id	sid	tid	token	lemma	pos
fumecheng-4103	1	1	plane	plane	NOUN
fumecheng-4103	1	2	thermoelastic	thermoelastic	ADJ
fumecheng-4103	1	3	waves	wave	NOUN
fumecheng-4103	1	4	in	in	ADP
fumecheng-4103	1	5	infinite	infinite	ADJ
fumecheng-4103	1	6	half	half	ADJ
fumecheng-4103	1	7	-	-	PUNCT
fumecheng-4103	1	8	space	space	NOUN
fumecheng-4103	1	9	caused	cause	VERB
fumecheng-4103	1	10	facta	facta	PROPN
fumecheng-4103	1	11	universitatis	universitatis	PROPN
fumecheng-4103	1	12	series	series	NOUN
fumecheng-4103	1	13	:	:	PUNCT
fumecheng-4103	1	14	mechanical	mechanical	ADJ
fumecheng-4103	1	15	engineering	engineering	NOUN
fumecheng-4103	1	16	vol	vol	NOUN
fumecheng-4103	1	17	.	.	PUNCT
fumecheng-4103	2	1	16	16	NUM
fumecheng-4103	2	2	,	,	PUNCT
fumecheng-4103	2	3	no	no	DET
fumecheng-4103	2	4	2	2	NUM
fumecheng-4103	2	5	,	,	PUNCT
fumecheng-4103	2	6	2018	2018	NUM
fumecheng-4103	2	7	,	,	PUNCT
fumecheng-4103	2	8	pp	pp	ADJ
fumecheng-4103	2	9	.	.	PUNCT
fumecheng-4103	3	1	127	127	NUM
fumecheng-4103	3	2	138	138	NUM
fumecheng-4103	3	3	https://doi.org/10.22190/fume180526023b	https://doi.org/10.22190/fume180526023b	PROPN
fumecheng-4103	3	4	©	©	PROPN
fumecheng-4103	3	5	2018	2018	NUM
fumecheng-4103	3	6	by	by	ADP
fumecheng-4103	3	7	university	university	PROPN
fumecheng-4103	3	8	of	of	ADP
fumecheng-4103	3	9	niš	niš	PROPN
fumecheng-4103	3	10	,	,	PUNCT
fumecheng-4103	3	11	serbia	serbia	PROPN
fumecheng-4103	3	12	|	|	ADV
fumecheng-4103	3	13	creative	creative	ADJ
fumecheng-4103	3	14	commons	common	NOUN
fumecheng-4103	3	15	license	license	NOUN
fumecheng-4103	3	16	:	:	PUNCT
fumecheng-4103	3	17	cc	cc	VERB
fumecheng-4103	3	18	by	by	ADP
fumecheng-4103	3	19	-	-	PUNCT
fumecheng-4103	3	20	nc	nc	VERB
fumecheng-4103	3	21	-	-	PUNCT
fumecheng-4103	3	22	nd	nd	ADV
fumecheng-4103	3	23	original	original	ADJ
fumecheng-4103	3	24	scientific	scientific	ADJ
fumecheng-4103	3	25	paper	paper	VERB
fumecheng-4103	3	26	fast	fast	ADJ
fumecheng-4103	3	27	numerical	numerical	ADJ
fumecheng-4103	3	28	implementation	implementation	NOUN
fumecheng-4103	3	29	of	of	ADP
fumecheng-4103	3	30	the	the	DET
fumecheng-4103	3	31	mdr	mdr	PROPN
fumecheng-4103	3	32	transformations	transformation	NOUN
fumecheng-4103	3	33	udc	udc	NOUN
fumecheng-4103	3	34	539.3	539.3	NUM
fumecheng-4103	3	35	justus	justus	PROPN
fumecheng-4103	3	36	benad	benad	PROPN
fumecheng-4103	3	37	berlin	berlin	PROPN
fumecheng-4103	3	38	university	university	PROPN
fumecheng-4103	3	39	of	of	ADP
fumecheng-4103	3	40	technology	technology	PROPN
fumecheng-4103	3	41	,	,	PUNCT
fumecheng-4103	3	42	berlin	berlin	PROPN
fumecheng-4103	3	43	,	,	PUNCT
fumecheng-4103	3	44	germany	germany	PROPN
fumecheng-4103	3	45	abstract	abstract	NOUN
fumecheng-4103	3	46	.	.	PUNCT
fumecheng-4103	4	1	in	in	ADP
fumecheng-4103	4	2	the	the	DET
fumecheng-4103	4	3	present	present	ADJ
fumecheng-4103	4	4	paper	paper	NOUN
fumecheng-4103	4	5	a	a	DET
fumecheng-4103	4	6	numerical	numerical	ADJ
fumecheng-4103	4	7	implementation	implementation	NOUN
fumecheng-4103	4	8	technique	technique	NOUN
fumecheng-4103	4	9	for	for	ADP
fumecheng-4103	4	10	the	the	DET
fumecheng-4103	4	11	transformations	transformation	NOUN
fumecheng-4103	4	12	of	of	ADP
fumecheng-4103	4	13	the	the	DET
fumecheng-4103	4	14	method	method	NOUN
fumecheng-4103	4	15	of	of	ADP
fumecheng-4103	4	16	dimensionality	dimensionality	NOUN
fumecheng-4103	4	17	reduction	reduction	NOUN
fumecheng-4103	4	18	(	(	PUNCT
fumecheng-4103	4	19	mdr	mdr	NOUN
fumecheng-4103	4	20	)	)	PUNCT
fumecheng-4103	4	21	is	be	AUX
fumecheng-4103	4	22	described	describe	VERB
fumecheng-4103	4	23	.	.	PUNCT
fumecheng-4103	5	1	the	the	DET
fumecheng-4103	5	2	mdr	mdr	PROPN
fumecheng-4103	5	3	has	have	AUX
fumecheng-4103	5	4	become	become	VERB
fumecheng-4103	5	5	,	,	PUNCT
fumecheng-4103	5	6	in	in	ADP
fumecheng-4103	5	7	the	the	DET
fumecheng-4103	5	8	past	past	ADJ
fumecheng-4103	5	9	few	few	ADJ
fumecheng-4103	5	10	years	year	NOUN
fumecheng-4103	5	11	,	,	PUNCT
fumecheng-4103	5	12	a	a	DET
fumecheng-4103	5	13	standard	standard	ADJ
fumecheng-4103	5	14	tool	tool	NOUN
fumecheng-4103	5	15	in	in	ADP
fumecheng-4103	5	16	contact	contact	NOUN
fumecheng-4103	5	17	mechanics	mechanic	NOUN
fumecheng-4103	5	18	for	for	ADP
fumecheng-4103	5	19	solving	solve	VERB
fumecheng-4103	5	20	axially	axially	ADV
fumecheng-4103	5	21	-	-	PUNCT
fumecheng-4103	5	22	symmetric	symmetric	ADJ
fumecheng-4103	5	23	contacts	contact	NOUN
fumecheng-4103	5	24	.	.	PUNCT
fumecheng-4103	6	1	the	the	DET
fumecheng-4103	6	2	numerical	numerical	ADJ
fumecheng-4103	6	3	implementation	implementation	NOUN
fumecheng-4103	6	4	of	of	ADP
fumecheng-4103	6	5	the	the	DET
fumecheng-4103	6	6	integral	integral	ADJ
fumecheng-4103	6	7	transformations	transformation	NOUN
fumecheng-4103	6	8	of	of	ADP
fumecheng-4103	6	9	the	the	DET
fumecheng-4103	6	10	mdr	mdr	PROPN
fumecheng-4103	6	11	can	can	AUX
fumecheng-4103	6	12	be	be	AUX
fumecheng-4103	6	13	performed	perform	VERB
fumecheng-4103	6	14	in	in	ADP
fumecheng-4103	6	15	several	several	ADJ
fumecheng-4103	6	16	different	different	ADJ
fumecheng-4103	6	17	ways	way	NOUN
fumecheng-4103	6	18	.	.	PUNCT
fumecheng-4103	7	1	in	in	ADP
fumecheng-4103	7	2	this	this	DET
fumecheng-4103	7	3	study	study	NOUN
fumecheng-4103	7	4	,	,	PUNCT
fumecheng-4103	7	5	the	the	DET
fumecheng-4103	7	6	focus	focus	NOUN
fumecheng-4103	7	7	is	be	AUX
fumecheng-4103	7	8	on	on	ADP
fumecheng-4103	7	9	a	a	DET
fumecheng-4103	7	10	simple	simple	ADJ
fumecheng-4103	7	11	and	and	CCONJ
fumecheng-4103	7	12	robust	robust	ADJ
fumecheng-4103	7	13	algorithm	algorithm	NOUN
fumecheng-4103	7	14	on	on	ADP
fumecheng-4103	7	15	the	the	DET
fumecheng-4103	7	16	uniform	uniform	ADJ
fumecheng-4103	7	17	grid	grid	NOUN
fumecheng-4103	7	18	using	use	VERB
fumecheng-4103	7	19	integration	integration	NOUN
fumecheng-4103	7	20	by	by	ADP
fumecheng-4103	7	21	parts	part	NOUN
fumecheng-4103	7	22	,	,	PUNCT
fumecheng-4103	7	23	a	a	DET
fumecheng-4103	7	24	central	central	ADJ
fumecheng-4103	7	25	difference	difference	NOUN
fumecheng-4103	7	26	scheme	scheme	NOUN
fumecheng-4103	7	27	to	to	PART
fumecheng-4103	7	28	obtain	obtain	VERB
fumecheng-4103	7	29	the	the	DET
fumecheng-4103	7	30	derivatives	derivative	NOUN
fumecheng-4103	7	31	,	,	PUNCT
fumecheng-4103	7	32	and	and	CCONJ
fumecheng-4103	7	33	a	a	DET
fumecheng-4103	7	34	trapezoidal	trapezoidal	ADJ
fumecheng-4103	7	35	rule	rule	NOUN
fumecheng-4103	7	36	to	to	PART
fumecheng-4103	7	37	perform	perform	VERB
fumecheng-4103	7	38	the	the	DET
fumecheng-4103	7	39	summation	summation	NOUN
fumecheng-4103	7	40	.	.	PUNCT
fumecheng-4103	8	1	the	the	DET
fumecheng-4103	8	2	results	result	NOUN
fumecheng-4103	8	3	are	be	AUX
fumecheng-4103	8	4	compared	compare	VERB
fumecheng-4103	8	5	to	to	ADP
fumecheng-4103	8	6	the	the	DET
fumecheng-4103	8	7	analytical	analytical	ADJ
fumecheng-4103	8	8	solutions	solution	NOUN
fumecheng-4103	8	9	for	for	ADP
fumecheng-4103	8	10	the	the	DET
fumecheng-4103	8	11	contact	contact	NOUN
fumecheng-4103	8	12	of	of	ADP
fumecheng-4103	8	13	a	a	DET
fumecheng-4103	8	14	cone	cone	NOUN
fumecheng-4103	8	15	and	and	CCONJ
fumecheng-4103	8	16	the	the	DET
fumecheng-4103	8	17	hertzian	hertzian	ADJ
fumecheng-4103	8	18	contact	contact	NOUN
fumecheng-4103	8	19	.	.	PUNCT
fumecheng-4103	9	1	for	for	ADP
fumecheng-4103	9	2	the	the	DET
fumecheng-4103	9	3	tested	test	VERB
fumecheng-4103	9	4	examples	example	NOUN
fumecheng-4103	9	5	,	,	PUNCT
fumecheng-4103	9	6	the	the	DET
fumecheng-4103	9	7	proposed	propose	VERB
fumecheng-4103	9	8	method	method	NOUN
fumecheng-4103	9	9	gives	give	VERB
fumecheng-4103	9	10	more	more	ADV
fumecheng-4103	9	11	accurate	accurate	ADJ
fumecheng-4103	9	12	results	result	NOUN
fumecheng-4103	9	13	with	with	ADP
fumecheng-4103	9	14	the	the	DET
fumecheng-4103	9	15	same	same	ADJ
fumecheng-4103	9	16	number	number	NOUN
fumecheng-4103	9	17	of	of	ADP
fumecheng-4103	9	18	discretization	discretization	NOUN
fumecheng-4103	9	19	points	point	NOUN
fumecheng-4103	9	20	than	than	ADP
fumecheng-4103	9	21	other	other	ADJ
fumecheng-4103	9	22	tested	test	VERB
fumecheng-4103	9	23	numerical	numerical	ADJ
fumecheng-4103	9	24	techniques	technique	NOUN
fumecheng-4103	9	25	.	.	PUNCT
fumecheng-4103	10	1	the	the	DET
fumecheng-4103	10	2	implementation	implementation	NOUN
fumecheng-4103	10	3	method	method	NOUN
fumecheng-4103	10	4	is	be	AUX
fumecheng-4103	10	5	further	far	ADV
fumecheng-4103	10	6	tested	test	VERB
fumecheng-4103	10	7	in	in	ADP
fumecheng-4103	10	8	a	a	DET
fumecheng-4103	10	9	wear	wear	NOUN
fumecheng-4103	10	10	simulation	simulation	NOUN
fumecheng-4103	10	11	of	of	ADP
fumecheng-4103	10	12	a	a	DET
fumecheng-4103	10	13	heterogeneous	heterogeneous	ADJ
fumecheng-4103	10	14	cylinder	cylinder	NOUN
fumecheng-4103	10	15	composed	compose	VERB
fumecheng-4103	10	16	of	of	ADP
fumecheng-4103	10	17	rings	ring	NOUN
fumecheng-4103	10	18	of	of	ADP
fumecheng-4103	10	19	different	different	ADJ
fumecheng-4103	10	20	material	material	NOUN
fumecheng-4103	10	21	having	have	VERB
fumecheng-4103	10	22	the	the	DET
fumecheng-4103	10	23	same	same	ADJ
fumecheng-4103	10	24	elastic	elastic	ADJ
fumecheng-4103	10	25	properties	property	NOUN
fumecheng-4103	10	26	but	but	CCONJ
fumecheng-4103	10	27	different	different	ADJ
fumecheng-4103	10	28	wear	wear	NOUN
fumecheng-4103	10	29	coefficients	coefficient	NOUN
fumecheng-4103	10	30	.	.	PUNCT
fumecheng-4103	11	1	these	these	DET
fumecheng-4103	11	2	discontinuous	discontinuous	ADJ
fumecheng-4103	11	3	transitions	transition	NOUN
fumecheng-4103	11	4	in	in	ADP
fumecheng-4103	11	5	the	the	DET
fumecheng-4103	11	6	material	material	NOUN
fumecheng-4103	11	7	properties	property	NOUN
fumecheng-4103	11	8	are	be	AUX
fumecheng-4103	11	9	handled	handle	VERB
fumecheng-4103	11	10	well	well	ADV
fumecheng-4103	11	11	with	with	ADP
fumecheng-4103	11	12	the	the	DET
fumecheng-4103	11	13	proposed	propose	VERB
fumecheng-4103	11	14	method	method	NOUN
fumecheng-4103	11	15	.	.	PUNCT
fumecheng-4103	12	1	key	key	ADJ
fumecheng-4103	12	2	words	word	NOUN
fumecheng-4103	12	3	:	:	PUNCT
fumecheng-4103	12	4	normal	normal	ADJ
fumecheng-4103	12	5	contact	contact	NOUN
fumecheng-4103	12	6	,	,	PUNCT
fumecheng-4103	12	7	method	method	NOUN
fumecheng-4103	12	8	of	of	ADP
fumecheng-4103	12	9	dimensionality	dimensionality	NOUN
fumecheng-4103	12	10	reduction	reduction	NOUN
fumecheng-4103	12	11	,	,	PUNCT
fumecheng-4103	12	12	stress	stress	NOUN
fumecheng-4103	12	13	,	,	PUNCT
fumecheng-4103	12	14	wear	wear	VERB
fumecheng-4103	12	15	1	1	NUM
fumecheng-4103	12	16	.	.	PUNCT
fumecheng-4103	13	1	introduction	introduction	NOUN
fumecheng-4103	13	2	the	the	DET
fumecheng-4103	13	3	method	method	NOUN
fumecheng-4103	13	4	of	of	ADP
fumecheng-4103	13	5	dimensionality	dimensionality	NOUN
fumecheng-4103	13	6	reduction	reduction	NOUN
fumecheng-4103	13	7	(	(	PUNCT
fumecheng-4103	13	8	mdr	mdr	PROPN
fumecheng-4103	13	9	)	)	PUNCT
fumecheng-4103	13	10	is	be	AUX
fumecheng-4103	13	11	a	a	DET
fumecheng-4103	13	12	simple	simple	ADJ
fumecheng-4103	13	13	and	and	CCONJ
fumecheng-4103	13	14	convenient	convenient	ADJ
fumecheng-4103	13	15	tool	tool	NOUN
fumecheng-4103	13	16	for	for	ADP
fumecheng-4103	13	17	the	the	DET
fumecheng-4103	13	18	calculation	calculation	NOUN
fumecheng-4103	13	19	of	of	ADP
fumecheng-4103	13	20	contact	contact	NOUN
fumecheng-4103	13	21	forces	force	NOUN
fumecheng-4103	13	22	between	between	ADP
fumecheng-4103	13	23	elastic	elastic	ADJ
fumecheng-4103	13	24	and	and	CCONJ
fumecheng-4103	13	25	viscoelastic	viscoelastic	NOUN
fumecheng-4103	13	26	bodies	body	NOUN
fumecheng-4103	13	27	.	.	PUNCT
fumecheng-4103	14	1	it	it	PRON
fumecheng-4103	14	2	is	be	AUX
fumecheng-4103	14	3	particularly	particularly	ADV
fumecheng-4103	14	4	easy	easy	ADJ
fumecheng-4103	14	5	to	to	PART
fumecheng-4103	14	6	use	use	VERB
fumecheng-4103	14	7	for	for	ADP
fumecheng-4103	14	8	the	the	DET
fumecheng-4103	14	9	simulation	simulation	NOUN
fumecheng-4103	14	10	of	of	ADP
fumecheng-4103	14	11	axially	axially	ADV
fumecheng-4103	14	12	-	-	PUNCT
fumecheng-4103	14	13	symmetric	symmetric	ADJ
fumecheng-4103	14	14	contacts	contact	NOUN
fumecheng-4103	14	15	.	.	PUNCT
fumecheng-4103	15	1	since	since	SCONJ
fumecheng-4103	15	2	it	it	PRON
fumecheng-4103	15	3	was	be	AUX
fumecheng-4103	15	4	first	first	ADV
fumecheng-4103	15	5	proposed	propose	VERB
fumecheng-4103	15	6	in	in	ADP
fumecheng-4103	15	7	2007	2007	NUM
fumecheng-4103	15	8	[	[	X
fumecheng-4103	15	9	1	1	X
fumecheng-4103	15	10	]	]	PUNCT
fumecheng-4103	15	11	the	the	DET
fumecheng-4103	15	12	mdr	mdr	PROPN
fumecheng-4103	15	13	has	have	AUX
fumecheng-4103	15	14	been	be	AUX
fumecheng-4103	15	15	applied	apply	VERB
fumecheng-4103	15	16	to	to	ADP
fumecheng-4103	15	17	a	a	DET
fumecheng-4103	15	18	wide	wide	ADJ
fumecheng-4103	15	19	range	range	NOUN
fumecheng-4103	15	20	of	of	ADP
fumecheng-4103	15	21	problems	problem	NOUN
fumecheng-4103	15	22	[	[	X
fumecheng-4103	15	23	2	2	NUM
fumecheng-4103	15	24	]	]	PUNCT
fumecheng-4103	15	25	.	.	PUNCT
fumecheng-4103	16	1	the	the	DET
fumecheng-4103	16	2	method	method	NOUN
fumecheng-4103	16	3	maps	map	VERB
fumecheng-4103	16	4	a	a	DET
fumecheng-4103	16	5	given	give	VERB
fumecheng-4103	16	6	three	three	NUM
fumecheng-4103	16	7	-	-	PUNCT
fumecheng-4103	16	8	dimensional	dimensional	ADJ
fumecheng-4103	16	9	contact	contact	NOUN
fumecheng-4103	16	10	problem	problem	NOUN
fumecheng-4103	16	11	to	to	ADP
fumecheng-4103	16	12	an	an	DET
fumecheng-4103	16	13	equivalent	equivalent	ADJ
fumecheng-4103	16	14	contact	contact	NOUN
fumecheng-4103	16	15	problem	problem	NOUN
fumecheng-4103	16	16	of	of	ADP
fumecheng-4103	16	17	a	a	DET
fumecheng-4103	16	18	transformed	transform	VERB
fumecheng-4103	16	19	indentation	indentation	NOUN
fumecheng-4103	16	20	profile	profile	NOUN
fumecheng-4103	16	21	with	with	ADP
fumecheng-4103	16	22	a	a	DET
fumecheng-4103	16	23	one	one	NUM
fumecheng-4103	16	24	-	-	PUNCT
fumecheng-4103	16	25	dimensional	dimensional	ADJ
fumecheng-4103	16	26	elastic	elastic	ADJ
fumecheng-4103	16	27	or	or	CCONJ
fumecheng-4103	16	28	viscoelastic	viscoelastic	NOUN
fumecheng-4103	16	29	foundation	foundation	NOUN
fumecheng-4103	16	30	of	of	ADP
fumecheng-4103	16	31	independent	independent	ADJ
fumecheng-4103	16	32	elements	element	NOUN
fumecheng-4103	16	33	.	.	PUNCT
fumecheng-4103	17	1	from	from	ADP
fumecheng-4103	17	2	a	a	DET
fumecheng-4103	17	3	numerical	numerical	ADJ
fumecheng-4103	17	4	perspective	perspective	NOUN
fumecheng-4103	17	5	,	,	PUNCT
fumecheng-4103	17	6	the	the	DET
fumecheng-4103	17	7	solution	solution	NOUN
fumecheng-4103	17	8	of	of	ADP
fumecheng-4103	17	9	the	the	DET
fumecheng-4103	17	10	contact	contact	NOUN
fumecheng-4103	17	11	problem	problem	NOUN
fumecheng-4103	17	12	in	in	ADP
fumecheng-4103	17	13	the	the	DET
fumecheng-4103	17	14	transformed	transform	VERB
fumecheng-4103	17	15	mdr	mdr	PROPN
fumecheng-4103	17	16	domain	domain	NOUN
fumecheng-4103	17	17	is	be	AUX
fumecheng-4103	17	18	then	then	ADV
fumecheng-4103	17	19	trivial	trivial	ADJ
fumecheng-4103	17	20	due	due	ADP
fumecheng-4103	17	21	to	to	ADP
fumecheng-4103	17	22	the	the	DET
fumecheng-4103	17	23	decoupled	decouple	VERB
fumecheng-4103	17	24	degrees	degree	NOUN
fumecheng-4103	17	25	of	of	ADP
fumecheng-4103	17	26	freedom	freedom	NOUN
fumecheng-4103	17	27	.	.	PUNCT
fumecheng-4103	18	1	a	a	DET
fumecheng-4103	18	2	variety	variety	NOUN
fumecheng-4103	18	3	received	receive	VERB
fumecheng-4103	18	4	may	may	AUX
fumecheng-4103	18	5	26	26	NUM
fumecheng-4103	18	6	,	,	PUNCT
fumecheng-4103	18	7	2018	2018	NUM
fumecheng-4103	18	8	/	/	SYM
fumecheng-4103	18	9	accepted	accept	VERB
fumecheng-4103	18	10	june	june	PROPN
fumecheng-4103	18	11	30	30	NUM
fumecheng-4103	18	12	,	,	PUNCT
fumecheng-4103	18	13	2018	2018	NUM
fumecheng-4103	18	14	corresponding	correspond	VERB
fumecheng-4103	18	15	author	author	NOUN
fumecheng-4103	18	16	:	:	PUNCT
fumecheng-4103	18	17	justus	justus	PROPN
fumecheng-4103	18	18	benad	benad	PROPN
fumecheng-4103	18	19	tu	tu	PROPN
fumecheng-4103	18	20	berlin	berlin	PROPN
fumecheng-4103	18	21	,	,	PUNCT
fumecheng-4103	18	22	institut	institut	PROPN
fumecheng-4103	18	23	für	für	PROPN
fumecheng-4103	18	24	mechanik	mechanik	PROPN
fumecheng-4103	18	25	,	,	PUNCT
fumecheng-4103	18	26	fg	fg	PROPN
fumecheng-4103	18	27	systemdynamik	systemdynamik	PROPN
fumecheng-4103	18	28	und	und	NOUN
fumecheng-4103	18	29	reibungsphysik	reibungsphysik	NOUN
fumecheng-4103	18	30	,	,	PUNCT
fumecheng-4103	18	31	str	str	NOUN
fumecheng-4103	18	32	.	.	PUNCT
fumecheng-4103	19	1	d.17	d.17	PROPN
fumecheng-4103	19	2	.	.	PROPN
fumecheng-4103	19	3	juni	juni	PROPN
fumecheng-4103	19	4	135	135	NUM
fumecheng-4103	19	5	,	,	PUNCT
fumecheng-4103	19	6	10623	10623	NUM
fumecheng-4103	19	7	berlin	berlin	PROPN
fumecheng-4103	19	8	,	,	PUNCT
fumecheng-4103	19	9	de	de	PROPN
fumecheng-4103	19	10	e	e	NOUN
fumecheng-4103	19	11	-	-	NOUN
fumecheng-4103	19	12	mail	mail	NOUN
fumecheng-4103	19	13	:	:	PUNCT
fumecheng-4103	19	14	mail@jbenad.com	mail@jbenad.com	X
fumecheng-4103	19	15	128	128	NUM
fumecheng-4103	19	16	j.	j.	PROPN
fumecheng-4103	19	17	benad	benad	PROPN
fumecheng-4103	19	18	of	of	ADP
fumecheng-4103	19	19	problems	problem	NOUN
fumecheng-4103	19	20	can	can	AUX
fumecheng-4103	19	21	be	be	AUX
fumecheng-4103	19	22	solved	solve	VERB
fumecheng-4103	19	23	directly	directly	ADV
fumecheng-4103	19	24	in	in	ADP
fumecheng-4103	19	25	this	this	DET
fumecheng-4103	19	26	domain	domain	NOUN
fumecheng-4103	19	27	after	after	SCONJ
fumecheng-4103	19	28	the	the	DET
fumecheng-4103	19	29	initial	initial	ADJ
fumecheng-4103	19	30	transformation	transformation	NOUN
fumecheng-4103	19	31	to	to	ADP
fumecheng-4103	19	32	the	the	DET
fumecheng-4103	19	33	equivalent	equivalent	ADJ
fumecheng-4103	19	34	problem	problem	NOUN
fumecheng-4103	19	35	was	be	AUX
fumecheng-4103	19	36	performed	perform	VERB
fumecheng-4103	19	37	(	(	PUNCT
fumecheng-4103	19	38	see	see	VERB
fumecheng-4103	19	39	for	for	ADP
fumecheng-4103	19	40	example	example	NOUN
fumecheng-4103	20	1	[	[	X
fumecheng-4103	20	2	3	3	NUM
fumecheng-4103	20	3	]	]	NUM
fumecheng-4103	20	4	)	)	PUNCT
fumecheng-4103	20	5	.	.	PUNCT
fumecheng-4103	21	1	however	however	ADV
fumecheng-4103	21	2	,	,	PUNCT
fumecheng-4103	21	3	there	there	PRON
fumecheng-4103	21	4	are	be	VERB
fumecheng-4103	21	5	other	other	ADJ
fumecheng-4103	21	6	problems	problem	NOUN
fumecheng-4103	21	7	which	which	PRON
fumecheng-4103	21	8	require	require	VERB
fumecheng-4103	21	9	multiple	multiple	ADJ
fumecheng-4103	21	10	transformations	transformation	NOUN
fumecheng-4103	21	11	to	to	ADP
fumecheng-4103	21	12	the	the	DET
fumecheng-4103	21	13	mdr	mdr	PROPN
fumecheng-4103	21	14	domain	domain	NOUN
fumecheng-4103	21	15	and	and	CCONJ
fumecheng-4103	21	16	back	back	ADV
fumecheng-4103	21	17	,	,	PUNCT
fumecheng-4103	21	18	for	for	ADP
fumecheng-4103	21	19	example	example	NOUN
fumecheng-4103	21	20	due	due	ADP
fumecheng-4103	21	21	to	to	ADP
fumecheng-4103	21	22	a	a	DET
fumecheng-4103	21	23	continuously	continuously	ADV
fumecheng-4103	21	24	changing	change	VERB
fumecheng-4103	21	25	indentation	indentation	NOUN
fumecheng-4103	21	26	profile	profile	NOUN
fumecheng-4103	21	27	as	as	SCONJ
fumecheng-4103	21	28	it	it	PRON
fumecheng-4103	21	29	appears	appear	VERB
fumecheng-4103	21	30	in	in	ADP
fumecheng-4103	21	31	wear	wear	NOUN
fumecheng-4103	21	32	simulations	simulation	NOUN
fumecheng-4103	21	33	,	,	PUNCT
fumecheng-4103	21	34	see	see	VERB
fumecheng-4103	21	35	[	[	X
fumecheng-4103	21	36	4	4	NUM
fumecheng-4103	21	37	-	-	SYM
fumecheng-4103	21	38	6	6	NUM
fumecheng-4103	21	39	]	]	PUNCT
fumecheng-4103	21	40	.	.	PUNCT
fumecheng-4103	22	1	with	with	ADP
fumecheng-4103	22	2	such	such	ADJ
fumecheng-4103	22	3	kinds	kind	NOUN
fumecheng-4103	22	4	of	of	ADP
fumecheng-4103	22	5	problems	problem	NOUN
fumecheng-4103	22	6	,	,	PUNCT
fumecheng-4103	22	7	the	the	DET
fumecheng-4103	22	8	main	main	ADJ
fumecheng-4103	22	9	difficulty	difficulty	NOUN
fumecheng-4103	22	10	in	in	ADP
fumecheng-4103	22	11	achieving	achieve	VERB
fumecheng-4103	22	12	an	an	DET
fumecheng-4103	22	13	accurate	accurate	ADJ
fumecheng-4103	22	14	and	and	CCONJ
fumecheng-4103	22	15	efficient	efficient	ADJ
fumecheng-4103	22	16	numerical	numerical	PROPN
fumecheng-4103	22	17	simulation	simulation	NOUN
fumecheng-4103	22	18	is	be	AUX
fumecheng-4103	22	19	the	the	DET
fumecheng-4103	22	20	implementation	implementation	NOUN
fumecheng-4103	22	21	of	of	ADP
fumecheng-4103	22	22	the	the	DET
fumecheng-4103	22	23	mdr	mdr	PROPN
fumecheng-4103	22	24	transformations	transformation	NOUN
fumecheng-4103	22	25	.	.	PUNCT
fumecheng-4103	23	1	these	these	PRON
fumecheng-4103	23	2	are	be	AUX
fumecheng-4103	23	3	given	give	VERB
fumecheng-4103	23	4	by	by	ADP
fumecheng-4103	23	5	abel	abel	NOUN
fumecheng-4103	23	6	-	-	PUNCT
fumecheng-4103	23	7	like	like	ADJ
fumecheng-4103	23	8	integral	integral	ADJ
fumecheng-4103	23	9	equations	equation	NOUN
fumecheng-4103	23	10	and	and	CCONJ
fumecheng-4103	23	11	it	it	PRON
fumecheng-4103	23	12	is	be	AUX
fumecheng-4103	23	13	well	well	ADV
fumecheng-4103	23	14	known	know	VERB
fumecheng-4103	23	15	that	that	SCONJ
fumecheng-4103	23	16	their	their	PRON
fumecheng-4103	23	17	numerical	numerical	ADJ
fumecheng-4103	23	18	treatment	treatment	NOUN
fumecheng-4103	23	19	is	be	AUX
fumecheng-4103	23	20	challenging	challenge	VERB
fumecheng-4103	23	21	[	[	X
fumecheng-4103	23	22	7	7	NUM
fumecheng-4103	23	23	,	,	PUNCT
fumecheng-4103	23	24	8	8	NUM
fumecheng-4103	23	25	]	]	PUNCT
fumecheng-4103	23	26	.	.	PUNCT
fumecheng-4103	24	1	this	this	DET
fumecheng-4103	24	2	work	work	NOUN
fumecheng-4103	24	3	is	be	AUX
fumecheng-4103	24	4	dedicated	dedicate	VERB
fumecheng-4103	24	5	to	to	ADP
fumecheng-4103	24	6	providing	provide	VERB
fumecheng-4103	24	7	a	a	DET
fumecheng-4103	24	8	simple	simple	ADJ
fumecheng-4103	24	9	and	and	CCONJ
fumecheng-4103	24	10	fast	fast	ADJ
fumecheng-4103	24	11	numerical	numerical	ADJ
fumecheng-4103	24	12	method	method	NOUN
fumecheng-4103	24	13	for	for	ADP
fumecheng-4103	24	14	the	the	DET
fumecheng-4103	24	15	implementation	implementation	NOUN
fumecheng-4103	24	16	of	of	ADP
fumecheng-4103	24	17	the	the	DET
fumecheng-4103	24	18	mdr	mdr	PROPN
fumecheng-4103	24	19	transformations	transformation	NOUN
fumecheng-4103	24	20	for	for	ADP
fumecheng-4103	24	21	axially	axially	ADV
fumecheng-4103	24	22	-	-	PUNCT
fumecheng-4103	24	23	symmetric	symmetric	ADJ
fumecheng-4103	24	24	contact	contact	NOUN
fumecheng-4103	24	25	problems	problem	NOUN
fumecheng-4103	24	26	.	.	PUNCT
fumecheng-4103	25	1	the	the	DET
fumecheng-4103	25	2	transformations	transformation	NOUN
fumecheng-4103	25	3	have	have	VERB
fumecheng-4103	25	4	an	an	DET
fumecheng-4103	25	5	integrable	integrable	ADJ
fumecheng-4103	25	6	singularity	singularity	NOUN
fumecheng-4103	25	7	which	which	PRON
fumecheng-4103	25	8	is	be	AUX
fumecheng-4103	25	9	handled	handle	VERB
fumecheng-4103	25	10	well	well	ADV
fumecheng-4103	25	11	with	with	ADP
fumecheng-4103	25	12	the	the	DET
fumecheng-4103	25	13	proposed	propose	VERB
fumecheng-4103	25	14	method	method	NOUN
fumecheng-4103	25	15	.	.	PUNCT
fumecheng-4103	26	1	the	the	DET
fumecheng-4103	26	2	parts	part	NOUN
fumecheng-4103	26	3	of	of	ADP
fumecheng-4103	26	4	this	this	DET
fumecheng-4103	26	5	work	work	NOUN
fumecheng-4103	26	6	are	be	AUX
fumecheng-4103	26	7	organized	organize	VERB
fumecheng-4103	26	8	as	as	SCONJ
fumecheng-4103	26	9	follows	follow	VERB
fumecheng-4103	26	10	:	:	PUNCT
fumecheng-4103	26	11	in	in	ADP
fumecheng-4103	26	12	section	section	NOUN
fumecheng-4103	26	13	2	2	NUM
fumecheng-4103	26	14	,	,	PUNCT
fumecheng-4103	26	15	the	the	DET
fumecheng-4103	26	16	mdr	mdr	NOUN
fumecheng-4103	26	17	transformations	transformation	NOUN
fumecheng-4103	26	18	are	be	AUX
fumecheng-4103	26	19	rewritten	rewrite	VERB
fumecheng-4103	26	20	using	use	VERB
fumecheng-4103	26	21	integration	integration	NOUN
fumecheng-4103	26	22	by	by	ADP
fumecheng-4103	26	23	parts	part	NOUN
fumecheng-4103	26	24	to	to	ADP
fumecheng-4103	26	25	a	a	DET
fumecheng-4103	26	26	form	form	NOUN
fumecheng-4103	26	27	which	which	PRON
fumecheng-4103	26	28	is	be	AUX
fumecheng-4103	26	29	well	well	ADV
fumecheng-4103	26	30	suited	suited	ADJ
fumecheng-4103	26	31	for	for	ADP
fumecheng-4103	26	32	numerical	numerical	ADJ
fumecheng-4103	26	33	implementation	implementation	NOUN
fumecheng-4103	26	34	.	.	PUNCT
fumecheng-4103	27	1	in	in	ADP
fumecheng-4103	27	2	section	section	NOUN
fumecheng-4103	27	3	3	3	NUM
fumecheng-4103	27	4	,	,	PUNCT
fumecheng-4103	27	5	this	this	DET
fumecheng-4103	27	6	numerical	numerical	ADJ
fumecheng-4103	27	7	implementation	implementation	NOUN
fumecheng-4103	27	8	technique	technique	NOUN
fumecheng-4103	27	9	is	be	AUX
fumecheng-4103	27	10	explained	explain	VERB
fumecheng-4103	27	11	in	in	ADP
fumecheng-4103	27	12	detail	detail	NOUN
fumecheng-4103	27	13	.	.	PUNCT
fumecheng-4103	28	1	section	section	NOUN
fumecheng-4103	28	2	4	4	NUM
fumecheng-4103	28	3	gives	give	VERB
fumecheng-4103	28	4	some	some	DET
fumecheng-4103	28	5	advice	advice	NOUN
fumecheng-4103	28	6	on	on	ADP
fumecheng-4103	28	7	optimizing	optimize	VERB
fumecheng-4103	28	8	the	the	DET
fumecheng-4103	28	9	implementation	implementation	NOUN
fumecheng-4103	28	10	for	for	ADP
fumecheng-4103	28	11	maximum	maximum	ADJ
fumecheng-4103	28	12	speed	speed	NOUN
fumecheng-4103	28	13	.	.	PUNCT
fumecheng-4103	29	1	section	section	NOUN
fumecheng-4103	29	2	5	5	NUM
fumecheng-4103	29	3	shows	show	VERB
fumecheng-4103	29	4	exemplary	exemplary	ADJ
fumecheng-4103	29	5	results	result	NOUN
fumecheng-4103	29	6	of	of	ADP
fumecheng-4103	29	7	the	the	DET
fumecheng-4103	29	8	newly	newly	ADV
fumecheng-4103	29	9	proposed	propose	VERB
fumecheng-4103	29	10	technique	technique	NOUN
fumecheng-4103	29	11	and	and	CCONJ
fumecheng-4103	29	12	highlights	highlight	NOUN
fumecheng-4103	29	13	its	its	PRON
fumecheng-4103	29	14	advantages	advantage	NOUN
fumecheng-4103	29	15	and	and	CCONJ
fumecheng-4103	29	16	weaknesses	weakness	NOUN
fumecheng-4103	29	17	.	.	PUNCT
fumecheng-4103	30	1	in	in	ADP
fumecheng-4103	30	2	section	section	NOUN
fumecheng-4103	30	3	6	6	NUM
fumecheng-4103	30	4	,	,	PUNCT
fumecheng-4103	30	5	a	a	DET
fumecheng-4103	30	6	small	small	ADJ
fumecheng-4103	30	7	addition	addition	NOUN
fumecheng-4103	30	8	to	to	ADP
fumecheng-4103	30	9	the	the	DET
fumecheng-4103	30	10	method	method	NOUN
fumecheng-4103	30	11	is	be	AUX
fumecheng-4103	30	12	presented	present	VERB
fumecheng-4103	30	13	to	to	PART
fumecheng-4103	30	14	further	far	ADV
fumecheng-4103	30	15	improve	improve	VERB
fumecheng-4103	30	16	it	it	PRON
fumecheng-4103	30	17	.	.	PUNCT
fumecheng-4103	31	1	in	in	ADP
fumecheng-4103	31	2	section	section	NOUN
fumecheng-4103	31	3	7	7	NUM
fumecheng-4103	31	4	,	,	PUNCT
fumecheng-4103	31	5	the	the	DET
fumecheng-4103	31	6	accuracy	accuracy	NOUN
fumecheng-4103	31	7	of	of	ADP
fumecheng-4103	31	8	the	the	DET
fumecheng-4103	31	9	introduced	introduce	VERB
fumecheng-4103	31	10	numerical	numerical	ADJ
fumecheng-4103	31	11	method	method	NOUN
fumecheng-4103	31	12	is	be	AUX
fumecheng-4103	31	13	compared	compare	VERB
fumecheng-4103	31	14	to	to	ADP
fumecheng-4103	31	15	other	other	ADJ
fumecheng-4103	31	16	known	know	VERB
fumecheng-4103	31	17	implementation	implementation	NOUN
fumecheng-4103	31	18	techniques	technique	NOUN
fumecheng-4103	31	19	which	which	PRON
fumecheng-4103	31	20	rely	rely	VERB
fumecheng-4103	31	21	on	on	ADP
fumecheng-4103	31	22	the	the	DET
fumecheng-4103	31	23	original	original	ADJ
fumecheng-4103	31	24	form	form	NOUN
fumecheng-4103	31	25	of	of	ADP
fumecheng-4103	31	26	the	the	DET
fumecheng-4103	31	27	transformations	transformation	NOUN
fumecheng-4103	31	28	.	.	PUNCT
fumecheng-4103	32	1	in	in	ADP
fumecheng-4103	32	2	section	section	NOUN
fumecheng-4103	32	3	8	8	NUM
fumecheng-4103	32	4	,	,	PUNCT
fumecheng-4103	32	5	an	an	DET
fumecheng-4103	32	6	exemplary	exemplary	ADJ
fumecheng-4103	32	7	wear	wear	NOUN
fumecheng-4103	32	8	simulation	simulation	NOUN
fumecheng-4103	32	9	is	be	AUX
fumecheng-4103	32	10	conducted	conduct	VERB
fumecheng-4103	32	11	with	with	ADP
fumecheng-4103	32	12	the	the	DET
fumecheng-4103	32	13	newly	newly	ADV
fumecheng-4103	32	14	introduced	introduce	VERB
fumecheng-4103	32	15	technique	technique	NOUN
fumecheng-4103	32	16	and	and	CCONJ
fumecheng-4103	32	17	compared	compare	VERB
fumecheng-4103	32	18	to	to	ADP
fumecheng-4103	32	19	the	the	DET
fumecheng-4103	32	20	results	result	NOUN
fumecheng-4103	32	21	of	of	ADP
fumecheng-4103	32	22	other	other	ADJ
fumecheng-4103	32	23	numerical	numerical	ADJ
fumecheng-4103	32	24	implementation	implementation	NOUN
fumecheng-4103	32	25	methods	method	NOUN
fumecheng-4103	32	26	.	.	PUNCT
fumecheng-4103	33	1	a	a	DET
fumecheng-4103	33	2	conclusion	conclusion	NOUN
fumecheng-4103	33	3	is	be	AUX
fumecheng-4103	33	4	presented	present	VERB
fumecheng-4103	33	5	in	in	ADP
fumecheng-4103	33	6	section	section	NOUN
fumecheng-4103	33	7	9	9	NUM
fumecheng-4103	33	8	.	.	PUNCT
fumecheng-4103	34	1	this	this	DET
fumecheng-4103	34	2	work	work	NOUN
fumecheng-4103	34	3	can	can	AUX
fumecheng-4103	34	4	be	be	AUX
fumecheng-4103	34	5	regarded	regard	VERB
fumecheng-4103	34	6	as	as	ADP
fumecheng-4103	34	7	a	a	DET
fumecheng-4103	34	8	small	small	ADJ
fumecheng-4103	34	9	addition	addition	NOUN
fumecheng-4103	34	10	to	to	ADP
fumecheng-4103	34	11	the	the	DET
fumecheng-4103	34	12	paper	paper	NOUN
fumecheng-4103	34	13	“	"	PUNCT
fumecheng-4103	34	14	method	method	NOUN
fumecheng-4103	34	15	of	of	ADP
fumecheng-4103	34	16	dimensionality	dimensionality	NOUN
fumecheng-4103	34	17	reduction	reduction	NOUN
fumecheng-4103	34	18	in	in	ADP
fumecheng-4103	34	19	contact	contact	NOUN
fumecheng-4103	34	20	mechanics	mechanic	NOUN
fumecheng-4103	34	21	and	and	CCONJ
fumecheng-4103	34	22	friction	friction	NOUN
fumecheng-4103	34	23	:	:	PUNCT
fumecheng-4103	34	24	a	a	DET
fumecheng-4103	34	25	users	user	NOUN
fumecheng-4103	34	26	handbook	handbook	NOUN
fumecheng-4103	34	27	”	"	PUNCT
fumecheng-4103	35	1	[	[	X
fumecheng-4103	35	2	9	9	NUM
fumecheng-4103	35	3	]	]	PUNCT
fumecheng-4103	35	4	.	.	PUNCT
fumecheng-4103	36	1	in	in	ADP
fumecheng-4103	36	2	the	the	DET
fumecheng-4103	36	3	following	following	NOUN
fumecheng-4103	36	4	,	,	PUNCT
fumecheng-4103	36	5	only	only	ADV
fumecheng-4103	36	6	homogeneous	homogeneous	ADJ
fumecheng-4103	36	7	elastic	elastic	ADJ
fumecheng-4103	36	8	material	material	NOUN
fumecheng-4103	36	9	is	be	AUX
fumecheng-4103	36	10	considered	consider	VERB
fumecheng-4103	36	11	.	.	PUNCT
fumecheng-4103	37	1	however	however	ADV
fumecheng-4103	37	2	,	,	PUNCT
fumecheng-4103	37	3	the	the	DET
fumecheng-4103	37	4	mdr	mdr	PROPN
fumecheng-4103	37	5	is	be	AUX
fumecheng-4103	37	6	applicable	applicable	ADJ
fumecheng-4103	37	7	also	also	ADV
fumecheng-4103	37	8	to	to	ADP
fumecheng-4103	37	9	gradient	gradient	ADJ
fumecheng-4103	37	10	media	medium	NOUN
fumecheng-4103	37	11	[	[	X
fumecheng-4103	37	12	10	10	NUM
fumecheng-4103	37	13	]	]	PUNCT
fumecheng-4103	37	14	and	and	CCONJ
fumecheng-4103	37	15	to	to	ADP
fumecheng-4103	37	16	viscoelastic	viscoelastic	ADJ
fumecheng-4103	37	17	media	medium	NOUN
fumecheng-4103	37	18	[	[	X
fumecheng-4103	37	19	11	11	NUM
fumecheng-4103	37	20	]	]	PUNCT
fumecheng-4103	37	21	,	,	PUNCT
fumecheng-4103	37	22	which	which	PRON
fumecheng-4103	37	23	can	can	AUX
fumecheng-4103	37	24	be	be	AUX
fumecheng-4103	37	25	treated	treat	VERB
fumecheng-4103	37	26	in	in	ADP
fumecheng-4103	37	27	a	a	DET
fumecheng-4103	37	28	similar	similar	ADJ
fumecheng-4103	37	29	manner	manner	NOUN
fumecheng-4103	37	30	as	as	SCONJ
fumecheng-4103	37	31	described	describe	VERB
fumecheng-4103	37	32	in	in	ADP
fumecheng-4103	37	33	the	the	DET
fumecheng-4103	37	34	present	present	ADJ
fumecheng-4103	37	35	paper	paper	NOUN
fumecheng-4103	37	36	.	.	PUNCT
fumecheng-4103	38	1	2	2	X
fumecheng-4103	38	2	.	.	X
fumecheng-4103	38	3	formulation	formulation	NOUN
fumecheng-4103	38	4	of	of	ADP
fumecheng-4103	38	5	the	the	DET
fumecheng-4103	38	6	mdr	mdr	PROPN
fumecheng-4103	38	7	transformations	transformation	NOUN
fumecheng-4103	38	8	for	for	ADP
fumecheng-4103	38	9	simple	simple	ADJ
fumecheng-4103	38	10	numerical	numerical	ADJ
fumecheng-4103	38	11	implementation	implementation	NOUN
fumecheng-4103	38	12	the	the	DET
fumecheng-4103	38	13	general	general	PROPN
fumecheng-4103	38	14	mdr	mdr	PROPN
fumecheng-4103	38	15	procedure	procedure	NOUN
fumecheng-4103	38	16	is	be	AUX
fumecheng-4103	38	17	fully	fully	ADV
fumecheng-4103	38	18	described	describe	VERB
fumecheng-4103	38	19	in	in	ADP
fumecheng-4103	38	20	[	[	X
fumecheng-4103	38	21	9	9	NUM
fumecheng-4103	38	22	]	]	PUNCT
fumecheng-4103	38	23	.	.	PUNCT
fumecheng-4103	39	1	three	three	NUM
fumecheng-4103	39	2	main	main	ADJ
fumecheng-4103	39	3	transformations	transformation	NOUN
fumecheng-4103	39	4	occur	occur	VERB
fumecheng-4103	39	5	in	in	ADP
fumecheng-4103	39	6	the	the	DET
fumecheng-4103	39	7	method	method	NOUN
fumecheng-4103	39	8	:	:	PUNCT
fumecheng-4103	39	9	the	the	DET
fumecheng-4103	39	10	transformation	transformation	NOUN
fumecheng-4103	39	11	of	of	ADP
fumecheng-4103	39	12	three	three	NUM
fumecheng-4103	39	13	-	-	PUNCT
fumecheng-4103	39	14	dimensional	dimensional	ADJ
fumecheng-4103	39	15	profile	profile	NOUN
fumecheng-4103	39	16	f(r	f(r	NOUN
fumecheng-4103	39	17	)	)	PUNCT
fumecheng-4103	39	18	to	to	ADP
fumecheng-4103	39	19	a	a	DET
fumecheng-4103	39	20	one	one	NUM
fumecheng-4103	39	21	-	-	PUNCT
fumecheng-4103	39	22	dimensional	dimensional	ADJ
fumecheng-4103	39	23	profile	profile	NOUN
fumecheng-4103	39	24	is	be	AUX
fumecheng-4103	39	25	2	2	NUM
fumecheng-4103	39	26	2	2	NUM
fumecheng-4103	39	27	0	0	NUM
fumecheng-4103	39	28	(	(	PUNCT
fumecheng-4103	39	29	)	)	PUNCT
fumecheng-4103	39	30	(	(	PUNCT
fumecheng-4103	39	31	)	)	PUNCT
fumecheng-4103	40	1	x	x	PUNCT
fumecheng-4103	40	2	f	f	NOUN
fumecheng-4103	40	3	r	r	NOUN
fumecheng-4103	40	4	g	g	NOUN
fumecheng-4103	40	5	x	x	SYM
fumecheng-4103	40	6	x	x	PROPN
fumecheng-4103	40	7	dr	dr	PROPN
fumecheng-4103	40	8	x	x	SYM
fumecheng-4103	40	9	r	r	NOUN
fumecheng-4103	40	10			CCONJ
fumecheng-4103	40	11			PROPN
fumecheng-4103	40	12			NOUN
fumecheng-4103	40	13			PUNCT
fumecheng-4103	40	14	,	,	PUNCT
fumecheng-4103	40	15	(	(	PUNCT
fumecheng-4103	40	16	1	1	X
fumecheng-4103	40	17	)	)	PUNCT
fumecheng-4103	40	18	the	the	DET
fumecheng-4103	40	19	transformation	transformation	NOUN
fumecheng-4103	40	20	of	of	ADP
fumecheng-4103	40	21	one	one	NUM
fumecheng-4103	40	22	-	-	PUNCT
fumecheng-4103	40	23	dimensional	dimensional	ADJ
fumecheng-4103	40	24	foundation	foundation	NOUN
fumecheng-4103	40	25	displacement	displacement	NOUN
fumecheng-4103	40	26	w1d(x	w1d(x	NOUN
fumecheng-4103	40	27	)	)	PUNCT
fumecheng-4103	40	28	to	to	ADP
fumecheng-4103	40	29	three	three	NUM
fumecheng-4103	40	30	-	-	PUNCT
fumecheng-4103	40	31	dimensional	dimensional	ADJ
fumecheng-4103	40	32	normal	normal	ADJ
fumecheng-4103	40	33	surface	surface	NOUN
fumecheng-4103	40	34	displacement	displacement	NOUN
fumecheng-4103	40	35	w(r	w(r	PROPN
fumecheng-4103	40	36	)	)	PUNCT
fumecheng-4103	40	37	is	be	AUX
fumecheng-4103	40	38	1d	1d	NUM
fumecheng-4103	40	39	2	2	NUM
fumecheng-4103	40	40	2	2	NUM
fumecheng-4103	40	41	0	0	NUM
fumecheng-4103	40	42	(	(	PUNCT
fumecheng-4103	40	43	)	)	PUNCT
fumecheng-4103	40	44	2	2	NUM
fumecheng-4103	40	45	(	(	PUNCT
fumecheng-4103	40	46	)	)	PUNCT
fumecheng-4103	40	47	r	r	NOUN
fumecheng-4103	40	48	w	w	PROPN
fumecheng-4103	40	49	x	x	X
fumecheng-4103	40	50	w	w	NOUN
fumecheng-4103	40	51	r	r	NOUN
fumecheng-4103	40	52	dx	dx	PROPN
fumecheng-4103	40	53	r	r	NOUN
fumecheng-4103	40	54	x	x	PROPN
fumecheng-4103	41	1			PROPN
fumecheng-4103	41	2			PROPN
fumecheng-4103	41	3			PUNCT
fumecheng-4103	41	4	,	,	PUNCT
fumecheng-4103	41	5	(	(	PUNCT
fumecheng-4103	41	6	2	2	X
fumecheng-4103	41	7	)	)	PUNCT
fumecheng-4103	41	8	and	and	CCONJ
fumecheng-4103	41	9	the	the	DET
fumecheng-4103	41	10	transformation	transformation	NOUN
fumecheng-4103	41	11	of	of	ADP
fumecheng-4103	41	12	one	one	NUM
fumecheng-4103	41	13	-	-	PUNCT
fumecheng-4103	41	14	dimensional	dimensional	ADJ
fumecheng-4103	41	15	force	force	NOUN
fumecheng-4103	41	16	density	density	NOUN
fumecheng-4103	41	17	q(x	q(x	NOUN
fumecheng-4103	41	18	)	)	PUNCT
fumecheng-4103	41	19	to	to	ADP
fumecheng-4103	41	20	three	three	NUM
fumecheng-4103	41	21	-	-	PUNCT
fumecheng-4103	41	22	dimensional	dimensional	ADJ
fumecheng-4103	41	23	pressure	pressure	NOUN
fumecheng-4103	41	24	distribution	distribution	NOUN
fumecheng-4103	41	25	p(r	p(r	NOUN
fumecheng-4103	41	26	)	)	PUNCT
fumecheng-4103	41	27	is	be	AUX
fumecheng-4103	41	28	fast	fast	ADJ
fumecheng-4103	41	29	numerical	numerical	ADJ
fumecheng-4103	41	30	implementation	implementation	NOUN
fumecheng-4103	41	31	of	of	ADP
fumecheng-4103	41	32	the	the	DET
fumecheng-4103	41	33	mdr	mdr	PROPN
fumecheng-4103	41	34	transformations	transformation	VERB
fumecheng-4103	41	35	129	129	NUM
fumecheng-4103	41	36	2	2	NUM
fumecheng-4103	41	37	2	2	NUM
fumecheng-4103	41	38	1	1	NUM
fumecheng-4103	41	39	(	(	PUNCT
fumecheng-4103	41	40	)	)	PUNCT
fumecheng-4103	42	1	(	(	PUNCT
fumecheng-4103	42	2	)	)	PUNCT
fumecheng-4103	42	3	r	r	NOUN
fumecheng-4103	42	4	q	q	NOUN
fumecheng-4103	43	1	x	x	X
fumecheng-4103	43	2	p	p	X
fumecheng-4103	43	3	r	r	NOUN
fumecheng-4103	43	4	dx	dx	PROPN
fumecheng-4103	43	5	x	x	PUNCT
fumecheng-4103	43	6	r	r	VERB
fumecheng-4103	43	7			NOUN
fumecheng-4103	43	8			CCONJ
fumecheng-4103	43	9			NUM
fumecheng-4103	43	10			PROPN
fumecheng-4103	43	11			PROPN
fumecheng-4103	43	12			PUNCT
fumecheng-4103	43	13	.	.	PUNCT
fumecheng-4103	44	1	(	(	PUNCT
fumecheng-4103	44	2	3	3	X
fumecheng-4103	44	3	)	)	PUNCT
fumecheng-4103	44	4	the	the	DET
fumecheng-4103	44	5	singularity	singularity	NOUN
fumecheng-4103	44	6	arising	arise	VERB
fumecheng-4103	44	7	at	at	ADP
fumecheng-4103	44	8	x	x	X
fumecheng-4103	44	9	=	=	NOUN
fumecheng-4103	44	10	r	r	NOUN
fumecheng-4103	44	11	in	in	ADP
fumecheng-4103	44	12	the	the	DET
fumecheng-4103	44	13	numerical	numerical	ADJ
fumecheng-4103	44	14	summation	summation	NOUN
fumecheng-4103	44	15	can	can	AUX
fumecheng-4103	44	16	be	be	AUX
fumecheng-4103	44	17	avoided	avoid	VERB
fumecheng-4103	44	18	when	when	SCONJ
fumecheng-4103	44	19	rewriting	rewrite	VERB
fumecheng-4103	44	20	eqs	eqs	PROPN
fumecheng-4103	44	21	.	.	PUNCT
fumecheng-4103	45	1	(	(	PUNCT
fumecheng-4103	45	2	1	1	NUM
fumecheng-4103	45	3	)	)	PUNCT
fumecheng-4103	45	4	,	,	PUNCT
fumecheng-4103	45	5	(	(	PUNCT
fumecheng-4103	45	6	2	2	X
fumecheng-4103	45	7	)	)	PUNCT
fumecheng-4103	45	8	and	and	CCONJ
fumecheng-4103	45	9	(	(	PUNCT
fumecheng-4103	45	10	3	3	X
fumecheng-4103	45	11	)	)	PUNCT
fumecheng-4103	45	12	to	to	ADP
fumecheng-4103	45	13	2	2	NUM
fumecheng-4103	45	14	2	2	NUM
fumecheng-4103	45	15	0	0	NUM
fumecheng-4103	45	16	(	(	PUNCT
fumecheng-4103	45	17	)	)	PUNCT
fumecheng-4103	45	18	(	(	PUNCT
fumecheng-4103	45	19	)	)	PUNCT
fumecheng-4103	45	20	atan	atan	PROPN
fumecheng-4103	45	21	(	(	PUNCT
fumecheng-4103	45	22	)	)	PUNCT
fumecheng-4103	45	23	2	2	NUM
fumecheng-4103	45	24	x	x	SYM
fumecheng-4103	45	25	r	r	NOUN
fumecheng-4103	45	26	g	g	NOUN
fumecheng-4103	45	27	x	x	PUNCT
fumecheng-4103	45	28	x	x	X
fumecheng-4103	45	29	f	f	NOUN
fumecheng-4103	45	30	x	x	PUNCT
fumecheng-4103	45	31	x	x	SYM
fumecheng-4103	45	32	f	f	NOUN
fumecheng-4103	45	33	r	r	NOUN
fumecheng-4103	45	34	dr	dr	PROPN
fumecheng-4103	45	35	x	x	PROPN
fumecheng-4103	45	36	r	r	NOUN
fumecheng-4103	45	37			PROPN
fumecheng-4103	45	38			NOUN
fumecheng-4103	45	39			NOUN
fumecheng-4103	45	40			ADJ
fumecheng-4103	45	41			PROPN
fumecheng-4103	45	42			PROPN
fumecheng-4103	45	43			PROPN
fumecheng-4103	45	44			NOUN
fumecheng-4103	46	1			PROPN
fumecheng-4103	46	2			NOUN
fumecheng-4103	46	3			NOUN
fumecheng-4103	46	4			PUNCT
fumecheng-4103	46	5	,	,	PUNCT
fumecheng-4103	46	6	(	(	PUNCT
fumecheng-4103	46	7	4	4	X
fumecheng-4103	46	8	)	)	PUNCT
fumecheng-4103	46	9	1d	1d	NUM
fumecheng-4103	46	10	1d	1d	NUM
fumecheng-4103	46	11	2	2	NUM
fumecheng-4103	46	12	2	2	NUM
fumecheng-4103	46	13	0	0	NUM
fumecheng-4103	46	14	2	2	NUM
fumecheng-4103	46	15	(	(	PUNCT
fumecheng-4103	46	16	)	)	PUNCT
fumecheng-4103	46	17	(	(	PUNCT
fumecheng-4103	46	18	)	)	PUNCT
fumecheng-4103	46	19	atan	atan	PROPN
fumecheng-4103	46	20	(	(	PUNCT
fumecheng-4103	46	21	)	)	PUNCT
fumecheng-4103	47	1	r	r	NOUN
fumecheng-4103	47	2	x	x	PUNCT
fumecheng-4103	47	3	w	w	NOUN
fumecheng-4103	47	4	r	r	NOUN
fumecheng-4103	47	5	w	w	NOUN
fumecheng-4103	47	6	r	r	NOUN
fumecheng-4103	47	7	w	w	PROPN
fumecheng-4103	47	8	x	x	SYM
fumecheng-4103	47	9	dx	dx	PROPN
fumecheng-4103	47	10	r	r	PROPN
fumecheng-4103	47	11	x	x	PROPN
fumecheng-4103	47	12			NOUN
fumecheng-4103	47	13			PROPN
fumecheng-4103	47	14			PROPN
fumecheng-4103	47	15			PROPN
fumecheng-4103	47	16			PROPN
fumecheng-4103	47	17			NOUN
fumecheng-4103	48	1			PROPN
fumecheng-4103	48	2			NOUN
fumecheng-4103	48	3			NOUN
fumecheng-4103	48	4			PUNCT
fumecheng-4103	48	5	,	,	PUNCT
fumecheng-4103	48	6	(	(	PUNCT
fumecheng-4103	48	7	5	5	NUM
fumecheng-4103	48	8	)	)	PUNCT
fumecheng-4103	48	9	and	and	CCONJ
fumecheng-4103	48	10	2	2	NUM
fumecheng-4103	48	11	21	21	NUM
fumecheng-4103	48	12	1	1	NUM
fumecheng-4103	48	13	(	(	PUNCT
fumecheng-4103	48	14	)	)	PUNCT
fumecheng-4103	48	15	log	log	NOUN
fumecheng-4103	48	16	(	(	PUNCT
fumecheng-4103	48	17	)	)	PUNCT
fumecheng-4103	48	18	(	(	PUNCT
fumecheng-4103	48	19	)	)	PUNCT
fumecheng-4103	48	20	log	log	NOUN
fumecheng-4103	48	21	(	(	PUNCT
fumecheng-4103	48	22	)	)	PUNCT
fumecheng-4103	48	23	(	(	PUNCT
fumecheng-4103	48	24	)	)	PUNCT
fumecheng-4103	49	1	r	r	NOUN
fumecheng-4103	49	2	p	p	NOUN
fumecheng-4103	49	3	r	r	NOUN
fumecheng-4103	49	4	r	r	NOUN
fumecheng-4103	49	5	q	q	NOUN
fumecheng-4103	49	6	r	r	NOUN
fumecheng-4103	49	7	x	x	PUNCT
fumecheng-4103	49	8	r	r	NOUN
fumecheng-4103	49	9	x	x	NOUN
fumecheng-4103	49	10	q	q	PUNCT
fumecheng-4103	49	11	x	x	X
fumecheng-4103	49	12	dx	dx	PROPN
fumecheng-4103	49	13			PROPN
fumecheng-4103	49	14			ADJ
fumecheng-4103	49	15			VERB
fumecheng-4103	49	16			PRON
fumecheng-4103	49	17			PROPN
fumecheng-4103	49	18			X
fumecheng-4103	49	19			X
fumecheng-4103	49	20			NUM
fumecheng-4103	49	21	(	(	PUNCT
fumecheng-4103	49	22	6	6	NUM
fumecheng-4103	49	23	)	)	PUNCT
fumecheng-4103	49	24	using	use	VERB
fumecheng-4103	49	25	integration	integration	NOUN
fumecheng-4103	49	26	by	by	ADP
fumecheng-4103	49	27	parts	part	NOUN
fumecheng-4103	49	28	.	.	PUNCT
fumecheng-4103	50	1	the	the	DET
fumecheng-4103	50	2	following	follow	VERB
fumecheng-4103	50	3	example	example	NOUN
fumecheng-4103	50	4	shall	shall	AUX
fumecheng-4103	50	5	illustrate	illustrate	VERB
fumecheng-4103	50	6	a	a	DET
fumecheng-4103	50	7	possible	possible	ADJ
fumecheng-4103	50	8	numerical	numerical	ADJ
fumecheng-4103	50	9	implementation	implementation	NOUN
fumecheng-4103	50	10	of	of	ADP
fumecheng-4103	50	11	the	the	DET
fumecheng-4103	50	12	three	three	NUM
fumecheng-4103	50	13	transformations	transformation	NOUN
fumecheng-4103	50	14	(	(	PUNCT
fumecheng-4103	50	15	4	4	NUM
fumecheng-4103	50	16	)	)	PUNCT
fumecheng-4103	50	17	,	,	PUNCT
fumecheng-4103	50	18	(	(	PUNCT
fumecheng-4103	50	19	5	5	NUM
fumecheng-4103	50	20	)	)	PUNCT
fumecheng-4103	50	21	and	and	CCONJ
fumecheng-4103	50	22	(	(	PUNCT
fumecheng-4103	50	23	6	6	NUM
fumecheng-4103	50	24	)	)	PUNCT
fumecheng-4103	50	25	.	.	PUNCT
fumecheng-4103	51	1	3	3	X
fumecheng-4103	51	2	.	.	X
fumecheng-4103	51	3	exemplary	exemplary	ADJ
fumecheng-4103	51	4	numerical	numerical	ADJ
fumecheng-4103	51	5	procedure	procedure	NOUN
fumecheng-4103	51	6	consider	consider	VERB
fumecheng-4103	51	7	a	a	DET
fumecheng-4103	51	8	uniform	uniform	ADJ
fumecheng-4103	51	9	discretization	discretization	NOUN
fumecheng-4103	51	10	of	of	ADP
fumecheng-4103	51	11	r∈	r∈	PROPN
fumecheng-4103	52	1	[	[	X
fumecheng-4103	52	2	0,l	0,l	X
fumecheng-4103	52	3	]	]	X
fumecheng-4103	52	4	and	and	CCONJ
fumecheng-4103	52	5	x∈	x∈	PROPN
fumecheng-4103	53	1	[	[	X
fumecheng-4103	53	2	0,l	0,l	X
fumecheng-4103	53	3	]	]	X
fumecheng-4103	53	4	with	with	ADP
fumecheng-4103	53	5	n	n	NOUN
fumecheng-4103	53	6	points	point	NOUN
fumecheng-4103	53	7	each	each	PRON
fumecheng-4103	53	8	and	and	CCONJ
fumecheng-4103	53	9	the	the	DET
fumecheng-4103	53	10	same	same	ADJ
fumecheng-4103	53	11	step	step	NOUN
fumecheng-4103	53	12	size	size	NOUN
fumecheng-4103	53	13	1	1	NUM
fumecheng-4103	53	14	l	l	NOUN
fumecheng-4103	53	15	h	h	NOUN
fumecheng-4103	53	16	n	n	CCONJ
fumecheng-4103	53	17			PROPN
fumecheng-4103	53	18			PROPN
fumecheng-4103	53	19	,	,	PUNCT
fumecheng-4103	53	20	(	(	PUNCT
fumecheng-4103	53	21	7	7	NUM
fumecheng-4103	53	22	)	)	PUNCT
fumecheng-4103	53	23	so	so	SCONJ
fumecheng-4103	53	24	that	that	SCONJ
fumecheng-4103	53	25	(	(	PUNCT
fumecheng-4103	53	26	1	1	NUM
fumecheng-4103	53	27	)	)	PUNCT
fumecheng-4103	53	28	,	,	PUNCT
fumecheng-4103	53	29	(	(	PUNCT
fumecheng-4103	53	30	1	1	NUM
fumecheng-4103	53	31	)	)	PUNCT
fumecheng-4103	53	32	,	,	PUNCT
fumecheng-4103	53	33	,	,	PUNCT
fumecheng-4103	53	34	{	{	PUNCT
fumecheng-4103	53	35	1,2	1,2	NUM
fumecheng-4103	53	36	,	,	PUNCT
fumecheng-4103	53	37	...	...	PUNCT
fumecheng-4103	53	38	,	,	PUNCT
fumecheng-4103	53	39	}	}	PUNCT
fumecheng-4103	53	40	n	n	CCONJ
fumecheng-4103	53	41	kr	kr	PROPN
fumecheng-4103	53	42	h	h	PROPN
fumecheng-4103	53	43	n	n	NOUN
fumecheng-4103	53	44	x	x	NOUN
fumecheng-4103	53	45	h	h	NOUN
fumecheng-4103	53	46	k	k	PROPN
fumecheng-4103	53	47	n	n	CCONJ
fumecheng-4103	53	48	k	k	PROPN
fumecheng-4103	53	49	n	n	ADJ
fumecheng-4103	53	50			PROPN
fumecheng-4103	53	51			PROPN
fumecheng-4103	53	52			PROPN
fumecheng-4103	53	53			NOUN
fumecheng-4103	53	54	.	.	PUNCT
fumecheng-4103	54	1	(	(	PUNCT
fumecheng-4103	54	2	8)	8)	NUM
fumecheng-4103	54	3	the	the	DET
fumecheng-4103	54	4	first	first	ADJ
fumecheng-4103	54	5	and	and	CCONJ
fumecheng-4103	54	6	second	second	ADJ
fumecheng-4103	54	7	derivatives	derivative	NOUN
fumecheng-4103	54	8	of	of	ADP
fumecheng-4103	54	9	a	a	DET
fumecheng-4103	54	10	discretized	discretized	ADJ
fumecheng-4103	54	11	indentation	indentation	NOUN
fumecheng-4103	54	12	profile	profile	NOUN
fumecheng-4103	54	13	fn	fn	NOUN
fumecheng-4103	54	14	=	=	SYM
fumecheng-4103	54	15	f(rn	f(rn	PROPN
fumecheng-4103	54	16	)	)	PUNCT
fumecheng-4103	54	17	can	can	AUX
fumecheng-4103	54	18	be	be	AUX
fumecheng-4103	54	19	obtained	obtain	VERB
fumecheng-4103	54	20	via	via	ADP
fumecheng-4103	54	21	central	central	ADJ
fumecheng-4103	54	22	differences	difference	NOUN
fumecheng-4103	54	23	:	:	PUNCT
fumecheng-4103	54	24	1	1	NUM
fumecheng-4103	54	25	1	1	NUM
fumecheng-4103	54	26	2	2	NUM
fumecheng-4103	54	27	n	n	CCONJ
fumecheng-4103	54	28	n	n	CCONJ
fumecheng-4103	54	29	n	n	NOUN
fumecheng-4103	54	30	f	f	NOUN
fumecheng-4103	54	31	f	f	X
fumecheng-4103	54	32	f	f	PROPN
fumecheng-4103	54	33	h	h	PROPN
fumecheng-4103	54	34			ADV
fumecheng-4103	54	35			PROPN
fumecheng-4103	54	36			NUM
fumecheng-4103	54	37			ADJ
fumecheng-4103	54	38	,	,	PUNCT
fumecheng-4103	54	39	(	(	PUNCT
fumecheng-4103	54	40	9	9	NUM
fumecheng-4103	54	41	)	)	SYM
fumecheng-4103	54	42	1	1	NUM
fumecheng-4103	54	43	1	1	NUM
fumecheng-4103	54	44	2	2	NUM
fumecheng-4103	54	45	2n	2n	NUM
fumecheng-4103	54	46	n	n	ADP
fumecheng-4103	54	47	n	n	CCONJ
fumecheng-4103	54	48	n	n	NOUN
fumecheng-4103	54	49	f	f	NOUN
fumecheng-4103	55	1	f	f	PROPN
fumecheng-4103	55	2	f	f	PROPN
fumecheng-4103	55	3	f	f	PROPN
fumecheng-4103	55	4	h	h	PROPN
fumecheng-4103	55	5			PROPN
fumecheng-4103	55	6			PROPN
fumecheng-4103	55	7			X
fumecheng-4103	55	8			PROPN
fumecheng-4103	55	9			PROPN
fumecheng-4103	55	10	.	.	PUNCT
fumecheng-4103	56	1	(	(	PUNCT
fumecheng-4103	56	2	10	10	NUM
fumecheng-4103	56	3	)	)	PUNCT
fumecheng-4103	56	4	some	some	DET
fumecheng-4103	56	5	care	care	NOUN
fumecheng-4103	56	6	must	must	AUX
fumecheng-4103	56	7	be	be	AUX
fumecheng-4103	56	8	taken	take	VERB
fumecheng-4103	56	9	at	at	ADP
fumecheng-4103	56	10	the	the	DET
fumecheng-4103	56	11	borders	border	NOUN
fumecheng-4103	56	12	.	.	PUNCT
fumecheng-4103	57	1	to	to	PART
fumecheng-4103	57	2	obtain	obtain	VERB
fumecheng-4103	57	3	f1	f1	PROPN
fumecheng-4103	57	4	′	′	NOUN
fumecheng-4103	57	5	and	and	CCONJ
fumecheng-4103	57	6	f1	f1	PROPN
fumecheng-4103	57	7	′′	′′	PROPN
fumecheng-4103	57	8	recall	recall	VERB
fumecheng-4103	57	9	that	that	SCONJ
fumecheng-4103	57	10	in	in	ADP
fumecheng-4103	57	11	the	the	DET
fumecheng-4103	57	12	present	present	ADJ
fumecheng-4103	57	13	framework	framework	NOUN
fumecheng-4103	57	14	of	of	ADP
fumecheng-4103	57	15	the	the	DET
fumecheng-4103	57	16	mdr	mdr	PROPN
fumecheng-4103	57	17	profile	profile	PROPN
fumecheng-4103	57	18	f	f	PROPN
fumecheng-4103	57	19	is	be	AUX
fumecheng-4103	57	20	axially	axially	ADV
fumecheng-4103	57	21	-	-	PUNCT
fumecheng-4103	57	22	symmetric	symmetric	ADJ
fumecheng-4103	57	23	and	and	CCONJ
fumecheng-4103	57	24	f(0	f(0	NOUN
fumecheng-4103	57	25	)	)	PUNCT
fumecheng-4103	57	26	=	=	SYM
fumecheng-4103	58	1	0	0	X
fumecheng-4103	58	2	.	.	PUNCT
fumecheng-4103	59	1	thus	thus	ADV
fumecheng-4103	59	2	,	,	PUNCT
fumecheng-4103	59	3	it	it	PRON
fumecheng-4103	59	4	is	be	AUX
fumecheng-4103	59	5	1	1	NUM
fumecheng-4103	59	6	0f	0f	NOUN
fumecheng-4103	59	7			PROPN
fumecheng-4103	59	8	,	,	PUNCT
fumecheng-4103	59	9	(	(	PUNCT
fumecheng-4103	59	10	11	11	NUM
fumecheng-4103	59	11	)	)	PUNCT
fumecheng-4103	59	12	and	and	CCONJ
fumecheng-4103	59	13	2	2	NUM
fumecheng-4103	59	14	1	1	NUM
fumecheng-4103	59	15	2	2	NUM
fumecheng-4103	59	16	2	2	NUM
fumecheng-4103	59	17	f	f	NOUN
fumecheng-4103	59	18	f	f	PROPN
fumecheng-4103	59	19	h	h	PROPN
fumecheng-4103	59	20			PROPN
fumecheng-4103	59	21			PRON
fumecheng-4103	59	22	.	.	PUNCT
fumecheng-4103	60	1	(	(	PUNCT
fumecheng-4103	60	2	12	12	NUM
fumecheng-4103	60	3	)	)	PUNCT
fumecheng-4103	60	4	130	130	NUM
fumecheng-4103	60	5	j.	j.	PROPN
fumecheng-4103	60	6	benad	benad	PROPN
fumecheng-4103	60	7	at	at	ADP
fumecheng-4103	60	8	the	the	DET
fumecheng-4103	60	9	other	other	ADJ
fumecheng-4103	60	10	border	border	NOUN
fumecheng-4103	60	11	the	the	DET
fumecheng-4103	60	12	values	value	NOUN
fumecheng-4103	60	13	for	for	ADP
fumecheng-4103	60	14	fn	fn	NOUN
fumecheng-4103	60	15	′	′	NOUN
fumecheng-4103	60	16	and	and	CCONJ
fumecheng-4103	60	17	fn	fn	PROPN
fumecheng-4103	60	18	′′	′′	PROPN
fumecheng-4103	60	19	can	can	AUX
fumecheng-4103	60	20	remain	remain	VERB
fumecheng-4103	60	21	undetermined	undetermined	ADJ
fumecheng-4103	60	22	.	.	PUNCT
fumecheng-4103	61	1	one	one	NUM
fumecheng-4103	61	2	-	-	PUNCT
fumecheng-4103	61	3	dimensional	dimensional	ADJ
fumecheng-4103	61	4	profile	profile	NOUN
fumecheng-4103	61	5	gk	gk	PROPN
fumecheng-4103	61	6	can	can	AUX
fumecheng-4103	61	7	now	now	ADV
fumecheng-4103	61	8	be	be	AUX
fumecheng-4103	61	9	obtained	obtain	VERB
fumecheng-4103	61	10	with	with	ADP
fumecheng-4103	61	11	eq	eq	NOUN
fumecheng-4103	61	12	.	.	PUNCT
fumecheng-4103	62	1	(	(	PUNCT
fumecheng-4103	62	2	4	4	NUM
fumecheng-4103	62	3	)	)	PUNCT
fumecheng-4103	62	4	.	.	PUNCT
fumecheng-4103	63	1	it	it	PRON
fumecheng-4103	63	2	is	be	AUX
fumecheng-4103	63	3	,	,	PUNCT
fumecheng-4103	63	4	for	for	ADP
fumecheng-4103	63	5	2,3	2,3	NUM
fumecheng-4103	63	6	,	,	PUNCT
fumecheng-4103	63	7	...	...	PUNCT
fumecheng-4103	63	8	,	,	PUNCT
fumecheng-4103	63	9	1	1	NUM
fumecheng-4103	63	10	2	2	X
fumecheng-4103	63	11	k	k	NOUN
fumecheng-4103	63	12	k	k	PROPN
fumecheng-4103	64	1	k	k	PROPN
fumecheng-4103	64	2	k	k	NOUN
fumecheng-4103	65	1	kg	kg	INTJ
fumecheng-4103	65	2	x	x	X
fumecheng-4103	66	1	f	f	X
fumecheng-4103	66	2	x	x	SYM
fumecheng-4103	66	3	t	t	PROPN
fumecheng-4103	66	4	k	k	PROPN
fumecheng-4103	66	5	n	n	PROPN
fumecheng-4103	66	6			PROPN
fumecheng-4103	66	7			PROPN
fumecheng-4103	66	8			PROPN
fumecheng-4103	66	9			PROPN
fumecheng-4103	66	10			PROPN
fumecheng-4103	66	11	,	,	PUNCT
fumecheng-4103	66	12	(	(	PUNCT
fumecheng-4103	66	13	13	13	NUM
fumecheng-4103	66	14	)	)	PUNCT
fumecheng-4103	66	15	where	where	SCONJ
fumecheng-4103	66	16	tk	tk	PROPN
fumecheng-4103	66	17	is	be	AUX
fumecheng-4103	66	18	the	the	DET
fumecheng-4103	66	19	result	result	NOUN
fumecheng-4103	66	20	of	of	ADP
fumecheng-4103	66	21	the	the	DET
fumecheng-4103	66	22	integral	integral	ADJ
fumecheng-4103	66	23	in	in	ADP
fumecheng-4103	66	24	(	(	PUNCT
fumecheng-4103	66	25	4	4	NUM
fumecheng-4103	66	26	)	)	PUNCT
fumecheng-4103	66	27	.	.	PUNCT
fumecheng-4103	67	1	using	use	VERB
fumecheng-4103	67	2	the	the	DET
fumecheng-4103	67	3	trapezoidal	trapezoidal	ADJ
fumecheng-4103	67	4	rule	rule	NOUN
fumecheng-4103	67	5	,	,	PUNCT
fumecheng-4103	67	6	it	it	PRON
fumecheng-4103	67	7	is	be	AUX
fumecheng-4103	67	8	1	1	NUM
fumecheng-4103	67	9	2	2	NUM
fumecheng-4103	67	10	2	2	NUM
fumecheng-4103	67	11	2	2	NUM
fumecheng-4103	67	12	,	,	PUNCT
fumecheng-4103	67	13	for	for	ADP
fumecheng-4103	67	14	2	2	NUM
fumecheng-4103	67	15	4	4	NUM
fumecheng-4103	67	16	atan	atan	ADJ
fumecheng-4103	67	17	,	,	PUNCT
fumecheng-4103	67	18	for	for	ADP
fumecheng-4103	67	19	3,4	3,4	NUM
fumecheng-4103	67	20	,	,	PUNCT
fumecheng-4103	67	21	...	...	PUNCT
fumecheng-4103	67	22	,	,	PUNCT
fumecheng-4103	67	23	1	1	NUM
fumecheng-4103	67	24	4	4	NUM
fumecheng-4103	67	25	k	k	NOUN
fumecheng-4103	67	26	k	k	PROPN
fumecheng-4103	67	27	k	k	PROPN
fumecheng-4103	67	28	n	n	CCONJ
fumecheng-4103	67	29	n	n	CCONJ
fumecheng-4103	67	30	k	k	PROPN
fumecheng-4103	67	31	n	n	CCONJ
fumecheng-4103	67	32	k	k	PROPN
fumecheng-4103	67	33	n	n	INTJ
fumecheng-4103	67	34	f	f	NOUN
fumecheng-4103	67	35	h	h	NOUN
fumecheng-4103	68	1	k	k	PROPN
fumecheng-4103	68	2	t	t	PROPN
fumecheng-4103	68	3	r	r	NOUN
fumecheng-4103	69	1	f	f	PROPN
fumecheng-4103	69	2	h	h	NOUN
fumecheng-4103	70	1	f	f	NOUN
fumecheng-4103	70	2	h	h	NOUN
fumecheng-4103	71	1	k	k	PROPN
fumecheng-4103	72	1	n	n	ADV
fumecheng-4103	72	2	x	x	SYM
fumecheng-4103	72	3	r	r	NOUN
fumecheng-4103	72	4			PROPN
fumecheng-4103	73	1			ADV
fumecheng-4103	73	2			NOUN
fumecheng-4103	73	3			ADV
fumecheng-4103	73	4			PROPN
fumecheng-4103	73	5			NOUN
fumecheng-4103	73	6			NUM
fumecheng-4103	73	7			NUM
fumecheng-4103	73	8			NUM
fumecheng-4103	73	9			NOUN
fumecheng-4103	73	10			PROPN
fumecheng-4103	73	11			PROPN
fumecheng-4103	73	12			NUM
fumecheng-4103	73	13			PROPN
fumecheng-4103	73	14			NOUN
fumecheng-4103	74	1			PROPN
fumecheng-4103	74	2			PROPN
fumecheng-4103	74	3			VERB
fumecheng-4103	74	4			PROPN
fumecheng-4103	74	5			PROPN
fumecheng-4103	74	6			NUM
fumecheng-4103	74	7			PROPN
fumecheng-4103	74	8			NOUN
fumecheng-4103	74	9			PROPN
fumecheng-4103	74	10			PROPN
fumecheng-4103	74	11			PROPN
fumecheng-4103	74	12			X
fumecheng-4103	74	13	(	(	PUNCT
fumecheng-4103	74	14	14	14	NUM
fumecheng-4103	74	15	)	)	PUNCT
fumecheng-4103	74	16	again	again	ADV
fumecheng-4103	74	17	,	,	PUNCT
fumecheng-4103	74	18	some	some	DET
fumecheng-4103	74	19	care	care	NOUN
fumecheng-4103	74	20	must	must	AUX
fumecheng-4103	74	21	be	be	AUX
fumecheng-4103	74	22	taken	take	VERB
fumecheng-4103	74	23	at	at	ADP
fumecheng-4103	74	24	the	the	DET
fumecheng-4103	74	25	borders	border	NOUN
fumecheng-4103	74	26	.	.	PUNCT
fumecheng-4103	75	1	to	to	PART
fumecheng-4103	75	2	obtain	obtain	VERB
fumecheng-4103	75	3	g1	g1	NOUN
fumecheng-4103	75	4	,	,	PUNCT
fumecheng-4103	75	5	recall	recall	VERB
fumecheng-4103	75	6	that	that	SCONJ
fumecheng-4103	75	7	in	in	ADP
fumecheng-4103	75	8	the	the	DET
fumecheng-4103	75	9	framework	framework	NOUN
fumecheng-4103	75	10	of	of	ADP
fumecheng-4103	75	11	the	the	DET
fumecheng-4103	75	12	mdr	mdr	PROPN
fumecheng-4103	75	13	it	it	PRON
fumecheng-4103	75	14	is	be	AUX
fumecheng-4103	75	15	g(0	g(0	NOUN
fumecheng-4103	75	16	)	)	PUNCT
fumecheng-4103	75	17	=	=	SYM
fumecheng-4103	76	1	0	0	X
fumecheng-4103	76	2	.	.	PUNCT
fumecheng-4103	77	1	thus	thus	ADV
fumecheng-4103	77	2	,	,	PUNCT
fumecheng-4103	77	3	it	it	PRON
fumecheng-4103	77	4	is	be	AUX
fumecheng-4103	77	5	1	1	NUM
fumecheng-4103	77	6	0	0	NUM
fumecheng-4103	77	7	g	g	NOUN
fumecheng-4103	77	8			NOUN
fumecheng-4103	77	9	.	.	PUNCT
fumecheng-4103	78	1	(	(	PUNCT
fumecheng-4103	78	2	15	15	NUM
fumecheng-4103	78	3	)	)	PUNCT
fumecheng-4103	78	4	at	at	ADP
fumecheng-4103	78	5	the	the	DET
fumecheng-4103	78	6	other	other	ADJ
fumecheng-4103	78	7	border	border	NOUN
fumecheng-4103	78	8	the	the	DET
fumecheng-4103	78	9	value	value	NOUN
fumecheng-4103	78	10	for	for	ADP
fumecheng-4103	78	11	gn	gn	PROPN
fumecheng-4103	78	12	can	can	AUX
fumecheng-4103	78	13	remain	remain	VERB
fumecheng-4103	78	14	undetermined	undetermined	ADJ
fumecheng-4103	78	15	.	.	PUNCT
fumecheng-4103	79	1	in	in	ADP
fumecheng-4103	79	2	a	a	DET
fumecheng-4103	79	3	quite	quite	ADV
fumecheng-4103	79	4	similar	similar	ADJ
fumecheng-4103	79	5	fashion	fashion	NOUN
fumecheng-4103	79	6	,	,	PUNCT
fumecheng-4103	79	7	normal	normal	ADJ
fumecheng-4103	79	8	surface	surface	NOUN
fumecheng-4103	79	9	displacement	displacement	NOUN
fumecheng-4103	79	10	wn	wn	NOUN
fumecheng-4103	79	11	can	can	AUX
fumecheng-4103	79	12	be	be	AUX
fumecheng-4103	79	13	obtained	obtain	VERB
fumecheng-4103	79	14	:	:	PUNCT
fumecheng-4103	79	15	the	the	DET
fumecheng-4103	79	16	first	first	ADJ
fumecheng-4103	79	17	derivative	derivative	NOUN
fumecheng-4103	79	18	in	in	ADP
fumecheng-4103	79	19	eq	eq	ADP
fumecheng-4103	79	20	.	.	PUNCT
fumecheng-4103	80	1	(	(	PUNCT
fumecheng-4103	80	2	5	5	X
fumecheng-4103	80	3	)	)	PUNCT
fumecheng-4103	80	4	can	can	AUX
fumecheng-4103	80	5	be	be	AUX
fumecheng-4103	80	6	obtained	obtain	VERB
fumecheng-4103	80	7	as	as	ADP
fumecheng-4103	80	8	in	in	ADP
fumecheng-4103	80	9	eq	eq	NOUN
fumecheng-4103	80	10	.	.	PUNCT
fumecheng-4103	81	1	(	(	PUNCT
fumecheng-4103	81	2	9	9	X
fumecheng-4103	81	3	)	)	PUNCT
fumecheng-4103	81	4	using	use	VERB
fumecheng-4103	81	5	central	central	ADJ
fumecheng-4103	81	6	differences	difference	NOUN
fumecheng-4103	81	7	,	,	PUNCT
fumecheng-4103	81	8	and	and	CCONJ
fumecheng-4103	81	9	the	the	DET
fumecheng-4103	81	10	integral	integral	ADJ
fumecheng-4103	81	11	can	can	AUX
fumecheng-4103	81	12	be	be	AUX
fumecheng-4103	81	13	calculated	calculate	VERB
fumecheng-4103	81	14	as	as	ADP
fumecheng-4103	81	15	in	in	ADP
fumecheng-4103	81	16	eq	eq	ADP
fumecheng-4103	81	17	.	.	PUNCT
fumecheng-4103	82	1	(	(	PUNCT
fumecheng-4103	82	2	14	14	NUM
fumecheng-4103	82	3	)	)	PUNCT
fumecheng-4103	82	4	using	use	VERB
fumecheng-4103	82	5	the	the	DET
fumecheng-4103	82	6	trapezoidal	trapezoidal	ADJ
fumecheng-4103	82	7	rule	rule	NOUN
fumecheng-4103	82	8	.	.	PUNCT
fumecheng-4103	83	1	subsequent	subsequent	ADJ
fumecheng-4103	83	2	smoothing	smoothing	NOUN
fumecheng-4103	83	3	of	of	ADP
fumecheng-4103	83	4	wn	wn	PROPN
fumecheng-4103	83	5	with	with	ADP
fumecheng-4103	83	6	wn	wn	PROPN
fumecheng-4103	83	7	:	:	PUNCT
fumecheng-4103	83	8	=	=	SYM
fumecheng-4103	83	9	(	(	PUNCT
fumecheng-4103	83	10	wn–1	wn–1	PROPN
fumecheng-4103	83	11	+	+	CCONJ
fumecheng-4103	83	12	wn	wn	PROPN
fumecheng-4103	83	13	+	+	CCONJ
fumecheng-4103	83	14	wn+1	wn+1	NOUN
fumecheng-4103	83	15	)	)	PUNCT
fumecheng-4103	83	16	/	/	SYM
fumecheng-4103	83	17	3	3	NUM
fumecheng-4103	83	18	increases	increase	VERB
fumecheng-4103	83	19	the	the	DET
fumecheng-4103	83	20	accuracy	accuracy	NOUN
fumecheng-4103	83	21	of	of	ADP
fumecheng-4103	83	22	wn	wn	PROPN
fumecheng-4103	83	23	.	.	PUNCT
fumecheng-4103	84	1	the	the	DET
fumecheng-4103	84	2	third	third	ADJ
fumecheng-4103	84	3	transformation	transformation	NOUN
fumecheng-4103	84	4	to	to	PART
fumecheng-4103	84	5	obtain	obtain	VERB
fumecheng-4103	84	6	pn	pn	PROPN
fumecheng-4103	84	7	is	be	AUX
fumecheng-4103	84	8	again	again	ADV
fumecheng-4103	84	9	similar	similar	ADJ
fumecheng-4103	84	10	to	to	ADP
fumecheng-4103	84	11	the	the	DET
fumecheng-4103	84	12	first	first	ADJ
fumecheng-4103	84	13	and	and	CCONJ
fumecheng-4103	84	14	second	second	ADJ
fumecheng-4103	84	15	transformation	transformation	NOUN
fumecheng-4103	84	16	.	.	PUNCT
fumecheng-4103	85	1	the	the	DET
fumecheng-4103	85	2	derivatives	derivative	NOUN
fumecheng-4103	85	3	in	in	ADP
fumecheng-4103	85	4	eq	eq	ADP
fumecheng-4103	85	5	.	.	PUNCT
fumecheng-4103	86	1	(	(	PUNCT
fumecheng-4103	86	2	6	6	NUM
fumecheng-4103	86	3	)	)	PUNCT
fumecheng-4103	86	4	can	can	AUX
fumecheng-4103	86	5	once	once	ADV
fumecheng-4103	86	6	more	more	ADJ
fumecheng-4103	86	7	be	be	AUX
fumecheng-4103	86	8	obtained	obtain	VERB
fumecheng-4103	86	9	as	as	ADP
fumecheng-4103	86	10	in	in	ADP
fumecheng-4103	86	11	eqs	eqs	PROPN
fumecheng-4103	86	12	.	.	PUNCT
fumecheng-4103	87	1	(	(	PUNCT
fumecheng-4103	87	2	9	9	NUM
fumecheng-4103	87	3	)	)	PUNCT
fumecheng-4103	87	4	and	and	CCONJ
fumecheng-4103	87	5	(	(	PUNCT
fumecheng-4103	87	6	10	10	NUM
fumecheng-4103	87	7	)	)	PUNCT
fumecheng-4103	87	8	using	use	VERB
fumecheng-4103	87	9	central	central	ADJ
fumecheng-4103	87	10	differences	difference	NOUN
fumecheng-4103	87	11	.	.	PUNCT
fumecheng-4103	88	1	then	then	ADV
fumecheng-4103	88	2	it	it	PRON
fumecheng-4103	88	3	is	be	AUX
fumecheng-4103	88	4	1	1	NUM
fumecheng-4103	88	5	1	1	NUM
fumecheng-4103	88	6	log	log	NOUN
fumecheng-4103	88	7	(	(	PUNCT
fumecheng-4103	88	8	)	)	PUNCT
fumecheng-4103	88	9	,	,	PUNCT
fumecheng-4103	88	10	for	for	ADP
fumecheng-4103	88	11	2,3	2,3	NUM
fumecheng-4103	88	12	,	,	PUNCT
fumecheng-4103	88	13	...	...	PUNCT
fumecheng-4103	88	14	,	,	PUNCT
fumecheng-4103	88	15	2n	2n	NUM
fumecheng-4103	88	16	n	n	CCONJ
fumecheng-4103	88	17	n	n	ADV
fumecheng-4103	88	18	np	np	INTJ
fumecheng-4103	88	19	r	r	NOUN
fumecheng-4103	88	20	q	q	PROPN
fumecheng-4103	88	21	s	s	NOUN
fumecheng-4103	88	22	n	n	CCONJ
fumecheng-4103	88	23	n	n	PRON
fumecheng-4103	88	24			PROPN
fumecheng-4103	88	25			NOUN
fumecheng-4103	88	26			PROPN
fumecheng-4103	88	27			VERB
fumecheng-4103	88	28			NUM
fumecheng-4103	88	29			NOUN
fumecheng-4103	88	30	(	(	PUNCT
fumecheng-4103	88	31	16	16	NUM
fumecheng-4103	88	32	)	)	PUNCT
fumecheng-4103	88	33	where	where	SCONJ
fumecheng-4103	88	34	sn	sn	PROPN
fumecheng-4103	88	35	is	be	AUX
fumecheng-4103	88	36	the	the	DET
fumecheng-4103	88	37	result	result	NOUN
fumecheng-4103	88	38	of	of	ADP
fumecheng-4103	88	39	the	the	DET
fumecheng-4103	88	40	integral	integral	ADJ
fumecheng-4103	88	41	in	in	ADP
fumecheng-4103	88	42	(	(	PUNCT
fumecheng-4103	88	43	6	6	NUM
fumecheng-4103	88	44	)	)	PUNCT
fumecheng-4103	88	45	.	.	PUNCT
fumecheng-4103	89	1	using	use	VERB
fumecheng-4103	89	2	the	the	DET
fumecheng-4103	89	3	trapezoidal	trapezoidal	ADJ
fumecheng-4103	89	4	rule	rule	NOUN
fumecheng-4103	89	5	,	,	PUNCT
fumecheng-4103	89	6	it	it	PRON
fumecheng-4103	89	7	is	be	AUX
fumecheng-4103	89	8	2	2	NUM
fumecheng-4103	89	9	2	2	NUM
fumecheng-4103	89	10	2	2	NUM
fumecheng-4103	89	11	1	1	NUM
fumecheng-4103	89	12	log	log	NOUN
fumecheng-4103	89	13	(	(	PUNCT
fumecheng-4103	89	14	)	)	PUNCT
fumecheng-4103	89	15	log	log	NOUN
fumecheng-4103	89	16	(	(	PUNCT
fumecheng-4103	89	17	)	)	PUNCT
fumecheng-4103	89	18	,	,	PUNCT
fumecheng-4103	89	19	for	for	ADP
fumecheng-4103	89	20	2,3	2,3	NUM
fumecheng-4103	89	21	,	,	PUNCT
fumecheng-4103	89	22	...	...	PUNCT
fumecheng-4103	89	23	,	,	PUNCT
fumecheng-4103	89	24	3	3	NUM
fumecheng-4103	89	25	2	2	NUM
fumecheng-4103	89	26	log	log	NOUN
fumecheng-4103	89	27	(	(	PUNCT
fumecheng-4103	89	28	)	)	PUNCT
fumecheng-4103	89	29	,	,	PUNCT
fumecheng-4103	89	30	for	for	ADP
fumecheng-4103	89	31	2	2	NUM
fumecheng-4103	89	32	2	2	NUM
fumecheng-4103	89	33	n	n	ADP
fumecheng-4103	89	34	n	n	CCONJ
fumecheng-4103	89	35	n	n	NOUN
fumecheng-4103	89	36	k	k	PROPN
fumecheng-4103	89	37	n	n	CCONJ
fumecheng-4103	89	38	k	k	PROPN
fumecheng-4103	89	39	k	k	PROPN
fumecheng-4103	89	40	k	k	PROPN
fumecheng-4103	89	41	n	n	CCONJ
fumecheng-4103	89	42	n	n	CCONJ
fumecheng-4103	89	43	n	n	CCONJ
fumecheng-4103	89	44	n	n	NOUN
fumecheng-4103	89	45	x	x	NOUN
fumecheng-4103	89	46	q	q	NOUN
fumecheng-4103	89	47	h	h	NOUN
fumecheng-4103	89	48	x	x	PUNCT
fumecheng-4103	89	49	r	r	NOUN
fumecheng-4103	89	50	x	x	X
fumecheng-4103	89	51	q	q	NOUN
fumecheng-4103	89	52	h	h	NOUN
fumecheng-4103	89	53	n	n	CCONJ
fumecheng-4103	89	54	n	n	NOUN
fumecheng-4103	89	55	s	s	NOUN
fumecheng-4103	89	56	x	x	X
fumecheng-4103	89	57	q	q	NOUN
fumecheng-4103	89	58	h	h	PROPN
fumecheng-4103	89	59	n	n	CCONJ
fumecheng-4103	89	60	n	n	ADV
fumecheng-4103	89	61			PROPN
fumecheng-4103	89	62			PROPN
fumecheng-4103	89	63			PROPN
fumecheng-4103	89	64			PROPN
fumecheng-4103	89	65			VERB
fumecheng-4103	89	66			PROPN
fumecheng-4103	89	67			VERB
fumecheng-4103	89	68			PROPN
fumecheng-4103	89	69			NOUN
fumecheng-4103	89	70			PROPN
fumecheng-4103	89	71			NUM
fumecheng-4103	89	72			VERB
fumecheng-4103	89	73			NUM
fumecheng-4103	89	74			PROPN
fumecheng-4103	89	75			NOUN
fumecheng-4103	89	76			X
fumecheng-4103	89	77	(	(	PUNCT
fumecheng-4103	89	78	17	17	NUM
fumecheng-4103	89	79	)	)	PUNCT
fumecheng-4103	89	80	note	note	NOUN
fumecheng-4103	89	81	that	that	SCONJ
fumecheng-4103	89	82	at	at	ADP
fumecheng-4103	89	83	kinks	kink	NOUN
fumecheng-4103	89	84	of	of	ADP
fumecheng-4103	89	85	q	q	NOUN
fumecheng-4103	89	86	the	the	DET
fumecheng-4103	89	87	term	term	NOUN
fumecheng-4103	89	88	qk	qk	VERB
fumecheng-4103	89	89	′′	′′	NOUN
fumecheng-4103	89	90	h	h	NOUN
fumecheng-4103	89	91	=	=	PUNCT
fumecheng-4103	89	92	(	(	PUNCT
fumecheng-4103	89	93	qk+1	qk+1	ADP
fumecheng-4103	89	94	–	–	PUNCT
fumecheng-4103	89	95	2qk	2qk	NOUN
fumecheng-4103	89	96	+	+	CCONJ
fumecheng-4103	89	97	qk–1	qk–1	NOUN
fumecheng-4103	89	98	)	)	PUNCT
fumecheng-4103	89	99	/	/	SYM
fumecheng-4103	89	100	h	h	NOUN
fumecheng-4103	89	101	converges	converge	VERB
fumecheng-4103	89	102	to	to	PART
fumecheng-4103	89	103	finite	finite	VERB
fumecheng-4103	89	104	values	value	NOUN
fumecheng-4103	89	105	for	for	ADP
fumecheng-4103	89	106	decreasing	decrease	VERB
fumecheng-4103	89	107	step	step	NOUN
fumecheng-4103	89	108	-	-	PUNCT
fumecheng-4103	89	109	sizes	size	NOUN
fumecheng-4103	89	110	h.	h.	NOUN
fumecheng-4103	89	111	note	note	PROPN
fumecheng-4103	89	112	also	also	ADV
fumecheng-4103	89	113	that	that	SCONJ
fumecheng-4103	89	114	the	the	DET
fumecheng-4103	89	115	summation	summation	NOUN
fumecheng-4103	89	116	in	in	ADP
fumecheng-4103	89	117	eq	eq	PROPN
fumecheng-4103	89	118	.	.	PUNCT
fumecheng-4103	90	1	(	(	PUNCT
fumecheng-4103	90	2	17	17	NUM
fumecheng-4103	90	3	)	)	PUNCT
fumecheng-4103	90	4	stops	stop	VERB
fumecheng-4103	90	5	at	at	ADP
fumecheng-4103	90	6	n	n	PROPN
fumecheng-4103	90	7	–	–	PUNCT
fumecheng-4103	90	8	2	2	NUM
fumecheng-4103	90	9	because	because	SCONJ
fumecheng-4103	90	10	qn	qn	NOUN
fumecheng-4103	90	11	′′	′′	PROPN
fumecheng-4103	90	12	and	and	CCONJ
fumecheng-4103	90	13	qn–1	qn–1	NUM
fumecheng-4103	90	14	′′	′′	PROPN
fumecheng-4103	90	15	are	be	AUX
fumecheng-4103	90	16	undetermined	undetermined	ADJ
fumecheng-4103	90	17	.	.	PUNCT
fumecheng-4103	91	1	this	this	PRON
fumecheng-4103	91	2	is	be	AUX
fumecheng-4103	91	3	not	not	PART
fumecheng-4103	91	4	problematic	problematic	ADJ
fumecheng-4103	91	5	because	because	SCONJ
fumecheng-4103	91	6	in	in	ADP
fumecheng-4103	91	7	the	the	DET
fumecheng-4103	91	8	framework	framework	NOUN
fumecheng-4103	91	9	of	of	ADP
fumecheng-4103	91	10	the	the	DET
fumecheng-4103	91	11	mdr	mdr	PROPN
fumecheng-4103	91	12	it	it	PRON
fumecheng-4103	91	13	is	be	AUX
fumecheng-4103	91	14	q	q	ADJ
fumecheng-4103	91	15	′′	′′	PROPN
fumecheng-4103	91	16	=	=	NOUN
fumecheng-4103	91	17	0	0	NUM
fumecheng-4103	91	18	for	for	ADP
fumecheng-4103	91	19	sufficiently	sufficiently	ADV
fumecheng-4103	91	20	large	large	ADJ
fumecheng-4103	91	21	x	x	NOUN
fumecheng-4103	91	22	in	in	ADP
fumecheng-4103	91	23	any	any	DET
fumecheng-4103	91	24	way	way	NOUN
fumecheng-4103	91	25	(	(	PUNCT
fumecheng-4103	91	26	x	x	X
fumecheng-4103	91	27	>	>	X
fumecheng-4103	91	28	a	a	X
fumecheng-4103	91	29	,	,	PUNCT
fumecheng-4103	91	30	where	where	SCONJ
fumecheng-4103	91	31	a	a	PRON
fumecheng-4103	91	32	is	be	AUX
fumecheng-4103	91	33	the	the	DET
fumecheng-4103	91	34	contact	contact	NOUN
fumecheng-4103	91	35	radius	radius	NOUN
fumecheng-4103	91	36	)	)	PUNCT
fumecheng-4103	91	37	.	.	PUNCT
fumecheng-4103	92	1	once	once	ADV
fumecheng-4103	92	2	again	again	ADV
fumecheng-4103	92	3	,	,	PUNCT
fumecheng-4103	92	4	some	some	DET
fumecheng-4103	92	5	care	care	NOUN
fumecheng-4103	92	6	must	must	AUX
fumecheng-4103	92	7	be	be	AUX
fumecheng-4103	92	8	taken	take	VERB
fumecheng-4103	92	9	at	at	ADP
fumecheng-4103	92	10	the	the	DET
fumecheng-4103	92	11	borders	border	NOUN
fumecheng-4103	92	12	.	.	PUNCT
fumecheng-4103	93	1	one	one	NUM
fumecheng-4103	93	2	way	way	NOUN
fumecheng-4103	93	3	to	to	PART
fumecheng-4103	93	4	approximate	approximate	ADJ
fumecheng-4103	93	5	p1	p1	PROPN
fumecheng-4103	93	6	is	be	AUX
fumecheng-4103	93	7	via	via	ADP
fumecheng-4103	93	8	taylor	taylor	PROPN
fumecheng-4103	93	9	series	series	PROPN
fumecheng-4103	93	10	.	.	PUNCT
fumecheng-4103	94	1	a	a	DET
fumecheng-4103	94	2	first	first	ADJ
fumecheng-4103	94	3	order	order	NOUN
fumecheng-4103	94	4	expansion	expansion	NOUN
fumecheng-4103	94	5	yields	yield	NOUN
fumecheng-4103	94	6	simply	simply	ADV
fumecheng-4103	94	7	3	3	NUM
fumecheng-4103	94	8	2	2	NUM
fumecheng-4103	94	9	1	1	NUM
fumecheng-4103	94	10	2	2	NUM
fumecheng-4103	94	11	2	2	NUM
fumecheng-4103	94	12	p	p	NOUN
fumecheng-4103	94	13	p	p	X
fumecheng-4103	94	14	p	p	X
fumecheng-4103	94	15	p	p	X
fumecheng-4103	94	16			PROPN
fumecheng-4103	94	17			PROPN
fumecheng-4103	94	18			PROPN
fumecheng-4103	94	19	.	.	PUNCT
fumecheng-4103	95	1	(	(	PUNCT
fumecheng-4103	95	2	18	18	NUM
fumecheng-4103	95	3	)	)	PUNCT
fumecheng-4103	95	4	fast	fast	ADJ
fumecheng-4103	95	5	numerical	numerical	ADJ
fumecheng-4103	95	6	implementation	implementation	NOUN
fumecheng-4103	95	7	of	of	ADP
fumecheng-4103	95	8	the	the	DET
fumecheng-4103	95	9	mdr	mdr	PROPN
fumecheng-4103	95	10	transformations	transformation	VERB
fumecheng-4103	95	11	131	131	NUM
fumecheng-4103	95	12	at	at	ADP
fumecheng-4103	95	13	the	the	DET
fumecheng-4103	95	14	other	other	ADJ
fumecheng-4103	95	15	border	border	NOUN
fumecheng-4103	95	16	the	the	DET
fumecheng-4103	95	17	values	value	NOUN
fumecheng-4103	95	18	for	for	ADP
fumecheng-4103	95	19	pn	pn	PROPN
fumecheng-4103	95	20	and	and	CCONJ
fumecheng-4103	95	21	pn–1	pn–1	PROPN
fumecheng-4103	95	22	remain	remain	VERB
fumecheng-4103	95	23	undetermined	undetermined	ADJ
fumecheng-4103	95	24	.	.	PUNCT
fumecheng-4103	96	1	again	again	ADV
fumecheng-4103	96	2	,	,	PUNCT
fumecheng-4103	96	3	this	this	PRON
fumecheng-4103	96	4	is	be	AUX
fumecheng-4103	96	5	not	not	PART
fumecheng-4103	96	6	problematic	problematic	ADJ
fumecheng-4103	96	7	as	as	ADV
fumecheng-4103	96	8	long	long	ADV
fumecheng-4103	96	9	as	as	SCONJ
fumecheng-4103	96	10	it	it	PRON
fumecheng-4103	96	11	is	be	AUX
fumecheng-4103	96	12	ensured	ensure	VERB
fumecheng-4103	96	13	that	that	SCONJ
fumecheng-4103	96	14	these	these	DET
fumecheng-4103	96	15	last	last	ADJ
fumecheng-4103	96	16	points	point	NOUN
fumecheng-4103	96	17	lie	lie	VERB
fumecheng-4103	96	18	outside	outside	ADP
fumecheng-4103	96	19	the	the	DET
fumecheng-4103	96	20	contact	contact	NOUN
fumecheng-4103	96	21	area	area	NOUN
fumecheng-4103	96	22	.	.	PUNCT
fumecheng-4103	97	1	then	then	ADV
fumecheng-4103	97	2	they	they	PRON
fumecheng-4103	97	3	can	can	AUX
fumecheng-4103	97	4	simply	simply	ADV
fumecheng-4103	97	5	be	be	AUX
fumecheng-4103	97	6	set	set	VERB
fumecheng-4103	97	7	to	to	ADP
fumecheng-4103	97	8	1	1	NUM
fumecheng-4103	97	9	0n	0n	NUM
fumecheng-4103	97	10	np	np	ADP
fumecheng-4103	97	11	p	p	NOUN
fumecheng-4103	97	12			PROPN
fumecheng-4103	97	13			PROPN
fumecheng-4103	97	14	.	.	PUNCT
fumecheng-4103	98	1	(	(	PUNCT
fumecheng-4103	98	2	19	19	NUM
fumecheng-4103	98	3	)	)	SYM
fumecheng-4103	98	4	4	4	NUM
fumecheng-4103	98	5	.	.	PUNCT
fumecheng-4103	98	6	performance	performance	NOUN
fumecheng-4103	98	7	often	often	ADV
fumecheng-4103	98	8	,	,	PUNCT
fumecheng-4103	98	9	the	the	DET
fumecheng-4103	98	10	mdr	mdr	PROPN
fumecheng-4103	98	11	transformations	transformation	NOUN
fumecheng-4103	98	12	need	need	VERB
fumecheng-4103	98	13	to	to	PART
fumecheng-4103	98	14	be	be	AUX
fumecheng-4103	98	15	performed	perform	VERB
fumecheng-4103	98	16	repeatedly	repeatedly	ADV
fumecheng-4103	98	17	.	.	PUNCT
fumecheng-4103	99	1	one	one	NUM
fumecheng-4103	99	2	example	example	NOUN
fumecheng-4103	99	3	is	be	AUX
fumecheng-4103	99	4	that	that	PRON
fumecheng-4103	99	5	of	of	ADP
fumecheng-4103	99	6	wear	wear	VERB
fumecheng-4103	99	7	simulations	simulation	NOUN
fumecheng-4103	99	8	where	where	SCONJ
fumecheng-4103	99	9	the	the	DET
fumecheng-4103	99	10	transformations	transformation	NOUN
fumecheng-4103	99	11	(	(	PUNCT
fumecheng-4103	99	12	1	1	NUM
fumecheng-4103	99	13	)	)	PUNCT
fumecheng-4103	99	14	and	and	CCONJ
fumecheng-4103	99	15	(	(	PUNCT
fumecheng-4103	99	16	3	3	X
fumecheng-4103	99	17	)	)	PUNCT
fumecheng-4103	99	18	need	need	VERB
fumecheng-4103	99	19	to	to	PART
fumecheng-4103	99	20	be	be	AUX
fumecheng-4103	99	21	performed	perform	VERB
fumecheng-4103	99	22	many	many	ADJ
fumecheng-4103	99	23	times	time	NOUN
fumecheng-4103	99	24	after	after	ADP
fumecheng-4103	99	25	each	each	DET
fumecheng-4103	99	26	other	other	ADJ
fumecheng-4103	99	27	for	for	ADP
fumecheng-4103	99	28	a	a	DET
fumecheng-4103	99	29	changing	change	VERB
fumecheng-4103	99	30	indentation	indentation	NOUN
fumecheng-4103	99	31	profile	profile	NOUN
fumecheng-4103	99	32	.	.	PUNCT
fumecheng-4103	100	1	in	in	ADP
fumecheng-4103	100	2	such	such	ADJ
fumecheng-4103	100	3	cases	case	NOUN
fumecheng-4103	100	4	,	,	PUNCT
fumecheng-4103	100	5	consider	consider	VERB
fumecheng-4103	100	6	optimizing	optimize	VERB
fumecheng-4103	100	7	the	the	DET
fumecheng-4103	100	8	implementation	implementation	NOUN
fumecheng-4103	100	9	of	of	ADP
fumecheng-4103	100	10	the	the	DET
fumecheng-4103	100	11	mdr	mdr	PROPN
fumecheng-4103	100	12	transformations	transformation	NOUN
fumecheng-4103	100	13	for	for	ADP
fumecheng-4103	100	14	maximum	maximum	ADJ
fumecheng-4103	100	15	speed	speed	NOUN
fumecheng-4103	100	16	.	.	PUNCT
fumecheng-4103	101	1	for	for	ADP
fumecheng-4103	101	2	example	example	NOUN
fumecheng-4103	101	3	,	,	PUNCT
fumecheng-4103	101	4	when	when	SCONJ
fumecheng-4103	101	5	using	use	VERB
fumecheng-4103	101	6	the	the	DET
fumecheng-4103	101	7	transformation	transformation	NOUN
fumecheng-4103	101	8	technique	technique	NOUN
fumecheng-4103	101	9	presented	present	VERB
fumecheng-4103	101	10	in	in	ADP
fumecheng-4103	101	11	the	the	DET
fumecheng-4103	101	12	example	example	NOUN
fumecheng-4103	101	13	above	above	ADV
fumecheng-4103	101	14	,	,	PUNCT
fumecheng-4103	101	15	note	note	VERB
fumecheng-4103	101	16	that	that	SCONJ
fumecheng-4103	101	17	the	the	DET
fumecheng-4103	101	18	summation	summation	NOUN
fumecheng-4103	101	19	in	in	ADP
fumecheng-4103	101	20	eqs	eqs	PROPN
fumecheng-4103	101	21	.	.	PUNCT
fumecheng-4103	102	1	(	(	PUNCT
fumecheng-4103	102	2	13	13	NUM
fumecheng-4103	102	3	)	)	PUNCT
fumecheng-4103	102	4	and	and	CCONJ
fumecheng-4103	102	5	(	(	PUNCT
fumecheng-4103	102	6	16	16	NUM
fumecheng-4103	102	7	)	)	PUNCT
fumecheng-4103	102	8	can	can	AUX
fumecheng-4103	102	9	be	be	AUX
fumecheng-4103	102	10	regarded	regard	VERB
fumecheng-4103	102	11	as	as	ADP
fumecheng-4103	102	12	a	a	DET
fumecheng-4103	102	13	matrix	matrix	NOUN
fumecheng-4103	102	14	vector	vector	NOUN
fumecheng-4103	102	15	product	product	NOUN
fumecheng-4103	102	16	in	in	ADP
fumecheng-4103	102	17	which	which	PRON
fumecheng-4103	102	18	the	the	DET
fumecheng-4103	102	19	matrix	matrix	NOUN
fumecheng-4103	102	20	is	be	AUX
fumecheng-4103	102	21	a	a	DET
fumecheng-4103	102	22	kernel	kernel	NOUN
fumecheng-4103	102	23	which	which	PRON
fumecheng-4103	102	24	is	be	AUX
fumecheng-4103	102	25	independent	independent	ADJ
fumecheng-4103	102	26	of	of	ADP
fumecheng-4103	102	27	the	the	DET
fumecheng-4103	102	28	indentation	indentation	NOUN
fumecheng-4103	102	29	profile	profile	NOUN
fumecheng-4103	102	30	and	and	CCONJ
fumecheng-4103	102	31	can	can	AUX
fumecheng-4103	102	32	be	be	AUX
fumecheng-4103	102	33	predefined	predefine	VERB
fumecheng-4103	102	34	.	.	PUNCT
fumecheng-4103	103	1	this	this	PRON
fumecheng-4103	103	2	enables	enable	VERB
fumecheng-4103	103	3	full	full	ADJ
fumecheng-4103	103	4	vectorization	vectorization	NOUN
fumecheng-4103	103	5	of	of	ADP
fumecheng-4103	103	6	the	the	DET
fumecheng-4103	103	7	transformations	transformation	NOUN
fumecheng-4103	103	8	when	when	SCONJ
fumecheng-4103	103	9	they	they	PRON
fumecheng-4103	103	10	are	be	AUX
fumecheng-4103	103	11	used	use	VERB
fumecheng-4103	103	12	repeatedly	repeatedly	ADV
fumecheng-4103	103	13	for	for	ADP
fumecheng-4103	103	14	changing	change	VERB
fumecheng-4103	103	15	indentation	indentation	NOUN
fumecheng-4103	103	16	profiles	profile	NOUN
fumecheng-4103	103	17	.	.	PUNCT
fumecheng-4103	104	1	also	also	ADV
fumecheng-4103	104	2	consider	consider	VERB
fumecheng-4103	104	3	the	the	DET
fumecheng-4103	104	4	possibility	possibility	NOUN
fumecheng-4103	104	5	of	of	ADP
fumecheng-4103	104	6	calculating	calculate	VERB
fumecheng-4103	104	7	the	the	DET
fumecheng-4103	104	8	derivatives	derivative	NOUN
fumecheng-4103	104	9	in	in	ADP
fumecheng-4103	104	10	the	the	DET
fumecheng-4103	104	11	transformations	transformation	NOUN
fumecheng-4103	104	12	such	such	ADJ
fumecheng-4103	104	13	as	as	ADP
fumecheng-4103	104	14	(	(	PUNCT
fumecheng-4103	104	15	9	9	NUM
fumecheng-4103	104	16	)	)	PUNCT
fumecheng-4103	104	17	and	and	CCONJ
fumecheng-4103	104	18	(	(	PUNCT
fumecheng-4103	104	19	10	10	NUM
fumecheng-4103	104	20	)	)	PUNCT
fumecheng-4103	104	21	via	via	ADP
fumecheng-4103	104	22	matrix	matrix	NOUN
fumecheng-4103	104	23	vector	vector	NOUN
fumecheng-4103	104	24	multiplication	multiplication	NOUN
fumecheng-4103	104	25	using	use	VERB
fumecheng-4103	104	26	predefined	predefine	VERB
fumecheng-4103	104	27	sparse	sparse	ADJ
fumecheng-4103	104	28	matrices	matrix	NOUN
fumecheng-4103	104	29	.	.	PUNCT
fumecheng-4103	105	1	5	5	X
fumecheng-4103	105	2	.	.	NOUN
fumecheng-4103	105	3	exemplary	exemplary	ADJ
fumecheng-4103	105	4	results	result	NOUN
fumecheng-4103	105	5	fig	fig	NOUN
fumecheng-4103	105	6	.	.	PUNCT
fumecheng-4103	106	1	1	1	NUM
fumecheng-4103	106	2	shows	show	VERB
fumecheng-4103	106	3	the	the	DET
fumecheng-4103	106	4	results	result	NOUN
fumecheng-4103	106	5	of	of	ADP
fumecheng-4103	106	6	the	the	DET
fumecheng-4103	106	7	previously	previously	ADV
fumecheng-4103	106	8	described	describe	VERB
fumecheng-4103	106	9	implementation	implementation	NOUN
fumecheng-4103	106	10	technique	technique	NOUN
fumecheng-4103	106	11	for	for	ADP
fumecheng-4103	106	12	a	a	DET
fumecheng-4103	106	13	conic	conic	ADJ
fumecheng-4103	106	14	and	and	CCONJ
fumecheng-4103	106	15	parabolic	parabolic	ADJ
fumecheng-4103	106	16	indenter	indenter	NOUN
fumecheng-4103	106	17	at	at	ADP
fumecheng-4103	106	18	an	an	DET
fumecheng-4103	106	19	exemplary	exemplary	ADJ
fumecheng-4103	106	20	indentation	indentation	NOUN
fumecheng-4103	106	21	depth	depth	NOUN
fumecheng-4103	106	22	d.	d.	NOUN
fumecheng-4103	106	23	it	it	PRON
fumecheng-4103	106	24	becomes	become	VERB
fumecheng-4103	106	25	apparent	apparent	ADJ
fumecheng-4103	106	26	that	that	SCONJ
fumecheng-4103	106	27	already	already	ADV
fumecheng-4103	106	28	for	for	ADP
fumecheng-4103	106	29	as	as	ADV
fumecheng-4103	106	30	few	few	ADJ
fumecheng-4103	106	31	as	as	ADP
fumecheng-4103	106	32	n	n	NOUN
fumecheng-4103	106	33	=	=	SYM
fumecheng-4103	106	34	51	51	NUM
fumecheng-4103	106	35	discretization	discretization	NOUN
fumecheng-4103	106	36	points	point	VERB
fumecheng-4103	106	37	a	a	DET
fumecheng-4103	106	38	fairly	fairly	ADV
fumecheng-4103	106	39	good	good	ADJ
fumecheng-4103	106	40	approximation	approximation	NOUN
fumecheng-4103	106	41	of	of	ADP
fumecheng-4103	106	42	the	the	DET
fumecheng-4103	106	43	analytical	analytical	ADJ
fumecheng-4103	106	44	solutions	solution	NOUN
fumecheng-4103	106	45	can	can	AUX
fumecheng-4103	106	46	be	be	AUX
fumecheng-4103	106	47	achieved	achieve	VERB
fumecheng-4103	106	48	.	.	PUNCT
fumecheng-4103	107	1	the	the	DET
fumecheng-4103	107	2	maximum	maximum	ADJ
fumecheng-4103	107	3	error	error	NOUN
fumecheng-4103	107	4	of	of	ADP
fumecheng-4103	107	5	gk	gk	PROPN
fumecheng-4103	107	6	,	,	PUNCT
fumecheng-4103	107	7	wn	wn	PROPN
fumecheng-4103	107	8	,	,	PUNCT
fumecheng-4103	107	9	and	and	CCONJ
fumecheng-4103	107	10	pn	pn	X
fumecheng-4103	107	11	with	with	ADP
fumecheng-4103	107	12	respect	respect	NOUN
fumecheng-4103	107	13	to	to	ADP
fumecheng-4103	107	14	the	the	DET
fumecheng-4103	107	15	analytical	analytical	ADJ
fumecheng-4103	107	16	solutions	solution	NOUN
fumecheng-4103	107	17	for	for	ADP
fumecheng-4103	107	18	g	g	PROPN
fumecheng-4103	107	19	,	,	PUNCT
fumecheng-4103	107	20	w	w	NOUN
fumecheng-4103	107	21	,	,	PUNCT
fumecheng-4103	107	22	and	and	CCONJ
fumecheng-4103	107	23	p	p	NOUN
fumecheng-4103	107	24	decreases	decrease	NOUN
fumecheng-4103	107	25	when	when	SCONJ
fumecheng-4103	107	26	the	the	DET
fumecheng-4103	107	27	number	number	NOUN
fumecheng-4103	107	28	of	of	ADP
fumecheng-4103	107	29	discretization	discretization	NOUN
fumecheng-4103	107	30	points	point	NOUN
fumecheng-4103	107	31	n	n	PRON
fumecheng-4103	107	32	is	be	AUX
fumecheng-4103	107	33	increased	increase	VERB
fumecheng-4103	107	34	as	as	SCONJ
fumecheng-4103	107	35	can	can	AUX
fumecheng-4103	107	36	be	be	AUX
fumecheng-4103	107	37	seen	see	VERB
fumecheng-4103	107	38	in	in	ADP
fumecheng-4103	107	39	fig	fig	NOUN
fumecheng-4103	107	40	.	.	PUNCT
fumecheng-4103	108	1	2	2	NUM
fumecheng-4103	108	2	.	.	X
fumecheng-4103	108	3	for	for	ADP
fumecheng-4103	108	4	most	most	ADJ
fumecheng-4103	108	5	n	n	CCONJ
fumecheng-4103	108	6	,	,	PUNCT
fumecheng-4103	108	7	the	the	DET
fumecheng-4103	108	8	maximum	maximum	ADJ
fumecheng-4103	108	9	error	error	NOUN
fumecheng-4103	108	10	of	of	ADP
fumecheng-4103	108	11	pressure	pressure	NOUN
fumecheng-4103	108	12	distribution	distribution	NOUN
fumecheng-4103	108	13	pn	pn	NOUN
fumecheng-4103	108	14	(	(	PUNCT
fumecheng-4103	108	15	a	a	DET
fumecheng-4103	108	16	thin	thin	ADJ
fumecheng-4103	108	17	grey	grey	NOUN
fumecheng-4103	108	18	oscillating	oscillating	NOUN
fumecheng-4103	108	19	line	line	NOUN
fumecheng-4103	108	20	in	in	ADP
fumecheng-4103	108	21	fig	fig	NOUN
fumecheng-4103	108	22	.	.	PUNCT
fumecheng-4103	108	23	2	2	NUM
fumecheng-4103	108	24	)	)	PUNCT
fumecheng-4103	108	25	is	be	AUX
fumecheng-4103	108	26	given	give	VERB
fumecheng-4103	108	27	by	by	ADP
fumecheng-4103	108	28	the	the	DET
fumecheng-4103	108	29	error	error	NOUN
fumecheng-4103	108	30	at	at	ADP
fumecheng-4103	108	31	the	the	DET
fumecheng-4103	108	32	very	very	ADV
fumecheng-4103	108	33	last	last	ADJ
fumecheng-4103	108	34	discretization	discretization	NOUN
fumecheng-4103	108	35	point	point	NOUN
fumecheng-4103	108	36	lying	lie	VERB
fumecheng-4103	108	37	within	within	ADP
fumecheng-4103	108	38	the	the	DET
fumecheng-4103	108	39	contact	contact	NOUN
fumecheng-4103	108	40	area	area	NOUN
fumecheng-4103	108	41	(	(	PUNCT
fumecheng-4103	108	42	highlighted	highlight	VERB
fumecheng-4103	108	43	with	with	ADP
fumecheng-4103	108	44	a	a	DET
fumecheng-4103	108	45	star	star	NOUN
fumecheng-4103	108	46	in	in	ADP
fumecheng-4103	108	47	fig	fig	NOUN
fumecheng-4103	108	48	.	.	PUNCT
fumecheng-4103	109	1	1	1	NUM
fumecheng-4103	109	2	)	)	PUNCT
fumecheng-4103	109	3	.	.	PUNCT
fumecheng-4103	110	1	index	index	NOUN
fumecheng-4103	110	2	n	n	PROPN
fumecheng-4103	110	3	of	of	ADP
fumecheng-4103	110	4	this	this	DET
fumecheng-4103	110	5	particular	particular	ADJ
fumecheng-4103	110	6	point	point	NOUN
fumecheng-4103	110	7	shall	shall	AUX
fumecheng-4103	110	8	be	be	AUX
fumecheng-4103	110	9	denoted	denote	VERB
fumecheng-4103	110	10	with	with	ADP
fumecheng-4103	110	11	n	n	NOUN
fumecheng-4103	110	12	=	=	SYM
fumecheng-4103	110	13	s.	s.	PROPN
fumecheng-4103	110	14	at	at	ADP
fumecheng-4103	110	15	all	all	DET
fumecheng-4103	110	16	other	other	ADJ
fumecheng-4103	110	17	points	point	NOUN
fumecheng-4103	110	18	a	a	DET
fumecheng-4103	110	19	much	much	ADV
fumecheng-4103	110	20	better	well	ADJ
fumecheng-4103	110	21	accuracy	accuracy	NOUN
fumecheng-4103	110	22	is	be	AUX
fumecheng-4103	110	23	achieved	achieve	VERB
fumecheng-4103	110	24	:	:	PUNCT
fumecheng-4103	110	25	if	if	SCONJ
fumecheng-4103	110	26	point	point	NOUN
fumecheng-4103	110	27	s	s	VERB
fumecheng-4103	110	28	would	would	AUX
fumecheng-4103	110	29	be	be	AUX
fumecheng-4103	110	30	disregarded	disregard	VERB
fumecheng-4103	110	31	in	in	ADP
fumecheng-4103	110	32	the	the	DET
fumecheng-4103	110	33	assessment	assessment	NOUN
fumecheng-4103	110	34	of	of	ADP
fumecheng-4103	110	35	the	the	DET
fumecheng-4103	110	36	maximum	maximum	ADJ
fumecheng-4103	110	37	error	error	NOUN
fumecheng-4103	110	38	,	,	PUNCT
fumecheng-4103	110	39	the	the	DET
fumecheng-4103	110	40	upper	upper	ADJ
fumecheng-4103	110	41	limit	limit	NOUN
fumecheng-4103	110	42	of	of	ADP
fumecheng-4103	110	43	the	the	DET
fumecheng-4103	110	44	grey	grey	NOUN
fumecheng-4103	110	45	oscillating	oscillating	NOUN
fumecheng-4103	110	46	line	line	NOUN
fumecheng-4103	110	47	would	would	AUX
fumecheng-4103	110	48	move	move	VERB
fumecheng-4103	110	49	down	down	ADP
fumecheng-4103	110	50	from	from	ADP
fumecheng-4103	110	51	the	the	DET
fumecheng-4103	110	52	dotted	dotted	ADJ
fumecheng-4103	110	53	line	line	NOUN
fumecheng-4103	110	54	to	to	ADP
fumecheng-4103	110	55	the	the	DET
fumecheng-4103	110	56	dashed	dash	VERB
fumecheng-4103	110	57	one	one	NUM
fumecheng-4103	110	58	.	.	PUNCT
fumecheng-4103	111	1	in	in	ADP
fumecheng-4103	111	2	the	the	DET
fumecheng-4103	111	3	exemplary	exemplary	ADJ
fumecheng-4103	111	4	case	case	NOUN
fumecheng-4103	111	5	of	of	ADP
fumecheng-4103	111	6	n	n	NOUN
fumecheng-4103	111	7	=	=	SYM
fumecheng-4103	111	8	51	51	NUM
fumecheng-4103	111	9	which	which	PRON
fumecheng-4103	111	10	is	be	AUX
fumecheng-4103	111	11	displayed	display	VERB
fumecheng-4103	111	12	in	in	ADP
fumecheng-4103	111	13	fig	fig	NOUN
fumecheng-4103	111	14	.	.	PUNCT
fumecheng-4103	112	1	1	1	NUM
fumecheng-4103	112	2	this	this	DET
fumecheng-4103	112	3	relatively	relatively	ADV
fumecheng-4103	112	4	high	high	ADJ
fumecheng-4103	112	5	error	error	NOUN
fumecheng-4103	112	6	of	of	ADP
fumecheng-4103	112	7	pn	pn	PROPN
fumecheng-4103	112	8	at	at	ADP
fumecheng-4103	112	9	the	the	DET
fumecheng-4103	112	10	point	point	NOUN
fumecheng-4103	113	1	n	n	NOUN
fumecheng-4103	113	2	=	=	SYM
fumecheng-4103	113	3	s	s	X
fumecheng-4103	113	4	does	do	AUX
fumecheng-4103	113	5	not	not	PART
fumecheng-4103	113	6	immediately	immediately	ADV
fumecheng-4103	113	7	become	become	VERB
fumecheng-4103	113	8	apparent	apparent	ADJ
fumecheng-4103	113	9	to	to	ADP
fumecheng-4103	113	10	the	the	DET
fumecheng-4103	113	11	viewer	viewer	NOUN
fumecheng-4103	113	12	due	due	ADP
fumecheng-4103	113	13	to	to	ADP
fumecheng-4103	113	14	the	the	DET
fumecheng-4103	113	15	large	large	ADJ
fumecheng-4103	113	16	slope	slope	NOUN
fumecheng-4103	113	17	of	of	ADP
fumecheng-4103	113	18	p	p	NOUN
fumecheng-4103	113	19	at	at	ADP
fumecheng-4103	113	20	the	the	DET
fumecheng-4103	113	21	end	end	NOUN
fumecheng-4103	113	22	of	of	ADP
fumecheng-4103	113	23	the	the	DET
fumecheng-4103	113	24	contact	contact	NOUN
fumecheng-4103	113	25	area	area	NOUN
fumecheng-4103	113	26	which	which	PRON
fumecheng-4103	113	27	puts	put	VERB
fumecheng-4103	113	28	the	the	DET
fumecheng-4103	113	29	numerical	numerical	ADJ
fumecheng-4103	113	30	value	value	NOUN
fumecheng-4103	113	31	close	close	ADV
fumecheng-4103	113	32	to	to	ADP
fumecheng-4103	113	33	the	the	DET
fumecheng-4103	113	34	analytical	analytical	ADJ
fumecheng-4103	113	35	curve	curve	NOUN
fumecheng-4103	113	36	even	even	ADV
fumecheng-4103	113	37	if	if	SCONJ
fumecheng-4103	113	38	there	there	PRON
fumecheng-4103	113	39	is	be	VERB
fumecheng-4103	113	40	a	a	DET
fumecheng-4103	113	41	relatively	relatively	ADV
fumecheng-4103	113	42	high	high	ADJ
fumecheng-4103	113	43	error	error	NOUN
fumecheng-4103	113	44	.	.	PUNCT
fumecheng-4103	114	1	132	132	NUM
fumecheng-4103	114	2	j.	j.	PROPN
fumecheng-4103	114	3	benad	benad	PROPN
fumecheng-4103	114	4	a	a	DET
fumecheng-4103	114	5	)	)	PUNCT
fumecheng-4103	114	6	b	b	NOUN
fumecheng-4103	114	7	)	)	PUNCT
fumecheng-4103	114	8	fig	fig	NOUN
fumecheng-4103	114	9	.	.	PUNCT
fumecheng-4103	115	1	1	1	NUM
fumecheng-4103	115	2	results	result	NOUN
fumecheng-4103	115	3	of	of	ADP
fumecheng-4103	115	4	the	the	DET
fumecheng-4103	115	5	mdr	mdr	PROPN
fumecheng-4103	115	6	transformations	transformation	NOUN
fumecheng-4103	115	7	carried	carry	VERB
fumecheng-4103	115	8	out	out	ADP
fumecheng-4103	115	9	with	with	ADP
fumecheng-4103	115	10	the	the	DET
fumecheng-4103	115	11	numerical	numerical	ADJ
fumecheng-4103	115	12	procedure	procedure	NOUN
fumecheng-4103	115	13	described	describe	VERB
fumecheng-4103	115	14	above	above	ADV
fumecheng-4103	115	15	for	for	ADP
fumecheng-4103	115	16	n	n	NOUN
fumecheng-4103	115	17	=	=	SYM
fumecheng-4103	115	18	51	51	NUM
fumecheng-4103	115	19	discretization	discretization	NOUN
fumecheng-4103	115	20	points	point	NOUN
fumecheng-4103	115	21	,	,	PUNCT
fumecheng-4103	115	22	exemplary	exemplary	ADJ
fumecheng-4103	115	23	input	input	NOUN
fumecheng-4103	115	24	parameters	parameter	NOUN
fumecheng-4103	115	25	of	of	ADP
fumecheng-4103	115	26	l	l	NOUN
fumecheng-4103	115	27	=	=	SYM
fumecheng-4103	115	28	1	1	NUM
fumecheng-4103	115	29	,	,	PUNCT
fumecheng-4103	115	30	e	e	NOUN
fumecheng-4103	115	31	*	*	PUNCT
fumecheng-4103	115	32	=	=	SYM
fumecheng-4103	115	33	1	1	NUM
fumecheng-4103	115	34	,	,	PUNCT
fumecheng-4103	115	35	d	d	NOUN
fumecheng-4103	115	36	=	=	SYM
fumecheng-4103	115	37	0.3	0.3	NUM
fumecheng-4103	115	38	and	and	CCONJ
fumecheng-4103	115	39	an	an	DET
fumecheng-4103	115	40	exemplary	exemplary	ADJ
fumecheng-4103	115	41	conic	conic	ADJ
fumecheng-4103	115	42	indenter	indenter	NOUN
fumecheng-4103	115	43	(	(	PUNCT
fumecheng-4103	115	44	left	leave	VERB
fumecheng-4103	115	45	)	)	PUNCT
fumecheng-4103	115	46	given	give	VERB
fumecheng-4103	115	47	with	with	ADP
fumecheng-4103	115	48	f(r	f(r	NOUN
fumecheng-4103	115	49	)	)	PUNCT
fumecheng-4103	116	1	=	=	SYM
fumecheng-4103	116	2	r	r	X
fumecheng-4103	116	3	tan(π/8	tan(π/8	PROPN
fumecheng-4103	116	4	)	)	PUNCT
fumecheng-4103	116	5	and	and	CCONJ
fumecheng-4103	116	6	an	an	DET
fumecheng-4103	116	7	exemplary	exemplary	ADJ
fumecheng-4103	116	8	parabolic	parabolic	NOUN
fumecheng-4103	116	9	indenter	indenter	NOUN
fumecheng-4103	116	10	(	(	PUNCT
fumecheng-4103	116	11	right	right	ADV
fumecheng-4103	116	12	)	)	PUNCT
fumecheng-4103	116	13	given	give	VERB
fumecheng-4103	116	14	with	with	ADP
fumecheng-4103	116	15	f(r	f(r	NOUN
fumecheng-4103	116	16	)	)	PUNCT
fumecheng-4103	117	1	=	=	SYM
fumecheng-4103	117	2	r	r	NOUN
fumecheng-4103	117	3	2	2	NUM
fumecheng-4103	117	4	/2	/2	NUM
fumecheng-4103	117	5	.	.	PUNCT
fumecheng-4103	118	1	the	the	DET
fumecheng-4103	118	2	pressure	pressure	NOUN
fumecheng-4103	118	3	which	which	PRON
fumecheng-4103	118	4	is	be	AUX
fumecheng-4103	118	5	obtained	obtain	VERB
fumecheng-4103	118	6	at	at	ADP
fumecheng-4103	118	7	last	last	ADJ
fumecheng-4103	118	8	discretization	discretization	NOUN
fumecheng-4103	118	9	point	point	NOUN
fumecheng-4103	118	10	within	within	ADP
fumecheng-4103	118	11	the	the	DET
fumecheng-4103	118	12	contact	contact	NOUN
fumecheng-4103	118	13	area	area	NOUN
fumecheng-4103	118	14	in	in	ADP
fumecheng-4103	118	15	this	this	DET
fumecheng-4103	118	16	example	example	NOUN
fumecheng-4103	118	17	is	be	AUX
fumecheng-4103	118	18	highlighted	highlight	VERB
fumecheng-4103	118	19	with	with	ADP
fumecheng-4103	118	20	a	a	DET
fumecheng-4103	118	21	star	star	NOUN
fumecheng-4103	118	22	a	a	PRON
fumecheng-4103	118	23	)	)	PUNCT
fumecheng-4103	118	24	b	b	NOUN
fumecheng-4103	118	25	)	)	PUNCT
fumecheng-4103	118	26	fig	fig	NOUN
fumecheng-4103	118	27	.	.	PUNCT
fumecheng-4103	119	1	2	2	NUM
fumecheng-4103	119	2	maximum	maximum	NOUN
fumecheng-4103	119	3	error	error	NOUN
fumecheng-4103	119	4	of	of	ADP
fumecheng-4103	119	5	gk	gk	PROPN
fumecheng-4103	119	6	,	,	PUNCT
fumecheng-4103	119	7	wn	wn	PROPN
fumecheng-4103	119	8	,	,	PUNCT
fumecheng-4103	119	9	and	and	CCONJ
fumecheng-4103	119	10	pn	pn	VERB
fumecheng-4103	119	11	for	for	ADP
fumecheng-4103	119	12	a	a	DET
fumecheng-4103	119	13	discretization	discretization	NOUN
fumecheng-4103	119	14	of	of	ADP
fumecheng-4103	119	15	n	n	NOUN
fumecheng-4103	119	16	=	=	SYM
fumecheng-4103	119	17	51	51	NUM
fumecheng-4103	119	18	,	,	PUNCT
fumecheng-4103	119	19	52	52	NUM
fumecheng-4103	119	20	,	,	PUNCT
fumecheng-4103	119	21	53	53	NUM
fumecheng-4103	119	22	…	…	SYM
fumecheng-4103	119	23	5000	5000	NUM
fumecheng-4103	119	24	,	,	PUNCT
fumecheng-4103	119	25	shown	show	VERB
fumecheng-4103	119	26	for	for	ADP
fumecheng-4103	119	27	the	the	DET
fumecheng-4103	119	28	exemplary	exemplary	ADJ
fumecheng-4103	119	29	inputs	input	NOUN
fumecheng-4103	119	30	l	l	NOUN
fumecheng-4103	119	31	=	=	SYM
fumecheng-4103	119	32	1	1	NUM
fumecheng-4103	119	33	,	,	PUNCT
fumecheng-4103	119	34	e	e	NOUN
fumecheng-4103	119	35	*	*	PUNCT
fumecheng-4103	119	36	=	=	SYM
fumecheng-4103	119	37	1	1	NUM
fumecheng-4103	119	38	,	,	PUNCT
fumecheng-4103	119	39	d	d	NOUN
fumecheng-4103	119	40	=	=	SYM
fumecheng-4103	119	41	0.3	0.3	NUM
fumecheng-4103	119	42	and	and	CCONJ
fumecheng-4103	119	43	the	the	DET
fumecheng-4103	119	44	exemplary	exemplary	ADJ
fumecheng-4103	119	45	conic	conic	ADJ
fumecheng-4103	119	46	indenter	indenter	NOUN
fumecheng-4103	119	47	(	(	PUNCT
fumecheng-4103	119	48	left	leave	VERB
fumecheng-4103	119	49	)	)	PUNCT
fumecheng-4103	119	50	given	give	VERB
fumecheng-4103	119	51	with	with	ADP
fumecheng-4103	119	52	f(r	f(r	NOUN
fumecheng-4103	119	53	)	)	PUNCT
fumecheng-4103	119	54	=	=	SYM
fumecheng-4103	119	55	r	r	X
fumecheng-4103	119	56	tan(π/8	tan(π/8	PROPN
fumecheng-4103	119	57	)	)	PUNCT
fumecheng-4103	119	58	and	and	CCONJ
fumecheng-4103	119	59	the	the	DET
fumecheng-4103	119	60	exemplary	exemplary	ADJ
fumecheng-4103	119	61	parabolic	parabolic	PROPN
fumecheng-4103	119	62	indenter	indenter	NOUN
fumecheng-4103	119	63	(	(	PUNCT
fumecheng-4103	119	64	right	right	ADV
fumecheng-4103	119	65	)	)	PUNCT
fumecheng-4103	119	66	given	give	VERB
fumecheng-4103	119	67	with	with	ADP
fumecheng-4103	119	68	f(r	f(r	NOUN
fumecheng-4103	119	69	)	)	PUNCT
fumecheng-4103	120	1	=	=	SYM
fumecheng-4103	120	2	r	r	NOUN
fumecheng-4103	120	3	2	2	NUM
fumecheng-4103	120	4	/2	/2	NUM
fumecheng-4103	120	5	.	.	PUNCT
fumecheng-4103	121	1	the	the	DET
fumecheng-4103	121	2	oscillating	oscillate	VERB
fumecheng-4103	121	3	thin	thin	ADJ
fumecheng-4103	121	4	grey	grey	ADJ
fumecheng-4103	121	5	line	line	NOUN
fumecheng-4103	121	6	shows	show	VERB
fumecheng-4103	121	7	the	the	DET
fumecheng-4103	121	8	maximum	maximum	ADJ
fumecheng-4103	121	9	error	error	NOUN
fumecheng-4103	121	10	of	of	ADP
fumecheng-4103	121	11	pn	pn	PROPN
fumecheng-4103	121	12	.	.	PUNCT
fumecheng-4103	122	1	its	its	PRON
fumecheng-4103	122	2	upper	upper	ADJ
fumecheng-4103	122	3	limit	limit	NOUN
fumecheng-4103	122	4	is	be	AUX
fumecheng-4103	122	5	marked	mark	VERB
fumecheng-4103	122	6	with	with	ADP
fumecheng-4103	122	7	the	the	DET
fumecheng-4103	122	8	dotted	dotted	ADJ
fumecheng-4103	122	9	black	black	ADJ
fumecheng-4103	122	10	line	line	NOUN
fumecheng-4103	122	11	.	.	PUNCT
fumecheng-4103	123	1	neglecting	neglect	VERB
fumecheng-4103	123	2	the	the	DET
fumecheng-4103	123	3	error	error	NOUN
fumecheng-4103	123	4	of	of	ADP
fumecheng-4103	123	5	pn	pn	PROPN
fumecheng-4103	123	6	at	at	ADP
fumecheng-4103	123	7	the	the	DET
fumecheng-4103	123	8	point	point	NOUN
fumecheng-4103	123	9	n	n	NOUN
fumecheng-4103	123	10	=	=	SYM
fumecheng-4103	123	11	s	s	PROPN
fumecheng-4103	123	12	in	in	ADP
fumecheng-4103	123	13	the	the	DET
fumecheng-4103	123	14	assessment	assessment	NOUN
fumecheng-4103	123	15	of	of	ADP
fumecheng-4103	123	16	the	the	DET
fumecheng-4103	123	17	maximum	maximum	ADJ
fumecheng-4103	123	18	error	error	NOUN
fumecheng-4103	123	19	would	would	AUX
fumecheng-4103	123	20	cause	cause	VERB
fumecheng-4103	123	21	a	a	DET
fumecheng-4103	123	22	much	much	ADV
fumecheng-4103	123	23	lower	low	ADJ
fumecheng-4103	123	24	upper	upper	ADJ
fumecheng-4103	123	25	limit	limit	NOUN
fumecheng-4103	123	26	which	which	PRON
fumecheng-4103	123	27	is	be	AUX
fumecheng-4103	123	28	marked	mark	VERB
fumecheng-4103	123	29	with	with	ADP
fumecheng-4103	123	30	the	the	DET
fumecheng-4103	123	31	dashed	dash	VERB
fumecheng-4103	123	32	black	black	ADJ
fumecheng-4103	123	33	line	line	NOUN
fumecheng-4103	123	34	.	.	PUNCT
fumecheng-4103	124	1	note	note	VERB
fumecheng-4103	124	2	also	also	ADV
fumecheng-4103	124	3	that	that	SCONJ
fumecheng-4103	124	4	the	the	DET
fumecheng-4103	124	5	maximum	maximum	ADJ
fumecheng-4103	124	6	error	error	NOUN
fumecheng-4103	124	7	of	of	ADP
fumecheng-4103	124	8	gk	gk	PROPN
fumecheng-4103	124	9	for	for	ADP
fumecheng-4103	124	10	the	the	DET
fumecheng-4103	124	11	exemplary	exemplary	ADJ
fumecheng-4103	124	12	conic	conic	ADJ
fumecheng-4103	124	13	indenter	indenter	NOUN
fumecheng-4103	124	14	lies	lie	VERB
fumecheng-4103	124	15	at	at	ADP
fumecheng-4103	124	16	around	around	ADP
fumecheng-4103	124	17	10	10	NUM
fumecheng-4103	124	18	-15	-15	PUNCT
fumecheng-4103	124	19	and	and	CCONJ
fumecheng-4103	124	20	is	be	AUX
fumecheng-4103	124	21	thus	thus	ADV
fumecheng-4103	124	22	outside	outside	ADP
fumecheng-4103	124	23	the	the	DET
fumecheng-4103	124	24	chosen	choose	VERB
fumecheng-4103	124	25	region	region	NOUN
fumecheng-4103	124	26	displayed	display	VERB
fumecheng-4103	124	27	in	in	ADP
fumecheng-4103	124	28	the	the	DET
fumecheng-4103	124	29	figure	figure	NOUN
fumecheng-4103	124	30	fast	fast	ADJ
fumecheng-4103	124	31	numerical	numerical	ADJ
fumecheng-4103	124	32	implementation	implementation	NOUN
fumecheng-4103	124	33	of	of	ADP
fumecheng-4103	124	34	the	the	DET
fumecheng-4103	124	35	mdr	mdr	PROPN
fumecheng-4103	124	36	transformations	transformation	VERB
fumecheng-4103	124	37	133	133	NUM
fumecheng-4103	124	38	6	6	NUM
fumecheng-4103	124	39	.	.	PUNCT
fumecheng-4103	125	1	adjustments	adjustment	NOUN
fumecheng-4103	125	2	if	if	SCONJ
fumecheng-4103	125	3	needed	need	VERB
fumecheng-4103	125	4	,	,	PUNCT
fumecheng-4103	125	5	one	one	NUM
fumecheng-4103	125	6	possible	possible	ADJ
fumecheng-4103	125	7	way	way	NOUN
fumecheng-4103	125	8	of	of	ADP
fumecheng-4103	125	9	obtaining	obtain	VERB
fumecheng-4103	125	10	better	well	ADJ
fumecheng-4103	125	11	results	result	NOUN
fumecheng-4103	125	12	for	for	ADP
fumecheng-4103	125	13	ps	ps	PROPN
fumecheng-4103	125	14	is	be	AUX
fumecheng-4103	125	15	by	by	ADP
fumecheng-4103	125	16	inserting	insert	VERB
fumecheng-4103	125	17	one	one	NUM
fumecheng-4103	125	18	or	or	CCONJ
fumecheng-4103	125	19	more	more	ADJ
fumecheng-4103	125	20	discretization	discretization	NOUN
fumecheng-4103	125	21	points	point	VERB
fumecheng-4103	125	22	on	on	ADP
fumecheng-4103	125	23	a	a	DET
fumecheng-4103	125	24	finer	fine	ADJ
fumecheng-4103	125	25	grid	grid	NOUN
fumecheng-4103	125	26	after	after	ADP
fumecheng-4103	125	27	point	point	NOUN
fumecheng-4103	125	28	s	s	VERB
fumecheng-4103	125	29	so	so	SCONJ
fumecheng-4103	125	30	that	that	SCONJ
fumecheng-4103	125	31	it	it	PRON
fumecheng-4103	125	32	is	be	AUX
fumecheng-4103	125	33	no	no	ADV
fumecheng-4103	125	34	longer	long	ADV
fumecheng-4103	125	35	the	the	DET
fumecheng-4103	125	36	last	last	ADJ
fumecheng-4103	125	37	point	point	NOUN
fumecheng-4103	125	38	in	in	ADP
fumecheng-4103	125	39	the	the	DET
fumecheng-4103	125	40	contact	contact	NOUN
fumecheng-4103	125	41	area	area	NOUN
fumecheng-4103	125	42	.	.	PUNCT
fumecheng-4103	126	1	for	for	ADP
fumecheng-4103	126	2	example	example	NOUN
fumecheng-4103	126	3	,	,	PUNCT
fumecheng-4103	126	4	one	one	PRON
fumecheng-4103	126	5	can	can	AUX
fumecheng-4103	126	6	use	use	VERB
fumecheng-4103	126	7	a	a	DET
fumecheng-4103	126	8	technique	technique	NOUN
fumecheng-4103	126	9	such	such	ADJ
fumecheng-4103	126	10	as	as	ADP
fumecheng-4103	126	11	the	the	DET
fumecheng-4103	126	12	one	one	NUM
fumecheng-4103	126	13	illustrated	illustrate	VERB
fumecheng-4103	126	14	in	in	ADP
fumecheng-4103	126	15	fig	fig	NOUN
fumecheng-4103	126	16	.	.	PUNCT
fumecheng-4103	127	1	3	3	X
fumecheng-4103	127	2	.	.	X
fumecheng-4103	127	3	here	here	ADV
fumecheng-4103	127	4	,	,	PUNCT
fumecheng-4103	127	5	a	a	DET
fumecheng-4103	127	6	new	new	ADJ
fumecheng-4103	127	7	discretization	discretization	NOUN
fumecheng-4103	127	8	point	point	NOUN
fumecheng-4103	127	9	is	be	AUX
fumecheng-4103	127	10	added	add	VERB
fumecheng-4103	127	11	right	right	ADV
fumecheng-4103	127	12	at	at	ADP
fumecheng-4103	127	13	contact	contact	NOUN
fumecheng-4103	127	14	radius	radius	NOUN
fumecheng-4103	127	15	a	a	PRON
fumecheng-4103	127	16	,	,	PUNCT
fumecheng-4103	127	17	which	which	PRON
fumecheng-4103	127	18	is	be	AUX
fumecheng-4103	127	19	approximated	approximate	VERB
fumecheng-4103	127	20	from	from	ADP
fumecheng-4103	127	21	gk	gk	PROPN
fumecheng-4103	127	22	with	with	ADP
fumecheng-4103	127	23	a	a	DET
fumecheng-4103	127	24	simple	simple	ADJ
fumecheng-4103	127	25	linear	linear	ADJ
fumecheng-4103	127	26	interpolation	interpolation	NOUN
fumecheng-4103	127	27	1	1	NUM
fumecheng-4103	127	28	1	1	NUM
fumecheng-4103	127	29	(	(	PUNCT
fumecheng-4103	127	30	)	)	PUNCT
fumecheng-4103	127	31	s	s	PART
fumecheng-4103	127	32	s	s	NOUN
fumecheng-4103	127	33	s	s	X
fumecheng-4103	127	34	s	s	X
fumecheng-4103	127	35	s	s	NOUN
fumecheng-4103	127	36	s	s	NOUN
fumecheng-4103	127	37	r	r	NOUN
fumecheng-4103	127	38	r	r	NOUN
fumecheng-4103	127	39	a	a	NOUN
fumecheng-4103	127	40	d	d	NOUN
fumecheng-4103	127	41	g	g	NOUN
fumecheng-4103	127	42	r	r	NOUN
fumecheng-4103	127	43	g	g	PROPN
fumecheng-4103	127	44	g	g	PROPN
fumecheng-4103	127	45			ADV
fumecheng-4103	127	46			VERB
fumecheng-4103	127	47			PROPN
fumecheng-4103	127	48			PROPN
fumecheng-4103	127	49			PROPN
fumecheng-4103	127	50			VERB
fumecheng-4103	127	51			PROPN
fumecheng-4103	127	52	,	,	PUNCT
fumecheng-4103	127	53	(	(	PUNCT
fumecheng-4103	127	54	20	20	NUM
fumecheng-4103	127	55	)	)	PUNCT
fumecheng-4103	127	56	another	another	DET
fumecheng-4103	127	57	discretization	discretization	NOUN
fumecheng-4103	127	58	point	point	NOUN
fumecheng-4103	127	59	is	be	AUX
fumecheng-4103	127	60	added	add	VERB
fumecheng-4103	127	61	in	in	ADP
fumecheng-4103	127	62	between	between	ADP
fumecheng-4103	127	63	rs	rs	NOUN
fumecheng-4103	127	64	and	and	CCONJ
fumecheng-4103	127	65	a	a	PRON
fumecheng-4103	127	66	at	at	ADP
fumecheng-4103	127	67	rs	rs	NOUN
fumecheng-4103	128	1	+	+	CCONJ
fumecheng-4103	128	2	(	(	PUNCT
fumecheng-4103	128	3	a	a	DET
fumecheng-4103	128	4	–	–	PUNCT
fumecheng-4103	128	5	rs	rs	NOUN
fumecheng-4103	128	6	)	)	PUNCT
fumecheng-4103	128	7	/	/	SYM
fumecheng-4103	128	8	2	2	NUM
fumecheng-4103	128	9	,	,	PUNCT
fumecheng-4103	128	10	and	and	CCONJ
fumecheng-4103	128	11	at	at	ADP
fumecheng-4103	128	12	both	both	PRON
fumecheng-4103	128	13	ends	end	VERB
fumecheng-4103	128	14	two	two	NUM
fumecheng-4103	128	15	more	more	ADJ
fumecheng-4103	128	16	points	point	NOUN
fumecheng-4103	128	17	are	be	AUX
fumecheng-4103	128	18	added	add	VERB
fumecheng-4103	128	19	,	,	PUNCT
fumecheng-4103	128	20	one	one	NUM
fumecheng-4103	128	21	at	at	ADP
fumecheng-4103	128	22	rs	rs	ADV
fumecheng-4103	128	23	–	–	PUNCT
fumecheng-4103	128	24	(	(	PUNCT
fumecheng-4103	128	25	a	a	DET
fumecheng-4103	128	26	–	–	PUNCT
fumecheng-4103	128	27	rs	rs	NOUN
fumecheng-4103	128	28	)	)	PUNCT
fumecheng-4103	128	29	/	/	SYM
fumecheng-4103	128	30	2	2	NUM
fumecheng-4103	128	31	and	and	CCONJ
fumecheng-4103	128	32	one	one	NUM
fumecheng-4103	128	33	at	at	ADP
fumecheng-4103	128	34	a	a	DET
fumecheng-4103	128	35	+	+	NOUN
fumecheng-4103	128	36	(	(	PUNCT
fumecheng-4103	128	37	a	a	DET
fumecheng-4103	128	38	–	–	PUNCT
fumecheng-4103	128	39	rs	rs	NOUN
fumecheng-4103	128	40	)	)	PUNCT
fumecheng-4103	128	41	/	/	SYM
fumecheng-4103	128	42	2	2	X
fumecheng-4103	128	43	.	.	PUNCT
fumecheng-4103	129	1	the	the	DET
fumecheng-4103	129	2	values	value	NOUN
fumecheng-4103	129	3	for	for	ADP
fumecheng-4103	129	4	the	the	DET
fumecheng-4103	129	5	one	one	NUM
fumecheng-4103	129	6	-	-	PUNCT
fumecheng-4103	129	7	dimensional	dimensional	ADJ
fumecheng-4103	129	8	profile	profile	NOUN
fumecheng-4103	129	9	are	be	AUX
fumecheng-4103	129	10	interpolated	interpolate	VERB
fumecheng-4103	129	11	linearly	linearly	ADV
fumecheng-4103	129	12	from	from	ADP
fumecheng-4103	129	13	gk	gk	PROPN
fumecheng-4103	129	14	to	to	ADP
fumecheng-4103	129	15	these	these	DET
fumecheng-4103	129	16	points	point	NOUN
fumecheng-4103	129	17	.	.	PUNCT
fumecheng-4103	130	1	the	the	DET
fumecheng-4103	130	2	resulting	result	VERB
fumecheng-4103	130	3	five	five	NUM
fumecheng-4103	130	4	equally	equally	ADV
fumecheng-4103	130	5	spaced	space	VERB
fumecheng-4103	130	6	points	point	NOUN
fumecheng-4103	130	7	are	be	AUX
fumecheng-4103	130	8	marked	mark	VERB
fumecheng-4103	130	9	with	with	ADP
fumecheng-4103	130	10	crosses	crosse	NOUN
fumecheng-4103	130	11	in	in	ADP
fumecheng-4103	130	12	fig	fig	NOUN
fumecheng-4103	130	13	.	.	PUNCT
fumecheng-4103	131	1	3	3	X
fumecheng-4103	131	2	.	.	X
fumecheng-4103	131	3	fig	fig	NOUN
fumecheng-4103	131	4	.	.	PUNCT
fumecheng-4103	132	1	3	3	NUM
fumecheng-4103	132	2	detailed	detailed	ADJ
fumecheng-4103	132	3	view	view	NOUN
fumecheng-4103	132	4	of	of	ADP
fumecheng-4103	132	5	the	the	DET
fumecheng-4103	132	6	graph	graph	NOUN
fumecheng-4103	132	7	in	in	ADP
fumecheng-4103	132	8	fig	fig	NOUN
fumecheng-4103	132	9	.	.	PUNCT
fumecheng-4103	133	1	1b	1b	NUM
fumecheng-4103	133	2	,	,	PUNCT
fumecheng-4103	133	3	here	here	ADV
fumecheng-4103	133	4	with	with	ADP
fumecheng-4103	133	5	additional	additional	ADJ
fumecheng-4103	133	6	discretization	discretization	NOUN
fumecheng-4103	133	7	points	point	NOUN
fumecheng-4103	133	8	at	at	ADP
fumecheng-4103	133	9	the	the	DET
fumecheng-4103	133	10	end	end	NOUN
fumecheng-4103	133	11	of	of	ADP
fumecheng-4103	133	12	the	the	DET
fumecheng-4103	133	13	contact	contact	NOUN
fumecheng-4103	133	14	area	area	NOUN
fumecheng-4103	133	15	which	which	PRON
fumecheng-4103	133	16	are	be	AUX
fumecheng-4103	133	17	marked	mark	VERB
fumecheng-4103	133	18	with	with	ADP
fumecheng-4103	133	19	black	black	ADJ
fumecheng-4103	133	20	crosses	crosse	NOUN
fumecheng-4103	133	21	the	the	DET
fumecheng-4103	133	22	desired	desire	VERB
fumecheng-4103	133	23	value	value	NOUN
fumecheng-4103	133	24	for	for	ADP
fumecheng-4103	133	25	the	the	DET
fumecheng-4103	133	26	pressure	pressure	NOUN
fumecheng-4103	133	27	at	at	ADP
fumecheng-4103	133	28	point	point	NOUN
fumecheng-4103	133	29	s	s	VERB
fumecheng-4103	133	30	can	can	AUX
fumecheng-4103	133	31	now	now	ADV
fumecheng-4103	133	32	be	be	AUX
fumecheng-4103	133	33	calculated	calculate	VERB
fumecheng-4103	133	34	as	as	ADP
fumecheng-4103	133	35	in	in	ADP
fumecheng-4103	133	36	eqs	eqs	PROPN
fumecheng-4103	133	37	.	.	PUNCT
fumecheng-4103	134	1	(	(	PUNCT
fumecheng-4103	134	2	16	16	NUM
fumecheng-4103	134	3	)	)	PUNCT
fumecheng-4103	134	4	and	and	CCONJ
fumecheng-4103	134	5	(	(	PUNCT
fumecheng-4103	134	6	17	17	NUM
fumecheng-4103	134	7	)	)	PUNCT
fumecheng-4103	134	8	using	use	VERB
fumecheng-4103	134	9	a	a	DET
fumecheng-4103	134	10	new	new	ADJ
fumecheng-4103	134	11	refined	refined	ADJ
fumecheng-4103	134	12	grid	grid	NOUN
fumecheng-4103	134	13	.	.	PUNCT
fumecheng-4103	135	1	the	the	DET
fumecheng-4103	135	2	three	three	NUM
fumecheng-4103	135	3	inner	inner	ADJ
fumecheng-4103	135	4	points	point	NOUN
fumecheng-4103	135	5	are	be	AUX
fumecheng-4103	135	6	used	use	VERB
fumecheng-4103	135	7	for	for	ADP
fumecheng-4103	135	8	the	the	DET
fumecheng-4103	135	9	summation	summation	NOUN
fumecheng-4103	135	10	while	while	SCONJ
fumecheng-4103	135	11	the	the	DET
fumecheng-4103	135	12	two	two	NUM
fumecheng-4103	135	13	additional	additional	ADJ
fumecheng-4103	135	14	outer	outer	ADJ
fumecheng-4103	135	15	points	point	NOUN
fumecheng-4103	135	16	are	be	AUX
fumecheng-4103	135	17	only	only	ADV
fumecheng-4103	135	18	there	there	ADV
fumecheng-4103	135	19	to	to	PART
fumecheng-4103	135	20	obtain	obtain	VERB
fumecheng-4103	135	21	the	the	DET
fumecheng-4103	135	22	derivatives	derivative	NOUN
fumecheng-4103	135	23	with	with	ADP
fumecheng-4103	135	24	the	the	DET
fumecheng-4103	135	25	central	central	ADJ
fumecheng-4103	135	26	difference	difference	NOUN
fumecheng-4103	135	27	scheme	scheme	NOUN
fumecheng-4103	135	28	.	.	PUNCT
fumecheng-4103	136	1	note	note	VERB
fumecheng-4103	136	2	that	that	SCONJ
fumecheng-4103	136	3	the	the	DET
fumecheng-4103	136	4	above	above	ADJ
fumecheng-4103	136	5	method	method	NOUN
fumecheng-4103	136	6	of	of	ADP
fumecheng-4103	136	7	obtaining	obtain	VERB
fumecheng-4103	136	8	a	a	DET
fumecheng-4103	136	9	more	more	ADV
fumecheng-4103	136	10	accurate	accurate	ADJ
fumecheng-4103	136	11	value	value	NOUN
fumecheng-4103	136	12	for	for	ADP
fumecheng-4103	136	13	ps	ps	PROPN
fumecheng-4103	136	14	does	do	AUX
fumecheng-4103	136	15	not	not	PART
fumecheng-4103	136	16	practically	practically	ADV
fumecheng-4103	136	17	increase	increase	VERB
fumecheng-4103	136	18	the	the	DET
fumecheng-4103	136	19	computational	computational	ADJ
fumecheng-4103	136	20	time	time	NOUN
fumecheng-4103	136	21	.	.	PUNCT
fumecheng-4103	137	1	it	it	PRON
fumecheng-4103	137	2	is	be	AUX
fumecheng-4103	137	3	a	a	DET
fumecheng-4103	137	4	simple	simple	ADJ
fumecheng-4103	137	5	addition	addition	NOUN
fumecheng-4103	137	6	of	of	ADP
fumecheng-4103	137	7	three	three	NUM
fumecheng-4103	137	8	values	value	NOUN
fumecheng-4103	137	9	,	,	PUNCT
fumecheng-4103	137	10	and	and	CCONJ
fumecheng-4103	137	11	the	the	DET
fumecheng-4103	137	12	three	three	NUM
fumecheng-4103	137	13	linear	linear	ADJ
fumecheng-4103	137	14	interpolations	interpolation	NOUN
fumecheng-4103	137	15	which	which	PRON
fumecheng-4103	137	16	are	be	AUX
fumecheng-4103	137	17	needed	need	VERB
fumecheng-4103	137	18	are	be	AUX
fumecheng-4103	137	19	also	also	ADV
fumecheng-4103	137	20	given	give	VERB
fumecheng-4103	137	21	with	with	ADP
fumecheng-4103	137	22	small	small	ADJ
fumecheng-4103	137	23	algebraic	algebraic	ADJ
fumecheng-4103	137	24	equations	equation	NOUN
fumecheng-4103	137	25	.	.	PUNCT
fumecheng-4103	138	1	compared	compare	VERB
fumecheng-4103	138	2	to	to	ADP
fumecheng-4103	138	3	the	the	DET
fumecheng-4103	138	4	time	time	NOUN
fumecheng-4103	138	5	for	for	ADP
fumecheng-4103	138	6	the	the	DET
fumecheng-4103	138	7	main	main	ADJ
fumecheng-4103	138	8	transformation	transformation	NOUN
fumecheng-4103	138	9	steps	step	NOUN
fumecheng-4103	138	10	,	,	PUNCT
fumecheng-4103	138	11	the	the	DET
fumecheng-4103	138	12	time	time	NOUN
fumecheng-4103	138	13	for	for	ADP
fumecheng-4103	138	14	these	these	DET
fumecheng-4103	138	15	additional	additional	ADJ
fumecheng-4103	138	16	steps	step	NOUN
fumecheng-4103	138	17	is	be	AUX
fumecheng-4103	138	18	negligible	negligible	ADJ
fumecheng-4103	138	19	.	.	PUNCT
fumecheng-4103	139	1	however	however	ADV
fumecheng-4103	139	2	,	,	PUNCT
fumecheng-4103	139	3	the	the	DET
fumecheng-4103	139	4	small	small	ADJ
fumecheng-4103	139	5	correction	correction	NOUN
fumecheng-4103	139	6	reduces	reduce	VERB
fumecheng-4103	139	7	the	the	DET
fumecheng-4103	139	8	maximum	maximum	ADJ
fumecheng-4103	139	9	error	error	NOUN
fumecheng-4103	139	10	norm	norm	NOUN
fumecheng-4103	139	11	(	(	PUNCT
fumecheng-4103	139	12	see	see	VERB
fumecheng-4103	139	13	fig	fig	NOUN
fumecheng-4103	139	14	.	.	PUNCT
fumecheng-4103	140	1	4	4	NUM
fumecheng-4103	140	2	)	)	PUNCT
fumecheng-4103	140	3	.	.	PUNCT
fumecheng-4103	141	1	at	at	ADP
fumecheng-4103	141	2	the	the	DET
fumecheng-4103	141	3	end	end	NOUN
fumecheng-4103	141	4	of	of	ADP
fumecheng-4103	141	5	this	this	DET
fumecheng-4103	141	6	section	section	NOUN
fumecheng-4103	141	7	it	it	PRON
fumecheng-4103	141	8	shall	shall	AUX
fumecheng-4103	141	9	be	be	AUX
fumecheng-4103	141	10	noted	note	VERB
fumecheng-4103	141	11	that	that	SCONJ
fumecheng-4103	141	12	higher	high	ADJ
fumecheng-4103	141	13	order	order	NOUN
fumecheng-4103	141	14	methods	method	NOUN
fumecheng-4103	141	15	for	for	ADP
fumecheng-4103	141	16	the	the	DET
fumecheng-4103	141	17	calculation	calculation	NOUN
fumecheng-4103	141	18	of	of	ADP
fumecheng-4103	141	19	the	the	DET
fumecheng-4103	141	20	derivatives	derivative	NOUN
fumecheng-4103	141	21	and	and	CCONJ
fumecheng-4103	141	22	for	for	ADP
fumecheng-4103	141	23	the	the	DET
fumecheng-4103	141	24	numerical	numerical	ADJ
fumecheng-4103	141	25	integration	integration	NOUN
fumecheng-4103	141	26	do	do	AUX
fumecheng-4103	141	27	not	not	PART
fumecheng-4103	141	28	necessarily	necessarily	ADV
fumecheng-4103	141	29	lead	lead	VERB
fumecheng-4103	141	30	to	to	ADP
fumecheng-4103	141	31	more	more	ADV
fumecheng-4103	141	32	accurate	accurate	ADJ
fumecheng-4103	141	33	results	result	NOUN
fumecheng-4103	141	34	.	.	PUNCT
fumecheng-4103	142	1	it	it	PRON
fumecheng-4103	142	2	is	be	AUX
fumecheng-4103	142	3	observed	observe	VERB
fumecheng-4103	142	4	that	that	SCONJ
fumecheng-4103	142	5	the	the	DET
fumecheng-4103	142	6	use	use	NOUN
fumecheng-4103	142	7	of	of	ADP
fumecheng-4103	142	8	more	more	ADJ
fumecheng-4103	142	9	neighboring	neighboring	NOUN
fumecheng-4103	142	10	points	point	NOUN
fumecheng-4103	142	11	than	than	ADP
fumecheng-4103	142	12	in	in	ADP
fumecheng-4103	142	13	eqs	eqs	PROPN
fumecheng-4103	142	14	.	.	PUNCT
fumecheng-4103	143	1	(	(	PUNCT
fumecheng-4103	143	2	9	9	NUM
fumecheng-4103	143	3	)	)	PUNCT
fumecheng-4103	143	4	and	and	CCONJ
fumecheng-4103	143	5	(	(	PUNCT
fumecheng-4103	143	6	10	10	NUM
fumecheng-4103	143	7	)	)	PUNCT
fumecheng-4103	143	8	for	for	ADP
fumecheng-4103	143	9	calculating	calculate	VERB
fumecheng-4103	143	10	the	the	DET
fumecheng-4103	143	11	derivatives	derivative	NOUN
fumecheng-4103	143	12	tends	tend	VERB
fumecheng-4103	143	13	to	to	PART
fumecheng-4103	143	14	decrease	decrease	VERB
fumecheng-4103	143	15	the	the	DET
fumecheng-4103	143	16	accuracy	accuracy	NOUN
fumecheng-4103	143	17	of	of	ADP
fumecheng-4103	143	18	the	the	DET
fumecheng-4103	143	19	transformations	transformation	NOUN
fumecheng-4103	143	20	for	for	ADP
fumecheng-4103	143	21	the	the	DET
fumecheng-4103	143	22	contact	contact	NOUN
fumecheng-4103	143	23	of	of	ADP
fumecheng-4103	143	24	the	the	DET
fumecheng-4103	143	25	cone	cone	NOUN
fumecheng-4103	143	26	and	and	CCONJ
fumecheng-4103	143	27	the	the	DET
fumecheng-4103	143	28	hertzian	hertzian	ADJ
fumecheng-4103	143	29	contact	contact	NOUN
fumecheng-4103	143	30	.	.	PUNCT
fumecheng-4103	144	1	it	it	PRON
fumecheng-4103	144	2	was	be	AUX
fumecheng-4103	144	3	also	also	ADV
fumecheng-4103	144	4	observed	observe	VERB
fumecheng-4103	144	5	that	that	SCONJ
fumecheng-4103	144	6	using	use	VERB
fumecheng-4103	144	7	simpson	simpson	PROPN
fumecheng-4103	144	8	’s	’s	PART
fumecheng-4103	144	9	rule	rule	NOUN
fumecheng-4103	144	10	to	to	PART
fumecheng-4103	144	11	perform	perform	VERB
fumecheng-4103	144	12	the	the	DET
fumecheng-4103	144	13	summation	summation	NOUN
fumecheng-4103	144	14	in	in	ADP
fumecheng-4103	144	15	eqs	eqs	PROPN
fumecheng-4103	144	16	.	.	PUNCT
fumecheng-4103	145	1	(	(	PUNCT
fumecheng-4103	145	2	13	13	NUM
fumecheng-4103	145	3	)	)	PUNCT
fumecheng-4103	145	4	and	and	CCONJ
fumecheng-4103	145	5	(	(	PUNCT
fumecheng-4103	145	6	16	16	NUM
fumecheng-4103	145	7	)	)	PUNCT
fumecheng-4103	145	8	instead	instead	ADV
fumecheng-4103	145	9	of	of	ADP
fumecheng-4103	145	10	the	the	DET
fumecheng-4103	145	11	trapezoidal	trapezoidal	ADJ
fumecheng-4103	145	12	rule	rule	NOUN
fumecheng-4103	145	13	decreases	decrease	VERB
fumecheng-4103	145	14	the	the	DET
fumecheng-4103	145	15	accuracy	accuracy	NOUN
fumecheng-4103	145	16	of	of	ADP
fumecheng-4103	145	17	the	the	DET
fumecheng-4103	145	18	transformations	transformation	NOUN
fumecheng-4103	145	19	.	.	PUNCT
fumecheng-4103	146	1	134	134	NUM
fumecheng-4103	146	2	j.	j.	PROPN
fumecheng-4103	146	3	benad	benad	PROPN
fumecheng-4103	146	4	a	a	DET
fumecheng-4103	146	5	)	)	PUNCT
fumecheng-4103	146	6	b	b	NOUN
fumecheng-4103	146	7	)	)	PUNCT
fumecheng-4103	146	8	fig	fig	NOUN
fumecheng-4103	146	9	.	.	PUNCT
fumecheng-4103	147	1	4	4	NUM
fumecheng-4103	147	2	maximum	maximum	NOUN
fumecheng-4103	147	3	error	error	NOUN
fumecheng-4103	147	4	of	of	ADP
fumecheng-4103	147	5	gk	gk	PROPN
fumecheng-4103	147	6	,	,	PUNCT
fumecheng-4103	147	7	wn	wn	PROPN
fumecheng-4103	147	8	,	,	PUNCT
fumecheng-4103	147	9	and	and	CCONJ
fumecheng-4103	147	10	pn	pn	PROPN
fumecheng-4103	147	11	as	as	SCONJ
fumecheng-4103	147	12	displayed	display	VERB
fumecheng-4103	147	13	in	in	ADP
fumecheng-4103	147	14	fig	fig	NOUN
fumecheng-4103	147	15	.	.	PUNCT
fumecheng-4103	148	1	2	2	NUM
fumecheng-4103	148	2	here	here	ADV
fumecheng-4103	148	3	however	however	ADV
fumecheng-4103	148	4	ps	ps	PROPN
fumecheng-4103	148	5	is	be	AUX
fumecheng-4103	148	6	corrected	correct	VERB
fumecheng-4103	148	7	with	with	ADP
fumecheng-4103	148	8	the	the	DET
fumecheng-4103	148	9	technique	technique	NOUN
fumecheng-4103	148	10	explained	explain	VERB
fumecheng-4103	148	11	above	above	ADV
fumecheng-4103	148	12	.	.	PUNCT
fumecheng-4103	149	1	the	the	DET
fumecheng-4103	149	2	old	old	ADJ
fumecheng-4103	149	3	upper	upper	ADJ
fumecheng-4103	149	4	limit	limit	NOUN
fumecheng-4103	149	5	of	of	ADP
fumecheng-4103	149	6	the	the	DET
fumecheng-4103	149	7	maximum	maximum	ADJ
fumecheng-4103	149	8	error	error	NOUN
fumecheng-4103	149	9	of	of	ADP
fumecheng-4103	149	10	pn	pn	PROPN
fumecheng-4103	149	11	from	from	ADP
fumecheng-4103	149	12	fig	fig	NOUN
fumecheng-4103	149	13	.	.	PUNCT
fumecheng-4103	150	1	2	2	NUM
fumecheng-4103	150	2	is	be	AUX
fumecheng-4103	150	3	shown	show	VERB
fumecheng-4103	150	4	with	with	ADP
fumecheng-4103	150	5	the	the	DET
fumecheng-4103	150	6	grey	grey	PROPN
fumecheng-4103	150	7	dotted	dotted	ADJ
fumecheng-4103	150	8	line	line	NOUN
fumecheng-4103	150	9	.	.	PUNCT
fumecheng-4103	151	1	the	the	DET
fumecheng-4103	151	2	new	new	ADJ
fumecheng-4103	151	3	upper	upper	ADJ
fumecheng-4103	151	4	limit	limit	NOUN
fumecheng-4103	151	5	of	of	ADP
fumecheng-4103	151	6	the	the	DET
fumecheng-4103	151	7	maximum	maximum	ADJ
fumecheng-4103	151	8	error	error	NOUN
fumecheng-4103	151	9	of	of	ADP
fumecheng-4103	151	10	pn	pn	PROPN
fumecheng-4103	151	11	after	after	ADP
fumecheng-4103	151	12	the	the	DET
fumecheng-4103	151	13	correction	correction	NOUN
fumecheng-4103	151	14	of	of	ADP
fumecheng-4103	151	15	ps	ps	PROPN
fumecheng-4103	151	16	is	be	AUX
fumecheng-4103	151	17	shown	show	VERB
fumecheng-4103	151	18	with	with	ADP
fumecheng-4103	151	19	the	the	DET
fumecheng-4103	151	20	black	black	ADJ
fumecheng-4103	151	21	dotted	dotted	ADJ
fumecheng-4103	151	22	line	line	NOUN
fumecheng-4103	151	23	.	.	PUNCT
fumecheng-4103	152	1	in	in	ADP
fumecheng-4103	152	2	the	the	DET
fumecheng-4103	152	3	case	case	NOUN
fumecheng-4103	152	4	of	of	ADP
fumecheng-4103	152	5	the	the	DET
fumecheng-4103	152	6	cone	cone	NOUN
fumecheng-4103	152	7	(	(	PUNCT
fumecheng-4103	152	8	a	a	X
fumecheng-4103	152	9	)	)	PUNCT
fumecheng-4103	152	10	this	this	DET
fumecheng-4103	152	11	upper	upper	ADJ
fumecheng-4103	152	12	limit	limit	NOUN
fumecheng-4103	152	13	falls	fall	VERB
fumecheng-4103	152	14	onto	onto	ADP
fumecheng-4103	152	15	the	the	DET
fumecheng-4103	152	16	dashed	dash	VERB
fumecheng-4103	152	17	line	line	NOUN
fumecheng-4103	152	18	marking	mark	VERB
fumecheng-4103	152	19	the	the	DET
fumecheng-4103	152	20	maximum	maximum	ADJ
fumecheng-4103	152	21	error	error	NOUN
fumecheng-4103	152	22	of	of	ADP
fumecheng-4103	152	23	pn	pn	NOUN
fumecheng-4103	152	24	when	when	SCONJ
fumecheng-4103	152	25	the	the	DET
fumecheng-4103	152	26	point	point	NOUN
fumecheng-4103	152	27	s	s	VERB
fumecheng-4103	152	28	is	be	AUX
fumecheng-4103	152	29	disregarded	disregard	VERB
fumecheng-4103	152	30	7	7	NUM
fumecheng-4103	152	31	.	.	PUNCT
fumecheng-4103	152	32	comparison	comparison	NOUN
fumecheng-4103	152	33	with	with	ADP
fumecheng-4103	152	34	other	other	ADJ
fumecheng-4103	152	35	numerical	numerical	PROPN
fumecheng-4103	152	36	techniques	technique	NOUN
fumecheng-4103	152	37	recall	recall	VERB
fumecheng-4103	152	38	that	that	SCONJ
fumecheng-4103	152	39	at	at	ADP
fumecheng-4103	152	40	the	the	DET
fumecheng-4103	152	41	beginning	beginning	NOUN
fumecheng-4103	152	42	of	of	ADP
fumecheng-4103	152	43	the	the	DET
fumecheng-4103	152	44	numerical	numerical	ADJ
fumecheng-4103	152	45	scheme	scheme	NOUN
fumecheng-4103	152	46	presented	present	VERB
fumecheng-4103	152	47	above	above	ADP
fumecheng-4103	152	48	the	the	DET
fumecheng-4103	152	49	mdr	mdr	PROPN
fumecheng-4103	152	50	transformations	transformation	NOUN
fumecheng-4103	152	51	were	be	AUX
fumecheng-4103	152	52	rewritten	rewrite	VERB
fumecheng-4103	152	53	using	use	VERB
fumecheng-4103	152	54	integration	integration	NOUN
fumecheng-4103	152	55	by	by	ADP
fumecheng-4103	152	56	parts	part	NOUN
fumecheng-4103	152	57	.	.	PUNCT
fumecheng-4103	153	1	however	however	ADV
fumecheng-4103	153	2	,	,	PUNCT
fumecheng-4103	153	3	the	the	DET
fumecheng-4103	153	4	mdr	mdr	NOUN
fumecheng-4103	153	5	transformations	transformation	NOUN
fumecheng-4103	153	6	can	can	AUX
fumecheng-4103	153	7	also	also	ADV
fumecheng-4103	153	8	be	be	AUX
fumecheng-4103	153	9	implemented	implement	VERB
fumecheng-4103	153	10	numerically	numerically	ADV
fumecheng-4103	153	11	using	use	VERB
fumecheng-4103	153	12	their	their	PRON
fumecheng-4103	153	13	original	original	ADJ
fumecheng-4103	153	14	form	form	NOUN
fumecheng-4103	153	15	of	of	ADP
fumecheng-4103	153	16	eqs	eqs	PROPN
fumecheng-4103	153	17	.	.	PUNCT
fumecheng-4103	154	1	(	(	PUNCT
fumecheng-4103	154	2	1	1	NUM
fumecheng-4103	154	3	)	)	PUNCT
fumecheng-4103	154	4	,	,	PUNCT
fumecheng-4103	154	5	(	(	PUNCT
fumecheng-4103	154	6	2	2	X
fumecheng-4103	154	7	)	)	PUNCT
fumecheng-4103	154	8	and	and	CCONJ
fumecheng-4103	154	9	(	(	PUNCT
fumecheng-4103	154	10	3	3	X
fumecheng-4103	154	11	)	)	PUNCT
fumecheng-4103	154	12	without	without	ADP
fumecheng-4103	154	13	rewriting	rewrite	VERB
fumecheng-4103	154	14	them	they	PRON
fumecheng-4103	154	15	to	to	ADP
fumecheng-4103	154	16	eqs	eqs	PROPN
fumecheng-4103	154	17	.	.	PUNCT
fumecheng-4103	155	1	(	(	PUNCT
fumecheng-4103	155	2	4	4	NUM
fumecheng-4103	155	3	)	)	PUNCT
fumecheng-4103	155	4	,	,	PUNCT
fumecheng-4103	155	5	(	(	PUNCT
fumecheng-4103	155	6	5	5	NUM
fumecheng-4103	155	7	)	)	PUNCT
fumecheng-4103	155	8	and	and	CCONJ
fumecheng-4103	155	9	(	(	PUNCT
fumecheng-4103	155	10	6	6	NUM
fumecheng-4103	155	11	)	)	PUNCT
fumecheng-4103	155	12	.	.	PUNCT
fumecheng-4103	156	1	here	here	ADV
fumecheng-4103	156	2	,	,	PUNCT
fumecheng-4103	156	3	two	two	NUM
fumecheng-4103	156	4	such	such	ADJ
fumecheng-4103	156	5	methods	method	NOUN
fumecheng-4103	156	6	which	which	PRON
fumecheng-4103	156	7	will	will	AUX
fumecheng-4103	156	8	be	be	AUX
fumecheng-4103	156	9	called	call	VERB
fumecheng-4103	156	10	“	"	PUNCT
fumecheng-4103	156	11	method	method	PROPN
fumecheng-4103	156	12	i	i	PRON
fumecheng-4103	156	13	”	"	PUNCT
fumecheng-4103	156	14	and	and	CCONJ
fumecheng-4103	156	15	“	"	PUNCT
fumecheng-4103	156	16	method	method	PROPN
fumecheng-4103	156	17	ii	ii	PROPN
fumecheng-4103	156	18	”	"	PUNCT
fumecheng-4103	156	19	shall	shall	AUX
fumecheng-4103	156	20	briefly	briefly	ADV
fumecheng-4103	156	21	be	be	AUX
fumecheng-4103	156	22	discussed	discuss	VERB
fumecheng-4103	156	23	.	.	PUNCT
fumecheng-4103	157	1	their	their	PRON
fumecheng-4103	157	2	accuracy	accuracy	NOUN
fumecheng-4103	157	3	will	will	AUX
fumecheng-4103	157	4	be	be	AUX
fumecheng-4103	157	5	compared	compare	VERB
fumecheng-4103	157	6	to	to	ADP
fumecheng-4103	157	7	the	the	DET
fumecheng-4103	157	8	partial	partial	ADJ
fumecheng-4103	157	9	integration	integration	NOUN
fumecheng-4103	157	10	methods	method	NOUN
fumecheng-4103	157	11	introduced	introduce	VERB
fumecheng-4103	157	12	above	above	ADP
fumecheng-4103	157	13	,	,	PUNCT
fumecheng-4103	157	14	which	which	PRON
fumecheng-4103	157	15	are	be	AUX
fumecheng-4103	157	16	referred	refer	VERB
fumecheng-4103	157	17	to	to	ADP
fumecheng-4103	157	18	as	as	ADP
fumecheng-4103	157	19	“	"	PUNCT
fumecheng-4103	157	20	method	method	PROPN
fumecheng-4103	157	21	iii	iii	NOUN
fumecheng-4103	157	22	”	"	PUNCT
fumecheng-4103	157	23	and	and	CCONJ
fumecheng-4103	157	24	“	"	PUNCT
fumecheng-4103	157	25	method	method	NOUN
fumecheng-4103	157	26	iv	iv	NUM
fumecheng-4103	157	27	”	"	PUNCT
fumecheng-4103	157	28	in	in	ADP
fumecheng-4103	157	29	the	the	DET
fumecheng-4103	157	30	following	following	NOUN
fumecheng-4103	157	31	.	.	PUNCT
fumecheng-4103	158	1	method	method	NOUN
fumecheng-4103	158	2	i	i	PRON
fumecheng-4103	158	3	–	–	PUNCT
fumecheng-4103	158	4	insertion	insertion	NOUN
fumecheng-4103	158	5	of	of	ADP
fumecheng-4103	158	6	h	h	NOUN
fumecheng-4103	158	7	at	at	ADP
fumecheng-4103	158	8	singularity	singularity	NOUN
fumecheng-4103	158	9	:	:	PUNCT
fumecheng-4103	158	10	one	one	NUM
fumecheng-4103	158	11	technique	technique	NOUN
fumecheng-4103	158	12	for	for	ADP
fumecheng-4103	158	13	the	the	DET
fumecheng-4103	158	14	implementation	implementation	NOUN
fumecheng-4103	158	15	of	of	ADP
fumecheng-4103	158	16	the	the	DET
fumecheng-4103	158	17	transformations	transformation	NOUN
fumecheng-4103	158	18	using	use	VERB
fumecheng-4103	158	19	their	their	PRON
fumecheng-4103	158	20	original	original	ADJ
fumecheng-4103	158	21	form	form	NOUN
fumecheng-4103	158	22	of	of	ADP
fumecheng-4103	158	23	eqs	eqs	PROPN
fumecheng-4103	158	24	.	.	PUNCT
fumecheng-4103	159	1	(	(	PUNCT
fumecheng-4103	159	2	1	1	NUM
fumecheng-4103	159	3	)	)	PUNCT
fumecheng-4103	159	4	,	,	PUNCT
fumecheng-4103	159	5	(	(	PUNCT
fumecheng-4103	159	6	2	2	X
fumecheng-4103	159	7	)	)	PUNCT
fumecheng-4103	159	8	and	and	CCONJ
fumecheng-4103	159	9	(	(	PUNCT
fumecheng-4103	159	10	3	3	X
fumecheng-4103	159	11	)	)	PUNCT
fumecheng-4103	159	12	is	be	AUX
fumecheng-4103	159	13	to	to	PART
fumecheng-4103	159	14	insert	insert	VERB
fumecheng-4103	159	15	a	a	DET
fumecheng-4103	159	16	single	single	ADJ
fumecheng-4103	159	17	increment	increment	NOUN
fumecheng-4103	159	18	h	h	NOUN
fumecheng-4103	159	19	at	at	ADP
fumecheng-4103	159	20	the	the	DET
fumecheng-4103	159	21	singularity	singularity	NOUN
fumecheng-4103	159	22	where	where	SCONJ
fumecheng-4103	159	23	x	x	X
fumecheng-4103	159	24	=	=	SYM
fumecheng-4103	159	25	r	r	NOUN
fumecheng-4103	159	26	,	,	PUNCT
fumecheng-4103	159	27	as	as	ADP
fumecheng-4103	159	28	in	in	ADP
fumecheng-4103	159	29	1	1	NUM
fumecheng-4103	159	30	2	2	NUM
fumecheng-4103	159	31	2	2	NUM
fumecheng-4103	159	32	1	1	NUM
fumecheng-4103	159	33	k	k	NOUN
fumecheng-4103	159	34	n	n	PRON
fumecheng-4103	159	35	k	k	PROPN
fumecheng-4103	159	36	k	k	PROPN
fumecheng-4103	159	37	k	k	PROPN
fumecheng-4103	159	38	n	n	CCONJ
fumecheng-4103	159	39	k	k	PROPN
fumecheng-4103	160	1	n	n	ADV
fumecheng-4103	160	2	f	f	NOUN
fumecheng-4103	160	3	f	f	NOUN
fumecheng-4103	160	4	g	g	PROPN
fumecheng-4103	160	5	x	x	PROPN
fumecheng-4103	160	6	h	h	NOUN
fumecheng-4103	160	7	hx	hx	NOUN
fumecheng-4103	160	8	r	r	PROPN
fumecheng-4103	160	9			PROPN
fumecheng-4103	160	10			PROPN
fumecheng-4103	160	11			NOUN
fumecheng-4103	160	12			PROPN
fumecheng-4103	160	13			PROPN
fumecheng-4103	160	14			PROPN
fumecheng-4103	160	15			PROPN
fumecheng-4103	160	16			NOUN
fumecheng-4103	160	17			VERB
fumecheng-4103	160	18			PROPN
fumecheng-4103	161	1			PROPN
fumecheng-4103	161	2			NOUN
fumecheng-4103	162	1			PROPN
fumecheng-4103	162	2			NOUN
fumecheng-4103	162	3			NOUN
fumecheng-4103	162	4			X
fumecheng-4103	162	5	,	,	PUNCT
fumecheng-4103	162	6	(	(	PUNCT
fumecheng-4103	162	7	21	21	NUM
fumecheng-4103	162	8	)	)	PUNCT
fumecheng-4103	162	9	where	where	SCONJ
fumecheng-4103	162	10	the	the	DET
fumecheng-4103	162	11	first	first	ADJ
fumecheng-4103	162	12	derivative	derivative	NOUN
fumecheng-4103	162	13	is	be	AUX
fumecheng-4103	162	14	computed	compute	VERB
fumecheng-4103	162	15	as	as	ADP
fumecheng-4103	162	16	in	in	ADP
fumecheng-4103	162	17	eq	eq	ADP
fumecheng-4103	162	18	.	.	PUNCT
fumecheng-4103	163	1	(	(	PUNCT
fumecheng-4103	163	2	9	9	X
fumecheng-4103	163	3	)	)	PUNCT
fumecheng-4103	163	4	using	use	VERB
fumecheng-4103	163	5	central	central	ADJ
fumecheng-4103	163	6	differences	difference	NOUN
fumecheng-4103	163	7	.	.	PUNCT
fumecheng-4103	164	1	this	this	DET
fumecheng-4103	164	2	method	method	NOUN
fumecheng-4103	164	3	,	,	PUNCT
fumecheng-4103	164	4	however	however	ADV
fumecheng-4103	164	5	,	,	PUNCT
fumecheng-4103	164	6	delivers	deliver	VERB
fumecheng-4103	164	7	only	only	ADV
fumecheng-4103	164	8	very	very	ADV
fumecheng-4103	164	9	poor	poor	ADJ
fumecheng-4103	164	10	results	result	NOUN
fumecheng-4103	164	11	.	.	PUNCT
fumecheng-4103	165	1	as	as	SCONJ
fumecheng-4103	165	2	can	can	AUX
fumecheng-4103	165	3	be	be	AUX
fumecheng-4103	165	4	seen	see	VERB
fumecheng-4103	165	5	in	in	ADP
fumecheng-4103	165	6	fig	fig	NOUN
fumecheng-4103	165	7	.	.	PUNCT
fumecheng-4103	166	1	5	5	NUM
fumecheng-4103	166	2	,	,	PUNCT
fumecheng-4103	166	3	the	the	DET
fumecheng-4103	166	4	technique	technique	NOUN
fumecheng-4103	166	5	requires	require	VERB
fumecheng-4103	166	6	a	a	DET
fumecheng-4103	166	7	number	number	NOUN
fumecheng-4103	166	8	of	of	ADP
fumecheng-4103	166	9	discretization	discretization	NOUN
fumecheng-4103	166	10	points	point	NOUN
fumecheng-4103	166	11	which	which	PRON
fumecheng-4103	166	12	is	be	AUX
fumecheng-4103	166	13	several	several	ADJ
fumecheng-4103	166	14	orders	order	NOUN
fumecheng-4103	166	15	of	of	ADP
fumecheng-4103	166	16	magnitude	magnitude	NOUN
fumecheng-4103	166	17	higher	high	ADJ
fumecheng-4103	166	18	in	in	ADP
fumecheng-4103	166	19	order	order	NOUN
fumecheng-4103	166	20	to	to	PART
fumecheng-4103	166	21	reach	reach	VERB
fumecheng-4103	166	22	the	the	DET
fumecheng-4103	166	23	accuracy	accuracy	NOUN
fumecheng-4103	166	24	which	which	PRON
fumecheng-4103	166	25	is	be	AUX
fumecheng-4103	166	26	achieved	achieve	VERB
fumecheng-4103	166	27	by	by	ADP
fumecheng-4103	166	28	the	the	DET
fumecheng-4103	166	29	other	other	ADJ
fumecheng-4103	166	30	implementation	implementation	NOUN
fumecheng-4103	166	31	techniques	technique	NOUN
fumecheng-4103	166	32	.	.	PUNCT
fumecheng-4103	167	1	this	this	DET
fumecheng-4103	167	2	method	method	NOUN
fumecheng-4103	167	3	is	be	AUX
fumecheng-4103	167	4	not	not	PART
fumecheng-4103	167	5	recommended	recommend	VERB
fumecheng-4103	167	6	.	.	PUNCT
fumecheng-4103	168	1	fast	fast	ADJ
fumecheng-4103	168	2	numerical	numerical	ADJ
fumecheng-4103	168	3	implementation	implementation	NOUN
fumecheng-4103	168	4	of	of	ADP
fumecheng-4103	168	5	the	the	DET
fumecheng-4103	168	6	mdr	mdr	PROPN
fumecheng-4103	168	7	transformations	transformation	VERB
fumecheng-4103	168	8	135	135	NUM
fumecheng-4103	168	9	method	method	PROPN
fumecheng-4103	168	10	ii	ii	NOUN
fumecheng-4103	168	11	–	–	PUNCT
fumecheng-4103	168	12	implementation	implementation	NOUN
fumecheng-4103	168	13	of	of	ADP
fumecheng-4103	168	14	the	the	DET
fumecheng-4103	168	15	kernel	kernel	NOUN
fumecheng-4103	168	16	with	with	ADP
fumecheng-4103	168	17	its	its	PRON
fumecheng-4103	168	18	antiderivative	antiderivative	NOUN
fumecheng-4103	168	19	:	:	PUNCT
fumecheng-4103	168	20	a	a	DET
fumecheng-4103	168	21	far	far	ADV
fumecheng-4103	168	22	better	well	ADJ
fumecheng-4103	168	23	technique	technique	NOUN
fumecheng-4103	168	24	for	for	ADP
fumecheng-4103	168	25	the	the	DET
fumecheng-4103	168	26	implementation	implementation	NOUN
fumecheng-4103	168	27	of	of	ADP
fumecheng-4103	168	28	the	the	DET
fumecheng-4103	168	29	transformations	transformation	NOUN
fumecheng-4103	168	30	using	use	VERB
fumecheng-4103	168	31	their	their	PRON
fumecheng-4103	168	32	original	original	ADJ
fumecheng-4103	168	33	form	form	NOUN
fumecheng-4103	168	34	is	be	AUX
fumecheng-4103	168	35	to	to	PART
fumecheng-4103	168	36	implement	implement	VERB
fumecheng-4103	168	37	the	the	DET
fumecheng-4103	168	38	kernel	kernel	NOUN
fumecheng-4103	168	39	of	of	ADP
fumecheng-4103	168	40	the	the	DET
fumecheng-4103	168	41	transformation	transformation	NOUN
fumecheng-4103	168	42	using	use	VERB
fumecheng-4103	168	43	its	its	PRON
fumecheng-4103	168	44	antiderivative	antiderivative	NOUN
fumecheng-4103	168	45	.	.	PUNCT
fumecheng-4103	169	1	for	for	ADP
fumecheng-4103	169	2	the	the	DET
fumecheng-4103	169	3	transformation	transformation	NOUN
fumecheng-4103	169	4	to	to	ADP
fumecheng-4103	169	5	gk	gk	PROPN
fumecheng-4103	169	6	,	,	PUNCT
fumecheng-4103	169	7	this	this	PRON
fumecheng-4103	169	8	translates	translate	VERB
fumecheng-4103	169	9	to	to	ADP
fumecheng-4103	169	10	1	1	NUM
fumecheng-4103	169	11	2	2	NUM
fumecheng-4103	169	12	2	2	NUM
fumecheng-4103	169	13	2	2	NUM
fumecheng-4103	169	14	2	2	NUM
fumecheng-4103	169	15	1	1	NUM
fumecheng-4103	169	16	1	1	NUM
fumecheng-4103	170	1	atan	atan	NOUN
fumecheng-4103	170	2	atann	atann	PROPN
fumecheng-4103	170	3	nk	nk	PROPN
fumecheng-4103	170	4	k	k	PROPN
fumecheng-4103	170	5	k	k	PROPN
fumecheng-4103	170	6	k	k	PROPN
fumecheng-4103	171	1	n	n	CCONJ
fumecheng-4103	172	1	k	k	PROPN
fumecheng-4103	173	1	n	n	CCONJ
fumecheng-4103	174	1	n	n	CCONJ
fumecheng-4103	175	1	n	n	NOUN
fumecheng-4103	176	1	r	r	NOUN
fumecheng-4103	176	2	r	r	NOUN
fumecheng-4103	176	3	g	g	NOUN
fumecheng-4103	176	4	x	x	SYM
fumecheng-4103	176	5	h	h	NOUN
fumecheng-4103	176	6	x	x	PUNCT
fumecheng-4103	176	7	r	r	NOUN
fumecheng-4103	176	8	x	x	SYM
fumecheng-4103	176	9	r	r	NOUN
fumecheng-4103	176	10	f	f	NOUN
fumecheng-4103	176	11	h	h	PROPN
fumecheng-4103	176	12			PROPN
fumecheng-4103	176	13			VERB
fumecheng-4103	176	14			PROPN
fumecheng-4103	176	15			NOUN
fumecheng-4103	176	16			NOUN
fumecheng-4103	177	1			PROPN
fumecheng-4103	177	2			PROPN
fumecheng-4103	178	1			PROPN
fumecheng-4103	178	2			PROPN
fumecheng-4103	178	3			PROPN
fumecheng-4103	178	4			PROPN
fumecheng-4103	178	5			PROPN
fumecheng-4103	178	6			PROPN
fumecheng-4103	178	7			NOUN
fumecheng-4103	178	8			X
fumecheng-4103	178	9	(	(	PUNCT
fumecheng-4103	178	10	22	22	NUM
fumecheng-4103	178	11	)	)	PUNCT
fumecheng-4103	178	12	and	and	CCONJ
fumecheng-4103	178	13	for	for	ADP
fumecheng-4103	178	14	the	the	DET
fumecheng-4103	178	15	transformation	transformation	NOUN
fumecheng-4103	178	16	to	to	ADP
fumecheng-4103	178	17	pn	pn	PROPN
fumecheng-4103	178	18	,	,	PUNCT
fumecheng-4103	178	19	one	one	PRON
fumecheng-4103	178	20	can	can	AUX
fumecheng-4103	178	21	use	use	VERB
fumecheng-4103	178	22	2	2	NUM
fumecheng-4103	178	23	2	2	NUM
fumecheng-4103	178	24	2	2	NUM
fumecheng-4103	178	25	2	2	NUM
fumecheng-4103	178	26	1	1	NUM
fumecheng-4103	178	27	1	1	NUM
fumecheng-4103	178	28	1	1	NUM
fumecheng-4103	178	29	log	log	NOUN
fumecheng-4103	178	30	(	(	PUNCT
fumecheng-4103	178	31	)	)	PUNCT
fumecheng-4103	178	32	log	log	NOUN
fumecheng-4103	178	33	(	(	PUNCT
fumecheng-4103	178	34	)	)	PUNCT
fumecheng-4103	178	35	n	n	CCONJ
fumecheng-4103	178	36	k	k	PROPN
fumecheng-4103	179	1	n	n	CCONJ
fumecheng-4103	179	2	k	k	PROPN
fumecheng-4103	179	3	k	k	PROPN
fumecheng-4103	180	1	n	n	CCONJ
fumecheng-4103	180	2	k	k	PROPN
fumecheng-4103	180	3	n	n	CCONJ
fumecheng-4103	180	4	k	k	PROPN
fumecheng-4103	180	5	k	k	PROPN
fumecheng-4103	181	1	n	n	PROPN
fumecheng-4103	181	2	x	x	SYM
fumecheng-4103	181	3	r	r	NOUN
fumecheng-4103	181	4	x	x	PUNCT
fumecheng-4103	181	5	x	x	SYM
fumecheng-4103	181	6	r	r	NOUN
fumecheng-4103	181	7	xp	xp	NOUN
fumecheng-4103	181	8	h	h	PROPN
fumecheng-4103	181	9	q	q	PROPN
fumecheng-4103	181	10	h	h	PROPN
fumecheng-4103	181	11			ADV
fumecheng-4103	181	12			PUNCT
fumecheng-4103	181	13			PROPN
fumecheng-4103	181	14			NOUN
fumecheng-4103	181	15			NOUN
fumecheng-4103	181	16			PUNCT
fumecheng-4103	181	17			PROPN
fumecheng-4103	181	18			PROPN
fumecheng-4103	181	19			PROPN
fumecheng-4103	181	20			PROPN
fumecheng-4103	181	21			PROPN
fumecheng-4103	181	22			PROPN
fumecheng-4103	181	23			PROPN
fumecheng-4103	181	24			PROPN
fumecheng-4103	181	25			NOUN
fumecheng-4103	181	26			X
fumecheng-4103	181	27	.	.	PUNCT
fumecheng-4103	182	1	(	(	PUNCT
fumecheng-4103	182	2	23	23	NUM
fumecheng-4103	182	3	)	)	PUNCT
fumecheng-4103	182	4	the	the	DET
fumecheng-4103	182	5	first	first	ADJ
fumecheng-4103	182	6	derivatives	derivative	NOUN
fumecheng-4103	182	7	can	can	AUX
fumecheng-4103	182	8	once	once	ADV
fumecheng-4103	182	9	more	more	ADV
fumecheng-4103	182	10	be	be	AUX
fumecheng-4103	182	11	obtained	obtain	VERB
fumecheng-4103	182	12	via	via	ADP
fumecheng-4103	182	13	central	central	ADJ
fumecheng-4103	182	14	differences	difference	NOUN
fumecheng-4103	182	15	.	.	PUNCT
fumecheng-4103	183	1	as	as	SCONJ
fumecheng-4103	183	2	can	can	AUX
fumecheng-4103	183	3	be	be	AUX
fumecheng-4103	183	4	seen	see	VERB
fumecheng-4103	183	5	in	in	ADP
fumecheng-4103	183	6	fig	fig	NOUN
fumecheng-4103	183	7	.	.	PUNCT
fumecheng-4103	184	1	5	5	NUM
fumecheng-4103	184	2	,	,	PUNCT
fumecheng-4103	184	3	the	the	DET
fumecheng-4103	184	4	method	method	PROPN
fumecheng-4103	184	5	ii	ii	PROPN
fumecheng-4103	184	6	provides	provide	VERB
fumecheng-4103	184	7	a	a	DET
fumecheng-4103	184	8	much	much	ADV
fumecheng-4103	184	9	better	well	ADJ
fumecheng-4103	184	10	accuracy	accuracy	NOUN
fumecheng-4103	184	11	than	than	ADP
fumecheng-4103	184	12	method	method	PROPN
fumecheng-4103	184	13	i.	i.	PROPN
fumecheng-4103	184	14	method	method	PROPN
fumecheng-4103	184	15	iii	iii	X
fumecheng-4103	184	16	–	–	PUNCT
fumecheng-4103	184	17	partial	partial	ADJ
fumecheng-4103	184	18	integration	integration	NOUN
fumecheng-4103	184	19	method	method	NOUN
fumecheng-4103	184	20	:	:	PUNCT
fumecheng-4103	184	21	this	this	DET
fumecheng-4103	184	22	technique	technique	NOUN
fumecheng-4103	184	23	was	be	AUX
fumecheng-4103	184	24	described	describe	VERB
fumecheng-4103	184	25	in	in	ADP
fumecheng-4103	184	26	great	great	ADJ
fumecheng-4103	184	27	detail	detail	NOUN
fumecheng-4103	184	28	in	in	ADP
fumecheng-4103	184	29	the	the	DET
fumecheng-4103	184	30	first	first	ADJ
fumecheng-4103	184	31	sections	section	NOUN
fumecheng-4103	184	32	of	of	ADP
fumecheng-4103	184	33	this	this	DET
fumecheng-4103	184	34	work	work	NOUN
fumecheng-4103	184	35	.	.	PUNCT
fumecheng-4103	185	1	here	here	ADV
fumecheng-4103	185	2	the	the	DET
fumecheng-4103	185	3	singularity	singularity	NOUN
fumecheng-4103	185	4	at	at	ADP
fumecheng-4103	185	5	x	x	X
fumecheng-4103	185	6	=	=	NOUN
fumecheng-4103	185	7	r	r	NOUN
fumecheng-4103	185	8	is	be	AUX
fumecheng-4103	185	9	avoided	avoid	VERB
fumecheng-4103	185	10	through	through	ADP
fumecheng-4103	185	11	partial	partial	ADJ
fumecheng-4103	185	12	integration	integration	NOUN
fumecheng-4103	185	13	of	of	ADP
fumecheng-4103	185	14	the	the	DET
fumecheng-4103	185	15	transformations	transformation	NOUN
fumecheng-4103	185	16	.	.	PUNCT
fumecheng-4103	186	1	this	this	PRON
fumecheng-4103	186	2	leads	lead	VERB
fumecheng-4103	186	3	to	to	ADP
fumecheng-4103	186	4	alternative	alternative	ADJ
fumecheng-4103	186	5	formulations	formulation	NOUN
fumecheng-4103	186	6	of	of	ADP
fumecheng-4103	186	7	the	the	DET
fumecheng-4103	186	8	transformations	transformation	NOUN
fumecheng-4103	186	9	in	in	ADP
fumecheng-4103	186	10	which	which	PRON
fumecheng-4103	186	11	the	the	DET
fumecheng-4103	186	12	second	second	ADJ
fumecheng-4103	186	13	derivative	derivative	NOUN
fumecheng-4103	186	14	of	of	ADP
fumecheng-4103	186	15	the	the	DET
fumecheng-4103	186	16	three	three	NUM
fumecheng-4103	186	17	-	-	PUNCT
fumecheng-4103	186	18	dimensional	dimensional	ADJ
fumecheng-4103	186	19	indentation	indentation	NOUN
fumecheng-4103	186	20	profile	profile	NOUN
fumecheng-4103	186	21	and	and	CCONJ
fumecheng-4103	186	22	the	the	DET
fumecheng-4103	186	23	deformed	deform	VERB
fumecheng-4103	186	24	elastic	elastic	ADJ
fumecheng-4103	186	25	foundation	foundation	NOUN
fumecheng-4103	186	26	occur	occur	VERB
fumecheng-4103	186	27	.	.	PUNCT
fumecheng-4103	187	1	thus	thus	ADV
fumecheng-4103	187	2	,	,	PUNCT
fumecheng-4103	187	3	singularities	singularity	NOUN
fumecheng-4103	187	4	now	now	ADV
fumecheng-4103	187	5	occur	occur	VERB
fumecheng-4103	187	6	at	at	ADP
fumecheng-4103	187	7	kinks	kink	NOUN
fumecheng-4103	187	8	of	of	ADP
fumecheng-4103	187	9	these	these	DET
fumecheng-4103	187	10	profiles	profile	NOUN
fumecheng-4103	187	11	;	;	PUNCT
fumecheng-4103	187	12	however	however	ADV
fumecheng-4103	187	13	,	,	PUNCT
fumecheng-4103	187	14	they	they	PRON
fumecheng-4103	187	15	disappear	disappear	VERB
fumecheng-4103	187	16	in	in	ADP
fumecheng-4103	187	17	the	the	DET
fumecheng-4103	187	18	numerical	numerical	ADJ
fumecheng-4103	187	19	integration	integration	NOUN
fumecheng-4103	187	20	,	,	PUNCT
fumecheng-4103	187	21	similarly	similarly	ADV
fumecheng-4103	187	22	to	to	PART
fumecheng-4103	187	23	method	method	VERB
fumecheng-4103	187	24	ii	ii	PROPN
fumecheng-4103	187	25	where	where	SCONJ
fumecheng-4103	187	26	small	small	ADJ
fumecheng-4103	187	27	increment	increment	NOUN
fumecheng-4103	187	28	h	h	NOUN
fumecheng-4103	187	29	cancels	cancel	VERB
fumecheng-4103	187	30	out	out	ADP
fumecheng-4103	187	31	in	in	ADP
fumecheng-4103	187	32	eqs	eqs	PROPN
fumecheng-4103	187	33	.	.	PUNCT
fumecheng-4103	188	1	(	(	PUNCT
fumecheng-4103	188	2	22	22	NUM
fumecheng-4103	188	3	)	)	PUNCT
fumecheng-4103	188	4	and	and	CCONJ
fumecheng-4103	188	5	(	(	PUNCT
fumecheng-4103	188	6	23	23	NUM
fumecheng-4103	188	7	)	)	PUNCT
fumecheng-4103	188	8	.	.	PUNCT
fumecheng-4103	189	1	recall	recall	NOUN
fumecheng-4103	189	2	,	,	PUNCT
fumecheng-4103	189	3	however	however	ADV
fumecheng-4103	189	4	,	,	PUNCT
fumecheng-4103	189	5	that	that	SCONJ
fumecheng-4103	189	6	the	the	DET
fumecheng-4103	189	7	singularity	singularity	NOUN
fumecheng-4103	189	8	which	which	PRON
fumecheng-4103	189	9	is	be	AUX
fumecheng-4103	189	10	overcome	overcome	VERB
fumecheng-4103	189	11	in	in	ADP
fumecheng-4103	189	12	method	method	PROPN
fumecheng-4103	189	13	ii	ii	PROPN
fumecheng-4103	189	14	occurs	occur	VERB
fumecheng-4103	189	15	in	in	ADP
fumecheng-4103	189	16	the	the	DET
fumecheng-4103	189	17	kernel	kernel	NOUN
fumecheng-4103	189	18	.	.	PUNCT
fumecheng-4103	190	1	method	method	PROPN
fumecheng-4103	190	2	iii	iii	PROPN
fumecheng-4103	190	3	,	,	PUNCT
fumecheng-4103	190	4	however	however	ADV
fumecheng-4103	190	5	,	,	PUNCT
fumecheng-4103	190	6	overcomes	overcome	VERB
fumecheng-4103	190	7	singularities	singularity	NOUN
fumecheng-4103	190	8	which	which	PRON
fumecheng-4103	190	9	may	may	AUX
fumecheng-4103	190	10	occur	occur	VERB
fumecheng-4103	190	11	through	through	ADP
fumecheng-4103	190	12	the	the	DET
fumecheng-4103	190	13	shape	shape	NOUN
fumecheng-4103	190	14	of	of	ADP
fumecheng-4103	190	15	the	the	DET
fumecheng-4103	190	16	indentation	indentation	NOUN
fumecheng-4103	190	17	profile	profile	NOUN
fumecheng-4103	190	18	or	or	CCONJ
fumecheng-4103	190	19	the	the	DET
fumecheng-4103	190	20	deformed	deform	VERB
fumecheng-4103	190	21	one	one	NUM
fumecheng-4103	190	22	-	-	PUNCT
fumecheng-4103	190	23	dimensional	dimensional	ADJ
fumecheng-4103	190	24	foundation	foundation	NOUN
fumecheng-4103	190	25	.	.	PUNCT
fumecheng-4103	191	1	also	also	ADV
fumecheng-4103	191	2	,	,	PUNCT
fumecheng-4103	191	3	the	the	DET
fumecheng-4103	191	4	singularity	singularity	NOUN
fumecheng-4103	191	5	in	in	ADP
fumecheng-4103	191	6	method	method	PROPN
fumecheng-4103	191	7	ii	ii	PROPN
fumecheng-4103	191	8	always	always	ADV
fumecheng-4103	191	9	influences	influence	VERB
fumecheng-4103	191	10	the	the	DET
fumecheng-4103	191	11	transformation	transformation	NOUN
fumecheng-4103	191	12	values	value	NOUN
fumecheng-4103	191	13	at	at	ADP
fumecheng-4103	191	14	all	all	DET
fumecheng-4103	191	15	discretization	discretization	NOUN
fumecheng-4103	191	16	points	point	NOUN
fumecheng-4103	191	17	whereas	whereas	SCONJ
fumecheng-4103	191	18	in	in	ADP
fumecheng-4103	191	19	method	method	NOUN
fumecheng-4103	191	20	iii	iii	NOUN
fumecheng-4103	191	21	the	the	DET
fumecheng-4103	191	22	singularities	singularity	NOUN
fumecheng-4103	191	23	through	through	ADP
fumecheng-4103	191	24	kinks	kink	NOUN
fumecheng-4103	191	25	may	may	AUX
fumecheng-4103	191	26	leave	leave	VERB
fumecheng-4103	191	27	transformation	transformation	NOUN
fumecheng-4103	191	28	values	value	NOUN
fumecheng-4103	191	29	at	at	ADP
fumecheng-4103	191	30	some	some	DET
fumecheng-4103	191	31	discretization	discretization	NOUN
fumecheng-4103	191	32	points	point	NOUN
fumecheng-4103	191	33	uninfluenced	uninfluenced	ADJ
fumecheng-4103	191	34	.	.	PUNCT
fumecheng-4103	192	1	in	in	ADP
fumecheng-4103	192	2	fig	fig	NOUN
fumecheng-4103	192	3	.	.	PUNCT
fumecheng-4103	193	1	5	5	NUM
fumecheng-4103	193	2	it	it	PRON
fumecheng-4103	193	3	can	can	AUX
fumecheng-4103	193	4	be	be	AUX
fumecheng-4103	193	5	seen	see	VERB
fumecheng-4103	193	6	that	that	SCONJ
fumecheng-4103	193	7	with	with	ADP
fumecheng-4103	193	8	method	method	NOUN
fumecheng-4103	193	9	iii	iii	NOUN
fumecheng-4103	193	10	the	the	DET
fumecheng-4103	193	11	number	number	NOUN
fumecheng-4103	193	12	of	of	ADP
fumecheng-4103	193	13	discretization	discretization	NOUN
fumecheng-4103	193	14	points	point	NOUN
fumecheng-4103	193	15	can	can	AUX
fumecheng-4103	193	16	substantially	substantially	ADV
fumecheng-4103	193	17	be	be	AUX
fumecheng-4103	193	18	reduced	reduce	VERB
fumecheng-4103	193	19	to	to	PART
fumecheng-4103	193	20	achieve	achieve	VERB
fumecheng-4103	193	21	the	the	DET
fumecheng-4103	193	22	same	same	ADJ
fumecheng-4103	193	23	accuracy	accuracy	NOUN
fumecheng-4103	193	24	as	as	ADP
fumecheng-4103	193	25	in	in	ADP
fumecheng-4103	193	26	method	method	PROPN
fumecheng-4103	193	27	ii	ii	PROPN
fumecheng-4103	193	28	.	.	PUNCT
fumecheng-4103	194	1	however	however	ADV
fumecheng-4103	194	2	,	,	PUNCT
fumecheng-4103	194	3	it	it	PRON
fumecheng-4103	194	4	stands	stand	VERB
fumecheng-4103	194	5	out	out	ADP
fumecheng-4103	194	6	that	that	SCONJ
fumecheng-4103	194	7	the	the	DET
fumecheng-4103	194	8	maximum	maximum	ADJ
fumecheng-4103	194	9	error	error	NOUN
fumecheng-4103	194	10	in	in	ADP
fumecheng-4103	194	11	method	method	NOUN
fumecheng-4103	194	12	iii	iii	NUM
fumecheng-4103	194	13	is	be	AUX
fumecheng-4103	194	14	still	still	ADV
fumecheng-4103	194	15	fairly	fairly	ADV
fumecheng-4103	194	16	close	close	ADJ
fumecheng-4103	194	17	to	to	ADP
fumecheng-4103	194	18	the	the	DET
fumecheng-4103	194	19	maximum	maximum	ADJ
fumecheng-4103	194	20	error	error	NOUN
fumecheng-4103	194	21	in	in	ADP
fumecheng-4103	194	22	method	method	PROPN
fumecheng-4103	194	23	ii	ii	PROPN
fumecheng-4103	194	24	.	.	PUNCT
fumecheng-4103	195	1	this	this	DET
fumecheng-4103	195	2	relatively	relatively	ADV
fumecheng-4103	195	3	high	high	ADJ
fumecheng-4103	195	4	maximum	maximum	ADJ
fumecheng-4103	195	5	error	error	NOUN
fumecheng-4103	195	6	of	of	ADP
fumecheng-4103	195	7	method	method	NOUN
fumecheng-4103	195	8	iii	iii	NOUN
fumecheng-4103	195	9	is	be	AUX
fumecheng-4103	195	10	generally	generally	ADV
fumecheng-4103	195	11	attained	attain	VERB
fumecheng-4103	195	12	at	at	ADP
fumecheng-4103	195	13	the	the	DET
fumecheng-4103	195	14	end	end	NOUN
fumecheng-4103	195	15	of	of	ADP
fumecheng-4103	195	16	the	the	DET
fumecheng-4103	195	17	contact	contact	NOUN
fumecheng-4103	195	18	area	area	NOUN
fumecheng-4103	195	19	.	.	PUNCT
fumecheng-4103	196	1	method	method	NOUN
fumecheng-4103	196	2	iv	iv	NUM
fumecheng-4103	196	3	–	–	PUNCT
fumecheng-4103	196	4	partial	partial	ADJ
fumecheng-4103	196	5	integration	integration	NOUN
fumecheng-4103	196	6	method	method	NOUN
fumecheng-4103	196	7	with	with	ADP
fumecheng-4103	196	8	small	small	ADJ
fumecheng-4103	196	9	adjustment	adjustment	NOUN
fumecheng-4103	196	10	:	:	PUNCT
fumecheng-4103	196	11	the	the	DET
fumecheng-4103	196	12	previously	previously	ADV
fumecheng-4103	196	13	described	describe	VERB
fumecheng-4103	196	14	relatively	relatively	ADV
fumecheng-4103	196	15	high	high	ADJ
fumecheng-4103	196	16	maximum	maximum	ADJ
fumecheng-4103	196	17	error	error	NOUN
fumecheng-4103	196	18	of	of	ADP
fumecheng-4103	196	19	method	method	NOUN
fumecheng-4103	196	20	iii	iii	NOUN
fumecheng-4103	196	21	is	be	AUX
fumecheng-4103	196	22	reduced	reduce	VERB
fumecheng-4103	196	23	in	in	ADP
fumecheng-4103	196	24	method	method	NOUN
fumecheng-4103	196	25	iv	iv	NUM
fumecheng-4103	196	26	.	.	PUNCT
fumecheng-4103	197	1	the	the	DET
fumecheng-4103	197	2	simple	simple	ADJ
fumecheng-4103	197	3	adjustment	adjustment	NOUN
fumecheng-4103	197	4	through	through	ADP
fumecheng-4103	197	5	the	the	DET
fumecheng-4103	197	6	insertion	insertion	NOUN
fumecheng-4103	197	7	of	of	ADP
fumecheng-4103	197	8	an	an	DET
fumecheng-4103	197	9	additional	additional	ADJ
fumecheng-4103	197	10	discretization	discretization	NOUN
fumecheng-4103	197	11	point	point	NOUN
fumecheng-4103	197	12	at	at	ADP
fumecheng-4103	197	13	the	the	DET
fumecheng-4103	197	14	end	end	NOUN
fumecheng-4103	197	15	of	of	ADP
fumecheng-4103	197	16	the	the	DET
fumecheng-4103	197	17	contact	contact	NOUN
fumecheng-4103	197	18	area	area	NOUN
fumecheng-4103	197	19	is	be	AUX
fumecheng-4103	197	20	described	describe	VERB
fumecheng-4103	197	21	in	in	ADP
fumecheng-4103	197	22	section	section	NOUN
fumecheng-4103	197	23	6	6	NUM
fumecheng-4103	197	24	above	above	ADP
fumecheng-4103	197	25	.	.	PUNCT
fumecheng-4103	198	1	in	in	ADP
fumecheng-4103	198	2	fig	fig	NOUN
fumecheng-4103	198	3	.	.	PUNCT
fumecheng-4103	199	1	5	5	NUM
fumecheng-4103	199	2	it	it	PRON
fumecheng-4103	199	3	can	can	AUX
fumecheng-4103	199	4	be	be	AUX
fumecheng-4103	199	5	seen	see	VERB
fumecheng-4103	199	6	that	that	SCONJ
fumecheng-4103	199	7	with	with	ADP
fumecheng-4103	199	8	the	the	DET
fumecheng-4103	199	9	method	method	NOUN
fumecheng-4103	199	10	iv	iv	VERB
fumecheng-4103	199	11	the	the	DET
fumecheng-4103	199	12	number	number	NOUN
fumecheng-4103	199	13	of	of	ADP
fumecheng-4103	199	14	discretization	discretization	NOUN
fumecheng-4103	199	15	points	point	NOUN
fumecheng-4103	199	16	can	can	AUX
fumecheng-4103	199	17	further	far	ADV
fumecheng-4103	199	18	be	be	AUX
fumecheng-4103	199	19	reduced	reduce	VERB
fumecheng-4103	199	20	to	to	PART
fumecheng-4103	199	21	achieve	achieve	VERB
fumecheng-4103	199	22	a	a	DET
fumecheng-4103	199	23	certain	certain	ADJ
fumecheng-4103	199	24	desired	desire	VERB
fumecheng-4103	199	25	accuracy	accuracy	NOUN
fumecheng-4103	199	26	.	.	PUNCT
fumecheng-4103	200	1	136	136	NUM
fumecheng-4103	200	2	j.	j.	PROPN
fumecheng-4103	200	3	benad	benad	PROPN
fumecheng-4103	200	4	a	a	DET
fumecheng-4103	200	5	)	)	PUNCT
fumecheng-4103	200	6	b	b	NOUN
fumecheng-4103	200	7	)	)	PUNCT
fumecheng-4103	200	8	fig	fig	NOUN
fumecheng-4103	200	9	.	.	PUNCT
fumecheng-4103	201	1	5	5	NUM
fumecheng-4103	201	2	upper	upper	ADJ
fumecheng-4103	201	3	limits	limit	NOUN
fumecheng-4103	201	4	of	of	ADP
fumecheng-4103	201	5	the	the	DET
fumecheng-4103	201	6	maximum	maximum	ADJ
fumecheng-4103	201	7	absolute	absolute	ADJ
fumecheng-4103	201	8	error	error	NOUN
fumecheng-4103	201	9	of	of	ADP
fumecheng-4103	201	10	pn	pn	PROPN
fumecheng-4103	201	11	(	(	PUNCT
fumecheng-4103	201	12	left	leave	VERB
fumecheng-4103	201	13	graph	graph	NOUN
fumecheng-4103	201	14	a	a	PRON
fumecheng-4103	201	15	)	)	PUNCT
fumecheng-4103	201	16	and	and	CCONJ
fumecheng-4103	201	17	the	the	DET
fumecheng-4103	201	18	mean	mean	ADJ
fumecheng-4103	201	19	absolute	absolute	ADJ
fumecheng-4103	201	20	error	error	NOUN
fumecheng-4103	201	21	of	of	ADP
fumecheng-4103	201	22	pn	pn	PROPN
fumecheng-4103	201	23	(	(	PUNCT
fumecheng-4103	201	24	right	right	ADJ
fumecheng-4103	201	25	graph	graph	NOUN
fumecheng-4103	201	26	b	b	NOUN
fumecheng-4103	201	27	)	)	PUNCT
fumecheng-4103	201	28	compared	compare	VERB
fumecheng-4103	201	29	for	for	ADP
fumecheng-4103	201	30	the	the	DET
fumecheng-4103	201	31	different	different	ADJ
fumecheng-4103	201	32	numerical	numerical	ADJ
fumecheng-4103	201	33	methods	method	NOUN
fumecheng-4103	201	34	:	:	PUNCT
fumecheng-4103	201	35	method	method	VERB
fumecheng-4103	201	36	i	i	PRON
fumecheng-4103	201	37	–	–	PUNCT
fumecheng-4103	201	38	insertion	insertion	NOUN
fumecheng-4103	201	39	of	of	ADP
fumecheng-4103	201	40	h	h	NOUN
fumecheng-4103	201	41	at	at	ADP
fumecheng-4103	201	42	singularity	singularity	NOUN
fumecheng-4103	201	43	,	,	PUNCT
fumecheng-4103	201	44	method	method	NOUN
fumecheng-4103	201	45	ii	ii	PROPN
fumecheng-4103	201	46	–	–	PUNCT
fumecheng-4103	201	47	implementation	implementation	NOUN
fumecheng-4103	201	48	of	of	ADP
fumecheng-4103	201	49	the	the	DET
fumecheng-4103	201	50	kernel	kernel	NOUN
fumecheng-4103	201	51	with	with	ADP
fumecheng-4103	201	52	its	its	PRON
fumecheng-4103	201	53	antiderivative	antiderivative	ADJ
fumecheng-4103	201	54	,	,	PUNCT
fumecheng-4103	201	55	method	method	NOUN
fumecheng-4103	201	56	iii	iii	NUM
fumecheng-4103	201	57	–	–	PUNCT
fumecheng-4103	201	58	partial	partial	ADJ
fumecheng-4103	201	59	integration	integration	NOUN
fumecheng-4103	201	60	method	method	NOUN
fumecheng-4103	201	61	(	(	PUNCT
fumecheng-4103	201	62	technique	technique	NOUN
fumecheng-4103	201	63	from	from	ADP
fumecheng-4103	201	64	this	this	DET
fumecheng-4103	201	65	paper	paper	NOUN
fumecheng-4103	201	66	)	)	PUNCT
fumecheng-4103	201	67	,	,	PUNCT
fumecheng-4103	201	68	method	method	NOUN
fumecheng-4103	201	69	iv	iv	NUM
fumecheng-4103	201	70	–	–	PUNCT
fumecheng-4103	201	71	partial	partial	ADJ
fumecheng-4103	201	72	integration	integration	NOUN
fumecheng-4103	201	73	method	method	NOUN
fumecheng-4103	201	74	with	with	ADP
fumecheng-4103	201	75	small	small	ADJ
fumecheng-4103	201	76	adjustment	adjustment	NOUN
fumecheng-4103	201	77	(	(	PUNCT
fumecheng-4103	201	78	refined	refined	ADJ
fumecheng-4103	201	79	technique	technique	NOUN
fumecheng-4103	201	80	from	from	ADP
fumecheng-4103	201	81	this	this	DET
fumecheng-4103	201	82	paper	paper	NOUN
fumecheng-4103	201	83	)	)	PUNCT
fumecheng-4103	201	84	.	.	PUNCT
fumecheng-4103	202	1	as	as	ADP
fumecheng-4103	202	2	before	before	ADV
fumecheng-4103	202	3	,	,	PUNCT
fumecheng-4103	202	4	the	the	DET
fumecheng-4103	202	5	curves	curve	NOUN
fumecheng-4103	202	6	are	be	AUX
fumecheng-4103	202	7	displayed	display	VERB
fumecheng-4103	202	8	for	for	ADP
fumecheng-4103	202	9	the	the	DET
fumecheng-4103	202	10	exemplary	exemplary	ADJ
fumecheng-4103	202	11	inputs	input	NOUN
fumecheng-4103	202	12	of	of	ADP
fumecheng-4103	202	13	l	l	NOUN
fumecheng-4103	202	14	=	=	SYM
fumecheng-4103	202	15	1	1	NUM
fumecheng-4103	202	16	,	,	PUNCT
fumecheng-4103	202	17	e	e	NOUN
fumecheng-4103	202	18	*	*	PUNCT
fumecheng-4103	202	19	=	=	SYM
fumecheng-4103	202	20	1	1	NUM
fumecheng-4103	202	21	,	,	PUNCT
fumecheng-4103	202	22	d	d	NOUN
fumecheng-4103	202	23	=	=	PUNCT
fumecheng-4103	202	24	0.3	0.3	NUM
fumecheng-4103	202	25	and	and	CCONJ
fumecheng-4103	202	26	here	here	ADV
fumecheng-4103	202	27	only	only	ADV
fumecheng-4103	202	28	for	for	ADP
fumecheng-4103	202	29	the	the	DET
fumecheng-4103	202	30	exemplary	exemplary	ADJ
fumecheng-4103	202	31	parabolic	parabolic	PROPN
fumecheng-4103	202	32	indenter	indenter	NOUN
fumecheng-4103	202	33	given	give	VERB
fumecheng-4103	202	34	with	with	ADP
fumecheng-4103	202	35	f(r	f(r	NOUN
fumecheng-4103	202	36	)	)	PUNCT
fumecheng-4103	203	1	=	=	SYM
fumecheng-4103	203	2	r	r	NOUN
fumecheng-4103	203	3	2	2	NUM
fumecheng-4103	203	4	/2	/2	NUM
fumecheng-4103	203	5	8	8	NUM
fumecheng-4103	203	6	.	.	PUNCT
fumecheng-4103	203	7	exemplary	exemplary	NOUN
fumecheng-4103	203	8	wear	wear	NOUN
fumecheng-4103	203	9	simulation	simulation	NOUN
fumecheng-4103	203	10	apart	apart	ADV
fumecheng-4103	203	11	from	from	ADP
fumecheng-4103	203	12	a	a	DET
fumecheng-4103	203	13	high	high	ADJ
fumecheng-4103	203	14	accuracy	accuracy	NOUN
fumecheng-4103	203	15	,	,	PUNCT
fumecheng-4103	203	16	method	method	NOUN
fumecheng-4103	203	17	iii	iii	NOUN
fumecheng-4103	203	18	and	and	CCONJ
fumecheng-4103	203	19	method	method	NOUN
fumecheng-4103	203	20	iv	iv	NUM
fumecheng-4103	203	21	may	may	AUX
fumecheng-4103	203	22	also	also	ADV
fumecheng-4103	203	23	show	show	VERB
fumecheng-4103	203	24	an	an	DET
fumecheng-4103	203	25	advantage	advantage	NOUN
fumecheng-4103	203	26	when	when	SCONJ
fumecheng-4103	203	27	they	they	PRON
fumecheng-4103	203	28	are	be	AUX
fumecheng-4103	203	29	used	use	VERB
fumecheng-4103	203	30	multiple	multiple	ADJ
fumecheng-4103	203	31	times	time	NOUN
fumecheng-4103	203	32	on	on	ADP
fumecheng-4103	203	33	a	a	DET
fumecheng-4103	203	34	changing	change	VERB
fumecheng-4103	203	35	indentation	indentation	NOUN
fumecheng-4103	203	36	profile	profile	NOUN
fumecheng-4103	203	37	,	,	PUNCT
fumecheng-4103	203	38	such	such	ADJ
fumecheng-4103	203	39	as	as	ADP
fumecheng-4103	203	40	in	in	ADP
fumecheng-4103	203	41	wear	wear	NOUN
fumecheng-4103	203	42	simulations	simulation	NOUN
fumecheng-4103	203	43	.	.	PUNCT
fumecheng-4103	204	1	as	as	ADP
fumecheng-4103	204	2	an	an	DET
fumecheng-4103	204	3	example	example	NOUN
fumecheng-4103	204	4	,	,	PUNCT
fumecheng-4103	204	5	consider	consider	VERB
fumecheng-4103	204	6	a	a	DET
fumecheng-4103	204	7	heterogeneous	heterogeneous	ADJ
fumecheng-4103	204	8	cylinder	cylinder	NOUN
fumecheng-4103	204	9	which	which	PRON
fumecheng-4103	204	10	is	be	AUX
fumecheng-4103	204	11	pressed	press	VERB
fumecheng-4103	204	12	onto	onto	ADP
fumecheng-4103	204	13	an	an	DET
fumecheng-4103	204	14	elastic	elastic	ADJ
fumecheng-4103	204	15	half	half	ADJ
fumecheng-4103	204	16	-	-	PUNCT
fumecheng-4103	204	17	space	space	NOUN
fumecheng-4103	204	18	with	with	ADP
fumecheng-4103	204	19	normal	normal	ADJ
fumecheng-4103	204	20	force	force	NOUN
fumecheng-4103	204	21	fn	fn	NOUN
fumecheng-4103	204	22	and	and	CCONJ
fumecheng-4103	204	23	moves	move	VERB
fumecheng-4103	204	24	tangentially	tangentially	ADV
fumecheng-4103	204	25	with	with	ADP
fumecheng-4103	204	26	velocity	velocity	NOUN
fumecheng-4103	204	27	v0	v0	NOUN
fumecheng-4103	204	28	.	.	PUNCT
fumecheng-4103	205	1	the	the	DET
fumecheng-4103	205	2	cylinder	cylinder	NOUN
fumecheng-4103	205	3	shall	shall	AUX
fumecheng-4103	205	4	be	be	AUX
fumecheng-4103	205	5	composed	compose	VERB
fumecheng-4103	205	6	of	of	ADP
fumecheng-4103	205	7	rings	ring	NOUN
fumecheng-4103	205	8	of	of	ADP
fumecheng-4103	205	9	different	different	ADJ
fumecheng-4103	205	10	material	material	NOUN
fumecheng-4103	205	11	having	have	VERB
fumecheng-4103	205	12	the	the	DET
fumecheng-4103	205	13	same	same	ADJ
fumecheng-4103	205	14	elastic	elastic	ADJ
fumecheng-4103	205	15	properties	property	NOUN
fumecheng-4103	205	16	but	but	CCONJ
fumecheng-4103	205	17	different	different	ADJ
fumecheng-4103	205	18	wear	wear	NOUN
fumecheng-4103	205	19	coefficients	coefficient	NOUN
fumecheng-4103	205	20	k1	k1	NOUN
fumecheng-4103	205	21	and	and	CCONJ
fumecheng-4103	205	22	k2	k2	PROPN
fumecheng-4103	205	23	(	(	PUNCT
fumecheng-4103	205	24	see	see	VERB
fumecheng-4103	205	25	fig	fig	NOUN
fumecheng-4103	205	26	.	.	PUNCT
fumecheng-4103	206	1	6a	6a	NOUN
fumecheng-4103	206	2	)	)	PUNCT
fumecheng-4103	206	3	.	.	PUNCT
fumecheng-4103	207	1	this	this	DET
fumecheng-4103	207	2	setup	setup	NOUN
fumecheng-4103	207	3	has	have	AUX
fumecheng-4103	207	4	recently	recently	ADV
fumecheng-4103	207	5	been	be	AUX
fumecheng-4103	207	6	studied	study	VERB
fumecheng-4103	207	7	with	with	ADP
fumecheng-4103	207	8	the	the	DET
fumecheng-4103	207	9	mdr	mdr	PROPN
fumecheng-4103	207	10	by	by	ADP
fumecheng-4103	207	11	li	li	PROPN
fumecheng-4103	207	12	et	et	PROPN
fumecheng-4103	207	13	al	al	PROPN
fumecheng-4103	207	14	.	.	PUNCT
fumecheng-4103	208	1	[	[	X
fumecheng-4103	208	2	6	6	NUM
fumecheng-4103	208	3	]	]	PUNCT
fumecheng-4103	208	4	using	use	VERB
fumecheng-4103	208	5	archard	archard	NOUN
fumecheng-4103	208	6	’s	’s	PART
fumecheng-4103	208	7	law	law	NOUN
fumecheng-4103	208	8	[	[	X
fumecheng-4103	208	9	12	12	NUM
fumecheng-4103	208	10	]	]	PUNCT
fumecheng-4103	208	11	n	n	CCONJ
fumecheng-4103	208	12	wear	wear	VERB
fumecheng-4103	208	13	0	0	NUM
fumecheng-4103	208	14	(	(	PUNCT
fumecheng-4103	208	15	)	)	PUNCT
fumecheng-4103	208	16	(	(	PUNCT
fumecheng-4103	208	17	)	)	PUNCT
fumecheng-4103	208	18	f	f	PROPN
fumecheng-4103	208	19	s	s	PROPN
fumecheng-4103	208	20	v	v	PROPN
fumecheng-4103	208	21	k	k	PROPN
fumecheng-4103	208	22	r	r	NOUN
fumecheng-4103	208	23	r	r	PROPN
fumecheng-4103	208	24			NOUN
fumecheng-4103	208	25			NUM
fumecheng-4103	208	26	(	(	PUNCT
fumecheng-4103	208	27	24	24	NUM
fumecheng-4103	208	28	)	)	PUNCT
fumecheng-4103	208	29	to	to	PART
fumecheng-4103	208	30	model	model	VERB
fumecheng-4103	208	31	the	the	DET
fumecheng-4103	208	32	change	change	NOUN
fumecheng-4103	208	33	of	of	ADP
fumecheng-4103	208	34	the	the	DET
fumecheng-4103	208	35	indentation	indentation	NOUN
fumecheng-4103	208	36	profile	profile	NOUN
fumecheng-4103	208	37	due	due	ADJ
fumecheng-4103	208	38	to	to	PART
fumecheng-4103	208	39	wear	wear	VERB
fumecheng-4103	208	40	.	.	PUNCT
fumecheng-4103	209	1	therein	therein	ADV
fumecheng-4103	209	2	,	,	PUNCT
fumecheng-4103	209	3	kwear(r	kwear(r	NOUN
fumecheng-4103	209	4	)	)	PUNCT
fumecheng-4103	209	5	and	and	CCONJ
fumecheng-4103	209	6	σ0(r	σ0(r	PROPN
fumecheng-4103	209	7	)	)	PUNCT
fumecheng-4103	209	8	are	be	AUX
fumecheng-4103	209	9	wear	wear	VERB
fumecheng-4103	209	10	coefficient	coefficient	NOUN
fumecheng-4103	209	11	,	,	PUNCT
fumecheng-4103	209	12	that	that	ADV
fumecheng-4103	209	13	is	is	ADV
fumecheng-4103	209	14	,	,	PUNCT
fumecheng-4103	209	15	hardness	hardness	ADJ
fumecheng-4103	209	16	,	,	PUNCT
fumecheng-4103	209	17	and	and	CCONJ
fumecheng-4103	209	18	with	with	ADP
fumecheng-4103	209	19	k(r	k(r	PROPN
fumecheng-4103	209	20	)	)	PUNCT
fumecheng-4103	209	21	=	=	SYM
fumecheng-4103	209	22	kwear(r	kwear(r	NOUN
fumecheng-4103	209	23	)	)	PUNCT
fumecheng-4103	209	24	/	/	SYM
fumecheng-4103	210	1	σ0(r	σ0(r	PROPN
fumecheng-4103	210	2	)	)	PUNCT
fumecheng-4103	210	3	the	the	DET
fumecheng-4103	210	4	linear	linear	ADJ
fumecheng-4103	210	5	wear	wear	NOUN
fumecheng-4103	210	6	is	be	AUX
fumecheng-4103	210	7	0	0	NUM
fumecheng-4103	210	8	(	(	PUNCT
fumecheng-4103	210	9	)	)	PUNCT
fumecheng-4103	210	10	(	(	PUNCT
fumecheng-4103	210	11	)	)	PUNCT
fumecheng-4103	211	1	(	(	PUNCT
fumecheng-4103	211	2	)	)	PUNCT
fumecheng-4103	211	3	f	f	X
fumecheng-4103	211	4	r	r	NOUN
fumecheng-4103	212	1	k	k	NOUN
fumecheng-4103	213	1	r	r	NOUN
fumecheng-4103	213	2	p	p	NOUN
fumecheng-4103	213	3	r	r	NOUN
fumecheng-4103	213	4	v	v	ADP
fumecheng-4103	213	5	t	t	NOUN
fumecheng-4103	213	6			NUM
fumecheng-4103	213	7			NOUN
fumecheng-4103	213	8	.	.	PUNCT
fumecheng-4103	214	1	(	(	PUNCT
fumecheng-4103	214	2	25	25	NUM
fumecheng-4103	214	3	)	)	PUNCT
fumecheng-4103	214	4	in	in	ADP
fumecheng-4103	214	5	the	the	DET
fumecheng-4103	214	6	following	following	NOUN
fumecheng-4103	214	7	,	,	PUNCT
fumecheng-4103	214	8	the	the	DET
fumecheng-4103	214	9	same	same	ADJ
fumecheng-4103	214	10	procedure	procedure	NOUN
fumecheng-4103	214	11	is	be	AUX
fumecheng-4103	214	12	adopted	adopt	VERB
fumecheng-4103	214	13	.	.	PUNCT
fumecheng-4103	215	1	it	it	PRON
fumecheng-4103	215	2	shows	show	VERB
fumecheng-4103	215	3	that	that	SCONJ
fumecheng-4103	215	4	the	the	DET
fumecheng-4103	215	5	numerical	numerical	ADJ
fumecheng-4103	215	6	method	method	NOUN
fumecheng-4103	215	7	which	which	PRON
fumecheng-4103	215	8	is	be	AUX
fumecheng-4103	215	9	used	use	VERB
fumecheng-4103	215	10	for	for	ADP
fumecheng-4103	215	11	the	the	DET
fumecheng-4103	215	12	mdr	mdr	PROPN
fumecheng-4103	215	13	transformations	transformation	NOUN
fumecheng-4103	215	14	has	have	VERB
fumecheng-4103	215	15	a	a	DET
fumecheng-4103	215	16	significant	significant	ADJ
fumecheng-4103	215	17	impact	impact	NOUN
fumecheng-4103	215	18	on	on	ADP
fumecheng-4103	215	19	the	the	DET
fumecheng-4103	215	20	quality	quality	NOUN
fumecheng-4103	215	21	of	of	ADP
fumecheng-4103	215	22	the	the	DET
fumecheng-4103	215	23	simulation	simulation	NOUN
fumecheng-4103	215	24	results	result	VERB
fumecheng-4103	215	25	.	.	PUNCT
fumecheng-4103	216	1	the	the	DET
fumecheng-4103	216	2	limiting	limit	VERB
fumecheng-4103	216	3	profile	profile	NOUN
fumecheng-4103	216	4	and	and	CCONJ
fumecheng-4103	216	5	pressure	pressure	NOUN
fumecheng-4103	216	6	reached	reach	VERB
fumecheng-4103	216	7	after	after	SCONJ
fumecheng-4103	216	8	a	a	DET
fumecheng-4103	216	9	long	long	ADJ
fumecheng-4103	216	10	enough	enough	ADJ
fumecheng-4103	216	11	wear	wear	NOUN
fumecheng-4103	216	12	process	process	NOUN
fumecheng-4103	216	13	are	be	AUX
fumecheng-4103	216	14	both	both	PRON
fumecheng-4103	216	15	displayed	display	VERB
fumecheng-4103	216	16	in	in	ADP
fumecheng-4103	216	17	fig	fig	NOUN
fumecheng-4103	216	18	.	.	PUNCT
fumecheng-4103	217	1	6b	6b	NOUN
fumecheng-4103	217	2	.	.	PUNCT
fumecheng-4103	218	1	profile	profile	PROPN
fumecheng-4103	218	2	f	f	PROPN
fumecheng-4103	218	3	is	be	AUX
fumecheng-4103	218	4	normalized	normalize	VERB
fumecheng-4103	218	5	with	with	ADP
fumecheng-4103	218	6	initial	initial	ADJ
fumecheng-4103	218	7	indentation	indentation	NOUN
fumecheng-4103	218	8	depth	depth	NOUN
fumecheng-4103	218	9	d0	d0	NOUN
fumecheng-4103	218	10	=	=	SYM
fumecheng-4103	218	11	fn	fn	NOUN
fumecheng-4103	218	12	/	/	SYM
fumecheng-4103	218	13	(	(	PUNCT
fumecheng-4103	218	14	2ae	2ae	NOUN
fumecheng-4103	218	15	*	*	PUNCT
fumecheng-4103	218	16	)	)	PUNCT
fumecheng-4103	218	17	and	and	CCONJ
fumecheng-4103	218	18	the	the	DET
fumecheng-4103	218	19	pressure	pressure	NOUN
fumecheng-4103	218	20	distribution	distribution	NOUN
fumecheng-4103	218	21	is	be	AUX
fumecheng-4103	218	22	normalized	normalize	VERB
fumecheng-4103	218	23	with	with	ADP
fumecheng-4103	218	24	p0	p0	NOUN
fumecheng-4103	218	25	=	=	SYM
fumecheng-4103	218	26	fn	fn	NOUN
fumecheng-4103	218	27	/	/	SYM
fumecheng-4103	218	28	(	(	PUNCT
fumecheng-4103	218	29	2πa	2πa	NOUN
fumecheng-4103	218	30	2	2	NUM
fumecheng-4103	218	31	)	)	PUNCT
fumecheng-4103	218	32	.	.	PUNCT
fumecheng-4103	219	1	as	as	SCONJ
fumecheng-4103	219	2	can	can	AUX
fumecheng-4103	219	3	be	be	AUX
fumecheng-4103	219	4	seen	see	VERB
fumecheng-4103	219	5	in	in	ADP
fumecheng-4103	219	6	fig	fig	NOUN
fumecheng-4103	219	7	.	.	PUNCT
fumecheng-4103	220	1	6b	6b	NOUN
fumecheng-4103	220	2	,	,	PUNCT
fumecheng-4103	220	3	the	the	DET
fumecheng-4103	220	4	use	use	NOUN
fumecheng-4103	220	5	of	of	ADP
fumecheng-4103	220	6	method	method	PROPN
fumecheng-4103	220	7	ii	ii	PROPN
fumecheng-4103	220	8	to	to	PART
fumecheng-4103	220	9	perform	perform	VERB
fumecheng-4103	220	10	the	the	DET
fumecheng-4103	220	11	transformations	transformation	NOUN
fumecheng-4103	220	12	leads	lead	VERB
fumecheng-4103	220	13	to	to	ADP
fumecheng-4103	220	14	an	an	DET
fumecheng-4103	220	15	oscillating	oscillating	NOUN
fumecheng-4103	220	16	error	error	NOUN
fumecheng-4103	220	17	in	in	ADP
fumecheng-4103	220	18	the	the	DET
fumecheng-4103	220	19	results	result	NOUN
fumecheng-4103	220	20	for	for	ADP
fumecheng-4103	220	21	both	both	CCONJ
fumecheng-4103	220	22	the	the	DET
fumecheng-4103	220	23	profile	profile	NOUN
fumecheng-4103	220	24	and	and	CCONJ
fumecheng-4103	220	25	the	the	DET
fumecheng-4103	220	26	pressure	pressure	NOUN
fumecheng-4103	220	27	(	(	PUNCT
fumecheng-4103	220	28	a	a	DET
fumecheng-4103	220	29	thin	thin	ADJ
fumecheng-4103	220	30	grey	grey	ADJ
fumecheng-4103	220	31	jagged	jagged	ADJ
fumecheng-4103	220	32	line	line	NOUN
fumecheng-4103	220	33	)	)	PUNCT
fumecheng-4103	220	34	.	.	PUNCT
fumecheng-4103	221	1	this	this	DET
fumecheng-4103	221	2	error	error	NOUN
fumecheng-4103	221	3	does	do	AUX
fumecheng-4103	221	4	not	not	PART
fumecheng-4103	221	5	occur	occur	VERB
fumecheng-4103	221	6	when	when	SCONJ
fumecheng-4103	221	7	method	method	NOUN
fumecheng-4103	221	8	iii	iii	NOUN
fumecheng-4103	221	9	or	or	CCONJ
fumecheng-4103	221	10	method	method	NOUN
fumecheng-4103	221	11	iv	iv	NUM
fumecheng-4103	221	12	are	be	AUX
fumecheng-4103	221	13	used	use	VERB
fumecheng-4103	221	14	(	(	PUNCT
fumecheng-4103	221	15	a	a	DET
fumecheng-4103	221	16	smooth	smooth	ADJ
fumecheng-4103	221	17	bold	bold	ADJ
fumecheng-4103	221	18	line	line	NOUN
fumecheng-4103	221	19	)	)	PUNCT
fumecheng-4103	221	20	.	.	PUNCT
fumecheng-4103	222	1	for	for	ADP
fumecheng-4103	222	2	an	an	DET
fumecheng-4103	222	3	increasing	increase	VERB
fumecheng-4103	222	4	fast	fast	ADJ
fumecheng-4103	222	5	numerical	numerical	ADJ
fumecheng-4103	222	6	implementation	implementation	NOUN
fumecheng-4103	222	7	of	of	ADP
fumecheng-4103	222	8	the	the	DET
fumecheng-4103	222	9	mdr	mdr	PROPN
fumecheng-4103	222	10	transformations	transformation	VERB
fumecheng-4103	222	11	137	137	NUM
fumecheng-4103	222	12	number	number	NOUN
fumecheng-4103	222	13	of	of	ADP
fumecheng-4103	222	14	discretization	discretization	NOUN
fumecheng-4103	222	15	points	point	NOUN
fumecheng-4103	222	16	or	or	CCONJ
fumecheng-4103	222	17	smaller	small	ADJ
fumecheng-4103	222	18	time	time	NOUN
fumecheng-4103	222	19	steps	step	NOUN
fumecheng-4103	222	20	in	in	ADP
fumecheng-4103	222	21	the	the	DET
fumecheng-4103	222	22	wear	wear	NOUN
fumecheng-4103	222	23	simulation	simulation	NOUN
fumecheng-4103	222	24	the	the	DET
fumecheng-4103	222	25	oscillating	oscillating	NOUN
fumecheng-4103	222	26	error	error	NOUN
fumecheng-4103	222	27	which	which	PRON
fumecheng-4103	222	28	occurs	occur	VERB
fumecheng-4103	222	29	with	with	ADP
fumecheng-4103	222	30	method	method	PROPN
fumecheng-4103	222	31	ii	ii	PROPN
fumecheng-4103	222	32	does	do	AUX
fumecheng-4103	222	33	not	not	PART
fumecheng-4103	222	34	vanish	vanish	VERB
fumecheng-4103	222	35	although	although	SCONJ
fumecheng-4103	222	36	it	it	PRON
fumecheng-4103	222	37	can	can	AUX
fumecheng-4103	222	38	be	be	AUX
fumecheng-4103	222	39	smoothed	smooth	VERB
fumecheng-4103	222	40	out	out	ADP
fumecheng-4103	222	41	in	in	ADP
fumecheng-4103	222	42	the	the	DET
fumecheng-4103	222	43	post	post	ADJ
fumecheng-4103	222	44	-	-	ADJ
fumecheng-4103	222	45	processing	processing	NOUN
fumecheng-4103	222	46	.	.	PUNCT
fumecheng-4103	223	1	method	method	PROPN
fumecheng-4103	223	2	iii	iii	PROPN
fumecheng-4103	223	3	and	and	CCONJ
fumecheng-4103	223	4	iv	iv	NUM
fumecheng-4103	223	5	,	,	PUNCT
fumecheng-4103	223	6	however	however	ADV
fumecheng-4103	223	7	,	,	PUNCT
fumecheng-4103	223	8	deliver	deliver	VERB
fumecheng-4103	223	9	the	the	DET
fumecheng-4103	223	10	undistorted	undistorted	ADJ
fumecheng-4103	223	11	results	result	NOUN
fumecheng-4103	223	12	straight	straight	ADV
fumecheng-4103	223	13	away	away	ADV
fumecheng-4103	223	14	without	without	ADP
fumecheng-4103	223	15	the	the	DET
fumecheng-4103	223	16	requirement	requirement	NOUN
fumecheng-4103	223	17	for	for	ADP
fumecheng-4103	223	18	subsequent	subsequent	ADJ
fumecheng-4103	223	19	corrections	correction	NOUN
fumecheng-4103	223	20	.	.	PUNCT
fumecheng-4103	224	1	note	note	VERB
fumecheng-4103	224	2	that	that	SCONJ
fumecheng-4103	224	3	these	these	DET
fumecheng-4103	224	4	raw	raw	ADJ
fumecheng-4103	224	5	results	result	NOUN
fumecheng-4103	224	6	of	of	ADP
fumecheng-4103	224	7	the	the	DET
fumecheng-4103	224	8	exemplary	exemplary	ADJ
fumecheng-4103	224	9	simulation	simulation	NOUN
fumecheng-4103	224	10	obtained	obtain	VERB
fumecheng-4103	224	11	using	use	VERB
fumecheng-4103	224	12	method	method	NOUN
fumecheng-4103	224	13	iii	iii	NOUN
fumecheng-4103	224	14	and	and	CCONJ
fumecheng-4103	224	15	method	method	NOUN
fumecheng-4103	224	16	iv	iv	NUM
fumecheng-4103	224	17	also	also	ADV
fumecheng-4103	224	18	reproduce	reproduce	VERB
fumecheng-4103	224	19	results	result	NOUN
fumecheng-4103	224	20	obtained	obtain	VERB
fumecheng-4103	224	21	for	for	ADP
fumecheng-4103	224	22	validation	validation	NOUN
fumecheng-4103	224	23	purposes	purpose	NOUN
fumecheng-4103	224	24	in	in	ADP
fumecheng-4103	224	25	[	[	X
fumecheng-4103	224	26	6	6	NUM
fumecheng-4103	224	27	]	]	PUNCT
fumecheng-4103	224	28	with	with	ADP
fumecheng-4103	224	29	the	the	DET
fumecheng-4103	224	30	boundary	boundary	ADJ
fumecheng-4103	224	31	element	element	NOUN
fumecheng-4103	224	32	method	method	NOUN
fumecheng-4103	224	33	(	(	PUNCT
fumecheng-4103	224	34	bem	bem	PROPN
fumecheng-4103	224	35	)	)	PUNCT
fumecheng-4103	225	1	[	[	X
fumecheng-4103	225	2	13	13	NUM
fumecheng-4103	225	3	]	]	PUNCT
fumecheng-4103	225	4	.	.	PUNCT
fumecheng-4103	226	1	a	a	DET
fumecheng-4103	226	2	)	)	PUNCT
fumecheng-4103	226	3	b	b	NOUN
fumecheng-4103	226	4	)	)	PUNCT
fumecheng-4103	226	5	fig	fig	NOUN
fumecheng-4103	226	6	.	.	PUNCT
fumecheng-4103	227	1	6	6	NUM
fumecheng-4103	227	2	left	leave	VERB
fumecheng-4103	227	3	graph	graph	NOUN
fumecheng-4103	227	4	a	a	PRON
fumecheng-4103	227	5	):	):	PUNCT
fumecheng-4103	227	6	a	a	DET
fumecheng-4103	227	7	heterogeneous	heterogeneous	ADJ
fumecheng-4103	227	8	cylinder	cylinder	NOUN
fumecheng-4103	227	9	composed	compose	VERB
fumecheng-4103	227	10	of	of	ADP
fumecheng-4103	227	11	rings	ring	NOUN
fumecheng-4103	227	12	of	of	ADP
fumecheng-4103	227	13	different	different	ADJ
fumecheng-4103	227	14	material	material	NOUN
fumecheng-4103	227	15	having	have	VERB
fumecheng-4103	227	16	the	the	DET
fumecheng-4103	227	17	same	same	ADJ
fumecheng-4103	227	18	elastic	elastic	ADJ
fumecheng-4103	227	19	properties	property	NOUN
fumecheng-4103	227	20	but	but	CCONJ
fumecheng-4103	227	21	different	different	ADJ
fumecheng-4103	227	22	wear	wear	NOUN
fumecheng-4103	227	23	coefficients	coefficient	NOUN
fumecheng-4103	227	24	k1	k1	PROPN
fumecheng-4103	227	25	and	and	CCONJ
fumecheng-4103	227	26	k2	k2	NOUN
fumecheng-4103	227	27	is	be	AUX
fumecheng-4103	227	28	pressed	press	VERB
fumecheng-4103	227	29	onto	onto	ADP
fumecheng-4103	227	30	an	an	DET
fumecheng-4103	227	31	elastic	elastic	ADJ
fumecheng-4103	227	32	half	half	ADJ
fumecheng-4103	227	33	-	-	PUNCT
fumecheng-4103	227	34	space	space	NOUN
fumecheng-4103	227	35	with	with	ADP
fumecheng-4103	227	36	the	the	DET
fumecheng-4103	227	37	normal	normal	ADJ
fumecheng-4103	227	38	force	force	NOUN
fumecheng-4103	227	39	fn	fn	NOUN
fumecheng-4103	227	40	and	and	CCONJ
fumecheng-4103	227	41	moves	move	VERB
fumecheng-4103	227	42	tangentially	tangentially	ADV
fumecheng-4103	227	43	with	with	ADP
fumecheng-4103	227	44	velocity	velocity	NOUN
fumecheng-4103	227	45	v0	v0	NOUN
fumecheng-4103	227	46	.	.	PUNCT
fumecheng-4103	228	1	right	right	ADJ
fumecheng-4103	228	2	graph	graph	NOUN
fumecheng-4103	228	3	b	b	NOUN
fumecheng-4103	228	4	):	):	PUNCT
fumecheng-4103	228	5	simulation	simulation	NOUN
fumecheng-4103	228	6	results	result	VERB
fumecheng-4103	228	7	for	for	ADP
fumecheng-4103	228	8	the	the	DET
fumecheng-4103	228	9	limiting	limit	VERB
fumecheng-4103	228	10	profile	profile	NOUN
fumecheng-4103	228	11	and	and	CCONJ
fumecheng-4103	228	12	pressure	pressure	NOUN
fumecheng-4103	228	13	after	after	ADP
fumecheng-4103	228	14	a	a	DET
fumecheng-4103	228	15	long	long	ADJ
fumecheng-4103	228	16	enough	enough	ADJ
fumecheng-4103	228	17	running	run	VERB
fumecheng-4103	228	18	-	-	PUNCT
fumecheng-4103	228	19	in	in	ADP
fumecheng-4103	228	20	process	process	NOUN
fumecheng-4103	228	21	as	as	SCONJ
fumecheng-4103	228	22	obtained	obtain	VERB
fumecheng-4103	228	23	with	with	ADP
fumecheng-4103	228	24	method	method	PROPN
fumecheng-4103	228	25	ii	ii	PROPN
fumecheng-4103	228	26	(	(	PUNCT
fumecheng-4103	228	27	a	a	DET
fumecheng-4103	228	28	thin	thin	ADJ
fumecheng-4103	228	29	grey	grey	ADJ
fumecheng-4103	228	30	jagged	jagged	ADJ
fumecheng-4103	228	31	line	line	NOUN
fumecheng-4103	228	32	)	)	PUNCT
fumecheng-4103	228	33	,	,	PUNCT
fumecheng-4103	228	34	and	and	CCONJ
fumecheng-4103	228	35	the	the	DET
fumecheng-4103	228	36	techniques	technique	NOUN
fumecheng-4103	228	37	from	from	ADP
fumecheng-4103	228	38	this	this	DET
fumecheng-4103	228	39	paper	paper	NOUN
fumecheng-4103	228	40	–	–	PUNCT
fumecheng-4103	228	41	method	method	NOUN
fumecheng-4103	228	42	iii	iii	NOUN
fumecheng-4103	228	43	and	and	CCONJ
fumecheng-4103	228	44	method	method	NOUN
fumecheng-4103	228	45	iv	iv	X
fumecheng-4103	228	46	(	(	PUNCT
fumecheng-4103	228	47	a	a	DET
fumecheng-4103	228	48	smooth	smooth	ADJ
fumecheng-4103	228	49	bold	bold	ADJ
fumecheng-4103	228	50	line	line	NOUN
fumecheng-4103	228	51	)	)	PUNCT
fumecheng-4103	228	52	with	with	ADP
fumecheng-4103	228	53	n	n	NOUN
fumecheng-4103	228	54	=	=	SYM
fumecheng-4103	228	55	201	201	NUM
fumecheng-4103	228	56	discretization	discretization	NOUN
fumecheng-4103	228	57	points	point	NOUN
fumecheng-4103	228	58	and	and	CCONJ
fumecheng-4103	228	59	k2	k2	ADJ
fumecheng-4103	228	60	/	/	SYM
fumecheng-4103	228	61	k1	k1	NOUN
fumecheng-4103	228	62	=	=	SYM
fumecheng-4103	228	63	10	10	NUM
fumecheng-4103	228	64	9	9	NUM
fumecheng-4103	228	65	.	.	PUNCT
fumecheng-4103	229	1	conclusion	conclusion	NOUN
fumecheng-4103	229	2	a	a	DET
fumecheng-4103	229	3	simple	simple	ADJ
fumecheng-4103	229	4	implementation	implementation	NOUN
fumecheng-4103	229	5	technique	technique	NOUN
fumecheng-4103	229	6	for	for	SCONJ
fumecheng-4103	229	7	the	the	DET
fumecheng-4103	229	8	mdr	mdr	PROPN
fumecheng-4103	229	9	transformations	transformation	NOUN
fumecheng-4103	229	10	is	be	AUX
fumecheng-4103	229	11	presented	present	VERB
fumecheng-4103	229	12	in	in	ADP
fumecheng-4103	229	13	this	this	DET
fumecheng-4103	229	14	work	work	NOUN
fumecheng-4103	229	15	.	.	PUNCT
fumecheng-4103	230	1	it	it	PRON
fumecheng-4103	230	2	relies	rely	VERB
fumecheng-4103	230	3	on	on	ADP
fumecheng-4103	230	4	integration	integration	NOUN
fumecheng-4103	230	5	by	by	ADP
fumecheng-4103	230	6	parts	part	NOUN
fumecheng-4103	230	7	of	of	ADP
fumecheng-4103	230	8	the	the	DET
fumecheng-4103	230	9	transformations	transformation	NOUN
fumecheng-4103	230	10	,	,	PUNCT
fumecheng-4103	230	11	a	a	DET
fumecheng-4103	230	12	central	central	ADJ
fumecheng-4103	230	13	difference	difference	NOUN
fumecheng-4103	230	14	scheme	scheme	NOUN
fumecheng-4103	230	15	to	to	PART
fumecheng-4103	230	16	obtain	obtain	VERB
fumecheng-4103	230	17	the	the	DET
fumecheng-4103	230	18	derivatives	derivative	NOUN
fumecheng-4103	230	19	,	,	PUNCT
fumecheng-4103	230	20	and	and	CCONJ
fumecheng-4103	230	21	the	the	DET
fumecheng-4103	230	22	trapezoidal	trapezoidal	ADJ
fumecheng-4103	230	23	rule	rule	NOUN
fumecheng-4103	230	24	to	to	PART
fumecheng-4103	230	25	perform	perform	VERB
fumecheng-4103	230	26	the	the	DET
fumecheng-4103	230	27	summation	summation	NOUN
fumecheng-4103	230	28	.	.	PUNCT
fumecheng-4103	231	1	it	it	PRON
fumecheng-4103	231	2	is	be	AUX
fumecheng-4103	231	3	shown	show	VERB
fumecheng-4103	231	4	that	that	SCONJ
fumecheng-4103	231	5	the	the	DET
fumecheng-4103	231	6	results	result	NOUN
fumecheng-4103	231	7	of	of	ADP
fumecheng-4103	231	8	the	the	DET
fumecheng-4103	231	9	method	method	NOUN
fumecheng-4103	231	10	for	for	ADP
fumecheng-4103	231	11	the	the	DET
fumecheng-4103	231	12	contact	contact	NOUN
fumecheng-4103	231	13	of	of	ADP
fumecheng-4103	231	14	a	a	DET
fumecheng-4103	231	15	cone	cone	NOUN
fumecheng-4103	231	16	and	and	CCONJ
fumecheng-4103	231	17	the	the	DET
fumecheng-4103	231	18	hertzian	hertzian	ADJ
fumecheng-4103	231	19	contact	contact	NOUN
fumecheng-4103	231	20	converge	converge	VERB
fumecheng-4103	231	21	to	to	ADP
fumecheng-4103	231	22	the	the	DET
fumecheng-4103	231	23	corresponding	corresponding	ADJ
fumecheng-4103	231	24	analytical	analytical	ADJ
fumecheng-4103	231	25	solutions	solution	NOUN
fumecheng-4103	231	26	for	for	ADP
fumecheng-4103	231	27	an	an	DET
fumecheng-4103	231	28	increasing	increase	VERB
fumecheng-4103	231	29	number	number	NOUN
fumecheng-4103	231	30	of	of	ADP
fumecheng-4103	231	31	discretization	discretization	NOUN
fumecheng-4103	231	32	points	point	NOUN
fumecheng-4103	231	33	.	.	PUNCT
fumecheng-4103	232	1	therein	therein	ADV
fumecheng-4103	232	2	,	,	PUNCT
fumecheng-4103	232	3	the	the	DET
fumecheng-4103	232	4	highest	high	ADJ
fumecheng-4103	232	5	error	error	NOUN
fumecheng-4103	232	6	occurs	occur	VERB
fumecheng-4103	232	7	at	at	ADP
fumecheng-4103	232	8	the	the	DET
fumecheng-4103	232	9	border	border	NOUN
fumecheng-4103	232	10	of	of	ADP
fumecheng-4103	232	11	the	the	DET
fumecheng-4103	232	12	contact	contact	NOUN
fumecheng-4103	232	13	area	area	NOUN
fumecheng-4103	232	14	.	.	PUNCT
fumecheng-4103	233	1	a	a	DET
fumecheng-4103	233	2	small	small	ADJ
fumecheng-4103	233	3	refinement	refinement	NOUN
fumecheng-4103	233	4	to	to	ADP
fumecheng-4103	233	5	the	the	DET
fumecheng-4103	233	6	numerical	numerical	ADJ
fumecheng-4103	233	7	method	method	NOUN
fumecheng-4103	233	8	has	have	AUX
fumecheng-4103	233	9	been	be	AUX
fumecheng-4103	233	10	presented	present	VERB
fumecheng-4103	233	11	to	to	PART
fumecheng-4103	233	12	reduce	reduce	VERB
fumecheng-4103	233	13	this	this	DET
fumecheng-4103	233	14	error	error	NOUN
fumecheng-4103	233	15	.	.	PUNCT
fumecheng-4103	234	1	the	the	DET
fumecheng-4103	234	2	introduced	introduce	VERB
fumecheng-4103	234	3	method	method	NOUN
fumecheng-4103	234	4	and	and	CCONJ
fumecheng-4103	234	5	its	its	PRON
fumecheng-4103	234	6	refinement	refinement	NOUN
fumecheng-4103	234	7	are	be	AUX
fumecheng-4103	234	8	then	then	ADV
fumecheng-4103	234	9	compared	compare	VERB
fumecheng-4103	234	10	to	to	ADP
fumecheng-4103	234	11	other	other	ADJ
fumecheng-4103	234	12	numerical	numerical	ADJ
fumecheng-4103	234	13	techniques	technique	NOUN
fumecheng-4103	234	14	which	which	PRON
fumecheng-4103	234	15	rely	rely	VERB
fumecheng-4103	234	16	on	on	ADP
fumecheng-4103	234	17	the	the	DET
fumecheng-4103	234	18	original	original	ADJ
fumecheng-4103	234	19	form	form	NOUN
fumecheng-4103	234	20	of	of	ADP
fumecheng-4103	234	21	the	the	DET
fumecheng-4103	234	22	transformations	transformation	NOUN
fumecheng-4103	234	23	.	.	PUNCT
fumecheng-4103	235	1	for	for	ADP
fumecheng-4103	235	2	the	the	DET
fumecheng-4103	235	3	tested	test	VERB
fumecheng-4103	235	4	examples	example	NOUN
fumecheng-4103	235	5	,	,	PUNCT
fumecheng-4103	235	6	the	the	DET
fumecheng-4103	235	7	newly	newly	ADV
fumecheng-4103	235	8	introduced	introduce	VERB
fumecheng-4103	235	9	method	method	NOUN
fumecheng-4103	235	10	and	and	CCONJ
fumecheng-4103	235	11	its	its	PRON
fumecheng-4103	235	12	refinement	refinement	NOUN
fumecheng-4103	235	13	deliver	deliver	VERB
fumecheng-4103	235	14	more	more	ADV
fumecheng-4103	235	15	accurate	accurate	ADJ
fumecheng-4103	235	16	results	result	NOUN
fumecheng-4103	235	17	at	at	ADP
fumecheng-4103	235	18	the	the	DET
fumecheng-4103	235	19	same	same	ADJ
fumecheng-4103	235	20	number	number	NOUN
fumecheng-4103	235	21	of	of	ADP
fumecheng-4103	235	22	discretization	discretization	NOUN
fumecheng-4103	235	23	points	point	NOUN
fumecheng-4103	235	24	(	(	PUNCT
fumecheng-4103	235	25	see	see	VERB
fumecheng-4103	235	26	fig	fig	NOUN
fumecheng-4103	235	27	.	.	PUNCT
fumecheng-4103	236	1	5	5	NUM
fumecheng-4103	236	2	)	)	PUNCT
fumecheng-4103	236	3	.	.	PUNCT
fumecheng-4103	237	1	furthermore	furthermore	ADV
fumecheng-4103	237	2	,	,	PUNCT
fumecheng-4103	237	3	it	it	PRON
fumecheng-4103	237	4	is	be	AUX
fumecheng-4103	237	5	shown	show	VERB
fumecheng-4103	237	6	that	that	SCONJ
fumecheng-4103	237	7	apart	apart	ADV
fumecheng-4103	237	8	from	from	ADP
fumecheng-4103	237	9	a	a	DET
fumecheng-4103	237	10	higher	high	ADJ
fumecheng-4103	237	11	accuracy	accuracy	NOUN
fumecheng-4103	237	12	when	when	SCONJ
fumecheng-4103	237	13	used	use	VERB
fumecheng-4103	237	14	once	once	ADV
fumecheng-4103	237	15	,	,	PUNCT
fumecheng-4103	237	16	the	the	DET
fumecheng-4103	237	17	presented	present	VERB
fumecheng-4103	237	18	method	method	NOUN
fumecheng-4103	237	19	and	and	CCONJ
fumecheng-4103	237	20	its	its	PRON
fumecheng-4103	237	21	refinement	refinement	NOUN
fumecheng-4103	237	22	may	may	AUX
fumecheng-4103	237	23	have	have	VERB
fumecheng-4103	237	24	another	another	DET
fumecheng-4103	237	25	benefit	benefit	NOUN
fumecheng-4103	237	26	when	when	SCONJ
fumecheng-4103	237	27	used	use	VERB
fumecheng-4103	237	28	multiple	multiple	ADJ
fumecheng-4103	237	29	times	time	NOUN
fumecheng-4103	237	30	in	in	ADP
fumecheng-4103	237	31	138	138	NUM
fumecheng-4103	237	32	j.	j.	PROPN
fumecheng-4103	237	33	benad	benad	PROPN
fumecheng-4103	237	34	wear	wear	VERB
fumecheng-4103	237	35	simulations	simulation	NOUN
fumecheng-4103	237	36	.	.	PUNCT
fumecheng-4103	238	1	in	in	ADP
fumecheng-4103	238	2	an	an	DET
fumecheng-4103	238	3	exemplary	exemplary	ADJ
fumecheng-4103	238	4	simulation	simulation	NOUN
fumecheng-4103	238	5	,	,	PUNCT
fumecheng-4103	238	6	the	the	DET
fumecheng-4103	238	7	wear	wear	NOUN
fumecheng-4103	238	8	of	of	ADP
fumecheng-4103	238	9	a	a	DET
fumecheng-4103	238	10	heterogeneous	heterogeneous	ADJ
fumecheng-4103	238	11	cylinder	cylinder	NOUN
fumecheng-4103	238	12	composed	compose	VERB
fumecheng-4103	238	13	of	of	ADP
fumecheng-4103	238	14	rings	ring	NOUN
fumecheng-4103	238	15	of	of	ADP
fumecheng-4103	238	16	different	different	ADJ
fumecheng-4103	238	17	material	material	NOUN
fumecheng-4103	238	18	having	have	VERB
fumecheng-4103	238	19	the	the	DET
fumecheng-4103	238	20	same	same	ADJ
fumecheng-4103	238	21	elastic	elastic	ADJ
fumecheng-4103	238	22	properties	property	NOUN
fumecheng-4103	238	23	but	but	CCONJ
fumecheng-4103	238	24	different	different	ADJ
fumecheng-4103	238	25	wear	wear	NOUN
fumecheng-4103	238	26	coefficients	coefficient	NOUN
fumecheng-4103	238	27	is	be	AUX
fumecheng-4103	238	28	modeled	model	VERB
fumecheng-4103	238	29	.	.	PUNCT
fumecheng-4103	239	1	these	these	DET
fumecheng-4103	239	2	discontinuous	discontinuous	ADJ
fumecheng-4103	239	3	transitions	transition	NOUN
fumecheng-4103	239	4	in	in	ADP
fumecheng-4103	239	5	the	the	DET
fumecheng-4103	239	6	material	material	NOUN
fumecheng-4103	239	7	properties	property	NOUN
fumecheng-4103	239	8	are	be	AUX
fumecheng-4103	239	9	handled	handle	VERB
fumecheng-4103	239	10	well	well	ADV
fumecheng-4103	239	11	by	by	ADP
fumecheng-4103	239	12	the	the	DET
fumecheng-4103	239	13	newly	newly	ADV
fumecheng-4103	239	14	introduced	introduce	VERB
fumecheng-4103	239	15	methods	method	NOUN
fumecheng-4103	239	16	,	,	PUNCT
fumecheng-4103	239	17	whereas	whereas	SCONJ
fumecheng-4103	239	18	the	the	DET
fumecheng-4103	239	19	tested	test	VERB
fumecheng-4103	239	20	numerical	numerical	ADJ
fumecheng-4103	239	21	techniques	technique	NOUN
fumecheng-4103	239	22	which	which	PRON
fumecheng-4103	239	23	rely	rely	VERB
fumecheng-4103	239	24	on	on	ADP
fumecheng-4103	239	25	the	the	DET
fumecheng-4103	239	26	original	original	ADJ
fumecheng-4103	239	27	form	form	NOUN
fumecheng-4103	239	28	of	of	ADP
fumecheng-4103	239	29	the	the	DET
fumecheng-4103	239	30	transformations	transformation	NOUN
fumecheng-4103	239	31	deliver	deliver	VERB
fumecheng-4103	239	32	results	result	NOUN
fumecheng-4103	239	33	with	with	ADP
fumecheng-4103	239	34	a	a	DET
fumecheng-4103	239	35	high	high	ADJ
fumecheng-4103	239	36	oscillating	oscillating	NOUN
fumecheng-4103	239	37	error	error	NOUN
fumecheng-4103	239	38	(	(	PUNCT
fumecheng-4103	239	39	see	see	VERB
fumecheng-4103	239	40	fig	fig	NOUN
fumecheng-4103	239	41	.	.	PUNCT
fumecheng-4103	240	1	6	6	NUM
fumecheng-4103	240	2	)	)	PUNCT
fumecheng-4103	240	3	.	.	PUNCT
fumecheng-4103	241	1	acknowledgments	acknowledgment	NOUN
fumecheng-4103	241	2	:	:	PUNCT
fumecheng-4103	241	3	the	the	DET
fumecheng-4103	241	4	author	author	NOUN
fumecheng-4103	241	5	would	would	AUX
fumecheng-4103	241	6	like	like	VERB
fumecheng-4103	241	7	to	to	PART
fumecheng-4103	241	8	thank	thank	VERB
fumecheng-4103	241	9	v.	v.	PROPN
fumecheng-4103	241	10	l.	l.	PROPN
fumecheng-4103	241	11	popov	popov	PROPN
fumecheng-4103	241	12	,	,	PUNCT
fumecheng-4103	241	13	m.	m.	NOUN
fumecheng-4103	241	14	heß	heß	PROPN
fumecheng-4103	241	15	,	,	PUNCT
fumecheng-4103	241	16	q.	q.	PROPN
fumecheng-4103	241	17	li	li	PROPN
fumecheng-4103	241	18	,	,	PUNCT
fumecheng-4103	241	19	e.	e.	PROPN
fumecheng-4103	241	20	willert	willert	PROPN
fumecheng-4103	241	21	and	and	CCONJ
fumecheng-4103	241	22	p.	p.	NOUN
fumecheng-4103	241	23	diercks	dierck	NOUN
fumecheng-4103	241	24	for	for	ADP
fumecheng-4103	241	25	many	many	ADJ
fumecheng-4103	241	26	valuable	valuable	ADJ
fumecheng-4103	241	27	discussions	discussion	NOUN
fumecheng-4103	241	28	on	on	ADP
fumecheng-4103	241	29	the	the	DET
fumecheng-4103	241	30	topic	topic	NOUN
fumecheng-4103	241	31	and	and	CCONJ
fumecheng-4103	241	32	critical	critical	ADJ
fumecheng-4103	241	33	comments	comment	NOUN
fumecheng-4103	241	34	.	.	PUNCT
fumecheng-4103	242	1	references	reference	NOUN
fumecheng-4103	242	2	1	1	NUM
fumecheng-4103	242	3	.	.	PUNCT
fumecheng-4103	243	1	popov	popov	PROPN
fumecheng-4103	243	2	,	,	PUNCT
fumecheng-4103	243	3	v.l	v.l	PROPN
fumecheng-4103	243	4	.	.	PROPN
fumecheng-4103	243	5	,	,	PUNCT
fumecheng-4103	243	6	psakhie	psakhie	PROPN
fumecheng-4103	243	7	,	,	PUNCT
fumecheng-4103	243	8	s.	s.	PROPN
fumecheng-4103	243	9	,	,	PUNCT
fumecheng-4103	243	10	2007	2007	NUM
fumecheng-4103	243	11	,	,	PUNCT
fumecheng-4103	243	12	numerical	numerical	PROPN
fumecheng-4103	243	13	simulation	simulation	NOUN
fumecheng-4103	243	14	methods	method	NOUN
fumecheng-4103	243	15	in	in	ADP
fumecheng-4103	243	16	tribology	tribology	NOUN
fumecheng-4103	243	17	,	,	PUNCT
fumecheng-4103	243	18	tribology	tribology	PROPN
fumecheng-4103	243	19	international	international	PROPN
fumecheng-4103	243	20	,	,	PUNCT
fumecheng-4103	243	21	40(6	40(6	PROPN
fumecheng-4103	243	22	)	)	PUNCT
fumecheng-4103	243	23	,	,	PUNCT
fumecheng-4103	243	24	pp	pp	ADP
fumecheng-4103	243	25	.	.	PUNCT
fumecheng-4103	244	1	916	916	NUM
fumecheng-4103	244	2	-	-	SYM
fumecheng-4103	244	3	923	923	NUM
fumecheng-4103	244	4	.	.	NOUN
fumecheng-4103	245	1	2	2	NUM
fumecheng-4103	245	2	.	.	X
fumecheng-4103	245	3	popov	popov	PROPN
fumecheng-4103	245	4	,	,	PUNCT
fumecheng-4103	245	5	v.l	v.l	PROPN
fumecheng-4103	245	6	.	.	PROPN
fumecheng-4103	245	7	,	,	PUNCT
fumecheng-4103	245	8	heß	heß	PROPN
fumecheng-4103	245	9	,	,	PUNCT
fumecheng-4103	245	10	m.	m.	NOUN
fumecheng-4103	245	11	,	,	PUNCT
fumecheng-4103	245	12	2016	2016	NUM
fumecheng-4103	245	13	,	,	PUNCT
fumecheng-4103	245	14	method	method	NOUN
fumecheng-4103	245	15	of	of	ADP
fumecheng-4103	245	16	dimensionality	dimensionality	NOUN
fumecheng-4103	245	17	reduction	reduction	NOUN
fumecheng-4103	245	18	in	in	ADP
fumecheng-4103	245	19	contact	contact	NOUN
fumecheng-4103	245	20	mechanics	mechanic	NOUN
fumecheng-4103	245	21	and	and	CCONJ
fumecheng-4103	245	22	friction	friction	NOUN
fumecheng-4103	245	23	,	,	PUNCT
fumecheng-4103	245	24	springer	springer	NOUN
fumecheng-4103	245	25	,	,	PUNCT
fumecheng-4103	245	26	berlin	berlin	PROPN
fumecheng-4103	245	27	.	.	PUNCT
fumecheng-4103	246	1	3	3	X
fumecheng-4103	246	2	.	.	X
fumecheng-4103	246	3	popov	popov	PROPN
fumecheng-4103	246	4	,	,	PUNCT
fumecheng-4103	246	5	m.	m.	NOUN
fumecheng-4103	246	6	,	,	PUNCT
fumecheng-4103	246	7	benad	benad	PROPN
fumecheng-4103	246	8	,	,	PUNCT
fumecheng-4103	246	9	j.	j.	PROPN
fumecheng-4103	246	10	,	,	PUNCT
fumecheng-4103	246	11	popov	popov	PROPN
fumecheng-4103	246	12	,	,	PUNCT
fumecheng-4103	246	13	v.l	v.l	PROPN
fumecheng-4103	246	14	.	.	PROPN
fumecheng-4103	246	15	,	,	PUNCT
fumecheng-4103	246	16	heß	heß	PROPN
fumecheng-4103	246	17	,	,	PUNCT
fumecheng-4103	246	18	m.	m.	NOUN
fumecheng-4103	246	19	,	,	PUNCT
fumecheng-4103	246	20	2015	2015	NUM
fumecheng-4103	246	21	,	,	PUNCT
fumecheng-4103	246	22	acoustic	acoustic	ADJ
fumecheng-4103	246	23	emission	emission	NOUN
fumecheng-4103	246	24	in	in	ADP
fumecheng-4103	246	25	rolling	rolling	ADJ
fumecheng-4103	246	26	contacts	contact	NOUN
fumecheng-4103	246	27	,	,	PUNCT
fumecheng-4103	246	28	method	method	NOUN
fumecheng-4103	246	29	of	of	ADP
fumecheng-4103	246	30	dimensionality	dimensionality	NOUN
fumecheng-4103	246	31	reduction	reduction	NOUN
fumecheng-4103	246	32	in	in	ADP
fumecheng-4103	246	33	contact	contact	NOUN
fumecheng-4103	246	34	mechanics	mechanic	NOUN
fumecheng-4103	246	35	and	and	CCONJ
fumecheng-4103	246	36	friction	friction	NOUN
fumecheng-4103	246	37	,	,	PUNCT
fumecheng-4103	246	38	springer	springer	NOUN
fumecheng-4103	246	39	,	,	PUNCT
fumecheng-4103	246	40	berlin	berlin	PROPN
fumecheng-4103	246	41	,	,	PUNCT
fumecheng-4103	246	42	pp	pp	PROPN
fumecheng-4103	246	43	.	.	PUNCT
fumecheng-4103	247	1	207	207	NUM
fumecheng-4103	247	2	-	-	SYM
fumecheng-4103	247	3	214	214	NUM
fumecheng-4103	247	4	.	.	PUNCT
fumecheng-4103	248	1	4	4	X
fumecheng-4103	248	2	.	.	X
fumecheng-4103	248	3	dimaki	dimaki	NOUN
fumecheng-4103	248	4	,	,	PUNCT
fumecheng-4103	248	5	a.	a.	PROPN
fumecheng-4103	248	6	,	,	PUNCT
fumecheng-4103	248	7	dmitriev	dmitriev	PROPN
fumecheng-4103	248	8	,	,	PUNCT
fumecheng-4103	248	9	a.	a.	NOUN
fumecheng-4103	248	10	,	,	PUNCT
fumecheng-4103	248	11	chai	chai	NOUN
fumecheng-4103	248	12	,	,	PUNCT
fumecheng-4103	248	13	y.	y.	PROPN
fumecheng-4103	248	14	,	,	PUNCT
fumecheng-4103	248	15	popov	popov	PROPN
fumecheng-4103	248	16	,	,	PUNCT
fumecheng-4103	248	17	v.l	v.l	PROPN
fumecheng-4103	248	18	.	.	PROPN
fumecheng-4103	248	19	,	,	PUNCT
fumecheng-4103	248	20	2014	2014	NUM
fumecheng-4103	248	21	,	,	PUNCT
fumecheng-4103	248	22	rapid	rapid	ADJ
fumecheng-4103	248	23	simulation	simulation	NOUN
fumecheng-4103	248	24	procedure	procedure	NOUN
fumecheng-4103	248	25	for	for	ADP
fumecheng-4103	248	26	fretting	fret	VERB
fumecheng-4103	248	27	wear	wear	NOUN
fumecheng-4103	248	28	on	on	ADP
fumecheng-4103	248	29	the	the	DET
fumecheng-4103	248	30	basis	basis	NOUN
fumecheng-4103	248	31	of	of	ADP
fumecheng-4103	248	32	the	the	DET
fumecheng-4103	248	33	method	method	NOUN
fumecheng-4103	248	34	of	of	ADP
fumecheng-4103	248	35	dimensionality	dimensionality	NOUN
fumecheng-4103	248	36	reduction	reduction	NOUN
fumecheng-4103	248	37	,	,	PUNCT
fumecheng-4103	248	38	international	international	ADJ
fumecheng-4103	248	39	journal	journal	NOUN
fumecheng-4103	248	40	of	of	ADP
fumecheng-4103	248	41	solids	solid	NOUN
fumecheng-4103	248	42	and	and	CCONJ
fumecheng-4103	248	43	structures	structure	NOUN
fumecheng-4103	248	44	,	,	PUNCT
fumecheng-4103	248	45	51(25	51(25	NOUN
fumecheng-4103	248	46	-	-	SYM
fumecheng-4103	248	47	26	26	NUM
fumecheng-4103	248	48	)	)	PUNCT
fumecheng-4103	248	49	,	,	PUNCT
fumecheng-4103	248	50	pp	pp	PROPN
fumecheng-4103	248	51	.	.	PUNCT
fumecheng-4103	249	1	4215	4215	NUM
fumecheng-4103	249	2	-	-	SYM
fumecheng-4103	249	3	4220	4220	NUM
fumecheng-4103	249	4	.	.	PUNCT
fumecheng-4103	250	1	5	5	X
fumecheng-4103	250	2	.	.	X
fumecheng-4103	250	3	dimaki	dimaki	NOUN
fumecheng-4103	250	4	,	,	PUNCT
fumecheng-4103	250	5	a.	a.	PROPN
fumecheng-4103	250	6	,	,	PUNCT
fumecheng-4103	250	7	dmitriev	dmitriev	PROPN
fumecheng-4103	250	8	,	,	PUNCT
fumecheng-4103	250	9	a.	a.	NOUN
fumecheng-4103	250	10	,	,	PUNCT
fumecheng-4103	250	11	menga	menga	NOUN
fumecheng-4103	250	12	,	,	PUNCT
fumecheng-4103	250	13	n.	n.	NOUN
fumecheng-4103	250	14	,	,	PUNCT
fumecheng-4103	250	15	papangelo	papangelo	NOUN
fumecheng-4103	250	16	,	,	PUNCT
fumecheng-4103	250	17	a.	a.	NOUN
fumecheng-4103	250	18	,	,	PUNCT
fumecheng-4103	250	19	ciavarella	ciavarella	NOUN
fumecheng-4103	250	20	,	,	PUNCT
fumecheng-4103	250	21	m.	m.	NOUN
fumecheng-4103	250	22	,	,	PUNCT
fumecheng-4103	250	23	popov	popov	PROPN
fumecheng-4103	250	24	,	,	PUNCT
fumecheng-4103	250	25	v.l	v.l	PROPN
fumecheng-4103	250	26	.	.	PROPN
fumecheng-4103	250	27	,	,	PUNCT
fumecheng-4103	250	28	2016	2016	NUM
fumecheng-4103	250	29	,	,	PUNCT
fumecheng-4103	250	30	fast	fast	ADJ
fumecheng-4103	250	31	high	high	ADJ
fumecheng-4103	250	32	-	-	PUNCT
fumecheng-4103	250	33	resolution	resolution	NOUN
fumecheng-4103	250	34	simulation	simulation	NOUN
fumecheng-4103	250	35	of	of	ADP
fumecheng-4103	250	36	the	the	DET
fumecheng-4103	250	37	gross	gross	ADJ
fumecheng-4103	250	38	slip	slip	NOUN
fumecheng-4103	250	39	wear	wear	NOUN
fumecheng-4103	250	40	of	of	ADP
fumecheng-4103	250	41	axially	axially	ADV
fumecheng-4103	250	42	symmetric	symmetric	ADJ
fumecheng-4103	250	43	contacts	contact	NOUN
fumecheng-4103	250	44	,	,	PUNCT
fumecheng-4103	250	45	tribology	tribology	NOUN
fumecheng-4103	250	46	transactions	transaction	NOUN
fumecheng-4103	250	47	,	,	PUNCT
fumecheng-4103	250	48	59(1	59(1	NUM
fumecheng-4103	250	49	)	)	PUNCT
fumecheng-4103	250	50	,	,	PUNCT
fumecheng-4103	250	51	pp	pp	ADP
fumecheng-4103	250	52	.	.	PUNCT
fumecheng-4103	251	1	189	189	NUM
fumecheng-4103	251	2	-	-	SYM
fumecheng-4103	251	3	194	194	NUM
fumecheng-4103	251	4	.	.	PUNCT
fumecheng-4103	252	1	6	6	NUM
fumecheng-4103	252	2	.	.	X
fumecheng-4103	252	3	li	li	PROPN
fumecheng-4103	252	4	,	,	PUNCT
fumecheng-4103	252	5	q.	q.	PROPN
fumecheng-4103	252	6	,	,	PUNCT
fumecheng-4103	252	7	forsbach	forsbach	PROPN
fumecheng-4103	252	8	,	,	PUNCT
fumecheng-4103	252	9	f.	f.	PROPN
fumecheng-4103	252	10	,	,	PUNCT
fumecheng-4103	252	11	schuster	schuster	PROPN
fumecheng-4103	252	12	,	,	PUNCT
fumecheng-4103	252	13	m.	m.	NOUN
fumecheng-4103	252	14	,	,	PUNCT
fumecheng-4103	252	15	pielsticker	pielsticker	PROPN
fumecheng-4103	252	16	,	,	PUNCT
fumecheng-4103	252	17	d.	d.	PROPN
fumecheng-4103	252	18	,	,	PUNCT
fumecheng-4103	252	19	popov	popov	PROPN
fumecheng-4103	252	20	,	,	PUNCT
fumecheng-4103	252	21	v.l	v.l	PROPN
fumecheng-4103	252	22	.	.	PROPN
fumecheng-4103	252	23	,	,	PUNCT
fumecheng-4103	252	24	2018	2018	NUM
fumecheng-4103	252	25	,	,	PUNCT
fumecheng-4103	252	26	wear	wear	VERB
fumecheng-4103	252	27	analysis	analysis	NOUN
fumecheng-4103	252	28	of	of	ADP
fumecheng-4103	252	29	a	a	DET
fumecheng-4103	252	30	heterogeneous	heterogeneous	ADJ
fumecheng-4103	252	31	annular	annular	ADJ
fumecheng-4103	252	32	cylinder	cylinder	NOUN
fumecheng-4103	252	33	,	,	PUNCT
fumecheng-4103	252	34	lubricants	lubricant	NOUN
fumecheng-4103	252	35	,	,	PUNCT
fumecheng-4103	252	36	6(1	6(1	NUM
fumecheng-4103	252	37	)	)	PUNCT
fumecheng-4103	252	38	,	,	PUNCT
fumecheng-4103	252	39	28	28	NUM
fumecheng-4103	252	40	.	.	X
fumecheng-4103	253	1	7	7	X
fumecheng-4103	253	2	.	.	X
fumecheng-4103	253	3	murio	murio	PROPN
fumecheng-4103	253	4	,	,	PUNCT
fumecheng-4103	253	5	d.	d.	PROPN
fumecheng-4103	253	6	,	,	PUNCT
fumecheng-4103	253	7	hinestroza	hinestroza	PROPN
fumecheng-4103	253	8	,	,	PUNCT
fumecheng-4103	253	9	d.	d.	PROPN
fumecheng-4103	253	10	,	,	PUNCT
fumecheng-4103	253	11	mejía	mejía	PROPN
fumecheng-4103	253	12	,	,	PUNCT
fumecheng-4103	253	13	c.	c.	PROPN
fumecheng-4103	253	14	,	,	PUNCT
fumecheng-4103	253	15	1992	1992	NUM
fumecheng-4103	253	16	,	,	PUNCT
fumecheng-4103	253	17	new	new	ADJ
fumecheng-4103	253	18	stable	stable	ADJ
fumecheng-4103	253	19	numerical	numerical	ADJ
fumecheng-4103	253	20	inversion	inversion	NOUN
fumecheng-4103	253	21	of	of	ADP
fumecheng-4103	253	22	abel	abel	PROPN
fumecheng-4103	253	23	's	's	PART
fumecheng-4103	253	24	integral	integral	ADJ
fumecheng-4103	253	25	equation	equation	NOUN
fumecheng-4103	253	26	,	,	PUNCT
fumecheng-4103	253	27	computers	computer	NOUN
fumecheng-4103	253	28	&	&	CCONJ
fumecheng-4103	253	29	mathematics	mathematics	PROPN
fumecheng-4103	253	30	with	with	ADP
fumecheng-4103	253	31	applications	application	NOUN
fumecheng-4103	253	32	,	,	PUNCT
fumecheng-4103	253	33	23(11	23(11	NUM
fumecheng-4103	253	34	)	)	PUNCT
fumecheng-4103	253	35	,	,	PUNCT
fumecheng-4103	253	36	pp	pp	ADJ
fumecheng-4103	253	37	.	.	PUNCT
fumecheng-4103	254	1	3	3	NUM
fumecheng-4103	254	2	-	-	SYM
fumecheng-4103	254	3	11	11	NUM
fumecheng-4103	254	4	.	.	NOUN
fumecheng-4103	255	1	8	8	NUM
fumecheng-4103	255	2	.	.	X
fumecheng-4103	256	1	hansen	hansen	PROPN
fumecheng-4103	256	2	,	,	PUNCT
fumecheng-4103	256	3	e.	e.	PROPN
fumecheng-4103	256	4	,	,	PUNCT
fumecheng-4103	256	5	law	law	NOUN
fumecheng-4103	256	6	,	,	PUNCT
fumecheng-4103	256	7	p.	p.	NOUN
fumecheng-4103	256	8	,	,	PUNCT
fumecheng-4103	256	9	1985	1985	NUM
fumecheng-4103	256	10	,	,	PUNCT
fumecheng-4103	256	11	recursive	recursive	ADJ
fumecheng-4103	256	12	methods	method	NOUN
fumecheng-4103	256	13	for	for	ADP
fumecheng-4103	256	14	computing	compute	VERB
fumecheng-4103	256	15	the	the	DET
fumecheng-4103	256	16	abel	abel	PROPN
fumecheng-4103	256	17	transform	transform	NOUN
fumecheng-4103	256	18	and	and	CCONJ
fumecheng-4103	256	19	its	its	PRON
fumecheng-4103	256	20	inverse	inverse	NOUN
fumecheng-4103	256	21	,	,	PUNCT
fumecheng-4103	256	22	journal	journal	NOUN
fumecheng-4103	256	23	of	of	ADP
fumecheng-4103	256	24	the	the	DET
fumecheng-4103	256	25	optical	optical	ADJ
fumecheng-4103	256	26	society	society	NOUN
fumecheng-4103	256	27	of	of	ADP
fumecheng-4103	256	28	america	america	PROPN
fumecheng-4103	256	29	a	a	X
fumecheng-4103	256	30	,	,	PUNCT
fumecheng-4103	256	31	2(4	2(4	NUM
fumecheng-4103	256	32	)	)	PUNCT
fumecheng-4103	256	33	,	,	PUNCT
fumecheng-4103	256	34	pp	pp	PROPN
fumecheng-4103	256	35	.	.	PUNCT
fumecheng-4103	257	1	510	510	NUM
fumecheng-4103	257	2	-	-	SYM
fumecheng-4103	257	3	520	520	NUM
fumecheng-4103	257	4	.	.	NOUN
fumecheng-4103	258	1	9	9	NUM
fumecheng-4103	258	2	.	.	X
fumecheng-4103	259	1	popov	popov	PROPN
fumecheng-4103	259	2	,	,	PUNCT
fumecheng-4103	259	3	v.l	v.l	PROPN
fumecheng-4103	259	4	.	.	PROPN
fumecheng-4103	259	5	,	,	PUNCT
fumecheng-4103	259	6	heß	heß	PROPN
fumecheng-4103	259	7	,	,	PUNCT
fumecheng-4103	259	8	m.	m.	NOUN
fumecheng-4103	259	9	,	,	PUNCT
fumecheng-4103	259	10	2014	2014	NUM
fumecheng-4103	259	11	,	,	PUNCT
fumecheng-4103	259	12	method	method	NOUN
fumecheng-4103	259	13	of	of	ADP
fumecheng-4103	259	14	dimensionality	dimensionality	NOUN
fumecheng-4103	259	15	reduction	reduction	NOUN
fumecheng-4103	259	16	in	in	ADP
fumecheng-4103	259	17	contact	contact	NOUN
fumecheng-4103	259	18	mechanics	mechanic	NOUN
fumecheng-4103	259	19	and	and	CCONJ
fumecheng-4103	259	20	friction	friction	NOUN
fumecheng-4103	259	21	:	:	PUNCT
fumecheng-4103	259	22	a	a	DET
fumecheng-4103	259	23	users	user	NOUN
fumecheng-4103	259	24	handbook	handbook	NOUN
fumecheng-4103	259	25	.	.	PUNCT
fumecheng-4103	260	1	i.	i.	PROPN
fumecheng-4103	260	2	axially	axially	ADV
fumecheng-4103	260	3	-	-	PUNCT
fumecheng-4103	260	4	symmetric	symmetric	ADJ
fumecheng-4103	260	5	contacts	contact	NOUN
fumecheng-4103	260	6	,	,	PUNCT
fumecheng-4103	260	7	facta	facta	PROPN
fumecheng-4103	260	8	universitatis	universitatis	PROPN
fumecheng-4103	260	9	-	-	PUNCT
fumecheng-4103	260	10	series	series	NOUN
fumecheng-4103	260	11	mechanical	mechanical	ADJ
fumecheng-4103	260	12	engineering	engineering	NOUN
fumecheng-4103	260	13	,	,	PUNCT
fumecheng-4103	260	14	12(1	12(1	NUM
fumecheng-4103	260	15	)	)	PUNCT
fumecheng-4103	260	16	,	,	PUNCT
fumecheng-4103	260	17	pp	pp	PROPN
fumecheng-4103	260	18	.	.	PUNCT
fumecheng-4103	261	1	1	1	NUM
fumecheng-4103	261	2	-	-	SYM
fumecheng-4103	261	3	14	14	NUM
fumecheng-4103	261	4	.	.	PUNCT
fumecheng-4103	262	1	10	10	NUM
fumecheng-4103	262	2	.	.	PUNCT
fumecheng-4103	263	1	heß	heß	PROPN
fumecheng-4103	263	2	,	,	PUNCT
fumecheng-4103	263	3	m.	m.	NOUN
fumecheng-4103	263	4	,	,	PUNCT
fumecheng-4103	263	5	2016	2016	NUM
fumecheng-4103	263	6	,	,	PUNCT
fumecheng-4103	263	7	a	a	DET
fumecheng-4103	263	8	simple	simple	ADJ
fumecheng-4103	263	9	method	method	NOUN
fumecheng-4103	263	10	for	for	ADP
fumecheng-4103	263	11	solving	solve	VERB
fumecheng-4103	263	12	adhesive	adhesive	ADJ
fumecheng-4103	263	13	and	and	CCONJ
fumecheng-4103	263	14	non	non	ADJ
fumecheng-4103	263	15	-	-	ADJ
fumecheng-4103	263	16	adhesive	adhesive	ADJ
fumecheng-4103	263	17	axisymmetric	axisymmetric	ADJ
fumecheng-4103	263	18	contact	contact	NOUN
fumecheng-4103	263	19	problems	problem	NOUN
fumecheng-4103	263	20	of	of	ADP
fumecheng-4103	263	21	elastically	elastically	ADV
fumecheng-4103	263	22	graded	grade	VERB
fumecheng-4103	263	23	materials	material	NOUN
fumecheng-4103	263	24	,	,	PUNCT
fumecheng-4103	263	25	international	international	ADJ
fumecheng-4103	263	26	journal	journal	NOUN
fumecheng-4103	263	27	of	of	ADP
fumecheng-4103	263	28	engineering	engineering	NOUN
fumecheng-4103	263	29	science	science	NOUN
fumecheng-4103	263	30	,	,	PUNCT
fumecheng-4103	263	31	104	104	NUM
fumecheng-4103	263	32	,	,	PUNCT
fumecheng-4103	263	33	pp	pp	ADJ
fumecheng-4103	263	34	.	.	PUNCT
fumecheng-4103	264	1	20	20	NUM
fumecheng-4103	264	2	-	-	SYM
fumecheng-4103	264	3	33	33	NUM
fumecheng-4103	264	4	.	.	PUNCT
fumecheng-4103	265	1	11	11	NUM
fumecheng-4103	265	2	.	.	PUNCT
fumecheng-4103	266	1	popov	popov	PROPN
fumecheng-4103	266	2	,	,	PUNCT
fumecheng-4103	266	3	v.l	v.l	PROPN
fumecheng-4103	266	4	.	.	PROPN
fumecheng-4103	266	5	,	,	PUNCT
fumecheng-4103	266	6	heß	heß	PROPN
fumecheng-4103	266	7	,	,	PUNCT
fumecheng-4103	266	8	m.	m.	NOUN
fumecheng-4103	266	9	,	,	PUNCT
fumecheng-4103	266	10	willert	willert	NOUN
fumecheng-4103	266	11	,	,	PUNCT
fumecheng-4103	266	12	e.	e.	PROPN
fumecheng-4103	266	13	,	,	PUNCT
fumecheng-4103	266	14	2017	2017	NUM
fumecheng-4103	266	15	,	,	PUNCT
fumecheng-4103	266	16	handbuch	handbuch	PROPN
fumecheng-4103	266	17	der	der	PROPN
fumecheng-4103	266	18	kontaktmechanik	kontaktmechanik	PROPN
fumecheng-4103	266	19	,	,	PUNCT
fumecheng-4103	266	20	springer	springer	NOUN
fumecheng-4103	266	21	,	,	PUNCT
fumecheng-4103	266	22	berlin	berlin	PROPN
fumecheng-4103	266	23	.	.	PUNCT
fumecheng-4103	267	1	12	12	NUM
fumecheng-4103	267	2	.	.	X
fumecheng-4103	267	3	archard	archard	NOUN
fumecheng-4103	267	4	,	,	PUNCT
fumecheng-4103	267	5	j.	j.	PROPN
fumecheng-4103	267	6	,	,	PUNCT
fumecheng-4103	267	7	hirst	hirst	PROPN
fumecheng-4103	267	8	,	,	PUNCT
fumecheng-4103	267	9	w.	w.	PROPN
fumecheng-4103	267	10	,	,	PUNCT
fumecheng-4103	267	11	1956	1956	NUM
fumecheng-4103	267	12	,	,	PUNCT
fumecheng-4103	267	13	the	the	DET
fumecheng-4103	267	14	wear	wear	NOUN
fumecheng-4103	267	15	of	of	ADP
fumecheng-4103	267	16	metals	metal	NOUN
fumecheng-4103	267	17	under	under	ADP
fumecheng-4103	267	18	unlubricated	unlubricated	ADJ
fumecheng-4103	267	19	conditions	condition	NOUN
fumecheng-4103	267	20	,	,	PUNCT
fumecheng-4103	267	21	proc	proc	NOUN
fumecheng-4103	267	22	.	.	PUNCT
fumecheng-4103	268	1	r.	r.	PROPN
fumecheng-4103	268	2	soc	soc	PROPN
fumecheng-4103	268	3	.	.	PUNCT
fumecheng-4103	269	1	lond	lond	PROPN
fumecheng-4103	269	2	.	.	PUNCT
fumecheng-4103	270	1	a	a	DET
fumecheng-4103	270	2	,	,	PUNCT
fumecheng-4103	270	3	236(1206	236(1206	NUM
fumecheng-4103	270	4	)	)	PUNCT
fumecheng-4103	270	5	,	,	PUNCT
fumecheng-4103	271	1	pp	pp	ADP
fumecheng-4103	271	2	.	.	PUNCT
fumecheng-4103	272	1	397	397	NUM
fumecheng-4103	272	2	-	-	SYM
fumecheng-4103	272	3	410	410	NUM
fumecheng-4103	272	4	.	.	NOUN
fumecheng-4103	273	1	13	13	NUM
fumecheng-4103	273	2	.	.	PUNCT
fumecheng-4103	274	1	pohrt	pohrt	PROPN
fumecheng-4103	274	2	,	,	PUNCT
fumecheng-4103	274	3	r.	r.	PROPN
fumecheng-4103	274	4	,	,	PUNCT
fumecheng-4103	274	5	li	li	PROPN
fumecheng-4103	274	6	,	,	PUNCT
fumecheng-4103	274	7	q.	q.	PROPN
fumecheng-4103	274	8	,	,	PUNCT
fumecheng-4103	274	9	2014	2014	NUM
fumecheng-4103	274	10	,	,	PUNCT
fumecheng-4103	274	11	complete	complete	ADJ
fumecheng-4103	274	12	boundary	boundary	ADJ
fumecheng-4103	274	13	element	element	NOUN
fumecheng-4103	274	14	formulation	formulation	NOUN
fumecheng-4103	274	15	for	for	ADP
fumecheng-4103	274	16	normal	normal	ADJ
fumecheng-4103	274	17	and	and	CCONJ
fumecheng-4103	274	18	tangential	tangential	ADJ
fumecheng-4103	274	19	contact	contact	NOUN
fumecheng-4103	274	20	problems	problem	NOUN
fumecheng-4103	274	21	,	,	PUNCT
fumecheng-4103	274	22	physical	physical	ADJ
fumecheng-4103	274	23	mesomechanics	mesomechanic	NOUN
fumecheng-4103	274	24	,	,	PUNCT
fumecheng-4103	274	25	17(4	17(4	NUM
fumecheng-4103	274	26	)	)	PUNCT
fumecheng-4103	274	27	,	,	PUNCT
fumecheng-4103	275	1	pp	pp	PROPN
fumecheng-4103	275	2	.	.	PUNCT
fumecheng-4103	276	1	334	334	NUM
fumecheng-4103	276	2	-	-	SYM
fumecheng-4103	276	3	340	340	NUM
fumecheng-4103	276	4	.	.	PUNCT