5	change	change	NOUN
fumecheng-7707	227	6	of	of	ADP
fumecheng-7707	227	7	profile	profile	NOUN
fumecheng-7707	227	8	during	during	ADP
fumecheng-7707	227	9	one	one	NUM
fumecheng-7707	227	10	fretting	fret	VERB
fumecheng-7707	227	11	cycle	cycle	NOUN
fumecheng-7707	227	12	is	be	AUX
fumecheng-7707	227	13	given	give	VERB
fumecheng-7707	227	14	by	by	ADP
fumecheng-7707	227	15	[	[	PUNCT
fumecheng-7707	227	16	9	9	NUM
fumecheng-7707	227	17	]	]	PUNCT
fumecheng-7707	227	18	wear	wear	NOUN
fumecheng-7707	227	19	0	0	NUM
fumecheng-7707	227	20	(	(	PUNCT
fumecheng-7707	227	21	;	;	PUNCT
fumecheng-7707	227	22	)	)	PUNCT
fumecheng-7707	227	23	(	(	PUNCT
fumecheng-7707	227	24	;	;	PUNCT
fumecheng-7707	227	25	)	)	PUNCT
fumecheng-7707	227	26	(	(	PUNCT
fumecheng-7707	227	27	;	;	PUNCT
fumecheng-7707	227	28	)	)	PUNCT
fumecheng-7707	227	29	,	,	PUNCT
fumecheng-7707	228	1	k	k	PROPN
fumecheng-7707	228	2	f	f	NOUN
fumecheng-7707	228	3	r	r	NOUN
fumecheng-7707	228	4	t	t	NOUN
fumecheng-7707	228	5	p	p	NOUN
fumecheng-7707	228	6	r	r	NOUN
fumecheng-7707	228	7	t	t	NOUN
fumecheng-7707	228	8	u	u	NOUN
fumecheng-7707	228	9	r	r	NOUN
fumecheng-7707	228	10	t	t	NOUN
fumecheng-7707	228	11	=	=	SYM
fumecheng-7707	228	12			X
fumecheng-7707	228	13			X
fumecheng-7707	228	14	(	(	PUNCT
fumecheng-7707	228	15	30	30	NUM
fumecheng-7707	228	16	)	)	PUNCT
fumecheng-7707	228	17	with	with	ADP
fumecheng-7707	228	18	the	the	DET
fumecheng-7707	228	19	wear	wear	NOUN
fumecheng-7707	228	20	coefficient	coefficient	NOUN
fumecheng-7707	228	21	kwear	kwear	PROPN
fumecheng-7707	228	22	,	,	PUNCT
fumecheng-7707	228	23	the	the	DET
fumecheng-7707	228	24	hardness	hardness	NOUN
fumecheng-7707	228	25	of	of	ADP
fumecheng-7707	228	26	the	the	DET
fumecheng-7707	228	27	worn	worn	ADJ
fumecheng-7707	228	28	body	body	NOUN
fumecheng-7707	228	29	σ0	σ0	NOUN
fumecheng-7707	228	30	and	and	CCONJ
fumecheng-7707	228	31	the	the	DET
fumecheng-7707	228	32	slip	slip	NOUN
fumecheng-7707	228	33	displacement	displacement	ADJ
fumecheng-7707	228	34	distribution	distribution	NOUN
fumecheng-7707	228	35	δu	δu	ADP
fumecheng-7707	228	36	,	,	PUNCT
fumecheng-7707	228	37	which	which	PRON
fumecheng-7707	228	38	can	can	AUX
fumecheng-7707	228	39	be	be	AUX
fumecheng-7707	228	40	calculated	calculate	VERB
fumecheng-7707	228	41	analytically	analytically	ADV
fumecheng-7707	228	42	,	,	PUNCT
fumecheng-7707	228	43	as	as	SCONJ
fumecheng-7707	228	44	is	be	AUX
fumecheng-7707	228	45	shown	show	VERB
fumecheng-7707	228	46	in	in	ADP
fumecheng-7707	228	47	another	another	DET
fumecheng-7707	228	48	manuscript	manuscript	NOUN
fumecheng-7707	228	49	[	[	X
fumecheng-7707	228	50	22	22	NUM
fumecheng-7707	228	51	]	]	PUNCT
fumecheng-7707	228	52	by	by	ADP
fumecheng-7707	228	53	the	the	DET
fumecheng-7707	228	54	author	author	NOUN
fumecheng-7707	228	55	.	.	PUNCT
fumecheng-7707	229	1	therefore	therefore	ADV
fumecheng-7707	229	2	,	,	PUNCT
fumecheng-7707	229	3	the	the	DET
fumecheng-7707	229	4	wear	wear	NOUN
fumecheng-7707	229	5	simulation	simulation	NOUN
fumecheng-7707	229	6	only	only	ADV
fumecheng-7707	229	7	requires	require	VERB
fumecheng-7707	229	8	the	the	DET
fumecheng-7707	229	9	two	two	NUM
fumecheng-7707	229	10	-	-	PUNCT
fumecheng-7707	229	11	step	step	NOUN
fumecheng-7707	229	12	transformation	transformation	NOUN
fumecheng-7707	229	13	f	f	PROPN
fumecheng-7707	229	14	→	→	SYM
fumecheng-7707	229	15	g	g	PROPN
fumecheng-7707	229	16	–	–	PUNCT
fumecheng-7707	229	17	see	see	VERB
fumecheng-7707	229	18	eq	eq	NOUN
fumecheng-7707	229	19	.	.	PUNCT
fumecheng-7707	230	1	(	(	PUNCT
fumecheng-7707	230	2	1	1	NUM
fumecheng-7707	230	3	)	)	PUNCT
fumecheng-7707	230	4	–	–	PUNCT
fumecheng-7707	230	5	and	and	CCONJ
fumecheng-7707	230	6	g	g	PROPN
fumecheng-7707	230	7	→	→	SYM
fumecheng-7707	230	8	p	p	X
fumecheng-7707	230	9	–	–	PUNCT
fumecheng-7707	230	10	see	see	VERB
fumecheng-7707	230	11	eq	eq	NOUN
fumecheng-7707	230	12	.	.	PUNCT
fumecheng-7707	231	1	(	(	PUNCT
fumecheng-7707	231	2	28	28	NUM
fumecheng-7707	231	3	)	)	PUNCT
fumecheng-7707	231	4	with	with	ADP
fumecheng-7707	231	5	k	k	PROPN
fumecheng-7707	231	6	=	=	SYM
fumecheng-7707	231	7	0	0	NUM
fumecheng-7707	231	8	–	–	PUNCT
fumecheng-7707	231	9	in	in	ADP
fumecheng-7707	231	10	every	every	DET
fumecheng-7707	231	11	fretting	fret	VERB
fumecheng-7707	231	12	cycle	cycle	NOUN
fumecheng-7707	231	13	.	.	PUNCT
fumecheng-7707	232	1	in	in	ADP
fumecheng-7707	232	2	fig	fig	NOUN
fumecheng-7707	232	3	.	.	PUNCT
fumecheng-7707	233	1	4	4	NUM
fumecheng-7707	233	2	the	the	DET
fumecheng-7707	233	3	results	result	NOUN
fumecheng-7707	233	4	for	for	ADP
fumecheng-7707	233	5	the	the	DET
fumecheng-7707	233	6	time	time	NOUN
fumecheng-7707	233	7	-	-	PUNCT
fumecheng-7707	233	8	evolution	evolution	NOUN
fumecheng-7707	233	9	of	of	ADP
fumecheng-7707	233	10	the	the	DET
fumecheng-7707	233	11	worn	worn	ADJ
fumecheng-7707	233	12	profile	profile	NOUN
fumecheng-7707	233	13	for	for	ADP
fumecheng-7707	233	14	different	different	ADJ
fumecheng-7707	233	15	numbers	number	NOUN
fumecheng-7707	233	16	of	of	ADP
fumecheng-7707	233	17	normalized	normalize	VERB
fumecheng-7707	233	18	fretting	fret	VERB
fumecheng-7707	233	19	cycles	cycle	NOUN
fumecheng-7707	233	20	are	be	AUX
fumecheng-7707	233	21	shown	show	VERB
fumecheng-7707	233	22	in	in	ADP
fumecheng-7707	233	23	normalized	normalize	VERB
fumecheng-7707	233	24	variables	variable	NOUN
fumecheng-7707	233	25	.	.	PUNCT
fumecheng-7707	234	1	the	the	DET
fumecheng-7707	234	2	characteristic	characteristic	ADJ
fumecheng-7707	234	3	number	number	NOUN
fumecheng-7707	234	4	of	of	ADP
fumecheng-7707	234	5	fretting	fret	VERB
fumecheng-7707	234	6	cycles	cycle	NOUN
fumecheng-7707	234	7	is	be	AUX
fumecheng-7707	234	8	given	give	VERB
fumecheng-7707	234	9	by	by	ADP
fumecheng-7707	234	10	[	[	X
fumecheng-7707	234	11	9	9	NUM
fumecheng-7707	234	12	]	]	SYM
fumecheng-7707	234	13	2	2	NUM
fumecheng-7707	234	14	0	0	NUM
fumecheng-7707	234	15	0	0	NUM
fumecheng-7707	234	16	0	0	NUM
fumecheng-7707	234	17	wear	wear	NOUN
fumecheng-7707	234	18	0	0	NUM
fumecheng-7707	234	19	,	,	PUNCT
fumecheng-7707	234	20	a	a	DET
fumecheng-7707	234	21	a	a	PROPN
fumecheng-7707	234	22	d	d	NOUN
fumecheng-7707	234	23	n	n	NOUN
fumecheng-7707	234	24	k	k	NOUN
fumecheng-7707	234	25	f	f	PUNCT
fumecheng-7707	234	26	u	u	PROPN
fumecheng-7707	234	27			PROPN
fumecheng-7707	234	28			PROPN
fumecheng-7707	234	29	=	=	PUNCT
fumecheng-7707	234	30	(	(	PUNCT
fumecheng-7707	234	31	31	31	NUM
fumecheng-7707	234	32	)	)	PUNCT
fumecheng-7707	234	33	with	with	ADP
fumecheng-7707	234	34	the	the	DET
fumecheng-7707	234	35	initial	initial	ADJ
fumecheng-7707	234	36	normal	normal	ADJ
fumecheng-7707	234	37	force	force	NOUN
fumecheng-7707	234	38	f0	f0	PROPN
fumecheng-7707	234	39	.	.	PUNCT
fumecheng-7707	235	1	the	the	DET
fumecheng-7707	235	2	number	number	NOUN
fumecheng-7707	235	3	of	of	ADP
fumecheng-7707	235	4	elements	element	NOUN
fumecheng-7707	235	5	was	be	AUX
fumecheng-7707	235	6	chosen	choose	VERB
fumecheng-7707	235	7	to	to	PART
fumecheng-7707	235	8	be	be	AUX
fumecheng-7707	235	9	n	n	PRON
fumecheng-7707	235	10	=	=	SYM
fumecheng-7707	235	11	2001	2001	NUM
fumecheng-7707	235	12	.	.	PUNCT
fumecheng-7707	236	1	the	the	DET
fumecheng-7707	236	2	results	result	NOUN
fumecheng-7707	236	3	on	on	ADP
fumecheng-7707	236	4	the	the	DET
fumecheng-7707	236	5	left	left	NOUN
fumecheng-7707	236	6	have	have	AUX
fumecheng-7707	236	7	been	be	AUX
fumecheng-7707	236	8	obtained	obtain	VERB
fumecheng-7707	236	9	with	with	ADP
fumecheng-7707	236	10	the	the	DET
fumecheng-7707	236	11	standard	standard	ADJ
fumecheng-7707	236	12	matrix	matrix	NOUN
fumecheng-7707	236	13	-	-	PUNCT
fumecheng-7707	236	14	vector	vector	NOUN
fumecheng-7707	236	15	multiplication	multiplication	NOUN
fumecheng-7707	236	16	procedure	procedure	NOUN
fumecheng-7707	236	17	;	;	PUNCT
fumecheng-7707	236	18	the	the	DET
fumecheng-7707	236	19	results	result	NOUN
fumecheng-7707	236	20	on	on	ADP
fumecheng-7707	236	21	the	the	DET
fumecheng-7707	236	22	right	right	NOUN
fumecheng-7707	236	23	were	be	AUX
fumecheng-7707	236	24	determined	determine	VERB
fumecheng-7707	236	25	with	with	ADP
fumecheng-7707	236	26	the	the	DET
fumecheng-7707	236	27	fft	fft	NOUN
fumecheng-7707	236	28	-	-	PUNCT
fumecheng-7707	236	29	based	base	VERB
fumecheng-7707	236	30	implementation	implementation	NOUN
fumecheng-7707	236	31	proposed	propose	VERB
fumecheng-7707	236	32	in	in	ADP
fumecheng-7707	236	33	the	the	DET
fumecheng-7707	236	34	present	present	ADJ
fumecheng-7707	236	35	manuscript	manuscript	NOUN
fumecheng-7707	236	36	.	.	PUNCT
fumecheng-7707	237	1	there	there	PRON
fumecheng-7707	237	2	are	be	VERB
fumecheng-7707	237	3	no	no	DET
fumecheng-7707	237	4	notable	notable	ADJ
fumecheng-7707	237	5	differences	difference	NOUN
fumecheng-7707	237	6	between	between	ADP
fumecheng-7707	237	7	both	both	DET
fumecheng-7707	237	8	variants	variant	NOUN
fumecheng-7707	237	9	.	.	PUNCT
fumecheng-7707	238	1	however	however	ADV
fumecheng-7707	238	2	,	,	PUNCT
fumecheng-7707	238	3	the	the	DET
fumecheng-7707	238	4	fft	fft	NOUN
fumecheng-7707	238	5	-	-	PUNCT
fumecheng-7707	238	6	based	base	VERB
fumecheng-7707	238	7	implementation	implementation	NOUN
fumecheng-7707	238	8	operates	operate	VERB
fumecheng-7707	238	9	faster	fast	ADV
fumecheng-7707	238	10	by	by	ADP
fumecheng-7707	238	11	a	a	DET
fumecheng-7707	238	12	factor	factor	NOUN
fumecheng-7707	238	13	of	of	ADP
fumecheng-7707	238	14	five	five	NUM
fumecheng-7707	238	15	.	.	PUNCT
fumecheng-7707	239	1	814	814	NUM
fumecheng-7707	239	2	e.	e.	PROPN
fumecheng-7707	239	3	willert	willert	PROPN
fumecheng-7707	239	4	moreover	moreover	ADV
fumecheng-7707	239	5	,	,	PUNCT
fumecheng-7707	239	6	this	this	DET
fumecheng-7707	239	7	speed	speed	NOUN
fumecheng-7707	239	8	advantage	advantage	NOUN
fumecheng-7707	239	9	of	of	ADP
fumecheng-7707	239	10	the	the	DET
fumecheng-7707	239	11	new	new	ADJ
fumecheng-7707	239	12	implementation	implementation	NOUN
fumecheng-7707	239	13	obviously	obviously	ADV
fumecheng-7707	239	14	increases	increase	VERB
fumecheng-7707	239	15	,	,	PUNCT
fumecheng-7707	239	16	if	if	SCONJ
fumecheng-7707	239	17	more	more	ADJ
fumecheng-7707	239	18	elements	element	NOUN
fumecheng-7707	239	19	are	be	AUX
fumecheng-7707	239	20	used	use	VERB
fumecheng-7707	239	21	for	for	ADP
fumecheng-7707	239	22	the	the	DET
fumecheng-7707	239	23	transformation	transformation	NOUN
fumecheng-7707	239	24	to	to	PART
fumecheng-7707	239	25	obtain	obtain	VERB
fumecheng-7707	239	26	a	a	DET
fumecheng-7707	239	27	finer	fine	ADJ
fumecheng-7707	239	28	resolution	resolution	NOUN
fumecheng-7707	239	29	.	.	PUNCT
fumecheng-7707	240	1	(	(	PUNCT
fumecheng-7707	240	2	a	a	X
fumecheng-7707	240	3	)	)	PUNCT
fumecheng-7707	240	4	(	(	PUNCT
fumecheng-7707	240	5	b	b	X
fumecheng-7707	240	6	)	)	PUNCT
fumecheng-7707	240	7	fig	fig	NOUN
fumecheng-7707	240	8	.	.	PUNCT
fumecheng-7707	241	1	4	4	NUM
fumecheng-7707	241	2	time	time	NOUN
fumecheng-7707	241	3	-	-	PUNCT
fumecheng-7707	241	4	evolution	evolution	NOUN
fumecheng-7707	241	5	of	of	ADP
fumecheng-7707	241	6	the	the	DET
fumecheng-7707	241	7	worn	worn	ADJ
fumecheng-7707	241	8	profile	profile	NOUN
fumecheng-7707	241	9	f	f	X
fumecheng-7707	241	10	,	,	PUNCT
fumecheng-7707	241	11	normalized	normalize	VERB
fumecheng-7707	241	12	for	for	ADP
fumecheng-7707	241	13	the	the	DET
fumecheng-7707	241	14	fixed	fix	VERB
fumecheng-7707	241	15	indentation	indentation	NOUN
fumecheng-7707	241	16	depth	depth	NOUN
fumecheng-7707	241	17	d	d	NOUN
fumecheng-7707	241	18	,	,	PUNCT
fumecheng-7707	241	19	as	as	ADP
fumecheng-7707	241	20	a	a	DET
fumecheng-7707	241	21	function	function	NOUN
fumecheng-7707	241	22	of	of	ADP
fumecheng-7707	241	23	the	the	DET
fumecheng-7707	241	24	radial	radial	ADJ
fumecheng-7707	241	25	coordinate	coordinate	NOUN
fumecheng-7707	241	26	r	r	NOUN
fumecheng-7707	241	27	,	,	PUNCT
fumecheng-7707	241	28	normalized	normalize	VERB
fumecheng-7707	241	29	for	for	ADP
fumecheng-7707	241	30	the	the	DET
fumecheng-7707	241	31	initial	initial	ADJ
fumecheng-7707	241	32	contact	contact	NOUN
fumecheng-7707	241	33	radius	radius	NOUN
fumecheng-7707	241	34	a0	a0	PROPN
fumecheng-7707	241	35	,	,	PUNCT
fumecheng-7707	241	36	for	for	ADP
fumecheng-7707	241	37	tangential	tangential	ADJ
fumecheng-7707	241	38	fretting	fretting	NOUN
fumecheng-7707	241	39	wear	wear	NOUN
fumecheng-7707	241	40	of	of	ADP
fumecheng-7707	241	41	an	an	DET
fumecheng-7707	241	42	initially	initially	ADV
fumecheng-7707	241	43	parabolic	parabolic	ADJ
fumecheng-7707	241	44	indenter	indenter	NOUN
fumecheng-7707	241	45	and	and	CCONJ
fumecheng-7707	241	46	different	different	ADJ
fumecheng-7707	241	47	numbers	number	NOUN
fumecheng-7707	241	48	of	of	ADP
fumecheng-7707	241	49	normalized	normalize	VERB
fumecheng-7707	241	50	cycles	cycle	NOUN
fumecheng-7707	241	51	,	,	PUNCT
fumecheng-7707	241	52	n	n	CCONJ
fumecheng-7707	241	53	/	/	SYM
fumecheng-7707	241	54	n0	n0	PROPN
fumecheng-7707	241	55	.	.	PUNCT
fumecheng-7707	242	1	the	the	DET
fumecheng-7707	242	2	dashed	dash	VERB
fumecheng-7707	242	3	black	black	ADJ
fumecheng-7707	242	4	line	line	NOUN
fumecheng-7707	242	5	denotes	denote	VERB
fumecheng-7707	242	6	the	the	DET
fumecheng-7707	242	7	limiting	limit	VERB
fumecheng-7707	242	8	no	no	DET
fumecheng-7707	242	9	-	-	PUNCT
fumecheng-7707	242	10	wear	wear	NOUN
fumecheng-7707	242	11	profile	profile	NOUN
fumecheng-7707	242	12	[	[	X
fumecheng-7707	242	13	23	23	NUM
fumecheng-7707	242	14	]	]	PUNCT
fumecheng-7707	242	15	.	.	PUNCT
fumecheng-7707	243	1	(	(	PUNCT
fumecheng-7707	243	2	a	a	X
fumecheng-7707	243	3	)	)	PUNCT
fumecheng-7707	243	4	results	result	NOUN
fumecheng-7707	243	5	for	for	ADP
fumecheng-7707	243	6	the	the	DET
fumecheng-7707	243	7	semi	semi	ADJ
fumecheng-7707	243	8	-	-	ADJ
fumecheng-7707	243	9	analytic	analytic	ADJ
fumecheng-7707	243	10	method	method	NOUN
fumecheng-7707	243	11	with	with	ADP
fumecheng-7707	243	12	matrix	matrix	NOUN
fumecheng-7707	243	13	-	-	PUNCT
fumecheng-7707	243	14	vector	vector	NOUN
fumecheng-7707	243	15	-	-	PUNCT
fumecheng-7707	243	16	multiplication	multiplication	NOUN
fumecheng-7707	243	17	(	(	PUNCT
fumecheng-7707	243	18	b	b	NOUN
fumecheng-7707	243	19	)	)	PUNCT
fumecheng-7707	243	20	results	result	NOUN
fumecheng-7707	243	21	for	for	ADP
fumecheng-7707	243	22	the	the	DET
fumecheng-7707	243	23	semi	semi	ADJ
fumecheng-7707	243	24	-	-	ADJ
fumecheng-7707	243	25	analytic	analytic	ADJ
fumecheng-7707	243	26	method	method	NOUN
fumecheng-7707	243	27	accelerated	accelerate	VERB
fumecheng-7707	243	28	by	by	ADP
fumecheng-7707	243	29	the	the	DET
fumecheng-7707	243	30	fft	fft	PROPN
fumecheng-7707	243	31	5	5	NUM
fumecheng-7707	243	32	.	.	PUNCT
fumecheng-7707	244	1	conclusions	conclusion	NOUN
fumecheng-7707	244	2	it	it	PRON
fumecheng-7707	244	3	has	have	AUX
fumecheng-7707	244	4	been	be	AUX
fumecheng-7707	244	5	shown	show	VERB
fumecheng-7707	244	6	,	,	PUNCT
fumecheng-7707	244	7	how	how	SCONJ
fumecheng-7707	244	8	the	the	DET
fumecheng-7707	244	9	abel	abel	NOUN
fumecheng-7707	244	10	-	-	PUNCT
fumecheng-7707	244	11	like	like	ADJ
fumecheng-7707	244	12	integral	integral	ADJ
fumecheng-7707	244	13	transform	transform	NOUN
fumecheng-7707	244	14	solution	solution	NOUN
fumecheng-7707	244	15	to	to	ADP
fumecheng-7707	244	16	the	the	DET
fumecheng-7707	244	17	general	general	ADJ
fumecheng-7707	244	18	axisymmetric	axisymmetric	ADJ
fumecheng-7707	244	19	boussinesq	boussinesq	ADJ
fumecheng-7707	244	20	problem	problem	NOUN
fumecheng-7707	244	21	can	can	AUX
fumecheng-7707	244	22	be	be	AUX
fumecheng-7707	244	23	written	write	VERB
fumecheng-7707	244	24	in	in	ADP
fumecheng-7707	244	25	terms	term	NOUN
fumecheng-7707	244	26	of	of	ADP
fumecheng-7707	244	27	real	real	ADJ
fumecheng-7707	244	28	convolutions	convolution	NOUN
fumecheng-7707	244	29	to	to	PART
fumecheng-7707	244	30	enable	enable	VERB
fumecheng-7707	244	31	the	the	DET
fumecheng-7707	244	32	evaluation	evaluation	NOUN
fumecheng-7707	244	33	of	of	ADP
fumecheng-7707	244	34	the	the	DET
fumecheng-7707	244	35	integral	integral	ADJ
fumecheng-7707	244	36	transforms	transform	NOUN
fumecheng-7707	244	37	based	base	VERB
fumecheng-7707	244	38	on	on	ADP
fumecheng-7707	244	39	the	the	DET
fumecheng-7707	244	40	1d	1d	NUM
fumecheng-7707	244	41	-	-	PUNCT
fumecheng-7707	244	42	fft	fft	NOUN
fumecheng-7707	244	43	.	.	PUNCT
fumecheng-7707	245	1	both	both	DET
fumecheng-7707	245	2	elastically	elastically	ADV
fumecheng-7707	245	3	homogeneous	homogeneous	ADJ
fumecheng-7707	245	4	materials	material	NOUN
fumecheng-7707	245	5	and	and	CCONJ
fumecheng-7707	245	6	those	those	PRON
fumecheng-7707	245	7	with	with	ADP
fumecheng-7707	245	8	an	an	DET
fumecheng-7707	245	9	elastic	elastic	ADJ
fumecheng-7707	245	10	grading	grading	NOUN
fumecheng-7707	245	11	in	in	ADP
fumecheng-7707	245	12	the	the	DET
fumecheng-7707	245	13	form	form	NOUN
fumecheng-7707	245	14	of	of	ADP
fumecheng-7707	245	15	a	a	DET
fumecheng-7707	245	16	power	power	NOUN
fumecheng-7707	245	17	-	-	PUNCT
fumecheng-7707	245	18	law	law	NOUN
fumecheng-7707	245	19	were	be	AUX
fumecheng-7707	245	20	considered	consider	VERB
fumecheng-7707	245	21	.	.	PUNCT
fumecheng-7707	246	1	while	while	SCONJ
fumecheng-7707	246	2	the	the	DET
fumecheng-7707	246	3	convolution	convolution	NOUN
fumecheng-7707	246	4	formulation	formulation	NOUN
fumecheng-7707	246	5	works	work	VERB
fumecheng-7707	246	6	perfectly	perfectly	ADV
fumecheng-7707	246	7	for	for	ADP
fumecheng-7707	246	8	the	the	DET
fumecheng-7707	246	9	profile	profile	ADJ
fumecheng-7707	246	10	transformation	transformation	NOUN
fumecheng-7707	246	11	and	and	CCONJ
fumecheng-7707	246	12	the	the	DET
fumecheng-7707	246	13	determination	determination	NOUN
fumecheng-7707	246	14	of	of	ADP
fumecheng-7707	246	15	the	the	DET
fumecheng-7707	246	16	contact	contact	NOUN
fumecheng-7707	246	17	stress	stress	NOUN
fumecheng-7707	246	18	distribution	distribution	NOUN
fumecheng-7707	246	19	,	,	PUNCT
fumecheng-7707	246	20	it	it	PRON
fumecheng-7707	246	21	is	be	AUX
fumecheng-7707	246	22	significantly	significantly	ADV
fumecheng-7707	246	23	more	more	ADV
fumecheng-7707	246	24	restrictive	restrictive	ADJ
fumecheng-7707	246	25	than	than	ADP
fumecheng-7707	246	26	the	the	DET
fumecheng-7707	246	27	standard	standard	ADJ
fumecheng-7707	246	28	formulation	formulation	NOUN
fumecheng-7707	246	29	in	in	ADP
fumecheng-7707	246	30	case	case	NOUN
fumecheng-7707	246	31	of	of	ADP
fumecheng-7707	246	32	the	the	DET
fumecheng-7707	246	33	determination	determination	NOUN
fumecheng-7707	246	34	of	of	ADP
fumecheng-7707	246	35	the	the	DET
fumecheng-7707	246	36	local	local	ADJ
fumecheng-7707	246	37	displacement	displacement	ADJ
fumecheng-7707	246	38	distribution	distribution	NOUN
fumecheng-7707	246	39	.	.	PUNCT
fumecheng-7707	247	1	moreover	moreover	ADV
fumecheng-7707	247	2	,	,	PUNCT
fumecheng-7707	247	3	it	it	PRON
fumecheng-7707	247	4	was	be	AUX
fumecheng-7707	247	5	demonstrated	demonstrate	VERB
fumecheng-7707	247	6	that	that	SCONJ
fumecheng-7707	247	7	the	the	DET
fumecheng-7707	247	8	fft	fft	PROPN
fumecheng-7707	247	9	-	-	PUNCT
fumecheng-7707	247	10	based	base	VERB
fumecheng-7707	247	11	solution	solution	NOUN
fumecheng-7707	247	12	operates	operate	VERB
fumecheng-7707	247	13	faster	fast	ADV
fumecheng-7707	247	14	than	than	ADP
fumecheng-7707	247	15	the	the	DET
fumecheng-7707	247	16	standard	standard	ADJ
fumecheng-7707	247	17	formulation	formulation	NOUN
fumecheng-7707	247	18	,	,	PUNCT
fumecheng-7707	247	19	if	if	SCONJ
fumecheng-7707	247	20	the	the	DET
fumecheng-7707	247	21	number	number	NOUN
fumecheng-7707	247	22	of	of	ADP
fumecheng-7707	247	23	array	array	NOUN
fumecheng-7707	247	24	elements	element	NOUN
fumecheng-7707	247	25	exceeds	exceed	VERB
fumecheng-7707	247	26	103	103	NUM
fumecheng-7707	247	27	(	(	PUNCT
fumecheng-7707	247	28	obviously	obviously	ADV
fumecheng-7707	247	29	,	,	PUNCT
fumecheng-7707	247	30	the	the	DET
fumecheng-7707	247	31	advantage	advantage	NOUN
fumecheng-7707	247	32	of	of	ADP
fumecheng-7707	247	33	the	the	DET
fumecheng-7707	247	34	fft	fft	NOUN
fumecheng-7707	247	35	will	will	AUX
fumecheng-7707	247	36	grow	grow	VERB
fumecheng-7707	247	37	,	,	PUNCT
fumecheng-7707	247	38	if	if	SCONJ
fumecheng-7707	247	39	the	the	DET
fumecheng-7707	247	40	number	number	NOUN
fumecheng-7707	247	41	of	of	ADP
fumecheng-7707	247	42	array	array	NOUN
fumecheng-7707	247	43	elements	element	NOUN
fumecheng-7707	247	44	further	further	ADJ
fumecheng-7707	247	45	increases	increase	NOUN
fumecheng-7707	247	46	)	)	PUNCT
fumecheng-7707	247	47	.	.	PUNCT
fumecheng-7707	248	1	while	while	SCONJ
fumecheng-7707	248	2	modern	modern	ADJ
fumecheng-7707	248	3	computers	computer	NOUN
fumecheng-7707	248	4	are	be	AUX
fumecheng-7707	248	5	,	,	PUNCT
fumecheng-7707	248	6	of	of	ADP
fumecheng-7707	248	7	course	course	NOUN
fumecheng-7707	248	8	,	,	PUNCT
fumecheng-7707	248	9	able	able	ADJ
fumecheng-7707	248	10	to	to	PART
fumecheng-7707	248	11	quickly	quickly	ADV
fumecheng-7707	248	12	perform	perform	VERB
fumecheng-7707	248	13	the	the	DET
fumecheng-7707	248	14	transformations	transformation	NOUN
fumecheng-7707	248	15	in	in	ADP
fumecheng-7707	248	16	the	the	DET
fumecheng-7707	248	17	traditional	traditional	ADJ
fumecheng-7707	248	18	form	form	NOUN
fumecheng-7707	248	19	,	,	PUNCT
fumecheng-7707	248	20	there	there	PRON
fumecheng-7707	248	21	might	might	AUX
fumecheng-7707	248	22	be	be	AUX
fumecheng-7707	248	23	applications	application	NOUN
fumecheng-7707	248	24	for	for	ADP
fumecheng-7707	248	25	which	which	PRON
fumecheng-7707	248	26	the	the	DET
fumecheng-7707	248	27	reduction	reduction	NOUN
fumecheng-7707	248	28	in	in	ADP
fumecheng-7707	248	29	calculation	calculation	NOUN
fumecheng-7707	248	30	time	time	NOUN
fumecheng-7707	248	31	and	and	CCONJ
fumecheng-7707	248	32	memory	memory	NOUN
fumecheng-7707	248	33	space	space	NOUN
fumecheng-7707	248	34	(	(	PUNCT
fumecheng-7707	248	35	for	for	ADP
fumecheng-7707	248	36	a	a	DET
fumecheng-7707	248	37	very	very	ADV
fumecheng-7707	248	38	fine	fine	ADJ
fumecheng-7707	248	39	discretization	discretization	NOUN
fumecheng-7707	248	40	)	)	PUNCT
fumecheng-7707	248	41	can	can	AUX
fumecheng-7707	248	42	come	come	VERB
fumecheng-7707	248	43	in	in	ADP
fumecheng-7707	248	44	handy	handy	ADJ
fumecheng-7707	248	45	,	,	PUNCT
fumecheng-7707	248	46	if	if	SCONJ
fumecheng-7707	248	47	the	the	DET
fumecheng-7707	248	48	contact	contact	NOUN
fumecheng-7707	248	49	simulation	simulation	NOUN
fumecheng-7707	248	50	is	be	AUX
fumecheng-7707	248	51	part	part	NOUN
fumecheng-7707	248	52	of	of	ADP
fumecheng-7707	248	53	a	a	DET
fumecheng-7707	248	54	more	more	ADV
fumecheng-7707	248	55	global	global	ADJ
fumecheng-7707	248	56	(	(	PUNCT
fumecheng-7707	248	57	hybrid	hybrid	NOUN
fumecheng-7707	248	58	)	)	PUNCT
fumecheng-7707	248	59	numerical	numerical	ADJ
fumecheng-7707	248	60	routine	routine	NOUN
fumecheng-7707	248	61	,	,	PUNCT
fumecheng-7707	248	62	e.g.	e.g.	ADV
fumecheng-7707	248	63	,	,	PUNCT
fumecheng-7707	248	64	for	for	ADP
fumecheng-7707	248	65	the	the	DET
fumecheng-7707	248	66	coupled	couple	VERB
fumecheng-7707	248	67	analysis	analysis	NOUN
fumecheng-7707	248	68	of	of	ADP
fumecheng-7707	248	69	wear	wear	NOUN
fumecheng-7707	248	70	and	and	CCONJ
fumecheng-7707	248	71	fatigue	fatigue	NOUN
fumecheng-7707	248	72	in	in	ADP
fumecheng-7707	248	73	fretting	fret	VERB
fumecheng-7707	248	74	.	.	PUNCT
fumecheng-7707	249	1	as	as	ADP
fumecheng-7707	249	2	the	the	DET
fumecheng-7707	249	3	main	main	ADJ
fumecheng-7707	249	4	numerical	numerical	ADJ
fumecheng-7707	249	5	issues	issue	NOUN
fumecheng-7707	249	6	in	in	ADP
fumecheng-7707	249	7	the	the	DET
fumecheng-7707	249	8	transformation	transformation	NOUN
fumecheng-7707	249	9	result	result	NOUN
fumecheng-7707	249	10	from	from	ADP
fumecheng-7707	249	11	the	the	DET
fumecheng-7707	249	12	finite	finite	ADJ
fumecheng-7707	249	13	difference	difference	NOUN
fumecheng-7707	249	14	derivatives	derivative	NOUN
fumecheng-7707	249	15	and	and	CCONJ
fumecheng-7707	249	16	the	the	DET
fumecheng-7707	249	17	trapezoidal	trapezoidal	ADJ
fumecheng-7707	249	18	rule	rule	NOUN
fumecheng-7707	249	19	,	,	PUNCT
fumecheng-7707	249	20	the	the	DET
fumecheng-7707	249	21	fft	fft	NOUN
fumecheng-7707	249	22	-	-	PUNCT
fumecheng-7707	249	23	based	base	VERB
fumecheng-7707	249	24	solution	solution	NOUN
fumecheng-7707	249	25	exhibits	exhibit	VERB
fumecheng-7707	249	26	practically	practically	ADV
fumecheng-7707	249	27	the	the	DET
fumecheng-7707	249	28	same	same	ADJ
fumecheng-7707	249	29	convergence	convergence	NOUN
fumecheng-7707	249	30	and	and	CCONJ
fumecheng-7707	249	31	stability	stability	NOUN
fumecheng-7707	249	32	as	as	ADP
fumecheng-7707	249	33	the	the	DET
fumecheng-7707	249	34	standard	standard	ADJ
fumecheng-7707	249	35	procedure	procedure	NOUN
fumecheng-7707	249	36	.	.	PUNCT
fumecheng-7707	250	1	the	the	DET
fumecheng-7707	250	2	fft	fft	PROPN
fumecheng-7707	250	3	-	-	PUNCT
fumecheng-7707	250	4	formulation	formulation	NOUN
fumecheng-7707	250	5	can	can	AUX
fumecheng-7707	250	6	be	be	AUX
fumecheng-7707	250	7	used	use	VERB
fumecheng-7707	250	8	for	for	ADP
fumecheng-7707	250	9	highly	highly	ADV
fumecheng-7707	250	10	transient	transient	ADJ
fumecheng-7707	250	11	contact	contact	NOUN
fumecheng-7707	250	12	simulations	simulation	NOUN
fumecheng-7707	250	13	;	;	PUNCT
fumecheng-7707	250	14	in	in	ADP
fumecheng-7707	250	15	this	this	DET
fumecheng-7707	250	16	case	case	NOUN
fumecheng-7707	250	17	,	,	PUNCT
fumecheng-7707	250	18	one	one	NUM
fumecheng-7707	250	19	,	,	PUNCT
fumecheng-7707	250	20	however	however	ADV
fumecheng-7707	250	21	,	,	PUNCT
fumecheng-7707	250	22	must	must	AUX
fumecheng-7707	250	23	keep	keep	VERB
fumecheng-7707	250	24	in	in	ADP
fumecheng-7707	250	25	mind	mind	NOUN
fumecheng-7707	250	26	that	that	SCONJ
fumecheng-7707	250	27	the	the	DET
fumecheng-7707	250	28	one	one	NUM
fumecheng-7707	250	29	-	-	PUNCT
fumecheng-7707	250	30	dimensional	dimensional	ADJ
fumecheng-7707	250	31	arrays	array	NOUN
fumecheng-7707	250	32	used	use	VERB
fumecheng-7707	250	33	for	for	ADP
fumecheng-7707	250	34	the	the	DET
fumecheng-7707	250	35	fft	fft	NOUN
fumecheng-7707	250	36	are	be	AUX
fumecheng-7707	250	37	equidistant	equidistant	ADJ
fumecheng-7707	250	38	in	in	ADP
fumecheng-7707	250	39	the	the	DET
fumecheng-7707	250	40	squares	square	NOUN
fumecheng-7707	250	41	of	of	ADP
fumecheng-7707	250	42	the	the	DET
fumecheng-7707	250	43	spatial	spatial	ADJ
fumecheng-7707	250	44	coordinates	coordinate	NOUN
fumecheng-7707	250	45	;	;	PUNCT
fumecheng-7707	250	46	this	this	PRON
fumecheng-7707	250	47	also	also	ADV
fumecheng-7707	250	48	leads	lead	VERB
fumecheng-7707	250	49	to	to	ADP
fumecheng-7707	250	50	a	a	DET
fumecheng-7707	250	51	finer	fine	ADJ
fumecheng-7707	250	52	resolution	resolution	NOUN
fumecheng-7707	250	53	at	at	ADP
fumecheng-7707	250	54	the	the	DET
fumecheng-7707	250	55	edge	edge	NOUN
fumecheng-7707	250	56	of	of	ADP
fumecheng-7707	250	57	contact	contact	NOUN
fumecheng-7707	250	58	,	,	PUNCT
fumecheng-7707	250	59	which	which	PRON
fumecheng-7707	250	60	might	might	AUX
fumecheng-7707	250	61	be	be	AUX
fumecheng-7707	250	62	beneficial	beneficial	ADJ
fumecheng-7707	250	63	in	in	ADP
fumecheng-7707	250	64	several	several	ADJ
fumecheng-7707	250	65	circumstances	circumstance	NOUN
fumecheng-7707	250	66	.	.	PUNCT
fumecheng-7707	251	1	fft	fft	NOUN
fumecheng-7707	251	2	-	-	PUNCT
fumecheng-7707	251	3	based	base	VERB
fumecheng-7707	251	4	implementation	implementation	NOUN
fumecheng-7707	251	5	of	of	ADP
fumecheng-7707	251	6	the	the	DET
fumecheng-7707	251	7	mdr	mdr	PROPN
fumecheng-7707	251	8	transformations	transformation	NOUN
fumecheng-7707	251	9	for	for	ADP
fumecheng-7707	251	10	homogeneous	homogeneous	ADJ
fumecheng-7707	251	11	and	and	CCONJ
fumecheng-7707	251	12	power	power	NOUN
fumecheng-7707	251	13	-	-	PUNCT
fumecheng-7707	251	14	law	law	NOUN
fumecheng-7707	251	15	graded	grade	VERB
fumecheng-7707	251	16	materials815	materials815	PROPN
fumecheng-7707	251	17	there	there	PRON
fumecheng-7707	251	18	exists	exist	VERB
fumecheng-7707	251	19	a	a	DET
fumecheng-7707	251	20	wide	wide	ADJ
fumecheng-7707	251	21	literature	literature	NOUN
fumecheng-7707	251	22	on	on	ADP
fumecheng-7707	251	23	the	the	DET
fumecheng-7707	251	24	numerical	numerical	ADJ
fumecheng-7707	251	25	implementation	implementation	NOUN
fumecheng-7707	251	26	of	of	ADP
fumecheng-7707	251	27	the	the	DET
fumecheng-7707	251	28	abel	abel	PROPN
fumecheng-7707	251	29	transform	transform	NOUN
fumecheng-7707	251	30	and	and	CCONJ
fumecheng-7707	251	31	its	its	PRON
fumecheng-7707	251	32	inversion	inversion	NOUN
fumecheng-7707	251	33	(	(	PUNCT
fumecheng-7707	251	34	see	see	VERB
fumecheng-7707	251	35	the	the	DET
fumecheng-7707	251	36	review	review	NOUN
fumecheng-7707	251	37	paper	paper	NOUN
fumecheng-7707	251	38	by	by	ADP
fumecheng-7707	251	39	hickstein	hickstein	ADV
fumecheng-7707	251	40	et	et	PROPN
fumecheng-7707	251	41	al	al	PROPN
fumecheng-7707	251	42	.	.	PUNCT
fumecheng-7707	252	1	[	[	X
fumecheng-7707	252	2	24	24	NUM
fumecheng-7707	252	3	]	]	PUNCT
fumecheng-7707	252	4	and	and	CCONJ
fumecheng-7707	252	5	the	the	DET
fumecheng-7707	252	6	references	reference	NOUN
fumecheng-7707	252	7	therein	therein	ADV
fumecheng-7707	252	8	)	)	PUNCT
fumecheng-7707	252	9	,	,	PUNCT
fumecheng-7707	252	10	mainly	mainly	ADV
fumecheng-7707	252	11	in	in	ADP
fumecheng-7707	252	12	the	the	DET
fumecheng-7707	252	13	framework	framework	NOUN
fumecheng-7707	252	14	of	of	ADP
fumecheng-7707	252	15	image	image	NOUN
fumecheng-7707	252	16	processing	processing	NOUN
fumecheng-7707	252	17	.	.	PUNCT
fumecheng-7707	253	1	however	however	ADV
fumecheng-7707	253	2	,	,	PUNCT
fumecheng-7707	253	3	the	the	DET
fumecheng-7707	253	4	algorithms	algorithm	NOUN
fumecheng-7707	253	5	used	use	VERB
fumecheng-7707	253	6	in	in	ADP
fumecheng-7707	253	7	that	that	DET
fumecheng-7707	253	8	context	context	NOUN
fumecheng-7707	253	9	are	be	AUX
fumecheng-7707	253	10	optimized	optimize	VERB
fumecheng-7707	253	11	to	to	PART
fumecheng-7707	253	12	handle	handle	VERB
fumecheng-7707	253	13	very	very	ADV
fumecheng-7707	253	14	noisy	noisy	ADJ
fumecheng-7707	253	15	data	datum	NOUN
fumecheng-7707	253	16	and	and	CCONJ
fumecheng-7707	253	17	therefore	therefore	ADV
fumecheng-7707	253	18	prioritize	prioritize	VERB
fumecheng-7707	253	19	stability	stability	NOUN
fumecheng-7707	253	20	over	over	ADP
fumecheng-7707	253	21	efficiency	efficiency	NOUN
fumecheng-7707	253	22	.	.	PUNCT
fumecheng-7707	254	1	this	this	PRON
fumecheng-7707	254	2	is	be	AUX
fumecheng-7707	254	3	usually	usually	ADV
fumecheng-7707	254	4	not	not	PART
fumecheng-7707	254	5	necessary	necessary	ADJ
fumecheng-7707	254	6	in	in	ADP
fumecheng-7707	254	7	the	the	DET
fumecheng-7707	254	8	framework	framework	NOUN
fumecheng-7707	254	9	of	of	ADP
fumecheng-7707	254	10	axisymmetric	axisymmetric	ADJ
fumecheng-7707	254	11	contact	contact	NOUN
fumecheng-7707	254	12	mechanics	mechanic	NOUN
fumecheng-7707	254	13	.	.	PUNCT
fumecheng-7707	255	1	acknowledgement	acknowledgement	NOUN
fumecheng-7707	255	2	:	:	PUNCT
fumecheng-7707	255	3	this	this	DET
fumecheng-7707	255	4	work	work	NOUN
fumecheng-7707	255	5	has	have	AUX
fumecheng-7707	255	6	been	be	AUX
fumecheng-7707	255	7	supported	support	VERB
fumecheng-7707	255	8	by	by	ADP
fumecheng-7707	255	9	the	the	DET
fumecheng-7707	255	10	german	german	ADJ
fumecheng-7707	255	11	research	research	NOUN
fumecheng-7707	255	12	foundation	foundation	NOUN
fumecheng-7707	255	13	under	under	ADP
fumecheng-7707	255	14	the	the	DET
fumecheng-7707	255	15	project	project	NOUN
fumecheng-7707	255	16	number	number	NOUN
fumecheng-7707	255	17	po	po	NOUN
fumecheng-7707	255	18	810/66	810/66	NUM
fumecheng-7707	255	19	-	-	SYM
fumecheng-7707	255	20	1	1	NUM
fumecheng-7707	255	21	.	.	PUNCT
fumecheng-7707	256	1	moreover	moreover	ADV
fumecheng-7707	256	2	,	,	PUNCT
fumecheng-7707	256	3	the	the	DET
fumecheng-7707	256	4	author	author	NOUN
fumecheng-7707	256	5	is	be	AUX
fumecheng-7707	256	6	very	very	ADV
fumecheng-7707	256	7	grateful	grateful	ADJ
fumecheng-7707	256	8	to	to	ADP
fumecheng-7707	256	9	mr	mr	PROPN
fumecheng-7707	256	10	.	.	PROPN
fumecheng-7707	256	11	justus	justus	PROPN
fumecheng-7707	256	12	benad	benad	PROPN
fumecheng-7707	256	13	for	for	ADP
fumecheng-7707	256	14	valuable	valuable	ADJ
fumecheng-7707	256	15	discussions	discussion	NOUN
fumecheng-7707	256	16	on	on	ADP
fumecheng-7707	256	17	the	the	DET
fumecheng-7707	256	18	topic	topic	NOUN
fumecheng-7707	256	19	.	.	PUNCT
fumecheng-7707	257	1	references	reference	NOUN
fumecheng-7707	257	2	1	1	NUM
fumecheng-7707	257	3	.	.	PUNCT
fumecheng-7707	258	1	popov	popov	PROPN
fumecheng-7707	258	2	,	,	PUNCT
fumecheng-7707	258	3	v.l	v.l	PROPN
fumecheng-7707	258	4	.	.	PROPN
fumecheng-7707	258	5	,	,	PUNCT
fumecheng-7707	258	6	heß	heß	PROPN
fumecheng-7707	258	7	,	,	PUNCT
fumecheng-7707	258	8	m.	m.	NOUN
fumecheng-7707	258	9	,	,	PUNCT
fumecheng-7707	258	10	willert	willert	NOUN
fumecheng-7707	258	11	,	,	PUNCT
fumecheng-7707	258	12	e.	e.	PROPN
fumecheng-7707	258	13	,	,	PUNCT
fumecheng-7707	258	14	2019	2019	NUM
fumecheng-7707	258	15	,	,	PUNCT
fumecheng-7707	258	16	handbook	handbook	NOUN
fumecheng-7707	258	17	of	of	ADP
fumecheng-7707	258	18	contact	contact	NOUN
fumecheng-7707	258	19	mechanics	mechanic	NOUN
fumecheng-7707	258	20	:	:	PUNCT
fumecheng-7707	258	21	exact	exact	ADJ
fumecheng-7707	258	22	solutions	solution	NOUN
fumecheng-7707	258	23	of	of	ADP
fumecheng-7707	258	24	axisymmetric	axisymmetric	ADJ
fumecheng-7707	258	25	contact	contact	NOUN
fumecheng-7707	258	26	problems	problem	NOUN
fumecheng-7707	258	27	,	,	PUNCT
fumecheng-7707	258	28	springer	springer	NOUN
fumecheng-7707	258	29	-	-	PUNCT
fumecheng-7707	258	30	verlag	verlag	PROPN
fumecheng-7707	258	31	,	,	PUNCT
fumecheng-7707	258	32	berlin	berlin	PROPN
fumecheng-7707	258	33	heidelberg	heidelberg	PROPN
fumecheng-7707	258	34	,	,	PUNCT
fumecheng-7707	258	35	347	347	NUM
fumecheng-7707	258	36	p.	p.	NOUN
fumecheng-7707	258	37	2	2	NUM
fumecheng-7707	258	38	.	.	PUNCT
fumecheng-7707	258	39	barquins	barquin	NOUN
fumecheng-7707	258	40	,	,	PUNCT
fumecheng-7707	258	41	m.	m.	NOUN
fumecheng-7707	258	42	,	,	PUNCT
fumecheng-7707	258	43	maugis	maugis	PROPN
fumecheng-7707	258	44	,	,	PUNCT
fumecheng-7707	258	45	d.	d.	PROPN
fumecheng-7707	258	46	,	,	PUNCT
fumecheng-7707	258	47	1982	1982	NUM
fumecheng-7707	258	48	,	,	PUNCT
fumecheng-7707	258	49	adhesive	adhesive	ADJ
fumecheng-7707	258	50	contact	contact	NOUN
fumecheng-7707	258	51	of	of	ADP
fumecheng-7707	258	52	axisymmetric	axisymmetric	ADJ
fumecheng-7707	258	53	punches	punch	NOUN
fumecheng-7707	258	54	on	on	ADP
fumecheng-7707	258	55	an	an	DET
fumecheng-7707	258	56	elastic	elastic	ADJ
fumecheng-7707	258	57	half	half	ADJ
fumecheng-7707	258	58	-	-	PUNCT
fumecheng-7707	258	59	space	space	NOUN
fumecheng-7707	258	60	:	:	PUNCT
fumecheng-7707	258	61	the	the	DET
fumecheng-7707	258	62	modified	modify	VERB
fumecheng-7707	258	63	hertz	hertz	NOUN
fumecheng-7707	258	64	-	-	PUNCT
fumecheng-7707	258	65	huber	huber	PROPN
fumecheng-7707	258	66	’s	’s	PART
fumecheng-7707	258	67	stress	stress	NOUN
fumecheng-7707	258	68	tensor	tensor	NOUN
fumecheng-7707	258	69	for	for	ADP
fumecheng-7707	258	70	contacting	contact	VERB
fumecheng-7707	258	71	spheres	sphere	NOUN
fumecheng-7707	258	72	,	,	PUNCT
fumecheng-7707	258	73	journal	journal	PROPN
fumecheng-7707	258	74	de	de	PROPN
fumecheng-7707	258	75	mécanique	mécanique	PROPN
fumecheng-7707	258	76	théorique	théorique	PROPN
fumecheng-7707	258	77	et	et	PROPN
fumecheng-7707	258	78	appliquée	appliquée	PROPN
fumecheng-7707	258	79	,	,	PUNCT
fumecheng-7707	258	80	1(2	1(2	NUM
fumecheng-7707	258	81	)	)	PUNCT
fumecheng-7707	258	82	,	,	PUNCT
fumecheng-7707	258	83	pp	pp	PROPN
fumecheng-7707	258	84	.	.	PUNCT
fumecheng-7707	259	1	331	331	NUM
fumecheng-7707	259	2	-	-	SYM
fumecheng-7707	259	3	357	357	NUM
fumecheng-7707	259	4	.	.	PUNCT
fumecheng-7707	260	1	3	3	NUM
fumecheng-7707	260	2	.	.	X
fumecheng-7707	260	3	jäger	jäger	PROPN
fumecheng-7707	260	4	,	,	PUNCT
fumecheng-7707	260	5	j.	j.	PROPN
fumecheng-7707	260	6	,	,	PUNCT
fumecheng-7707	260	7	1998	1998	NUM
fumecheng-7707	260	8	,	,	PUNCT
fumecheng-7707	260	9	a	a	DET
fumecheng-7707	260	10	new	new	ADJ
fumecheng-7707	260	11	principle	principle	NOUN
fumecheng-7707	260	12	in	in	ADP
fumecheng-7707	260	13	contact	contact	NOUN
fumecheng-7707	260	14	mechanics	mechanic	NOUN
fumecheng-7707	260	15	,	,	PUNCT
fumecheng-7707	260	16	journal	journal	NOUN
fumecheng-7707	260	17	of	of	ADP
fumecheng-7707	260	18	tribology	tribology	NOUN
fumecheng-7707	260	19	,	,	PUNCT
fumecheng-7707	260	20	120(4	120(4	NUM
fumecheng-7707	260	21	)	)	PUNCT
fumecheng-7707	260	22	,	,	PUNCT
fumecheng-7707	260	23	pp	pp	PROPN
fumecheng-7707	260	24	.	.	PUNCT
fumecheng-7707	261	1	677	677	NUM
fumecheng-7707	261	2	-	-	SYM
fumecheng-7707	261	3	684	684	NUM
fumecheng-7707	261	4	.	.	PUNCT
fumecheng-7707	262	1	4	4	NUM
fumecheng-7707	262	2	.	.	X
fumecheng-7707	262	3	ciavarella	ciavarella	NOUN
fumecheng-7707	262	4	,	,	PUNCT
fumecheng-7707	262	5	m.	m.	NOUN
fumecheng-7707	262	6	,	,	PUNCT
fumecheng-7707	262	7	1998	1998	NUM
fumecheng-7707	262	8	,	,	PUNCT
fumecheng-7707	262	9	tangential	tangential	ADJ
fumecheng-7707	262	10	loading	loading	NOUN
fumecheng-7707	262	11	of	of	ADP
fumecheng-7707	262	12	general	general	ADJ
fumecheng-7707	262	13	three	three	NUM
fumecheng-7707	262	14	-	-	PUNCT
fumecheng-7707	262	15	dimensional	dimensional	ADJ
fumecheng-7707	262	16	contacts	contact	NOUN
fumecheng-7707	262	17	,	,	PUNCT
fumecheng-7707	262	18	journal	journal	NOUN
fumecheng-7707	262	19	of	of	ADP
fumecheng-7707	262	20	applied	apply	VERB
fumecheng-7707	262	21	mechanics	mechanic	NOUN
fumecheng-7707	262	22	,	,	PUNCT
fumecheng-7707	262	23	65(4	65(4	PROPN
fumecheng-7707	262	24	)	)	PUNCT
fumecheng-7707	262	25	,	,	PUNCT
fumecheng-7707	262	26	pp	pp	PROPN
fumecheng-7707	262	27	.	.	PUNCT
fumecheng-7707	263	1	998	998	NUM
fumecheng-7707	263	2	-	-	SYM
fumecheng-7707	263	3	1003	1003	NUM
fumecheng-7707	263	4	.	.	PUNCT
fumecheng-7707	264	1	5	5	X
fumecheng-7707	264	2	.	.	X
fumecheng-7707	264	3	lee	lee	PROPN
fumecheng-7707	264	4	,	,	PUNCT
fumecheng-7707	264	5	e.h	e.h	PROPN
fumecheng-7707	264	6	.	.	PROPN
fumecheng-7707	264	7	,	,	PUNCT
fumecheng-7707	264	8	radok	radok	PROPN
fumecheng-7707	264	9	,	,	PUNCT
fumecheng-7707	264	10	j.r.m	j.r.m	PROPN
fumecheng-7707	264	11	.	.	PROPN
fumecheng-7707	264	12	,	,	PUNCT
fumecheng-7707	264	13	1960	1960	NUM
fumecheng-7707	264	14	,	,	PUNCT
fumecheng-7707	264	15	the	the	DET
fumecheng-7707	264	16	contact	contact	NOUN
fumecheng-7707	264	17	problem	problem	NOUN
fumecheng-7707	264	18	for	for	ADP
fumecheng-7707	264	19	viscoelastic	viscoelastic	ADJ
fumecheng-7707	264	20	bodies	body	NOUN
fumecheng-7707	264	21	,	,	PUNCT
fumecheng-7707	264	22	journal	journal	NOUN
fumecheng-7707	264	23	of	of	ADP
fumecheng-7707	264	24	applied	apply	VERB
fumecheng-7707	264	25	mechanics	mechanic	NOUN
fumecheng-7707	264	26	,	,	PUNCT
fumecheng-7707	264	27	27(3	27(3	NUM
fumecheng-7707	264	28	)	)	PUNCT
fumecheng-7707	264	29	,	,	PUNCT
fumecheng-7707	264	30	pp	pp	PROPN
fumecheng-7707	264	31	.	.	PUNCT
fumecheng-7707	265	1	438	438	NUM
fumecheng-7707	265	2	-	-	SYM
fumecheng-7707	265	3	444	444	NUM
fumecheng-7707	265	4	.	.	NOUN
fumecheng-7707	266	1	6	6	NUM
fumecheng-7707	266	2	.	.	X
fumecheng-7707	266	3	schubert	schubert	PROPN
fumecheng-7707	266	4	,	,	PUNCT
fumecheng-7707	266	5	g.	g.	PROPN
fumecheng-7707	266	6	,	,	PUNCT
fumecheng-7707	266	7	1942	1942	NUM
fumecheng-7707	266	8	,	,	PUNCT
fumecheng-7707	266	9	zur	zur	NOUN
fumecheng-7707	266	10	frage	frage	NOUN
fumecheng-7707	266	11	der	der	NOUN
fumecheng-7707	266	12	druckverteilung	druckverteilung	AUX
fumecheng-7707	266	13	unter	unter	NOUN
fumecheng-7707	266	14	elastisch	elastisch	PROPN
fumecheng-7707	266	15	gelagerten	gelagerten	VERB
fumecheng-7707	266	16	tragwerken	tragwerken	VERB
fumecheng-7707	266	17	,	,	PUNCT
fumecheng-7707	266	18	ingenieur	ingenieur	PROPN
fumecheng-7707	266	19	-	-	PUNCT
fumecheng-7707	266	20	archiv	archiv	PROPN
fumecheng-7707	266	21	,	,	PUNCT
fumecheng-7707	266	22	13(3	13(3	NUM
fumecheng-7707	266	23	)	)	PUNCT
fumecheng-7707	266	24	,	,	PUNCT
fumecheng-7707	267	1	pp	pp	ADP
fumecheng-7707	267	2	.	.	PUNCT
fumecheng-7707	268	1	132	132	NUM
fumecheng-7707	268	2	-	-	SYM
fumecheng-7707	268	3	147	147	NUM
fumecheng-7707	268	4	.	.	PUNCT
fumecheng-7707	269	1	7	7	X
fumecheng-7707	269	2	.	.	X
fumecheng-7707	269	3	popov	popov	PROPN
fumecheng-7707	269	4	,	,	PUNCT
fumecheng-7707	269	5	v.l	v.l	PROPN
fumecheng-7707	269	6	.	.	PROPN
fumecheng-7707	269	7	,	,	PUNCT
fumecheng-7707	269	8	heß	heß	PROPN
fumecheng-7707	269	9	,	,	PUNCT
fumecheng-7707	269	10	m.	m.	NOUN
fumecheng-7707	269	11	,	,	PUNCT
fumecheng-7707	269	12	2015	2015	NUM
fumecheng-7707	269	13	,	,	PUNCT
fumecheng-7707	269	14	method	method	NOUN
fumecheng-7707	269	15	of	of	ADP
fumecheng-7707	269	16	dimensionality	dimensionality	NOUN
fumecheng-7707	269	17	reduction	reduction	NOUN
fumecheng-7707	269	18	in	in	ADP
fumecheng-7707	269	19	contact	contact	NOUN
fumecheng-7707	269	20	mechanics	mechanic	NOUN
fumecheng-7707	269	21	and	and	CCONJ
fumecheng-7707	269	22	friction	friction	NOUN
fumecheng-7707	269	23	,	,	PUNCT
fumecheng-7707	269	24	springerverlag	springerverlag	NOUN
fumecheng-7707	269	25	,	,	PUNCT
fumecheng-7707	269	26	berlin	berlin	PROPN
fumecheng-7707	269	27	heidelberg	heidelberg	PROPN
fumecheng-7707	269	28	,	,	PUNCT
fumecheng-7707	269	29	265	265	NUM
fumecheng-7707	269	30	p.	p.	NOUN
fumecheng-7707	269	31	8	8	NUM
fumecheng-7707	269	32	.	.	PUNCT
fumecheng-7707	270	1	benad	benad	PROPN
fumecheng-7707	270	2	,	,	PUNCT
fumecheng-7707	270	3	j.	j.	PROPN
fumecheng-7707	270	4	,	,	PUNCT
fumecheng-7707	270	5	2018	2018	NUM
fumecheng-7707	270	6	,	,	PUNCT
fumecheng-7707	270	7	fast	fast	ADJ
fumecheng-7707	270	8	numerical	numerical	ADJ
fumecheng-7707	270	9	implementation	implementation	NOUN
fumecheng-7707	270	10	of	of	ADP
fumecheng-7707	270	11	the	the	DET
fumecheng-7707	270	12	mdr	mdr	PROPN
fumecheng-7707	270	13	transformations	transformation	NOUN
fumecheng-7707	270	14	,	,	PUNCT
fumecheng-7707	270	15	facta	facta	PROPN
fumecheng-7707	270	16	universitatis	universitatis	PROPN
fumecheng-7707	270	17	-	-	PUNCT
fumecheng-7707	270	18	series	series	NOUN
fumecheng-7707	270	19	mechanical	mechanical	ADJ
fumecheng-7707	270	20	engineering	engineering	NOUN
fumecheng-7707	270	21	,	,	PUNCT
fumecheng-7707	270	22	16(2	16(2	NUM
fumecheng-7707	270	23	)	)	PUNCT
fumecheng-7707	270	24	,	,	PUNCT
fumecheng-7707	270	25	pp	pp	ADP
fumecheng-7707	270	26	.	.	PUNCT
fumecheng-7707	271	1	127	127	NUM
fumecheng-7707	271	2	-	-	SYM
fumecheng-7707	271	3	138	138	NUM
fumecheng-7707	271	4	.	.	NOUN
fumecheng-7707	272	1	9	9	X
fumecheng-7707	272	2	.	.	X
fumecheng-7707	272	3	dimaki	dimaki	NOUN
fumecheng-7707	272	4	,	,	PUNCT
fumecheng-7707	272	5	a.v	a.v	PROPN
fumecheng-7707	272	6	.	.	PROPN
fumecheng-7707	272	7	,	,	PUNCT
fumecheng-7707	272	8	dmitriev	dmitriev	PROPN
fumecheng-7707	272	9	,	,	PUNCT
fumecheng-7707	272	10	a.i	a.i	PROPN
fumecheng-7707	272	11	.	.	PROPN
fumecheng-7707	272	12	,	,	PUNCT
fumecheng-7707	272	13	chai	chai	NOUN
fumecheng-7707	272	14	,	,	PUNCT
fumecheng-7707	272	15	y.s	y.s	PROPN
fumecheng-7707	272	16	.	.	PROPN
fumecheng-7707	272	17	,	,	PUNCT
fumecheng-7707	272	18	popov	popov	PROPN
fumecheng-7707	272	19	,	,	PUNCT
fumecheng-7707	272	20	v.l	v.l	PROPN
fumecheng-7707	272	21	.	.	PROPN
fumecheng-7707	272	22	,	,	PUNCT
fumecheng-7707	272	23	2014	2014	NUM
fumecheng-7707	272	24	,	,	PUNCT
fumecheng-7707	272	25	rapid	rapid	ADJ
fumecheng-7707	272	26	simulation	simulation	NOUN
fumecheng-7707	272	27	procedure	procedure	NOUN
fumecheng-7707	272	28	for	for	ADP
fumecheng-7707	272	29	fretting	fret	VERB
fumecheng-7707	272	30	wear	wear	NOUN
fumecheng-7707	272	31	on	on	ADP
fumecheng-7707	272	32	the	the	DET
fumecheng-7707	272	33	basis	basis	NOUN
fumecheng-7707	272	34	of	of	ADP
fumecheng-7707	272	35	the	the	DET
fumecheng-7707	272	36	method	method	NOUN
fumecheng-7707	272	37	of	of	ADP
fumecheng-7707	272	38	dimensionality	dimensionality	NOUN
fumecheng-7707	272	39	reduction	reduction	NOUN
fumecheng-7707	272	40	,	,	PUNCT
fumecheng-7707	272	41	international	international	ADJ
fumecheng-7707	272	42	journal	journal	NOUN
fumecheng-7707	272	43	of	of	ADP
fumecheng-7707	272	44	solids	solid	NOUN
fumecheng-7707	272	45	and	and	CCONJ
fumecheng-7707	272	46	structures	structure	NOUN
fumecheng-7707	272	47	,	,	PUNCT
fumecheng-7707	272	48	51(25	51(25	NOUN
fumecheng-7707	272	49	-	-	SYM
fumecheng-7707	272	50	26	26	NUM
fumecheng-7707	272	51	)	)	PUNCT
fumecheng-7707	272	52	,	,	PUNCT
fumecheng-7707	272	53	pp	pp	PROPN
fumecheng-7707	272	54	.	.	PUNCT
fumecheng-7707	273	1	4215	4215	NUM
fumecheng-7707	273	2	-	-	SYM
fumecheng-7707	273	3	4220	4220	NUM
fumecheng-7707	273	4	.	.	PUNCT
fumecheng-7707	274	1	10	10	NUM
fumecheng-7707	274	2	.	.	PUNCT
fumecheng-7707	275	1	liu	liu	PROPN
fumecheng-7707	275	2	,	,	PUNCT
fumecheng-7707	275	3	z.	z.	PROPN
fumecheng-7707	275	4	,	,	PUNCT
fumecheng-7707	275	5	meyers	meyers	PROPN
fumecheng-7707	275	6	,	,	PUNCT
fumecheng-7707	275	7	m.a	m.a	PROPN
fumecheng-7707	275	8	.	.	PROPN
fumecheng-7707	275	9	,	,	PUNCT
fumecheng-7707	275	10	zhang	zhang	PROPN
fumecheng-7707	275	11	,	,	PUNCT
fumecheng-7707	275	12	z.	z.	PROPN
fumecheng-7707	275	13	,	,	PUNCT
fumecheng-7707	275	14	ritchie	ritchie	PROPN
fumecheng-7707	275	15	,	,	PUNCT
fumecheng-7707	275	16	r.o	r.o	PROPN
fumecheng-7707	275	17	.	.	PROPN
fumecheng-7707	275	18	,	,	PUNCT
fumecheng-7707	275	19	2017	2017	NUM
fumecheng-7707	275	20	,	,	PUNCT
fumecheng-7707	275	21	functional	functional	ADJ
fumecheng-7707	275	22	gradients	gradient	NOUN
fumecheng-7707	275	23	and	and	CCONJ
fumecheng-7707	275	24	heterogeneities	heterogeneity	NOUN
fumecheng-7707	275	25	in	in	ADP
fumecheng-7707	275	26	biological	biological	ADJ
fumecheng-7707	275	27	materials	material	NOUN
fumecheng-7707	275	28	:	:	PUNCT
fumecheng-7707	275	29	design	design	NOUN
fumecheng-7707	275	30	principles	principle	NOUN
fumecheng-7707	275	31	,	,	PUNCT
fumecheng-7707	275	32	functions	function	NOUN
fumecheng-7707	275	33	,	,	PUNCT
fumecheng-7707	275	34	and	and	CCONJ
fumecheng-7707	275	35	bioinspired	bioinspired	ADJ
fumecheng-7707	275	36	applications	application	NOUN
fumecheng-7707	275	37	,	,	PUNCT
fumecheng-7707	275	38	progress	progress	NOUN
fumecheng-7707	275	39	in	in	ADP
fumecheng-7707	275	40	materials	material	NOUN
fumecheng-7707	275	41	science	science	NOUN
fumecheng-7707	275	42	,	,	PUNCT
fumecheng-7707	275	43	88	88	NUM
fumecheng-7707	275	44	,	,	PUNCT
fumecheng-7707	275	45	pp	pp	ADJ
fumecheng-7707	275	46	.	.	PUNCT
fumecheng-7707	276	1	467	467	NUM
fumecheng-7707	276	2	-	-	SYM
fumecheng-7707	276	3	498	498	NUM
fumecheng-7707	276	4	.	.	PUNCT
fumecheng-7707	277	1	11	11	NUM
fumecheng-7707	277	2	.	.	PUNCT
fumecheng-7707	278	1	selvadurai	selvadurai	PROPN
fumecheng-7707	278	2	,	,	PUNCT
fumecheng-7707	278	3	a.p	a.p	PROPN
fumecheng-7707	278	4	.	.	PROPN
fumecheng-7707	278	5	,	,	PUNCT
fumecheng-7707	278	6	2007	2007	NUM
fumecheng-7707	278	7	,	,	PUNCT
fumecheng-7707	278	8	the	the	DET
fumecheng-7707	278	9	analytical	analytical	ADJ
fumecheng-7707	278	10	method	method	NOUN
fumecheng-7707	278	11	in	in	ADP
fumecheng-7707	278	12	geomechanics	geomechanic	NOUN
fumecheng-7707	278	13	,	,	PUNCT
fumecheng-7707	278	14	applied	apply	VERB
fumecheng-7707	278	15	mechanics	mechanic	NOUN
fumecheng-7707	278	16	reviews	review	NOUN
fumecheng-7707	278	17	,	,	PUNCT
fumecheng-7707	278	18	60	60	NUM
fumecheng-7707	278	19	,	,	PUNCT
fumecheng-7707	278	20	3	3	NUM
fumecheng-7707	278	21	,	,	PUNCT
fumecheng-7707	278	22	pp	pp	ADJ
fumecheng-7707	278	23	.	.	PUNCT
fumecheng-7707	279	1	87	87	NUM
fumecheng-7707	279	2	-	-	SYM
fumecheng-7707	279	3	106	106	NUM
fumecheng-7707	279	4	.	.	PUNCT
fumecheng-7707	280	1	12	12	NUM
fumecheng-7707	280	2	.	.	PUNCT
fumecheng-7707	281	1	giannakopoulos	giannakopoulos	PROPN
fumecheng-7707	281	2	,	,	PUNCT
fumecheng-7707	281	3	a.e	a.e	PROPN
fumecheng-7707	281	4	.	.	PROPN
fumecheng-7707	281	5	,	,	PUNCT
fumecheng-7707	281	6	suresh	suresh	PROPN
fumecheng-7707	281	7	,	,	PUNCT
fumecheng-7707	281	8	s.	s.	PROPN
fumecheng-7707	281	9	,	,	PUNCT
fumecheng-7707	281	10	1997	1997	NUM
fumecheng-7707	281	11	,	,	PUNCT
fumecheng-7707	281	12	indentation	indentation	NOUN
fumecheng-7707	281	13	of	of	ADP
fumecheng-7707	281	14	solids	solid	NOUN
fumecheng-7707	281	15	with	with	ADP
fumecheng-7707	281	16	gradients	gradient	NOUN
fumecheng-7707	281	17	in	in	ADP
fumecheng-7707	281	18	elastic	elastic	ADJ
fumecheng-7707	281	19	properties	property	NOUN
fumecheng-7707	281	20	:	:	PUNCT
fumecheng-7707	281	21	part	part	PROPN
fumecheng-7707	281	22	ii	ii	PROPN
fumecheng-7707	281	23	.	.	PUNCT
fumecheng-7707	282	1	axisymmetric	axisymmetric	PROPN
fumecheng-7707	282	2	indentors	indentor	NOUN
fumecheng-7707	282	3	,	,	PUNCT
fumecheng-7707	282	4	international	international	ADJ
fumecheng-7707	282	5	journal	journal	NOUN
fumecheng-7707	282	6	of	of	ADP
fumecheng-7707	282	7	solids	solid	NOUN
fumecheng-7707	282	8	and	and	CCONJ
fumecheng-7707	282	9	structures	structure	NOUN
fumecheng-7707	282	10	,	,	PUNCT
fumecheng-7707	282	11	34(19	34(19	NUM
fumecheng-7707	282	12	)	)	PUNCT
fumecheng-7707	282	13	,	,	PUNCT
fumecheng-7707	282	14	pp	pp	ADJ
fumecheng-7707	282	15	.	.	PUNCT
fumecheng-7707	282	16	2393	2393	NUM
fumecheng-7707	282	17	-	-	SYM
fumecheng-7707	282	18	2428	2428	NUM
fumecheng-7707	282	19	.	.	PUNCT
fumecheng-7707	283	1	13	13	NUM
fumecheng-7707	283	2	.	.	PUNCT
fumecheng-7707	284	1	jin	jin	PROPN
fumecheng-7707	284	2	,	,	PUNCT
fumecheng-7707	284	3	f.	f.	PROPN
fumecheng-7707	284	4	,	,	PUNCT
fumecheng-7707	284	5	guo	guo	PROPN
fumecheng-7707	284	6	,	,	PUNCT
fumecheng-7707	284	7	x.	x.	PROPN
fumecheng-7707	284	8	,	,	PUNCT
fumecheng-7707	284	9	zhang	zhang	PROPN
fumecheng-7707	284	10	,	,	PUNCT
fumecheng-7707	284	11	w.	w.	PROPN
fumecheng-7707	284	12	,	,	PUNCT
fumecheng-7707	284	13	2013	2013	NUM
fumecheng-7707	284	14	,	,	PUNCT
fumecheng-7707	284	15	a	a	DET
fumecheng-7707	284	16	unified	unified	ADJ
fumecheng-7707	284	17	treatment	treatment	NOUN
fumecheng-7707	284	18	of	of	ADP
fumecheng-7707	284	19	axisymmetric	axisymmetric	ADJ
fumecheng-7707	284	20	adhesive	adhesive	ADJ
fumecheng-7707	284	21	contact	contact	NOUN
fumecheng-7707	284	22	on	on	ADP
fumecheng-7707	284	23	a	a	DET
fumecheng-7707	284	24	power	power	NOUN
fumecheng-7707	284	25	-	-	PUNCT
fumecheng-7707	284	26	law	law	NOUN
fumecheng-7707	284	27	graded	grade	VERB
fumecheng-7707	284	28	elastic	elastic	ADJ
fumecheng-7707	284	29	half	half	ADJ
fumecheng-7707	284	30	-	-	PUNCT
fumecheng-7707	284	31	space	space	NOUN
fumecheng-7707	284	32	,	,	PUNCT
fumecheng-7707	284	33	journal	journal	NOUN
fumecheng-7707	284	34	of	of	ADP
fumecheng-7707	284	35	applied	apply	VERB
fumecheng-7707	284	36	mechanics	mechanic	NOUN
fumecheng-7707	284	37	,	,	PUNCT
fumecheng-7707	284	38	80(6	80(6	NOUN
fumecheng-7707	284	39	)	)	PUNCT
fumecheng-7707	284	40	,	,	PUNCT
fumecheng-7707	284	41	061024	061024	NUM
fumecheng-7707	284	42	.	.	PUNCT
fumecheng-7707	285	1	14	14	NUM
fumecheng-7707	285	2	.	.	PUNCT
fumecheng-7707	286	1	chen	chen	PROPN
fumecheng-7707	286	2	,	,	PUNCT
fumecheng-7707	286	3	s.	s.	PROPN
fumecheng-7707	286	4	,	,	PUNCT
fumecheng-7707	286	5	yan	yan	PROPN
fumecheng-7707	286	6	,	,	PUNCT
fumecheng-7707	286	7	c.	c.	PROPN
fumecheng-7707	286	8	,	,	PUNCT
fumecheng-7707	286	9	zhang	zhang	PROPN
fumecheng-7707	286	10	,	,	PUNCT
fumecheng-7707	286	11	p.	p.	PROPN
fumecheng-7707	286	12	,	,	PUNCT
fumecheng-7707	286	13	gao	gao	PROPN
fumecheng-7707	286	14	,	,	PUNCT
fumecheng-7707	286	15	h.	h.	PROPN
fumecheng-7707	286	16	,	,	PUNCT
fumecheng-7707	286	17	2009	2009	NUM
fumecheng-7707	286	18	,	,	PUNCT
fumecheng-7707	286	19	mechanics	mechanic	NOUN
fumecheng-7707	286	20	of	of	ADP
fumecheng-7707	286	21	adhesive	adhesive	ADJ
fumecheng-7707	286	22	contact	contact	NOUN
fumecheng-7707	286	23	on	on	ADP
fumecheng-7707	286	24	a	a	DET
fumecheng-7707	286	25	power	power	NOUN
fumecheng-7707	286	26	-	-	PUNCT
fumecheng-7707	286	27	law	law	NOUN
fumecheng-7707	286	28	graded	grade	VERB
fumecheng-7707	286	29	elastic	elastic	ADJ
fumecheng-7707	286	30	halfspace	halfspace	NOUN
fumecheng-7707	286	31	,	,	PUNCT
fumecheng-7707	286	32	journal	journal	NOUN
fumecheng-7707	286	33	of	of	ADP
fumecheng-7707	286	34	the	the	DET
fumecheng-7707	286	35	mechanics	mechanic	NOUN
fumecheng-7707	286	36	and	and	CCONJ
fumecheng-7707	286	37	physics	physic	NOUN
fumecheng-7707	286	38	of	of	ADP
fumecheng-7707	286	39	solids	solid	NOUN
fumecheng-7707	286	40	,	,	PUNCT
fumecheng-7707	286	41	57(9	57(9	NOUN
fumecheng-7707	286	42	)	)	PUNCT
fumecheng-7707	286	43	,	,	PUNCT
fumecheng-7707	286	44	pp	pp	ADP
fumecheng-7707	286	45	.	.	PUNCT
fumecheng-7707	286	46	1437	1437	NUM
fumecheng-7707	286	47	-	-	SYM
fumecheng-7707	286	48	1448	1448	NUM
fumecheng-7707	286	49	.	.	PUNCT
fumecheng-7707	287	1	15	15	NUM
fumecheng-7707	287	2	.	.	PUNCT
fumecheng-7707	288	1	heß	heß	PROPN
fumecheng-7707	288	2	,	,	PUNCT
fumecheng-7707	288	3	m.	m.	NOUN
fumecheng-7707	288	4	,	,	PUNCT
fumecheng-7707	288	5	2016	2016	NUM
fumecheng-7707	288	6	,	,	PUNCT
fumecheng-7707	288	7	a	a	DET
fumecheng-7707	288	8	simple	simple	ADJ
fumecheng-7707	288	9	method	method	NOUN
fumecheng-7707	288	10	for	for	ADP
fumecheng-7707	288	11	solving	solve	VERB
fumecheng-7707	288	12	adhesive	adhesive	ADJ
fumecheng-7707	288	13	and	and	CCONJ
fumecheng-7707	288	14	non	non	ADJ
fumecheng-7707	288	15	-	-	ADJ
fumecheng-7707	288	16	adhesive	adhesive	ADJ
fumecheng-7707	288	17	axisymmetric	axisymmetric	ADJ
fumecheng-7707	288	18	contact	contact	NOUN
fumecheng-7707	288	19	problems	problem	NOUN
fumecheng-7707	288	20	of	of	ADP
fumecheng-7707	288	21	elastically	elastically	ADV
fumecheng-7707	288	22	graded	grade	VERB
fumecheng-7707	288	23	materials	material	NOUN
fumecheng-7707	288	24	,	,	PUNCT
fumecheng-7707	288	25	international	international	ADJ
fumecheng-7707	288	26	journal	journal	NOUN
fumecheng-7707	288	27	of	of	ADP
fumecheng-7707	288	28	engineering	engineering	NOUN
fumecheng-7707	288	29	science	science	NOUN
fumecheng-7707	288	30	,	,	PUNCT
fumecheng-7707	288	31	104	104	NUM
fumecheng-7707	288	32	,	,	PUNCT
fumecheng-7707	288	33	pp	pp	ADJ
fumecheng-7707	288	34	.	.	PUNCT
fumecheng-7707	289	1	20	20	NUM
fumecheng-7707	289	2	-	-	SYM
fumecheng-7707	289	3	33	33	NUM
fumecheng-7707	289	4	.	.	PUNCT
fumecheng-7707	290	1	16	16	NUM
fumecheng-7707	290	2	.	.	PUNCT
fumecheng-7707	291	1	heß	heß	PROPN
fumecheng-7707	291	2	,	,	PUNCT
fumecheng-7707	291	3	m.	m.	NOUN
fumecheng-7707	291	4	,	,	PUNCT
fumecheng-7707	291	5	2016	2016	NUM
fumecheng-7707	291	6	,	,	PUNCT
fumecheng-7707	291	7	normal	normal	ADJ
fumecheng-7707	291	8	,	,	PUNCT
fumecheng-7707	291	9	tangential	tangential	ADJ
fumecheng-7707	291	10	and	and	CCONJ
fumecheng-7707	291	11	adhesive	adhesive	ADJ
fumecheng-7707	291	12	contacts	contact	NOUN
fumecheng-7707	291	13	between	between	ADP
fumecheng-7707	291	14	power	power	NOUN
fumecheng-7707	291	15	-	-	PUNCT
fumecheng-7707	291	16	law	law	NOUN
fumecheng-7707	291	17	graded	grade	VERB
fumecheng-7707	291	18	materials	material	NOUN
fumecheng-7707	291	19	,	,	PUNCT
fumecheng-7707	291	20	presentation	presentation	NOUN
fumecheng-7707	291	21	at	at	ADP
fumecheng-7707	291	22	the	the	DET
fumecheng-7707	291	23	workshop	workshop	NOUN
fumecheng-7707	291	24	on	on	ADP
fumecheng-7707	291	25	tribology	tribology	NOUN
fumecheng-7707	291	26	and	and	CCONJ
fumecheng-7707	291	27	contact	contact	NOUN
fumecheng-7707	291	28	mechanics	mechanic	NOUN
fumecheng-7707	291	29	in	in	ADP
fumecheng-7707	291	30	biological	biological	ADJ
fumecheng-7707	291	31	and	and	CCONJ
fumecheng-7707	291	32	medical	medical	ADJ
fumecheng-7707	291	33	applications	application	NOUN
fumecheng-7707	291	34	,	,	PUNCT
fumecheng-7707	291	35	technische	technische	PROPN
fumecheng-7707	291	36	universität	universität	PROPN
fumecheng-7707	291	37	berlin	berlin	PROPN
fumecheng-7707	291	38	,	,	PUNCT
fumecheng-7707	291	39	november	november	PROPN
fumecheng-7707	291	40	14	14	NUM
fumecheng-7707	291	41	-	-	SYM
fumecheng-7707	291	42	17	17	NUM
fumecheng-7707	291	43	,	,	PUNCT
fumecheng-7707	291	44	berlin	berlin	PROPN
fumecheng-7707	291	45	.	.	PUNCT
fumecheng-7707	292	1	17	17	NUM
fumecheng-7707	292	2	.	.	PUNCT
fumecheng-7707	292	3	paulino	paulino	PROPN
fumecheng-7707	292	4	,	,	PUNCT
fumecheng-7707	292	5	g.h	g.h	PROPN
fumecheng-7707	292	6	.	.	PROPN
fumecheng-7707	292	7	,	,	PUNCT
fumecheng-7707	292	8	jin	jin	PROPN
fumecheng-7707	292	9	,	,	PUNCT
fumecheng-7707	292	10	z.h	z.h	PROPN
fumecheng-7707	292	11	.	.	PROPN
fumecheng-7707	292	12	,	,	PUNCT
fumecheng-7707	292	13	2001	2001	NUM
fumecheng-7707	292	14	,	,	PUNCT
fumecheng-7707	292	15	correspondence	correspondence	NOUN
fumecheng-7707	292	16	principle	principle	NOUN
fumecheng-7707	292	17	in	in	ADP
fumecheng-7707	292	18	viscoelastic	viscoelastic	NOUN
fumecheng-7707	292	19	functionally	functionally	ADV
fumecheng-7707	292	20	graded	grade	VERB
fumecheng-7707	292	21	materials	material	NOUN
fumecheng-7707	292	22	,	,	PUNCT
fumecheng-7707	292	23	journal	journal	NOUN
fumecheng-7707	292	24	of	of	ADP
fumecheng-7707	292	25	applied	apply	VERB
fumecheng-7707	292	26	mechanics	mechanic	NOUN
fumecheng-7707	292	27	,	,	PUNCT
fumecheng-7707	292	28	68(1	68(1	NOUN
fumecheng-7707	292	29	)	)	PUNCT
fumecheng-7707	292	30	,	,	PUNCT
fumecheng-7707	292	31	pp	pp	ADP
fumecheng-7707	292	32	.	.	PUNCT
fumecheng-7707	293	1	129	129	NUM
fumecheng-7707	293	2	-	-	SYM
fumecheng-7707	293	3	132	132	NUM
fumecheng-7707	293	4	.	.	NOUN
fumecheng-7707	294	1	18	18	NUM
fumecheng-7707	294	2	.	.	PUNCT
fumecheng-7707	294	3	willert	willert	PROPN
fumecheng-7707	294	4	,	,	PUNCT
fumecheng-7707	294	5	e.	e.	PROPN
fumecheng-7707	294	6	,	,	PUNCT
fumecheng-7707	294	7	2020	2020	NUM
fumecheng-7707	294	8	,	,	PUNCT
fumecheng-7707	294	9	ratio	ratio	NOUN
fumecheng-7707	294	10	of	of	ADP
fumecheng-7707	294	11	loss	loss	NOUN
fumecheng-7707	294	12	and	and	CCONJ
fumecheng-7707	294	13	storage	storage	NOUN
fumecheng-7707	294	14	moduli	modulus	NOUN
fumecheng-7707	294	15	determines	determine	VERB
fumecheng-7707	294	16	restitution	restitution	NOUN
fumecheng-7707	294	17	coefficient	coefficient	NOUN
fumecheng-7707	294	18	in	in	ADP
fumecheng-7707	294	19	low	low	ADJ
fumecheng-7707	294	20	-	-	PUNCT
fumecheng-7707	294	21	velocity	velocity	NOUN
fumecheng-7707	294	22	viscoelastic	viscoelastic	NOUN
fumecheng-7707	294	23	impacts	impact	NOUN
fumecheng-7707	294	24	,	,	PUNCT
fumecheng-7707	294	25	frontiers	frontier	NOUN
fumecheng-7707	294	26	in	in	ADP
fumecheng-7707	294	27	mechanical	mechanical	ADJ
fumecheng-7707	294	28	engineering	engineering	NOUN
fumecheng-7707	294	29	,	,	PUNCT
fumecheng-7707	294	30	6	6	NUM
fumecheng-7707	294	31	,	,	PUNCT
fumecheng-7707	294	32	3	3	NUM
fumecheng-7707	294	33	.	.	NOUN
fumecheng-7707	294	34	19	19	NUM
fumecheng-7707	294	35	.	.	PUNCT
fumecheng-7707	295	1	willert	willert	PROPN
fumecheng-7707	295	2	,	,	PUNCT
fumecheng-7707	295	3	e.	e.	PROPN
fumecheng-7707	295	4	,	,	PUNCT
fumecheng-7707	295	5	dmitriev	dmitriev	PROPN
fumecheng-7707	295	6	,	,	PUNCT
fumecheng-7707	295	7	a.i	a.i	PROPN
fumecheng-7707	295	8	.	.	PROPN
fumecheng-7707	295	9	,	,	PUNCT
fumecheng-7707	295	10	psakhie	psakhie	PROPN
fumecheng-7707	295	11	,	,	PUNCT
fumecheng-7707	295	12	s.g	s.g	PROPN
fumecheng-7707	295	13	.	.	PROPN
fumecheng-7707	295	14	,	,	PUNCT
fumecheng-7707	295	15	popov	popov	PROPN
fumecheng-7707	295	16	,	,	PUNCT
fumecheng-7707	295	17	v.l	v.l	PROPN
fumecheng-7707	295	18	.	.	PROPN
fumecheng-7707	295	19	,	,	PUNCT
fumecheng-7707	295	20	2019	2019	NUM
fumecheng-7707	295	21	,	,	PUNCT
fumecheng-7707	295	22	effect	effect	NOUN
fumecheng-7707	295	23	of	of	ADP
fumecheng-7707	295	24	elastic	elastic	ADJ
fumecheng-7707	295	25	grading	grading	NOUN
fumecheng-7707	295	26	on	on	ADP
fumecheng-7707	295	27	fretting	fret	VERB
fumecheng-7707	295	28	wear	wear	NOUN
fumecheng-7707	295	29	,	,	PUNCT
fumecheng-7707	295	30	scientific	scientific	ADJ
fumecheng-7707	295	31	reports	report	NOUN
fumecheng-7707	295	32	,	,	PUNCT
fumecheng-7707	295	33	9	9	NUM
fumecheng-7707	295	34	,	,	PUNCT
fumecheng-7707	295	35	7791	7791	NUM
fumecheng-7707	295	36	.	.	PUNCT
fumecheng-7707	296	1	20	20	NUM
fumecheng-7707	296	2	.	.	X
fumecheng-7707	297	1	bracewell	bracewell	PROPN
fumecheng-7707	297	2	,	,	PUNCT
fumecheng-7707	297	3	r.n	r.n	PROPN
fumecheng-7707	297	4	.	.	PROPN
fumecheng-7707	297	5	,	,	PUNCT
fumecheng-7707	297	6	2000	2000	NUM
fumecheng-7707	297	7	,	,	PUNCT
fumecheng-7707	297	8	the	the	DET
fumecheng-7707	297	9	fourier	fourier	NOUN
fumecheng-7707	297	10	transform	transform	NOUN
fumecheng-7707	297	11	and	and	CCONJ
fumecheng-7707	297	12	its	its	PRON
fumecheng-7707	297	13	applications	application	NOUN
fumecheng-7707	297	14	,	,	PUNCT
fumecheng-7707	297	15	3rd	3rd	ADJ
fumecheng-7707	297	16	edition	edition	NOUN
fumecheng-7707	297	17	,	,	PUNCT
fumecheng-7707	297	18	new	new	PROPN
fumecheng-7707	297	19	york	york	PROPN
fumecheng-7707	297	20	:	:	PUNCT
fumecheng-7707	297	21	mcgraw	mcgraw	PROPN
fumecheng-7707	297	22	-	-	PUNCT
fumecheng-7707	297	23	hill	hill	NOUN
fumecheng-7707	297	24	book	book	NOUN
fumecheng-7707	297	25	company	company	NOUN
fumecheng-7707	297	26	,	,	PUNCT
fumecheng-7707	297	27	636	636	NUM
fumecheng-7707	297	28	p.	p.	NOUN
fumecheng-7707	297	29	816	816	NUM
fumecheng-7707	297	30	e.	e.	PROPN
fumecheng-7707	297	31	willert	willert	PROPN
fumecheng-7707	297	32	21	21	NUM
fumecheng-7707	297	33	.	.	PUNCT
fumecheng-7707	298	1	willert	willert	PROPN
fumecheng-7707	298	2	,	,	PUNCT
fumecheng-7707	298	3	e.	e.	PROPN
fumecheng-7707	298	4	,	,	PUNCT
fumecheng-7707	298	5	2020	2020	NUM
fumecheng-7707	298	6	,	,	PUNCT
fumecheng-7707	298	7	stoßprobleme	stoßprobleme	NOUN
fumecheng-7707	298	8	in	in	ADP
fumecheng-7707	298	9	physik	physik	PROPN
fumecheng-7707	298	10	,	,	PUNCT
fumecheng-7707	298	11	technik	technik	X
fumecheng-7707	298	12	und	und	PROPN
fumecheng-7707	298	13	medizin	medizin	PROPN
fumecheng-7707	298	14	:	:	PUNCT
fumecheng-7707	298	15	grundlagen	grundlagen	PROPN
fumecheng-7707	298	16	und	und	NOUN
fumecheng-7707	298	17	anwendungen	anwendungen	NOUN
fumecheng-7707	298	18	,	,	PUNCT
fumecheng-7707	298	19	springer	springer	NOUN
fumecheng-7707	298	20	vieweg	vieweg	NOUN
fumecheng-7707	298	21	,	,	PUNCT
fumecheng-7707	298	22	berlin	berlin	PROPN
fumecheng-7707	298	23	,	,	PUNCT
fumecheng-7707	298	24	241	241	NUM
fumecheng-7707	298	25	p.	p.	NOUN
fumecheng-7707	298	26	22	22	NUM
fumecheng-7707	298	27	.	.	PUNCT
fumecheng-7707	299	1	willert	willert	PROPN
fumecheng-7707	299	2	,	,	PUNCT
fumecheng-7707	299	3	e.	e.	PROPN
fumecheng-7707	299	4	,	,	PUNCT
fumecheng-7707	299	5	2021	2021	NUM
fumecheng-7707	299	6	,	,	PUNCT
fumecheng-7707	299	7	a	a	DET
fumecheng-7707	299	8	simple	simple	ADJ
fumecheng-7707	299	9	semi	semi	ADJ
fumecheng-7707	299	10	-	-	ADJ
fumecheng-7707	299	11	analytic	analytic	ADJ
fumecheng-7707	299	12	contact	contact	NOUN
fumecheng-7707	299	13	mechanical	mechanical	ADJ
fumecheng-7707	299	14	model	model	NOUN
fumecheng-7707	299	15	for	for	ADP
fumecheng-7707	299	16	tangential	tangential	ADJ
fumecheng-7707	299	17	and	and	CCONJ
fumecheng-7707	299	18	torsional	torsional	ADJ
fumecheng-7707	299	19	fretting	fretting	NOUN
fumecheng-7707	299	20	wear	wear	NOUN
fumecheng-7707	299	21	of	of	ADP
fumecheng-7707	299	22	axisymmetric	axisymmetric	ADJ
fumecheng-7707	299	23	contacts	contact	NOUN
fumecheng-7707	299	24	,	,	PUNCT
fumecheng-7707	299	25	symmetry	symmetry	NOUN
fumecheng-7707	299	26	,	,	PUNCT
fumecheng-7707	299	27	submitted	submit	VERB
fumecheng-7707	299	28	manuscript	manuscript	NOUN
fumecheng-7707	299	29	.	.	PUNCT
fumecheng-7707	300	1	23	23	NUM
fumecheng-7707	300	2	.	.	PUNCT
fumecheng-7707	301	1	popov	popov	PROPN
fumecheng-7707	301	2	,	,	PUNCT
fumecheng-7707	301	3	v.l	v.l	PROPN
fumecheng-7707	301	4	.	.	PROPN
fumecheng-7707	301	5	,	,	PUNCT
fumecheng-7707	301	6	2014	2014	NUM
fumecheng-7707	301	7	,	,	PUNCT
fumecheng-7707	301	8	analytic	analytic	ADJ
fumecheng-7707	301	9	solution	solution	NOUN
fumecheng-7707	301	10	for	for	ADP
fumecheng-7707	301	11	the	the	DET
fumecheng-7707	301	12	limiting	limit	VERB
fumecheng-7707	301	13	shape	shape	NOUN
fumecheng-7707	301	14	of	of	ADP
fumecheng-7707	301	15	profiles	profile	NOUN
fumecheng-7707	301	16	due	due	ADJ
fumecheng-7707	301	17	to	to	ADP
fumecheng-7707	301	18	fretting	fret	VERB
fumecheng-7707	301	19	wear	wear	NOUN
fumecheng-7707	301	20	,	,	PUNCT
fumecheng-7707	301	21	scientific	scientific	ADJ
fumecheng-7707	301	22	reports	report	NOUN
fumecheng-7707	301	23	,	,	PUNCT
fumecheng-7707	301	24	4	4	NUM
fumecheng-7707	301	25	,	,	PUNCT
fumecheng-7707	301	26	3749	3749	NUM
fumecheng-7707	301	27	.	.	PUNCT
fumecheng-7707	302	1	24	24	NUM
fumecheng-7707	302	2	.	.	PUNCT
fumecheng-7707	303	1	hickstein	hickstein	PROPN
fumecheng-7707	303	2	,	,	PUNCT
fumecheng-7707	303	3	d.d	d.d	PROPN
fumecheng-7707	303	4	.	.	PROPN
fumecheng-7707	303	5	,	,	PUNCT
fumecheng-7707	303	6	gibson	gibson	PROPN
fumecheng-7707	303	7	,	,	PUNCT
fumecheng-7707	303	8	s.t	s.t	PROPN
fumecheng-7707	303	9	.	.	PROPN
fumecheng-7707	303	10	,	,	PUNCT
fumecheng-7707	303	11	yurchak	yurchak	PROPN
fumecheng-7707	303	12	,	,	PUNCT
fumecheng-7707	303	13	r.	r.	PROPN
fumecheng-7707	303	14	,	,	PUNCT
fumecheng-7707	303	15	das	das	PROPN
fumecheng-7707	303	16	,	,	PUNCT
fumecheng-7707	303	17	d.d	d.d	PROPN
fumecheng-7707	303	18	.	.	PROPN
fumecheng-7707	303	19	,	,	PUNCT
fumecheng-7707	303	20	ryazanov	ryazanov	PROPN
fumecheng-7707	303	21	,	,	PUNCT
fumecheng-7707	303	22	m.	m.	NOUN
fumecheng-7707	303	23	,	,	PUNCT
fumecheng-7707	303	24	2019	2019	NUM
fumecheng-7707	303	25	,	,	PUNCT
fumecheng-7707	303	26	a	a	DET
fumecheng-7707	303	27	direct	direct	ADJ
fumecheng-7707	303	28	comparison	comparison	NOUN
fumecheng-7707	303	29	of	of	ADP
fumecheng-7707	303	30	high	high	ADJ
fumecheng-7707	303	31	-	-	PUNCT
fumecheng-7707	303	32	speed	speed	NOUN
fumecheng-7707	303	33	methods	method	NOUN
fumecheng-7707	303	34	for	for	ADP
fumecheng-7707	303	35	the	the	DET
fumecheng-7707	303	36	numerical	numerical	PROPN
fumecheng-7707	303	37	abel	abel	PROPN
fumecheng-7707	303	38	transform	transform	PROPN
fumecheng-7707	303	39	,	,	PUNCT
fumecheng-7707	303	40	review	review	NOUN
fumecheng-7707	303	41	of	of	ADP
fumecheng-7707	303	42	scientific	scientific	ADJ
fumecheng-7707	303	43	instruments	instrument	NOUN
fumecheng-7707	303	44	,	,	PUNCT
fumecheng-7707	303	45	90	90	NUM
fumecheng-7707	303	46	,	,	PUNCT
fumecheng-7707	303	47	065115	065115	NUM
fumecheng-7707	303	48	.	.	PUNCT